LMFDB - Embedded newform 507.2.k.k.89.8

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			89.8
Character	$\chi$	$=$	507.89
Dual form			507.2.k.k.188.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26815 - 0.339800i) q^{2} +(1.60126 + 0.660289i) q^{3} +(-0.239309 - 0.138165i) q^{4} +(2.12536 - 2.12536i) q^{5} +(-1.80627 - 1.38145i) q^{6} +(-0.755945 - 2.82123i) q^{7} +(2.11323 + 2.11323i) q^{8} +(2.12804 + 2.11458i) q^{9} +(-3.41747 + 1.97308i) q^{10} +(0.689573 - 2.57352i) q^{11} +(-0.291966 - 0.379251i) q^{12} +3.83461i q^{14} +(4.80659 - 1.99989i) q^{15} +(-1.68549 - 2.91935i) q^{16} +(0.0994162 - 0.172194i) q^{17} +(-1.98013 - 3.40472i) q^{18} +(-5.12548 + 1.37337i) q^{19} +(-0.802269 + 0.214967i) q^{20} +(0.652364 - 5.01665i) q^{21} +(-1.74897 + 3.02930i) q^{22} +(-1.65038 - 2.85855i) q^{23} +(1.98848 + 4.77917i) q^{24} -4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(-0.208891 + 0.779591i) q^{28} +(3.23258 - 1.86633i) q^{29} +(-6.77505 + 0.902881i) q^{30} +(-0.550550 - 0.550550i) q^{31} +(-0.401535 - 1.49855i) q^{32} +(2.80345 - 3.66555i) q^{33} +(-0.184586 + 0.184586i) q^{34} +(-7.60277 - 4.38946i) q^{35} +(-0.217097 - 0.800060i) q^{36} +(-4.92878 - 1.32066i) q^{37} +6.96655 q^{38} +8.98276 q^{40} +(3.68005 + 0.986066i) q^{41} +(-2.53195 + 6.14019i) q^{42} +(10.0942 + 5.82790i) q^{43} +(-0.520592 + 0.520592i) q^{44} +(9.01709 - 0.0285911i) q^{45} +(1.12160 + 4.18587i) q^{46} +(4.29586 + 4.29586i) q^{47} +(-0.771281 - 5.78754i) q^{48} +(-1.32568 + 0.765385i) q^{49} +(-1.37086 + 5.11610i) q^{50} +(0.272889 - 0.210083i) q^{51} -13.6276i q^{53} +(-0.922602 - 6.75928i) q^{54} +(-4.00407 - 6.93525i) q^{55} +(4.36442 - 7.55939i) q^{56} +(-9.11402 - 1.18519i) q^{57} +(-4.73357 + 1.26836i) q^{58} +(3.22482 - 0.864088i) q^{59} +(-1.42658 - 0.185512i) q^{60} +(1.35047 - 2.33909i) q^{61} +(0.511103 + 0.885257i) q^{62} +(4.35704 - 7.60218i) q^{63} +8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(-1.95320 + 7.28944i) q^{67} +(-0.0475824 + 0.0274717i) q^{68} +(-0.755216 - 5.66699i) q^{69} +(8.14992 + 8.14992i) q^{70} +(-1.38405 - 5.16536i) q^{71} +(0.0284280 + 8.96564i) q^{72} +(-3.46215 + 3.46215i) q^{73} +(5.80168 + 3.34960i) q^{74} +(2.66381 - 6.45995i) q^{75} +(1.41633 + 0.379503i) q^{76} -7.78177 q^{77} -11.1376 q^{79} +(-9.78695 - 2.62241i) q^{80} +(0.0570734 + 8.99982i) q^{81} +(-4.33179 - 2.50096i) q^{82} +(-1.84014 + 1.84014i) q^{83} +(-0.849243 + 1.11040i) q^{84} +(-0.154679 - 0.577269i) q^{85} +(-10.8207 - 10.8207i) q^{86} +(6.40850 - 0.854033i) q^{87} +(6.89568 - 3.98122i) q^{88} +(-0.284349 + 1.06120i) q^{89} +(-11.4447 - 3.02775i) q^{90} +0.912102i q^{92} +(-0.518049 - 1.24509i) q^{93} +(-3.98807 - 6.90753i) q^{94} +(-7.97458 + 13.8124i) q^{95} +(0.346516 - 2.66469i) q^{96} +(11.7496 - 3.14829i) q^{97} +(1.94125 - 0.520155i) 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−1.26815	−	0.339800i	−0.896718	−	0.240275i	−0.219112	−	0.975700i	$-0.570316\pi$
$2$	−1.26815	−	0.339800i	−0.896718	−	0.240275i	−0.677606	+	0.735425i	$0.736983\pi$
$3$	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	−0.0483414	−	0.998831i	$-0.515394\pi$
$5$	2.12536	−	2.12536i	0.950489	−	0.950489i	0.998831	+	0.0483414i	$0.0153935\pi$
$6$	−1.80627	−	1.38145i	−0.737405	−	0.563976i
$7$	−0.755945	−	2.82123i	−0.285720	−	1.06632i	−0.948311	−	0.317342i	$-0.897210\pi$
$7$	−0.755945	−	2.82123i	−0.285720	−	1.06632i	0.662591	−	0.748982i	$-0.269457\pi$
$8$	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
$11$	0.689573	−	2.57352i	0.207914	−	0.775946i	−0.780627	−	0.624997i	$-0.785100\pi$
$11$	0.689573	−	2.57352i	0.207914	−	0.775946i	0.988541	−	0.150949i	$-0.0482331\pi$
$12$	−0.291966	−	0.379251i	−0.0842833	−	0.109480i
$13$		0			0
$13$		0			0
$14$			3.83461i			1.02484i
$15$	4.80659	−	1.99989i	1.24106	−	0.516369i
$16$	−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
$19$	−5.12548	+	1.37337i	−1.17586	+	0.315072i	−0.793285	−	0.608850i	$-0.791631\pi$
$19$	−5.12548	+	1.37337i	−1.17586	+	0.315072i	−0.382580	+	0.923922i	$0.624964\pi$
$20$	−0.802269	+	0.214967i	−0.179393	+	0.0480681i
$21$	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	$0.945159\pi$
$24$	1.98848	+	4.77917i	0.405897	+	0.975544i
$25$		−	4.03430i		−	0.806861i
$26$		0			0
$27$	2.01129	+	4.79111i	0.387073	+	0.922049i
$28$	−0.208891	+	0.779591i	−0.0394766	+	0.147329i
$29$	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	$-0.272274\pi$
$31$	−0.550550	−	0.550550i	−0.0988817	−	0.0988817i	−0.754817	+	0.655935i	$0.772274\pi$
$32$	−0.401535	−	1.49855i	−0.0709820	−	0.264908i
$33$	2.80345	−	3.66555i	0.488018	−	0.638090i
$34$	−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
$37$	−4.92878	−	1.32066i	−0.810287	−	0.217116i	−0.170191	−	0.985411i	$-0.554439\pi$
$37$	−4.92878	−	1.32066i	−0.810287	−	0.217116i	−0.640096	+	0.768295i	$0.721105\pi$
$38$	6.96655			1.13012
$39$		0			0
$40$	8.98276			1.42030
$41$	3.68005	+	0.986066i	0.574727	+	0.153998i	0.534464	−	0.845192i	$-0.320514\pi$
$41$	3.68005	+	0.986066i	0.574727	+	0.153998i	0.0402633	+	0.999189i	$0.487180\pi$
$42$	−2.53195	+	6.14019i	−0.390689	+	0.947451i
$43$	10.0942	+	5.82790i	1.53936	+	0.888747i	0.998876	+	0.0473894i	$0.0150902\pi$
$43$	10.0942	+	5.82790i	1.53936	+	0.888747i	0.540479	+	0.841358i	$0.318243\pi$
$44$	−0.520592	+	0.520592i	−0.0784823	+	0.0784823i
$45$	9.01709	−	0.0285911i	1.34419	−	0.00426212i
$46$	1.12160	+	4.18587i	0.165371	+	0.617173i
$47$	4.29586	+	4.29586i	0.626616	+	0.626616i	0.947215	−	0.320599i	$-0.103884\pi$
$47$	4.29586	+	4.29586i	0.626616	+	0.626616i	−0.320599	+	0.947215i	$0.603884\pi$
$48$	−0.771281	−	5.78754i	−0.111325	−	0.835360i
$49$	−1.32568	+	0.765385i	−0.189384	+	0.109341i
$50$	−1.37086	+	5.11610i	−0.193868	+	0.723526i
$51$	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	$-0.385454\pi$
$54$	−0.922602	−	6.75928i	−0.125550	−	0.919822i
$55$	−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
$58$	−4.73357	+	1.26836i	−0.621548	+	0.166543i
$59$	3.22482	−	0.864088i	0.419836	−	0.112495i	−0.0427154	−	0.999087i	$-0.513601\pi$
$59$	3.22482	−	0.864088i	0.419836	−	0.112495i	0.462551	+	0.886593i	$0.346934\pi$
$60$	−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
$63$	4.35704	−	7.60218i	0.548935	−	0.957785i
$64$			8.77879i			1.09735i
$65$		0			0
$66$	−4.80075	+	3.69585i	−0.590932	+	0.454928i
$67$	−1.95320	+	7.28944i	−0.238621	+	0.890547i	0.737862	+	0.674952i	$0.235836\pi$
$67$	−1.95320	+	7.28944i	−0.238621	+	0.890547i	−0.976483	+	0.215595i	$0.930831\pi$
$68$	−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
$71$	−1.38405	−	5.16536i	−0.164257	−	0.613016i	−0.998134	−	0.0610649i	$-0.980550\pi$
$71$	−1.38405	−	5.16536i	−0.164257	−	0.613016i	0.833877	−	0.551951i	$-0.186116\pi$
$72$	0.0284280	+	8.96564i	0.00335027	+	1.05661i
$73$	−3.46215	+	3.46215i	−0.405214	+	0.405214i	−0.880066	−	0.474852i	$-0.842502\pi$
$73$	−3.46215	+	3.46215i	−0.405214	+	0.405214i	0.474852	+	0.880066i	$0.342502\pi$
$74$	5.80168	+	3.34960i	0.674431	+	0.389383i
$75$	2.66381	−	6.45995i	0.307590	−	0.745931i
$76$	1.41633	+	0.379503i	0.162464	+	0.0435320i
$77$	−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	$0.715530\pi$
$80$	−9.78695	−	2.62241i	−1.09421	−	0.293194i
$81$	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	−0.800848	−	0.598867i	$-0.795618\pi$
$83$	−1.84014	+	1.84014i	−0.201981	+	0.201981i	0.598867	+	0.800848i	$0.295618\pi$
$84$	−0.849243	+	1.11040i	−0.0926600	+	0.121154i
$85$	−0.154679	−	0.577269i	−0.0167773	−	0.0626136i
$86$	−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
$89$	−0.284349	+	1.06120i	−0.0301409	+	0.112487i	−0.979357	−	0.202136i	$-0.935212\pi$
$89$	−0.284349	+	1.06120i	−0.0301409	+	0.112487i	0.949217	+	0.314624i	$0.101878\pi$
$90$	−11.4447	−	3.02775i	−1.20638	−	0.319153i
$91$		0			0
$92$			0.912102i			0.0950932i
$93$	−0.518049	−	1.24509i	−0.0537191	−	0.129110i
$94$	−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
$97$	11.7496	−	3.14829i	1.19299	−	0.319661i	0.392923	−	0.919571i	$-0.371464\pi$
$97$	11.7496	−	3.14829i	1.19299	−	0.319661i	0.800067	+	0.599911i	$0.204797\pi$
$98$	1.94125	−	0.520155i	0.196095	−	0.0525436i
$99$	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	$0.621836\pi$
$102$	−0.417450	+	0.173689i	−0.0413337	+	0.0171978i
$103$		−	5.68798i		−	0.560453i	−0.959934	−	0.280226i	$-0.909590\pi$
$103$		−	5.68798i		−	0.560453i	0.959934	−	0.280226i	$-0.0904096\pi$
$104$		0			0
$105$	−9.27566	−	12.0487i	−0.905212	−	1.17583i
$106$	−4.63065	+	17.2818i	−0.449769	+	1.67856i
$107$	−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	$-0.0882618\pi$
$109$	7.18355	+	7.18355i	0.688060	+	0.688060i	−0.273743	+	0.961803i	$0.588262\pi$
$110$	2.72116	+	10.1555i	0.259453	+	0.968291i
$111$	−7.02022	−	5.36914i	−0.666330	−	0.509616i
$112$	−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
$115$	−9.58310	−	2.56778i	−0.893628	−	0.239447i
$116$	−1.03145			−0.0957674
$117$		0			0
$118$	−4.38317			−0.403504
$119$	−0.560951	−	0.150306i	−0.0514223	−	0.0137786i
$120$	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
$123$	5.24161	+	4.00884i	0.472620	+	0.361465i
$124$	0.0556848	+	0.207818i	0.00500064	+	0.0186627i
$125$	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	−0.821952	−	0.569557i	$-0.807115\pi$
$127$	−8.33573	+	4.81263i	−0.739676	+	0.427052i	0.0822755	+	0.996610i	$0.473781\pi$
$128$	2.17996	−	8.13573i	0.192683	−	0.719103i
$129$	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	$0.825965\pi$
$132$	−1.17734	+	0.489860i	−0.102475	+	0.0426368i
$133$	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
$136$	0.573976	−	0.153796i	0.0492180	−	0.0131879i
$137$	−16.8029	+	4.50231i	−1.43557	+	0.384659i	−0.890979	−	0.454045i	$-0.849980\pi$
$137$	−16.8029	+	4.50231i	−1.43557	+	0.384659i	−0.544587	+	0.838704i	$0.683314\pi$
$138$	−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
$141$	4.04226	+	9.71528i	0.340420	+	0.818174i
$142$			7.02076i			0.589169i
$143$		0			0
$144$	2.58644	−	9.77660i	0.215536	−	0.814717i
$145$	2.90377	−	10.8370i	0.241145	−	0.899964i
$146$	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
$149$	4.08308	+	15.2383i	0.334499	+	1.24837i	0.904412	+	0.426661i	$0.140310\pi$
$149$	4.08308	+	15.2383i	0.334499	+	1.24837i	−0.569913	+	0.821705i	$0.693023\pi$
$150$	−5.57320	+	7.28702i	−0.455050	+	0.594983i
$151$	−8.56897	+	8.56897i	−0.697333	+	0.697333i	−0.963834	−	0.266502i	$-0.914132\pi$
$151$	−8.56897	+	8.56897i	−0.697333	+	0.697333i	0.266502	+	0.963834i	$0.414132\pi$
$152$	−13.7336	−	7.92908i	−1.11394	−	0.643133i
$153$	0.575680	−	0.156211i	0.0465410	−	0.0126289i
$154$	9.86845	+	2.64424i	0.795222	+	0.213079i
$155$	−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	$0.541620\pi$
$158$	14.1242	+	3.78456i	1.12366	+	0.301084i
$159$	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
$162$	2.98576	−	11.4325i	0.234583	−	0.898223i
$163$	1.50848	+	5.62972i	0.118153	+	0.440954i	0.999503	−	0.0315098i	$-0.0100315\pi$
$163$	1.50848	+	5.62972i	0.118153	+	0.440954i	−0.881350	+	0.472463i	$0.843365\pi$
$164$	−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
$167$	0.409254	−	1.52736i	0.0316690	−	0.118190i	−0.948282	−	0.317429i	$-0.897180\pi$
$167$	0.409254	−	1.52736i	0.0316690	−	0.118190i	0.979951	+	0.199239i	$0.0638470\pi$
$168$	11.9799	−	9.22274i	0.924272	−	0.711550i
$169$		0			0
$170$			0.784624i			0.0601779i
$171$	−13.8113	−	7.91567i	−1.05618	−	0.605327i
$172$	−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
$175$	−11.3817	+	3.04971i	−0.860374	+	0.230537i
$176$	−8.67529	+	2.32454i	−0.653925	+	0.175219i
$177$	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	$-0.375202\pi$
$180$	−2.16182	−	1.23901i	−0.161133	−	0.0923501i
$181$		−	9.29621i		−	0.690982i	−0.938422	−	0.345491i	$-0.887712\pi$
$181$		−	9.29621i		−	0.690982i	0.938422	−	0.345491i	$-0.112288\pi$
$182$		0			0
$183$	3.70692	−	2.85377i	0.274024	−	0.210957i
$184$	2.55313	−	9.52842i	0.188219	−	0.702444i
$185$	−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
$188$	−0.434500	−	1.62158i	−0.0316892	−	0.118266i
$189$	11.9964	−	9.29612i	0.872607	−	0.676193i
$190$	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
$193$	−3.83737	−	1.02822i	−0.276220	−	0.0740130i	0.118050	−	0.993008i	$-0.462336\pi$
$193$	−3.83737	−	1.02822i	−0.276220	−	0.0740130i	−0.394270	+	0.918995i	$0.629002\pi$
$194$	−15.9700			−1.14658
$195$		0			0
$196$	0.422998			0.0302142
$197$	6.65511	+	1.78323i	0.474157	+	0.127050i	0.487981	−	0.872855i	$-0.337734\pi$
$197$	6.65511	+	1.78323i	0.474157	+	0.127050i	−0.0138237	+	0.999904i	$0.504400\pi$
$198$	−10.1276	+	2.74812i	−0.719734	+	0.195300i
$199$	5.49109	+	3.17028i	0.389253	+	0.224735i	0.681836	−	0.731505i	$-0.261182\pi$
$199$	5.49109	+	3.17028i	0.389253	+	0.224735i	−0.292584	+	0.956240i	$0.594515\pi$
$200$	8.52542	−	8.52542i	0.602838	−	0.602838i
$201$	−7.94071	+	10.3826i	−0.560094	+	0.732330i
$202$	−4.21142	−	15.7172i	−0.296315	−	1.10586i
$203$	−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
$206$	−1.93277	+	7.21321i	−0.134663	+	0.502568i
$207$	2.53256	−	9.57296i	0.176025	−	0.665367i
$208$		0			0
$209$			14.1376i			0.977916i
$210$	7.66880	+	18.4314i	0.529197	+	1.27189i
$211$	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
$214$	9.85182	−	2.63979i	0.673457	−	0.180452i
$215$	33.8402	−	9.06747i	2.30789	−	0.618396i
$216$	−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
$219$	−7.82981	+	3.25776i	−0.529089	+	0.220139i
$220$			2.21289i			0.149193i
$221$		0			0
$222$	7.07826	+	9.19435i	0.475062	+	0.617084i
$223$	−0.799768	+	2.98478i	−0.0535565	+	0.199875i	−0.987520	−	0.157492i	$-0.949659\pi$
$223$	−0.799768	+	2.98478i	−0.0535565	+	0.199875i	0.933964	+	0.357368i	$0.116326\pi$
$224$	−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
$227$	−6.70715	−	25.0314i	−0.445169	−	1.66139i	−0.715489	−	0.698624i	$-0.753796\pi$
$227$	−6.70715	−	25.0314i	−0.445169	−	1.66139i	0.270320	−	0.962770i	$-0.412870\pi$
$228$	2.01732	+	1.54287i	0.133600	+	0.102179i
$229$	19.6410	−	19.6410i	1.29791	−	1.29791i	0.368147	−	0.929768i	$-0.379992\pi$
$229$	19.6410	−	19.6410i	1.29791	−	1.29791i	0.929768	−	0.368147i	$-0.120008\pi$
$230$	11.2803	+	6.51267i	0.743799	+	0.429433i
$231$	−12.4606	−	5.13822i	−0.819847	−	0.338070i
$232$	10.7752	+	2.88720i	0.707425	+	0.189554i
$233$	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
$236$	−0.891116	−	0.238774i	−0.0580067	−	0.0155428i
$237$	−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	−0.830878	−	0.556455i	$-0.812161\pi$
$239$	−4.24248	+	4.24248i	−0.274423	+	0.274423i	0.556455	+	0.830878i	$0.312161\pi$
$240$	−13.9399	−	10.6614i	−0.899814	−	0.688188i
$241$	6.38724	+	23.8375i	0.411438	+	1.53551i	0.791864	+	0.610697i	$0.209111\pi$
$241$	6.38724	+	23.8375i	0.411438	+	1.53551i	−0.380426	+	0.924811i	$0.624223\pi$
$242$	−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
$245$	−1.19084	+	4.44427i	−0.0760799	+	0.283934i
$246$	−5.28494	−	6.86491i	−0.336956	−	0.437691i
$247$		0			0
$248$		−	2.32688i		−	0.147757i
$249$	−4.16156	+	1.73151i	−0.263728	+	0.109730i
$250$	−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
$253$	−8.49459	+	2.27612i	−0.534051	+	0.143098i
$254$	12.2063	−	3.27066i	0.765891	−	0.205220i
$255$	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	$0.663448\pi$
$258$	−10.1819	−	24.4714i	−0.633897	−	1.52353i
$259$			14.9036i			0.926062i
$260$		0			0
$261$	10.8255	+	2.86394i	0.670084	+	0.177273i
$262$	4.04406	−	15.0926i	0.249843	−	0.932426i
$263$	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
$266$	−5.26633	−	19.6542i	−0.322899	−	1.20508i
$267$	−1.15602	+	1.51151i	−0.0707470	+	0.0925026i
$268$	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
$271$	−5.86962	−	1.57276i	−0.356554	−	0.0955383i	0.0760956	−	0.997101i	$-0.475755\pi$
$271$	−5.86962	−	1.57276i	−0.356554	−	0.0955383i	−0.432650	+	0.901562i	$0.642421\pi$
$272$	−0.670260			−0.0406405
$273$		0			0
$274$	22.8384			1.37972
$275$	−10.3824	−	2.78195i	−0.626080	−	0.167758i
$276$	−0.602251	+	1.46051i	−0.0362513	+	0.0879123i
$277$	−24.0591	−	13.8905i	−1.44557	−	0.834600i	−0.447356	−	0.894356i	$-0.647634\pi$
$277$	−24.0591	−	13.8905i	−1.44557	−	0.834600i	−0.998213	+	0.0597558i	$0.980968\pi$
$278$	2.16218	−	2.16218i	0.129679	−	0.129679i
$279$	−0.00740621	−	2.33577i	−0.000443398	−	0.139839i
$280$	−6.79047	−	25.3424i	−0.405808	−	1.51450i
$281$	11.6187	+	11.6187i	0.693113	+	0.693113i	0.962916	−	0.269803i	$-0.0869585\pi$
$281$	11.6187	+	11.6187i	0.693113	+	0.693113i	−0.269803	+	0.962916i	$0.586958\pi$
$282$	−1.82494	−	13.6940i	−0.108674	−	0.815466i
$283$	−23.0251	+	13.2935i	−1.36870	+	0.790219i	−0.990762	−	0.135612i	$-0.956700\pi$
$283$	−23.0251	+	13.2935i	−1.36870	+	0.790219i	−0.377938	+	0.925831i	$0.623367\pi$
$284$	−0.382456	+	1.42735i	−0.0226946	+	0.0846974i
$285$	−21.8895	+	16.8516i	−1.29662	+	0.998203i
$286$		0			0
$287$		−	11.1277i		−	0.656845i
$288$	2.31433	−	4.03804i	0.136373	−	0.237944i
$289$	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
$292$	1.30687	−	0.350176i	0.0764790	−	0.0204925i
$293$	−2.79628	+	0.749260i	−0.163360	+	0.0437722i	−0.339572	−	0.940580i	$-0.610282\pi$
$293$	−2.79628	+	0.749260i	−0.163360	+	0.0437722i	0.176212	+	0.984352i	$0.443616\pi$
$294$	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
$297$	13.7170	−	1.87228i	0.795938	−	0.108641i
$298$		−	20.7118i		−	1.19980i
$299$		0			0
$300$	−1.53001	+	1.17788i	−0.0883354	+	0.0680049i
$301$	8.81115	−	32.8837i	0.507866	−	1.89538i
$302$	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
$305$	−2.10116	−	7.84164i	−0.120312	−	0.449011i
$306$	−0.783129	+	0.00248313i	−0.0447685	+	0.000141951i
$307$	−13.9565	+	13.9565i	−0.796541	+	0.796541i	−0.982548	−	0.186007i	$-0.940445\pi$
$307$	−13.9565	+	13.9565i	−0.796541	+	0.796541i	0.186007	+	0.982548i	$0.440445\pi$
$308$	1.86225	+	1.07517i	0.106111	+	0.0612635i
$309$	3.75571	−	9.10790i	0.213655	−	0.518130i
$310$	2.96777	+	0.795211i	0.168558	+	0.0451649i
$311$	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	$0.736859\pi$
$314$	4.14344	+	1.11023i	0.233828	+	0.0626539i
$315$	−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	0.249973	−	0.968253i	$-0.419578\pi$
$317$	21.6899	−	21.6899i	1.21823	−	1.21823i	0.968253	−	0.249973i	$-0.0804218\pi$
$318$	−18.8259	+	24.6151i	−1.05570	+	1.38034i
$319$	−2.57394	−	9.60608i	−0.144113	−	0.537837i
$320$	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
$323$	−0.273070	+	1.01911i	−0.0151940	+	0.0567049i
$324$	1.22980	−	2.16162i	0.0683224	−	0.120090i
$325$		0			0
$326$		−	7.65191i		−	0.423800i
$327$	6.75948	+	16.2459i	0.373800	+	0.898402i
$328$	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
$331$	0.640966	−	0.171746i	0.0352307	−	0.00944003i	−0.241161	−	0.970485i	$-0.577528\pi$
$331$	0.640966	−	0.171746i	0.0352307	−	0.00944003i	0.276391	+	0.961045i	$0.410861\pi$
$332$	0.694605	−	0.186119i	0.0381214	−	0.0102146i
$333$	−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
$336$	−15.7449	+	6.55102i	−0.858956	+	0.357388i
$337$		−	25.0872i		−	1.36659i	−0.730143	−	0.683294i	$-0.760547\pi$
$337$		−	25.0872i		−	1.36659i	0.730143	−	0.683294i	$-0.239453\pi$
$338$		0			0
$339$	18.0547	+	23.4522i	0.980596	+	1.27375i
$340$	−0.0427425	+	0.159517i	−0.00231804	+	0.00865103i
$341$	−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
$344$	9.01573	+	33.6472i	0.486096	+	1.81413i
$345$	−13.6495	−	10.4393i	−0.734864	−	0.562033i
$346$	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
$349$	28.9532	+	7.75800i	1.54983	+	0.415276i	0.929427	−	0.369006i	$-0.120302\pi$
$349$	28.9532	+	7.75800i	1.54983	+	0.415276i	0.620405	+	0.784282i	$0.286968\pi$
$350$	15.4700			0.826905
$351$		0			0
$352$	−4.13344			−0.220313
$353$	6.50846	+	1.74394i	0.346410	+	0.0928203i	0.427829	−	0.903860i	$-0.359279\pi$
$353$	6.50846	+	1.74394i	0.346410	+	0.0928203i	−0.0814189	+	0.996680i	$0.525945\pi$
$354$	−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
$357$	−0.798980	−	0.611069i	−0.0422865	−	0.0323412i
$358$	5.53970	+	20.6744i	0.292782	+	1.09268i
$359$	−6.76884	−	6.76884i	−0.357246	−	0.357246i	0.505551	−	0.862797i	$-0.331289\pi$
$359$	−6.76884	−	6.76884i	−0.357246	−	0.357246i	−0.862797	+	0.505551i	$0.831289\pi$
$360$	19.1156	+	18.9948i	1.00748	+	1.00111i
$361$	7.92989	−	4.57832i	0.417363	−	0.240964i
$362$	−3.15885	+	11.7890i	−0.166025	+	0.619616i
$363$	4.12223	+	5.35459i	0.216361	+	0.281043i
$364$		0			0
$365$			14.7166i			0.770303i
$366$	−5.67065	+	2.35940i	−0.296410	+	0.123328i
$367$	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
$370$	19.4497	−	5.21154i	1.01114	−	0.270935i
$371$	−38.4465	+	10.3017i	−1.99604	+	0.534838i
$372$	−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
$375$	1.93129	+	4.64172i	0.0997313	+	0.239697i
$376$			18.1563i			0.936340i
$377$		0			0
$378$	−18.3720	+	7.71252i	−0.944955	+	0.396689i
$379$	−8.01497	+	29.9123i	−0.411701	+	1.53649i	0.379651	+	0.925130i	$0.376044\pi$
$379$	−8.01497	+	29.9123i	−0.411701	+	1.53649i	−0.791352	+	0.611360i	$0.790623\pi$
$380$	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
$383$	2.65388	+	9.90441i	0.135607	+	0.506092i	0.999995	+	0.00326604i	$0.00103961\pi$
$383$	2.65388	+	9.90441i	0.135607	+	0.506092i	−0.864388	+	0.502826i	$0.832294\pi$
$384$	8.86261	−	11.5880i	0.452268	−	0.591346i
$385$	−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
$388$	−3.24677	−	0.869969i	−0.164830	−	0.0441660i
$389$	−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
$392$	−4.41892	−	1.18405i	−0.223189	−	0.0598033i
$393$	−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
$396$	−2.20868	+	0.00700321i	−0.110990	+	0.000351925i
$397$	−0.888280	−	3.31510i	−0.0445815	−	0.166380i	0.940046	−	0.341048i	$-0.110782\pi$
$397$	−0.888280	−	3.31510i	−0.0445815	−	0.166380i	−0.984628	+	0.174667i	$0.944115\pi$
$398$	−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
$401$	5.16404	−	19.2725i	0.257880	−	0.962421i	−0.708586	−	0.705625i	$-0.750666\pi$
$401$	5.16404	−	19.2725i	0.257880	−	0.962421i	0.966466	−	0.256796i	$-0.0826668\pi$
$402$	13.5980	−	10.4684i	0.678207	−	0.522117i
$403$		0			0
$404$		−	3.42479i		−	0.170390i
$405$	19.2491	+	19.0065i	0.956498	+	0.944443i
$406$	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
$409$	5.35240	−	1.43417i	0.264659	−	0.0709152i	−0.124049	−	0.992276i	$-0.539588\pi$
$409$	5.35240	−	1.43417i	0.264659	−	0.0709152i	0.388708	+	0.921361i	$0.372921\pi$
$410$	−14.5220	+	3.89117i	−0.717193	+	0.192171i
$411$	−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
$414$	−6.46456	+	11.2794i	−0.317716	+	0.554352i
$415$			7.82191i			0.383962i
$416$		0			0
$417$	−3.19652	+	2.46083i	−0.156534	+	0.120508i
$418$	4.80394	−	17.9286i	0.234969	−	0.876914i
$419$	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	$-0.0283154\pi$
$421$	18.6143	+	18.6143i	0.907208	+	0.907208i	−0.0888383	+	0.996046i	$0.528315\pi$
$422$	−0.272613	−	1.01740i	−0.0132706	−	0.0495265i
$423$	0.0577896	+	18.2257i	0.00280983	+	0.886164i
$424$	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
$427$	−7.61997	−	2.04177i	−0.368756	−	0.0988080i
$428$	2.14672			0.103765
$429$		0			0
$430$	−45.9956			−2.21811
$431$	−10.9232	−	2.92686i	−0.526152	−	0.140982i	−0.0140414	−	0.999901i	$-0.504470\pi$
$431$	−10.9232	−	2.92686i	−0.526152	−	0.140982i	−0.512111	+	0.858919i	$0.671136\pi$
$432$	10.5969	−	13.9470i	0.509845	−	0.671027i
$433$	−5.37469	−	3.10308i	−0.258291	−	0.149124i	0.365264	−	0.930904i	$-0.380979\pi$
$433$	−5.37469	−	3.10308i	−0.258291	−	0.149124i	−0.623555	+	0.781780i	$0.714312\pi$
$434$	2.11114	−	2.11114i	0.101338	−	0.101338i
$435$	11.8052	−	15.4355i	0.566017	−	0.740075i
$436$	−0.726573	−	2.71161i	−0.0347965	−	0.129862i
$437$	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	$-0.290311\pi$
$439$	33.5869	−	19.3914i	1.60301	−	0.925501i	0.990880	−	0.134748i	$-0.0430224\pi$
$440$	6.19427	−	23.1173i	0.295300	−	1.10208i
$441$	−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	$-0.143267\pi$
$444$	0.938174	+	2.25484i	0.0445238	+	0.107010i
$445$	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
$448$	24.7669	−	6.63628i	1.17013	−	0.313535i
$449$	1.87306	−	0.501884i	0.0883950	−	0.0236854i	−0.214350	−	0.976757i	$-0.568763\pi$
$449$	1.87306	−	0.501884i	0.0883950	−	0.0236854i	0.302745	+	0.953071i	$0.402097\pi$
$450$	−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
$453$	−19.3791	+	8.06311i	−0.910510	+	0.378838i
$454$			34.0227i			1.59676i
$455$		0			0
$456$	−16.7555	−	21.7646i	−0.784646	−	1.01922i
$457$	1.50820	−	5.62868i	0.0705507	−	0.263299i	−0.921637	−	0.388053i	$-0.873148\pi$
$457$	1.50820	−	5.62868i	0.0705507	−	0.263299i	0.992188	+	0.124755i	$0.0398143\pi$
$458$	−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
$461$	3.70361	+	13.8221i	0.172494	+	0.643758i	0.996965	+	0.0778529i	$0.0248064\pi$
$461$	3.70361	+	13.8221i	0.172494	+	0.643758i	−0.824470	+	0.565905i	$0.808527\pi$
$462$	14.0559	+	10.7501i	0.653942	+	0.500142i
$463$	−2.99038	+	2.99038i	−0.138975	+	0.138975i	−0.773172	−	0.634197i	$-0.781331\pi$
$463$	−2.99038	+	2.99038i	−0.138975	+	0.138975i	0.634197	+	0.773172i	$0.281331\pi$
$464$	−10.8969	−	6.29136i	−0.505878	−	0.292069i
$465$	−3.74731	−	1.54523i	−0.173777	−	0.0716584i
$466$	−18.3313	−	4.91185i	−0.849181	−	0.227537i
$467$	−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
$470$	−23.1571	−	6.20491i	−1.06816	−	0.286211i
$471$	−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
$474$	20.1175	+	15.3861i	0.924028	+	0.706707i
$475$	5.54058	+	20.6777i	0.254219	+	0.948759i
$476$	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
$479$	0.528588	−	1.97272i	0.0241518	−	0.0901358i	−0.952798	−	0.303605i	$-0.901810\pi$
$479$	0.528588	−	1.97272i	0.0241518	−	0.0901358i	0.976950	+	0.213469i	$0.0684763\pi$
$480$	−4.92695	−	6.39989i	−0.224883	−	0.292114i
$481$		0			0
$482$		−	32.3999i		−	1.47578i
$483$	−15.4170	+	6.41457i	−0.701496	+	0.291873i
$484$	−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
$487$	−24.2264	+	6.49144i	−1.09780	+	0.294155i	−0.761869	−	0.647731i	$-0.775718\pi$
$487$	−24.2264	+	6.49144i	−1.09780	+	0.294155i	−0.335933	+	0.941886i	$0.609052\pi$
$488$	7.79690	−	2.08917i	0.352949	−	0.0945724i
$489$	−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	$0.887698\pi$
$492$	−0.700482	−	1.68356i	−0.0315802	−	0.0759007i
$493$		−	0.742173i		−	0.0334258i
$494$		0			0
$495$	6.14436	−	23.2254i	0.276169	−	1.04390i
$496$	−0.679304	+	2.53520i	−0.0305016	+	0.113834i
$497$	−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	$-0.161030\pi$
$499$	8.71539	+	8.71539i	0.390154	+	0.390154i	−0.484588	+	0.874742i	$0.661030\pi$
$500$	−0.207593	−	0.774749i	−0.00928385	−	0.0346478i
$501$	1.66382	−	2.17546i	0.0743339	−	0.0971925i
$502$	−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
$505$	35.9829	+	9.64160i	1.60122	+	0.429046i
$506$	11.5458			0.513276
$507$		0			0
$508$	2.65975			0.118008
$509$	−28.9544	−	7.75830i	−1.28338	−	0.343881i	−0.448238	−	0.893914i	$-0.647948\pi$
$509$	−28.9544	−	7.75830i	−1.28338	−	0.343881i	−0.835142	+	0.550034i	$0.814615\pi$
$510$	−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
$513$	−16.8888	−	21.7945i	−0.745658	−	0.962249i
$514$	−5.54254	−	20.6850i	−0.244471	−	0.912377i
$515$	−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
$518$	5.06423	−	18.9000i	0.222509	−	0.830416i
$519$	−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	$-0.0415786\pi$
$522$	−12.7553	−	7.31042i	−0.558282	−	0.319968i
$523$	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
$526$	−14.5789	+	3.90641i	−0.635672	+	0.170328i
$527$	−0.149535	+	0.0400678i	−0.00651385	+	0.00174538i
$528$	−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
$531$	8.68971	+	4.98034i	0.377102	+	0.216128i
$532$		−	4.28266i		−	0.185677i
$533$		0			0
$534$	1.97961	−	1.52400i	0.0856662	−	0.0659500i
$535$	−6.04351	+	22.5547i	−0.261284	+	0.975124i
$536$	−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
$539$	1.05558	+	3.93947i	0.0454669	+	0.169685i
$540$	−2.64353	−	3.41139i	−0.113759	−	0.146803i
$541$	−5.67009	+	5.67009i	−0.243776	+	0.243776i	−0.818410	−	0.574634i	$-0.805144\pi$
$541$	−5.67009	+	5.67009i	−0.243776	+	0.243776i	0.574634	+	0.818410i	$0.305144\pi$
$542$	6.90914	+	3.98899i	0.296773	+	0.171342i
$543$	6.13819	−	14.8856i	0.263415	−	0.638802i
$544$	−0.297960	−	0.0798382i	−0.0127749	−	0.00342303i
$545$	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	$0.715980\pi$
$548$	4.64314	+	1.24413i	0.198345	+	0.0531465i
$549$	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
$552$	10.3797	−	13.5716i	0.441791	−	0.577647i
$553$	8.41943	+	31.4217i	0.358031	+	1.33619i
$554$	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
$557$	−9.67941	+	36.1240i	−0.410130	+	1.53062i	0.384265	+	0.923223i	$0.374455\pi$
$557$	−9.67941	+	36.1240i	−0.410130	+	1.53062i	−0.794395	+	0.607402i	$0.792212\pi$
$558$	−0.784303	+	2.96463i	−0.0332022	+	0.125503i
$559$		0			0
$560$			29.5936i			1.25056i
$561$	−0.352477	−	0.847152i	−0.0148816	−	0.0357668i
$562$	−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
$565$	49.6109	−	13.2932i	2.08715	−	0.559250i
$566$	33.7164	−	9.03429i	1.41721	−	0.379740i
$567$	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	$0.991023\pi$
$570$	33.4854	−	13.9323i	1.40255	−	0.583561i
$571$		−	21.9369i		−	0.918032i	−0.888428	−	0.459016i	$-0.848202\pi$
$571$		−	21.9369i		−	0.918032i	0.888428	−	0.459016i	$-0.151798\pi$
$572$		0			0
$573$	2.14307	+	2.78375i	0.0895279	+	0.116293i
$574$	−3.78118	+	14.1115i	−0.157823	+	0.589004i
$575$	−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	$-0.436265\pi$
$577$	−18.7633	−	18.7633i	−0.781126	−	0.781126i	−0.980021	+	0.198895i	$0.936265\pi$
$578$	−5.76316	−	21.5084i	−0.239716	−	0.894632i
$579$	−5.46569	−	4.18022i	−0.227146	−	0.173724i
$580$	−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
$583$	−35.0709	−	9.39722i	−1.45249	−	0.389193i
$584$	−14.6327			−0.605504
$585$		0			0
$586$	3.80070			0.157005
$587$	11.8276	+	3.16920i	0.488178	+	0.130807i	0.494508	−	0.869173i	$-0.335348\pi$
$587$	11.8276	+	3.16920i	0.488178	+	0.130807i	−0.00632980	+	0.999980i	$0.502015\pi$
$588$	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
$591$	9.47908	+	7.24970i	0.389917	+	0.298213i
$592$	4.45193	+	16.6148i	0.182973	+	0.682865i
$593$	−32.4467	−	32.4467i	−1.33243	−	1.33243i	−0.903194	−	0.429232i	$-0.858784\pi$
$593$	−32.4467	−	32.4467i	−1.33243	−	1.33243i	−0.429232	−	0.903194i	$-0.641216\pi$
$594$	−18.0314	−	2.28668i	−0.739836	−	0.0938237i
$595$	−1.51168	+	0.872768i	−0.0619728	+	0.0357800i
$596$	1.12828	−	4.21079i	0.0462161	−	0.172481i
$597$	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	$-0.0760708\pi$
$600$	19.2806	−	8.02213i	0.787128	−	0.327502i
$601$	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
$604$	3.23457	−	0.866700i	0.131613	−	0.0352655i
$605$	11.3271	−	3.03509i	0.460513	−	0.123394i
$606$	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
$609$	−7.25389	−	17.4342i	−0.293942	−	0.706470i
$610$			10.6583i			0.431544i
$611$		0			0
$612$	−0.159348	−	0.0421562i	−0.00644128	−	0.00170406i
$613$	0.930978	−	3.47446i	0.0376019	−	0.140332i	−0.944573	−	0.328301i	$-0.893524\pi$
$613$	0.930978	−	3.47446i	0.0376019	−	0.140332i	0.982175	+	0.187969i	$0.0601905\pi$
$614$	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
$617$	1.71888	+	6.41496i	0.0691997	+	0.258257i	0.991856	−	0.127368i	$-0.0406528\pi$
$617$	1.71888	+	6.41496i	0.0691997	+	0.258257i	−0.922656	+	0.385624i	$0.873986\pi$
$618$	−7.85767	+	10.2740i	−0.316082	+	0.413281i
$619$	13.3334	−	13.3334i	0.535916	−	0.535916i	−0.386411	−	0.922327i	$-0.626285\pi$
$619$	13.3334	−	13.3334i	0.535916	−	0.535916i	0.922327	+	0.386411i	$0.126285\pi$
$620$	0.560039	+	0.323339i	0.0224917	+	0.0129856i
$621$	10.3762	−	13.6565i	0.416383	−	0.548018i
$622$	−34.2090	−	9.16628i	−1.37166	−	0.367534i
$623$	3.20885			0.128560
$624$		0			0
$625$	28.8959			1.15584
$626$	30.3925	+	8.14365i	1.21473	+	0.325486i
$627$	−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
$630$	0.109636	+	34.5770i	0.00436800	+	1.37758i
$631$	0.381334	+	1.42316i	0.0151807	+	0.0566550i	0.973101	−	0.230380i	$-0.0739970\pi$
$631$	0.381334	+	1.42316i	0.0151807	+	0.0566550i	−0.957920	+	0.287035i	$0.907330\pi$
$632$	−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
$635$	−7.48784	+	27.9450i	−0.297146	+	1.10896i
$636$	−5.16828	+	3.97879i	−0.204936	+	0.157769i
$637$		0			0
$638$			13.0566i			0.516915i
$639$	7.97727	−	13.9188i	0.315576	−	0.550618i
$640$	−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
$643$	−46.9319	+	12.5754i	−1.85081	+	0.495924i	−0.999583	−	0.0288681i	$-0.990810\pi$
$643$	−46.9319	+	12.5754i	−1.85081	+	0.495924i	−0.851230	+	0.524792i	$0.824143\pi$
$644$	2.57325	−	0.689499i	0.101400	−	0.0271701i
$645$	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	$-0.432107\pi$
$648$	−18.8981	+	19.1393i	−0.742388	+	0.751864i
$649$		−	8.89499i		−	0.349159i
$650$		0			0
$651$	−3.12107	+	2.40275i	−0.122324	+	0.0941714i
$652$	0.416839	−	1.55566i	0.0163247	−	0.0609245i
$653$	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
$656$	−3.32401	−	12.4054i	−0.129781	−	0.484348i
$657$	−14.6886	+	0.0465742i	−0.573056	+	0.00181703i
$658$	−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
$661$	16.8775	+	4.52232i	0.656459	+	0.175898i	0.571647	−	0.820499i	$-0.306304\pi$
$661$	16.8775	+	4.52232i	0.656459	+	0.175898i	0.0848116	+	0.996397i	$0.472971\pi$
$662$	−0.871200			−0.0338602
$663$		0			0
$664$	−7.77728			−0.301817
$665$	44.9962	+	12.0567i	1.74488	+	0.467538i
$666$	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
$669$	−3.25145	+	4.25131i	−0.125708	+	0.164365i
$670$	−7.70763	−	28.7653i	−0.297772	−	1.11130i
$671$	−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	−0.958005	−	0.286751i	$-0.907425\pi$
$673$	−30.8369	+	17.8037i	−1.18867	+	0.686281i	−0.230669	+	0.973032i	$0.574091\pi$
$674$	−8.52464	+	31.8144i	−0.328357	+	1.22544i
$675$	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	$0.898076\pi$
$678$	−14.9270	−	35.8760i	−0.573267	−	1.37781i
$679$	−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
$682$	2.63067	−	0.704886i	0.100734	−	0.0269915i
$683$	−37.1052	+	9.94232i	−1.41979	+	0.380432i	−0.885410	−	0.464811i	$-0.846122\pi$
$683$	−37.1052	+	9.94232i	−1.41979	+	0.380432i	−0.534382	+	0.845243i	$0.679456\pi$
$684$	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
$687$	44.4190	−	18.4815i	1.69469	−	0.705114i
$688$		−	39.2915i		−	1.49797i
$689$		0			0
$690$	13.7624	+	17.8767i	0.523924	+	0.680554i
$691$	−4.99988	+	18.6598i	−0.190204	+	0.709853i	0.803252	+	0.595640i	$0.203101\pi$
$691$	−4.99988	+	18.6598i	−0.190204	+	0.709853i	−0.993456	+	0.114213i	$0.963565\pi$
$692$	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
$695$	1.81185	+	6.76192i	0.0687274	+	0.256494i
$696$	15.3474	+	11.7379i	0.581742	+	0.444923i
$697$	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
$700$	3.14510	+	0.842728i	0.118874	+	0.0318521i
$701$	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
$704$	22.5924	+	6.05362i	0.851483	+	0.228154i
$705$	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
$708$	−1.26924	−	0.970732i	−0.0477011	−	0.0364823i
$709$	−11.2814	−	42.1029i	−0.423683	−	1.58121i	−0.766782	−	0.641907i	$-0.778143\pi$
$709$	−11.2814	−	42.1029i	−0.423683	−	1.58121i	0.343099	−	0.939299i	$-0.388523\pi$
$710$	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
$713$	−0.665155	+	2.48239i	−0.0249102	+	0.0929663i
$714$	0.805586	+	1.04642i	0.0301483	+	0.0391613i
$715$		0			0
$716$			4.50497i			0.168359i
$717$	−9.59455	+	3.99203i	−0.358315	+	0.149085i
$718$	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
$721$	−16.0471	+	4.29980i	−0.597624	+	0.160133i
$722$	−11.6120	+	3.11143i	−0.432154	+	0.115795i
$723$	−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
$726$	−3.40812	−	8.19116i	−0.126487	−	0.304003i
$727$			26.2936i			0.975176i	0.873074	+	0.487588i	$0.162123\pi$
$727$			26.2936i			0.975176i	−0.873074	+	0.487588i	$0.837877\pi$
$728$		0			0
$729$	−18.9094	+	19.2726i	−0.700349	+	0.713801i
$730$	5.00071	−	18.6629i	0.185084	−	0.690745i
$731$	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	$-0.297750\pi$
$733$	−5.72217	−	5.72217i	−0.211353	−	0.211353i	−0.804842	+	0.593489i	$0.797750\pi$
$734$	−4.08668	−	15.2517i	−0.150842	−	0.562951i
$735$	−4.84134	+	6.33012i	−0.178576	+	0.233490i
$736$	−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
$739$	19.8431	+	5.31693i	0.729939	+	0.195587i	0.604602	−	0.796528i	$-0.293332\pi$
$739$	19.8431	+	5.31693i	0.729939	+	0.195587i	0.125337	+	0.992114i	$0.459999\pi$
$740$	4.23811			0.155796
$741$		0			0
$742$	52.2565			1.91840
$743$	−33.2196	−	8.90116i	−1.21871	−	0.326552i	−0.408535	−	0.912743i	$-0.633960\pi$
$743$	−33.2196	−	8.90116i	−1.21871	−	0.326552i	−0.810173	+	0.586191i	$0.800627\pi$
$744$	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
$747$	−7.80701	+	0.0247543i	−0.285643	+	0.000905711i
$748$	0.0378875	+	0.141398i	0.00138531	+	0.00517003i
$749$	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	−0.891382	−	0.453252i	$-0.850264\pi$
$751$	−25.8847	+	14.9445i	−0.944546	+	0.545334i	−0.0531635	+	0.998586i	$0.516930\pi$
$752$	5.30051	−	19.7818i	0.193290	−	0.721367i
$753$	29.8233	−	22.9594i	1.08682	−	0.836687i
$754$		0			0
$755$			36.4243i			1.32562i
$756$	−4.15524	+	0.567166i	−0.151125	+	0.0206276i
$757$	−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
$760$	−46.0409	+	12.3366i	−1.67008	+	0.447496i
$761$	25.5783	−	6.85369i	0.927214	−	0.248446i	0.236547	−	0.971620i	$-0.423984\pi$
$761$	25.5783	−	6.85369i	0.927214	−	0.248446i	0.690666	+	0.723174i	$0.257317\pi$
$762$	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
$765$	0.891522	−	1.55553i	0.0322330	−	0.0562403i
$766$		−	13.4621i		−	0.486404i
$767$		0			0
$768$	8.92027	−	6.86726i	0.321882	−	0.247801i
$769$	3.17804	−	11.8606i	0.114603	−	0.427704i	−0.884654	−	0.466248i	$-0.845605\pi$
$769$	3.17804	−	11.8606i	0.114603	−	0.427704i	0.999257	+	0.0385441i	$0.0122720\pi$
$770$	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
$773$	−5.96678	−	22.2683i	−0.214610	−	0.800937i	−0.986303	−	0.164941i	$-0.947256\pi$
$773$	−5.96678	−	22.2683i	−0.214610	−	0.800937i	0.771693	−	0.635995i	$-0.219410\pi$
$774$	−0.145564	−	45.9080i	−0.00523219	−	1.65013i
$775$	−2.22108	+	2.22108i	−0.0797837	+	0.0797837i
$776$	31.4827	+	18.1765i	1.13016	+	0.652500i
$777$	−9.84066	+	23.8644i	−0.353032	+	0.856131i
$778$	38.1807	+	10.2305i	1.36884	+	0.366780i
$779$	−20.2162			−0.724321
$780$		0			0
$781$	−14.2476			−0.509818
$782$	0.832286	+	0.223010i	0.0297625	+	0.00797484i
$783$	15.4434	+	11.7339i	0.551903	+	0.419335i
$784$	4.46886	+	2.58010i	0.159602	+	0.0921463i
$785$	−6.94420	+	6.94420i	−0.247849	+	0.247849i
$786$	16.4411	−	21.4969i	0.586434	−	0.766769i
$787$	−12.8168	−	47.8331i	−0.456871	−	1.70507i	−0.682528	−	0.730859i	$-0.739120\pi$
$787$	−12.8168	−	47.8331i	−0.456871	−	1.70507i	0.225657	−	0.974207i	$-0.427547\pi$
$788$	−1.34625	−	1.34625i	−0.0479581	−	0.0479581i
$789$	19.7375	−	2.63034i	0.702675	−	0.0936425i
$790$	38.0625	−	21.9754i	1.35420	−	0.781849i
$791$	12.9174	−	48.2086i	0.459292	−	1.71410i
$792$	23.0929	+	6.10931i	0.820570	+	0.217085i
$793$		0			0
$794$			4.50589i			0.159908i
$795$	−27.2537	−	65.5023i	−0.966588	−	2.32313i
$796$	−0.876045	−	1.51735i	−0.0310506	−	0.0537812i
$797$	−2.55365	+	4.42306i	−0.0904550	+	0.156673i	−0.907703	−	0.419614i	$-0.862165\pi$
$797$	−2.55365	+	4.42306i	−0.0904550	+	0.156673i	0.817248	+	0.576287i	$0.195499\pi$
$798$	4.54473	−	34.9487i	0.160882	−	1.23717i
$799$	1.16680	−	0.312643i	0.0412784	−	0.0110605i
$800$	−6.04560	+	1.61991i	−0.213744	+	0.0572726i
$801$	−2.84911	+	1.65700i	−0.100668	+	0.0585472i
$802$	−13.0976	+	22.6856i	−0.462491	+	0.801058i
$803$	6.52251	+	11.2973i	0.230175	+	0.398674i
$804$	3.33480	−	1.38752i	0.117609	−	0.0489339i
$805$			28.9772i			1.02131i
$806$		0			0
$807$	−11.7692	−	15.2877i	−0.414295	−	0.538151i
$808$	−9.58659	+	35.7776i	−0.337255	+	1.25865i
$809$	−0.216848	+	0.125197i	−0.00762398	+	0.00440171i	−0.503807	−	0.863816i	$-0.668068\pi$
$809$	−0.216848	+	0.125197i	−0.00762398	+	0.00440171i	0.496183	+	0.868218i	$0.334734\pi$
$810$	−17.9524	−	30.6440i	−0.630783	−	1.07672i
$811$	−0.345058	−	0.345058i	−0.0121166	−	0.0121166i	0.701023	−	0.713139i	$-0.252727\pi$
$811$	−0.345058	−	0.345058i	−0.0121166	−	0.0121166i	−0.713139	+	0.701023i	$0.752727\pi$
$812$	0.779717	+	2.90994i	0.0273627	+	0.102119i
$813$	−8.36028	−	6.39404i	−0.293208	−	0.224249i
$814$	12.6210	−	12.6210i	0.442364	−	0.442364i
$815$	15.1712	+	8.75912i	0.531425	+	0.306818i
$816$	−1.07326	−	0.442566i	−0.0375715	−	0.0154929i
$817$	−59.7416	−	16.0077i	−2.09009	−	0.560039i
$818$	−7.27498			−0.254364
$819$		0			0
$820$	−3.16436			−0.110504
$821$	27.7769	+	7.44280i	0.969421	+	0.259756i	0.708583	−	0.705627i	$-0.249335\pi$
$821$	27.7769	+	7.44280i	0.969421	+	0.259756i	0.260838	+	0.965383i	$0.416001\pi$
$822$	36.5702	+	15.0800i	1.27553	+	0.525975i
$823$	1.74844	+	1.00946i	0.0609468	+	0.0351877i	0.530164	−	0.847895i	$-0.322130\pi$
$823$	1.74844	+	1.00946i	0.0609468	+	0.0351877i	−0.469217	+	0.883083i	$0.655464\pi$
$824$	12.0200	−	12.0200i	0.418737	−	0.418737i
$825$	−14.7879	−	11.3100i	−0.514850	−	0.393763i
$826$	3.31344	+	12.3659i	0.115289	+	0.430265i
$827$	0.657151	+	0.657151i	0.0228514	+	0.0228514i	0.718440	−	0.695589i	$-0.244856\pi$
$827$	0.657151	+	0.657151i	0.0228514	+	0.0228514i	−0.695589	+	0.718440i	$0.744856\pi$
$828$	−1.92872	+	1.94099i	−0.0670275	+	0.0674539i
$829$	−40.2809	+	23.2562i	−1.39902	+	0.807722i	−0.994289	−	0.106716i	$-0.965966\pi$
$829$	−40.2809	+	23.2562i	−1.39902	+	0.807722i	−0.404726	+	0.914438i	$0.632633\pi$
$830$	2.65788	−	9.91936i	0.0922565	−	0.344306i
$831$	−29.3530	−	38.1282i	−1.01824	−	1.32265i
$832$		0			0
$833$			0.304367i			0.0105457i
$834$	4.88986	−	2.03453i	0.169322	−	0.0704501i
$835$	−2.37637	−	4.11600i	−0.0822377	−	0.142440i
$836$	1.95332	−	3.38325i	0.0675570	−	0.117012i
$837$	1.53043	−	3.74506i	0.0528993	−	0.129448i
$838$	−43.6675	+	11.7007i	−1.50847	+	0.404193i
$839$	41.9982	−	11.2534i	1.44994	−	0.388510i	0.553937	−	0.832558i	$-0.313125\pi$
$839$	41.9982	−	11.2534i	1.44994	−	0.388510i	0.896003	+	0.444048i	$0.146458\pi$
$840$	5.86003	−	45.0633i	0.202190	−	1.55483i
$841$	−7.53364	+	13.0486i	−0.259781	+	0.449953i
$842$	−17.2806	−	29.9309i	−0.595530	−	1.03149i
$843$	10.9328	+	26.2762i	0.376545	+	0.905000i
$844$		−	0.221693i		−	0.00763098i
$845$		0			0
$846$	6.11981	−	23.1326i	0.210403	−	0.795314i
$847$	2.94930	−	11.0069i	0.101339	−	0.378203i
$848$	−39.7838	+	22.9692i	−1.36618	+	0.788765i
$849$	−45.6466	+	6.08313i	−1.56659	+	0.208773i
$850$	0.744677	+	0.744677i	0.0255422	+	0.0255422i
$851$	4.35920	+	16.2688i	0.149431	+	0.557686i
$852$	−1.55487	+	2.03301i	−0.0532690	+	0.0696499i
$853$	−0.0191114	+	0.0191114i	−0.000654362	+	0.000654362i	−0.707434	−	0.706780i	$-0.750147\pi$
$853$	−0.0191114	+	0.0191114i	−0.000654362	+	0.000654362i	0.706780	+	0.707434i	$0.250147\pi$
$854$	8.96948	+	5.17853i	0.306929	+	0.177206i
$855$	−46.1776	+	12.5303i	−1.57924	+	0.428528i
$856$	−22.4260	−	6.00903i	−0.766505	−	0.205384i
$857$	−5.89068			−0.201222			−0.100611	−	0.994926i	$-0.532080\pi$
$857$	−5.89068			−0.201222			−0.100611	+	0.994926i	$0.532080\pi$
$858$		0			0
$859$	11.6341			0.396949			0.198475	−	0.980106i	$-0.436401\pi$
$859$	11.6341			0.396949			0.198475	+	0.980106i	$0.436401\pi$
$860$	−9.35109	−	2.50562i	−0.318870	−	0.0854408i
$861$	7.34747	−	17.8182i	0.250401	−	0.607243i
$862$	12.8577	+	7.42341i	0.437936	+	0.252842i
$863$	19.9075	−	19.9075i	0.677660	−	0.677660i	−0.281811	−	0.959470i	$-0.590935\pi$
$863$	19.9075	−	19.9075i	0.677660	−	0.677660i	0.959470	+	0.281811i	$0.0909350\pi$
$864$	6.37210	−	4.93781i	0.216783	−	0.167988i
$865$	9.66445	+	36.0682i	0.328601	+	1.22636i
$866$	5.76148	+	5.76148i	0.195783	+	0.195783i
$867$	3.88056	+	29.1190i	0.131791	+	0.988932i
$868$	0.544208	−	0.314199i	0.0184716	−	0.0106646i
$869$	−7.68020	+	28.6629i	−0.260533	+	0.972323i
$870$	−20.2158	+	15.5631i	−0.685379	+	0.527638i
$871$		0			0
$872$			30.3610i			1.02815i
$873$	31.6609	+	18.1458i	1.07156	+	0.614142i
$874$	−11.4975	−	19.9142i	−0.388908	−	0.673608i
$875$	4.23889	−	7.34198i	0.143301	−	0.248204i
$876$	2.32385	+	0.302194i	0.0785158	+	0.0102102i
$877$	13.4570	−	3.60580i	0.454412	−	0.121759i	−0.0243510	−	0.999703i	$-0.507752\pi$
$877$	13.4570	−	3.60580i	0.454412	−	0.121759i	0.478763	+	0.877944i	$0.341085\pi$
$878$	−49.1824	+	13.1784i	−1.65983	+	0.444749i
$879$	−4.97228	−	0.646595i	−0.167711	−	0.0218091i
$880$	−13.4976	+	23.3786i	−0.455005	+	0.788092i
$881$	3.83326	+	6.63940i	0.129146	+	0.223687i	0.923346	−	0.383969i	$-0.125443\pi$
$881$	3.83326	+	6.63940i	0.129146	+	0.223687i	−0.794200	+	0.607656i	$0.792110\pi$
$882$	5.23095	+	2.99802i	0.176135	+	0.100948i
$883$			7.52156i			0.253121i	0.991959	+	0.126560i	$0.0403937\pi$
$883$			7.52156i			0.253121i	−0.991959	+	0.126560i	$0.959606\pi$
$884$		0			0
$885$	13.7723	−	10.6026i	0.462951	−	0.356403i
$886$	−6.22283	+	23.2239i	−0.209060	+	0.780222i
$887$	−36.5051	+	21.0762i	−1.22572	+	0.707670i	−0.966132	−	0.258049i	$-0.916920\pi$
$887$	−36.5051	+	21.0762i	−1.22572	+	0.707670i	−0.259589	+	0.965719i	$0.583587\pi$
$888$	−3.48911	−	26.1816i	−0.117087	−	0.878597i
$889$	19.8789	+	19.8789i	0.666716	+	0.666716i
$890$	−1.12208	−	4.18768i	−0.0376123	−	0.140371i
$891$	23.2006	+	6.05915i	0.777249	+	0.202989i
$892$	0.603784	−	0.603784i	0.0202162	−	0.0202162i
$893$	−27.9181	−	16.1185i	−0.934245	−	0.539386i
$894$	13.6758	−	33.1649i	0.457387	−	1.10920i
$895$	−47.3319	−	12.6826i	−1.58213	−	0.423931i
$896$	−24.6007			−0.821850
$897$		0			0
$898$	−2.54586			−0.0849564
$899$	−2.80720	−	0.752187i	−0.0936254	−	0.0250868i
$900$	−3.22768	+	0.875834i	−0.107589	+	0.0291945i
$901$	−2.34659	−	1.35480i	−0.0781762	−	0.0451351i
$902$	−9.42336	+	9.42336i	−0.313764	+	0.313764i
$903$	35.8216	−	46.8372i	1.19207	−	1.55865i
$904$	13.2174	+	49.3279i	0.439603	+	1.64062i
$905$	−19.7578	−	19.7578i	−0.656771	−	0.656771i
$906$	27.3155	−	3.64021i	0.907496	−	0.120938i
$907$	32.3487	−	18.6765i	1.07412	−	0.620143i	0.144815	−	0.989459i	$-0.453741\pi$
$907$	32.3487	−	18.6765i	1.07412	−	0.620143i	0.929304	+	0.369316i	$0.120408\pi$
$908$	−1.85339	+	6.91694i	−0.0615069	+	0.229547i
$909$	−9.50935	+	35.9449i	−0.315405	+	1.19222i
$910$		0			0
$911$			20.5977i			0.682434i	0.939985	+	0.341217i	$0.110839\pi$
$911$			20.5977i			0.682434i	−0.939985	+	0.341217i	$0.889161\pi$
$912$	11.9016	+	28.6047i	0.394102	+	0.947195i
$913$	3.46673	+	6.00455i	0.114732	+	0.198722i
$914$	−3.82525	+	6.62553i	−0.126528	+	0.219153i
$915$	1.81326	−	13.9438i	0.0599444	−	0.460969i
$916$	−7.41398	+	1.98657i	−0.244965	+	0.0656381i
$917$	33.5762	−	8.99672i	1.10878	−	0.297098i
$918$	−1.25563	−	0.513116i	−0.0414419	−	0.0169353i
$919$	19.6678	−	34.0657i	0.648782	−	1.12372i	−0.334632	−	0.942349i	$-0.608612\pi$
$919$	19.6678	−	34.0657i	0.648782	−	1.12372i	0.983414	−	0.181375i	$-0.0580546\pi$
$920$	−14.8250	−	25.6776i	−0.488765	−	0.846567i
$921$	−31.5633	+	13.1326i	−1.04005	+	0.432734i
$922$		−	18.7869i		−	0.618715i
$923$		0			0
$924$	2.27201	+	2.95124i	0.0747437	+	0.0970888i
$925$	−5.32796	+	19.8842i	−0.175182	+	0.653789i
$926$	4.80838	−	2.77612i	0.158013	−	0.0912289i
$927$	12.0277	−	12.1042i	0.395041	−	0.397555i
$928$	−4.09478	−	4.09478i	−0.134418	−	0.134418i
$929$	−5.44472	−	20.3200i	−0.178635	−	0.666676i	−0.995904	−	0.0904192i	$-0.971179\pi$
$929$	−5.44472	−	20.3200i	−0.178635	−	0.666676i	0.817268	−	0.576257i	$-0.195487\pi$
$930$	4.22708	+	3.23292i	0.138611	+	0.106012i
$931$	5.74361	−	5.74361i	0.188239	−	0.188239i
$932$	−3.45925	−	1.99720i	−0.113311	−	0.0654204i
$933$	43.1947	+	17.8117i	1.41413	+	0.583127i
$934$	47.5689	+	12.7460i	1.55650	+	0.417063i
$935$	−1.59228			−0.0520730
$936$		0			0
$937$	2.05438			0.0671138			0.0335569	−	0.999437i	$-0.489317\pi$
$937$	2.05438			0.0671138			0.0335569	+	0.999437i	$0.489317\pi$
$938$	−27.9521	−	7.48976i	−0.912670	−	0.244549i
$939$	−38.3757	−	15.8245i	−1.25234	−	0.516413i
$940$	−4.36990	−	2.52297i	−0.142531	−	0.0822901i
$941$	−41.3493	+	41.3493i	−1.34795	+	1.34795i	−0.460059	+	0.887888i	$0.652172\pi$
$941$	−41.3493	+	41.3493i	−1.34795	+	1.34795i	−0.887888	+	0.460059i	$0.847828\pi$
$942$	5.90163	+	4.51363i	0.192285	+	0.147062i
$943$	−3.25477	−	12.1470i	−0.105990	−	0.395560i
$944$	−7.95798	−	7.95798i	−0.259010	−	0.259010i
$945$	5.73900	−	45.2542i	0.186690	−	1.47212i
$946$	−35.3089	+	20.3856i	−1.14799	+	0.662793i
$947$	7.83402	−	29.2370i	0.254571	−	0.950074i	−0.713757	−	0.700393i	$-0.753008\pi$
$947$	7.83402	−	29.2370i	0.254571	−	0.950074i	0.968328	−	0.249680i	$-0.0803255\pi$
$948$	3.25181	+	4.22395i	0.105614	+	0.137188i
$949$		0			0
$950$		−	28.1052i		−	0.911852i
$951$	49.0527	−	20.4094i	1.59064	−	0.661822i
$952$	−0.867788	−	1.50305i	−0.0281252	−	0.0487142i
$953$	−4.74184	+	8.21310i	−0.153603	+	0.266048i	−0.932550	−	0.361042i	$-0.882421\pi$
$953$	−4.74184	+	8.21310i	−0.153603	+	0.266048i	0.778946	+	0.627091i	$0.215754\pi$
$954$	−46.3981	+	26.9845i	−1.50219	+	0.873654i
$955$	5.88875	−	1.57789i	0.190556	−	0.0510592i
$956$	1.60143	−	0.429101i	0.0517938	−	0.0138781i
$957$	2.22125	−	17.0813i	0.0718030	−	0.552161i
$958$	−1.34066	+	2.32209i	−0.0433147	+	0.0750233i
$959$	25.4041	+	44.0012i	0.820341	+	1.42087i
$960$	17.5566	+	42.1961i	0.566637	+	1.36187i
$961$		−	30.3938i		−	0.980445i
$962$		0			0
$963$	−22.5308	−	5.96062i	−0.726046	−	0.192078i
$964$	1.76499	−	6.58703i	0.0568465	−	0.212154i
$965$	−10.3411	+	5.97046i	−0.332893	+	0.192196i
$966$	21.7307	−	2.89596i	0.699174	−	0.0931759i
$967$	−17.7922	−	17.7922i	−0.572158	−	0.572158i	0.360573	−	0.932731i	$-0.382581\pi$
$967$	−17.7922	−	17.7922i	−0.572158	−	0.572158i	−0.932731	+	0.360573i	$0.882581\pi$
$968$	3.01778	+	11.2625i	0.0969950	+	0.361990i
$969$	−1.11016	+	1.45155i	−0.0356636	+	0.0466306i
$970$	−33.9421	+	33.9421i	−1.08981	+	1.08981i
$971$	−16.0499	−	9.26639i	−0.515065	−	0.297373i	0.219848	−	0.975534i	$-0.429444\pi$
$971$	−16.0499	−	9.26639i	−0.515065	−	0.297373i	−0.734913	+	0.678161i	$0.762777\pi$
$972$	3.39653	−	2.64929i	0.108944	−	0.0849759i
$973$	6.57078	+	1.76063i	0.210649	+	0.0564434i
$974$	32.9285			1.05510
$975$		0			0
$976$	−9.10483			−0.291439
$977$	−29.7416	−	7.96925i	−0.951519	−	0.254959i	−0.250512	−	0.968113i	$-0.580599\pi$
$977$	−29.7416	−	7.96925i	−0.951519	−	0.254959i	−0.701007	+	0.713155i	$0.747266\pi$
$978$	5.05248	−	12.2527i	0.161560	−	0.391797i
$979$	2.53495	+	1.46355i	0.0810174	+	0.0467754i
$980$	0.899023	−	0.899023i	0.0287182	−	0.0287182i
$981$	0.0966359	+	30.4771i	0.00308535	+	0.973058i
$982$	2.55943	+	9.55192i	0.0816747	+	0.304814i
$983$	19.1428	+	19.1428i	0.610561	+	0.610561i	0.943092	−	0.332531i	$-0.107903\pi$
$983$	19.1428	+	19.1428i	0.610561	+	0.610561i	−0.332531	+	0.943092i	$0.607903\pi$
$984$	2.60512	+	19.5483i	0.0830483	+	0.623178i
$985$	17.9345	−	10.3545i	0.571441	−	0.329921i
$986$	−0.252190	+	0.941188i	−0.00803138	+	0.0299735i
$987$	24.3533	−	18.7483i	0.775173	−	0.596766i
$988$		0			0
$989$		−	38.4731i		−	1.22337i
$990$	−15.6840	+	27.3654i	−0.498469	+	0.869731i
$991$	−3.12167	−	5.40689i	−0.0991631	−	0.171755i	0.812175	−	0.583413i	$-0.198283\pi$
$991$	−3.12167	−	5.40689i	−0.0991631	−	0.171755i	−0.911338	+	0.411658i	$0.864950\pi$
$992$	−0.603961	+	1.04609i	−0.0191758	+	0.0332134i
$993$	1.13975	+	0.148213i	0.0361689	+	0.00470341i
$994$	19.8071	−	5.30731i	0.628244	−	0.168338i
$995$	18.4085	−	4.93255i	0.583589	−	0.156372i
$996$	1.23513	+	0.160617i	0.0391367	+	0.00508933i
$997$	0.917609	−	1.58935i	0.0290610	−	0.0503351i	−0.851129	−	0.524956i	$-0.824082\pi$
$997$	0.917609	−	1.58935i	0.0290610	−	0.0503351i	0.880190	+	0.474621i	$0.157415\pi$
$998$	−8.09094	−	14.0139i	−0.256114	−	0.443603i
$999$	−3.58578	−	26.2706i	−0.113449	−	0.831164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.k.89.8		96
3.2	odd	2	inner	507.2.k.k.89.17		96
13.2	odd	12		507.2.f.g.239.8	yes	48
13.3	even	3		507.2.f.g.437.18	yes	48
13.4	even	6	inner	507.2.k.k.488.7		96
13.5	odd	4	inner	507.2.k.k.80.8		96
13.6	odd	12	inner	507.2.k.k.188.17		96
13.7	odd	12	inner	507.2.k.k.188.7		96
13.8	odd	4	inner	507.2.k.k.80.18		96
13.9	even	3	inner	507.2.k.k.488.17		96
13.10	even	6		507.2.f.g.437.8	yes	48
13.11	odd	12		507.2.f.g.239.18	yes	48
13.12	even	2	inner	507.2.k.k.89.18		96
39.2	even	12		507.2.f.g.239.17	yes	48
39.5	even	4	inner	507.2.k.k.80.17		96
39.8	even	4	inner	507.2.k.k.80.7		96
39.11	even	12		507.2.f.g.239.7	✓	48
39.17	odd	6	inner	507.2.k.k.488.18		96
39.20	even	12	inner	507.2.k.k.188.18		96
39.23	odd	6		507.2.f.g.437.17	yes	48
39.29	odd	6		507.2.f.g.437.7	yes	48
39.32	even	12	inner	507.2.k.k.188.8		96
39.35	odd	6	inner	507.2.k.k.488.8		96
39.38	odd	2	inner	507.2.k.k.89.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.7	✓	48	39.11	even	12
507.2.f.g.239.8	yes	48	13.2	odd	12
507.2.f.g.239.17	yes	48	39.2	even	12
507.2.f.g.239.18	yes	48	13.11	odd	12
507.2.f.g.437.7	yes	48	39.29	odd	6
507.2.f.g.437.8	yes	48	13.10	even	6
507.2.f.g.437.17	yes	48	39.23	odd	6
507.2.f.g.437.18	yes	48	13.3	even	3
507.2.k.k.80.7		96	39.8	even	4	inner
507.2.k.k.80.8		96	13.5	odd	4	inner
507.2.k.k.80.17		96	39.5	even	4	inner
507.2.k.k.80.18		96	13.8	odd	4	inner
507.2.k.k.89.7		96	39.38	odd	2	inner
507.2.k.k.89.8		96	1.1	even	1	trivial
507.2.k.k.89.17		96	3.2	odd	2	inner
507.2.k.k.89.18		96	13.12	even	2	inner
507.2.k.k.188.7		96	13.7	odd	12	inner
507.2.k.k.188.8		96	39.32	even	12	inner
507.2.k.k.188.17		96	13.6	odd	12	inner
507.2.k.k.188.18		96	39.20	even	12	inner
507.2.k.k.488.7		96	13.4	even	6	inner
507.2.k.k.488.8		96	39.35	odd	6	inner
507.2.k.k.488.17		96	13.9	even	3	inner
507.2.k.k.488.18		96	39.17	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.26815 - 0.339800i) q^{2} +(1.60126 + 0.660289i) q^{3} +(-0.239309 - 0.138165i) q^{4} +(2.12536 - 2.12536i) q^{5} +(-1.80627 - 1.38145i) q^{6} +(-0.755945 - 2.82123i) q^{7} +(2.11323 + 2.11323i) q^{8} +(2.12804 + 2.11458i) q^{9} +(-3.41747 + 1.97308i) q^{10} +(0.689573 - 2.57352i) q^{11} +(-0.291966 - 0.379251i) q^{12} +3.83461i q^{14} +(4.80659 - 1.99989i) q^{15} +(-1.68549 - 2.91935i) q^{16} +(0.0994162 - 0.172194i) q^{17} +(-1.98013 - 3.40472i) q^{18} +(-5.12548 + 1.37337i) q^{19} +(-0.802269 + 0.214967i) q^{20} +(0.652364 - 5.01665i) q^{21} +(-1.74897 + 3.02930i) q^{22} +(-1.65038 - 2.85855i) q^{23} +(1.98848 + 4.77917i) q^{24} -4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(-0.208891 + 0.779591i) q^{28} +(3.23258 - 1.86633i) q^{29} +(-6.77505 + 0.902881i) q^{30} +(-0.550550 - 0.550550i) q^{31} +(-0.401535 - 1.49855i) q^{32} +(2.80345 - 3.66555i) q^{33} +(-0.184586 + 0.184586i) q^{34} +(-7.60277 - 4.38946i) q^{35} +(-0.217097 - 0.800060i) q^{36} +(-4.92878 - 1.32066i) q^{37} +6.96655 q^{38} +8.98276 q^{40} +(3.68005 + 0.986066i) q^{41} +(-2.53195 + 6.14019i) q^{42} +(10.0942 + 5.82790i) q^{43} +(-0.520592 + 0.520592i) q^{44} +(9.01709 - 0.0285911i) q^{45} +(1.12160 + 4.18587i) q^{46} +(4.29586 + 4.29586i) q^{47} +(-0.771281 - 5.78754i) q^{48} +(-1.32568 + 0.765385i) q^{49} +(-1.37086 + 5.11610i) q^{50} +(0.272889 - 0.210083i) q^{51} -13.6276i q^{53} +(-0.922602 - 6.75928i) q^{54} +(-4.00407 - 6.93525i) q^{55} +(4.36442 - 7.55939i) q^{56} +(-9.11402 - 1.18519i) q^{57} +(-4.73357 + 1.26836i) q^{58} +(3.22482 - 0.864088i) q^{59} +(-1.42658 - 0.185512i) q^{60} +(1.35047 - 2.33909i) q^{61} +(0.511103 + 0.885257i) q^{62} +(4.35704 - 7.60218i) q^{63} +8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(-1.95320 + 7.28944i) q^{67} +(-0.0475824 + 0.0274717i) q^{68} +(-0.755216 - 5.66699i) q^{69} +(8.14992 + 8.14992i) q^{70} +(-1.38405 - 5.16536i) q^{71} +(0.0284280 + 8.96564i) q^{72} +(-3.46215 + 3.46215i) q^{73} +(5.80168 + 3.34960i) q^{74} +(2.66381 - 6.45995i) q^{75} +(1.41633 + 0.379503i) q^{76} -7.78177 q^{77} -11.1376 q^{79} +(-9.78695 - 2.62241i) q^{80} +(0.0570734 + 8.99982i) q^{81} +(-4.33179 - 2.50096i) q^{82} +(-1.84014 + 1.84014i) q^{83} +(-0.849243 + 1.11040i) q^{84} +(-0.154679 - 0.577269i) q^{85} +(-10.8207 - 10.8207i) q^{86} +(6.40850 - 0.854033i) q^{87} +(6.89568 - 3.98122i) q^{88} +(-0.284349 + 1.06120i) q^{89} +(-11.4447 - 3.02775i) q^{90} +0.912102i q^{92} +(-0.518049 - 1.24509i) q^{93} +(-3.98807 - 6.90753i) q^{94} +(-7.97458 + 13.8124i) q^{95} +(0.346516 - 2.66469i) q^{96} +(11.7496 - 3.14829i) q^{97} +(1.94125 - 0.520155i) 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

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