LMFDB - Embedded newform 930.2.br.b.761.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			761.8
Character	$\chi$	$=$	930.761
Dual form			930.2.br.b.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.668302 + 1.59793i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.141806 - 1.72624i) q^{6} +(0.349465 - 3.32494i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.10675 + 2.13580i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.668302 + 1.59793i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.141806 - 1.72624i) q^{6} +(0.349465 - 3.32494i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.10675 + 2.13580i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.04488 - 1.35567i) q^{11} +(-0.398571 + 1.68557i) q^{12} +(-0.767976 + 3.61304i) q^{13} +(-1.35982 + 3.05421i) q^{14} +(0.220198 - 1.71800i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.24674 - 1.00031i) q^{17} +(2.66363 - 1.38024i) q^{18} +(5.45440 - 1.15937i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(5.54655 - 1.66364i) q^{21} +(-3.31478 + 0.348398i) q^{22} +(2.39951 - 1.74334i) q^{23} +(0.899933 - 1.47991i) q^{24} +(0.500000 + 0.866025i) q^{25} +(1.84688 - 3.19889i) q^{26} +(-4.82079 - 1.93907i) q^{27} +(2.23707 - 2.48452i) q^{28} +(-0.463163 + 1.42547i) q^{29} +(-0.740311 + 1.56587i) q^{30} +(-1.60598 - 5.33112i) q^{31} -1.00000i q^{32} +(4.20116 + 3.95951i) q^{33} +(1.82766 + 1.64563i) q^{34} +(-1.96511 + 2.70475i) q^{35} +(-2.95978 + 0.489581i) q^{36} +(10.2925 - 5.94236i) q^{37} +(-5.54571 - 0.582877i) q^{38} +(-6.28662 + 1.18743i) q^{39} +(0.104528 + 0.994522i) q^{40} +(4.72947 - 4.25843i) q^{41} +(-5.78918 - 0.131764i) q^{42} +(-2.42388 - 11.4035i) q^{43} +(3.26021 + 0.692978i) q^{44} +(2.89239 - 0.796280i) q^{45} +(-2.82079 + 0.916530i) q^{46} +(7.66790 - 2.49145i) q^{47} +(-1.31320 + 1.12938i) q^{48} +(-4.08604 - 0.868514i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(0.0969279 - 4.25863i) q^{51} +(-2.74500 + 2.47161i) q^{52} +(0.935941 + 8.90488i) q^{53} +(3.98564 + 3.33387i) q^{54} +(-3.31478 - 0.348398i) q^{55} +(-2.89534 + 1.67162i) q^{56} +(5.49777 + 7.94093i) q^{57} +(0.880989 - 1.21258i) q^{58} +(9.40535 + 8.46861i) q^{59} +(1.18796 - 1.26046i) q^{60} +10.1925i q^{61} +(-0.120033 + 5.56647i) q^{62} +(6.36515 + 7.75118i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.47161 - 2.74500i) q^{65} +(-2.77199 - 5.06395i) q^{66} +(-6.36095 + 11.0175i) q^{67} +(-1.22968 - 2.12987i) q^{68} +(4.38933 + 2.66916i) q^{69} +(2.70475 - 1.96511i) q^{70} +(12.8607 - 1.35172i) q^{71} +(2.96621 + 0.449004i) q^{72} +(1.97090 + 4.42672i) q^{73} +(-11.6250 + 2.47097i) q^{74} +(-1.04970 + 1.37773i) q^{75} +(5.09416 + 2.26807i) q^{76} +(-3.44343 - 10.5978i) q^{77} +(6.34587 + 0.813358i) q^{78} +(0.269267 - 0.604785i) q^{79} +(0.207912 - 0.978148i) q^{80} +(-0.123244 - 8.99916i) q^{81} +(-5.81392 + 2.58852i) q^{82} +(-0.713673 - 0.792614i) q^{83} +(5.46512 + 1.91427i) q^{84} +(1.44558 + 1.98966i) q^{85} +(-1.21862 + 11.5944i) q^{86} +(-2.58733 + 0.212543i) q^{87} +(-2.88650 - 1.66652i) q^{88} +(-3.28978 - 2.39017i) q^{89} +(-2.99689 - 0.136491i) q^{90} +(11.7448 + 3.81610i) q^{91} +2.96595 q^{92} +(7.44547 - 6.12903i) q^{93} -8.06251 q^{94} +(-5.30333 - 1.72316i) q^{95} +(1.59793 - 0.668302i) q^{96} +(-15.6402 - 11.3633i) q^{97} +(3.61766 + 2.08866i) q^{98} +(-3.51936 + 9.35930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.668302	+	1.59793i	0.385844	+	0.922564i
$3$	0.668302	+	1.59793i	0.385844	+	0.922564i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−0.141806	−	1.72624i	−0.0578920	−	0.704733i
$7$	0.349465	−	3.32494i	0.132085	−	1.25671i	−0.704831	−	0.709376i	$-0.748977\pi$
$7$	0.349465	−	3.32494i	0.132085	−	1.25671i	0.836916	−	0.547332i	$-0.184356\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−2.10675	+	2.13580i	−0.702249	+	0.711932i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	3.04488	−	1.35567i	0.918067	−	0.408750i	0.107372	−	0.994219i	$-0.465756\pi$
$11$	3.04488	−	1.35567i	0.918067	−	0.408750i	0.810695	+	0.585469i	$0.199090\pi$
$12$	−0.398571	+	1.68557i	−0.115058	+	0.486582i
$13$	−0.767976	+	3.61304i	−0.212998	+	1.00208i	0.733580	+	0.679603i	$0.237848\pi$
$13$	−0.767976	+	3.61304i	−0.212998	+	1.00208i	−0.946578	+	0.322475i	$0.895485\pi$
$14$	−1.35982	+	3.05421i	−0.363428	+	0.816272i
$15$	0.220198	−	1.71800i	0.0568548	−	0.443585i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.24674	−	1.00031i	−0.544914	−	0.242611i	0.115769	−	0.993276i	$-0.463067\pi$
$17$	−2.24674	−	1.00031i	−0.544914	−	0.242611i	−0.660683	+	0.750665i	$0.729733\pi$
$18$	2.66363	−	1.38024i	0.627824	−	0.325326i
$19$	5.45440	−	1.15937i	1.25132	−	0.265977i	0.465846	−	0.884866i	$-0.345750\pi$
$19$	5.45440	−	1.15937i	1.25132	−	0.265977i	0.785479	+	0.618888i	$0.212417\pi$
$20$	−0.406737	−	0.913545i	−0.0909491	−	0.204275i
$21$	5.54655	−	1.66364i	1.21036	−	0.363036i
$22$	−3.31478	+	0.348398i	−0.706714	+	0.0742786i
$23$	2.39951	−	1.74334i	0.500332	−	0.363512i	−0.308812	−	0.951123i	$-0.599931\pi$
$23$	2.39951	−	1.74334i	0.500332	−	0.363512i	0.809144	+	0.587611i	$0.199931\pi$
$24$	0.899933	−	1.47991i	0.183698	−	0.302084i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	1.84688	−	3.19889i	0.362203	−	0.627354i
$27$	−4.82079	−	1.93907i	−0.927761	−	0.373175i
$28$	2.23707	−	2.48452i	0.422767	−	0.469530i
$29$	−0.463163	+	1.42547i	−0.0860073	+	0.264703i	−0.984806	−	0.173659i	$-0.944441\pi$
$29$	−0.463163	+	1.42547i	−0.0860073	+	0.264703i	0.898799	+	0.438362i	$0.144441\pi$
$30$	−0.740311	+	1.56587i	−0.135162	+	0.285887i
$31$	−1.60598	−	5.33112i	−0.288442	−	0.957497i
$31$	−1.60598	−	5.33112i	−0.288442	−	0.957497i
$32$		−	1.00000i		−	0.176777i
$33$	4.20116	+	3.95951i	0.731329	+	0.689262i
$34$	1.82766	+	1.64563i	0.313441	+	0.282224i
$35$	−1.96511	+	2.70475i	−0.332165	+	0.457186i
$36$	−2.95978	+	0.489581i	−0.493297	+	0.0815968i
$37$	10.2925	−	5.94236i	1.69207	−	0.976918i	0.739229	−	0.673454i	$-0.235190\pi$
$37$	10.2925	−	5.94236i	1.69207	−	0.976918i	0.952843	−	0.303464i	$-0.0981431\pi$
$38$	−5.54571	−	0.582877i	−0.899632	−	0.0945552i
$39$	−6.28662	+	1.18743i	−1.00667	+	0.190141i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	4.72947	−	4.25843i	0.738619	−	0.665055i	−0.211346	−	0.977411i	$-0.567785\pi$
$41$	4.72947	−	4.25843i	0.738619	−	0.665055i	0.949965	+	0.312356i	$0.101118\pi$
$42$	−5.78918	−	0.131764i	−0.893290	−	0.0203316i
$43$	−2.42388	−	11.4035i	−0.369639	−	1.73901i	−0.632848	−	0.774276i	$-0.718114\pi$
$43$	−2.42388	−	11.4035i	−0.369639	−	1.73901i	0.263209	−	0.964739i	$-0.415219\pi$
$44$	3.26021	+	0.692978i	0.491494	+	0.104470i
$45$	2.89239	−	0.796280i	0.431173	−	0.118702i
$46$	−2.82079	+	0.916530i	−0.415903	+	0.135135i
$47$	7.66790	−	2.49145i	1.11848	−	0.363416i	0.309292	−	0.950967i	$-0.399908\pi$
$47$	7.66790	−	2.49145i	1.11848	−	0.363416i	0.809187	+	0.587552i	$0.199908\pi$
$48$	−1.31320	+	1.12938i	−0.189545	+	0.163012i
$49$	−4.08604	−	0.868514i	−0.583719	−	0.124073i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	0.0969279	−	4.25863i	0.0135726	−	0.596328i
$52$	−2.74500	+	2.47161i	−0.380663	+	0.342750i
$53$	0.935941	+	8.90488i	0.128561	+	1.22318i	0.848520	+	0.529163i	$0.177494\pi$
$53$	0.935941	+	8.90488i	0.128561	+	1.22318i	−0.719959	+	0.694017i	$0.755839\pi$
$54$	3.98564	+	3.33387i	0.542376	+	0.453683i
$55$	−3.31478	−	0.348398i	−0.446965	−	0.0469779i
$56$	−2.89534	+	1.67162i	−0.386906	+	0.223380i
$57$	5.49777	+	7.94093i	0.728197	+	1.05180i
$58$	0.880989	−	1.21258i	0.115680	−	0.159219i
$59$	9.40535	+	8.46861i	1.22447	+	1.10252i	0.991510	+	0.130033i	$0.0415085\pi$
$59$	9.40535	+	8.46861i	1.22447	+	1.10252i	0.232962	+	0.972486i	$0.425158\pi$
$60$	1.18796	−	1.26046i	0.153365	−	0.162725i
$61$			10.1925i			1.30501i	0.757783	+	0.652506i	$0.226282\pi$
$61$			10.1925i			1.30501i	−0.757783	+	0.652506i	$0.773718\pi$
$62$	−0.120033	+	5.56647i	−0.0152442	+	0.706942i
$63$	6.36515	+	7.75118i	0.801933	+	0.976557i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	2.47161	−	2.74500i	0.306565	−	0.340475i
$66$	−2.77199	−	5.06395i	−0.341208	−	0.623329i
$67$	−6.36095	+	11.0175i	−0.777113	+	1.34600i	0.156486	+	0.987680i	$0.449983\pi$
$67$	−6.36095	+	11.0175i	−0.777113	+	1.34600i	−0.933599	+	0.358319i	$0.883350\pi$
$68$	−1.22968	−	2.12987i	−0.149121	−	0.258284i
$69$	4.38933	+	2.66916i	0.528413	+	0.321329i
$70$	2.70475	−	1.96511i	0.323279	−	0.234876i
$71$	12.8607	−	1.35172i	1.52629	−	0.160419i	0.696116	−	0.717929i	$-0.254910\pi$
$71$	12.8607	−	1.35172i	1.52629	−	0.160419i	0.830170	+	0.557510i	$0.188243\pi$
$72$	2.96621	+	0.449004i	0.349571	+	0.0529156i
$73$	1.97090	+	4.42672i	0.230677	+	0.518108i	0.991384	−	0.130986i	$-0.0418144\pi$
$73$	1.97090	+	4.42672i	0.230677	+	0.518108i	−0.760707	+	0.649095i	$0.775148\pi$
$74$	−11.6250	+	2.47097i	−1.35138	+	0.287245i
$75$	−1.04970	+	1.37773i	−0.121208	+	0.159087i
$76$	5.09416	+	2.26807i	0.584340	+	0.260165i
$77$	−3.44343	−	10.5978i	−0.392416	−	1.20773i
$78$	6.34587	+	0.813358i	0.718528	+	0.0920946i
$79$	0.269267	−	0.604785i	0.0302950	−	0.0680436i	−0.897764	−	0.440476i	$-0.854810\pi$
$79$	0.269267	−	0.604785i	0.0302950	−	0.0680436i	0.928059	+	0.372433i	$0.121476\pi$
$80$	0.207912	−	0.978148i	0.0232452	−	0.109360i
$81$	−0.123244	−	8.99916i	−0.0136938	−	0.999906i
$82$	−5.81392	+	2.58852i	−0.642040	+	0.285855i
$83$	−0.713673	−	0.792614i	−0.0783358	−	0.0870007i	0.702703	−	0.711484i	$-0.251976\pi$
$83$	−0.713673	−	0.792614i	−0.0783358	−	0.0870007i	−0.781038	+	0.624483i	$0.785310\pi$
$84$	5.46512	+	1.91427i	0.596293	+	0.208864i
$85$	1.44558	+	1.98966i	0.156795	+	0.215809i
$86$	−1.21862	+	11.5944i	−0.131407	+	1.25025i
$87$	−2.58733	+	0.212543i	−0.277391	+	0.0227870i
$88$	−2.88650	−	1.66652i	−0.307702	−	0.177652i
$89$	−3.28978	−	2.39017i	−0.348716	−	0.253357i	0.399614	−	0.916683i	$-0.369144\pi$
$89$	−3.28978	−	2.39017i	−0.348716	−	0.253357i	−0.748330	+	0.663326i	$0.769144\pi$
$90$	−2.99689	−	0.136491i	−0.315900	−	0.0143874i
$91$	11.7448	+	3.81610i	1.23118	+	0.400036i
$92$	2.96595			0.309222
$93$	7.44547	−	6.12903i	0.772059	−	0.635551i
$94$	−8.06251			−0.831584
$95$	−5.30333	−	1.72316i	−0.544110	−	0.176792i
$96$	1.59793	−	0.668302i	0.163088	−	0.0682082i
$97$	−15.6402	−	11.3633i	−1.58802	−	1.15376i	−0.906698	−	0.421780i	$-0.861405\pi$
$97$	−15.6402	−	11.3633i	−1.58802	−	1.15376i	−0.681322	−	0.731984i	$-0.738595\pi$
$98$	3.61766	+	2.08866i	0.365439	+	0.210987i
$99$	−3.51936	+	9.35930i	−0.353709	+	0.940645i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	10.5296	+	14.4927i	1.04773	+	1.44208i	0.890758	+	0.454477i	$0.150174\pi$
$101$	10.5296	+	14.4927i	1.04773	+	1.44208i	0.156974	+	0.987603i	$0.449826\pi$
$102$	−1.40817	+	4.02025i	−0.139430	+	0.398064i
$103$	−5.71141	−	6.34317i	−0.562762	−	0.625011i	0.392863	−	0.919597i	$-0.371485\pi$
$103$	−5.71141	−	6.34317i	−0.562762	−	0.625011i	−0.955625	+	0.294586i	$0.904818\pi$
$104$	3.37442	−	1.50239i	0.330889	−	0.147321i
$105$	−5.63528	−	1.33252i	−0.549947	−	0.130041i
$106$	1.86163	−	8.75827i	0.180817	−	0.850678i
$107$	1.29495	−	2.90850i	0.125187	−	0.281176i	−0.840069	−	0.542479i	$-0.817486\pi$
$107$	1.29495	−	2.90850i	0.125187	−	0.281176i	0.965257	+	0.261304i	$0.0841524\pi$
$108$	−2.76034	−	4.40233i	−0.265614	−	0.423614i
$109$	−2.82151	−	8.68372i	−0.270252	−	0.831749i	−0.990437	−	0.137967i	$-0.955943\pi$
$109$	−2.82151	−	8.68372i	−0.270252	−	0.831749i	0.720185	−	0.693782i	$-0.244057\pi$
$110$	3.04488	+	1.35567i	0.290318	+	0.129258i
$111$	16.3739	+	12.4753i	1.55415	+	1.18411i
$112$	3.27019	−	0.695101i	0.309004	−	0.0656808i
$113$	−3.64515	−	8.18713i	−0.342907	−	0.770181i	−0.999868	−	0.0162564i	$-0.994825\pi$
$113$	−3.64515	−	8.18713i	−0.342907	−	0.770181i	0.656961	−	0.753924i	$-0.271841\pi$
$114$	−2.77481	−	9.25117i	−0.259885	−	0.866452i
$115$	−2.94970	+	0.310026i	−0.275061	+	0.0289101i
$116$	−1.21258	+	0.880989i	−0.112585	+	0.0817978i
$117$	−6.09879	−	9.25200i	−0.563833	−	0.855348i
$118$	−6.32807	−	10.9605i	−0.582546	−	1.00900i
$119$	−4.11113	+	7.12068i	−0.376866	+	0.652752i
$120$	−1.51932	+	0.831670i	−0.138694	+	0.0759207i
$121$	0.0730396	−	0.0811187i	0.00663996	−	0.00737442i
$122$	3.14965	−	9.69362i	0.285156	−	0.877619i
$123$	9.96538	+	4.71143i	0.898548	+	0.424815i
$124$	1.83429	−	5.25694i	0.164724	−	0.472087i
$125$		−	1.00000i		−	0.0894427i
$126$	−3.65837	−	9.33875i	−0.325913	−	0.831962i
$127$	6.54841	+	5.89622i	0.581078	+	0.523205i	0.906412	−	0.422394i	$-0.138810\pi$
$127$	6.54841	+	5.89622i	0.581078	+	0.523205i	−0.325335	+	0.945599i	$0.605477\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	16.6021	−	11.4942i	1.46173	−	1.01200i
$130$	−3.19889	+	1.84688i	−0.280561	+	0.161982i
$131$	−4.28845	−	0.450734i	−0.374683	−	0.0393808i	−0.0846846	−	0.996408i	$-0.526988\pi$
$131$	−4.28845	−	0.450734i	−0.374683	−	0.0393808i	−0.289999	+	0.957027i	$0.593655\pi$
$132$	1.07147	+	5.67269i	0.0932596	+	0.493744i
$133$	−1.94870	−	18.5407i	−0.168974	−	1.60768i
$134$	9.45421	−	8.51261i	0.816719	−	0.735377i
$135$	3.20539	+	4.08968i	0.275876	+	0.351984i
$136$	0.511330	+	2.40562i	0.0438462	+	0.206280i
$137$	−20.0356	−	4.25871i	−1.71176	−	0.363846i	−0.755226	−	0.655464i	$-0.772473\pi$
$137$	−20.0356	−	4.25871i	−1.71176	−	0.363846i	−0.956535	+	0.291618i	$0.905806\pi$
$138$	−3.34969	−	3.89490i	−0.285144	−	0.331556i
$139$	5.03220	−	1.63506i	0.426826	−	0.138684i	−0.0877237	−	0.996145i	$-0.527959\pi$
$139$	5.03220	−	1.63506i	0.426826	−	0.138684i	0.514549	+	0.857461i	$0.327959\pi$
$140$	−3.17962	+	1.03312i	−0.268727	+	0.0873147i
$141$	9.10563	+	10.5877i	0.766832	+	0.891646i
$142$	−12.6490	−	2.68862i	−1.06148	−	0.225624i
$143$	2.55970	+	12.0424i	0.214052	+	1.00704i
$144$	−2.68228	−	1.34364i	−0.223524	−	0.111970i
$145$	1.11385	−	1.00291i	0.0924999	−	0.0832873i
$146$	−0.506508	−	4.81910i	−0.0419189	−	0.398832i
$147$	−1.34288	−	7.10962i	−0.110759	−	0.586391i
$148$	11.8196	+	1.24229i	0.971566	+	0.102116i
$149$	6.76707	−	3.90697i	0.554380	−	0.320071i	−0.196507	−	0.980502i	$-0.562960\pi$
$149$	6.76707	−	3.90697i	0.554380	−	0.320071i	0.750887	+	0.660431i	$0.229626\pi$
$150$	1.42406	−	0.985925i	0.116274	−	0.0805005i
$151$	5.11107	−	7.03478i	0.415933	−	0.572482i	−0.548720	−	0.836006i	$-0.684885\pi$
$151$	5.11107	−	7.03478i	0.415933	−	0.572482i	0.964653	+	0.263524i	$0.0848847\pi$
$152$	−4.14396	−	3.73124i	−0.336120	−	0.302644i
$153$	6.86976	−	2.69117i	0.555388	−	0.217568i
$154$			11.1432i			0.897943i
$155$	−1.27474	+	5.41987i	−0.102390	+	0.435335i
$156$	−5.78394	−	2.73453i	−0.463086	−	0.218938i
$157$	−0.964998	+	2.96996i	−0.0770152	+	0.237028i	−0.982151	−	0.188094i	$-0.939769\pi$
$157$	−0.964998	+	2.96996i	−0.0770152	+	0.237028i	0.905136	+	0.425123i	$0.139769\pi$
$158$	−0.442977	+	0.491976i	−0.0352414	+	0.0391395i
$159$	−13.6039	+	7.44671i	−1.07886	+	0.590563i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−4.95796	−	8.58744i	−0.390742	−	0.676785i
$162$	−2.66368	+	8.59679i	−0.209278	+	0.675428i
$163$	−11.3453	+	8.24288i	−0.888636	+	0.645632i	−0.935522	−	0.353268i	$-0.885070\pi$
$163$	−11.3453	+	8.24288i	−0.888636	+	0.645632i	0.0468858	+	0.998900i	$0.485070\pi$
$164$	6.32926	−	0.665233i	0.494233	−	0.0519459i
$165$	−1.65856	−	5.52962i	−0.129119	−	0.430480i
$166$	0.433812	+	0.974358i	0.0336703	+	0.0756248i
$167$	−10.0189	+	2.12958i	−0.775286	+	0.164792i	−0.578531	−	0.815660i	$-0.696374\pi$
$167$	−10.0189	+	2.12958i	−0.775286	+	0.164792i	−0.196755	+	0.980453i	$0.563040\pi$
$168$	−4.60610	−	3.50939i	−0.355368	−	0.270756i
$169$	−0.588205	−	0.261886i	−0.0452466	−	0.0201451i
$170$	−0.759984	−	2.33899i	−0.0582881	−	0.179392i
$171$	−9.01486	+	14.0920i	−0.689383	+	1.07764i
$172$	4.74183	−	10.6503i	0.361561	−	0.812080i
$173$	1.29442	−	6.08977i	0.0984130	−	0.462997i	−0.901152	−	0.433503i	$-0.857277\pi$
$173$	1.29442	−	6.08977i	0.0984130	−	0.462997i	0.999565	−	0.0294936i	$-0.00938945\pi$
$174$	2.52638	+	0.597389i	0.191524	+	0.0452880i
$175$	3.05421	−	1.35982i	0.230877	−	0.102793i
$176$	2.23024	+	2.47693i	0.168111	+	0.186706i
$177$	−7.24662	+	20.6886i	−0.544689	+	1.55505i
$178$	2.39017	+	3.28978i	0.179150	+	0.246579i
$179$	0.584082	−	5.55717i	0.0436564	−	0.415362i	−0.950767	−	0.309905i	$-0.899703\pi$
$179$	0.584082	−	5.55717i	0.0436564	−	0.415362i	0.994424	−	0.105457i	$-0.0336306\pi$
$180$	2.80804	+	1.05590i	0.209299	+	0.0787023i
$181$	−4.37862	−	2.52800i	−0.325460	−	0.187904i	0.328364	−	0.944551i	$-0.393503\pi$
$181$	−4.37862	−	2.52800i	−0.325460	−	0.187904i	−0.653824	+	0.756647i	$0.726836\pi$
$182$	−9.99069	−	7.25866i	−0.740559	−	0.538048i
$183$	−16.2868	+	6.81165i	−1.20396	+	0.503531i
$184$	−2.82079	−	0.916530i	−0.207951	−	0.0675675i
$185$	−11.8847			−0.873782
$186$	−8.97504	+	3.52828i	−0.658082	+	0.258706i
$187$	−8.19714			−0.599435
$188$	7.66790	+	2.49145i	0.559239	+	0.181708i
$189$	−8.13198	+	15.3512i	−0.591515	+	1.11663i
$190$	4.51128	+	3.27764i	0.327283	+	0.237785i
$191$	−21.0648	−	12.1618i	−1.52420	−	0.879996i	−0.999589	−	0.0286516i	$-0.990879\pi$
$191$	−21.0648	−	12.1618i	−1.52420	−	0.879996i	−0.524608	−	0.851344i	$-0.675788\pi$
$192$	−1.72624	+	0.141806i	−0.124580	+	0.0102340i
$193$	−0.184318	+	1.75367i	−0.0132675	+	0.126232i	−0.999151	−	0.0412017i	$-0.986881\pi$
$193$	−0.184318	+	1.75367i	−0.0132675	+	0.126232i	0.985883	+	0.167434i	$0.0535480\pi$
$194$	11.3633	+	15.6402i	0.815834	+	1.12290i
$195$	6.03809	+	2.11496i	0.432397	+	0.151456i
$196$	−2.79517	−	3.10435i	−0.199655	−	0.221740i
$197$	12.7147	−	5.66094i	0.905883	−	0.403325i	0.0997180	−	0.995016i	$-0.468206\pi$
$197$	12.7147	−	5.66094i	0.905883	−	0.403325i	0.806165	+	0.591691i	$0.201539\pi$
$198$	6.23930	−	7.81368i	0.443407	−	0.555294i
$199$	1.75227	−	8.24376i	0.124215	−	0.584385i	−0.871379	−	0.490611i	$-0.836774\pi$
$199$	1.75227	−	8.24376i	0.124215	−	0.584385i	0.995594	−	0.0937737i	$-0.0298930\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	−21.8562	−	2.80133i	−1.54162	−	0.197591i
$202$	−5.53573	−	17.0372i	−0.389492	−	1.19873i
$203$	4.57774	+	2.03814i	0.321294	+	0.143049i
$204$	2.58158	−	3.38833i	0.180747	−	0.237231i
$205$	−6.22506	+	1.32318i	−0.434777	+	0.0924147i
$206$	3.47173	+	7.79763i	0.241887	+	0.543287i
$207$	−1.33172	+	8.79763i	−0.0925613	+	0.611478i
$208$	−3.67353	+	0.386103i	−0.254713	+	0.0267714i
$209$	15.0363	−	10.9245i	1.04008	−	0.755664i
$210$	4.94769	+	3.00870i	0.341423	+	0.207620i
$211$	−1.76506	−	3.05717i	−0.121511	−	0.210464i	0.798852	−	0.601527i	$-0.205441\pi$
$211$	−1.76506	−	3.05717i	−0.121511	−	0.210464i	−0.920364	+	0.391063i	$0.872107\pi$
$212$	−4.47697	+	7.75433i	−0.307479	+	0.532570i
$213$	10.7548	+	19.6471i	0.736906	+	1.34620i
$214$	−2.13035	+	2.36599i	−0.145627	+	0.161736i
$215$	−3.60259	+	11.0876i	−0.245695	+	0.756171i
$216$	1.26485	+	5.03986i	0.0860619	+	0.342919i
$217$	−18.2869	+	3.47673i	−1.24139	+	0.236016i
$218$			9.13060i			0.618402i
$219$	−5.75642	+	6.10775i	−0.388983	+	0.412723i
$220$	−2.47693	−	2.23024i	−0.166995	−	0.150363i
$221$	5.33961	−	7.34934i	0.359181	−	0.494370i
$222$	−11.7174	−	16.9246i	−0.786424	−	1.13590i
$223$	4.55052	−	2.62725i	0.304726	−	0.175933i	−0.339838	−	0.940484i	$-0.610372\pi$
$223$	4.55052	−	2.62725i	0.304726	−	0.175933i	0.644564	+	0.764550i	$0.277039\pi$
$224$	−3.32494	−	0.349465i	−0.222157	−	0.0233496i
$225$	−2.90303	−	0.756598i	−0.193535	−	0.0504398i
$226$	0.936777	+	8.91284i	0.0623135	+	0.592873i
$227$	7.29169	−	6.56547i	0.483966	−	0.435765i	−0.390680	−	0.920527i	$-0.627760\pi$
$227$	7.29169	−	6.56547i	0.483966	−	0.435765i	0.874647	+	0.484761i	$0.161093\pi$
$228$	−0.219770	+	9.65585i	−0.0145546	+	0.639475i
$229$	0.00473030	+	0.0222543i	0.000312587	+	0.00147061i	0.978304	−	0.207176i	$-0.0664274\pi$
$229$	0.00473030	+	0.0222543i	0.000312587	+	0.00147061i	−0.977991	+	0.208647i	$0.933094\pi$
$230$	2.90114	+	0.616656i	0.191295	+	0.0406611i
$231$	14.6333	−	12.5849i	0.962798	−	0.828025i
$232$	1.42547	−	0.463163i	0.0935867	−	0.0304082i
$233$	−12.7632	+	4.14700i	−0.836142	+	0.271679i	−0.695630	−	0.718400i	$-0.744875\pi$
$233$	−12.7632	+	4.14700i	−0.836142	+	0.271679i	−0.140512	+	0.990079i	$0.544875\pi$
$234$	2.94127	+	10.6838i	0.192277	+	0.698422i
$235$	−7.88632	−	1.67629i	−0.514447	−	0.109349i
$236$	2.63136	+	12.3796i	0.171287	+	0.805842i
$237$	1.14635	+	0.0260914i	0.0744637	+	0.00169482i
$238$	6.11033	−	5.50176i	0.396074	−	0.356626i
$239$	2.74962	+	26.1608i	0.177858	+	1.69220i	0.611600	+	0.791167i	$0.290526\pi$
$239$	2.74962	+	26.1608i	0.177858	+	1.69220i	−0.433742	+	0.901037i	$0.642807\pi$
$240$	1.70196	−	0.321470i	0.109861	−	0.0207508i
$241$	3.39797	+	0.357141i	0.218883	+	0.0230055i	0.213335	−	0.976979i	$-0.431567\pi$
$241$	3.39797	+	0.357141i	0.218883	+	0.0230055i	0.00554769	+	0.999985i	$0.498234\pi$
$242$	−0.0945318	+	0.0545780i	−0.00607673	+	0.00350840i
$243$	14.2976	−	6.21109i	0.917194	−	0.398441i
$244$	−5.99099	+	8.24588i	−0.383534	+	0.527889i
$245$	3.10435	+	2.79517i	0.198330	+	0.178577i
$246$	−8.02173	−	7.56031i	−0.511447	−	0.482028i
$247$			20.5973i			1.31058i
$248$	−3.36900	+	4.43282i	−0.213932	+	0.281484i
$249$	0.789591	−	1.67010i	0.0500383	−	0.105838i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−17.4824	+	19.4162i	−1.10348	+	1.22554i	−0.131292	+	0.991344i	$0.541913\pi$
$251$	−17.4824	+	19.4162i	−1.10348	+	1.22554i	−0.972189	+	0.234196i	$0.924754\pi$
$252$	0.593484	+	10.0122i	0.0373860	+	0.630708i
$253$	4.94282	−	8.56121i	0.310752	−	0.538239i
$254$	−4.40588	−	7.63121i	−0.276449	−	0.478824i
$255$	−2.21326	+	3.63962i	−0.138600	+	0.227922i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−21.0066	+	2.20788i	−1.31035	+	0.137724i	−0.733817	−	0.679347i	$-0.762263\pi$
$257$	−21.0066	+	2.20788i	−1.31035	+	0.137724i	−0.576537	+	0.817071i	$0.695596\pi$
$258$	−19.3414	+	5.80128i	−1.20414	+	0.361172i
$259$	−16.1611	−	36.2984i	−1.00420	−	2.25548i
$260$	3.61304	−	0.767976i	0.224071	−	0.0476279i
$261$	−2.06875	−	3.99233i	−0.128052	−	0.247119i
$262$	3.93927	+	1.75388i	0.243369	+	0.108355i
$263$	3.30860	+	10.1828i	0.204017	+	0.627901i	0.999752	+	0.0222557i	$0.00708481\pi$
$263$	3.30860	+	10.1828i	0.204017	+	0.627901i	−0.795735	+	0.605645i	$0.792915\pi$
$264$	0.733928	−	5.72615i	0.0451701	−	0.352420i
$265$	3.64189	−	8.17982i	0.223720	−	0.502483i
$266$	−3.87606	+	18.2354i	−0.237656	+	1.11809i
$267$	1.62075	−	6.85418i	0.0991880	−	0.419469i
$268$	−11.6220	+	5.17446i	−0.709928	+	0.316080i
$269$	0.794498	+	0.882379i	0.0484414	+	0.0537996i	0.766879	−	0.641792i	$-0.221809\pi$
$269$	0.794498	+	0.882379i	0.0484414	+	0.0537996i	−0.718437	+	0.695592i	$0.755142\pi$
$270$	−1.78473	−	4.88004i	−0.108615	−	0.296990i
$271$	9.99794	+	13.7610i	0.607331	+	0.835920i	0.996355	−	0.0853080i	$-0.0271874\pi$
$271$	9.99794	+	13.7610i	0.607331	+	0.835920i	−0.389023	+	0.921228i	$0.627187\pi$
$272$	0.257073	−	2.44589i	0.0155873	−	0.148304i
$273$	1.75118	+	21.3176i	0.105986	+	1.29020i
$274$	17.7390	+	10.2416i	1.07165	+	0.618719i
$275$	2.69649	+	1.95911i	0.162604	+	0.118139i
$276$	1.98215	+	4.73938i	0.119311	+	0.285277i
$277$	7.40924	+	2.40741i	0.445178	+	0.144647i	0.523024	−	0.852318i	$-0.324804\pi$
$277$	7.40924	+	2.40741i	0.445178	+	0.144647i	−0.0778452	+	0.996965i	$0.524804\pi$
$278$	−5.29117			−0.317343
$279$	14.7696	+	7.80128i	0.884231	+	0.467050i
$280$	3.34325			0.199797
$281$	0.311686	+	0.101273i	0.0185936	+	0.00604144i	0.318299	−	0.947990i	$-0.396888\pi$
$281$	0.311686	+	0.101273i	0.0185936	+	0.00604144i	−0.299705	+	0.954032i	$0.596888\pi$
$282$	−5.38819	−	12.8833i	−0.320862	−	0.767190i
$283$	11.0458	+	8.02524i	0.656604	+	0.477051i	0.865514	−	0.500884i	$-0.166992\pi$
$283$	11.0458	+	8.02524i	0.656604	+	0.477051i	−0.208910	+	0.977935i	$0.566992\pi$
$284$	11.1991	+	6.46578i	0.664542	+	0.383673i
$285$	−0.790745	−	9.62593i	−0.0468397	−	0.570191i
$286$	1.28690	−	12.2440i	0.0760958	−	0.724004i
$287$	−12.5062	−	17.2133i	−0.738219	−	1.01607i
$288$	2.13580	+	2.10675i	0.125853	+	0.124141i
$289$	−7.32802	−	8.13859i	−0.431060	−	0.478740i
$290$	−1.36925	+	0.609628i	−0.0804050	+	0.0357986i
$291$	7.70531	−	32.5860i	0.451693	−	1.91022i
$292$	−1.00747	+	4.73976i	−0.0589576	+	0.277373i
$293$	10.6444	−	23.9078i	0.621855	−	1.39671i	−0.278026	−	0.960574i	$-0.589680\pi$
$293$	10.6444	−	23.9078i	0.621855	−	1.39671i	0.899881	−	0.436136i	$-0.143653\pi$
$294$	−0.919836	+	7.17662i	−0.0536459	+	0.418549i
$295$	−3.91096	−	12.0367i	−0.227705	−	0.700804i
$296$	−10.8572	−	4.83395i	−0.631064	−	0.280968i
$297$	−17.3075	+	0.631147i	−1.00428	+	0.0366229i
$298$	−7.64319	+	1.62461i	−0.442758	+	0.0941111i
$299$	4.45601	+	10.0084i	0.257698	+	0.578799i
$300$	−1.65903	+	0.497612i	−0.0957842	+	0.0287296i
$301$	−38.7629	+	4.07414i	−2.23426	+	0.234830i
$302$	−7.03478	+	5.11107i	−0.404806	+	0.294109i
$303$	−16.1214	+	26.5110i	−0.926150	+	1.52302i
$304$	2.78813	+	4.82918i	0.159910	+	0.276972i
$305$	5.09624	−	8.82694i	0.291810	−	0.505429i
$306$	−7.36515	+	0.436579i	−0.421038	+	0.0249575i
$307$	−18.3546	+	20.3849i	−1.04755	+	1.16343i	−0.0613122	+	0.998119i	$0.519529\pi$
$307$	−18.3546	+	20.3849i	−1.04755	+	1.16343i	−0.986242	+	0.165308i	$0.947138\pi$
$308$	3.44343	−	10.5978i	0.196208	−	0.603866i
$309$	6.31898	−	13.3656i	0.359474	−	0.760341i
$310$	2.88719	−	4.76069i	0.163981	−	0.270389i
$311$			21.6877i			1.22980i	0.788607	+	0.614898i	$0.210803\pi$
$311$			21.6877i			1.22980i	−0.788607	+	0.614898i	$0.789197\pi$
$312$	4.65584	+	4.38803i	0.263585	+	0.248423i
$313$	5.09545	+	4.58797i	0.288012	+	0.259327i	0.800453	−	0.599395i	$-0.204592\pi$
$313$	5.09545	+	4.58797i	0.288012	+	0.259327i	−0.512441	+	0.858722i	$0.671259\pi$
$314$	1.83553	−	2.52640i	0.103585	−	0.142573i
$315$	−1.63679	−	9.89529i	−0.0922227	−	0.557537i
$316$	0.573326	−	0.331010i	0.0322521	−	0.0186207i
$317$	−31.8889	−	3.35166i	−1.79106	−	0.188248i	−0.850068	−	0.526674i	$-0.823439\pi$
$317$	−31.8889	−	3.35166i	−1.79106	−	0.188248i	−0.940993	+	0.338426i	$0.890106\pi$
$318$	15.2392	−	2.87842i	0.854572	−	0.161414i
$319$	0.522188	+	4.96829i	0.0292369	+	0.278171i
$320$	0.743145	−	0.669131i	0.0415431	−	0.0374055i
$321$	5.51299	+	0.125478i	0.307705	+	0.00700347i
$322$	2.06164	+	9.69923i	0.114890	+	0.540517i
$323$	−13.4143	−	2.85130i	−0.746393	−	0.158651i
$324$	5.18986	−	7.35291i	0.288326	−	0.408495i
$325$	−3.51298	+	1.14143i	−0.194865	+	0.0633154i
$326$	13.3373	−	4.33354i	0.738682	−	0.240012i
$327$	11.9903	−	10.3119i	0.663067	−	0.570250i
$328$	−6.22506	−	1.32318i	−0.343721	−	0.0730602i
$329$	−5.60425	−	26.3659i	−0.308973	−	1.45360i
$330$	−0.131361	+	5.77150i	−0.00723120	+	0.317711i
$331$	−12.1437	+	10.9342i	−0.667477	+	0.600999i	−0.931598	−	0.363491i	$-0.881585\pi$
$331$	−12.1437	+	10.9342i	−0.667477	+	0.600999i	0.264121	+	0.964490i	$0.414918\pi$
$332$	−0.111487	−	1.06072i	−0.00611862	−	0.0582148i
$333$	−8.99195	+	34.5017i	−0.492756	+	1.89068i
$334$	10.1866	+	1.07066i	0.557387	+	0.0585838i
$335$	11.0175	−	6.36095i	0.601949	−	0.347536i
$336$	3.29620	+	4.76099i	0.179822	+	0.259733i
$337$	−3.67952	+	5.06443i	−0.200436	+	0.275877i	−0.897389	−	0.441240i	$-0.854539\pi$
$337$	−3.67952	+	5.06443i	−0.200436	+	0.275877i	0.696953	+	0.717117i	$0.254539\pi$
$338$	0.478489	+	0.430834i	0.0260264	+	0.0234343i
$339$	10.6464	−	11.2962i	0.578233	−	0.613523i
$340$			2.45936i			0.133378i
$341$	−12.1172	−	14.0555i	−0.656186	−	0.761146i
$342$	12.9283	−	10.6165i	0.699082	−	0.574076i
$343$	2.91617	−	8.97505i	0.157458	−	0.484607i
$344$	−7.80089	+	8.66376i	−0.420596	+	0.467119i
$345$	−2.46669	−	4.50622i	−0.132802	−	0.242607i
$346$	−3.11291	+	5.39172i	−0.167351	+	0.289861i
$347$	−5.53100	−	9.57997i	−0.296920	−	0.514280i	0.678510	−	0.734591i	$-0.262626\pi$
$347$	−5.53100	−	9.57997i	−0.296920	−	0.514280i	−0.975430	+	0.220311i	$0.929293\pi$
$348$	−2.21812	−	1.34884i	−0.118904	−	0.0723057i
$349$	14.2437	−	10.3487i	0.762450	−	0.553952i	−0.137211	−	0.990542i	$-0.543814\pi$
$349$	14.2437	−	10.3487i	0.762450	−	0.553952i	0.899661	+	0.436589i	$0.143814\pi$
$350$	−3.32494	+	0.349465i	−0.177725	+	0.0186797i
$351$	10.7082	−	15.9286i	0.571562	−	0.850203i
$352$	−1.35567	−	3.04488i	−0.0722574	−	0.162293i
$353$	10.1776	−	2.16332i	0.541700	−	0.115142i	0.0710681	−	0.997471i	$-0.477359\pi$
$353$	10.1776	−	2.16332i	0.541700	−	0.115142i	0.470632	+	0.882330i	$0.344026\pi$
$354$	13.2851	−	17.4367i	0.706095	−	0.926753i
$355$	−11.8136	−	5.25974i	−0.626999	−	0.279158i
$356$	−1.25658	−	3.86737i	−0.0665988	−	0.204970i
$357$	−14.1258	−	1.81052i	−0.747617	−	0.0958229i
$358$	−2.27276	+	5.10469i	−0.120119	+	0.269791i
$359$	1.58902	−	7.47576i	0.0838654	−	0.394556i	−0.916114	−	0.400917i	$-0.868692\pi$
$359$	1.58902	−	7.47576i	0.0838654	−	0.394556i	0.999980	+	0.00636130i	$0.00202488\pi$
$360$	−2.34431	−	1.87195i	−0.123556	−	0.0986606i
$361$	11.0490	−	4.91932i	0.581525	−	0.258911i
$362$	3.38312	+	3.75733i	0.177813	+	0.197481i
$363$	0.178434	+	0.0625002i	0.00936537	+	0.00328041i
$364$	7.25866	+	9.99069i	0.380457	+	0.523654i
$365$	0.506508	−	4.81910i	0.0265119	−	0.252243i
$366$	17.5946	−	1.44535i	0.919685	−	0.0755498i
$367$	31.3719	+	18.1126i	1.63760	+	0.945470i	0.981656	+	0.190662i	$0.0610635\pi$
$367$	31.3719	+	18.1126i	1.63760	+	0.945470i	0.655946	+	0.754808i	$0.272270\pi$
$368$	2.39951	+	1.74334i	0.125083	+	0.0908780i
$369$	−0.868648	+	19.0726i	−0.0452200	+	0.992881i
$370$	11.3030	+	3.67258i	0.587617	+	0.190928i
$371$	29.9352			1.55416
$372$	9.62606	−	0.582152i	0.499088	−	0.0301832i
$373$	−15.3449			−0.794528			−0.397264	−	0.917704i	$-0.630040\pi$
$373$	−15.3449			−0.794528			−0.397264	+	0.917704i	$0.630040\pi$
$374$	7.79595	+	2.53306i	0.403119	+	0.130981i
$375$	1.59793	−	0.668302i	0.0825166	−	0.0345109i
$376$	−6.52271	−	4.73902i	−0.336383	−	0.244396i
$377$	−4.79459	−	2.76816i	−0.246934	−	0.142567i
$378$	12.4777	−	12.0869i	0.641786	−	0.621684i
$379$	3.01568	−	28.6923i	0.154905	−	1.47382i	−0.590406	−	0.807107i	$-0.701032\pi$
$379$	3.01568	−	28.6923i	0.154905	−	1.47382i	0.745311	−	0.666717i	$-0.232301\pi$
$380$	−3.27764	−	4.51128i	−0.168139	−	0.231424i
$381$	−5.04541	+	14.4043i	−0.258484	+	0.737957i
$382$	16.2756	+	18.0759i	0.832734	+	0.924845i
$383$	−4.24482	+	1.88991i	−0.216900	+	0.0965701i	−0.512310	−	0.858800i	$-0.671210\pi$
$383$	−4.24482	+	1.88991i	−0.216900	+	0.0965701i	0.295410	+	0.955370i	$0.404544\pi$
$384$	1.68557	+	0.398571i	0.0860163	+	0.0203395i
$385$	−2.31680	+	10.8997i	−0.118075	+	0.555499i
$386$	0.717212	−	1.61088i	0.0365051	−	0.0819918i
$387$	29.4620	+	18.8473i	1.49764	+	0.958063i
$388$	−5.97402	−	18.3861i	−0.303285	−	0.933415i
$389$	7.35426	+	3.27433i	0.372876	+	0.166015i	0.584614	−	0.811311i	$-0.301246\pi$
$389$	7.35426	+	3.27433i	0.372876	+	0.166015i	−0.211739	+	0.977326i	$0.567913\pi$
$390$	−5.08901	−	3.87732i	−0.257692	−	0.196336i
$391$	−7.13494	+	1.51658i	−0.360830	+	0.0766967i
$392$	1.69907	+	3.81617i	0.0858159	+	0.192746i
$393$	−2.14574	−	7.15386i	−0.108238	−	0.360864i
$394$	−13.8417	+	1.45482i	−0.697335	+	0.0732928i
$395$	−0.535585	+	0.389125i	−0.0269482	+	0.0195790i
$396$	−8.34848	+	5.50320i	−0.419527	+	0.276546i
$397$	8.16499	+	14.1422i	0.409789	+	0.709775i	0.994866	−	0.101202i	$-0.0322690\pi$
$397$	8.16499	+	14.1422i	0.409789	+	0.709775i	−0.585077	+	0.810978i	$0.698936\pi$
$398$	−4.21396	+	7.29880i	−0.211227	+	0.365856i
$399$	28.3243	−	15.5047i	1.41799	−	0.776204i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	−5.07436	+	15.6173i	−0.253401	+	0.779889i	0.740739	+	0.671793i	$0.234476\pi$
$401$	−5.07436	+	15.6173i	−0.253401	+	0.779889i	−0.994140	+	0.108096i	$0.965524\pi$
$402$	19.9208	+	9.41815i	0.993559	+	0.469735i
$403$	20.4949	−	1.70829i	1.02092	−	0.0850958i
$404$			17.9140i			0.891254i
$405$	−4.39285	+	7.85512i	−0.218282	+	0.390324i
$406$	−3.72387	−	3.35299i	−0.184812	−	0.166406i
$407$	23.2835	−	32.0470i	1.15412	−	1.58851i
$408$	−3.50228	+	2.42475i	−0.173389	+	0.120043i
$409$	−16.6654	+	9.62179i	−0.824052	+	0.475767i	−0.851812	−	0.523848i	$-0.824496\pi$
$409$	−16.6654	+	9.62179i	−0.824052	+	0.475767i	0.0277595	+	0.999615i	$0.491163\pi$
$410$	6.32926	+	0.665233i	0.312580	+	0.0328535i
$411$	−6.58475	−	34.8616i	−0.324802	−	1.71960i
$412$	−0.892210	−	8.48881i	−0.0439561	−	0.418214i
$413$	31.4444	−	28.3127i	1.54728	−	1.39318i
$414$	3.98516	−	7.95552i	0.195860	−	0.390993i
$415$	0.221752	+	1.04326i	0.0108854	+	0.0512116i
$416$	3.61304	+	0.767976i	0.177144	+	0.0376531i
$417$	5.97574	+	6.94838i	0.292633	+	0.340264i
$418$	−17.6762	+	5.74335i	−0.864572	+	0.280916i
$419$	−24.4554	+	7.94605i	−1.19473	+	0.388190i	−0.837818	−	0.545950i	$-0.816169\pi$
$419$	−24.4554	+	7.94605i	−1.19473	+	0.388190i	−0.356907	+	0.934140i	$0.616169\pi$
$420$	−3.77580	−	4.39037i	−0.184240	−	0.214228i
$421$	20.6806	+	4.39581i	1.00791	+	0.214238i	0.682149	−	0.731213i	$-0.261045\pi$
$421$	20.6806	+	4.39581i	1.00791	+	0.214238i	0.325763	+	0.945451i	$0.394379\pi$
$422$	0.733952	+	3.45297i	0.0357282	+	0.168088i
$423$	−10.8331	+	21.6259i	−0.526723	+	1.05149i
$424$	6.65407	−	5.99135i	0.323150	−	0.290966i
$425$	−0.257073	−	2.44589i	−0.0124699	−	0.118643i
$426$	−4.15711	−	22.0090i	−0.201412	−	1.06634i
$427$	33.8893	+	3.56191i	1.64002	+	0.172373i
$428$	2.75721	−	1.59188i	0.133275	−	0.0769463i
$429$	−17.5323	+	12.1382i	−0.846466	+	0.586037i
$430$	6.85254	−	9.43172i	0.330459	−	0.454838i
$431$	9.23624	+	8.31635i	0.444894	+	0.400584i	0.860897	−	0.508779i	$-0.169903\pi$
$431$	9.23624	+	8.31635i	0.444894	+	0.400584i	−0.416003	+	0.909363i	$0.636570\pi$
$432$	0.354462	−	5.18405i	0.0170540	−	0.249418i
$433$			24.5415i			1.17939i	0.807626	+	0.589695i	$0.200752\pi$
$433$			24.5415i			1.17939i	−0.807626	+	0.589695i	$0.799248\pi$
$434$	18.4662	+	2.34439i	0.886406	+	0.112534i
$435$	2.34697	+	1.10960i	0.112528	+	0.0532012i
$436$	2.82151	−	8.68372i	0.135126	−	0.415875i
$437$	11.0667	−	12.2908i	0.529391	−	0.587949i
$438$	7.36208	−	4.02998i	0.351774	−	0.192560i
$439$	1.08376	−	1.87713i	0.0517251	−	0.0895905i	−0.839004	−	0.544126i	$-0.816861\pi$
$439$	1.08376	−	1.87713i	0.0517251	−	0.0895905i	0.890729	+	0.454535i	$0.150195\pi$
$440$	1.66652	+	2.88650i	0.0794482	+	0.137608i
$441$	10.4632	−	6.89720i	0.498248	−	0.328438i
$442$	−7.34934	+	5.33961i	−0.349573	+	0.253979i
$443$	0.622280	−	0.0654043i	0.0295654	−	0.00310745i	−0.0897342	−	0.995966i	$-0.528602\pi$
$443$	0.622280	−	0.0654043i	0.0295654	−	0.00310745i	0.119300	+	0.992858i	$0.461935\pi$
$444$	5.91398	+	19.7171i	0.280665	+	0.935733i
$445$	1.65395	+	3.71483i	0.0784048	+	0.176100i
$446$	−5.13967	+	1.09247i	−0.243370	+	0.0517300i
$447$	10.7655	+	8.20226i	0.509191	+	0.387953i
$448$	3.05421	+	1.35982i	0.144298	+	0.0642456i
$449$	−4.66988	−	14.3724i	−0.220385	−	0.678277i	−0.998727	−	0.0504360i	$-0.983939\pi$
$449$	−4.66988	−	14.3724i	−0.220385	−	0.678277i	0.778342	−	0.627841i	$-0.216061\pi$
$450$	2.52714	+	1.61665i	0.119131	+	0.0762097i
$451$	8.62765	−	19.3780i	0.406260	−	0.912476i
$452$	1.86329	−	8.76609i	0.0876418	−	0.412322i
$453$	14.6568	+	3.46576i	0.688637	+	0.162836i
$454$	−8.96365	+	3.99087i	−0.420685	+	0.187301i
$455$	−8.26321	−	9.17722i	−0.387385	−	0.430235i
$456$	3.19284	−	9.11535i	0.149518	−	0.426865i
$457$	7.20835	+	9.92144i	0.337192	+	0.464105i	0.943619	−	0.331034i	$-0.107398\pi$
$457$	7.20835	+	9.92144i	0.337192	+	0.464105i	−0.606426	+	0.795140i	$0.707398\pi$
$458$	0.00237818	−	0.0226269i	0.000111125	−	0.00105728i
$459$	8.89137	+	9.17888i	0.415013	+	0.428433i
$460$	−2.56859	−	1.48298i	−0.119761	−	0.0691441i
$461$	−3.45805	−	2.51242i	−0.161058	−	0.117015i	0.504337	−	0.863507i	$-0.331737\pi$
$461$	−3.45805	−	2.51242i	−0.161058	−	0.117015i	−0.665395	+	0.746492i	$0.731737\pi$
$462$	−17.8060	+	7.44701i	−0.828410	+	0.346466i
$463$	7.91194	+	2.57075i	0.367699	+	0.119473i	0.487038	−	0.873381i	$-0.338077\pi$
$463$	7.91194	+	2.57075i	0.367699	+	0.119473i	−0.119339	+	0.992854i	$0.538077\pi$
$464$	−1.49883			−0.0695814
$465$	−9.51248	+	1.58516i	−0.441131	+	0.0735101i
$466$	13.4200			0.621668
$467$	−9.51582	−	3.09188i	−0.440340	−	0.143075i	0.0804527	−	0.996758i	$-0.474363\pi$
$467$	−9.51582	−	3.09188i	−0.440340	−	0.143075i	−0.520792	+	0.853683i	$0.674363\pi$
$468$	0.504166	−	11.0698i	0.0233051	−	0.511702i
$469$	34.4095	+	25.0000i	1.58888	+	1.15439i
$470$	6.98234	+	4.03125i	0.322071	+	0.185948i
$471$	−5.39069	+	0.442831i	−0.248390	+	0.0204046i
$472$	1.32293	−	12.5868i	0.0608927	−	0.579355i
$473$	−22.8398	−	31.4363i	−1.05018	−	1.44544i
$474$	−1.08218	−	0.379057i	−0.0497064	−	0.0174107i
$475$	3.73124	+	4.14396i	0.171201	+	0.190138i
$476$	−7.51140	+	3.34429i	−0.344285	+	0.153285i
$477$	−20.9908	−	16.7613i	−0.961102	−	0.767449i
$478$	5.46911	−	25.7301i	0.250151	−	1.17687i
$479$	5.14214	−	11.5494i	0.234951	−	0.527708i	−0.757137	−	0.653256i	$-0.773402\pi$
$479$	5.14214	−	11.5494i	0.234951	−	0.527708i	0.992087	+	0.125549i	$0.0400691\pi$
$480$	−1.71800	−	0.220198i	−0.0784155	−	0.0100506i
$481$	13.5656	+	41.7507i	0.618540	+	1.90367i
$482$	−3.12130	−	1.38969i	−0.142171	−	0.0632988i
$483$	10.4087	−	13.6615i	0.473612	−	0.621618i
$484$	0.106771	−	0.0226948i	0.00485321	−	0.00103158i
$485$	7.86317	+	17.6610i	0.357048	+	0.801943i
$486$	−15.5172	+	1.48888i	−0.703874	+	0.0675370i
$487$	−1.75963	+	0.184945i	−0.0797364	+	0.00838064i	−0.144313	−	0.989532i	$-0.546097\pi$
$487$	−1.75963	+	0.184945i	−0.0797364	+	0.00838064i	0.0645762	+	0.997913i	$0.479430\pi$
$488$	8.24588	−	5.99099i	0.373274	−	0.271199i
$489$	−20.7536	−	12.6203i	−0.938512	−	0.570711i
$490$	−2.08866	−	3.61766i	−0.0943560	−	0.163429i
$491$	−3.59194	+	6.22142i	−0.162102	+	0.280769i	−0.935622	−	0.353003i	$-0.885161\pi$
$491$	−3.59194	+	6.22142i	−0.162102	+	0.280769i	0.773520	+	0.633771i	$0.218494\pi$
$492$	5.29285	+	9.66913i	0.238620	+	0.435918i
$493$	2.46652	−	2.73935i	0.111087	−	0.123374i
$494$	6.36493	−	19.5892i	0.286372	−	0.881362i
$495$	7.72751	−	6.34571i	0.347326	−	0.285218i
$496$	4.57392	−	3.17478i	0.205375	−	0.142552i
$497$		−	43.2334i		−	1.93928i
$498$	−1.26704	+	1.34437i	−0.0567772	+	0.0602424i
$499$	−25.9527	−	23.3679i	−1.16180	−	1.04609i	−0.998225	−	0.0595607i	$-0.981030\pi$
$499$	−25.9527	−	23.3679i	−1.16180	−	1.04609i	−0.163577	−	0.986531i	$-0.552303\pi$
$500$	0.587785	−	0.809017i	0.0262866	−	0.0361803i
$501$	−10.0986	−	14.5863i	−0.451171	−	0.651667i
$502$	22.6267	−	13.0635i	1.00988	−	0.583054i
$503$	6.20250	+	0.651909i	0.276556	+	0.0290672i	0.241791	−	0.970328i	$-0.422265\pi$
$503$	6.20250	+	0.651909i	0.276556	+	0.0290672i	0.0347647	+	0.999396i	$0.488932\pi$
$504$	2.52950	−	9.70554i	0.112673	−	0.432319i
$505$	−1.87252	−	17.8159i	−0.0833261	−	0.792795i
$506$	−7.34646	+	6.61478i	−0.326590	+	0.294063i
$507$	0.0253761	−	1.11493i	0.00112699	−	0.0495157i
$508$	1.83207	+	8.61920i	0.0812848	+	0.382415i
$509$	−16.1192	−	3.42624i	−0.714470	−	0.151865i	−0.163685	−	0.986513i	$-0.552338\pi$
$509$	−16.1192	−	3.42624i	−0.714470	−	0.151865i	−0.550785	+	0.834647i	$0.685672\pi$
$510$	3.22964	−	2.77755i	0.143011	−	0.122992i
$511$	15.4073	−	5.00614i	0.681580	−	0.221459i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−28.5426	−	4.98740i	−1.26019	−	0.220199i
$514$	20.6607	+	4.39157i	0.911305	+	0.193704i
$515$	1.77465	+	8.34905i	0.0782002	+	0.367903i
$516$	20.1874	+	0.459473i	0.888702	+	0.0202272i
$517$	19.9703	−	17.9813i	0.878292	−	0.790817i
$518$	4.15329	+	39.5159i	0.182485	+	1.73623i
$519$	10.5961	−	2.00141i	0.465116	−	0.0878523i
$520$	−3.67353	−	0.386103i	−0.161095	−	0.0169317i
$521$	−25.0911	+	14.4864i	−1.09926	+	0.634659i	−0.936027	−	0.351928i	$-0.885526\pi$
$521$	−25.0911	+	14.4864i	−1.09926	+	0.634659i	−0.163235	+	0.986587i	$0.552193\pi$
$522$	0.733797	+	4.43621i	0.0321174	+	0.194167i
$523$	−6.82526	+	9.39417i	−0.298448	+	0.410778i	−0.931735	−	0.363138i	$-0.881705\pi$
$523$	−6.82526	+	9.39417i	−0.298448	+	0.410778i	0.633287	+	0.773917i	$0.281705\pi$
$524$	−3.20449	−	2.88534i	−0.139989	−	0.126047i
$525$	4.21403	+	3.97164i	0.183915	+	0.173336i
$526$		−	10.7069i		−	0.466842i
$527$	−1.72458	+	13.5841i	−0.0751238	+	0.591733i
$528$	−2.46748	+	5.21910i	−0.107383	+	0.227132i
$529$	−4.38901	+	13.5080i	−0.190826	+	0.587303i
$530$	−5.99135	+	6.65407i	−0.260248	+	0.289034i
$531$	−37.9019	+	2.24668i	−1.64480	+	0.0974977i
$532$	9.32140	−	16.1451i	0.404134	−	0.699981i
$533$	11.7538	+	20.3582i	0.509113	+	0.881809i
$534$	−3.65948	+	6.01788i	−0.158361	+	0.260419i
$535$	−2.57571	+	1.87136i	−0.111358	+	0.0809061i
$536$	12.6522	−	1.32980i	0.546492	−	0.0574386i
$537$	9.27030	−	2.78055i	0.400043	−	0.119989i
$538$	−0.482942	−	1.08471i	−0.0208211	−	0.0467650i
$539$	−13.6189	+	2.89479i	−0.586608	+	0.124687i
$540$	0.189361	+	5.19270i	0.00814879	+	0.223458i
$541$	−4.45776	−	1.98472i	−0.191654	−	0.0853299i	0.308666	−	0.951171i	$-0.400118\pi$
$541$	−4.45776	−	1.98472i	−0.191654	−	0.0853299i	−0.500320	+	0.865841i	$0.666784\pi$
$542$	−5.25623	−	16.1770i	−0.225774	−	0.694862i
$543$	1.11332	−	8.68618i	0.0477770	−	0.372759i
$544$	−1.00031	+	2.24674i	−0.0428880	+	0.0963280i
$545$	−1.89836	+	8.93107i	−0.0813167	+	0.382565i
$546$	4.92202	−	20.8154i	0.210643	−	0.890815i
$547$	5.60296	−	2.49460i	0.239565	−	0.106661i	−0.283443	−	0.958989i	$-0.591477\pi$
$547$	5.60296	−	2.49460i	0.239565	−	0.106661i	0.523008	+	0.852328i	$0.324810\pi$
$548$	−13.7060	−	15.2220i	−0.585490	−	0.650253i
$549$	−21.7690	−	21.4729i	−0.929080	−	0.916443i
$550$	−1.95911	−	2.69649i	−0.0835368	−	0.114979i
$551$	−0.873633	+	8.31206i	−0.0372180	+	0.354106i
$552$	−0.420589	−	5.11993i	−0.0179015	−	0.217919i
$553$	−1.91677	−	1.10665i	−0.0815094	−	0.0470595i
$554$	−6.30268	−	4.57916i	−0.267775	−	0.194550i
$555$	−7.94258	−	18.9909i	−0.337144	−	0.806120i
$556$	5.03220	+	1.63506i	0.213413	+	0.0693420i
$557$	−5.86114			−0.248344			−0.124172	−	0.992261i	$-0.539628\pi$
$557$	−5.86114			−0.248344			−0.124172	+	0.992261i	$0.539628\pi$
$558$	−11.6360	−	11.9835i	−0.492590	−	0.507302i
$559$	43.0628			1.82136
$560$	−3.17962	−	1.03312i	−0.134363	−	0.0436573i
$561$	−5.47816	−	13.0984i	−0.231288	−	0.553017i
$562$	−0.265136	−	0.192633i	−0.0111841	−	0.00812571i
$563$	8.55975	+	4.94197i	0.360750	+	0.208279i	0.669410	−	0.742893i	$-0.266547\pi$
$563$	8.55975	+	4.94197i	0.360750	+	0.208279i	−0.308660	+	0.951173i	$0.599880\pi$
$564$	1.14331	+	13.9178i	0.0481420	+	0.586045i
$565$	−0.936777	+	8.91284i	−0.0394105	+	0.374966i
$566$	−8.02524	−	11.0458i	−0.337326	−	0.464289i
$567$	−29.9647	−	2.73511i	−1.25840	−	0.114864i
$568$	−8.65290	−	9.61002i	−0.363068	−	0.403228i
$569$	33.2243	−	14.7924i	1.39284	−	0.620131i	0.433180	−	0.901307i	$-0.357391\pi$
$569$	33.2243	−	14.7924i	1.39284	−	0.620131i	0.959656	+	0.281177i	$0.0907247\pi$
$570$	−2.22253	+	9.39916i	−0.0930916	+	0.393687i
$571$	−7.27467	+	34.2246i	−0.304436	+	1.43226i	0.514065	+	0.857751i	$0.328139\pi$
$571$	−7.27467	+	34.2246i	−0.304436	+	1.43226i	−0.818501	+	0.574506i	$0.805194\pi$
$572$	−5.00752	+	11.2471i	−0.209375	+	0.470264i
$573$	5.35599	−	41.7878i	0.223750	−	1.74571i
$574$	6.57491	+	20.2355i	0.274432	+	0.844614i
$575$	2.70953	+	1.20636i	0.112995	+	0.0503087i
$576$	−1.38024	−	2.66363i	−0.0575101	−	0.110985i
$577$	−33.3893	+	7.09712i	−1.39002	+	0.295457i	−0.841307	−	0.540557i	$-0.818213\pi$
$577$	−33.3893	+	7.09712i	−1.39002	+	0.295457i	−0.548708	+	0.836014i	$0.684880\pi$
$578$	4.45440	+	10.0047i	0.185278	+	0.416142i
$579$	−2.92542	+	0.877455i	−0.121576	+	0.0364658i
$580$	1.49062	−	0.156670i	0.0618945	−	0.00650538i
$581$	−2.88479	+	2.09593i	−0.119681	+	0.0869536i
$582$	−17.3978	+	28.6100i	−0.721162	+	1.18592i
$583$	14.9219	+	25.8455i	0.618002	+	1.07041i
$584$	2.42282	−	4.19646i	0.100257	−	0.173651i
$585$	0.655706	+	11.0619i	0.0271101	+	0.457352i
$586$	−17.5114	+	19.4484i	−0.723389	+	0.803405i
$587$	7.13378	−	21.9555i	0.294443	−	0.906201i	−0.688965	−	0.724794i	$-0.741935\pi$
$587$	7.13378	−	21.9555i	0.294443	−	0.906201i	0.983408	−	0.181407i	$-0.0580652\pi$
$588$	3.09251	−	6.54113i	0.127533	−	0.269752i
$589$	−14.9404	−	27.2161i	−0.615607	−	1.12142i
$590$			12.6561i			0.521045i
$591$	17.5430	+	16.5339i	0.721623	+	0.680115i
$592$	8.83207	+	7.95243i	0.362996	+	0.326843i
$593$	−9.28284	+	12.7767i	−0.381201	+	0.524678i	−0.955902	−	0.293685i	$-0.905118\pi$
$593$	−9.28284	+	12.7767i	−0.381201	+	0.524678i	0.574701	+	0.818363i	$0.305118\pi$
$594$	16.6554	+	4.74805i	0.683380	+	0.194815i
$595$	7.12068	−	4.11113i	0.291919	−	0.168540i
$596$	7.77113	+	0.816779i	0.318318	+	0.0334566i
$597$	14.3440	−	2.70932i	0.587060	−	0.110885i
$598$	−1.14516	−	10.8955i	−0.0468292	−	0.445550i
$599$	−27.5853	+	24.8379i	−1.12711	+	1.01485i	−0.127370	+	0.991855i	$0.540654\pi$
$599$	−27.5853	+	24.8379i	−1.12711	+	1.01485i	−0.999736	+	0.0229955i	$0.992680\pi$
$600$	1.73160	+	0.0394118i	0.0706924	+	0.00160898i
$601$	9.13746	+	42.9884i	0.372725	+	1.75353i	0.620014	+	0.784591i	$0.287127\pi$
$601$	9.13746	+	42.9884i	0.372725	+	1.75353i	−0.247289	+	0.968942i	$0.579540\pi$
$602$	38.1247	+	8.10365i	1.55385	+	0.330280i
$603$	−10.1302	−	36.7967i	−0.412533	−	1.49848i
$604$	8.26988	−	2.68705i	0.336497	−	0.109334i
$605$	−0.103813	+	0.0337310i	−0.00422062	+	0.00137136i
$606$	23.5247	−	20.2317i	0.955626	−	0.821856i
$607$	−5.87357	−	1.24847i	−0.238401	−	0.0506736i	0.0871617	−	0.996194i	$-0.472220\pi$
$607$	−5.87357	−	1.24847i	−0.238401	−	0.0506736i	−0.325562	+	0.945521i	$0.605554\pi$
$608$	−1.15937	−	5.45440i	−0.0470186	−	0.221205i
$609$	−0.197491	+	8.67699i	−0.00800274	+	0.351609i
$610$	−7.57448	+	6.82010i	−0.306682	+	0.276138i
$611$	3.11296	+	29.6178i	0.125937	+	1.19821i
$612$	7.13959	+	1.86075i	0.288601	+	0.0752162i
$613$	3.98199	+	0.418524i	0.160831	+	0.0169040i	0.184602	−	0.982813i	$-0.440900\pi$
$613$	3.98199	+	0.418524i	0.160831	+	0.0169040i	−0.0237707	+	0.999717i	$0.507567\pi$
$614$	23.7556	−	13.7153i	0.958697	−	0.553504i
$615$	−6.27456	−	9.06291i	−0.253015	−	0.365452i
$616$	−6.54980	+	9.01503i	−0.263899	+	0.363226i
$617$	6.28753	+	5.66131i	0.253126	+	0.227916i	0.785918	−	0.618330i	$-0.212191\pi$
$617$	6.28753	+	5.66131i	0.253126	+	0.227916i	−0.532792	+	0.846246i	$0.678857\pi$
$618$	−10.1399	+	10.7587i	−0.407886	+	0.432780i
$619$			25.7898i			1.03658i	0.855205	+	0.518290i	$0.173431\pi$
$619$			25.7898i			1.03658i	−0.855205	+	0.518290i	$0.826569\pi$
$620$	−4.21701	+	3.63549i	−0.169359	+	0.146005i
$621$	−14.9480	+	3.75147i	−0.599842	+	0.150541i
$622$	6.70186	−	20.6262i	0.268720	−	0.827036i
$623$	−9.09681	+	10.1030i	−0.364456	+	0.404769i
$624$	−3.07199	−	5.61200i	−0.122978	−	0.224660i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.42831	−	5.93800i	−0.137023	−	0.237330i
$627$	27.5053	+	16.7260i	1.09846	+	0.667974i
$628$	−2.52640	+	1.83553i	−0.100814	+	0.0732458i
$629$	−29.0687	+	3.05524i	−1.15904	+	0.121820i
$630$	−1.50113	+	9.91678i	−0.0598066	+	0.395094i
$631$	−2.12476	−	4.77228i	−0.0845853	−	0.189982i	0.866301	−	0.499523i	$-0.166491\pi$
$631$	−2.12476	−	4.77228i	−0.0845853	−	0.189982i	−0.950886	+	0.309541i	$0.899825\pi$
$632$	−0.647553	+	0.137642i	−0.0257583	+	0.00547509i
$633$	3.70554	−	4.86354i	0.147282	−	0.193308i
$634$	29.2925	+	13.0418i	1.16335	+	0.517958i
$635$	−2.72298	−	8.38048i	−0.108058	−	0.332569i
$636$	−15.3828	−	1.97163i	−0.609969	−	0.0781804i
$637$	6.27595	−	14.0960i	0.248662	−	0.558505i
$638$	1.03866	−	4.88649i	0.0411207	−	0.193458i
$639$	−24.2073	+	30.3156i	−0.957625	+	1.19927i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	−10.6230	−	11.7981i	−0.419585	−	0.465996i	0.495882	−	0.868390i	$-0.334845\pi$
$641$	−10.6230	−	11.7981i	−0.419585	−	0.465996i	−0.915467	+	0.402394i	$0.868178\pi$
$642$	−5.20439	−	1.82295i	−0.205401	−	0.0719459i
$643$	13.4584	+	18.5239i	0.530746	+	0.730510i	0.987244	−	0.159215i	$-0.0508963\pi$
$643$	13.4584	+	18.5239i	0.530746	+	0.730510i	−0.456497	+	0.889725i	$0.650896\pi$
$644$	1.03650	−	9.86160i	0.0408437	−	0.388601i
$645$	−20.1249	+	1.65321i	−0.792416	+	0.0650949i
$646$	11.8767	+	6.85701i	0.467282	+	0.269785i
$647$	31.8360	+	23.1302i	1.25160	+	0.909341i	0.998314	−	0.0580499i	$-0.0184883\pi$
$647$	31.8360	+	23.1302i	1.25160	+	0.909341i	0.253287	+	0.967391i	$0.418488\pi$
$648$	−7.20803	+	5.38928i	−0.283158	+	0.211711i
$649$	40.1188	+	13.0354i	1.57480	+	0.511684i
$650$	3.69376			0.144881
$651$	−17.7767	−	26.8976i	−0.696724	−	1.05420i
$652$	−14.0236			−0.549207
$653$	29.0304	+	9.43254i	1.13605	+	0.369124i	0.815871	−	0.578234i	$-0.196258\pi$
$653$	29.0304	+	9.43254i	1.13605	+	0.369124i	0.320176	+	0.947358i	$0.396258\pi$
$654$	−14.5900	+	6.10199i	−0.570516	+	0.238607i
$655$	3.48854	+	2.53457i	0.136308	+	0.0990339i
$656$	5.51150	+	3.18206i	0.215188	+	0.124239i
$657$	−13.6068	−	5.11653i	−0.530850	−	0.199615i
$658$	−2.81756	+	26.8073i	−0.109840	+	1.04506i
$659$	7.35711	+	10.1262i	0.286592	+	0.394461i	0.927904	−	0.372820i	$-0.121609\pi$
$659$	7.35711	+	10.1262i	0.286592	+	0.394461i	−0.641311	+	0.767281i	$0.721609\pi$
$660$	1.90842	−	5.44843i	0.0742853	−	0.212080i
$661$	−17.0185	−	18.9009i	−0.661941	−	0.735160i	0.314900	−	0.949125i	$-0.398029\pi$
$661$	−17.0185	−	18.9009i	−0.661941	−	0.735160i	−0.976841	+	0.213964i	$0.931362\pi$
$662$	14.9282	−	6.64646i	0.580200	−	0.258322i
$663$	15.3122	+	3.62073i	0.594676	+	0.140618i
$664$	−0.221752	+	1.04326i	−0.00860564	+	0.0404863i
$665$	−7.58271	+	17.0311i	−0.294045	+	0.660436i
$666$	19.2135	−	30.0344i	0.744506	−	1.16381i
$667$	1.37372	+	4.22788i	0.0531907	+	0.163704i
$668$	−9.35720	−	4.16610i	−0.362041	−	0.161191i
$669$	7.23927	+	5.51562i	0.279886	+	0.213246i
$670$	−12.4439	+	2.64503i	−0.480749	+	0.102186i
$671$	13.8176	+	31.0349i	0.533423	+	1.19809i
$672$	−1.66364	−	5.54655i	−0.0641763	−	0.213963i
$673$	23.1679	−	2.43505i	0.893058	−	0.0938641i	0.353129	−	0.935575i	$-0.385118\pi$
$673$	23.1679	−	2.43505i	0.893058	−	0.0938641i	0.539929	+	0.841711i	$0.318451\pi$
$674$	5.06443	−	3.67952i	0.195074	−	0.141730i
$675$	−0.731109	−	5.14446i	−0.0281404	−	0.198010i
$676$	−0.321936	−	0.557609i	−0.0123821	−	0.0214465i
$677$	12.0325	−	20.8409i	0.462447	−	0.800982i	−0.536635	−	0.843814i	$-0.680305\pi$
$677$	12.0325	−	20.8409i	0.462447	−	0.800982i	0.999082	+	0.0428325i	$0.0136382\pi$
$678$	−13.6160	+	7.45337i	−0.522920	+	0.286245i
$679$	−43.2478	+	48.0315i	−1.65970	+	1.84328i
$680$	0.759984	−	2.33899i	0.0291441	−	0.0896962i
$681$	15.3642	+	7.26388i	0.588757	+	0.278353i
$682$	7.18081	+	17.1120i	0.274967	+	0.655252i
$683$		−	39.5421i		−	1.51304i	−0.653973	−	0.756518i	$-0.726899\pi$
$683$		−	39.5421i		−	1.51304i	0.653973	−	0.756518i	$-0.273101\pi$
$684$	−15.5762	+	6.10185i	−0.595572	+	0.233310i
$685$	15.2220	+	13.7060i	0.581604	+	0.523678i
$686$	−5.54689	+	7.63463i	−0.211781	+	0.291492i
$687$	−0.0323995	+	0.0224313i	−0.00123612	+	0.000855807i
$688$	10.0963	−	5.82912i	0.384919	−	0.222233i
$689$	−32.8925	−	3.45714i	−1.25310	−	0.131707i
$690$	0.953464	+	5.04792i	0.0362978	+	0.192171i
$691$	−3.85251	−	36.6542i	−0.146556	−	1.39439i	−0.782498	−	0.622653i	$-0.786055\pi$
$691$	−3.85251	−	36.6542i	−0.146556	−	1.39439i	0.635942	−	0.771737i	$-0.280612\pi$
$692$	4.62669	−	4.16589i	0.175880	−	0.158363i
$693$	29.8892	+	14.9724i	1.13540	+	0.568754i
$694$	2.29992	+	10.8203i	0.0873037	+	0.410732i
$695$	−5.17554	−	1.10010i	−0.196320	−	0.0417290i
$696$	1.69275	+	1.96827i	0.0641634	+	0.0746069i
$697$	−14.8856	+	4.83663i	−0.563834	+	0.183201i
$698$	−16.7445	+	5.44063i	−0.633790	+	0.205931i
$699$	−15.1562	−	17.6232i	−0.573262	−	0.666569i
$700$	3.27019	+	0.695101i	0.123602	+	0.0262723i
$701$	9.09483	+	42.7878i	0.343507	+	1.61607i	0.722979	+	0.690870i	$0.242773\pi$
$701$	9.09483	+	42.7878i	0.343507	+	1.61607i	−0.379471	+	0.925203i	$0.623894\pi$
$702$	−15.1063	+	11.8399i	−0.570151	+	0.446870i
$703$	49.2499	−	44.3448i	1.85749	−	1.67249i
$704$	0.348398	+	3.31478i	0.0131307	+	0.124931i
$705$	−2.59185	−	13.7220i	−0.0976148	−	0.516802i
$706$	−10.3480	−	1.08762i	−0.389452	−	0.0409331i
$707$	51.8671	−	29.9455i	1.95066	−	1.12622i
$708$	−18.0231	+	12.4780i	−0.677350	+	0.468952i
$709$	5.38739	−	7.41511i	0.202328	−	0.278480i	−0.695781	−	0.718254i	$-0.744941\pi$
$709$	5.38739	−	7.41511i	0.202328	−	0.278480i	0.898108	+	0.439774i	$0.144941\pi$
$710$	9.61002	+	8.65290i	0.360658	+	0.324738i
$711$	0.724418	+	1.84923i	0.0271678	+	0.0693515i
$712$			4.06639i			0.152394i
$713$	−13.1475	−	9.99229i	−0.492378	−	0.374214i
$714$	12.8750	+	6.08702i	0.481833	+	0.227801i
$715$	3.80445	−	11.7089i	0.142278	−	0.437888i
$716$	3.73896	−	4.15253i	0.139731	−	0.155187i
$717$	−39.9656	+	21.8770i	−1.49254	+	0.817012i
$718$	−3.82139	+	6.61884i	−0.142613	+	0.247013i
$719$	−22.2250	−	38.4948i	−0.828851	−	1.43561i	−0.898940	−	0.438072i	$-0.855662\pi$
$719$	−22.2250	−	38.4948i	−0.828851	−	1.43561i	0.0700889	−	0.997541i	$-0.477672\pi$
$720$	1.65111	+	2.50477i	0.0615331	+	0.0933471i
$721$	−23.0866	+	16.7734i	−0.859788	+	0.624673i
$722$	−12.0283	+	1.26423i	−0.447649	+	0.0470498i
$723$	1.70018	+	5.66839i	0.0632305	+	0.210810i
$724$	−2.05646	−	4.61888i	−0.0764276	−	0.171659i
$725$	−1.46608	+	0.311624i	−0.0544487	+	0.0115734i
$726$	−0.150387	−	0.114580i	−0.00558140	−	0.00425248i
$727$	18.0736	+	8.04690i	0.670314	+	0.298443i	0.713532	−	0.700623i	$-0.247094\pi$
$727$	18.0736	+	8.04690i	0.670314	+	0.298443i	−0.0432183	+	0.999066i	$0.513761\pi$
$728$	−3.81610	−	11.7448i	−0.141434	−	0.435290i
$729$	19.4800	+	18.6957i	0.721481	+	0.692434i
$730$	−1.97090	+	4.42672i	−0.0729464	+	0.163840i
$731$	−5.96120	+	28.0453i	−0.220483	+	1.03729i
$732$	−17.1801	−	4.06242i	−0.634995	−	0.150151i
$733$	−20.3502	+	9.06049i	−0.751652	+	0.334657i	−0.746549	−	0.665330i	$-0.768291\pi$
$733$	−20.3502	+	9.06049i	−0.751652	+	0.334657i	−0.00510234	+	0.999987i	$0.501624\pi$
$734$	−24.2394	−	26.9206i	−0.894692	−	0.993656i
$735$	−2.39184	+	6.82855i	−0.0882243	+	0.251875i
$736$	−1.74334	−	2.39951i	−0.0642605	−	0.0884470i
$737$	−4.43228	+	42.1703i	−0.163265	+	1.55336i
$738$	6.71989	−	17.8707i	0.247363	−	0.657830i
$739$	−32.8246	−	18.9513i	−1.20747	−	0.697134i	−0.245266	−	0.969456i	$-0.578875\pi$
$739$	−32.8246	−	18.9513i	−1.20747	−	0.697134i	−0.962206	+	0.272321i	$0.912209\pi$
$740$	−9.61494	−	6.98566i	−0.353452	−	0.256798i
$741$	−32.9131	+	13.7652i	−1.20909	+	0.505679i
$742$	−28.4701	−	9.25049i	−1.04517	−	0.339596i
$743$	−28.4714			−1.04451			−0.522257	−	0.852788i	$-0.674910\pi$
$743$	−28.4714			−1.04451			−0.522257	+	0.852788i	$0.674910\pi$
$744$	−9.33483	−	2.42096i	−0.342231	−	0.0887566i
$745$	−7.81394			−0.286281
$746$	14.5939	+	4.74183i	0.534319	+	0.173611i
$747$	3.19639	+	0.145577i	0.116950	+	0.00532639i
$748$	−6.63163	−	4.81816i	−0.242476	−	0.176169i
$749$	−9.21804	−	5.32204i	−0.336820	−	0.194463i
$750$	−1.72624	+	0.141806i	−0.0630332	+	0.00517802i
$751$	3.50646	−	33.3617i	0.127952	−	1.21739i	−0.722514	−	0.691357i	$-0.757013\pi$
$751$	3.50646	−	33.3617i	0.127952	−	1.21739i	0.850466	−	0.526030i	$-0.176320\pi$
$752$	4.73902	+	6.52271i	0.172814	+	0.237859i
$753$	−42.7092	−	14.9598i	−1.55641	−	0.545165i
$754$	3.70452	+	4.11428i	0.134911	+	0.149833i
$755$	−7.94371	+	3.53677i	−0.289101	+	0.128716i
$756$	−15.6021	+	7.63950i	−0.567443	+	0.277846i
$757$	3.36697	−	15.8403i	0.122375	−	0.575727i	−0.873643	−	0.486568i	$-0.838249\pi$
$757$	3.36697	−	15.8403i	0.122375	−	0.575727i	0.996017	−	0.0891591i	$-0.0284180\pi$
$758$	−11.7345	+	26.3561i	−0.426216	+	0.957296i
$759$	16.9835	+	2.17679i	0.616462	+	0.0790126i
$760$	1.72316	+	5.30333i	0.0625055	+	0.192372i
$761$	41.9952	+	18.6975i	1.52233	+	0.677783i	0.986079	−	0.166279i	$-0.0531751\pi$
$761$	41.9952	+	18.6975i	1.52233	+	0.677783i	0.536246	+	0.844061i	$0.319842\pi$
$762$	9.24966	−	12.1402i	0.335080	−	0.439794i
$763$	−29.8588	+	6.34669i	−1.08096	+	0.229765i
$764$	−9.89329	−	22.2207i	−0.357926	−	0.803916i
$765$	−7.29497	−	1.10426i	−0.263750	−	0.0399247i
$766$	4.62108	−	0.485695i	0.166966	−	0.0175489i
$767$	−37.8205	+	27.4782i	−1.36562	+	0.992181i
$768$	−1.47991	−	0.899933i	−0.0534015	−	0.0324735i
$769$	−1.38395	−	2.39708i	−0.0499066	−	0.0864408i	0.839993	−	0.542597i	$-0.182559\pi$
$769$	−1.38395	−	2.39708i	−0.0499066	−	0.0864408i	−0.889900	+	0.456157i	$0.849226\pi$
$770$	5.57159	−	9.65028i	0.200786	−	0.347772i
$771$	−17.5668	−	32.0914i	−0.632651	−	1.15575i
$772$	−1.17990	+	1.31041i	−0.0424655	+	0.0471627i
$773$	0.504226	−	1.55185i	0.0181357	−	0.0558161i	−0.941579	−	0.336792i	$-0.890658\pi$
$773$	0.504226	−	1.55185i	0.0181357	−	0.0558161i	0.959715	+	0.280976i	$0.0906581\pi$
$774$	−22.1959	−	27.0291i	−0.797815	−	0.971542i
$775$	3.81390	−	4.05638i	0.136999	−	0.145709i
$776$			19.3323i			0.693990i
$777$	47.2018	−	50.0826i	1.69335	−	1.79670i
$778$	−5.98249	−	5.38666i	−0.214483	−	0.193121i
$779$	20.8593	−	28.7104i	0.747363	−	1.02866i
$780$	3.64177	+	5.26014i	0.130396	+	0.188343i
$781$	37.3269	−	21.5507i	1.33566	−	0.771145i
$782$	7.25438	+	0.762466i	0.259416	+	0.0272657i
$783$	4.99690	−	5.97378i	0.178575	−	0.213486i
$784$	−0.436649	−	4.15444i	−0.0155946	−	0.148373i
$785$	2.32069	−	2.08956i	0.0828290	−	0.0745796i
$786$	−0.169947	+	7.46679i	−0.00606179	+	0.266332i
$787$	10.8041	+	50.8291i	0.385123	+	1.81186i	0.561427	+	0.827527i	$0.310253\pi$
$787$	10.8041	+	50.8291i	0.385123	+	1.81186i	−0.176303	+	0.984336i	$0.556414\pi$
$788$	13.6138	+	2.89370i	0.484972	+	0.103084i
$789$	−14.0603	+	12.0921i	−0.500560	+	0.430491i
$790$	0.629618	−	0.204575i	0.0224008	−	0.00727846i
$791$	−28.4955	+	9.25876i	−1.01318	+	0.329204i
$792$	9.64046	−	2.65403i	0.342559	−	0.0943070i
$793$	−36.8258	−	7.82758i	−1.30772	−	0.277965i
$794$	−3.39519	−	15.9731i	−0.120491	−	0.566865i
$795$	15.5046	+	0.352891i	0.549893	+	0.0125157i
$796$	6.26317	−	5.63939i	0.221992	−	0.199883i
$797$	2.43639	+	23.1807i	0.0863014	+	0.821103i	0.948977	+	0.315345i	$0.102120\pi$
$797$	2.43639	+	23.1807i	0.0863014	+	0.821103i	−0.862676	+	0.505758i	$0.831213\pi$
$798$	−31.7293	+	5.99310i	−1.12320	+	0.212153i
$799$	−19.7200	−	2.07265i	−0.697643	−	0.0733252i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	12.0356	−	1.99083i	0.425258	−	0.0703424i
$802$	9.65200	−	13.2848i	0.340824	−	0.469104i
$803$	12.0023	+	10.8070i	0.423553	+	0.381369i
$804$	−16.0354	−	15.1131i	−0.565526	−	0.532996i
$805$			9.91592i			0.349490i
$806$	−20.0197	−	4.70860i	−0.705164	−	0.165853i
$807$	−0.879014	+	1.85924i	−0.0309427	+	0.0654485i
$808$	5.53573	−	17.0372i	0.194746	−	0.599367i
$809$	−0.641532	+	0.712493i	−0.0225551	+	0.0250499i	−0.754317	−	0.656511i	$-0.772032\pi$
$809$	−0.641532	+	0.712493i	−0.0225551	+	0.0250499i	0.731762	+	0.681561i	$0.238698\pi$
$810$	6.60521	−	6.11320i	0.232083	−	0.214796i
$811$	−1.21103	+	2.09757i	−0.0425251	+	0.0736556i	−0.886505	−	0.462720i	$-0.846874\pi$
$811$	−1.21103	+	2.09757i	−0.0425251	+	0.0736556i	0.843979	+	0.536376i	$0.180207\pi$
$812$	2.50548	+	4.33962i	0.0879251	+	0.152291i
$813$	−15.3074	+	25.1725i	−0.536854	+	0.882837i
$814$	−32.0470	+	23.2835i	−1.12325	+	0.816086i
$815$	13.9468	−	1.46587i	0.488535	−	0.0513471i
$816$	4.08015	−	1.22381i	0.142834	−	0.0428418i
$817$	−26.4417	−	59.3890i	−0.925077	−	2.07776i
$818$	18.8231	−	4.00097i	0.658133	−	0.139890i
$819$	−32.8936	+	17.0448i	−1.14940	+	0.595595i
$820$	−5.81392	−	2.58852i	−0.203031	−	0.0903952i
$821$	−7.76156	−	23.8876i	−0.270880	−	0.833684i	−0.990280	−	0.139088i	$-0.955583\pi$
$821$	−7.76156	−	23.8876i	−0.270880	−	0.833684i	0.719400	−	0.694596i	$-0.244417\pi$
$822$	−4.51037	+	35.1902i	−0.157317	+	1.22740i
$823$	−9.02178	+	20.2632i	−0.314479	+	0.706332i	−0.999759	−	0.0219477i	$-0.993013\pi$
$823$	−9.02178	+	20.2632i	−0.314479	+	0.706332i	0.685280	+	0.728280i	$0.259680\pi$
$824$	−1.77465	+	8.34905i	−0.0618227	+	0.290853i
$825$	−1.32845	+	5.61807i	−0.0462508	+	0.195596i
$826$	−38.6545	+	17.2101i	−1.34496	+	0.598816i
$827$	31.7592	+	35.2722i	1.10438	+	1.22653i	0.971912	+	0.235346i	$0.0756222\pi$
$827$	31.7592	+	35.2722i	1.10438	+	1.22653i	0.132464	+	0.991188i	$0.457711\pi$
$828$	−6.24851	+	6.33467i	−0.217151	+	0.220145i
$829$	0.151697	+	0.208793i	0.00526865	+	0.00725167i	0.811643	−	0.584154i	$-0.198573\pi$
$829$	0.151697	+	0.208793i	0.00526865	+	0.00725167i	−0.806375	+	0.591405i	$0.798573\pi$
$830$	0.111487	−	1.06072i	0.00386976	−	0.0368183i
$831$	1.10474	+	13.4483i	0.0383231	+	0.466517i
$832$	−3.19889	−	1.84688i	−0.110902	−	0.0640291i
$833$	8.31146	+	6.03863i	0.287975	+	0.209226i
$834$	−3.53610	−	8.45490i	−0.122445	−	0.292769i
$835$	9.74142	+	3.16518i	0.337116	+	0.109536i
$836$	18.5859			0.642806
$837$	−2.59536	+	28.8143i	−0.0897087	+	0.995968i
$838$	25.7139			0.888274
$839$	−5.03145	−	1.63482i	−0.173705	−	0.0564401i	0.220873	−	0.975303i	$-0.429109\pi$
$839$	−5.03145	−	1.63482i	−0.173705	−	0.0564401i	−0.394578	+	0.918862i	$0.629109\pi$
$840$	2.23430	+	5.34227i	0.0770907	+	0.184326i
$841$	21.6440	+	15.7253i	0.746346	+	0.542252i
$842$	−18.3101	−	10.5713i	−0.631007	−	0.364312i
$843$	0.0464735	+	0.565733i	0.00160063	+	0.0194849i
$844$	0.368997	−	3.51077i	0.0127014	−	0.120846i
$845$	0.378458	+	0.520903i	0.0130193	+	0.0179196i
$846$	16.9857	−	17.2199i	0.583979	−	0.592031i
$847$	−0.244190	−	0.271200i	−0.00839045	−	0.00931854i
$848$	−8.17982	+	3.64189i	−0.280896	+	0.125063i
$849$	−5.44183	+	23.0137i	−0.186763	+	0.789826i
$850$	−0.511330	+	2.40562i	−0.0175385	+	0.0825120i
$851$	14.3373	−	32.2020i	0.491475	−	1.10387i
$852$	−2.84750	+	22.2164i	−0.0975537	+	0.761121i
$853$	13.7080	+	42.1889i	0.469353	+	1.44452i	0.853424	+	0.521217i	$0.174522\pi$
$853$	13.7080	+	42.1889i	0.469353	+	1.44452i	−0.384071	+	0.923303i	$0.625478\pi$
$854$	−31.1300	−	13.8600i	−1.06525	−	0.474278i
$855$	14.8531	−	7.69658i	0.507965	−	0.263217i
$856$	−3.11418	+	0.661939i	−0.106440	+	0.0226246i
$857$	−11.1097	−	24.9528i	−0.379501	−	0.852373i	−0.997792	−	0.0664234i	$-0.978841\pi$
$857$	−11.1097	−	24.9528i	−0.379501	−	0.852373i	0.618291	−	0.785950i	$-0.287825\pi$
$858$	20.4251	−	6.12632i	0.697301	−	0.209149i
$859$	2.51737	−	0.264587i	0.0858917	−	0.00902758i	−0.0614851	−	0.998108i	$-0.519584\pi$
$859$	2.51737	−	0.264587i	0.0858917	−	0.00902758i	0.147377	+	0.989080i	$0.452917\pi$
$860$	−9.43172	+	6.85254i	−0.321619	+	0.233670i
$861$	19.1478	−	31.4878i	0.652554	−	1.07310i
$862$	−6.21429	−	10.7635i	−0.211660	−	0.366605i
$863$	−23.1581	+	40.1111i	−0.788312	+	1.36540i	0.138688	+	0.990336i	$0.455711\pi$
$863$	−23.1581	+	40.1111i	−0.788312	+	1.36540i	−0.927000	+	0.375061i	$0.877622\pi$
$864$	−1.93907	+	4.82079i	−0.0659686	+	0.164007i
$865$	−4.16589	+	4.62669i	−0.141644	+	0.157312i
$866$	7.58375	−	23.3404i	0.257706	−	0.793138i
$867$	8.10755	−	17.1487i	0.275347	−	0.582399i
$868$	−16.8379	−	7.93602i	−0.571517	−	0.269366i
$869$		−	2.20654i		−	0.0748516i
$870$	−1.88921	−	1.78054i	−0.0640503	−	0.0603661i
$871$	−34.9216	−	31.4435i	−1.18327	−	1.06542i
$872$	−5.36683	+	7.38681i	−0.181744	+	0.250149i
$873$	57.2195	−	9.46473i	1.93659	−	0.320333i
$874$	−14.3231	+	8.26945i	−0.484486	+	0.279718i
$875$	−3.32494	−	0.349465i	−0.112403	−	0.0118141i
$876$	−8.24709	+	1.55773i	−0.278643	+	0.0526308i
$877$	2.49394	+	23.7283i	0.0842145	+	0.801247i	0.952368	+	0.304951i	$0.0986402\pi$
$877$	2.49394	+	23.7283i	0.0842145	+	0.801247i	−0.868153	+	0.496296i	$0.834693\pi$
$878$	−1.61078	+	1.45036i	−0.0543613	+	0.0489471i
$879$	45.3167	+	1.03142i	1.52849	+	0.0347890i
$880$	−0.692978	−	3.26021i	−0.0233603	−	0.109901i
$881$	24.9989	+	5.31368i	0.842235	+	0.179022i	0.608774	−	0.793344i	$-0.291662\pi$
$881$	24.9989	+	5.31368i	0.842235	+	0.179022i	0.233461	+	0.972366i	$0.424995\pi$
$882$	−12.0825	+	3.32632i	−0.406837	+	0.112003i
$883$	11.8873	−	3.86242i	0.400040	−	0.129981i	−0.102086	−	0.994776i	$-0.532552\pi$
$883$	11.8873	−	3.86242i	0.400040	−	0.129981i	0.502125	+	0.864795i	$0.332552\pi$
$884$	8.63967	−	2.80720i	0.290584	−	0.0944163i
$885$	16.6201	−	14.2936i	0.558678	−	0.480474i
$886$	−0.612035	−	0.130092i	−0.0205617	−	0.00437053i
$887$	9.82766	+	46.2355i	0.329980	+	1.55244i	0.760187	+	0.649705i	$0.225108\pi$
$887$	9.82766	+	46.2355i	0.329980	+	1.55244i	−0.430206	+	0.902731i	$0.641559\pi$
$888$	0.468399	−	20.5796i	0.0157184	−	0.690607i
$889$	21.8930	−	19.7125i	0.734267	−	0.661137i
$890$	−0.425054	−	4.04412i	−0.0142478	−	0.135559i
$891$	−12.5751	−	27.2343i	−0.421283	−	0.912384i
$892$	5.22571	+	0.549244i	0.174970	+	0.0183901i
$893$	38.9353	−	22.4793i	1.30292	−	0.752241i
$894$	−7.70396	−	11.1275i	−0.257659	−	0.372160i
$895$	−3.28442	+	4.52061i	−0.109786	+	0.151107i
$896$	−2.48452	−	2.23707i	−0.0830019	−	0.0747353i
$897$	−13.0147	+	13.8090i	−0.434548	+	0.461069i
$898$			15.1121i			0.504296i
$899$	8.34318	+	0.179909i	0.278261	+	0.00600031i
$900$	−1.90388	−	2.31846i	−0.0634627	−	0.0772819i
$901$	6.80484	−	20.9432i	0.226702	−	0.697718i
$902$	−14.1935	+	15.7635i	−0.472593	+	0.524867i
$903$	−32.4155	−	59.2175i	−1.07872	−	1.97064i
$904$	−4.48097	+	7.76126i	−0.149035	+	0.258136i
$905$	2.52800	+	4.37862i	0.0840334	+	0.145550i
$906$	−12.8685	−	7.82534i	−0.427526	−	0.259979i
$907$	13.4971	−	9.80625i	0.448165	−	0.325611i	−0.340706	−	0.940170i	$-0.610666\pi$
$907$	13.4971	−	9.80625i	0.448165	−	0.325611i	0.788871	+	0.614559i	$0.210666\pi$
$908$	9.75819	−	1.02563i	0.323837	−	0.0340366i
$909$	−53.1366	−	8.04346i	−1.76243	−	0.266785i
$910$	5.02286	+	11.2815i	0.166506	+	0.373979i
$911$	−2.22362	+	0.472644i	−0.0736717	+	0.0156594i	−0.244600	−	0.969624i	$-0.578657\pi$
$911$	−2.22362	+	0.472644i	−0.0736717	+	0.0156594i	0.170928	+	0.985283i	$0.445323\pi$
$912$	−5.85337	+	7.68257i	−0.193824	+	0.254395i
$913$	−3.24757	−	1.44591i	−0.107479	−	0.0478527i
$914$	−3.78965	−	11.6634i	−0.125351	−	0.385789i
$915$	17.5106	+	2.24436i	0.578884	+	0.0741962i
$916$	−0.00925387	+	0.0207845i	−0.000305756	+	0.000686740i
$917$	−2.99732	+	14.1013i	−0.0989803	+	0.465666i
$918$	−5.61976	−	11.4772i	−0.185480	−	0.378804i
$919$	−15.9247	+	7.09012i	−0.525306	+	0.233881i	−0.652216	−	0.758033i	$-0.726161\pi$
$919$	−15.9247	+	7.09012i	−0.525306	+	0.233881i	0.126910	+	0.991914i	$0.459494\pi$
$920$	1.98461	+	2.20413i	0.0654306	+	0.0726681i
$921$	−44.8400	−	15.7061i	−1.47753	−	0.517534i
$922$	2.51242	+	3.45805i	0.0827422	+	0.113885i
$923$	−4.99292	+	47.5044i	−0.164344	+	1.56363i
$924$	19.2358	−	1.58017i	0.632810	−	0.0519837i
$925$	10.2925	+	5.94236i	0.338414	+	0.195384i
$926$	−6.73030	−	4.88985i	−0.221171	−	0.160690i
$927$	25.5802	+	1.16503i	0.840164	+	0.0382646i
$928$	1.42547	+	0.463163i	0.0467934	+	0.0152041i
$929$	27.5698			0.904535			0.452268	−	0.891882i	$-0.350615\pi$
$929$	27.5698			0.904535			0.452268	+	0.891882i	$0.350615\pi$
$930$	9.53675	+	1.43194i	0.312722	+	0.0469552i
$931$	−23.2938			−0.763423
$932$	−12.7632	−	4.14700i	−0.418071	−	0.135840i
$933$	−34.6553	+	14.4939i	−1.13457	+	0.474509i
$934$	8.09464	+	5.88110i	0.264865	+	0.192435i
$935$	7.09894	+	4.09857i	0.232160	+	0.134038i
$936$	−3.90025	+	10.3722i	−0.127484	+	0.339027i
$937$	2.14545	−	20.4126i	0.0700887	−	0.666850i	−0.901920	−	0.431904i	$-0.857842\pi$
$937$	2.14545	−	20.4126i	0.0700887	−	0.666850i	0.972008	−	0.234946i	$-0.0754913\pi$
$938$	−25.0000	−	34.4095i	−0.816277	−	1.12351i
$939$	−3.92594	+	11.2083i	−0.128118	+	0.365770i
$940$	−5.39487	−	5.99161i	−0.175961	−	0.195425i
$941$	14.5134	−	6.46180i	0.473124	−	0.210649i	−0.156301	−	0.987709i	$-0.549957\pi$
$941$	14.5134	−	6.46180i	0.473124	−	0.210649i	0.629425	+	0.777061i	$0.283290\pi$
$942$	5.26369	+	1.24466i	0.171500	+	0.0405531i
$943$	3.92448	−	18.4632i	0.127799	−	0.601245i
$944$	−5.14772	+	11.5620i	−0.167544	+	0.376310i
$945$	14.7181	−	9.22851i	0.478780	−	0.300204i
$946$	12.0076	+	36.9556i	0.390401	+	1.20153i
$947$	22.0232	+	9.80536i	0.715658	+	0.318631i	0.732066	−	0.681234i	$-0.238556\pi$
$947$	22.0232	+	9.80536i	0.715658	+	0.318631i	−0.0164078	+	0.999865i	$0.505223\pi$
$948$	0.912084	+	0.694918i	0.0296231	+	0.0225699i
$949$	−17.5075	+	3.72134i	−0.568319	+	0.120800i
$950$	−2.26807	−	5.09416i	−0.0735858	−	0.165276i
$951$	−15.9557	−	53.1961i	−0.517399	−	1.72500i
$952$	8.17721	−	0.859460i	0.265025	−	0.0278552i
$953$	42.9889	−	31.2333i	1.39255	−	1.01174i	0.396966	−	0.917833i	$-0.370063\pi$
$953$	42.9889	−	31.2333i	1.39255	−	1.01174i	0.995581	−	0.0939112i	$-0.0299370\pi$
$954$	14.7839	+	22.4275i	0.478646	+	0.726117i
$955$	12.1618	+	21.0648i	0.393546	+	0.681642i
$956$	−13.1525	+	22.7807i	−0.425381	+	0.736782i
$957$	−7.58999	+	4.15473i	−0.245349	+	0.134303i
$958$	−8.45944	+	9.39517i	−0.273312	+	0.303544i
$959$	−21.1617	+	65.1290i	−0.683346	+	2.10312i
$960$	1.56587	+	0.740311i	0.0505381	+	0.0238934i
$961$	−25.8417	+	17.1233i	−0.833603	+	0.552364i
$962$		−	43.8993i		−	1.41537i
$963$	3.48384	+	8.89322i	0.112265	+	0.286580i
$964$	2.53910	+	2.28621i	0.0817787	+	0.0736339i
$965$	1.03646	−	1.42657i	0.0333649	−	0.0459228i
$966$	−14.1209	+	9.77636i	−0.454332	+	0.314549i
$967$	−42.1643	+	24.3436i	−1.35591	+	0.782837i	−0.989070	−	0.147445i	$-0.952895\pi$
$967$	−42.1643	+	24.3436i	−1.35591	+	0.782837i	−0.366844	+	0.930283i	$0.619562\pi$
$968$	−0.108558	−	0.0114099i	−0.00348918	−	0.000366728i
$969$	−4.40864	−	23.3407i	−0.141626	−	0.749810i
$970$	−2.02078	−	19.2264i	−0.0648833	−	0.617323i
$971$	3.88163	−	3.49503i	0.124567	−	0.112161i	−0.604493	−	0.796611i	$-0.706624\pi$
$971$	3.88163	−	3.49503i	0.124567	−	0.112161i	0.729060	+	0.684450i	$0.239957\pi$
$972$	15.2178	+	3.37907i	0.488112	+	0.108384i
$973$	−3.67789	−	17.3031i	−0.117908	−	0.554713i
$974$	1.73066	+	0.367863i	0.0554539	+	0.0117871i
$975$	−4.17166	−	4.85066i	−0.133600	−	0.155345i
$976$	−9.69362	+	3.14965i	−0.310285	+	0.100818i
$977$	45.1510	−	14.6705i	1.44451	−	0.469349i	0.521209	−	0.853429i	$-0.325481\pi$
$977$	45.1510	−	14.6705i	1.44451	−	0.469349i	0.923300	+	0.384080i	$0.125481\pi$
$978$	15.8380	+	18.4159i	0.506443	+	0.588874i
$979$	−13.2573	−	2.81792i	−0.423704	−	0.0900611i
$980$	0.868514	+	4.08604i	0.0277436	+	0.130524i
$981$	24.4908	+	12.2682i	0.781933	+	0.391694i
$982$	5.33866	−	4.80695i	0.170363	−	0.153396i
$983$	−4.02598	−	38.3046i	−0.128409	−	1.22173i	−0.849009	−	0.528378i	$-0.822801\pi$
$983$	−4.02598	−	38.3046i	−0.128409	−	1.22173i	0.720601	−	0.693350i	$-0.243866\pi$
$984$	−2.04587	−	10.8315i	−0.0652201	−	0.345295i
$985$	−13.8417	−	1.45482i	−0.441033	−	0.0463545i
$986$	−3.19231	+	1.84308i	−0.101664	+	0.0586956i
$987$	38.3855	−	26.5756i	1.22183	−	0.845911i
$988$	−12.1068	+	16.6636i	−0.385169	+	0.530140i
$989$	−25.6963	−	23.1371i	−0.817095	−	0.735716i
$990$	−9.31023	+	3.64720i	−0.295898	+	0.115916i
$991$		−	2.46354i		−	0.0782568i	−0.999234	−	0.0391284i	$-0.987542\pi$
$991$		−	2.46354i		−	0.0782568i	0.999234	−	0.0391284i	$-0.0124581\pi$
$992$	−5.33112	+	1.60598i	−0.169263	+	0.0509898i
$993$	−25.5877	−	12.0974i	−0.812002	−	0.383898i
$994$	−13.3599	+	41.1174i	−0.423749	+	1.30417i
$995$	−5.63939	+	6.26317i	−0.178781	+	0.198556i
$996$	1.62045	−	0.887032i	0.0513461	−	0.0281067i
$997$	−0.340357	+	0.589515i	−0.0107792	+	0.0186701i	−0.871365	−	0.490636i	$-0.836765\pi$
$997$	−0.340357	+	0.589515i	−0.0107792	+	0.0186701i	0.860585	+	0.509306i	$0.170098\pi$
$998$	17.4614	+	30.2440i	0.552731	+	0.957358i
$999$	−61.1405	+	8.68902i	−1.93440	+	0.274908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.761.8	yes	176
3.2	odd	2	inner	930.2.br.b.761.21	yes	176
31.11	odd	30	inner	930.2.br.b.11.21	yes	176
93.11	even	30	inner	930.2.br.b.11.8	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.8	✓	176	93.11	even	30	inner
930.2.br.b.11.21	yes	176	31.11	odd	30	inner
930.2.br.b.761.8	yes	176	1.1	even	1	trivial
930.2.br.b.761.21	yes	176	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.668302 + 1.59793i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.141806 - 1.72624i) q^{6} +(0.349465 - 3.32494i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.10675 + 2.13580i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.668302 + 1.59793i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.141806 - 1.72624i) q^{6} +(0.349465 - 3.32494i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.10675 + 2.13580i) q^{9} +(0.669131 + 0.743145i) q^{10} +(3.04488 - 1.35567i) q^{11} +(-0.398571 + 1.68557i) q^{12} +(-0.767976 + 3.61304i) q^{13} +(-1.35982 + 3.05421i) q^{14} +(0.220198 - 1.71800i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.24674 - 1.00031i) q^{17} +(2.66363 - 1.38024i) q^{18} +(5.45440 - 1.15937i) q^{19} +(-0.406737 - 0.913545i) q^{20} +(5.54655 - 1.66364i) q^{21} +(-3.31478 + 0.348398i) q^{22} +(2.39951 - 1.74334i) q^{23} +(0.899933 - 1.47991i) q^{24} +(0.500000 + 0.866025i) q^{25} +(1.84688 - 3.19889i) q^{26} +(-4.82079 - 1.93907i) q^{27} +(2.23707 - 2.48452i) q^{28} +(-0.463163 + 1.42547i) q^{29} +(-0.740311 + 1.56587i) q^{30} +(-1.60598 - 5.33112i) q^{31} -1.00000i q^{32} +(4.20116 + 3.95951i) q^{33} +(1.82766 + 1.64563i) q^{34} +(-1.96511 + 2.70475i) q^{35} +(-2.95978 + 0.489581i) q^{36} +(10.2925 - 5.94236i) q^{37} +(-5.54571 - 0.582877i) q^{38} +(-6.28662 + 1.18743i) q^{39} +(0.104528 + 0.994522i) q^{40} +(4.72947 - 4.25843i) q^{41} +(-5.78918 - 0.131764i) q^{42} +(-2.42388 - 11.4035i) q^{43} +(3.26021 + 0.692978i) q^{44} +(2.89239 - 0.796280i) q^{45} +(-2.82079 + 0.916530i) q^{46} +(7.66790 - 2.49145i) q^{47} +(-1.31320 + 1.12938i) q^{48} +(-4.08604 - 0.868514i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(0.0969279 - 4.25863i) q^{51} +(-2.74500 + 2.47161i) q^{52} +(0.935941 + 8.90488i) q^{53} +(3.98564 + 3.33387i) q^{54} +(-3.31478 - 0.348398i) q^{55} +(-2.89534 + 1.67162i) q^{56} +(5.49777 + 7.94093i) q^{57} +(0.880989 - 1.21258i) q^{58} +(9.40535 + 8.46861i) q^{59} +(1.18796 - 1.26046i) q^{60} +10.1925i q^{61} +(-0.120033 + 5.56647i) q^{62} +(6.36515 + 7.75118i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.47161 - 2.74500i) q^{65} +(-2.77199 - 5.06395i) q^{66} +(-6.36095 + 11.0175i) q^{67} +(-1.22968 - 2.12987i) q^{68} +(4.38933 + 2.66916i) q^{69} +(2.70475 - 1.96511i) q^{70} +(12.8607 - 1.35172i) q^{71} +(2.96621 + 0.449004i) q^{72} +(1.97090 + 4.42672i) q^{73} +(-11.6250 + 2.47097i) q^{74} +(-1.04970 + 1.37773i) q^{75} +(5.09416 + 2.26807i) q^{76} +(-3.44343 - 10.5978i) q^{77} +(6.34587 + 0.813358i) q^{78} +(0.269267 - 0.604785i) q^{79} +(0.207912 - 0.978148i) q^{80} +(-0.123244 - 8.99916i) q^{81} +(-5.81392 + 2.58852i) q^{82} +(-0.713673 - 0.792614i) q^{83} +(5.46512 + 1.91427i) q^{84} +(1.44558 + 1.98966i) q^{85} +(-1.21862 + 11.5944i) q^{86} +(-2.58733 + 0.212543i) q^{87} +(-2.88650 - 1.66652i) q^{88} +(-3.28978 - 2.39017i) q^{89} +(-2.99689 - 0.136491i) q^{90} +(11.7448 + 3.81610i) q^{91} +2.96595 q^{92} +(7.44547 - 6.12903i) q^{93} -8.06251 q^{94} +(-5.30333 - 1.72316i) q^{95} +(1.59793 - 0.668302i) q^{96} +(-15.6402 - 11.3633i) q^{97} +(3.61766 + 2.08866i) q^{98} +(-3.51936 + 9.35930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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