LMFDB - Embedded newform 920.2.bv.a.217.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.26
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44284 - 0.313871i) q^{3} +(-0.625712 + 2.14674i) q^{5} +(2.34294 - 1.27934i) q^{7} +(-0.745622 + 0.340514i) q^{9} +O(q^{10})$	\(q+(1.44284 - 0.313871i) q^{3} +(-0.625712 + 2.14674i) q^{5} +(2.34294 - 1.27934i) q^{7} +(-0.745622 + 0.340514i) q^{9} +(4.30034 + 3.72626i) q^{11} +(-2.02873 + 3.71534i) q^{13} +(-0.229005 + 3.29379i) q^{15} +(-2.53026 - 1.89413i) q^{17} +(-0.894860 + 6.22389i) q^{19} +(2.97894 - 2.58127i) q^{21} +(-1.71282 - 4.47954i) q^{23} +(-4.21697 - 2.68648i) q^{25} +(-4.51514 + 3.37999i) q^{27} +(2.66650 - 0.383384i) q^{29} +(5.88992 - 3.78522i) q^{31} +(7.37427 + 4.02666i) q^{33} +(1.28041 + 5.83019i) q^{35} +(7.38779 + 2.75550i) q^{37} +(-1.76100 + 5.99741i) q^{39} +(2.17029 - 4.75228i) q^{41} +(0.0789002 + 0.362698i) q^{43} +(-0.264450 - 1.81372i) q^{45} +(1.20693 + 1.20693i) q^{47} +(0.0681750 - 0.106082i) q^{49} +(-4.24528 - 1.93875i) q^{51} +(2.10676 + 3.85824i) q^{53} +(-10.6901 + 6.90013i) q^{55} +(0.662356 + 9.26095i) q^{57} +(-3.63836 - 12.3911i) q^{59} +(7.08717 + 11.0279i) q^{61} +(-1.31131 + 1.75171i) q^{63} +(-6.70647 - 6.67989i) q^{65} +(-7.83763 - 0.560559i) q^{67} +(-3.87732 - 5.92566i) q^{69} +(4.92875 + 5.68808i) q^{71} +(0.604698 + 0.807782i) q^{73} +(-6.92762 - 2.55258i) q^{75} +(14.8426 + 3.22881i) q^{77} +(13.4247 - 3.94186i) q^{79} +(-3.84339 + 4.43550i) q^{81} +(1.57582 - 4.22495i) q^{83} +(5.64942 - 4.24663i) q^{85} +(3.72700 - 1.39010i) q^{87} +(-1.64702 - 1.05848i) q^{89} +11.3003i q^{91} +(7.31015 - 7.31015i) q^{93} +(-12.8011 - 5.81539i) q^{95} +(-4.70004 - 12.6013i) q^{97} +(-4.47527 - 1.31406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	1.44284	−	0.313871i	0.833024	−	0.181213i	0.224225	−	0.974537i	$-0.428015\pi$
$3$	1.44284	−	0.313871i	0.833024	−	0.181213i	0.608800	+	0.793324i	$0.291651\pi$
$4$		0			0
$5$	−0.625712	+	2.14674i	−0.279827	+	0.960050i
$5$	−0.625712	+	2.14674i	−0.279827	+	0.960050i
$6$		0			0
$7$	2.34294	−	1.27934i	0.885549	−	0.483546i	0.0289807	−	0.999580i	$-0.490774\pi$
$7$	2.34294	−	1.27934i	0.885549	−	0.483546i	0.856568	+	0.516034i	$0.172592\pi$
$8$		0			0
$9$	−0.745622	+	0.340514i	−0.248541	+	0.113505i
$10$		0			0
$11$	4.30034	+	3.72626i	1.29660	+	1.12351i	0.984861	+	0.173344i	$0.0554571\pi$
$11$	4.30034	+	3.72626i	1.29660	+	1.12351i	0.311740	+	0.950168i	$0.399088\pi$
$12$		0			0
$13$	−2.02873	+	3.71534i	−0.562669	+	1.03045i	0.429203	+	0.903208i	$0.358795\pi$
$13$	−2.02873	+	3.71534i	−0.562669	+	1.03045i	−0.991872	+	0.127243i	$0.959387\pi$
$14$		0			0
$15$	−0.229005	+	3.29379i	−0.0591288	+	0.850454i
$16$		0			0
$17$	−2.53026	−	1.89413i	−0.613678	−	0.459394i	0.246671	−	0.969099i	$-0.420663\pi$
$17$	−2.53026	−	1.89413i	−0.613678	−	0.459394i	−0.860349	+	0.509705i	$0.829754\pi$
$18$		0			0
$19$	−0.894860	+	6.22389i	−0.205295	+	1.42786i	0.582956	+	0.812504i	$0.301896\pi$
$19$	−0.894860	+	6.22389i	−0.205295	+	1.42786i	−0.788251	+	0.615354i	$0.789013\pi$
$20$		0			0
$21$	2.97894	−	2.58127i	0.650059	−	0.563279i
$22$		0			0
$23$	−1.71282	−	4.47954i	−0.357147	−	0.934048i
$23$	−1.71282	−	4.47954i	−0.357147	−	0.934048i
$24$		0			0
$25$	−4.21697	−	2.68648i	−0.843394	−	0.537296i
$26$		0			0
$27$	−4.51514	+	3.37999i	−0.868939	+	0.650479i
$28$		0			0
$29$	2.66650	−	0.383384i	0.495156	−	0.0711927i	0.109787	−	0.993955i	$-0.464983\pi$
$29$	2.66650	−	0.383384i	0.495156	−	0.0711927i	0.385369	+	0.922763i	$0.374074\pi$
$30$		0			0
$31$	5.88992	−	3.78522i	1.05786	−	0.679846i	0.108521	−	0.994094i	$-0.465389\pi$
$31$	5.88992	−	3.78522i	1.05786	−	0.679846i	0.949341	+	0.314248i	$0.101752\pi$
$32$		0			0
$33$	7.37427	+	4.02666i	1.28370	+	0.700951i
$34$		0			0
$35$	1.28041	+	5.83019i	0.216428	+	0.985481i
$36$		0			0
$37$	7.38779	+	2.75550i	1.21455	+	0.453002i	0.873398	−	0.487008i	$-0.161912\pi$
$37$	7.38779	+	2.75550i	1.21455	+	0.453002i	0.341148	+	0.940010i	$0.389184\pi$
$38$		0			0
$39$	−1.76100	+	5.99741i	−0.281985	+	0.960354i
$40$		0			0
$41$	2.17029	−	4.75228i	0.338943	−	0.742181i	−0.661024	−	0.750365i	$-0.729878\pi$
$41$	2.17029	−	4.75228i	0.338943	−	0.742181i	0.999967	+	0.00818408i	$0.00260510\pi$
$42$		0			0
$43$	0.0789002	+	0.362698i	0.0120322	+	0.0553110i	0.982772	−	0.184825i	$-0.0591717\pi$
$43$	0.0789002	+	0.362698i	0.0120322	+	0.0553110i	−0.970739	+	0.240136i	$0.922808\pi$
$44$		0			0
$45$	−0.264450	−	1.81372i	−0.0394218	−	0.270373i
$46$		0			0
$47$	1.20693	+	1.20693i	0.176050	+	0.176050i	0.789631	−	0.613582i	$-0.210272\pi$
$47$	1.20693	+	1.20693i	0.176050	+	0.176050i	−0.613582	+	0.789631i	$0.710272\pi$
$48$		0			0
$49$	0.0681750	−	0.106082i	0.00973928	−	0.0151546i
$50$		0			0
$51$	−4.24528	−	1.93875i	−0.594457	−	0.271480i
$52$		0			0
$53$	2.10676	+	3.85824i	0.289385	+	0.529970i	0.981415	−	0.191900i	$-0.0614648\pi$
$53$	2.10676	+	3.85824i	0.289385	+	0.529970i	−0.692029	+	0.721870i	$0.743283\pi$
$54$		0			0
$55$	−10.6901	+	6.90013i	−1.44145	+	0.930414i
$56$		0			0
$57$	0.662356	+	9.26095i	0.0877312	+	1.22664i
$58$		0			0
$59$	−3.63836	−	12.3911i	−0.473674	−	1.61318i	−0.756487	−	0.654009i	$-0.773086\pi$
$59$	−3.63836	−	12.3911i	−0.473674	−	1.61318i	0.282813	−	0.959175i	$-0.408732\pi$
$60$		0			0
$61$	7.08717	+	11.0279i	0.907420	+	1.41197i	0.911193	+	0.411980i	$0.135163\pi$
$61$	7.08717	+	11.0279i	0.907420	+	1.41197i	−0.00377339	+	0.999993i	$0.501201\pi$
$62$		0			0
$63$	−1.31131	+	1.75171i	−0.165210	+	0.220695i
$64$		0			0
$65$	−6.70647	−	6.67989i	−0.831835	−	0.828538i
$66$		0			0
$67$	−7.83763	−	0.560559i	−0.957519	−	0.0684831i	−0.416175	−	0.909284i	$-0.636630\pi$
$67$	−7.83763	−	0.560559i	−0.957519	−	0.0684831i	−0.541344	+	0.840801i	$0.682084\pi$
$68$		0			0
$69$	−3.87732	−	5.92566i	−0.466774	−	0.713365i
$70$		0			0
$71$	4.92875	+	5.68808i	0.584935	+	0.675051i	0.968658	−	0.248397i	$-0.0799037\pi$
$71$	4.92875	+	5.68808i	0.584935	+	0.675051i	−0.383723	+	0.923448i	$0.625358\pi$
$72$		0			0
$73$	0.604698	+	0.807782i	0.0707745	+	0.0945437i	0.834532	−	0.550960i	$-0.185738\pi$
$73$	0.604698	+	0.807782i	0.0707745	+	0.0945437i	−0.763757	+	0.645504i	$0.776647\pi$
$74$		0			0
$75$	−6.92762	−	2.55258i	−0.799933	−	0.294747i
$76$		0			0
$77$	14.8426	+	3.22881i	1.69147	+	0.367958i
$78$		0			0
$79$	13.4247	−	3.94186i	1.51040	−	0.443494i	0.581414	−	0.813608i	$-0.302500\pi$
$79$	13.4247	−	3.94186i	1.51040	−	0.443494i	0.928986	+	0.370114i	$0.120681\pi$
$80$		0			0
$81$	−3.84339	+	4.43550i	−0.427043	+	0.492834i
$82$		0			0
$83$	1.57582	−	4.22495i	0.172969	−	0.463748i	−0.821320	−	0.570468i	$-0.806762\pi$
$83$	1.57582	−	4.22495i	0.172969	−	0.463748i	0.994289	+	0.106720i	$0.0340347\pi$
$84$		0			0
$85$	5.64942	−	4.24663i	0.612765	−	0.460611i
$86$		0			0
$87$	3.72700	−	1.39010i	0.399576	−	0.149034i
$88$		0			0
$89$	−1.64702	−	1.05848i	−0.174584	−	0.112198i	0.450431	−	0.892811i	$-0.351271\pi$
$89$	−1.64702	−	1.05848i	−0.174584	−	0.112198i	−0.625014	+	0.780613i	$0.714907\pi$
$90$		0			0
$91$			11.3003i			1.18459i
$92$		0			0
$93$	7.31015	−	7.31015i	0.758027	−	0.758027i
$94$		0			0
$95$	−12.8011	−	5.81539i	−1.31337	−	0.596647i
$96$		0			0
$97$	−4.70004	−	12.6013i	−0.477217	−	1.27947i	−0.923163	−	0.384408i	$-0.874405\pi$
$97$	−4.70004	−	12.6013i	−0.477217	−	1.27947i	0.445946	−	0.895060i	$-0.352867\pi$
$98$		0			0
$99$	−4.47527	−	1.31406i	−0.449782	−	0.132068i
$100$		0			0
$101$	−5.44003	−	11.9120i	−0.541304	−	1.18529i	−0.960726	−	0.277498i	$-0.910495\pi$
$101$	−5.44003	−	11.9120i	−0.541304	−	1.18529i	0.419423	−	0.907791i	$-0.362233\pi$
$102$		0			0
$103$	−8.56003	+	0.612225i	−0.843445	+	0.0603244i	−0.486372	−	0.873752i	$-0.661680\pi$
$103$	−8.56003	+	0.612225i	−0.843445	+	0.0603244i	−0.357073	+	0.934076i	$0.616225\pi$
$104$		0			0
$105$	3.67735	+	8.01015i	0.358872	+	0.781710i
$106$		0			0
$107$	0.259683	−	1.19374i	0.0251045	−	0.115404i	−0.962889	−	0.269896i	$-0.913011\pi$
$107$	0.259683	−	1.19374i	0.0251045	−	0.115404i	0.987994	+	0.154493i	$0.0493743\pi$
$108$		0			0
$109$	−0.0682258	−	0.474521i	−0.00653485	−	0.0454509i	0.986293	−	0.165003i	$-0.0527633\pi$
$109$	−0.0682258	−	0.474521i	−0.00653485	−	0.0454509i	−0.992828	+	0.119552i	$0.961854\pi$
$110$		0			0
$111$	11.5243	+	1.65694i	1.09384	+	0.157270i
$112$		0			0
$113$	0.776119	−	10.8516i	0.0730112	−	1.02083i	−0.820459	−	0.571706i	$-0.806282\pi$
$113$	0.776119	−	10.8516i	0.0730112	−	1.02083i	0.893470	−	0.449123i	$-0.148264\pi$
$114$		0			0
$115$	10.6881	−	0.874066i	0.996673	−	0.0815071i
$116$		0			0
$117$	0.247539	−	3.46105i	0.0228850	−	0.319974i
$118$		0			0
$119$	−8.35150	−	1.20076i	−0.765581	−	0.110074i
$120$		0			0
$121$	3.04240	+	21.1604i	0.276582	+	1.92367i
$122$		0			0
$123$	1.63978	−	7.53797i	0.147854	−	0.679676i
$124$		0			0
$125$	8.40578	−	7.37176i	0.751836	−	0.659350i
$126$		0			0
$127$	3.54210	−	0.253336i	0.314310	−	0.0224799i	0.0867069	−	0.996234i	$-0.472366\pi$
$127$	3.54210	−	0.253336i	0.314310	−	0.0224799i	0.227603	+	0.973754i	$0.426911\pi$
$128$		0			0
$129$	0.227681	+	0.498551i	0.0200462	+	0.0438950i
$130$		0			0
$131$	−5.33036	−	1.56513i	−0.465716	−	0.136746i	0.0404521	−	0.999181i	$-0.487120\pi$
$131$	−5.33036	−	1.56513i	−0.465716	−	0.136746i	−0.506168	+	0.862435i	$0.668938\pi$
$132$		0			0
$133$	5.86589	+	15.7270i	0.508637	+	1.36371i
$134$		0			0
$135$	−4.43078	−	11.8077i	−0.381340	−	1.01625i
$136$		0			0
$137$	11.0716	−	11.0716i	0.945911	−	0.945911i	−0.0526996	−	0.998610i	$-0.516783\pi$
$137$	11.0716	−	11.0716i	0.945911	−	0.945911i	0.998610	+	0.0526996i	$0.0167826\pi$
$138$		0			0
$139$			16.5983i			1.40785i	0.710273	+	0.703927i	$0.248572\pi$
$139$			16.5983i			1.40785i	−0.710273	+	0.703927i	$0.751428\pi$
$140$		0			0
$141$	2.12024	+	1.36259i	0.178556	+	0.114751i
$142$		0			0
$143$	−22.5686	+	8.41765i	−1.88728	+	0.703919i
$144$		0			0
$145$	−0.845434	+	5.96416i	−0.0702094	+	0.495296i
$146$		0			0
$147$	0.0650695	−	0.174458i	0.00536684	−	0.0143891i
$148$		0			0
$149$	3.50317	−	4.04287i	0.286991	−	0.331205i	−0.593887	−	0.804548i	$-0.702408\pi$
$149$	3.50317	−	4.04287i	0.286991	−	0.331205i	0.880878	+	0.473343i	$0.156953\pi$
$150$		0			0
$151$	−4.00628	+	1.17635i	−0.326027	+	0.0957300i	−0.440650	−	0.897679i	$-0.645252\pi$
$151$	−4.00628	+	1.17635i	−0.326027	+	0.0957300i	0.114623	+	0.993409i	$0.463434\pi$
$152$		0			0
$153$	2.53159	+	0.550715i	0.204667	+	0.0445226i
$154$		0			0
$155$	4.44049	+	15.0126i	0.356669	+	1.20584i
$156$		0			0
$157$	−11.4040	−	15.2340i	−0.910138	−	1.21580i	−0.975955	−	0.217970i	$-0.930056\pi$
$157$	−11.4040	−	15.2340i	−0.910138	−	1.21580i	0.0658176	−	0.997832i	$-0.479034\pi$
$158$		0			0
$159$	4.25070	+	4.90558i	0.337103	+	0.389037i
$160$		0			0
$161$	−9.74390	−	8.30402i	−0.767927	−	0.654448i
$162$		0			0
$163$	−4.94367	−	0.353578i	−0.387218	−	0.0276944i	−0.123627	−	0.992329i	$-0.539453\pi$
$163$	−4.94367	−	0.353578i	−0.387218	−	0.0276944i	−0.263591	+	0.964634i	$0.584907\pi$
$164$		0			0
$165$	−13.2583	+	13.3111i	−1.03216	+	1.03627i
$166$		0			0
$167$	2.76858	−	3.69838i	0.214239	−	0.286190i	−0.680529	−	0.732721i	$-0.738250\pi$
$167$	2.76858	−	3.69838i	0.214239	−	0.286190i	0.894768	+	0.446532i	$0.147341\pi$
$168$		0			0
$169$	−2.65970	−	4.13857i	−0.204592	−	0.318352i
$170$		0			0
$171$	−1.45209	−	4.94538i	−0.111044	−	0.378182i
$172$		0			0
$173$	−0.621041	−	8.68329i	−0.0472169	−	0.660178i	−0.964859	−	0.262769i	$-0.915364\pi$
$173$	−0.621041	−	8.68329i	−0.0472169	−	0.660178i	0.917642	−	0.397409i	$-0.130090\pi$
$174$		0			0
$175$	−13.3170	−	0.899319i	−1.00667	−	0.0679821i
$176$		0			0
$177$	−9.13877	−	16.7364i	−0.686912	−	1.25799i
$178$		0			0
$179$	−12.4191	−	5.67161i	−0.928247	−	0.423916i	−0.106851	−	0.994275i	$-0.534077\pi$
$179$	−12.4191	−	5.67161i	−0.928247	−	0.423916i	−0.821396	+	0.570359i	$0.806804\pi$
$180$		0			0
$181$	12.0358	−	18.7281i	0.894615	−	1.39205i	−0.0251939	−	0.999683i	$-0.508020\pi$
$181$	12.0358	−	18.7281i	0.894615	−	1.39205i	0.919809	−	0.392366i	$-0.128343\pi$
$182$		0			0
$183$	13.6870	+	13.6870i	1.01177	+	1.01177i
$184$		0			0
$185$	−10.5380	+	14.1355i	−0.774767	+	1.03926i
$186$		0			0
$187$	−3.82295	−	17.5738i	−0.279562	−	1.28513i
$188$		0			0
$189$	−6.25454	+	13.6955i	−0.454951	+	0.996204i
$190$		0			0
$191$	−6.21863	+	21.1787i	−0.449964	+	1.53244i	0.352544	+	0.935795i	$0.385317\pi$
$191$	−6.21863	+	21.1787i	−0.449964	+	1.53244i	−0.802508	+	0.596642i	$0.796501\pi$
$192$		0			0
$193$	15.0863	+	5.62691i	1.08594	+	0.405034i	0.827771	−	0.561067i	$-0.189609\pi$
$193$	15.0863	+	5.62691i	1.08594	+	0.405034i	0.258167	+	0.966100i	$0.416882\pi$
$194$		0			0
$195$	−11.7730	−	7.53305i	−0.843081	−	0.539453i
$196$		0			0
$197$	−17.9458	−	9.79914i	−1.27858	−	0.698160i	−0.310929	−	0.950433i	$-0.600640\pi$
$197$	−17.9458	−	9.79914i	−1.27858	−	0.698160i	−0.967656	+	0.252273i	$0.918822\pi$
$198$		0			0
$199$	20.5088	−	13.1802i	1.45383	−	0.934318i	0.454783	−	0.890602i	$-0.349717\pi$
$199$	20.5088	−	13.1802i	1.45383	−	0.934318i	0.999044	−	0.0437156i	$-0.0139195\pi$
$200$		0			0
$201$	−11.4844	+	1.65121i	−0.810047	+	0.116467i
$202$		0			0
$203$	5.75697	−	4.30961i	0.404060	−	0.302475i
$204$		0			0
$205$	8.84391	+	7.63260i	0.617686	+	0.533084i
$206$		0			0
$207$	2.80246	+	2.75680i	0.194784	+	0.191611i
$208$		0			0
$209$	−27.0401	+	23.4303i	−1.87040	+	1.62071i
$210$		0			0
$211$	−2.54477	+	17.6992i	−0.175189	+	1.21847i	0.692522	+	0.721397i	$0.256499\pi$
$211$	−2.54477	+	17.6992i	−0.175189	+	1.21847i	−0.867711	+	0.497069i	$0.834410\pi$
$212$		0			0
$213$	8.89673	+	6.66001i	0.609594	+	0.456336i
$214$		0			0
$215$	−0.827987	−	0.0575667i	−0.0564682	−	0.00392602i
$216$		0			0
$217$	8.95715	−	16.4038i	0.608051	−	1.11356i
$218$		0			0
$219$	1.12602	+	0.975704i	0.0760895	+	0.0659319i
$220$		0			0
$221$	12.1706	−	5.55811i	0.818681	−	0.373879i
$222$		0			0
$223$	20.3019	−	11.0857i	1.35951	−	0.742351i	0.376593	−	0.926379i	$-0.377096\pi$
$223$	20.3019	−	11.0857i	1.35951	−	0.742351i	0.982921	+	0.184028i	$0.0589137\pi$
$224$		0			0
$225$	4.05905	+	0.567161i	0.270603	+	0.0378107i
$226$		0			0
$227$	−16.5160	+	3.59284i	−1.09621	+	0.238465i	−0.724079	−	0.689717i	$-0.757735\pi$
$227$	−16.5160	+	3.59284i	−1.09621	+	0.238465i	−0.372127	+	0.928182i	$0.621371\pi$
$228$		0			0
$229$	−20.0396			−1.32425			−0.662127	−	0.749392i	$-0.730346\pi$
$229$	−20.0396			−1.32425			−0.662127	+	0.749392i	$0.730346\pi$
$230$		0			0
$231$	22.4290			1.47572
$232$		0			0
$233$	7.58130	−	1.64921i	0.496667	−	0.108043i	0.0427476	−	0.999086i	$-0.486389\pi$
$233$	7.58130	−	1.64921i	0.496667	−	0.108043i	0.453920	+	0.891043i	$0.350025\pi$
$234$		0			0
$235$	−3.34617	+	1.83578i	−0.218280	+	0.119753i
$236$		0			0
$237$	18.1325	−	9.90110i	1.17783	−	0.643146i
$238$		0			0
$239$	4.43610	−	2.02590i	0.286947	−	0.131044i	−0.266741	−	0.963768i	$-0.585947\pi$
$239$	4.43610	−	2.02590i	0.286947	−	0.131044i	0.553689	+	0.832724i	$0.313220\pi$
$240$		0			0
$241$	−21.5563	−	18.6786i	−1.38856	−	1.20320i	−0.952975	−	0.303048i	$-0.901996\pi$
$241$	−21.5563	−	18.6786i	−1.38856	−	1.20320i	−0.435586	−	0.900147i	$-0.643459\pi$
$242$		0			0
$243$	3.95583	−	7.24456i	0.253767	−	0.464739i
$244$		0			0
$245$	0.185073	+	0.212731i	0.0118239	+	0.0135909i
$246$		0			0
$247$	−21.3085	−	15.9513i	−1.35582	−	1.01496i
$248$		0			0
$249$	0.947575	−	6.59053i	0.0600501	−	0.417658i
$250$		0			0
$251$	−2.22358	+	1.92675i	−0.140351	+	0.121615i	−0.722207	−	0.691677i	$-0.756872\pi$
$251$	−2.22358	+	1.92675i	−0.140351	+	0.121615i	0.581856	+	0.813292i	$0.302327\pi$
$252$		0			0
$253$	9.32625	−	25.6459i	0.586337	−	1.61235i
$254$		0			0
$255$	6.81831	−	7.90039i	0.426979	−	0.494742i
$256$		0			0
$257$	0.694162	−	0.519643i	0.0433006	−	0.0324144i	−0.577408	−	0.816456i	$-0.695936\pi$
$257$	0.694162	−	0.519643i	0.0433006	−	0.0324144i	0.620709	+	0.784041i	$0.286845\pi$
$258$		0			0
$259$	20.8344	−	2.99554i	1.29459	−	0.186134i
$260$		0			0
$261$	−1.85765	+	1.19384i	−0.114986	+	0.0738967i
$262$		0			0
$263$	−6.28523	−	3.43200i	−0.387564	−	0.211626i	0.273640	−	0.961832i	$-0.411772\pi$
$263$	−6.28523	−	3.43200i	−0.387564	−	0.211626i	−0.661204	+	0.750206i	$0.729954\pi$
$264$		0			0
$265$	−9.60085	+	2.10851i	−0.589776	+	0.129525i
$266$		0			0
$267$	−2.70861	−	1.01026i	−0.165764	−	0.0618269i
$268$		0			0
$269$	−1.56863	+	5.34228i	−0.0956413	+	0.325725i	−0.993391	−	0.114782i	$-0.963383\pi$
$269$	−1.56863	+	5.34228i	−0.0956413	+	0.325725i	0.897749	+	0.440507i	$0.145201\pi$
$270$		0			0
$271$	4.01179	−	8.78461i	0.243699	−	0.533627i	−0.747772	−	0.663956i	$-0.768876\pi$
$271$	4.01179	−	8.78461i	0.243699	−	0.533627i	0.991471	+	0.130329i	$0.0416035\pi$
$272$		0			0
$273$	3.54683	+	16.3045i	0.214664	+	0.986794i
$274$		0			0
$275$	−8.12385	−	27.2663i	−0.489887	−	1.64422i
$276$		0			0
$277$	13.8262	+	13.8262i	0.830735	+	0.830735i	0.987617	−	0.156882i	$-0.0501443\pi$
$277$	13.8262	+	13.8262i	0.830735	+	0.830735i	−0.156882	+	0.987617i	$0.550144\pi$
$278$		0			0
$279$	−3.10273	+	4.82795i	−0.185756	+	0.289042i
$280$		0			0
$281$	12.4534	+	5.68727i	0.742907	+	0.339274i	0.750654	−	0.660696i	$-0.229739\pi$
$281$	12.4534	+	5.68727i	0.742907	+	0.339274i	−0.00774708	+	0.999970i	$0.502466\pi$
$282$		0			0
$283$	−5.72111	−	10.4774i	−0.340085	−	0.622819i	0.650533	−	0.759478i	$-0.274545\pi$
$283$	−5.72111	−	10.4774i	−0.340085	−	0.622819i	−0.990618	+	0.136659i	$0.956364\pi$
$284$		0			0
$285$	−20.2953	−	4.37278i	−1.20219	−	0.259021i
$286$		0			0
$287$	−0.994924	−	13.9109i	−0.0587285	−	0.821132i
$288$		0			0
$289$	−1.97496	−	6.72610i	−0.116174	−	0.395653i
$290$		0			0
$291$	−10.7366	−	16.7065i	−0.629390	−	0.979350i
$292$		0			0
$293$	5.01085	−	6.69371i	0.292737	−	0.391051i	−0.629928	−	0.776654i	$-0.716916\pi$
$293$	5.01085	−	6.69371i	0.292737	−	0.391051i	0.922665	+	0.385603i	$0.126007\pi$
$294$		0			0
$295$	28.8770	−	0.0573326i	1.68128	−	0.00333803i
$296$		0			0
$297$	−32.0114	−	2.28950i	−1.85749	−	0.132850i
$298$		0			0
$299$	20.1179	+	2.72408i	1.16345	+	0.157537i
$300$		0			0
$301$	0.648874	+	0.748841i	0.0374005	+	0.0431625i
$302$		0			0
$303$	−11.5879	−	15.4797i	−0.665709	−	0.889284i
$304$		0			0
$305$	−28.1085	+	8.31404i	−1.60949	+	0.476061i
$306$		0			0
$307$	−6.22207	−	1.35353i	−0.355112	−	0.0772499i	0.0314705	−	0.999505i	$-0.489981\pi$
$307$	−6.22207	−	1.35353i	−0.355112	−	0.0772499i	−0.386583	+	0.922255i	$0.626345\pi$
$308$		0			0
$309$	−12.1586	+	3.57009i	−0.691679	+	0.203095i
$310$		0			0
$311$	−20.8046	+	24.0098i	−1.17972	+	1.36147i	−0.261601	+	0.965176i	$0.584250\pi$
$311$	−20.8046	+	24.0098i	−1.17972	+	1.36147i	−0.918122	+	0.396297i	$0.870295\pi$
$312$		0			0
$313$	−7.22005	+	19.3577i	−0.408102	+	1.09416i	0.556592	+	0.830786i	$0.312109\pi$
$313$	−7.22005	+	19.3577i	−0.408102	+	1.09416i	−0.964693	+	0.263376i	$0.915164\pi$
$314$		0			0
$315$	−2.93996	−	3.91111i	−0.165648	−	0.220366i
$316$		0			0
$317$	−2.41268	+	0.899884i	−0.135510	+	0.0505425i	−0.416304	−	0.909225i	$-0.636675\pi$
$317$	−2.41268	+	0.899884i	−0.135510	+	0.0505425i	0.280794	+	0.959768i	$0.409402\pi$
$318$		0			0
$319$	12.8954	+	8.28739i	0.722005	+	0.464005i
$320$		0			0
$321$		−	1.80389i		−	0.100683i
$322$		0			0
$323$	14.0531	−	14.0531i	0.781934	−	0.781934i
$324$		0			0
$325$	18.5363	−	10.2173i	1.02821	−	0.566756i
$326$		0			0
$327$	−0.247377	−	0.663244i	−0.0136800	−	0.0366775i
$328$		0			0
$329$	4.37186	+	1.28369i	0.241029	+	0.0707724i
$330$		0			0
$331$	11.0397	+	24.1735i	0.606796	+	1.32870i	0.924744	+	0.380590i	$0.124279\pi$
$331$	11.0397	+	24.1735i	0.606796	+	1.32870i	−0.317948	+	0.948108i	$0.602994\pi$
$332$		0			0
$333$	−6.44678	+	0.461083i	−0.353282	+	0.0252672i
$334$		0			0
$335$	6.10748	−	16.4746i	0.333687	−	0.900104i
$336$		0			0
$337$	1.55087	−	7.12923i	0.0844812	−	0.388354i	−0.915419	−	0.402503i	$-0.868140\pi$
$337$	1.55087	−	7.12923i	0.0844812	−	0.388354i	0.999900	+	0.0141490i	$0.00450392\pi$
$338$		0			0
$339$	−2.28617	−	15.9007i	−0.124168	−	0.863607i
$340$		0			0
$341$	39.4334	+	5.66967i	2.13544	+	0.307030i
$342$		0			0
$343$	−1.30905	+	18.3030i	−0.0706822	+	0.988267i
$344$		0			0
$345$	15.1469	−	4.61583i	0.815483	−	0.248508i
$346$		0			0
$347$	0.853436	−	11.9326i	0.0458148	−	0.640575i	−0.921723	−	0.387849i	$-0.873218\pi$
$347$	0.853436	−	11.9326i	0.0458148	−	0.640575i	0.967538	−	0.252726i	$-0.0813272\pi$
$348$		0			0
$349$	−6.02675	−	0.866516i	−0.322604	−	0.0463835i	−0.0208898	−	0.999782i	$-0.506650\pi$
$349$	−6.02675	−	0.866516i	−0.322604	−	0.0463835i	−0.301715	+	0.953398i	$0.597559\pi$
$350$		0			0
$351$	−3.39782	−	23.6324i	−0.181362	−	1.26140i
$352$		0			0
$353$	−5.00738	+	23.0186i	−0.266516	+	1.22515i	0.628034	+	0.778186i	$0.283860\pi$
$353$	−5.00738	+	23.0186i	−0.266516	+	1.22515i	−0.894550	+	0.446968i	$0.852504\pi$
$354$		0			0
$355$	−15.2948	+	7.02164i	−0.811764	+	0.372670i
$356$		0			0
$357$	−12.4268	+	0.888780i	−0.657694	+	0.0470392i
$358$		0			0
$359$	−0.882729	−	1.93291i	−0.0465886	−	0.102015i	0.884906	−	0.465769i	$-0.154222\pi$
$359$	−0.882729	−	1.93291i	−0.0465886	−	0.102015i	−0.931495	+	0.363754i	$0.881495\pi$
$360$		0			0
$361$	−19.7057	−	5.78610i	−1.03714	−	0.304532i
$362$		0			0
$363$	11.0313	+	29.5761i	0.578994	+	1.55234i
$364$		0			0
$365$	−2.11246	+	0.792689i	−0.110571	+	0.0414912i
$366$		0			0
$367$	15.8099	−	15.8099i	0.825271	−	0.825271i	−0.161587	−	0.986858i	$-0.551661\pi$
$367$	15.8099	−	15.8099i	0.825271	−	0.825271i	0.986858	+	0.161587i	$0.0516614\pi$
$368$		0			0
$369$			4.28241i			0.222934i
$370$		0			0
$371$	9.87203	+	6.34437i	0.512530	+	0.329383i
$372$		0			0
$373$	7.67031	−	2.86088i	0.397154	−	0.148131i	−0.142949	−	0.989730i	$-0.545658\pi$
$373$	7.67031	−	2.86088i	0.397154	−	0.148131i	0.540102	+	0.841599i	$0.318386\pi$
$374$		0			0
$375$	9.81442	−	13.2746i	0.506814	−	0.685498i
$376$		0			0
$377$	−3.98520	+	10.6847i	−0.205248	+	0.550292i
$378$		0			0
$379$	9.48650	−	10.9480i	0.487289	−	0.562361i	−0.457850	−	0.889029i	$-0.651380\pi$
$379$	9.48650	−	10.9480i	0.487289	−	0.562361i	0.945139	+	0.326668i	$0.105926\pi$
$380$		0			0
$381$	5.03116	−	1.47728i	0.257754	−	0.0756835i
$382$		0			0
$383$	−9.15590	−	1.99174i	−0.467845	−	0.101773i	−0.0275379	−	0.999621i	$-0.508767\pi$
$383$	−9.15590	−	1.99174i	−0.467845	−	0.101773i	−0.440307	+	0.897847i	$0.645130\pi$
$384$		0			0
$385$	−16.2186	+	29.8429i	−0.826578	+	1.52094i
$386$		0			0
$387$	−0.182333	−	0.243569i	−0.00926853	−	0.0123813i
$388$		0			0
$389$	7.31352	+	8.44025i	0.370810	+	0.427938i	0.910232	−	0.414098i	$-0.135903\pi$
$389$	7.31352	+	8.44025i	0.370810	+	0.427938i	−0.539422	+	0.842035i	$0.681357\pi$
$390$		0			0
$391$	−4.15095	+	14.5787i	−0.209923	+	0.737276i
$392$		0			0
$393$	−8.18211	−	0.585196i	−0.412733	−	0.0295192i
$394$		0			0
$395$	0.0621151	+	31.2859i	0.00312535	+	1.57416i
$396$		0			0
$397$	−15.6849	+	20.9526i	−0.787203	+	1.05158i	0.210063	+	0.977688i	$0.432633\pi$
$397$	−15.6849	+	20.9526i	−0.787203	+	1.05158i	−0.997266	+	0.0738928i	$0.976458\pi$
$398$		0			0
$399$	13.3998	+	20.8505i	0.670829	+	1.04383i
$400$		0			0
$401$	−3.80989	−	12.9753i	−0.190257	−	0.647955i	−0.998270	−	0.0587911i	$-0.981275\pi$
$401$	−3.80989	−	12.9753i	−0.190257	−	0.647955i	0.808014	−	0.589164i	$-0.200543\pi$
$402$		0			0
$403$	2.11434	+	29.5623i	0.105323	+	1.47260i
$404$		0			0
$405$	−7.11701	−	11.0261i	−0.353647	−	0.547891i
$406$		0			0
$407$	21.5023	+	39.3785i	1.06583	+	1.95192i
$408$		0			0
$409$	8.55531	+	3.90708i	0.423033	+	0.193193i	0.615545	−	0.788102i	$-0.288936\pi$
$409$	8.55531	+	3.90708i	0.423033	+	0.193193i	−0.192512	+	0.981295i	$0.561663\pi$
$410$		0			0
$411$	12.4995	−	19.4496i	0.616555	−	0.959379i
$412$		0			0
$413$	−24.3769	−	24.3769i	−1.19951	−	1.19951i
$414$		0			0
$415$	8.08384	+	6.02648i	0.396820	+	0.295828i
$416$		0			0
$417$	5.20974	+	23.9488i	0.255122	+	1.17278i
$418$		0			0
$419$	−14.0325	+	30.7269i	−0.685534	+	1.50111i	0.171138	+	0.985247i	$0.445256\pi$
$419$	−14.0325	+	30.7269i	−0.685534	+	1.50111i	−0.856671	+	0.515862i	$0.827472\pi$
$420$		0			0
$421$	−7.25121	+	24.6953i	−0.353402	+	1.20358i	0.570612	+	0.821220i	$0.306706\pi$
$421$	−7.25121	+	24.6953i	−0.353402	+	1.20358i	−0.924014	+	0.382358i	$0.875112\pi$
$422$		0			0
$423$	−1.31089	−	0.488938i	−0.0637379	−	0.0237730i
$424$		0			0
$425$	5.58149	+	14.7850i	0.270742	+	0.717177i
$426$		0			0
$427$	30.7133	+	16.7707i	1.48632	+	0.811592i
$428$		0			0
$429$	−29.9208	+	19.2289i	−1.44459	+	0.928382i
$430$		0			0
$431$	−22.4270	+	3.22451i	−1.08027	+	0.155319i	−0.659393	−	0.751799i	$-0.729186\pi$
$431$	−22.4270	+	3.22451i	−1.08027	+	0.155319i	−0.420876	+	0.907118i	$0.638277\pi$
$432$		0			0
$433$	−5.19189	+	3.88660i	−0.249506	+	0.186778i	−0.716709	−	0.697372i	$-0.754353\pi$
$433$	−5.19189	+	3.88660i	−0.249506	+	0.186778i	0.467203	+	0.884150i	$0.345262\pi$
$434$		0			0
$435$	0.652148	+	8.87068i	0.0312681	+	0.425317i
$436$		0			0
$437$	29.4129	−	6.65182i	1.40701	−	0.318200i
$438$		0			0
$439$	−18.8767	+	16.3568i	−0.900937	+	0.780667i	−0.976285	−	0.216491i	$-0.930539\pi$
$439$	−18.8767	+	16.3568i	−0.900937	+	0.780667i	0.0753474	+	0.997157i	$0.475993\pi$
$440$		0			0
$441$	−0.0147102	+	0.102312i	−0.000700487	+	0.00487199i
$442$		0			0
$443$	16.1355	+	12.0789i	0.766621	+	0.573885i	0.909426	−	0.415865i	$-0.136521\pi$
$443$	16.1355	+	12.0789i	0.766621	+	0.573885i	−0.142805	+	0.989751i	$0.545612\pi$
$444$		0			0
$445$	3.30283	−	2.87342i	0.156569	−	0.136213i
$446$		0			0
$447$	3.78557	−	6.93276i	0.179052	−	0.327908i
$448$		0			0
$449$	−0.979881	−	0.849072i	−0.0462435	−	0.0400702i	0.631432	−	0.775431i	$-0.282467\pi$
$449$	−0.979881	−	0.849072i	−0.0462435	−	0.0400702i	−0.677676	+	0.735361i	$0.737013\pi$
$450$		0			0
$451$	27.0412	−	12.3493i	1.27332	−	0.581507i
$452$		0			0
$453$	−5.41120	+	2.95474i	−0.254241	+	0.138826i
$454$		0			0
$455$	−24.2587	−	7.07072i	−1.13727	−	0.331481i
$456$		0			0
$457$	26.6871	−	5.80543i	1.24837	−	0.271566i	0.460640	−	0.887587i	$-0.347620\pi$
$457$	26.6871	−	5.80543i	1.24837	−	0.271566i	0.787730	+	0.616021i	$0.211256\pi$
$458$		0			0
$459$	17.8266			0.832075
$460$		0			0
$461$	33.2390			1.54809			0.774046	−	0.633129i	$-0.218230\pi$
$461$	33.2390			1.54809			0.774046	+	0.633129i	$0.218230\pi$
$462$		0			0
$463$	31.1041	−	6.76628i	1.44553	−	0.314456i	0.579715	−	0.814819i	$-0.303164\pi$
$463$	31.1041	−	6.76628i	1.44553	−	0.314456i	0.865816	+	0.500363i	$0.166800\pi$
$464$		0			0
$465$	11.1189	+	20.2670i	0.515628	+	0.939861i
$466$		0			0
$467$	11.8228	−	6.45572i	0.547093	−	0.298735i	−0.181831	−	0.983330i	$-0.558203\pi$
$467$	11.8228	−	6.45572i	0.547093	−	0.298735i	0.728924	+	0.684595i	$0.240021\pi$
$468$		0			0
$469$	−19.0803	+	8.71367i	−0.881045	+	0.402360i
$470$		0			0
$471$	−21.2356	−	18.4008i	−0.978487	−	0.847864i
$472$		0			0
$473$	−1.01221	+	1.85373i	−0.0465416	+	0.0852345i
$474$		0			0
$475$	20.4940	−	23.8419i	0.940327	−	1.09394i
$476$		0			0
$477$	−2.88463	−	2.15941i	−0.132078	−	0.0988724i
$478$		0			0
$479$	2.09533	−	14.5734i	0.0957382	−	0.665874i	−0.884279	−	0.466960i	$-0.845349\pi$
$479$	2.09533	−	14.5734i	0.0957382	−	0.665874i	0.980017	−	0.198914i	$-0.0637416\pi$
$480$		0			0
$481$	−25.2255	+	21.8580i	−1.15018	+	0.996639i
$482$		0			0
$483$	−16.6653	−	8.92305i	−0.758297	−	0.406013i
$484$		0			0
$485$	29.9926	−	2.20497i	1.36189	−	0.100123i
$486$		0			0
$487$	−17.1852	+	12.8647i	−0.778737	+	0.582955i	−0.912985	−	0.407992i	$-0.866229\pi$
$487$	−17.1852	+	12.8647i	−0.778737	+	0.582955i	0.134248	+	0.990948i	$0.457138\pi$
$488$		0			0
$489$	−7.24391	+	1.04152i	−0.327581	+	0.0470990i
$490$		0			0
$491$	1.27257	−	0.817831i	0.0574303	−	0.0369082i	−0.511611	−	0.859217i	$-0.670951\pi$
$491$	1.27257	−	0.817831i	0.0574303	−	0.0369082i	0.569041	+	0.822309i	$0.307315\pi$
$492$		0			0
$493$	−7.47311	−	4.08063i	−0.336572	−	0.183782i
$494$		0			0
$495$	5.62117	−	8.78501i	0.252653	−	0.394857i
$496$		0			0
$497$	18.8248	+	7.02129i	0.844408	+	0.314948i
$498$		0			0
$499$	−6.22186	+	21.1897i	−0.278529	+	0.948582i	0.694807	+	0.719196i	$0.255490\pi$
$499$	−6.22186	+	21.1897i	−0.278529	+	0.948582i	−0.973336	+	0.229385i	$0.926328\pi$
$500$		0			0
$501$	2.83380	−	6.20515i	0.126605	−	0.277226i
$502$		0			0
$503$	−0.986310	−	4.53399i	−0.0439774	−	0.202161i	0.949916	−	0.312505i	$-0.101168\pi$
$503$	−0.986310	−	4.53399i	−0.0439774	−	0.202161i	−0.993893	+	0.110345i	$0.964805\pi$
$504$		0			0
$505$	28.9759	−	4.22483i	1.28941	−	0.188003i
$506$		0			0
$507$	−5.13650	−	5.13650i	−0.228120	−	0.228120i
$508$		0			0
$509$	6.66402	−	10.3694i	0.295377	−	0.459616i	−0.661568	−	0.749886i	$-0.730109\pi$
$509$	6.66402	−	10.3694i	0.295377	−	0.459616i	0.956945	+	0.290269i	$0.0937449\pi$
$510$		0			0
$511$	2.45020	+	1.11897i	0.108391	+	0.0495003i
$512$		0			0
$513$	−16.9963	−	31.1263i	−0.750403	−	1.37426i
$514$		0			0
$515$	4.04183	−	18.7592i	0.178104	−	0.826630i
$516$		0			0
$517$	0.692870	+	9.68759i	0.0304724	+	0.426060i
$518$		0			0
$519$	−3.62149	−	12.3337i	−0.158966	−	0.541388i
$520$		0			0
$521$	13.3199	+	20.7261i	0.583554	+	0.908028i	0.999999	−	0.00113295i	$-0.000360630\pi$
$521$	13.3199	+	20.7261i	0.583554	+	0.908028i	−0.416445	+	0.909161i	$0.636724\pi$
$522$		0			0
$523$	20.6696	−	27.6114i	0.903819	−	1.20736i	−0.0738628	−	0.997268i	$-0.523533\pi$
$523$	20.6696	−	27.6114i	0.903819	−	1.20736i	0.977682	−	0.210092i	$-0.0673764\pi$
$524$		0			0
$525$	−19.4966	+	2.88226i	−0.850903	+	0.125792i
$526$		0			0
$527$	−22.0728	−	1.57867i	−0.961504	−	0.0687681i
$528$		0			0
$529$	−17.1325	+	15.3453i	−0.744892	+	0.667185i
$530$		0			0
$531$	6.93218	+	8.00016i	0.300831	+	0.347177i
$532$		0			0
$533$	13.2534	+	17.7045i	0.574068	+	0.766866i
$534$		0			0
$535$	2.40017	+	1.30441i	0.103768	+	0.0563946i
$536$		0			0
$537$	−19.6989	−	4.28524i	−0.850072	−	0.184922i
$538$		0			0
$539$	0.688466	−	0.202152i	0.0296543	−	0.00870730i
$540$		0			0
$541$	2.45870	−	2.83749i	0.105708	−	0.121993i	−0.700430	−	0.713721i	$-0.747008\pi$
$541$	2.45870	−	2.83749i	0.105708	−	0.121993i	0.806138	+	0.591728i	$0.201554\pi$
$542$		0			0
$543$	11.4876	−	30.7994i	0.492979	−	1.32173i
$544$		0			0
$545$	1.06136	+	0.150451i	0.0454637	+	0.00644460i
$546$		0			0
$547$	−25.3040	+	9.43790i	−1.08192	+	0.403536i	−0.826293	−	0.563240i	$-0.809555\pi$
$547$	−25.3040	+	9.43790i	−1.08192	+	0.403536i	−0.255627	+	0.966775i	$0.582282\pi$
$548$		0			0
$549$	−9.03949	−	5.80933i	−0.385796	−	0.247936i
$550$		0			0
$551$			16.9390i			0.721628i
$552$		0			0
$553$	26.4104	−	26.4104i	1.12308	−	1.12308i
$554$		0			0
$555$	−10.7679	+	23.7028i	−0.457072	+	1.00613i
$556$		0			0
$557$	−12.6108	−	33.8108i	−0.534336	−	1.43261i	−0.871139	−	0.491036i	$-0.836618\pi$
$557$	−12.6108	−	33.8108i	−0.534336	−	1.43261i	0.336803	−	0.941575i	$-0.390654\pi$
$558$		0			0
$559$	−1.50762	−	0.442676i	−0.0637654	−	0.0187232i
$560$		0			0
$561$	−11.0318	−	24.1563i	−0.465764	−	1.01988i
$562$		0			0
$563$	−3.11308	+	0.222652i	−0.131201	+	0.00938367i	−0.136785	−	0.990601i	$-0.543677\pi$
$563$	−3.11308	+	0.222652i	−0.131201	+	0.00938367i	0.00558434	+	0.999984i	$0.498222\pi$
$564$		0			0
$565$	22.8098	+	8.45608i	0.959617	+	0.355750i
$566$		0			0
$567$	−3.33030	+	15.3091i	−0.139859	+	0.642923i
$568$		0			0
$569$	−2.12558	−	14.7837i	−0.0891090	−	0.619767i	−0.984618	−	0.174723i	$-0.944097\pi$
$569$	−2.12558	−	14.7837i	−0.0891090	−	0.619767i	0.895509	−	0.445044i	$-0.146812\pi$
$570$		0			0
$571$	11.5081	+	1.65461i	0.481598	+	0.0692433i	0.378838	−	0.925463i	$-0.376324\pi$
$571$	11.5081	+	1.65461i	0.481598	+	0.0692433i	0.102760	+	0.994706i	$0.467233\pi$
$572$		0			0
$573$	−2.32511	+	32.5093i	−0.0971330	+	1.35810i
$574$		0			0
$575$	−4.81130	+	23.4915i	−0.200645	+	0.979664i
$576$		0			0
$577$	−2.20262	+	30.7966i	−0.0916961	+	1.28208i	0.718337	+	0.695695i	$0.244904\pi$
$577$	−2.20262	+	30.7966i	−0.0916961	+	1.28208i	−0.810033	+	0.586384i	$0.800551\pi$
$578$		0			0
$579$	23.5333	+	3.38357i	0.978010	+	0.140617i
$580$		0			0
$581$	−1.71309	−	11.9148i	−0.0710711	−	0.494310i
$582$		0			0
$583$	−5.31705	+	24.4421i	−0.220210	+	1.01229i
$584$		0			0
$585$	7.27508	+	2.69702i	0.300788	+	0.111508i
$586$		0			0
$587$	27.4383	−	1.96242i	1.13250	−	0.0809979i	0.507520	−	0.861640i	$-0.330562\pi$
$587$	27.4383	−	1.96242i	1.13250	−	0.0809979i	0.624978	+	0.780642i	$0.285108\pi$
$588$		0			0
$589$	18.2882	+	40.0455i	0.753550	+	1.65005i
$590$		0			0
$591$	−28.9686	−	8.50594i	−1.19161	−	0.349888i
$592$		0			0
$593$	−13.6117	−	36.4945i	−0.558967	−	1.49865i	−0.841967	−	0.539529i	$-0.818602\pi$
$593$	−13.6117	−	36.4945i	−0.558967	−	1.49865i	0.283000	−	0.959120i	$-0.408670\pi$
$594$		0			0
$595$	7.80336	−	17.1771i	0.319907	−	0.704194i
$596$		0			0
$597$	25.4540	−	25.4540i	1.04176	−	1.04176i
$598$		0			0
$599$			5.03096i			0.205560i	0.994704	+	0.102780i	$0.0327737\pi$
$599$			5.03096i			0.205560i	−0.994704	+	0.102780i	$0.967226\pi$
$600$		0			0
$601$	−14.7055	−	9.45064i	−0.599849	−	0.385500i	0.205189	−	0.978722i	$-0.434219\pi$
$601$	−14.7055	−	9.45064i	−0.599849	−	0.385500i	−0.805038	+	0.593223i	$0.797855\pi$
$602$		0			0
$603$	6.03479	−	2.25086i	0.245756	−	0.0916621i
$604$		0			0
$605$	−47.3294	−	6.70906i	−1.92422	−	0.272762i
$606$		0			0
$607$	3.35091	−	8.98413i	0.136009	−	0.364655i	−0.851034	−	0.525111i	$-0.824024\pi$
$607$	3.35091	−	8.98413i	0.136009	−	0.364655i	0.987043	+	0.160456i	$0.0512965\pi$
$608$		0			0
$609$	6.95372	−	8.02503i	0.281779	−	0.325190i
$610$		0			0
$611$	−6.93272	+	2.03563i	−0.280468	+	0.0823528i
$612$		0			0
$613$	25.9669	+	5.64875i	1.04879	+	0.228151i	0.703759	−	0.710439i	$-0.251504\pi$
$613$	25.9669	+	5.64875i	1.04879	+	0.228151i	0.345034	+	0.938590i	$0.387867\pi$
$614$		0			0
$615$	15.1560	+	8.23679i	0.611149	+	0.332139i
$616$		0			0
$617$	22.5510	+	30.1246i	0.907870	+	1.21277i	0.976584	+	0.215136i	$0.0690194\pi$
$617$	22.5510	+	30.1246i	0.907870	+	1.21277i	−0.0687143	+	0.997636i	$0.521890\pi$
$618$		0			0
$619$	2.52597	+	2.91512i	0.101527	+	0.117169i	0.804239	−	0.594306i	$-0.202573\pi$
$619$	2.52597	+	2.91512i	0.101527	+	0.117169i	−0.702712	+	0.711475i	$0.748028\pi$
$620$		0			0
$621$	22.8744	+	14.4364i	0.917918	+	0.579314i
$622$		0			0
$623$	−5.21303	−	0.372843i	−0.208856	−	0.0149376i
$624$		0			0
$625$	10.5656	+	22.6576i	0.422626	+	0.906304i
$626$		0			0
$627$	−31.6604	+	42.2933i	−1.26439	+	1.68903i
$628$		0			0
$629$	−13.4738	−	20.9656i	−0.537234	−	0.835952i
$630$		0			0
$631$	0.718028	+	2.44538i	0.0285842	+	0.0973490i	0.972550	−	0.232695i	$-0.0747545\pi$
$631$	0.718028	+	2.44538i	0.0285842	+	0.0973490i	−0.943965	+	0.330044i	$0.892936\pi$
$632$		0			0
$633$	1.88358	+	26.3359i	0.0748656	+	1.04676i
$634$		0			0
$635$	−1.67249	+	7.76247i	−0.0663706	+	0.308044i
$636$		0			0
$637$	0.255824	+	0.468506i	0.0101361	+	0.0185629i
$638$		0			0
$639$	−5.61186	−	2.56285i	−0.222002	−	0.101385i
$640$		0			0
$641$	15.3133	−	23.8280i	0.604841	−	0.941151i	−0.394908	−	0.918721i	$-0.629223\pi$
$641$	15.3133	−	23.8280i	0.604841	−	0.941151i	0.999748	−	0.0224299i	$-0.00714027\pi$
$642$		0			0
$643$	−8.13783	−	8.13783i	−0.320925	−	0.320925i	0.528197	−	0.849122i	$-0.322868\pi$
$643$	−8.13783	−	8.13783i	−0.320925	−	0.320925i	−0.849122	+	0.528197i	$0.822868\pi$
$644$		0			0
$645$	−1.21272	+	0.176821i	−0.0477509	+	0.00696233i
$646$		0			0
$647$	4.74461	+	21.8106i	0.186530	+	0.857465i	0.971334	+	0.237720i	$0.0764001\pi$
$647$	4.74461	+	21.8106i	0.186530	+	0.857465i	−0.784804	+	0.619744i	$0.787236\pi$
$648$		0			0
$649$	30.5264	−	66.8434i	1.19826	−	2.62383i
$650$		0			0
$651$	7.77507	−	26.4795i	0.304729	−	1.03781i
$652$		0			0
$653$	−45.7707	−	17.0716i	−1.79114	−	0.668063i	−0.998278	−	0.0586684i	$-0.981315\pi$
$653$	−45.7707	−	17.0716i	−1.79114	−	0.668063i	−0.792867	−	0.609394i	$-0.791413\pi$
$654$		0			0
$655$	6.69521	−	10.4636i	0.261603	−	0.408845i
$656$		0			0
$657$	−0.725937	−	0.396392i	−0.0283215	−	0.0154647i
$658$		0			0
$659$	−20.8524	+	13.4010i	−0.812295	+	0.522030i	−0.879607	−	0.475702i	$-0.842194\pi$
$659$	−20.8524	+	13.4010i	−0.812295	+	0.522030i	0.0673115	+	0.997732i	$0.478558\pi$
$660$		0			0
$661$	38.2610	−	5.50110i	1.48818	−	0.213968i	0.650239	−	0.759729i	$-0.274669\pi$
$661$	38.2610	−	5.50110i	1.48818	−	0.213968i	0.837941	+	0.545761i	$0.183759\pi$
$662$		0			0
$663$	15.8157	−	11.8395i	0.614229	−	0.459806i
$664$		0			0
$665$	−37.4322	+	2.75191i	−1.45156	+	0.106715i
$666$		0			0
$667$	−6.28460	−	11.2880i	−0.243341	−	0.437073i
$668$		0			0
$669$	25.8129	−	22.3670i	0.997985	−	0.864758i
$670$		0			0
$671$	−10.6155	+	73.8322i	−0.409806	+	2.85026i
$672$		0			0
$673$	35.9502	+	26.9120i	1.38578	+	1.03738i	0.993046	+	0.117730i	$0.0375617\pi$
$673$	35.9502	+	26.9120i	1.38578	+	1.03738i	0.392734	+	0.919652i	$0.371529\pi$
$674$		0			0
$675$	28.1205	−	2.12348i	1.08236	−	0.0817328i
$676$		0			0
$677$	20.9441	−	38.3562i	0.804947	−	1.47415i	−0.0740151	−	0.997257i	$-0.523581\pi$
$677$	20.9441	−	38.3562i	0.804947	−	1.47415i	0.878962	−	0.476892i	$-0.158237\pi$
$678$		0			0
$679$	−27.1333	−	23.5112i	−1.04128	−	0.902275i
$680$		0			0
$681$	−22.7023	+	10.3678i	−0.869953	+	0.397294i
$682$		0			0
$683$	−12.0667	+	6.58890i	−0.461718	+	0.252117i	−0.693232	−	0.720714i	$-0.743814\pi$
$683$	−12.0667	+	6.58890i	−0.461718	+	0.252117i	0.231514	+	0.972832i	$0.425632\pi$
$684$		0			0
$685$	16.8402	+	30.6955i	0.643431	+	1.17281i
$686$		0			0
$687$	−28.9139	+	6.28984i	−1.10314	+	0.239972i
$688$		0			0
$689$	−18.6087			−0.708936
$690$		0			0
$691$	43.2777			1.64636			0.823181	−	0.567779i	$-0.192197\pi$
$691$	43.2777			1.64636			0.823181	+	0.567779i	$0.192197\pi$
$692$		0			0
$693$	−12.1664	+	2.64665i	−0.462165	+	0.100538i
$694$		0			0
$695$	−35.6323	−	10.3858i	−1.35161	−	0.393955i
$696$		0			0
$697$	−14.4928	+	7.91368i	−0.548955	+	0.299752i
$698$		0			0
$699$	10.4210	−	4.75910i	0.394157	−	0.180006i
$700$		0			0
$701$	0.556046	+	0.481817i	0.0210016	+	0.0181980i	0.665298	−	0.746578i	$-0.268304\pi$
$701$	0.556046	+	0.481817i	0.0210016	+	0.0181980i	−0.644297	+	0.764776i	$0.722850\pi$
$702$		0			0
$703$	−23.7610	+	43.5150i	−0.896163	+	1.64120i
$704$		0			0
$705$	−4.25179	+	3.69900i	−0.160132	+	0.139312i
$706$		0			0
$707$	−27.9852	−	20.9495i	−1.05249	−	0.787887i
$708$		0			0
$709$	0.239731	−	1.66737i	0.00900328	−	0.0626192i	−0.984824	−	0.173553i	$-0.944475\pi$
$709$	0.239731	−	1.66737i	0.00900328	−	0.0626192i	0.993828	+	0.110934i	$0.0353842\pi$
$710$		0			0
$711$	−8.66751	+	7.51044i	−0.325057	+	0.281664i
$712$		0			0
$713$	−27.0444	−	19.9007i	−1.01282	−	0.745289i
$714$		0			0
$715$	−3.94904	−	53.7159i	−0.147686	−	2.00886i
$716$		0			0
$717$	5.76471	−	4.31541i	0.215287	−	0.161162i
$718$		0			0
$719$	19.5089	−	2.80496i	0.727559	−	0.104607i	0.231424	−	0.972853i	$-0.425661\pi$
$719$	19.5089	−	2.80496i	0.727559	−	0.104607i	0.496134	+	0.868246i	$0.334752\pi$
$720$		0			0
$721$	−19.2724	+	12.3856i	−0.717742	+	0.461265i
$722$		0			0
$723$	−36.9649	−	20.1844i	−1.37474	−	0.750665i
$724$		0			0
$725$	−12.2745	−	5.54677i	−0.455863	−	0.206002i
$726$		0			0
$727$	−21.4693	−	8.00763i	−0.796252	−	0.296987i	−0.0817797	−	0.996650i	$-0.526060\pi$
$727$	−21.4693	−	8.00763i	−0.796252	−	0.296987i	−0.714472	+	0.699664i	$0.753333\pi$
$728$		0			0
$729$	8.39425	−	28.5882i	0.310898	−	1.05882i
$730$		0			0
$731$	0.487360	−	1.06717i	0.0180256	−	0.0394707i
$732$		0			0
$733$	9.58464	+	44.0599i	0.354017	+	1.62739i	0.718042	+	0.696000i	$0.245039\pi$
$733$	9.58464	+	44.0599i	0.354017	+	1.62739i	−0.364025	+	0.931389i	$0.618598\pi$
$734$		0			0
$735$	0.333801	+	0.248848i	0.0123124	+	0.00917889i
$736$		0			0
$737$	−31.6157	−	31.6157i	−1.16458	−	1.16458i
$738$		0			0
$739$	7.64381	−	11.8940i	0.281182	−	0.437528i	−0.671720	−	0.740805i	$-0.734444\pi$
$739$	7.64381	−	11.8940i	0.281182	−	0.437528i	0.952902	+	0.303277i	$0.0980807\pi$
$740$		0			0
$741$	−35.7514	−	16.3271i	−1.31336	−	0.599791i
$742$		0			0
$743$	−16.4309	−	30.0909i	−0.602791	−	1.10393i	−0.983785	−	0.179351i	$-0.942600\pi$
$743$	−16.4309	−	30.0909i	−0.602791	−	1.10393i	0.380995	−	0.924577i	$-0.375582\pi$
$744$		0			0
$745$	6.48701	+	10.0501i	0.237666	+	0.368206i
$746$		0			0
$747$	0.263685	+	3.68680i	0.00964774	+	0.134893i
$748$		0			0
$749$	−0.918785	−	3.12910i	−0.0335717	−	0.114335i
$750$		0			0
$751$	−8.55726	−	13.3154i	−0.312259	−	0.485884i	0.649281	−	0.760548i	$-0.275070\pi$
$751$	−8.55726	−	13.3154i	−0.312259	−	0.485884i	−0.961540	+	0.274664i	$0.911433\pi$
$752$		0			0
$753$	−2.60353	+	3.47791i	−0.0948779	+	0.126742i
$754$		0			0
$755$	−0.0185367	−	9.33649i	−0.000674620	−	0.339790i
$756$		0			0
$757$	24.9928	+	1.78752i	0.908380	+	0.0649686i	0.517704	−	0.855560i	$-0.326787\pi$
$757$	24.9928	+	1.78752i	0.908380	+	0.0649686i	0.390676	+	0.920528i	$0.372241\pi$
$758$		0			0
$759$	5.40679	−	39.9302i	0.196254	−	1.44938i
$760$		0			0
$761$	−19.2250	−	22.1868i	−0.696906	−	0.804272i	0.291425	−	0.956594i	$-0.405871\pi$
$761$	−19.2250	−	22.1868i	−0.696906	−	0.804272i	−0.988331	+	0.152321i	$0.951325\pi$
$762$		0			0
$763$	−0.766924	−	1.02449i	−0.0277645	−	0.0370891i
$764$		0			0
$765$	−2.76629	+	5.09008i	−0.100015	+	0.184032i
$766$		0			0
$767$	53.4184	+	11.6205i	1.92883	+	0.419591i
$768$		0			0
$769$	−37.0056	+	10.8658i	−1.33446	+	0.391832i	−0.869688	−	0.493601i	$-0.835680\pi$
$769$	−37.0056	+	10.8658i	−1.33446	+	0.391832i	−0.464767	+	0.885433i	$0.653862\pi$
$770$		0			0
$771$	0.838464	−	0.967639i	0.0301965	−	0.0348487i
$772$		0			0
$773$	6.11486	−	16.3946i	0.219936	−	0.589672i	−0.779383	−	0.626547i	$-0.784468\pi$
$773$	6.11486	−	16.3946i	0.219936	−	0.589672i	0.999320	+	0.0368749i	$0.0117403\pi$
$774$		0			0
$775$	−35.0066	+	0.139005i	−1.25747	+	0.00499320i
$776$		0			0
$777$	29.1205	−	10.8614i	1.04469	−	0.389650i
$778$		0			0
$779$	27.6355	+	17.7603i	0.990146	+	0.636328i
$780$		0			0
$781$			42.8265i			1.53245i
$782$		0			0
$783$	−10.7438	+	10.7438i	−0.383951	+	0.383951i
$784$		0			0
$785$	39.8389	−	14.9493i	1.42191	−	0.533564i
$786$		0			0
$787$	−3.02207	−	8.10248i	−0.107725	−	0.288822i	0.871891	−	0.489699i	$-0.162893\pi$
$787$	−3.02207	−	8.10248i	−0.107725	−	0.288822i	−0.979616	+	0.200877i	$0.935621\pi$
$788$		0			0
$789$	−10.1458	−	2.97907i	−0.361200	−	0.106058i
$790$		0			0
$791$	−12.0645	−	26.4175i	−0.428963	−	0.939299i
$792$		0			0
$793$	−55.3503	+	3.95873i	−1.96555	+	0.140579i
$794$		0			0
$795$	−13.1907	+	6.05567i	−0.467826	+	0.214773i
$796$		0			0
$797$	−7.49186	+	34.4395i	−0.265375	+	1.21991i	0.630707	+	0.776021i	$0.282765\pi$
$797$	−7.49186	+	34.4395i	−0.265375	+	1.21991i	−0.896082	+	0.443889i	$0.853599\pi$
$798$		0			0
$799$	−0.767769	−	5.33995i	−0.0271617	−	0.188914i
$800$		0			0
$801$	1.58848	+	0.228389i	0.0561262	+	0.00806972i
$802$		0			0
$803$	−0.409603	+	5.72700i	−0.0144546	+	0.202101i
$804$		0			0
$805$	23.9234	−	15.7217i	0.843190	−	0.554116i
$806$		0			0
$807$	−0.586505	+	8.20041i	−0.0206459	+	0.288668i
$808$		0			0
$809$	26.0032	+	3.73870i	0.914224	+	0.131446i	0.583342	−	0.812226i	$-0.301745\pi$
$809$	26.0032	+	3.73870i	0.914224	+	0.131446i	0.330882	+	0.943672i	$0.392654\pi$
$810$		0			0
$811$	−0.868677	−	6.04178i	−0.0305034	−	0.212156i	0.968869	−	0.247573i	$-0.0796330\pi$
$811$	−0.868677	−	6.04178i	−0.0305034	−	0.212156i	−0.999373	+	0.0354175i	$0.988724\pi$
$812$		0			0
$813$	3.03115	−	13.9340i	0.106307	−	0.488686i
$814$		0			0
$815$	3.85235	−	10.3915i	0.134942	−	0.363999i
$816$		0			0
$817$	−2.32800	+	0.166502i	−0.0814464	+	0.00582516i
$818$		0			0
$819$	−3.84790	−	8.42573i	−0.134457	−	0.294419i
$820$		0			0
$821$	−18.9847	−	5.57442i	−0.662572	−	0.194549i	−0.0668793	−	0.997761i	$-0.521304\pi$
$821$	−18.9847	−	5.57442i	−0.662572	−	0.194549i	−0.595693	+	0.803212i	$0.703122\pi$
$822$		0			0
$823$	−2.34888	−	6.29760i	−0.0818770	−	0.219521i	0.889560	−	0.456818i	$-0.151011\pi$
$823$	−2.34888	−	6.29760i	−0.0818770	−	0.219521i	−0.971437	+	0.237298i	$0.923738\pi$
$824$		0			0
$825$	−20.2795	−	36.7911i	−0.706043	−	1.28090i
$826$		0			0
$827$	−19.9829	+	19.9829i	−0.694872	+	0.694872i	−0.963300	−	0.268428i	$-0.913496\pi$
$827$	−19.9829	+	19.9829i	−0.694872	+	0.694872i	0.268428	+	0.963300i	$0.413496\pi$
$828$		0			0
$829$		−	14.9670i		−	0.519827i	−0.965632	−	0.259914i	$-0.916306\pi$
$829$		−	14.9670i		−	0.519827i	0.965632	−	0.259914i	$-0.0836941\pi$
$830$		0			0
$831$	24.2886	+	15.6094i	0.842563	+	0.541482i
$832$		0			0
$833$	−0.373434	+	0.139284i	−0.0129387	+	0.00482590i
$834$		0			0
$835$	6.20713	+	8.25753i	0.214807	+	0.285764i
$836$		0			0
$837$	−13.7998	+	36.9987i	−0.476991	+	1.27886i
$838$		0			0
$839$	10.3915	−	11.9925i	0.358756	−	0.414026i	−0.547467	−	0.836827i	$-0.684408\pi$
$839$	10.3915	−	11.9925i	0.358756	−	0.414026i	0.906222	+	0.422801i	$0.138953\pi$
$840$		0			0
$841$	−20.8621	+	6.12566i	−0.719382	+	0.211230i
$842$		0			0
$843$	19.7533	+	4.29707i	0.680340	+	0.147999i
$844$		0			0
$845$	10.5486	−	3.12012i	0.362884	−	0.107335i
$846$		0			0
$847$	34.1996	+	45.6853i	1.17511	+	1.56976i
$848$		0			0
$849$	−11.5432	−	13.3216i	−0.396162	−	0.457195i
$850$		0			0
$851$	−0.310546	−	37.8136i	−0.0106454	−	1.29623i
$852$		0			0
$853$	−20.7243	−	1.48223i	−0.709586	−	0.0507506i	−0.288120	−	0.957594i	$-0.593030\pi$
$853$	−20.7243	−	1.48223i	−0.709586	−	0.0507506i	−0.421467	+	0.906844i	$0.638485\pi$
$854$		0			0
$855$	11.5250	−	0.0228818i	0.394147	−	0.000782542i
$856$		0			0
$857$	9.80836	−	13.1024i	0.335047	−	0.447570i	−0.601103	−	0.799172i	$-0.705272\pi$
$857$	9.80836	−	13.1024i	0.335047	−	0.447570i	0.936150	+	0.351601i	$0.114363\pi$
$858$		0			0
$859$	−15.6239	−	24.3113i	−0.533081	−	0.829490i	0.465371	−	0.885116i	$-0.345921\pi$
$859$	−15.6239	−	24.3113i	−0.533081	−	0.829490i	−0.998452	+	0.0556255i	$0.982285\pi$
$860$		0			0
$861$	−5.80173	−	19.7589i	−0.197722	−	0.673381i
$862$		0			0
$863$	0.571782	+	7.99456i	0.0194637	+	0.272138i	0.997859	+	0.0653968i	$0.0208313\pi$
$863$	0.571782	+	7.99456i	0.0194637	+	0.272138i	−0.978396	+	0.206741i	$0.933714\pi$
$864$		0			0
$865$	19.0293	+	4.10003i	0.647017	+	0.139405i
$866$		0			0
$867$	−4.96068	−	9.08480i	−0.168473	−	0.308536i
$868$		0			0
$869$	72.4193	+	33.0728i	2.45666	+	1.12192i
$870$		0			0
$871$	17.9831	−	27.9823i	0.609335	−	0.948143i
$872$		0			0
$873$	7.79537	+	7.79537i	0.263833	+	0.263833i
$874$		0			0
$875$	10.2632	−	28.0255i	0.346961	−	0.947435i
$876$		0			0
$877$	3.24159	+	14.9014i	0.109461	+	0.503183i	0.998933	+	0.0461929i	$0.0147089\pi$
$877$	3.24159	+	14.9014i	0.109461	+	0.503183i	−0.889472	+	0.456990i	$0.848927\pi$
$878$		0			0
$879$	5.12890	−	11.2307i	0.172993	−	0.378803i
$880$		0			0
$881$	8.07049	−	27.4856i	0.271902	−	0.926012i	−0.704437	−	0.709766i	$-0.748801\pi$
$881$	8.07049	−	27.4856i	0.271902	−	0.926012i	0.976339	−	0.216246i	$-0.0693813\pi$
$882$		0			0
$883$	−11.6391	−	4.34118i	−0.391688	−	0.146092i	0.145901	−	0.989299i	$-0.453392\pi$
$883$	−11.6391	−	4.34118i	−0.391688	−	0.146092i	−0.537589	+	0.843207i	$0.680665\pi$
$884$		0			0
$885$	41.6469	−	9.14637i	1.39995	−	0.307452i
$886$		0			0
$887$	16.1536	+	8.82055i	0.542386	+	0.296165i	0.726990	−	0.686648i	$-0.240919\pi$
$887$	16.1536	+	8.82055i	0.542386	+	0.296165i	−0.184604	+	0.982813i	$0.559100\pi$
$888$		0			0
$889$	7.97482	−	5.12511i	0.267467	−	0.171891i
$890$		0			0
$891$	−33.0557	+	4.75269i	−1.10741	+	0.159221i
$892$		0			0
$893$	−8.59186	+	6.43179i	−0.287516	+	0.215232i
$894$		0			0
$895$	19.9462	−	23.1118i	0.666730	−	0.772541i
$896$		0			0
$897$	29.8819	−	2.38400i	0.997727	−	0.0795995i
$898$		0			0
$899$	14.2543	−	12.3514i	0.475406	−	0.411942i
$900$		0			0
$901$	1.97736	−	13.7528i	0.0658753	−	0.458173i
$902$		0			0
$903$	1.17126	+	0.876795i	0.0389771	+	0.0291779i
$904$		0			0
$905$	32.6734	+	37.5561i	1.08610	+	1.24841i
$906$		0			0
$907$	−21.9971	+	40.2847i	−0.730402	+	1.33763i	0.203136	+	0.979151i	$0.434887\pi$
$907$	−21.9971	+	40.2847i	−0.730402	+	1.33763i	−0.933537	+	0.358480i	$0.883295\pi$
$908$		0			0
$909$	8.11241	+	7.02944i	0.269072	+	0.233152i
$910$		0			0
$911$	−14.1816	+	6.47653i	−0.469858	+	0.214577i	−0.636250	−	0.771483i	$-0.719515\pi$
$911$	−14.1816	+	6.47653i	−0.469858	+	0.214577i	0.166392	+	0.986060i	$0.446788\pi$
$912$		0			0
$913$	22.5198	−	12.2968i	0.745298	−	0.406963i
$914$		0			0
$915$	−37.9465	+	20.8183i	−1.25447	+	0.688230i
$916$		0			0
$917$	−14.4911	+	3.15234i	−0.478537	+	0.104099i
$918$		0			0
$919$	−31.2609			−1.03120			−0.515601	−	0.856829i	$-0.672431\pi$
$919$	−31.2609			−1.03120			−0.515601	+	0.856829i	$0.672431\pi$
$920$		0			0
$921$	−9.40229			−0.309816
$922$		0			0
$923$	−31.1323	+	6.77242i	−1.02473	+	0.222917i
$924$		0			0
$925$	−23.7515	−	31.4670i	−0.780944	−	1.03463i
$926$		0			0
$927$	6.17407	−	3.37130i	0.202783	−	0.110728i
$928$		0			0
$929$	30.7294	−	14.0336i	1.00820	−	0.460428i	0.158308	−	0.987390i	$-0.449396\pi$
$929$	30.7294	−	14.0336i	1.00820	−	0.460428i	0.849889	+	0.526961i	$0.176669\pi$
$930$		0			0
$931$	0.599238	+	0.519242i	0.0196392	+	0.0170175i
$932$		0			0
$933$	−22.4818	+	41.1723i	−0.736021	+	1.34792i
$934$		0			0
$935$	40.1185	+	2.78928i	1.31201	+	0.0912193i
$936$		0			0
$937$	−2.18852	−	1.63830i	−0.0714957	−	0.0535210i	0.562932	−	0.826503i	$-0.309673\pi$
$937$	−2.18852	−	1.63830i	−0.0714957	−	0.0535210i	−0.634428	+	0.772982i	$0.718764\pi$
$938$		0			0
$939$	−4.34157	+	30.1963i	−0.141682	+	0.985418i
$940$		0			0
$941$	4.73266	−	4.10088i	0.154280	−	0.133685i	−0.574300	−	0.818645i	$-0.694726\pi$
$941$	4.73266	−	4.10088i	0.154280	−	0.133685i	0.728581	+	0.684960i	$0.240180\pi$
$942$		0			0
$943$	−25.0053	−	1.58213i	−0.814285	−	0.0515212i
$944$		0			0
$945$	−25.4872	−	21.9963i	−0.829098	−	0.715541i
$946$		0			0
$947$	−31.2878	+	23.4217i	−1.01672	+	0.761104i	−0.971298	−	0.237864i	$-0.923553\pi$
$947$	−31.2878	+	23.4217i	−1.01672	+	0.761104i	−0.0454172	+	0.998968i	$0.514462\pi$
$948$		0			0
$949$	−4.22796	+	0.607888i	−0.137245	+	0.0197329i
$950$		0			0
$951$	−3.19867	+	2.05566i	−0.103724	+	0.0666593i
$952$		0			0
$953$	−10.1934	−	5.56604i	−0.330198	−	0.180302i	0.305595	−	0.952162i	$-0.401145\pi$
$953$	−10.1934	−	5.56604i	−0.330198	−	0.180302i	−0.635793	+	0.771860i	$0.719327\pi$
$954$		0			0
$955$	−41.5740	−	26.6015i	−1.34530	−	0.860805i
$956$		0			0
$957$	21.2072	+	7.90988i	0.685532	+	0.255690i
$958$		0			0
$959$	11.7757	−	40.1045i	0.380259	−	1.29504i
$960$		0			0
$961$	7.48541	−	16.3908i	0.241465	−	0.528735i
$962$		0			0
$963$	0.212861	+	0.978506i	0.00685935	+	0.0315319i
$964$		0			0
$965$	−21.5192	+	28.8656i	−0.692727	+	0.929215i
$966$		0			0
$967$	19.6049	+	19.6049i	0.630450	+	0.630450i	0.948181	−	0.317731i	$-0.102921\pi$
$967$	19.6049	+	19.6049i	0.630450	+	0.630450i	−0.317731	+	0.948181i	$0.602921\pi$
$968$		0			0
$969$	15.8655	−	24.6872i	0.509674	−	0.793068i
$970$		0			0
$971$	−47.0886	−	21.5047i	−1.51115	−	0.690117i	−0.524263	−	0.851556i	$-0.675659\pi$
$971$	−47.0886	−	21.5047i	−1.51115	−	0.690117i	−0.986883	+	0.161439i	$0.948387\pi$
$972$		0			0
$973$	21.2350	+	38.8890i	0.680762	+	1.24672i
$974$		0			0
$975$	23.5380	−	20.5600i	0.753819	−	0.658447i
$976$		0			0
$977$	−0.0310414	−	0.434016i	−0.000993104	−	0.0138854i	0.996931	−	0.0782802i	$-0.0249429\pi$
$977$	−0.0310414	−	0.434016i	−0.000993104	−	0.0138854i	−0.997925	+	0.0643948i	$0.979488\pi$
$978$		0			0
$979$	−3.13858	−	10.6890i	−0.100310	−	0.341623i
$980$		0			0
$981$	0.212452	+	0.330581i	0.00678306	+	0.0105546i
$982$		0			0
$983$	−2.38990	+	3.19253i	−0.0762259	+	0.101826i	−0.837034	−	0.547152i	$-0.815712\pi$
$983$	−2.38990	+	3.19253i	−0.0762259	+	0.101826i	0.760808	+	0.648977i	$0.224803\pi$
$984$		0			0
$985$	32.2651	−	32.3935i	1.02805	−	1.03214i
$986$		0			0
$987$	6.71082	+	0.479967i	0.213608	+	0.0152775i
$988$		0			0
$989$	1.48958	−	0.974672i	0.0473659	−	0.0309928i
$990$		0			0
$991$	−14.9111	−	17.2083i	−0.473667	−	0.546640i	0.467761	−	0.883855i	$-0.345061\pi$
$991$	−14.9111	−	17.2083i	−0.473667	−	0.546640i	−0.941428	+	0.337214i	$0.890515\pi$
$992$		0			0
$993$	23.5159	+	31.4135i	0.746254	+	0.996879i
$994$		0			0
$995$	15.4618	+	52.2739i	0.490172	+	1.65719i
$996$		0			0
$997$	−55.0061	−	11.9658i	−1.74206	−	0.378962i	−0.774692	−	0.632339i	$-0.782095\pi$
$997$	−55.0061	−	11.9658i	−1.74206	−	0.378962i	−0.967368	+	0.253377i	$0.918459\pi$
$998$		0			0
$999$	−42.6705	+	12.5292i	−1.35003	+	0.396406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.26	yes	720
5.3	odd	4	inner	920.2.bv.a.33.26	✓	720
23.7	odd	22	inner	920.2.bv.a.697.26	yes	720
115.53	even	44	inner	920.2.bv.a.513.26	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.26	✓	720	5.3	odd	4	inner
920.2.bv.a.217.26	yes	720	1.1	even	1	trivial
920.2.bv.a.513.26	yes	720	115.53	even	44	inner
920.2.bv.a.697.26	yes	720	23.7	odd	22	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44284 - 0.313871i) q^{3} +(-0.625712 + 2.14674i) q^{5} +(2.34294 - 1.27934i) q^{7} +(-0.745622 + 0.340514i) q^{9} +O(q^{10})\)	\(q+(1.44284 - 0.313871i) q^{3} +(-0.625712 + 2.14674i) q^{5} +(2.34294 - 1.27934i) q^{7} +(-0.745622 + 0.340514i) q^{9} +(4.30034 + 3.72626i) q^{11} +(-2.02873 + 3.71534i) q^{13} +(-0.229005 + 3.29379i) q^{15} +(-2.53026 - 1.89413i) q^{17} +(-0.894860 + 6.22389i) q^{19} +(2.97894 - 2.58127i) q^{21} +(-1.71282 - 4.47954i) q^{23} +(-4.21697 - 2.68648i) q^{25} +(-4.51514 + 3.37999i) q^{27} +(2.66650 - 0.383384i) q^{29} +(5.88992 - 3.78522i) q^{31} +(7.37427 + 4.02666i) q^{33} +(1.28041 + 5.83019i) q^{35} +(7.38779 + 2.75550i) q^{37} +(-1.76100 + 5.99741i) q^{39} +(2.17029 - 4.75228i) q^{41} +(0.0789002 + 0.362698i) q^{43} +(-0.264450 - 1.81372i) q^{45} +(1.20693 + 1.20693i) q^{47} +(0.0681750 - 0.106082i) q^{49} +(-4.24528 - 1.93875i) q^{51} +(2.10676 + 3.85824i) q^{53} +(-10.6901 + 6.90013i) q^{55} +(0.662356 + 9.26095i) q^{57} +(-3.63836 - 12.3911i) q^{59} +(7.08717 + 11.0279i) q^{61} +(-1.31131 + 1.75171i) q^{63} +(-6.70647 - 6.67989i) q^{65} +(-7.83763 - 0.560559i) q^{67} +(-3.87732 - 5.92566i) q^{69} +(4.92875 + 5.68808i) q^{71} +(0.604698 + 0.807782i) q^{73} +(-6.92762 - 2.55258i) q^{75} +(14.8426 + 3.22881i) q^{77} +(13.4247 - 3.94186i) q^{79} +(-3.84339 + 4.43550i) q^{81} +(1.57582 - 4.22495i) q^{83} +(5.64942 - 4.24663i) q^{85} +(3.72700 - 1.39010i) q^{87} +(-1.64702 - 1.05848i) q^{89} +11.3003i q^{91} +(7.31015 - 7.31015i) q^{93} +(-12.8011 - 5.81539i) q^{95} +(-4.70004 - 12.6013i) q^{97} +(-4.47527 - 1.31406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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