LMFDB - Embedded newform 507.2.k.k.188.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.7
Character	$\chi$	$=$	507.188
Dual form			507.2.k.k.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26815 + 0.339800i) q^{2} +(-0.228800 - 1.71687i) q^{3} +(-0.239309 + 0.138165i) q^{4} +(2.12536 + 2.12536i) q^{5} +(0.873546 + 2.09951i) q^{6} +(0.755945 - 2.82123i) q^{7} +(2.11323 - 2.11323i) q^{8} +(-2.89530 + 0.785641i) q^{9} +(-3.41747 - 1.97308i) q^{10} +(0.689573 + 2.57352i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(3.16269 - 4.13525i) q^{15} +(-1.68549 + 2.91935i) q^{16} +(-0.0994162 - 0.172194i) q^{17} +(3.40472 - 1.98013i) q^{18} +(5.12548 + 1.37337i) q^{19} +(-0.802269 - 0.214967i) q^{20} +(-5.01665 - 0.652364i) q^{21} +(-1.74897 - 3.02930i) q^{22} +(1.65038 - 2.85855i) q^{23} +(-4.11166 - 3.14464i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(0.208891 + 0.779591i) q^{28} +(-3.23258 - 1.86633i) q^{29} +(-2.60561 + 6.31880i) q^{30} +(0.550550 - 0.550550i) q^{31} +(-0.401535 + 1.49855i) q^{32} +(4.26063 - 1.77273i) q^{33} +(0.184586 + 0.184586i) q^{34} +(7.60277 - 4.38946i) q^{35} +(0.584324 - 0.588041i) q^{36} +(4.92878 - 1.32066i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(3.68005 - 0.986066i) q^{41} +(6.58353 - 0.877359i) q^{42} +(10.0942 - 5.82790i) q^{43} +(-0.520592 - 0.520592i) q^{44} +(-7.82332 - 4.48378i) q^{45} +(-1.12160 + 4.18587i) q^{46} +(4.29586 - 4.29586i) q^{47} +(5.39780 + 2.22582i) q^{48} +(-1.32568 - 0.765385i) q^{49} +(-1.37086 - 5.11610i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(-4.17864 - 5.39241i) q^{54} +(-4.00407 + 6.93525i) q^{55} +(-4.36442 - 7.55939i) q^{56} +(1.18519 - 9.11402i) q^{57} +(4.73357 + 1.26836i) q^{58} +(3.22482 + 0.864088i) q^{59} +(-0.185512 + 1.42658i) q^{60} +(1.35047 + 2.33909i) q^{61} +(-0.511103 + 0.885257i) q^{62} +(0.0277830 + 8.76220i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(1.95320 + 7.28944i) q^{67} +(0.0475824 + 0.0274717i) q^{68} +(-5.28537 - 2.17946i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(-1.38405 + 5.16536i) q^{71} +(-4.45820 + 7.77869i) q^{72} +(3.46215 + 3.46215i) q^{73} +(-5.80168 + 3.34960i) q^{74} +(6.92638 - 0.923049i) q^{75} +(-1.41633 + 0.379503i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(-9.78695 + 2.62241i) q^{80} +(7.76554 - 4.54934i) q^{81} +(-4.33179 + 2.50096i) q^{82} +(-1.84014 - 1.84014i) q^{83} +(1.29066 - 0.537009i) q^{84} +(0.154679 - 0.577269i) q^{85} +(-10.8207 + 10.8207i) q^{86} +(-2.46463 + 5.97694i) q^{87} +(6.89568 + 3.98122i) q^{88} +(-0.284349 - 1.06120i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(-1.07119 - 0.819258i) q^{93} +(-3.98807 + 6.90753i) q^{94} +(7.97458 + 13.8124i) q^{95} +(2.66469 + 0.346516i) q^{96} +(-11.7496 - 3.14829i) q^{97} +(1.94125 + 0.520155i) 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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	−0.677606	−	0.735425i	$-0.736983\pi$
$2$	−1.26815	+	0.339800i	−0.896718	+	0.240275i	−0.219112	+	0.975700i	$0.570316\pi$
$3$	−0.228800	−	1.71687i	−0.132098	−	0.991237i
$3$	−0.228800	−	1.71687i	−0.132098	−	0.991237i
$4$	−0.239309	+	0.138165i	−0.119655	+	0.0690826i
$5$	2.12536	+	2.12536i	0.950489	+	0.950489i	0.998831	−	0.0483414i	$-0.0153935\pi$
$5$	2.12536	+	2.12536i	0.950489	+	0.950489i	−0.0483414	+	0.998831i	$0.515394\pi$
$6$	0.873546	+	2.09951i	0.356624	+	0.857120i
$7$	0.755945	−	2.82123i	0.285720	−	1.06632i	−0.662591	−	0.748982i	$-0.730543\pi$
$7$	0.755945	−	2.82123i	0.285720	−	1.06632i	0.948311	−	0.317342i	$-0.102790\pi$
$8$	2.11323	−	2.11323i	0.747141	−	0.747141i
$9$	−2.89530	+	0.785641i	−0.965100	+	0.261880i
$10$	−3.41747	−	1.97308i	−1.08070	−	0.623942i
$11$	0.689573	+	2.57352i	0.207914	+	0.775946i	0.988541	+	0.150949i	$0.0482331\pi$
$11$	0.689573	+	2.57352i	0.207914	+	0.775946i	−0.780627	+	0.624997i	$0.785100\pi$
$12$	0.291966	+	0.379251i	0.0842833	+	0.109480i
$13$		0			0
$13$		0			0
$14$			3.83461i			1.02484i
$15$	3.16269	−	4.13525i	0.816602	−	1.06772i
$16$	−1.68549	+	2.91935i	−0.421373	+	0.729839i
$17$	−0.0994162	−	0.172194i	−0.0241120	−	0.0417632i	0.853718	−	0.520736i	$-0.174342\pi$
$17$	−0.0994162	−	0.172194i	−0.0241120	−	0.0417632i	−0.877830	+	0.478973i	$0.841009\pi$
$18$	3.40472	−	1.98013i	0.802499	−	0.466722i
$19$	5.12548	+	1.37337i	1.17586	+	0.315072i	0.793285	−	0.608850i	$-0.208369\pi$
$19$	5.12548	+	1.37337i	1.17586	+	0.315072i	0.382580	+	0.923922i	$0.375036\pi$
$20$	−0.802269	−	0.214967i	−0.179393	−	0.0480681i
$21$	−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	−0.641066	−	0.767485i	$-0.721508\pi$
$23$	1.65038	−	2.85855i	0.344129	−	0.596048i	0.985195	+	0.171437i	$0.0548410\pi$
$24$	−4.11166	−	3.14464i	−0.839289	−	0.641897i
$25$			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	$-0.445987\pi$
$29$	−3.23258	−	1.86633i	−0.600274	−	0.346568i	−0.769149	+	0.639069i	$0.779320\pi$
$30$	−2.60561	+	6.31880i	−0.475716	+	1.15365i
$31$	0.550550	−	0.550550i	0.0988817	−	0.0988817i	−0.655935	−	0.754817i	$-0.727726\pi$
$31$	0.550550	−	0.550550i	0.0988817	−	0.0988817i	0.754817	+	0.655935i	$0.227726\pi$
$32$	−0.401535	+	1.49855i	−0.0709820	+	0.264908i
$33$	4.26063	−	1.77273i	0.741681	−	0.308593i
$34$	0.184586	+	0.184586i	0.0316563	+	0.0316563i
$35$	7.60277	−	4.38946i	1.28510	−	0.741955i
$36$	0.584324	−	0.588041i	0.0973873	−	0.0980069i
$37$	4.92878	−	1.32066i	0.810287	−	0.217116i	0.170191	−	0.985411i	$-0.445561\pi$
$37$	4.92878	−	1.32066i	0.810287	−	0.217116i	0.640096	+	0.768295i	$0.278895\pi$
$38$	−6.96655			−1.13012
$39$		0			0
$40$	8.98276			1.42030
$41$	3.68005	−	0.986066i	0.574727	−	0.153998i	0.0402633	−	0.999189i	$-0.487180\pi$
$41$	3.68005	−	0.986066i	0.574727	−	0.153998i	0.534464	+	0.845192i	$0.320514\pi$
$42$	6.58353	−	0.877359i	1.01586	−	0.135379i
$43$	10.0942	−	5.82790i	1.53936	−	0.888747i	0.540479	−	0.841358i	$-0.318243\pi$
$43$	10.0942	−	5.82790i	1.53936	−	0.888747i	0.998876	−	0.0473894i	$-0.0150902\pi$
$44$	−0.520592	−	0.520592i	−0.0784823	−	0.0784823i
$45$	−7.82332	−	4.48378i	−1.16623	−	0.668403i
$46$	−1.12160	+	4.18587i	−0.165371	+	0.617173i
$47$	4.29586	−	4.29586i	0.626616	−	0.626616i	−0.320599	−	0.947215i	$-0.603884\pi$
$47$	4.29586	−	4.29586i	0.626616	−	0.626616i	0.947215	+	0.320599i	$0.103884\pi$
$48$	5.39780	+	2.22582i	0.779105	+	0.321270i
$49$	−1.32568	−	0.765385i	−0.189384	−	0.109341i
$50$	−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	$-0.385454\pi$
$54$	−4.17864	−	5.39241i	−0.568641	−	0.733814i
$55$	−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
$58$	4.73357	+	1.26836i	0.621548	+	0.166543i
$59$	3.22482	+	0.864088i	0.419836	+	0.112495i	0.462551	−	0.886593i	$-0.346934\pi$
$59$	3.22482	+	0.864088i	0.419836	+	0.112495i	−0.0427154	+	0.999087i	$0.513601\pi$
$60$	−0.185512	+	1.42658i	−0.0239495	+	0.184170i
$61$	1.35047	+	2.33909i	0.172910	+	0.299489i	0.939436	−	0.342724i	$-0.111350\pi$
$61$	1.35047	+	2.33909i	0.172910	+	0.299489i	−0.766526	+	0.642213i	$0.778016\pi$
$62$	−0.511103	+	0.885257i	−0.0649102	+	0.112428i
$63$	0.0277830	+	8.76220i	0.00350032	+	1.10393i
$64$		−	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	0.976483	+	0.215595i	$0.0691690\pi$
$67$	1.95320	+	7.28944i	0.238621	+	0.890547i	−0.737862	+	0.674952i	$0.764164\pi$
$68$	0.0475824	+	0.0274717i	0.00577022	+	0.00333144i
$69$	−5.28537	−	2.17946i	−0.636284	−	0.262376i
$70$	−8.14992	+	8.14992i	−0.974102	+	0.974102i
$71$	−1.38405	+	5.16536i	−0.164257	+	0.613016i	0.833877	+	0.551951i	$0.186116\pi$
$71$	−1.38405	+	5.16536i	−0.164257	+	0.613016i	−0.998134	+	0.0610649i	$0.980550\pi$
$72$	−4.45820	+	7.77869i	−0.525404	+	0.916727i
$73$	3.46215	+	3.46215i	0.405214	+	0.405214i	0.880066	−	0.474852i	$-0.157498\pi$
$73$	3.46215	+	3.46215i	0.405214	+	0.405214i	−0.474852	+	0.880066i	$0.657498\pi$
$74$	−5.80168	+	3.34960i	−0.674431	+	0.389383i
$75$	6.92638	−	0.923049i	0.799790	−	0.106585i
$76$	−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
$81$	7.76554	−	4.54934i	0.862837	−	0.505482i
$82$	−4.33179	+	2.50096i	−0.478366	+	0.276185i
$83$	−1.84014	−	1.84014i	−0.201981	−	0.201981i	0.598867	−	0.800848i	$-0.295618\pi$
$83$	−1.84014	−	1.84014i	−0.201981	−	0.201981i	−0.800848	+	0.598867i	$0.795618\pi$
$84$	1.29066	−	0.537009i	0.140823	−	0.0585925i
$85$	0.154679	−	0.577269i	0.0167773	−	0.0626136i
$86$	−10.8207	+	10.8207i	−1.16682	+	1.16682i
$87$	−2.46463	+	5.97694i	−0.264236	+	0.640795i
$88$	6.89568	+	3.98122i	0.735082	+	0.424400i
$89$	−0.284349	−	1.06120i	−0.0301409	−	0.112487i	0.949217	−	0.314624i	$-0.101878\pi$
$89$	−0.284349	−	1.06120i	−0.0301409	−	0.112487i	−0.979357	+	0.202136i	$0.935212\pi$
$90$	11.4447	+	3.02775i	1.20638	+	0.319153i
$91$		0			0
$92$			0.912102i			0.0950932i
$93$	−1.07119	−	0.819258i	−0.111077	−	0.0849531i
$94$	−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
$97$	−11.7496	−	3.14829i	−1.19299	−	0.319661i	−0.392923	−	0.919571i	$-0.628536\pi$
$97$	−11.7496	−	3.14829i	−1.19299	−	0.319661i	−0.800067	+	0.599911i	$0.795203\pi$
$98$	1.94125	+	0.520155i	0.196095	+	0.0525436i
$99$	−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	0.373483	+	0.927637i	$0.378164\pi$
$101$	−6.19691	+	10.7334i	−0.616616	+	1.06801i	−0.990099	+	0.140373i	$0.955170\pi$
$102$	0.274678	−	0.359144i	0.0271971	−	0.0355606i
$103$			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
$106$	4.63065	+	17.2818i	0.449769	+	1.67856i
$107$	6.72785	+	3.88433i	0.650406	+	0.375512i	0.788612	−	0.614891i	$-0.210800\pi$
$107$	6.72785	+	3.88433i	0.650406	+	0.375512i	−0.138206	+	0.990404i	$0.544134\pi$
$108$	−1.14328	−	0.868665i	−0.110013	−	0.0835874i
$109$	−7.18355	+	7.18355i	−0.688060	+	0.688060i	−0.961803	−	0.273743i	$-0.911738\pi$
$109$	−7.18355	+	7.18355i	−0.688060	+	0.688060i	0.273743	+	0.961803i	$0.411738\pi$
$110$	2.72116	−	10.1555i	0.259453	−	0.968291i
$111$	−3.39512	−	8.15992i	−0.322250	−	0.774506i
$112$	6.96202	+	6.96202i	0.657849	+	0.657849i
$113$	−14.7985	+	8.54390i	−1.39212	+	0.803743i	−0.993550	−	0.113394i	$-0.963828\pi$
$113$	−14.7985	+	8.54390i	−1.39212	+	0.803743i	−0.398573	+	0.917136i	$0.630495\pi$
$114$	1.59395	+	11.9607i	0.149287	+	1.12022i
$115$	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
$120$	−2.05526	−	15.4222i	−0.187618	−	1.40785i
$121$	3.37877	−	1.95074i	0.307161	−	0.177340i
$122$	−2.50742	−	2.50742i	−0.227011	−	0.227011i
$123$	−2.53494	−	6.09256i	−0.228568	−	0.549348i
$124$	−0.0556848	+	0.207818i	−0.00500064	+	0.0186627i
$125$	2.05245	−	2.05245i	0.183577	−	0.183577i
$126$	−3.01263	−	11.1023i	−0.268386	−	0.989076i
$127$	−8.33573	−	4.81263i	−0.739676	−	0.427052i	0.0822755	−	0.996610i	$-0.473781\pi$
$127$	−8.33573	−	4.81263i	−0.739676	−	0.427052i	−0.821952	+	0.569557i	$0.807115\pi$
$128$	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	$0.825965\pi$
$132$	−0.774679	+	1.01290i	−0.0674272	+	0.0881618i
$133$	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
$136$	−0.573976	−	0.153796i	−0.0492180	−	0.0131879i
$137$	−16.8029	−	4.50231i	−1.43557	−	0.384659i	−0.544587	−	0.838704i	$-0.683314\pi$
$137$	−16.8029	−	4.50231i	−1.43557	−	0.384659i	−0.890979	+	0.454045i	$0.849980\pi$
$138$	7.44322	+	0.967917i	0.633609	+	0.0823945i
$139$	−1.16453	−	2.01702i	−0.0987737	−	0.171081i	0.812404	−	0.583096i	$-0.198159\pi$
$139$	−1.16453	−	2.01702i	−0.0987737	−	0.171081i	−0.911177	+	0.412014i	$0.864825\pi$
$140$	−1.21294	+	2.10088i	−0.102512	+	0.177557i
$141$	−8.35834	−	6.39255i	−0.703899	−	0.538350i
$142$		−	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
$147$	−1.01075	+	2.45115i	−0.0833653	+	0.202168i
$148$	−0.997033	+	0.997033i	−0.0819556	+	0.0819556i
$149$	4.08308	−	15.2383i	0.334499	−	1.24837i	−0.569913	−	0.821705i	$-0.693023\pi$
$149$	4.08308	−	15.2383i	0.334499	−	1.24837i	0.904412	−	0.426661i	$-0.140310\pi$
$150$	−8.47004	+	3.52415i	−0.691576	+	0.287746i
$151$	8.56897	+	8.56897i	0.697333	+	0.697333i	0.963834	−	0.266502i	$-0.0858678\pi$
$151$	8.56897	+	8.56897i	0.697333	+	0.697333i	−0.266502	+	0.963834i	$0.585868\pi$
$152$	13.7336	−	7.92908i	1.11394	−	0.643133i
$153$	0.423123	+	0.420448i	0.0342074	+	0.0339912i
$154$	−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
$159$	−23.3968	+	3.11800i	−1.85549	+	0.247273i
$160$	−4.03836	+	2.33155i	−0.319260	+	0.184325i
$161$	−6.81701	−	6.81701i	−0.537256	−	0.537256i
$162$	−8.30200	+	8.40797i	−0.652267	+	0.660593i
$163$	−1.50848	+	5.62972i	−0.118153	+	0.440954i	−0.999503	−	0.0315098i	$-0.989968\pi$
$163$	−1.50848	+	5.62972i	−0.118153	+	0.440954i	0.881350	+	0.472463i	$0.156635\pi$
$164$	−0.744429	+	0.744429i	−0.0581302	+	0.0581302i
$165$	12.8231	+	5.28769i	0.998275	+	0.411646i
$166$	2.95885	+	1.70829i	0.229651	+	0.132589i
$167$	0.409254	+	1.52736i	0.0316690	+	0.118190i	0.979951	−	0.199239i	$-0.0638470\pi$
$167$	0.409254	+	1.52736i	0.0316690	+	0.118190i	−0.948282	+	0.317429i	$0.897180\pi$
$168$	−11.9799	+	9.22274i	−0.924272	+	0.711550i
$169$		0			0
$170$			0.784624i			0.0601779i
$171$	−15.9188	+	0.0504748i	−1.21734	+	0.00385991i
$172$	−1.61043	+	2.78934i	−0.122794	+	0.212685i
$173$	6.21160	+	10.7588i	0.472259	+	0.817977i	0.999496	−	0.0317413i	$-0.0101053\pi$
$173$	6.21160	+	10.7588i	0.472259	+	0.817977i	−0.527237	+	0.849718i	$0.676772\pi$
$174$	1.09456	−	8.41714i	0.0829787	−	0.638101i
$175$	11.3817	+	3.04971i	0.860374	+	0.230537i
$176$	−8.67529	−	2.32454i	−0.653925	−	0.175219i
$177$	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	−0.382096	−	0.924123i	$-0.624798\pi$
$179$	8.15142	−	14.1187i	0.609265	−	1.05528i	0.991362	−	0.131156i	$-0.0418689\pi$
$180$	2.49170	−	0.00790061i	0.185720	−	0.000588876i
$181$			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
$184$	−2.55313	−	9.52842i	−0.188219	−	0.702444i
$185$	13.2823	+	7.66855i	0.976535	+	0.563803i
$186$	1.63681	+	0.674952i	0.120017	+	0.0494899i
$187$	0.374590	−	0.374590i	0.0273928	−	0.0273928i
$188$	−0.434500	+	1.62158i	−0.0316892	+	0.118266i
$189$	15.0372	−	2.05249i	1.09380	−	0.149297i
$190$	−14.8064	−	14.8064i	−1.07417	−	1.07417i
$191$	−1.75656	+	1.01415i	−0.127100	+	0.0733813i	−0.562202	−	0.827000i	$-0.690046\pi$
$191$	−1.75656	+	1.01415i	−0.127100	+	0.0733813i	0.435102	+	0.900381i	$0.356712\pi$
$192$	−15.0721	+	2.00859i	−1.08773	+	0.144957i
$193$	3.83737	−	1.02822i	0.276220	−	0.0740130i	−0.118050	−	0.993008i	$-0.537664\pi$
$193$	3.83737	−	1.02822i	0.276220	−	0.0740130i	0.394270	+	0.918995i	$0.370998\pi$
$194$	15.9700			1.14658
$195$		0			0
$196$	0.422998			0.0302142
$197$	6.65511	−	1.78323i	0.474157	−	0.127050i	−0.0138237	−	0.999904i	$-0.504400\pi$
$197$	6.65511	−	1.78323i	0.474157	−	0.127050i	0.487981	+	0.872855i	$0.337734\pi$
$198$	7.44372	+	7.39667i	0.529002	+	0.525658i
$199$	5.49109	−	3.17028i	0.389253	−	0.224735i	−0.292584	−	0.956240i	$-0.594515\pi$
$199$	5.49109	−	3.17028i	0.389253	−	0.224735i	0.681836	+	0.731505i	$0.261182\pi$
$200$	8.52542	+	8.52542i	0.602838	+	0.602838i
$201$	12.0681	−	5.02122i	0.851221	−	0.354169i
$202$	4.21142	−	15.7172i	0.296315	−	1.10586i
$203$	−7.70898	+	7.70898i	−0.541065	+	0.541065i
$204$	0.0362786	−	0.0879785i	0.00254001	−	0.00615973i
$205$	9.91717	+	5.72568i	0.692645	+	0.399899i
$206$	−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
$210$	15.8571	+	12.1277i	1.09424	+	0.836889i
$211$	0.401137	−	0.694790i	0.0276154	−	0.0478313i	−0.851887	−	0.523725i	$-0.824542\pi$
$211$	0.401137	−	0.694790i	0.0276154	−	0.0478313i	0.879503	+	0.475894i	$0.157875\pi$
$212$	1.88286	+	3.26121i	0.129315	+	0.223981i
$213$	9.18494	+	1.19441i	0.629342	+	0.0818396i
$214$	−9.85182	−	2.63979i	−0.673457	−	0.180452i
$215$	33.8402	+	9.06747i	2.30789	+	0.618396i
$216$	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
$219$	5.15193	−	6.73621i	0.348135	−	0.455191i
$220$		−	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	$-0.0503410\pi$
$223$	0.799768	+	2.98478i	0.0535565	+	0.199875i	−0.933964	+	0.357368i	$0.883674\pi$
$224$	3.92421	+	2.26564i	0.262197	+	0.151380i
$225$	−3.16952	−	11.6805i	−0.211301	−	0.778701i
$226$	15.8635	−	15.8635i	1.05522	−	1.05522i
$227$	−6.70715	+	25.0314i	−0.445169	+	1.66139i	0.270320	+	0.962770i	$0.412870\pi$
$227$	−6.70715	+	25.0314i	−0.445169	+	1.66139i	−0.715489	+	0.698624i	$0.753796\pi$
$228$	0.975614	+	2.34482i	0.0646116	+	0.155289i
$229$	−19.6410	−	19.6410i	−1.29791	−	1.29791i	−0.929768	−	0.368147i	$-0.879992\pi$
$229$	−19.6410	−	19.6410i	−1.29791	−	1.29791i	−0.368147	−	0.929768i	$-0.620008\pi$
$230$	−11.2803	+	6.51267i	−0.743799	+	0.429433i
$231$	−1.78047	−	13.3603i	−0.117146	−	0.879043i
$232$	−10.7752	+	2.88720i	−0.707425	+	0.189554i
$233$	−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
$236$	−0.891116	+	0.238774i	−0.0580067	+	0.0155428i
$237$	2.54829	+	19.1219i	0.165529	+	1.24210i
$238$	0.660297	−	0.381222i	0.0428007	−	0.0247110i
$239$	−4.24248	−	4.24248i	−0.274423	−	0.274423i	0.556455	−	0.830878i	$-0.312161\pi$
$239$	−4.24248	−	4.24248i	−0.274423	−	0.274423i	−0.830878	+	0.556455i	$0.812161\pi$
$240$	6.74159	+	16.2029i	0.435168	+	1.04590i
$241$	−6.38724	+	23.8375i	−0.411438	+	1.53551i	0.380426	+	0.924811i	$0.375777\pi$
$241$	−6.38724	+	23.8375i	−0.411438	+	1.53551i	−0.791864	+	0.610697i	$0.790889\pi$
$242$	−3.62193	+	3.62193i	−0.232827	+	0.232827i
$243$	−9.58739	−	12.2915i	−0.615031	−	0.788503i
$244$	−0.646361	−	0.373177i	−0.0413790	−	0.0238902i
$245$	−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
$249$	−2.73826	+	3.58031i	−0.173530	+	0.226893i
$250$	−1.90540	+	3.30024i	−0.120508	+	0.208726i
$251$	−10.8649	−	18.8186i	−0.685789	−	1.18782i	−0.973188	−	0.230010i	$-0.926124\pi$
$251$	−10.8649	−	18.8186i	−0.685789	−	1.18782i	0.287400	−	0.957811i	$-0.407209\pi$
$252$	−1.21728	−	2.09304i	−0.0766814	−	0.131849i
$253$	8.49459	+	2.27612i	0.534051	+	0.143098i
$254$	12.2063	+	3.27066i	0.765891	+	0.205220i
$255$	−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	0.491217	+	0.871037i	$0.336552\pi$
$257$	−8.15559	+	14.1259i	−0.508732	+	0.881149i	−0.999949	+	0.0101119i	$0.996781\pi$
$258$	21.0535	+	16.1019i	1.31073	+	1.00246i
$259$		−	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	$-0.448663\pi$
$263$	−9.95602	−	5.74811i	−0.613914	−	0.354444i	−0.774496	+	0.632579i	$0.781996\pi$
$264$	5.25752	−	12.7499i	0.323578	−	0.784702i
$265$	28.9635	−	28.9635i	1.77922	−	1.77922i
$266$	−5.26633	+	19.6542i	−0.322899	+	1.20508i
$267$	−1.75689	+	0.730994i	−0.107520	+	0.0447361i
$268$	−1.47457	−	1.47457i	−0.0900734	−	0.0900734i
$269$	9.64658	−	5.56946i	0.588162	−	0.339576i	−0.176208	−	0.984353i	$-0.556383\pi$
$269$	9.64658	−	5.56946i	0.588162	−	0.339576i	0.764371	+	0.644777i	$0.223050\pi$
$270$	2.57970	−	20.3419i	0.156995	−	1.23797i
$271$	5.86962	−	1.57276i	0.356554	−	0.0955383i	−0.0760956	−	0.997101i	$-0.524245\pi$
$271$	5.86962	−	1.57276i	0.356554	−	0.0955383i	0.432650	+	0.901562i	$0.357579\pi$
$272$	0.670260			0.0406405
$273$		0			0
$274$	22.8384			1.37972
$275$	−10.3824	+	2.78195i	−0.626080	+	0.167758i
$276$	1.56596	−	0.208689i	0.0942599	−	0.0125616i
$277$	−24.0591	+	13.8905i	−1.44557	+	0.834600i	−0.998213	−	0.0597558i	$-0.980968\pi$
$277$	−24.0591	+	13.8905i	−1.44557	+	0.834600i	−0.447356	+	0.894356i	$0.647634\pi$
$278$	2.16218	+	2.16218i	0.129679	+	0.129679i
$279$	−1.16147	+	2.02654i	−0.0695356	+	0.121326i
$280$	6.79047	−	25.3424i	0.405808	−	1.51450i
$281$	11.6187	−	11.6187i	0.693113	−	0.693113i	−0.269803	−	0.962916i	$-0.586958\pi$
$281$	11.6187	−	11.6187i	0.693113	−	0.693113i	0.962916	+	0.269803i	$0.0869585\pi$
$282$	12.7718	+	5.26655i	0.760551	+	0.313619i
$283$	−23.0251	−	13.2935i	−1.36870	−	0.790219i	−0.377938	−	0.925831i	$-0.623367\pi$
$283$	−23.0251	−	13.2935i	−1.36870	−	0.790219i	−0.990762	+	0.135612i	$0.956700\pi$
$284$	−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
$288$	−0.0147574	−	4.65421i	−0.000869591	−	0.274252i
$289$	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
$292$	−1.30687	−	0.350176i	−0.0764790	−	0.0204925i
$293$	−2.79628	−	0.749260i	−0.163360	−	0.0437722i	0.176212	−	0.984352i	$-0.443616\pi$
$293$	−2.79628	−	0.749260i	−0.163360	−	0.0437722i	−0.339572	+	0.940580i	$0.610282\pi$
$294$	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
$297$	−10.9431	+	8.47992i	−0.634982	+	0.492055i
$298$			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
$303$	19.8457	+	8.18351i	1.14010	+	0.470131i
$304$	−12.6483	+	12.6483i	−0.725429	+	0.725429i
$305$	−2.10116	+	7.84164i	−0.120312	+	0.449011i
$306$	−0.679451	−	0.389414i	−0.0388416	−	0.0222613i
$307$	13.9565	+	13.9565i	0.796541	+	0.796541i	0.982548	−	0.186007i	$-0.0595549\pi$
$307$	13.9565	+	13.9565i	0.796541	+	0.796541i	−0.186007	+	0.982548i	$0.559555\pi$
$308$	−1.86225	+	1.07517i	−0.106111	+	0.0612635i
$309$	9.76553	−	1.30141i	0.555541	−	0.0740346i
$310$	−2.96777	+	0.795211i	−0.168558	+	0.0451649i
$311$	−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	$0.736859\pi$
$314$	4.14344	−	1.11023i	0.233828	−	0.0626539i
$315$	−18.5638	+	18.6819i	−1.04595	+	1.05260i
$316$	2.66533	−	1.53883i	0.149937	−	0.0865660i
$317$	21.6899	+	21.6899i	1.21823	+	1.21823i	0.968253	+	0.249973i	$0.0804218\pi$
$317$	21.6899	+	21.6899i	1.21823	+	1.21823i	0.249973	+	0.968253i	$0.419578\pi$
$318$	28.6112	−	11.9043i	1.60444	−	0.667562i
$319$	2.57394	−	9.60608i	0.144113	−	0.537837i
$320$	18.6581	−	18.6581i	1.04302	−	1.04302i
$321$	5.12956	−	12.4396i	0.286304	−	0.694311i
$322$	10.9614	+	6.32857i	0.610856	+	0.352678i
$323$	−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
$327$	13.9768	+	10.6896i	0.772921	+	0.591139i
$328$	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
$331$	−0.640966	−	0.171746i	−0.0352307	−	0.00944003i	0.241161	−	0.970485i	$-0.422472\pi$
$331$	−0.640966	−	0.171746i	−0.0352307	−	0.00944003i	−0.276391	+	0.961045i	$0.589139\pi$
$332$	0.694605	+	0.186119i	0.0381214	+	0.0102146i
$333$	−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
$336$	10.3600	−	13.5458i	0.565184	−	0.738985i
$337$			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
$340$	0.0427425	+	0.159517i	0.00231804	+	0.00865103i
$341$	1.79650	+	1.03721i	0.0972858	+	0.0561680i
$342$	20.1702	−	5.47321i	1.09068	−	0.295957i
$343$	11.2955	−	11.2955i	0.609900	−	0.609900i
$344$	9.01573	−	33.6472i	0.486096	−	1.81413i
$345$	−6.60117	−	15.8654i	−0.355395	−	0.854167i
$346$	−11.5331	−	11.5331i	−0.620023	−	0.620023i
$347$	14.2117	−	8.20511i	0.762923	−	0.440474i	−0.0674214	−	0.997725i	$-0.521477\pi$
$347$	14.2117	−	8.20511i	0.762923	−	0.440474i	0.830344	+	0.557251i	$0.188144\pi$
$348$	−0.235995	−	1.77086i	−0.0126507	−	0.0949282i
$349$	−28.9532	+	7.75800i	−1.54983	+	0.415276i	−0.929427	−	0.369006i	$-0.879698\pi$
$349$	−28.9532	+	7.75800i	−1.54983	+	0.415276i	−0.620405	+	0.784282i	$0.713032\pi$
$350$	−15.4700			−0.826905
$351$		0			0
$352$	−4.13344			−0.220313
$353$	6.50846	−	1.74394i	0.346410	−	0.0928203i	−0.0814189	−	0.996680i	$-0.525945\pi$
$353$	6.50846	−	1.74394i	0.346410	−	0.0928203i	0.427829	+	0.903860i	$0.359279\pi$
$354$	1.00287	+	7.52535i	0.0533020	+	0.399968i
$355$	−13.9199	+	8.03664i	−0.738790	+	0.426540i
$356$	0.214669	+	0.214669i	0.0113774	+	0.0113774i
$357$	0.386403	+	0.928692i	0.0204506	+	0.0491516i
$358$	−5.53970	+	20.6744i	−0.292782	+	1.09268i
$359$	−6.76884	+	6.76884i	−0.357246	+	0.357246i	−0.862797	−	0.505551i	$-0.831289\pi$
$359$	−6.76884	+	6.76884i	−0.357246	+	0.357246i	0.505551	+	0.862797i	$0.331289\pi$
$360$	−26.0078	+	7.05723i	−1.37073	+	0.371948i
$361$	7.92989	+	4.57832i	0.417363	+	0.240964i
$362$	−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
$366$	−3.73123	+	4.87862i	−0.195034	+	0.255010i
$367$	6.01337	−	10.4155i	0.313895	−	0.543682i	−0.665307	−	0.746570i	$-0.731699\pi$
$367$	6.01337	−	10.4155i	0.313895	−	0.543682i	0.979202	+	0.202888i	$0.0650326\pi$
$368$	5.56341	+	9.63611i	0.290013	+	0.502317i
$369$	−9.88015	+	5.74615i	−0.514340	+	0.299133i
$370$	−19.4497	−	5.21154i	−1.01114	−	0.270935i
$371$	−38.4465	−	10.3017i	−1.99604	−	0.534838i
$372$	0.369539	+	0.0480548i	0.0191597	+	0.00249152i
$373$	−6.67932	−	11.5689i	−0.345842	−	0.599016i	0.639664	−	0.768654i	$-0.279073\pi$
$373$	−6.67932	−	11.5689i	−0.345842	−	0.599016i	−0.985506	+	0.169638i	$0.945740\pi$
$374$	−0.347751	+	0.602323i	−0.0179818	+	0.0311454i
$375$	−3.99340	−	3.05420i	−0.206218	−	0.157718i
$376$		−	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	0.791352	+	0.611360i	$0.209377\pi$
$379$	8.01497	+	29.9123i	0.411701	+	1.53649i	−0.379651	+	0.925130i	$0.623956\pi$
$380$	−3.81678	−	2.20362i	−0.195797	−	0.113043i
$381$	−6.35546	+	15.4125i	−0.325600	+	0.789607i
$382$	1.88297	−	1.88297i	0.0963413	−	0.0963413i
$383$	2.65388	−	9.90441i	0.135607	−	0.506092i	−0.864388	−	0.502826i	$-0.832294\pi$
$383$	2.65388	−	9.90441i	0.135607	−	0.506092i	0.999995	−	0.00326604i	$-0.00103961\pi$
$384$	13.4692	−	5.60417i	0.687349	−	0.285987i
$385$	16.5390	+	16.5390i	0.842908	+	0.842908i
$386$	−4.51698	+	2.60788i	−0.229908	+	0.132738i
$387$	−24.6472	+	24.8040i	−1.25289	+	1.26086i
$388$	3.24677	−	0.869969i	0.164830	−	0.0441660i
$389$	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
$392$	−4.41892	+	1.18405i	−0.223189	+	0.0598033i
$393$	20.4330	−	2.72302i	1.03071	−	0.137358i
$394$	−7.83374	+	4.52281i	−0.394658	+	0.227856i
$395$	−23.6714	−	23.6714i	−1.19104	−	1.19104i
$396$	1.91627	+	1.09827i	0.0962962	+	0.0551903i
$397$	0.888280	−	3.31510i	0.0445815	−	0.166380i	−0.940046	−	0.341048i	$-0.889218\pi$
$397$	0.888280	−	3.31510i	0.0445815	−	0.166380i	0.984628	+	0.174667i	$0.0558850\pi$
$398$	−5.88626	+	5.88626i	−0.295052	+	0.295052i
$399$	−24.8168	−	10.2334i	−1.24239	−	0.512310i
$400$	−11.7776	−	6.79978i	−0.588878	−	0.339989i
$401$	5.16404	+	19.2725i	0.257880	+	0.962421i	0.966466	+	0.256796i	$0.0826668\pi$
$401$	5.16404	+	19.2725i	0.257880	+	0.962421i	−0.708586	+	0.705625i	$0.750666\pi$
$402$	−13.5980	+	10.4684i	−0.678207	+	0.522117i
$403$		0			0
$404$		−	3.42479i		−	0.170390i
$405$	26.1735	+	6.83558i	1.30057	+	0.339663i
$406$	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
$409$	−5.35240	−	1.43417i	−0.264659	−	0.0709152i	0.124049	−	0.992276i	$-0.460412\pi$
$409$	−5.35240	−	1.43417i	−0.264659	−	0.0709152i	−0.388708	+	0.921361i	$0.627079\pi$
$410$	−14.5220	−	3.89117i	−0.717193	−	0.192171i
$411$	−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
$414$	−0.0412217	−	13.0005i	−0.00202594	−	0.638941i
$415$		−	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	$-0.651428\pi$
$419$	−29.8207	−	17.2170i	−1.45684	−	0.841106i	−0.998854	+	0.0478553i	$0.984761\pi$
$420$	3.88446	+	1.60179i	0.189542	+	0.0781591i
$421$	−18.6143	+	18.6143i	−0.907208	+	0.907208i	−0.996046	−	0.0888383i	$-0.971685\pi$
$421$	−18.6143	+	18.6143i	−0.907208	+	0.907208i	0.0888383	+	0.996046i	$0.471685\pi$
$422$	−0.272613	+	1.01740i	−0.0132706	+	0.0495265i
$423$	−9.06281	+	15.8128i	−0.440649	+	0.768846i
$424$	−28.7983	−	28.7983i	−1.39857	−	1.39857i
$425$	0.694683	−	0.401075i	0.0336971	−	0.0194550i
$426$	−12.0537	+	1.60635i	−0.584006	+	0.0778279i
$427$	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	−0.512111	−	0.858919i	$-0.671136\pi$
$431$	−10.9232	+	2.92686i	−0.526152	+	0.140982i	−0.0140414	+	0.999901i	$0.504470\pi$
$432$	−17.3770	−	2.20369i	−0.836049	−	0.106025i
$433$	−5.37469	+	3.10308i	−0.258291	+	0.149124i	−0.623555	−	0.781780i	$-0.714312\pi$
$433$	−5.37469	+	3.10308i	−0.258291	+	0.149124i	0.365264	+	0.930904i	$0.380979\pi$
$434$	2.11114	+	2.11114i	0.101338	+	0.101338i
$435$	−17.9414	+	7.46490i	−0.860223	+	0.357915i
$436$	0.726573	−	2.71161i	0.0347965	−	0.129862i
$437$	12.3848	−	12.3848i	0.592447	−	0.592447i
$438$	−4.24446	+	10.2932i	−0.202808	+	0.491826i
$439$	33.5869	+	19.3914i	1.60301	+	0.925501i	0.990880	+	0.134748i	$0.0430224\pi$
$439$	33.5869	+	19.3914i	1.60301	+	0.925501i	0.612135	+	0.790753i	$0.290311\pi$
$440$	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	$-0.143267\pi$
$444$	1.93990	+	1.48366i	0.0920636	+	0.0704113i
$445$	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
$448$	−24.7669	−	6.63628i	−1.17013	−	0.313535i
$449$	1.87306	+	0.501884i	0.0883950	+	0.0236854i	0.302745	−	0.953071i	$-0.402097\pi$
$449$	1.87306	+	0.501884i	0.0883950	+	0.0236854i	−0.214350	+	0.976757i	$0.568763\pi$
$450$	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
$453$	12.7512	−	16.6724i	0.599106	−	0.783338i
$454$		−	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	$-0.126852\pi$
$457$	−1.50820	−	5.62868i	−0.0705507	−	0.263299i	−0.992188	+	0.124755i	$0.960186\pi$
$458$	31.5818	+	18.2337i	1.47572	+	0.852007i
$459$	0.625045	−	0.822646i	0.0291746	−	0.0383978i
$460$	−1.93854	+	1.93854i	−0.0903851	+	0.0903851i
$461$	3.70361	−	13.8221i	0.172494	−	0.643758i	−0.824470	−	0.565905i	$-0.808527\pi$
$461$	3.70361	−	13.8221i	0.172494	−	0.643758i	0.996965	−	0.0778529i	$-0.0248064\pi$
$462$	6.79773	+	16.3379i	0.316259	+	0.760106i
$463$	2.99038	+	2.99038i	0.138975	+	0.138975i	0.773172	−	0.634197i	$-0.218669\pi$
$463$	2.99038	+	2.99038i	0.138975	+	0.138975i	−0.634197	+	0.773172i	$0.718669\pi$
$464$	10.8969	−	6.29136i	0.505878	−	0.292069i
$465$	−0.535446	−	4.01788i	−0.0248307	−	0.186325i
$466$	18.3313	−	4.91185i	0.849181	−	0.227537i
$467$	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
$470$	−23.1571	+	6.20491i	−1.06816	+	0.286211i
$471$	0.747560	+	5.60955i	0.0344458	+	0.258474i
$472$	8.64081	−	4.98877i	0.397726	−	0.229627i
$473$	21.9589	+	21.9589i	1.00967	+	1.00967i
$474$	−9.72922	−	23.3835i	−0.446878	−	1.07404i
$475$	−5.54058	+	20.6777i	−0.254219	+	0.948759i
$476$	0.113474	−	0.113474i	0.00520106	−	0.00520106i
$477$	10.7064	+	39.4560i	0.490212	+	1.80656i
$478$	6.82169	+	3.93851i	0.312017	+	0.180143i
$479$	0.528588	+	1.97272i	0.0241518	+	0.0901358i	0.976950	−	0.213469i	$-0.0684763\pi$
$479$	0.528588	+	1.97272i	0.0241518	+	0.0901358i	−0.952798	+	0.303605i	$0.901810\pi$
$480$	4.92695	+	6.39989i	0.224883	+	0.292114i
$481$		0			0
$482$		−	32.3999i		−	1.47578i
$483$	−10.1442	+	13.2637i	−0.461577	+	0.603518i
$484$	−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
$487$	24.2264	+	6.49144i	1.09780	+	0.294155i	0.761869	−	0.647731i	$-0.224282\pi$
$487$	24.2264	+	6.49144i	1.09780	+	0.294155i	0.335933	+	0.941886i	$0.390948\pi$
$488$	7.79690	+	2.08917i	0.352949	+	0.0945724i
$489$	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	−0.768445	−	0.639916i	$-0.778969\pi$
$491$	3.76608	−	6.52305i	0.169961	−	0.294381i	0.938406	+	0.345535i	$0.112302\pi$
$492$	1.44842	+	1.10776i	0.0652996	+	0.0499419i
$493$			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
$498$	2.25594	−	5.47083i	0.101091	−	0.245154i
$499$	−8.71539	+	8.71539i	−0.390154	+	0.390154i	−0.874742	−	0.484588i	$-0.838970\pi$
$499$	−8.71539	+	8.71539i	−0.390154	+	0.390154i	0.484588	+	0.874742i	$0.338970\pi$
$500$	−0.207593	+	0.774749i	−0.00928385	+	0.0346478i
$501$	2.52864	−	1.05210i	0.112971	−	0.0470042i
$502$	20.1729	+	20.1729i	0.900362	+	0.900362i
$503$	2.03490	−	1.17485i	0.0907316	−	0.0523839i	−0.453948	−	0.891028i	$-0.649985\pi$
$503$	2.03490	−	1.17485i	0.0907316	−	0.0523839i	0.544679	+	0.838644i	$0.316651\pi$
$504$	18.5753	+	18.4579i	0.827409	+	0.822178i
$505$	−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	−0.835142	−	0.550034i	$-0.814615\pi$
$509$	−28.9544	+	7.75830i	−1.28338	+	0.343881i	−0.448238	+	0.893914i	$0.647948\pi$
$510$	1.34710	−	0.179522i	0.0596506	−	0.00794937i
$511$	12.3847	−	7.15031i	0.547867	−	0.316311i
$512$	−17.9453	−	17.9453i	−0.793080	−	0.793080i
$513$	3.72888	+	27.3189i	0.164634	+	1.20616i
$514$	5.54254	−	20.6850i	0.244471	−	0.912377i
$515$	−12.0890	+	12.0890i	−0.532705	+	0.532705i
$516$	5.15741	+	2.12670i	0.227042	+	0.0936226i
$517$	14.0178	+	8.09318i	0.616502	+	0.355938i
$518$	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	$-0.0415786\pi$
$522$	−14.7016	+	0.0466154i	−0.643471	+	0.00204030i
$523$	0.429973	−	0.744735i	0.0188014	−	0.0325650i	−0.856472	−	0.516194i	$-0.827348\pi$
$523$	0.429973	−	0.744735i	0.0188014	−	0.0325650i	0.875273	+	0.483629i	$0.160682\pi$
$524$	−1.64434	−	2.84809i	−0.0718335	−	0.124419i
$525$	2.63184	−	20.2387i	0.114863	−	0.883288i
$526$	14.5789	+	3.90641i	0.635672	+	0.170328i
$527$	−0.149535	−	0.0400678i	−0.00651385	−	0.00174538i
$528$	−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
$531$	−10.0157	+	0.0317575i	−0.434644	+	0.00137816i
$532$			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
$537$	−26.1050	−	10.7646i	−1.12651	−	0.464526i
$538$	−10.3408	+	10.3408i	−0.445824	+	0.445824i
$539$	1.05558	−	3.93947i	0.0454669	−	0.169685i
$540$	−0.583665	−	4.27612i	−0.0251169	−	0.184015i
$541$	5.67009	+	5.67009i	0.243776	+	0.243776i	0.818410	−	0.574634i	$-0.194856\pi$
$541$	5.67009	+	5.67009i	0.243776	+	0.243776i	−0.574634	+	0.818410i	$0.694856\pi$
$542$	−6.90914	+	3.98899i	−0.296773	+	0.171342i
$543$	15.9604	−	2.12697i	0.684926	−	0.0912772i
$544$	0.297960	−	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
$549$	−5.74771	−	5.71137i	−0.245306	−	0.243755i
$550$	12.2211	−	7.05585i	0.521109	−	0.300863i
$551$	−14.0053	−	14.0053i	−0.596647	−	0.596647i
$552$	−15.7749	+	6.56351i	−0.671425	+	0.279361i
$553$	−8.41943	+	31.4217i	−0.358031	+	1.33619i
$554$	25.7905	−	25.7905i	1.09573	−	1.09573i
$555$	10.1269	−	24.5586i	0.429864	−	1.04245i
$556$	0.557363	+	0.321794i	0.0236375	+	0.0136471i
$557$	−9.67941	−	36.1240i	−0.410130	−	1.53062i	−0.794395	−	0.607402i	$-0.792212\pi$
$557$	−9.67941	−	36.1240i	−0.410130	−	1.53062i	0.384265	−	0.923223i	$-0.374455\pi$
$558$	0.784303	−	2.96463i	0.0332022	−	0.125503i
$559$		0			0
$560$			29.5936i			1.25056i
$561$	−0.728830	−	0.557417i	−0.0307712	−	0.0235342i
$562$	−10.7862	+	18.6823i	−0.454989	+	0.788064i
$563$	−6.70261	−	11.6093i	−0.282481	−	0.489272i	0.689514	−	0.724272i	$-0.257824\pi$
$563$	−6.70261	−	11.6093i	−0.282481	−	0.489272i	−0.971995	+	0.235000i	$0.924491\pi$
$564$	2.88346	+	0.374965i	0.121415	+	0.0157889i
$565$	−49.6109	−	13.2932i	−2.08715	−	0.559250i
$566$	33.7164	+	9.03429i	1.41721	+	0.379740i
$567$	−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	−0.524223	−	0.851581i	$-0.675644\pi$
$569$	11.3396	−	19.6407i	0.475380	−	0.823382i	0.999602	+	0.0281995i	$0.00897737\pi$
$570$	−22.0330	+	28.8084i	−0.922861	+	1.20665i
$571$			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
$574$	3.78118	+	14.1115i	0.157823	+	0.589004i
$575$	11.5322	+	6.65814i	0.480928	+	0.277664i
$576$	6.89698	+	25.4172i	0.287374	+	1.05905i
$577$	18.7633	−	18.7633i	0.781126	−	0.781126i	−0.198895	−	0.980021i	$-0.563735\pi$
$577$	18.7633	−	18.7633i	0.781126	−	0.781126i	0.980021	+	0.198895i	$0.0637354\pi$
$578$	−5.76316	+	21.5084i	−0.239716	+	0.894632i
$579$	−2.64332	−	6.35302i	−0.109852	−	0.264023i
$580$	2.19219	+	2.19219i	0.0910259	+	0.0910259i
$581$	−6.58249	+	3.80040i	−0.273088	+	0.157667i
$582$	−3.65395	−	27.4185i	−0.151461	−	1.13653i
$583$	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	−0.00632980	−	0.999980i	$-0.502015\pi$
$587$	11.8276	−	3.16920i	0.488178	−	0.130807i	0.494508	+	0.869173i	$0.335348\pi$
$588$	−0.0967820	−	0.726234i	−0.00399122	−	0.0299494i
$589$	3.57794	−	2.06572i	0.147426	−	0.0851166i
$590$	−9.31581	−	9.31581i	−0.383526	−	0.383526i
$591$	−4.58427	−	11.0180i	−0.188572	−	0.453219i
$592$	−4.45193	+	16.6148i	−0.182973	+	0.682865i
$593$	−32.4467	+	32.4467i	−1.33243	+	1.33243i	−0.429232	+	0.903194i	$0.641216\pi$
$593$	−32.4467	+	32.4467i	−1.33243	+	1.33243i	−0.903194	+	0.429232i	$0.858784\pi$
$594$	10.9960	−	14.4723i	0.451172	−	0.593805i
$595$	−1.51168	−	0.872768i	−0.0619728	−	0.0357800i
$596$	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	$-0.0760708\pi$
$600$	12.6864	−	16.5877i	0.517922	−	0.677189i
$601$	2.26709	−	3.92671i	0.0924764	−	0.160174i	−0.816076	−	0.577944i	$-0.803855\pi$
$601$	2.26709	−	3.92671i	0.0924764	−	0.160174i	0.908553	+	0.417771i	$0.137188\pi$
$602$	22.3477	+	38.7074i	0.910826	+	1.57760i
$603$	−11.3820	−	19.5706i	−0.463510	−	0.796977i
$604$	−3.23457	−	0.866700i	−0.131613	−	0.0352655i
$605$	11.3271	+	3.03509i	0.460513	+	0.123394i
$606$	−27.9481	−	3.63437i	−1.13531	−	0.147636i
$607$	−6.51641	−	11.2868i	−0.264493	−	0.458115i	0.702938	−	0.711251i	$-0.251871\pi$
$607$	−6.51641	−	11.2868i	−0.264493	−	0.458115i	−0.967431	+	0.253136i	$0.918538\pi$
$608$	−4.11611	+	7.12932i	−0.166930	+	0.289132i
$609$	14.9992	+	11.4715i	0.607797	+	0.464850i
$610$		−	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	$-0.106476\pi$
$613$	−0.930978	−	3.47446i	−0.0376019	−	0.140332i	−0.982175	+	0.187969i	$0.939809\pi$
$614$	−22.4414	−	12.9565i	−0.905661	−	0.522884i
$615$	7.56121	−	18.3365i	0.304897	−	0.739401i
$616$	16.4447	−	16.4447i	0.662575	−	0.662575i
$617$	1.71888	−	6.41496i	0.0691997	−	0.258257i	−0.922656	−	0.385624i	$-0.873986\pi$
$617$	1.71888	−	6.41496i	0.0691997	−	0.258257i	0.991856	+	0.127368i	$0.0406528\pi$
$618$	−11.9419	+	4.96871i	−0.480375	+	0.199871i
$619$	−13.3334	−	13.3334i	−0.535916	−	0.535916i	0.386411	−	0.922327i	$-0.373715\pi$
$619$	−13.3334	−	13.3334i	−0.535916	−	0.535916i	−0.922327	+	0.386411i	$0.873715\pi$
$620$	−0.560039	+	0.323339i	−0.0224917	+	0.0129856i
$621$	17.0150	+	2.15779i	0.682789	+	0.0865892i
$622$	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
$627$	24.2724	−	3.23468i	0.969346	−	0.129181i
$628$	0.781896	−	0.451428i	0.0312011	−	0.0180139i
$629$	−0.717411	−	0.717411i	−0.0286051	−	0.0286051i
$630$	17.1936	−	29.9994i	0.685008	−	1.19520i
$631$	−0.381334	+	1.42316i	−0.0151807	+	0.0566550i	−0.973101	−	0.230380i	$-0.926003\pi$
$631$	−0.381334	+	1.42316i	−0.0151807	+	0.0566550i	0.957920	+	0.287035i	$0.0926697\pi$
$632$	−23.5364	+	23.5364i	−0.936227	+	0.936227i
$633$	−1.28465	−	0.529733i	−0.0510601	−	0.0210550i
$634$	−34.8763	−	20.1358i	−1.38511	−	0.799696i
$635$	−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
$639$	−0.0508676	−	16.0426i	−0.00201229	−	0.634637i
$640$	−12.6581	+	21.9245i	−0.500357	+	0.866644i
$641$	7.43034	+	12.8697i	0.293481	+	0.508323i	0.974630	−	0.223821i	$-0.0718530\pi$
$641$	7.43034	+	12.8697i	0.293481	+	0.508323i	−0.681150	+	0.732144i	$0.738520\pi$
$642$	−2.27808	+	17.5183i	−0.0899086	+	0.691392i
$643$	46.9319	+	12.5754i	1.85081	+	0.495924i	0.999583	−	0.0288681i	$-0.00919027\pi$
$643$	46.9319	+	12.5754i	1.85081	+	0.495924i	0.851230	+	0.524792i	$0.175857\pi$
$644$	2.57325	+	0.689499i	0.101400	+	0.0271701i
$645$	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	−0.211678	−	0.977340i	$-0.567893\pi$
$647$	18.8371	−	32.6268i	0.740562	−	1.28269i	0.952240	−	0.305351i	$-0.0987739\pi$
$648$	6.79658	−	26.0242i	0.266995	−	1.02233i
$649$			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	$-0.476859\pi$
$653$	−19.2876	−	11.1357i	−0.754782	−	0.435774i	−0.827419	+	0.561585i	$0.810192\pi$
$654$	−21.3571	−	8.80675i	−0.835128	−	0.344371i
$655$	−25.2945	+	25.2945i	−0.988339	+	0.988339i
$656$	−3.32401	+	12.4054i	−0.129781	+	0.484348i
$657$	−12.7440	−	7.30396i	−0.497190	−	0.284955i
$658$	16.4729	+	16.4729i	0.642182	+	0.642182i
$659$	−23.2104	+	13.4005i	−0.904148	+	0.522010i	−0.878544	−	0.477662i	$-0.841484\pi$
$659$	−23.2104	+	13.4005i	−0.904148	+	0.522010i	−0.0256043	+	0.999672i	$0.508151\pi$
$660$	−3.79925	+	0.506310i	−0.147886	+	0.0197081i
$661$	−16.8775	+	4.52232i	−0.656459	+	0.175898i	−0.571647	−	0.820499i	$-0.693696\pi$
$661$	−16.8775	+	4.52232i	−0.656459	+	0.175898i	−0.0848116	+	0.996397i	$0.527029\pi$
$662$	0.871200			0.0338602
$663$		0			0
$664$	−7.77728			−0.301817
$665$	44.9962	−	12.0567i	1.74488	−	0.467538i
$666$	14.1660	−	14.2561i	0.548922	−	0.552414i
$667$	−10.6700	+	6.16031i	−0.413143	+	0.238528i
$668$	−0.308966	−	0.308966i	−0.0119543	−	0.0119543i
$669$	4.94149	−	2.05602i	0.191049	−	0.0794902i
$670$	7.70763	−	28.7653i	0.297772	−	1.11130i
$671$	−5.08844	+	5.08844i	−0.196437	+	0.196437i
$672$	2.99196	−	7.25574i	0.115417	−	0.279896i
$673$	−30.8369	−	17.8037i	−1.18867	−	0.686281i	−0.230669	−	0.973032i	$-0.574091\pi$
$673$	−30.8369	−	17.8037i	−1.18867	−	0.686281i	−0.958005	+	0.286751i	$0.907425\pi$
$674$	−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	$0.898076\pi$
$678$	−30.8651	−	23.6060i	−1.18537	−	0.906583i
$679$	−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
$682$	−2.63067	−	0.704886i	−0.100734	−	0.0269915i
$683$	−37.1052	−	9.94232i	−1.41979	−	0.380432i	−0.534382	−	0.845243i	$-0.679456\pi$
$683$	−37.1052	−	9.94232i	−1.41979	−	0.380432i	−0.885410	+	0.464811i	$0.846122\pi$
$684$	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
$687$	−29.2272	+	38.2150i	−1.11509	+	1.45799i
$688$			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	0.993456	+	0.114213i	$0.0364347\pi$
$691$	4.99988	+	18.6598i	0.190204	+	0.709853i	−0.803252	+	0.595640i	$0.796899\pi$
$692$	−2.97299	−	1.71645i	−0.113016	−	0.0652498i
$693$	−22.5306	+	6.11368i	−0.855865	+	0.232239i
$694$	−15.2344	+	15.2344i	−0.578292	+	0.578292i
$695$	1.81185	−	6.76192i	0.0687274	−	0.256494i
$696$	7.42231	+	17.8390i	0.281342	+	0.676186i
$697$	−0.535651	−	0.535651i	−0.0202892	−	0.0202892i
$698$	34.0809	−	19.6766i	1.28998	−	0.744771i
$699$	3.30734	+	24.8176i	0.125095	+	0.938689i
$700$	−3.14510	+	0.842728i	−0.118874	+	0.0318521i
$701$	−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
$704$	22.5924	−	6.05362i	0.851483	−	0.228154i
$705$	−4.17800	−	31.3509i	−0.157353	−	1.18074i
$706$	−7.66111	+	4.42315i	−0.288330	+	0.166467i
$707$	25.5967	+	25.5967i	0.962664	+	0.962664i
$708$	0.613831	+	1.47530i	0.0230692	+	0.0554452i
$709$	11.2814	−	42.1029i	0.423683	−	1.58121i	−0.343099	−	0.939299i	$-0.611477\pi$
$709$	11.2814	−	42.1029i	0.423683	−	1.58121i	0.766782	−	0.641907i	$-0.221857\pi$
$710$	14.9216	−	14.9216i	0.559999	−	0.559999i
$711$	32.2468	−	8.75017i	1.20935	−	0.328157i
$712$	−2.84346	−	1.64168i	−0.106563	−	0.0615244i
$713$	−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
$717$	−6.31311	+	8.25447i	−0.235767	+	0.308269i
$718$	6.28386	−	10.8840i	0.234512	−	0.406186i
$719$	17.7809	+	30.7974i	0.663116	+	1.14855i	0.979793	+	0.200017i	$0.0640996\pi$
$719$	17.7809	+	30.7974i	0.663116	+	1.14855i	−0.316677	+	0.948534i	$0.602567\pi$
$720$	26.2759	−	15.2817i	0.979245	−	0.569515i
$721$	16.0471	+	4.29980i	0.597624	+	0.160133i
$722$	−11.6120	−	3.11143i	−0.432154	−	0.115795i
$723$	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
$726$	7.04710	+	5.38970i	0.261542	+	0.200030i
$727$		−	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
$730$	−5.00071	−	18.6629i	−0.185084	−	0.690745i
$731$	−2.00706	−	1.15878i	−0.0742338	−	0.0428589i
$732$	−0.492809	+	1.19510i	−0.0182147	+	0.0441722i
$733$	5.72217	−	5.72217i	0.211353	−	0.211353i	−0.593489	−	0.804842i	$-0.702250\pi$
$733$	5.72217	−	5.72217i	0.211353	−	0.211353i	0.804842	+	0.593489i	$0.202250\pi$
$734$	−4.08668	+	15.2517i	−0.150842	+	0.562951i
$735$	−7.35779	+	3.06137i	−0.271396	+	0.112920i
$736$	3.62099	+	3.62099i	0.133471	+	0.133471i
$737$	−17.4127	+	10.0532i	−0.641403	+	0.370314i
$738$	10.5770	−	10.6443i	0.389344	−	0.391821i
$739$	−19.8431	+	5.31693i	−0.729939	+	0.195587i	−0.604602	−	0.796528i	$-0.706668\pi$
$739$	−19.8431	+	5.31693i	−0.729939	+	0.195587i	−0.125337	+	0.992114i	$0.540001\pi$
$740$	−4.23811			−0.155796
$741$		0			0
$742$	52.2565			1.91840
$743$	−33.2196	+	8.90116i	−1.21871	+	0.326552i	−0.810173	−	0.586191i	$-0.800627\pi$
$743$	−33.2196	+	8.90116i	−1.21871	+	0.326552i	−0.408535	+	0.912743i	$0.633960\pi$
$744$	−3.99496	+	0.532391i	−0.146462	+	0.0195184i
$745$	41.0648	−	23.7087i	1.50450	−	0.868621i
$746$	12.4015	+	12.4015i	0.454051	+	0.454051i
$747$	6.77344	+	3.88207i	0.247827	+	0.142037i
$748$	−0.0378875	+	0.141398i	−0.00138531	+	0.00517003i
$749$	16.0445	−	16.0445i	0.586252	−	0.586252i
$750$	6.10205	+	2.51623i	0.222815	+	0.0918796i
$751$	−25.8847	−	14.9445i	−0.944546	−	0.545334i	−0.0531635	−	0.998586i	$-0.516930\pi$
$751$	−25.8847	−	14.9445i	−0.944546	−	0.545334i	−0.891382	+	0.453252i	$0.850264\pi$
$752$	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
$756$	−3.31496	+	2.56880i	−0.120564	+	0.0934264i
$757$	−11.1534	+	19.3182i	−0.405376	+	0.702132i	−0.994365	−	0.106009i	$-0.966193\pi$
$757$	−11.1534	+	19.3182i	−0.405376	+	0.702132i	0.588989	+	0.808141i	$0.299526\pi$
$758$	−20.3284	−	35.2098i	−0.738360	−	1.27888i
$759$	1.96424	−	15.1049i	0.0712975	−	0.548274i
$760$	46.0409	+	12.3366i	1.67008	+	0.447496i
$761$	25.5783	+	6.85369i	0.927214	+	0.248446i	0.690666	−	0.723174i	$-0.257317\pi$
$761$	25.5783	+	6.85369i	0.927214	+	0.248446i	0.236547	+	0.971620i	$0.423984\pi$
$762$	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
$765$	0.00568485	+	1.79289i	0.000205536	+	0.0648221i
$766$			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	$-0.154395\pi$
$769$	−3.17804	−	11.8606i	−0.114603	−	0.427704i	−0.999257	+	0.0385441i	$0.987728\pi$
$770$	−26.5940	−	15.3540i	−0.958380	−	0.553321i
$771$	26.1184	+	10.7701i	0.940630	+	0.387876i
$772$	−0.776254	+	0.776254i	−0.0279380	+	0.0279380i
$773$	−5.96678	+	22.2683i	−0.214610	+	0.800937i	0.771693	+	0.635995i	$0.219410\pi$
$773$	−5.96678	+	22.2683i	−0.214610	+	0.800937i	−0.986303	+	0.164941i	$0.947256\pi$
$774$	22.8279	−	39.8303i	0.820534	−	1.43167i
$775$	2.22108	+	2.22108i	0.0797837	+	0.0797837i
$776$	−31.4827	+	18.1765i	−1.13016	+	0.652500i
$777$	−25.5875	+	3.40994i	−0.917947	+	0.122331i
$778$	−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
$783$	2.44013	−	19.2413i	0.0872031	−	0.687630i
$784$	4.46886	−	2.58010i	0.159602	−	0.0921463i
$785$	−6.94420	−	6.94420i	−0.247849	−	0.247849i
$786$	−24.9868	+	10.3963i	−0.891251	+	0.370825i
$787$	12.8168	−	47.8331i	0.456871	−	1.70507i	−0.225657	−	0.974207i	$-0.572453\pi$
$787$	12.8168	−	47.8331i	0.456871	−	1.70507i	0.682528	−	0.730859i	$-0.260880\pi$
$788$	−1.34625	+	1.34625i	−0.0479581	+	0.0479581i
$789$	−7.59083	+	18.4084i	−0.270241	+	0.655356i
$790$	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
$795$	−56.3535	−	43.0998i	−1.99865	−	1.52859i
$796$	−0.876045	+	1.51735i	−0.0310506	+	0.0537812i
$797$	2.55365	+	4.42306i	0.0904550	+	0.156673i	0.907703	−	0.419614i	$-0.137835\pi$
$797$	2.55365	+	4.42306i	0.0904550	+	0.156673i	−0.817248	+	0.576287i	$0.804501\pi$
$798$	34.9487	+	4.54473i	1.23717	+	0.160882i
$799$	−1.16680	−	0.312643i	−0.0412784	−	0.0110605i
$800$	−6.04560	−	1.61991i	−0.213744	−	0.0572726i
$801$	1.65700	+	2.84911i	0.0585472	+	0.100668i
$802$	−13.0976	−	22.6856i	−0.462491	−	0.801058i
$803$	−6.52251	+	11.2973i	−0.230175	+	0.398674i
$804$	−2.19426	+	2.86902i	−0.0773856	+	0.101183i
$805$		−	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	$-0.331932\pi$
$809$	0.216848	+	0.125197i	0.00762398	+	0.00440171i	−0.496183	+	0.868218i	$0.665266\pi$
$810$	−35.5147	+	0.225220i	−1.24786	+	0.00791344i
$811$	0.345058	−	0.345058i	0.0121166	−	0.0121166i	−0.701023	−	0.713139i	$-0.747273\pi$
$811$	0.345058	−	0.345058i	0.0121166	−	0.0121166i	0.713139	+	0.701023i	$0.247273\pi$
$812$	0.779717	−	2.90994i	0.0273627	−	0.102119i
$813$	−4.04320	−	9.71754i	−0.141801	−	0.340809i
$814$	−12.6210	−	12.6210i	−0.442364	−	0.442364i
$815$	−15.1712	+	8.75912i	−0.531425	+	0.306818i
$816$	−0.153356	−	1.15075i	−0.00536852	−	0.0402844i
$817$	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	0.260838	−	0.965383i	$-0.416001\pi$
$821$	27.7769	−	7.44280i	0.969421	−	0.259756i	0.708583	+	0.705627i	$0.249335\pi$
$822$	−5.22544	−	39.2107i	−0.182258	−	1.36763i
$823$	1.74844	−	1.00946i	0.0609468	−	0.0351877i	−0.469217	−	0.883083i	$-0.655464\pi$
$823$	1.74844	−	1.00946i	0.0609468	−	0.0351877i	0.530164	+	0.847895i	$0.322130\pi$
$824$	12.0200	+	12.0200i	0.418737	+	0.418737i
$825$	7.15174	+	17.1887i	0.248991	+	0.598433i
$826$	−3.31344	+	12.3659i	−0.115289	+	0.430265i
$827$	0.657151	−	0.657151i	0.0228514	−	0.0228514i	−0.695589	−	0.718440i	$-0.744856\pi$
$827$	0.657151	−	0.657151i	0.0228514	−	0.0228514i	0.718440	+	0.695589i	$0.244856\pi$
$828$	−0.716585	−	2.64081i	−0.0249031	−	0.0917745i
$829$	−40.2809	−	23.2562i	−1.39902	−	0.807722i	−0.404726	−	0.914438i	$-0.632633\pi$
$829$	−40.2809	−	23.2562i	−1.39902	−	0.807722i	−0.994289	+	0.106716i	$0.965966\pi$
$830$	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
$834$	3.21747	−	4.20688i	0.111412	−	0.145673i
$835$	−2.37637	+	4.11600i	−0.0822377	+	0.142440i
$836$	−1.95332	−	3.38325i	−0.0675570	−	0.117012i
$837$	3.74506	+	1.53043i	0.129448	+	0.0528993i
$838$	43.6675	+	11.7007i	1.50847	+	0.404193i
$839$	41.9982	+	11.2534i	1.44994	+	0.388510i	0.896003	−	0.444048i	$-0.146458\pi$
$839$	41.9982	+	11.2534i	1.44994	+	0.388510i	0.553937	+	0.832558i	$0.313125\pi$
$840$	−45.0633	−	5.86003i	−1.55483	−	0.202190i
$841$	−7.53364	−	13.0486i	−0.259781	−	0.449953i
$842$	17.2806	−	29.9309i	0.595530	−	1.03149i
$843$	−22.6062	−	17.2895i	−0.778598	−	0.595480i
$844$			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
$849$	−17.5552	+	42.5727i	−0.602492	+	1.46109i
$850$	−0.744677	+	0.744677i	−0.0255422	+	0.0255422i
$851$	4.35920	−	16.2688i	0.149431	−	0.557686i
$852$	−2.36307	+	0.983206i	−0.0809573	+	0.0336841i
$853$	0.0191114	+	0.0191114i	0.000654362	+	0.000654362i	0.707434	−	0.706780i	$-0.249853\pi$
$853$	0.0191114	+	0.0191114i	0.000654362	+	0.000654362i	−0.706780	+	0.707434i	$0.749853\pi$
$854$	−8.96948	+	5.17853i	−0.306929	+	0.177206i
$855$	−33.9404	−	33.7258i	−1.16074	−	1.15340i
$856$	22.4260	−	6.00903i	0.766505	−	0.205384i
$857$	5.89068			0.201222			0.100611	−	0.994926i	$-0.467920\pi$
$857$	5.89068			0.201222			0.100611	+	0.994926i	$0.467920\pi$
$858$		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
$861$	−19.1048	+	2.54601i	−0.651089	+	0.0867678i
$862$	12.8577	−	7.42341i	0.437936	−	0.252842i
$863$	19.9075	+	19.9075i	0.677660	+	0.677660i	0.959470	−	0.281811i	$-0.0909350\pi$
$863$	19.9075	+	19.9075i	0.677660	+	0.677660i	−0.281811	+	0.959470i	$0.590935\pi$
$864$	−7.98731	+	1.09022i	−0.271734	+	0.0370901i
$865$	−9.66445	+	36.0682i	−0.328601	+	1.22636i
$866$	5.76148	−	5.76148i	0.195783	−	0.195783i
$867$	−27.1580	−	11.1988i	−0.922335	−	0.380332i
$868$	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
$873$	36.4920	−	0.115708i	1.23507	−	0.00391612i
$874$	−11.4975	+	19.9142i	−0.388908	+	0.673608i
$875$	−4.23889	−	7.34198i	−0.143301	−	0.248204i
$876$	−0.302194	+	2.32385i	−0.0102102	+	0.0785158i
$877$	−13.4570	−	3.60580i	−0.454412	−	0.121759i	0.0243510	−	0.999703i	$-0.492248\pi$
$877$	−13.4570	−	3.60580i	−0.454412	−	0.121759i	−0.478763	+	0.877944i	$0.658915\pi$
$878$	−49.1824	−	13.1784i	−1.65983	−	0.444749i
$879$	−0.646595	+	4.97228i	−0.0218091	+	0.167711i
$880$	−13.4976	−	23.3786i	−0.455005	−	0.788092i
$881$	−3.83326	+	6.63940i	−0.129146	+	0.223687i	−0.923346	−	0.383969i	$-0.874557\pi$
$881$	−3.83326	+	6.63940i	−0.129146	+	0.223687i	0.794200	+	0.607656i	$0.207890\pi$
$882$	−6.02915	+	0.0191171i	−0.203012	+	0.000643705i
$883$		−	7.52156i		−	0.253121i	−0.991959	−	0.126560i	$-0.959606\pi$
$883$		−	7.52156i		−	0.253121i	0.991959	−	0.126560i	$-0.0403937\pi$
$884$		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	$-0.0830797\pi$
$887$	36.5051	+	21.0762i	1.22572	+	0.707670i	0.259589	+	0.965719i	$0.416413\pi$
$888$	−24.4185	−	10.0691i	−0.819431	−	0.337898i
$889$	−19.8789	+	19.8789i	−0.666716	+	0.666716i
$890$	−1.12208	+	4.18768i	−0.0376123	+	0.140371i
$891$	17.0627	+	16.8477i	0.571623	+	0.564418i
$892$	−0.603784	−	0.603784i	−0.0202162	−	0.0202162i
$893$	27.9181	−	16.1185i	0.934245	−	0.539386i
$894$	35.5596	−	4.73887i	1.18929	−	0.158491i
$895$	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
$900$	2.37234	+	2.35734i	0.0790779	+	0.0785780i
$901$	−2.34659	+	1.35480i	−0.0781762	+	0.0451351i
$902$	−9.42336	−	9.42336i	−0.313764	−	0.313764i
$903$	−54.4411	+	22.6514i	−1.81169	+	0.753792i
$904$	−13.2174	+	49.3279i	−0.439603	+	1.64062i
$905$	−19.7578	+	19.7578i	−0.656771	+	0.656771i
$906$	−10.5052	+	25.4760i	−0.349012	+	0.846383i
$907$	32.3487	+	18.6765i	1.07412	+	0.620143i	0.929304	−	0.369316i	$-0.120408\pi$
$907$	32.3487	+	18.6765i	1.07412	+	0.620143i	0.144815	+	0.989459i	$0.453741\pi$
$908$	−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	$0.889161\pi$
$912$	24.6094	+	18.8216i	0.814899	+	0.623244i
$913$	3.46673	−	6.00455i	0.114732	−	0.198722i
$914$	3.82525	+	6.62553i	0.126528	+	0.219153i
$915$	13.9438	+	1.81326i	0.460969	+	0.0599444i
$916$	7.41398	+	1.98657i	0.244965	+	0.0656381i
$917$	33.5762	+	8.99672i	1.10878	+	0.297098i
$918$	−0.513116	+	1.25563i	−0.0169353	+	0.0414419i
$919$	19.6678	+	34.0657i	0.648782	+	1.12372i	0.983414	+	0.181375i	$0.0580546\pi$
$919$	19.6678	+	34.0657i	0.648782	+	1.12372i	−0.334632	+	0.942349i	$0.608612\pi$
$920$	14.8250	−	25.6776i	0.488765	−	0.846567i
$921$	20.7683	−	27.1548i	0.684339	−	0.894782i
$922$			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
$927$	−4.46871	−	16.4684i	−0.146772	−	0.540893i
$928$	4.09478	−	4.09478i	0.134418	−	0.134418i
$929$	−5.44472	+	20.3200i	−0.178635	+	0.666676i	0.817268	+	0.576257i	$0.195487\pi$
$929$	−5.44472	+	20.3200i	−0.178635	+	0.666676i	−0.995904	+	0.0904192i	$0.971179\pi$
$930$	2.04430	+	4.91333i	0.0670353	+	0.161115i
$931$	−5.74361	−	5.74361i	−0.188239	−	0.188239i
$932$	3.45925	−	1.99720i	0.113311	−	0.0654204i
$933$	6.17200	+	46.3135i	0.202062	+	1.51624i
$934$	−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
$939$	5.48343	+	41.1466i	0.178945	+	1.34277i
$940$	−4.36990	+	2.52297i	−0.142531	+	0.0822901i
$941$	−41.3493	−	41.3493i	−1.34795	−	1.34795i	−0.887888	−	0.460059i	$-0.847828\pi$
$941$	−41.3493	−	41.3493i	−1.34795	−	1.34795i	−0.460059	−	0.887888i	$-0.652172\pi$
$942$	−2.85414	−	6.85973i	−0.0929930	−	0.223502i
$943$	3.25477	−	12.1470i	0.105990	−	0.395560i
$944$	−7.95798	+	7.95798i	−0.259010	+	0.259010i
$945$	36.3218	+	27.5972i	1.18155	+	0.897737i
$946$	−35.3089	−	20.3856i	−1.14799	−	0.662793i
$947$	7.83402	+	29.2370i	0.254571	+	0.950074i	0.968328	+	0.249680i	$0.0803255\pi$
$947$	7.83402	+	29.2370i	0.254571	+	0.950074i	−0.713757	+	0.700393i	$0.753008\pi$
$948$	−3.25181	−	4.22395i	−0.105614	−	0.137188i
$949$		0			0
$950$		−	28.1052i		−	0.911852i
$951$	32.2761	−	42.2014i	1.04663	−	1.36848i
$952$	−0.867788	+	1.50305i	−0.0281252	+	0.0487142i
$953$	4.74184	+	8.21310i	0.153603	+	0.266048i	0.932550	−	0.361042i	$-0.117579\pi$
$953$	4.74184	+	8.21310i	0.153603	+	0.266048i	−0.778946	+	0.627091i	$0.784246\pi$
$954$	−26.9845	−	46.3981i	−0.873654	−	1.50219i
$955$	−5.88875	−	1.57789i	−0.190556	−	0.0510592i
$956$	1.60143	+	0.429101i	0.0517938	+	0.0138781i
$957$	−17.0813	−	2.22125i	−0.552161	−	0.0718030i
$958$	−1.34066	−	2.32209i	−0.0433147	−	0.0750233i
$959$	−25.4041	+	44.0012i	−0.820341	+	1.42087i
$960$	−36.3025	−	27.7646i	−1.17166	−	0.896097i
$961$			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
$966$	8.35738	−	20.2673i	0.268894	−	0.652090i
$967$	17.7922	−	17.7922i	0.572158	−	0.572158i	−0.360573	−	0.932731i	$-0.617419\pi$
$967$	17.7922	−	17.7922i	0.572158	−	0.572158i	0.932731	+	0.360573i	$0.117419\pi$
$968$	3.01778	−	11.2625i	0.0969950	−	0.361990i
$969$	−1.68721	+	0.701999i	−0.0542008	+	0.0225515i
$970$	33.9421	+	33.9421i	1.08981	+	1.08981i
$971$	16.0499	−	9.26639i	0.515065	−	0.297373i	−0.219848	−	0.975534i	$-0.570556\pi$
$971$	16.0499	−	9.26639i	0.515065	−	0.297373i	0.734913	+	0.678161i	$0.237223\pi$
$972$	3.99261	+	1.61684i	0.128063	+	0.0518600i
$973$	−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	−0.701007	−	0.713155i	$-0.747266\pi$
$977$	−29.7416	+	7.96925i	−0.951519	+	0.254959i	−0.250512	+	0.968113i	$0.580599\pi$
$978$	−13.1374	+	1.75076i	−0.420086	+	0.0559831i
$979$	2.53495	−	1.46355i	0.0810174	−	0.0467754i
$980$	0.899023	+	0.899023i	0.0287182	+	0.0287182i
$981$	15.1549	−	26.4422i	0.483857	−	0.844236i
$982$	−2.55943	+	9.55192i	−0.0816747	+	0.304814i
$983$	19.1428	−	19.1428i	0.610561	−	0.610561i	−0.332531	−	0.943092i	$-0.607903\pi$
$983$	19.1428	−	19.1428i	0.610561	−	0.610561i	0.943092	+	0.332531i	$0.107903\pi$
$984$	−18.2319	−	7.51807i	−0.581212	−	0.239667i
$985$	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
$990$	0.100010	+	31.5412i	0.00317852	+	1.00244i
$991$	−3.12167	+	5.40689i	−0.0991631	+	0.171755i	−0.911338	−	0.411658i	$-0.864950\pi$
$991$	−3.12167	+	5.40689i	−0.0991631	+	0.171755i	0.812175	+	0.583413i	$0.198283\pi$
$992$	0.603961	+	1.04609i	0.0191758	+	0.0332134i
$993$	−0.148213	+	1.13975i	−0.00470341	+	0.0361689i
$994$	−19.8071	−	5.30731i	−0.628244	−	0.168338i
$995$	18.4085	+	4.93255i	0.583589	+	0.156372i
$996$	0.160617	−	1.23513i	0.00508933	−	0.0391367i
$997$	0.917609	+	1.58935i	0.0290610	+	0.0503351i	0.880190	−	0.474621i	$-0.157415\pi$
$997$	0.917609	+	1.58935i	0.0290610	+	0.0503351i	−0.851129	+	0.524956i	$0.824082\pi$
$998$	8.09094	−	14.0139i	0.256114	−	0.443603i
$999$	16.2407	+	20.9581i	0.513832	+	0.663085i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.7	✓	48	39.35	odd	6
507.2.f.g.239.8	yes	48	13.4	even	6
507.2.f.g.239.17	yes	48	39.17	odd	6
507.2.f.g.239.18	yes	48	13.9	even	3
507.2.f.g.437.7	yes	48	39.32	even	12
507.2.f.g.437.8	yes	48	13.7	odd	12
507.2.f.g.437.17	yes	48	39.20	even	12
507.2.f.g.437.18	yes	48	13.6	odd	12
507.2.k.k.80.7		96	39.29	odd	6	inner
507.2.k.k.80.8		96	13.10	even	6	inner
507.2.k.k.80.17		96	39.23	odd	6	inner
507.2.k.k.80.18		96	13.3	even	3	inner
507.2.k.k.89.7		96	39.11	even	12	inner
507.2.k.k.89.8		96	13.2	odd	12	inner
507.2.k.k.89.17		96	39.2	even	12	inner
507.2.k.k.89.18		96	13.11	odd	12	inner
507.2.k.k.188.7		96	1.1	even	1	trivial
507.2.k.k.188.8		96	39.38	odd	2	inner
507.2.k.k.188.17		96	13.12	even	2	inner
507.2.k.k.188.18		96	3.2	odd	2	inner
507.2.k.k.488.7		96	13.8	odd	4	inner
507.2.k.k.488.8		96	39.5	even	4	inner
507.2.k.k.488.17		96	13.5	odd	4	inner
507.2.k.k.488.18		96	39.8	even	4	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} +(-0.228800 - 1.71687i) q^{3} +(-0.239309 + 0.138165i) q^{4} +(2.12536 + 2.12536i) q^{5} +(0.873546 + 2.09951i) q^{6} +(0.755945 - 2.82123i) q^{7} +(2.11323 - 2.11323i) q^{8} +(-2.89530 + 0.785641i) q^{9} +(-3.41747 - 1.97308i) q^{10} +(0.689573 + 2.57352i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(3.16269 - 4.13525i) q^{15} +(-1.68549 + 2.91935i) q^{16} +(-0.0994162 - 0.172194i) q^{17} +(3.40472 - 1.98013i) q^{18} +(5.12548 + 1.37337i) q^{19} +(-0.802269 - 0.214967i) q^{20} +(-5.01665 - 0.652364i) q^{21} +(-1.74897 - 3.02930i) q^{22} +(1.65038 - 2.85855i) q^{23} +(-4.11166 - 3.14464i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(0.208891 + 0.779591i) q^{28} +(-3.23258 - 1.86633i) q^{29} +(-2.60561 + 6.31880i) q^{30} +(0.550550 - 0.550550i) q^{31} +(-0.401535 + 1.49855i) q^{32} +(4.26063 - 1.77273i) q^{33} +(0.184586 + 0.184586i) q^{34} +(7.60277 - 4.38946i) q^{35} +(0.584324 - 0.588041i) q^{36} +(4.92878 - 1.32066i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(3.68005 - 0.986066i) q^{41} +(6.58353 - 0.877359i) q^{42} +(10.0942 - 5.82790i) q^{43} +(-0.520592 - 0.520592i) q^{44} +(-7.82332 - 4.48378i) q^{45} +(-1.12160 + 4.18587i) q^{46} +(4.29586 - 4.29586i) q^{47} +(5.39780 + 2.22582i) q^{48} +(-1.32568 - 0.765385i) q^{49} +(-1.37086 - 5.11610i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(-4.17864 - 5.39241i) q^{54} +(-4.00407 + 6.93525i) q^{55} +(-4.36442 - 7.55939i) q^{56} +(1.18519 - 9.11402i) q^{57} +(4.73357 + 1.26836i) q^{58} +(3.22482 + 0.864088i) q^{59} +(-0.185512 + 1.42658i) q^{60} +(1.35047 + 2.33909i) q^{61} +(-0.511103 + 0.885257i) q^{62} +(0.0277830 + 8.76220i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(1.95320 + 7.28944i) q^{67} +(0.0475824 + 0.0274717i) q^{68} +(-5.28537 - 2.17946i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(-1.38405 + 5.16536i) q^{71} +(-4.45820 + 7.77869i) q^{72} +(3.46215 + 3.46215i) q^{73} +(-5.80168 + 3.34960i) q^{74} +(6.92638 - 0.923049i) q^{75} +(-1.41633 + 0.379503i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(-9.78695 + 2.62241i) q^{80} +(7.76554 - 4.54934i) q^{81} +(-4.33179 + 2.50096i) q^{82} +(-1.84014 - 1.84014i) q^{83} +(1.29066 - 0.537009i) q^{84} +(0.154679 - 0.577269i) q^{85} +(-10.8207 + 10.8207i) q^{86} +(-2.46463 + 5.97694i) q^{87} +(6.89568 + 3.98122i) q^{88} +(-0.284349 - 1.06120i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(-1.07119 - 0.819258i) q^{93} +(-3.98807 + 6.90753i) q^{94} +(7.97458 + 13.8124i) q^{95} +(2.66469 + 0.346516i) q^{96} +(-11.7496 - 3.14829i) q^{97} +(1.94125 + 0.520155i) 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

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