LMFDB - Embedded newform 570.2.bb.b.71.5

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			71.5
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.b.281.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-0.950784 + 1.44776i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.398282 + 1.68564i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.19202 - 2.75301i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-0.950784 + 1.44776i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.398282 + 1.68564i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.19202 - 2.75301i) q^{9} +(0.342020 - 0.939693i) q^{10} +(-1.46419 - 0.845352i) q^{11} +(0.202260 + 1.72020i) q^{12} +(-6.08847 + 1.07356i) q^{13} +(-3.47540 - 2.91621i) q^{14} +(0.497896 + 1.65895i) 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} +(7.84500 + 0.451517i) q^{21} +(-1.66502 - 0.293587i) q^{22} +(3.51661 + 4.19093i) q^{23} +(0.778405 + 1.54728i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(-5.35411 + 3.09120i) q^{26} +(5.11906 + 0.891764i) q^{27} +(-4.26321 - 1.55168i) q^{28} +(-0.0705953 - 0.0256946i) q^{29} +(1.03526 + 1.38861i) q^{30} +(-0.204974 + 0.118342i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(2.61600 - 1.31605i) q^{33} +(-4.67263 - 5.56863i) q^{34} +(-4.46789 - 0.787809i) q^{35} +(-2.68274 - 1.34272i) 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} +(7.52632 - 2.25886i) q^{42} +(0.125793 + 0.105553i) q^{43} +(-1.66502 + 0.293587i) q^{44} +(-2.87515 - 0.856464i) q^{45} +(4.73792 + 2.73544i) q^{46} +(4.05435 - 11.1392i) q^{47} +(1.26066 + 1.18774i) q^{48} +(-6.79132 + 11.7629i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(12.2534 + 2.89524i) q^{51} +(-3.97397 + 4.73599i) q^{52} +(2.78447 - 2.33645i) q^{53} +(5.11534 - 0.912837i) q^{54} +(-1.58874 + 0.578254i) q^{55} -4.53681 q^{56} +(-6.29898 + 4.16207i) q^{57} -0.0751260 q^{58} +(7.99509 - 2.90997i) q^{59} +(1.44776 + 0.950784i) q^{60} +(-4.59785 + 3.85805i) q^{61} +(-0.152137 + 0.181310i) q^{62} +(-8.11259 + 10.9284i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.09120 + 5.35411i) q^{65} +(2.00812 - 2.13141i) q^{66} +(-3.16159 + 8.68641i) q^{67} +(-6.29542 - 3.63466i) q^{68} +(-9.41100 + 1.10654i) q^{69} +(-4.46789 + 0.787809i) q^{70} +(9.83511 + 8.25264i) q^{71} +(-2.98019 - 0.344188i) 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} +(0.615291 - 10.6905i) q^{78} +(-0.925456 - 0.163183i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(-6.15818 + 6.56329i) q^{81} +(-0.549253 - 3.11497i) q^{82} +(-8.21102 + 4.74063i) q^{83} +(6.29985 - 4.69679i) q^{84} +(-6.83093 - 2.48626i) q^{85} +(0.154308 + 0.0561635i) q^{86} +(0.104321 - 0.0777751i) q^{87} +(-1.46419 + 0.845352i) q^{88} +(-0.540172 - 3.06346i) q^{89} +(-2.99468 + 0.178545i) q^{90} +(18.0291 + 21.4863i) q^{91} +(5.38776 + 0.950007i) q^{92} +(0.0235555 - 0.409271i) 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} +(-0.581920 + 5.03862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * 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
$3$	−0.950784	+	1.44776i	−0.548935	+	0.835865i
$3$	−0.950784	+	1.44776i	−0.548935	+	0.835865i
$4$	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
$6$	−0.398282	+	1.68564i	−0.162598	+	0.688158i
$7$	−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
$9$	−1.19202	−	2.75301i	−0.397340	−	0.917672i
$10$	0.342020	−	0.939693i	0.108156	−	0.297157i
$11$	−1.46419	−	0.845352i	−0.441470	−	0.254883i	0.262751	−	0.964864i	$-0.415370\pi$
$11$	−1.46419	−	0.845352i	−0.441470	−	0.254883i	−0.704221	+	0.709981i	$0.748704\pi$
$12$	0.202260	+	1.72020i	0.0583873	+	0.496579i
$13$	−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
$15$	0.497896	+	1.65895i	0.128556	+	0.428338i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.48626	−	6.83093i	−0.603006	−	1.65674i	−0.745149	−	0.666899i	$-0.767621\pi$
$17$	−2.48626	−	6.83093i	−0.603006	−	1.65674i	0.142143	−	0.989846i	$-0.454601\pi$
$18$	−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
$21$	7.84500	+	0.451517i	1.71192	+	0.0985291i
$22$	−1.66502	−	0.293587i	−0.354983	−	0.0625931i
$23$	3.51661	+	4.19093i	0.733264	+	0.873870i	0.995847	−	0.0910394i	$-0.0290189\pi$
$23$	3.51661	+	4.19093i	0.733264	+	0.873870i	−0.262583	+	0.964909i	$0.584574\pi$
$24$	0.778405	+	1.54728i	0.158891	+	0.315838i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	−5.35411	+	3.09120i	−1.05003	+	0.606234i
$27$	5.11906	+	0.891764i	0.985163	+	0.171620i
$28$	−4.26321	−	1.55168i	−0.805670	−	0.293240i
$29$	−0.0705953	−	0.0256946i	−0.0131092	−	0.00477137i	0.335457	−	0.942055i	$-0.391109\pi$
$29$	−0.0705953	−	0.0256946i	−0.0131092	−	0.00477137i	−0.348566	+	0.937284i	$0.613331\pi$
$30$	1.03526	+	1.38861i	0.189012	+	0.253524i
$31$	−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
$33$	2.61600	−	1.31605i	0.455387	−	0.229095i
$34$	−4.67263	−	5.56863i	−0.801350	−	0.955012i
$35$	−4.46789	−	0.787809i	−0.755211	−	0.133164i
$36$	−2.68274	−	1.34272i	−0.447124	−	0.223786i
$37$		−	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	$-0.865003\pi$
$41$	0.549253	−	3.11497i	0.0857789	−	0.486476i	0.997186	−	0.0749699i	$-0.0238861\pi$
$42$	7.52632	−	2.25886i	1.16134	−	0.348550i
$43$	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
$45$	−2.87515	−	0.856464i	−0.428602	−	0.127674i
$46$	4.73792	+	2.73544i	0.698568	+	0.403318i
$47$	4.05435	−	11.1392i	0.591388	−	1.62483i	−0.176542	−	0.984293i	$-0.556491\pi$
$47$	4.05435	−	11.1392i	0.591388	−	1.62483i	0.767931	−	0.640533i	$-0.221287\pi$
$48$	1.26066	+	1.18774i	0.181961	+	0.171436i
$49$	−6.79132	+	11.7629i	−0.970189	+	1.68042i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	12.2534	+	2.89524i	1.71583	+	0.405415i
$52$	−3.97397	+	4.73599i	−0.551090	+	0.656764i
$53$	2.78447	−	2.33645i	0.382477	−	0.320936i	−0.431197	−	0.902258i	$-0.641909\pi$
$53$	2.78447	−	2.33645i	0.382477	−	0.320936i	0.813674	+	0.581322i	$0.197464\pi$
$54$	5.11534	−	0.912837i	0.696110	−	0.124221i
$55$	−1.58874	+	0.578254i	−0.214226	+	0.0779718i
$56$	−4.53681			−0.606257
$57$	−6.29898	+	4.16207i	−0.834320	+	0.551280i
$58$	−0.0751260			−0.00986453
$59$	7.99509	−	2.90997i	1.04087	−	0.378846i	0.235661	−	0.971835i	$-0.424275\pi$
$59$	7.99509	−	2.90997i	1.04087	−	0.378846i	0.805211	+	0.592989i	$0.202052\pi$
$60$	1.44776	+	0.950784i	0.186905	+	0.122746i
$61$	−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
$63$	−8.11259	+	10.9284i	−1.02209	+	1.37685i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−3.09120	+	5.35411i	−0.383416	+	0.664096i
$66$	2.00812	−	2.13141i	0.247182	−	0.262358i
$67$	−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
$69$	−9.41100	+	1.10654i	−1.13295	+	0.133211i
$70$	−4.46789	+	0.787809i	−0.534015	+	0.0941612i
$71$	9.83511	+	8.25264i	1.16721	+	0.979408i	0.999979	−	0.00650962i	$-0.00207209\pi$
$71$	9.83511	+	8.25264i	1.16721	+	0.979408i	0.167234	+	0.985917i	$0.446517\pi$
$72$	−2.98019	−	0.344188i	−0.351219	−	0.0405630i
$73$	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
$78$	0.615291	−	10.6905i	0.0696680	−	1.21046i
$79$	−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
$81$	−6.15818	+	6.56329i	−0.684242	+	0.729255i
$82$	−0.549253	−	3.11497i	−0.0606548	−	0.343991i
$83$	−8.21102	+	4.74063i	−0.901276	+	0.520352i	−0.877614	−	0.479368i	$-0.840866\pi$
$83$	−8.21102	+	4.74063i	−0.901276	+	0.520352i	−0.0236622	+	0.999720i	$0.507533\pi$
$84$	6.29985	−	4.69679i	0.687370	−	0.512462i
$85$	−6.83093	−	2.48626i	−0.740919	−	0.269672i
$86$	0.154308	+	0.0561635i	0.0166395	+	0.00605627i
$87$	0.104321	−	0.0777751i	0.0111843	−	0.00833837i
$88$	−1.46419	+	0.845352i	−0.156083	+	0.0901148i
$89$	−0.540172	−	3.06346i	−0.0572581	−	0.324727i	0.942702	−	0.333635i	$-0.108275\pi$
$89$	−0.540172	−	3.06346i	−0.0572581	−	0.324727i	−0.999960	+	0.00890859i	$0.997164\pi$
$90$	−2.99468	+	0.178545i	−0.315667	+	0.0188203i
$91$	18.0291	+	21.4863i	1.88997	+	2.25238i
$92$	5.38776	+	0.950007i	0.561713	+	0.0990451i
$93$	0.0235555	−	0.409271i	0.00244259	−	0.0424394i
$94$		−	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
$99$	−0.581920	+	5.03862i	−0.0584852	+	0.506400i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	11.0474	−	1.94795i	1.09926	−	0.193828i	0.405540	−	0.914077i	$-0.367084\pi$
$101$	11.0474	−	1.94795i	1.09926	−	0.193828i	0.693716	+	0.720249i	$0.255972\pi$
$102$	12.5047	−	1.47029i	1.23815	−	0.145580i
$103$	−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
$105$	5.38855	−	5.71939i	0.525869	−	0.558155i
$106$	1.81744	−	3.14789i	0.176525	−	0.305750i
$107$	3.66274	+	6.34406i	0.354091	+	0.613303i	0.986962	−	0.160954i	$-0.0514570\pi$
$107$	3.66274	+	6.34406i	0.354091	+	0.613303i	−0.632871	+	0.774257i	$0.718124\pi$
$108$	4.49464	−	2.60734i	0.432497	−	0.250891i
$109$	−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
$111$	0.0101080	+	0.00663823i	0.000959412	+	0.000630072i
$112$	−4.26321	+	1.55168i	−0.402835	+	0.146620i
$113$	3.58755			0.337488			0.168744	−	0.985660i	$-0.446029\pi$
$113$	3.58755			0.337488			0.168744	+	0.985660i	$0.446029\pi$
$114$	−4.49559	+	6.06545i	−0.421051	+	0.568081i
$115$	5.47087			0.510162
$116$	−0.0705953	+	0.0256946i	−0.00655461	+	0.00238568i
$117$	10.2131	+	15.4820i	0.944202	+	1.43131i
$118$	6.51765	−	5.46896i	0.599999	−	0.503459i
$119$	−21.1989	+	25.2638i	−1.94330	+	2.31593i
$120$	1.68564	+	0.398282i	0.153877	+	0.0363580i
$121$	−4.07076	−	7.05077i	−0.370069	−	0.640979i
$122$	−3.00103	+	5.19794i	−0.271701	+	0.470600i
$123$	3.98751	+	3.75685i	0.359541	+	0.338744i
$124$	−0.0809506	+	0.222410i	−0.00726958	+	0.0199730i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	−3.88561	+	13.0440i	−0.346158	+	1.16205i
$127$	−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
$129$	−0.272417	+	0.0817602i	−0.0239850	+	0.00719858i
$130$	−1.07356	+	6.08847i	−0.0941576	+	0.533994i
$131$	0.481979	+	1.32423i	0.0421107	+	0.115698i	0.958966	−	0.283522i	$-0.0915030\pi$
$131$	0.481979	+	1.32423i	0.0421107	+	0.115698i	−0.916855	+	0.399221i	$0.869281\pi$
$132$	1.15803	−	2.68968i	0.100793	−	0.234107i
$133$	−2.32398	−	19.6385i	−0.201514	−	1.70287i
$134$			9.24389i			0.798550i
$135$	3.97360	−	3.34821i	0.341993	−	0.288168i
$136$	−7.15889	−	1.26231i	−0.613870	−	0.108242i
$137$	−5.91522	−	7.04949i	−0.505372	−	0.602279i	0.451686	−	0.892177i	$-0.350823\pi$
$137$	−5.91522	−	7.04949i	−0.505372	−	0.602279i	−0.957057	+	0.289899i	$0.906378\pi$
$138$	−8.46499	+	4.25856i	−0.720588	+	0.362512i
$139$	−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
$141$	12.2721	+	16.4608i	1.03350	+	1.38625i
$142$	12.0645	+	4.39114i	1.01243	+	0.368496i
$143$	9.82223	+	3.57500i	0.821376	+	0.298956i
$144$	−2.91818	+	0.695854i	−0.243182	+	0.0579878i
$145$	−0.0650610	+	0.0375630i	−0.00540302	+	0.00311944i
$146$	−2.59990	−	14.7447i	−0.215169	−	1.22028i
$147$	−10.5728	−	21.0162i	−0.872030	−	1.73339i
$148$	−0.00448784	−	0.00534840i	−0.000368898	−	0.000439636i
$149$	0.442672	+	0.0780551i	0.0362651	+	0.00639452i	0.191751	−	0.981444i	$-0.438583\pi$
$149$	0.442672	+	0.0780551i	0.0362651	+	0.00639452i	−0.155486	+	0.987838i	$0.549694\pi$
$150$	1.72919	+	0.0995230i	0.141188	+	0.00812602i
$151$			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
$156$	−3.07819	−	10.2563i	−0.246453	−	0.821158i
$157$	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
$159$	0.735187	+	6.25271i	0.0583041	+	0.495872i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	8.48905	−	23.3235i	0.669031	−	1.83815i
$162$	−3.54202	+	8.27370i	−0.278287	+	0.650043i
$163$	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
$165$	0.673376	−	2.84991i	0.0524222	−	0.221865i
$166$	−6.09444	+	7.26307i	−0.473020	+	0.563724i
$167$	2.93371	−	2.46168i	0.227018	−	0.190490i	−0.522183	−	0.852833i	$-0.674882\pi$
$167$	2.93371	−	2.46168i	0.227018	−	0.190490i	0.749201	+	0.662343i	$0.230438\pi$
$168$	4.31353	−	6.56821i	0.332796	−	0.506749i
$169$	23.7010	−	8.62645i	1.82315	−	0.663573i
$170$	−7.26933			−0.557532
$171$	−0.0367134	−	13.0766i	−0.00280754	−	0.999996i
$172$	0.164211			0.0125210
$173$	−3.33329	+	1.21322i	−0.253426	+	0.0922394i	−0.465609	−	0.884990i	$-0.654165\pi$
$173$	−3.33329	+	1.21322i	−0.253426	+	0.0922394i	0.212184	+	0.977230i	$0.431943\pi$
$174$	0.0714286	−	0.108764i	0.00541499	−	0.00824541i
$175$	−3.47540	+	2.91621i	−0.262715	+	0.220444i
$176$	−1.08676	+	1.29515i	−0.0819178	+	0.0976259i
$177$	−3.38866	+	14.3417i	−0.254707	+	1.07799i
$178$	−1.55536	−	2.69397i	−0.116579	−	0.201921i
$179$	6.83477	−	11.8382i	0.510855	−	0.884826i	−0.489066	−	0.872247i	$-0.662662\pi$
$179$	6.83477	−	11.8382i	0.510855	−	0.884826i	0.999921	−	0.0125797i	$-0.00400435\pi$
$180$	−2.75301	+	1.19202i	−0.205198	+	0.0888479i
$181$	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
$183$	−1.21398	−	10.3248i	−0.0897396	−	0.763228i
$184$	5.38776	−	0.950007i	0.397191	−	0.0700355i
$185$	−0.00534840	−	0.00448784i	−0.000393222	−	0.000329953i
$186$	−0.117844	−	0.392645i	−0.00864074	−	0.0287901i
$187$	−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	$0.0491906\pi$
$191$			4.25450i			0.307845i	−0.988083	+	0.153923i	$0.950809\pi$
$192$	1.72919	+	0.0995230i	0.124793	+	0.00718245i
$193$	−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
$195$	−4.81241	−	9.56592i	−0.344624	−	0.685030i
$196$	2.35860	+	13.3763i	0.168472	+	0.955450i
$197$	−10.2138	+	5.89693i	−0.727702	+	0.420139i	−0.817581	−	0.575814i	$-0.804685\pi$
$197$	−10.2138	+	5.89693i	−0.727702	+	0.420139i	0.0898788	+	0.995953i	$0.471352\pi$
$198$	1.17648	+	4.93378i	0.0836090	+	0.350628i
$199$	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
$201$	−9.56985	−	12.8361i	−0.675005	−	0.905391i
$202$	9.71490	−	5.60890i	0.683538	−	0.394641i
$203$	0.0591849	+	0.335654i	0.00415397	+	0.0235583i
$204$	11.2477	−	5.65848i	0.787497	−	0.396173i
$205$	−2.03315	−	2.42301i	−0.142001	−	0.169231i
$206$	−4.77292	−	0.841594i	−0.332545	−	0.0586367i
$207$	7.34583	−	14.6770i	0.510571	−	1.02012i
$208$			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
$213$	−21.2989	+	6.39240i	−1.45938	+	0.438000i
$214$	5.61165	+	4.70873i	0.383604	+	0.321882i
$215$	0.161716	−	0.0285150i	0.0110290	−	0.00194470i
$216$	3.33182	−	3.98735i	0.226702	−	0.271305i
$217$	0.929929	+	0.536895i	0.0631277	+	0.0364468i
$218$	−3.39966	+	9.34050i	−0.230254	+	0.632618i
$219$	18.8749	+	17.7831i	1.27545	+	1.20167i
$220$	−0.845352	+	1.46419i	−0.0569936	+	0.0987158i
$221$	22.4709	+	38.9208i	1.51156	+	2.61810i
$222$	0.0117689	+	0.00278074i	0.000789874	+	0.000186631i
$223$	−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
$225$	−2.50420	+	1.65197i	−0.166947	+	0.110131i
$226$	3.37119	−	1.22701i	0.224248	−	0.0816197i
$227$	1.65314			0.109723			0.0548613	−	0.998494i	$-0.482528\pi$
$227$	1.65314			0.109723			0.0548613	+	0.998494i	$0.482528\pi$
$228$	−2.14997	+	7.23724i	−0.142385	+	0.479298i
$229$	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
$231$	−11.1049	−	7.29289i	−0.730649	−	0.479837i
$232$	−0.0575498	+	0.0482901i	−0.00377833	+	0.00317040i
$233$	13.9801	−	16.6608i	0.915866	−	1.09149i	−0.0796438	−	0.996823i	$-0.525378\pi$
$233$	13.9801	−	16.6608i	0.915866	−	1.09149i	0.995509	−	0.0946628i	$-0.0301773\pi$
$234$	14.8923	+	11.0552i	0.973542	+	0.722700i
$235$	−5.92707	−	10.2660i	−0.386639	−	0.669679i
$236$	4.25410	−	7.36831i	0.276918	−	0.479636i
$237$	1.11616	−	1.18469i	0.0725022	−	0.0769536i
$238$	−11.2797	+	30.9907i	−0.731153	+	2.00883i
$239$	10.5904	+	6.11437i	0.685036	+	0.395506i	0.801750	−	0.597660i	$-0.203903\pi$
$239$	10.5904	+	6.11437i	0.685036	+	0.395506i	−0.116714	+	0.993166i	$0.537236\pi$
$240$	1.72020	−	0.202260i	0.111038	−	0.0130558i
$241$	−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
$243$	−3.64698	−	15.1558i	−0.233954	−	0.972248i
$244$	−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
$249$	0.943604	−	16.3949i	0.0597985	−	1.03898i
$250$	−0.984808	−	0.173648i	−0.0622847	−	0.0109825i
$251$	−14.3816	−	17.1393i	−0.907756	−	1.08182i	−0.996317	−	0.0857509i	$-0.972671\pi$
$251$	−14.3816	−	17.1393i	−0.907756	−	1.08182i	0.0885604	−	0.996071i	$-0.471773\pi$
$252$	0.810027	+	13.5863i	0.0510269	+	0.855857i
$253$	−1.60618	−	9.10910i	−0.100980	−	0.572684i
$254$	−0.636138	+	0.367274i	−0.0399148	+	0.0230448i
$255$	10.0942	−	7.52566i	0.632126	−	0.471275i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	6.07802	+	2.21222i	0.379136	+	0.137994i	0.524557	−	0.851376i	$-0.324231\pi$
$257$	6.07802	+	2.21222i	0.379136	+	0.137994i	−0.145420	+	0.989370i	$0.546453\pi$
$258$	−0.228025	+	0.170002i	−0.0141962	+	0.0105838i
$259$	−0.0274316	+	0.0158377i	−0.00170452	+	0.000984104i
$260$	1.07356	+	6.08847i	0.0665795	+	0.377591i
$261$	0.0134134	+	0.224978i	0.000830269	+	0.0139258i
$262$	0.905825	+	1.07952i	0.0559620	+	0.0666929i
$263$	9.26722	+	1.63406i	0.571441	+	0.100761i	0.451900	−	0.892069i	$-0.350746\pi$
$263$	9.26722	+	1.63406i	0.571441	+	0.100761i	0.119542	+	0.992829i	$0.461858\pi$
$264$	0.168264	−	2.92355i	0.0103559	−	0.179932i
$265$		−	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	−0.995919	−	0.0902484i	$-0.971234\pi$
$269$	−0.478825	+	2.71555i	−0.0291945	+	0.165570i	0.966725	+	0.255819i	$0.0823450\pi$
$270$	2.58881	−	4.50534i	0.157550	−	0.274186i
$271$	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
$273$	−48.2488	+	5.67305i	−2.92015	+	0.343349i
$274$	−7.96956	−	4.60123i	−0.481459	−	0.277970i
$275$	−0.578254	+	1.58874i	−0.0348701	+	0.0958047i
$276$	−6.49798	+	6.89693i	−0.391132	+	0.415147i
$277$	−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
$279$	0.570130	+	0.423231i	0.0341328	+	0.0253382i
$280$	−2.91621	+	3.47540i	−0.174277	+	0.207695i
$281$	23.7180	−	19.9018i	1.41490	−	1.18724i	0.460889	−	0.887458i	$-0.347531\pi$
$281$	23.7180	−	19.9018i	1.41490	−	1.18724i	0.954008	−	0.299782i	$-0.0969139\pi$
$282$	17.1620	+	11.2707i	1.02198	+	0.671162i
$283$	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
$285$	−0.860574	+	7.50063i	−0.0509760	+	0.444299i
$286$	10.4526			0.618075
$287$	−13.4846	+	4.90800i	−0.795972	+	0.289710i
$288$	−2.50420	+	1.65197i	−0.147561	+	0.0973430i
$289$	−27.4574	+	23.0395i	−1.61514	+	1.35527i
$290$	−0.0482901	+	0.0575498i	−0.00283569	+	0.00337944i
$291$	9.66946	+	2.28470i	0.566834	+	0.133931i
$292$	−7.48610	−	12.9663i	−0.438091	−	0.758796i
$293$	0.503132	−	0.871450i	0.0293933	−	0.0509106i	−0.850955	−	0.525239i	$-0.823976\pi$
$293$	0.503132	−	0.871450i	0.0293933	−	0.0509106i	0.880348	+	0.474329i	$0.157309\pi$
$294$	−17.1232	−	16.1327i	−0.998642	−	0.940876i
$295$	2.90997	−	7.99509i	0.169425	−	0.465492i
$296$	−0.00604645	−	0.00349092i	−0.000351443	−	0.000202906i
$297$	−6.74143	−	5.63312i	−0.391177	−	0.326867i
$298$	0.442672	−	0.0780551i	0.0256433	−	0.00452161i
$299$	−25.9100	−	21.7411i	−1.49841	−	1.25732i
$300$	1.65895	−	0.497896i	0.0957792	−	0.0287461i
$301$	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
$306$	−9.76064	+	19.5017i	−0.557979	+	1.11484i
$307$	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
$309$	7.49898	−	3.77258i	0.426602	−	0.214614i
$310$	0.0410997	+	0.233088i	0.00233431	+	0.0132385i
$311$	−4.19540	+	2.42222i	−0.237899	+	0.137351i	−0.614211	−	0.789142i	$-0.710526\pi$
$311$	−4.19540	+	2.42222i	−0.237899	+	0.137351i	0.376311	+	0.926493i	$0.377192\pi$
$312$	−6.40040	−	8.58493i	−0.362352	−	0.486026i
$313$	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
$315$	3.15696	+	13.2392i	0.177874	+	0.745947i
$316$	−0.813832	+	0.469866i	−0.0457816	+	0.0264320i
$317$	0.867738	+	4.92119i	0.0487370	+	0.276401i	0.999431	−	0.0337292i	$-0.0107384\pi$
$317$	0.867738	+	4.92119i	0.0487370	+	0.276401i	−0.950694	+	0.310130i	$0.899627\pi$
$318$	2.82940	+	5.62417i	0.158665	+	0.315388i
$319$	0.0816441	+	0.0972997i	0.00457119	+	0.00544774i
$320$	−0.984808	−	0.173648i	−0.0550524	−	0.00970723i
$321$	−12.6672	−	0.729055i	−0.707012	−	0.0406919i
$322$		−	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
$327$	−4.94907	−	16.4898i	−0.273684	−	0.911890i
$328$	−2.42301	−	2.03315i	−0.133789	−	0.112262i
$329$	−52.9629	+	9.33880i	−2.91994	+	0.514865i
$330$	−0.341961	−	2.90835i	−0.0188243	−	0.160099i
$331$	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
$333$	−0.0192211	+	0.00832249i	−0.00105331	+	0.000456070i
$334$	1.91485	−	3.31661i	0.104776	−	0.181477i
$335$	4.62194	+	8.00544i	0.252524	+	0.437384i
$336$	1.80693	−	7.64742i	0.0985760	−	0.417201i
$337$	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
$339$	−3.41098	+	5.19391i	−0.185259	+	0.282094i
$340$	−6.83093	+	2.48626i	−0.370459	+	0.134836i
$341$	0.400162			0.0216700
$342$	−4.50698	−	12.2755i	−0.243709	−	0.663781i
$343$	29.8642			1.61252
$344$	0.154308	−	0.0561635i	0.00831973	−	0.00302813i
$345$	−5.20162	+	7.92051i	−0.280046	+	0.426426i
$346$	−2.71733	+	2.28011i	−0.146084	+	0.122579i
$347$	−3.05181	+	3.63701i	−0.163830	+	0.195245i	−0.841714	−	0.539924i	$-0.818453\pi$
$347$	−3.05181	+	3.63701i	−0.163830	+	0.195245i	0.677884	+	0.735169i	$0.262897\pi$
$348$	0.0299213	−	0.126635i	0.00160395	−	0.00678836i
$349$	−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
$351$	−32.1246	+	0.0661454i	−1.71469	+	0.00353058i
$352$	−0.578254	+	1.58874i	−0.0308211	+	0.0846802i
$353$	14.5648	+	8.40901i	0.775208	+	0.447566i	0.834729	−	0.550661i	$-0.185624\pi$
$353$	14.5648	+	8.40901i	0.775208	+	0.447566i	−0.0595214	+	0.998227i	$0.518957\pi$
$354$	1.72086	+	14.6358i	0.0914628	+	0.777884i
$355$	12.6438	−	2.22944i	0.671062	−	0.118326i
$356$	−2.38295	−	1.99953i	−0.126296	−	0.105975i
$357$	−16.4204	−	54.7113i	−0.869060	−	2.89563i
$358$	2.37369	−	13.4619i	0.125453	−	0.711482i
$359$	7.90680	+	21.7238i	0.417305	+	1.14654i	0.953223	+	0.302267i	$0.0977433\pi$
$359$	7.90680	+	21.7238i	0.417305	+	1.14654i	−0.535918	+	0.844270i	$0.680035\pi$
$360$	−2.17929	+	2.06172i	−0.114859	+	0.108662i
$361$	13.0782	+	13.7826i	0.688326	+	0.725401i
$362$		−	21.6757i		−	1.13925i
$363$	14.0782	+	0.810269i	0.738916	+	0.0425281i
$364$	27.6223	+	4.87055i	1.44780	+	0.255286i
$365$	−9.62395	−	11.4694i	−0.503740	−	0.600334i
$366$	−4.67204	−	9.28690i	−0.244211	−	0.485434i
$367$	−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
$369$	−9.23027	+	2.20100i	−0.480509	+	0.114580i
$370$	−0.00656079	−	0.00238793i	−0.000341079	−	0.000124143i
$371$	−15.4962	−	5.64016i	−0.804523	−	0.292822i
$372$	−0.245030	−	0.328661i	−0.0127042	−	0.0170403i
$373$	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
$375$	1.54728	−	0.778405i	0.0799014	−	0.0401967i
$376$	−7.61969	−	9.08080i	−0.392956	−	0.468306i
$377$	0.457403	+	0.0806524i	0.0235574	+	0.00415381i
$378$	−15.1902	−	18.0275i	−0.781300	−	0.927233i
$379$			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	$-0.595504\pi$
$383$	6.04562	−	34.2864i	0.308917	−	1.75195i	0.604470	−	0.796628i	$-0.293385\pi$
$384$	1.65895	−	0.497896i	0.0846577	−	0.0254082i
$385$	5.87587	+	4.93044i	0.299462	+	0.251278i
$386$	−20.0283	+	3.53154i	−1.01942	+	0.179750i
$387$	0.140641	−	0.472131i	0.00714918	−	0.0239998i
$388$	−4.96786	−	2.86819i	−0.252205	−	0.145610i
$389$	1.67725	−	4.60821i	0.0850400	−	0.233645i	−0.889883	−	0.456190i	$-0.849214\pi$
$389$	1.67725	−	4.60821i	0.0850400	−	0.233645i	0.974923	+	0.222544i	$0.0714361\pi$
$390$	−7.79392	−	7.34308i	−0.394661	−	0.371832i
$391$	19.8848	−	34.4415i	1.00562	−	1.74178i
$392$	6.79132	+	11.7629i	0.343014	+	0.594117i
$393$	−2.37542	−	0.561264i	−0.119824	−	0.0283120i
$394$	−7.58095	+	9.03462i	−0.381923	+	0.455158i
$395$	−0.719877	+	0.604048i	−0.0362209	+	0.0303930i
$396$	2.79298	+	4.23386i	0.140353	+	0.212759i
$397$	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
$399$	30.6414	+	15.3074i	1.53399	+	0.766328i
$400$	−1.00000			−0.0500000
$401$	17.2532	−	6.27966i	0.861585	−	0.313591i	0.126830	−	0.991924i	$-0.459520\pi$
$401$	17.2532	−	6.27966i	0.861585	−	0.313591i	0.734754	+	0.678333i	$0.237297\pi$
$402$	−13.3829	−	8.78894i	−0.667480	−	0.438352i
$403$	1.12093	−	0.940574i	0.0558376	−	0.0468533i
$404$	7.21067	−	8.59334i	0.358744	−	0.427534i
$405$	1.06937	+	8.93624i	0.0531376	+	0.444045i
$406$	0.170416	+	0.295169i	0.00845761	+	0.0146490i
$407$	−0.00590211	+	0.0102228i	−0.000292557	+	0.000506723i
$408$	8.63407	−	9.16418i	0.427450	−	0.453694i
$409$	−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
$411$	15.8301	−	1.86128i	0.780840	−	0.0918104i
$412$	−4.77292	+	0.841594i	−0.235145	+	0.0414624i
$413$	−29.5694	−	24.8116i	−1.45501	−	1.22090i
$414$	1.88301	−	16.3042i	0.0925449	−	0.801310i
$415$	−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	$0.0199035\pi$
$419$			2.55820i			0.124976i	−0.998046	+	0.0624880i	$0.980096\pi$
$420$	0.451517	−	7.84500i	0.0220318	−	0.382797i
$421$	−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
$423$	−35.4994	+	2.11650i	−1.72604	+	0.102908i
$424$	−0.631189	−	3.57965i	−0.0306532	−	0.173843i
$425$	−6.29542	+	3.63466i	−0.305373	+	0.176307i
$426$	−17.8281	+	13.2915i	−0.863774	+	0.643978i
$427$	25.5881	+	9.31329i	1.23829	+	0.450702i
$428$	6.88371	+	2.50546i	0.332737	+	0.121106i
$429$	−14.5146	+	10.8212i	−0.700770	+	0.522452i
$430$	0.142211	−	0.0821056i	0.00685802	−	0.00395948i
$431$	−0.0624841	−	0.354365i	−0.00300975	−	0.0170692i	0.983266	−	0.182176i	$-0.0583141\pi$
$431$	−0.0624841	−	0.354365i	−0.00300975	−	0.0170692i	−0.986276	+	0.165107i	$0.947203\pi$
$432$	1.76713	−	4.88644i	0.0850211	−	0.235099i
$433$	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
$435$	0.00747676	−	0.129907i	0.000358483	−	0.00622857i
$436$			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
$441$	40.4789	+	4.67499i	1.92757	+	0.222618i
$442$	34.4275	+	28.8881i	1.63755	+	1.37407i
$443$	−19.5392	+	3.44528i	−0.928333	+	0.163690i	−0.617317	−	0.786714i	$-0.711780\pi$
$443$	−19.5392	+	3.44528i	−0.928333	+	0.163690i	−0.311016	+	0.950405i	$0.600669\pi$
$444$	0.0120102	−	0.00141214i	0.000569978	−	6.70174e-5i
$445$	−2.69397	−	1.55536i	−0.127706	−	0.0737312i
$446$	−4.46562	+	12.2692i	−0.211453	+	0.580963i
$447$	−0.533891	+	0.566670i	−0.0252522	+	0.0268026i
$448$	−2.26841	+	3.92899i	−0.107172	+	0.185627i
$449$	19.8715	+	34.4184i	0.937792	+	1.62430i	0.769578	+	0.638553i	$0.220467\pi$
$449$	19.8715	+	34.4184i	0.937792	+	1.62430i	0.168214	+	0.985751i	$0.446200\pi$
$450$	−1.78817	+	2.40883i	−0.0842952	+	0.113553i
$451$	−3.43745	+	4.09660i	−0.161863	+	0.192901i
$452$	2.74822	−	2.30603i	0.129265	−	0.108467i
$453$	−9.74981	−	6.40297i	−0.458086	−	0.300838i
$454$	1.55344	−	0.565406i	0.0729066	−	0.0265358i
$455$	28.0484			1.31493
$456$	0.454970	+	7.53611i	0.0213059	+	0.352911i
$457$	−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
$459$	−6.63571	−	37.1851i	−0.309728	−	1.73565i
$460$	4.19093	−	3.51661i	0.195403	−	0.163963i
$461$	−4.96863	+	5.92139i	−0.231412	+	0.275786i	−0.869238	−	0.494395i	$-0.835390\pi$
$461$	−4.96863	+	5.92139i	−0.231412	+	0.275786i	0.637825	+	0.770181i	$0.279834\pi$
$462$	−12.9295	−	3.05498i	−0.601535	−	0.142130i
$463$	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
$465$	−0.298379	−	0.281119i	−0.0138370	−	0.0130366i
$466$	7.43865	−	20.4375i	0.344589	−	0.946749i
$467$	−30.6485	−	17.6949i	−1.41824	−	0.818822i	−0.422098	−	0.906550i	$-0.638706\pi$
$467$	−30.6485	−	17.6949i	−1.41824	−	0.818822i	−0.996144	+	0.0877280i	$0.972039\pi$
$468$	17.7753	+	5.29500i	0.821664	+	0.244761i
$469$	41.3006	−	7.28241i	1.90709	−	0.336271i
$470$	−9.08080	−	7.61969i	−0.418866	−	0.351470i
$471$	−23.6112	+	7.08638i	−1.08795	+	0.326523i
$472$	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
$477$	−9.75143	−	4.88060i	−0.446487	−	0.223467i
$478$	12.0430	+	2.12350i	0.550832	+	0.0971265i
$479$	−7.83555	−	9.33805i	−0.358015	−	0.426666i	0.556732	−	0.830692i	$-0.312055\pi$
$479$	−7.83555	−	9.33805i	−0.358015	−	0.426666i	−0.914748	+	0.404026i	$0.867611\pi$
$480$	1.54728	−	0.778405i	0.0706235	−	0.0355292i
$481$	0.00749544	+	0.0425088i	0.000341763	+	0.00193823i
$482$	−23.8853	+	13.7902i	−1.08795	+	0.628126i
$483$	25.6955	+	34.4657i	1.16919	+	1.56824i
$484$	−7.65053	−	2.78456i	−0.347751	−	0.126571i
$485$	−5.39044	−	1.96196i	−0.244767	−	0.0890880i
$486$	−8.61064	−	12.9945i	−0.390587	−	0.589442i
$487$	−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
$489$	0.852250	+	1.69407i	0.0385401	+	0.0766085i
$490$	8.73076	+	10.4049i	0.394415	+	0.470046i
$491$	1.81626	+	0.320255i	0.0819666	+	0.0144529i	0.214481	−	0.976728i	$-0.431194\pi$
$491$	1.81626	+	0.320255i	0.0819666	+	0.0144529i	−0.132514	+	0.991181i	$0.542305\pi$
$492$	5.46946	+	0.314793i	0.246582	+	0.0141920i
$493$			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
$498$	−4.72069	−	15.7289i	−0.211539	−	0.704829i
$499$	−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
$501$	0.774592	+	6.58784i	0.0346062	+	0.294323i
$502$	−19.3762	−	11.1869i	−0.864803	−	0.499294i
$503$	−2.81655	+	7.73842i	−0.125584	+	0.345039i	−0.986512	−	0.163687i	$-0.947661\pi$
$503$	−2.81655	+	7.73842i	−0.125584	+	0.345039i	0.860928	+	0.508726i	$0.169883\pi$
$504$	5.40797	+	12.4899i	0.240890	+	0.556345i
$505$	5.60890	−	9.71490i	0.249593	−	0.432308i
$506$	−4.62481	−	8.01041i	−0.205598	−	0.356106i
$507$	−10.0455	+	42.5152i	−0.446135	+	1.88817i
$508$	−0.472159	+	0.562697i	−0.0209487	+	0.0249656i
$509$	−22.9498	+	19.2572i	−1.01723	+	0.853559i	−0.989277	−	0.146050i	$-0.953344\pi$
$509$	−22.9498	+	19.2572i	−1.01723	+	0.853559i	−0.0279547	+	0.999609i	$0.508899\pi$
$510$	6.91156	−	10.5242i	0.306049	−	0.466021i
$511$	−63.8296	+	23.2321i	−2.82366	+	1.02773i
$512$	−1.00000			−0.0441942
$513$	18.9668	+	12.3799i	0.837403	+	0.546587i
$514$	6.46809			0.285295
$515$	−4.55427	+	1.65762i	−0.200685	+	0.0730433i
$516$	−0.156129	+	0.237738i	−0.00687321	+	0.0104658i
$517$	−15.3529	+	12.8826i	−0.675221	+	0.566578i
$518$	−0.0203605	+	0.0242647i	−0.000894589	+	0.00106613i
$519$	1.41279	−	5.97932i	0.0620146	−	0.262463i
$520$	3.09120	+	5.35411i	0.135558	+	0.234793i
$521$	−1.56894	+	2.71749i	−0.0687366	+	0.119055i	−0.898345	−	0.439290i	$-0.855230\pi$
$521$	−1.56894	+	2.71749i	−0.0687366	+	0.119055i	0.829609	+	0.558345i	$0.188563\pi$
$522$	0.0895516	+	0.206823i	0.00391957	+	0.00905239i
$523$	−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
$525$	−0.917613	−	7.80423i	−0.0400479	−	0.340604i
$526$	9.26722	−	1.63406i	0.404070	−	0.0712485i
$527$	1.31800	+	1.10594i	0.0574131	+	0.0481753i
$528$	−0.841795	−	2.80478i	−0.0366344	−	0.122063i
$529$	−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
$534$	5.37903	+	0.309589i	0.232773	+	0.0133972i
$535$	7.21420	+	1.27206i	0.311897	+	0.0549958i
$536$	5.94185	+	7.08123i	0.256649	+	0.305862i
$537$	10.6404	+	21.1507i	0.459169	+	0.912718i
$538$	0.478825	+	2.71555i	0.0206436	+	0.117076i
$539$	19.8876	−	11.4821i	0.856620	−	0.494570i
$540$	0.891764	−	5.11906i	0.0383754	−	0.220289i
$541$	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
$543$	22.4400	+	30.0990i	0.962994	+	1.29167i
$544$	−6.29542	+	3.63466i	−0.269914	+	0.155835i
$545$	1.72605	+	9.78894i	0.0739361	+	0.419312i
$546$	−43.3988	+	21.8330i	−1.85730	+	0.934366i
$547$	−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
$549$	16.1020	+	8.05907i	0.687217	+	0.343953i
$550$			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
$555$	0.0115825	−	0.00347624i	0.000491650	−	0.000147558i
$556$	−13.5855	−	11.3996i	−0.576154	−	0.483450i
$557$	31.3589	−	5.52942i	1.32872	−	0.234289i	0.536177	−	0.844105i	$-0.319868\pi$
$557$	31.3589	−	5.52942i	1.32872	−	0.234289i	0.792543	+	0.609816i	$0.208757\pi$
$558$	0.680500	+	0.202711i	0.0288079	+	0.00858144i
$559$	−0.879205	−	0.507609i	−0.0371864	−	0.0214696i
$560$	−1.55168	+	4.26321i	−0.0655705	+	0.180153i
$561$	−15.4939	−	14.5977i	−0.654153	−	0.616313i
$562$	15.4808	−	26.8136i	0.653019	−	1.13106i
$563$	5.37938	+	9.31737i	0.226714	+	0.392680i	0.956832	−	0.290641i	$-0.0938684\pi$
$563$	5.37938	+	9.31737i	0.226714	+	0.392680i	−0.730118	+	0.683321i	$0.760535\pi$
$564$	19.9818	+	4.72129i	0.841385	+	0.198802i
$565$	2.30603	−	2.74822i	0.0970154	−	0.115618i
$566$	10.1391	−	8.50775i	0.426180	−	0.357607i
$567$	39.7564	+	9.30723i	1.66961	+	0.390867i
$568$	12.0645	−	4.39114i	0.506217	−	0.184248i
$569$	−22.9976			−0.964111			−0.482056	−	0.876141i	$-0.660110\pi$
$569$	−22.9976			−0.964111			−0.482056	+	0.876141i	$0.660110\pi$
$570$	1.75669	+	7.34262i	0.0735797	+	0.307548i
$571$	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
$573$	−6.15950	−	4.04511i	−0.257317	−	0.168987i
$574$	−10.9928	+	9.22402i	−0.458829	+	0.385003i
$575$	3.51661	−	4.19093i	0.146653	−	0.174774i
$576$	−1.78817	+	2.40883i	−0.0745071	+	0.100368i
$577$	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
$579$	24.1554	−	25.6385i	1.00387	−	1.06550i
$580$	−0.0256946	+	0.0705953i	−0.00106691	+	0.00293131i
$581$	37.2518	+	21.5074i	1.54547	+	0.892275i
$582$	9.86773	−	1.16024i	0.409031	−	0.0480934i
$583$	−6.05212	+	1.06715i	−0.250653	+	0.0441969i
$584$	−11.4694	−	9.62395i	−0.474606	−	0.398242i
$585$	18.4247	+	2.12791i	0.761769	+	0.0879782i
$586$	0.174736	−	0.990976i	0.00721827	−	0.0409368i
$587$	5.18214	+	14.2378i	0.213890	+	0.587658i	0.999518	−	0.0310413i	$-0.00988233\pi$
$587$	5.18214	+	14.2378i	0.213890	+	0.587658i	−0.785628	+	0.618699i	$0.787660\pi$
$588$	−21.6082	−	9.30328i	−0.891107	−	0.383661i
$589$	−1.02453	+	0.121241i	−0.0422151	+	0.00499565i
$590$		−	8.50819i		−	0.350277i
$591$	1.17376	−	20.3938i	0.0482821	−	0.838890i
$592$	−0.00687577	−	0.00121238i	−0.000282593	−	4.98287e-5i
$593$	16.9365	+	20.1841i	0.695497	+	0.828861i	0.992009	−	0.126168i	$-0.0402678\pi$
$593$	16.9365	+	20.1841i	0.695497	+	0.828861i	−0.296512	+	0.955029i	$0.595823\pi$
$594$	−8.26151	−	2.98769i	−0.338974	−	0.122587i
$595$	5.72684	+	32.4785i	0.234778	+	1.33149i
$596$	0.389280	−	0.224751i	0.0159455	−	0.00920615i
$597$	−25.7627	+	19.2071i	−1.05440	+	0.786096i
$598$	−31.7833	−	11.5682i	−1.29972	−	0.473058i
$599$	−0.698047	−	0.254068i	−0.0285214	−	0.0103810i	0.327720	−	0.944775i	$-0.393720\pi$
$599$	−0.698047	−	0.254068i	−0.0285214	−	0.0103810i	−0.356241	+	0.934394i	$0.615942\pi$
$600$	1.38861	−	1.03526i	0.0566897	−	0.0422644i
$601$	−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
$603$	27.6825	−	1.65045i	1.12732	−	0.0672116i
$604$	4.32880	+	5.15886i	0.176136	+	0.209911i
$605$	−8.01784	−	1.41376i	−0.325971	−	0.0574775i
$606$	−1.11643	+	19.3977i	−0.0453519	+	0.787978i
$607$			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
$612$	−2.50202	+	21.6640i	−0.101138	+	0.875714i
$613$	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
$615$	5.44103	−	0.639751i	0.219404	−	0.0257973i
$616$	6.64276	+	3.83520i	0.267644	+	0.154525i
$617$	7.98580	−	21.9408i	0.321496	−	0.883303i	−0.668689	−	0.743542i	$-0.733144\pi$
$617$	7.98580	−	21.9408i	0.321496	−	0.883303i	0.990185	−	0.139761i	$-0.0446334\pi$
$618$	5.75644	−	6.10987i	0.231558	−	0.245775i
$619$	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
$621$	14.2644	+	24.5896i	0.572411	+	0.986747i
$622$	−3.11394	+	3.71105i	−0.124858	+	0.148800i
$623$	−10.8110	+	9.07151i	−0.433134	+	0.363442i
$624$	−8.95063	−	5.87813i	−0.358312	−	0.235313i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	12.8287			0.512736
$627$	12.7413	−	0.769220i	0.508840	−	0.0307197i
$628$	14.2326			0.567944
$629$	−0.0476925	+	0.0173587i	−0.00190162	+	0.000692135i
$630$	7.49466	+	11.3611i	0.298594	+	0.452636i
$631$	−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
$633$	36.4199	+	8.60528i	1.44756	+	0.342029i
$634$	2.49855	+	4.32762i	0.0992302	+	0.171872i
$635$	−0.367274	+	0.636138i	−0.0145748	+	0.0252443i
$636$	4.58235	+	4.31728i	0.181702	+	0.171191i
$637$	28.7206	−	78.9091i	1.13795	−	3.12649i
$638$	0.109999	+	0.0635079i	0.00435490	+	0.00251430i
$639$	10.9960	−	36.9135i	0.434995	−	1.46028i
$640$	−0.984808	+	0.173648i	−0.0389279	+	0.00686405i
$641$	−34.2258	−	28.7189i	−1.35184	−	1.13433i	−0.978411	−	0.206668i	$-0.933738\pi$
$641$	−34.2258	−	28.7189i	−1.35184	−	1.13433i	−0.373427	−	0.927659i	$-0.621818\pi$
$642$	−12.1526	+	3.64733i	−0.479624	+	0.143949i
$643$	−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	$0.413804\pi$
$647$			49.0186i			1.92712i	−0.267495	+	0.963559i	$0.586196\pi$
$648$	2.60489	+	8.61479i	0.102330	+	0.338421i
$649$	−14.1663	−	2.49790i	−0.556075	−	0.0980511i
$650$	3.97397	+	4.73599i	0.155872	+	0.185761i
$651$	−1.66146	+	0.835843i	−0.0651176	+	0.0327593i
$652$	−0.190122	−	1.07823i	−0.00744574	−	0.0422269i
$653$	35.8908	−	20.7216i	1.40451	−	0.810897i	0.409663	−	0.912237i	$-0.365646\pi$
$653$	35.8908	−	20.7216i	1.40451	−	0.810897i	0.994852	+	0.101340i	$0.0323130\pi$
$654$	−10.2905	−	13.8027i	−0.402389	−	0.539728i
$655$	1.32423	+	0.481979i	0.0517418	+	0.0188325i
$656$	−2.97227	−	1.08182i	−0.116048	−	0.0422379i
$657$	−43.6916	+	10.4185i	−1.70457	+	0.406463i
$658$	−46.5748	+	26.8900i	−1.81568	+	1.04828i
$659$	4.20535	+	23.8497i	0.163817	+	0.929053i	0.950276	+	0.311410i	$0.100801\pi$
$659$	4.20535	+	23.8497i	0.163817	+	0.929053i	−0.786459	+	0.617643i	$0.788088\pi$
$660$	−1.31605	−	2.61600i	−0.0512273	−	0.101828i
$661$	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
$663$	−77.7130	−	4.47275i	−3.01812	−	0.173707i
$664$			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
$669$	−6.50084	−	21.6602i	−0.251337	−	0.837431i
$670$	7.08123	+	5.94185i	0.273572	+	0.229554i
$671$	9.99355	−	1.76213i	0.385797	−	0.0680263i
$672$	−0.917613	−	7.80423i	−0.0353977	−	0.301055i
$673$	−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
$675$	−0.0106990	−	5.19614i	−0.000411804	−	0.200000i
$676$	12.6110	−	21.8429i	0.485039	−	0.840113i
$677$	−8.82920	−	15.2926i	−0.339334	−	0.587743i	0.644974	−	0.764205i	$-0.276868\pi$
$677$	−8.82920	−	15.2926i	−0.339334	−	0.587743i	−0.984308	+	0.176461i	$0.943535\pi$
$678$	−1.42885	+	6.04730i	−0.0548748	+	0.232245i
$679$	−16.7285	+	19.9362i	−0.641980	+	0.765082i
$680$	−5.56863	+	4.67263i	−0.213547	+	0.179187i
$681$	−1.57178	+	2.39335i	−0.0602306	+	0.0917133i
$682$	0.376029	−	0.136863i	0.0143989	−	0.00524077i
$683$	34.8153			1.33217			0.666085	−	0.745876i	$-0.267969\pi$
$683$	34.8153			1.33217			0.666085	+	0.745876i	$0.267969\pi$
$684$	−8.43363	−	9.99369i	−0.322468	−	0.382118i
$685$	−9.20246			−0.351608
$686$	28.0632	−	10.2142i	1.07146	−	0.389979i
$687$	−14.6642	+	22.3292i	−0.559475	+	0.851913i
$688$	0.125793	−	0.105553i	0.00479581	−	0.00402417i
$689$	−14.4449	+	17.2147i	−0.550305	+	0.655829i
$690$	−2.17895	+	9.22191i	−0.0829511	+	0.351072i
$691$	−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
$693$	21.1167	−	9.14326i	0.802158	−	0.347324i
$694$	−1.62384	+	4.46145i	−0.0616399	+	0.169354i
$695$	−15.3586	−	8.86731i	−0.582586	−	0.336356i
$696$	−0.0151949	−	0.129232i	−0.000575963	−	0.00489852i
$697$	−22.6437	+	3.99270i	−0.857692	+	0.151234i
$698$	−5.10580	−	4.28427i	−0.193257	−	0.162162i
$699$	10.8288	+	36.0806i	0.409584	+	1.36470i
$700$	−0.787809	+	4.46789i	−0.0297764	+	0.168870i
$701$	−13.0837	−	35.9471i	−0.494163	−	1.35770i	−0.896838	−	0.442360i	$-0.854141\pi$
$701$	−13.0837	−	35.9471i	−0.494163	−	1.35770i	0.402674	−	0.915343i	$-0.368081\pi$
$702$	−30.1646	+	11.0494i	−1.13849	+	0.417034i
$703$	0.0120138	−	0.0279615i	0.000453111	−	0.00105459i
$704$			1.69070i			0.0637208i
$705$	20.4980	+	1.17976i	0.772001	+	0.0444323i
$706$	16.5625	+	2.92042i	0.623339	+	0.109911i
$707$	−32.7134	−	38.9863i	−1.23031	−	1.46623i
$708$	6.62282	+	13.1646i	0.248901	+	0.494755i
$709$	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
$711$	0.653916	+	2.74231i	0.0245238	+	0.102845i
$712$	−2.92312	−	1.06393i	−0.109549	−	0.0398725i
$713$	−1.21678	−	0.442871i	−0.0455686	−	0.0165856i
$714$	−34.1425	−	45.7957i	−1.27775	−	1.71386i
$715$	9.05222	−	5.22630i	0.338534	−	0.195453i
$716$	−2.37369	−	13.4619i	−0.0887090	−	0.503094i
$717$	−18.9213	+	9.51891i	−0.706630	+	0.355490i
$718$	14.8599	+	17.7094i	0.554568	+	0.660908i
$719$	−10.3694	−	1.82841i	−0.386714	−	0.0681881i	−0.0230888	−	0.999733i	$-0.507350\pi$
$719$	−10.3694	−	1.82841i	−0.386714	−	0.0681881i	−0.363625	+	0.931545i	$0.618461\pi$
$720$	−1.34272	+	2.68274i	−0.0500401	+	0.0999799i
$721$			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
$726$	13.5063	−	4.05364i	0.501267	−	0.150445i
$727$	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
$729$	25.4095	+	9.12998i	0.941093	+	0.338148i
$730$	−12.9663	−	7.48610i	−0.479905	−	0.277073i
$731$	0.408271	−	1.12172i	0.0151004	−	0.0414881i
$732$	−7.56659	−	7.12890i	−0.279669	−	0.263492i
$733$	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
$735$	−22.8954	−	5.40972i	−0.844510	−	0.199540i
$736$	3.51661	−	4.19093i	0.129624	−	0.154480i
$737$	11.9723	−	10.0459i	0.441004	−	0.370046i
$738$	−7.92083	+	5.22520i	−0.291570	+	0.192342i
$739$	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
$741$	33.8829	−	32.1030i	1.24472	−	1.17933i
$742$	−16.4907			−0.605393
$743$	−22.8177	+	8.30497i	−0.837101	+	0.304680i	−0.724770	−	0.688991i	$-0.758054\pi$
$743$	−22.8177	+	8.30497i	−0.837101	+	0.304680i	−0.112331	+	0.993671i	$0.535832\pi$
$744$	−0.342661	−	0.225035i	−0.0125626	−	0.00825019i
$745$	0.344338	−	0.288934i	0.0126156	−	0.0105857i
$746$	14.5283	−	17.3141i	0.531918	−	0.633915i
$747$	22.8387	+	16.9541i	0.835625	+	0.620319i
$748$	6.14514	+	10.6437i	0.224688	+	0.389172i
$749$	16.6172	−	28.7818i	0.607178	−	1.05166i
$750$	1.18774	−	1.26066i	0.0433701	−	0.0460329i
$751$	−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
$753$	38.4873	−	4.52530i	1.40256	−	0.164911i
$754$	0.457403	−	0.0806524i	0.0166576	−	0.00293719i
$755$	5.15886	+	4.32880i	0.187750	+	0.157541i
$756$	−20.4399	−	11.7449i	−0.743391	−	0.427159i
$757$	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	$0.148066\pi$
$761$			24.7487i			0.897138i	−0.893748	+	0.448569i	$0.851934\pi$
$762$	0.0731045	−	1.27017i	0.00264830	−	0.0460135i
$763$	44.4106	+	7.83078i	1.60777	+	0.283493i
$764$	2.73474	+	3.25914i	0.0989395	+	0.117912i
$765$	1.29790	+	21.7693i	0.0469259	+	0.787072i
$766$	−6.04562	−	34.2864i	−0.218437	−	1.23882i
$767$	−45.5538	+	26.3005i	−1.64485	+	0.949657i
$768$	1.38861	−	1.03526i	0.0501071	−	0.0373568i
$769$	−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
$771$	−8.98165	+	6.69617i	−0.323466	+	0.241157i
$772$	−17.6126	+	10.1687i	−0.633892	+	0.365978i
$773$	−3.03360	−	17.2044i	−0.109111	−	0.618798i	−0.989498	−	0.144544i	$-0.953829\pi$
$773$	−3.03360	−	17.2044i	−0.109111	−	0.618798i	0.880388	−	0.474255i	$-0.157282\pi$
$774$	−0.0293191	−	0.491760i	−0.00105385	−	0.0176760i
$775$	0.152137	+	0.181310i	0.00546493	+	0.00651286i
$776$	−5.64924	−	0.996113i	−0.202796	−	0.0357584i
$777$	0.00315242	−	0.0547726i	0.000113092	−	0.00196496i
$778$		−	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
$783$	−0.338468	−	0.194487i	−0.0120959	−	0.00695038i
$784$	10.4049	+	8.73076i	0.371604	+	0.311813i
$785$	14.0164	−	2.47147i	0.500267	−	0.0882106i
$786$	−2.42413	+	0.285027i	−0.0864658	+	0.0101666i
$787$	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
$789$	−11.1769	+	11.8631i	−0.397907	+	0.422337i
$790$	−0.469866	+	0.813832i	−0.0167171	+	0.0289548i
$791$	−8.13801	−	14.0954i	−0.289354	−	0.501176i
$792$	4.07261	+	3.02327i	0.144714	+	0.107427i
$793$	23.8520	−	28.4257i	0.847010	−	1.00943i
$794$	10.1189	−	8.49076i	0.359106	−	0.301326i
$795$	5.26242	+	3.45598i	0.186639	+	0.122571i
$796$	17.4340	−	6.34547i	0.617933	−	0.224909i
$797$	−50.4058			−1.78546			−0.892732	−	0.450587i	$-0.851215\pi$
$797$	−50.4058			−1.78546			−0.892732	+	0.450587i	$0.851215\pi$
$798$	34.0289	+	3.90426i	1.20461	+	0.138209i
$799$	−86.1716			−3.04853
$800$	−0.939693	+	0.342020i	−0.0332232	+	0.0120922i
$801$	−7.78987	+	5.13881i	−0.275241	+	0.181571i
$802$	14.0650	−	11.8019i	0.496651	−	0.416739i
$803$	−16.2712	+	19.3913i	−0.574199	+	0.684304i
$804$	−15.5818	−	3.68167i	−0.549529	−	0.129842i
$805$	−12.4102	−	21.4950i	−0.437401	−	0.757600i
$806$	0.731636	−	1.26723i	0.0257708	−	0.0446363i
$807$	−3.47621	−	3.27513i	−0.122368	−	0.115290i
$808$	3.83671	−	10.5413i	0.134975	−	0.370841i
$809$	−25.5990	−	14.7796i	−0.900012	−	0.519622i	−0.0228079	−	0.999740i	$-0.507261\pi$
$809$	−25.5990	−	14.7796i	−0.900012	−	0.519622i	−0.877204	+	0.480118i	$0.840594\pi$
$810$	4.06126	+	8.03157i	0.142698	+	0.282201i
$811$	−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
$813$	−4.98220	+	1.49530i	−0.174733	+	0.0524424i
$814$	−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
$819$	37.6610	−	75.2466i	1.31598	−	2.62933i
$820$	−3.11497	−	0.549253i	−0.108779	−	0.0191807i
$821$	3.09504	+	3.68852i	0.108018	+	0.128730i	0.817344	−	0.576149i	$-0.195445\pi$
$821$	3.09504	+	3.68852i	0.108018	+	0.128730i	−0.709327	+	0.704880i	$0.751001\pi$
$822$	14.2388	−	7.16324i	0.496635	−	0.249847i
$823$	−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
$825$	−1.75032	−	2.34772i	−0.0609384	−	0.0817372i
$826$	−36.2722	−	13.2020i	−1.26207	−	0.459356i
$827$	36.7299	+	13.3686i	1.27722	+	0.464872i	0.889513	−	0.456909i	$-0.151044\pi$
$827$	36.7299	+	13.3686i	1.27722	+	0.464872i	0.387711	+	0.921781i	$0.373266\pi$
$828$	−3.80693	−	15.9650i	−0.132300	−	0.554822i
$829$	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
$831$	−25.5243	−	50.7362i	−0.885428	−	1.76002i
$832$	3.97397	+	4.73599i	0.137773	+	0.164191i
$833$	97.2367	+	17.1455i	3.36905	+	0.594055i
$834$	30.6665	+	1.76500i	1.06189	+	0.0611170i
$835$		−	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	−0.971489	−	0.237085i	$-0.923808\pi$
$839$	0.651722	−	3.69610i	0.0224999	−	0.127604i	0.993989	+	0.109482i	$0.0349191\pi$
$840$	−2.25886	−	7.52632i	−0.0779381	−	0.259683i
$841$	−22.2110	−	18.6372i	−0.765895	−	0.642663i
$842$	−11.2145	+	1.97742i	−0.386478	+	0.0681465i
$843$	6.26229	+	53.2603i	0.215685	+	1.83438i
$844$	−18.7114	−	10.8030i	−0.644072	−	0.371855i
$845$	8.62645	−	23.7010i	0.296759	−	0.815338i
$846$	−32.6346	+	14.1304i	−1.12200	+	0.485812i
$847$	−18.4683	+	31.9880i	−0.634577	+	1.09912i
$848$	−1.81744	−	3.14789i	−0.0624110	−	0.108099i
$849$	−5.27154	+	22.3106i	−0.180919	+	0.765698i
$850$	−4.67263	+	5.56863i	−0.160270	+	0.191002i
$851$	0.0292604	−	0.0245524i	0.00100303	−	0.000841646i
$852$	−12.2069	+	18.5875i	−0.418203	+	0.636798i
$853$	−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
$855$	−10.0409	−	8.37738i	−0.343391	−	0.286500i
$856$	7.32549			0.250380
$857$	19.8023	−	7.20746i	0.676435	−	0.246202i	0.0191188	−	0.999817i	$-0.493914\pi$
$857$	19.8023	−	7.20746i	0.676435	−	0.246202i	0.657316	+	0.753615i	$0.271692\pi$
$858$	−9.93816	+	15.1329i	−0.339283	+	0.516627i
$859$	−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
$861$	5.71535	−	24.1889i	0.194779	−	0.824357i
$862$	−0.179916	−	0.311623i	−0.00612796	−	0.0106139i
$863$	−25.3332	+	43.8784i	−0.862352	+	1.49364i	0.00729976	+	0.999973i	$0.497676\pi$
$863$	−25.3332	+	43.8784i	−0.862352	+	1.49364i	−0.869652	+	0.493665i	$0.835657\pi$
$864$	−0.0106990	−	5.19614i	−0.000363987	−	0.176776i
$865$	−1.21322	+	3.33329i	−0.0412507	+	0.113335i
$866$	12.1805	+	7.03242i	0.413911	+	0.238971i
$867$	−7.24961	−	61.6574i	−0.246210	−	2.09399i
$868$	1.05748	−	0.186462i	0.0358931	−	0.00632892i
$869$	1.21710	+	1.02127i	0.0412872	+	0.0346441i
$870$	−0.0374050	−	0.124630i	−0.00126815	−	0.00422535i
$871$	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
$876$	25.8898	+	1.49008i	0.874734	+	0.0503451i
$877$	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
$879$	0.783281	+	1.55697i	0.0264194	+	0.0525154i
$880$	0.293587	+	1.66502i	0.00989683	+	0.0561277i
$881$	−14.2451	+	8.22439i	−0.479929	+	0.277087i	−0.720387	−	0.693573i	$-0.756036\pi$
$881$	−14.2451	+	8.22439i	−0.479929	+	0.277087i	0.240458	+	0.970660i	$0.422702\pi$
$882$	39.6366	−	9.45154i	1.33464	−	0.318250i
$883$	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
$885$	8.80821	+	11.8145i	0.296085	+	0.397142i
$886$	−17.1824	+	9.92029i	−0.577255	+	0.333279i
$887$	6.00539	+	34.0582i	0.201641	+	1.14356i	0.902638	+	0.430400i	$0.141627\pi$
$887$	6.00539	+	34.0582i	0.201641	+	1.14356i	−0.700997	+	0.713164i	$0.747261\pi$
$888$	0.0108029	−	0.00543470i	0.000362521	−	0.000182377i
$889$	2.14209	+	2.55285i	0.0718435	+	0.0856198i
$890$	−3.06346	−	0.540172i	−0.102688	−	0.0181066i
$891$	14.5650	−	4.40409i	0.487947	−	0.147543i
$892$			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
$897$	56.1107	−	16.8404i	1.87348	−	0.562285i
$898$	30.4448	+	25.5462i	1.01596	+	0.852489i
$899$	0.0175110	−	0.00308765i	0.000584023	−	0.000102979i
$900$	−0.856464	+	2.87515i	−0.0285488	+	0.0958382i
$901$	−22.8830	−	13.2115i	−0.762345	−	0.440140i
$902$	−1.82903	+	5.02522i	−0.0609001	+	0.167322i
$903$	0.939188	+	0.884861i	0.0312542	+	0.0294463i
$904$	1.79377	−	3.10691i	0.0596600	−	0.103334i
$905$	−10.8378	−	18.7717i	−0.360262	−	0.623992i
$906$	−11.3518	−	2.68219i	−0.377137	−	0.0891098i
$907$	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
$909$	−18.5314	−	28.0916i	−0.614649	−	0.931740i
$910$	26.3568	−	9.59311i	0.873721	−	0.318008i
$911$	−14.0631			−0.465932			−0.232966	−	0.972485i	$-0.574843\pi$
$911$	−14.0631			−0.465932			−0.232966	+	0.972485i	$0.574843\pi$
$912$	3.00503	+	6.92602i	0.0995066	+	0.229343i
$913$	16.0300			0.530516
$914$	−23.1522	+	8.42672i	−0.765807	+	0.278731i
$915$	−8.68955	−	5.70667i	−0.287268	−	0.188657i
$916$	11.8149	−	9.91390i	0.390376	−	0.327564i
$917$	4.10955	−	4.89758i	0.135709	−	0.161732i
$918$	−18.9536	−	32.6730i	−0.625561	−	1.07837i
$919$	−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
$921$	−4.21759	+	4.47653i	−0.138974	+	0.147507i
$922$	−2.64375	+	7.26366i	−0.0870674	+	0.239216i
$923$	−68.7405	−	39.6874i	−2.26262	−	1.30633i
$924$	−13.1946	+	1.55141i	−0.434071	+	0.0510377i
$925$	−0.00687577	+	0.00121238i	−0.000226074	+	3.98630e-5i
$926$	27.3299	+	22.9325i	0.898117	+	0.753609i
$927$	−1.66812	+	14.4436i	−0.0547884	+	0.474391i
$928$	−0.0130455	+	0.0739847i	−0.000428239	+	0.00242867i
$929$	−1.21958	−	3.35077i	−0.0400131	−	0.109935i	0.918077	−	0.396402i	$-0.129741\pi$
$929$	−1.21958	−	3.35077i	−0.0400131	−	0.109935i	−0.958090	+	0.286467i	$0.907519\pi$
$930$	−0.376532	−	0.162114i	−0.0123470	−	0.00531592i
$931$	−47.4392	+	35.4231i	−1.55476	+	1.16095i
$932$		−	21.7491i		−	0.712417i
$933$	0.482133	−	8.37694i	0.0157843	−	0.274249i
$934$	−34.8522	−	6.14538i	−1.14040	−	0.201083i
$935$	7.90004	+	9.41490i	0.258359	+	0.307900i
$936$	18.5143	−	1.10384i	0.605159	−	0.0360801i
$937$	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
$939$	−17.8140	+	13.2810i	−0.581337	+	0.433410i
$940$	−11.1392	−	4.05435i	−0.363322	−	0.132238i
$941$	−24.0938	−	8.76941i	−0.785434	−	0.285875i	−0.0819973	−	0.996633i	$-0.526130\pi$
$941$	−24.0938	−	8.76941i	−0.785434	−	0.285875i	−0.703437	+	0.710758i	$0.748352\pi$
$942$	−19.7636	+	14.7345i	−0.643932	+	0.480077i
$943$	14.9861	−	8.65225i	0.488016	−	0.281756i
$944$	−1.47743	−	8.37893i	−0.0480863	−	0.272711i
$945$	−22.1688	−	8.01714i	−0.721152	−	0.260798i
$946$	−0.178459	−	0.212679i	−0.00580219	−	0.00691478i
$947$	14.7708	+	2.60449i	0.479986	+	0.0846345i	0.408406	−	0.912800i	$-0.366085\pi$
$947$	14.7708	+	2.60449i	0.479986	+	0.0846345i	0.0715801	+	0.997435i	$0.477196\pi$
$948$	0.0935250	−	1.62497i	0.00303755	−	0.0527767i
$949$			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	$-0.834667\pi$
$953$	3.62464	−	20.5563i	0.117414	−	0.665885i	0.985527	−	0.169519i	$-0.0542215\pi$
$954$	−10.8326	−	1.25108i	−0.350719	−	0.0405052i
$955$	3.25914	+	2.73474i	0.105463	+	0.0884942i
$956$	12.0430	−	2.12350i	0.389497	−	0.0686788i
$957$	−0.218493	+	0.0256901i	−0.00706286	+	0.000830444i
$958$	−10.5568	−	6.09498i	−0.341075	−	0.196920i
$959$	−14.2793	+	39.2320i	−0.461102	+	1.26687i
$960$	1.18774	−	1.26066i	0.0383342	−	0.0406877i
$961$	−15.4720	+	26.7983i	−0.499096	+	0.864460i
$962$	0.0215823	+	0.0373816i	0.000695840	+	0.00120523i
$963$	13.0992	−	17.6458i	0.422117	−	0.568629i
$964$	−17.7283	+	21.1278i	−0.570991	+	0.680481i
$965$	−15.5793	+	13.0726i	−0.501515	+	0.420821i
$966$	35.9339	+	23.5988i	1.15615	+	0.759278i
$967$	−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
$969$	44.0917	+	32.6799i	1.41643	+	1.04983i
$970$	−5.73639			−0.184184
$971$	−33.2457	+	12.1005i	−1.06691	+	0.388322i	−0.815019	−	0.579435i	$-0.803273\pi$
$971$	−33.2457	+	12.1005i	−1.06691	+	0.388322i	−0.251887	+	0.967757i	$0.581051\pi$
$972$	−12.5357	−	9.26582i	−0.402084	−	0.297201i
$973$	−61.6349	+	51.7178i	−1.97592	+	1.65800i
$974$	−13.3313	+	15.8876i	−0.427162	+	0.509071i
$975$	−10.4213	−	2.46234i	−0.333748	−	0.0788578i
$976$	3.00103	+	5.19794i	0.0960607	+	0.166382i
$977$	−6.32362	+	10.9528i	−0.202311	+	0.350412i	−0.949273	−	0.314455i	$-0.898178\pi$
$977$	−6.32362	+	10.9528i	−0.202311	+	0.350412i	0.746962	+	0.664867i	$0.231512\pi$
$978$	1.38026	+	1.30042i	0.0441358	+	0.0415828i
$979$	−1.79879	+	4.94214i	−0.0574896	+	0.157951i
$980$	11.7629	+	6.79132i	0.375753	+	0.216941i
$981$	28.5788	+	8.51321i	0.912452	+	0.271806i
$982$	1.81626	−	0.320255i	0.0579591	−	0.0102198i
$983$	−14.4524	−	12.1270i	−0.460958	−	0.386790i	0.382525	−	0.923945i	$-0.375055\pi$
$983$	−14.4524	−	12.1270i	−0.460958	−	0.386790i	−0.843484	+	0.537155i	$0.819499\pi$
$984$	5.24728	−	1.57486i	0.167277	−	0.0502046i
$985$	−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
$990$	4.53572	+	2.27013i	0.144155	+	0.0721496i
$991$	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
$993$	−55.9408	+	28.1426i	−1.77523	+	0.893079i
$994$	−10.1145	−	57.3624i	−0.320814	−	1.81942i
$995$	16.0673	−	9.27646i	0.509368	−	0.294084i
$996$	−9.81560	−	13.1658i	−0.311019	−	0.417173i
$997$	−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
$999$	0.00622616	−	0.0357405i	0.000196987	−	0.00113078i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.950784 + 1.44776i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.398282 + 1.68564i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.19202 - 2.75301i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-0.950784 + 1.44776i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-0.398282 + 1.68564i) q^{6} +(-2.26841 - 3.92899i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.19202 - 2.75301i) q^{9} +(0.342020 - 0.939693i) q^{10} +(-1.46419 - 0.845352i) q^{11} +(0.202260 + 1.72020i) q^{12} +(-6.08847 + 1.07356i) q^{13} +(-3.47540 - 2.91621i) q^{14} +(0.497896 + 1.65895i) 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} +(7.84500 + 0.451517i) q^{21} +(-1.66502 - 0.293587i) q^{22} +(3.51661 + 4.19093i) q^{23} +(0.778405 + 1.54728i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(-5.35411 + 3.09120i) q^{26} +(5.11906 + 0.891764i) q^{27} +(-4.26321 - 1.55168i) q^{28} +(-0.0705953 - 0.0256946i) q^{29} +(1.03526 + 1.38861i) q^{30} +(-0.204974 + 0.118342i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(2.61600 - 1.31605i) q^{33} +(-4.67263 - 5.56863i) q^{34} +(-4.46789 - 0.787809i) q^{35} +(-2.68274 - 1.34272i) 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} +(7.52632 - 2.25886i) q^{42} +(0.125793 + 0.105553i) q^{43} +(-1.66502 + 0.293587i) q^{44} +(-2.87515 - 0.856464i) q^{45} +(4.73792 + 2.73544i) q^{46} +(4.05435 - 11.1392i) q^{47} +(1.26066 + 1.18774i) q^{48} +(-6.79132 + 11.7629i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(12.2534 + 2.89524i) q^{51} +(-3.97397 + 4.73599i) q^{52} +(2.78447 - 2.33645i) q^{53} +(5.11534 - 0.912837i) q^{54} +(-1.58874 + 0.578254i) q^{55} -4.53681 q^{56} +(-6.29898 + 4.16207i) q^{57} -0.0751260 q^{58} +(7.99509 - 2.90997i) q^{59} +(1.44776 + 0.950784i) q^{60} +(-4.59785 + 3.85805i) q^{61} +(-0.152137 + 0.181310i) q^{62} +(-8.11259 + 10.9284i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.09120 + 5.35411i) q^{65} +(2.00812 - 2.13141i) q^{66} +(-3.16159 + 8.68641i) q^{67} +(-6.29542 - 3.63466i) q^{68} +(-9.41100 + 1.10654i) q^{69} +(-4.46789 + 0.787809i) q^{70} +(9.83511 + 8.25264i) q^{71} +(-2.98019 - 0.344188i) 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} +(0.615291 - 10.6905i) q^{78} +(-0.925456 - 0.163183i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(-6.15818 + 6.56329i) q^{81} +(-0.549253 - 3.11497i) q^{82} +(-8.21102 + 4.74063i) q^{83} +(6.29985 - 4.69679i) q^{84} +(-6.83093 - 2.48626i) q^{85} +(0.154308 + 0.0561635i) q^{86} +(0.104321 - 0.0777751i) q^{87} +(-1.46419 + 0.845352i) q^{88} +(-0.540172 - 3.06346i) q^{89} +(-2.99468 + 0.178545i) q^{90} +(18.0291 + 21.4863i) q^{91} +(5.38776 + 0.950007i) q^{92} +(0.0235555 - 0.409271i) 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} +(-0.581920 + 5.03862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more