LMFDB - Embedded newform 372.2.ba.a.43.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(43,372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("372.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 0, 19])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.ba (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			43.14
Character	$\chi$	$=$	372.43
Dual form			372.2.ba.a.199.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17786 + 0.782714i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.774717 + 1.84386i) q^{4} +(-0.969598 + 1.67939i) q^{5} +(-0.757672 - 1.19412i) q^{6} +(1.41801 + 1.27678i) q^{7} +(-0.530704 + 2.77819i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-2.45654 + 1.21917i) q^{10} +(-3.63168 - 0.771938i) q^{11} +(0.0422255 - 1.99955i) q^{12} +(0.0373439 - 0.00392500i) q^{13} +(0.670865 + 2.61377i) q^{14} +(1.56884 - 1.13983i) q^{15} +(-2.79963 + 2.85694i) q^{16} +(0.452842 + 2.13045i) q^{17} +(0.206473 + 1.39906i) q^{18} +(2.50099 + 0.262865i) q^{19} +(-3.84773 - 0.486747i) q^{20} +(-0.776103 - 1.74316i) q^{21} +(-3.67342 - 3.75181i) q^{22} +(-1.45114 + 4.46616i) q^{23} +(1.61482 - 2.32215i) q^{24} +(0.619759 + 1.07345i) q^{25} +(0.0470581 + 0.0246065i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.25565 + 3.60376i) q^{28} +(5.00044 - 6.88252i) q^{29} +(2.74004 - 0.114608i) q^{30} +(2.01762 + 5.18933i) q^{31} +(-5.53374 + 1.17377i) q^{32} +(3.00373 + 2.18234i) q^{33} +(-1.13415 + 2.86383i) q^{34} +(-3.51912 + 1.14343i) q^{35} +(-0.851867 + 1.80951i) q^{36} +(5.38035 - 3.10635i) q^{37} +(2.74007 + 2.26718i) q^{38} +(-0.0357118 - 0.0116035i) q^{39} +(-4.15111 - 3.58499i) q^{40} +(1.01242 - 0.450758i) q^{41} +(0.450251 - 2.66066i) q^{42} +(0.778877 - 7.41052i) q^{43} +(-1.39018 - 7.29435i) q^{44} +(-1.89682 + 0.403182i) q^{45} +(-5.20497 + 4.12468i) q^{46} +(-1.57081 - 2.16203i) q^{47} +(3.71961 - 1.47123i) q^{48} +(-0.351119 - 3.34067i) q^{49} +(-0.110217 + 1.74948i) q^{50} +(0.452842 - 2.13045i) q^{51} +(0.0361681 + 0.0658161i) q^{52} +(6.72502 - 6.05524i) q^{53} +(0.380426 - 1.36209i) q^{54} +(4.81766 - 5.35056i) q^{55} +(-4.29969 + 3.26191i) q^{56} +(-2.17785 - 1.25738i) q^{57} +(11.2769 - 4.19274i) q^{58} +(2.38530 - 5.35748i) q^{59} +(3.31710 + 2.00968i) q^{60} -2.37245i q^{61} +(-1.68528 + 7.69154i) q^{62} +1.90812i q^{63} +(-7.43671 - 2.94880i) q^{64} +(-0.0296169 + 0.0665207i) q^{65} +(1.82983 + 4.92156i) q^{66} +(4.37145 + 2.52386i) q^{67} +(-3.57743 + 2.48548i) q^{68} +(3.14223 - 3.48980i) q^{69} +(-5.04002 - 1.40766i) q^{70} +(-1.82734 + 1.64534i) q^{71} +(-2.41971 + 1.46458i) q^{72} +(-1.27485 + 5.99771i) q^{73} +(8.76869 + 0.552429i) q^{74} +(-0.129565 - 1.23273i) q^{75} +(1.45287 + 4.81512i) q^{76} +(-4.16417 - 5.73149i) q^{77} +(-0.0329814 - 0.0416194i) q^{78} +(15.4937 - 3.29329i) q^{79} +(-2.08341 - 7.47175i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.54530 + 0.261504i) q^{82} +(-12.9124 + 5.74896i) q^{83} +(2.61287 - 2.78148i) q^{84} +(-4.01695 - 1.30518i) q^{85} +(6.71773 - 8.11893i) q^{86} +(-7.36750 + 4.25363i) q^{87} +(4.07194 - 9.67985i) q^{88} +(-10.0884 + 3.27793i) q^{89} +(-2.54977 - 1.00978i) q^{90} +(0.0579654 + 0.0421143i) q^{91} +(-9.35918 + 0.784307i) q^{92} +(0.267502 - 5.56133i) q^{93} +(-0.157942 - 3.77607i) q^{94} +(-2.86641 + 3.94527i) q^{95} +(5.53274 + 1.17848i) q^{96} +(-0.939717 - 2.89215i) q^{97} +(2.20122 - 4.20967i) q^{98} +(-1.85641 - 3.21540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) $ 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{30}\right)$

Coefficient data

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

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

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

$2$	1.17786	+	0.782714i	0.832874	+	0.553463i
$2$	1.17786	+	0.782714i	0.832874	+	0.553463i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	0.774717	+	1.84386i	0.387359	+	0.921929i
$5$	−0.969598	+	1.67939i	−0.433617	+	0.751047i	−0.997182	−	0.0750248i	$-0.976096\pi$
$5$	−0.969598	+	1.67939i	−0.433617	+	0.751047i	0.563564	+	0.826072i	$0.309430\pi$
$6$	−0.757672	−	1.19412i	−0.309318	−	0.487499i
$7$	1.41801	+	1.27678i	0.535958	+	0.482578i	0.892090	−	0.451857i	$-0.149238\pi$
$7$	1.41801	+	1.27678i	0.535958	+	0.482578i	−0.356133	+	0.934435i	$0.615905\pi$
$8$	−0.530704	+	2.77819i	−0.187632	+	0.982239i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−2.45654	+	1.21917i	−0.776825	+	0.385537i
$11$	−3.63168	−	0.771938i	−1.09499	−	0.232748i	−0.375206	−	0.926942i	$-0.622428\pi$
$11$	−3.63168	−	0.771938i	−1.09499	−	0.232748i	−0.719788	+	0.694193i	$0.755761\pi$
$12$	0.0422255	−	1.99955i	0.0121895	−	0.577222i
$13$	0.0373439	−	0.00392500i	0.0103573	−	0.00108860i	−0.0993484	−	0.995053i	$-0.531676\pi$
$13$	0.0373439	−	0.00392500i	0.0103573	−	0.00108860i	0.109706	+	0.993964i	$0.465009\pi$
$14$	0.670865	+	2.61377i	0.179296	+	0.698560i
$15$	1.56884	−	1.13983i	0.405073	−	0.294303i
$16$	−2.79963	+	2.85694i	−0.699907	+	0.714234i
$17$	0.452842	+	2.13045i	0.109830	+	0.516711i	0.998327	+	0.0578273i	$0.0184173\pi$
$17$	0.452842	+	2.13045i	0.109830	+	0.516711i	−0.888496	+	0.458884i	$0.848249\pi$
$18$	0.206473	+	1.39906i	0.0486663	+	0.329762i
$19$	2.50099	+	0.262865i	0.573767	+	0.0603053i	0.386968	−	0.922093i	$-0.373522\pi$
$19$	2.50099	+	0.262865i	0.573767	+	0.0603053i	0.186798	+	0.982398i	$0.440189\pi$
$20$	−3.84773	−	0.486747i	−0.860378	−	0.108840i
$21$	−0.776103	−	1.74316i	−0.169360	−	0.380388i
$22$	−3.67342	−	3.75181i	−0.783175	−	0.799888i
$23$	−1.45114	+	4.46616i	−0.302584	+	0.931258i	0.677984	+	0.735077i	$0.262854\pi$
$23$	−1.45114	+	4.46616i	−0.302584	+	0.931258i	−0.980568	+	0.196181i	$0.937146\pi$
$24$	1.61482	−	2.32215i	0.329623	−	0.474006i
$25$	0.619759	+	1.07345i	0.123952	+	0.214691i
$26$	0.0470581	+	0.0246065i	0.00922885	+	0.00482573i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−1.25565	+	3.60376i	−0.237295	+	0.681046i
$29$	5.00044	−	6.88252i	0.928559	−	1.27805i	−0.0318602	−	0.999492i	$-0.510143\pi$
$29$	5.00044	−	6.88252i	0.928559	−	1.27805i	0.960419	−	0.278559i	$-0.0898569\pi$
$30$	2.74004	−	0.114608i	0.500261	−	0.0209244i
$31$	2.01762	+	5.18933i	0.362376	+	0.932032i
$31$	2.01762	+	5.18933i	0.362376	+	0.932032i
$32$	−5.53374	+	1.17377i	−0.978236	+	0.207495i
$33$	3.00373	+	2.18234i	0.522883	+	0.379897i
$34$	−1.13415	+	2.86383i	−0.194505	+	0.491142i
$35$	−3.51912	+	1.14343i	−0.594840	+	0.193275i
$36$	−0.851867	+	1.80951i	−0.141978	+	0.301585i
$37$	5.38035	−	3.10635i	0.884524	−	0.510680i	0.0123767	−	0.999923i	$-0.496060\pi$
$37$	5.38035	−	3.10635i	0.884524	−	0.510680i	0.872147	+	0.489243i	$0.162727\pi$
$38$	2.74007	+	2.26718i	0.444499	+	0.367785i
$39$	−0.0357118	−	0.0116035i	−0.00571846	−	0.00185804i
$40$	−4.15111	−	3.58499i	−0.656348	−	0.566837i
$41$	1.01242	−	0.450758i	0.158113	−	0.0703965i	−0.326154	−	0.945317i	$-0.605753\pi$
$41$	1.01242	−	0.450758i	0.158113	−	0.0703965i	0.484267	+	0.874920i	$0.339086\pi$
$42$	0.450251	−	2.66066i	0.0694752	−	0.410549i
$43$	0.778877	−	7.41052i	0.118778	−	1.13009i	−0.759022	−	0.651065i	$-0.774322\pi$
$43$	0.778877	−	7.41052i	0.118778	−	1.13009i	0.877799	−	0.479029i	$-0.159011\pi$
$44$	−1.39018	−	7.29435i	−0.209578	−	1.09966i
$45$	−1.89682	+	0.403182i	−0.282761	+	0.0601028i
$46$	−5.20497	+	4.12468i	−0.767431	+	0.608152i
$47$	−1.57081	−	2.16203i	−0.229126	−	0.315365i	0.678938	−	0.734195i	$-0.262440\pi$
$47$	−1.57081	−	2.16203i	−0.229126	−	0.315365i	−0.908065	+	0.418830i	$0.862440\pi$
$48$	3.71961	−	1.47123i	0.536879	−	0.212354i
$49$	−0.351119	−	3.34067i	−0.0501598	−	0.477239i
$50$	−0.110217	+	1.74948i	−0.0155871	+	0.247413i
$51$	0.452842	−	2.13045i	0.0634106	−	0.298323i
$52$	0.0361681	+	0.0658161i	0.00501561	+	0.00912705i
$53$	6.72502	−	6.05524i	0.923753	−	0.831751i	−0.0623213	−	0.998056i	$-0.519850\pi$
$53$	6.72502	−	6.05524i	0.923753	−	0.831751i	0.986074	+	0.166305i	$0.0531837\pi$
$54$	0.380426	−	1.36209i	0.0517694	−	0.185356i
$55$	4.81766	−	5.35056i	0.649613	−	0.721469i
$56$	−4.29969	+	3.26191i	−0.574571	+	0.435891i
$57$	−2.17785	−	1.25738i	−0.288464	−	0.166544i
$58$	11.2769	−	4.19274i	1.48073	−	0.550534i
$59$	2.38530	−	5.35748i	0.310540	−	0.697484i	−0.689090	−	0.724676i	$-0.741990\pi$
$59$	2.38530	−	5.35748i	0.310540	−	0.697484i	0.999630	+	0.0271913i	$0.00865632\pi$
$60$	3.31710	+	2.00968i	0.428235	+	0.259448i
$61$		−	2.37245i		−	0.303762i	−0.988399	−	0.151881i	$-0.951467\pi$
$61$		−	2.37245i		−	0.303762i	0.988399	−	0.151881i	$-0.0485330\pi$
$62$	−1.68528	+	7.69154i	−0.214031	+	0.976827i
$63$			1.90812i			0.240401i
$64$	−7.43671	−	2.94880i	−0.929588	−	0.368600i
$65$	−0.0296169	+	0.0665207i	−0.00367353	+	0.00825088i
$66$	1.82983	+	4.92156i	0.225237	+	0.605802i
$67$	4.37145	+	2.52386i	0.534057	+	0.308338i	0.742667	−	0.669661i	$-0.233560\pi$
$67$	4.37145	+	2.52386i	0.534057	+	0.308338i	−0.208610	+	0.977999i	$0.566894\pi$
$68$	−3.57743	+	2.48548i	−0.433827	+	0.301408i
$69$	3.14223	−	3.48980i	0.378280	−	0.420123i
$70$	−5.04002	−	1.40766i	−0.602397	−	0.168248i
$71$	−1.82734	+	1.64534i	−0.216865	+	0.195266i	−0.770402	−	0.637558i	$-0.779944\pi$
$71$	−1.82734	+	1.64534i	−0.216865	+	0.195266i	0.553537	+	0.832825i	$0.313278\pi$
$72$	−2.41971	+	1.46458i	−0.285166	+	0.172603i
$73$	−1.27485	+	5.99771i	−0.149210	+	0.701979i	0.838400	+	0.545055i	$0.183491\pi$
$73$	−1.27485	+	5.99771i	−0.149210	+	0.701979i	−0.987611	+	0.156924i	$0.949842\pi$
$74$	8.76869	+	0.552429i	1.01934	+	0.0642186i
$75$	−0.129565	−	1.23273i	−0.0149609	−	0.142343i
$76$	1.45287	+	4.81512i	0.166656	+	0.552332i
$77$	−4.16417	−	5.73149i	−0.474551	−	0.653164i
$78$	−0.0329814	−	0.0416194i	−0.00373440	−	0.00471247i
$79$	15.4937	−	3.29329i	1.74318	−	0.370524i	0.777221	−	0.629228i	$-0.216629\pi$
$79$	15.4937	−	3.29329i	1.74318	−	0.370524i	0.965957	+	0.258704i	$0.0832956\pi$
$80$	−2.08341	−	7.47175i	−0.232932	−	0.835368i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	1.54530	+	0.261504i	0.170650	+	0.0288783i
$83$	−12.9124	+	5.74896i	−1.41732	+	0.631030i	−0.965339	−	0.261000i	$-0.915948\pi$
$83$	−12.9124	+	5.74896i	−1.41732	+	0.631030i	−0.451977	+	0.892029i	$0.649281\pi$
$84$	2.61287	−	2.78148i	0.285088	−	0.303484i
$85$	−4.01695	−	1.30518i	−0.435699	−	0.141567i
$86$	6.71773	−	8.11893i	0.724392	−	0.875487i
$87$	−7.36750	+	4.25363i	−0.789879	+	0.456037i
$88$	4.07194	−	9.67985i	0.434071	−	1.03188i
$89$	−10.0884	+	3.27793i	−1.06937	+	0.347460i	−0.790242	−	0.612794i	$-0.790045\pi$
$89$	−10.0884	+	3.27793i	−1.06937	+	0.347460i	−0.279128	+	0.960254i	$0.590045\pi$
$90$	−2.54977	−	1.00978i	−0.268769	−	0.106440i
$91$	0.0579654	+	0.0421143i	0.00607643	+	0.00441478i
$92$	−9.35918	+	0.784307i	−0.975762	+	0.0817696i
$93$	0.267502	−	5.56133i	0.0277387	−	0.576684i
$94$	−0.157942	−	3.77607i	−0.0162905	−	0.389472i
$95$	−2.86641	+	3.94527i	−0.294087	+	0.404776i
$96$	5.53274	+	1.17848i	0.564683	+	0.120278i
$97$	−0.939717	−	2.89215i	−0.0954138	−	0.293653i	0.891948	−	0.452139i	$-0.149339\pi$
$97$	−0.939717	−	2.89215i	−0.0954138	−	0.293653i	−0.987361	+	0.158485i	$0.949339\pi$
$98$	2.20122	−	4.20967i	0.222357	−	0.425241i
$99$	−1.85641	−	3.21540i	−0.186576	−	0.323159i
$100$	−1.49916	+	1.97437i	−0.149916	+	0.197437i
$101$	−2.76783	+	8.51850i	−0.275409	+	0.847623i	0.713702	+	0.700450i	$0.247017\pi$
$101$	−2.76783	+	8.51850i	−0.275409	+	0.847623i	−0.989111	+	0.147173i	$0.952983\pi$
$102$	2.20092	−	2.15494i	0.217924	−	0.213370i
$103$	−2.26081	−	5.07787i	−0.222765	−	0.500338i	0.767242	−	0.641358i	$-0.221628\pi$
$103$	−2.26081	−	5.07787i	−0.222765	−	0.500338i	−0.990007	+	0.141020i	$0.954962\pi$
$104$	−0.00891416	+	0.105832i	−0.000874105	+	0.0103776i
$105$	3.67995	+	0.386779i	0.359127	+	0.0377457i
$106$	12.6607	−	1.86846i	1.22971	−	0.181481i
$107$	2.81384	+	13.2381i	0.272024	+	1.27977i	0.875822	+	0.482635i	$0.160320\pi$
$107$	2.81384	+	13.2381i	0.272024	+	1.27977i	−0.603798	+	0.797138i	$0.706347\pi$
$108$	1.51421	−	1.30658i	0.145705	−	0.125726i
$109$	−0.393847	+	0.286147i	−0.0377237	+	0.0274079i	−0.606487	−	0.795093i	$-0.707422\pi$
$109$	−0.393847	+	0.286147i	−0.0377237	+	0.0274079i	0.568764	+	0.822501i	$0.307422\pi$
$110$	9.86250	−	2.53136i	0.940352	−	0.241356i
$111$	−6.17866	+	0.649403i	−0.586452	+	0.0616386i
$112$	−7.61759	+	0.476652i	−0.719794	+	0.0450394i
$113$	18.2598	+	3.88124i	1.71774	+	0.365116i	0.958366	−	0.285541i	$-0.0921734\pi$
$113$	18.2598	+	3.88124i	1.71774	+	0.365116i	0.759371	+	0.650658i	$0.225507\pi$
$114$	−1.58104	−	3.18566i	−0.148078	−	0.298364i
$115$	−6.09341	−	6.76741i	−0.568213	−	0.631065i
$116$	16.5643	+	3.88810i	1.53796	+	0.361001i
$117$	0.0279048	+	0.0251256i	0.00257980	+	0.00232286i
$118$	7.00293	−	4.44336i	0.644672	−	0.409044i
$119$	−2.07799	+	3.59919i	−0.190489	+	0.329937i
$120$	2.33408	+	4.96346i	0.213071	+	0.453100i
$121$	2.54424	+	1.13277i	0.231295	+	0.102979i
$122$	1.85695	−	2.79442i	0.168121	−	0.252995i
$123$	−1.10823			−0.0999257
$124$	−8.00531	+	7.74048i	−0.718898	+	0.695115i
$125$	−12.0997			−1.08223
$126$	−1.49351	+	2.24750i	−0.133053	+	0.200224i
$127$	12.0394	+	5.36026i	1.06832	+	0.475647i	0.864122	−	0.503283i	$-0.167875\pi$
$127$	12.0394	+	5.36026i	1.06832	+	0.475647i	0.204198	+	0.978930i	$0.434541\pi$
$128$	−6.45135	−	9.29409i	−0.570224	−	0.821489i
$129$	−3.72567	+	6.45305i	−0.328027	+	0.568160i
$130$	−0.0869514	+	0.0551706i	−0.00762614	+	0.00483879i
$131$	12.9802	+	11.6874i	1.13409	+	1.02113i	0.999543	+	0.0302270i	$0.00962302\pi$
$131$	12.9802	+	11.6874i	1.13409	+	1.02113i	0.134542	+	0.990908i	$0.457044\pi$
$132$	−1.69688	+	7.22915i	−0.147695	+	0.629217i
$133$	3.21081	+	3.56597i	0.278413	+	0.309208i
$134$	3.17350	+	6.39435i	0.274149	+	0.552388i
$135$	1.89682	+	0.403182i	0.163252	+	0.0347003i
$136$	−6.15914	+	0.127441i	−0.528142	+	0.0109280i
$137$	−8.11165	+	0.852569i	−0.693025	+	0.0728399i	−0.444491	−	0.895783i	$-0.646615\pi$
$137$	−8.11165	+	0.852569i	−0.693025	+	0.0728399i	−0.248534	+	0.968623i	$0.579949\pi$
$138$	6.43264	−	1.65104i	0.547582	−	0.140546i
$139$	−0.550550	+	0.399998i	−0.0466970	+	0.0339274i	−0.610889	−	0.791716i	$-0.709188\pi$
$139$	−0.550550	+	0.399998i	−0.0466970	+	0.0339274i	0.564192	+	0.825644i	$0.309188\pi$
$140$	−4.83465	−	5.60292i	−0.408602	−	0.473533i
$141$	0.555628	+	2.61402i	0.0467923	+	0.220140i
$142$	−3.44019	+	0.507703i	−0.288694	+	0.0426055i
$143$	−0.138651	−	0.0145728i	−0.0115946	−	0.00121864i
$144$	−3.99643	−	0.168864i	−0.333036	−	0.0140720i
$145$	6.71003	+	15.0710i	0.557238	+	1.25158i
$146$	−6.19610	+	6.06663i	−0.512793	+	0.502078i
$147$	−1.03801	+	3.19467i	−0.0856136	+	0.263492i
$148$	9.89591	+	7.51406i	0.813439	+	0.617652i
$149$	−2.56452	−	4.44188i	−0.210094	−	0.363893i	0.741650	−	0.670787i	$-0.234044\pi$
$149$	−2.56452	−	4.44188i	−0.210094	−	0.363893i	−0.951744	+	0.306894i	$0.900710\pi$
$150$	0.812264	−	1.55340i	0.0663211	−	0.126834i
$151$	−5.90363	−	18.1695i	−0.480430	−	1.47861i	−0.838492	−	0.544914i	$-0.816562\pi$
$151$	−5.90363	−	18.1695i	−0.480430	−	1.47861i	0.358061	−	0.933698i	$-0.383438\pi$
$152$	−2.05758	+	6.80873i	−0.166891	+	0.552261i
$153$	−1.28023	+	1.76208i	−0.103500	+	0.142456i
$154$	−0.418700	−	10.0103i	−0.0337398	−	0.806649i
$155$	−10.6712	−	1.64319i	−0.857133	−	0.131984i
$156$	−0.00627139	−	0.0748369i	−0.000502113	−	0.00599174i
$157$	−2.15538	−	1.56597i	−0.172018	−	0.124978i	0.498445	−	0.866921i	$-0.333904\pi$
$157$	−2.15538	−	1.56597i	−0.172018	−	0.124978i	−0.670463	+	0.741943i	$0.733904\pi$
$158$	20.8271	+	8.24810i	1.65692	+	0.656184i
$159$	−8.60650	+	2.79642i	−0.682540	+	0.221771i
$160$	3.39428	−	10.4314i	0.268342	−	0.824675i
$161$	−7.76004	+	4.48026i	−0.611577	+	0.353094i
$162$	−0.901546	+	1.08959i	−0.0708322	+	0.0856065i
$163$	12.1065	+	3.93365i	0.948256	+	0.308107i	0.742007	−	0.670392i	$-0.233874\pi$
$163$	12.1065	+	3.93365i	0.948256	+	0.308107i	0.206249	+	0.978499i	$0.433874\pi$
$164$	1.61547	+	1.51755i	0.126147	+	0.118500i
$165$	−6.57742	+	2.92846i	−0.512051	+	0.227980i
$166$	−19.7088	−	3.33522i	−1.52970	−	0.258863i
$167$	2.15395	−	20.4935i	0.166678	−	1.58584i	−0.516957	−	0.856011i	$-0.672935\pi$
$167$	2.15395	−	20.4935i	0.166678	−	1.58584i	0.683635	−	0.729824i	$-0.260398\pi$
$168$	5.25470	−	1.23106i	0.405409	−	0.0949786i
$169$	−12.7145	+	2.70256i	−0.978042	+	0.207889i
$170$	−3.70982	−	4.68145i	−0.284530	−	0.359051i
$171$	1.47814	+	2.03449i	0.113036	+	0.155581i
$172$	14.2674	−	4.30492i	1.08788	−	0.328247i
$173$	0.418189	+	3.97881i	0.0317944	+	0.302503i	0.998850	+	0.0479390i	$0.0152653\pi$
$173$	0.418189	+	3.97881i	0.0317944	+	0.302503i	−0.967056	+	0.254564i	$0.918068\pi$
$174$	−12.0073	−	0.756461i	−0.910269	−	0.0573472i
$175$	−0.491743	+	2.31347i	−0.0371723	+	0.174882i
$176$	12.3727	−	8.21435i	0.932630	−	0.619180i
$177$	−4.35817	+	3.92411i	−0.327580	+	0.294954i
$178$	−14.4484	−	4.03541i	−1.08296	−	0.302466i
$179$	7.05081	−	7.83072i	0.527002	−	0.585295i	−0.419596	−	0.907711i	$-0.637828\pi$
$179$	7.05081	−	7.83072i	0.527002	−	0.585295i	0.946598	+	0.322416i	$0.104495\pi$
$180$	−2.21291	−	3.18512i	−0.164940	−	0.237405i
$181$	−18.1830	−	10.4980i	−1.35153	−	0.780308i	−0.363069	−	0.931762i	$-0.618271\pi$
$181$	−18.1830	−	10.4980i	−1.35153	−	0.780308i	−0.988464	+	0.151454i	$0.951604\pi$
$182$	0.0353118	+	0.0949752i	0.00261748	+	0.00704003i
$183$	−0.964964	+	2.16735i	−0.0713322	+	0.160215i
$184$	−11.6377	−	6.40176i	−0.857944	−	0.471944i
$185$			12.0476i			0.885759i
$186$	4.66802	−	6.34111i	0.342276	−	0.464952i
$187$		−	8.08671i		−	0.591358i
$188$	2.76955	−	4.57132i	0.201990	−	0.333398i
$189$	0.776103	−	1.74316i	0.0564532	−	0.126796i
$190$	−6.46425	+	2.40341i	−0.468966	+	0.174362i
$191$	−14.2787	−	8.24382i	−1.03317	−	0.596502i	−0.115280	−	0.993333i	$-0.536776\pi$
$191$	−14.2787	−	8.24382i	−1.03317	−	0.596502i	−0.917892	+	0.396831i	$0.870110\pi$
$192$	5.59438	+	5.71864i	0.403740	+	0.412707i
$193$	2.65492	−	2.94858i	0.191105	−	0.212244i	−0.639976	−	0.768395i	$-0.721056\pi$
$193$	2.65492	−	2.94858i	0.191105	−	0.212244i	0.831081	+	0.556151i	$0.187722\pi$
$194$	1.15687	−	4.14208i	0.0830585	−	0.297384i
$195$	0.0541128	−	0.0487234i	0.00387510	−	0.00348916i
$196$	5.88771	−	3.23549i	0.420550	−	0.231106i
$197$	−0.812121	+	3.82073i	−0.0578613	+	0.272216i	−0.997562	−	0.0697811i	$-0.977770\pi$
$197$	−0.812121	+	3.82073i	−0.0578613	+	0.272216i	0.939701	+	0.341997i	$0.111103\pi$
$198$	0.330142	−	5.24033i	0.0234622	−	0.372414i
$199$	1.74591	+	16.6112i	0.123764	+	1.17754i	0.863396	+	0.504527i	$0.168333\pi$
$199$	1.74591	+	16.6112i	0.123764	+	1.17754i	−0.739632	+	0.673012i	$0.765000\pi$
$200$	−3.31117	+	1.15212i	−0.234135	+	0.0814674i
$201$	−2.96697	−	4.08369i	−0.209274	−	0.288041i
$202$	−9.92767	+	7.86720i	−0.698509	+	0.553534i
$203$	15.8782	−	3.37501i	1.11443	−	0.236879i
$204$	4.27908	−	0.815523i	0.299596	−	0.0570980i
$205$	−0.224639	+	2.13730i	−0.0156895	+	0.149276i
$206$	1.31160	−	7.75060i	0.0913832	−	0.540010i
$207$	−4.29000	+	1.91003i	−0.298176	+	0.132756i
$208$	−0.0933355	+	0.117678i	−0.00647165	+	0.00815948i
$209$	−8.87989	−	2.88525i	−0.614235	−	0.199577i
$210$	4.03174	+	3.33592i	0.278216	+	0.230200i
$211$	−21.4440	+	12.3807i	−1.47626	+	0.852321i	−0.999641	−	0.0267871i	$-0.991472\pi$
$211$	−21.4440	+	12.3807i	−1.47626	+	0.852321i	−0.476622	+	0.879108i	$0.658139\pi$
$212$	16.3750	+	7.70889i	1.12464	+	0.529449i
$213$	2.33858	−	0.759850i	0.160237	−	0.0520641i
$214$	−7.04731	+	17.7950i	−0.481744	+	1.21644i
$215$	11.6900	+	8.49327i	0.797250	+	0.579236i
$216$	2.80621	−	0.353779i	0.190939	−	0.0240716i
$217$	−3.76464	+	9.93460i	−0.255561	+	0.674404i
$218$	−0.687868	+	0.0287715i	−0.0465883	+	0.00194865i
$219$	3.60413	−	4.96065i	0.243544	−	0.335210i
$220$	13.5980	+	4.73792i	0.916776	+	0.319430i
$221$	0.0252729	+	0.0777821i	0.00170004	+	0.00523219i
$222$	−7.78590	−	4.07122i	−0.522556	−	0.273242i
$223$	1.62929	+	2.82201i	0.109105	+	0.188976i	0.915408	−	0.402527i	$-0.131868\pi$
$223$	1.62929	+	2.82201i	0.109105	+	0.188976i	−0.806303	+	0.591503i	$0.798535\pi$
$224$	−9.34555	−	5.40096i	−0.624426	−	0.360867i
$225$	−0.383032	+	1.17885i	−0.0255355	+	0.0785902i
$226$	18.4696	+	18.8638i	1.22858	+	1.25480i
$227$	−8.14071	−	18.2843i	−0.540318	−	1.21357i	−0.953076	−	0.302733i	$-0.902101\pi$
$227$	−8.14071	−	18.2843i	−0.540318	−	1.21357i	0.412758	−	0.910841i	$-0.364566\pi$
$228$	0.631218	−	4.98977i	0.0418034	−	0.330455i
$229$	−20.6135	−	2.16656i	−1.36218	−	0.143171i	−0.604919	−	0.796287i	$-0.706795\pi$
$229$	−20.6135	−	2.16656i	−1.36218	−	0.143171i	−0.757258	+	0.653116i	$0.773461\pi$
$230$	−1.88024	−	12.7405i	−0.123979	−	0.840082i
$231$	1.47295	+	6.92970i	0.0969131	+	0.455941i
$232$	16.4672	+	17.5448i	1.08112	+	1.15187i
$233$	6.90304	−	5.01535i	0.452233	−	0.328567i	−0.338244	−	0.941059i	$-0.609833\pi$
$233$	6.90304	−	5.01535i	0.452233	−	0.328567i	0.790477	+	0.612492i	$0.209833\pi$
$234$	0.0132018	+	0.0514359i	0.000863031	+	0.00336247i
$235$	5.15396	−	0.541703i	0.336207	−	0.0353368i
$236$	11.7264	+	0.247631i	0.763321	+	0.0161194i
$237$	−15.4937	−	3.29329i	−1.00642	−	0.213922i
$238$	−5.26472	+	2.61287i	−0.341261	+	0.169367i
$239$	−7.79273	−	8.65470i	−0.504070	−	0.559826i	0.436379	−	0.899763i	$-0.356261\pi$
$239$	−7.79273	−	8.65470i	−0.504070	−	0.559826i	−0.940448	+	0.339937i	$0.889594\pi$
$240$	−1.13575	+	7.67319i	−0.0733123	+	0.495302i
$241$	12.7501	+	11.4802i	0.821306	+	0.739508i	0.968343	−	0.249623i	$-0.0803068\pi$
$241$	12.7501	+	11.4802i	0.821306	+	0.739508i	−0.147037	+	0.989131i	$0.546974\pi$
$242$	2.11013	+	3.32566i	0.135644	+	0.213782i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.37447	−	1.83798i	0.280047	−	0.117665i
$245$	5.95074	+	2.64944i	0.380179	+	0.169267i
$246$	−1.30534	−	0.867427i	−0.0832255	−	0.0553051i
$247$	0.0944285			0.00600834
$248$	−15.4877	+	2.85134i	−0.983472	+	0.181060i
$249$	14.1343			0.895728
$250$	−14.2517	−	9.47057i	−0.901358	−	0.598971i
$251$	1.93173	+	0.860062i	0.121930	+	0.0542866i	0.466795	−	0.884366i	$-0.345409\pi$
$251$	1.93173	+	0.860062i	0.121930	+	0.0542866i	−0.344865	+	0.938652i	$0.612075\pi$
$252$	−3.51831	+	1.47825i	−0.221632	+	0.0931213i
$253$	8.71769	−	15.0995i	0.548076	−	0.949296i
$254$	9.98514	+	15.7370i	0.626523	+	0.987429i
$255$	3.13880	+	2.82618i	0.196559	+	0.176983i
$256$	−0.324177	−	15.9967i	−0.0202610	−	0.999795i
$257$	2.95232	+	3.27888i	0.184161	+	0.204531i	0.828155	−	0.560499i	$-0.189391\pi$
$257$	2.95232	+	3.27888i	0.184161	+	0.204531i	−0.643994	+	0.765030i	$0.722724\pi$
$258$	−9.43922	+	4.68467i	−0.587660	+	0.291655i
$259$	11.5955	+	2.46470i	0.720511	+	0.153149i
$260$	−0.145600	−	0.00307469i	−0.00902970	−	0.000190684i
$261$	8.46066	−	0.889251i	0.523702	−	0.0550432i
$262$	6.14097	+	23.9260i	0.379390	+	1.47815i
$263$	11.4420	−	8.31311i	0.705545	−	0.512608i	−0.176189	−	0.984356i	$-0.556377\pi$
$263$	11.4420	−	8.31311i	0.705545	−	0.512608i	0.881733	+	0.471748i	$0.156377\pi$
$264$	−7.65705	+	7.18677i	−0.471259	+	0.442315i
$265$	3.64856	+	17.1651i	0.224129	+	1.05444i
$266$	0.990759	+	6.71336i	0.0607473	+	0.411623i
$267$	10.5495	+	1.10880i	0.645618	+	0.0678572i
$268$	−1.26700	+	10.0156i	−0.0773943	+	0.611801i
$269$	2.17231	+	4.87908i	0.132448	+	0.297483i	0.967579	−	0.252568i	$-0.0812751\pi$
$269$	2.17231	+	4.87908i	0.132448	+	0.297483i	−0.835131	+	0.550051i	$0.814608\pi$
$270$	1.91862	+	1.95956i	0.116763	+	0.119255i
$271$	−4.78971	+	14.7412i	−0.290954	+	0.895465i	0.693596	+	0.720364i	$0.256025\pi$
$271$	−4.78971	+	14.7412i	−0.290954	+	0.895465i	−0.984550	+	0.175101i	$0.943975\pi$
$272$	−7.35436	−	4.67074i	−0.445924	−	0.283205i
$273$	−0.0358246	−	0.0620500i	−0.00216820	−	0.00375544i
$274$	−10.2217	−	5.34490i	−0.617517	−	0.322897i
$275$	−1.42213	−	4.37687i	−0.0857577	−	0.263935i
$276$	8.86905	+	3.09022i	0.533854	+	0.186010i
$277$	−13.3207	+	18.3344i	−0.800363	+	1.10160i	0.192377	+	0.981321i	$0.438380\pi$
$277$	−13.3207	+	18.3344i	−0.800363	+	1.10160i	−0.992740	+	0.120284i	$0.961620\pi$
$278$	−0.961556	+	0.0402191i	−0.0576703	+	0.00241218i
$279$	−2.50637	+	4.97173i	−0.150053	+	0.297650i
$280$	−1.30906	−	10.3836i	−0.0782313	−	0.620540i
$281$	−3.10652	−	2.25702i	−0.185320	−	0.134643i	0.491257	−	0.871014i	$-0.336537\pi$
$281$	−3.10652	−	2.25702i	−0.185320	−	0.134643i	−0.676577	+	0.736372i	$0.736537\pi$
$282$	−1.39158	+	3.51386i	−0.0828674	+	0.209247i
$283$	−15.7580	+	5.12010i	−0.936718	+	0.304358i	−0.737307	−	0.675558i	$-0.763903\pi$
$283$	−15.7580	+	5.12010i	−0.936718	+	0.304358i	−0.199411	+	0.979916i	$0.563903\pi$
$284$	−4.44945	−	2.09468i	−0.264026	−	0.124296i
$285$	4.22328	−	2.43831i	0.250166	−	0.144433i
$286$	−0.151905	−	0.125689i	−0.00898236	−	0.00743214i
$287$	2.01114	+	0.653459i	0.118714	+	0.0385725i
$288$	−4.57507	−	3.32696i	−0.269589	−	0.196043i
$289$	11.1965	−	4.98500i	0.658618	−	0.293236i
$290$	−3.89278	+	23.0036i	−0.228592	+	1.35082i
$291$	−0.317870	+	3.02433i	−0.0186339	+	0.177289i
$292$	−12.0466	+	2.29588i	−0.704973	+	0.134356i
$293$	0.912218	−	0.193898i	0.0532924	−	0.0113276i	−0.181188	−	0.983448i	$-0.557994\pi$
$293$	0.912218	−	0.193898i	0.0532924	−	0.0113276i	0.234481	+	0.972121i	$0.424661\pi$
$294$	−3.72314	+	2.95041i	−0.217138	+	0.172071i
$295$	6.68453	+	9.20046i	0.389188	+	0.535672i
$296$	5.77465	+	16.5962i	0.335645	+	0.964635i
$297$	0.388095	+	3.69248i	0.0225196	+	0.214259i
$298$	0.456071	−	7.23920i	0.0264195	−	0.419356i
$299$	−0.0366616	+	0.172479i	−0.00212020	+	0.00997474i
$300$	2.17260	−	1.19392i	0.125435	−	0.0689307i
$301$	10.5661	−	9.51374i	0.609019	−	0.548363i
$302$	7.26786	−	26.0220i	0.418219	−	1.49740i
$303$	5.99332	−	6.65626i	0.344307	−	0.382392i
$304$	−7.75283	+	6.40925i	−0.444655	+	0.367596i
$305$	3.98428	+	2.30033i	0.228139	+	0.131716i
$306$	−2.88713	+	1.07344i	−0.165046	+	0.0613642i
$307$	7.30819	−	16.4145i	0.417100	−	0.936823i	−0.575769	−	0.817613i	$-0.695297\pi$
$307$	7.30819	−	16.4145i	0.417100	−	0.936823i	0.992869	−	0.119210i	$-0.0380362\pi$
$308$	7.34200	−	12.1184i	0.418349	−	0.690511i
$309$			5.55842i			0.316208i
$310$	−11.2831	−	10.2880i	−0.640835	−	0.584317i
$311$		−	31.7869i		−	1.80247i	−0.433328	−	0.901236i	$-0.642661\pi$
$311$		−	31.7869i		−	1.80247i	0.433328	−	0.901236i	$-0.357339\pi$
$312$	0.0511891	−	0.0930562i	0.00289801	−	0.00526827i
$313$	10.4688	−	23.5133i	0.591731	−	1.32905i	−0.331009	−	0.943628i	$-0.607389\pi$
$313$	10.4688	−	23.5133i	0.591731	−	1.32905i	0.922740	−	0.385422i	$-0.125944\pi$
$314$	−1.31303	−	3.53154i	−0.0740984	−	0.199297i
$315$	−3.20449	−	1.85011i	−0.180552	−	0.104242i
$316$	18.0756	+	26.0168i	1.01683	+	1.46356i
$317$	5.88475	−	6.53568i	0.330520	−	0.367080i	−0.554863	−	0.831942i	$-0.687229\pi$
$317$	5.88475	−	6.53568i	0.330520	−	0.367080i	0.885383	+	0.464862i	$0.153896\pi$
$318$	−12.3261	−	3.44263i	−0.691212	−	0.193053i
$319$	−23.4729	+	21.1351i	−1.31423	+	1.18334i
$320$	12.1628	−	9.63000i	0.679922	−	0.538334i
$321$	2.81384	−	13.2381i	0.157053	−	0.738877i
$322$	−12.6470	−	0.796765i	−0.704791	−	0.0444020i
$323$	0.572533	+	5.44728i	0.0318566	+	0.303095i
$324$	−1.91474	+	0.577737i	−0.106374	+	0.0320965i
$325$	0.0273575	+	0.0376544i	0.00151752	+	0.00208869i
$326$	11.1809	+	14.1092i	0.619252	+	0.781439i
$327$	0.476183	−	0.101216i	0.0263330	−	0.00559725i
$328$	0.714997	+	3.05191i	0.0394791	+	0.168514i
$329$	0.533023	−	5.07137i	0.0293865	−	0.279594i
$330$	−10.0394	−	1.69892i	−0.552653	−	0.0935227i
$331$	−25.0907	+	11.1711i	−1.37911	+	0.614018i	−0.956350	−	0.292225i	$-0.905604\pi$
$331$	−25.0907	+	11.1711i	−1.37911	+	0.614018i	−0.422757	+	0.906243i	$0.638938\pi$
$332$	−20.6037	−	19.3548i	−1.13077	−	1.06223i
$333$	5.90862	+	1.91983i	0.323791	+	0.105206i
$334$	18.5776	−	22.4526i	1.01652	−	1.22855i
$335$	−8.47710	+	4.89425i	−0.463153	+	0.267402i
$336$	7.15289	+	2.66291i	0.390222	+	0.145274i
$337$	7.36296	−	2.39237i	0.401086	−	0.130321i	−0.101526	−	0.994833i	$-0.532372\pi$
$337$	7.36296	−	2.39237i	0.401086	−	0.130321i	0.502612	+	0.864512i	$0.332372\pi$
$338$	−17.0913	−	6.76861i	−0.929644	−	0.368164i
$339$	−15.1025	−	10.9726i	−0.820256	−	0.595951i
$340$	−0.705420	−	8.41783i	−0.0382568	−	0.456521i
$341$	−3.32152	−	20.4035i	−0.179871	−	1.10491i
$342$	0.148625	+	3.55331i	0.00803670	+	0.192141i
$343$	11.6184	−	15.9913i	0.627334	−	0.863451i
$344$	20.1745	+	6.09667i	1.08774	+	0.328710i
$345$	2.81405	+	8.66075i	0.151503	+	0.466279i
$346$	−2.62170	+	5.01381i	−0.140943	+	0.269544i
$347$	6.07633	+	10.5245i	0.326194	+	0.564985i	0.981753	−	0.190159i	$-0.0609002\pi$
$347$	6.07633	+	10.5245i	0.326194	+	0.564985i	−0.655559	+	0.755144i	$0.727567\pi$
$348$	−13.5508	−	10.2893i	−0.726400	−	0.551563i
$349$	6.49234	−	19.9814i	0.347527	−	1.06958i	−0.612690	−	0.790324i	$-0.709912\pi$
$349$	6.49234	−	19.9814i	0.347527	−	1.06958i	0.960217	−	0.279255i	$-0.0900876\pi$
$350$	−2.38999	+	2.34005i	−0.127750	+	0.125081i
$351$	−0.0152728	−	0.0343033i	−0.000815201	−	0.00183097i
$352$	21.0029	+	0.00894627i	1.11946	+	0.000476838i
$353$	35.9403	+	3.77748i	1.91291	+	0.201055i	0.985098	−	0.171993i	$-0.0550206\pi$
$353$	35.9403	+	3.77748i	1.91291	+	0.201055i	0.927812	+	0.373048i	$0.121687\pi$
$354$	−8.20477	+	1.21086i	−0.436079	+	0.0643566i
$355$	−0.991394	−	4.66414i	−0.0526177	−	0.247547i
$356$	−13.8597	−	16.0622i	−0.734563	−	0.851292i
$357$	3.36226	−	2.44283i	0.177950	−	0.129288i
$358$	14.4341	−	3.70473i	0.762866	−	0.195801i
$359$	24.4141	−	2.56602i	1.28853	−	0.135429i	0.564633	−	0.825342i	$-0.309018\pi$
$359$	24.4141	−	2.56602i	1.28853	−	0.135429i	0.723893	+	0.689913i	$0.242351\pi$
$360$	−0.113465	−	5.48370i	−0.00598013	−	0.289016i
$361$	−12.3989	−	2.63548i	−0.652576	−	0.138709i
$362$	−13.2002	−	26.5973i	−0.693786	−	1.39792i
$363$	−1.86354	−	2.06967i	−0.0978107	−	0.108630i
$364$	−0.0327461	+	0.139507i	−0.00171636	+	0.00731214i
$365$	−8.83642	−	7.95635i	−0.462520	−	0.416454i
$366$	−2.83301	+	1.79754i	−0.148084	+	0.0939590i
$367$	−12.6769	+	21.9570i	−0.661728	+	1.14615i	0.318434	+	0.947945i	$0.396843\pi$
$367$	−12.6769	+	21.9570i	−0.661728	+	1.14615i	−0.980161	+	0.198201i	$0.936490\pi$
$368$	−8.69687	−	16.6494i	−0.453356	−	0.867910i
$369$	1.01242	+	0.450758i	0.0527044	+	0.0234655i
$370$	−9.42985	+	14.1904i	−0.490235	+	0.737726i
$371$	17.2674			0.896478
$372$	10.4616	−	3.81522i	0.542406	−	0.197810i
$373$	32.2537			1.67003			0.835017	−	0.550225i	$-0.185458\pi$
$373$	32.2537			1.67003			0.835017	+	0.550225i	$0.185458\pi$
$374$	6.32958	−	9.52502i	0.327295	−	0.492527i
$375$	11.0536	+	4.92137i	0.570804	+	0.254139i
$376$	6.84018	−	3.21661i	0.352756	−	0.165884i
$377$	0.159722	−	0.276647i	0.00822611	−	0.0142480i
$378$	2.27853	−	1.44573i	0.117195	−	0.0743603i
$379$	2.26969	+	2.04364i	0.116586	+	0.104975i	0.725362	−	0.688368i	$-0.241672\pi$
$379$	2.26969	+	2.04364i	0.116586	+	0.104975i	−0.608776	+	0.793342i	$0.708339\pi$
$380$	−9.49518	−	2.22878i	−0.487092	−	0.114334i
$381$	−8.81828	−	9.79369i	−0.451774	−	0.501746i
$382$	−10.3658	−	20.8862i	−0.530360	−	1.06863i
$383$	19.3022	+	4.10281i	0.986296	+	0.209644i	0.672702	−	0.739914i	$-0.265134\pi$
$383$	19.3022	+	4.10281i	0.986296	+	0.209644i	0.313594	+	0.949557i	$0.398467\pi$
$384$	2.11335	+	11.1146i	0.107846	+	0.567188i
$385$	13.6630	−	1.43604i	0.696331	−	0.0731873i
$386$	5.43502	−	1.39498i	0.276635	−	0.0710028i
$387$	6.02826	−	4.37979i	0.306434	−	0.222637i
$388$	4.60470	−	3.97330i	0.233768	−	0.201714i
$389$	−5.66184	−	26.6368i	−0.287067	−	1.35054i	−0.851193	−	0.524853i	$-0.824120\pi$
$389$	−5.66184	−	26.6368i	−0.287067	−	1.35054i	0.564126	−	0.825689i	$-0.309213\pi$
$390$	0.101874	−	0.0150346i	0.00515859	−	0.000761305i
$391$	−10.1721	−	1.06913i	−0.514424	−	0.0540682i
$392$	9.46737	+	0.797434i	0.478174	+	0.0402765i
$393$	−7.10430	−	15.9565i	−0.358364	−	0.804900i
$394$	−3.94711	+	3.86463i	−0.198852	+	0.194697i
$395$	−9.49193	+	29.2132i	−0.477591	+	1.46987i
$396$	4.49054	−	5.91398i	0.225658	−	0.297189i
$397$	−9.55080	−	16.5425i	−0.479341	−	0.830243i	0.520378	−	0.853936i	$-0.325791\pi$
$397$	−9.55080	−	16.5425i	−0.479341	−	0.830243i	−0.999719	+	0.0236929i	$0.992458\pi$
$398$	−10.9454	+	20.9323i	−0.548643	+	1.04924i
$399$	−1.48281	−	4.56363i	−0.0742335	−	0.228467i
$400$	−4.80189	−	1.23466i	−0.240094	−	0.0617330i
$401$	15.1618	−	20.8684i	0.757144	−	1.04212i	−0.240302	−	0.970698i	$-0.577246\pi$
$401$	15.1618	−	20.8684i	0.757144	−	1.04212i	0.997446	−	0.0714217i	$-0.0227536\pi$
$402$	−0.298324	−	7.13231i	−0.0148790	−	0.355727i
$403$	0.0957140	+	0.185871i	0.00476786	+	0.00925888i
$404$	−17.8512	+	1.49594i	−0.888130	+	0.0744260i
$405$	−1.56884	−	1.13983i	−0.0779564	−	0.0566386i
$406$	21.3439	+	8.45277i	1.05928	+	0.419504i
$407$	−21.9376	+	7.12797i	−1.08741	+	0.353320i
$408$	5.67849	+	2.38872i	0.281127	+	0.118259i
$409$	−32.8402	+	18.9603i	−1.62384	+	0.937526i	−0.637963	+	0.770067i	$0.720223\pi$
$409$	−32.8402	+	18.9603i	−1.62384	+	0.937526i	−0.985879	+	0.167459i	$0.946444\pi$
$410$	−1.93749	+	2.34162i	−0.0956858	+	0.115644i
$411$	7.75714	+	2.52045i	0.382631	+	0.124324i
$412$	7.61139	−	8.10254i	0.374986	−	0.399183i
$413$	10.2227	−	4.55145i	0.503027	−	0.223962i
$414$	−6.54804	−	1.10809i	−0.321819	−	0.0544598i
$415$	2.86505	−	27.2591i	0.140640	−	1.33810i
$416$	−0.202044	+	0.0655530i	−0.00990604	+	0.00321400i
$417$	0.665646	−	0.141487i	0.0325968	−	0.00692867i
$418$	−8.20096	−	10.3488i	−0.401122	−	0.506179i
$419$	18.5020	+	25.4658i	0.903882	+	1.24409i	0.969213	+	0.246223i	$0.0791896\pi$
$419$	18.5020	+	25.4658i	0.903882	+	1.24409i	−0.0653313	+	0.997864i	$0.520810\pi$
$420$	2.13776	+	7.08495i	0.104312	+	0.345710i
$421$	−2.99499	−	28.4954i	−0.145967	−	1.38878i	−0.784950	−	0.619559i	$-0.787311\pi$
$421$	−2.99499	−	28.4954i	−0.145967	−	1.38878i	0.638983	−	0.769221i	$-0.279355\pi$
$422$	−34.9486	−	2.20177i	−1.70127	−	0.107180i
$423$	0.555628	−	2.61402i	0.0270155	−	0.127098i
$424$	13.2536	+	21.8970i	0.643653	+	1.06341i
$425$	−2.00629	+	1.80647i	−0.0973195	+	0.0876269i
$426$	3.34927	+	0.935440i	0.162273	+	0.0453222i
$427$	3.02911	−	3.36417i	0.146589	−	0.162803i
$428$	−22.2292	+	15.4441i	−1.07449	+	0.746517i
$429$	0.120737	+	0.0697074i	0.00582923	+	0.00336551i
$430$	7.12138	+	19.1538i	0.343424	+	0.923679i
$431$	11.0168	−	24.7442i	0.530661	−	1.19189i	−0.427069	−	0.904219i	$-0.640454\pi$
$431$	11.0168	−	24.7442i	0.530661	−	1.19189i	0.957731	−	0.287666i	$-0.0928794\pi$
$432$	3.58224	+	1.77976i	0.172351	+	0.0856288i
$433$			12.1411i			0.583464i	0.956500	+	0.291732i	$0.0942316\pi$
$433$			12.1411i			0.583464i	−0.956500	+	0.291732i	$0.905768\pi$
$434$	−12.2102	+	8.75495i	−0.586107	+	0.420251i
$435$		−	16.4972i		−	0.790982i
$436$	−0.832734	−	0.504515i	−0.0398807	−	0.0241619i
$437$	−4.80329	+	10.7884i	−0.229772	+	0.516077i
$438$	8.12794	−	3.02196i	0.388368	−	0.144395i
$439$	−17.4201	−	10.0575i	−0.831416	−	0.480018i	0.0229213	−	0.999737i	$-0.492703\pi$
$439$	−17.4201	−	10.0575i	−0.831416	−	0.480018i	−0.854337	+	0.519719i	$0.826037\pi$
$440$	12.3081	+	16.2240i	0.586767	+	0.773447i
$441$	2.24766	−	2.49628i	0.107031	−	0.118870i
$442$	−0.0311131	+	0.111398i	−0.00147990	+	0.00529866i
$443$	−29.7862	+	26.8196i	−1.41518	+	1.27424i	−0.503105	+	0.864226i	$0.667809\pi$
$443$	−29.7862	+	26.8196i	−1.41518	+	1.27424i	−0.912080	+	0.410012i	$0.865524\pi$
$444$	−5.98412	−	10.8895i	−0.283994	−	0.516791i
$445$	4.27679	−	20.1207i	0.202739	−	0.953812i
$446$	−0.289751	+	4.59921i	−0.0137201	+	0.217779i
$447$	0.536131	+	5.10094i	0.0253581	+	0.241266i
$448$	−6.78035	−	13.6765i	−0.320342	−	0.646153i
$449$	−1.90779	−	2.62584i	−0.0900341	−	0.123921i	0.761624	−	0.648019i	$-0.224402\pi$
$449$	−1.90779	−	2.62584i	−0.0900341	−	0.123921i	−0.851658	+	0.524098i	$0.824402\pi$
$450$	−1.37386	+	1.08872i	−0.0647646	+	0.0513228i
$451$	−4.02474	+	0.855485i	−0.189518	+	0.0402832i
$452$	6.98972	+	36.6754i	0.328769	+	1.72506i
$453$	−1.99697	+	18.9999i	−0.0938257	+	0.892692i
$454$	4.72277	−	27.9083i	0.221651	−	1.30980i
$455$	−0.126930	+	0.0565127i	−0.00595055	+	0.00264936i
$456$	4.64905	−	5.38319i	0.217712	−	0.252091i
$457$	9.97168	+	3.24000i	0.466456	+	0.151561i	0.532809	−	0.846236i	$-0.321136\pi$
$457$	9.97168	+	3.24000i	0.466456	+	0.151561i	−0.0663533	+	0.997796i	$0.521136\pi$
$458$	−22.5840	−	18.6864i	−1.05528	−	0.873157i
$459$	1.88625	−	1.08903i	0.0880425	−	0.0508313i
$460$	7.75749	−	16.4782i	0.361695	−	0.768300i
$461$	−2.88570	+	0.937621i	−0.134401	+	0.0436694i	−0.375445	−	0.926845i	$-0.622510\pi$
$461$	−2.88570	+	0.937621i	−0.134401	+	0.0436694i	0.241044	+	0.970514i	$0.422510\pi$
$462$	−3.68904	+	9.31512i	−0.171630	+	0.433379i
$463$	−12.8328	−	9.32355i	−0.596389	−	0.433302i	0.248206	−	0.968707i	$-0.420159\pi$
$463$	−12.8328	−	9.32355i	−0.596389	−	0.433302i	−0.844595	+	0.535405i	$0.820159\pi$
$464$	5.66355	+	33.5544i	0.262924	+	1.55773i
$465$	9.08030	+	5.84150i	0.421089	+	0.270893i
$466$	12.0564	−	0.504284i	0.558502	−	0.0233605i
$467$	−0.152458	+	0.209840i	−0.00705491	+	0.00971025i	−0.812530	−	0.582920i	$-0.801910\pi$
$467$	−0.152458	+	0.209840i	−0.00705491	+	0.00971025i	0.805475	+	0.592630i	$0.201910\pi$
$468$	−0.0247097	+	0.0709177i	−0.00114221	+	0.00327817i
$469$	2.97634	+	9.16025i	0.137435	+	0.422981i
$470$	6.49465	+	3.39603i	0.299576	+	0.156647i
$471$	1.33210	+	2.30726i	0.0613797	+	0.106313i
$472$	13.6182	+	9.47007i	0.626829	+	0.435895i
$473$	−8.54910	+	26.3114i	−0.393088	+	1.20980i
$474$	−15.6717	−	16.0062i	−0.719827	−	0.735188i
$475$	1.26784	+	2.84761i	0.0581724	+	0.130657i
$476$	−8.24625	−	1.04317i	−0.377966	−	0.0478137i
$477$	8.99984	+	0.945921i	0.412074	+	0.0433108i
$478$	−2.40460	−	16.2935i	−0.109984	−	0.745248i
$479$	−1.24574	−	5.86075i	−0.0569193	−	0.267784i	0.940481	−	0.339847i	$-0.110375\pi$
$479$	−1.24574	−	5.86075i	−0.0569193	−	0.267784i	−0.997400	+	0.0720625i	$0.977042\pi$
$480$	−7.34367	+	8.14899i	−0.335191	+	0.371949i
$481$	0.188731	−	0.137121i	0.00860538	−	0.00625218i
$482$	6.03211	+	23.5018i	0.274755	+	1.07048i
$483$	8.91144	−	0.936630i	0.405485	−	0.0426181i
$484$	−0.117599	+	5.56880i	−0.00534541	+	0.253127i
$485$	5.76821	+	1.22607i	0.261921	+	0.0556730i
$486$	1.26678	−	0.628701i	0.0574624	−	0.0285185i
$487$	3.72604	+	4.13819i	0.168843	+	0.187519i	0.821628	−	0.570024i	$-0.193066\pi$
$487$	3.72604	+	4.13819i	0.168843	+	0.187519i	−0.652785	+	0.757543i	$0.726399\pi$
$488$	6.59113	+	1.25907i	0.298367	+	0.0569955i
$489$	−9.45990	−	8.51773i	−0.427792	−	0.385185i
$490$	4.93540	+	7.77841i	0.222959	+	0.351393i
$491$	−0.00363974	+	0.00630422i	−0.000164259	+	0.000284505i	−0.866108	−	0.499858i	$-0.833386\pi$
$491$	−0.00363974	+	0.00630422i	−0.000164259	+	0.000284505i	0.865943	+	0.500142i	$0.166719\pi$
$492$	−0.858564	−	2.04342i	−0.0387071	−	0.0921244i
$493$	16.9273	+	7.53652i	0.762367	+	0.339428i
$494$	0.111224	+	0.0739105i	0.00500419	+	0.00332539i
$495$	7.19988			0.323611
$496$	−20.4742	−	8.76398i	−0.919318	−	0.393514i
$497$	−4.69193			−0.210462
$498$	16.6483	+	11.0632i	0.746028	+	0.495752i
$499$	−4.97938	−	2.21696i	−0.222907	−	0.0992448i	0.292245	−	0.956344i	$-0.405598\pi$
$499$	−4.97938	−	2.21696i	−0.222907	−	0.0992448i	−0.515152	+	0.857099i	$0.672265\pi$
$500$	−9.37380	−	22.3100i	−0.419209	−	0.997735i
$501$	−10.3032	+	17.8457i	−0.460313	+	0.797285i
$502$	1.60213	+	2.52503i	0.0715065	+	0.112698i
$503$	15.9801	+	14.3886i	0.712519	+	0.641555i	0.943488	−	0.331406i	$-0.107523\pi$
$503$	15.9801	+	14.3886i	0.712519	+	0.641555i	−0.230969	+	0.972961i	$0.574190\pi$
$504$	−5.30113	−	1.01265i	−0.236131	−	0.0451070i
$505$	−11.6222	−	12.9078i	−0.517182	−	0.574389i
$506$	22.0868	−	10.9616i	0.981878	−	0.487304i
$507$	12.7145	+	2.70256i	0.564673	+	0.120025i
$508$	−0.556478	+	26.3515i	−0.0246897	+	1.16916i
$509$	−14.4408	+	1.51779i	−0.640076	+	0.0672747i	−0.419006	−	0.907983i	$-0.637622\pi$
$509$	−14.4408	+	1.51779i	−0.640076	+	0.0672747i	−0.221070	+	0.975258i	$0.570955\pi$
$510$	1.48497	+	5.78563i	0.0657557	+	0.256192i
$511$	−9.46553	+	6.87711i	−0.418730	+	0.304226i
$512$	12.1390	−	19.0957i	0.536474	−	0.843917i
$513$	−0.522849	−	2.45981i	−0.0230844	−	0.108603i
$514$	0.910996	+	6.17289i	0.0401823	+	0.272275i
$515$	10.7198	+	1.12670i	0.472372	+	0.0496483i
$516$	−14.7849	−	1.87032i	−0.650867	−	0.0823363i
$517$	4.03573	+	9.06440i	0.177491	+	0.398652i
$518$	11.7288	+	11.9791i	0.515332	+	0.526330i
$519$	1.23629	−	3.80491i	0.0542672	−	0.167017i
$520$	−0.169090	−	0.117584i	−0.00741507	−	0.00515642i
$521$	19.3797	+	33.5667i	0.849042	+	1.47058i	0.882064	+	0.471129i	$0.156153\pi$
$521$	19.3797	+	33.5667i	0.849042	+	1.47058i	−0.0330225	+	0.999455i	$0.510513\pi$
$522$	10.6615	+	5.57486i	0.466642	+	0.244005i
$523$	−5.18921	−	15.9707i	−0.226908	−	0.698352i	−0.998092	−	0.0617395i	$-0.980335\pi$
$523$	−5.18921	−	15.9707i	−0.226908	−	0.698352i	0.771184	−	0.636612i	$-0.219665\pi$
$524$	−11.4940	+	32.9881i	−0.502116	+	1.44109i
$525$	1.39020	−	1.91345i	0.0606734	−	0.0835097i
$526$	19.9839	−	0.835868i	0.871339	−	0.0364456i
$527$	−10.1420	+	6.64840i	−0.441792	+	0.289609i
$528$	−14.6441	+	2.47174i	−0.637304	+	0.107569i
$529$	0.766658	+	0.557009i	0.0333329	+	0.0242178i
$530$	−9.13788	+	23.0739i	−0.396924	+	1.00227i
$531$	5.57746	−	1.81223i	0.242041	−	0.0786440i
$532$	−4.08767	+	8.68289i	−0.177223	+	0.376451i
$533$	0.0360384	−	0.0208068i	0.00156100	−	0.000901242i
$534$	11.5580	+	9.56324i	0.500162	+	0.413842i
$535$	−24.9602	−	8.11006i	−1.07912	−	0.350629i
$536$	−9.33171	+	10.8053i	−0.403068	+	0.466718i
$537$	−9.62627	+	4.28589i	−0.415404	+	0.184950i
$538$	−1.26025	+	7.44718i	−0.0543332	+	0.321071i
$539$	−1.30364	+	12.4033i	−0.0561517	+	0.534248i
$540$	0.726089	+	3.80982i	0.0312459	+	0.163948i
$541$	0.624525	−	0.132747i	0.0268504	−	0.00570724i	−0.194467	−	0.980909i	$-0.562298\pi$
$541$	0.624525	−	0.132747i	0.0268504	−	0.00570724i	0.221317	+	0.975202i	$0.428964\pi$
$542$	−17.1798	+	13.6141i	−0.737934	+	0.584777i
$543$	12.3411	+	16.9861i	0.529607	+	0.728942i
$544$	−5.00657	−	11.2578i	−0.214655	−	0.482676i
$545$	−0.0986793	−	0.938871i	−0.00422696	−	0.0402168i
$546$	0.00637101	−	0.101127i	0.000272654	−	0.00432783i
$547$	5.60237	−	26.3571i	0.239540	−	1.12695i	−0.679774	−	0.733422i	$-0.737922\pi$
$547$	5.60237	−	26.3571i	0.239540	−	1.12695i	0.919314	−	0.393525i	$-0.128745\pi$
$548$	−7.85625	−	14.2962i	−0.335602	−	0.610705i
$549$	1.76308	−	1.58748i	0.0752463	−	0.0677521i
$550$	1.75076	−	6.26846i	0.0746528	−	0.267288i
$551$	14.3152	−	15.8987i	0.609849	−	0.677306i
$552$	8.02775	+	10.5818i	0.341684	+	0.450391i
$553$	26.1750	+	15.1122i	1.11308	+	0.642635i
$554$	−30.0405	+	11.1690i	−1.27630	+	0.474527i
$555$	4.90021	−	11.0061i	0.208002	−	0.467181i
$556$	−1.16406	−	0.705251i	−0.0493671	−	0.0299093i
$557$		−	5.28154i		−	0.223786i	−0.993720	−	0.111893i	$-0.964309\pi$
$557$		−	5.28154i		−	0.223786i	0.993720	−	0.111893i	$-0.0356914\pi$
$558$	−6.84361	+	3.89424i	−0.289713	+	0.164856i
$559$		−	0.279795i		−	0.0118341i
$560$	6.58551	−	13.2551i	0.278289	−	0.560130i
$561$	−3.28916	+	7.38757i	−0.138868	+	0.311904i
$562$	−1.89245	−	5.08998i	−0.0798283	−	0.214708i
$563$	19.3542	+	11.1741i	0.815681	+	0.470933i	0.848925	−	0.528514i	$-0.177251\pi$
$563$	19.3542	+	11.1741i	0.815681	+	0.470933i	−0.0332441	+	0.999447i	$0.510584\pi$
$564$	−4.38943	+	3.04963i	−0.184829	+	0.128412i
$565$	−24.2228	+	26.9021i	−1.01906	+	1.13178i
$566$	−22.5684	−	6.30327i	−0.948619	−	0.264946i
$567$	−1.41801	+	1.27678i	−0.0595509	+	0.0536198i
$568$	−3.60130	−	5.94989i	−0.151107	−	0.249652i
$569$	−7.24472	+	34.0837i	−0.303715	+	1.42887i	0.516244	+	0.856442i	$0.327330\pi$
$569$	−7.24472	+	34.0837i	−0.303715	+	1.42887i	−0.819958	+	0.572423i	$0.806003\pi$
$570$	6.88294	+	0.433627i	0.288295	+	0.0181626i
$571$	−2.39536	−	22.7904i	−0.100243	−	0.953747i	−0.922856	−	0.385145i	$-0.874151\pi$
$571$	−2.39536	−	22.7904i	−0.100243	−	0.953747i	0.822613	−	0.568601i	$-0.192515\pi$
$572$	−0.0805452	−	0.266943i	−0.00336776	−	0.0111614i
$573$	9.69119	+	13.3388i	0.404855	+	0.557235i
$574$	1.85737	+	2.34383i	0.0775252	+	0.0978296i
$575$	−5.69358	+	1.21021i	−0.237438	+	0.0504691i
$576$	−2.78474	−	7.49968i	−0.116031	−	0.312487i
$577$	−0.500056	+	4.75771i	−0.0208176	+	0.198066i	−0.999988	−	0.00497580i	$-0.998416\pi$
$577$	−0.500056	+	4.75771i	−0.0208176	+	0.198066i	0.979170	+	0.203042i	$0.0650828\pi$
$578$	17.0898	+	2.89201i	0.710841	+	0.120292i
$579$	−3.62468	+	1.61381i	−0.150637	+	0.0670678i
$580$	−22.5904	+	24.0481i	−0.938015	+	0.998543i
$581$	−25.6500	−	8.33420i	−1.06414	−	0.345761i
$582$	−2.74159	+	3.31344i	−0.113643	+	0.137347i
$583$	−29.0974	+	16.7994i	−1.20509	+	0.695761i
$584$	−15.9862	−	6.72480i	−0.661515	−	0.278274i
$585$	−0.0692521	+	0.0225014i	−0.00286322	+	0.000930318i
$586$	1.22623	+	0.485621i	0.0506553	+	0.0200608i
$587$	−15.6835	−	11.3947i	−0.647326	−	0.470310i	0.215033	−	0.976607i	$-0.431014\pi$
$587$	−15.6835	−	11.3947i	−0.647326	−	0.470310i	−0.862359	+	0.506297i	$0.831014\pi$
$588$	−6.69468	+	0.561019i	−0.276084	+	0.0231360i
$589$	3.68196	+	13.5088i	0.151713	+	0.556622i
$590$	0.672117	+	16.0689i	0.0276706	+	0.661548i
$591$	2.29594	−	3.16009i	0.0944424	−	0.129989i
$592$	−6.18834	+	24.0679i	−0.254339	+	0.989186i
$593$	6.50065	+	20.0069i	0.266950	+	0.821586i	0.991238	+	0.132089i	$0.0421685\pi$
$593$	6.50065	+	20.0069i	0.266950	+	0.821586i	−0.724288	+	0.689497i	$0.757832\pi$
$594$	−2.43303	+	4.65300i	−0.0998286	+	0.190915i
$595$	−4.02963	−	6.97953i	−0.165199	−	0.286133i
$596$	6.20342	−	8.16981i	0.254102	−	0.334648i
$597$	5.16142	−	15.8852i	0.211243	−	0.650139i
$598$	−0.178184	+	0.174461i	−0.00728650	+	0.00713425i
$599$	−8.83182	−	19.8366i	−0.360858	−	0.810501i	−0.999170	−	0.0407233i	$-0.987034\pi$
$599$	−8.83182	−	19.8366i	−0.360858	−	0.810501i	0.638312	−	0.769778i	$-0.279633\pi$
$600$	3.49352	+	0.294258i	0.142622	+	0.0120130i
$601$	−32.4500	−	3.41064i	−1.32366	−	0.139123i	−0.583810	−	0.811890i	$-0.698439\pi$
$601$	−32.4500	−	3.41064i	−1.32366	−	0.139123i	−0.739854	+	0.672767i	$0.765105\pi$
$602$	19.8919	−	2.93565i	0.810734	−	0.119648i
$603$	1.04948	+	4.93741i	0.0427381	+	0.201067i
$604$	28.9283	−	24.9617i	1.17708	−	1.01568i
$605$	−4.36926	+	3.17445i	−0.177636	+	0.129060i
$606$	12.2693	−	3.14910i	0.498404	−	0.127923i
$607$	38.6074	−	4.05780i	1.56703	−	0.164701i	0.719135	−	0.694871i	$-0.244538\pi$
$607$	38.6074	−	4.05780i	1.56703	−	0.164701i	0.847892	+	0.530170i	$0.177872\pi$
$608$	−14.1484	+	1.48096i	−0.573792	+	0.0600609i
$609$	−15.8782	−	3.37501i	−0.643416	−	0.136762i
$610$	2.89244	+	5.82802i	0.117111	+	0.235970i
$611$	−0.0671462	−	0.0745734i	−0.00271644	−	0.00301692i
$612$	−4.24084	−	0.995442i	−0.171426	−	0.0402384i
$613$	18.1727	+	16.3628i	0.733990	+	0.660887i	0.948839	−	0.315760i	$-0.102259\pi$
$613$	18.1727	+	16.3628i	0.733990	+	0.660887i	−0.214849	+	0.976647i	$0.568926\pi$
$614$	21.4559	−	13.6137i	0.865888	−	0.549406i
$615$	1.07454	−	1.86115i	0.0433295	−	0.0750489i
$616$	18.1331	−	8.52714i	0.730604	−	0.343568i
$617$	−31.2814	−	13.9274i	−1.25934	−	0.560695i	−0.334985	−	0.942223i	$-0.608731\pi$
$617$	−31.2814	−	13.9274i	−1.25934	−	0.560695i	−0.924357	+	0.381528i	$0.875398\pi$
$618$	−4.35066	+	6.54705i	−0.175009	+	0.263361i
$619$	34.3580			1.38096			0.690482	−	0.723350i	$-0.257398\pi$
$619$	34.3580			1.38096			0.690482	+	0.723350i	$0.257398\pi$
$620$	−5.23737	−	20.9492i	−0.210338	−	0.841341i
$621$	4.69599			0.188444
$622$	24.8801	−	37.4406i	0.997601	−	1.50123i
$623$	−18.4907	−	8.23258i	−0.740814	−	0.329832i
$624$	0.133130	−	0.0695409i	0.00532947	−	0.00278387i
$625$	8.63300	−	14.9528i	0.345320	−	0.598112i
$626$	30.7350	−	19.5013i	1.22842	−	0.779430i
$627$	6.93865	+	6.24759i	0.277103	+	0.249505i
$628$	1.21762	−	5.18739i	0.0485885	−	0.207000i
$629$	9.05438	+	10.0559i	0.361022	+	0.400955i
$630$	−2.32633	−	4.68737i	−0.0926834	−	0.186749i
$631$	21.4720	+	4.56400i	0.854785	+	0.181690i	0.614407	−	0.788989i	$-0.289395\pi$
$631$	21.4720	+	4.56400i	0.854785	+	0.181690i	0.240378	+	0.970679i	$0.422729\pi$
$632$	0.926811	+	44.7922i	0.0368666	+	1.78174i
$633$	24.6257	−	2.58827i	0.978784	−	0.102874i
$634$	12.0470	−	3.09205i	0.478447	−	0.122801i
$635$	−20.6753	+	15.0215i	−0.820475	+	0.596110i
$636$	−11.8238	−	13.7027i	−0.468845	−	0.543349i
$637$	−0.0262243	−	0.123375i	−0.00103904	−	0.00488832i
$638$	−44.1906	+	6.52165i	−1.74952	+	0.258195i
$639$	−2.44546	−	0.257028i	−0.0967407	−	0.0101679i
$640$	21.8636	−	1.82281i	0.864236	−	0.0720530i
$641$	−12.5858	−	28.2681i	−0.497108	−	1.11652i	−0.971679	−	0.236305i	$-0.924064\pi$
$641$	−12.5858	−	28.2681i	−0.497108	−	1.11652i	0.474571	−	0.880217i	$-0.342603\pi$
$642$	13.6759	−	13.3902i	0.539746	−	0.528468i
$643$	−2.06537	+	6.35655i	−0.0814501	+	0.250678i	−0.983486	−	0.180983i	$-0.942072\pi$
$643$	−2.06537	+	6.35655i	−0.0814501	+	0.250678i	0.902036	+	0.431661i	$0.142072\pi$
$644$	−14.2728	−	10.8375i	−0.562428	−	0.427057i
$645$	−7.22481	−	12.5137i	−0.284476	−	0.492728i
$646$	−3.58930	+	6.86428i	−0.141219	+	0.270071i
$647$	−8.45355	−	26.0173i	−0.332343	−	1.02285i	−0.968016	−	0.250889i	$-0.919277\pi$
$647$	−8.45355	−	26.0173i	−0.332343	−	1.02285i	0.635673	−	0.771959i	$-0.280723\pi$
$648$	−2.70750	−	0.818197i	−0.106361	−	0.0321418i
$649$	−12.7983	+	17.6154i	−0.502378	+	0.691464i
$650$	0.00275075	+	0.0657648i	0.000107893	+	0.00257951i
$651$	7.47994	−	7.54449i	0.293162	−	0.295692i
$652$	2.12604	+	25.3702i	0.0832622	+	0.993573i
$653$	34.4135	+	25.0029i	1.34670	+	0.978438i	0.999168	+	0.0407717i	$0.0129816\pi$
$653$	34.4135	+	25.0029i	1.34670	+	0.978438i	0.347536	+	0.937667i	$0.387018\pi$
$654$	0.640101	+	0.253497i	0.0250299	+	0.00991252i
$655$	−32.2134	+	10.4668i	−1.25868	+	0.408970i
$656$	−1.54661	+	4.15437i	−0.0603849	+	0.162201i
$657$	−5.31021	+	3.06585i	−0.207171	+	0.119610i
$658$	4.59726	−	5.55617i	0.179220	−	0.216602i
$659$	−42.5693	−	13.8316i	−1.65827	−	0.538803i	−0.677758	−	0.735285i	$-0.737048\pi$
$659$	−42.5693	−	13.8316i	−1.65827	−	0.538803i	−0.980507	+	0.196482i	$0.937048\pi$
$660$	−10.4953	−	9.85911i	−0.408529	−	0.383765i
$661$	−36.7447	+	16.3598i	−1.42920	+	0.636323i	−0.967995	−	0.250969i	$-0.919251\pi$
$661$	−36.7447	+	16.3598i	−1.42920	+	0.636323i	−0.461209	+	0.887292i	$0.652584\pi$
$662$	−38.2971	−	6.48082i	−1.48846	−	0.251884i
$663$	0.00854885	−	0.0813369i	0.000332010	−	0.00315886i
$664$	−9.11905	−	38.9240i	−0.353888	−	1.51055i
$665$	−9.10185	+	1.93466i	−0.352955	+	0.0750228i
$666$	5.45686	+	6.88605i	0.211449	+	0.266829i
$667$	23.4820	+	32.3203i	0.909228	+	1.25145i
$668$	39.4558	−	11.9051i	1.52659	−	0.460621i
$669$	−0.340614	−	3.24073i	−0.0131689	−	0.125294i
$670$	−13.8156	−	0.870389i	−0.533745	−	0.0336260i
$671$	−1.83139	+	8.61601i	−0.0707000	+	0.332617i
$672$	6.34081	+	8.73520i	0.244602	+	0.336968i
$673$	−16.1531	+	14.5443i	−0.622657	+	0.560643i	−0.918910	−	0.394467i	$-0.870929\pi$
$673$	−16.1531	+	14.5443i	−0.622657	+	0.560643i	0.296254	+	0.955109i	$0.404263\pi$
$674$	10.5451	+	2.94521i	0.406182	+	0.113445i
$675$	0.829400	−	0.921142i	0.0319236	−	0.0354548i
$676$	−14.8333	−	21.3501i	−0.570512	−	0.821157i
$677$	−15.3926	−	8.88690i	−0.591584	−	0.341551i	0.174139	−	0.984721i	$-0.444286\pi$
$677$	−15.3926	−	8.88690i	−0.591584	−	0.341551i	−0.765724	+	0.643170i	$0.777619\pi$
$678$	−9.20025	−	24.7452i	−0.353334	−	0.950333i
$679$	2.36012	−	5.30092i	0.0905731	−	0.203430i
$680$	5.75787	−	10.4672i	0.220804	−	0.401398i
$681$			20.0147i			0.766964i
$682$	12.0578	−	26.6323i	0.461718	−	1.01980i
$683$			10.0774i			0.385601i	0.981238	+	0.192801i	$0.0617571\pi$
$683$			10.0774i			0.385601i	−0.981238	+	0.192801i	$0.938243\pi$
$684$	−2.60617	+	4.30164i	−0.0996493	+	0.164477i
$685$	6.43324	−	14.4493i	0.245802	−	0.552080i
$686$	26.2015	−	9.74170i	1.00038	−	0.371940i
$687$	17.9501	+	10.3635i	0.684840	+	0.395393i
$688$	18.9908	+	22.9719i	0.724019	+	0.875796i
$689$	0.227372	−	0.252522i	0.00866217	−	0.00962032i
$690$	−3.46433	+	12.4038i	−0.131885	+	0.472203i
$691$	−28.0732	+	25.2772i	−1.06796	+	0.961591i	−0.999350	−	0.0360525i	$-0.988522\pi$
$691$	−28.0732	+	25.2772i	−1.06796	+	0.961591i	−0.0686055	+	0.997644i	$0.521855\pi$
$692$	−7.01238	+	3.85353i	−0.266571	+	0.146489i
$693$	1.47295	−	6.92970i	0.0559528	−	0.263237i
$694$	−1.08061	+	17.1525i	−0.0410193	+	0.651098i
$695$	−0.137942	−	1.31243i	−0.00523242	−	0.0497832i
$696$	−7.90744	−	22.7258i	−0.299731	−	0.861418i
$697$	1.41878	+	1.95279i	0.0537403	+	0.0739672i
$698$	23.2868	−	18.4537i	0.881418	−	0.698481i
$699$	−8.34617	+	1.77403i	−0.315681	+	0.0671001i
$700$	−4.64667	+	0.885579i	−0.175628	+	0.0334717i
$701$	4.47890	−	42.6139i	0.169166	−	1.60951i	−0.499751	−	0.866169i	$-0.666575\pi$
$701$	4.47890	−	42.6139i	0.169166	−	1.60951i	0.668917	−	0.743337i	$-0.266758\pi$
$702$	0.00886041	−	0.0523587i	0.000334414	−	0.00197615i
$703$	14.2728	−	6.35464i	0.538307	−	0.239670i
$704$	24.7315	+	16.4498i	0.932103	+	0.619975i
$705$	−4.92871	−	1.60143i	−0.185626	−	0.0603135i
$706$	39.3760	+	32.5803i	1.48194	+	1.22618i
$707$	−14.8011	+	8.54541i	−0.556652	+	0.321383i
$708$	−10.6118	−	4.99576i	−0.398818	−	0.187752i
$709$	−12.2195	+	3.97037i	−0.458915	+	0.149110i	−0.529346	−	0.848406i	$-0.677563\pi$
$709$	−12.2195	+	3.97037i	−0.458915	+	0.149110i	0.0704310	+	0.997517i	$0.477563\pi$
$710$	2.48296	−	6.26969i	0.0931840	−	0.235297i
$711$	12.8147	+	9.31042i	0.480589	+	0.349168i
$712$	−3.75274	−	29.7672i	−0.140640	−	1.11557i
$713$	−26.1042	+	1.48056i	−0.977611	+	0.0554473i
$714$	5.87232	−	0.245622i	0.219766	−	0.00919216i
$715$	0.158909	−	0.218720i	0.00594287	−	0.00817966i
$716$	19.9011	+	6.93410i	0.743740	+	0.259140i
$717$	3.59883	+	11.0760i	0.134401	+	0.413643i
$718$	30.7649	+	16.0868i	1.14813	+	0.600355i
$719$	3.71423	+	6.43323i	0.138517	+	0.239919i	0.926936	−	0.375221i	$-0.122433\pi$
$719$	3.71423	+	6.43323i	0.138517	+	0.239919i	−0.788418	+	0.615139i	$0.789100\pi$
$720$	4.15852	−	6.54785i	0.154979	−	0.244024i
$721$	3.27748	−	10.0870i	0.122060	−	0.375661i
$722$	−12.5414	−	12.8091i	−0.466743	−	0.476704i
$723$	−6.97836	−	15.6737i	−0.259528	−	0.582910i
$724$	5.27008	−	41.6599i	0.195861	−	1.54828i
$725$	10.4871	+	1.10224i	0.389483	+	0.0409363i
$726$	−0.575033	−	3.89641i	−0.0213415	−	0.144609i
$727$	6.34406	+	29.8465i	0.235288	+	1.10694i	0.924144	+	0.382045i	$0.124780\pi$
$727$	6.34406	+	29.8465i	0.235288	+	1.10694i	−0.688855	+	0.724899i	$0.741886\pi$
$728$	−0.147764	+	0.138689i	−0.00547651	+	0.00514015i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−4.18054	−	16.2879i	−0.154729	−	0.602841i
$731$	16.1405	−	1.69643i	0.596978	−	0.0627449i
$732$	−4.74385	−	0.100178i	−0.175338	−	0.00370269i
$733$	−14.4213	−	3.06535i	−0.532663	−	0.113221i	−0.0662755	−	0.997801i	$-0.521112\pi$
$733$	−14.4213	−	3.06535i	−0.532663	−	0.113221i	−0.466388	+	0.884580i	$0.654445\pi$
$734$	−32.1177	+	15.9399i	−1.18548	+	0.588354i
$735$	−4.35865	−	4.84077i	−0.160771	−	0.178555i
$736$	2.78800	−	26.4178i	0.102767	−	0.973775i
$737$	−13.9275	−	12.5403i	−0.513025	−	0.461929i
$738$	0.839674	+	1.32336i	0.0309088	+	0.0487137i
$739$	1.42470	−	2.46765i	0.0524083	−	0.0907739i	−0.838631	−	0.544700i	$-0.816644\pi$
$739$	1.42470	−	2.46765i	0.0524083	−	0.0907739i	0.891039	+	0.453926i	$0.149977\pi$
$740$	−22.2141	+	9.33350i	−0.816607	+	0.343106i
$741$	−0.0862647	−	0.0384075i	−0.00316901	−	0.00141094i
$742$	20.3386	+	13.5154i	0.746653	+	0.496167i
$743$	−5.58523			−0.204902			−0.102451	−	0.994738i	$-0.532668\pi$
$743$	−5.58523			−0.204902			−0.102451	+	0.994738i	$0.532668\pi$
$744$	15.3085	+	3.69460i	0.561237	+	0.135451i
$745$	9.94621			0.364401
$746$	37.9904	+	25.2454i	1.39093	+	0.924301i
$747$	−12.9124	−	5.74896i	−0.472439	−	0.210343i
$748$	14.9107	−	6.26491i	0.545191	−	0.229068i
$749$	−12.9121	+	22.3644i	−0.471797	+	0.817177i
$750$	9.16756	+	14.4485i	0.334752	+	0.527584i
$751$	1.08745	+	0.979145i	0.0396816	+	0.0357295i	0.688733	−	0.725015i	$-0.258167\pi$
$751$	1.08745	+	0.979145i	0.0396816	+	0.0357295i	−0.649051	+	0.760745i	$0.724834\pi$
$752$	10.5745	+	1.56519i	0.385612	+	0.0570764i
$753$	−1.41491	−	1.57141i	−0.0515620	−	0.0572654i
$754$	0.404666	−	0.200835i	0.0147371	−	0.00731398i
$755$	36.2379	+	7.70260i	1.31883	+	0.280326i
$756$	3.81539	+	0.0805714i	0.138764	+	0.00293036i
$757$	−23.6597	+	2.48674i	−0.859927	+	0.0903820i	−0.524219	−	0.851584i	$-0.675643\pi$
$757$	−23.6597	+	2.48674i	−0.859927	+	0.0903820i	−0.335709	+	0.941966i	$0.608976\pi$
$758$	1.07380	+	4.18364i	0.0390021	+	0.151957i
$759$	−14.1055	+	10.2483i	−0.511998	+	0.371988i
$760$	−9.43951	−	10.0572i	−0.342407	−	0.364813i
$761$	−0.893451	−	4.20336i	−0.0323876	−	0.152372i	0.958982	−	0.283466i	$-0.0914843\pi$
$761$	−0.893451	−	4.20336i	−0.0323876	−	0.152372i	−0.991370	+	0.131094i	$0.958151\pi$
$762$	−2.72105	−	18.4378i	−0.0985734	−	0.667931i
$763$	−0.923826	−	0.0970980i	−0.0334448	−	0.00351518i
$764$	4.13847	−	32.7146i	0.149725	−	1.18357i
$765$	−1.71792	−	3.85851i	−0.0621115	−	0.139505i
$766$	19.5240	+	19.9406i	0.705430	+	0.720485i
$767$	0.0680484	−	0.209431i	0.00245708	−	0.00756213i
$768$	−6.21030	+	14.7456i	−0.224095	+	0.532085i
$769$	−24.8219	−	42.9928i	−0.895101	−	1.55036i	−0.833679	−	0.552249i	$-0.813770\pi$
$769$	−24.8219	−	42.9928i	−0.895101	−	1.55036i	−0.0614220	−	0.998112i	$-0.519564\pi$
$770$	17.2171	+	9.00276i	0.620462	+	0.324437i
$771$	−1.36344	−	4.19622i	−0.0491029	−	0.151123i
$772$	7.49358	+	2.61097i	0.269700	+	0.0939709i
$773$	12.7662	−	17.5711i	0.459168	−	0.631990i	−0.515168	−	0.857089i	$-0.672271\pi$
$773$	12.7662	−	17.5711i	0.459168	−	0.631990i	0.974336	+	0.225099i	$0.0722706\pi$
$774$	10.5286	−	0.440380i	0.378442	−	0.0158291i
$775$	−4.32008	+	5.38197i	−0.155182	+	0.193326i
$776$	8.53367	−	1.07584i	0.306341	−	0.0386203i
$777$	−9.59055	−	6.96794i	−0.344059	−	0.249974i
$778$	14.1802	−	35.8061i	0.508384	−	1.28371i
$779$	2.65054	−	0.861212i	0.0949653	−	0.0308561i
$780$	0.131761	+	0.0620296i	0.00471781	+	0.00222101i
$781$	7.90642	−	4.56477i	0.282914	−	0.163340i
$782$	−11.1445	−	9.22112i	−0.398526	−	0.329746i
$783$	−8.09089	−	2.62889i	−0.289145	−	0.0939488i
$784$	10.5271	+	8.34951i	0.375967	+	0.298197i
$785$	4.71973	−	2.10136i	0.168454	−	0.0750008i
$786$	4.12151	−	24.3552i	0.147009	−	0.868721i
$787$	3.83440	−	36.4819i	0.136682	−	1.30044i	−0.684181	−	0.729313i	$-0.739840\pi$
$787$	3.83440	−	36.4819i	0.136682	−	1.30044i	0.820862	−	0.571126i	$-0.193493\pi$
$788$	−7.67405	+	1.46255i	−0.273377	+	0.0521011i
$789$	−13.8340	+	2.94052i	−0.492505	+	0.104685i
$790$	−34.0458	+	26.9796i	−1.21129	+	0.959891i
$791$	20.9371	+	28.8174i	0.744437	+	1.02463i
$792$	9.91819	−	3.45104i	0.352428	−	0.122627i
$793$	−0.00931189	−	0.0885967i	−0.000330675	−	0.00314616i
$794$	1.69850	−	26.9603i	0.0602776	−	0.956785i
$795$	3.64856	−	17.1651i	0.129401	−	0.608784i
$796$	−29.2762	+	16.0882i	−1.03767	+	0.570231i
$797$	8.74352	−	7.87270i	0.309711	−	0.278865i	−0.499586	−	0.866264i	$-0.666515\pi$
$797$	8.74352	−	7.87270i	0.309711	−	0.278865i	0.809298	+	0.587399i	$0.199848\pi$
$798$	1.82547	−	6.53594i	0.0646208	−	0.231370i
$799$	3.89479	−	4.32560i	0.137788	−	0.153029i
$800$	−4.68957	−	5.21276i	−0.165802	−	0.184299i
$801$	−9.18645	−	5.30380i	−0.324587	−	0.187400i
$802$	34.1925	−	12.7128i	1.20738	−	0.448904i
$803$	9.25973	−	20.7977i	0.326769	−	0.733935i
$804$	5.23118	−	8.63438i	0.184489	−	0.304511i
$805$		−	17.3762i		−	0.612431i
$806$	−0.0327458	+	0.293847i	−0.00115342	+	0.0103503i
$807$		−	5.34082i		−	0.188006i
$808$	−22.1971	−	12.2104i	−0.780892	−	0.429559i
$809$	−6.24620	+	14.0292i	−0.219605	+	0.493240i	−0.989429	−	0.145015i	$-0.953677\pi$
$809$	−6.24620	+	14.0292i	−0.219605	+	0.493240i	0.769825	+	0.638255i	$0.220344\pi$
$810$	−0.955718	−	2.57052i	−0.0335805	−	0.0903188i
$811$	−3.43033	−	1.98050i	−0.120455	−	0.0695449i	0.438562	−	0.898701i	$-0.355488\pi$
$811$	−3.43033	−	1.98050i	−0.120455	−	0.0695449i	−0.559017	+	0.829156i	$0.688821\pi$
$812$	18.5241	+	26.6624i	0.650069	+	0.935667i
$813$	10.3714	−	11.5186i	0.363741	−	0.403975i
$814$	−31.4187	−	8.77514i	−1.10122	−	0.307568i
$815$	−18.3446	+	16.5176i	−0.642584	+	0.578585i
$816$	4.81879	+	7.25822i	0.168691	+	0.254089i
$817$	3.89593	−	18.3289i	0.136301	−	0.641247i
$818$	−53.5217	−	3.37188i	−1.87134	−	0.117895i
$819$	0.00748938	+	0.0712567i	0.000261700	+	0.00248991i
$820$	−4.11491	+	1.24160i	−0.143699	+	0.0433586i
$821$	19.7755	+	27.2187i	0.690171	+	0.949939i	1.00000		0.000853715i	$-0.000271746\pi$
$821$	19.7755	+	27.2187i	0.690171	+	0.949939i	−0.309829	+	0.950792i	$0.600272\pi$
$822$	7.16404	+	9.04036i	0.249875	+	0.315319i
$823$	−40.3616	+	8.57913i	−1.40692	+	0.299050i	−0.847922	−	0.530120i	$-0.822147\pi$
$823$	−40.3616	+	8.57913i	−1.40692	+	0.299050i	−0.558996	+	0.829170i	$0.688813\pi$
$824$	15.3071	−	3.58613i	0.533249	−	0.124929i
$825$	−0.481051	+	4.57690i	−0.0167481	+	0.159347i
$826$	15.6034	+	2.64049i	0.542913	+	0.0918744i
$827$	−23.8199	+	10.6053i	−0.828298	+	0.368782i	−0.776688	−	0.629885i	$-0.783102\pi$
$827$	−23.8199	+	10.6053i	−0.828298	+	0.368782i	−0.0516099	+	0.998667i	$0.516435\pi$
$828$	−6.84537	−	6.43042i	−0.237893	−	0.223473i
$829$	49.0534	+	15.9384i	1.70369	+	0.553564i	0.989264	−	0.146143i	$-0.0466858\pi$
$829$	49.0534	+	15.9384i	1.70369	+	0.553564i	0.714431	+	0.699706i	$0.246686\pi$
$830$	24.7107	−	29.8650i	0.857722	−	1.03663i
$831$	19.6263	−	11.3313i	0.680829	−	0.393077i
$832$	−0.289290	−	0.0809305i	−0.0100293	−	0.00280576i
$833$	6.95815	−	2.26084i	0.241085	−	0.0783334i
$834$	0.894783	+	0.354358i	0.0309838	+	0.0122704i
$835$	32.3282	+	23.4878i	1.11876	+	0.812829i
$836$	−1.55941	−	18.6085i	−0.0539333	−	0.643589i
$837$	4.31187	−	3.52247i	0.149040	−	0.121754i
$838$	1.86034	+	44.4770i	0.0642645	+	1.53643i
$839$	22.6890	−	31.2287i	0.783311	−	1.07813i	−0.211598	−	0.977357i	$-0.567867\pi$
$839$	22.6890	−	31.2287i	0.783311	−	1.07813i	0.994909	−	0.100778i	$-0.0321332\pi$
$840$	−3.02751	+	10.0183i	−0.104459	+	0.345666i
$841$	−13.4031	−	41.2506i	−0.462177	−	1.42244i
$842$	18.7761	−	35.9078i	0.647066	−	1.23747i
$843$	1.91994	+	3.32543i	0.0661262	+	0.114534i
$844$	−39.4412	−	29.9481i	−1.35762	−	1.03086i
$845$	7.78933	−	23.9731i	0.267961	−	0.824700i
$846$	2.70049	−	2.64406i	0.0928446	−	0.0909047i
$847$	2.16146	+	4.85473i	0.0742688	+	0.166810i
$848$	−1.52812	+	36.1654i	−0.0524760	+	1.24192i
$849$	16.4782	+	1.73193i	0.565531	+	0.0594397i
$850$	−3.77709	+	0.557423i	−0.129553	+	0.0191195i
$851$	6.06578	+	28.5372i	0.207932	+	0.978244i
$852$	3.21279	+	3.72334i	0.110068	+	0.127559i
$853$	−33.8660	+	24.6051i	−1.15955	+	0.842463i	−0.989721	−	0.143011i	$-0.954322\pi$
$853$	−33.8660	+	24.6051i	−1.15955	+	0.842463i	−0.169830	+	0.985473i	$0.554322\pi$
$854$	6.20105	−	1.59160i	0.212196	−	0.0544633i
$855$	−4.84991	+	0.509746i	−0.165863	+	0.0174330i
$856$	−38.2712	+	0.791882i	−1.30808	+	0.0270660i
$857$	42.1793	+	8.96548i	1.44082	+	0.306255i	0.861047	−	0.508525i	$-0.169809\pi$
$857$	42.1793	+	8.96548i	1.44082	+	0.306255i	0.579770	+	0.814780i	$0.303142\pi$
$858$	0.0876503	+	0.176608i	0.00299233	+	0.00602930i
$859$	−31.8740	−	35.3997i	−1.08753	−	1.20782i	−0.976841	−	0.213965i	$-0.931362\pi$
$859$	−31.8740	−	35.3997i	−1.08753	−	1.20782i	−0.110685	−	0.993856i	$-0.535305\pi$
$860$	−6.60396	+	28.1346i	−0.225193	+	0.959380i
$861$	−1.57148	−	1.41497i	−0.0535560	−	0.0482220i
$862$	32.3439	−	20.5222i	1.10164	−	0.698989i
$863$	21.4608	−	37.1712i	0.730534	−	1.26532i	−0.226121	−	0.974099i	$-0.572605\pi$
$863$	21.4608	−	37.1712i	0.730534	−	1.26532i	0.956655	−	0.291223i	$-0.0940621\pi$
$864$	2.82634	+	4.90018i	0.0961540	+	0.166708i
$865$	−7.08746	−	3.15554i	−0.240981	−	0.107292i
$866$	−9.50301	+	14.3005i	−0.322926	+	0.485952i
$867$	−12.2561			−0.416239
$868$	−21.2345	+	0.755037i	−0.720747	+	0.0256276i
$869$	−58.8104			−1.99501
$870$	12.9126	−	19.4315i	0.437779	−	0.658789i
$871$	0.173153	+	0.0770927i	0.00586707	+	0.00261219i
$872$	−0.585954	−	1.24604i	−0.0198429	−	0.0421963i
$873$	1.52049	−	2.63357i	0.0514609	−	0.0891329i
$874$	−14.1018	+	8.94760i	−0.477001	+	0.302657i
$875$	−17.1574	−	15.4486i	−0.580027	−	0.522259i
$876$	11.9389	+	2.80240i	0.403379	+	0.0946842i
$877$	20.3150	+	22.5621i	0.685990	+	0.761869i	0.981080	−	0.193600i	$-0.0620165\pi$
$877$	20.3150	+	22.5621i	0.685990	+	0.761869i	−0.295091	+	0.955469i	$0.595350\pi$
$878$	−12.6463	−	25.4813i	−0.426793	−	0.859952i
$879$	−0.912218	−	0.193898i	−0.0307684	−	0.00654002i
$880$	1.79854	+	28.7433i	0.0606289	+	0.968937i
$881$	−21.0820	+	2.21581i	−0.710271	+	0.0746524i	−0.452772	−	0.891626i	$-0.649565\pi$
$881$	−21.0820	+	2.21581i	−0.710271	+	0.0746524i	−0.257498	+	0.966279i	$0.582898\pi$
$882$	4.60130	−	1.18100i	0.154934	−	0.0397662i
$883$	6.56782	−	4.77180i	0.221025	−	0.160584i	−0.471763	−	0.881725i	$-0.656382\pi$
$883$	6.56782	−	4.77180i	0.221025	−	0.160584i	0.692788	+	0.721141i	$0.256382\pi$
$884$	−0.123840	+	0.106859i	−0.00416518	+	0.00359405i
$885$	−2.36445	−	11.1239i	−0.0794803	−	0.373925i
$886$	−56.0761	+	8.27572i	−1.88391	+	0.278028i
$887$	9.79486	+	1.02948i	0.328879	+	0.0345666i	0.267529	−	0.963550i	$-0.413793\pi$
$887$	9.79486	+	1.02948i	0.328879	+	0.0345666i	0.0613500	+	0.998116i	$0.480459\pi$
$888$	1.47487	−	17.5101i	0.0494936	−	0.587602i
$889$	10.2280	+	22.9725i	0.343037	+	0.770474i
$890$	20.7862	−	20.3519i	0.696756	−	0.682197i
$891$	1.14732	−	3.53110i	0.0384368	−	0.118296i
$892$	−3.94115	+	5.19044i	−0.131960	+	0.173789i
$893$	−3.36026	−	5.82014i	−0.112447	−	0.194764i
$894$	−3.36109	+	6.42784i	−0.112412	+	0.214979i
$895$	6.31440	+	19.4337i	0.211067	+	0.649598i
$896$	2.71846	−	21.4161i	0.0908173	−	0.715461i
$897$	0.103646	−	0.142656i	0.00346063	−	0.00476315i
$898$	−0.191825	−	4.58614i	−0.00640127	−	0.153041i
$899$	45.8047	+	12.0626i	1.52767	+	0.402312i
$900$	−2.47038	+	0.207020i	−0.0823460	+	0.00690065i
$901$	15.9458	+	11.5853i	0.531231	+	0.385962i
$902$	−5.41019	−	2.14258i	−0.180140	−	0.0713401i
$903$	−13.5222	+	4.39362i	−0.449990	+	0.146211i
$904$	−20.4734	+	48.6694i	−0.680935	+	1.61872i
$905$	35.2604	−	20.3576i	1.17210	−	0.676710i
$906$	−17.2236	+	20.8162i	−0.572217	+	0.691571i
$907$	−16.4330	−	5.33940i	−0.545648	−	0.177292i	0.0232054	−	0.999731i	$-0.492613\pi$
$907$	−16.4330	−	5.33940i	−0.545648	−	0.177292i	−0.568853	+	0.822439i	$0.692613\pi$
$908$	27.4070	−	29.1755i	0.909532	−	0.968223i
$909$	−8.18252	+	3.64309i	−0.271397	+	0.120834i
$910$	−0.193739	−	0.0327855i	−0.00642238	−	0.00108683i
$911$	3.80091	−	36.1633i	0.125930	−	1.19814i	−0.730878	−	0.682508i	$-0.760889\pi$
$911$	3.80091	−	36.1633i	0.125930	−	1.19814i	0.856808	−	0.515635i	$-0.172444\pi$
$912$	9.68944	−	2.70178i	0.320849	−	0.0894649i
$913$	51.3315	−	10.9108i	1.69882	−	0.361096i
$914$	9.20927	+	11.6212i	0.304616	+	0.384397i
$915$	−2.70420	−	3.72201i	−0.0893980	−	0.123046i
$916$	−11.9748	−	39.6868i	−0.395658	−	1.31129i
$917$	3.48376	+	33.1458i	0.115044	+	1.09457i
$918$	3.07413	+	0.193671i	0.101462	+	0.00639210i
$919$	−6.30389	+	29.6575i	−0.207946	+	0.978310i	0.743081	+	0.669202i	$0.233364\pi$
$919$	−6.30389	+	29.6575i	−0.207946	+	0.978310i	−0.951027	+	0.309108i	$0.899969\pi$
$920$	22.0350	−	13.3372i	0.726472	−	0.439713i
$921$	−13.3527	+	12.0228i	−0.439987	+	0.396166i
$922$	−4.13285	−	1.15429i	−0.136108	−	0.0380146i
$923$	−0.0617820	+	0.0686158i	−0.00203358	+	0.00225852i
$924$	−11.6363	+	8.08447i	−0.382805	+	0.265959i
$925$	6.66905	+	3.85038i	0.219277	+	0.126600i
$926$	−7.81755	−	21.0263i	−0.256901	−	0.690965i
$927$	2.26081	−	5.07787i	0.0742549	−	0.166779i
$928$	−19.5927	+	43.9554i	−0.643160	+	1.44291i
$929$		−	15.3304i		−	0.502975i	−0.967861	−	0.251488i	$-0.919080\pi$
$929$		−	15.3304i		−	0.502975i	0.967861	−	0.251488i	$-0.0809198\pi$
$930$	6.12311	+	13.9878i	0.200785	+	0.458677i
$931$		−	8.44728i		−	0.276848i
$932$	14.5955	+	8.84275i	0.478091	+	0.289654i
$933$	−12.9289	+	29.0388i	−0.423274	+	0.950688i
$934$	−0.343819	+	0.127832i	−0.0112501	+	0.00418279i
$935$	13.5808	+	7.84085i	0.444138	+	0.256423i
$936$	−0.0846129	+	0.0641906i	−0.00276566	+	0.00209814i
$937$	−9.22310	+	10.2433i	−0.301306	+	0.334634i	−0.874717	−	0.484634i	$-0.838953\pi$
$937$	−9.22310	+	10.2433i	−0.301306	+	0.334634i	0.573412	+	0.819267i	$0.305620\pi$
$938$	−3.66413	+	13.1191i	−0.119638	+	0.428355i
$939$	−19.1274	+	17.2224i	−0.624200	+	0.562032i
$940$	4.99168	+	9.08351i	0.162811	+	0.296271i
$941$	−4.76424	+	22.4140i	−0.155310	+	0.730676i	0.829704	+	0.558203i	$0.188509\pi$
$941$	−4.76424	+	22.4140i	−0.155310	+	0.730676i	−0.985014	+	0.172473i	$0.944824\pi$
$942$	−0.236898	+	3.76028i	−0.00771857	+	0.122517i
$943$	0.543991	+	5.17573i	0.0177148	+	0.168545i
$944$	8.62802	+	21.8136i	0.280818	+	0.709972i
$945$	2.17494	+	2.99354i	0.0707507	+	0.0973799i
$946$	−30.6640	+	24.2997i	−0.996973	+	0.790052i
$947$	−50.2039	+	10.6712i	−1.63141	+	0.346766i	−0.930444	−	0.366433i	$-0.880579\pi$
$947$	−50.2039	+	10.6712i	−1.63141	+	0.346766i	−0.700962	+	0.713199i	$0.747246\pi$
$948$	−5.93088	−	31.1195i	−0.192626	−	1.01072i
$949$	−0.0240670	+	0.228982i	−0.000781246	+	0.00743306i
$950$	−0.735528	+	4.34645i	−0.0238637	+	0.141017i
$951$	−8.03429	+	3.57709i	−0.260530	+	0.115995i
$952$	−8.89644	−	7.68317i	−0.288335	−	0.249013i
$953$	−7.32576	−	2.38028i	−0.237305	−	0.0771049i	0.187950	−	0.982179i	$-0.439816\pi$
$953$	−7.32576	−	2.38028i	−0.237305	−	0.0771049i	−0.425255	+	0.905074i	$0.639816\pi$
$954$	9.86018	+	8.15847i	0.319235	+	0.264140i
$955$	27.6892	−	15.9864i	0.896002	−	0.517307i
$956$	9.92088	−	21.0736i	0.320864	−	0.681570i
$957$	30.0400	−	9.76058i	0.971055	−	0.315515i
$958$	3.11998	−	7.87821i	0.100802	−	0.254533i
$959$	−12.5910	−	9.14787i	−0.406583	−	0.295400i
$960$	−15.0282	+	3.85039i	−0.485031	+	0.124271i
$961$	−22.8584	+	20.9402i	−0.737368	+	0.675492i
$962$	0.329625	−	0.0137873i	0.0106275	−	0.000444519i
$963$	−7.95498	+	10.9491i	−0.256346	+	0.352829i
$964$	−11.2902	+	32.4033i	−0.363634	+	1.04364i
$965$	2.37763	+	7.31759i	0.0765386	+	0.235562i
$966$	11.2296	+	5.87189i	0.361305	+	0.188925i
$967$	−1.96450	−	3.40261i	−0.0631739	−	0.109420i	0.832709	−	0.553711i	$-0.186789\pi$
$967$	−1.96450	−	3.40261i	−0.0631739	−	0.109420i	−0.895883	+	0.444291i	$0.853456\pi$
$968$	−4.49730	+	6.46723i	−0.144549	+	0.207865i
$969$	1.69258	−	5.20921i	0.0543733	−	0.167344i
$970$	5.83449	+	5.95900i	0.187334	+	0.191332i
$971$	23.8195	+	53.4994i	0.764403	+	1.71688i	0.694688	+	0.719311i	$0.255542\pi$
$971$	23.8195	+	53.4994i	0.764403	+	1.71688i	0.0697150	+	0.997567i	$0.477791\pi$
$972$	1.98419	+	0.251005i	0.0636428	+	0.00805097i
$973$	−1.29140	−	0.135731i	−0.0414003	−	0.00435134i
$974$	1.14974	+	7.79064i	0.0368402	+	0.249628i
$975$	−0.00967692	−	0.0455263i	−0.000309910	−	0.00145801i
$976$	6.77795	+	6.64199i	0.216957	+	0.212605i
$977$	14.2714	−	10.3688i	0.456583	−	0.331727i	−0.335607	−	0.942002i	$-0.608941\pi$
$977$	14.2714	−	10.3688i	0.456583	−	0.331727i	0.792189	+	0.610276i	$0.208941\pi$
$978$	−4.47551	−	17.4371i	−0.143111	−	0.557577i
$979$	39.1683	−	4.11676i	1.25182	−	0.131572i
$980$	−0.275053	+	13.0249i	−0.00878624	+	0.416065i
$981$	−0.476183	−	0.101216i	−0.0152034	−	0.00323157i
$982$	−0.00922151	+	0.00457662i	−0.000294270	+	0.000146046i
$983$	−17.3564	−	19.2763i	−0.553584	−	0.614817i	0.399791	−	0.916606i	$-0.369083\pi$
$983$	−17.3564	−	19.2763i	−0.553584	−	0.614817i	−0.953375	+	0.301789i	$0.902416\pi$
$984$	0.588142	−	3.07888i	0.0187493	−	0.0981510i
$985$	−5.62908	−	5.06844i	−0.179357	−	0.161494i
$986$	14.0391	+	22.1262i	0.447096	+	0.704642i
$987$	−2.54965	+	4.41613i	−0.0811564	+	0.140567i
$988$	0.0731553	+	0.174113i	0.00232738	+	0.00553926i
$989$	31.9663	+	14.2323i	1.01647	+	0.452561i
$990$	8.48047	+	5.63545i	0.269527	+	0.179106i
$991$	0.813756			0.0258498			0.0129249	−	0.999916i	$-0.495886\pi$
$991$	0.813756			0.0258498			0.0129249	+	0.999916i	$0.495886\pi$
$992$	−17.2561	−	26.3482i	−0.547881	−	0.836556i
$993$	27.4651			0.871580
$994$	−5.52645	−	3.67244i	−0.175288	−	0.116483i
$995$	−29.5896	−	13.1741i	−0.938053	−	0.417648i
$996$	10.9501	+	26.0617i	0.346968	+	0.825797i
$997$	22.2476	−	38.5339i	0.704588	−	1.22038i	−0.262252	−	0.964999i	$-0.584465\pi$
$997$	22.2476	−	38.5339i	0.704588	−	1.22038i	0.966840	−	0.255383i	$-0.0822014\pi$
$998$	−4.12977	−	6.50870i	−0.130726	−	0.206029i
$999$	−4.61693	−	4.15710i	−0.146073	−	0.131525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.ba.a.43.14	✓	128
4.3	odd	2		372.2.ba.b.43.13	yes	128
31.13	odd	30		372.2.ba.b.199.13	yes	128
124.75	even	30	inner	372.2.ba.a.199.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.ba.a.43.14	✓	128	1.1	even	1	trivial
372.2.ba.a.199.14	yes	128	124.75	even	30	inner
372.2.ba.b.43.13	yes	128	4.3	odd	2
372.2.ba.b.199.13	yes	128	31.13	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17786 + 0.782714i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.774717 + 1.84386i) q^{4} +(-0.969598 + 1.67939i) q^{5} +(-0.757672 - 1.19412i) q^{6} +(1.41801 + 1.27678i) q^{7} +(-0.530704 + 2.77819i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-2.45654 + 1.21917i) q^{10} +(-3.63168 - 0.771938i) q^{11} +(0.0422255 - 1.99955i) q^{12} +(0.0373439 - 0.00392500i) q^{13} +(0.670865 + 2.61377i) q^{14} +(1.56884 - 1.13983i) q^{15} +(-2.79963 + 2.85694i) q^{16} +(0.452842 + 2.13045i) q^{17} +(0.206473 + 1.39906i) q^{18} +(2.50099 + 0.262865i) q^{19} +(-3.84773 - 0.486747i) q^{20} +(-0.776103 - 1.74316i) q^{21} +(-3.67342 - 3.75181i) q^{22} +(-1.45114 + 4.46616i) q^{23} +(1.61482 - 2.32215i) q^{24} +(0.619759 + 1.07345i) q^{25} +(0.0470581 + 0.0246065i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.25565 + 3.60376i) q^{28} +(5.00044 - 6.88252i) q^{29} +(2.74004 - 0.114608i) q^{30} +(2.01762 + 5.18933i) q^{31} +(-5.53374 + 1.17377i) q^{32} +(3.00373 + 2.18234i) q^{33} +(-1.13415 + 2.86383i) q^{34} +(-3.51912 + 1.14343i) q^{35} +(-0.851867 + 1.80951i) q^{36} +(5.38035 - 3.10635i) q^{37} +(2.74007 + 2.26718i) q^{38} +(-0.0357118 - 0.0116035i) q^{39} +(-4.15111 - 3.58499i) q^{40} +(1.01242 - 0.450758i) q^{41} +(0.450251 - 2.66066i) q^{42} +(0.778877 - 7.41052i) q^{43} +(-1.39018 - 7.29435i) q^{44} +(-1.89682 + 0.403182i) q^{45} +(-5.20497 + 4.12468i) q^{46} +(-1.57081 - 2.16203i) q^{47} +(3.71961 - 1.47123i) q^{48} +(-0.351119 - 3.34067i) q^{49} +(-0.110217 + 1.74948i) q^{50} +(0.452842 - 2.13045i) q^{51} +(0.0361681 + 0.0658161i) q^{52} +(6.72502 - 6.05524i) q^{53} +(0.380426 - 1.36209i) q^{54} +(4.81766 - 5.35056i) q^{55} +(-4.29969 + 3.26191i) q^{56} +(-2.17785 - 1.25738i) q^{57} +(11.2769 - 4.19274i) q^{58} +(2.38530 - 5.35748i) q^{59} +(3.31710 + 2.00968i) q^{60} -2.37245i q^{61} +(-1.68528 + 7.69154i) q^{62} +1.90812i q^{63} +(-7.43671 - 2.94880i) q^{64} +(-0.0296169 + 0.0665207i) q^{65} +(1.82983 + 4.92156i) q^{66} +(4.37145 + 2.52386i) q^{67} +(-3.57743 + 2.48548i) q^{68} +(3.14223 - 3.48980i) q^{69} +(-5.04002 - 1.40766i) q^{70} +(-1.82734 + 1.64534i) q^{71} +(-2.41971 + 1.46458i) q^{72} +(-1.27485 + 5.99771i) q^{73} +(8.76869 + 0.552429i) q^{74} +(-0.129565 - 1.23273i) q^{75} +(1.45287 + 4.81512i) q^{76} +(-4.16417 - 5.73149i) q^{77} +(-0.0329814 - 0.0416194i) q^{78} +(15.4937 - 3.29329i) q^{79} +(-2.08341 - 7.47175i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.54530 + 0.261504i) q^{82} +(-12.9124 + 5.74896i) q^{83} +(2.61287 - 2.78148i) q^{84} +(-4.01695 - 1.30518i) q^{85} +(6.71773 - 8.11893i) q^{86} +(-7.36750 + 4.25363i) q^{87} +(4.07194 - 9.67985i) q^{88} +(-10.0884 + 3.27793i) q^{89} +(-2.54977 - 1.00978i) q^{90} +(0.0579654 + 0.0421143i) q^{91} +(-9.35918 + 0.784307i) q^{92} +(0.267502 - 5.56133i) q^{93} +(-0.157942 - 3.77607i) q^{94} +(-2.86641 + 3.94527i) q^{95} +(5.53274 + 1.17848i) q^{96} +(-0.939717 - 2.89215i) q^{97} +(2.20122 - 4.20967i) q^{98} +(-1.85641 - 3.21540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{3} + 2 q^{4} + 3 q^{6} - 6 q^{8} + 16 q^{9} - 2 q^{10} + 12 q^{11} - 9 q^{12} - 6 q^{13} + 5 q^{14} + 10 q^{16} + 3 q^{18} + 18 q^{19} - 11 q^{20} - 10 q^{21} + 10 q^{22} + 48 q^{23} - 3 q^{24}+ \cdots + 2 q^{99}+O(q^{100}) \) 128 * q - 16 * q^3 + 2 * q^4 + 3 * q^6 - 6 * q^8 + 16 * q^9 - 2 * q^10 + 12 * q^11 - 9 * q^12 - 6 * q^13 + 5 * q^14 + 10 * q^16 + 3 * q^18 + 18 * q^19 - 11 * q^20 - 10 * q^21 + 10 * q^22 + 48 * q^23 - 3 * q^24 - 68 * q^25 - 20 * q^26 + 32 * q^27 + 21 * q^28 + 26 * q^30 + 30 * q^32 + 4 * q^33 - 20 * q^34 - q^36 - 6 * q^37 + 3 * q^38 + 10 * q^39 - 54 * q^40 - 5 * q^42 - 40 * q^43 - 51 * q^44 - 41 * q^46 + 15 * q^48 + 8 * q^49 - 37 * q^50 + 121 * q^52 - 12 * q^53 - 5 * q^54 - 8 * q^55 - 109 * q^56 + 18 * q^57 - 58 * q^58 - 62 * q^59 + 7 * q^60 - 3 * q^62 - 16 * q^64 + 25 * q^66 + 48 * q^67 - 111 * q^68 + 24 * q^69 - 133 * q^70 - 2 * q^72 + 18 * q^73 - 14 * q^74 - 22 * q^75 - 81 * q^76 - 75 * q^78 - 10 * q^79 - 5 * q^80 + 16 * q^81 + 16 * q^82 - 26 * q^83 - 15 * q^84 + 38 * q^86 + 85 * q^88 + 20 * q^89 - 2 * q^90 + 54 * q^91 - 56 * q^92 + 14 * q^93 - 28 * q^94 + 40 * q^95 - 38 * q^96 - 10 * q^97 - 9 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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