LMFDB - Embedded newform 570.2.bb.b.41.2

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			41.2
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.b.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-1.50714 - 0.853538i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(0.605893 + 1.62262i) q^{6} +(1.94656 + 3.37154i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.54295 + 2.57280i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.50714 - 0.853538i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(0.605893 + 1.62262i) q^{6} +(1.94656 + 3.37154i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.54295 + 2.57280i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(-5.53533 - 3.19583i) q^{11} +(0.578858 - 1.63246i) q^{12} +(-0.211111 + 0.580022i) q^{13} +(0.676032 - 3.83397i) q^{14} +(-1.33603 - 1.10228i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.63698 + 3.14263i) q^{17} +(0.471800 - 2.96267i) q^{18} +(-4.23138 - 1.04663i) q^{19} +1.00000i q^{20} +(-0.0560032 - 6.74284i) q^{21} +(2.18607 + 6.00619i) q^{22} +(-4.59141 + 0.809589i) q^{23} +(-1.49276 + 0.878453i) q^{24} +(0.939693 + 0.342020i) q^{25} +(0.534551 - 0.308623i) q^{26} +(-0.129455 - 5.19454i) q^{27} +(-2.98230 + 2.50245i) q^{28} +(-2.91651 + 2.44724i) q^{29} +(0.314924 + 1.70318i) q^{30} +(-0.249618 + 0.144117i) q^{31} +(0.939693 + 0.342020i) q^{32} +(5.61477 + 9.54118i) q^{33} +(4.04009 - 0.712376i) q^{34} +(1.33152 + 3.65833i) q^{35} +(-2.26579 + 1.96627i) q^{36} -1.09998i q^{37} +(2.56866 + 3.52164i) q^{38} +(0.813245 - 0.693984i) q^{39} +(0.642788 - 0.766044i) q^{40} +(1.36238 - 0.495867i) q^{41} +(-4.29131 + 5.20131i) q^{42} +(-1.72239 + 9.76814i) q^{43} +(2.18607 - 6.00619i) q^{44} +(1.07274 + 2.80165i) q^{45} +(4.03762 + 2.33112i) q^{46} +(6.17725 + 7.36176i) q^{47} +(1.70818 + 0.286590i) q^{48} +(-4.07817 + 7.06360i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(6.65665 - 2.48562i) q^{51} +(-0.607869 - 0.107184i) q^{52} +(1.58814 + 9.00681i) q^{53} +(-3.23982 + 4.06246i) q^{54} +(-4.89629 - 4.10848i) q^{55} +3.89311 q^{56} +(5.48395 + 5.18906i) q^{57} +3.80723 q^{58} +(-7.42818 - 6.23299i) q^{59} +(0.853538 - 1.50714i) q^{60} +(-1.21786 - 6.90682i) q^{61} +(0.283856 + 0.0500514i) q^{62} +(-5.67086 + 10.2102i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.308623 + 0.534551i) q^{65} +(1.83179 - 10.9181i) q^{66} +(-1.90164 - 2.26629i) q^{67} +(-3.55279 - 2.05121i) q^{68} +(7.61092 + 2.69878i) q^{69} +(1.33152 - 3.65833i) q^{70} +(0.250147 - 1.41866i) q^{71} +(2.99959 - 0.0498300i) q^{72} +(-14.7800 + 5.37947i) q^{73} +(-0.707053 + 0.842633i) q^{74} +(-1.12432 - 1.31754i) q^{75} +(0.295956 - 4.34884i) q^{76} -24.8834i q^{77} +(-1.06907 + 0.00887921i) q^{78} +(-0.407155 - 1.11865i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(-4.23863 + 7.93940i) q^{81} +(-1.36238 - 0.495867i) q^{82} +(2.08501 - 1.20378i) q^{83} +(6.63068 - 1.22603i) q^{84} +(-3.14263 + 2.63698i) q^{85} +(7.59827 - 6.37570i) q^{86} +(6.48440 - 1.19899i) q^{87} +(-5.53533 + 3.19583i) q^{88} +(10.7454 + 3.91101i) q^{89} +(0.979094 - 2.83573i) q^{90} +(-2.36651 + 0.417279i) q^{91} +(-1.59458 - 4.38107i) q^{92} +(0.499220 - 0.00414631i) q^{93} -9.61009i q^{94} +(-3.98535 - 1.76550i) q^{95} +(-1.12432 - 1.31754i) q^{96} +(-5.99172 + 7.14066i) q^{97} +(7.66445 - 2.78963i) q^{98} +(-0.318496 - 19.1723i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−1.50714	−	0.853538i	−0.870148	−	0.492790i
$3$	−1.50714	−	0.853538i	−0.870148	−	0.492790i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$6$	0.605893	+	1.62262i	0.247355	+	0.662432i
$7$	1.94656	+	3.37154i	0.735729	+	1.27432i	0.954403	+	0.298523i	$0.0964938\pi$
$7$	1.94656	+	3.37154i	0.735729	+	1.27432i	−0.218673	+	0.975798i	$0.570173\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.54295	+	2.57280i	0.514316	+	0.857601i
$10$	−0.642788	−	0.766044i	−0.203267	−	0.242245i
$11$	−5.53533	−	3.19583i	−1.66897	−	0.963578i	−0.968197	−	0.250190i	$-0.919507\pi$
$11$	−5.53533	−	3.19583i	−1.66897	−	0.963578i	−0.700769	−	0.713388i	$-0.747160\pi$
$12$	0.578858	−	1.63246i	0.167102	−	0.471250i
$13$	−0.211111	+	0.580022i	−0.0585516	+	0.160869i	−0.965520	−	0.260330i	$-0.916169\pi$
$13$	−0.211111	+	0.580022i	−0.0585516	+	0.160869i	0.906968	+	0.421200i	$0.138391\pi$
$14$	0.676032	−	3.83397i	0.180677	−	1.02467i
$15$	−1.33603	−	1.10228i	−0.344961	−	0.284608i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.63698	+	3.14263i	−0.639561	+	0.762200i	−0.984301	−	0.176499i	$-0.943523\pi$
$17$	−2.63698	+	3.14263i	−0.639561	+	0.762200i	0.344739	+	0.938698i	$0.387967\pi$
$18$	0.471800	−	2.96267i	0.111204	−	0.698308i
$19$	−4.23138	−	1.04663i	−0.970745	−	0.240113i
$19$	−4.23138	−	1.04663i	−0.970745	−	0.240113i
$20$			1.00000i			0.223607i
$21$	−0.0560032	−	6.74284i	−0.0122209	−	1.47141i
$22$	2.18607	+	6.00619i	0.466073	+	1.28052i
$23$	−4.59141	+	0.809589i	−0.957375	+	0.168811i	−0.630442	−	0.776236i	$-0.717126\pi$
$23$	−4.59141	+	0.809589i	−0.957375	+	0.168811i	−0.326933	+	0.945047i	$0.606015\pi$
$24$	−1.49276	+	0.878453i	−0.304707	+	0.179314i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	0.534551	−	0.308623i	0.104834	−	0.0605260i
$27$	−0.129455	−	5.19454i	−0.0249136	−	0.999690i
$28$	−2.98230	+	2.50245i	−0.563601	+	0.472918i
$29$	−2.91651	+	2.44724i	−0.541582	+	0.454441i	−0.872078	−	0.489366i	$-0.837228\pi$
$29$	−2.91651	+	2.44724i	−0.541582	+	0.454441i	0.330497	+	0.943807i	$0.392784\pi$
$30$	0.314924	+	1.70318i	0.0574969	+	0.310957i
$31$	−0.249618	+	0.144117i	−0.0448328	+	0.0258842i	−0.522249	−	0.852793i	$-0.674907\pi$
$31$	−0.249618	+	0.144117i	−0.0448328	+	0.0258842i	0.477416	+	0.878677i	$0.341573\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	5.61477	+	9.54118i	0.977406	+	1.66091i
$34$	4.04009	−	0.712376i	0.692869	−	0.122172i
$35$	1.33152	+	3.65833i	0.225069	+	0.618371i
$36$	−2.26579	+	1.96627i	−0.377631	+	0.327711i
$37$		−	1.09998i		−	0.180836i	−0.995904	−	0.0904178i	$-0.971180\pi$
$37$		−	1.09998i		−	0.180836i	0.995904	−	0.0904178i	$-0.0288202\pi$
$38$	2.56866	+	3.52164i	0.416692	+	0.571286i
$39$	0.813245	−	0.693984i	0.130223	−	0.111126i
$40$	0.642788	−	0.766044i	0.101634	−	0.121122i
$41$	1.36238	−	0.495867i	0.212769	−	0.0774415i	−0.233437	−	0.972372i	$-0.574997\pi$
$41$	1.36238	−	0.495867i	0.212769	−	0.0774415i	0.446206	+	0.894930i	$0.352775\pi$
$42$	−4.29131	+	5.20131i	−0.662164	+	0.802580i
$43$	−1.72239	+	9.76814i	−0.262662	+	1.48963i	0.512950	+	0.858418i	$0.328552\pi$
$43$	−1.72239	+	9.76814i	−0.262662	+	1.48963i	−0.775612	+	0.631210i	$0.782559\pi$
$44$	2.18607	−	6.00619i	0.329563	−	0.905467i
$45$	1.07274	+	2.80165i	0.159915	+	0.417645i
$46$	4.03762	+	2.33112i	0.595314	+	0.343705i
$47$	6.17725	+	7.36176i	0.901044	+	1.07382i	0.996920	+	0.0784291i	$0.0249904\pi$
$47$	6.17725	+	7.36176i	0.901044	+	1.07382i	−0.0958757	+	0.995393i	$0.530565\pi$
$48$	1.70818	+	0.286590i	0.246554	+	0.0413658i
$49$	−4.07817	+	7.06360i	−0.582596	+	1.00909i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	6.65665	−	2.48562i	0.932118	−	0.348057i
$52$	−0.607869	−	0.107184i	−0.0842963	−	0.0148637i
$53$	1.58814	+	9.00681i	0.218148	+	1.23718i	0.875359	+	0.483473i	$0.160625\pi$
$53$	1.58814	+	9.00681i	0.218148	+	1.23718i	−0.657211	+	0.753707i	$0.728264\pi$
$54$	−3.23982	+	4.06246i	−0.440883	+	0.552831i
$55$	−4.89629	−	4.10848i	−0.660216	−	0.553987i
$56$	3.89311			0.520239
$57$	5.48395	+	5.18906i	0.726367	+	0.687307i
$58$	3.80723			0.499913
$59$	−7.42818	−	6.23299i	−0.967067	−	0.811466i	0.0150210	−	0.999887i	$-0.495218\pi$
$59$	−7.42818	−	6.23299i	−0.967067	−	0.811466i	−0.982088	+	0.188421i	$0.939663\pi$
$60$	0.853538	−	1.50714i	0.110191	−	0.194571i
$61$	−1.21786	−	6.90682i	−0.155931	−	0.884328i	−0.957930	−	0.287002i	$-0.907341\pi$
$61$	−1.21786	−	6.90682i	−0.155931	−	0.884328i	0.801999	−	0.597325i	$-0.203770\pi$
$62$	0.283856	+	0.0500514i	0.0360497	+	0.00635654i
$63$	−5.67086	+	10.2102i	−0.714461	+	1.28637i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.308623	+	0.534551i	−0.0382800	+	0.0663029i
$66$	1.83179	−	10.9181i	0.225477	−	1.34392i
$67$	−1.90164	−	2.26629i	−0.232323	−	0.276871i	0.637271	−	0.770640i	$-0.280063\pi$
$67$	−1.90164	−	2.26629i	−0.232323	−	0.276871i	−0.869593	+	0.493769i	$0.835619\pi$
$68$	−3.55279	−	2.05121i	−0.430839	−	0.248745i
$69$	7.61092	+	2.69878i	0.916247	+	0.324894i
$70$	1.33152	−	3.65833i	0.159147	−	0.437254i
$71$	0.250147	−	1.41866i	0.0296870	−	0.168363i	−0.966360	−	0.257194i	$-0.917202\pi$
$71$	0.250147	−	1.41866i	0.0296870	−	0.168363i	0.996047	+	0.0888309i	$0.0283131\pi$
$72$	2.99959	−	0.0498300i	0.353505	−	0.00587252i
$73$	−14.7800	+	5.37947i	−1.72986	+	0.629619i	−0.998621	−	0.0524980i	$-0.983282\pi$
$73$	−14.7800	+	5.37947i	−1.72986	+	0.629619i	−0.731243	+	0.682117i	$0.761059\pi$
$74$	−0.707053	+	0.842633i	−0.0821933	+	0.0979541i
$75$	−1.12432	−	1.31754i	−0.129826	−	0.152136i
$76$	0.295956	−	4.34884i	0.0339485	−	0.498846i
$77$		−	24.8834i		−	2.83573i
$78$	−1.06907	+	0.00887921i	−0.121048	+	0.00100537i
$79$	−0.407155	−	1.11865i	−0.0458085	−	0.125858i	0.914679	−	0.404181i	$-0.132444\pi$
$79$	−0.407155	−	1.11865i	−0.0458085	−	0.125858i	−0.960487	+	0.278323i	$0.910221\pi$
$80$	−0.984808	+	0.173648i	−0.110105	+	0.0194145i
$81$	−4.23863	+	7.93940i	−0.470959	+	0.882155i
$82$	−1.36238	−	0.495867i	−0.150450	−	0.0547594i
$83$	2.08501	−	1.20378i	0.228860	−	0.132132i	−0.381186	−	0.924498i	$-0.624484\pi$
$83$	2.08501	−	1.20378i	0.228860	−	0.132132i	0.610046	+	0.792366i	$0.291151\pi$
$84$	6.63068	−	1.22603i	0.723466	−	0.133771i
$85$	−3.14263	+	2.63698i	−0.340866	+	0.286021i
$86$	7.59827	−	6.37570i	0.819342	−	0.687510i
$87$	6.48440	−	1.19899i	0.695200	−	0.128545i
$88$	−5.53533	+	3.19583i	−0.590069	+	0.340676i
$89$	10.7454	+	3.91101i	1.13901	+	0.414566i	0.841556	−	0.540170i	$-0.181640\pi$
$89$	10.7454	+	3.91101i	1.13901	+	0.414566i	0.297454	+	0.954736i	$0.403862\pi$
$90$	0.979094	−	2.83573i	0.103206	−	0.298912i
$91$	−2.36651	+	0.417279i	−0.248077	+	0.0437427i
$92$	−1.59458	−	4.38107i	−0.166246	−	0.456758i
$93$	0.499220	−	0.00414631i	0.0517667	−	0.000429952i
$94$		−	9.61009i		−	0.991205i
$95$	−3.98535	−	1.76550i	−0.408888	−	0.181136i
$96$	−1.12432	−	1.31754i	−0.114751	−	0.134470i
$97$	−5.99172	+	7.14066i	−0.608367	+	0.725024i	−0.979024	−	0.203746i	$-0.934688\pi$
$97$	−5.99172	+	7.14066i	−0.608367	+	0.725024i	0.370657	+	0.928770i	$0.379133\pi$
$98$	7.66445	−	2.78963i	0.774226	−	0.281795i
$99$	−0.318496	−	19.1723i	−0.0320101	−	1.92689i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	0.207307	−	0.569570i	0.0206278	−	0.0566744i	−0.928951	−	0.370202i	$-0.879289\pi$
$101$	0.207307	−	0.569570i	0.0206278	−	0.0566744i	0.949579	+	0.313527i	$0.101511\pi$
$102$	−6.69702	−	2.37471i	−0.663104	−	0.235132i
$103$	0.0346776	+	0.0200211i	0.00341689	+	0.00197274i	0.501707	−	0.865037i	$-0.332705\pi$
$103$	0.0346776	+	0.0200211i	0.00341689	+	0.00197274i	−0.498291	+	0.867010i	$0.666039\pi$
$104$	0.396759	+	0.472839i	0.0389054	+	0.0463656i
$105$	1.11573	−	6.65012i	0.108884	−	0.648986i
$106$	4.57288	−	7.92045i	0.444157	−	0.769302i
$107$	1.07773	+	1.86669i	0.104188	+	0.180460i	0.913406	−	0.407049i	$-0.133442\pi$
$107$	1.07773	+	1.86669i	0.104188	+	0.180460i	−0.809218	+	0.587509i	$0.800109\pi$
$108$	5.09314	−	1.02951i	0.490088	−	0.0990647i
$109$	−0.686499	−	0.121048i	−0.0657547	−	0.0115943i	0.140674	−	0.990056i	$-0.455073\pi$
$109$	−0.686499	−	0.121048i	−0.0657547	−	0.0115943i	−0.206429	+	0.978462i	$0.566184\pi$
$110$	1.10990	+	6.29455i	0.105825	+	0.600162i
$111$	−0.938874	+	1.65782i	−0.0891140	+	0.157354i
$112$	−2.98230	−	2.50245i	−0.281801	−	0.236459i
$113$	14.4597			1.36025			0.680126	−	0.733095i	$-0.261925\pi$
$113$	14.4597			1.36025			0.680126	+	0.733095i	$0.261925\pi$
$114$	−0.865486	−	7.50006i	−0.0810602	−	0.702445i
$115$	−4.66224			−0.434756
$116$	−2.91651	−	2.44724i	−0.270791	−	0.227220i
$117$	−1.81802	+	0.351797i	−0.168076	+	0.0325237i
$118$	1.68383	+	9.54949i	0.155009	+	0.879102i
$119$	−15.7285	−	2.77336i	−1.44183	−	0.254234i
$120$	−1.62262	+	0.605893i	−0.148124	+	0.0553103i
$121$	14.9266	+	25.8537i	1.35696	+	2.35033i
$122$	−3.50668	+	6.07375i	−0.317480	+	0.549892i
$123$	−2.47655	−	0.415504i	−0.223303	−	0.0374648i
$124$	−0.185274	−	0.220800i	−0.0166381	−	0.0198285i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	10.9071	−	4.17631i	0.971684	−	0.372056i
$127$	7.44977	−	20.4681i	0.661060	−	1.81625i	0.0890053	−	0.996031i	$-0.471631\pi$
$127$	7.44977	−	20.4681i	0.661060	−	1.81625i	0.572055	−	0.820216i	$-0.306147\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	10.9334	−	13.2518i	0.962629	−	1.16676i
$130$	0.580022	−	0.211111i	0.0508713	−	0.0185156i
$131$	−11.3770	+	13.5586i	−0.994017	+	1.18462i	−0.0112197	+	0.999937i	$0.503571\pi$
$131$	−11.3770	+	13.5586i	−0.994017	+	1.18462i	−0.982797	+	0.184687i	$0.940873\pi$
$132$	−8.42123	+	7.18628i	−0.732974	+	0.625485i
$133$	−4.70788	−	16.3036i	−0.408225	−	1.41370i
$134$			2.95843i			0.255569i
$135$	0.774534	−	5.13810i	0.0666613	−	0.442217i
$136$	1.40311	+	3.85501i	0.120315	+	0.330564i
$137$	−0.0513943	+	0.00906220i	−0.00439091	+	0.000774236i	−0.175843	−	0.984418i	$-0.556265\pi$
$137$	−0.0513943	+	0.00906220i	−0.00439091	+	0.000774236i	0.171452	+	0.985192i	$0.445154\pi$
$138$	−4.09556	−	6.95958i	−0.348637	−	0.592439i
$139$	−4.49012	−	1.63427i	−0.380847	−	0.138617i	0.144501	−	0.989505i	$-0.453842\pi$
$139$	−4.49012	−	1.63427i	−0.380847	−	0.138617i	−0.525348	+	0.850888i	$0.676065\pi$
$140$	−3.37154	+	1.94656i	−0.284947	+	0.164514i
$141$	−3.02645	−	16.3677i	−0.254873	−	1.37841i
$142$	−1.10352	+	0.925962i	−0.0926052	+	0.0777050i
$143$	3.02222	−	2.53594i	0.252731	−	0.212066i
$144$	−2.32985	−	1.88992i	−0.194154	−	0.157494i
$145$	−3.29716	+	1.90361i	−0.273814	+	0.158087i
$146$	14.7800	+	5.37947i	1.22320	+	0.445208i
$147$	12.1754	−	7.16496i	1.00421	−	0.590956i
$148$	1.08327	−	0.191009i	0.0890441	−	0.0157009i
$149$	−3.50624	−	9.63331i	−0.287242	−	0.789191i	−0.996450	−	0.0841915i	$-0.973169\pi$
$149$	−3.50624	−	9.63331i	−0.287242	−	0.789191i	0.709207	−	0.705000i	$-0.249053\pi$
$150$	0.0143852	+	1.73199i	0.00117455	+	0.141416i
$151$		−	9.30320i		−	0.757083i	−0.925584	−	0.378542i	$-0.876426\pi$
$151$		−	9.30320i		−	0.757083i	0.925584	−	0.378542i	$-0.123574\pi$
$152$	−3.02210	+	3.14117i	−0.245124	+	0.254782i
$153$	−12.1541	−	1.93552i	−0.982600	−	0.156477i
$154$	−15.9948	+	19.0618i	−1.28889	+	1.53604i
$155$	−0.270852	+	0.0985820i	−0.0217553	+	0.00791830i
$156$	0.824660	+	0.680381i	0.0660256	+	0.0544740i
$157$	3.94205	−	22.3565i	0.314610	−	1.78424i	−0.259790	−	0.965665i	$-0.583653\pi$
$157$	3.94205	−	22.3565i	0.314610	−	1.78424i	0.574400	−	0.818575i	$-0.305236\pi$
$158$	−0.407155	+	1.11865i	−0.0323915	+	0.0889949i
$159$	5.29409	−	14.9301i	0.419849	−	1.18403i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−11.6670	−	13.9042i	−0.919488	−	1.09580i
$162$	8.35032	−	3.35739i	0.656063	−	0.263782i
$163$	2.34099	−	4.05472i	0.183361	−	0.317590i	−0.759662	−	0.650318i	$-0.774636\pi$
$163$	2.34099	−	4.05472i	0.183361	−	0.317590i	0.943023	+	0.332728i	$0.107969\pi$
$164$	0.724909	+	1.25558i	0.0566059	+	0.0980443i
$165$	3.87266	+	10.3712i	0.301486	+	0.807398i
$166$	−2.37099	−	0.418069i	−0.184024	−	0.0324484i
$167$	1.06545	+	6.04249i	0.0824474	+	0.467582i	0.997878	+	0.0651071i	$0.0207389\pi$
$167$	1.06545	+	6.04249i	0.0824474	+	0.467582i	−0.915431	+	0.402475i	$0.868150\pi$
$168$	−5.86747	−	3.32292i	−0.452685	−	0.256369i
$169$	9.66672	+	8.11134i	0.743594	+	0.623949i
$170$	4.10241			0.314641
$171$	−3.83603	−	12.5014i	−0.293348	−	0.956006i
$172$	−9.91883			−0.756304
$173$	14.9932	+	12.5808i	1.13991	+	0.956501i	0.999436	−	0.0335828i	$-0.0106918\pi$
$173$	14.9932	+	12.5808i	1.13991	+	0.956501i	0.140478	+	0.990084i	$0.455136\pi$
$174$	−5.73803	−	3.24961i	−0.434999	−	0.246352i
$175$	0.676032	+	3.83397i	0.0511032	+	0.289821i
$176$	6.29455	+	1.10990i	0.474469	+	0.0836618i
$177$	5.87523	+	15.7342i	0.441609	+	1.18266i
$178$	−5.71751	−	9.90302i	−0.428545	−	0.742262i
$179$	−11.1893	+	19.3805i	−0.836331	+	1.44857i	0.0566110	+	0.998396i	$0.481971\pi$
$179$	−11.1893	+	19.3805i	−0.836331	+	1.44857i	−0.892942	+	0.450172i	$0.851363\pi$
$180$	−2.57280	+	1.54295i	−0.191765	+	0.115004i
$181$	11.9995	+	14.3004i	0.891915	+	1.06294i	0.997648	+	0.0685483i	$0.0218367\pi$
$181$	11.9995	+	14.3004i	0.891915	+	1.06294i	−0.105733	+	0.994395i	$0.533719\pi$
$182$	2.08107	+	1.20151i	0.154259	+	0.0890616i
$183$	−4.05975	+	11.4490i	−0.300105	+	0.846337i
$184$	−1.59458	+	4.38107i	−0.117554	+	0.322977i
$185$	0.191009	−	1.08327i	0.0140433	−	0.0796435i
$186$	−0.385090	−	0.317716i	−0.0282361	−	0.0232961i
$187$	24.6399	−	8.96817i	1.80184	−	0.655818i
$188$	−6.17725	+	7.36176i	−0.450522	+	0.536911i
$189$	17.2616	−	10.5479i	1.25560	−	0.767249i
$190$	1.91811	+	3.91418i	0.139155	+	0.283965i
$191$		−	13.4638i		−	0.974209i	−0.873344	−	0.487104i	$-0.838053\pi$
$191$		−	13.4638i		−	0.974209i	0.873344	−	0.487104i	$-0.161947\pi$
$192$	0.0143852	+	1.73199i	0.00103816	+	0.124996i
$193$	−4.56420	−	12.5400i	−0.328539	−	0.902652i	−0.988482	−	0.151337i	$-0.951642\pi$
$193$	−4.56420	−	12.5400i	−0.328539	−	0.902652i	0.659944	−	0.751315i	$-0.270580\pi$
$194$	9.17985	−	1.61866i	0.659075	−	0.116213i
$195$	0.921399	−	0.542223i	0.0659827	−	0.0388294i
$196$	−7.66445	−	2.78963i	−0.547461	−	0.199259i
$197$	−6.87247	+	3.96782i	−0.489643	+	0.282696i	−0.724426	−	0.689352i	$-0.757895\pi$
$197$	−6.87247	+	3.96782i	−0.489643	+	0.282696i	0.234783	+	0.972048i	$0.424562\pi$
$198$	−12.0797	+	14.8916i	−0.858470	+	1.05830i
$199$	−17.2023	+	14.4345i	−1.21944	+	1.02323i	−0.220588	+	0.975367i	$0.570798\pi$
$199$	−17.2023	+	14.4345i	−1.21944	+	1.02323i	−0.998854	+	0.0478658i	$0.984758\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	0.931680	+	5.03874i	0.0657156	+	0.355405i
$202$	−0.524919	+	0.303062i	−0.0369332	+	0.0213234i
$203$	−13.9281	−	5.06941i	−0.977561	−	0.355803i
$204$	3.60378	+	6.12390i	0.252315	+	0.428759i
$205$	1.42779	−	0.251758i	0.0997214	−	0.0175836i
$206$	−0.0136953	−	0.0376274i	−0.000954194	−	0.00262163i
$207$	−9.16722	−	10.5636i	−0.637166	−	0.734224i
$208$		−	0.617247i		−	0.0427984i
$209$	20.0773	+	19.3162i	1.38877	+	1.33613i
$210$	−5.12932	+	4.37711i	−0.353956	+	0.302050i
$211$	−1.54597	+	1.84241i	−0.106429	+	0.126837i	−0.816629	−	0.577163i	$-0.804160\pi$
$211$	−1.54597	+	1.84241i	−0.106429	+	0.126837i	0.710200	+	0.704000i	$0.248604\pi$
$212$	−8.59420	+	3.12803i	−0.590252	+	0.214834i
$213$	−1.58788	+	1.92460i	−0.108800	+	0.131872i
$214$	0.374293	−	2.12272i	0.0255861	−	0.145106i
$215$	−3.39244	+	9.32065i	−0.231363	+	0.635663i
$216$	−4.56333	−	2.48516i	−0.310495	−	0.169094i
$217$	−0.971793	−	0.561065i	−0.0659696	−	0.0380876i
$218$	0.448080	+	0.534001i	0.0303478	+	0.0361671i
$219$	26.8671	+	4.50764i	1.81551	+	0.304598i
$220$	3.19583	−	5.53533i	0.215463	−	0.373192i
$221$	−1.26610	−	2.19295i	−0.0851671	−	0.147514i
$222$	1.78485	−	0.666470i	0.119791	−	0.0447306i
$223$	−13.1022	−	2.31026i	−0.877385	−	0.154707i	−0.283225	−	0.959053i	$-0.591404\pi$
$223$	−13.1022	−	2.31026i	−0.877385	−	0.154707i	−0.594160	+	0.804347i	$0.702516\pi$
$224$	0.676032	+	3.83397i	0.0451693	+	0.256168i
$225$	0.569946	+	2.94536i	0.0379964	+	0.196358i
$226$	−11.0768	−	9.29450i	−0.736815	−	0.618261i
$227$	−7.08756			−0.470418			−0.235209	−	0.971945i	$-0.575577\pi$
$227$	−7.08756			−0.470418			−0.235209	+	0.971945i	$0.575577\pi$
$228$	−4.15795	+	6.30170i	−0.275367	+	0.417341i
$229$	20.1737			1.33312			0.666559	−	0.745453i	$-0.267767\pi$
$229$	20.1737			1.33312			0.666559	+	0.745453i	$0.267767\pi$
$230$	3.57148	+	2.99683i	0.235497	+	0.197605i
$231$	−21.2389	+	37.5028i	−1.39742	+	2.46751i
$232$	0.661118	+	3.74939i	0.0434045	+	0.246159i
$233$	−2.78216	−	0.490569i	−0.182265	−	0.0321383i	0.0817705	−	0.996651i	$-0.473943\pi$
$233$	−2.78216	−	0.490569i	−0.182265	−	0.0321383i	−0.264036	+	0.964513i	$0.585054\pi$
$234$	1.61881	+	0.899106i	0.105825	+	0.0587764i
$235$	4.80504	+	8.32258i	0.313447	+	0.542905i
$236$	4.84840	−	8.39768i	0.315604	−	0.546642i
$237$	−0.341169	+	2.03348i	−0.0221613	+	0.132089i
$238$	10.2661	+	12.2346i	0.665450	+	0.793052i
$239$	−8.66890	−	5.00499i	−0.560744	−	0.323746i	0.192700	−	0.981258i	$-0.438276\pi$
$239$	−8.66890	−	5.00499i	−0.560744	−	0.323746i	−0.753444	+	0.657512i	$0.771609\pi$
$240$	1.63246	+	0.578858i	0.105375	+	0.0373651i
$241$	3.70205	−	10.1713i	0.238470	−	0.655190i	−0.761506	−	0.648158i	$-0.775539\pi$
$241$	3.70205	−	10.1713i	0.238470	−	0.655190i	0.999975	−	0.00703182i	$-0.00223832\pi$
$242$	5.18396	−	29.3997i	0.333237	−	1.88988i
$243$	13.1648	−	8.34796i	0.844521	−	0.535522i
$244$	6.59041	−	2.39871i	0.421908	−	0.153562i
$245$	−5.24279	+	6.24812i	−0.334950	+	0.399178i
$246$	1.63006	+	1.91019i	0.103929	+	0.121789i
$247$	1.50036	−	2.23334i	0.0954655	−	0.142104i
$248$			0.288235i			0.0183029i
$249$	−4.16988	+	0.0346332i	−0.264255	+	0.00219479i
$250$	−0.342020	−	0.939693i	−0.0216313	−	0.0594314i
$251$	15.9964	−	2.82059i	1.00968	−	0.178034i	0.355745	−	0.934583i	$-0.384227\pi$
$251$	15.9964	−	2.82059i	1.00968	−	0.178034i	0.653937	+	0.756549i	$0.273116\pi$
$252$	−11.0398	−	3.81172i	−0.695444	−	0.240116i
$253$	28.0023	+	10.1920i	1.76049	+	0.640766i
$254$	−18.8635	+	10.8908i	−1.18360	+	0.683351i
$255$	6.98715	−	1.29195i	0.437552	−	0.0809048i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	16.9856	−	14.2526i	1.05953	−	0.889052i	0.0654679	−	0.997855i	$-0.479146\pi$
$257$	16.9856	−	14.2526i	1.05953	−	0.889052i	0.994063	+	0.108802i	$0.0347016\pi$
$258$	−16.8936	+	3.12368i	−1.05175	+	0.194472i
$259$	3.70862	−	2.14117i	0.230442	−	0.133046i
$260$	−0.580022	−	0.211111i	−0.0359715	−	0.0130925i
$261$	−10.7963	−	3.72763i	−0.668273	−	0.230735i
$262$	17.4306	−	3.07349i	1.07687	−	0.189881i
$263$	3.16022	+	8.68265i	0.194868	+	0.535395i	0.998189	−	0.0601507i	$-0.0191581\pi$
$263$	3.16022	+	8.68265i	0.194868	+	0.535395i	−0.803321	+	0.595546i	$0.796936\pi$
$264$	11.0703	−	0.0919451i	0.681329	−	0.00565883i
$265$			9.14575i			0.561819i
$266$	−6.87329	+	15.5154i	−0.421428	+	0.951312i
$267$	−12.8566	−	15.0660i	−0.786814	−	0.922027i
$268$	1.90164	−	2.26629i	0.116161	−	0.138436i
$269$	−16.3121	+	5.93711i	−0.994565	+	0.361992i	−0.787486	−	0.616332i	$-0.788618\pi$
$269$	−16.3121	+	5.93711i	−0.994565	+	0.361992i	−0.207078	+	0.978324i	$0.566396\pi$
$270$	−3.89604	+	3.43815i	−0.237105	+	0.209239i
$271$	−0.106051	+	0.601445i	−0.00644213	+	0.0365352i	−0.987859	−	0.155351i	$-0.950349\pi$
$271$	−0.106051	+	0.601445i	−0.00644213	+	0.0365352i	0.981417	+	0.191886i	$0.0614603\pi$
$272$	1.40311	−	3.85501i	0.0850759	−	0.233744i
$273$	3.92282	+	1.39100i	0.237420	+	0.0841874i
$274$	0.0451954	+	0.0260936i	0.00273035	+	0.00157637i
$275$	−4.10848	−	4.89629i	−0.247750	−	0.295257i
$276$	−1.33615	+	7.96393i	−0.0804270	+	0.479372i
$277$	0.638404	−	1.10575i	0.0383580	−	0.0664380i	−0.846209	−	0.532851i	$-0.821121\pi$
$277$	0.638404	−	1.10575i	0.0383580	−	0.0664380i	0.884567	+	0.466413i	$0.154454\pi$
$278$	2.38914	+	4.13812i	0.143291	+	0.248188i
$279$	−0.755933	−	0.419854i	−0.0452566	−	0.0251360i
$280$	3.83397	+	0.676032i	0.229123	+	0.0404006i
$281$	−4.62942	−	26.2548i	−0.276168	−	1.56623i	−0.735226	−	0.677822i	$-0.762924\pi$
$281$	−4.62942	−	26.2548i	−0.276168	−	1.56623i	0.459058	−	0.888406i	$-0.348187\pi$
$282$	−8.20257	+	14.4838i	−0.488456	+	0.862495i
$283$	0.210982	+	0.177035i	0.0125416	+	0.0105236i	0.649037	−	0.760757i	$-0.275172\pi$
$283$	0.210982	+	0.177035i	0.0125416	+	0.0105236i	−0.636495	+	0.771281i	$0.719617\pi$
$284$	1.44054			0.0854804
$285$	4.49956	+	6.06250i	0.266531	+	0.359112i
$286$	−3.94523			−0.233286
$287$	4.32379	+	3.62809i	0.255225	+	0.214160i
$288$	0.569946	+	2.94536i	0.0335844	+	0.173557i
$289$	0.0295588	+	0.167636i	0.00173875	+	0.00986095i
$290$	3.74939	+	0.661118i	0.220172	+	0.0388222i
$291$	15.1252	−	5.64782i	0.886654	−	0.331081i
$292$	−7.86426	−	13.6213i	−0.460221	−	0.797126i
$293$	0.770482	−	1.33451i	0.0450120	−	0.0779631i	−0.842642	−	0.538475i	$-0.819001\pi$
$293$	0.770482	−	1.33451i	0.0450120	−	0.0779631i	0.887654	+	0.460512i	$0.152334\pi$
$294$	−13.9325	−	2.33753i	−0.812558	−	0.136327i
$295$	−6.23299	−	7.42818i	−0.362899	−	0.432486i
$296$	−0.952610	−	0.549990i	−0.0553693	−	0.0319675i
$297$	−15.8843	+	29.1672i	−0.921699	+	1.69245i
$298$	−3.50624	+	9.63331i	−0.203111	+	0.558043i
$299$	0.499716	−	2.83403i	0.0288994	−	0.163896i
$300$	1.10228	−	1.33603i	0.0636403	−	0.0771357i
$301$	−36.2864	+	13.2072i	−2.09151	+	0.761248i
$302$	−5.97998	+	7.12666i	−0.344109	+	0.410093i
$303$	−0.798590	+	0.681479i	−0.0458778	+	0.0391499i
$304$	4.33416	−	0.463708i	0.248581	−	0.0265955i
$305$		−	7.01337i		−	0.401584i
$306$	8.06644	+	9.29519i	0.461128	+	0.531370i
$307$	3.35259	+	9.21116i	0.191342	+	0.525709i	0.997852	−	0.0655126i	$-0.0208683\pi$
$307$	3.35259	+	9.21116i	0.191342	+	0.525709i	−0.806509	+	0.591221i	$0.798646\pi$
$308$	24.5054	−	4.32096i	1.39632	−	0.246210i
$309$	−0.0351752	−	0.0597733i	−0.00200105	−	0.00340038i
$310$	0.270852	+	0.0985820i	0.0153834	+	0.00559908i
$311$	20.5276	−	11.8516i	1.16402	−	0.672045i	0.211753	−	0.977323i	$-0.432083\pi$
$311$	20.5276	−	11.8516i	1.16402	−	0.672045i	0.952263	+	0.305278i	$0.0987495\pi$
$312$	−0.194386	−	1.05128i	−0.0110049	−	0.0595172i
$313$	−16.5122	+	13.8554i	−0.933327	+	0.783155i	−0.976412	−	0.215917i	$-0.930726\pi$
$313$	−16.5122	+	13.8554i	−0.933327	+	0.783155i	0.0430844	+	0.999071i	$0.486282\pi$
$314$	−17.3902	+	14.5921i	−0.981388	+	0.823482i
$315$	−7.35769	+	9.07036i	−0.414559	+	0.511057i
$316$	1.03095	−	0.595221i	0.0579956	−	0.0334838i
$317$	−22.5638	−	8.21257i	−1.26731	−	0.461264i	−0.381096	−	0.924536i	$-0.624453\pi$
$317$	−22.5638	−	8.21257i	−1.26731	−	0.461264i	−0.886216	+	0.463272i	$0.846675\pi$
$318$	−13.6524	+	8.03412i	−0.765587	+	0.450531i
$319$	23.9648	−	4.22564i	1.34177	−	0.236590i
$320$	−0.342020	−	0.939693i	−0.0191195	−	0.0525304i
$321$	−0.0310068	−	3.73325i	−0.00173063	−	0.208370i
$322$			18.1506i			1.01150i
$323$	14.4472	−	10.5377i	0.803865	−	0.586334i
$324$	−8.55481	−	2.79557i	−0.475267	−	0.155310i
$325$	−0.396759	+	0.472839i	−0.0220082	+	0.0262284i
$326$	−4.39963	+	1.60133i	−0.243673	+	0.0886897i
$327$	0.931331	+	0.768389i	0.0515027	+	0.0424920i
$328$	0.251758	−	1.42779i	0.0139010	−	0.0788367i
$329$	−12.7961	+	35.1569i	−0.705470	+	1.93826i
$330$	3.69986	−	10.4341i	0.203671	−	0.574379i
$331$	26.7957	+	15.4705i	1.47283	+	0.850337i	0.999533	−	0.0305677i	$-0.00973153\pi$
$331$	26.7957	+	15.4705i	1.47283	+	0.850337i	0.473294	+	0.880905i	$0.343065\pi$
$332$	1.54755	+	1.84430i	0.0849329	+	0.101219i
$333$	2.83003	−	1.69721i	0.155085	−	0.0930065i
$334$	3.06786	−	5.31368i	0.167866	−	0.290752i
$335$	−1.47921	−	2.56208i	−0.0808181	−	0.139981i
$336$	2.35881	+	6.31704i	0.128684	+	0.344623i
$337$	−32.9914	−	5.81728i	−1.79716	−	0.316887i	−0.827521	−	0.561435i	$-0.810249\pi$
$337$	−32.9914	−	5.81728i	−1.79716	−	0.316887i	−0.969637	+	0.244547i	$0.921361\pi$
$338$	−2.19127	−	12.4273i	−0.119189	−	0.675956i
$339$	−21.7928	−	12.3419i	−1.18362	−	0.670319i
$340$	−3.14263	−	2.63698i	−0.170433	−	0.143010i
$341$	1.84230			0.0997659
$342$	−5.09718	+	12.0424i	−0.275624	+	0.651177i
$343$	−4.50175			−0.243072
$344$	7.59827	+	6.37570i	0.409671	+	0.343755i
$345$	7.02665	+	3.97940i	0.378302	+	0.214244i
$346$	−3.39869	−	19.2749i	−0.182715	−	1.03623i
$347$	16.1221	+	2.84277i	0.865482	+	0.152608i	0.588726	−	0.808333i	$-0.299630\pi$
$347$	16.1221	+	2.84277i	0.865482	+	0.152608i	0.276756	+	0.960940i	$0.410741\pi$
$348$	2.30677	+	6.17768i	0.123656	+	0.331158i
$349$	7.48295	+	12.9609i	0.400553	+	0.693779i	0.993793	−	0.111247i	$-0.0354846\pi$
$349$	7.48295	+	12.9609i	0.400553	+	0.693779i	−0.593239	+	0.805026i	$0.702151\pi$
$350$	1.94656	−	3.37154i	0.104048	−	0.180216i
$351$	3.04028	+	1.02154i	0.162278	+	0.0545256i
$352$	−4.10848	−	4.89629i	−0.218982	−	0.260973i
$353$	0.987569	+	0.570173i	0.0525630	+	0.0303473i	0.526051	−	0.850453i	$-0.323672\pi$
$353$	0.987569	+	0.570173i	0.0525630	+	0.0303473i	−0.473488	+	0.880800i	$0.657005\pi$
$354$	5.61308	−	15.8296i	0.298332	−	0.841336i
$355$	0.492694	−	1.35367i	0.0261495	−	0.0718451i
$356$	−1.98567	+	11.2613i	−0.105240	+	0.596847i
$357$	21.3379	+	17.6047i	1.12932	+	0.931741i
$358$	21.0291	−	7.65396i	1.11142	−	0.404525i
$359$	−4.58551	+	5.46480i	−0.242014	+	0.288421i	−0.873355	−	0.487084i	$-0.838060\pi$
$359$	−4.58551	+	5.46480i	−0.242014	+	0.288421i	0.631341	+	0.775506i	$0.282505\pi$
$360$	2.96267	+	0.471800i	0.156146	+	0.0248660i
$361$	16.8091	+	8.85736i	0.884691	+	0.466177i
$362$		−	18.6679i		−	0.981163i
$363$	−0.429444	−	51.7055i	−0.0225400	−	2.71384i
$364$	−0.821879	−	2.25809i	−0.0430781	−	0.118356i
$365$	−15.4896	+	2.73123i	−0.810761	+	0.142959i
$366$	10.4692	−	6.16092i	0.547236	−	0.322036i
$367$	23.9261	+	8.70840i	1.24893	+	0.454575i	0.880041	−	0.474898i	$-0.157515\pi$
$367$	23.9261	+	8.70840i	1.24893	+	0.454575i	0.368892	+	0.929472i	$0.379737\pi$
$368$	4.03762	−	2.33112i	0.210475	−	0.121518i
$369$	3.37786	+	2.74005i	0.175844	+	0.142641i
$370$	−0.842633	+	0.707053i	−0.0438064	+	0.0367579i
$371$	−27.2754	+	22.8867i	−1.41607	+	1.18822i
$372$	0.0907719	+	0.490915i	0.00470630	+	0.0254528i
$373$	−13.9606	+	8.06016i	−0.722853	+	0.417339i	−0.815802	−	0.578331i	$-0.803704\pi$
$373$	−13.9606	+	8.06016i	−0.722853	+	0.417339i	0.0929488	+	0.995671i	$0.470371\pi$
$374$	−24.6399	−	8.96817i	−1.27410	−	0.463733i
$375$	−0.878453	−	1.49276i	−0.0453631	−	0.0770856i
$376$	9.46409	−	1.66877i	0.488073	−	0.0860605i
$377$	−0.803747	−	2.20828i	−0.0413951	−	0.113732i
$378$	−20.0032	−	3.01535i	−1.02885	−	0.155093i
$379$			0.335569i			0.0172370i	0.999963	+	0.00861851i	$0.00274339\pi$
$379$			0.335569i			0.0172370i	−0.999963	+	0.00861851i	$0.997257\pi$
$380$	1.04663	−	4.23138i	0.0536909	−	0.217065i
$381$	−28.6981	+	24.4896i	−1.47025	+	1.25464i
$382$	−8.65439	+	10.3139i	−0.442797	+	0.527705i
$383$	−22.4759	+	8.18055i	−1.14846	+	0.418007i	−0.844963	−	0.534825i	$-0.820378\pi$
$383$	−22.4759	+	8.18055i	−1.14846	+	0.418007i	−0.303501	+	0.952831i	$0.598155\pi$
$384$	1.10228	−	1.33603i	0.0562506	−	0.0681789i
$385$	4.32096	−	24.5054i	0.220217	−	1.24891i
$386$	−4.56420	+	12.5400i	−0.232312	+	0.638271i
$387$	−27.7891	+	10.6404i	−1.41260	+	0.540880i
$388$	−8.07263	−	4.66073i	−0.409825	−	0.236613i
$389$	−15.1033	−	17.9994i	−0.765767	−	0.912605i	0.232431	−	0.972613i	$-0.425332\pi$
$389$	−15.1033	−	17.9994i	−0.765767	−	0.912605i	−0.998198	+	0.0600076i	$0.980888\pi$
$390$	−1.05437	−	0.176897i	−0.0533899	−	0.00895753i
$391$	9.56321	−	16.5640i	0.483632	−	0.837676i
$392$	4.07817	+	7.06360i	0.205979	+	0.356765i
$393$	28.7196	−	10.7240i	1.44871	−	0.540956i
$394$	7.81508	+	1.37801i	0.393718	+	0.0694232i
$395$	−0.206718	−	1.17236i	−0.0104011	−	0.0589876i
$396$	18.8257	−	3.64289i	0.946029	−	0.183062i
$397$	26.3621	+	22.1204i	1.32307	+	1.11019i	0.985643	+	0.168841i	$0.0540024\pi$
$397$	26.3621	+	22.1204i	1.32307	+	1.11019i	0.337431	+	0.941350i	$0.390442\pi$
$398$	22.4561			1.12562
$399$	−6.82028	+	28.5901i	−0.341441	+	1.43130i
$400$	−1.00000			−0.0500000
$401$	−11.0555	−	9.27669i	−0.552087	−	0.463256i	0.323560	−	0.946208i	$-0.395120\pi$
$401$	−11.0555	−	9.27669i	−0.552087	−	0.463256i	−0.875647	+	0.482952i	$0.839565\pi$
$402$	2.52513	−	4.45877i	0.125942	−	0.222383i
$403$	−0.0308941	−	0.175209i	−0.00153894	−	0.00872778i
$404$	0.596916	+	0.105252i	0.0296977	+	0.00523650i
$405$	−5.55290	+	7.08275i	−0.275926	+	0.351945i
$406$	7.41099	+	12.8362i	0.367801	+	0.637050i
$407$	−3.51534	+	6.08875i	−0.174249	+	0.301808i
$408$	1.17571	−	7.00764i	0.0582064	−	0.346930i
$409$	−22.4068	−	26.7034i	−1.10795	−	1.32040i	−0.942510	−	0.334177i	$-0.891542\pi$
$409$	−22.4068	−	26.7034i	−1.10795	−	1.32040i	−0.165435	−	0.986221i	$-0.552903\pi$
$410$	−1.25558	−	0.724909i	−0.0620087	−	0.0358007i
$411$	0.0851934	+	0.0302090i	0.00420228	+	0.00149010i
$412$	−0.0136953	+	0.0376274i	−0.000674717	+	0.00185377i
$413$	6.55535	−	37.1773i	0.322568	−	1.82937i
$414$	0.232320	+	13.9848i	0.0114179	+	0.687315i
$415$	2.26237	−	0.823435i	0.111055	−	0.0404208i
$416$	−0.396759	+	0.472839i	−0.0194527	+	0.0231828i
$417$	5.37233	+	6.29556i	0.263084	+	0.308295i
$418$	−2.96386	−	27.7025i	−0.144967	−	1.35497i
$419$			2.55795i			0.124964i	0.998046	+	0.0624821i	$0.0199016\pi$
$419$			2.55795i			0.124964i	−0.998046	+	0.0624821i	$0.980098\pi$
$420$	6.74284	−	0.0560032i	0.329017	−	0.00273267i
$421$	−7.74506	−	21.2794i	−0.377471	−	1.03709i	−0.972401	−	0.233315i	$-0.925043\pi$
$421$	−7.74506	−	21.2794i	−0.377471	−	1.03709i	0.594930	−	0.803777i	$-0.297180\pi$
$422$	2.36856	−	0.417641i	0.115300	−	0.0203304i
$423$	−9.40918	+	27.2516i	−0.457490	+	1.32502i
$424$	8.59420	+	3.12803i	0.417371	+	0.151911i
$425$	−3.55279	+	2.05121i	−0.172336	+	0.0994981i
$426$	2.45350	−	0.453660i	0.118872	−	0.0219799i
$427$	20.9160	−	17.5506i	1.01219	−	0.849332i
$428$	−1.65118	+	1.38551i	−0.0798129	+	0.0669710i
$429$	−6.71943	+	1.24245i	−0.324417	+	0.0599858i
$430$	8.58996	−	4.95942i	0.414245	−	0.239164i
$431$	35.4391	+	12.8988i	1.70704	+	0.621312i	0.996596	−	0.0824399i	$-0.0262713\pi$
$431$	35.4391	+	12.8988i	1.70704	+	0.621312i	0.710445	+	0.703752i	$0.248493\pi$
$432$	1.89828	+	4.83699i	0.0913313	+	0.232720i
$433$	−9.73483	+	1.71651i	−0.467826	+	0.0824904i	−0.402592	−	0.915380i	$-0.631891\pi$
$433$	−9.73483	+	1.71651i	−0.467826	+	0.0824904i	−0.0652344	+	0.997870i	$0.520780\pi$
$434$	0.383791	+	1.05446i	0.0184226	+	0.0506156i
$435$	6.59408	−	0.0547677i	0.316162	−	0.00262591i
$436$		−	0.697089i		−	0.0333845i
$437$	20.2753	+	1.37982i	0.969901	+	0.0660057i
$438$	−17.6839	−	20.7229i	−0.844970	−	0.990177i
$439$	20.1496	−	24.0133i	0.961687	−	1.14609i	−0.0275275	−	0.999621i	$-0.508763\pi$
$439$	20.1496	−	24.0133i	0.961687	−	1.14609i	0.989215	−	0.146473i	$-0.0467922\pi$
$440$	−6.00619	+	2.18607i	−0.286334	+	0.104217i
$441$	−24.4656	+	0.406430i	−1.16503	+	0.0193538i
$442$	−0.439712	+	2.49373i	−0.0209150	+	0.118615i
$443$	0.0761116	−	0.209115i	0.00361617	−	0.00993534i	−0.937871	−	0.346983i	$-0.887206\pi$
$443$	0.0761116	−	0.209115i	0.00361617	−	0.00993534i	0.941488	+	0.337048i	$0.109428\pi$
$444$	−1.79567	−	0.636732i	−0.0852188	−	0.0302180i
$445$	9.90302	+	5.71751i	0.469448	+	0.271036i
$446$	8.55183	+	10.1917i	0.404941	+	0.482590i
$447$	−2.93800	+	17.5115i	−0.138962	+	0.828264i
$448$	1.94656	−	3.37154i	0.0919662	−	0.159290i
$449$	0.394469	+	0.683241i	0.0186162	+	0.0322441i	0.875183	−	0.483791i	$-0.160741\pi$
$449$	0.394469	+	0.683241i	0.0186162	+	0.0322441i	−0.856567	+	0.516035i	$0.827407\pi$
$450$	1.45664	−	2.62263i	0.0686666	−	0.123632i
$451$	−9.12596	−	1.60915i	−0.429724	−	0.0757720i
$452$	2.51090	+	14.2400i	0.118103	+	0.669793i
$453$	−7.94063	+	14.0212i	−0.373083	+	0.658775i
$454$	5.42938	+	4.55579i	0.254814	+	0.213814i
$455$	−2.40301			−0.112655
$456$	7.23583	−	2.15471i	0.338849	−	0.100904i
$457$	13.1718			0.616149			0.308074	−	0.951362i	$-0.400315\pi$
$457$	13.1718			0.616149			0.308074	+	0.951362i	$0.400315\pi$
$458$	−15.4540	−	12.9674i	−0.722117	−	0.605928i
$459$	16.6659	+	13.2911i	0.777897	+	0.620374i
$460$	−0.809589	−	4.59141i	−0.0377473	−	0.214076i
$461$	5.30552	+	0.935506i	0.247103	+	0.0435708i	0.295827	−	0.955241i	$-0.404405\pi$
$461$	5.30552	+	0.935506i	0.247103	+	0.0435708i	−0.0487249	+	0.998812i	$0.515516\pi$
$462$	40.3763	−	15.0767i	1.87848	−	0.701432i
$463$	1.66265	+	2.87980i	0.0772700	+	0.133836i	0.902071	−	0.431587i	$-0.142046\pi$
$463$	1.66265	+	2.87980i	0.0772700	+	0.133836i	−0.824801	+	0.565423i	$0.808713\pi$
$464$	1.90361	−	3.29716i	0.0883731	−	0.153067i
$465$	0.492355	+	0.0826053i	0.0228324	+	0.00383073i
$466$	1.81592	+	2.16413i	0.0841211	+	0.100252i
$467$	29.3454	+	16.9426i	1.35794	+	0.784010i	0.989347	−	0.145579i	$-0.0465046\pi$
$467$	29.3454	+	16.9426i	1.35794	+	0.784010i	0.368598	+	0.929589i	$0.379838\pi$
$468$	−0.662148	−	1.72931i	−0.0306078	−	0.0799373i
$469$	3.93922	−	10.8229i	0.181896	−	0.499756i
$470$	1.66877	−	9.46409i	0.0769748	−	0.436546i
$471$	−25.0233	+	30.3297i	−1.15301	+	1.39752i
$472$	−9.11202	+	3.31650i	−0.419415	+	0.152654i
$473$	40.7513	−	48.5655i	1.87375	−	2.23304i
$474$	1.56845	−	1.33844i	0.0720412	−	0.0614765i
$475$	−3.61823	−	2.43073i	−0.166016	−	0.111529i
$476$		−	15.9712i		−	0.732037i
$477$	−20.7223	+	17.9830i	−0.948810	+	0.823385i
$478$	3.42362	+	9.40631i	0.156593	+	0.430234i
$479$	21.7831	−	3.84095i	0.995297	−	0.175498i	0.347802	−	0.937568i	$-0.386928\pi$
$479$	21.7831	−	3.84095i	0.995297	−	0.175498i	0.647494	+	0.762070i	$0.275817\pi$
$480$	−0.878453	−	1.49276i	−0.0400957	−	0.0681347i
$481$	0.638013	+	0.232218i	0.0290909	+	0.0105882i
$482$	−9.37391	+	5.41203i	−0.426970	+	0.246511i
$483$	5.71606	+	30.9138i	0.260090	+	1.40663i
$484$	−22.8689	+	19.1893i	−1.03950	+	0.872240i
$485$	−7.14066	+	5.99172i	−0.324241	+	0.272070i
$486$	−15.4508	−	2.06725i	−0.700861	−	0.0937724i
$487$	−33.7469	+	19.4838i	−1.52922	+	0.882895i	−0.529824	+	0.848108i	$0.677742\pi$
$487$	−33.7469	+	19.4838i	−1.52922	+	0.882895i	−0.999395	+	0.0347873i	$0.988925\pi$
$488$	−6.59041	−	2.39871i	−0.298334	−	0.108585i
$489$	−6.98906	+	4.11291i	−0.316056	+	0.185992i
$490$	8.03242	−	1.41633i	0.362868	−	0.0639834i
$491$	2.49106	+	6.84414i	0.112420	+	0.308872i	0.983125	−	0.182934i	$-0.0585594\pi$
$491$	2.49106	+	6.84414i	0.112420	+	0.308872i	−0.870705	+	0.491805i	$0.836337\pi$
$492$	−0.0208559	−	2.51107i	−0.000940257	−	0.113208i
$493$		−	15.6188i		−	0.703436i
$494$	−2.58490	+	0.746426i	−0.116300	+	0.0335833i
$495$	3.01558	−	18.9363i	0.135540	−	0.851126i
$496$	0.185274	−	0.220800i	0.00831903	−	0.00991423i
$497$	5.26997	−	1.91811i	0.236391	−	0.0860391i
$498$	3.21657	+	2.65381i	0.144138	+	0.118920i
$499$	6.56073	−	37.2077i	0.293698	−	1.66565i	−0.378747	−	0.925500i	$-0.623645\pi$
$499$	6.56073	−	37.2077i	0.293698	−	1.66565i	0.672446	−	0.740146i	$-0.265244\pi$
$500$	−0.342020	+	0.939693i	−0.0152956	+	0.0420243i
$501$	3.55171	−	10.0163i	0.158679	−	0.447495i
$502$	−14.0670	−	8.12157i	−0.627839	−	0.362483i
$503$	−7.16294	−	8.53646i	−0.319380	−	0.380622i	0.582338	−	0.812946i	$-0.302138\pi$
$503$	−7.16294	−	8.53646i	−0.319380	−	0.380622i	−0.901718	+	0.432325i	$0.857693\pi$
$504$	6.00687	+	10.0162i	0.267567	+	0.446158i
$505$	0.303062	−	0.524919i	0.0134861	−	0.0233586i
$506$	−14.8997	−	25.8071i	−0.662373	−	1.14726i
$507$	−7.64577	−	20.4758i	−0.339561	−	0.909364i
$508$	21.4507	+	3.78234i	0.951723	+	0.167814i
$509$	1.20463	+	6.83182i	0.0533944	+	0.302815i	0.999796	−	0.0201762i	$-0.00642271\pi$
$509$	1.20463	+	6.83182i	0.0533944	+	0.302815i	−0.946402	+	0.322991i	$0.895312\pi$
$510$	−6.18291	−	3.50156i	−0.273784	−	0.155052i
$511$	−46.9071	−	39.3597i	−2.07505	−	1.74117i
$512$	−1.00000			−0.0441942
$513$	−4.88898	+	22.1156i	−0.215854	+	0.976426i
$514$	−22.1731			−0.978013
$515$	0.0306741	+	0.0257387i	0.00135166	+	0.00113418i
$516$	14.9491	+	8.46610i	0.658097	+	0.372699i
$517$	−10.6662	−	60.4912i	−0.469100	−	2.66040i
$518$	−4.21729	−	0.743622i	−0.185297	−	0.0326729i
$519$	−11.8587	−	31.7583i	−0.520539	−	1.39404i
$520$	0.308623	+	0.534551i	0.0135340	+	0.0234416i
$521$	2.84075	−	4.92032i	0.124455	−	0.215563i	−0.797065	−	0.603894i	$-0.793615\pi$
$521$	2.84075	−	4.92032i	0.124455	−	0.215563i	0.921520	+	0.388331i	$0.126948\pi$
$522$	5.87435	+	9.79525i	0.257113	+	0.428726i
$523$	15.7819	+	18.8082i	0.690095	+	0.822423i	0.991367	−	0.131115i	$-0.0418556\pi$
$523$	15.7819	+	18.8082i	0.690095	+	0.822423i	−0.301272	+	0.953538i	$0.597411\pi$
$524$	−15.3283	−	8.84977i	−0.669618	−	0.386604i
$525$	2.25356	−	6.35535i	0.0983535	−	0.277370i
$526$	3.16022	−	8.68265i	0.137792	−	0.378581i
$527$	0.205331	−	1.16449i	0.00894438	−	0.0507261i
$528$	−8.53943	−	7.04541i	−0.371631	−	0.306612i
$529$	−1.18732	+	0.432150i	−0.0516227	+	0.0187891i
$530$	5.87878	−	7.00605i	0.255358	−	0.304323i
$531$	4.57495	−	28.7284i	0.198536	−	1.24671i
$532$	15.2384	−	7.46744i	0.660667	−	0.323754i
$533$			0.894896i			0.0387623i
$534$	0.164495	+	19.8053i	0.00711839	+	0.857061i
$535$	0.737213	+	2.02547i	0.0318725	+	0.0875689i
$536$	−2.91348	+	0.513726i	−0.125843	+	0.0221896i
$537$	33.4059	−	19.6586i	1.44157	−	0.848333i
$538$	16.3121	+	5.93711i	0.703263	+	0.255967i
$539$	45.1480	−	26.0662i	1.94466	−	1.12275i
$540$	5.19454	−	0.129455i	0.223537	−	0.00557085i
$541$	−13.4150	+	11.2565i	−0.576757	+	0.483957i	−0.883880	−	0.467713i	$-0.845078\pi$
$541$	−13.4150	+	11.2565i	−0.576757	+	0.483957i	0.307123	+	0.951670i	$0.400634\pi$
$542$	0.467841	−	0.392565i	0.0200955	−	0.0168621i
$543$	−5.87896	−	31.7948i	−0.252290	−	1.36444i
$544$	−3.55279	+	2.05121i	−0.152325	+	0.0879447i
$545$	−0.655050	−	0.238419i	−0.0280592	−	0.0102127i
$546$	−2.11093	−	3.58711i	−0.0903397	−	0.153514i
$547$	−37.7411	+	6.65478i	−1.61369	+	0.284538i	−0.906412	−	0.422394i	$-0.861190\pi$
$547$	−37.7411	+	6.65478i	−1.61369	+	0.284538i	−0.707282	+	0.706932i	$0.750079\pi$
$548$	−0.0178491	−	0.0490399i	−0.000762474	−	0.00209488i
$549$	15.8908	−	13.7902i	0.678202	−	0.588550i
$550$			6.39165i			0.272541i
$551$	14.9022	−	7.30270i	0.634855	−	0.311105i
$552$	6.14267	−	5.24186i	0.261449	−	0.223108i
$553$	2.97901	−	3.55025i	0.126681	−	0.150972i
$554$	−1.19981	+	0.436694i	−0.0509749	+	0.0185534i
$555$	−1.21249	+	1.46960i	−0.0514673	+	0.0623812i
$556$	0.829741	−	4.70569i	0.0351888	−	0.199566i
$557$	−6.80022	+	18.6835i	−0.288135	+	0.791644i	0.708193	+	0.706019i	$0.249511\pi$
$557$	−6.80022	+	18.6835i	−0.288135	+	0.791644i	−0.996327	+	0.0856245i	$0.972711\pi$
$558$	0.309202	+	0.807531i	0.0130896	+	0.0341855i
$559$	−5.30213	−	3.06118i	−0.224256	−	0.129474i
$560$	−2.50245	−	2.98230i	−0.105748	−	0.126025i
$561$	−44.7904	−	7.51474i	−1.89105	−	0.317273i
$562$	−13.3299	+	23.0880i	−0.562288	+	0.973911i
$563$	−16.5917	−	28.7376i	−0.699255	−	1.21115i	−0.968725	−	0.248136i	$-0.920182\pi$
$563$	−16.5917	−	28.7376i	−0.699255	−	1.21115i	0.269470	−	0.963009i	$-0.413151\pi$
$564$	15.5935	−	5.82269i	0.656605	−	0.245180i
$565$	14.2400	+	2.51090i	0.599081	+	0.105634i
$566$	−0.0478257	−	0.271233i	−0.00201026	−	0.0114008i
$567$	−35.0187	+	1.16380i	−1.47065	+	0.0488751i
$568$	−1.10352	−	0.925962i	−0.0463026	−	0.0388525i
$569$	−43.5630			−1.82625			−0.913127	−	0.407674i	$-0.866340\pi$
$569$	−43.5630			−1.82625			−0.913127	+	0.407674i	$0.866340\pi$
$570$	0.450035	−	7.53641i	0.0188499	−	0.315665i
$571$	−19.5447			−0.817921			−0.408960	−	0.912552i	$-0.634109\pi$
$571$	−19.5447			−0.817921			−0.408960	+	0.912552i	$0.634109\pi$
$572$	3.02222	+	2.53594i	0.126365	+	0.106033i
$573$	−11.4919	+	20.2919i	−0.480081	+	0.847706i
$574$	−0.980124	−	5.55856i	−0.0409096	−	0.232010i
$575$	−4.59141	−	0.809589i	−0.191475	−	0.0337622i
$576$	1.45664	−	2.62263i	0.0606933	−	0.109276i
$577$	12.3114	+	21.3239i	0.512528	+	0.887725i	0.999894	+	0.0145275i	$0.00462439\pi$
$577$	12.3114	+	21.3239i	0.512528	+	0.887725i	−0.487366	+	0.873198i	$0.662042\pi$
$578$	0.0851111	−	0.147417i	0.00354015	−	0.00613173i
$579$	−3.82450	+	22.7953i	−0.158941	+	0.947342i
$580$	−2.44724	−	2.91651i	−0.101616	−	0.121101i
$581$	8.11718	+	4.68646i	0.336757	+	0.194427i
$582$	−15.2169	−	5.39581i	−0.630761	−	0.223663i
$583$	19.9933	−	54.9311i	0.828037	−	2.27501i
$584$	−2.73123	+	15.4896i	−0.113019	+	0.640963i
$585$	−1.85149	+	0.0307574i	−0.0765495	+	0.00127166i
$586$	−1.44803	+	0.527040i	−0.0598176	+	0.0217718i
$587$	−21.4430	+	25.5547i	−0.885045	+	1.05476i	0.113082	+	0.993586i	$0.463928\pi$
$587$	−21.4430	+	25.5547i	−0.885045	+	1.05476i	−0.998127	+	0.0611704i	$0.980517\pi$
$588$	9.17035	+	10.7463i	0.378179	+	0.443168i
$589$	1.20707	−	0.348557i	0.0497364	−	0.0143620i
$590$			9.69681i			0.399211i
$591$	13.7445	−	0.114156i	0.565372	−	0.00469574i
$592$	0.376215	+	1.03364i	0.0154623	+	0.0424824i
$593$	10.7884	−	1.90228i	0.443026	−	0.0781174i	0.0523144	−	0.998631i	$-0.483340\pi$
$593$	10.7884	−	1.90228i	0.443026	−	0.0781174i	0.390711	+	0.920513i	$0.372229\pi$
$594$	30.9164	−	12.1332i	1.26851	−	0.497830i
$595$	−15.0080	−	5.46246i	−0.615267	−	0.223939i
$596$	8.87811	−	5.12578i	0.363661	−	0.209960i
$597$	38.2467	−	7.07195i	1.56533	−	0.289435i
$598$	−2.20449	+	1.84978i	−0.0901482	+	0.0756433i
$599$	9.99216	−	8.38442i	0.408269	−	0.342578i	−0.415411	−	0.909634i	$-0.636362\pi$
$599$	9.99216	−	8.38442i	0.408269	−	0.342578i	0.823679	+	0.567056i	$0.191918\pi$
$600$	−1.70318	+	0.314924i	−0.0695320	+	0.0128567i
$601$	25.1892	−	14.5430i	1.02749	−	0.593222i	0.111225	−	0.993795i	$-0.464522\pi$
$601$	25.1892	−	14.5430i	1.02749	−	0.593222i	0.916265	+	0.400574i	$0.131189\pi$
$602$	36.2864	+	13.2072i	1.47892	+	0.538284i
$603$	2.89658	−	8.38931i	0.117958	−	0.341639i
$604$	9.16186	−	1.61548i	0.372791	−	0.0657331i
$605$	10.2104	+	28.0529i	0.415112	+	1.14051i
$606$	1.04980	−	0.00871921i	0.0426453	−	0.000354194i
$607$			28.8148i			1.16956i	0.811193	+	0.584778i	$0.198819\pi$
$607$			28.8148i			1.16956i	−0.811193	+	0.584778i	$0.801181\pi$
$608$	−3.61823	−	2.43073i	−0.146739	−	0.0985790i
$609$	16.6647	+	19.5285i	0.675287	+	0.791334i
$610$	−4.50811	+	5.37255i	−0.182528	+	0.217528i
$611$	−5.57407	+	2.02879i	−0.225503	+	0.0820762i
$612$	−0.204423	−	12.3055i	−0.00826332	−	0.497422i
$613$	−3.02376	+	17.1486i	−0.122128	+	0.692625i	0.860844	+	0.508870i	$0.169936\pi$
$613$	−3.02376	+	17.1486i	−0.122128	+	0.692625i	−0.982972	+	0.183755i	$0.941175\pi$
$614$	3.35259	−	9.21116i	0.135299	−	0.371732i
$615$	−2.36677	−	0.839240i	−0.0954374	−	0.0338414i
$616$	−21.5497	−	12.4417i	−0.868262	−	0.501291i
$617$	−23.5726	−	28.0928i	−0.948998	−	1.13097i	−0.991268	−	0.131866i	$-0.957903\pi$
$617$	−23.5726	−	28.0928i	−0.948998	−	1.13097i	0.0422692	−	0.999106i	$-0.486541\pi$
$618$	−0.0114757	+	0.0683992i	−0.000461621	+	0.00275142i
$619$	−16.5923	+	28.7387i	−0.666900	+	1.15511i	0.311866	+	0.950126i	$0.399046\pi$
$619$	−16.5923	+	28.7387i	−0.666900	+	1.15511i	−0.978766	+	0.204979i	$0.934287\pi$
$620$	−0.144117	−	0.249618i	−0.00578789	−	0.0100249i
$621$	4.79982	+	23.7455i	0.192610	+	0.952872i
$622$	−23.3432	−	4.11603i	−0.935976	−	0.165038i
$623$	7.73044	+	43.8415i	0.309714	+	1.75647i
$624$	−0.526843	+	0.930278i	−0.0210906	+	0.0372409i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	21.5552			0.861519
$627$	−13.7722	−	46.2489i	−0.550007	−	1.84700i
$628$	22.7014			0.905882
$629$	3.45683	+	2.90062i	0.137833	+	0.115655i
$630$	11.4666	−	2.21886i	0.456842	−	0.0884016i
$631$	6.13993	+	34.8213i	0.244427	+	1.38621i	0.821820	+	0.569747i	$0.192959\pi$
$631$	6.13993	+	34.8213i	0.244427	+	1.38621i	−0.577393	+	0.816466i	$0.695930\pi$
$632$	−1.17236	−	0.206718i	−0.0466338	−	0.00822280i
$633$	3.90256	−	1.45723i	0.155113	−	0.0579198i
$634$	12.0060	+	20.7950i	0.476818	+	0.825873i
$635$	10.8908	−	18.8635i	0.432189	−	0.748574i
$636$	15.6226	+	2.62109i	0.619475	+	0.103933i
$637$	−3.23610	−	3.85663i	−0.128219	−	0.152805i
$638$	−21.0743	−	12.1672i	−0.834339	−	0.481706i
$639$	4.03588	−	1.54533i	0.159657	−	0.0611323i
$640$	−0.342020	+	0.939693i	−0.0135195	+	0.0371446i
$641$	−1.72828	+	9.80159i	−0.0682631	+	0.387139i	0.931465	+	0.363830i	$0.118531\pi$
$641$	−1.72828	+	9.80159i	−0.0682631	+	0.387139i	−0.999728	+	0.0233089i	$0.992580\pi$
$642$	−2.37593	+	2.87976i	−0.0937706	+	0.113655i
$643$	16.0753	−	5.85093i	0.633948	−	0.230738i	−0.00500085	−	0.999987i	$-0.501592\pi$
$643$	16.0753	−	5.85093i	0.633948	−	0.230738i	0.638949	+	0.769249i	$0.279370\pi$
$644$	11.6670	−	13.9042i	0.459744	−	0.547902i
$645$	13.0684	−	11.1520i	0.514568	−	0.439108i
$646$	−17.8407	−	1.21414i	−0.701934	−	0.0477695i
$647$			44.1128i			1.73425i	0.498088	+	0.867127i	$0.334036\pi$
$647$			44.1128i			1.73425i	−0.498088	+	0.867127i	$0.665964\pi$
$648$	4.75641	+	7.64046i	0.186849	+	0.300146i
$649$	21.1979	+	58.2408i	0.832092	+	2.28615i
$650$	0.607869	−	0.107184i	0.0238426	−	0.00420409i
$651$	0.985739	+	1.67507i	0.0386342	+	0.0656510i
$652$	4.39963	+	1.60133i	0.172303	+	0.0627131i
$653$	18.7417	−	10.8205i	0.733419	−	0.423440i	−0.0862526	−	0.996273i	$-0.527489\pi$
$653$	18.7417	−	10.8205i	0.733419	−	0.423440i	0.819672	+	0.572834i	$0.194156\pi$
$654$	−0.219530	−	1.18727i	−0.00858430	−	0.0464259i
$655$	−13.5586	+	11.3770i	−0.529780	+	0.444538i
$656$	−1.11063	+	0.931926i	−0.0433626	+	0.0363856i
$657$	−36.6450	−	29.7257i	−1.42966	−	1.15971i
$658$	32.4008	−	18.7066i	1.26311	−	0.729259i
$659$	19.7397	+	7.18465i	0.768949	+	0.279874i	0.696557	−	0.717502i	$-0.254715\pi$
$659$	19.7397	+	7.18465i	0.768949	+	0.279874i	0.0723920	+	0.997376i	$0.476937\pi$
$660$	−9.54118	+	5.61477i	−0.371390	+	0.218555i
$661$	29.5993	−	5.21915i	1.15128	−	0.203001i	0.434744	−	0.900554i	$-0.356839\pi$
$661$	29.5993	−	5.21915i	1.15128	−	0.203001i	0.716534	+	0.697552i	$0.245728\pi$
$662$	−10.5825	−	29.0751i	−0.411299	−	1.13003i
$663$	0.0364262	+	4.38575i	0.00141468	+	0.170328i
$664$		−	2.40756i		−	0.0934315i
$665$	−1.80527	−	16.8734i	−0.0700053	−	0.654322i
$666$	−3.25887	−	0.518970i	−0.126279	−	0.0201097i
$667$	11.4096	−	13.5974i	0.441782	−	0.526495i
$668$	−5.76568	+	2.09854i	−0.223081	+	0.0811948i
$669$	17.7749	+	14.6651i	0.687217	+	0.566985i
$670$	−0.513726	+	2.91348i	−0.0198470	+	0.112558i
$671$	−15.3317	+	42.1236i	−0.591875	+	1.62616i
$672$	2.25356	−	6.35535i	0.0869330	−	0.245163i
$673$	−29.4764	−	17.0182i	−1.13623	−	0.656004i	−0.190738	−	0.981641i	$-0.561088\pi$
$673$	−29.4764	−	17.0182i	−1.13623	−	0.656004i	−0.945495	+	0.325637i	$0.894421\pi$
$674$	21.5336	+	25.6628i	0.829445	+	0.988493i
$675$	1.65499	−	4.92555i	0.0637006	−	0.189584i
$676$	−6.30950	+	10.9284i	−0.242673	+	0.420322i
$677$	15.0264	+	26.0265i	0.577511	+	1.00028i	0.995764	+	0.0919477i	$0.0293093\pi$
$677$	15.0264	+	26.0265i	0.577511	+	1.00028i	−0.418253	+	0.908331i	$0.637357\pi$
$678$	8.76102	+	23.4626i	0.336465	+	0.901074i
$679$	−35.7382	−	6.30161i	−1.37151	−	0.241834i
$680$	0.712376	+	4.04009i	0.0273184	+	0.154930i
$681$	10.6819	+	6.04950i	0.409333	+	0.231817i
$682$	−1.41128	−	1.18420i	−0.0540407	−	0.0453455i
$683$	−39.0044			−1.49246			−0.746230	−	0.665688i	$-0.768138\pi$
$683$	−39.0044			−1.49246			−0.746230	+	0.665688i	$0.768138\pi$
$684$	11.6454	−	5.94859i	0.445271	−	0.227450i
$685$	−0.0521871			−0.00199397
$686$	3.44854	+	2.89367i	0.131666	+	0.110481i
$687$	−30.4046	−	17.2190i	−1.16001	−	0.656947i
$688$	−1.72239	−	9.76814i	−0.0656654	−	0.372407i
$689$	−5.55942	−	0.980276i	−0.211797	−	0.0373456i
$690$	−2.82482	−	7.56504i	−0.107539	−	0.287996i
$691$	20.5470	+	35.5884i	0.781643	+	1.35385i	0.930984	+	0.365060i	$0.118951\pi$
$691$	20.5470	+	35.5884i	0.781643	+	1.35385i	−0.149341	+	0.988786i	$0.547715\pi$
$692$	−9.78613	+	16.9501i	−0.372013	+	0.644345i
$693$	64.0202	−	38.3938i	2.43193	−	1.45846i
$694$	−10.5230	−	12.5408i	−0.399447	−	0.476042i
$695$	−4.13812	−	2.38914i	−0.156968	−	0.0906254i
$696$	2.20384	−	6.21514i	0.0835365	−	0.235584i
$697$	−2.03425	+	5.58906i	−0.0770528	+	0.211701i
$698$	2.59880	−	14.7385i	0.0983661	−	0.557862i
$699$	3.77438	+	3.11403i	0.142760	+	0.117784i
$700$	−3.65833	+	1.33152i	−0.138272	+	0.0503269i
$701$	13.1399	−	15.6596i	0.496289	−	0.591454i	−0.458516	−	0.888686i	$-0.651619\pi$
$701$	13.1399	−	15.6596i	0.496289	−	0.591454i	0.954805	+	0.297232i	$0.0960634\pi$
$702$	−1.67236	−	2.73680i	−0.0631190	−	0.103294i
$703$	−1.15127	+	4.65443i	−0.0434210	+	0.175545i
$704$			6.39165i			0.240894i
$705$	−0.138243	−	16.6446i	−0.00520653	−	0.626871i
$706$	−0.390022	−	1.07158i	−0.0146787	−	0.0403293i
$707$	2.32386	−	0.409759i	0.0873978	−	0.0154106i
$708$	−14.4750	+	8.51819i	−0.544002	+	0.320133i
$709$	−29.2433	−	10.6437i	−1.09826	−	0.399732i	−0.271583	−	0.962415i	$-0.587547\pi$
$709$	−29.2433	−	10.6437i	−1.09826	−	0.399732i	−0.826673	+	0.562683i	$0.809769\pi$
$710$	−1.24754	+	0.720270i	−0.0468195	+	0.0270313i
$711$	2.24984	−	2.77354i	0.0843757	−	0.104016i
$712$	8.75973	−	7.35029i	0.328285	−	0.275464i
$713$	1.02942	−	0.863790i	0.0385523	−	0.0323492i
$714$	−5.02970	−	27.2018i	−0.188232	−	1.01800i
$715$	3.41667	−	1.97261i	0.127776	−	0.0737716i
$716$	−21.0291	−	7.65396i	−0.785894	−	0.286042i
$717$	8.79330	+	14.9425i	0.328392	+	0.558036i
$718$	7.02542	−	1.23877i	0.262186	−	0.0462305i
$719$	2.14737	+	5.89985i	0.0800833	+	0.220027i	0.973272	−	0.229655i	$-0.0737596\pi$
$719$	2.14737	+	5.89985i	0.0800833	+	0.220027i	−0.893189	+	0.449682i	$0.851537\pi$
$720$	−1.96627	−	2.26579i	−0.0732785	−	0.0844409i
$721$			0.155889i			0.00580561i
$722$	−7.18314	−	17.5898i	−0.267329	−	0.654626i
$723$	−14.2611	+	12.1697i	−0.530375	+	0.452597i
$724$	−11.9995	+	14.3004i	−0.445957	+	0.531471i
$725$	−3.57762	+	1.30215i	−0.132870	+	0.0483606i
$726$	−32.9067	+	39.8848i	−1.22128	+	1.48026i
$727$	−1.92695	+	10.9283i	−0.0714665	+	0.405307i	0.927998	+	0.372585i	$0.121529\pi$
$727$	−1.92695	+	10.9283i	−0.0714665	+	0.405307i	−0.999465	+	0.0327216i	$0.989583\pi$
$728$	−0.821879	+	2.25809i	−0.0304608	+	0.0836905i
$729$	−26.9665	+	1.34492i	−0.998759	+	0.0498117i
$730$	13.6213	+	7.86426i	0.504147	+	0.291069i
$731$	−26.1558	−	31.1712i	−0.967406	−	1.15291i
$732$	−11.9801	−	2.00996i	−0.442796	−	0.0742904i
$733$	−13.3635	+	23.1463i	−0.493593	+	0.854928i	−0.999973	−	0.00738236i	$-0.997650\pi$
$733$	−13.3635	+	23.1463i	−0.493593	+	0.854928i	0.506380	+	0.862311i	$0.330983\pi$
$734$	−12.7308	−	22.0504i	−0.469903	−	0.813896i
$735$	13.2346	−	4.94187i	0.488167	−	0.182284i
$736$	−4.59141	−	0.809589i	−0.169242	−	0.0298419i
$737$	3.28356	+	18.6220i	0.120951	+	0.685949i
$738$	−0.826318	−	4.27024i	−0.0304172	−	0.157190i
$739$	3.79311	+	3.18280i	0.139532	+	0.117081i	0.709882	−	0.704320i	$-0.248748\pi$
$739$	3.79311	+	3.18280i	0.139532	+	0.117081i	−0.570350	+	0.821402i	$0.693193\pi$
$740$	1.09998			0.0404360
$741$	−4.16749	+	2.08535i	−0.153097	+	0.0766071i
$742$	35.6055			1.30712
$743$	10.0791	+	8.45734i	0.369765	+	0.310270i	0.808669	−	0.588264i	$-0.200189\pi$
$743$	10.0791	+	8.45734i	0.369765	+	0.310270i	−0.438903	+	0.898534i	$0.644633\pi$
$744$	0.246019	−	0.434410i	0.00901950	−	0.0159262i
$745$	−1.78016	−	10.0958i	−0.0652201	−	0.369882i
$746$	15.8754	+	2.79927i	0.581241	+	0.102488i
$747$	6.31415	+	3.50695i	0.231023	+	0.128313i
$748$	13.1106	+	22.7082i	0.479371	+	0.830295i
$749$	−4.19574	+	7.26723i	−0.153309	+	0.265539i
$750$	−0.286590	+	1.70818i	−0.0104648	+	0.0623738i
$751$	22.0945	+	26.3312i	0.806240	+	0.960839i	0.999795	−	0.0202503i	$-0.00644631\pi$
$751$	22.0945	+	26.3312i	0.806240	+	0.960839i	−0.193555	+	0.981089i	$0.562002\pi$
$752$	−8.32258	−	4.80504i	−0.303493	−	0.175222i
$753$	−26.5162	−	9.40247i	−0.966306	−	0.342645i
$754$	−0.803747	+	2.20828i	−0.0292707	+	0.0804207i
$755$	1.61548	−	9.16186i	0.0587935	−	0.333434i
$756$	13.3851	+	15.1677i	0.486812	+	0.551644i
$757$	−28.1802	+	10.2568i	−1.02423	+	0.372789i	−0.798880	−	0.601490i	$-0.794574\pi$
$757$	−28.1802	+	10.2568i	−1.02423	+	0.372789i	−0.225348	+	0.974278i	$0.572352\pi$
$758$	0.215700	−	0.257061i	0.00783456	−	0.00933686i
$759$	−33.5041	−	39.2618i	−1.21612	−	1.42511i
$760$	−3.52164	+	2.56866i	−0.127743	+	0.0931753i
$761$			21.7356i			0.787913i	0.919129	+	0.393957i	$0.128894\pi$
$761$			21.7356i			0.787913i	−0.919129	+	0.393957i	$0.871106\pi$
$762$	37.7256	−	0.313333i	1.36666	−	0.0113509i
$763$	−0.928191	−	2.55018i	−0.0336028	−	0.0923228i
$764$	13.2593	−	2.33797i	0.479704	−	0.0845848i
$765$	−11.6333	−	4.01665i	−0.420604	−	0.145222i
$766$	22.4759	+	8.18055i	0.812086	+	0.295575i
$767$	5.18344	−	2.99266i	0.187163	−	0.108059i
$768$	−1.70318	+	0.314924i	−0.0614582	+	0.0113638i
$769$	−3.10391	+	2.60449i	−0.111930	+	0.0939203i	−0.697035	−	0.717037i	$-0.745498\pi$
$769$	−3.10391	+	2.60449i	−0.111930	+	0.0939203i	0.585105	+	0.810958i	$0.301053\pi$
$770$	−19.0618	+	15.9948i	−0.686940	+	0.576411i
$771$	−37.7648	+	6.98283i	−1.36007	+	0.251481i
$772$	11.5570	−	6.67242i	0.415944	−	0.240146i
$773$	−20.8952	−	7.60522i	−0.751547	−	0.273541i	−0.0622906	−	0.998058i	$-0.519841\pi$
$773$	−20.8952	−	7.60522i	−0.751547	−	0.273541i	−0.689257	+	0.724517i	$0.742063\pi$
$774$	28.1272	+	9.71147i	1.01101	+	0.349072i
$775$	−0.283856	+	0.0500514i	−0.0101964	+	0.00179790i
$776$	3.18813	+	8.75931i	0.114447	+	0.314441i
$777$	−7.41698	+	0.0616023i	−0.266083	+	0.00220997i
$778$			23.4965i			0.842392i
$779$	−6.28375	+	0.672292i	−0.225139	+	0.0240874i
$780$	0.693984	+	0.813245i	0.0248486	+	0.0291188i
$781$	−5.91843	+	7.05330i	−0.211778	+	0.252387i
$782$	−17.9730	+	6.54162i	−0.642712	+	0.233928i
$783$	13.0898	+	14.8331i	0.467793	+	0.530092i
$784$	1.41633	−	8.03242i	0.0505833	−	0.286872i
$785$	7.76432	−	21.3323i	0.277120	−	0.761382i
$786$	−28.8938	−	10.2455i	−1.03061	−	0.365446i
$787$	11.0583	+	6.38449i	0.394184	+	0.227582i	0.683972	−	0.729509i	$-0.260251\pi$
$787$	11.0583	+	6.38449i	0.394184	+	0.227582i	−0.289787	+	0.957091i	$0.593585\pi$
$788$	−5.10093	−	6.07906i	−0.181713	−	0.216557i
$789$	2.64806	−	15.7833i	0.0942735	−	0.561902i
$790$	−0.595221	+	1.03095i	−0.0211770	+	0.0366796i
$791$	28.1466	+	48.7513i	1.00078	+	1.73340i
$792$	−16.7630	−	9.31033i	−0.595646	−	0.330828i
$793$	4.26321	+	0.751719i	0.151391	+	0.0266943i
$794$	−5.97580	−	33.8904i	−0.212073	−	1.20273i
$795$	7.80624	−	13.7839i	0.276859	−	0.488866i
$796$	−17.2023	−	14.4345i	−0.609721	−	0.511616i
$797$	17.9987			0.637548			0.318774	−	0.947831i	$-0.396729\pi$
$797$	17.9987			0.637548			0.318774	+	0.947831i	$0.396729\pi$
$798$	23.6020	−	17.5173i	0.835502	−	0.620106i
$799$	−39.4245			−1.39474
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	6.51734	+	33.6803i	0.230279	+	1.19003i
$802$	2.50608	+	14.2127i	0.0884929	+	0.501868i
$803$	99.0039	+	17.4571i	3.49377	+	0.616046i
$804$	−4.80040	+	1.79249i	−0.169297	+	0.0632164i
$805$	−9.07532	−	15.7189i	−0.319863	−	0.554019i
$806$	−0.0889559	+	0.154076i	−0.00313334	+	0.00542710i
$807$	29.6521	+	4.97491i	1.04380	+	0.175125i
$808$	−0.389609	−	0.464318i	−0.0137064	−	0.0163346i
$809$	4.62741	+	2.67164i	0.162691	+	0.0939297i	0.579135	−	0.815232i	$-0.303390\pi$
$809$	4.62741	+	2.67164i	0.162691	+	0.0939297i	−0.416444	+	0.909161i	$0.636724\pi$
$810$	8.80647	−	1.85637i	0.309428	−	0.0652261i
$811$	−2.73391	+	7.51135i	−0.0960005	+	0.263759i	−0.978393	−	0.206756i	$-0.933710\pi$
$811$	−2.73391	+	7.51135i	−0.0960005	+	0.263759i	0.882392	+	0.470515i	$0.155932\pi$
$812$	2.57381	−	14.5968i	0.0903230	−	0.512247i
$813$	0.673189	−	0.815943i	0.0236098	−	0.0286164i
$814$	6.60668	−	2.40464i	0.231564	−	0.0842825i
$815$	3.00952	−	3.58661i	0.105419	−	0.125633i
$816$	−5.40507	+	4.61243i	−0.189215	+	0.161467i
$817$	17.5117	−	39.5300i	0.612657	−	1.38298i
$818$			34.8588i			1.21881i
$819$	−4.72497	−	5.44471i	−0.165104	−	0.190254i
$820$	0.495867	+	1.36238i	0.0173164	+	0.0475765i
$821$	−28.7055	+	5.06155i	−1.00183	+	0.176649i	−0.650421	−	0.759574i	$-0.725408\pi$
$821$	−28.7055	+	5.06155i	−1.00183	+	0.176649i	−0.351407	+	0.936223i	$0.614296\pi$
$822$	−0.0458440	−	0.0779027i	−0.00159899	−	0.00271717i
$823$	5.68615	+	2.06959i	0.198207	+	0.0721414i	0.439216	−	0.898381i	$-0.355256\pi$
$823$	5.68615	+	2.06959i	0.198207	+	0.0721414i	−0.241009	+	0.970523i	$0.577478\pi$
$824$	0.0346776	−	0.0200211i	0.00120805	−	0.000697469i
$825$	2.01288	+	10.8861i	0.0700796	+	0.379007i
$826$	−28.9188	+	24.2657i	−1.00621	+	0.844313i
$827$	5.42049	−	4.54833i	0.188489	−	0.158161i	−0.543660	−	0.839305i	$-0.682962\pi$
$827$	5.42049	−	4.54833i	0.188489	−	0.158161i	0.732149	+	0.681145i	$0.238517\pi$
$828$	8.81128	−	10.8623i	0.306213	−	0.377491i
$829$	8.76307	−	5.05936i	0.304354	−	0.175719i	−0.340043	−	0.940410i	$-0.610442\pi$
$829$	8.76307	−	5.05936i	0.304354	−	0.175719i	0.644397	+	0.764691i	$0.277108\pi$
$830$	−2.26237	−	0.823435i	−0.0785279	−	0.0285818i
$831$	−1.90596	+	1.12162i	−0.0661171	+	0.0389084i
$832$	0.607869	−	0.107184i	0.0210741	−	0.00371593i
$833$	−11.4442	−	31.4427i	−0.396519	−	1.08943i
$834$	−0.0687365	−	8.27595i	−0.00238015	−	0.286573i
$835$			6.13571i			0.212335i
$836$	−15.5364	+	23.1265i	−0.537336	+	0.799845i
$837$	0.780937	+	1.27800i	0.0269931	+	0.0441740i
$838$	1.64422	−	1.95951i	0.0567987	−	0.0676900i
$839$	−52.2701	+	19.0248i	−1.80457	+	0.656808i	−0.806740	+	0.590907i	$0.798770\pi$
$839$	−52.2701	+	19.0248i	−1.80457	+	0.656808i	−0.997826	+	0.0659012i	$0.979008\pi$
$840$	−5.20131	−	4.29131i	−0.179462	−	0.148064i
$841$	−2.51877	+	14.2847i	−0.0868541	+	0.492574i
$842$	−7.74506	+	21.2794i	−0.266912	+	0.733335i
$843$	−15.4322	+	43.5210i	−0.531514	+	1.49894i
$844$	−2.08288	−	1.20255i	−0.0716955	−	0.0413934i
$845$	8.11134	+	9.66672i	0.279039	+	0.332545i
$846$	24.7249	−	14.8279i	0.850058	−	0.509792i
$847$	−58.1110	+	100.651i	−1.99672	+	3.45842i
$848$	−4.57288	−	7.92045i	−0.157033	−	0.271989i
$849$	−0.166873	−	0.446897i	−0.00572708	−	0.0153375i
$850$	4.04009	+	0.712376i	0.138574	+	0.0244343i
$851$	0.890532	+	5.05046i	0.0305270	+	0.173127i
$852$	−2.17110	−	1.22956i	−0.0743806	−	0.0421239i
$853$	3.16157	+	2.65287i	0.108250	+	0.0908326i	0.695306	−	0.718714i	$-0.255269\pi$
$853$	3.16157	+	2.65287i	0.108250	+	0.0908326i	−0.587056	+	0.809546i	$0.699713\pi$
$854$	−27.3038			−0.934318
$855$	−1.60690	−	12.9776i	−0.0549549	−	0.443824i
$856$	2.15547			0.0736723
$857$	11.6763	+	9.79761i	0.398856	+	0.334680i	0.820051	−	0.572290i	$-0.193945\pi$
$857$	11.6763	+	9.79761i	0.398856	+	0.334680i	−0.421195	+	0.906970i	$0.638389\pi$
$858$	5.94601	+	3.36740i	0.202994	+	0.114961i
$859$	−1.61623	−	9.16607i	−0.0551449	−	0.312742i	0.944741	−	0.327816i	$-0.106313\pi$
$859$	−1.61623	−	9.16607i	−0.0551449	−	0.312742i	−0.999886	+	0.0150740i	$0.995202\pi$
$860$	−9.76814	−	1.72239i	−0.333091	−	0.0587329i
$861$	−3.41985	−	9.15857i	−0.116548	−	0.312123i
$862$	−18.8568	−	32.6609i	−0.642264	−	1.11243i
$863$	−1.34181	+	2.32408i	−0.0456757	+	0.0791126i	−0.887959	−	0.459922i	$-0.847877\pi$
$863$	−1.34181	+	2.32408i	−0.0456757	+	0.0791126i	0.842284	+	0.539034i	$0.181211\pi$
$864$	1.65499	−	4.92555i	0.0563039	−	0.167570i
$865$	12.5808	+	14.9932i	0.427760	+	0.509785i
$866$	8.56067	+	4.94250i	0.290903	+	0.167953i
$867$	0.0985345	−	0.277881i	0.00334641	−	0.00943732i
$868$	0.383791	−	1.05446i	0.0130267	−	0.0357906i
$869$	−1.32127	+	7.49329i	−0.0448210	+	0.254192i
$870$	−5.08657	−	4.19664i	−0.172451	−	0.142279i
$871$	1.71596	−	0.624557i	0.0581429	−	0.0211623i
$872$	−0.448080	+	0.534001i	−0.0151739	+	0.0180836i
$873$	−27.6164	−	4.39786i	−0.934674	−	0.148845i
$874$	−14.6449	−	14.0897i	−0.495370	−	0.476592i
$875$			3.89311i			0.131611i
$876$	0.226258	+	27.2416i	0.00764453	+	0.920410i
$877$	−0.952898	−	2.61806i	−0.0321771	−	0.0884058i	0.922564	−	0.385844i	$-0.126090\pi$
$877$	−0.952898	−	2.61806i	−0.0321771	−	0.0884058i	−0.954741	+	0.297439i	$0.903868\pi$
$878$	−30.8710	+	5.44338i	−1.04184	+	0.183705i
$879$	−2.30028	+	1.35366i	−0.0775866	+	0.0456580i
$880$	6.00619	+	2.18607i	0.202469	+	0.0736925i
$881$	−17.0334	+	9.83426i	−0.573871	+	0.331325i	−0.758694	−	0.651447i	$-0.774162\pi$
$881$	−17.0334	+	9.83426i	−0.573871	+	0.331325i	0.184823	+	0.982772i	$0.440829\pi$
$882$	19.0030	+	15.4149i	0.639865	+	0.519045i
$883$	−5.58456	+	4.68600i	−0.187935	+	0.157697i	−0.731901	−	0.681411i	$-0.761367\pi$
$883$	−5.58456	+	4.68600i	−0.187935	+	0.157697i	0.543966	+	0.839108i	$0.316922\pi$
$884$	1.93978	−	1.62767i	0.0652418	−	0.0547444i
$885$	3.05375	+	16.5154i	0.102651	+	0.555159i
$886$	−0.192721	+	0.111268i	−0.00647460	+	0.00373811i
$887$	−41.2714	−	15.0216i	−1.38576	−	0.504374i	−0.461839	−	0.886964i	$-0.652810\pi$
$887$	−41.2714	−	15.0216i	−1.38576	−	0.504374i	−0.923919	+	0.382589i	$0.875032\pi$
$888$	0.966281	+	1.64200i	0.0324263	+	0.0551019i
$889$	83.5102	−	14.7251i	2.80084	−	0.493864i
$890$	−3.91101	−	10.7454i	−0.131097	−	0.360187i
$891$	48.8352	−	30.4013i	1.63604	−	1.01848i
$892$		−	13.3043i		−	0.445460i
$893$	−18.4332	−	37.6157i	−0.616845	−	1.25876i
$894$	13.5068	−	11.5260i	0.451734	−	0.385489i
$895$	−14.3847	+	17.1431i	−0.480829	+	0.573030i
$896$	−3.65833	+	1.33152i	−0.122216	+	0.0444831i
$897$	−3.17210	+	3.84476i	−0.105913	+	0.128373i
$898$	0.136998	−	0.776953i	0.00457167	−	0.0259272i
$899$	0.375324	−	1.03119i	0.0125178	−	0.0343923i
$900$	−2.80165	+	1.07274i	−0.0933882	+	0.0357581i
$901$	−32.4930	−	18.7598i	−1.08250	−	0.624980i
$902$	5.95654	+	7.09873i	0.198331	+	0.236362i
$903$	65.9615	+	11.0667i	2.19506	+	0.368278i
$904$	7.22984	−	12.5224i	0.240461	−	0.416490i
$905$	9.33395	+	16.1669i	0.310271	+	0.537405i
$906$	15.0955	−	5.63675i	0.501516	−	0.187268i
$907$	42.9396	+	7.57142i	1.42579	+	0.251405i	0.832696	−	0.553731i	$-0.186796\pi$
$907$	42.9396	+	7.57142i	1.42579	+	0.251405i	0.593091	+	0.805135i	$0.297907\pi$
$908$	−1.23074	−	6.97988i	−0.0408436	−	0.231635i
$909$	1.78526	−	0.345458i	0.0592132	−	0.0114581i
$910$	1.84081	+	1.54463i	0.0610224	+	0.0512039i
$911$	−6.19660			−0.205303			−0.102651	−	0.994717i	$-0.532733\pi$
$911$	−6.19660			−0.205303			−0.102651	+	0.994717i	$0.532733\pi$
$912$	−6.92799	−	3.00050i	−0.229409	−	0.0993564i
$913$	−15.3883			−0.509278
$914$	−10.0901	−	8.46664i	−0.333752	−	0.280052i
$915$	−5.98617	+	10.5701i	−0.197897	+	0.349438i
$916$	3.50313	+	19.8672i	0.115747	+	0.656432i
$917$	−67.8595	−	11.9655i	−2.24092	−	0.395134i
$918$	−4.22347	−	20.8942i	−0.139395	−	0.689610i
$919$	−1.42692	−	2.47150i	−0.0470697	−	0.0815271i	0.841531	−	0.540209i	$-0.181655\pi$
$919$	−1.42692	−	2.47150i	−0.0470697	−	0.0815271i	−0.888600	+	0.458682i	$0.848322\pi$
$920$	−2.33112	+	4.03762i	−0.0768547	+	0.133116i
$921$	2.80925	−	16.7441i	0.0925679	−	0.551736i
$922$	−3.46293	−	4.12696i	−0.114046	−	0.135914i
$923$	0.770043	+	0.444585i	0.0253463	+	0.0146337i
$924$	−40.6212	−	14.4040i	−1.33634	−	0.473856i
$925$	0.376215	−	1.03364i	0.0123699	−	0.0339860i
$926$	0.577433	−	3.27479i	0.0189756	−	0.107616i
$927$	0.00199531	+	0.120110i	6.55344e−5	+	0.00394494i
$928$	−3.57762	+	1.30215i	−0.117441	+	0.0427451i
$929$	−3.41429	+	4.06899i	−0.112019	+	0.133499i	−0.819140	−	0.573593i	$-0.805549\pi$
$929$	−3.41429	+	4.06899i	−0.112019	+	0.133499i	0.707121	+	0.707092i	$0.249994\pi$
$930$	−0.324068	−	0.379759i	−0.0106266	−	0.0124528i
$931$	24.6492	−	25.6204i	0.807846	−	0.839675i
$932$		−	2.82508i		−	0.0925385i
$933$	−41.0539	+	0.340976i	−1.34404	+	0.0111631i
$934$	−11.5894	−	31.8417i	−0.379217	−	1.04189i
$935$	25.8228	−	4.55326i	0.844497	−	0.148908i
$936$	−0.604343	+	1.75035i	−0.0197536	+	0.0572119i
$937$	−2.65505	−	0.966361i	−0.0867368	−	0.0315696i	0.298287	−	0.954476i	$-0.403585\pi$
$937$	−2.65505	−	0.966361i	−0.0867368	−	0.0315696i	−0.385024	+	0.922907i	$0.625807\pi$
$938$	−9.97445	+	5.75875i	−0.325677	+	0.188030i
$939$	36.7124	−	6.78825i	1.19806	−	0.221526i
$940$	−7.36176	+	6.17725i	−0.240114	+	0.201480i
$941$	16.1434	−	13.5460i	0.526261	−	0.441585i	−0.340547	−	0.940228i	$-0.610612\pi$
$941$	16.1434	−	13.5460i	0.526261	−	0.441585i	0.866808	+	0.498642i	$0.166168\pi$
$942$	38.6645	−	7.14919i	1.25976	−	0.232933i
$943$	−5.85381	+	3.37970i	−0.190626	+	0.110058i
$944$	9.11202	+	3.31650i	0.296571	+	0.107943i
$945$	18.8310	−	7.39024i	0.612572	−	0.240405i
$946$	−62.4346	+	11.0089i	−2.02992	+	0.357930i
$947$	−8.12789	−	22.3312i	−0.264121	−	0.725666i	−0.998879	−	0.0473371i	$-0.984927\pi$
$947$	−8.12789	−	22.3312i	−0.264121	−	0.725666i	0.734758	−	0.678329i	$-0.237296\pi$
$948$	−2.06183	+	0.0171247i	−0.0669652	+	0.000556185i
$949$		−	9.70837i		−	0.315147i
$950$	1.20928	+	4.18780i	0.0392343	+	0.135870i
$951$	26.9972	+	31.6366i	0.875443	+	1.02589i
$952$	−10.2661	+	12.2346i	−0.332725	+	0.396526i
$953$	−35.7063	+	12.9960i	−1.15664	+	0.420983i	−0.847896	−	0.530162i	$-0.822131\pi$
$953$	−35.7063	+	12.9960i	−1.15664	+	0.420983i	−0.308745	+	0.951145i	$0.599909\pi$
$954$	27.4335	−	0.455733i	0.888191	−	0.0147549i
$955$	2.33797	−	13.2593i	0.0756549	−	0.429061i
$956$	3.42362	−	9.40631i	0.110728	−	0.304222i
$957$	−39.7250	−	14.0862i	−1.28413	−	0.455343i
$958$	−19.1558	−	11.0596i	−0.618895	−	0.357319i
$959$	−0.130595	−	0.155638i	−0.00421715	−	0.00502580i
$960$	−0.286590	+	1.70818i	−0.00924967	+	0.0551311i
$961$	−15.4585	+	26.7748i	−0.498660	+	0.863704i
$962$	−0.339479	−	0.587996i	−0.0109453	−	0.0189577i
$963$	−3.13973	+	5.65299i	−0.101177	+	0.182165i
$964$	10.6596	+	1.87958i	0.343323	+	0.0605371i
$965$	−2.31731	−	13.1421i	−0.0745967	−	0.423059i
$966$	15.4922	−	27.3556i	0.498455	−	0.880151i
$967$	15.1475	+	12.7103i	0.487111	+	0.408735i	0.852990	−	0.521928i	$-0.174787\pi$
$967$	15.1475	+	12.7103i	0.487111	+	0.408735i	−0.365879	+	0.930663i	$0.619231\pi$
$968$	29.8532			0.959519
$969$	−30.7683	+	3.55058i	−0.988421	+	0.114061i
$970$	9.32147			0.299294
$971$	2.79448	+	2.34485i	0.0896792	+	0.0752498i	0.686525	−	0.727106i	$-0.259135\pi$
$971$	2.79448	+	2.34485i	0.0896792	+	0.0752498i	−0.596846	+	0.802356i	$0.703580\pi$
$972$	10.5072	+	11.5152i	0.337018	+	0.369349i
$973$	−3.23028	−	18.3198i	−0.103558	−	0.587306i
$974$	38.3756	+	6.76665i	1.22963	+	0.216817i
$975$	1.00156	−	0.373986i	0.0320755	−	0.0119771i
$976$	3.50668	+	6.07375i	0.112246	+	0.194416i
$977$	26.7706	−	46.3681i	0.856468	−	1.48345i	−0.0188091	−	0.999823i	$-0.505987\pi$
$977$	26.7706	−	46.3681i	0.856468	−	1.48345i	0.875277	−	0.483622i	$-0.160679\pi$
$978$	7.99766	+	1.34181i	0.255737	+	0.0429064i
$979$	−46.9805	−	55.9892i	−1.50150	−	1.78942i
$980$	−7.06360	−	4.07817i	−0.225638	−	0.130272i
$981$	−0.747798	−	1.95300i	−0.0238754	−	0.0623544i
$982$	2.49106	−	6.84414i	0.0794930	−	0.218405i
$983$	−4.90260	+	27.8040i	−0.156369	+	0.886811i	0.801155	+	0.598457i	$0.204219\pi$
$983$	−4.90260	+	27.8040i	−0.156369	+	0.886811i	−0.957524	+	0.288354i	$0.906892\pi$
$984$	−1.59811	+	1.93700i	−0.0509459	+	0.0617493i
$985$	−7.45707	+	2.71415i	−0.237602	+	0.0864800i
$986$	−10.0396	+	11.9647i	−0.319725	+	0.381034i
$987$	49.2932	−	42.0645i	1.56902	−	1.33893i
$988$	2.45994	+	1.08975i	0.0782613	+	0.0346695i
$989$		−	46.2440i		−	1.47047i
$990$	−14.4821	+	12.5677i	−0.460272	+	0.399428i
$991$	−11.6099	−	31.8980i	−0.368801	−	1.01327i	−0.975818	−	0.218584i	$-0.929856\pi$
$991$	−11.6099	−	31.8980i	−0.368801	−	1.01327i	0.607017	−	0.794689i	$-0.292366\pi$
$992$	−0.283856	+	0.0500514i	−0.00901243	+	0.00158913i
$993$	−27.1803	−	46.1874i	−0.862540	−	1.46571i
$994$	−5.26997	−	1.91811i	−0.167153	−	0.0608389i
$995$	−19.4475	+	11.2280i	−0.616528	+	0.355952i
$996$	−0.758198	−	4.10051i	−0.0240244	−	0.129930i
$997$	−25.2540	+	21.1906i	−0.799802	+	0.671113i	−0.948150	−	0.317822i	$-0.897049\pi$
$997$	−25.2540	+	21.1906i	−0.799802	+	0.671113i	0.148349	+	0.988935i	$0.452604\pi$
$998$	−28.9425	+	24.2856i	−0.916158	+	0.768748i
$999$	−5.71389	+	0.142398i	−0.180779	+	0.00450526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.41.2	yes	84
3.2	odd	2		570.2.bb.a.41.9	✓	84
19.13	odd	18		570.2.bb.a.431.9	yes	84
57.32	even	18	inner	570.2.bb.b.431.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.9	✓	84	3.2	odd	2
570.2.bb.a.431.9	yes	84	19.13	odd	18
570.2.bb.b.41.2	yes	84	1.1	even	1	trivial
570.2.bb.b.431.2	yes	84	57.32	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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.50714 - 0.853538i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(0.605893 + 1.62262i) q^{6} +(1.94656 + 3.37154i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.54295 + 2.57280i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.50714 - 0.853538i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(0.605893 + 1.62262i) q^{6} +(1.94656 + 3.37154i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.54295 + 2.57280i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(-5.53533 - 3.19583i) q^{11} +(0.578858 - 1.63246i) q^{12} +(-0.211111 + 0.580022i) q^{13} +(0.676032 - 3.83397i) q^{14} +(-1.33603 - 1.10228i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.63698 + 3.14263i) q^{17} +(0.471800 - 2.96267i) q^{18} +(-4.23138 - 1.04663i) q^{19} +1.00000i q^{20} +(-0.0560032 - 6.74284i) q^{21} +(2.18607 + 6.00619i) q^{22} +(-4.59141 + 0.809589i) q^{23} +(-1.49276 + 0.878453i) q^{24} +(0.939693 + 0.342020i) q^{25} +(0.534551 - 0.308623i) q^{26} +(-0.129455 - 5.19454i) q^{27} +(-2.98230 + 2.50245i) q^{28} +(-2.91651 + 2.44724i) q^{29} +(0.314924 + 1.70318i) q^{30} +(-0.249618 + 0.144117i) q^{31} +(0.939693 + 0.342020i) q^{32} +(5.61477 + 9.54118i) q^{33} +(4.04009 - 0.712376i) q^{34} +(1.33152 + 3.65833i) q^{35} +(-2.26579 + 1.96627i) q^{36} -1.09998i q^{37} +(2.56866 + 3.52164i) q^{38} +(0.813245 - 0.693984i) q^{39} +(0.642788 - 0.766044i) q^{40} +(1.36238 - 0.495867i) q^{41} +(-4.29131 + 5.20131i) q^{42} +(-1.72239 + 9.76814i) q^{43} +(2.18607 - 6.00619i) q^{44} +(1.07274 + 2.80165i) q^{45} +(4.03762 + 2.33112i) q^{46} +(6.17725 + 7.36176i) q^{47} +(1.70818 + 0.286590i) q^{48} +(-4.07817 + 7.06360i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(6.65665 - 2.48562i) q^{51} +(-0.607869 - 0.107184i) q^{52} +(1.58814 + 9.00681i) q^{53} +(-3.23982 + 4.06246i) q^{54} +(-4.89629 - 4.10848i) q^{55} +3.89311 q^{56} +(5.48395 + 5.18906i) q^{57} +3.80723 q^{58} +(-7.42818 - 6.23299i) q^{59} +(0.853538 - 1.50714i) q^{60} +(-1.21786 - 6.90682i) q^{61} +(0.283856 + 0.0500514i) q^{62} +(-5.67086 + 10.2102i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.308623 + 0.534551i) q^{65} +(1.83179 - 10.9181i) q^{66} +(-1.90164 - 2.26629i) q^{67} +(-3.55279 - 2.05121i) q^{68} +(7.61092 + 2.69878i) q^{69} +(1.33152 - 3.65833i) q^{70} +(0.250147 - 1.41866i) q^{71} +(2.99959 - 0.0498300i) q^{72} +(-14.7800 + 5.37947i) q^{73} +(-0.707053 + 0.842633i) q^{74} +(-1.12432 - 1.31754i) q^{75} +(0.295956 - 4.34884i) q^{76} -24.8834i q^{77} +(-1.06907 + 0.00887921i) q^{78} +(-0.407155 - 1.11865i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(-4.23863 + 7.93940i) q^{81} +(-1.36238 - 0.495867i) q^{82} +(2.08501 - 1.20378i) q^{83} +(6.63068 - 1.22603i) q^{84} +(-3.14263 + 2.63698i) q^{85} +(7.59827 - 6.37570i) q^{86} +(6.48440 - 1.19899i) q^{87} +(-5.53533 + 3.19583i) q^{88} +(10.7454 + 3.91101i) q^{89} +(0.979094 - 2.83573i) q^{90} +(-2.36651 + 0.417279i) q^{91} +(-1.59458 - 4.38107i) q^{92} +(0.499220 - 0.00414631i) q^{93} -9.61009i q^{94} +(-3.98535 - 1.76550i) q^{95} +(-1.12432 - 1.31754i) q^{96} +(-5.99172 + 7.14066i) q^{97} +(7.66445 - 2.78963i) q^{98} +(-0.318496 - 19.1723i) 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

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