LMFDB - Embedded newform 135.2.q.a.2.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(2,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.761943 - 1.08817i) q^{2} +(1.60100 - 0.660916i) q^{3} +(0.0804885 - 0.221140i) q^{4} +(1.62191 + 1.53928i) q^{5} +(-1.93906 - 1.23857i) q^{6} +(1.77434 + 0.827388i) q^{7} +(-2.86825 + 0.768546i) q^{8} +(2.12638 - 2.11625i) q^{9} +(0.439192 - 2.93776i) q^{10} +(-2.76562 + 3.29594i) q^{11} +(-0.0172933 - 0.407241i) q^{12} +(-4.15220 - 2.90740i) q^{13} +(-0.451609 - 2.56120i) q^{14} +(3.61402 + 1.39244i) q^{15} +(2.66120 + 2.23301i) q^{16} +(-3.09176 - 0.828434i) q^{17} +(-3.92301 - 0.701399i) q^{18} +(0.776109 + 0.448087i) q^{19} +(0.470943 - 0.234776i) q^{20} +(3.38755 + 0.151957i) q^{21} +(5.69379 + 0.498142i) q^{22} +(-2.36525 - 5.07230i) q^{23} +(-4.08412 + 3.12611i) q^{24} +(0.261212 + 4.99317i) q^{25} +6.73356i q^{26} +(2.00567 - 4.79346i) q^{27} +(0.325783 - 0.325783i) q^{28} +(-1.14702 + 6.50507i) q^{29} +(-1.23847 - 4.99362i) q^{30} +(2.27652 + 0.828586i) q^{31} +(-0.115398 + 1.31900i) q^{32} +(-2.24941 + 7.10463i) q^{33} +(1.45427 + 3.99557i) q^{34} +(1.60424 + 4.07317i) q^{35} +(-0.296839 - 0.640563i) q^{36} +(-1.86654 + 6.96604i) q^{37} +(-0.103757 - 1.18595i) q^{38} +(-8.56920 - 1.91049i) q^{39} +(-5.83507 - 3.16854i) q^{40} +(8.33680 - 1.47000i) q^{41} +(-2.41576 - 3.80200i) q^{42} +(1.28541 - 0.112459i) q^{43} +(0.506265 + 0.876877i) q^{44} +(6.70631 - 0.159269i) q^{45} +(-3.71732 + 6.43859i) q^{46} +(3.48305 - 7.46943i) q^{47} +(5.73641 + 1.81622i) q^{48} +(-2.03580 - 2.42617i) q^{49} +(5.23438 - 4.08876i) q^{50} +(-5.49742 + 0.717071i) q^{51} +(-0.977148 + 0.684206i) q^{52} +(0.947342 + 0.947342i) q^{53} +(-6.74430 + 1.46984i) q^{54} +(-9.55899 + 1.08866i) q^{55} +(-5.72514 - 1.00950i) q^{56} +(1.53869 + 0.204443i) q^{57} +(7.95258 - 3.70835i) q^{58} +(3.72879 - 3.12883i) q^{59} +(0.598812 - 0.687130i) q^{60} +(-7.90101 + 2.87573i) q^{61} +(-0.832940 - 3.10857i) q^{62} +(5.52388 - 1.99560i) q^{63} +(7.54029 - 4.35339i) q^{64} +(-2.25919 - 11.1070i) q^{65} +(9.44496 - 2.96559i) q^{66} +(5.53556 - 7.90560i) q^{67} +(-0.432051 + 0.617033i) q^{68} +(-7.13912 - 6.55750i) q^{69} +(3.20995 - 4.84921i) q^{70} +(4.92123 - 2.84127i) q^{71} +(-4.47256 + 7.70415i) q^{72} +(-1.32285 - 4.93694i) q^{73} +(9.00242 - 3.27661i) q^{74} +(3.71826 + 7.82141i) q^{75} +(0.161558 - 0.135563i) q^{76} +(-7.63418 + 3.55988i) q^{77} +(4.45032 + 10.7804i) q^{78} +(0.410612 + 0.0724019i) q^{79} +(0.879000 + 7.71810i) q^{80} +(0.0429919 - 8.99990i) q^{81} +(-7.95178 - 7.95178i) q^{82} +(-7.59392 + 5.31732i) q^{83} +(0.306263 - 0.736893i) q^{84} +(-3.73937 - 6.10274i) q^{85} +(-1.10179 - 1.31306i) q^{86} +(2.46293 + 11.1727i) q^{87} +(5.39942 - 11.5791i) q^{88} +(0.974450 - 1.68780i) q^{89} +(-5.28314 - 7.17624i) q^{90} +(-4.96186 - 8.59420i) q^{91} +(-1.31207 + 0.114791i) q^{92} +(4.19233 - 0.178025i) q^{93} +(-10.7819 + 1.90114i) q^{94} +(0.569049 + 1.92141i) q^{95} +(0.686998 + 2.18799i) q^{96} +(1.17718 + 13.4552i) q^{97} +(-1.08892 + 4.06390i) q^{98} +(1.09426 + 12.8612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.761943	−	1.08817i	−0.538775	−	0.769451i	0.453797	−	0.891105i	$-0.350069\pi$
$2$	−0.761943	−	1.08817i	−0.538775	−	0.769451i	−0.992573	+	0.121654i	$0.961180\pi$
$3$	1.60100	−	0.660916i	0.924336	−	0.381580i
$3$	1.60100	−	0.660916i	0.924336	−	0.381580i
$4$	0.0804885	−	0.221140i	0.0402443	−	0.110570i
$5$	1.62191	+	1.53928i	0.725342	+	0.688389i
$5$	1.62191	+	1.53928i	0.725342	+	0.688389i
$6$	−1.93906	−	1.23857i	−0.791616	−	0.505645i
$7$	1.77434	+	0.827388i	0.670638	+	0.312723i	0.727947	−	0.685633i	$-0.240474\pi$
$7$	1.77434	+	0.827388i	0.670638	+	0.312723i	−0.0573098	+	0.998356i	$0.518252\pi$
$8$	−2.86825	+	0.768546i	−1.01408	+	0.271722i
$9$	2.12638	−	2.11625i	0.708794	−	0.705416i
$10$	0.439192	−	2.93776i	0.138885	−	0.929002i
$11$	−2.76562	+	3.29594i	−0.833867	+	0.993764i	0.166104	+	0.986108i	$0.446881\pi$
$11$	−2.76562	+	3.29594i	−0.833867	+	0.993764i	−0.999971	+	0.00765542i	$0.997563\pi$
$12$	−0.0172933	−	0.407241i	−0.00499215	−	0.117560i
$13$	−4.15220	−	2.90740i	−1.15161	−	0.806368i	−0.167844	−	0.985814i	$-0.553681\pi$
$13$	−4.15220	−	2.90740i	−1.15161	−	0.806368i	−0.983768	+	0.179446i	$0.942569\pi$
$14$	−0.451609	−	2.56120i	−0.120698	−	0.684510i
$15$	3.61402	+	1.39244i	0.933135	+	0.359526i
$16$	2.66120	+	2.23301i	0.665301	+	0.558253i
$17$	−3.09176	−	0.828434i	−0.749861	−	0.200925i	−0.136405	−	0.990653i	$-0.543555\pi$
$17$	−3.09176	−	0.828434i	−0.749861	−	0.200925i	−0.613456	+	0.789729i	$0.710221\pi$
$18$	−3.92301	−	0.701399i	−0.924663	−	0.165321i
$19$	0.776109	+	0.448087i	0.178052	+	0.102798i	0.586377	−	0.810038i	$-0.300554\pi$
$19$	0.776109	+	0.448087i	0.178052	+	0.102798i	−0.408325	+	0.912836i	$0.633887\pi$
$20$	0.470943	−	0.234776i	0.105306	−	0.0524975i
$21$	3.38755	+	0.151957i	0.739223	+	0.0331597i
$22$	5.69379	+	0.498142i	1.21392	+	0.106204i
$23$	−2.36525	−	5.07230i	−0.493189	−	1.05765i	−0.982624	−	0.185607i	$-0.940575\pi$
$23$	−2.36525	−	5.07230i	−0.493189	−	1.05765i	0.489435	−	0.872040i	$-0.337203\pi$
$24$	−4.08412	+	3.12611i	−0.833667	+	0.638115i
$25$	0.261212	+	4.99317i	0.0522423	+	0.998634i
$26$			6.73356i			1.32056i
$27$	2.00567	−	4.79346i	0.385991	−	0.922503i
$28$	0.325783	−	0.325783i	0.0615672	−	0.0615672i
$29$	−1.14702	+	6.50507i	−0.212996	+	1.20796i	0.671354	+	0.741137i	$0.265713\pi$
$29$	−1.14702	+	6.50507i	−0.212996	+	1.20796i	−0.884350	+	0.466825i	$0.845398\pi$
$30$	−1.23847	−	4.99362i	−0.226112	−	0.911705i
$31$	2.27652	+	0.828586i	0.408875	+	0.148818i	0.538266	−	0.842775i	$-0.319080\pi$
$31$	2.27652	+	0.828586i	0.408875	+	0.148818i	−0.129390	+	0.991594i	$0.541302\pi$
$32$	−0.115398	+	1.31900i	−0.0203996	+	0.233169i
$33$	−2.24941	+	7.10463i	−0.391573	+	1.23676i
$34$	1.45427	+	3.99557i	0.249405	+	0.685235i
$35$	1.60424	+	4.07317i	0.271166	+	0.688491i
$36$	−0.296839	−	0.640563i	−0.0494731	−	0.106760i
$37$	−1.86654	+	6.96604i	−0.306858	+	1.14521i	0.624476	+	0.781044i	$0.285312\pi$
$37$	−1.86654	+	6.96604i	−0.306858	+	1.14521i	−0.931334	+	0.364166i	$0.881354\pi$
$38$	−0.103757	−	1.18595i	−0.0168317	−	0.192387i
$39$	−8.56920	−	1.91049i	−1.37217	−	0.305922i
$40$	−5.83507	−	3.16854i	−0.922606	−	0.500990i
$41$	8.33680	−	1.47000i	1.30199	−	0.229576i	0.520697	−	0.853742i	$-0.325672\pi$
$41$	8.33680	−	1.47000i	1.30199	−	0.229576i	0.781292	+	0.624166i	$0.214561\pi$
$42$	−2.41576	−	3.80200i	−0.372761	−	0.586662i
$43$	1.28541	−	0.112459i	0.196024	−	0.0171499i	0.0112790	−	0.999936i	$-0.496410\pi$
$43$	1.28541	−	0.112459i	0.196024	−	0.0171499i	0.184745	+	0.982787i	$0.440854\pi$
$44$	0.506265	+	0.876877i	0.0763223	+	0.132194i
$45$	6.70631	−	0.159269i	0.999718	−	0.0237424i
$46$	−3.71732	+	6.43859i	−0.548090	+	0.949319i
$47$	3.48305	−	7.46943i	0.508055	−	1.08953i	−0.470283	−	0.882516i	$-0.655848\pi$
$47$	3.48305	−	7.46943i	0.508055	−	1.08953i	0.978338	−	0.207013i	$-0.0663741\pi$
$48$	5.73641	+	1.81622i	0.827979	+	0.262148i
$49$	−2.03580	−	2.42617i	−0.290829	−	0.346596i
$50$	5.23438	−	4.08876i	0.740253	−	0.578238i
$51$	−5.49742	+	0.717071i	−0.769792	+	0.100410i
$52$	−0.977148	+	0.684206i	−0.135506	+	0.0948823i
$53$	0.947342	+	0.947342i	0.130127	+	0.130127i	0.769171	−	0.639043i	$-0.220670\pi$
$53$	0.947342	+	0.947342i	0.130127	+	0.130127i	−0.639043	+	0.769171i	$0.720670\pi$
$54$	−6.74430	+	1.46984i	−0.917783	+	0.200021i
$55$	−9.55899	+	1.08866i	−1.28893	+	0.146794i
$56$	−5.72514	−	1.00950i	−0.765054	−	0.134900i
$57$	1.53869	+	0.204443i	0.203805	+	0.0270791i
$58$	7.95258	−	3.70835i	1.04422	−	0.486930i
$59$	3.72879	−	3.12883i	0.485447	−	0.407339i	−0.366944	−	0.930243i	$-0.619596\pi$
$59$	3.72879	−	3.12883i	0.485447	−	0.407339i	0.852391	+	0.522904i	$0.175151\pi$
$60$	0.598812	−	0.687130i	0.0773062	−	0.0887081i
$61$	−7.90101	+	2.87573i	−1.01162	+	0.368200i	−0.794055	−	0.607846i	$-0.792034\pi$
$61$	−7.90101	+	2.87573i	−1.01162	+	0.368200i	−0.217566	+	0.976046i	$0.569812\pi$
$62$	−0.832940	−	3.10857i	−0.105783	−	0.394789i
$63$	5.52388	−	1.99560i	0.695944	−	0.251422i
$64$	7.54029	−	4.35339i	0.942536	−	0.544173i
$65$	−2.25919	−	11.1070i	−0.280219	−	1.37765i
$66$	9.44496	−	2.96559i	1.16259	−	0.365039i
$67$	5.53556	−	7.90560i	0.676276	−	0.965822i	−0.323532	−	0.946217i	$-0.604870\pi$
$67$	5.53556	−	7.90560i	0.676276	−	0.965822i	0.999808	−	0.0196049i	$-0.00624085\pi$
$68$	−0.432051	+	0.617033i	−0.0523939	+	0.0748262i
$69$	−7.13912	−	6.55750i	−0.859449	−	0.789430i
$70$	3.20995	−	4.84921i	0.383662	−	0.579591i
$71$	4.92123	−	2.84127i	0.584043	−	0.337197i	−0.178696	−	0.983904i	$-0.557188\pi$
$71$	4.92123	−	2.84127i	0.584043	−	0.337197i	0.762738	+	0.646707i	$0.223854\pi$
$72$	−4.47256	+	7.70415i	−0.527097	+	0.907943i
$73$	−1.32285	−	4.93694i	−0.154828	−	0.577825i	−0.999120	−	0.0419419i	$-0.986646\pi$
$73$	−1.32285	−	4.93694i	−0.154828	−	0.577825i	0.844292	−	0.535883i	$-0.180021\pi$
$74$	9.00242	−	3.27661i	1.04651	−	0.380898i
$75$	3.71826	+	7.82141i	0.429348	+	0.903139i
$76$	0.161558	−	0.135563i	0.0185320	−	0.0155502i
$77$	−7.63418	+	3.55988i	−0.869996	+	0.405686i
$78$	4.45032	+	10.7804i	0.503899	+	1.22064i
$79$	0.410612	+	0.0724019i	0.0461974	+	0.00814585i	0.196699	−	0.980464i	$-0.436978\pi$
$79$	0.410612	+	0.0724019i	0.0461974	+	0.00814585i	−0.150502	+	0.988610i	$0.548089\pi$
$80$	0.879000	+	7.71810i	0.0982752	+	0.862910i
$81$	0.0429919	−	8.99990i	0.00477688	−	0.999989i
$82$	−7.95178	−	7.95178i	−0.878127	−	0.878127i
$83$	−7.59392	+	5.31732i	−0.833541	+	0.583652i	−0.910560	−	0.413378i	$-0.864349\pi$
$83$	−7.59392	+	5.31732i	−0.833541	+	0.583652i	0.0770185	+	0.997030i	$0.475460\pi$
$84$	0.306263	−	0.736893i	0.0334160	−	0.0804016i
$85$	−3.73937	−	6.10274i	−0.405592	−	0.661935i
$86$	−1.10179	−	1.31306i	−0.118809	−	0.141591i
$87$	2.46293	+	11.1727i	0.264054	+	1.19784i
$88$	5.39942	−	11.5791i	0.575580	−	1.23434i
$89$	0.974450	−	1.68780i	0.103292	−	0.178906i	−0.809747	−	0.586779i	$-0.800396\pi$
$89$	0.974450	−	1.68780i	0.103292	−	0.178906i	0.913039	+	0.407872i	$0.133729\pi$
$90$	−5.28314	−	7.17624i	−0.556892	−	0.756442i
$91$	−4.96186	−	8.59420i	−0.520144	−	0.900917i
$92$	−1.31207	+	0.114791i	−0.136792	+	0.0119678i
$93$	4.19233	−	0.178025i	0.434724	−	0.0184604i
$94$	−10.7819	+	1.90114i	−1.11207	+	0.196087i
$95$	0.569049	+	1.92141i	0.0583832	+	0.197132i
$96$	0.686998	+	2.18799i	0.0701164	+	0.223310i
$97$	1.17718	+	13.4552i	0.119524	+	1.36617i	0.784883	+	0.619644i	$0.212723\pi$
$97$	1.17718	+	13.4552i	0.119524	+	1.36617i	−0.665359	+	0.746524i	$0.731721\pi$
$98$	−1.08892	+	4.06390i	−0.109997	+	0.410516i
$99$	1.09426	+	12.8612i	0.109977	+	1.29260i
$100$	1.12522	+	0.344129i	0.112522	+	0.0344129i
$101$	−1.45521	−	3.99814i	−0.144798	−	0.397830i	0.845999	−	0.533185i	$-0.179005\pi$
$101$	−1.45521	−	3.99814i	−0.144798	−	0.397830i	−0.990797	+	0.135354i	$0.956783\pi$
$102$	4.96901	+	5.43575i	0.492006	+	0.538219i
$103$	−1.16385	+	13.3028i	−0.114677	+	1.31077i	0.692912	+	0.721022i	$0.256327\pi$
$103$	−1.16385	+	13.3028i	−0.114677	+	1.31077i	−0.807589	+	0.589745i	$0.799228\pi$
$104$	14.1440	+	5.14800i	1.38694	+	0.504803i
$105$	5.26041	+	5.46086i	0.513363	+	0.532925i
$106$	0.309046	−	1.75269i	0.0300172	−	0.170236i
$107$	10.2616	−	10.2616i	0.992026	−	0.992026i	−0.00794276	−	0.999968i	$-0.502528\pi$
$107$	10.2616	−	10.2616i	0.992026	−	0.992026i	0.999968	+	0.00794276i	$0.00252829\pi$
$108$	−0.898596	−	0.829353i	−0.0864674	−	0.0798045i
$109$			14.3459i			1.37409i	0.726615	+	0.687045i	$0.241092\pi$
$109$			14.3459i			1.37409i	−0.726615	+	0.687045i	$0.758908\pi$
$110$	8.46805	+	9.57229i	0.807397	+	0.912682i
$111$	1.61563	+	12.3862i	0.153349	+	1.17565i
$112$	2.87431	+	6.16397i	0.271597	+	0.582441i
$113$	−13.5865	−	1.18867i	−1.27811	−	0.111821i	−0.572198	−	0.820116i	$-0.693909\pi$
$113$	−13.5865	−	1.18867i	−1.27811	−	0.111821i	−0.705916	+	0.708295i	$0.749465\pi$
$114$	−0.949930	−	1.83013i	−0.0889691	−	0.171408i
$115$	3.97147	−	11.8676i	0.370341	−	1.10666i
$116$	1.34621	+	0.777236i	0.124993	+	0.0721646i
$117$	−14.9819	+	2.60484i	−1.38508	+	0.240817i
$118$	−6.24582	−	1.67356i	−0.574974	−	0.154064i
$119$	−4.80039	−	4.02801i	−0.440051	−	0.369247i
$120$	−11.4361	−	1.21633i	−1.04397	−	0.111035i
$121$	−1.30443	−	7.39778i	−0.118584	−	0.672525i
$122$	9.14940	+	6.40648i	0.828348	+	0.580016i
$123$	12.3756	−	7.86339i	1.11587	−	0.709018i
$124$	0.366468	−	0.436739i	0.0329098	−	0.0392204i
$125$	−7.26225	+	8.50058i	−0.649555	+	0.760315i
$126$	−6.38043	−	4.49038i	−0.568414	−	0.400035i
$127$	−3.47767	+	0.931838i	−0.308593	+	0.0826872i	−0.409792	−	0.912179i	$-0.634399\pi$
$127$	−3.47767	+	0.931838i	−0.308593	+	0.0826872i	0.101199	+	0.994866i	$0.467732\pi$
$128$	−8.08251	−	3.76894i	−0.714400	−	0.333130i
$129$	1.98362	−	1.02960i	0.174648	−	0.0906510i
$130$	−10.3649	+	10.9213i	−0.909058	+	0.957858i
$131$	0.189922	−	0.521807i	0.0165936	−	0.0455905i	−0.931119	−	0.364715i	$-0.881167\pi$
$131$	0.189922	−	0.521807i	0.0165936	−	0.0455905i	0.947713	+	0.319124i	$0.103389\pi$
$132$	1.39007	+	1.06928i	0.120990	+	0.0930687i
$133$	1.00634	+	1.43720i	0.0872607	+	0.124621i
$134$	−12.8204			−1.10751
$135$	10.6315	−	4.68730i	0.915016	−	0.403418i
$136$	9.50463			0.815015
$137$	−3.46624	−	4.95031i	−0.296141	−	0.422934i	0.643315	−	0.765601i	$-0.277558\pi$
$137$	−3.46624	−	4.95031i	−0.296141	−	0.422934i	−0.939457	+	0.342668i	$0.888670\pi$
$138$	−1.69606	+	12.7650i	−0.144378	+	1.08663i
$139$	6.33390	−	17.4022i	0.537234	−	1.47604i	−0.313061	−	0.949733i	$-0.601354\pi$
$139$	6.33390	−	17.4022i	0.537234	−	1.47604i	0.850295	−	0.526306i	$-0.176423\pi$
$140$	1.02986	−	0.0269197i	0.0870395	−	0.00227513i
$141$	0.639692	−	14.2605i	0.0538718	−	1.20095i
$142$	−6.84148	−	3.19024i	−0.574125	−	0.267719i
$143$	21.0660	−	5.64463i	1.76163	−	0.472027i
$144$	10.3843	−	0.883525i	0.865362	−	0.0736271i
$145$	−11.8735	+	8.78508i	−0.986042	+	0.729561i
$146$	−4.36428	+	5.20115i	−0.361190	+	0.430450i
$147$	−4.86281	−	2.53880i	−0.401078	−	0.209397i
$148$	1.39024	+	0.973455i	0.114277	+	0.0800175i
$149$	−1.50609	−	8.54145i	−0.123384	−	0.699743i	−0.982255	−	0.187551i	$-0.939945\pi$
$149$	−1.50609	−	8.54145i	−0.123384	−	0.699743i	0.858871	−	0.512192i	$-0.171166\pi$
$150$	5.67790	−	10.0056i	0.463599	−	0.816951i
$151$	−12.2052	−	10.2414i	−0.993244	−	0.833431i	−0.00721007	−	0.999974i	$-0.502295\pi$
$151$	−12.2052	−	10.2414i	−0.993244	−	0.833431i	−0.986034	+	0.166543i	$0.946740\pi$
$152$	−2.57045	−	0.688750i	−0.208491	−	0.0558650i
$153$	−8.32742	+	4.78136i	−0.673232	+	0.386550i
$154$	9.69056	+	5.59485i	0.780887	+	0.450846i
$155$	2.41689	+	4.84811i	0.194130	+	0.389409i
$156$	−1.11221	+	1.74122i	−0.0890479	+	0.139410i
$157$	13.2243	+	1.15698i	1.05541	+	0.0923367i	0.601630	−	0.798775i	$-0.294518\pi$
$157$	13.2243	+	1.15698i	1.05541	+	0.0923367i	0.453784	+	0.891112i	$0.350074\pi$
$158$	−0.234077	−	0.501981i	−0.0186222	−	0.0399354i
$159$	2.14280	+	0.890578i	0.169935	+	0.0706274i
$160$	−2.21748	+	1.96168i	−0.175307	+	0.155084i
$161$		−	10.9570i		−	0.863530i
$162$	−9.82616	+	6.81063i	−0.772016	+	0.535094i
$163$	5.24760	−	5.24760i	0.411024	−	0.411024i	−0.471071	−	0.882095i	$-0.656133\pi$
$163$	5.24760	−	5.24760i	0.411024	−	0.411024i	0.882095	+	0.471071i	$0.156133\pi$
$164$	0.345940	−	1.96192i	0.0270133	−	0.153200i
$165$	−14.5844	+	8.06062i	−1.13539	+	0.627519i
$166$	11.5723	+	4.21196i	0.898183	+	0.326912i
$167$	−0.717512	+	8.20120i	−0.0555227	+	0.634628i	0.916546	+	0.399930i	$0.130966\pi$
$167$	−0.717512	+	8.20120i	−0.0555227	+	0.634628i	−0.972068	+	0.234698i	$0.924590\pi$
$168$	−9.83313	+	2.16763i	−0.758642	+	0.167237i
$169$	4.34150	+	11.9282i	0.333962	+	0.917553i
$170$	−3.79162	+	8.71900i	−0.290804	+	0.668717i
$171$	2.59856	−	0.689635i	0.198717	−	0.0527377i
$172$	0.0785918	−	0.293309i	0.00599257	−	0.0223646i
$173$	0.677506	+	7.74393i	0.0515098	+	0.588760i	0.977461	+	0.211116i	$0.0677099\pi$
$173$	0.677506	+	7.74393i	0.0515098	+	0.588760i	−0.925951	+	0.377643i	$0.876735\pi$
$174$	10.2811	−	11.1930i	0.779412	−	0.848542i
$175$	−3.66781	+	9.07571i	−0.277261	+	0.686059i
$176$	−14.7198	+	2.59549i	−1.10954	+	0.195643i
$177$	3.90189	−	7.47366i	0.293284	−	0.561755i
$178$	−2.57908	+	0.225641i	−0.193310	+	0.0169125i
$179$	−2.19929	−	3.80928i	−0.164382	−	0.284719i	0.772053	−	0.635558i	$-0.219230\pi$
$179$	−2.19929	−	3.80928i	−0.164382	−	0.284719i	−0.936436	+	0.350839i	$0.885896\pi$
$180$	0.504561	−	1.49586i	0.0376077	−	0.111495i
$181$	−2.85830	+	4.95072i	−0.212456	+	0.367984i	−0.952483	−	0.304593i	$-0.901479\pi$
$181$	−2.85830	+	4.95072i	−0.212456	+	0.367984i	0.740027	+	0.672577i	$0.234813\pi$
$182$	−5.57127	+	11.9476i	−0.412970	+	0.885617i
$183$	−10.7489	+	9.82594i	−0.794580	+	0.726355i
$184$	10.6824	+	12.7308i	0.787519	+	0.938529i
$185$	−13.7501	+	8.42517i	−1.01093	+	0.619431i
$186$	−3.38804	−	4.42631i	−0.248423	−	0.324553i
$187$	11.2811	−	7.89911i	0.824956	−	0.577640i
$188$	−1.37145	−	1.37145i	−0.100023	−	0.100023i
$189$	7.52479	−	6.84577i	0.547348	−	0.497957i
$190$	1.65723	−	2.08323i	0.120228	−	0.151133i
$191$	14.2067	+	2.50503i	1.02796	+	0.181258i	0.662104	−	0.749412i	$-0.269664\pi$
$191$	14.2067	+	2.50503i	1.02796	+	0.181258i	0.365860	+	0.930670i	$0.380775\pi$
$192$	9.19475	−	11.9532i	0.663574	−	0.862651i
$193$	15.7247	−	7.33254i	1.13189	−	0.527808i	0.235852	−	0.971789i	$-0.424212\pi$
$193$	15.7247	−	7.33254i	1.13189	−	0.527808i	0.896036	+	0.443981i	$0.146434\pi$
$194$	13.7446	−	11.5331i	0.986802	−	0.828025i
$195$	−10.9577	−	16.2891i	−0.784699	−	1.16648i
$196$	−0.700384	+	0.254919i	−0.0500274	+	0.0182085i
$197$	−3.52289	−	13.1476i	−0.250995	−	0.936727i	−0.970275	−	0.242006i	$-0.922195\pi$
$197$	−3.52289	−	13.1476i	−0.250995	−	0.936727i	0.719280	−	0.694721i	$-0.244472\pi$
$198$	13.1613	−	10.9902i	0.935336	−	0.781041i
$199$	7.78555	−	4.49499i	0.551903	−	0.318641i	−0.197986	−	0.980205i	$-0.563440\pi$
$199$	7.78555	−	4.49499i	0.551903	−	0.318641i	0.749889	+	0.661564i	$0.230107\pi$
$200$	−4.58670	−	14.1209i	−0.324329	−	0.998500i
$201$	3.63748	−	16.3154i	0.256568	−	1.15080i
$202$	−3.24187	+	4.62987i	−0.228097	+	0.325756i
$203$	−7.41743	+	10.5932i	−0.520601	+	0.743496i
$204$	−0.283906	+	1.27342i	−0.0198774	+	0.0891570i
$205$	15.7843	+	10.4485i	1.10242	+	0.729753i
$206$	15.3625	−	8.86955i	1.07036	−	0.617971i
$207$	−15.7637	−	5.78018i	−1.09565	−	0.401750i
$208$	−4.55757	−	17.0091i	−0.316011	−	1.17937i
$209$	−3.62329	+	1.31877i	−0.250628	+	0.0912212i
$210$	1.93420	−	9.88507i	0.133472	−	0.682135i
$211$	−14.3607	+	12.0500i	−0.988631	+	0.829559i	−0.985369	−	0.170435i	$-0.945483\pi$
$211$	−14.3607	+	12.0500i	−0.988631	+	0.829559i	−0.00326162	+	0.999995i	$0.501038\pi$
$212$	0.285746	−	0.133245i	0.0196251	−	0.00915134i
$213$	6.00103	−	7.80139i	0.411184	−	0.534542i
$214$	−18.9851	−	3.34758i	−1.29779	−	0.228836i
$215$	2.25794	+	1.79622i	0.153990	+	0.122501i
$216$	−2.06876	+	15.2903i	−0.140762	+	1.04037i
$217$	3.35376	+	3.35376i	0.227668	+	0.227668i
$218$	15.6108	−	10.9308i	1.05729	−	0.740326i
$219$	−5.38077	−	7.02973i	−0.363599	−	0.475025i
$220$	−0.528643	+	2.20150i	−0.0356411	+	0.148425i
$221$	10.4290	+	12.4288i	0.701530	+	0.836051i
$222$	12.2473	−	11.1957i	0.821984	−	0.751405i
$223$	−7.00968	+	15.0323i	−0.469403	+	1.00664i	0.518999	+	0.854775i	$0.326305\pi$
$223$	−7.00968	+	15.0323i	−0.469403	+	1.00664i	−0.988402	+	0.151862i	$0.951473\pi$
$224$	−1.29608	+	2.24488i	−0.0865981	+	0.149992i
$225$	11.1222	+	10.0646i	0.741482	+	0.670973i
$226$	9.05870	+	15.6901i	0.602576	+	1.04369i
$227$	18.0248	−	1.57696i	1.19634	−	0.104667i	0.528478	−	0.848947i	$-0.322763\pi$
$227$	18.0248	−	1.57696i	1.19634	−	0.104667i	0.667867	+	0.744281i	$0.267207\pi$
$228$	0.169058	−	0.323812i	0.0111961	−	0.0214450i
$229$	−18.7074	+	3.29862i	−1.23622	+	0.217979i	−0.753294	−	0.657684i	$-0.771536\pi$
$229$	−18.7074	+	3.29862i	−1.23622	+	0.217979i	−0.482924	+	0.875662i	$0.660425\pi$
$230$	−15.9400	+	4.72083i	−1.05105	+	0.311282i
$231$	−9.86952	+	10.7449i	−0.649367	+	0.706963i
$232$	−1.70951	−	19.5397i	−0.112235	−	1.28285i
$233$	−1.95750	+	7.30551i	−0.128240	+	0.478600i	−0.999934	−	0.0114509i	$-0.996355\pi$
$233$	−1.95750	+	7.30551i	−0.128240	+	0.478600i	0.871694	+	0.490050i	$0.163022\pi$
$234$	14.2499	+	14.3181i	0.931544	+	0.936005i
$235$	17.1468	−	6.75337i	1.11853	−	0.440541i
$236$	−0.391785	−	1.07642i	−0.0255031	−	0.0700691i
$237$	0.705239	−	0.155464i	0.0458102	−	0.0100985i
$238$	−0.725521	+	8.29275i	−0.0470286	+	0.537539i
$239$	−11.7518	−	4.27731i	−0.760162	−	0.276676i	−0.0672867	−	0.997734i	$-0.521434\pi$
$239$	−11.7518	−	4.27731i	−0.760162	−	0.276676i	−0.692875	+	0.721057i	$0.743656\pi$
$240$	6.50829	+	11.7757i	0.420108	+	0.760119i
$241$	2.97320	−	16.8619i	0.191521	−	1.08617i	−0.725766	−	0.687942i	$-0.758514\pi$
$241$	2.97320	−	16.8619i	0.191521	−	1.08617i	0.917287	−	0.398227i	$-0.130374\pi$
$242$	−7.05612	+	7.05612i	−0.453585	+	0.453585i
$243$	−5.87934	−	14.4372i	−0.377160	−	0.926148i
$244$			1.97870i			0.126673i
$245$	0.432674	−	7.06872i	0.0276425	−	0.451604i
$246$	−17.9862	−	7.47531i	−1.14676	−	0.476609i
$247$	−1.91979	−	4.11700i	−0.122153	−	0.261958i
$248$	−7.16645	−	0.626983i	−0.455070	−	0.0398134i
$249$	−8.64354	+	13.5320i	−0.547762	+	0.857553i
$250$	14.7835	+	1.42558i	0.934989	+	0.0901619i
$251$	4.66370	+	2.69259i	0.294370	+	0.169955i	0.639911	−	0.768449i	$-0.278971\pi$
$251$	4.66370	+	2.69259i	0.294370	+	0.169955i	−0.345541	+	0.938404i	$0.612304\pi$
$252$	0.00330126	−	1.38218i	0.000207960	−	0.0870690i
$253$	23.2594	+	6.23233i	1.46231	+	0.391823i
$254$	3.66378	+	3.07428i	0.229886	+	0.192897i
$255$	−10.0201	−	7.29906i	−0.627484	−	0.457085i
$256$	−0.966651	−	5.48215i	−0.0604157	−	0.342634i
$257$	−10.0445	−	7.03325i	−0.626560	−	0.438722i	0.216692	−	0.976240i	$-0.430473\pi$
$257$	−10.0445	−	7.03325i	−0.626560	−	0.438722i	−0.843252	+	0.537518i	$0.819362\pi$
$258$	−2.63178	−	1.37401i	−0.163847	−	0.0855424i
$259$	−9.07550	+	10.8158i	−0.563924	+	0.672059i
$260$	−2.63804	−	0.394384i	−0.163604	−	0.0244586i
$261$	11.3273	+	16.2596i	0.701145	+	1.00645i
$262$	−0.712524	+	0.190920i	−0.0440199	+	0.0117951i
$263$	12.3505	+	5.75913i	0.761563	+	0.355123i	0.764289	−	0.644873i	$-0.223090\pi$
$263$	12.3505	+	5.75913i	0.761563	+	0.355123i	−0.00272594	+	0.999996i	$0.500868\pi$
$264$	0.991650	−	22.1067i	0.0610318	−	1.36057i
$265$	0.0782794	+	2.99474i	0.00480867	+	0.183965i
$266$	0.797143	−	2.19013i	0.0488760	−	0.134286i
$267$	0.444600	−	3.34619i	0.0272091	−	0.204783i
$268$	−1.30270	−	1.86045i	−0.0795749	−	0.113645i
$269$	−12.3342			−0.752028			−0.376014	−	0.926614i	$-0.622706\pi$
$269$	−12.3342			−0.752028			−0.376014	+	0.926614i	$0.622706\pi$
$270$	−13.2012	−	7.99743i	−0.803398	−	0.486708i
$271$	19.7578			1.20020			0.600099	−	0.799926i	$-0.295128\pi$
$271$	19.7578			1.20020			0.600099	+	0.799926i	$0.295128\pi$
$272$	−6.37789	−	9.10856i	−0.386716	−	0.552288i
$273$	−13.6240	−	10.4799i	−0.824560	−	0.634273i
$274$	−2.74569	+	7.54371i	−0.165873	+	0.455732i
$275$	−17.1796	−	12.9483i	−1.03597	−	0.780811i
$276$	−2.02475	+	1.05094i	−0.121875	+	0.0632594i
$277$	−1.83776	−	0.856962i	−0.110420	−	0.0514898i	0.366623	−	0.930370i	$-0.380514\pi$
$277$	−1.83776	−	0.856962i	−0.110420	−	0.0514898i	−0.477044	+	0.878880i	$0.658292\pi$
$278$	−23.7626	+	6.36718i	−1.42519	+	0.381878i
$279$	6.59425	−	3.05579i	0.394787	−	0.182946i
$280$	−7.73179	−	10.4499i	−0.462063	−	0.624503i
$281$	−16.8041	+	20.0263i	−1.00245	+	1.19467i	−0.0216244	+	0.999766i	$0.506884\pi$
$281$	−16.8041	+	20.0263i	−1.00245	+	1.19467i	−0.980822	+	0.194903i	$0.937561\pi$
$282$	−16.0053	+	10.1696i	−0.953100	+	0.605593i
$283$	−1.89971	−	1.33019i	−0.112926	−	0.0790717i	0.515749	−	0.856740i	$-0.327514\pi$
$283$	−1.89971	−	1.33019i	−0.112926	−	0.0790717i	−0.628675	+	0.777668i	$0.716403\pi$
$284$	−0.232218	−	1.31697i	−0.0137796	−	0.0781480i
$285$	2.18094	+	2.70008i	0.129187	+	0.159939i
$286$	−22.1934	−	18.6225i	−1.31232	−	1.10117i
$287$	16.0086	+	4.28949i	0.944956	+	0.253200i
$288$	2.54596	+	3.04891i	0.150022	+	0.179659i
$289$	−5.84978	−	3.37737i	−0.344105	−	0.198669i
$290$	18.6066	+	6.22665i	1.09262	+	0.365642i
$291$	10.7774	+	20.7637i	0.631783	+	1.21719i
$292$	−1.19823	−	0.104832i	−0.0701211	−	0.00613480i
$293$	5.09445	+	10.9251i	0.297621	+	0.638250i	0.997075	−	0.0764274i	$-0.0243513\pi$
$293$	5.09445	+	10.9251i	0.297621	+	0.638250i	−0.699454	+	0.714677i	$0.746574\pi$
$294$	0.942540	+	7.22598i	0.0549701	+	0.421427i
$295$	10.8639	+	0.664978i	0.632523	+	0.0387165i
$296$		−	21.4149i		−	1.24471i
$297$	10.2521	+	19.8675i	0.594885	+	1.15283i
$298$	−8.14698	+	8.14698i	−0.471942	+	0.471942i
$299$	−4.92621	+	27.9379i	−0.284890	+	1.61569i
$300$	2.02891	−	0.192725i	0.117139	−	0.0111270i
$301$	2.37381	+	0.863996i	0.136824	+	0.0497999i
$302$	−1.84467	+	21.0846i	−0.106149	+	1.21328i
$303$	−4.97222	−	5.43925i	−0.285646	−	0.312477i
$304$	1.06480	+	2.92551i	0.0610704	+	0.167790i
$305$	−17.2413	−	7.49771i	−0.987236	−	0.429317i
$306$	11.5479	+	5.41851i	0.660152	+	0.309756i
$307$	−6.08202	+	22.6984i	−0.347119	+	1.29547i	0.542998	+	0.839734i	$0.317289\pi$
$307$	−6.08202	+	22.6984i	−0.347119	+	1.29547i	−0.890117	+	0.455732i	$0.849378\pi$
$308$	0.172769	+	1.97476i	0.00984441	+	0.112522i
$309$	6.92874	+	22.0670i	0.394162	+	1.25535i
$310$	3.43402	−	6.32397i	0.195039	−	0.359177i
$311$	3.91683	−	0.690642i	0.222103	−	0.0391627i	−0.0614891	−	0.998108i	$-0.519585\pi$
$311$	3.91683	−	0.690642i	0.222103	−	0.0391627i	0.283592	+	0.958945i	$0.408474\pi$
$312$	26.0469	−	1.10607i	1.47462	−	0.0626189i
$313$	−0.911077	+	0.0797089i	−0.0514971	+	0.00450541i	−0.112875	−	0.993609i	$-0.536006\pi$
$313$	−0.911077	+	0.0797089i	−0.0514971	+	0.00450541i	0.0613781	+	0.998115i	$0.480450\pi$
$314$	−8.81718	−	15.2718i	−0.497582	−	0.861838i
$315$	12.0311	+	5.26613i	0.677873	+	0.296713i
$316$	0.0490605	−	0.0849753i	0.00275987	−	0.00478023i
$317$	−11.1443	+	23.8990i	−0.625924	+	1.34230i	0.296096	+	0.955158i	$0.404315\pi$
$317$	−11.1443	+	23.8990i	−0.625924	+	1.34230i	−0.922021	+	0.387141i	$0.873463\pi$
$318$	−0.663597	−	3.01030i	−0.0372127	−	0.168809i
$319$	−18.2681	−	21.7711i	−1.02282	−	1.21895i
$320$	18.9308	+	4.54582i	1.05826	+	0.254119i
$321$	9.64673	−	23.2108i	0.538428	−	1.29550i
$322$	−11.9230	+	8.34859i	−0.664444	+	0.465249i
$323$	−2.02833	−	2.02833i	−0.112859	−	0.112859i
$324$	−1.98678	−	0.733896i	−0.110377	−	0.0407720i
$325$	13.4325	−	21.4921i	0.745103	−	1.19217i
$326$	−9.70865	−	1.71190i	−0.537712	−	0.0948132i
$327$	9.48144	+	22.9678i	0.524325	+	1.27012i
$328$	−22.7823	+	10.6235i	−1.25794	+	0.586587i
$329$	12.3602	−	10.3715i	0.681442	−	0.571798i
$330$	19.8838	+	9.72854i	1.09457	+	0.535539i
$331$	−12.0746	+	4.39481i	−0.663682	+	0.241561i	−0.651825	−	0.758369i	$-0.725996\pi$
$331$	−12.0746	+	4.39481i	−0.663682	+	0.241561i	−0.0118569	+	0.999930i	$0.503774\pi$
$332$	0.564651	+	2.10731i	0.0309893	+	0.115653i
$333$	10.7729	+	18.7625i	0.590350	+	1.02818i
$334$	9.47099	−	5.46808i	0.518229	−	0.299200i
$335$	21.1472	−	4.30140i	1.15539	−	0.235011i
$336$	8.67563	+	7.96883i	0.473294	+	0.434735i
$337$	4.87543	−	6.96283i	0.265581	−	0.379290i	−0.664106	−	0.747638i	$-0.731188\pi$
$337$	4.87543	−	6.96283i	0.265581	−	0.379290i	0.929688	+	0.368349i	$0.120077\pi$
$338$	9.67189	−	13.8129i	0.526081	−	0.751322i
$339$	−22.5376	+	7.07650i	−1.22408	+	0.384343i
$340$	−1.65054	+	0.335725i	−0.0895130	+	0.0182073i
$341$	−9.02697	+	5.21173i	−0.488838	+	0.282231i
$342$	−2.73040	−	2.30221i	−0.147643	−	0.124489i
$343$	−5.15177	−	19.2267i	−0.278169	−	1.03814i
$344$	−3.60046	+	1.31046i	−0.194124	+	0.0706553i
$345$	−1.48519	−	21.6248i	−0.0799598	−	1.16424i
$346$	7.91047	−	6.63767i	0.425270	−	0.356844i
$347$	4.76851	−	2.22359i	0.255987	−	0.119369i	−0.290389	−	0.956909i	$-0.593785\pi$
$347$	4.76851	−	2.22359i	0.255987	−	0.119369i	0.546376	+	0.837540i	$0.316007\pi$
$348$	2.66897	+	0.354620i	0.143072	+	0.0190096i
$349$	20.3047	+	3.58026i	1.08688	+	0.191647i	0.688258	−	0.725466i	$-0.258376\pi$
$349$	20.3047	+	3.58026i	1.08688	+	0.191647i	0.398627	+	0.917113i	$0.369487\pi$
$350$	12.6706	−	2.92398i	0.677270	−	0.156293i
$351$	−22.2644	+	14.0721i	−1.18839	+	0.751115i
$352$	−4.02821	−	4.02821i	−0.214704	−	0.214704i
$353$	23.6027	−	16.5268i	1.25624	−	0.879631i	0.259948	−	0.965623i	$-0.416295\pi$
$353$	23.6027	−	16.5268i	1.25624	−	0.879631i	0.996296	+	0.0859911i	$0.0274057\pi$
$354$	−11.1056	+	1.44859i	−0.590257	+	0.0769918i
$355$	12.3553	+	2.96687i	0.655754	+	0.157465i
$356$	−0.294808	−	0.351339i	−0.0156248	−	0.0186209i
$357$	−10.3476	−	3.27617i	−0.547652	−	0.173393i
$358$	−2.46940	+	5.29565i	−0.130512	+	0.279884i
$359$	−8.91393	+	15.4394i	−0.470459	+	0.814860i	−0.999429	−	0.0337810i	$-0.989245\pi$
$359$	−8.91393	+	15.4394i	−0.470459	+	0.814860i	0.528970	+	0.848641i	$0.322578\pi$
$360$	−19.1130	+	5.61093i	−1.00734	+	0.295722i
$361$	−9.09844	−	15.7590i	−0.478865	−	0.829419i
$362$	7.56508	−	0.661859i	0.397612	−	0.0347865i
$363$	−6.97769	−	10.9817i	−0.366234	−	0.576390i
$364$	−2.29990	+	0.405534i	−0.120547	+	0.0212558i
$365$	5.45380	−	10.0435i	0.285465	−	0.525702i
$366$	18.8823	+	4.20977i	0.986994	+	0.220048i
$367$	−1.91117	−	21.8448i	−0.0997623	−	1.14029i	−0.866790	−	0.498674i	$-0.833821\pi$
$367$	−1.91117	−	21.8448i	−0.0997623	−	1.14029i	0.767028	−	0.641614i	$-0.221735\pi$
$368$	5.03210	−	18.7800i	0.262316	−	0.978978i
$369$	14.6163	−	20.7685i	0.760895	−	1.08117i
$370$	19.6448	+	8.54289i	1.02128	+	0.444124i
$371$	0.897087	+	2.46473i	0.0465744	+	0.127962i
$372$	0.298066	−	0.941423i	0.0154540	−	0.0488105i
$373$	−1.50421	+	17.1932i	−0.0778848	+	0.890228i	0.852280	+	0.523086i	$0.175219\pi$
$373$	−1.50421	+	17.1932i	−0.0778848	+	0.890228i	−0.930165	+	0.367142i	$0.880336\pi$
$374$	−17.1911	−	6.25706i	−0.888932	−	0.323545i
$375$	−6.00867	+	18.4091i	−0.310286	+	0.950643i
$376$	−4.24967	+	24.1011i	−0.219160	+	1.24292i
$377$	23.6755	−	23.6755i	1.21935	−	1.21935i
$378$	−13.1828	−	2.97215i	−0.678051	−	0.152871i
$379$		−	27.1687i		−	1.39556i	−0.716312	−	0.697780i	$-0.754171\pi$
$379$		−	27.1687i		−	1.39556i	0.716312	−	0.697780i	$-0.245829\pi$
$380$	0.470703	+	0.0288116i	0.0241466	+	0.00147800i
$381$	−4.95187	+	3.79031i	−0.253692	+	0.194184i
$382$	−8.09883	−	17.3680i	−0.414372	−	0.888624i
$383$	7.32022	+	0.640436i	0.374046	+	0.0327248i	0.272629	−	0.962119i	$-0.412107\pi$
$383$	7.32022	+	0.640436i	0.374046	+	0.0327248i	0.101417	+	0.994844i	$0.467662\pi$
$384$	−15.4310	−	0.692197i	−0.787461	−	0.0353235i
$385$	−17.8616	−	5.97735i	−0.910314	−	0.304634i
$386$	−19.9604	−	11.5241i	−1.01596	−	0.586562i
$387$	2.49529	−	2.95939i	0.126843	−	0.150434i
$388$	3.07024	+	0.822667i	0.155868	+	0.0417646i
$389$	23.9421	+	20.0898i	1.21391	+	1.01859i	0.999120	+	0.0419334i	$0.0133517\pi$
$389$	23.9421	+	20.0898i	1.21391	+	1.01859i	0.214792	+	0.976660i	$0.431093\pi$
$390$	−9.37608	+	24.3352i	−0.474776	+	1.23226i
$391$	3.11072	+	17.6418i	0.157316	+	0.892182i
$392$	7.70382	+	5.39427i	0.389102	+	0.272452i
$393$	−0.0408056	−	0.960934i	−0.00205837	−	0.0484727i
$394$	−11.6225	+	13.8512i	−0.585535	+	0.697814i
$395$	0.554530	+	0.749477i	0.0279014	+	0.0377103i
$396$	2.93220	+	0.793192i	0.147349	+	0.0398594i
$397$	−15.9305	+	4.26857i	−0.799531	+	0.214234i	−0.635378	−	0.772201i	$-0.719156\pi$
$397$	−15.9305	+	4.26857i	−0.799531	+	0.214234i	−0.164153	+	0.986435i	$0.552489\pi$
$398$	−10.8234	−	5.04706i	−0.542530	−	0.252986i
$399$	2.56101	+	1.63585i	0.128211	+	0.0818949i
$400$	−10.4547	+	13.8711i	−0.522734	+	0.693557i
$401$	−0.517022	+	1.42051i	−0.0258188	+	0.0709367i	−0.951932	−	0.306308i	$-0.900906\pi$
$401$	−0.517022	+	1.42051i	−0.0258188	+	0.0709367i	0.926114	+	0.377245i	$0.123128\pi$
$402$	−20.5254	+	8.47320i	−1.02371	+	0.422605i
$403$	−7.04354	−	10.0592i	−0.350864	−	0.501085i
$404$	−1.00128			−0.0498155
$405$	13.9231	−	14.5309i	0.691846	−	0.722045i
$406$	17.1788			0.852571
$407$	−17.7975	−	25.4175i	−0.882189	−	1.25990i
$408$	15.2169	−	6.28176i	0.753348	−	0.310993i
$409$	8.02778	−	22.0561i	0.396948	−	1.09061i	−0.566815	−	0.823845i	$-0.691825\pi$
$409$	8.02778	−	22.0561i	0.396948	−	1.09061i	0.963763	−	0.266760i	$-0.0859532\pi$
$410$	−0.657060	−	25.1371i	−0.0324499	−	1.24143i
$411$	−8.82118	−	5.63453i	−0.435117	−	0.277931i
$412$	2.84812	+	1.32810i	0.140317	+	0.0654308i
$413$	9.20490	−	2.46645i	0.452944	−	0.121366i
$414$	5.72121	+	21.5577i	0.281182	+	1.05950i
$415$	−20.5016	−	3.06496i	−1.00638	−	0.150453i
$416$	4.31402	−	5.14125i	0.211512	−	0.252070i
$417$	−1.36086	−	32.0471i	−0.0666418	−	1.56935i
$418$	4.19579	+	2.93792i	0.205223	+	0.143698i
$419$	2.76242	+	15.6665i	0.134953	+	0.765357i	0.974892	+	0.222677i	$0.0714794\pi$
$419$	2.76242	+	15.6665i	0.134953	+	0.765357i	−0.839939	+	0.542680i	$0.817409\pi$
$420$	1.63102	−	0.723752i	0.0795856	−	0.0353155i
$421$	27.8051	+	23.3312i	1.35514	+	1.13709i	0.977452	+	0.211160i	$0.0677241\pi$
$421$	27.8051	+	23.3312i	1.35514	+	1.13709i	0.377685	+	0.925934i	$0.376720\pi$
$422$	24.0545	+	6.44539i	1.17096	+	0.313756i
$423$	−8.40087	−	23.2539i	−0.408464	−	1.13064i
$424$	−3.44529	−	1.98914i	−0.167318	−	0.0966012i
$425$	3.32891	−	15.6541i	0.161476	−	0.759334i
$426$	−13.0617	−	0.585914i	−0.632840	−	0.0283876i
$427$	−16.3984	−	1.43468i	−0.793576	−	0.0694289i
$428$	−1.44331	−	3.09519i	−0.0697652	−	0.149612i
$429$	29.9960	−	22.9599i	1.44822	−	1.10851i
$430$	0.234166	−	3.82563i	0.0112925	−	0.184488i
$431$			10.7570i			0.518146i	0.965858	+	0.259073i	$0.0834169\pi$
$431$			10.7570i			0.518146i	−0.965858	+	0.259073i	$0.916583\pi$
$432$	16.0414	−	8.27769i	0.771790	−	0.398261i
$433$	−25.8369	+	25.8369i	−1.24164	+	1.24164i	−0.282321	+	0.959320i	$0.591104\pi$
$433$	−25.8369	+	25.8369i	−1.24164	+	1.24164i	−0.959320	+	0.282321i	$0.908896\pi$
$434$	1.09408	−	6.20483i	0.0525175	−	0.297842i
$435$	−13.2033	+	21.9123i	−0.633048	+	1.05061i
$436$	3.17246	+	1.15468i	0.151933	+	0.0552992i
$437$	0.437136	−	4.99649i	0.0209111	−	0.239015i
$438$	−3.54968	+	11.2114i	−0.169610	+	0.535703i
$439$	−4.76440	−	13.0901i	−0.227393	−	0.624756i	0.772556	−	0.634947i	$-0.218978\pi$
$439$	−4.76440	−	13.0901i	−0.227393	−	0.624756i	−0.999948	+	0.0101913i	$0.996756\pi$
$440$	26.5809	−	10.4691i	1.26720	−	0.499093i
$441$	−9.46327	−	0.850709i	−0.450632	−	0.0405100i
$442$	5.57831	−	20.8185i	0.265333	−	0.990237i
$443$	0.993879	+	11.3601i	0.0472206	+	0.539734i	0.982555	+	0.185970i	$0.0595428\pi$
$443$	0.993879	+	11.3601i	0.0472206	+	0.539734i	−0.935335	+	0.353764i	$0.884902\pi$
$444$	2.86914	+	0.639668i	0.136163	+	0.0303573i
$445$	4.17847	−	1.23751i	0.198079	−	0.0586635i
$446$	21.6986	−	3.82606i	1.02746	−	0.181169i
$447$	−8.05642	−	12.6794i	−0.381056	−	0.599717i
$448$	16.9810	−	1.48564i	0.802276	−	0.0701900i
$449$	−0.807925	−	1.39937i	−0.0381283	−	0.0660402i	0.846332	−	0.532657i	$-0.178806\pi$
$449$	−0.807925	−	1.39937i	−0.0381283	−	0.0660402i	−0.884460	+	0.466616i	$0.845473\pi$
$450$	2.47747	−	19.7715i	0.116789	−	0.932038i
$451$	−18.2114	+	31.5431i	−0.857541	+	1.48530i
$452$	−1.35642	+	2.90886i	−0.0638008	+	0.136821i
$453$	−26.3092	−	8.32980i	−1.23611	−	0.391368i
$454$	−15.4498	−	18.4124i	−0.725097	−	0.864137i
$455$	5.18119	−	21.5768i	0.242898	−	1.01153i
$456$	−4.57049	+	0.596164i	−0.214033	+	0.0279180i
$457$	4.53775	−	3.17737i	0.212267	−	0.148631i	−0.462608	−	0.886563i	$-0.653086\pi$
$457$	4.53775	−	3.17737i	0.212267	−	0.148631i	0.674875	+	0.737932i	$0.264197\pi$
$458$	17.8434	+	17.8434i	0.833768	+	0.833768i
$459$	−10.1721	+	13.1587i	−0.474793	+	0.614194i
$460$	−2.30475	−	1.83346i	−0.107460	−	0.0854855i
$461$	14.9666	+	2.63902i	0.697065	+	0.122911i	0.510942	−	0.859615i	$-0.329297\pi$
$461$	14.9666	+	2.63902i	0.697065	+	0.122911i	0.186123	+	0.982527i	$0.440408\pi$
$462$	19.2123	+	2.55269i	0.893836	+	0.118762i
$463$	−29.9580	+	13.9696i	−1.39226	+	0.649224i	−0.966749	−	0.255727i	$-0.917685\pi$
$463$	−29.9580	+	13.9696i	−1.39226	+	0.649224i	−0.425516	+	0.904951i	$0.639907\pi$
$464$	−17.5784	+	14.7500i	−0.816056	+	0.684752i
$465$	7.07363	+	6.16444i	0.328032	+	0.285869i
$466$	9.44112	−	3.43629i	0.437352	−	0.159183i
$467$	5.87822	+	21.9378i	0.272012	+	1.01516i	0.957818	+	0.287377i	$0.0927831\pi$
$467$	5.87822	+	21.9378i	0.272012	+	1.01516i	−0.685806	+	0.727784i	$0.740550\pi$
$468$	−0.629839	+	3.52277i	−0.0291143	+	0.162840i
$469$	16.3630	−	9.44716i	0.755571	−	0.436229i
$470$	−20.4137	−	13.5129i	−0.941613	−	0.623303i
$471$	21.9367	−	6.88783i	1.01079	−	0.317374i
$472$	−8.29047	+	11.8400i	−0.381600	+	0.544981i
$473$	−3.18431	+	4.54767i	−0.146415	+	0.209102i
$474$	−0.706524	−	0.648964i	−0.0324517	−	0.0298079i
$475$	−2.03464	+	3.99229i	−0.0933559	+	0.183179i
$476$	−1.27713	+	0.737352i	−0.0585372	+	0.0337965i
$477$	4.01922	+	0.00959972i	0.184027	+	0.000439541i
$478$	4.29979	+	16.0470i	0.196668	+	0.733974i
$479$	−21.4594	+	7.81060i	−0.980507	+	0.356875i	−0.782037	−	0.623232i	$-0.785819\pi$
$479$	−21.4594	+	7.81060i	−0.980507	+	0.356875i	−0.198470	+	0.980107i	$0.563597\pi$
$480$	−2.25368	+	4.60621i	−0.102866	+	0.210244i
$481$	28.0033	−	23.4976i	1.27684	−	1.07140i
$482$	−20.6140	+	9.61245i	−0.938941	+	0.437835i
$483$	−7.24163	−	17.5421i	−0.329506	−	0.798191i
$484$	−1.74094	−	0.306975i	−0.0791336	−	0.0139534i
$485$	−18.8021	+	23.6352i	−0.853758	+	1.07322i
$486$	−11.2304	+	17.3981i	−0.509421	+	0.789192i
$487$	13.1004	+	13.1004i	0.593634	+	0.593634i	0.938611	−	0.344977i	$-0.112113\pi$
$487$	13.1004	+	13.1004i	0.593634	+	0.593634i	−0.344977	+	0.938611i	$0.612113\pi$
$488$	20.4520	−	14.3206i	0.925817	−	0.648264i
$489$	4.93317	−	11.8696i	0.223086	−	0.536762i
$490$	−8.02163	+	4.91514i	−0.362380	+	0.222044i
$491$	−5.95862	−	7.10121i	−0.268909	−	0.320473i	0.614644	−	0.788805i	$-0.289300\pi$
$491$	−5.95862	−	7.10121i	−0.268909	−	0.320473i	−0.883553	+	0.468332i	$0.844855\pi$
$492$	−0.742816	−	3.36967i	−0.0334887	−	0.151916i
$493$	8.93533	−	19.1619i	0.402427	−	0.863007i
$494$	−3.01722	+	5.22597i	−0.135751	+	0.235128i
$495$	−18.0222	+	22.5441i	−0.810037	+	1.01328i
$496$	4.20804	+	7.28854i	0.188947	+	0.327265i
$497$	11.0828	−	0.969617i	0.497131	−	0.0434933i
$498$	21.3109	−	0.904958i	0.954965	−	0.0405521i
$499$	20.3482	−	3.58794i	0.910911	−	0.160618i	0.301494	−	0.953468i	$-0.402515\pi$
$499$	20.3482	−	3.58794i	0.910911	−	0.160618i	0.609417	+	0.792850i	$0.291404\pi$
$500$	1.29529	+	2.29018i	0.0579273	+	0.102420i
$501$	4.27157	+	13.6043i	0.190840	+	0.607796i
$502$	−0.623488	−	7.12650i	−0.0278276	−	0.318071i
$503$	1.21585	−	4.53760i	0.0542119	−	0.202322i	−0.933508	−	0.358557i	$-0.883269\pi$
$503$	1.21585	−	4.53760i	0.0542119	−	0.202322i	0.987720	+	0.156235i	$0.0499357\pi$
$504$	−14.3102	+	9.96924i	−0.637426	+	0.444065i
$505$	3.79406	−	8.72462i	0.168833	−	0.388241i
$506$	−10.9405	−	30.0588i	−0.486365	−	1.33628i
$507$	14.8343	+	16.2276i	0.658813	+	0.720694i
$508$	−0.0738452	+	0.844055i	−0.00327635	+	0.0374489i
$509$	30.3526	+	11.0475i	1.34536	+	0.489670i	0.911496	−	0.411309i	$-0.134928\pi$
$509$	30.3526	+	11.0475i	1.34536	+	0.489670i	0.433862	+	0.900979i	$0.357151\pi$
$510$	−0.307840	+	16.4650i	−0.0136314	+	0.729084i
$511$	1.73758	−	9.85432i	0.0768661	−	0.435929i
$512$	−17.8410	+	17.8410i	−0.788469	+	0.788469i
$513$	3.70450	−	2.82154i	0.163558	−	0.124574i
$514$			16.2891i			0.718480i
$515$	−22.3645	+	19.7846i	−0.985497	+	0.871812i
$516$	−0.0680271	−	0.521529i	−0.00299472	−	0.0229590i
$517$	14.9860	+	32.1376i	0.659083	+	1.41341i
$518$	18.6844	+	1.63467i	0.820945	+	0.0718234i
$519$	6.20277	+	11.9502i	0.272271	+	0.524557i
$520$	15.0162	+	30.1213i	0.658502	+	1.32091i
$521$	−2.29310	−	1.32392i	−0.100463	−	0.0580021i	0.448927	−	0.893568i	$-0.351806\pi$
$521$	−2.29310	−	1.32392i	−0.100463	−	0.0580021i	−0.549390	+	0.835566i	$0.685140\pi$
$522$	9.06243	−	24.7150i	0.396652	−	1.08175i
$523$	−12.5901	−	3.37351i	−0.550527	−	0.147513i	−0.0271764	−	0.999631i	$-0.508652\pi$
$523$	−12.5901	−	3.37351i	−0.550527	−	0.147513i	−0.523351	+	0.852117i	$0.675318\pi$
$524$	−0.100106	−	0.0839990i	−0.00437316	−	0.00366951i
$525$	0.126120	+	16.9543i	0.00550432	+	0.739946i
$526$	−3.14347	−	17.8275i	−0.137062	−	0.777317i
$527$	−6.35202	−	4.44773i	−0.276698	−	0.193746i
$528$	−21.8509	+	13.8839i	−0.950938	+	0.604219i
$529$	−5.34967	+	6.37549i	−0.232594	+	0.277195i
$530$	3.19913	−	2.36700i	0.138961	−	0.102816i
$531$	1.30746	−	14.5441i	0.0567388	−	0.631161i
$532$	0.398822	−	0.106864i	0.0172911	−	0.00463314i
$533$	−38.8899	−	18.1347i	−1.68451	−	0.785499i
$534$	−3.97997	+	2.06581i	−0.172230	+	0.0893962i
$535$	32.4389	−	0.847922i	1.40246	−	0.0366589i
$536$	−9.80156	+	26.9296i	−0.423363	+	1.16318i
$537$	−6.03866	−	4.64510i	−0.260587	−	0.200451i
$538$	9.39794	+	13.4217i	0.405174	+	0.578649i
$539$	13.6268			0.586947
$540$	−0.180835	−	2.72833i	−0.00778190	−	0.117409i
$541$	−42.0435			−1.80759			−0.903796	−	0.427963i	$-0.859231\pi$
$541$	−42.0435			−1.80759			−0.903796	+	0.427963i	$0.859231\pi$
$542$	−15.0543	−	21.4998i	−0.646637	−	0.923494i
$543$	−1.30412	+	9.81518i	−0.0559651	+	0.421210i
$544$	1.44949	−	3.98243i	0.0621463	−	0.170745i
$545$	−22.0824	+	23.2678i	−0.945908	+	0.996685i
$546$	−1.02321	+	22.8103i	−0.0437894	+	0.976189i
$547$	−20.8870	−	9.73975i	−0.893062	−	0.416442i	−0.0787671	−	0.996893i	$-0.525098\pi$
$547$	−20.8870	−	9.73975i	−0.893062	−	0.416442i	−0.814295	+	0.580451i	$0.802876\pi$
$548$	−1.37371	+	0.368084i	−0.0586818	+	0.0157238i
$549$	−10.7148	+	22.8354i	−0.457296	+	0.974591i
$550$	−1.00002	+	28.5602i	−0.0426412	+	1.21781i
$551$	−3.80505	+	4.53468i	−0.162101	+	0.193184i
$552$	25.5165	+	13.3218i	1.08606	+	0.567014i
$553$	0.668660	+	0.468201i	0.0284343	+	0.0199099i
$554$	0.467751	+	2.65275i	0.0198728	+	0.112704i
$555$	−16.4455	+	22.5763i	−0.698073	+	0.958311i
$556$	−3.33853	−	2.80136i	−0.141585	−	0.118804i
$557$	−34.3132	−	9.19419i	−1.45390	−	0.389570i	−0.556519	−	0.830835i	$-0.687863\pi$
$557$	−34.3132	−	9.19419i	−1.45390	−	0.389570i	−0.897377	+	0.441265i	$0.854530\pi$
$558$	−8.34966	−	4.84731i	−0.353469	−	0.205203i
$559$	−5.66426	−	3.27026i	−0.239572	−	0.138317i
$560$	−4.82622	+	14.4218i	−0.203945	+	0.609433i
$561$	12.8404	−	20.1023i	0.542120	−	0.848720i
$562$	34.5957	+	3.02674i	1.45933	+	0.127675i
$563$	1.97748	+	4.24073i	0.0833410	+	0.178725i	0.943562	−	0.331196i	$-0.107452\pi$
$563$	1.97748	+	4.24073i	0.0833410	+	0.178725i	−0.860221	+	0.509922i	$0.829674\pi$
$564$	−3.10209	−	1.28927i	−0.130622	−	0.0542881i
$565$	−20.2065	−	22.8415i	−0.850094	−	0.960947i
$566$			3.08073i			0.129493i
$567$	7.52269	−	15.9333i	0.315923	−	0.669136i
$568$	−11.9317	+	11.9317i	−0.500642	+	0.500642i
$569$	−1.37633	+	7.80556i	−0.0576988	+	0.327226i	−0.999971	−	0.00762185i	$-0.997574\pi$
$569$	−1.37633	+	7.80556i	−0.0576988	+	0.327226i	0.942272	+	0.334848i	$0.108685\pi$
$570$	1.27639	−	4.43053i	0.0534620	−	0.185574i
$571$	4.65824	+	1.69546i	0.194941	+	0.0709528i	0.437646	−	0.899147i	$-0.355812\pi$
$571$	4.65824	+	1.69546i	0.194941	+	0.0709528i	−0.242705	+	0.970100i	$0.578035\pi$
$572$	0.447319	−	5.11288i	0.0187033	−	0.213780i
$573$	24.4006	−	5.37891i	1.01935	−	0.224707i
$574$	−7.52995	−	20.6884i	−0.314294	−	0.863516i
$575$	24.7090	−	13.1350i	1.03044	−	0.547769i
$576$	6.82068	−	25.2141i	0.284195	−	1.05059i
$577$	−5.90200	+	22.0266i	−0.245703	+	0.916977i	0.727325	+	0.686293i	$0.240763\pi$
$577$	−5.90200	+	22.0266i	−0.245703	+	0.916977i	−0.973029	+	0.230684i	$0.925904\pi$
$578$	0.782053	+	8.93890i	0.0325291	+	0.371809i
$579$	20.3290	−	22.1321i	0.844844	−	0.919777i
$580$	0.987055	+	3.33281i	0.0409852	+	0.138388i
$581$	−17.8737	+	3.15161i	−0.741526	+	0.130751i
$582$	14.3826	−	27.5484i	0.596179	−	1.14192i
$583$	−5.74237	+	0.502393i	−0.237825	+	0.0208070i
$584$	7.58853	+	13.1437i	0.314015	+	0.543891i
$585$	−28.3090	−	18.8366i	−1.17043	−	0.778798i
$586$	8.00664	−	13.8679i	0.330751	−	0.572878i
$587$	−15.8151	+	33.9155i	−0.652758	+	1.39984i	0.249384	+	0.968405i	$0.419772\pi$
$587$	−15.8151	+	33.9155i	−0.652758	+	1.39984i	−0.902142	+	0.431439i	$0.858006\pi$
$588$	−0.952832	+	0.871019i	−0.0392941	+	0.0359202i
$589$	1.39555	+	1.66315i	0.0575026	+	0.0685290i
$590$	−7.55410	−	12.3285i	−0.310997	−	0.507555i
$591$	−14.3296	−	18.7209i	−0.589440	−	0.770075i
$592$	−20.5225	+	14.3700i	−0.843470	+	0.590604i
$593$	5.46266	+	5.46266i	0.224324	+	0.224324i	0.810317	−	0.585992i	$-0.199295\pi$
$593$	5.46266	+	5.46266i	0.224324	+	0.224324i	−0.585992	+	0.810317i	$0.699295\pi$
$594$	13.8077	−	26.2939i	0.566535	−	1.07885i
$595$	−1.58558	−	13.9222i	−0.0650024	−	0.570756i
$596$	−2.01008	−	0.354432i	−0.0823362	−	0.0145181i
$597$	9.49383	−	12.3421i	0.388556	−	0.505126i
$598$	34.1546	−	15.9266i	1.39669	−	0.651286i
$599$	1.79656	−	1.50749i	0.0734055	−	0.0615946i	−0.605347	−	0.795962i	$-0.706965\pi$
$599$	1.79656	−	1.50749i	0.0734055	−	0.0615946i	0.678752	+	0.734367i	$0.262521\pi$
$600$	−16.6760	−	19.5761i	−0.680796	−	0.799192i
$601$	38.1639	−	13.8905i	1.55674	−	0.566607i	0.586753	−	0.809766i	$-0.300406\pi$
$601$	38.1639	−	13.8905i	1.55674	−	0.566607i	0.969987	+	0.243159i	$0.0781836\pi$
$602$	−0.868536	−	3.24142i	−0.0353989	−	0.132110i
$603$	−4.95949	−	28.5249i	−0.201966	−	1.16162i
$604$	−3.24716	+	1.87475i	−0.132125	+	0.0762824i
$605$	9.27161	−	14.0064i	0.376944	−	0.569443i
$606$	−2.13027	+	9.55500i	−0.0865362	+	0.388146i
$607$	1.07501	−	1.53527i	0.0436332	−	0.0623147i	−0.796743	−	0.604319i	$-0.793445\pi$
$607$	1.07501	−	1.53527i	0.0436332	−	0.0623147i	0.840376	+	0.542004i	$0.182334\pi$
$608$	−0.680588	+	0.971981i	−0.0276015	+	0.0394190i
$609$	−4.87408	+	21.8619i	−0.197508	+	0.885891i
$610$	4.97816	+	24.4743i	0.201560	+	0.990935i
$611$	−36.1789	+	20.8879i	−1.46364	+	0.845035i
$612$	0.387089	+	2.22637i	0.0156472	+	0.0899958i
$613$	4.71349	+	17.5910i	0.190376	+	0.710494i	0.993415	+	0.114568i	$0.0365482\pi$
$613$	4.71349	+	17.5910i	0.190376	+	0.710494i	−0.803039	+	0.595926i	$0.796785\pi$
$614$	29.3338	−	10.6766i	1.18382	−	0.430874i
$615$	32.1762	+	6.29587i	1.29747	+	0.253874i
$616$	19.1608	−	16.0778i	0.772012	−	0.647795i
$617$	16.8885	−	7.87526i	0.679907	−	0.317046i	−0.0518073	−	0.998657i	$-0.516498\pi$
$617$	16.8885	−	7.87526i	0.679907	−	0.317046i	0.731715	+	0.681611i	$0.238720\pi$
$618$	18.7333	−	24.3534i	0.753564	−	0.979639i
$619$	28.0130	+	4.93945i	1.12594	+	0.198533i	0.705447	−	0.708763i	$-0.250746\pi$
$619$	28.0130	+	4.93945i	1.12594	+	0.198533i	0.420492	+	0.907296i	$0.361858\pi$
$620$	1.26665	−	0.144256i	0.0508697	−	0.00579345i
$621$	−29.0578	+	1.16440i	−1.16605	+	0.0467259i
$622$	−3.73594	−	3.73594i	−0.149797	−	0.149797i
$623$	3.12547	−	2.18848i	0.125219	−	0.0876795i
$624$	−18.5382	−	24.2193i	−0.742123	−	0.969549i
$625$	−24.8635	+	2.60855i	−0.994541	+	0.104342i
$626$	0.780926	+	0.930671i	0.0312121	+	0.0371971i
$627$	−4.92928	+	4.50604i	−0.196857	+	0.179954i
$628$	1.32026	−	2.83130i	0.0526840	−	0.112981i
$629$	11.5418	−	19.9910i	0.460202	−	0.797093i
$630$	−3.43655	−	17.1043i	−0.136916	−	0.681452i
$631$	−16.2016	−	28.0619i	−0.644974	−	1.11713i	−0.984307	−	0.176462i	$-0.943535\pi$
$631$	−16.2016	−	28.0619i	−0.644974	−	1.11713i	0.339333	−	0.940666i	$-0.389799\pi$
$632$	−1.23338	+	0.107907i	−0.0490613	+	0.00429231i
$633$	−15.0273	+	28.7833i	−0.597283	+	1.14403i
$634$	34.4974	−	6.08282i	1.37007	−	0.241580i
$635$	−7.07484	−	3.84175i	−0.280756	−	0.152455i
$636$	0.369414	−	0.402179i	0.0146482	−	0.0159475i
$637$	1.39919	+	15.9928i	0.0554380	+	0.633659i
$638$	−9.77134	+	36.4671i	−0.386851	+	1.44375i
$639$	4.45157	−	16.4562i	0.176102	−	0.650996i
$640$	−7.30768	−	18.5542i	−0.288861	−	0.733418i
$641$	−7.10695	−	19.5262i	−0.280708	−	0.771238i	−0.997279	−	0.0737239i	$-0.976512\pi$
$641$	−7.10695	−	19.5262i	−0.280708	−	0.771238i	0.716571	−	0.697514i	$-0.245711\pi$
$642$	−32.6075	+	7.18807i	−1.28692	+	0.283691i
$643$	3.44122	−	39.3334i	0.135709	−	1.55116i	−0.557351	−	0.830277i	$-0.688182\pi$
$643$	3.44122	−	39.3334i	0.135709	−	1.55116i	0.693060	−	0.720880i	$-0.256262\pi$
$644$	−2.42303	−	0.881910i	−0.0954807	−	0.0347521i
$645$	4.80210	+	1.38343i	0.189082	+	0.0544726i
$646$	−0.661691	+	3.75263i	−0.0260339	+	0.147645i
$647$	−27.7872	+	27.7872i	−1.09243	+	1.09243i	−0.0971593	+	0.995269i	$0.530976\pi$
$647$	−27.7872	+	27.7872i	−1.09243	+	1.09243i	−0.995269	+	0.0971593i	$0.969024\pi$
$648$	6.79352	+	25.8470i	0.266875	+	1.01537i
$649$			20.9430i			0.822086i
$650$	−33.6218	+	1.75888i	−1.31876	+	0.0689891i
$651$	7.58592	+	3.15281i	0.297315	+	0.123568i
$652$	−0.738085	−	1.58283i	−0.0289056	−	0.0619884i
$653$	16.8852	+	1.47726i	0.660770	+	0.0578098i	0.412608	−	0.910909i	$-0.364618\pi$
$653$	16.8852	+	1.47726i	0.660770	+	0.0578098i	0.248162	+	0.968719i	$0.420174\pi$
$654$	17.7685	−	27.8175i	0.694802	−	1.08775i
$655$	1.11125	−	0.553982i	0.0434200	−	0.0216459i
$656$	25.4684	+	14.7042i	0.994375	+	0.574103i
$657$	−13.2607	−	7.69833i	−0.517348	−	0.300341i
$658$	−20.7037	−	5.54754i	−0.807115	−	0.216266i
$659$	−36.7210	−	30.8125i	−1.43045	−	1.20029i	−0.945449	−	0.325770i	$-0.894376\pi$
$659$	−36.7210	−	30.8125i	−1.43045	−	1.20029i	−0.484997	−	0.874516i	$-0.661179\pi$
$660$	0.608652	+	3.87399i	0.0236917	+	0.150795i
$661$	−0.726513	−	4.12026i	−0.0282581	−	0.160259i	0.967413	−	0.253202i	$-0.0814838\pi$
$661$	−0.726513	−	4.12026i	−0.0282581	−	0.160259i	−0.995671	+	0.0929427i	$0.970373\pi$
$662$	13.9825	+	9.79064i	0.543445	+	0.380524i
$663$	24.9112	+	13.0058i	0.967470	+	0.505102i
$664$	17.6947	−	21.0877i	0.686687	−	0.818361i
$665$	−0.580065	+	3.88006i	−0.0224939	+	0.150462i
$666$	12.2084	−	26.0187i	0.473068	−	1.00820i
$667$	35.7087	−	9.56811i	1.38264	−	0.370479i
$668$	1.75587	+	0.818774i	0.0679365	+	0.0316793i
$669$	−1.28739	+	28.6995i	−0.0497732	+	1.10959i
$670$	−20.7936	−	19.7342i	−0.803326	−	0.762400i
$671$	12.3730	−	33.9945i	0.477653	−	1.31234i
$672$	−0.591347	+	4.45065i	−0.0228117	+	0.171687i
$673$	13.6940	+	19.5570i	0.527863	+	0.753867i	0.991208	−	0.132311i	$-0.0422398\pi$
$673$	13.6940	+	19.5570i	0.527863	+	0.753867i	−0.463345	+	0.886178i	$0.653351\pi$
$674$	−11.2915			−0.434933
$675$	24.4585	+	8.76254i	0.941408	+	0.337270i
$676$	2.98725			0.114894
$677$	−12.6903	−	18.1236i	−0.487727	−	0.696547i	0.497565	−	0.867427i	$-0.334228\pi$
$677$	−12.6903	−	18.1236i	−0.487727	−	0.696547i	−0.985292	+	0.170880i	$0.945339\pi$
$678$	24.8728	+	19.1328i	0.955235	+	0.734791i
$679$	−9.04396	+	24.8481i	−0.347075	+	0.953581i
$680$	15.4157	+	14.6303i	0.591165	+	0.561047i
$681$	27.8153	−	14.4376i	1.06589	−	0.553248i
$682$	12.5493	+	5.85182i	0.480537	+	0.224078i
$683$	24.3829	−	6.53337i	0.932985	−	0.249993i	0.239858	−	0.970808i	$-0.422899\pi$
$683$	24.3829	−	6.53337i	0.932985	−	0.249993i	0.693127	+	0.720815i	$0.256232\pi$
$684$	0.0566484	−	0.630155i	0.00216601	−	0.0240946i
$685$	1.99798	−	13.3645i	0.0763389	−	0.510632i
$686$	−16.9965	+	20.2556i	−0.648929	+	0.773363i
$687$	−27.7703	+	17.6451i	−1.05950	+	0.673201i
$688$	3.67187	+	2.57107i	0.139989	+	0.0980212i
$689$	−1.17925	−	6.68785i	−0.0449258	−	0.254787i
$690$	−22.3998	+	18.0930i	−0.852747	+	0.688790i
$691$	25.5999	+	21.4808i	0.973865	+	0.817170i	0.983153	−	0.182787i	$-0.0585118\pi$
$691$	25.5999	+	21.4808i	0.973865	+	0.817170i	−0.00928734	+	0.999957i	$0.502956\pi$
$692$	1.76703	+	0.473473i	0.0671723	+	0.0179988i
$693$	−8.69959	+	23.7255i	−0.330470	+	0.901256i
$694$	−6.05298	−	3.49469i	−0.229768	−	0.132657i
$695$	37.0600	−	18.4753i	1.40577	−	0.700807i
$696$	−15.6510	−	30.1532i	−0.593251	−	1.14295i
$697$	−26.9931	−	2.36159i	−1.02244	−	0.0894517i
$698$	−11.5751	−	24.8229i	−0.438124	−	0.939559i
$699$	1.69437	+	12.9898i	0.0640868	+	0.491321i
$700$	1.71179	+	1.54159i	0.0646996	+	0.0582667i
$701$		−	12.4042i		−	0.468499i	−0.972177	−	0.234249i	$-0.924737\pi$
$701$		−	12.4042i		−	0.468499i	0.972177	−	0.234249i	$-0.0752632\pi$
$702$	32.2771	+	13.5053i	1.21822	+	0.509724i
$703$	−4.57003	+	4.57003i	−0.172362	+	0.172362i
$704$	−6.50508	+	36.8922i	−0.245170	+	1.39043i
$705$	22.9885	−	22.1447i	0.865798	−	0.834018i
$706$	−35.9678	−	13.0912i	−1.35367	−	0.492694i
$707$	0.725989	−	8.29809i	0.0273036	−	0.312082i
$708$	−1.33867	−	1.46441i	−0.0503103	−	0.0550359i
$709$	4.29127	+	11.7902i	0.161162	+	0.442789i	0.993821	−	0.110998i	$-0.0354046\pi$
$709$	4.29127	+	11.7902i	0.161162	+	0.442789i	−0.832659	+	0.553786i	$0.813182\pi$
$710$	−6.18562	−	15.7053i	−0.232142	−	0.589408i
$711$	1.02634	−	0.715002i	0.0384906	−	0.0268147i
$712$	−1.49782	+	5.58994i	−0.0561332	+	0.209492i
$713$	−1.18171	−	13.5070i	−0.0442554	−	0.505842i
$714$	4.31925	+	13.7562i	0.161644	+	0.514812i
$715$	42.8560	+	23.2715i	1.60272	+	0.870305i
$716$	−1.01940	+	0.179748i	−0.0380969	+	0.00671750i
$717$	−21.6416	+	0.918999i	−0.808219	+	0.0343206i
$718$	23.5926	−	2.06408i	0.880466	−	0.0770308i
$719$	−9.10268	−	15.7663i	−0.339473	−	0.587984i	0.644861	−	0.764300i	$-0.276915\pi$
$719$	−9.10268	−	15.7663i	−0.339473	−	0.587984i	−0.984334	+	0.176316i	$0.943582\pi$
$720$	18.2025	+	14.5514i	0.678367	+	0.542300i
$721$	−13.0717	+	22.6408i	−0.486815	+	0.843188i
$722$	−10.2159	+	21.9081i	−0.380196	+	0.815334i
$723$	−6.38419	−	28.9608i	−0.237431	−	1.07707i
$724$	0.864744	+	1.03056i	0.0321380	+	0.0383005i
$725$	−32.7806	−	4.02807i	−1.21744	−	0.149599i
$726$	−6.63333	+	15.9603i	−0.246186	+	0.592344i
$727$	8.06014	−	5.64377i	0.298934	−	0.209316i	−0.414480	−	0.910058i	$-0.636037\pi$
$727$	8.06014	−	5.64377i	0.298934	−	0.209316i	0.713414	+	0.700742i	$0.247148\pi$
$728$	20.8369	+	20.8369i	0.772267	+	0.772267i
$729$	−18.9546	−	19.2282i	−0.702022	−	0.712155i
$730$	−15.0845	+	1.71795i	−0.558304	+	0.0635841i
$731$	−4.06735	−	0.717184i	−0.150436	−	0.0265260i
$732$	1.30775	+	3.16789i	0.0483359	+	0.117088i
$733$	−33.5024	+	15.6224i	−1.23744	+	0.577027i	−0.927533	−	0.373740i	$-0.878075\pi$
$733$	−33.5024	+	15.6224i	−1.23744	+	0.577027i	−0.309905	+	0.950767i	$0.600297\pi$
$734$	−22.3146	+	18.7242i	−0.823646	+	0.691121i
$735$	−3.97912	−	11.6030i	−0.146772	−	0.427982i
$736$	6.96332	−	2.53444i	0.256671	−	0.0934207i
$737$	10.7471	+	40.1088i	0.395875	+	1.47743i
$738$	−33.7364	−	0.0805779i	−1.24186	−	0.00296611i
$739$	7.02338	−	4.05495i	0.258359	−	0.149164i	−0.365227	−	0.930919i	$-0.619009\pi$
$739$	7.02338	−	4.05495i	0.258359	−	0.149164i	0.623586	+	0.781755i	$0.285675\pi$
$740$	0.756423	+	3.71883i	0.0278067	+	0.136707i
$741$	−5.79457	−	5.32249i	−0.212869	−	0.195526i
$742$	1.99851	−	2.85416i	0.0733675	−	0.104780i
$743$	17.8592	−	25.5056i	0.655190	−	0.935709i	−0.344805	−	0.938674i	$-0.612055\pi$
$743$	17.8592	−	25.5056i	0.655190	−	0.935709i	0.999996	+	0.00296531i	$0.000943888\pi$
$744$	−11.8878	+	3.73262i	−0.435829	+	0.136844i
$745$	10.7050	−	16.1718i	0.392200	−	0.592489i
$746$	19.8552	−	11.4634i	0.726949	−	0.419704i
$747$	−4.89480	+	27.3773i	−0.179091	+	1.00168i
$748$	−0.838814	−	3.13050i	−0.0306701	−	0.114462i
$749$	26.6979	−	9.71724i	0.975519	−	0.355060i
$750$	24.6105	−	7.48827i	0.898648	−	0.273433i
$751$	−13.4156	+	11.2570i	−0.489541	+	0.410774i	−0.853862	−	0.520500i	$-0.825746\pi$
$751$	−13.4156	+	11.2570i	−0.489541	+	0.410774i	0.364321	+	0.931273i	$0.381301\pi$
$752$	25.9484	−	12.1000i	0.946243	−	0.441240i
$753$	9.24615	+	1.22851i	0.336949	+	0.0447695i
$754$	−43.8023	−	7.72353i	−1.59519	−	0.281274i
$755$	−4.03140	−	35.3979i	−0.146718	−	1.28826i
$756$	−0.908217	−	2.21504i	−0.0330315	−	0.0805603i
$757$	−20.1777	−	20.1777i	−0.733371	−	0.733371i	0.237915	−	0.971286i	$-0.423536\pi$
$757$	−20.1777	−	20.1777i	−0.733371	−	0.733371i	−0.971286	+	0.237915i	$0.923536\pi$
$758$	−29.5641	+	20.7010i	−1.07381	+	0.751893i
$759$	41.3572	−	5.39455i	1.50117	−	0.195810i
$760$	−3.10887	−	5.07375i	−0.112771	−	0.184044i
$761$	23.7584	+	28.3141i	0.861240	+	1.02639i	0.999353	+	0.0359689i	$0.0114517\pi$
$761$	23.7584	+	28.3141i	0.861240	+	1.02639i	−0.138113	+	0.990416i	$0.544104\pi$
$762$	7.89754	+	2.50046i	0.286098	+	0.0905820i
$763$	−11.8696	+	25.4545i	−0.429710	+	0.921516i
$764$	1.69744	−	2.94006i	0.0614113	−	0.106368i
$765$	−20.8662	−	5.06331i	−0.754420	−	0.183065i
$766$	−4.88069	−	8.45360i	−0.176346	−	0.305441i
$767$	−24.5794	+	2.15042i	−0.887512	+	0.0776472i
$768$	−5.17084	−	8.13803i	−0.186587	−	0.293656i
$769$	−8.53754	+	1.50540i	−0.307872	+	0.0542861i	−0.325450	−	0.945559i	$-0.605516\pi$
$769$	−8.53754	+	1.50540i	−0.307872	+	0.0542861i	0.0175779	+	0.999845i	$0.494405\pi$
$770$	7.10520	+	23.9909i	0.256054	+	0.864571i
$771$	−20.7296	−	4.62163i	−0.746559	−	0.166444i
$772$	−0.355865	−	4.06755i	−0.0128078	−	0.146394i
$773$	3.05417	−	11.3983i	0.109851	−	0.409969i	−0.889000	−	0.457908i	$-0.848599\pi$
$773$	3.05417	−	11.3983i	0.109851	−	0.409969i	0.998850	+	0.0479396i	$0.0152655\pi$
$774$	−5.12158	−	0.460409i	−0.184091	−	0.0165491i
$775$	−3.54262	+	11.5835i	−0.127255	+	0.416092i
$776$	−13.7174	−	37.6882i	−0.492425	−	1.35293i
$777$	−7.38154	+	23.3141i	−0.264811	+	0.836390i
$778$	3.61856	−	41.3603i	0.129732	−	1.48284i
$779$	7.12895	+	2.59472i	0.255421	+	0.0929657i
$780$	−4.48414	+	1.11211i	−0.160558	+	0.0398200i
$781$	−4.24560	+	24.0780i	−0.151919	+	0.861578i
$782$	16.8270	−	16.8270i	0.601733	−	0.601733i
$783$	28.8813	+	18.5452i	1.03213	+	0.662752i
$784$		−	11.0025i		−	0.392947i
$785$	19.6678	+	22.2325i	0.701972	+	0.793510i
$786$	−1.01457	+	0.776581i	−0.0361884	+	0.0276997i
$787$	7.93722	+	17.0214i	0.282931	+	0.606748i	0.995490	−	0.0948643i	$-0.0302417\pi$
$787$	7.93722	+	17.0214i	0.282931	+	0.606748i	−0.712559	+	0.701612i	$0.752464\pi$
$788$	−3.19101	−	0.279178i	−0.113675	−	0.00994529i
$789$	23.5794	+	1.05771i	0.839448	+	0.0376556i
$790$	0.393037	−	1.17448i	0.0139836	−	0.0417862i
$791$	−23.1237	−	13.3505i	−0.822183	−	0.474687i
$792$	−13.0230	−	36.0481i	−0.462753	−	1.28091i
$793$	41.1675	+	11.0308i	1.46190	+	0.391715i
$794$	16.7831	+	14.0827i	0.595610	+	0.499776i
$795$	2.10459	+	4.74283i	0.0746422	+	0.168211i
$796$	−0.367376	−	2.08349i	−0.0130213	−	0.0738475i
$797$	17.6670	+	12.3706i	0.625797	+	0.438188i	0.842981	−	0.537943i	$-0.180798\pi$
$797$	17.6670	+	12.3706i	0.625797	+	0.438188i	−0.217184	+	0.976131i	$0.569687\pi$
$798$	−0.171269	−	4.03324i	−0.00606287	−	0.142775i
$799$	−16.9567	+	20.2082i	−0.599884	+	0.714914i
$800$	−6.61615	−	0.231662i	−0.233916	−	0.00819049i
$801$	−1.49974	−	5.65108i	−0.0529909	−	0.199671i
$802$	1.93969	−	0.519739i	0.0684929	−	0.0183526i
$803$	19.9304	+	9.29368i	0.703327	+	0.327967i
$804$	−3.31521	−	2.11759i	−0.116919	−	0.0746818i
$805$	16.8659	−	17.7713i	0.594444	−	0.626354i
$806$	−5.57934	+	15.3291i	−0.196524	+	0.539945i
$807$	−19.7470	+	8.15185i	−0.695126	+	0.286959i
$808$	7.24665	+	10.3493i	0.254936	+	0.364087i
$809$	4.46938			0.157135			0.0785676	−	0.996909i	$-0.474965\pi$
$809$	4.46938			0.157135			0.0785676	+	0.996909i	$0.474965\pi$
$810$	−26.4207	−	4.07899i	−0.928328	−	0.143321i
$811$	37.9099			1.33120			0.665598	−	0.746311i	$-0.268177\pi$
$811$	37.9099			1.33120			0.665598	+	0.746311i	$0.268177\pi$
$812$	1.74556	+	2.49292i	0.0612573	+	0.0874845i
$813$	31.6321	−	13.0582i	1.10939	−	0.457971i
$814$	−14.0978	+	38.7333i	−0.494127	+	1.35760i
$815$	16.5887	−	0.433612i	0.581077	−	0.0151888i
$816$	−16.2310	−	10.3675i	−0.568197	−	0.362936i
$817$	1.04801	+	0.488696i	0.0366653	+	0.0170973i
$818$	−30.1175	+	8.06996i	−1.05303	+	0.282159i
$819$	−28.7383	−	7.77401i	−1.00420	−	0.271646i
$820$	3.58104	−	2.64957i	0.125055	−	0.0925269i
$821$	23.1674	−	27.6099i	0.808549	−	0.963591i	−0.191290	−	0.981533i	$-0.561267\pi$
$821$	23.1674	−	27.6099i	0.808549	−	0.963591i	0.999839	+	0.0179428i	$0.00571166\pi$
$822$	0.589922	+	13.8921i	0.0205759	+	0.484544i
$823$	−2.18095	−	1.52711i	−0.0760230	−	0.0532319i	0.534947	−	0.844886i	$-0.320332\pi$
$823$	−2.18095	−	1.52711i	−0.0760230	−	0.0532319i	−0.610970	+	0.791654i	$0.709220\pi$
$824$	−6.88563	−	39.0504i	−0.239872	−	1.36038i
$825$	−36.0622	−	9.37590i	−1.25553	−	0.326427i
$826$	−9.69752	−	8.13719i	−0.337420	−	0.283129i
$827$	39.8859	+	10.6874i	1.38697	+	0.371637i	0.873647	−	0.486560i	$-0.161748\pi$
$827$	39.8859	+	10.6874i	1.38697	+	0.371637i	0.513321	+	0.858197i	$0.328415\pi$
$828$	−2.54703	+	3.02075i	−0.0885153	+	0.104978i
$829$	−19.6326	−	11.3349i	−0.681869	−	0.393677i	0.118690	−	0.992931i	$-0.462131\pi$
$829$	−19.6326	−	11.3349i	−0.681869	−	0.393677i	−0.800559	+	0.599254i	$0.795464\pi$
$830$	12.2858	+	24.6445i	0.426447	+	0.855422i
$831$	−3.50863	−	0.157388i	−0.121713	−	0.00545974i
$832$	−43.9658	−	3.84651i	−1.52424	−	0.133354i
$833$	4.28428	+	9.18766i	0.148441	+	0.318334i
$834$	−33.8357	+	25.8989i	−1.17164	+	0.896806i
$835$	−13.7877	+	12.1972i	−0.477144	+	0.422101i
$836$			0.907402i			0.0313832i
$837$	8.53774	−	9.25056i	0.295108	−	0.319746i
$838$	14.9429	−	14.9429i	0.516195	−	0.516195i
$839$	1.44230	−	8.17971i	0.0497938	−	0.282395i	−0.949736	−	0.313052i	$-0.898649\pi$
$839$	1.44230	−	8.17971i	0.0497938	−	0.282395i	0.999530	+	0.0306567i	$0.00975985\pi$
$840$	−19.2851	−	11.6203i	−0.665399	−	0.400937i
$841$	−13.7493	−	5.00432i	−0.474112	−	0.172563i
$842$	4.20240	−	48.0337i	0.144824	−	1.65535i
$843$	−13.6676	+	43.1681i	−0.470736	+	1.48679i
$844$	1.50888	+	4.14562i	0.0519379	+	0.142698i
$845$	−11.3193	+	26.0293i	−0.389396	+	0.895435i
$846$	−18.9031	+	26.8597i	−0.649902	+	0.923455i
$847$	3.80634	−	14.2054i	0.130787	−	0.488105i
$848$	0.405641	+	4.63650i	0.0139298	+	0.159218i
$849$	−3.92057	−	0.874084i	−0.134554	−	0.0299985i
$850$	−19.5707	+	8.30510i	−0.671269	+	0.284863i
$851$	39.7487	−	7.00876i	1.36257	−	0.240257i
$852$	−1.24219	−	1.95499i	−0.0425567	−	0.0669770i
$853$	−6.11455	+	0.534954i	−0.209358	+	0.0183165i	−0.191352	−	0.981521i	$-0.561287\pi$
$853$	−6.11455	+	0.534954i	−0.209358	+	0.0183165i	−0.0180058	+	0.999838i	$0.505732\pi$
$854$	10.9335	+	18.9374i	0.374137	+	0.648024i
$855$	5.27619	+	2.88140i	0.180442	+	0.0985417i
$856$	−21.5463	+	37.3193i	−0.736439	+	1.27555i
$857$	14.6042	−	31.3187i	0.498869	−	1.06983i	−0.482181	−	0.876072i	$-0.660155\pi$
$857$	14.6042	−	31.3187i	0.498869	−	1.06983i	0.981050	−	0.193756i	$-0.0620670\pi$
$858$	−47.8395	−	15.1466i	−1.63321	−	0.517095i
$859$	14.4078	+	17.1705i	0.491587	+	0.585850i	0.953620	−	0.301012i	$-0.0973245\pi$
$859$	14.4078	+	17.1705i	0.491587	+	0.585850i	−0.462034	+	0.886862i	$0.652880\pi$
$860$	0.578954	−	0.354746i	0.0197422	−	0.0120968i
$861$	28.4647	−	3.71287i	0.970073	−	0.126534i
$862$	11.7054	−	8.19621i	0.398688	−	0.279164i
$863$	−34.4337	−	34.4337i	−1.17214	−	1.17214i	−0.981700	−	0.190436i	$-0.939010\pi$
$863$	−34.4337	−	34.4337i	−1.17214	−	1.17214i	−0.190436	−	0.981700i	$-0.560990\pi$
$864$	6.09114	+	3.19864i	0.207225	+	0.108820i
$865$	−10.8212	+	13.6029i	−0.367933	+	0.462511i
$866$	47.8011	+	8.42862i	1.62435	+	0.286416i
$867$	−11.5976	−	1.54095i	−0.393876	−	0.0523334i
$868$	1.01159	−	0.471713i	0.0343357	−	0.0160110i
$869$	−1.37423	+	1.15312i	−0.0466175	+	0.0391168i
$870$	33.9044	−	2.32855i	1.14947	−	0.0789451i
$871$	−45.9694	+	16.7315i	−1.55762	+	0.566926i
$872$	−11.0255	−	41.1477i	−0.373370	−	1.39344i
$873$	30.9776	+	26.1197i	1.04843	+	0.884017i
$874$	−5.77009	+	3.33137i	−0.195176	+	0.112685i
$875$	−19.9190	+	9.07422i	−0.673384	+	0.306765i
$876$	−1.98765	+	0.624094i	−0.0671564	+	0.0210862i
$877$	−7.94910	+	11.3525i	−0.268422	+	0.383347i	−0.930623	−	0.365980i	$-0.880734\pi$
$877$	−7.94910	+	11.3525i	−0.268422	+	0.383347i	0.662201	+	0.749327i	$0.269623\pi$
$878$	−10.6140	+	15.1584i	−0.358206	+	0.511571i
$879$	15.3768	+	14.1240i	0.518645	+	0.476391i
$880$	−27.8694	−	18.4482i	−0.939477	−	0.621890i
$881$	−20.3929	+	11.7738i	−0.687054	+	0.396671i	−0.802507	−	0.596642i	$-0.796501\pi$
$881$	−20.3929	+	11.7738i	−0.687054	+	0.396671i	0.115453	+	0.993313i	$0.463168\pi$
$882$	6.28476	+	10.9458i	0.211619	+	0.368565i
$883$	4.25489	+	15.8795i	0.143188	+	0.534386i	0.999829	+	0.0184733i	$0.00588057\pi$
$883$	4.25489	+	15.8795i	0.143188	+	0.534386i	−0.856641	+	0.515913i	$0.827453\pi$
$884$	3.58792	−	1.30590i	0.120675	−	0.0439221i
$885$	17.8326	−	6.11552i	0.599437	−	0.205571i
$886$	11.6044	−	9.73725i	0.389857	−	0.327129i
$887$	9.29073	−	4.33234i	0.311952	−	0.145466i	−0.260336	−	0.965518i	$-0.583833\pi$
$887$	9.29073	−	4.33234i	0.311952	−	0.145466i	0.572289	+	0.820052i	$0.306056\pi$
$888$	−14.1534	−	34.2851i	−0.474958	−	1.15053i
$889$	−6.94156	−	1.22398i	−0.232812	−	0.0410511i
$890$	−4.53038	−	3.60397i	−0.151859	−	0.120805i
$891$	29.5442	+	25.0320i	0.989769	+	0.838604i
$892$	2.76005	+	2.76005i	0.0924133	+	0.0924133i
$893$	6.05018	−	4.23638i	0.202461	−	0.141765i
$894$	−7.65882	+	18.4278i	−0.256149	+	0.616316i
$895$	2.29650	−	9.56364i	0.0767636	−	0.319677i
$896$	−11.2227	−	13.3748i	−0.374926	−	0.446819i
$897$	10.5778	+	47.9843i	0.353181	+	1.60215i
$898$	−0.907153	+	1.94540i	−0.0302721	+	0.0649187i
$899$	−8.00123	+	13.8585i	−0.266856	+	0.462208i
$900$	3.12090	−	1.64949i	0.104030	−	0.0549830i
$901$	−2.14414	−	3.71376i	−0.0714317	−	0.123723i
$902$	48.2002	−	4.21697i	1.60489	−	0.140410i
$903$	4.37149	−	0.185633i	0.145474	−	0.00617748i
$904$	39.8832	−	7.03248i	1.32649	−	0.233897i
$905$	−12.2565	+	3.62991i	−0.407419	+	0.120662i
$906$	10.9819	+	34.9756i	0.364848	+	1.16199i
$907$	−1.17717	−	13.4551i	−0.0390872	−	0.446769i	−0.990370	−	0.138448i	$-0.955789\pi$
$907$	−1.17717	−	13.4551i	−0.0390872	−	0.446769i	0.951283	−	0.308321i	$-0.0997669\pi$
$908$	1.10206	−	4.11293i	0.0365730	−	0.136492i
$909$	−11.5554	−	5.42200i	−0.383268	−	0.179836i
$910$	−27.4269	+	10.8023i	−0.909193	+	0.358092i
$911$	4.95701	+	13.6193i	0.164233	+	0.451227i	0.994323	−	0.106403i	$-0.0339332\pi$
$911$	4.95701	+	13.6193i	0.164233	+	0.451227i	−0.830090	+	0.557629i	$0.811711\pi$
$912$	3.63825	+	3.97999i	0.120475	+	0.131791i
$913$	3.47635	−	39.7348i	0.115050	−	1.31503i
$914$	−6.91502	−	2.51686i	−0.228729	−	0.0832504i
$915$	−32.5587	−	0.608735i	−1.07636	−	0.0201242i
$916$	−0.776272	+	4.40246i	−0.0256488	+	0.145461i
$917$	0.768724	−	0.768724i	0.0253855	−	0.0253855i
$918$	22.0694	+	1.04280i	0.728399	+	0.0344176i
$919$		−	11.7599i		−	0.387925i	−0.981009	−	0.193962i	$-0.937866\pi$
$919$		−	11.7599i		−	0.387925i	0.981009	−	0.193962i	$-0.0621340\pi$
$920$	−2.27036	+	37.0916i	−0.0748517	+	1.22287i
$921$	5.26444	+	40.3597i	0.173469	+	1.32990i
$922$	−8.53202	−	18.2970i	−0.280987	−	0.602579i
$923$	−28.6946	−	2.51046i	−0.944496	−	0.0826327i
$924$	1.58175	+	3.04739i	0.0520357	+	0.100252i
$925$	−35.2702	−	7.50037i	−1.15968	−	0.246610i
$926$	38.0276	+	21.9552i	1.24966	+	0.721494i
$927$	25.6773	+	30.7499i	0.843353	+	1.00996i
$928$	−8.44784	−	2.26359i	−0.277314	−	0.0743061i
$929$	−36.0388	−	30.2401i	−1.18239	−	0.992146i	−0.999960	−	0.00892776i	$-0.997158\pi$
$929$	−36.0388	−	30.2401i	−1.18239	−	0.992146i	−0.182433	−	0.983218i	$-0.558397\pi$
$930$	1.31824	−	12.3943i	0.0432269	−	0.406424i
$931$	−0.492867	−	2.79519i	−0.0161531	−	0.0916086i
$932$	1.45799	+	1.02089i	0.0477579	+	0.0334405i
$933$	5.81437	−	3.69441i	0.190354	−	0.120950i
$934$	19.3932	−	23.1119i	0.634563	−	0.756243i
$935$	30.4560	+	4.55313i	0.996016	+	0.148903i
$936$	40.9700	−	18.9856i	1.33915	−	0.620565i
$937$	36.6017	−	9.80740i	1.19573	−	0.320394i	0.394580	−	0.918862i	$-0.370890\pi$
$937$	36.6017	−	9.80740i	1.19573	−	0.320394i	0.801147	+	0.598468i	$0.204224\pi$
$938$	−22.7477	−	10.6074i	−0.742740	−	0.346346i
$939$	−1.40595	+	0.729759i	−0.0458814	+	0.0238148i
$940$	−0.113324	−	4.33542i	−0.00369621	−	0.141406i
$941$	−3.79401	+	10.4240i	−0.123681	+	0.339811i	−0.986045	−	0.166477i	$-0.946761\pi$
$941$	−3.79401	+	10.4240i	−0.123681	+	0.339811i	0.862364	+	0.506289i	$0.168983\pi$
$942$	−24.2096	−	18.6227i	−0.788793	−	0.606760i
$943$	−27.1749	−	38.8098i	−0.884937	−	1.26382i
$944$	16.9098			0.550367
$945$	22.7422	+	0.479540i	0.739802	+	0.0155994i
$946$	7.37489			0.239778
$947$	−9.12331	−	13.0294i	−0.296468	−	0.423400i	0.643090	−	0.765791i	$-0.277652\pi$
$947$	−9.12331	−	13.0294i	−0.296468	−	0.423400i	−0.939558	+	0.342391i	$0.888763\pi$
$948$	0.0223842	−	0.168470i	0.000727006	−	0.00547165i
$949$	−8.86092	+	24.3452i	−0.287638	+	0.790278i
$950$	5.89457	−	0.827864i	0.191245	−	0.0268594i
$951$	−2.04674	+	45.6276i	−0.0663701	+	1.47958i
$952$	16.8644	+	7.86402i	0.546580	+	0.254874i
$953$	−35.2746	+	9.45180i	−1.14266	+	0.306174i	−0.780019	−	0.625756i	$-0.784790\pi$
$953$	−35.2746	+	9.45180i	−1.14266	+	0.306174i	−0.362638	+	0.931930i	$0.618124\pi$
$954$	−3.05197	−	4.38090i	−0.0988113	−	0.141837i
$955$	19.1862	+	25.9311i	0.620849	+	0.839112i
$956$	−1.89177	+	2.25453i	−0.0611843	+	0.0729167i
$957$	−43.6361	−	22.7818i	−1.41055	−	0.736430i
$958$	24.8501	+	17.4002i	0.802871	+	0.562176i
$959$	−2.05447	−	11.6515i	−0.0663422	−	0.376245i
$960$	33.3125	−	5.23382i	1.07516	−	0.168921i
$961$	−19.2514	−	16.1538i	−0.621012	−	0.521091i
$962$	−46.9062	−	12.5685i	−1.51232	−	0.405224i
$963$	0.103984	−	43.5361i	0.00335084	−	1.40293i
$964$	−3.48953	−	2.01468i	−0.112390	−	0.0648886i
$965$	36.7910	+	12.3120i	1.18434	+	0.396337i
$966$	−13.5710	+	21.2462i	−0.436640	+	0.683584i
$967$	−1.95128	−	0.170714i	−0.0627488	−	0.00548981i	0.0557381	−	0.998445i	$-0.482249\pi$
$967$	−1.95128	−	0.170714i	−0.0627488	−	0.00548981i	−0.118487	+	0.992956i	$0.537804\pi$
$968$	9.42696	+	20.2162i	0.302994	+	0.649773i
$969$	−4.58790	−	1.90679i	−0.147385	−	0.0612550i
$970$	40.0452	+	2.45115i	1.28577	+	0.0787017i
$971$			27.5442i			0.883934i	0.897031	+	0.441967i	$0.145719\pi$
$971$			27.5442i			0.883934i	−0.897031	+	0.441967i	$0.854281\pi$
$972$	−3.66587	+	0.138130i	−0.117583	+	0.00443052i
$973$	25.6369	−	25.6369i	0.821881	−	0.821881i
$974$	4.27366	−	24.2371i	0.136937	−	0.776607i
$975$	7.30101	−	43.2865i	0.233819	−	1.38628i
$976$	−27.4477	−	9.99016i	−0.878581	−	0.319777i
$977$	2.84484	−	32.5167i	0.0910146	−	1.04030i	−0.804108	−	0.594483i	$-0.797357\pi$
$977$	2.84484	−	32.5167i	0.0910146	−	1.04030i	0.895123	−	0.445819i	$-0.147088\pi$
$978$	−16.6749	+	3.67586i	−0.533205	+	0.117541i
$979$	2.86792	+	7.87954i	0.0916591	+	0.251831i
$980$	−1.52835	−	0.664633i	−0.0488215	−	0.0212309i
$981$	30.3595	+	30.5049i	0.969305	+	0.973946i
$982$	−3.18718	+	11.8947i	−0.101707	+	0.379575i
$983$	2.79155	+	31.9076i	0.0890367	+	1.01769i	0.900952	+	0.433919i	$0.142870\pi$
$983$	2.79155	+	31.9076i	0.0890367	+	1.01769i	−0.811915	+	0.583775i	$0.801575\pi$
$984$	−29.4531	+	32.0654i	−0.938930	+	1.02221i
$985$	14.5240	−	26.7470i	0.462775	−	0.852230i
$986$	−27.6596	+	4.87713i	−0.880860	+	0.155319i
$987$	12.9340	−	24.7738i	0.411695	−	0.788558i
$988$	−1.06496	+	0.0931716i	−0.0338808	+	0.00296418i
$989$	−3.61075	−	6.25401i	−0.114815	−	0.198866i
$990$	38.2636	+	2.43385i	1.21610	+	0.0773529i
$991$	24.5859	−	42.5840i	0.780995	−	1.35272i	−0.150367	−	0.988630i	$-0.548046\pi$
$991$	24.5859	−	42.5840i	0.780995	−	1.35272i	0.931362	−	0.364094i	$-0.118621\pi$
$992$	−1.35561	+	2.90712i	−0.0430407	+	0.0923012i
$993$	−16.4269	+	15.0164i	−0.521291	+	0.476531i
$994$	−9.49956	−	11.3211i	−0.301308	−	0.359084i
$995$	19.5466	+	4.69368i	0.619667	+	0.148800i
$996$	2.29676	+	3.00060i	0.0727755	+	0.0950778i
$997$	25.7299	−	18.0163i	0.814874	−	0.570581i	−0.0901563	−	0.995928i	$-0.528737\pi$
$997$	25.7299	−	18.0163i	0.814874	−	0.570581i	0.905031	+	0.425347i	$0.139848\pi$
$998$	−19.4085	−	19.4085i	−0.614364	−	0.614364i
$999$	29.6478	+	22.9188i	0.938014	+	0.725118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.2.6	✓	192
3.2	odd	2		405.2.r.a.332.11		192
5.2	odd	4		675.2.ba.b.218.11		192
5.3	odd	4	inner	135.2.q.a.83.6	yes	192
5.4	even	2		675.2.ba.b.407.11		192
15.8	even	4		405.2.r.a.8.11		192
27.13	even	9		405.2.r.a.152.11		192
27.14	odd	18	inner	135.2.q.a.122.6	yes	192
135.13	odd	36		405.2.r.a.233.11		192
135.14	odd	18		675.2.ba.b.257.11		192
135.68	even	36	inner	135.2.q.a.68.6	yes	192
135.122	even	36		675.2.ba.b.68.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	1.1	even	1	trivial
135.2.q.a.68.6	yes	192	135.68	even	36	inner
135.2.q.a.83.6	yes	192	5.3	odd	4	inner
135.2.q.a.122.6	yes	192	27.14	odd	18	inner
405.2.r.a.8.11		192	15.8	even	4
405.2.r.a.152.11		192	27.13	even	9
405.2.r.a.233.11		192	135.13	odd	36
405.2.r.a.332.11		192	3.2	odd	2
675.2.ba.b.68.11		192	135.122	even	36
675.2.ba.b.218.11		192	5.2	odd	4
675.2.ba.b.257.11		192	135.14	odd	18
675.2.ba.b.407.11		192	5.4	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.761943 - 1.08817i) q^{2} +(1.60100 - 0.660916i) q^{3} +(0.0804885 - 0.221140i) q^{4} +(1.62191 + 1.53928i) q^{5} +(-1.93906 - 1.23857i) q^{6} +(1.77434 + 0.827388i) q^{7} +(-2.86825 + 0.768546i) q^{8} +(2.12638 - 2.11625i) q^{9} +(0.439192 - 2.93776i) q^{10} +(-2.76562 + 3.29594i) q^{11} +(-0.0172933 - 0.407241i) q^{12} +(-4.15220 - 2.90740i) q^{13} +(-0.451609 - 2.56120i) q^{14} +(3.61402 + 1.39244i) q^{15} +(2.66120 + 2.23301i) q^{16} +(-3.09176 - 0.828434i) q^{17} +(-3.92301 - 0.701399i) q^{18} +(0.776109 + 0.448087i) q^{19} +(0.470943 - 0.234776i) q^{20} +(3.38755 + 0.151957i) q^{21} +(5.69379 + 0.498142i) q^{22} +(-2.36525 - 5.07230i) q^{23} +(-4.08412 + 3.12611i) q^{24} +(0.261212 + 4.99317i) q^{25} +6.73356i q^{26} +(2.00567 - 4.79346i) q^{27} +(0.325783 - 0.325783i) q^{28} +(-1.14702 + 6.50507i) q^{29} +(-1.23847 - 4.99362i) q^{30} +(2.27652 + 0.828586i) q^{31} +(-0.115398 + 1.31900i) q^{32} +(-2.24941 + 7.10463i) q^{33} +(1.45427 + 3.99557i) q^{34} +(1.60424 + 4.07317i) q^{35} +(-0.296839 - 0.640563i) q^{36} +(-1.86654 + 6.96604i) q^{37} +(-0.103757 - 1.18595i) q^{38} +(-8.56920 - 1.91049i) q^{39} +(-5.83507 - 3.16854i) q^{40} +(8.33680 - 1.47000i) q^{41} +(-2.41576 - 3.80200i) q^{42} +(1.28541 - 0.112459i) q^{43} +(0.506265 + 0.876877i) q^{44} +(6.70631 - 0.159269i) q^{45} +(-3.71732 + 6.43859i) q^{46} +(3.48305 - 7.46943i) q^{47} +(5.73641 + 1.81622i) q^{48} +(-2.03580 - 2.42617i) q^{49} +(5.23438 - 4.08876i) q^{50} +(-5.49742 + 0.717071i) q^{51} +(-0.977148 + 0.684206i) q^{52} +(0.947342 + 0.947342i) q^{53} +(-6.74430 + 1.46984i) q^{54} +(-9.55899 + 1.08866i) q^{55} +(-5.72514 - 1.00950i) q^{56} +(1.53869 + 0.204443i) q^{57} +(7.95258 - 3.70835i) q^{58} +(3.72879 - 3.12883i) q^{59} +(0.598812 - 0.687130i) q^{60} +(-7.90101 + 2.87573i) q^{61} +(-0.832940 - 3.10857i) q^{62} +(5.52388 - 1.99560i) q^{63} +(7.54029 - 4.35339i) q^{64} +(-2.25919 - 11.1070i) q^{65} +(9.44496 - 2.96559i) q^{66} +(5.53556 - 7.90560i) q^{67} +(-0.432051 + 0.617033i) q^{68} +(-7.13912 - 6.55750i) q^{69} +(3.20995 - 4.84921i) q^{70} +(4.92123 - 2.84127i) q^{71} +(-4.47256 + 7.70415i) q^{72} +(-1.32285 - 4.93694i) q^{73} +(9.00242 - 3.27661i) q^{74} +(3.71826 + 7.82141i) q^{75} +(0.161558 - 0.135563i) q^{76} +(-7.63418 + 3.55988i) q^{77} +(4.45032 + 10.7804i) q^{78} +(0.410612 + 0.0724019i) q^{79} +(0.879000 + 7.71810i) q^{80} +(0.0429919 - 8.99990i) q^{81} +(-7.95178 - 7.95178i) q^{82} +(-7.59392 + 5.31732i) q^{83} +(0.306263 - 0.736893i) q^{84} +(-3.73937 - 6.10274i) q^{85} +(-1.10179 - 1.31306i) q^{86} +(2.46293 + 11.1727i) q^{87} +(5.39942 - 11.5791i) q^{88} +(0.974450 - 1.68780i) q^{89} +(-5.28314 - 7.17624i) q^{90} +(-4.96186 - 8.59420i) q^{91} +(-1.31207 + 0.114791i) q^{92} +(4.19233 - 0.178025i) q^{93} +(-10.7819 + 1.90114i) q^{94} +(0.569049 + 1.92141i) q^{95} +(0.686998 + 2.18799i) q^{96} +(1.17718 + 13.4552i) q^{97} +(-1.08892 + 4.06390i) q^{98} +(1.09426 + 12.8612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22}+ \cdots + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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