LMFDB - Embedded newform 18.9.d.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,9,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

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("18.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, 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:	$7.33281498110$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 5476 x^{14} - 38192 x^{13} + 11414542 x^{12} - 67991120 x^{11} + \cdots + 19\!\cdots\!29 $ x^16 - 8x^15 + 5476x^14 - 38192x^13 + 11414542x^12 - 67991120x^11 + 11330952892x^10 - 56032421816x^9 + 5575009041895x^8 - 21964587980304x^7 + 1366797007396500x^6 - 4023749554164360x^5 + 166750774096111110x^4 - 326820812596206264x^3 + 9443577280676906808x^2 - 9280833855293027160*x + 190324219382219227329
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.1
Root			$0.500000 - 14.2466i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.9.d.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+(-9.79796 - 5.65685i) q^{2} +(-69.4086 - 41.7547i) q^{3} +(64.0000 + 110.851i) q^{4} +(-719.139 + 415.195i) q^{5} +(443.862 + 801.745i) q^{6} +(1343.41 - 2326.85i) q^{7} -1448.15i q^{8} +(3074.10 + 5796.26i) q^{9} +9394.80 q^{10} +(21366.9 + 12336.2i) q^{11} +(186.409 - 10366.3i) q^{12} +(-4848.77 - 8398.31i) q^{13} +(-26325.3 + 15198.9i) q^{14} +(67250.8 + 1209.31i) q^{15} +(-8192.00 + 14189.0i) q^{16} +42669.1i q^{17} +(2668.74 - 74181.3i) q^{18} +101194. q^{19} +(-92049.8 - 53145.0i) q^{20} +(-190401. + 105410. i) q^{21} +(-139568. - 241739. i) q^{22} +(-396990. + 229203. i) q^{23} +(-60467.2 + 100514. i) q^{24} +(149462. - 258875. i) q^{25} +109715. i q^{26} +(28652.4 - 530668. i) q^{27} +343913. q^{28} +(577159. + 333223. i) q^{29} +(-652079. - 392277. i) q^{30} +(709545. + 1.22897e6i) q^{31} +(160530. - 92681.9i) q^{32} +(-967951. - 1.74840e6i) q^{33} +(241373. - 418071. i) q^{34} +2.23111e6i q^{35} +(-445781. + 711728. i) q^{36} +1.62583e6 q^{37} +(-991496. - 572441. i) q^{38} +(-14122.7 + 785373. i) q^{39} +(601267. + 1.04142e6i) q^{40} +(1.99920e6 - 1.15424e6i) q^{41} +(2.46183e6 + 44269.1i) q^{42} +(812997. - 1.40815e6i) q^{43} +3.15806e6i q^{44} +(-4.61728e6 - 2.89197e6i) q^{45} +5.18626e6 q^{46} +(-3.38272e6 - 1.95301e6i) q^{47} +(1.16105e6 - 642781. i) q^{48} +(-727099. - 1.25937e6i) q^{49} +(-2.92884e6 + 1.69097e6i) q^{50} +(1.78164e6 - 2.96160e6i) q^{51} +(620642. - 1.07498e6i) q^{52} +6.96433e6i q^{53} +(-3.28265e6 + 5.03738e6i) q^{54} -2.04877e7 q^{55} +(-3.36964e6 - 1.94547e6i) q^{56} +(-7.02374e6 - 4.22533e6i) q^{57} +(-3.76999e6 - 6.52981e6i) q^{58} +(5.94959e6 - 3.43500e6i) q^{59} +(4.16999e6 + 7.53223e6i) q^{60} +(1.26576e6 - 2.19236e6i) q^{61} -1.60552e7i q^{62} +(1.76168e7 + 633783. i) q^{63} -2.09715e6 q^{64} +(6.97388e6 + 4.02637e6i) q^{65} +(-406511. + 2.26063e7i) q^{66} +(1.58375e7 + 2.74313e7i) q^{67} +(-4.72993e6 + 2.73083e6i) q^{68} +(3.71248e7 + 667585. i) q^{69} +(1.26211e7 - 2.18603e7i) q^{70} -1.75496e7i q^{71} +(8.39388e6 - 4.45177e6i) q^{72} -2.86971e7 q^{73} +(-1.59299e7 - 9.19711e6i) q^{74} +(-2.11832e7 + 1.17274e7i) q^{75} +(6.47643e6 + 1.12175e7i) q^{76} +(5.74089e7 - 3.31451e7i) q^{77} +(4.58112e6 - 7.61517e6i) q^{78} +(-3.40323e7 + 5.89457e7i) q^{79} -1.36051e7i q^{80} +(-2.41466e7 + 3.56365e7i) q^{81} -2.61174e7 q^{82} +(4.73759e7 + 2.73525e7i) q^{83} +(-2.38705e7 - 1.43600e7i) q^{84} +(-1.77160e7 - 3.06851e7i) q^{85} +(-1.59314e7 + 9.19801e6i) q^{86} +(-2.61462e7 - 4.72276e7i) q^{87} +(1.78647e7 - 3.09425e7i) q^{88} -7.04968e6i q^{89} +(2.88805e7 + 5.44547e7i) q^{90} -2.60555e7 q^{91} +(-5.08148e7 - 2.93379e7i) q^{92} +(2.06665e6 - 1.14928e8i) q^{93} +(2.20958e7 + 3.82711e7i) q^{94} +(-7.27727e7 + 4.20153e7i) q^{95} +(-1.50120e7 - 269949. i) q^{96} +(5.14341e7 - 8.90865e7i) q^{97} +1.64524e7i q^{98} +(-5.81985e6 + 1.61771e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 126 q^{3} + 1024 q^{4} - 882 q^{5} + 384 q^{6} - 1846 q^{7} - 28662 q^{9} + 45756 q^{11} + 5376 q^{12} - 3370 q^{13} - 94464 q^{14} + 128754 q^{15} - 131072 q^{16} - 236544 q^{18} + 362180 q^{19}+ \cdots + 366888330 q^{99}+O(q^{100}) $ 16 * q + 126 * q^3 + 1024 * q^4 - 882 * q^5 + 384 * q^6 - 1846 * q^7 - 28662 * q^9 + 45756 * q^11 + 5376 * q^12 - 3370 * q^13 - 94464 * q^14 + 128754 * q^15 - 131072 * q^16 - 236544 * q^18 + 362180 * q^19 - 112896 * q^20 - 299166 * q^21 - 61824 * q^22 + 1311138 * q^23 - 147456 * q^24 + 963394 * q^25 - 208656 * q^27 - 472576 * q^28 - 2851290 * q^29 - 1253376 * q^30 + 542438 * q^31 + 3875796 * q^33 + 220416 * q^34 - 3655680 * q^36 + 3343328 * q^37 - 1314432 * q^38 - 5896002 * q^39 + 9218592 * q^41 + 14237952 * q^42 + 339512 * q^43 - 32740578 * q^45 + 7417344 * q^46 - 34980606 * q^47 - 1376256 * q^48 - 2364654 * q^49 + 27744768 * q^50 + 50877810 * q^51 + 431360 * q^52 - 5648256 * q^54 - 4584276 * q^55 - 12091392 * q^56 - 34049898 * q^57 - 7852800 * q^58 + 93924216 * q^59 + 18604800 * q^60 - 841954 * q^61 - 14043234 * q^63 - 33554432 * q^64 - 126568134 * q^65 - 35179776 * q^66 + 29946644 * q^67 - 5476608 * q^68 + 70499610 * q^69 - 34359552 * q^70 - 11894784 * q^72 - 7547764 * q^73 + 35124480 * q^74 + 114494910 * q^75 + 23179520 * q^76 + 9309294 * q^77 + 23014656 * q^78 + 33813002 * q^79 - 46018134 * q^81 - 137346048 * q^82 + 114200226 * q^83 - 15040512 * q^84 - 125696772 * q^85 - 171379584 * q^86 - 159599970 * q^87 + 7913472 * q^88 + 129745152 * q^90 + 268578316 * q^91 + 167825664 * q^92 + 120711534 * q^93 - 11832576 * q^94 - 143949240 * q^95 - 25165824 * q^96 - 89415484 * q^97 + 366888330 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$3$	−69.4086	−	41.7547i	−0.856896	−	0.515490i
$3$	−69.4086	−	41.7547i	−0.856896	−	0.515490i
$4$	64.0000	+	110.851i	0.250000	+	0.433013i
$5$	−719.139	+	415.195i	−1.15062	+	0.664312i	−0.949039	−	0.315159i	$-0.897942\pi$
$5$	−719.139	+	415.195i	−1.15062	+	0.664312i	−0.201584	+	0.979471i	$0.564609\pi$
$6$	443.862	+	801.745i	0.342486	+	0.618630i
$7$	1343.41	−	2326.85i	0.559521	−	0.969119i	−0.438015	−	0.898967i	$-0.644318\pi$
$7$	1343.41	−	2326.85i	0.559521	−	0.969119i	0.997536	−	0.0701513i	$-0.0223482\pi$
$8$		−	1448.15i		−	0.353553i
$9$	3074.10	+	5796.26i	0.468541	+	0.883442i
$10$	9394.80			0.939480
$11$	21366.9	+	12336.2i	1.45939	+	0.842577i	0.998981	−	0.0451321i	$-0.0143709\pi$
$11$	21366.9	+	12336.2i	1.45939	+	0.842577i	0.460405	+	0.887709i	$0.347704\pi$
$12$	186.409	−	10366.3i	0.00898963	−	0.499919i
$13$	−4848.77	−	8398.31i	−0.169769	−	0.294048i	0.768570	−	0.639766i	$-0.220969\pi$
$13$	−4848.77	−	8398.31i	−0.169769	−	0.294048i	−0.938339	+	0.345718i	$0.887635\pi$
$14$	−26325.3	+	15198.9i	−0.685270	+	0.395641i
$15$	67250.8	+	1209.31i	1.32841	+	0.0238877i
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$			42669.1i			0.510879i	0.966825	+	0.255440i	$0.0822202\pi$
$17$			42669.1i			0.510879i	−0.966825	+	0.255440i	$0.917780\pi$
$18$	2668.74	−	74181.3i	0.0254224	−	0.706650i
$19$	101194.			0.776499			0.388250	−	0.921554i	$-0.373080\pi$
$19$	101194.			0.776499			0.388250	+	0.921554i	$0.373080\pi$
$20$	−92049.8	−	53145.0i	−0.575311	−	0.332156i
$21$	−190401.	+	105410.i	−0.979022	+	0.542006i
$22$	−139568.	−	241739.i	−0.595792	−	1.03194i
$23$	−396990.	+	229203.i	−1.41863	+	0.819046i	−0.996179	−	0.0873406i	$-0.972163\pi$
$23$	−396990.	+	229203.i	−1.41863	+	0.819046i	−0.422450	+	0.906386i	$0.638830\pi$
$24$	−60467.2	+	100514.i	−0.182253	+	0.302958i
$25$	149462.	−	258875.i	0.382622	−	0.662721i
$26$			109715.i			0.240089i
$27$	28652.4	−	530668.i	0.0539146	−	0.998546i
$28$	343913.			0.559521
$29$	577159.	+	333223.i	0.816025	+	0.471132i	0.849044	−	0.528322i	$-0.177179\pi$
$29$	577159.	+	333223.i	0.816025	+	0.471132i	−0.0330188	+	0.999455i	$0.510512\pi$
$30$	−652079.	−	392277.i	−0.805036	−	0.484292i
$31$	709545.	+	1.22897e6i	0.768305	+	1.33074i	0.938482	+	0.345329i	$0.112233\pi$
$31$	709545.	+	1.22897e6i	0.768305	+	1.33074i	−0.170177	+	0.985413i	$0.554434\pi$
$32$	160530.	−	92681.9i	0.153093	−	0.0883883i
$33$	−967951.	−	1.74840e6i	−0.816202	−	1.47430i
$34$	241373.	−	418071.i	0.180623	−	0.312848i
$35$			2.23111e6i			1.48679i
$36$	−445781.	+	711728.i	−0.265406	+	0.423745i
$37$	1.62583e6			0.867500			0.433750	−	0.901033i	$-0.357190\pi$
$37$	1.62583e6			0.867500			0.433750	+	0.901033i	$0.357190\pi$
$38$	−991496.	−	572441.i	−0.475507	−	0.274534i
$39$	−14122.7	+	785373.i	−0.00610464	+	0.339483i
$40$	601267.	+	1.04142e6i	0.234870	+	0.406807i
$41$	1.99920e6	−	1.15424e6i	0.707491	−	0.408470i	−0.102641	−	0.994719i	$-0.532729\pi$
$41$	1.99920e6	−	1.15424e6i	0.707491	−	0.408470i	0.810131	+	0.586249i	$0.199396\pi$
$42$	2.46183e6	+	44269.1i	0.791154	+	0.0142267i
$43$	812997.	−	1.40815e6i	0.237802	−	0.411885i	−0.722281	−	0.691599i	$-0.756906\pi$
$43$	812997.	−	1.40815e6i	0.237802	−	0.411885i	0.960083	+	0.279714i	$0.0902398\pi$
$44$			3.15806e6i			0.842577i
$45$	−4.61728e6	−	2.89197e6i	−1.12600	−	0.705251i
$46$	5.18626e6			1.15831
$47$	−3.38272e6	−	1.95301e6i	−0.693226	−	0.400234i	0.111594	−	0.993754i	$-0.464405\pi$
$47$	−3.38272e6	−	1.95301e6i	−0.693226	−	0.400234i	−0.804819	+	0.593520i	$0.797738\pi$
$48$	1.16105e6	−	642781.i	0.218719	−	0.121087i
$49$	−727099.	−	1.25937e6i	−0.126127	−	0.218459i
$50$	−2.92884e6	+	1.69097e6i	−0.468614	+	0.270555i
$51$	1.78164e6	−	2.96160e6i	0.263353	−	0.437770i
$52$	620642.	−	1.07498e6i	0.0848844	−	0.147024i
$53$			6.96433e6i			0.882624i	0.897354	+	0.441312i	$0.145487\pi$
$53$			6.96433e6i			0.882624i	−0.897354	+	0.441312i	$0.854513\pi$
$54$	−3.28265e6	+	5.03738e6i	−0.386055	+	0.592420i
$55$	−2.04877e7			−2.23894
$56$	−3.36964e6	−	1.94547e6i	−0.342635	−	0.197821i
$57$	−7.02374e6	−	4.22533e6i	−0.665379	−	0.400277i
$58$	−3.76999e6	−	6.52981e6i	−0.333141	−	0.577017i
$59$	5.94959e6	−	3.43500e6i	0.490997	−	0.283477i	−0.233991	−	0.972239i	$-0.575179\pi$
$59$	5.94959e6	−	3.43500e6i	0.490997	−	0.283477i	0.724988	+	0.688761i	$0.241845\pi$
$60$	4.16999e6	+	7.53223e6i	0.321759	+	0.581190i
$61$	1.26576e6	−	2.19236e6i	0.0914182	−	0.158341i	−0.816690	−	0.577077i	$-0.804193\pi$
$61$	1.26576e6	−	2.19236e6i	0.0914182	−	0.158341i	0.908108	+	0.418736i	$0.137527\pi$
$62$		−	1.60552e7i		−	1.08655i
$63$	1.76168e7	+	633783.i	1.11832	+	0.0402326i
$64$	−2.09715e6			−0.125000
$65$	6.97388e6	+	4.02637e6i	0.390680	+	0.225559i
$66$	−406511.	+	2.26063e7i	−0.0214238	+	1.19139i
$67$	1.58375e7	+	2.74313e7i	0.785936	+	1.36128i	0.928439	+	0.371486i	$0.121152\pi$
$67$	1.58375e7	+	2.74313e7i	0.785936	+	1.36128i	−0.142503	+	0.989794i	$0.545515\pi$
$68$	−4.72993e6	+	2.73083e6i	−0.221217	+	0.127720i
$69$	3.71248e7	+	667585.i	1.63783	+	0.0294517i
$70$	1.26211e7	−	2.18603e7i	0.525659	−	0.910467i
$71$		−	1.75496e7i		−	0.690612i	−0.938490	−	0.345306i	$-0.887775\pi$
$71$		−	1.75496e7i		−	0.690612i	0.938490	−	0.345306i	$-0.112225\pi$
$72$	8.39388e6	−	4.45177e6i	0.312344	−	0.165654i
$73$	−2.86971e7			−1.01052			−0.505261	−	0.862966i	$-0.668604\pi$
$73$	−2.86971e7			−1.01052			−0.505261	+	0.862966i	$0.668604\pi$
$74$	−1.59299e7	−	9.19711e6i	−0.531233	−	0.306707i
$75$	−2.11832e7	+	1.17274e7i	−0.669493	+	0.370645i
$76$	6.47643e6	+	1.12175e7i	0.194125	+	0.336234i
$77$	5.74089e7	−	3.31451e7i	1.63311	−	0.942879i
$78$	4.58112e6	−	7.61517e6i	0.123764	−	0.205732i
$79$	−3.40323e7	+	5.89457e7i	−0.873741	+	1.51336i	−0.0156441	+	0.999878i	$0.504980\pi$
$79$	−3.40323e7	+	5.89457e7i	−0.873741	+	1.51336i	−0.858097	+	0.513487i	$0.828353\pi$
$80$		−	1.36051e7i		−	0.332156i
$81$	−2.41466e7	+	3.56365e7i	−0.560939	+	0.827857i
$82$	−2.61174e7			−0.577664
$83$	4.73759e7	+	2.73525e7i	0.998263	+	0.576347i	0.907734	−	0.419547i	$-0.137811\pi$
$83$	4.73759e7	+	2.73525e7i	0.998263	+	0.576347i	0.0905288	+	0.995894i	$0.471144\pi$
$84$	−2.38705e7	−	1.43600e7i	−0.479451	−	0.288427i
$85$	−1.77160e7	−	3.06851e7i	−0.339383	−	0.587829i
$86$	−1.59314e7	+	9.19801e6i	−0.291247	+	0.168151i
$87$	−2.61462e7	−	4.72276e7i	−0.456385	−	0.824364i
$88$	1.78647e7	−	3.09425e7i	0.297896	−	0.515971i
$89$		−	7.04968e6i		−	0.112359i	−0.998421	−	0.0561797i	$-0.982108\pi$
$89$		−	7.04968e6i		−	0.112359i	0.998421	−	0.0561797i	$-0.0178920\pi$
$90$	2.88805e7	+	5.44547e7i	0.440185	+	0.829976i
$91$	−2.60555e7			−0.379957
$92$	−5.08148e7	−	2.93379e7i	−0.709314	−	0.409523i
$93$	2.06665e6	−	1.14928e8i	0.0276271	−	1.53636i
$94$	2.20958e7	+	3.82711e7i	0.283008	+	0.490185i
$95$	−7.27727e7	+	4.20153e7i	−0.893458	+	0.515838i
$96$	−1.50120e7	−	269949.i	−0.176748	−	0.00317832i
$97$	5.14341e7	−	8.90865e7i	0.580984	−	1.00629i	−0.414379	−	0.910104i	$-0.636001\pi$
$97$	5.14341e7	−	8.90865e7i	0.580984	−	1.00629i	0.995363	−	0.0961894i	$-0.0306655\pi$
$98$			1.64524e7i			0.178371i
$99$	−5.81985e6	+	1.61771e8i	−0.0605859	+	1.68406i
$100$	3.82622e7			0.382622
$101$	−8.11338e7	−	4.68426e7i	−0.779680	−	0.450148i	0.0566370	−	0.998395i	$-0.481962\pi$
$101$	−8.11338e7	−	4.68426e7i	−0.779680	−	0.450148i	−0.836317	+	0.548246i	$0.815296\pi$
$102$	−3.42098e7	+	1.89392e7i	−0.316045	+	0.174969i
$103$	4.68590e7	+	8.11622e7i	0.416336	+	0.721116i	0.995568	−	0.0940475i	$-0.0299806\pi$
$103$	4.68590e7	+	8.11622e7i	0.416336	+	0.721116i	−0.579231	+	0.815163i	$0.696647\pi$
$104$	−1.21621e7	+	7.02177e6i	−0.103962	+	0.0600224i
$105$	9.31592e7	−	1.54858e8i	0.766423	−	1.27402i
$106$	3.93962e7	−	6.82362e7i	0.312055	−	0.540495i
$107$			1.34556e8i			1.02652i	0.858232	+	0.513262i	$0.171563\pi$
$107$			1.34556e8i			1.02652i	−0.858232	+	0.513262i	$0.828437\pi$
$108$	6.06590e7	−	3.07866e7i	0.445862	−	0.226291i
$109$	−5.31868e7			−0.376788			−0.188394	−	0.982093i	$-0.560328\pi$
$109$	−5.31868e7			−0.376788			−0.188394	+	0.982093i	$0.560328\pi$
$110$	2.00737e8	+	1.15896e8i	1.37106	+	0.791584i
$111$	−1.12847e8	−	6.78862e7i	−0.743357	−	0.447187i
$112$	2.20104e7	+	3.81232e7i	0.139880	+	0.242280i
$113$	−1.14368e8	+	6.60307e7i	−0.701443	+	0.404978i	−0.807885	−	0.589341i	$-0.799388\pi$
$113$	−1.14368e8	+	6.60307e7i	−0.701443	+	0.404978i	0.106442	+	0.994319i	$0.466054\pi$
$114$	4.49163e7	+	8.11319e7i	0.265940	+	0.480366i
$115$	1.90328e8	−	3.29657e8i	1.08820	−	1.88483i
$116$			8.53051e7i			0.471132i
$117$	3.37732e7	−	5.39220e7i	0.180231	−	0.287755i
$118$	−7.77251e7			−0.400897
$119$	9.92849e7	+	5.73222e7i	0.495103	+	0.285848i
$120$	1.75128e6	−	9.73895e7i	0.00844558	−	0.469664i
$121$	1.97183e8	+	3.41530e8i	0.919872	+	1.59326i
$122$	−2.48038e7	+	1.43205e7i	−0.111964	+	0.0646424i
$123$	−1.86956e8	−	3.36188e6i	−0.816808	−	0.0146880i
$124$	−9.08218e7	+	1.57308e8i	−0.384152	+	0.665371i
$125$		−	7.61481e7i		−	0.311903i
$126$	−1.69024e8	−	1.05866e8i	−0.670603	−	0.420023i
$127$	5.72307e7			0.219996			0.109998	−	0.993932i	$-0.464916\pi$
$127$	5.72307e7			0.219996			0.109998	+	0.993932i	$0.464916\pi$
$128$	2.05478e7	+	1.18633e7i	0.0765466	+	0.0441942i
$129$	−1.15226e8	+	6.37914e7i	−0.416094	+	0.230358i
$130$	−4.55532e7	−	7.89004e7i	−0.159494	−	0.276252i
$131$	−9.79607e7	+	5.65576e7i	−0.332634	+	0.192046i	−0.657010	−	0.753882i	$-0.728179\pi$
$131$	−9.79607e7	+	5.65576e7i	−0.332634	+	0.192046i	0.324376	+	0.945928i	$0.394846\pi$
$132$	1.31864e8	−	2.19196e8i	0.434340	−	0.722001i
$133$	1.35945e8	−	2.35464e8i	0.434468	−	0.752520i
$134$		−	3.58361e8i		−	1.11148i
$135$	1.99726e8	+	3.93521e8i	0.601311	+	1.18477i
$136$	6.17915e7			0.180623
$137$	−1.19042e8	−	6.87289e7i	−0.337923	−	0.195100i	0.321430	−	0.946933i	$-0.395836\pi$
$137$	−1.19042e8	−	6.87289e7i	−0.337923	−	0.195100i	−0.659353	+	0.751833i	$0.729170\pi$
$138$	−3.59971e8	−	2.16551e8i	−0.992547	−	0.597094i
$139$	−9.70841e7	−	1.68155e8i	−0.260069	−	0.450453i	0.706191	−	0.708022i	$-0.250412\pi$
$139$	−9.70841e7	−	1.68155e8i	−0.260069	−	0.450453i	−0.966260	+	0.257568i	$0.917079\pi$
$140$	−2.47321e8	+	1.42791e8i	−0.643798	+	0.371697i
$141$	1.53242e8	+	2.76800e8i	0.387706	+	0.700310i
$142$	−9.92757e7	+	1.71950e8i	−0.244168	+	0.422912i
$143$		−	2.39261e8i		−	0.572173i
$144$	−1.07426e8	−	3.86475e6i	−0.249838	−	0.00898818i
$145$	−5.53410e8			−1.25192
$146$	2.81173e8	+	1.62335e8i	0.618816	+	0.357274i
$147$	−2.11778e6	+	1.17771e8i	−0.00453536	+	0.252214i
$148$	1.04053e8	+	1.80226e8i	0.216875	+	0.375638i
$149$	6.70921e8	−	3.87357e8i	1.36121	−	0.785897i	0.371429	−	0.928461i	$-0.378868\pi$
$149$	6.70921e8	−	3.87357e8i	1.36121	−	0.785897i	0.989786	+	0.142564i	$0.0455347\pi$
$150$	2.73892e8	+	4.92518e6i	0.541022	+	0.00972875i
$151$	−3.48071e8	+	6.02877e8i	−0.669515	+	1.15963i	0.308525	+	0.951216i	$0.400165\pi$
$151$	−3.48071e8	+	6.02877e8i	−0.669515	+	1.15963i	−0.978040	+	0.208418i	$0.933169\pi$
$152$		−	1.46545e8i		−	0.274534i
$153$	−2.47322e8	+	1.31169e8i	−0.451332	+	0.239368i
$154$	−7.49987e8			−1.33343
$155$	−1.02052e9	−	5.89200e8i	−1.76806	−	1.02079i
$156$	−8.79635e7	+	4.86984e7i	−0.148527	+	0.0822273i
$157$	−4.99364e6	−	8.64924e6i	−0.00821900	−	0.0142357i	0.861887	−	0.507101i	$-0.169283\pi$
$157$	−4.99364e6	−	8.64924e6i	−0.00821900	−	0.0142357i	−0.870106	+	0.492865i	$0.835950\pi$
$158$	6.66894e8	−	3.85032e8i	1.07011	−	0.617829i
$159$	2.90793e8	−	4.83384e8i	0.454984	−	0.756317i
$160$	−7.69622e7	+	1.33302e8i	−0.117435	+	0.203403i
$161$			1.23165e9i			1.83309i
$162$	4.38178e8	−	2.12572e8i	0.636195	−	0.308635i
$163$	1.22877e9			1.74068			0.870340	−	0.492451i	$-0.163899\pi$
$163$	1.22877e9			1.74068			0.870340	+	0.492451i	$0.163899\pi$
$164$	2.55898e8	+	1.47743e8i	0.353745	+	0.204235i
$165$	1.42202e9	+	8.55456e8i	1.91854	+	1.15415i
$166$	−3.09458e8	−	5.35997e8i	−0.407539	−	0.705878i
$167$	7.41092e8	−	4.27870e8i	0.952809	−	0.550105i	0.0588569	−	0.998266i	$-0.481254\pi$
$167$	7.41092e8	−	4.27870e8i	0.952809	−	0.550105i	0.893953	+	0.448162i	$0.147921\pi$
$168$	1.52650e8	+	2.75730e8i	0.191628	+	0.346136i
$169$	3.60844e8	−	6.25001e8i	0.442357	−	0.766185i
$170$			4.00868e8i			0.479961i
$171$	3.11081e8	+	5.86548e8i	0.363822	+	0.685992i
$172$	2.08127e8			0.237802
$173$	−3.96513e8	−	2.28927e8i	−0.442663	−	0.255572i	0.262064	−	0.965051i	$-0.415597\pi$
$173$	−3.96513e8	−	2.28927e8i	−0.442663	−	0.255572i	−0.704727	+	0.709479i	$0.748930\pi$
$174$	−1.09806e7	+	6.10639e8i	−0.0119793	+	0.666174i
$175$	−4.01577e8	−	6.95551e8i	−0.428170	−	0.741612i
$176$	−3.50075e8	+	2.02116e8i	−0.364846	+	0.210644i
$177$	−5.56380e8	−	1.00049e7i	−0.566863	−	0.0101934i
$178$	−3.98790e7	+	6.90725e7i	−0.0397250	+	0.0688058i
$179$		−	1.46762e9i		−	1.42956i	−0.699350	−	0.714779i	$-0.746527\pi$
$179$		−	1.46762e9i		−	1.42956i	0.699350	−	0.714779i	$-0.253473\pi$
$180$	2.50723e7	−	6.96918e8i	0.0238838	−	0.663883i
$181$	−1.59274e9			−1.48399			−0.741993	−	0.670408i	$-0.766119\pi$
$181$	−1.59274e9			−1.48399			−0.741993	+	0.670408i	$0.766119\pi$
$182$	2.55291e8	+	1.47392e8i	0.232675	+	0.134335i
$183$	−1.79396e8	+	9.93173e7i	−0.159959	+	0.0885566i
$184$	3.31921e8	+	5.74904e8i	0.289576	+	0.501561i
$185$	−1.16920e9	+	6.75039e8i	−0.998165	+	0.576291i
$186$	−6.70379e8	+	1.11437e9i	−0.560104	+	0.931057i
$187$	−5.26374e8	+	9.11706e8i	−0.430455	+	0.745570i
$188$		−	4.99972e8i		−	0.400234i
$189$	−1.19630e9	−	7.79575e8i	−0.937543	−	0.610957i
$190$	9.50699e8			0.729505
$191$	−1.60894e8	−	9.28923e7i	−0.120895	−	0.0697985i	0.438333	−	0.898813i	$-0.355569\pi$
$191$	−1.60894e8	−	9.28923e7i	−0.120895	−	0.0697985i	−0.559228	+	0.829014i	$0.688902\pi$
$192$	1.45560e8	+	8.75659e7i	0.107112	+	0.0644362i
$193$	−5.85324e8	−	1.01381e9i	−0.421859	−	0.730681i	0.574262	−	0.818671i	$-0.305289\pi$
$193$	−5.85324e8	−	1.01381e9i	−0.421859	−	0.730681i	−0.996121	+	0.0879903i	$0.971956\pi$
$194$	−1.00790e9	+	5.81910e8i	−0.711557	+	0.410818i
$195$	−3.15927e8	−	5.70657e8i	−0.218499	−	0.394672i
$196$	9.30687e7	−	1.61200e8i	0.0630637	−	0.109230i
$197$			1.90415e9i			1.26426i	0.774864	+	0.632128i	$0.217818\pi$
$197$			1.90415e9i			1.26426i	−0.774864	+	0.632128i	$0.782182\pi$
$198$	9.72135e8	−	1.55210e9i	0.632508	−	1.00985i
$199$	1.59363e9			1.01619			0.508096	−	0.861300i	$-0.330349\pi$
$199$	1.59363e9			1.01619			0.508096	+	0.861300i	$0.330349\pi$
$200$	−3.74891e8	−	2.16444e8i	−0.234307	−	0.135277i
$201$	4.61289e7	−	2.56526e9i	0.0282611	−	1.57162i
$202$	5.29964e8	+	9.17924e8i	0.318303	+	0.551317i
$203$	1.55072e9	−	8.95310e8i	0.913166	−	0.527217i
$204$	4.42322e8	+	7.95392e6i	0.255398	+	0.00459262i
$205$	−9.58469e8	+	1.66012e9i	−0.542703	+	0.939990i
$206$		−	1.06030e9i		−	0.588788i
$207$	−2.54890e9	−	1.59647e9i	−1.38826	−	0.869520i
$208$	1.58884e8			0.0848844
$209$	2.16220e9	+	1.24835e9i	1.13321	+	0.654260i
$210$	−1.78878e9	+	9.90305e8i	−0.919771	+	0.509204i
$211$	4.36444e8	+	7.55944e8i	0.220191	+	0.381382i	0.954866	−	0.297038i	$-0.0959987\pi$
$211$	4.36444e8	+	7.55944e8i	0.220191	+	0.381382i	−0.734675	+	0.678419i	$0.762665\pi$
$212$	−7.72004e8	+	4.45717e8i	−0.382187	+	0.220656i
$213$	−7.32779e8	+	1.21809e9i	−0.356004	+	0.591783i
$214$	7.61166e8	−	1.31838e9i	0.362931	−	0.628615i
$215$			1.35021e9i			0.631899i
$216$	−7.68489e8	−	4.14931e7i	−0.353039	−	0.0190617i
$217$	3.81284e9			1.71953
$218$	5.21122e8	+	3.00870e8i	0.230735	+	0.133215i
$219$	1.99182e9	+	1.19824e9i	0.865913	+	0.520914i
$220$	−1.31121e9	−	2.27108e9i	−0.559734	−	0.969488i
$221$	3.58349e8	−	2.06893e8i	0.150223	−	0.0867314i
$222$	7.21646e8	+	1.30350e9i	0.297107	+	0.536661i
$223$	1.69943e8	−	2.94349e8i	0.0687199	−	0.119026i	−0.829618	−	0.558331i	$-0.811442\pi$
$223$	1.69943e8	−	2.94349e8i	0.0687199	−	0.119026i	0.898338	+	0.439305i	$0.144775\pi$
$224$		−	4.98039e8i		−	0.197821i
$225$	1.95997e9	+	7.05118e7i	0.764749	+	0.0275126i
$226$	1.49410e9			0.572726
$227$	−7.86249e8	−	4.53941e8i	−0.296113	−	0.170961i	0.344583	−	0.938756i	$-0.388020\pi$
$227$	−7.86249e8	−	4.53941e8i	−0.296113	−	0.170961i	−0.640695	+	0.767795i	$0.721354\pi$
$228$	1.88635e7	−	1.04901e9i	0.00698044	−	0.388187i
$229$	1.91967e7	+	3.32497e7i	0.00698047	+	0.0120905i	0.869495	−	0.493943i	$-0.164445\pi$
$229$	1.91967e7	+	3.32497e7i	0.00698047	+	0.0120905i	−0.862514	+	0.506033i	$0.831111\pi$
$230$	−3.72964e9	+	2.15331e9i	−1.33277	+	0.769477i
$231$	−5.36863e9	−	9.65397e7i	−1.88545	−	0.0339045i
$232$	4.82558e8	−	8.35816e8i	0.166570	−	0.288508i
$233$			3.39626e9i			1.15233i	0.817334	+	0.576165i	$0.195451\pi$
$233$			3.39626e9i			1.15233i	−0.817334	+	0.576165i	$0.804549\pi$
$234$	−6.35937e8	+	3.37275e8i	−0.212105	+	0.112492i
$235$	3.24353e9			1.06352
$236$	7.61547e8	+	4.39680e8i	0.245499	+	0.141739i
$237$	4.82339e9	−	2.67033e9i	1.52883	−	0.846391i
$238$	−6.48526e8	−	1.12328e9i	−0.202125	−	0.350090i
$239$	−2.60050e8	+	1.50140e8i	−0.0797012	+	0.0460155i	−0.539321	−	0.842100i	$-0.681319\pi$
$239$	−2.60050e8	+	1.50140e8i	−0.0797012	+	0.0460155i	0.459620	+	0.888116i	$0.347986\pi$
$240$	−5.68077e8	+	9.44312e8i	−0.171223	+	0.284623i
$241$	−2.67282e9	+	4.62946e9i	−0.792321	+	1.37234i	0.132205	+	0.991222i	$0.457794\pi$
$241$	−2.67282e9	+	4.62946e9i	−0.792321	+	1.37234i	−0.924526	+	0.381119i	$0.875539\pi$
$242$		−	4.46173e9i		−	1.30089i
$243$	3.16397e9	−	1.46525e9i	0.907418	−	0.420229i
$244$	3.24035e8			0.0914182
$245$	1.04577e9	+	6.03776e8i	0.290250	+	0.167576i
$246$	1.81277e9	+	1.09052e9i	0.494998	+	0.297780i
$247$	−4.90667e8	−	8.49860e8i	−0.131825	−	0.228328i
$248$	1.77974e9	−	1.02753e9i	0.470489	−	0.271637i
$249$	−2.14620e9	−	3.87666e9i	−0.558306	−	1.00846i
$250$	−4.30759e8	+	7.46096e8i	−0.110274	+	0.191001i
$251$		−	2.15800e8i		−	0.0543696i	−0.999630	−	0.0271848i	$-0.991346\pi$
$251$		−	2.15800e8i		−	0.0543696i	0.999630	−	0.0271848i	$-0.00865425\pi$
$252$	1.05722e9	+	1.99341e9i	0.262158	+	0.494304i
$253$	−1.13099e10			−2.76044
$254$	−5.60744e8	−	3.23746e8i	−0.134719	−	0.0777802i
$255$	−5.16004e7	+	2.86953e9i	−0.0122037	+	0.678657i
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	1.30255e9	−	7.52028e8i	0.298581	−	0.172386i	−0.343224	−	0.939254i	$-0.611519\pi$
$257$	1.30255e9	−	7.52028e8i	0.298581	−	0.172386i	0.641805	+	0.766868i	$0.278186\pi$
$258$	1.48984e9	+	2.67905e7i	0.336248	+	0.00604647i
$259$	2.18416e9	−	3.78308e9i	0.485384	−	0.840710i
$260$			1.03075e9i			0.225559i
$261$	−1.57205e8	+	4.36972e9i	−0.0338770	+	0.941655i
$262$	1.27975e9			0.271595
$263$	−4.86114e9	−	2.80658e9i	−1.01605	−	0.586616i	−0.103092	−	0.994672i	$-0.532874\pi$
$263$	−4.86114e9	−	2.80658e9i	−1.01605	−	0.586616i	−0.912957	+	0.408055i	$0.866207\pi$
$264$	−2.53196e9	+	1.40174e9i	−0.521243	+	0.288571i
$265$	−2.89156e9	−	5.00832e9i	−0.586338	−	1.01557i
$266$	−2.66397e9	+	1.53804e9i	−0.532112	+	0.307215i
$267$	−2.94357e8	+	4.89308e8i	−0.0579201	+	0.0962803i
$268$	−2.02720e9	+	3.51121e9i	−0.392968	+	0.680640i
$269$		−	5.36842e9i		−	1.02527i	−0.858607	−	0.512634i	$-0.828670\pi$
$269$		−	5.36842e9i		−	1.02527i	0.858607	−	0.512634i	$-0.171330\pi$
$270$	2.69184e8	−	4.98552e9i	0.0506516	−	0.938113i
$271$	−3.34972e9			−0.621056			−0.310528	−	0.950564i	$-0.600506\pi$
$271$	−3.34972e9			−0.621056			−0.310528	+	0.950564i	$0.600506\pi$
$272$	−6.05431e8	−	3.49546e8i	−0.110609	−	0.0638599i
$273$	1.80848e9	+	1.08794e9i	0.325583	+	0.195864i
$274$	7.77578e8	+	1.34681e9i	0.137956	+	0.238948i
$275$	6.38706e9	−	3.68757e9i	1.11679	−	0.644777i
$276$	2.30199e9	+	4.15806e9i	0.396704	+	0.716563i
$277$	4.05893e8	−	7.03028e8i	0.0689434	−	0.119413i	−0.829493	−	0.558517i	$-0.811371\pi$
$277$	4.05893e8	−	7.03028e8i	0.0689434	−	0.119413i	0.898436	+	0.439104i	$0.144704\pi$
$278$			2.19676e9i			0.367793i
$279$	−4.94221e9	+	7.89068e9i	−0.815652	+	1.30226i
$280$	3.23099e9			0.525659
$281$	−9.24159e8	−	5.33564e8i	−0.148225	−	0.0855778i	0.424053	−	0.905637i	$-0.360607\pi$
$281$	−9.24159e8	−	5.33564e8i	−0.148225	−	0.0855778i	−0.572278	+	0.820060i	$0.693940\pi$
$282$	6.43573e7	−	3.57895e9i	0.0101766	−	0.565925i
$283$	4.18292e9	+	7.24503e9i	0.652130	+	1.12952i	0.982605	+	0.185707i	$0.0594577\pi$
$283$	4.18292e9	+	7.24503e9i	0.652130	+	1.12952i	−0.330475	+	0.943815i	$0.607209\pi$
$284$	1.94540e9	−	1.12318e9i	0.299044	−	0.172653i
$285$	6.80538e9	+	1.22376e8i	1.03151	+	0.0185488i
$286$	−1.35346e9	+	2.34427e9i	−0.202294	+	0.350383i
$287$		−	6.20246e9i		−	0.914190i
$288$	1.03069e9	+	6.45560e8i	0.149816	+	0.0938353i
$289$	5.15510e9			0.739002
$290$	5.42229e9	+	3.13056e9i	0.766639	+	0.442619i
$291$	−7.28974e9	+	4.03575e9i	−1.01658	+	0.562798i
$292$	−1.83661e9	−	3.18111e9i	−0.252631	−	0.437569i
$293$	−1.17267e9	+	6.77039e8i	−0.159112	+	0.0918636i	−0.577442	−	0.816432i	$-0.695949\pi$
$293$	−1.17267e9	+	6.77039e8i	−0.159112	+	0.0918636i	0.418330	+	0.908295i	$0.362616\pi$
$294$	6.86964e8	−	1.14194e9i	0.0919484	−	0.152845i
$295$	−2.85239e9	+	4.94048e9i	−0.376635	+	0.652351i
$296$		−	2.35446e9i		−	0.306707i
$297$	7.15862e9	−	1.09853e10i	0.920034	−	1.41184i
$298$	−8.76488e9			−1.11143
$299$	3.84983e9	+	2.22270e9i	0.481678	+	0.278097i
$300$	−2.65572e9	−	1.59763e9i	−0.327867	−	0.197238i
$301$	−2.18438e9	−	3.78345e9i	−0.266110	−	0.460916i
$302$	6.82078e9	−	3.93798e9i	0.819985	−	0.473419i
$303$	3.67548e9	+	6.63899e9i	0.436058	+	0.787647i
$304$	−8.28983e8	+	1.43584e9i	−0.0970624	+	0.168117i
$305$			2.10215e9i			0.242921i
$306$	3.16525e9	+	1.13873e8i	0.361013	+	0.0129878i
$307$	3.34624e9			0.376707			0.188354	−	0.982101i	$-0.439685\pi$
$307$	3.34624e9			0.376707			0.188354	+	0.982101i	$0.439685\pi$
$308$	7.34834e9	+	4.24257e9i	0.816557	+	0.471439i
$309$	1.36484e8	−	7.58993e9i	0.0149708	−	0.832538i
$310$	6.66603e9	+	1.15459e10i	0.721806	+	1.25021i
$311$	−7.07501e9	+	4.08476e9i	−0.756285	+	0.436641i	−0.827960	−	0.560787i	$-0.810499\pi$
$311$	−7.07501e9	+	4.08476e9i	−0.756285	+	0.436641i	0.0716755	+	0.997428i	$0.477165\pi$
$312$	1.13734e9	+	2.04519e7i	0.120025	+	0.00215832i
$313$	6.49273e9	−	1.12457e10i	0.676472	−	1.17168i	−0.299564	−	0.954076i	$-0.596841\pi$
$313$	6.49273e9	−	1.12457e10i	0.676472	−	1.17168i	0.976036	−	0.217608i	$-0.0698255\pi$
$314$			1.12993e8i			0.0116234i
$315$	−1.29321e10	+	6.85864e9i	−1.31349	+	0.696620i
$316$	−8.71227e9			−0.873741
$317$	−2.27583e9	−	1.31395e9i	−0.225374	−	0.130120i	0.383062	−	0.923723i	$-0.374869\pi$
$317$	−2.27583e9	−	1.31395e9i	−0.225374	−	0.130120i	−0.608436	+	0.793603i	$0.708203\pi$
$318$	−5.58361e9	+	3.09120e9i	−0.546018	+	0.302287i
$319$	8.22139e9	+	1.42399e10i	0.793930	+	1.37513i
$320$	1.50814e9	−	8.70728e8i	0.143828	−	0.0830391i
$321$	5.61836e9	−	9.33937e9i	0.529163	−	0.879625i
$322$	6.96727e9	−	1.20677e10i	0.648096	−	1.12254i
$323$			4.31787e9i			0.396697i
$324$	−5.49574e9	−	3.95941e8i	−0.498707	−	0.0359295i
$325$	−2.89882e9			−0.259829
$326$	−1.20394e10	−	6.95095e9i	−1.06594	−	0.615423i
$327$	3.69162e9	+	2.22080e9i	0.322868	+	0.194231i
$328$	−1.67152e9	−	2.89515e9i	−0.144416	−	0.250136i
$329$	−9.08876e9	+	5.24740e9i	−0.775749	+	0.447879i
$330$	−9.09370e9	−	1.64259e10i	−0.766805	−	1.38507i
$331$	5.38121e9	−	9.32053e9i	0.448299	−	0.776477i	−0.549976	−	0.835180i	$-0.685363\pi$
$331$	5.38121e9	−	9.32053e9i	0.448299	−	0.776477i	0.998275	+	0.0587032i	$0.0186965\pi$
$332$			7.00223e9i			0.576347i
$333$	4.99797e9	+	9.42376e9i	0.406459	+	0.766386i
$334$	−9.68158e9			−0.777966
$335$	−2.27787e10	−	1.31513e10i	−1.80863	−	1.04421i
$336$	6.41085e7	−	3.56511e9i	0.00502989	−	0.279715i
$337$	−6.49324e9	−	1.12466e10i	−0.503433	−	0.871972i	−0.999992	−	0.00396864i	$-0.998737\pi$
$337$	−6.49324e9	−	1.12466e10i	−0.503433	−	0.871972i	0.496559	−	0.868003i	$-0.334597\pi$
$338$	−7.07107e9	+	4.08249e9i	−0.541775	+	0.312794i
$339$	1.06952e10	+	1.92324e8i	0.809826	+	0.0145624i
$340$	2.26765e9	−	3.92769e9i	0.169692	−	0.293915i
$341$			3.50123e10i			2.58942i
$342$	2.70061e8	−	7.50671e9i	0.0197405	−	0.548713i
$343$	1.15818e10			0.836758
$344$	−2.03922e9	−	1.17735e9i	−0.145623	−	0.0840757i
$345$	−2.69751e10	+	1.49340e10i	−1.90409	+	1.05414i
$346$	2.59001e9	+	4.48603e9i	0.180716	+	0.313010i
$347$	2.11272e9	−	1.21978e9i	0.145722	−	0.0841324i	−0.425366	−	0.905021i	$-0.639855\pi$
$347$	2.11272e9	−	1.21978e9i	0.145722	−	0.0841324i	0.571088	+	0.820889i	$0.306521\pi$
$348$	3.56188e9	−	5.92090e9i	0.242864	−	0.403711i
$349$	1.08992e10	−	1.88779e10i	0.734669	−	1.27248i	−0.220200	−	0.975455i	$-0.570671\pi$
$349$	1.08992e10	−	1.88779e10i	0.734669	−	1.27248i	0.954869	−	0.297029i	$-0.0959957\pi$
$350$			9.08664e9i			0.605524i
$351$	−4.59565e9	+	2.33245e9i	−0.302774	+	0.153668i
$352$	4.57336e9			0.297896
$353$	1.22820e10	+	7.09100e9i	0.790987	+	0.456677i	0.840310	−	0.542106i	$-0.182373\pi$
$353$	1.22820e10	+	7.09100e9i	0.790987	+	0.456677i	−0.0493227	+	0.998783i	$0.515706\pi$
$354$	5.39479e9	+	3.24539e9i	0.343527	+	0.206659i
$355$	7.28652e9	+	1.26206e10i	0.458782	+	0.794634i
$356$	7.81466e8	−	4.51180e8i	0.0486530	−	0.0280898i
$357$	−4.49775e9	−	8.12425e9i	−0.276900	−	0.500162i
$358$	−8.30212e9	+	1.43797e10i	−0.505425	+	0.875422i
$359$		−	1.62366e10i		−	0.977499i	−0.872424	−	0.488750i	$-0.837453\pi$
$359$		−	1.62366e10i		−	0.977499i	0.872424	−	0.488750i	$-0.162547\pi$
$360$	−4.18802e9	+	6.68654e9i	−0.249344	+	0.398099i
$361$	−6.74331e9			−0.397049
$362$	1.56056e10	+	9.00988e9i	0.908752	+	0.524668i
$363$	5.74322e8	−	3.19384e10i	0.0330772	−	1.83945i
$364$	−1.66755e9	−	2.88829e9i	−0.0949892	−	0.164526i
$365$	2.06372e10	−	1.19149e10i	1.16273	−	0.671303i
$366$	2.31954e9	+	4.17104e7i	0.129264	+	0.00232445i
$367$	4.72220e9	−	8.17909e9i	0.260303	−	0.450859i	−0.706019	−	0.708193i	$-0.749511\pi$
$367$	4.72220e9	−	8.17909e9i	0.260303	−	0.450859i	0.966323	+	0.257334i	$0.0828440\pi$
$368$		−	7.51051e9i		−	0.409523i
$369$	1.28360e10	+	8.03965e9i	0.692348	+	0.433642i
$370$	1.52744e10			0.814998
$371$	1.62050e10	+	9.35595e9i	0.855367	+	0.493847i
$372$	1.28722e10	−	7.12629e9i	0.672170	−	0.372127i
$373$	6.87407e9	+	1.19062e10i	0.355123	+	0.615091i	0.987139	−	0.159864i	$-0.0511056\pi$
$373$	6.87407e9	+	1.19062e10i	0.355123	+	0.615091i	−0.632016	+	0.774955i	$0.717772\pi$
$374$	1.03148e10	−	5.95524e9i	0.527198	−	0.304378i
$375$	−3.17954e9	+	5.28533e9i	−0.160783	+	0.267268i
$376$	−2.82827e9	+	4.89870e9i	−0.141504	+	0.245092i
$377$		−	6.46288e9i		−	0.319934i
$378$	7.31131e9	+	1.44055e10i	0.358120	+	0.705605i
$379$	−8.10058e9			−0.392608			−0.196304	−	0.980543i	$-0.562894\pi$
$379$	−8.10058e9			−0.392608			−0.196304	+	0.980543i	$0.562894\pi$
$380$	−9.31490e9	−	5.37796e9i	−0.446729	−	0.257919i
$381$	−3.97230e9	−	2.38965e9i	−0.188513	−	0.113406i
$382$	1.05096e9	+	1.82031e9i	0.0493550	+	0.0854854i
$383$	−3.26313e10	+	1.88397e10i	−1.51649	+	0.875544i	−0.516675	+	0.856182i	$0.672830\pi$
$383$	−3.26313e10	+	1.88397e10i	−1.51649	+	0.875544i	−0.999813	+	0.0193625i	$0.993836\pi$
$384$	−9.30846e8	−	1.68138e9i	−0.0428108	−	0.0773288i
$385$	−2.75233e10	+	4.76718e10i	−1.25273	+	2.16980i
$386$			1.32444e10i			0.596599i
$387$	1.06613e10	+	3.83549e8i	0.475296	+	0.0170992i
$388$	1.31671e10			0.580984
$389$	−7.44708e9	−	4.29957e9i	−0.325228	−	0.187770i	0.328493	−	0.944507i	$-0.393459\pi$
$389$	−7.44708e9	−	4.29957e9i	−0.325228	−	0.187770i	−0.653720	+	0.756736i	$0.726793\pi$
$390$	−1.32680e8	+	7.37842e9i	−0.00573518	+	0.318937i
$391$	−9.77988e9	−	1.69392e10i	−0.418433	−	0.724748i
$392$	−1.82377e9	+	1.05295e9i	−0.0772369	+	0.0445928i
$393$	9.16086e9	+	1.64732e8i	0.384031	+	0.00690571i
$394$	1.07715e10	−	1.86567e10i	0.446982	−	0.774196i
$395$		−	5.65202e10i		−	2.32175i
$396$	−1.83049e10	+	9.70818e9i	−0.744368	+	0.394782i
$397$	−7.53858e9			−0.303478			−0.151739	−	0.988421i	$-0.548487\pi$
$397$	−7.53858e9			−0.303478			−0.151739	+	0.988421i	$0.548487\pi$
$398$	−1.56144e10	−	9.01495e9i	−0.622289	−	0.359278i
$399$	−1.92675e10	+	1.06669e10i	−0.760210	+	0.420868i
$400$	2.44878e9	+	4.24141e9i	0.0956555	+	0.165680i
$401$	−2.42910e9	+	1.40244e9i	−0.0939436	+	0.0542384i	−0.546236	−	0.837631i	$-0.683940\pi$
$401$	−2.42910e9	+	1.40244e9i	−0.0939436	+	0.0542384i	0.452292	+	0.891870i	$0.350606\pi$
$402$	−1.49633e10	+	2.48733e10i	−0.572957	+	0.952423i
$403$	6.88084e9	−	1.19180e10i	0.260868	−	0.451837i
$404$		−	1.19917e10i		−	0.450148i
$405$	2.56864e9	−	3.56532e10i	0.0954736	−	1.32519i
$406$	−2.02585e10			−0.745597
$407$	3.47390e10	+	2.00566e10i	1.26602	+	0.730935i
$408$	−4.28886e9	−	2.58008e9i	−0.154775	−	0.0931093i
$409$	4.31779e9	+	7.47864e9i	0.154301	+	0.267257i	0.932804	−	0.360383i	$-0.117354\pi$
$409$	4.31779e9	+	7.47864e9i	0.154301	+	0.267257i	−0.778503	+	0.627641i	$0.784021\pi$
$410$	1.87821e10	−	1.08438e10i	0.664673	−	0.383749i
$411$	5.39277e9	+	9.74092e9i	0.188993	+	0.341376i
$412$	−5.99795e9	+	1.03888e10i	−0.208168	+	0.360558i
$413$		−	1.84584e10i		−	0.634446i
$414$	1.59431e10	+	3.00609e10i	0.542713	+	1.02330i
$415$	−4.54265e10			−1.53150
$416$	−1.55674e9	−	8.98786e8i	−0.0519809	−	0.0300112i
$417$	−2.82771e8	+	1.57251e10i	−0.00935171	+	0.520054i
$418$	−1.41234e10	−	2.44625e10i	−0.462632	−	0.801302i
$419$	2.20697e10	−	1.27420e10i	0.716046	−	0.413409i	−0.0972497	−	0.995260i	$-0.531005\pi$
$419$	2.20697e10	−	1.27420e10i	0.716046	−	0.413409i	0.813296	+	0.581851i	$0.197671\pi$
$420$	2.31284e10	+	4.15899e8i	0.743273	+	0.0133657i
$421$	7.22114e7	−	1.25074e8i	0.00229867	−	0.00398142i	−0.864874	−	0.501989i	$-0.832602\pi$
$421$	7.22114e7	−	1.25074e8i	0.00229867	−	0.00398142i	0.867172	+	0.498008i	$0.165935\pi$
$422$		−	9.87561e9i		−	0.311397i
$423$	9.21377e8	−	2.56109e10i	0.0287790	−	0.799951i
$424$	1.00854e10			0.312055
$425$	1.10460e10	+	6.37740e9i	0.338570	+	0.195474i
$426$	1.40703e10	−	7.78961e9i	0.427234	−	0.236525i
$427$	−3.40087e9	−	5.89049e9i	−0.102301	−	0.177190i
$428$	−1.49157e10	+	8.61161e9i	−0.444498	+	0.256631i
$429$	−9.99026e9	+	1.66068e10i	−0.294949	+	0.490293i
$430$	7.63794e9	−	1.32293e10i	0.223410	−	0.386957i
$431$			6.31640e9i			0.183046i	0.995803	+	0.0915231i	$0.0291735\pi$
$431$			6.31640e9i			0.183046i	−0.995803	+	0.0915231i	$0.970826\pi$
$432$	7.29491e9	+	4.75378e9i	0.209452	+	0.136491i
$433$	−3.96241e10			−1.12722			−0.563609	−	0.826042i	$-0.690587\pi$
$433$	−3.96241e10			−1.12722			−0.563609	+	0.826042i	$0.690587\pi$
$434$	−3.73581e10	−	2.15687e10i	−1.05299	−	0.607946i
$435$	3.84114e10	+	2.31075e10i	1.07276	+	0.645350i
$436$	−3.40395e9	−	5.89582e9i	−0.0941971	−	0.163154i
$437$	−4.01731e10	+	2.31940e10i	−1.10156	+	0.635988i
$438$	−1.27375e10	−	2.30077e10i	−0.346090	−	0.625140i
$439$	−1.57438e10	+	2.72691e10i	−0.423889	+	0.734196i	−0.996316	−	0.0857589i	$-0.972669\pi$
$439$	−1.57438e10	+	2.72691e10i	−0.423889	+	0.734196i	0.572427	+	0.819955i	$0.306002\pi$
$440$			2.96693e10i			0.791584i
$441$	5.06448e9	−	8.08589e9i	0.133900	−	0.213783i
$442$	−4.68145e9			−0.122657
$443$	3.86111e10	+	2.22921e10i	1.00253	+	0.578810i	0.908995	−	0.416806i	$-0.136851\pi$
$443$	3.86111e10	+	2.22921e10i	1.00253	+	0.578810i	0.0935330	+	0.995616i	$0.470184\pi$
$444$	3.03070e8	−	1.68539e10i	0.00779850	−	0.433680i
$445$	2.92699e9	+	5.06970e9i	0.0746417	+	0.129283i
$446$	−3.33018e9	+	1.92268e9i	−0.0841644	+	0.0485923i
$447$	−6.27416e10	−	1.12823e9i	−1.57154	−	0.0282597i
$448$	−2.81733e9	+	4.87977e9i	−0.0699401	+	0.121140i
$449$		−	2.35548e10i		−	0.579553i	−0.957094	−	0.289777i	$-0.906419\pi$
$449$		−	2.35548e10i		−	0.579553i	0.957094	−	0.289777i	$-0.0935810\pi$
$450$	−1.88048e10	−	1.17781e10i	−0.458584	−	0.287228i
$451$	5.69555e10			1.37667
$452$	−1.46392e10	−	8.45192e9i	−0.350722	−	0.202489i
$453$	4.93321e10	−	2.73112e10i	1.17148	−	0.648557i
$454$	5.13576e9	+	8.89540e9i	0.120887	+	0.209383i
$455$	1.87376e10	−	1.08181e10i	0.437187	−	0.252410i
$456$	−6.11893e9	+	1.01715e10i	−0.141519	+	0.235247i
$457$	−2.05058e10	+	3.55170e10i	−0.470122	+	0.814276i	−0.999416	−	0.0341626i	$-0.989124\pi$
$457$	−2.05058e10	+	3.55170e10i	−0.470122	+	0.814276i	0.529294	+	0.848439i	$0.322457\pi$
$458$		−	4.34372e8i		−	0.00987188i
$459$	2.26432e10	+	1.22257e9i	0.510136	+	0.0275438i
$460$	4.87239e10			1.08820
$461$	−3.37174e9	−	1.94668e9i	−0.0746536	−	0.0431013i	0.462209	−	0.886771i	$-0.347057\pi$
$461$	−3.37174e9	−	1.94668e9i	−0.0746536	−	0.0431013i	−0.536862	+	0.843670i	$0.680390\pi$
$462$	5.20555e10	+	3.13155e10i	1.14261	+	0.687370i
$463$	−2.67932e10	−	4.64073e10i	−0.583044	−	1.00986i	−0.995116	−	0.0987107i	$-0.968528\pi$
$463$	−2.67932e10	−	4.64073e10i	−0.583044	−	1.00986i	0.412072	−	0.911151i	$-0.364805\pi$
$464$	−9.45617e9	+	5.45952e9i	−0.204006	+	0.117783i
$465$	4.62313e10	+	8.35071e10i	0.988835	+	1.78612i
$466$	1.92121e10	−	3.32764e10i	0.407410	−	0.705655i
$467$			4.53162e10i			0.952766i	0.879238	+	0.476383i	$0.158052\pi$
$467$			4.53162e10i			0.952766i	−0.879238	+	0.476383i	$0.841948\pi$
$468$	8.13880e9	+	2.92801e8i	0.169659	+	0.00610365i
$469$	8.51049e10			1.75899
$470$	−3.17800e10	−	1.83482e10i	−0.651272	−	0.376012i
$471$	−1.45447e7	+	8.08839e8i	−0.000295543	+	0.0164353i
$472$	−4.97441e9	−	8.61593e9i	−0.100224	−	0.173594i
$473$	3.47424e10	−	2.00585e10i	0.694089	−	0.400733i
$474$	−6.23650e10	−	1.12146e9i	−1.23546	−	0.0222162i
$475$	1.51247e10	−	2.61967e10i	0.297106	−	0.514602i
$476$			1.46745e10i			0.285848i
$477$	−4.03671e10	+	2.14090e10i	−0.779747	+	0.413545i
$478$	3.39728e9			0.0650758
$479$	4.92416e9	+	2.84297e9i	0.0935385	+	0.0540045i	0.546040	−	0.837759i	$-0.316135\pi$
$479$	4.92416e9	+	2.84297e9i	0.0935385	+	0.0540045i	−0.452501	+	0.891764i	$0.649468\pi$
$480$	1.09078e10	−	6.03880e9i	0.205482	−	0.113759i
$481$	−7.88329e9	−	1.36543e10i	−0.147274	−	0.255087i
$482$	5.23763e10	−	3.02395e10i	0.970392	−	0.560256i
$483$	5.14272e10	−	8.54872e10i	0.944940	−	1.57077i
$484$	−2.52394e10	+	4.37159e10i	−0.459936	+	0.796632i
$485$			8.54208e10i			1.54382i
$486$	−3.92892e10	−	3.54169e9i	−0.704251	−	0.0634841i
$487$	3.64760e10			0.648472			0.324236	−	0.945976i	$-0.394893\pi$
$487$	3.64760e10			0.648472			0.324236	+	0.945976i	$0.394893\pi$
$488$	−3.17488e9	−	1.83302e9i	−0.0559820	−	0.0323212i
$489$	−8.52869e10	−	5.13067e10i	−1.49158	−	0.897303i
$490$	−6.83095e9	−	1.18316e10i	−0.118494	−	0.205238i
$491$	−5.07409e10	+	2.92952e10i	−0.873035	+	0.504047i	−0.868356	−	0.495942i	$-0.834823\pi$
$491$	−5.07409e10	+	2.92952e10i	−0.873035	+	0.504047i	−0.00467962	+	0.999989i	$0.501490\pi$
$492$	−1.15925e10	−	2.09395e10i	−0.197842	−	0.357360i
$493$	−1.42183e10	+	2.46269e10i	−0.240692	+	0.416890i
$494$			1.11025e10i			0.186429i
$495$	−6.29811e10	−	1.18752e11i	−1.04903	−	1.97797i
$496$	−2.32504e10			−0.384152
$497$	−4.08354e10	−	2.35763e10i	−0.669285	−	0.386412i
$498$	−9.01340e8	+	5.01241e10i	−0.0146545	+	0.814946i
$499$	3.18425e10	+	5.51528e10i	0.513576	+	0.889541i	0.999876	+	0.0157483i	$0.00501306\pi$
$499$	3.18425e10	+	5.51528e10i	0.513576	+	0.889541i	−0.486300	+	0.873792i	$0.661654\pi$
$500$	8.44112e9	−	4.87348e9i	0.135058	−	0.0779757i
$501$	−6.93037e10	−	1.24623e9i	−1.10003	−	0.0197810i
$502$	−1.22075e9	+	2.11440e9i	−0.0192225	+	0.0332944i
$503$			1.09134e10i			0.170486i	0.996360	+	0.0852430i	$0.0271667\pi$
$503$			1.09134e10i			0.170486i	−0.996360	+	0.0852430i	$0.972833\pi$
$504$	9.17815e8	−	2.55119e10i	0.0142244	−	0.395385i
$505$	7.77953e10			1.19616
$506$	1.10814e11	+	6.39786e10i	1.69041	+	0.975961i
$507$	−5.11424e10	+	2.83135e10i	−0.774014	+	0.428510i
$508$	3.66277e9	+	6.34410e9i	0.0549989	+	0.0952609i
$509$	−9.71431e9	+	5.60856e9i	−0.144724	+	0.0835565i	−0.570614	−	0.821219i	$-0.693295\pi$
$509$	−9.71431e9	+	5.60856e9i	−0.144724	+	0.0835565i	0.425889	+	0.904775i	$0.359961\pi$
$510$	1.67381e10	−	2.78237e10i	0.247415	−	0.411276i
$511$	−3.85519e10	+	6.67739e10i	−0.565409	+	0.979316i
$512$			3.03700e9i			0.0441942i
$513$	2.89946e9	−	5.37005e10i	0.0418646	−	0.775370i
$514$	−1.70165e10			−0.243790
$515$	−6.73963e10	−	3.89113e10i	−0.958092	−	0.553155i
$516$	−1.44458e10	−	8.69029e9i	−0.203771	−	0.122584i
$517$	−4.81854e10	−	8.34596e10i	−0.674456	−	1.16819i
$518$	−4.28006e10	+	2.47110e10i	−0.594472	+	0.343218i
$519$	1.79626e10	+	3.24458e10i	0.247572	+	0.447186i
$520$	5.83081e9	−	1.00993e10i	0.0797472	−	0.138126i
$521$		−	1.03375e11i		−	1.40302i	−0.712658	−	0.701511i	$-0.752509\pi$
$521$		−	1.03375e11i		−	1.40302i	0.712658	−	0.701511i	$-0.247491\pi$
$522$	2.62592e10	−	4.19251e10i	0.353671	−	0.564666i
$523$	−6.50405e10			−0.869314			−0.434657	−	0.900596i	$-0.643130\pi$
$523$	−6.50405e10			−0.869314			−0.434657	+	0.900596i	$0.643130\pi$
$524$	−1.25390e10	−	7.23938e9i	−0.166317	−	0.0960232i
$525$	−1.16965e9	+	6.50449e10i	−0.0153964	+	0.856202i
$526$	3.17528e10	+	5.49975e10i	0.414800	+	0.718456i
$527$	−5.24390e10	+	3.02757e10i	−0.679849	+	0.392511i
$528$	3.27375e10	+	5.88691e8i	0.421220	+	0.00757446i
$529$	6.59121e10	−	1.14163e11i	0.841671	−	1.45782i
$530$			6.54284e10i			0.829207i
$531$	3.81998e10	+	2.39259e10i	0.480488	+	0.300947i
$532$	3.48020e10			0.434468
$533$	−1.93873e10	−	1.11933e10i	−0.240220	−	0.138691i
$534$	5.65204e9	−	3.12909e9i	0.0695089	−	0.0384815i
$535$	−5.58672e10	−	9.67648e10i	−0.681933	−	1.18114i
$536$	3.97248e10	−	2.29351e10i	0.481285	−	0.277870i
$537$	−6.12800e10	+	1.01865e11i	−0.736923	+	1.22498i
$538$	−3.03684e10	+	5.25995e10i	−0.362487	+	0.627845i
$539$		−	3.58785e10i		−	0.425088i
$540$	−3.08398e10	+	4.73252e10i	−0.362691	+	0.556567i
$541$	9.26356e10			1.08141			0.540703	−	0.841214i	$-0.318158\pi$
$541$	9.26356e10			1.08141			0.540703	+	0.841214i	$0.318158\pi$
$542$	3.28204e10	+	1.89489e10i	0.380318	+	0.219577i
$543$	1.10550e11	+	6.65042e10i	1.27162	+	0.764979i
$544$	3.95466e9	+	6.84967e9i	0.0451558	+	0.0782121i
$545$	3.82487e10	−	2.20829e10i	0.433541	−	0.250305i
$546$	−1.15651e10	−	2.08899e10i	−0.130130	−	0.235053i
$547$	−6.17442e9	+	1.06944e10i	−0.0689679	+	0.119456i	−0.898447	−	0.439081i	$-0.855304\pi$
$547$	−6.17442e9	+	1.06944e10i	−0.0689679	+	0.119456i	0.829479	+	0.558537i	$0.188637\pi$
$548$		−	1.75946e10i		−	0.195100i
$549$	1.65986e10	+	5.97150e8i	0.182718	+	0.00657347i
$550$	−8.34402e10			−0.911852
$551$	5.84051e10	+	3.37202e10i	0.633643	+	0.365834i
$552$	9.66766e8	−	5.37625e10i	0.0104127	−	0.579059i
$553$	9.14387e10	+	1.58376e11i	0.977753	+	1.69352i
$554$	−7.95385e9	+	4.59216e9i	−0.0844381	+	0.0487503i
$555$	1.09339e11	+	1.96615e9i	1.15240	+	0.0207226i
$556$	1.24268e10	−	2.15238e10i	0.130035	−	0.225227i
$557$		−	1.17871e9i		−	0.0122458i	−0.999981	−	0.00612290i	$-0.998051\pi$
$557$		−	1.17871e9i		−	0.0122458i	0.999981	−	0.00612290i	$-0.00194899\pi$
$558$	9.30600e10	−	4.93552e10i	0.959901	−	0.509091i
$559$	−1.57681e10			−0.161485
$560$	−3.16571e10	−	1.82772e10i	−0.321899	−	0.185848i
$561$	7.46028e10	−	4.13016e10i	0.753189	−	0.416981i
$562$	6.03658e9	+	1.04557e10i	0.0605126	+	0.104811i
$563$	−4.60975e10	+	2.66144e10i	−0.458822	+	0.264901i	−0.711549	−	0.702637i	$-0.752006\pi$
$563$	−4.60975e10	+	2.66144e10i	−0.458822	+	0.264901i	0.252727	+	0.967538i	$0.418673\pi$
$564$	−2.08762e10	+	3.47023e10i	−0.206317	+	0.342959i
$565$	5.48312e10	−	9.49705e10i	0.538064	−	0.931955i
$566$		−	9.46487e10i		−	0.922251i
$567$	5.04822e10	+	1.04060e11i	0.488435	+	1.00682i
$568$	−2.54146e10			−0.244168
$569$	−7.89230e9	−	4.55662e9i	−0.0752930	−	0.0434704i	0.461881	−	0.886942i	$-0.347175\pi$
$569$	−7.89230e9	−	4.55662e9i	−0.0752930	−	0.0434704i	−0.537174	+	0.843472i	$0.680508\pi$
$570$	−6.59866e10	−	3.96961e10i	−0.625110	−	0.376052i
$571$	−8.93207e10	−	1.54708e11i	−0.840248	−	1.45535i	−0.889685	−	0.456575i	$-0.849076\pi$
$571$	−8.93207e10	−	1.54708e11i	−0.840248	−	1.45535i	0.0494367	−	0.998777i	$-0.484257\pi$
$572$	2.65224e10	−	1.53127e10i	0.247758	−	0.143043i
$573$	7.28874e9	+	1.31656e10i	0.0676136	+	0.122130i
$574$	−3.50864e10	+	6.07715e10i	−0.323215	+	0.559825i
$575$			1.37028e11i			1.25354i
$576$	−6.44685e9	−	1.21556e10i	−0.0585676	−	0.110430i
$577$	−1.57035e11			−1.41675			−0.708374	−	0.705837i	$-0.750571\pi$
$577$	−1.57035e11			−1.41675			−0.708374	+	0.705837i	$0.750571\pi$
$578$	−5.05095e10	−	2.91617e10i	−0.452545	−	0.261277i
$579$	−1.70484e9	+	9.48072e10i	−0.0151694	+	0.843581i
$580$	−3.54183e10	−	6.13462e10i	−0.312979	−	0.542096i
$581$	1.27290e11	−	7.34911e10i	1.11710	−	0.644957i
$582$	9.42542e10	+	1.69490e9i	0.821503	+	0.0147724i
$583$	−8.59131e10	+	1.48806e11i	−0.743679	+	1.28809i
$584$			4.15578e10i			0.357274i
$585$	−1.89953e9	+	5.27999e10i	−0.0162189	+	0.450827i
$586$	1.53197e10			0.129915
$587$	7.02172e10	+	4.05399e10i	0.591413	+	0.341452i	0.765656	−	0.643250i	$-0.222414\pi$
$587$	7.02172e10	+	4.05399e10i	0.591413	+	0.341452i	−0.174243	+	0.984703i	$0.555748\pi$
$588$	−1.31906e10	+	7.30259e9i	−0.110346	+	0.0610896i
$589$	7.18018e10	+	1.24364e11i	0.596588	+	1.03332i
$590$	5.58952e10	−	3.22711e10i	0.461282	−	0.266321i
$591$	7.95070e10	−	1.32164e11i	0.651711	−	1.08334i
$592$	−1.33188e10	+	2.30689e10i	−0.108437	+	0.187819i
$593$		−	2.32095e11i		−	1.87693i	−0.345379	−	0.938463i	$-0.612250\pi$
$593$		−	2.32095e11i		−	1.87693i	0.345379	−	0.938463i	$-0.387750\pi$
$594$	−1.32282e11	+	6.71378e10i	−1.06256	+	0.539289i
$595$	−9.51995e10			−0.759569
$596$	8.58779e10	+	4.95816e10i	0.680607	+	0.392949i
$597$	−1.10612e11	−	6.65416e10i	−0.870771	−	0.523837i
$598$	−2.51470e10	−	4.35558e10i	−0.196644	−	0.340598i
$599$	−6.67859e9	+	3.85589e9i	−0.0518773	+	0.0299514i	−0.525714	−	0.850661i	$-0.676202\pi$
$599$	−6.67859e9	+	3.85589e9i	−0.0518773	+	0.0299514i	0.473837	+	0.880613i	$0.342869\pi$
$600$	1.69831e10	+	3.06765e10i	0.131043	+	0.236701i
$601$	8.64971e10	−	1.49817e11i	0.662985	−	1.14832i	−0.316842	−	0.948478i	$-0.602623\pi$
$601$	8.64971e10	−	1.49817e11i	0.662985	−	1.14832i	0.979827	−	0.199846i	$-0.0640441\pi$
$602$			4.94268e10i			0.376337i
$603$	−1.10313e11	+	1.76125e11i	−0.834369	+	1.33214i
$604$	−8.91062e10			−0.669515
$605$	−2.83604e11	−	1.63739e11i	−2.11685	−	1.22216i
$606$	1.54359e9	−	8.58403e10i	0.0114457	−	0.636503i
$607$	6.33224e10	+	1.09678e11i	0.466448	+	0.807911i	0.999266	−	0.0383189i	$-0.0122003\pi$
$607$	6.33224e10	+	1.09678e11i	0.466448	+	0.807911i	−0.532818	+	0.846230i	$0.678867\pi$
$608$	1.62447e10	−	9.37887e9i	0.118877	−	0.0686335i
$609$	−1.45017e11	−	2.60772e9i	−1.05426	−	0.0189579i
$610$	1.18916e10	−	2.05968e10i	0.0858855	−	0.148758i
$611$			3.78789e10i			0.271789i
$612$	−3.03688e10	−	1.90211e10i	−0.216482	−	0.135591i
$613$	−1.90947e11			−1.35230			−0.676148	−	0.736765i	$-0.736352\pi$
$613$	−1.90947e11			−1.35230			−0.676148	+	0.736765i	$0.736352\pi$
$614$	−3.27863e10	−	1.89292e10i	−0.230685	−	0.133186i
$615$	1.35844e11	−	7.52057e10i	0.949595	−	0.525715i
$616$	−4.79992e10	−	8.31370e10i	−0.333358	−	0.577393i
$617$	3.94255e10	−	2.27623e10i	0.272043	−	0.157064i	−0.357773	−	0.933809i	$-0.616464\pi$
$617$	3.94255e10	−	2.27623e10i	0.272043	−	0.157064i	0.629816	+	0.776745i	$0.283130\pi$
$618$	−4.42724e10	+	7.35938e10i	−0.303514	+	0.504530i
$619$	2.52527e10	−	4.37390e10i	0.172007	−	0.297925i	−0.767114	−	0.641510i	$-0.778308\pi$
$619$	2.52527e10	−	4.37390e10i	0.172007	−	0.297925i	0.939121	+	0.343585i	$0.111642\pi$
$620$		−	1.50835e11i		−	1.02079i
$621$	1.10256e11	+	2.17237e11i	0.741370	+	1.46072i
$622$	9.24275e10			0.617504
$623$	−1.64036e10	−	9.47061e9i	−0.108890	−	0.0628674i
$624$	−1.10279e10	−	6.63417e9i	−0.0727371	−	0.0437570i
$625$	8.99998e10	+	1.55884e11i	0.589823	+	1.02160i
$626$	−1.27231e11	+	7.34569e10i	−0.828506	+	0.478338i
$627$	−9.79510e10	−	1.76928e11i	−0.633780	−	1.14479i
$628$	6.39186e8	−	1.10710e9i	0.00410950	−	0.00711786i
$629$			6.93730e10i			0.443188i
$630$	1.65506e11	+	5.95426e9i	1.05064	+	0.0377977i
$631$	7.46120e10			0.470642			0.235321	−	0.971918i	$-0.424386\pi$
$631$	7.46120e10			0.470642			0.235321	+	0.971918i	$0.424386\pi$
$632$	8.53625e10	+	4.92840e10i	0.535055	+	0.308914i
$633$	1.27121e9	−	7.06926e10i	0.00791774	−	0.440310i
$634$	1.48657e10	+	2.57481e10i	0.0920085	+	0.159363i
$635$	−4.11568e10	+	2.37619e10i	−0.253132	+	0.146146i
$636$	7.21945e10	+	1.29821e9i	0.441241	+	0.00793447i
$637$	−7.05107e9	+	1.22128e10i	−0.0428250	+	0.0741751i
$638$		−	1.86029e11i		−	1.12279i
$639$	1.01722e11	−	5.39492e10i	0.610116	−	0.323580i
$640$	−1.97023e10			−0.117435
$641$	2.44739e11	+	1.41300e11i	1.44968	+	0.836972i	0.998462	−	0.0554435i	$-0.0176573\pi$
$641$	2.44739e11	+	1.41300e11i	1.44968	+	0.836972i	0.451215	+	0.892415i	$0.350991\pi$
$642$	−1.07880e11	+	5.97245e10i	−0.635039	+	0.351571i
$643$	8.57408e10	+	1.48507e11i	0.501584	+	0.868769i	0.999998	+	0.00183012i	$0.000582545\pi$
$643$	8.57408e10	+	1.48507e11i	0.501584	+	0.868769i	−0.498414	+	0.866939i	$0.666084\pi$
$644$	−1.36530e11	+	7.88257e10i	−0.793752	+	0.458273i
$645$	5.63776e10	−	9.37162e10i	0.325737	−	0.541472i
$646$	2.44256e10	−	4.23063e10i	0.140254	−	0.242927i
$647$		−	6.51359e10i		−	0.371709i	−0.982577	−	0.185855i	$-0.940495\pi$
$647$		−	6.51359e10i		−	0.371709i	0.982577	−	0.185855i	$-0.0595053\pi$
$648$	5.16072e10	+	3.49680e10i	0.292692	+	0.198322i
$649$	1.69499e11			0.955406
$650$	2.84025e10	+	1.63982e10i	0.159112	+	0.0918635i
$651$	−2.64644e11	−	1.59204e11i	−1.47346	−	0.886400i
$652$	7.86411e10	+	1.36210e11i	0.435170	+	0.753737i
$653$	2.27135e10	−	1.31137e10i	0.124920	−	0.0721226i	−0.436238	−	0.899831i	$-0.643689\pi$
$653$	2.27135e10	−	1.31137e10i	0.124920	−	0.0721226i	0.561158	+	0.827709i	$0.310356\pi$
$654$	−2.36076e10	−	4.26422e10i	−0.129045	−	0.233093i
$655$	4.69649e10	−	8.13456e10i	0.255158	−	0.441946i
$656$			3.78221e10i			0.204235i
$657$	−8.82175e10	−	1.66336e11i	−0.473471	−	0.892738i
$658$	1.18735e11			0.633396
$659$	2.34946e11	+	1.35646e11i	1.24574	+	0.719228i	0.970257	−	0.242078i	$-0.0778289\pi$
$659$	2.34946e11	+	1.35646e11i	1.24574	+	0.719228i	0.275483	+	0.961306i	$0.411162\pi$
$660$	−3.81909e9	+	2.12382e11i	−0.0201272	+	1.11929i
$661$	−1.12700e11	−	1.95203e11i	−0.590364	−	1.02254i	−0.994183	−	0.107702i	$-0.965651\pi$
$661$	−1.12700e11	−	1.95203e11i	−0.590364	−	1.02254i	0.403819	−	0.914839i	$-0.367682\pi$
$662$	−1.05450e11	+	6.08815e10i	−0.549052	+	0.316995i
$663$	−3.35112e10	−	6.02605e8i	−0.173435	−	0.00311873i
$664$	3.96106e10	−	6.86076e10i	0.203769	−	0.352939i
$665$			2.25775e11i			1.15449i
$666$	4.33893e9	−	1.20606e11i	0.0220539	−	0.613018i
$667$	−3.05502e11			−1.54352
$668$	9.48597e10	+	5.47673e10i	0.476405	+	0.275052i
$669$	−2.40859e10	+	1.33345e10i	−0.120243	+	0.0665688i
$670$	1.48790e11	+	2.57712e11i	0.738370	+	1.27890i
$671$	5.40907e10	−	3.12293e10i	0.266829	−	0.154054i
$672$	−2.07955e10	+	3.45682e10i	−0.101974	+	0.169512i
$673$	−7.58538e10	+	1.31383e11i	−0.369757	+	0.640439i	−0.989527	−	0.144345i	$-0.953893\pi$
$673$	−7.58538e10	+	1.31383e11i	−0.369757	+	0.640439i	0.619770	+	0.784784i	$0.287226\pi$
$674$			1.46925e11i			0.711962i
$675$	−1.33094e11	−	8.67320e10i	−0.641128	−	0.417796i
$676$	9.23761e10			0.442357
$677$	−2.20192e11	−	1.27128e11i	−1.04821	−	0.605183i	−0.126061	−	0.992023i	$-0.540233\pi$
$677$	−2.20192e11	−	1.27128e11i	−1.04821	−	0.605183i	−0.922147	+	0.386839i	$0.873567\pi$
$678$	−1.03704e11	−	6.23858e10i	−0.490766	−	0.295234i
$679$	−1.38194e11	−	2.39359e11i	−0.650145	−	1.12608i
$680$	−4.44367e10	+	2.56555e10i	−0.207829	+	0.119990i
$681$	3.56183e10	+	6.43370e10i	0.165609	+	0.299138i
$682$	1.98059e11	−	3.43049e11i	0.915499	−	1.58569i
$683$			2.98251e11i			1.37056i	0.728279	+	0.685281i	$0.240321\pi$
$683$			2.98251e11i			1.37056i	−0.728279	+	0.685281i	$0.759679\pi$
$684$	−4.51104e10	+	7.20227e10i	−0.206088	+	0.329037i
$685$	1.14144e11			0.518429
$686$	−1.13478e11	−	6.55166e10i	−0.512408	−	0.295839i
$687$	5.59131e7	−	3.10936e9i	0.000251008	−	0.0139587i
$688$	1.33201e10	+	2.30712e10i	0.0594505	+	0.102971i
$689$	5.84886e10	−	3.37684e10i	0.259534	−	0.149842i
$690$	3.48780e11	+	6.27182e9i	1.53870	+	0.0276693i
$691$	1.50423e11	−	2.60541e11i	0.659785	−	1.14278i	−0.320886	−	0.947118i	$-0.603981\pi$
$691$	1.50423e11	−	2.60541e11i	0.659785	−	1.14278i	0.980671	−	0.195663i	$-0.0626860\pi$
$692$		−	5.86053e10i		−	0.255572i
$693$	3.68598e11	+	2.30866e11i	1.59816	+	1.00098i
$694$	−2.76005e10			−0.118981
$695$	1.39634e11	+	8.06177e10i	0.598483	+	0.345534i
$696$	−6.83929e10	+	3.78637e10i	−0.291457	+	0.161356i
$697$	4.92504e10	+	8.53041e10i	0.208679	+	0.361442i
$698$	−2.13579e11	+	1.23310e11i	−0.899782	+	0.519489i
$699$	1.41810e11	−	2.35729e11i	0.594014	−	0.987426i
$700$	5.14018e10	−	8.90305e10i	0.214085	−	0.370806i
$701$			2.33302e11i			0.966156i	0.875577	+	0.483078i	$0.160481\pi$
$701$			2.33302e11i			0.966156i	−0.875577	+	0.483078i	$0.839519\pi$
$702$	5.82223e10	+	3.14360e9i	0.239740	+	0.0129443i
$703$	1.64525e11			0.673613
$704$	−4.48096e10	−	2.58708e10i	−0.182423	−	0.105322i
$705$	−2.25129e11	−	1.35433e11i	−0.911327	−	0.548235i
$706$	−8.02255e10	−	1.38955e11i	−0.322919	−	0.559312i
$707$	−2.17992e11	+	1.25858e11i	−0.872494	+	0.503735i
$708$	−3.44992e10	−	6.23157e10i	−0.137302	−	0.248007i
$709$	−1.36103e11	+	2.35737e11i	−0.538620	+	0.932918i	0.460358	+	0.887733i	$0.347721\pi$
$709$	−1.36103e11	+	2.35737e11i	−0.538620	+	0.932918i	−0.998979	+	0.0451845i	$0.985612\pi$
$710$		−	1.64875e11i		−	0.648816i
$711$	−4.46283e11	−	1.60555e10i	−1.74635	−	0.0628268i
$712$	−1.02090e10			−0.0397250
$713$	−5.63365e11	−	3.25259e11i	−2.17988	−	1.25855i
$714$	−1.88892e9	+	1.05044e11i	−0.00726811	+	0.404184i
$715$	9.93400e10	+	1.72062e11i	0.380102	+	0.658356i
$716$	1.62688e11	−	9.39278e10i	0.619017	−	0.357390i
$717$	2.43187e10	+	4.37303e8i	0.0920162	+	0.00165465i
$718$	−9.18479e10	+	1.59085e11i	−0.345598	+	0.598594i
$719$		−	4.94299e11i		−	1.84958i	−0.380473	−	0.924792i	$-0.624239\pi$
$719$		−	4.94299e11i		−	1.84958i	0.380473	−	0.924792i	$-0.375761\pi$
$720$	7.88588e10	−	4.18234e10i	0.293441	−	0.155629i
$721$	2.51803e11			0.931796
$722$	6.60706e10	+	3.81459e10i	0.243142	+	0.140378i
$723$	3.78818e11	−	2.09721e11i	1.38636	−	0.767520i
$724$	−1.01935e11	−	1.76557e11i	−0.370996	−	0.642585i
$725$	1.72526e11	−	9.96081e10i	0.624458	−	0.360531i
$726$	−1.86298e11	+	3.09683e11i	−0.670598	+	1.11473i
$727$	7.37697e10	−	1.27773e11i	0.264083	−	0.457405i	−0.703240	−	0.710952i	$-0.748264\pi$
$727$	7.37697e10	−	1.27773e11i	0.264083	−	0.457405i	0.967323	+	0.253548i	$0.0815974\pi$
$728$			3.77324e10i			0.134335i
$729$	−2.80788e11	−	3.04098e10i	−0.994186	−	0.107672i
$730$	−2.69603e11			−0.949365
$731$	6.00847e10	+	3.46899e10i	0.210423	+	0.121488i
$732$	−2.24908e10	−	1.35300e10i	−0.0783359	−	0.0471251i
$733$	2.03374e10	+	3.52254e10i	0.0704497	+	0.122022i	0.899098	−	0.437746i	$-0.144223\pi$
$733$	2.03374e10	+	3.52254e10i	0.0704497	+	0.122022i	−0.828649	+	0.559769i	$0.810890\pi$
$734$	−9.25358e10	+	5.34256e10i	−0.318805	+	0.184062i
$735$	−4.73750e10	−	8.55731e10i	−0.162330	−	0.293216i
$736$	−4.24859e10	+	7.35877e10i	−0.144788	+	0.250780i
$737$			7.81495e11i			2.64884i
$738$	−8.02875e10	−	1.51383e11i	−0.270659	−	0.510332i
$739$	−4.39058e11			−1.47212			−0.736062	−	0.676915i	$-0.763317\pi$
$739$	−4.39058e11			−1.47212			−0.736062	+	0.676915i	$0.763317\pi$
$740$	−1.49658e11	−	8.64049e10i	−0.499082	−	0.288145i
$741$	−1.42914e9	+	7.94752e10i	−0.00474025	+	0.263608i
$742$	−1.05850e11	−	1.83338e11i	−0.349202	−	0.604836i
$743$	2.39798e11	−	1.38447e11i	0.786846	−	0.454286i	−0.0520049	−	0.998647i	$-0.516561\pi$
$743$	2.39798e11	−	1.38447e11i	0.786846	−	0.454286i	0.838851	+	0.544361i	$0.183228\pi$
$744$	−1.66433e11	−	2.99283e9i	−0.543186	−	0.00976766i
$745$	−3.21657e11	+	5.57127e11i	−1.04416	+	1.80854i
$746$		−	1.55543e11i		−	0.502220i
$747$	−1.29041e10	+	3.58687e11i	−0.0414425	+	1.15195i
$748$	−1.34752e11			−0.430455
$749$	3.13093e11	+	1.80764e11i	0.994824	+	0.574362i
$750$	6.10514e10	−	3.37993e10i	0.192952	−	0.106822i
$751$	−2.18499e10	−	3.78451e10i	−0.0686893	−	0.118973i	0.829635	−	0.558306i	$-0.188548\pi$
$751$	−2.18499e10	−	3.78451e10i	−0.0686893	−	0.118973i	−0.898325	+	0.439332i	$0.855215\pi$
$752$	5.54225e10	−	3.19982e10i	0.173306	−	0.100059i
$753$	−9.01064e9	+	1.49783e10i	−0.0280269	+	0.0465890i
$754$	−3.65596e10	+	6.33231e10i	−0.113114	+	0.195919i
$755$		−	5.78070e11i		−	1.77907i
$756$	9.85393e9	−	1.82504e11i	0.0301663	−	0.558707i
$757$	−2.44223e11			−0.743708			−0.371854	−	0.928291i	$-0.621278\pi$
$757$	−2.44223e11			−0.743708			−0.371854	+	0.928291i	$0.621278\pi$
$758$	7.93691e10	+	4.58238e10i	0.240422	+	0.138808i
$759$	7.85006e11	+	4.72242e11i	2.36541	+	1.42298i
$760$	6.08447e10	+	1.05386e11i	0.182376	+	0.315885i
$761$	3.60019e11	−	2.07857e11i	1.07346	−	0.619764i	0.144337	−	0.989529i	$-0.453895\pi$
$761$	3.60019e11	−	2.07857e11i	1.07346	−	0.619764i	0.929125	+	0.369765i	$0.120562\pi$
$762$	2.54025e10	+	4.58844e10i	0.0753455	+	0.136096i
$763$	−7.14516e10	+	1.23758e11i	−0.210821	+	0.365153i
$764$		−	2.37804e10i		−	0.0697985i
$765$	1.23398e11	−	1.97016e11i	0.360298	−	0.575248i
$766$	4.26293e11			1.23821
$767$	−5.76964e10	−	3.33110e10i	−0.166712	−	0.0962512i
$768$	−3.90928e8	+	2.17398e10i	−0.00112370	+	0.0624899i
$769$	−5.75903e10	−	9.97493e10i	−0.164681	−	0.285236i	0.771861	−	0.635792i	$-0.219326\pi$
$769$	−5.75903e10	−	9.97493e10i	−0.164681	−	0.285236i	−0.936542	+	0.350555i	$0.885993\pi$
$770$	5.39345e11	−	3.11391e11i	1.53428	−	0.885815i
$771$	−1.21809e11	−	2.19039e9i	−0.344716	−	0.00619874i
$772$	7.49215e10	−	1.29768e11i	0.210929	−	0.365340i
$773$		−	1.78665e11i		−	0.500406i	−0.968193	−	0.250203i	$-0.919503\pi$
$773$		−	1.78665e11i		−	0.500406i	0.968193	−	0.250203i	$-0.0804973\pi$
$774$	−1.02289e11	−	6.40672e10i	−0.285013	−	0.178514i
$775$	4.24199e11			1.17588
$776$	−1.29011e11	−	7.44845e10i	−0.355779	−	0.205409i
$777$	−3.09561e11	+	1.71379e11i	−0.849301	+	0.470190i
$778$	4.86441e10	+	8.42541e10i	0.132774	+	0.229971i
$779$	2.02307e11	−	1.16802e11i	0.549366	−	0.317177i
$780$	4.30387e10	−	7.15429e10i	0.116273	−	0.193281i
$781$	2.16495e11	−	3.74981e11i	0.581894	−	1.00787i
$782$			2.21293e11i			0.591754i
$783$	1.93368e11	−	2.96732e11i	0.514443	−	0.789437i
$784$	2.38256e10			0.0630637
$785$	7.18225e9	+	4.14667e9i	0.0189139	+	0.0109200i
$786$	−8.88258e10	−	5.34357e10i	−0.232728	−	0.140004i
$787$	2.61255e11	+	4.52507e11i	0.681029	+	1.17958i	0.974667	+	0.223660i	$0.0718005\pi$
$787$	2.61255e11	+	4.52507e11i	0.681029	+	1.17958i	−0.293638	+	0.955917i	$0.594866\pi$
$788$	−2.11077e11	+	1.21865e11i	−0.547439	+	0.316064i
$789$	2.20217e11	+	3.97776e11i	0.568254	+	1.02643i
$790$	−3.19727e11	+	5.53783e11i	−0.820862	+	1.42178i
$791$			3.54825e11i			0.906376i
$792$	2.34269e11	+	8.42805e9i	0.595407	+	0.0214203i
$793$	−2.45495e10			−0.0620798
$794$	7.38627e10	+	4.26446e10i	0.185842	+	0.107296i
$795$	−8.42207e9	+	4.68356e11i	−0.0210839	+	1.17249i
$796$	1.01993e11	+	1.76656e11i	0.254048	+	0.440024i
$797$	1.67664e11	−	9.68008e10i	0.415534	−	0.239908i	−0.277631	−	0.960688i	$-0.589549\pi$
$797$	1.67664e11	−	9.68008e10i	0.415534	−	0.239908i	0.693165	+	0.720779i	$0.256216\pi$
$798$	2.49123e11	+	4.47977e9i	0.614331	+	0.0110470i
$799$	8.33335e10	−	1.44338e11i	0.204471	−	0.354155i
$800$		−	5.54096e10i		−	0.135277i
$801$	4.08618e10	−	2.16714e10i	0.0992630	−	0.0526450i
$802$	3.17336e10			0.0767047
$803$	−6.13166e11	−	3.54012e11i	−1.47474	−	0.851443i
$804$	2.87314e11	−	1.59063e11i	0.687595	−	0.380667i
$805$	−5.11376e11	−	8.85729e11i	−1.21775	−	2.10920i
$806$	−1.34836e11	+	7.78478e10i	−0.319497	+	0.184462i
$807$	−2.24156e11	+	3.72614e11i	−0.528515	+	0.878547i
$808$	−6.78354e10	+	1.17494e11i	−0.159151	+	0.275658i
$809$		−	4.05968e11i		−	0.947760i	−0.880590	−	0.473880i	$-0.842853\pi$
$809$		−	4.05968e11i		−	0.947760i	0.880590	−	0.473880i	$-0.157147\pi$
$810$	−2.26852e11	+	3.34798e11i	−0.526991	+	0.777755i
$811$	−3.49637e11			−0.808229			−0.404115	−	0.914708i	$-0.632420\pi$
$811$	−3.49637e11			−0.808229			−0.404115	+	0.914708i	$0.632420\pi$
$812$	1.98492e11	+	1.14600e11i	0.456583	+	0.263608i
$813$	2.32499e11	+	1.39866e11i	0.532180	+	0.320148i
$814$	−2.26914e11	−	3.93027e11i	−0.516849	−	0.895209i
$815$	−8.83654e11	+	5.10178e11i	−2.00287	+	1.15636i
$816$	2.74269e10	+	4.95410e10i	0.0618609	+	0.111739i
$817$	8.22706e10	−	1.42497e11i	0.184653	−	0.319828i
$818$		−	9.77005e10i		−	0.218215i
$819$	−8.00972e10	−	1.51025e11i	−0.178025	−	0.335670i
$820$	−2.45368e11			−0.542703
$821$	−1.48992e11	−	8.60206e10i	−0.327937	−	0.189334i	0.326988	−	0.945029i	$-0.393966\pi$
$821$	−1.48992e11	−	8.60206e10i	−0.327937	−	0.189334i	−0.654925	+	0.755694i	$0.727300\pi$
$822$	2.26481e9	−	1.25947e11i	0.00496071	−	0.275868i
$823$	−1.51520e11	−	2.62440e11i	−0.330271	−	0.572046i	0.652294	−	0.757966i	$-0.273807\pi$
$823$	−1.51520e11	−	2.62440e11i	−0.330271	−	0.572046i	−0.982565	+	0.185920i	$0.940473\pi$
$824$	1.17535e11	−	6.78591e10i	0.254953	−	0.147197i
$825$	−5.97290e11	−	1.07406e10i	−1.28935	−	0.0231852i
$826$	−1.04417e11	+	1.80855e11i	−0.224311	+	0.388517i
$827$		−	7.71110e11i		−	1.64852i	−0.566211	−	0.824260i	$-0.691591\pi$
$827$		−	7.71110e11i		−	1.64852i	0.566211	−	0.824260i	$-0.308409\pi$
$828$	1.38408e10	−	3.84723e11i	0.0294469	−	0.818516i
$829$	1.56682e11			0.331742			0.165871	−	0.986147i	$-0.446956\pi$
$829$	1.56682e11			0.331742			0.165871	+	0.986147i	$0.446956\pi$
$830$	4.45087e11	+	2.56971e11i	0.937847	+	0.541466i
$831$	−5.75271e10	+	3.18482e10i	−0.120634	+	0.0667853i
$832$	1.01686e10	+	1.76125e10i	0.0212211	+	0.0367560i
$833$	5.37364e10	−	3.10247e10i	0.111606	−	0.0644359i
$834$	9.17251e10	−	1.52474e11i	0.189594	−	0.315161i
$835$	−3.55299e11	+	6.15396e11i	−0.730883	+	1.26593i
$836$			3.19577e11i			0.654260i
$837$	6.72505e11	−	3.41320e11i	1.37023	−	0.695441i
$838$	−2.88318e11			−0.584649
$839$	4.22447e11	+	2.43900e11i	0.852559	+	0.492225i	0.861513	−	0.507735i	$-0.169517\pi$
$839$	4.22447e11	+	2.43900e11i	0.852559	+	0.492225i	−0.00895468	+	0.999960i	$0.502850\pi$
$840$	−2.24258e11	−	1.34909e11i	−0.450435	−	0.270972i
$841$	−2.80482e10	−	4.85809e10i	−0.0560688	−	0.0971140i
$842$	−1.41505e9	+	8.16978e8i	−0.00281529	+	0.00162541i
$843$	4.18658e10	+	7.56218e10i	0.0828990	+	0.149740i
$844$	−5.58649e10	+	9.67608e10i	−0.110095	+	0.190691i
$845$			5.99283e11i			1.17545i
$846$	−1.53905e11	+	2.45722e11i	−0.300449	+	0.479693i
$847$	1.05959e12			2.05875
$848$	−9.88166e10	−	5.70518e10i	−0.191094	−	0.110328i
$849$	1.21834e10	−	6.77524e11i	0.0234496	−	1.30405i
$850$	−7.21521e10	−	1.24971e11i	−0.138221	−	0.239405i
$851$	−6.45441e11	+	3.72645e11i	−1.23066	+	0.710522i
$852$	−1.81925e11	−	3.27141e9i	−0.345250	−	0.00620835i
$853$	−5.07020e10	+	8.78185e10i	−0.0957699	+	0.165878i	−0.909930	−	0.414763i	$-0.863865\pi$
$853$	−5.07020e10	+	8.78185e10i	−0.0957699	+	0.165878i	0.814160	+	0.580641i	$0.197198\pi$
$854$			7.69530e10i			0.144675i
$855$	−4.67242e11	−	2.92650e11i	−0.874334	−	0.547627i
$856$	1.94859e11			0.362931
$857$	2.37864e11	+	1.37331e11i	0.440967	+	0.254592i	0.704008	−	0.710192i	$-0.251392\pi$
$857$	2.37864e11	+	1.37331e11i	0.440967	+	0.254592i	−0.263041	+	0.964785i	$0.584725\pi$
$858$	1.91826e11	−	1.06199e11i	0.353964	−	0.195961i
$859$	−2.10607e11	−	3.64783e11i	−0.386813	−	0.669980i	0.605206	−	0.796069i	$-0.293091\pi$
$859$	−2.10607e11	−	3.64783e11i	−0.386813	−	0.669980i	−0.992019	+	0.126089i	$0.959757\pi$
$860$	−1.49673e11	+	8.64135e10i	−0.273620	+	0.157975i
$861$	−2.58982e11	+	4.30504e11i	−0.471255	+	0.783366i
$862$	3.57310e10	−	6.18879e10i	0.0647166	−	0.112092i
$863$		−	8.61056e11i		−	1.55235i	−0.630520	−	0.776173i	$-0.717158\pi$
$863$		−	8.61056e11i		−	1.55235i	0.630520	−	0.776173i	$-0.282842\pi$
$864$	−4.45838e10	−	8.78436e10i	−0.0800058	−	0.157636i
$865$	3.80198e11			0.679117
$866$	3.88235e11	+	2.24148e11i	0.690277	+	0.398532i
$867$	−3.57808e11	−	2.15250e11i	−0.633248	−	0.380948i
$868$	2.44022e11	+	4.22658e11i	0.429882	+	0.744578i
$869$	−1.45433e12	+	8.39656e11i	−2.55025	+	1.47239i
$870$	−2.45638e11	−	4.43694e11i	−0.428764	−	0.774473i
$871$	1.53585e11	−	2.66016e11i	0.266855	−	0.462206i
$872$			7.70227e10i			0.133215i
$873$	6.74482e11	+	2.42651e10i	1.16122	+	0.0417759i
$874$	5.24819e11			0.899423
$875$	−1.77186e11	−	1.02298e11i	−0.302271	−	0.174516i
$876$	−5.34939e9	+	2.97483e11i	−0.00908423	+	0.505180i
$877$	−3.14825e11	−	5.45294e11i	−0.532196	−	0.921790i	−0.999293	−	0.0375845i	$-0.988034\pi$
$877$	−3.14825e11	−	5.45294e11i	−0.532196	−	0.921790i	0.467098	−	0.884206i	$-0.345300\pi$
$878$	3.08514e11	−	1.78121e11i	0.519155	−	0.299734i
$879$	1.09663e11	+	1.97197e9i	0.183697	+	0.00330328i
$880$	1.67835e11	−	2.90699e11i	0.279867	−	0.484744i
$881$			8.26944e11i			1.37269i	0.727276	+	0.686345i	$0.240786\pi$
$881$			8.26944e11i			1.37269i	−0.727276	+	0.686345i	$0.759214\pi$
$882$	−9.53623e10	+	5.05762e10i	−0.157580	+	0.0835741i
$883$	1.00813e12			1.65834			0.829168	−	0.558999i	$-0.188815\pi$
$883$	1.00813e12			1.65834			0.829168	+	0.558999i	$0.188815\pi$
$884$	4.58687e10	+	2.64823e10i	0.0751116	+	0.0433657i
$885$	4.04268e11	−	2.23811e11i	0.659017	−	0.364845i
$886$	−2.52206e11	−	4.36834e11i	−0.409281	−	0.708895i
$887$	8.45160e11	−	4.87954e11i	1.36535	−	0.788286i	0.375022	−	0.927016i	$-0.377635\pi$
$887$	8.45160e11	−	4.87954e11i	1.36535	−	0.788286i	0.990330	+	0.138730i	$0.0443019\pi$
$888$	−9.83097e10	+	1.63420e11i	−0.158105	+	0.262816i
$889$	7.68843e10	−	1.33167e11i	0.123092	−	0.213202i
$890$		−	6.62303e10i		−	0.105559i
$891$	−9.55555e11	+	4.63565e11i	−1.51616	+	0.735529i
$892$	4.35053e10			0.0687199
$893$	−3.42312e11	−	1.97634e11i	−0.538289	−	0.310781i
$894$	6.08358e11	+	3.65975e11i	0.952377	+	0.572929i
$895$	6.09349e11	+	1.05542e12i	0.949673	+	1.64488i
$896$	5.52083e10	−	3.18745e10i	0.0856588	−	0.0494551i
$897$	−1.74403e11	−	3.15023e11i	−0.269392	−	0.486600i
$898$	−1.33246e11	+	2.30789e11i	−0.204903	+	0.354902i
$899$			9.45747e11i			1.44789i
$900$	1.17622e11	+	2.21778e11i	0.179274	+	0.338024i
$901$	−2.97162e11			−0.450914
$902$	−5.58048e11	−	3.22189e11i	−0.843034	−	0.486726i
$903$	−6.36231e9	+	3.53812e11i	−0.00956893	+	0.532134i
$904$	9.56226e10	+	1.65623e11i	0.143181	+	0.247998i
$905$	1.14540e12	−	6.61297e11i	1.70751	−	0.985830i
$906$	−6.37849e11	−	1.14699e10i	−0.946684	−	0.0170234i
$907$	2.98209e11	−	5.16514e11i	0.440648	−	0.763225i	−0.557089	−	0.830453i	$-0.688082\pi$
$907$	2.98209e11	−	5.16514e11i	0.440648	−	0.763225i	0.997738	+	0.0672273i	$0.0214153\pi$
$908$		−	1.16209e11i		−	0.170961i
$909$	2.20990e10	−	6.14271e11i	0.0323681	−	0.899715i
$910$	−2.44786e11			−0.356962
$911$	1.16083e12	+	6.70203e11i	1.68536	+	0.973045i	0.957989	+	0.286804i	$0.0925927\pi$
$911$	1.16083e12	+	6.70203e11i	1.68536	+	0.973045i	0.727374	+	0.686241i	$0.240741\pi$
$912$	1.17491e11	−	6.50457e10i	0.169835	−	0.0940241i
$913$	6.74849e11	+	1.16887e12i	0.971234	+	1.68223i
$914$	4.01829e11	−	2.31996e11i	0.575780	−	0.332427i
$915$	8.77747e10	−	1.45907e11i	0.125223	−	0.208158i
$916$	−2.45718e9	+	4.25596e9i	−0.00349024	+	0.00604527i
$917$			3.03920e11i			0.429816i
$918$	−2.14941e11	−	1.40068e11i	−0.302655	−	0.197227i
$919$	−3.60905e11			−0.505977			−0.252988	−	0.967469i	$-0.581413\pi$
$919$	−3.60905e11			−0.505977			−0.252988	+	0.967469i	$0.581413\pi$
$920$	−4.77394e11	−	2.75624e11i	−0.666386	−	0.384738i
$921$	−2.32258e11	−	1.39721e11i	−0.322799	−	0.194189i
$922$	2.20241e10	+	3.81469e10i	0.0304772	+	0.0527880i
$923$	−1.47387e11	+	8.50941e10i	−0.203073	+	0.117244i
$924$	−3.32891e11	−	6.01298e11i	−0.456682	−	0.824901i
$925$	2.43000e11	−	4.20888e11i	0.331924	−	0.574910i
$926$			6.06262e11i			0.824549i
$927$	−3.26388e11	+	5.21108e11i	−0.441993	+	0.705681i
$928$	1.23535e11			0.166570
$929$	8.27772e10	+	4.77914e10i	0.111134	+	0.0641634i	0.554537	−	0.832159i	$-0.312895\pi$
$929$	8.27772e10	+	4.77914e10i	0.111134	+	0.0641634i	−0.443403	+	0.896323i	$0.646229\pi$
$930$	1.94158e10	−	1.07972e12i	0.0259551	−	1.44338i
$931$	−7.35782e10	−	1.27441e11i	−0.0979378	−	0.169633i
$932$	−3.76479e11	+	2.17360e11i	−0.498973	+	0.288082i
$933$	6.61624e11	+	1.18974e10i	0.873141	+	0.0157010i
$934$	2.56347e11	−	4.44006e11i	0.336854	−	0.583448i
$935$		−	8.74192e11i		−	1.14383i
$936$	−7.80873e10	−	4.89089e10i	−0.101737	−	0.0637213i
$937$	−1.26218e12			−1.63743			−0.818714	−	0.574201i	$-0.805313\pi$
$937$	−1.26218e12			−1.63743			−0.818714	+	0.574201i	$0.805313\pi$
$938$	−8.33855e11	−	4.81426e11i	−1.07716	−	0.621897i
$939$	−9.20213e11	+	5.09449e11i	−1.18366	+	0.655297i
$940$	2.07586e11	+	3.59549e11i	0.265880	+	0.460519i
$941$	−5.84641e11	+	3.37543e11i	−0.745643	+	0.430497i	−0.824118	−	0.566419i	$-0.808328\pi$
$941$	−5.84641e11	+	3.37543e11i	−0.745643	+	0.430497i	0.0784743	+	0.996916i	$0.474995\pi$
$942$	4.71799e9	−	7.84270e9i	0.00599175	−	0.00996006i
$943$	−5.29109e11	+	9.16443e11i	−0.669111	+	1.15893i
$944$			1.12558e11i			0.141739i
$945$	1.18398e12	+	6.39267e10i	1.48462	+	0.0801595i
$946$	−4.53873e11			−0.566722
$947$	4.41361e11	+	2.54820e11i	0.548775	+	0.316835i	0.748628	−	0.662991i	$-0.230713\pi$
$947$	4.41361e11	+	2.54820e11i	0.548775	+	0.316835i	−0.199853	+	0.979826i	$0.564046\pi$
$948$	6.04706e11	+	3.63778e11i	0.748705	+	0.450405i
$949$	1.39145e11	+	2.41007e11i	0.171555	+	0.297142i
$950$	−2.96381e11	+	1.71116e11i	−0.363879	+	0.210085i
$951$	1.03099e11	+	1.86226e11i	0.126047	+	0.227677i
$952$	8.30113e10	−	1.43780e11i	0.101062	−	0.175045i
$953$		−	1.54025e12i		−	1.86732i	−0.358160	−	0.933660i	$-0.616596\pi$
$953$		−	1.54025e12i		−	1.86732i	0.358160	−	0.933660i	$-0.383404\pi$
$954$	5.16623e11	+	1.85860e10i	0.623706	+	0.0224384i
$955$	1.54274e11			0.185472
$956$	−3.32864e10	−	1.92179e10i	−0.0398506	−	0.0230078i
$957$	2.39460e10	−	1.33165e12i	0.0285486	−	1.58760i
$958$	−3.21645e10	−	5.57106e10i	−0.0381869	−	0.0661417i
$959$	−3.19844e11	+	1.84662e11i	−0.378150	+	0.218325i
$960$	−1.41035e11	−	2.53612e9i	−0.166051	−	0.00298596i
$961$	−5.80464e11	+	1.00539e12i	−0.680584	+	1.17881i
$962$			1.78379e11i			0.208277i
$963$	−7.79924e11	+	4.13639e11i	−0.906875	+	0.480969i
$964$	−6.84242e11			−0.792321
$965$	8.41859e11	+	4.86048e11i	0.970801	+	0.560492i
$966$	−9.87470e11	+	5.46684e11i	−1.13401	+	0.627809i
$967$	−4.00962e11	−	6.94486e11i	−0.458561	−	0.794251i	0.540324	−	0.841457i	$-0.318302\pi$
$967$	−4.00962e11	−	6.94486e11i	−0.458561	−	0.794251i	−0.998885	+	0.0472059i	$0.984968\pi$
$968$	4.94589e11	−	2.85551e11i	0.563304	−	0.325224i
$969$	1.80291e11	−	2.99697e11i	0.204493	−	0.339928i
$970$	4.83213e11	−	8.36949e11i	0.545823	−	0.945393i
$971$		−	5.82235e11i		−	0.654970i	−0.944856	−	0.327485i	$-0.893799\pi$
$971$		−	5.82235e11i		−	0.654970i	0.944856	−	0.327485i	$-0.106201\pi$
$972$	3.64919e11	+	2.56954e11i	0.408819	+	0.287866i
$973$	−5.21695e11			−0.582057
$974$	−3.57390e11	−	2.06339e11i	−0.397106	−	0.229269i
$975$	2.01203e11	+	1.21039e11i	0.222647	+	0.133939i
$976$	2.07382e10	+	3.59197e10i	0.0228545	+	0.0395852i
$977$	1.00625e12	−	5.80962e11i	1.10441	−	0.637631i	0.167033	−	0.985951i	$-0.446581\pi$
$977$	1.00625e12	−	5.80962e11i	1.10441	−	0.637631i	0.937375	+	0.348321i	$0.113248\pi$
$978$	5.45403e11	+	9.85157e11i	0.596159	+	1.07684i
$979$	8.69660e10	−	1.50630e11i	0.0946714	−	0.163976i
$980$			1.54567e11i			0.167576i
$981$	−1.63501e11	−	3.08284e11i	−0.176541	−	0.332871i
$982$	6.62876e11			0.712830
$983$	−1.19414e12	−	6.89439e11i	−1.27892	−	0.738383i	−0.302268	−	0.953223i	$-0.597744\pi$
$983$	−1.19414e12	−	6.89439e11i	−1.27892	−	0.738383i	−0.976649	+	0.214840i	$0.931077\pi$
$984$	−4.86853e9	+	2.70742e11i	−0.00519299	+	0.288785i
$985$	−7.90592e11	−	1.36935e12i	−0.839861	−	1.45468i
$986$	2.78621e11	−	1.60862e11i	0.294786	−	0.170195i
$987$	8.49941e11	+	1.52838e10i	0.895613	+	0.0161051i
$988$	6.28054e10	−	1.08782e11i	0.0659127	−	0.114164i
$989$			7.45364e11i			0.779082i
$990$	−5.46763e10	+	1.51980e12i	−0.0569192	+	1.58214i
$991$	−8.57390e11			−0.888963			−0.444482	−	0.895788i	$-0.646612\pi$
$991$	−8.57390e11			−0.888963			−0.444482	+	0.895788i	$0.646612\pi$
$992$	2.27806e11	+	1.31524e11i	0.235244	+	0.135818i
$993$	−7.62678e11	+	4.22234e11i	−0.784412	+	0.434266i
$994$	2.66736e11	+	4.62000e11i	0.273235	+	0.473256i
$995$	−1.14604e12	+	6.61669e11i	−1.16925	+	0.675070i
$996$	2.92376e11	−	4.86015e11i	0.297101	−	0.493869i
$997$	7.94454e11	−	1.37603e12i	0.804060	−	1.39267i	−0.112865	−	0.993610i	$-0.536003\pi$
$997$	7.94454e11	−	1.37603e12i	0.804060	−	1.39267i	0.916924	−	0.399062i	$-0.130664\pi$
$998$		−	7.20514e11i		−	0.726307i
$999$	4.65841e10	−	8.62778e11i	0.0467709	−	0.866238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.9.d.a.11.1	yes	16
3.2	odd	2		54.9.d.a.35.8		16
4.3	odd	2		144.9.q.b.65.8		16
9.2	odd	6		162.9.b.c.161.7		16
9.4	even	3		54.9.d.a.17.8		16
9.5	odd	6	inner	18.9.d.a.5.1	✓	16
9.7	even	3		162.9.b.c.161.10		16
12.11	even	2		432.9.q.c.305.7		16
36.23	even	6		144.9.q.b.113.8		16
36.31	odd	6		432.9.q.c.17.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.1	✓	16	9.5	odd	6	inner
18.9.d.a.11.1	yes	16	1.1	even	1	trivial
54.9.d.a.17.8		16	9.4	even	3
54.9.d.a.35.8		16	3.2	odd	2
144.9.q.b.65.8		16	4.3	odd	2
144.9.q.b.113.8		16	36.23	even	6
162.9.b.c.161.7		16	9.2	odd	6
162.9.b.c.161.10		16	9.7	even	3
432.9.q.c.17.7		16	36.31	odd	6
432.9.q.c.305.7		16	12.11	even	2

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

\(f(q)\)	\(=\)	\(q+(-9.79796 - 5.65685i) q^{2} +(-69.4086 - 41.7547i) q^{3} +(64.0000 + 110.851i) q^{4} +(-719.139 + 415.195i) q^{5} +(443.862 + 801.745i) q^{6} +(1343.41 - 2326.85i) q^{7} -1448.15i q^{8} +(3074.10 + 5796.26i) q^{9} +9394.80 q^{10} +(21366.9 + 12336.2i) q^{11} +(186.409 - 10366.3i) q^{12} +(-4848.77 - 8398.31i) q^{13} +(-26325.3 + 15198.9i) q^{14} +(67250.8 + 1209.31i) q^{15} +(-8192.00 + 14189.0i) q^{16} +42669.1i q^{17} +(2668.74 - 74181.3i) q^{18} +101194. q^{19} +(-92049.8 - 53145.0i) q^{20} +(-190401. + 105410. i) q^{21} +(-139568. - 241739. i) q^{22} +(-396990. + 229203. i) q^{23} +(-60467.2 + 100514. i) q^{24} +(149462. - 258875. i) q^{25} +109715. i q^{26} +(28652.4 - 530668. i) q^{27} +343913. q^{28} +(577159. + 333223. i) q^{29} +(-652079. - 392277. i) q^{30} +(709545. + 1.22897e6i) q^{31} +(160530. - 92681.9i) q^{32} +(-967951. - 1.74840e6i) q^{33} +(241373. - 418071. i) q^{34} +2.23111e6i q^{35} +(-445781. + 711728. i) q^{36} +1.62583e6 q^{37} +(-991496. - 572441. i) q^{38} +(-14122.7 + 785373. i) q^{39} +(601267. + 1.04142e6i) q^{40} +(1.99920e6 - 1.15424e6i) q^{41} +(2.46183e6 + 44269.1i) q^{42} +(812997. - 1.40815e6i) q^{43} +3.15806e6i q^{44} +(-4.61728e6 - 2.89197e6i) q^{45} +5.18626e6 q^{46} +(-3.38272e6 - 1.95301e6i) q^{47} +(1.16105e6 - 642781. i) q^{48} +(-727099. - 1.25937e6i) q^{49} +(-2.92884e6 + 1.69097e6i) q^{50} +(1.78164e6 - 2.96160e6i) q^{51} +(620642. - 1.07498e6i) q^{52} +6.96433e6i q^{53} +(-3.28265e6 + 5.03738e6i) q^{54} -2.04877e7 q^{55} +(-3.36964e6 - 1.94547e6i) q^{56} +(-7.02374e6 - 4.22533e6i) q^{57} +(-3.76999e6 - 6.52981e6i) q^{58} +(5.94959e6 - 3.43500e6i) q^{59} +(4.16999e6 + 7.53223e6i) q^{60} +(1.26576e6 - 2.19236e6i) q^{61} -1.60552e7i q^{62} +(1.76168e7 + 633783. i) q^{63} -2.09715e6 q^{64} +(6.97388e6 + 4.02637e6i) q^{65} +(-406511. + 2.26063e7i) q^{66} +(1.58375e7 + 2.74313e7i) q^{67} +(-4.72993e6 + 2.73083e6i) q^{68} +(3.71248e7 + 667585. i) q^{69} +(1.26211e7 - 2.18603e7i) q^{70} -1.75496e7i q^{71} +(8.39388e6 - 4.45177e6i) q^{72} -2.86971e7 q^{73} +(-1.59299e7 - 9.19711e6i) q^{74} +(-2.11832e7 + 1.17274e7i) q^{75} +(6.47643e6 + 1.12175e7i) q^{76} +(5.74089e7 - 3.31451e7i) q^{77} +(4.58112e6 - 7.61517e6i) q^{78} +(-3.40323e7 + 5.89457e7i) q^{79} -1.36051e7i q^{80} +(-2.41466e7 + 3.56365e7i) q^{81} -2.61174e7 q^{82} +(4.73759e7 + 2.73525e7i) q^{83} +(-2.38705e7 - 1.43600e7i) q^{84} +(-1.77160e7 - 3.06851e7i) q^{85} +(-1.59314e7 + 9.19801e6i) q^{86} +(-2.61462e7 - 4.72276e7i) q^{87} +(1.78647e7 - 3.09425e7i) q^{88} -7.04968e6i q^{89} +(2.88805e7 + 5.44547e7i) q^{90} -2.60555e7 q^{91} +(-5.08148e7 - 2.93379e7i) q^{92} +(2.06665e6 - 1.14928e8i) q^{93} +(2.20958e7 + 3.82711e7i) q^{94} +(-7.27727e7 + 4.20153e7i) q^{95} +(-1.50120e7 - 269949. i) q^{96} +(5.14341e7 - 8.90865e7i) q^{97} +1.64524e7i q^{98} +(-5.81985e6 + 1.61771e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 126 q^{3} + 1024 q^{4} - 882 q^{5} + 384 q^{6} - 1846 q^{7} - 28662 q^{9} + 45756 q^{11} + 5376 q^{12} - 3370 q^{13} - 94464 q^{14} + 128754 q^{15} - 131072 q^{16} - 236544 q^{18} + 362180 q^{19}+ \cdots + 366888330 q^{99}+O(q^{100}) \) 16 * q + 126 * q^3 + 1024 * q^4 - 882 * q^5 + 384 * q^6 - 1846 * q^7 - 28662 * q^9 + 45756 * q^11 + 5376 * q^12 - 3370 * q^13 - 94464 * q^14 + 128754 * q^15 - 131072 * q^16 - 236544 * q^18 + 362180 * q^19 - 112896 * q^20 - 299166 * q^21 - 61824 * q^22 + 1311138 * q^23 - 147456 * q^24 + 963394 * q^25 - 208656 * q^27 - 472576 * q^28 - 2851290 * q^29 - 1253376 * q^30 + 542438 * q^31 + 3875796 * q^33 + 220416 * q^34 - 3655680 * q^36 + 3343328 * q^37 - 1314432 * q^38 - 5896002 * q^39 + 9218592 * q^41 + 14237952 * q^42 + 339512 * q^43 - 32740578 * q^45 + 7417344 * q^46 - 34980606 * q^47 - 1376256 * q^48 - 2364654 * q^49 + 27744768 * q^50 + 50877810 * q^51 + 431360 * q^52 - 5648256 * q^54 - 4584276 * q^55 - 12091392 * q^56 - 34049898 * q^57 - 7852800 * q^58 + 93924216 * q^59 + 18604800 * q^60 - 841954 * q^61 - 14043234 * q^63 - 33554432 * q^64 - 126568134 * q^65 - 35179776 * q^66 + 29946644 * q^67 - 5476608 * q^68 + 70499610 * q^69 - 34359552 * q^70 - 11894784 * q^72 - 7547764 * q^73 + 35124480 * q^74 + 114494910 * q^75 + 23179520 * q^76 + 9309294 * q^77 + 23014656 * q^78 + 33813002 * q^79 - 46018134 * q^81 - 137346048 * q^82 + 114200226 * q^83 - 15040512 * q^84 - 125696772 * q^85 - 171379584 * q^86 - 159599970 * q^87 + 7913472 * q^88 + 129745152 * q^90 + 268578316 * q^91 + 167825664 * q^92 + 120711534 * q^93 - 11832576 * q^94 - 143949240 * q^95 - 25165824 * q^96 - 89415484 * q^97 + 366888330 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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