LMFDB - Embedded newform 966.2.q.d.673.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 10 x^{18} - 14 x^{17} + 77 x^{16} + 12 x^{15} - 226 x^{14} - 793 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 10x^18 - 14x^17 + 77x^16 + 12x^15 - 226x^14 - 793x^13 + 690x^12 + 6105x^11 + 13883x^10 + 24365x^9 + 36461x^8 + 41912x^7 + 45709x^6 + 33023x^5 + 25949x^4 + 12217x^3 + 2895x^2 - 172*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			673.2
Root			$-0.665158 - 0.427471i$ of defining polynomial
Character	$\chi$	$=$	966.673
Dual form			966.2.q.d.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.08057 - 1.33710i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.08057 - 1.33710i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.351971 - 2.44801i) q^{10} +(-0.895337 - 1.96052i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(-0.276831 - 1.92540i) q^{13} +(0.841254 + 0.540641i) q^{14} +(2.37300 - 0.696776i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.12587 - 4.76151i) q^{17} +(0.841254 - 0.540641i) q^{18} +(-1.20393 - 1.38940i) q^{19} +(-2.37300 - 0.696776i) q^{20} +(-0.415415 + 0.909632i) q^{21} -2.15528 q^{22} +(-1.07870 + 4.67294i) q^{23} -1.00000 q^{24} +(0.463865 - 1.01572i) q^{25} +(-1.86641 - 0.548027i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(5.17145 - 5.96817i) q^{29} +(0.351971 - 2.44801i) q^{30} +(2.37961 - 0.698716i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.306729 - 2.13335i) q^{33} +(-2.61727 - 5.73103i) q^{34} +(1.02740 + 2.24969i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.446985 - 0.287260i) q^{37} +(-1.76398 + 0.517950i) q^{38} +(0.276831 - 1.92540i) q^{39} +(-1.61959 + 1.86911i) q^{40} +(1.47782 - 0.949736i) q^{41} +(0.654861 + 0.755750i) q^{42} +(3.09798 + 0.909648i) q^{43} +(-0.895337 + 1.96052i) q^{44} +2.47318 q^{45} +(3.80255 + 2.92243i) q^{46} -0.732419 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.731237 - 0.843892i) q^{50} +(5.30022 - 3.40624i) q^{51} +(-1.27384 + 1.47009i) q^{52} +(-0.824746 + 5.73623i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-4.48423 - 2.88184i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(-0.763718 - 1.67231i) q^{57} +(-3.28054 - 7.18339i) q^{58} +(0.692610 + 4.81721i) q^{59} +(-2.08057 - 1.33710i) q^{60} +(-7.96193 + 2.33783i) q^{61} +(0.352951 - 2.45483i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-3.15043 - 3.63579i) q^{65} +(-2.06798 - 0.607214i) q^{66} +(-3.48889 + 7.63961i) q^{67} -6.30038 q^{68} +(-2.35153 + 4.17975i) q^{69} +2.47318 q^{70} +(-2.53543 + 5.55182i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(1.81790 + 2.09797i) q^{73} +(-0.446985 + 0.287260i) q^{74} +(0.731237 - 0.843892i) q^{75} +(-0.261638 + 1.81973i) q^{76} +(2.06798 - 0.607214i) q^{77} +(-1.63641 - 1.05166i) q^{78} +(-1.10981 - 7.71891i) q^{79} +(1.02740 + 2.24969i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.250002 - 1.73880i) q^{82} +(3.95720 + 2.54314i) q^{83} +(0.959493 - 0.281733i) q^{84} +(2.21755 - 15.4234i) q^{85} +(2.11439 - 2.44014i) q^{86} +(6.64340 - 4.26945i) q^{87} +(1.41141 + 1.62886i) q^{88} +(2.90371 + 0.852606i) q^{89} +(1.02740 - 2.24969i) q^{90} +1.94520 q^{91} +(4.23798 - 2.24490i) q^{92} +2.48007 q^{93} +(-0.304258 + 0.666232i) q^{94} +(-4.36263 - 1.28098i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-2.01807 + 1.29693i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(0.306729 - 2.13335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$3$	0.959493	+	0.281733i	0.553964	+	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	2.08057	−	1.33710i	0.930461	−	0.597971i	0.0147858	−	0.999891i	$-0.495293\pi$
$5$	2.08057	−	1.33710i	0.930461	−	0.597971i	0.915675	+	0.401920i	$0.131657\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$7$	−0.142315	+	0.989821i	−0.0537900	+	0.374117i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.351971	−	2.44801i	−0.111303	−	0.774128i
$11$	−0.895337	−	1.96052i	−0.269954	−	0.591118i	0.725299	−	0.688434i	$-0.241701\pi$
$11$	−0.895337	−	1.96052i	−0.269954	−	0.591118i	−0.995254	+	0.0973162i	$0.968974\pi$
$12$	−0.415415	−	0.909632i	−0.119920	−	0.262588i
$13$	−0.276831	−	1.92540i	−0.0767792	−	0.534011i	−0.991518	−	0.129966i	$-0.958513\pi$
$13$	−0.276831	−	1.92540i	−0.0767792	−	0.534011i	0.914739	−	0.404045i	$-0.132396\pi$
$14$	0.841254	+	0.540641i	0.224834	+	0.144492i
$15$	2.37300	−	0.696776i	0.612706	−	0.179907i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	4.12587	−	4.76151i	1.00067	−	1.15484i	0.0127430	−	0.999919i	$-0.495944\pi$
$17$	4.12587	−	4.76151i	1.00067	−	1.15484i	0.987928	−	0.154917i	$-0.0495109\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	−1.20393	−	1.38940i	−0.276199	−	0.318751i	0.600654	−	0.799509i	$-0.294907\pi$
$19$	−1.20393	−	1.38940i	−0.276199	−	0.318751i	−0.876853	+	0.480758i	$0.840362\pi$
$20$	−2.37300	−	0.696776i	−0.530619	−	0.155804i
$21$	−0.415415	+	0.909632i	−0.0906510	+	0.198498i
$22$	−2.15528			−0.459508
$23$	−1.07870	+	4.67294i	−0.224925	+	0.974376i
$23$	−1.07870	+	4.67294i	−0.224925	+	0.974376i
$24$	−1.00000			−0.204124
$25$	0.463865	−	1.01572i	0.0927729	−	0.203144i
$26$	−1.86641	−	0.548027i	−0.366033	−	0.107477i
$27$	0.654861	+	0.755750i	0.126028	+	0.145444i
$28$	0.841254	−	0.540641i	0.158982	−	0.102172i
$29$	5.17145	−	5.96817i	0.960314	−	1.10826i	−0.0337457	−	0.999430i	$-0.510744\pi$
$29$	5.17145	−	5.96817i	0.960314	−	1.10826i	0.994060	−	0.108832i	$-0.0347109\pi$
$30$	0.351971	−	2.44801i	0.0642607	−	0.446943i
$31$	2.37961	−	0.698716i	0.427390	−	0.125493i	−0.0609611	−	0.998140i	$-0.519417\pi$
$31$	2.37961	−	0.698716i	0.427390	−	0.125493i	0.488352	+	0.872647i	$0.337598\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−0.306729	−	2.13335i	−0.0533947	−	0.371368i
$34$	−2.61727	−	5.73103i	−0.448858	−	0.982863i
$35$	1.02740	+	2.24969i	0.173662	+	0.380266i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−0.446985	−	0.287260i	−0.0734839	−	0.0472252i	0.503383	−	0.864063i	$-0.332089\pi$
$37$	−0.446985	−	0.287260i	−0.0734839	−	0.0472252i	−0.576867	+	0.816838i	$0.695725\pi$
$38$	−1.76398	+	0.517950i	−0.286155	+	0.0840226i
$39$	0.276831	−	1.92540i	0.0443285	−	0.308311i
$40$	−1.61959	+	1.86911i	−0.256080	+	0.295532i
$41$	1.47782	−	0.949736i	0.230796	−	0.148324i	−0.420132	−	0.907463i	$-0.638016\pi$
$41$	1.47782	−	0.949736i	0.230796	−	0.148324i	0.650928	+	0.759139i	$0.274380\pi$
$42$	0.654861	+	0.755750i	0.101047	+	0.116615i
$43$	3.09798	+	0.909648i	0.472437	+	0.138720i	0.509280	−	0.860601i	$-0.329912\pi$
$43$	3.09798	+	0.909648i	0.472437	+	0.138720i	−0.0368428	+	0.999321i	$0.511730\pi$
$44$	−0.895337	+	1.96052i	−0.134977	+	0.295559i
$45$	2.47318			0.368680
$46$	3.80255	+	2.92243i	0.560655	+	0.430889i
$47$	−0.732419			−0.106834			−0.0534172	−	0.998572i	$-0.517011\pi$
$47$	−0.732419			−0.106834			−0.0534172	+	0.998572i	$0.517011\pi$
$48$	−0.415415	+	0.909632i	−0.0599600	+	0.131294i
$49$	−0.959493	−	0.281733i	−0.137070	−	0.0402475i
$50$	−0.731237	−	0.843892i	−0.103412	−	0.119344i
$51$	5.30022	−	3.40624i	0.742179	−	0.476969i
$52$	−1.27384	+	1.47009i	−0.176650	+	0.203864i
$53$	−0.824746	+	5.73623i	−0.113288	+	0.787932i	0.851397	+	0.524523i	$0.175756\pi$
$53$	−0.824746	+	5.73623i	−0.113288	+	0.787932i	−0.964684	+	0.263410i	$0.915153\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	−4.48423	−	2.88184i	−0.604653	−	0.388587i
$56$	−0.142315	−	0.989821i	−0.0190176	−	0.132270i
$57$	−0.763718	−	1.67231i	−0.101157	−	0.221503i
$58$	−3.28054	−	7.18339i	−0.430756	−	0.943225i
$59$	0.692610	+	4.81721i	0.0901701	+	0.627147i	0.983924	+	0.178589i	$0.0571532\pi$
$59$	0.692610	+	4.81721i	0.0901701	+	0.627147i	−0.893754	+	0.448558i	$0.851938\pi$
$60$	−2.08057	−	1.33710i	−0.268601	−	0.172619i
$61$	−7.96193	+	2.33783i	−1.01942	+	0.299329i	−0.748402	−	0.663245i	$-0.769179\pi$
$61$	−7.96193	+	2.33783i	−1.01942	+	0.299329i	−0.271019	+	0.962574i	$0.587361\pi$
$62$	0.352951	−	2.45483i	0.0448248	−	0.311763i
$63$	−0.654861	+	0.755750i	−0.0825047	+	0.0952155i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−3.15043	−	3.63579i	−0.390763	−	0.450965i
$66$	−2.06798	−	0.607214i	−0.254551	−	0.0747428i
$67$	−3.48889	+	7.63961i	−0.426236	+	0.933327i	0.567686	+	0.823245i	$0.307839\pi$
$67$	−3.48889	+	7.63961i	−0.426236	+	0.933327i	−0.993922	+	0.110082i	$0.964889\pi$
$68$	−6.30038			−0.764033
$69$	−2.35153	+	4.17975i	−0.283091	+	0.503183i
$70$	2.47318			0.295602
$71$	−2.53543	+	5.55182i	−0.300900	+	0.658879i	−0.998330	−	0.0577739i	$-0.981600\pi$
$71$	−2.53543	+	5.55182i	−0.300900	+	0.658879i	0.697430	+	0.716653i	$0.254327\pi$
$72$	−0.959493	−	0.281733i	−0.113077	−	0.0332025i
$73$	1.81790	+	2.09797i	0.212769	+	0.245548i	0.852095	−	0.523387i	$-0.175332\pi$
$73$	1.81790	+	2.09797i	0.212769	+	0.245548i	−0.639326	+	0.768936i	$0.720787\pi$
$74$	−0.446985	+	0.287260i	−0.0519610	+	0.0333933i
$75$	0.731237	−	0.843892i	0.0844359	−	0.0974443i
$76$	−0.261638	+	1.81973i	−0.0300119	+	0.208738i
$77$	2.06798	−	0.607214i	0.235668	−	0.0691984i
$78$	−1.63641	−	1.05166i	−0.185287	−	0.119077i
$79$	−1.10981	−	7.71891i	−0.124864	−	0.868445i	−0.951924	−	0.306333i	$-0.900898\pi$
$79$	−1.10981	−	7.71891i	−0.124864	−	0.868445i	0.827061	−	0.562112i	$-0.190011\pi$
$80$	1.02740	+	2.24969i	0.114866	+	0.251522i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.250002	−	1.73880i	−0.0276081	−	0.192019i
$83$	3.95720	+	2.54314i	0.434359	+	0.279146i	0.739494	−	0.673164i	$-0.235065\pi$
$83$	3.95720	+	2.54314i	0.434359	+	0.279146i	−0.305134	+	0.952309i	$0.598701\pi$
$84$	0.959493	−	0.281733i	0.104689	−	0.0307395i
$85$	2.21755	−	15.4234i	0.240527	−	1.67290i
$86$	2.11439	−	2.44014i	0.228001	−	0.263127i
$87$	6.64340	−	4.26945i	0.712247	−	0.457734i
$88$	1.41141	+	1.62886i	0.150457	+	0.173637i
$89$	2.90371	+	0.852606i	0.307793	+	0.0903761i	0.431981	−	0.901883i	$-0.357815\pi$
$89$	2.90371	+	0.852606i	0.307793	+	0.0903761i	−0.124189	+	0.992259i	$0.539633\pi$
$90$	1.02740	−	2.24969i	0.108297	−	0.237138i
$91$	1.94520			0.203913
$92$	4.23798	−	2.24490i	0.441839	−	0.234047i
$93$	2.48007			0.257171
$94$	−0.304258	+	0.666232i	−0.0313818	+	0.0687166i
$95$	−4.36263	−	1.28098i	−0.447597	−	0.131426i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	−2.01807	+	1.29693i	−0.204904	+	0.131684i	−0.639068	−	0.769150i	$-0.720680\pi$
$97$	−2.01807	+	1.29693i	−0.204904	+	0.131684i	0.434165	+	0.900833i	$0.357044\pi$
$98$	−0.654861	+	0.755750i	−0.0661509	+	0.0763422i
$99$	0.306729	−	2.13335i	0.0308274	−	0.214409i
$100$	−1.07140	+	0.314591i	−0.107140	+	0.0314591i
$101$	−2.72800	−	1.75318i	−0.271446	−	0.174448i	0.397835	−	0.917457i	$-0.369762\pi$
$101$	−2.72800	−	1.75318i	−0.271446	−	0.174448i	−0.669281	+	0.743009i	$0.733398\pi$
$102$	−0.896637	−	6.23625i	−0.0887803	−	0.617481i
$103$	−5.80436	−	12.7098i	−0.571921	−	1.25233i	−0.945768	−	0.324842i	$-0.894689\pi$
$103$	−5.80436	−	12.7098i	−0.571921	−	1.25233i	0.373847	−	0.927490i	$-0.378038\pi$
$104$	0.808067	+	1.76942i	0.0792375	+	0.173506i
$105$	0.351971	+	2.44801i	0.0343488	+	0.238901i
$106$	4.87525	+	3.13313i	0.473526	+	0.304317i
$107$	−1.67853	+	0.492862i	−0.162270	+	0.0476468i	−0.361858	−	0.932233i	$-0.617858\pi$
$107$	−1.67853	+	0.492862i	−0.162270	+	0.0476468i	0.199589	+	0.979880i	$0.436039\pi$
$108$	0.142315	−	0.989821i	0.0136943	−	0.0952456i
$109$	1.83066	−	2.11269i	0.175345	−	0.202359i	−0.661273	−	0.750145i	$-0.729984\pi$
$109$	1.83066	−	2.11269i	0.175345	−	0.202359i	0.836619	+	0.547786i	$0.184529\pi$
$110$	−4.48423	+	2.88184i	−0.427554	+	0.274772i
$111$	−0.347949	−	0.401554i	−0.0330258	−	0.0381138i
$112$	−0.959493	−	0.281733i	−0.0906636	−	0.0266212i
$113$	−1.30062	+	2.84796i	−0.122352	+	0.267913i	−0.960890	−	0.276929i	$-0.910683\pi$
$113$	−1.30062	+	2.84796i	−0.122352	+	0.267913i	0.838538	+	0.544842i	$0.183411\pi$
$114$	−1.83844			−0.172186
$115$	4.00389	+	11.1647i	0.373364	+	1.04112i
$116$	−7.89703			−0.733220
$117$	0.808067	−	1.76942i	0.0747058	−	0.163583i
$118$	4.66961	+	1.37112i	0.429872	+	0.126222i
$119$	4.12587	+	4.76151i	0.378218	+	0.436487i
$120$	−2.08057	+	1.33710i	−0.189929	+	0.122060i
$121$	4.16148	−	4.80260i	0.378316	−	0.436600i
$122$	−1.18094	+	8.21360i	−0.106917	+	0.743625i
$123$	1.68553	−	0.494915i	0.151979	−	0.0446250i
$124$	−2.08637	−	1.34083i	−0.187361	−	0.120410i
$125$	1.36683	+	9.50652i	0.122253	+	0.850289i
$126$	0.415415	+	0.909632i	0.0370081	+	0.0810365i
$127$	0.868795	+	1.90240i	0.0770931	+	0.168810i	0.944254	−	0.329218i	$-0.106785\pi$
$127$	0.868795	+	1.90240i	0.0770931	+	0.168810i	−0.867161	+	0.498028i	$0.834058\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	2.71621	+	1.74560i	0.239149	+	0.153692i
$130$	−4.61597	+	1.35537i	−0.404847	+	0.118874i
$131$	−2.98845	+	20.7851i	−0.261102	+	1.81601i	0.263501	+	0.964659i	$0.415123\pi$
$131$	−2.98845	+	20.7851i	−0.261102	+	1.81601i	−0.524603	+	0.851347i	$0.675786\pi$
$132$	−1.41141	+	1.62886i	−0.122848	+	0.141774i
$133$	1.54660	−	0.993938i	0.134107	−	0.0861854i
$134$	5.49990	+	6.34722i	0.475119	+	0.548316i
$135$	2.37300	+	0.696776i	0.204235	+	0.0599689i
$136$	−2.61727	+	5.73103i	−0.224429	+	0.491431i
$137$	−10.0571			−0.859233			−0.429617	−	0.903011i	$-0.641351\pi$
$137$	−10.0571			−0.859233			−0.429617	+	0.903011i	$0.641351\pi$
$138$	2.82517	+	3.87536i	0.240495	+	0.329892i
$139$	−9.50455			−0.806166			−0.403083	−	0.915163i	$-0.632061\pi$
$139$	−9.50455			−0.806166			−0.403083	+	0.915163i	$0.632061\pi$
$140$	1.02740	−	2.24969i	0.0868309	−	0.190133i
$141$	−0.702751	−	0.206346i	−0.0591823	−	0.0173775i
$142$	3.99685	+	4.61262i	0.335409	+	0.387082i
$143$	−3.52693	+	2.26662i	−0.294937	+	0.189544i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	2.77952	−	19.3320i	0.230827	−	1.60543i
$146$	2.66356	−	0.782092i	0.220438	−	0.0647264i
$147$	−0.841254	−	0.540641i	−0.0693854	−	0.0445913i
$148$	0.0756165	+	0.525924i	0.00621563	+	0.0432307i
$149$	−0.0344979	−	0.0755398i	−0.00282618	−	0.00618846i	0.908214	−	0.418507i	$-0.137446\pi$
$149$	−0.0344979	−	0.0755398i	−0.00282618	−	0.00618846i	−0.911040	+	0.412318i	$0.864719\pi$
$150$	−0.463865	−	1.01572i	−0.0378744	−	0.0829333i
$151$	1.59373	+	11.0847i	0.129696	+	0.902056i	0.945938	+	0.324347i	$0.105144\pi$
$151$	1.59373	+	11.0847i	0.129696	+	0.902056i	−0.816242	+	0.577710i	$0.803947\pi$
$152$	1.54660	+	0.993938i	0.125446	+	0.0806190i
$153$	6.04517	−	1.77502i	0.488723	−	0.143502i
$154$	0.306729	−	2.13335i	0.0247169	−	0.171910i
$155$	4.01669	−	4.63551i	0.322629	−	0.372333i
$156$	−1.63641	+	1.05166i	−0.131018	+	0.0841999i
$157$	11.0329	+	12.7326i	0.880520	+	1.01617i	0.999728	+	0.0233048i	$0.00741883\pi$
$157$	11.0329	+	12.7326i	0.880520	+	1.01617i	−0.119209	+	0.992869i	$0.538036\pi$
$158$	−7.48240	−	2.19703i	−0.595268	−	0.174786i
$159$	−2.40742	+	5.27152i	−0.190921	+	0.418058i
$160$	2.47318			0.195522
$161$	−4.47186	−	1.73275i	−0.352432	−	0.136560i
$162$	1.00000			0.0785674
$163$	4.35535	−	9.53689i	0.341138	−	0.746987i	−0.658848	−	0.752276i	$-0.728956\pi$
$163$	4.35535	−	9.53689i	0.341138	−	0.746987i	0.999986	+	0.00528867i	$0.00168344\pi$
$164$	−1.68553	−	0.494915i	−0.131618	−	0.0386464i
$165$	−3.49068	−	4.02846i	−0.271749	−	0.313615i
$166$	3.95720	−	2.54314i	0.307138	−	0.197386i
$167$	−2.92559	+	3.37632i	−0.226389	+	0.261267i	−0.857568	−	0.514370i	$-0.828026\pi$
$167$	−2.92559	+	3.37632i	−0.226389	+	0.261267i	0.631179	+	0.775637i	$0.282571\pi$
$168$	0.142315	−	0.989821i	0.0109798	−	0.0763664i
$169$	8.84286	−	2.59650i	0.680220	−	0.199731i
$170$	−13.1084	−	8.42426i	−1.00537	−	0.646111i
$171$	−0.261638	−	1.81973i	−0.0200080	−	0.139158i
$172$	−1.34128	−	2.93699i	−0.102271	−	0.223943i
$173$	9.85149	+	21.5718i	0.748995	+	1.64007i	0.768163	+	0.640254i	$0.221171\pi$
$173$	9.85149	+	21.5718i	0.748995	+	1.64007i	−0.0191683	+	0.999816i	$0.506102\pi$
$174$	−1.12386	−	7.81664i	−0.0851999	−	0.592578i
$175$	0.939368	+	0.603695i	0.0710096	+	0.0456351i
$176$	2.06798	−	0.607214i	0.155880	−	0.0457705i
$177$	−0.692610	+	4.81721i	−0.0520597	+	0.362083i
$178$	1.98180	−	2.28712i	0.148542	−	0.171427i
$179$	−15.7957	+	10.1513i	−1.18063	+	0.758744i	−0.975502	−	0.219991i	$-0.929397\pi$
$179$	−15.7957	+	10.1513i	−1.18063	+	0.758744i	−0.205127	+	0.978735i	$0.565761\pi$
$180$	−1.61959	−	1.86911i	−0.120717	−	0.139315i
$181$	4.22787	+	1.24141i	0.314255	+	0.0922736i	0.435057	−	0.900403i	$-0.356728\pi$
$181$	4.22787	+	1.24141i	0.314255	+	0.0922736i	−0.120802	+	0.992677i	$0.538547\pi$
$182$	0.808067	−	1.76942i	0.0598979	−	0.131158i
$183$	−8.29806			−0.613411
$184$	−0.281512	−	4.78756i	−0.0207533	−	0.352944i
$185$	−1.31408			−0.0966132
$186$	1.03026	−	2.25595i	0.0755422	−	0.165414i
$187$	−13.0291	−	3.82568i	−0.952779	−	0.279761i
$188$	0.479633	+	0.553526i	0.0349808	+	0.0403700i
$189$	−0.841254	+	0.540641i	−0.0611922	+	0.0393258i
$190$	−2.97753	+	3.43625i	−0.216012	+	0.249292i
$191$	−3.00995	+	20.9346i	−0.217792	+	1.51478i	0.528371	+	0.849014i	$0.322803\pi$
$191$	−3.00995	+	20.9346i	−0.217792	+	1.51478i	−0.746163	+	0.665763i	$0.768106\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	−20.4981	−	13.1733i	−1.47549	−	0.948238i	−0.997558	−	0.0698387i	$-0.977752\pi$
$193$	−20.4981	−	13.1733i	−1.47549	−	0.948238i	−0.477928	−	0.878399i	$-0.658612\pi$
$194$	0.341396	+	2.37446i	0.0245108	+	0.170477i
$195$	−1.99850	−	4.37610i	−0.143115	−	0.313379i
$196$	0.415415	+	0.909632i	0.0296725	+	0.0649737i
$197$	1.78409	+	12.4086i	0.127111	+	0.884077i	0.949190	+	0.314703i	$0.101905\pi$
$197$	1.78409	+	12.4086i	0.127111	+	0.884077i	−0.822079	+	0.569373i	$0.807186\pi$
$198$	−1.81314	−	1.16523i	−0.128854	−	0.0828096i
$199$	6.58112	−	1.93239i	0.466523	−	0.136984i	−0.0400188	−	0.999199i	$-0.512742\pi$
$199$	6.58112	−	1.93239i	0.466523	−	0.136984i	0.506542	+	0.862215i	$0.330924\pi$
$200$	−0.158913	+	1.10526i	−0.0112368	+	0.0781539i
$201$	−5.49990	+	6.34722i	−0.387933	+	0.447698i
$202$	−2.72800	+	1.75318i	−0.191942	+	0.123353i
$203$	5.17145	+	5.96817i	0.362965	+	0.418884i
$204$	−6.04517	−	1.77502i	−0.423246	−	0.124276i
$205$	1.80481	−	3.95199i	0.126054	−	0.276019i
$206$	−13.9724			−0.973506
$207$	−3.43385	+	3.34794i	−0.238669	+	0.232698i
$208$	1.94520			0.134876
$209$	−1.64603	+	3.60430i	−0.113858	+	0.249315i
$210$	2.37300	+	0.696776i	0.163753	+	0.0480821i
$211$	5.93333	+	6.84743i	0.408467	+	0.471396i	0.922289	−	0.386500i	$-0.126316\pi$
$211$	5.93333	+	6.84743i	0.408467	+	0.471396i	−0.513822	+	0.857897i	$0.671771\pi$
$212$	4.87525	−	3.13313i	0.334833	−	0.215184i
$213$	−3.99685	+	4.61262i	−0.273860	+	0.316051i
$214$	−0.248965	+	1.73159i	−0.0170189	+	0.118369i
$215$	7.66186	−	2.24972i	0.522534	−	0.153430i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	0.352951	+	2.45483i	0.0239599	+	0.166644i
$218$	−1.16129	−	2.54287i	−0.0786525	−	0.172225i
$219$	1.15320	+	2.52515i	0.0779257	+	0.170634i
$220$	0.758597	+	5.27615i	0.0511446	+	0.355718i
$221$	−10.3100	−	6.62583i	−0.693526	−	0.445702i
$222$	−0.509810	+	0.149694i	−0.0342162	+	0.0100468i
$223$	−0.907301	+	6.31041i	−0.0607573	+	0.422577i	0.936629	+	0.350323i	$0.113928\pi$
$223$	−0.907301	+	6.31041i	−0.0607573	+	0.422577i	−0.997386	+	0.0722536i	$0.976981\pi$
$224$	−0.654861	+	0.755750i	−0.0437547	+	0.0504956i
$225$	0.939368	−	0.603695i	0.0626246	−	0.0402464i
$226$	2.05030	+	2.36617i	0.136384	+	0.157395i
$227$	28.4379	+	8.35011i	1.88749	+	0.554217i	0.994580	+	0.103979i	$0.0331574\pi$
$227$	28.4379	+	8.35011i	1.88749	+	0.554217i	0.892909	+	0.450238i	$0.148661\pi$
$228$	−0.763718	+	1.67231i	−0.0505784	+	0.110751i
$229$	−9.96039			−0.658201			−0.329100	−	0.944295i	$-0.606745\pi$
$229$	−9.96039			−0.658201			−0.329100	+	0.944295i	$0.606745\pi$
$230$	11.8191	+	0.995937i	0.779327	+	0.0656702i
$231$	2.15528			0.141807
$232$	−3.28054	+	7.18339i	−0.215378	+	0.471612i
$233$	−16.8667	−	4.95251i	−1.10498	−	0.324450i	−0.322148	−	0.946689i	$-0.604405\pi$
$233$	−16.8667	−	4.95251i	−1.10498	−	0.324450i	−0.782827	+	0.622239i	$0.786223\pi$
$234$	−1.27384	−	1.47009i	−0.0832734	−	0.0961026i
$235$	−1.52385	+	0.979320i	−0.0994051	+	0.0638838i
$236$	3.18704	−	3.67804i	0.207459	−	0.239420i
$237$	1.10981	−	7.71891i	0.0720900	−	0.501397i
$238$	6.04517	−	1.77502i	0.391850	−	0.115058i
$239$	5.45268	+	3.50423i	0.352705	+	0.226670i	0.704981	−	0.709227i	$-0.250956\pi$
$239$	5.45268	+	3.50423i	0.352705	+	0.226670i	−0.352276	+	0.935896i	$0.614592\pi$
$240$	0.351971	+	2.44801i	0.0227196	+	0.158018i
$241$	−0.115125	−	0.252089i	−0.00741586	−	0.0162385i	0.905888	−	0.423518i	$-0.139205\pi$
$241$	−0.115125	−	0.252089i	−0.00741586	−	0.0162385i	−0.913304	+	0.407279i	$0.866478\pi$
$242$	−2.63986	−	5.78048i	−0.169697	−	0.371584i
$243$	0.142315	+	0.989821i	0.00912950	+	0.0634971i
$244$	6.98078	+	4.48627i	0.446898	+	0.287204i
$245$	−2.37300	+	0.696776i	−0.151605	+	0.0445154i
$246$	0.250002	−	1.73880i	0.0159396	−	0.110862i
$247$	−2.34188	+	2.70267i	−0.149010	+	0.171967i
$248$	−2.08637	+	1.34083i	−0.132484	+	0.0851426i
$249$	3.08042	+	3.55500i	0.195214	+	0.225289i
$250$	9.21524	+	2.70584i	0.582823	+	0.171132i
$251$	9.94466	−	21.7758i	0.627702	−	1.37447i	−0.282081	−	0.959390i	$-0.591025\pi$
$251$	9.94466	−	21.7758i	0.627702	−	1.37447i	0.909783	−	0.415084i	$-0.136248\pi$
$252$	1.00000			0.0629941
$253$	10.1272	−	2.06905i	0.636690	−	0.130080i
$254$	2.09139			0.131226
$255$	6.47299	−	14.1739i	0.405354	−	0.887602i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	18.1223	+	20.9143i	1.13044	+	1.30460i	0.946880	+	0.321587i	$0.104216\pi$
$257$	18.1223	+	20.9143i	1.13044	+	1.30460i	0.183559	+	0.983009i	$0.441238\pi$
$258$	2.71621	−	1.74560i	0.169104	−	0.108676i
$259$	0.347949	−	0.401554i	0.0216205	−	0.0249514i
$260$	−0.684654	+	4.76188i	−0.0424605	+	0.295319i
$261$	7.57714	−	2.22485i	0.469013	−	0.137715i
$262$	17.6654	+	11.3529i	1.09137	+	0.701382i
$263$	−1.79580	−	12.4901i	−0.110734	−	0.770171i	−0.967209	−	0.253982i	$-0.918260\pi$
$263$	−1.79580	−	12.4901i	−0.110734	−	0.770171i	0.856475	−	0.516188i	$-0.172650\pi$
$264$	0.895337	+	1.96052i	0.0551042	+	0.120661i
$265$	5.95399	+	13.0374i	0.365751	+	0.800882i
$266$	−0.261638	−	1.81973i	−0.0160421	−	0.111575i
$267$	2.54588	+	1.63614i	0.155805	+	0.100130i
$268$	8.05837	−	2.36615i	0.492243	−	0.144536i
$269$	1.11591	−	7.76133i	0.0680383	−	0.473217i	−0.927107	−	0.374797i	$-0.877712\pi$
$269$	1.11591	−	7.76133i	0.0680383	−	0.473217i	0.995145	−	0.0984192i	$-0.0313786\pi$
$270$	1.61959	−	1.86911i	0.0985651	−	0.113750i
$271$	−10.6562	+	6.84830i	−0.647316	+	0.416004i	−0.822684	−	0.568498i	$-0.807525\pi$
$271$	−10.6562	+	6.84830i	−0.647316	+	0.416004i	0.175369	+	0.984503i	$0.443888\pi$
$272$	4.12587	+	4.76151i	0.250168	+	0.288709i
$273$	1.86641	+	0.548027i	0.112960	+	0.0331681i
$274$	−4.17786	+	9.14823i	−0.252394	+	0.552665i
$275$	−2.40665			−0.145127
$276$	4.69877	−	0.959988i	0.282833	−	0.0577845i
$277$	−14.0731			−0.845570			−0.422785	−	0.906230i	$-0.638948\pi$
$277$	−14.0731			−0.845570			−0.422785	+	0.906230i	$0.638948\pi$
$278$	−3.94833	+	8.64565i	−0.236805	+	0.518531i
$279$	2.37961	+	0.698716i	0.142463	+	0.0418310i
$280$	−1.61959	−	1.86911i	−0.0967890	−	0.111700i
$281$	24.5497	−	15.7771i	1.46451	−	0.941185i	0.466108	−	0.884728i	$-0.345656\pi$
$281$	24.5497	−	15.7771i	1.46451	−	0.941185i	0.998405	−	0.0564577i	$-0.0179806\pi$
$282$	−0.479633	+	0.553526i	−0.0285617	+	0.0329620i
$283$	−0.139714	+	0.971732i	−0.00830513	+	0.0577635i	−0.993553	−	0.113373i	$-0.963835\pi$
$283$	−0.139714	+	0.971732i	−0.00830513	+	0.0577635i	0.985247	+	0.171136i	$0.0547437\pi$
$284$	5.85614	−	1.71952i	0.347498	−	0.102035i
$285$	−3.82502	−	2.45819i	−0.226575	−	0.145611i
$286$	0.596650	+	4.14979i	0.0352807	+	0.245382i
$287$	0.729753	+	1.59794i	0.0430760	+	0.0943233i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	−3.22980	−	22.4638i	−0.189988	−	1.32140i
$290$	−16.4303	−	10.5591i	−0.964823	−	0.620054i
$291$	−2.30171	+	0.675843i	−0.134929	+	0.0396186i
$292$	0.395067	−	2.74775i	0.0231196	−	0.160800i
$293$	3.48831	−	4.02573i	0.203789	−	0.235185i	−0.644650	−	0.764478i	$-0.722997\pi$
$293$	3.48831	−	4.02573i	0.203789	−	0.235185i	0.848440	+	0.529292i	$0.177542\pi$
$294$	−0.841254	+	0.540641i	−0.0490629	+	0.0315308i
$295$	7.88213	+	9.09646i	0.458915	+	0.529616i
$296$	0.509810	+	0.149694i	0.0296321	+	0.00870076i
$297$	0.895337	−	1.96052i	0.0519528	−	0.113761i
$298$	−0.0830444			−0.00481063
$299$	9.29593	+	0.783323i	0.537597	+	0.0453008i
$300$	−1.11663			−0.0644686
$301$	−1.34128	+	2.93699i	−0.0773099	+	0.169285i
$302$	10.7450	+	3.15502i	0.618306	+	0.181551i
$303$	−2.12357	−	2.45073i	−0.121996	−	0.140791i
$304$	1.54660	−	0.993938i	0.0887035	−	0.0570063i
$305$	−13.4395	+	15.5100i	−0.769541	+	0.888098i
$306$	0.896637	−	6.23625i	0.0512573	−	0.356503i
$307$	20.6422	−	6.06108i	1.17811	−	0.345924i	0.366665	−	0.930353i	$-0.380500\pi$
$307$	20.6422	−	6.06108i	1.17811	−	0.345924i	0.811445	+	0.584429i	$0.198681\pi$
$308$	−1.81314	−	1.16523i	−0.103313	−	0.0663954i
$309$	−1.98849	−	13.8302i	−0.113121	−	0.786774i
$310$	−2.54802	−	5.57938i	−0.144718	−	0.316887i
$311$	7.70959	+	16.8816i	0.437171	+	0.957270i	0.992109	+	0.125379i	$0.0400145\pi$
$311$	7.70959	+	16.8816i	0.437171	+	0.957270i	−0.554938	+	0.831891i	$0.687258\pi$
$312$	0.276831	+	1.92540i	0.0156725	+	0.109005i
$313$	−8.07013	−	5.18636i	−0.456151	−	0.293150i	0.292317	−	0.956321i	$-0.405574\pi$
$313$	−8.07013	−	5.18636i	−0.456151	−	0.293150i	−0.748468	+	0.663171i	$0.769210\pi$
$314$	16.1652	−	4.74654i	0.912257	−	0.267863i
$315$	−0.351971	+	2.44801i	−0.0198313	+	0.137930i
$316$	−5.10679	+	5.89355i	−0.287279	+	0.331538i
$317$	−12.1247	+	7.79204i	−0.680988	+	0.437645i	−0.834872	−	0.550444i	$-0.814458\pi$
$317$	−12.1247	+	7.79204i	−0.680988	+	0.437645i	0.153884	+	0.988089i	$0.450822\pi$
$318$	3.79506	+	4.37973i	0.212816	+	0.245603i
$319$	−16.3309	−	4.79518i	−0.914354	−	0.268479i
$320$	1.02740	−	2.24969i	0.0574332	−	0.125761i
$321$	−1.74940			−0.0976418
$322$	−3.43385	+	3.34794i	−0.191361	+	0.186573i
$323$	−11.5829			−0.644490
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−2.08409	−	0.611943i	−0.115604	−	0.0339445i
$326$	−6.86578	−	7.92354i	−0.380261	−	0.438844i
$327$	2.35172	−	1.51136i	0.130050	−	0.0835784i
$328$	−1.15038	+	1.32761i	−0.0635193	+	0.0733052i
$329$	0.104234	−	0.724964i	0.00574661	−	0.0399686i
$330$	−5.11449	+	1.50175i	−0.281543	+	0.0826686i
$331$	−10.8057	−	6.94437i	−0.593933	−	0.381697i	0.208869	−	0.977944i	$-0.433022\pi$
$331$	−10.8057	−	6.94437i	−0.593933	−	0.381697i	−0.802802	+	0.596246i	$0.796658\pi$
$332$	−0.669440	−	4.65606i	−0.0367403	−	0.255534i
$333$	−0.220723	−	0.483317i	−0.0120956	−	0.0264856i
$334$	1.85587	+	4.06379i	0.101549	+	0.222360i
$335$	2.95605	+	20.5598i	0.161506	+	1.12330i
$336$	−0.841254	−	0.540641i	−0.0458941	−	0.0294944i
$337$	0.558361	−	0.163950i	0.0304158	−	0.00893090i	−0.266489	−	0.963838i	$-0.585864\pi$
$337$	0.558361	−	0.163950i	0.0304158	−	0.00893090i	0.296905	+	0.954907i	$0.404045\pi$
$338$	1.31160	−	9.12237i	0.0713416	−	0.496192i
$339$	−2.05030	+	2.36617i	−0.111357	+	0.128513i
$340$	−13.1084	+	8.42426i	−0.710903	+	0.456869i
$341$	−3.50040	−	4.03967i	−0.189557	−	0.218761i
$342$	−1.76398	−	0.517950i	−0.0953848	−	0.0280075i
$343$	0.415415	−	0.909632i	0.0224303	−	0.0491155i
$344$	−3.22876			−0.174083
$345$	0.696230	+	11.8405i	0.0374838	+	0.637472i
$346$	23.7148			1.27492
$347$	7.98749	−	17.4902i	0.428791	−	0.938921i	−0.564731	−	0.825275i	$-0.691020\pi$
$347$	7.98749	−	17.4902i	0.428791	−	0.938921i	0.993521	−	0.113645i	$-0.0362528\pi$
$348$	−7.57714	−	2.22485i	−0.406177	−	0.119264i
$349$	6.79637	+	7.84343i	0.363802	+	0.419849i	0.907910	−	0.419166i	$-0.137677\pi$
$349$	6.79637	+	7.84343i	0.363802	+	0.419849i	−0.544108	+	0.839015i	$0.683132\pi$
$350$	0.939368	−	0.603695i	0.0502114	−	0.0322689i
$351$	1.27384	−	1.47009i	0.0679924	−	0.0784674i
$352$	0.306729	−	2.13335i	0.0163487	−	0.113708i
$353$	−5.52214	+	1.62145i	−0.293914	+	0.0863010i	−0.425366	−	0.905022i	$-0.639854\pi$
$353$	−5.52214	+	1.62145i	−0.293914	+	0.0863010i	0.131451	+	0.991323i	$0.458036\pi$
$354$	4.09417	+	2.63116i	0.217602	+	0.139845i
$355$	2.14820	+	14.9411i	0.114015	+	0.792991i
$356$	−1.25717	−	2.75282i	−0.0666298	−	0.145899i
$357$	2.61727	+	5.73103i	0.138521	+	0.303318i
$358$	2.67217	+	18.5853i	0.141228	+	0.982264i
$359$	−21.4994	−	13.8168i	−1.13469	−	0.729223i	−0.168159	−	0.985760i	$-0.553782\pi$
$359$	−21.4994	−	13.8168i	−1.13469	−	0.729223i	−0.966535	+	0.256536i	$0.917419\pi$
$360$	−2.37300	+	0.696776i	−0.125068	+	0.0367233i
$361$	2.22297	−	15.4611i	0.116999	−	0.813744i
$362$	2.88555	−	3.33010i	0.151661	−	0.175026i
$363$	5.34596	−	3.43564i	0.280590	−	0.180324i
$364$	−1.27384	−	1.47009i	−0.0667672	−	0.0770535i
$365$	6.58747	+	1.93426i	0.344804	+	0.101244i
$366$	−3.44714	+	7.54818i	−0.180185	+	0.394550i
$367$	19.4649			1.01606			0.508029	−	0.861340i	$-0.330374\pi$
$367$	19.4649			1.01606			0.508029	+	0.861340i	$0.330374\pi$
$368$	−4.47186	−	1.73275i	−0.233112	−	0.0903260i
$369$	1.75669			0.0914494
$370$	−0.545889	+	1.19533i	−0.0283794	+	0.0621423i
$371$	−5.56047	−	1.63270i	−0.288685	−	0.0847657i
$372$	−1.62410	−	1.87431i	−0.0842057	−	0.0971785i
$373$	−20.2790	+	13.0325i	−1.05001	+	0.674799i	−0.947442	−	0.319927i	$-0.896341\pi$
$373$	−20.2790	+	13.0325i	−1.05001	+	0.674799i	−0.102565	+	0.994726i	$0.532705\pi$
$374$	−8.89242	+	10.2624i	−0.459816	+	0.530656i
$375$	−1.36683	+	9.50652i	−0.0705829	+	0.490915i
$376$	0.702751	−	0.206346i	0.0362416	−	0.0106415i
$377$	−12.9228	−	8.30496i	−0.665556	−	0.427727i
$378$	0.142315	+	0.989821i	0.00731989	+	0.0509109i
$379$	−5.91177	−	12.9450i	−0.303667	−	0.664939i	0.694863	−	0.719143i	$-0.255465\pi$
$379$	−5.91177	−	12.9450i	−0.303667	−	0.664939i	−0.998530	+	0.0542039i	$0.982738\pi$
$380$	1.88881	+	4.13592i	0.0968940	+	0.212168i
$381$	0.297636	+	2.07010i	0.0152484	+	0.106055i
$382$	17.7924	+	11.4345i	0.910340	+	0.585040i
$383$	−18.6668	+	5.48108i	−0.953831	+	0.280070i	−0.721381	−	0.692538i	$-0.756492\pi$
$383$	−18.6668	+	5.48108i	−0.953831	+	0.280070i	−0.232450	+	0.972608i	$0.574674\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	3.49068	−	4.02846i	0.177901	−	0.205309i
$386$	−20.4981	+	13.1733i	−1.04333	+	0.670505i
$387$	2.11439	+	2.44014i	0.107480	+	0.124039i
$388$	2.30171	+	0.675843i	0.116852	+	0.0343107i
$389$	7.01295	−	15.3562i	0.355571	−	0.778592i	−0.644333	−	0.764745i	$-0.722865\pi$
$389$	7.01295	−	15.3562i	0.355571	−	0.778592i	0.999904	−	0.0138468i	$-0.00440770\pi$
$390$	−4.81084			−0.243607
$391$	17.7997	+	24.4162i	0.900168	+	1.23478i
$392$	1.00000			0.0505076
$393$	−8.72325	+	19.1013i	−0.440030	+	0.963531i
$394$	12.0284	+	3.53186i	0.605982	+	0.177932i
$395$	−12.6300	−	14.5758i	−0.635486	−	0.733389i
$396$	−1.81314	+	1.16523i	−0.0911137	+	0.0585552i
$397$	10.0951	−	11.6503i	0.506657	−	0.584713i	−0.443583	−	0.896233i	$-0.646293\pi$
$397$	10.0951	−	11.6503i	0.506657	−	0.584713i	0.950240	+	0.311520i	$0.100838\pi$
$398$	0.976131	−	6.78914i	0.0489290	−	0.340309i
$399$	1.76398	−	0.517950i	0.0883092	−	0.0259299i
$400$	0.939368	+	0.603695i	0.0469684	+	0.0301848i
$401$	−4.71987	−	32.8274i	−0.235699	−	1.63932i	−0.672738	−	0.739881i	$-0.734882\pi$
$401$	−4.71987	−	32.8274i	−0.235699	−	1.63932i	0.437039	−	0.899443i	$-0.356027\pi$
$402$	3.48889	+	7.63961i	0.174010	+	0.381029i
$403$	−2.00406	−	4.38828i	−0.0998294	−	0.218596i
$404$	0.461496	+	3.20977i	0.0229603	+	0.159692i
$405$	2.08057	+	1.33710i	0.103385	+	0.0664412i
$406$	7.57714	−	2.22485i	0.376047	−	0.110417i
$407$	−0.162975	+	1.13352i	−0.00807837	+	0.0561863i
$408$	−4.12587	+	4.76151i	−0.204261	+	0.235730i
$409$	−25.5385	+	16.4126i	−1.26280	+	0.811551i	−0.988665	−	0.150141i	$-0.952027\pi$
$409$	−25.5385	+	16.4126i	−1.26280	+	0.811551i	−0.274133	+	0.961692i	$0.588391\pi$
$410$	−2.84511	−	3.28343i	−0.140510	−	0.162157i
$411$	−9.64969	−	2.83340i	−0.475984	−	0.139762i
$412$	−5.80436	+	12.7098i	−0.285960	+	0.626166i
$413$	−4.86674			−0.239477
$414$	1.61892	+	4.51432i	0.0795656	+	0.221867i
$415$	11.6337			0.571075
$416$	0.808067	−	1.76942i	0.0396187	−	0.0867529i
$417$	−9.11955	−	2.67774i	−0.446586	−	0.131130i
$418$	2.59480	+	2.99456i	0.126916	+	0.146469i
$419$	12.8854	−	8.28096i	0.629494	−	0.404551i	−0.186628	−	0.982431i	$-0.559756\pi$
$419$	12.8854	−	8.28096i	0.629494	−	0.404551i	0.816122	+	0.577879i	$0.196120\pi$
$420$	1.61959	−	1.86911i	0.0790279	−	0.0912030i
$421$	3.73753	−	25.9951i	0.182156	−	1.26692i	−0.669495	−	0.742816i	$-0.733490\pi$
$421$	3.73753	−	25.9951i	0.182156	−	1.26692i	0.851652	−	0.524108i	$-0.175601\pi$
$422$	8.69344	−	2.55262i	0.423190	−	0.124260i
$423$	−0.616150	−	0.395976i	−0.0299583	−	0.0192530i
$424$	−0.824746	−	5.73623i	−0.0400532	−	0.278576i
$425$	−2.92252	−	6.39943i	−0.141763	−	0.310418i
$426$	2.53543	+	5.55182i	0.122842	+	0.268986i
$427$	−1.18094	−	8.21360i	−0.0571496	−	0.397484i
$428$	1.47169	+	0.945795i	0.0711366	+	0.0457167i
$429$	−4.02264	+	1.18115i	−0.194215	+	0.0570267i
$430$	1.13643	−	7.90404i	0.0548035	−	0.381167i
$431$	−0.0244443	+	0.0282103i	−0.00117744	+	0.00135884i	−0.756338	−	0.654181i	$-0.773013\pi$
$431$	−0.0244443	+	0.0282103i	−0.00117744	+	0.00135884i	0.755161	+	0.655540i	$0.227559\pi$
$432$	−0.841254	+	0.540641i	−0.0404748	+	0.0260116i
$433$	−15.4672	−	17.8501i	−0.743305	−	0.857820i	0.250596	−	0.968092i	$-0.419373\pi$
$433$	−15.4672	−	17.8501i	−0.743305	−	0.857820i	−0.993901	+	0.110272i	$0.964828\pi$
$434$	2.37961	+	0.698716i	0.114225	+	0.0335395i
$435$	8.11338	−	17.7658i	0.389007	−	0.851806i
$436$	−2.79550			−0.133880
$437$	7.79128	−	4.12712i	0.372708	−	0.197427i
$438$	2.77601			0.132643
$439$	−1.54815	+	3.38997i	−0.0738889	+	0.161794i	−0.942972	−	0.332872i	$-0.891982\pi$
$439$	−1.54815	+	3.38997i	−0.0738889	+	0.161794i	0.869083	+	0.494666i	$0.164710\pi$
$440$	5.11449	+	1.50175i	0.243824	+	0.0715931i
$441$	−0.654861	−	0.755750i	−0.0311838	−	0.0359881i
$442$	−10.3100	+	6.62583i	−0.490397	+	0.315159i
$443$	−25.6830	+	29.6398i	−1.22024	+	1.40823i	−0.335564	+	0.942017i	$0.608927\pi$
$443$	−25.6830	+	29.6398i	−1.22024	+	1.40823i	−0.884673	+	0.466211i	$0.845619\pi$
$444$	−0.0756165	+	0.525924i	−0.00358860	+	0.0249593i
$445$	7.18140	−	2.10865i	0.340431	−	0.0999596i
$446$	5.36325	+	3.44675i	0.253957	+	0.163208i
$447$	−0.0118184	−	0.0821991i	−0.000558993	−	0.00388788i
$448$	0.415415	+	0.909632i	0.0196265	+	0.0429761i
$449$	−7.38411	−	16.1689i	−0.348478	−	0.763060i	−0.999990	−	0.00442197i	$-0.998592\pi$
$449$	−7.38411	−	16.1689i	−0.348478	−	0.763060i	0.651512	−	0.758638i	$-0.274135\pi$
$450$	−0.158913	−	1.10526i	−0.00749123	−	0.0521026i
$451$	−3.18512	−	2.04695i	−0.149981	−	0.0963871i
$452$	3.00407	−	0.882073i	0.141299	−	0.0414892i
$453$	−1.59373	+	11.0847i	−0.0748801	+	0.520803i
$454$	19.4091	−	22.3992i	0.910912	−	1.05125i
$455$	4.04714	−	2.60094i	0.189733	−	0.121934i
$456$	1.20393	+	1.38940i	0.0563790	+	0.0650648i
$457$	−18.0364	−	5.29597i	−0.843709	−	0.247735i	−0.168813	−	0.985648i	$-0.553993\pi$
$457$	−18.0364	−	5.29597i	−0.843709	−	0.247735i	−0.674896	+	0.737913i	$0.735811\pi$
$458$	−4.13769	+	9.06029i	−0.193342	+	0.423359i
$459$	6.30038			0.294076
$460$	5.81576	−	10.3373i	0.271161	−	0.481978i
$461$	1.75590			0.0817806			0.0408903	−	0.999164i	$-0.486981\pi$
$461$	1.75590			0.0817806			0.0408903	+	0.999164i	$0.486981\pi$
$462$	0.895337	−	1.96052i	0.0416549	−	0.0912114i
$463$	−27.7707	−	8.15420i	−1.29061	−	0.378958i	−0.436809	−	0.899554i	$-0.643892\pi$
$463$	−27.7707	−	8.15420i	−1.29061	−	0.378958i	−0.853803	+	0.520596i	$0.825710\pi$
$464$	5.17145	+	5.96817i	0.240079	+	0.277065i
$465$	5.15997	−	3.31611i	0.239288	−	0.153781i
$466$	−11.5117	+	13.2852i	−0.533267	+	0.615423i
$467$	4.96865	−	34.5577i	0.229921	−	1.59914i	−0.468507	−	0.883460i	$-0.655208\pi$
$467$	4.96865	−	34.5577i	0.229921	−	1.59914i	0.698429	−	0.715680i	$-0.253883\pi$
$468$	−1.86641	+	0.548027i	−0.0862748	+	0.0253326i
$469$	−7.06533	−	4.54061i	−0.326247	−	0.209666i
$470$	0.257790	+	1.79297i	0.0118910	+	0.0827035i
$471$	6.99878	+	15.3252i	0.322487	+	0.706147i
$472$	−2.02172	−	4.42695i	−0.0930571	−	0.203767i
$473$	−0.990355	−	6.88807i	−0.0455366	−	0.316714i
$474$	−6.56034	−	4.21607i	−0.301326	−	0.193651i
$475$	−1.96971	+	0.578358i	−0.0903763	+	0.0265369i
$476$	0.896637	−	6.23625i	0.0410973	−	0.285838i
$477$	−3.79506	+	4.37973i	−0.173764	+	0.200534i
$478$	5.45268	−	3.50423i	0.249400	−	0.160280i
$479$	−26.4387	−	30.5119i	−1.20802	−	1.39412i	−0.896004	−	0.444046i	$-0.853543\pi$
$479$	−26.4387	−	30.5119i	−1.20802	−	1.39412i	−0.312012	−	0.950078i	$-0.601003\pi$
$480$	2.37300	+	0.696776i	0.108312	+	0.0318033i
$481$	−0.429352	+	0.940150i	−0.0195768	+	0.0428671i
$482$	−0.277133			−0.0126230
$483$	−3.80255	−	2.92243i	−0.173022	−	0.132975i
$484$	−6.35475			−0.288852
$485$	−2.46460	+	5.39673i	−0.111912	+	0.245053i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	14.1824	+	16.3674i	0.642667	+	0.741678i	0.979844	−	0.199764i	$-0.0640174\pi$
$487$	14.1824	+	16.3674i	0.642667	+	0.741678i	−0.337177	+	0.941441i	$0.609472\pi$
$488$	6.98078	−	4.48627i	0.316005	−	0.203084i
$489$	6.86578	−	7.92354i	0.310481	−	0.358315i
$490$	−0.351971	+	2.44801i	−0.0159004	+	0.110590i
$491$	27.1243	−	7.96442i	1.22410	−	0.359429i	0.395082	−	0.918646i	$-0.370716\pi$
$491$	27.1243	−	7.96442i	1.22410	−	0.359429i	0.829022	+	0.559217i	$0.188898\pi$
$492$	−1.47782	−	0.949736i	−0.0666252	−	0.0428174i
$493$	−7.08077	−	49.2478i	−0.318902	−	2.21801i
$494$	1.48559	+	3.25298i	0.0668397	+	0.146359i
$495$	−2.21433	−	4.84871i	−0.0995268	−	0.217933i
$496$	0.352951	+	2.45483i	0.0158480	+	0.110225i
$497$	−5.13448	−	3.29973i	−0.230313	−	0.148013i
$498$	4.51339	−	1.32525i	0.202250	−	0.0593859i
$499$	−5.77044	+	40.1343i	−0.258320	+	1.79666i	0.286475	+	0.958088i	$0.407517\pi$
$499$	−5.77044	+	40.1343i	−0.258320	+	1.79666i	−0.544795	+	0.838569i	$0.683393\pi$
$500$	6.28947	−	7.25843i	0.281274	−	0.324607i
$501$	−3.75830	+	2.41532i	−0.167909	+	0.107908i
$502$	−15.6768	−	18.0920i	−0.699689	−	0.807484i
$503$	14.4278	+	4.23639i	0.643305	+	0.188891i	0.587083	−	0.809527i	$-0.300276\pi$
$503$	14.4278	+	4.23639i	0.643305	+	0.188891i	0.0562224	+	0.998418i	$0.482094\pi$
$504$	0.415415	−	0.909632i	0.0185041	−	0.0405182i
$505$	−8.01999			−0.356885
$506$	2.32491	−	10.0715i	0.103355	−	0.447734i
$507$	9.21618			0.409305
$508$	0.868795	−	1.90240i	0.0385465	−	0.0844052i
$509$	1.59607	+	0.468648i	0.0707445	+	0.0207725i	0.316913	−	0.948455i	$-0.397354\pi$
$509$	1.59607	+	0.468648i	0.0707445	+	0.0207725i	−0.246169	+	0.969227i	$0.579172\pi$
$510$	−10.2040	−	11.7761i	−0.451842	−	0.521453i
$511$	−2.33533	+	1.50082i	−0.103309	+	0.0663925i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	0.261638	−	1.81973i	0.0115516	−	0.0803431i
$514$	26.5526	−	7.79654i	1.17118	−	0.343890i
$515$	−29.0707	−	18.6826i	−1.28101	−	0.823254i
$516$	−0.459501	−	3.19590i	−0.0202284	−	0.140692i
$517$	0.655763	+	1.43592i	0.0288404	+	0.0631517i
$518$	−0.220723	−	0.483317i	−0.00969803	−	0.0212357i
$519$	3.37497	+	23.4734i	0.148145	+	1.03037i
$520$	4.04714	+	2.60094i	0.177479	+	0.114059i
$521$	−3.34861	+	0.983240i	−0.146705	+	0.0430765i	−0.354261	−	0.935147i	$-0.615267\pi$
$521$	−3.34861	+	0.983240i	−0.146705	+	0.0430765i	0.207555	+	0.978223i	$0.433449\pi$
$522$	1.12386	−	7.81664i	0.0491902	−	0.342125i
$523$	−8.66153	+	9.99594i	−0.378742	+	0.437092i	−0.912832	−	0.408336i	$-0.866109\pi$
$523$	−8.66153	+	9.99594i	−0.378742	+	0.437092i	0.534089	+	0.845428i	$0.320655\pi$
$524$	17.6654	−	11.3529i	0.771716	−	0.495952i
$525$	0.731237	+	0.843892i	0.0319138	+	0.0368305i
$526$	−12.1074	−	3.55504i	−0.527906	−	0.155007i
$527$	6.49101	−	14.2133i	0.282753	−	0.619143i
$528$	2.15528			0.0937967
$529$	−20.6728	−	10.0814i	−0.898817	−	0.438323i
$530$	14.3326			0.622570
$531$	−2.02172	+	4.42695i	−0.0877351	+	0.192113i
$532$	−1.76398	−	0.517950i	−0.0764780	−	0.0224560i
$533$	−2.23773	−	2.58248i	−0.0969269	−	0.111860i
$534$	2.54588	−	1.63614i	0.110171	−	0.0708027i
$535$	−2.83330	+	3.26981i	−0.122494	+	0.141366i
$536$	1.19524	−	8.31309i	0.0516266	−	0.359071i
$537$	−18.0159	+	5.28993i	−0.777442	+	0.228277i
$538$	−6.59639	−	4.23924i	−0.284390	−	0.182767i
$539$	0.306729	+	2.13335i	0.0132118	+	0.0918897i
$540$	−1.02740	−	2.24969i	−0.0442121	−	0.0968111i
$541$	−3.37453	−	7.38919i	−0.145082	−	0.317686i	0.823115	−	0.567875i	$-0.192234\pi$
$541$	−3.37453	−	7.38919i	−0.145082	−	0.317686i	−0.968197	+	0.250189i	$0.919507\pi$
$542$	1.80270	+	12.5381i	0.0774327	+	0.538556i
$543$	3.70686	+	2.38226i	0.159077	+	0.102232i
$544$	6.04517	−	1.77502i	0.259184	−	0.0761034i
$545$	0.983932	−	6.84340i	0.0421470	−	0.293139i
$546$	1.27384	−	1.47009i	0.0545152	−	0.0629139i
$547$	21.8289	−	14.0286i	0.933337	−	0.599819i	0.0168390	−	0.999858i	$-0.494640\pi$
$547$	21.8289	−	14.0286i	0.933337	−	0.599819i	0.916498	+	0.400039i	$0.131003\pi$
$548$	6.58598	+	7.60063i	0.281339	+	0.324683i
$549$	−7.96193	−	2.33783i	−0.339807	−	0.0997764i
$550$	−0.999760	+	2.18917i	−0.0426299	+	0.0933465i
$551$	−14.5182			−0.618498
$552$	1.07870	−	4.67294i	0.0459127	−	0.198894i
$553$	7.79829			0.331617
$554$	−5.84618	+	12.8013i	−0.248380	+	0.543877i
$555$	−1.26085	−	0.370220i	−0.0535202	−	0.0157149i
$556$	6.22416	+	7.18306i	0.263963	+	0.304630i
$557$	34.3818	−	22.0958i	1.45680	−	0.936231i	0.457920	−	0.888993i	$-0.348595\pi$
$557$	34.3818	−	22.0958i	1.45680	−	0.936231i	0.998884	−	0.0472375i	$-0.0150418\pi$
$558$	1.62410	−	1.87431i	0.0687536	−	0.0793459i
$559$	0.893823	−	6.21668i	0.0378047	−	0.262937i
$560$	−2.37300	+	0.696776i	−0.100278	+	0.0294442i
$561$	−11.4235	−	7.34142i	−0.482299	−	0.309955i
$562$	−4.15307	−	28.8853i	−0.175187	−	1.21845i
$563$	1.28821	+	2.82078i	0.0542914	+	0.118882i	0.934834	−	0.355086i	$-0.115549\pi$
$563$	1.28821	+	2.82078i	0.0542914	+	0.118882i	−0.880542	+	0.473968i	$0.842821\pi$
$564$	0.304258	+	0.666232i	0.0128116	+	0.0280534i
$565$	1.10198	+	7.66444i	0.0463607	+	0.322445i
$566$	0.825879	+	0.530760i	0.0347143	+	0.0223095i
$567$	−0.959493	+	0.281733i	−0.0402949	+	0.0118317i
$568$	0.868600	−	6.04124i	0.0364456	−	0.253485i
$569$	17.3665	−	20.0420i	0.728040	−	0.840203i	−0.264210	−	0.964465i	$-0.585111\pi$
$569$	17.3665	−	20.0420i	0.728040	−	0.840203i	0.992249	+	0.124263i	$0.0396565\pi$
$570$	−3.82502	+	2.45819i	−0.160212	+	0.102962i
$571$	17.8588	+	20.6102i	0.747369	+	0.862510i	0.994310	−	0.106521i	$-0.0339710\pi$
$571$	17.8588	+	20.6102i	0.747369	+	0.862510i	−0.246942	+	0.969030i	$0.579426\pi$
$572$	4.02264	+	1.18115i	0.168195	+	0.0493866i
$573$	−8.78599	+	19.2386i	−0.367040	+	0.803705i
$574$	1.75669			0.0733226
$575$	4.24604	+	3.26328i	0.177072	+	0.136088i
$576$	1.00000			0.0416667
$577$	13.7879	−	30.1913i	0.573998	−	1.25688i	−0.370643	−	0.928775i	$-0.620863\pi$
$577$	13.7879	−	30.1913i	0.573998	−	1.25688i	0.944641	−	0.328105i	$-0.106410\pi$
$578$	−21.7755	−	6.39385i	−0.905740	−	0.265949i
$579$	−15.9564	−	18.4147i	−0.663127	−	0.765289i
$580$	−16.4303	+	10.5591i	−0.682233	+	0.438444i
$581$	−3.08042	+	3.55500i	−0.127797	+	0.147486i
$582$	−0.341396	+	2.37446i	−0.0141513	+	0.0984247i
$583$	11.9844	−	3.51894i	0.496343	−	0.145739i
$584$	−2.33533	−	1.50082i	−0.0966365	−	0.0621045i
$585$	−0.684654	−	4.76188i	−0.0283070	−	0.196879i
$586$	−2.21283	−	4.84543i	−0.0914112	−	0.200163i
$587$	−1.80462	−	3.95156i	−0.0744846	−	0.163099i	0.868727	−	0.495292i	$-0.164939\pi$
$587$	−1.80462	−	3.95156i	−0.0744846	−	0.163099i	−0.943211	+	0.332193i	$0.892211\pi$
$588$	0.142315	+	0.989821i	0.00586897	+	0.0408195i
$589$	−3.83567	−	2.46504i	−0.158046	−	0.101570i
$590$	11.5488	−	3.39103i	0.475456	−	0.139606i
$591$	−1.78409	+	12.4086i	−0.0733876	+	0.510422i
$592$	0.347949	−	0.401554i	0.0143006	−	0.0165038i
$593$	22.3430	−	14.3590i	0.917516	−	0.589651i	0.00557984	−	0.999984i	$-0.498224\pi$
$593$	22.3430	−	14.3590i	0.917516	−	0.589651i	0.911936	+	0.410333i	$0.134588\pi$
$594$	−1.41141	−	1.62886i	−0.0579109	−	0.0668327i
$595$	14.9508	+	4.38995i	0.612923	+	0.179970i
$596$	−0.0344979	+	0.0755398i	−0.00141309	+	0.00309423i
$597$	6.85895			0.280718
$598$	4.57420	−	8.13047i	0.187053	−	0.332480i
$599$	−12.3054			−0.502783			−0.251392	−	0.967885i	$-0.580888\pi$
$599$	−12.3054			−0.502783			−0.251392	+	0.967885i	$0.580888\pi$
$600$	−0.463865	+	1.01572i	−0.0189372	+	0.0414667i
$601$	−4.99738	−	1.46736i	−0.203847	−	0.0598550i	0.178215	−	0.983992i	$-0.442968\pi$
$601$	−4.99738	−	1.46736i	−0.203847	−	0.0598550i	−0.382062	+	0.924137i	$0.624786\pi$
$602$	2.11439	+	2.44014i	0.0861761	+	0.0994525i
$603$	−7.06533	+	4.54061i	−0.287722	+	0.184908i
$604$	7.33355	−	8.46337i	0.298398	−	0.344370i
$605$	2.23668	−	15.5565i	0.0909341	−	0.632461i
$606$	−3.11143	+	0.913597i	−0.126393	+	0.0371123i
$607$	−33.3254	−	21.4169i	−1.35264	−	0.869286i	−0.354793	−	0.934945i	$-0.615449\pi$
$607$	−33.3254	−	21.4169i	−1.35264	−	0.869286i	−0.997842	+	0.0656592i	$0.979085\pi$
$608$	−0.261638	−	1.81973i	−0.0106108	−	0.0737999i
$609$	3.28054	+	7.18339i	0.132934	+	0.291086i
$610$	8.52541	+	18.6680i	0.345184	+	0.755847i
$611$	0.202757	+	1.41020i	0.00820266	+	0.0570507i
$612$	−5.30022	−	3.40624i	−0.214249	−	0.137689i
$613$	9.90170	−	2.90740i	0.399926	−	0.117429i	−0.0755834	−	0.997139i	$-0.524082\pi$
$613$	9.90170	−	2.90740i	0.399926	−	0.117429i	0.475509	+	0.879711i	$0.342264\pi$
$614$	3.06171	−	21.2946i	0.123560	−	0.859381i
$615$	2.84511	−	3.28343i	0.114726	−	0.132401i
$616$	−1.81314	+	1.16523i	−0.0730535	+	0.0469486i
$617$	5.18143	+	5.97969i	0.208596	+	0.240733i	0.850401	−	0.526135i	$-0.176359\pi$
$617$	5.18143	+	5.97969i	0.208596	+	0.240733i	−0.641805	+	0.766868i	$0.721814\pi$
$618$	−13.4065	−	3.93649i	−0.539287	−	0.158349i
$619$	−11.6541	+	25.5190i	−0.468420	+	1.02570i	0.517067	+	0.855945i	$0.327024\pi$
$619$	−11.6541	+	25.5190i	−0.468420	+	1.02570i	−0.985487	+	0.169751i	$0.945704\pi$
$620$	−6.13366			−0.246334
$621$	−4.23798	+	2.24490i	−0.170064	+	0.0900846i
$622$	18.5588			0.744138
$623$	−1.25717	+	2.75282i	−0.0503674	+	0.110289i
$624$	1.86641	+	0.548027i	0.0747162	+	0.0219387i
$625$	19.2112	+	22.1709i	0.768447	+	0.886835i
$626$	−8.07013	+	5.18636i	−0.322547	+	0.207289i
$627$	−2.59480	+	2.99456i	−0.103626	+	0.119591i
$628$	2.39767	−	16.6762i	0.0956776	−	0.665452i
$629$	−3.21199	+	0.943126i	−0.128071	+	0.0376049i
$630$	2.08057	+	1.33710i	0.0828920	+	0.0532715i
$631$	−2.41829	−	16.8196i	−0.0962705	−	0.669576i	−0.979620	−	0.200861i	$-0.935626\pi$
$631$	−2.41829	−	16.8196i	−0.0962705	−	0.669576i	0.883349	−	0.468715i	$-0.155283\pi$
$632$	3.23953	+	7.09357i	0.128861	+	0.282167i
$633$	3.76385	+	8.24167i	0.149599	+	0.327577i
$634$	2.05113	+	14.2659i	0.0814607	+	0.566571i
$635$	4.35129	+	2.79641i	0.172676	+	0.110972i
$636$	5.56047	−	1.63270i	0.220487	−	0.0647408i
$637$	−0.276831	+	1.92540i	−0.0109685	+	0.0762873i
$638$	−11.1459	+	12.8631i	−0.441272	+	0.509255i
$639$	−5.13448	+	3.29973i	−0.203117	+	0.130535i
$640$	−1.61959	−	1.86911i	−0.0640199	−	0.0738829i
$641$	−15.0146	−	4.40869i	−0.593042	−	0.174133i	−0.0285792	−	0.999592i	$-0.509098\pi$
$641$	−15.0146	−	4.40869i	−0.593042	−	0.174133i	−0.564462	+	0.825459i	$0.690916\pi$
$642$	−0.726726	+	1.59131i	−0.0286816	+	0.0628039i
$643$	2.65128			0.104556			0.0522782	−	0.998633i	$-0.483352\pi$
$643$	2.65128			0.104556			0.0522782	+	0.998633i	$0.483352\pi$
$644$	1.61892	+	4.51432i	0.0637944	+	0.177889i
$645$	7.98532			0.314422
$646$	−4.81171	+	10.5362i	−0.189314	+	0.414540i
$647$	38.5310	+	11.3137i	1.51481	+	0.444788i	0.930361	−	0.366644i	$-0.119493\pi$
$647$	38.5310	+	11.3137i	1.51481	+	0.444788i	0.584447	+	0.811432i	$0.301312\pi$
$648$	−0.654861	−	0.755750i	−0.0257254	−	0.0296886i
$649$	8.82409	−	5.67090i	0.346376	−	0.222602i
$650$	−1.42240	+	1.64154i	−0.0557913	+	0.0643866i
$651$	−0.352951	+	2.45483i	−0.0138332	+	0.0962122i
$652$	−10.0597	+	2.95378i	−0.393966	+	0.115679i
$653$	−18.6538	−	11.9881i	−0.729981	−	0.469130i	0.122115	−	0.992516i	$-0.461032\pi$
$653$	−18.6538	−	11.9881i	−0.729981	−	0.469130i	−0.852096	+	0.523386i	$0.824669\pi$
$654$	−0.397841	−	2.76704i	−0.0155568	−	0.108200i
$655$	21.5742	+	47.2409i	0.842973	+	1.84585i
$656$	0.729753	+	1.59794i	0.0284921	+	0.0623890i
$657$	0.395067	+	2.74775i	0.0154130	+	0.107200i
$658$	−0.616150	−	0.395976i	−0.0240200	−	0.0154367i
$659$	13.1386	−	3.85785i	0.511808	−	0.150280i	−0.0156235	−	0.999878i	$-0.504973\pi$
$659$	13.1386	−	3.85785i	0.511808	−	0.150280i	0.527431	+	0.849598i	$0.323155\pi$
$660$	−0.758597	+	5.27615i	−0.0295283	+	0.205374i
$661$	−13.9723	+	16.1248i	−0.543458	+	0.627184i	−0.959346	−	0.282232i	$-0.908925\pi$
$661$	−13.9723	+	16.1248i	−0.543458	+	0.627184i	0.415888	+	0.909416i	$0.363471\pi$
$662$	−10.8057	+	6.94437i	−0.419974	+	0.269901i
$663$	−8.02566	−	9.26210i	−0.311691	−	0.359710i
$664$	−4.51339	−	1.32525i	−0.175154	−	0.0514297i
$665$	1.88881	−	4.13592i	0.0732450	−	0.160384i
$666$	−0.531332			−0.0205887
$667$	22.3105	+	30.6038i	0.863865	+	1.18498i
$668$	4.46751			0.172853
$669$	−2.64840	+	5.79918i	−0.102393	+	0.224209i
$670$	19.9298	+	5.85192i	0.769956	+	0.226080i
$671$	11.7120	+	13.5163i	0.452136	+	0.521793i
$672$	−0.841254	+	0.540641i	−0.0324521	+	0.0208557i
$673$	19.0716	−	22.0098i	0.735156	−	0.848416i	−0.257886	−	0.966175i	$-0.583026\pi$
$673$	19.0716	−	22.0098i	0.735156	−	0.848416i	0.993042	+	0.117760i	$0.0375712\pi$
$674$	0.0828177	−	0.576010i	0.00319002	−	0.0221871i
$675$	1.07140	−	0.314591i	0.0412381	−	0.0121086i
$676$	−7.75315	−	4.98264i	−0.298198	−	0.191640i
$677$	0.550830	+	3.83110i	0.0211701	+	0.147241i	0.997665	−	0.0683000i	$-0.0217575\pi$
$677$	0.550830	+	3.83110i	0.0211701	+	0.147241i	−0.976495	+	0.215541i	$0.930848\pi$
$678$	1.30062	+	2.84796i	0.0499499	+	0.109375i
$679$	−0.996531	−	2.18210i	−0.0382434	−	0.0837413i
$680$	2.21755	+	15.4234i	0.0850391	+	0.591460i
$681$	24.9334	+	16.0238i	0.955452	+	0.614032i
$682$	−5.12873	+	1.50593i	−0.196389	+	0.0576651i
$683$	5.08514	−	35.3679i	0.194577	−	1.35332i	−0.625124	−	0.780525i	$-0.714952\pi$
$683$	5.08514	−	35.3679i	0.194577	−	1.35332i	0.819702	−	0.572791i	$-0.194139\pi$
$684$	−1.20393	+	1.38940i	−0.0460332	+	0.0531252i
$685$	−20.9245	+	13.4473i	−0.799483	+	0.513796i
$686$	−0.654861	−	0.755750i	−0.0250027	−	0.0288547i
$687$	−9.55692	−	2.80617i	−0.364619	−	0.107062i
$688$	−1.34128	+	2.93699i	−0.0511357	+	0.111972i
$689$	11.2729			0.429463
$690$	11.0597	+	4.28541i	0.421037	+	0.163143i
$691$	−50.4371			−1.91872			−0.959359	−	0.282189i	$-0.908940\pi$
$691$	−50.4371			−1.91872			−0.959359	+	0.282189i	$0.908940\pi$
$692$	9.85149	−	21.5718i	0.374497	−	0.820035i
$693$	2.06798	+	0.607214i	0.0785561	+	0.0230661i
$694$	−12.5915	−	14.5313i	−0.477966	−	0.551602i
$695$	−19.7749	+	12.7086i	−0.750105	+	0.482063i
$696$	−5.17145	+	5.96817i	−0.196023	+	0.226223i
$697$	1.57511	−	10.9551i	0.0596615	−	0.414955i
$698$	9.95796	−	2.92392i	0.376914	−	0.110672i
$699$	−14.7882	−	9.50381i	−0.559341	−	0.359467i
$700$	−0.158913	−	1.10526i	−0.00600634	−	0.0417750i
$701$	21.7903	+	47.7140i	0.823007	+	1.80213i	0.536037	+	0.844195i	$0.319921\pi$
$701$	21.7903	+	47.7140i	0.823007	+	1.80213i	0.286971	+	0.957939i	$0.407352\pi$
$702$	−0.808067	−	1.76942i	−0.0304985	−	0.0667824i
$703$	0.139017	+	0.966882i	0.00524311	+	0.0364667i
$704$	−1.81314	−	1.16523i	−0.0683353	−	0.0439164i
$705$	−1.73803	+	0.510332i	−0.0654581	+	0.0192202i
$706$	−0.819061	+	5.69669i	−0.0308258	+	0.214398i
$707$	2.12357	−	2.45073i	0.0798651	−	0.0921692i
$708$	4.09417	−	2.63116i	0.153868	−	0.0988851i
$709$	−9.14213	−	10.5506i	−0.343340	−	0.396235i	0.557649	−	0.830077i	$-0.311703\pi$
$709$	−9.14213	−	10.5506i	−0.343340	−	0.396235i	−0.900989	+	0.433841i	$0.857158\pi$
$710$	14.4833	+	4.25268i	0.543548	+	0.159600i
$711$	3.23953	−	7.09357i	0.121492	−	0.266030i
$712$	−3.02630			−0.113415
$713$	0.698169	+	11.8735i	0.0261466	+	0.444666i
$714$	6.30038			0.235786
$715$	−4.30733	+	9.43173i	−0.161085	+	0.352727i
$716$	18.0159	+	5.28993i	0.673284	+	0.197694i
$717$	4.24456	+	4.89848i	0.158516	+	0.182937i
$718$	−21.4994	+	13.8168i	−0.802350	+	0.515639i
$719$	−12.6668	+	14.6183i	−0.472392	+	0.545169i	−0.941075	−	0.338197i	$-0.890183\pi$
$719$	−12.6668	+	14.6183i	−0.472392	+	0.545169i	0.468684	+	0.883366i	$0.344728\pi$
$720$	−0.351971	+	2.44801i	−0.0131172	+	0.0912319i
$721$	13.4065	−	3.93649i	0.499283	−	0.146603i
$722$	−13.1405	−	8.44487i	−0.489038	−	0.314286i
$723$	−0.0394401	−	0.274312i	−0.00146679	−	0.0102018i
$724$	−1.83047	−	4.00816i	−0.0680287	−	0.148962i
$725$	−3.66315	−	8.02118i	−0.136046	−	0.297899i
$726$	−0.904375	−	6.29007i	−0.0335645	−	0.233446i
$727$	40.5055	+	26.0313i	1.50227	+	0.965448i	0.994588	+	0.103901i	$0.0331326\pi$
$727$	40.5055	+	26.0313i	1.50227	+	0.965448i	0.507678	+	0.861547i	$0.330504\pi$
$728$	−1.86641	+	0.548027i	−0.0691737	+	0.0203112i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	4.49599	−	5.18865i	0.166404	−	0.192041i
$731$	17.1131	−	10.9979i	0.632952	−	0.406774i
$732$	5.43408	+	6.27126i	0.200849	+	0.231792i
$733$	−17.5467	−	5.15219i	−0.648104	−	0.190300i	−0.0588733	−	0.998265i	$-0.518751\pi$
$733$	−17.5467	−	5.15219i	−0.648104	−	0.190300i	−0.589230	+	0.807965i	$0.700569\pi$
$734$	8.08600	−	17.7059i	0.298460	−	0.653535i
$735$	−2.47318			−0.0912247
$736$	−3.43385	+	3.34794i	−0.126573	+	0.123407i
$737$	18.1013			0.666771
$738$	0.729753	−	1.59794i	0.0268626	−	0.0588209i
$739$	−9.43715	−	2.77100i	−0.347151	−	0.101933i	0.103509	−	0.994629i	$-0.466993\pi$
$739$	−9.43715	−	2.77100i	−0.347151	−	0.101933i	−0.450660	+	0.892696i	$0.648811\pi$
$740$	0.860540	+	0.993116i	0.0316341	+	0.0365077i
$741$	−3.00845	+	1.93341i	−0.110518	+	0.0710257i
$742$	−3.79506	+	4.37973i	−0.139321	+	0.160785i
$743$	1.06602	−	7.41435i	0.0391086	−	0.272006i	−0.960879	−	0.276968i	$-0.910670\pi$
$743$	1.06602	−	7.41435i	0.0391086	−	0.272006i	0.999988	+	0.00496200i	$0.00157946\pi$
$744$	−2.37961	+	0.698716i	−0.0872407	+	0.0256162i
$745$	−0.172780	−	0.111039i	−0.00633016	−	0.00406815i
$746$	3.43060	+	23.8603i	0.125603	+	0.873589i
$747$	1.95408	+	4.27885i	0.0714962	+	0.156555i
$748$	5.64096	+	12.3520i	0.206254	+	0.451633i
$749$	−0.248965	−	1.73159i	−0.00909699	−	0.0632709i
$750$	8.07964	+	5.19247i	0.295027	+	0.189602i
$751$	−34.5147	+	10.1344i	−1.25946	+	0.369811i	−0.842294	−	0.539019i	$-0.818795\pi$
$751$	−34.5147	+	10.1344i	−1.25946	+	0.369811i	−0.417167	+	0.908830i	$0.636977\pi$
$752$	0.104234	−	0.724964i	0.00380103	−	0.0264367i
$753$	15.6768	−	18.0920i	0.571294	−	0.659308i
$754$	−12.9228	+	8.30496i	−0.470620	+	0.302449i
$755$	18.1372	+	20.9315i	0.660080	+	0.761773i
$756$	0.959493	+	0.281733i	0.0348964	+	0.0102465i
$757$	14.3608	−	31.4458i	0.521952	−	1.14292i	−0.446743	−	0.894662i	$-0.647416\pi$
$757$	14.3608	−	31.4458i	0.521952	−	1.14292i	0.968695	−	0.248253i	$-0.0798565\pi$
$758$	−14.2310			−0.516893
$759$	10.2999	+	0.867922i	0.373862	+	0.0315036i
$760$	4.54681			0.164930
$761$	−2.58751	+	5.66586i	−0.0937973	+	0.205387i	−0.950715	−	0.310065i	$-0.899649\pi$
$761$	−2.58751	+	5.66586i	−0.0937973	+	0.205387i	0.856918	+	0.515453i	$0.172376\pi$
$762$	2.00667	+	0.589213i	0.0726942	+	0.0213449i
$763$	1.83066	+	2.11269i	0.0662744	+	0.0764847i
$764$	17.7924	−	11.4345i	0.643708	−	0.413686i
$765$	10.2040	−	11.7761i	0.368927	−	0.425765i
$766$	−2.76872	+	19.2569i	−0.100038	+	0.695779i
$767$	9.08334	−	2.66711i	0.327980	−	0.0963037i
$768$	−0.841254	−	0.540641i	−0.0303561	−	0.0195087i
$769$	0.276091	+	1.92026i	0.00995610	+	0.0692462i	0.994194	−	0.107605i	$-0.0343181\pi$
$769$	0.276091	+	1.92026i	0.00995610	+	0.0692462i	−0.984238	+	0.176851i	$0.943409\pi$
$770$	−2.21433	−	4.84871i	−0.0797990	−	0.174735i
$771$	11.4960	+	25.1727i	0.414018	+	0.906574i
$772$	3.46767	+	24.1181i	0.124804	+	0.868031i
$773$	−28.5059	−	18.3196i	−1.02529	−	0.658912i	−0.0839811	−	0.996467i	$-0.526764\pi$
$773$	−28.5059	−	18.3196i	−1.02529	−	0.658912i	−0.941306	+	0.337556i	$0.890400\pi$
$774$	3.09798	−	0.909648i	0.111354	−	0.0326966i
$775$	0.394115	−	2.74113i	0.0141570	−	0.0984643i
$776$	1.57093	−	1.81295i	0.0563932	−	0.0650812i
$777$	0.446985	−	0.287260i	0.0160355	−	0.0103054i
$778$	−11.0552	−	12.7584i	−0.396349	−	0.457411i
$779$	−3.09875	−	0.909875i	−0.111024	−	0.0325996i
$780$	−1.99850	+	4.37610i	−0.0715577	+	0.156689i
$781$	13.1545			0.470705
$782$	29.6040	−	6.04828i	1.05864	−	0.216286i
$783$	7.89703			0.282217
$784$	0.415415	−	0.909632i	0.0148363	−	0.0324869i
$785$	39.9795	+	11.7391i	1.42693	+	0.418985i
$786$	13.7513	+	15.8699i	0.490494	+	0.566060i
$787$	−19.9983	+	12.8521i	−0.712862	+	0.458129i	−0.846147	−	0.532949i	$-0.821084\pi$
$787$	−19.9983	+	12.8521i	−0.712862	+	0.458129i	0.133285	+	0.991078i	$0.457447\pi$
$788$	8.20947	−	9.47423i	0.292450	−	0.337506i
$789$	1.79580	−	12.4901i	0.0639322	−	0.444658i
$790$	−18.5053	+	5.43366i	−0.658391	+	0.193321i
$791$	−2.63387	−	1.69269i	−0.0936497	−	0.0601850i
$792$	0.306729	+	2.13335i	0.0108991	+	0.0758052i
$793$	6.70539	+	14.6828i	0.238115	+	0.521400i
$794$	−6.40387	−	14.0225i	−0.227265	−	0.497641i
$795$	2.03975	+	14.1867i	0.0723423	+	0.503152i
$796$	−5.77012	−	3.70823i	−0.204516	−	0.131435i
$797$	−33.8606	+	9.94237i	−1.19940	+	0.352177i	−0.819625	−	0.572900i	$-0.805818\pi$
$797$	−33.8606	+	9.94237i	−1.19940	+	0.352177i	−0.379779	+	0.925077i	$0.624000\pi$
$798$	0.261638	−	1.81973i	0.00926188	−	0.0644178i
$799$	−3.02187	+	3.48742i	−0.106906	+	0.123376i
$800$	0.939368	−	0.603695i	0.0332117	−	0.0213439i
$801$	1.98180	+	2.28712i	0.0700235	+	0.0808115i
$802$	−31.8216	−	9.34366i	−1.12366	−	0.329936i
$803$	2.48546	−	5.44241i	0.0877101	−	0.192058i
$804$	8.39857			0.296195
$805$	−11.6209	+	2.37422i	−0.409583	+	0.0836804i
$806$	−4.82424			−0.169927
$807$	3.25733	−	7.13255i	0.114663	−	0.251078i
$808$	3.11143	+	0.913597i	0.109460	+	0.0321402i
$809$	12.3686	+	14.2741i	0.434856	+	0.501851i	0.930305	−	0.366786i	$-0.119542\pi$
$809$	12.3686	+	14.2741i	0.434856	+	0.501851i	−0.495449	+	0.868637i	$0.664996\pi$
$810$	2.08057	−	1.33710i	0.0731039	−	0.0469810i
$811$	−12.1713	+	14.0464i	−0.427392	+	0.493237i	−0.928075	−	0.372394i	$-0.878537\pi$
$811$	−12.1713	+	14.0464i	−0.427392	+	0.493237i	0.500683	+	0.865631i	$0.333082\pi$
$812$	1.12386	−	7.81664i	0.0394399	−	0.274310i
$813$	−12.1539	+	3.56871i	−0.426256	+	0.125160i
$814$	0.963380	+	0.619127i	0.0337665	+	0.0217004i
$815$	−3.69018	−	25.6658i	−0.129261	−	0.899032i
$816$	2.61727	+	5.73103i	0.0916228	+	0.200626i
$817$	−2.46586	−	5.39949i	−0.0862696	−	0.188904i
$818$	4.32035	+	30.0487i	0.151057	+	1.05063i
$819$	1.63641	+	1.05166i	0.0571808	+	0.0367479i
$820$	−4.16862	+	1.22402i	−0.145574	+	0.0427445i
$821$	−5.85159	+	40.6987i	−0.204222	+	1.42039i	0.587357	+	0.809328i	$0.300168\pi$
$821$	−5.85159	+	40.6987i	−0.204222	+	1.42039i	−0.791579	+	0.611066i	$0.790741\pi$
$822$	−6.58598	+	7.60063i	−0.229712	+	0.265102i
$823$	−1.96900	+	1.26540i	−0.0686349	+	0.0441090i	−0.574508	−	0.818499i	$-0.694807\pi$
$823$	−1.96900	+	1.26540i	−0.0686349	+	0.0441090i	0.505873	+	0.862608i	$0.331170\pi$
$824$	9.15001	+	10.5597i	0.318756	+	0.367864i
$825$	−2.30917	−	0.678033i	−0.0803949	−	0.0236061i
$826$	−2.02172	+	4.42695i	−0.0703446	+	0.154033i
$827$	33.6067			1.16862			0.584309	−	0.811531i	$-0.301366\pi$
$827$	33.6067			1.16862			0.584309	+	0.811531i	$0.301366\pi$
$828$	4.77889	+	0.402695i	0.166078	+	0.0139946i
$829$	−44.0398			−1.52957			−0.764783	−	0.644288i	$-0.777154\pi$
$829$	−44.0398			−1.52957			−0.764783	+	0.644288i	$0.777154\pi$
$830$	4.83281	−	10.5824i	0.167749	−	0.367320i
$831$	−13.5030	−	3.96485i	−0.468415	−	0.137539i
$832$	−1.27384	−	1.47009i	−0.0441624	−	0.0509661i
$833$	−5.30022	+	3.40624i	−0.183642	+	0.118019i
$834$	−6.22416	+	7.18306i	−0.215525	+	0.248729i
$835$	−1.57243	+	10.9365i	−0.0544162	+	0.378473i
$836$	3.80187	−	1.11633i	0.131490	−	0.0386090i
$837$	2.08637	+	1.34083i	0.0721154	+	0.0463457i
$838$	−2.17983	−	15.1610i	−0.0753009	−	0.523729i
$839$	14.5049	+	31.7613i	0.500765	+	1.09652i	0.976220	+	0.216782i	$0.0695561\pi$
$839$	14.5049	+	31.7613i	0.500765	+	1.09652i	−0.475455	+	0.879740i	$0.657717\pi$
$840$	−1.02740	−	2.24969i	−0.0354486	−	0.0776215i
$841$	−4.74805	−	33.0234i	−0.163726	−	1.13874i
$842$	−22.0934	−	14.1985i	−0.761387	−	0.489314i
$843$	28.0002	−	8.22160i	0.964379	−	0.283167i
$844$	1.28944	−	8.96822i	0.0443842	−	0.308699i
$845$	14.9264	−	17.2260i	0.513485	−	0.592593i
$846$	−0.616150	+	0.395976i	−0.0211837	+	0.0136139i
$847$	4.16148	+	4.80260i	0.142990	+	0.165019i
$848$	−5.56047	−	1.63270i	−0.190947	−	0.0560672i
$849$	−0.407823	+	0.893008i	−0.0139964	+	0.0306479i
$850$	−7.03519			−0.241305
$851$	1.82451	−	1.77887i	0.0625435	−	0.0609788i
$852$	6.10337			0.209098
$853$	−20.5325	+	44.9599i	−0.703019	+	1.53940i	0.133253	+	0.991082i	$0.457458\pi$
$853$	−20.5325	+	44.9599i	−0.703019	+	1.53940i	−0.836272	+	0.548315i	$0.815269\pi$
$854$	−7.96193	−	2.33783i	−0.272452	−	0.0799991i
$855$	−2.97753	−	3.43625i	−0.101829	−	0.117517i
$856$	1.47169	−	0.945795i	0.0503012	−	0.0323266i
$857$	15.0681	−	17.3895i	0.514715	−	0.594013i	−0.437584	−	0.899177i	$-0.644166\pi$
$857$	15.0681	−	17.3895i	0.514715	−	0.594013i	0.952300	+	0.305164i	$0.0987113\pi$
$858$	−0.596650	+	4.14979i	−0.0203693	+	0.141672i
$859$	−49.4241	+	14.5122i	−1.68633	+	0.495151i	−0.977625	−	0.210355i	$-0.932538\pi$
$859$	−49.4241	+	14.5122i	−1.68633	+	0.495151i	−0.708704	+	0.705506i	$0.750720\pi$
$860$	−6.71768	−	4.31719i	−0.229071	−	0.147215i
$861$	0.250002	+	1.73880i	0.00852006	+	0.0592583i
$862$	0.0155064	+	0.0339543i	0.000528151	+	0.00115649i
$863$	−7.30784	−	16.0019i	−0.248762	−	0.544712i	0.743520	−	0.668713i	$-0.233155\pi$
$863$	−7.30784	−	16.0019i	−0.248762	−	0.544712i	−0.992282	+	0.124001i	$0.960427\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	49.3404	+	31.7092i	1.67762	+	1.07814i
$866$	−22.6623	+	6.65425i	−0.770096	+	0.226121i
$867$	3.22980	−	22.4638i	0.109690	−	0.762909i
$868$	1.62410	−	1.87431i	0.0551255	−	0.0636183i
$869$	−14.1394	+	9.08683i	−0.479646	+	0.308250i
$870$	−12.7899	−	14.7604i	−0.433620	−	0.500424i
$871$	15.6752	+	4.60265i	0.531133	+	0.155955i
$872$	−1.16129	+	2.54287i	−0.0393263	+	0.0861125i
$873$	−2.39888			−0.0811898
$874$	−0.517544	−	8.80167i	−0.0175062	−	0.297721i
$875$	−9.60428			−0.324684
$876$	1.15320	−	2.52515i	0.0389629	−	0.0853168i
$877$	52.7209	+	15.4803i	1.78026	+	0.522731i	0.995302	−	0.0968197i	$-0.0308670\pi$
$877$	52.7209	+	15.4803i	1.78026	+	0.522731i	0.784957	+	0.619551i	$0.212685\pi$
$878$	2.44050	+	2.81649i	0.0823628	+	0.0950518i
$879$	4.48119	−	2.87988i	0.151147	−	0.0971361i
$880$	3.49068	−	4.02846i	0.117671	−	0.135799i
$881$	6.46763	−	44.9834i	0.217900	−	1.51553i	−0.527870	−	0.849325i	$-0.677009\pi$
$881$	6.46763	−	44.9834i	0.217900	−	1.51553i	0.745770	−	0.666203i	$-0.232082\pi$
$882$	−0.959493	+	0.281733i	−0.0323078	+	0.00948643i
$883$	−17.0823	−	10.9781i	−0.574866	−	0.369444i	0.220672	−	0.975348i	$-0.429175\pi$
$883$	−17.0823	−	10.9781i	−0.574866	−	0.369444i	−0.795538	+	0.605904i	$0.792811\pi$
$884$	1.74414	+	12.1308i	0.0586619	+	0.408002i
$885$	5.00008	+	10.9486i	0.168076	+	0.368035i
$886$	16.2922	+	35.6749i	0.547347	+	1.19852i
$887$	5.20272	+	36.1857i	0.174690	+	1.21500i	0.868813	+	0.495140i	$0.164883\pi$
$887$	5.20272	+	36.1857i	0.174690	+	1.21500i	−0.694123	+	0.719856i	$0.744208\pi$
$888$	0.446985	+	0.287260i	0.0149998	+	0.00963981i
$889$	−2.00667	+	0.589213i	−0.0673017	+	0.0197616i
$890$	1.06517	−	7.40840i	0.0357045	−	0.248330i
$891$	1.41141	−	1.62886i	0.0472841	−	0.0545687i
$892$	5.36325	−	3.44675i	0.179575	−	0.115406i
$893$	0.881778	+	1.01763i	0.0295076	+	0.0340536i
$894$	−0.0796805	−	0.0233963i	−0.00266491	−	0.000782489i
$895$	−19.2908	+	42.2411i	−0.644822	+	1.41196i
$896$	1.00000			0.0334077
$897$	8.69869	+	3.37056i	0.290441	+	0.112540i
$898$	−17.7753			−0.593168
$899$	8.13597	−	17.8153i	0.271350	−	0.594173i
$900$	−1.07140	−	0.314591i	−0.0357133	−	0.0104864i
$901$	23.9103	+	27.5940i	0.796568	+	0.919289i
$902$	−3.18512	+	2.04695i	−0.106053	+	0.0681560i
$903$	−2.11439	+	2.44014i	−0.0703625	+	0.0812027i
$904$	0.445572	−	3.09902i	0.0148195	−	0.103072i
$905$	10.4563	−	3.07024i	0.347579	−	0.102058i
$906$	9.42090	+	6.05444i	0.312988	+	0.201145i
$907$	−5.19606	−	36.1394i	−0.172532	−	1.19999i	−0.873510	−	0.486805i	$-0.838162\pi$
$907$	−5.19606	−	36.1394i	−0.172532	−	1.19999i	0.700978	−	0.713183i	$-0.252747\pi$
$908$	−12.3123	−	26.9601i	−0.408597	−	0.894702i
$909$	−1.34710	−	2.94974i	−0.0446805	−	0.0978366i
$910$	−0.684654	−	4.76188i	−0.0226961	−	0.157855i
$911$	−47.7483	−	30.6859i	−1.58197	−	1.01667i	−0.975071	−	0.221891i	$-0.928777\pi$
$911$	−47.7483	−	30.6859i	−1.58197	−	1.01667i	−0.606899	−	0.794779i	$-0.707587\pi$
$912$	1.76398	−	0.517950i	0.0584110	−	0.0171510i
$913$	1.44283	−	10.0351i	0.0477508	−	0.332114i
$914$	−12.3100	+	14.2065i	−0.407178	+	0.469909i
$915$	−17.2647	+	11.0954i	−0.570754	+	0.366802i
$916$	6.52267	+	7.52756i	0.215515	+	0.248718i
$917$	−20.1483	−	5.91607i	−0.665355	−	0.195366i
$918$	2.61727	−	5.73103i	0.0863828	−	0.189152i
$919$	9.79790			0.323203			0.161601	−	0.986856i	$-0.448334\pi$
$919$	9.79790			0.323203			0.161601	+	0.986856i	$0.448334\pi$
$920$	−6.98717	−	9.58446i	−0.230360	−	0.315990i
$921$	21.5136			0.708897
$922$	0.729429	−	1.59723i	0.0240225	−	0.0526019i
$923$	11.3914	+	3.34481i	0.374952	+	0.110096i
$924$	−1.41141	−	1.62886i	−0.0464320	−	0.0535854i
$925$	−0.499117	+	0.320763i	−0.0164109	+	0.0105466i
$926$	−18.9537	+	21.8737i	−0.622857	+	0.718815i
$927$	1.98849	−	13.8302i	0.0653105	−	0.454244i
$928$	7.57714	−	2.22485i	0.248732	−	0.0730343i
$929$	30.7487	+	19.7610i	1.00883	+	0.648337i	0.937091	−	0.349086i	$-0.113508\pi$
$929$	30.7487	+	19.7610i	1.00883	+	0.648337i	0.0717416	+	0.997423i	$0.477144\pi$
$930$	−0.872911	−	6.07123i	−0.0286239	−	0.199083i
$931$	0.763718	+	1.67231i	0.0250298	+	0.0548077i
$932$	7.30249	+	15.9902i	0.239201	+	0.523777i
$933$	2.64119	+	18.3699i	0.0864686	+	0.601402i
$934$	−29.3707	−	18.8754i	−0.961040	−	0.617623i
$935$	−32.2232	+	9.46159i	−1.05381	+	0.309427i
$936$	−0.276831	+	1.92540i	−0.00904852	+	0.0629338i
$937$	17.2740	−	19.9353i	0.564317	−	0.651256i	−0.399841	−	0.916584i	$-0.630935\pi$
$937$	17.2740	−	19.9353i	0.564317	−	0.651256i	0.964158	+	0.265328i	$0.0854802\pi$
$938$	−7.06533	+	4.54061i	−0.230691	+	0.148256i
$939$	−6.28207	−	7.24989i	−0.205008	−	0.236591i
$940$	1.73803	+	0.510332i	0.0566883	+	0.0166452i
$941$	1.88606	−	4.12990i	0.0614839	−	0.134631i	−0.876396	−	0.481591i	$-0.840059\pi$
$941$	1.88606	−	4.12990i	0.0614839	−	0.134631i	0.937880	+	0.346960i	$0.112786\pi$
$942$	16.8477			0.548927
$943$	2.84393	+	7.93024i	0.0926112	+	0.258244i
$944$	−4.86674			−0.158399
$945$	−1.02740	+	2.24969i	−0.0334212	+	0.0731823i
$946$	−6.67702	−	1.96055i	−0.217089	−	0.0637430i
$947$	3.76778	+	4.34825i	0.122436	+	0.141299i	0.813658	−	0.581343i	$-0.197473\pi$
$947$	3.76778	+	4.34825i	0.122436	+	0.141299i	−0.691222	+	0.722643i	$0.742927\pi$
$948$	−6.56034	+	4.21607i	−0.213070	+	0.136932i
$949$	3.53618	−	4.08097i	0.114789	−	0.132474i
$950$	−0.292153	+	2.03197i	−0.00947868	+	0.0659257i
$951$	−13.8288	+	4.06050i	−0.448429	+	0.131671i
$952$	−5.30022	−	3.40624i	−0.171781	−	0.110397i
$953$	−0.897091	−	6.23940i	−0.0290596	−	0.202114i	0.970119	−	0.242628i	$-0.0780095\pi$
$953$	−0.897091	−	6.23940i	−0.0290596	−	0.202114i	−0.999179	+	0.0405141i	$0.987100\pi$
$954$	2.40742	+	5.27152i	0.0779431	+	0.170672i
$955$	21.7294	+	47.5806i	0.703145	+	1.53967i
$956$	−0.922431	−	6.41565i	−0.0298335	−	0.207497i
$957$	−14.3184	−	9.20189i	−0.462849	−	0.297455i
$958$	−38.7376	+	11.3744i	−1.25156	+	0.367490i
$959$	1.43127	−	9.95470i	0.0462181	−	0.321454i
$960$	1.61959	−	1.86911i	0.0522720	−	0.0603251i
$961$	−20.9045	+	13.4345i	−0.674340	+	0.433372i
$962$	0.676831	+	0.781105i	0.0218219	+	0.0251838i
$963$	−1.67853	−	0.492862i	−0.0540900	−	0.0158823i
$964$	−0.115125	+	0.252089i	−0.00370793	+	0.00811923i
$965$	−60.2619			−1.93990
$966$	−4.23798	+	2.24490i	−0.136355	+	0.0722284i
$967$	3.23720			0.104101			0.0520506	−	0.998644i	$-0.483424\pi$
$967$	3.23720			0.104101			0.0520506	+	0.998644i	$0.483424\pi$
$968$	−2.63986	+	5.78048i	−0.0848483	+	0.185792i
$969$	−11.1137	−	3.26328i	−0.357024	−	0.104832i
$970$	3.88520	+	4.48376i	0.124746	+	0.143965i
$971$	40.8234	−	26.2356i	1.31009	−	0.841942i	0.315815	−	0.948821i	$-0.397722\pi$
$971$	40.8234	−	26.2356i	1.31009	−	0.841942i	0.994272	+	0.106879i	$0.0340858\pi$
$972$	0.654861	−	0.755750i	0.0210047	−	0.0242407i
$973$	1.35264	−	9.40781i	0.0433636	−	0.301601i
$974$	20.7799	−	6.10153i	0.665831	−	0.195506i
$975$	−1.82726	−	1.17431i	−0.0585193	−	0.0376080i
$976$	−1.18094	−	8.21360i	−0.0378009	−	0.262911i
$977$	20.5438	+	44.9846i	0.657254	+	1.43919i	0.885059	+	0.465479i	$0.154118\pi$
$977$	20.5438	+	44.9846i	0.657254	+	1.43919i	−0.227804	+	0.973707i	$0.573155\pi$
$978$	−4.35535	−	9.53689i	−0.139269	−	0.304956i
$979$	−0.928253	−	6.45614i	−0.0296671	−	0.206339i
$980$	2.08057	+	1.33710i	0.0664615	+	0.0427122i
$981$	2.68226	−	0.787582i	0.0856379	−	0.0251456i
$982$	4.02316	−	27.9817i	0.128384	−	0.892932i
$983$	21.8661	−	25.2348i	0.697420	−	0.804866i	−0.290981	−	0.956729i	$-0.593982\pi$
$983$	21.8661	−	25.2348i	0.697420	−	0.804866i	0.988402	+	0.151863i	$0.0485272\pi$
$984$	−1.47782	+	0.949736i	−0.0471111	+	0.0302765i
$985$	20.3035	+	23.4315i	0.646924	+	0.746590i
$986$	−47.7388	−	14.0174i	−1.52031	−	0.446405i
$987$	0.304258	−	0.666232i	0.00968464	−	0.0212064i
$988$	3.57615			0.113773
$989$	−7.59253	+	13.4954i	−0.241428	+	0.429130i
$990$	−5.33041			−0.169412
$991$	4.40295	−	9.64111i	0.139864	−	0.306260i	−0.826718	−	0.562616i	$-0.809795\pi$
$991$	4.40295	−	9.64111i	0.139864	−	0.306260i	0.966582	+	0.256356i	$0.0825221\pi$
$992$	2.37961	+	0.698716i	0.0755527	+	0.0221843i
$993$	−8.41150	−	9.70738i	−0.266931	−	0.308055i
$994$	−5.13448	+	3.29973i	−0.162856	+	0.104661i
$995$	11.1087	−	12.8201i	0.352169	−	0.406425i
$996$	0.669440	−	4.65606i	0.0212120	−	0.147533i
$997$	−26.7696	+	7.86025i	−0.847800	+	0.248937i	−0.676647	−	0.736308i	$-0.736568\pi$
$997$	−26.7696	+	7.86025i	−0.847800	+	0.248937i	−0.171154	+	0.985244i	$0.554749\pi$
$998$	34.1103	+	21.9214i	1.07974	+	0.693908i
$999$	−0.0756165	−	0.525924i	−0.00239240	−	0.0166395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.673.2	yes	20
23.4	even	11	inner	966.2.q.d.211.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.211.2	✓	20	23.4	even	11	inner
966.2.q.d.673.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.08057 - 1.33710i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(0.959493 + 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(2.08057 - 1.33710i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.142315 + 0.989821i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.351971 - 2.44801i) q^{10} +(-0.895337 - 1.96052i) q^{11} +(-0.415415 - 0.909632i) q^{12} +(-0.276831 - 1.92540i) q^{13} +(0.841254 + 0.540641i) q^{14} +(2.37300 - 0.696776i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(4.12587 - 4.76151i) q^{17} +(0.841254 - 0.540641i) q^{18} +(-1.20393 - 1.38940i) q^{19} +(-2.37300 - 0.696776i) q^{20} +(-0.415415 + 0.909632i) q^{21} -2.15528 q^{22} +(-1.07870 + 4.67294i) q^{23} -1.00000 q^{24} +(0.463865 - 1.01572i) q^{25} +(-1.86641 - 0.548027i) q^{26} +(0.654861 + 0.755750i) q^{27} +(0.841254 - 0.540641i) q^{28} +(5.17145 - 5.96817i) q^{29} +(0.351971 - 2.44801i) q^{30} +(2.37961 - 0.698716i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.306729 - 2.13335i) q^{33} +(-2.61727 - 5.73103i) q^{34} +(1.02740 + 2.24969i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.446985 - 0.287260i) q^{37} +(-1.76398 + 0.517950i) q^{38} +(0.276831 - 1.92540i) q^{39} +(-1.61959 + 1.86911i) q^{40} +(1.47782 - 0.949736i) q^{41} +(0.654861 + 0.755750i) q^{42} +(3.09798 + 0.909648i) q^{43} +(-0.895337 + 1.96052i) q^{44} +2.47318 q^{45} +(3.80255 + 2.92243i) q^{46} -0.732419 q^{47} +(-0.415415 + 0.909632i) q^{48} +(-0.959493 - 0.281733i) q^{49} +(-0.731237 - 0.843892i) q^{50} +(5.30022 - 3.40624i) q^{51} +(-1.27384 + 1.47009i) q^{52} +(-0.824746 + 5.73623i) q^{53} +(0.959493 - 0.281733i) q^{54} +(-4.48423 - 2.88184i) q^{55} +(-0.142315 - 0.989821i) q^{56} +(-0.763718 - 1.67231i) q^{57} +(-3.28054 - 7.18339i) q^{58} +(0.692610 + 4.81721i) q^{59} +(-2.08057 - 1.33710i) q^{60} +(-7.96193 + 2.33783i) q^{61} +(0.352951 - 2.45483i) q^{62} +(-0.654861 + 0.755750i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-3.15043 - 3.63579i) q^{65} +(-2.06798 - 0.607214i) q^{66} +(-3.48889 + 7.63961i) q^{67} -6.30038 q^{68} +(-2.35153 + 4.17975i) q^{69} +2.47318 q^{70} +(-2.53543 + 5.55182i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(1.81790 + 2.09797i) q^{73} +(-0.446985 + 0.287260i) q^{74} +(0.731237 - 0.843892i) q^{75} +(-0.261638 + 1.81973i) q^{76} +(2.06798 - 0.607214i) q^{77} +(-1.63641 - 1.05166i) q^{78} +(-1.10981 - 7.71891i) q^{79} +(1.02740 + 2.24969i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.250002 - 1.73880i) q^{82} +(3.95720 + 2.54314i) q^{83} +(0.959493 - 0.281733i) q^{84} +(2.21755 - 15.4234i) q^{85} +(2.11439 - 2.44014i) q^{86} +(6.64340 - 4.26945i) q^{87} +(1.41141 + 1.62886i) q^{88} +(2.90371 + 0.852606i) q^{89} +(1.02740 - 2.24969i) q^{90} +1.94520 q^{91} +(4.23798 - 2.24490i) q^{92} +2.48007 q^{93} +(-0.304258 + 0.666232i) q^{94} +(-4.36263 - 1.28098i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-2.01807 + 1.29693i) q^{97} +(-0.654861 + 0.755750i) q^{98} +(0.306729 - 2.13335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Introduction

L-functions

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