LMFDB - Embedded newform 570.2.bh.b.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			67.3
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.b.553.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.430308 + 2.19427i) q^{5} +(0.766044 + 0.642788i) q^{6} +(0.0612713 - 0.0164176i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.430308 + 2.19427i) q^{5} +(0.766044 + 0.642788i) q^{6} +(0.0612713 - 0.0164176i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(0.906096 - 2.04426i) q^{10} +(0.978646 + 1.69506i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-0.239255 - 2.73470i) q^{13} +(-0.0596073 - 0.0216953i) q^{14} +(-0.237427 - 2.22343i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-0.519831 + 0.742395i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-3.00247 + 3.15993i) q^{19} +(-1.91477 + 1.15484i) q^{20} +(-0.0624690 + 0.0110150i) q^{21} +(0.170589 - 1.94984i) q^{22} +(-1.49330 + 3.20238i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(-4.62967 + 1.88843i) q^{25} +(-1.37257 + 2.37737i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(0.0363835 + 0.0519610i) q^{28} +(-1.22265 + 6.93401i) q^{29} +(-1.08082 + 1.95751i) q^{30} +(-0.927411 - 0.535441i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-0.827187 - 1.77391i) q^{33} +(0.851641 - 0.309972i) q^{34} +(0.0623902 + 0.127381i) q^{35} +(0.173648 + 0.984808i) q^{36} +(5.68967 - 5.68967i) q^{37} +(4.27194 - 0.866313i) q^{38} +2.74515i q^{39} +(2.23088 + 0.152274i) q^{40} +(7.43026 + 8.85504i) q^{41} +(0.0574896 + 0.0268078i) q^{42} +(-8.08894 + 3.77193i) q^{43} +(-1.25812 + 1.49937i) q^{44} +(0.0427391 + 2.23566i) q^{45} +(3.06005 - 1.76672i) q^{46} +(-4.82273 + 3.37691i) q^{47} +(0.819152 - 0.573576i) q^{48} +(-6.05869 + 3.49799i) q^{49} +(4.87556 + 1.10856i) q^{50} +(0.582557 - 0.694264i) q^{51} +(2.48795 - 1.16015i) q^{52} +(3.93536 + 1.83509i) q^{53} +(0.642788 + 0.766044i) q^{54} +(-3.29832 + 2.87682i) q^{55} -0.0634327i q^{56} +(3.26646 - 2.88622i) q^{57} +(4.97872 - 4.97872i) q^{58} +(-0.306498 - 1.73824i) q^{59} +(2.00813 - 0.983565i) q^{60} +(8.28535 - 3.01562i) q^{61} +(0.452574 + 0.970549i) q^{62} +(0.0631913 - 0.00552853i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(5.89773 - 1.70176i) q^{65} +(-0.339880 + 1.92756i) q^{66} +(0.603609 + 0.862044i) q^{67} +(-0.875416 - 0.234567i) q^{68} +(1.76672 - 3.06005i) q^{69} +(0.0219559 - 0.140130i) q^{70} +(-5.35062 + 14.7007i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.457621 + 5.23064i) q^{73} +(-7.92417 + 1.39725i) q^{74} +(4.77664 - 1.47774i) q^{75} +(-3.99627 - 1.74064i) q^{76} +(0.0877918 + 0.0877918i) q^{77} +(1.57455 - 2.24869i) q^{78} +(1.75469 - 1.47236i) q^{79} +(-1.74009 - 1.40431i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-1.00747 - 11.5154i) q^{82} +(0.907126 + 3.38544i) q^{83} +(-0.0317164 - 0.0549344i) q^{84} +(-1.85271 - 0.821192i) q^{85} +(8.78956 + 1.54984i) q^{86} +(1.82234 - 6.80106i) q^{87} +(1.89060 - 0.506584i) q^{88} +(-8.08005 - 6.77997i) q^{89} +(1.24731 - 1.85586i) q^{90} +(-0.0595567 - 0.163631i) q^{91} +(-3.51999 - 0.307959i) q^{92} +(0.877215 + 0.614233i) q^{93} +5.88747 q^{94} +(-8.22573 - 5.22851i) q^{95} -1.00000 q^{96} +(-4.56101 - 3.19365i) q^{97} +(6.96935 + 0.609740i) q^{98} +(0.669433 + 1.83925i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	0.430308	+	2.19427i	0.192440	+	0.981309i
$5$	0.430308	+	2.19427i	0.192440	+	0.981309i
$6$	0.766044	+	0.642788i	0.312736	+	0.262417i
$7$	0.0612713	−	0.0164176i	0.0231584	−	0.00620527i	−0.247221	−	0.968959i	$-0.579517\pi$
$7$	0.0612713	−	0.0164176i	0.0231584	−	0.00620527i	0.270380	+	0.962754i	$0.412851\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	0.906096	−	2.04426i	0.286533	−	0.646451i
$11$	0.978646	+	1.69506i	0.295073	+	0.511081i	0.975002	−	0.222197i	$-0.0713227\pi$
$11$	0.978646	+	1.69506i	0.295073	+	0.511081i	−0.679929	+	0.733278i	$0.737989\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	−0.239255	−	2.73470i	−0.0663575	−	0.758470i	−0.954365	−	0.298641i	$-0.903467\pi$
$13$	−0.239255	−	2.73470i	−0.0663575	−	0.758470i	0.888008	−	0.459828i	$-0.152089\pi$
$14$	−0.0596073	−	0.0216953i	−0.0159307	−	0.00579830i
$15$	−0.237427	−	2.22343i	−0.0613034	−	0.574086i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.519831	+	0.742395i	−0.126078	+	0.180057i	−0.877228	−	0.480073i	$-0.840610\pi$
$17$	−0.519831	+	0.742395i	−0.126078	+	0.180057i	0.751151	+	0.660130i	$0.229499\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−3.00247	+	3.15993i	−0.688815	+	0.724937i
$19$	−3.00247	+	3.15993i	−0.688815	+	0.724937i
$20$	−1.91477	+	1.15484i	−0.428155	+	0.258231i
$21$	−0.0624690	+	0.0110150i	−0.0136319	+	0.00240367i
$22$	0.170589	−	1.94984i	0.0363697	−	0.415708i
$23$	−1.49330	+	3.20238i	−0.311374	+	0.667743i	−0.998256	−	0.0590253i	$-0.981201\pi$
$23$	−1.49330	+	3.20238i	−0.311374	+	0.667743i	0.686883	+	0.726768i	$0.258979\pi$
$24$	−0.342020	+	0.939693i	−0.0698146	+	0.191814i
$25$	−4.62967	+	1.88843i	−0.925934	+	0.377685i
$26$	−1.37257	+	2.37737i	−0.269184	+	0.466240i
$27$	−0.965926	−	0.258819i	−0.185893	−	0.0498097i
$28$	0.0363835	+	0.0519610i	0.00687584	+	0.00981971i
$29$	−1.22265	+	6.93401i	−0.227041	+	1.28761i	0.631704	+	0.775210i	$0.282356\pi$
$29$	−1.22265	+	6.93401i	−0.227041	+	1.28761i	−0.858745	+	0.512404i	$0.828755\pi$
$30$	−1.08082	+	1.95751i	−0.197329	+	0.357390i
$31$	−0.927411	−	0.535441i	−0.166568	−	0.0961681i	0.414399	−	0.910096i	$-0.363992\pi$
$31$	−0.927411	−	0.535441i	−0.166568	−	0.0961681i	−0.580967	+	0.813927i	$0.697325\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	−0.827187	−	1.77391i	−0.143995	−	0.308798i
$34$	0.851641	−	0.309972i	0.146055	−	0.0531598i
$35$	0.0623902	+	0.127381i	0.0105459	+	0.0215314i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	5.68967	−	5.68967i	0.935377	−	0.935377i	−0.0626583	−	0.998035i	$-0.519958\pi$
$37$	5.68967	−	5.68967i	0.935377	−	0.935377i	0.998035	+	0.0626583i	$0.0199578\pi$
$38$	4.27194	−	0.866313i	0.693001	−	0.140535i
$39$			2.74515i			0.439575i
$40$	2.23088	+	0.152274i	0.352733	+	0.0240766i
$41$	7.43026	+	8.85504i	1.16041	+	1.38292i	0.909909	+	0.414809i	$0.136152\pi$
$41$	7.43026	+	8.85504i	1.16041	+	1.38292i	0.250503	+	0.968116i	$0.419404\pi$
$42$	0.0574896	+	0.0268078i	0.00887083	+	0.00413654i
$43$	−8.08894	+	3.77193i	−1.23355	+	0.575215i	−0.926434	−	0.376457i	$-0.877142\pi$
$43$	−8.08894	+	3.77193i	−1.23355	+	0.575215i	−0.307118	+	0.951672i	$0.599364\pi$
$44$	−1.25812	+	1.49937i	−0.189669	+	0.226039i
$45$	0.0427391	+	2.23566i	0.00637117	+	0.333272i
$46$	3.06005	−	1.76672i	0.451179	−	0.260488i
$47$	−4.82273	+	3.37691i	−0.703468	+	0.492573i	−0.869742	−	0.493506i	$-0.835715\pi$
$47$	−4.82273	+	3.37691i	−0.703468	+	0.492573i	0.166275	+	0.986079i	$0.446826\pi$
$48$	0.819152	−	0.573576i	0.118234	−	0.0827886i
$49$	−6.05869	+	3.49799i	−0.865528	+	0.499713i
$50$	4.87556	+	1.10856i	0.689508	+	0.156774i
$51$	0.582557	−	0.694264i	0.0815743	−	0.0972164i
$52$	2.48795	−	1.16015i	0.345016	−	0.160884i
$53$	3.93536	+	1.83509i	0.540563	+	0.252069i	0.673669	−	0.739033i	$-0.264717\pi$
$53$	3.93536	+	1.83509i	0.540563	+	0.252069i	−0.133106	+	0.991102i	$0.542495\pi$
$54$	0.642788	+	0.766044i	0.0874723	+	0.104245i
$55$	−3.29832	+	2.87682i	−0.444745	+	0.387910i
$56$		−	0.0634327i		−	0.00847655i
$57$	3.26646	−	2.88622i	0.432653	−	0.382289i
$58$	4.97872	−	4.97872i	0.653738	−	0.653738i
$59$	−0.306498	−	1.73824i	−0.0399027	−	0.226299i	0.958335	−	0.285648i	$-0.0922088\pi$
$59$	−0.306498	−	1.73824i	−0.0399027	−	0.226299i	−0.998237	+	0.0593485i	$0.981098\pi$
$60$	2.00813	−	0.983565i	0.259249	−	0.126978i
$61$	8.28535	−	3.01562i	1.06083	−	0.386111i	0.248090	−	0.968737i	$-0.420197\pi$
$61$	8.28535	−	3.01562i	1.06083	−	0.386111i	0.812740	+	0.582627i	$0.197975\pi$
$62$	0.452574	+	0.970549i	0.0574770	+	0.123260i
$63$	0.0631913	−	0.00552853i	0.00796136	−	0.000696529i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	5.89773	−	1.70176i	0.731523	−	0.211077i
$66$	−0.339880	+	1.92756i	−0.0418364	+	0.237266i
$67$	0.603609	+	0.862044i	0.0737426	+	0.105315i	0.854329	−	0.519732i	$-0.173968\pi$
$67$	0.603609	+	0.862044i	0.0737426	+	0.105315i	−0.780586	+	0.625048i	$0.785079\pi$
$68$	−0.875416	−	0.234567i	−0.106160	−	0.0284454i
$69$	1.76672	−	3.06005i	0.212688	−	0.368386i
$70$	0.0219559	−	0.140130i	0.00262423	−	0.0167488i
$71$	−5.35062	+	14.7007i	−0.635002	+	1.74465i	0.0318816	+	0.999492i	$0.489850\pi$
$71$	−5.35062	+	14.7007i	−0.635002	+	1.74465i	−0.666884	+	0.745162i	$0.732372\pi$
$72$	0.422618	−	0.906308i	0.0498060	−	0.106809i
$73$	−0.457621	+	5.23064i	−0.0535605	+	0.612200i	0.921221	+	0.389039i	$0.127193\pi$
$73$	−0.457621	+	5.23064i	−0.0535605	+	0.612200i	−0.974782	+	0.223160i	$0.928363\pi$
$74$	−7.92417	+	1.39725i	−0.921166	+	0.162426i
$75$	4.77664	−	1.47774i	0.551559	−	0.170635i
$76$	−3.99627	−	1.74064i	−0.458403	−	0.199666i
$77$	0.0877918	+	0.0877918i	0.0100048	+	0.0100048i
$78$	1.57455	−	2.24869i	0.178283	−	0.254614i
$79$	1.75469	−	1.47236i	0.197419	−	0.165654i	−0.538720	−	0.842485i	$-0.681092\pi$
$79$	1.75469	−	1.47236i	0.197419	−	0.165654i	0.736138	+	0.676831i	$0.236647\pi$
$80$	−1.74009	−	1.40431i	−0.194548	−	0.157007i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	−1.00747	−	11.5154i	−0.111257	−	1.27167i
$83$	0.907126	+	3.38544i	0.0995700	+	0.371600i	0.997673	−	0.0681855i	$-0.0217210\pi$
$83$	0.907126	+	3.38544i	0.0995700	+	0.371600i	−0.898103	+	0.439786i	$0.855054\pi$
$84$	−0.0317164	−	0.0549344i	−0.00346054	−	0.00599383i
$85$	−1.85271	−	0.821192i	−0.200954	−	0.0890708i
$86$	8.78956	+	1.54984i	0.947803	+	0.167123i
$87$	1.82234	−	6.80106i	0.195375	−	0.729151i
$88$	1.89060	−	0.506584i	0.201539	−	0.0540021i
$89$	−8.08005	−	6.77997i	−0.856484	−	0.718675i	0.104724	−	0.994501i	$-0.466604\pi$
$89$	−8.08005	−	6.77997i	−0.856484	−	0.718675i	−0.961208	+	0.275826i	$0.911049\pi$
$90$	1.24731	−	1.85586i	0.131478	−	0.195625i
$91$	−0.0595567	−	0.163631i	−0.00624324	−	0.0171532i
$92$	−3.51999	−	0.307959i	−0.366984	−	0.0321070i
$93$	0.877215	+	0.614233i	0.0909630	+	0.0636930i
$94$	5.88747			0.607246
$95$	−8.22573	−	5.22851i	−0.843943	−	0.536434i
$96$	−1.00000			−0.102062
$97$	−4.56101	−	3.19365i	−0.463100	−	0.324266i	0.318634	−	0.947878i	$-0.396776\pi$
$97$	−4.56101	−	3.19365i	−0.463100	−	0.324266i	−0.781735	+	0.623611i	$0.785665\pi$
$98$	6.96935	+	0.609740i	0.704011	+	0.0615930i
$99$	0.669433	+	1.83925i	0.0672806	+	0.184852i
$100$	−3.35798	−	3.70459i	−0.335798	−	0.370459i
$101$	1.52915	+	1.28311i	0.152156	+	0.127674i	0.715688	−	0.698420i	$-0.246113\pi$
$101$	1.52915	+	1.28311i	0.152156	+	0.127674i	−0.563532	+	0.826094i	$0.690558\pi$
$102$	−0.875416	+	0.234567i	−0.0866791	+	0.0232256i
$103$	1.96187	−	7.32180i	0.193309	−	0.721438i	−0.799389	−	0.600813i	$-0.794843\pi$
$103$	1.96187	−	7.32180i	0.193309	−	0.721438i	0.992698	−	0.120625i	$-0.0384899\pi$
$104$	−2.70344	−	0.476690i	−0.265094	−	0.0467433i
$105$	−0.0510508	−	0.132334i	−0.00498205	−	0.0129145i
$106$	−2.17109	−	3.76044i	−0.210875	−	0.365247i
$107$	−4.50655	−	16.8187i	−0.435665	−	1.62592i	−0.739471	−	0.673188i	$-0.764924\pi$
$107$	−4.50655	−	16.8187i	−0.435665	−	1.62592i	0.303807	−	0.952734i	$-0.401742\pi$
$108$	−0.0871557	−	0.996195i	−0.00838657	−	0.0958589i
$109$	4.24051	+	1.54342i	0.406168	+	0.147833i	0.537021	−	0.843569i	$-0.319550\pi$
$109$	4.24051	+	1.54342i	0.406168	+	0.147833i	−0.130854	+	0.991402i	$0.541772\pi$
$110$	4.35190	−	0.464714i	0.414937	−	0.0443087i
$111$	−6.16391	+	5.17214i	−0.585053	+	0.490917i
$112$	−0.0363835	+	0.0519610i	−0.00343792	+	0.00490986i
$113$	3.32761	+	3.32761i	0.313035	+	0.313035i	0.846084	−	0.533049i	$-0.178954\pi$
$113$	3.32761	+	3.32761i	0.313035	+	0.313035i	−0.533049	+	0.846084i	$0.678954\pi$
$114$	−4.33119	+	0.490692i	−0.405653	+	0.0459575i
$115$	−7.66948	−	1.89869i	−0.715182	−	0.177053i
$116$	−6.93401	+	1.22265i	−0.643807	+	0.113520i
$117$	0.239255	−	2.73470i	0.0221192	−	0.252823i
$118$	−0.745944	+	1.59968i	−0.0686697	+	0.147263i
$119$	−0.0196624	+	0.0540219i	−0.00180245	+	0.00495218i
$120$	−2.20912	−	0.346128i	−0.201664	−	0.0315971i
$121$	3.58450	−	6.20854i	0.325864	−	0.564413i
$122$	−8.51665	−	2.28203i	−0.771061	−	0.206605i
$123$	−6.63022	−	9.46893i	−0.597827	−	0.853785i
$124$	0.185957	−	1.05461i	0.0166994	−	0.0947071i
$125$	−6.13591	−	9.34616i	−0.548812	−	0.835946i
$126$	−0.0549344	−	0.0317164i	−0.00489394	−	0.00282552i
$127$	−13.5738	+	1.18755i	−1.20448	+	0.105378i	−0.671664	−	0.740856i	$-0.734420\pi$
$127$	−13.5738	+	1.18755i	−1.20448	+	0.105378i	−0.532812	+	0.846234i	$0.678865\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	8.38690	−	3.05258i	0.738426	−	0.268765i
$130$	−5.80722	−	1.98880i	−0.509327	−	0.174429i
$131$	−0.283488	−	1.60774i	−0.0247685	−	0.140469i	0.969916	−	0.243440i	$-0.0782761\pi$
$131$	−0.283488	−	1.60774i	−0.0247685	−	0.140469i	−0.994684	+	0.102972i	$0.967165\pi$
$132$	1.38401	−	1.38401i	0.120463	−	0.120463i
$133$	−0.132087	+	0.242906i	−0.0114534	+	0.0210627i
$134$		−	1.05236i		−	0.0909101i
$135$	0.152274	−	2.23088i	0.0131057	−	0.192003i
$136$	0.582557	+	0.694264i	0.0499538	+	0.0595327i
$137$	9.13343	+	4.25899i	0.780322	+	0.363870i	0.771613	−	0.636092i	$-0.219450\pi$
$137$	9.13343	+	4.25899i	0.780322	+	0.363870i	0.00870871	+	0.999962i	$0.497228\pi$
$138$	−3.20238	+	1.49330i	−0.272605	+	0.127118i
$139$	7.51017	−	8.95027i	0.637004	−	0.759152i	−0.346889	−	0.937906i	$-0.612762\pi$
$139$	7.51017	−	8.95027i	0.637004	−	0.759152i	0.983894	+	0.178754i	$0.0572066\pi$
$140$	−0.0983606	+	0.102195i	−0.00831299	+	0.00863702i
$141$	5.09870	−	2.94373i	0.429388	−	0.247907i
$142$	12.8150	−	8.97313i	1.07541	−	0.753008i
$143$	4.40135	−	3.08186i	0.368059	−	0.257718i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	−15.7412	+	0.300925i	−1.30724	+	0.0249905i
$146$	3.37503	−	4.02221i	0.279320	−	0.332880i
$147$	6.34051	−	2.95663i	0.522956	−	0.243859i
$148$	7.29253	+	3.40056i	0.599442	+	0.279524i
$149$	2.96488	+	3.53341i	0.242893	+	0.289468i	0.873694	−	0.486476i	$-0.161718\pi$
$149$	2.96488	+	3.53341i	0.242893	+	0.289468i	−0.630801	+	0.775945i	$0.717274\pi$
$150$	−4.76039	−	1.52928i	−0.388684	−	0.124865i
$151$			9.97778i			0.811980i	0.913877	+	0.405990i	$0.133073\pi$
$151$			9.97778i			0.811980i	−0.913877	+	0.405990i	$0.866927\pi$
$152$	2.27516	+	3.71802i	0.184540	+	0.301571i
$153$	−0.640849	+	0.640849i	−0.0518096	+	0.0518096i
$154$	−0.0215595	−	0.122270i	−0.00173732	−	0.00985281i
$155$	0.775832	−	2.26540i	0.0623163	−	0.181961i
$156$	−2.57959	+	0.938896i	−0.206533	+	0.0751718i
$157$	2.28088	+	4.89137i	0.182034	+	0.390374i	0.976057	−	0.217514i	$-0.0697948\pi$
$157$	2.28088	+	4.89137i	0.182034	+	0.390374i	−0.794023	+	0.607888i	$0.792017\pi$
$158$	−2.28188	+	0.199638i	−0.181536	+	0.0158824i
$159$	−3.76044	−	2.17109i	−0.298223	−	0.172179i
$160$	0.619914	+	2.14842i	0.0490085	+	0.169847i
$161$	−0.0389207	+	0.220730i	−0.00306738	+	0.0173960i
$162$	−0.573576	−	0.819152i	−0.0450644	−	0.0643587i
$163$	8.41938	+	2.25597i	0.659457	+	0.176701i	0.573001	−	0.819555i	$-0.305779\pi$
$163$	8.41938	+	2.25597i	0.659457	+	0.176701i	0.0864558	+	0.996256i	$0.472446\pi$
$164$	−5.77972	+	10.0108i	−0.451320	+	0.781709i
$165$	3.53650	−	2.57840i	0.275316	−	0.200728i
$166$	1.19873	−	3.29350i	0.0930399	−	0.255625i
$167$	8.60116	−	18.4452i	0.665577	−	1.42734i	−0.225845	−	0.974163i	$-0.572514\pi$
$167$	8.60116	−	18.4452i	0.665577	−	1.42734i	0.891423	−	0.453172i	$-0.149708\pi$
$168$	−0.00552853	+	0.0631913i	−0.000426535	+	0.00487532i
$169$	5.38115	−	0.948843i	0.413935	−	0.0729879i
$170$	1.04663	+	1.73535i	0.0802729	+	0.133095i
$171$	−3.50558	+	2.59055i	−0.268078	+	0.198104i
$172$	−6.31104	−	6.31104i	−0.481212	−	0.481212i
$173$	−0.966964	+	1.38097i	−0.0735169	+	0.104993i	−0.854227	−	0.519901i	$-0.825969\pi$
$173$	−0.966964	+	1.38097i	−0.0735169	+	0.104993i	0.780710	+	0.624894i	$0.214858\pi$
$174$	−5.39370	+	4.52585i	−0.408896	+	0.343104i
$175$	−0.252663	+	0.191714i	−0.0190995	+	0.0144922i
$176$	−1.83925	−	0.669433i	−0.138639	−	0.0504604i
$177$	0.153835	+	1.75834i	0.0115629	+	0.132165i
$178$	2.72996	+	10.1884i	0.204619	+	0.763649i
$179$	−10.4663	−	18.1281i	−0.782287	−	1.35496i	−0.930607	−	0.366021i	$-0.880720\pi$
$179$	−10.4663	−	18.1281i	−0.782287	−	1.35496i	0.148320	−	0.988939i	$-0.452614\pi$
$180$	−2.08622	+	0.804802i	−0.155497	+	0.0599864i
$181$	7.49019	+	1.32072i	0.556741	+	0.0981685i	0.444937	−	0.895562i	$-0.353226\pi$
$181$	7.49019	+	1.32072i	0.556741	+	0.0981685i	0.111804	+	0.993730i	$0.464337\pi$
$182$	−0.0450687	+	0.168199i	−0.00334072	+	0.0124677i
$183$	−8.51665	+	2.28203i	−0.629569	+	0.168692i
$184$	2.70677	+	2.27125i	0.199546	+	0.167439i
$185$	14.9330	+	10.0364i	1.09790	+	0.737890i
$186$	−0.366263	−	1.00630i	−0.0268557	−	0.0737855i
$187$	−1.76714	−	0.154605i	−0.129226	−	0.0113058i
$188$	−4.82273	−	3.37691i	−0.351734	−	0.246287i
$189$	−0.0634327			−0.00461405
$190$	3.73918	+	9.00103i	0.271269	+	0.653003i
$191$	6.79727			0.491833			0.245917	−	0.969291i	$-0.420911\pi$
$191$	6.79727			0.491833			0.245917	+	0.969291i	$0.420911\pi$
$192$	0.819152	+	0.573576i	0.0591172	+	0.0413943i
$193$	22.1449	+	1.93743i	1.59403	+	0.139459i	0.849300	−	0.527911i	$-0.177024\pi$
$193$	22.1449	+	1.93743i	1.59403	+	0.139459i	0.744726	+	0.667370i	$0.232580\pi$
$194$	1.90436	+	5.23218i	0.136725	+	0.375648i
$195$	−6.02360	+	1.18126i	−0.431359	+	0.0845917i
$196$	−5.35923	−	4.49693i	−0.382802	−	0.321209i
$197$	−11.2894	+	3.02498i	−0.804335	+	0.215521i	−0.637486	−	0.770462i	$-0.720026\pi$
$197$	−11.2894	+	3.02498i	−0.804335	+	0.215521i	−0.166849	+	0.985983i	$0.553359\pi$
$198$	0.506584	−	1.89060i	0.0360014	−	0.134359i
$199$	3.04873	+	0.537573i	0.216119	+	0.0381075i	0.280659	−	0.959808i	$-0.409447\pi$
$199$	3.04873	+	0.537573i	0.216119	+	0.0381075i	−0.0645404	+	0.997915i	$0.520558\pi$
$200$	0.625833	+	4.96068i	0.0442531	+	0.350773i
$201$	−0.526180	−	0.911371i	−0.0371139	−	0.0642832i
$202$	−0.516643	−	1.92814i	−0.0363509	−	0.135663i
$203$	0.0389262	+	0.444929i	0.00273209	+	0.0312279i
$204$	0.851641	+	0.309972i	0.0596268	+	0.0217024i
$205$	−16.2331	+	20.1144i	−1.13377	+	1.40485i
$206$	−5.80668	+	4.87238i	−0.404571	+	0.339475i
$207$	−2.02670	+	2.89442i	−0.140865	+	0.201176i
$208$	1.94111	+	1.94111i	0.134592	+	0.134592i
$209$	−8.29464	−	1.99694i	−0.573752	−	0.138131i
$210$	−0.0340855	+	0.137683i	−0.00235212	+	0.00950106i
$211$	16.5633	−	2.92055i	1.14026	−	0.201059i	0.428541	−	0.903522i	$-0.359028\pi$
$211$	16.5633	−	2.92055i	1.14026	−	0.201059i	0.711720	+	0.702463i	$0.247917\pi$
$212$	−0.378446	+	4.32566i	−0.0259918	+	0.297088i
$213$	6.61151	−	14.1784i	0.453013	−	0.971490i
$214$	−5.95524	+	16.3619i	−0.407092	+	1.11848i
$215$	−11.7574	−	16.1262i	−0.801847	−	1.09980i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−0.0656144	−	0.0175813i	−0.00445419	−	0.00119350i
$218$	−2.58836	−	3.69656i	−0.175306	−	0.250362i
$219$	0.911760	−	5.17085i	0.0616110	−	0.349414i
$220$	−3.83141	−	2.11547i	−0.258314	−	0.142625i
$221$	2.15460	+	1.24396i	0.144934	+	0.0836778i
$222$	8.01580	−	0.701291i	0.537985	−	0.0470676i
$223$	7.43424	+	15.9428i	0.497833	+	1.06761i	0.981342	+	0.192268i	$0.0615843\pi$
$223$	7.43424	+	15.9428i	0.497833	+	1.06761i	−0.483509	+	0.875339i	$0.660638\pi$
$224$	0.0596073	−	0.0216953i	0.00398268	−	0.00144958i
$225$	−4.88726	+	1.05580i	−0.325817	+	0.0703869i
$226$	−0.817180	−	4.63446i	−0.0543580	−	0.308280i
$227$	−1.49044	+	1.49044i	−0.0989242	+	0.0989242i	−0.754837	−	0.655913i	$-0.772284\pi$
$227$	−1.49044	+	1.49044i	−0.0989242	+	0.0989242i	0.655913	+	0.754837i	$0.272284\pi$
$228$	3.82935	+	2.08232i	0.253605	+	0.137905i
$229$		−	17.5361i		−	1.15882i	−0.815037	−	0.579409i	$-0.803284\pi$
$229$		−	17.5361i		−	1.15882i	0.815037	−	0.579409i	$-0.196716\pi$
$230$	5.19343	+	5.95435i	0.342444	+	0.392618i
$231$	−0.0798062	−	0.0951093i	−0.00525086	−	0.00625773i
$232$	6.38129	+	2.97565i	0.418952	+	0.195361i
$233$	3.32232	−	1.54922i	0.217652	−	0.101493i	−0.310734	−	0.950497i	$-0.600575\pi$
$233$	3.32232	−	1.54922i	0.217652	−	0.101493i	0.528387	+	0.849004i	$0.322797\pi$
$234$	−1.76455	+	2.10290i	−0.115352	+	0.137471i
$235$	−9.48513	−	9.12928i	−0.618742	−	0.595529i
$236$	1.52858	−	0.882527i	0.0995022	−	0.0574476i
$237$	−1.87634	+	1.31383i	−0.121882	+	0.0853424i
$238$	0.0470922	−	0.0329743i	0.00305253	−	0.00213741i
$239$	−3.48438	+	2.01171i	−0.225386	+	0.130126i	−0.608442	−	0.793599i	$-0.708205\pi$
$239$	−3.48438	+	2.01171i	−0.225386	+	0.130126i	0.383056	+	0.923725i	$0.374872\pi$
$240$	1.61107	+	1.55063i	0.103994	+	0.100093i
$241$	−1.73648	+	2.06945i	−0.111856	+	0.133305i	−0.819067	−	0.573697i	$-0.805509\pi$
$241$	−1.73648	+	2.06945i	−0.111856	+	0.133305i	0.707211	+	0.707002i	$0.249953\pi$
$242$	−6.49733	+	3.02975i	−0.417664	+	0.194760i
$243$	−0.906308	−	0.422618i	−0.0581397	−	0.0271110i
$244$	5.66751	+	6.75428i	0.362825	+	0.432398i
$245$	−10.2826	−	11.7892i	−0.656934	−	0.753185i
$246$			11.5594i			0.737002i
$247$	9.35982	+	7.45484i	0.595551	+	0.474340i
$248$	−0.757228	+	0.757228i	−0.0480840	+	0.0480840i
$249$	−0.608614	−	3.45162i	−0.0385693	−	0.218737i
$250$	−0.334493	+	11.1753i	−0.0211552	+	0.706790i
$251$	20.8452	−	7.58704i	1.31574	−	0.478890i	0.413648	−	0.910437i	$-0.364254\pi$
$251$	20.8452	−	7.58704i	1.31574	−	0.478890i	0.902090	+	0.431547i	$0.142032\pi$
$252$	0.0268078	+	0.0574896i	0.00168873	+	0.00362150i
$253$	−6.88965	+	0.602766i	−0.433149	+	0.0378956i
$254$	11.8001	+	6.81280i	0.740405	+	0.427473i
$255$	1.77408	+	0.979541i	0.111097	+	0.0613413i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	8.20231	+	11.7141i	0.511646	+	0.730706i	0.988985	−	0.148013i	$-0.0472876\pi$
$257$	8.20231	+	11.7141i	0.511646	+	0.730706i	−0.477339	+	0.878719i	$0.658399\pi$
$258$	−8.62104	−	2.31000i	−0.536722	−	0.143814i
$259$	0.255203	−	0.442025i	0.0158575	−	0.0274661i
$260$	3.61627	+	4.96002i	0.224271	+	0.307607i
$261$	−2.40816	+	6.61636i	−0.149061	+	0.409542i
$262$	−0.689942	+	1.47959i	−0.0426248	+	0.0914092i
$263$	−2.06306	+	23.5808i	−0.127213	+	1.45406i	0.617447	+	0.786613i	$0.288167\pi$
$263$	−2.06306	+	23.5808i	−0.127213	+	1.45406i	−0.744660	+	0.667444i	$0.767388\pi$
$264$	−1.92756	+	0.339880i	−0.118633	+	0.0209182i
$265$	−2.33327	+	9.42490i	−0.143331	+	0.578967i
$266$	0.247525	−	0.123215i	0.0151767	−	0.00755481i
$267$	7.45839	+	7.45839i	0.456446	+	0.456446i
$268$	−0.603609	+	0.862044i	−0.0368713	+	0.0526577i
$269$	15.2209	−	12.7718i	0.928034	−	0.778713i	−0.0474298	−	0.998875i	$-0.515103\pi$
$269$	15.2209	−	12.7718i	0.928034	−	0.778713i	0.975463	+	0.220162i	$0.0706586\pi$
$270$	−1.40431	+	1.74009i	−0.0854638	+	0.105898i
$271$	−17.6872	−	6.43760i	−1.07442	−	0.391056i	−0.256591	−	0.966520i	$-0.582599\pi$
$271$	−17.6872	−	6.43760i	−1.07442	−	0.391056i	−0.817827	+	0.575464i	$0.804822\pi$
$272$	−0.0789890	−	0.902849i	−0.00478941	−	0.0547432i
$273$	0.0450687	+	0.168199i	0.00272768	+	0.0101799i
$274$	−5.03881	−	8.72748i	−0.304406	−	0.527247i
$275$	−7.73181	−	5.99949i	−0.466246	−	0.361783i
$276$	3.47976	+	0.613575i	0.209457	+	0.0369329i
$277$	−5.92482	+	22.1117i	−0.355988	+	1.32857i	0.523248	+	0.852180i	$0.324720\pi$
$277$	−5.92482	+	22.1117i	−0.355988	+	1.32857i	−0.879236	+	0.476386i	$0.841947\pi$
$278$	−11.2856	+	3.02398i	−0.676868	+	0.181366i
$279$	−0.820343	−	0.688350i	−0.0491127	−	0.0412104i
$280$	0.139189	−	0.0272956i	0.00831812	−	0.00163122i
$281$	−0.0882518	−	0.242470i	−0.00526466	−	0.0144645i	0.937032	−	0.349242i	$-0.113561\pi$
$281$	−0.0882518	−	0.242470i	−0.00526466	−	0.0144645i	−0.942297	+	0.334778i	$0.891339\pi$
$282$	−5.86507	−	0.513127i	−0.349260	−	0.0305563i
$283$	8.26492	+	5.78716i	0.491298	+	0.344011i	0.792827	−	0.609446i	$-0.208608\pi$
$283$	8.26492	+	5.78716i	0.491298	+	0.344011i	−0.301529	+	0.953457i	$0.597497\pi$
$284$	−15.6442			−0.928311
$285$	7.73874	+	5.92553i	0.458403	+	0.350998i
$286$	−5.37305			−0.317715
$287$	0.600640	+	0.420573i	0.0354547	+	0.0248256i
$288$	0.996195	+	0.0871557i	0.0587013	+	0.00513570i
$289$	5.53342	+	15.2029i	0.325495	+	0.894290i
$290$	13.0671	+	8.78230i	0.767324	+	0.515714i
$291$	4.26531	+	3.57902i	0.250037	+	0.209806i
$292$	−5.07171	+	1.35896i	−0.296799	+	0.0795271i
$293$	5.77946	−	21.5692i	0.337639	−	1.26009i	−0.563340	−	0.826225i	$-0.690484\pi$
$293$	5.77946	−	21.5692i	0.337639	−	1.26009i	0.900979	−	0.433862i	$-0.142850\pi$
$294$	−6.88969	−	1.21484i	−0.401815	−	0.0708508i
$295$	3.68228	−	1.42052i	0.214391	−	0.0827058i
$296$	−4.02321	−	6.96840i	−0.233844	−	0.405030i
$297$	−0.506584	−	1.89060i	−0.0293950	−	0.109704i
$298$	−0.402009	−	4.59498i	−0.0232878	−	0.266180i
$299$	9.11484	+	3.31753i	0.527125	+	0.191858i
$300$	3.02233	+	3.98316i	0.174494	+	0.229968i
$301$	−0.433694	+	0.363912i	−0.0249977	+	0.0209756i
$302$	5.72302	−	8.17332i	0.329323	−	0.470322i
$303$	−1.41150	−	1.41150i	−0.0810883	−	0.0810883i
$304$	0.268866	−	4.35060i	0.0154205	−	0.249524i
$305$	10.1823	+	16.8827i	0.583039	+	0.966699i
$306$	0.892529	−	0.157377i	0.0510225	−	0.00899664i
$307$	−1.62473	+	18.5707i	−0.0927280	+	1.05989i	0.797179	+	0.603743i	$0.206325\pi$
$307$	−1.62473	+	18.5707i	−0.0927280	+	1.05989i	−0.889907	+	0.456143i	$0.849231\pi$
$308$	−0.0524707	+	0.112524i	−0.00298980	+	0.00641164i
$309$	−2.59254	+	7.12295i	−0.147485	+	0.405210i
$310$	−1.93490	+	1.41071i	−0.109895	+	0.0801228i
$311$	−1.94895	+	3.37568i	−0.110515	+	0.191417i	−0.915978	−	0.401229i	$-0.868583\pi$
$311$	−1.94895	+	3.37568i	−0.110515	+	0.191417i	0.805463	+	0.592646i	$0.201917\pi$
$312$	2.65161	+	0.710496i	0.150118	+	0.0402239i
$313$	−17.9648	−	25.6564i	−1.01543	−	1.45018i	−0.888834	−	0.458229i	$-0.848484\pi$
$313$	−17.9648	−	25.6564i	−1.01543	−	1.45018i	−0.126596	−	0.991954i	$-0.540405\pi$
$314$	0.937184	−	5.31503i	0.0528883	−	0.299945i
$315$	0.0393228	+	0.136280i	0.00221559	+	0.00767851i
$316$	1.98371	+	1.14530i	0.111592	+	0.0644279i
$317$	12.5565	−	1.09855i	0.705242	−	0.0617006i	0.271108	−	0.962549i	$-0.412610\pi$
$317$	12.5565	−	1.09855i	0.705242	−	0.0617006i	0.434134	+	0.900848i	$0.357054\pi$
$318$	1.83509	+	3.93536i	0.102907	+	0.220684i
$319$	−12.9501	+	4.71347i	−0.725069	+	0.263903i
$320$	0.724479	−	2.11545i	0.0404996	−	0.118257i
$321$	3.02356	+	17.1474i	0.168758	+	0.957077i
$322$	0.158488	−	0.158488i	0.00883218	−	0.00883218i
$323$	−0.785137	−	3.87165i	−0.0436862	−	0.215424i
$324$			1.00000i			0.0555556i
$325$	6.27196	+	12.2089i	0.347905	+	0.677231i
$326$	−5.60278	−	6.67714i	−0.310309	−	0.369812i
$327$	−4.08986	−	1.90713i	−0.226170	−	0.105465i
$328$	10.4764	−	4.88523i	0.578463	−	0.269742i
$329$	−0.240054	+	0.286086i	−0.0132346	+	0.0157724i
$330$	−4.37584	+	0.0836529i	−0.240882	+	0.00460494i
$331$	16.9022	−	9.75848i	0.929028	−	0.536374i	0.0425238	−	0.999095i	$-0.486460\pi$
$331$	16.9022	−	9.75848i	0.929028	−	0.536374i	0.886504	+	0.462721i	$0.153127\pi$
$332$	−2.87102	+	2.01031i	−0.157568	+	0.110330i
$333$	6.59124	−	4.61523i	0.361198	−	0.252913i
$334$	−17.6254	+	10.1760i	−0.964420	+	0.556808i
$335$	−1.63182	+	1.69543i	−0.0891559	+	0.0926311i
$336$	0.0407738	−	0.0485923i	0.00222439	−	0.00265093i
$337$	−14.0092	+	6.53262i	−0.763132	+	0.355854i	−0.764904	−	0.644144i	$-0.777214\pi$
$337$	−14.0092	+	6.53262i	−0.763132	+	0.355854i	0.00177208	+	0.999998i	$0.499436\pi$
$338$	−4.95222	−	2.30926i	−0.269365	−	0.125607i
$339$	−3.02493	−	3.60497i	−0.164292	−	0.195795i
$340$	0.138006	−	2.02184i	0.00748441	−	0.109650i
$341$		−	2.09603i		−	0.113506i
$342$	4.35748	−	0.111337i	0.235625	−	0.00602039i
$343$	−0.627771	+	0.627771i	−0.0338965	+	0.0338965i
$344$	1.54984	+	8.78956i	0.0835616	+	0.473902i
$345$	7.47481	+	2.55990i	0.402430	+	0.137820i
$346$	1.58418	−	0.576595i	0.0851661	−	0.0309979i
$347$	−3.08958	−	6.62563i	−0.165858	−	0.355683i	0.805759	−	0.592243i	$-0.201758\pi$
$347$	−3.08958	−	6.62563i	−0.165858	−	0.355683i	−0.971617	+	0.236561i	$0.923980\pi$
$348$	7.01419	−	0.613662i	0.376000	−	0.0328957i
$349$	21.1779	+	12.2270i	1.13362	+	0.654498i	0.944844	−	0.327521i	$-0.106213\pi$
$349$	21.1779	+	12.2270i	1.13362	+	0.654498i	0.188781	+	0.982019i	$0.439546\pi$
$350$	0.316932	−	0.0121220i	0.0169407	−	0.000647948i
$351$	−0.476690	+	2.70344i	−0.0254438	+	0.144299i
$352$	1.12266	+	1.60332i	0.0598378	+	0.0854572i
$353$	34.3453	+	9.20281i	1.82802	+	0.489816i	0.997719	−	0.0675024i	$-0.0215030\pi$
$353$	34.3453	+	9.20281i	1.82802	+	0.489816i	0.830299	+	0.557318i	$0.188170\pi$
$354$	0.882527	−	1.52858i	0.0469058	−	0.0812432i
$355$	−34.5598	−	5.41489i	−1.83424	−	0.287393i
$356$	3.60755	−	9.91165i	0.191200	−	0.525316i
$357$	0.0242959	−	0.0521027i	0.00128587	−	0.00275756i
$358$	−1.82439	+	20.8529i	−0.0964222	+	1.10211i
$359$	−2.71046	+	0.477928i	−0.143053	+	0.0252241i	−0.244716	−	0.969595i	$-0.578695\pi$
$359$	−2.71046	+	0.477928i	−0.143053	+	0.0252241i	0.101663	+	0.994819i	$0.467584\pi$
$360$	2.17054	+	0.537348i	0.114398	+	0.0283208i
$361$	−0.970292	−	18.9752i	−0.0510680	−	0.998695i
$362$	−5.37807	−	5.37807i	−0.282665	−	0.282665i
$363$	−4.11197	+	5.87251i	−0.215823	+	0.308227i
$364$	0.133393	−	0.111930i	0.00699169	−	0.00586673i
$365$	−11.6744	+	1.24664i	−0.611064	+	0.0652520i
$366$	8.28535	+	3.01562i	0.433082	+	0.157629i
$367$	0.0399756	+	0.456923i	0.00208671	+	0.0238512i	0.997167	−	0.0752239i	$-0.0239672\pi$
$367$	0.0399756	+	0.456923i	0.00208671	+	0.0238512i	−0.995080	+	0.0990751i	$0.968412\pi$
$368$	−0.914521	−	3.41304i	−0.0476727	−	0.177917i
$369$	5.77972	+	10.0108i	0.300880	+	0.521139i
$370$	−6.47577	−	16.7866i	−0.336659	−	0.872691i
$371$	0.271252	+	0.0478291i	0.0140827	+	0.00248316i
$372$	−0.277165	+	1.03439i	−0.0143703	+	0.0536308i
$373$	−30.2170	+	8.09661i	−1.56458	+	0.419227i	−0.934108	−	0.356989i	$-0.883803\pi$
$373$	−30.2170	+	8.09661i	−1.56458	+	0.419227i	−0.630467	+	0.776216i	$0.717137\pi$
$374$	1.35888	+	1.14023i	0.0702659	+	0.0589601i
$375$	5.29799	+	9.84537i	0.273587	+	0.508413i
$376$	2.01363	+	5.53241i	0.103845	+	0.285312i
$377$	19.2550	+	1.68459i	0.991681	+	0.0867609i
$378$	0.0519610	+	0.0363835i	0.00267259	+	0.00187137i
$379$	34.2125			1.75738			0.878690	−	0.477392i	$-0.158418\pi$
$379$	34.2125			1.75738			0.878690	+	0.477392i	$0.158418\pi$
$380$	2.09982	−	9.51792i	0.107719	−	0.488259i
$381$	13.6256			0.698061
$382$	−5.56800	−	3.89876i	−0.284884	−	0.199478i
$383$	−20.6617	−	1.80767i	−1.05576	−	0.0923675i	−0.453969	−	0.891017i	$-0.649992\pi$
$383$	−20.6617	−	1.80767i	−1.05576	−	0.0923675i	−0.601796	+	0.798650i	$0.705548\pi$
$384$	−0.342020	−	0.939693i	−0.0174536	−	0.0479535i
$385$	−0.154862	+	0.230417i	−0.00789248	+	0.0117431i
$386$	−17.0288	−	14.2889i	−0.866743	−	0.727284i
$387$	−8.62104	+	2.31000i	−0.438232	+	0.117424i
$388$	1.44110	−	5.37824i	0.0731605	−	0.273039i
$389$	−18.6208	−	3.28335i	−0.944112	−	0.166472i	−0.319657	−	0.947533i	$-0.603568\pi$
$389$	−18.6208	−	3.28335i	−0.944112	−	0.166472i	−0.624455	+	0.781061i	$0.714679\pi$
$390$	5.61179	+	2.48737i	0.284164	+	0.125953i
$391$	−1.60117	−	2.77331i	−0.0809748	−	0.140252i
$392$	1.81069	+	6.75759i	0.0914538	+	0.341310i
$393$	0.142285	+	1.62633i	0.00717735	+	0.0820375i
$394$	10.9828	+	3.99740i	0.553304	+	0.201386i
$395$	3.98583	+	3.21671i	0.200549	+	0.161850i
$396$	−1.49937	+	1.25812i	−0.0753463	+	0.0632231i
$397$	−3.09321	+	4.41756i	−0.155244	+	0.221711i	−0.889238	−	0.457444i	$-0.848765\pi$
$397$	−3.09321	+	4.41756i	−0.155244	+	0.221711i	0.733994	+	0.679155i	$0.237654\pi$
$398$	−2.18903	−	2.18903i	−0.109726	−	0.109726i
$399$	0.152755	−	0.230470i	0.00764732	−	0.0115379i
$400$	2.33268	−	4.42251i	0.116634	−	0.221126i
$401$	−19.5290	+	3.44349i	−0.975233	+	0.171960i	−0.638484	−	0.769635i	$-0.720438\pi$
$401$	−19.5290	+	3.44349i	−0.975233	+	0.171960i	−0.336748	+	0.941595i	$0.609327\pi$
$402$	−0.0917193	+	1.04836i	−0.00457454	+	0.0522873i
$403$	−1.24238	+	2.66430i	−0.0618875	+	0.132718i
$404$	−0.682726	+	1.87577i	−0.0339669	+	0.0933232i
$405$	−0.346128	+	2.20912i	−0.0171993	+	0.109772i
$406$	0.223314	−	0.386792i	0.0110829	−	0.0191961i
$407$	15.2125	+	4.07619i	0.754058	+	0.202049i
$408$	−0.519831	−	0.742395i	−0.0257355	−	0.0367540i
$409$	6.55506	−	37.1756i	0.324127	−	1.83822i	−0.191613	−	0.981471i	$-0.561372\pi$
$409$	6.55506	−	37.1756i	0.324127	−	1.83822i	0.515740	−	0.856745i	$-0.327517\pi$
$410$	24.8345	−	7.16585i	1.22649	−	0.353896i
$411$	−8.72748	−	5.03881i	−0.430495	−	0.248546i
$412$	7.55124	−	0.660648i	0.372023	−	0.0325478i
$413$	−0.0473173	−	0.101472i	−0.00232833	−	0.00499312i
$414$	3.32035	−	1.20851i	0.163186	−	0.0593949i
$415$	−7.03824	+	3.44726i	−0.345494	+	0.169220i
$416$	−0.476690	−	2.70344i	−0.0233716	−	0.132547i
$417$	−8.26166	+	8.26166i	−0.404575	+	0.404575i
$418$	5.64918	+	6.39341i	0.276310	+	0.312712i
$419$		−	4.40572i		−	0.215234i	−0.994192	−	0.107617i	$-0.965678\pi$
$419$		−	4.40572i		−	0.215234i	0.994192	−	0.107617i	$-0.0343220\pi$
$420$	0.106893	−	0.0932331i	0.00521585	−	0.00454931i
$421$	−17.4083	−	20.7464i	−0.848426	−	1.01112i	−0.999744	−	0.0226300i	$-0.992796\pi$
$421$	−17.4083	−	20.7464i	−0.848426	−	1.01112i	0.151317	−	0.988485i	$-0.451648\pi$
$422$	−15.2430	−	7.10792i	−0.742017	−	0.346008i
$423$	−5.33586	+	2.48815i	−0.259438	+	0.120978i
$424$	2.79110	−	3.32631i	0.135548	−	0.161540i
$425$	1.00469	−	4.41871i	0.0487344	−	0.214339i
$426$	−13.5482	+	7.82209i	−0.656415	+	0.378981i
$427$	0.458145	−	0.320796i	0.0221712	−	0.0155244i
$428$	14.2630	−	9.98709i	0.689430	−	0.482744i
$429$	−4.65320	+	2.68653i	−0.224659	+	0.129707i
$430$	0.381453	+	19.9536i	0.0183953	+	0.962249i
$431$	−0.844879	+	1.00689i	−0.0406964	+	0.0485000i	−0.786009	−	0.618215i	$-0.787856\pi$
$431$	−0.844879	+	1.00689i	−0.0406964	+	0.0485000i	0.745312	+	0.666715i	$0.232300\pi$
$432$	0.906308	−	0.422618i	0.0436048	−	0.0203332i
$433$	5.03732	+	2.34894i	0.242078	+	0.112883i	0.539871	−	0.841747i	$-0.318473\pi$
$433$	5.03732	+	2.34894i	0.242078	+	0.112883i	−0.297793	+	0.954630i	$0.596251\pi$
$434$	0.0436639	+	0.0520366i	0.00209593	+	0.00249784i
$435$	15.7076	+	1.07216i	0.753120	+	0.0514061i
$436$			4.51266i			0.216117i
$437$	−5.63572	−	14.3338i	−0.269593	−	0.685677i
$438$	−3.71275	+	3.71275i	−0.177402	+	0.177402i
$439$	3.91562	+	22.2066i	0.186882	+	1.05986i	0.923513	+	0.383567i	$0.125304\pi$
$439$	3.91562	+	22.2066i	0.186882	+	1.05986i	−0.736631	+	0.676295i	$0.763584\pi$
$440$	1.92512	+	3.93050i	0.0917767	+	0.187379i
$441$	−6.57407	+	2.39276i	−0.313051	+	0.113941i
$442$	−1.05144	−	2.25482i	−0.0500119	−	0.107251i
$443$	−30.1543	+	2.63816i	−1.43267	+	0.125343i	−0.776904	−	0.629620i	$-0.783211\pi$
$443$	−30.1543	+	2.63816i	−1.43267	+	0.125343i	−0.655768	+	0.754962i	$0.727655\pi$
$444$	−6.96840	−	4.02321i	−0.330706	−	0.190933i
$445$	11.4002	−	20.6473i	0.540421	−	0.978776i
$446$	3.05463	−	17.3237i	0.144641	−	0.820299i
$447$	−2.64564	−	3.77837i	−0.125135	−	0.178711i
$448$	−0.0612713	−	0.0164176i	−0.00289480	−	0.000775659i
$449$	11.0998	−	19.2254i	0.523831	−	0.907302i	−0.475784	−	0.879562i	$-0.657836\pi$
$449$	11.0998	−	19.2254i	0.523831	−	0.907302i	0.999615	−	0.0277402i	$-0.00883112\pi$
$450$	4.60899	+	1.93835i	0.217270	+	0.0913748i
$451$	−7.73827	+	21.2607i	−0.364381	+	1.00113i
$452$	−1.98882	+	4.26504i	−0.0935463	+	0.200611i
$453$	0.869621	−	9.93981i	0.0408583	−	0.467013i
$454$	2.07578	−	0.366017i	0.0974214	−	0.0171780i
$455$	0.333423	−	0.201095i	0.0156311	−	0.00942749i
$456$	−1.94245	−	3.90216i	−0.0909638	−	0.182735i
$457$	2.71355	+	2.71355i	0.126935	+	0.126935i	0.767720	−	0.640785i	$-0.221391\pi$
$457$	2.71355	+	2.71355i	0.126935	+	0.126935i	−0.640785	+	0.767720i	$0.721391\pi$
$458$	−10.0583	+	14.3647i	−0.469993	+	0.671219i
$459$	0.694264	−	0.582557i	0.0324055	−	0.0271914i
$460$	−0.838934	−	7.85634i	−0.0391155	−	0.366304i
$461$	−17.9524	−	6.53413i	−0.836125	−	0.304325i	−0.111755	−	0.993736i	$-0.535647\pi$
$461$	−17.9524	−	6.53413i	−0.836125	−	0.304325i	−0.724370	+	0.689411i	$0.757869\pi$
$462$	0.0108209	+	0.123684i	0.000503436	+	0.00575430i
$463$	4.44669	+	16.5953i	0.206655	+	0.771248i	0.988939	+	0.148325i	$0.0473882\pi$
$463$	4.44669	+	16.5953i	0.206655	+	0.771248i	−0.782283	+	0.622923i	$0.785945\pi$
$464$	−3.52049	−	6.09767i	−0.163435	−	0.283077i
$465$	−0.970322	+	2.18916i	−0.0449976	+	0.101520i
$466$	−3.61008	−	0.636554i	−0.167234	−	0.0294878i
$467$	7.13056	−	26.6116i	0.329963	−	1.23144i	−0.579265	−	0.815139i	$-0.696660\pi$
$467$	7.13056	−	26.6116i	0.329963	−	1.23144i	0.909228	−	0.416299i	$-0.136673\pi$
$468$	2.65161	−	0.710496i	0.122571	−	0.0328427i
$469$	0.0511366	+	0.0429087i	0.00236127	+	0.00198134i
$470$	2.53343	+	12.9187i	0.116858	+	0.595896i
$471$	−1.84589	−	5.07155i	−0.0850542	−	0.233684i
$472$	−1.75834	−	0.153835i	−0.0809340	−	0.00708081i
$473$	−14.3099	−	10.0199i	−0.657969	−	0.460715i
$474$	2.29059			0.105210
$475$	7.93317	−	20.2994i	0.363999	−	0.931399i
$476$	−0.0574889			−0.00263500
$477$	3.55691	+	2.49058i	0.162860	+	0.114036i
$478$	4.00810	+	0.350664i	0.183326	+	0.0160390i
$479$	9.64414	+	26.4970i	0.440652	+	1.21068i	0.939064	+	0.343741i	$0.111694\pi$
$479$	9.64414	+	26.4970i	0.440652	+	1.21068i	−0.498413	+	0.866940i	$0.666084\pi$
$480$	−0.430308	−	2.19427i	−0.0196408	−	0.100154i
$481$	−16.9208	−	14.1983i	−0.771524	−	0.647386i
$482$	2.60943	−	0.699194i	0.118856	−	0.0318474i
$483$	0.0580106	−	0.216498i	0.00263957	−	0.00985102i
$484$	7.06009	+	1.24489i	0.320913	+	0.0565857i
$485$	5.04511	−	11.3824i	0.229087	−	0.516846i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	1.13844	+	4.24872i	0.0515877	+	0.192528i	0.986911	−	0.161266i	$-0.0515579\pi$
$487$	1.13844	+	4.24872i	0.0515877	+	0.192528i	−0.935323	+	0.353795i	$0.884891\pi$
$488$	−0.768459	−	8.78353i	−0.0347865	−	0.397612i
$489$	−8.19072	−	2.98118i	−0.370397	−	0.134814i
$490$	1.66103	+	15.5550i	0.0750379	+	0.702705i
$491$	−29.5016	+	24.7548i	−1.33139	+	1.11717i	−0.347640	+	0.937628i	$0.613017\pi$
$491$	−29.5016	+	24.7548i	−1.33139	+	1.11717i	−0.983750	+	0.179541i	$0.942539\pi$
$492$	6.63022	−	9.46893i	0.298913	−	0.426892i
$493$	−4.51220	−	4.51220i	−0.203219	−	0.203219i
$494$	−3.39119	−	11.4752i	−0.152577	−	0.516294i
$495$	−3.74776	+	2.26036i	−0.168449	+	0.101596i
$496$	1.05461	−	0.185957i	0.0473535	−	0.00834971i
$497$	−0.0864892	+	0.988576i	−0.00387957	+	0.0443437i
$498$	−1.48122	+	3.17649i	−0.0663751	+	0.142342i
$499$	10.5253	−	28.9182i	0.471179	−	1.29455i	−0.445626	−	0.895219i	$-0.647019\pi$
$499$	10.5253	−	28.9182i	0.471179	−	1.29455i	0.916805	−	0.399335i	$-0.130759\pi$
$500$	6.68391	−	8.96244i	0.298914	−	0.400813i
$501$	−10.1760	+	17.6254i	−0.454632	+	0.787445i
$502$	−21.4272	−	5.74139i	−0.956341	−	0.256251i
$503$	−5.58023	−	7.96939i	−0.248810	−	0.355338i	0.675247	−	0.737591i	$-0.264037\pi$
$503$	−5.58023	−	7.96939i	−0.248810	−	0.355338i	−0.924057	+	0.382254i	$0.875148\pi$
$504$	0.0110150	−	0.0624690i	0.000490646	−	0.00278259i
$505$	−2.15748	+	3.90749i	−0.0960066	+	0.173881i
$506$	5.98940	+	3.45798i	0.266262	+	0.153726i
$507$	−5.44338	+	0.476234i	−0.241749	+	0.0211503i
$508$	−5.75843	−	12.3490i	−0.255489	−	0.547898i
$509$	11.5695	−	4.21094i	0.512808	−	0.186647i	−0.0726379	−	0.997358i	$-0.523142\pi$
$509$	11.5695	−	4.21094i	0.512808	−	0.186647i	0.585446	+	0.810712i	$0.300920\pi$
$510$	−0.891403	−	1.81997i	−0.0394720	−	0.0805895i
$511$	0.0578354	+	0.328001i	0.00255849	+	0.0145099i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.71802	−	2.27516i	0.164154	−	0.100451i
$514$		−	14.3003i		−	0.630759i
$515$	16.9102	+	1.15425i	0.745154	+	0.0508624i
$516$	5.73698	+	6.83707i	0.252556	+	0.300985i
$517$	−10.4438	−	4.87004i	−0.459319	−	0.214184i
$518$	−0.462585	+	0.215707i	−0.0203248	+	0.00947762i
$519$	1.08364	−	1.29144i	0.0475667	−	0.0566878i
$520$	−0.117325	−	6.13721i	−0.00514505	−	0.269135i
$521$	15.1379	−	8.73986i	0.663203	−	0.382900i	−0.130293	−	0.991475i	$-0.541592\pi$
$521$	15.1379	−	8.73986i	0.663203	−	0.382900i	0.793496	+	0.608575i	$0.208259\pi$
$522$	5.76763	−	4.03854i	0.252442	−	0.176762i
$523$	26.4596	−	18.5272i	1.15700	−	0.810139i	0.172410	−	0.985025i	$-0.444845\pi$
$523$	26.4596	−	18.5272i	1.15700	−	0.810139i	0.984589	+	0.174886i	$0.0559556\pi$
$524$	1.41382	−	0.816271i	0.0617632	−	0.0356590i
$525$	0.268410	−	0.168964i	0.0117144	−	0.00737419i
$526$	15.2154	−	18.1330i	0.663422	−	0.790635i
$527$	0.879606	−	0.410167i	0.0383162	−	0.0178672i
$528$	1.77391	+	0.827187i	0.0771995	+	0.0359987i
$529$	6.75880	+	8.05482i	0.293861	+	0.350210i
$530$	7.31720	−	6.38212i	0.317839	−	0.277222i
$531$		−	1.76505i		−	0.0765968i
$532$	−0.273434	−	0.0410424i	−0.0118549	−	0.00177941i
$533$	22.4382	−	22.4382i	0.971904	−	0.971904i
$534$	−1.83160	−	10.3875i	−0.0792610	−	0.449512i
$535$	34.9656	−	17.1258i	1.51169	−	0.740413i
$536$	0.988896	−	0.359929i	0.0427138	−	0.0155465i
$537$	8.84649	+	18.9714i	0.381754	+	0.818674i
$538$	−19.7938	+	1.73174i	−0.853373	+	0.0746605i
$539$	−11.8586	−	6.84658i	−0.510787	−	0.294903i
$540$	2.14842	−	0.619914i	0.0924533	−	0.0266769i
$541$	5.77074	−	32.7275i	0.248104	−	1.40707i	−0.565069	−	0.825043i	$-0.691151\pi$
$541$	5.77074	−	32.7275i	0.248104	−	1.40707i	0.813173	−	0.582022i	$-0.197738\pi$
$542$	10.7960	+	15.4183i	0.463729	+	0.662273i
$543$	−7.34658	−	1.96851i	−0.315272	−	0.0844768i
$544$	−0.453149	+	0.784877i	−0.0194286	+	0.0336513i
$545$	−1.56196	+	9.96899i	−0.0669070	+	0.427025i
$546$	0.0595567	−	0.163631i	0.00254879	−	0.00700275i
$547$	−11.1617	+	23.9364i	−0.477241	+	1.02345i	0.509399	+	0.860530i	$0.329868\pi$
$547$	−11.1617	+	23.9364i	−0.477241	+	1.02345i	−0.986640	+	0.162916i	$0.947910\pi$
$548$	−0.878323	+	10.0393i	−0.0375201	+	0.428857i
$549$	8.68313	−	1.53107i	0.370587	−	0.0653445i
$550$	2.89237	+	9.34928i	0.123331	+	0.398655i
$551$	−18.2400	−	24.6827i	−0.777050	−	1.05152i
$552$	−2.49852	−	2.49852i	−0.106344	−	0.106344i
$553$	0.0833398	−	0.119022i	0.00354397	−	0.00506131i
$554$	17.5361	−	14.7145i	0.745038	−	0.625161i
$555$	−14.0015	−	11.2997i	−0.594329	−	0.479645i
$556$	10.9791	+	3.99608i	0.465619	+	0.169471i
$557$	1.89997	+	21.7167i	0.0805042	+	0.920168i	0.923840	+	0.382780i	$0.125033\pi$
$557$	1.89997	+	21.7167i	0.0805042	+	0.920168i	−0.843335	+	0.537388i	$0.819411\pi$
$558$	0.277165	+	1.03439i	0.0117333	+	0.0437893i
$559$	12.2504	+	21.2184i	0.518138	+	0.897442i
$560$	−0.129673	−	0.0574761i	−0.00547968	−	0.00242881i
$561$	1.74694	+	0.308033i	0.0737558	+	0.0130051i
$562$	−0.0667833	+	0.249239i	−0.00281708	+	0.0105135i
$563$	−25.5063	+	6.83440i	−1.07496	+	0.288036i	−0.752531	−	0.658557i	$-0.771167\pi$
$563$	−25.5063	+	6.83440i	−1.07496	+	0.288036i	−0.322432	+	0.946593i	$0.604500\pi$
$564$	4.51006	+	3.78439i	0.189908	+	0.159352i
$565$	−5.86979	+	8.73359i	−0.246944	+	0.367425i
$566$	−3.45085	−	9.48112i	−0.145050	−	0.398521i
$567$	0.0631913	+	0.00552853i	0.00265379	+	0.000232176i
$568$	12.8150	+	8.97313i	0.537704	+	0.376504i
$569$	−26.9704			−1.13066			−0.565330	−	0.824865i	$-0.691251\pi$
$569$	−26.9704			−1.13066			−0.565330	+	0.824865i	$0.691251\pi$
$570$	−2.94046	−	9.29267i	−0.123162	−	0.389227i
$571$	10.9427			0.457937			0.228968	−	0.973434i	$-0.426465\pi$
$571$	10.9427			0.457937			0.228968	+	0.973434i	$0.426465\pi$
$572$	4.40135	+	3.08186i	0.184030	+	0.128859i
$573$	−6.77141	−	0.592421i	−0.282880	−	0.0247488i
$574$	−0.250785	−	0.689026i	−0.0104676	−	0.0287594i
$575$	0.866001	−	17.6459i	0.0361147	−	0.735887i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−28.1995	+	7.55604i	−1.17396	+	0.314562i	−0.792529	−	0.609835i	$-0.791236\pi$
$577$	−28.1995	+	7.55604i	−1.17396	+	0.314562i	−0.381433	+	0.924397i	$0.624569\pi$
$578$	4.18734	−	15.6274i	0.174170	−	0.650012i
$579$	−21.8918	−	3.86011i	−0.909792	−	0.160421i
$580$	−5.66660	−	14.6890i	−0.235293	−	0.609927i
$581$	0.111162	+	0.192538i	0.00461176	+	0.00798780i
$582$	−1.44110	−	5.37824i	−0.0597353	−	0.222935i
$583$	0.740730	+	8.46659i	0.0306779	+	0.350650i
$584$	4.93397	+	1.79582i	0.204169	+	0.0743114i
$585$	6.10363	−	0.651772i	0.252354	−	0.0269475i
$586$	−17.1059	+	14.3535i	−0.706636	+	0.592938i
$587$	−0.957570	+	1.36755i	−0.0395232	+	0.0564449i	−0.838427	−	0.545013i	$-0.816525\pi$
$587$	−0.957570	+	1.36755i	−0.0395232	+	0.0564449i	0.798904	+	0.601458i	$0.205413\pi$
$588$	4.94690	+	4.94690i	0.204007	+	0.204007i
$589$	4.47648	−	1.32290i	0.184450	−	0.0545093i
$590$	−3.83112	−	0.948449i	−0.157725	−	0.0390470i
$591$	11.5101	−	2.02954i	0.473461	−	0.0834839i
$592$	−0.701291	+	8.01580i	−0.0288229	+	0.329447i
$593$	1.15320	−	2.47305i	0.0473563	−	0.101556i	−0.881206	−	0.472732i	$-0.843268\pi$
$593$	1.15320	−	2.47305i	0.0473563	−	0.101556i	0.928562	+	0.371176i	$0.121046\pi$
$594$	−0.669433	+	1.83925i	−0.0274672	+	0.0754655i
$595$	−0.127000	−	0.0198985i	−0.00520648	−	0.000815761i
$596$	−2.30627	+	3.99457i	−0.0944684	+	0.163624i
$597$	−2.99027	−	0.801241i	−0.122384	−	0.0327926i
$598$	−5.56358	−	7.94562i	−0.227512	−	0.324920i
$599$	−1.03310	+	5.85903i	−0.0422115	+	0.239393i	−0.998612	−	0.0526641i	$-0.983229\pi$
$599$	−1.03310	+	5.85903i	−0.0422115	+	0.239393i	0.956401	+	0.292057i	$0.0943399\pi$
$600$	−0.191100	−	4.99635i	−0.00780163	−	0.203975i
$601$	−32.7171	−	18.8892i	−1.33456	−	0.770508i	−0.348564	−	0.937285i	$-0.613331\pi$
$601$	−32.7171	−	18.8892i	−1.33456	−	0.770508i	−0.985995	+	0.166777i	$0.946664\pi$
$602$	0.563993	−	0.0493430i	0.0229866	−	0.00201107i
$603$	0.444747	+	0.953763i	0.0181115	+	0.0388402i
$604$	−9.37605	+	3.41260i	−0.381506	+	0.138857i
$605$	15.1657	+	5.19380i	0.616573	+	0.211158i
$606$	0.346629	+	1.96583i	0.0140808	+	0.0798564i
$607$	6.98489	−	6.98489i	0.283508	−	0.283508i	−0.550998	−	0.834506i	$-0.685753\pi$
$607$	6.98489	−	6.98489i	0.283508	−	0.283508i	0.834506	+	0.550998i	$0.185753\pi$
$608$	−2.71564	+	3.40959i	−0.110134	+	0.138277i
$609$		−	0.446628i		−	0.0180983i
$610$	1.34261	−	19.6698i	0.0543608	−	0.796408i
$611$	10.3887	+	12.3808i	0.420282	+	0.500873i
$612$	−0.821384	−	0.383018i	−0.0332025	−	0.0154826i
$613$	9.45941	−	4.41100i	0.382062	−	0.178158i	−0.222093	−	0.975026i	$-0.571289\pi$
$613$	9.45941	−	4.41100i	0.382062	−	0.178158i	0.604155	+	0.796867i	$0.293511\pi$
$614$	11.9826	−	14.2803i	0.483579	−	0.576307i
$615$	17.9244	−	18.6231i	0.722781	−	0.750955i
$616$	0.107523	−	0.0620782i	0.00433221	−	0.00250120i
$617$	−6.38710	+	4.47230i	−0.257135	+	0.180048i	−0.695035	−	0.718976i	$-0.744611\pi$
$617$	−6.38710	+	4.47230i	−0.257135	+	0.180048i	0.437900	+	0.899024i	$0.355722\pi$
$618$	6.20924	−	4.34776i	0.249772	−	0.174892i
$619$	−5.02706	+	2.90237i	−0.202055	+	0.116656i	−0.597613	−	0.801784i	$-0.703884\pi$
$619$	−5.02706	+	2.90237i	−0.202055	+	0.116656i	0.395559	+	0.918441i	$0.370551\pi$
$620$	2.39413	−	0.0457686i	0.0961505	−	0.00183811i
$621$	2.27125	−	2.70677i	0.0911421	−	0.108619i
$622$	3.53269	−	1.64732i	0.141648	−	0.0660516i
$623$	−0.606386	−	0.282762i	−0.0242943	−	0.0113286i
$624$	−1.76455	−	2.10290i	−0.0706384	−	0.0841836i
$625$	17.8677	−	17.4856i	0.714708	−	0.699423i
$626$			31.3206i			1.25182i
$627$	8.08903	+	2.71226i	0.323045	+	0.108317i
$628$	−3.81627	+	3.81627i	−0.152286	+	0.152286i
$629$	1.26632	+	7.18166i	0.0504915	+	0.286351i
$630$	0.0459557	−	0.134189i	0.00183092	−	0.00534621i
$631$	19.6267	−	7.14353i	0.781326	−	0.284379i	0.0796005	−	0.996827i	$-0.474636\pi$
$631$	19.6267	−	7.14353i	0.781326	−	0.284379i	0.701726	+	0.712447i	$0.252413\pi$
$632$	−0.968046	−	2.07598i	−0.0385068	−	0.0825781i
$633$	−16.7548	+	1.46585i	−0.665942	+	0.0582624i
$634$	−10.9158	−	6.30222i	−0.433520	−	0.250293i
$635$	−8.44670	−	29.2735i	−0.335197	−	1.16168i
$636$	0.754013	−	4.27622i	0.0298985	−	0.169563i
$637$	11.0155	+	15.7318i	0.436451	+	0.623317i
$638$	13.3117	+	3.56685i	0.527014	+	0.141213i
$639$	−7.82209	+	13.5482i	−0.309437	+	0.535960i
$640$	−1.80683	+	1.31733i	−0.0714213	+	0.0520721i
$641$	−11.8611	+	32.5881i	−0.468485	+	1.28715i	0.450470	+	0.892791i	$0.351256\pi$
$641$	−11.8611	+	32.5881i	−0.468485	+	1.28715i	−0.918956	+	0.394361i	$0.870966\pi$
$642$	7.35862	−	15.7806i	0.290421	−	0.622811i
$643$	2.67675	−	30.5954i	0.105561	−	1.20657i	−0.739970	−	0.672639i	$-0.765161\pi$
$643$	2.67675	−	30.5954i	0.105561	−	1.20657i	0.845531	−	0.533926i	$-0.179284\pi$
$644$	−0.220730	+	0.0389207i	−0.00869800	+	0.00153369i
$645$	10.3072	+	17.0896i	0.405844	+	0.672903i
$646$	−1.57754	+	3.62181i	−0.0620675	+	0.142498i
$647$	25.1774	+	25.1774i	0.989825	+	0.989825i	0.999949	−	0.0101236i	$-0.00322249\pi$
$647$	25.1774	+	25.1774i	0.989825	+	0.989825i	−0.0101236	+	0.999949i	$0.503222\pi$
$648$	0.573576	−	0.819152i	0.0225322	−	0.0321793i
$649$	2.64647	−	2.22065i	0.103883	−	0.0871683i
$650$	1.86508	−	13.5984i	0.0731544	−	0.533374i
$651$	0.0638324	+	0.0232331i	0.00250179	+	0.000910576i
$652$	0.759683	+	8.68321i	0.0297515	+	0.340061i
$653$	10.1462	+	37.8662i	0.397052	+	1.48182i	0.818257	+	0.574852i	$0.194940\pi$
$653$	10.1462	+	37.8662i	0.397052	+	1.48182i	−0.421206	+	0.906965i	$0.638393\pi$
$654$	2.25633	+	3.90808i	0.0882295	+	0.152818i
$655$	3.40584	−	1.31387i	0.133077	−	0.0513373i
$656$	−11.3838	−	2.00727i	−0.444463	−	0.0783709i
$657$	−1.35896	+	5.07171i	−0.0530181	+	0.197866i
$658$	0.360733	−	0.0966581i	0.0140628	−	0.00376812i
$659$	−1.20050	−	1.00734i	−0.0467647	−	0.0392402i	0.619106	−	0.785308i	$-0.287495\pi$
$659$	−1.20050	−	1.00734i	−0.0467647	−	0.0392402i	−0.665870	+	0.746067i	$0.731940\pi$
$660$	3.63246	+	2.44135i	0.141393	+	0.0950295i
$661$	−1.39745	−	3.83947i	−0.0543547	−	0.149338i	0.909544	−	0.415608i	$-0.136431\pi$
$661$	−1.39745	−	3.83947i	−0.0543547	−	0.149338i	−0.963899	+	0.266270i	$0.914209\pi$
$662$	−19.4427	−	1.70101i	−0.755662	−	0.0661118i
$663$	−2.03798	−	1.42701i	−0.0791488	−	0.0554206i
$664$	3.50487			0.136015
$665$	−0.589841	−	0.185311i	−0.0228731	−	0.00718604i
$666$	−8.04641			−0.311792
$667$	−20.3796	−	14.2699i	−0.789100	−	0.552534i
$668$	20.2746	+	1.77380i	0.784449	+	0.0686304i
$669$	−6.01644	−	16.5300i	−0.232609	−	0.639089i
$670$	2.30917	−	0.452839i	0.0892109	−	0.0174947i
$671$	13.2201	+	11.0930i	0.510356	+	0.428239i
$672$	−0.0612713	+	0.0164176i	−0.00236359	+	0.000633323i
$673$	−10.5127	+	39.2339i	−0.405234	+	1.51235i	0.398390	+	0.917216i	$0.369569\pi$
$673$	−10.5127	+	39.2339i	−0.405234	+	1.51235i	−0.803624	+	0.595138i	$0.797097\pi$
$674$	15.2227	+	2.68416i	0.586355	+	0.103390i
$675$	4.96068	−	0.625833i	0.190937	−	0.0240883i
$676$	2.73208	+	4.73211i	0.105080	+	0.182004i
$677$	−5.63840	−	21.0428i	−0.216701	−	0.808740i	−0.985561	−	0.169322i	$-0.945842\pi$
$677$	−5.63840	−	21.0428i	−0.216701	−	0.808740i	0.768860	−	0.639418i	$-0.220825\pi$
$678$	0.410151	+	4.68805i	0.0157518	+	0.180043i
$679$	−0.331891	−	0.120799i	−0.0127368	−	0.00463582i
$680$	−1.27273	+	1.57704i	−0.0488068	+	0.0604766i
$681$	1.61467	−	1.35487i	0.0618744	−	0.0519188i
$682$	−1.20223	+	1.71697i	−0.0460359	+	0.0657461i
$683$	−23.9160	−	23.9160i	−0.915118	−	0.915118i	0.0815507	−	0.996669i	$-0.474013\pi$
$683$	−23.9160	−	23.9160i	−0.915118	−	0.915118i	−0.996669	+	0.0815507i	$0.974013\pi$
$684$	−3.63330	−	2.40814i	−0.138923	−	0.0920777i
$685$	−5.41520	+	21.8739i	−0.206904	+	0.835760i
$686$	0.874315	−	0.154165i	0.0333815	−	0.00588606i
$687$	−1.52837	+	17.4694i	−0.0583110	+	0.666498i
$688$	3.77193	−	8.08894i	0.143804	−	0.308388i
$689$	4.07686	−	11.2011i	0.155316	−	0.426727i
$690$	−4.65471	−	6.38432i	−0.177202	−	0.243047i
$691$	6.56856	−	11.3771i	0.249880	−	0.432804i	−0.713613	−	0.700541i	$-0.752942\pi$
$691$	6.56856	−	11.3771i	0.249880	−	0.432804i	0.963492	+	0.267736i	$0.0862756\pi$
$692$	−1.62841	−	0.436330i	−0.0619027	−	0.0165868i
$693$	0.0712132	+	0.101703i	0.00270516	+	0.00386338i
$694$	−1.26947	+	7.19952i	−0.0481884	+	0.273290i
$695$	22.8710	+	12.6280i	0.867548	+	0.479007i
$696$	−6.09767	−	3.52049i	−0.231131	−	0.133444i
$697$	−10.4364	+	0.913068i	−0.395308	+	0.0345849i
$698$	−10.3347	−	22.1629i	−0.391176	−	0.838879i
$699$	−3.44470	+	1.25377i	−0.130290	+	0.0474218i
$700$	−0.266568	−	0.171855i	−0.0100753	−	0.00649550i
$701$	5.98161	+	33.9234i	0.225922	+	1.28127i	0.860914	+	0.508750i	$0.169892\pi$
$701$	5.98161	+	33.9234i	0.225922	+	1.28127i	−0.634992	+	0.772519i	$0.718997\pi$
$702$	1.94111	−	1.94111i	0.0732626	−	0.0732626i
$703$	0.895860	+	35.0621i	0.0337880	+	1.32239i
$704$		−	1.95729i		−	0.0737682i
$705$	8.65337	+	9.92122i	0.325905	+	0.373655i
$706$	−22.8555	−	27.2382i	−0.860180	−	1.02512i
$707$	0.114758	+	0.0535126i	0.00431593	+	0.00201255i
$708$	−1.59968	+	0.745944i	−0.0601197	+	0.0280343i
$709$	−21.1784	+	25.2395i	−0.795373	+	0.947888i	−0.999518	−	0.0310523i	$-0.990114\pi$
$709$	−21.1784	+	25.2395i	−0.795373	+	0.947888i	0.204145	+	0.978941i	$0.434559\pi$
$710$	25.2039	+	24.2583i	0.945884	+	0.910398i
$711$	1.98371	−	1.14530i	0.0743950	−	0.0429519i
$712$	−8.64022	+	6.04994i	−0.323806	+	0.226731i
$713$	3.09959	−	2.17035i	0.116080	−	0.0812804i
$714$	−0.0497869	+	0.0287445i	−0.00186323	+	0.00107573i
$715$	8.65637	+	8.33161i	0.323730	+	0.311585i
$716$	13.4552	−	16.0353i	0.502844	−	0.599267i
$717$	3.64645	−	1.70037i	0.136179	−	0.0635014i
$718$	2.49441	+	1.16316i	0.0930906	+	0.0434088i
$719$	32.5165	+	38.7516i	1.21266	+	1.44519i	0.860651	+	0.509196i	$0.170057\pi$
$719$	32.5165	+	38.7516i	1.21266	+	1.44519i	0.352009	+	0.935996i	$0.385499\pi$
$720$	−1.46979	−	1.68514i	−0.0547760	−	0.0628015i
$721$		−	0.480825i		−	0.0179069i
$722$	−10.0889	+	16.1001i	−0.375471	+	0.599184i
$723$	1.91023	−	1.91023i	0.0710423	−	0.0710423i
$724$	1.32072	+	7.49019i	0.0490842	+	0.278371i
$725$	−7.43389	−	34.4111i	−0.276088	−	1.27800i
$726$	6.73666	−	2.45195i	0.250021	−	0.0910002i
$727$	0.522821	+	1.12119i	0.0193904	+	0.0415827i	0.915764	−	0.401716i	$-0.131586\pi$
$727$	0.522821	+	1.12119i	0.0193904	+	0.0415827i	−0.896374	+	0.443298i	$0.853808\pi$
$728$	−0.173470	+	0.0151766i	−0.00642921	+	0.000562483i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	10.2781	+	5.67495i	0.380410	+	0.210039i
$731$	1.40461	−	7.96596i	0.0519515	−	0.294632i
$732$	−5.05727	−	7.22253i	−0.186922	−	0.266952i
$733$	−25.7844	−	6.90892i	−0.952370	−	0.255187i	−0.251002	−	0.967987i	$-0.580760\pi$
$733$	−25.7844	−	6.90892i	−0.952370	−	0.255187i	−0.701367	+	0.712800i	$0.747427\pi$
$734$	0.229334	−	0.397218i	0.00846488	−	0.0146616i
$735$	9.21602	+	12.6405i	0.339938	+	0.466254i
$736$	−1.20851	+	3.32035i	−0.0445462	+	0.122390i
$737$	−0.870500	+	1.86679i	−0.0320653	+	0.0687642i
$738$	1.00747	−	11.5154i	0.0370855	−	0.423889i
$739$	−30.3072	+	5.34398i	−1.11487	+	0.196581i	−0.700586	−	0.713568i	$-0.747078\pi$
$739$	−30.3072	+	5.34398i	−1.11487	+	0.196581i	−0.414281	+	0.910149i	$0.635967\pi$
$740$	−4.32373	+	17.4651i	−0.158943	+	0.642029i
$741$	−8.67447	−	8.24223i	−0.318665	−	0.302786i
$742$	−0.194763	−	0.194763i	−0.00714998	−	0.00714998i
$743$	−29.8626	+	42.6483i	−1.09555	+	1.56461i	−0.304864	+	0.952396i	$0.598611\pi$
$743$	−29.8626	+	42.6483i	−1.09555	+	1.56461i	−0.790690	+	0.612217i	$0.790278\pi$
$744$	0.820343	−	0.688350i	0.0300753	−	0.0252361i
$745$	−6.47745	+	8.02621i	−0.237315	+	0.294058i
$746$	29.3963	+	10.6994i	1.07628	+	0.391732i
$747$	0.305469	+	3.49153i	0.0111765	+	0.127748i
$748$	−0.459116	−	1.71344i	−0.0167869	−	0.0626497i
$749$	−0.552244	−	0.956515i	−0.0201786	−	0.0349503i
$750$	1.30722	−	11.1037i	0.0477327	−	0.405448i
$751$	36.1436	+	6.37310i	1.31890	+	0.232558i	0.788419	−	0.615139i	$-0.210900\pi$
$751$	36.1436	+	6.37310i	1.31890	+	0.232558i	0.530481	+	0.847697i	$0.322011\pi$
$752$	1.52379	−	5.68686i	0.0555669	−	0.207378i
$753$	−21.4272	+	5.74139i	−0.780849	+	0.209228i
$754$	−14.8065	−	12.4241i	−0.539221	−	0.452460i
$755$	−21.8940	+	4.29352i	−0.796803	+	0.156257i
$756$	−0.0216953	−	0.0596073i	−0.000789049	−	0.00216790i
$757$	45.2590	+	3.95965i	1.64497	+	0.143916i	0.871658	−	0.490114i	$-0.163045\pi$
$757$	45.2590	+	3.95965i	1.64497	+	0.143916i	0.773309	+	0.634030i	$0.218600\pi$
$758$	−28.0253	−	19.6235i	−1.01792	−	0.712758i
$759$	6.91597			0.251034
$760$	−7.17933	+	6.59221i	−0.260422	+	0.239125i
$761$	44.3283			1.60690			0.803450	−	0.595373i	$-0.202996\pi$
$761$	44.3283			1.60690			0.803450	+	0.595373i	$0.202996\pi$
$762$	−11.1614	−	7.81532i	−0.404336	−	0.283119i
$763$	0.285161	+	0.0249484i	0.0103235	+	0.000903191i
$764$	2.32480	+	6.38735i	0.0841085	+	0.231086i
$765$	−1.68196	−	1.13044i	−0.0608114	−	0.0408710i
$766$	15.8883	+	13.3318i	0.574066	+	0.481699i
$767$	−4.68023	+	1.25406i	−0.168993	+	0.0452816i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	43.2793	+	7.63130i	1.56069	+	0.275192i	0.886274	−	0.463160i	$-0.153285\pi$
$769$	43.2793	+	7.63130i	1.56069	+	0.275192i	0.674415	+	0.738352i	$0.264396\pi$
$770$	0.259017	−	0.0999213i	0.00933432	−	0.00360091i
$771$	−7.15015	−	12.3844i	−0.257506	−	0.446014i
$772$	5.75342	+	21.4721i	0.207070	+	0.772796i
$773$	0.792105	+	9.05380i	0.0284900	+	0.325643i	0.997044	+	0.0768376i	$0.0244823\pi$
$773$	0.792105	+	9.05380i	0.0284900	+	0.325643i	−0.968554	+	0.248805i	$0.919962\pi$
$774$	8.38690	+	3.05258i	0.301461	+	0.109723i
$775$	5.30475	+	0.727568i	0.190552	+	0.0261350i
$776$	−4.26531	+	3.57902i	−0.153116	+	0.128479i
$777$	−0.292757	+	0.418100i	−0.0105026	+	0.0149993i
$778$	13.3700	+	13.3700i	0.479338	+	0.479338i
$779$	−50.2905	−	3.10794i	−1.80184	−	0.111354i
$780$	−3.17021	−	5.25632i	−0.113512	−	0.188206i
$781$	−30.1550	+	5.31714i	−1.07903	+	0.190262i
$782$	−0.279103	+	3.19016i	−0.00998069	+	0.114080i
$783$	2.97565	−	6.38129i	0.106341	−	0.228049i
$784$	2.39276	−	6.57407i	0.0854559	−	0.234788i
$785$	−9.75151	+	7.10967i	−0.348046	+	0.253755i
$786$	0.816271	−	1.41382i	0.0291154	−	0.0504294i
$787$	−18.8784	−	5.05845i	−0.672942	−	0.180314i	−0.0938625	−	0.995585i	$-0.529921\pi$
$787$	−18.8784	−	5.05845i	−0.672942	−	0.180314i	−0.579080	+	0.815271i	$0.696588\pi$
$788$	−6.70375	−	9.57394i	−0.238811	−	0.341058i
$789$	4.11041	−	23.3113i	0.146334	−	0.829904i
$790$	−1.41997	−	4.92115i	−0.0505203	−	0.175087i
$791$	0.258519	+	0.149256i	0.00919186	+	0.00530692i
$792$	1.94984	−	0.170589i	0.0692847	−	0.00606162i
$793$	−10.2291	−	21.9364i	−0.363247	−	0.778986i
$794$	5.06762	−	1.84446i	0.179843	−	0.0654576i
$795$	3.14582	−	9.18568i	0.111571	−	0.325782i
$796$	0.537573	+	3.04873i	0.0190538	+	0.108059i
$797$	−2.81973	+	2.81973i	−0.0998800	+	0.0998800i	−0.755281	−	0.655401i	$-0.772500\pi$
$797$	−2.81973	+	2.81973i	−0.0998800	+	0.0998800i	0.655401	+	0.755281i	$0.272500\pi$
$798$	−0.257322	+	0.101173i	−0.00910909	+	0.00358149i
$799$		−	5.33580i		−	0.188767i
$800$	−4.44747	+	2.28474i	−0.157242	+	0.0807779i
$801$	−6.77997	−	8.08005i	−0.239558	−	0.285495i
$802$	17.9723	+	8.38064i	0.634626	+	0.295931i
$803$	−9.31412	+	4.34324i	−0.328688	+	0.153270i
$804$	0.676445	−	0.806155i	0.0238564	−	0.0284309i
$805$	−0.501091	+	0.00957935i	−0.0176611	+	0.000337628i
$806$	2.54588	−	1.46986i	0.0896748	−	0.0517738i
$807$	−16.2761	+	11.3966i	−0.572946	+	0.401181i
$808$	1.63516	−	1.14495i	0.0575246	−	0.0402792i
$809$	−19.9641	+	11.5263i	−0.701902	+	0.405243i	−0.808055	−	0.589107i	$-0.799480\pi$
$809$	−19.9641	+	11.5263i	−0.701902	+	0.405243i	0.106154	+	0.994350i	$0.466146\pi$
$810$	1.55063	−	1.61107i	0.0544835	−	0.0566073i
$811$	5.48905	−	6.54159i	0.192746	−	0.229706i	−0.661012	−	0.750375i	$-0.729873\pi$
$811$	5.48905	−	6.54159i	0.192746	−	0.229706i	0.853759	+	0.520669i	$0.174317\pi$
$812$	−0.404783	+	0.188753i	−0.0142051	+	0.00662394i
$813$	17.0588	+	7.95464i	0.598277	+	0.278981i
$814$	−10.1234	−	12.0646i	−0.354824	−	0.422863i
$815$	−1.32728	+	19.4452i	−0.0464926	+	0.681135i
$816$			0.906297i			0.0317268i
$817$	12.3678	−	36.8856i	0.432694	−	1.29046i
$818$	−26.6926	+	26.6926i	−0.933287	+	0.933287i
$819$	−0.0302377	−	0.171487i	−0.00105659	−	0.00599223i
$820$	−24.4534	−	8.37457i	−0.853950	−	0.292453i
$821$	−35.5693	+	12.9462i	−1.24138	+	0.451824i	−0.877479	−	0.479615i	$-0.840776\pi$
$821$	−35.5693	+	12.9462i	−1.24138	+	0.451824i	−0.363898	+	0.931439i	$0.618554\pi$
$822$	4.25899	+	9.13343i	0.148549	+	0.318565i
$823$	−2.51293	+	0.219853i	−0.0875954	+	0.00766360i	−0.130869	−	0.991400i	$-0.541777\pi$
$823$	−2.51293	+	0.219853i	−0.0875954	+	0.00766360i	0.0432738	+	0.999063i	$0.486221\pi$
$824$	−6.56455	−	3.79004i	−0.228687	−	0.132032i
$825$	7.17950	+	6.65053i	0.249958	+	0.231542i
$826$	−0.0194420	+	0.110261i	−0.000676475	+	0.00383648i
$827$	30.7836	+	43.9635i	1.07045	+	1.52876i	0.829730	+	0.558165i	$0.188494\pi$
$827$	30.7836	+	43.9635i	1.07045	+	1.52876i	0.240719	+	0.970595i	$0.422617\pi$
$828$	−3.41304	−	0.914521i	−0.118611	−	0.0317818i
$829$	4.17533	−	7.23188i	0.145015	−	0.251174i	−0.784363	−	0.620301i	$-0.787010\pi$
$829$	4.17533	−	7.23188i	0.145015	−	0.251174i	0.929379	+	0.369128i	$0.120344\pi$
$830$	7.74266	+	1.21313i	0.268752	+	0.0421085i
$831$	7.82944	−	21.5112i	0.271600	−	0.746216i
$832$	−1.16015	+	2.48795i	−0.0402209	+	0.0862541i
$833$	0.552605	−	6.31631i	0.0191466	−	0.218847i
$834$	11.5062	−	2.02886i	0.398429	−	0.0702538i
$835$	44.1750	+	10.9362i	1.52874	+	0.378461i
$836$	−0.960427	−	8.47741i	−0.0332171	−	0.293197i
$837$	0.757228	+	0.757228i	0.0261736	+	0.0261736i
$838$	−2.52702	+	3.60896i	−0.0872944	+	0.124669i
$839$	−33.8250	+	28.3825i	−1.16777	+	0.979874i	−0.999982	−	0.00594987i	$-0.998106\pi$
$839$	−33.8250	+	28.3825i	−1.16777	+	0.979874i	−0.167786	+	0.985824i	$0.553662\pi$
$840$	−0.141038	+	0.0150606i	−0.00486627	+	0.000519642i
$841$	−19.3345	−	7.03719i	−0.666708	−	0.242662i
$842$	2.36039	+	26.9794i	0.0813444	+	0.929771i
$843$	0.0667833	+	0.249239i	0.00230014	+	0.00858424i
$844$	8.40938	+	14.5655i	0.289463	+	0.501364i
$845$	4.39757	+	11.3994i	0.151281	+	0.392152i
$846$	5.79803	+	1.02235i	0.199340	+	0.0351491i
$847$	0.117698	−	0.439255i	0.00404415	−	0.0150930i
$848$	−4.19423	+	1.12384i	−0.144030	+	0.0385928i
$849$	−7.72908	−	6.48547i	−0.265261	−	0.222581i
$850$	−3.35746	+	3.04333i	−0.115160	+	0.104385i
$851$	9.72415	+	26.7169i	0.333339	+	0.915843i
$852$	15.5846	+	1.36348i	0.533921	+	0.0467120i
$853$	10.5661	+	7.39843i	0.361775	+	0.253317i	0.740305	−	0.672272i	$-0.234681\pi$
$853$	10.5661	+	7.39843i	0.361775	+	0.253317i	−0.378530	+	0.925589i	$0.623570\pi$
$854$	−0.559292			−0.0191386
$855$	−7.19285	−	6.57746i	−0.245990	−	0.224944i
$856$	−17.4120			−0.595129
$857$	−9.74959	−	6.82674i	−0.333040	−	0.233197i	0.395080	−	0.918647i	$-0.370717\pi$
$857$	−9.74959	−	6.82674i	−0.333040	−	0.233197i	−0.728120	+	0.685450i	$0.759606\pi$
$858$	5.35261	+	0.468293i	0.182735	+	0.0159872i
$859$	−15.5384	−	42.6913i	−0.530162	−	1.45661i	−0.858878	−	0.512180i	$-0.828838\pi$
$859$	−15.5384	−	42.6913i	−0.530162	−	1.45661i	0.328716	−	0.944429i	$-0.393384\pi$
$860$	11.1325	−	16.5638i	0.379614	−	0.564822i
$861$	−0.561699	−	0.471322i	−0.0191427	−	0.0160626i
$862$	1.26961	−	0.340191i	0.0432431	−	0.0115870i
$863$	11.4140	−	42.5976i	0.388537	−	1.45004i	−0.443979	−	0.896037i	$-0.646434\pi$
$863$	11.4140	−	42.5976i	0.388537	−	1.45004i	0.832516	−	0.554001i	$-0.186900\pi$
$864$	−0.984808	−	0.173648i	−0.0335038	−	0.00590763i
$865$	−3.44631	−	1.52754i	−0.117178	−	0.0519380i
$866$	−2.77903	−	4.81343i	−0.0944354	−	0.163567i
$867$	−4.18734	−	15.6274i	−0.142209	−	0.530733i
$868$	−0.00592040	−	0.0676705i	−0.000200952	−	0.00229689i
$869$	4.21298	+	1.53340i	0.142915	+	0.0520170i
$870$	−12.2519	−	9.88775i	−0.415379	−	0.335226i
$871$	2.21301	−	1.85694i	0.0749851	−	0.0629200i
$872$	2.58836	−	3.69656i	0.0876528	−	0.125181i
$873$	−3.93715	−	3.93715i	−0.133252	−	0.133252i
$874$	−3.60501	+	14.9741i	−0.121941	+	0.506505i
$875$	−0.529397	−	0.471914i	−0.0178969	−	0.0159536i
$876$	5.17085	−	0.911760i	0.174707	−	0.0308055i
$877$	−1.45162	+	16.5921i	−0.0490176	+	0.560274i	0.931487	+	0.363776i	$0.118513\pi$
$877$	−1.45162	+	16.5921i	−0.0490176	+	0.560274i	−0.980504	+	0.196498i	$0.937043\pi$
$878$	9.52968	−	20.4365i	0.321611	−	0.689697i
$879$	−7.63735	+	20.9834i	−0.257601	+	0.707754i
$880$	0.677474	−	4.32389i	0.0228377	−	0.145758i
$881$	6.98155	−	12.0924i	0.235214	−	0.407403i	−0.724121	−	0.689673i	$-0.757754\pi$
$881$	6.98155	−	12.0924i	0.235214	−	0.407403i	0.959335	+	0.282270i	$0.0910875\pi$
$882$	6.75759	+	1.81069i	0.227540	+	0.0609692i
$883$	5.79070	+	8.26997i	0.194872	+	0.278307i	0.904682	−	0.426087i	$-0.140108\pi$
$883$	5.79070	+	8.26997i	0.194872	+	0.278307i	−0.709810	+	0.704393i	$0.751219\pi$
$884$	−0.432023	+	2.45012i	−0.0145305	+	0.0824065i
$885$	−3.79208	+	1.09418i	−0.127469	+	0.0367805i
$886$	26.2141	+	15.1347i	0.880680	+	0.508461i
$887$	−3.06847	+	0.268456i	−0.103029	+	0.00901389i	−0.138554	−	0.990355i	$-0.544245\pi$
$887$	−3.06847	+	0.268456i	−0.103029	+	0.00901389i	0.0355245	+	0.999369i	$0.488690\pi$
$888$	3.40056	+	7.29253i	0.114115	+	0.244721i
$889$	−0.812185	+	0.295611i	−0.0272398	+	0.00991448i
$890$	−21.1813	+	10.3744i	−0.709999	+	0.347751i
$891$	0.339880	+	1.92756i	0.0113864	+	0.0645756i
$892$	−12.4387	+	12.4387i	−0.416477	+	0.416477i
$893$	3.80933	−	25.3786i	0.127474	−	0.849262i
$894$			4.61254i			0.154266i
$895$	35.2744	−	30.7666i	1.17909	−	1.02841i
$896$	0.0407738	+	0.0485923i	0.00136216	+	0.00162335i
$897$	−8.79101	−	4.09931i	−0.293523	−	0.136872i
$898$	−20.1196	+	9.38195i	−0.671401	+	0.313080i
$899$	4.84666	−	5.77602i	0.161645	−	0.192641i
$900$	−2.66367	−	4.23141i	−0.0887890	−	0.141047i
$901$	−3.40808	+	1.96766i	−0.113540	+	0.0655521i
$902$	18.5335	−	12.9773i	0.617097	−	0.432096i
$903$	0.463761	−	0.324729i	0.0154330	−	0.0108063i
$904$	4.07548	−	2.35298i	0.135548	−	0.0782589i
$905$	0.325062	+	17.0038i	0.0108054	+	0.565227i
$906$	−6.41359	+	7.64342i	−0.213077	+	0.253936i
$907$	11.2742	−	5.25724i	0.374353	−	0.174564i	−0.226330	−	0.974051i	$-0.572673\pi$
$907$	11.2742	−	5.25724i	0.374353	−	0.174564i	0.600684	+	0.799487i	$0.294895\pi$
$908$	−1.91032	−	0.890797i	−0.0633962	−	0.0295621i
$909$	1.28311	+	1.52915i	0.0425579	+	0.0507185i
$910$	−0.388467	−	0.0265158i	−0.0128776	−	0.000878991i
$911$			34.7964i			1.15286i	0.817148	+	0.576428i	$0.195554\pi$
$911$			34.7964i			1.15286i	−0.817148	+	0.576428i	$0.804446\pi$
$912$	−0.647023	+	4.31061i	−0.0214251	+	0.142739i
$913$	−4.85079	+	4.85079i	−0.160538	+	0.160538i
$914$	−0.666383	−	3.77924i	−0.0220420	−	0.125006i
$915$	−8.67218	−	17.7059i	−0.286693	−	0.585338i
$916$	16.4785	−	5.99770i	0.544466	−	0.198169i
$917$	−0.0437649	−	0.0938542i	−0.00144525	−	0.00309934i
$918$	−0.902849	+	0.0789890i	−0.0297984	+	0.00260703i
$919$	23.3985	+	13.5091i	0.771844	+	0.445624i	0.833532	−	0.552471i	$-0.186315\pi$
$919$	23.3985	+	13.5091i	0.771844	+	0.445624i	−0.0616883	+	0.998095i	$0.519648\pi$
$920$	−3.81900	+	6.91673i	−0.125909	+	0.228038i
$921$	3.23709	−	18.3584i	0.106666	−	0.604931i
$922$	10.9579	+	15.6495i	0.360879	+	0.515389i
$923$	41.4822	+	11.1151i	1.36540	+	0.365859i
$924$	0.0620782	−	0.107523i	0.00204222	−	0.00353723i
$925$	−15.5968	+	37.0858i	−0.512819	+	1.21938i
$926$	5.87614	−	16.1446i	0.193102	−	0.530544i
$927$	3.20348	−	6.86989i	0.105216	−	0.225637i
$928$	−0.613662	+	7.01419i	−0.0201444	+	0.230252i
$929$	−31.4756	+	5.55000i	−1.03268	+	0.182090i	−0.664208	−	0.747548i	$-0.731231\pi$
$929$	−31.4756	+	5.55000i	−1.03268	+	0.182090i	−0.368474	+	0.929638i	$0.620120\pi$
$930$	2.05049	−	1.23670i	0.0672383	−	0.0405530i
$931$	7.13768	−	29.6477i	0.233928	−	0.971663i
$932$	2.59209	+	2.59209i	0.0849068	+	0.0849068i
$933$	2.23574	−	3.19297i	0.0731949	−	0.104533i
$934$	−21.1048	+	17.7090i	−0.690570	+	0.579457i
$935$	−0.421169	−	3.94411i	−0.0137737	−	0.128986i
$936$	−2.57959	−	0.938896i	−0.0843167	−	0.0306888i
$937$	−0.317655	−	3.63081i	−0.0103773	−	0.118613i	0.989239	−	0.146308i	$-0.0467390\pi$
$937$	−0.317655	−	3.63081i	−0.0103773	−	0.118613i	−0.999616	+	0.0276945i	$0.991183\pi$
$938$	−0.0172772	−	0.0644795i	−0.000564122	−	0.00210533i
$939$	15.6603	+	27.1245i	0.511055	+	0.885174i
$940$	5.33461	−	12.0355i	0.173996	−	0.392555i
$941$	−51.6361	−	9.10484i	−1.68329	−	0.296809i	−0.751479	−	0.659757i	$-0.770659\pi$
$941$	−51.6361	−	9.10484i	−1.68329	−	0.296809i	−0.931810	+	0.362947i	$0.881770\pi$
$942$	−1.39685	+	5.21313i	−0.0455119	+	0.169853i
$943$	−39.4528	+	10.5713i	−1.28476	+	0.344250i
$944$	1.35211	+	1.13455i	0.0440074	+	0.0369266i
$945$	−0.0272956	−	0.139189i	−0.000887926	−	0.00452781i
$946$	5.97480	+	16.4156i	0.194257	+	0.533718i
$947$	−9.14466	−	0.800054i	−0.297162	−	0.0259983i	−0.0623999	−	0.998051i	$-0.519875\pi$
$947$	−9.14466	−	0.800054i	−0.297162	−	0.0259983i	−0.234762	+	0.972053i	$0.575431\pi$
$948$	−1.87634	−	1.31383i	−0.0609408	−	0.0426712i
$949$	14.4137			0.467889
$950$	−18.1417	+	12.0780i	−0.588595	+	0.391862i
$951$	−12.6044			−0.408727
$952$	0.0470922	+	0.0329743i	0.00152627	+	0.00106870i
$953$	21.4091	+	1.87305i	0.693509	+	0.0606741i	0.428460	−	0.903561i	$-0.359056\pi$
$953$	21.4091	+	1.87305i	0.693509	+	0.0606741i	0.265049	+	0.964235i	$0.414612\pi$
$954$	−1.48512	−	4.08032i	−0.0480824	−	0.132105i
$955$	2.92492	+	14.9151i	0.0946482	+	0.482640i
$956$	−3.08211	−	2.58620i	−0.0996827	−	0.0836437i
$957$	13.3117	−	3.56685i	0.430305	−	0.115300i
$958$	7.29807	−	27.2368i	0.235790	−	0.879980i
$959$	0.629540	+	0.111005i	0.0203289	+	0.00358453i
$960$	−0.906096	+	2.04426i	−0.0292441	+	0.0659781i
$961$	−14.9266	−	25.8536i	−0.481503	−	0.833988i
$962$	5.71695	+	21.3359i	0.184322	+	0.687898i
$963$	−1.51755	−	17.3457i	−0.0489025	−	0.558958i
$964$	−2.53856	−	0.923959i	−0.0817614	−	0.0297587i
$965$	5.27789	+	49.4257i	0.169901	+	1.59107i
$966$	−0.171698	+	0.144072i	−0.00552429	+	0.00463543i
$967$	11.9631	−	17.0850i	0.384706	−	0.549417i	−0.579363	−	0.815070i	$-0.696699\pi$
$967$	11.9631	−	17.0850i	0.384706	−	0.549417i	0.964069	+	0.265653i	$0.0855875\pi$
$968$	−5.06925	−	5.06925i	−0.162932	−	0.162932i
$969$	0.444713	+	3.92535i	0.0142862	+	0.126100i
$970$	−10.6614	+	6.43013i	−0.342316	+	0.206459i
$971$	28.3008	−	4.99020i	0.908217	−	0.160143i	0.300024	−	0.953932i	$-0.403005\pi$
$971$	28.3008	−	4.99020i	0.908217	−	0.160143i	0.608194	+	0.793789i	$0.291894\pi$
$972$	0.0871557	−	0.996195i	0.00279552	−	0.0319530i
$973$	0.313216	−	0.671694i	0.0100412	−	0.0215335i
$974$	1.50441	−	4.13334i	0.0482044	−	0.132441i
$975$	−5.18401	−	12.7091i	−0.166021	−	0.407018i
$976$	−4.40854	+	7.63582i	−0.141114	+	0.244417i
$977$	1.32239	+	0.354333i	0.0423070	+	0.0113361i	0.279910	−	0.960026i	$-0.409695\pi$
$977$	1.32239	+	0.354333i	0.0423070	+	0.0113361i	−0.237603	+	0.971362i	$0.576362\pi$
$978$	4.99951	+	7.14004i	0.159867	+	0.228313i
$979$	3.58497	−	20.3314i	0.114576	−	0.649794i
$980$	7.56137	−	13.6947i	0.241539	−	0.437460i
$981$	3.90808	+	2.25633i	0.124775	+	0.0720391i
$982$	38.3651	−	3.35651i	1.22428	−	0.107111i
$983$	−17.5243	−	37.5809i	−0.558937	−	1.19864i	−0.959326	−	0.282299i	$-0.908903\pi$
$983$	−17.5243	−	37.5809i	−0.558937	−	1.19864i	0.400389	−	0.916345i	$-0.368875\pi$
$984$	−10.8623	+	3.95356i	−0.346278	+	0.126035i
$985$	−11.4955	−	23.4703i	−0.366279	−	0.747826i
$986$	1.10809	+	6.28428i	0.0352887	+	0.200132i
$987$	0.264075	−	0.264075i	0.00840559	−	0.00840559i
$988$	−3.80401	+	11.3451i	−0.121022	+	0.360934i
$989$		−	31.5365i		−	1.00280i
$990$	4.36648	+	0.298045i	0.138776	+	0.00947249i
$991$	14.9812	+	17.8539i	0.475893	+	0.567147i	0.949571	−	0.313551i	$-0.101519\pi$
$991$	14.9812	+	17.8539i	0.475893	+	0.567147i	−0.473679	+	0.880698i	$0.657074\pi$
$992$	−0.970549	−	0.452574i	−0.0308150	−	0.0143693i
$993$	−17.6884	+	8.24822i	−0.561323	+	0.261749i
$994$	0.637872	−	0.760186i	0.0202321	−	0.0241116i
$995$	0.132310	+	6.92106i	0.00419451	+	0.219412i
$996$	3.03530	−	1.75243i	0.0961773	−	0.0555280i
$997$	−11.7506	+	8.22785i	−0.372145	+	0.260579i	−0.744655	−	0.667449i	$-0.767386\pi$
$997$	−11.7506	+	8.22785i	−0.372145	+	0.260579i	0.372510	+	0.928028i	$0.378497\pi$
$998$	−25.2086	+	17.6513i	−0.797965	+	0.558741i
$999$	−6.96840	+	4.02321i	−0.220470	+	0.127289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.67.3	✓	120
5.3	odd	4	inner	570.2.bh.b.523.5	yes	120
19.2	odd	18	inner	570.2.bh.b.97.5	yes	120
95.78	even	36	inner	570.2.bh.b.553.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.67.3	✓	120	1.1	even	1	trivial
570.2.bh.b.97.5	yes	120	19.2	odd	18	inner
570.2.bh.b.523.5	yes	120	5.3	odd	4	inner
570.2.bh.b.553.3	yes	120	95.78	even	36	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.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.430308 + 2.19427i) q^{5} +(0.766044 + 0.642788i) q^{6} +(0.0612713 - 0.0164176i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.430308 + 2.19427i) q^{5} +(0.766044 + 0.642788i) q^{6} +(0.0612713 - 0.0164176i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(0.906096 - 2.04426i) q^{10} +(0.978646 + 1.69506i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-0.239255 - 2.73470i) q^{13} +(-0.0596073 - 0.0216953i) q^{14} +(-0.237427 - 2.22343i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-0.519831 + 0.742395i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-3.00247 + 3.15993i) q^{19} +(-1.91477 + 1.15484i) q^{20} +(-0.0624690 + 0.0110150i) q^{21} +(0.170589 - 1.94984i) q^{22} +(-1.49330 + 3.20238i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(-4.62967 + 1.88843i) q^{25} +(-1.37257 + 2.37737i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(0.0363835 + 0.0519610i) q^{28} +(-1.22265 + 6.93401i) q^{29} +(-1.08082 + 1.95751i) q^{30} +(-0.927411 - 0.535441i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-0.827187 - 1.77391i) q^{33} +(0.851641 - 0.309972i) q^{34} +(0.0623902 + 0.127381i) q^{35} +(0.173648 + 0.984808i) q^{36} +(5.68967 - 5.68967i) q^{37} +(4.27194 - 0.866313i) q^{38} +2.74515i q^{39} +(2.23088 + 0.152274i) q^{40} +(7.43026 + 8.85504i) q^{41} +(0.0574896 + 0.0268078i) q^{42} +(-8.08894 + 3.77193i) q^{43} +(-1.25812 + 1.49937i) q^{44} +(0.0427391 + 2.23566i) q^{45} +(3.06005 - 1.76672i) q^{46} +(-4.82273 + 3.37691i) q^{47} +(0.819152 - 0.573576i) q^{48} +(-6.05869 + 3.49799i) q^{49} +(4.87556 + 1.10856i) q^{50} +(0.582557 - 0.694264i) q^{51} +(2.48795 - 1.16015i) q^{52} +(3.93536 + 1.83509i) q^{53} +(0.642788 + 0.766044i) q^{54} +(-3.29832 + 2.87682i) q^{55} -0.0634327i q^{56} +(3.26646 - 2.88622i) q^{57} +(4.97872 - 4.97872i) q^{58} +(-0.306498 - 1.73824i) q^{59} +(2.00813 - 0.983565i) q^{60} +(8.28535 - 3.01562i) q^{61} +(0.452574 + 0.970549i) q^{62} +(0.0631913 - 0.00552853i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(5.89773 - 1.70176i) q^{65} +(-0.339880 + 1.92756i) q^{66} +(0.603609 + 0.862044i) q^{67} +(-0.875416 - 0.234567i) q^{68} +(1.76672 - 3.06005i) q^{69} +(0.0219559 - 0.140130i) q^{70} +(-5.35062 + 14.7007i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.457621 + 5.23064i) q^{73} +(-7.92417 + 1.39725i) q^{74} +(4.77664 - 1.47774i) q^{75} +(-3.99627 - 1.74064i) q^{76} +(0.0877918 + 0.0877918i) q^{77} +(1.57455 - 2.24869i) q^{78} +(1.75469 - 1.47236i) q^{79} +(-1.74009 - 1.40431i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-1.00747 - 11.5154i) q^{82} +(0.907126 + 3.38544i) q^{83} +(-0.0317164 - 0.0549344i) q^{84} +(-1.85271 - 0.821192i) q^{85} +(8.78956 + 1.54984i) q^{86} +(1.82234 - 6.80106i) q^{87} +(1.89060 - 0.506584i) q^{88} +(-8.08005 - 6.77997i) q^{89} +(1.24731 - 1.85586i) q^{90} +(-0.0595567 - 0.163631i) q^{91} +(-3.51999 - 0.307959i) q^{92} +(0.877215 + 0.614233i) q^{93} +5.88747 q^{94} +(-8.22573 - 5.22851i) q^{95} -1.00000 q^{96} +(-4.56101 - 3.19365i) q^{97} +(6.96935 + 0.609740i) q^{98} +(0.669433 + 1.83925i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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