LMFDB - Embedded newform 570.2.bb.a.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.6
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.a.281.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.398282 - 1.68564i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.950784 + 1.44776i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.68274 + 1.34272i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.398282 - 1.68564i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.950784 + 1.44776i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.68274 + 1.34272i) q^{9} +(0.342020 - 0.939693i) q^{10} +(1.46419 + 0.845352i) q^{11} +(-1.38861 - 1.03526i) q^{12} +(-6.08847 + 1.07356i) q^{13} +(3.47540 + 2.91621i) q^{14} +(1.54728 + 0.778405i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.48626 + 6.83093i) q^{17} +(2.06172 - 2.17929i) q^{18} +(4.00488 + 1.72073i) q^{19} +1.00000i q^{20} +(-5.71939 + 5.38855i) q^{21} +(-1.66502 - 0.293587i) q^{22} +(-3.51661 - 4.19093i) q^{23} +(1.65895 + 0.497896i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(5.35411 - 3.09120i) q^{26} +(3.33182 + 3.98735i) q^{27} +(-4.26321 - 1.55168i) q^{28} +(0.0705953 + 0.0256946i) q^{29} +(-1.72020 - 0.202260i) q^{30} +(-0.204974 + 0.118342i) q^{31} +(0.173648 + 0.984808i) q^{32} +(0.841795 - 2.80478i) q^{33} +(-4.67263 - 5.56863i) q^{34} +(4.46789 + 0.787809i) q^{35} +(-1.19202 + 2.75301i) q^{36} -0.00698184i q^{37} +(-4.35188 - 0.247203i) q^{38} +(4.23456 + 9.83538i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-0.549253 + 3.11497i) q^{41} +(3.53148 - 7.01973i) q^{42} +(0.125793 + 0.105553i) q^{43} +(1.66502 - 0.293587i) q^{44} +(0.695854 - 2.91818i) q^{45} +(4.73792 + 2.73544i) q^{46} +(-4.05435 + 11.1392i) q^{47} +(-1.72919 + 0.0995230i) q^{48} +(-6.79132 + 11.7629i) q^{49} +(0.500000 + 0.866025i) q^{50} +(10.5242 - 6.91156i) q^{51} +(-3.97397 + 4.73599i) q^{52} +(-2.78447 + 2.33645i) q^{53} +(-4.49464 - 2.60734i) q^{54} +(-1.58874 + 0.578254i) q^{55} +4.53681 q^{56} +(1.30545 - 7.43611i) q^{57} -0.0751260 q^{58} +(-7.99509 + 2.90997i) q^{59} +(1.68564 - 0.398282i) q^{60} +(-4.59785 + 3.85805i) q^{61} +(0.152137 - 0.181310i) q^{62} +(11.3611 + 7.49466i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.09120 - 5.35411i) q^{65} +(0.168264 + 2.92355i) q^{66} +(-3.16159 + 8.68641i) q^{67} +(6.29542 + 3.63466i) q^{68} +(-5.66379 + 7.59690i) q^{69} +(-4.46789 + 0.787809i) q^{70} +(-9.83511 - 8.25264i) q^{71} +(0.178545 - 2.99468i) q^{72} +(2.59990 - 14.7447i) q^{73} +(0.00238793 + 0.00656079i) q^{74} +(-1.59087 + 0.684939i) q^{75} +(4.17398 - 1.25614i) q^{76} -7.67040i q^{77} +(-7.34308 - 7.79392i) q^{78} +(-0.925456 - 0.163183i) q^{79} +(0.642788 + 0.766044i) q^{80} +(5.39423 - 7.20433i) q^{81} +(-0.549253 - 3.11497i) q^{82} +(8.21102 - 4.74063i) q^{83} +(-0.917613 + 7.80423i) q^{84} +(-6.83093 - 2.48626i) q^{85} +(-0.154308 - 0.0561635i) q^{86} +(0.0151949 - 0.129232i) q^{87} +(-1.46419 + 0.845352i) q^{88} +(0.540172 + 3.06346i) q^{89} +(0.344188 + 2.98019i) q^{90} +(18.0291 + 21.4863i) q^{91} +(-5.38776 - 0.950007i) q^{92} +(0.281119 + 0.298379i) q^{93} -11.8541i q^{94} +(-3.89244 + 1.96186i) q^{95} +(1.59087 - 0.684939i) q^{96} +(-1.96196 - 5.39044i) q^{97} +(2.35860 - 13.3763i) q^{98} +(-5.06312 - 0.301867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−0.398282	−	1.68564i	−0.229948	−	0.973203i
$3$	−0.398282	−	1.68564i	−0.229948	−	0.973203i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.642788	+	0.766044i	−0.287463	+	0.342585i
$5$	−0.642788	+	0.766044i	−0.287463	+	0.342585i
$6$	0.950784	+	1.44776i	0.388156	+	0.591046i
$7$	−2.26841	−	3.92899i	−0.857377	−	1.48502i	−0.874423	−	0.485165i	$-0.838759\pi$
$7$	−2.26841	−	3.92899i	−0.857377	−	1.48502i	0.0170460	−	0.999855i	$-0.494574\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.68274	+	1.34272i	−0.894248	+	0.447572i
$10$	0.342020	−	0.939693i	0.108156	−	0.297157i
$11$	1.46419	+	0.845352i	0.441470	+	0.254883i	0.704221	−	0.709981i	$-0.251296\pi$
$11$	1.46419	+	0.845352i	0.441470	+	0.254883i	−0.262751	+	0.964864i	$0.584630\pi$
$12$	−1.38861	−	1.03526i	−0.400857	−	0.298854i
$13$	−6.08847	+	1.07356i	−1.68864	+	0.297753i	−0.933704	−	0.358047i	$-0.883443\pi$
$13$	−6.08847	+	1.07356i	−1.68864	+	0.297753i	−0.754935	+	0.655799i	$0.772332\pi$
$14$	3.47540	+	2.91621i	0.928839	+	0.779389i
$15$	1.54728	+	0.778405i	0.399507	+	0.200983i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	2.48626	+	6.83093i	0.603006	+	1.65674i	0.745149	+	0.666899i	$0.232379\pi$
$17$	2.48626	+	6.83093i	0.603006	+	1.65674i	−0.142143	+	0.989846i	$0.545399\pi$
$18$	2.06172	−	2.17929i	0.485952	−	0.513664i
$19$	4.00488	+	1.72073i	0.918783	+	0.394762i
$19$	4.00488	+	1.72073i	0.918783	+	0.394762i
$20$			1.00000i			0.223607i
$21$	−5.71939	+	5.38855i	−1.24807	+	1.17588i
$22$	−1.66502	−	0.293587i	−0.354983	−	0.0625931i
$23$	−3.51661	−	4.19093i	−0.733264	−	0.873870i	0.262583	−	0.964909i	$-0.415426\pi$
$23$	−3.51661	−	4.19093i	−0.733264	−	0.873870i	−0.995847	+	0.0910394i	$0.970981\pi$
$24$	1.65895	+	0.497896i	0.338631	+	0.101633i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	5.35411	−	3.09120i	1.05003	−	0.606234i
$27$	3.33182	+	3.98735i	0.641209	+	0.767366i
$28$	−4.26321	−	1.55168i	−0.805670	−	0.293240i
$29$	0.0705953	+	0.0256946i	0.0131092	+	0.00477137i	0.348566	−	0.937284i	$-0.386669\pi$
$29$	0.0705953	+	0.0256946i	0.0131092	+	0.00477137i	−0.335457	+	0.942055i	$0.608891\pi$
$30$	−1.72020	−	0.202260i	−0.314064	−	0.0369274i
$31$	−0.204974	+	0.118342i	−0.0368144	+	0.0212548i	−0.518294	−	0.855202i	$-0.673433\pi$
$31$	−0.204974	+	0.118342i	−0.0368144	+	0.0212548i	0.481480	+	0.876457i	$0.340099\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	0.841795	−	2.80478i	0.146538	−	0.488250i
$34$	−4.67263	−	5.56863i	−0.801350	−	0.955012i
$35$	4.46789	+	0.787809i	0.755211	+	0.133164i
$36$	−1.19202	+	2.75301i	−0.198670	+	0.458836i
$37$		−	0.00698184i		−	0.00114781i	−1.00000		0.000573904i	$-0.999817\pi$
$37$		−	0.00698184i		−	0.00114781i	1.00000		0.000573904i	$-0.000182679\pi$
$38$	−4.35188	−	0.247203i	−0.705969	−	0.0401017i
$39$	4.23456	+	9.83538i	0.678073	+	1.57492i
$40$	−0.342020	−	0.939693i	−0.0540781	−	0.148578i
$41$	−0.549253	+	3.11497i	−0.0857789	+	0.486476i	0.911407	+	0.411506i	$0.134997\pi$
$41$	−0.549253	+	3.11497i	−0.0857789	+	0.486476i	−0.997186	+	0.0749699i	$0.976114\pi$
$42$	3.53148	−	7.01973i	0.544919	−	1.08317i
$43$	0.125793	+	0.105553i	0.0191833	+	0.0160967i	0.652329	−	0.757936i	$-0.273792\pi$
$43$	0.125793	+	0.105553i	0.0191833	+	0.0160967i	−0.633146	+	0.774033i	$0.718237\pi$
$44$	1.66502	−	0.293587i	0.251011	−	0.0442600i
$45$	0.695854	−	2.91818i	0.103732	−	0.435017i
$46$	4.73792	+	2.73544i	0.698568	+	0.403318i
$47$	−4.05435	+	11.1392i	−0.591388	+	1.62483i	0.176542	+	0.984293i	$0.443509\pi$
$47$	−4.05435	+	11.1392i	−0.591388	+	1.62483i	−0.767931	+	0.640533i	$0.778713\pi$
$48$	−1.72919	+	0.0995230i	−0.249587	+	0.0143649i
$49$	−6.79132	+	11.7629i	−0.970189	+	1.68042i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	10.5242	−	6.91156i	1.47369	−	0.967812i
$52$	−3.97397	+	4.73599i	−0.551090	+	0.656764i
$53$	−2.78447	+	2.33645i	−0.382477	+	0.320936i	−0.813674	−	0.581322i	$-0.802536\pi$
$53$	−2.78447	+	2.33645i	−0.382477	+	0.320936i	0.431197	+	0.902258i	$0.358091\pi$
$54$	−4.49464	−	2.60734i	−0.611643	−	0.354814i
$55$	−1.58874	+	0.578254i	−0.214226	+	0.0779718i
$56$	4.53681			0.606257
$57$	1.30545	−	7.43611i	0.172911	−	0.984937i
$58$	−0.0751260			−0.00986453
$59$	−7.99509	+	2.90997i	−1.04087	+	0.378846i	−0.805211	−	0.592989i	$-0.797948\pi$
$59$	−7.99509	+	2.90997i	−1.04087	+	0.378846i	−0.235661	+	0.971835i	$0.575725\pi$
$60$	1.68564	−	0.398282i	0.217615	−	0.0514179i
$61$	−4.59785	+	3.85805i	−0.588694	+	0.493973i	−0.887789	−	0.460250i	$-0.847760\pi$
$61$	−4.59785	+	3.85805i	−0.588694	+	0.493973i	0.299095	+	0.954223i	$0.403315\pi$
$62$	0.152137	−	0.181310i	0.0193215	−	0.0230264i
$63$	11.3611	+	7.49466i	1.43136	+	0.944238i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.09120	−	5.35411i	0.383416	−	0.664096i
$66$	0.168264	+	2.92355i	0.0207118	+	0.359864i
$67$	−3.16159	+	8.68641i	−0.386250	+	1.06121i	0.582425	+	0.812884i	$0.302104\pi$
$67$	−3.16159	+	8.68641i	−0.386250	+	1.06121i	−0.968676	+	0.248330i	$0.920118\pi$
$68$	6.29542	+	3.63466i	0.763432	+	0.440768i
$69$	−5.66379	+	7.59690i	−0.681840	+	0.914559i
$70$	−4.46789	+	0.787809i	−0.534015	+	0.0941612i
$71$	−9.83511	−	8.25264i	−1.16721	−	0.979408i	−0.167234	−	0.985917i	$-0.553483\pi$
$71$	−9.83511	−	8.25264i	−1.16721	−	0.979408i	−0.999979	+	0.00650962i	$0.997928\pi$
$72$	0.178545	−	2.99468i	0.0210418	−	0.352927i
$73$	2.59990	−	14.7447i	0.304295	−	1.72574i	−0.322511	−	0.946566i	$-0.604527\pi$
$73$	2.59990	−	14.7447i	0.304295	−	1.72574i	0.626805	−	0.779176i	$-0.284362\pi$
$74$	0.00238793	+	0.00656079i	0.000277591	+	0.000762676i
$75$	−1.59087	+	0.684939i	−0.183698	+	0.0790899i
$76$	4.17398	−	1.25614i	0.478789	−	0.144089i
$77$		−	7.67040i		−	0.874123i
$78$	−7.34308	−	7.79392i	−0.831441	−	0.882488i
$79$	−0.925456	−	0.163183i	−0.104122	−	0.0183595i	0.121344	−	0.992610i	$-0.461279\pi$
$79$	−0.925456	−	0.163183i	−0.104122	−	0.0183595i	−0.225466	+	0.974251i	$0.572391\pi$
$80$	0.642788	+	0.766044i	0.0718658	+	0.0856464i
$81$	5.39423	−	7.20433i	0.599358	−	0.800481i
$82$	−0.549253	−	3.11497i	−0.0606548	−	0.343991i
$83$	8.21102	−	4.74063i	0.901276	−	0.520352i	0.0236622	−	0.999720i	$-0.492467\pi$
$83$	8.21102	−	4.74063i	0.901276	−	0.520352i	0.877614	+	0.479368i	$0.159134\pi$
$84$	−0.917613	+	7.80423i	−0.100120	+	0.851511i
$85$	−6.83093	−	2.48626i	−0.740919	−	0.269672i
$86$	−0.154308	−	0.0561635i	−0.0166395	−	0.00605627i
$87$	0.0151949	−	0.129232i	0.00162907	−	0.0138551i
$88$	−1.46419	+	0.845352i	−0.156083	+	0.0901148i
$89$	0.540172	+	3.06346i	0.0572581	+	0.324727i	0.999960	−	0.00890859i	$-0.00283573\pi$
$89$	0.540172	+	3.06346i	0.0572581	+	0.324727i	−0.942702	+	0.333635i	$0.891725\pi$
$90$	0.344188	+	2.98019i	0.0362806	+	0.314140i
$91$	18.0291	+	21.4863i	1.88997	+	2.25238i
$92$	−5.38776	−	0.950007i	−0.561713	−	0.0990451i
$93$	0.281119	+	0.298379i	0.0291507	+	0.0309404i
$94$		−	11.8541i		−	1.22266i
$95$	−3.89244	+	1.96186i	−0.399356	+	0.201282i
$96$	1.59087	−	0.684939i	0.162367	−	0.0699062i
$97$	−1.96196	−	5.39044i	−0.199207	−	0.547316i	0.799359	−	0.600854i	$-0.205173\pi$
$97$	−1.96196	−	5.39044i	−0.199207	−	0.547316i	−0.998566	+	0.0535375i	$0.982950\pi$
$98$	2.35860	−	13.3763i	0.238255	−	1.35121i
$99$	−5.06312	−	0.301867i	−0.508863	−	0.0303388i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	−11.0474	+	1.94795i	−1.09926	+	0.193828i	−0.693716	−	0.720249i	$-0.744028\pi$
$101$	−11.0474	+	1.94795i	−1.09926	+	0.193828i	−0.405540	+	0.914077i	$0.632916\pi$
$102$	−7.52566	+	10.0942i	−0.745151	+	0.999479i
$103$	−4.19723	−	2.42327i	−0.413566	−	0.238772i	0.278755	−	0.960362i	$-0.410078\pi$
$103$	−4.19723	−	2.42327i	−0.413566	−	0.238772i	−0.692321	+	0.721590i	$0.743412\pi$
$104$	2.11450	−	5.80955i	0.207344	−	0.569674i
$105$	−0.451517	−	7.84500i	−0.0440636	−	0.765594i
$106$	1.81744	−	3.14789i	0.176525	−	0.305750i
$107$	−3.66274	−	6.34406i	−0.354091	−	0.613303i	0.632871	−	0.774257i	$-0.281876\pi$
$107$	−3.66274	−	6.34406i	−0.354091	−	0.613303i	−0.986962	+	0.160954i	$0.948543\pi$
$108$	5.11534	+	0.912837i	0.492224	+	0.0878378i
$109$	−6.38928	+	7.61445i	−0.611982	+	0.729332i	−0.979670	−	0.200618i	$-0.935705\pi$
$109$	−6.38928	+	7.61445i	−0.611982	+	0.729332i	0.367688	+	0.929949i	$0.380150\pi$
$110$	1.29515	−	1.08676i	0.123488	−	0.103619i
$111$	−0.0117689	+	0.00278074i	−0.00111705	+	0.000263936i
$112$	−4.26321	+	1.55168i	−0.402835	+	0.146620i
$113$	−3.58755			−0.337488			−0.168744	−	0.985660i	$-0.553971\pi$
$113$	−3.58755			−0.337488			−0.168744	+	0.985660i	$0.553971\pi$
$114$	1.31658	+	7.43415i	0.123309	+	0.696272i
$115$	5.47087			0.510162
$116$	0.0705953	−	0.0256946i	0.00655461	−	0.00238568i
$117$	14.8923	−	11.0552i	1.37680	−	1.02205i
$118$	6.51765	−	5.46896i	0.599999	−	0.503459i
$119$	21.1989	−	25.2638i	1.94330	−	2.31593i
$120$	−1.44776	+	0.950784i	−0.132162	+	0.0867943i
$121$	−4.07076	−	7.05077i	−0.370069	−	0.640979i
$122$	3.00103	−	5.19794i	0.271701	−	0.470600i
$123$	5.46946	−	0.314793i	0.493165	−	0.0283840i
$124$	−0.0809506	+	0.222410i	−0.00726958	+	0.0199730i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	−13.2392	−	3.15696i	−1.17945	−	0.281244i
$127$	−0.723389	+	0.127553i	−0.0641904	+	0.0113185i	−0.205651	−	0.978625i	$-0.565931\pi$
$127$	−0.723389	+	0.127553i	−0.0641904	+	0.0113185i	0.141461	+	0.989944i	$0.454820\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	0.127823	−	0.254081i	0.0112542	−	0.0223706i
$130$	−1.07356	+	6.08847i	−0.0941576	+	0.533994i
$131$	−0.481979	−	1.32423i	−0.0421107	−	0.115698i	0.916855	−	0.399221i	$-0.130719\pi$
$131$	−0.481979	−	1.32423i	−0.0421107	−	0.115698i	−0.958966	+	0.283522i	$0.908497\pi$
$132$	−1.15803	−	2.68968i	−0.100793	−	0.234107i
$133$	−2.32398	−	19.6385i	−0.201514	−	1.70287i
$134$		−	9.24389i		−	0.798550i
$135$	−5.19614	−	0.0106990i	−0.447213	−	0.000920822i
$136$	−7.15889	−	1.26231i	−0.613870	−	0.108242i
$137$	5.91522	+	7.04949i	0.505372	+	0.602279i	0.957057	−	0.289899i	$-0.0936216\pi$
$137$	5.91522	+	7.04949i	0.505372	+	0.602279i	−0.451686	+	0.892177i	$0.649177\pi$
$138$	2.72393	−	9.07588i	0.231876	−	0.772590i
$139$	−3.07958	−	17.4652i	−0.261207	−	1.48138i	−0.779623	−	0.626249i	$-0.784589\pi$
$139$	−3.07958	−	17.4652i	−0.261207	−	1.48138i	0.518416	−	0.855129i	$-0.326522\pi$
$140$	3.92899	−	2.26841i	0.332061	−	0.191715i
$141$	20.3915	+	2.39761i	1.71727	+	0.201915i
$142$	12.0645	+	4.39114i	1.01243	+	0.368496i
$143$	−9.82223	−	3.57500i	−0.821376	−	0.298956i
$144$	0.856464	+	2.87515i	0.0713720	+	0.239596i
$145$	−0.0650610	+	0.0375630i	−0.00540302	+	0.00311944i
$146$	2.59990	+	14.7447i	0.215169	+	1.22028i
$147$	22.5329	+	6.76275i	1.85848	+	0.557782i
$148$	−0.00448784	−	0.00534840i	−0.000368898	−	0.000439636i
$149$	−0.442672	−	0.0780551i	−0.0362651	−	0.00639452i	0.155486	−	0.987838i	$-0.450306\pi$
$149$	−0.442672	−	0.0780551i	−0.0362651	−	0.00639452i	−0.191751	+	0.981444i	$0.561417\pi$
$150$	1.26066	−	1.18774i	0.102933	−	0.0969786i
$151$			6.73441i			0.548039i	0.961724	+	0.274019i	$0.0883532\pi$
$151$			6.73441i			0.548039i	−0.961724	+	0.274019i	$0.911647\pi$
$152$	−3.49264	+	2.60797i	−0.283290	+	0.211534i
$153$	−15.8420	−	14.9873i	−1.28075	−	1.21165i
$154$	2.62343	+	7.20782i	0.211402	+	0.580822i
$155$	0.0410997	−	0.233088i	0.00330121	−	0.0187221i
$156$	9.56592	+	4.81241i	0.765887	+	0.385301i
$157$	10.9028	+	9.14857i	0.870141	+	0.730135i	0.964128	−	0.265438i	$-0.0855167\pi$
$157$	10.9028	+	9.14857i	0.870141	+	0.730135i	−0.0939868	+	0.995573i	$0.529961\pi$
$158$	0.925456	−	0.163183i	0.0736253	−	0.0129821i
$159$	5.04741	+	3.76304i	0.400286	+	0.298429i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−8.48905	+	23.3235i	−0.669031	+	1.83815i
$162$	−2.60489	+	8.61479i	−0.204659	+	0.676842i
$163$	0.547434	−	0.948183i	0.0428783	−	0.0742674i	−0.843790	−	0.536674i	$-0.819681\pi$
$163$	0.547434	−	0.948183i	0.0428783	−	0.0742674i	0.886668	+	0.462406i	$0.153014\pi$
$164$	1.58151	+	2.73926i	0.123495	+	0.213900i
$165$	1.60749	+	2.44773i	0.125143	+	0.190556i
$166$	−6.09444	+	7.26307i	−0.473020	+	0.563724i
$167$	−2.93371	+	2.46168i	−0.227018	+	0.190490i	−0.749201	−	0.662343i	$-0.769562\pi$
$167$	−2.93371	+	2.46168i	−0.227018	+	0.190490i	0.522183	+	0.852833i	$0.325118\pi$
$168$	−1.80693	−	7.64742i	−0.139408	−	0.590011i
$169$	23.7010	−	8.62645i	1.82315	−	0.663573i
$170$	7.26933			0.557532
$171$	−13.0545	+	0.761154i	−0.998305	+	0.0582069i
$172$	0.164211			0.0125210
$173$	3.33329	−	1.21322i	0.253426	−	0.0922394i	−0.212184	−	0.977230i	$-0.568057\pi$
$173$	3.33329	−	1.21322i	0.253426	−	0.0922394i	0.465609	+	0.884990i	$0.345835\pi$
$174$	0.0299213	+	0.126635i	0.00226833	+	0.00960018i
$175$	−3.47540	+	2.91621i	−0.262715	+	0.220444i
$176$	1.08676	−	1.29515i	0.0819178	−	0.0976259i
$177$	8.08945	+	12.3178i	0.608041	+	0.925864i
$178$	−1.55536	−	2.69397i	−0.116579	−	0.201921i
$179$	−6.83477	+	11.8382i	−0.510855	+	0.884826i	0.489066	+	0.872247i	$0.337338\pi$
$179$	−6.83477	+	11.8382i	−0.510855	+	0.884826i	−0.999921	+	0.0125797i	$0.995996\pi$
$180$	−1.34272	−	2.68274i	−0.100080	−	0.199960i
$181$	7.41352	−	20.3685i	0.551043	−	1.51398i	−0.281246	−	0.959636i	$-0.590748\pi$
$181$	7.41352	−	20.3685i	0.551043	−	1.51398i	0.832289	−	0.554342i	$-0.187030\pi$
$182$	−24.2906	−	14.0242i	−1.80054	−	1.03954i
$183$	8.33452	+	6.21371i	0.616105	+	0.459331i
$184$	5.38776	−	0.950007i	0.397191	−	0.0700355i
$185$	0.00534840	+	0.00448784i	0.000393222	+	0.000329953i
$186$	−0.366217	−	0.184236i	−0.0268523	−	0.0135088i
$187$	−2.13418	+	12.1036i	−0.156067	+	0.885100i
$188$	4.05435	+	11.1392i	0.295694	+	0.812413i
$189$	8.10836	−	22.1356i	0.589797	−	1.61013i
$190$	2.98671	−	3.17484i	0.216678	−	0.230327i
$191$		−	4.25450i		−	0.307845i	−0.988083	−	0.153923i	$-0.950809\pi$
$191$		−	4.25450i		−	0.307845i	0.988083	−	0.153923i	$-0.0491906\pi$
$192$	−1.26066	+	1.18774i	−0.0909806	+	0.0857178i
$193$	−20.0283	−	3.53154i	−1.44167	−	0.254205i	−0.602520	−	0.798104i	$-0.705837\pi$
$193$	−20.0283	−	3.53154i	−1.44167	−	0.254205i	−0.839151	+	0.543898i	$0.816948\pi$
$194$	3.68728	+	4.39433i	0.264731	+	0.315494i
$195$	−10.2563	−	3.07819i	−0.734466	−	0.220434i
$196$	2.35860	+	13.3763i	0.168472	+	0.955450i
$197$	10.2138	−	5.89693i	0.727702	−	0.420139i	−0.0898788	−	0.995953i	$-0.528648\pi$
$197$	10.2138	−	5.89693i	0.727702	−	0.420139i	0.817581	+	0.575814i	$0.195315\pi$
$198$	4.86102	−	1.44803i	0.345458	−	0.102907i
$199$	17.4340	+	6.34547i	1.23587	+	0.449819i	0.875603	−	0.483032i	$-0.160464\pi$
$199$	17.4340	+	6.34547i	1.23587	+	0.449819i	0.360264	+	0.932850i	$0.382687\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	15.9013	+	1.86966i	1.12159	+	0.131876i
$202$	9.71490	−	5.60890i	0.683538	−	0.394641i
$203$	−0.0591849	−	0.335654i	−0.00415397	−	0.0235583i
$204$	3.61937	−	12.0594i	0.253407	−	0.844328i
$205$	−2.03315	−	2.42301i	−0.142001	−	0.169231i
$206$	4.77292	+	0.841594i	0.332545	+	0.0586367i
$207$	15.0614	+	6.52139i	1.04684	+	0.453268i
$208$			6.18240i			0.428672i
$209$	4.40930	+	5.90501i	0.304998	+	0.408458i
$210$	3.10744	+	7.21746i	0.214433	+	0.498052i
$211$	−7.38969	−	20.3030i	−0.508728	−	1.39772i	−0.882551	−	0.470217i	$-0.844175\pi$
$211$	−7.38969	−	20.3030i	−0.508728	−	1.39772i	0.373823	−	0.927500i	$-0.378047\pi$
$212$	−0.631189	+	3.57965i	−0.0433502	+	0.245851i
$213$	−9.99380	+	19.8653i	−0.684764	+	1.36115i
$214$	5.61165	+	4.70873i	0.383604	+	0.321882i
$215$	−0.161716	+	0.0285150i	−0.0110290	+	0.00194470i
$216$	−5.11906	+	0.891764i	−0.348308	+	0.0606769i
$217$	0.929929	+	0.536895i	0.0631277	+	0.0364468i
$218$	3.39966	−	9.34050i	0.230254	−	0.632618i
$219$	−25.8898	+	1.49008i	−1.74947	+	0.100690i
$220$	−0.845352	+	1.46419i	−0.0569936	+	0.0987158i
$221$	−22.4709	−	38.9208i	−1.51156	−	2.61810i
$222$	0.0101080	−	0.00663823i	0.000678407	−	0.000445529i
$223$	−8.39262	+	10.0019i	−0.562012	+	0.669779i	−0.969971	−	0.243221i	$-0.921796\pi$
$223$	−8.39262	+	10.0019i	−0.562012	+	0.669779i	0.407959	+	0.913000i	$0.366240\pi$
$224$	3.47540	−	2.91621i	0.232210	−	0.194847i
$225$	1.78817	+	2.40883i	0.119211	+	0.160588i
$226$	3.37119	−	1.22701i	0.224248	−	0.0816197i
$227$	−1.65314			−0.109723			−0.0548613	−	0.998494i	$-0.517472\pi$
$227$	−1.65314			−0.109723			−0.0548613	+	0.998494i	$0.517472\pi$
$228$	−3.77981	−	6.53552i	−0.250324	−	0.432825i
$229$	15.4233			1.01920			0.509600	−	0.860412i	$-0.329793\pi$
$229$	15.4233			1.01920			0.509600	+	0.860412i	$0.329793\pi$
$230$	−5.14094	+	1.87115i	−0.338984	+	0.123380i
$231$	−12.9295	+	3.05498i	−0.850699	+	0.201003i
$232$	−0.0575498	+	0.0482901i	−0.00377833	+	0.00317040i
$233$	−13.9801	+	16.6608i	−0.915866	+	1.09149i	0.0796438	+	0.996823i	$0.474622\pi$
$233$	−13.9801	+	16.6608i	−0.915866	+	1.09149i	−0.995509	+	0.0946628i	$0.969823\pi$
$234$	−10.2131	+	15.4820i	−0.667652	+	1.01209i
$235$	−5.92707	−	10.2660i	−0.386639	−	0.669679i
$236$	−4.25410	+	7.36831i	−0.276918	+	0.479636i
$237$	0.0935250	+	1.62497i	0.00607510	+	0.105553i
$238$	−11.2797	+	30.9907i	−0.731153	+	2.00883i
$239$	−10.5904	−	6.11437i	−0.685036	−	0.395506i	0.116714	−	0.993166i	$-0.462764\pi$
$239$	−10.5904	−	6.11437i	−0.685036	−	0.395506i	−0.801750	+	0.597660i	$0.796097\pi$
$240$	1.03526	−	1.38861i	0.0668259	−	0.0896343i
$241$	−27.1614	+	4.78928i	−1.74962	+	0.308505i	−0.954558	−	0.298026i	$-0.903672\pi$
$241$	−27.1614	+	4.78928i	−1.74962	+	0.308505i	−0.795060	+	0.606530i	$0.792561\pi$
$242$	6.23677	+	5.23327i	0.400915	+	0.336407i
$243$	−14.2923	−	6.22336i	−0.916851	−	0.399228i
$244$	−1.04225	+	5.91088i	−0.0667231	+	0.378405i
$245$	−4.64554	−	12.7635i	−0.296793	−	0.815431i
$246$	−5.03195	+	2.16648i	−0.320825	+	0.138129i
$247$	−26.2309	−	6.17711i	−1.66903	−	0.393040i
$248$		−	0.236684i		−	0.0150294i
$249$	−11.2613	−	11.9527i	−0.713655	−	0.757471i
$250$	−0.984808	−	0.173648i	−0.0622847	−	0.0109825i
$251$	14.3816	+	17.1393i	0.907756	+	1.08182i	0.996317	+	0.0857509i	$0.0273289\pi$
$251$	14.3816	+	17.1393i	0.907756	+	1.08182i	−0.0885604	+	0.996071i	$0.528227\pi$
$252$	13.5206	−	1.56152i	0.851715	−	0.0983663i
$253$	−1.60618	−	9.10910i	−0.100980	−	0.572684i
$254$	0.636138	−	0.367274i	0.0399148	−	0.0230448i
$255$	−1.47029	+	12.5047i	−0.0920732	+	0.783075i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−6.07802	−	2.21222i	−0.379136	−	0.137994i	0.145420	−	0.989370i	$-0.453547\pi$
$257$	−6.07802	−	2.21222i	−0.379136	−	0.137994i	−0.524557	+	0.851376i	$0.675769\pi$
$258$	−0.0332133	+	0.282476i	−0.00206777	+	0.0175862i
$259$	−0.0274316	+	0.0158377i	−0.00170452	+	0.000984104i
$260$	−1.07356	−	6.08847i	−0.0665795	−	0.377591i
$261$	−0.223890	+	0.0258575i	−0.0138584	+	0.00160054i
$262$	0.905825	+	1.07952i	0.0559620	+	0.0666929i
$263$	−9.26722	−	1.63406i	−0.571441	−	0.100761i	−0.119542	−	0.992829i	$-0.538142\pi$
$263$	−9.26722	−	1.63406i	−0.571441	−	0.100761i	−0.451900	+	0.892069i	$0.649254\pi$
$264$	2.00812	+	2.13141i	0.123591	+	0.131179i
$265$		−	3.63487i		−	0.223288i
$266$	8.90058	+	17.6593i	0.545729	+	1.08276i
$267$	4.94875	−	2.13065i	0.302859	−	0.130394i
$268$	3.16159	+	8.68641i	0.193125	+	0.530607i
$269$	0.478825	−	2.71555i	0.0291945	−	0.165570i	−0.966725	−	0.255819i	$-0.917655\pi$
$269$	0.478825	−	2.71555i	0.0291945	−	0.165570i	0.995919	+	0.0902484i	$0.0287661\pi$
$270$	4.88644	−	1.76713i	0.297379	−	0.107544i
$271$	2.30061	+	1.93044i	0.139752	+	0.117266i	0.709984	−	0.704218i	$-0.248702\pi$
$271$	2.30061	+	1.93044i	0.139752	+	0.117266i	−0.570232	+	0.821484i	$0.693147\pi$
$272$	7.15889	−	1.26231i	0.434071	−	0.0765385i
$273$	29.0374	−	38.9482i	1.75742	−	2.35725i
$274$	−7.96956	−	4.60123i	−0.481459	−	0.277970i
$275$	0.578254	−	1.58874i	0.0348701	−	0.0958047i
$276$	0.544478	+	9.46018i	0.0327737	+	0.569436i
$277$	−16.3953	+	28.3974i	−0.985096	+	1.70624i	−0.343585	+	0.939122i	$0.611641\pi$
$277$	−16.3953	+	28.3974i	−0.985096	+	1.70624i	−0.641511	+	0.767114i	$0.721692\pi$
$278$	8.86731	+	15.3586i	0.531826	+	0.921149i
$279$	0.390993	−	0.592703i	0.0234082	−	0.0354842i
$280$	−2.91621	+	3.47540i	−0.174277	+	0.207695i
$281$	−23.7180	+	19.9018i	−1.41490	+	1.18724i	−0.460889	+	0.887458i	$0.652469\pi$
$281$	−23.7180	+	19.9018i	−1.41490	+	1.18724i	−0.954008	+	0.299782i	$0.903086\pi$
$282$	−19.9818	+	4.72129i	−1.18990	+	0.281148i
$283$	12.4375	−	4.52688i	0.739332	−	0.269095i	0.0552226	−	0.998474i	$-0.482413\pi$
$283$	12.4375	−	4.52688i	0.739332	−	0.269095i	0.684110	+	0.729379i	$0.260191\pi$
$284$	−12.8388			−0.761844
$285$	4.85727	+	5.77987i	0.287720	+	0.342370i
$286$	10.4526			0.618075
$287$	13.4846	−	4.90800i	0.795972	−	0.289710i
$288$	−1.78817	−	2.40883i	−0.105369	−	0.141941i
$289$	−27.4574	+	23.0395i	−1.61514	+	1.35527i
$290$	0.0482901	−	0.0575498i	0.00283569	−	0.00337944i
$291$	−8.30491	+	5.45406i	−0.486842	+	0.319723i
$292$	−7.48610	−	12.9663i	−0.438091	−	0.758796i
$293$	−0.503132	+	0.871450i	−0.0293933	+	0.0509106i	−0.880348	−	0.474329i	$-0.842691\pi$
$293$	−0.503132	+	0.871450i	−0.0293933	+	0.0509106i	0.850955	+	0.525239i	$0.176024\pi$
$294$	−23.4870	+	1.35179i	−1.36979	+	0.0788378i
$295$	2.90997	−	7.99509i	0.169425	−	0.465492i
$296$	0.00604645	+	0.00349092i	0.000351443	+	0.000202906i
$297$	1.50771	+	8.65481i	0.0874861	+	0.502203i
$298$	0.442672	−	0.0780551i	0.0256433	−	0.00452161i
$299$	25.9100	+	21.7411i	1.49841	+	1.25732i
$300$	−0.778405	+	1.54728i	−0.0449412	+	0.0893324i
$301$	0.129367	−	0.733677i	0.00745659	−	0.0422884i
$302$	−2.30330	−	6.32828i	−0.132540	−	0.364151i
$303$	7.68351	+	17.8460i	0.441406	+	1.02523i
$304$	2.39003	−	3.64524i	0.137077	−	0.209069i
$305$		−	6.00207i		−	0.343677i
$306$	20.0126	+	8.66518i	1.14404	+	0.495355i
$307$	3.49699	+	0.616613i	0.199584	+	0.0351920i	0.272546	−	0.962143i	$-0.412134\pi$
$307$	3.49699	+	0.616613i	0.199584	+	0.0351920i	−0.0729625	+	0.997335i	$0.523245\pi$
$308$	−4.93044	−	5.87587i	−0.280938	−	0.334809i
$309$	−2.41308	+	8.04016i	−0.137275	+	0.457389i
$310$	0.0410997	+	0.233088i	0.00233431	+	0.0132385i
$311$	4.19540	−	2.42222i	0.237899	−	0.137351i	−0.376311	−	0.926493i	$-0.622808\pi$
$311$	4.19540	−	2.42222i	0.237899	−	0.137351i	0.614211	+	0.789142i	$0.289474\pi$
$312$	−10.6350	−	1.25045i	−0.602086	−	0.0707927i
$313$	12.0550	+	4.38766i	0.681388	+	0.248005i	0.659444	−	0.751754i	$-0.270792\pi$
$313$	12.0550	+	4.38766i	0.681388	+	0.248005i	0.0219448	+	0.999759i	$0.493014\pi$
$314$	−13.3743	−	4.86785i	−0.754756	−	0.274709i
$315$	−13.0440	+	3.88561i	−0.734946	+	0.218930i
$316$	−0.813832	+	0.469866i	−0.0457816	+	0.0264320i
$317$	−0.867738	−	4.92119i	−0.0487370	−	0.276401i	0.950694	−	0.310130i	$-0.100373\pi$
$317$	−0.867738	−	4.92119i	−0.0487370	−	0.276401i	−0.999431	+	0.0337292i	$0.989262\pi$
$318$	−6.03005	−	1.80979i	−0.338148	−	0.101488i
$319$	0.0816441	+	0.0972997i	0.00457119	+	0.00544774i
$320$	0.984808	+	0.173648i	0.0550524	+	0.00970723i
$321$	−9.23498	+	8.70078i	−0.515446	+	0.485630i
$322$		−	24.8203i		−	1.38318i
$323$	−1.79700	+	31.6353i	−0.0999879	+	1.76023i
$324$	−0.498635	−	8.98618i	−0.0277019	−	0.499232i
$325$	2.11450	+	5.80955i	0.117292	+	0.322256i
$326$	−0.190122	+	1.07823i	−0.0105299	+	0.0597179i
$327$	15.3799	+	7.73731i	0.850512	+	0.427874i
$328$	−2.42301	−	2.03315i	−0.133789	−	0.112262i
$329$	52.9629	−	9.33880i	2.91994	−	0.514865i
$330$	−2.34772	−	1.75032i	−0.129238	−	0.0963520i
$331$	31.3105	+	18.0771i	1.72098	+	0.993608i	0.916933	+	0.399041i	$0.130657\pi$
$331$	31.3105	+	18.0771i	1.72098	+	0.993608i	0.804046	+	0.594567i	$0.202676\pi$
$332$	3.24278	−	8.90948i	0.177971	−	0.488971i
$333$	0.00937464	+	0.0187305i	0.000513727	+	0.00102642i
$334$	1.91485	−	3.31661i	0.104776	−	0.181477i
$335$	−4.62194	−	8.00544i	−0.252524	−	0.437384i
$336$	4.31353	+	6.56821i	0.235322	+	0.358325i
$337$	10.1517	−	12.0983i	0.552998	−	0.659037i	−0.415051	−	0.909798i	$-0.636236\pi$
$337$	10.1517	−	12.0983i	0.552998	−	0.659037i	0.968049	+	0.250761i	$0.0806808\pi$
$338$	−19.3212	+	16.2124i	−1.05094	+	0.881839i
$339$	1.42885	+	6.04730i	0.0776047	+	0.328444i
$340$	−6.83093	+	2.48626i	−0.370459	+	0.134836i
$341$	−0.400162			−0.0216700
$342$	12.0069	−	5.18016i	0.649259	−	0.280111i
$343$	29.8642			1.61252
$344$	−0.154308	+	0.0561635i	−0.00831973	+	0.00302813i
$345$	−2.17895	−	9.22191i	−0.117311	−	0.496491i
$346$	−2.71733	+	2.28011i	−0.146084	+	0.122579i
$347$	3.05181	−	3.63701i	0.163830	−	0.195245i	−0.677884	−	0.735169i	$-0.737103\pi$
$347$	3.05181	−	3.63701i	0.163830	−	0.195245i	0.841714	+	0.539924i	$0.181547\pi$
$348$	−0.0714286	−	0.108764i	−0.00382897	−	0.00583038i
$349$	−3.33257	−	5.77218i	−0.178389	−	0.308978i	0.762940	−	0.646469i	$-0.223755\pi$
$349$	−3.33257	−	5.77218i	−0.178389	−	0.308978i	−0.941329	+	0.337491i	$0.890422\pi$
$350$	2.26841	−	3.92899i	0.121251	−	0.210014i
$351$	−24.5664	−	20.7000i	−1.31126	−	1.10488i
$352$	−0.578254	+	1.58874i	−0.0308211	+	0.0846802i
$353$	−14.5648	−	8.40901i	−0.775208	−	0.447566i	0.0595214	−	0.998227i	$-0.481043\pi$
$353$	−14.5648	−	8.40901i	−0.775208	−	0.447566i	−0.834729	+	0.550661i	$0.814376\pi$
$354$	−11.8145	−	8.80821i	−0.627936	−	0.468151i
$355$	12.6438	−	2.22944i	0.671062	−	0.118326i
$356$	2.38295	+	1.99953i	0.126296	+	0.105975i
$357$	−51.0287	−	25.6715i	−2.70073	−	1.35868i
$358$	2.37369	−	13.4619i	0.125453	−	0.711482i
$359$	−7.90680	−	21.7238i	−0.417305	−	1.14654i	−0.953223	−	0.302267i	$-0.902257\pi$
$359$	−7.90680	−	21.7238i	−0.417305	−	1.14654i	0.535918	−	0.844270i	$-0.319965\pi$
$360$	2.17929	+	2.06172i	0.114859	+	0.108662i
$361$	13.0782	+	13.7826i	0.688326	+	0.725401i
$362$			21.6757i			1.13925i
$363$	−10.2637	+	9.67002i	−0.538706	+	0.507544i
$364$	27.6223	+	4.87055i	1.44780	+	0.255286i
$365$	9.62395	+	11.4694i	0.503740	+	0.600334i
$366$	−9.95710	−	2.98841i	−0.520466	−	0.156207i
$367$	−0.745187	−	4.22617i	−0.0388984	−	0.220604i	0.959162	−	0.282858i	$-0.0912824\pi$
$367$	−0.745187	−	4.22617i	−0.0388984	−	0.220604i	−0.998060	+	0.0622535i	$0.980171\pi$
$368$	−4.73792	+	2.73544i	−0.246981	+	0.142595i
$369$	−2.70901	−	9.09415i	−0.141026	−	0.473423i
$370$	−0.00656079	−	0.00238793i	−0.000341079	−	0.000124143i
$371$	15.4962	+	5.64016i	0.804523	+	0.292822i
$372$	0.407144	+	0.0478715i	0.0211094	+	0.00248202i
$373$	19.5739	−	11.3010i	1.01350	−	0.585143i	0.101283	−	0.994858i	$-0.467705\pi$
$373$	19.5739	−	11.3010i	1.01350	−	0.585143i	0.912214	+	0.409715i	$0.134372\pi$
$374$	−2.13418	−	12.1036i	−0.110356	−	0.625860i
$375$	0.497896	−	1.65895i	0.0257113	−	0.0856676i
$376$	−7.61969	−	9.08080i	−0.392956	−	0.468306i
$377$	−0.457403	−	0.0806524i	−0.0235574	−	0.00415381i
$378$	−0.0485392	+	23.5739i	−0.00249659	+	1.21251i
$379$			4.19480i			0.215473i	0.994180	+	0.107736i	$0.0343602\pi$
$379$			4.19480i			0.215473i	−0.994180	+	0.107736i	$0.965640\pi$
$380$	−1.72073	+	4.00488i	−0.0882714	+	0.205446i
$381$	0.503121	+	1.16857i	0.0257756	+	0.0598676i
$382$	1.45513	+	3.99793i	0.0744507	+	0.204552i
$383$	−6.04562	+	34.2864i	−0.308917	+	1.75195i	0.295554	+	0.955326i	$0.404496\pi$
$383$	−6.04562	+	34.2864i	−0.308917	+	1.75195i	−0.604470	+	0.796628i	$0.706615\pi$
$384$	0.778405	−	1.54728i	0.0397228	−	0.0789595i
$385$	5.87587	+	4.93044i	0.299462	+	0.251278i
$386$	20.0283	−	3.53154i	1.01942	−	0.179750i
$387$	−0.479198	−	0.114267i	−0.0243590	−	0.00580852i
$388$	−4.96786	−	2.86819i	−0.252205	−	0.145610i
$389$	−1.67725	+	4.60821i	−0.0850400	+	0.233645i	−0.974923	−	0.222544i	$-0.928564\pi$
$389$	−1.67725	+	4.60821i	−0.0850400	+	0.233645i	0.889883	+	0.456190i	$0.150786\pi$
$390$	10.6905	−	0.615291i	0.541336	−	0.0311565i
$391$	19.8848	−	34.4415i	1.00562	−	1.74178i
$392$	−6.79132	−	11.7629i	−0.343014	−	0.594117i
$393$	−2.04020	+	1.33986i	−0.102915	+	0.0675868i
$394$	−7.58095	+	9.03462i	−0.381923	+	0.455158i
$395$	0.719877	−	0.604048i	0.0362209	−	0.0303930i
$396$	−4.07261	+	3.02327i	−0.204656	+	0.151925i
$397$	12.4127	−	4.51784i	0.622973	−	0.226744i	−0.0111968	−	0.999937i	$-0.503564\pi$
$397$	12.4127	−	4.51784i	0.622973	−	0.226744i	0.634170	+	0.773194i	$0.281342\pi$
$398$	−18.5529			−0.929974
$399$	−32.1777	+	11.7390i	−1.61090	+	0.587686i
$400$	−1.00000			−0.0500000
$401$	−17.2532	+	6.27966i	−0.861585	+	0.313591i	−0.734754	−	0.678333i	$-0.762703\pi$
$401$	−17.2532	+	6.27966i	−0.861585	+	0.313591i	−0.126830	+	0.991924i	$0.540480\pi$
$402$	−15.5818	+	3.68167i	−0.777151	+	0.183625i
$403$	1.12093	−	0.940574i	0.0558376	−	0.0468533i
$404$	−7.21067	+	8.59334i	−0.358744	+	0.427534i
$405$	2.05149	+	8.76307i	0.101939	+	0.435440i
$406$	0.170416	+	0.295169i	0.00845761	+	0.0146490i
$407$	0.00590211	−	0.0102228i	0.000292557	−	0.000506723i
$408$	0.723465	+	12.5700i	0.0358169	+	0.622310i
$409$	−1.10438	+	3.03426i	−0.0546080	+	0.150034i	−0.963997	−	0.265911i	$-0.914327\pi$
$409$	−1.10438	+	3.03426i	−0.0546080	+	0.150034i	0.909389	+	0.415946i	$0.136549\pi$
$410$	2.73926	+	1.58151i	0.135282	+	0.0781052i
$411$	9.52696	−	12.7786i	0.469930	−	0.630322i
$412$	−4.77292	+	0.841594i	−0.235145	+	0.0414624i
$413$	29.5694	+	24.8116i	1.45501	+	1.22090i
$414$	−16.3835	−	0.976799i	−0.805207	−	0.0480071i
$415$	−1.64640	+	9.33722i	−0.0808188	+	0.458346i
$416$	−2.11450	−	5.80955i	−0.103672	−	0.284837i
$417$	−28.2134	+	12.1471i	−1.38162	+	0.594847i
$418$	−6.16302	−	4.04082i	−0.301443	−	0.197643i
$419$		−	2.55820i		−	0.124976i	−0.998046	−	0.0624880i	$-0.980096\pi$
$419$		−	2.55820i		−	0.124976i	0.998046	−	0.0624880i	$-0.0199035\pi$
$420$	−5.38855	−	5.71939i	−0.262934	−	0.279078i
$421$	−11.2145	−	1.97742i	−0.546562	−	0.0963737i	−0.106453	−	0.994318i	$-0.533949\pi$
$421$	−11.2145	−	1.97742i	−0.546562	−	0.0963737i	−0.440110	+	0.897944i	$0.645060\pi$
$422$	13.8881	+	16.5512i	0.676061	+	0.805698i
$423$	−4.08006	−	35.3276i	−0.198379	−	1.71769i
$424$	−0.631189	−	3.57965i	−0.0306532	−	0.173843i
$425$	6.29542	−	3.63466i	0.305373	−	0.176307i
$426$	2.59677	−	22.0854i	0.125814	−	1.07004i
$427$	25.5881	+	9.31329i	1.23829	+	0.450702i
$428$	−6.88371	−	2.50546i	−0.332737	−	0.121106i
$429$	−2.11414	+	17.9806i	−0.102072	+	0.868110i
$430$	0.142211	−	0.0821056i	0.00685802	−	0.00395948i
$431$	0.0624841	+	0.354365i	0.00300975	+	0.0170692i	0.986276	−	0.165107i	$-0.0527970\pi$
$431$	0.0624841	+	0.354365i	0.00300975	+	0.0170692i	−0.983266	+	0.182176i	$0.941686\pi$
$432$	4.50534	−	2.58881i	0.216763	−	0.124554i
$433$	9.04071	+	10.7743i	0.434469	+	0.517780i	0.938206	−	0.346077i	$-0.112487\pi$
$433$	9.04071	+	10.7743i	0.434469	+	0.517780i	−0.503737	+	0.863857i	$0.668042\pi$
$434$	−1.05748	−	0.186462i	−0.0507605	−	0.00895044i
$435$	0.0892302	+	0.0947086i	0.00427826	+	0.00454093i
$436$			9.93995i			0.476037i
$437$	−6.87217	−	22.8353i	−0.328740	−	1.09236i
$438$	23.8188	−	10.2550i	1.13811	−	0.490005i
$439$	−9.61057	−	26.4048i	−0.458687	−	1.26023i	−0.926463	−	0.376386i	$-0.877167\pi$
$439$	−9.61057	−	26.4048i	−0.458687	−	1.26023i	0.467775	−	0.883847i	$-0.345056\pi$
$440$	0.293587	−	1.66502i	0.0139962	−	0.0793766i
$441$	2.42512	−	40.6757i	0.115482	−	1.93694i
$442$	34.4275	+	28.8881i	1.63755	+	1.37407i
$443$	19.5392	−	3.44528i	0.928333	−	0.163690i	0.311016	−	0.950405i	$-0.399331\pi$
$443$	19.5392	−	3.44528i	0.928333	−	0.163690i	0.617317	+	0.786714i	$0.288220\pi$
$444$	−0.00722804	+	0.00969504i	−0.000343028	+	0.000460106i
$445$	−2.69397	−	1.55536i	−0.127706	−	0.0737312i
$446$	4.46562	−	12.2692i	0.211453	−	0.580963i
$447$	0.0447357	+	0.777273i	0.00211593	+	0.0367638i
$448$	−2.26841	+	3.92899i	−0.107172	+	0.185627i
$449$	−19.8715	−	34.4184i	−0.937792	−	1.62430i	−0.769578	−	0.638553i	$-0.779533\pi$
$449$	−19.8715	−	34.4184i	−0.937792	−	1.62430i	−0.168214	−	0.985751i	$-0.553800\pi$
$450$	−2.50420	−	1.65197i	−0.118049	−	0.0778744i
$451$	−3.43745	+	4.09660i	−0.161863	+	0.192901i
$452$	−2.74822	+	2.30603i	−0.129265	+	0.108467i
$453$	11.3518	−	2.68219i	0.533353	−	0.126020i
$454$	1.55344	−	0.565406i	0.0729066	−	0.0265358i
$455$	−28.0484			−1.31493
$456$	5.78714	+	4.84861i	0.271008	+	0.227057i
$457$	−24.6381			−1.15252			−0.576260	−	0.817266i	$-0.695489\pi$
$457$	−24.6381			−1.15252			−0.576260	+	0.817266i	$0.695489\pi$
$458$	−14.4932	+	5.27508i	−0.677220	+	0.246488i
$459$	−18.9536	+	32.6730i	−0.884677	+	1.52505i
$460$	4.19093	−	3.51661i	0.195403	−	0.163963i
$461$	4.96863	−	5.92139i	0.231412	−	0.275786i	−0.637825	−	0.770181i	$-0.720166\pi$
$461$	4.96863	−	5.92139i	0.231412	−	0.275786i	0.869238	+	0.494395i	$0.164610\pi$
$462$	11.1049	−	7.29289i	0.516647	−	0.339296i
$463$	17.8383	+	30.8969i	0.829018	+	1.43590i	0.898810	+	0.438339i	$0.144433\pi$
$463$	17.8383	+	30.8969i	0.829018	+	1.43590i	−0.0697920	+	0.997562i	$0.522234\pi$
$464$	0.0375630	−	0.0650610i	0.00174382	−	0.00302038i
$465$	−0.409271	+	0.0235555i	−0.0189795	+	0.00109236i
$466$	7.43865	−	20.4375i	0.344589	−	0.946749i
$467$	30.6485	+	17.6949i	1.41824	+	0.818822i	0.996144	−	0.0877280i	$-0.0279606\pi$
$467$	30.6485	+	17.6949i	1.41824	+	0.818822i	0.422098	+	0.906550i	$0.361294\pi$
$468$	4.30205	−	18.0414i	0.198862	−	0.833962i
$469$	41.3006	−	7.28241i	1.90709	−	0.336271i
$470$	9.08080	+	7.61969i	0.418866	+	0.351470i
$471$	11.0788	−	22.0219i	0.510482	−	1.01472i
$472$	1.47743	−	8.37893i	0.0680043	−	0.385672i
$473$	0.0949558	+	0.260889i	0.00436607	+	0.0119957i
$474$	−0.643659	−	1.49499i	−0.0295642	−	0.0686671i
$475$	0.999144	−	4.24284i	0.0458439	−	0.194675i
$476$		−	32.9796i		−	1.51162i
$477$	4.33284	−	10.0069i	0.198387	−	0.458182i
$478$	12.0430	+	2.12350i	0.550832	+	0.0971265i
$479$	7.83555	+	9.33805i	0.358015	+	0.426666i	0.914748	−	0.404026i	$-0.132389\pi$
$479$	7.83555	+	9.33805i	0.358015	+	0.426666i	−0.556732	+	0.830692i	$0.687945\pi$
$480$	−0.497896	+	1.65895i	−0.0227258	+	0.0757201i
$481$	0.00749544	+	0.0425088i	0.000341763	+	0.00193823i
$482$	23.8853	−	13.7902i	1.08795	−	0.628126i
$483$	42.6959	+	5.02015i	1.94273	+	0.228425i
$484$	−7.65053	−	2.78456i	−0.347751	−	0.126571i
$485$	5.39044	+	1.96196i	0.244767	+	0.0890880i
$486$	15.5589	+	0.959787i	0.705765	+	0.0435368i
$487$	−17.9612	+	10.3699i	−0.813899	+	0.469905i	−0.848308	−	0.529503i	$-0.822378\pi$
$487$	−17.9612	+	10.3699i	−0.813899	+	0.469905i	0.0344093	+	0.999408i	$0.489045\pi$
$488$	−1.04225	−	5.91088i	−0.0471803	−	0.267573i
$489$	−1.81633	−	0.545131i	−0.0821371	−	0.0246517i
$490$	8.73076	+	10.4049i	0.394415	+	0.470046i
$491$	−1.81626	−	0.320255i	−0.0819666	−	0.0144529i	0.132514	−	0.991181i	$-0.457695\pi$
$491$	−1.81626	−	0.320255i	−0.0819666	−	0.0144529i	−0.214481	+	0.976728i	$0.568806\pi$
$492$	3.98751	−	3.75685i	0.179771	−	0.169372i
$493$			0.546115i			0.0245958i
$494$	26.7617	−	3.16693i	1.20407	−	0.142487i
$495$	3.48575	−	3.68454i	0.156673	−	0.165608i
$496$	0.0809506	+	0.222410i	0.00363479	+	0.00998650i
$497$	−10.1145	+	57.3624i	−0.453699	+	2.57306i
$498$	14.6702	+	7.38027i	0.657388	+	0.330718i
$499$	−27.5497	−	23.1169i	−1.23329	−	1.03486i	−0.998018	−	0.0629281i	$-0.979956\pi$
$499$	−27.5497	−	23.1169i	−1.23329	−	1.03486i	−0.235276	−	0.971929i	$-0.575599\pi$
$500$	0.984808	−	0.173648i	0.0440419	−	0.00776578i
$501$	5.31794	+	3.96474i	0.237588	+	0.177131i
$502$	−19.3762	−	11.1869i	−0.864803	−	0.499294i
$503$	2.81655	−	7.73842i	0.125584	−	0.345039i	−0.860928	−	0.508726i	$-0.830117\pi$
$503$	2.81655	−	7.73842i	0.125584	−	0.345039i	0.986512	+	0.163687i	$0.0523388\pi$
$504$	−12.1711	+	6.09165i	−0.542144	+	0.271344i
$505$	5.60890	−	9.71490i	0.249593	−	0.432308i
$506$	4.62481	+	8.01041i	0.205598	+	0.356106i
$507$	−23.9807	−	36.5155i	−1.06502	−	1.62171i
$508$	−0.472159	+	0.562697i	−0.0209487	+	0.0249656i
$509$	22.9498	−	19.2572i	1.01723	−	0.853559i	0.0279547	−	0.999609i	$-0.491101\pi$
$509$	22.9498	−	19.2572i	1.01723	−	0.853559i	0.989277	+	0.146050i	$0.0466561\pi$
$510$	−2.89524	−	12.2534i	−0.128203	−	0.542592i
$511$	−63.8296	+	23.2321i	−2.82366	+	1.02773i
$512$	1.00000			0.0441942
$513$	6.48241	+	21.7020i	0.286205	+	0.958168i
$514$	6.46809			0.285295
$515$	4.55427	−	1.65762i	0.200685	−	0.0730433i
$516$	−0.0654023	−	0.276800i	−0.00287917	−	0.0121855i
$517$	−15.3529	+	12.8826i	−0.675221	+	0.566578i
$518$	0.0203605	−	0.0242647i	0.000894589	−	0.00106613i
$519$	−3.37264	−	5.13552i	−0.148042	−	0.225424i
$520$	3.09120	+	5.35411i	0.135558	+	0.234793i
$521$	1.56894	−	2.71749i	0.0687366	−	0.119055i	−0.829609	−	0.558345i	$-0.811437\pi$
$521$	1.56894	−	2.71749i	0.0687366	−	0.119055i	0.898345	+	0.439290i	$0.144770\pi$
$522$	0.201544	−	0.100873i	0.00882133	−	0.00441509i
$523$	−6.83817	+	18.7877i	−0.299012	+	0.821530i	0.695653	+	0.718378i	$0.255115\pi$
$523$	−6.83817	+	18.7877i	−0.299012	+	0.821530i	−0.994666	+	0.103152i	$0.967107\pi$
$524$	−1.22041	−	0.704606i	−0.0533140	−	0.0307809i
$525$	6.29985	+	4.69679i	0.274948	+	0.204985i
$526$	9.26722	−	1.63406i	0.404070	−	0.0712485i
$527$	−1.31800	−	1.10594i	−0.0574131	−	0.0481753i
$528$	−2.61600	−	1.31605i	−0.113847	−	0.0572738i
$529$	−1.20346	+	6.82518i	−0.0523245	+	0.296747i
$530$	1.24320	+	3.41566i	0.0540011	+	0.148367i
$531$	17.5415	−	18.5418i	0.761236	−	0.804647i
$532$	−14.4036	−	13.5501i	−0.624477	−	0.587472i
$533$		−	19.5551i		−	0.847024i
$534$	−3.92158	+	3.69473i	−0.169703	+	0.159887i
$535$	7.21420	+	1.27206i	0.311897	+	0.0549958i
$536$	−5.94185	−	7.08123i	−0.256649	−	0.305862i
$537$	22.6770	+	6.80602i	0.978586	+	0.293701i
$538$	0.478825	+	2.71555i	0.0206436	+	0.117076i
$539$	−19.8876	+	11.4821i	−0.856620	+	0.494570i
$540$	−3.98735	+	3.33182i	−0.171588	+	0.143379i
$541$	11.2837	+	4.10695i	0.485126	+	0.176571i	0.572992	−	0.819561i	$-0.305783\pi$
$541$	11.2837	+	4.10695i	0.485126	+	0.176571i	−0.0878662	+	0.996132i	$0.528005\pi$
$542$	−2.82212	−	1.02717i	−0.121220	−	0.0441206i
$543$	−37.2865	−	4.38411i	−1.60012	−	0.188140i
$544$	−6.29542	+	3.63466i	−0.269914	+	0.155835i
$545$	−1.72605	−	9.78894i	−0.0739361	−	0.419312i
$546$	−13.9652	+	46.5307i	−0.597655	+	1.99133i
$547$	−8.52193	−	10.1560i	−0.364372	−	0.434241i	0.552445	−	0.833549i	$-0.313695\pi$
$547$	−8.52193	−	10.1560i	−0.364372	−	0.434241i	−0.916817	+	0.399308i	$0.869250\pi$
$548$	9.06265	+	1.59799i	0.387137	+	0.0682627i
$549$	7.15458	−	16.5238i	0.305350	−	0.705218i
$550$			1.69070i			0.0720918i
$551$	0.238513	+	0.224379i	0.0101610	+	0.00955888i
$552$	−3.74721	−	8.70344i	−0.159492	−	0.370443i
$553$	1.45816	+	4.00627i	0.0620074	+	0.170364i
$554$	5.69401	−	32.2924i	0.241915	−	1.37197i
$555$	0.00543470	−	0.0108029i	0.000230690	−	0.000458557i
$556$	−13.5855	−	11.3996i	−0.576154	−	0.483450i
$557$	−31.3589	+	5.52942i	−1.32872	+	0.234289i	−0.792543	−	0.609816i	$-0.791243\pi$
$557$	−31.3589	+	5.52942i	−1.32872	+	0.234289i	−0.536177	+	0.844105i	$0.680132\pi$
$558$	−0.164697	+	0.690686i	−0.00697219	+	0.0292391i
$559$	−0.879205	−	0.507609i	−0.0371864	−	0.0214696i
$560$	1.55168	−	4.26321i	0.0655705	−	0.180153i
$561$	21.2522	−	1.22317i	0.897269	−	0.0516421i
$562$	15.4808	−	26.8136i	0.653019	−	1.13106i
$563$	−5.37938	−	9.31737i	−0.226714	−	0.392680i	0.730118	−	0.683321i	$-0.239465\pi$
$563$	−5.37938	−	9.31737i	−0.226714	−	0.392680i	−0.956832	+	0.290641i	$0.906132\pi$
$564$	17.1620	−	11.2707i	0.722649	−	0.474583i
$565$	2.30603	−	2.74822i	0.0970154	−	0.115618i
$566$	−10.1391	+	8.50775i	−0.426180	+	0.357607i
$567$	−40.5420	−	4.85154i	−1.70261	−	0.203746i
$568$	12.0645	−	4.39114i	0.506217	−	0.184248i
$569$	22.9976			0.964111			0.482056	−	0.876141i	$-0.339890\pi$
$569$	22.9976			0.964111			0.482056	+	0.876141i	$0.339890\pi$
$570$	−6.54117	−	3.77002i	−0.273980	−	0.157909i
$571$	34.8811			1.45973			0.729864	−	0.683592i	$-0.239583\pi$
$571$	34.8811			1.45973			0.729864	+	0.683592i	$0.239583\pi$
$572$	−9.82223	+	3.57500i	−0.410688	+	0.149478i
$573$	−7.17155	+	1.69449i	−0.299596	+	0.0707884i
$574$	−10.9928	+	9.22402i	−0.458829	+	0.385003i
$575$	−3.51661	+	4.19093i	−0.146653	+	0.174774i
$576$	2.50420	+	1.65197i	0.104342	+	0.0688319i
$577$	13.6910	+	23.7135i	0.569963	+	0.987204i	0.996569	+	0.0827669i	$0.0263757\pi$
$577$	13.6910	+	23.7135i	0.569963	+	0.987204i	−0.426606	+	0.904437i	$0.640291\pi$
$578$	17.9216	−	31.0411i	0.745439	−	1.29114i
$579$	2.02403	+	35.1670i	0.0841158	+	1.46149i
$580$	−0.0256946	+	0.0705953i	−0.00106691	+	0.00293131i
$581$	−37.2518	−	21.5074i	−1.54547	−	0.892275i
$582$	5.93866	−	7.96559i	0.246166	−	0.330184i
$583$	−6.05212	+	1.06715i	−0.250653	+	0.0441969i
$584$	11.4694	+	9.62395i	0.474606	+	0.398242i
$585$	−1.10384	+	18.5143i	−0.0456381	+	0.765473i
$586$	0.174736	−	0.990976i	0.00721827	−	0.0409368i
$587$	−5.18214	−	14.2378i	−0.213890	−	0.587658i	0.785628	−	0.618699i	$-0.212340\pi$
$587$	−5.18214	−	14.2378i	−0.213890	−	0.587658i	−0.999518	+	0.0310413i	$0.990118\pi$
$588$	21.6082	−	9.30328i	0.891107	−	0.383661i
$589$	−1.02453	+	0.121241i	−0.0422151	+	0.00499565i
$590$			8.50819i			0.350277i
$591$	−14.0080	−	14.8681i	−0.576214	−	0.611592i
$592$	−0.00687577	−	0.00121238i	−0.000282593	−	4.98287e-5i
$593$	−16.9365	−	20.1841i	−0.695497	−	0.828861i	0.296512	−	0.955029i	$-0.404177\pi$
$593$	−16.9365	−	20.1841i	−0.695497	−	0.828861i	−0.992009	+	0.126168i	$0.959732\pi$
$594$	−4.37690	−	7.61719i	−0.179586	−	0.312537i
$595$	5.72684	+	32.4785i	0.234778	+	1.33149i
$596$	−0.389280	+	0.224751i	−0.0159455	+	0.00920615i
$597$	3.75251	−	31.9148i	0.153580	−	1.30618i
$598$	−31.7833	−	11.5682i	−1.29972	−	0.473058i
$599$	0.698047	+	0.254068i	0.0285214	+	0.0103810i	0.356241	−	0.934394i	$-0.384058\pi$
$599$	0.698047	+	0.254068i	0.0285214	+	0.0103810i	−0.327720	+	0.944775i	$0.606280\pi$
$600$	0.202260	−	1.72020i	0.00825721	−	0.0702269i
$601$	−25.4578	+	14.6981i	−1.03845	+	0.599547i	−0.919393	−	0.393341i	$-0.871319\pi$
$601$	−25.4578	+	14.6981i	−1.03845	+	0.599547i	−0.119053	+	0.992888i	$0.537986\pi$
$602$	0.129367	+	0.733677i	0.00527261	+	0.0299024i
$603$	−3.18164	−	27.5485i	−0.129566	−	1.12186i
$604$	4.32880	+	5.15886i	0.176136	+	0.209911i
$605$	8.01784	+	1.41376i	0.325971	+	0.0574775i
$606$	−13.3238	−	14.1419i	−0.541244	−	0.574474i
$607$			13.4574i			0.546220i	0.961983	+	0.273110i	$0.0880523\pi$
$607$			13.4574i			0.546220i	−0.961983	+	0.273110i	$0.911948\pi$
$608$	−0.999144	+	4.24284i	−0.0405207	+	0.172070i
$609$	−0.542219	+	0.233449i	−0.0219718	+	0.00945984i
$610$	2.05283	+	5.64010i	0.0831166	+	0.228361i
$611$	12.7262	−	72.1736i	0.514845	−	2.91983i
$612$	−21.7693	−	1.29790i	−0.879973	−	0.0524647i
$613$	25.6359	+	21.5110i	1.03542	+	0.868822i	0.991486	−	0.130212i	$-0.0415658\pi$
$613$	25.6359	+	21.5110i	1.03542	+	0.868822i	0.0439361	+	0.999034i	$0.486010\pi$
$614$	−3.49699	+	0.616613i	−0.141127	+	0.0248845i
$615$	−3.27456	+	4.39220i	−0.132043	+	0.177110i
$616$	6.64276	+	3.83520i	0.267644	+	0.154525i
$617$	−7.98580	+	21.9408i	−0.321496	+	0.883303i	0.668689	+	0.743542i	$0.266856\pi$
$617$	−7.98580	+	21.9408i	−0.321496	+	0.883303i	−0.990185	+	0.139761i	$0.955367\pi$
$618$	−0.482343	−	8.38060i	−0.0194027	−	0.337117i
$619$	20.0043	−	34.6485i	0.804042	−	1.39264i	−0.112894	−	0.993607i	$-0.536012\pi$
$619$	20.0043	−	34.6485i	0.804042	−	1.39264i	0.916936	−	0.399034i	$-0.130655\pi$
$620$	−0.118342	−	0.204974i	−0.00475272	−	0.00823196i
$621$	4.99402	−	27.9854i	0.200403	−	1.12302i
$622$	−3.11394	+	3.71105i	−0.124858	+	0.148800i
$623$	10.8110	−	9.07151i	0.433134	−	0.363442i
$624$	10.4213	−	2.46234i	0.417185	−	0.0985723i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	−12.8287			−0.512736
$627$	8.19756	−	9.78433i	0.327379	−	0.390749i
$628$	14.2326			0.567944
$629$	0.0476925	−	0.0173587i	0.00190162	−	0.000692135i
$630$	10.9284	−	8.11259i	0.435397	−	0.323213i
$631$	−19.9319	+	16.7248i	−0.793476	+	0.665805i	−0.946603	−	0.322401i	$-0.895510\pi$
$631$	−19.9319	+	16.7248i	−0.793476	+	0.665805i	0.153127	+	0.988207i	$0.451066\pi$
$632$	0.604048	−	0.719877i	0.0240277	−	0.0286352i
$633$	−31.2803	+	20.5427i	−1.24328	+	0.816497i
$634$	2.49855	+	4.32762i	0.0992302	+	0.171872i
$635$	0.367274	−	0.636138i	0.0145748	−	0.0252443i
$636$	6.28538	−	0.361753i	0.249231	−	0.0143445i
$637$	28.7206	−	78.9091i	1.13795	−	3.12649i
$638$	−0.109999	−	0.0635079i	−0.00435490	−	0.00251430i
$639$	37.4660	+	8.93395i	1.48213	+	0.353421i
$640$	−0.984808	+	0.173648i	−0.0389279	+	0.00686405i
$641$	34.2258	+	28.7189i	1.35184	+	1.13433i	0.978411	+	0.206668i	$0.0662620\pi$
$641$	34.2258	+	28.7189i	1.35184	+	1.13433i	0.373427	+	0.927659i	$0.378182\pi$
$642$	5.70220	−	11.3346i	0.225048	−	0.447341i
$643$	−0.362355	+	2.05502i	−0.0142899	+	0.0810420i	−0.991119	−	0.132980i	$-0.957545\pi$
$643$	−0.362355	+	2.05502i	−0.0142899	+	0.0810420i	0.976829	+	0.214022i	$0.0686565\pi$
$644$	8.48905	+	23.3235i	0.334515	+	0.919074i
$645$	0.112475	+	0.261238i	0.00442868	+	0.0102862i
$646$	−9.13127	−	30.3420i	−0.359265	−	1.19379i
$647$		−	49.0186i		−	1.92712i	−0.267495	−	0.963559i	$-0.586196\pi$
$647$		−	49.0186i		−	1.92712i	0.267495	−	0.963559i	$-0.413804\pi$
$648$	3.54202	+	8.27370i	0.139144	+	0.325022i
$649$	−14.1663	−	2.49790i	−0.556075	−	0.0980511i
$650$	−3.97397	−	4.73599i	−0.155872	−	0.185761i
$651$	0.534636	−	1.78136i	0.0209540	−	0.0698169i
$652$	−0.190122	−	1.07823i	−0.00744574	−	0.0422269i
$653$	−35.8908	+	20.7216i	−1.40451	+	0.810897i	−0.994852	−	0.101340i	$-0.967687\pi$
$653$	−35.8908	+	20.7216i	−1.40451	+	0.810897i	−0.409663	+	0.912237i	$0.634354\pi$
$654$	−17.0987	−	2.01045i	−0.668613	−	0.0786148i
$655$	1.32423	+	0.481979i	0.0517418	+	0.0188325i
$656$	2.97227	+	1.08182i	0.116048	+	0.0422379i
$657$	12.8232	+	43.0473i	0.500279	+	1.67943i
$658$	−46.5748	+	26.8900i	−1.81568	+	1.04828i
$659$	−4.20535	−	23.8497i	−0.163817	−	0.929053i	−0.950276	−	0.311410i	$-0.899199\pi$
$659$	−4.20535	−	23.8497i	−0.163817	−	0.929053i	0.786459	−	0.617643i	$-0.211912\pi$
$660$	2.80478	+	0.841795i	0.109176	+	0.0327668i
$661$	6.46407	+	7.70357i	0.251423	+	0.299634i	0.876963	−	0.480558i	$-0.159566\pi$
$661$	6.46407	+	7.70357i	0.251423	+	0.299634i	−0.625540	+	0.780192i	$0.715121\pi$
$662$	−35.6050	−	6.27811i	−1.38383	−	0.244006i
$663$	−56.6566	+	53.3793i	−2.20036	+	2.07308i
$664$			9.48127i			0.367944i
$665$	16.5378	+	10.8431i	0.641307	+	0.420477i
$666$	−0.0152155	−	0.0143946i	−0.000589588	−	0.000557779i
$667$	−0.140572	−	0.386218i	−0.00544297	−	0.0149544i
$668$	−0.665019	+	3.77151i	−0.0257304	+	0.145924i
$669$	20.2023	+	10.1633i	0.781065	+	0.392937i
$670$	7.08123	+	5.94185i	0.273572	+	0.229554i
$671$	−9.99355	+	1.76213i	−0.385797	+	0.0680263i
$672$	−6.29985	−	4.69679i	−0.243022	−	0.181183i
$673$	−17.6165	−	10.1709i	−0.679065	−	0.392058i	0.120438	−	0.992721i	$-0.461570\pi$
$673$	−17.6165	−	10.1709i	−0.679065	−	0.392058i	−0.799503	+	0.600663i	$0.794903\pi$
$674$	−5.40160	+	14.8408i	−0.208062	+	0.571646i
$675$	3.34821	−	3.97360i	0.128873	−	0.152944i
$676$	12.6110	−	21.8429i	0.485039	−	0.840113i
$677$	8.82920	+	15.2926i	0.339334	+	0.587743i	0.984308	−	0.176461i	$-0.0564650\pi$
$677$	8.82920	+	15.2926i	0.339334	+	0.587743i	−0.644974	+	0.764205i	$0.723132\pi$
$678$	−3.41098	−	5.19391i	−0.130998	−	0.199471i
$679$	−16.7285	+	19.9362i	−0.641980	+	0.765082i
$680$	5.56863	−	4.67263i	0.213547	−	0.179187i
$681$	0.658414	+	2.78659i	0.0252305	+	0.106782i
$682$	0.376029	−	0.136863i	0.0143989	−	0.00524077i
$683$	−34.8153			−1.33217			−0.666085	−	0.745876i	$-0.732031\pi$
$683$	−34.8153			−1.33217			−0.666085	+	0.745876i	$0.732031\pi$
$684$	−9.51109	+	8.97437i	−0.363665	+	0.343143i
$685$	−9.20246			−0.351608
$686$	−28.0632	+	10.2142i	−1.07146	+	0.389979i
$687$	−6.14281	−	25.9981i	−0.234363	−	0.991888i
$688$	0.125793	−	0.105553i	0.00479581	−	0.00402417i
$689$	14.4449	−	17.2147i	0.550305	−	0.655829i
$690$	5.20162	+	7.92051i	0.198022	+	0.301529i
$691$	−13.8603	−	24.0067i	−0.527269	−	0.913257i	−0.999495	−	0.0317796i	$-0.989883\pi$
$691$	−13.8603	−	24.0067i	−0.527269	−	0.913257i	0.472225	−	0.881478i	$-0.343451\pi$
$692$	1.77361	−	3.07198i	0.0674225	−	0.116779i
$693$	10.2992	+	20.5777i	0.391233	+	0.781683i
$694$	−1.62384	+	4.46145i	−0.0616399	+	0.169354i
$695$	15.3586	+	8.86731i	0.582586	+	0.336356i
$696$	0.104321	+	0.0777751i	0.00395426	+	0.00294806i
$697$	−22.6437	+	3.99270i	−0.857692	+	0.151234i
$698$	5.10580	+	4.28427i	0.193257	+	0.162162i
$699$	33.6521	+	16.9296i	1.27284	+	0.640338i
$700$	−0.787809	+	4.46789i	−0.0297764	+	0.168870i
$701$	13.0837	+	35.9471i	0.494163	+	1.35770i	0.896838	+	0.442360i	$0.145859\pi$
$701$	13.0837	+	35.9471i	0.494163	+	1.35770i	−0.402674	+	0.915343i	$0.631919\pi$
$702$	30.1646	+	11.0494i	1.13849	+	0.417034i
$703$	0.0120138	−	0.0279615i	0.000453111	−	0.00105459i
$704$		−	1.69070i		−	0.0637208i
$705$	−14.9441	+	14.0796i	−0.562827	+	0.530270i
$706$	16.5625	+	2.92042i	0.623339	+	0.109911i
$707$	32.7134	+	38.9863i	1.23031	+	1.46623i
$708$	14.1146	+	4.23620i	0.530460	+	0.159206i
$709$	6.26828	+	35.5492i	0.235410	+	1.33508i	0.841748	+	0.539871i	$0.181527\pi$
$709$	6.26828	+	35.5492i	0.235410	+	1.33508i	−0.606338	+	0.795207i	$0.707362\pi$
$710$	−11.1187	+	6.41941i	−0.417279	+	0.240916i
$711$	2.70187	−	0.804847i	0.101328	−	0.0301841i
$712$	−2.92312	−	1.06393i	−0.109549	−	0.0398725i
$713$	1.21678	+	0.442871i	0.0455686	+	0.0165856i
$714$	56.7315	+	6.67043i	2.12312	+	0.249635i
$715$	9.05222	−	5.22630i	0.338534	−	0.195453i
$716$	2.37369	+	13.4619i	0.0887090	+	0.503094i
$717$	−6.08865	+	20.2868i	−0.227385	+	0.757625i
$718$	14.8599	+	17.7094i	0.554568	+	0.660908i
$719$	10.3694	+	1.82841i	0.386714	+	0.0681881i	0.363625	−	0.931545i	$-0.381539\pi$
$719$	10.3694	+	1.82841i	0.386714	+	0.0681881i	0.0230888	+	0.999733i	$0.492650\pi$
$720$	−2.75301	−	1.19202i	−0.102599	−	0.0444239i
$721$			21.9879i			0.818871i
$722$	−17.0034	−	8.47842i	−0.632802	−	0.315534i
$723$	18.8909	+	43.8767i	0.702559	+	1.63179i
$724$	−7.41352	−	20.3685i	−0.275521	−	0.756989i
$725$	0.0130455	−	0.0739847i	0.000484497	−	0.00274772i
$726$	6.33740	−	12.5972i	0.235203	−	0.467528i
$727$	5.84919	+	4.90805i	0.216934	+	0.182030i	0.744779	−	0.667312i	$-0.232555\pi$
$727$	5.84919	+	4.90805i	0.216934	+	0.182030i	−0.527844	+	0.849341i	$0.676999\pi$
$728$	−27.6223	+	4.87055i	−1.02375	+	0.180515i
$729$	−4.79796	+	26.5703i	−0.177702	+	0.984084i
$730$	−12.9663	−	7.48610i	−0.479905	−	0.277073i
$731$	−0.408271	+	1.12172i	−0.0151004	+	0.0414881i
$732$	10.3787	−	0.597344i	0.383608	−	0.0220785i
$733$	6.30638	−	10.9230i	0.232931	−	0.403449i	−0.725738	−	0.687971i	$-0.758502\pi$
$733$	6.30638	−	10.9230i	0.232931	−	0.403449i	0.958669	+	0.284522i	$0.0918349\pi$
$734$	2.14568	+	3.71643i	0.0791985	+	0.137176i
$735$	−19.6644	+	12.9142i	−0.725333	+	0.476346i
$736$	3.51661	−	4.19093i	0.129624	−	0.154480i
$737$	−11.9723	+	10.0459i	−0.441004	+	0.370046i
$738$	5.65602	+	7.61917i	0.208201	+	0.280465i
$739$	28.6421	−	10.4249i	1.05362	−	0.383485i	0.243589	−	0.969878i	$-0.421675\pi$
$739$	28.6421	−	10.4249i	1.05362	−	0.383485i	0.810026	+	0.586394i	$0.199453\pi$
$740$	0.00698184			0.000256658
$741$	0.0349382	+	46.6761i	0.00128349	+	1.71469i
$742$	−16.4907			−0.605393
$743$	22.8177	−	8.30497i	0.837101	−	0.304680i	0.112331	−	0.993671i	$-0.464168\pi$
$743$	22.8177	−	8.30497i	0.837101	−	0.304680i	0.724770	+	0.688991i	$0.241946\pi$
$744$	−0.398963	+	0.0942668i	−0.0146267	+	0.00345599i
$745$	0.344338	−	0.288934i	0.0126156	−	0.0105857i
$746$	−14.5283	+	17.3141i	−0.531918	+	0.633915i
$747$	−15.6627	+	23.7430i	−0.573069	+	0.868710i
$748$	6.14514	+	10.6437i	0.224688	+	0.389172i
$749$	−16.6172	+	28.7818i	−0.607178	+	1.05166i
$750$	0.0995230	+	1.72919i	0.00363407	+	0.0631411i
$751$	−4.28501	+	11.7730i	−0.156362	+	0.429601i	−0.992994	−	0.118164i	$-0.962299\pi$
$751$	−4.28501	+	11.7730i	−0.156362	+	0.429601i	0.836632	+	0.547765i	$0.184521\pi$
$752$	10.2660	+	5.92707i	0.374362	+	0.216138i
$753$	23.1627	−	31.0684i	0.844095	−	1.13219i
$754$	0.457403	−	0.0806524i	0.0166576	−	0.00293719i
$755$	−5.15886	−	4.32880i	−0.187750	−	0.157541i
$756$	−8.01714	−	22.1688i	−0.291581	−	0.806273i
$757$	4.66442	−	26.4532i	0.169531	−	0.961459i	−0.774737	−	0.632283i	$-0.782118\pi$
$757$	4.66442	−	26.4532i	0.169531	−	0.961459i	0.944269	−	0.329176i	$-0.106771\pi$
$758$	−1.43471	−	3.94183i	−0.0521109	−	0.143174i
$759$	−14.7149	+	6.33542i	−0.534118	+	0.229961i
$760$	0.247203	−	4.35188i	0.00896701	−	0.157859i
$761$		−	24.7487i		−	0.897138i	−0.893748	−	0.448569i	$-0.851934\pi$
$761$		−	24.7487i		−	0.897138i	0.893748	−	0.448569i	$-0.148066\pi$
$762$	−0.872453	−	0.926018i	−0.0316056	−	0.0335461i
$763$	44.4106	+	7.83078i	1.60777	+	0.283493i
$764$	−2.73474	−	3.25914i	−0.0989395	−	0.117912i
$765$	21.6640	−	2.50202i	0.783263	−	0.0904606i
$766$	−6.04562	−	34.2864i	−0.218437	−	1.23882i
$767$	45.5538	−	26.3005i	1.64485	−	0.949657i
$768$	−0.202260	+	1.72020i	−0.00729841	+	0.0620724i
$769$	−32.4415	−	11.8077i	−1.16987	−	0.425798i	−0.317257	−	0.948340i	$-0.602762\pi$
$769$	−32.4415	−	11.8077i	−1.16987	−	0.425798i	−0.852614	+	0.522542i	$0.824984\pi$
$770$	−7.20782	−	2.62343i	−0.259752	−	0.0945419i
$771$	−1.30823	+	11.1264i	−0.0471149	+	0.400708i
$772$	−17.6126	+	10.1687i	−0.633892	+	0.365978i
$773$	3.03360	+	17.2044i	0.109111	+	0.618798i	0.989498	+	0.144544i	$0.0461714\pi$
$773$	3.03360	+	17.2044i	0.109111	+	0.618798i	−0.880388	+	0.474255i	$0.842718\pi$
$774$	0.489380	−	0.0565195i	0.0175904	−	0.00203155i
$775$	0.152137	+	0.181310i	0.00546493	+	0.00651286i
$776$	5.64924	+	0.996113i	0.202796	+	0.0357584i
$777$	0.0376220	+	0.0399319i	0.00134968	+	0.00143255i
$778$		−	4.90395i		−	0.175815i
$779$	−7.55970	+	11.5300i	−0.270854	+	0.413104i
$780$	−9.83538	+	4.23456i	−0.352163	+	0.151622i
$781$	−7.42411	−	20.3976i	−0.265655	−	0.729882i
$782$	−6.90591	+	39.1654i	−0.246955	+	1.40055i
$783$	0.132757	+	0.367098i	0.00474437	+	0.0131190i
$784$	10.4049	+	8.73076i	0.371604	+	0.311813i
$785$	−14.0164	+	2.47147i	−0.500267	+	0.0882106i
$786$	1.45890	−	1.95684i	0.0520374	−	0.0697983i
$787$	18.7295	+	10.8135i	0.667634	+	0.385459i	0.795180	−	0.606374i	$-0.207377\pi$
$787$	18.7295	+	10.8135i	0.667634	+	0.385459i	−0.127546	+	0.991833i	$0.540710\pi$
$788$	4.03374	−	11.0826i	0.143696	−	0.394802i
$789$	0.936530	+	16.2720i	0.0333413	+	0.579298i
$790$	−0.469866	+	0.813832i	−0.0167171	+	0.0289548i
$791$	8.13801	+	14.0954i	0.289354	+	0.501176i
$792$	2.79298	−	4.23386i	0.0992444	−	0.150444i
$793$	23.8520	−	28.4257i	0.847010	−	1.00943i
$794$	−10.1189	+	8.49076i	−0.359106	+	0.301326i
$795$	−6.12707	+	1.44770i	−0.217305	+	0.0513447i
$796$	17.4340	−	6.34547i	0.617933	−	0.224909i
$797$	50.4058			1.78546			0.892732	−	0.450587i	$-0.148785\pi$
$797$	50.4058			1.78546			0.892732	+	0.450587i	$0.148785\pi$
$798$	26.2222	−	22.0365i	0.928256	−	0.780084i
$799$	−86.1716			−3.04853
$800$	0.939693	−	0.342020i	0.0332232	−	0.0120922i
$801$	−5.56251	−	7.49319i	−0.196541	−	0.264759i
$802$	14.0650	−	11.8019i	0.496651	−	0.416739i
$803$	16.2712	−	19.3913i	0.574199	−	0.684304i
$804$	13.3829	−	8.78894i	0.471980	−	0.309962i
$805$	−12.4102	−	21.4950i	−0.437401	−	0.757600i
$806$	−0.731636	+	1.26723i	−0.0257708	+	0.0446363i
$807$	−4.76815	+	0.274429i	−0.167847	+	0.00966037i
$808$	3.83671	−	10.5413i	0.134975	−	0.370841i
$809$	25.5990	+	14.7796i	0.900012	+	0.519622i	0.877204	−	0.480118i	$-0.159406\pi$
$809$	25.5990	+	14.7796i	0.900012	+	0.519622i	0.0228079	+	0.999740i	$0.492739\pi$
$810$	−4.92492	−	7.53294i	−0.173044	−	0.264681i
$811$	−21.4263	+	3.77804i	−0.752380	+	0.132665i	−0.536670	−	0.843792i	$-0.680318\pi$
$811$	−21.4263	+	3.77804i	−0.752380	+	0.132665i	−0.215710	+	0.976457i	$0.569207\pi$
$812$	−0.261093	−	0.219083i	−0.00916256	−	0.00768830i
$813$	2.33773	−	4.64685i	0.0819878	−	0.162972i
$814$	−0.00204978	+	0.0116249i	−7.18448e−5	+	0.000407452i
$815$	0.374467	+	1.02884i	0.0131170	+	0.0360387i
$816$	−4.97904	−	11.5645i	−0.174301	−	0.404840i
$817$	0.322159	+	0.639183i	0.0112709	+	0.0223622i
$818$		−	3.22899i		−	0.112899i
$819$	−77.2176	−	33.4342i	−2.69820	−	1.16829i
$820$	−3.11497	−	0.549253i	−0.108779	−	0.0191807i
$821$	−3.09504	−	3.68852i	−0.108018	−	0.128730i	0.709327	−	0.704880i	$-0.248999\pi$
$821$	−3.09504	−	3.68852i	−0.108018	−	0.128730i	−0.817344	+	0.576149i	$0.804555\pi$
$822$	−4.58187	+	15.2664i	−0.159811	+	0.532476i
$823$	−7.58580	−	43.0212i	−0.264424	−	1.49962i	−0.770669	−	0.637235i	$-0.780078\pi$
$823$	−7.58580	−	43.0212i	−0.264424	−	1.49962i	0.506245	−	0.862390i	$-0.331033\pi$
$824$	4.19723	−	2.42327i	0.146218	−	0.0844188i
$825$	−2.90835	−	0.341961i	−0.101256	−	0.0119055i
$826$	−36.2722	−	13.2020i	−1.26207	−	0.459356i
$827$	−36.7299	−	13.3686i	−1.27722	−	0.464872i	−0.387711	−	0.921781i	$-0.626734\pi$
$827$	−36.7299	−	13.3686i	−1.27722	−	0.464872i	−0.889513	+	0.456909i	$0.848956\pi$
$828$	15.7296	−	4.68561i	0.546640	−	0.162836i
$829$	10.9611	−	6.32838i	0.380694	−	0.219794i	−0.297426	−	0.954745i	$-0.596128\pi$
$829$	10.9611	−	6.32838i	0.380694	−	0.219794i	0.678120	+	0.734951i	$0.262795\pi$
$830$	−1.64640	−	9.33722i	−0.0571475	−	0.324100i
$831$	54.3977	+	16.3263i	1.88703	+	0.566352i
$832$	3.97397	+	4.73599i	0.137773	+	0.164191i
$833$	−97.2367	−	17.1455i	−3.36905	−	0.594055i
$834$	22.3574	−	21.0641i	0.774173	−	0.729391i
$835$		−	3.82969i		−	0.132532i
$836$	7.17339	+	1.68926i	0.248097	+	0.0584242i
$837$	−1.15481	−	0.423010i	−0.0399160	−	0.0146214i
$838$	0.874954	+	2.40392i	0.0302248	+	0.0830419i
$839$	−0.651722	+	3.69610i	−0.0224999	+	0.127604i	−0.993989	−	0.109482i	$-0.965081\pi$
$839$	−0.651722	+	3.69610i	−0.0224999	+	0.127604i	0.971489	+	0.237085i	$0.0761920\pi$
$840$	7.01973	+	3.53148i	0.242204	+	0.121848i
$841$	−22.2110	−	18.6372i	−0.765895	−	0.642663i
$842$	11.2145	−	1.97742i	0.386478	−	0.0681465i
$843$	42.9936	+	32.0534i	1.48078	+	1.10398i
$844$	−18.7114	−	10.8030i	−0.644072	−	0.371855i
$845$	−8.62645	+	23.7010i	−0.296759	+	0.815338i
$846$	15.9167	+	31.8016i	0.547229	+	1.09336i
$847$	−18.4683	+	31.9880i	−0.634577	+	1.09912i
$848$	1.81744	+	3.14789i	0.0624110	+	0.108099i
$849$	−12.5843	−	19.1621i	−0.431892	−	0.657643i
$850$	−4.67263	+	5.56863i	−0.160270	+	0.191002i
$851$	−0.0292604	+	0.0245524i	−0.00100303	+	0.000841646i
$852$	5.11347	+	21.6416i	0.175184	+	0.741429i
$853$	−18.7440	+	6.82226i	−0.641782	+	0.233590i	−0.642351	−	0.766410i	$-0.722041\pi$
$853$	−18.7440	+	6.82226i	−0.641782	+	0.233590i	0.000569321		1.00000i	$0.499819\pi$
$854$	−27.2302			−0.931800
$855$	7.80821	−	10.4896i	0.267035	−	0.358737i
$856$	7.32549			0.250380
$857$	−19.8023	+	7.20746i	−0.676435	+	0.246202i	−0.657316	−	0.753615i	$-0.728308\pi$
$857$	−19.8023	+	7.20746i	−0.676435	+	0.246202i	−0.0191188	+	0.999817i	$0.506086\pi$
$858$	−4.16308	−	17.6193i	−0.142125	−	0.601513i
$859$	−32.0239	+	26.8712i	−1.09264	+	0.916835i	−0.996908	−	0.0785719i	$-0.974964\pi$
$859$	−32.0239	+	26.8712i	−1.09264	+	0.916835i	−0.0957331	+	0.995407i	$0.530520\pi$
$860$	−0.105553	+	0.125793i	−0.00359932	+	0.00428951i
$861$	−13.6438	−	20.7754i	−0.464979	−	0.708024i
$862$	−0.179916	−	0.311623i	−0.00612796	−	0.0106139i
$863$	25.3332	−	43.8784i	0.862352	−	1.49364i	−0.00729976	−	0.999973i	$-0.502324\pi$
$863$	25.3332	−	43.8784i	0.862352	−	1.49364i	0.869652	−	0.493665i	$-0.164343\pi$
$864$	−3.34821	+	3.97360i	−0.113908	+	0.135185i
$865$	−1.21322	+	3.33329i	−0.0412507	+	0.113335i
$866$	−12.1805	−	7.03242i	−0.413911	−	0.238971i
$867$	49.7720	+	37.1070i	1.69035	+	1.26022i
$868$	1.05748	−	0.186462i	0.0358931	−	0.00632892i
$869$	−1.21710	−	1.02127i	−0.0412872	−	0.0346441i
$870$	−0.116241	−	0.0584785i	−0.00394095	−	0.00198261i
$871$	9.92389	−	56.2812i	0.336258	−	1.90701i
$872$	−3.39966	−	9.34050i	−0.115127	−	0.316309i
$873$	12.5013	+	11.8268i	0.423104	+	0.400277i
$874$	14.2679	+	19.1078i	0.482618	+	0.646330i
$875$		−	4.53681i		−	0.153372i
$876$	−18.8749	+	17.7831i	−0.637724	+	0.600835i
$877$	23.9350	+	4.22039i	0.808229	+	0.142513i	0.562469	−	0.826818i	$-0.309851\pi$
$877$	23.9350	+	4.22039i	0.808229	+	0.142513i	0.245760	+	0.969331i	$0.420963\pi$
$878$	18.0620	+	21.5254i	0.609562	+	0.726447i
$879$	1.66934	+	0.501015i	0.0563053	+	0.0168988i
$880$	0.293587	+	1.66502i	0.00989683	+	0.0561277i
$881$	14.2451	−	8.22439i	0.479929	−	0.277087i	−0.240458	−	0.970660i	$-0.577298\pi$
$881$	14.2451	−	8.22439i	0.479929	−	0.277087i	0.720387	+	0.693573i	$0.243964\pi$
$882$	11.6330	+	39.0521i	0.391705	+	1.31495i
$883$	4.07953	+	1.48483i	0.137287	+	0.0499684i	0.409750	−	0.912198i	$-0.365616\pi$
$883$	4.07953	+	1.48483i	0.137287	+	0.0499684i	−0.272463	+	0.962166i	$0.587838\pi$
$884$	−42.2316	−	15.3710i	−1.42040	−	0.516984i
$885$	−14.6358	−	1.72086i	−0.491977	−	0.0578462i
$886$	−17.1824	+	9.92029i	−0.577255	+	0.333279i
$887$	−6.00539	−	34.0582i	−0.201641	−	1.14356i	−0.902638	−	0.430400i	$-0.858373\pi$
$887$	−6.00539	−	34.0582i	−0.201641	−	1.14356i	0.700997	−	0.713164i	$-0.252739\pi$
$888$	0.00347624	−	0.0115825i	0.000116655	−	0.000388683i
$889$	2.14209	+	2.55285i	0.0718435	+	0.0856198i
$890$	3.06346	+	0.540172i	0.102688	+	0.0181066i
$891$	13.9884	−	5.98850i	0.468628	−	0.200622i
$892$			13.0566i			0.437167i
$893$	−35.4048	+	37.6350i	−1.18478	+	1.25941i
$894$	−0.307881	−	0.715097i	−0.0102971	−	0.0239164i
$895$	−4.67526	−	12.8452i	−0.156277	−	0.429367i
$896$	0.787809	−	4.46789i	0.0263188	−	0.149262i
$897$	26.3281	−	52.3340i	0.879069	−	1.74738i
$898$	30.4448	+	25.5462i	1.01596	+	0.852489i
$899$	−0.0175110	+	0.00308765i	−0.000584023	+	0.000102979i
$900$	2.91818	+	0.695854i	0.0972727	+	0.0231951i
$901$	−22.8830	−	13.2115i	−0.762345	−	0.440140i
$902$	1.82903	−	5.02522i	0.0609001	−	0.167322i
$903$	−1.28824	+	0.0741441i	−0.0428698	+	0.00246736i
$904$	1.79377	−	3.10691i	0.0596600	−	0.103334i
$905$	10.8378	+	18.7717i	0.360262	+	0.623992i
$906$	−9.74981	+	6.40297i	−0.323916	+	0.212724i
$907$	34.5064	−	41.1232i	1.14577	−	1.36547i	0.225472	−	0.974250i	$-0.427608\pi$
$907$	34.5064	−	41.1232i	1.14577	−	1.36547i	0.920296	−	0.391223i	$-0.127948\pi$
$908$	−1.26638	+	1.06262i	−0.0420262	+	0.0352642i
$909$	27.0217	−	20.0594i	0.896255	−	0.665327i
$910$	26.3568	−	9.59311i	0.873721	−	0.318008i
$911$	14.0631			0.465932			0.232966	−	0.972485i	$-0.425157\pi$
$911$	14.0631			0.465932			0.232966	+	0.972485i	$0.425157\pi$
$912$	−7.09645	−	2.57688i	−0.234987	−	0.0853292i
$913$	16.0300			0.530516
$914$	23.1522	−	8.42672i	0.765807	−	0.278731i
$915$	−10.1173	+	2.39051i	−0.334468	+	0.0790279i
$916$	11.8149	−	9.91390i	0.390376	−	0.327564i
$917$	−4.10955	+	4.89758i	−0.135709	+	0.161732i
$918$	6.63571	−	37.1851i	0.219011	−	1.22729i
$919$	−3.05640	−	5.29384i	−0.100821	−	0.174628i	0.811202	−	0.584766i	$-0.198814\pi$
$919$	−3.05640	−	5.29384i	−0.100821	−	0.174628i	−0.912023	+	0.410139i	$0.865480\pi$
$920$	−2.73544	+	4.73792i	−0.0901847	+	0.156204i
$921$	−0.353400	−	6.14024i	−0.0116449	−	0.202328i
$922$	−2.64375	+	7.26366i	−0.0870674	+	0.239216i
$923$	68.7405	+	39.6874i	2.26262	+	1.30633i
$924$	−7.94088	+	10.6512i	−0.261236	+	0.350398i
$925$	−0.00687577	+	0.00121238i	−0.000226074	+	3.98630e-5i
$926$	−27.3299	−	22.9325i	−0.898117	−	0.753609i
$927$	14.5139	+	0.865329i	0.476698	+	0.0284211i
$928$	−0.0130455	+	0.0739847i	−0.000428239	+	0.00242867i
$929$	1.21958	+	3.35077i	0.0400131	+	0.109935i	0.958090	−	0.286467i	$-0.0924808\pi$
$929$	1.21958	+	3.35077i	0.0400131	+	0.109935i	−0.918077	+	0.396402i	$0.870259\pi$
$930$	0.376532	−	0.162114i	0.0123470	−	0.00531592i
$931$	−47.4392	+	35.4231i	−1.55476	+	1.16095i
$932$			21.7491i			0.712417i
$933$	−5.75393	−	6.10720i	−0.188375	−	0.199941i
$934$	−34.8522	−	6.14538i	−1.14040	−	0.201083i
$935$	−7.90004	−	9.41490i	−0.258359	−	0.307900i
$936$	2.12791	+	18.4247i	0.0695529	+	0.602231i
$937$	2.20099	+	12.4824i	0.0719032	+	0.407783i	0.999422	+	0.0340060i	$0.0108265\pi$
$937$	2.20099	+	12.4824i	0.0719032	+	0.407783i	−0.927518	+	0.373778i	$0.878062\pi$
$938$	−36.3192	+	20.9689i	−1.18586	+	0.684658i
$939$	2.59472	−	22.0679i	0.0846754	−	0.720157i
$940$	−11.1392	−	4.05435i	−0.363322	−	0.132238i
$941$	24.0938	+	8.76941i	0.785434	+	0.285875i	0.703437	−	0.710758i	$-0.251648\pi$
$941$	24.0938	+	8.76941i	0.785434	+	0.285875i	0.0819973	+	0.996633i	$0.473870\pi$
$942$	−2.87869	+	24.4830i	−0.0937927	+	0.797699i
$943$	14.9861	−	8.65225i	0.488016	−	0.281756i
$944$	1.47743	+	8.37893i	0.0480863	+	0.272711i
$945$	11.7449	+	20.4399i	0.382062	+	0.664909i
$946$	−0.178459	−	0.212679i	−0.00580219	−	0.00691478i
$947$	−14.7708	−	2.60449i	−0.479986	−	0.0846345i	−0.0715801	−	0.997435i	$-0.522804\pi$
$947$	−14.7708	−	2.60449i	−0.479986	−	0.0846345i	−0.408406	+	0.912800i	$0.633915\pi$
$948$	1.11616	+	1.18469i	0.0362511	+	0.0384768i
$949$			92.5641i			3.00476i
$950$	0.512249	+	4.32870i	0.0166195	+	0.140441i
$951$	−7.94973	+	3.42271i	−0.257788	+	0.110989i
$952$	11.2797	+	30.9907i	0.365576	+	1.00441i
$953$	−3.62464	+	20.5563i	−0.117414	+	0.665885i	0.868113	+	0.496366i	$0.165333\pi$
$953$	−3.62464	+	20.5563i	−0.117414	+	0.665885i	−0.985527	+	0.169519i	$0.945779\pi$
$954$	−0.648989	+	10.8853i	−0.0210118	+	0.352424i
$955$	3.25914	+	2.73474i	0.105463	+	0.0884942i
$956$	−12.0430	+	2.12350i	−0.389497	+	0.0686788i
$957$	0.131495	−	0.176375i	0.00425062	−	0.00570140i
$958$	−10.5568	−	6.09498i	−0.341075	−	0.196920i
$959$	14.2793	−	39.2320i	0.461102	−	1.26687i
$960$	−0.0995230	−	1.72919i	−0.00321209	−	0.0558093i
$961$	−15.4720	+	26.7983i	−0.499096	+	0.864460i
$962$	−0.0215823	−	0.0373816i	−0.000695840	−	0.00120523i
$963$	18.3445	+	12.1015i	0.591142	+	0.389964i
$964$	−17.7283	+	21.1278i	−0.570991	+	0.680481i
$965$	15.5793	−	13.0726i	0.501515	−	0.420821i
$966$	−41.8380	+	9.88548i	−1.34612	+	0.318060i
$967$	−32.9627	+	11.9974i	−1.06001	+	0.385812i	−0.812432	−	0.583056i	$-0.801857\pi$
$967$	−32.9627	+	11.9974i	−1.06001	+	0.385812i	−0.247577	+	0.968868i	$0.579634\pi$
$968$	8.14152			0.261678
$969$	54.0413	−	9.57065i	1.73606	−	0.307454i
$970$	−5.73639			−0.184184
$971$	33.2457	−	12.1005i	1.06691	−	0.388322i	0.251887	−	0.967757i	$-0.418949\pi$
$971$	33.2457	−	12.1005i	1.06691	−	0.388322i	0.815019	+	0.579435i	$0.196727\pi$
$972$	−14.9488	+	4.41955i	−0.479484	+	0.141757i
$973$	−61.6349	+	51.7178i	−1.97592	+	1.65800i
$974$	13.3313	−	15.8876i	0.427162	−	0.509071i
$975$	8.95063	−	5.87813i	0.286650	−	0.188251i
$976$	3.00103	+	5.19794i	0.0960607	+	0.166382i
$977$	6.32362	−	10.9528i	0.202311	−	0.350412i	−0.746962	−	0.664867i	$-0.768488\pi$
$977$	6.32362	−	10.9528i	0.202311	−	0.350412i	0.949273	+	0.314455i	$0.101822\pi$
$978$	1.89323	−	0.108965i	0.0605389	−	0.00348430i
$979$	−1.79879	+	4.94214i	−0.0574896	+	0.157951i
$980$	−11.7629	−	6.79132i	−0.375753	−	0.216941i
$981$	6.91676	−	29.0066i	0.220835	−	0.926109i
$982$	1.81626	−	0.320255i	0.0579591	−	0.0102198i
$983$	14.4524	+	12.1270i	0.460958	+	0.386790i	0.843484	−	0.537155i	$-0.180501\pi$
$983$	14.4524	+	12.1270i	0.460958	+	0.386790i	−0.382525	+	0.923945i	$0.624945\pi$
$984$	−2.46211	+	4.89409i	−0.0784893	+	0.156018i
$985$	−2.04798	+	11.6147i	−0.0652542	+	0.370075i
$986$	−0.186782	−	0.513181i	−0.00594837	−	0.0163430i
$987$	−36.8360	−	85.5568i	−1.17250	−	2.72330i
$988$	−24.0646	+	12.1290i	−0.765598	+	0.385874i
$989$		−	0.898379i		−	0.0285668i
$990$	−2.01535	+	4.65453i	−0.0640521	+	0.147931i
$991$	28.2284	+	4.97742i	0.896704	+	0.158113i	0.602960	−	0.797771i	$-0.293988\pi$
$991$	28.2284	+	4.97742i	0.896704	+	0.158113i	0.293744	+	0.955884i	$0.405099\pi$
$992$	−0.152137	−	0.181310i	−0.00483037	−	0.00575661i
$993$	18.0011	−	59.9779i	0.571246	−	1.90334i
$994$	−10.1145	−	57.3624i	−0.320814	−	1.81942i
$995$	−16.0673	+	9.27646i	−0.509368	+	0.294084i
$996$	−16.3097	−	1.91768i	−0.516792	−	0.0607639i
$997$	−35.3852	−	12.8792i	−1.12066	−	0.407887i	−0.285767	−	0.958299i	$-0.592248\pi$
$997$	−35.3852	−	12.8792i	−1.12066	−	0.407887i	−0.834893	+	0.550412i	$0.814471\pi$
$998$	33.7947	+	12.3003i	1.06975	+	0.389358i
$999$	0.0278391	−	0.0232622i	0.000880789	−	0.000735985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.a.71.6	✓	84
3.2	odd	2		570.2.bb.b.71.5	yes	84
19.15	odd	18		570.2.bb.b.281.5	yes	84
57.53	even	18	inner	570.2.bb.a.281.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.71.6	✓	84	1.1	even	1	trivial
570.2.bb.a.281.6	yes	84	57.53	even	18	inner
570.2.bb.b.71.5	yes	84	3.2	odd	2
570.2.bb.b.281.5	yes	84	19.15	odd	18

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.398282 - 1.68564i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.950784 + 1.44776i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.68274 + 1.34272i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.398282 - 1.68564i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.950784 + 1.44776i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.68274 + 1.34272i) q^{9} +(0.342020 - 0.939693i) q^{10} +(1.46419 + 0.845352i) q^{11} +(-1.38861 - 1.03526i) q^{12} +(-6.08847 + 1.07356i) q^{13} +(3.47540 + 2.91621i) q^{14} +(1.54728 + 0.778405i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.48626 + 6.83093i) q^{17} +(2.06172 - 2.17929i) q^{18} +(4.00488 + 1.72073i) q^{19} +1.00000i q^{20} +(-5.71939 + 5.38855i) q^{21} +(-1.66502 - 0.293587i) q^{22} +(-3.51661 - 4.19093i) q^{23} +(1.65895 + 0.497896i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(5.35411 - 3.09120i) q^{26} +(3.33182 + 3.98735i) q^{27} +(-4.26321 - 1.55168i) q^{28} +(0.0705953 + 0.0256946i) q^{29} +(-1.72020 - 0.202260i) q^{30} +(-0.204974 + 0.118342i) q^{31} +(0.173648 + 0.984808i) q^{32} +(0.841795 - 2.80478i) q^{33} +(-4.67263 - 5.56863i) q^{34} +(4.46789 + 0.787809i) q^{35} +(-1.19202 + 2.75301i) q^{36} -0.00698184i q^{37} +(-4.35188 - 0.247203i) q^{38} +(4.23456 + 9.83538i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-0.549253 + 3.11497i) q^{41} +(3.53148 - 7.01973i) q^{42} +(0.125793 + 0.105553i) q^{43} +(1.66502 - 0.293587i) q^{44} +(0.695854 - 2.91818i) q^{45} +(4.73792 + 2.73544i) q^{46} +(-4.05435 + 11.1392i) q^{47} +(-1.72919 + 0.0995230i) q^{48} +(-6.79132 + 11.7629i) q^{49} +(0.500000 + 0.866025i) q^{50} +(10.5242 - 6.91156i) q^{51} +(-3.97397 + 4.73599i) q^{52} +(-2.78447 + 2.33645i) q^{53} +(-4.49464 - 2.60734i) q^{54} +(-1.58874 + 0.578254i) q^{55} +4.53681 q^{56} +(1.30545 - 7.43611i) q^{57} -0.0751260 q^{58} +(-7.99509 + 2.90997i) q^{59} +(1.68564 - 0.398282i) q^{60} +(-4.59785 + 3.85805i) q^{61} +(0.152137 - 0.181310i) q^{62} +(11.3611 + 7.49466i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.09120 - 5.35411i) q^{65} +(0.168264 + 2.92355i) q^{66} +(-3.16159 + 8.68641i) q^{67} +(6.29542 + 3.63466i) q^{68} +(-5.66379 + 7.59690i) q^{69} +(-4.46789 + 0.787809i) q^{70} +(-9.83511 - 8.25264i) q^{71} +(0.178545 - 2.99468i) q^{72} +(2.59990 - 14.7447i) q^{73} +(0.00238793 + 0.00656079i) q^{74} +(-1.59087 + 0.684939i) q^{75} +(4.17398 - 1.25614i) q^{76} -7.67040i q^{77} +(-7.34308 - 7.79392i) q^{78} +(-0.925456 - 0.163183i) q^{79} +(0.642788 + 0.766044i) q^{80} +(5.39423 - 7.20433i) q^{81} +(-0.549253 - 3.11497i) q^{82} +(8.21102 - 4.74063i) q^{83} +(-0.917613 + 7.80423i) q^{84} +(-6.83093 - 2.48626i) q^{85} +(-0.154308 - 0.0561635i) q^{86} +(0.0151949 - 0.129232i) q^{87} +(-1.46419 + 0.845352i) q^{88} +(0.540172 + 3.06346i) q^{89} +(0.344188 + 2.98019i) q^{90} +(18.0291 + 21.4863i) q^{91} +(-5.38776 - 0.950007i) q^{92} +(0.281119 + 0.298379i) q^{93} -11.8541i q^{94} +(-3.89244 + 1.96186i) q^{95} +(1.59087 - 0.684939i) q^{96} +(-1.96196 - 5.39044i) q^{97} +(2.35860 - 13.3763i) q^{98} +(-5.06312 - 0.301867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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