LMFDB - Embedded newform 12.9.d.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,9,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	12.d (of order $2$, degree $1$, 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:	$4.88854332073$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 40x^{6} - 395x^{5} + 403x^{4} + 8998x^{3} + 74584x^{2} + 217224x + 269328 $ x^8 - 3x^7 - 40x^6 - 395x^5 + 403x^4 + 8998x^3 + 74584x^2 + 217224*x + 269328
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.2
Root			$-1.97054 + 1.25304i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.9.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-15.8645 + 2.07809i) q^{2} -46.7654i q^{3} +(247.363 - 65.9356i) q^{4} -374.901 q^{5} +(97.1827 + 741.908i) q^{6} +4472.52i q^{7} +(-3787.26 + 1560.08i) q^{8} -2187.00 q^{9} +(5947.61 - 779.079i) q^{10} +12939.6i q^{11} +(-3083.50 - 11568.0i) q^{12} +17549.0 q^{13} +(-9294.30 - 70954.2i) q^{14} +17532.4i q^{15} +(56841.0 - 32620.1i) q^{16} -99303.3 q^{17} +(34695.6 - 4544.78i) q^{18} +115642. i q^{19} +(-92736.8 + 24719.4i) q^{20} +209159. q^{21} +(-26889.7 - 205281. i) q^{22} +10924.8i q^{23} +(72957.6 + 177113. i) q^{24} -250074. q^{25} +(-278405. + 36468.4i) q^{26} +102276. i q^{27} +(294898. + 1.10634e6i) q^{28} +31214.2 q^{29} +(-36433.9 - 278142. i) q^{30} -1.20904e6i q^{31} +(-833965. + 635621. i) q^{32} +605127. q^{33} +(1.57539e6 - 206361. i) q^{34} -1.67675e6i q^{35} +(-540983. + 144201. i) q^{36} -1.24040e6 q^{37} +(-240314. - 1.83459e6i) q^{38} -820684. i q^{39} +(1.41985e6 - 584875. i) q^{40} +2.96280e6 q^{41} +(-3.31820e6 + 434651. i) q^{42} +2.69350e6i q^{43} +(853183. + 3.20079e6i) q^{44} +819909. q^{45} +(-22702.7 - 173316. i) q^{46} +8.92341e6i q^{47} +(-1.52549e6 - 2.65819e6i) q^{48} -1.42386e7 q^{49} +(3.96729e6 - 519676. i) q^{50} +4.64396e6i q^{51} +(4.34097e6 - 1.15710e6i) q^{52} +1.11107e7 q^{53} +(-212539. - 1.62255e6i) q^{54} -4.85109e6i q^{55} +(-6.97747e6 - 1.69386e7i) q^{56} +5.40802e6 q^{57} +(-495196. + 64865.9i) q^{58} -6.19748e6i q^{59} +(1.15601e6 + 4.33687e6i) q^{60} -2.13656e6 q^{61} +(2.51249e6 + 1.91807e7i) q^{62} -9.78140e6i q^{63} +(1.19095e7 - 1.18169e7i) q^{64} -6.57914e6 q^{65} +(-9.60002e6 + 1.25751e6i) q^{66} +2.55543e6i q^{67} +(-2.45640e7 + 6.54763e6i) q^{68} +510901. q^{69} +(3.48445e6 + 2.66008e7i) q^{70} -2.55352e7i q^{71} +(8.28275e6 - 3.41189e6i) q^{72} +3.32867e7 q^{73} +(1.96783e7 - 2.57766e6i) q^{74} +1.16948e7i q^{75} +(7.62490e6 + 2.86055e7i) q^{76} -5.78728e7 q^{77} +(1.70546e6 + 1.30197e7i) q^{78} -2.18934e7i q^{79} +(-2.13098e7 + 1.22293e7i) q^{80} +4.78297e6 q^{81} +(-4.70033e7 + 6.15697e6i) q^{82} +3.75220e7i q^{83} +(5.17382e7 - 1.37910e7i) q^{84} +3.72290e7 q^{85} +(-5.59733e6 - 4.27309e7i) q^{86} -1.45974e6i q^{87} +(-2.01868e7 - 4.90058e7i) q^{88} +3.61031e7 q^{89} +(-1.30074e7 + 1.70385e6i) q^{90} +7.84881e7i q^{91} +(720332. + 2.70238e6i) q^{92} -5.65411e7 q^{93} +(-1.85437e7 - 1.41565e8i) q^{94} -4.33542e7i q^{95} +(2.97251e7 + 3.90007e7i) q^{96} -1.26353e7 q^{97} +(2.25888e8 - 2.95892e7i) q^{98} -2.82990e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9} + 36628 q^{10} - 11340 q^{12} - 2864 q^{13} + 52728 q^{14} + 99440 q^{16} - 193200 q^{17} - 13122 q^{18} + 335592 q^{20} + 121824 q^{21}+ \cdots + 691081830 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 - 52 * q^4 - 336 * q^5 + 1134 * q^6 - 12960 * q^8 - 17496 * q^9 + 36628 * q^10 - 11340 * q^12 - 2864 * q^13 + 52728 * q^14 + 99440 * q^16 - 193200 * q^17 - 13122 * q^18 + 335592 * q^20 + 121824 * q^21 - 556968 * q^22 + 221616 * q^24 - 579048 * q^25 + 21564 * q^26 - 594672 * q^28 + 2063472 * q^29 + 46980 * q^30 - 3602784 * q^32 - 920160 * q^33 + 1568476 * q^34 + 113724 * q^36 + 7470352 * q^37 + 3659400 * q^38 + 1749184 * q^40 - 8865456 * q^41 - 5288328 * q^42 + 2395920 * q^44 + 734832 * q^45 - 13649856 * q^46 + 10916208 * q^48 - 18923896 * q^49 + 14581842 * q^50 + 18592888 * q^52 + 8706672 * q^53 - 2480058 * q^54 - 45565632 * q^56 - 2325024 * q^57 - 8816444 * q^58 + 28348056 * q^60 + 13457296 * q^61 + 80783976 * q^62 + 1268864 * q^64 + 7293408 * q^65 - 51205608 * q^66 - 117288264 * q^68 - 8636544 * q^69 - 60373104 * q^70 + 28343520 * q^72 + 94738960 * q^73 + 119548428 * q^74 + 144621360 * q^76 - 56971392 * q^77 - 140630580 * q^78 - 163857888 * q^80 + 38263752 * q^81 - 188383460 * q^82 + 199712304 * q^84 - 201200416 * q^85 + 240327384 * q^86 + 156323520 * q^88 + 188992272 * q^89 - 80105436 * q^90 - 387657984 * q^92 - 54802656 * q^93 - 38749872 * q^94 + 246092256 * q^96 - 123291632 * q^97 + 691081830 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	−15.8645	+	2.07809i	−0.991530	+	0.129881i
$2$	−15.8645	+	2.07809i	−0.991530	+	0.129881i
$3$		−	46.7654i		−	0.577350i
$3$		−	46.7654i		−	0.577350i
$4$	247.363	−	65.9356i	0.966262	−	0.257561i
$5$	−374.901			−0.599842			−0.299921	−	0.953964i	$-0.596960\pi$
$5$	−374.901			−0.599842			−0.299921	+	0.953964i	$0.596960\pi$
$6$	97.1827	+	741.908i	0.0749866	+	0.572460i
$7$			4472.52i			1.86277i	0.364031	+	0.931387i	$0.381400\pi$
$7$			4472.52i			1.86277i	−0.364031	+	0.931387i	$0.618600\pi$
$8$	−3787.26	+	1560.08i	−0.924625	+	0.380878i
$9$	−2187.00			−0.333333
$10$	5947.61	−	779.079i	0.594761	−	0.0779079i
$11$			12939.6i			0.883795i	0.897066	+	0.441897i	$0.145694\pi$
$11$			12939.6i			0.883795i	−0.897066	+	0.441897i	$0.854306\pi$
$12$	−3083.50	−	11568.0i	−0.148703	−	0.557872i
$13$	17549.0			0.614438			0.307219	−	0.951639i	$-0.400602\pi$
$13$	17549.0			0.614438			0.307219	+	0.951639i	$0.400602\pi$
$14$	−9294.30	−	70954.2i	−0.241938	−	1.84700i
$15$			17532.4i			0.346319i
$16$	56841.0	−	32620.1i	0.867325	−	0.497743i
$17$	−99303.3			−1.18896			−0.594481	−	0.804110i	$-0.702643\pi$
$17$	−99303.3			−1.18896			−0.594481	+	0.804110i	$0.702643\pi$
$18$	34695.6	−	4544.78i	0.330510	−	0.0432936i
$19$			115642.i			0.887359i	0.896185	+	0.443680i	$0.146327\pi$
$19$			115642.i			0.887359i	−0.896185	+	0.443680i	$0.853673\pi$
$20$	−92736.8	+	24719.4i	−0.579605	+	0.154496i
$21$	209159.			1.07547
$22$	−26889.7	−	205281.i	−0.114788	−	0.876309i
$23$			10924.8i			0.0390392i	0.999809	+	0.0195196i	$0.00621368\pi$
$23$			10924.8i			0.0390392i	−0.999809	+	0.0195196i	$0.993786\pi$
$24$	72957.6	+	177113.i	0.219900	+	0.533833i
$25$	−250074.			−0.640189
$26$	−278405.	+	36468.4i	−0.609234	+	0.0798037i
$27$			102276.i			0.192450i
$28$	294898.	+	1.10634e6i	0.479778	+	1.79993i
$29$	31214.2			0.0441326			0.0220663	−	0.999757i	$-0.492976\pi$
$29$	31214.2			0.0441326			0.0220663	+	0.999757i	$0.492976\pi$
$30$	−36433.9	−	278142.i	−0.0449802	−	0.343386i
$31$		−	1.20904e6i		−	1.30916i	−0.755993	−	0.654580i	$-0.772845\pi$
$31$		−	1.20904e6i		−	1.30916i	0.755993	−	0.654580i	$-0.227155\pi$
$32$	−833965.	+	635621.i	−0.795331	+	0.606176i
$33$	605127.			0.510259
$34$	1.57539e6	−	206361.i	1.17889	−	0.154423i
$35$		−	1.67675e6i		−	1.11737i
$36$	−540983.	+	144201.i	−0.322087	+	0.0858537i
$37$	−1.24040e6			−0.661842			−0.330921	−	0.943659i	$-0.607359\pi$
$37$	−1.24040e6			−0.661842			−0.330921	+	0.943659i	$0.607359\pi$
$38$	−240314.	−	1.83459e6i	−0.115251	−	0.879843i
$39$		−	820684.i		−	0.354746i
$40$	1.41985e6	−	584875.i	0.554629	−	0.228467i
$41$	2.96280e6			1.04850			0.524249	−	0.851565i	$-0.324346\pi$
$41$	2.96280e6			1.04850			0.524249	+	0.851565i	$0.324346\pi$
$42$	−3.31820e6	+	434651.i	−1.06636	+	0.139683i
$43$			2.69350e6i			0.787848i	0.919143	+	0.393924i	$0.128883\pi$
$43$			2.69350e6i			0.787848i	−0.919143	+	0.393924i	$0.871117\pi$
$44$	853183.	+	3.20079e6i	0.227631	+	0.853977i
$45$	819909.			0.199947
$46$	−22702.7	−	173316.i	−0.00507044	−	0.0387085i
$47$			8.92341e6i			1.82869i	0.404939	+	0.914344i	$0.367293\pi$
$47$			8.92341e6i			1.82869i	−0.404939	+	0.914344i	$0.632707\pi$
$48$	−1.52549e6	−	2.65819e6i	−0.287372	−	0.500750i
$49$	−1.42386e7			−2.46992
$50$	3.96729e6	−	519676.i	0.634767	−	0.0831482i
$51$			4.64396e6i			0.686448i
$52$	4.34097e6	−	1.15710e6i	0.593708	−	0.158255i
$53$	1.11107e7			1.40811			0.704055	−	0.710146i	$-0.251371\pi$
$53$	1.11107e7			1.40811			0.704055	+	0.710146i	$0.251371\pi$
$54$	−212539.	−	1.62255e6i	−0.0249955	−	0.190820i
$55$		−	4.85109e6i		−	0.530137i
$56$	−6.97747e6	−	1.69386e7i	−0.709490	−	1.72237i
$57$	5.40802e6			0.512317
$58$	−495196.	+	64865.9i	−0.0437588	+	0.00573197i
$59$		−	6.19748e6i		−	0.511454i	−0.966749	−	0.255727i	$-0.917685\pi$
$59$		−	6.19748e6i		−	0.511454i	0.966749	−	0.255727i	$-0.0823149\pi$
$60$	1.15601e6	+	4.33687e6i	0.0891983	+	0.334635i
$61$	−2.13656e6			−0.154310			−0.0771552	−	0.997019i	$-0.524584\pi$
$61$	−2.13656e6			−0.154310			−0.0771552	+	0.997019i	$0.524584\pi$
$62$	2.51249e6	+	1.91807e7i	0.170035	+	1.29807i
$63$		−	9.78140e6i		−	0.620924i
$64$	1.19095e7	−	1.18169e7i	0.709864	−	0.704339i
$65$	−6.57914e6			−0.368566
$66$	−9.60002e6	+	1.25751e6i	−0.505937	+	0.0662728i
$67$			2.55543e6i			0.126813i	0.997988	+	0.0634067i	$0.0201965\pi$
$67$			2.55543e6i			0.126813i	−0.997988	+	0.0634067i	$0.979803\pi$
$68$	−2.45640e7	+	6.54763e6i	−1.14885	+	0.306230i
$69$	510901.			0.0225393
$70$	3.48445e6	+	2.66008e7i	0.145125	+	1.10791i
$71$		−	2.55352e7i		−	1.00486i	−0.864618	−	0.502431i	$-0.832439\pi$
$71$		−	2.55352e7i		−	1.00486i	0.864618	−	0.502431i	$-0.167561\pi$
$72$	8.28275e6	−	3.41189e6i	0.308208	−	0.126959i
$73$	3.32867e7			1.17214			0.586070	−	0.810260i	$-0.300674\pi$
$73$	3.32867e7			1.17214			0.586070	+	0.810260i	$0.300674\pi$
$74$	1.96783e7	−	2.57766e6i	0.656236	−	0.0859604i
$75$			1.16948e7i			0.369613i
$76$	7.62490e6	+	2.86055e7i	0.228549	+	0.857422i
$77$	−5.78728e7			−1.64631
$78$	1.70546e6	+	1.30197e7i	0.0460747	+	0.351741i
$79$		−	2.18934e7i		−	0.562088i	−0.959695	−	0.281044i	$-0.909319\pi$
$79$		−	2.18934e7i		−	0.562088i	0.959695	−	0.281044i	$-0.0906807\pi$
$80$	−2.13098e7	+	1.22293e7i	−0.520258	+	0.298567i
$81$	4.78297e6			0.111111
$82$	−4.70033e7	+	6.15697e6i	−1.03962	+	0.136180i
$83$			3.75220e7i			0.790630i	0.918546	+	0.395315i	$0.129364\pi$
$83$			3.75220e7i			0.790630i	−0.918546	+	0.395315i	$0.870636\pi$
$84$	5.17382e7	−	1.37910e7i	1.03919	−	0.277000i
$85$	3.72290e7			0.713190
$86$	−5.59733e6	−	4.27309e7i	−0.102326	−	0.781175i
$87$		−	1.45974e6i		−	0.0254800i
$88$	−2.01868e7	−	4.90058e7i	−0.336618	−	0.817179i
$89$	3.61031e7			0.575420			0.287710	−	0.957718i	$-0.407106\pi$
$89$	3.61031e7			0.575420			0.287710	+	0.957718i	$0.407106\pi$
$90$	−1.30074e7	+	1.70385e6i	−0.198254	+	0.0259693i
$91$			7.84881e7i			1.14456i
$92$	720332.	+	2.70238e6i	0.0100550	+	0.0377221i
$93$	−5.65411e7			−0.755844
$94$	−1.85437e7	−	1.41565e8i	−0.237511	−	1.81320i
$95$		−	4.33542e7i		−	0.532276i
$96$	2.97251e7	+	3.90007e7i	0.349976	+	0.459184i
$97$	−1.26353e7			−0.142724			−0.0713621	−	0.997450i	$-0.522735\pi$
$97$	−1.26353e7			−0.142724			−0.0713621	+	0.997450i	$0.522735\pi$
$98$	2.25888e8	−	2.95892e7i	2.44900	−	0.320795i
$99$		−	2.82990e7i		−	0.294598i
$100$	−6.18591e7	+	1.64888e7i	−0.618591	+	0.164888i
$101$	6.19037e6			0.0594882			0.0297441	−	0.999558i	$-0.490531\pi$
$101$	6.19037e6			0.0594882			0.0297441	+	0.999558i	$0.490531\pi$
$102$	−9.65056e6	−	7.36739e7i	−0.0891563	−	0.680633i
$103$		−	1.93155e7i		−	0.171616i	−0.996312	−	0.0858079i	$-0.972653\pi$
$103$		−	1.93155e7i		−	0.171616i	0.996312	−	0.0858079i	$-0.0273471\pi$
$104$	−6.64626e7	+	2.73778e7i	−0.568125	+	0.234026i
$105$	−7.84140e7			−0.645114
$106$	−1.76265e8	+	2.30890e7i	−1.39618	+	0.182886i
$107$			2.27863e8i			1.73836i	0.494498	+	0.869179i	$0.335352\pi$
$107$			2.27863e8i			1.73836i	−0.494498	+	0.869179i	$0.664648\pi$
$108$	6.74362e6	+	2.52993e7i	0.0495677	+	0.185957i
$109$	1.49887e8			1.06184			0.530920	−	0.847422i	$-0.321846\pi$
$109$	1.49887e8			1.06184			0.530920	+	0.847422i	$0.321846\pi$
$110$	1.00810e7	+	7.69600e7i	0.0688546	+	0.525647i
$111$			5.80077e7i			0.382114i
$112$	1.45894e8	+	2.54222e8i	0.927182	+	1.61563i
$113$	−9.43384e7			−0.578595			−0.289298	−	0.957239i	$-0.593422\pi$
$113$	−9.43384e7			−0.578595			−0.289298	+	0.957239i	$0.593422\pi$
$114$	−8.57954e7	+	1.12384e7i	−0.507978	+	0.0665401i
$115$		−	4.09571e6i		−	0.0234174i
$116$	7.72123e6	−	2.05813e6i	0.0426437	−	0.0113668i
$117$	−3.83796e7			−0.204813
$118$	1.28789e7	+	9.83197e7i	0.0664280	+	0.507122i
$119$		−	4.44136e8i		−	2.21477i
$120$	−2.73519e7	−	6.63999e7i	−0.131905	−	0.320215i
$121$	4.69246e7			0.218907
$122$	3.38954e7	−	4.43996e6i	0.153003	−	0.0200419i
$123$		−	1.38557e8i		−	0.605350i
$124$	−7.97186e7	−	2.99071e8i	−0.337189	−	1.26499i
$125$	2.40199e8			0.983855
$126$	2.03266e7	+	1.55177e8i	0.0806461	+	0.615665i
$127$		−	2.82897e8i		−	1.08746i	−0.839260	−	0.543731i	$-0.817011\pi$
$127$		−	2.82897e8i		−	1.08746i	0.839260	−	0.543731i	$-0.182989\pi$
$128$	−1.64382e8	+	2.12217e8i	−0.612371	+	0.790571i
$129$	1.25962e8			0.454864
$130$	1.04375e8	−	1.36720e7i	0.365444	−	0.0478696i
$131$			9.98571e7i			0.339073i	0.985524	+	0.169537i	$0.0542271\pi$
$131$			9.98571e7i			0.339073i	−0.985524	+	0.169537i	$0.945773\pi$
$132$	1.49686e8	−	3.98994e7i	0.493044	−	0.131423i
$133$	−5.17209e8			−1.65295
$134$	−5.31042e6	−	4.05406e7i	−0.0164706	−	0.125739i
$135$		−	3.83434e7i		−	0.115440i
$136$	3.76088e8	−	1.54921e8i	1.09934	−	0.452850i
$137$	−1.18390e8			−0.336074			−0.168037	−	0.985781i	$-0.553743\pi$
$137$	−1.18390e8			−0.336074			−0.168037	+	0.985781i	$0.553743\pi$
$138$	−8.10517e6	+	1.06170e6i	−0.0223484	+	0.00292742i
$139$			2.90295e8i			0.777642i	0.921313	+	0.388821i	$0.127118\pi$
$139$			2.90295e8i			0.777642i	−0.921313	+	0.388821i	$0.872882\pi$
$140$	−1.10558e8	−	4.14767e8i	−0.287791	−	1.07967i
$141$	4.17307e8			1.05579
$142$	5.30645e7	+	4.05103e8i	0.130512	+	0.996350i
$143$			2.27077e8i			0.543037i
$144$	−1.24311e8	+	7.13401e7i	−0.289108	+	0.165914i
$145$	−1.17022e7			−0.0264726
$146$	−5.28076e8	+	6.91728e7i	−1.16221	+	0.152238i
$147$			6.65875e8i			1.42601i
$148$	−3.06829e8	+	8.17864e7i	−0.639512	+	0.170465i
$149$	−1.78016e8			−0.361173			−0.180586	−	0.983559i	$-0.557800\pi$
$149$	−1.78016e8			−0.361173			−0.180586	+	0.983559i	$0.557800\pi$
$150$	−2.43029e7	−	1.85532e8i	−0.0480056	−	0.366483i
$151$		−	9.14545e6i		−	0.0175913i	−0.999961	−	0.00879563i	$-0.997200\pi$
$151$		−	9.14545e6i		−	0.0175913i	0.999961	−	0.00879563i	$-0.00279977\pi$
$152$	−1.80410e8	−	4.37965e8i	−0.337976	−	0.820475i
$153$	2.17176e8			0.396321
$154$	9.18121e8	−	1.20265e8i	1.63236	−	0.213824i
$155$			4.53270e8i			0.785290i
$156$	−5.41123e7	−	2.03007e8i	−0.0913688	−	0.342778i
$157$	−2.24414e8			−0.369361			−0.184681	−	0.982799i	$-0.559125\pi$
$157$	−2.24414e8			−0.369361			−0.184681	+	0.982799i	$0.559125\pi$
$158$	4.54964e7	+	3.47327e8i	0.0730044	+	0.557327i
$159$		−	5.19594e8i		−	0.812973i
$160$	3.12655e8	−	2.38295e8i	0.477073	−	0.363610i
$161$	−4.88612e7			−0.0727212
$162$	−7.58793e7	+	9.93944e6i	−0.110170	+	0.0144312i
$163$			7.18722e8i			1.01815i	0.860723	+	0.509074i	$0.170012\pi$
$163$			7.18722e8i			1.01815i	−0.860723	+	0.509074i	$0.829988\pi$
$164$	7.32888e8	−	1.95354e8i	1.01312	−	0.270052i
$165$	−2.26863e8			−0.306075
$166$	−7.79740e7	−	5.95266e8i	−0.102688	−	0.783933i
$167$		−	2.91809e8i		−	0.375174i	−0.982248	−	0.187587i	$-0.939933\pi$
$167$		−	2.91809e8i		−	0.375174i	0.982248	−	0.187587i	$-0.0600667\pi$
$168$	−7.92141e8	+	3.26304e8i	−0.994409	+	0.409624i
$169$	−5.07764e8			−0.622465
$170$	−5.90618e8	+	7.73651e7i	−0.707149	+	0.0926296i
$171$		−	2.52908e8i		−	0.295786i
$172$	1.77597e8	+	6.66271e8i	0.202919	+	0.761268i
$173$	1.20998e9			1.35080			0.675402	−	0.737450i	$-0.263970\pi$
$173$	1.20998e9			1.35080			0.675402	+	0.737450i	$0.263970\pi$
$174$	3.03348e6	+	2.31580e7i	0.00330936	+	0.0252642i
$175$		−	1.11846e9i		−	1.19253i
$176$	4.22092e8	+	7.35502e8i	0.439903	+	0.766537i
$177$	−2.89827e8			−0.295288
$178$	−5.72757e8	+	7.50255e7i	−0.570546	+	0.0747359i
$179$		−	1.45368e9i		−	1.41598i	−0.706223	−	0.707990i	$-0.749602\pi$
$179$		−	1.45368e9i		−	1.41598i	0.706223	−	0.707990i	$-0.250398\pi$
$180$	2.02815e8	−	5.40612e7i	0.193202	−	0.0514987i
$181$	2.11074e8			0.196662			0.0983311	−	0.995154i	$-0.468650\pi$
$181$	2.11074e8			0.196662			0.0983311	+	0.995154i	$0.468650\pi$
$182$	−1.63105e8	−	1.24517e9i	−0.148656	−	1.13486i
$183$			9.99169e7i			0.0890912i
$184$	−1.70435e7	−	4.13750e7i	−0.0148692	−	0.0360966i
$185$	4.65027e8			0.397001
$186$	8.96994e8	−	1.17497e8i	0.749442	−	0.0981696i
$187$		−	1.28495e9i		−	1.05080i
$188$	5.88371e8	+	2.20732e9i	0.470999	+	1.76699i
$189$	−4.57431e8			−0.358491
$190$	9.00939e7	+	6.87791e8i	0.0691323	+	0.527767i
$191$			1.66532e9i			1.25130i	0.780102	+	0.625652i	$0.215167\pi$
$191$			1.66532e9i			1.25130i	−0.780102	+	0.625652i	$0.784833\pi$
$192$	−5.52619e8	−	5.56954e8i	−0.406650	−	0.409840i
$193$	7.57046e8			0.545624			0.272812	−	0.962067i	$-0.412046\pi$
$193$	7.57046e8			0.545624			0.272812	+	0.962067i	$0.412046\pi$
$194$	2.00452e8	−	2.62572e7i	0.141515	−	0.0185371i
$195$			3.07676e8i			0.212792i
$196$	−3.52211e9	+	9.38833e8i	−2.38659	+	0.636156i
$197$	−7.31378e8			−0.485598			−0.242799	−	0.970077i	$-0.578066\pi$
$197$	−7.31378e8			−0.485598			−0.242799	+	0.970077i	$0.578066\pi$
$198$	5.88079e7	+	4.48949e8i	0.0382626	+	0.292103i
$199$			1.02039e9i			0.650663i	0.945600	+	0.325331i	$0.105476\pi$
$199$			1.02039e9i			0.650663i	−0.945600	+	0.325331i	$0.894524\pi$
$200$	9.47096e8	−	3.90135e8i	0.591935	−	0.243834i
$201$	1.19506e8			0.0732157
$202$	−9.82069e7	+	1.28641e7i	−0.0589843	+	0.00772637i
$203$			1.39606e8i			0.0822091i
$204$	3.06202e8	+	1.14874e9i	0.176802	+	0.663288i
$205$	−1.11076e9			−0.628933
$206$	4.01394e7	+	3.06430e8i	0.0222896	+	0.170162i
$207$		−	2.38925e7i		−	0.0130131i
$208$	9.97501e8	−	5.72449e8i	0.532918	−	0.305832i
$209$	−1.49636e9			−0.784244
$210$	1.24400e9	−	1.62951e8i	0.639650	−	0.0837878i
$211$			1.81728e9i			0.916834i	0.888737	+	0.458417i	$0.151583\pi$
$211$			1.81728e9i			0.916834i	−0.888737	+	0.458417i	$0.848417\pi$
$212$	2.74837e9	−	7.32589e8i	1.36060	−	0.362674i
$213$	−1.19416e9			−0.580157
$214$	−4.73520e8	−	3.61493e9i	−0.225779	−	1.72363i
$215$		−	1.00980e9i		−	0.472584i
$216$	−1.59558e8	−	3.87346e8i	−0.0733000	−	0.177944i
$217$	5.40744e9			2.43867
$218$	−2.37789e9	+	3.11480e8i	−1.05285	+	0.137913i
$219$		−	1.55667e9i		−	0.676735i
$220$	−3.19860e8	−	1.19998e9i	−0.136543	−	0.512252i
$221$	−1.74267e9			−0.730544
$222$	−1.20545e8	−	9.20261e8i	−0.0496293	−	0.378878i
$223$			2.10749e9i			0.852207i	0.904674	+	0.426104i	$0.140114\pi$
$223$			2.10749e9i			0.852207i	−0.904674	+	0.426104i	$0.859886\pi$
$224$	−2.84283e9	−	3.72992e9i	−1.12917	−	1.48152i
$225$	5.46912e8			0.213396
$226$	1.49663e9	−	1.96044e8i	0.573694	−	0.0751483i
$227$		−	9.20581e7i		−	0.0346704i	−0.999850	−	0.0173352i	$-0.994482\pi$
$227$		−	9.20581e7i		−	0.0346704i	0.999850	−	0.0173352i	$-0.00551824\pi$
$228$	1.33774e9	−	3.56581e8i	0.495033	−	0.131953i
$229$	3.72077e9			1.35298			0.676490	−	0.736452i	$-0.263500\pi$
$229$	3.72077e9			1.35298			0.676490	+	0.736452i	$0.263500\pi$
$230$	8.51126e6	+	6.49763e7i	0.00304146	+	0.0232190i
$231$			2.70644e9i			0.950497i
$232$	−1.18216e8	+	4.86965e7i	−0.0408061	+	0.0168092i
$233$	−4.16272e9			−1.41239			−0.706193	−	0.708020i	$-0.749589\pi$
$233$	−4.16272e9			−1.41239			−0.706193	+	0.708020i	$0.749589\pi$
$234$	6.08872e8	−	7.97563e7i	0.203078	−	0.0266012i
$235$		−	3.34540e9i		−	1.09692i
$236$	−4.08634e8	−	1.53303e9i	−0.131731	−	0.494199i
$237$	−1.02385e9			−0.324522
$238$	9.22955e8	+	7.04598e9i	0.287655	+	2.19601i
$239$			1.41116e9i			0.432499i	0.976338	+	0.216250i	$0.0693825\pi$
$239$			1.41116e9i			0.432499i	−0.976338	+	0.216250i	$0.930618\pi$
$240$	5.71908e8	+	9.96559e8i	0.172378	+	0.300371i
$241$	−5.52118e9			−1.63668			−0.818339	−	0.574736i	$-0.805105\pi$
$241$	−5.52118e9			−1.63668			−0.818339	+	0.574736i	$0.805105\pi$
$242$	−7.44434e8	+	9.75136e7i	−0.217053	+	0.0284318i
$243$		−	2.23677e8i		−	0.0641500i
$244$	−5.28506e8	+	1.40875e8i	−0.149104	+	0.0397444i
$245$	5.33808e9			1.48157
$246$	2.87933e8	+	2.19813e9i	0.0786233	+	0.600223i
$247$			2.02939e9i			0.545228i
$248$	1.88619e9	+	4.57894e9i	0.498631	+	1.21048i
$249$	1.75473e9			0.456470
$250$	−3.81063e9	+	4.99155e8i	−0.975521	+	0.127784i
$251$			6.67446e8i			0.168159i	0.996459	+	0.0840797i	$0.0267950\pi$
$251$			6.67446e8i			0.168159i	−0.996459	+	0.0840797i	$0.973205\pi$
$252$	−6.44943e8	−	2.41956e9i	−0.159926	−	0.599976i
$253$	−1.41363e8			−0.0345026
$254$	5.87886e8	+	4.48802e9i	0.141240	+	1.07825i
$255$		−	1.74103e9i		−	0.411760i
$256$	2.16683e9	−	3.70832e9i	0.504504	−	0.863409i
$257$	−1.30371e9			−0.298846			−0.149423	−	0.988773i	$-0.547742\pi$
$257$	−1.30371e9			−0.298846			−0.149423	+	0.988773i	$0.547742\pi$
$258$	−1.99833e9	+	2.61761e8i	−0.451011	+	0.0590781i
$259$		−	5.54770e9i		−	1.23286i
$260$	−1.62744e9	+	4.33799e8i	−0.356131	+	0.0949283i
$261$	−6.82654e7			−0.0147109
$262$	−2.07512e8	−	1.58418e9i	−0.0440391	−	0.336201i
$263$		−	5.57666e9i		−	1.16560i	−0.812614	−	0.582802i	$-0.801956\pi$
$263$		−	5.57666e9i		−	1.16560i	0.812614	−	0.582802i	$-0.198044\pi$
$264$	−2.29178e9	+	9.44045e8i	−0.471798	+	0.194347i
$265$	−4.16540e9			−0.844644
$266$	8.20525e9	−	1.07481e9i	1.63895	−	0.214686i
$267$		−	1.68838e9i		−	0.332219i
$268$	1.68494e8	+	6.32119e8i	0.0326622	+	0.122535i
$269$	7.68316e9			1.46734			0.733670	−	0.679506i	$-0.237806\pi$
$269$	7.68316e9			1.46734			0.733670	+	0.679506i	$0.237806\pi$
$270$	7.96810e7	+	6.08297e8i	0.0149934	+	0.114462i
$271$			3.30747e9i			0.613224i	0.951835	+	0.306612i	$0.0991954\pi$
$271$			3.30747e9i			0.613224i	−0.951835	+	0.306612i	$0.900805\pi$
$272$	−5.64450e9	+	3.23928e9i	−1.03122	+	0.591798i
$273$	3.67053e9			0.660812
$274$	1.87820e9	−	2.46026e8i	0.333227	−	0.0436495i
$275$		−	3.23587e9i		−	0.565796i
$276$	1.26378e8	−	3.36866e7i	0.0217789	−	0.00580524i
$277$	−6.82083e9			−1.15856			−0.579280	−	0.815129i	$-0.696666\pi$
$277$	−6.82083e9			−1.15856			−0.579280	+	0.815129i	$0.696666\pi$
$278$	−6.03258e8	−	4.60537e9i	−0.101001	−	0.771055i
$279$			2.64416e9i			0.436387i
$280$	2.61586e9	+	6.35031e9i	0.425582	+	1.03315i
$281$	4.59488e9			0.736969			0.368484	−	0.929634i	$-0.379877\pi$
$281$	4.59488e9			0.736969			0.368484	+	0.929634i	$0.379877\pi$
$282$	−6.62035e9	+	8.67201e8i	−1.04685	+	0.137127i
$283$		−	6.87759e9i		−	1.07224i	−0.844143	−	0.536118i	$-0.819890\pi$
$283$		−	6.87759e9i		−	1.07224i	0.844143	−	0.536118i	$-0.180110\pi$
$284$	−1.68368e9	−	6.31647e9i	−0.258813	−	0.970959i
$285$	−2.02747e9			−0.307310
$286$	−4.71887e8	−	3.60246e9i	−0.0705301	−	0.538438i
$287$			1.32512e10i			1.95311i
$288$	1.82388e9	−	1.39010e9i	0.265110	−	0.202059i
$289$	2.88539e9			0.413631
$290$	1.85650e8	−	2.43183e7i	0.0262484	−	0.00343828i
$291$			5.90893e8i			0.0824018i
$292$	8.23390e9	−	2.19478e9i	1.13259	−	0.301898i
$293$	−3.84587e9			−0.521825			−0.260912	−	0.965363i	$-0.584023\pi$
$293$	−3.84587e9			−0.521825			−0.260912	+	0.965363i	$0.584023\pi$
$294$	−1.38375e9	−	1.05638e10i	−0.185211	−	1.41393i
$295$			2.32344e9i			0.306792i
$296$	4.69772e9	−	1.93512e9i	0.611955	−	0.252081i
$297$	−1.32341e9			−0.170086
$298$	2.82414e9	−	3.69934e8i	0.358114	−	0.0469094i
$299$			1.91718e8i			0.0239872i
$300$	7.71104e8	+	2.89286e9i	0.0951980	+	0.357143i
$301$	−1.20467e10			−1.46758
$302$	1.90051e7	+	1.45088e8i	0.00228477	+	0.0174423i
$303$		−	2.89495e8i		−	0.0343455i
$304$	3.77224e9	+	6.57318e9i	0.441677	+	0.769629i
$305$	8.00999e8			0.0925619
$306$	−3.44539e9	+	4.51312e8i	−0.392964	+	0.0514744i
$307$			1.59131e10i			1.79144i	0.444621	+	0.895719i	$0.353338\pi$
$307$			1.59131e10i			1.79144i	−0.444621	+	0.895719i	$0.646662\pi$
$308$	−1.43156e10	+	3.81588e9i	−1.59077	+	0.424025i
$309$	−9.03297e8			−0.0990824
$310$	−9.41936e8	−	7.19089e9i	−0.101994	−	0.778638i
$311$			4.82439e9i			0.515704i	0.966184	+	0.257852i	$0.0830147\pi$
$311$			4.82439e9i			0.515704i	−0.966184	+	0.257852i	$0.916985\pi$
$312$	1.28033e9	+	3.10815e9i	0.135115	+	0.328007i
$313$	9.94627e9			1.03629			0.518147	−	0.855292i	$-0.326622\pi$
$313$	9.94627e9			1.03629			0.518147	+	0.855292i	$0.326622\pi$
$314$	3.56021e9	−	4.66353e8i	0.366233	−	0.0479729i
$315$			3.66706e9i			0.372457i
$316$	−1.44355e9	−	5.41561e9i	−0.144772	−	0.543124i
$317$	1.13655e10			1.12552			0.562760	−	0.826621i	$-0.309740\pi$
$317$	1.13655e10			1.12552			0.562760	+	0.826621i	$0.309740\pi$
$318$	1.07976e9	+	8.24309e9i	0.105589	+	0.806086i
$319$			4.03900e8i			0.0390042i
$320$	−4.46490e9	+	4.43015e9i	−0.425806	+	0.422492i
$321$	1.06561e10			1.00364
$322$	7.75158e8	−	1.01538e8i	0.0721052	−	0.00944508i
$323$		−	1.14836e10i		−	1.05504i
$324$	1.18313e9	−	3.15368e8i	0.107362	−	0.0286179i
$325$	−4.38854e9			−0.393357
$326$	−1.49357e9	−	1.14022e10i	−0.132238	−	1.00952i
$327$		−	7.00954e9i		−	0.613054i
$328$	−1.12209e10	+	4.62220e9i	−0.969467	+	0.399350i
$329$	−3.99101e10			−3.40643
$330$	3.59906e9	−	4.71442e8i	0.303482	−	0.0397532i
$331$		−	3.51927e9i		−	0.293185i	−0.989197	−	0.146592i	$-0.953169\pi$
$331$		−	3.51927e9i		−	0.293185i	0.989197	−	0.146592i	$-0.0468305\pi$
$332$	2.47403e9	+	9.28155e9i	0.203635	+	0.763955i
$333$	2.71275e9			0.220614
$334$	6.06406e8	+	4.62940e9i	0.0487279	+	0.371996i
$335$		−	9.58035e8i		−	0.0760680i
$336$	1.18888e10	−	6.82278e9i	0.932784	−	0.535309i
$337$	1.46645e10			1.13697			0.568484	−	0.822695i	$-0.307530\pi$
$337$	1.46645e10			1.13697			0.568484	+	0.822695i	$0.307530\pi$
$338$	8.05541e9	−	1.05518e9i	0.617193	−	0.0808462i
$339$			4.41177e9i			0.334052i
$340$	9.20907e9	−	2.45471e9i	0.689128	−	0.183690i
$341$	1.56445e10			1.15703
$342$	5.25566e8	+	4.01225e9i	0.0384169	+	0.293281i
$343$		−	3.78993e10i		−	2.73814i
$344$	−4.20206e9	−	1.02010e10i	−0.300074	−	0.728464i
$345$	−1.91537e8			−0.0135200
$346$	−1.91956e10	+	2.51444e9i	−1.33936	+	0.175443i
$347$		−	1.68810e10i		−	1.16434i	−0.813066	−	0.582172i	$-0.802203\pi$
$347$		−	1.68810e10i		−	1.16434i	0.813066	−	0.582172i	$-0.197797\pi$
$348$	−9.62490e7	−	3.61086e8i	−0.00656265	−	0.0246203i
$349$	1.01348e10			0.683145			0.341572	−	0.939855i	$-0.389041\pi$
$349$	1.01348e10			0.683145			0.341572	+	0.939855i	$0.389041\pi$
$350$	2.32426e9	+	1.77438e10i	0.154886	+	1.18243i
$351$			1.79484e9i			0.118249i
$352$	−8.22471e9	−	1.07912e10i	−0.535735	−	0.702909i
$353$	1.91125e9			0.123089			0.0615445	−	0.998104i	$-0.480397\pi$
$353$	1.91125e9			0.123089			0.0615445	+	0.998104i	$0.480397\pi$
$354$	4.59796e9	−	6.02287e8i	0.292787	−	0.0383522i
$355$			9.57319e9i			0.602758i
$356$	8.93058e9	−	2.38048e9i	0.556006	−	0.148206i
$357$	−2.07702e10			−1.27870
$358$	3.02088e9	+	2.30619e10i	0.183908	+	1.40399i
$359$		−	8.33129e9i		−	0.501573i	−0.968042	−	0.250787i	$-0.919311\pi$
$359$		−	8.33129e9i		−	0.501573i	0.968042	−	0.250787i	$-0.0806892\pi$
$360$	−3.10521e9	+	1.27912e9i	−0.184876	+	0.0761556i
$361$	3.61059e9			0.212593
$362$	−3.34858e9	+	4.38631e8i	−0.194996	+	0.0255426i
$363$		−	2.19445e9i		−	0.126386i
$364$	5.17516e9	+	1.94151e10i	0.294794	+	1.10594i
$365$	−1.24792e10			−0.703099
$366$	−2.07636e8	−	1.58513e9i	−0.0115712	−	0.0883366i
$367$			2.75727e10i			1.51990i	0.649981	+	0.759950i	$0.274777\pi$
$367$			2.75727e10i			1.51990i	−0.649981	+	0.759950i	$0.725223\pi$
$368$	3.56367e8	+	6.20975e8i	0.0194315	+	0.0338597i
$369$	−6.47965e9			−0.349499
$370$	−7.37741e9	+	9.66368e8i	−0.393638	+	0.0515627i
$371$			4.96927e10i			2.62299i
$372$	−1.39862e10	+	3.72807e9i	−0.730344	+	0.194676i
$373$	1.13007e10			0.583809			0.291905	−	0.956447i	$-0.405711\pi$
$373$	1.13007e10			0.583809			0.291905	+	0.956447i	$0.405711\pi$
$374$	2.67024e9	+	2.03850e10i	0.136478	+	1.04190i
$375$		−	1.12330e10i		−	0.568029i
$376$	−1.39212e10	−	3.37953e10i	−0.696507	−	1.69085i
$377$	5.47777e8			0.0271168
$378$	7.25690e9	−	9.50583e8i	0.355454	−	0.0465610i
$379$			2.00812e10i			0.973267i	0.873606	+	0.486634i	$0.161775\pi$
$379$			2.00812e10i			0.973267i	−0.873606	+	0.486634i	$0.838225\pi$
$380$	−2.85859e9	−	1.07242e10i	−0.137093	−	0.514318i
$381$	−1.32298e10			−0.627846
$382$	−3.46068e9	−	2.64194e10i	−0.162520	−	1.24071i
$383$		−	2.28867e10i		−	1.06363i	−0.846862	−	0.531813i	$-0.821511\pi$
$383$		−	2.28867e10i		−	1.06363i	0.846862	−	0.531813i	$-0.178489\pi$
$384$	9.92442e9	+	7.68739e9i	0.456436	+	0.353552i
$385$	2.16966e10			0.987526
$386$	−1.20101e10	+	1.57321e9i	−0.541002	+	0.0708660i
$387$		−	5.89067e9i		−	0.262616i
$388$	−3.12550e9	+	8.33114e8i	−0.137909	+	0.0367602i
$389$	3.25250e10			1.42043			0.710214	−	0.703986i	$-0.248598\pi$
$389$	3.25250e10			1.42043			0.710214	+	0.703986i	$0.248598\pi$
$390$	−6.39378e8	−	4.88111e9i	−0.0276375	−	0.210989i
$391$		−	1.08487e9i		−	0.0464161i
$392$	5.39254e10	−	2.22134e10i	2.28375	−	0.940741i
$393$	4.66985e9			0.195764
$394$	1.16029e10	−	1.51987e9i	0.481485	−	0.0630698i
$395$			8.20786e9i			0.337164i
$396$	−1.86591e9	−	7.00013e9i	−0.0758770	−	0.284659i
$397$	−3.95474e10			−1.59205			−0.796024	−	0.605264i	$-0.793067\pi$
$397$	−3.95474e10			−1.59205			−0.796024	+	0.605264i	$0.793067\pi$
$398$	−2.12047e9	−	1.61880e10i	−0.0845085	−	0.645151i
$399$			2.41875e10i			0.954331i
$400$	−1.42144e10	+	8.15743e9i	−0.555252	+	0.318650i
$401$	−4.03775e10			−1.56157			−0.780786	−	0.624798i	$-0.785181\pi$
$401$	−4.03775e10			−1.56157			−0.780786	+	0.624798i	$0.785181\pi$
$402$	−1.89590e9	+	2.48344e8i	−0.0725956	+	0.00950931i
$403$		−	2.12174e10i		−	0.804398i
$404$	1.53127e9	−	4.08166e8i	0.0574812	−	0.0153218i
$405$	−1.79314e9			−0.0666491
$406$	−2.90114e8	−	2.21477e9i	−0.0106774	−	0.0815127i
$407$		−	1.60503e10i		−	0.584932i
$408$	−7.24493e9	−	1.75879e10i	−0.261453	−	0.634707i
$409$	−2.14604e9			−0.0766912			−0.0383456	−	0.999265i	$-0.512209\pi$
$409$	−2.14604e9			−0.0766912			−0.0383456	+	0.999265i	$0.512209\pi$
$410$	1.76216e10	−	2.30826e9i	0.623606	−	0.0816862i
$411$			5.53657e9i			0.194032i
$412$	−1.27358e9	−	4.77794e9i	−0.0442015	−	0.165826i
$413$	2.77183e10			0.952723
$414$	4.96507e7	+	3.79041e8i	0.00169015	+	0.0129028i
$415$		−	1.40670e10i		−	0.474253i
$416$	−1.46352e10	+	1.11545e10i	−0.488682	+	0.372458i
$417$	1.35757e10			0.448972
$418$	2.37390e10	−	3.10957e9i	0.777601	−	0.101858i
$419$			5.54260e10i			1.79828i	0.437662	+	0.899140i	$0.355807\pi$
$419$			5.54260e10i			1.79828i	−0.437662	+	0.899140i	$0.644193\pi$
$420$	−1.93967e10	+	5.17028e9i	−0.623349	+	0.166156i
$421$	7.84742e9			0.249803			0.124902	−	0.992169i	$-0.460138\pi$
$421$	7.84742e9			0.249803			0.124902	+	0.992169i	$0.460138\pi$
$422$	−3.77646e9	−	2.88301e10i	−0.119079	−	0.909068i
$423$		−	1.95155e10i		−	0.609562i
$424$	−4.20790e10	+	1.73335e10i	−1.30197	+	0.536318i
$425$	2.48332e10			0.761161
$426$	1.89448e10	−	2.48158e9i	0.575243	−	0.0753512i
$427$		−	9.55580e9i		−	0.287445i
$428$	1.50243e10	+	5.63649e10i	0.447733	+	1.67971i
$429$	1.06194e10			0.313523
$430$	2.09845e9	+	1.60199e10i	0.0613796	+	0.468582i
$431$		−	2.02028e10i		−	0.585468i	−0.956194	−	0.292734i	$-0.905435\pi$
$431$		−	2.02028e10i		−	0.585468i	0.956194	−	0.292734i	$-0.0945651\pi$
$432$	3.33625e9	+	5.81346e9i	0.0957907	+	0.166917i
$433$	−4.24666e10			−1.20808			−0.604040	−	0.796954i	$-0.706443\pi$
$433$	−4.24666e10			−1.20808			−0.604040	+	0.796954i	$0.706443\pi$
$434$	−8.57862e10	+	1.12372e10i	−2.41801	+	0.316736i
$435$			5.47259e8i			0.0152840i
$436$	3.70766e10	−	9.88292e9i	1.02602	−	0.273489i
$437$	−1.26336e9			−0.0346418
$438$	3.23489e9	+	2.46957e10i	0.0878948	+	0.671003i
$439$			3.13705e9i			0.0844624i	0.999108	+	0.0422312i	$0.0134466\pi$
$439$			3.13705e9i			0.0844624i	−0.999108	+	0.0422312i	$0.986553\pi$
$440$	7.56807e9	+	1.83724e10i	0.201918	+	0.490178i
$441$	3.11399e10			0.823308
$442$	2.76466e10	−	3.62143e9i	0.724356	−	0.0948836i
$443$		−	7.34157e10i		−	1.90623i	−0.302616	−	0.953113i	$-0.597860\pi$
$443$		−	7.34157e10i		−	1.90623i	0.302616	−	0.953113i	$-0.402140\pi$
$444$	3.82477e9	+	1.43490e10i	0.0984178	+	0.369223i
$445$	−1.35351e10			−0.345161
$446$	−4.37955e9	−	3.34342e10i	−0.110685	−	0.844989i
$447$			8.32501e9i			0.208523i
$448$	5.28511e10	+	5.32656e10i	1.31202	+	1.32232i
$449$	−6.05149e10			−1.48894			−0.744469	−	0.667657i	$-0.767297\pi$
$449$	−6.05149e10			−1.48894			−0.744469	+	0.667657i	$0.767297\pi$
$450$	−8.67647e9	+	1.13653e9i	−0.211589	+	0.0277161i
$451$			3.83376e10i			0.926656i
$452$	−2.33358e10	+	6.22026e9i	−0.559075	+	0.149024i
$453$	−4.27690e8			−0.0101563
$454$	1.91305e8	+	1.46045e9i	0.00450301	+	0.0343767i
$455$		−	2.94253e10i		−	0.686555i
$456$	−2.04816e10	+	8.43693e9i	−0.473701	+	0.195130i
$457$	2.60402e10			0.597008			0.298504	−	0.954408i	$-0.403512\pi$
$457$	2.60402e10			0.597008			0.298504	+	0.954408i	$0.403512\pi$
$458$	−5.90281e10	+	7.73210e9i	−1.34152	+	0.175726i
$459$		−	1.01563e10i		−	0.228816i
$460$	−2.70053e8	−	1.01313e9i	−0.00603140	−	0.0226273i
$461$	4.25451e10			0.941990			0.470995	−	0.882136i	$-0.343895\pi$
$461$	4.25451e10			0.941990			0.470995	+	0.882136i	$0.343895\pi$
$462$	−5.62423e9	−	4.29363e10i	−0.123451	−	0.942446i
$463$		−	2.22263e10i		−	0.483663i	−0.970318	−	0.241832i	$-0.922252\pi$
$463$		−	2.22263e10i		−	0.483663i	0.970318	−	0.241832i	$-0.0777481\pi$
$464$	1.77424e9	−	1.01821e9i	0.0382773	−	0.0219667i
$465$	2.11973e10			0.453387
$466$	6.60393e10	−	8.65050e9i	1.40042	−	0.183442i
$467$			6.05685e10i			1.27344i	0.771094	+	0.636721i	$0.219710\pi$
$467$			6.05685e10i			1.27344i	−0.771094	+	0.636721i	$0.780290\pi$
$468$	−9.49370e9	+	2.53058e9i	−0.197903	+	0.0527518i
$469$	−1.14292e10			−0.236225
$470$	6.95204e9	+	5.30730e10i	0.142469	+	1.08763i
$471$			1.04948e10i			0.213251i
$472$	9.66854e9	+	2.34715e10i	0.194802	+	0.472903i
$473$	−3.48529e10			−0.696296
$474$	1.62429e10	−	2.12766e9i	0.321773	−	0.0421491i
$475$		−	2.89189e10i		−	0.568078i
$476$	−2.92844e10	−	1.09863e11i	−0.570438	−	2.14005i
$477$	−2.42990e10			−0.469370
$478$	−2.93252e9	−	2.23873e10i	−0.0561733	−	0.428836i
$479$			4.26641e10i			0.810439i	0.914219	+	0.405219i	$0.132805\pi$
$479$			4.26641e10i			0.810439i	−0.914219	+	0.405219i	$0.867195\pi$
$480$	−1.11440e10	−	1.46214e10i	−0.209930	−	0.275438i
$481$	−2.17677e10			−0.406661
$482$	8.75905e10	−	1.14735e10i	1.62282	−	0.212573i
$483$			2.28501e9i			0.0419856i
$484$	1.16074e10	−	3.09400e9i	0.211521	−	0.0563819i
$485$	4.73698e9			0.0856120
$486$	4.64822e8	+	3.54852e9i	0.00833185	+	0.0636067i
$487$		−	6.59829e10i		−	1.17305i	−0.809932	−	0.586523i	$-0.800496\pi$
$487$		−	6.59829e10i		−	1.17305i	0.809932	−	0.586523i	$-0.199504\pi$
$488$	8.09171e9	−	3.33320e9i	0.142679	−	0.0587735i
$489$	3.36113e10			0.587828
$490$	−8.46858e10	+	1.10930e10i	−1.46902	+	0.192427i
$491$		−	4.15778e10i		−	0.715379i	−0.933841	−	0.357689i	$-0.883565\pi$
$491$		−	4.15778e10i		−	0.715379i	0.933841	−	0.357689i	$-0.116435\pi$
$492$	−9.13581e9	−	3.42738e10i	−0.155915	−	0.584927i
$493$	−3.09967e9			−0.0524720
$494$	−4.21726e9	−	3.21952e10i	−0.0708145	−	0.540609i
$495$			1.06093e10i			0.176712i
$496$	−3.94389e10	−	6.87229e10i	−0.651625	−	1.13547i
$497$	1.14207e11			1.87183
$498$	−2.78378e10	+	3.64648e9i	−0.452604	+	0.0592867i
$499$			7.89968e10i			1.27411i	0.770818	+	0.637056i	$0.219848\pi$
$499$			7.89968e10i			1.27411i	−0.770818	+	0.637056i	$0.780152\pi$
$500$	5.94163e10	−	1.58377e10i	0.950662	−	0.253403i
$501$	−1.36466e10			−0.216607
$502$	−1.38701e9	−	1.05887e10i	−0.0218407	−	0.166735i
$503$			4.75631e10i			0.743017i	0.928430	+	0.371508i	$0.121159\pi$
$503$			4.75631e10i			0.743017i	−0.928430	+	0.371508i	$0.878841\pi$
$504$	1.52597e10	+	3.70447e10i	0.236497	+	0.574122i
$505$	−2.32078e9			−0.0356835
$506$	2.24264e9	−	2.93764e8i	0.0342104	−	0.00448123i
$507$			2.37458e10i			0.359381i
$508$	−1.86530e10	−	6.99783e10i	−0.280088	−	1.05077i
$509$	−5.08975e10			−0.758272			−0.379136	−	0.925341i	$-0.623779\pi$
$509$	−5.08975e10			−0.758272			−0.379136	+	0.925341i	$0.623779\pi$
$510$	3.61801e9	+	2.76205e10i	0.0534797	+	0.408273i
$511$			1.48875e11i			2.18343i
$512$	−2.66694e10	+	6.33333e10i	−0.388090	+	0.921621i
$513$	−1.18273e10			−0.170772
$514$	2.06826e10	−	2.70922e9i	0.296315	−	0.0388143i
$515$			7.24141e9i			0.102942i
$516$	3.11584e10	−	8.30540e9i	0.439518	−	0.117155i
$517$	−1.15466e11			−1.61618
$518$	1.15286e10	+	8.80114e10i	0.160125	+	1.22242i
$519$		−	5.65850e10i		−	0.779887i
$520$	2.49169e10	−	1.02640e10i	0.340785	−	0.140379i
$521$	−1.88555e10			−0.255910			−0.127955	−	0.991780i	$-0.540841\pi$
$521$	−1.88555e10			−0.255910			−0.127955	+	0.991780i	$0.540841\pi$
$522$	1.08299e9	−	1.41862e8i	0.0145863	−	0.00191066i
$523$		−	2.61334e10i		−	0.349293i	−0.984631	−	0.174646i	$-0.944122\pi$
$523$		−	2.61334e10i		−	0.349293i	0.984631	−	0.174646i	$-0.0558782\pi$
$524$	6.58414e9	+	2.47010e10i	0.0873321	+	0.327634i
$525$	−5.23052e10			−0.688506
$526$	1.15888e10	+	8.84708e10i	0.151390	+	1.15573i
$527$			1.20061e11i			1.55654i
$528$	3.43960e10	−	1.97393e10i	0.442560	−	0.253978i
$529$	7.81916e10			0.998476
$530$	6.60819e10	−	8.65609e9i	0.837489	−	0.109703i
$531$			1.35539e10i			0.170485i
$532$	−1.27938e11	+	3.41025e10i	−1.59718	+	0.425735i
$533$	5.19941e10			0.644237
$534$	3.50860e9	+	2.67852e10i	0.0431488	+	0.329405i
$535$		−	8.54262e10i		−	1.04274i
$536$	−3.98667e9	−	9.67810e9i	−0.0483004	−	0.117255i
$537$	−6.79819e10			−0.817516
$538$	−1.21889e11	+	1.59663e10i	−1.45491	+	0.190579i
$539$		−	1.84243e11i		−	2.18291i
$540$	−2.52819e9	−	9.48473e9i	−0.0297328	−	0.111545i
$541$	1.45275e11			1.69591			0.847956	−	0.530067i	$-0.177833\pi$
$541$	1.45275e11			1.69591			0.847956	+	0.530067i	$0.177833\pi$
$542$	−6.87323e9	−	5.24713e10i	−0.0796460	−	0.608030i
$543$		−	9.87096e9i		−	0.113543i
$544$	8.28155e10	−	6.31193e10i	0.945618	−	0.720720i
$545$	−5.61930e10			−0.636937
$546$	−5.82310e10	+	7.62769e9i	−0.655214	+	0.0858267i
$547$		−	1.46238e11i		−	1.63347i	−0.577015	−	0.816734i	$-0.695782\pi$
$547$		−	1.46238e11i		−	1.63347i	0.577015	−	0.816734i	$-0.304218\pi$
$548$	−2.92854e10	+	7.80615e9i	−0.324735	+	0.0865595i
$549$	4.67265e9			0.0514368
$550$	6.72442e9	+	5.13353e10i	0.0734860	+	0.561003i
$551$			3.60965e9i			0.0391615i
$552$	−1.93492e9	+	7.97045e8i	−0.0208404	+	0.00858472i
$553$	9.79185e10			1.04704
$554$	1.08209e11	−	1.41743e10i	1.14875	−	0.150474i
$555$		−	2.17472e10i		−	0.229208i
$556$	1.91408e10	+	7.18081e10i	0.200290	+	0.751406i
$557$	7.17684e10			0.745611			0.372806	−	0.927909i	$-0.378396\pi$
$557$	7.17684e10			0.745611			0.372806	+	0.927909i	$0.378396\pi$
$558$	−5.49481e9	−	4.19483e10i	−0.0566782	−	0.432690i
$559$			4.72681e10i			0.484084i
$560$	−5.46958e10	−	9.53083e10i	−0.556163	−	0.969123i
$561$	−6.00911e10			−0.606679
$562$	−7.28954e10	+	9.54858e9i	−0.730726	+	0.0957180i
$563$		−	1.13670e11i		−	1.13139i	−0.824614	−	0.565696i	$-0.808608\pi$
$563$		−	1.13670e11i		−	1.13139i	0.824614	−	0.565696i	$-0.191392\pi$
$564$	1.03226e11	−	2.75154e10i	1.02017	−	0.271931i
$565$	3.53676e10			0.347066
$566$	1.42923e10	+	1.09109e11i	0.139263	+	1.06315i
$567$			2.13919e10i			0.206975i
$568$	3.98369e10	+	9.67086e10i	0.382730	+	0.929120i
$569$	−1.57868e11			−1.50607			−0.753034	−	0.657982i	$-0.771410\pi$
$569$	−1.57868e11			−1.50607			−0.753034	+	0.657982i	$0.771410\pi$
$570$	3.21648e10	−	4.21328e9i	0.304706	−	0.0399136i
$571$		−	7.63897e10i		−	0.718606i	−0.933221	−	0.359303i	$-0.883015\pi$
$571$		−	7.63897e10i		−	0.718606i	0.933221	−	0.359303i	$-0.116985\pi$
$572$	1.49725e10	+	5.61706e10i	0.139865	+	0.524716i
$573$	7.78791e10			0.722441
$574$	−2.75372e10	−	2.10223e11i	−0.253672	−	1.93657i
$575$		−	2.73200e9i		−	0.0249925i
$576$	−2.60462e10	+	2.58435e10i	−0.236621	+	0.234780i
$577$	2.03064e10			0.183202			0.0916010	−	0.995796i	$-0.470802\pi$
$577$	2.03064e10			0.183202			0.0916010	+	0.995796i	$0.470802\pi$
$578$	−4.57752e10	+	5.99611e9i	−0.410128	+	0.0537227i
$579$		−	3.54036e10i		−	0.315016i
$580$	−2.89470e9	+	7.71594e8i	−0.0255795	+	0.00681831i
$581$	−1.67818e11			−1.47276
$582$	−1.22793e9	−	9.37421e9i	−0.0107024	−	0.0817039i
$583$			1.43768e11i			1.24448i
$584$	−1.26066e11	+	5.19298e10i	−1.08379	+	0.446443i
$585$	1.43886e10			0.122855
$586$	6.10128e10	−	7.99207e9i	0.517405	−	0.0677749i
$587$			1.14252e11i			0.962306i	0.876637	+	0.481153i	$0.159782\pi$
$587$			1.14252e11i			0.962306i	−0.876637	+	0.481153i	$0.840218\pi$
$588$	4.39049e10	+	1.64713e11i	0.367285	+	1.37790i
$589$	1.39815e11			1.16170
$590$	−4.82832e9	−	3.68602e10i	−0.0398463	−	0.304193i
$591$			3.42032e10i			0.280360i
$592$	−7.05054e10	+	4.04619e10i	−0.574032	+	0.329427i
$593$	−3.24685e10			−0.262569			−0.131285	−	0.991345i	$-0.541910\pi$
$593$	−3.24685e10			−0.262569			−0.131285	+	0.991345i	$0.541910\pi$
$594$	2.09952e10	−	2.75017e9i	0.168646	−	0.0220909i
$595$			1.66507e11i			1.32851i
$596$	−4.40347e10	+	1.17376e10i	−0.348988	+	0.0930241i
$597$	4.77191e10			0.375660
$598$	−3.98408e8	−	3.04151e9i	−0.00311547	−	0.0237840i
$599$		−	1.02381e11i		−	0.795267i	−0.917544	−	0.397633i	$-0.869832\pi$
$599$		−	1.02381e11i		−	0.795267i	0.917544	−	0.397633i	$-0.130168\pi$
$600$	−1.82448e10	−	4.42913e10i	−0.140778	−	0.341754i
$601$	−1.86440e11			−1.42903			−0.714516	−	0.699619i	$-0.753353\pi$
$601$	−1.86440e11			−1.42903			−0.714516	+	0.699619i	$0.753353\pi$
$602$	1.91115e11	−	2.50342e10i	1.45515	−	0.190611i
$603$		−	5.58873e9i		−	0.0422711i
$604$	−6.03011e8	−	2.26225e9i	−0.00453083	−	0.0169978i
$605$	−1.75921e10			−0.131310
$606$	6.01596e8	+	4.59268e9i	0.00446082	+	0.0340546i
$607$			1.44933e11i			1.06761i	0.845608	+	0.533805i	$0.179238\pi$
$607$			1.44933e11i			1.06761i	−0.845608	+	0.533805i	$0.820762\pi$
$608$	−7.35042e10	−	9.64410e10i	−0.537896	−	0.705744i
$609$	6.52872e9			0.0474634
$610$	−1.27074e10	+	1.66455e9i	−0.0917779	+	0.0120220i
$611$			1.56597e11i			1.12362i
$612$	5.37214e10	−	1.43197e10i	0.382950	−	0.102077i
$613$	−1.17256e11			−0.830413			−0.415206	−	0.909727i	$-0.636291\pi$
$613$	−1.17256e11			−0.830413			−0.415206	+	0.909727i	$0.636291\pi$
$614$	−3.30689e10	−	2.52453e11i	−0.232673	−	1.77626i
$615$			5.19450e10i			0.363115i
$616$	2.19180e11	−	9.02860e10i	1.52222	−	0.627043i
$617$	2.27194e11			1.56768			0.783838	−	0.620965i	$-0.213259\pi$
$617$	2.27194e11			1.56768			0.783838	+	0.620965i	$0.213259\pi$
$618$	1.43303e10	−	1.87713e9i	0.0982431	−	0.0128689i
$619$		−	2.58584e11i		−	1.76132i	−0.473747	−	0.880661i	$-0.657099\pi$
$619$		−	2.58584e11i		−	1.76132i	0.473747	−	0.880661i	$-0.342901\pi$
$620$	2.98866e10	+	1.12122e11i	0.202260	+	0.758796i
$621$	−1.11734e9			−0.00751310
$622$	−1.00255e10	−	7.65363e10i	−0.0669800	−	0.511336i
$623$			1.61472e11i			1.07188i
$624$	−2.67708e10	−	4.66485e10i	−0.176572	−	0.307680i
$625$	7.63422e9			0.0500316
$626$	−1.57792e11	+	2.06692e10i	−1.02752	+	0.134595i
$627$			6.99778e10i			0.452783i
$628$	−5.55118e10	+	1.47969e10i	−0.356900	+	0.0951331i
$629$	1.23176e11			0.786905
$630$	−7.62048e9	−	5.81760e10i	−0.0483749	−	0.369302i
$631$		−	1.44941e11i		−	0.914268i	−0.889398	−	0.457134i	$-0.848876\pi$
$631$		−	1.44941e11i		−	0.914268i	0.889398	−	0.457134i	$-0.151124\pi$
$632$	3.41553e10	+	8.29160e10i	0.214087	+	0.519721i
$633$	8.49855e10			0.529335
$634$	−1.80308e11	+	2.36186e10i	−1.11599	+	0.146183i
$635$			1.06059e11i			0.652305i
$636$	−3.42598e10	−	1.28528e11i	−0.209390	−	0.785545i
$637$	−2.49873e11			−1.51762
$638$	−8.39341e8	−	6.40766e9i	−0.00506589	−	0.0386738i
$639$			5.58455e10i			0.334954i
$640$	6.16270e10	−	7.95605e10i	0.367326	−	0.474218i
$641$	9.48881e10			0.562056			0.281028	−	0.959700i	$-0.409325\pi$
$641$	9.48881e10			0.562056			0.281028	+	0.959700i	$0.409325\pi$
$642$	−1.69054e11	+	2.21444e10i	−0.995140	+	0.130354i
$643$			1.08538e11i			0.634949i	0.948267	+	0.317475i	$0.102835\pi$
$643$			1.08538e11i			0.634949i	−0.948267	+	0.317475i	$0.897165\pi$
$644$	−1.20865e10	+	3.22170e9i	−0.0702677	+	0.0187301i
$645$	−4.72234e10			−0.272847
$646$	2.38639e10	+	1.82181e11i	0.137029	+	1.04610i
$647$		−	2.25310e11i		−	1.28577i	−0.765963	−	0.642884i	$-0.777738\pi$
$647$		−	2.25310e11i		−	1.28577i	0.765963	−	0.642884i	$-0.222262\pi$
$648$	−1.81144e10	+	7.46180e9i	−0.102736	+	0.0423198i
$649$	8.01931e10			0.452021
$650$	6.96219e10	−	9.11979e9i	0.390025	−	0.0510895i
$651$		−	2.52881e11i		−	1.40797i
$652$	4.73894e10	+	1.77785e11i	0.262235	+	0.983798i
$653$	−2.14348e11			−1.17887			−0.589436	−	0.807815i	$-0.700650\pi$
$653$	−2.14348e11			−1.17887			−0.589436	+	0.807815i	$0.700650\pi$
$654$	1.45665e10	+	1.11203e11i	0.0796239	+	0.607861i
$655$		−	3.74366e10i		−	0.203390i
$656$	1.68409e11	−	9.66468e10i	0.909387	−	0.521882i
$657$	−7.27980e10			−0.390713
$658$	6.33153e11	−	8.29369e10i	3.37758	−	0.442429i
$659$		−	2.90756e11i		−	1.54165i	−0.637044	−	0.770827i	$-0.719843\pi$
$659$		−	2.90756e11i		−	1.54165i	0.637044	−	0.770827i	$-0.280157\pi$
$660$	−5.61175e10	+	1.49584e10i	−0.295749	+	0.0788330i
$661$	6.50949e10			0.340990			0.170495	−	0.985359i	$-0.445463\pi$
$661$	6.50949e10			0.340990			0.170495	+	0.985359i	$0.445463\pi$
$662$	7.31337e9	+	5.58314e10i	0.0380790	+	0.290701i
$663$			8.14967e10i			0.421780i
$664$	−5.85371e10	−	1.42106e11i	−0.301134	−	0.731036i
$665$	1.93902e11			0.991509
$666$	−4.30364e10	+	5.63734e9i	−0.218745	+	0.0286535i
$667$			3.41007e8i			0.00172290i
$668$	−1.92406e10	−	7.21828e10i	−0.0966302	−	0.362516i
$669$	9.85574e10			0.492022
$670$	1.99088e9	+	1.51987e10i	0.00987976	+	0.0754237i
$671$		−	2.76463e10i		−	0.136379i
$672$	−1.74431e11	+	1.32946e11i	−0.855357	+	0.651925i
$673$	−2.72275e11			−1.32724			−0.663618	−	0.748072i	$-0.730980\pi$
$673$	−2.72275e11			−1.32724			−0.663618	+	0.748072i	$0.730980\pi$
$674$	−2.32645e11	+	3.04742e10i	−1.12734	+	0.147670i
$675$		−	2.55765e10i		−	0.123204i
$676$	−1.25602e11	+	3.34798e10i	−0.601465	+	0.160323i
$677$	1.04438e11			0.497170			0.248585	−	0.968610i	$-0.420034\pi$
$677$	1.04438e11			0.497170			0.248585	+	0.968610i	$0.420034\pi$
$678$	−9.16806e9	−	6.99904e10i	−0.0433869	−	0.331223i
$679$		−	5.65115e10i		−	0.265863i
$680$	−1.40996e11	+	5.80800e10i	−0.659433	+	0.271638i
$681$	−4.30513e9			−0.0200169
$682$	−2.48192e11	+	3.25107e10i	−1.14723	+	0.150276i
$683$			3.01459e11i			1.38531i	0.721271	+	0.692653i	$0.243558\pi$
$683$			3.01459e11i			1.38531i	−0.721271	+	0.692653i	$0.756442\pi$
$684$	−1.66757e10	−	6.25601e10i	−0.0761831	−	0.285807i
$685$	4.43847e10			0.201591
$686$	7.87583e10	+	6.01253e11i	0.355631	+	2.71494i
$687$		−	1.74003e11i		−	0.781143i
$688$	8.78620e10	+	1.53101e11i	0.392146	+	0.683320i
$689$	1.94981e11			0.865197
$690$	3.03864e9	−	3.98032e8i	0.0134055	−	0.00175599i
$691$			5.88076e10i			0.257941i	0.991648	+	0.128971i	$0.0411673\pi$
$691$			5.88076e10i			0.257941i	−0.991648	+	0.128971i	$0.958833\pi$
$692$	2.99303e11	−	7.97805e10i	1.30523	−	0.347915i
$693$	1.26568e11			0.548770
$694$	3.50803e10	+	2.67809e11i	0.151226	+	1.15448i
$695$		−	1.08832e11i		−	0.466462i
$696$	2.27731e9	+	5.52843e9i	0.00970477	+	0.0235594i
$697$	−2.94216e11			−1.24662
$698$	−1.60783e11	+	2.10610e10i	−0.677358	+	0.0887273i
$699$			1.94671e11i			0.815441i
$700$	−7.37464e10	−	2.76666e11i	−0.307149	−	1.15229i
$701$	−1.04963e11			−0.434676			−0.217338	−	0.976096i	$-0.569737\pi$
$701$	−1.04963e11			−0.434676			−0.217338	+	0.976096i	$0.569737\pi$
$702$	−3.72983e9	−	2.84741e10i	−0.0153582	−	0.117247i
$703$		−	1.43442e11i		−	0.587291i
$704$	1.52906e11	+	1.54105e11i	0.622491	+	0.627374i
$705$	−1.56449e11			−0.633309
$706$	−3.03210e10	+	3.97176e9i	−0.122046	+	0.0159869i
$707$			2.76865e10i			0.110813i
$708$	−7.16926e10	+	1.91099e10i	−0.285326	+	0.0760548i
$709$	1.19072e11			0.471219			0.235610	−	0.971848i	$-0.424291\pi$
$709$	1.19072e11			0.471219			0.235610	+	0.971848i	$0.424291\pi$
$710$	−1.98939e10	−	1.51874e11i	−0.0782866	−	0.597653i
$711$			4.78808e10i			0.187363i
$712$	−1.36732e11	+	5.63236e10i	−0.532047	+	0.219165i
$713$	1.32085e10			0.0511086
$714$	3.29508e11	−	4.31623e10i	1.26787	−	0.166078i
$715$		−	8.51316e10i		−	0.325737i
$716$	−9.58494e10	−	3.59587e11i	−0.364701	−	1.36821i
$717$	6.59935e10			0.249703
$718$	1.73132e10	+	1.32171e11i	0.0651447	+	0.497325i
$719$			2.89449e11i			1.08307i	0.840679	+	0.541534i	$0.182156\pi$
$719$			2.89449e11i			1.08307i	−0.840679	+	0.541534i	$0.817844\pi$
$720$	4.66045e10	−	2.67455e10i	0.173419	−	0.0995224i
$721$	8.63889e10			0.319681
$722$	−5.72801e10	+	7.50313e9i	−0.210792	+	0.0276117i
$723$			2.58200e11i			0.944937i
$724$	5.22120e10	−	1.39173e10i	0.190027	−	0.0506525i
$725$	−7.80585e9			−0.0282532
$726$	4.56026e9	+	3.48138e10i	0.0164151	+	0.125315i
$727$		−	5.53322e10i		−	0.198080i	−0.995083	−	0.0990399i	$-0.968423\pi$
$727$		−	5.53322e10i		−	0.198080i	0.995083	−	0.0990399i	$-0.0315771\pi$
$728$	−1.22448e11	−	2.97255e11i	−0.435938	−	1.05829i
$729$	−1.04604e10			−0.0370370
$730$	1.97977e11	−	2.59330e10i	0.697144	−	0.0913190i
$731$		−	2.67473e11i		−	0.936721i
$732$	6.58809e9	+	2.47158e10i	0.0229464	+	0.0860854i
$733$	1.07487e11			0.372339			0.186170	−	0.982518i	$-0.440393\pi$
$733$	1.07487e11			0.372339			0.186170	+	0.982518i	$0.440393\pi$
$734$	−5.72986e10	−	4.37426e11i	−0.197406	−	1.50703i
$735$		−	2.49637e11i		−	0.855382i
$736$	−6.94401e9	−	9.11087e9i	−0.0236646	−	0.0310491i
$737$	−3.30664e10			−0.112077
$738$	1.02796e11	−	1.34653e10i	0.346539	−	0.0453932i
$739$			3.18755e11i			1.06876i	0.845245	+	0.534379i	$0.179455\pi$
$739$			3.18755e11i			1.06876i	−0.845245	+	0.534379i	$0.820545\pi$
$740$	1.15030e11	−	3.06618e10i	0.383607	−	0.102252i
$741$	9.49052e10			0.314787
$742$	−1.03266e11	−	7.88348e11i	−0.340676	−	2.60077i
$743$			1.52531e10i			0.0500497i	0.999687	+	0.0250249i	$0.00796649\pi$
$743$			1.52531e10i			0.0500497i	−0.999687	+	0.0250249i	$0.992034\pi$
$744$	2.14136e11	−	8.82084e10i	0.698873	−	0.287885i
$745$	6.67386e10			0.216647
$746$	−1.79280e11	+	2.34839e10i	−0.578864	+	0.0758255i
$747$		−	8.20605e10i		−	0.263543i
$748$	−8.47239e10	−	3.17849e11i	−0.270645	−	1.01535i
$749$	−1.01912e12			−3.23817
$750$	2.33432e10	+	1.78206e11i	0.0737760	+	0.563217i
$751$		−	8.51300e10i		−	0.267623i	−0.991007	−	0.133811i	$-0.957278\pi$
$751$		−	8.51300e10i		−	0.267623i	0.991007	−	0.133811i	$-0.0427216\pi$
$752$	2.91082e11	+	5.07215e11i	0.910216	+	1.58607i
$753$	3.12133e10			0.0970869
$754$	−8.69019e9	+	1.13833e9i	−0.0268871	+	0.00352194i
$755$			3.42864e9i			0.0105520i
$756$	−1.13151e11	+	3.01610e10i	−0.346396	+	0.0923333i
$757$	4.85502e11			1.47845			0.739226	−	0.673457i	$-0.235191\pi$
$757$	4.85502e11			1.47845			0.739226	+	0.673457i	$0.235191\pi$
$758$	−4.17305e10	−	3.18577e11i	−0.126409	−	0.965024i
$759$			6.61087e9i			0.0199201i
$760$	6.76359e10	+	1.64194e11i	0.202732	+	0.492156i
$761$	3.60091e11			1.07368			0.536839	−	0.843685i	$-0.319618\pi$
$761$	3.60091e11			1.07368			0.536839	+	0.843685i	$0.319618\pi$
$762$	2.09884e11	−	2.74927e10i	0.622528	−	0.0815451i
$763$			6.70374e11i			1.97797i
$764$	1.09804e11	+	4.11938e11i	0.322287	+	1.20909i
$765$	−8.14197e10			−0.237730
$766$	4.75607e10	+	3.63086e11i	0.138144	+	1.05462i
$767$		−	1.08759e11i		−	0.314257i
$768$	−1.73421e11	−	1.01333e11i	−0.498490	−	0.291275i
$769$	2.93454e11			0.839139			0.419570	−	0.907723i	$-0.362181\pi$
$769$	2.93454e11			0.839139			0.419570	+	0.907723i	$0.362181\pi$
$770$	−3.44205e11	+	4.50875e10i	−0.979161	+	0.128261i
$771$			6.09683e10i			0.172539i
$772$	1.87265e11	−	4.99163e10i	0.527215	−	0.140531i
$773$	−3.89598e11			−1.09118			−0.545592	−	0.838051i	$-0.683695\pi$
$773$	−3.89598e11			−1.09118			−0.545592	+	0.838051i	$0.683695\pi$
$774$	1.22414e10	+	9.34525e10i	0.0341087	+	0.260392i
$775$			3.02349e11i			0.838111i
$776$	4.78531e10	−	1.97120e10i	0.131966	−	0.0543605i
$777$	−2.59440e11			−0.711793
$778$	−5.15992e11	+	6.75899e10i	−1.40840	+	0.184486i
$779$			3.42623e11i			0.930394i
$780$	2.02868e10	+	7.61076e10i	0.0548069	+	0.205613i
$781$	3.30416e11			0.888091
$782$	2.25445e9	+	1.72108e10i	0.00602856	+	0.0460230i
$783$			3.19246e9i			0.00849333i
$784$	−8.09337e11	+	4.64465e11i	−2.14223	+	1.22939i
$785$	8.41332e10			0.221559
$786$	−7.40848e10	+	9.70438e9i	−0.194106	+	0.0254260i
$787$		−	1.71711e11i		−	0.447609i	−0.974634	−	0.223805i	$-0.928152\pi$
$787$		−	1.71711e11i		−	0.447609i	0.974634	−	0.223805i	$-0.0718477\pi$
$788$	−1.80916e11	+	4.82239e10i	−0.469215	+	0.125071i
$789$	−2.60795e11			−0.672962
$790$	−1.70567e10	−	1.30213e11i	−0.0437911	−	0.334308i
$791$		−	4.21930e11i		−	1.07779i
$792$	4.41486e10	+	1.07176e11i	0.112206	+	0.272393i
$793$	−3.74944e10			−0.0948143
$794$	6.27399e11	−	8.21832e10i	1.57856	−	0.206776i
$795$			1.94797e11i			0.487655i
$796$	6.72804e10	+	2.52408e11i	0.167585	+	0.628711i
$797$	5.13006e11			1.27142			0.635710	−	0.771928i	$-0.280707\pi$
$797$	5.13006e11			1.27142			0.635710	+	0.771928i	$0.280707\pi$
$798$	−5.02638e10	−	3.83722e11i	−0.123949	−	0.946247i
$799$		−	8.86124e11i		−	2.17424i
$800$	2.08553e11	−	1.58952e11i	0.509162	−	0.388067i
$801$	−7.89575e10			−0.191807
$802$	6.40568e11	−	8.39081e10i	1.54835	−	0.202818i
$803$			4.30718e11i			1.03593i
$804$	2.95613e10	−	7.87968e9i	0.0707456	−	0.0188575i
$805$	1.83181e10			0.0436212
$806$	4.40916e10	+	3.36602e11i	0.104476	+	0.797585i
$807$		−	3.59306e11i		−	0.847170i
$808$	−2.34446e10	+	9.65745e9i	−0.0550043	+	0.0226578i
$809$	−6.85342e11			−1.59997			−0.799987	−	0.600017i	$-0.795161\pi$
$809$	−6.85342e11			−1.59997			−0.799987	+	0.600017i	$0.795161\pi$
$810$	2.84473e10	−	3.72631e9i	0.0660846	−	0.00865643i
$811$		−	4.87378e11i		−	1.12663i	−0.826241	−	0.563317i	$-0.809525\pi$
$811$		−	4.87378e11i		−	1.12663i	0.826241	−	0.563317i	$-0.190475\pi$
$812$	9.20501e9	+	3.45334e10i	0.0211739	+	0.0794355i
$813$	1.54675e11			0.354045
$814$	3.33540e10	+	2.54630e11i	0.0759714	+	0.579978i
$815$		−	2.69450e11i		−	0.610728i
$816$	1.51486e11	+	2.63967e11i	0.341675	+	0.595373i
$817$	−3.11480e11			−0.699104
$818$	3.40459e10	−	4.45967e9i	0.0760416	−	0.00996070i
$819$		−	1.71654e11i		−	0.381520i
$820$	−2.74761e11	+	7.32386e10i	−0.607714	+	0.161989i
$821$	9.57797e10			0.210815			0.105407	−	0.994429i	$-0.466385\pi$
$821$	9.57797e10			0.210815			0.105407	+	0.994429i	$0.466385\pi$
$822$	−1.15055e10	−	8.78348e10i	−0.0252010	−	0.192389i
$823$			6.07905e9i			0.0132506i	0.999978	+	0.00662531i	$0.00210892\pi$
$823$			6.07905e9i			0.0132506i	−0.999978	+	0.00662531i	$0.997891\pi$
$824$	3.01337e10	+	7.31529e10i	0.0653647	+	0.158680i
$825$	−1.51327e11			−0.326662
$826$	−4.39737e11	+	5.76012e10i	−0.944653	+	0.123740i
$827$		−	7.37214e11i		−	1.57605i	−0.615640	−	0.788027i	$-0.711103\pi$
$827$		−	7.37214e11i		−	1.57605i	0.615640	−	0.788027i	$-0.288897\pi$
$828$	−1.57537e9	−	5.91011e9i	−0.00335166	−	0.0125740i
$829$	2.05577e11			0.435269			0.217634	−	0.976030i	$-0.430166\pi$
$829$	2.05577e11			0.435269			0.217634	+	0.976030i	$0.430166\pi$
$830$	2.92326e10	+	2.23166e11i	0.0615963	+	0.470236i
$831$			3.18979e11i			0.668894i
$832$	2.09000e11	−	2.07374e11i	0.436167	−	0.432773i
$833$	1.41394e12			2.93665
$834$	−2.15372e11	+	2.82116e10i	−0.445169	+	0.0583127i
$835$			1.09400e11i			0.225045i
$836$	−3.70144e11	+	9.86635e10i	−0.757785	+	0.201991i
$837$	1.23655e11			0.251948
$838$	−1.15180e11	−	8.79304e11i	−0.233562	−	1.78305i
$839$			3.05355e11i			0.616250i	0.951346	+	0.308125i	$0.0997015\pi$
$839$			3.05355e11i			0.616250i	−0.951346	+	0.308125i	$0.900298\pi$
$840$	2.96975e11	−	1.22332e11i	0.596489	−	0.245710i
$841$	−4.99272e11			−0.998052
$842$	−1.24495e11	+	1.63077e10i	−0.247688	+	0.0324446i
$843$		−	2.14881e11i		−	0.425489i
$844$	1.19823e11	+	4.49527e11i	0.236141	+	0.885902i
$845$	1.90362e11			0.373381
$846$	4.05550e10	+	3.09603e11i	0.0791704	+	0.604399i
$847$			2.09871e11i			0.407774i
$848$	6.31541e11	−	3.62431e11i	1.22129	−	0.700877i
$849$	−3.21633e11			−0.619056
$850$	−3.93965e11	+	5.16056e10i	−0.754714	+	0.0988601i
$851$		−	1.35511e10i		−	0.0258378i
$852$	−2.95392e11	+	7.87379e10i	−0.560584	+	0.149426i
$853$	−6.05342e11			−1.14342			−0.571709	−	0.820457i	$-0.693719\pi$
$853$	−6.05342e11			−1.14342			−0.571709	+	0.820457i	$0.693719\pi$
$854$	1.98578e10	+	1.51598e11i	0.0373336	+	0.285011i
$855$			9.48156e10i			0.177425i
$856$	−3.55484e11	−	8.62978e11i	−0.662102	−	1.60733i
$857$	−4.98335e11			−0.923843			−0.461921	−	0.886921i	$-0.652840\pi$
$857$	−4.98335e11			−0.923843			−0.461921	+	0.886921i	$0.652840\pi$
$858$	−1.68471e11	+	2.20680e10i	−0.310867	+	0.0407206i
$859$			7.49759e11i			1.37705i	0.725214	+	0.688524i	$0.241741\pi$
$859$			7.49759e11i			1.37705i	−0.725214	+	0.688524i	$0.758259\pi$
$860$	−6.65815e10	−	2.49786e11i	−0.121719	−	0.456640i
$861$	6.19697e11			1.12763
$862$	4.19833e10	+	3.20507e11i	0.0760410	+	0.580509i
$863$		−	3.32171e10i		−	0.0598850i	−0.999552	−	0.0299425i	$-0.990468\pi$
$863$		−	3.32171e10i		−	0.0598850i	0.999552	−	0.0299425i	$-0.00953242\pi$
$864$	−6.50087e10	−	8.52945e10i	−0.116659	−	0.153061i
$865$	−4.53622e11			−0.810269
$866$	6.73710e11	−	8.82494e10i	1.19785	−	0.156906i
$867$		−	1.34936e11i		−	0.238810i
$868$	1.33760e12	−	3.56543e11i	2.35639	−	0.628106i
$869$	2.83292e11			0.496770
$870$	−1.13725e9	−	8.68198e9i	−0.00198509	−	0.0151545i
$871$			4.48452e10i			0.0779190i
$872$	−5.67663e11	+	2.33836e11i	−0.981804	+	0.404432i
$873$	2.76333e10			0.0475747
$874$	2.00425e10	−	2.62537e9i	0.0343484	−	0.00449930i
$875$			1.07429e12i			1.83270i
$876$	−1.02640e11	−	3.85062e11i	−0.174301	−	0.653904i
$877$	1.59141e10			0.0269020			0.0134510	−	0.999910i	$-0.495718\pi$
$877$	1.59141e10			0.0269020			0.0134510	+	0.999910i	$0.495718\pi$
$878$	−6.51907e9	−	4.97676e10i	−0.0109700	−	0.0837469i
$879$			1.79854e11i			0.301276i
$880$	−1.58243e11	−	2.75741e11i	−0.263872	−	0.459801i
$881$	1.50297e11			0.249486			0.124743	−	0.992189i	$-0.460189\pi$
$881$	1.50297e11			0.249486			0.124743	+	0.992189i	$0.460189\pi$
$882$	−4.94018e11	+	6.47115e10i	−0.816335	+	0.106932i
$883$		−	8.12117e11i		−	1.33591i	−0.744203	−	0.667953i	$-0.767171\pi$
$883$		−	8.12117e11i		−	1.33591i	0.744203	−	0.667953i	$-0.232829\pi$
$884$	−4.31073e11	+	1.14904e11i	−0.705897	+	0.188160i
$885$	1.08657e11			0.177126
$886$	1.52565e11	+	1.16470e12i	0.247582	+	1.89008i
$887$			8.54543e11i			1.38051i	0.723566	+	0.690255i	$0.242502\pi$
$887$			8.54543e11i			1.38051i	−0.723566	+	0.690255i	$0.757498\pi$
$888$	−9.04964e10	−	2.19690e11i	−0.145539	−	0.353313i
$889$	1.26526e12			2.02569
$890$	2.14727e11	−	2.81272e10i	0.342237	−	0.0448297i
$891$			6.18899e10i			0.0981994i
$892$	1.38958e11	+	5.21314e11i	0.219495	+	0.823456i
$893$	−1.03192e12			−1.62270
$894$	−1.73001e10	−	1.32072e11i	−0.0270831	−	0.206757i
$895$			5.44987e11i			0.849365i
$896$	−9.49146e11	−	7.35202e11i	−1.47265	−	1.14071i
$897$	8.96579e9			0.0138490
$898$	9.60036e11	−	1.25755e11i	1.47633	−	0.193384i
$899$		−	3.77391e10i		−	0.0577767i
$900$	1.35286e11	−	3.60610e10i	0.206197	−	0.0549626i
$901$	−1.10333e12			−1.67419
$902$	−7.96690e10	−	6.08206e11i	−0.120355	−	0.918807i
$903$			5.63369e11i			0.847309i
$904$	3.57285e11	−	1.47175e11i	0.534984	−	0.220374i
$905$	−7.91320e10			−0.117966
$906$	6.78508e9	−	8.88779e8i	0.0100703	−	0.00131911i
$907$			3.08390e11i			0.455692i	0.973697	+	0.227846i	$0.0731683\pi$
$907$			3.08390e11i			0.455692i	−0.973697	+	0.227846i	$0.926832\pi$
$908$	−6.06991e9	−	2.27718e10i	−0.00892974	−	0.0335007i
$909$	−1.35383e10			−0.0198294
$910$	6.11485e10	+	4.66817e11i	0.0891702	+	0.680740i
$911$		−	1.27670e12i		−	1.85360i	−0.375555	−	0.926800i	$-0.622548\pi$
$911$		−	1.27670e12i		−	1.85360i	0.375555	−	0.926800i	$-0.377452\pi$
$912$	3.07397e11	−	1.76410e11i	0.444345	−	0.255002i
$913$	−4.85521e11			−0.698754
$914$	−4.13115e11	+	5.41140e10i	−0.591951	+	0.0775398i
$915$		−	3.74590e10i		−	0.0534407i
$916$	9.20382e11	−	2.45332e11i	1.30733	−	0.348475i
$917$	−4.46613e11			−0.631617
$918$	2.11058e10	+	1.61125e11i	0.0297188	+	0.226878i
$919$			9.02035e11i			1.26462i	0.774714	+	0.632312i	$0.217894\pi$
$919$			9.02035e11i			1.26462i	−0.774714	+	0.632312i	$0.782106\pi$
$920$	6.38962e9	+	1.55115e10i	0.00891916	+	0.0216523i
$921$	7.44183e11			1.03429
$922$	−6.74956e11	+	8.84127e10i	−0.934011	+	0.122346i
$923$		−	4.48117e11i		−	0.617425i
$924$	1.78451e11	+	6.69474e11i	0.244811	+	0.918429i
$925$	3.10191e11			0.423704
$926$	4.61882e10	+	3.52608e11i	0.0628185	+	0.479566i
$927$			4.22430e10i			0.0572052i
$928$	−2.60315e10	+	1.98404e10i	−0.0351000	+	0.0267521i
$929$	4.51064e11			0.605585			0.302793	−	0.953056i	$-0.402081\pi$
$929$	4.51064e11			0.605585			0.302793	+	0.953056i	$0.402081\pi$
$930$	−3.36284e11	+	4.40500e10i	−0.449547	+	0.0588862i
$931$		−	1.64658e12i		−	2.19171i
$932$	−1.02970e12	+	2.74471e11i	−1.36473	+	0.363775i
$933$	2.25614e11			0.297742
$934$	−1.25867e11	−	9.60888e11i	−0.165396	−	1.26266i
$935$			4.81729e11i			0.630313i
$936$	1.45354e11	−	5.98751e10i	0.189375	−	0.0780087i
$937$	−1.78546e10			−0.0231628			−0.0115814	−	0.999933i	$-0.503687\pi$
$937$	−1.78546e10			−0.0231628			−0.0115814	+	0.999933i	$0.503687\pi$
$938$	1.81318e11	−	2.37509e10i	0.234224	−	0.0306810i
$939$		−	4.65141e11i		−	0.598304i
$940$	−2.20581e11	−	8.27528e11i	−0.282525	−	1.05992i
$941$	4.03037e11			0.514028			0.257014	−	0.966408i	$-0.417261\pi$
$941$	4.03037e11			0.514028			0.257014	+	0.966408i	$0.417261\pi$
$942$	−2.18092e10	−	1.66495e11i	−0.0276972	−	0.211445i
$943$			3.23679e10i			0.0409325i
$944$	−2.02162e11	−	3.52271e11i	−0.254573	−	0.443597i
$945$	1.71491e11			0.215038
$946$	5.52922e11	−	7.24274e10i	0.690398	−	0.0904354i
$947$		−	1.09600e12i		−	1.36273i	−0.731942	−	0.681367i	$-0.761386\pi$
$947$		−	1.09600e12i		−	1.36273i	0.731942	−	0.681367i	$-0.238614\pi$
$948$	−2.53263e11	+	6.75083e10i	−0.313573	+	0.0835841i
$949$	5.84148e11			0.720208
$950$	6.00962e10	+	4.58784e11i	0.0737824	+	0.563266i
$951$		−	5.31514e11i		−	0.649819i
$952$	6.92886e11	+	1.68206e12i	0.843557	+	2.04783i
$953$	1.08909e12			1.32036			0.660179	−	0.751108i	$-0.270480\pi$
$953$	1.08909e12			1.32036			0.660179	+	0.751108i	$0.270480\pi$
$954$	3.85491e11	−	5.04956e10i	0.465394	−	0.0609621i
$955$		−	6.24329e11i		−	0.750586i
$956$	9.30458e10	+	3.49069e11i	0.111395	+	0.417907i
$957$	1.88885e10			0.0225191
$958$	−8.86598e10	−	6.76843e11i	−0.105260	−	0.803574i
$959$		−	5.29503e11i		−	0.626029i
$960$	2.07178e11	+	2.08803e11i	0.243926	+	0.245839i
$961$	−6.08880e11			−0.713901
$962$	3.45333e11	−	4.52353e10i	0.403216	−	0.0528174i
$963$		−	4.98337e11i		−	0.579452i
$964$	−1.36573e12	+	3.64042e11i	−1.58146	+	0.421545i
$965$	−2.83818e11			−0.327288
$966$	−4.74847e9	−	3.62505e10i	−0.00545312	−	0.0416300i
$967$		−	3.98199e11i		−	0.455402i	−0.973731	−	0.227701i	$-0.926879\pi$
$967$		−	3.98199e11i		−	0.455402i	0.973731	−	0.227701i	$-0.0731208\pi$
$968$	−1.77716e11	+	7.32060e10i	−0.202407	+	0.0833768i
$969$	−5.37034e11			−0.609126
$970$	−7.51497e10	+	9.84387e9i	−0.0848868	+	0.0111193i
$971$			6.52799e11i			0.734349i	0.930152	+	0.367175i	$0.119675\pi$
$971$			6.52799e11i			0.734349i	−0.930152	+	0.367175i	$0.880325\pi$
$972$	−1.47483e10	−	5.53295e10i	−0.0165226	−	0.0619857i
$973$	−1.29835e12			−1.44857
$974$	1.37118e11	+	1.04678e12i	0.152356	+	1.16311i
$975$			2.05232e11i			0.227105i
$976$	−1.21444e11	+	6.96947e10i	−0.133837	+	0.0768070i
$977$	−7.17862e11			−0.787885			−0.393943	−	0.919135i	$-0.628889\pi$
$977$	−7.17862e11			−0.787885			−0.393943	+	0.919135i	$0.628889\pi$
$978$	−5.33226e11	+	6.98474e10i	−0.582849	+	0.0763475i
$979$			4.67161e11i			0.508553i
$980$	1.32044e12	−	3.51970e11i	1.43158	−	0.381594i
$981$	−3.27804e11			−0.353947
$982$	8.64025e10	+	6.59611e11i	0.0929139	+	0.709319i
$983$			9.40181e11i			1.00693i	0.864017	+	0.503463i	$0.167941\pi$
$983$			9.40181e11i			1.00693i	−0.864017	+	0.503463i	$0.832059\pi$
$984$	2.16159e11	+	5.24750e11i	0.230565	+	0.559722i
$985$	2.74195e11			0.291282
$986$	4.91746e10	−	6.44140e9i	0.0520276	−	0.00681510i
$987$			1.86641e12i			1.96670i
$988$	1.33809e11	+	5.01996e11i	0.140429	+	0.526833i
$989$	−2.94258e10			−0.0307570
$990$	−2.20472e10	−	1.68311e11i	−0.0229515	−	0.175216i
$991$			8.13083e10i			0.0843025i	0.999111	+	0.0421512i	$0.0134211\pi$
$991$			8.13083e10i			0.0843025i	−0.999111	+	0.0421512i	$0.986579\pi$
$992$	7.68490e11	+	1.00829e12i	0.793581	+	1.04122i
$993$	−1.64580e11			−0.169270
$994$	−1.81183e12	+	2.37332e11i	−1.85597	+	0.243114i
$995$		−	3.82547e11i		−	0.390295i
$996$	4.34055e11	−	1.15699e11i	0.441070	−	0.117569i
$997$	1.94960e12			1.97318			0.986588	−	0.163232i	$-0.0521919\pi$
$997$	1.94960e12			1.97318			0.986588	+	0.163232i	$0.0521919\pi$
$998$	−1.64163e11	−	1.25324e12i	−0.165482	−	1.26332i
$999$		−	1.26863e11i		−	0.127371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.9.d.a.7.2	yes	8
3.2	odd	2		36.9.d.c.19.7		8
4.3	odd	2	inner	12.9.d.a.7.1	✓	8
8.3	odd	2		192.9.g.e.127.3		8
8.5	even	2		192.9.g.e.127.7		8
12.11	even	2		36.9.d.c.19.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.9.d.a.7.1	✓	8	4.3	odd	2	inner
12.9.d.a.7.2	yes	8	1.1	even	1	trivial
36.9.d.c.19.7		8	3.2	odd	2
36.9.d.c.19.8		8	12.11	even	2
192.9.g.e.127.3		8	8.3	odd	2
192.9.g.e.127.7		8	8.5	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.8645 + 2.07809i) q^{2} -46.7654i q^{3} +(247.363 - 65.9356i) q^{4} -374.901 q^{5} +(97.1827 + 741.908i) q^{6} +4472.52i q^{7} +(-3787.26 + 1560.08i) q^{8} -2187.00 q^{9} +(5947.61 - 779.079i) q^{10} +12939.6i q^{11} +(-3083.50 - 11568.0i) q^{12} +17549.0 q^{13} +(-9294.30 - 70954.2i) q^{14} +17532.4i q^{15} +(56841.0 - 32620.1i) q^{16} -99303.3 q^{17} +(34695.6 - 4544.78i) q^{18} +115642. i q^{19} +(-92736.8 + 24719.4i) q^{20} +209159. q^{21} +(-26889.7 - 205281. i) q^{22} +10924.8i q^{23} +(72957.6 + 177113. i) q^{24} -250074. q^{25} +(-278405. + 36468.4i) q^{26} +102276. i q^{27} +(294898. + 1.10634e6i) q^{28} +31214.2 q^{29} +(-36433.9 - 278142. i) q^{30} -1.20904e6i q^{31} +(-833965. + 635621. i) q^{32} +605127. q^{33} +(1.57539e6 - 206361. i) q^{34} -1.67675e6i q^{35} +(-540983. + 144201. i) q^{36} -1.24040e6 q^{37} +(-240314. - 1.83459e6i) q^{38} -820684. i q^{39} +(1.41985e6 - 584875. i) q^{40} +2.96280e6 q^{41} +(-3.31820e6 + 434651. i) q^{42} +2.69350e6i q^{43} +(853183. + 3.20079e6i) q^{44} +819909. q^{45} +(-22702.7 - 173316. i) q^{46} +8.92341e6i q^{47} +(-1.52549e6 - 2.65819e6i) q^{48} -1.42386e7 q^{49} +(3.96729e6 - 519676. i) q^{50} +4.64396e6i q^{51} +(4.34097e6 - 1.15710e6i) q^{52} +1.11107e7 q^{53} +(-212539. - 1.62255e6i) q^{54} -4.85109e6i q^{55} +(-6.97747e6 - 1.69386e7i) q^{56} +5.40802e6 q^{57} +(-495196. + 64865.9i) q^{58} -6.19748e6i q^{59} +(1.15601e6 + 4.33687e6i) q^{60} -2.13656e6 q^{61} +(2.51249e6 + 1.91807e7i) q^{62} -9.78140e6i q^{63} +(1.19095e7 - 1.18169e7i) q^{64} -6.57914e6 q^{65} +(-9.60002e6 + 1.25751e6i) q^{66} +2.55543e6i q^{67} +(-2.45640e7 + 6.54763e6i) q^{68} +510901. q^{69} +(3.48445e6 + 2.66008e7i) q^{70} -2.55352e7i q^{71} +(8.28275e6 - 3.41189e6i) q^{72} +3.32867e7 q^{73} +(1.96783e7 - 2.57766e6i) q^{74} +1.16948e7i q^{75} +(7.62490e6 + 2.86055e7i) q^{76} -5.78728e7 q^{77} +(1.70546e6 + 1.30197e7i) q^{78} -2.18934e7i q^{79} +(-2.13098e7 + 1.22293e7i) q^{80} +4.78297e6 q^{81} +(-4.70033e7 + 6.15697e6i) q^{82} +3.75220e7i q^{83} +(5.17382e7 - 1.37910e7i) q^{84} +3.72290e7 q^{85} +(-5.59733e6 - 4.27309e7i) q^{86} -1.45974e6i q^{87} +(-2.01868e7 - 4.90058e7i) q^{88} +3.61031e7 q^{89} +(-1.30074e7 + 1.70385e6i) q^{90} +7.84881e7i q^{91} +(720332. + 2.70238e6i) q^{92} -5.65411e7 q^{93} +(-1.85437e7 - 1.41565e8i) q^{94} -4.33542e7i q^{95} +(2.97251e7 + 3.90007e7i) q^{96} -1.26353e7 q^{97} +(2.25888e8 - 2.95892e7i) q^{98} -2.82990e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 52 q^{4} - 336 q^{5} + 1134 q^{6} - 12960 q^{8} - 17496 q^{9} + 36628 q^{10} - 11340 q^{12} - 2864 q^{13} + 52728 q^{14} + 99440 q^{16} - 193200 q^{17} - 13122 q^{18} + 335592 q^{20} + 121824 q^{21}+ \cdots + 691081830 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 52 * q^4 - 336 * q^5 + 1134 * q^6 - 12960 * q^8 - 17496 * q^9 + 36628 * q^10 - 11340 * q^12 - 2864 * q^13 + 52728 * q^14 + 99440 * q^16 - 193200 * q^17 - 13122 * q^18 + 335592 * q^20 + 121824 * q^21 - 556968 * q^22 + 221616 * q^24 - 579048 * q^25 + 21564 * q^26 - 594672 * q^28 + 2063472 * q^29 + 46980 * q^30 - 3602784 * q^32 - 920160 * q^33 + 1568476 * q^34 + 113724 * q^36 + 7470352 * q^37 + 3659400 * q^38 + 1749184 * q^40 - 8865456 * q^41 - 5288328 * q^42 + 2395920 * q^44 + 734832 * q^45 - 13649856 * q^46 + 10916208 * q^48 - 18923896 * q^49 + 14581842 * q^50 + 18592888 * q^52 + 8706672 * q^53 - 2480058 * q^54 - 45565632 * q^56 - 2325024 * q^57 - 8816444 * q^58 + 28348056 * q^60 + 13457296 * q^61 + 80783976 * q^62 + 1268864 * q^64 + 7293408 * q^65 - 51205608 * q^66 - 117288264 * q^68 - 8636544 * q^69 - 60373104 * q^70 + 28343520 * q^72 + 94738960 * q^73 + 119548428 * q^74 + 144621360 * q^76 - 56971392 * q^77 - 140630580 * q^78 - 163857888 * q^80 + 38263752 * q^81 - 188383460 * q^82 + 199712304 * q^84 - 201200416 * q^85 + 240327384 * q^86 + 156323520 * q^88 + 188992272 * q^89 - 80105436 * q^90 - 387657984 * q^92 - 54802656 * q^93 - 38749872 * q^94 + 246092256 * q^96 - 123291632 * q^97 + 691081830 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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