LMFDB - Embedded newform 966.2.be.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	966.19
Dual form			966.2.be.a.661.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.25010 + 1.16001i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.37319 - 2.26149i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.25010 + 1.16001i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.37319 - 2.26149i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-2.35018 + 0.940871i) q^{10} +(0.316455 + 3.31406i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(-2.62261 - 0.377074i) q^{13} +(1.58194 - 2.12072i) q^{14} +(0.713211 - 2.42897i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-2.10249 + 6.07474i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(2.12280 + 6.13342i) q^{19} +(-2.42897 + 0.713211i) q^{20} +(0.689107 + 2.55443i) q^{21} +3.32914i q^{22} +(-4.49177 - 1.68049i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.817062 - 1.14740i) q^{25} +(-2.57489 - 0.624662i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.77637 - 1.96075i) q^{28} +(0.0928484 + 0.107153i) q^{29} +(0.940871 - 2.35018i) q^{30} +(2.23813 - 0.542965i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-2.61688 - 2.05794i) q^{33} +(-2.67041 + 5.84738i) q^{34} +(-0.466474 + 6.68151i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-0.551937 + 0.0262920i) q^{37} +(1.53017 + 6.30744i) q^{38} +(2.08271 - 1.63786i) q^{39} +(-2.48577 + 0.479093i) q^{40} +(-4.05770 + 6.31390i) q^{41} +(0.443173 + 2.60837i) q^{42} +(0.00611032 + 0.0208098i) q^{43} +(-0.316455 + 3.31406i) q^{44} +(1.26576 + 2.19236i) q^{45} +(-4.31169 - 2.09985i) q^{46} +(-8.26842 - 4.77378i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-3.22869 - 6.21092i) q^{49} +(0.922430 - 1.06454i) q^{50} +(-2.94561 - 5.71369i) q^{51} +(-2.50385 - 0.866592i) q^{52} +(-1.37215 - 1.74483i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-4.55640 - 7.08990i) q^{55} +(1.95470 - 1.78301i) q^{56} +(-5.90387 - 2.69621i) q^{57} +(0.0822425 + 0.115493i) q^{58} +(5.22946 + 13.0626i) q^{59} +(1.16001 - 2.25010i) q^{60} +(-3.85888 + 3.67943i) q^{61} +(2.27961 - 0.327758i) q^{62} +(-2.32427 - 1.26403i) q^{63} +(0.841254 + 0.540641i) q^{64} +(6.33855 - 2.19379i) q^{65} +(-2.40941 - 2.29737i) q^{66} +(-0.139503 - 0.0993395i) q^{67} +(-3.21414 + 5.56706i) q^{68} +(4.31590 - 2.09117i) q^{69} +(-1.09948 + 6.60691i) q^{70} +(2.60362 + 5.70113i) q^{71} +(0.235759 - 0.971812i) q^{72} +(0.221518 - 1.14934i) q^{73} +(-0.551937 - 0.0262920i) q^{74} +(0.266577 + 1.38313i) q^{75} +(0.923679 + 6.42433i) q^{76} +(7.92928 + 3.83519i) q^{77} +(2.22897 - 1.43247i) q^{78} +(4.54022 - 5.77337i) q^{79} +(-2.52006 + 0.240636i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-4.63950 + 5.89960i) q^{82} +(6.80019 - 4.37022i) q^{83} +(0.193224 + 2.63869i) q^{84} +(-2.31594 - 16.1077i) q^{85} +(0.00410455 + 0.0212964i) q^{86} +(-0.141623 - 0.00674633i) q^{87} +(-0.630043 + 3.26898i) q^{88} +(-2.29186 + 9.44719i) q^{89} +(1.05163 + 2.30275i) q^{90} +(-4.45410 + 5.41321i) q^{91} +(-4.09256 - 2.50019i) q^{92} +(-1.15153 + 1.99450i) q^{93} +(-7.77721 - 5.53812i) q^{94} +(-11.8913 - 11.3384i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(3.49704 + 2.24741i) q^{97} +(-2.62368 - 6.48971i) q^{98} +(3.29525 - 0.473786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$3$	−0.690079	+	0.723734i	−0.398417	+	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	−2.25010	+	1.16001i	−1.00628	+	0.518772i	−0.880882	−	0.473335i	$-0.843050\pi$
$5$	−2.25010	+	1.16001i	−1.00628	+	0.518772i	−0.125395	+	0.992107i	$0.540020\pi$
$6$	−0.755750	+	0.654861i	−0.308533	+	0.267346i
$7$	1.37319	−	2.26149i	0.519018	−	0.854763i
$7$	1.37319	−	2.26149i	0.519018	−	0.854763i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	−2.35018	+	0.940871i	−0.743193	+	0.297529i
$11$	0.316455	+	3.31406i	0.0954147	+	0.999228i	0.908724	+	0.417397i	$0.137057\pi$
$11$	0.316455	+	3.31406i	0.0954147	+	0.999228i	−0.813310	+	0.581831i	$0.802337\pi$
$12$	−0.814576	+	0.580057i	−0.235148	+	0.167448i
$13$	−2.62261	−	0.377074i	−0.727381	−	0.104582i	−0.231330	−	0.972875i	$-0.574308\pi$
$13$	−2.62261	−	0.377074i	−0.727381	−	0.104582i	−0.496051	+	0.868294i	$0.665217\pi$
$14$	1.58194	−	2.12072i	0.422792	−	0.566787i
$15$	0.713211	−	2.42897i	0.184150	−	0.627159i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	−2.10249	+	6.07474i	−0.509928	+	1.47334i	0.336934	+	0.941528i	$0.390610\pi$
$17$	−2.10249	+	6.07474i	−0.509928	+	1.47334i	−0.846862	+	0.531812i	$0.821511\pi$
$18$	0.0475819	−	0.998867i	0.0112152	−	0.235435i
$19$	2.12280	+	6.13342i	0.487003	+	1.40710i	0.874407	+	0.485194i	$0.161251\pi$
$19$	2.12280	+	6.13342i	0.487003	+	1.40710i	−0.387403	+	0.921910i	$0.626628\pi$
$20$	−2.42897	+	0.713211i	−0.543135	+	0.159479i
$21$	0.689107	+	2.55443i	0.150376	+	0.557423i
$22$			3.32914i			0.709774i
$23$	−4.49177	−	1.68049i	−0.936598	−	0.350406i
$23$	−4.49177	−	1.68049i	−0.936598	−	0.350406i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.817062	−	1.14740i	0.163412	−	0.229481i
$26$	−2.57489	−	0.624662i	−0.504978	−	0.122506i
$27$	0.755750	+	0.654861i	0.145444	+	0.126028i
$28$	1.77637	−	1.96075i	0.335702	−	0.370546i
$29$	0.0928484	+	0.107153i	0.0172415	+	0.0198978i	0.764305	−	0.644855i	$-0.223082\pi$
$29$	0.0928484	+	0.107153i	0.0172415	+	0.0198978i	−0.747063	+	0.664753i	$0.768537\pi$
$30$	0.940871	−	2.35018i	0.171779	−	0.429082i
$31$	2.23813	−	0.542965i	0.401980	−	0.0975193i	−0.0296715	−	0.999560i	$-0.509446\pi$
$31$	2.23813	−	0.542965i	0.401980	−	0.0975193i	0.431652	+	0.902040i	$0.357931\pi$
$32$	0.888835	+	0.458227i	0.157125	+	0.0810038i
$33$	−2.61688	−	2.05794i	−0.455540	−	0.358241i
$34$	−2.67041	+	5.84738i	−0.457971	+	1.00282i
$35$	−0.466474	+	6.68151i	−0.0788485	+	1.12938i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	−0.551937	+	0.0262920i	−0.0907379	+	0.00432238i	−0.0929018	−	0.995675i	$-0.529614\pi$
$37$	−0.551937	+	0.0262920i	−0.0907379	+	0.00432238i	0.00216384	+	0.999998i	$0.499311\pi$
$38$	1.53017	+	6.30744i	0.248226	+	1.02320i
$39$	2.08271	−	1.63786i	0.333500	−	0.262268i
$40$	−2.48577	+	0.479093i	−0.393035	+	0.0757513i
$41$	−4.05770	+	6.31390i	−0.633706	+	0.986066i	0.364782	+	0.931093i	$0.381144\pi$
$41$	−4.05770	+	6.31390i	−0.633706	+	0.986066i	−0.998488	+	0.0549728i	$0.982493\pi$
$42$	0.443173	+	2.60837i	0.0683830	+	0.402480i
$43$	0.00611032	+	0.0208098i	0.000931816	+	0.00317347i	0.959958	−	0.280145i	$-0.0903827\pi$
$43$	0.00611032	+	0.0208098i	0.000931816	+	0.00317347i	−0.959026	+	0.283319i	$0.908565\pi$
$44$	−0.316455	+	3.31406i	−0.0477073	+	0.499614i
$45$	1.26576	+	2.19236i	0.188688	+	0.326818i
$46$	−4.31169	−	2.09985i	−0.635723	−	0.309606i
$47$	−8.26842	−	4.77378i	−1.20607	−	0.696327i	−0.244174	−	0.969731i	$-0.578517\pi$
$47$	−8.26842	−	4.77378i	−1.20607	−	0.696327i	−0.961899	+	0.273405i	$0.911850\pi$
$48$	−0.909632	+	0.415415i	−0.131294	+	0.0599600i
$49$	−3.22869	−	6.21092i	−0.461241	−	0.887275i
$50$	0.922430	−	1.06454i	0.130451	−	0.150549i
$51$	−2.94561	−	5.71369i	−0.412468	−	0.800077i
$52$	−2.50385	−	0.866592i	−0.347222	−	0.120175i
$53$	−1.37215	−	1.74483i	−0.188479	−	0.239671i	0.682625	−	0.730769i	$-0.260838\pi$
$53$	−1.37215	−	1.74483i	−0.188479	−	0.239671i	−0.871104	+	0.491098i	$0.836596\pi$
$54$	0.690079	+	0.723734i	0.0939079	+	0.0984877i
$55$	−4.55640	−	7.08990i	−0.614385	−	0.956001i
$56$	1.95470	−	1.78301i	0.261208	−	0.238265i
$57$	−5.90387	−	2.69621i	−0.781986	−	0.357121i
$58$	0.0822425	+	0.115493i	0.0107990	+	0.0151650i
$59$	5.22946	+	13.0626i	0.680818	+	1.70060i	0.713042	+	0.701121i	$0.247317\pi$
$59$	5.22946	+	13.0626i	0.680818	+	1.70060i	−0.0322240	+	0.999481i	$0.510259\pi$
$60$	1.16001	−	2.25010i	0.149757	−	0.290487i
$61$	−3.85888	+	3.67943i	−0.494078	+	0.471103i	−0.895672	−	0.444715i	$-0.853305\pi$
$61$	−3.85888	+	3.67943i	−0.494078	+	0.471103i	0.401594	+	0.915818i	$0.368456\pi$
$62$	2.27961	−	0.327758i	0.289511	−	0.0416253i
$63$	−2.32427	−	1.26403i	−0.292830	−	0.159253i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	6.33855	−	2.19379i	0.786201	−	0.272107i
$66$	−2.40941	−	2.29737i	−0.296578	−	0.282786i
$67$	−0.139503	−	0.0993395i	−0.0170430	−	0.0121363i	0.571504	−	0.820600i	$-0.306360\pi$
$67$	−0.139503	−	0.0993395i	−0.0170430	−	0.0121363i	−0.588547	+	0.808463i	$0.700300\pi$
$68$	−3.21414	+	5.56706i	−0.389772	+	0.675105i
$69$	4.31590	−	2.09117i	0.519573	−	0.251748i
$70$	−1.09948	+	6.60691i	−0.131413	+	0.789677i
$71$	2.60362	+	5.70113i	0.308993	+	0.676599i	0.998880	−	0.0473174i	$-0.0150672\pi$
$71$	2.60362	+	5.70113i	0.308993	+	0.676599i	−0.689887	+	0.723917i	$0.742340\pi$
$72$	0.235759	−	0.971812i	0.0277845	−	0.114529i
$73$	0.221518	−	1.14934i	0.0259267	−	0.134521i	−0.966659	−	0.256067i	$-0.917573\pi$
$73$	0.221518	−	1.14934i	0.0259267	−	0.134521i	0.992586	+	0.121546i	$0.0387853\pi$
$74$	−0.551937	−	0.0262920i	−0.0641614	−	0.00305639i
$75$	0.266577	+	1.38313i	0.0307817	+	0.159711i
$76$	0.923679	+	6.42433i	0.105953	+	0.736921i
$77$	7.92928	+	3.83519i	0.903625	+	0.437060i
$78$	2.22897	−	1.43247i	0.252381	−	0.162195i
$79$	4.54022	−	5.77337i	0.510815	−	0.649554i	−0.460413	−	0.887705i	$-0.652299\pi$
$79$	4.54022	−	5.77337i	0.510815	−	0.649554i	0.971228	+	0.238150i	$0.0765411\pi$
$80$	−2.52006	+	0.240636i	−0.281751	+	0.0269039i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	−4.63950	+	5.89960i	−0.512347	+	0.651502i
$83$	6.80019	−	4.37022i	0.746418	−	0.479694i	−0.111317	−	0.993785i	$-0.535507\pi$
$83$	6.80019	−	4.37022i	0.746418	−	0.479694i	0.857736	+	0.514091i	$0.171871\pi$
$84$	0.193224	+	2.63869i	0.0210825	+	0.287904i
$85$	−2.31594	−	16.1077i	−0.251199	−	1.74713i
$86$	0.00410455	+	0.0212964i	0.000442605	+	0.00229645i
$87$	−0.141623	−	0.00674633i	−0.0151836	−	0.000723282i
$88$	−0.630043	+	3.26898i	−0.0671629	+	0.348474i
$89$	−2.29186	+	9.44719i	−0.242937	+	1.00140i	0.711428	+	0.702758i	$0.248049\pi$
$89$	−2.29186	+	9.44719i	−0.242937	+	1.00140i	−0.954365	+	0.298641i	$0.903467\pi$
$90$	1.05163	+	2.30275i	0.110852	+	0.242731i
$91$	−4.45410	+	5.41321i	−0.466916	+	0.567459i
$92$	−4.09256	−	2.50019i	−0.426679	−	0.260663i
$93$	−1.15153	+	1.99450i	−0.119408	+	0.206820i
$94$	−7.77721	−	5.53812i	−0.802158	−	0.571214i
$95$	−11.8913	−	11.3384i	−1.22003	−	1.16329i
$96$	−0.945001	+	0.327068i	−0.0964487	+	0.0333812i
$97$	3.49704	+	2.24741i	0.355070	+	0.228190i	0.706000	−	0.708212i	$-0.250498\pi$
$97$	3.49704	+	2.24741i	0.355070	+	0.228190i	−0.350929	+	0.936402i	$0.614134\pi$
$98$	−2.62368	−	6.48971i	−0.265032	−	0.655559i
$99$	3.29525	−	0.473786i	0.331185	−	0.0476173i
$100$	1.01944	−	0.972038i	0.101944	−	0.0972038i
$101$	7.65212	−	14.8430i	0.761414	−	1.47694i	−0.113957	−	0.993486i	$-0.536352\pi$
$101$	7.65212	−	14.8430i	0.761414	−	1.47694i	0.875371	−	0.483452i	$-0.160617\pi$
$102$	−2.38915	−	5.96782i	−0.236561	−	0.590902i
$103$	−2.94022	−	4.12896i	−0.289708	−	0.406838i	0.643914	−	0.765098i	$-0.277310\pi$
$103$	−2.94022	−	4.12896i	−0.289708	−	0.406838i	−0.933622	+	0.358260i	$0.883370\pi$
$104$	−2.41014	−	1.10067i	−0.236334	−	0.107930i
$105$	−4.51373	−	4.94837i	−0.440495	−	0.482912i
$106$	−1.20008	−	1.86736i	−0.116562	−	0.181374i
$107$	6.89400	+	7.23022i	0.666468	+	0.698971i	0.966993	−	0.254802i	$-0.0820104\pi$
$107$	6.89400	+	7.23022i	0.666468	+	0.698971i	−0.300525	+	0.953774i	$0.597162\pi$
$108$	0.618159	+	0.786053i	0.0594824	+	0.0756380i
$109$	17.3984	+	6.02164i	1.66646	+	0.576768i	0.987530	−	0.157432i	$-0.0503214\pi$
$109$	17.3984	+	6.02164i	1.66646	+	0.576768i	0.678933	+	0.734200i	$0.262443\pi$
$110$	−3.86183	−	7.49091i	−0.368211	−	0.714230i
$111$	0.361852	−	0.417599i	0.0343455	−	0.0396368i
$112$	2.11534	−	1.58913i	0.199881	−	0.150159i
$113$	8.65634	−	3.95322i	0.814320	−	0.371887i	0.0356838	−	0.999363i	$-0.488639\pi$
$113$	8.65634	−	3.95322i	0.814320	−	0.371887i	0.778636	+	0.627476i	$0.215912\pi$
$114$	−5.62084	−	3.24520i	−0.526440	−	0.303940i
$115$	12.0563	−	1.42921i	1.12426	−	0.133275i
$116$	0.0708917	+	0.122788i	0.00658213	+	0.0114006i
$117$	−0.251858	+	2.63758i	−0.0232843	+	0.243844i
$118$	3.96411	+	13.5005i	0.364926	+	1.24282i
$119$	10.8509	+	13.0965i	0.994696	+	1.20056i
$120$	1.36864	−	2.12965i	0.124939	−	0.194410i
$121$	−0.0816534	+	0.0157374i	−0.00742304	+	0.00143067i
$122$	−4.19115	+	3.29596i	−0.379449	+	0.298402i
$123$	−1.76945	−	7.29379i	−0.159546	−	0.657658i
$124$	2.30044	−	0.109584i	0.206586	−	0.00984089i
$125$	1.29389	−	8.99918i	0.115729	−	0.804911i
$126$	−2.19359	−	1.47924i	−0.195421	−	0.131781i
$127$	−1.87807	+	4.11240i	−0.166652	+	0.364917i	−0.974471	−	0.224514i	$-0.927921\pi$
$127$	−1.87807	+	4.11240i	−0.166652	+	0.364917i	0.807819	+	0.589431i	$0.200648\pi$
$128$	0.786053	+	0.618159i	0.0694779	+	0.0546381i
$129$	−0.0192774	−	0.00993819i	−0.00169728	−	0.000875009i
$130$	6.51838	−	1.58134i	0.571700	−	0.138693i
$131$	2.95340	−	7.37723i	0.258040	−	0.644552i	−0.741615	−	0.670825i	$-0.765940\pi$
$131$	2.95340	−	7.37723i	0.258040	−	0.644552i	0.999655	+	0.0262739i	$0.00836419\pi$
$132$	−2.18012	−	2.51599i	−0.189755	−	0.218989i
$133$	16.7857	+	3.62168i	1.45550	+	0.314039i
$134$	−0.129428	−	0.112150i	−0.0111809	−	0.00968831i
$135$	−2.46016	−	0.596828i	−0.211737	−	0.0513668i
$136$	−3.72877	+	5.23633i	−0.319740	+	0.449012i
$137$	17.5751	−	10.1470i	1.50154	−	0.866917i	0.501546	−	0.865131i	$-0.332765\pi$
$137$	17.5751	−	10.1470i	1.50154	−	0.866917i	0.999998	−	0.00178630i	$-0.000568598\pi$
$138$	4.49514	−	1.67145i	0.382651	−	0.142283i
$139$		−	0.0487391i		−	0.00413400i	−0.999998	−	0.00206700i	$-0.999342\pi$
$139$		−	0.0487391i		−	0.00413400i	0.999998	−	0.00206700i	$-0.000657947\pi$
$140$	−1.72253	+	6.47248i	−0.145580	+	0.547025i
$141$	9.16081	−	2.68986i	0.771479	−	0.226527i
$142$	2.04990	+	5.92280i	0.172024	+	0.497031i
$143$	0.419711	−	8.81082i	0.0350980	−	0.736798i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	−0.333217	−	0.133400i	−0.0276721	−	0.0110783i
$146$	0.329767	−	1.12308i	0.0272917	−	0.0929471i
$147$	6.72311	+	1.94932i	0.554512	+	0.160777i
$148$	−0.546939	−	0.0786379i	−0.0449581	−	0.00646400i
$149$	−1.02600	+	0.730614i	−0.0840535	+	0.0598542i	−0.621311	−	0.783564i	$-0.713400\pi$
$149$	−1.02600	+	0.730614i	−0.0840535	+	0.0598542i	0.537258	+	0.843418i	$0.319460\pi$
$150$	0.133895	+	1.40221i	0.0109325	+	0.114490i
$151$	2.46981	−	0.988763i	0.200990	−	0.0804644i	−0.268983	−	0.963145i	$-0.586688\pi$
$151$	2.46981	−	0.988763i	0.200990	−	0.0804644i	0.469974	+	0.882680i	$0.344263\pi$
$152$	0.308825	+	6.48304i	0.0250490	+	0.525844i
$153$	6.16790	+	1.81106i	0.498645	+	0.146415i
$154$	7.52882	+	4.57155i	0.606689	+	0.368386i
$155$	−4.40618	+	3.81798i	−0.353913	+	0.306668i
$156$	2.35504	−	1.21411i	0.188554	−	0.0972063i
$157$	−14.2685	−	2.75002i	−1.13875	−	0.219476i	−0.415187	−	0.909736i	$-0.636284\pi$
$157$	−14.2685	−	2.75002i	−1.13875	−	0.219476i	−0.723561	+	0.690260i	$0.757496\pi$
$158$	5.06846	−	5.31565i	0.403225	−	0.422890i
$159$	2.20968	+	0.210999i	0.175239	+	0.0167333i
$160$	−2.53152			−0.200134
$161$	−9.96847	+	7.85045i	−0.785625	+	0.618703i
$162$	−1.00000			−0.0785674
$163$	−15.3297	−	1.46381i	−1.20072	−	0.114655i	−0.524534	−	0.851389i	$-0.675761\pi$
$163$	−15.3297	−	1.46381i	−1.20072	−	0.114655i	−0.676182	+	0.736735i	$0.736367\pi$
$164$	−5.17928	+	5.43188i	−0.404434	+	0.424158i
$165$	8.27547	+	1.59497i	0.644245	+	0.124168i
$166$	7.18482	−	3.70403i	0.557650	−	0.287489i
$167$	−14.6097	+	12.6594i	−1.13054	+	0.979615i	−0.999930	−	0.0118197i	$-0.996238\pi$
$167$	−14.6097	+	12.6594i	−1.13054	+	0.979615i	−0.130605	+	0.991434i	$0.541692\pi$
$168$	−0.0584735	+	2.64511i	−0.00451133	+	0.204074i
$169$	−5.73752	−	1.68469i	−0.441347	−	0.129591i
$170$	−0.774317	−	16.2549i	−0.0593874	−	1.24669i
$171$	6.02547	−	2.41223i	0.460779	−	0.184468i
$172$	0.00206161	+	0.0215902i	0.000157196	+	0.00164624i
$173$	11.7607	−	8.37476i	0.894150	−	0.636721i	−0.0378089	−	0.999285i	$-0.512038\pi$
$173$	11.7607	−	8.37476i	0.894150	−	0.636721i	0.931959	+	0.362564i	$0.118098\pi$
$174$	−0.140340	−	0.0201779i	−0.0106392	−	0.00152968i
$175$	−1.47286	−	3.42338i	−0.111338	−	0.258783i
$176$	−0.937926	+	3.19428i	−0.0706989	+	0.240778i
$177$	−13.0626	−	5.22946i	−0.981843	−	0.393071i
$178$	−3.17950	+	9.18655i	−0.238313	+	0.688561i
$179$	−0.591155	+	12.4099i	−0.0441850	+	0.927557i	0.862580	+	0.505921i	$0.168847\pi$
$179$	−0.591155	+	12.4099i	−0.0441850	+	0.927557i	−0.906765	+	0.421636i	$0.861456\pi$
$180$	0.827979	+	2.39229i	0.0617139	+	0.178311i
$181$	14.4762	−	4.25061i	1.07601	−	0.315945i	0.304729	−	0.952439i	$-0.401434\pi$
$181$	14.4762	−	4.25061i	1.07601	−	0.315945i	0.771282	+	0.636494i	$0.219616\pi$
$182$	−4.94849	+	4.96531i	−0.366806	+	0.368053i
$183$		−	5.33190i		−	0.394145i
$184$	−3.83637	−	2.87789i	−0.282821	−	0.212161i
$185$	1.21142	−	0.699412i	0.0890652	−	0.0514218i
$186$	−1.33590	+	1.87601i	−0.0979530	+	0.137556i
$187$	−20.7974	−	5.04540i	−1.52086	−	0.368956i
$188$	−7.21556	−	6.25232i	−0.526249	−	0.455997i
$189$	2.51875	−	0.809872i	0.183212	−	0.0589095i
$190$	−10.7597	−	12.4174i	−0.780592	−	0.900851i
$191$	−1.83174	+	4.57547i	−0.132540	+	0.331069i	−0.979761	−	0.200172i	$-0.935850\pi$
$191$	−1.83174	+	4.57547i	−0.132540	+	0.331069i	0.847221	+	0.531241i	$0.178274\pi$
$192$	−0.971812	+	0.235759i	−0.0701345	+	0.0170144i
$193$	11.6063	+	5.98348i	0.835443	+	0.430701i	0.822191	−	0.569212i	$-0.192751\pi$
$193$	11.6063	+	5.98348i	0.835443	+	0.430701i	0.0132516	+	0.999912i	$0.495782\pi$
$194$	3.26757	+	2.56965i	0.234598	+	0.184490i
$195$	−2.78638	+	6.10132i	−0.199537	+	0.436924i
$196$	−1.99492	−	6.70972i	−0.142494	−	0.479266i
$197$	−0.754284	+	5.24616i	−0.0537405	+	0.373773i	0.945148	+	0.326642i	$0.105917\pi$
$197$	−0.754284	+	5.24616i	−0.0537405	+	0.373773i	−0.998889	+	0.0471315i	$0.984992\pi$
$198$	3.32537	−	0.158407i	0.236324	−	0.0112575i
$199$	−6.39666	−	26.3674i	−0.453447	−	1.86914i	−0.493183	−	0.869926i	$-0.664167\pi$
$199$	−6.39666	−	26.3674i	−0.453447	−	1.86914i	0.0397355	−	0.999210i	$-0.487348\pi$
$200$	1.10723	−	0.870732i	0.0782927	−	0.0615701i
$201$	0.168163	−	0.0324108i	0.0118613	−	0.00228608i
$202$	9.02839	−	14.0485i	0.635235	−	0.988446i
$203$	0.369824	−	0.0628345i	0.0259565	−	0.00441012i
$204$	−1.81106	−	6.16790i	−0.126799	−	0.431839i
$205$	1.80606	−	18.9139i	0.126141	−	1.32100i
$206$	−2.53442	−	4.38975i	−0.176582	−	0.305848i
$207$	−1.46486	+	4.56664i	−0.101815	+	0.317403i
$208$	−2.29460	−	1.32479i	−0.159102	−	0.0918576i
$209$	−19.6548	+	8.97604i	−1.35955	+	0.620886i
$210$	−4.02292	−	5.35502i	−0.277608	−	0.369532i
$211$	−8.55354	+	9.87131i	−0.588850	+	0.679569i	−0.969483	−	0.245157i	$-0.921161\pi$
$211$	−8.55354	+	9.87131i	−0.588850	+	0.679569i	0.380633	+	0.924726i	$0.375706\pi$
$212$	−1.01714	−	1.97298i	−0.0698576	−	0.135505i
$213$	−5.92280	−	2.04990i	−0.405824	−	0.140457i
$214$	6.17551	+	7.85279i	0.422149	+	0.536806i
$215$	−0.0378885	−	0.0397363i	−0.00258397	−	0.00270999i
$216$	0.540641	+	0.841254i	0.0367859	+	0.0572401i
$217$	1.84547	−	5.80711i	0.125279	−	0.394212i
$218$	16.7472	+	7.64819i	1.13426	+	0.518001i
$219$	0.678955	+	0.953459i	0.0458795	+	0.0644288i
$220$	−3.13229	−	7.82408i	−0.211179	−	0.527499i
$221$	7.80463	−	15.1389i	0.524996	−	1.01835i
$222$	0.399909	−	0.381312i	0.0268401	−	0.0255920i
$223$	−13.9920	+	2.01175i	−0.936977	+	0.134717i	−0.593853	−	0.804573i	$-0.702394\pi$
$223$	−13.9920	+	2.01175i	−0.936977	+	0.134717i	−0.343124	+	0.939290i	$0.611485\pi$
$224$	2.25682	−	1.38086i	0.150790	−	0.0922626i
$225$	−1.18498	−	0.761541i	−0.0789987	−	0.0507694i
$226$	8.99292	−	3.11248i	0.598200	−	0.207039i
$227$	16.6782	+	15.9027i	1.10697	+	1.05550i	0.998111	+	0.0614409i	$0.0195696\pi$
$227$	16.6782	+	15.9027i	1.10697	+	1.05550i	0.108863	+	0.994057i	$0.465279\pi$
$228$	−5.28692	−	3.76480i	−0.350135	−	0.249330i
$229$	−2.04459	+	3.54134i	−0.135110	+	0.234018i	−0.925640	−	0.378406i	$-0.876472\pi$
$229$	−2.04459	+	3.54134i	−0.135110	+	0.234018i	0.790529	+	0.612424i	$0.209806\pi$
$230$	12.1376	−	0.276717i	0.800329	−	0.0182462i
$231$	−8.24748	+	3.09211i	−0.542645	+	0.203446i
$232$	0.0588990	+	0.128971i	0.00386691	+	0.00846734i
$233$	3.86460	−	15.9301i	0.253178	−	1.04361i	−0.693249	−	0.720698i	$-0.743822\pi$
$233$	3.86460	−	15.9301i	0.253178	−	1.04361i	0.946427	−	0.322917i	$-0.104663\pi$
$234$	−0.501436	+	2.60170i	−0.0327799	+	0.170078i
$235$	24.1424	+	1.15005i	1.57488	+	0.0750207i
$236$	2.66285	+	13.8162i	0.173337	+	0.899358i
$237$	1.04527	+	7.26999i	0.0678974	+	0.472237i
$238$	9.55681	+	14.0687i	0.619476	+	0.911937i
$239$	−21.1378	+	13.5845i	−1.36729	+	0.878706i	−0.998704	−	0.0508868i	$-0.983795\pi$
$239$	−21.1378	+	13.5845i	−1.36729	+	0.878706i	−0.368589	+	0.929593i	$0.620159\pi$
$240$	1.56488	−	1.98991i	0.101013	−	0.128448i
$241$	18.9158	−	1.80624i	1.21847	−	0.116350i	0.534060	−	0.845447i	$-0.320666\pi$
$241$	18.9158	−	1.80624i	1.21847	−	0.116350i	0.684411	+	0.729097i	$0.260060\pi$
$242$	−0.0827796	+	0.00790449i	−0.00532127	+	0.000508120i
$243$	0.618159	−	0.786053i	0.0396549	−	0.0504253i
$244$	−4.48548	+	2.88264i	−0.287153	+	0.184542i
$245$	14.4696	+	10.2299i	0.924430	+	0.653566i
$246$	−1.06812	−	7.42896i	−0.0681010	−	0.473653i
$247$	−3.25451	−	16.8860i	−0.207080	−	1.07443i
$248$	2.30044	+	0.109584i	0.146078	+	0.00695856i
$249$	−1.52979	+	7.93733i	−0.0969468	+	0.503008i
$250$	2.14346	−	8.83544i	0.135564	−	0.558802i
$251$	−2.84838	−	6.23707i	−0.179788	−	0.393681i	0.798185	−	0.602412i	$-0.205794\pi$
$251$	−2.84838	−	6.23707i	−0.179788	−	0.393681i	−0.977973	+	0.208732i	$0.933066\pi$
$252$	−2.04305	−	1.68106i	−0.128700	−	0.105897i
$253$	4.14781	−	15.4178i	0.260770	−	0.969308i
$254$	−2.26048	+	3.91526i	−0.141835	+	0.245665i
$255$	13.2559	+	9.43946i	0.830115	+	0.591122i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	−24.1485	+	8.35789i	−1.50635	+	0.521351i	−0.950712	−	0.310076i	$-0.899645\pi$
$257$	−24.1485	+	8.35789i	−1.50635	+	0.521351i	−0.555633	+	0.831427i	$0.687524\pi$
$258$	−0.0182454	−	0.0117256i	−0.00113591	−	0.000730005i
$259$	−0.698457	+	1.28431i	−0.0434000	+	0.0798029i
$260$	6.63919	−	0.954571i	0.411745	−	0.0592000i
$261$	0.102613	−	0.0978418i	0.00635162	−	0.00605625i
$262$	3.64127	−	7.06309i	0.224959	−	0.436359i
$263$	2.04502	+	5.10821i	0.126101	+	0.314985i	0.977962	−	0.208783i	$-0.0669501\pi$
$263$	2.04502	+	5.10821i	0.126101	+	0.314985i	−0.851861	+	0.523768i	$0.824526\pi$
$264$	−1.93109	−	2.71184i	−0.118850	−	0.166902i
$265$	5.11150	+	2.33434i	0.313997	+	0.143398i
$266$	16.3654	+	5.20086i	1.00343	+	0.318885i
$267$	−5.25568	−	8.17800i	−0.321643	−	0.500486i
$268$	−0.118182	−	0.123945i	−0.00721910	−	0.00757117i
$269$	−12.3525	−	15.7074i	−0.753142	−	0.957698i	0.246793	−	0.969068i	$-0.420623\pi$
$269$	−12.3525	−	15.7074i	−0.753142	−	0.957698i	−0.999935	+	0.0113698i	$0.996381\pi$
$270$	−2.39229	−	0.827979i	−0.145590	−	0.0503892i
$271$	5.53267	+	10.7319i	0.336086	+	0.651916i	0.994953	−	0.100344i	$-0.0319943\pi$
$271$	5.53267	+	10.7319i	0.336086	+	0.651916i	−0.658867	+	0.752260i	$0.728964\pi$
$272$	−4.20963	+	4.85818i	−0.255247	+	0.294570i
$273$	−0.844048	−	6.95913i	−0.0510841	−	0.421185i
$274$	18.4601	−	8.43044i	1.11521	−	0.509301i
$275$	4.06113	+	2.34469i	0.244895	+	0.141390i
$276$	4.63366	−	1.23659i	0.278914	−	0.0744342i
$277$	13.1668	+	22.8056i	0.791119	+	1.37026i	0.925275	+	0.379297i	$0.123834\pi$
$277$	13.1668	+	22.8056i	0.791119	+	1.37026i	−0.134156	+	0.990960i	$0.542832\pi$
$278$	0.00463295	−	0.0485184i	0.000277866	−	0.00290994i
$279$	−0.648844	−	2.20976i	−0.0388453	−	0.132295i
$280$	−2.32998	+	6.27944i	−0.139243	+	0.375268i
$281$	8.31072	−	12.9317i	0.495776	−	0.771443i	−0.499726	−	0.866184i	$-0.666566\pi$
$281$	8.31072	−	12.9317i	0.495776	−	0.771443i	0.995502	+	0.0947410i	$0.0302023\pi$
$282$	9.37502	−	1.80689i	0.558274	−	0.107598i
$283$	−2.62315	+	2.06287i	−0.155930	+	0.122625i	−0.693076	−	0.720865i	$-0.743745\pi$
$283$	−2.62315	+	2.06287i	−0.155930	+	0.122625i	0.537146	+	0.843489i	$0.319502\pi$
$284$	1.47762	+	6.09084i	0.0876807	+	0.361425i
$285$	16.4119	−	0.781797i	0.972159	−	0.0463097i
$286$	1.25533	−	8.73103i	0.0742293	−	0.516276i
$287$	8.70684	+	17.8466i	0.513948	+	1.05345i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	−19.1191	−	15.0354i	−1.12465	−	0.884437i
$290$	−0.319027	−	0.164470i	−0.0187339	−	0.00965802i
$291$	−4.03976	+	0.980035i	−0.236815	+	0.0574507i
$292$	0.435030	−	1.08665i	0.0254582	−	0.0635915i
$293$	14.3607	+	16.5731i	0.838961	+	0.968213i	0.999824	−	0.0187640i	$-0.00597310\pi$
$293$	14.3607	+	16.5731i	0.838961	+	0.968213i	−0.160863	+	0.986977i	$0.551428\pi$
$294$	6.50737	+	2.57956i	0.379517	+	0.150443i
$295$	−26.9195	−	23.3259i	−1.56732	−	1.35809i
$296$	−0.536987	−	0.130272i	−0.0312118	−	0.00757189i
$297$	−1.93109	+	2.71184i	−0.112053	+	0.157357i
$298$	−1.09081	+	0.629778i	−0.0631888	+	0.0364821i
$299$	11.1465	+	6.10099i	0.644617	+	0.352830i
$300$			1.40859i			0.0813250i
$301$	0.0554519	+	0.0147575i	0.00319620	+	0.000850607i
$302$	2.55261	−	0.749515i	0.146886	−	0.0431297i
$303$	5.46185	+	15.7810i	0.313775	+	0.906593i
$304$	−0.308825	+	6.48304i	−0.0177123	+	0.371828i
$305$	4.41470	−	12.7554i	0.252785	−	0.730374i
$306$	5.96782	+	2.38915i	0.341157	+	0.136579i
$307$	7.07731	−	24.1031i	0.403923	−	1.37564i	−0.467017	−	0.884248i	$-0.654671\pi$
$307$	7.07731	−	24.1031i	0.403923	−	1.37564i	0.870940	−	0.491389i	$-0.163511\pi$
$308$	7.06017	+	5.26650i	0.402291	+	0.300087i
$309$	5.01725	+	0.721372i	0.285421	+	0.0410374i
$310$	−4.74915	+	3.38186i	−0.269734	+	0.192077i
$311$	−1.59577	−	16.7116i	−0.0904878	−	0.947631i	−0.920723	−	0.390217i	$-0.872400\pi$
$311$	−1.59577	−	16.7116i	−0.0904878	−	0.947631i	0.830235	−	0.557413i	$-0.188206\pi$
$312$	2.45978	−	0.984749i	0.139258	−	0.0557504i
$313$	−0.181392	−	3.80789i	−0.0102529	−	0.215235i	−0.998180	−	0.0603124i	$-0.980790\pi$
$313$	−0.181392	−	3.80789i	−0.0102529	−	0.215235i	0.987927	−	0.154922i	$-0.0495127\pi$
$314$	−13.9425	−	4.09388i	−0.786819	−	0.231031i
$315$	6.69613	+	0.148027i	0.377284	+	0.00834037i
$316$	5.55079	−	4.80979i	0.312257	−	0.270572i
$317$	−3.69396	+	1.90437i	−0.207473	+	0.106960i	−0.558832	−	0.829281i	$-0.688750\pi$
$317$	−3.69396	+	1.90437i	−0.207473	+	0.106960i	0.351358	+	0.936241i	$0.385720\pi$
$318$	2.17962	+	0.420088i	0.122227	+	0.0235574i
$319$	−0.325729	+	0.341614i	−0.0182373	+	0.0191267i
$320$	−2.52006	−	0.240636i	−0.140875	−	0.0134520i
$321$	−9.99016			−0.557596
$322$	−10.6696	+	6.86734i	−0.594592	+	0.382702i
$323$	−41.7221			−2.32148
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	−2.57549	+	2.70110i	−0.142863	+	0.149830i
$326$	−15.1212	−	2.91437i	−0.837484	−	0.161412i
$327$	−16.3643	+	8.43640i	−0.904949	+	0.466534i
$328$	−5.67216	+	4.91496i	−0.313193	+	0.271383i
$329$	−22.1500	+	12.1437i	−1.22117	+	0.669501i
$330$	8.08639	+	2.37438i	0.445141	+	0.130705i
$331$	−1.36701	−	28.6971i	−0.0751378	−	1.57734i	−0.650544	−	0.759469i	$-0.725459\pi$
$331$	−1.36701	−	28.6971i	−0.0751378	−	1.57734i	0.575406	−	0.817868i	$-0.304844\pi$
$332$	7.50438	−	3.00430i	0.411856	−	0.164882i
$333$	0.0525245	+	0.550061i	0.00287832	+	0.0301432i
$334$	−15.7469	+	11.2133i	−0.861634	+	0.613567i
$335$	0.429131	+	0.0616997i	0.0234459	+	0.00337101i
$336$	−0.309642	+	2.62757i	−0.0168924	+	0.143346i
$337$	0.608893	−	2.07370i	0.0331685	−	0.112961i	−0.941245	−	0.337725i	$-0.890343\pi$
$337$	0.608893	−	2.07370i	0.0331685	−	0.112961i	0.974413	+	0.224763i	$0.0721609\pi$
$338$	−5.55140	−	2.22244i	−0.301956	−	0.120885i
$339$	−3.11248	+	8.99292i	−0.169047	+	0.488428i
$340$	0.774317	−	16.2549i	0.0419932	−	0.881546i
$341$	2.50769	+	7.24548i	0.135799	+	0.392365i
$342$	6.22748	−	1.82855i	0.336744	−	0.0988769i
$343$	−18.4796	−	1.22714i	−0.997802	−	0.0662595i
$344$			0.0216884i			0.00116936i
$345$	−7.28544	+	9.71184i	−0.392235	+	0.522868i
$346$	12.5035	−	7.21891i	0.672194	−	0.388091i
$347$	3.71080	−	5.21109i	0.199206	−	0.279746i	−0.702874	−	0.711314i	$-0.748100\pi$
$347$	3.71080	−	5.21109i	0.199206	−	0.279746i	0.902080	+	0.431568i	$0.142040\pi$
$348$	−0.137787	−	0.0334267i	−0.00738615	−	0.00179186i
$349$	17.9565	+	15.5594i	0.961189	+	0.832875i	0.985988	−	0.166817i	$-0.0533490\pi$
$349$	17.9565	+	15.5594i	0.961189	+	0.832875i	−0.0247985	+	0.999692i	$0.507894\pi$
$350$	−1.14078	−	3.54789i	−0.0609771	−	0.189643i
$351$	−1.73510	−	2.00242i	−0.0926130	−	0.106881i
$352$	−1.23732	+	3.09066i	−0.0659491	+	0.164733i
$353$	27.1191	−	6.57901i	1.44340	−	0.350166i	0.563814	−	0.825902i	$-0.309333\pi$
$353$	27.1191	−	6.57901i	1.44340	−	0.350166i	0.879588	+	0.475736i	$0.157818\pi$
$354$	−12.5063	−	6.44746i	−0.664704	−	0.342679i
$355$	−12.4718	−	9.80791i	−0.661933	−	0.520550i
$356$	−4.03834	+	8.84273i	−0.214031	+	0.468664i
$357$	−16.9664	−	1.18452i	−0.897955	−	0.0626913i
$358$	−1.76811	+	12.2975i	−0.0934476	+	0.649942i
$359$	−21.2231	+	1.01098i	−1.12011	+	0.0533576i	−0.599456	−	0.800408i	$-0.704616\pi$
$359$	−21.2231	+	1.01098i	−1.12011	+	0.0533576i	−0.520658	+	0.853766i	$0.674313\pi$
$360$	0.596828	+	2.46016i	0.0314556	+	0.129662i
$361$	−18.1776	+	14.2950i	−0.956716	+	0.752370i
$362$	14.8147	−	2.85531i	0.778645	−	0.150072i
$363$	0.0449576	−	0.0699554i	0.00235966	−	0.00367171i
$364$	−5.39806	+	4.47245i	−0.282935	+	0.234420i
$365$	0.834812	+	2.84311i	0.0436960	+	0.148815i
$366$	0.506829	−	5.30775i	0.0264924	−	0.277441i
$367$	11.2133	+	19.4221i	0.585332	+	1.01382i	0.994834	+	0.101516i	$0.0323692\pi$
$367$	11.2133	+	19.4221i	0.585332	+	1.01382i	−0.409502	+	0.912309i	$0.634297\pi$
$368$	−3.54544	−	3.22953i	−0.184819	−	0.168351i
$369$	6.49982	+	3.75267i	0.338367	+	0.195356i
$370$	1.27242	−	0.581093i	0.0661497	−	0.0302096i
$371$	−5.83014	+	0.707118i	−0.302686	+	0.0367117i
$372$	−1.50818	+	1.74053i	−0.0781953	+	0.0902422i
$373$	11.0138	+	21.3638i	0.570274	+	1.10618i	0.980925	+	0.194384i	$0.0622709\pi$
$373$	11.0138	+	21.3638i	0.570274	+	1.10618i	−0.410652	+	0.911792i	$0.634699\pi$
$374$	−20.2236	−	6.99947i	−1.04574	−	0.361934i
$375$	5.62013	+	7.14658i	0.290222	+	0.369048i
$376$	−6.58857	−	6.90989i	−0.339779	−	0.356350i
$377$	−0.203101	−	0.316031i	−0.0104602	−	0.0162764i
$378$	2.58433	−	0.566782i	0.132924	−	0.0291521i
$379$	−2.17167	−	0.991769i	−0.111551	−	0.0509437i	0.358858	−	0.933392i	$-0.383166\pi$
$379$	−2.17167	−	0.991769i	−0.111551	−	0.0509437i	−0.470409	+	0.882449i	$0.655894\pi$
$380$	−9.53065	−	13.3839i	−0.488912	−	0.686581i
$381$	−1.68027	−	4.19711i	−0.0860828	−	0.215024i
$382$	−2.25837	+	4.38063i	−0.115548	+	0.224133i
$383$	−7.26399	+	6.92620i	−0.371173	+	0.353912i	−0.852591	−	0.522578i	$-0.824970\pi$
$383$	−7.26399	+	6.92620i	−0.371173	+	0.353912i	0.481419	+	0.876491i	$0.340122\pi$
$384$	−0.989821	+	0.142315i	−0.0505116	+	0.00726247i
$385$	−22.2906	+	0.568469i	−1.13603	+	0.0289719i
$386$	10.9850	+	7.05964i	0.559123	+	0.359326i
$387$	0.0204955	−	0.00709357i	0.00104185	−	0.000360587i
$388$	3.00852	+	2.86861i	0.152734	+	0.145632i
$389$	23.4750	+	16.7165i	1.19023	+	0.847559i	0.991192	−	0.132433i	$-0.0422789\pi$
$389$	23.4750	+	16.7165i	1.19023	+	0.847559i	0.199038	+	0.979992i	$0.436218\pi$
$390$	−3.35373	+	5.80883i	−0.169823	+	0.294141i
$391$	19.6524	−	23.7531i	0.993865	−	1.20125i
$392$	−1.34808	−	6.86896i	−0.0680885	−	0.346935i
$393$	3.30108	+	7.22835i	0.166517	+	0.364622i
$394$	−1.24955	+	5.15070i	−0.0629513	+	0.259489i
$395$	−3.51882	+	18.2574i	−0.177051	+	0.918628i
$396$	3.32537	+	0.158407i	0.167106	+	0.00796024i
$397$	−1.22316	−	6.34637i	−0.0613888	−	0.318515i	0.938233	−	0.346003i	$-0.112461\pi$
$397$	−1.22316	−	6.34637i	−0.0613888	−	0.318515i	−0.999622	+	0.0274879i	$0.991249\pi$
$398$	−3.86132	−	26.8561i	−0.193550	−	1.34617i
$399$	−14.2046	+	9.64914i	−0.711119	+	0.483061i
$400$	1.18498	−	0.761541i	0.0592490	−	0.0380770i
$401$	−3.72422	+	4.73573i	−0.185978	+	0.236491i	−0.870098	−	0.492879i	$-0.835944\pi$
$401$	−3.72422	+	4.73573i	−0.185978	+	0.236491i	0.684119	+	0.729370i	$0.260187\pi$
$402$	0.170483	−	0.0162791i	0.00850291	−	0.000811929i
$403$	−6.07448	+	0.580043i	−0.302591	+	0.0288940i
$404$	10.3229	−	13.1266i	0.513583	−	0.653074i
$405$	2.12965	−	1.36864i	0.105823	−	0.0680084i
$406$	0.374122	−	0.0273960i	0.0185674	−	0.00135964i
$407$	−0.261797	−	1.82083i	−0.0129768	−	0.0902554i
$408$	−1.21656	−	6.31212i	−0.0602288	−	0.312497i
$409$	24.3285	+	1.15891i	1.20296	+	0.0573043i	0.639470	−	0.768816i	$-0.279154\pi$
$409$	24.3285	+	1.15891i	1.20296	+	0.0573043i	0.563494	+	0.826120i	$0.309457\pi$
$410$	3.59576	−	18.6566i	0.177582	−	0.921383i
$411$	−4.78449	+	19.7220i	−0.236002	+	0.972812i
$412$	−2.10567	−	4.61078i	−0.103739	−	0.227157i
$413$	36.7219	+	6.11103i	1.80697	+	0.300704i
$414$	−1.89231	+	4.40672i	−0.0930021	+	0.216578i
$415$	−10.2316	+	17.7217i	−0.502252	+	0.869926i
$416$	−2.15828	−	1.53691i	−0.105819	−	0.0753530i
$417$	0.0352742	+	0.0336339i	0.00172738	+	0.00164706i
$418$	−20.4190	+	7.06709i	−0.998727	+	0.345663i
$419$	15.8506	+	10.1866i	0.774352	+	0.497646i	0.867155	−	0.498039i	$-0.165946\pi$
$419$	15.8506	+	10.1866i	0.774352	+	0.497646i	−0.0928027	+	0.995685i	$0.529583\pi$
$420$	−3.49568	−	5.71318i	−0.170571	−	0.278774i
$421$	−24.3631	+	3.50288i	−1.18738	+	0.170720i	−0.707566	−	0.706648i	$-0.750207\pi$
$421$	−24.3631	+	3.50288i	−1.18738	+	0.170720i	−0.479819	+	0.877368i	$0.659298\pi$
$422$	−9.45314	+	9.01355i	−0.460172	+	0.438773i
$423$	−4.37494	+	8.48620i	−0.212717	+	0.412613i
$424$	−0.824992	−	2.06073i	−0.0400652	−	0.100078i
$425$	5.25231	+	7.37584i	0.254775	+	0.357781i
$426$	−5.70113	−	2.60362i	−0.276221	−	0.126146i
$427$	3.02202	+	13.7794i	0.146246	+	0.666831i
$428$	5.40109	+	8.40426i	0.261071	+	0.406235i
$429$	6.08706	+	6.38392i	0.293886	+	0.308219i
$430$	−0.0339397	−	0.0431579i	−0.00163672	−	0.00208126i
$431$	4.28072	+	1.48157i	0.206195	+	0.0713648i	0.428213	−	0.903678i	$-0.359143\pi$
$431$	4.28072	+	1.48157i	0.206195	+	0.0713648i	−0.222018	+	0.975043i	$0.571264\pi$
$432$	0.458227	+	0.888835i	0.0220464	+	0.0427641i
$433$	3.22047	−	3.71662i	0.154766	−	0.178609i	−0.673072	−	0.739577i	$-0.735025\pi$
$433$	3.22047	−	3.71662i	0.154766	−	0.178609i	0.827837	+	0.560968i	$0.189571\pi$
$434$	2.38912	−	5.60539i	0.114681	−	0.269067i
$435$	0.326492	−	0.149104i	0.0156541	−	0.00714898i
$436$	15.9444	+	9.20549i	0.763597	+	0.440863i
$437$	0.772037	−	31.1172i	0.0369316	−	1.48854i
$438$	0.585249	+	1.01368i	0.0279643	+	0.0484355i
$439$	−2.38428	+	24.9693i	−0.113796	+	1.19172i	0.740545	+	0.672007i	$0.234568\pi$
$439$	−2.38428	+	24.9693i	−0.113796	+	1.19172i	−0.854340	+	0.519714i	$0.826038\pi$
$440$	−2.37438	−	8.08639i	−0.113194	−	0.385504i
$441$	−6.05026	+	3.52056i	−0.288108	+	0.167646i
$442$	9.20833	−	14.3284i	0.437996	−	0.681535i
$443$	−21.1495	+	4.07624i	−1.00485	+	0.193668i	−0.665024	−	0.746822i	$-0.731579\pi$
$443$	−21.1495	+	4.07624i	−1.00485	+	0.193668i	−0.339821	+	0.940490i	$0.610367\pi$
$444$	0.434344	−	0.341572i	0.0206131	−	0.0162103i
$445$	−5.80189	−	23.9157i	−0.275036	−	1.13371i
$446$	−14.1199	+	0.672615i	−0.668598	+	0.0318492i
$447$	0.179253	−	1.24674i	0.00847840	−	0.0589686i
$448$	2.37786	−	1.16008i	0.112343	−	0.0548088i
$449$	2.44494	−	5.35366i	0.115384	−	0.252655i	−0.843125	−	0.537717i	$-0.819287\pi$
$449$	2.44494	−	5.35366i	0.115384	−	0.252655i	0.958509	+	0.285062i	$0.0920142\pi$
$450$	−1.10723	−	0.870732i	−0.0521951	−	0.0410467i
$451$	−22.2087	−	11.4494i	−1.04577	−	0.539131i
$452$	9.24806	−	2.24356i	0.434992	−	0.105528i
$453$	−0.988763	+	2.46981i	−0.0464561	+	0.116042i
$454$	15.0911	+	17.4160i	0.708260	+	0.817375i
$455$	3.74280	−	17.3471i	0.175465	−	0.813244i
$456$	−4.90511	−	4.25030i	−0.229703	−	0.199039i
$457$	−11.7014	−	2.83874i	−0.547370	−	0.132790i	−0.0474682	−	0.998873i	$-0.515115\pi$
$457$	−11.7014	−	2.83874i	−0.547370	−	0.132790i	−0.499901	+	0.866082i	$0.666630\pi$
$458$	−2.37196	+	3.33095i	−0.110834	+	0.155645i
$459$	−5.56706	+	3.21414i	−0.259848	+	0.150023i
$460$	12.1089	+	0.878287i	0.564582	+	0.0409504i
$461$			21.5309i			1.00279i	0.865217	+	0.501397i	$0.167180\pi$
$461$			21.5309i			1.00279i	−0.865217	+	0.501397i	$0.832820\pi$
$462$	−8.50406	+	2.29413i	−0.395645	+	0.106733i
$463$	3.97380	−	1.16681i	0.184678	−	0.0542264i	−0.188086	−	0.982153i	$-0.560228\pi$
$463$	3.97380	−	1.16681i	0.184678	−	0.0542264i	0.372764	+	0.927926i	$0.378410\pi$
$464$	0.0463728	+	0.133985i	0.00215280	+	0.00622012i
$465$	0.277413	−	5.82361i	0.0128647	−	0.270064i
$466$	5.36135	−	15.4906i	0.248360	−	0.717588i
$467$	−6.15227	−	2.46300i	−0.284693	−	0.113974i	0.224921	−	0.974377i	$-0.427788\pi$
$467$	−6.15227	−	2.46300i	−0.284693	−	0.113974i	−0.509614	+	0.860403i	$0.670212\pi$
$468$	−0.746472	+	2.54225i	−0.0345057	+	0.117516i
$469$	−0.416220	+	0.179072i	−0.0192192	+	0.00826879i
$470$	23.9238	+	3.43972i	1.10352	+	0.158663i
$471$	11.8367	−	8.42885i	0.545405	−	0.388381i
$472$	1.33748	+	14.0068i	0.0615626	+	0.644713i
$473$	−0.0670315	+	0.0268354i	−0.00308211	+	0.00123389i
$474$	0.349477	+	7.33643i	0.0160520	+	0.336974i
$475$	8.77197	+	2.57568i	0.402486	+	0.118180i
$476$	8.17622	+	14.9134i	0.374757	+	0.683555i
$477$	−1.67756	+	1.45362i	−0.0768104	+	0.0665566i
$478$	−22.3334	+	11.5137i	−1.02151	+	0.526623i
$479$	4.87613	+	0.939796i	0.222796	+	0.0429404i	0.299427	−	0.954119i	$-0.403204\pi$
$479$	4.87613	+	0.939796i	0.222796	+	0.0429404i	−0.0766315	+	0.997059i	$0.524417\pi$
$480$	1.74695	−	1.83215i	0.0797369	−	0.0836257i
$481$	1.45743	+	0.139168i	0.0664531	+	0.00634550i
$482$	19.0018			0.865508
$483$	1.19739	−	12.6320i	0.0544831	−	0.574774i
$484$	−0.0831561			−0.00377982
$485$	−10.4757	−	1.00031i	−0.475678	−	0.0454217i
$486$	0.690079	−	0.723734i	0.0313026	−	0.0328292i
$487$	−11.4676	−	2.21019i	−0.519645	−	0.100153i	−0.0773165	−	0.997007i	$-0.524635\pi$
$487$	−11.4676	−	2.21019i	−0.519645	−	0.100153i	−0.442328	+	0.896853i	$0.645847\pi$
$488$	−4.73918	+	2.44322i	−0.214533	+	0.110599i
$489$	11.6381	−	10.0845i	0.526294	−	0.456037i
$490$	13.4317	+	11.5590i	0.606781	+	0.522183i
$491$	−31.6219	−	9.28503i	−1.42708	−	0.419028i	−0.525185	−	0.850988i	$-0.676004\pi$
$491$	−31.6219	−	9.28503i	−1.42708	−	0.419028i	−0.901892	+	0.431961i	$0.857822\pi$
$492$	−0.357119	−	7.49685i	−0.0161002	−	0.337984i
$493$	−0.846138	+	0.338742i	−0.0381081	+	0.0152562i
$494$	−1.63466	−	17.1189i	−0.0735468	−	0.770217i
$495$	−6.86506	+	4.88859i	−0.308562	+	0.219726i
$496$	2.27961	+	0.327758i	0.102357	+	0.0147168i
$497$	16.4683	+	1.94068i	0.738705	+	0.0870516i
$498$	−2.27736	+	7.75597i	−0.102051	+	0.347553i
$499$	34.9713	+	14.0004i	1.56553	+	0.626744i	0.982593	−	0.185773i	$-0.0594790\pi$
$499$	34.9713	+	14.0004i	1.56553	+	0.626744i	0.582937	+	0.812517i	$0.301903\pi$
$500$	2.97361	−	8.59169i	0.132984	−	0.384232i
$501$	0.919828	−	19.3096i	0.0410949	−	0.862688i
$502$	−2.24261	−	6.47959i	−0.100092	−	0.289198i
$503$	−28.7123	+	8.43070i	−1.28022	+	0.375906i	−0.849983	−	0.526810i	$-0.823388\pi$
$503$	−28.7123	+	8.43070i	−1.28022	+	0.375906i	−0.430236	+	0.902716i	$0.641570\pi$
$504$	−1.87400	−	1.86765i	−0.0834746	−	0.0831918i
$505$			42.2749i			1.88121i
$506$	5.59458	−	14.9537i	0.248709	−	0.664773i
$507$	5.17860	−	2.98987i	0.229990	−	0.132785i
$508$	−2.62241	+	3.68266i	−0.116351	+	0.163392i
$509$	−26.2553	−	6.36946i	−1.16374	−	0.282321i	−0.393045	−	0.919519i	$-0.628578\pi$
$509$	−26.2553	−	6.36946i	−1.16374	−	0.282321i	−0.770700	+	0.637198i	$0.780093\pi$
$510$	12.2986	+	10.6568i	0.544590	+	0.471890i
$511$	−2.29505	−	2.07923i	−0.101527	−	0.0919798i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−2.41223	+	6.02547i	−0.106503	+	0.266031i
$514$	−24.8337	+	6.02458i	−1.09537	+	0.265733i
$515$	11.4054	+	5.87991i	0.502583	+	0.259100i
$516$	−0.0170482	−	0.0134069i	−0.000750506	−	0.000590204i
$517$	13.2040	−	28.9128i	0.580712	−	1.27158i
$518$	−0.817375	+	1.21210i	−0.0359134	+	0.0532565i
$519$	−2.05472	+	14.2909i	−0.0901921	+	0.627300i
$520$	6.69986	−	0.319154i	0.293808	−	0.0139958i
$521$	−10.4558	−	43.0992i	−0.458075	−	1.88821i	−0.459433	−	0.888213i	$-0.651947\pi$
$521$	−10.4558	−	43.0992i	−0.458075	−	1.88821i	0.00135764	−	0.999999i	$-0.499568\pi$
$522$	0.111449	−	0.0876447i	0.00487800	−	0.00383610i
$523$	29.4606	−	5.67807i	1.28822	−	0.248285i	0.501267	−	0.865293i	$-0.332867\pi$
$523$	29.4606	−	5.67807i	1.28822	−	0.248285i	0.786957	+	0.617008i	$0.211655\pi$
$524$	4.29618	−	6.68498i	0.187679	−	0.292035i
$525$	3.49401	+	1.29645i	0.152491	+	0.0565816i
$526$	1.55019	+	5.27947i	0.0675916	+	0.230196i
$527$	−1.40727	+	14.7376i	−0.0613018	+	0.641982i
$528$	−1.66457	−	2.88312i	−0.0724411	−	0.125472i
$529$	17.3519	+	15.0967i	0.754431	+	0.656379i
$530$	4.86646	+	2.80965i	0.211386	+	0.122043i
$531$	12.7989	−	5.84508i	0.555427	−	0.253655i
$532$	15.7969	+	6.73294i	0.684885	+	0.291910i
$533$	13.0226	−	15.0288i	0.564070	−	0.650971i
$534$	−4.45452	−	8.64056i	−0.192766	−	0.373914i
$535$	−23.8993	−	8.27164i	−1.03326	−	0.357614i
$536$	−0.105865	−	0.134618i	−0.00457266	−	0.00581461i
$537$	−8.57350	−	8.99163i	−0.369974	−	0.388017i
$538$	−10.8034	−	16.8105i	−0.465769	−	0.724751i
$539$	19.5617	−	12.6655i	0.842580	−	0.545544i
$540$	−2.30275	−	1.05163i	−0.0990946	−	0.0452550i
$541$	−7.20410	−	10.1167i	−0.309729	−	0.434953i	0.630144	−	0.776478i	$-0.282996\pi$
$541$	−7.20410	−	10.1167i	−0.309729	−	0.434953i	−0.939873	+	0.341525i	$0.889056\pi$
$542$	4.48749	+	11.2092i	0.192754	+	0.481477i
$543$	−6.91344	+	13.4102i	−0.296684	+	0.575487i
$544$	−4.65237	+	4.43603i	−0.199469	+	0.190193i
$545$	−46.1333	+	6.63297i	−1.97613	+	0.284125i
$546$	−0.178719	−	7.00785i	−0.00764847	−	0.299908i
$547$	19.8282	+	12.7428i	0.847793	+	0.544844i	0.890886	−	0.454228i	$-0.150085\pi$
$547$	19.8282	+	12.7428i	0.847793	+	0.544844i	−0.0430926	+	0.999071i	$0.513721\pi$
$548$	19.1779	−	6.63752i	0.819237	−	0.283541i
$549$	3.85888	+	3.67943i	0.164693	+	0.157034i
$550$	3.81986	+	2.72011i	0.162879	+	0.115986i
$551$	−0.460115	+	0.796942i	−0.0196016	+	0.0339509i
$552$	4.73023	−	0.790537i	0.201332	−	0.0336475i
$553$	−6.82182	−	18.1956i	−0.290093	−	0.773756i
$554$	10.9394	+	23.9540i	0.464771	+	1.01771i
$555$	−0.329785	+	1.35939i	−0.0139986	+	0.0577031i
$556$	0.00922394	−	0.0478584i	0.000391182	−	0.00202965i
$557$	14.3612	+	0.684107i	0.608502	+	0.0289865i	0.349572	−	0.936910i	$-0.386327\pi$
$557$	14.3612	+	0.684107i	0.608502	+	0.0289865i	0.258930	+	0.965896i	$0.416630\pi$
$558$	−0.435855	−	2.26143i	−0.0184512	−	0.0957340i
$559$	−0.00817813	−	0.0568801i	−0.000345898	−	0.00240577i
$560$	−2.91632	+	6.02953i	−0.123237	+	0.254794i
$561$	18.0034	−	11.5701i	0.760103	−	0.488489i
$562$	9.50233	−	12.0832i	0.400832	−	0.509699i
$563$	−17.2297	+	1.64523i	−0.726144	+	0.0693383i	−0.451580	−	0.892231i	$-0.649139\pi$
$563$	−17.2297	+	1.64523i	−0.726144	+	0.0693383i	−0.274564	+	0.961569i	$0.588533\pi$
$564$	9.50432	−	0.907552i	0.400204	−	0.0382149i
$565$	−14.8919	+	18.9366i	−0.626507	+	0.796668i
$566$	−2.80736	+	1.80418i	−0.118002	+	0.0758353i
$567$	−1.15201	+	2.38178i	−0.0483797	+	0.100025i
$568$	0.891960	+	6.20372i	0.0374258	+	0.260302i
$569$	−3.34122	−	17.3359i	−0.140071	−	0.726759i	−0.982252	−	0.187564i	$-0.939941\pi$
$569$	−3.34122	−	17.3359i	−0.140071	−	0.726759i	0.842181	−	0.539195i	$-0.181271\pi$
$570$	16.4119	+	0.781797i	0.687420	+	0.0327459i
$571$	−5.40758	+	28.0572i	−0.226300	+	1.17416i	0.673948	+	0.738779i	$0.264597\pi$
$571$	−5.40758	+	28.0572i	−0.226300	+	1.17416i	−0.900248	+	0.435377i	$0.856615\pi$
$572$	2.07958	−	8.57216i	0.0869518	−	0.358420i
$573$	−2.04738	−	4.48313i	−0.0855304	−	0.187285i
$574$	6.97098	+	18.5935i	0.290963	+	0.776077i
$575$	−5.59825	+	3.78080i	−0.233463	+	0.157670i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−12.3400	−	8.78726i	−0.513720	−	0.365819i	0.293603	−	0.955927i	$-0.405145\pi$
$577$	−12.3400	−	8.78726i	−0.513720	−	0.365819i	−0.807324	+	0.590109i	$0.799085\pi$
$578$	−17.6033	−	16.7847i	−0.732201	−	0.698153i
$579$	−12.3397	+	4.27083i	−0.512822	+	0.177490i
$580$	−0.301949	−	0.194051i	−0.0125377	−	0.00805752i
$581$	−0.545241	−	21.3797i	−0.0226204	−	0.886981i
$582$	−4.11462	+	0.591594i	−0.170557	+	0.0245223i
$583$	5.34825	−	5.09955i	0.221502	−	0.211202i
$584$	0.536353	−	1.04038i	0.0221944	−	0.0430512i
$585$	−2.49291	−	6.22699i	−0.103069	−	0.257454i
$586$	12.7203	+	17.8632i	0.525471	+	0.737920i
$587$	−28.6510	−	13.0845i	−1.18255	−	0.540053i	−0.275594	−	0.961274i	$-0.588874\pi$
$587$	−28.6510	−	13.0845i	−1.18255	−	0.540053i	−0.906958	+	0.421221i	$0.861602\pi$
$588$	6.23270	+	3.18645i	0.257032	+	0.131407i
$589$	8.08133	+	12.5748i	0.332986	+	0.518136i
$590$	−24.5804	−	25.7792i	−1.01196	−	1.06131i
$591$	−3.27631	−	4.16617i	−0.134769	−	0.171373i
$592$	−0.522173	−	0.180726i	−0.0214612	−	0.00742778i
$593$	−9.87888	−	19.1624i	−0.405677	−	0.786903i	0.594171	−	0.804339i	$-0.297480\pi$
$593$	−9.87888	−	19.1624i	−0.405677	−	0.786903i	−0.999848	+	0.0174353i	$0.994450\pi$
$594$	−2.18012	+	2.51599i	−0.0894515	+	0.103232i
$595$	−39.6076	−	16.8815i	−1.62376	−	0.692074i
$596$	−1.14573	+	0.523238i	−0.0469310	+	0.0214327i
$597$	23.4972	+	13.5661i	0.961676	+	0.555224i
$598$	10.5161	+	7.13291i	0.430034	+	0.291686i
$599$	17.5634	+	30.4207i	0.717620	+	1.24296i	0.961940	+	0.273260i	$0.0881020\pi$
$599$	17.5634	+	30.4207i	0.717620	+	1.24296i	−0.244320	+	0.969695i	$0.578565\pi$
$600$	−0.133895	+	1.40221i	−0.00546624	+	0.0572450i
$601$	12.8209	+	43.6639i	0.522974	+	1.78109i	0.618641	+	0.785674i	$0.287683\pi$
$601$	12.8209	+	43.6639i	0.522974	+	1.78109i	−0.0956670	+	0.995413i	$0.530498\pi$
$602$	0.0537981	+	0.0199617i	0.00219265	+	0.000813578i
$603$	−0.0925892	+	0.144072i	−0.00377052	+	0.00586705i
$604$	2.61230	−	0.503480i	0.106293	−	0.0204863i
$605$	0.165473	−	0.130129i	0.00672744	−	0.00529052i
$606$	3.93704	+	16.2287i	0.159931	+	0.659246i
$607$	11.8915	−	0.566464i	0.482663	−	0.0229921i	0.195159	−	0.980772i	$-0.437478\pi$
$607$	11.8915	−	0.566464i	0.482663	−	0.0229921i	0.287504	+	0.957780i	$0.407175\pi$
$608$	−0.923679	+	6.42433i	−0.0374601	+	0.260541i
$609$	−0.209732	+	0.311015i	−0.00849877	+	0.0126030i
$610$	5.60719	−	12.2780i	0.227028	−	0.497123i
$611$	19.8848	+	15.6376i	0.804452	+	0.632628i
$612$	5.71369	+	2.94561i	0.230962	+	0.119069i
$613$	−32.7696	+	7.94981i	−1.32355	+	0.321090i	−0.834424	−	0.551123i	$-0.814200\pi$
$613$	−32.7696	+	7.94981i	−1.32355	+	0.321090i	−0.489127	+	0.872213i	$0.662684\pi$
$614$	9.33641	−	23.3212i	0.376787	−	0.941168i
$615$	12.4423	+	14.3592i	0.501722	+	0.579019i
$616$	6.52759	+	5.91377i	0.263004	+	0.238273i
$617$	25.5701	+	22.1566i	1.02941	+	0.891992i	0.994217	−	0.107388i	$-0.0342487\pi$
$617$	25.5701	+	22.1566i	1.02941	+	0.891992i	0.0351969	+	0.999380i	$0.488794\pi$
$618$	4.92596	+	1.19503i	0.198151	+	0.0480710i
$619$	−24.9711	+	35.0671i	−1.00367	+	1.40946i	−0.0933193	+	0.995636i	$0.529748\pi$
$619$	−24.9711	+	35.0671i	−1.00367	+	1.40946i	−0.910355	+	0.413828i	$0.864192\pi$
$620$	−5.04912	+	2.91511i	−0.202777	+	0.117074i
$621$	−2.29416	−	4.21151i	−0.0920616	−	0.169002i
$622$		−	16.7877i		−	0.673124i
$623$	18.2176	+	18.1558i	0.729871	+	0.727398i
$624$	2.54225	−	0.746472i	0.101772	−	0.0298828i
$625$	9.83128	+	28.4056i	0.393251	+	1.13622i
$626$	0.181392	−	3.80789i	0.00724989	−	0.152194i
$627$	7.06709	−	20.4190i	0.282232	−	0.815457i
$628$	−13.4902	−	5.40066i	−0.538317	−	0.215510i
$629$	1.00072	−	3.40815i	0.0399015	−	0.135892i
$630$	6.65174	+	0.783865i	0.265012	+	0.0312299i
$631$	16.2150	+	2.33136i	0.645508	+	0.0928101i	0.457291	−	0.889317i	$-0.348820\pi$
$631$	16.2150	+	2.33136i	0.645508	+	0.0928101i	0.188218	+	0.982127i	$0.439729\pi$
$632$	5.98286	−	4.26037i	0.237985	−	0.169469i
$633$	−1.24159	−	13.0025i	−0.0493486	−	0.516802i
$634$	−3.85825	+	1.54461i	−0.153231	+	0.0613444i
$635$	−0.544569	−	11.4319i	−0.0216106	−	0.453662i
$636$	2.12982	+	0.625372i	0.0844529	+	0.0247976i
$637$	6.12560	+	17.5063i	0.242705	+	0.693624i
$638$	−0.356726	+	0.309105i	−0.0141229	+	0.0122376i
$639$	5.57078	−	2.87194i	0.220377	−	0.113612i
$640$	−2.48577	−	0.479093i	−0.0982587	−	0.0189378i
$641$	−34.5504	+	36.2354i	−1.36466	+	1.43121i	−0.574172	+	0.818735i	$0.694676\pi$
$641$	−34.5504	+	36.2354i	−1.36466	+	1.43121i	−0.790487	+	0.612478i	$0.790173\pi$
$642$	−9.94492	−	0.949625i	−0.392495	−	0.0374787i
$643$	40.7987			1.60894			0.804471	−	0.593992i	$-0.202449\pi$
$643$	40.7987			1.60894			0.804471	+	0.593992i	$0.202449\pi$
$644$	−11.2740	+	5.82204i	−0.444259	+	0.229421i
$645$	0.0549046			0.00216186
$646$	−41.5332	−	3.96594i	−1.63410	−	0.156038i
$647$	23.3712	−	24.5111i	0.918818	−	0.963629i	−0.0806333	−	0.996744i	$-0.525694\pi$
$647$	23.3712	−	24.5111i	0.918818	−	0.963629i	0.999452	+	0.0331150i	$0.0105428\pi$
$648$	−0.981929	−	0.189251i	−0.0385738	−	0.00743449i
$649$	−41.6353	+	21.4645i	−1.63433	+	0.842555i
$650$	−2.82058	+	2.44405i	−0.110632	+	0.0958635i
$651$	2.92928	+	5.34300i	0.114808	+	0.209409i
$652$	−14.7757	−	4.33853i	−0.578660	−	0.169910i
$653$	−1.10483	−	23.1932i	−0.0432353	−	0.907620i	−0.911445	−	0.411423i	$-0.865032\pi$
$653$	−1.10483	−	23.1932i	−0.0432353	−	0.907620i	0.868209	−	0.496198i	$-0.165271\pi$
$654$	−17.0922	+	6.84267i	−0.668356	+	0.267569i
$655$	1.91220	+	20.0255i	0.0747160	+	0.782461i
$656$	−6.11368	+	4.35353i	−0.238699	+	0.169977i
$657$	−1.15858	−	0.166579i	−0.0452006	−	0.00649887i
$658$	−23.2040	+	9.98318i	−0.904587	+	0.389185i
$659$	3.93795	−	13.4114i	0.153401	−	0.522434i	−0.846551	−	0.532308i	$-0.821325\pi$
$659$	3.93795	−	13.4114i	0.153401	−	0.522434i	0.999951	+	0.00987376i	$0.00314297\pi$
$660$	7.82408	+	3.13229i	0.304552	+	0.121924i
$661$	−6.51848	+	18.8339i	−0.253540	+	0.732554i	0.744360	+	0.667778i	$0.232755\pi$
$661$	−6.51848	+	18.8339i	−0.253540	+	0.732554i	−0.997900	+	0.0647762i	$0.979367\pi$
$662$	1.36701	−	28.6971i	0.0531305	−	1.11535i
$663$	5.57070	+	16.0955i	0.216348	+	0.625097i
$664$	7.75597	−	2.27736i	0.300990	−	0.0883787i
$665$	−41.9707	+	11.3224i	−1.62756	+	0.439064i
$666$			0.552563i			0.0214114i
$667$	−0.236984	−	0.637336i	−0.00917606	−	0.0246777i
$668$	−16.7415	+	9.66573i	−0.647749	+	0.373978i
$669$	8.19964	−	11.5148i	0.317017	−	0.445188i
$670$	0.421322	+	0.102212i	0.0162771	+	0.00394878i
$671$	−13.4150	−	11.6242i	−0.517881	−	0.448747i
$672$	−0.558006	+	2.58624i	−0.0215256	+	0.0997663i
$673$	−18.3692	−	21.1992i	−0.708082	−	0.817171i	0.281738	−	0.959491i	$-0.409089\pi$
$673$	−18.3692	−	21.1992i	−0.708082	−	0.817171i	−0.989821	+	0.142321i	$0.954544\pi$
$674$	0.803253	−	2.00643i	0.0309401	−	0.0772847i
$675$	1.36888	−	0.332088i	0.0526884	−	0.0127821i
$676$	−5.31500	−	2.74007i	−0.204423	−	0.105387i
$677$	−3.53041	−	2.77635i	−0.135685	−	0.106704i	0.548010	−	0.836472i	$-0.315386\pi$
$677$	−3.53041	−	2.77635i	−0.135685	−	0.106704i	−0.683695	+	0.729768i	$0.739628\pi$
$678$	−3.95322	+	8.65634i	−0.151822	+	0.332445i
$679$	9.88460	−	4.82240i	0.379336	−	0.185067i
$680$	2.31594	−	16.1077i	0.0888121	−	0.617702i
$681$	−23.0186	+	1.09651i	−0.882075	+	0.0420184i
$682$	1.80760	+	7.45105i	0.0692167	+	0.285315i
$683$	2.74703	−	2.16029i	0.105112	−	0.0826611i	−0.564220	−	0.825625i	$-0.690823\pi$
$683$	2.74703	−	2.16029i	0.105112	−	0.0826611i	0.669332	+	0.742964i	$0.266580\pi$
$684$	6.37310	−	1.22831i	0.243682	−	0.0469658i
$685$	−27.7752	+	43.2191i	−1.06124	+	1.65132i
$686$	−18.2792	−	2.97818i	−0.697904	−	0.113707i
$687$	−1.15206	−	3.92354i	−0.0439537	−	0.149693i
$688$	−0.00206161	+	0.0215902i	−7.85982e−5	+	0.000823118i
$689$	2.94068	+	5.09341i	0.112031	+	0.194043i
$690$	−8.17562	+	8.97534i	−0.311241	+	0.341685i
$691$	4.00362	+	2.31149i	0.152305	+	0.0879332i	0.574216	−	0.818704i	$-0.305307\pi$
$691$	4.00362	+	2.31149i	0.152305	+	0.0879332i	−0.421911	+	0.906637i	$0.638640\pi$
$692$	13.1331	−	5.99769i	0.499246	−	0.227998i
$693$	3.45355	−	8.10278i	0.131190	−	0.307799i
$694$	4.18934	−	4.83476i	0.159025	−	0.183525i
$695$	0.0565378	+	0.109668i	0.00214460	+	0.00415995i
$696$	−0.133985	−	0.0463728i	−0.00507871	−	0.00175776i
$697$	−29.8240	−	37.9244i	−1.12967	−	1.43649i
$698$	16.3962	+	17.1958i	0.620604	+	0.650871i
$699$	8.86227	+	13.7900i	0.335202	+	0.521584i
$700$	−0.798363	−	3.64026i	−0.0301753	−	0.137589i
$701$	3.58804	+	1.63860i	0.135519	+	0.0618892i	0.482020	−	0.876160i	$-0.339903\pi$
$701$	3.58804	+	1.63860i	0.135519	+	0.0618892i	−0.346502	+	0.938049i	$0.612630\pi$
$702$	−1.53691	−	2.15828i	−0.0580068	−	0.0814591i
$703$	−1.33291	−	3.32945i	−0.0502717	−	0.125573i
$704$	−1.52550	+	2.95906i	−0.0574944	+	0.111524i
$705$	−17.4925	+	16.6791i	−0.658806	+	0.628170i
$706$	27.6216	−	3.97139i	1.03955	−	0.149465i
$707$	−23.0596	−	37.6875i	−0.867245	−	1.41739i
$708$	−11.8368	−	7.60707i	−0.444855	−	0.285891i
$709$	−9.38999	+	3.24991i	−0.352648	+	0.122053i	−0.497648	−	0.867379i	$-0.665803\pi$
$709$	−9.38999	+	3.24991i	−0.352648	+	0.122053i	0.145000	+	0.989432i	$0.453682\pi$
$710$	−11.4830	−	10.9490i	−0.430949	−	0.410909i
$711$	−5.98286	−	4.26037i	−0.224375	−	0.159777i
$712$	−4.86061	+	8.41882i	−0.182159	+	0.315508i
$713$	−10.9656	−	1.32228i	−0.410665	−	0.0495199i
$714$	−16.7769	−	2.79191i	−0.627861	−	0.104485i
$715$	9.27624	+	20.3121i	0.346912	+	0.759630i
$716$	−2.92906	+	12.0737i	−0.109464	+	0.451216i
$717$	4.75524	−	24.6725i	0.177588	−	0.921412i
$718$	−21.2231	−	1.01098i	−0.792040	−	0.0377295i
$719$	3.16830	+	16.4387i	0.118158	+	0.613061i	0.991936	+	0.126737i	$0.0404503\pi$
$719$	3.16830	+	16.4387i	0.118158	+	0.613061i	−0.873779	+	0.486324i	$0.838338\pi$
$720$	0.360273	+	2.50575i	0.0134266	+	0.0933839i
$721$	−13.3751	+	0.979425i	−0.498114	+	0.0364757i
$722$	−19.4541	+	12.5024i	−0.724008	+	0.465291i
$723$	−11.7461	+	14.9364i	−0.436843	+	0.555491i
$724$	15.0191	−	1.43415i	0.558179	−	0.0532996i
$725$	0.198810	−	0.0189841i	0.00738363	−	0.000705051i
$726$	0.0514037	−	0.0653651i	0.00190777	−	0.00242593i
$727$	25.6818	−	16.5047i	0.952486	−	0.612126i	0.0305771	−	0.999532i	$-0.490265\pi$
$727$	25.6818	−	16.5047i	0.952486	−	0.612126i	0.921909	+	0.387407i	$0.126629\pi$
$728$	−5.79875	+	3.93908i	−0.214916	+	0.145992i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	0.560777	+	2.90959i	0.0207553	+	0.107689i
$731$	−0.139261	−	0.00663383i	−0.00515076	−	0.000245361i
$732$	1.00907	−	5.23554i	0.0372962	−	0.193511i
$733$	−0.401579	+	1.65533i	−0.0148326	+	0.0611410i	−0.978747	−	0.205072i	$-0.934257\pi$
$733$	−0.401579	+	1.65533i	−0.0148326	+	0.0611410i	0.963914	+	0.266213i	$0.0857724\pi$
$734$	9.31639	+	20.4000i	0.343874	+	0.752979i
$735$	−17.3889	+	3.41270i	−0.641400	+	0.125879i
$736$	−3.22240	−	3.55192i	−0.118779	−	0.130926i
$737$	0.285071	−	0.493757i	0.0105007	−	0.0181878i
$738$	6.11368	+	4.35353i	0.225048	+	0.160256i
$739$	23.3480	+	22.2623i	0.858870	+	0.818930i	0.984905	−	0.173095i	$-0.0553768\pi$
$739$	23.3480	+	22.2623i	0.858870	+	0.818930i	−0.126036	+	0.992026i	$0.540225\pi$
$740$	1.32189	−	0.457511i	0.0485937	−	0.0168184i
$741$	14.4669	+	9.29729i	0.531454	+	0.341544i
$742$	−5.87096	+	0.149725i	−0.215530	+	0.00549659i
$743$	−25.3635	+	3.64672i	−0.930496	+	0.133785i	−0.590862	−	0.806772i	$-0.701212\pi$
$743$	−25.3635	+	3.64672i	−0.930496	+	0.133785i	−0.339634	+	0.940558i	$0.610303\pi$
$744$	−1.66680	+	1.58929i	−0.0611077	+	0.0582661i
$745$	1.46110	−	2.83413i	0.0535304	−	0.103835i
$746$	8.93318	+	22.3140i	0.327067	+	0.816974i
$747$	−4.68884	−	6.58455i	−0.171556	−	0.240916i
$748$	−19.4667	−	8.89015i	−0.711774	−	0.325056i
$749$	25.8179	−	5.66224i	0.943364	−	0.206894i
$750$	4.91536	+	7.64845i	0.179483	+	0.279282i
$751$	28.2624	+	29.6408i	1.03131	+	1.08161i	0.996615	+	0.0822096i	$0.0261977\pi$
$751$	28.2624	+	29.6408i	1.03131	+	1.08161i	0.0346956	+	0.999398i	$0.488954\pi$
$752$	−5.90190	−	7.50488i	−0.215220	−	0.273675i
$753$	6.47959	+	2.24261i	0.236129	+	0.0817252i
$754$	−0.172140	−	0.333905i	−0.00626898	−	0.0121601i
$755$	−4.41035	+	5.08982i	−0.160509	+	0.185238i
$756$	2.62650	−	0.318559i	0.0955250	−	0.0115859i
$757$	21.3812	−	9.76449i	0.777114	−	0.354896i	0.0129486	−	0.999916i	$-0.495878\pi$
$757$	21.3812	−	9.76449i	0.777114	−	0.354896i	0.764166	+	0.645020i	$0.223151\pi$
$758$	−2.06756	−	1.19371i	−0.0750973	−	0.0433574i
$759$	8.29607	+	13.6414i	0.301128	+	0.495152i
$760$	−8.21527	−	14.2293i	−0.297999	−	0.516150i
$761$	3.96963	−	41.5718i	0.143899	−	1.50698i	−0.578604	−	0.815609i	$-0.696402\pi$
$761$	3.96963	−	41.5718i	0.143899	−	1.50698i	0.722503	−	0.691368i	$-0.242992\pi$
$762$	−1.27370	−	4.33782i	−0.0461413	−	0.157143i
$763$	37.5092	−	31.0774i	1.35792	−	1.12508i
$764$	−2.66455	+	4.14613i	−0.0964001	+	0.150002i
$765$	−15.9793	+	3.07975i	−0.577731	+	0.111349i
$766$	−7.88947	+	6.20435i	−0.285058	+	0.224172i
$767$	−8.78928	−	36.2299i	−0.317363	−	1.30819i
$768$	−0.998867	+	0.0475819i	−0.0360435	+	0.00171696i
$769$	1.44038	−	10.0181i	0.0519415	−	0.361261i	−0.947230	−	0.320556i	$-0.896130\pi$
$769$	1.44038	−	10.0181i	0.0519415	−	0.361261i	0.999171	−	0.0407056i	$-0.0129606\pi$
$770$	−22.2437	−	1.55296i	−0.801606	−	0.0559647i
$771$	10.6155	−	23.2447i	0.382308	−	0.837139i
$772$	10.2642	+	8.07187i	0.369417	+	0.290513i
$773$	−21.9829	−	11.3330i	−0.790671	−	0.407619i	0.0150708	−	0.999886i	$-0.495203\pi$
$773$	−21.9829	−	11.3330i	−0.790671	−	0.407619i	−0.805742	+	0.592267i	$0.798233\pi$
$774$	0.0210770	−	0.00511323i	0.000757598	−	0.000183791i
$775$	1.20569	−	3.01167i	0.0433098	−	0.108183i
$776$	2.72221	+	3.14160i	0.0977218	+	0.112777i
$777$	−0.447505	−	1.39177i	−0.0160542	−	0.0499294i
$778$	21.7797	+	18.8722i	0.780840	+	0.676602i
$779$	−47.3395	−	11.4844i	−1.69611	−	0.411473i
$780$	−3.89071	+	5.46373i	−0.139310	+	0.195633i
$781$	−18.0700	+	10.4327i	−0.646594	+	0.373311i
$782$	21.8213	−	21.7775i	0.780328	−	0.778760i
$783$			0.141783i			0.00506693i
$784$	−0.689042	−	6.96600i	−0.0246086	−	0.248786i
$785$	35.2956	−	10.3637i	1.25975	−	0.369897i
$786$	2.59903	+	7.50940i	0.0927043	+	0.267852i
$787$	−0.472363	+	9.91612i	−0.0168379	+	0.353471i	0.974689	+	0.223567i	$0.0717701\pi$
$787$	−0.472363	+	9.91612i	−0.0168379	+	0.353471i	−0.991527	+	0.129905i	$0.958533\pi$
$788$	−1.73349	+	5.00860i	−0.0617532	+	0.178424i
$789$	−5.10821	−	2.04502i	−0.181857	−	0.0728045i
$790$	−5.23836	+	17.8402i	−0.186373	+	0.634727i
$791$	2.94665	−	25.0048i	0.104771	−	0.889067i
$792$	3.29525	+	0.473786i	0.117092	+	0.0168352i
$793$	11.5077	−	8.19463i	0.408652	−	0.291000i
$794$	−0.614363	−	6.43390i	−0.0218029	−	0.228331i
$795$	−5.21678	+	2.08848i	−0.185020	+	0.0740709i
$796$	−1.29100	−	27.1015i	−0.0457584	−	0.960587i
$797$	36.6224	+	10.7533i	1.29723	+	0.380902i	0.856226	−	0.516602i	$-0.172803\pi$
$797$	36.6224	+	10.7533i	1.29723	+	0.380902i	0.441007	+	0.897504i	$0.354621\pi$
$798$	−15.0575	+	8.25521i	−0.533029	+	0.292231i
$799$	46.3837	−	40.1917i	1.64094	−	1.42188i
$800$	1.25200	−	0.645453i	0.0442650	−	0.0228202i
$801$	9.54554	+	1.83975i	0.337275	+	0.0650044i
$802$	−4.15751	+	4.36027i	−0.146807	+	0.153967i
$803$	3.87910	+	0.370409i	0.136891	+	0.0130715i
$804$	0.171258			0.00603981
$805$	13.3235	−	29.2279i	0.469591	−	1.03015i
$806$	−6.10211			−0.214938
$807$	19.8922	+	1.89947i	0.700237	+	0.0668646i
$808$	11.5239	−	12.0859i	0.405410	−	0.425182i
$809$	19.7548	+	3.80743i	0.694542	+	0.133862i	0.524292	−	0.851539i	$-0.324330\pi$
$809$	19.7548	+	3.80743i	0.694542	+	0.133862i	0.170251	+	0.985401i	$0.445542\pi$
$810$	2.25010	−	1.16001i	0.0790606	−	0.0407586i
$811$	−40.8324	+	35.3815i	−1.43382	+	1.24241i	−0.509677	+	0.860366i	$0.670235\pi$
$811$	−40.8324	+	35.3815i	−1.43382	+	1.24241i	−0.924143	+	0.382046i	$0.875220\pi$
$812$	0.375032	+	0.00829057i	0.0131610	+	0.000290942i
$813$	−11.5850	−	3.40167i	−0.406304	−	0.119302i
$814$	−0.0875297	−	1.83748i	−0.00306792	−	0.0644035i
$815$	36.1915	−	14.4889i	1.26773	−	0.507524i
$816$	−0.611048	−	6.39918i	−0.0213909	−	0.224016i
$817$	−0.114665	+	0.0816523i	−0.00401161	+	0.00285665i
$818$	24.1081	+	3.46623i	0.842921	+	0.121194i
$819$	5.61902	+	4.19148i	0.196344	+	0.146462i
$820$	5.35290	−	18.2303i	0.186931	−	0.636630i
$821$	−29.6184	−	11.8574i	−1.03369	−	0.413827i	−0.208106	−	0.978106i	$-0.566730\pi$
$821$	−29.6184	−	11.8574i	−1.03369	−	0.413827i	−0.825584	+	0.564280i	$0.809154\pi$
$822$	−6.63752	+	19.1779i	−0.231510	+	0.668905i
$823$	−0.995080	+	20.8893i	−0.0346863	+	0.728155i	0.912809	+	0.408386i	$0.133908\pi$
$823$	−0.995080	+	20.8893i	−0.0346863	+	0.728155i	−0.947496	+	0.319769i	$0.896395\pi$
$824$	−1.65786	−	4.79006i	−0.0577542	−	0.166870i
$825$	−4.49943	+	1.32115i	−0.156650	+	0.0459967i
$826$	35.9748	+	9.57400i	1.25172	+	0.333122i
$827$			51.5037i			1.79096i	0.445102	+	0.895480i	$0.353167\pi$
$827$			51.5037i			1.79096i	−0.445102	+	0.895480i	$0.646833\pi$
$828$	−2.30263	+	4.20689i	−0.0800219	+	0.146199i
$829$	−45.7350	+	26.4051i	−1.58844	+	0.917087i	−0.594876	+	0.803817i	$0.702799\pi$
$829$	−45.7350	+	26.4051i	−1.58844	+	0.917087i	−0.993564	+	0.113270i	$0.963868\pi$
$830$	−11.8699	+	16.6689i	−0.412009	+	0.578586i
$831$	−25.5914	−	6.20840i	−0.887755	−	0.215367i
$832$	−2.00242	−	1.73510i	−0.0694213	−	0.0601539i
$833$	44.5180	−	6.55504i	1.54246	−	0.227119i
$834$	0.0319173	+	0.0368346i	0.00110521	+	0.00127548i
$835$	18.1884	−	45.4324i	0.629436	−	1.57225i
$836$	−20.9983	+	5.09414i	−0.726242	+	0.176184i
$837$	2.04703	+	1.05532i	0.0707558	+	0.0364772i
$838$	14.8105	+	11.6471i	0.511621	+	0.402343i
$839$	3.77260	−	8.26084i	0.130245	−	0.285196i	−0.833263	−	0.552877i	$-0.813530\pi$
$839$	3.77260	−	8.26084i	0.130245	−	0.285196i	0.963508	+	0.267681i	$0.0862573\pi$
$840$	−2.93677	−	6.01959i	−0.101328	−	0.207696i
$841$	4.12427	−	28.6849i	0.142216	−	0.989135i
$842$	−24.5857	+	1.17116i	−0.847281	+	0.0403610i
$843$	3.62408	+	14.9387i	0.124820	+	0.514515i
$844$	−10.2671	+	8.07416i	−0.353409	+	0.277924i
$845$	14.8643	−	2.86485i	0.511346	−	0.0985539i
$846$	−5.16180	+	8.03191i	−0.177466	+	0.276143i
$847$	−0.0765358	+	0.206269i	−0.00262980	+	0.00708748i
$848$	−0.625372	−	2.12982i	−0.0214754	−	0.0731384i
$849$	0.317213	−	3.32200i	0.0108867	−	0.114011i
$850$	4.52741	+	7.84170i	0.155289	+	0.268968i
$851$	2.52336	+	0.809427i	0.0864996	+	0.0277468i
$852$	−5.42782	−	3.13375i	−0.185954	−	0.107361i
$853$	42.5499	−	19.4319i	1.45688	−	0.665335i	0.479639	−	0.877466i	$-0.340768\pi$
$853$	42.5499	−	19.4319i	1.45688	−	0.665335i	0.977241	+	0.212132i	$0.0680405\pi$
$854$	1.69853	+	14.0042i	0.0581224	+	0.479215i
$855$	−10.7597	+	12.4174i	−0.367975	+	0.424665i
$856$	4.57776	+	8.87961i	0.156464	+	0.303499i
$857$	−35.9942	−	12.4577i	−1.22954	−	0.425547i	−0.366372	−	0.930469i	$-0.619400\pi$
$857$	−35.9942	−	12.4577i	−1.22954	−	0.425547i	−0.863165	+	0.504922i	$0.831521\pi$
$858$	5.45266	+	6.93362i	0.186151	+	0.236710i
$859$	31.2560	+	32.7804i	1.06644	+	1.11845i	0.992631	+	0.121179i	$0.0386676\pi$
$859$	31.2560	+	32.7804i	1.06644	+	1.11845i	0.0738109	+	0.997272i	$0.476484\pi$
$860$	−0.0296836	−	0.0461887i	−0.00101220	−	0.00157502i
$861$	−18.9246	−	6.01417i	−0.644950	−	0.204962i
$862$	4.12050	+	1.88177i	0.140345	+	0.0640934i
$863$	23.6847	+	33.2605i	0.806237	+	1.13220i	0.988835	+	0.149013i	$0.0476097\pi$
$863$	23.6847	+	33.2605i	0.806237	+	1.13220i	−0.182599	+	0.983188i	$0.558451\pi$
$864$	0.371662	+	0.928368i	0.0126442	+	0.0315837i
$865$	−16.7480	+	32.4866i	−0.569450	+	1.10458i
$866$	3.55917	−	3.39366i	0.120946	−	0.115321i
$867$	24.0753	−	3.46151i	0.817641	−	0.117559i
$868$	2.91113	−	5.35291i	0.0988101	−	0.181690i
$869$	20.5701	+	13.2196i	0.697792	+	0.448444i
$870$	0.339187	−	0.117394i	0.0114995	−	0.00398002i
$871$	0.328403	+	0.313132i	0.0111275	+	0.0106101i
$872$	14.9971	+	10.6794i	0.507867	+	0.361651i
$873$	2.07847	−	3.60001i	0.0703455	−	0.121842i
$874$	3.72642	−	30.9030i	0.126048	−	1.04531i
$875$	−18.5748	−	15.2837i	−0.627944	−	0.516684i
$876$	0.486242	+	1.06472i	0.0164286	+	0.0359736i
$877$	5.30607	−	21.8719i	0.179173	−	0.738562i	−0.809329	−	0.587355i	$-0.800169\pi$
$877$	5.30607	−	21.8719i	0.179173	−	0.738562i	0.988502	−	0.151206i	$-0.0483158\pi$
$878$	−4.74697	+	24.6296i	−0.160203	+	0.831210i
$879$	−21.9046	−	1.04344i	−0.738822	−	0.0351945i
$880$	−1.59497	−	8.27547i	−0.0537663	−	0.278966i
$881$	−2.91653	−	20.2849i	−0.0982603	−	0.683415i	−0.978099	−	0.208142i	$-0.933258\pi$
$881$	−2.91653	−	20.2849i	−0.0982603	−	0.683415i	0.879838	−	0.475273i	$-0.157651\pi$
$882$	−6.35752	+	2.92950i	−0.214069	+	0.0986415i
$883$	17.8353	−	11.4621i	0.600206	−	0.385729i	−0.204967	−	0.978769i	$-0.565709\pi$
$883$	17.8353	−	11.4621i	0.600206	−	0.385729i	0.805173	+	0.593040i	$0.202072\pi$
$884$	10.5286	−	13.3883i	0.354117	−	0.450296i
$885$	35.4584	−	3.38586i	1.19192	−	0.113815i
$886$	−21.4412	+	2.04739i	−0.720333	+	0.0687834i
$887$	28.7182	−	36.5182i	0.964263	−	1.22616i	−0.00981590	−	0.999952i	$-0.503125\pi$
$887$	28.7182	−	36.5182i	0.964263	−	1.22616i	0.974079	−	0.226208i	$-0.0726330\pi$
$888$	0.464846	−	0.298738i	0.0155992	−	0.0100250i
$889$	6.72121	+	9.89436i	0.225422	+	0.331846i
$890$	−3.50229	−	24.3589i	−0.117397	−	0.816514i
$891$	−0.630043	−	3.26898i	−0.0211072	−	0.109515i
$892$	−14.1199	−	0.672615i	−0.472770	−	0.0225208i
$893$	11.7274	−	60.8475i	0.392442	−	2.03618i
$894$	0.296952	−	1.22405i	0.00993155	−	0.0409384i
$895$	−13.0654	−	28.6092i	−0.436728	−	0.956302i
$896$	2.47736	−	0.928801i	0.0827629	−	0.0310291i
$897$	−12.1074	+	3.85692i	−0.404256	+	0.128779i
$898$	2.94276	−	5.09701i	0.0982013	−	0.170090i
$899$	0.265987	+	0.189409i	0.00887116	+	0.00631713i
$900$	−1.01944	−	0.972038i	−0.0339815	−	0.0324013i
$901$	13.4843	−	4.66697i	0.449228	−	0.155479i
$902$	−21.0198	−	13.5086i	−0.699884	−	0.449788i
$903$	−0.0489467	+	0.0299486i	−0.00162884	+	0.000996628i
$904$	9.41945	−	1.35431i	0.313286	−	0.0450438i
$905$	−27.6423	+	26.3569i	−0.918861	+	0.876132i
$906$	−1.21906	+	2.36464i	−0.0405004	+	0.0785598i
$907$	−13.6094	−	33.9946i	−0.451892	−	1.12877i	−0.963059	−	0.269290i	$-0.913211\pi$
$907$	−13.6094	−	33.9946i	−0.451892	−	1.12877i	0.511167	−	0.859481i	$-0.329213\pi$
$908$	13.3672	+	18.7717i	0.443608	+	0.622960i
$909$	−15.1903	−	6.93719i	−0.503831	−	0.230092i
$910$	5.37480	−	16.9128i	0.178173	−	0.560653i
$911$	15.4129	+	23.9830i	0.510654	+	0.794593i	0.996854	−	0.0792544i	$-0.0252540\pi$
$911$	15.4129	+	23.9830i	0.510654	+	0.794593i	−0.486201	+	0.873847i	$0.661618\pi$
$912$	−4.47888	−	4.69732i	−0.148311	−	0.155544i
$913$	16.6351	+	21.1533i	0.550543	+	0.700072i
$914$	−11.3786	−	3.93817i	−0.376371	−	0.130263i
$915$	6.18505	+	11.9973i	0.204471	+	0.396619i
$916$	−2.67785	+	3.09040i	−0.0884785	+	0.102110i
$917$	−12.6280	−	16.8094i	−0.417012	−	0.555097i
$918$	−5.84738	+	2.67041i	−0.192992	+	0.0881366i
$919$	15.4483	+	8.91909i	0.509593	+	0.294214i	0.732666	−	0.680588i	$-0.238276\pi$
$919$	15.4483	+	8.91909i	0.509593	+	0.294214i	−0.223073	+	0.974802i	$0.571609\pi$
$920$	11.9706	+	2.02534i	0.394659	+	0.0667734i
$921$	12.5603	+	21.7551i	0.413877	+	0.716856i
$922$	−2.04664	+	21.4334i	−0.0674025	+	0.705871i
$923$	−4.67852	−	15.9336i	−0.153995	−	0.524460i
$924$	−8.68362	+	1.47538i	−0.285670	+	0.0485365i
$925$	−0.420800	+	0.654777i	−0.0138358	+	0.0215289i
$926$	4.06672	−	0.783796i	0.133641	−	0.0257571i
$927$	−3.98438	+	3.13335i	−0.130864	+	0.102913i
$928$	0.0334267	+	0.137787i	0.00109729	+	0.00452307i
$929$	56.6074	−	2.69654i	1.85723	−	0.0884707i	0.911085	−	0.412220i	$-0.135246\pi$
$929$	56.6074	−	2.69654i	1.85723	−	0.0884707i	0.946143	+	0.323749i	$0.104943\pi$
$930$	0.829726	−	5.77087i	0.0272078	−	0.189234i
$931$	31.2404	−	32.9874i	1.02386	−	1.08112i
$932$	6.80955	−	14.9108i	0.223054	−	0.488420i
$933$	13.1960	+	10.3774i	0.432018	+	0.339742i
$934$	−5.89029	−	3.03666i	−0.192736	−	0.0993625i
$935$	52.6490	−	12.7725i	1.72181	−	0.417706i
$936$	−0.984749	+	2.45978i	−0.0321875	+	0.0804005i
$937$	9.45233	+	10.9086i	0.308794	+	0.356367i	0.888841	−	0.458216i	$-0.151511\pi$
$937$	9.45233	+	10.9086i	0.308794	+	0.356367i	−0.580047	+	0.814583i	$0.696966\pi$
$938$	−0.431357	+	0.138697i	−0.0140843	+	0.00452862i
$939$	2.88107	+	2.49646i	0.0940203	+	0.0814690i
$940$	23.4885	+	5.69825i	0.766110	+	0.185856i
$941$	−9.89246	+	13.8920i	−0.322485	+	0.452867i	−0.943714	−	0.330762i	$-0.892694\pi$
$941$	−9.89246	+	13.8920i	−0.322485	+	0.452867i	0.621229	+	0.783629i	$0.286634\pi$
$942$	12.5843	−	7.26554i	0.410018	−	0.236724i
$943$	28.8367	−	21.5416i	0.939051	−	0.701493i
$944$			14.0705i			0.457955i
$945$	−4.72799	+	4.74407i	−0.153802	+	0.154325i
$946$	−0.0692788	+	0.0203421i	−0.00225245	+	0.000661379i
$947$	0.574999	+	1.66135i	0.0186850	+	0.0539867i	0.953958	−	0.299941i	$-0.0969671\pi$
$947$	0.574999	+	1.66135i	0.0186850	+	0.0539867i	−0.935273	+	0.353928i	$0.884846\pi$
$948$	−0.349477	+	7.33643i	−0.0113505	+	0.238276i
$949$	−1.01434	+	2.93075i	−0.0329270	+	0.0951363i
$950$	8.48741	+	3.39785i	0.275368	+	0.110241i
$951$	1.17087	−	3.98761i	0.0379680	−	0.129307i
$952$	6.72159	+	15.6231i	0.217848	+	0.506347i
$953$	33.2926	+	4.78675i	1.07845	+	0.155058i	0.658570	−	0.752520i	$-0.271162\pi$
$953$	33.2926	+	4.78675i	1.07845	+	0.155058i	0.419884	+	0.907578i	$0.362071\pi$
$954$	−1.80814	+	1.28757i	−0.0585408	+	0.0416867i
$955$	−1.18598	−	12.4201i	−0.0383773	−	0.401906i
$956$	−23.3267	+	9.33861i	−0.754440	+	0.302032i
$957$	−0.0224595	−	0.471482i	−0.000726011	−	0.0152408i
$958$	4.76471	+	1.39905i	0.153941	+	0.0452011i
$959$	1.18666	−	53.6798i	0.0383193	−	1.73341i
$960$	1.91319	−	1.65779i	0.0617481	−	0.0535050i
$961$	−22.8395	+	11.7746i	−0.736757	+	0.379825i
$962$	1.43760	+	0.277075i	0.0463501	+	0.00893326i
$963$	6.89400	−	7.23022i	0.222156	−	0.232990i
$964$	18.9158	+	1.80624i	0.609235	+	0.0581749i
$965$	−33.0564			−1.06412
$966$	2.39271	−	12.4609i	0.0769842	−	0.400924i
$967$	−48.2530			−1.55171			−0.775856	−	0.630910i	$-0.782682\pi$
$967$	−48.2530			−1.55171			−0.775856	+	0.630910i	$0.782682\pi$
$968$	−0.0827796	−	0.00790449i	−0.00266064	−	0.000254060i
$969$	28.7915	−	30.1957i	0.924918	−	0.970026i
$970$	−10.3332	−	1.99156i	−0.331779	−	0.0639451i
$971$	19.6691	−	10.1401i	0.631211	−	0.325412i	−0.112762	−	0.993622i	$-0.535970\pi$
$971$	19.6691	−	10.1401i	0.631211	−	0.325412i	0.743972	+	0.668210i	$0.232939\pi$
$972$	0.755750	−	0.654861i	0.0242407	−	0.0210047i
$973$	−0.110223	−	0.0669282i	−0.00353359	−	0.00214562i
$974$	−11.2055	−	3.29024i	−0.359049	−	0.105426i
$975$	−0.177584	−	3.72794i	−0.00568723	−	0.119390i
$976$	−4.94996	+	1.98167i	−0.158444	+	0.0634316i
$977$	−0.730127	−	7.64623i	−0.0233588	−	0.244625i	−0.999609	−	0.0279765i	$-0.991094\pi$
$977$	−0.730127	−	7.64623i	−0.0233588	−	0.244625i	0.976250	−	0.216648i	$-0.0695124\pi$
$978$	12.5440	−	8.93256i	0.401114	−	0.285632i
$979$	−32.0338	−	4.60577i	−1.02381	−	0.147201i
$980$	12.2721	+	12.7834i	0.392018	+	0.408352i
$981$	5.18697	−	17.6652i	0.165607	−	0.564006i
$982$	−30.5961	−	12.2488i	−0.976362	−	0.390876i
$983$	17.5739	−	50.7766i	0.560522	−	1.61952i	−0.206888	−	0.978365i	$-0.566334\pi$
$983$	17.5739	−	50.7766i	0.560522	−	1.61952i	0.767410	−	0.641157i	$-0.221545\pi$
$984$	0.357119	−	7.49685i	0.0113845	−	0.238991i
$985$	−4.38838	−	12.6794i	−0.139825	−	0.403999i
$986$	−0.874506	+	0.256778i	−0.0278499	+	0.00817748i
$987$	6.49646	−	24.4108i	0.206785	−	0.777004i
$988$		−	17.1968i		−	0.547103i
$989$	0.00752458	−	0.103741i	0.000239268	−	0.00329878i
$990$	−7.29867	+	4.21389i	−0.231967	+	0.133926i
$991$	16.8643	−	23.6826i	0.535712	−	0.752302i	−0.454671	−	0.890660i	$-0.650243\pi$
$991$	16.8643	−	23.6826i	0.535712	−	0.752302i	0.990382	+	0.138358i	$0.0441825\pi$
$992$	2.23813	+	0.542965i	0.0710607	+	0.0172391i
$993$	21.7124	+	18.8139i	0.689023	+	0.597042i
$994$	16.2093	+	3.49731i	0.514127	+	0.110928i
$995$	44.9796	+	51.9092i	1.42595	+	1.64563i
$996$	−3.00430	+	7.50438i	−0.0951949	+	0.237785i
$997$	52.2258	−	12.6698i	1.65401	−	0.401258i	0.703188	−	0.711004i	$-0.251759\pi$
$997$	52.2258	−	12.6698i	1.65401	−	0.401258i	0.950819	+	0.309746i	$0.100244\pi$
$998$	33.4821	+	17.2612i	1.05986	+	0.546395i
$999$	−0.434344	−	0.341572i	−0.0137420	−	0.0108069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.19.2	✓	320
7.3	odd	6	inner	966.2.be.a.157.2	yes	320
23.17	odd	22	inner	966.2.be.a.523.2	yes	320
161.17	even	66	inner	966.2.be.a.661.2	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.19.2	✓	320	1.1	even	1	trivial
966.2.be.a.157.2	yes	320	7.3	odd	6	inner
966.2.be.a.523.2	yes	320	23.17	odd	22	inner
966.2.be.a.661.2	yes	320	161.17	even	66	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.25010 + 1.16001i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.37319 - 2.26149i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(0.995472 + 0.0950560i) q^{2} +(-0.690079 + 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.25010 + 1.16001i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.37319 - 2.26149i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-2.35018 + 0.940871i) q^{10} +(0.316455 + 3.31406i) q^{11} +(-0.814576 + 0.580057i) q^{12} +(-2.62261 - 0.377074i) q^{13} +(1.58194 - 2.12072i) q^{14} +(0.713211 - 2.42897i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-2.10249 + 6.07474i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(2.12280 + 6.13342i) q^{19} +(-2.42897 + 0.713211i) q^{20} +(0.689107 + 2.55443i) q^{21} +3.32914i q^{22} +(-4.49177 - 1.68049i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.817062 - 1.14740i) q^{25} +(-2.57489 - 0.624662i) q^{26} +(0.755750 + 0.654861i) q^{27} +(1.77637 - 1.96075i) q^{28} +(0.0928484 + 0.107153i) q^{29} +(0.940871 - 2.35018i) q^{30} +(2.23813 - 0.542965i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-2.61688 - 2.05794i) q^{33} +(-2.67041 + 5.84738i) q^{34} +(-0.466474 + 6.68151i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-0.551937 + 0.0262920i) q^{37} +(1.53017 + 6.30744i) q^{38} +(2.08271 - 1.63786i) q^{39} +(-2.48577 + 0.479093i) q^{40} +(-4.05770 + 6.31390i) q^{41} +(0.443173 + 2.60837i) q^{42} +(0.00611032 + 0.0208098i) q^{43} +(-0.316455 + 3.31406i) q^{44} +(1.26576 + 2.19236i) q^{45} +(-4.31169 - 2.09985i) q^{46} +(-8.26842 - 4.77378i) q^{47} +(-0.909632 + 0.415415i) q^{48} +(-3.22869 - 6.21092i) q^{49} +(0.922430 - 1.06454i) q^{50} +(-2.94561 - 5.71369i) q^{51} +(-2.50385 - 0.866592i) q^{52} +(-1.37215 - 1.74483i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-4.55640 - 7.08990i) q^{55} +(1.95470 - 1.78301i) q^{56} +(-5.90387 - 2.69621i) q^{57} +(0.0822425 + 0.115493i) q^{58} +(5.22946 + 13.0626i) q^{59} +(1.16001 - 2.25010i) q^{60} +(-3.85888 + 3.67943i) q^{61} +(2.27961 - 0.327758i) q^{62} +(-2.32427 - 1.26403i) q^{63} +(0.841254 + 0.540641i) q^{64} +(6.33855 - 2.19379i) q^{65} +(-2.40941 - 2.29737i) q^{66} +(-0.139503 - 0.0993395i) q^{67} +(-3.21414 + 5.56706i) q^{68} +(4.31590 - 2.09117i) q^{69} +(-1.09948 + 6.60691i) q^{70} +(2.60362 + 5.70113i) q^{71} +(0.235759 - 0.971812i) q^{72} +(0.221518 - 1.14934i) q^{73} +(-0.551937 - 0.0262920i) q^{74} +(0.266577 + 1.38313i) q^{75} +(0.923679 + 6.42433i) q^{76} +(7.92928 + 3.83519i) q^{77} +(2.22897 - 1.43247i) q^{78} +(4.54022 - 5.77337i) q^{79} +(-2.52006 + 0.240636i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-4.63950 + 5.89960i) q^{82} +(6.80019 - 4.37022i) q^{83} +(0.193224 + 2.63869i) q^{84} +(-2.31594 - 16.1077i) q^{85} +(0.00410455 + 0.0212964i) q^{86} +(-0.141623 - 0.00674633i) q^{87} +(-0.630043 + 3.26898i) q^{88} +(-2.29186 + 9.44719i) q^{89} +(1.05163 + 2.30275i) q^{90} +(-4.45410 + 5.41321i) q^{91} +(-4.09256 - 2.50019i) q^{92} +(-1.15153 + 1.99450i) q^{93} +(-7.77721 - 5.53812i) q^{94} +(-11.8913 - 11.3384i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(3.49704 + 2.24741i) q^{97} +(-2.62368 - 6.48971i) q^{98} +(3.29525 - 0.473786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

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