LMFDB - Embedded newform 552.2.t.a.451.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			451.14
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.476922 - 1.33137i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.54509 - 1.26992i) q^{4} +(0.175998 + 1.22409i) q^{5} +(1.31850 - 0.511428i) q^{6} +(1.83825 - 4.02520i) q^{7} +(-2.42762 + 1.45143i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.476922 - 1.33137i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.54509 - 1.26992i) q^{4} +(0.175998 + 1.22409i) q^{5} +(1.31850 - 0.511428i) q^{6} +(1.83825 - 4.02520i) q^{7} +(-2.42762 + 1.45143i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(1.71366 + 0.349478i) q^{10} +(0.205881 - 0.701166i) q^{11} +(-0.0520784 - 1.99932i) q^{12} +(1.90431 - 0.869671i) q^{13} +(-4.48233 - 4.36709i) q^{14} +(-0.809853 + 0.934620i) q^{15} +(0.774611 + 3.92428i) q^{16} +(2.50116 - 3.89187i) q^{17} +(1.24995 + 0.661541i) q^{18} +(0.534105 + 0.831084i) q^{19} +(1.28257 - 2.11484i) q^{20} +(4.24584 - 1.24669i) q^{21} +(-0.835322 - 0.608505i) q^{22} +(-2.21033 - 4.25611i) q^{23} +(-2.68667 - 0.884185i) q^{24} +(3.33004 - 0.977787i) q^{25} +(-0.249644 - 2.95011i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-7.95193 + 3.88487i) q^{28} +(-2.81514 + 4.38045i) q^{29} +(0.858088 + 1.52396i) q^{30} +(-1.18530 - 1.02706i) q^{31} +(5.59410 + 0.840283i) q^{32} +(0.664729 - 0.303571i) q^{33} +(-3.98867 - 5.18608i) q^{34} +(5.25074 + 1.54176i) q^{35} +(1.47688 - 1.34864i) q^{36} +(0.690569 - 4.80301i) q^{37} +(1.36121 - 0.314729i) q^{38} +(1.90431 + 0.869671i) q^{39} +(-2.20395 - 2.71618i) q^{40} +(0.851099 + 5.91953i) q^{41} +(0.365128 - 6.24735i) q^{42} +(5.62116 - 4.87076i) q^{43} +(-1.20853 + 0.821912i) q^{44} -1.23668 q^{45} +(-6.72061 + 0.912940i) q^{46} -3.21000i q^{47} +(-2.45851 + 3.15527i) q^{48} +(-8.23904 - 9.50836i) q^{49} +(0.286372 - 4.89984i) q^{50} +(4.57919 - 0.658388i) q^{51} +(-4.04675 - 1.07460i) q^{52} +(-4.99279 + 10.9327i) q^{53} +(0.318580 + 1.37786i) q^{54} +(0.894526 + 0.128613i) q^{55} +(1.37975 + 12.4397i) q^{56} +(-0.278327 + 0.947894i) q^{57} +(4.48939 + 5.83713i) q^{58} +(3.58635 + 7.85300i) q^{59} +(2.43819 - 0.415625i) q^{60} +(-6.08332 + 7.02052i) q^{61} +(-1.93270 + 1.08824i) q^{62} +(3.72262 + 2.39238i) q^{63} +(3.78668 - 7.04706i) q^{64} +(1.39971 + 2.17800i) q^{65} +(-0.0871421 - 1.02978i) q^{66} +(-2.30995 - 7.86698i) q^{67} +(-8.80688 + 2.83703i) q^{68} +(1.76909 - 4.45761i) q^{69} +(4.55684 - 6.25538i) q^{70} +(2.19649 + 7.48057i) q^{71} +(-1.09117 - 2.60947i) q^{72} +(-11.2800 + 7.24919i) q^{73} +(-6.06524 - 3.21006i) q^{74} +(2.91967 + 1.87636i) q^{75} +(0.230168 - 1.96237i) q^{76} +(-2.44387 - 2.11763i) q^{77} +(2.06606 - 2.12058i) q^{78} +(6.41315 + 14.0428i) q^{79} +(-4.66735 + 1.63886i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(8.28699 + 1.69002i) q^{82} +(8.31810 + 1.19596i) q^{83} +(-8.14340 - 3.46562i) q^{84} +(5.20421 + 2.37668i) q^{85} +(-3.80393 - 9.80682i) q^{86} +(-5.15405 + 0.741040i) q^{87} +(0.517896 + 2.00099i) q^{88} +(-11.8620 + 10.2785i) q^{89} +(-0.589800 + 1.64648i) q^{90} -9.26391i q^{91} +(-1.98974 + 9.38301i) q^{92} -1.56837i q^{93} +(-4.27370 - 1.53092i) q^{94} +(-0.923322 + 0.800063i) q^{95} +(3.02831 + 4.77800i) q^{96} +(3.23341 - 0.464894i) q^{97} +(-16.5885 + 6.43446i) q^{98} +(0.664729 + 0.303571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.476922	−	1.33137i	0.337235	−	0.941421i
$2$	0.476922	−	1.33137i	0.337235	−	0.941421i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	−1.54509	−	1.26992i	−0.772545	−	0.634960i
$5$	0.175998	+	1.22409i	0.0787087	+	0.547431i	0.990578	+	0.136950i	$0.0437300\pi$
$5$	0.175998	+	1.22409i	0.0787087	+	0.547431i	−0.911869	+	0.410481i	$0.865361\pi$
$6$	1.31850	−	0.511428i	0.538275	−	0.208790i
$7$	1.83825	−	4.02520i	0.694792	−	1.52138i	−0.151383	−	0.988475i	$-0.548373\pi$
$7$	1.83825	−	4.02520i	0.694792	−	1.52138i	0.846174	−	0.532906i	$-0.178900\pi$
$8$	−2.42762	+	1.45143i	−0.858293	+	0.513160i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	1.71366	+	0.349478i	0.541906	+	0.110515i
$11$	0.205881	−	0.701166i	0.0620754	−	0.211409i	−0.922615	−	0.385722i	$-0.873952\pi$
$11$	0.205881	−	0.701166i	0.0620754	−	0.211409i	0.984690	+	0.174313i	$0.0557704\pi$
$12$	−0.0520784	−	1.99932i	−0.0150337	−	0.577155i
$13$	1.90431	−	0.869671i	0.528162	−	0.241203i	−0.133443	−	0.991057i	$-0.542603\pi$
$13$	1.90431	−	0.869671i	0.528162	−	0.241203i	0.661604	+	0.749853i	$0.269876\pi$
$14$	−4.48233	−	4.36709i	−1.19795	−	1.16715i
$15$	−0.809853	+	0.934620i	−0.209103	+	0.241318i
$16$	0.774611	+	3.92428i	0.193653	+	0.981070i
$17$	2.50116	−	3.89187i	0.606619	−	0.943918i	−0.393083	−	0.919503i	$-0.628591\pi$
$17$	2.50116	−	3.89187i	0.606619	−	0.943918i	0.999702	−	0.0244150i	$-0.00777231\pi$
$18$	1.24995	+	0.661541i	0.294615	+	0.155927i
$19$	0.534105	+	0.831084i	0.122532	+	0.190664i	0.897101	−	0.441826i	$-0.145669\pi$
$19$	0.534105	+	0.831084i	0.122532	+	0.190664i	−0.774568	+	0.632490i	$0.782033\pi$
$20$	1.28257	−	2.11484i	0.286790	−	0.472892i
$21$	4.24584	−	1.24669i	0.926517	−	0.272050i
$22$	−0.835322	−	0.608505i	−0.178091	−	0.129734i
$23$	−2.21033	−	4.25611i	−0.460886	−	0.887459i
$23$	−2.21033	−	4.25611i	−0.460886	−	0.887459i
$24$	−2.68667	−	0.884185i	−0.548415	−	0.180484i
$25$	3.33004	−	0.977787i	0.666008	−	0.195557i
$26$	−0.249644	−	2.95011i	−0.0489593	−	0.578564i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	−7.95193	+	3.88487i	−1.50277	+	0.734172i
$29$	−2.81514	+	4.38045i	−0.522759	+	0.813429i	−0.997784	−	0.0665438i	$-0.978803\pi$
$29$	−2.81514	+	4.38045i	−0.522759	+	0.813429i	0.475025	+	0.879973i	$0.342439\pi$
$30$	0.858088	+	1.52396i	0.156665	+	0.278235i
$31$	−1.18530	−	1.02706i	−0.212885	−	0.184466i	0.541890	−	0.840449i	$-0.317709\pi$
$31$	−1.18530	−	1.02706i	−0.212885	−	0.184466i	−0.754776	+	0.655983i	$0.772254\pi$
$32$	5.59410	+	0.840283i	0.988906	+	0.148542i
$33$	0.664729	−	0.303571i	0.115714	−	0.0528450i
$34$	−3.98867	−	5.18608i	−0.684051	−	0.889406i
$35$	5.25074	+	1.54176i	0.887537	+	0.260604i
$36$	1.47688	−	1.34864i	0.246147	−	0.224773i
$37$	0.690569	−	4.80301i	0.113529	−	0.789610i	−0.850911	−	0.525309i	$-0.823950\pi$
$37$	0.690569	−	4.80301i	0.113529	−	0.789610i	0.964440	−	0.264301i	$-0.0851413\pi$
$38$	1.36121	−	0.314729i	0.220817	−	0.0510558i
$39$	1.90431	+	0.869671i	0.304934	+	0.139259i
$40$	−2.20395	−	2.71618i	−0.348474	−	0.429466i
$41$	0.851099	+	5.91953i	0.132919	+	0.924475i	0.941721	+	0.336394i	$0.109207\pi$
$41$	0.851099	+	5.91953i	0.132919	+	0.924475i	−0.808802	+	0.588081i	$0.799884\pi$
$42$	0.365128	−	6.24735i	0.0563404	−	0.963987i
$43$	5.62116	−	4.87076i	0.857219	−	0.742784i	−0.110752	−	0.993848i	$-0.535326\pi$
$43$	5.62116	−	4.87076i	0.857219	−	0.742784i	0.967971	+	0.251064i	$0.0807804\pi$
$44$	−1.20853	+	0.821912i	−0.182192	+	0.123908i
$45$	−1.23668			−0.184353
$46$	−6.72061	+	0.912940i	−0.990899	+	0.134606i
$47$		−	3.21000i		−	0.468227i	−0.972209	−	0.234113i	$-0.924781\pi$
$47$		−	3.21000i		−	0.468227i	0.972209	−	0.234113i	$-0.0752187\pi$
$48$	−2.45851	+	3.15527i	−0.354856	+	0.455424i
$49$	−8.23904	−	9.50836i	−1.17701	−	1.35834i
$50$	0.286372	−	4.89984i	0.0404991	−	0.692942i
$51$	4.57919	−	0.658388i	0.641215	−	0.0921928i
$52$	−4.04675	−	1.07460i	−0.561183	−	0.149021i
$53$	−4.99279	+	10.9327i	−0.685812	+	1.50172i	0.170554	+	0.985348i	$0.445444\pi$
$53$	−4.99279	+	10.9327i	−0.685812	+	1.50172i	−0.856366	+	0.516370i	$0.827283\pi$
$54$	0.318580	+	1.37786i	0.0433533	+	0.187503i
$55$	0.894526	+	0.128613i	0.120618	+	0.0173422i
$56$	1.37975	+	12.4397i	0.184377	+	1.66233i
$57$	−0.278327	+	0.947894i	−0.0368653	+	0.125552i
$58$	4.48939	+	5.83713i	0.589486	+	0.766452i
$59$	3.58635	+	7.85300i	0.466902	+	1.02237i	0.985860	+	0.167573i	$0.0535931\pi$
$59$	3.58635	+	7.85300i	0.466902	+	1.02237i	−0.518957	+	0.854800i	$0.673680\pi$
$60$	2.43819	−	0.415625i	0.314769	−	0.0536570i
$61$	−6.08332	+	7.02052i	−0.778889	+	0.898886i	−0.997029	−	0.0770318i	$-0.975456\pi$
$61$	−6.08332	+	7.02052i	−0.778889	+	0.898886i	0.218140	+	0.975918i	$0.430001\pi$
$62$	−1.93270	+	1.08824i	−0.245453	+	0.138206i
$63$	3.72262	+	2.39238i	0.469006	+	0.301412i
$64$	3.78668	−	7.04706i	0.473334	−	0.880883i
$65$	1.39971	+	2.17800i	0.173613	+	0.270147i
$66$	−0.0871421	−	1.02978i	−0.0107264	−	0.126757i
$67$	−2.30995	−	7.86698i	−0.282206	−	0.961105i	−0.971582	−	0.236702i	$-0.923934\pi$
$67$	−2.30995	−	7.86698i	−0.282206	−	0.961105i	0.689377	−	0.724403i	$-0.257885\pi$
$68$	−8.80688	+	2.83703i	−1.06799	+	0.344041i
$69$	1.76909	−	4.45761i	0.212973	−	0.536634i
$70$	4.55684	−	6.25538i	0.544647	−	0.747661i
$71$	2.19649	+	7.48057i	0.260676	+	0.887781i	0.980978	+	0.194120i	$0.0621851\pi$
$71$	2.19649	+	7.48057i	0.260676	+	0.887781i	−0.720302	+	0.693661i	$0.755997\pi$
$72$	−1.09117	−	2.60947i	−0.128596	−	0.307529i
$73$	−11.2800	+	7.24919i	−1.32022	+	0.848454i	−0.995258	−	0.0972730i	$-0.968988\pi$
$73$	−11.2800	+	7.24919i	−1.32022	+	0.848454i	−0.324962	+	0.945727i	$0.605352\pi$
$74$	−6.06524	−	3.21006i	−0.705069	−	0.373162i
$75$	2.91967	+	1.87636i	0.337135	+	0.216663i
$76$	0.230168	−	1.96237i	0.0264021	−	0.225099i
$77$	−2.44387	−	2.11763i	−0.278505	−	0.241326i
$78$	2.06606	−	2.12058i	0.233936	−	0.240108i
$79$	6.41315	+	14.0428i	0.721535	+	1.57994i	0.811740	+	0.584019i	$0.198521\pi$
$79$	6.41315	+	14.0428i	0.721535	+	1.57994i	−0.0902046	+	0.995923i	$0.528752\pi$
$80$	−4.66735	+	1.63886i	−0.521826	+	0.183230i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	8.28699	+	1.69002i	0.915145	+	0.186632i
$83$	8.31810	+	1.19596i	0.913030	+	0.131274i	0.582790	−	0.812623i	$-0.301961\pi$
$83$	8.31810	+	1.19596i	0.913030	+	0.131274i	0.330241	+	0.943897i	$0.392870\pi$
$84$	−8.14340	−	3.46562i	−0.888518	−	0.378130i
$85$	5.20421	+	2.37668i	0.564476	+	0.257788i
$86$	−3.80393	−	9.80682i	−0.410188	−	1.05750i
$87$	−5.15405	+	0.741040i	−0.552572	+	0.0794479i
$88$	0.517896	+	2.00099i	0.0552079	+	0.213306i
$89$	−11.8620	+	10.2785i	−1.25737	+	1.08952i	−0.265253	+	0.964179i	$0.585456\pi$
$89$	−11.8620	+	10.2785i	−1.25737	+	1.08952i	−0.992114	+	0.125336i	$0.959999\pi$
$90$	−0.589800	+	1.64648i	−0.0621704	+	0.173554i
$91$		−	9.26391i		−	0.971121i
$92$	−1.98974	+	9.38301i	−0.207445	+	0.978247i
$93$		−	1.56837i		−	0.162632i
$94$	−4.27370	−	1.53092i	−0.440798	−	0.157902i
$95$	−0.923322	+	0.800063i	−0.0947308	+	0.0820847i
$96$	3.02831	+	4.77800i	0.309076	+	0.487653i
$97$	3.23341	−	0.464894i	0.328303	−	0.0472028i	0.0238073	−	0.999717i	$-0.492421\pi$
$97$	3.23341	−	0.464894i	0.328303	−	0.0472028i	0.304496	+	0.952514i	$0.401512\pi$
$98$	−16.5885	+	6.43446i	−1.67569	+	0.649979i
$99$	0.664729	+	0.303571i	0.0668078	+	0.0305101i
$100$	−6.38692	−	2.71811i	−0.638692	−	0.271811i
$101$	−6.24934	−	0.898519i	−0.621833	−	0.0894060i	−0.175805	−	0.984425i	$-0.556253\pi$
$101$	−6.24934	−	0.898519i	−0.621833	−	0.0894060i	−0.446028	+	0.895019i	$0.647162\pi$
$102$	1.30736	−	6.41060i	0.129448	−	0.634744i
$103$	−14.4446	−	4.24132i	−1.42327	−	0.417910i	−0.522661	−	0.852541i	$-0.675061\pi$
$103$	−14.4446	−	4.24132i	−1.42327	−	0.417910i	−0.900609	+	0.434631i	$0.856879\pi$
$104$	−3.36068	+	4.87522i	−0.329542	+	0.478054i
$105$	2.27332	+	4.97788i	0.221854	+	0.485791i
$106$	12.1743	+	11.8613i	1.18247	+	1.15207i
$107$	13.7069	+	11.8771i	1.32509	+	1.14820i	0.977590	+	0.210519i	$0.0675153\pi$
$107$	13.7069	+	11.8771i	1.32509	+	1.14820i	0.347501	+	0.937679i	$0.387030\pi$
$108$	1.98638	+	0.232985i	0.191140	+	0.0224190i
$109$	4.78810	+	3.07713i	0.458617	+	0.294735i	0.749477	−	0.662030i	$-0.230305\pi$
$109$	4.78810	+	3.07713i	0.458617	+	0.294735i	−0.290860	+	0.956766i	$0.593941\pi$
$110$	0.597851	−	1.12961i	0.0570029	−	0.107704i
$111$	4.08210	−	2.62341i	0.387456	−	0.249003i
$112$	17.2199	+	4.09583i	1.62713	+	0.387020i
$113$	−1.08571	−	3.69760i	−0.102135	−	0.347841i	0.892531	−	0.450986i	$-0.148928\pi$
$113$	−1.08571	−	3.69760i	−0.102135	−	0.347841i	−0.994666	+	0.103145i	$0.967109\pi$
$114$	1.12926	+	0.822627i	0.105765	+	0.0770461i
$115$	4.82085	−	3.45472i	0.449547	−	0.322154i
$116$	9.91247	−	3.19319i	0.920349	−	0.296480i
$117$	0.589807	+	2.00870i	0.0545277	+	0.185704i
$118$	12.1657	−	1.02948i	1.11994	−	0.0947715i
$119$	−11.0678	−	17.2219i	−1.01459	−	1.57873i
$120$	0.609475	−	3.44435i	0.0556372	−	0.314425i
$121$	8.80454	+	5.65834i	0.800413	+	0.514394i
$122$	6.44564	+	11.4474i	0.583561	+	1.03640i
$123$	−3.91633	+	4.51968i	−0.353123	+	0.407526i
$124$	0.527100	+	3.09214i	0.0473350	+	0.277682i
$125$	4.35166	+	9.52880i	0.389224	+	0.852282i
$126$	4.96054	−	3.81520i	0.441920	−	0.339885i
$127$	1.77915	−	6.05923i	0.157874	−	0.537670i	−0.842125	−	0.539283i	$-0.818695\pi$
$127$	1.77915	−	6.05923i	0.157874	−	0.537670i	0.999999	+	0.00161305i	$0.000513451\pi$
$128$	−7.57630	−	8.40236i	−0.669656	−	0.742671i
$129$	7.36215	+	1.05852i	0.648202	+	0.0931973i
$130$	3.56727	−	0.824801i	0.312870	−	0.0723398i
$131$	4.84277	−	10.6042i	0.423115	−	0.926492i	−0.571280	−	0.820755i	$-0.693553\pi$
$131$	4.84277	−	10.6042i	0.423115	−	0.926492i	0.994394	−	0.105736i	$-0.0337199\pi$
$132$	−1.41258	−	0.375106i	−0.122949	−	0.0326488i
$133$	4.32709	−	0.622142i	0.375207	−	0.0539466i
$134$	−11.5755	−	0.676534i	−0.999973	−	0.0584436i
$135$	−0.809853	−	0.934620i	−0.0697011	−	0.0804393i
$136$	−0.423054	+	13.0783i	−0.0362766	+	1.12145i
$137$		−	11.5339i		−	0.985407i	−0.870197	−	0.492703i	$-0.836009\pi$
$137$		−	11.5339i		−	0.985407i	0.870197	−	0.492703i	$-0.163991\pi$
$138$	−5.09101	−	4.48125i	−0.433376	−	0.381469i
$139$	−9.23301			−0.783134			−0.391567	−	0.920150i	$-0.628067\pi$
$139$	−9.23301			−0.783134			−0.391567	+	0.920150i	$0.628067\pi$
$140$	−6.15497	−	9.05017i	−0.520190	−	0.764879i
$141$	2.42596	−	2.10210i	0.204302	−	0.177029i
$142$	11.0070	+	0.643304i	0.923684	+	0.0539849i
$143$	−0.217722	−	1.51429i	−0.0182068	−	0.126631i
$144$	−3.99458	+	0.208243i	−0.332881	+	0.0173536i
$145$	−5.85753	−	2.67505i	−0.486442	−	0.222150i
$146$	4.27169	+	18.4751i	0.353528	+	1.52901i
$147$	1.79051	−	12.4533i	0.147679	−	1.02713i
$148$	−7.16643	+	6.54412i	−0.589077	+	0.537924i
$149$	8.89000	+	2.61034i	0.728297	+	0.213847i	0.624803	−	0.780783i	$-0.285179\pi$
$149$	8.89000	+	2.61034i	0.728297	+	0.213847i	0.103495	+	0.994630i	$0.466998\pi$
$150$	3.89059	−	2.99229i	0.317665	−	0.244319i
$151$	10.3104	−	4.70860i	0.839048	−	0.383180i	0.0509281	−	0.998702i	$-0.483782\pi$
$151$	10.3104	−	4.70860i	0.839048	−	0.383180i	0.788120	+	0.615522i	$0.211055\pi$
$152$	−2.50287	−	1.24234i	−0.203009	−	0.100767i
$153$	3.49631	+	3.02957i	0.282660	+	0.244926i
$154$	−3.98488	+	2.24375i	−0.321111	+	0.180807i
$155$	1.04861	−	1.63167i	0.0842266	−	0.131059i
$156$	−1.83793	−	3.76204i	−0.147152	−	0.301205i
$157$	3.51065	−	2.25616i	0.280181	−	0.180061i	−0.393002	−	0.919538i	$-0.628563\pi$
$157$	3.51065	−	2.25616i	0.280181	−	0.180061i	0.673182	+	0.739477i	$0.264927\pi$
$158$	21.7548	−	1.84093i	1.73072	−	0.146457i
$159$	−11.5319	+	3.38608i	−0.914543	+	0.268534i
$160$	−0.0440340	+	6.99558i	−0.00348120	+	0.553049i
$161$	−21.1948	+	1.07326i	−1.67038	+	0.0845845i
$162$	−0.832694	+	1.14308i	−0.0654226	+	0.0898085i
$163$	−8.04721	+	2.36288i	−0.630306	+	0.185075i	−0.581255	−	0.813722i	$-0.697438\pi$
$163$	−8.04721	+	2.36288i	−0.630306	+	0.185075i	−0.0490516	+	0.998796i	$0.515620\pi$
$164$	6.20229	−	10.2270i	0.484318	−	0.798597i
$165$	0.488590	+	0.760262i	0.0380367	+	0.0591863i
$166$	5.55936	−	10.5041i	0.431490	−	0.815275i
$167$	0.339519	−	0.528302i	0.0262728	−	0.0408813i	−0.827869	−	0.560922i	$-0.810447\pi$
$167$	0.339519	−	0.528302i	0.0262728	−	0.0408813i	0.854142	+	0.520041i	$0.174083\pi$
$168$	−8.49779	+	9.18904i	−0.655619	+	0.708950i
$169$	−5.64311	+	6.51249i	−0.434085	+	0.500961i
$170$	5.64625	−	5.79524i	0.433048	−	0.444474i
$171$	−0.898636	+	0.410393i	−0.0687204	+	0.0313835i
$172$	−14.8707	+	0.387352i	−1.13388	+	0.0295353i
$173$	−1.64828	+	5.61354i	−0.125317	+	0.426790i	−0.998121	−	0.0612817i	$-0.980481\pi$
$173$	−1.64828	+	5.61354i	−0.125317	+	0.426790i	0.872804	+	0.488071i	$0.162299\pi$
$174$	−1.47148	+	7.21536i	−0.111553	+	0.546995i
$175$	2.18564	−	15.2015i	0.165219	−	1.14912i
$176$	2.91105	+	0.264804i	0.219428	+	0.0199603i
$177$	−3.58635	+	7.85300i	−0.269566	+	0.590268i
$178$	8.02720	+	20.6947i	0.601664	+	1.55113i
$179$	0.302070	+	2.10094i	0.0225778	+	0.157032i	0.997991	−	0.0633505i	$-0.0201786\pi$
$179$	0.302070	+	2.10094i	0.0225778	+	0.157032i	−0.975414	+	0.220382i	$0.929270\pi$
$180$	1.91078	+	1.57048i	0.142421	+	0.117057i
$181$	4.92883	+	5.68818i	0.366357	+	0.422799i	0.908760	−	0.417320i	$-0.137031\pi$
$181$	4.92883	+	5.68818i	0.366357	+	0.422799i	−0.542402	+	0.840119i	$0.682485\pi$
$182$	−12.3337	−	4.41816i	−0.914234	−	0.327496i
$183$	−9.28948			−0.686698
$184$	11.5433	+	7.12405i	0.850984	+	0.525192i
$185$	6.00087			0.441193
$186$	−2.08808	−	0.747991i	−0.153106	−	0.0548453i
$187$	−2.21391	−	2.55499i	−0.161897	−	0.186839i
$188$	−4.07644	+	4.95974i	−0.297305	+	0.361726i
$189$	0.629755	+	4.38004i	0.0458079	+	0.318601i
$190$	0.624827	+	1.61085i	0.0453297	+	0.116863i
$191$	−1.57355	+	3.44560i	−0.113858	+	0.249315i	−0.957979	−	0.286838i	$-0.907396\pi$
$191$	−1.57355	+	3.44560i	−0.113858	+	0.249315i	0.844121	+	0.536153i	$0.180123\pi$
$192$	7.80556	−	1.75307i	0.563318	−	0.126517i
$193$	3.16042	−	21.9812i	0.227492	−	1.58224i	−0.481127	−	0.876651i	$-0.659773\pi$
$193$	3.16042	−	21.9812i	0.227492	−	1.58224i	0.708619	−	0.705591i	$-0.249318\pi$
$194$	0.923138	−	4.52658i	0.0662775	−	0.324990i
$195$	−0.729402	+	2.48412i	−0.0522336	+	0.177891i
$196$	0.655217	+	25.1542i	0.0468012	+	1.79673i
$197$	−10.2317	+	4.67265i	−0.728976	+	0.332912i	−0.745096	−	0.666958i	$-0.767596\pi$
$197$	−10.2317	+	4.67265i	−0.728976	+	0.332912i	0.0161191	+	0.999870i	$0.494869\pi$
$198$	0.721190	−	0.740220i	0.0512527	−	0.0526051i
$199$	−1.71397	+	1.97803i	−0.121500	+	0.140219i	−0.813241	−	0.581927i	$-0.802299\pi$
$199$	−1.71397	+	1.97803i	−0.121500	+	0.140219i	0.691740	+	0.722146i	$0.256844\pi$
$200$	−6.66487	+	7.20703i	−0.471278	+	0.509614i
$201$	4.43277	−	6.89752i	0.312663	−	0.486514i
$202$	−4.17671	+	7.89166i	−0.293872	+	0.555255i
$203$	12.4572	+	19.3838i	0.874327	+	1.36048i
$204$	−7.91137	−	4.79793i	−0.553906	−	0.335922i
$205$	−7.09626	+	2.08365i	−0.495624	+	0.145528i
$206$	−12.5357	+	17.2083i	−0.873405	+	1.19896i
$207$	4.52735	−	1.58213i	0.314672	−	0.109965i
$208$	4.88793	+	6.79940i	0.338917	+	0.471454i
$209$	0.692689	−	0.203392i	0.0479143	−	0.0140689i
$210$	7.71160	−	0.652571i	0.532151	−	0.0450317i
$211$	−8.10079	+	5.20606i	−0.557681	+	0.358400i	−0.788919	−	0.614497i	$-0.789359\pi$
$211$	−8.10079	+	5.20606i	−0.557681	+	0.358400i	0.231238	+	0.972897i	$0.425722\pi$
$212$	21.5979	−	10.5515i	1.48335	−	0.724683i
$213$	−4.21504	+	6.55873i	−0.288810	+	0.449397i
$214$	22.3498	−	12.5845i	1.52780	−	0.860256i
$215$	6.95158	+	6.02358i	0.474094	+	0.410804i
$216$	1.25754	−	2.53349i	0.0855647	−	0.172382i
$217$	−6.31300	+	2.88305i	−0.428555	+	0.195714i
$218$	6.38035	−	4.90719i	0.432132	−	0.332357i
$219$	−12.8654	−	3.77762i	−0.869362	−	0.255268i
$220$	−1.21880	−	1.33470i	−0.0821712	−	0.0899851i
$221$	1.37834	−	9.58653i	0.0927169	−	0.644860i
$222$	−1.54588	−	6.68595i	−0.103753	−	0.448731i
$223$	−1.33536	−	0.609838i	−0.0894222	−	0.0408377i	0.370202	−	0.928951i	$-0.379289\pi$
$223$	−1.33536	−	0.609838i	−0.0894222	−	0.0408377i	−0.459624	+	0.888114i	$0.652016\pi$
$224$	13.6656	−	20.9727i	0.913073	−	1.40130i
$225$	0.493921	+	3.43530i	0.0329281	+	0.229020i
$226$	−5.44068	−	0.317981i	−0.361908	−	0.0211518i
$227$	2.04965	−	1.77603i	0.136040	−	0.117879i	−0.584183	−	0.811622i	$-0.698585\pi$
$227$	2.04965	−	1.77603i	0.136040	−	0.117879i	0.720223	+	0.693743i	$0.244040\pi$
$228$	1.63379	−	1.11113i	0.108200	−	0.0735863i
$229$	20.4354			1.35041			0.675205	−	0.737630i	$-0.264055\pi$
$229$	20.4354			1.35041			0.675205	+	0.737630i	$0.264055\pi$
$230$	−2.30034	−	8.06597i	−0.151680	−	0.531854i
$231$		−	3.23370i		−	0.212762i
$232$	0.476163	−	14.7201i	0.0312616	−	0.966419i
$233$	−10.4023	−	12.0049i	−0.681479	−	0.786468i	0.304648	−	0.952465i	$-0.401461\pi$
$233$	−10.4023	−	12.0049i	−0.681479	−	0.786468i	−0.986126	+	0.165997i	$0.946916\pi$
$234$	2.95561	+	0.172741i	0.193214	+	0.0112924i
$235$	3.92934	−	0.564953i	0.256322	−	0.0368535i
$236$	4.43145	−	16.6880i	0.288463	−	1.08629i
$237$	−6.41315	+	14.0428i	−0.416579	+	0.912180i
$238$	−28.2072	+	6.52188i	−1.82840	+	0.422750i
$239$	3.92517	+	0.564354i	0.253898	+	0.0365050i	0.268088	−	0.963394i	$-0.413608\pi$
$239$	3.92517	+	0.564354i	0.253898	+	0.0365050i	−0.0141906	+	0.999899i	$0.504517\pi$
$240$	−4.29503	−	2.45412i	−0.277243	−	0.158413i
$241$	−4.39578	+	14.9707i	−0.283157	+	0.964344i	0.687962	+	0.725747i	$0.258506\pi$
$241$	−4.39578	+	14.9707i	−0.283157	+	0.964344i	−0.971119	+	0.238597i	$0.923312\pi$
$242$	11.7324	−	9.02352i	0.754188	−	0.580054i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	18.3148	−	3.12202i	1.17248	−	0.199867i
$245$	10.1891	−	11.7588i	0.650955	−	0.751242i
$246$	4.14959	+	7.36962i	0.264568	+	0.469870i
$247$	1.73987	+	1.11815i	0.110705	+	0.0711461i
$248$	4.36816	+	0.772943i	0.277379	+	0.0490819i
$249$	4.54335	+	7.06959i	0.287923	+	0.448017i
$250$	14.7618	−	1.24917i	0.933616	−	0.0790045i
$251$	−5.28298	−	17.9922i	−0.333458	−	1.13566i	−0.940162	−	0.340727i	$-0.889327\pi$
$251$	−5.28298	−	17.9922i	−0.333458	−	1.13566i	0.606704	−	0.794928i	$-0.292491\pi$
$252$	−2.71365	−	8.42387i	−0.170944	−	0.530654i
$253$	−3.43930	+	0.673559i	−0.216227	+	0.0423463i
$254$	−7.21856	−	5.25849i	−0.452933	−	0.329947i
$255$	1.61186	+	5.48948i	0.100938	+	0.343764i
$256$	−14.8000	+	6.07958i	−0.924997	+	0.379974i
$257$	−11.0677	+	7.11275i	−0.690381	+	0.443681i	−0.838221	−	0.545330i	$-0.816404\pi$
$257$	−11.0677	+	7.11275i	−0.690381	+	0.443681i	0.147840	+	0.989011i	$0.452768\pi$
$258$	4.92045	−	9.29692i	0.306334	−	0.578801i
$259$	−18.0636	−	11.6088i	−1.12242	−	0.721335i
$260$	0.603195	−	5.14272i	0.0374086	−	0.318938i
$261$	−3.93522	−	3.40989i	−0.243584	−	0.211067i
$262$	−11.8085	−	11.5049i	−0.729529	−	0.710774i
$263$	−5.40570	−	11.8368i	−0.333330	−	0.729891i	0.666549	−	0.745461i	$-0.267771\pi$
$263$	−5.40570	−	11.8368i	−0.333330	−	0.729891i	−0.999879	+	0.0155706i	$0.995044\pi$
$264$	−1.17309	+	1.70177i	−0.0721990	+	0.104736i
$265$	−14.2613	−	4.18750i	−0.876066	−	0.257236i
$266$	1.23538	−	6.05767i	0.0757463	−	0.371420i
$267$	−15.5359	−	2.23372i	−0.950781	−	0.136702i
$268$	−6.42134	+	15.0887i	−0.392246	+	0.921686i
$269$	−0.291963	−	0.133335i	−0.0178013	−	0.00812958i	0.406494	−	0.913653i	$-0.366751\pi$
$269$	−0.291963	−	0.133335i	−0.0178013	−	0.00812958i	−0.424296	+	0.905524i	$0.639478\pi$
$270$	−1.63056	+	0.632473i	−0.0992329	+	0.0384911i
$271$	4.69708	−	0.675338i	0.285327	−	0.0410239i	0.00183483	−	0.999998i	$-0.499416\pi$
$271$	4.69708	−	0.675338i	0.285327	−	0.0410239i	0.283493	+	0.958974i	$0.408507\pi$
$272$	17.2102	+	6.80055i	1.04352	+	0.412344i
$273$	7.00119	−	6.06657i	0.423732	−	0.367165i
$274$	−15.3559	−	5.50077i	−0.927682	−	0.332313i
$275$		−	2.53622i		−	0.152940i
$276$	−8.39421	+	4.64082i	−0.505272	+	0.279344i
$277$		−	24.3777i		−	1.46471i	−0.680920	−	0.732357i	$-0.738420\pi$
$277$		−	24.3777i		−	1.46471i	0.680920	−	0.732357i	$-0.261580\pi$
$278$	−4.40343	+	12.2926i	−0.264100	+	0.737258i
$279$	1.18530	−	1.02706i	0.0709618	−	0.0614887i
$280$	−14.9846	+	3.87831i	−0.895499	+	0.231773i
$281$	−15.2914	+	2.19857i	−0.912209	+	0.131156i	−0.582410	−	0.812895i	$-0.697890\pi$
$281$	−15.2914	+	2.19857i	−0.912209	+	0.131156i	−0.329799	+	0.944051i	$0.606981\pi$
$282$	−1.64168	−	4.23238i	−0.0977609	−	0.252035i
$283$	−3.59708	−	1.64273i	−0.213824	−	0.0976504i	0.305624	−	0.952152i	$-0.401135\pi$
$283$	−3.59708	−	1.64273i	−0.213824	−	0.0976504i	−0.519448	+	0.854502i	$0.673862\pi$
$284$	6.10594	−	14.3475i	0.362321	−	0.851369i
$285$	−1.20929	−	0.173870i	−0.0716324	−	0.0102992i
$286$	−2.11991	−	0.432329i	−0.125353	−	0.0255642i
$287$	25.3918	+	7.45570i	1.49883	+	0.440096i
$288$	−1.62785	+	5.41757i	−0.0959221	+	0.319234i
$289$	−1.82885	−	4.00463i	−0.107579	−	0.235566i
$290$	−6.35506	+	6.52275i	−0.373182	+	0.383029i
$291$	2.46878	+	2.13921i	0.144722	+	0.125403i
$292$	26.6345	+	3.12398i	1.55866	+	0.182817i
$293$	−8.40438	−	5.40117i	−0.490989	−	0.315540i	0.271614	−	0.962406i	$-0.412443\pi$
$293$	−8.40438	−	5.40117i	−0.490989	−	0.315540i	−0.762603	+	0.646867i	$0.776079\pi$
$294$	−15.7260	−	8.32309i	−0.917160	−	0.485413i
$295$	−8.98161	+	5.77213i	−0.522930	+	0.336066i
$296$	5.29482	+	12.6622i	0.307755	+	0.735976i
$297$	0.205881	+	0.701166i	0.0119464	+	0.0406858i
$298$	7.71516	−	10.5909i	0.446927	−	0.613517i
$299$	−7.91058	−	6.18270i	−0.457480	−	0.357555i
$300$	−2.12833	−	6.60690i	−0.122879	−	0.381449i
$301$	−9.27271	−	31.5799i	−0.534470	−	1.82024i
$302$	−1.35163	−	15.9726i	−0.0777777	−	0.919119i
$303$	−3.41339	−	5.31134i	−0.196094	−	0.305129i
$304$	−2.84768	+	2.73974i	−0.163326	+	0.157135i
$305$	−9.66442	−	6.21095i	−0.553383	−	0.355638i
$306$	5.70094	−	3.21001i	0.325901	−	0.183504i
$307$	−18.3143	+	21.1358i	−1.04525	+	1.20628i	−0.0672376	+	0.997737i	$0.521419\pi$
$307$	−18.3143	+	21.1358i	−1.04525	+	1.20628i	−0.978013	+	0.208546i	$0.933127\pi$
$308$	1.08679	+	6.37544i	0.0619255	+	0.363275i
$309$	−6.25383	−	13.6940i	−0.355768	−	0.779023i
$310$	−1.67225	−	2.17427i	−0.0949776	−	0.123490i
$311$	2.00260	−	6.82024i	0.113557	−	0.386740i	−0.883027	−	0.469322i	$-0.844498\pi$
$311$	2.00260	−	6.82024i	0.113557	−	0.386740i	0.996584	+	0.0825817i	$0.0263165\pi$
$312$	−5.88522	+	0.652756i	−0.333185	+	0.0369551i
$313$	20.8212	+	2.99364i	1.17688	+	0.169210i	0.702878	−	0.711311i	$-0.251898\pi$
$313$	20.8212	+	2.99364i	1.17688	+	0.169210i	0.474007	+	0.880521i	$0.342807\pi$
$314$	−1.32947	−	5.74999i	−0.0750266	−	0.324491i
$315$	−2.27332	+	4.97788i	−0.128087	+	0.280472i
$316$	7.92437	−	29.8416i	0.445781	−	1.67872i
$317$	−25.3622	+	3.64654i	−1.42449	+	0.204810i	−0.811069	−	0.584950i	$-0.801114\pi$
$317$	−25.3622	+	3.64654i	−1.42449	+	0.204810i	−0.613416	+	0.789760i	$0.710205\pi$
$318$	−0.991708	+	16.9682i	−0.0556122	+	0.951528i
$319$	2.49184	+	2.87573i	0.139516	+	0.161010i
$320$	9.29270	+	3.39497i	0.519478	+	0.189785i
$321$			18.1368i			1.01230i
$322$	−8.67937	+	28.7300i	−0.483682	+	1.60106i
$323$	4.57035			0.254301
$324$	1.12473	+	1.65378i	0.0624848	+	0.0918767i
$325$	5.49108	−	4.75805i	0.304590	−	0.263929i
$326$	−0.692033	+	11.8407i	−0.0383282	+	0.655797i
$327$	0.810003	+	5.63370i	0.0447933	+	0.311544i
$328$	−10.6580	−	13.1350i	−0.588487	−	0.725262i
$329$	−12.9209	−	5.90077i	−0.712351	−	0.325320i
$330$	1.24521	−	0.287909i	0.0685465	−	0.0158489i
$331$	2.46620	−	17.1528i	0.135554	−	0.942802i	−0.802583	−	0.596540i	$-0.796542\pi$
$331$	2.46620	−	17.1528i	0.135554	−	0.942802i	0.938138	−	0.346262i	$-0.112549\pi$
$332$	−11.3334	−	12.4112i	−0.622004	−	0.681152i
$333$	4.65585	+	1.36708i	0.255139	+	0.0749155i
$334$	−0.541441	−	0.703985i	−0.0296264	−	0.0385203i
$335$	9.22336	−	4.21217i	0.503926	−	0.230135i
$336$	8.18123	+	15.6962i	0.446323	+	0.856295i
$337$	7.93637	+	6.87690i	0.432322	+	0.374609i	0.843663	−	0.536872i	$-0.180394\pi$
$337$	7.93637	+	6.87690i	0.432322	+	0.374609i	−0.411342	+	0.911481i	$0.634940\pi$
$338$	5.97921	+	10.6190i	0.325226	+	0.577598i
$339$	2.08347	−	3.24194i	0.113159	−	0.176078i
$340$	−5.02278	−	10.2811i	−0.272399	−	0.557572i
$341$	−0.964172	+	0.619636i	−0.0522128	+	0.0335551i
$342$	0.117806	+	1.39214i	0.00637021	+	0.0752784i
$343$	−23.6976	+	6.95823i	−1.27955	+	0.375709i
$344$	−6.57645	+	19.9831i	−0.354578	+	1.07742i
$345$	5.76789	+	1.38100i	0.310533	+	0.0743505i
$346$	6.68760	+	4.87170i	0.359527	+	0.261904i
$347$	−31.6329	+	9.28826i	−1.69814	+	0.498620i	−0.980288	−	0.197572i	$-0.936694\pi$
$347$	−31.6329	+	9.28826i	−1.69814	+	0.498620i	−0.717856	+	0.696192i	$0.754876\pi$
$348$	8.90453	+	5.40025i	0.477333	+	0.289484i
$349$	−7.84283	−	12.2037i	−0.419817	−	0.653248i	0.565349	−	0.824852i	$-0.308741\pi$
$349$	−7.84283	−	12.2037i	−0.419817	−	0.653248i	−0.985166	+	0.171604i	$0.945105\pi$
$350$	−19.1964	−	10.1598i	−1.02609	−	0.543065i
$351$	−1.13183	+	1.76116i	−0.0604127	+	0.0940039i
$352$	1.74089	−	3.74939i	0.0927900	−	0.199843i
$353$	18.6407	−	21.5125i	0.992142	−	1.14499i	0.00271018	−	0.999996i	$-0.499137\pi$
$353$	18.6407	−	21.5125i	0.992142	−	1.14499i	0.989432	−	0.144997i	$-0.0463172\pi$
$354$	8.74484	+	8.52002i	0.464783	+	0.452834i
$355$	−8.77033	+	4.00528i	−0.465481	+	0.212578i
$356$	31.3807	−	0.817404i	1.66317	−	0.0433224i
$357$	5.76754	−	19.6424i	0.305250	−	1.03959i
$358$	2.94119	+	0.599819i	0.155447	+	0.0317014i
$359$	0.558026	−	3.88116i	0.0294515	−	0.204840i	−0.969783	−	0.243971i	$-0.921550\pi$
$359$	0.558026	−	3.88116i	0.0294515	−	0.204840i	0.999234	+	0.0391311i	$0.0124590\pi$
$360$	3.00219	−	1.79496i	0.158229	−	0.0946027i
$361$	7.48745	−	16.3952i	0.394076	−	0.862907i
$362$	9.92374	−	3.84928i	0.521580	−	0.202314i
$363$	1.48946	+	10.3595i	0.0781766	+	0.543730i
$364$	−11.7644	+	14.3136i	−0.616623	+	0.750235i
$365$	−10.8589	−	12.5319i	−0.568383	−	0.655948i
$366$	−4.43036	+	12.3677i	−0.231579	+	0.646472i
$367$	20.8520			1.08847			0.544233	−	0.838934i	$-0.316821\pi$
$367$	20.8520			1.08847			0.544233	+	0.838934i	$0.316821\pi$
$368$	14.9900	−	11.9708i	0.781408	−	0.624021i
$369$	−5.98040			−0.311327
$370$	2.86195	−	7.98938i	0.148786	−	0.415348i
$371$	34.8282	+	40.1939i	1.80819	+	2.08676i
$372$	−1.99170	+	2.42328i	−0.103265	+	0.125641i
$373$	3.33657	+	23.2063i	0.172761	+	1.20158i	0.873018	+	0.487688i	$0.162160\pi$
$373$	3.33657	+	23.2063i	0.172761	+	1.20158i	−0.700257	+	0.713891i	$0.746931\pi$
$374$	−4.45749	+	1.72900i	−0.230492	+	0.0894045i
$375$	−4.35166	+	9.52880i	−0.224719	+	0.492065i
$376$	4.65910	+	7.79266i	0.240275	+	0.401876i
$377$	−1.55137	+	10.7900i	−0.0798995	+	0.555713i
$378$	6.13180	+	1.25050i	0.315386	+	0.0643189i
$379$	9.28894	−	31.6352i	0.477141	−	1.62499i	−0.271799	−	0.962354i	$-0.587619\pi$
$379$	9.28894	−	31.6352i	0.477141	−	1.62499i	0.748940	−	0.662638i	$-0.230563\pi$
$380$	2.44263	−	0.0636257i	0.125304	−	0.00326393i
$381$	5.74436	−	2.62336i	0.294292	−	0.134399i
$382$	3.83690	+	3.73826i	0.196313	+	0.191266i
$383$	14.2698	−	16.4682i	0.729154	−	0.841488i	−0.263222	−	0.964735i	$-0.584785\pi$
$383$	14.2698	−	16.4682i	0.729154	−	0.841488i	0.992376	+	0.123247i	$0.0393307\pi$
$384$	1.38866	−	11.2282i	0.0708649	−	0.572985i
$385$	2.16205	−	3.36422i	0.110188	−	0.171457i
$386$	−27.7578	−	14.6910i	−1.41284	−	0.747753i
$387$	4.02121	+	6.25713i	0.204410	+	0.318068i
$388$	−5.58629	−	3.38786i	−0.283601	−	0.171993i
$389$	14.2448	−	4.18265i	0.722240	−	0.212069i	0.100103	−	0.994977i	$-0.468083\pi$
$389$	14.2448	−	4.18265i	0.722240	−	0.212069i	0.622137	+	0.782908i	$0.286265\pi$
$390$	2.95941	+	2.15583i	0.149855	+	0.109165i
$391$	−22.0926	−	2.04285i	−1.11727	−	0.103311i
$392$	33.8020	+	11.1243i	1.70726	+	0.561860i
$393$	11.1854	−	3.28434i	0.564231	−	0.165673i
$394$	1.34131	+	15.8506i	0.0675743	+	0.798543i
$395$	−16.0610	+	10.3218i	−0.808118	+	0.519346i
$396$	−0.641555	−	1.31320i	−0.0322394	−	0.0659907i
$397$	13.7123	−	21.3368i	0.688203	−	1.07086i	−0.304759	−	0.952430i	$-0.598576\pi$
$397$	13.7123	−	21.3368i	0.688203	−	1.07086i	0.992962	−	0.118435i	$-0.0377878\pi$
$398$	1.81606	+	3.22530i	0.0910309	+	0.161670i
$399$	3.30383	+	2.86278i	0.165398	+	0.143318i
$400$	6.41660	+	12.3106i	0.320830	+	0.615530i
$401$	6.39527	−	2.92062i	0.319364	−	0.145849i	−0.249282	−	0.968431i	$-0.580195\pi$
$401$	6.39527	−	2.92062i	0.319364	−	0.145849i	0.568646	+	0.822582i	$0.307467\pi$
$402$	−7.06907	−	9.19124i	−0.352573	−	0.458417i
$403$	−3.15038	−	0.925036i	−0.156932	−	0.0460793i
$404$	8.51475	+	9.32445i	0.423625	+	0.463909i
$405$	0.175998	−	1.22409i	0.00874541	−	0.0608256i
$406$	31.7482	−	7.34061i	1.57564	−	0.364308i
$407$	−3.22553	−	1.47305i	−0.159884	−	0.0730164i
$408$	−10.1609	+	8.24471i	−0.503041	+	0.408174i
$409$	−0.679935	−	4.72905i	−0.0336206	−	0.233836i	0.966082	−	0.258237i	$-0.0831415\pi$
$409$	−0.679935	−	4.72905i	−0.0336206	−	0.233836i	−0.999702	+	0.0244003i	$0.992232\pi$
$410$	−0.610254	+	10.4415i	−0.0301383	+	0.515668i
$411$	8.71673	−	7.55309i	0.429965	−	0.372566i
$412$	16.9321	+	24.8967i	0.834184	+	1.22657i
$413$	38.2025			1.87982
$414$	0.0527948	−	6.78212i	0.00259472	−	0.333323i
$415$			10.3926i			0.510153i
$416$	11.3837	−	3.26486i	0.558131	−	0.160073i
$417$	−6.04634	−	6.97784i	−0.296090	−	0.341706i
$418$	0.0595689	−	1.01923i	0.00291361	−	0.0498521i
$419$	−7.70676	+	1.10806i	−0.376500	+	0.0541325i	−0.327967	−	0.944689i	$-0.606364\pi$
$419$	−7.70676	+	1.10806i	−0.376500	+	0.0541325i	−0.0485326	+	0.998822i	$0.515454\pi$
$420$	2.80902	−	10.5782i	0.137066	−	0.516164i
$421$	−16.9905	+	37.2040i	−0.828066	+	1.81321i	−0.339897	+	0.940463i	$0.610392\pi$
$421$	−16.9905	+	37.2040i	−0.828066	+	1.81321i	−0.488169	+	0.872749i	$0.662335\pi$
$422$	3.06775	+	13.2680i	0.149336	+	0.645877i
$423$	3.17733	+	0.456831i	0.154487	+	0.0222119i
$424$	−3.74748	−	33.7871i	−0.181994	−	1.64085i
$425$	4.52352	−	15.4057i	0.219423	−	0.747286i
$426$	6.72185	+	8.73978i	0.325675	+	0.423444i
$427$	17.0764	+	37.3920i	0.826383	+	1.80953i
$428$	−6.09543	−	35.7577i	−0.294634	−	1.72841i
$429$	1.00184	−	1.15619i	0.0483695	−	0.0558214i
$430$	11.3350	−	6.38234i	0.546621	−	0.307784i
$431$	17.7959	+	11.4367i	0.857199	+	0.550888i	0.893812	−	0.448441i	$-0.148021\pi$
$431$	17.7959	+	11.4367i	0.857199	+	0.550888i	−0.0366134	+	0.999330i	$0.511657\pi$
$432$	−2.77327	−	2.88253i	−0.133429	−	0.138686i
$433$	22.2808	+	34.6695i	1.07074	+	1.66611i	0.652530	+	0.757763i	$0.273708\pi$
$433$	22.2808	+	34.6695i	1.07074	+	1.66611i	0.418215	+	0.908348i	$0.362656\pi$
$434$	0.827598	+	9.77993i	0.0397260	+	0.469452i
$435$	−1.81420	−	6.17861i	−0.0869844	−	0.296242i
$436$	−3.49035	−	10.8349i	−0.167158	−	0.518900i
$437$	2.35663	−	4.11018i	0.112733	−	0.196617i
$438$	−11.1652	+	15.3270i	−0.533493	+	0.732350i
$439$	7.26853	+	24.7543i	0.346908	+	1.18146i	0.929539	+	0.368723i	$0.120205\pi$
$439$	7.26853	+	24.7543i	0.346908	+	1.18146i	−0.582631	+	0.812737i	$0.697977\pi$
$440$	−2.35824	+	0.986122i	−0.112425	+	0.0470115i
$441$	10.5841	−	6.80200i	0.504006	−	0.323905i
$442$	−12.1059	−	6.40710i	−0.575817	−	0.304755i
$443$	−1.40668	−	0.904021i	−0.0668336	−	0.0429513i	0.506797	−	0.862065i	$-0.330829\pi$
$443$	−1.40668	−	0.904021i	−0.0668336	−	0.0429513i	−0.573631	+	0.819114i	$0.694466\pi$
$444$	−9.63873	−	1.13054i	−0.457434	−	0.0536529i
$445$	−14.6695	−	12.7112i	−0.695400	−	0.602567i
$446$	−1.44878	+	1.48701i	−0.0686018	+	0.0704120i
$447$	3.84895	+	8.42802i	0.182049	+	0.398632i
$448$	−21.4050	−	28.1964i	−1.01129	−	1.33215i
$449$	36.6064	+	10.7486i	1.72756	+	0.507258i	0.986442	−	0.164112i	$-0.0524759\pi$
$449$	36.6064	+	10.7486i	1.72756	+	0.507258i	0.741122	+	0.671371i	$0.234294\pi$
$450$	4.80921	+	0.980777i	0.226708	+	0.0462343i
$451$	4.32579	+	0.621955i	0.203694	+	0.0292867i
$452$	−3.01813	+	7.09190i	−0.141961	+	0.333575i
$453$	10.3104	+	4.70860i	0.484424	+	0.221229i
$454$	−1.38703	−	3.57586i	−0.0650965	−	0.167824i
$455$	11.3399	−	1.63043i	0.531622	−	0.0764357i
$456$	−0.700134	−	2.70510i	−0.0327868	−	0.126678i
$457$	8.02012	−	6.94947i	0.375165	−	0.325083i	−0.446785	−	0.894641i	$-0.647431\pi$
$457$	8.02012	−	6.94947i	0.375165	−	0.325083i	0.821951	+	0.569559i	$0.192886\pi$
$458$	9.74610	−	27.2071i	0.455406	−	1.27130i
$459$			4.62628i			0.215936i
$460$	−11.8359	−	0.784241i	−0.551850	−	0.0365654i
$461$			35.2790i			1.64311i	0.570132	+	0.821553i	$0.306892\pi$
$461$			35.2790i			1.64311i	−0.570132	+	0.821553i	$0.693108\pi$
$462$	−4.30526	−	1.54222i	−0.200299	−	0.0717508i
$463$	−27.1924	+	23.5623i	−1.26374	+	1.09503i	−0.272608	+	0.962125i	$0.587886\pi$
$463$	−27.1924	+	23.5623i	−1.26374	+	1.09503i	−0.991128	+	0.132908i	$0.957568\pi$
$464$	−19.3707	−	7.65427i	−0.899264	−	0.355341i
$465$	1.91983	−	0.276030i	0.0890300	−	0.0128006i
$466$	−20.9441	+	8.12392i	−0.970216	+	0.376334i
$467$	−3.45882	−	1.57959i	−0.160055	−	0.0730946i	0.333777	−	0.942652i	$-0.391677\pi$
$467$	−3.45882	−	1.57959i	−0.160055	−	0.0730946i	−0.493832	+	0.869558i	$0.664404\pi$
$468$	1.63958	−	3.85263i	0.0757895	−	0.178088i
$469$	−35.9124	−	5.16343i	−1.65828	−	0.238425i
$470$	1.12183	−	5.50084i	0.0517459	−	0.253735i
$471$	4.00408	+	1.17570i	0.184498	+	0.0541736i
$472$	−20.1044	−	13.8588i	−0.925380	−	0.637901i
$473$	−2.25792	−	4.94416i	−0.103819	−	0.227333i
$474$	15.6376	+	15.2356i	0.718260	+	0.699795i
$475$	2.59121	+	2.24530i	0.118893	+	0.103021i
$476$	−4.76959	+	40.6646i	−0.218614	+	1.86386i
$477$	−10.1108	−	6.49785i	−0.462944	−	0.297516i
$478$	2.62336	−	4.95669i	0.119990	−	0.226714i
$479$	6.83104	−	4.39004i	0.312118	−	0.200586i	−0.375198	−	0.926945i	$-0.622425\pi$
$479$	6.83104	−	4.39004i	0.312118	−	0.200586i	0.687316	+	0.726359i	$0.258789\pi$
$480$	−5.31574	+	4.54785i	−0.242629	+	0.207580i
$481$	−2.86198	−	9.74701i	−0.130495	−	0.444425i
$482$	17.8350	+	12.9922i	0.812363	+	0.591780i
$483$	−14.6908	−	15.3151i	−0.668452	−	0.696862i
$484$	−6.41819	−	19.9237i	−0.291736	−	0.905623i
$485$	1.13815	+	3.87617i	0.0516806	+	0.176008i
$486$	−1.40918	+	0.119247i	−0.0639216	+	0.00540917i
$487$	−8.34119	−	12.9791i	−0.377976	−	0.588141i	0.599194	−	0.800604i	$-0.295488\pi$
$487$	−8.34119	−	12.9791i	−0.377976	−	0.588141i	−0.977169	+	0.212463i	$0.931852\pi$
$488$	4.57815	−	25.8727i	0.207243	−	1.17120i
$489$	−7.05555	−	4.53432i	−0.319063	−	0.205049i
$490$	−10.7959	−	19.1734i	−0.487710	−	0.866167i
$491$	−7.77485	+	8.97266i	−0.350874	+	0.404930i	−0.903562	−	0.428458i	$-0.859057\pi$
$491$	−7.77485	+	8.97266i	−0.350874	+	0.404930i	0.552687	+	0.833389i	$0.313602\pi$
$492$	11.7907	−	2.00990i	0.531567	−	0.0906133i
$493$	10.0070	+	21.9124i	0.450695	+	0.986883i
$494$	2.31845	−	1.78314i	0.104312	−	0.0802275i
$495$	−0.254609	+	0.867117i	−0.0114438	+	0.0389740i
$496$	3.11235	−	5.44701i	0.139748	−	0.244578i
$497$	34.1485	+	4.90981i	1.53177	+	0.220235i
$498$	11.5791	−	2.67724i	0.518870	−	0.119970i
$499$	−15.5691	+	34.0916i	−0.696970	+	1.52615i	0.146637	+	0.989190i	$0.453155\pi$
$499$	−15.5691	+	34.0916i	−0.696970	+	1.52615i	−0.843607	+	0.536961i	$0.819572\pi$
$500$	5.37710	−	20.2491i	0.240471	−	0.905568i
$501$	0.621602	−	0.0893729i	0.0277711	−	0.00399289i
$502$	−26.4738	−	1.54727i	−1.18158	−	0.0690578i
$503$	−8.08435	−	9.32984i	−0.360463	−	0.415997i	0.546331	−	0.837569i	$-0.316024\pi$
$503$	−8.08435	−	9.32984i	−0.360463	−	0.415997i	−0.906795	+	0.421572i	$0.861478\pi$
$504$	−12.5095	−	0.404655i	−0.557217	−	0.0180248i
$505$		−	7.80791i		−	0.347447i
$506$	−0.743522	+	4.90021i	−0.0330536	+	0.217841i
$507$	−8.61726			−0.382706
$508$	−10.4437	+	7.10269i	−0.463364	+	0.315131i
$509$	−24.8196	+	21.5063i	−1.10011	+	0.953252i	−0.999133	−	0.0416366i	$-0.986743\pi$
$509$	−24.8196	+	21.5063i	−1.10011	+	0.953252i	−0.100979	+	0.994889i	$0.532197\pi$
$510$	8.07726	+	0.472077i	0.357667	+	0.0209039i
$511$	8.44408	+	58.7299i	0.373544	+	2.59806i
$512$	1.03574	+	22.6037i	0.0457738	+	0.998952i
$513$	−0.898636	−	0.410393i	−0.0396757	−	0.0181193i
$514$	4.19129	+	18.1274i	0.184870	+	0.799564i
$515$	2.64955	−	18.4280i	0.116753	−	0.812034i
$516$	−10.0310	−	10.9848i	−0.441589	−	0.483581i
$517$	−2.25074	−	0.660877i	−0.0989875	−	0.0290653i
$518$	−24.0705	+	18.5129i	−1.05760	+	0.813410i
$519$	−5.32183	+	2.43040i	−0.233602	+	0.106683i
$520$	−6.55919	−	3.25575i	−0.287639	−	0.142774i
$521$	2.52519	+	2.18809i	0.110631	+	0.0958620i	0.708420	−	0.705792i	$-0.249408\pi$
$521$	2.52519	+	2.18809i	0.110631	+	0.0958620i	−0.597789	+	0.801654i	$0.703954\pi$
$522$	−6.41662	+	3.61299i	−0.280848	+	0.158136i
$523$	4.99151	−	7.76694i	0.218264	−	0.339625i	−0.714805	−	0.699324i	$-0.753484\pi$
$523$	4.99151	−	7.76694i	0.218264	−	0.339625i	0.933068	+	0.359699i	$0.117121\pi$
$524$	−20.9490	+	10.2345i	−0.915160	+	0.447096i
$525$	12.9198	−	8.30305i	0.563866	−	0.362375i
$526$	−18.3373	+	1.55174i	−0.799545	+	0.0676591i
$527$	−6.96181	+	2.04417i	−0.303261	+	0.0890456i
$528$	1.70621	+	2.37343i	0.0742531	+	0.103290i
$529$	−13.2289	+	18.8148i	−0.575168	+	0.818035i
$530$	−12.3767	+	16.9900i	−0.537608	+	0.737998i
$531$	−8.28346	+	2.43224i	−0.359471	+	0.105550i
$532$	−7.47582	−	4.53379i	−0.324118	−	0.196565i
$533$	6.76880	+	10.5325i	0.293189	+	0.456211i
$534$	−10.3833	+	19.6187i	−0.449330	+	0.848984i
$535$	−12.1262	+	18.8688i	−0.524263	+	0.815769i
$536$	17.0261	+	15.7453i	0.735415	+	0.680093i
$537$	−1.38997	+	1.60411i	−0.0599817	+	0.0692226i
$538$	−0.316762	+	0.325120i	−0.0136566	+	0.0140169i
$539$	−8.36320	+	3.81934i	−0.360228	+	0.164511i
$540$	0.0644043	+	2.47252i	0.00277152	+	0.106400i
$541$	−0.914518	+	3.11456i	−0.0393182	+	0.133905i	−0.976813	−	0.214093i	$-0.931320\pi$
$541$	−0.914518	+	3.11456i	−0.0393182	+	0.133905i	0.937495	+	0.347999i	$0.113139\pi$
$542$	1.34102	−	6.57564i	0.0576016	−	0.282448i
$543$	−1.07114	+	7.44993i	−0.0459669	+	0.319707i
$544$	17.2620	−	19.6698i	0.740101	−	0.843338i
$545$	−2.92399	+	6.40265i	−0.125250	+	0.274259i
$546$	−4.73782	−	12.2145i	−0.202760	−	0.522731i
$547$	−2.01238	−	13.9964i	−0.0860430	−	0.598442i	−0.986533	−	0.163565i	$-0.947701\pi$
$547$	−2.01238	−	13.9964i	−0.0860430	−	0.598442i	0.900490	−	0.434877i	$-0.143208\pi$
$548$	−14.6471	+	17.8209i	−0.625693	+	0.761271i
$549$	−6.08332	−	7.02052i	−0.259630	−	0.299629i
$550$	−3.37664	−	1.20958i	−0.143980	−	0.0515765i
$551$	−5.14410			−0.219146
$552$	2.17526	+	13.3891i	0.0925851	+	0.569878i
$553$	68.3141			2.90501
$554$	−32.4557	−	11.6263i	−1.37891	−	0.493953i
$555$	3.92973	+	4.53515i	0.166808	+	0.192507i
$556$	14.2658	+	11.7252i	0.605006	+	0.497258i
$557$	1.55921	+	10.8445i	0.0660659	+	0.459498i	0.995822	+	0.0913210i	$0.0291089\pi$
$557$	1.55921	+	10.8445i	0.0660659	+	0.459498i	−0.929756	+	0.368177i	$0.879982\pi$
$558$	−0.802109	−	2.06790i	−0.0339560	−	0.0875410i
$559$	6.46849	−	14.1640i	0.273588	−	0.599074i
$560$	−1.98301	+	21.7996i	−0.0837973	+	0.921203i
$561$	0.481128	−	3.34632i	0.0203133	−	0.141282i
$562$	−4.36570	+	21.4071i	−0.184156	+	0.903002i
$563$	7.56910	−	25.7780i	0.318999	−	1.08641i	−0.631420	−	0.775441i	$-0.717528\pi$
$563$	7.56910	−	25.7780i	0.318999	−	1.08641i	0.950419	−	0.310971i	$-0.100654\pi$
$564$	−6.41782	+	0.167172i	−0.270239	+	0.00703920i
$565$	4.33512	−	1.97978i	0.182380	−	0.0832901i
$566$	−3.90261	+	4.00559i	−0.164039	+	0.168368i
$567$	−2.89781	+	3.34425i	−0.121697	+	0.140446i
$568$	−16.1898	−	14.9719i	−0.679309	−	0.628208i
$569$	17.2572	−	26.8527i	0.723460	−	1.12573i	−0.263484	−	0.964664i	$-0.584872\pi$
$569$	17.2572	−	26.8527i	0.723460	−	1.12573i	0.986944	−	0.161062i	$-0.0514919\pi$
$570$	−0.808225	+	1.52710i	−0.0338528	+	0.0639630i
$571$	−18.8554	−	29.3396i	−0.789075	−	1.22783i	−0.969706	−	0.244274i	$-0.921450\pi$
$571$	−18.8554	−	29.3396i	−0.789075	−	1.22783i	0.180631	−	0.983551i	$-0.442186\pi$
$572$	−1.58662	+	2.61620i	−0.0663400	+	0.109389i
$573$	−3.63447	+	1.06718i	−0.151832	+	0.0445819i
$574$	22.0362	−	30.2501i	0.919773	−	1.26261i
$575$	−11.5221	−	12.0118i	−0.480503	−	0.500925i
$576$	6.43643	+	4.75103i	0.268185	+	0.197960i
$577$	9.67550	−	2.84098i	0.402796	−	0.118272i	−0.0740583	−	0.997254i	$-0.523595\pi$
$577$	9.67550	−	2.84098i	0.402796	−	0.118272i	0.476854	+	0.878982i	$0.341777\pi$
$578$	−6.20386	+	0.524983i	−0.258046	+	0.0218364i
$579$	18.6819	−	12.0061i	0.776394	−	0.498958i
$580$	5.65333	+	11.5718i	0.234742	+	0.480492i
$581$	20.1047	−	31.2835i	0.834084	−	1.29786i
$582$	4.02549	−	2.26662i	0.166862	−	0.0939544i
$583$	6.63770	+	5.75160i	0.274905	+	0.238207i
$584$	16.8617	−	33.9704i	0.697744	−	1.40571i
$585$	−2.35503	+	1.07550i	−0.0973684	+	0.0444666i
$586$	−11.1992	+	8.61340i	−0.462634	+	0.355816i
$587$	25.1896	+	7.39633i	1.03969	+	0.305279i	0.756643	−	0.653828i	$-0.226838\pi$
$587$	25.1896	+	7.39633i	1.03969	+	0.305279i	0.283042	+	0.959107i	$0.408656\pi$
$588$	−18.5812	+	16.9677i	−0.766276	+	0.699735i
$589$	0.220504	−	1.53364i	0.00908572	−	0.0631925i
$590$	3.40131	+	14.7107i	0.140030	+	0.605630i
$591$	−10.2317	−	4.67265i	−0.420875	−	0.192207i
$592$	19.3833	−	1.01048i	0.796648	−	0.0415304i
$593$	−4.76892	−	33.1686i	−0.195836	−	1.36207i	−0.816206	−	0.577761i	$-0.803927\pi$
$593$	−4.76892	−	33.1686i	−0.195836	−	1.36207i	0.620370	−	0.784309i	$-0.286982\pi$
$594$	1.03170	+	0.0602979i	0.0423312	+	0.00247405i
$595$	19.1332	−	16.5791i	0.784387	−	0.679675i
$596$	−10.4209	−	15.3228i	−0.426858	−	0.627646i
$597$	−2.61731			−0.107119
$598$	−12.0042	+	7.58324i	−0.490888	+	0.310102i
$599$		−	39.2585i		−	1.60406i	−0.597285	−	0.802029i	$-0.703754\pi$
$599$		−	39.2585i		−	1.60406i	0.597285	−	0.802029i	$-0.296246\pi$
$600$	−9.81127	−	0.317374i	−0.400543	−	0.0129567i
$601$	−15.4433	−	17.8225i	−0.629944	−	0.726994i	0.347619	−	0.937636i	$-0.386990\pi$
$601$	−15.4433	−	17.8225i	−0.629944	−	0.726994i	−0.977563	+	0.210642i	$0.932445\pi$
$602$	−46.4669	−	2.71577i	−1.89385	−	0.110686i
$603$	8.11565	−	1.16685i	0.330495	−	0.0475180i
$604$	−21.9100	−	5.81815i	−0.891506	−	0.236737i
$605$	−5.37674	+	11.7734i	−0.218596	+	0.478658i
$606$	−8.69928	+	2.01139i	−0.353384	+	0.0817072i
$607$	27.0325	+	3.88668i	1.09721	+	0.157756i	0.667063	−	0.745001i	$-0.267551\pi$
$607$	27.0325	+	3.88668i	1.09721	+	0.157756i	0.430151	+	0.902757i	$0.358460\pi$
$608$	2.28949	+	5.09796i	0.0928511	+	0.206750i
$609$	−6.49158	+	22.1083i	−0.263052	+	0.895873i
$610$	−12.8782	+	9.90478i	−0.521425	+	0.401033i
$611$	−2.79164	−	6.11285i	−0.112938	−	0.247299i
$612$	−1.55481	−	9.12099i	−0.0628494	−	0.368694i
$613$	7.44027	−	8.58653i	0.300510	−	0.346807i	−0.585332	−	0.810793i	$-0.699036\pi$
$613$	7.44027	−	8.58653i	0.300510	−	0.346807i	0.885842	+	0.463987i	$0.153581\pi$
$614$	19.4051	+	34.4632i	0.783125	+	1.39082i
$615$	−6.22178	−	3.99849i	−0.250886	−	0.161235i
$616$	9.00638	+	1.59367i	0.362878	+	0.0642109i
$617$	−1.73083	−	2.69322i	−0.0696806	−	0.108425i	0.804665	−	0.593730i	$-0.202345\pi$
$617$	−1.73083	−	2.69322i	−0.0696806	−	0.108425i	−0.874345	+	0.485304i	$0.838709\pi$
$618$	−21.2143	+	1.79520i	−0.853366	+	0.0722135i
$619$	13.3916	+	45.6075i	0.538252	+	1.83312i	0.552933	+	0.833226i	$0.313509\pi$
$619$	13.3916	+	45.6075i	0.538252	+	1.83312i	−0.0146806	+	0.999892i	$0.504673\pi$
$620$	−3.69229	+	1.18943i	−0.148286	+	0.0477686i
$621$	4.16047	+	2.38547i	0.166954	+	0.0957255i
$622$	−8.12518	−	5.91893i	−0.325790	−	0.237327i
$623$	19.5676	+	66.6412i	0.783960	+	2.66992i
$624$	−1.93773	+	8.14672i	−0.0775713	+	0.326130i
$625$	3.70011	−	2.37792i	0.148005	−	0.0951167i
$626$	13.9157	−	26.2930i	0.556185	−	1.05088i
$627$	0.607328	+	0.390306i	0.0242544	+	0.0155873i
$628$	−8.28942	−	0.972274i	−0.330784	−	0.0387979i
$629$	−16.9655	−	14.7007i	−0.676459	−	0.586155i
$630$	5.54320	+	5.40069i	0.220846	+	0.215169i
$631$	−19.5919	−	42.9003i	−0.779942	−	1.70783i	−0.703429	−	0.710765i	$-0.748349\pi$
$631$	−19.5919	−	42.9003i	−0.779942	−	1.70783i	−0.0765122	−	0.997069i	$-0.524378\pi$
$632$	−35.9509	−	24.7824i	−1.43005	−	0.985791i
$633$	−9.23936	−	2.71292i	−0.367232	−	0.107829i
$634$	−7.24092	+	35.5056i	−0.287574	+	1.41011i
$635$	7.73019	+	1.11143i	0.306763	+	0.0441059i
$636$	22.1180	+	9.41283i	0.877034	+	0.373243i
$637$	−23.9589	−	10.9416i	−0.949285	−	0.433524i
$638$	5.01707	−	1.94605i	0.198628	−	0.0770450i
$639$	−7.71702	+	1.10954i	−0.305281	+	0.0438927i
$640$	8.95186	−	10.7529i	0.353853	−	0.425045i
$641$	−10.2819	+	8.90928i	−0.406109	+	0.351895i	−0.833836	−	0.552013i	$-0.813860\pi$
$641$	−10.2819	+	8.90928i	−0.406109	+	0.351895i	0.427727	+	0.903908i	$0.359315\pi$
$642$	24.1467	+	8.64982i	0.952996	+	0.341381i
$643$			49.7801i			1.96314i	0.191111	+	0.981568i	$0.438791\pi$
$643$			49.7801i			1.96314i	−0.191111	+	0.981568i	$0.561209\pi$
$644$	34.1108	+	25.2574i	1.34416	+	0.995281i
$645$			9.19825i			0.362181i
$646$	2.17970	−	6.08483i	0.0857592	−	0.239404i
$647$	−34.7448	+	30.1065i	−1.36596	+	1.18361i	−0.402604	+	0.915374i	$0.631895\pi$
$647$	−34.7448	+	30.1065i	−1.36596	+	1.18361i	−0.963354	+	0.268234i	$0.913560\pi$
$648$	2.73820	−	0.708702i	0.107567	−	0.0278404i
$649$	6.24461	−	0.897840i	0.245123	−	0.0352433i
$650$	−3.71591	−	9.57988i	−0.145750	−	0.375754i
$651$	−6.31300	−	2.88305i	−0.247426	−	0.112996i
$652$	15.4343	+	6.56845i	0.604455	+	0.257241i
$653$	−20.9353	−	3.01005i	−0.819263	−	0.117792i	−0.280075	−	0.959978i	$-0.590359\pi$
$653$	−20.9353	−	3.01005i	−0.819263	−	0.117792i	−0.539187	+	0.842186i	$0.681269\pi$
$654$	7.88684	+	1.60842i	0.308400	+	0.0628942i
$655$	13.8328	+	4.06168i	0.540493	+	0.158703i
$656$	−22.5706	+	7.92528i	−0.881234	+	0.309430i
$657$	−5.57010	−	12.1968i	−0.217310	−	0.475843i
$658$	−14.0184	+	14.3883i	−0.546492	+	0.560913i
$659$	−20.0271	−	17.3536i	−0.780147	−	0.676001i	0.170817	−	0.985303i	$-0.445359\pi$
$659$	−20.0271	−	17.3536i	−0.780147	−	0.676001i	−0.950964	+	0.309302i	$0.899905\pi$
$660$	0.210554	−	1.79514i	0.00819581	−	0.0698759i
$661$	19.3448	+	12.4322i	0.752426	+	0.483555i	0.859779	−	0.510666i	$-0.170601\pi$
$661$	19.3448	+	12.4322i	0.752426	+	0.483555i	−0.107353	+	0.994221i	$0.534238\pi$
$662$	−21.6605	−	11.4640i	−0.841860	−	0.445559i
$663$	8.14763	−	5.23617i	0.316428	−	0.203356i
$664$	−21.9291	+	9.16984i	−0.851012	+	0.355859i
$665$	1.52312	+	5.18727i	0.0590640	+	0.201154i
$666$	4.04056	−	5.54666i	0.156569	−	0.214929i
$667$	24.8660	+	2.29930i	0.962817	+	0.0890292i
$668$	−1.19549	+	0.385113i	−0.0462549	+	0.0149005i
$669$	−0.413589	−	1.40856i	−0.0159903	−	0.0544579i
$670$	−1.20913	−	14.2886i	−0.0467127	−	0.552016i
$671$	3.67011	+	5.71080i	0.141683	+	0.220463i
$672$	24.7992	−	3.40640i	0.956650	−	0.131405i
$673$	37.2842	+	23.9611i	1.43720	+	0.923632i	0.999702	+	0.0244118i	$0.00777130\pi$
$673$	37.2842	+	23.9611i	1.43720	+	0.923632i	0.437497	+	0.899220i	$0.355865\pi$
$674$	12.9407	−	7.28649i	0.498458	−	0.280665i
$675$	−2.27277	+	2.62292i	−0.0874791	+	0.100956i
$676$	16.9895	−	2.89610i	0.653440	−	0.111389i
$677$	−2.69503	−	5.90128i	−0.103578	−	0.226805i	0.850746	−	0.525576i	$-0.176150\pi$
$677$	−2.69503	−	5.90128i	−0.103578	−	0.226805i	−0.954325	+	0.298772i	$0.903423\pi$
$678$	−3.32257	−	4.32002i	−0.127603	−	0.165909i
$679$	4.07251	−	13.8697i	0.156289	−	0.532270i
$680$	−16.0834	+	1.78389i	−0.616772	+	0.0684090i
$681$	2.68446	+	0.385968i	0.102869	+	0.0147903i
$682$	0.365129	+	1.57919i	0.0139815	+	0.0604702i
$683$	12.4250	−	27.2069i	0.475429	−	1.04104i	−0.508267	−	0.861200i	$-0.669714\pi$
$683$	12.4250	−	27.2069i	0.475429	−	1.04104i	0.983695	−	0.179844i	$-0.0575592\pi$
$684$	1.90964	+	0.507100i	0.0730169	+	0.0193895i
$685$	14.1185	−	2.02994i	0.539442	−	0.0775600i
$686$	−2.03791	+	34.8687i	−0.0778077	+	1.33129i
$687$	13.3824	+	15.4441i	0.510569	+	0.589228i
$688$	23.4685	+	18.2861i	0.894726	+	0.697150i
$689$			25.1613i			0.958570i
$690$	4.58945	−	7.02056i	0.174717	−	0.267268i
$691$	31.1812			1.18619			0.593094	−	0.805133i	$-0.297906\pi$
$691$	31.1812			1.18619			0.593094	+	0.805133i	$0.297906\pi$
$692$	9.67549	−	6.58024i	0.367807	−	0.250143i
$693$	2.44387	−	2.11763i	0.0928350	−	0.0804420i
$694$	−2.72032	+	46.5449i	−0.103262	+	1.76682i
$695$	−1.62499	−	11.3021i	−0.0616394	−	0.428712i
$696$	11.4365	−	9.27973i	0.433499	−	0.351747i
$697$	25.1668	+	11.4933i	0.953260	+	0.435339i
$698$	−19.9880	+	4.62150i	−0.756558	+	0.174926i
$699$	2.26064	−	15.7231i	0.0855053	−	0.594702i
$700$	−22.6817	+	20.7121i	−0.857286	+	0.782843i
$701$	−20.0940	−	5.90014i	−0.758941	−	0.222845i	−0.120708	−	0.992688i	$-0.538516\pi$
$701$	−20.0940	−	5.90014i	−0.758941	−	0.222845i	−0.638233	+	0.769843i	$0.720335\pi$
$702$	1.80496	+	2.34682i	0.0681240	+	0.0885751i
$703$	4.36054	−	1.99139i	0.164461	−	0.0751068i
$704$	−4.16155	−	4.10594i	−0.156844	−	0.154748i
$705$	3.00013	+	2.59963i	0.112991	+	0.0979077i
$706$	−19.7509	−	35.0774i	−0.743335	−	1.32015i
$707$	−15.1045	+	23.5031i	−0.568065	+	0.883926i
$708$	15.5139	−	7.57923i	0.583048	−	0.284845i
$709$	−1.90619	+	1.22503i	−0.0715884	+	0.0460071i	−0.575945	−	0.817488i	$-0.695366\pi$
$709$	−1.90619	+	1.22503i	−0.0715884	+	0.0460071i	0.504357	+	0.863495i	$0.331730\pi$
$710$	1.14974	+	13.5868i	0.0431489	+	0.509902i
$711$	−14.8126	+	4.34937i	−0.555515	+	0.163114i
$712$	13.8779	−	42.1691i	0.520095	−	1.58035i
$713$	−1.75140	+	7.31490i	−0.0655903	+	0.273945i
$714$	−23.4007	−	17.0466i	−0.875748	−	0.637954i
$715$	1.81531	−	0.533023i	0.0678887	−	0.0199339i
$716$	2.20130	−	3.62975i	0.0822665	−	0.135650i
$717$	2.14393	+	3.33602i	0.0800664	+	0.124586i
$718$	−4.90112	−	2.59395i	−0.182908	−	0.0968053i
$719$	20.7821	−	32.3376i	0.775042	−	1.20599i	−0.199084	−	0.979982i	$-0.563797\pi$
$719$	20.7821	−	32.3376i	0.775042	−	1.20599i	0.974126	−	0.226006i	$-0.0725669\pi$
$720$	−0.957946	−	4.85308i	−0.0357005	−	0.180864i
$721$	−43.6249	+	50.3458i	−1.62468	+	1.87498i
$722$	−18.2572	−	17.7878i	−0.679462	−	0.661994i
$723$	−14.1927	+	6.48158i	−0.527832	+	0.241053i
$724$	−0.391970	−	15.0480i	−0.0145675	−	0.559254i
$725$	−5.09139	+	17.3397i	−0.189089	+	0.643979i
$726$	14.5026	+	2.95762i	0.538243	+	0.109768i
$727$	3.36225	−	23.3849i	0.124699	−	0.867299i	−0.827423	−	0.561580i	$-0.810194\pi$
$727$	3.36225	−	23.3849i	0.124699	−	0.867299i	0.952122	−	0.305720i	$-0.0988971\pi$
$728$	13.4460	+	22.4892i	0.498340	+	0.833507i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−21.8634	+	8.48053i	−0.809202	+	0.313878i
$731$	−4.89700	−	34.0594i	−0.181122	−	1.25973i
$732$	14.3531	+	11.7969i	0.530506	+	0.436026i
$733$	9.05965	+	10.4554i	0.334626	+	0.386179i	0.897980	−	0.440037i	$-0.145035\pi$
$733$	9.05965	+	10.4554i	0.334626	+	0.386179i	−0.563354	+	0.826216i	$0.690489\pi$
$734$	9.94478	−	27.7617i	0.367068	−	1.02470i
$735$	15.5591			0.573907
$736$	−8.78848	−	25.6664i	−0.323948	−	0.946075i
$737$	−5.99163			−0.220705
$738$	−2.85218	+	7.96212i	−0.104990	+	0.293090i
$739$	−19.0633	−	22.0002i	−0.701254	−	0.809290i	0.287668	−	0.957730i	$-0.407120\pi$
$739$	−19.0633	−	22.0002i	−0.701254	−	0.809290i	−0.988921	+	0.148440i	$0.952575\pi$
$740$	−9.27189	−	7.62062i	−0.340841	−	0.280140i
$741$	0.294334	+	2.04714i	0.0108126	+	0.0752036i
$742$	70.1233	−	27.1999i	2.57431	−	0.998539i
$743$	−16.1984	+	35.4695i	−0.594260	+	1.30125i	0.338573	+	0.940940i	$0.390056\pi$
$743$	−16.1984	+	35.4695i	−0.594260	+	1.30125i	−0.932833	+	0.360308i	$0.882671\pi$
$744$	2.27639	+	3.80741i	0.0834564	+	0.139586i
$745$	−1.63068	+	11.3416i	−0.0597433	+	0.415524i
$746$	32.4875	+	6.62541i	1.18945	+	0.242573i
$747$	−2.36758	+	8.06323i	−0.0866252	+	0.295018i
$748$	0.176063	+	6.75917i	0.00643751	+	0.247140i
$749$	73.0040	−	33.3398i	2.66751	−	1.21821i
$750$	10.6110	+	10.3382i	0.387457	+	0.377496i
$751$	1.45464	−	1.67874i	0.0530806	−	0.0612582i	−0.728588	−	0.684952i	$-0.759823\pi$
$751$	1.45464	−	1.67874i	0.0530806	−	0.0612582i	0.781669	+	0.623694i	$0.214369\pi$
$752$	12.5969	−	2.48650i	0.459363	−	0.0906733i
$753$	10.1380	−	15.7750i	0.369448	−	0.574872i
$754$	13.6256	+	7.21143i	0.496215	+	0.262625i
$755$	7.57837	+	11.7922i	0.275805	+	0.429161i
$756$	4.58927	−	7.56730i	0.166910	−	0.275220i
$757$	−5.03249	+	1.47767i	−0.182909	+	0.0537069i	−0.371904	−	0.928271i	$-0.621295\pi$
$757$	−5.03249	+	1.47767i	−0.182909	+	0.0537069i	0.188995	+	0.981978i	$0.439477\pi$
$758$	−37.6881	−	27.4545i	−1.36889	−	0.997194i
$759$	−2.76130	−	2.15816i	−0.100229	−	0.0783363i
$760$	1.08024	−	3.28239i	0.0391843	−	0.119065i
$761$	−48.2097	+	14.1556i	−1.74760	+	0.513142i	−0.990181	−	0.139789i	$-0.955358\pi$
$761$	−48.2097	+	14.1556i	−1.74760	+	0.513142i	−0.757418	+	0.652930i	$0.773540\pi$
$762$	−0.753052	−	8.89901i	−0.0272802	−	0.322377i
$763$	21.1878	−	13.6165i	0.767048	−	0.492952i
$764$	6.80691	−	3.32548i	0.246265	−	0.120312i
$765$	−3.09313	+	4.81300i	−0.111832	+	0.174015i
$766$	−15.1197	−	26.8525i	−0.546298	−	0.970219i
$767$	13.6591	+	11.8356i	0.493200	+	0.427360i
$768$	−14.2866	−	7.20378i	−0.515521	−	0.259944i
$769$	6.34962	−	2.89977i	0.228973	−	0.104569i	−0.297625	−	0.954683i	$-0.596195\pi$
$769$	6.34962	−	2.89977i	0.228973	−	0.104569i	0.526598	+	0.850114i	$0.323467\pi$
$770$	−3.44789	−	4.48296i	−0.124253	−	0.161555i
$771$	−12.6232	−	3.70652i	−0.454615	−	0.133487i
$772$	−32.7975	+	29.9495i	−1.18041	+	1.07791i
$773$	−0.775966	+	5.39696i	−0.0279096	+	0.194115i	−0.999006	−	0.0445714i	$-0.985808\pi$
$773$	−0.775966	+	5.39696i	−0.0279096	+	0.194115i	0.971097	+	0.238687i	$0.0767169\pi$
$774$	10.2484	−	2.36956i	0.368369	−	0.0851720i
$775$	−4.95133	−	2.26120i	−0.177857	−	0.0812246i
$776$	−7.17473	+	5.82167i	−0.257558	+	0.208986i
$777$	−3.05582	−	21.2537i	−0.109627	−	0.762473i
$778$	1.22500	−	20.9599i	0.0439185	−	0.751449i
$779$	−4.46505	+	3.86898i	−0.159977	+	0.138621i
$780$	4.28162	−	2.91190i	0.153307	−	0.104263i
$781$	5.69734			0.203867
$782$	−13.2562	+	28.4392i	−0.474042	+	1.01698i
$783$		−	5.20705i		−	0.186085i
$784$	30.9314	−	39.6976i	1.10469	−	1.41777i
$785$	3.37961	+	3.90028i	0.120624	+	0.139207i
$786$	0.961910	−	16.4583i	0.0343102	−	0.587049i
$787$	−27.9652	+	4.02078i	−0.996851	+	0.143325i	−0.621380	−	0.783509i	$-0.713428\pi$
$787$	−27.9652	+	4.02078i	−0.996851	+	0.143325i	−0.375470	+	0.926835i	$0.622519\pi$
$788$	21.7427	+	5.77373i	0.774553	+	0.205681i
$789$	5.40570	−	11.8368i	0.192448	−	0.421403i
$790$	6.08227	+	26.3059i	0.216397	+	0.935920i
$791$	−16.8794	−	2.42689i	−0.600162	−	0.0862903i
$792$	−2.05432	+	0.227854i	−0.0729972	+	0.00809645i
$793$	−5.47900	+	18.6598i	−0.194565	+	0.662627i
$794$	−21.8675	−	28.4322i	−0.776048	−	1.00902i
$795$	−6.17448	−	13.5202i	−0.218986	−	0.479513i
$796$	5.16019	−	0.879630i	0.182898	−	0.0311777i
$797$	−14.9918	+	17.3014i	−0.531035	+	0.612847i	−0.956359	−	0.292194i	$-0.905615\pi$
$797$	−14.9918	+	17.3014i	−0.531035	+	0.612847i	0.425324	+	0.905041i	$0.360160\pi$
$798$	5.38709	−	3.03329i	0.190701	−	0.107377i
$799$	−12.4929	−	8.02871i	−0.441968	−	0.284035i
$800$	19.4502	−	2.67166i	0.687667	−	0.0944576i
$801$	−8.48571	−	13.2040i	−0.299828	−	0.466541i
$802$	−0.838382	−	9.90737i	−0.0296043	−	0.349841i
$803$	2.76056	+	9.40159i	0.0974179	+	0.331775i
$804$	−15.6083	+	5.02804i	−0.550463	+	0.177325i
$805$	−5.04401	−	25.7555i	−0.177778	−	0.907762i
$806$	−2.73405	+	3.75315i	−0.0963028	+	0.132199i
$807$	−0.0904272	−	0.307967i	−0.00318319	−	0.0108409i
$808$	16.4752	−	6.88924i	0.579594	−	0.242363i
$809$	35.8136	−	23.0160i	1.25914	−	0.809200i	0.270974	−	0.962587i	$-0.412654\pi$
$809$	35.8136	−	23.0160i	1.25914	−	0.809200i	0.988166	+	0.153387i	$0.0490180\pi$
$810$	−1.54578	−	0.818115i	−0.0543133	−	0.0287456i
$811$	−4.66890	−	3.00052i	−0.163947	−	0.105363i	0.456094	−	0.889931i	$-0.349248\pi$
$811$	−4.66890	−	3.00052i	−0.163947	−	0.105363i	−0.620042	+	0.784569i	$0.712884\pi$
$812$	5.36835	−	45.7695i	0.188392	−	1.60619i
$813$	3.58632	+	3.10757i	0.125778	+	0.108987i
$814$	−3.49950	+	3.59184i	−0.122658	+	0.125894i
$815$	−4.30867	−	9.43467i	−0.150926	−	0.330482i
$816$	6.13079	+	17.4600i	0.214621	+	0.611224i
$817$	7.05030	+	2.07016i	0.246659	+	0.0724256i
$818$	−6.62039	−	1.35014i	−0.231477	−	0.0472067i
$819$	9.16961	+	1.31839i	0.320412	+	0.0460683i
$820$	13.6104	+	5.79225i	0.475297	+	0.202274i
$821$	−37.2711	−	17.0211i	−1.30077	−	0.594042i	−0.359957	−	0.932969i	$-0.617209\pi$
$821$	−37.2711	−	17.0211i	−1.30077	−	0.594042i	−0.940813	+	0.338927i	$0.889936\pi$
$822$	−5.89875	−	15.2074i	−0.205743	−	0.530420i
$823$	40.7124	−	5.85356i	1.41915	−	0.204042i	0.610350	−	0.792132i	$-0.291029\pi$
$823$	40.7124	−	5.85356i	1.41915	−	0.204042i	0.808796	+	0.588089i	$0.200120\pi$
$824$	41.2220	−	10.6691i	1.43604	−	0.371675i
$825$	1.91674	−	1.66087i	0.0667325	−	0.0578240i
$826$	18.2196	−	50.8616i	0.633941	−	1.76970i
$827$			16.0467i			0.558000i	0.960291	+	0.279000i	$0.0900030\pi$
$827$			16.0467i			0.558000i	−0.960291	+	0.279000i	$0.909997\pi$
$828$	−9.00434	−	3.30483i	−0.312922	−	0.114851i
$829$		−	43.6802i		−	1.51707i	−0.651629	−	0.758537i	$-0.725914\pi$
$829$		−	43.6802i		−	1.51707i	0.651629	−	0.758537i	$-0.274086\pi$
$830$	13.8364	+	4.95647i	0.480269	+	0.172041i
$831$	18.4234	−	15.9640i	0.639102	−	0.553785i
$832$	1.08239	−	16.7130i	0.0375252	−	0.579418i
$833$	−57.6125	+	8.28342i	−1.99615	+	0.287004i
$834$	−12.1737	+	4.72202i	−0.421541	+	0.163510i
$835$	0.706445	+	0.322623i	0.0244476	+	0.0111648i
$836$	−1.32856	−	0.565400i	−0.0459492	−	0.0195548i
$837$	1.55241	+	0.223202i	0.0536590	+	0.00771500i
$838$	−2.20028	+	10.7890i	−0.0760074	+	0.372700i
$839$	−10.2208	−	3.00109i	−0.352861	−	0.103609i	0.100498	−	0.994937i	$-0.467956\pi$
$839$	−10.2208	−	3.00109i	−0.352861	−	0.103609i	−0.453359	+	0.891328i	$0.649774\pi$
$840$	−12.7438	−	8.78482i	−0.439704	−	0.303105i
$841$	0.783741	+	1.71615i	0.0270256	+	0.0591777i
$842$	41.4291	+	40.3640i	1.42774	+	1.39104i
$843$	−11.6753	−	10.1167i	−0.402119	−	0.348438i
$844$	19.1277	+	2.24351i	0.658403	+	0.0772248i
$845$	−8.96507	−	5.76150i	−0.308408	−	0.198202i
$846$	2.12355	−	4.01232i	0.0730091	−	0.137947i
$847$	38.9608	−	25.0386i	1.33871	−	0.860337i
$848$	−46.7704	−	11.1245i	−1.60610	−	0.382018i
$849$	−1.11409	−	3.79426i	−0.0382356	−	0.130219i
$850$	−18.3533	−	13.3698i	−0.629513	−	0.458580i
$851$	−21.9685	+	7.67712i	−0.753071	+	0.263168i
$852$	14.8417	−	4.78107i	0.508468	−	0.163797i
$853$	13.4116	+	45.6757i	0.459205	+	1.56391i	0.785637	+	0.618687i	$0.212335\pi$
$853$	13.4116	+	45.6757i	0.459205	+	1.56391i	−0.326433	+	0.945220i	$0.605847\pi$
$854$	57.9267	−	4.90187i	1.98221	−	0.167739i
$855$	−0.660517	−	1.02778i	−0.0225892	−	0.0351495i
$856$	−50.5138	−	8.93837i	−1.72653	−	0.305507i
$857$	−10.0086	−	6.43214i	−0.341887	−	0.219718i	0.358418	−	0.933561i	$-0.383316\pi$
$857$	−10.0086	−	6.43214i	−0.341887	−	0.219718i	−0.700305	+	0.713844i	$0.746953\pi$
$858$	−1.06152	−	1.88524i	−0.0362395	−	0.0643610i
$859$	−0.0214755	+	0.0247841i	−0.000732735	+	0.000845621i	−0.756116	−	0.654438i	$-0.772905\pi$
$859$	−0.0214755	+	0.0247841i	−0.000732735	+	0.000845621i	0.755383	+	0.655283i	$0.227451\pi$
$860$	−3.09136	−	18.1349i	−0.105415	−	0.618395i
$861$	10.9934	+	24.0723i	0.374656	+	0.820381i
$862$	23.7138	−	18.2385i	0.807695	−	0.621206i
$863$	−14.6713	+	49.9659i	−0.499417	+	1.70086i	0.194585	+	0.980886i	$0.437664\pi$
$863$	−14.6713	+	49.9659i	−0.499417	+	1.70086i	−0.694002	+	0.719973i	$0.744154\pi$
$864$	−5.16035	+	2.31751i	−0.175559	+	0.0788432i
$865$	−7.16159	−	1.02968i	−0.243501	−	0.0350102i
$866$	56.7841	−	13.1293i	1.92960	−	0.446150i
$867$	1.82885	−	4.00463i	0.0621110	−	0.136004i
$868$	13.4154	+	3.56243i	0.455348	+	0.120917i
$869$	11.1667	−	1.60553i	0.378804	−	0.0544638i
$870$	−9.09125	−	0.531340i	−0.308222	−	0.0180141i
$871$	−11.2406	−	12.9723i	−0.380872	−	0.439550i
$872$	−16.0899	−	0.520476i	−0.544874	−	0.0176255i
$873$			3.26666i			0.110560i
$874$	−4.34824	−	5.09778i	−0.147081	−	0.172435i
$875$	46.3547			1.56708
$876$	15.0809	+	22.1748i	0.509537	+	0.749216i
$877$	25.4529	−	22.0551i	0.859485	−	0.744748i	−0.108941	−	0.994048i	$-0.534746\pi$
$877$	25.4529	−	22.0551i	0.859485	−	0.744748i	0.968426	+	0.249300i	$0.0802006\pi$
$878$	36.4237	+	2.12879i	1.22924	+	0.0718432i
$879$	−1.42177	−	9.88862i	−0.0479551	−	0.333535i
$880$	0.188194	+	3.61000i	0.00634403	+	0.121693i
$881$	−15.6787	−	7.16022i	−0.528228	−	0.241234i	0.133405	−	0.991062i	$-0.457409\pi$
$881$	−15.6787	−	7.16022i	−0.528228	−	0.241234i	−0.661633	+	0.749828i	$0.730136\pi$
$882$	−4.00818	−	17.3354i	−0.134962	−	0.583713i
$883$	−0.0668046	+	0.464637i	−0.00224816	+	0.0156363i	−0.990915	−	0.134492i	$-0.957060\pi$
$883$	−0.0668046	+	0.464637i	−0.00224816	+	0.0156363i	0.988666	+	0.150129i	$0.0479688\pi$
$884$	−14.3038	+	13.0617i	−0.481088	+	0.439312i
$885$	−10.2440	−	3.00791i	−0.344348	−	0.101110i
$886$	−1.87446	+	1.44167i	−0.0629739	+	0.0484338i
$887$	−32.4033	+	14.7981i	−1.08800	+	0.496872i	−0.876939	−	0.480602i	$-0.840418\pi$
$887$	−32.4033	+	14.7981i	−1.08800	+	0.496872i	−0.211058	+	0.977473i	$0.567691\pi$
$888$	−6.10208	+	12.2935i	−0.204773	+	0.412544i
$889$	−21.1191	−	18.2998i	−0.708312	−	0.613756i
$890$	−23.9195	+	13.4683i	−0.801782	+	0.451457i
$891$	−0.395082	+	0.614760i	−0.0132358	+	0.0205952i
$892$	1.28881	+	2.63805i	0.0431524	+	0.0883285i
$893$	2.66778	−	1.71448i	0.0892738	−	0.0573728i
$894$	13.0565	−	1.10486i	0.436673	−	0.0369522i
$895$	−2.51858	+	0.739523i	−0.0841870	+	0.0247195i
$896$	−47.7483	+	15.0505i	−1.59516	+	0.502801i
$897$	−0.507756	−	10.0272i	−0.0169535	−	0.334799i
$898$	31.7688	−	43.6104i	1.06014	−	1.45530i
$899$	7.83578	−	2.30079i	0.261338	−	0.0767357i
$900$	3.59940	−	5.93508i	0.119980	−	0.197836i
$901$	30.0609	+	46.7756i	1.00147	+	1.55832i
$902$	2.89112	−	5.46261i	0.0962637	−	0.181885i
$903$	17.7942	−	27.6883i	0.592154	−	0.921409i
$904$	8.00253	+	7.40053i	0.266160	+	0.246138i
$905$	−6.09539	+	7.03446i	−0.202618	+	0.233833i
$906$	11.1861	−	11.4813i	0.371635	−	0.381441i
$907$	−36.4033	+	16.6249i	−1.20875	+	0.552019i	−0.914841	−	0.403813i	$-0.867685\pi$
$907$	−36.4033	+	16.6249i	−1.20875	+	0.552019i	−0.293912	+	0.955833i	$0.594957\pi$
$908$	−5.42230	+	0.141240i	−0.179945	+	0.00468722i
$909$	1.77875	−	6.05786i	0.0589973	−	0.200926i
$910$	3.23753	−	15.8752i	0.107323	−	0.526256i
$911$	6.79980	−	47.2936i	0.225287	−	1.56691i	−0.492291	−	0.870431i	$-0.663840\pi$
$911$	6.79980	−	47.2936i	0.225287	−	1.56691i	0.717579	−	0.696478i	$-0.245250\pi$
$912$	−3.93540	−	0.357983i	−0.130314	−	0.0118540i
$913$	2.55111	−	5.58614i	0.0844293	−	0.184874i
$914$	−5.42735	−	13.9921i	−0.179521	−	0.462818i
$915$	−1.63493	−	11.3712i	−0.0540491	−	0.375920i
$916$	−31.5746	−	25.9513i	−1.04325	−	0.857456i
$917$	−33.7817	−	38.9862i	−1.11557	−	1.28744i
$918$	6.15929	+	2.20637i	0.203287	+	0.0728212i
$919$	−46.6324			−1.53826			−0.769130	−	0.639093i	$-0.779310\pi$
$919$	−46.6324			−1.53826			−0.769130	+	0.639093i	$0.779310\pi$
$920$	−6.68890	+	15.3839i	−0.220526	+	0.507192i
$921$	−27.9667			−0.921533
$922$	46.9694	+	16.8253i	1.54685	+	0.554112i
$923$	10.6884	+	12.3351i	0.351815	+	0.406016i
$924$	−4.10654	+	4.99637i	−0.135095	+	0.164368i
$925$	−2.39670	−	16.6694i	−0.0788031	−	0.548088i
$926$	18.4015	+	47.4405i	0.604711	+	1.55899i
$927$	6.25383	−	13.6940i	0.205403	−	0.449769i
$928$	−19.4290	+	22.1391i	−0.637788	+	0.726753i
$929$	−1.78174	+	12.3923i	−0.0584569	+	0.406577i	0.939493	+	0.342569i	$0.111297\pi$
$929$	−1.78174	+	12.3923i	−0.0584569	+	0.406577i	−0.997949	+	0.0640074i	$0.979612\pi$
$930$	0.548112	−	2.68765i	0.0179733	−	0.0881315i
$931$	3.50173	−	11.9258i	0.114765	−	0.390852i
$932$	0.827254	+	31.7588i	0.0270976	+	1.04029i
$933$	6.46582	−	2.95284i	0.211681	−	0.0966717i
$934$	−3.75260	+	3.85162i	−0.122789	+	0.126029i
$935$	2.73790	−	3.15970i	0.0895388	−	0.103333i
$936$	−4.34732	−	4.02029i	−0.142097	−	0.131407i
$937$	−26.0486	+	40.5325i	−0.850972	+	1.32414i	0.0935243	+	0.995617i	$0.470187\pi$
$937$	−26.0486	+	40.5325i	−0.850972	+	1.32414i	−0.944496	+	0.328522i	$0.893450\pi$
$938$	−24.0019	+	45.3501i	−0.783688	+	1.48073i
$939$	11.3726	+	17.6960i	0.371129	+	0.577489i
$940$	−6.78863	−	4.11703i	−0.221421	−	0.134283i
$941$	39.9005	−	11.7158i	1.30072	−	0.381925i	0.443220	−	0.896413i	$-0.353836\pi$
$941$	39.9005	−	11.7158i	1.30072	−	0.381925i	0.857498	+	0.514488i	$0.172018\pi$
$942$	3.47493	−	4.77019i	0.113219	−	0.155421i
$943$	23.3129	−	16.7065i	0.759173	−	0.544038i
$944$	−28.0394	+	20.1568i	−0.912603	+	0.656049i
$945$	−5.25074	+	1.54176i	−0.170807	+	0.0501533i
$946$	−7.65936	+	0.648151i	−0.249027	+	0.0210732i
$947$	−16.8451	+	10.8257i	−0.547393	+	0.351788i	−0.784924	−	0.619592i	$-0.787298\pi$
$947$	−16.8451	+	10.8257i	−0.547393	+	0.351788i	0.237531	+	0.971380i	$0.423662\pi$
$948$	27.7422	−	13.5533i	0.901023	−	0.440190i
$949$	−15.1762	+	23.6146i	−0.492640	+	0.766562i
$950$	4.22513	−	2.37903i	0.137081	−	0.0771859i
$951$	−19.3646	−	16.7795i	−0.627940	−	0.544113i
$952$	51.8649	+	25.7439i	1.68095	+	0.834365i
$953$	15.6739	−	7.15805i	0.507729	−	0.231872i	−0.145045	−	0.989425i	$-0.546333\pi$
$953$	15.6739	−	7.15805i	0.507729	−	0.231872i	0.652774	+	0.757553i	$0.273605\pi$
$954$	−13.4731	+	10.3623i	−0.436209	+	0.335492i
$955$	−4.49467	−	1.31975i	−0.145444	−	0.0427063i
$956$	−5.34805	−	5.85662i	−0.172968	−	0.189417i
$957$	−0.541528	+	3.76641i	−0.0175051	+	0.121751i
$958$	−2.58690	−	11.1883i	−0.0835788	−	0.361479i
$959$	−46.4262	−	21.2021i	−1.49918	−	0.684652i
$960$	3.51968	+	9.24619i	0.113597	+	0.298420i
$961$	−4.06170	−	28.2497i	−0.131022	−	0.911281i
$962$	−14.3418	−	0.838210i	−0.462399	−	0.0270250i
$963$	−13.7069	+	11.8771i	−0.441697	+	0.382733i
$964$	25.8034	−	17.5487i	0.831071	−	0.565207i
$965$	27.4633			0.884073
$966$	−27.3964	+	12.2547i	−0.881466	+	0.394289i
$967$		−	34.5213i		−	1.11013i	−0.831807	−	0.555065i	$-0.812693\pi$
$967$		−	34.5213i		−	1.11013i	0.831807	−	0.555065i	$-0.187307\pi$
$968$	−29.5868	−	0.957070i	−0.950955	−	0.0307614i
$969$	2.99295	+	3.45404i	0.0961473	+	0.110960i
$970$	5.70342	+	0.333338i	0.183126	+	0.0107028i
$971$	−22.9742	+	3.30319i	−0.737277	+	0.106004i	−0.500715	−	0.865612i	$-0.666930\pi$
$971$	−22.9742	+	3.30319i	−0.737277	+	0.106004i	−0.236562	+	0.971616i	$0.576021\pi$
$972$	−0.513305	+	1.93301i	−0.0164643	+	0.0620012i
$973$	−16.9725	+	37.1647i	−0.544115	+	1.19145i
$974$	−21.2581	+	4.91517i	−0.681155	+	0.157492i
$975$	7.19179	+	1.03402i	0.230322	+	0.0331152i
$976$	−32.2627	−	18.4345i	−1.03270	−	0.590073i
$977$	8.51234	−	28.9904i	0.272334	−	0.927484i	−0.703815	−	0.710383i	$-0.748522\pi$
$977$	8.51234	−	28.9904i	0.272334	−	0.927484i	0.976149	−	0.217101i	$-0.0696601\pi$
$978$	−9.40181	+	7.23102i	−0.300637	+	0.231223i
$979$	4.76475	+	10.4334i	0.152282	+	0.333451i
$980$	−30.6757	+	5.22913i	−0.979901	+	0.167039i
$981$	−3.72722	+	4.30145i	−0.119001	+	0.137335i
$982$	8.23793	+	14.6305i	0.262883	+	0.466877i
$983$	11.9526	+	7.68149i	0.381230	+	0.245002i	0.717194	−	0.696873i	$-0.245426\pi$
$983$	11.9526	+	7.68149i	0.381230	+	0.245002i	−0.335965	+	0.941875i	$0.609062\pi$
$984$	2.94733	−	16.6564i	0.0939575	−	0.530986i
$985$	−7.52051	−	11.7021i	−0.239623	−	0.372861i
$986$	33.9460	−	2.87258i	1.08106	−	0.0914817i
$987$	−4.00187	−	13.6291i	−0.127381	−	0.433820i
$988$	−1.26830	−	3.93714i	−0.0403501	−	0.125257i
$989$	−33.1551	−	13.1582i	−1.05427	−	0.418408i
$990$	1.03303	+	0.752526i	0.0328317	+	0.0239168i
$991$	−4.72729	−	16.0997i	−0.150167	−	0.511423i	0.849707	−	0.527255i	$-0.176779\pi$
$991$	−4.72729	−	16.0997i	−0.150167	−	0.511423i	−0.999875	+	0.0158315i	$0.994960\pi$
$992$	−5.76763	−	6.74148i	−0.183123	−	0.214042i
$993$	14.5782	−	9.36886i	0.462626	−	0.297312i
$994$	22.8229	−	43.1226i	0.723899	−	1.36777i
$995$	−2.72295	−	1.74993i	−0.0863233	−	0.0554766i
$996$	1.95792	−	16.6928i	0.0620391	−	0.528933i
$997$	18.1585	+	15.7344i	0.575086	+	0.498315i	0.893153	−	0.449754i	$-0.148488\pi$
$997$	18.1585	+	15.7344i	0.575086	+	0.498315i	−0.318067	+	0.948068i	$0.603034\pi$
$998$	37.9633	+	36.9873i	1.20171	+	1.17081i
$999$	2.01576	+	4.41390i	0.0637758	+	0.139650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.451.14	yes	240
8.3	odd	2	inner	552.2.t.a.451.18	yes	240
23.5	odd	22	inner	552.2.t.a.235.18	yes	240
184.51	even	22	inner	552.2.t.a.235.14	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.14	✓	240	184.51	even	22	inner
552.2.t.a.235.18	yes	240	23.5	odd	22	inner
552.2.t.a.451.14	yes	240	1.1	even	1	trivial
552.2.t.a.451.18	yes	240	8.3	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.476922 - 1.33137i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.54509 - 1.26992i) q^{4} +(0.175998 + 1.22409i) q^{5} +(1.31850 - 0.511428i) q^{6} +(1.83825 - 4.02520i) q^{7} +(-2.42762 + 1.45143i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.476922 - 1.33137i) q^{2} +(0.654861 + 0.755750i) q^{3} +(-1.54509 - 1.26992i) q^{4} +(0.175998 + 1.22409i) q^{5} +(1.31850 - 0.511428i) q^{6} +(1.83825 - 4.02520i) q^{7} +(-2.42762 + 1.45143i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(1.71366 + 0.349478i) q^{10} +(0.205881 - 0.701166i) q^{11} +(-0.0520784 - 1.99932i) q^{12} +(1.90431 - 0.869671i) q^{13} +(-4.48233 - 4.36709i) q^{14} +(-0.809853 + 0.934620i) q^{15} +(0.774611 + 3.92428i) q^{16} +(2.50116 - 3.89187i) q^{17} +(1.24995 + 0.661541i) q^{18} +(0.534105 + 0.831084i) q^{19} +(1.28257 - 2.11484i) q^{20} +(4.24584 - 1.24669i) q^{21} +(-0.835322 - 0.608505i) q^{22} +(-2.21033 - 4.25611i) q^{23} +(-2.68667 - 0.884185i) q^{24} +(3.33004 - 0.977787i) q^{25} +(-0.249644 - 2.95011i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-7.95193 + 3.88487i) q^{28} +(-2.81514 + 4.38045i) q^{29} +(0.858088 + 1.52396i) q^{30} +(-1.18530 - 1.02706i) q^{31} +(5.59410 + 0.840283i) q^{32} +(0.664729 - 0.303571i) q^{33} +(-3.98867 - 5.18608i) q^{34} +(5.25074 + 1.54176i) q^{35} +(1.47688 - 1.34864i) q^{36} +(0.690569 - 4.80301i) q^{37} +(1.36121 - 0.314729i) q^{38} +(1.90431 + 0.869671i) q^{39} +(-2.20395 - 2.71618i) q^{40} +(0.851099 + 5.91953i) q^{41} +(0.365128 - 6.24735i) q^{42} +(5.62116 - 4.87076i) q^{43} +(-1.20853 + 0.821912i) q^{44} -1.23668 q^{45} +(-6.72061 + 0.912940i) q^{46} -3.21000i q^{47} +(-2.45851 + 3.15527i) q^{48} +(-8.23904 - 9.50836i) q^{49} +(0.286372 - 4.89984i) q^{50} +(4.57919 - 0.658388i) q^{51} +(-4.04675 - 1.07460i) q^{52} +(-4.99279 + 10.9327i) q^{53} +(0.318580 + 1.37786i) q^{54} +(0.894526 + 0.128613i) q^{55} +(1.37975 + 12.4397i) q^{56} +(-0.278327 + 0.947894i) q^{57} +(4.48939 + 5.83713i) q^{58} +(3.58635 + 7.85300i) q^{59} +(2.43819 - 0.415625i) q^{60} +(-6.08332 + 7.02052i) q^{61} +(-1.93270 + 1.08824i) q^{62} +(3.72262 + 2.39238i) q^{63} +(3.78668 - 7.04706i) q^{64} +(1.39971 + 2.17800i) q^{65} +(-0.0871421 - 1.02978i) q^{66} +(-2.30995 - 7.86698i) q^{67} +(-8.80688 + 2.83703i) q^{68} +(1.76909 - 4.45761i) q^{69} +(4.55684 - 6.25538i) q^{70} +(2.19649 + 7.48057i) q^{71} +(-1.09117 - 2.60947i) q^{72} +(-11.2800 + 7.24919i) q^{73} +(-6.06524 - 3.21006i) q^{74} +(2.91967 + 1.87636i) q^{75} +(0.230168 - 1.96237i) q^{76} +(-2.44387 - 2.11763i) q^{77} +(2.06606 - 2.12058i) q^{78} +(6.41315 + 14.0428i) q^{79} +(-4.66735 + 1.63886i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(8.28699 + 1.69002i) q^{82} +(8.31810 + 1.19596i) q^{83} +(-8.14340 - 3.46562i) q^{84} +(5.20421 + 2.37668i) q^{85} +(-3.80393 - 9.80682i) q^{86} +(-5.15405 + 0.741040i) q^{87} +(0.517896 + 2.00099i) q^{88} +(-11.8620 + 10.2785i) q^{89} +(-0.589800 + 1.64648i) q^{90} -9.26391i q^{91} +(-1.98974 + 9.38301i) q^{92} -1.56837i q^{93} +(-4.27370 - 1.53092i) q^{94} +(-0.923322 + 0.800063i) q^{95} +(3.02831 + 4.77800i) q^{96} +(3.23341 - 0.464894i) q^{97} +(-16.5885 + 6.43446i) q^{98} +(0.664729 + 0.303571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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