LMFDB - Embedded newform 507.2.k.k.80.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.7
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.339800 + 1.26815i) q^{2} +(-0.228800 + 1.71687i) q^{3} +(0.239309 + 0.138165i) q^{4} +(-2.12536 - 2.12536i) q^{5} +(-2.09951 - 0.873546i) q^{6} +(-2.82123 + 0.755945i) q^{7} +(-2.11323 + 2.11323i) q^{8} +(-2.89530 - 0.785641i) q^{9} +(3.41747 - 1.97308i) q^{10} +(2.57352 + 0.689573i) q^{11} +(-0.291966 + 0.379251i) q^{12} -3.83461i q^{14} +(4.13525 - 3.16269i) q^{15} +(-1.68549 - 2.91935i) q^{16} +(0.0994162 - 0.172194i) q^{17} +(1.98013 - 3.40472i) q^{18} +(-1.37337 - 5.12548i) q^{19} +(-0.214967 - 0.802269i) q^{20} +(-0.652364 - 5.01665i) q^{21} +(-1.74897 + 3.02930i) q^{22} +(-1.65038 - 2.85855i) q^{23} +(-3.14464 - 4.11166i) q^{24} +4.03430i q^{25} +(2.01129 - 4.79111i) q^{27} +(-0.779591 - 0.208891i) q^{28} +(-3.23258 + 1.86633i) q^{29} +(2.60561 + 6.31880i) q^{30} +(0.550550 - 0.550550i) q^{31} +(-1.49855 + 0.401535i) q^{32} +(-1.77273 + 4.26063i) q^{33} +(0.184586 + 0.184586i) q^{34} +(7.60277 + 4.38946i) q^{35} +(-0.584324 - 0.588041i) q^{36} +(-1.32066 + 4.92878i) q^{37} +6.96655 q^{38} +8.98276 q^{40} +(0.986066 - 3.68005i) q^{41} +(6.58353 + 0.877359i) q^{42} +(-10.0942 - 5.82790i) q^{43} +(0.520592 + 0.520592i) q^{44} +(4.48378 + 7.82332i) q^{45} +(4.18587 - 1.12160i) q^{46} +(-4.29586 + 4.29586i) q^{47} +(5.39780 - 2.22582i) q^{48} +(1.32568 - 0.765385i) q^{49} +(-5.11610 - 1.37086i) q^{50} +(0.272889 + 0.210083i) q^{51} +13.6276i q^{53} +(5.39241 + 4.17864i) q^{54} +(-4.00407 - 6.93525i) q^{55} +(4.36442 - 7.55939i) q^{56} +(9.11402 - 1.18519i) q^{57} +(-1.26836 - 4.73357i) q^{58} +(0.864088 + 3.22482i) q^{59} +(1.42658 - 0.185512i) q^{60} +(1.35047 - 2.33909i) q^{61} +(0.511103 + 0.885257i) q^{62} +(8.76220 + 0.0277830i) q^{63} -8.77879i q^{64} +(-4.80075 - 3.69585i) q^{66} +(-7.28944 - 1.95320i) q^{67} +(0.0475824 - 0.0274717i) q^{68} +(5.28537 - 2.17946i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(-5.16536 + 1.38405i) q^{71} +(7.77869 - 4.45820i) q^{72} +(3.46215 + 3.46215i) q^{73} +(-5.80168 - 3.34960i) q^{74} +(-6.92638 - 0.923049i) q^{75} +(0.379503 - 1.41633i) q^{76} -7.78177 q^{77} -11.1376 q^{79} +(-2.62241 + 9.78695i) q^{80} +(7.76554 + 4.54934i) q^{81} +(4.33179 + 2.50096i) q^{82} +(1.84014 + 1.84014i) q^{83} +(0.537009 - 1.29066i) q^{84} +(-0.577269 + 0.154679i) q^{85} +(10.8207 - 10.8207i) q^{86} +(-2.46463 - 5.97694i) q^{87} +(-6.89568 + 3.98122i) q^{88} +(-1.06120 - 0.284349i) q^{89} +(-11.4447 + 3.02775i) q^{90} -0.912102i q^{92} +(0.819258 + 1.07119i) q^{93} +(-3.98807 - 6.90753i) q^{94} +(-7.97458 + 13.8124i) q^{95} +(-0.346516 - 2.66469i) q^{96} +(3.14829 + 11.7496i) q^{97} +(0.520155 + 1.94125i) q^{98} +(-6.90936 - 4.01839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−0.339800	+	1.26815i	−0.240275	+	0.896718i	0.735425	+	0.677606i	$0.236983\pi$
$2$	−0.339800	+	1.26815i	−0.240275	+	0.896718i	−0.975700	+	0.219112i	$0.929684\pi$
$3$	−0.228800	+	1.71687i	−0.132098	+	0.991237i
$3$	−0.228800	+	1.71687i	−0.132098	+	0.991237i
$4$	0.239309	+	0.138165i	0.119655	+	0.0690826i
$5$	−2.12536	−	2.12536i	−0.950489	−	0.950489i	0.0483414	−	0.998831i	$-0.484606\pi$
$5$	−2.12536	−	2.12536i	−0.950489	−	0.950489i	−0.998831	+	0.0483414i	$0.984606\pi$
$6$	−2.09951	−	0.873546i	−0.857120	−	0.356624i
$7$	−2.82123	+	0.755945i	−1.06632	+	0.285720i	−0.748982	−	0.662591i	$-0.769457\pi$
$7$	−2.82123	+	0.755945i	−1.06632	+	0.285720i	−0.317342	+	0.948311i	$0.602790\pi$
$8$	−2.11323	+	2.11323i	−0.747141	+	0.747141i
$9$	−2.89530	−	0.785641i	−0.965100	−	0.261880i
$10$	3.41747	−	1.97308i	1.08070	−	0.623942i
$11$	2.57352	+	0.689573i	0.775946	+	0.207914i	0.624997	−	0.780627i	$-0.285100\pi$
$11$	2.57352	+	0.689573i	0.775946	+	0.207914i	0.150949	+	0.988541i	$0.451767\pi$
$12$	−0.291966	+	0.379251i	−0.0842833	+	0.109480i
$13$		0			0
$13$		0			0
$14$		−	3.83461i		−	1.02484i
$15$	4.13525	−	3.16269i	1.06772	−	0.816602i
$16$	−1.68549	−	2.91935i	−0.421373	−	0.729839i
$17$	0.0994162	−	0.172194i	0.0241120	−	0.0417632i	−0.853718	−	0.520736i	$-0.825658\pi$
$17$	0.0994162	−	0.172194i	0.0241120	−	0.0417632i	0.877830	+	0.478973i	$0.158991\pi$
$18$	1.98013	−	3.40472i	0.466722	−	0.802499i
$19$	−1.37337	−	5.12548i	−0.315072	−	1.17586i	−0.923922	−	0.382580i	$-0.875036\pi$
$19$	−1.37337	−	5.12548i	−0.315072	−	1.17586i	0.608850	−	0.793285i	$-0.291631\pi$
$20$	−0.214967	−	0.802269i	−0.0480681	−	0.179393i
$21$	−0.652364	−	5.01665i	−0.142358	−	1.09472i
$22$	−1.74897	+	3.02930i	−0.372881	+	0.645848i
$23$	−1.65038	−	2.85855i	−0.344129	−	0.596048i	0.641066	−	0.767485i	$-0.278492\pi$
$23$	−1.65038	−	2.85855i	−0.344129	−	0.596048i	−0.985195	+	0.171437i	$0.945159\pi$
$24$	−3.14464	−	4.11166i	−0.641897	−	0.839289i
$25$			4.03430i			0.806861i
$26$		0			0
$27$	2.01129	−	4.79111i	0.387073	−	0.922049i
$28$	−0.779591	−	0.208891i	−0.147329	−	0.0394766i
$29$	−3.23258	+	1.86633i	−0.600274	+	0.346568i	−0.769149	−	0.639069i	$-0.779320\pi$
$29$	−3.23258	+	1.86633i	−0.600274	+	0.346568i	0.168875	+	0.985637i	$0.445987\pi$
$30$	2.60561	+	6.31880i	0.475716	+	1.15365i
$31$	0.550550	−	0.550550i	0.0988817	−	0.0988817i	−0.655935	−	0.754817i	$-0.727726\pi$
$31$	0.550550	−	0.550550i	0.0988817	−	0.0988817i	0.754817	+	0.655935i	$0.227726\pi$
$32$	−1.49855	+	0.401535i	−0.264908	+	0.0709820i
$33$	−1.77273	+	4.26063i	−0.308593	+	0.741681i
$34$	0.184586	+	0.184586i	0.0316563	+	0.0316563i
$35$	7.60277	+	4.38946i	1.28510	+	0.741955i
$36$	−0.584324	−	0.588041i	−0.0973873	−	0.0980069i
$37$	−1.32066	+	4.92878i	−0.217116	+	0.810287i	0.768295	+	0.640096i	$0.221105\pi$
$37$	−1.32066	+	4.92878i	−0.217116	+	0.810287i	−0.985411	+	0.170191i	$0.945561\pi$
$38$	6.96655			1.13012
$39$		0			0
$40$	8.98276			1.42030
$41$	0.986066	−	3.68005i	0.153998	−	0.574727i	−0.845192	−	0.534464i	$-0.820514\pi$
$41$	0.986066	−	3.68005i	0.153998	−	0.574727i	0.999189	−	0.0402633i	$-0.0128197\pi$
$42$	6.58353	+	0.877359i	1.01586	+	0.135379i
$43$	−10.0942	−	5.82790i	−1.53936	−	0.888747i	−0.998876	−	0.0473894i	$-0.984910\pi$
$43$	−10.0942	−	5.82790i	−1.53936	−	0.888747i	−0.540479	−	0.841358i	$-0.681757\pi$
$44$	0.520592	+	0.520592i	0.0784823	+	0.0784823i
$45$	4.48378	+	7.82332i	0.668403	+	1.16623i
$46$	4.18587	−	1.12160i	0.617173	−	0.165371i
$47$	−4.29586	+	4.29586i	−0.626616	+	0.626616i	−0.947215	−	0.320599i	$-0.896116\pi$
$47$	−4.29586	+	4.29586i	−0.626616	+	0.626616i	0.320599	+	0.947215i	$0.396116\pi$
$48$	5.39780	−	2.22582i	0.779105	−	0.321270i
$49$	1.32568	−	0.765385i	0.189384	−	0.109341i
$50$	−5.11610	−	1.37086i	−0.723526	−	0.193868i
$51$	0.272889	+	0.210083i	0.0382120	+	0.0294175i
$52$		0			0
$53$			13.6276i			1.87189i	0.352142	+	0.935947i	$0.385454\pi$
$53$			13.6276i			1.87189i	−0.352142	+	0.935947i	$0.614546\pi$
$54$	5.39241	+	4.17864i	0.733814	+	0.568641i
$55$	−4.00407	−	6.93525i	−0.539908	−	0.935149i
$56$	4.36442	−	7.55939i	0.583220	−	1.01017i
$57$	9.11402	−	1.18519i	1.20718	−	0.156982i
$58$	−1.26836	−	4.73357i	−0.166543	−	0.621548i
$59$	0.864088	+	3.22482i	0.112495	+	0.419836i	0.999087	−	0.0427154i	$-0.0136009\pi$
$59$	0.864088	+	3.22482i	0.112495	+	0.419836i	−0.886593	+	0.462551i	$0.846934\pi$
$60$	1.42658	−	0.185512i	0.184170	−	0.0239495i
$61$	1.35047	−	2.33909i	0.172910	−	0.299489i	−0.766526	−	0.642213i	$-0.778016\pi$
$61$	1.35047	−	2.33909i	0.172910	−	0.299489i	0.939436	+	0.342724i	$0.111350\pi$
$62$	0.511103	+	0.885257i	0.0649102	+	0.112428i
$63$	8.76220	+	0.0277830i	1.10393	+	0.00350032i
$64$		−	8.77879i		−	1.09735i
$65$		0			0
$66$	−4.80075	−	3.69585i	−0.590932	−	0.454928i
$67$	−7.28944	−	1.95320i	−0.890547	−	0.238621i	−0.215595	−	0.976483i	$-0.569169\pi$
$67$	−7.28944	−	1.95320i	−0.890547	−	0.238621i	−0.674952	+	0.737862i	$0.735836\pi$
$68$	0.0475824	−	0.0274717i	0.00577022	−	0.00333144i
$69$	5.28537	−	2.17946i	0.636284	−	0.262376i
$70$	−8.14992	+	8.14992i	−0.974102	+	0.974102i
$71$	−5.16536	+	1.38405i	−0.613016	+	0.164257i	−0.551951	−	0.833877i	$-0.686116\pi$
$71$	−5.16536	+	1.38405i	−0.613016	+	0.164257i	−0.0610649	+	0.998134i	$0.519450\pi$
$72$	7.77869	−	4.45820i	0.916727	−	0.525404i
$73$	3.46215	+	3.46215i	0.405214	+	0.405214i	0.880066	−	0.474852i	$-0.157498\pi$
$73$	3.46215	+	3.46215i	0.405214	+	0.405214i	−0.474852	+	0.880066i	$0.657498\pi$
$74$	−5.80168	−	3.34960i	−0.674431	−	0.389383i
$75$	−6.92638	−	0.923049i	−0.799790	−	0.106585i
$76$	0.379503	−	1.41633i	0.0435320	−	0.162464i
$77$	−7.78177			−0.886815
$78$		0			0
$79$	−11.1376			−1.25308			−0.626540	−	0.779389i	$-0.715530\pi$
$79$	−11.1376			−1.25308			−0.626540	+	0.779389i	$0.715530\pi$
$80$	−2.62241	+	9.78695i	−0.293194	+	1.09421i
$81$	7.76554	+	4.54934i	0.862837	+	0.505482i
$82$	4.33179	+	2.50096i	0.478366	+	0.276185i
$83$	1.84014	+	1.84014i	0.201981	+	0.201981i	0.800848	−	0.598867i	$-0.204382\pi$
$83$	1.84014	+	1.84014i	0.201981	+	0.201981i	−0.598867	+	0.800848i	$0.704382\pi$
$84$	0.537009	−	1.29066i	0.0585925	−	0.140823i
$85$	−0.577269	+	0.154679i	−0.0626136	+	0.0167773i
$86$	10.8207	−	10.8207i	1.16682	−	1.16682i
$87$	−2.46463	−	5.97694i	−0.264236	−	0.640795i
$88$	−6.89568	+	3.98122i	−0.735082	+	0.424400i
$89$	−1.06120	−	0.284349i	−0.112487	−	0.0301409i	0.202136	−	0.979357i	$-0.435212\pi$
$89$	−1.06120	−	0.284349i	−0.112487	−	0.0301409i	−0.314624	+	0.949217i	$0.601878\pi$
$90$	−11.4447	+	3.02775i	−1.20638	+	0.319153i
$91$		0			0
$92$		−	0.912102i		−	0.0950932i
$93$	0.819258	+	1.07119i	0.0849531	+	0.111077i
$94$	−3.98807	−	6.90753i	−0.411338	−	0.712458i
$95$	−7.97458	+	13.8124i	−0.818175	+	1.41712i
$96$	−0.346516	−	2.66469i	−0.0353661	−	0.271964i
$97$	3.14829	+	11.7496i	0.319661	+	1.19299i	0.919571	+	0.392923i	$0.128536\pi$
$97$	3.14829	+	11.7496i	0.319661	+	1.19299i	−0.599911	+	0.800067i	$0.704797\pi$
$98$	0.520155	+	1.94125i	0.0525436	+	0.196095i
$99$	−6.90936	−	4.01839i	−0.694417	−	0.403863i
$100$	−0.557400	+	0.965446i	−0.0557400	+	0.0965446i
$101$	6.19691	+	10.7334i	0.616616	+	1.06801i	0.990099	+	0.140373i	$0.0448302\pi$
$101$	6.19691	+	10.7334i	0.616616	+	1.06801i	−0.373483	+	0.927637i	$0.621836\pi$
$102$	−0.359144	+	0.274678i	−0.0355606	+	0.0271971i
$103$			5.68798i			0.560453i	0.959934	+	0.280226i	$0.0904096\pi$
$103$			5.68798i			0.560453i	−0.959934	+	0.280226i	$0.909590\pi$
$104$		0			0
$105$	−9.27566	+	12.0487i	−0.905212	+	1.17583i
$106$	−17.2818	−	4.63065i	−1.67856	−	0.449769i
$107$	6.72785	−	3.88433i	0.650406	−	0.375512i	−0.138206	−	0.990404i	$-0.544134\pi$
$107$	6.72785	−	3.88433i	0.650406	−	0.375512i	0.788612	+	0.614891i	$0.210800\pi$
$108$	1.14328	−	0.868665i	0.110013	−	0.0835874i
$109$	−7.18355	+	7.18355i	−0.688060	+	0.688060i	−0.961803	−	0.273743i	$-0.911738\pi$
$109$	−7.18355	+	7.18355i	−0.688060	+	0.688060i	0.273743	+	0.961803i	$0.411738\pi$
$110$	10.1555	−	2.72116i	0.968291	−	0.259453i
$111$	−8.15992	−	3.39512i	−0.774506	−	0.322250i
$112$	6.96202	+	6.96202i	0.657849	+	0.657849i
$113$	−14.7985	−	8.54390i	−1.39212	−	0.803743i	−0.398573	−	0.917136i	$-0.630495\pi$
$113$	−14.7985	−	8.54390i	−1.39212	−	0.803743i	−0.993550	+	0.113394i	$0.963828\pi$
$114$	−1.59395	+	11.9607i	−0.149287	+	1.12022i
$115$	−2.56778	+	9.58310i	−0.239447	+	0.893628i
$116$	−1.03145			−0.0957674
$117$		0			0
$118$	−4.38317			−0.403504
$119$	−0.150306	+	0.560951i	−0.0137786	+	0.0514223i
$120$	−2.05526	+	15.4222i	−0.187618	+	1.40785i
$121$	−3.37877	−	1.95074i	−0.307161	−	0.177340i
$122$	2.50742	+	2.50742i	0.227011	+	0.227011i
$123$	6.09256	+	2.53494i	0.549348	+	0.228568i
$124$	0.207818	−	0.0556848i	0.0186627	−	0.00500064i
$125$	−2.05245	+	2.05245i	−0.183577	+	0.183577i
$126$	−3.01263	+	11.1023i	−0.268386	+	0.989076i
$127$	8.33573	−	4.81263i	0.739676	−	0.427052i	−0.0822755	−	0.996610i	$-0.526219\pi$
$127$	8.33573	−	4.81263i	0.739676	−	0.427052i	0.821952	+	0.569557i	$0.192885\pi$
$128$	8.13573	+	2.17996i	0.719103	+	0.192683i
$129$	12.3153	−	15.9971i	1.08430	−	1.40846i
$130$		0			0
$131$		−	11.9013i		−	1.03982i	−0.854221	−	0.519910i	$-0.825965\pi$
$131$		−	11.9013i		−	1.03982i	0.854221	−	0.519910i	$-0.174035\pi$
$132$	−1.01290	+	0.774679i	−0.0881618	+	0.0674272i
$133$	7.74916	+	13.4219i	0.671937	+	1.16383i
$134$	4.95390	−	8.58041i	0.427952	−	0.741234i
$135$	−14.4575	+	5.90811i	−1.24431	+	0.508489i
$136$	0.153796	+	0.573976i	0.0131879	+	0.0492180i
$137$	−4.50231	−	16.8029i	−0.384659	−	1.43557i	−0.838704	−	0.544587i	$-0.816686\pi$
$137$	−4.50231	−	16.8029i	−0.384659	−	1.43557i	0.454045	−	0.890979i	$-0.349980\pi$
$138$	0.967917	+	7.44322i	0.0823945	+	0.633609i
$139$	−1.16453	+	2.01702i	−0.0987737	+	0.171081i	−0.911177	−	0.412014i	$-0.864825\pi$
$139$	−1.16453	+	2.01702i	−0.0987737	+	0.171081i	0.812404	+	0.583096i	$0.198159\pi$
$140$	1.21294	+	2.10088i	0.102512	+	0.177557i
$141$	−6.39255	−	8.35834i	−0.538350	−	0.703899i
$142$		−	7.02076i		−	0.589169i
$143$		0			0
$144$	2.58644	+	9.77660i	0.215536	+	0.814717i
$145$	10.8370	+	2.90377i	0.899964	+	0.241145i
$146$	−5.56697	+	3.21409i	−0.460725	+	0.266000i
$147$	1.01075	+	2.45115i	0.0833653	+	0.202168i
$148$	−0.997033	+	0.997033i	−0.0819556	+	0.0819556i
$149$	15.2383	−	4.08308i	1.24837	−	0.334499i	0.426661	−	0.904412i	$-0.359690\pi$
$149$	15.2383	−	4.08308i	1.24837	−	0.334499i	0.821705	+	0.569913i	$0.193023\pi$
$150$	3.52415	−	8.47004i	0.287746	−	0.691576i
$151$	8.56897	+	8.56897i	0.697333	+	0.697333i	0.963834	−	0.266502i	$-0.0858678\pi$
$151$	8.56897	+	8.56897i	0.697333	+	0.697333i	−0.266502	+	0.963834i	$0.585868\pi$
$152$	13.7336	+	7.92908i	1.11394	+	0.643133i
$153$	−0.423123	+	0.420448i	−0.0342074	+	0.0339912i
$154$	2.64424	−	9.86845i	0.213079	−	0.795222i
$155$	−2.34023			−0.187972
$156$		0			0
$157$	−3.26731			−0.260759			−0.130380	−	0.991464i	$-0.541620\pi$
$157$	−3.26731			−0.260759			−0.130380	+	0.991464i	$0.541620\pi$
$158$	3.78456	−	14.1242i	0.301084	−	1.12366i
$159$	−23.3968	−	3.11800i	−1.85549	−	0.247273i
$160$	4.03836	+	2.33155i	0.319260	+	0.184325i
$161$	6.81701	+	6.81701i	0.537256	+	0.537256i
$162$	−8.40797	+	8.30200i	−0.660593	+	0.652267i
$163$	5.62972	−	1.50848i	0.440954	−	0.118153i	−0.0315098	−	0.999503i	$-0.510032\pi$
$163$	5.62972	−	1.50848i	0.440954	−	0.118153i	0.472463	+	0.881350i	$0.343365\pi$
$164$	0.744429	−	0.744429i	0.0581302	−	0.0581302i
$165$	12.8231	−	5.28769i	0.998275	−	0.411646i
$166$	−2.95885	+	1.70829i	−0.229651	+	0.132589i
$167$	1.52736	+	0.409254i	0.118190	+	0.0316690i	0.317429	−	0.948282i	$-0.397180\pi$
$167$	1.52736	+	0.409254i	0.118190	+	0.0316690i	−0.199239	+	0.979951i	$0.563847\pi$
$168$	11.9799	+	9.22274i	0.924272	+	0.711550i
$169$		0			0
$170$		−	0.784624i		−	0.0601779i
$171$	−0.0504748	+	15.9188i	−0.00385991	+	1.21734i
$172$	−1.61043	−	2.78934i	−0.122794	−	0.212685i
$173$	−6.21160	+	10.7588i	−0.472259	+	0.817977i	−0.999496	−	0.0317413i	$-0.989895\pi$
$173$	−6.21160	+	10.7588i	−0.472259	+	0.817977i	0.527237	+	0.849718i	$0.323228\pi$
$174$	8.41714	−	1.09456i	0.638101	−	0.0829787i
$175$	−3.04971	−	11.3817i	−0.230537	−	0.860374i
$176$	−2.32454	−	8.67529i	−0.175219	−	0.653925i
$177$	−5.73431	+	0.745689i	−0.431017	+	0.0560494i
$178$	0.721194	−	1.24914i	0.0540557	−	0.0936273i
$179$	−8.15142	−	14.1187i	−0.609265	−	1.05528i	−0.991362	−	0.131156i	$-0.958131\pi$
$179$	−8.15142	−	14.1187i	−0.609265	−	1.05528i	0.382096	−	0.924123i	$-0.375202\pi$
$180$	−0.00790061	+	2.49170i	−0.000588876	+	0.185720i
$181$			9.29621i			0.690982i	0.938422	+	0.345491i	$0.112288\pi$
$181$			9.29621i			0.690982i	−0.938422	+	0.345491i	$0.887712\pi$
$182$		0			0
$183$	3.70692	+	2.85377i	0.274024	+	0.210957i
$184$	9.52842	+	2.55313i	0.702444	+	0.188219i
$185$	13.2823	−	7.66855i	0.976535	−	0.563803i
$186$	−1.63681	+	0.674952i	−0.120017	+	0.0494899i
$187$	0.374590	−	0.374590i	0.0273928	−	0.0273928i
$188$	−1.62158	+	0.434500i	−0.118266	+	0.0316892i
$189$	−2.05249	+	15.0372i	−0.149297	+	1.09380i
$190$	−14.8064	−	14.8064i	−1.07417	−	1.07417i
$191$	−1.75656	−	1.01415i	−0.127100	−	0.0733813i	0.435102	−	0.900381i	$-0.356712\pi$
$191$	−1.75656	−	1.01415i	−0.127100	−	0.0733813i	−0.562202	+	0.827000i	$0.690046\pi$
$192$	15.0721	+	2.00859i	1.08773	+	0.144957i
$193$	−1.02822	+	3.83737i	−0.0740130	+	0.276220i	−0.993008	−	0.118050i	$-0.962336\pi$
$193$	−1.02822	+	3.83737i	−0.0740130	+	0.276220i	0.918995	+	0.394270i	$0.129002\pi$
$194$	−15.9700			−1.14658
$195$		0			0
$196$	0.422998			0.0302142
$197$	1.78323	−	6.65511i	0.127050	−	0.474157i	−0.872855	−	0.487981i	$-0.837734\pi$
$197$	1.78323	−	6.65511i	0.127050	−	0.474157i	0.999904	+	0.0138237i	$0.00440036\pi$
$198$	7.44372	−	7.39667i	0.529002	−	0.525658i
$199$	−5.49109	−	3.17028i	−0.389253	−	0.224735i	0.292584	−	0.956240i	$-0.405485\pi$
$199$	−5.49109	−	3.17028i	−0.389253	−	0.224735i	−0.681836	+	0.731505i	$0.738818\pi$
$200$	−8.52542	−	8.52542i	−0.602838	−	0.602838i
$201$	5.02122	−	12.0681i	0.354169	−	0.851221i
$202$	−15.7172	+	4.21142i	−1.10586	+	0.296315i
$203$	7.70898	−	7.70898i	0.541065	−	0.541065i
$204$	0.0362786	+	0.0879785i	0.00254001	+	0.00615973i
$205$	−9.91717	+	5.72568i	−0.692645	+	0.399899i
$206$	−7.21321	−	1.93277i	−0.502568	−	0.134663i
$207$	2.53256	+	9.57296i	0.176025	+	0.665367i
$208$		0			0
$209$		−	14.1376i		−	0.977916i
$210$	−12.1277	−	15.8571i	−0.836889	−	1.09424i
$211$	0.401137	+	0.694790i	0.0276154	+	0.0478313i	0.879503	−	0.475894i	$-0.157875\pi$
$211$	0.401137	+	0.694790i	0.0276154	+	0.0478313i	−0.851887	+	0.523725i	$0.824542\pi$
$212$	−1.88286	+	3.26121i	−0.129315	+	0.223981i
$213$	−1.19441	−	9.18494i	−0.0818396	−	0.629342i
$214$	2.63979	+	9.85182i	0.180452	+	0.673457i
$215$	9.06747	+	33.8402i	0.618396	+	2.30789i
$216$	5.87440	+	14.3751i	0.399702	+	0.978098i
$217$	−1.13704	+	1.96941i	−0.0771873	+	0.133692i
$218$	−6.66886	−	11.5508i	−0.451672	−	0.782319i
$219$	−6.73621	+	5.15193i	−0.455191	+	0.348135i
$220$		−	2.21289i		−	0.149193i
$221$		0			0
$222$	7.07826	−	9.19435i	0.475062	−	0.617084i
$223$	−2.98478	−	0.799768i	−0.199875	−	0.0535565i	0.157492	−	0.987520i	$-0.449659\pi$
$223$	−2.98478	−	0.799768i	−0.199875	−	0.0535565i	−0.357368	+	0.933964i	$0.616326\pi$
$224$	3.92421	−	2.26564i	0.262197	−	0.151380i
$225$	3.16952	−	11.6805i	0.211301	−	0.778701i
$226$	15.8635	−	15.8635i	1.05522	−	1.05522i
$227$	−25.0314	+	6.70715i	−1.66139	+	0.445169i	−0.962770	−	0.270320i	$-0.912870\pi$
$227$	−25.0314	+	6.70715i	−1.66139	+	0.445169i	−0.698624	+	0.715489i	$0.746204\pi$
$228$	2.34482	+	0.975614i	0.155289	+	0.0646116i
$229$	−19.6410	−	19.6410i	−1.29791	−	1.29791i	−0.929768	−	0.368147i	$-0.879992\pi$
$229$	−19.6410	−	19.6410i	−1.29791	−	1.29791i	−0.368147	−	0.929768i	$-0.620008\pi$
$230$	−11.2803	−	6.51267i	−0.743799	−	0.429433i
$231$	1.78047	−	13.3603i	0.117146	−	0.879043i
$232$	2.88720	−	10.7752i	0.189554	−	0.707425i
$233$	14.4551			0.946988			0.473494	−	0.880797i	$-0.342993\pi$
$233$	14.4551			0.946988			0.473494	+	0.880797i	$0.342993\pi$
$234$		0			0
$235$	18.2605			1.19118
$236$	−0.238774	+	0.891116i	−0.0155428	+	0.0580067i
$237$	2.54829	−	19.1219i	0.165529	−	1.24210i
$238$	−0.660297	−	0.381222i	−0.0428007	−	0.0247110i
$239$	4.24248	+	4.24248i	0.274423	+	0.274423i	0.830878	−	0.556455i	$-0.187839\pi$
$239$	4.24248	+	4.24248i	0.274423	+	0.274423i	−0.556455	+	0.830878i	$0.687839\pi$
$240$	−16.2029	−	6.74159i	−1.04590	−	0.435168i
$241$	23.8375	−	6.38724i	1.53551	−	0.411438i	0.610697	−	0.791864i	$-0.290889\pi$
$241$	23.8375	−	6.38724i	1.53551	−	0.411438i	0.924811	+	0.380426i	$0.124223\pi$
$242$	3.62193	−	3.62193i	0.232827	−	0.232827i
$243$	−9.58739	+	12.2915i	−0.615031	+	0.788503i
$244$	0.646361	−	0.373177i	0.0413790	−	0.0238902i
$245$	−4.44427	−	1.19084i	−0.283934	−	0.0760799i
$246$	−5.28494	+	6.86491i	−0.336956	+	0.437691i
$247$		0			0
$248$			2.32688i			0.147757i
$249$	−3.58031	+	2.73826i	−0.226893	+	0.173530i
$250$	−1.90540	−	3.30024i	−0.120508	−	0.208726i
$251$	10.8649	−	18.8186i	0.685789	−	1.18782i	−0.287400	−	0.957811i	$-0.592791\pi$
$251$	10.8649	−	18.8186i	0.685789	−	1.18782i	0.973188	−	0.230010i	$-0.0738759\pi$
$252$	2.09304	+	1.21728i	0.131849	+	0.0766814i
$253$	−2.27612	−	8.49459i	−0.143098	−	0.534051i
$254$	3.27066	+	12.2063i	0.205220	+	0.765891i
$255$	−0.133484	−	1.02649i	−0.00835912	−	0.0642812i
$256$	3.24975	−	5.62873i	0.203109	−	0.351796i
$257$	8.15559	+	14.1259i	0.508732	+	0.881149i	0.999949	+	0.0101119i	$0.00321879\pi$
$257$	8.15559	+	14.1259i	0.508732	+	0.881149i	−0.491217	+	0.871037i	$0.663448\pi$
$258$	16.1019	+	21.0535i	1.00246	+	1.31073i
$259$		−	14.9036i		−	0.926062i
$260$		0			0
$261$	10.8255	−	2.86394i	0.670084	−	0.177273i
$262$	15.0926	+	4.04406i	0.932426	+	0.249843i
$263$	−9.95602	+	5.74811i	−0.613914	+	0.354444i	−0.774496	−	0.632579i	$-0.781996\pi$
$263$	−9.95602	+	5.74811i	−0.613914	+	0.354444i	0.160582	+	0.987023i	$0.448663\pi$
$264$	−5.25752	−	12.7499i	−0.323578	−	0.784702i
$265$	28.9635	−	28.9635i	1.77922	−	1.77922i
$266$	−19.6542	+	5.26633i	−1.20508	+	0.322899i
$267$	0.730994	−	1.75689i	0.0447361	−	0.107520i
$268$	−1.47457	−	1.47457i	−0.0900734	−	0.0900734i
$269$	9.64658	+	5.56946i	0.588162	+	0.339576i	0.764371	−	0.644777i	$-0.223050\pi$
$269$	9.64658	+	5.56946i	0.588162	+	0.339576i	−0.176208	+	0.984353i	$0.556383\pi$
$270$	−2.57970	−	20.3419i	−0.156995	−	1.23797i
$271$	−1.57276	+	5.86962i	−0.0955383	+	0.356554i	−0.997101	−	0.0760956i	$-0.975755\pi$
$271$	−1.57276	+	5.86962i	−0.0955383	+	0.356554i	0.901562	+	0.432650i	$0.142421\pi$
$272$	−0.670260			−0.0406405
$273$		0			0
$274$	22.8384			1.37972
$275$	−2.78195	+	10.3824i	−0.167758	+	0.626080i
$276$	1.56596	+	0.208689i	0.0942599	+	0.0125616i
$277$	24.0591	+	13.8905i	1.44557	+	0.834600i	0.998213	−	0.0597558i	$-0.0190322\pi$
$277$	24.0591	+	13.8905i	1.44557	+	0.834600i	0.447356	+	0.894356i	$0.352366\pi$
$278$	−2.16218	−	2.16218i	−0.129679	−	0.129679i
$279$	−2.02654	+	1.16147i	−0.121326	+	0.0695356i
$280$	−25.3424	+	6.79047i	−1.51450	+	0.405808i
$281$	−11.6187	+	11.6187i	−0.693113	+	0.693113i	−0.962916	−	0.269803i	$-0.913042\pi$
$281$	−11.6187	+	11.6187i	−0.693113	+	0.693113i	0.269803	+	0.962916i	$0.413042\pi$
$282$	12.7718	−	5.26655i	0.760551	−	0.313619i
$283$	23.0251	−	13.2935i	1.36870	−	0.790219i	0.377938	−	0.925831i	$-0.376633\pi$
$283$	23.0251	−	13.2935i	1.36870	−	0.790219i	0.990762	+	0.135612i	$0.0432999\pi$
$284$	−1.42735	−	0.382456i	−0.0846974	−	0.0226946i
$285$	−21.8895	−	16.8516i	−1.29662	−	0.998203i
$286$		0			0
$287$			11.1277i			0.656845i
$288$	4.65421	+	0.0147574i	0.274252	+	0.000869591i
$289$	8.48023	+	14.6882i	0.498837	+	0.864011i
$290$	−7.36482	+	12.7563i	−0.432477	+	0.749073i
$291$	−20.8929	+	2.71691i	−1.22476	+	0.159268i
$292$	0.350176	+	1.30687i	0.0204925	+	0.0764790i
$293$	−0.749260	−	2.79628i	−0.0437722	−	0.163360i	0.940580	−	0.339572i	$-0.110282\pi$
$293$	−0.749260	−	2.79628i	−0.0437722	−	0.163360i	−0.984352	+	0.176212i	$0.943616\pi$
$294$	−3.45188	+	0.448883i	−0.201318	+	0.0261794i
$295$	5.01740	−	8.69039i	0.292124	−	0.505974i
$296$	−7.62480	−	13.2065i	−0.443182	−	0.767614i
$297$	8.47992	−	10.9431i	0.492055	−	0.634982i
$298$			20.7118i			1.19980i
$299$		0			0
$300$	−1.53001	−	1.17788i	−0.0883354	−	0.0680049i
$301$	32.8837	+	8.81115i	1.89538	+	0.507866i
$302$	−13.7785	+	7.95501i	−0.792862	+	0.457759i
$303$	−19.8457	+	8.18351i	−1.14010	+	0.470131i
$304$	−12.6483	+	12.6483i	−0.725429	+	0.725429i
$305$	−7.84164	+	2.10116i	−0.449011	+	0.120312i
$306$	−0.389414	−	0.679451i	−0.0222613	−	0.0388416i
$307$	13.9565	+	13.9565i	0.796541	+	0.796541i	0.982548	−	0.186007i	$-0.0595549\pi$
$307$	13.9565	+	13.9565i	0.796541	+	0.796541i	−0.186007	+	0.982548i	$0.559555\pi$
$308$	−1.86225	−	1.07517i	−0.106111	−	0.0612635i
$309$	−9.76553	−	1.30141i	−0.555541	−	0.0740346i
$310$	0.795211	−	2.96777i	0.0451649	−	0.168558i
$311$	26.9755			1.52964			0.764821	−	0.644243i	$-0.222828\pi$
$311$	26.9755			1.52964			0.764821	+	0.644243i	$0.222828\pi$
$312$		0			0
$313$	−23.9660			−1.35464			−0.677320	−	0.735689i	$-0.736859\pi$
$313$	−23.9660			−1.35464			−0.677320	+	0.735689i	$0.736859\pi$
$314$	1.11023	−	4.14344i	0.0626539	−	0.233828i
$315$	−18.5638	−	18.6819i	−1.04595	−	1.05260i
$316$	−2.66533	−	1.53883i	−0.149937	−	0.0865660i
$317$	−21.6899	−	21.6899i	−1.21823	−	1.21823i	−0.968253	−	0.249973i	$-0.919578\pi$
$317$	−21.6899	−	21.6899i	−1.21823	−	1.21823i	−0.249973	−	0.968253i	$-0.580422\pi$
$318$	11.9043	−	28.6112i	0.667562	−	1.60444i
$319$	−9.60608	+	2.57394i	−0.537837	+	0.144113i
$320$	−18.6581	+	18.6581i	−1.04302	+	1.04302i
$321$	5.12956	+	12.4396i	0.286304	+	0.694311i
$322$	−10.9614	+	6.32857i	−0.610856	+	0.352678i
$323$	−1.01911	−	0.273070i	−0.0567049	−	0.0151940i
$324$	1.22980	+	2.16162i	0.0683224	+	0.120090i
$325$		0			0
$326$			7.65191i			0.423800i
$327$	−10.6896	−	13.9768i	−0.591139	−	0.772921i
$328$	5.69301	+	9.86058i	0.314344	+	0.544460i
$329$	8.87216	−	15.3670i	0.489138	−	0.847212i
$330$	2.34831	+	18.0583i	0.129270	+	0.994079i
$331$	0.171746	+	0.640966i	0.00944003	+	0.0352307i	0.970485	−	0.241161i	$-0.0775281\pi$
$331$	0.171746	+	0.640966i	0.00944003	+	0.0352307i	−0.961045	+	0.276391i	$0.910861\pi$
$332$	0.186119	+	0.694605i	0.0102146	+	0.0381214i
$333$	7.69597	−	13.2327i	0.421737	−	0.725150i
$334$	−1.03799	+	1.79785i	−0.0567964	+	0.0983742i
$335$	11.3414	+	19.6439i	0.619648	+	1.07326i
$336$	−13.5458	+	10.3600i	−0.738985	+	0.565184i
$337$			25.0872i			1.36659i	0.730143	+	0.683294i	$0.239453\pi$
$337$			25.0872i			1.36659i	−0.730143	+	0.683294i	$0.760547\pi$
$338$		0			0
$339$	18.0547	−	23.4522i	0.980596	−	1.27375i
$340$	−0.159517	−	0.0427425i	−0.00865103	−	0.00231804i
$341$	1.79650	−	1.03721i	0.0972858	−	0.0561680i
$342$	−20.1702	−	5.47321i	−1.09068	−	0.295957i
$343$	11.2955	−	11.2955i	0.609900	−	0.609900i
$344$	33.6472	−	9.01573i	1.81413	−	0.486096i
$345$	−15.8654	−	6.60117i	−0.854167	−	0.355395i
$346$	−11.5331	−	11.5331i	−0.620023	−	0.620023i
$347$	14.2117	+	8.20511i	0.762923	+	0.440474i	0.830344	−	0.557251i	$-0.188144\pi$
$347$	14.2117	+	8.20511i	0.762923	+	0.440474i	−0.0674214	+	0.997725i	$0.521477\pi$
$348$	0.235995	−	1.77086i	0.0126507	−	0.0949282i
$349$	7.75800	−	28.9532i	0.415276	−	1.54983i	−0.369006	−	0.929427i	$-0.620302\pi$
$349$	7.75800	−	28.9532i	0.415276	−	1.54983i	0.784282	−	0.620405i	$-0.213032\pi$
$350$	15.4700			0.826905
$351$		0			0
$352$	−4.13344			−0.220313
$353$	1.74394	−	6.50846i	0.0928203	−	0.346410i	−0.903860	−	0.427829i	$-0.859279\pi$
$353$	1.74394	−	6.50846i	0.0928203	−	0.346410i	0.996680	+	0.0814189i	$0.0259452\pi$
$354$	1.00287	−	7.52535i	0.0533020	−	0.399968i
$355$	13.9199	+	8.03664i	0.738790	+	0.426540i
$356$	−0.214669	−	0.214669i	−0.0113774	−	0.0113774i
$357$	−0.928692	−	0.386403i	−0.0491516	−	0.0204506i
$358$	20.6744	−	5.53970i	1.09268	−	0.292782i
$359$	6.76884	−	6.76884i	0.357246	−	0.357246i	−0.505551	−	0.862797i	$-0.668711\pi$
$359$	6.76884	−	6.76884i	0.357246	−	0.357246i	0.862797	+	0.505551i	$0.168711\pi$
$360$	−26.0078	−	7.05723i	−1.37073	−	0.371948i
$361$	−7.92989	+	4.57832i	−0.417363	+	0.240964i
$362$	−11.7890	−	3.15885i	−0.619616	−	0.166025i
$363$	4.12223	−	5.35459i	0.216361	−	0.281043i
$364$		0			0
$365$		−	14.7166i		−	0.770303i
$366$	−4.87862	+	3.73123i	−0.255010	+	0.195034i
$367$	6.01337	+	10.4155i	0.313895	+	0.543682i	0.979202	−	0.202888i	$-0.0650326\pi$
$367$	6.01337	+	10.4155i	0.313895	+	0.543682i	−0.665307	+	0.746570i	$0.731699\pi$
$368$	−5.56341	+	9.63611i	−0.290013	+	0.502317i
$369$	−5.74615	+	9.88015i	−0.299133	+	0.514340i
$370$	5.21154	+	19.4497i	0.270935	+	1.01114i
$371$	−10.3017	−	38.4465i	−0.534838	−	1.99604i
$372$	0.0480548	+	0.369539i	0.00249152	+	0.0191597i
$373$	−6.67932	+	11.5689i	−0.345842	+	0.599016i	−0.985506	−	0.169638i	$-0.945740\pi$
$373$	−6.67932	+	11.5689i	−0.345842	+	0.599016i	0.639664	+	0.768654i	$0.279073\pi$
$374$	0.347751	+	0.602323i	0.0179818	+	0.0311454i
$375$	−3.05420	−	3.99340i	−0.157718	−	0.206218i
$376$		−	18.1563i		−	0.936340i
$377$		0			0
$378$	−18.3720	−	7.71252i	−0.944955	−	0.396689i
$379$	−29.9123	−	8.01497i	−1.53649	−	0.411701i	−0.611360	−	0.791352i	$-0.709377\pi$
$379$	−29.9123	−	8.01497i	−1.53649	−	0.411701i	−0.925130	+	0.379651i	$0.876044\pi$
$380$	−3.81678	+	2.20362i	−0.195797	+	0.113043i
$381$	6.35546	+	15.4125i	0.325600	+	0.789607i
$382$	1.88297	−	1.88297i	0.0963413	−	0.0963413i
$383$	9.90441	−	2.65388i	0.506092	−	0.135607i	0.00326604	−	0.999995i	$-0.498960\pi$
$383$	9.90441	−	2.65388i	0.506092	−	0.135607i	0.502826	+	0.864388i	$0.332294\pi$
$384$	−5.60417	+	13.4692i	−0.285987	+	0.687349i
$385$	16.5390	+	16.5390i	0.842908	+	0.842908i
$386$	−4.51698	−	2.60788i	−0.229908	−	0.132738i
$387$	24.6472	+	24.8040i	1.25289	+	1.26086i
$388$	−0.869969	+	3.24677i	−0.0441660	+	0.164830i
$389$	−30.1074			−1.52650			−0.763252	−	0.646101i	$-0.776398\pi$
$389$	−30.1074			−1.52650			−0.763252	+	0.646101i	$0.776398\pi$
$390$		0			0
$391$	−0.656299			−0.0331905
$392$	−1.18405	+	4.41892i	−0.0598033	+	0.223189i
$393$	20.4330	+	2.72302i	1.03071	+	0.137358i
$394$	7.83374	+	4.52281i	0.394658	+	0.227856i
$395$	23.6714	+	23.6714i	1.19104	+	1.19104i
$396$	−1.09827	−	1.91627i	−0.0551903	−	0.0962962i
$397$	−3.31510	+	0.888280i	−0.166380	+	0.0445815i	−0.341048	−	0.940046i	$-0.610782\pi$
$397$	−3.31510	+	0.888280i	−0.166380	+	0.0445815i	0.174667	+	0.984628i	$0.444115\pi$
$398$	5.88626	−	5.88626i	0.295052	−	0.295052i
$399$	−24.8168	+	10.2334i	−1.24239	+	0.512310i
$400$	11.7776	−	6.79978i	0.588878	−	0.339989i
$401$	19.2725	+	5.16404i	0.962421	+	0.257880i	0.705625	−	0.708586i	$-0.250666\pi$
$401$	19.2725	+	5.16404i	0.962421	+	0.257880i	0.256796	+	0.966466i	$0.417333\pi$
$402$	13.5980	+	10.4684i	0.678207	+	0.522117i
$403$		0			0
$404$			3.42479i			0.170390i
$405$	−6.83558	−	26.1735i	−0.339663	−	1.30057i
$406$	7.15664	+	12.3957i	0.355178	+	0.615186i
$407$	−6.79751	+	11.7736i	−0.336940	+	0.583598i
$408$	−1.02063	+	0.132723i	−0.0505288	+	0.00657076i
$409$	1.43417	+	5.35240i	0.0709152	+	0.264659i	0.992276	−	0.124049i	$-0.0395881\pi$
$409$	1.43417	+	5.35240i	0.0709152	+	0.264659i	−0.921361	+	0.388708i	$0.872921\pi$
$410$	−3.89117	−	14.5220i	−0.192171	−	0.717193i
$411$	29.8785	−	3.88540i	1.47380	−	0.191653i
$412$	−0.785880	+	1.36118i	−0.0387175	+	0.0670608i
$413$	−4.87557	−	8.44474i	−0.239911	−	0.415538i
$414$	−13.0005	−	0.0412217i	−0.638941	−	0.00202594i
$415$		−	7.82191i		−	0.383962i
$416$		0			0
$417$	−3.19652	−	2.46083i	−0.156534	−	0.120508i
$418$	17.9286	+	4.80394i	0.876914	+	0.234969i
$419$	−29.8207	+	17.2170i	−1.45684	+	0.841106i	−0.998854	−	0.0478553i	$-0.984761\pi$
$419$	−29.8207	+	17.2170i	−1.45684	+	0.841106i	−0.457983	+	0.888961i	$0.651428\pi$
$420$	−3.88446	+	1.60179i	−0.189542	+	0.0781591i
$421$	−18.6143	+	18.6143i	−0.907208	+	0.907208i	−0.996046	−	0.0888383i	$-0.971685\pi$
$421$	−18.6143	+	18.6143i	−0.907208	+	0.907208i	0.0888383	+	0.996046i	$0.471685\pi$
$422$	−1.01740	+	0.272613i	−0.0495265	+	0.0132706i
$423$	15.8128	−	9.06281i	0.768846	−	0.440649i
$424$	−28.7983	−	28.7983i	−1.39857	−	1.39857i
$425$	0.694683	+	0.401075i	0.0336971	+	0.0194550i
$426$	12.0537	+	1.60635i	0.584006	+	0.0778279i
$427$	−2.04177	+	7.61997i	−0.0988080	+	0.368756i
$428$	2.14672			0.103765
$429$		0			0
$430$	−45.9956			−2.21811
$431$	−2.92686	+	10.9232i	−0.140982	+	0.526152i	0.858919	+	0.512111i	$0.171136\pi$
$431$	−2.92686	+	10.9232i	−0.140982	+	0.526152i	−0.999901	+	0.0140414i	$0.995530\pi$
$432$	−17.3770	+	2.20369i	−0.836049	+	0.106025i
$433$	5.37469	+	3.10308i	0.258291	+	0.149124i	0.623555	−	0.781780i	$-0.285688\pi$
$433$	5.37469	+	3.10308i	0.258291	+	0.149124i	−0.365264	+	0.930904i	$0.619021\pi$
$434$	−2.11114	−	2.11114i	−0.101338	−	0.101338i
$435$	−7.46490	+	17.9414i	−0.357915	+	0.860223i
$436$	−2.71161	+	0.726573i	−0.129862	+	0.0347965i
$437$	−12.3848	+	12.3848i	−0.592447	+	0.592447i
$438$	−4.24446	−	10.2932i	−0.202808	−	0.491826i
$439$	−33.5869	+	19.3914i	−1.60301	+	0.925501i	−0.612135	+	0.790753i	$0.709689\pi$
$439$	−33.5869	+	19.3914i	−1.60301	+	0.925501i	−0.990880	+	0.134748i	$0.956978\pi$
$440$	23.1173	+	6.19427i	1.10208	+	0.295300i
$441$	−4.43957	+	1.17451i	−0.211408	+	0.0559288i
$442$		0			0
$443$			18.3132i			0.870087i	0.900409	+	0.435043i	$0.143267\pi$
$443$			18.3132i			0.870087i	−0.900409	+	0.435043i	$0.856733\pi$
$444$	−1.48366	−	1.93990i	−0.0704113	−	0.0920636i
$445$	1.65110	+	2.85978i	0.0782694	+	0.135567i
$446$	2.02845	−	3.51338i	0.0960500	−	0.166364i
$447$	3.52361	+	27.0963i	0.166661	+	1.28161i
$448$	6.63628	+	24.7669i	0.313535	+	1.17013i
$449$	0.501884	+	1.87306i	0.0236854	+	0.0883950i	0.976757	−	0.214350i	$-0.0687635\pi$
$449$	0.501884	+	1.87306i	0.0236854	+	0.0883950i	−0.953071	+	0.302745i	$0.902097\pi$
$450$	13.7357	+	7.98846i	0.647505	+	0.376580i
$451$	5.07532	−	8.79072i	0.238988	−	0.413939i
$452$	−2.36094	−	4.08927i	−0.111049	−	0.192343i
$453$	−16.6724	+	12.7512i	−0.783338	+	0.599106i
$454$		−	34.0227i		−	1.59676i
$455$		0			0
$456$	−16.7555	+	21.7646i	−0.784646	+	1.01922i
$457$	5.62868	+	1.50820i	0.263299	+	0.0705507i	0.388053	−	0.921637i	$-0.373148\pi$
$457$	5.62868	+	1.50820i	0.263299	+	0.0705507i	−0.124755	+	0.992188i	$0.539814\pi$
$458$	31.5818	−	18.2337i	1.47572	−	0.852007i
$459$	−0.625045	−	0.822646i	−0.0291746	−	0.0383978i
$460$	−1.93854	+	1.93854i	−0.0903851	+	0.0903851i
$461$	13.8221	−	3.70361i	0.643758	−	0.172494i	0.0778529	−	0.996965i	$-0.475194\pi$
$461$	13.8221	−	3.70361i	0.643758	−	0.172494i	0.565905	+	0.824470i	$0.308527\pi$
$462$	16.3379	+	6.79773i	0.760106	+	0.316259i
$463$	2.99038	+	2.99038i	0.138975	+	0.138975i	0.773172	−	0.634197i	$-0.218669\pi$
$463$	2.99038	+	2.99038i	0.138975	+	0.138975i	−0.634197	+	0.773172i	$0.718669\pi$
$464$	10.8969	+	6.29136i	0.505878	+	0.292069i
$465$	0.535446	−	4.01788i	0.0248307	−	0.186325i
$466$	−4.91185	+	18.3313i	−0.227537	+	0.849181i
$467$	−37.5105			−1.73578			−0.867888	−	0.496759i	$-0.834523\pi$
$467$	−37.5105			−1.73578			−0.867888	+	0.496759i	$0.834523\pi$
$468$		0			0
$469$	22.0417			1.01779
$470$	−6.20491	+	23.1571i	−0.286211	+	1.06816i
$471$	0.747560	−	5.60955i	0.0344458	−	0.258474i
$472$	−8.64081	−	4.98877i	−0.397726	−	0.229627i
$473$	−21.9589	−	21.9589i	−1.00967	−	1.00967i
$474$	23.3835	+	9.72922i	1.07404	+	0.446878i
$475$	20.6777	−	5.54058i	0.948759	−	0.254219i
$476$	−0.113474	+	0.113474i	−0.00520106	+	0.00520106i
$477$	10.7064	−	39.4560i	0.490212	−	1.80656i
$478$	−6.82169	+	3.93851i	−0.312017	+	0.180143i
$479$	1.97272	+	0.528588i	0.0901358	+	0.0241518i	0.303605	−	0.952798i	$-0.401810\pi$
$479$	1.97272	+	0.528588i	0.0901358	+	0.0241518i	−0.213469	+	0.976950i	$0.568476\pi$
$480$	−4.92695	+	6.39989i	−0.224883	+	0.292114i
$481$		0			0
$482$			32.3999i			1.47578i
$483$	−13.2637	+	10.1442i	−0.603518	+	0.461577i
$484$	−0.539048	−	0.933658i	−0.0245022	−	0.0424390i
$485$	18.2808	−	31.6633i	0.830090	−	1.43776i
$486$	−12.3297	−	16.3349i	−0.559288	−	0.740967i
$487$	−6.49144	−	24.2264i	−0.294155	−	1.09780i	−0.941886	−	0.335933i	$-0.890948\pi$
$487$	−6.49144	−	24.2264i	−0.294155	−	1.09780i	0.647731	−	0.761869i	$-0.275718\pi$
$488$	2.08917	+	7.79690i	0.0945724	+	0.352949i
$489$	1.30178	+	10.0106i	0.0588687	+	0.452697i
$490$	3.02033	−	5.23136i	0.136444	−	0.236329i
$491$	−3.76608	−	6.52305i	−0.169961	−	0.294381i	0.768445	−	0.639916i	$-0.221031\pi$
$491$	−3.76608	−	6.52305i	−0.169961	−	0.294381i	−0.938406	+	0.345535i	$0.887698\pi$
$492$	1.10776	+	1.44842i	0.0499419	+	0.0652996i
$493$			0.742173i			0.0334258i
$494$		0			0
$495$	6.14436	+	23.2254i	0.276169	+	1.04390i
$496$	−2.53520	−	0.679304i	−0.113834	−	0.0305016i
$497$	13.5264	−	7.80946i	0.606741	−	0.350302i
$498$	−2.25594	−	5.47083i	−0.101091	−	0.245154i
$499$	−8.71539	+	8.71539i	−0.390154	+	0.390154i	−0.874742	−	0.484588i	$-0.838970\pi$
$499$	−8.71539	+	8.71539i	−0.390154	+	0.390154i	0.484588	+	0.874742i	$0.338970\pi$
$500$	−0.774749	+	0.207593i	−0.0346478	+	0.00928385i
$501$	−1.05210	+	2.52864i	−0.0470042	+	0.112971i
$502$	20.1729	+	20.1729i	0.900362	+	0.900362i
$503$	2.03490	+	1.17485i	0.0907316	+	0.0523839i	0.544679	−	0.838644i	$-0.316651\pi$
$503$	2.03490	+	1.17485i	0.0907316	+	0.0523839i	−0.453948	+	0.891028i	$0.649985\pi$
$504$	−18.5753	+	18.4579i	−0.827409	+	0.822178i
$505$	9.64160	−	35.9829i	0.429046	−	1.60122i
$506$	11.5458			0.513276
$507$		0			0
$508$	2.65975			0.118008
$509$	−7.75830	+	28.9544i	−0.343881	+	1.28338i	0.550034	+	0.835142i	$0.314615\pi$
$509$	−7.75830	+	28.9544i	−0.343881	+	1.28338i	−0.893914	+	0.448238i	$0.852052\pi$
$510$	1.34710	+	0.179522i	0.0596506	+	0.00794937i
$511$	−12.3847	−	7.15031i	−0.547867	−	0.316311i
$512$	17.9453	+	17.9453i	0.793080	+	0.793080i
$513$	−27.3189	−	3.72888i	−1.20616	−	0.164634i
$514$	−20.6850	+	5.54254i	−0.912377	+	0.244471i
$515$	12.0890	−	12.0890i	0.532705	−	0.532705i
$516$	5.15741	−	2.12670i	0.227042	−	0.0936226i
$517$	−14.0178	+	8.09318i	−0.616502	+	0.355938i
$518$	18.9000	+	5.06423i	0.830416	+	0.222509i
$519$	−17.0503	−	13.1261i	−0.748424	−	0.576174i
$520$		0			0
$521$			5.94611i			0.260504i	0.991481	+	0.130252i	$0.0415786\pi$
$521$			5.94611i			0.260504i	−0.991481	+	0.130252i	$0.958421\pi$
$522$	−0.0466154	+	14.7016i	−0.00204030	+	0.643471i
$523$	0.429973	+	0.744735i	0.0188014	+	0.0325650i	0.875273	−	0.483629i	$-0.160682\pi$
$523$	0.429973	+	0.744735i	0.0188014	+	0.0325650i	−0.856472	+	0.516194i	$0.827348\pi$
$524$	1.64434	−	2.84809i	0.0718335	−	0.124419i
$525$	20.2387	−	2.63184i	0.883288	−	0.114863i
$526$	−3.90641	−	14.5789i	−0.170328	−	0.635672i
$527$	−0.0400678	−	0.149535i	−0.00174538	−	0.00651385i
$528$	15.4262	−	2.00603i	0.671340	−	0.0873011i
$529$	6.05247	−	10.4832i	0.263151	−	0.455791i
$530$	26.8883	+	46.5719i	1.16795	+	2.02295i
$531$	0.0317575	−	10.0157i	0.00137816	−	0.434644i
$532$			4.28266i			0.185677i
$533$		0			0
$534$	1.97961	+	1.52400i	0.0856662	+	0.0659500i
$535$	−22.5547	−	6.04351i	−0.975124	−	0.261284i
$536$	19.5318	−	11.2767i	0.843647	−	0.487080i
$537$	26.1050	−	10.7646i	1.12651	−	0.464526i
$538$	−10.3408	+	10.3408i	−0.445824	+	0.445824i
$539$	3.93947	−	1.05558i	0.169685	−	0.0454669i
$540$	−4.27612	−	0.583665i	−0.184015	−	0.0251169i
$541$	5.67009	+	5.67009i	0.243776	+	0.243776i	0.818410	−	0.574634i	$-0.194856\pi$
$541$	5.67009	+	5.67009i	0.243776	+	0.243776i	−0.574634	+	0.818410i	$0.694856\pi$
$542$	−6.90914	−	3.98899i	−0.296773	−	0.171342i
$543$	−15.9604	−	2.12697i	−0.684926	−	0.0912772i
$544$	−0.0798382	+	0.297960i	−0.00342303	+	0.0127749i
$545$	30.5353			1.30799
$546$		0			0
$547$	−29.3587			−1.25529			−0.627643	−	0.778501i	$-0.715980\pi$
$547$	−29.3587			−1.25529			−0.627643	+	0.778501i	$0.715980\pi$
$548$	1.24413	−	4.64314i	0.0531465	−	0.198345i
$549$	−5.74771	+	5.71137i	−0.245306	+	0.243755i
$550$	−12.2211	−	7.05585i	−0.521109	−	0.300863i
$551$	14.0053	+	14.0053i	0.596647	+	0.596647i
$552$	−6.56351	+	15.7749i	−0.279361	+	0.671425i
$553$	31.4217	−	8.41943i	1.33619	−	0.358031i
$554$	−25.7905	+	25.7905i	−1.09573	+	1.09573i
$555$	10.1269	+	24.5586i	0.429864	+	1.04245i
$556$	−0.557363	+	0.321794i	−0.0236375	+	0.0136471i
$557$	−36.1240	−	9.67941i	−1.53062	−	0.410130i	−0.607402	−	0.794395i	$-0.707788\pi$
$557$	−36.1240	−	9.67941i	−1.53062	−	0.410130i	−0.923223	+	0.384265i	$0.874455\pi$
$558$	−0.784303	−	2.96463i	−0.0332022	−	0.125503i
$559$		0			0
$560$		−	29.5936i		−	1.25056i
$561$	0.557417	+	0.728830i	0.0235342	+	0.0307712i
$562$	−10.7862	−	18.6823i	−0.454989	−	0.788064i
$563$	6.70261	−	11.6093i	0.282481	−	0.489272i	−0.689514	−	0.724272i	$-0.742176\pi$
$563$	6.70261	−	11.6093i	0.282481	−	0.489272i	0.971995	+	0.235000i	$0.0755091\pi$
$564$	−0.374965	−	2.88346i	−0.0157889	−	0.121415i
$565$	13.2932	+	49.6109i	0.559250	+	2.08715i
$566$	9.03429	+	33.7164i	0.379740	+	1.41721i
$567$	−25.3474	−	6.96439i	−1.06449	−	0.292477i
$568$	7.99078	−	13.8404i	0.335286	−	0.580732i
$569$	−11.3396	−	19.6407i	−0.475380	−	0.823382i	0.524223	−	0.851581i	$-0.324356\pi$
$569$	−11.3396	−	19.6407i	−0.475380	−	0.823382i	−0.999602	+	0.0281995i	$0.991023\pi$
$570$	28.8084	−	22.0330i	1.20665	−	0.922861i
$571$			21.9369i			0.918032i	0.888428	+	0.459016i	$0.151798\pi$
$571$			21.9369i			0.918032i	−0.888428	+	0.459016i	$0.848202\pi$
$572$		0			0
$573$	2.14307	−	2.78375i	0.0895279	−	0.116293i
$574$	−14.1115	−	3.78118i	−0.589004	−	0.157823i
$575$	11.5322	−	6.65814i	0.480928	−	0.277664i
$576$	−6.89698	+	25.4172i	−0.287374	+	1.05905i
$577$	18.7633	−	18.7633i	0.781126	−	0.781126i	−0.198895	−	0.980021i	$-0.563735\pi$
$577$	18.7633	−	18.7633i	0.781126	−	0.781126i	0.980021	+	0.198895i	$0.0637354\pi$
$578$	−21.5084	+	5.76316i	−0.894632	+	0.239716i
$579$	−6.35302	−	2.64332i	−0.264023	−	0.109852i
$580$	2.19219	+	2.19219i	0.0910259	+	0.0910259i
$581$	−6.58249	−	3.80040i	−0.273088	−	0.157667i
$582$	3.65395	−	27.4185i	0.151461	−	1.13653i
$583$	−9.39722	+	35.0709i	−0.389193	+	1.45249i
$584$	−14.6327			−0.605504
$585$		0			0
$586$	3.80070			0.157005
$587$	3.16920	−	11.8276i	0.130807	−	0.488178i	−0.869173	−	0.494508i	$-0.835348\pi$
$587$	3.16920	−	11.8276i	0.130807	−	0.488178i	0.999980	+	0.00632980i	$0.00201485\pi$
$588$	−0.0967820	+	0.726234i	−0.00399122	+	0.0299494i
$589$	−3.57794	−	2.06572i	−0.147426	−	0.0851166i
$590$	9.31581	+	9.31581i	0.383526	+	0.383526i
$591$	11.0180	+	4.58427i	0.453219	+	0.188572i
$592$	16.6148	−	4.45193i	0.682865	−	0.182973i
$593$	32.4467	−	32.4467i	1.33243	−	1.33243i	0.429232	−	0.903194i	$-0.358784\pi$
$593$	32.4467	−	32.4467i	1.33243	−	1.33243i	0.903194	−	0.429232i	$-0.141216\pi$
$594$	10.9960	+	14.4723i	0.451172	+	0.593805i
$595$	1.51168	−	0.872768i	0.0619728	−	0.0357800i
$596$	4.21079	+	1.12828i	0.172481	+	0.0462161i
$597$	6.69933	−	8.70213i	0.274185	−	0.356155i
$598$		0			0
$599$			11.5870i			0.473430i	0.971579	+	0.236715i	$0.0760708\pi$
$599$			11.5870i			0.473430i	−0.971579	+	0.236715i	$0.923929\pi$
$600$	16.5877	−	12.6864i	0.677189	−	0.517922i
$601$	2.26709	+	3.92671i	0.0924764	+	0.160174i	0.908553	−	0.417771i	$-0.137188\pi$
$601$	2.26709	+	3.92671i	0.0924764	+	0.160174i	−0.816076	+	0.577944i	$0.803855\pi$
$602$	−22.3477	+	38.7074i	−0.910826	+	1.57760i
$603$	19.5706	+	11.3820i	0.796977	+	0.463510i
$604$	0.866700	+	3.23457i	0.0352655	+	0.131613i
$605$	3.03509	+	11.3271i	0.123394	+	0.460513i
$606$	−3.63437	−	27.9481i	−0.147636	−	1.13531i
$607$	−6.51641	+	11.2868i	−0.264493	+	0.458115i	−0.967431	−	0.253136i	$-0.918538\pi$
$607$	−6.51641	+	11.2868i	−0.264493	+	0.458115i	0.702938	+	0.711251i	$0.251871\pi$
$608$	4.11611	+	7.12932i	0.166930	+	0.289132i
$609$	11.4715	+	14.9992i	0.464850	+	0.607797i
$610$		−	10.6583i		−	0.431544i
$611$		0			0
$612$	−0.159348	+	0.0421562i	−0.00644128	+	0.00170406i
$613$	3.47446	+	0.930978i	0.140332	+	0.0376019i	0.328301	−	0.944573i	$-0.393524\pi$
$613$	3.47446	+	0.930978i	0.140332	+	0.0376019i	−0.187969	+	0.982175i	$0.560191\pi$
$614$	−22.4414	+	12.9565i	−0.905661	+	0.522884i
$615$	−7.56121	−	18.3365i	−0.304897	−	0.739401i
$616$	16.4447	−	16.4447i	0.662575	−	0.662575i
$617$	6.41496	−	1.71888i	0.258257	−	0.0691997i	−0.127368	−	0.991856i	$-0.540653\pi$
$617$	6.41496	−	1.71888i	0.258257	−	0.0691997i	0.385624	+	0.922656i	$0.373986\pi$
$618$	4.96871	−	11.9419i	0.199871	−	0.480375i
$619$	−13.3334	−	13.3334i	−0.535916	−	0.535916i	0.386411	−	0.922327i	$-0.373715\pi$
$619$	−13.3334	−	13.3334i	−0.535916	−	0.535916i	−0.922327	+	0.386411i	$0.873715\pi$
$620$	−0.560039	−	0.323339i	−0.0224917	−	0.0129856i
$621$	−17.0150	+	2.15779i	−0.682789	+	0.0865892i
$622$	−9.16628	+	34.2090i	−0.367534	+	1.37166i
$623$	3.20885			0.128560
$624$		0			0
$625$	28.8959			1.15584
$626$	8.14365	−	30.3925i	0.325486	−	1.21473i
$627$	24.2724	+	3.23468i	0.969346	+	0.129181i
$628$	−0.781896	−	0.451428i	−0.0312011	−	0.0180139i
$629$	0.717411	+	0.717411i	0.0286051	+	0.0286051i
$630$	29.9994	−	17.1936i	1.19520	−	0.685008i
$631$	1.42316	−	0.381334i	0.0566550	−	0.0151807i	−0.230380	−	0.973101i	$-0.573997\pi$
$631$	1.42316	−	0.381334i	0.0566550	−	0.0151807i	0.287035	+	0.957920i	$0.407330\pi$
$632$	23.5364	−	23.5364i	0.936227	−	0.936227i
$633$	−1.28465	+	0.529733i	−0.0510601	+	0.0210550i
$634$	34.8763	−	20.1358i	1.38511	−	0.799696i
$635$	−27.9450	−	7.48784i	−1.10896	−	0.297146i
$636$	−5.16828	−	3.97879i	−0.204936	−	0.157769i
$637$		0			0
$638$		−	13.0566i		−	0.516915i
$639$	16.0426	+	0.0508676i	0.634637	+	0.00201229i
$640$	−12.6581	−	21.9245i	−0.500357	−	0.866644i
$641$	−7.43034	+	12.8697i	−0.293481	+	0.508323i	−0.974630	−	0.223821i	$-0.928147\pi$
$641$	−7.43034	+	12.8697i	−0.293481	+	0.508323i	0.681150	+	0.732144i	$0.261480\pi$
$642$	−17.5183	+	2.27808i	−0.691392	+	0.0899086i
$643$	−12.5754	−	46.9319i	−0.495924	−	1.85081i	−0.524792	−	0.851230i	$-0.675857\pi$
$643$	−12.5754	−	46.9319i	−0.495924	−	1.85081i	0.0288681	−	0.999583i	$-0.490810\pi$
$644$	0.689499	+	2.57325i	0.0271701	+	0.101400i
$645$	−60.1740	+	7.82503i	−2.36935	+	0.308110i
$646$	0.692588	−	1.19960i	0.0272495	−	0.0471975i
$647$	−18.8371	−	32.6268i	−0.740562	−	1.28269i	−0.952240	−	0.305351i	$-0.901226\pi$
$647$	−18.8371	−	32.6268i	−0.740562	−	1.28269i	0.211678	−	0.977340i	$-0.432107\pi$
$648$	−26.0242	+	6.79658i	−1.02233	+	0.266995i
$649$			8.89499i			0.349159i
$650$		0			0
$651$	−3.12107	−	2.40275i	−0.122324	−	0.0941714i
$652$	1.55566	+	0.416839i	0.0609245	+	0.0163247i
$653$	−19.2876	+	11.1357i	−0.754782	+	0.435774i	−0.827419	−	0.561585i	$-0.810192\pi$
$653$	−19.2876	+	11.1357i	−0.754782	+	0.435774i	0.0726369	+	0.997358i	$0.476859\pi$
$654$	21.3571	−	8.80675i	0.835128	−	0.344371i
$655$	−25.2945	+	25.2945i	−0.988339	+	0.988339i
$656$	−12.4054	+	3.32401i	−0.484348	+	0.129781i
$657$	−7.30396	−	12.7440i	−0.284955	−	0.497190i
$658$	16.4729	+	16.4729i	0.642182	+	0.642182i
$659$	−23.2104	−	13.4005i	−0.904148	−	0.522010i	−0.0256043	−	0.999672i	$-0.508151\pi$
$659$	−23.2104	−	13.4005i	−0.904148	−	0.522010i	−0.878544	+	0.477662i	$0.841484\pi$
$660$	3.79925	+	0.506310i	0.147886	+	0.0197081i
$661$	4.52232	−	16.8775i	0.175898	−	0.656459i	−0.820499	−	0.571647i	$-0.806304\pi$
$661$	4.52232	−	16.8775i	0.175898	−	0.656459i	0.996397	−	0.0848116i	$-0.0270288\pi$
$662$	−0.871200			−0.0338602
$663$		0			0
$664$	−7.77728			−0.301817
$665$	12.0567	−	44.9962i	0.467538	−	1.74488i
$666$	14.1660	+	14.2561i	0.548922	+	0.552414i
$667$	10.6700	+	6.16031i	0.413143	+	0.238528i
$668$	0.308966	+	0.308966i	0.0119543	+	0.0119543i
$669$	2.05602	−	4.94149i	0.0794902	−	0.191049i
$670$	−28.7653	+	7.70763i	−1.11130	+	0.297772i
$671$	5.08844	−	5.08844i	0.196437	−	0.196437i
$672$	2.99196	+	7.25574i	0.115417	+	0.279896i
$673$	30.8369	−	17.8037i	1.18867	−	0.686281i	0.230669	−	0.973032i	$-0.425909\pi$
$673$	30.8369	−	17.8037i	1.18867	−	0.686281i	0.958005	+	0.286751i	$0.0925753\pi$
$674$	−31.8144	−	8.52464i	−1.22544	−	0.328357i
$675$	19.3288	+	8.11416i	0.743965	+	0.312314i
$676$		0			0
$677$		−	16.3795i		−	0.629517i	−0.949172	−	0.314758i	$-0.898076\pi$
$677$		−	16.3795i		−	0.629517i	0.949172	−	0.314758i	$-0.101924\pi$
$678$	23.6060	+	30.8651i	0.906583	+	1.18537i
$679$	−17.7641	−	30.7683i	−0.681723	−	1.18078i
$680$	0.893032	−	1.54678i	0.0342462	−	0.0593162i
$681$	−5.78813	−	44.5104i	−0.221801	−	1.70564i
$682$	0.704886	+	2.63067i	0.0269915	+	0.100734i
$683$	−9.94232	−	37.1052i	−0.380432	−	1.41979i	−0.845243	−	0.534382i	$-0.820544\pi$
$683$	−9.94232	−	37.1052i	−0.380432	−	1.41979i	0.464811	−	0.885410i	$-0.346122\pi$
$684$	−2.21150	+	3.80253i	−0.0845588	+	0.145394i
$685$	−26.1431	+	45.2812i	−0.998876	+	1.73010i
$686$	10.4862	+	18.1626i	0.400364	+	0.693451i
$687$	38.2150	−	29.2272i	1.45799	−	1.11509i
$688$			39.2915i			1.49797i
$689$		0			0
$690$	13.7624	−	17.8767i	0.523924	−	0.680554i
$691$	−18.6598	−	4.99988i	−0.709853	−	0.190204i	−0.114213	−	0.993456i	$-0.536435\pi$
$691$	−18.6598	−	4.99988i	−0.709853	−	0.190204i	−0.595640	+	0.803252i	$0.703101\pi$
$692$	−2.97299	+	1.71645i	−0.113016	+	0.0652498i
$693$	22.5306	+	6.11368i	0.855865	+	0.232239i
$694$	−15.2344	+	15.2344i	−0.578292	+	0.578292i
$695$	6.76192	−	1.81185i	0.256494	−	0.0687274i
$696$	17.8390	+	7.42231i	0.676186	+	0.281342i
$697$	−0.535651	−	0.535651i	−0.0202892	−	0.0202892i
$698$	34.0809	+	19.6766i	1.28998	+	0.744771i
$699$	−3.30734	+	24.8176i	−0.125095	+	0.938689i
$700$	0.842728	−	3.14510i	0.0318521	−	0.118874i
$701$	12.7471			0.481453			0.240726	−	0.970593i	$-0.422614\pi$
$701$	12.7471			0.481453			0.240726	+	0.970593i	$0.422614\pi$
$702$		0			0
$703$	27.0761			1.02120
$704$	6.05362	−	22.5924i	0.228154	−	0.851483i
$705$	−4.17800	+	31.3509i	−0.157353	+	1.18074i
$706$	7.66111	+	4.42315i	0.288330	+	0.166467i
$707$	−25.5967	−	25.5967i	−0.962664	−	0.962664i
$708$	−1.47530	−	0.613831i	−0.0554452	−	0.0230692i
$709$	−42.1029	+	11.2814i	−1.58121	+	0.423683i	−0.939299	−	0.343099i	$-0.888523\pi$
$709$	−42.1029	+	11.2814i	−1.58121	+	0.423683i	−0.641907	+	0.766782i	$0.721857\pi$
$710$	−14.9216	+	14.9216i	−0.559999	+	0.559999i
$711$	32.2468	+	8.75017i	1.20935	+	0.328157i
$712$	2.84346	−	1.64168i	0.106563	−	0.0615244i
$713$	−2.48239	−	0.665155i	−0.0929663	−	0.0249102i
$714$	0.805586	−	1.04642i	0.0301483	−	0.0391613i
$715$		0			0
$716$		−	4.50497i		−	0.168359i
$717$	−8.25447	+	6.31311i	−0.308269	+	0.235767i
$718$	6.28386	+	10.8840i	0.234512	+	0.406186i
$719$	−17.7809	+	30.7974i	−0.663116	+	1.14855i	0.316677	+	0.948534i	$0.397433\pi$
$719$	−17.7809	+	30.7974i	−0.663116	+	1.14855i	−0.979793	+	0.200017i	$0.935900\pi$
$720$	15.2817	−	26.2759i	0.569515	−	0.979245i
$721$	−4.29980	−	16.0471i	−0.160133	−	0.597624i
$722$	−3.11143	−	11.6120i	−0.115795	−	0.432154i
$723$	5.51205	+	42.3873i	0.204995	+	1.57640i
$724$	−1.28441	+	2.22467i	−0.0477348	+	0.0826791i
$725$	−7.52933	−	13.0412i	−0.279632	−	0.484338i
$726$	5.38970	+	7.04710i	0.200030	+	0.261542i
$727$		−	26.2936i		−	0.975176i	−0.873074	−	0.487588i	$-0.837877\pi$
$727$		−	26.2936i		−	0.975176i	0.873074	−	0.487588i	$-0.162123\pi$
$728$		0			0
$729$	−18.9094	−	19.2726i	−0.700349	−	0.713801i
$730$	18.6629	+	5.00071i	0.690745	+	0.185084i
$731$	−2.00706	+	1.15878i	−0.0742338	+	0.0428589i
$732$	0.492809	+	1.19510i	0.0182147	+	0.0441722i
$733$	5.72217	−	5.72217i	0.211353	−	0.211353i	−0.593489	−	0.804842i	$-0.702250\pi$
$733$	5.72217	−	5.72217i	0.211353	−	0.211353i	0.804842	+	0.593489i	$0.202250\pi$
$734$	−15.2517	+	4.08668i	−0.562951	+	0.150842i
$735$	3.06137	−	7.35779i	0.112920	−	0.271396i
$736$	3.62099	+	3.62099i	0.133471	+	0.133471i
$737$	−17.4127	−	10.0532i	−0.641403	−	0.370314i
$738$	−10.5770	−	10.6443i	−0.389344	−	0.391821i
$739$	5.31693	−	19.8431i	0.195587	−	0.729939i	−0.796528	−	0.604602i	$-0.793332\pi$
$739$	5.31693	−	19.8431i	0.195587	−	0.729939i	0.992114	−	0.125337i	$-0.0400012\pi$
$740$	4.23811			0.155796
$741$		0			0
$742$	52.2565			1.91840
$743$	−8.90116	+	33.2196i	−0.326552	+	1.21871i	0.586191	+	0.810173i	$0.300627\pi$
$743$	−8.90116	+	33.2196i	−0.326552	+	1.21871i	−0.912743	+	0.408535i	$0.866040\pi$
$744$	−3.99496	−	0.532391i	−0.146462	−	0.0195184i
$745$	−41.0648	−	23.7087i	−1.50450	−	0.868621i
$746$	−12.4015	−	12.4015i	−0.454051	−	0.454051i
$747$	−3.88207	−	6.77344i	−0.142037	−	0.247827i
$748$	0.141398	−	0.0378875i	0.00517003	−	0.00138531i
$749$	−16.0445	+	16.0445i	−0.586252	+	0.586252i
$750$	6.10205	−	2.51623i	0.222815	−	0.0918796i
$751$	25.8847	−	14.9445i	0.944546	−	0.545334i	0.0531635	−	0.998586i	$-0.483070\pi$
$751$	25.8847	−	14.9445i	0.944546	−	0.545334i	0.891382	+	0.453252i	$0.149736\pi$
$752$	19.7818	+	5.30051i	0.721367	+	0.193290i
$753$	29.8233	+	22.9594i	1.08682	+	0.836687i
$754$		0			0
$755$		−	36.4243i		−	1.32562i
$756$	−2.56880	+	3.31496i	−0.0934264	+	0.120564i
$757$	−11.1534	−	19.3182i	−0.405376	−	0.702132i	0.588989	−	0.808141i	$-0.299526\pi$
$757$	−11.1534	−	19.3182i	−0.405376	−	0.702132i	−0.994365	+	0.106009i	$0.966193\pi$
$758$	20.3284	−	35.2098i	0.738360	−	1.27888i
$759$	15.1049	−	1.96424i	0.548274	−	0.0712975i
$760$	−12.3366	−	46.0409i	−0.447496	−	1.67008i
$761$	6.85369	+	25.5783i	0.248446	+	0.927214i	0.971620	+	0.236547i	$0.0760159\pi$
$761$	6.85369	+	25.5783i	0.248446	+	0.927214i	−0.723174	+	0.690666i	$0.757317\pi$
$762$	−21.7050	+	2.82251i	−0.786288	+	0.102249i
$763$	14.8361	−	25.6968i	0.537101	−	0.930287i
$764$	−0.280241	−	0.485391i	−0.0101387	−	0.0175608i
$765$	1.79289	+	0.00568485i	0.0648221	+	0.000205536i
$766$			13.4621i			0.486404i
$767$		0			0
$768$	8.92027	+	6.86726i	0.321882	+	0.247801i
$769$	11.8606	+	3.17804i	0.427704	+	0.114603i	0.466248	−	0.884654i	$-0.345605\pi$
$769$	11.8606	+	3.17804i	0.427704	+	0.114603i	−0.0385441	+	0.999257i	$0.512272\pi$
$770$	−26.5940	+	15.3540i	−0.958380	+	0.553321i
$771$	−26.1184	+	10.7701i	−0.940630	+	0.387876i
$772$	−0.776254	+	0.776254i	−0.0279380	+	0.0279380i
$773$	−22.2683	+	5.96678i	−0.800937	+	0.214610i	−0.635995	−	0.771693i	$-0.719410\pi$
$773$	−22.2683	+	5.96678i	−0.800937	+	0.214610i	−0.164941	+	0.986303i

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.339800 + 1.26815i) q^{2} +(-0.228800 + 1.71687i) q^{3} +(0.239309 + 0.138165i) q^{4} +(-2.12536 - 2.12536i) q^{5} +(-2.09951 - 0.873546i) q^{6} +(-2.82123 + 0.755945i) q^{7} +(-2.11323 + 2.11323i) q^{8} +(-2.89530 - 0.785641i) q^{9} +(3.41747 - 1.97308i) q^{10} +(2.57352 + 0.689573i) q^{11} +(-0.291966 + 0.379251i) q^{12} -3.83461i q^{14} +(4.13525 - 3.16269i) q^{15} +(-1.68549 - 2.91935i) q^{16} +(0.0994162 - 0.172194i) q^{17} +(1.98013 - 3.40472i) q^{18} +(-1.37337 - 5.12548i) q^{19} +(-0.214967 - 0.802269i) q^{20} +(-0.652364 - 5.01665i) q^{21} +(-1.74897 + 3.02930i) q^{22} +(-1.65038 - 2.85855i) q^{23} +(-3.14464 - 4.11166i) q^{24} +4.03430i q^{25} +(2.01129 - 4.79111i) q^{27} +(-0.779591 - 0.208891i) q^{28} +(-3.23258 + 1.86633i) q^{29} +(2.60561 + 6.31880i) q^{30} +(0.550550 - 0.550550i) q^{31} +(-1.49855 + 0.401535i) q^{32} +(-1.77273 + 4.26063i) q^{33} +(0.184586 + 0.184586i) q^{34} +(7.60277 + 4.38946i) q^{35} +(-0.584324 - 0.588041i) q^{36} +(-1.32066 + 4.92878i) q^{37} +6.96655 q^{38} +8.98276 q^{40} +(0.986066 - 3.68005i) q^{41} +(6.58353 + 0.877359i) q^{42} +(-10.0942 - 5.82790i) q^{43} +(0.520592 + 0.520592i) q^{44} +(4.48378 + 7.82332i) q^{45} +(4.18587 - 1.12160i) q^{46} +(-4.29586 + 4.29586i) q^{47} +(5.39780 - 2.22582i) q^{48} +(1.32568 - 0.765385i) q^{49} +(-5.11610 - 1.37086i) q^{50} +(0.272889 + 0.210083i) q^{51} +13.6276i q^{53} +(5.39241 + 4.17864i) q^{54} +(-4.00407 - 6.93525i) q^{55} +(4.36442 - 7.55939i) q^{56} +(9.11402 - 1.18519i) q^{57} +(-1.26836 - 4.73357i) q^{58} +(0.864088 + 3.22482i) q^{59} +(1.42658 - 0.185512i) q^{60} +(1.35047 - 2.33909i) q^{61} +(0.511103 + 0.885257i) q^{62} +(8.76220 + 0.0277830i) q^{63} -8.77879i q^{64} +(-4.80075 - 3.69585i) q^{66} +(-7.28944 - 1.95320i) q^{67} +(0.0475824 - 0.0274717i) q^{68} +(5.28537 - 2.17946i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(-5.16536 + 1.38405i) q^{71} +(7.77869 - 4.45820i) q^{72} +(3.46215 + 3.46215i) q^{73} +(-5.80168 - 3.34960i) q^{74} +(-6.92638 - 0.923049i) q^{75} +(0.379503 - 1.41633i) q^{76} -7.78177 q^{77} -11.1376 q^{79} +(-2.62241 + 9.78695i) q^{80} +(7.76554 + 4.54934i) q^{81} +(4.33179 + 2.50096i) q^{82} +(1.84014 + 1.84014i) q^{83} +(0.537009 - 1.29066i) q^{84} +(-0.577269 + 0.154679i) q^{85} +(10.8207 - 10.8207i) q^{86} +(-2.46463 - 5.97694i) q^{87} +(-6.89568 + 3.98122i) q^{88} +(-1.06120 - 0.284349i) q^{89} +(-11.4447 + 3.02775i) q^{90} -0.912102i q^{92} +(0.819258 + 1.07119i) q^{93} +(-3.98807 - 6.90753i) q^{94} +(-7.97458 + 13.8124i) q^{95} +(-0.346516 - 2.66469i) q^{96} +(3.14829 + 11.7496i) q^{97} +(0.520155 + 1.94125i) q^{98} +(-6.90936 - 4.01839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Introduction

L-functions

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Varieties

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