LMFDB - Embedded newform 507.2.f.g.239.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(239,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("507.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.f (of order $4$, degree $2$, 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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.18
Character	$\chi$	$=$	507.239
Dual form			507.2.f.g.437.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.928351 + 0.928351i) q^{2} +(-1.37245 + 1.05658i) q^{3} -0.276330i q^{4} +(2.12536 + 2.12536i) q^{5} +(-2.25500 - 0.293240i) q^{6} +(2.06528 + 2.06528i) q^{7} +(2.11323 - 2.11323i) q^{8} +(0.767265 - 2.90022i) q^{9} +3.94616i q^{10} +(1.88395 - 1.88395i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(-5.16258 - 0.671341i) q^{15} +3.37098 q^{16} +0.198832 q^{17} +(3.40472 - 1.98013i) q^{18} +(-3.75211 + 3.75211i) q^{19} +(0.587301 - 0.587301i) q^{20} +(-5.01665 - 0.652364i) q^{21} +3.49793 q^{22} -3.30077 q^{23} +(-0.667511 + 5.13312i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(0.570700 - 0.570700i) q^{28} +3.73266i q^{29} +(-4.16944 - 5.41592i) q^{30} +(0.550550 - 0.550550i) q^{31} +(-1.09701 - 1.09701i) q^{32} +(-0.595087 + 4.57618i) q^{33} +(0.184586 + 0.184586i) q^{34} +8.77893i q^{35} +(-0.801420 - 0.212019i) q^{36} +(-3.60812 - 3.60812i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(-2.69398 - 2.69398i) q^{41} +(-4.05158 - 5.26283i) q^{42} +11.6558i q^{43} +(-0.520592 - 0.520592i) q^{44} +(7.79473 - 4.53331i) q^{45} +(-3.06427 - 3.06427i) q^{46} +(4.29586 - 4.29586i) q^{47} +(-4.62652 + 3.56172i) q^{48} +1.53077i q^{49} +(-3.74525 + 3.74525i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(-2.58064 + 6.31501i) q^{54} +8.00814 q^{55} +8.72884 q^{56} +(1.18519 - 9.11402i) q^{57} +(-3.46521 + 3.46521i) q^{58} +(-2.36073 + 2.36073i) q^{59} +(-0.185512 + 1.42658i) q^{60} -2.70094 q^{61} +1.02221 q^{62} +(7.57440 - 4.40516i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(5.33624 - 5.33624i) q^{67} -0.0549435i q^{68} +(4.53015 - 3.48753i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(-3.78131 - 3.78131i) q^{71} +(-4.50744 - 7.75026i) q^{72} +(3.46215 + 3.46215i) q^{73} -6.69920i q^{74} +(-4.26258 - 5.53690i) q^{75} +(1.03682 + 1.03682i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(7.16454 + 7.16454i) q^{80} +(-7.82261 - 4.45048i) q^{81} -5.00192i q^{82} +(-1.84014 - 1.84014i) q^{83} +(-0.180268 + 1.38625i) q^{84} +(0.422590 + 0.422590i) q^{85} +(-10.8207 + 10.8207i) q^{86} +(-3.94386 - 5.12290i) q^{87} -7.96245i q^{88} +(-0.776855 + 0.776855i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(-0.173903 + 1.33731i) q^{93} +7.97613 q^{94} -15.9492 q^{95} +(2.66469 + 0.346516i) q^{96} +(8.60129 - 8.60129i) q^{97} +(-1.42109 + 1.42109i) q^{98} +(-4.01839 - 6.90936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) $ 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.928351	+	0.928351i	0.656443	+	0.656443i	0.954537	−	0.298094i	$-0.0963508\pi$
$2$	0.928351	+	0.928351i	0.656443	+	0.656443i	−0.298094	+	0.954537i	$0.596351\pi$
$3$	−1.37245	+	1.05658i	−0.792387	+	0.610018i
$3$	−1.37245	+	1.05658i	−0.792387	+	0.610018i
$4$		−	0.276330i		−	0.138165i
$5$	2.12536	+	2.12536i	0.950489	+	0.950489i	0.998831	−	0.0483414i	$-0.0153935\pi$
$5$	2.12536	+	2.12536i	0.950489	+	0.950489i	−0.0483414	+	0.998831i	$0.515394\pi$
$6$	−2.25500	−	0.293240i	−0.920599	−	0.119715i
$7$	2.06528	+	2.06528i	0.780603	+	0.780603i	0.979932	−	0.199330i	$-0.0638765\pi$
$7$	2.06528	+	2.06528i	0.780603	+	0.780603i	−0.199330	+	0.979932i	$0.563876\pi$
$8$	2.11323	−	2.11323i	0.747141	−	0.747141i
$9$	0.767265	−	2.90022i	0.255755	−	0.966742i
$10$			3.94616i			1.24788i
$11$	1.88395	−	1.88395i	0.568032	−	0.568032i	−0.363545	−	0.931577i	$-0.618434\pi$
$11$	1.88395	−	1.88395i	0.568032	−	0.568032i	0.931577	+	0.363545i	$0.118434\pi$
$12$	0.291966	+	0.379251i	0.0842833	+	0.109480i
$13$		0			0
$13$		0			0
$14$			3.83461i			1.02484i
$15$	−5.16258	−	0.671341i	−1.33297	−	0.173340i
$16$	3.37098			0.842745
$17$	0.198832			0.0482240			0.0241120	−	0.999709i	$-0.492324\pi$
$17$	0.198832			0.0482240			0.0241120	+	0.999709i	$0.492324\pi$
$18$	3.40472	−	1.98013i	0.802499	−	0.466722i
$19$	−3.75211	+	3.75211i	−0.860793	+	0.860793i	−0.991430	−	0.130637i	$-0.958298\pi$
$19$	−3.75211	+	3.75211i	−0.860793	+	0.860793i	0.130637	+	0.991430i	$0.458298\pi$
$20$	0.587301	−	0.587301i	0.131325	−	0.131325i
$21$	−5.01665	−	0.652364i	−1.09472	−	0.142358i
$22$	3.49793			0.745761
$23$	−3.30077			−0.688257			−0.344129	−	0.938923i	$-0.611826\pi$
$23$	−3.30077			−0.688257			−0.344129	+	0.938923i	$0.611826\pi$
$24$	−0.667511	+	5.13312i	−0.136255	+	1.04779i
$25$			4.03430i			0.806861i
$26$		0			0
$27$	2.01129	+	4.79111i	0.387073	+	0.922049i
$28$	0.570700	−	0.570700i	0.107852	−	0.107852i
$29$			3.73266i			0.693137i	0.938025	+	0.346568i	$0.112653\pi$
$29$			3.73266i			0.693137i	−0.938025	+	0.346568i	$0.887347\pi$
$30$	−4.16944	−	5.41592i	−0.761232	−	0.988808i
$31$	0.550550	−	0.550550i	0.0988817	−	0.0988817i	−0.655935	−	0.754817i	$-0.727726\pi$
$31$	0.550550	−	0.550550i	0.0988817	−	0.0988817i	0.754817	+	0.655935i	$0.227726\pi$
$32$	−1.09701	−	1.09701i	−0.193926	−	0.193926i
$33$	−0.595087	+	4.57618i	−0.103591	+	0.796611i
$34$	0.184586	+	0.184586i	0.0316563	+	0.0316563i
$35$			8.77893i			1.48391i
$36$	−0.801420	−	0.212019i	−0.133570	−	0.0353365i
$37$	−3.60812	−	3.60812i	−0.593171	−	0.593171i	0.345315	−	0.938487i	$-0.387772\pi$
$37$	−3.60812	−	3.60812i	−0.593171	−	0.593171i	−0.938487	+	0.345315i	$0.887772\pi$
$38$	−6.96655			−1.13012
$39$		0			0
$40$	8.98276			1.42030
$41$	−2.69398	−	2.69398i	−0.420729	−	0.420729i	0.464726	−	0.885455i	$-0.346153\pi$
$41$	−2.69398	−	2.69398i	−0.420729	−	0.420729i	−0.885455	+	0.464726i	$0.846153\pi$
$42$	−4.05158	−	5.26283i	−0.625173	−	0.812072i
$43$			11.6558i			1.77749i	0.458398	+	0.888747i	$0.348423\pi$
$43$			11.6558i			1.77749i	−0.458398	+	0.888747i	$0.651577\pi$
$44$	−0.520592	−	0.520592i	−0.0784823	−	0.0784823i
$45$	7.79473	−	4.53331i	1.16197	−	0.675785i
$46$	−3.06427	−	3.06427i	−0.451802	−	0.451802i
$47$	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	$0.103884\pi$
$48$	−4.62652	+	3.56172i	−0.667780	+	0.514090i
$49$			1.53077i			0.218681i
$50$	−3.74525	+	3.74525i	−0.529658	+	0.529658i
$51$	−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	$-0.385454\pi$
$54$	−2.58064	+	6.31501i	−0.351181	+	0.859364i
$55$	8.00814			1.07982
$56$	8.72884			1.16644
$57$	1.18519	−	9.11402i	0.156982	−	1.20718i
$58$	−3.46521	+	3.46521i	−0.455005	+	0.455005i
$59$	−2.36073	+	2.36073i	−0.307341	+	0.307341i	−0.843877	−	0.536536i	$-0.819732\pi$
$59$	−2.36073	+	2.36073i	−0.307341	+	0.307341i	0.536536	+	0.843877i	$0.319732\pi$
$60$	−0.185512	+	1.42658i	−0.0239495	+	0.184170i
$61$	−2.70094			−0.345820			−0.172910	−	0.984938i	$-0.555317\pi$
$61$	−2.70094			−0.345820			−0.172910	+	0.984938i	$0.555317\pi$
$62$	1.02221			0.129820
$63$	7.57440	−	4.40516i	0.954284	−	0.554998i
$64$		−	8.77879i		−	1.09735i
$65$		0			0
$66$	−4.80075	+	3.69585i	−0.590932	+	0.454928i
$67$	5.33624	−	5.33624i	0.651925	−	0.651925i	−0.301531	−	0.953456i	$-0.597498\pi$
$67$	5.33624	−	5.33624i	0.651925	−	0.651925i	0.953456	+	0.301531i	$0.0974977\pi$
$68$		−	0.0549435i		−	0.00666287i
$69$	4.53015	−	3.48753i	0.545366	−	0.419850i
$70$	−8.14992	+	8.14992i	−0.974102	+	0.974102i
$71$	−3.78131	−	3.78131i	−0.448759	−	0.448759i	0.446183	−	0.894942i	$-0.352783\pi$
$71$	−3.78131	−	3.78131i	−0.448759	−	0.448759i	−0.894942	+	0.446183i	$0.852783\pi$
$72$	−4.50744	−	7.75026i	−0.531207	−	0.913377i
$73$	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	$0.657498\pi$
$74$		−	6.69920i		−	0.778766i
$75$	−4.26258	−	5.53690i	−0.492200	−	0.639346i
$76$	1.03682	+	1.03682i	0.118932	+	0.118932i
$77$	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	$0.715530\pi$
$80$	7.16454	+	7.16454i	0.801020	+	0.801020i
$81$	−7.82261	−	4.45048i	−0.869179	−	0.494498i
$82$		−	5.00192i		−	0.552370i
$83$	−1.84014	−	1.84014i	−0.201981	−	0.201981i	0.598867	−	0.800848i	$-0.295618\pi$
$83$	−1.84014	−	1.84014i	−0.201981	−	0.201981i	−0.800848	+	0.598867i	$0.795618\pi$
$84$	−0.180268	+	1.38625i	−0.0196689	+	0.151252i
$85$	0.422590	+	0.422590i	0.0458364	+	0.0458364i
$86$	−10.8207	+	10.8207i	−1.16682	+	1.16682i
$87$	−3.94386	−	5.12290i	−0.422826	−	0.549233i
$88$		−	7.96245i		−	0.848800i
$89$	−0.776855	+	0.776855i	−0.0823464	+	0.0823464i	−0.747080	−	0.664734i	$-0.768545\pi$
$89$	−0.776855	+	0.776855i	−0.0823464	+	0.0823464i	0.664734	+	0.747080i	$0.268545\pi$
$90$	11.4447	+	3.02775i	1.20638	+	0.319153i
$91$		0			0
$92$			0.912102i			0.0950932i
$93$	−0.173903	+	1.33731i	−0.0180329	+	0.138672i
$94$	7.97613			0.822675
$95$	−15.9492			−1.63635
$96$	2.66469	+	0.346516i	0.271964	+	0.0353661i
$97$	8.60129	−	8.60129i	0.873329	−	0.873329i	−0.119505	−	0.992834i	$-0.538131\pi$
$97$	8.60129	−	8.60129i	0.873329	−	0.873329i	0.992834	+	0.119505i	$0.0381306\pi$
$98$	−1.42109	+	1.42109i	−0.143552	+	0.143552i
$99$	−4.01839	−	6.90936i	−0.403863	−	0.694417i
$100$	1.11480			0.111480
$101$	12.3938			1.23323			0.616616	−	0.787264i	$-0.288503\pi$
$101$	12.3938			1.23323			0.616616	+	0.787264i	$0.288503\pi$
$102$	−0.448367	−	0.0583056i	−0.0443949	−	0.00577312i
$103$			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
$106$	12.6512	−	12.6512i	1.22879	−	1.22879i
$107$		−	7.76865i		−	0.751024i	−0.926818	−	0.375512i	$-0.877467\pi$
$107$		−	7.76865i		−	0.751024i	0.926818	−	0.375512i	$-0.122533\pi$
$108$	1.32393	−	0.555781i	0.127395	−	0.0534801i
$109$	−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	$0.411738\pi$
$110$	7.43436	+	7.43436i	0.708838	+	0.708838i
$111$	8.76426	+	1.13970i	0.831867	+	0.108176i
$112$	6.96202	+	6.96202i	0.657849	+	0.657849i
$113$		−	17.0878i		−	1.60749i	−0.594977	−	0.803743i	$-0.702839\pi$
$113$		−	17.0878i		−	1.60749i	0.594977	−	0.803743i	$-0.297161\pi$
$114$	9.56127	−	7.36073i	0.895495	−	0.689396i
$115$	−7.01531	−	7.01531i	−0.654181	−	0.654181i
$116$	1.03145			0.0957674
$117$		0			0
$118$	−4.38317			−0.403504
$119$	0.410645	+	0.410645i	0.0376438	+	0.0376438i
$120$	−12.3284	+	9.49103i	−1.12543	+	0.866408i
$121$			3.90147i			0.354679i
$122$	−2.50742	−	2.50742i	−0.227011	−	0.227011i
$123$	6.54378	+	0.850953i	0.590033	+	0.0767279i
$124$	−0.152134	−	0.152134i	−0.0136620	−	0.0136620i
$125$	2.05245	−	2.05245i	0.183577	−	0.183577i
$126$	11.1212	+	2.94216i	0.990758	+	0.262109i
$127$			9.62527i			0.854104i	0.904227	+	0.427052i	$0.140448\pi$
$127$			9.62527i			0.854104i	−0.904227	+	0.427052i	$0.859552\pi$
$128$	5.95577	−	5.95577i	0.526420	−	0.526420i
$129$	−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	$0.825965\pi$
$132$	1.26454	+	0.164441i	0.110064	+	0.0143127i
$133$	−15.4983			−1.34387
$134$	9.90780			0.855904
$135$	−5.90811	+	14.4575i	−0.508489	+	1.24431i
$136$	0.420179	−	0.420179i	0.0360301	−	0.0360301i
$137$	12.3006	−	12.3006i	1.05091	−	1.05091i	0.0522743	−	0.998633i	$-0.483353\pi$
$137$	12.3006	−	12.3006i	1.05091	−	1.05091i	0.998633	−	0.0522743i	$-0.0166470\pi$
$138$	7.44322	+	0.967917i	0.633609	+	0.0823945i
$139$	2.32905			0.197547			0.0987737	−	0.995110i	$-0.468508\pi$
$139$	2.32905			0.197547			0.0987737	+	0.995110i	$0.468508\pi$
$140$	2.42588			0.205025
$141$	−1.35694	+	10.4348i	−0.114275	+	0.878770i
$142$		−	7.02076i		−	0.589169i
$143$		0			0
$144$	2.58644	−	9.77660i	0.215536	−	0.814717i
$145$	−7.93324	+	7.93324i	−0.658819	+	0.658819i
$146$			6.42818i			0.532000i
$147$	−1.61738	−	2.10091i	−0.133400	−	0.173280i
$148$	−0.997033	+	0.997033i	−0.0819556	+	0.0819556i
$149$	11.1552	+	11.1552i	0.913867	+	0.913867i	0.996574	−	0.0827065i	$-0.0263564\pi$
$149$	11.1552	+	11.1552i	0.913867	+	0.913867i	−0.0827065	+	0.996574i	$0.526356\pi$
$150$	1.18302	−	9.09735i	0.0965931	−	0.742795i
$151$	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	$0.585868\pi$
$152$			15.8582i			1.28627i
$153$	0.152557	−	0.576659i	0.0123335	−	0.0466201i
$154$	7.22421	+	7.22421i	0.582143	+	0.582143i
$155$	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	$0.541620\pi$
$158$	−10.3396	−	10.3396i	−0.822576	−	0.822576i
$159$	14.3987	+	18.7033i	1.14189	+	1.48326i
$160$		−	4.66310i		−	0.368650i
$161$	−6.81701	−	6.81701i	−0.537256	−	0.537256i
$162$	−3.13052	−	11.3937i	−0.245956	−	0.895176i
$163$	−4.12124	−	4.12124i	−0.322800	−	0.322800i	0.527040	−	0.849840i	$-0.323302\pi$
$163$	−4.12124	−	4.12124i	−0.322800	−	0.322800i	−0.849840	+	0.527040i	$0.823302\pi$
$164$	−0.744429	+	0.744429i	−0.0581302	+	0.0581302i
$165$	−10.9908	+	8.46126i	−0.855633	+	0.658708i
$166$		−	3.41659i		−	0.265179i
$167$	1.11810	−	1.11810i	0.0865215	−	0.0865215i	−0.662521	−	0.749043i	$-0.730514\pi$
$167$	1.11810	−	1.11810i	0.0865215	−	0.0865215i	0.749043	+	0.662521i	$0.230514\pi$
$168$	−11.9799	+	9.22274i	−0.924272	+	0.711550i
$169$		0			0
$170$			0.784624i			0.0601779i
$171$	8.00310	+	13.7608i	0.612012	+	1.05232i
$172$	3.22085			0.245588
$173$	−12.4232			−0.944518			−0.472259	−	0.881460i	$-0.656561\pi$
$173$	−12.4232			−0.944518			−0.472259	+	0.881460i	$0.656561\pi$
$174$	1.09456	−	8.41714i	0.0829787	−	0.638101i
$175$	−8.33197	+	8.33197i	−0.629838	+	0.629838i
$176$	6.35076	−	6.35076i	0.478706	−	0.478706i
$177$	0.745689	−	5.73431i	0.0560494	−	0.431017i
$178$	−1.44239			−0.108111
$179$	−16.3028			−1.21853			−0.609265	−	0.792966i	$-0.708536\pi$
$179$	−16.3028			−1.21853			−0.609265	+	0.792966i	$0.708536\pi$
$180$	−1.25269	−	2.15392i	−0.0933700	−	0.160544i
$181$			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
$184$	−6.97529	+	6.97529i	−0.514225	+	0.514225i
$185$		−	15.3371i		−	1.12761i
$186$	−1.40293	+	1.08005i	−0.102868	+	0.0791928i
$187$	0.374590	−	0.374590i	0.0273928	−	0.0273928i
$188$	−1.18708	−	1.18708i	−0.0865765	−	0.0865765i
$189$	−5.74110	+	14.0489i	−0.417604	+	1.02190i
$190$	−14.8064	−	14.8064i	−1.07417	−	1.07417i
$191$		−	2.02830i		−	0.146763i	−0.997304	−	0.0733813i	$-0.976621\pi$
$191$		−	2.02830i		−	0.146763i	0.997304	−	0.0733813i	$-0.0233790\pi$
$192$	9.27552	+	12.0485i	0.669403	+	0.869525i
$193$	−2.80915	−	2.80915i	−0.202207	−	0.202207i	0.598738	−	0.800945i	$-0.295669\pi$
$193$	−2.80915	−	2.80915i	−0.202207	−	0.202207i	−0.800945	+	0.598738i	$0.795669\pi$
$194$	15.9700			1.14658
$195$		0			0
$196$	0.422998			0.0302142
$197$	−4.87188	−	4.87188i	−0.347107	−	0.347107i	0.511924	−	0.859031i	$-0.328933\pi$
$197$	−4.87188	−	4.87188i	−0.347107	−	0.347107i	−0.859031	+	0.511924i	$0.828933\pi$
$198$	2.68384	−	10.1448i	0.190732	−	0.720958i
$199$			6.34056i			0.449470i	0.974420	+	0.224735i	$0.0721517\pi$
$199$			6.34056i			0.449470i	−0.974420	+	0.224735i	$0.927848\pi$
$200$	8.52542	+	8.52542i	0.602838	+	0.602838i
$201$	−1.68557	+	12.9619i	−0.118891	+	0.914264i
$202$	11.5058	+	11.5058i	0.809547	+	0.809547i
$203$	−7.70898	+	7.70898i	−0.541065	+	0.541065i
$204$	0.0580523	+	0.0754074i	0.00406448	+	0.00527958i
$205$		−	11.4514i		−	0.799797i
$206$	−5.28044	+	5.28044i	−0.367905	+	0.367905i
$207$	−2.53256	+	9.57296i	−0.176025	+	0.665367i
$208$		0			0
$209$			14.1376i			0.977916i
$210$	2.57433	−	19.7965i	0.177646	−	1.36609i
$211$	−0.802275			−0.0552309			−0.0276154	−	0.999619i	$-0.508791\pi$
$211$	−0.802275			−0.0552309			−0.0276154	+	0.999619i	$0.508791\pi$
$212$	−3.76572			−0.258631
$213$	9.18494	+	1.19441i	0.629342	+	0.0818396i
$214$	7.21203	−	7.21203i	0.493005	−	0.493005i
$215$	−24.7728	+	24.7728i	−1.68949	+	1.68949i
$216$	14.3751	+	5.87440i	0.978098	+	0.399702i
$217$	2.27408			0.154375
$218$	−13.3377			−0.903344
$219$	−8.40969	−	1.09360i	−0.568274	−	0.0738984i
$220$		−	2.21289i		−	0.149193i
$221$		0			0
$222$	7.07826	+	9.19435i	0.475062	+	0.617084i
$223$	2.18501	−	2.18501i	0.146319	−	0.146319i	−0.630152	−	0.776471i	$-0.717008\pi$
$223$	2.18501	−	2.18501i	0.146319	−	0.146319i	0.776471	+	0.630152i	$0.217008\pi$
$224$		−	4.53128i		−	0.302759i
$225$	11.7004	+	3.09538i	0.780026	+	0.206359i
$226$	15.8635	−	15.8635i	1.05522	−	1.05522i
$227$	−18.3243	−	18.3243i	−1.21622	−	1.21622i	−0.968944	−	0.247281i	$-0.920463\pi$
$227$	−18.3243	−	18.3243i	−1.21622	−	1.21622i	−0.247281	−	0.968944i	$-0.579537\pi$
$228$	−2.51848	−	0.327503i	−0.166790	−	0.0216894i
$229$	−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	$-0.620008\pi$
$230$		−	13.0253i		−	0.858865i
$231$	−10.6801	+	8.22208i	−0.702701	+	0.540973i
$232$	7.88797	+	7.88797i	0.517871	+	0.517871i
$233$	−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
$236$	0.652342	+	0.652342i	0.0424638	+	0.0424638i
$237$	15.2859	−	11.7678i	0.992925	−	0.764402i
$238$			0.762445i			0.0494220i
$239$	−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	$0.812161\pi$
$240$	−17.4029	−	2.26308i	−1.12336	−	0.146081i
$241$	−17.4503	−	17.4503i	−1.12407	−	1.12407i	−0.991123	−	0.132947i	$-0.957556\pi$
$241$	−17.4503	−	17.4503i	−1.12407	−	1.12407i	−0.132947	−	0.991123i	$-0.542444\pi$
$242$	−3.62193	+	3.62193i	−0.232827	+	0.232827i
$243$	15.4385	−	2.15715i	0.990379	−	0.138381i
$244$			0.746353i			0.0477804i
$245$	−3.25343	+	3.25343i	−0.207854	+	0.207854i
$246$	5.28494	+	6.86491i	0.336956	+	0.437691i
$247$		0			0
$248$		−	2.32688i		−	0.147757i
$249$	4.46977	+	0.581248i	0.283260	+	0.0368351i
$250$	3.81079			0.241016
$251$	21.7299			1.37158			0.685789	−	0.727801i	$-0.259457\pi$
$251$	21.7299			1.37158			0.685789	+	0.727801i	$0.259457\pi$
$252$	−1.21728	−	2.09304i	−0.0766814	−	0.131849i
$253$	−6.21847	+	6.21847i	−0.390952	+	0.390952i
$254$	−8.93562	+	8.93562i	−0.560671	+	0.560671i
$255$	−1.02649	−	0.133484i	−0.0642812	−	0.00835912i
$256$	−6.49950			−0.406219
$257$	16.3112			1.01746			0.508732	−	0.860925i	$-0.330115\pi$
$257$	16.3112			1.01746			0.508732	+	0.860925i	$0.330115\pi$
$258$	3.41795	−	26.2838i	0.212792	−	1.63636i
$259$		−	14.9036i		−	0.926062i
$260$		0			0
$261$	10.8255	+	2.86394i	0.670084	+	0.177273i
$262$	−11.0486	+	11.0486i	−0.682583	+	0.682583i
$263$			11.4962i			0.708887i	0.935077	+	0.354444i	$0.115330\pi$
$263$			11.4962i			0.708887i	−0.935077	+	0.354444i	$0.884670\pi$
$264$	8.41298	+	10.9281i	0.517783	+	0.672578i
$265$	28.9635	−	28.9635i	1.77922	−	1.77922i
$266$	−14.3879	−	14.3879i	−0.882177	−	0.882177i
$267$	0.245387	−	1.88701i	0.0150174	−	0.115483i
$268$	−1.47457	−	1.47457i	−0.0900734	−	0.0900734i
$269$			11.1389i			0.679151i	0.940579	+	0.339576i	$0.110283\pi$
$269$			11.1389i			0.679151i	−0.940579	+	0.339576i	$0.889717\pi$
$270$	−18.9065	+	7.93687i	−1.15061	+	0.483023i
$271$	−4.29686	−	4.29686i	−0.261016	−	0.261016i	0.564451	−	0.825467i	$-0.309088\pi$
$271$	−4.29686	−	4.29686i	−0.261016	−	0.261016i	−0.825467	+	0.564451i	$0.809088\pi$
$272$	0.670260			0.0406405
$273$		0			0
$274$	22.8384			1.37972
$275$	7.60042	+	7.60042i	0.458323	+	0.458323i
$276$	−0.963712	−	1.25182i	−0.0580086	−	0.0753507i
$277$		−	27.7810i		−	1.66920i	−0.550857	−	0.834600i	$-0.685699\pi$
$277$		−	27.7810i		−	1.66920i	0.550857	−	0.834600i	$-0.314301\pi$
$278$	2.16218	+	2.16218i	0.129679	+	0.129679i
$279$	−1.17430	−	2.01914i	−0.0703035	−	0.120883i
$280$	18.5519	+	18.5519i	1.10869	+	1.10869i
$281$	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	$0.0869585\pi$
$282$	−10.9469	+	8.42744i	−0.651877	+	0.501847i
$283$			26.5871i			1.58044i	0.612824	+	0.790219i	$0.290033\pi$
$283$			26.5871i			1.58044i	−0.612824	+	0.790219i	$0.709967\pi$
$284$	−1.04489	+	1.04489i	−0.0620028	+	0.0620028i
$285$	21.8895	−	16.8516i	1.29662	−	0.998203i
$286$		0			0
$287$		−	11.1277i		−	0.656845i
$288$	−4.02329	+	2.33989i	−0.237074	+	0.137879i
$289$	−16.9605			−0.997674
$290$	−14.7296			−0.864955
$291$	−2.71691	+	20.8929i	−0.159268	+	1.22476i
$292$	0.956698	−	0.956698i	0.0559865	−	0.0559865i
$293$	2.04702	−	2.04702i	0.119588	−	0.119588i	−0.644780	−	0.764368i	$-0.723051\pi$
$293$	2.04702	−	2.04702i	0.119588	−	0.119588i	0.764368	+	0.644780i	$0.223051\pi$
$294$	0.448883	−	3.45188i	0.0261794	−	0.201318i
$295$	−10.0348			−0.584249
$296$	−15.2496			−0.886365
$297$	12.8154	+	5.23703i	0.743623	+	0.303883i
$298$			20.7118i			1.19980i
$299$		0			0
$300$	−1.53001	+	1.17788i	−0.0883354	+	0.0680049i
$301$	−24.0725	+	24.0725i	−1.38752	+	1.38752i
$302$			15.9100i			0.915519i
$303$	−17.0100	+	13.0951i	−0.977197	+	0.752294i
$304$	−12.6483	+	12.6483i	−0.725429	+	0.725429i
$305$	−5.74048	−	5.74048i	−0.328699	−	0.328699i
$306$	0.676968	−	0.393715i	0.0386997	−	0.0225072i
$307$	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	$0.559555\pi$
$308$		−	2.15034i		−	0.122527i
$309$	−6.00982	−	7.80649i	−0.341887	−	0.444096i
$310$	2.17256	+	2.17256i	0.123393	+	0.123393i
$311$	−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	$0.736859\pi$
$314$	−3.03321	−	3.03321i	−0.171174	−	0.171174i
$315$	25.4609	+	6.73576i	1.43456	+	0.379517i
$316$			3.07766i			0.173132i
$317$	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	$0.419578\pi$
$318$	−3.99615	+	30.7302i	−0.224093	+	1.72326i
$319$	7.03214	+	7.03214i	0.393724	+	0.393724i
$320$	18.6581	−	18.6581i	1.04302	−	1.04302i
$321$	8.20823	+	10.6621i	0.458139	+	0.595102i
$322$		−	12.6571i		−	0.705355i
$323$	−0.746041	+	0.746041i	−0.0415108	+	0.0415108i
$324$	−1.22980	+	2.16162i	−0.0683224	+	0.120090i
$325$		0			0
$326$		−	7.65191i		−	0.423800i
$327$	2.26908	−	17.4491i	0.125481	−	0.964939i
$328$	−11.3860			−0.628688
$329$	17.7443			0.978276
$330$	−18.0583	−	2.34831i	−0.994079	−	0.129270i
$331$	0.469219	−	0.469219i	0.0257906	−	0.0257906i	−0.694094	−	0.719885i	$-0.744195\pi$
$331$	0.469219	−	0.469219i	0.0257906	−	0.0257906i	0.719885	+	0.694094i	$0.244195\pi$
$332$	−0.508486	+	0.508486i	−0.0279068	+	0.0279068i
$333$	−13.2327	+	7.69597i	−0.725150	+	0.421737i
$334$	2.07598			0.113593
$335$	22.6828			1.23930
$336$	−16.9110	−	2.19911i	−0.922571	−	0.119971i
$337$			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
$340$	0.116775	−	0.116775i	0.00633299	−	0.00633299i
$341$		−	2.07442i		−	0.112336i
$342$	−5.34519	+	20.2045i	−0.289035	+	1.09254i
$343$	11.2955	−	11.2955i	0.609900	−	0.609900i
$344$	24.6314	+	24.6314i	1.32804	+	1.32804i
$345$	17.0405	+	2.21594i	0.917428	+	0.119302i
$346$	−11.5331	−	11.5331i	−0.620023	−	0.620023i
$347$			16.4102i			0.880947i	0.897766	+	0.440474i	$0.145189\pi$
$347$			16.4102i			0.880947i	−0.897766	+	0.440474i	$0.854811\pi$
$348$	−1.41561	+	1.08981i	−0.0758849	+	0.0584199i
$349$	21.1952	+	21.1952i	1.13456	+	1.13456i	0.989410	+	0.145145i	$0.0463649\pi$
$349$	21.1952	+	21.1952i	1.13456	+	1.13456i	0.145145	+	0.989410i	$0.453635\pi$
$350$	−15.4700			−0.826905
$351$		0			0
$352$	−4.13344			−0.220313
$353$	−4.76452	−	4.76452i	−0.253590	−	0.253590i	0.568851	−	0.822441i	$-0.307388\pi$
$353$	−4.76452	−	4.76452i	−0.253590	−	0.253590i	−0.822441	+	0.568851i	$0.807388\pi$
$354$	6.01571	−	4.63118i	0.319731	−	0.246145i
$355$		−	16.0733i		−	0.853081i
$356$	0.214669	+	0.214669i	0.0113774	+	0.0113774i
$357$	−0.997472	−	0.129711i	−0.0527918	−	0.00686505i
$358$	−15.1347	−	15.1347i	−0.799896	−	0.799896i
$359$	−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	$0.331289\pi$
$360$	6.89216	−	26.0520i	0.363248	−	1.37306i
$361$		−	9.15665i		−	0.481929i
$362$	−8.63014	+	8.63014i	−0.453590	+	0.453590i
$363$	−4.12223	−	5.35459i	−0.216361	−	0.281043i
$364$		0			0
$365$			14.7166i			0.770303i
$366$	6.09063	+	0.792025i	0.318362	+	0.0413998i
$367$	−12.0267			−0.627790			−0.313895	−	0.949458i	$-0.601634\pi$
$367$	−12.0267			−0.627790			−0.313895	+	0.949458i	$0.601634\pi$
$368$	−11.1268			−0.580026
$369$	−9.88015	+	5.74615i	−0.514340	+	0.299133i
$370$	14.2382	−	14.2382i	0.740209	−	0.740209i
$371$	28.1448	−	28.1448i	1.46121	−	1.46121i
$372$	0.369539	+	0.0480548i	0.0191597	+	0.00249152i
$373$	13.3586			0.691684			0.345842	−	0.938293i	$-0.387593\pi$
$373$	13.3586			0.691684			0.345842	+	0.938293i	$0.387593\pi$
$374$	0.695502			0.0359636
$375$	−0.648313	+	4.98549i	−0.0334787	+	0.257449i
$376$		−	18.1563i		−	0.936340i
$377$		0			0
$378$	−18.3720	+	7.71252i	−0.944955	+	0.396689i
$379$	21.8973	−	21.8973i	1.12479	−	1.12479i	0.133777	−	0.991011i	$-0.457289\pi$
$379$	21.8973	−	21.8973i	1.12479	−	1.12479i	0.991011	−	0.133777i	$-0.0427107\pi$
$380$			4.40724i			0.226087i
$381$	−10.1699	−	13.2102i	−0.521019	−	0.676781i
$382$	1.88297	−	1.88297i	0.0963413	−	0.0963413i
$383$	7.25053	+	7.25053i	0.370485	+	0.370485i	0.867654	−	0.497169i	$-0.165627\pi$
$383$	7.25053	+	7.25053i	0.370485	+	0.370485i	−0.497169	+	0.867654i	$0.665627\pi$
$384$	−1.88126	+	14.4668i	−0.0960026	+	0.738255i
$385$	16.5390	+	16.5390i	0.842908	+	0.842908i
$386$		−	5.21576i		−	0.265475i
$387$	33.8045	+	8.94310i	1.71838	+	0.454603i
$388$	−2.37680	−	2.37680i	−0.120664	−	0.120664i
$389$	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
$392$	3.23487	+	3.23487i	0.163386	+	0.163386i
$393$	−12.5747	−	16.3340i	−0.634310	−	0.823941i
$394$		−	9.04562i		−	0.455712i
$395$	−23.6714	−	23.6714i	−1.19104	−	1.19104i
$396$	−1.90927	+	1.11040i	−0.0959443	+	0.0557998i
$397$	2.42682	+	2.42682i	0.121799	+	0.121799i	0.765379	−	0.643580i	$-0.222552\pi$
$397$	2.42682	+	2.42682i	0.121799	+	0.121799i	−0.643580	+	0.765379i	$0.722552\pi$
$398$	−5.88626	+	5.88626i	−0.295052	+	0.295052i
$399$	21.2707	−	16.3753i	1.06487	−	0.819788i
$400$			13.5996i			0.679978i
$401$	14.1084	−	14.1084i	0.704541	−	0.704541i	−0.260841	−	0.965382i	$-0.584000\pi$
$401$	14.1084	−	14.1084i	0.704541	−	0.704541i	0.965382	+	0.260841i	$0.0839998\pi$
$402$	−13.5980	+	10.4684i	−0.678207	+	0.522117i
$403$		0			0
$404$		−	3.42479i		−	0.170390i
$405$	−7.16698	−	26.0847i	−0.356130	−	1.29616i
$406$	−14.3133			−0.710356
$407$	−13.5950			−0.673880
$408$	−0.132723	+	1.02063i	−0.00657076	+	0.0505288i
$409$	3.91823	−	3.91823i	0.193744	−	0.193744i	−0.603568	−	0.797312i	$-0.706255\pi$
$409$	3.91823	−	3.91823i	0.193744	−	0.193744i	0.797312	+	0.603568i	$0.206255\pi$
$410$	10.6309	−	10.6309i	0.525021	−	0.525021i
$411$	−3.88540	+	29.8785i	−0.191653	+	1.47380i
$412$	1.57176			0.0774351
$413$	−9.75114			−0.479822
$414$	−11.2382	+	6.53596i	−0.552326	+	0.321225i
$415$		−	7.82191i		−	0.383962i
$416$		0			0
$417$	−3.19652	+	2.46083i	−0.156534	+	0.120508i
$418$	−13.1246	+	13.1246i	−0.641946	+	0.641946i
$419$			34.4340i			1.68221i	0.540871	+	0.841106i	$0.318095\pi$
$419$			34.4340i			1.68221i	−0.540871	+	0.841106i	$0.681905\pi$
$420$	−3.32942	+	2.56315i	−0.162459	+	0.125069i
$421$	−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	$0.471685\pi$
$422$	−0.744792	−	0.744792i	−0.0362559	−	0.0362559i
$423$	−9.16290	−	15.7550i	−0.445515	−	0.766036i
$424$	−28.7983	−	28.7983i	−1.39857	−	1.39857i
$425$			0.802150i			0.0389100i
$426$	7.41801	+	9.63567i	0.359404	+	0.466850i
$427$	−5.57821	−	5.57821i	−0.269948	−	0.269948i
$428$	−2.14672			−0.103765
$429$		0			0
$430$	−45.9956			−2.21811
$431$	7.99634	+	7.99634i	0.385170	+	0.385170i	0.872961	−	0.487791i	$-0.162197\pi$
$431$	7.99634	+	7.99634i	0.385170	+	0.385170i	−0.487791	+	0.872961i	$0.662197\pi$
$432$	6.78002	+	16.1507i	0.326204	+	0.777052i
$433$		−	6.20615i		−	0.298249i	−0.988818	−	0.149124i	$-0.952355\pi$
$433$		−	6.20615i		−	0.298249i	0.988818	−	0.149124i	$-0.0476455\pi$
$434$	2.11114	+	2.11114i	0.101338	+	0.101338i
$435$	2.50589	−	19.2701i	0.120148	−	0.923932i
$436$	1.98503	+	1.98503i	0.0950659	+	0.0950659i
$437$	12.3848	−	12.3848i	0.592447	−	0.592447i
$438$	−6.79190	−	8.82238i	−0.324530	−	0.421550i
$439$		−	38.7828i		−	1.85100i	−0.378745	−	0.925501i	$-0.623644\pi$
$439$		−	38.7828i		−	1.85100i	0.378745	−	0.925501i	$-0.376356\pi$
$440$	16.9231	−	16.9231i	0.806775	−	0.806775i
$441$	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	$-0.143267\pi$
$444$	0.314935	−	2.42183i	0.0149461	−	0.114935i
$445$	−3.30219			−0.156539
$446$	4.05691			0.192100
$447$	−27.0963	−	3.52361i	−1.28161	−	0.166661i
$448$	18.1307	−	18.1307i	0.856593	−	0.856593i
$449$	−1.37117	+	1.37117i	−0.0647096	+	0.0647096i	−0.738721	−	0.674011i	$-0.764570\pi$
$449$	−1.37117	+	1.37117i	−0.0647096	+	0.0647096i	0.674011	+	0.738721i	$0.264570\pi$
$450$	7.98846	+	13.7357i	0.376580	+	0.647505i
$451$	−10.1506			−0.477975
$452$	−4.72188			−0.222099
$453$	−20.8144	−	2.70670i	−0.977944	−	0.127172i
$454$		−	34.0227i		−	1.59676i
$455$		0			0
$456$	−16.7555	−	21.7646i	−0.784646	−	1.01922i
$457$	−4.12048	+	4.12048i	−0.192748	+	0.192748i	−0.796882	−	0.604134i	$-0.793519\pi$
$457$	−4.12048	+	4.12048i	−0.192748	+	0.192748i	0.604134	+	0.796882i	$0.293519\pi$
$458$		−	36.4675i		−	1.70401i
$459$	0.399910	+	0.952628i	0.0186662	+	0.0444649i
$460$	−1.93854	+	1.93854i	−0.0903851	+	0.0903851i
$461$	10.1185	+	10.1185i	0.471264	+	0.471264i	0.902323	−	0.431060i	$-0.141860\pi$
$461$	10.1185	+	10.1185i	0.471264	+	0.471264i	−0.431060	+	0.902323i	$0.641860\pi$
$462$	−17.5479	−	2.28193i	−0.816401	−	0.106165i
$463$	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	$0.718669\pi$
$464$			12.5827i			0.584138i
$465$	−3.21186	+	2.47265i	−0.148947	+	0.114666i
$466$	−13.4194	−	13.4194i	−0.621643	−	0.621643i
$467$	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
$470$	16.9521	+	16.9521i	0.781944	+	0.781944i
$471$	4.48423	−	3.45218i	0.206622	−	0.159068i
$472$			9.97755i			0.459254i
$473$	21.9589	+	21.9589i	1.00967	+	1.00967i
$474$	25.1153	+	3.26600i	1.15358	+	0.150012i
$475$	−15.1371	−	15.1371i	−0.694540	−	0.694540i
$476$	0.113474	−	0.113474i	0.00520106	−	0.00520106i
$477$	−39.5231	−	10.4560i	−1.80964	−	0.478746i
$478$		−	7.87701i		−	0.360286i
$479$	1.44413	−	1.44413i	0.0659840	−	0.0659840i	−0.673345	−	0.739329i	$-0.735143\pi$
$479$	1.44413	−	1.44413i	0.0659840	−	0.0659840i	0.739329	+	0.673345i	$0.235143\pi$
$480$	4.92695	+	6.39989i	0.224883	+	0.292114i
$481$		0			0
$482$		−	32.3999i		−	1.47578i
$483$	16.5588	+	2.15330i	0.753450	+	0.0979786i
$484$	1.07810			0.0490043
$485$	36.5617			1.66018
$486$	16.3349	+	12.3297i	0.740967	+	0.559288i
$487$	−17.7349	+	17.7349i	−0.803647	+	0.803647i	−0.983664	−	0.180017i	$-0.942385\pi$
$487$	−17.7349	+	17.7349i	−0.803647	+	0.803647i	0.180017	+	0.983664i	$0.442385\pi$
$488$	−5.70772	+	5.70772i	−0.258377	+	0.258377i
$489$	10.0106	+	1.30178i	0.452697	+	0.0588687i
$490$	−6.04065			−0.272889
$491$	−7.53217			−0.339922			−0.169961	−	0.985451i	$-0.554364\pi$
$491$	−7.53217			−0.339922			−0.169961	+	0.985451i	$0.554364\pi$
$492$	0.235144	−	1.80825i	0.0106011	−	0.0815221i
$493$			0.742173i			0.0334258i
$494$		0			0
$495$	6.14436	−	23.2254i	0.276169	−	1.04390i
$496$	1.85589	−	1.85589i	0.0833321	−	0.0833321i
$497$		−	15.6189i		−	0.700604i
$498$	3.60991	+	4.68911i	0.161764	+	0.210124i
$499$	−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	$0.338970\pi$
$500$	−0.567155	−	0.567155i	−0.0253640	−	0.0253640i
$501$	−0.353178	+	2.71592i	−0.0157788	+	0.121338i
$502$	20.1729	+	20.1729i	0.900362	+	0.900362i
$503$			2.34970i			0.104768i	0.998627	+	0.0523839i	$0.0166819\pi$
$503$			2.34970i			0.104768i	−0.998627	+	0.0523839i	$0.983318\pi$
$504$	6.69733	−	25.3156i	0.298323	−	1.12765i
$505$	26.3413	+	26.3413i	1.17217	+	1.17217i
$506$	−11.5458			−0.513276
$507$		0			0
$508$	2.65975			0.118008
$509$	21.1961	+	21.1961i	0.939499	+	0.939499i	0.998271	−	0.0587720i	$-0.0187185\pi$
$509$	21.1961	+	21.1961i	0.939499	+	0.939499i	−0.0587720	+	0.998271i	$0.518718\pi$
$510$	−0.829020	−	1.07686i	−0.0367096	−	0.0476842i
$511$			14.3006i			0.632622i
$512$	−17.9453	−	17.9453i	−0.793080	−	0.793080i
$513$	−25.5233	−	10.4302i	−1.12688	−	0.460503i
$514$	15.1425	+	15.1425i	0.667907	+	0.667907i
$515$	−12.0890	+	12.0890i	−0.532705	+	0.532705i
$516$	−4.42048	+	3.40310i	−0.194601	+	0.149813i
$517$		−	16.1864i		−	0.711876i
$518$	13.8357	−	13.8357i	0.607907	−	0.607907i
$519$	17.0503	−	13.1261i	0.748424	−	0.576174i
$520$		0			0
$521$		−	5.94611i		−	0.260504i	−0.991481	−	0.130252i	$-0.958421\pi$
$521$		−	5.94611i		−	0.260504i	0.991481	−	0.130252i	$-0.0415786\pi$
$522$	7.39116	+	12.7086i	0.323502	+	0.556242i
$523$	−0.859946			−0.0376028			−0.0188014	−	0.999823i	$-0.505985\pi$
$523$	−0.859946			−0.0376028			−0.0188014	+	0.999823i	$0.505985\pi$
$524$	3.28869			0.143667
$525$	2.63184	−	20.2387i	0.114863	−	0.883288i
$526$	−10.6725	+	10.6725i	−0.465344	+	0.465344i
$527$	0.109467	−	0.109467i	0.00476847	−	0.00476847i
$528$	−2.00603	+	15.4262i	−0.0873011	+	0.671340i
$529$	−12.1049			−0.526302
$530$	53.7766			2.33591
$531$	5.03534	+	8.65796i	0.218515	+	0.375723i
$532$			4.28266i			0.185677i
$533$		0			0
$534$	1.97961	−	1.52400i	0.0856662	−	0.0659500i
$535$	16.5112	−	16.5112i	0.713841	−	0.713841i
$536$		−	22.5534i		−	0.974160i
$537$	22.3749	−	17.2253i	0.965548	−	0.743326i
$538$	−10.3408	+	10.3408i	−0.445824	+	0.445824i
$539$	2.88389	+	2.88389i	0.124218	+	0.124218i
$540$	3.99506	+	1.63259i	0.171920	+	0.0702555i
$541$	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	$0.694856\pi$
$542$		−	7.97798i		−	0.342684i
$543$	−9.82221	−	12.7586i	−0.421512	−	0.547525i
$544$	−0.218122	−	0.218122i	−0.00935190	−	0.00935190i
$545$	−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	$0.715980\pi$
$548$	−3.39902	−	3.39902i	−0.145199	−	0.145199i
$549$	−2.07234	+	7.83335i	−0.0884453	+	0.334319i
$550$			14.1117i			0.601725i
$551$	−14.0053	−	14.0053i	−0.596647	−	0.596647i
$552$	2.20330	−	16.9432i	0.0937786	−	0.721152i
$553$	−23.0023	−	23.0023i	−0.978158	−	0.978158i
$554$	25.7905	−	25.7905i	1.09573	−	1.09573i
$555$	16.2049	+	21.0495i	0.687860	+	0.893501i
$556$		−	0.643588i		−	0.0272942i
$557$	−26.4446	+	26.4446i	−1.12050	+	1.12050i	−0.128828	+	0.991667i	$0.541122\pi$
$557$	−26.4446	+	26.4446i	−1.12050	+	1.12050i	−0.991667	+	0.128828i	$0.958878\pi$
$558$	0.784303	−	2.96463i	0.0332022	−	0.125503i
$559$		0			0
$560$			29.5936i			1.25056i
$561$	−0.118323	+	0.909894i	−0.00499558	+	0.0384157i
$562$	21.5724			0.909978
$563$	13.4052			0.564963			0.282481	−	0.959273i	$-0.408842\pi$
$563$	13.4052			0.564963			0.282481	+	0.959273i	$0.408842\pi$
$564$	2.88346	+	0.374965i	0.121415	+	0.0157889i
$565$	36.3177	−	36.3177i	1.52790	−	1.52790i
$566$	−24.6821	+	24.6821i	−1.03747	+	1.03747i
$567$	−6.96439	−	25.3474i	−0.292477	−	1.06449i
$568$	−15.9816			−0.670572
$569$	−22.6791			−0.950759			−0.475380	−	0.879781i	$-0.657689\pi$
$569$	−22.6791			−0.950759			−0.475380	+	0.879781i	$0.657689\pi$
$570$	35.9653	+	4.67693i	1.50642	+	0.195895i
$571$			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
$574$	10.3304	−	10.3304i	0.431181	−	0.431181i
$575$		−	13.3163i		−	0.555328i
$576$	−25.4605	−	6.73566i	−1.06085	−	0.280652i
$577$	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	$0.0637354\pi$
$578$	−15.7453	−	15.7453i	−0.654916	−	0.654916i
$579$	6.82354	+	0.887333i	0.283577	+	0.0368763i
$580$	2.19219	+	2.19219i	0.0910259	+	0.0910259i
$581$		−	7.60081i		−	0.315335i
$582$	−21.9181	+	16.8737i	−0.908537	+	0.699436i
$583$	−25.6737	−	25.6737i	−1.06330	−	1.06330i
$584$	14.6327			0.605504
$585$		0			0
$586$	3.80070			0.157005
$587$	−8.65842	−	8.65842i	−0.357371	−	0.357371i	0.505472	−	0.862843i	$-0.331318\pi$
$587$	−8.65842	−	8.65842i	−0.357371	−	0.357371i	−0.862843	+	0.505472i	$0.831318\pi$
$588$	−0.580546	+	0.446933i	−0.0239413	+	0.0184312i
$589$			4.13145i			0.170233i
$590$	−9.31581	−	9.31581i	−0.383526	−	0.383526i
$591$	11.8340	+	1.53889i	0.486785	+	0.0633015i
$592$	−12.1629	−	12.1629i	−0.499892	−	0.499892i
$593$	−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	$0.858784\pi$
$594$	7.03536	+	16.7590i	0.288664	+	0.687628i
$595$			1.74554i			0.0715600i
$596$	3.08251	−	3.08251i	0.126265	−	0.126265i
$597$	−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	$-0.0760708\pi$
$600$	−20.7086	−	2.69294i	−0.845424	−	0.109939i
$601$	−4.53417			−0.184953			−0.0924764	−	0.995715i	$-0.529478\pi$
$601$	−4.53417			−0.184953			−0.0924764	+	0.995715i	$0.529478\pi$
$602$	−44.6955			−1.82165
$603$	−11.3820	−	19.5706i	−0.463510	−	0.796977i
$604$	2.36787	−	2.36787i	0.0963472	−	0.0963472i
$605$	−8.29203	+	8.29203i	−0.337119	+	0.337119i
$606$	−27.9481	−	3.63437i	−1.13531	−	0.147636i
$607$	13.0328			0.528986			0.264493	−	0.964388i	$-0.414795\pi$
$607$	13.0328			0.528986			0.264493	+	0.964388i	$0.414795\pi$
$608$	8.23223			0.333861
$609$	2.43505	−	18.7254i	0.0986733	−	0.758792i
$610$		−	10.6583i		−	0.431544i
$611$		0			0
$612$	−0.159348	−	0.0421562i	−0.00644128	−	0.00170406i
$613$	−2.54348	+	2.54348i	−0.102730	+	0.102730i	−0.756604	−	0.653874i	$-0.773143\pi$
$613$	−2.54348	+	2.54348i	−0.102730	+	0.102730i	0.653874	+	0.756604i	$0.273143\pi$
$614$			25.9131i			1.04577i
$615$	12.0993	+	15.7165i	0.487891	+	0.633749i
$616$	16.4447	−	16.4447i	0.662575	−	0.662575i
$617$	4.69608	+	4.69608i	0.189057	+	0.189057i	0.795288	−	0.606231i	$-0.207319\pi$
$617$	4.69608	+	4.69608i	0.189057	+	0.189057i	−0.606231	+	0.795288i	$0.707319\pi$
$618$	1.66794	−	12.8264i	0.0670945	−	0.515953i
$619$	−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	$0.873715\pi$
$620$		−	0.646677i		−	0.0259712i
$621$	−6.63880	−	15.8143i	−0.266406	−	0.634607i
$622$	−25.0427	−	25.0427i	−1.00412	−	1.00412i
$623$	−3.20885			−0.128560
$624$		0			0
$625$	28.8959			1.15584
$626$	−22.2489	−	22.2489i	−0.889243	−	0.889243i
$627$	−14.9375	−	19.4032i	−0.596547	−	0.774888i
$628$			0.902856i			0.0360279i
$629$	−0.717411	−	0.717411i	−0.0286051	−	0.0286051i
$630$	17.3835	+	29.8898i	0.692573	+	1.19084i
$631$	−1.04182	−	1.04182i	−0.0414743	−	0.0414743i	0.686065	−	0.727540i	$-0.259336\pi$
$631$	−1.04182	−	1.04182i	−0.0414743	−	0.0414743i	−0.727540	+	0.686065i	$0.759336\pi$
$632$	−23.5364	+	23.5364i	−0.936227	+	0.936227i
$633$	1.10109	−	0.847670i	0.0437642	−	0.0336918i
$634$			40.2717i			1.59939i
$635$	−20.4571	+	20.4571i	−0.811817	+	0.811817i
$636$	5.16828	−	3.97879i	0.204936	−	0.157769i
$637$		0			0
$638$			13.0566i			0.516915i
$639$	−13.8679	+	8.06538i	−0.548606	+	0.319061i
$640$	25.3163			1.00071
$641$	−14.8607			−0.586961			−0.293481	−	0.955965i	$-0.594814\pi$
$641$	−14.8607			−0.586961			−0.293481	+	0.955965i	$0.594814\pi$
$642$	−2.27808	+	17.5183i	−0.0899086	+	0.691392i
$643$	−34.3565	+	34.3565i	−1.35489	+	1.35489i	−0.474791	+	0.880099i	$0.657476\pi$
$643$	−34.3565	+	34.3565i	−1.35489	+	1.35489i	−0.880099	+	0.474791i	$0.842524\pi$
$644$	−1.88375	+	1.88375i	−0.0742300	+	0.0742300i
$645$	7.82503	−	60.1740i	0.308110	−	2.36935i
$646$	−1.38518			−0.0544990
$647$	−37.6742			−1.48112			−0.740562	−	0.671988i	$-0.765441\pi$
$647$	−37.6742			−1.48112			−0.740562	+	0.671988i	$0.765441\pi$
$648$	−25.9359	+	7.12609i	−1.01886	+	0.279939i
$649$			8.89499i			0.349159i
$650$		0			0
$651$	−3.12107	+	2.40275i	−0.122324	+	0.0941714i
$652$	−1.13882	+	1.13882i	−0.0445998	+	0.0445998i
$653$			22.2714i			0.871548i	0.900056	+	0.435774i	$0.143525\pi$
$653$			22.2714i			0.871548i	−0.900056	+	0.435774i	$0.856475\pi$
$654$	18.3054	−	14.0924i	0.715798	−	0.551056i
$655$	−25.2945	+	25.2945i	−0.988339	+	0.988339i
$656$	−9.08136	−	9.08136i	−0.354568	−	0.354568i
$657$	12.6974	−	7.38463i	0.495373	−	0.288102i
$658$	16.4729	+	16.4729i	0.642182	+	0.642182i
$659$		−	26.8010i		−	1.04402i	−0.852939	−	0.522010i	$-0.825182\pi$
$659$		−	26.8010i		−	1.04402i	0.852939	−	0.522010i	$-0.174818\pi$
$660$	2.33810	+	3.03709i	0.0910106	+	0.118219i
$661$	12.3552	+	12.3552i	0.480561	+	0.480561i	0.905311	−	0.424750i	$-0.139638\pi$
$661$	12.3552	+	12.3552i	0.480561	+	0.480561i	−0.424750	+	0.905311i	$0.639638\pi$
$662$	0.871200			0.0338602
$663$		0			0
$664$	−7.77728			−0.301817
$665$	−32.9395	−	32.9395i	−1.27734	−	1.27734i
$666$	−19.4292	−	5.14006i	−0.752866	−	0.199173i
$667$		−	12.3206i		−	0.477057i
$668$	−0.308966	−	0.308966i	−0.0119543	−	0.0119543i
$669$	−0.690183	+	5.30747i	−0.0266840	+	0.205199i
$670$	21.0576	+	21.0576i	0.813527	+	0.813527i
$671$	−5.08844	+	5.08844i	−0.196437	+	0.196437i
$672$	4.78768	+	6.21898i	0.184689	+	0.239902i
$673$			35.6073i			1.37256i	0.727336	+	0.686281i	$0.240758\pi$
$673$			35.6073i			1.37256i	−0.727336	+	0.686281i	$0.759242\pi$
$674$	−23.2897	+	23.2897i	−0.897087	+	0.897087i
$675$	−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	$0.898076\pi$
$678$	−5.01083	+	38.5330i	−0.192440	+	1.47985i
$679$	35.5282			1.36345
$680$	1.78606			0.0684924
$681$	44.5104	+	5.78813i	1.70564	+	0.221801i
$682$	1.92579	−	1.92579i	0.0737421	−	0.0737421i
$683$	27.1629	−	27.1629i	1.03936	−	1.03936i	0.0401670	−	0.999193i	$-0.487211\pi$
$683$	27.1629	−	27.1629i	1.03936	−	1.03936i	0.999193	−	0.0401670i	$-0.0127890\pi$
$684$	3.80253	−	2.21150i	0.145394	−	0.0845588i
$685$	52.2862			1.99775
$686$	20.9724			0.800729
$687$	47.7088	+	6.20404i	1.82020	+	0.236699i
$688$			39.2915i			1.49797i
$689$		0			0
$690$	13.7624	+	17.8767i	0.523924	+	0.680554i
$691$	13.6599	−	13.6599i	0.519648	−	0.519648i	−0.397817	−	0.917465i	$-0.630232\pi$
$691$	13.6599	−	13.6599i	0.519648	−	0.519648i	0.917465	+	0.397817i	$0.130232\pi$
$692$			3.43291i			0.130500i
$693$	5.97068	−	22.5689i	0.226807	−	0.857321i
$694$	−15.2344	+	15.2344i	−0.578292	+	0.578292i
$695$	4.95007	+	4.95007i	0.187767	+	0.187767i
$696$	−19.1602	−	2.49159i	−0.726265	−	0.0944435i
$697$	−0.535651	−	0.535651i	−0.0202892	−	0.0202892i
$698$			39.3532i			1.48954i
$699$	19.8390	−	15.2731i	0.750381	−	0.577680i
$700$	2.30238	+	2.30238i	0.0870216	+	0.0870216i
$701$	−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
$704$	−16.5388	−	16.5388i	−0.623329	−	0.623329i
$705$	−25.0617	+	19.2937i	−0.943879	+	0.726644i
$706$		−	8.84629i		−	0.332935i
$707$	25.5967	+	25.5967i	0.962664	+	0.962664i
$708$	−1.58456	−	0.206057i	−0.0595515	−	0.00774408i
$709$	30.8214	+	30.8214i	1.15752	+	1.15752i	0.985007	+	0.172517i	$0.0551899\pi$
$709$	30.8214	+	30.8214i	1.15752	+	1.15752i	0.172517	+	0.985007i	$0.444810\pi$
$710$	14.9216	−	14.9216i	0.559999	−	0.559999i
$711$	−8.54551	+	32.3016i	−0.320482	+	1.21140i
$712$			3.28335i			0.123049i
$713$	−1.81724	+	1.81724i	−0.0680560	+	0.0680560i
$714$	−0.805586	−	1.04642i	−0.0301483	−	0.0391613i
$715$		0			0
$716$			4.50497i			0.168359i
$717$	10.3051	+	1.34008i	0.384852	+	0.0500462i
$718$	−12.5677			−0.469023
$719$	−35.5618			−1.32623			−0.663116	−	0.748517i	$-0.730766\pi$
$719$	−35.5618			−1.32623			−0.663116	+	0.748517i	$0.730766\pi$
$720$	26.2759	−	15.2817i	0.979245	−	0.569515i
$721$	−11.7473	+	11.7473i	−0.437491	+	0.437491i
$722$	8.50058	−	8.50058i	0.316359	−	0.316359i
$723$	42.3873	+	5.51205i	1.57640	+	0.204995i
$724$	2.56883			0.0954696
$725$	−15.0587			−0.559265
$726$	1.14407	−	8.79781i	0.0424603	−	0.326518i
$727$		−	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
$730$	−13.6622	+	13.6622i	−0.505660	+	0.505660i
$731$			2.31755i			0.0857178i
$732$	−0.788584	−	1.02434i	−0.0291469	−	0.0378606i
$733$	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	$0.202250\pi$
$734$	−11.1650	−	11.1650i	−0.412109	−	0.412109i
$735$	1.02767	−	7.90271i	0.0379061	−	0.291496i
$736$	3.62099	+	3.62099i	0.133471	+	0.133471i
$737$		−	20.1064i		−	0.740629i
$738$	−14.5067	−	3.83780i	−0.533999	−	0.141271i
$739$	14.5261	+	14.5261i	0.534352	+	0.534352i	0.921865	−	0.387512i	$-0.126665\pi$
$739$	14.5261	+	14.5261i	0.534352	+	0.534352i	−0.387512	+	0.921865i	$0.626665\pi$
$740$	−4.23811			−0.155796
$741$		0			0
$742$	52.2565			1.91840
$743$	24.3184	+	24.3184i	0.892156	+	0.892156i	0.994726	−	0.102570i	$-0.0327065\pi$
$743$	24.3184	+	24.3184i	0.892156	+	0.892156i	−0.102570	+	0.994726i	$0.532706\pi$
$744$	2.45854	+	3.19354i	0.0901345	+	0.117081i
$745$			47.4175i			1.73724i
$746$	12.4015	+	12.4015i	0.454051	+	0.454051i
$747$	−6.74869	+	3.92494i	−0.246922	+	0.143606i
$748$	−0.103511	−	0.103511i	−0.00378473	−	0.00378473i
$749$	16.0445	−	16.0445i	0.586252	−	0.586252i
$750$	−5.23014	+	4.02642i	−0.190978	+	0.147024i
$751$			29.8891i			1.09067i	0.838219	+	0.545334i	$0.183597\pi$
$751$			29.8891i			1.09067i	−0.838219	+	0.545334i	$0.816403\pi$
$752$	14.4813	−	14.4813i	0.528077	−	0.528077i
$753$	−29.8233	+	22.9594i	−1.08682	+	0.836687i
$754$		0			0
$755$			36.4243i			1.32562i
$756$	3.88213	+	1.58644i	0.141192	+	0.0576983i
$757$	22.3067			0.810752			0.405376	−	0.914150i	$-0.367141\pi$
$757$	22.3067			0.810752			0.405376	+	0.914150i	$0.367141\pi$
$758$	40.6567			1.47672
$759$	1.96424	−	15.1049i	0.0712975	−	0.548274i
$760$	−33.7043	+	33.7043i	−1.22258	+	1.22258i
$761$	−18.7246	+	18.7246i	−0.678767	+	0.678767i	−0.959721	−	0.280954i	$-0.909349\pi$
$761$	−18.7246	+	18.7246i	−0.678767	+	0.678767i	0.280954	+	0.959721i	$0.409349\pi$
$762$	2.82251	−	21.7050i	0.102249	−	0.786288i
$763$	−29.6721			−1.07420
$764$	−0.560481			−0.0202775
$765$	1.54985	−	0.901368i	0.0560348	−	0.0325890i
$766$			13.4621i			0.486404i
$767$		0			0
$768$	8.92027	−	6.86726i	0.321882	−	0.247801i
$769$	−8.68256	+	8.68256i	−0.313101	+	0.313101i	−0.846110	−	0.533009i	$-0.821061\pi$
$769$	−8.68256	+	8.68256i	−0.313101	+	0.313101i	0.533009	+	0.846110i	$0.321061\pi$
$770$			30.7081i			1.10664i
$771$	−22.3864	+	17.2341i	−0.806225	+	0.620671i
$772$	−0.776254	+	0.776254i	−0.0279380	+	0.0279380i
$773$	−16.3016	−	16.3016i	−0.586326	−	0.586326i	0.350308	−	0.936634i	$-0.386077\pi$
$773$	−16.3016	−	16.3016i	−0.586326	−	0.586326i	−0.936634	+	0.350308i	$0.886077\pi$
$774$	23.0801	+	39.6847i	0.829596	+	1.42644i
$775$	2.22108	+	2.22108i	0.0797837	+	0.0797837i
$776$		−	36.3531i		−	1.30500i
$777$	15.7468	+	20.4545i	0.564915	+	0.733800i
$778$	27.9502	+	27.9502i	1.00206	+	1.00206i
$779$	20.2162			0.724321
$780$		0			0
$781$	−14.2476			−0.509818
$782$	−0.609276	−	0.609276i	−0.0217877	−	0.0217877i
$783$	−17.8836	+	7.50746i	−0.639106	+	0.268295i
$784$			5.16019i			0.184293i
$785$	−6.94420	−	6.94420i	−0.247849	−	0.247849i
$786$	3.48993	−	26.8374i	0.124482	−	0.957258i
$787$	35.0163	+	35.0163i	1.24819	+	1.24819i	0.956516	+	0.291678i	$0.0942137\pi$
$787$	35.0163	+	35.0163i	1.24819	+	1.24819i	0.291678	+	0.956516i	$0.405786\pi$
$788$	−1.34625	+	1.34625i	−0.0479581	+	0.0479581i
$789$	−12.1467	−	15.7780i	−0.432434	−	0.561713i
$790$		−	43.9508i		−	1.56370i
$791$	35.2911	−	35.2911i	1.25481	−	1.25481i
$792$	−23.0929	−	6.10931i	−0.820570	−	0.217085i
$793$		0			0
$794$			4.50589i			0.159908i
$795$	−9.14877	+	70.3535i	−0.324473	+	2.49518i
$796$	1.75209			0.0621012
$797$	−5.10731			−0.180910			−0.0904550	−	0.995901i	$-0.528832\pi$
$797$	−5.10731			−0.180910			−0.0904550	+	0.995901i	$0.528832\pi$
$798$	34.9487	+	4.54473i	1.23717	+	0.160882i
$799$	0.854157	−	0.854157i	0.0302179	−	0.0302179i
$800$	4.42568	−	4.42568i	0.156472	−	0.156472i
$801$	1.65700	+	2.84911i	0.0585472	+	0.100668i
$802$	26.1951			0.924982
$803$	13.0450			0.460349
$804$	3.58178	+	0.465774i	0.126319	+	0.0164266i
$805$		−	28.9772i		−	1.02131i
$806$		0			0
$807$	−11.7692	−	15.2877i	−0.414295	−	0.538151i
$808$	26.1910	−	26.1910i	0.921398	−	0.921398i
$809$		−	0.250395i		−	0.00880341i	−0.999990	−	0.00440171i	$-0.998599\pi$
$809$		−	0.250395i		−	0.00880341i	0.999990	−	0.00440171i	$-0.00140111\pi$
$810$	17.5623	−	30.8692i	0.617076	−	1.08463i
$811$	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	$0.247273\pi$
$812$	2.13023	+	2.13023i	0.0747563	+	0.0747563i
$813$	10.4372	+	1.35726i	0.366050	+	0.0476011i
$814$	−12.6210	−	12.6210i	−0.442364	−	0.442364i
$815$		−	17.5182i		−	0.613637i
$816$	−0.919902	+	0.708186i	−0.0322030	+	0.0247915i
$817$	−43.7339	−	43.7339i	−1.53005	−	1.53005i
$818$	7.27498			0.254364
$819$		0			0
$820$	−3.16436			−0.110504
$821$	−20.3341	−	20.3341i	−0.709665	−	0.709665i	0.256799	−	0.966465i	$-0.417332\pi$
$821$	−20.3341	−	20.3341i	−0.709665	−	0.709665i	−0.966465	+	0.256799i	$0.917332\pi$
$822$	−31.3447	+	24.1307i	−1.09327	+	0.841655i
$823$			2.01893i			0.0703754i	0.999381	+	0.0351877i	$0.0112029\pi$
$823$			2.01893i			0.0703754i	−0.999381	+	0.0351877i	$0.988797\pi$
$824$	12.0200	+	12.0200i	0.418737	+	0.418737i
$825$	−18.4617	−	2.40076i	−0.642754	−	0.0835837i
$826$	−9.05248	−	9.05248i	−0.314976	−	0.314976i
$827$	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	$0.244856\pi$
$828$	2.64530	+	0.699824i	0.0919306	+	0.0243206i
$829$			46.5124i			1.61544i	0.589564	+	0.807722i	$0.299300\pi$
$829$			46.5124i			1.61544i	−0.589564	+	0.807722i	$0.700700\pi$
$830$	7.26148	−	7.26148i	0.252049	−	0.252049i
$831$	29.3530	+	38.1282i	1.01824	+	1.32265i
$832$		0			0
$833$			0.304367i			0.0105457i
$834$	−5.25201	−	0.682971i	−0.181862	−	0.0236493i
$835$	4.75274			0.164475
$836$	3.90664			0.135114
$837$	3.74506	+	1.53043i	0.129448	+	0.0528993i
$838$	−31.9668	+	31.9668i	−1.10428	+	1.10428i
$839$	−30.7448	+	30.7448i	−1.06143	+	1.06143i	−0.0634447	+	0.997985i	$0.520209\pi$
$839$	−30.7448	+	30.7448i	−1.06143	+	1.06143i	−0.997985	+	0.0634447i	$0.979791\pi$
$840$	−45.0633	−	5.86003i	−1.55483	−	0.202190i
$841$	15.0673			0.519561
$842$	−34.5613			−1.19106
$843$	−3.67002	+	28.2222i	−0.126402	+	0.972026i
$844$			0.221693i			0.00763098i
$845$		0			0
$846$	6.11981	−	23.1326i	0.210403	−	0.795314i
$847$	−8.05764	+	8.05764i	−0.276864	+	0.276864i
$848$		−	45.9383i		−	1.57753i
$849$	−28.0915	−	36.4896i	−0.964097	−	1.25232i
$850$	−0.744677	+	0.744677i	−0.0255422	+	0.0255422i
$851$	11.9096	+	11.9096i	0.408254	+	0.408254i
$852$	0.330052	−	2.53808i	0.0113074	−	0.0869531i
$853$	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	$0.749853\pi$
$854$		−	10.3571i		−	0.354411i
$855$	−12.2372	+	46.2561i	−0.418505	+	1.58193i
$856$	−16.4170	−	16.4170i	−0.561121	−	0.561121i
$857$	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	$0.436401\pi$
$860$	6.84547	+	6.84547i	0.233429	+	0.233429i
$861$	11.7573	+	15.2722i	0.400687	+	0.520475i
$862$			14.8468i			0.505685i
$863$	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	$0.590935\pi$
$864$	3.04950	−	7.46232i	0.103746	−	0.253873i
$865$	−26.4038	−	26.4038i	−0.897755	−	0.897755i
$866$	5.76148	−	5.76148i	0.195783	−	0.195783i
$867$	23.2775	−	17.9201i	0.790544	−	0.608600i
$868$		−	0.628398i		−	0.0213292i
$869$	−20.9827	+	20.9827i	−0.711790	+	0.711790i
$870$	20.2158	−	15.5631i	0.685379	−	0.527638i
$871$		0			0
$872$			30.3610i			1.02815i
$873$	−18.3462	−	31.5452i	−0.620925	−	1.06764i
$874$	22.9949			0.777815
$875$	8.47779			0.286601
$876$	−0.302194	+	2.32385i	−0.0102102	+	0.0785158i
$877$	9.85124	−	9.85124i	0.332653	−	0.332653i	−0.520940	−	0.853593i	$-0.674419\pi$
$877$	9.85124	−	9.85124i	0.332653	−	0.332653i	0.853593	+	0.520940i	$0.174419\pi$
$878$	36.0040	−	36.0040i	1.21508	−	1.21508i
$879$	−0.646595	+	4.97228i	−0.0218091	+	0.167711i
$880$	26.9953			0.910010
$881$	7.66652			0.258292			0.129146	−	0.991626i	$-0.458776\pi$
$881$	7.66652			0.258292			0.129146	+	0.991626i	$0.458776\pi$
$882$	3.03113	+	5.21183i	0.102063	+	0.175492i
$883$		−	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
$886$	17.0011	−	17.0011i	0.571162	−	0.571162i
$887$		−	42.1524i		−	1.41534i	−0.706543	−	0.707670i	$-0.749746\pi$
$887$		−	42.1524i		−	1.41534i	0.706543	−	0.707670i	$-0.250254\pi$
$888$	20.9294	−	16.1125i	0.702344	−	0.540699i
$889$	−19.8789	+	19.8789i	−0.666716	+	0.666716i
$890$	−3.06559	−	3.06559i	−0.102759	−	0.102759i
$891$	−23.1219	+	6.35291i	−0.774612	+	0.212831i
$892$	−0.603784	−	0.603784i	−0.0202162	−	0.0202162i
$893$			32.2371i			1.07877i
$894$	−21.8838	−	28.4260i	−0.731902	−	0.950709i
$895$	−34.6494	−	34.6494i	−1.15820	−	1.15820i
$896$	24.6007			0.821850
$897$		0			0
$898$	−2.54586			−0.0849564
$899$	2.05501	+	2.05501i	0.0685385	+	0.0685385i
$900$	0.855348	−	3.23317i	0.0285116	−	0.107772i
$901$		−	2.70961i		−	0.0902701i
$902$	−9.42336	−	9.42336i	−0.313764	−	0.313764i
$903$	7.60383	−	58.4731i	0.253040	−	1.94586i
$904$	−36.1105	−	36.1105i	−1.20102	−	1.20102i
$905$	−19.7578	+	19.7578i	−0.656771	+	0.656771i
$906$	−16.8103	−	21.8358i	−0.558483	−	0.725445i
$907$		−	37.3530i		−	1.24029i	−0.784489	−	0.620143i	$-0.787075\pi$
$907$		−	37.3530i		−	1.24029i	0.784489	−	0.620143i	$-0.212925\pi$
$908$	−5.06355	+	5.06355i	−0.168040	+	0.168040i
$909$	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	$0.889161\pi$
$912$	3.99524	−	30.7232i	0.132296	−	1.01735i
$913$	−6.93345			−0.229464
$914$	−7.65050			−0.253056
$915$	13.9438	+	1.81326i	0.460969	+	0.0599444i
$916$	−5.42741	+	5.42741i	−0.179327	+	0.179327i
$917$	−24.5795	+	24.5795i	−0.811687	+	0.811687i
$918$	−0.513116	+	1.25563i	−0.0169353	+	0.0414419i
$919$	−39.3357			−1.29756			−0.648782	−	0.760974i	$-0.724721\pi$
$919$	−39.3357			−1.29756			−0.648782	+	0.760974i	$0.724721\pi$
$920$	−29.6500			−0.977531
$921$	−33.9009	−	4.40848i	−1.11707	−	0.145264i
$922$			18.7869i			0.618715i
$923$		0			0
$924$	2.27201	+	2.95124i	0.0747437	+	0.0970888i
$925$	14.5562	−	14.5562i	0.478606	−	0.478606i
$926$			5.55224i			0.182458i
$927$	16.4964	+	4.36418i	0.541813	+	0.143339i
$928$	4.09478	−	4.09478i	0.134418	−	0.134418i
$929$	−14.8752	−	14.8752i	−0.488041	−	0.488041i	0.419647	−	0.907688i	$-0.362154\pi$
$929$	−14.8752	−	14.8752i	−0.488041	−	0.488041i	−0.907688	+	0.419647i	$0.862154\pi$
$930$	−5.27722	−	0.686250i	−0.173047	−	0.0225030i
$931$	−5.74361	−	5.74361i	−0.188239	−	0.188239i
$932$			3.99439i			0.130841i
$933$	37.0227	−	28.5019i	1.21207	−	0.933110i
$934$	34.8228	+	34.8228i	1.13944	+	1.13944i
$935$	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	$0.489317\pi$
$938$	20.4624	+	20.4624i	0.668121	+	0.668121i
$939$	32.8923	−	25.3221i	1.07340	−	0.826355i
$940$		−	5.04593i		−	0.164580i
$941$	−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	$-0.652172\pi$
$942$	7.36777	+	0.958105i	0.240055	+	0.0312167i
$943$	8.89220	+	8.89220i	0.289570	+	0.289570i
$944$	−7.95798	+	7.95798i	−0.259010	+	0.259010i
$945$	−42.0608	+	17.6570i	−1.36824	+	0.574382i
$946$			40.7712i			1.32559i
$947$	21.4029	−	21.4029i	0.695502	−	0.695502i	−0.267935	−	0.963437i	$-0.586341\pi$
$947$	21.4029	−	21.4029i	0.695502	−	0.695502i	0.963437	+	0.267935i	$0.0863412\pi$
$948$	−3.25181	−	4.22395i	−0.105614	−	0.137188i
$949$		0			0
$950$		−	28.1052i		−	0.911852i
$951$	−52.6856	−	6.85123i	−1.70845	−	0.222166i
$952$	1.73558			0.0562504
$953$	−9.48367			−0.307206			−0.153603	−	0.988133i	$-0.549088\pi$
$953$	−9.48367			−0.307206			−0.153603	+	0.988133i	$0.549088\pi$
$954$	−26.9845	−	46.3981i	−0.873654	−	1.50219i
$955$	4.31087	−	4.31087i	0.139496	−	0.139496i
$956$	−1.17233	+	1.17233i	−0.0379157	+	0.0379157i
$957$	−17.0813	−	2.22125i	−0.552161	−	0.0718030i
$958$	2.68132			0.0866295
$959$	50.8082			1.64068
$960$	−5.89356	+	45.3212i	−0.190214	+	1.46273i
$961$			30.3938i			0.980445i
$962$		0			0
$963$	−22.5308	−	5.96062i	−0.726046	−	0.192078i
$964$	−4.82204	+	4.82204i	−0.155307	+	0.155307i
$965$		−	11.9409i		−	0.384392i
$966$	13.3733	+	17.3714i	0.430280	+	0.558914i
$967$	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	$0.117419\pi$
$968$	8.24472	+	8.24472i	0.264995	+	0.264995i
$969$	0.235654	−	1.81216i	0.00757028	−	0.0582150i
$970$	33.9421	+	33.9421i	1.08981	+	1.08981i
$971$			18.5328i			0.594745i	0.954761	+	0.297373i	$0.0961104\pi$
$971$			18.5328i			0.594745i	−0.954761	+	0.297373i	$0.903890\pi$
$972$	−0.596086	−	4.26612i	−0.0191195	−	0.136836i
$973$	4.81014	+	4.81014i	0.154206	+	0.154206i
$974$	−32.9285			−1.05510
$975$		0			0
$976$	−9.10483			−0.291439
$977$	21.7724	+	21.7724i	0.696561	+	0.696561i	0.963667	−	0.267107i	$-0.0860676\pi$
$977$	21.7724	+	21.7724i	0.696561	+	0.696561i	−0.267107	+	0.963667i	$0.586068\pi$
$978$	8.08488	+	10.5019i	0.258526	+	0.335814i
$979$			2.92711i			0.0935508i
$980$	0.899023	+	0.899023i	0.0287182	+	0.0287182i
$981$	15.3222	+	26.3456i	0.489201	+	0.841151i
$982$	−6.99249	−	6.99249i	−0.223139	−	0.223139i
$983$	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	$0.107903\pi$
$984$	15.6268	−	12.0303i	0.498164	−	0.383511i
$985$		−	20.7090i		−	0.659843i
$986$	−0.688997	+	0.688997i	−0.0219421	+	0.0219421i
$987$	−24.3533	+	18.7483i	−0.775173	+	0.596766i
$988$		0			0
$989$		−	38.4731i		−	1.22337i
$990$	27.2654	−	15.8572i	0.866552	−	0.503974i
$991$	6.24334			0.198326			0.0991631	−	0.995071i	$-0.468383\pi$
$991$	6.24334			0.198326			0.0991631	+	0.995071i	$0.468383\pi$
$992$	−1.20792			−0.0383515
$993$	−0.148213	+	1.13975i	−0.00470341	+	0.0361689i
$994$	14.4998	−	14.4998i	0.459907	−	0.459907i
$995$	−13.4760	+	13.4760i	−0.427217	+	0.427217i
$996$	0.160617	−	1.23513i	0.00508933	−	0.0391367i
$997$	−1.83522			−0.0581220			−0.0290610	−	0.999578i	$-0.509252\pi$
$997$	−1.83522			−0.0581220			−0.0290610	+	0.999578i	$0.509252\pi$
$998$	−16.1819			−0.512228
$999$	10.0299	−	24.5439i	0.317332	−	0.776534i

Twists

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

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

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.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.928351 + 0.928351i) q^{2} +(-1.37245 + 1.05658i) q^{3} -0.276330i q^{4} +(2.12536 + 2.12536i) q^{5} +(-2.25500 - 0.293240i) q^{6} +(2.06528 + 2.06528i) q^{7} +(2.11323 - 2.11323i) q^{8} +(0.767265 - 2.90022i) q^{9} +3.94616i q^{10} +(1.88395 - 1.88395i) q^{11} +(0.291966 + 0.379251i) q^{12} +3.83461i q^{14} +(-5.16258 - 0.671341i) q^{15} +3.37098 q^{16} +0.198832 q^{17} +(3.40472 - 1.98013i) q^{18} +(-3.75211 + 3.75211i) q^{19} +(0.587301 - 0.587301i) q^{20} +(-5.01665 - 0.652364i) q^{21} +3.49793 q^{22} -3.30077 q^{23} +(-0.667511 + 5.13312i) q^{24} +4.03430i q^{25} +(2.01129 + 4.79111i) q^{27} +(0.570700 - 0.570700i) q^{28} +3.73266i q^{29} +(-4.16944 - 5.41592i) q^{30} +(0.550550 - 0.550550i) q^{31} +(-1.09701 - 1.09701i) q^{32} +(-0.595087 + 4.57618i) q^{33} +(0.184586 + 0.184586i) q^{34} +8.77893i q^{35} +(-0.801420 - 0.212019i) q^{36} +(-3.60812 - 3.60812i) q^{37} -6.96655 q^{38} +8.98276 q^{40} +(-2.69398 - 2.69398i) q^{41} +(-4.05158 - 5.26283i) q^{42} +11.6558i q^{43} +(-0.520592 - 0.520592i) q^{44} +(7.79473 - 4.53331i) q^{45} +(-3.06427 - 3.06427i) q^{46} +(4.29586 - 4.29586i) q^{47} +(-4.62652 + 3.56172i) q^{48} +1.53077i q^{49} +(-3.74525 + 3.74525i) q^{50} +(-0.272889 + 0.210083i) q^{51} -13.6276i q^{53} +(-2.58064 + 6.31501i) q^{54} +8.00814 q^{55} +8.72884 q^{56} +(1.18519 - 9.11402i) q^{57} +(-3.46521 + 3.46521i) q^{58} +(-2.36073 + 2.36073i) q^{59} +(-0.185512 + 1.42658i) q^{60} -2.70094 q^{61} +1.02221 q^{62} +(7.57440 - 4.40516i) q^{63} -8.77879i q^{64} +(-4.80075 + 3.69585i) q^{66} +(5.33624 - 5.33624i) q^{67} -0.0549435i q^{68} +(4.53015 - 3.48753i) q^{69} +(-8.14992 + 8.14992i) q^{70} +(-3.78131 - 3.78131i) q^{71} +(-4.50744 - 7.75026i) q^{72} +(3.46215 + 3.46215i) q^{73} -6.69920i q^{74} +(-4.26258 - 5.53690i) q^{75} +(1.03682 + 1.03682i) q^{76} +7.78177 q^{77} -11.1376 q^{79} +(7.16454 + 7.16454i) q^{80} +(-7.82261 - 4.45048i) q^{81} -5.00192i q^{82} +(-1.84014 - 1.84014i) q^{83} +(-0.180268 + 1.38625i) q^{84} +(0.422590 + 0.422590i) q^{85} +(-10.8207 + 10.8207i) q^{86} +(-3.94386 - 5.12290i) q^{87} -7.96245i q^{88} +(-0.776855 + 0.776855i) q^{89} +(11.4447 + 3.02775i) q^{90} +0.912102i q^{92} +(-0.173903 + 1.33731i) q^{93} +7.97613 q^{94} -15.9492 q^{95} +(2.66469 + 0.346516i) q^{96} +(8.60129 - 8.60129i) q^{97} +(-1.42109 + 1.42109i) q^{98} +(-4.01839 - 6.90936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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