LMFDB - Embedded newform 1183.2.e.j.170.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.10
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.j.508.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.689527 - 1.19430i) q^{2} +(-1.44060 - 2.49520i) q^{3} +(0.0491037 + 0.0850501i) q^{4} +(0.402974 - 0.697972i) q^{5} -3.97334 q^{6} +(1.26180 + 2.32548i) q^{7} +2.89354 q^{8} +(-2.65067 + 4.59109i) q^{9} +O(q^{10})$	\(q+(0.689527 - 1.19430i) q^{2} +(-1.44060 - 2.49520i) q^{3} +(0.0491037 + 0.0850501i) q^{4} +(0.402974 - 0.697972i) q^{5} -3.97334 q^{6} +(1.26180 + 2.32548i) q^{7} +2.89354 q^{8} +(-2.65067 + 4.59109i) q^{9} +(-0.555723 - 0.962541i) q^{10} +(2.63579 + 4.56532i) q^{11} +(0.141478 - 0.245047i) q^{12} +(3.64736 + 0.0965159i) q^{14} -2.32210 q^{15} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +(3.65541 + 6.33136i) q^{18} +(2.92234 - 5.06165i) q^{19} +0.0791501 q^{20} +(3.98477 - 6.49853i) q^{21} +7.26980 q^{22} +(0.802438 - 1.38986i) q^{23} +(-4.16844 - 7.21995i) q^{24} +(2.17522 + 3.76760i) q^{25} +6.63060 q^{27} +(-0.135823 + 0.221506i) q^{28} +2.28015 q^{29} +(-1.60115 + 2.77328i) q^{30} +(1.73795 + 3.01022i) q^{31} +(0.277517 + 0.480674i) q^{32} +(7.59424 - 13.1536i) q^{33} +0.772411 q^{34} +(2.13159 + 0.0564059i) q^{35} -0.520630 q^{36} +(0.620979 - 1.07557i) q^{37} +(-4.03007 - 6.98029i) q^{38} +(1.16602 - 2.01961i) q^{40} -0.927702 q^{41} +(-5.01357 - 9.23991i) q^{42} +4.44711 q^{43} +(-0.258854 + 0.448348i) q^{44} +(2.13630 + 3.70018i) q^{45} +(-1.10661 - 1.91670i) q^{46} +(-1.92209 + 3.32915i) q^{47} -10.9311 q^{48} +(-3.81571 + 5.86859i) q^{49} +5.99951 q^{50} +(0.806883 - 1.39756i) q^{51} +(-2.72727 - 4.72377i) q^{53} +(4.57198 - 7.91890i) q^{54} +4.24862 q^{55} +(3.65108 + 6.72888i) q^{56} -16.8397 q^{57} +(1.57223 - 2.72318i) q^{58} +(-5.49698 - 9.52106i) q^{59} +(-0.114024 - 0.197495i) q^{60} +(-3.65107 + 6.32385i) q^{61} +4.79346 q^{62} +(-14.0211 - 0.371024i) q^{63} +8.35330 q^{64} +(-10.4729 - 18.1396i) q^{66} +(-3.67278 - 6.36144i) q^{67} +(-0.0275031 + 0.0476367i) q^{68} -4.62397 q^{69} +(1.53716 - 2.50686i) q^{70} -9.31460 q^{71} +(-7.66982 + 13.2845i) q^{72} +(-2.50073 - 4.33139i) q^{73} +(-0.856364 - 1.48327i) q^{74} +(6.26726 - 10.8552i) q^{75} +0.573991 q^{76} +(-7.29072 + 11.8900i) q^{77} +(-5.68437 + 9.84562i) q^{79} +(-1.52886 - 2.64806i) q^{80} +(-1.60006 - 2.77138i) q^{81} +(-0.639676 + 1.10795i) q^{82} +5.81962 q^{83} +(0.748368 + 0.0198032i) q^{84} +0.451413 q^{85} +(3.06641 - 5.31117i) q^{86} +(-3.28479 - 5.68943i) q^{87} +(7.62677 + 13.2100i) q^{88} +(2.50473 - 4.33832i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(5.00739 - 8.67305i) q^{93} +(2.65067 + 4.59109i) q^{94} +(-2.35526 - 4.07942i) q^{95} +(0.799583 - 1.38492i) q^{96} +10.6483 q^{97} +(4.37780 + 8.60364i) q^{98} -27.9464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.689527	−	1.19430i	0.487570	−	0.844495i	−0.512328	−	0.858790i	$-0.671217\pi$
$2$	0.689527	−	1.19430i	0.487570	−	0.844495i	0.999898	+	0.0142944i	$0.00455022\pi$
$3$	−1.44060	−	2.49520i	−0.831732	−	1.44060i	−0.896664	−	0.442712i	$-0.854016\pi$
$3$	−1.44060	−	2.49520i	−0.831732	−	1.44060i	0.0649323	−	0.997890i	$-0.479317\pi$
$4$	0.0491037	+	0.0850501i	0.0245518	+	0.0425250i
$5$	0.402974	−	0.697972i	0.180216	−	0.312142i	−0.761738	−	0.647885i	$-0.775654\pi$
$5$	0.402974	−	0.697972i	0.180216	−	0.312142i	0.941954	+	0.335742i	$0.108987\pi$
$6$	−3.97334			−1.62211
$7$	1.26180	+	2.32548i	0.476916	+	0.878949i
$7$	1.26180	+	2.32548i	0.476916	+	0.878949i
$8$	2.89354			1.02302
$9$	−2.65067	+	4.59109i	−0.883555	+	1.53036i
$10$	−0.555723	−	0.962541i	−0.175735	−	0.304382i
$11$	2.63579	+	4.56532i	0.794720	+	1.37650i	0.923017	+	0.384760i	$0.125716\pi$
$11$	2.63579	+	4.56532i	0.794720	+	1.37650i	−0.128296	+	0.991736i	$0.540951\pi$
$12$	0.141478	−	0.245047i	0.0408411	−	0.0707389i
$13$		0			0
$13$		0			0
$14$	3.64736	+	0.0965159i	0.974798	+	0.0257950i
$15$	−2.32210			−0.599564
$16$	1.89697	−	3.28565i	0.474243	−	0.821412i
$17$	0.280051	+	0.485062i	0.0679223	+	0.117645i	0.897987	−	0.440023i	$-0.145030\pi$
$17$	0.280051	+	0.485062i	0.0679223	+	0.117645i	−0.830064	+	0.557668i	$0.811696\pi$
$18$	3.65541	+	6.33136i	0.861589	+	1.49232i
$19$	2.92234	−	5.06165i	0.670431	−	1.16122i	−0.307351	−	0.951596i	$-0.599442\pi$
$19$	2.92234	−	5.06165i	0.670431	−	1.16122i	0.977782	−	0.209625i	$-0.0672243\pi$
$20$	0.0791501			0.0176985
$21$	3.98477	−	6.49853i	0.869548	−	1.41810i
$22$	7.26980			1.54993
$23$	0.802438	−	1.38986i	0.167320	−	0.289807i	−0.770157	−	0.637855i	$-0.779822\pi$
$23$	0.802438	−	1.38986i	0.167320	−	0.289807i	0.937477	+	0.348048i	$0.113155\pi$
$24$	−4.16844	−	7.21995i	−0.850880	−	1.47377i
$25$	2.17522	+	3.76760i	0.435045	+	0.753520i
$26$		0			0
$27$	6.63060			1.27606
$28$	−0.135823	+	0.221506i	−0.0256682	+	0.0418607i
$29$	2.28015			0.423414			0.211707	−	0.977333i	$-0.432098\pi$
$29$	2.28015			0.423414			0.211707	+	0.977333i	$0.432098\pi$
$30$	−1.60115	+	2.77328i	−0.292329	+	0.506329i
$31$	1.73795	+	3.01022i	0.312145	+	0.540651i	0.978827	−	0.204692i	$-0.0656191\pi$
$31$	1.73795	+	3.01022i	0.312145	+	0.540651i	−0.666681	+	0.745343i	$0.732286\pi$
$32$	0.277517	+	0.480674i	0.0490585	+	0.0849719i
$33$	7.59424	−	13.1536i	1.32199	−	2.28975i
$34$	0.772411			0.132467
$35$	2.13159	+	0.0564059i	0.360305	+	0.00953433i
$36$	−0.520630			−0.0867716
$37$	0.620979	−	1.07557i	0.102088	−	0.176822i	−0.810457	−	0.585799i	$-0.800781\pi$
$37$	0.620979	−	1.07557i	0.102088	−	0.176822i	0.912545	+	0.408977i	$0.134114\pi$
$38$	−4.03007	−	6.98029i	−0.653764	−	1.13235i
$39$		0			0
$40$	1.16602	−	2.01961i	0.184364	−	0.319329i
$41$	−0.927702			−0.144883			−0.0724413	−	0.997373i	$-0.523079\pi$
$41$	−0.927702			−0.144883			−0.0724413	+	0.997373i	$0.523079\pi$
$42$	−5.01357	−	9.23991i	−0.773610	−	1.42575i
$43$	4.44711			0.678179			0.339089	−	0.940754i	$-0.389881\pi$
$43$	4.44711			0.678179			0.339089	+	0.940754i	$0.389881\pi$
$44$	−0.258854	+	0.448348i	−0.0390237	+	0.0675910i
$45$	2.13630	+	3.70018i	0.318461	+	0.551590i
$46$	−1.10661	−	1.91670i	−0.163160	−	0.282602i
$47$	−1.92209	+	3.32915i	−0.280365	+	0.485607i	−0.971475	−	0.237143i	$-0.923789\pi$
$47$	−1.92209	+	3.32915i	−0.280365	+	0.485607i	0.691109	+	0.722750i	$0.257122\pi$
$48$	−10.9311			−1.57777
$49$	−3.81571	+	5.86859i	−0.545101	+	0.838370i
$50$	5.99951			0.848458
$51$	0.806883	−	1.39756i	0.112986	−	0.195698i
$52$		0			0
$53$	−2.72727	−	4.72377i	−0.374620	−	0.648860i	0.615650	−	0.788019i	$-0.288893\pi$
$53$	−2.72727	−	4.72377i	−0.374620	−	0.648860i	−0.990270	+	0.139159i	$0.955560\pi$
$54$	4.57198	−	7.91890i	0.622168	−	1.07763i
$55$	4.24862			0.572884
$56$	3.65108	+	6.72888i	0.487896	+	0.899184i
$57$	−16.8397			−2.23048
$58$	1.57223	−	2.72318i	0.206444	−	0.357571i
$59$	−5.49698	−	9.52106i	−0.715646	−	1.23954i	−0.962710	−	0.270537i	$-0.912799\pi$
$59$	−5.49698	−	9.52106i	−0.715646	−	1.23954i	0.247063	−	0.968999i	$-0.420534\pi$
$60$	−0.114024	−	0.197495i	−0.0147204	−	0.0254965i
$61$	−3.65107	+	6.32385i	−0.467472	+	0.809686i	−0.999309	−	0.0371610i	$-0.988169\pi$
$61$	−3.65107	+	6.32385i	−0.467472	+	0.809686i	0.531837	+	0.846847i	$0.321502\pi$
$62$	4.79346			0.608770
$63$	−14.0211	−	0.371024i	−1.76649	−	0.0467446i
$64$	8.35330			1.04416
$65$		0			0
$66$	−10.4729	−	18.1396i	−1.28912	−	2.23283i
$67$	−3.67278	−	6.36144i	−0.448701	−	0.777174i	0.549600	−	0.835428i	$-0.314780\pi$
$67$	−3.67278	−	6.36144i	−0.448701	−	0.777174i	−0.998302	+	0.0582541i	$0.981447\pi$
$68$	−0.0275031	+	0.0476367i	−0.00333524	+	0.00577680i
$69$	−4.62397			−0.556661
$70$	1.53716	−	2.50686i	0.183725	−	0.299627i
$71$	−9.31460			−1.10544			−0.552720	−	0.833367i	$-0.686410\pi$
$71$	−9.31460			−1.10544			−0.552720	+	0.833367i	$0.686410\pi$
$72$	−7.66982	+	13.2845i	−0.903896	+	1.56559i
$73$	−2.50073	−	4.33139i	−0.292688	−	0.506951i	0.681756	−	0.731579i	$-0.261216\pi$
$73$	−2.50073	−	4.33139i	−0.292688	−	0.506951i	−0.974444	+	0.224629i	$0.927883\pi$
$74$	−0.856364	−	1.48327i	−0.0995503	−	0.172426i
$75$	6.26726	−	10.8552i	0.723681	−	1.25345i
$76$	0.573991			0.0658413
$77$	−7.29072	+	11.8900i	−0.830854	+	1.35499i
$78$		0			0
$79$	−5.68437	+	9.84562i	−0.639542	+	1.10772i	0.345992	+	0.938238i	$0.387543\pi$
$79$	−5.68437	+	9.84562i	−0.639542	+	1.10772i	−0.985533	+	0.169481i	$0.945791\pi$
$80$	−1.52886	−	2.64806i	−0.170932	−	0.296062i
$81$	−1.60006	−	2.77138i	−0.177784	−	0.307931i
$82$	−0.639676	+	1.10795i	−0.0706404	+	0.122353i
$83$	5.81962			0.638786			0.319393	−	0.947622i	$-0.396521\pi$
$83$	5.81962			0.638786			0.319393	+	0.947622i	$0.396521\pi$
$84$	0.748368	+	0.0198032i	0.0816536	+	0.00216071i
$85$	0.451413			0.0489626
$86$	3.06641	−	5.31117i	0.330659	−	0.572719i
$87$	−3.28479	−	5.68943i	−0.352167	−	0.609971i
$88$	7.62677	+	13.2100i	0.813016	+	1.40819i
$89$	2.50473	−	4.33832i	0.265501	−	0.459861i	−0.702194	−	0.711986i	$-0.747796\pi$
$89$	2.50473	−	4.33832i	0.265501	−	0.459861i	0.967695	+	0.252125i	$0.0811294\pi$
$90$	5.89215			0.621087
$91$		0			0
$92$	0.157611			0.0164320
$93$	5.00739	−	8.67305i	0.519242	−	0.899354i
$94$	2.65067	+	4.59109i	0.273395	+	0.473534i
$95$	−2.35526	−	4.07942i	−0.241644	−	0.418540i
$96$	0.799583	−	1.38492i	0.0816071	−	0.141348i
$97$	10.6483			1.08117			0.540586	−	0.841289i	$-0.318202\pi$
$97$	10.6483			1.08117			0.540586	+	0.841289i	$0.318202\pi$
$98$	4.37780	+	8.60364i	0.442225	+	0.869099i
$99$	−27.9464			−2.80872
$100$	−0.213623	+	0.370006i	−0.0213623	+	0.0370006i
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	0.752031	−	0.659127i	$-0.229074\pi$
$101$	−1.95777	−	3.39096i	−0.194805	−	0.337413i	−0.946837	+	0.321715i	$0.895741\pi$
$102$	−1.11274	−	1.92732i	−0.110177	−	0.190833i
$103$	−4.22690	+	7.32120i	−0.416488	+	0.721379i	−0.995583	−	0.0938810i	$-0.970073\pi$
$103$	−4.22690	+	7.32120i	−0.416488	+	0.721379i	0.579095	+	0.815260i	$0.303406\pi$
$104$		0			0
$105$	−2.93003	−	5.40000i	−0.285942	−	0.526986i
$106$	−7.52212			−0.730613
$107$	4.83761	−	8.37899i	0.467670	−	0.810028i	−0.531648	−	0.846965i	$-0.678427\pi$
$107$	4.83761	−	8.37899i	0.467670	−	0.810028i	0.999318	+	0.0369379i	$0.0117604\pi$
$108$	0.325587	+	0.563933i	0.0313296	+	0.0542645i
$109$	−7.28189	−	12.6126i	−0.697478	−	1.20807i	−0.969338	−	0.245731i	$-0.920972\pi$
$109$	−7.28189	−	12.6126i	−0.697478	−	1.20807i	0.271860	−	0.962337i	$-0.412361\pi$
$110$	2.92954	−	5.07411i	0.279321	−	0.483798i
$111$	−3.57833			−0.339640
$112$	10.0343	+	0.265526i	0.948153	+	0.0250899i
$113$	19.5114			1.83548			0.917741	−	0.397180i	$-0.130011\pi$
$113$	19.5114			1.83548			0.917741	+	0.397180i	$0.130011\pi$
$114$	−11.6115	+	20.1116i	−1.08751	+	1.88363i
$115$	−0.646723	−	1.12016i	−0.0603073	−	0.104455i
$116$	0.111964	+	0.193927i	0.0103956	+	0.0180057i
$117$		0			0
$118$	−15.1613			−1.39571
$119$	−0.774634	+	1.26331i	−0.0710106	+	0.115807i
$120$	−6.71910			−0.613367
$121$	−8.39477	+	14.5402i	−0.763161	+	1.32183i
$122$	5.03503	+	8.72093i	0.455850	+	0.789556i
$123$	1.33645	+	2.31480i	0.120503	+	0.208718i
$124$	−0.170680	+	0.295626i	−0.0153275	+	0.0265480i
$125$	7.53598			0.674038
$126$	−10.1110	+	16.4895i	−0.900763	+	1.46900i
$127$	−1.91731			−0.170134			−0.0850670	−	0.996375i	$-0.527110\pi$
$127$	−1.91731			−0.170134			−0.0850670	+	0.996375i	$0.527110\pi$
$128$	5.20480	−	9.01498i	0.460044	−	0.796819i
$129$	−6.40652	−	11.0964i	−0.564063	−	0.976985i
$130$		0			0
$131$	−7.79078	+	13.4940i	−0.680684	+	1.17898i	0.294089	+	0.955778i	$0.404984\pi$
$131$	−7.79078	+	13.4940i	−0.680684	+	1.17898i	−0.974772	+	0.223201i	$0.928349\pi$
$132$	1.49162			0.129829
$133$	15.4582	+	0.409052i	1.34039	+	0.0354693i
$134$	−10.1299			−0.875093
$135$	2.67196	−	4.62797i	0.229966	−	0.398312i
$136$	0.810339	+	1.40355i	0.0694860	+	0.120353i
$137$	−3.92553	−	6.79921i	−0.335380	−	0.580896i	0.648178	−	0.761489i	$-0.275531\pi$
$137$	−3.92553	−	6.79921i	−0.335380	−	0.580896i	−0.983558	+	0.180594i	$0.942198\pi$
$138$	−3.18836	+	5.52240i	−0.271411	+	0.470098i
$139$	9.92481			0.841812			0.420906	−	0.907104i	$-0.361712\pi$
$139$	9.92481			0.841812			0.420906	+	0.907104i	$0.361712\pi$
$140$	0.0998717	+	0.184062i	0.00844070	+	0.0155561i
$141$	11.0759			0.932755
$142$	−6.42267	+	11.1244i	−0.538979	+	0.933538i
$143$		0			0
$144$	10.0565	+	17.4183i	0.838039	+	1.45153i
$145$	0.918843	−	1.59148i	0.0763058	−	0.132165i
$146$	−6.89728			−0.570823
$147$	20.1402	+	1.06664i	1.66114	+	0.0879750i
$148$	0.121969			0.0100258
$149$	3.95962	−	6.85827i	0.324385	−	0.561851i	−0.657003	−	0.753888i	$-0.728176\pi$
$149$	3.95962	−	6.85827i	0.324385	−	0.561851i	0.981388	+	0.192037i	$0.0615093\pi$
$150$	−8.64290	−	14.9699i	−0.705690	−	1.22229i
$151$	−0.750582	−	1.30005i	−0.0610815	−	0.105796i	0.833868	−	0.551965i	$-0.186122\pi$
$151$	−0.750582	−	1.30005i	−0.0610815	−	0.105796i	−0.894949	+	0.446168i	$0.852788\pi$
$152$	8.45592	−	14.6461i	0.685866	−	1.18795i
$153$	−2.96928			−0.240052
$154$	9.17305	+	16.9058i	0.739185	+	1.36231i
$155$	2.80140			0.225014
$156$		0			0
$157$	−1.92846	−	3.34019i	−0.153908	−	0.266576i	0.778753	−	0.627331i	$-0.215853\pi$
$157$	−1.92846	−	3.34019i	−0.153908	−	0.266576i	−0.932661	+	0.360754i	$0.882519\pi$
$158$	7.83906	+	13.5777i	0.623642	+	1.08018i
$159$	−7.85782	+	13.6102i	−0.623166	+	1.07936i
$160$	0.447329			0.0353644
$161$	4.24462	+	0.112320i	0.334523	+	0.00885209i
$162$	−4.41314			−0.346729
$163$	−7.18042	+	12.4369i	−0.562414	+	0.974130i	0.434871	+	0.900493i	$0.356794\pi$
$163$	−7.18042	+	12.4369i	−0.562414	+	0.974130i	−0.997285	+	0.0736372i	$0.976539\pi$
$164$	−0.0455536	−	0.0789011i	−0.00355714	−	0.00616114i
$165$	−6.12057	−	10.6011i	−0.476486	−	0.825297i
$166$	4.01279	−	6.95035i	0.311453	−	0.539452i
$167$	−4.52138			−0.349875			−0.174937	−	0.984580i	$-0.555972\pi$
$167$	−4.52138			−0.349875			−0.174937	+	0.984580i	$0.555972\pi$
$168$	11.5301	−	18.8038i	0.889567	−	1.45074i
$169$		0			0
$170$	0.311262	−	0.539121i	0.0238727	−	0.0413487i
$171$	15.4923	+	26.8335i	1.18473	+	2.05201i
$172$	0.218370	+	0.378227i	0.0166505	+	0.0288396i
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	−0.209642	−	0.977778i	$-0.567230\pi$
$173$	9.75896	−	16.9030i	0.741960	−	1.28511i	0.951602	−	0.307334i	$-0.0994369\pi$
$174$	−9.05982			−0.686823
$175$	−6.01677	+	9.81240i	−0.454825	+	0.741748i
$176$	20.0001			1.50756
$177$	−15.8379	+	27.4321i	−1.19045	+	2.06192i
$178$	−3.45416	−	5.98278i	−0.258900	−	0.448428i
$179$	−10.4098	−	18.0303i	−0.778065	−	1.34765i	−0.933055	−	0.359733i	$-0.882868\pi$
$179$	−10.4098	−	18.0303i	−0.778065	−	1.34765i	0.154990	−	0.987916i	$-0.450465\pi$
$180$	−0.209800	+	0.363385i	−0.0156376	+	0.0270851i
$181$	−16.5522			−1.23031			−0.615157	−	0.788405i	$-0.710907\pi$
$181$	−16.5522			−1.23031			−0.615157	+	0.788405i	$0.710907\pi$
$182$		0			0
$183$	21.0390			1.55525
$184$	2.32189	−	4.02163i	0.171172	−	0.296478i
$185$	−0.500477	−	0.866851i	−0.0367958	−	0.0637322i
$186$	−6.90546	−	11.9606i	−0.506333	−	0.876995i
$187$	−1.47631	+	2.55704i	−0.107958	+	0.186990i
$188$	−0.377527			−0.0275340
$189$	8.36651	+	15.4193i	0.608574	+	1.12159i
$190$	−6.49606			−0.471274
$191$	2.12504	−	3.68068i	0.153762	−	0.266324i	−0.778845	−	0.627216i	$-0.784194\pi$
$191$	2.12504	−	3.68068i	0.153762	−	0.266324i	0.932608	+	0.360892i	$0.117528\pi$
$192$	−12.0338	−	20.8431i	−0.868463	−	1.50422i
$193$	−5.79861	−	10.0435i	−0.417393	−	0.722946i	0.578283	−	0.815836i	$-0.303723\pi$
$193$	−5.79861	−	10.0435i	−0.417393	−	0.722946i	−0.995676	+	0.0928898i	$0.970390\pi$
$194$	7.34231	−	12.7172i	0.527147	−	0.913045i
$195$		0			0
$196$	−0.686490	−	0.0363570i	−0.0490350	−	0.00259693i
$197$	14.4213			1.02748			0.513738	−	0.857947i	$-0.328260\pi$
$197$	14.4213			1.02748			0.513738	+	0.857947i	$0.328260\pi$
$198$	−19.2698	+	33.3763i	−1.36944	+	2.37195i
$199$	−3.52962	−	6.11348i	−0.250208	−	0.433373i	0.713375	−	0.700783i	$-0.247166\pi$
$199$	−3.52962	−	6.11348i	−0.250208	−	0.433373i	−0.963583	+	0.267409i	$0.913832\pi$
$200$	6.29410	+	10.9017i	0.445060	+	0.770867i
$201$	−10.5820	+	18.3286i	−0.746398	+	1.29280i
$202$	−5.39974			−0.379925
$203$	2.87710	+	5.30245i	0.201933	+	0.372159i
$204$	0.158484			0.0110961
$205$	−0.373840	+	0.647509i	−0.0261101	+	0.0452240i
$206$	5.82912	+	10.0963i	0.406134	+	0.703445i
$207$	4.25399	+	7.36812i	0.295673	+	0.512120i
$208$		0			0
$209$	30.8107			2.13122
$210$	−8.46954	−	0.224120i	−0.584454	−	0.0154657i
$211$	−26.4226			−1.81901			−0.909505	−	0.415693i	$-0.863539\pi$
$211$	−26.4226			−1.81901			−0.909505	+	0.415693i	$0.863539\pi$
$212$	0.267838	−	0.463909i	0.0183952	−	0.0318614i
$213$	13.4186	+	23.2417i	0.919429	+	1.59250i
$214$	−6.67133	−	11.5551i	−0.456043	−	0.789890i
$215$	1.79207	−	3.10396i	0.122218	−	0.211688i
$216$	19.1859			1.30544
$217$	−4.80725	+	7.83987i	−0.326338	+	0.532205i
$218$	−20.0842			−1.36028
$219$	−7.20511	+	12.4796i	−0.486876	+	0.843294i
$220$	0.208623	+	0.361345i	0.0140654	+	0.0243619i
$221$		0			0
$222$	−2.46736	+	4.27359i	−0.165598	+	0.286825i
$223$	−23.0005			−1.54023			−0.770115	−	0.637905i	$-0.779801\pi$
$223$	−23.0005			−1.54023			−0.770115	+	0.637905i	$0.779801\pi$
$224$	−0.767625	+	1.25188i	−0.0512891	+	0.0836444i
$225$	−23.0632			−1.53754
$226$	13.4537	−	23.3024i	0.894925	−	1.55006i
$227$	−0.226684	−	0.392628i	−0.0150455	−	0.0260596i	0.858405	−	0.512973i	$-0.171456\pi$
$227$	−0.226684	−	0.392628i	−0.0150455	−	0.0260596i	−0.873450	+	0.486914i	$0.838123\pi$
$228$	−0.826893	−	1.43222i	−0.0547623	−	0.0948511i
$229$	8.66674	−	15.0112i	0.572714	−	0.991970i	−0.423571	−	0.905863i	$-0.639224\pi$
$229$	8.66674	−	15.0112i	0.572714	−	0.991970i	0.996286	−	0.0861077i	$-0.0274429\pi$
$230$	−1.78373			−0.117616
$231$	40.1709	+	1.06300i	2.64305	+	0.0699400i
$232$	6.59772			0.433162
$233$	−3.90756	+	6.76809i	−0.255992	+	0.443392i	−0.965165	−	0.261643i	$-0.915736\pi$
$233$	−3.90756	+	6.76809i	−0.255992	+	0.443392i	0.709172	+	0.705035i	$0.249069\pi$
$234$		0			0
$235$	1.54910	+	2.68313i	0.101052	+	0.175028i
$236$	0.539844	−	0.935038i	0.0351409	−	0.0608658i
$237$	32.7557			2.12771
$238$	0.974630	+	1.79623i	0.0631759	+	0.116432i
$239$	13.5314			0.875276			0.437638	−	0.899151i	$-0.355815\pi$
$239$	13.5314			0.875276			0.437638	+	0.899151i	$0.355815\pi$
$240$	−4.40496	+	7.62961i	−0.284339	+	0.492489i
$241$	11.2796	+	19.5369i	0.726583	+	1.25848i	0.958319	+	0.285701i	$0.0922263\pi$
$241$	11.2796	+	19.5369i	0.726583	+	1.25848i	−0.231736	+	0.972779i	$0.574440\pi$
$242$	11.5768	+	20.0517i	0.744188	+	1.28897i
$243$	5.33581	−	9.24189i	0.342292	−	0.592868i
$244$	−0.717125			−0.0459092
$245$	2.55848	+	5.02815i	0.163455	+	0.321237i
$246$	3.68607			0.235015
$247$		0			0
$248$	5.02884	+	8.71020i	0.319331	+	0.553098i
$249$	−8.38375	−	14.5211i	−0.531299	−	0.920236i
$250$	5.19626	−	9.00019i	0.328641	−	0.569222i
$251$	−6.73236			−0.424943			−0.212471	−	0.977167i	$-0.568151\pi$
$251$	−6.73236			−0.424943			−0.212471	+	0.977167i	$0.568151\pi$
$252$	−0.656932	−	1.21071i	−0.0413828	−	0.0762678i
$253$	8.46023			0.531890
$254$	−1.32204	+	2.28984i	−0.0829521	+	0.143677i
$255$	−0.650306	−	1.12636i	−0.0407238	−	0.0705356i
$256$	1.17560	+	2.03620i	0.0734750	+	0.127262i
$257$	−8.26907	+	14.3225i	−0.515811	+	0.893410i	0.484021	+	0.875056i	$0.339176\pi$
$257$	−8.26907	+	14.3225i	−0.515811	+	0.893410i	−0.999832	+	0.0183536i	$0.994158\pi$
$258$	−17.6699			−1.10008
$259$	3.28476	+	0.0869209i	0.204105	+	0.00540100i
$260$		0			0
$261$	−6.04392	+	10.4684i	−0.374110	+	0.647977i
$262$	10.7439	+	18.6090i	0.663761	+	1.14967i
$263$	5.01137	+	8.67994i	0.309014	+	0.535228i	0.978147	−	0.207915i	$-0.0666676\pi$
$263$	5.01137	+	8.67994i	0.309014	+	0.535228i	−0.669133	+	0.743143i	$0.733334\pi$
$264$	21.9743	−	38.0606i	1.35242	−	2.34247i
$265$	−4.39608			−0.270049
$266$	11.1474	−	18.1796i	0.683489	−	1.11466i
$267$	−14.4333			−0.883302
$268$	0.360694	−	0.624740i	0.0220329	−	0.0381621i
$269$	7.86149	+	13.6165i	0.479323	+	0.830212i	0.999719	−	0.0237130i	$-0.00754880\pi$
$269$	7.86149	+	13.6165i	0.479323	+	0.830212i	−0.520395	+	0.853925i	$0.674215\pi$
$270$	−3.68478	−	6.38223i	−0.224249	−	0.388410i
$271$	−2.60809	+	4.51734i	−0.158430	+	0.274409i	−0.934303	−	0.356481i	$-0.883977\pi$
$271$	−2.60809	+	4.51734i	−0.158430	+	0.274409i	0.775873	+	0.630890i	$0.217310\pi$
$272$	2.12499			0.128847
$273$		0			0
$274$	−10.8270			−0.654085
$275$	−11.4669	+	19.8612i	−0.691478	+	1.19767i
$276$	−0.227054	−	0.393269i	−0.0136671	−	0.0236720i
$277$	9.63619	+	16.6904i	0.578983	+	1.00283i	0.995596	+	0.0937439i	$0.0298835\pi$
$277$	9.63619	+	16.6904i	0.578983	+	1.00283i	−0.416614	+	0.909084i	$0.636783\pi$
$278$	6.84343	−	11.8532i	0.410442	−	0.710906i
$279$	−18.4269			−1.10319
$280$	6.16786	+	0.163213i	0.368600	+	0.00975383i
$281$	−2.14283			−0.127831			−0.0639153	−	0.997955i	$-0.520359\pi$
$281$	−2.14283			−0.127831			−0.0639153	+	0.997955i	$0.520359\pi$
$282$	7.63711	−	13.2279i	0.454783	−	0.787707i
$283$	7.87512	+	13.6401i	0.468127	+	0.810820i	0.999337	−	0.0364203i	$-0.0115955\pi$
$283$	7.87512	+	13.6401i	0.468127	+	0.810820i	−0.531209	+	0.847241i	$0.678262\pi$
$284$	−0.457381	−	0.792207i	−0.0271406	−	0.0470089i
$285$	−6.78597	+	11.7537i	−0.401966	+	0.696226i
$286$		0			0
$287$	−1.17058	−	2.15735i	−0.0690969	−	0.127344i
$288$	−2.94242			−0.173384
$289$	8.34314	−	14.4507i	0.490773	−	0.850044i
$290$	−1.26714	−	2.19474i	−0.0744087	−	0.128880i
$291$	−15.3400	−	26.5696i	−0.899246	−	1.55754i
$292$	0.245590	−	0.425374i	0.0143721	−	0.0248932i
$293$	23.1487			1.35236			0.676182	−	0.736735i	$-0.263633\pi$
$293$	23.1487			1.35236			0.676182	+	0.736735i	$0.263633\pi$
$294$	15.1611	−	23.3179i	0.884214	−	1.35993i
$295$	−8.86057			−0.515882
$296$	1.79683	−	3.11220i	0.104439	−	0.180893i
$297$	17.4769	+	30.2708i	1.01411	+	1.75649i
$298$	−5.46054	−	9.45793i	−0.316320	−	0.547883i
$299$		0			0
$300$	1.23098			0.0710708
$301$	5.61138	+	10.3417i	0.323434	+	0.596084i
$302$	−2.07019			−0.119126
$303$	−5.64073	+	9.77003i	−0.324052	+	0.561274i
$304$	−11.0872	−	19.2036i	−0.635894	−	1.10140i
$305$	2.94258	+	5.09669i	0.168491	+	0.291836i
$306$	−2.04740	+	3.54621i	−0.117042	+	0.202723i
$307$	4.23590			0.241756			0.120878	−	0.992667i	$-0.461429\pi$
$307$	4.23590			0.241756			0.120878	+	0.992667i	$0.461429\pi$
$308$	−1.36925	−	0.0362328i	−0.0780201	−	0.00206456i
$309$	24.3571			1.38563
$310$	1.93164	−	3.34570i	0.109710	−	0.190023i
$311$	−13.6251	−	23.5993i	−0.772606	−	1.33819i	−0.936130	−	0.351654i	$-0.885619\pi$
$311$	−13.6251	−	23.5993i	−0.772606	−	1.33819i	0.163524	−	0.986539i	$-0.447714\pi$
$312$		0			0
$313$	−1.34849	+	2.33565i	−0.0762209	+	0.132018i	−0.901617	−	0.432536i	$-0.857619\pi$
$313$	−1.34849	+	2.33565i	−0.0762209	+	0.132018i	0.825396	+	0.564555i	$0.190952\pi$
$314$	−5.31891			−0.300163
$315$	−5.90910	+	9.63681i	−0.332940	+	0.542973i
$316$	−1.11649			−0.0628077
$317$	−12.0352	+	20.8456i	−0.675966	+	1.17081i	0.300220	+	0.953870i	$0.402940\pi$
$317$	−12.0352	+	20.8456i	−0.675966	+	1.17081i	−0.976186	+	0.216937i	$0.930393\pi$
$318$	10.8364	+	18.7691i	0.607674	+	1.05252i
$319$	6.01000	+	10.4096i	0.336496	+	0.582828i
$320$	3.36617	−	5.83037i	0.188174	−	0.325928i
$321$	−27.8763			−1.55590
$322$	3.06092	−	4.99188i	0.170579	−	0.278187i
$323$	3.27362			0.182149
$324$	0.157138	−	0.272170i	0.00872986	−	0.0151206i
$325$		0			0
$326$	9.90220	+	17.1511i	0.548432	+	0.949912i
$327$	−20.9806	+	36.3394i	−1.16023	+	2.00958i
$328$	−2.68434			−0.148218
$329$	−10.1672	−	0.269042i	−0.560535	−	0.0148328i
$330$	−16.8812			−0.929279
$331$	0.309862	−	0.536696i	0.0170315	−	0.0294995i	−0.857384	−	0.514677i	$-0.827912\pi$
$331$	0.309862	−	0.536696i	0.0170315	−	0.0294995i	0.874416	+	0.485178i	$0.161245\pi$
$332$	0.285765	+	0.494959i	0.0156834	+	0.0271644i
$333$	3.29201	+	5.70194i	0.180401	+	0.312464i
$334$	−3.11762	+	5.39987i	−0.170588	+	0.295468i
$335$	−5.92014			−0.323452
$336$	−13.7929	−	25.4201i	−0.752465	−	1.38678i
$337$	5.72118			0.311652			0.155826	−	0.987784i	$-0.450196\pi$
$337$	5.72118			0.311652			0.155826	+	0.987784i	$0.450196\pi$
$338$		0			0
$339$	−28.1082	−	48.6848i	−1.52663	−	2.64420i
$340$	0.0221660	+	0.0383927i	0.00120212	+	0.00208214i
$341$	−9.16174	+	15.8686i	−0.496136	+	0.859333i
$342$	42.7295			2.31055
$343$	−18.4620	−	1.46836i	−0.996852	−	0.0792837i
$344$	12.8679			0.693792
$345$	−1.86334	+	3.22740i	−0.100319	+	0.173757i
$346$	−13.4581	−	23.3102i	−0.723514	−	1.25316i
$347$	0.932429	+	1.61501i	0.0500554	+	0.0866985i	0.889968	−	0.456024i	$-0.150727\pi$
$347$	0.932429	+	1.61501i	0.0500554	+	0.0866985i	−0.839912	+	0.542722i	$0.817394\pi$
$348$	0.322591	−	0.558744i	0.0172927	−	0.0299518i
$349$	−22.3172			−1.19461			−0.597307	−	0.802012i	$-0.703763\pi$
$349$	−22.3172			−1.19461			−0.597307	+	0.802012i	$0.703763\pi$
$350$	7.57019	+	13.9517i	0.404644	+	0.745751i
$351$		0			0
$352$	−1.46295	+	2.53391i	−0.0779756	+	0.135058i
$353$	−1.16600	−	2.01956i	−0.0620597	−	0.107491i	0.833326	−	0.552781i	$-0.186434\pi$
$353$	−1.16600	−	2.01956i	−0.0620597	−	0.107491i	−0.895386	+	0.445291i	$0.853100\pi$
$354$	21.8414	+	37.8304i	1.16086	+	2.01066i
$355$	−3.75354	+	6.50133i	−0.199217	+	0.345055i
$356$	0.491966			0.0260741
$357$	4.26813	+	0.112943i	0.225893	+	0.00597756i
$358$	−28.7114			−1.51744
$359$	−1.63553	+	2.83281i	−0.0863197	+	0.149510i	−0.905953	−	0.423379i	$-0.860844\pi$
$359$	−1.63553	+	2.83281i	−0.0863197	+	0.149510i	0.819633	+	0.572889i	$0.194177\pi$
$360$	6.18147	+	10.7066i	0.325792	+	0.564289i
$361$	−7.58017	−	13.1292i	−0.398956	−	0.691013i
$362$	−11.4132	+	19.7682i	−0.599863	+	1.03899i
$363$	48.3741			2.53898
$364$		0			0
$365$	−4.03092			−0.210988
$366$	14.5070	−	25.1268i	0.758291	−	1.31340i
$367$	−2.07645	−	3.59652i	−0.108390	−	0.187737i	0.806728	−	0.590923i	$-0.201236\pi$
$367$	−2.07645	−	3.59652i	−0.108390	−	0.187737i	−0.915118	+	0.403186i	$0.867903\pi$
$368$	−3.04440	−	5.27306i	−0.158700	−	0.274877i
$369$	2.45903	−	4.25916i	0.128012	−	0.221723i
$370$	−1.38037			−0.0717620
$371$	7.54376	−	12.3027i	0.391653	−	0.638724i
$372$	0.983525			0.0509934
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	−0.685637	−	0.727944i	$-0.740476\pi$
$373$	5.55446	−	9.62061i	0.287599	−	0.498136i	0.973236	+	0.229807i	$0.0738096\pi$
$374$	2.03591	+	3.52630i	0.105275	+	0.182341i
$375$	−10.8563	−	18.8037i	−0.560619	−	0.971021i
$376$	−5.56165	+	9.63305i	−0.286820	+	0.496787i
$377$		0			0
$378$	24.1842	+	0.639958i	1.24390	+	0.0329159i
$379$	4.64030			0.238356			0.119178	−	0.992873i	$-0.461974\pi$
$379$	4.64030			0.238356			0.119178	+	0.992873i	$0.461974\pi$
$380$	0.231304	−	0.400630i	0.0118656	−	0.0205519i
$381$	2.76208	+	4.78407i	0.141506	+	0.245095i
$382$	−2.93055	−	5.07586i	−0.149940	−	0.259703i
$383$	−1.83466	+	3.17773i	−0.0937469	+	0.162374i	−0.909085	−	0.416611i	$-0.863218\pi$
$383$	−1.83466	+	3.17773i	−0.0937469	+	0.162374i	0.815338	+	0.578985i	$0.196551\pi$
$384$	−29.9922			−1.53053
$385$	5.36092	+	9.88008i	0.273218	+	0.503535i
$386$	−15.9932			−0.814033
$387$	−11.7878	+	20.4171i	−0.599208	+	1.03786i
$388$	0.522872	+	0.905640i	0.0265448	+	0.0459769i
$389$	−8.44156	−	14.6212i	−0.428004	−	0.741324i	0.568692	−	0.822551i	$-0.307450\pi$
$389$	−8.44156	−	14.6212i	−0.428004	−	0.741324i	−0.996696	+	0.0812262i	$0.974116\pi$
$390$		0			0
$391$	0.898894			0.0454590
$392$	−11.0409	+	16.9810i	−0.557651	+	0.857671i
$393$	44.8937			2.26459
$394$	9.94390	−	17.2233i	0.500966	−	0.867699i
$395$	4.58131	+	7.93506i	0.230511	+	0.399256i
$396$	−1.37227	−	2.37684i	−0.0689592	−	0.119441i
$397$	8.35428	−	14.4700i	0.419289	−	0.726230i	−0.576579	−	0.817041i	$-0.695613\pi$
$397$	8.35428	−	14.4700i	0.419289	−	0.726230i	0.995868	+	0.0908114i	$0.0289461\pi$
$398$	−9.73508			−0.487976
$399$	−21.2484	−	39.1604i	−1.06375	−	1.96047i
$400$	16.5053			0.825267
$401$	12.6567	−	21.9221i	0.632046	−	1.09474i	−0.355087	−	0.934833i	$-0.615549\pi$
$401$	12.6567	−	21.9221i	0.632046	−	1.09474i	0.987133	−	0.159902i	$-0.0511179\pi$
$402$	14.5932	+	25.2761i	0.727842	+	1.26066i
$403$		0			0
$404$	0.192267	−	0.333017i	0.00956566	−	0.0165682i
$405$	−2.57913			−0.128158
$406$	8.31654	+	0.220071i	0.412743	+	0.0109219i
$407$	6.54708			0.324527
$408$	2.33475	−	4.04391i	0.115587	−	0.200203i
$409$	2.86671	+	4.96529i	0.141750	+	0.245518i	0.928156	−	0.372192i	$-0.121394\pi$
$409$	2.86671	+	4.96529i	0.141750	+	0.245518i	−0.786406	+	0.617710i	$0.788060\pi$
$410$	0.515546	+	0.892951i	0.0254610	+	0.0440997i
$411$	−11.3102	+	19.5899i	−0.557893	+	0.966299i
$412$	−0.830225			−0.0409022
$413$	15.2049	−	24.7968i	0.748185	−	1.22017i
$414$	11.7330			0.576644
$415$	2.34516	−	4.06193i	0.115119	−	0.199392i
$416$		0			0
$417$	−14.2977	−	24.7643i	−0.700161	−	1.21272i
$418$	21.2448	−	36.7971i	1.03912	−	1.79981i
$419$	−34.3458			−1.67790			−0.838950	−	0.544208i	$-0.816830\pi$
$419$	−34.3458			−1.67790			−0.838950	+	0.544208i	$0.816830\pi$
$420$	0.315395	−	0.514359i	0.0153897	−	0.0250982i
$421$	2.94167			0.143368			0.0716842	−	0.997427i	$-0.477163\pi$
$421$	2.94167			0.143368			0.0716842	+	0.997427i	$0.477163\pi$
$422$	−18.2191	+	31.5565i	−0.886894	+	1.53614i
$423$	−10.1896	−	17.6489i	−0.495437	−	0.858121i
$424$	−7.89148	−	13.6684i	−0.383244	−	0.663798i
$425$	−1.21835	+	2.11024i	−0.0590985	+	0.102362i
$426$	37.0100			1.79314
$427$	−19.3129	−	0.511055i	−0.934617	−	0.0247317i
$428$	0.950178			0.0459286
$429$		0			0
$430$	−2.47137	−	4.28053i	−0.119180	−	0.206426i
$431$	−19.8478	−	34.3773i	−0.956033	−	1.65590i	−0.731985	−	0.681321i	$-0.761406\pi$
$431$	−19.8478	−	34.3773i	−0.956033	−	1.65590i	−0.224048	−	0.974578i	$-0.571927\pi$
$432$	12.5781	−	21.7858i	0.605162	−	1.04817i
$433$	−9.83653			−0.472714			−0.236357	−	0.971666i	$-0.575953\pi$
$433$	−9.83653			−0.472714			−0.236357	+	0.971666i	$0.575953\pi$
$434$	6.04840	+	11.1471i	0.290332	+	0.535078i
$435$	−5.29475			−0.253864
$436$	0.715135	−	1.23865i	0.0342488	−	0.0593206i
$437$	−4.69000	−	8.12331i	−0.224353	−	0.388591i
$438$	9.93624	+	17.2101i	0.474772	+	0.822329i
$439$	−14.2733	+	24.7220i	−0.681226	+	1.17992i	0.293381	+	0.955996i	$0.405220\pi$
$439$	−14.2733	+	24.7220i	−0.681226	+	1.17992i	−0.974607	+	0.223922i	$0.928114\pi$
$440$	12.2936			0.586073
$441$	−16.8290	−	33.0739i	−0.801383	−	1.57495i
$442$		0			0
$443$	−1.66951	+	2.89167i	−0.0793207	+	0.137387i	−0.902957	−	0.429731i	$-0.858608\pi$
$443$	−1.66951	+	2.89167i	−0.0793207	+	0.137387i	0.823636	+	0.567118i	$0.191942\pi$
$444$	−0.175709	−	0.304337i	−0.00833880	−	0.0144432i
$445$	−2.01868	−	3.49646i	−0.0956947	−	0.165748i
$446$	−15.8595	+	27.4695i	−0.750969	+	1.30072i
$447$	−22.8170			−1.07921
$448$	10.5402	+	19.4254i	0.497978	+	0.917766i
$449$	−18.1851			−0.858206			−0.429103	−	0.903256i	$-0.641170\pi$
$449$	−18.1851			−0.858206			−0.429103	+	0.903256i	$0.641170\pi$
$450$	−15.9027	+	27.5443i	−0.749660	+	1.29845i
$451$	−2.44523	−	4.23526i	−0.115141	−	0.199430i
$452$	0.958084	+	1.65945i	0.0450645	+	0.0780539i
$453$	−2.16258	+	3.74570i	−0.101607	+	0.175988i
$454$	−0.625219			−0.0293430
$455$		0			0
$456$	−48.7265			−2.28183
$457$	−4.36466	+	7.55982i	−0.204170	+	0.353633i	−0.949868	−	0.312651i	$-0.898783\pi$
$457$	−4.36466	+	7.55982i	−0.204170	+	0.353633i	0.745698	+	0.666284i	$0.232116\pi$
$458$	−11.9519	−	20.7013i	−0.558476	−	0.967309i
$459$	1.85691	+	3.21625i	0.0866729	+	0.150122i
$460$	0.0635130	−	0.110008i	0.00296131	−	0.00512914i
$461$	−2.27124			−0.105782			−0.0528910	−	0.998600i	$-0.516844\pi$
$461$	−2.27124			−0.105782			−0.0528910	+	0.998600i	$0.516844\pi$
$462$	28.9685	−	47.2430i	1.34774	−	2.19794i
$463$	−5.48326			−0.254829			−0.127414	−	0.991850i	$-0.540668\pi$
$463$	−5.48326			−0.254829			−0.127414	+	0.991850i	$0.540668\pi$
$464$	4.32538	−	7.49178i	0.200801	−	0.347797i
$465$	−4.03570	−	6.99003i	−0.187151	−	0.324155i
$466$	5.38873	+	9.33356i	0.249628	+	0.432369i
$467$	−9.44095	+	16.3522i	−0.436875	+	0.756690i	−0.997447	−	0.0714164i	$-0.977248\pi$
$467$	−9.44095	+	16.3522i	−0.436875	+	0.756690i	0.560572	+	0.828106i	$0.310581\pi$
$468$		0			0
$469$	10.1591	−	16.5679i	0.469103	−	0.765032i
$470$	4.27260			0.197080
$471$	−5.55629	+	9.62377i	−0.256020	+	0.443440i
$472$	−15.9058	−	27.5496i	−0.732122	−	1.26807i
$473$	11.7217	+	20.3025i	0.538962	+	0.933510i
$474$	22.5859	−	39.1200i	1.03741	−	1.79684i
$475$	25.4270			1.16667
$476$	−0.145482	−	0.00384971i	−0.00666814	−	0.000176451i
$477$	28.9163			1.32399
$478$	9.33030	−	16.1606i	0.426758	−	0.739166i
$479$	−16.5677	−	28.6961i	−0.756997	−	1.31116i	−0.944375	−	0.328869i	$-0.893332\pi$
$479$	−16.5677	−	28.6961i	−0.756997	−	1.31116i	0.187378	−	0.982288i	$-0.440001\pi$
$480$	−0.644422	−	1.11617i	−0.0294137	−	0.0509461i
$481$		0			0
$482$	31.1104			1.41704
$483$	−5.83454	−	10.7530i	−0.265481	−	0.489276i
$484$	−1.64886			−0.0749480
$485$	4.29100	−	7.43222i	0.194844	−	0.337480i
$486$	−7.35838	−	12.7451i	−0.333783	−	0.578129i
$487$	−7.97814	−	13.8185i	−0.361524	−	0.626178i	0.626688	−	0.779270i	$-0.284410\pi$
$487$	−7.97814	−	13.8185i	−0.361524	−	0.626178i	−0.988212	+	0.153093i	$0.951077\pi$
$488$	−10.5645	+	18.2983i	−0.478234	+	0.828326i
$489$	41.3765			1.87111
$490$	7.76924	+	0.411465i	0.350979	+	0.0185881i
$491$	−31.6928			−1.43028			−0.715138	−	0.698983i	$-0.753636\pi$
$491$	−31.6928			−1.43028			−0.715138	+	0.698983i	$0.753636\pi$
$492$	−0.131249	+	0.227330i	−0.00591717	+	0.0102488i
$493$	0.638559	+	1.10602i	0.0287593	+	0.0498125i
$494$		0			0
$495$	−11.2617	+	19.5058i	−0.506174	+	0.876720i
$496$	13.1874			0.592130
$497$	−11.7532	−	21.6609i	−0.527202	−	0.971624i
$498$	−23.1233			−1.03618
$499$	−12.1092	+	20.9738i	−0.542083	+	0.938916i	0.456701	+	0.889620i	$0.349031\pi$
$499$	−12.1092	+	20.9738i	−0.542083	+	0.938916i	−0.998784	+	0.0492955i	$0.984302\pi$
$500$	0.370044	+	0.640935i	0.0165489	+	0.0286635i
$501$	6.51351	+	11.2817i	0.291002	+	0.504030i
$502$	−4.64215	+	8.04043i	−0.207189	+	0.358862i
$503$	0.854498			0.0381002			0.0190501	−	0.999819i	$-0.493936\pi$
$503$	0.854498			0.0381002			0.0190501	+	0.999819i	$0.493936\pi$
$504$	−40.5706	−	1.07357i	−1.80716	−	0.0478208i
$505$	−3.15572			−0.140428
$506$	5.83356	−	10.1040i	0.259333	−	0.449179i
$507$		0			0
$508$	−0.0941471	−	0.163068i	−0.00417710	−	0.00723495i
$509$	0.650000	−	1.12583i	0.0288108	−	0.0499017i	−0.851261	−	0.524743i	$-0.824161\pi$
$509$	0.650000	−	1.12583i	0.0288108	−	0.0499017i	0.880071	+	0.474842i	$0.157495\pi$
$510$	−1.79362			−0.0794227
$511$	6.91713	−	11.2807i	0.305996	−	0.499031i
$512$	24.0616			1.06338
$513$	19.3769	−	33.5618i	0.855511	−	1.48179i
$514$	11.4035	+	19.7514i	0.502987	+	0.871199i
$515$	3.40666	+	5.90051i	0.150115	+	0.260007i
$516$	0.629167	−	1.08975i	0.0276976	−	0.0479736i
$517$	−20.2649			−0.891248
$518$	2.36874	−	3.86305i	0.104077	−	0.169732i
$519$	−56.2351			−2.46845
$520$		0			0
$521$	12.5228	+	21.6901i	0.548632	+	0.950259i	0.998369	+	0.0570974i	$0.0181846\pi$
$521$	12.5228	+	21.6901i	0.548632	+	0.950259i	−0.449736	+	0.893161i	$0.648482\pi$
$522$	8.33490	+	14.4365i	0.364809	+	0.631867i
$523$	−6.41197	+	11.1059i	−0.280376	+	0.485625i	−0.971477	−	0.237133i	$-0.923792\pi$
$523$	−6.41197	+	11.1059i	−0.280376	+	0.485625i	0.691101	+	0.722758i	$0.257126\pi$
$524$	−1.53022			−0.0668482
$525$	33.1516	+	0.877253i	1.44686	+	0.0382865i
$526$	13.8219			0.602664
$527$	−0.973429	+	1.68603i	−0.0424032	+	0.0734446i
$528$	−28.8121	−	49.9040i	−1.25389	−	2.17179i
$529$	10.2122	+	17.6880i	0.444008	+	0.769045i
$530$	−3.03122	+	5.25022i	−0.131668	+	0.228055i
$531$	58.2827			2.52925
$532$	0.724263	+	1.33480i	0.0314008	+	0.0578711i
$533$		0			0
$534$	−9.95213	+	17.2376i	−0.430671	+	0.745944i
$535$	−3.89886	−	6.75303i	−0.168563	−	0.291959i
$536$	−10.6273	−	18.4071i	−0.459031	−	0.795066i
$537$	−29.9928	+	51.9490i	−1.29428	+	2.24176i
$538$	21.6828			0.934814
$539$	−36.8494	−	1.95157i	−1.58722	−	0.0840602i
$540$	0.524813			0.0225843
$541$	−14.3725	+	24.8938i	−0.617920	+	1.07027i	0.371944	+	0.928255i	$0.378691\pi$
$541$	−14.3725	+	24.8938i	−0.617920	+	1.07027i	−0.989865	+	0.142014i	$0.954642\pi$
$542$	3.59670	+	6.22966i	0.154491	+	0.267587i
$543$	23.8451	+	41.3009i	1.02329	+	1.77239i
$544$	−0.155438	+	0.269226i	−0.00666434	+	0.0115430i
$545$	−11.7376			−0.502785
$546$		0			0
$547$	−8.88085			−0.379718			−0.189859	−	0.981811i	$-0.560803\pi$
$547$	−8.88085			−0.379718			−0.189859	+	0.981811i	$0.560803\pi$
$548$	0.385516	−	0.667733i	0.0164684	−	0.0285241i
$549$	−19.3556	−	33.5248i	−0.826075	−	1.43080i
$550$	15.8134	+	27.3897i	0.674287	+	1.16790i
$551$	6.66339	−	11.5413i	0.283870	−	0.491677i
$552$	−13.3797			−0.569476
$553$	−30.0683	−	0.795664i	−1.27864	−	0.0338351i
$554$	26.5777			1.12918
$555$	−1.44198	+	2.49757i	−0.0612084	+	0.106016i
$556$	0.487345	+	0.844106i	0.0206680	+	0.0357981i
$557$	19.3637	+	33.5389i	0.820465	+	1.42109i	0.905336	+	0.424695i	$0.139619\pi$
$557$	19.3637	+	33.5389i	0.820465	+	1.42109i	−0.0848711	+	0.996392i	$0.527048\pi$
$558$	−12.7059	+	22.0072i	−0.537882	+	0.931639i
$559$		0			0
$560$	4.22890	−	6.89666i	0.178704	−	0.291437i
$561$	8.50710			0.359170
$562$	−1.47754	+	2.55918i	−0.0623263	+	0.107952i
$563$	−3.45441	−	5.98321i	−0.145586	−	0.252162i	0.784005	−	0.620754i	$-0.213173\pi$
$563$	−3.45441	−	5.98321i	−0.145586	−	0.252162i	−0.929591	+	0.368592i	$0.879840\pi$
$564$	0.543865	+	0.942002i	0.0229009	+	0.0396655i
$565$	7.86260	−	13.6184i	0.330782	−	0.572932i
$566$	21.7205			0.912979
$567$	4.42583	−	7.21784i	0.185868	−	0.303121i
$568$	−26.9522			−1.13089
$569$	1.41872	−	2.45730i	0.0594759	−	0.103015i	−0.834754	−	0.550623i	$-0.814390\pi$
$569$	1.41872	−	2.45730i	0.0594759	−	0.103015i	0.894230	+	0.447607i	$0.147724\pi$
$570$	9.35823	+	16.2089i	0.391973	+	0.678917i
$571$	23.3362	+	40.4195i	0.976589	+	1.69150i	0.674588	+	0.738195i	$0.264321\pi$
$571$	23.3362	+	40.4195i	0.976589	+	1.69150i	0.302001	+	0.953307i	$0.402345\pi$
$572$		0			0
$573$	−12.2453			−0.511557
$574$	−3.38366	−	0.0895379i	−0.141231	−	0.00373724i
$575$	6.98193			0.291167
$576$	−22.1418	+	38.3507i	−0.922576	+	1.59795i
$577$	−5.70441	−	9.88033i	−0.237478	−	0.411323i	0.722512	−	0.691358i	$-0.242987\pi$
$577$	−5.70441	−	9.88033i	−0.237478	−	0.411323i	−0.959990	+	0.280035i	$0.909654\pi$
$578$	−11.5057	−	19.9284i	−0.478572	−	0.828911i
$579$	−16.7070	+	28.9373i	−0.694318	+	1.20259i
$580$	0.180474			0.00749379
$581$	7.34321	+	13.5334i	0.304648	+	0.561460i
$582$	−42.3094			−1.75378
$583$	14.3770	−	24.9017i	0.595436	−	1.03132i
$584$	−7.23597	−	12.5331i	−0.299426	−	0.518622i
$585$		0			0
$586$	15.9617	−	27.6465i	0.659371	−	1.14206i
$587$	46.4410			1.91683			0.958413	−	0.285384i	$-0.0921211\pi$
$587$	46.4410			1.91683			0.958413	+	0.285384i	$0.0921211\pi$
$588$	0.898240	+	1.76530i	0.0370428	+	0.0727998i
$589$	20.3156			0.837088
$590$	−6.10961	+	10.5821i	−0.251529	+	0.435660i
$591$	−20.7754	−	35.9840i	−0.854585	−	1.48018i
$592$	−2.35596	−	4.08064i	−0.0968292	−	0.167713i
$593$	10.1303	−	17.5462i	0.416001	−	0.720535i	−0.579532	−	0.814950i	$-0.696765\pi$
$593$	10.1303	−	17.5462i	0.416001	−	0.720535i	0.995533	+	0.0944146i	$0.0300979\pi$
$594$	48.2031			1.97780
$595$	0.569594	+	1.04975i	0.0233511	+	0.0430356i
$596$	0.777728			0.0318570
$597$	−10.1696	+	17.6142i	−0.416212	+	0.720901i
$598$		0			0
$599$	19.4938	+	33.7642i	0.796494	+	1.37957i	0.921886	+	0.387462i	$0.126648\pi$
$599$	19.4938	+	33.7642i	0.796494	+	1.37957i	−0.125391	+	0.992107i	$0.540019\pi$
$600$	18.1346	−	31.4100i	0.740342	−	1.28231i
$601$	19.1390			0.780697			0.390348	−	0.920667i	$-0.372355\pi$
$601$	19.1390			0.780697			0.390348	+	0.920667i	$0.372355\pi$
$602$	16.2202	+	0.429217i	0.661087	+	0.0174936i
$603$	38.9412			1.58581
$604$	0.0737127	−	0.127674i	0.00299933	−	0.00519499i
$605$	6.76575	+	11.7186i	0.275067	+	0.476430i
$606$	7.77888	+	13.4734i	0.315995	+	0.547320i
$607$	−21.6668	+	37.5280i	−0.879428	+	1.52321i	−0.0274572	+	0.999623i	$0.508741\pi$
$607$	−21.6668	+	37.5280i	−0.879428	+	1.52321i	−0.851970	+	0.523590i	$0.824592\pi$
$608$	3.24400			0.131562
$609$	9.08589	−	14.8177i	0.368179	−	0.600442i
$610$	8.11595			0.328605
$611$		0			0
$612$	−0.145803	−	0.252538i	−0.00589373	−	0.0102082i
$613$	−5.15478	−	8.92834i	−0.208200	−	0.360612i	0.742948	−	0.669349i	$-0.233427\pi$
$613$	−5.15478	−	8.92834i	−0.208200	−	0.360612i	−0.951147	+	0.308737i	$0.900094\pi$
$614$	2.92077	−	5.05892i	0.117873	−	0.204161i
$615$	2.15422			0.0868664
$616$	−21.0960	+	34.4042i	−0.849982	+	1.38619i
$617$	−11.0699			−0.445659			−0.222829	−	0.974857i	$-0.571529\pi$
$617$	−11.0699			−0.445659			−0.222829	+	0.974857i	$0.571529\pi$
$618$	16.7949	−	29.0896i	0.675589	−	1.17015i
$619$	−16.8808	−	29.2384i	−0.678498	−	1.17519i	−0.975433	−	0.220295i	$-0.929298\pi$
$619$	−16.8808	−	29.2384i	−0.678498	−	1.17519i	0.296936	−	0.954897i	$-0.404035\pi$
$620$	0.137559	+	0.238259i	0.00552450	+	0.00956871i
$621$	5.32065	−	9.21563i	0.213510	−	0.369810i
$622$	−37.5794			−1.50680
$623$	13.2491	+	0.350597i	0.530816	+	0.0140464i
$624$		0			0
$625$	−7.83931	+	13.5781i	−0.313573	+	0.543124i
$626$	1.85964	+	3.22098i	0.0743260	+	0.128736i
$627$	−44.3860	−	76.8787i	−1.77260	−	3.07024i
$628$	0.189389	−	0.328031i	0.00755745	−	0.0130899i
$629$	0.695623			0.0277363
$630$	7.43473	+	13.7021i	0.296207	+	0.545904i
$631$	−38.5975			−1.53654			−0.768271	−	0.640125i	$-0.778883\pi$
$631$	−38.5975			−1.53654			−0.768271	+	0.640125i	$0.778883\pi$
$632$	−16.4480	+	28.4887i	−0.654265	+	1.13322i
$633$	38.0645	+	65.9296i	1.51293	+	2.62047i
$634$	16.5972	+	28.7473i	0.659161	+	1.14170i
$635$	−0.772627	+	1.33823i	−0.0306608	+	0.0531060i
$636$	−1.54339			−0.0611995
$637$		0			0
$638$	16.5763			0.656260
$639$	24.6899	−	42.7641i	0.976717	−	1.69172i
$640$	−4.19480	−	7.26560i	−0.165814	−	0.287198i
$641$	−9.76141	−	16.9073i	−0.385553	−	0.667797i	0.606293	−	0.795241i	$-0.292656\pi$
$641$	−9.76141	−	16.9073i	−0.385553	−	0.667797i	−0.991846	+	0.127445i	$0.959322\pi$
$642$	−19.2215	+	33.2926i	−0.758611	+	1.31395i
$643$	12.4718			0.491839			0.245920	−	0.969290i	$-0.420910\pi$
$643$	12.4718			0.491839			0.245920	+	0.969290i	$0.420910\pi$
$644$	0.198873	+	0.366520i	0.00783671	+	0.0144429i
$645$	−10.3266			−0.406611
$646$	2.25725	−	3.90967i	0.0888103	−	0.153824i
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	−0.966164	−	0.257929i	$-0.916960\pi$
$647$	−17.9695	−	31.1241i	−0.706455	−	1.22362i	0.259709	−	0.965687i	$-0.416373\pi$
$648$	−4.62984	−	8.01911i	−0.181877	−	0.315021i
$649$	28.9778	−	50.1910i	1.13748	−	1.97017i
$650$		0			0
$651$	26.4873	+	0.700904i	1.03812	+	0.0274706i
$652$	−1.41034			−0.0552332
$653$	−2.42944	+	4.20791i	−0.0950713	+	0.164668i	−0.909638	−	0.415401i	$-0.863641\pi$
$653$	−2.42944	+	4.20791i	−0.0950713	+	0.164668i	0.814567	+	0.580069i	$0.196975\pi$
$654$	28.9334	+	50.1141i	1.13138	+	1.95962i
$655$	6.27897	+	10.8755i	0.245340	+	0.424941i
$656$	−1.75982	+	3.04810i	−0.0687095	+	0.119008i
$657$	26.5144			1.03442
$658$	−7.33186	+	11.9571i	−0.285826	+	0.466137i
$659$	−23.6206			−0.920127			−0.460063	−	0.887886i	$-0.652173\pi$
$659$	−23.6206			−0.920127			−0.460063	+	0.887886i	$0.652173\pi$
$660$	0.601085	−	1.04111i	0.0233972	−	0.0405251i
$661$	8.19662	+	14.1970i	0.318812	+	0.552198i	0.980240	−	0.197810i	$-0.0633829\pi$
$661$	8.19662	+	14.1970i	0.318812	+	0.552198i	−0.661429	+	0.750008i	$0.730050\pi$
$662$	−0.427316	−	0.740134i	−0.0166081	−	0.0287661i
$663$		0			0
$664$	16.8393			0.653492
$665$	6.51475	−	10.6245i	0.252631	−	0.412002i
$666$	9.07974			0.351833
$667$	1.82968	−	3.16910i	0.0708456	−	0.122708i
$668$	−0.222016	−	0.384544i	−0.00859007	−	0.0148784i
$669$	33.1346	+	57.3908i	1.28106	+	2.21886i
$670$	−4.08210	+	7.07040i	−0.157705	+	0.273154i
$671$	−38.4939			−1.48604
$672$	4.22951	+	0.111921i	0.163157	+	0.00431744i
$673$	−14.2536			−0.549434			−0.274717	−	0.961525i	$-0.588584\pi$
$673$	−14.2536			−0.549434			−0.274717	+	0.961525i	$0.588584\pi$
$674$	3.94491	−	6.83278i	0.151952	−	0.263189i
$675$	14.4230	+	24.9814i	0.555143	+	0.961536i
$676$		0			0
$677$	5.13574	−	8.89537i	0.197383	−	0.341877i	−0.750296	−	0.661102i	$-0.770089\pi$
$677$	5.13574	−	8.89537i	0.197383	−	0.341877i	0.947679	+	0.319225i	$0.103423\pi$
$678$	−77.5255			−2.97735
$679$	13.4361	+	24.7624i	0.515629	+	0.950295i
$680$	1.30618			0.0500898
$681$	−0.653122	+	1.13124i	−0.0250277	+	0.0433492i
$682$	12.6345	+	21.8837i	0.483802	+	0.837969i
$683$	−1.11101	−	1.92432i	−0.0425115	−	0.0736321i	0.843987	−	0.536364i	$-0.180203\pi$
$683$	−1.11101	−	1.92432i	−0.0425115	−	0.0736321i	−0.886498	+	0.462732i	$0.846869\pi$
$684$	−1.52146	+	2.63524i	−0.0581744	+	0.100761i
$685$	−6.32754			−0.241763
$686$	−14.4837	+	21.0366i	−0.552989	+	0.803181i
$687$	−49.9413			−1.90538
$688$	8.43604	−	14.6117i	0.321621	−	0.557064i
$689$		0			0
$690$	2.56965	+	4.45076i	0.0978249	+	0.169438i
$691$	−1.32007	+	2.28643i	−0.0502179	+	0.0869800i	−0.890042	−	0.455879i	$-0.849325\pi$
$691$	−1.32007	+	2.28643i	−0.0502179	+	0.0869800i	0.839824	+	0.542859i	$0.182658\pi$
$692$	1.91680			0.0728659
$693$	−35.2628	−	64.9887i	−1.33952	−	2.46872i
$694$	2.57174			0.0976220
$695$	3.99944	−	6.92724i	0.151708	−	0.262765i
$696$	−9.50469	−	16.4626i	−0.360274	−	0.624014i
$697$	−0.259804	−	0.449993i	−0.00984077	−	0.0170447i
$698$	−15.3884	+	26.6534i	−0.582458	+	1.00885i
$699$	22.5169			0.851668
$700$	−1.12999	−	0.0299017i	−0.0427097	−	0.00113018i
$701$	8.89991			0.336145			0.168072	−	0.985775i	$-0.446246\pi$
$701$	8.89991			0.336145			0.168072	+	0.985775i	$0.446246\pi$
$702$		0			0
$703$	−3.62943	−	6.28635i	−0.136886	−	0.237094i
$704$	22.0175	+	38.1355i	0.829818	+	1.43729i
$705$	4.46328	−	7.73063i	0.168097	−	0.291152i
$706$	−3.21594			−0.121034
$707$	5.41528	−	8.83147i	0.203663	−	0.332142i
$708$	−3.11080			−0.116911
$709$	20.2972	−	35.1558i	0.762278	−	1.32030i	−0.179396	−	0.983777i	$-0.557414\pi$
$709$	20.2972	−	35.1558i	0.762278	−	1.32030i	0.941674	−	0.336527i	$-0.109252\pi$
$710$	5.17634	+	8.96569i	0.194265	+	0.336476i
$711$	−30.1347	−	52.1949i	−1.13014	−	1.95746i
$712$	7.24754	−	12.5531i	0.271613	−	0.470448i
$713$	5.57839			0.208912
$714$	3.07788	−	5.01954i	0.115187	−	0.187851i
$715$		0			0
$716$	1.02232	−	1.77071i	0.0382059	−	0.0661745i
$717$	−19.4934	−	33.7636i	−0.727995	−	1.26092i
$718$	2.25548	+	3.90661i	0.0841738	+	0.145793i
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	−0.969024	−	0.246968i	$-0.920566\pi$
$719$	−7.25674	+	12.5690i	−0.270631	+	0.468746i	0.698393	+	0.715715i	$0.253899\pi$
$720$	16.2100			0.604110
$721$	−22.3588	−	0.591655i	−0.832685	−	0.0220344i
$722$	−20.9069			−0.778076
$723$	32.4988	−	56.2896i	1.20864	−	2.09343i
$724$	−0.812773	−	1.40776i	−0.0302065	−	0.0523191i
$725$	4.95984	+	8.59070i	0.184204	+	0.319051i
$726$	33.3552	−	57.7730i	1.23793	−	2.14416i
$727$	−30.6942			−1.13839			−0.569193	−	0.822204i	$-0.692744\pi$
$727$	−30.6942			−1.13839			−0.569193	+	0.822204i	$0.692744\pi$
$728$		0			0
$729$	−40.3475			−1.49435
$730$	−2.77943	+	4.81411i	−0.102871	+	0.178178i
$731$	1.24542	+	2.15713i	0.0460635	+	0.0797842i
$732$	1.03309	+	1.78937i	0.0381842	+	0.0661369i
$733$	6.63218	−	11.4873i	0.244965	−	0.424292i	−0.717157	−	0.696912i	$-0.754557\pi$
$733$	6.63218	−	11.4873i	0.244965	−	0.424292i	0.962122	+	0.272620i	$0.0878901\pi$
$734$	−5.72708			−0.211390
$735$	8.86046	−	13.6275i	0.326823	−	0.502656i
$736$	0.890761			0.0328339
$737$	19.3613	−	33.5348i	0.713184	−	1.23527i
$738$	−3.39113	−	5.87361i	−0.124829	−	0.216211i
$739$	−3.62737	−	6.28279i	−0.133435	−	0.231116i	0.791564	−	0.611087i	$-0.209267\pi$
$739$	−3.62737	−	6.28279i	−0.133435	−	0.231116i	−0.924999	+	0.379971i	$0.875934\pi$
$740$	0.0491505	−	0.0851312i	0.00180681	−	0.00312948i
$741$		0			0
$742$	−9.49142	−	17.4925i	−0.348441	−	0.642171i
$743$	46.2694			1.69746			0.848730	−	0.528827i	$-0.177368\pi$
$743$	46.2694			1.69746			0.848730	+	0.528827i	$0.177368\pi$
$744$	14.4891	−	25.0959i	0.531196	−	0.920059i
$745$	−3.19125	−	5.52741i	−0.116918	−	0.202509i
$746$	−7.65991	−	13.2673i	−0.280449	−	0.485752i
$747$	−15.4259	+	26.7184i	−0.564403	+	0.977574i
$748$	−0.289969			−0.0106023
$749$	25.5893	+	0.677140i	0.935012	+	0.0247421i
$750$	−29.9430			−1.09336
$751$	18.0130	−	31.1995i	0.657305	−	1.13848i	−0.324006	−	0.946055i	$-0.605030\pi$
$751$	18.0130	−	31.1995i	0.657305	−	1.13848i	0.981311	−	0.192430i	$-0.0616368\pi$
$752$	7.29229	+	12.6306i	0.265922	+	0.460591i
$753$	9.69865	+	16.7985i	0.353438	+	0.612173i
$754$		0			0
$755$	−1.20986			−0.0440313
$756$	−0.900589	+	1.46872i	−0.0327541	+	0.0534168i
$757$	−10.5626			−0.383906			−0.191953	−	0.981404i	$-0.561482\pi$
$757$	−10.5626			−0.383906			−0.191953	+	0.981404i	$0.561482\pi$
$758$	3.19961	−	5.54189i	0.116215	−	0.201291i
$759$	−12.1878	−	21.1099i	−0.442390	−	0.766242i
$760$	−6.81504	−	11.8040i	−0.247207	−	0.428176i
$761$	−3.90601	+	6.76541i	−0.141593	+	0.245246i	−0.928097	−	0.372340i	$-0.878556\pi$
$761$	−3.90601	+	6.76541i	−0.141593	+	0.245246i	0.786504	+	0.617585i	$0.211889\pi$
$762$	7.61813			0.275976
$763$	20.1420	−	32.8485i	0.729191	−	1.18919i
$764$	0.417389			0.0151006
$765$	−1.19654	+	2.07248i	−0.0432612	+	0.0749305i
$766$	2.53010	+	4.38226i	0.0914163	+	0.158338i
$767$		0			0
$768$	3.38714	−	5.86671i	0.122223	−	0.211696i
$769$	−25.2915			−0.912033			−0.456017	−	0.889971i	$-0.650724\pi$
$769$	−25.2915			−0.912033			−0.456017	+	0.889971i	$0.650724\pi$
$770$	15.4962	+	0.410059i	0.558446	+	0.0147775i
$771$	47.6497			1.71606
$772$	0.569467	−	0.986345i	0.0204956	−	0.0354993i
$773$	−23.3002	−	40.3572i	−0.838051	−	1.45155i	−0.891522	−	0.452977i	$-0.850362\pi$
$773$	−23.3002	−	40.3572i	−0.838051	−	1.45155i	0.0534716	−	0.998569i	$-0.482971\pi$
$774$	16.2560	+	28.1563i	0.584311	+	1.01206i
$775$	−7.56086	+	13.0958i	−0.271594	+	0.470415i
$776$	30.8114			1.10606
$777$	−4.51515	−	8.32134i	−0.161980	−	0.298526i
$778$	−23.2827			−0.834727
$779$	−2.71106	+	4.69570i	−0.0971339	+	0.168241i
$780$		0			0
$781$	−24.5513	−	42.5241i	−0.878515	−	1.52163i
$782$	0.619812	−	1.07355i	0.0221644	−	0.0383899i
$783$	15.1188			0.540302
$784$	12.0438	+	23.6696i	0.430137	+	0.845344i
$785$	−3.10848			−0.110946
$786$	30.9554	−	53.6163i	1.10414	−	1.91243i
$787$	−19.8666	−	34.4099i	−0.708167	−	1.22658i	−0.965536	−	0.260268i	$-0.916189\pi$
$787$	−19.8666	−	34.4099i	−0.708167	−	1.22658i	0.257369	−	0.966313i	$-0.417144\pi$
$788$	0.708140	+	1.22653i	0.0252265	+	0.0436935i
$789$	14.4388	−	25.0087i	0.514034	−	0.890333i
$790$	12.6358			0.449560
$791$	24.6196	+	45.3734i	0.875371	+	1.61329i
$792$	−80.8641			−2.87338
$793$		0			0
$794$	−11.5210	−	19.9550i	−0.408865	−	0.708175i
$795$	6.33300	+	10.9691i	0.224608	+	0.389033i
$796$	0.346635	−	0.600389i	0.0122861	−	0.0212802i
$797$	−2.78598			−0.0986844			−0.0493422	−	0.998782i	$-0.515712\pi$
$797$	−2.78598			−0.0986844			−0.0493422	+	0.998782i	$0.515712\pi$
$798$	−61.4205	−	1.62530i	−2.17426	−	0.0575350i
$799$	−2.15313			−0.0761723
$800$	−1.20732	+	2.09115i	−0.0426853	+	0.0739332i
$801$	13.2784	+	22.9989i	0.469169	+	0.812625i
$802$	−17.4543	−	30.2317i	−0.616333	−	1.06752i
$803$	13.1828	−	22.8333i	0.465210	−	0.805768i
$804$	−2.07847			−0.0733018
$805$	1.78887	−	2.91736i	0.0630493	−	0.102823i
$806$		0			0
$807$	22.6505	−	39.2319i	0.797337	−	1.38103i
$808$	−5.66489	−	9.81188i	−0.199290	−	0.345181i
$809$	20.7293	+	35.9042i	0.728803	+	1.26232i	0.957389	+	0.288801i	$0.0932565\pi$
$809$	20.7293	+	35.9042i	0.728803	+	1.26232i	−0.228586	+	0.973524i	$0.573410\pi$
$810$	−1.77838	+	3.08024i	−0.0624859	+	0.108229i
$811$	−27.8622			−0.978375			−0.489188	−	0.872179i	$-0.662707\pi$
$811$	−27.8622			−0.978375			−0.489188	+	0.872179i	$0.662707\pi$
$812$	−0.309698	+	0.505068i	−0.0108683	+	0.0177244i
$813$	15.0289			0.527085
$814$	4.51439	−	7.81915i	0.158229	−	0.274061i
$815$	5.78705	+	10.0235i	0.202712	+	0.351107i
$816$	−3.06127	−	5.30227i	−0.107166	−	0.185617i
$817$	12.9960	−	22.5097i	0.454672	−	0.787515i
$818$	7.90671			0.276452
$819$		0			0
$820$	−0.0734276			−0.00256420
$821$	11.2101	−	19.4164i	0.391235	−	0.677638i	−0.601378	−	0.798965i	$-0.705381\pi$
$821$	11.2101	−	19.4164i	0.391235	−	0.677638i	0.992613	+	0.121326i	$0.0387148\pi$
$822$	15.5974	+	27.0156i	0.544023	+	0.942276i
$823$	1.18083	+	2.04525i	0.0411611	+	0.0712931i	0.885872	−	0.463930i	$-0.153561\pi$
$823$	1.18083	+	2.04525i	0.0411611	+	0.0712931i	−0.844711	+	0.535223i	$0.820228\pi$
$824$	−12.2307	+	21.1842i	−0.426077	+	0.737987i
$825$	66.0767			2.30050
$826$	−19.1305	−	35.2573i	−0.665637	−	1.22676i
$827$	43.3148			1.50620			0.753102	−	0.657904i	$-0.228557\pi$
$827$	43.3148			1.50620			0.753102	+	0.657904i	$0.228557\pi$
$828$	−0.417773	+	0.723604i	−0.0145186	+	0.0251470i
$829$	27.4640	+	47.5690i	0.953864	+	1.65214i	0.736947	+	0.675951i	$0.236267\pi$
$829$	27.4640	+	47.5690i	0.953864	+	1.65214i	0.216917	+	0.976190i	$0.430400\pi$
$830$	−3.23410	−	5.60162i	−0.112257	−	0.194435i
$831$	27.7638	−	48.0884i	0.963117	−	1.66817i
$832$		0			0
$833$	−3.91523	−	0.207353i	−0.135655	−	0.00718437i
$834$	−39.4346			−1.36551
$835$	−1.82200	+	3.15579i	−0.0630529	+	0.109211i
$836$	1.51292	+	2.62045i	0.0523254	+	0.0906303i
$837$	11.5237	+	19.9596i	0.398316	+	0.689903i
$838$	−23.6824	+	41.0190i	−0.818093	+	1.41698i
$839$	14.7410			0.508917			0.254459	−	0.967084i	$-0.418103\pi$
$839$	14.7410			0.508917			0.254459	+	0.967084i	$0.418103\pi$
$840$	−8.47817	−	15.6251i	−0.292525	−	0.539118i
$841$	−23.8009			−0.820721
$842$	2.02837	−	3.51323i	0.0699021	−	0.121074i
$843$	3.08697	+	5.34678i	0.106321	+	0.184153i
$844$	−1.29745	−	2.24725i	−0.0446600	−	0.0773535i
$845$		0			0
$846$	−28.1041			−0.966239
$847$	−44.4054	−	1.17505i	−1.52579	−	0.0403752i
$848$	−20.6942			−0.710642
$849$	22.6898	−	39.2999i	0.778713	−	1.34877i
$850$	1.68017	+	2.91013i	0.0576292	+	0.0998168i
$851$	−0.996594	−	1.72615i	−0.0341628	−	0.0591717i
$852$	−1.31781	+	2.28251i	−0.0451474	+	0.0781975i
$853$	24.1038			0.825297			0.412649	−	0.910890i	$-0.364604\pi$
$853$	24.1038			0.825297			0.412649	+	0.910890i	$0.364604\pi$
$854$	−13.9271	+	22.7130i	−0.476577	+	0.777221i
$855$	24.9720			0.854024
$856$	13.9978	−	24.2450i	0.478436	−	0.828676i
$857$	9.29249	+	16.0951i	0.317425	+	0.549797i	0.979950	−	0.199243i	$-0.0638483\pi$
$857$	9.29249	+	16.0951i	0.317425	+	0.549797i	−0.662525	+	0.749040i	$0.730515\pi$
$858$		0			0
$859$	−14.7487	+	25.5456i	−0.503221	+	0.871604i	0.496772	+	0.867881i	$0.334518\pi$
$859$	−14.7487	+	25.5456i	−0.503221	+	0.871604i	−0.999993	+	0.00372294i	$0.998815\pi$
$860$	0.351989			0.0120027
$861$	−3.69668	+	6.02870i	−0.125982	+	0.205458i
$862$	−54.7423			−1.86453
$863$	9.32173	−	16.1457i	0.317315	−	0.549606i	−0.662612	−	0.748963i	$-0.730552\pi$
$863$	9.32173	−	16.1457i	0.317315	−	0.549606i	0.979927	+	0.199357i	$0.0638853\pi$
$864$	1.84010	+	3.18716i	0.0626016	+	0.108429i
$865$	−7.86522	−	13.6230i	−0.267425	−	0.463194i
$866$	−6.78256	+	11.7477i	−0.230481	+	0.399204i
$867$	−48.0766			−1.63277
$868$	−0.902836	−	0.0238907i	−0.0306442	−	0.000810903i
$869$	−59.9312			−2.03303
$870$	−3.65087	+	6.32350i	−0.123776	+	0.214387i
$871$		0			0
$872$	−21.0705	−	36.4951i	−0.713536	−	1.23588i
$873$	−28.2251	+	48.8873i	−0.955276	+	1.65459i
$874$	−12.9355			−0.437551
$875$	9.50891	+	17.5248i	0.321460	+	0.592445i
$876$	−1.41519			−0.0478148
$877$	−18.8759	+	32.6941i	−0.637395	+	1.10400i	0.348608	+	0.937269i	$0.386655\pi$
$877$	−18.8759	+	32.6941i	−0.637395	+	1.10400i	−0.986002	+	0.166731i	$0.946679\pi$
$878$	19.6836	+	34.0930i	0.664290	+	1.15058i
$879$	−33.3481	−	57.7606i	−1.12480	−	1.94822i
$880$	8.05950	−	13.9595i	0.271686	−	0.470574i
$881$	29.8298			1.00499			0.502497	−	0.864579i	$-0.332415\pi$
$881$	29.8298			1.00499			0.502497	+	0.864579i	$0.332415\pi$
$882$	−51.1042	−	2.70652i	−1.72077	−	0.0911332i
$883$	32.3979			1.09028			0.545138	−	0.838346i	$-0.316477\pi$
$883$	32.3979			1.09028			0.545138	+	0.838346i	$0.316477\pi$
$884$		0			0
$885$	12.7646	+	22.1089i	0.429076	+	0.743181i
$886$	2.30234	+	3.98777i	0.0773487	+	0.133972i
$887$	12.9599	−	22.4472i	0.435151	−	0.753703i	−0.562157	−	0.827030i	$-0.690028\pi$
$887$	12.9599	−	22.4472i	0.435151	−	0.753703i	0.997308	+	0.0733272i	$0.0233617\pi$
$888$	−10.3541			−0.347459
$889$	−2.41927	−	4.45867i	−0.0811397	−	0.149539i
$890$	−5.56775			−0.186631
$891$	8.43483	−	14.6096i	0.282577	−	0.489439i
$892$	−1.12941	−	1.95620i	−0.0378155	−	0.0654984i
$893$	11.2340	+	19.4579i	0.375931	+	0.651132i
$894$	−15.7329	+	27.2502i	−0.526188	+	0.911384i
$895$	−16.7795			−0.560878
$896$	27.5316	+	0.728536i	0.919765	+	0.0243387i
$897$		0			0
$898$	−12.5391	+	21.7184i	−0.418435	+	0.724751i
$899$	3.96280	+	6.86376i	0.132167	+	0.228919i
$900$	−1.13249	−	1.96152i	−0.0377495	−	0.0653841i
$901$	1.52755	−	2.64579i	0.0508901	−	0.0881442i
$902$	−6.74420			−0.224557
$903$	17.7207	−	28.8997i	0.589709	−	0.961722i
$904$	56.4572			1.87774
$905$	−6.67010	+	11.5529i	−0.221722	+	0.384033i
$906$	2.98231	+	5.16552i	0.0990808	+	0.171613i
$907$	−7.77113	−	13.4600i	−0.258036	−	0.446931i	0.707680	−	0.706533i	$-0.249742\pi$
$907$	−7.77113	−	13.4600i	−0.258036	−	0.446931i	−0.965716	+	0.259602i	$0.916409\pi$
$908$	0.0222620	−	0.0385589i	0.000738791	−	0.00127962i
$909$	20.7576			0.688485
$910$		0			0
$911$	23.6358			0.783090			0.391545	−	0.920159i	$-0.371941\pi$
$911$	23.6358			0.783090			0.391545	+	0.920159i	$0.371941\pi$
$912$	−31.9445	+	55.3294i	−1.05779	+	1.83214i
$913$	15.3393	+	26.5684i	0.507656	+	0.879287i
$914$	6.01911	+	10.4254i	0.199094	+	0.344842i
$915$	8.47816	−	14.6846i	0.280279	−	0.485458i
$916$	1.70228			0.0562448
$917$	−41.2105	−	1.09051i	−1.36089	−	0.0360117i
$918$	5.12155			0.169036
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	0.221651	+	0.975126i	$0.428856\pi$
$919$	−22.2409	+	38.5223i	−0.733659	+	1.27073i	−0.955309	+	0.295608i	$0.904478\pi$
$920$	−1.87132	−	3.24123i	−0.0616957	−	0.106860i
$921$	−6.10224	−	10.5694i	−0.201076	−	0.348273i
$922$	−1.56608	+	2.71253i	−0.0515761	+	0.0893324i
$923$		0			0
$924$	1.88213	+	3.46874i	0.0619176	+	0.114113i
$925$	5.40307			0.177652
$926$	−3.78086	+	6.54864i	−0.124247	+	0.215202i
$927$	−22.4082	−	38.8121i	−0.735981	−	1.27476i
$928$	0.632782	+	1.09601i	0.0207721	+	0.0359783i
$929$	−1.47135	+	2.54846i	−0.0482735	+	0.0836121i	−0.889152	−	0.457611i	$-0.848705\pi$
$929$	−1.47135	+	2.54846i	−0.0482735	+	0.0836121i	0.840879	+	0.541223i	$0.182039\pi$
$930$	−11.1309			−0.364996
$931$	18.5539	+	36.4638i	0.608080	+	1.19505i
$932$	−0.767502			−0.0251404
$933$	−39.2566	+	67.9944i	−1.28520	+	2.22604i
$934$	13.0196	+	22.5506i	0.426014	+	0.737878i
$935$	1.18983	+	2.06085i	0.0389116	+	0.0673968i
$936$		0			0
$937$	−0.951020			−0.0310685			−0.0155342	−	0.999879i	$-0.504945\pi$
$937$	−0.951020			−0.0310685			−0.0155342	+	0.999879i	$0.504945\pi$
$938$	−12.7820	−	23.5569i	−0.417346	−	0.769161i
$939$	7.77052			0.253581
$940$	−0.152133	+	0.263503i	−0.00496205	+	0.00859451i
$941$	−11.0346	−	19.1125i	−0.359718	−	0.623050i	0.628196	−	0.778056i	$-0.283794\pi$
$941$	−11.0346	−	19.1125i	−0.359718	−	0.623050i	−0.987914	+	0.155006i	$0.950460\pi$
$942$	7.66242	+	13.2717i	0.249655	+	0.432416i
$943$	−0.744423	+	1.28938i	−0.0242417	+	0.0419879i
$944$	−41.7105			−1.35756
$945$	14.1337	+	0.374005i	0.459771	+	0.0121664i
$946$	32.3296			1.05113
$947$	−25.5859	+	44.3160i	−0.831429	+	1.44008i	0.0654762	+	0.997854i	$0.479143\pi$
$947$	−25.5859	+	44.3160i	−0.831429	+	1.44008i	−0.896905	+	0.442223i	$0.854190\pi$
$948$	1.60842	+	2.78587i	0.0522392	+	0.0904809i
$949$		0			0
$950$	17.5326	−	30.3674i	0.568833	−	0.985248i
$951$	69.3519			2.24889
$952$	−2.24144	+	3.65543i	−0.0726454	+	0.118473i
$953$	45.8470			1.48513			0.742565	−	0.669773i	$-0.233609\pi$
$953$	45.8470			1.48513			0.742565	+	0.669773i	$0.233609\pi$
$954$	19.9386	−	34.5347i	0.645536	−	1.11810i
$955$	−1.71267	−	2.96644i	−0.0554208	−	0.0959916i
$956$	0.664444	+	1.15085i	0.0214896	+	0.0372212i
$957$	17.3160	−	29.9923i	0.559748	−	0.969512i
$958$	−45.6955			−1.47635
$959$	10.8582	−	17.7080i	0.350629	−	0.571821i
$960$	−19.3972			−0.626042
$961$	9.45905	−	16.3836i	0.305131	−	0.528502i
$962$		0			0
$963$	25.6458	+	44.4198i	0.826424	+	1.43141i
$964$	−1.10774	+	1.91866i	−0.0356779	+	0.0617960i
$965$	−9.34676			−0.300883
$966$	−16.8653	−	0.446287i	−0.542632	−	0.0143590i
$967$	−19.2609			−0.619387			−0.309694	−	0.950836i	$-0.600227\pi$
$967$	−19.2609			−0.619387			−0.309694	+	0.950836i	$0.600227\pi$
$968$	−24.2906	+	42.0726i	−0.780730	+	1.35226i
$969$	−4.71598	−	8.16832i	−0.151499	−	0.262404i
$970$	−5.91752	−	10.2494i	−0.190000	−	0.329090i
$971$	−23.6663	+	40.9912i	−0.759487	+	1.31547i	0.183625	+	0.982996i	$0.441217\pi$
$971$	−23.6663	+	40.9912i	−0.759487	+	1.31547i	−0.943112	+	0.332474i	$0.892117\pi$
$972$	1.04803			0.0336156
$973$	12.5232	+	23.0800i	0.401474	+	0.739909i
$974$	−22.0046			−0.705072
$975$		0			0
$976$	13.8520	+	23.9923i	0.443390	+	0.767975i
$977$	−23.9285	−	41.4454i	−0.765541	−	1.32596i	−0.939960	−	0.341285i	$-0.889138\pi$
$977$	−23.9285	−	41.4454i	−0.765541	−	1.32596i	0.174418	−	0.984672i	$-0.444195\pi$
$978$	28.5302	−	49.4158i	0.912297	−	1.58014i
$979$	26.4078			0.843995
$980$	−0.302014	+	0.464499i	−0.00964747	+	0.0148379i
$981$	77.2074			2.46504
$982$	−21.8531	+	37.8506i	−0.697359	+	1.20786i
$983$	−7.88432	−	13.6560i	−0.251471	−	0.435560i	0.712460	−	0.701712i	$-0.247581\pi$
$983$	−7.88432	−	13.6560i	−0.251471	−	0.435560i	−0.963931	+	0.266152i	$0.914248\pi$
$984$	3.86707	+	6.69796i	0.123278	+	0.213523i
$985$	5.81142	−	10.0657i	0.185167	−	0.320719i
$986$	1.76122			0.0560885
$987$	13.9755	+	25.7567i	0.444846	+	0.819844i
$988$		0			0
$989$	3.56853	−	6.18088i	0.113473	−	0.196541i
$990$	15.5305	+	26.8995i	0.493590	+	0.854924i
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	0.946172	−	0.323663i	$-0.104914\pi$
$991$	6.06892	+	10.5117i	0.192786	+	0.333914i	−0.753387	+	0.657578i	$0.771581\pi$
$992$	−0.964622	+	1.67077i	−0.0306268	+	0.0530471i
$993$	−1.78555			−0.0566627
$994$	−33.9737	−	0.899007i	−1.07758	−	0.0285148i
$995$	−5.68938			−0.180366
$996$	0.823346	−	1.42608i	0.0260887	−	0.0451870i
$997$	−16.8938	−	29.2609i	−0.535032	−	0.926703i	−0.999162	−	0.0409358i	$-0.986966\pi$
$997$	−16.8938	−	29.2609i	−0.535032	−	0.926703i	0.464129	−	0.885767i	$-0.346367\pi$
$998$	16.6993	+	28.9240i	0.528607	+	0.915574i
$999$	4.11746	−	7.13166i	0.130271	−	0.225636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.j.170.10		24
7.2	even	3		8281.2.a.cp.1.3		12
7.4	even	3	inner	1183.2.e.j.508.10		24
7.5	odd	6		8281.2.a.co.1.3		12
13.6	odd	12		91.2.k.b.23.5	yes	12
13.11	odd	12		91.2.u.b.30.2	yes	12
13.12	even	2	inner	1183.2.e.j.170.3		24
39.11	even	12		819.2.do.e.667.5		12
39.32	even	12		819.2.bm.f.478.2		12
91.6	even	12		637.2.k.i.569.5		12
91.11	odd	12		91.2.k.b.4.2	✓	12
91.12	odd	6		8281.2.a.co.1.10		12
91.19	even	12		637.2.q.i.491.5		12
91.24	even	12		637.2.k.i.459.2		12
91.25	even	6	inner	1183.2.e.j.508.3		24
91.32	odd	12		91.2.u.b.88.2	yes	12
91.37	odd	12		637.2.q.g.589.5		12
91.45	even	12		637.2.u.g.361.2		12
91.51	even	6		8281.2.a.cp.1.10		12
91.58	odd	12		637.2.q.g.491.5		12
91.76	even	12		637.2.u.g.30.2		12
91.89	even	12		637.2.q.i.589.5		12
273.11	even	12		819.2.bm.f.550.5		12
273.32	even	12		819.2.do.e.361.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.2	✓	12	91.11	odd	12
91.2.k.b.23.5	yes	12	13.6	odd	12
91.2.u.b.30.2	yes	12	13.11	odd	12
91.2.u.b.88.2	yes	12	91.32	odd	12
637.2.k.i.459.2		12	91.24	even	12
637.2.k.i.569.5		12	91.6	even	12
637.2.q.g.491.5		12	91.58	odd	12
637.2.q.g.589.5		12	91.37	odd	12
637.2.q.i.491.5		12	91.19	even	12
637.2.q.i.589.5		12	91.89	even	12
637.2.u.g.30.2		12	91.76	even	12
637.2.u.g.361.2		12	91.45	even	12
819.2.bm.f.478.2		12	39.32	even	12
819.2.bm.f.550.5		12	273.11	even	12
819.2.do.e.361.5		12	273.32	even	12
819.2.do.e.667.5		12	39.11	even	12
1183.2.e.j.170.3		24	13.12	even	2	inner
1183.2.e.j.170.10		24	1.1	even	1	trivial
1183.2.e.j.508.3		24	91.25	even	6	inner
1183.2.e.j.508.10		24	7.4	even	3	inner
8281.2.a.co.1.3		12	7.5	odd	6
8281.2.a.co.1.10		12	91.12	odd	6
8281.2.a.cp.1.3		12	7.2	even	3
8281.2.a.cp.1.10		12	91.51	even	6

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.689527 - 1.19430i) q^{2} +(-1.44060 - 2.49520i) q^{3} +(0.0491037 + 0.0850501i) q^{4} +(0.402974 - 0.697972i) q^{5} -3.97334 q^{6} +(1.26180 + 2.32548i) q^{7} +2.89354 q^{8} +(-2.65067 + 4.59109i) q^{9} +O(q^{10})\)	\(q+(0.689527 - 1.19430i) q^{2} +(-1.44060 - 2.49520i) q^{3} +(0.0491037 + 0.0850501i) q^{4} +(0.402974 - 0.697972i) q^{5} -3.97334 q^{6} +(1.26180 + 2.32548i) q^{7} +2.89354 q^{8} +(-2.65067 + 4.59109i) q^{9} +(-0.555723 - 0.962541i) q^{10} +(2.63579 + 4.56532i) q^{11} +(0.141478 - 0.245047i) q^{12} +(3.64736 + 0.0965159i) q^{14} -2.32210 q^{15} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +(3.65541 + 6.33136i) q^{18} +(2.92234 - 5.06165i) q^{19} +0.0791501 q^{20} +(3.98477 - 6.49853i) q^{21} +7.26980 q^{22} +(0.802438 - 1.38986i) q^{23} +(-4.16844 - 7.21995i) q^{24} +(2.17522 + 3.76760i) q^{25} +6.63060 q^{27} +(-0.135823 + 0.221506i) q^{28} +2.28015 q^{29} +(-1.60115 + 2.77328i) q^{30} +(1.73795 + 3.01022i) q^{31} +(0.277517 + 0.480674i) q^{32} +(7.59424 - 13.1536i) q^{33} +0.772411 q^{34} +(2.13159 + 0.0564059i) q^{35} -0.520630 q^{36} +(0.620979 - 1.07557i) q^{37} +(-4.03007 - 6.98029i) q^{38} +(1.16602 - 2.01961i) q^{40} -0.927702 q^{41} +(-5.01357 - 9.23991i) q^{42} +4.44711 q^{43} +(-0.258854 + 0.448348i) q^{44} +(2.13630 + 3.70018i) q^{45} +(-1.10661 - 1.91670i) q^{46} +(-1.92209 + 3.32915i) q^{47} -10.9311 q^{48} +(-3.81571 + 5.86859i) q^{49} +5.99951 q^{50} +(0.806883 - 1.39756i) q^{51} +(-2.72727 - 4.72377i) q^{53} +(4.57198 - 7.91890i) q^{54} +4.24862 q^{55} +(3.65108 + 6.72888i) q^{56} -16.8397 q^{57} +(1.57223 - 2.72318i) q^{58} +(-5.49698 - 9.52106i) q^{59} +(-0.114024 - 0.197495i) q^{60} +(-3.65107 + 6.32385i) q^{61} +4.79346 q^{62} +(-14.0211 - 0.371024i) q^{63} +8.35330 q^{64} +(-10.4729 - 18.1396i) q^{66} +(-3.67278 - 6.36144i) q^{67} +(-0.0275031 + 0.0476367i) q^{68} -4.62397 q^{69} +(1.53716 - 2.50686i) q^{70} -9.31460 q^{71} +(-7.66982 + 13.2845i) q^{72} +(-2.50073 - 4.33139i) q^{73} +(-0.856364 - 1.48327i) q^{74} +(6.26726 - 10.8552i) q^{75} +0.573991 q^{76} +(-7.29072 + 11.8900i) q^{77} +(-5.68437 + 9.84562i) q^{79} +(-1.52886 - 2.64806i) q^{80} +(-1.60006 - 2.77138i) q^{81} +(-0.639676 + 1.10795i) q^{82} +5.81962 q^{83} +(0.748368 + 0.0198032i) q^{84} +0.451413 q^{85} +(3.06641 - 5.31117i) q^{86} +(-3.28479 - 5.68943i) q^{87} +(7.62677 + 13.2100i) q^{88} +(2.50473 - 4.33832i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(5.00739 - 8.67305i) q^{93} +(2.65067 + 4.59109i) q^{94} +(-2.35526 - 4.07942i) q^{95} +(0.799583 - 1.38492i) q^{96} +10.6483 q^{97} +(4.37780 + 8.60364i) q^{98} -27.9464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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