LMFDB - Embedded newform 54.9.f.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	54.11
Dual form			54.9.f.a.5.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.27231 + 8.66680i) q^{2} +(-80.6183 - 7.85385i) q^{3} +(-22.2270 - 126.055i) q^{4} +(208.139 - 571.857i) q^{5} +(654.349 - 641.588i) q^{6} +(-808.155 + 4583.27i) q^{7} +(1254.14 + 724.077i) q^{8} +(6437.63 + 1266.33i) q^{9} +(3442.52 + 5962.62i) q^{10} +(-2304.87 - 6332.57i) q^{11} +(801.881 + 10336.9i) q^{12} +(-28817.9 + 24181.1i) q^{13} +(-33845.2 - 40335.1i) q^{14} +(-21271.1 + 44467.4i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-25788.7 + 14889.1i) q^{17} +(-57791.5 + 46584.6i) q^{18} +(36420.7 - 63082.5i) q^{19} +(-76711.9 - 13526.4i) q^{20} +(101148. - 363149. i) q^{21} +(71644.8 + 26076.6i) q^{22} +(453226. - 79916.0i) q^{23} +(-95419.8 - 68223.7i) q^{24} +(15537.9 + 13037.9i) q^{25} -425611. i q^{26} +(-509046. - 152649. i) q^{27} +595709. q^{28} +(-488689. + 582397. i) q^{29} +(-230701. - 507733. i) q^{30} +(-266191. - 1.50964e6i) q^{31} +(63398.2 - 174185. i) q^{32} +(136079. + 528623. i) q^{33} +(58502.5 - 331784. i) q^{34} +(2.45277e6 + 1.41611e6i) q^{35} +(16538.4 - 839645. i) q^{36} +(-1.42819e6 - 2.47370e6i) q^{37} +(281861. + 774407. i) q^{38} +(2.51316e6 - 1.72311e6i) q^{39} +(675103. - 566479. i) q^{40} +(-2.69268e6 - 3.20902e6i) q^{41} +(2.41176e6 + 3.51756e6i) q^{42} +(2.67475e6 - 973529. i) q^{43} +(-747024. + 431294. i) q^{44} +(2.06408e6 - 3.41783e6i) q^{45} +(-2.60338e6 + 4.50919e6i) q^{46} +(-390402. - 68838.4i) q^{47} +(1.28520e6 - 330840. i) q^{48} +(-1.49361e7 - 5.43631e6i) q^{49} +(-225993. + 39848.7i) q^{50} +(2.19598e6 - 997795. i) q^{51} +(3.68869e6 + 3.09518e6i) q^{52} +34340.3i q^{53} +(5.02492e6 - 3.30169e6i) q^{54} -4.10105e6 q^{55} +(-4.33218e6 + 5.16289e6i) q^{56} +(-3.43162e6 + 4.79956e6i) q^{57} +(-1.49362e6 - 8.47075e6i) q^{58} +(5.31298e6 - 1.45973e7i) q^{59} +(6.07815e6 + 1.69296e6i) q^{60} +(-669659. + 3.79782e6i) q^{61} +(1.50196e7 + 8.67158e6i) q^{62} +(-1.10065e7 + 2.84820e7i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(7.82999e6 + 2.15127e7i) q^{65} +(-5.57108e6 - 2.66494e6i) q^{66} +(5.68875e6 - 4.77343e6i) q^{67} +(2.45006e6 + 2.91987e6i) q^{68} +(-3.71660e7 + 2.88312e6i) q^{69} +(-3.01104e7 + 1.09593e7i) q^{70} +(-2.44321e7 + 1.41059e7i) q^{71} +(7.15677e6 + 6.24950e6i) q^{72} +(6.47054e6 - 1.12073e7i) q^{73} +(3.18253e7 + 5.61166e6i) q^{74} +(-1.15024e6 - 1.17312e6i) q^{75} +(-8.76141e6 - 3.18889e6i) q^{76} +(3.08866e7 - 5.44614e6i) q^{77} +(-3.34268e6 + 3.43121e7i) q^{78} +(5.72766e6 + 4.80607e6i) q^{79} +9.97060e6i q^{80} +(3.98395e7 + 1.63043e7i) q^{81} +4.73939e7 q^{82} +(2.51217e7 - 2.99388e7i) q^{83} +(-4.80251e7 - 4.67861e6i) q^{84} +(3.14681e6 + 1.78464e7i) q^{85} +(-1.10142e7 + 3.02613e7i) q^{86} +(4.39714e7 - 4.31138e7i) q^{87} +(1.69465e6 - 9.61082e6i) q^{88} +(-2.94822e7 - 1.70215e7i) q^{89} +(1.46110e7 + 4.27445e7i) q^{90} +(-8.75391e7 - 1.51622e8i) q^{91} +(-2.01477e7 - 5.53553e7i) q^{92} +(9.60337e6 + 1.23796e8i) q^{93} +(3.43573e6 - 2.88292e6i) q^{94} +(-2.84936e7 - 3.39573e7i) q^{95} +(-6.47908e6 + 1.35446e7i) q^{96} +(-1.27634e8 + 4.64551e7i) q^{97} +(1.55736e8 - 8.99140e7i) q^{98} +(-6.81877e6 - 4.36855e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25}+ \cdots + 26756370 q^{99}+O(q^{100}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.27231	+	8.66680i	−0.454519	+	0.541675i
$2$	−7.27231	+	8.66680i	−0.454519	+	0.541675i
$3$	−80.6183	−	7.85385i	−0.995288	−	0.0969611i
$3$	−80.6183	−	7.85385i	−0.995288	−	0.0969611i
$4$	−22.2270	−	126.055i	−0.0868241	−	0.492404i
$5$	208.139	−	571.857i	0.333022	−	0.914971i	−0.654299	−	0.756236i	$-0.727036\pi$
$5$	208.139	−	571.857i	0.333022	−	0.914971i	0.987321	−	0.158735i	$-0.0507415\pi$
$6$	654.349	−	641.588i	0.504899	−	0.495052i
$7$	−808.155	+	4583.27i	−0.336591	+	1.90890i	0.0743355	+	0.997233i	$0.476316\pi$
$7$	−808.155	+	4583.27i	−0.336591	+	1.90890i	−0.410926	+	0.911669i	$0.634795\pi$
$8$	1254.14	+	724.077i	0.306186	+	0.176777i
$9$	6437.63	+	1266.33i	0.981197	+	0.193008i
$10$	3442.52	+	5962.62i	0.344252	+	0.596262i
$11$	−2304.87	−	6332.57i	−0.157425	−	0.432523i	0.835756	−	0.549101i	$-0.185030\pi$
$11$	−2304.87	−	6332.57i	−0.157425	−	0.432523i	−0.993182	+	0.116578i	$0.962807\pi$
$12$	801.881	+	10336.9i	0.0386710	+	0.498502i
$13$	−28817.9	+	24181.1i	−1.00899	+	0.846646i	−0.988205	−	0.153137i	$-0.951062\pi$
$13$	−28817.9	+	24181.1i	−1.00899	+	0.846646i	−0.0207890	+	0.999784i	$0.506618\pi$
$14$	−33845.2	−	40335.1i	−0.881018	−	1.04996i
$15$	−21271.1	+	44467.4i	−0.420169	+	0.878369i
$16$	−15395.9	+	5603.66i	−0.234923	+	0.0855050i
$17$	−25788.7	+	14889.1i	−0.308769	+	0.178268i	−0.646376	−	0.763019i	$-0.723716\pi$
$17$	−25788.7	+	14889.1i	−0.308769	+	0.178268i	0.337606	+	0.941287i	$0.390383\pi$
$18$	−57791.5	+	46584.6i	−0.550521	+	0.443764i
$19$	36420.7	−	63082.5i	0.279469	−	0.484055i	−0.691784	−	0.722105i	$-0.743175\pi$
$19$	36420.7	−	63082.5i	0.279469	−	0.484055i	0.971253	+	0.238050i	$0.0765082\pi$
$20$	−76711.9	−	13526.4i	−0.479449	−	0.0845399i
$21$	101148.	−	363149.i	0.520094	−	1.86727i
$22$	71644.8	+	26076.6i	0.305840	+	0.111317i
$23$	453226.	−	79916.0i	1.61958	−	0.285576i	0.710973	−	0.703220i	$-0.248255\pi$
$23$	453226.	−	79916.0i	1.61958	−	0.285576i	0.908611	+	0.417643i	$0.137144\pi$
$24$	−95419.8	−	68223.7i	−0.287603	−	0.205632i
$25$	15537.9	+	13037.9i	0.0397771	+	0.0333769i
$26$		−	425611.i		−	0.931364i
$27$	−509046.	−	152649.i	−0.957860	−	0.287237i
$28$	595709.			0.969175
$29$	−488689.	+	582397.i	−0.690941	+	0.823432i	−0.991469	−	0.130341i	$-0.958393\pi$
$29$	−488689.	+	582397.i	−0.690941	+	0.823432i	0.300528	+	0.953773i	$0.402837\pi$
$30$	−230701.	−	507733.i	−0.284816	−	0.626831i
$31$	−266191.	−	1.50964e6i	−0.288235	−	1.63466i	−0.693496	−	0.720461i	$-0.743930\pi$
$31$	−266191.	−	1.50964e6i	−0.288235	−	1.63466i	0.405261	−	0.914201i	$-0.367181\pi$
$32$	63398.2	−	174185.i	0.0604612	−	0.166116i
$33$	136079.	+	528623.i	0.114746	+	0.445749i
$34$	58502.5	−	331784.i	0.0437783	−	0.248279i
$35$	2.45277e6	+	1.41611e6i	1.63450	+	0.943677i
$36$	16538.4	−	839645.i	0.00984656	−	0.499903i
$37$	−1.42819e6	−	2.47370e6i	−0.762042	−	1.31990i	−0.941796	−	0.336184i	$-0.890863\pi$
$37$	−1.42819e6	−	2.47370e6i	−0.762042	−	1.31990i	0.179754	−	0.983712i	$-0.442470\pi$
$38$	281861.	+	774407.i	0.135176	+	0.371394i
$39$	2.51316e6	−	1.72311e6i	1.08633	−	0.744824i
$40$	675103.	−	566479.i	0.263712	−	0.221281i
$41$	−2.69268e6	−	3.20902e6i	−0.952906	−	1.13563i	−0.990662	−	0.136342i	$-0.956465\pi$
$41$	−2.69268e6	−	3.20902e6i	−0.952906	−	1.13563i	0.0377562	−	0.999287i	$-0.487979\pi$
$42$	2.41176e6	+	3.51756e6i	0.775062	+	1.13043i
$43$	2.67475e6	−	973529.i	0.782365	−	0.284757i	0.0802063	−	0.996778i	$-0.474442\pi$
$43$	2.67475e6	−	973529.i	0.782365	−	0.284757i	0.702158	+	0.712021i	$0.252220\pi$
$44$	−747024.	+	431294.i	−0.199308	+	0.115070i
$45$	2.06408e6	−	3.41783e6i	0.503357	−	0.833490i
$46$	−2.60338e6	+	4.50919e6i	−0.581443	+	1.00709i
$47$	−390402.	−	68838.4i	−0.0800056	−	0.0141072i	0.133502	−	0.991049i	$-0.457378\pi$
$47$	−390402.	−	68838.4i	−0.0800056	−	0.0141072i	−0.213508	+	0.976941i	$0.568489\pi$
$48$	1.28520e6	−	330840.i	0.242107	−	0.0623237i
$49$	−1.49361e7	−	5.43631e6i	−2.59092	−	0.943018i
$50$	−225993.	+	39848.7i	−0.0361589	+	0.00637579i
$51$	2.19598e6	−	997795.i	0.324599	−	0.147489i
$52$	3.68869e6	+	3.09518e6i	0.504497	+	0.423323i
$53$			34340.3i			0.00435212i	0.999998	+	0.00217606i	$0.000692662\pi$
$53$			34340.3i			0.00435212i	−0.999998	+	0.00217606i	$0.999307\pi$
$54$	5.02492e6	−	3.30169e6i	0.590955	−	0.388294i
$55$	−4.10105e6			−0.448172
$56$	−4.33218e6	+	5.16289e6i	−0.440509	+	0.524978i
$57$	−3.43162e6	+	4.79956e6i	−0.325087	+	0.454676i
$58$	−1.49362e6	−	8.47075e6i	−0.131986	−	0.748531i
$59$	5.31298e6	−	1.45973e7i	0.438460	−	1.20466i	−0.502034	−	0.864848i	$-0.667415\pi$
$59$	5.31298e6	−	1.45973e7i	0.438460	−	1.20466i	0.940494	−	0.339811i	$-0.110363\pi$
$60$	6.07815e6	+	1.69296e6i	0.468993	+	0.130629i
$61$	−669659.	+	3.79782e6i	−0.0483653	+	0.274293i	−0.999394	−	0.0348094i	$-0.988918\pi$
$61$	−669659.	+	3.79782e6i	−0.0483653	+	0.274293i	0.951029	+	0.309103i	$0.100029\pi$
$62$	1.50196e7	+	8.67158e6i	1.01646	+	0.586856i
$63$	−1.10065e7	+	2.84820e7i	−0.698696	+	1.80804i
$64$	1.04858e6	+	1.81619e6i	0.0625000	+	0.108253i
$65$	7.82999e6	+	2.15127e7i	0.438639	+	1.20515i
$66$	−5.57108e6	−	2.66494e6i	−0.293605	−	0.140447i
$67$	5.68875e6	−	4.77343e6i	0.282304	−	0.236882i	−0.490629	−	0.871368i	$-0.663233\pi$
$67$	5.68875e6	−	4.77343e6i	0.282304	−	0.236882i	0.772934	+	0.634487i	$0.218789\pi$
$68$	2.45006e6	+	2.91987e6i	0.114588	+	0.136561i
$69$	−3.71660e7	+	2.88312e6i	−1.63964	+	0.127194i
$70$	−3.01104e7	+	1.09593e7i	−1.25408	+	0.456447i
$71$	−2.44321e7	+	1.41059e7i	−0.961452	+	0.555094i	−0.896620	−	0.442802i	$-0.853985\pi$
$71$	−2.44321e7	+	1.41059e7i	−0.961452	+	0.555094i	−0.0648322	+	0.997896i	$0.520651\pi$
$72$	7.15677e6	+	6.24950e6i	0.266310	+	0.232549i
$73$	6.47054e6	−	1.12073e7i	0.227850	−	0.394648i	−0.729321	−	0.684172i	$-0.760164\pi$
$73$	6.47054e6	−	1.12073e7i	0.227850	−	0.394648i	0.957171	+	0.289524i	$0.0934970\pi$
$74$	3.18253e7	+	5.61166e6i	1.06132	+	0.187139i
$75$	−1.15024e6	−	1.17312e6i	−0.0363534	−	0.0370765i
$76$	−8.76141e6	−	3.18889e6i	−0.262615	−	0.0955841i
$77$	3.08866e7	−	5.44614e6i	0.878631	−	0.154926i
$78$	−3.34268e6	+	3.43121e7i	−0.0903061	+	0.926976i
$79$	5.72766e6	+	4.80607e6i	0.147051	+	0.123391i	0.713346	−	0.700812i	$-0.247179\pi$
$79$	5.72766e6	+	4.80607e6i	0.147051	+	0.123391i	−0.566294	+	0.824203i	$0.691623\pi$
$80$			9.97060e6i			0.243423i
$81$	3.98395e7	+	1.63043e7i	0.925495	+	0.378759i
$82$	4.73939e7			1.04826
$83$	2.51217e7	−	2.99388e7i	0.529341	−	0.630844i	−0.433422	−	0.901191i	$-0.642694\pi$
$83$	2.51217e7	−	2.99388e7i	0.529341	−	0.630844i	0.962763	+	0.270347i	$0.0871384\pi$
$84$	−4.80251e7	−	4.67861e6i	−0.964608	−	0.0939722i
$85$	3.14681e6	+	1.78464e7i	0.0602830	+	0.341882i
$86$	−1.10142e7	+	3.02613e7i	−0.201354	+	0.553215i
$87$	4.39714e7	−	4.31138e7i	0.767526	−	0.752557i
$88$	1.69465e6	−	9.61082e6i	0.0282585	−	0.160262i
$89$	−2.94822e7	−	1.70215e7i	−0.469894	−	0.271293i	0.246301	−	0.969193i	$-0.420785\pi$
$89$	−2.94822e7	−	1.70215e7i	−0.469894	−	0.271293i	−0.716195	+	0.697900i	$0.754118\pi$
$90$	1.46110e7	+	4.27445e7i	0.222695	+	0.651494i
$91$	−8.75391e7	−	1.51622e8i	−1.27655	−	2.21104i
$92$	−2.01477e7	−	5.53553e7i	−0.281238	−	0.772694i
$93$	9.60337e6	+	1.23796e8i	0.128378	+	1.65491i
$94$	3.43573e6	−	2.88292e6i	0.0440056	−	0.0369251i
$95$	−2.84936e7	−	3.39573e7i	−0.349826	−	0.416907i
$96$	−6.47908e6	+	1.35446e7i	−0.0762831	+	0.159471i
$97$	−1.27634e8	+	4.64551e7i	−1.44172	+	0.524743i	−0.940266	−	0.340441i	$-0.889424\pi$
$97$	−1.27634e8	+	4.64551e7i	−1.44172	+	0.524743i	−0.501454	+	0.865184i	$0.667201\pi$
$98$	1.55736e8	−	8.99140e7i	1.68843	−	0.974817i
$99$	−6.81877e6	−	4.36855e7i	−0.0709848	−	0.454775i
$100$	1.29813e6	−	2.24843e6i	0.0129813	−	0.0224843i
$101$	1.52432e8	+	2.68778e7i	1.46484	+	0.258291i	0.848503	−	0.529191i	$-0.177505\pi$
$101$	1.52432e8	+	2.68778e7i	1.46484	+	0.258291i	0.616337	+	0.787482i	$0.288616\pi$
$102$	−7.32215e6	+	2.62884e7i	−0.0676454	+	0.242864i
$103$	8.46933e6	+	3.08258e6i	0.0752489	+	0.0273884i	0.379370	−	0.925245i	$-0.376141\pi$
$103$	8.46933e6	+	3.08258e6i	0.0752489	+	0.0273884i	−0.304121	+	0.952633i	$0.598363\pi$
$104$	−5.36506e7	+	9.46004e6i	−0.458607	+	0.0808649i
$105$	−1.86616e8	−	1.33428e8i	−1.53530	−	1.09771i
$106$	−297621.	−	249734.i	−0.00235744	−	0.00197812i
$107$		−	1.30990e7i		−	0.0999319i	−0.998751	−	0.0499659i	$-0.984089\pi$
$107$		−	1.30990e7i		−	0.0999319i	0.998751	−	0.0499659i	$-0.0159113\pi$
$108$	−7.92775e6	+	6.75609e7i	−0.0582713	+	0.496593i
$109$	−3.69259e7			−0.261592			−0.130796	−	0.991409i	$-0.541753\pi$
$109$	−3.69259e7			−0.261592			−0.130796	+	0.991409i	$0.541753\pi$
$110$	2.98241e7	−	3.55430e7i	0.203703	−	0.242764i
$111$	9.57103e7	+	2.10642e8i	0.630473	+	1.38757i
$112$	−1.32408e7	−	7.50923e7i	−0.0841477	−	0.477225i
$113$	1.96169e7	−	5.38970e7i	0.120314	−	0.330561i	−0.864886	−	0.501968i	$-0.832609\pi$
$113$	1.96169e7	−	5.38970e7i	0.120314	−	0.330561i	0.985200	+	0.171408i	$0.0548316\pi$
$114$	−1.66411e7	−	6.46451e7i	−0.0985286	−	0.382751i
$115$	4.86334e7	−	2.75814e8i	0.278063	−	1.57697i
$116$	8.42764e7	+	4.86570e7i	0.465451	+	0.268728i
$117$	−2.16140e8	+	1.19176e8i	−1.15343	+	0.635983i
$118$	8.78742e7	+	1.52203e8i	0.453245	+	0.785044i
$119$	−4.73996e7	−	1.30229e8i	−0.236367	−	0.649413i
$120$	−5.88747e7	+	4.03664e7i	−0.283925	+	0.194668i
$121$	1.29419e8	−	1.08596e8i	0.603751	−	0.506607i
$122$	−2.80450e7	−	3.34228e7i	−0.126595	−	0.150870i
$123$	1.91877e8	+	2.79853e8i	0.838304	+	1.22267i
$124$	−1.84382e8	+	6.71096e7i	−0.779888	+	0.283856i
$125$	2.16559e8	−	1.25031e8i	0.887027	−	0.512125i
$126$	−1.66805e8	−	3.02522e8i	−0.661802	−	1.20026i
$127$	7.79555e7	−	1.35023e8i	0.299662	−	0.519030i	−0.676396	−	0.736538i	$-0.736459\pi$
$127$	7.79555e7	−	1.35023e8i	0.299662	−	0.519030i	0.976059	+	0.217508i	$0.0697927\pi$
$128$	−2.33661e7	−	4.12008e6i	−0.0870455	−	0.0153485i
$129$	−2.23280e8	+	5.74772e7i	−0.806289	+	0.207557i
$130$	−2.43389e8	−	8.85862e7i	−0.852171	−	0.310165i
$131$	2.07082e8	−	3.65141e7i	0.703164	−	0.123987i	0.189377	−	0.981904i	$-0.439353\pi$
$131$	2.07082e8	−	3.65141e7i	0.703164	−	0.123987i	0.513787	+	0.857918i	$0.328242\pi$
$132$	6.36112e7	−	2.89032e7i	0.209526	−	0.0952030i
$133$	2.59691e8	+	2.17906e8i	0.829946	+	0.696408i
$134$			8.40171e7i			0.260585i
$135$	−1.93246e8	+	2.59329e8i	−0.581802	+	0.780757i
$136$	−4.31235e7			−0.126054
$137$	1.86230e8	−	2.21940e8i	0.528649	−	0.630019i	−0.433954	−	0.900935i	$-0.642882\pi$
$137$	1.86230e8	−	2.21940e8i	0.528649	−	0.630019i	0.962603	+	0.270916i	$0.0873265\pi$
$138$	2.45295e8	−	3.43077e8i	0.676352	−	0.945966i
$139$	−5.40792e7	−	3.06699e8i	−0.144868	−	0.821585i	−0.967473	−	0.252973i	$-0.918592\pi$
$139$	−5.40792e7	−	3.06699e8i	−0.144868	−	0.821585i	0.822606	−	0.568612i	$-0.192519\pi$
$140$	1.23990e8	−	3.40660e8i	0.322757	−	0.886766i
$141$	3.09329e7	+	8.61580e6i	0.0782608	+	0.0217981i
$142$	5.54250e7	−	3.14331e8i	0.136318	−	0.773096i
$143$	2.19550e8	+	1.26757e8i	0.525035	+	0.303129i
$144$	−1.06209e8	+	1.65780e7i	−0.247009	+	0.0385551i
$145$	2.31333e8	+	4.00680e8i	0.523317	+	0.906412i
$146$	5.00757e7	+	1.37582e8i	0.110209	+	0.302796i
$147$	1.16143e9	+	5.55572e8i	2.48728	+	1.18979i
$148$	−2.80079e8	+	2.35014e8i	−0.583758	+	0.489831i
$149$	−1.85737e8	−	2.21353e8i	−0.376838	−	0.449098i	0.543976	−	0.839101i	$-0.316918\pi$
$149$	−1.85737e8	−	2.21353e8i	−0.376838	−	0.449098i	−0.920813	+	0.390003i	$0.872474\pi$
$150$	1.85322e7	−	1.43762e6i	0.0366067	−	0.00283974i
$151$	−8.24893e8	+	3.00236e8i	−1.58668	+	0.577505i	−0.976643	−	0.214868i	$-0.931068\pi$
$151$	−8.24893e8	+	3.00236e8i	−1.58668	+	0.577505i	−0.610038	+	0.792372i	$0.708846\pi$
$152$	9.13532e7	−	5.27428e7i	0.171139	−	0.0988073i
$153$	−1.84873e8	+	6.31937e7i	−0.337371	+	0.115321i
$154$	−1.77416e8	+	3.07294e8i	−0.315435	+	0.546350i
$155$	−9.18705e8	−	1.61992e8i	−1.59166	−	0.280652i
$156$	−2.73067e8	−	2.78498e8i	−0.461074	−	0.470245i
$157$	−4.67660e8	−	1.70214e8i	−0.769717	−	0.280154i	−0.0728391	−	0.997344i	$-0.523206\pi$
$157$	−4.67660e8	−	1.70214e8i	−0.769717	−	0.280154i	−0.696878	+	0.717190i	$0.745428\pi$
$158$	−8.33066e7	+	1.46892e7i	−0.133675	+	0.0235706i
$159$	269704.	−	2.76846e6i	0.000421986	−	0.00433161i
$160$	−8.64132e7	−	7.25093e7i	−0.131856	−	0.110640i
$161$			2.14184e9i			3.18775i
$162$	−4.31032e8	+	2.26711e8i	−0.625820	+	0.329165i
$163$	6.53890e8			0.926306			0.463153	−	0.886278i	$-0.346718\pi$
$163$	6.53890e8			0.926306			0.463153	+	0.886278i	$0.346718\pi$
$164$	−3.44664e8	+	4.10754e8i	−0.476453	+	0.567814i
$165$	3.30620e8	+	3.22090e7i	0.446060	+	0.0434552i
$166$	7.67814e7	+	4.35449e8i	0.101117	+	0.573462i
$167$	−4.24548e8	+	1.16644e9i	−0.545834	+	1.49967i	0.293450	+	0.955974i	$0.405196\pi$
$167$	−4.24548e8	+	1.16644e9i	−0.545834	+	1.49967i	−0.839284	+	0.543693i	$0.817026\pi$
$168$	3.89802e8	−	3.82200e8i	0.489336	−	0.479792i
$169$	1.04096e8	−	5.90356e8i	0.127610	−	0.723714i
$170$	−1.77556e8	−	1.02512e8i	−0.212589	−	0.122738i
$171$	3.14346e8	−	3.59982e8i	0.367641	−	0.421013i
$172$	−1.82170e8	−	3.15528e8i	−0.208144	−	0.360516i
$173$	1.56927e8	+	4.31152e8i	0.175191	+	0.481334i	0.995947	−	0.0899458i	$-0.0286694\pi$
$173$	1.56927e8	+	4.31152e8i	0.175191	+	0.481334i	−0.820755	+	0.571280i	$0.806447\pi$
$174$	5.38853e7	+	6.94629e8i	0.0587860	+	0.757802i
$175$	−7.23131e7	+	6.06779e7i	−0.0771019	+	0.0646962i
$176$	7.09711e7	+	8.45800e7i	0.0739658	+	0.0881490i
$177$	−5.42968e8	+	1.13508e9i	−0.553199	+	1.15647i
$178$	3.61926e8	−	1.31730e8i	0.360529	−	0.131222i
$179$	3.92103e8	−	2.26381e8i	0.381933	−	0.220509i	−0.296726	−	0.954963i	$-0.595895\pi$
$179$	3.92103e8	−	2.26381e8i	0.381933	−	0.220509i	0.678659	+	0.734453i	$0.262561\pi$
$180$	−4.76714e8	−	1.84220e8i	−0.454117	−	0.175488i
$181$	6.48174e8	−	1.12267e9i	0.603917	−	1.04602i	−0.388304	−	0.921531i	$-0.626939\pi$
$181$	6.48174e8	−	1.12267e9i	0.603917	−	1.04602i	0.992222	−	0.124484i	$-0.0397276\pi$
$182$	1.95069e9	+	3.43960e8i	1.77788	+	0.313489i
$183$	8.38143e7	−	3.00915e8i	0.0747332	−	0.268311i
$184$	6.26274e8	+	2.27945e8i	0.546377	+	0.198865i
$185$	−1.71186e9	+	3.01847e8i	−1.46144	+	0.257692i
$186$	−1.14275e9	−	8.17050e8i	−0.954773	−	0.682648i
$187$	1.53726e8	+	1.28991e8i	0.125713	+	0.105486i
$188$			5.07423e7i			0.0406199i
$189$	1.11102e9	−	2.20973e9i	0.870714	−	1.73178i
$190$	5.01516e8			0.384831
$191$	1.23458e8	−	1.47132e8i	0.0927655	−	0.110554i	−0.717665	−	0.696389i	$-0.754789\pi$
$191$	1.23458e8	−	1.47132e8i	0.0927655	−	0.110554i	0.810430	+	0.585835i	$0.199233\pi$
$192$	−7.02704e7	−	1.54653e8i	−0.0517092	−	0.113803i
$193$	2.02415e7	+	1.14795e8i	0.0145886	+	0.0827361i	0.991233	−	0.132127i	$-0.0421806\pi$
$193$	2.02415e7	+	1.14795e8i	0.0145886	+	0.0827361i	−0.976644	+	0.214863i	$0.931070\pi$
$194$	5.25580e8	−	1.44402e9i	0.371049	−	1.01945i
$195$	−4.62283e8	−	1.79581e9i	−0.319720	−	1.24200i
$196$	−3.53291e8	+	2.00361e9i	−0.239391	+	1.35766i
$197$	−1.96751e9	−	1.13594e9i	−1.30633	−	0.754208i	−0.324845	−	0.945767i	$-0.605312\pi$
$197$	−1.96751e9	−	1.13594e9i	−1.30633	−	0.754208i	−0.981481	+	0.191559i	$0.938646\pi$
$198$	4.28202e8	+	2.58597e8i	0.278604	+	0.168253i
$199$	−2.53993e8	−	4.39928e8i	−0.161960	−	0.280524i	0.773611	−	0.633660i	$-0.218448\pi$
$199$	−2.53993e8	−	4.39928e8i	−0.161960	−	0.280524i	−0.935572	+	0.353137i	$0.885115\pi$
$200$	1.00463e7	+	2.76019e7i	0.00627893	+	0.0172512i
$201$	−4.96107e8	+	3.40147e8i	−0.303943	+	0.208393i
$202$	−1.34148e9	+	1.12563e9i	−0.805708	+	0.676069i
$203$	−2.27435e9	−	2.71046e9i	−1.33929	−	1.59610i
$204$	−1.74587e8	−	2.54637e8i	−0.100807	−	0.147028i
$205$	−2.39555e9	+	8.71908e8i	−1.35641	+	0.493691i
$206$	−8.83078e7	+	5.09845e7i	−0.0490377	+	0.0283119i
$207$	3.01890e9	+	5.94631e7i	1.64425	+	0.0323867i
$208$	3.08175e8	−	5.33775e8i	0.164644	−	0.285171i
$209$	−4.83419e8	−	8.52398e7i	−0.253360	−	0.0446743i
$210$	2.51352e9	−	6.47037e8i	1.29243	−	0.332699i
$211$	1.98173e9	+	7.21292e8i	0.999806	+	0.363900i	0.789510	−	0.613738i	$-0.210335\pi$
$211$	1.98173e9	+	7.21292e8i	0.999806	+	0.363900i	0.210296	+	0.977638i	$0.432557\pi$
$212$	4.32878e6	−	763281.i	0.00214300	−	0.000377869i
$213$	2.08046e9	−	9.45307e8i	1.01074	−	0.459256i
$214$	1.13527e8	+	9.52602e7i	0.0541306	+	0.0454210i
$215$		−	1.73220e9i		−	0.810671i
$216$	−5.27884e8	−	5.60032e8i	−0.242507	−	0.257275i
$217$	7.13424e9			3.21743
$218$	2.68537e8	−	3.20030e8i	0.118899	−	0.141698i
$219$	−6.09665e8	+	8.52696e8i	−0.265042	+	0.370696i
$220$	9.11539e7	+	5.16960e8i	0.0389121	+	0.220681i
$221$	3.83141e8	−	1.05267e9i	0.160616	−	0.441290i
$222$	−2.52163e9	−	7.02354e8i	−1.03817	−	0.289164i
$223$	−1.07941e8	+	6.12162e8i	−0.0436481	+	0.247541i	−0.998823	−	0.0485009i	$-0.984556\pi$
$223$	−1.07941e8	+	6.12162e8i	−0.0436481	+	0.247541i	0.955175	+	0.296042i	$0.0956667\pi$
$224$	7.47102e8	+	4.31339e8i	0.296748	+	0.171328i
$225$	8.35172e7	+	1.03609e8i	0.0325871	+	0.0404267i
$226$	3.24455e8	+	5.61972e8i	0.124371	+	0.215417i
$227$	−5.66505e8	−	1.55646e9i	−0.213354	−	0.586184i	0.786138	−	0.618050i	$-0.212077\pi$
$227$	−5.66505e8	−	1.55646e9i	−0.213354	−	0.586184i	−0.999492	+	0.0318660i	$0.989855\pi$
$228$	6.81285e8	+	3.25894e8i	0.252110	+	0.120597i
$229$	1.41138e8	−	1.18429e8i	0.0513217	−	0.0430640i	−0.616766	−	0.787147i	$-0.711558\pi$
$229$	1.41138e8	−	1.18429e8i	0.0513217	−	0.0430640i	0.668088	+	0.744083i	$0.267113\pi$
$230$	2.03675e9	+	2.42730e9i	0.727823	+	0.867386i
$231$	−2.53280e9	+	1.96480e8i	−0.889513	+	0.0690034i
$232$	−1.03459e9	+	3.76558e8i	−0.357120	+	0.129981i
$233$	−1.64102e9	+	9.47443e8i	−0.556788	+	0.321462i	−0.751855	−	0.659328i	$-0.770841\pi$
$233$	−1.64102e9	+	9.47443e8i	−0.556788	+	0.321462i	0.195067	+	0.980790i	$0.437508\pi$
$234$	5.38963e8	−	2.73993e9i	0.179761	−	0.913852i
$235$	−1.20623e8	+	2.08926e8i	−0.0395513	+	0.0685048i
$236$	−1.95816e9	−	3.45276e8i	−0.631248	−	0.111306i
$237$	−4.24008e8	−	4.32442e8i	−0.134394	−	0.137067i
$238$	1.47338e9	+	5.36266e8i	0.459205	+	0.167137i
$239$	6.53182e7	−	1.15174e7i	0.0200190	−	0.00352989i	−0.163630	−	0.986522i	$-0.552320\pi$
$239$	6.53182e7	−	1.15174e7i	0.0200190	−	0.00352989i	0.183649	+	0.982992i	$0.441209\pi$
$240$	7.83076e7	−	8.03813e8i	0.0236025	−	0.242276i
$241$	−3.35963e9	−	2.81906e9i	−0.995917	−	0.835674i	−0.00950371	−	0.999955i	$-0.503025\pi$
$241$	−3.35963e9	−	2.81906e9i	−0.995917	−	0.835674i	−0.986414	+	0.164281i	$0.947470\pi$
$242$			1.91140e9i			0.557300i
$243$	−3.08375e9	−	1.62732e9i	−0.884410	−	0.466711i
$244$	4.93621e8			0.139262
$245$	−6.21758e9	+	7.40982e9i	−1.72567	+	2.05657i
$246$	−3.82082e9	−	3.72225e8i	−1.04332	−	0.101640i
$247$	4.75835e8	+	2.69860e9i	0.127841	+	0.725020i
$248$	7.59259e8	−	2.08605e9i	0.200717	−	0.551464i
$249$	−2.26040e9	+	2.21632e9i	−0.588015	+	0.576547i
$250$	−4.91271e8	+	2.78614e9i	−0.125765	+	0.713251i
$251$	5.21406e9	+	3.01034e9i	1.31366	+	0.758439i	0.982699	−	0.185207i	$-0.0592956\pi$
$251$	5.21406e9	+	3.01034e9i	1.31366	+	0.758439i	0.330956	+	0.943646i	$0.392629\pi$
$252$	3.83496e9	+	7.54363e8i	0.950952	+	0.187059i
$253$	−1.55070e9	−	2.68589e9i	−0.378482	−	0.655550i
$254$	6.03300e8	+	1.65755e9i	0.144943	+	0.398229i
$255$	−1.13527e8	−	1.46347e9i	−0.0268497	−	0.346116i
$256$	2.05633e8	−	1.72547e8i	0.0478778	−	0.0401742i
$257$	−5.51616e9	−	6.57390e9i	−1.26446	−	1.50692i	−0.770505	−	0.637434i	$-0.779996\pi$
$257$	−5.51616e9	−	6.57390e9i	−1.26446	−	1.50692i	−0.493953	−	0.869489i	$-0.664448\pi$
$258$	1.12562e9	−	2.35311e9i	0.254046	−	0.531085i
$259$	1.24918e10	−	4.54665e9i	2.77605	−	1.01040i
$260$	2.53776e9	−	1.46517e9i	0.555337	−	0.320624i
$261$	−3.88351e9	+	3.13042e9i	−0.836879	+	0.674591i
$262$	−1.18950e9	+	2.06028e9i	−0.252441	+	0.437241i
$263$	−3.56775e9	−	6.29090e8i	−0.745712	−	0.131489i	−0.212135	−	0.977240i	$-0.568042\pi$
$263$	−3.56775e9	−	6.29090e8i	−0.745712	−	0.131489i	−0.533577	+	0.845751i	$0.679153\pi$
$264$	−2.12101e8	+	7.61499e8i	−0.0436644	+	0.156767i
$265$	1.96377e7	+	7.14755e6i	0.00398206	+	0.00144935i
$266$	−3.77711e9	+	6.66006e8i	−0.754454	+	0.133031i
$267$	2.24312e9	+	1.60380e9i	0.441375	+	0.315576i
$268$	−7.28160e8	−	6.10999e8i	−0.141152	−	0.118441i
$269$			2.99749e9i			0.572465i	0.958160	+	0.286233i	$0.0924030\pi$
$269$			2.99749e9i			0.572465i	−0.958160	+	0.286233i	$0.907597\pi$
$270$	−8.42209e8	−	3.56074e9i	−0.158477	−	0.670017i
$271$	−4.06312e9			−0.753325			−0.376663	−	0.926351i	$-0.622928\pi$
$271$	−4.06312e9			−0.753325			−0.376663	+	0.926351i	$0.622928\pi$
$272$	3.13607e8	−	3.73743e8i	0.0572942	−	0.0682806i
$273$	5.86644e9	+	1.29111e10i	1.05615	+	2.32440i
$274$	5.69190e8	+	3.22804e9i	0.100985	+	0.572712i
$275$	4.67503e7	−	1.28445e8i	0.00817436	−	0.0224589i
$276$	1.18952e9	+	4.62089e9i	0.204991	+	0.796323i
$277$	5.01418e8	−	2.84368e9i	0.0851689	−	0.483017i	−0.912151	−	0.409854i	$-0.865580\pi$
$277$	5.01418e8	−	2.84368e9i	0.0851689	−	0.483017i	0.997320	−	0.0731627i	$-0.0233092\pi$
$278$	3.05138e9	+	1.76171e9i	0.510877	+	0.294955i
$279$	1.98065e8	−	1.00556e10i	0.0326882	−	1.65956i
$280$	2.05074e9	+	3.55199e9i	0.333640	+	0.577882i
$281$	1.18431e9	+	3.25387e9i	0.189951	+	0.521885i	0.997711	−	0.0676261i	$-0.0215425\pi$
$281$	1.18431e9	+	3.25387e9i	0.189951	+	0.521885i	−0.807760	+	0.589512i	$0.799320\pi$
$282$	−2.99625e8	+	2.05433e8i	−0.0473786	+	0.0324843i
$283$	−5.07471e9	+	4.25819e9i	−0.791163	+	0.663864i	−0.946033	−	0.324070i	$-0.894949\pi$
$283$	−5.07471e9	+	4.25819e9i	−0.791163	+	0.663864i	0.154870	+	0.987935i	$0.450504\pi$
$284$	2.32117e9	+	2.76627e9i	0.356808	+	0.425227i
$285$	2.03041e9	+	2.96137e9i	0.307754	+	0.448862i
$286$	−2.69521e9	+	9.80976e8i	−0.402836	+	0.146620i
$287$	1.68839e10	−	9.74792e9i	2.48854	−	1.43676i
$288$	6.28710e8	−	1.04106e9i	0.0913861	−	0.151323i
$289$	−3.04451e9	+	5.27324e9i	−0.436441	+	0.755938i
$290$	−5.15494e9	−	9.08954e8i	−0.728838	−	0.128514i
$291$	1.06545e10	−	2.74271e9i	1.48581	−	0.382480i
$292$	−1.55656e9	−	5.66542e8i	−0.214109	−	0.0779293i
$293$	2.26858e9	−	4.00012e8i	0.307811	−	0.0542753i	−0.0176092	−	0.999845i	$-0.505605\pi$
$293$	2.26858e9	−	4.00012e8i	0.307811	−	0.0542753i	0.325420	+	0.945570i	$0.394494\pi$
$294$	−1.32613e10	+	6.02560e9i	−1.77500	+	0.806512i
$295$	−7.24172e9	−	6.07652e9i	−0.956211	−	0.802356i
$296$		−	4.13648e9i		−	0.538845i
$297$	2.06619e8	+	3.57540e9i	0.0265549	+	0.459514i
$298$	3.26916e9			0.414545
$299$	−1.11286e10	+	1.32625e10i	−1.39237	+	1.65936i
$300$	−1.22312e8	+	1.71069e8i	−0.0151003	+	0.0211197i
$301$	2.30034e9	+	1.30459e10i	0.280237	+	1.58930i
$302$	3.39679e9	−	9.33259e9i	0.408357	−	1.12195i
$303$	−1.20777e10	−	3.36402e9i	−1.43289	−	0.399106i
$304$	−2.07238e8	+	1.17530e9i	−0.0242647	+	0.137612i
$305$	2.03243e9	+	1.17342e9i	0.234864	+	0.135599i
$306$	7.96765e8	−	2.06182e9i	0.0908750	−	0.235161i
$307$	−3.93188e9	−	6.81021e9i	−0.442636	−	0.766668i	0.555248	−	0.831685i	$-0.312623\pi$
$307$	−3.93188e9	−	6.81021e9i	−0.442636	−	0.766668i	−0.997884	+	0.0650169i	$0.979290\pi$
$308$	−1.37303e9	−	3.77237e9i	−0.152573	−	0.419190i
$309$	−6.58573e8	−	3.15030e8i	−0.0722387	−	0.0345555i
$310$	8.08507e9	−	6.78418e9i	0.875461	−	0.734599i
$311$	−1.55726e9	−	1.85588e9i	−0.166464	−	0.198384i	0.676363	−	0.736568i	$-0.263555\pi$
$311$	−1.55726e9	−	1.85588e9i	−0.166464	−	0.198384i	−0.842827	+	0.538184i	$0.819111\pi$
$312$	4.39952e9	−	3.41290e8i	0.464287	−	0.0360168i
$313$	−7.11159e9	+	2.58841e9i	−0.740951	+	0.269684i	−0.684793	−	0.728738i	$-0.740107\pi$
$313$	−7.11159e9	+	2.58841e9i	−0.740951	+	0.269684i	−0.0561581	+	0.998422i	$0.517885\pi$
$314$	4.87618e9	−	2.81526e9i	0.501604	−	0.289601i
$315$	1.39968e10	+	1.22224e10i	1.42163	+	1.24140i
$316$	4.78523e8	−	8.28826e8i	0.0479904	−	0.0831219i
$317$	1.30171e10	+	2.29527e9i	1.28907	+	0.227298i	0.775829	−	0.630944i	$-0.217332\pi$
$317$	1.30171e10	+	2.29527e9i	1.28907	+	0.227298i	0.513245	+	0.858242i	$0.328443\pi$
$318$	2.20323e7	+	2.24706e7i	0.00215453	+	0.00219738i
$319$	4.81443e9	+	1.75231e9i	0.464925	+	0.169219i
$320$	1.25685e9	−	2.21616e8i	0.119862	−	0.0211350i
$321$	−1.02878e8	+	1.05602e9i	−0.00968950	+	0.0994610i
$322$	−1.85629e10	−	1.55761e10i	−1.72672	−	1.44889i
$323$			2.16909e9i			0.199282i
$324$	1.16973e9	−	5.38439e9i	0.106147	−	0.488603i
$325$	−7.63039e8			−0.0683933
$326$	−4.75529e9	+	5.66714e9i	−0.421024	+	0.501757i
$327$	2.97691e9	+	2.90010e8i	0.260360	+	0.0253643i
$328$	−1.05342e9	−	5.97426e9i	−0.0910139	−	0.516165i
$329$	6.31010e8	−	1.73369e9i	0.0538583	−	0.147975i
$330$	−2.68352e9	+	2.63118e9i	−0.226282	+	0.221868i
$331$	3.15619e9	−	1.78997e10i	0.262937	−	1.49119i	−0.511909	−	0.859040i	$-0.671062\pi$
$331$	3.15619e9	−	1.78997e10i	0.262937	−	1.49119i	0.774846	−	0.632150i	$-0.217827\pi$
$332$	−4.33233e9	−	2.50127e9i	−0.356590	−	0.205877i
$333$	−6.06165e9	−	1.77333e10i	−0.492963	−	1.44216i
$334$	−7.02182e9	−	1.21622e10i	−0.564240	−	0.977293i
$335$	−1.54567e9	−	4.24669e9i	−0.122726	−	0.337187i
$336$	4.77688e8	+	6.15781e9i	0.0374789	+	0.483136i
$337$	−1.14032e10	+	9.56846e9i	−0.884115	+	0.741861i	−0.967021	−	0.254697i	$-0.918024\pi$
$337$	−1.14032e10	+	9.56846e9i	−0.884115	+	0.741861i	0.0829057	+	0.996557i	$0.473580\pi$
$338$	4.35948e9	+	5.19543e9i	0.334017	+	0.398066i
$339$	−2.00478e9	+	4.19102e9i	−0.151799	+	0.317337i
$340$	2.17970e9	−	7.93345e8i	0.163110	−	0.0593672i
$341$	−8.94639e9	+	5.16520e9i	−0.661653	+	0.382006i
$342$	8.33865e8	+	5.34228e9i	0.0609525	+	0.390501i
$343$	2.35722e10	−	4.08282e10i	1.70303	−	2.94974i
$344$	4.05942e9	+	7.15785e8i	0.289888	+	0.0511150i
$345$	−6.08695e9	+	2.18537e10i	−0.429658	+	1.54258i
$346$	−4.87793e9	−	1.77542e9i	−0.340354	−	0.123879i
$347$	2.42670e10	−	4.27893e9i	1.67378	−	0.295132i	0.745359	−	0.666664i	$-0.232278\pi$
$347$	2.42670e10	−	4.27893e9i	1.67378	−	0.295132i	0.928420	+	0.371531i	$0.121167\pi$
$348$	−6.41208e9	−	4.58454e9i	−0.437202	−	0.312593i
$349$	−1.55872e10	−	1.30792e10i	−1.05067	−	0.881618i	−0.0575079	−	0.998345i	$-0.518315\pi$
$349$	−1.55872e10	−	1.30792e10i	−1.05067	−	0.881618i	−0.993164	+	0.116727i	$0.962760\pi$
$350$		−	1.06799e9i		−	0.0711698i
$351$	1.83608e10	−	7.91024e9i	1.20966	−	0.521148i
$352$	−1.24916e9			−0.0813670
$353$	6.55825e9	−	7.81582e9i	0.422366	−	0.503357i	−0.512337	−	0.858784i	$-0.671220\pi$
$353$	6.55825e9	−	7.81582e9i	0.422366	−	0.503357i	0.934704	+	0.355428i	$0.115665\pi$
$354$	−5.88890e9	−	1.29605e10i	−0.374991	−	0.825292i
$355$	2.98127e9	+	1.69076e10i	0.187710	+	1.06456i
$356$	−1.49036e9	+	4.09473e9i	−0.0927878	+	0.254932i
$357$	2.79848e9	+	1.08711e10i	0.172286	+	0.669272i
$358$	−8.89497e8	+	5.04459e9i	−0.0541517	+	0.307110i
$359$	1.49833e10	+	8.65060e9i	0.902047	+	0.520797i	0.877864	−	0.478910i	$-0.158968\pi$
$359$	1.49833e10	+	8.65060e9i	0.902047	+	0.520797i	0.0241833	+	0.999708i	$0.492301\pi$
$360$	5.06342e9	−	2.79188e9i	0.301463	−	0.166221i
$361$	5.83885e9	+	1.01132e10i	0.343794	+	0.595469i
$362$	5.01624e9	+	1.37820e10i	0.292108	+	0.802561i
$363$	−1.12865e10	+	7.73837e9i	−0.650028	+	0.445680i
$364$	−1.71671e10	+	1.44049e10i	−0.977892	+	0.820548i
$365$	−5.06220e9	−	6.03290e9i	−0.285212	−	0.339903i
$366$	1.99845e9	+	2.91475e9i	0.111370	+	0.162434i
$367$	−2.63458e10	+	9.58908e9i	−1.45227	+	0.528583i	−0.943224	−	0.332158i	$-0.892223\pi$
$367$	−2.63458e10	+	9.58908e9i	−1.45227	+	0.528583i	−0.509045	+	0.860740i	$0.670001\pi$
$368$	−6.53001e9	+	3.77010e9i	−0.356060	+	0.205571i
$369$	−1.32708e10	−	2.40683e10i	−0.715802	−	1.29819i
$370$	9.83314e9	−	1.70315e10i	0.524669	−	0.908753i
$371$	−1.57391e8	−	2.77523e7i	−0.00830777	−	0.00146488i
$372$	1.53917e10	−	3.96216e9i	0.803736	−	0.206900i
$373$	1.95992e10	+	7.13352e9i	1.01252	+	0.368526i	0.794399	−	0.607396i	$-0.207786\pi$
$373$	1.95992e10	+	7.13352e9i	1.01252	+	0.368526i	0.218118	+	0.975922i	$0.430008\pi$
$374$	−2.23588e9	+	3.94247e8i	−0.114278	+	0.0201503i
$375$	−1.84406e10	+	8.37893e9i	−0.932504	+	0.423705i
$376$	−4.39774e8	−	3.69014e8i	−0.0220028	−	0.0184625i
$377$		−	2.86005e10i		−	1.41582i
$378$	1.10716e10	+	2.56989e10i	0.542305	+	1.25877i
$379$	−9.38168e9			−0.454699			−0.227350	−	0.973813i	$-0.573006\pi$
$379$	−9.38168e9			−0.454699			−0.227350	+	0.973813i	$0.573006\pi$
$380$	−3.64718e9	+	4.34654e9i	−0.174913	+	0.208453i
$381$	−7.34509e9	+	1.02731e10i	−0.348576	+	0.487529i
$382$	3.77336e8	+	2.13998e9i	0.0177204	+	0.100498i
$383$	−1.93666e9	+	5.32094e9i	−0.0900034	+	0.247282i	−0.976525	−	0.215405i	$-0.930893\pi$
$383$	−1.93666e9	+	5.32094e9i	−0.0900034	+	0.247282i	0.886521	+	0.462688i	$0.153115\pi$
$384$	1.85138e9	+	5.15667e8i	0.0851472	+	0.0237162i
$385$	3.31428e9	−	1.87962e10i	0.150851	−	0.855516i
$386$	−1.14211e9	−	6.59398e8i	−0.0514469	−	0.0297029i
$387$	1.84519e10	−	2.88011e9i	0.822614	−	0.128400i
$388$	8.69285e9	+	1.50564e10i	0.383562	+	0.664348i
$389$	−6.25611e9	−	1.71885e10i	−0.273216	−	0.750655i	−0.998090	−	0.0617737i	$-0.980324\pi$
$389$	−6.25611e9	−	1.71885e10i	−0.273216	−	0.750655i	0.724874	−	0.688881i	$-0.241898\pi$
$390$	1.89258e10	+	9.05321e9i	0.818082	+	0.391331i
$391$	−1.04982e10	+	8.80906e9i	−0.449168	+	0.376897i
$392$	−1.47957e10	−	1.76328e10i	−0.626600	−	0.746753i
$393$	−1.69814e10	+	1.31732e9i	−0.711873	+	0.0552231i
$394$	2.41533e10	−	8.79109e9i	1.00229	−	0.364802i
$395$	3.94053e9	−	2.27507e9i	0.161870	−	0.0934557i
$396$	−5.35523e9	+	1.83054e9i	−0.217770	+	0.0744386i
$397$	−2.05364e10	+	3.55700e10i	−0.826726	+	1.43193i	0.0738664	+	0.997268i	$0.476466\pi$
$397$	−2.05364e10	+	3.55700e10i	−0.826726	+	1.43193i	−0.900593	+	0.434664i	$0.856867\pi$
$398$	5.65988e9	+	9.97990e8i	0.225567	+	0.0397735i
$399$	−1.92244e10	−	1.96068e10i	−0.758511	−	0.773599i
$400$	−3.12280e8	−	1.13661e8i	−0.0121985	−	0.00443987i
$401$	5.68533e9	−	1.00248e9i	0.219876	−	0.0387701i	−0.0626247	−	0.998037i	$-0.519947\pi$
$401$	5.68533e9	−	1.00248e9i	0.219876	−	0.0387701i	0.282501	+	0.959267i	$0.408836\pi$
$402$	6.59858e8	−	6.77332e9i	0.0252666	−	0.259357i
$403$	4.41759e10	+	3.70680e10i	1.67481	+	1.40533i
$404$		−	1.98123e10i		−	0.743719i
$405$	1.76159e10	−	1.93889e10i	0.654763	−	0.720666i
$406$	4.00308e10			1.47330
$407$	−1.23731e10	+	1.47456e10i	−0.450920	+	0.537386i
$408$	3.47654e9	+	3.38685e8i	0.125461	+	0.0122224i
$409$	−3.40118e9	−	1.92890e10i	−0.121545	−	0.689314i	−0.983300	−	0.181990i	$-0.941746\pi$
$409$	−3.40118e9	−	1.92890e10i	−0.121545	−	0.689314i	0.861756	−	0.507324i	$-0.169365\pi$
$410$	9.86452e9	−	2.71025e10i	0.349092	−	0.959123i
$411$	−1.67566e10	+	1.64298e10i	−0.587245	+	0.575792i
$412$	2.00329e8	−	1.13612e9i	0.00695272	−	0.0394308i
$413$	6.26096e10	+	3.61477e10i	2.15199	+	1.24245i
$414$	−2.24698e10	+	2.57318e10i	−0.764887	+	0.875929i
$415$	−1.18919e10	−	2.05974e10i	−0.400922	−	0.694417i
$416$	2.38498e9	+	6.55268e9i	0.0796363	+	0.218799i
$417$	1.95101e9	+	2.51503e10i	0.0645232	+	0.831760i
$418$	4.25433e9	−	3.56981e9i	0.139356	−	0.116934i
$419$	−4.21037e9	−	5.01772e9i	−0.136604	−	0.162798i	0.693405	−	0.720548i	$-0.256110\pi$
$419$	−4.21037e9	−	5.01772e9i	−0.136604	−	0.162798i	−0.830010	+	0.557749i	$0.811665\pi$
$420$	−1.26714e10	+	2.64897e10i	−0.407218	+	0.851293i
$421$	−4.93249e10	+	1.79528e10i	−1.57014	+	0.571483i	−0.973030	−	0.230678i	$-0.925905\pi$
$421$	−4.93249e10	+	1.79528e10i	−1.57014	+	0.571483i	−0.597107	+	0.802162i	$0.703683\pi$
$422$	−2.06631e10	+	1.19298e10i	−0.651547	+	0.376171i
$423$	−2.42609e9	−	9.37534e8i	−0.0757785	−	0.0292837i
$424$	−2.48651e7	+	4.30675e7i	−0.000769353	+	0.00133256i
$425$	−5.94825e8	−	1.04884e8i	−0.0182320	−	0.00321479i
$426$	−6.93697e9	+	2.49055e10i	−0.210636	+	0.756236i
$427$	−1.68653e10	−	6.13846e9i	−0.507320	−	0.184649i
$428$	−1.65120e9	+	2.91152e8i	−0.0492068	+	0.00867649i
$429$	−1.67042e10	−	1.19432e10i	−0.493170	−	0.352609i
$430$	1.50127e10	+	1.25971e10i	0.439120	+	0.368466i
$431$			5.46765e9i			0.158450i	0.996857	+	0.0792248i	$0.0252445\pi$
$431$			5.46765e9i			0.158450i	−0.996857	+	0.0792248i	$0.974755\pi$
$432$	8.69263e9	−	5.02339e8i	0.249584	−	0.0144232i
$433$	5.74008e10			1.63292			0.816462	−	0.577399i	$-0.195932\pi$
$433$	5.74008e10			1.63292			0.816462	+	0.577399i	$0.195932\pi$
$434$	−5.18824e10	+	6.18310e10i	−1.46238	+	1.74280i
$435$	−1.55028e10	−	3.41190e10i	−0.432965	−	0.952882i
$436$	8.20751e8	+	4.65471e9i	0.0227125	+	0.128809i
$437$	1.14655e10	−	3.15012e10i	0.314389	−	0.863777i
$438$	−2.95648e9	−	1.14849e10i	−0.0803300	−	0.312055i
$439$	4.09034e8	−	2.31975e9i	0.0110129	−	0.0624572i	−0.978806	−	0.204789i	$-0.934349\pi$
$439$	4.09034e8	−	2.31975e9i	0.0110129	−	0.0624572i	0.989819	+	0.142332i	$0.0454601\pi$
$440$	−5.14329e9	−	2.96948e9i	−0.137224	−	0.0792263i
$441$	−8.92692e10	−	5.39110e10i	−2.36019	−	1.42536i
$442$	6.33697e9	+	1.09760e10i	0.166032	+	0.287577i
$443$	−9.87952e8	−	2.71438e9i	−0.0256520	−	0.0704782i	0.926206	−	0.377019i	$-0.123051\pi$
$443$	−9.87952e8	−	2.71438e9i	−0.0256520	−	0.0704782i	−0.951858	+	0.306540i	$0.900829\pi$
$444$	2.44252e10	−	1.67467e10i	0.628502	−	0.430922i
$445$	−1.58703e10	+	1.33167e10i	−0.404710	+	0.339592i
$446$	−4.52051e9	−	5.38733e9i	−0.114248	−	0.136155i
$447$	1.32354e10	+	1.93039e10i	0.331517	+	0.483520i
$448$	−9.17149e9	+	3.33815e9i	−0.227682	+	0.0828693i
$449$	−1.65503e10	+	9.55529e9i	−0.407211	+	0.235103i	−0.689591	−	0.724199i	$-0.742210\pi$
$449$	−1.65503e10	+	9.55529e9i	−0.407211	+	0.235103i	0.282380	+	0.959303i	$0.408876\pi$
$450$	−1.50532e9	−	2.96502e7i	−0.0367096	−	0.000723067i
$451$	−1.41150e10	+	2.44479e10i	−0.341174	+	0.590930i
$452$	−7.23003e9	−	1.27485e9i	−0.173215	−	0.0305426i
$453$	6.88595e10	−	1.77260e10i	1.63520	−	0.420937i
$454$	1.76093e10	+	6.40927e9i	0.414495	+	0.150864i
$455$	−1.04926e11	+	1.85014e10i	−2.44816	+	0.431676i
$456$	−7.77898e9	+	3.53456e9i	−0.179913	+	0.0817479i
$457$	1.70069e10	+	1.42705e10i	0.389907	+	0.327171i	0.816577	−	0.577237i	$-0.195869\pi$
$457$	1.70069e10	+	1.42705e10i	0.389907	+	0.327171i	−0.426670	+	0.904407i	$0.640313\pi$
$458$			2.08446e9i			0.0473731i
$459$	1.54005e10	−	3.64261e9i	0.346963	−	0.0820658i
$460$	−3.58488e10			−0.800651
$461$	1.08079e10	−	1.28803e10i	0.239297	−	0.285183i	−0.633008	−	0.774145i	$-0.718180\pi$
$461$	1.08079e10	−	1.28803e10i	0.239297	−	0.285183i	0.872305	+	0.488963i	$0.162625\pi$
$462$	1.67164e10	−	2.33801e10i	0.366924	−	0.513191i
$463$	3.11709e9	+	1.76779e10i	0.0678305	+	0.384686i	0.999757	+	0.0220390i	$0.00701580\pi$
$463$	3.11709e9	+	1.76779e10i	0.0678305	+	0.384686i	−0.931927	+	0.362647i	$0.881873\pi$
$464$	4.26027e9	−	1.17050e10i	0.0919105	−	0.252522i
$465$	7.27922e10	+	2.02749e10i	1.55694	+	0.433658i
$466$	3.72270e9	−	2.11125e10i	0.0789432	−	0.447709i
$467$	1.26576e10	+	7.30789e9i	0.266125	+	0.153647i	0.627125	−	0.778918i	$-0.284231\pi$
$467$	1.26576e10	+	7.30789e9i	0.266125	+	0.153647i	−0.361000	+	0.932566i	$0.617565\pi$
$468$	1.98269e10	+	2.45967e10i	0.413306	+	0.512736i
$469$	1.72805e10	+	2.99308e10i	0.357163	+	0.618624i
$470$	−9.33509e8	−	2.56480e9i	−0.0191305	−	0.0525607i
$471$	3.63651e10	+	1.73953e10i	0.738926	+	0.353467i
$472$	1.72328e10	−	1.44600e10i	0.347206	−	0.291340i
$473$	−1.23299e10	−	1.46942e10i	−0.246328	−	0.293562i
$474$	6.83141e9	−	5.29942e8i	0.135331	−	0.0104982i
$475$	1.38836e9	−	5.05323e8i	0.0272727	−	0.00992646i
$476$	−1.53626e10	+	8.86958e9i	−0.299251	+	0.172773i
$477$	−4.34861e7	+	2.21070e8i	−0.000839996	+	0.00427029i
$478$	−3.75196e8	+	6.49858e8i	−0.00718698	+	0.0124482i
$479$	−9.35117e9	−	1.64886e9i	−0.177633	−	0.0313215i	0.0841240	−	0.996455i	$-0.473191\pi$
$479$	−9.35117e9	−	1.64886e9i	−0.177633	−	0.0313215i	−0.261757	+	0.965134i	$0.584302\pi$
$480$	6.39701e9	+	6.52426e9i	0.120507	+	0.122904i
$481$	1.00974e11	+	3.67516e10i	1.88638	+	0.686587i
$482$	4.88646e10	−	8.61614e9i	0.905328	−	0.159634i
$483$	1.68217e10	−	1.72672e11i	0.309088	−	3.17273i
$484$	−1.65657e10	−	1.39003e10i	−0.301876	−	0.253304i
$485$			8.26577e10i			1.49388i
$486$	3.65296e10	−	1.48918e10i	0.654787	−	0.266934i
$487$	−1.09510e11			−1.94687			−0.973435	−	0.228964i	$-0.926466\pi$
$487$	−1.09510e11			−1.94687			−0.973435	+	0.228964i	$0.926466\pi$
$488$	−3.58976e9	+	4.27811e9i	−0.0632975	+	0.0754350i
$489$	−5.27155e10	−	5.13555e9i	−0.921941	−	0.0898156i
$490$	−1.90033e10	−	1.07773e11i	−0.329644	−	1.86950i
$491$	−1.59722e10	+	4.38833e10i	−0.274814	+	0.755045i	0.723116	+	0.690727i	$0.242709\pi$
$491$	−1.59722e10	+	4.38833e10i	−0.274814	+	0.755045i	−0.997929	+	0.0643180i	$0.979513\pi$
$492$	3.10122e10	−	3.04074e10i	0.529264	−	0.518942i
$493$	3.93129e9	−	2.22954e10i	0.0665498	−	0.377423i
$494$	−2.68486e10	−	1.55011e10i	−0.450831	−	0.260288i
$495$	−2.64011e10	−	5.19328e9i	−0.439745	−	0.0865009i
$496$	1.25578e10	+	2.17507e10i	0.207485	+	0.359374i
$497$	−4.49062e10	−	1.23379e11i	−0.736005	−	2.02216i
$498$	−2.77004e9	−	3.57082e10i	−0.0450369	−	0.580565i
$499$	−1.51236e10	+	1.26902e10i	−0.243923	+	0.204676i	−0.756550	−	0.653936i	$-0.773117\pi$
$499$	−1.51236e10	+	1.26902e10i	−0.243923	+	0.204676i	0.512627	+	0.858611i	$0.328672\pi$
$500$	−2.05742e10	−	2.45194e10i	−0.329188	−	0.392311i
$501$	4.33873e10	−	9.07018e10i	0.688672	−	1.43968i
$502$	−6.40083e10	+	2.32971e10i	−1.00791	+	0.366849i
$503$	1.03427e11	−	5.97137e10i	1.61571	−	0.932828i	0.627692	−	0.778462i	$-0.284000\pi$
$503$	1.03427e11	−	5.97137e10i	1.61571	−	0.932828i	0.988014	−	0.154367i	$-0.0493337\pi$
$504$	−3.44269e10	+	2.77509e10i	−0.533551	+	0.430085i
$505$	4.70972e10	−	8.15748e10i	0.724152	−	1.25427i
$506$	3.45552e10	+	6.09302e9i	0.527123	+	0.0929459i
$507$	−1.30286e10	+	4.67760e10i	−0.197181	+	0.707931i
$508$	−1.87531e10	−	6.82556e9i	−0.281590	−	0.102491i
$509$	−4.55739e10	+	8.03591e9i	−0.678962	+	0.119719i	−0.502486	−	0.864586i	$-0.667581\pi$
$509$	−4.55739e10	+	8.03591e9i	−0.678962	+	0.119719i	−0.176476	+	0.984305i	$0.556470\pi$
$510$	1.35092e10	+	9.65886e9i	0.199686	+	0.142773i
$511$	4.61370e10	+	3.87135e10i	0.676652	+	0.567778i
$512$			3.03700e9i			0.0441942i
$513$	−2.81693e10	+	2.65523e10i	−0.406731	+	0.383383i
$514$	9.70900e10			1.39098
$515$	3.52559e9	−	4.20164e9i	0.0501191	−	0.0597296i
$516$	1.22081e10	+	2.68681e10i	0.172207	+	0.378999i
$517$	4.63900e8	+	2.63091e9i	0.00649326	+	0.0368251i
$518$	−5.14395e10	+	1.41329e11i	−0.714460	+	1.96296i
$519$	−9.26496e9	−	3.59913e10i	−0.127695	−	0.496053i
$520$	−5.75698e9	+	3.26494e10i	−0.0787374	+	0.446542i
$521$	−1.06319e11	−	6.13835e10i	−1.44298	−	0.833106i	−0.444935	−	0.895563i	$-0.646773\pi$
$521$	−1.06319e11	−	6.13835e10i	−1.44298	−	0.833106i	−0.998048	+	0.0624566i	$0.980106\pi$
$522$	1.11136e9	−	5.64230e10i	0.0149683	−	0.759931i
$523$	8.51271e9	+	1.47445e10i	0.113779	+	0.197071i	0.917291	−	0.398218i	$-0.130371\pi$
$523$	8.51271e9	+	1.47445e10i	0.113779	+	0.197071i	−0.803512	+	0.595288i	$0.797038\pi$
$524$	−9.20560e9	−	2.52922e10i	−0.122103	−	0.335476i
$525$	6.30632e9	−	4.32382e9i	0.0830116	−	0.0569154i
$526$	3.13980e10	−	2.63460e10i	0.410165	−	0.344169i
$527$	2.93420e10	+	3.49684e10i	0.380406	+	0.453350i
$528$	−5.05729e9	−	7.37610e9i	−0.0650702	−	0.0949054i
$529$	1.25439e11	−	4.56560e10i	1.60181	−	0.583009i
$530$	−2.04758e8	+	1.18217e8i	−0.00259500	+	0.00149823i
$531$	5.26880e10	−	8.72440e10i	0.662725	−	1.09738i
$532$	2.16961e10	−	3.75788e10i	0.270855	−	0.469134i
$533$	1.55195e11	+	2.73650e10i	1.92295	+	0.339068i
$534$	−3.02125e10	+	7.77737e9i	−0.371553	+	0.0956462i
$535$	−7.49077e9	−	2.72642e9i	−0.0914347	−	0.0332795i
$536$	1.05908e10	−	1.86745e9i	0.128313	−	0.0226250i
$537$	−3.33886e10	+	1.51709e10i	−0.401515	+	0.182438i
$538$	−2.59787e10	−	2.17987e10i	−0.310090	−	0.260197i
$539$			1.07114e11i			1.26909i
$540$	3.69851e10	+	1.85956e10i	0.434962	+	0.218693i
$541$	−4.41827e10			−0.515778			−0.257889	−	0.966175i	$-0.583027\pi$
$541$	−4.41827e10			−0.515778			−0.257889	+	0.966175i	$0.583027\pi$
$542$	2.95483e10	−	3.52143e10i	0.342401	−	0.408058i
$543$	−6.10720e10	+	8.54172e10i	−0.702495	+	0.982530i
$544$	9.58504e8	+	5.43595e9i	0.0109446	+	0.0620697i
$545$	−7.68571e9	+	2.11163e10i	−0.0871161	+	0.239349i
$546$	−1.54560e11	−	4.30499e10i	−1.73911	−	0.484397i
$547$	−1.14275e10	+	6.48085e10i	−0.127644	+	0.723907i	0.852058	+	0.523448i	$0.175355\pi$
$547$	−1.14275e10	+	6.48085e10i	−0.127644	+	0.723907i	−0.979702	+	0.200459i	$0.935757\pi$
$548$	−3.21161e10	−	1.85422e10i	−0.356123	−	0.205608i
$549$	−9.12031e9	+	2.36010e10i	−0.100397	+	0.259801i
$550$	7.73228e8	+	1.33927e9i	0.00845001	+	0.0146358i
$551$	1.89407e10	+	5.20391e10i	0.205489	+	0.564577i
$552$	−4.86989e10	−	2.32952e10i	−0.524521	−	0.250905i
$553$	−2.66564e10	+	2.23674e10i	−0.285037	+	0.239174i
$554$	2.09992e10	+	2.50258e10i	0.222927	+	0.265674i
$555$	1.40378e11	−	1.08897e10i	1.47954	−	0.114775i
$556$	−3.74590e10	+	1.36340e10i	−0.391974	+	0.142667i
$557$	−1.45491e11	+	8.39991e10i	−1.51152	+	0.872678i	−0.511613	+	0.859216i	$0.670952\pi$
$557$	−1.45491e11	+	8.39991e10i	−1.51152	+	0.872678i	−0.999909	+	0.0134620i	$0.995715\pi$
$558$	8.57097e10	+	7.48442e10i	0.884084	+	0.772008i
$559$	−5.35396e10	+	9.27333e10i	−0.548312	+	0.949705i
$560$	−4.56980e10	−	8.05779e9i	−0.464670	−	0.0819339i
$561$	−1.13800e10	−	1.16064e10i	−0.114893	−	0.117178i
$562$	−3.68134e10	−	1.33990e10i	−0.369029	−	0.134315i
$563$	−4.17694e10	+	7.36508e9i	−0.415743	+	0.0733067i	−0.377607	−	0.925966i	$-0.623253\pi$
$563$	−4.17694e10	+	7.36508e9i	−0.415743	+	0.0733067i	−0.0381357	+	0.999273i	$0.512142\pi$
$564$	3.98523e8	−	4.09076e9i	0.00393855	−	0.0404285i
$565$	−2.67383e10	−	2.24361e10i	−0.262386	−	0.220168i
$566$		−	7.49484e10i		−	0.730293i
$567$	−1.06924e11	+	1.69419e11i	−1.03453	+	1.63919i
$568$	−4.08550e10			−0.392511
$569$	4.96494e9	−	5.91699e9i	0.0473658	−	0.0564484i	−0.741841	−	0.670575i	$-0.766047\pi$
$569$	4.96494e9	−	5.91699e9i	0.0473658	−	0.0564484i	0.789207	+	0.614127i	$0.210492\pi$
$570$	−4.04314e10	−	3.93883e9i	−0.383018	−	0.0373136i
$571$	−1.20307e9	−	6.82293e9i	−0.0113174	−	0.0641839i	0.978626	−	0.205648i	$-0.0659302\pi$
$571$	−1.20307e9	−	6.82293e9i	−0.0113174	−	0.0641839i	−0.989943	+	0.141464i	$0.954819\pi$
$572$	1.10985e10	−	3.04928e10i	0.103676	−	0.284848i
$573$	−1.11085e10	+	1.08919e10i	−0.103048	+	0.101038i
$574$	−3.83016e10	+	2.17219e11i	−0.352833	+	2.00102i
$575$	8.08412e9	+	4.66737e9i	0.0739540	+	0.0426973i
$576$	4.45046e9	+	1.30198e10i	0.0404310	+	0.118281i
$577$	3.42329e9	+	5.92932e9i	0.0308845	+	0.0534936i	0.881055	−	0.473015i	$-0.156834\pi$
$577$	3.42329e9	+	5.92932e9i	0.0308845	+	0.0534936i	−0.850170	+	0.526508i	$0.823501\pi$
$578$	−2.35615e10	−	6.47348e10i	−0.211102	−	0.579998i
$579$	−7.30252e8	−	9.41358e9i	−0.00649769	−	0.0837608i
$580$	4.53660e10	−	3.80666e10i	0.400884	−	0.336382i
$581$	1.16916e11	+	1.39335e11i	1.02605	+	1.22280i
$582$	−5.37125e10	+	1.12287e11i	−0.468148	+	0.978669i
$583$	2.17462e8	−	7.91498e7i	0.00188239	−	0.000685134i
$584$	1.62299e10	−	9.37035e9i	0.139529	−	0.0805572i
$585$	2.31644e10	+	1.48406e11i	0.197787	+	1.26715i
$586$	−1.30310e10	+	2.25703e10i	−0.110506	+	0.191403i
$587$	1.17881e11	+	2.07856e10i	0.992867	+	0.175069i	0.646405	−	0.762995i	$-0.276272\pi$
$587$	1.17881e11	+	2.07856e10i	0.992867	+	0.175069i	0.346462	+	0.938064i	$0.387383\pi$
$588$	4.42178e10	−	1.58753e11i	0.369903	−	1.32805i
$589$	−1.04927e11	−	3.81903e10i	−0.871819	−	0.317316i
$590$	1.05328e11	−	1.85722e10i	0.869233	−	0.153269i
$591$	1.49696e11	+	1.07030e11i	1.22704	+	0.877317i
$592$	3.58501e10	+	3.00818e10i	0.291879	+	0.244916i
$593$		−	1.43481e11i		−	1.16031i	−0.814506	−	0.580155i	$-0.802992\pi$
$593$		−	1.43481e11i		−	1.16031i	0.814506	−	0.580155i	$-0.197008\pi$
$594$	−3.24899e10	−	2.42107e10i	−0.260977	−	0.194474i
$595$	−8.43382e10			−0.672910
$596$	−2.37744e10	+	2.83332e10i	−0.188419	+	0.224549i
$597$	1.70213e10	+	3.74611e10i	0.133997	+	0.294906i
$598$	−3.40131e10	−	1.92898e11i	−0.265976	−	1.50842i
$599$	3.73399e10	−	1.02591e11i	0.290046	−	0.796894i	−0.706013	−	0.708199i	$-0.749508\pi$
$599$	3.73399e10	−	1.02591e11i	0.290046	−	0.796894i	0.996059	−	0.0886950i	$-0.0282696\pi$
$600$	−5.93133e8	−	2.30412e9i	−0.00457665	−	0.0177787i
$601$	1.76969e9	−	1.00364e10i	0.0135644	−	0.0769275i	−0.977274	−	0.211979i	$-0.932009\pi$
$601$	1.76969e9	−	1.00364e10i	0.0135644	−	0.0769275i	0.990839	+	0.135052i	$0.0431201\pi$
$602$	−1.29795e11	−	7.49370e10i	−0.988260	−	0.570572i
$603$	4.26668e10	−	2.35258e10i	0.322716	−	0.177940i
$604$	5.61813e10	+	9.73088e10i	0.422128	+	0.731147i
$605$	−3.51640e10	−	9.66124e10i	−0.262468	−	0.721126i
$606$	1.16988e11	−	8.02109e10i	0.867464	−	0.594761i
$607$	−6.80673e10	+	5.71152e10i	−0.501399	+	0.420724i	−0.858090	−	0.513499i	$-0.828349\pi$
$607$	−6.80673e10	+	5.71152e10i	−0.501399	+	0.420724i	0.356691	+	0.934222i	$0.383905\pi$
$608$	−8.67902e9	−	1.03433e10i	−0.0635121	−	0.0756908i
$609$	1.62067e11	+	2.36376e11i	1.17822	+	1.71844i
$610$	−2.49503e10	+	9.08116e9i	−0.180201	+	0.0655876i
$611$	1.29151e10	−	7.45656e9i	0.0926690	−	0.0535025i
$612$	1.20751e10	+	2.18996e10i	0.0860764	+	0.156110i
$613$	4.78807e10	−	8.29318e10i	0.339093	−	0.587326i	−0.645170	−	0.764039i	$-0.723213\pi$
$613$	4.78807e10	−	8.29318e10i	0.339093	−	0.587326i	0.984262	+	0.176713i	$0.0565466\pi$
$614$	8.76166e10	+	1.54492e10i	0.616472	+	0.108701i
$615$	1.99973e11	−	5.14775e10i	1.39788	−	0.359846i
$616$	4.26795e10	+	1.55341e10i	0.296412	+	0.107885i
$617$	−1.02462e11	+	1.80668e10i	−0.707004	+	0.124664i	−0.515577	−	0.856843i	$-0.672423\pi$
$617$	−1.02462e11	+	1.80668e10i	−0.707004	+	0.124664i	−0.191427	+	0.981507i	$0.561311\pi$
$618$	7.51965e9	−	3.41673e9i	0.0515518	−	0.0234238i
$619$	−8.74309e10	−	7.33632e10i	−0.595528	−	0.499708i	0.294477	−	0.955659i	$-0.404855\pi$
$619$	−8.74309e10	−	7.33632e10i	−0.595528	−	0.499708i	−0.890005	+	0.455951i	$0.849299\pi$
$620$			1.19408e11i			0.808105i
$621$	−2.42912e11	−	2.85038e10i	−1.63336	−	0.191662i
$622$	2.74094e10			0.183121
$623$	1.01841e11	−	1.21369e11i	0.676034	−	0.805666i
$624$	−2.90368e10	+	4.06117e10i	−0.191518	+	0.267863i
$625$	−2.50493e10	−	1.42062e11i	−0.164163	−	0.931016i
$626$	2.92845e10	−	8.04585e10i	0.190695	−	0.523931i
$627$	3.83030e10	+	1.06686e10i	0.247835	+	0.0690298i
$628$	−1.10618e10	+	6.27344e10i	−0.0711190	+	0.403336i
$629$	7.36624e10	+	4.25290e10i	0.470590	+	0.271695i
$630$	−2.07718e11	+	3.24222e10i	−1.31859	+	0.205817i
$631$	−8.73812e10	−	1.51349e11i	−0.551189	−	0.954688i	−0.998189	−	0.0601538i	$-0.980841\pi$
$631$	−8.73812e10	−	1.51349e11i	−0.551189	−	0.954688i	0.447000	−	0.894534i	$-0.352492\pi$
$632$	3.70331e9	+	1.01748e10i	0.0232125	+	0.0637757i
$633$	−1.54099e11	−	7.37136e10i	−0.959811	−	0.459127i
$634$	−1.14557e11	+	9.61249e10i	−0.709031	+	0.594948i
$635$	−6.09882e10	−	7.26829e10i	−0.375103	−	0.447031i
$636$	−3.54974e8	+	2.75369e7i	−0.00216954	+	0.000168301i
$637$	5.61884e11	−	2.04509e11i	3.41263	−	1.24209i
$638$	−5.01990e10	+	2.89824e10i	−0.302979	+	0.174925i
$639$	−1.75148e11	+	5.98694e10i	−1.05051	+	0.359089i
$640$	−7.21948e9	+	1.25045e10i	−0.0430315	+	0.0745327i
$641$	7.99764e9	+	1.41020e9i	0.0473729	+	0.00835312i	0.197284	−	0.980346i	$-0.436788\pi$
$641$	7.99764e9	+	1.41020e9i	0.0473729	+	0.00835312i	−0.149911	+	0.988699i	$0.547899\pi$
$642$	−8.40418e9	−	8.57134e9i	−0.0494715	−	0.0504555i
$643$	1.09381e11	+	3.98115e10i	0.639880	+	0.232897i	0.641526	−	0.767101i	$-0.278302\pi$
$643$	1.09381e11	+	3.98115e10i	0.639880	+	0.232897i	−0.00164564	+	0.999999i	$0.500524\pi$
$644$	2.69991e11	−	4.76067e10i	1.56966	−	0.276773i
$645$	−1.36044e10	+	1.39647e11i	−0.0786035	+	0.806851i
$646$	−1.87991e10	−	1.57743e10i	−0.107946	−	0.0905774i
$647$			2.68470e11i			1.53207i	0.642800	+	0.766034i	$0.277773\pi$
$647$			2.68470e11i			1.53207i	−0.642800	+	0.766034i	$0.722227\pi$
$648$	3.81587e10	+	4.92948e10i	0.216418	+	0.279577i
$649$	−1.04684e11			−0.590067
$650$	5.54906e9	−	6.61311e9i	0.0310861	−	0.0370469i
$651$	−5.75150e11	−	5.60312e10i	−3.20227	−	0.311965i
$652$	−1.45340e10	−	8.24264e10i	−0.0804257	−	0.456117i
$653$	1.68626e10	−	4.63295e10i	0.0927408	−	0.254803i	−0.884646	−	0.466264i	$-0.845600\pi$
$653$	1.68626e10	−	4.63295e10i	0.0927408	−	0.254803i	0.977387	+	0.211461i	$0.0678220\pi$
$654$	−2.41625e10	+	2.36912e10i	−0.132078	+	0.129502i
$655$	2.22209e10	−	1.26021e11i	0.120725	−	0.684665i
$656$	5.94386e10	+	3.43169e10i	0.320962	+	0.185307i
$657$	5.58471e10	−	6.39547e10i	0.299736	−	0.343250i
$658$	1.04366e10	+	1.80768e10i	0.0556745	+	0.0964311i
$659$	−5.50314e10	−	1.51198e11i	−0.291789	−	0.801684i	−0.995805	−	0.0914998i	$-0.970834\pi$
$659$	−5.50314e10	−	1.51198e11i	−0.291789	−	0.801684i	0.704016	−	0.710184i	$-0.251388\pi$
$660$	−3.28856e9	−	4.23923e10i	−0.0173312	−	0.223415i
$661$	−1.27976e10	+	1.07385e10i	−0.0670384	+	0.0562519i	−0.675691	−	0.737185i	$-0.736155\pi$
$661$	−1.27976e10	+	1.07385e10i	−0.0670384	+	0.0562519i	0.608653	+	0.793437i	$0.291710\pi$
$662$	1.32180e11	+	1.57526e11i	0.688231	+	0.820201i
$663$	−3.91557e10	+	8.18555e10i	−0.202647	+	0.423637i
$664$	5.31841e10	−	1.93574e10i	0.273596	−	0.0995807i
$665$	1.78663e11	−	1.03151e11i	0.913583	−	0.527457i
$666$	1.97773e11	+	7.64271e10i	1.00524	+	0.388464i
$667$	−1.74944e11	+	3.03012e11i	−0.883884	+	1.53093i
$668$	1.56472e11	+	2.75902e10i	0.785833	+	0.138564i
$669$	1.35098e10	−	4.85037e10i	0.0674443	−	0.242142i
$670$	4.80458e10	+	1.74872e10i	0.238427	+	0.0867804i
$671$	2.55934e10	−	4.51281e9i	0.126252	−	0.0222616i
$672$	−5.68424e10	−	4.06415e10i	−0.278738	−	0.199293i
$673$	1.65026e11	+	1.38473e11i	0.804435	+	0.675001i	0.949273	−	0.314455i	$-0.101822\pi$
$673$	1.65026e11	+	1.38473e11i	0.804435	+	0.675001i	−0.144838	+	0.989455i	$0.546266\pi$
$674$		−	1.68415e11i		−	0.816094i
$675$	−5.91929e9	−	9.00872e9i	−0.0285138	−	0.0433959i
$676$	−7.67313e10			−0.367439
$677$	1.44588e11	−	1.72314e11i	0.688302	−	0.820286i	−0.302847	−	0.953039i	$-0.597937\pi$
$677$	1.44588e11	−	1.72314e11i	0.688302	−	0.820286i	0.991149	+	0.132753i	$0.0423817\pi$
$678$	−2.17433e10	−	4.78535e10i	−0.102898	−	0.226462i
$679$	−1.09768e11	−	6.22526e11i	−0.516413	−	2.92873i
$680$	−8.97567e9	+	2.46605e10i	−0.0419789	+	0.115336i
$681$	3.34465e10	+	1.29928e11i	0.155511	+	0.604109i
$682$	2.02952e10	−	1.15100e11i	0.0938113	−	0.532030i
$683$	−2.85374e11	−	1.64761e11i	−1.31139	−	0.757131i	−0.329063	−	0.944308i	$-0.606733\pi$
$683$	−2.85374e11	−	1.64761e11i	−1.31139	−	0.757131i	−0.982326	+	0.187177i	$0.940066\pi$
$684$	−5.23646e10	−	3.16238e10i	−0.239229	−	0.144474i
$685$	−8.81563e10	−	1.52691e11i	−0.400397	−	0.693508i
$686$	1.82426e11	+	5.01211e11i	0.823740	+	2.26321i
$687$	−1.23084e10	+	8.43904e9i	−0.0552554	+	0.0378849i
$688$	−3.57249e10	+	2.99768e10i	−0.159447	+	0.133792i
$689$	−8.30386e8	−	9.89615e8i	−0.00368471	−	0.00439126i
$690$	−1.45136e11	−	2.11681e11i	−0.640291	−	0.933869i
$691$	−2.25153e10	+	8.19488e9i	−0.0987563	+	0.0359443i	−0.390926	−	0.920422i	$-0.627845\pi$
$691$	−2.25153e10	+	8.19488e9i	−0.0987563	+	0.0359443i	0.292169	+	0.956367i	$0.405623\pi$
$692$	5.08611e10	−	2.93647e10i	0.221800	−	0.128056i
$693$	2.05733e11	+	4.05231e9i	0.892013	+	0.0175699i
$694$	−1.39393e11	+	2.41435e11i	−0.600899	+	1.04079i
$695$	−1.86644e11	−	3.29103e10i	−0.799970	−	0.141056i
$696$	8.63640e10	−	2.22320e10i	0.368041	−	0.0947419i
$697$	1.17220e11	+	4.26647e10i	0.496674	+	0.180775i
$698$	2.26710e11	−	3.99752e10i	0.955102	−	0.168410i
$699$	1.39737e11	−	6.34930e10i	0.585334	−	0.265960i
$700$	9.25608e9	+	7.76677e9i	0.0385509	+	0.0323481i
$701$		−	4.21785e11i		−	1.74670i	−0.487091	−	0.873351i	$-0.661942\pi$
$701$		−	4.21785e11i		−	1.74670i	0.487091	−	0.873351i	$-0.338058\pi$
$702$	−6.49693e10	+	2.16656e11i	−0.267522	+	0.892116i
$703$	−2.08063e11			−0.851869
$704$	9.08430e9	−	1.08262e10i	0.0369829	−	0.0440745i
$705$	1.13653e10	−	1.58959e10i	0.0460072	−	0.0643471i
$706$	2.00445e10	+	1.13678e11i	0.0806821	+	0.457571i
$707$	−2.46377e11	+	6.76915e11i	−0.986104	+	2.70930i
$708$	1.55152e11	+	4.32147e10i	0.617481	+	0.171988i
$709$	−1.96979e10	+	1.11712e11i	−0.0779533	+	0.442095i	0.920703	+	0.390265i	$0.127617\pi$
$709$	−1.96979e10	+	1.11712e11i	−0.0779533	+	0.442095i	−0.998656	+	0.0518302i	$0.983495\pi$
$710$	−1.68216e11	−	9.71195e10i	−0.661963	−	0.382185i
$711$	3.07865e10	+	3.81928e10i	0.120471	+	0.149453i
$712$	−2.46498e10	−	4.26948e10i	−0.0959167	−	0.166133i
$713$	−2.41289e11	−	6.62937e11i	−0.933642	−	2.56516i
$714$	−1.14570e11	−	5.48045e10i	−0.440835	−	0.210874i
$715$	1.18184e11	−	9.91678e10i	0.452203	−	0.379443i
$716$	−3.72517e10	−	4.43949e10i	−0.141741	−	0.168920i
$717$	−5.35630e9	+	4.15511e8i	−0.0202670	+	0.00157219i
$718$	−1.83936e11	+	6.69473e10i	−0.692101	+	0.251904i
$719$	−1.50686e11	+	8.69985e10i	−0.563841	+	0.325534i	−0.754686	−	0.656086i	$-0.772211\pi$
$719$	−1.50686e11	+	8.69985e10i	−0.563841	+	0.325534i	0.190845	+	0.981620i	$0.438877\pi$
$720$	−1.26261e10	+	6.41871e10i	−0.0469827	+	0.238846i
$721$	−2.09729e10	+	3.63260e10i	−0.0776098	+	0.134424i
$722$	−1.30111e11	−	2.29421e10i	−0.478812	−	0.0844274i
$723$	2.48707e11	+	2.53654e11i	0.910197	+	0.928301i
$724$	−1.55926e11	−	5.67523e10i	−0.567497	−	0.206552i
$725$	−1.51864e10	+	2.67778e9i	−0.0549672	+	0.00969220i
$726$	1.50118e10	−	1.54094e11i	0.0540364	−	0.554674i
$727$	−2.31003e11	−	1.93835e11i	−0.826953	−	0.693896i	0.127636	−	0.991821i	$-0.459261\pi$
$727$	−2.31003e11	−	1.93835e11i	−0.826953	−	0.693896i	−0.954589	+	0.297925i	$0.903705\pi$
$728$		−	2.53540e11i		−	0.902655i
$729$	2.35826e11	+	1.55411e11i	0.834990	+	0.550265i
$730$	8.90998e10			0.313751
$731$	−5.44833e10	+	6.49307e10i	−0.190807	+	0.227395i
$732$	−3.97949e10	−	3.87682e9i	−0.138606	−	0.0135030i
$733$	5.67847e10	+	3.22042e11i	0.196705	+	1.11557i	0.909970	+	0.414675i	$0.136105\pi$
$733$	5.67847e10	+	3.22042e11i	0.196705	+	1.11557i	−0.713265	+	0.700895i	$0.752784\pi$
$734$	1.08488e11	−	2.98069e11i	0.373764	−	1.02691i
$735$	5.59447e11	−	5.48536e11i	1.91694	−	1.87956i
$736$	1.48135e10	−	8.40117e10i	0.0504832	−	0.286305i
$737$	−4.33399e10	−	2.50223e10i	−0.146899	−	0.0848119i
$738$	3.05105e11	+	6.00163e10i	1.02855	+	0.202322i
$739$	−1.78330e11	−	3.08877e11i	−0.597925	−	1.03564i	−0.993127	−	0.117042i	$-0.962659\pi$
$739$	−1.78330e11	−	3.08877e11i	−0.597925	−	1.03564i	0.395202	−	0.918594i	$-0.370675\pi$
$740$	7.60990e10	+	2.09080e11i	0.253777	+	0.697246i
$741$	−1.71667e10	−	2.21293e11i	−0.0569395	−	0.733999i
$742$	1.38512e9	−	1.16225e9i	0.00456954	−	0.00383430i
$743$	3.85547e11	+	4.59477e11i	1.26509	+	1.50768i	0.768749	+	0.639551i	$0.220880\pi$
$743$	3.85547e11	+	4.59477e11i	1.26509	+	1.50768i	0.496343	+	0.868127i	$0.334676\pi$
$744$	−7.75937e10	+	1.62211e11i	−0.253241	+	0.529404i
$745$	−1.65241e11	+	6.01430e10i	−0.536406	+	0.195236i
$746$	−2.04356e11	+	1.17985e11i	−0.659831	+	0.380953i
$747$	1.99636e11	−	1.60923e11i	0.641147	−	0.516815i
$748$	1.28432e10	−	2.22451e10i	0.0410267	−	0.0710603i
$749$	6.00364e10	+	1.05860e10i	0.190760	+	0.0336362i
$750$	6.14874e10	−	2.20755e11i	0.194331	−	0.697696i
$751$	5.82770e11	+	2.12111e11i	1.83205	+	0.666812i	0.992302	+	0.123838i	$0.0395202\pi$
$751$	5.82770e11	+	2.12111e11i	1.83205	+	0.666812i	0.839749	+	0.542975i	$0.182702\pi$
$752$	6.39635e9	−	1.12785e9i	0.0200014	−	0.00352679i
$753$	−3.96706e11	−	2.83639e11i	−1.23393	−	0.882239i
$754$	2.47875e11	+	2.07992e11i	0.766915	+	0.643518i
$755$			5.34211e11i			1.64409i
$756$	−3.03243e11	−	9.09347e10i	−0.928333	−	0.278383i
$757$	−1.73730e11			−0.529042			−0.264521	−	0.964380i	$-0.585214\pi$
$757$	−1.73730e11			−0.529042			−0.264521	+	0.964380i	$0.585214\pi$
$758$	6.82265e10	−	8.13092e10i	0.206670	−	0.246299i
$759$	1.03920e11	+	2.28711e11i	0.313136	+	0.689159i
$760$	−1.11472e10	−	6.32188e10i	−0.0334126	−	0.189492i
$761$	−1.65093e11	+	4.53591e11i	−0.492256	+	1.35246i	0.406354	+	0.913716i	$0.366800\pi$
$761$	−1.65093e11	+	4.53591e11i	−0.492256	+	1.35246i	−0.898610	+	0.438747i	$0.855422\pi$
$762$	−3.56189e10	−	1.38367e11i	−0.105648	−	0.410406i
$763$	2.98419e10	−	1.69242e11i	0.0880496	−	0.499354i
$764$	−2.12909e10	−	1.22923e10i	−0.0624913	−	0.0360794i
$765$	−2.34145e9	+	1.18874e11i	−0.00683658	+	0.347089i
$766$	−3.20315e10	−	5.54802e10i	−0.0930384	−	0.161147i
$767$	1.99869e11	+	5.49136e11i	0.577517	+	1.58671i
$768$	−1.79330e10	+	1.22954e10i	−0.0515475	+	0.0353427i
$769$	−4.15701e11	+	3.48815e11i	−1.18871	+	0.997446i	−0.188829	+	0.982010i	$0.560469\pi$
$769$	−4.15701e11	+	3.48815e11i	−1.18871	+	0.997446i	−0.999881	+	0.0154358i	$0.995086\pi$
$770$	1.38801e11	+	1.65416e11i	0.394847	+	0.470561i
$771$	3.93073e11	+	5.73300e11i	1.11239	+	1.62243i
$772$	1.40207e10	−	5.10310e9i	0.0394729	−	0.0143670i
$773$	1.22712e11	−	7.08481e10i	0.343693	−	0.198431i	−0.318211	−	0.948020i	$-0.603082\pi$
$773$	1.22712e11	−	7.08481e10i	0.343693	−	0.198431i	0.661904	+	0.749589i	$0.269749\pi$
$774$	−1.09226e11	+	1.80864e11i	−0.304343	+	0.503950i
$775$	1.55465e10	−	2.69273e10i	0.0430948	−	0.0746425i
$776$	−1.93708e11	−	3.41560e10i	−0.534197	−	0.0941934i
$777$	−1.04278e12	+	2.68435e11i	−2.86094	+	0.736470i
$778$	1.94466e11	+	7.07799e10i	0.530793	+	0.193193i
$779$	−3.00502e11	+	5.29866e10i	−0.816014	+	0.143885i
$780$	−2.16097e11	+	9.81888e10i	−0.583808	+	0.265267i
$781$	1.45639e11	+	1.22206e11i	0.391448	+	0.328464i
$782$		−	1.55048e11i		−	0.414610i
$783$	3.37668e11	−	2.21869e11i	0.898344	−	0.590268i
$784$	2.60419e11			0.689300
$785$	−1.94676e11	+	2.32006e11i	−0.512666	+	0.610971i
$786$	1.12077e11	−	1.56754e11i	0.293647	−	0.410704i
$787$	−5.17348e10	−	2.93403e11i	−0.134860	−	0.764830i	−0.974957	−	0.222394i	$-0.928613\pi$
$787$	−5.17348e10	−	2.93403e11i	−0.134860	−	0.764830i	0.840097	−	0.542437i	$-0.182498\pi$
$788$	−9.94598e10	+	2.73264e11i	−0.257954	+	0.708724i
$789$	2.82685e11	+	7.87368e10i	0.729449	+	0.203175i
$790$	−8.93922e9	+	5.06968e10i	−0.0229504	+	0.130158i
$791$	2.31171e11	+	1.33467e11i	0.590511	+	0.340932i
$792$	2.30800e10	−	5.97249e10i	0.0586590	−	0.151794i
$793$	−7.25373e10	−	1.25638e11i	−0.183429	−	0.317709i
$794$	−1.58932e11	−	4.36661e11i	−0.399879	−	1.09866i
$795$	−1.52703e9	−	7.30456e8i	−0.00382277	−	0.00182863i
$796$	−4.98098e10	+	4.17954e10i	−0.124069	+	0.104106i
$797$	−1.47296e11	−	1.75541e11i	−0.365055	−	0.435056i	0.551983	−	0.833856i	$-0.313871\pi$
$797$	−1.47296e11	−	1.75541e11i	−0.365055	−	0.435056i	−0.917038	+	0.398799i	$0.869427\pi$
$798$	3.09735e11	−	2.40275e10i	0.763797	−	0.0592511i
$799$	1.10929e10	−	4.03749e9i	0.0272181	−	0.00990659i
$800$	3.25608e9	−	1.87990e9i	0.00794940	−	0.00458959i
$801$	−1.68241e11	−	1.46913e11i	−0.408697	−	0.356886i
$802$	−3.26572e10	+	5.65640e10i	−0.0789372	+	0.136723i
$803$	−8.58847e10	−	1.51438e10i	−0.206564	−	0.0364227i
$804$	5.39044e10	+	5.49766e10i	0.129003	+	0.131569i
$805$	1.22483e12	+	4.45801e11i	2.91670	+	1.06159i
$806$	−6.42522e11	+	1.13294e11i	−1.52247	+	0.268452i
$807$	2.35419e10	−	2.41653e11i	0.0555068	−	0.569768i
$808$	1.71709e11	+	1.44081e11i	0.402854	+	0.338035i
$809$		−	8.80448e10i		−	0.205546i	−0.994705	−	0.102773i	$-0.967228\pi$
$809$		−	8.80448e10i		−	0.205546i	0.994705	−	0.102773i	$-0.0327716\pi$
$810$	3.99320e10	+	2.93676e11i	0.0927643	+	0.682226i
$811$	3.75493e8			0.000867998			0.000433999	−	1.00000i	$-0.499862\pi$
$811$	3.75493e8			0.000867998			0.000433999		1.00000i	$0.499862\pi$
$812$	−2.91117e11	+	3.46939e11i	−0.669643	+	0.798049i
$813$	3.27562e11	+	3.19111e10i	0.749776	+	0.0730432i
$814$	−3.78168e10	−	2.14470e11i	−0.0861366	−	0.488505i
$815$	1.36100e11	−	3.73931e11i	0.308480	−	0.847543i
$816$	−2.82178e10	+	2.76675e10i	−0.0636448	+	0.0624036i
$817$	3.60036e10	−	2.04186e11i	0.0808086	−	0.458288i
$818$	1.91909e11	+	1.10798e11i	0.428629	+	0.247469i
$819$	−3.71541e11	−	1.08694e12i	−0.825794	−	2.41585i
$820$	1.63155e11	+	2.82592e11i	0.360864	+	0.625035i
$821$	−6.98628e10	−	1.91946e11i	−0.153771	−	0.422481i	0.838756	−	0.544507i	$-0.183283\pi$
$821$	−6.98628e10	−	1.91946e11i	−0.153771	−	0.422481i	−0.992527	+	0.122026i	$0.961061\pi$
$822$	−2.05346e10	−	2.64709e11i	−0.0449780	−	0.579805i
$823$	−4.68555e11	+	3.93165e11i	−1.02132	+	0.856989i	−0.989793	−	0.142514i	$-0.954481\pi$
$823$	−4.68555e11	+	3.93165e11i	−1.02132	+	0.856989i	−0.0315268	+	0.999503i	$0.510037\pi$
$824$	8.38969e9	+	9.99844e9i	0.0181986	+	0.0216882i
$825$	−4.77772e9	+	9.98789e9i	−0.0103135	+	0.0215604i
$826$	−7.68602e11	+	2.79748e11i	−1.65113	+	0.600962i
$827$	−4.31359e11	+	2.49045e11i	−0.922183	+	0.532422i	−0.884331	−	0.466861i	$-0.845385\pi$
$827$	−4.31359e11	+	2.49045e11i	−0.922183	+	0.532422i	−0.0378519	+	0.999283i	$0.512052\pi$
$828$	−5.96054e10	−	3.81871e11i	−0.126813	−	0.812447i
$829$	−2.91062e11	+	5.04134e11i	−0.616265	+	1.06740i	0.373896	+	0.927471i	$0.378022\pi$
$829$	−2.91062e11	+	5.04134e11i	−0.616265	+	1.06740i	−0.990161	+	0.139932i	$0.955312\pi$
$830$	2.64995e11	+	4.67259e10i	0.558375	+	0.0984566i
$831$	−6.27573e10	+	2.25315e11i	−0.131601	+	0.472483i
$832$	−7.41351e10	−	2.69830e10i	−0.154714	−	0.0563114i
$833$	4.66126e11	−	8.21905e10i	0.968106	−	0.170703i
$834$	−2.32161e11	−	1.65991e11i	−0.479871	−	0.343101i
$835$	5.78669e11	+	4.85561e11i	1.19038	+	0.998844i
$836$			6.28322e10i			0.128634i
$837$	−9.49430e10	+	8.09112e11i	−0.193447	+	1.64857i
$838$	7.41067e10			0.150273
$839$	4.52293e11	−	5.39022e11i	0.912793	−	1.08782i	−0.0830329	−	0.996547i	$-0.526461\pi$
$839$	4.52293e11	−	5.39022e11i	0.912793	−	1.08782i	0.995826	−	0.0912770i	$-0.0290949\pi$
$840$	−1.37430e11	−	3.02461e11i	−0.276036	−	0.607509i
$841$	−1.35025e10	−	7.65765e10i	−0.0269917	−	0.153078i
$842$	2.03113e11	−	5.58047e11i	0.404100	−	1.11025i
$843$	−6.99219e10	−	2.71623e11i	−0.138453	−	0.537844i
$844$	4.68748e10	−	2.65840e11i	0.0923783	−	0.523904i
$845$	−3.15933e11	−	1.82404e11i	−0.619680	−	0.357773i
$846$	2.57687e10	−	1.42084e10i	0.0503050	−	0.0277373i
$847$	3.93133e11	+	6.80927e11i	0.763847	+	1.32302i
$848$	−1.92431e8	−	5.28701e8i	−0.000372128	−	0.00102241i
$849$	4.42558e11	−	3.03432e11i	0.851804	−	0.584024i
$850$	5.23476e9	−	4.39249e9i	0.0100282	−	0.00841462i
$851$	−8.44981e11	−	1.00701e12i	−1.61112	−	1.92006i
$852$	−1.65403e11	−	2.41242e11i	−0.313896	−	0.457820i
$853$	6.49207e11	−	2.36292e11i	1.22627	−	0.446327i	0.353954	−	0.935263i	$-0.384837\pi$
$853$	6.49207e11	−	2.36292e11i	1.22627	−	0.446327i	0.872320	+	0.488936i	$0.162615\pi$
$854$	1.75850e11	−	1.01527e11i	0.330607	−	0.190876i
$855$	−1.40430e11	−	2.54687e11i	−0.262782	−	0.476587i
$856$	9.48471e9	−	1.64280e10i	0.0176656	−	0.0305978i
$857$	−6.63284e11	−	1.16955e11i	−1.22963	−	0.216818i	−0.479166	−	0.877724i	$-0.659061\pi$
$857$	−6.63284e11	−	1.16955e11i	−1.22963	−	0.216818i	−0.750468	+	0.660906i	$0.770172\pi$
$858$	2.24988e11	−	5.79169e10i	0.415155	−	0.106870i
$859$	−3.76675e11	−	1.37098e11i	−0.691821	−	0.251802i	−0.0279066	−	0.999611i	$-0.508884\pi$
$859$	−3.76675e11	−	1.37098e11i	−0.691821	−	0.251802i	−0.663915	+	0.747808i	$0.731106\pi$
$860$	−2.18353e11	+	3.85016e10i	−0.399178	+	0.0703858i
$861$	−1.43771e12	+	6.53258e11i	−2.61613	+	1.18870i
$862$	−4.73870e10	−	3.97624e10i	−0.0858283	−	0.0720185i
$863$		−	3.60967e11i		−	0.650766i	−0.945582	−	0.325383i	$-0.894507\pi$
$863$		−	3.60967e11i		−	0.650766i	0.945582	−	0.325383i	$-0.105493\pi$
$864$	−5.88618e10	+	7.89905e10i	−0.105628	+	0.141749i
$865$	2.79220e11			0.498749
$866$	−4.17436e11	+	4.97481e11i	−0.742196	+	0.884515i
$867$	2.86858e11	−	4.01209e11i	0.507681	−	0.710058i
$868$	−1.58572e11	−	8.99309e11i	−0.279350	−	1.58427i
$869$	1.72333e10	−	4.73481e10i	0.0302197	−	0.0830278i
$870$	4.08444e11	+	1.13764e11i	0.712943	+	0.198577i
$871$	−4.85111e10	+	2.75120e11i	−0.0842885	+	0.478024i
$872$	−4.63102e10	−	2.67372e10i	−0.0800960	−	0.0462435i
$873$	−8.80491e11	+	1.37434e11i	−1.51589	+	0.236612i
$874$	1.89634e11	+	3.28456e11i	0.324991	+	0.562900i
$875$	3.98036e11	+	1.09359e12i	0.679032	+	1.86562i
$876$	1.21038e11	+	5.78987e10i	0.205544	+	0.0983224i
$877$	−2.12214e11	+	1.78069e11i	−0.358737	+	0.301016i	−0.804287	−	0.594241i	$-0.797453\pi$
$877$	−2.12214e11	+	1.78069e11i	−0.358737	+	0.301016i	0.445550	+	0.895257i	$0.353008\pi$
$878$	1.71302e10	+	2.04149e10i	0.0288259	+	0.0343534i
$879$	−1.86031e11	+	1.44312e10i	−0.311623	+	0.0241739i
$880$	6.31395e10	−	2.29809e10i	0.105286	−	0.0383209i
$881$	−7.06464e10	+	4.07877e10i	−0.117270	+	0.0677058i	−0.557488	−	0.830185i	$-0.688235\pi$
$881$	−7.06464e10	+	4.07877e10i	−0.117270	+	0.0677058i	0.440218	+	0.897891i	$0.354901\pi$
$882$	1.11643e12	−	3.81621e11i	1.84483	−	0.630606i
$883$	3.99517e11	−	6.91984e11i	0.657192	−	1.13829i	−0.324147	−	0.946007i	$-0.605077\pi$
$883$	3.99517e11	−	6.91984e11i	0.657192	−	1.13829i	0.981339	−	0.192284i	$-0.0615893\pi$
$884$	−1.41211e11	−	2.48993e10i	−0.231238	−	0.0407735i
$885$	5.36091e11	+	5.46755e11i	0.873908	+	0.891291i
$886$	3.07097e10	+	1.11774e10i	0.0498356	+	0.0181387i
$887$	7.75909e11	−	1.36814e11i	1.25348	−	0.221022i	0.492794	−	0.870146i	$-0.335975\pi$
$887$	7.75909e11	−	1.36814e11i	1.25348	−	0.221022i	0.760683	+	0.649124i	$0.224864\pi$
$888$	−3.24873e10	+	3.33476e11i	−0.0522470	+	0.536306i
$889$	5.55847e11	+	4.66411e11i	0.889914	+	0.746727i
$890$		−	2.34388e11i		−	0.373573i
$891$	1.14234e10	−	2.89866e11i	0.0181252	−	0.459924i
$892$	7.95655e10			0.125680
$893$	−1.85612e10	+	2.21204e10i	−0.0291877	+	0.0347846i
$894$	−2.63555e11	−	2.56755e10i	−0.412592	−	0.0401947i
$895$	−4.78454e10	−	2.71345e11i	−0.0745673	−	0.422892i
$896$	3.77669e10	−	1.03764e11i	0.0585975	−	0.160995i
$897$	1.00133e12	−	9.81798e11i	1.54670	−	1.51654i
$898$	3.75448e10	−	2.12927e11i	0.0577356	−	0.327435i
$899$	1.00930e12	+	5.82718e11i	1.54519	+	0.892113i
$900$	1.12042e10	−	1.28307e10i	0.0170769	−	0.0195560i
$901$	−5.11297e8	−	8.85593e8i	−0.000775844	−	0.00134380i
$902$	−1.09237e11	−	3.00125e11i	−0.165022	−	0.453395i
$903$	−8.29892e10	−	1.06980e12i	−0.124816	−	1.60899i
$904$	6.36279e10	−	5.33902e10i	0.0952739	−	0.0799443i
$905$	−5.07096e11	−	6.04334e11i	−0.755956	−	0.900913i
$906$	−3.47140e11	+	7.25700e11i	−0.515219	+	1.07707i
$907$	−7.06335e10	+	2.57085e10i	−0.104371	+	0.0379881i	−0.393678	−	0.919248i	$-0.628798\pi$
$907$	−7.06335e10	+	2.57085e10i	−0.104371	+	0.0379881i	0.289307	+	0.957236i	$0.406575\pi$
$908$	−1.83608e11	+	1.06006e11i	−0.270115	+	0.155951i
$909$	9.47264e11	+	3.66058e11i	1.38744	+	0.536161i
$910$	6.02710e11	−	1.04392e12i	0.878907	−	1.52231i
$911$	−5.26413e10	−	9.28208e9i	−0.0764281	−	0.0134763i	0.135303	−	0.990804i	$-0.456799\pi$
$911$	−5.26413e10	−	9.28208e9i	−0.0764281	−	0.0134763i	−0.211731	+	0.977328i	$0.567910\pi$
$912$	2.59378e10	−	9.31233e10i	0.0374933	−	0.134611i
$913$	−2.47492e11	−	9.00796e10i	−0.356186	−	0.129641i
$914$	−2.47359e11	+	4.36161e10i	−0.354441	+	0.0624974i
$915$	−1.54635e11	−	1.10562e11i	−0.220609	−	0.157732i
$916$	−1.80656e10	−	1.51589e10i	−0.0256608	−	0.0215320i
$917$			9.78622e11i			1.38400i
$918$	−8.04271e10	+	1.59963e11i	−0.113248	+	0.225242i
$919$	1.85878e11			0.260595			0.130297	−	0.991475i	$-0.458407\pi$
$919$	1.85878e11			0.260595			0.130297	+	0.991475i	$0.458407\pi$
$920$	2.60704e11	−	3.10694e11i	0.363911	−	0.433693i
$921$	2.63495e11	+	5.79908e11i	0.366213	+	0.805974i
$922$	3.30330e10	+	1.87339e11i	0.0457114	+	0.259242i
$923$	3.62986e11	−	9.97296e11i	0.500130	−	1.37410i
$924$	8.10638e10	+	3.14906e11i	0.111209	+	0.432009i
$925$	1.00606e10	−	5.70567e10i	0.0137423	−	0.0779362i
$926$	−1.75879e11	−	1.01544e11i	−0.239205	−	0.138105i
$927$	5.06189e10	+	3.05695e10i	0.0685478	+	0.0413971i
$928$	7.04629e10	+	1.22045e11i	0.0950098	+	0.164562i
$929$	1.17933e11	+	3.24018e11i	0.158333	+	0.435017i	0.993340	−	0.115223i	$-0.0367584\pi$
$929$	1.17933e11	+	3.24018e11i	0.158333	+	0.435017i	−0.835006	+	0.550240i	$0.814536\pi$
$930$	−7.05086e11	+	4.83430e11i	−0.942563	+	0.646252i
$931$	−8.86921e11	+	7.44215e11i	−1.18055	+	0.990603i
$932$	1.55905e11	+	1.85801e11i	0.206632	+	0.246254i
$933$	1.10968e11	+	1.61848e11i	0.146444	+	0.213590i
$934$	−1.55386e11	+	5.65560e10i	−0.204186	+	0.0743176i
$935$	1.05761e11	−	6.10610e10i	0.138382	−	0.0798947i
$936$	−3.57362e11	−	7.03894e9i	−0.465592	−	0.00917073i
$937$	2.26937e11	−	3.93066e11i	0.294406	−	0.509926i	−0.680441	−	0.732803i	$-0.738212\pi$
$937$	2.26937e11	−	3.93066e11i	0.294406	−	0.509926i	0.974846	+	0.222878i	$0.0715450\pi$
$938$	−3.85074e11	−	6.78989e10i	−0.497430	−	0.0877104i
$939$	5.93654e11	−	1.52820e11i	0.763609	−	0.196570i
$940$	2.90173e10	+	1.05614e10i	0.0371660	+	0.0135273i
$941$	−9.58616e11	+	1.69030e11i	−1.22260	+	0.215578i	−0.747446	−	0.664322i	$-0.768720\pi$
$941$	−9.58616e11	+	1.69030e11i	−1.22260	+	0.215578i	−0.475158	+	0.879900i	$0.657609\pi$
$942$	−4.15220e11	+	1.88665e11i	−0.527321	+	0.239601i
$943$	−1.47685e12	−	1.23922e12i	−1.86762	−	1.56712i
$944$			2.54511e11i			0.320493i
$945$	−1.03240e12	−	1.09528e12i	−1.29456	−	1.37340i
$946$	2.17018e11			0.270976
$947$	8.00877e11	−	9.54448e11i	0.995786	−	1.18673i	0.0133915	−	0.999910i	$-0.495737\pi$
$947$	8.00877e11	−	9.54448e11i	0.995786	−	1.18673i	0.982394	−	0.186821i	$-0.0598183\pi$
$948$	−4.50872e10	+	6.30604e10i	−0.0558239	+	0.0780770i
$949$	8.45374e10	+	4.79435e11i	0.104228	+	0.591106i
$950$	−5.71707e9	+	1.57075e10i	−0.00701907	+	0.0192847i
$951$	−1.03139e12	−	2.87275e11i	−1.26096	−	0.351217i
$952$	3.48505e10	−	1.97647e11i	0.0424288	−	0.240626i
$953$	5.26504e11	+	3.03977e11i	0.638308	+	0.368527i	0.783962	−	0.620808i	$-0.213196\pi$
$953$	5.26504e11	+	3.03977e11i	0.638308	+	0.368527i	−0.145655	+	0.989335i	$0.546529\pi$
$954$	−1.59973e9	−	1.98458e9i	−0.00193131	−	0.00239593i
$955$	−5.84418e10	−	1.01224e11i	−0.0702604	−	0.121694i
$956$	−2.90365e9	−	7.97772e9i	−0.00347627	−	0.00955096i
$957$	−3.74369e11	−	1.79080e11i	−0.446326	−	0.213501i
$958$	8.22950e10	−	6.90537e10i	0.0977038	−	0.0819832i
$959$	8.66710e11	+	1.03290e12i	1.02471	+	1.22120i
$960$	−1.03066e11	+	7.99524e9i	−0.121347	+	0.00941340i
$961$	−1.40671e12	+	5.12002e11i	−1.64935	+	0.600314i
$962$	−1.05283e12	+	6.07854e11i	−1.22930	+	0.709739i
$963$	1.65877e10	−	8.43268e10i	0.0192877	−	0.0980529i
$964$	−2.80684e11	+	4.86159e11i	−0.325019	+	0.562950i
$965$	6.98595e10	+	1.23181e10i	0.0805594	+	0.0142048i
$966$	1.37418e12	+	1.40151e12i	1.57810	+	1.60949i
$967$	−1.17995e11	−	4.29467e10i	−0.134945	−	0.0491161i	0.273665	−	0.961825i	$-0.411764\pi$
$967$	−1.17995e11	−	4.29467e10i	−0.134945	−	0.0491161i	−0.408610	+	0.912709i	$0.633986\pi$
$968$	2.40942e11	−	4.24845e10i	0.274417	−	0.0483871i
$969$	1.70357e10	−	1.74868e11i	0.0193226	−	0.198343i
$970$	−7.16378e11	−	6.01112e11i	−0.809199	−	0.678999i
$971$		−	7.98948e11i		−	0.898755i	−0.893342	−	0.449378i	$-0.851646\pi$
$971$		−	7.98948e11i		−	0.898755i	0.893342	−	0.449378i	$-0.148354\pi$
$972$	−1.36590e11	+	4.24893e11i	−0.153022	+	0.476009i
$973$	1.44939e12			1.61709
$974$	7.96389e11	−	9.49099e11i	0.884890	−	1.05457i
$975$	6.15150e10	+	5.99279e9i	0.0680710	+	0.00663149i
$976$	−1.09717e10	−	6.22235e10i	−0.0120913	−	0.0685733i
$977$	−1.25204e11	+	3.43994e11i	−0.137416	+	0.377549i	−0.989244	−	0.146273i	$-0.953272\pi$
$977$	−1.25204e11	+	3.43994e11i	−0.137416	+	0.377549i	0.851828	+	0.523822i	$0.175494\pi$
$978$	4.27873e11	−	4.19528e11i	0.467691	−	0.458570i
$979$	−3.98376e10	+	2.25930e11i	−0.0433673	+	0.245948i
$980$	1.07225e12	+	6.19061e11i	1.16249	+	0.671165i
$981$	−2.37716e11	−	4.67603e10i	−0.256674	−	0.0504896i
$982$	−2.64173e11	−	4.57561e11i	−0.284081	−	0.492043i
$983$	1.21663e11	+	3.34265e11i	0.130300	+	0.357995i	0.987637	−	0.156760i	$-0.0501050\pi$
$983$	1.21663e11	+	3.34265e11i	0.130300	+	0.357995i	−0.857337	+	0.514755i	$0.827883\pi$
$984$	3.80043e10	+	4.89909e11i	0.0405371	+	0.522558i
$985$	−1.05911e12	+	8.88699e11i	−1.12511	+	0.944082i
$986$	1.64641e11	+	1.96211e11i	0.174192	+	0.207594i
$987$	−6.44871e10	+	1.34811e11i	−0.0679523	+	0.142055i
$988$	3.29596e11	−	1.19963e11i	0.345903	−	0.125898i
$989$	1.13447e12	−	6.54984e11i	1.18579	−	0.684613i
$990$	2.37006e11	−	1.91046e11i	0.246728	−	0.198883i
$991$	1.76447e11	−	3.05615e11i	0.182945	−	0.316869i	−0.759937	−	0.649996i	$-0.774770\pi$
$991$	1.76447e11	−	3.05615e11i	0.182945	−	0.316869i	0.942882	+	0.333127i	$0.108104\pi$
$992$	−2.79833e11	−	4.93422e10i	−0.288970	−	0.0509532i
$993$	−3.95028e11	+	1.41825e12i	−0.406285	+	1.45867i
$994$	1.39587e12	+	5.08056e11i	1.42988	+	0.520434i
$995$	−3.04441e11	+	5.36812e10i	−0.310607	+	0.0547684i
$996$	3.29620e11	+	2.35674e11i	0.334948	+	0.239483i
$997$	−9.75186e11	−	8.18279e11i	−0.986977	−	0.828172i	−0.00184966	−	0.999998i	$-0.500589\pi$
$997$	−9.75186e11	−	8.18279e11i	−0.986977	−	0.828172i	−0.985127	+	0.171826i	$0.945033\pi$
$998$		−	2.23360e11i		−	0.225156i
$999$	3.49406e11	+	1.47724e12i	0.350807	+	1.48316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.9.f.a.11.1	yes	144
27.5	odd	18	inner	54.9.f.a.5.1	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.9.f.a.5.1	✓	144	27.5	odd	18	inner
54.9.f.a.11.1	yes	144	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.27231 + 8.66680i) q^{2} +(-80.6183 - 7.85385i) q^{3} +(-22.2270 - 126.055i) q^{4} +(208.139 - 571.857i) q^{5} +(654.349 - 641.588i) q^{6} +(-808.155 + 4583.27i) q^{7} +(1254.14 + 724.077i) q^{8} +(6437.63 + 1266.33i) q^{9} +(3442.52 + 5962.62i) q^{10} +(-2304.87 - 6332.57i) q^{11} +(801.881 + 10336.9i) q^{12} +(-28817.9 + 24181.1i) q^{13} +(-33845.2 - 40335.1i) q^{14} +(-21271.1 + 44467.4i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-25788.7 + 14889.1i) q^{17} +(-57791.5 + 46584.6i) q^{18} +(36420.7 - 63082.5i) q^{19} +(-76711.9 - 13526.4i) q^{20} +(101148. - 363149. i) q^{21} +(71644.8 + 26076.6i) q^{22} +(453226. - 79916.0i) q^{23} +(-95419.8 - 68223.7i) q^{24} +(15537.9 + 13037.9i) q^{25} -425611. i q^{26} +(-509046. - 152649. i) q^{27} +595709. q^{28} +(-488689. + 582397. i) q^{29} +(-230701. - 507733. i) q^{30} +(-266191. - 1.50964e6i) q^{31} +(63398.2 - 174185. i) q^{32} +(136079. + 528623. i) q^{33} +(58502.5 - 331784. i) q^{34} +(2.45277e6 + 1.41611e6i) q^{35} +(16538.4 - 839645. i) q^{36} +(-1.42819e6 - 2.47370e6i) q^{37} +(281861. + 774407. i) q^{38} +(2.51316e6 - 1.72311e6i) q^{39} +(675103. - 566479. i) q^{40} +(-2.69268e6 - 3.20902e6i) q^{41} +(2.41176e6 + 3.51756e6i) q^{42} +(2.67475e6 - 973529. i) q^{43} +(-747024. + 431294. i) q^{44} +(2.06408e6 - 3.41783e6i) q^{45} +(-2.60338e6 + 4.50919e6i) q^{46} +(-390402. - 68838.4i) q^{47} +(1.28520e6 - 330840. i) q^{48} +(-1.49361e7 - 5.43631e6i) q^{49} +(-225993. + 39848.7i) q^{50} +(2.19598e6 - 997795. i) q^{51} +(3.68869e6 + 3.09518e6i) q^{52} +34340.3i q^{53} +(5.02492e6 - 3.30169e6i) q^{54} -4.10105e6 q^{55} +(-4.33218e6 + 5.16289e6i) q^{56} +(-3.43162e6 + 4.79956e6i) q^{57} +(-1.49362e6 - 8.47075e6i) q^{58} +(5.31298e6 - 1.45973e7i) q^{59} +(6.07815e6 + 1.69296e6i) q^{60} +(-669659. + 3.79782e6i) q^{61} +(1.50196e7 + 8.67158e6i) q^{62} +(-1.10065e7 + 2.84820e7i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(7.82999e6 + 2.15127e7i) q^{65} +(-5.57108e6 - 2.66494e6i) q^{66} +(5.68875e6 - 4.77343e6i) q^{67} +(2.45006e6 + 2.91987e6i) q^{68} +(-3.71660e7 + 2.88312e6i) q^{69} +(-3.01104e7 + 1.09593e7i) q^{70} +(-2.44321e7 + 1.41059e7i) q^{71} +(7.15677e6 + 6.24950e6i) q^{72} +(6.47054e6 - 1.12073e7i) q^{73} +(3.18253e7 + 5.61166e6i) q^{74} +(-1.15024e6 - 1.17312e6i) q^{75} +(-8.76141e6 - 3.18889e6i) q^{76} +(3.08866e7 - 5.44614e6i) q^{77} +(-3.34268e6 + 3.43121e7i) q^{78} +(5.72766e6 + 4.80607e6i) q^{79} +9.97060e6i q^{80} +(3.98395e7 + 1.63043e7i) q^{81} +4.73939e7 q^{82} +(2.51217e7 - 2.99388e7i) q^{83} +(-4.80251e7 - 4.67861e6i) q^{84} +(3.14681e6 + 1.78464e7i) q^{85} +(-1.10142e7 + 3.02613e7i) q^{86} +(4.39714e7 - 4.31138e7i) q^{87} +(1.69465e6 - 9.61082e6i) q^{88} +(-2.94822e7 - 1.70215e7i) q^{89} +(1.46110e7 + 4.27445e7i) q^{90} +(-8.75391e7 - 1.51622e8i) q^{91} +(-2.01477e7 - 5.53553e7i) q^{92} +(9.60337e6 + 1.23796e8i) q^{93} +(3.43573e6 - 2.88292e6i) q^{94} +(-2.84936e7 - 3.39573e7i) q^{95} +(-6.47908e6 + 1.35446e7i) q^{96} +(-1.27634e8 + 4.64551e7i) q^{97} +(1.55736e8 - 8.99140e7i) q^{98} +(-6.81877e6 - 4.36855e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25}+ \cdots + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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