LMFDB - Embedded newform 370.2.x.a.9.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(9,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 8]))

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

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

chi := DirichletCharacter("370.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.x (of order $18$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			9.9
Character	$\chi$	$=$	370.9
Dual form			370.2.x.a.329.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.984808 + 0.173648i) q^{2} +(2.61244 + 0.460644i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.38577 + 1.75489i) q^{5} -2.65274 q^{6} +(2.09125 - 2.49226i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(3.79359 + 1.38075i) q^{9} +(-1.66945 - 1.48759i) q^{10} +(0.0622047 + 0.107742i) q^{11} +(2.61244 - 0.460644i) q^{12} +(-2.13136 - 5.85586i) q^{13} +(-1.62670 + 2.81754i) q^{14} +(2.81188 + 5.22289i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.61191 + 4.42868i) q^{17} +(-3.97572 - 0.701027i) q^{18} +(-0.307373 + 1.74320i) q^{19} +(1.90241 + 1.17509i) q^{20} +(6.61132 - 5.54755i) q^{21} +(-0.0799689 - 0.0953032i) q^{22} +(-7.34121 - 4.23845i) q^{23} +(-2.49276 + 0.907292i) q^{24} +(-1.15926 + 4.86376i) q^{25} +(3.11584 + 5.39679i) q^{26} +(2.38247 + 1.37552i) q^{27} +(1.11273 - 3.05720i) q^{28} +(1.23037 + 2.13106i) q^{29} +(-3.67611 - 4.65527i) q^{30} -5.35817 q^{31} +(-0.642788 + 0.766044i) q^{32} +(0.112876 + 0.310124i) q^{33} +(0.818388 - 4.64131i) q^{34} +(7.27163 + 0.216203i) q^{35} +4.03705 q^{36} +(2.12868 + 5.69813i) q^{37} -1.77009i q^{38} +(-2.87058 - 16.2799i) q^{39} +(-2.07756 - 0.826889i) q^{40} +(-3.81283 + 1.38776i) q^{41} +(-5.54755 + 6.61132i) q^{42} -2.22479i q^{43} +(0.0953032 + 0.0799689i) q^{44} +(2.83399 + 8.57073i) q^{45} +(7.96568 + 2.89927i) q^{46} +(8.31733 + 4.80201i) q^{47} +(2.29734 - 1.32637i) q^{48} +(-0.622472 - 3.53021i) q^{49} +(0.297062 - 4.99117i) q^{50} +(-6.25107 + 10.8272i) q^{51} +(-4.00564 - 4.77374i) q^{52} +(4.66659 + 5.56142i) q^{53} +(-2.58513 - 0.940909i) q^{54} +(-0.102873 + 0.258468i) q^{55} +(-0.564949 + 3.20398i) q^{56} +(-1.60599 + 4.41242i) q^{57} +(-1.58173 - 1.88504i) q^{58} +(5.60374 - 4.70210i) q^{59} +(4.42864 + 3.94619i) q^{60} +(0.127159 - 0.0462822i) q^{61} +(5.27677 - 0.930436i) q^{62} +(11.3745 - 6.56709i) q^{63} +(0.500000 - 0.866025i) q^{64} +(7.32278 - 11.8552i) q^{65} +(-0.165013 - 0.285811i) q^{66} +(-6.98181 + 8.32060i) q^{67} +4.71291i q^{68} +(-17.2261 - 14.4544i) q^{69} +(-7.19870 + 1.04979i) q^{70} +(1.01311 - 5.74563i) q^{71} +(-3.97572 + 0.701027i) q^{72} -9.15252i q^{73} +(-3.08581 - 5.24193i) q^{74} +(-5.26895 + 12.1723i) q^{75} +(0.307373 + 1.74320i) q^{76} +(0.398606 + 0.0702850i) q^{77} +(5.65395 + 15.5341i) q^{78} +(0.898957 + 0.754314i) q^{79} +(2.18958 + 0.453562i) q^{80} +(-3.68725 - 3.09397i) q^{81} +(3.51392 - 2.02876i) q^{82} +(-1.33054 + 3.65563i) q^{83} +(4.31523 - 7.47420i) q^{84} +(-10.0056 + 3.30844i) q^{85} +(0.386330 + 2.19099i) q^{86} +(2.23261 + 6.13404i) q^{87} +(-0.107742 - 0.0622047i) q^{88} +(-11.3243 + 9.50225i) q^{89} +(-4.27923 - 7.94840i) q^{90} +(-19.0515 - 6.93418i) q^{91} +(-8.34812 - 1.47200i) q^{92} +(-13.9979 - 2.46821i) q^{93} +(-9.02483 - 3.28477i) q^{94} +(-3.48507 + 1.87628i) q^{95} +(-2.03212 + 1.70515i) q^{96} +(-1.40174 - 0.809293i) q^{97} +(1.22603 + 3.36849i) q^{98} +(0.0872144 + 0.494617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 12 q^{9} + 12 q^{11} - 6 q^{14} + 6 q^{19} - 24 q^{21} + 30 q^{25} + 48 q^{26} + 24 q^{30} - 192 q^{31} + 12 q^{34} + 30 q^{35} + 84 q^{36} + 24 q^{39} + 12 q^{40} - 108 q^{41} + 6 q^{44} - 30 q^{45}+ \cdots - 90 q^{99}+O(q^{100}) $ 108 * q - 12 * q^9 + 12 * q^11 - 6 * q^14 + 6 * q^19 - 24 * q^21 + 30 * q^25 + 48 * q^26 + 24 * q^30 - 192 * q^31 + 12 * q^34 + 30 * q^35 + 84 * q^36 + 24 * q^39 + 12 * q^40 - 108 * q^41 + 6 * q^44 - 30 * q^45 - 54 * q^46 + 60 * q^49 - 12 * q^50 + 30 * q^55 - 48 * q^59 + 24 * q^61 + 54 * q^64 - 6 * q^65 - 120 * q^69 - 12 * q^70 + 12 * q^71 - 60 * q^74 - 156 * q^75 - 6 * q^76 + 12 * q^80 + 120 * q^81 - 24 * q^84 - 30 * q^85 + 12 * q^86 + 54 * q^89 + 18 * q^90 - 138 * q^91 + 6 * q^94 + 84 * q^95 - 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	2.61244	+	0.460644i	1.50829	+	0.265953i	0.865821	−	0.500354i	$-0.166797\pi$
$3$	2.61244	+	0.460644i	1.50829	+	0.265953i	0.642474	+	0.766307i	$0.277908\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	1.38577	+	1.75489i	0.619737	+	0.784809i
$5$	1.38577	+	1.75489i	0.619737	+	0.784809i
$6$	−2.65274			−1.08298
$7$	2.09125	−	2.49226i	0.790419	−	0.941984i	−0.208935	−	0.977930i	$-0.567000\pi$
$7$	2.09125	−	2.49226i	0.790419	−	0.941984i	0.999354	+	0.0359452i	$0.0114442\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	3.79359	+	1.38075i	1.26453	+	0.460251i
$10$	−1.66945	−	1.48759i	−0.527928	−	0.470417i
$11$	0.0622047	+	0.107742i	0.0187554	+	0.0324854i	0.875251	−	0.483669i	$-0.160696\pi$
$11$	0.0622047	+	0.107742i	0.0187554	+	0.0324854i	−0.856495	+	0.516155i	$0.827363\pi$
$12$	2.61244	−	0.460644i	0.754147	−	0.132977i
$13$	−2.13136	−	5.85586i	−0.591132	−	1.62412i	−0.768407	−	0.639961i	$-0.778950\pi$
$13$	−2.13136	−	5.85586i	−0.591132	−	1.62412i	0.177275	−	0.984161i	$-0.443272\pi$
$14$	−1.62670	+	2.81754i	−0.434755	+	0.753018i
$15$	2.81188	+	5.22289i	0.726024	+	1.34854i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.61191	+	4.42868i	−0.390945	+	1.07411i	0.575625	+	0.817713i	$0.304759\pi$
$17$	−1.61191	+	4.42868i	−0.390945	+	1.07411i	−0.966571	+	0.256400i	$0.917464\pi$
$18$	−3.97572	−	0.701027i	−0.937086	−	0.165234i
$19$	−0.307373	+	1.74320i	−0.0705162	+	0.399917i	0.929036	+	0.369990i	$0.120639\pi$
$19$	−0.307373	+	1.74320i	−0.0705162	+	0.399917i	−0.999552	+	0.0299275i	$0.990472\pi$
$20$	1.90241	+	1.17509i	0.425392	+	0.262758i
$21$	6.61132	−	5.54755i	1.44271	−	1.21058i
$22$	−0.0799689	−	0.0953032i	−0.0170494	−	0.0203187i
$23$	−7.34121	−	4.23845i	−1.53075	−	0.883778i	−0.999327	−	0.0366706i	$-0.988325\pi$
$23$	−7.34121	−	4.23845i	−1.53075	−	0.883778i	−0.531421	−	0.847108i	$-0.678342\pi$
$24$	−2.49276	+	0.907292i	−0.508833	+	0.185200i
$25$	−1.15926	+	4.86376i	−0.231851	+	0.972751i
$26$	3.11584	+	5.39679i	0.611066	+	1.05840i
$27$	2.38247	+	1.37552i	0.458506	+	0.264718i
$28$	1.11273	−	3.05720i	0.210286	−	0.577757i
$29$	1.23037	+	2.13106i	0.228474	+	0.395728i	0.957356	−	0.288911i	$-0.0932931\pi$
$29$	1.23037	+	2.13106i	0.228474	+	0.395728i	−0.728882	+	0.684639i	$0.759960\pi$
$30$	−3.67611	−	4.65527i	−0.671162	−	0.849931i
$31$	−5.35817			−0.962356			−0.481178	−	0.876623i	$-0.659791\pi$
$31$	−5.35817			−0.962356			−0.481178	+	0.876623i	$0.659791\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	0.112876	+	0.310124i	0.0196491	+	0.0539856i
$34$	0.818388	−	4.64131i	0.140352	−	0.795977i
$35$	7.27163	+	0.216203i	1.22913	+	0.0365450i
$36$	4.03705			0.672842
$37$	2.12868	+	5.69813i	0.349952	+	0.936767i
$37$	2.12868	+	5.69813i	0.349952	+	0.936767i
$38$		−	1.77009i		−	0.287146i
$39$	−2.87058	−	16.2799i	−0.459661	−	2.60687i
$40$	−2.07756	−	0.826889i	−0.328491	−	0.130743i
$41$	−3.81283	+	1.38776i	−0.595464	+	0.216731i	−0.622131	−	0.782913i	$-0.713733\pi$
$41$	−3.81283	+	1.38776i	−0.595464	+	0.216731i	0.0266671	+	0.999644i	$0.491511\pi$
$42$	−5.54755	+	6.61132i	−0.856006	+	1.02015i
$43$		−	2.22479i		−	0.339277i	−0.985506	−	0.169639i	$-0.945740\pi$
$43$		−	2.22479i		−	0.339277i	0.985506	−	0.169639i	$-0.0542600\pi$
$44$	0.0953032	+	0.0799689i	0.0143675	+	0.0120558i
$45$	2.83399	+	8.57073i	0.422467	+	1.27765i
$46$	7.96568	+	2.89927i	1.17448	+	0.427474i
$47$	8.31733	+	4.80201i	1.21321	+	0.700445i	0.963456	−	0.267865i	$-0.0863182\pi$
$47$	8.31733	+	4.80201i	1.21321	+	0.700445i	0.249750	+	0.968310i	$0.419652\pi$
$48$	2.29734	−	1.32637i	0.331593	−	0.191445i
$49$	−0.622472	−	3.53021i	−0.0889245	−	0.504316i
$50$	0.297062	−	4.99117i	0.0420109	−	0.705858i
$51$	−6.25107	+	10.8272i	−0.875324	+	1.51611i
$52$	−4.00564	−	4.77374i	−0.555483	−	0.661998i
$53$	4.66659	+	5.56142i	0.641005	+	0.763920i	0.984529	−	0.175224i	$-0.0560650\pi$
$53$	4.66659	+	5.56142i	0.641005	+	0.763920i	−0.343524	+	0.939144i	$0.611621\pi$
$54$	−2.58513	−	0.940909i	−0.351791	−	0.128042i
$55$	−0.102873	+	0.258468i	−0.0138714	+	0.0348518i
$56$	−0.564949	+	3.20398i	−0.0754944	+	0.428150i
$57$	−1.60599	+	4.41242i	−0.212718	+	0.584439i
$58$	−1.58173	−	1.88504i	−0.207692	−	0.247517i
$59$	5.60374	−	4.70210i	0.729545	−	0.612161i	−0.200462	−	0.979701i	$-0.564244\pi$
$59$	5.60374	−	4.70210i	0.729545	−	0.612161i	0.930008	+	0.367540i	$0.119800\pi$
$60$	4.42864	+	3.94619i	0.571735	+	0.509451i
$61$	0.127159	−	0.0462822i	0.0162811	−	0.00592583i	−0.333867	−	0.942620i	$-0.608354\pi$
$61$	0.127159	−	0.0462822i	0.0162811	−	0.00592583i	0.350148	+	0.936694i	$0.386131\pi$
$62$	5.27677	−	0.930436i	0.670150	−	0.118166i
$63$	11.3745	−	6.56709i	1.43306	−	0.827376i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	7.32278	−	11.8552i	0.908280	−	1.47046i
$66$	−0.165013	−	0.285811i	−0.0203117	−	0.0351810i
$67$	−6.98181	+	8.32060i	−0.852964	+	1.01652i	0.146662	+	0.989187i	$0.453147\pi$
$67$	−6.98181	+	8.32060i	−0.852964	+	1.01652i	−0.999626	+	0.0273364i	$0.991297\pi$
$68$			4.71291i			0.571524i
$69$	−17.2261	−	14.4544i	−2.07378	−	1.74011i
$70$	−7.19870	+	1.04979i	−0.860409	+	0.125474i
$71$	1.01311	−	5.74563i	0.120234	−	0.681881i	−0.863791	−	0.503851i	$-0.831916\pi$
$71$	1.01311	−	5.74563i	0.120234	−	0.681881i	0.984025	−	0.178031i	$-0.0569727\pi$
$72$	−3.97572	+	0.701027i	−0.468543	+	0.0826168i
$73$		−	9.15252i		−	1.07122i	−0.844465	−	0.535611i	$-0.820081\pi$
$73$		−	9.15252i		−	1.07122i	0.844465	−	0.535611i	$-0.179919\pi$
$74$	−3.08581	−	5.24193i	−0.358718	−	0.609361i
$75$	−5.26895	+	12.1723i	−0.608406	+	1.40553i
$76$	0.307373	+	1.74320i	0.0352581	+	0.199959i
$77$	0.398606	+	0.0702850i	0.0454254	+	0.00800972i
$78$	5.65395	+	15.5341i	0.640183	+	1.75889i
$79$	0.898957	+	0.754314i	0.101141	+	0.0848670i	0.691956	−	0.721940i	$-0.256749\pi$
$79$	0.898957	+	0.754314i	0.101141	+	0.0848670i	−0.590815	+	0.806807i	$0.701194\pi$
$80$	2.18958	+	0.453562i	0.244803	+	0.0507098i
$81$	−3.68725	−	3.09397i	−0.409695	−	0.343775i
$82$	3.51392	−	2.02876i	0.388048	−	0.224039i
$83$	−1.33054	+	3.65563i	−0.146046	+	0.401257i	−0.991048	−	0.133505i	$-0.957377\pi$
$83$	−1.33054	+	3.65563i	−0.146046	+	0.401257i	0.845002	+	0.534763i	$0.179599\pi$
$84$	4.31523	−	7.47420i	0.470830	−	0.815502i
$85$	−10.0056	+	3.30844i	−1.08526	+	0.358851i
$86$	0.386330	+	2.19099i	0.0416591	+	0.236260i
$87$	2.23261	+	6.13404i	0.239361	+	0.657638i
$88$	−0.107742	−	0.0622047i	−0.0114853	−	0.00663105i
$89$	−11.3243	+	9.50225i	−1.20038	+	1.00724i	−0.200759	+	0.979641i	$0.564341\pi$
$89$	−11.3243	+	9.50225i	−1.20038	+	1.00724i	−0.999619	+	0.0275959i	$0.991215\pi$
$90$	−4.27923	−	7.94840i	−0.451071	−	0.837835i
$91$	−19.0515	−	6.93418i	−1.99714	−	0.726899i
$92$	−8.34812	−	1.47200i	−0.870352	−	0.153466i
$93$	−13.9979	−	2.46821i	−1.45152	−	0.255941i
$94$	−9.02483	−	3.28477i	−0.930840	−	0.338798i
$95$	−3.48507	+	1.87628i	−0.357560	+	0.192502i
$96$	−2.03212	+	1.70515i	−0.207402	+	0.174031i
$97$	−1.40174	−	0.809293i	−0.142325	−	0.0821712i	0.427147	−	0.904182i	$-0.359519\pi$
$97$	−1.40174	−	0.809293i	−0.142325	−	0.0821712i	−0.569471	+	0.822011i	$0.692852\pi$
$98$	1.22603	+	3.36849i	0.123848	+	0.340269i
$99$	0.0872144	+	0.494617i	0.00876538	+	0.0497109i
$100$	0.574159	+	4.96692i	0.0574159	+	0.496692i
$101$	3.80356	−	6.58797i	0.378469	−	0.655527i	−0.612371	−	0.790571i	$-0.709784\pi$
$101$	3.80356	−	6.58797i	0.378469	−	0.655527i	0.990840	+	0.135044i	$0.0431174\pi$
$102$	4.27598	−	11.7482i	0.423385	−	1.16324i
$103$	0.748500	−	0.432146i	0.0737519	−	0.0425807i	−0.462671	−	0.886530i	$-0.653109\pi$
$103$	0.748500	−	0.432146i	0.0737519	−	0.0425807i	0.536422	+	0.843950i	$0.319775\pi$
$104$	4.77374	+	4.00564i	0.468104	+	0.392786i
$105$	18.8971	+	3.91445i	1.84417	+	0.382012i
$106$	−5.56142	−	4.66659i	−0.540173	−	0.453259i
$107$	−7.01548	−	19.2749i	−0.678212	−	1.86337i	−0.461511	−	0.887135i	$-0.652692\pi$
$107$	−7.01548	−	19.2749i	−0.678212	−	1.86337i	−0.216701	−	0.976238i	$-0.569530\pi$
$108$	2.70924	+	0.477712i	0.260697	+	0.0459679i
$109$	−2.66608	−	15.1201i	−0.255364	−	1.44824i	−0.795137	−	0.606429i	$-0.792601\pi$
$109$	−2.66608	−	15.1201i	−0.255364	−	1.44824i	0.539774	−	0.841810i	$-0.318510\pi$
$110$	0.0564275	−	0.272405i	0.00538015	−	0.0259728i
$111$	2.93624	+	15.8666i	0.278695	+	1.50599i
$112$		−	3.25341i		−	0.307418i
$113$	−6.37898	+	1.12479i	−0.600084	+	0.105811i	−0.465435	−	0.885082i	$-0.654102\pi$
$113$	−6.37898	+	1.12479i	−0.600084	+	0.105811i	−0.134650	+	0.990893i	$0.542991\pi$
$114$	0.815382	−	4.62426i	0.0763675	−	0.433102i
$115$	−2.73527	−	18.7565i	−0.255065	−	1.74906i
$116$	1.88504	+	1.58173i	0.175021	+	0.146860i
$117$		−	25.1576i		−	2.32582i
$118$	−4.70210	+	5.60374i	−0.432863	+	0.515866i
$119$	7.66651	+	13.2788i	0.702787	+	1.21726i
$120$	−5.04660	−	3.11722i	−0.460690	−	0.284562i
$121$	5.49226	−	9.51288i	0.499296	−	0.864807i
$122$	−0.117191	+	0.0676601i	−0.0106099	+	0.00612566i
$123$	−10.6001	+	1.86908i	−0.955775	+	0.168529i
$124$	−5.03503	+	1.83260i	−0.452159	+	0.164573i
$125$	−10.1418	+	4.70571i	−0.907111	+	0.420891i
$126$	−10.0614	+	8.44249i	−0.896338	+	0.752117i
$127$	7.60677	+	9.06540i	0.674992	+	0.804424i	0.989454	−	0.144846i	$-0.0462687\pi$
$127$	7.60677	+	9.06540i	0.674992	+	0.804424i	−0.314462	+	0.949270i	$0.601824\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	1.02484	−	5.81213i	0.0902318	−	0.511730i
$130$	−5.15290	+	12.9467i	−0.451939	+	1.13550i
$131$	18.7130	+	6.81096i	1.63496	+	0.595077i	0.986147	−	0.165872i	$-0.0530437\pi$
$131$	18.7130	+	6.81096i	1.63496	+	0.595077i	0.648812	+	0.760948i	$0.275266\pi$
$132$	0.212137	+	0.252815i	0.0184642	+	0.0220047i
$133$	3.70170	+	4.41152i	0.320978	+	0.382527i
$134$	5.43089	−	9.40657i	0.469157	−	0.812604i
$135$	0.887684	+	6.08712i	0.0763997	+	0.523895i
$136$	−0.818388	−	4.64131i	−0.0701762	−	0.397989i
$137$	−9.87870	+	5.70347i	−0.843995	+	0.487281i	−0.858620	−	0.512613i	$-0.828678\pi$
$137$	−9.87870	+	5.70347i	−0.843995	+	0.487281i	0.0146254	+	0.999893i	$0.495344\pi$
$138$	19.4744	+	11.2435i	1.65777	+	0.957113i
$139$	7.95448	+	2.89519i	0.674690	+	0.245567i	0.656566	−	0.754269i	$-0.272008\pi$
$139$	7.95448	+	2.89519i	0.674690	+	0.245567i	0.0181240	+	0.999836i	$0.494231\pi$
$140$	6.90704	−	2.28388i	0.583752	−	0.193023i
$141$	19.5165	+	16.3763i	1.64359	+	1.37913i
$142$			5.83427i			0.489601i
$143$	0.498340	−	0.593898i	0.0416733	−	0.0496643i
$144$	3.79359	−	1.38075i	0.316132	−	0.115063i
$145$	−2.03476	+	5.11233i	−0.168978	+	0.424556i
$146$	1.58932	+	9.01347i	0.131533	+	0.745960i
$147$		−	9.50922i		−	0.784307i
$148$	3.94918	+	4.62644i	0.324621	+	0.380291i
$149$	6.02167			0.493314			0.246657	−	0.969103i	$-0.420668\pi$
$149$	6.02167			0.493314			0.246657	+	0.969103i	$0.420668\pi$
$150$	3.07521	−	12.9023i	0.251090	−	1.05347i
$151$	3.37427	−	19.1364i	0.274594	−	1.55730i	−0.465654	−	0.884967i	$-0.654181\pi$
$151$	3.37427	−	19.1364i	0.274594	−	1.55730i	0.740248	−	0.672334i	$-0.234708\pi$
$152$	−0.605406	−	1.66334i	−0.0491049	−	0.134915i
$153$	−12.2298	+	14.5750i	−0.988724	+	1.17831i
$154$	−0.404755			−0.0326161
$155$	−7.42522	−	9.40298i	−0.596408	−	0.755266i
$156$	−8.26552	−	14.3163i	−0.661771	−	1.14622i
$157$	−1.64797	+	4.52776i	−0.131522	+	0.361355i	−0.987921	−	0.154961i	$-0.950475\pi$
$157$	−1.64797	+	4.52776i	−0.131522	+	0.361355i	0.856398	+	0.516316i	$0.172697\pi$
$158$	−1.01628	−	0.586752i	−0.0808513	−	0.0466795i
$159$	9.62935	+	16.6785i	0.763657	+	1.32269i
$160$	−2.23508	−	0.0664544i	−0.176699	−	0.00525368i
$161$	−25.9156	+	9.43252i	−2.04244	+	0.743386i
$162$	4.16850	+	2.40668i	0.327508	+	0.189087i
$163$	9.49111	+	11.3111i	0.743401	+	0.885951i	0.996678	−	0.0814431i	$-0.0259529\pi$
$163$	9.49111	+	11.3111i	0.743401	+	0.885951i	−0.253277	+	0.967394i	$0.581508\pi$
$164$	−3.10825	+	2.60813i	−0.242713	+	0.203661i
$165$	−0.387811	+	0.627846i	−0.0301911	+	0.0488777i
$166$	0.675533	−	3.83114i	0.0524315	−	0.297354i
$167$	13.0721	+	2.30496i	1.01155	+	0.178363i	0.654771	−	0.755828i	$-0.272765\pi$
$167$	13.0721	+	2.30496i	1.01155	+	0.178363i	0.356775	+	0.934190i	$0.383876\pi$
$168$	−2.95179	+	8.10998i	−0.227736	+	0.625699i
$169$	−19.7898	+	16.6056i	−1.52229	+	1.27735i
$170$	9.27907	−	4.99563i	0.711672	−	0.383147i
$171$	−3.57297	+	6.18857i	−0.273232	+	0.473252i
$172$	−0.760923	−	2.09062i	−0.0580198	−	0.159408i
$173$	2.57744	−	0.454472i	0.195959	−	0.0345529i	−0.0748071	−	0.997198i	$-0.523834\pi$
$173$	2.57744	−	0.454472i	0.195959	−	0.0345529i	0.270766	+	0.962645i	$0.412723\pi$
$174$	−3.26386	−	5.65316i	−0.247432	−	0.428565i
$175$	9.69743	+	13.0605i	0.733057	+	0.987281i
$176$	0.116907	+	0.0425506i	0.00881217	+	0.00320737i
$177$	16.8055	−	9.70263i	1.26318	−	0.729295i
$178$	9.50225	−	11.3243i	0.712224	−	0.848795i
$179$	−0.806271			−0.0602635			−0.0301318	−	0.999546i	$-0.509593\pi$
$179$	−0.806271			−0.0602635			−0.0301318	+	0.999546i	$0.509593\pi$
$180$	5.59445	+	7.08457i	0.416985	+	0.528053i
$181$	7.10400	−	2.58564i	0.528036	−	0.192189i	−0.0642251	−	0.997935i	$-0.520458\pi$
$181$	7.10400	−	2.58564i	0.528036	−	0.192189i	0.592261	+	0.805746i	$0.298235\pi$
$182$	19.9662	+	3.52057i	1.47999	+	0.260962i
$183$	0.353516	−	0.0623344i	0.0261327	−	0.00460789i
$184$	8.47690			0.624926
$185$	−7.04971	+	11.6319i	−0.518305	+	0.855196i
$186$	14.2139			1.04221
$187$	−0.577423	+	0.101815i	−0.0422253	+	0.00744546i
$188$	9.45811	+	1.66772i	0.689804	+	0.121631i
$189$	8.41048	−	3.06116i	0.611772	−	0.222667i
$190$	3.10631	−	2.45295i	0.225355	−	0.177955i
$191$	27.3426			1.97844			0.989221	−	0.146428i	$-0.0467776\pi$
$191$	27.3426			1.97844			0.989221	+	0.146428i	$0.0467776\pi$
$192$	1.70515	−	2.03212i	0.123059	−	0.146656i
$193$	11.7272	−	6.77071i	0.844143	−	0.487366i	−0.0145271	−	0.999894i	$-0.504624\pi$
$193$	11.7272	−	6.77071i	0.844143	−	0.487366i	0.858670	+	0.512528i	$0.171291\pi$
$194$	1.52097	+	0.553589i	0.109199	+	0.0397454i
$195$	24.5914	−	27.5978i	1.76103	−	1.97632i
$196$	−1.79234	−	3.10442i	−0.128024	−	0.221744i
$197$	−25.3327	+	4.46683i	−1.80488	+	0.318249i	−0.971959	−	0.235149i	$-0.924442\pi$
$197$	−25.3327	+	4.46683i	−1.80488	+	0.318249i	−0.832918	+	0.553397i	$0.813331\pi$
$198$	−0.171779	−	0.471958i	−0.0122078	−	0.0335406i
$199$	4.88903	−	8.46804i	0.346574	−	0.600284i	−0.639065	−	0.769153i	$-0.720678\pi$
$199$	4.88903	−	8.46804i	0.346574	−	0.600284i	0.985638	+	0.168870i	$0.0540116\pi$
$200$	−1.42793	−	4.79176i	−0.100970	−	0.338829i
$201$	−22.0724	+	18.5210i	−1.55687	+	1.30637i
$202$	−2.60179	+	7.14836i	−0.183061	+	0.502957i
$203$	7.88417	+	1.39019i	0.553360	+	0.0975723i
$204$	−2.17097	+	12.3122i	−0.151999	+	0.862026i
$205$	−7.71908	−	4.76797i	−0.539124	−	0.333009i
$206$	−0.662087	+	0.555557i	−0.0461298	+	0.0387075i
$207$	−21.9973	−	26.2153i	−1.52892	−	1.82209i
$208$	−5.39679	−	3.11584i	−0.374200	−	0.216044i
$209$	−0.206935	+	0.0753183i	−0.0143140	+	0.00520988i
$210$	−19.2898	−	0.573532i	−1.33112	−	0.0395775i
$211$	−1.59289	−	2.75897i	−0.109659	−	0.189936i	0.805973	−	0.591952i	$-0.201643\pi$
$211$	−1.59289	−	2.75897i	−0.109659	−	0.189936i	−0.915632	+	0.402017i	$0.868309\pi$
$212$	6.28727	+	3.62996i	0.431812	+	0.249307i
$213$	5.29339	−	14.5435i	0.362697	−	0.996502i
$214$	10.2559	+	17.7638i	0.701082	+	1.21431i
$215$	3.90425	−	3.08306i	0.266268	−	0.210263i
$216$	−2.75103			−0.187184
$217$	−11.2053	+	13.3539i	−0.760664	+	0.906524i
$218$	5.25114	+	14.4274i	0.355652	+	0.977147i
$219$	4.21606	−	23.9104i	0.284895	−	1.61572i
$220$	−0.00826755	+	0.278065i	−0.000557398	+	0.0187472i
$221$	29.3693			1.97559
$222$	−5.64684	−	15.1157i	−0.378991	−	1.01450i
$223$		−	5.96950i		−	0.399747i	−0.979822	−	0.199874i	$-0.935947\pi$
$223$		−	5.96950i		−	0.399747i	0.979822	−	0.199874i	$-0.0640531\pi$
$224$	0.564949	+	3.20398i	0.0377472	+	0.214075i
$225$	−11.1134	+	16.8504i	−0.740892	+	1.12336i
$226$	6.08675	−	2.21540i	0.404885	−	0.147366i
$227$	9.03348	−	10.7657i	0.599573	−	0.714543i	−0.377842	−	0.925870i	$-0.623334\pi$
$227$	9.03348	−	10.7657i	0.599573	−	0.714543i	0.977416	+	0.211327i	$0.0677784\pi$
$228$			4.69560i			0.310973i
$229$	−13.4234	−	11.2635i	−0.887042	−	0.744316i	0.0805729	−	0.996749i	$-0.474325\pi$
$229$	−13.4234	−	11.2635i	−0.887042	−	0.744316i	−0.967615	+	0.252432i	$0.918769\pi$
$230$	5.95075	+	17.9966i	0.392381	+	1.18666i
$231$	1.00896	+	0.367231i	0.0663846	+	0.0241620i
$232$	−2.13106	−	1.23037i	−0.139911	−	0.0807777i
$233$	8.01457	−	4.62722i	0.525052	−	0.303139i	−0.213947	−	0.976845i	$-0.568632\pi$
$233$	8.01457	−	4.62722i	0.525052	−	0.303139i	0.738999	+	0.673706i	$0.235299\pi$
$234$	4.36857	+	24.7754i	0.285582	+	1.61962i
$235$	3.09896	+	21.2505i	0.202154	+	1.38623i
$236$	3.65758	−	6.33512i	0.238088	−	0.412381i
$237$	2.00100	+	2.38470i	0.129979	+	0.154903i
$238$	−9.85587	−	11.7458i	−0.638861	−	0.761365i
$239$	2.11096	+	0.768325i	0.136546	+	0.0496988i	0.409389	−	0.912360i	$-0.365742\pi$
$239$	2.11096	+	0.768325i	0.136546	+	0.0496988i	−0.272843	+	0.962059i	$0.587964\pi$
$240$	5.51123	+	2.19353i	0.355749	+	0.141591i
$241$	−3.16438	+	17.9461i	−0.203836	+	1.15601i	0.695425	+	0.718598i	$0.255216\pi$
$241$	−3.16438	+	17.9461i	−0.203836	+	1.15601i	−0.899261	+	0.437412i	$0.855895\pi$
$242$	−3.75693	+	10.3221i	−0.241504	+	0.663528i
$243$	−13.5125	−	16.1036i	−0.866828	−	1.03305i
$244$	0.103661	−	0.0869821i	0.00663623	−	0.00556846i
$245$	5.33252	−	5.98445i	0.340682	−	0.382332i
$246$	10.1145	−	3.68136i	0.644874	−	0.234715i
$247$	10.8630	−	1.91545i	0.691199	−	0.121877i
$248$	4.64031	−	2.67908i	0.294660	−	0.170122i
$249$	−5.15990	+	8.93722i	−0.326996	+	0.566373i
$250$	9.17060	−	6.39533i	0.579999	−	0.404476i
$251$	−7.01443	−	12.1494i	−0.442747	−	0.766860i	0.555145	−	0.831753i	$-0.312663\pi$
$251$	−7.01443	−	12.1494i	−0.442747	−	0.766860i	−0.997892	+	0.0648932i	$0.979329\pi$
$252$	8.44249	−	10.0614i	0.531827	−	0.633807i
$253$		−	1.05461i		−	0.0663026i
$254$	−9.06540	−	7.60677i	−0.568814	−	0.477291i
$255$	−27.6630	+	4.03410i	−1.73233	+	0.252625i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	21.0952	−	3.71965i	1.31588	−	0.232025i	0.528732	−	0.848789i	$-0.322668\pi$
$257$	21.0952	−	3.71965i	1.31588	−	0.232025i	0.787148	+	0.616764i	$0.211557\pi$
$258$			5.90180i			0.367430i
$259$	18.6528	+	6.61102i	1.15903	+	0.410789i
$260$	2.82645	−	13.6448i	0.175289	−	0.846213i
$261$	1.72504	+	9.78321i	0.106778	+	0.605566i
$262$	−19.6114	−	3.45802i	−1.21160	−	0.213637i
$263$	4.34907	+	11.9490i	0.268175	+	0.736804i	0.998554	+	0.0537622i	$0.0171213\pi$
$263$	4.34907	+	11.9490i	0.268175	+	0.736804i	−0.730379	+	0.683042i	$0.760656\pi$
$264$	−0.252815	−	0.212137i	−0.0155597	−	0.0130561i
$265$	−3.29283	+	15.8962i	−0.202277	+	0.976496i
$266$	−4.41152	−	3.70170i	−0.270487	−	0.226966i
$267$	−33.9614	+	19.6076i	−2.07840	+	1.19997i
$268$	−3.71494	+	10.2067i	−0.226926	+	0.623475i
$269$	5.81907	−	10.0789i	0.354795	−	0.614522i	−0.632288	−	0.774733i	$-0.717884\pi$
$269$	5.81907	−	10.0789i	0.354795	−	0.614522i	0.987083	+	0.160211i	$0.0512174\pi$
$270$	−1.93121	−	5.84049i	−0.117530	−	0.355441i
$271$	−2.78689	−	15.8052i	−0.169292	−	0.960100i	−0.944528	−	0.328430i	$-0.893481\pi$
$271$	−2.78689	−	15.8052i	−0.169292	−	0.960100i	0.775237	−	0.631671i	$-0.217630\pi$
$272$	1.61191	+	4.42868i	0.0977363	+	0.268528i
$273$	−46.5768	−	26.8911i	−2.81895	−	1.62752i
$274$	8.73823	−	7.33224i	0.527896	−	0.442957i
$275$	−0.596141	+	0.177648i	−0.0359487	+	0.0107126i
$276$	−21.1309	−	7.69103i	−1.27193	−	0.462945i
$277$	15.0833	+	2.65958i	0.906265	+	0.159799i	0.607307	−	0.794467i	$-0.292250\pi$
$277$	15.0833	+	2.65958i	0.906265	+	0.159799i	0.298958	+	0.954266i	$0.403361\pi$
$278$	−8.33637	−	1.46993i	−0.499983	−	0.0881604i
$279$	−20.3267	−	7.39831i	−1.21693	−	0.442925i
$280$	−6.40552	+	3.44858i	−0.382803	+	0.206092i
$281$	−12.5602	+	10.5392i	−0.749278	+	0.628719i	−0.935312	−	0.353824i	$-0.884881\pi$
$281$	−12.5602	+	10.5392i	−0.749278	+	0.628719i	0.186034	+	0.982543i	$0.440437\pi$
$282$	−22.0637	−	12.7385i	−1.31388	−	0.758567i
$283$	−0.762634	−	2.09532i	−0.0453339	−	0.124554i	0.914960	−	0.403545i	$-0.132222\pi$
$283$	−0.762634	−	2.09532i	−0.0453339	−	0.124554i	−0.960294	+	0.278991i	$0.910000\pi$
$284$	−1.01311	−	5.74563i	−0.0601170	−	0.340941i
$285$	−9.96883	+	3.29629i	−0.590503	+	0.195255i
$286$	−0.387640	+	0.671412i	−0.0229216	+	0.0397014i
$287$	−4.51494	+	12.4047i	−0.266508	+	0.732226i
$288$	−3.49619	+	2.01853i	−0.206015	+	0.118943i
$289$	−3.99223	−	3.34988i	−0.234837	−	0.197052i
$290$	1.11610	−	5.38800i	0.0655396	−	0.316394i
$291$	−3.28916	−	2.75993i	−0.192814	−	0.161790i
$292$	−3.13035	−	8.60056i	−0.183190	−	0.503309i
$293$	−30.5728	−	5.39081i	−1.78608	−	0.314935i	−0.819845	−	0.572586i	$-0.805940\pi$
$293$	−30.5728	−	5.39081i	−1.78608	−	0.314935i	−0.966238	+	0.257652i	$0.917051\pi$
$294$	1.65126	+	9.36475i	0.0963034	+	0.546163i
$295$	16.0172	+	3.31788i	0.932556	+	0.193175i
$296$	−4.69256	−	3.87039i	−0.272749	−	0.224962i
$297$			0.342255i			0.0198596i
$298$	−5.93018	+	1.04565i	−0.343526	+	0.0605730i
$299$	−9.17302	+	52.0228i	−0.530489	+	3.00855i
$300$	−0.788029	+	13.2403i	−0.0454969	+	0.764429i
$301$	−5.54474	−	4.65259i	−0.319594	−	0.268171i
$302$			19.4316i			1.11817i
$303$	12.9713	−	15.4586i	0.745182	−	0.888073i
$304$	0.885045	+	1.53294i	0.0507608	+	0.0879203i
$305$	0.257434	+	0.159014i	0.0147406	+	0.00910509i
$306$	9.51312	−	16.4772i	0.543829	−	0.941940i
$307$	−16.2296	+	9.37014i	−0.926270	+	0.534782i	−0.885630	−	0.464392i	$-0.846273\pi$
$307$	−16.2296	+	9.37014i	−0.926270	+	0.534782i	−0.0406400	+	0.999174i	$0.512940\pi$
$308$	0.398606	−	0.0702850i	0.0227127	−	0.00400486i
$309$	2.15448	−	0.784166i	0.122564	−	0.0446096i
$310$	8.94522	+	7.97075i	0.508054	+	0.452708i
$311$	−25.3178	+	21.2441i	−1.43564	+	1.20464i	−0.493357	+	0.869827i	$0.664230\pi$
$311$	−25.3178	+	21.2441i	−1.43564	+	1.20464i	−0.942283	+	0.334818i	$0.891325\pi$
$312$	10.6259	+	12.6635i	0.601576	+	0.716930i
$313$	7.88099	−	21.6528i	0.445460	−	1.22389i	−0.490393	−	0.871501i	$-0.663147\pi$
$313$	7.88099	−	21.6528i	0.445460	−	1.22389i	0.935853	−	0.352390i	$-0.114631\pi$
$314$	0.836697	−	4.74515i	0.0472176	−	0.267784i
$315$	27.2871	+	10.8605i	1.53745	+	0.611921i
$316$	1.10273	+	0.401362i	0.0620336	+	0.0225784i
$317$	9.65872	+	11.5108i	0.542488	+	0.646512i	0.965744	−	0.259498i	$-0.0835572\pi$
$317$	9.65872	+	11.5108i	0.542488	+	0.646512i	−0.423256	+	0.906010i	$0.639113\pi$
$318$	−12.3793	−	14.7530i	−0.694194	−	0.827309i
$319$	−0.153070	+	0.265124i	−0.00857026	+	0.0148441i
$320$	2.21266	−	0.322673i	0.123692	−	0.0180380i
$321$	−9.44869	−	53.5862i	−0.527374	−	2.99089i
$322$	23.8840	−	13.7894i	1.33100	−	0.768454i
$323$	−7.22462	−	4.17113i	−0.401988	−	0.232088i
$324$	−4.52308	−	1.64627i	−0.251282	−	0.0914593i
$325$	30.9523	−	3.57797i	1.71692	−	0.198470i
$326$	−11.3111	−	9.49111i	−0.626462	−	0.525664i
$327$		−	40.7284i		−	2.25229i
$328$	2.60813	−	3.10825i	0.144010	−	0.171624i
$329$	29.3615	−	10.6867i	1.61875	−	0.589177i
$330$	0.272895	−	0.685650i	0.0150224	−	0.0377438i
$331$	0.997568	+	5.65749i	0.0548313	+	0.310964i	0.999872	−	0.0159885i	$-0.00508951\pi$
$331$	0.997568	+	5.65749i	0.0548313	+	0.310964i	−0.945041	+	0.326952i	$0.893978\pi$
$332$			3.89024i			0.213505i
$333$	0.207610	+	24.5556i	0.0113770	+	1.34564i
$334$	−13.2737			−0.726305
$335$	−24.2769	−	0.721812i	−1.32639	−	0.0394368i
$336$	1.49866	−	8.49935i	0.0817588	−	0.463677i
$337$	10.5449	+	28.9719i	0.574417	+	1.57820i	0.797449	+	0.603387i	$0.206182\pi$
$337$	10.5449	+	28.9719i	0.574417	+	1.57820i	−0.223032	+	0.974811i	$0.571595\pi$
$338$	16.6056	−	19.7898i	0.903226	−	1.07642i
$339$	−17.1829			−0.933245
$340$	−8.27062	+	6.53103i	−0.448537	+	0.354195i
$341$	−0.333304	−	0.577299i	−0.0180494	−	0.0312625i
$342$	2.44406	−	6.71499i	0.132159	−	0.363105i
$343$	9.62281	+	5.55573i	0.519583	+	0.299981i
$344$	1.11239	+	1.92672i	0.0599763	+	0.103882i
$345$	1.49436	−	50.2604i	0.0804538	−	2.70593i
$346$	−2.45936	+	0.895135i	−0.132216	+	0.0481227i
$347$	1.49886	+	0.865365i	0.0804628	+	0.0464552i	0.539692	−	0.841863i	$-0.318541\pi$
$347$	1.49886	+	0.865365i	0.0804628	+	0.0464552i	−0.459229	+	0.888318i	$0.651874\pi$
$348$	4.19593	+	5.00052i	0.224926	+	0.268056i
$349$	1.92593	−	1.61604i	0.103092	−	0.0865048i	−0.589785	−	0.807561i	$-0.700787\pi$
$349$	1.92593	−	1.61604i	0.103092	−	0.0865048i	0.692877	+	0.721056i	$0.256343\pi$
$350$	−11.8180	−	11.1781i	−0.631701	−	0.597497i
$351$	2.97695	−	16.8831i	0.158898	−	0.901153i
$352$	−0.122519	−	0.0216035i	−0.00653031	−	0.00115147i
$353$	−5.99902	+	16.4822i	−0.319296	+	0.877258i	0.671392	+	0.741103i	$0.265697\pi$
$353$	−5.99902	+	16.4822i	−0.319296	+	0.877258i	−0.990688	+	0.136155i	$0.956525\pi$
$354$	−14.8653	+	12.4735i	−0.790082	+	0.662957i
$355$	11.4869	−	6.18426i	0.609660	−	0.328227i
$356$	−7.39144	+	12.8023i	−0.391745	+	0.678523i
$357$	13.9115	+	38.2216i	0.736276	+	2.02290i
$358$	0.794022	−	0.140007i	0.0419654	−	0.00739962i
$359$	−2.81046	−	4.86786i	−0.148330	−	0.256916i	0.782280	−	0.622927i	$-0.214057\pi$
$359$	−2.81046	−	4.86786i	−0.148330	−	0.256916i	−0.930611	+	0.366011i	$0.880723\pi$
$360$	−6.73968	−	6.00547i	−0.355212	−	0.316516i
$361$	14.9099	+	5.42676i	0.784731	+	0.285619i
$362$	−6.54708	+	3.77996i	−0.344107	+	0.198670i
$363$	18.7303	−	22.3219i	0.983084	−	1.17159i
$364$	−20.2742			−1.06266
$365$	16.0616	−	12.6833i	0.840705	−	0.663876i
$366$	−0.337321	+	0.122775i	−0.0176321	+	0.00641755i
$367$	26.7060	+	4.70899i	1.39404	+	0.245807i	0.819693	−	0.572804i	$-0.194144\pi$
$367$	26.7060	+	4.70899i	1.39404	+	0.245807i	0.574349	+	0.818611i	$0.305255\pi$
$368$	−8.34812	+	1.47200i	−0.435176	+	0.0767332i
$369$	−16.3805			−0.852732
$370$	4.92275	−	12.6794i	0.255922	−	0.659169i
$371$	23.6195			1.22626
$372$	−13.9979	+	2.46821i	−0.725758	+	0.127971i
$373$	−29.1022	−	5.13150i	−1.50685	−	0.265699i	−0.641602	−	0.767037i	$-0.721730\pi$
$373$	−29.1022	−	5.13150i	−1.50685	−	0.265699i	−0.865251	+	0.501338i	$0.832841\pi$
$374$	0.550970	−	0.200537i	0.0284900	−	0.0103695i
$375$	−28.6626	+	7.62163i	−1.48013	+	0.393579i
$376$	−9.60402			−0.495289
$377$	9.85684	−	11.7469i	0.507653	−	0.604997i
$378$	−7.75114	+	4.47512i	−0.398675	+	0.230175i
$379$	22.0060	+	8.00953i	1.13037	+	0.411422i	0.838427	−	0.545013i	$-0.183475\pi$
$379$	22.0060	+	8.00953i	1.13037	+	0.411422i	0.291945	+	0.956435i	$0.405698\pi$
$380$	−2.63317	+	2.95509i	−0.135079	+	0.151593i
$381$	15.6963	+	27.1868i	0.804147	+	1.39282i
$382$	−26.9272	+	4.74800i	−1.37772	+	0.242929i
$383$	−0.0827565	−	0.227371i	−0.00422866	−	0.0116181i	0.937560	−	0.347823i	$-0.113079\pi$
$383$	−0.0827565	−	0.227371i	−0.00422866	−	0.0116181i	−0.941789	+	0.336205i	$0.890857\pi$
$384$	−1.32637	+	2.29734i	−0.0676861	+	0.117236i
$385$	0.429036	+	0.796907i	0.0218657	+	0.0406142i
$386$	−10.3733	+	8.70426i	−0.527989	+	0.443035i
$387$	3.07188	−	8.43993i	0.156153	−	0.429026i
$388$	−1.59400	−	0.281064i	−0.0809229	−	0.0142689i
$389$	−0.294635	+	1.67096i	−0.0149386	+	0.0847208i	−0.991366	−	0.131127i	$-0.958140\pi$
$389$	−0.294635	+	1.67096i	−0.0149386	+	0.0847208i	0.976427	+	0.215848i	$0.0692515\pi$
$390$	−19.4255	+	31.4488i	−0.983647	+	1.59247i
$391$	30.6041	−	25.6799i	1.54772	−	1.29869i
$392$	2.30418	+	2.74602i	0.116379	+	0.138695i
$393$	45.7491	+	26.4133i	2.30774	+	1.33237i
$394$	24.1721	−	8.79794i	1.21777	−	0.443234i
$395$	−0.0779845	+	2.62288i	−0.00392383	+	0.131971i
$396$	0.251124	+	0.434959i	0.0126194	+	0.0218575i
$397$	7.64307	+	4.41273i	0.383595	+	0.221468i	0.679381	−	0.733786i	$-0.262248\pi$
$397$	7.64307	+	4.41273i	0.383595	+	0.221468i	−0.295787	+	0.955254i	$0.595582\pi$
$398$	−3.34429	+	9.18836i	−0.167634	+	0.460571i
$399$	7.63835	+	13.2300i	0.382396	+	0.662329i
$400$	2.23832	+	4.47101i	0.111916	+	0.223550i
$401$	−17.8573			−0.891751			−0.445875	−	0.895095i	$-0.647108\pi$
$401$	−17.8573			−0.891751			−0.445875	+	0.895095i	$0.647108\pi$
$402$	18.5210	−	22.0724i	0.923742	−	1.10087i
$403$	11.4202	+	31.3767i	0.568879	+	1.56298i
$404$	1.32096	−	7.49156i	0.0657204	−	0.372719i
$405$	0.319869	−	10.7583i	0.0158944	−	0.534582i
$406$	−8.00579			−0.397321
$407$	−0.481513	+	0.583799i	−0.0238677	+	0.0289378i
$408$		−	12.5021i		−	0.618948i
$409$	−0.621905	−	3.52700i	−0.0307512	−	0.174399i	0.965564	−	0.260166i	$-0.0837772\pi$
$409$	−0.621905	−	3.52700i	−0.0307512	−	0.174399i	−0.996315	+	0.0857667i	$0.972666\pi$
$410$	8.42976	+	3.35513i	0.416316	+	0.165698i
$411$	−28.4348	+	10.3494i	−1.40259	+	0.510500i
$412$	0.555557	−	0.662087i	0.0273703	−	0.0326187i
$413$		−	23.7992i		−	1.17108i
$414$	26.2153	+	21.9973i	1.28841	+	1.08111i
$415$	−8.25904	+	2.73093i	−0.405421	+	0.134056i
$416$	5.85586	+	2.13136i	0.287107	+	0.104498i
$417$	19.4470	+	11.2277i	0.952322	+	0.549823i
$418$	0.190713	−	0.110108i	0.00932806	−	0.00538556i
$419$	0.292638	+	1.65963i	0.0142963	+	0.0810784i	0.991121	−	0.132962i	$-0.0424488\pi$
$419$	0.292638	+	1.65963i	0.0142963	+	0.0810784i	−0.976825	+	0.214040i	$0.931338\pi$
$420$	19.0963	−	2.78482i	0.931805	−	0.135885i
$421$	−5.62872	+	9.74922i	−0.274327	+	0.475148i	−0.969965	−	0.243244i	$-0.921788\pi$
$421$	−5.62872	+	9.74922i	−0.274327	+	0.475148i	0.695638	+	0.718392i	$0.255122\pi$
$422$	2.04778	+	2.44046i	0.0996846	+	0.118799i
$423$	24.9221	+	29.7010i	1.21175	+	1.44411i
$424$	−6.82209	−	2.48304i	−0.331310	−	0.120587i
$425$	−19.6714	−	12.9739i	−0.954204	−	0.629327i
$426$	−2.68752	+	15.2417i	−0.130211	+	0.738463i
$427$	0.150575	−	0.413701i	0.00728684	−	0.0200204i
$428$	−13.1848	−	15.7130i	−0.637311	−	0.759518i
$429$	1.57546	−	1.32197i	0.0760640	−	0.0638252i
$430$	−3.30957	+	3.71418i	−0.159602	+	0.179114i
$431$	−2.78306	+	1.01295i	−0.134055	+	0.0487921i	−0.408177	−	0.912903i	$-0.633835\pi$
$431$	−2.78306	+	1.01295i	−0.134055	+	0.0487921i	0.274121	+	0.961695i	$0.411613\pi$
$432$	2.70924	−	0.477712i	0.130348	−	0.0229839i
$433$	−16.0594	+	9.27188i	−0.771764	+	0.445578i	−0.833503	−	0.552514i	$-0.813668\pi$
$433$	−16.0594	+	9.27188i	−0.771764	+	0.445578i	0.0617397	+	0.998092i	$0.480335\pi$
$434$	8.71616	−	15.0968i	0.418389	−	0.724671i
$435$	−7.67066	+	12.4184i	−0.367780	+	0.595416i
$436$	−7.67666	−	13.2964i	−0.367645	−	0.636780i
$437$	9.64495	−	11.4944i	0.461381	−	0.549852i
$438$			24.2793i			1.16011i
$439$	8.69993	+	7.30011i	0.415225	+	0.348415i	0.826343	−	0.563167i	$-0.190417\pi$
$439$	8.69993	+	7.30011i	0.415225	+	0.348415i	−0.411118	+	0.911582i	$0.634862\pi$
$440$	−0.0401436	−	0.275276i	−0.00191377	−	0.0131233i
$441$	2.51295	−	14.2517i	0.119664	−	0.678650i
$442$	−28.9231	+	5.09992i	−1.37573	+	0.242579i
$443$		−	8.42323i		−	0.400200i	−0.979775	−	0.200100i	$-0.935873\pi$
$443$		−	8.42323i		−	0.400200i	0.979775	−	0.200100i	$-0.0641267\pi$
$444$	8.18586	+	13.9055i	0.388484	+	0.659925i
$445$	−32.3684	−	6.70496i	−1.53441	−	0.317845i
$446$	1.03659	+	5.87881i	0.0490841	+	0.278370i
$447$	15.7313	+	2.77385i	0.744063	+	0.131198i
$448$	−1.11273	−	3.05720i	−0.0525716	−	0.144439i
$449$	−5.64012	−	4.73262i	−0.266174	−	0.223346i	0.499926	−	0.866068i	$-0.333361\pi$
$449$	−5.64012	−	4.73262i	−0.266174	−	0.223346i	−0.766100	+	0.642722i	$0.777805\pi$
$450$	8.01850	−	18.5243i	0.377996	−	0.873242i
$451$	−0.386695	−	0.324476i	−0.0182088	−	0.0152790i
$452$	−5.60958	+	3.23869i	−0.263853	+	0.152335i
$453$	17.6302	−	48.4385i	0.828338	−	2.27584i
$454$	−7.02680	+	12.1708i	−0.329784	+	0.571203i
$455$	−14.2324	−	43.0424i	−0.667225	−	2.01786i
$456$	−0.815382	−	4.62426i	−0.0381837	−	0.216551i
$457$	−2.39975	−	6.59326i	−0.112256	−	0.308420i	0.870825	−	0.491593i	$-0.163585\pi$
$457$	−2.39975	−	6.59326i	−0.112256	−	0.308420i	−0.983081	+	0.183173i	$0.941363\pi$
$458$	15.1753	+	8.76149i	0.709097	+	0.409397i
$459$	−9.93205	+	8.33398i	−0.463588	+	0.388997i
$460$	−8.98542	−	16.6899i	−0.418948	−	0.778169i
$461$	−8.35772	−	3.04196i	−0.389258	−	0.141678i	0.139975	−	0.990155i	$-0.455298\pi$
$461$	−8.35772	−	3.04196i	−0.389258	−	0.141678i	−0.529232	+	0.848477i	$0.677520\pi$
$462$	−1.05740	−	0.186448i	−0.0491947	−	0.00867435i
$463$	29.0606	+	5.12417i	1.35056	+	0.238140i	0.801677	−	0.597758i	$-0.203941\pi$
$463$	29.0606	+	5.12417i	1.35056	+	0.238140i	0.548885	+	0.835898i	$0.315053\pi$
$464$	2.31234	+	0.841622i	0.107348	+	0.0390713i
$465$	−15.0665	−	27.9851i	−0.698694	−	1.29778i
$466$	−7.08931	+	5.94863i	−0.328406	+	0.275565i
$467$	−25.2848	−	14.5982i	−1.17004	−	0.675522i	−0.216350	−	0.976316i	$-0.569415\pi$
$467$	−25.2848	−	14.5982i	−1.17004	−	0.675522i	−0.953689	+	0.300793i	$0.902749\pi$
$468$	−8.60440	−	23.6404i	−0.397739	−	1.09278i
$469$	6.13634	+	34.8009i	0.283350	+	1.60696i
$470$	−6.74198	−	20.3895i	−0.310984	−	0.940497i
$471$	−6.39092	+	11.0694i	−0.294478	+	0.510051i
$472$	−2.50193	+	6.87401i	−0.115161	+	0.316402i
$473$	0.239703	−	0.138392i	0.0110215	−	0.00636329i
$474$	−2.38470	−	2.00100i	−0.109533	−	0.0919091i
$475$	−8.12217	−	3.51580i	−0.372671	−	0.161316i
$476$	11.7458	+	9.85587i	0.538366	+	0.451743i
$477$	10.0242	+	27.5411i	0.458975	+	1.26102i
$478$	−2.21230	−	0.390089i	−0.101188	−	0.0178422i
$479$	0.783733	+	4.44477i	0.0358097	+	0.203087i	0.997464	−	0.0711792i	$-0.0226762\pi$
$479$	0.783733	+	4.44477i	0.0358097	+	0.203087i	−0.961654	+	0.274266i	$0.911565\pi$
$480$	−5.80841	−	1.20319i	−0.265116	−	0.0549176i
$481$	28.8305	−	24.6100i	1.31456	−	1.12212i
$482$		−	18.2230i		−	0.830033i
$483$	−72.0481	+	12.7040i	−3.27830	+	0.578053i
$484$	1.90744	−	10.8176i	0.0867019	−	0.491711i
$485$	−0.522274	−	3.58139i	−0.0237152	−	0.162622i
$486$	16.1036	+	13.5125i	0.730473	+	0.612940i
$487$		−	21.9873i		−	0.996338i	−0.867080	−	0.498169i	$-0.834006\pi$
$487$		−	21.9873i		−	0.996338i	0.867080	−	0.498169i	$-0.165994\pi$
$488$	−0.0869821	+	0.103661i	−0.00393750	+	0.00469252i
$489$	19.5846	+	33.9215i	0.885646	+	1.53398i
$490$	−4.21232	+	6.81951i	−0.190293	+	0.308074i
$491$	−11.5059	+	19.9287i	−0.519252	+	0.899371i	0.480498	+	0.876996i	$0.340456\pi$
$491$	−11.5059	+	19.9287i	−0.519252	+	0.899371i	−0.999750	+	0.0223747i	$0.992877\pi$
$492$	−9.32154	+	5.38179i	−0.420247	+	0.242630i
$493$	−11.4210	+	2.01384i	−0.514378	+	0.0906987i
$494$	−10.3654	+	3.77269i	−0.466361	+	0.169742i
$495$	−0.747138	+	0.838480i	−0.0335814	+	0.0376869i
$496$	−4.10460	+	3.44417i	−0.184302	+	0.154648i
$497$	−12.2009	−	14.5405i	−0.547286	−	0.652230i
$498$	3.52958	−	9.69745i	0.158164	−	0.434553i
$499$	−2.48624	+	14.1002i	−0.111299	+	0.631211i	0.877217	+	0.480095i	$0.159398\pi$
$499$	−2.48624	+	14.1002i	−0.111299	+	0.631211i	−0.988516	+	0.151116i	$0.951713\pi$
$500$	−7.92074	+	7.89062i	−0.354226	+	0.352879i
$501$	33.0882	+	12.0431i	1.47827	+	0.538047i
$502$	9.01758	+	10.7467i	0.402474	+	0.479650i
$503$	−13.6272	−	16.2402i	−0.607606	−	0.724116i	0.371281	−	0.928521i	$-0.378919\pi$
$503$	−13.6272	−	16.2402i	−0.607606	−	0.724116i	−0.978887	+	0.204404i	$0.934474\pi$
$504$	−6.56709	+	11.3745i	−0.292522	+	0.506662i
$505$	16.8320	−	2.45461i	0.749015	−	0.109229i
$506$	0.183131	+	1.03859i	0.00814115	+	0.0461708i
$507$	−59.3490	+	34.2652i	−2.63578	+	1.52177i
$508$	10.2486	+	5.91702i	0.454707	+	0.262525i
$509$	−33.4117	−	12.1609i	−1.48095	−	0.539020i	−0.529898	−	0.848062i	$-0.677770\pi$
$509$	−33.4117	−	12.1609i	−1.48095	−	0.539020i	−0.951049	+	0.309041i	$0.899992\pi$
$510$	26.5422	−	8.77645i	1.17531	−	0.388628i
$511$	−22.8104	−	19.1402i	−1.00907	−	0.846713i
$512$			1.00000i			0.0441942i
$513$	−3.13010	+	3.73031i	−0.138197	+	0.164697i
$514$	−20.1288	+	7.32627i	−0.887842	+	0.323148i
$515$	1.79562	+	0.714674i	0.0791245	+	0.0314923i
$516$	−1.02484	−	5.81213i	−0.0451159	−	0.255865i
$517$			1.19483i			0.0525486i
$518$	−19.5174	−	3.27156i	−0.857546	−	0.143744i
$519$	6.94276			0.304753
$520$	−0.414122	+	13.9283i	−0.0181604	+	0.610796i
$521$	−0.796753	+	4.51861i	−0.0349064	+	0.197964i	−0.997274	−	0.0737869i	$-0.976492\pi$
$521$	−0.796753	+	4.51861i	−0.0349064	+	0.197964i	0.962368	+	0.271751i	$0.0876026\pi$
$522$	−3.39767	−	9.33503i	−0.148712	−	0.408583i
$523$	−0.554308	+	0.660599i	−0.0242382	+	0.0288860i	−0.778027	−	0.628230i	$-0.783780\pi$
$523$	−0.554308	+	0.660599i	−0.0242382	+	0.0288860i	0.753789	+	0.657116i	$0.228224\pi$
$524$	19.9139			0.869944
$525$	19.3177	+	38.5869i	0.843096	+	1.68407i
$526$	−6.35791	−	11.0122i	−0.277218	−	0.480156i
$527$	8.63688	−	23.7296i	0.376228	−	1.03368i
$528$	0.285811	+	0.165013i	0.0124383	+	0.00718128i
$529$	24.4289	+	42.3122i	1.06213	+	1.83966i
$530$	0.482453	−	16.2265i	0.0209564	−	0.704834i
$531$	27.7507	−	10.1004i	1.20428	−	0.438322i
$532$	4.98729	+	2.87941i	0.216226	+	0.124838i
$533$	16.2530	+	19.3696i	0.703996	+	0.838989i
$534$	30.0406	−	25.2070i	1.29998	−	1.09082i
$535$	24.1033	−	39.0220i	1.04208	−	1.68707i
$536$	1.88613	−	10.6968i	0.0814683	−	0.462030i
$537$	−2.10634	−	0.371404i	−0.0908951	−	0.0160273i
$538$	−3.98048	+	10.9363i	−0.171610	+	0.471496i
$539$	0.341631	−	0.286662i	0.0147151	−	0.0123474i
$540$	2.91607	+	5.41641i	0.125488	+	0.233085i
$541$	6.93311	−	12.0085i	0.298078	−	0.516286i	−0.677618	−	0.735414i	$-0.736988\pi$
$541$	6.93311	−	12.0085i	0.298078	−	0.516286i	0.975696	+	0.219128i	$0.0703212\pi$
$542$	5.48910	+	15.0812i	0.235777	+	0.647792i
$543$	19.7499	−	3.48243i	0.847547	−	0.149445i
$544$	−2.35645	−	4.08150i	−0.101032	−	0.174993i
$545$	22.8394	−	25.6317i	0.978333	−	1.09794i
$546$	50.5388	+	18.3946i	2.16286	+	0.787216i
$547$	−25.1975	+	14.5478i	−1.07737	+	0.622018i	−0.930185	−	0.367092i	$-0.880354\pi$
$547$	−25.1975	+	14.5478i	−1.07737	+	0.622018i	−0.147182	+	0.989109i	$0.547020\pi$
$548$	−7.33224	+	8.73823i	−0.313218	+	0.373279i
$549$	0.546295			0.0233153
$550$	0.556236	−	0.278468i	0.0237180	−	0.0118739i
$551$	−4.09305	+	1.48975i	−0.174370	+	0.0634654i
$552$	22.1454	+	3.90484i	0.942572	+	0.166201i
$553$	3.75989	−	0.662970i	0.159887	−	0.0281923i
$554$	−15.3159			−0.650712
$555$	−23.7751	+	27.1403i	−1.00920	+	1.15204i
$556$	8.46498			0.358995
$557$	−2.68552	+	0.473530i	−0.113789	+	0.0200641i	−0.230253	−	0.973131i	$-0.573955\pi$
$557$	−2.68552	+	0.473530i	−0.113789	+	0.0200641i	0.116464	+	0.993195i	$0.462844\pi$
$558$	21.3026	+	3.75622i	0.901810	+	0.159013i
$559$	−13.0280	+	4.74182i	−0.551028	+	0.200558i
$560$	5.70937	−	4.50849i	0.241265	−	0.190519i
$561$	−1.55538			−0.0656684
$562$	10.5392	−	12.5602i	0.444571	−	0.529820i
$563$	−1.29221	+	0.746060i	−0.0544603	+	0.0314427i	−0.526983	−	0.849876i	$-0.676677\pi$
$563$	−1.29221	+	0.746060i	−0.0544603	+	0.0314427i	0.472523	+	0.881319i	$0.343343\pi$
$564$	23.9406	+	8.71365i	1.00808	+	0.366911i
$565$	−10.8137	−	9.63569i	−0.454936	−	0.405377i
$566$	1.11490	+	1.93106i	0.0468626	+	0.0811684i
$567$	−15.4219	+	2.71930i	−0.647661	+	0.114200i
$568$	1.99544	+	5.48242i	0.0837267	+	0.230037i
$569$	0.464658	−	0.804812i	0.0194795	−	0.0337395i	−0.856121	−	0.516775i	$-0.827132\pi$
$569$	0.464658	−	0.804812i	0.0194795	−	0.0337395i	0.875601	+	0.483035i	$0.160466\pi$
$570$	9.24499	−	4.97728i	0.387230	−	0.208475i
$571$	−10.4105	+	8.73548i	−0.435667	+	0.365568i	−0.834085	−	0.551636i	$-0.814004\pi$
$571$	−10.4105	+	8.73548i	−0.435667	+	0.365568i	0.398418	+	0.917204i	$0.369559\pi$
$572$	0.265161	−	0.728524i	0.0110869	−	0.0304611i
$573$	71.4310	+	12.5952i	2.98407	+	0.526173i
$574$	2.29229	−	13.0002i	0.0956785	−	0.542620i
$575$	29.1251	−	30.7924i	1.21460	−	1.28413i
$576$	3.09256	−	2.59497i	0.128857	−	0.108124i
$577$	7.04419	+	8.39494i	0.293254	+	0.349486i	0.892475	−	0.451098i	$-0.148967\pi$
$577$	7.04419	+	8.39494i	0.293254	+	0.349486i	−0.599221	+	0.800584i	$0.704523\pi$
$578$	4.51328	+	2.60574i	0.187728	+	0.108385i
$579$	33.7556	−	12.2860i	1.40283	−	0.510590i
$580$	−0.163527	+	5.49995i	−0.00679008	+	0.228373i
$581$	6.32827	+	10.9609i	0.262541	+	0.454734i
$582$	3.71845	+	2.14685i	0.154135	+	0.0889896i
$583$	−0.308914	+	0.848733i	−0.0127939	+	0.0351509i
$584$	4.57626	+	7.92632i	0.189367	+	0.327993i
$585$	44.1487	−	34.8628i	1.82533	−	1.44140i
$586$	31.0444			1.28243
$587$	−12.1206	+	14.4448i	−0.500271	+	0.596200i	−0.955799	−	0.294022i	$-0.905006\pi$
$587$	−12.1206	+	14.4448i	−0.500271	+	0.596200i	0.455528	+	0.890222i	$0.349451\pi$
$588$	−3.25234	−	8.93574i	−0.134124	−	0.368504i
$589$	1.64696	−	9.34035i	0.0678616	−	0.384862i
$590$	−16.3500	−	0.486125i	−0.673118	−	0.0200134i
$591$	−68.2377			−2.80693
$592$	5.29335	+	2.99674i	0.217555	+	0.123165i
$593$			22.9711i			0.943311i	0.881783	+	0.471655i	$0.156343\pi$
$593$			22.9711i			0.943311i	−0.881783	+	0.471655i	$0.843657\pi$
$594$	−0.0594319	−	0.337055i	−0.00243852	−	0.0138295i
$595$	−12.6787	+	31.8552i	−0.519776	+	1.30594i
$596$	5.65852	−	2.05953i	0.231782	−	0.0843617i
$597$	16.6731	−	19.8702i	0.682383	−	0.813232i
$598$		−	52.8253i		−	2.16019i
$599$	13.2057	+	11.0809i	0.539570	+	0.452753i	0.871391	−	0.490589i	$-0.163219\pi$
$599$	13.2057	+	11.0809i	0.539570	+	0.452753i	−0.331821	+	0.943342i	$0.607663\pi$
$600$	−1.52310	−	13.1760i	−0.0621801	−	0.537907i
$601$	−17.2811	−	6.28980i	−0.704910	−	0.256566i	−0.0354044	−	0.999373i	$-0.511272\pi$
$601$	−17.2811	−	6.28980i	−0.704910	−	0.256566i	−0.669506	+	0.742807i	$0.733494\pi$
$602$	6.26842	+	3.61907i	0.255482	+	0.147502i
$603$	−37.9748	+	21.9248i	−1.54645	+	0.892846i
$604$	−3.37427	−	19.1364i	−0.137297	−	0.778650i
$605$	24.3051	−	3.54441i	0.988141	−	0.144101i
$606$	−10.0899	+	17.4762i	−0.409873	+	0.709922i
$607$	20.1792	+	24.0486i	0.819049	+	0.976104i	0.999973	−	0.00739272i	$-0.00235320\pi$
$607$	20.1792	+	24.0486i	0.819049	+	0.976104i	−0.180924	+	0.983497i	$0.557909\pi$
$608$	−1.13779	−	1.35597i	−0.0461436	−	0.0549917i
$609$	19.9566	+	7.26359i	0.808680	+	0.294336i
$610$	−0.281136	−	0.111895i	−0.0113829	−	0.00453049i
$611$	10.3927	−	58.9399i	0.420443	−	2.38445i
$612$	−6.50736	+	17.8788i	−0.263044	+	0.722709i
$613$	−3.34601	−	3.98762i	−0.135144	−	0.161058i	0.694228	−	0.719755i	$-0.255746\pi$
$613$	−3.34601	−	3.98762i	−0.135144	−	0.161058i	−0.829372	+	0.558697i	$0.811302\pi$
$614$	14.3559	−	12.0460i	0.579357	−	0.486138i
$615$	−17.9693	−	16.0118i	−0.724593	−	0.645658i
$616$	−0.380345	+	0.138434i	−0.0153245	+	0.00557768i
$617$	−10.8427	+	1.91187i	−0.436513	+	0.0769689i	−0.387586	−	0.921833i	$-0.626691\pi$
$617$	−10.8427	+	1.91187i	−0.436513	+	0.0769689i	−0.0489263	+	0.998802i	$0.515580\pi$
$618$	−1.98558	+	1.14637i	−0.0798717	+	0.0461139i
$619$	−12.3360	+	21.3667i	−0.495828	+	0.858799i	−0.999988	−	0.00481106i	$-0.998469\pi$
$619$	−12.3360	+	21.3667i	−0.495828	+	0.858799i	0.504161	+	0.863610i	$0.331802\pi$
$620$	−10.1934	−	6.29634i	−0.409378	−	0.252867i
$621$	−11.6601	−	20.1959i	−0.467905	−	0.810435i
$622$	21.2441	−	25.3178i	0.851813	−	1.01515i
$623$			48.0948i			1.92688i
$624$	−12.6635	−	10.6259i	−0.506946	−	0.425378i
$625$	−22.3123	−	11.2767i	−0.892490	−	0.451067i
$626$	−4.00128	+	22.6924i	−0.159924	+	0.906971i
$627$	−0.575302	+	0.101441i	−0.0229753	+	0.00405117i
$628$			4.81835i			0.192273i
$629$	−28.6665	+	0.242366i	−1.14301	+	0.00966378i
$630$	−28.7584	−	5.95717i	−1.14576	−	0.237339i
$631$	−2.77327	−	15.7280i	−0.110402	−	0.626122i	−0.988924	−	0.148420i	$-0.952581\pi$
$631$	−2.77327	−	15.7280i	−0.110402	−	0.626122i	0.878522	−	0.477702i	$-0.158530\pi$
$632$	−1.15568	−	0.203777i	−0.0459703	−	0.00810581i
$633$	−2.89044	−	7.94142i	−0.114885	−	0.315643i
$634$	−11.5108	−	9.65872i	−0.457153	−	0.383597i
$635$	−5.36747	+	25.9116i	−0.213002	+	1.02827i
$636$	14.7530	+	12.3793i	0.584996	+	0.490870i
$637$	−19.3457	+	11.1693i	−0.766505	+	0.442542i
$638$	0.104706	−	0.287677i	0.00414534	−	0.0113892i
$639$	11.7766	−	20.3977i	0.465876	−	0.806921i
$640$	−2.12302	+	0.701996i	−0.0839196	+	0.0277488i
$641$	1.88975	+	10.7173i	0.0746405	+	0.423307i	0.999115	+	0.0420632i	$0.0133931\pi$
$641$	1.88975	+	10.7173i	0.0746405	+	0.423307i	−0.924474	+	0.381244i	$0.875496\pi$
$642$	18.6103	+	51.1313i	0.734489	+	2.01799i
$643$	−17.8979	−	10.3334i	−0.705825	−	0.407508i	0.103689	−	0.994610i	$-0.466935\pi$
$643$	−17.8979	−	10.3334i	−0.705825	−	0.407508i	−0.809513	+	0.587102i	$0.800269\pi$
$644$	−21.1266	+	17.7273i	−0.832505	+	0.698555i
$645$	11.6198	−	6.25584i	0.457530	−	0.246323i
$646$	7.83917	+	2.85322i	0.308428	+	0.112259i
$647$	−26.6214	−	4.69407i	−1.04660	−	0.184543i	−0.376194	−	0.926541i	$-0.622767\pi$
$647$	−26.6214	−	4.69407i	−1.04660	−	0.184543i	−0.670402	+	0.741998i	$0.733878\pi$
$648$	4.74024	+	0.835832i	0.186214	+	0.0328346i
$649$	0.855192	+	0.311264i	0.0335692	+	0.0122182i
$650$	−29.8607	+	8.89841i	−1.17123	+	0.349024i
$651$	−35.4246	+	29.7247i	−1.38840	+	1.16500i
$652$	12.7873	+	7.38277i	0.500791	+	0.289132i
$653$	1.25703	+	3.45366i	0.0491914	+	0.135152i	0.961855	−	0.273559i	$-0.0882007\pi$
$653$	1.25703	+	3.45366i	0.0491914	+	0.135152i	−0.912664	+	0.408711i	$0.865979\pi$
$654$	7.07242	+	40.1097i	0.276553	+	1.56841i
$655$	13.9795	+	42.2776i	0.546224	+	1.65192i
$656$	−2.02876	+	3.51392i	−0.0792099	+	0.137196i
$657$	12.6374	−	34.7209i	0.493031	−	1.35459i
$658$	−27.0597	+	15.6229i	−1.05490	+	0.609044i
$659$	−17.3527	−	14.5606i	−0.675965	−	0.567202i	0.238859	−	0.971054i	$-0.423227\pi$
$659$	−17.3527	−	14.5606i	−0.675965	−	0.567202i	−0.914824	+	0.403852i	$0.867671\pi$
$660$	−0.149688	+	0.722621i	−0.00582658	+	0.0281280i
$661$	−24.4097	−	20.4821i	−0.949426	−	0.796663i	0.0297746	−	0.999557i	$-0.490521\pi$
$661$	−24.4097	−	20.4821i	−0.949426	−	0.796663i	−0.979201	+	0.202893i	$0.934965\pi$
$662$	−1.96483	−	5.39831i	−0.0763651	−	0.209811i
$663$	76.7256	+	13.5288i	2.97978	+	0.525415i
$664$	−0.675533	−	3.83114i	−0.0262158	−	0.148677i
$665$	−2.61199	+	12.6094i	−0.101289	+	0.488973i
$666$	−4.46848	−	24.1464i	−0.173150	−	0.935656i
$667$		−	20.8594i		−	0.807681i
$668$	13.0721	−	2.30496i	0.505773	−	0.0891814i
$669$	2.74981	−	15.5950i	0.106314	−	0.602936i
$670$	24.0335	−	3.50480i	0.928493	−	0.135402i
$671$	0.0128964	+	0.0108214i	0.000497862	+	0.000417756i
$672$			8.63046i			0.332927i
$673$	6.08410	−	7.25075i	0.234525	−	0.279496i	−0.635927	−	0.771749i	$-0.719382\pi$
$673$	6.08410	−	7.25075i	0.234525	−	0.279496i	0.870452	+	0.492253i	$0.163827\pi$
$674$	−15.4156	−	26.7006i	−0.593787	−	1.02847i
$675$	−9.45207	+	9.99316i	−0.363810	+	0.384637i
$676$	−12.9169	+	22.3727i	−0.496803	+	0.860488i
$677$	30.5077	−	17.6136i	1.17250	−	0.676946i	0.218236	−	0.975896i	$-0.429970\pi$
$677$	30.5077	−	17.6136i	1.17250	−	0.676946i	0.954269	+	0.298950i	$0.0966364\pi$
$678$	16.9218	−	2.98377i	0.649878	−	0.114591i
$679$	−4.94835	+	1.80105i	−0.189900	+	0.0691180i
$680$	7.01087	−	7.86798i	0.268854	−	0.301723i
$681$	28.5586	−	23.9635i	1.09437	−	0.918284i
$682$	0.428487	+	0.510651i	0.0164076	+	0.0195538i
$683$	3.38068	−	9.28834i	0.129358	−	0.355408i	−0.858058	−	0.513553i	$-0.828329\pi$
$683$	3.38068	−	9.28834i	0.129358	−	0.355408i	0.987416	+	0.158145i	$0.0505512\pi$
$684$	−1.24088	+	7.03738i	−0.0474462	+	0.269081i
$685$	−23.6986	−	9.43228i	−0.905477	−	0.360389i
$686$	−10.4414	−	3.80034i	−0.398653	−	0.145098i
$687$	−29.8793	−	35.6088i	−1.13997	−	1.35856i
$688$	−1.43007	−	1.70429i	−0.0545208	−	0.0649753i
$689$	22.6207	−	39.1802i	0.861781	−	1.49265i
$690$	7.25596	+	49.7563i	0.276230	+	1.89419i
$691$	1.40211	+	7.95176i	0.0533388	+	0.302499i	0.999793	−	0.0203384i	$-0.00647437\pi$
$691$	1.40211	+	7.95176i	0.0533388	+	0.302499i	−0.946454	+	0.322838i	$0.895363\pi$
$692$	2.26656	−	1.30860i	0.0861617	−	0.0497455i
$693$	1.41510	+	0.817009i	0.0537552	+	0.0310356i
$694$	−1.62635	−	0.591944i	−0.0617355	−	0.0224699i
$695$	5.94238	+	17.9713i	0.225407	+	0.681690i
$696$	−5.00052	−	4.19593i	−0.189544	−	0.159046i
$697$		−	19.1227i		−	0.724326i
$698$	−1.61604	+	1.92593i	−0.0611682	+	0.0728974i
$699$	23.0691	−	8.39647i	0.872554	−	0.317584i
$700$	13.5796	+	8.95614i	0.513259	+	0.338510i
$701$	6.64346	+	37.6769i	0.250920	+	1.42304i	0.806332	+	0.591463i	$0.201449\pi$
$701$	6.64346	+	37.6769i	0.250920	+	1.42304i	−0.555412	+	0.831575i	$0.687440\pi$
$702$			17.1435i			0.647042i
$703$	−10.5873	+	1.95926i	−0.399307	+	0.0738947i
$704$	0.124409			0.00468886
$705$	−1.69306	+	56.9432i	−0.0637643	+	2.14460i
$706$	3.04578	−	17.2735i	0.114630	−	0.650097i
$707$	−8.46469	−	23.2565i	−0.318347	−	0.874652i
$708$	12.4735	−	14.8653i	0.468782	−	0.558672i
$709$	−7.80154			−0.292993			−0.146497	−	0.989211i	$-0.546800\pi$
$709$	−7.80154			−0.292993			−0.146497	+	0.989211i	$0.546800\pi$
$710$	−10.2385	+	8.08499i	−0.384243	+	0.303424i
$711$	2.36875	+	4.10279i	0.0888351	+	0.153867i
$712$	5.05604	−	13.8914i	0.189483	−	0.520601i
$713$	39.3355	+	22.7103i	1.47312	+	0.850509i
$714$	−20.3373	−	35.2252i	−0.761104	−	1.31827i
$715$	1.73281	+	0.0515207i	0.0648035	+	0.00192676i
$716$	−0.757647	+	0.275761i	−0.0283146	+	0.0103057i
$717$	5.16083	+	2.97960i	0.192735	+	0.111275i
$718$	3.61306	+	4.30587i	0.134838	+	0.160694i
$719$	9.50555	−	7.97610i	0.354497	−	0.297458i	−0.448096	−	0.893986i	$-0.647898\pi$
$719$	9.50555	−	7.97610i	0.354497	−	0.297458i	0.802593	+	0.596527i	$0.203453\pi$
$720$	7.68013	+	4.74391i	0.286221	+	0.176795i
$721$	0.488281	−	2.76918i	0.0181845	−	0.103130i
$722$	−15.6257	−	2.75524i	−0.581529	−	0.102539i
$723$	−16.5335	+	45.4255i	−0.614889	+	1.68939i
$724$	5.79123	−	4.85942i	0.215229	−	0.180599i
$725$	−11.7913	+	3.51377i	−0.437917	+	0.130498i
$726$	−14.5696	+	25.2352i	−0.540727	+	0.936567i
$727$	5.43556	+	14.9341i	0.201594	+	0.553874i	0.998755	−	0.0498929i	$-0.0158880\pi$
$727$	5.43556	+	14.9341i	0.201594	+	0.553874i	−0.797161	+	0.603767i	$0.793666\pi$
$728$	19.9662	−	3.52057i	0.739996	−	0.130481i
$729$	−20.6626	−	35.7887i	−0.765281	−	1.32551i
$730$	−13.6152	+	15.2797i	−0.503921	+	0.565528i
$731$	9.85288	+	3.58616i	0.364422	+	0.132639i
$732$	0.310877	−	0.179485i	0.0114903	−	0.00663395i
$733$	−33.4889	+	39.9105i	−1.23694	+	1.47413i	−0.409755	+	0.912196i	$0.634386\pi$
$733$	−33.4889	+	39.9105i	−1.23694	+	1.47413i	−0.827184	+	0.561931i	$0.810059\pi$
$734$	−27.1180			−1.00094
$735$	16.6876	−	13.1776i	0.615532	−	0.486064i
$736$	7.96568	−	2.89927i	0.293619	−	0.106869i
$737$	−1.33078	−	0.234652i	−0.0490198	−	0.00864352i
$738$	16.1316	−	2.84444i	0.593812	−	0.104705i
$739$	16.1448			0.593895			0.296947	−	0.954894i	$-0.404031\pi$
$739$	16.1448			0.593895			0.296947	+	0.954894i	$0.404031\pi$
$740$	−2.64621	+	13.3416i	−0.0972767	+	0.490446i
$741$	29.2614			1.07495
$742$	−23.2607	+	4.10148i	−0.853926	+	0.150570i
$743$	−31.3707	−	5.53150i	−1.15088	−	0.202931i	−0.434520	−	0.900662i	$-0.643082\pi$
$743$	−31.3707	−	5.53150i	−1.15088	−	0.202931i	−0.716360	+	0.697731i	$0.754193\pi$
$744$	13.3567	−	4.86142i	0.489679	−	0.178228i
$745$	8.34468	+	10.5673i	0.305725	+	0.387158i
$746$	29.5511			1.08194
$747$	−10.0950	+	12.0308i	−0.369358	+	0.440184i
$748$	−0.507777	+	0.293165i	−0.0185662	+	0.0107192i
$749$	−62.7091	−	22.8242i	−2.29134	−	0.833979i
$750$	26.9036	−	12.4830i	0.982382	−	0.455816i
$751$	3.87246	+	6.70730i	0.141308	+	0.244753i	0.927990	−	0.372606i	$-0.121536\pi$
$751$	3.87246	+	6.70730i	0.141308	+	0.244753i	−0.786681	+	0.617359i	$0.788202\pi$
$752$	9.45811	−	1.66772i	0.344902	−	0.0608155i
$753$	−12.7283	−	34.9706i	−0.463844	−	1.27440i
$754$	−7.66726	+	13.2801i	−0.279225	+	0.483632i
$755$	38.2583	−	20.5973i	1.39236	−	0.749613i
$756$	6.85628	−	5.75310i	0.249361	−	0.209238i
$757$	14.6997	−	40.3870i	0.534269	−	1.46789i	−0.319675	−	0.947527i	$-0.603574\pi$
$757$	14.6997	−	40.3870i	0.534269	−	1.46789i	0.853944	−	0.520365i	$-0.174204\pi$
$758$	−23.0625	−	4.06654i	−0.837668	−	0.147704i
$759$	0.485799	−	2.75510i	0.0176334	−	0.100004i
$760$	2.08002	−	3.36744i	0.0754502	−	0.122150i
$761$	−2.77362	+	2.32734i	−0.100544	+	0.0843660i	−0.691674	−	0.722210i	$-0.743126\pi$
$761$	−2.77362	+	2.32734i	−0.100544	+	0.0843660i	0.591130	+	0.806576i	$0.298682\pi$
$762$	−20.1788	−	24.0482i	−0.731001	−	0.871174i
$763$	−43.2585	−	24.9753i	−1.56606	−	0.904167i
$764$	25.6937	−	9.35173i	0.929564	−	0.338334i
$765$	−42.5252	−	1.26438i	−1.53750	−	0.0457137i
$766$	0.120982	+	0.209547i	0.00437125	+	0.00757123i
$767$	−39.4784	−	22.7929i	−1.42548	−	0.823003i
$768$	0.907292	−	2.49276i	0.0327391	−	0.0899499i
$769$	20.1460	+	34.8940i	0.726485	+	1.25831i	0.958360	+	0.285563i	$0.0921806\pi$
$769$	20.1460	+	34.8940i	0.726485	+	1.25831i	−0.231875	+	0.972746i	$0.574486\pi$
$770$	−0.560899	−	0.710299i	−0.0202134	−	0.0255974i
$771$	56.8233			2.04644
$772$	8.70426	−	10.3733i	0.313273	−	0.373344i
$773$	14.2847	+	39.2469i	0.513784	+	1.41161i	0.877264	+	0.480009i	$0.159367\pi$
$773$	14.2847	+	39.2469i	0.513784	+	1.41161i	−0.363479	+	0.931602i	$0.618411\pi$
$774$	−1.55964	+	8.84514i	−0.0560600	+	0.317932i
$775$	6.21149	−	26.0608i	0.223123	−	0.936133i
$776$	1.61859			0.0581038
$777$	45.6841	+	25.8632i	1.63891	+	0.927838i
$778$		−	1.69673i		−	0.0608308i
$779$	−1.24717	−	7.07307i	−0.0446846	−	0.253419i
$780$	13.6693	−	34.3442i	0.489441	−	1.22972i
$781$	0.682065	−	0.248251i	0.0244062	−	0.00888314i
$782$	−25.6799	+	30.6041i	−0.918312	+	1.09440i
$783$			6.76958i			0.241925i
$784$	−2.74602	−	2.30418i	−0.0980721	−	0.0822922i
$785$	−10.2294	+	3.38246i	−0.365104	+	0.120725i
$786$	−49.6407	−	18.0677i	−1.77063	−	0.644455i
$787$	5.89312	+	3.40240i	0.210067	+	0.121282i	0.601343	−	0.798991i	$-0.294633\pi$
$787$	5.89312	+	3.40240i	0.210067	+	0.121282i	−0.391275	+	0.920274i	$0.627966\pi$
$788$	−22.2772	+	12.8617i	−0.793591	+	0.458180i
$789$	5.85747	+	33.2194i	0.208531	+	1.18264i
$790$	−0.378658	−	2.59657i	−0.0134720	−	0.0923819i
$791$	−10.5368	+	18.2503i	−0.374645	+	0.648905i
$792$	−0.322839	−	0.384744i	−0.0114716	−	0.0136713i
$793$	−0.542044	−	0.645983i	−0.0192486	−	0.0229395i
$794$	−8.29321	−	3.01848i	−0.294315	−	0.107122i
$795$	−15.9248	+	40.0111i	−0.564795	+	1.41905i
$796$	1.69794	−	9.62950i	0.0601819	−	0.341309i
$797$	−15.2588	+	41.9231i	−0.540493	+	1.48499i	0.305706	+	0.952126i	$0.401108\pi$
$797$	−15.2588	+	41.9231i	−0.540493	+	1.48499i	−0.846199	+	0.532867i	$0.821115\pi$
$798$	−9.81967	−	11.7026i	−0.347613	−	0.414269i
$799$	−34.6733	+	29.0944i	−1.22665	+	1.02929i
$800$	−2.98070	−	4.01440i	−0.105384	−	0.141931i
$801$	−56.0802	+	20.4115i	−1.98149	+	0.721205i
$802$	17.5860	−	3.10089i	0.620983	−	0.109496i
$803$	0.986109	−	0.569330i	0.0347990	−	0.0200912i
$804$	−14.4068	+	24.9532i	−0.508087	+	0.880032i
$805$	−52.4662	−	32.4076i	−1.84919	−	1.14222i
$806$	−16.6952	−	28.9169i	−0.588063	−	1.01855i
$807$	19.8448	−	23.6501i	0.698569	−	0.832522i
$808$			7.60713i			0.267618i
$809$	16.3379	+	13.7092i	0.574411	+	0.481988i	0.883106	−	0.469173i	$-0.155448\pi$
$809$	16.3379	+	13.7092i	0.574411	+	0.481988i	−0.308695	+	0.951161i	$0.599892\pi$
$810$	1.55314	+	10.6504i	0.0545719	+	0.374216i
$811$	0.598461	−	3.39404i	0.0210148	−	0.119181i	−0.972496	−	0.232920i	$-0.925172\pi$
$811$	0.598461	−	3.39404i	0.0210148	−	0.119181i	0.993511	+	0.113740i	$0.0362829\pi$
$812$	7.88417	−	1.39019i	0.276680	−	0.0487861i
$813$		−	42.5741i		−	1.49314i
$814$	0.372822	−	0.658543i	0.0130674	−	0.0230819i
$815$	−6.69709	+	32.3304i	−0.234589	+	1.13248i
$816$	2.17097	+	12.3122i	0.0759993	+	0.431013i
$817$	3.87825	+	0.683840i	0.135683	+	0.0239245i
$818$	1.22491	+	3.36542i	0.0428281	+	0.117669i
$819$	−62.6992	−	52.6108i	−2.19089	−	1.83837i
$820$	−8.88430	−	1.84034i	−0.310253	−	0.0642675i
$821$	−32.5122	−	27.2810i	−1.13468	−	0.952114i	−0.135433	−	0.990787i	$-0.543243\pi$
$821$	−32.5122	−	27.2810i	−1.13468	−	0.952114i	−0.999252	+	0.0386729i	$0.987687\pi$
$822$	26.2057	−	15.1299i	0.914028	−	0.527714i
$823$	14.9362	−	41.0368i	0.520642	−	1.43045i	−0.349166	−	0.937061i	$-0.613535\pi$
$823$	14.9362	−	41.0368i	0.520642	−	1.43045i	0.869808	−	0.493391i	$-0.164243\pi$
$824$	−0.432146	+	0.748500i	−0.0150545	+	0.0260752i
$825$	−1.63922	+	0.189488i	−0.0570702	+	0.00659711i
$826$	4.13269	+	23.4377i	0.143795	+	0.815501i
$827$	−9.38199	−	25.7768i	−0.326244	−	0.896348i	−0.989053	−	0.147559i	$-0.952858\pi$
$827$	−9.38199	−	25.7768i	−0.326244	−	0.896348i	0.662809	−	0.748788i	$-0.269364\pi$
$828$	−29.6369	−	17.1109i	−1.02995	−	0.594643i
$829$	28.8267	−	24.1885i	1.00119	−	0.840100i	0.0140429	−	0.999901i	$-0.495530\pi$
$829$	28.8267	−	24.1885i	1.00119	−	0.840100i	0.987149	+	0.159802i	$0.0510854\pi$
$830$	7.65935	−	4.12361i	0.265860	−	0.143133i
$831$	38.1790	+	13.8960i	1.32442	+	0.482048i
$832$	−6.13700	−	1.08212i	−0.212762	−	0.0375157i
$833$	16.6376	+	2.93365i	0.576457	+	0.101645i
$834$	−21.1012	−	7.68021i	−0.730674	−	0.265944i
$835$	14.0700	+	26.1341i	0.486912	+	0.904409i
$836$	−0.168695	+	0.141552i	−0.00583445	+	0.00489568i
$837$	−12.7657	−	7.37025i	−0.441246	−	0.254753i
$838$	−0.576385	−	1.58360i	−0.0199109	−	0.0547047i
$839$	−7.07968	−	40.1508i	−0.244418	−	1.38616i	−0.821841	−	0.569716i	$-0.807053\pi$
$839$	−7.07968	−	40.1508i	−0.244418	−	1.38616i	0.577424	−	0.816445i	$-0.304058\pi$
$840$	−18.3226	+	6.05855i	−0.632190	+	0.209040i
$841$	11.4724	−	19.8707i	0.395599	−	0.685198i
$842$	3.85027	−	10.5785i	0.132689	−	0.364560i
$843$	−37.6676	+	21.7474i	−1.29734	+	0.749021i
$844$	−2.44046	−	2.04778i	−0.0840039	−	0.0704877i
$845$	−56.5652	−	11.7172i	−1.94590	−	0.403085i
$846$	−29.7010	−	24.9221i	−1.02114	−	0.856840i
$847$	−12.2228	−	33.5819i	−0.419981	−	1.15389i
$848$	7.14962	+	1.26067i	0.245519	+	0.0432916i
$849$	−1.02714	−	5.82521i	−0.0352514	−	0.199921i
$850$	21.6255	+	9.36090i	0.741747	+	0.321076i
$851$	8.52419	−	50.8535i	0.292205	−	1.74324i
$852$		−	15.4768i		−	0.530227i
$853$	16.9093	−	2.98157i	0.578964	−	0.102087i	0.123505	−	0.992344i	$-0.460586\pi$
$853$	16.9093	−	2.98157i	0.578964	−	0.102087i	0.455459	+	0.890257i	$0.349475\pi$
$854$	−0.0764489	+	0.433563i	−0.00261603	+	0.0148362i
$855$	−15.8116	+	2.30580i	−0.540745	+	0.0788568i
$856$	15.7130	+	13.1848i	0.537060	+	0.450647i
$857$		−	10.2382i		−	0.349729i	−0.984593	−	0.174864i	$-0.944051\pi$
$857$		−	10.2382i		−	0.349729i	0.984593	−	0.174864i	$-0.0559487\pi$
$858$	−1.32197	+	1.57546i	−0.0451313	+	0.0537853i
$859$	−13.9161	−	24.1035i	−0.474813	−	0.822400i	0.524771	−	0.851243i	$-0.324151\pi$
$859$	−13.9161	−	24.1035i	−0.474813	−	0.822400i	−0.999584	+	0.0288434i	$0.990818\pi$
$860$	2.61433	−	4.23246i	0.0891479	−	0.144326i
$861$	−17.5092	+	30.3268i	−0.596711	+	1.03353i
$862$	2.56488	−	1.48084i	0.0873602	−	0.0504374i
$863$	20.3816	−	3.59383i	0.693799	−	0.122335i	0.184381	−	0.982855i	$-0.440972\pi$
$863$	20.3816	−	3.59383i	0.693799	−	0.122335i	0.509418	+	0.860519i	$0.329861\pi$
$864$	−2.58513	+	0.940909i	−0.0879478	+	0.0320104i
$865$	4.36930	+	3.89332i	0.148561	+	0.132377i
$866$	14.2053	−	11.9197i	0.482717	−	0.405048i
$867$	−8.88637	−	10.5904i	−0.301797	−	0.359667i
$868$	−5.96220	+	16.3810i	−0.202370	+	0.556008i
$869$	−0.0253518	+	0.143777i	−0.000860000	+	0.00487731i
$870$	5.39769	−	13.5617i	0.182999	−	0.459785i
$871$	63.6050	+	23.1503i	2.15517	+	0.784419i
$872$	9.86892	+	11.7613i	0.334204	+	0.398289i
$873$	−4.20018	−	5.00557i	−0.142154	−	0.169413i
$874$	−7.50244	+	12.9946i	−0.253774	+	0.439549i
$875$	−9.48124	+	35.1168i	−0.320524	+	1.18716i
$876$	−4.21606	−	23.9104i	−0.142447	−	0.807859i
$877$	−12.1853	+	7.03519i	−0.411469	+	0.237562i	−0.691421	−	0.722452i	$-0.743015\pi$
$877$	−12.1853	+	7.03519i	−0.411469	+	0.237562i	0.279952	+	0.960014i	$0.409682\pi$
$878$	−9.83541	−	5.67848i	−0.331929	−	0.191639i
$879$	−77.3865	−	28.1664i	−2.61018	−	0.950028i
$880$	0.0873349	+	0.264124i	0.00294406	+	0.00890360i
$881$	−8.43965	−	7.08171i	−0.284339	−	0.238589i	0.489451	−	0.872031i	$-0.337197\pi$
$881$	−8.43965	−	7.08171i	−0.284339	−	0.238589i	−0.773790	+	0.633442i	$0.781642\pi$
$882$			14.4715i			0.487281i
$883$	17.9615	−	21.4057i	0.604452	−	0.720358i	−0.373862	−	0.927484i	$-0.621967\pi$
$883$	17.9615	−	21.4057i	0.604452	−	0.720358i	0.978314	+	0.207126i	$0.0664112\pi$
$884$	27.5981	−	10.0449i	0.928225	−	0.337846i
$885$	40.3156	+	16.0460i	1.35519	+	0.539381i
$886$	1.46268	+	8.29527i	0.0491397	+	0.278685i
$887$		−	15.5073i		−	0.520683i	−0.965517	−	0.260341i	$-0.916165\pi$
$887$		−	15.5073i		−	0.520683i	0.965517	−	0.260341i	$-0.0838351\pi$
$888$	−10.4762	−	12.2728i	−0.351557	−	0.411847i
$889$	38.5010			1.29128
$890$	33.0409	+	0.982387i	1.10753	+	0.0329297i
$891$	0.103985	−	0.589731i	0.00348364	−	0.0197567i
$892$	−2.04169	−	5.60949i	−0.0683608	−	0.187820i
$893$	−10.9274	+	13.0227i	−0.365671	+	0.435789i
$894$	−15.9739			−0.534249
$895$	−1.11731	−	1.41491i	−0.0373476	−	0.0472954i
$896$	1.62670	+	2.81754i	0.0543444	+	0.0941272i
$897$	−47.9280	+	131.681i	−1.60027	+	4.39670i
$898$	6.37625	+	3.68133i	0.212778	+	0.122847i
$899$	−6.59253	−	11.4186i	−0.219873	−	0.380831i
$900$	−4.67998	+	19.6352i	−0.155999	+	0.654508i
$901$	−32.1519	+	11.7023i	−1.07113	+	0.389861i
$902$	0.437165	+	0.252397i	0.0145560	+	0.00840392i
$903$	−12.3421	−	14.7088i	−0.410721	−	0.489478i
$904$	4.96197	−	4.16358i	0.165033	−	0.138479i
$905$	14.3821	+	8.88359i	0.478076	+	0.295301i
$906$	−8.95107	+	50.7641i	−0.297380	+	1.68652i
$907$	43.1993	+	7.61721i	1.43441	+	0.252925i	0.836205	−	0.548418i	$-0.184770\pi$
$907$	43.1993	+	7.61721i	1.43441	+	0.252925i	0.598205	+	0.801343i	$0.295881\pi$
$908$	4.80661	−	13.2061i	0.159513	−	0.438259i
$909$	23.5255	−	19.7402i	0.780292	−	0.654743i
$910$	21.4904	+	39.9171i	0.712400	+	1.32324i
$911$	−4.77070	+	8.26310i	−0.158060	+	0.273769i	−0.934169	−	0.356830i	$-0.883857\pi$
$911$	−4.77070	+	8.26310i	−0.158060	+	0.273769i	0.776109	+	0.630599i	$0.217191\pi$
$912$	1.60599	+	4.41242i	0.0531796	+	0.146110i
$913$	−0.476630	+	0.0840427i	−0.0157741	+	0.00278141i
$914$	3.50820	+	6.07638i	0.116041	+	0.200989i
$915$	0.599284	+	0.533999i	0.0198117	+	0.0176535i
$916$	−16.4662	−	5.99321i	−0.544059	−	0.198021i
$917$	56.1082	−	32.3941i	1.85286	−	1.06975i
$918$	8.33398	−	9.93205i	0.275062	−	0.327806i
$919$	48.1342			1.58780			0.793901	−	0.608048i	$-0.208047\pi$
$919$	48.1342			1.58780			0.793901	+	0.608048i	$0.208047\pi$
$920$	11.7471	+	14.8760i	0.387290	+	0.490447i
$921$	−46.7151	+	17.0029i	−1.53932	+	0.560265i
$922$	8.75897	+	1.54444i	0.288461	+	0.0508635i
$923$	−35.8049	+	6.31337i	−1.17853	+	0.207807i
$924$	1.07371			0.0353225
$925$	−30.1820	+	3.74777i	−0.992379	+	0.123226i
$926$	−29.5089			−0.969724
$927$	3.43619	−	0.605893i	0.112859	−	0.0199001i
$928$	−2.42336	−	0.427303i	−0.0795505	−	0.0140269i
$929$	43.2031	−	15.7246i	1.41745	−	0.515909i	0.484141	−	0.874990i	$-0.339132\pi$
$929$	43.2031	−	15.7246i	1.41745	−	0.515909i	0.933306	+	0.359081i	$0.116910\pi$
$930$	19.6972	+	24.9437i	0.645897	+	0.817936i
$931$	6.34519			0.207955
$932$	5.94863	−	7.08931i	0.194854	−	0.232218i
$933$	−75.9273	+	43.8366i	−2.48575	+	1.43515i
$934$	27.4356	+	9.98573i	0.897719	+	0.326743i
$935$	−0.978852	−	0.872218i	−0.0320119	−	0.0285246i
$936$	12.5788	+	21.7871i	0.411151	+	0.712134i
$937$	25.3840	−	4.47588i	0.829259	−	0.146221i	0.257122	−	0.966379i	$-0.417226\pi$
$937$	25.3840	−	4.47588i	0.829259	−	0.146221i	0.572137	+	0.820158i	$0.306115\pi$
$938$	−12.0862	−	33.2067i	−0.394630	−	1.08424i
$939$	30.5629	−	52.9365i	0.997383	−	1.72752i
$940$	10.1802	+	18.9090i	0.332040	+	0.616744i
$941$	−34.0940	+	28.6083i	−1.11143	+	0.932603i	−0.998140	−	0.0609589i	$-0.980584\pi$
$941$	−34.0940	+	28.6083i	−1.11143	+	0.932603i	−0.113292	+	0.993562i	$0.536140\pi$
$942$	4.37165	−	12.0110i	0.142436	−	0.391340i
$943$	33.8727	+	5.97268i	1.10305	+	0.194497i
$944$	1.27027	−	7.20403i	0.0413436	−	0.234471i
$945$	17.0270	+	10.5174i	0.553889	+	0.342129i
$946$	−0.212029	+	0.177914i	−0.00689367	+	0.00578448i
$947$	19.8592	+	23.6673i	0.645339	+	0.769085i	0.985203	−	0.171390i	$-0.0548257\pi$
$947$	19.8592	+	23.6673i	0.645339	+	0.769085i	−0.339865	+	0.940474i	$0.610381\pi$
$948$	2.69594	+	1.55650i	0.0875602	+	0.0505529i
$949$	−53.5959	+	19.5073i	−1.73980	+	0.633234i
$950$	8.60929	+	2.05199i	0.279322	+	0.0665752i
$951$	19.9305	+	34.5206i	0.646290	+	1.11941i
$952$	−13.2788	−	7.66651i	−0.430368	−	0.248473i
$953$	17.0316	−	46.7940i	0.551708	−	1.51581i	−0.279668	−	0.960097i	$-0.590224\pi$
$953$	17.0316	−	46.7940i	0.551708	−	1.51581i	0.831377	−	0.555709i	$-0.187553\pi$
$954$	−14.6543	−	25.3821i	−0.474452	−	0.821774i
$955$	37.8907	+	47.9832i	1.22611	+	1.55270i
$956$	2.24643			0.0726548
$957$	−0.522014	+	0.622112i	−0.0168743	+	0.0201100i
$958$	−1.54365	−	4.24115i	−0.0498732	−	0.137025i
$959$	−6.44434	+	36.5477i	−0.208099	+	1.18019i
$960$	5.92910	+	0.176286i	0.191361	+	0.00568962i
$961$	−2.29002			−0.0738716
$962$	−24.1190	+	29.2425i	−0.777628	+	0.942815i
$963$		−	82.8076i		−	2.66844i
$964$	3.16438	+	17.9461i	0.101918	+	0.578005i
$965$	28.1331	+	11.1973i	0.905637	+	0.360452i
$966$	68.7475	−	25.0221i	2.21192	−	0.805071i
$967$	−30.8841	+	36.8062i	−0.993165	+	1.18361i	−0.0101746	+	0.999948i	$0.503239\pi$
$967$	−30.8841	+	36.8062i	−0.993165	+	1.18361i	−0.982990	+	0.183659i	$0.941206\pi$
$968$			10.9845i			0.353056i
$969$	−16.9525	−	14.2248i	−0.544592	−	0.456967i
$970$	1.13624	+	3.43628i	0.0364825	+	0.110332i
$971$	1.99793	+	0.727189i	0.0641168	+	0.0233366i	0.373879	−	0.927477i	$-0.378027\pi$
$971$	1.99793	+	0.727189i	0.0641168	+	0.0233366i	−0.309763	+	0.950814i	$0.600250\pi$
$972$	−18.2054	−	10.5109i	−0.583937	−	0.337136i
$973$	23.8504	−	13.7700i	0.764608	−	0.441446i
$974$	3.81805	+	21.6532i	0.122338	+	0.693814i
$975$	82.5092	+	4.91074i	2.64241	+	0.157269i
$976$	0.0676601	−	0.117191i	0.00216575	−	0.00375118i
$977$	13.1442	+	15.6647i	0.420522	+	0.501158i	0.934163	−	0.356847i	$-0.116148\pi$
$977$	13.1442	+	15.6647i	0.420522	+	0.501158i	−0.513641	+	0.858005i	$0.671704\pi$
$978$	−25.1775	−	30.0054i	−0.805087	−	0.959465i
$979$	−1.72822	−	0.629020i	−0.0552341	−	0.0201036i
$980$	2.96413	−	7.44737i	0.0946855	−	0.237898i
$981$	10.7631	−	61.0405i	0.343639	−	1.94887i
$982$	7.87047	−	21.6239i	0.251157	−	0.690047i
$983$	2.93803	+	3.50141i	0.0937087	+	0.111678i	0.810861	−	0.585239i	$-0.198999\pi$
$983$	2.93803	+	3.50141i	0.0937087	+	0.111678i	−0.717152	+	0.696917i	$0.754555\pi$
$984$	8.24538	−	6.91870i	0.262853	−	0.220560i
$985$	−42.9441	−	38.2659i	−1.36831	−	1.21925i
$986$	10.8978	−	3.96649i	0.347058	−	0.126319i
$987$	81.6279	−	14.3932i	2.59824	−	0.458141i
$988$	9.55280	−	5.51531i	0.303915	−	0.175465i
$989$	−9.42966	+	16.3326i	−0.299846	+	0.519348i
$990$	0.590187	−	0.955481i	0.0187574	−	0.0303672i
$991$	−22.4132	−	38.8207i	−0.711977	−	1.23318i	−0.964114	−	0.265489i	$-0.914467\pi$
$991$	−22.4132	−	38.8207i	−0.711977	−	1.23318i	0.252137	−	0.967692i	$-0.418867\pi$
$992$	3.44417	−	4.10460i	0.109352	−	0.130321i
$993$			15.2394i			0.483607i
$994$	14.5405	+	12.2009i	0.461197	+	0.386990i
$995$	21.6355	−	3.15511i	0.685893	−	0.100024i
$996$	−1.79202	+	10.1630i	−0.0567822	+	0.322028i
$997$	−29.3514	+	5.17544i	−0.929567	+	0.163908i	−0.617876	−	0.786276i	$-0.712007\pi$
$997$	−29.3514	+	5.17544i	−0.929567	+	0.163908i	−0.311691	+	0.950183i	$0.600895\pi$
$998$		−	14.3177i		−	0.453219i
$999$	−2.76638	+	16.5036i	−0.0875244	+	0.522152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.x.a.9.9	✓	108
5.4	even	2	inner	370.2.x.a.9.10	yes	108
37.33	even	9	inner	370.2.x.a.329.10	yes	108
185.144	even	18	inner	370.2.x.a.329.9	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.x.a.9.9	✓	108	1.1	even	1	trivial
370.2.x.a.9.10	yes	108	5.4	even	2	inner
370.2.x.a.329.9	yes	108	185.144	even	18	inner
370.2.x.a.329.10	yes	108	37.33	even	9	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(2.61244 + 0.460644i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.38577 + 1.75489i) q^{5} -2.65274 q^{6} +(2.09125 - 2.49226i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(3.79359 + 1.38075i) q^{9} +(-1.66945 - 1.48759i) q^{10} +(0.0622047 + 0.107742i) q^{11} +(2.61244 - 0.460644i) q^{12} +(-2.13136 - 5.85586i) q^{13} +(-1.62670 + 2.81754i) q^{14} +(2.81188 + 5.22289i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.61191 + 4.42868i) q^{17} +(-3.97572 - 0.701027i) q^{18} +(-0.307373 + 1.74320i) q^{19} +(1.90241 + 1.17509i) q^{20} +(6.61132 - 5.54755i) q^{21} +(-0.0799689 - 0.0953032i) q^{22} +(-7.34121 - 4.23845i) q^{23} +(-2.49276 + 0.907292i) q^{24} +(-1.15926 + 4.86376i) q^{25} +(3.11584 + 5.39679i) q^{26} +(2.38247 + 1.37552i) q^{27} +(1.11273 - 3.05720i) q^{28} +(1.23037 + 2.13106i) q^{29} +(-3.67611 - 4.65527i) q^{30} -5.35817 q^{31} +(-0.642788 + 0.766044i) q^{32} +(0.112876 + 0.310124i) q^{33} +(0.818388 - 4.64131i) q^{34} +(7.27163 + 0.216203i) q^{35} +4.03705 q^{36} +(2.12868 + 5.69813i) q^{37} -1.77009i q^{38} +(-2.87058 - 16.2799i) q^{39} +(-2.07756 - 0.826889i) q^{40} +(-3.81283 + 1.38776i) q^{41} +(-5.54755 + 6.61132i) q^{42} -2.22479i q^{43} +(0.0953032 + 0.0799689i) q^{44} +(2.83399 + 8.57073i) q^{45} +(7.96568 + 2.89927i) q^{46} +(8.31733 + 4.80201i) q^{47} +(2.29734 - 1.32637i) q^{48} +(-0.622472 - 3.53021i) q^{49} +(0.297062 - 4.99117i) q^{50} +(-6.25107 + 10.8272i) q^{51} +(-4.00564 - 4.77374i) q^{52} +(4.66659 + 5.56142i) q^{53} +(-2.58513 - 0.940909i) q^{54} +(-0.102873 + 0.258468i) q^{55} +(-0.564949 + 3.20398i) q^{56} +(-1.60599 + 4.41242i) q^{57} +(-1.58173 - 1.88504i) q^{58} +(5.60374 - 4.70210i) q^{59} +(4.42864 + 3.94619i) q^{60} +(0.127159 - 0.0462822i) q^{61} +(5.27677 - 0.930436i) q^{62} +(11.3745 - 6.56709i) q^{63} +(0.500000 - 0.866025i) q^{64} +(7.32278 - 11.8552i) q^{65} +(-0.165013 - 0.285811i) q^{66} +(-6.98181 + 8.32060i) q^{67} +4.71291i q^{68} +(-17.2261 - 14.4544i) q^{69} +(-7.19870 + 1.04979i) q^{70} +(1.01311 - 5.74563i) q^{71} +(-3.97572 + 0.701027i) q^{72} -9.15252i q^{73} +(-3.08581 - 5.24193i) q^{74} +(-5.26895 + 12.1723i) q^{75} +(0.307373 + 1.74320i) q^{76} +(0.398606 + 0.0702850i) q^{77} +(5.65395 + 15.5341i) q^{78} +(0.898957 + 0.754314i) q^{79} +(2.18958 + 0.453562i) q^{80} +(-3.68725 - 3.09397i) q^{81} +(3.51392 - 2.02876i) q^{82} +(-1.33054 + 3.65563i) q^{83} +(4.31523 - 7.47420i) q^{84} +(-10.0056 + 3.30844i) q^{85} +(0.386330 + 2.19099i) q^{86} +(2.23261 + 6.13404i) q^{87} +(-0.107742 - 0.0622047i) q^{88} +(-11.3243 + 9.50225i) q^{89} +(-4.27923 - 7.94840i) q^{90} +(-19.0515 - 6.93418i) q^{91} +(-8.34812 - 1.47200i) q^{92} +(-13.9979 - 2.46821i) q^{93} +(-9.02483 - 3.28477i) q^{94} +(-3.48507 + 1.87628i) q^{95} +(-2.03212 + 1.70515i) q^{96} +(-1.40174 - 0.809293i) q^{97} +(1.22603 + 3.36849i) q^{98} +(0.0872144 + 0.494617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 12 q^{9} + 12 q^{11} - 6 q^{14} + 6 q^{19} - 24 q^{21} + 30 q^{25} + 48 q^{26} + 24 q^{30} - 192 q^{31} + 12 q^{34} + 30 q^{35} + 84 q^{36} + 24 q^{39} + 12 q^{40} - 108 q^{41} + 6 q^{44} - 30 q^{45}+ \cdots - 90 q^{99}+O(q^{100}) \) 108 * q - 12 * q^9 + 12 * q^11 - 6 * q^14 + 6 * q^19 - 24 * q^21 + 30 * q^25 + 48 * q^26 + 24 * q^30 - 192 * q^31 + 12 * q^34 + 30 * q^35 + 84 * q^36 + 24 * q^39 + 12 * q^40 - 108 * q^41 + 6 * q^44 - 30 * q^45 - 54 * q^46 + 60 * q^49 - 12 * q^50 + 30 * q^55 - 48 * q^59 + 24 * q^61 + 54 * q^64 - 6 * q^65 - 120 * q^69 - 12 * q^70 + 12 * q^71 - 60 * q^74 - 156 * q^75 - 6 * q^76 + 12 * q^80 + 120 * q^81 - 24 * q^84 - 30 * q^85 + 12 * q^86 + 54 * q^89 + 18 * q^90 - 138 * q^91 + 6 * q^94 + 84 * q^95 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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