LMFDB - Embedded newform 507.2.k.k.80.18

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			80.18
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.18

$q$-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} +(1.60126 + 0.660289i) q^{3} +(0.239309 + 0.138165i) q^{4} +(2.12536 + 2.12536i) q^{5} +(1.38145 - 1.80627i) q^{6} +(-2.82123 + 0.755945i) q^{7} +(2.11323 - 2.11323i) q^{8} +(2.12804 + 2.11458i) q^{9} +(3.41747 - 1.97308i) q^{10} +(-2.57352 - 0.689573i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(1.99989 + 4.80659i) q^{15} +(-1.68549 - 2.91935i) q^{16} +(-0.0994162 + 0.172194i) q^{17} +(3.40472 - 1.98013i) q^{18} +(-1.37337 - 5.12548i) q^{19} +(0.214967 + 0.802269i) q^{20} +(-5.01665 - 0.652364i) q^{21} +(-1.74897 + 3.02930i) q^{22} +(1.65038 + 2.85855i) q^{23} +(4.77917 - 1.98848i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(-0.779591 - 0.208891i) q^{28} +(3.23258 - 1.86633i) q^{29} +(6.77505 - 0.902881i) q^{30} +(0.550550 - 0.550550i) q^{31} +(1.49855 - 0.401535i) q^{32} +(-3.66555 - 2.80345i) q^{33} +(0.184586 + 0.184586i) q^{34} +(-7.60277 - 4.38946i) q^{35} +(0.217097 + 0.800060i) q^{36} +(-1.32066 + 4.92878i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(-0.986066 + 3.68005i) q^{41} +(-2.53195 + 6.14019i) q^{42} +(-10.0942 - 5.82790i) q^{43} +(-0.520592 - 0.520592i) q^{44} +(0.0285911 + 9.01709i) q^{45} +(4.18587 - 1.12160i) q^{46} +(4.29586 - 4.29586i) q^{47} +(-0.771281 - 5.78754i) q^{48} +(1.32568 - 0.765385i) q^{49} +(5.11610 + 1.37086i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(6.75928 - 0.922602i) q^{54} +(-4.00407 - 6.93525i) q^{55} +(-4.36442 + 7.55939i) q^{56} +(1.18519 - 9.11402i) q^{57} +(-1.26836 - 4.73357i) q^{58} +(-0.864088 - 3.22482i) q^{59} +(-0.185512 + 1.42658i) q^{60} +(1.35047 - 2.33909i) q^{61} +(-0.511103 - 0.885257i) q^{62} +(-7.60218 - 4.35704i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(-7.28944 - 1.95320i) q^{67} +(-0.0475824 + 0.0274717i) q^{68} +(0.755216 + 5.66699i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(5.16536 - 1.38405i) q^{71} +(8.96564 - 0.0284280i) q^{72} +(3.46215 + 3.46215i) q^{73} +(5.80168 + 3.34960i) q^{74} +(-2.66381 + 6.45995i) q^{75} +(0.379503 - 1.41633i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(2.62241 - 9.78695i) q^{80} +(0.0570734 + 8.99982i) q^{81} +(4.33179 + 2.50096i) q^{82} +(-1.84014 - 1.84014i) q^{83} +(-1.11040 - 0.849243i) q^{84} +(-0.577269 + 0.154679i) q^{85} +(-10.8207 + 10.8207i) q^{86} +(6.40850 - 0.854033i) q^{87} +(-6.89568 + 3.98122i) q^{88} +(1.06120 + 0.284349i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(1.24509 - 0.518049i) q^{93} +(-3.98807 - 6.90753i) q^{94} +(7.97458 - 13.8124i) q^{95} +(2.66469 + 0.346516i) q^{96} +(3.14829 + 11.7496i) q^{97} +(-0.520155 - 1.94125i) q^{98} +(-4.01839 - 6.90936i) 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	$-0.0703159\pi$
$3$	1.60126	+	0.660289i	0.924485	+	0.381218i
$3$	1.60126	+	0.660289i	0.924485	+	0.381218i
$4$	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	$0.515394\pi$
$6$	1.38145	−	1.80627i	0.563976	−	0.737405i
$7$	−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
$9$	2.12804	+	2.11458i	0.709345	+	0.704861i
$10$	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
$15$	1.99989	+	4.80659i	0.516369	+	1.24106i
$16$	−1.68549	−	2.91935i	−0.421373	−	0.729839i
$17$	−0.0994162	+	0.172194i	−0.0241120	+	0.0417632i	−0.877830	−	0.478973i	$-0.841009\pi$
$17$	−0.0994162	+	0.172194i	−0.0241120	+	0.0417632i	0.853718	+	0.520736i	$0.174342\pi$
$18$	3.40472	−	1.98013i	0.802499	−	0.466722i
$19$	−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
$21$	−5.01665	−	0.652364i	−1.09472	−	0.142358i
$22$	−1.74897	+	3.02930i	−0.372881	+	0.645848i
$23$	1.65038	+	2.85855i	0.344129	+	0.596048i	0.985195	−	0.171437i	$-0.0548410\pi$
$23$	1.65038	+	2.85855i	0.344129	+	0.596048i	−0.641066	+	0.767485i	$0.721508\pi$
$24$	4.77917	−	1.98848i	0.975544	−	0.405897i
$25$			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	−0.168875	−	0.985637i	$-0.554013\pi$
$29$	3.23258	−	1.86633i	0.600274	−	0.346568i	0.769149	+	0.639069i	$0.220680\pi$
$30$	6.77505	−	0.902881i	1.23695	−	0.164843i
$31$	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
$33$	−3.66555	−	2.80345i	−0.638090	−	0.488018i
$34$	0.184586	+	0.184586i	0.0316563	+	0.0316563i
$35$	−7.60277	−	4.38946i	−1.28510	−	0.741955i
$36$	0.217097	+	0.800060i	0.0361828	+	0.133343i
$37$	−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	$0.179486\pi$
$41$	−0.986066	+	3.68005i	−0.153998	+	0.574727i	−0.999189	+	0.0402633i	$0.987180\pi$
$42$	−2.53195	+	6.14019i	−0.390689	+	0.947451i
$43$	−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
$45$	0.0285911	+	9.01709i	0.00426212	+	1.34419i
$46$	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	$0.103884\pi$
$48$	−0.771281	−	5.78754i	−0.111325	−	0.835360i
$49$	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	$-0.614546\pi$
$53$		−	13.6276i		−	1.87189i	0.352142	−	0.935947i	$-0.385454\pi$
$54$	6.75928	−	0.922602i	0.919822	−	0.125550i
$55$	−4.00407	−	6.93525i	−0.539908	−	0.935149i
$56$	−4.36442	+	7.55939i	−0.583220	+	1.01017i
$57$	1.18519	−	9.11402i	0.156982	−	1.20718i
$58$	−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	$0.986399\pi$
$60$	−0.185512	+	1.42658i	−0.0239495	+	0.184170i
$61$	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
$63$	−7.60218	−	4.35704i	−0.957785	−	0.548935i
$64$		−	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
$69$	0.755216	+	5.66699i	0.0909173	+	0.682226i
$70$	−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	$0.313884\pi$
$72$	8.96564	−	0.0284280i	1.05661	−	0.00335027i
$73$	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
$75$	−2.66381	+	6.45995i	−0.307590	+	0.745931i
$76$	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
$81$	0.0570734	+	8.99982i	0.00634148	+	0.999980i
$82$	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	$0.795618\pi$
$84$	−1.11040	−	0.849243i	−0.121154	−	0.0926600i
$85$	−0.577269	+	0.154679i	−0.0626136	+	0.0167773i
$86$	−10.8207	+	10.8207i	−1.16682	+	1.16682i
$87$	6.40850	−	0.854033i	0.687063	−	0.0915619i
$88$	−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
$93$	1.24509	−	0.518049i	0.129110	−	0.0537191i
$94$	−3.98807	−	6.90753i	−0.411338	−	0.712458i
$95$	7.97458	−	13.8124i	0.818175	−	1.41712i
$96$	2.66469	+	0.346516i	0.271964	+	0.0353661i
$97$	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
$99$	−4.01839	−	6.90936i	−0.403863	−	0.694417i
$100$	−0.557400	+	0.965446i	−0.0557400	+	0.0965446i
$101$	−6.19691	−	10.7334i	−0.616616	−	1.06801i	−0.990099	−	0.140373i	$-0.955170\pi$
$101$	−6.19691	−	10.7334i	−0.616616	−	1.06801i	0.373483	−	0.927637i	$-0.378164\pi$
$102$	0.173689	+	0.417450i	0.0171978	+	0.0413337i
$103$			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	−0.788612	−	0.614891i	$-0.789200\pi$
$107$	−6.72785	+	3.88433i	−0.650406	+	0.375512i	0.138206	+	0.990404i	$0.455866\pi$
$108$	−0.180644	+	1.42445i	−0.0173825	+	0.137067i
$109$	−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
$111$	−5.36914	+	7.02022i	−0.509616	+	0.666330i
$112$	6.96202	+	6.96202i	0.657849	+	0.657849i
$113$	14.7985	+	8.54390i	1.39212	+	0.803743i	0.993550	−	0.113394i	$-0.0361721\pi$
$113$	14.7985	+	8.54390i	1.39212	+	0.803743i	0.398573	+	0.917136i	$0.369505\pi$
$114$	−11.1552	−	4.59994i	−1.04478	−	0.430823i
$115$	−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
$120$	14.3837	+	5.93122i	1.31304	+	0.541444i
$121$	−3.37877	−	1.95074i	−0.307161	−	0.177340i
$122$	−2.50742	−	2.50742i	−0.227011	−	0.227011i
$123$	−4.00884	+	5.24161i	−0.361465	+	0.472620i
$124$	0.207818	−	0.0556848i	0.0186627	−	0.00500064i
$125$	2.05245	−	2.05245i	0.183577	−	0.183577i
$126$	−8.10860	+	8.16019i	−0.722372	+	0.726967i
$127$	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	$0.174035\pi$
$131$			11.9013i			1.03982i	−0.854221	+	0.519910i	$0.825965\pi$
$132$	−0.489860	−	1.17734i	−0.0426368	−	0.102475i
$133$	7.74916	+	13.4219i	0.671937	+	1.16383i
$134$	−4.95390	+	8.58041i	−0.427952	+	0.741234i
$135$	−5.90811	+	14.4575i	−0.508489	+	1.24431i
$136$	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	$0.650020\pi$
$138$	7.44322	+	0.967917i	0.633609	+	0.0823945i
$139$	−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
$141$	9.71528	−	4.04226i	0.818174	−	0.340420i
$142$		−	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
$147$	2.62814	−	0.350240i	0.216765	−	0.0288873i
$148$	−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	$0.640310\pi$
$150$	7.28702	+	5.57320i	0.594983	+	0.455050i
$151$	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
$153$	−0.575680	+	0.156211i	−0.0465410	+	0.0126289i
$154$	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
$159$	8.99815	−	21.8212i	0.713600	−	1.73054i
$160$	4.03836	+	2.33155i	0.319260	+	0.184325i
$161$	−6.81701	−	6.81701i	−0.537256	−	0.537256i
$162$	11.4325	+	2.98576i	0.898223	+	0.234583i
$163$	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
$165$	−1.83226	−	13.7489i	−0.142641	−	1.07035i
$166$	−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
$171$	7.91567	−	13.8113i	0.605327	−	1.05618i
$172$	−1.61043	−	2.78934i	−0.122794	−	0.212685i
$173$	6.21160	−	10.7588i	0.472259	−	0.817977i	−0.527237	−	0.849718i	$-0.676772\pi$
$173$	6.21160	−	10.7588i	0.472259	−	0.817977i	0.999496	+	0.0317413i	$0.0101053\pi$
$174$	1.09456	−	8.41714i	0.0829787	−	0.638101i
$175$	−3.04971	−	11.3817i	−0.230537	−	0.860374i
$176$	2.32454	+	8.67529i	0.175219	+	0.653925i
$177$	0.745689	−	5.73431i	0.0560494	−	0.431017i
$178$	0.721194	−	1.24914i	0.0540557	−	0.0936273i
$179$	8.15142	+	14.1187i	0.609265	+	1.05528i	0.991362	+	0.131156i	$0.0418689\pi$
$179$	8.15142	+	14.1187i	0.609265	+	1.05528i	−0.382096	+	0.924123i	$0.624798\pi$
$180$	−1.23901	+	2.16182i	−0.0923501	+	0.161133i
$181$			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
$186$	−0.233881	−	1.75500i	−0.0171490	−	0.128683i
$187$	0.374590	−	0.374590i	0.0273928	−	0.0273928i
$188$	1.62158	−	0.434500i	0.118266	−	0.0316892i
$189$	−9.29612	−	11.9964i	−0.676193	−	0.872607i
$190$	−14.8064	−	14.8064i	−1.07417	−	1.07417i
$191$	1.75656	+	1.01415i	0.127100	+	0.0733813i	0.562202	−	0.827000i	$-0.309954\pi$
$191$	1.75656	+	1.01415i	0.127100	+	0.0733813i	−0.435102	+	0.900381i	$0.643288\pi$
$192$	5.79654	−	14.0571i	0.418329	−	1.01448i
$193$	−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	−0.999904	−	0.0138237i	$-0.995600\pi$
$197$	−1.78323	+	6.65511i	−0.127050	+	0.474157i	0.872855	+	0.487981i	$0.162266\pi$
$198$	−10.1276	+	2.74812i	−0.719734	+	0.195300i
$199$	−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
$201$	−10.3826	−	7.94071i	−0.732330	−	0.560094i
$202$	−15.7172	+	4.21142i	−1.10586	+	0.296315i
$203$	−7.70898	+	7.70898i	−0.541065	+	0.541065i
$204$	−0.0943309	+	0.0125711i	−0.00660449	+	0.000880151i
$205$	−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
$210$	−18.4314	+	7.66880i	−1.27189	+	0.529197i
$211$	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
$213$	9.18494	+	1.19441i	0.629342	+	0.0818396i
$214$	2.63979	+	9.85182i	0.180452	+	0.673457i
$215$	−9.06747	−	33.8402i	−0.618396	−	2.30789i
$216$	14.3751	+	5.87440i	0.978098	+	0.399702i
$217$	−1.13704	+	1.96941i	−0.0771873	+	0.133692i
$218$	6.66886	+	11.5508i	0.451672	+	0.782319i
$219$	3.25776	+	7.82981i	0.220139	+	0.529089i
$220$		−	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
$225$	−8.53087	+	8.58514i	−0.568725	+	0.572343i
$226$	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	$0.0871296\pi$
$228$	1.54287	−	2.01732i	0.102179	−	0.133600i
$229$	−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
$231$	12.4606	+	5.13822i	0.819847	+	0.338070i
$232$	2.88720	−	10.7752i	0.189554	−	0.707425i
$233$	−14.4551			−0.946988			−0.473494	−	0.880797i	$-0.657007\pi$
$233$	−14.4551			−0.946988			−0.473494	+	0.880797i	$0.657007\pi$
$234$		0			0
$235$	18.2605			1.19118
$236$	0.238774	−	0.891116i	0.0155428	−	0.0580067i
$237$	−17.8342	−	7.35405i	−1.15845	−	0.477697i
$238$	−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	$0.812161\pi$
$240$	10.6614	−	13.9399i	0.688188	−	0.899814i
$241$	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
$243$	−5.85110	+	14.4487i	−0.375348	+	0.926884i
$244$	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
$249$	−1.73151	−	4.16156i	−0.109730	−	0.263728i
$250$	−1.90540	−	3.30024i	−0.120508	−	0.208726i
$251$	−10.8649	+	18.8186i	−0.685789	+	1.18782i	0.287400	+	0.957811i	$0.407209\pi$
$251$	−10.8649	+	18.8186i	−0.685789	+	1.18782i	−0.973188	+	0.230010i	$0.926124\pi$
$252$	−1.21728	−	2.09304i	−0.0766814	−	0.131849i
$253$	−2.27612	−	8.49459i	−0.143098	−	0.534051i
$254$	−3.27066	−	12.2063i	−0.205220	−	0.765891i
$255$	−1.02649	−	0.133484i	−0.0642812	−	0.00835912i
$256$	3.24975	−	5.62873i	0.203109	−	0.351796i
$257$	−8.15559	−	14.1259i	−0.508732	−	0.881149i	−0.999949	−	0.0101119i	$-0.996781\pi$
$257$	−8.15559	−	14.1259i	−0.508732	−	0.881149i	0.491217	−	0.871037i	$-0.336552\pi$
$258$	−24.4714	+	10.1819i	−1.52353	+	0.633897i
$259$		−	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	−0.160582	−	0.987023i	$-0.551337\pi$
$263$	9.95602	−	5.74811i	0.613914	−	0.354444i	0.774496	+	0.632579i	$0.218004\pi$
$264$	−13.6705	+	1.82181i	−0.841361	+	0.112125i
$265$	28.9635	−	28.9635i	1.77922	−	1.77922i
$266$	19.6542	−	5.26633i	1.20508	−	0.322899i
$267$	1.51151	+	1.15602i	0.0925026	+	0.0707470i
$268$	−1.47457	−	1.47457i	−0.0900734	−	0.0900734i
$269$	−9.64658	−	5.56946i	−0.588162	−	0.339576i	0.176208	−	0.984353i	$-0.443617\pi$
$269$	−9.64658	−	5.56946i	−0.588162	−	0.339576i	−0.764371	+	0.644777i	$0.776950\pi$
$270$	16.3268	+	12.4050i	0.993615	+	0.754947i
$271$	−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
$276$	−0.602251	+	1.46051i	−0.0362513	+	0.0879123i
$277$	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
$279$	2.33577	−	0.00740621i	0.139839	−	0.000443398i
$280$	−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	$0.0869585\pi$
$282$	−1.82494	−	13.6940i	−0.108674	−	0.815466i
$283$	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
$288$	4.03804	+	2.31433i	0.237944	+	0.136373i
$289$	8.48023	+	14.6882i	0.498837	+	0.864011i
$290$	7.36482	−	12.7563i	0.432477	−	0.749073i
$291$	−2.71691	+	20.8929i	−0.159268	+	1.22476i
$292$	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	$0.889718\pi$
$294$	0.448883	−	3.45188i	0.0261794	−	0.201318i
$295$	5.01740	−	8.69039i	0.292124	−	0.505974i
$296$	7.62480	+	13.2065i	0.443182	+	0.767614i
$297$	−1.87228	−	13.7170i	−0.108641	−	0.795938i
$298$			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
$303$	−2.83571	−	21.2786i	−0.162907	−	1.22242i
$304$	−12.6483	+	12.6483i	−0.725429	+	0.725429i
$305$	7.84164	−	2.10116i	0.449011	−	0.120312i
$306$	0.00248313	+	0.783129i	0.000141951	+	0.0447685i
$307$	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
$309$	−3.75571	+	9.10790i	−0.213655	+	0.518130i
$310$	0.795211	−	2.96777i	0.0451649	−	0.168558i
$311$	−26.9755			−1.52964			−0.764821	−	0.644243i	$-0.777172\pi$
$311$	−26.9755			−1.52964			−0.764821	+	0.644243i	$0.777172\pi$
$312$		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
$315$	−6.89709	−	25.4176i	−0.388607	−	1.43212i
$316$	−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	$0.419578\pi$
$318$	−24.6151	−	18.8259i	−1.38034	−	1.05570i
$319$	−9.60608	+	2.57394i	−0.537837	+	0.144113i
$320$	18.6581	−	18.6581i	1.04302	−	1.04302i
$321$	−13.3378	+	1.77747i	−0.744443	+	0.0992087i
$322$	−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
$327$	−16.2459	+	6.75948i	−0.898402	+	0.373800i
$328$	5.69301	+	9.86058i	0.314344	+	0.544460i
$329$	−8.87216	+	15.3670i	−0.489138	+	0.847212i
$330$	−18.0583	−	2.34831i	−0.994079	−	0.129270i
$331$	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
$333$	−13.2327	+	7.69597i	−0.725150	+	0.421737i
$334$	−1.03799	+	1.79785i	−0.0567964	+	0.0983742i
$335$	−11.3414	−	19.6439i	−0.619648	−	1.07326i
$336$	6.55102	+	15.7449i	0.357388	+	0.858956i
$337$			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
$342$	−14.8251	−	14.7313i	−0.801647	−	0.796580i
$343$	11.2955	−	11.2955i	0.609900	−	0.609900i
$344$	−33.6472	+	9.01573i	−1.81413	+	0.486096i
$345$	−10.4393	+	13.6495i	−0.562033	+	0.734864i
$346$	−11.5331	−	11.5331i	−0.620023	−	0.620023i
$347$	−14.2117	−	8.20511i	−0.762923	−	0.440474i	0.0674214	−	0.997725i	$-0.478523\pi$
$347$	−14.2117	−	8.20511i	−0.762923	−	0.440474i	−0.830344	+	0.557251i	$0.811856\pi$
$348$	1.65161	+	0.681053i	0.0885356	+	0.0365083i
$349$	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	−0.996680	−	0.0814189i	$-0.974055\pi$
$353$	−1.74394	+	6.50846i	−0.0928203	+	0.346410i	0.903860	+	0.427829i	$0.140721\pi$
$354$	−7.01858	−	2.89416i	−0.373033	−	0.153823i
$355$	13.9199	+	8.03664i	0.738790	+	0.426540i
$356$	0.214669	+	0.214669i	0.0113774	+	0.0113774i
$357$	0.611069	−	0.798980i	0.0323412	−	0.0422865i
$358$	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	$0.331289\pi$
$360$	19.1156	+	18.9948i	1.00748	+	1.00111i
$361$	−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
$366$	−2.35940	−	5.67065i	−0.123328	−	0.296410i
$367$	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
$369$	−9.88015	+	5.74615i	−0.514340	+	0.299133i
$370$	5.21154	+	19.4497i	0.270935	+	1.01114i
$371$	10.3017	+	38.4465i	0.534838	+	1.99604i
$372$	0.369539	+	0.0480548i	0.0191597	+	0.00249152i
$373$	−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
$375$	4.64172	−	1.93129i	0.239697	−	0.0997313i
$376$		−	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
$381$	16.5254	−	2.20226i	0.846620	−	0.112825i
$382$	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	$0.501040\pi$
$384$	−11.5880	−	8.86261i	−0.591346	−	0.452268i
$385$	16.5390	+	16.5390i	0.842908	+	0.842908i
$386$	4.51698	+	2.60788i	0.229908	+	0.132738i
$387$	−9.15729	−	33.7471i	−0.465491	−	1.71546i
$388$	−0.869969	+	3.24677i	−0.0441660	+	0.164830i
$389$	30.1074			1.52650			0.763252	−	0.646101i	$-0.223602\pi$
$389$	30.1074			1.52650			0.763252	+	0.646101i	$0.223602\pi$
$390$		0			0
$391$	−0.656299			−0.0331905
$392$	1.18405	−	4.41892i	0.0598033	−	0.223189i
$393$	−7.85830	+	19.0570i	−0.396399	+	0.961299i
$394$	7.83374	+	4.52281i	0.394658	+	0.227856i
$395$	−23.6714	−	23.6714i	−1.19104	−	1.19104i
$396$	−0.00700321	−	2.20868i	−0.000351925	−	0.110990i
$397$	−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
$399$	3.54602	+	26.6086i	0.177523	+	1.33210i
$400$	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
$405$	−19.0065	+	19.2491i	−0.944443	+	0.956498i
$406$	7.15664	+	12.3957i	0.355178	+	0.615186i
$407$	6.79751	−	11.7736i	0.336940	−	0.583598i
$408$	−0.132723	+	1.02063i	−0.00657076	+	0.0505288i
$409$	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
$411$	−3.88540	+	29.8785i	−0.191653	+	1.47380i
$412$	−0.785880	+	1.36118i	−0.0387175	+	0.0670608i
$413$	4.87557	+	8.44474i	0.239911	+	0.415538i
$414$	11.2794	+	6.46456i	0.554352	+	0.317716i
$415$		−	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	0.457983	−	0.888961i	$-0.348572\pi$
$419$	29.8207	−	17.2170i	1.45684	−	0.841106i	0.998854	+	0.0478553i	$0.0152386\pi$
$420$	−0.555043	−	4.16493i	−0.0270833	−	0.203228i
$421$	−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
$423$	18.2257	−	0.0577896i	0.886164	−	0.00280983i
$424$	−28.7983	−	28.7983i	−1.39857	−	1.39857i
$425$	−0.694683	−	0.401075i	−0.0336971	−	0.0194550i
$426$	4.63573	−	11.2420i	0.224602	−	0.544678i
$427$	−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	$-0.00446966\pi$
$432$	10.5969	−	13.9470i	0.509845	−	0.671027i
$433$	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
$435$	15.4355	+	11.8052i	0.740075	+	0.566017i
$436$	−2.71161	+	0.726573i	−0.129862	+	0.0347965i
$437$	12.3848	−	12.3848i	0.592447	−	0.592447i
$438$	11.0364	−	1.47077i	0.527338	−	0.0702760i
$439$	−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	$-0.856733\pi$
$443$		−	18.3132i		−	0.870087i	0.900409	−	0.435043i	$-0.143267\pi$
$444$	−2.25484	+	0.938174i	−0.107010	+	0.0445238i
$445$	1.65110	+	2.85978i	0.0782694	+	0.135567i
$446$	−2.02845	+	3.51338i	−0.0960500	+	0.166364i
$447$	−27.0963	−	3.52361i	−1.28161	−	0.166661i
$448$	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	$0.931237\pi$
$450$	7.98846	+	13.7357i	0.376580	+	0.647505i
$451$	5.07532	−	8.79072i	0.238988	−	0.413939i
$452$	2.36094	+	4.08927i	0.111049	+	0.192343i
$453$	8.06311	+	19.3791i	0.378838	+	0.910510i
$454$		−	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
$459$	−1.02495	−	0.129982i	−0.0478408	−	0.00606702i
$460$	−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	$0.524806\pi$
$462$	10.7501	−	14.0559i	0.500142	−	0.653942i
$463$	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
$465$	3.74731	+	1.54523i	0.173777	+	0.0716584i
$466$	−4.91185	+	18.3313i	−0.227537	+	0.849181i
$467$	37.5105			1.73578			0.867888	−	0.496759i	$-0.165477\pi$
$467$	37.5105			1.73578			0.867888	+	0.496759i	$0.165477\pi$
$468$		0			0
$469$	22.0417			1.01779
$470$	6.20491	−	23.1571i	0.286211	−	1.06816i
$471$	−5.23179	−	2.15737i	−0.241068	−	0.0994063i
$472$	−8.64081	−	4.98877i	−0.397726	−	0.229627i
$473$	21.9589	+	21.9589i	1.00967	+	1.00967i
$474$	−15.3861	+	20.1175i	−0.706707	+	0.924028i
$475$	20.6777	−	5.54058i	0.948759	−	0.254219i
$476$	0.113474	−	0.113474i	0.00520106	−	0.00520106i
$477$	28.8167	−	29.0000i	1.31942	−	1.32782i
$478$	−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
$483$	−6.41457	−	15.4170i	−0.291873	−	0.701496i
$484$	−0.539048	−	0.933658i	−0.0245022	−	0.0424390i
$485$	−18.2808	+	31.6633i	−0.830090	+	1.43776i
$486$	16.3349	+	12.3297i	0.740967	+	0.559288i
$487$	−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
$489$	10.0106	+	1.30178i	0.452697	+	0.0588687i
$490$	3.02033	−	5.23136i	0.136444	−	0.236329i
$491$	3.76608	+	6.52305i	0.169961	+	0.294381i	0.938406	−	0.345535i	$-0.112302\pi$
$491$	3.76608	+	6.52305i	0.169961	+	0.294381i	−0.768445	+	0.639916i	$0.778969\pi$
$492$	−1.68356	+	0.700482i	−0.0759007	+	0.0315802i
$493$			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
$498$	−5.86584	+	0.781716i	−0.262855	+	0.0350295i
$499$	−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
$501$	−2.17546	−	1.66382i	−0.0971925	−	0.0743339i
$502$	20.1729	+	20.1729i	0.900362	+	0.900362i
$503$	−2.03490	−	1.17485i	−0.0907316	−	0.0523839i	0.453948	−	0.891028i	$-0.350015\pi$
$503$	−2.03490	−	1.17485i	−0.0907316	−	0.0523839i	−0.544679	+	0.838644i	$0.683349\pi$
$504$	−25.2726	+	6.85774i	−1.12573	+	0.305468i
$505$	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	$-0.147948\pi$
$510$	−0.518079	+	1.25638i	−0.0229409	+	0.0556336i
$511$	−12.3847	−	7.15031i	−0.547867	−	0.316311i
$512$	−17.9453	−	17.9453i	−0.793080	−	0.793080i
$513$	21.7945	−	16.8888i	0.962249	−	0.745658i
$514$	−20.6850	+	5.54254i	−0.912377	+	0.244471i
$515$	−12.0890	+	12.0890i	−0.532705	+	0.532705i
$516$	−0.736932	−	5.52980i	−0.0324416	−	0.243436i
$517$	−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	$-0.958421\pi$
$521$		−	5.94611i		−	0.260504i	0.991481	−	0.130252i	$-0.0415786\pi$
$522$	7.31042	−	12.7553i	0.319968	−	0.558282i
$523$	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
$525$	2.63184	−	20.2387i	0.114863	−	0.883288i
$526$	−3.90641	−	14.5789i	−0.170328	−	0.635672i
$527$	0.0400678	+	0.149535i	0.00174538	+	0.00651385i
$528$	−2.00603	+	15.4262i	−0.0873011	+	0.671340i
$529$	6.05247	−	10.4832i	0.263151	−	0.455791i
$530$	−26.8883	−	46.5719i	−1.16795	−	2.02295i
$531$	4.98034	−	8.68971i	0.216128	−	0.377102i
$532$			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
$537$	3.73009	+	27.9899i	0.160965	+	1.20785i
$538$	−10.3408	+	10.3408i	−0.445824	+	0.445824i
$539$	−3.93947	+	1.05558i	−0.169685	+	0.0454669i
$540$	−3.41139	+	2.64353i	−0.146803	+	0.113759i
$541$	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
$543$	−6.13819	+	14.8856i	−0.263415	+	0.638802i
$544$	−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
$549$	7.82005	−	2.12197i	0.333751	−	0.0905636i
$550$	−12.2211	−	7.05585i	−0.521109	−	0.300863i
$551$	−14.0053	−	14.0053i	−0.596647	−	0.596647i
$552$	13.5716	+	10.3797i	0.577647	+	0.441791i
$553$	31.4217	−	8.41943i	1.33619	−	0.358031i
$554$	25.7905	−	25.7905i	1.09573	−	1.09573i
$555$	−26.3318	+	3.50913i	−1.11772	+	0.148954i
$556$	−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
$561$	0.847152	−	0.352477i	0.0357668	−	0.0148816i
$562$	−10.7862	−	18.6823i	−0.454989	−	0.788064i
$563$	−6.70261	+	11.6093i	−0.282481	+	0.489272i	−0.971995	−	0.235000i	$-0.924491\pi$
$563$	−6.70261	+	11.6093i	−0.282481	+	0.489272i	0.689514	+	0.724272i	$0.257824\pi$
$564$	2.88346	+	0.374965i	0.121415	+	0.0157889i
$565$	13.2932	+	49.6109i	0.559250	+	2.08715i
$566$	−9.03429	−	33.7164i	−0.379740	−	1.41721i
$567$	−6.96439	−	25.3474i	−0.292477	−	1.06449i
$568$	7.99078	−	13.8404i	0.335286	−	0.580732i
$569$	11.3396	+	19.6407i	0.475380	+	0.823382i	0.999602	−	0.0281995i	$-0.00897737\pi$
$569$	11.3396	+	19.6407i	0.475380	+	0.823382i	−0.524223	+	0.851581i	$0.675644\pi$
$570$	−13.9323	−	33.4854i	−0.583561	−	1.40255i
$571$			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
$576$	18.5635	−	18.6816i	0.773478	−	0.778399i
$577$	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
$579$	−4.18022	+	5.46569i	−0.173724	+	0.227146i
$580$	2.19219	+	2.19219i	0.0910259	+	0.0910259i
$581$	6.58249	+	3.80040i	0.273088	+	0.157667i
$582$	25.5721	+	10.5448i	1.06000	+	0.437098i
$583$	−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	$0.164652\pi$
$588$	0.677328	+	0.279301i	0.0279325	+	0.0115182i
$589$	−3.57794	−	2.06572i	−0.147426	−	0.0851166i
$590$	−9.31581	−	9.31581i	−0.383526	−	0.383526i
$591$	−7.24970	+	9.47908i	−0.298213	+	0.389917i
$592$	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	$0.858784\pi$
$594$	−18.0314	−	2.28668i	−0.739836	−	0.0938237i
$595$	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	$-0.923929\pi$
$599$		−	11.5870i		−	0.473430i	0.971579	−	0.236715i	$-0.0760708\pi$
$600$	8.02213	+	19.2806i	0.327502	+	0.787128i
$601$	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
$603$	−11.3820	−	19.5706i	−0.463510	−	0.796977i
$604$	0.866700	+	3.23457i	0.0352655	+	0.131613i
$605$	−3.03509	−	11.3271i	−0.123394	−	0.460513i
$606$	−27.9481	−	3.63437i	−1.13531	−	0.147636i
$607$	−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
$609$	−17.4342	+	7.25389i	−0.706470	+	0.293942i
$610$		−	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
$615$	−19.6605	+	2.62007i	−0.792789	+	0.105652i
$616$	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	$0.459347\pi$
$618$	10.2740	+	7.85767i	0.413281	+	0.316082i
$619$	−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
$621$	−10.3762	+	13.6565i	−0.416383	+	0.548018i
$622$	−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
$627$	−9.33488	+	22.6378i	−0.372799	+	0.904069i
$628$	−0.781896	−	0.451428i	−0.0312011	−	0.0180139i
$629$	−0.717411	−	0.717411i	−0.0286051	−	0.0286051i
$630$	−34.5770	+	0.109636i	−1.37758	+	0.00436800i
$631$	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
$633$	0.183561	+	1.37740i	0.00729588	+	0.0547469i
$634$	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
$639$	13.9188	+	7.97727i	0.550618	+	0.315576i
$640$	−12.6581	−	21.9245i	−0.500357	−	0.866644i
$641$	7.43034	−	12.8697i	0.293481	−	0.508323i	−0.681150	−	0.732144i	$-0.738520\pi$
$641$	7.43034	−	12.8697i	0.293481	−	0.508323i	0.974630	+	0.223821i	$0.0718530\pi$
$642$	−2.27808	+	17.5183i	−0.0899086	+	0.691392i
$643$	−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
$645$	7.82503	−	60.1740i	0.308110	−	2.36935i
$646$	0.692588	−	1.19960i	0.0272495	−	0.0471975i
$647$	18.8371	+	32.6268i	0.740562	+	1.28269i	0.952240	+	0.305351i	$0.0987739\pi$
$647$	18.8371	+	32.6268i	0.740562	+	1.28269i	−0.211678	+	0.977340i	$0.567893\pi$
$648$	19.1393	+	18.8981i	0.751864	+	0.742388i
$649$			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	−0.0726369	−	0.997358i	$-0.523141\pi$
$653$	19.2876	−	11.1357i	0.754782	−	0.435774i	0.827419	+	0.561585i	$0.189808\pi$
$654$	3.05167	+	22.8992i	0.119330	+	0.895428i
$655$	−25.2945	+	25.2945i	−0.988339	+	0.988339i
$656$	12.4054	−	3.32401i	0.484348	−	0.129781i
$657$	0.0465742	+	14.6886i	0.00181703	+	0.573056i
$658$	16.4729	+	16.4729i	0.642182	+	0.642182i
$659$	23.2104	+	13.4005i	0.904148	+	0.522010i	0.878544	−	0.477662i	$-0.158516\pi$
$659$	23.2104	+	13.4005i	0.904148	+	0.522010i	0.0256043	+	0.999672i	$0.491849\pi$
$660$	1.46115	−	3.54340i	0.0568751	−	0.137927i
$661$	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
$666$	5.26317	+	19.3962i	0.203944	+	0.751587i
$667$	10.6700	+	6.16031i	0.413143	+	0.238528i
$668$	−0.308966	−	0.308966i	−0.0119543	−	0.0119543i
$669$	−4.25131	−	3.25145i	−0.164365	−	0.125708i
$670$	−28.7653	+	7.70763i	−1.11130	+	0.297772i
$671$	−5.08844	+	5.08844i	−0.196437	+	0.196437i
$672$	−7.77963	+	1.03676i	−0.300106	+	0.0399938i
$673$	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	$0.101924\pi$
$677$			16.3795i			0.629517i	−0.949172	+	0.314758i	$0.898076\pi$
$678$	35.8760	−	14.9270i	1.37781	−	0.573267i
$679$	−17.7641	−	30.7683i	−0.681723	−	1.18078i
$680$	−0.893032	+	1.54678i	−0.0342462	+	0.0593162i
$681$	44.5104	+	5.78813i	1.70564	+	0.221801i
$682$	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	$0.653878\pi$
$684$	3.80253	−	2.21150i	0.145394	−	0.0845588i
$685$	−26.1431	+	45.2812i	−0.998876	+	1.73010i
$686$	−10.4862	−	18.1626i	−0.400364	−	0.693451i
$687$	−18.4815	−	44.4190i	−0.705114	−	1.69469i
$688$			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
$693$	16.5599	+	16.4552i	0.629058	+	0.625081i
$694$	−15.2344	+	15.2344i	−0.578292	+	0.578292i
$695$	−6.76192	+	1.81185i	−0.256494	+	0.0687274i
$696$	11.7379	−	15.3474i	0.444923	−	0.581742i
$697$	−0.535651	−	0.535651i	−0.0202892	−	0.0202892i
$698$	−34.0809	−	19.6766i	−1.28998	−	0.744771i
$699$	−23.1464	−	9.54457i	−0.875476	−	0.361009i
$700$	0.842728	−	3.14510i	0.0318521	−	0.118874i
$701$	−12.7471			−0.481453			−0.240726	−	0.970593i	$-0.577386\pi$
$701$	−12.7471			−0.481453			−0.240726	+	0.970593i	$0.577386\pi$
$702$		0			0
$703$	27.0761			1.02120
$704$	−6.05362	+	22.5924i	−0.228154	+	0.851483i
$705$	29.2397	+	12.0572i	1.10123	+	0.454101i
$706$	7.66111	+	4.42315i	0.288330	+	0.166467i
$707$	25.5967	+	25.5967i	0.962664	+	0.962664i
$708$	0.970732	−	1.26924i	0.0364823	−	0.0477011i
$709$	−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
$711$	−23.7013	−	23.5514i	−0.888866	−	0.883247i
$712$	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
$717$	−3.99203	−	9.59455i	−0.149085	−	0.358315i
$718$	6.28386	+	10.8840i	0.234512	+	0.406186i
$719$	17.7809	−	30.7974i	0.663116	−	1.14855i	−0.316677	−	0.948534i	$-0.602567\pi$
$719$	17.7809	−	30.7974i	0.663116	−	1.14855i	0.979793	−	0.200017i	$-0.0640996\pi$
$720$	26.2759	−	15.2817i	0.979245	−	0.569515i
$721$	−4.29980	−	16.0471i	−0.160133	−	0.597624i
$722$	3.11143	+	11.6120i	0.115795	+	0.432154i
$723$	42.3873	+	5.51205i	1.57640	+	0.204995i
$724$	−1.28441	+	2.22467i	−0.0477348	+	0.0826791i
$725$	7.52933	+	13.0412i	0.279632	+	0.484338i
$726$	−8.19116	+	3.40812i	−0.304003	+	0.126487i
$727$		−	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
$732$	1.28139	−	0.170766i	0.0473617	−	0.00631168i
$733$	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
$735$	6.33012	+	4.84134i	0.233490	+	0.178576i
$736$	3.62099	+	3.62099i	0.133471	+	0.133471i
$737$	17.4127	+	10.0532i	0.641403	+	0.370314i
$738$	3.92971	+	14.4821i	0.144655	+	0.533092i
$739$	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	$-0.699373\pi$
$743$	8.90116	−	33.2196i	0.326552	−	1.21871i	0.912743	−	0.408535i	$-0.133960\pi$
$744$	1.53641	−	3.72593i	0.0563277	−	0.136599i
$745$	−41.0648	−	23.7087i	−1.50450	−	0.868621i
$746$	12.4015	+	12.4015i	0.454051	+	0.454051i
$747$	−0.0247543	−	7.80701i	−0.000905711	−	0.285643i
$748$	0.141398	−	0.0378875i	0.00517003	−	0.00138531i
$749$	16.0445	−	16.0445i	0.586252	−	0.586252i
$750$	−0.871910	−	6.54264i	−0.0318377	−	0.238904i
$751$	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
$756$	−0.567166	−	4.15524i	−0.0206276	−	0.151125i
$757$	−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
$759$	1.96424	−	15.1049i	0.0712975	−	0.548274i
$760$	−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	$-0.242683\pi$
$762$	2.82251	−	21.7050i	0.102249	−	0.786288i
$763$	14.8361	−	25.6968i	0.537101	−	0.930287i
$764$	0.280241	+	0.485391i	0.0101387	+	0.0175608i
$765$	−1.55553	−	0.891522i	−0.0562403	−	0.0322330i
$766$			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
$771$	−3.73200	−	28.0042i	−0.134405	−	1.00855i
$772$	−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	+	0.771693i	$0.280590\pi$

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} +(1.60126 + 0.660289i) q^{3} +(0.239309 + 0.138165i) q^{4} +(2.12536 + 2.12536i) q^{5} +(1.38145 - 1.80627i) q^{6} +(-2.82123 + 0.755945i) q^{7} +(2.11323 - 2.11323i) q^{8} +(2.12804 + 2.11458i) q^{9} +(3.41747 - 1.97308i) q^{10} +(-2.57352 - 0.689573i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(1.99989 + 4.80659i) q^{15} +(-1.68549 - 2.91935i) q^{16} +(-0.0994162 + 0.172194i) q^{17} +(3.40472 - 1.98013i) q^{18} +(-1.37337 - 5.12548i) q^{19} +(0.214967 + 0.802269i) q^{20} +(-5.01665 - 0.652364i) q^{21} +(-1.74897 + 3.02930i) q^{22} +(1.65038 + 2.85855i) q^{23} +(4.77917 - 1.98848i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(-0.779591 - 0.208891i) q^{28} +(3.23258 - 1.86633i) q^{29} +(6.77505 - 0.902881i) q^{30} +(0.550550 - 0.550550i) q^{31} +(1.49855 - 0.401535i) q^{32} +(-3.66555 - 2.80345i) q^{33} +(0.184586 + 0.184586i) q^{34} +(-7.60277 - 4.38946i) q^{35} +(0.217097 + 0.800060i) q^{36} +(-1.32066 + 4.92878i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(-0.986066 + 3.68005i) q^{41} +(-2.53195 + 6.14019i) q^{42} +(-10.0942 - 5.82790i) q^{43} +(-0.520592 - 0.520592i) q^{44} +(0.0285911 + 9.01709i) q^{45} +(4.18587 - 1.12160i) q^{46} +(4.29586 - 4.29586i) q^{47} +(-0.771281 - 5.78754i) q^{48} +(1.32568 - 0.765385i) q^{49} +(5.11610 + 1.37086i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(6.75928 - 0.922602i) q^{54} +(-4.00407 - 6.93525i) q^{55} +(-4.36442 + 7.55939i) q^{56} +(1.18519 - 9.11402i) q^{57} +(-1.26836 - 4.73357i) q^{58} +(-0.864088 - 3.22482i) q^{59} +(-0.185512 + 1.42658i) q^{60} +(1.35047 - 2.33909i) q^{61} +(-0.511103 - 0.885257i) q^{62} +(-7.60218 - 4.35704i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(-7.28944 - 1.95320i) q^{67} +(-0.0475824 + 0.0274717i) q^{68} +(0.755216 + 5.66699i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(5.16536 - 1.38405i) q^{71} +(8.96564 - 0.0284280i) q^{72} +(3.46215 + 3.46215i) q^{73} +(5.80168 + 3.34960i) q^{74} +(-2.66381 + 6.45995i) q^{75} +(0.379503 - 1.41633i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(2.62241 - 9.78695i) q^{80} +(0.0570734 + 8.99982i) q^{81} +(4.33179 + 2.50096i) q^{82} +(-1.84014 - 1.84014i) q^{83} +(-1.11040 - 0.849243i) q^{84} +(-0.577269 + 0.154679i) q^{85} +(-10.8207 + 10.8207i) q^{86} +(6.40850 - 0.854033i) q^{87} +(-6.89568 + 3.98122i) q^{88} +(1.06120 + 0.284349i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(1.24509 - 0.518049i) q^{93} +(-3.98807 - 6.90753i) q^{94} +(7.97458 - 13.8124i) q^{95} +(2.66469 + 0.346516i) q^{96} +(3.14829 + 11.7496i) q^{97} +(-0.520155 - 1.94125i) q^{98} +(-4.01839 - 6.90936i) 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

Fields

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Groups

Database

Properties

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