LMFDB - Embedded newform 507.2.k.k.80.17

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			80.17
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.17

$q$-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	$-0.763017\pi$
$2$	0.339800	−	1.26815i	0.240275	−	0.896718i	0.975700	−	0.219112i	$-0.0703159\pi$
$3$	−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	0.998831	−	0.0483414i	$-0.0153935\pi$
$5$	2.12536	+	2.12536i	0.950489	+	0.950489i	−0.0483414	+	0.998831i	$0.515394\pi$
$6$	2.09951	+	0.873546i	0.857120	+	0.356624i
$7$	2.82123	−	0.755945i	1.06632	−	0.285720i	0.317342	−	0.948311i	$-0.397210\pi$
$7$	2.82123	−	0.755945i	1.06632	−	0.285720i	0.748982	+	0.662591i	$0.230543\pi$
$8$	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	−0.150949	−	0.988541i	$-0.548233\pi$
$11$	−2.57352	−	0.689573i	−0.775946	−	0.207914i	−0.624997	+	0.780627i	$0.714900\pi$
$12$	−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	$0.124964\pi$
$19$	1.37337	+	5.12548i	0.315072	+	1.17586i	−0.608850	+	0.793285i	$0.708369\pi$
$20$	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	−0.754817	−	0.655935i	$-0.772274\pi$
$31$	−0.550550	+	0.550550i	−0.0988817	+	0.0988817i	0.655935	+	0.754817i	$0.272274\pi$
$32$	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	$-0.778895\pi$
$37$	1.32066	−	4.92878i	0.217116	−	0.810287i	0.985411	−	0.170191i	$-0.0544386\pi$
$38$	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	$0.179486\pi$
$41$	−0.986066	+	3.68005i	−0.153998	+	0.574727i	−0.999189	+	0.0402633i	$0.987180\pi$
$42$	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	−0.320599	−	0.947215i	$-0.603884\pi$
$47$	4.29586	−	4.29586i	0.626616	−	0.626616i	0.947215	+	0.320599i	$0.103884\pi$
$48$	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	0.886593	−	0.462551i	$-0.153066\pi$
$59$	−0.864088	−	3.22482i	−0.112495	−	0.419836i	−0.999087	+	0.0427154i	$0.986399\pi$
$60$	−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	0.674952	−	0.737862i	$-0.264164\pi$
$67$	7.28944	+	1.95320i	0.890547	+	0.238621i	0.215595	+	0.976483i	$0.430831\pi$
$68$	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	0.0610649	−	0.998134i	$-0.480550\pi$
$71$	5.16536	−	1.38405i	0.613016	−	0.164257i	0.551951	+	0.833877i	$0.313884\pi$
$72$	−7.77869	+	4.45820i	−0.916727	+	0.525404i
$73$	−3.46215	−	3.46215i	−0.405214	−	0.405214i	0.474852	−	0.880066i	$-0.342502\pi$
$73$	−3.46215	−	3.46215i	−0.405214	−	0.405214i	−0.880066	+	0.474852i	$0.842502\pi$
$74$	−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	0.598867	−	0.800848i	$-0.295618\pi$
$83$	−1.84014	−	1.84014i	−0.201981	−	0.201981i	−0.800848	+	0.598867i	$0.795618\pi$
$84$	−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	0.314624	−	0.949217i	$-0.398122\pi$
$89$	1.06120	+	0.284349i	0.112487	+	0.0301409i	−0.202136	+	0.979357i	$0.564788\pi$
$90$	−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	$-0.871464\pi$
$97$	−3.14829	−	11.7496i	−0.319661	−	1.19299i	0.599911	−	0.800067i	$-0.295203\pi$
$98$	−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	−0.273743	−	0.961803i	$-0.588262\pi$
$109$	7.18355	−	7.18355i	0.688060	−	0.688060i	0.961803	+	0.273743i	$0.0882618\pi$
$110$	−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	$0.183314\pi$
$137$	4.50231	+	16.8029i	0.384659	+	1.43557i	−0.454045	+	0.890979i	$0.650020\pi$
$138$	−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	−0.821705	−	0.569913i	$-0.806977\pi$
$149$	−15.2383	+	4.08308i	−1.24837	+	0.334499i	−0.426661	+	0.904412i	$0.640310\pi$
$150$	−3.52415	+	8.47004i	−0.287746	+	0.691576i
$151$	−8.56897	−	8.56897i	−0.697333	−	0.697333i	0.266502	−	0.963834i	$-0.414132\pi$
$151$	−8.56897	−	8.56897i	−0.697333	−	0.697333i	−0.963834	+	0.266502i	$0.914132\pi$
$152$	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	−0.472463	−	0.881350i	$-0.656635\pi$
$163$	−5.62972	+	1.50848i	−0.440954	+	0.118153i	0.0315098	+	0.999503i	$0.489968\pi$
$164$	−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	0.199239	−	0.979951i	$-0.436153\pi$
$167$	−1.52736	−	0.409254i	−0.118190	−	0.0316690i	−0.317429	+	0.948282i	$0.602820\pi$
$168$	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	−0.918995	−	0.394270i	$-0.870998\pi$
$193$	1.02822	−	3.83737i	0.0740130	−	0.276220i	0.993008	+	0.118050i	$0.0376642\pi$
$194$	−15.9700			−1.14658
$195$		0			0
$196$	0.422998			0.0302142
$197$	−1.78323	+	6.65511i	−0.127050	+	0.474157i	−0.999904	−	0.0138237i	$-0.995600\pi$
$197$	−1.78323	+	6.65511i	−0.127050	+	0.474157i	0.872855	+	0.487981i	$0.162266\pi$
$198$	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	0.357368	−	0.933964i	$-0.383674\pi$
$223$	2.98478	+	0.799768i	0.199875	+	0.0535565i	−0.157492	+	0.987520i	$0.550341\pi$
$224$	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	0.698624	−	0.715489i	$-0.253796\pi$
$227$	25.0314	−	6.70715i	1.66139	−	0.445169i	0.962770	+	0.270320i	$0.0871296\pi$
$228$	−2.34482	−	0.975614i	−0.155289	−	0.0646116i
$229$	19.6410	+	19.6410i	1.29791	+	1.29791i	0.929768	+	0.368147i	$0.120008\pi$
$229$	19.6410	+	19.6410i	1.29791	+	1.29791i	0.368147	+	0.929768i	$0.379992\pi$
$230$	−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	0.556455	−	0.830878i	$-0.312161\pi$
$239$	−4.24248	−	4.24248i	−0.274423	−	0.274423i	−0.830878	+	0.556455i	$0.812161\pi$
$240$	16.2029	+	6.74159i	1.04590	+	0.435168i
$241$	−23.8375	+	6.38724i	−1.53551	+	0.411438i	−0.924811	−	0.380426i	$-0.875777\pi$
$241$	−23.8375	+	6.38724i	−1.53551	+	0.411438i	−0.610697	+	0.791864i	$0.709111\pi$
$242$	−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	−0.901562	−	0.432650i	$-0.857579\pi$
$271$	1.57276	−	5.86962i	0.0955383	−	0.356554i	0.997101	+	0.0760956i	$0.0242454\pi$
$272$	−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	−0.269803	−	0.962916i	$-0.586958\pi$
$281$	11.6187	−	11.6187i	0.693113	−	0.693113i	0.962916	+	0.269803i	$0.0869585\pi$
$282$	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	0.984352	−	0.176212i	$-0.0563844\pi$
$293$	0.749260	+	2.79628i	0.0437722	+	0.163360i	−0.940580	+	0.339572i	$0.889718\pi$
$294$	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	0.186007	−	0.982548i	$-0.440445\pi$
$307$	−13.9565	−	13.9565i	−0.796541	−	0.796541i	−0.982548	+	0.186007i	$0.940445\pi$
$308$	−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	$0.0804218\pi$
$317$	21.6899	+	21.6899i	1.21823	+	1.21823i	0.249973	+	0.968253i	$0.419578\pi$
$318$	−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	0.961045	−	0.276391i	$-0.0891386\pi$
$331$	−0.171746	−	0.640966i	−0.00944003	−	0.0352307i	−0.970485	+	0.241161i	$0.922472\pi$
$332$	−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	$0.379698\pi$
$349$	−7.75800	+	28.9532i	−0.415276	+	1.54983i	−0.784282	+	0.620405i	$0.786968\pi$
$350$	15.4700			0.826905
$351$		0			0
$352$	−4.13344			−0.220313
$353$	−1.74394	+	6.50846i	−0.0928203	+	0.346410i	−0.996680	−	0.0814189i	$-0.974055\pi$
$353$	−1.74394	+	6.50846i	−0.0928203	+	0.346410i	0.903860	+	0.427829i	$0.140721\pi$
$354$	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	−0.862797	−	0.505551i	$-0.831289\pi$
$359$	−6.76884	+	6.76884i	−0.357246	+	0.357246i	0.505551	+	0.862797i	$0.331289\pi$
$360$	−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	0.925130	−	0.379651i	$-0.123956\pi$
$379$	29.9123	+	8.01497i	1.53649	+	0.411701i	0.611360	+	0.791352i	$0.290623\pi$
$380$	−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	−0.502826	−	0.864388i	$-0.667706\pi$
$383$	−9.90441	+	2.65388i	−0.506092	+	0.135607i	−0.00326604	+	0.999995i	$0.501040\pi$
$384$	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	−0.174667	−	0.984628i	$-0.555885\pi$
$397$	3.31510	−	0.888280i	0.166380	−	0.0445815i	0.341048	+	0.940046i	$0.389218\pi$
$398$	−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	−0.256796	−	0.966466i	$-0.582667\pi$
$401$	−19.2725	−	5.16404i	−0.962421	−	0.257880i	−0.705625	+	0.708586i	$0.749334\pi$
$402$	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	0.921361	−	0.388708i	$-0.127079\pi$
$409$	−1.43417	−	5.35240i	−0.0709152	−	0.264659i	−0.992276	+	0.124049i	$0.960412\pi$
$410$	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	−0.0888383	−	0.996046i	$-0.528315\pi$
$421$	18.6143	−	18.6143i	0.907208	−	0.907208i	0.996046	+	0.0888383i	$0.0283154\pi$
$422$	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	$-0.828864\pi$
$431$	2.92686	−	10.9232i	0.140982	−	0.526152i	0.999901	−	0.0140414i	$-0.00446966\pi$
$432$	−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	0.953071	−	0.302745i	$-0.0979032\pi$
$449$	−0.501884	−	1.87306i	−0.0236854	−	0.0883950i	−0.976757	+	0.214350i	$0.931237\pi$
$450$	−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	0.124755	−	0.992188i	$-0.460186\pi$
$457$	−5.62868	−	1.50820i	−0.263299	−	0.0705507i	−0.388053	+	0.921637i	$0.626852\pi$
$458$	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	−0.565905	−	0.824470i	$-0.691473\pi$
$461$	−13.8221	+	3.70361i	−0.643758	+	0.172494i	−0.0778529	+	0.996965i	$0.524806\pi$
$462$	−16.3379	−	6.79773i	−0.760106	−	0.316259i
$463$	−2.99038	−	2.99038i	−0.138975	−	0.138975i	0.634197	−	0.773172i	$-0.281331\pi$
$463$	−2.99038	−	2.99038i	−0.138975	−	0.138975i	−0.773172	+	0.634197i	$0.781331\pi$
$464$	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	0.213469	−	0.976950i	$-0.431524\pi$
$479$	−1.97272	−	0.528588i	−0.0901358	−	0.0241518i	−0.303605	+	0.952798i	$0.598190\pi$
$480$	−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	$0.109052\pi$
$487$	6.49144	+	24.2264i	0.294155	+	1.09780i	−0.647731	+	0.761869i	$0.724282\pi$
$488$	−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	−0.484588	−	0.874742i	$-0.661030\pi$
$499$	8.71539	−	8.71539i	0.390154	−	0.390154i	0.874742	+	0.484588i	$0.161030\pi$
$500$	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	$-0.685385\pi$
$509$	7.75830	−	28.9544i	0.343881	−	1.28338i	0.893914	−	0.448238i	$-0.147948\pi$
$510$	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	0.574634	−	0.818410i	$-0.305144\pi$
$541$	−5.67009	−	5.67009i	−0.243776	−	0.243776i	−0.818410	+	0.574634i	$0.805144\pi$
$542$	−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	0.923223	−	0.384265i	$-0.125545\pi$
$557$	36.1240	+	9.67941i	1.53062	+	0.410130i	0.607402	+	0.794395i	$0.292212\pi$
$558$	−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	−0.980021	−	0.198895i	$-0.936265\pi$
$577$	−18.7633	+	18.7633i	−0.781126	+	0.781126i	0.198895	+	0.980021i	$0.436265\pi$
$578$	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	−0.999980	−	0.00632980i	$-0.997985\pi$
$587$	−3.16920	+	11.8276i	−0.130807	+	0.488178i	0.869173	+	0.494508i	$0.164652\pi$
$588$	−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	$0.641216\pi$
$593$	−32.4467	+	32.4467i	−1.33243	+	1.33243i	−0.903194	+	0.429232i	$0.858784\pi$
$594$	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	0.187969	−	0.982175i	$-0.439809\pi$
$613$	−3.47446	−	0.930978i	−0.140332	−	0.0376019i	−0.328301	+	0.944573i	$0.606476\pi$
$614$	−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	−0.385624	−	0.922656i	$-0.626014\pi$
$617$	−6.41496	+	1.71888i	−0.258257	+	0.0691997i	0.127368	+	0.991856i	$0.459347\pi$
$618$	−4.96871	+	11.9419i	−0.199871	+	0.480375i
$619$	13.3334	+	13.3334i	0.535916	+	0.535916i	0.922327	−	0.386411i	$-0.126285\pi$
$619$	13.3334	+	13.3334i	0.535916	+	0.535916i	−0.386411	+	0.922327i	$0.626285\pi$
$620$	−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	−0.287035	−	0.957920i	$-0.592670\pi$
$631$	−1.42316	+	0.381334i	−0.0566550	+	0.0151807i	0.230380	+	0.973101i	$0.426003\pi$
$632$	−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	$0.324143\pi$
$643$	12.5754	+	46.9319i	0.495924	+	1.85081i	−0.0288681	+	0.999583i	$0.509190\pi$
$644$	−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	$0.193696\pi$
$661$	−4.52232	+	16.8775i	−0.175898	+	0.656459i	−0.996397	+	0.0848116i	$0.972971\pi$
$662$	−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	$0.179456\pi$
$683$	9.94232	+	37.1052i	0.380432	+	1.41979i	−0.464811	+	0.885410i	$0.653878\pi$
$684$	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	0.595640	−	0.803252i	$-0.296899\pi$
$691$	18.6598	+	4.99988i	0.709853	+	0.190204i	0.114213	+	0.993456i	$0.463565\pi$
$692$	−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	0.641907	−	0.766782i	$-0.278143\pi$
$709$	42.1029	−	11.2814i	1.58121	−	0.423683i	0.939299	+	0.343099i	$0.111477\pi$
$710$	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	−0.804842	−	0.593489i	$-0.797750\pi$
$733$	−5.72217	+	5.72217i	−0.211353	+	0.211353i	0.593489	+	0.804842i	$0.297750\pi$
$734$	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	$0.206668\pi$
$739$	−5.31693	+	19.8431i	−0.195587	+	0.729939i	−0.992114	+	0.125337i	$0.959999\pi$
$740$	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	$-0.699373\pi$
$743$	8.90116	−	33.2196i	0.326552	−	1.21871i	0.912743	−	0.408535i	$-0.133960\pi$
$744$	−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	$-0.923984\pi$
$761$	−6.85369	−	25.5783i	−0.248446	−	0.927214i	0.723174	−	0.690666i	$-0.242683\pi$
$762$	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	0.0385441	−	0.999257i	$-0.487728\pi$
$769$	−11.8606	−	3.17804i	−0.427704	−	0.114603i	−0.466248	+	0.884654i	$0.654395\pi$
$770$	−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	0.164941	−	0.986303i	$-0.447256\pi$
$773$	22.2683	−	5.96678i	0.800937	−	0.214610i	0.635995	+	0

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

Modular forms

Varieties

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