LMFDB - Embedded newform 308.2.l.a.243.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(199,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("308.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			243.1
Character	$\chi$	$=$	308.243
Dual form			308.2.l.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40939 - 0.116729i) q^{2} +(-0.800821 - 1.38706i) q^{3} +(1.97275 + 0.329032i) q^{4} +(-0.235555 - 0.135998i) q^{5} +(0.966757 + 2.04839i) q^{6} +(1.80804 - 1.93157i) q^{7} +(-2.74196 - 0.694010i) q^{8} +(0.217373 - 0.376500i) q^{9} +O(q^{10})$	\(q+(-1.40939 - 0.116729i) q^{2} +(-0.800821 - 1.38706i) q^{3} +(1.97275 + 0.329032i) q^{4} +(-0.235555 - 0.135998i) q^{5} +(0.966757 + 2.04839i) q^{6} +(1.80804 - 1.93157i) q^{7} +(-2.74196 - 0.694010i) q^{8} +(0.217373 - 0.376500i) q^{9} +(0.316113 + 0.219169i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.12343 - 2.99982i) q^{12} +1.72503i q^{13} +(-2.77371 + 2.51129i) q^{14} +0.435639i q^{15} +(3.78348 + 1.29819i) q^{16} +(3.81998 - 2.20547i) q^{17} +(-0.350311 + 0.505261i) q^{18} +(1.05375 - 1.82515i) q^{19} +(-0.419943 - 0.345794i) q^{20} +(-4.12713 - 0.961027i) q^{21} +(1.27893 - 0.603604i) q^{22} +(-8.26541 - 4.77204i) q^{23} +(1.23318 + 4.35905i) q^{24} +(-2.46301 - 4.26606i) q^{25} +(0.201360 - 2.43124i) q^{26} -5.50123 q^{27} +(4.20237 - 3.21560i) q^{28} -2.98320 q^{29} +(0.0508515 - 0.613984i) q^{30} +(-0.259539 - 0.449535i) q^{31} +(-5.18085 - 2.27130i) q^{32} +(1.38706 + 0.800821i) q^{33} +(-5.64127 + 2.66246i) q^{34} +(-0.688582 + 0.209101i) q^{35} +(0.552702 - 0.671218i) q^{36} +(2.87244 - 4.97521i) q^{37} +(-1.69819 + 2.44934i) q^{38} +(2.39272 - 1.38144i) q^{39} +(0.551498 + 0.536377i) q^{40} +5.45198i q^{41} +(5.70455 + 1.83621i) q^{42} +4.88474i q^{43} +(-1.87297 + 0.701425i) q^{44} +(-0.102406 + 0.0591242i) q^{45} +(11.0921 + 7.69046i) q^{46} +(5.13284 - 8.89035i) q^{47} +(-1.22921 - 6.28754i) q^{48} +(-0.461949 - 6.98474i) q^{49} +(2.97336 + 6.30003i) q^{50} +(-6.11823 - 3.53236i) q^{51} +(-0.567589 + 3.40305i) q^{52} +(-1.74001 - 3.01379i) q^{53} +(7.75337 + 0.642151i) q^{54} +0.271995 q^{55} +(-6.29812 + 4.04150i) q^{56} -3.37546 q^{57} +(4.20449 + 0.348225i) q^{58} +(4.17378 + 7.22920i) q^{59} +(-0.143339 + 0.859405i) q^{60} +(12.4475 + 7.18655i) q^{61} +(0.313318 + 0.663865i) q^{62} +(-0.334219 - 1.10060i) q^{63} +(7.03670 + 3.80589i) q^{64} +(0.234600 - 0.406339i) q^{65} +(-1.86143 - 1.29058i) q^{66} +(-2.34085 + 1.35149i) q^{67} +(8.26153 - 3.09394i) q^{68} +15.2862i q^{69} +(0.994888 - 0.214328i) q^{70} +9.88555i q^{71} +(-0.857322 + 0.881490i) q^{72} +(5.22985 - 3.01945i) q^{73} +(-4.62913 + 6.67671i) q^{74} +(-3.94486 + 6.83269i) q^{75} +(2.67932 - 3.25384i) q^{76} +(-0.600026 + 2.57681i) q^{77} +(-3.53353 + 1.66768i) q^{78} +(-2.90246 - 1.67574i) q^{79} +(-0.714664 - 0.820339i) q^{80} +(3.75338 + 6.50105i) q^{81} +(0.636401 - 7.68395i) q^{82} +12.3799 q^{83} +(-7.82559 - 3.25382i) q^{84} -1.19975 q^{85} +(0.570189 - 6.88449i) q^{86} +(2.38901 + 4.13789i) q^{87} +(2.72161 - 0.769951i) q^{88} +(-2.25107 - 1.29965i) q^{89} +(0.151232 - 0.0713753i) q^{90} +(3.33202 + 3.11893i) q^{91} +(-14.7354 - 12.1336i) q^{92} +(-0.415688 + 0.719994i) q^{93} +(-8.27193 + 11.9308i) q^{94} +(-0.496431 + 0.286615i) q^{95} +(0.998499 + 9.00506i) q^{96} -6.64920i q^{97} +(-0.164253 + 9.89813i) q^{98} +0.434745i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 12 q^{8} - 40 q^{9}+O(q^{10}) $ 80 * q + 12 * q^8 - 40 * q^9	$ 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38} - 60 q^{40} + 4 q^{44} + 24 q^{45} - 10 q^{46} - 24 q^{49} - 64 q^{50} + 54 q^{52} - 30 q^{54} + 38 q^{56} + 80 q^{57} + 10 q^{58} - 12 q^{60} - 36 q^{64} - 16 q^{65} + 30 q^{66} + 60 q^{68} - 22 q^{70} - 38 q^{72} - 72 q^{73} + 28 q^{74} - 24 q^{78} + 42 q^{80} - 64 q^{81} - 90 q^{82} + 88 q^{84} - 2 q^{86} + 12 q^{88} - 120 q^{89} + 36 q^{92} + 8 q^{93} - 54 q^{94} - 42 q^{96} + 78 q^{98}+O(q^{100}) $ 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.40939	−	0.116729i	−0.996588	−	0.0825396i
$2$	−1.40939	−	0.116729i	−0.996588	−	0.0825396i
$3$	−0.800821	−	1.38706i	−0.462354	−	0.800821i	0.536724	−	0.843758i	$-0.319662\pi$
$3$	−0.800821	−	1.38706i	−0.462354	−	0.800821i	−0.999078	+	0.0429374i	$0.986328\pi$
$4$	1.97275	+	0.329032i	0.986374	+	0.164516i
$5$	−0.235555	−	0.135998i	−0.105343	−	0.0608199i	0.446403	−	0.894832i	$-0.352705\pi$
$5$	−0.235555	−	0.135998i	−0.105343	−	0.0608199i	−0.551746	+	0.834012i	$0.686038\pi$
$6$	0.966757	+	2.04839i	0.394677	+	0.836251i
$7$	1.80804	−	1.93157i	0.683377	−	0.730066i
$7$	1.80804	−	1.93157i	0.683377	−	0.730066i
$8$	−2.74196	−	0.694010i	−0.969430	−	0.245369i
$9$	0.217373	−	0.376500i	0.0724575	−	0.125500i
$10$	0.316113	+	0.219169i	0.0999637	+	0.0693074i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−1.12343	−	2.99982i	−0.324306	−	0.865974i
$13$			1.72503i			0.478437i	0.970966	+	0.239218i	$0.0768912\pi$
$13$			1.72503i			0.478437i	−0.970966	+	0.239218i	$0.923109\pi$
$14$	−2.77371	+	2.51129i	−0.741304	+	0.671169i
$15$			0.435639i			0.112481i
$16$	3.78348	+	1.29819i	0.945869	+	0.324548i
$17$	3.81998	−	2.20547i	0.926481	−	0.534904i	0.0407839	−	0.999168i	$-0.487014\pi$
$17$	3.81998	−	2.20547i	0.926481	−	0.534904i	0.885697	+	0.464264i	$0.153681\pi$
$18$	−0.350311	+	0.505261i	−0.0825690	+	0.119091i
$19$	1.05375	−	1.82515i	0.241747	−	0.418718i	−0.719465	−	0.694529i	$-0.755613\pi$
$19$	1.05375	−	1.82515i	0.241747	−	0.418718i	0.961212	+	0.275811i	$0.0889463\pi$
$20$	−0.419943	−	0.345794i	−0.0939020	−	0.0773219i
$21$	−4.12713	−	0.961027i	−0.900614	−	0.209713i
$22$	1.27893	−	0.603604i	0.272669	−	0.128689i
$23$	−8.26541	−	4.77204i	−1.72346	−	0.995038i	−0.911475	−	0.411355i	$-0.865056\pi$
$23$	−8.26541	−	4.77204i	−1.72346	−	0.995038i	−0.811981	−	0.583683i	$-0.801611\pi$
$24$	1.23318	+	4.35905i	0.251723	+	0.889787i
$25$	−2.46301	−	4.26606i	−0.492602	−	0.853211i
$26$	0.201360	−	2.43124i	0.0394900	−	0.476804i
$27$	−5.50123			−1.05871
$28$	4.20237	−	3.21560i	0.794173	−	0.607692i
$29$	−2.98320			−0.553967			−0.276983	−	0.960875i	$-0.589335\pi$
$29$	−2.98320			−0.553967			−0.276983	+	0.960875i	$0.589335\pi$
$30$	0.0508515	−	0.613984i	0.00928416	−	0.112098i
$31$	−0.259539	−	0.449535i	−0.0466146	−	0.0807388i	0.841777	−	0.539826i	$-0.181510\pi$
$31$	−0.259539	−	0.449535i	−0.0466146	−	0.0807388i	−0.888391	+	0.459087i	$0.848177\pi$
$32$	−5.18085	−	2.27130i	−0.915853	−	0.401513i
$33$	1.38706	+	0.800821i	0.241457	+	0.139405i
$34$	−5.64127	+	2.66246i	−0.967470	+	0.456607i
$35$	−0.688582	+	0.209101i	−0.116392	+	0.0353446i
$36$	0.552702	−	0.671218i	0.0921170	−	0.111870i
$37$	2.87244	−	4.97521i	0.472226	−	0.817920i	−0.527269	−	0.849698i	$-0.676784\pi$
$37$	2.87244	−	4.97521i	0.472226	−	0.817920i	0.999495	+	0.0317790i	$0.0101173\pi$
$38$	−1.69819	+	2.44934i	−0.275483	+	0.397335i
$39$	2.39272	−	1.38144i	0.383142	−	0.221207i
$40$	0.551498	+	0.536377i	0.0871995	+	0.0848087i
$41$			5.45198i			0.851456i	0.904851	+	0.425728i	$0.139982\pi$
$41$			5.45198i			0.851456i	−0.904851	+	0.425728i	$0.860018\pi$
$42$	5.70455	+	1.83621i	0.880231	+	0.283334i
$43$			4.88474i			0.744916i	0.928049	+	0.372458i	$0.121485\pi$
$43$			4.88474i			0.744916i	−0.928049	+	0.372458i	$0.878515\pi$
$44$	−1.87297	+	0.701425i	−0.282360	+	0.105744i
$45$	−0.102406	+	0.0591242i	−0.0152658	+	0.00881372i
$46$	11.0921	+	7.69046i	1.63545	+	1.13390i
$47$	5.13284	−	8.89035i	0.748702	−	1.29679i	−0.199743	−	0.979848i	$-0.564011\pi$
$47$	5.13284	−	8.89035i	0.748702	−	1.29679i	0.948445	−	0.316942i	$-0.102656\pi$
$48$	−1.22921	−	6.28754i	−0.177421	−	0.907528i
$49$	−0.461949	−	6.98474i	−0.0659927	−	0.997820i
$50$	2.97336	+	6.30003i	0.420497	+	0.890959i
$51$	−6.11823	−	3.53236i	−0.856724	−	0.494630i
$52$	−0.567589	+	3.40305i	−0.0787105	+	0.471918i
$53$	−1.74001	−	3.01379i	−0.239009	−	0.413976i	0.721421	−	0.692497i	$-0.243489\pi$
$53$	−1.74001	−	3.01379i	−0.239009	−	0.413976i	−0.960430	+	0.278520i	$0.910156\pi$
$54$	7.75337	+	0.642151i	1.05510	+	0.0873856i
$55$	0.271995			0.0366758
$56$	−6.29812	+	4.04150i	−0.841621	+	0.540068i
$57$	−3.37546			−0.447090
$58$	4.20449	+	0.348225i	0.552076	+	0.0457242i
$59$	4.17378	+	7.22920i	0.543380	+	0.941161i	0.998707	+	0.0508372i	$0.0161890\pi$
$59$	4.17378	+	7.22920i	0.543380	+	0.941161i	−0.455327	+	0.890324i	$0.650478\pi$
$60$	−0.143339	+	0.859405i	−0.0185050	+	0.110949i
$61$	12.4475	+	7.18655i	1.59373	+	0.920143i	0.992658	+	0.120951i	$0.0385944\pi$
$61$	12.4475	+	7.18655i	1.59373	+	0.920143i	0.601076	+	0.799192i	$0.294739\pi$
$62$	0.313318	+	0.663865i	0.0397914	+	0.0843109i
$63$	−0.334219	−	1.10060i	−0.0421076	−	0.138663i
$64$	7.03670	+	3.80589i	0.879588	+	0.475737i
$65$	0.234600	−	0.406339i	0.0290985	−	0.0504001i
$66$	−1.86143	−	1.29058i	−0.229126	−	0.158859i
$67$	−2.34085	+	1.35149i	−0.285980	+	0.165111i	−0.636128	−	0.771584i	$-0.719465\pi$
$67$	−2.34085	+	1.35149i	−0.285980	+	0.165111i	0.350147	+	0.936695i	$0.386132\pi$
$68$	8.26153	−	3.09394i	1.00186	−	0.375195i
$69$			15.2862i			1.84024i
$70$	0.994888	−	0.214328i	0.118912	−	0.0256171i
$71$			9.88555i			1.17320i	0.809877	+	0.586600i	$0.199534\pi$
$71$			9.88555i			1.17320i	−0.809877	+	0.586600i	$0.800466\pi$
$72$	−0.857322	+	0.881490i	−0.101036	+	0.103885i
$73$	5.22985	−	3.01945i	0.612108	−	0.353400i	−0.161682	−	0.986843i	$-0.551692\pi$
$73$	5.22985	−	3.01945i	0.612108	−	0.353400i	0.773790	+	0.633442i	$0.218359\pi$
$74$	−4.62913	+	6.67671i	−0.538125	+	0.776151i
$75$	−3.94486	+	6.83269i	−0.455513	+	0.788972i
$76$	2.67932	−	3.25384i	0.307339	−	0.373241i
$77$	−0.600026	+	2.57681i	−0.0683793	+	0.293655i
$78$	−3.53353	+	1.66768i	−0.400093	+	0.188828i
$79$	−2.90246	−	1.67574i	−0.326552	−	0.188535i	0.327757	−	0.944762i	$-0.393707\pi$
$79$	−2.90246	−	1.67574i	−0.326552	−	0.188535i	−0.654309	+	0.756227i	$0.727041\pi$
$80$	−0.714664	−	0.820339i	−0.0799019	−	0.0917167i
$81$	3.75338	+	6.50105i	0.417042	+	0.722338i
$82$	0.636401	−	7.68395i	0.0702788	−	0.848550i
$83$	12.3799			1.35887			0.679435	−	0.733735i	$-0.262225\pi$
$83$	12.3799			1.35887			0.679435	+	0.733735i	$0.262225\pi$
$84$	−7.82559	−	3.25382i	−0.853841	−	0.355021i
$85$	−1.19975			−0.130131
$86$	0.570189	−	6.88449i	0.0614850	−	0.742374i
$87$	2.38901	+	4.13789i	0.256129	+	0.443628i
$88$	2.72161	−	0.769951i	0.290125	−	0.0820770i
$89$	−2.25107	−	1.29965i	−0.238613	−	0.137763i	0.375926	−	0.926650i	$-0.377325\pi$
$89$	−2.25107	−	1.29965i	−0.238613	−	0.137763i	−0.614539	+	0.788887i	$0.710658\pi$
$90$	0.151232	−	0.0713753i	0.0159412	−	0.00752361i
$91$	3.33202	+	3.11893i	0.349291	+	0.326953i
$92$	−14.7354	−	12.1336i	−1.53627	−	1.26502i
$93$	−0.415688	+	0.719994i	−0.0431049	+	0.0746599i
$94$	−8.27193	+	11.9308i	−0.853184	+	1.23057i
$95$	−0.496431	+	0.286615i	−0.0509328	+	0.0294061i
$96$	0.998499	+	9.00506i	0.101909	+	0.919075i
$97$		−	6.64920i		−	0.675124i	−0.941303	−	0.337562i	$-0.890398\pi$
$97$		−	6.64920i		−	0.675124i	0.941303	−	0.337562i	$-0.109602\pi$
$98$	−0.164253	+	9.89813i	−0.0165921	+	0.999862i
$99$			0.434745i			0.0436935i
$100$	−3.45523	−	9.22627i	−0.345523	−	0.922627i
$101$	−8.54982	+	4.93624i	−0.850739	+	0.491174i	−0.860900	−	0.508774i	$-0.830099\pi$
$101$	−8.54982	+	4.93624i	−0.850739	+	0.491174i	0.0101613	+	0.999948i	$0.496765\pi$
$102$	8.21064	+	5.69264i	0.812974	+	0.563656i
$103$	−1.94255	+	3.36459i	−0.191405	+	0.331523i	−0.945716	−	0.324994i	$-0.894638\pi$
$103$	−1.94255	+	3.36459i	−0.191405	+	0.331523i	0.754311	+	0.656517i	$0.227971\pi$
$104$	1.19719	−	4.72996i	0.117394	−	0.463811i
$105$	0.841468	+	0.787654i	0.0821188	+	0.0768671i
$106$	2.10056	+	4.45071i	0.204024	+	0.432292i
$107$	7.47406	+	4.31515i	0.722544	+	0.417161i	0.815688	−	0.578492i	$-0.196358\pi$
$107$	7.47406	+	4.31515i	0.722544	+	0.417161i	−0.0931441	+	0.995653i	$0.529692\pi$
$108$	−10.8525	−	1.81008i	−1.04429	−	0.174175i
$109$	−4.83682	−	8.37762i	−0.463283	−	0.802430i	0.535839	−	0.844320i	$-0.319995\pi$
$109$	−4.83682	−	8.37762i	−0.463283	−	0.802430i	−0.999122	+	0.0418899i	$0.986662\pi$
$110$	−0.383347	−	0.0317496i	−0.0365507	−	0.00302721i
$111$	−9.20123			−0.873342
$112$	9.34825	−	4.96087i	0.883327	−	0.468758i
$113$	15.7813			1.48458			0.742290	−	0.670078i	$-0.233740\pi$
$113$	15.7813			1.48458			0.742290	+	0.670078i	$0.233740\pi$
$114$	4.75733	+	0.394013i	0.445565	+	0.0369027i
$115$	1.29797	+	2.24815i	0.121036	+	0.209641i
$116$	−5.88511	−	0.981568i	−0.546419	−	0.0911363i
$117$	0.649474	+	0.374974i	0.0600439	+	0.0346663i
$118$	−5.03862	−	10.6759i	−0.463843	−	0.982800i
$119$	2.64667	−	11.3661i	0.242620	−	1.04193i
$120$	0.302337	−	1.19450i	0.0275995	−	0.109043i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−16.7044	−	11.5816i	−1.51235	−	1.04855i
$123$	7.56223	−	4.36606i	0.681863	−	0.393674i
$124$	−0.364094	−	0.972216i	−0.0326966	−	0.0873076i
$125$			2.69983i			0.241480i
$126$	0.342572	+	1.59019i	0.0305187	+	0.141665i
$127$			14.7968i			1.31300i	0.754325	+	0.656501i	$0.227964\pi$
$127$			14.7968i			1.31300i	−0.754325	+	0.656501i	$0.772036\pi$
$128$	−9.47319	−	6.18537i	−0.837319	−	0.546714i
$129$	6.77543	−	3.91180i	0.596544	−	0.344415i
$130$	−0.378073	+	0.545304i	−0.0331592	+	0.0478263i
$131$	5.61464	−	9.72484i	0.490553	−	0.849663i	−0.509388	−	0.860537i	$-0.670128\pi$
$131$	5.61464	−	9.72484i	0.490553	−	0.849663i	0.999941	+	0.0108742i	$0.00346143\pi$
$132$	2.47283	+	2.03621i	0.215232	+	0.177229i
$133$	−1.62018	−	5.33534i	−0.140487	−	0.462633i
$134$	3.45692	−	1.63153i	0.298633	−	0.140943i
$135$	1.29584	+	0.748154i	0.111528	+	0.0643908i
$136$	−12.0048	+	3.39620i	−1.02941	+	0.291222i
$137$	−7.76953	−	13.4572i	−0.663796	−	1.14973i	−0.979610	−	0.200908i	$-0.935611\pi$
$137$	−7.76953	−	13.4572i	−0.663796	−	1.14973i	0.315814	−	0.948821i	$-0.397722\pi$
$138$	1.78433	−	21.5442i	0.151893	−	1.83396i
$139$	9.29058			0.788017			0.394008	−	0.919107i	$-0.371088\pi$
$139$	9.29058			0.788017			0.394008	+	0.919107i	$0.371088\pi$
$140$	−1.42720	+	0.185939i	−0.120621	+	0.0157147i
$141$	−16.4420			−1.38466
$142$	1.15393	−	13.9326i	0.0968354	−	1.16920i
$143$	−0.862514	−	1.49392i	−0.0721271	−	0.124928i
$144$	1.31119	−	1.14229i	0.109266	−	0.0951907i
$145$	0.702707	+	0.405708i	0.0583566	+	0.0336922i
$146$	−7.72334	+	3.64511i	−0.639188	+	0.301671i
$147$	−9.31833	+	6.23428i	−0.768563	+	0.514195i
$148$	7.30360	−	8.86972i	0.600352	−	0.729086i
$149$	−3.91288	+	6.77732i	−0.320556	+	0.555219i	−0.980603	−	0.196005i	$-0.937203\pi$
$149$	−3.91288	+	6.77732i	−0.320556	+	0.555219i	0.660047	+	0.751224i	$0.270536\pi$
$150$	6.35741	−	9.16944i	0.519080	−	0.748682i
$151$	8.13242	−	4.69525i	0.661807	−	0.382094i	−0.131158	−	0.991361i	$-0.541870\pi$
$151$	8.13242	−	4.69525i	0.661807	−	0.382094i	0.792965	+	0.609267i	$0.208536\pi$
$152$	−4.15601	+	4.27317i	−0.337097	+	0.346600i
$153$		−	1.91763i		−	0.155031i
$154$	1.14646	−	3.56169i	0.0923842	−	0.287009i
$155$			0.141187i			0.0113404i
$156$	5.17478	−	1.93795i	0.414314	−	0.155160i
$157$	−11.5730	+	6.68166i	−0.923625	+	0.533255i	−0.884790	−	0.465991i	$-0.845698\pi$
$157$	−11.5730	+	6.68166i	−0.923625	+	0.533255i	−0.0388349	+	0.999246i	$0.512365\pi$
$158$	3.89509	+	2.70056i	0.309876	+	0.214845i
$159$	−2.78688	+	4.82702i	−0.221014	+	0.382807i
$160$	0.911482	+	1.23960i	0.0720590	+	0.0979988i
$161$	−24.1618	+	7.33719i	−1.90421	+	0.578251i
$162$	−4.53111	−	9.60062i	−0.355998	−	0.754296i
$163$	4.34350	+	2.50772i	0.340209	+	0.196420i	0.660365	−	0.750945i	$-0.270402\pi$
$163$	4.34350	+	2.50772i	0.340209	+	0.196420i	−0.320155	+	0.947365i	$0.603735\pi$
$164$	−1.79387	+	10.7554i	−0.140078	+	0.839854i
$165$	−0.217819	−	0.377274i	−0.0169572	−	0.0293707i
$166$	−17.4481	−	1.44509i	−1.35423	−	0.112161i
$167$	12.7142			0.983855			0.491928	−	0.870636i	$-0.336292\pi$
$167$	12.7142			0.983855			0.491928	+	0.870636i	$0.336292\pi$
$168$	10.6495	+	5.49937i	0.821625	+	0.424285i
$169$	10.0243			0.771098
$170$	1.69091	+	0.140045i	0.129687	+	0.0107410i
$171$	−0.458112	−	0.793474i	−0.0350327	−	0.0606785i
$172$	−1.60723	+	9.63636i	−0.122550	+	0.734766i
$173$	9.16310	+	5.29032i	0.696658	+	0.402215i	0.806101	−	0.591778i	$-0.201574\pi$
$173$	9.16310	+	5.29032i	0.696658	+	0.402215i	−0.109444	+	0.993993i	$0.534907\pi$
$174$	−2.88403	−	6.11075i	−0.218638	−	0.463255i
$175$	−12.6934	−	2.95574i	−0.959533	−	0.223433i
$176$	−3.92568	+	0.767469i	−0.295910	+	0.0578502i
$177$	6.68490	−	11.5786i	0.502468	−	0.870300i
$178$	3.02092	+	2.09448i	0.226427	+	0.156988i
$179$	15.0451	−	8.68631i	1.12453	−	0.649246i	0.181974	−	0.983303i	$-0.441751\pi$
$179$	15.0451	−	8.68631i	1.12453	−	0.649246i	0.942553	+	0.334058i	$0.108418\pi$
$180$	−0.221475	+	0.0829424i	−0.0165078	+	0.00618216i
$181$			15.5759i			1.15774i	0.815418	+	0.578872i	$0.196507\pi$
$181$			15.5759i			1.15774i	−0.815418	+	0.578872i	$0.803493\pi$
$182$	−4.33204	−	4.78472i	−0.321112	−	0.354667i
$183$		−	23.0205i		−	1.70173i
$184$	19.3516	+	18.8210i	1.42662	+	1.38750i
$185$	−1.35323	+	0.781289i	−0.0994916	+	0.0574415i
$186$	0.669910	−	0.966227i	0.0491202	−	0.0708472i
$187$	−2.20547	+	3.81998i	−0.161280	+	0.279344i
$188$	13.0510	−	15.8496i	0.951843	−	1.15595i
$189$	−9.94647	+	10.6260i	−0.723499	+	0.772930i
$190$	0.733120	−	0.346004i	0.0531861	−	0.0251017i
$191$	−4.28524	−	2.47409i	−0.310069	−	0.179019i	0.336888	−	0.941545i	$-0.390626\pi$
$191$	−4.28524	−	2.47409i	−0.310069	−	0.179019i	−0.646957	+	0.762526i	$0.723959\pi$
$192$	−0.356124	−	12.8082i	−0.0257011	−	0.924351i
$193$	0.0753312	+	0.130477i	0.00542246	+	0.00939197i	0.868724	−	0.495297i	$-0.164941\pi$
$193$	0.0753312	+	0.130477i	0.00542246	+	0.00939197i	−0.863301	+	0.504689i	$0.831607\pi$
$194$	−0.776152	+	9.37130i	−0.0557244	+	0.672820i
$195$	−0.751489			−0.0538152
$196$	1.38689	−	13.9311i	0.0990637	−	0.995081i
$197$	−13.2707			−0.945500			−0.472750	−	0.881197i	$-0.656739\pi$
$197$	−13.2707			−0.945500			−0.472750	+	0.881197i	$0.656739\pi$
$198$	0.0507472	−	0.612724i	0.00360644	−	0.0435444i
$199$	10.1408	+	17.5644i	0.718865	+	1.24511i	0.961450	+	0.274980i	$0.0886714\pi$
$199$	10.1408	+	17.5644i	0.718865	+	1.24511i	−0.242585	+	0.970130i	$0.577995\pi$
$200$	3.79279	+	13.4067i	0.268191	+	0.947998i
$201$	3.74920	+	2.16460i	0.264448	+	0.152679i
$202$	12.6262	−	5.95907i	0.888377	−	0.419279i
$203$	−5.39376	+	5.76227i	−0.378568	+	0.404432i
$204$	−10.9075	−	8.98156i	−0.763676	−	0.628835i
$205$	0.741455	−	1.28424i	0.0517855	−	0.0896951i
$206$	3.13055	−	4.51527i	0.218116	−	0.314594i
$207$	−3.59334	+	2.07462i	−0.249755	+	0.144196i
$208$	−2.23942	+	6.52661i	−0.155276	+	0.452539i
$209$			2.10750i			0.145779i
$210$	−1.09401	−	1.20833i	−0.0754940	−	0.0833829i
$211$		−	1.47447i		−	0.101506i	−0.998711	−	0.0507532i	$-0.983838\pi$
$211$		−	1.47447i		−	0.101506i	0.998711	−	0.0507532i	$-0.0161622\pi$
$212$	−2.44098	−	6.51798i	−0.167647	−	0.447657i
$213$	13.7119	−	7.91655i	0.939522	−	0.542433i
$214$	−10.0301	−	6.95415i	−0.685646	−	0.475376i
$215$	0.664312	−	1.15062i	0.0453057	−	0.0784718i
$216$	15.0842	+	3.81791i	1.02635	+	0.259776i
$217$	−1.33757	−	0.311460i	−0.0908000	−	0.0211433i
$218$	5.83905	+	12.3719i	0.395470	+	0.837932i
$219$	−8.37634	−	4.83608i	−0.566021	−	0.326792i
$220$	0.536578	+	0.0894950i	0.0361761	+	0.00603375i
$221$	3.80449	+	6.58957i	0.255918	+	0.443263i
$222$	12.9681	+	1.07405i	0.870362	+	0.0720853i
$223$	−11.6973			−0.783308			−0.391654	−	0.920113i	$-0.628097\pi$
$223$	−11.6973			−0.783308			−0.391654	+	0.920113i	$0.628097\pi$
$224$	−13.7544	+	5.90058i	−0.919004	+	0.394249i
$225$	−2.14156			−0.142771
$226$	−22.2420	−	1.84213i	−1.47951	−	0.122537i
$227$	−0.960086	−	1.66292i	−0.0637231	−	0.110372i	0.832404	−	0.554170i	$-0.186964\pi$
$227$	−0.960086	−	1.66292i	−0.0637231	−	0.110372i	−0.896127	+	0.443798i	$0.853631\pi$
$228$	−6.65893	−	1.11063i	−0.440999	−	0.0735535i
$229$	−20.0500	−	11.5759i	−1.32494	−	0.764955i	−0.340429	−	0.940270i	$-0.610572\pi$
$229$	−20.0500	−	11.5759i	−1.32494	−	0.764955i	−0.984512	+	0.175315i	$0.943906\pi$
$230$	−1.56692	−	3.32003i	−0.103320	−	0.218916i
$231$	4.05471	−	1.23129i	0.266781	−	0.0810131i
$232$	8.17982	+	2.07037i	0.537032	+	0.135926i
$233$	−3.89145	+	6.74019i	−0.254937	+	0.441564i	−0.964878	−	0.262697i	$-0.915388\pi$
$233$	−3.89145	+	6.74019i	−0.254937	+	0.441564i	0.709941	+	0.704261i	$0.248721\pi$
$234$	−0.871590	−	0.604296i	−0.0569776	−	0.0395041i
$235$	−2.41813	+	1.39611i	−0.157741	+	0.0910721i
$236$	5.85518	+	15.6347i	0.381140	+	1.01773i
$237$			5.36786i			0.348680i
$238$	−5.05694	+	15.7104i	−0.327793	+	1.01835i
$239$		−	14.8217i		−	0.958733i	−0.877615	−	0.479367i	$-0.840866\pi$
$239$		−	14.8217i		−	0.958733i	0.877615	−	0.479367i	$-0.159134\pi$
$240$	−0.565543	+	1.64823i	−0.0365057	+	0.106393i
$241$	5.91823	−	3.41689i	0.381227	−	0.220101i	−0.297125	−	0.954839i	$-0.596028\pi$
$241$	5.91823	−	3.41689i	0.381227	−	0.220101i	0.678352	+	0.734737i	$0.262695\pi$
$242$	−0.805784	+	1.16220i	−0.0517978	+	0.0747091i
$243$	−2.24027	+	3.88027i	−0.143714	+	0.248919i
$244$	22.1911	+	18.2729i	1.42064	+	1.16980i
$245$	−0.841093	+	1.70811i	−0.0537355	+	0.109127i
$246$	−11.1678	+	5.27074i	−0.712030	+	0.336050i
$247$	3.14843	+	1.81775i	0.200330	+	0.115661i
$248$	0.399665	+	1.41273i	0.0253787	+	0.0897084i
$249$	−9.91408	−	17.1717i	−0.628279	−	1.08821i
$250$	0.315147	−	3.80510i	0.0199317	−	0.240656i
$251$	−18.6466			−1.17696			−0.588482	−	0.808510i	$-0.700274\pi$
$251$	−18.6466			−1.17696			−0.588482	+	0.808510i	$0.700274\pi$
$252$	−0.297197	−	2.28118i	−0.0187216	−	0.143701i
$253$	9.54407			0.600031
$254$	1.72721	−	20.8544i	0.108375	−	1.30852i
$255$	0.960786	+	1.66413i	0.0601667	+	0.104212i
$256$	12.6294	+	9.82337i	0.789337	+	0.613961i
$257$	25.3607	+	14.6420i	1.58195	+	0.913342i	0.994574	+	0.104031i	$0.0331741\pi$
$257$	25.3607	+	14.6420i	1.58195	+	0.913342i	0.587380	+	0.809311i	$0.300159\pi$
$258$	−10.0058	+	4.72236i	−0.622936	+	0.294001i
$259$	−4.41648	−	14.5437i	−0.274427	−	0.903703i
$260$	0.596504	−	0.724413i	0.0369936	−	0.0449262i
$261$	−0.648466	+	1.12318i	−0.0401390	+	0.0695229i
$262$	−9.04837	+	13.0507i	−0.559010	+	0.806274i
$263$	1.05778	−	0.610707i	0.0652253	−	0.0376578i	−0.467033	−	0.884240i	$-0.654677\pi$
$263$	1.05778	−	0.610707i	0.0652253	−	0.0376578i	0.532258	+	0.846582i	$0.321344\pi$
$264$	−3.24749	−	3.15845i	−0.199869	−	0.194389i
$265$			0.946551i			0.0581462i
$266$	1.66068	+	7.70869i	0.101823	+	0.472650i
$267$			4.16316i			0.254781i
$268$	−5.06259	+	1.89594i	−0.309247	+	0.115813i
$269$	24.5928	−	14.1987i	1.49945	−	0.865708i	0.499451	−	0.866342i	$-0.333535\pi$
$269$	24.5928	−	14.1987i	1.49945	−	0.865708i	1.00000		0.000633644i	$0.000201695\pi$
$270$	−1.73901	−	1.20570i	−0.105833	−	0.0733766i
$271$	−11.5278	+	19.9667i	−0.700261	+	1.21289i	0.268113	+	0.963387i	$0.413600\pi$
$271$	−11.5278	+	19.9667i	−0.700261	+	1.21289i	−0.968375	+	0.249501i	$0.919734\pi$
$272$	17.3159	−	3.38525i	1.04993	−	0.205261i
$273$	1.65780	−	7.11942i	0.100335	−	0.430887i
$274$	9.37945	+	19.8734i	0.566633	+	1.20059i
$275$	4.26606	+	2.46301i	0.257253	+	0.148525i
$276$	−5.02964	+	30.1558i	−0.302749	+	1.81517i
$277$	−8.43761	−	14.6144i	−0.506967	−	0.878092i	−0.999967	−	0.00806306i	$-0.997433\pi$
$277$	−8.43761	−	14.6144i	−0.506967	−	0.878092i	0.493001	−	0.870029i	$-0.335900\pi$
$278$	−13.0940	−	1.08448i	−0.785328	−	0.0650426i
$279$	−0.225667			−0.0135103
$280$	2.03318	−	0.0954651i	0.121506	−	0.00570513i
$281$	29.7931			1.77730			0.888652	−	0.458582i	$-0.151642\pi$
$281$	29.7931			1.77730			0.888652	+	0.458582i	$0.151642\pi$
$282$	23.1731	+	1.91925i	1.37994	+	0.114289i
$283$	0.490972	+	0.850388i	0.0291852	+	0.0505503i	0.880249	−	0.474512i	$-0.157375\pi$
$283$	0.490972	+	0.850388i	0.0291852	+	0.0505503i	−0.851064	+	0.525062i	$0.824042\pi$
$284$	−3.25266	+	19.5017i	−0.193010	+	1.15721i
$285$	0.795105	+	0.459054i	0.0470979	+	0.0271920i
$286$	1.04123	+	2.20619i	0.0615695	+	0.130455i
$287$	10.5309	+	9.85742i	0.621619	+	0.581865i
$288$	−1.98132	+	1.45687i	−0.116750	+	0.0858471i
$289$	1.22815	−	2.12723i	0.0722444	−	0.125131i
$290$	−0.943029	−	0.653826i	−0.0553766	−	0.0383940i
$291$	−9.22285	+	5.32482i	−0.540653	+	0.312146i
$292$	11.3107	−	4.23584i	0.661907	−	0.247884i
$293$			15.2735i			0.892287i	0.894961	+	0.446144i	$0.147203\pi$
$293$			15.2735i			0.892287i	−0.894961	+	0.446144i	$0.852797\pi$
$294$	13.8609	−	7.69880i	0.808382	−	0.449003i
$295$		−	2.27049i		−	0.132193i
$296$	−11.3290	+	11.6483i	−0.658482	+	0.677046i
$297$	4.76420	−	2.75061i	0.276447	−	0.159607i
$298$	6.30588	−	9.09512i	0.365290	−	0.526866i
$299$	8.23190	−	14.2581i	0.476063	−	0.824565i
$300$	−10.0304	+	12.1812i	−0.579105	+	0.703282i
$301$	9.43523	+	8.83182i	0.543838	+	0.509058i
$302$	−12.0098	+	5.66815i	−0.691087	+	0.326165i
$303$	13.6937	+	7.90609i	0.786685	+	0.454193i
$304$	6.35623	−	5.53743i	0.364555	−	0.317594i
$305$	−1.95471	−	3.38565i	−0.111926	−	0.193862i
$306$	−0.223842	+	2.70268i	−0.0127962	+	0.154502i
$307$	−15.0250			−0.857525			−0.428762	−	0.903417i	$-0.641050\pi$
$307$	−15.0250			−0.857525			−0.428762	+	0.903417i	$0.641050\pi$
$308$	−2.03155	+	4.88598i	−0.115759	+	0.278404i
$309$	6.22254			0.353988
$310$	0.0164805	−	0.198987i	0.000936031	−	0.0113017i
$311$	6.30433	+	10.9194i	0.357486	+	0.619183i	0.987540	−	0.157368i	$-0.0503008\pi$
$311$	6.30433	+	10.9194i	0.357486	+	0.619183i	−0.630055	+	0.776551i	$0.716967\pi$
$312$	−7.51948	+	2.12728i	−0.425707	+	0.120433i
$313$	9.27497	+	5.35490i	0.524252	+	0.302677i	0.738673	−	0.674064i	$-0.235453\pi$
$313$	9.27497	+	5.35490i	0.524252	+	0.302677i	−0.214421	+	0.976741i	$0.568786\pi$
$314$	17.0908	−	8.06616i	0.964488	−	0.455200i
$315$	−0.0709522	+	0.304704i	−0.00399770	+	0.0171681i
$316$	−5.17445	−	4.26081i	−0.291086	−	0.239689i
$317$	−8.21776	+	14.2336i	−0.461555	+	0.799437i	−0.999039	−	0.0438370i	$-0.986042\pi$
$317$	−8.21776	+	14.2336i	−0.461555	+	0.799437i	0.537483	+	0.843274i	$0.319375\pi$
$318$	4.49125	−	6.47783i	0.251857	−	0.363259i
$319$	2.58353	−	1.49160i	0.144650	−	0.0835136i
$320$	−1.13994	−	1.85347i	−0.0637243	−	0.103612i
$321$		−	13.8226i		−	0.771505i
$322$	34.9098	−	7.52057i	1.94544	−	0.419105i
$323$		−	9.29603i		−	0.517245i
$324$	5.26543	+	14.0599i	0.292524	+	0.781106i
$325$	7.35907	−	4.24876i	0.408208	−	0.235679i
$326$	−5.82896	−	4.04137i	−0.322836	−	0.223831i
$327$	−7.74685	+	13.4179i	−0.428402	+	0.742014i
$328$	3.78372	−	14.9491i	0.208921	−	0.825426i
$329$	−7.89194	−	25.9886i	−0.435097	−	1.43280i
$330$	0.262953	+	0.557151i	0.0144751	+	0.0306702i
$331$	−6.74610	−	3.89486i	−0.370799	−	0.214081i	0.303008	−	0.952988i	$-0.402009\pi$
$331$	−6.74610	−	3.89486i	−0.370799	−	0.214081i	−0.673808	+	0.738907i	$0.735342\pi$
$332$	24.4224	+	4.07338i	1.34036	+	0.223556i
$333$	−1.24878	−	2.16295i	−0.0684326	−	0.118529i
$334$	−17.9193	−	1.48411i	−0.980498	−	0.0812070i
$335$	0.735197			0.0401681
$336$	−14.3673	−	8.99384i	−0.783801	−	0.490654i
$337$	−7.73427			−0.421312			−0.210656	−	0.977560i	$-0.567560\pi$
$337$	−7.73427			−0.421312			−0.210656	+	0.977560i	$0.567560\pi$
$338$	−14.1281	−	1.17012i	−0.768467	−	0.0636461i
$339$	−12.6380	−	21.8897i	−0.686402	−	1.18888i
$340$	−2.36681	−	0.394756i	−0.128358	−	0.0214087i
$341$	0.449535	+	0.259539i	0.0243437	+	0.0140548i
$342$	0.553037	+	1.17179i	0.0299048	+	0.0633630i
$343$	−14.3268	−	11.7364i	−0.773572	−	0.633708i
$344$	3.39005	−	13.3938i	0.182779	−	0.722143i
$345$	2.07888	−	3.60073i	0.111923	−	0.193857i
$346$	−12.2968	−	8.52571i	−0.661082	−	0.458345i
$347$	−17.8247	+	10.2911i	−0.956882	+	0.552456i	−0.895212	−	0.445641i	$-0.852976\pi$
$347$	−17.8247	+	10.2911i	−0.956882	+	0.552456i	−0.0616698	+	0.998097i	$0.519643\pi$
$348$	3.35142	+	8.94907i	0.179655	+	0.479721i
$349$		−	25.3916i		−	1.35918i	−0.733591	−	0.679591i	$-0.762157\pi$
$349$		−	25.3916i		−	1.35918i	0.733591	−	0.679591i	$-0.237843\pi$
$350$	17.5450	+	5.64747i	0.937817	+	0.301870i
$351$		−	9.48978i		−	0.506527i
$352$	5.62240	−	0.623422i	0.299675	−	0.0332285i
$353$	27.1204	−	15.6580i	1.44347	−	0.833390i	0.445394	−	0.895335i	$-0.353064\pi$
$353$	27.1204	−	15.6580i	1.44347	−	0.833390i	0.998080	+	0.0619452i	$0.0197304\pi$
$354$	−10.7732	+	15.5384i	−0.572587	+	0.825856i
$355$	1.34441	−	2.32859i	0.0713539	−	0.123589i
$356$	−4.01316	−	3.30456i	−0.212697	−	0.175141i
$357$	−17.8851	+	5.43114i	−0.946578	+	0.287447i
$358$	−22.2184	+	10.4862i	−1.17428	+	0.554212i
$359$	7.58393	+	4.37858i	0.400265	+	0.231093i	0.686598	−	0.727037i	$-0.259103\pi$
$359$	7.58393	+	4.37858i	0.400265	+	0.231093i	−0.286334	+	0.958130i	$0.592437\pi$
$360$	0.321827	−	0.0910455i	0.0169618	−	0.00479852i
$361$	7.27922	+	12.6080i	0.383117	+	0.663578i
$362$	1.81815	−	21.9524i	0.0955598	−	1.15379i
$363$	−1.60164			−0.0840644
$364$	5.54701	+	7.24920i	0.290742	+	0.379962i
$365$	−1.64255			−0.0859752
$366$	−2.68716	+	32.4449i	−0.140460	+	1.69592i
$367$	5.57199	+	9.65096i	0.290855	+	0.503776i	0.974012	−	0.226495i	$-0.0727268\pi$
$367$	5.57199	+	9.65096i	0.290855	+	0.503776i	−0.683157	+	0.730272i	$0.739394\pi$
$368$	−25.0769	−	28.7850i	−1.30723	−	1.50052i
$369$	2.05267	+	1.18511i	0.106858	+	0.0616944i
$370$	1.99843	−	0.943179i	0.103893	−	0.0490335i
$371$	−8.96739	−	2.08811i	−0.465564	−	0.108409i
$372$	−1.05695	+	1.28359i	−0.0548003	+	0.0665511i
$373$	−15.6835	+	27.1647i	−0.812063	+	1.40653i	0.0993544	+	0.995052i	$0.468322\pi$
$373$	−15.6835	+	27.1647i	−0.812063	+	1.40653i	−0.911418	+	0.411483i	$0.865011\pi$
$374$	3.55426	−	5.12639i	0.183786	−	0.265079i
$375$	3.74483	−	2.16208i	0.193382	−	0.111649i
$376$	−20.2440	+	20.8147i	−1.04401	+	1.07344i
$377$		−	5.14611i		−	0.265038i
$378$	15.2588	−	13.8152i	0.784828	−	0.710575i
$379$		−	37.0868i		−	1.90502i	−0.304507	−	0.952510i	$-0.598492\pi$
$379$		−	37.0868i		−	1.90502i	0.304507	−	0.952510i	$-0.401508\pi$
$380$	−1.07364	+	0.402077i	−0.0550765	+	0.0206261i
$381$	20.5241	−	11.8496i	1.05148	−	0.607072i
$382$	5.75077	+	3.98716i	0.294235	+	0.204001i
$383$	−2.80474	+	4.85795i	−0.143315	+	0.248230i	−0.928743	−	0.370724i	$-0.879110\pi$
$383$	−2.80474	+	4.85795i	−0.143315	+	0.248230i	0.785428	+	0.618953i	$0.212443\pi$
$384$	−0.993163	+	18.0933i	−0.0506822	+	0.923318i
$385$	0.491779	−	0.525378i	0.0250634	−	0.0267758i
$386$	−0.0909404	−	0.192687i	−0.00462874	−	0.00980749i
$387$	1.83910	+	1.06181i	0.0934870	+	0.0539747i
$388$	2.18780	−	13.1172i	0.111069	−	0.665925i
$389$	7.14485	+	12.3752i	0.362258	+	0.627450i	0.988332	−	0.152314i	$-0.0486725\pi$
$389$	7.14485	+	12.3752i	0.362258	+	0.627450i	−0.626074	+	0.779764i	$0.715339\pi$
$390$	1.05914	+	0.0877202i	0.0536316	+	0.00444189i
$391$	−42.0982			−2.12900
$392$	−3.58083	+	19.4725i	−0.180859	+	0.983509i
$393$	−17.9853			−0.907237
$394$	18.7036	+	1.54907i	0.942274	+	0.0780412i
$395$	0.455792	+	0.789455i	0.0229334	+	0.0397218i
$396$	−0.143045	+	0.857643i	−0.00718828	+	0.0430982i
$397$	−18.3609	−	10.6007i	−0.921507	−	0.532032i	−0.0373914	−	0.999301i	$-0.511905\pi$
$397$	−18.3609	−	10.6007i	−0.921507	−	0.532032i	−0.884115	+	0.467268i	$0.845238\pi$
$398$	−12.2421	−	25.9388i	−0.613641	−	1.30020i
$399$	−6.10298	+	6.51995i	−0.305531	+	0.326406i
$400$	−3.78057	−	19.3380i	−0.189028	−	0.966900i
$401$	−8.00747	+	13.8693i	−0.399874	+	0.692602i	−0.993710	−	0.111984i	$-0.964279\pi$
$401$	−8.00747	+	13.8693i	−0.399874	+	0.692602i	0.593836	+	0.804586i	$0.297613\pi$
$402$	−5.03141	−	3.48840i	−0.250944	−	0.173986i
$403$	0.775461	−	0.447712i	0.0386284	−	0.0223021i
$404$	−18.4908	+	6.92480i	−0.919953	+	0.344522i
$405$		−	2.04180i		−	0.101458i
$406$	8.27453	−	7.49167i	0.410658	−	0.371805i
$407$			5.74488i			0.284763i
$408$	14.3245	+	13.9317i	0.709167	+	0.689723i
$409$	−31.4995	+	18.1862i	−1.55755	+	0.899251i	−0.560057	+	0.828454i	$0.689221\pi$
$409$	−31.4995	+	18.1862i	−1.55755	+	0.899251i	−0.997491	+	0.0707970i	$0.977446\pi$
$410$	−1.19491	+	1.72344i	−0.0590122	+	0.0851147i
$411$	−12.4440	+	21.5537i	−0.613818	+	1.06316i
$412$	−4.93922	+	5.99834i	−0.243338	+	0.295517i
$413$	21.5101	+	5.00875i	1.05844	+	0.246465i
$414$	5.30658	−	2.50450i	0.260804	−	0.123089i
$415$	−2.91614	−	1.68364i	−0.143148	−	0.0826464i
$416$	3.91806	−	8.93712i	0.192099	−	0.438178i
$417$	−7.44009	−	12.8866i	−0.364343	−	0.631060i
$418$	0.246005	−	2.97028i	0.0120325	−	0.145281i
$419$	19.9458			0.974416			0.487208	−	0.873286i	$-0.338015\pi$
$419$	19.9458			0.974416			0.487208	+	0.873286i	$0.338015\pi$
$420$	1.40084	+	1.83071i	0.0683541	+	0.0893296i
$421$	−9.41632			−0.458923			−0.229462	−	0.973318i	$-0.573697\pi$
$421$	−9.41632			−0.458923			−0.229462	+	0.973318i	$0.573697\pi$
$422$	−0.172112	+	2.07809i	−0.00837829	+	0.101160i
$423$	−2.23148	−	3.86503i	−0.108498	−	0.187924i
$424$	2.67945	+	9.47129i	0.130126	+	0.459967i
$425$	−18.8173	−	10.8642i	−0.912772	−	0.526989i
$426$	−20.2494	+	9.55693i	−0.981088	+	0.463035i
$427$	36.3869	−	11.0496i	1.76089	−	0.534727i
$428$	13.3246	+	10.9719i	0.644070	+	0.530347i
$429$	−1.38144	+	2.39272i	−0.0666965	+	0.115522i
$430$	−1.07058	+	1.54413i	−0.0516282	+	0.0744645i
$431$	26.4161	−	15.2514i	1.27242	−	0.734632i	0.296977	−	0.954885i	$-0.404021\pi$
$431$	26.4161	−	15.2514i	1.27242	−	0.734632i	0.975443	+	0.220252i	$0.0706881\pi$
$432$	−20.8138	−	7.14166i	−1.00140	−	0.343603i
$433$		−	24.2470i		−	1.16523i	−0.812747	−	0.582617i	$-0.802029\pi$
$433$		−	24.2470i		−	1.16523i	0.812747	−	0.582617i	$-0.197971\pi$
$434$	1.84880	+	0.595101i	0.0887450	+	0.0285658i
$435$		−	1.29960i		−	0.0623109i
$436$	−6.78533	−	18.1184i	−0.324958	−	0.867714i
$437$	−17.4193	+	10.0571i	−0.833280	+	0.481095i
$438$	11.2410	+	7.79368i	0.537116	+	0.372396i
$439$	18.1995	−	31.5225i	0.868617	−	1.50449i	0.00520569	−	0.999986i	$-0.498343\pi$
$439$	18.1995	−	31.5225i	0.868617	−	1.50449i	0.863411	−	0.504501i	$-0.168324\pi$
$440$	−0.745800	−	0.188767i	−0.0355546	−	0.00899912i
$441$	−2.73017	−	1.34437i	−0.130008	−	0.0640175i
$442$	−4.59281	−	9.73136i	−0.218458	−	0.462873i
$443$	−15.0900	−	8.71222i	−0.716948	−	0.413930i	0.0966804	−	0.995315i	$-0.469178\pi$
$443$	−15.0900	−	8.71222i	−0.716948	−	0.413930i	−0.813628	+	0.581385i	$0.802511\pi$
$444$	−18.1517	−	3.02750i	−0.861443	−	0.143679i
$445$	0.353499	+	0.612279i	0.0167575	+	0.0290248i
$446$	16.4860	+	1.36541i	0.780635	+	0.0646539i
$447$	12.5341			0.592841
$448$	20.0740	−	6.71068i	0.948409	−	0.317050i
$449$	29.4688			1.39072			0.695358	−	0.718663i	$-0.255246\pi$
$449$	29.4688			1.39072			0.695358	+	0.718663i	$0.255246\pi$
$450$	3.01829	+	0.249982i	0.142284	+	0.0117842i
$451$	−2.72599	−	4.72155i	−0.128362	−	0.222329i
$452$	31.1326	+	5.19255i	1.46435	+	0.244237i
$453$	−13.0252	−	7.52011i	−0.611978	−	0.353326i
$454$	1.15902	+	2.45576i	0.0543957	+	0.115255i
$455$	−0.360706	−	1.18782i	−0.0169102	−	0.0556861i
$456$	9.25538	+	2.34260i	0.433423	+	0.109702i
$457$	−2.22054	+	3.84608i	−0.103872	+	0.179912i	−0.913277	−	0.407339i	$-0.866457\pi$
$457$	−2.22054	+	3.84608i	−0.103872	+	0.179912i	0.809405	+	0.587251i	$0.199790\pi$
$458$	26.9070	+	18.6553i	1.25728	+	0.871705i
$459$	−21.0146	+	12.1328i	−0.980876	+	0.566309i
$460$	1.82086	+	4.86211i	0.0848979	+	0.226697i
$461$			34.4810i			1.60594i	0.596021	+	0.802969i	$0.296748\pi$
$461$			34.4810i			1.60594i	−0.596021	+	0.802969i	$0.703252\pi$
$462$	−5.85839	+	1.26207i	−0.272557	+	0.0587167i
$463$			16.0840i			0.747486i	0.927532	+	0.373743i	$0.121926\pi$
$463$			16.0840i			0.747486i	−0.927532	+	0.373743i	$0.878074\pi$
$464$	−11.2869	−	3.87277i	−0.523980	−	0.179789i
$465$	0.195835	−	0.113065i	0.00908162	−	0.00524327i
$466$	6.27133	−	9.04529i	0.290514	−	0.419015i
$467$	17.0469	−	29.5261i	0.788837	−	1.36631i	−0.137843	−	0.990454i	$-0.544017\pi$
$467$	17.0469	−	29.5261i	0.788837	−	1.36631i	0.926680	−	0.375852i	$-0.122650\pi$
$468$	1.15787	+	0.953427i	0.0535226	+	0.0440722i
$469$	−1.62186	+	6.96508i	−0.0748905	+	0.321617i
$470$	3.57105	−	1.68539i	0.164720	−	0.0777414i
$471$	18.5358	+	10.7016i	0.854083	+	0.493105i
$472$	−6.42721	−	22.7188i	−0.295836	−	1.04572i
$473$	−2.44237	−	4.23031i	−0.112300	−	0.194510i
$474$	0.626582	−	7.56539i	0.0287799	−	0.347490i
$475$	−10.3816			−0.476340
$476$	8.96104	−	21.5517i	0.410729	−	0.987821i
$477$	−1.51293			−0.0692721
$478$	−1.73011	+	20.8895i	−0.0791335	+	0.955462i
$479$	−3.46764	−	6.00613i	−0.158441	−	0.274427i	0.775866	−	0.630898i	$-0.217313\pi$
$479$	−3.46764	−	6.00613i	−0.158441	−	0.274427i	−0.934307	+	0.356471i	$0.883980\pi$
$480$	0.989465	−	2.25698i	0.0451627	−	0.103016i
$481$	8.58238	+	4.95504i	0.391323	+	0.225930i
$482$	−8.73993	+	4.12490i	−0.398093	+	0.187884i
$483$	29.5264	+	27.6381i	1.34350	+	1.25758i
$484$	1.27132	−	1.54393i	0.0577875	−	0.0701789i
$485$	−0.904275	+	1.56625i	−0.0410610	+	0.0711197i
$486$	3.61035	−	5.20730i	0.163769	−	0.236208i
$487$	2.84581	−	1.64303i	0.128956	−	0.0744528i	−0.434134	−	0.900848i	$-0.642946\pi$
$487$	2.84581	−	1.64303i	0.128956	−	0.0744528i	0.563090	+	0.826395i	$0.309612\pi$
$488$	−29.1429	−	28.3439i	−1.31924	−	1.28307i
$489$		−	8.03295i		−	0.363262i
$490$	1.38481	−	2.30921i	0.0625594	−	0.104320i
$491$			11.2694i			0.508582i	0.967128	+	0.254291i	$0.0818420\pi$
$491$			11.2694i			0.508582i	−0.967128	+	0.254291i	$0.918158\pi$
$492$	16.3550	−	6.12492i	0.737338	−	0.276133i
$493$	−11.3958	+	6.57935i	−0.513239	+	0.296319i
$494$	−4.22518	−	2.92943i	−0.190100	−	0.131801i
$495$	0.0591242	−	0.102406i	0.00265744	−	0.00460282i
$496$	−0.398376	−	2.03774i	−0.0178876	−	0.0914971i
$497$	19.0947	+	17.8735i	0.856513	+	0.801737i
$498$	11.9684	+	25.3588i	0.536315	+	1.13636i
$499$	12.4058	+	7.16251i	0.555361	+	0.320638i	0.751282	−	0.659982i	$-0.229436\pi$
$499$	12.4058	+	7.16251i	0.555361	+	0.320638i	−0.195920	+	0.980620i	$0.562769\pi$
$500$	−0.888329	+	5.32608i	−0.0397273	+	0.238190i
$501$	−10.1818	−	17.6354i	−0.454889	−	0.787892i
$502$	26.2803	+	2.17659i	1.17295	+	0.0971462i
$503$	−10.0242			−0.446958			−0.223479	−	0.974709i	$-0.571741\pi$
$503$	−10.0242			−0.446958			−0.223479	+	0.974709i	$0.571741\pi$
$504$	0.152587	+	3.24975i	0.00679677	+	0.144756i
$505$	2.68527			0.119493
$506$	−13.4513	−	1.11407i	−0.597983	−	0.0495263i
$507$	−8.02765	−	13.9043i	−0.356520	−	0.617511i
$508$	−4.86861	+	29.1903i	−0.216010	+	1.29511i
$509$	−21.5897	−	12.4648i	−0.956946	−	0.552493i	−0.0617145	−	0.998094i	$-0.519657\pi$
$509$	−21.5897	−	12.4648i	−0.956946	−	0.552493i	−0.895232	+	0.445601i	$0.852990\pi$
$510$	−1.15987	−	2.45756i	−0.0513598	−	0.108822i
$511$	3.62350	−	15.5611i	0.160294	−	0.688384i
$512$	−16.6530	−	15.3192i	−0.735967	−	0.677017i
$513$	−5.79692	+	10.0406i	−0.255940	+	0.443302i
$514$	−34.0339	−	23.5965i	−1.50117	−	1.04080i
$515$	0.915153	−	0.528364i	0.0403265	−	0.0232825i
$516$	14.6533	−	5.48766i	0.645077	−	0.241581i
$517$			10.2657i			0.451484i
$518$	4.52687	+	21.0133i	0.198899	+	0.923271i
$519$		−	16.9464i		−	0.743864i
$520$	−0.925266	+	0.951350i	−0.0405756	+	0.0417195i
$521$	−18.0714	+	10.4335i	−0.791720	+	0.457100i	−0.840568	−	0.541706i	$-0.817779\pi$
$521$	−18.0714	+	10.4335i	−0.791720	+	0.457100i	0.0488474	+	0.998806i	$0.484445\pi$
$522$	1.04505	−	1.50730i	0.0457405	−	0.0659726i
$523$	−13.4795	+	23.3471i	−0.589415	+	1.02090i	0.404894	+	0.914364i	$0.367309\pi$
$523$	−13.4795	+	23.3471i	−0.589415	+	1.02090i	−0.994309	+	0.106534i	$0.966025\pi$
$524$	14.2760	−	17.3373i	0.623652	−	0.757382i
$525$	6.06537	+	19.9736i	0.264714	+	0.871719i
$526$	−1.56210	+	0.737251i	−0.0681110	+	0.0321457i
$527$	−1.98287	−	1.14481i	−0.0863750	−	0.0498687i
$528$	4.20830	+	4.83056i	0.183143	+	0.210223i
$529$	34.0446	+	58.9671i	1.48020	+	2.56378i
$530$	0.110490	−	1.33406i	0.00479936	−	0.0579477i
$531$	3.62906			0.157488
$532$	−1.44071	−	11.0584i	−0.0624628	−	0.479442i
$533$	−9.40482			−0.407368
$534$	0.485960	−	5.86750i	0.0210295	−	0.253912i
$535$	−1.17370	−	2.03291i	−0.0507434	−	0.0878902i
$536$	7.35647	−	2.08116i	0.317751	−	0.0898925i
$537$	−24.0969	−	13.9124i	−1.03986	−	0.600363i
$538$	−36.3182	+	17.1408i	−1.56579	+	0.738990i
$539$	3.89243	+	5.81799i	0.167659	+	0.250598i
$540$	2.31020	+	1.90229i	0.0994152	+	0.0818616i
$541$	18.0081	−	31.1910i	0.774230	−	1.34100i	−0.160997	−	0.986955i	$-0.551471\pi$
$541$	18.0081	−	31.1910i	0.774230	−	1.34100i	0.935227	−	0.354050i	$-0.115196\pi$
$542$	18.5778	−	26.7951i	0.797983	−	1.15095i
$543$	21.6047	−	12.4735i	0.927146	−	0.535288i
$544$	−24.8000	+	2.74987i	−1.06329	+	0.117900i
$545$			2.63118i			0.112707i
$546$	−3.16752	+	9.84051i	−0.135557	+	0.421135i
$547$			16.6691i			0.712721i	0.934349	+	0.356360i	$0.115982\pi$
$547$			16.6691i			0.712721i	−0.934349	+	0.356360i	$0.884018\pi$
$548$	−10.8995	−	29.1042i	−0.465603	−	1.24327i
$549$	5.41147	−	3.12432i	0.230956	−	0.133343i
$550$	−5.72503	−	3.96931i	−0.244116	−	0.169252i
$551$	−3.14355	+	5.44479i	−0.133920	+	0.231956i
$552$	10.6088	−	41.9141i	0.451539	−	1.78398i
$553$	−8.48458	+	2.57651i	−0.360801	+	0.109564i
$554$	10.1859	+	21.5822i	0.432759	+	0.916940i
$555$	2.16739	+	1.25134i	0.0920007	+	0.0531166i
$556$	18.3280	+	3.05690i	0.777280	+	0.129641i
$557$	−1.66802	−	2.88909i	−0.0706761	−	0.122415i	0.828522	−	0.559957i	$-0.189182\pi$
$557$	−1.66802	−	2.88909i	−0.0706761	−	0.122415i	−0.899198	+	0.437542i	$0.855849\pi$
$558$	0.318052	+	0.0263417i	0.0134642	+	0.00111513i
$559$	−8.42631			−0.356395
$560$	−2.87669	−	0.102783i	−0.121562	−	0.00434339i
$561$	7.06473			0.298273
$562$	−41.9900	−	3.47770i	−1.77124	−	0.146698i
$563$	−9.21051	−	15.9531i	−0.388177	−	0.672342i	0.604028	−	0.796963i	$-0.293562\pi$
$563$	−9.21051	−	15.9531i	−0.388177	−	0.672342i	−0.992204	+	0.124622i	$0.960228\pi$
$564$	−32.4358	−	5.40992i	−1.36580	−	0.227799i
$565$	−3.71736	−	2.14622i	−0.156391	−	0.0902921i
$566$	−0.592705	−	1.25584i	−0.0249133	−	0.0527868i
$567$	19.3435	+	4.50425i	0.812352	+	0.189161i
$568$	6.86067	−	27.1058i	0.287867	−	1.13733i
$569$	−4.44688	+	7.70222i	−0.186423	+	0.322894i	−0.944055	−	0.329788i	$-0.893023\pi$
$569$	−4.44688	+	7.70222i	−0.186423	+	0.322894i	0.757632	+	0.652682i	$0.226356\pi$
$570$	−1.06703	−	0.739797i	−0.0446928	−	0.0309867i
$571$	−11.1115	+	6.41525i	−0.465003	+	0.268470i	−0.714146	−	0.699997i	$-0.753185\pi$
$571$	−11.1115	+	6.41525i	−0.465003	+	0.268470i	0.249142	+	0.968467i	$0.419851\pi$
$572$	−1.20998	−	3.23092i	−0.0505917	−	0.135092i
$573$			7.92519i			0.331080i
$574$	−13.6915	−	15.1222i	−0.571471	−	0.631188i
$575$			47.0143i			1.96063i
$576$	2.96251	−	1.82202i	0.123438	−	0.0759176i
$577$	9.13579	−	5.27455i	0.380328	−	0.219582i	−0.297633	−	0.954680i	$-0.596197\pi$
$577$	9.13579	−	5.27455i	0.380328	−	0.219582i	0.677961	+	0.735098i	$0.262864\pi$
$578$	−1.97925	+	2.85473i	−0.0823261	+	0.118741i
$579$	0.120653	−	0.208978i	0.00501419	−	0.00868483i
$580$	1.25277	+	1.03157i	0.0520186	+	0.0428337i
$581$	22.3834	−	23.9127i	0.928620	−	0.992065i
$582$	13.6201	−	6.42816i	0.564573	−	0.266456i
$583$	3.01379	+	1.74001i	0.124819	+	0.0720641i
$584$	−16.4356	+	4.64966i	−0.680109	+	0.192404i
$585$	−0.101991	−	0.176654i	−0.00421681	−	0.00730373i
$586$	1.78285	−	21.5263i	0.0736490	−	0.889242i
$587$	27.1036			1.11868			0.559342	−	0.828937i	$-0.311054\pi$
$587$	27.1036			1.11868			0.559342	+	0.828937i	$0.311054\pi$
$588$	−20.4340	+	9.23264i	−0.842684	+	0.380748i
$589$	−1.09396			−0.0450757
$590$	−0.265032	+	3.20001i	−0.0109112	+	0.131742i
$591$	10.6275	+	18.4073i	0.437156	+	0.757176i
$592$	17.3266	−	15.0946i	0.712119	−	0.620385i
$593$	−16.2551	−	9.38488i	−0.667516	−	0.385391i	0.127619	−	0.991823i	$-0.459267\pi$
$593$	−16.2551	−	9.38488i	−0.667516	−	0.385391i	−0.795135	+	0.606433i	$0.792600\pi$
$594$	−7.03569	+	3.32056i	−0.288678	+	0.136244i
$595$	−2.16920	+	2.31741i	−0.0889287	+	0.0950044i
$596$	−9.94909	+	12.0825i	−0.407531	+	0.494918i
$597$	16.2420	−	28.1319i	0.664740	−	1.15136i
$598$	−13.2663	+	19.1343i	−0.542498	+	0.782458i
$599$	−6.61802	+	3.82092i	−0.270405	+	0.156118i	−0.629072	−	0.777347i	$-0.716565\pi$
$599$	−6.61802	+	3.82092i	−0.270405	+	0.156118i	0.358667	+	0.933466i	$0.383231\pi$
$600$	15.5586	−	15.9972i	0.635177	−	0.653083i
$601$		−	21.8393i		−	0.890842i	−0.895321	−	0.445421i	$-0.853054\pi$
$601$		−	21.8393i		−	0.890842i	0.895321	−	0.445421i	$-0.146946\pi$
$602$	−12.2670	−	13.5488i	−0.499964	−	0.552209i
$603$			1.17511i			0.0478541i
$604$	17.5881	−	6.58673i	0.715650	−	0.268010i
$605$	−0.235555	+	0.135998i	−0.00957666	+	0.00552909i
$606$	−18.3769	−	12.7412i	−0.746512	−	0.517576i
$607$	−21.0737	+	36.5006i	−0.855353	+	1.48152i	0.0209637	+	0.999780i	$0.493327\pi$
$607$	−21.0737	+	36.5006i	−0.855353	+	1.48152i	−0.876317	+	0.481735i	$0.840007\pi$
$608$	−9.60478	+	7.06244i	−0.389525	+	0.286420i
$609$	12.3121	+	2.86694i	0.498910	+	0.116174i
$610$	2.35974	+	4.99986i	0.0955429	+	0.202439i
$611$	15.3361	+	8.85430i	0.620432	+	0.358207i
$612$	0.630961	−	3.78300i	0.0255051	−	0.152919i
$613$	−3.22667	−	5.58876i	−0.130324	−	0.225728i	0.793477	−	0.608600i	$-0.208268\pi$
$613$	−3.22667	−	5.58876i	−0.130324	−	0.225728i	−0.923801	+	0.382872i	$0.874935\pi$
$614$	21.1761	+	1.75385i	0.854599	+	0.0707797i
$615$	−2.37509			−0.0957729
$616$	3.43358	−	6.64910i	0.138343	−	0.267900i
$617$	−17.3938			−0.700249			−0.350124	−	0.936703i	$-0.613861\pi$
$617$	−17.3938			−0.700249			−0.350124	+	0.936703i	$0.613861\pi$
$618$	−8.76997	−	0.726348i	−0.352780	−	0.0292180i
$619$	−16.0795	−	27.8505i	−0.646290	−	1.11941i	−0.984002	−	0.178158i	$-0.942986\pi$
$619$	−16.0795	−	27.8505i	−0.646290	−	1.11941i	0.337711	−	0.941250i	$-0.390347\pi$
$620$	−0.0464549	+	0.278526i	−0.00186567	+	0.0111859i
$621$	45.4699	+	26.2521i	1.82464	+	1.05346i
$622$	−7.61063	−	16.1256i	−0.305159	−	0.646577i
$623$	−6.58040	+	1.99827i	−0.263638	+	0.0800589i
$624$	10.8462	−	2.12042i	0.434195	−	0.0848849i
$625$	−11.9479	+	20.6943i	−0.477915	+	0.827773i
$626$	−12.4470	−	8.62979i	−0.497480	−	0.344916i
$627$	2.92323	−	1.68773i	0.116743	−	0.0674014i
$628$	−25.0291	+	9.37337i	−0.998768	+	0.374038i
$629$		−	25.3403i		−	1.01038i
$630$	0.135567	−	0.421164i	0.00540111	−	0.0167796i
$631$			18.3194i			0.729285i	0.931148	+	0.364642i	$0.118809\pi$
$631$			18.3194i			0.729285i	−0.931148	+	0.364642i	$0.881191\pi$
$632$	6.79545	+	6.60914i	0.270309	+	0.262897i
$633$	−2.04517	+	1.18078i	−0.0812884	+	0.0469319i
$634$	13.2435	−	19.1014i	0.525966	−	0.758613i
$635$	2.01233	−	3.48545i	0.0798567	−	0.138316i
$636$	−7.08606	+	8.60552i	−0.280980	+	0.341231i
$637$	12.0489	−	0.796876i	0.477394	−	0.0315734i
$638$	−3.81531	+	1.80067i	−0.151049	+	0.0712893i
$639$	3.72191	+	2.14885i	0.147237	+	0.0850071i
$640$	1.39026	+	2.74532i	0.0549548	+	0.108518i
$641$	−16.6245	−	28.7945i	−0.656629	−	1.13731i	−0.981483	−	0.191550i	$-0.938648\pi$
$641$	−16.6245	−	28.7945i	−0.656629	−	1.13731i	0.324854	−	0.945764i	$-0.394685\pi$
$642$	−1.61350	+	19.4815i	−0.0636797	+	0.768872i
$643$	37.9140			1.49518			0.747590	−	0.664160i	$-0.231211\pi$
$643$	37.9140			1.49518			0.747590	+	0.664160i	$0.231211\pi$
$644$	−50.0793	+	6.52444i	−1.97340	+	0.257099i
$645$	−2.12798			−0.0837891
$646$	−1.08511	+	13.1017i	−0.0426932	+	0.515480i
$647$	2.21767	+	3.84112i	0.0871856	+	0.151010i	0.906320	−	0.422591i	$-0.138879\pi$
$647$	2.21767	+	3.84112i	0.0871856	+	0.151010i	−0.819135	+	0.573601i	$0.805546\pi$
$648$	−5.77984	−	20.4305i	−0.227053	−	0.802586i
$649$	−7.22920	−	4.17378i	−0.283771	−	0.163835i
$650$	−10.8677	+	5.12914i	−0.426268	+	0.201181i
$651$	0.639137	+	2.10471i	0.0250497	+	0.0824902i
$652$	7.74352	+	6.37626i	0.303260	+	0.249714i
$653$	6.71253	−	11.6264i	0.262681	−	0.454978i	−0.704272	−	0.709930i	$-0.748726\pi$
$653$	6.71253	−	11.6264i	0.262681	−	0.454978i	0.966954	+	0.254952i	$0.0820598\pi$
$654$	12.4846	−	18.0068i	0.488186	−	0.704122i
$655$	−2.64511	+	1.52715i	−0.103353	+	0.0596708i
$656$	−7.07772	+	20.6274i	−0.276339	+	0.805366i
$657$		−	2.62539i		−	0.102426i
$658$	8.08920	+	37.5492i	0.315350	+	1.46382i
$659$			37.8173i			1.47315i	0.676354	+	0.736577i	$0.263559\pi$
$659$			37.8173i			1.47315i	−0.676354	+	0.736577i	$0.736441\pi$
$660$	−0.305568	−	0.815936i	−0.0118942	−	0.0317603i
$661$	−8.41265	+	4.85704i	−0.327214	+	0.188917i	−0.654604	−	0.755972i	$-0.727164\pi$
$661$	−8.41265	+	4.85704i	−0.327214	+	0.188917i	0.327390	+	0.944889i	$0.393831\pi$
$662$	9.05323	+	6.27684i	0.351864	+	0.243956i
$663$	6.09343	−	10.5541i	0.236649	−	0.409889i
$664$	−33.9452	−	8.59177i	−1.31733	−	0.333425i
$665$	−0.343953	+	1.47711i	−0.0133379	+	0.0572797i
$666$	1.50754	+	3.19420i	0.0584158	+	0.123773i
$667$	24.6574	+	14.2359i	0.954738	+	0.551218i
$668$	25.0819	+	4.18338i	0.970450	+	0.161860i
$669$	9.36743	+	16.2249i	0.362166	+	0.627289i
$670$	−1.03618	−	0.0858185i	−0.0400311	−	0.00331546i
$671$	−14.3731			−0.554867
$672$	19.1993	+	14.3529i	0.740628	+	0.553674i
$673$	−6.76158			−0.260640			−0.130320	−	0.991472i	$-0.541600\pi$
$673$	−6.76158			−0.260640			−0.130320	+	0.991472i	$0.541600\pi$
$674$	10.9006	+	0.902810i	0.419875	+	0.0347750i
$675$	13.5496	+	23.4686i	0.521524	+	0.903305i
$676$	19.7754	+	3.29830i	0.760591	+	0.126858i
$677$	−11.9063	−	6.87412i	−0.457598	−	0.264194i	0.253436	−	0.967352i	$-0.418439\pi$
$677$	−11.9063	−	6.87412i	−0.457598	−	0.264194i	−0.711034	+	0.703158i	$0.751773\pi$
$678$	15.2567	+	32.3262i	0.585930	+	1.24148i
$679$	−12.8434	−	12.0220i	−0.492885	−	0.461364i
$680$	3.28967	+	0.832639i	0.126153	+	0.0319302i
$681$	−1.53771	+	2.66340i	−0.0589253	+	0.102062i
$682$	−0.603273	−	0.418265i	−0.0231005	−	0.0160162i
$683$	7.73191	−	4.46402i	0.295853	−	0.170811i	−0.344725	−	0.938704i	$-0.612028\pi$
$683$	7.73191	−	4.46402i	0.295853	−	0.170811i	0.640579	+	0.767893i	$0.278695\pi$
$684$	−0.642663	−	1.71606i	−0.0245728	−	0.0656151i
$685$			4.22655i			0.161488i
$686$	18.8220	+	18.2135i	0.718627	+	0.695396i
$687$			37.0808i			1.41472i
$688$	−6.34134	+	18.4813i	−0.241761	+	0.704593i
$689$	5.19888	−	3.00158i	0.198062	−	0.114351i
$690$	−3.35026	+	4.83216i	−0.127542	+	0.183957i
$691$	2.77991	−	4.81495i	0.105753	−	0.183169i	−0.808293	−	0.588781i	$-0.799608\pi$
$691$	2.77991	−	4.81495i	0.105753	−	0.183169i	0.914046	+	0.405612i	$0.132941\pi$
$692$	16.3358	+	13.4514i	0.620994	+	0.511346i
$693$	0.839742	+	0.786038i	0.0318992	+	0.0298591i
$694$	26.3232	−	12.4235i	0.999216	−	0.471590i
$695$	−2.18844	−	1.26350i	−0.0830122	−	0.0479271i
$696$	−3.67884	−	13.0039i	−0.139446	−	0.492912i
$697$	12.0241	+	20.8264i	0.455447	+	0.788857i
$698$	−2.96393	+	35.7866i	−0.112186	+	1.35454i
$699$	12.4654			0.471485
$700$	−24.0684	−	10.0075i	−0.909701	−	0.378247i
$701$	10.0731			0.380455			0.190227	−	0.981740i	$-0.439078\pi$
$701$	10.0731			0.380455			0.190227	+	0.981740i	$0.439078\pi$
$702$	−1.10773	+	13.3748i	−0.0418085	+	0.504799i
$703$	−6.05366	−	10.4853i	−0.228318	−	0.395459i
$704$	−7.99691	+	0.222350i	−0.301395	+	0.00838012i
$705$	3.87298	+	2.23606i	0.145865	+	0.0842151i
$706$	−40.0509	+	18.9024i	−1.50734	+	0.711402i
$707$	−5.92374	+	25.4395i	−0.222785	+	0.956752i
$708$	16.9973	−	20.6421i	0.638799	−	0.775777i
$709$	3.47065	−	6.01135i	0.130343	−	0.225761i	−0.793466	−	0.608615i	$-0.791725\pi$
$709$	3.47065	−	6.01135i	0.130343	−	0.225761i	0.923809	+	0.382854i	$0.125059\pi$
$710$	−2.16661	+	3.12495i	−0.0813114	+	0.117277i
$711$	−1.26183	+	0.728518i	−0.0473223	+	0.0273216i
$712$	5.27036	+	5.12586i	0.197515	+	0.192100i
$713$			4.95412i			0.185533i
$714$	25.8410	−	5.56689i	0.967074	−	0.208336i
$715$			0.469199i			0.0175471i
$716$	32.5384	−	12.1856i	1.21602	−	0.455397i
$717$	−20.5586	+	11.8695i	−0.767774	+	0.443274i
$718$	−10.1776	−	7.05639i	−0.379824	−	0.263342i
$719$	22.1401	−	38.3478i	0.825687	−	1.43013i	−0.0757065	−	0.997130i	$-0.524121\pi$
$719$	22.1401	−	38.3478i	0.825687	−	1.43013i	0.901393	−	0.433001i	$-0.142545\pi$
$720$	−0.464206	+	0.0907521i	−0.0172999	+	0.00338213i
$721$	2.98674	+	9.83551i	0.111232	+	0.366294i
$722$	−8.78754	−	18.6192i	−0.327038	−	0.692936i
$723$	−9.47888	−	5.47263i	−0.352523	−	0.203529i
$724$	−5.12495	+	30.7273i	−0.190467	+	1.14197i
$725$	7.34765	+	12.7265i	0.272885	+	0.472651i
$726$	2.25733	+	0.186957i	0.0837775	+	0.00693864i
$727$	−12.4882			−0.463161			−0.231580	−	0.972816i	$-0.574390\pi$
$727$	−12.4882			−0.463161			−0.231580	+	0.972816i	$0.574390\pi$
$728$	−6.97170	−	10.8644i	−0.258388	−	0.402663i
$729$	29.6965			1.09987
$730$	2.31499	+	0.191733i	0.0856818	+	0.00709635i
$731$	10.7731	+	18.6596i	0.398458	+	0.690150i
$732$	7.57449	−	45.4137i	0.279961	−	1.67854i
$733$	24.4899	+	14.1392i	0.904554	+	0.522245i	0.878675	−	0.477420i	$-0.158428\pi$
$733$	24.4899	+	14.1392i	0.904554	+	0.522245i	0.0258793	+	0.999665i	$0.491761\pi$
$734$	−6.72655	−	14.2524i	−0.248281	−	0.526064i
$735$	3.04282	−	0.201243i	0.112236	−	0.00742296i
$736$	31.9831	+	43.4964i	1.17891	+	1.60330i
$737$	1.35149	−	2.34085i	0.0497828	−	0.0862263i
$738$	−2.75467	−	1.90988i	−0.101401	−	0.0703038i
$739$	−28.9115	+	16.6921i	−1.06353	+	0.614028i	−0.926406	−	0.376526i	$-0.877119\pi$
$739$	−28.9115	+	16.6921i	−1.06353	+	0.614028i	−0.137122	+	0.990554i	$0.543785\pi$
$740$	−2.92666	+	1.09603i	−0.107586	+	0.0402909i
$741$		−	5.82276i		−	0.213905i
$742$	12.3948	+	3.98971i	0.455027	+	0.146467i
$743$		−	5.66014i		−	0.207651i	−0.994596	−	0.103825i	$-0.966892\pi$
$743$		−	5.66014i		−	0.207651i	0.994596	−	0.103825i	$-0.0331083\pi$
$744$	1.63948	−	1.68570i	0.0601064	−	0.0618009i
$745$	1.84340	−	1.06429i	0.0675368	−	0.0389924i
$746$	25.2751	−	36.4549i	0.925387	−	1.33471i
$747$	2.69105	−	4.66103i	0.0984604	−	0.170538i
$748$	−5.60772	+	6.81019i	−0.205039	+	0.249005i
$749$	21.8485	−	6.63470i	0.798325	−	0.242427i
$750$	−5.53029	+	2.61008i	−0.201938	+	0.0953066i
$751$	−33.3985	−	19.2827i	−1.21873	−	0.703634i	−0.254084	−	0.967182i	$-0.581774\pi$
$751$	−33.3985	−	19.2827i	−1.21873	−	0.703634i	−0.964646	+	0.263548i	$0.915107\pi$
$752$	30.9614	−	26.9730i	1.12905	−	0.983604i
$753$	14.9326	+	25.8640i	0.544174	+	0.942538i
$754$	−0.600698	+	7.25287i	−0.0218761	+	0.264134i
$755$	−2.55417			−0.0929558
$756$	−23.1182	+	17.6898i	−0.840800	+	0.643371i
$757$	−37.2566			−1.35411			−0.677057	−	0.735930i	$-0.736745\pi$
$757$	−37.2566			−1.35411			−0.677057	+	0.735930i	$0.736745\pi$
$758$	−4.32909	+	52.2697i	−0.157240	+	1.89852i
$759$	−7.64309	−	13.2382i	−0.277427	−	0.480517i
$760$	1.56011	−	0.441358i	0.0565911	−	0.0160098i
$761$	−2.72004	−	1.57042i	−0.0986014	−	0.0569276i	0.449888	−	0.893085i	$-0.351464\pi$
$761$	−2.72004	−	1.57042i	−0.0986014	−	0.0569276i	−0.548490	+	0.836157i	$0.684797\pi$
$762$	−30.3095	+	14.3049i	−1.09800	+	0.518212i
$763$	−24.9272	−	5.80444i	−0.902424	−	0.210135i
$764$	−7.63965	−	6.29073i	−0.276393	−	0.227591i
$765$	−0.260793	+	0.451707i	−0.00942899	+	0.0163315i
$766$	4.52003	−	6.51934i	0.163315	−	0.235553i
$767$	−12.4706	+	7.19989i	−0.450286	+	0.259973i
$768$	3.51175	−	25.3845i	0.126720	−	0.915984i
$769$			24.2179i			0.873320i	0.899627	+	0.436660i	$0.143839\pi$
$769$			24.2179i			0.873320i	−0.899627	+	0.436660i	$0.856161\pi$
$770$	−0.754434	+	0.683057i	−0.0271879	+	0.0246157i
$771$		−	46.9024i		−	1.68915i
$772$	0.105678	+	0.282185i	0.00380344	+	0.0101561i
$773$	−27.6423	+	15.9593i	−0.994226	+	0.574017i	−0.906535	−	0.422131i	$-0.861282\pi$
$773$	−27.6423	+	15.9593i	−0.994226	+	0.574017i	−0.0876910	+	0.996148i	$0.527949\pi$
$774$	−2.46807	−	1.71118i	−0.0887129	−	0.0615069i
$775$	−1.27849	+	2.21442i	−0.0459249	+	0.0795442i
$776$	−4.61461	+	18.2318i	−0.165655	+	0.654485i
$777$	−16.6362	+	17.7729i	−0.596822	+	0.637598i
$778$	−8.62532	−	18.2755i	−0.309233	−	0.655209i
$779$	9.95067	+	5.74502i	0.356520	+	0.205837i
$780$	−1.48250	−	0.247264i	−0.0530820	−	0.00885346i
$781$	−4.94278	−	8.56114i	−0.176866	−	0.306342i
$782$	59.3327	+	4.91407i	2.12173	+	0.175727i
$783$	16.4113			0.586491
$784$	7.31977	−	27.0263i	0.261421	−	0.965225i
$785$	3.63476			0.129730
$786$	25.3482	+	2.09940i	0.904141	+	0.0748829i
$787$	−13.6974	−	23.7246i	−0.488260	−	0.845691i	0.511649	−	0.859195i	$-0.329035\pi$
$787$	−13.6974	−	23.7246i	−0.488260	−	0.845691i	−0.999909	+	0.0135038i	$0.995701\pi$
$788$	−26.1798	−	4.36649i	−0.932617	−	0.155550i
$789$	−1.69418	−	0.978134i	−0.0603143	−	0.0348225i
$790$	−0.550236	−	1.16585i	−0.0195765	−	0.0414791i
$791$	28.5333	−	30.4828i	1.01453	−	1.08384i
$792$	0.301717	−	1.19205i	0.0107211	−	0.0423578i
$793$	−12.3970	+	21.4722i	−0.440230	+	0.762501i
$794$	24.6402	+	17.0837i	0.874449	+	0.606278i
$795$	1.31292	−	0.758017i	0.0465646	−	0.0268841i
$796$	14.2261	+	37.9869i	0.504230	+	1.34641i
$797$			15.8243i			0.560526i	0.959923	+	0.280263i	$0.0904216\pi$
$797$			15.8243i			0.560526i	−0.959923	+	0.280263i	$0.909578\pi$
$798$	9.36253	−	8.47674i	0.331430	−	0.300073i
$799$		−	45.2812i		−	1.60194i
$800$	3.07099	+	27.6960i	0.108576	+	0.979203i
$801$	−0.978640	+	0.565018i	−0.0345785	+	0.0199639i
$802$	12.9046	−	18.6126i	0.455677	−	0.657233i
$803$	−3.01945	+	5.22985i	−0.106554	+	0.184557i
$804$	6.68401	+	5.50382i	0.235727	+	0.194105i
$805$	6.68925	+	1.55763i	0.235765	+	0.0548993i
$806$	−1.14519	+	0.540482i	−0.0403374	+	0.0190377i
$807$	−39.3889	−	22.7412i	−1.38655	−	0.800528i
$808$	26.8691	−	7.60132i	0.945250	−	0.267414i
$809$	−20.6958	−	35.8462i	−0.727625	−	1.26028i	−0.957884	−	0.287155i	$-0.907291\pi$
$809$	−20.6958	−	35.8462i	−0.727625	−	1.26028i	0.230259	−	0.973129i	$-0.426043\pi$
$810$	−0.238337	+	2.87769i	−0.00837430	+	0.101112i
$811$	54.4393			1.91162			0.955812	−	0.293979i	$-0.0949794\pi$
$811$	54.4393			1.91162			0.955812	+	0.293979i	$0.0949794\pi$
$812$	−12.5365	+	9.59280i	−0.439945	+	0.336641i
$813$	36.9267			1.29507
$814$	0.670591	−	8.09676i	0.0235042	−	0.283791i
$815$	−0.682088	−	1.18141i	−0.0238925	−	0.0413830i
$816$	−18.5625	−	21.3073i	−0.649818	−	0.745904i
$817$	8.91537	+	5.14729i	0.311909	+	0.180081i
$818$	46.5178	−	21.9546i	1.62646	−	0.767623i
$819$	1.89857	−	0.576537i	0.0663413	−	0.0201458i
$820$	1.88526	−	2.28952i	0.0658361	−	0.0799534i
$821$	−5.35663	+	9.27796i	−0.186948	+	0.323803i	−0.944231	−	0.329283i	$-0.893193\pi$
$821$	−5.35663	+	9.27796i	−0.186948	+	0.323803i	0.757283	+	0.653086i	$0.226526\pi$
$822$	20.0544	−	28.9249i	0.699476	−	1.00887i
$823$	10.8159	−	6.24458i	0.377019	−	0.217672i	−0.299501	−	0.954096i	$-0.596820\pi$
$823$	10.8159	−	6.24458i	0.377019	−	0.217672i	0.676521	+	0.736424i	$0.263487\pi$
$824$	7.66146	−	7.87744i	0.266899	−	0.274424i
$825$		−	7.88972i		−	0.274685i
$826$	−29.7314	−	9.57012i	−1.03449	−	0.332987i
$827$			12.8688i			0.447493i	0.974647	+	0.223747i	$0.0718288\pi$
$827$			12.8688i			0.447493i	−0.974647	+	0.223747i	$0.928171\pi$
$828$	−7.77138	+	2.91038i	−0.270074	+	0.101143i
$829$	−0.0415827	+	0.0240078i	−0.00144423	+	0.000833825i	−0.500722	−	0.865608i	$-0.666932\pi$
$829$	−0.0415827	+	0.0240078i	−0.00144423	+	0.000833825i	0.499278	+	0.866442i	$0.333599\pi$
$830$	3.91345	+	2.71329i	0.135838	+	0.0941798i
$831$	−13.5140	+	23.4070i	−0.468796	+	0.811979i
$832$	−6.56528	+	12.1385i	−0.227610	+	0.420827i
$833$	−17.1692	−	25.6627i	−0.594879	−	0.889161i
$834$	8.98174	+	19.0307i	0.311012	+	0.658980i
$835$	−2.99489	−	1.72910i	−0.103642	−	0.0598380i
$836$	−0.693434	+	4.15757i	−0.0239829	+	0.143792i
$837$	1.42778	+	2.47299i	0.0493514	+	0.0854792i
$838$	−28.1114	−	2.32825i	−0.971092	−	0.0804279i
$839$	−3.71609			−0.128294			−0.0641468	−	0.997940i	$-0.520433\pi$
$839$	−3.71609			−0.128294			−0.0641468	+	0.997940i	$0.520433\pi$
$840$	−1.76063	−	2.74370i	−0.0607476	−	0.0946667i
$841$	−20.1005			−0.693121
$842$	13.2713	+	1.09915i	0.457358	+	0.0378793i
$843$	−23.8589	−	41.3248i	−0.821744	−	1.42330i
$844$	0.485146	−	2.90875i	0.0166994	−	0.100123i
$845$	−2.36126	−	1.36328i	−0.0812300	−	0.0468981i
$846$	2.69386	+	5.70781i	0.0926168	+	0.196239i
$847$	−0.768769	−	2.53160i	−0.0264152	−	0.0869868i
$848$	−2.67082	−	13.6615i	−0.0917162	−	0.469138i
$849$	0.786361	−	1.36202i	0.0269878	−	0.0467443i
$850$	25.2527	+	17.5083i	0.866160	+	0.600531i
$851$	−47.4838	+	27.4148i	−1.62772	+	0.939766i
$852$	29.6549	−	11.1057i	1.01596	−	0.380476i
$853$		−	39.2257i		−	1.34306i	−0.740976	−	0.671532i	$-0.765637\pi$
$853$		−	39.2257i		−	1.34306i	0.740976	−	0.671532i	$-0.234363\pi$
$854$	−52.5731	+	11.3258i	−1.79901	+	0.387560i
$855$			0.249209i			0.00852276i
$856$	−17.4988	−	17.0190i	−0.598097	−	0.581699i
$857$	−12.0729	+	6.97030i	−0.412403	+	0.238101i	−0.691822	−	0.722068i	$-0.743192\pi$
$857$	−12.0729	+	6.97030i	−0.412403	+	0.238101i	0.279419	+	0.960169i	$0.409858\pi$
$858$	2.22628	−	3.21102i	0.0760040	−	0.109622i
$859$	0.285995	−	0.495358i	0.00975803	−	0.0169014i	−0.861105	−	0.508427i	$-0.830227\pi$
$859$	0.285995	−	0.495358i	0.00975803	−	0.0169014i	0.870863	+	0.491525i	$0.163561\pi$
$860$	1.68911	−	2.05131i	0.0575983	−	0.0699491i
$861$	5.23949	−	22.5010i	0.178561	−	0.766833i
$862$	−39.0108	+	18.4116i	−1.32871	+	0.627100i
$863$	−31.3569	−	18.1039i	−1.06740	−	0.616264i	−0.139930	−	0.990161i	$-0.544688\pi$
$863$	−31.3569	−	18.1039i	−1.06740	−	0.616264i	−0.927470	+	0.373898i	$0.878021\pi$
$864$	28.5010	+	12.4949i	0.969625	+	0.425086i
$865$	−1.43894	−	2.49232i	−0.0489254	−	0.0847413i
$866$	−2.83031	+	34.1734i	−0.0961779	+	1.16126i
$867$	−3.93413			−0.133610
$868$	−2.53620	−	1.05454i	−0.0860844	−	0.0357933i
$869$	3.35147			0.113691
$870$	−0.151700	+	1.83164i	−0.00514312	+	0.0620983i
$871$	−2.33136	−	4.03803i	−0.0789951	−	0.136824i
$872$	7.44823	+	26.3279i	0.252229	+	0.891575i
$873$	−2.50342	−	1.44535i	−0.0847281	−	0.0489178i
$874$	25.7246	−	12.1410i	0.870146	−	0.410674i
$875$	5.21491	+	4.88141i	0.176296	+	0.165022i
$876$	−14.9332	−	12.2965i	−0.504546	−	0.415459i
$877$	22.7114	−	39.3374i	0.766911	−	1.32833i	−0.172320	−	0.985041i	$-0.555126\pi$
$877$	22.7114	−	39.3374i	0.766911	−	1.32833i	0.939231	−	0.343287i	$-0.111540\pi$
$878$	−29.3298	+	42.3031i	−0.989832	+	1.42766i
$879$	21.1853	−	12.2313i	0.714562	−	0.412553i
$880$	1.02909	+	0.353102i	0.0346905	+	0.0119031i
$881$			5.37839i			0.181202i	0.995887	+	0.0906012i	$0.0288789\pi$
$881$			5.37839i			0.181202i	−0.995887	+	0.0906012i	$0.971121\pi$
$882$	3.69094	+	2.21342i	0.124281	+	0.0745298i
$883$			36.3357i			1.22279i	0.791325	+	0.611396i	$0.209392\pi$
$883$			36.3357i			1.22279i	−0.791325	+	0.611396i	$0.790608\pi$
$884$	5.33713	+	14.2514i	0.179507	+	0.479325i
$885$	−3.14932	+	1.81826i	−0.105863	+	0.0611201i
$886$	20.2507	+	14.0403i	0.680336	+	0.471694i
$887$	−17.2464	+	29.8716i	−0.579077	+	1.00299i	0.416509	+	0.909132i	$0.363253\pi$
$887$	−17.2464	+	29.8716i	−0.579077	+	1.00299i	−0.995586	+	0.0938585i	$0.970080\pi$
$888$	25.2294	+	6.38574i	0.846644	+	0.214292i
$889$	28.5811	+	26.7532i	0.958578	+	0.897275i
$890$	−0.426747	−	0.904202i	−0.0143046	−	0.0303089i
$891$	−6.50105	−	3.75338i	−0.217793	−	0.125743i
$892$	−23.0758	−	3.84878i	−0.772635	−	0.128867i
$893$	−10.8175	−	18.7364i	−0.361993	−	0.626990i
$894$	−17.6654	−	1.46308i	−0.590819	−	0.0489329i
$895$	−4.72527			−0.157948
$896$	−29.0754	+	7.11473i	−0.971342	+	0.237687i
$897$	−26.3691			−0.880439
$898$	−41.5329	−	3.43985i	−1.38597	−	0.114789i
$899$	0.774257	+	1.34105i	0.0258229	+	0.0447266i
$900$	−4.22476	−	0.704642i	−0.140825	−	0.0234881i
$901$	−13.2936	−	7.67508i	−0.442875	−	0.255694i
$902$	3.29084	+	6.97270i	0.109573	+	0.232165i
$903$	4.69436	−	20.1600i	0.156219	−	0.670881i
$904$	−43.2717	−	10.9524i	−1.43920	−	0.364271i
$905$	2.11828	−	3.66897i	0.0704140	−	0.121961i
$906$	17.4798	+	12.1192i	0.580727	+	0.402633i
$907$	−0.611225	+	0.352891i	−0.0202954	+	0.0117175i	−0.510113	−	0.860107i	$-0.670397\pi$
$907$	−0.611225	+	0.352891i	−0.0202954	+	0.0117175i	0.489818	+	0.871825i	$0.337063\pi$
$908$	−1.34686	−	3.59642i	−0.0446970	−	0.119351i
$909$			4.29201i			0.142357i
$910$	0.369721	+	1.71621i	0.0122561	+	0.0568918i
$911$		−	38.4748i		−	1.27473i	−0.770563	−	0.637363i	$-0.780025\pi$
$911$		−	38.4748i		−	1.27473i	0.770563	−	0.637363i	$-0.219975\pi$
$912$	−12.7710	−	4.38200i	−0.422889	−	0.145103i
$913$	−10.7213	+	6.18995i	−0.354823	+	0.204857i
$914$	3.57854	−	5.16142i	0.118368	−	0.170725i
$915$	−3.13074	+	5.42259i	−0.103499	+	0.179265i
$916$	−35.7448	−	29.4334i	−1.18104	−	0.972506i
$917$	−8.63272	−	28.4280i	−0.285077	−	0.938776i
$918$	31.0339	−	14.6468i	1.02427	−	0.483416i
$919$	36.3317	+	20.9761i	1.19847	+	0.691938i	0.960214	−	0.279265i	$-0.0900906\pi$
$919$	36.3317	+	20.9761i	1.19847	+	0.691938i	0.238257	+	0.971202i	$0.423424\pi$
$920$	−1.99875	−	7.06514i	−0.0658967	−	0.232931i
$921$	12.0324	+	20.8407i	0.396480	+	0.686724i
$922$	4.02491	−	48.5970i	0.132553	−	1.60046i
$923$	−17.0529			−0.561302
$924$	8.40407	−	1.09490i	0.276473	−	0.0360196i
$925$	−28.2994			−0.930478
$926$	1.87746	−	22.6686i	0.0616971	−	0.744935i
$927$	0.844514	+	1.46274i	0.0277375	+	0.0480427i
$928$	15.4555	+	6.77574i	0.507352	+	0.222425i
$929$	−46.1440	−	26.6412i	−1.51393	−	0.874071i	−0.999867	−	0.0163213i	$-0.994805\pi$
$929$	−46.1440	−	26.6412i	−1.51393	−	0.874071i	−0.514068	−	0.857749i	$-0.671862\pi$
$930$	−0.289205	+	0.136493i	−0.00948340	+	0.00447579i
$931$	−13.2350	−	6.51704i	−0.433759	−	0.213587i
$932$	−9.89459	+	12.0163i	−0.324108	+	0.393606i
$933$	10.0973	−	17.4890i	0.330570	−	0.572564i
$934$	−27.4723	+	39.6239i	−0.898920	+	1.29653i
$935$	1.03902	−	0.599876i	0.0339794	−	0.0196180i
$936$	−1.52060	−	1.47890i	−0.0497022	−	0.0483395i
$937$		−	47.4828i		−	1.55120i	−0.631227	−	0.775598i	$-0.717448\pi$
$937$		−	47.4828i		−	1.55120i	0.631227	−	0.775598i	$-0.282552\pi$
$938$	3.09885	−	9.62718i	0.101181	−	0.314338i
$939$		−	17.1533i		−	0.559776i
$940$	−5.22973	+	1.95853i	−0.170575	+	0.0638802i
$941$	−3.69513	+	2.13339i	−0.120458	+	0.0695464i	−0.559018	−	0.829155i	$-0.688822\pi$
$941$	−3.69513	+	2.13339i	−0.120458	+	0.0695464i	0.438560	+	0.898702i	$0.355489\pi$
$942$	−24.8749	−	17.2464i	−0.810468	−	0.561918i
$943$	26.0170	−	45.0628i	0.847231	−	1.46745i
$944$	6.40649	+	32.7699i	0.208514	+	1.06657i
$945$	3.78805	−	1.15031i	0.123225	−	0.0374197i
$946$	2.94845	+	6.24724i	0.0958623	+	0.203115i
$947$	−0.391056	−	0.225776i	−0.0127076	−	0.00733675i	0.493633	−	0.869670i	$-0.335669\pi$
$947$	−0.391056	−	0.225776i	−0.0127076	−	0.00733675i	−0.506340	+	0.862334i	$0.669002\pi$
$948$	−1.76619	+	10.5894i	−0.0573633	+	0.343929i
$949$	5.20865	+	9.02164i	0.169080	+	0.292855i
$950$	14.6317	+	1.21183i	0.474714	+	0.0393169i
$951$	26.3238			0.853608
$952$	−15.1453	+	29.3287i	−0.490862	+	0.950549i
$953$	−43.0013			−1.39295			−0.696475	−	0.717581i	$-0.745249\pi$
$953$	−43.0013			−1.39295			−0.696475	+	0.717581i	$0.745249\pi$
$954$	2.13230	+	0.176602i	0.0690357	+	0.00571769i
$955$	0.672939	+	1.16556i	0.0217758	+	0.0377168i
$956$	4.87680	−	29.2394i	0.157727	−	0.945670i
$957$	−4.13789	−	2.38901i	−0.133759	−	0.0772257i
$958$	4.18617	+	8.86974i	0.135249	+	0.286568i
$959$	−40.0413	−	9.32385i	−1.29300	−	0.301083i
$960$	−1.65799	+	3.06546i	−0.0535115	+	0.0989372i
$961$	15.3653	−	26.6134i	0.495654	−	0.858498i
$962$	−11.5175	−	7.98538i	−0.371339	−	0.257459i
$963$	3.24931	−	1.87599i	0.104708	−	0.0604529i
$964$	12.7994	−	4.79338i	0.412242	−	0.154384i
$965$		−	0.0409794i		−	0.00131917i
$966$	−38.3880	−	42.3994i	−1.23511	−	1.36418i
$967$		−	14.4689i		−	0.465290i	−0.972562	−	0.232645i	$-0.925262\pi$
$967$		−	14.4689i		−	0.465290i	0.972562	−	0.232645i	$-0.0747380\pi$
$968$	−1.97201	+	2.02760i	−0.0633828	+	0.0651696i
$969$	−12.8942	+	7.44446i	−0.414221	+	0.239150i
$970$	1.45730	−	2.10190i	0.0467911	−	0.0674879i
$971$	26.2647	−	45.4917i	0.842873	−	1.45990i	−0.0445821	−	0.999006i	$-0.514196\pi$
$971$	26.2647	−	45.4917i	0.842873	−	1.45990i	0.887455	−	0.460894i	$-0.152471\pi$
$972$	−5.69623	+	6.91768i	−0.182707	+	0.221885i
$973$	16.7978	−	17.9454i	0.538512	−	0.575304i
$974$	−4.20264	+	1.98348i	−0.134661	+	0.0635547i
$975$	−11.7866	−	6.80499i	−0.377473	−	0.217934i
$976$	37.7652	+	43.3494i	1.20883	+	1.38758i
$977$	26.7174	+	46.2759i	0.854765	+	1.48050i	0.876863	+	0.480741i	$0.159632\pi$
$977$	26.7174	+	46.2759i	0.854765	+	1.48050i	−0.0220974	+	0.999756i	$0.507034\pi$
$978$	−0.937674	+	11.3215i	−0.0299835	+	0.362023i
$979$	2.59931			0.0830742
$980$	−2.22129	+	3.09293i	−0.0709565	+	0.0988000i
$981$	−4.20557			−0.134273
$982$	1.31546	−	15.8830i	0.0419781	−	0.506846i
$983$	−19.8539	−	34.3880i	−0.633241	−	1.09681i	−0.986885	−	0.161426i	$-0.948391\pi$
$983$	−19.8539	−	34.3880i	−0.633241	−	1.09681i	0.353643	−	0.935380i	$-0.384943\pi$
$984$	−23.7654	+	6.72329i	−0.757614	+	0.214331i
$985$	3.12598	+	1.80479i	0.0996020	+	0.0575053i
$986$	16.8291	−	7.94264i	0.535946	−	0.252945i
$987$	−29.7278	+	31.7588i	−0.946246	+	1.01089i
$988$	5.61297	+	4.62190i	0.178572	+	0.147042i
$989$	23.3101	−	40.3743i	0.741219	−	1.28383i
$990$	−0.0952827	+	0.137429i	−0.00302828	+	0.00436777i
$991$	7.08359	−	4.08971i	0.225018	−	0.129914i	−0.383254	−	0.923643i	$-0.625197\pi$
$991$	7.08359	−	4.08971i	0.225018	−	0.129914i	0.608271	+	0.793729i	$0.291863\pi$
$992$	0.323605	+	2.91846i	0.0102745	+	0.0926613i
$993$			12.4763i			0.395925i
$994$	−24.8254	−	27.4196i	−0.787415	−	0.869697i
$995$		−	5.51651i		−	0.174885i
$996$	−13.9080	−	37.1375i	−0.440691	−	1.17675i
$997$	44.7360	−	25.8284i	1.41680	−	0.817992i	0.420788	−	0.907159i	$-0.361754\pi$
$997$	44.7360	−	25.8284i	1.41680	−	0.817992i	0.996017	+	0.0891667i	$0.0284204\pi$
$998$	−16.6486	−	11.5429i	−0.527001	−	0.365383i
$999$	−15.8019	+	27.3698i	−0.499951	+	0.865941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.l.a.243.1	yes	80
4.3	odd	2	inner	308.2.l.a.243.27	yes	80
7.3	odd	6	inner	308.2.l.a.199.27	yes	80
28.3	even	6	inner	308.2.l.a.199.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.l.a.199.1	✓	80	28.3	even	6	inner
308.2.l.a.199.27	yes	80	7.3	odd	6	inner
308.2.l.a.243.1	yes	80	1.1	even	1	trivial
308.2.l.a.243.27	yes	80	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40939 - 0.116729i) q^{2} +(-0.800821 - 1.38706i) q^{3} +(1.97275 + 0.329032i) q^{4} +(-0.235555 - 0.135998i) q^{5} +(0.966757 + 2.04839i) q^{6} +(1.80804 - 1.93157i) q^{7} +(-2.74196 - 0.694010i) q^{8} +(0.217373 - 0.376500i) q^{9} +O(q^{10})\)	\(q+(-1.40939 - 0.116729i) q^{2} +(-0.800821 - 1.38706i) q^{3} +(1.97275 + 0.329032i) q^{4} +(-0.235555 - 0.135998i) q^{5} +(0.966757 + 2.04839i) q^{6} +(1.80804 - 1.93157i) q^{7} +(-2.74196 - 0.694010i) q^{8} +(0.217373 - 0.376500i) q^{9} +(0.316113 + 0.219169i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.12343 - 2.99982i) q^{12} +1.72503i q^{13} +(-2.77371 + 2.51129i) q^{14} +0.435639i q^{15} +(3.78348 + 1.29819i) q^{16} +(3.81998 - 2.20547i) q^{17} +(-0.350311 + 0.505261i) q^{18} +(1.05375 - 1.82515i) q^{19} +(-0.419943 - 0.345794i) q^{20} +(-4.12713 - 0.961027i) q^{21} +(1.27893 - 0.603604i) q^{22} +(-8.26541 - 4.77204i) q^{23} +(1.23318 + 4.35905i) q^{24} +(-2.46301 - 4.26606i) q^{25} +(0.201360 - 2.43124i) q^{26} -5.50123 q^{27} +(4.20237 - 3.21560i) q^{28} -2.98320 q^{29} +(0.0508515 - 0.613984i) q^{30} +(-0.259539 - 0.449535i) q^{31} +(-5.18085 - 2.27130i) q^{32} +(1.38706 + 0.800821i) q^{33} +(-5.64127 + 2.66246i) q^{34} +(-0.688582 + 0.209101i) q^{35} +(0.552702 - 0.671218i) q^{36} +(2.87244 - 4.97521i) q^{37} +(-1.69819 + 2.44934i) q^{38} +(2.39272 - 1.38144i) q^{39} +(0.551498 + 0.536377i) q^{40} +5.45198i q^{41} +(5.70455 + 1.83621i) q^{42} +4.88474i q^{43} +(-1.87297 + 0.701425i) q^{44} +(-0.102406 + 0.0591242i) q^{45} +(11.0921 + 7.69046i) q^{46} +(5.13284 - 8.89035i) q^{47} +(-1.22921 - 6.28754i) q^{48} +(-0.461949 - 6.98474i) q^{49} +(2.97336 + 6.30003i) q^{50} +(-6.11823 - 3.53236i) q^{51} +(-0.567589 + 3.40305i) q^{52} +(-1.74001 - 3.01379i) q^{53} +(7.75337 + 0.642151i) q^{54} +0.271995 q^{55} +(-6.29812 + 4.04150i) q^{56} -3.37546 q^{57} +(4.20449 + 0.348225i) q^{58} +(4.17378 + 7.22920i) q^{59} +(-0.143339 + 0.859405i) q^{60} +(12.4475 + 7.18655i) q^{61} +(0.313318 + 0.663865i) q^{62} +(-0.334219 - 1.10060i) q^{63} +(7.03670 + 3.80589i) q^{64} +(0.234600 - 0.406339i) q^{65} +(-1.86143 - 1.29058i) q^{66} +(-2.34085 + 1.35149i) q^{67} +(8.26153 - 3.09394i) q^{68} +15.2862i q^{69} +(0.994888 - 0.214328i) q^{70} +9.88555i q^{71} +(-0.857322 + 0.881490i) q^{72} +(5.22985 - 3.01945i) q^{73} +(-4.62913 + 6.67671i) q^{74} +(-3.94486 + 6.83269i) q^{75} +(2.67932 - 3.25384i) q^{76} +(-0.600026 + 2.57681i) q^{77} +(-3.53353 + 1.66768i) q^{78} +(-2.90246 - 1.67574i) q^{79} +(-0.714664 - 0.820339i) q^{80} +(3.75338 + 6.50105i) q^{81} +(0.636401 - 7.68395i) q^{82} +12.3799 q^{83} +(-7.82559 - 3.25382i) q^{84} -1.19975 q^{85} +(0.570189 - 6.88449i) q^{86} +(2.38901 + 4.13789i) q^{87} +(2.72161 - 0.769951i) q^{88} +(-2.25107 - 1.29965i) q^{89} +(0.151232 - 0.0713753i) q^{90} +(3.33202 + 3.11893i) q^{91} +(-14.7354 - 12.1336i) q^{92} +(-0.415688 + 0.719994i) q^{93} +(-8.27193 + 11.9308i) q^{94} +(-0.496431 + 0.286615i) q^{95} +(0.998499 + 9.00506i) q^{96} -6.64920i q^{97} +(-0.164253 + 9.89813i) q^{98} +0.434745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 12 q^{8} - 40 q^{9}+O(q^{10}) \) 80 * q + 12 * q^8 - 40 * q^9	\( 80 q + 12 q^{8} - 40 q^{9} - 18 q^{10} - 30 q^{12} - 4 q^{14} - 4 q^{16} - 10 q^{18} - 8 q^{21} + 40 q^{25} + 30 q^{26} + 16 q^{28} - 16 q^{29} + 36 q^{30} - 20 q^{32} - 20 q^{36} - 8 q^{37} - 12 q^{38} - 60 q^{40} + 4 q^{44} + 24 q^{45} - 10 q^{46} - 24 q^{49} - 64 q^{50} + 54 q^{52} - 30 q^{54} + 38 q^{56} + 80 q^{57} + 10 q^{58} - 12 q^{60} - 36 q^{64} - 16 q^{65} + 30 q^{66} + 60 q^{68} - 22 q^{70} - 38 q^{72} - 72 q^{73} + 28 q^{74} - 24 q^{78} + 42 q^{80} - 64 q^{81} - 90 q^{82} + 88 q^{84} - 2 q^{86} + 12 q^{88} - 120 q^{89} + 36 q^{92} + 8 q^{93} - 54 q^{94} - 42 q^{96} + 78 q^{98}+O(q^{100}) \) 80 * q + 12 * q^8 - 40 * q^9 - 18 * q^10 - 30 * q^12 - 4 * q^14 - 4 * q^16 - 10 * q^18 - 8 * q^21 + 40 * q^25 + 30 * q^26 + 16 * q^28 - 16 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^36 - 8 * q^37 - 12 * q^38 - 60 * q^40 + 4 * q^44 + 24 * q^45 - 10 * q^46 - 24 * q^49 - 64 * q^50 + 54 * q^52 - 30 * q^54 + 38 * q^56 + 80 * q^57 + 10 * q^58 - 12 * q^60 - 36 * q^64 - 16 * q^65 + 30 * q^66 + 60 * q^68 - 22 * q^70 - 38 * q^72 - 72 * q^73 + 28 * q^74 - 24 * q^78 + 42 * q^80 - 64 * q^81 - 90 * q^82 + 88 * q^84 - 2 * q^86 + 12 * q^88 - 120 * q^89 + 36 * q^92 + 8 * q^93 - 54 * q^94 - 42 * q^96 + 78 * q^98

Introduction

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