LMFDB - Embedded newform 135.2.q.a.68.6

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			68.6
Character	$\chi$	$=$	135.68
Dual form			135.2.q.a.2.6

$q$-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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.992573	−	0.121654i	$-0.961180\pi$
$2$	−0.761943	+	1.08817i	−0.538775	+	0.769451i	0.453797	+	0.891105i	$0.350069\pi$
$3$	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	−0.0573098	−	0.998356i	$-0.518252\pi$
$7$	1.77434	−	0.827388i	0.670638	−	0.312723i	0.727947	+	0.685633i	$0.240474\pi$
$8$	−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	−0.999971	−	0.00765542i	$-0.997563\pi$
$11$	−2.76562	−	3.29594i	−0.833867	−	0.993764i	0.166104	−	0.986108i	$-0.446881\pi$
$12$	−0.0172933	+	0.407241i	−0.00499215	+	0.117560i
$13$	−4.15220	+	2.90740i	−1.15161	+	0.806368i	−0.983768	−	0.179446i	$-0.942569\pi$
$13$	−4.15220	+	2.90740i	−1.15161	+	0.806368i	−0.167844	+	0.985814i	$0.553681\pi$
$14$	−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	−0.613456	−	0.789729i	$-0.710221\pi$
$17$	−3.09176	+	0.828434i	−0.749861	+	0.200925i	−0.136405	+	0.990653i	$0.543555\pi$
$18$	−3.92301	+	0.701399i	−0.924663	+	0.165321i
$19$	0.776109	−	0.448087i	0.178052	−	0.102798i	−0.408325	−	0.912836i	$-0.633887\pi$
$19$	0.776109	−	0.448087i	0.178052	−	0.102798i	0.586377	+	0.810038i	$0.300554\pi$
$20$	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	0.489435	+	0.872040i	$0.337203\pi$
$23$	−2.36525	+	5.07230i	−0.493189	+	1.05765i	−0.982624	+	0.185607i	$0.940575\pi$
$24$	−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	−0.884350	−	0.466825i	$-0.845398\pi$
$29$	−1.14702	−	6.50507i	−0.212996	−	1.20796i	0.671354	−	0.741137i	$-0.265713\pi$
$30$	−1.23847	+	4.99362i	−0.226112	+	0.911705i
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	−0.129390	−	0.991594i	$-0.541302\pi$
$31$	2.27652	−	0.828586i	0.408875	−	0.148818i	0.538266	+	0.842775i	$0.319080\pi$
$32$	−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	−0.931334	−	0.364166i	$-0.881354\pi$
$37$	−1.86654	−	6.96604i	−0.306858	−	1.14521i	0.624476	−	0.781044i	$-0.285312\pi$
$38$	−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	0.781292	−	0.624166i	$-0.214561\pi$
$41$	8.33680	+	1.47000i	1.30199	+	0.229576i	0.520697	+	0.853742i	$0.325672\pi$
$42$	−2.41576	+	3.80200i	−0.372761	+	0.586662i
$43$	1.28541	+	0.112459i	0.196024	+	0.0171499i	0.184745	−	0.982787i	$-0.440854\pi$
$43$	1.28541	+	0.112459i	0.196024	+	0.0171499i	0.0112790	+	0.999936i	$0.496410\pi$
$44$	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	0.978338	+	0.207013i	$0.0663741\pi$
$47$	3.48305	+	7.46943i	0.508055	+	1.08953i	−0.470283	+	0.882516i	$0.655848\pi$
$48$	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	−0.639043	−	0.769171i	$-0.720670\pi$
$53$	0.947342	−	0.947342i	0.130127	−	0.130127i	0.769171	+	0.639043i	$0.220670\pi$
$54$	−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	0.852391	−	0.522904i	$-0.175151\pi$
$59$	3.72879	+	3.12883i	0.485447	+	0.407339i	−0.366944	+	0.930243i	$0.619596\pi$
$60$	0.598812	+	0.687130i	0.0773062	+	0.0887081i
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.217566	−	0.976046i	$-0.569812\pi$
$61$	−7.90101	−	2.87573i	−1.01162	−	0.368200i	−0.794055	+	0.607846i	$0.792034\pi$
$62$	−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	0.999808	+	0.0196049i	$0.00624085\pi$
$67$	5.53556	+	7.90560i	0.676276	+	0.965822i	−0.323532	+	0.946217i	$0.604870\pi$
$68$	−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	0.762738	−	0.646707i	$-0.223854\pi$
$71$	4.92123	+	2.84127i	0.584043	+	0.337197i	−0.178696	+	0.983904i	$0.557188\pi$
$72$	−4.47256	−	7.70415i	−0.527097	−	0.907943i
$73$	−1.32285	+	4.93694i	−0.154828	+	0.577825i	0.844292	+	0.535883i	$0.180021\pi$
$73$	−1.32285	+	4.93694i	−0.154828	+	0.577825i	−0.999120	+	0.0419419i	$0.986646\pi$
$74$	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	−0.150502	−	0.988610i	$-0.548089\pi$
$79$	0.410612	−	0.0724019i	0.0461974	−	0.00814585i	0.196699	+	0.980464i	$0.436978\pi$
$80$	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	0.0770185	−	0.997030i	$-0.475460\pi$
$83$	−7.59392	−	5.31732i	−0.833541	−	0.583652i	−0.910560	+	0.413378i	$0.864349\pi$
$84$	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	0.913039	−	0.407872i	$-0.133729\pi$
$89$	0.974450	+	1.68780i	0.103292	+	0.178906i	−0.809747	+	0.586779i	$0.800396\pi$
$90$	−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	−0.665359	−	0.746524i	$-0.731721\pi$
$97$	1.17718	−	13.4552i	0.119524	−	1.36617i	0.784883	−	0.619644i	$-0.212723\pi$
$98$	−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	−0.990797	−	0.135354i	$-0.956783\pi$
$101$	−1.45521	+	3.99814i	−0.144798	+	0.397830i	0.845999	+	0.533185i	$0.179005\pi$
$102$	4.96901	−	5.43575i	0.492006	−	0.538219i
$103$	−1.16385	−	13.3028i	−0.114677	−	1.31077i	−0.807589	−	0.589745i	$-0.799228\pi$
$103$	−1.16385	−	13.3028i	−0.114677	−	1.31077i	0.692912	−	0.721022i	$-0.256327\pi$
$104$	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	0.999968	−	0.00794276i	$-0.00252829\pi$
$107$	10.2616	+	10.2616i	0.992026	+	0.992026i	−0.00794276	+	0.999968i	$0.502528\pi$
$108$	−0.898596	+	0.829353i	−0.0864674	+	0.0798045i
$109$		−	14.3459i		−	1.37409i	−0.726615	−	0.687045i	$-0.758908\pi$
$109$		−	14.3459i		−	1.37409i	0.726615	−	0.687045i	$-0.241092\pi$
$110$	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	−0.705916	−	0.708295i	$-0.749465\pi$
$113$	−13.5865	+	1.18867i	−1.27811	+	0.111821i	−0.572198	+	0.820116i	$0.693909\pi$
$114$	−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	0.101199	−	0.994866i	$-0.467732\pi$
$127$	−3.47767	−	0.931838i	−0.308593	−	0.0826872i	−0.409792	+	0.912179i	$0.634399\pi$
$128$	−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	0.947713	−	0.319124i	$-0.103389\pi$
$131$	0.189922	+	0.521807i	0.0165936	+	0.0455905i	−0.931119	+	0.364715i	$0.881167\pi$
$132$	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	−0.939457	−	0.342668i	$-0.888670\pi$
$137$	−3.46624	+	4.95031i	−0.296141	+	0.422934i	0.643315	+	0.765601i	$0.277558\pi$
$138$	−1.69606	−	12.7650i	−0.144378	−	1.08663i
$139$	6.33390	+	17.4022i	0.537234	+	1.47604i	0.850295	+	0.526306i	$0.176423\pi$
$139$	6.33390	+	17.4022i	0.537234	+	1.47604i	−0.313061	+	0.949733i	$0.601354\pi$
$140$	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	0.858871	+	0.512192i	$0.171166\pi$
$149$	−1.50609	+	8.54145i	−0.123384	+	0.699743i	−0.982255	+	0.187551i	$0.939945\pi$
$150$	5.67790	+	10.0056i	0.463599	+	0.816951i
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.986034	−	0.166543i	$-0.946740\pi$
$151$	−12.2052	+	10.2414i	−0.993244	+	0.833431i	−0.00721007	+	0.999974i	$0.502295\pi$
$152$	−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	0.453784	−	0.891112i	$-0.350074\pi$
$157$	13.2243	−	1.15698i	1.05541	−	0.0923367i	0.601630	+	0.798775i	$0.294518\pi$
$158$	−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	0.882095	−	0.471071i	$-0.156133\pi$
$163$	5.24760	+	5.24760i	0.411024	+	0.411024i	−0.471071	+	0.882095i	$0.656133\pi$
$164$	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	−0.972068	−	0.234698i	$-0.924590\pi$
$167$	−0.717512	−	8.20120i	−0.0555227	−	0.634628i	0.916546	−	0.399930i	$-0.130966\pi$
$168$	−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	−0.925951	−	0.377643i	$-0.876735\pi$
$173$	0.677506	−	7.74393i	0.0515098	−	0.588760i	0.977461	−	0.211116i	$-0.0677099\pi$
$174$	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	−0.936436	−	0.350839i	$-0.885896\pi$
$179$	−2.19929	+	3.80928i	−0.164382	+	0.284719i	0.772053	+	0.635558i	$0.219230\pi$
$180$	0.504561	+	1.49586i	0.0376077	+	0.111495i
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	0.740027	−	0.672577i	$-0.234813\pi$
$181$	−2.85830	−	4.95072i	−0.212456	−	0.367984i	−0.952483	+	0.304593i	$0.901479\pi$
$182$	−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	0.365860	−	0.930670i	$-0.380775\pi$
$191$	14.2067	−	2.50503i	1.02796	−	0.181258i	0.662104	+	0.749412i	$0.269664\pi$
$192$	9.19475	+	11.9532i	0.663574	+	0.862651i
$193$	15.7247	+	7.33254i	1.13189	+	0.527808i	0.896036	−	0.443981i	$-0.146434\pi$
$193$	15.7247	+	7.33254i	1.13189	+	0.527808i	0.235852	+	0.971789i	$0.424212\pi$
$194$	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	0.719280	+	0.694721i	$0.244472\pi$
$197$	−3.52289	+	13.1476i	−0.250995	+	0.936727i	−0.970275	+	0.242006i	$0.922195\pi$
$198$	13.1613	+	10.9902i	0.935336	+	0.781041i
$199$	7.78555	+	4.49499i	0.551903	+	0.318641i	0.749889	−	0.661564i	$-0.230107\pi$
$199$	7.78555	+	4.49499i	0.551903	+	0.318641i	−0.197986	+	0.980205i	$0.563440\pi$
$200$	−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	−0.00326162	−	0.999995i	$-0.501038\pi$
$211$	−14.3607	−	12.0500i	−0.988631	−	0.829559i	−0.985369	+	0.170435i	$0.945483\pi$
$212$	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	−0.988402	−	0.151862i	$-0.951473\pi$
$223$	−7.00968	−	15.0323i	−0.469403	−	1.00664i	0.518999	−	0.854775i	$-0.326305\pi$
$224$	−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	0.667867	−	0.744281i	$-0.267207\pi$
$227$	18.0248	+	1.57696i	1.19634	+	0.104667i	0.528478	+	0.848947i	$0.322763\pi$
$228$	0.169058	+	0.323812i	0.0111961	+	0.0214450i
$229$	−18.7074	−	3.29862i	−1.23622	−	0.217979i	−0.482924	−	0.875662i	$-0.660425\pi$
$229$	−18.7074	−	3.29862i	−1.23622	−	0.217979i	−0.753294	+	0.657684i	$0.771536\pi$
$230$	−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	0.871694	−	0.490050i	$-0.163022\pi$
$233$	−1.95750	−	7.30551i	−0.128240	−	0.478600i	−0.999934	+	0.0114509i	$0.996355\pi$
$234$	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	−0.692875	−	0.721057i	$-0.743656\pi$
$239$	−11.7518	+	4.27731i	−0.760162	+	0.276676i	−0.0672867	+	0.997734i	$0.521434\pi$
$240$	6.50829	−	11.7757i	0.420108	−	0.760119i
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	0.917287	+	0.398227i	$0.130374\pi$
$241$	2.97320	+	16.8619i	0.191521	+	1.08617i	−0.725766	+	0.687942i	$0.758514\pi$
$242$	−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	−0.345541	−	0.938404i	$-0.612304\pi$
$251$	4.66370	−	2.69259i	0.294370	−	0.169955i	0.639911	+	0.768449i	$0.278971\pi$
$252$	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	−0.843252	−	0.537518i	$-0.819362\pi$
$257$	−10.0445	+	7.03325i	−0.626560	+	0.438722i	0.216692	+	0.976240i	$0.430473\pi$
$258$	−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	−0.00272594	−	0.999996i	$-0.500868\pi$
$263$	12.3505	−	5.75913i	0.761563	−	0.355123i	0.764289	+	0.644873i	$0.223090\pi$
$264$	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	−0.477044	−	0.878880i	$-0.658292\pi$
$277$	−1.83776	+	0.856962i	−0.110420	+	0.0514898i	0.366623	+	0.930370i	$0.380514\pi$
$278$	−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	−0.980822	−	0.194903i	$-0.937561\pi$
$281$	−16.8041	−	20.0263i	−1.00245	−	1.19467i	−0.0216244	−	0.999766i	$-0.506884\pi$
$282$	−16.0053	−	10.1696i	−0.953100	−	0.605593i
$283$	−1.89971	+	1.33019i	−0.112926	+	0.0790717i	−0.628675	−	0.777668i	$-0.716403\pi$
$283$	−1.89971	+	1.33019i	−0.112926	+	0.0790717i	0.515749	+	0.856740i	$0.327514\pi$
$284$	−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	−0.699454	−	0.714677i	$-0.746574\pi$
$293$	5.09445	−	10.9251i	0.297621	−	0.638250i	0.997075	+	0.0764274i	$0.0243513\pi$
$294$	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	−0.890117	−	0.455732i	$-0.849378\pi$
$307$	−6.08202	−	22.6984i	−0.347119	−	1.29547i	0.542998	−	0.839734i	$-0.317289\pi$
$308$	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	0.283592	−	0.958945i	$-0.408474\pi$
$311$	3.91683	+	0.690642i	0.222103	+	0.0391627i	−0.0614891	+	0.998108i	$0.519585\pi$
$312$	26.0469	+	1.10607i	1.47462	+	0.0626189i
$313$	−0.911077	−	0.0797089i	−0.0514971	−	0.00450541i	0.0613781	−	0.998115i	$-0.480450\pi$
$313$	−0.911077	−	0.0797089i	−0.0514971	−	0.00450541i	−0.112875	+	0.993609i	$0.536006\pi$
$314$	−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	−0.922021	−	0.387141i	$-0.873463\pi$
$317$	−11.1443	−	23.8990i	−0.625924	−	1.34230i	0.296096	−	0.955158i	$-0.404315\pi$
$318$	−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	−0.0118569	−	0.999930i	$-0.503774\pi$
$331$	−12.0746	−	4.39481i	−0.663682	−	0.241561i	−0.651825	+	0.758369i	$0.725996\pi$
$332$	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	0.929688	−	0.368349i	$-0.120077\pi$
$337$	4.87543	+	6.96283i	0.265581	+	0.379290i	−0.664106	+	0.747638i	$0.731188\pi$
$338$	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	0.546376	−	0.837540i	$-0.316007\pi$
$347$	4.76851	+	2.22359i	0.255987	+	0.119369i	−0.290389	+	0.956909i	$0.593785\pi$
$348$	2.66897	−	0.354620i	0.143072	−	0.0190096i
$349$	20.3047	−	3.58026i	1.08688	−	0.191647i	0.398627	−	0.917113i	$-0.369487\pi$
$349$	20.3047	−	3.58026i	1.08688	−	0.191647i	0.688258	+	0.725466i	$0.258376\pi$
$350$	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	0.996296	−	0.0859911i	$-0.0274057\pi$
$353$	23.6027	+	16.5268i	1.25624	+	0.879631i	0.259948	+	0.965623i	$0.416295\pi$
$354$	−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	0.528970	−	0.848641i	$-0.322578\pi$
$359$	−8.91393	−	15.4394i	−0.470459	−	0.814860i	−0.999429	+	0.0337810i	$0.989245\pi$
$360$	−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	0.767028	+	0.641614i	$0.221735\pi$
$367$	−1.91117	+	21.8448i	−0.0997623	+	1.14029i	−0.866790	+	0.498674i	$0.833821\pi$
$368$	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	−0.930165	−	0.367142i	$-0.880336\pi$
$373$	−1.50421	−	17.1932i	−0.0778848	−	0.890228i	0.852280	−	0.523086i	$-0.175219\pi$
$374$	−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	$0.245829\pi$
$379$			27.1687i			1.39556i	−0.716312	+	0.697780i	$0.754171\pi$
$380$	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	0.101417	−	0.994844i	$-0.467662\pi$
$383$	7.32022	−	0.640436i	0.374046	−	0.0327248i	0.272629	+	0.962119i	$0.412107\pi$
$384$	−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	0.214792	−	0.976660i	$-0.431093\pi$
$389$	23.9421	−	20.0898i	1.21391	−	1.01859i	0.999120	−	0.0419334i	$-0.0133517\pi$
$390$	−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	−0.164153	−	0.986435i	$-0.552489\pi$
$397$	−15.9305	−	4.26857i	−0.799531	−	0.214234i	−0.635378	+	0.772201i	$0.719156\pi$
$398$	−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	0.926114	−	0.377245i	$-0.123128\pi$
$401$	−0.517022	−	1.42051i	−0.0258188	−	0.0709367i	−0.951932	+	0.306308i	$0.900906\pi$
$402$	−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	0.963763	+	0.266760i	$0.0859532\pi$
$409$	8.02778	+	22.0561i	0.396948	+	1.09061i	−0.566815	+	0.823845i	$0.691825\pi$
$410$	−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	−0.839939	−	0.542680i	$-0.817409\pi$
$419$	2.76242	−	15.6665i	0.134953	−	0.765357i	0.974892	−	0.222677i	$-0.0714794\pi$
$420$	1.63102	+	0.723752i	0.0795856	+	0.0353155i
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.377685	−	0.925934i	$-0.376720\pi$
$421$	27.8051	−	23.3312i	1.35514	−	1.13709i	0.977452	−	0.211160i	$-0.0677241\pi$
$422$	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	$-0.916583\pi$
$431$		−	10.7570i		−	0.518146i	0.965858	−	0.259073i	$-0.0834169\pi$
$432$	16.0414	+	8.27769i	0.771790	+	0.398261i
$433$	−25.8369	−	25.8369i	−1.24164	−	1.24164i	−0.959320	−	0.282321i	$-0.908896\pi$
$433$	−25.8369	−	25.8369i	−1.24164	−	1.24164i	−0.282321	−	0.959320i	$-0.591104\pi$
$434$	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	−0.999948	−	0.0101913i	$-0.996756\pi$
$439$	−4.76440	+	13.0901i	−0.227393	+	0.624756i	0.772556	+	0.634947i	$0.218978\pi$
$440$	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	−0.935335	−	0.353764i	$-0.884902\pi$
$443$	0.993879	−	11.3601i	0.0472206	−	0.539734i	0.982555	−	0.185970i	$-0.0595428\pi$
$444$	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	−0.884460	−	0.466616i	$-0.845473\pi$
$449$	−0.807925	+	1.39937i	−0.0381283	+	0.0660402i	0.846332	+	0.532657i	$0.178806\pi$
$450$	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	0.674875	−	0.737932i	$-0.264197\pi$
$457$	4.53775	+	3.17737i	0.212267	+	0.148631i	−0.462608	+	0.886563i	$0.653086\pi$
$458$	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	0.186123	−	0.982527i	$-0.440408\pi$
$461$	14.9666	−	2.63902i	0.697065	−	0.122911i	0.510942	+	0.859615i	$0.329297\pi$
$462$	19.2123	−	2.55269i	0.893836	−	0.118762i
$463$	−29.9580	−	13.9696i	−1.39226	−	0.649224i	−0.425516	−	0.904951i	$-0.639907\pi$
$463$	−29.9580	−	13.9696i	−1.39226	−	0.649224i	−0.966749	+	0.255727i	$0.917685\pi$
$464$	−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	−0.685806	−	0.727784i	$-0.740550\pi$
$467$	5.87822	−	21.9378i	0.272012	−	1.01516i	0.957818	−	0.287377i	$-0.0927831\pi$
$468$	−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	−0.198470	−	0.980107i	$-0.563597\pi$
$479$	−21.4594	−	7.81060i	−0.980507	−	0.356875i	−0.782037	+	0.623232i	$0.785819\pi$
$480$	−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	−0.344977	−	0.938611i	$-0.612113\pi$
$487$	13.1004	−	13.1004i	0.593634	−	0.593634i	0.938611	+	0.344977i	$0.112113\pi$
$488$	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	−0.883553	−	0.468332i	$-0.844855\pi$
$491$	−5.95862	+	7.10121i	−0.268909	+	0.320473i	0.614644	+	0.788805i	$0.289300\pi$
$492$	−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	0.609417	−	0.792850i	$-0.291404\pi$
$499$	20.3482	+	3.58794i	0.910911	+	0.160618i	0.301494	+	0.953468i	$0.402515\pi$
$500$	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	0.987720	−	0.156235i	$-0.0499357\pi$
$503$	1.21585	+	4.53760i	0.0542119	+	0.202322i	−0.933508	+	0.358557i	$0.883269\pi$
$504$	−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	0.433862	−	0.900979i	$-0.357151\pi$
$509$	30.3526	−	11.0475i	1.34536	−	0.489670i	0.911496	+	0.411309i	$0.134928\pi$
$510$	−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	−0.549390	−	0.835566i	$-0.685140\pi$
$521$	−2.29310	+	1.32392i	−0.100463	+	0.0580021i	0.448927	+	0.893568i	$0.351806\pi$
$522$	9.06243	+	24.7150i	0.396652	+	1.08175i
$523$	−12.5901	+	3.37351i	−0.550527	+	0.147513i	−0.523351	−	0.852117i	$-0.675318\pi$
$523$	−12.5901	+	3.37351i	−0.550527	+	0.147513i	−0.0271764	+	0.999631i	$0.508652\pi$
$524$	−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	−0.814295	−	0.580451i	$-0.802876\pi$
$547$	−20.8870	+	9.73975i	−0.893062	+	0.416442i	−0.0787671	+	0.996893i	$0.525098\pi$
$548$	−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	−0.897377	−	0.441265i	$-0.854530\pi$
$557$	−34.3132	+	9.19419i	−1.45390	+	0.389570i	−0.556519	+	0.830835i	$0.687863\pi$
$558$	−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	−0.860221	−	0.509922i	$-0.829674\pi$
$563$	1.97748	−	4.24073i	0.0833410	−	0.178725i	0.943562	+	0.331196i	$0.107452\pi$
$564$	−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	0.942272	−	0.334848i	$-0.108685\pi$
$569$	−1.37633	−	7.80556i	−0.0576988	−	0.327226i	−0.999971	+	0.00762185i	$0.997574\pi$
$570$	1.27639	+	4.43053i	0.0534620	+	0.185574i
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	−0.242705	−	0.970100i	$-0.578035\pi$
$571$	4.65824	−	1.69546i	0.194941	−	0.0709528i	0.437646	+	0.899147i	$0.355812\pi$
$572$	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	−0.973029	−	0.230684i	$-0.925904\pi$
$577$	−5.90200	−	22.0266i	−0.245703	−	0.916977i	0.727325	−	0.686293i	$-0.240763\pi$
$578$	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	−0.902142	−	0.431439i	$-0.858006\pi$
$587$	−15.8151	−	33.9155i	−0.652758	−	1.39984i	0.249384	−	0.968405i	$-0.419772\pi$
$588$	−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	−0.585992	−	0.810317i	$-0.699295\pi$
$593$	5.46266	−	5.46266i	0.224324	−	0.224324i	0.810317	+	0.585992i	$0.199295\pi$
$594$	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	0.678752	−	0.734367i	$-0.262521\pi$
$599$	1.79656	+	1.50749i	0.0734055	+	0.0615946i	−0.605347	+	0.795962i	$0.706965\pi$
$600$	−16.6760	+	19.5761i	−0.680796	+	0.799192i
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.969987	−	0.243159i	$-0.0781836\pi$
$601$	38.1639	+	13.8905i	1.55674	+	0.566607i	0.586753	+	0.809766i	$0.300406\pi$
$602$	−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	0.840376	−	0.542004i	$-0.182334\pi$
$607$	1.07501	+	1.53527i	0.0436332	+	0.0623147i	−0.796743	+	0.604319i	$0.793445\pi$
$608$	−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	−0.803039	−	0.595926i	$-0.796785\pi$
$613$	4.71349	−	17.5910i	0.190376	−	0.710494i	0.993415	−	0.114568i	$-0.0365482\pi$
$614$	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	0.731715	−	0.681611i	$-0.238720\pi$
$617$	16.8885	+	7.87526i	0.679907	+	0.317046i	−0.0518073	+	0.998657i	$0.516498\pi$
$618$	18.7333	+	24.3534i	0.753564	+	0.979639i
$619$	28.0130	−	4.93945i	1.12594	−	0.198533i	0.420492	−	0.907296i	$-0.361858\pi$
$619$	28.0130	−	4.93945i	1.12594	−	0.198533i	0.705447	+	0.708763i	$0.250746\pi$
$620$	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	0.339333	+	0.940666i	$0.389799\pi$
$631$	−16.2016	+	28.0619i	−0.644974	+	1.11713i	−0.984307	+	0.176462i	$0.943535\pi$
$632$	−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	0.716571	+	0.697514i	$0.245711\pi$
$641$	−7.10695	+	19.5262i	−0.280708	+	0.771238i	−0.997279	+	0.0737239i	$0.976512\pi$
$642$	−32.6075	−	7.18807i	−1.28692	−	0.283691i
$643$	3.44122	+	39.3334i	0.135709	+	1.55116i	0.693060	+	0.720880i	$0.256262\pi$
$643$	3.44122	+	39.3334i	0.135709	+	1.55116i	−0.557351	+	0.830277i	$0.688182\pi$
$644$	−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	−0.995269	−	0.0971593i	$-0.969024\pi$
$647$	−27.7872	−	27.7872i	−1.09243	−	1.09243i	−0.0971593	−	0.995269i	$-0.530976\pi$
$648$	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	0.248162	−	0.968719i	$-0.420174\pi$
$653$	16.8852	−	1.47726i	0.660770	−	0.0578098i	0.412608	+	0.910909i	$0.364618\pi$
$654$	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	−0.484997	+	0.874516i	$0.661179\pi$
$659$	−36.7210	+	30.8125i	−1.43045	+	1.20029i	−0.945449	+	0.325770i	$0.894376\pi$
$660$	0.608652	−	3.87399i	0.0236917	−	0.150795i
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	−0.995671	−	0.0929427i	$-0.970373\pi$
$661$	−0.726513	+	4.12026i	−0.0282581	+	0.160259i	0.967413	+	0.253202i	$0.0814838\pi$
$662$	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	−0.463345	−	0.886178i	$-0.653351\pi$
$673$	13.6940	−	19.5570i	0.527863	−	0.753867i	0.991208	+	0.132311i	$0.0422398\pi$
$674$	−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	−0.985292	−	0.170880i	$-0.945339\pi$
$677$	−12.6903	+	18.1236i	−0.487727	+	0.696547i	0.497565	+	0.867427i	$0.334228\pi$
$678$	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	0.693127	−	0.720815i	$-0.256232\pi$
$683$	24.3829	+	6.53337i	0.932985	+	0.249993i	0.239858	+	0.970808i	$0.422899\pi$
$684$	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	−0.00928734	−	0.999957i	$-0.502956\pi$
$691$	25.5999	−	21.4808i	0.973865	−	0.817170i	0.983153	+	0.182787i	$0.0585118\pi$
$692$	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	$0.0752632\pi$
$701$			12.4042i			0.468499i	−0.972177	+	0.234249i	$0.924737\pi$
$702$	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	−0.832659	−	0.553786i	$-0.813182\pi$
$709$	4.29127	−	11.7902i	0.161162	−	0.442789i	0.993821	+	0.110998i	$0.0354046\pi$
$710$	−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	−0.984334	−	0.176316i	$-0.943582\pi$
$719$	−9.10268	+	15.7663i	−0.339473	+	0.587984i	0.644861	+	0.764300i	$0.276915\pi$
$720$	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	0.713414	−	0.700742i	$-0.247148\pi$
$727$	8.06014	+	5.64377i	0.298934	+	0.209316i	−0.414480	+	0.910058i	$0.636037\pi$
$728$	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	−0.309905	−	0.950767i	$-0.600297\pi$
$733$	−33.5024	−	15.6224i	−1.23744	−	0.577027i	−0.927533	+	0.373740i	$0.878075\pi$
$734$	−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	0.623586	−	0.781755i	$-0.285675\pi$
$739$	7.02338	+	4.05495i	0.258359	+	0.149164i	−0.365227	+	0.930919i	$0.619009\pi$
$740$	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	0.999996	−	0.00296531i	$-0.000943888\pi$
$743$	17.8592	+	25.5056i	0.655190	+	0.935709i	−0.344805	+	0.938674i	$0.612055\pi$
$744$	−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	0.364321	−	0.931273i	$-0.381301\pi$
$751$	−13.4156	−	11.2570i	−0.489541	−	0.410774i	−0.853862	+	0.520500i	$0.825746\pi$
$752$	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	−0.971286	−	0.237915i	$-0.923536\pi$
$757$	−20.1777	+	20.1777i	−0.733371	+	0.733371i	0.237915	+	0.971286i	$0.423536\pi$
$758$	−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	−0.138113	−	0.990416i	$-0.544104\pi$
$761$	23.7584	−	28.3141i	0.861240	−	1.02639i	0.999353	−	0.0359689i	$-0.0114517\pi$
$762$	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	0.0175779	−	0.999845i	$-0.494405\pi$
$769$	−8.53754	−	1.50540i	−0.307872	−	0.0542861i	−0.325450	+	0.945559i	$0.605516\pi$
$770$	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	0.998850	−	0.0479396i	$-0.0152655\pi$
$773$	3.05417	+	11.3983i	0.109851	+	0.409969i	−0.889000	+	0.457908i	$0.848599\pi$
$774$	−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	−0.712559	−	0.701612i	$-0.752464\pi$
$787$	7.93722	−	17.0214i	0.282931	−	0.606748i	0.995490	+	0.0948643i	$0.0302417\pi$
$788$	−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	−0.217184	−	0.976131i	$-0.569687\pi$
$797$	17.6670	−	12.3706i	0.625797	−	0.438188i	0.842981	+	0.537943i	$0.180798\pi$
$798$	−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	0.999839	−	0.0179428i	$-0.00571166\pi$
$821$	23.1674	+	27.6099i	0.808549	+	0.963591i	−0.191290	+	0.981533i	$0.561267\pi$
$822$	0.589922	−	13.8921i	0.0205759	−	0.484544i
$823$	−2.18095	+	1.52711i	−0.0760230	+	0.0532319i	−0.610970	−	0.791654i	$-0.709220\pi$
$823$	−2.18095	+	1.52711i	−0.0760230	+	0.0532319i	0.534947	+	0.844886i	$0.320332\pi$
$824$	−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	0.513321	−	0.858197i	$-0.328415\pi$
$827$	39.8859	−	10.6874i	1.38697	−	0.371637i	0.873647	+	0.486560i	$0.161748\pi$
$828$	−2.54703	−	3.02075i	−0.0885153	−	0.104978i
$829$	−19.6326	+	11.3349i	−0.681869	+	0.393677i	−0.800559	−	0.599254i	$-0.795464\pi$
$829$	−19.6326	+	11.3349i	−0.681869	+	0.393677i	0.118690	+	0.992931i	$0.462131\pi$
$830$	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	0.999530	−	0.0306567i	$-0.00975985\pi$
$839$	1.44230	+	8.17971i	0.0497938	+	0.282395i	−0.949736	+	0.313052i	$0.898649\pi$
$840$	−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	−0.0180058	−	0.999838i	$-0.505732\pi$
$853$	−6.11455	−	0.534954i	−0.209358	−	0.0183165i	−0.191352	+	0.981521i	$0.561287\pi$
$854$	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	0.981050	+	0.193756i	$0.0620670\pi$
$857$	14.6042	+	31.3187i	0.498869	+	1.06983i	−0.482181	+	0.876072i	$0.660155\pi$
$858$	−47.8395	+	15.1466i	−1.63321	+	0.517095i
$859$	14.4078	−	17.1705i	0.491587	−	0.585850i	−0.462034	−	0.886862i	$-0.652880\pi$
$859$	14.4078	−	17.1705i	0.491587	−	0.585850i	0.953620	+	0.301012i	$0.0973245\pi$
$860$	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	−0.190436	+	0.981700i	$0.560990\pi$
$863$	−34.4337	+	34.4337i	−1.17214	+	1.17214i	−0.981700	+	0.190436i	$0.939010\pi$
$864$	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	0.662201	−	0.749327i	$-0.269623\pi$
$877$	−7.94910	−	11.3525i	−0.268422	−	0.383347i	−0.930623	+	0.365980i	$0.880734\pi$
$878$	−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	0.115453	−	0.993313i	$-0.463168\pi$
$881$	−20.3929	−	11.7738i	−0.687054	−	0.396671i	−0.802507	+	0.596642i	$0.796501\pi$
$882$	6.28476	−	10.9458i	0.211619	−	0.368565i
$883$	4.25489	−	15.8795i	0.143188	−	0.534386i	−0.856641	−	0.515913i	$-0.827453\pi$
$883$	4.25489	−	15.8795i	0.143188	−	0.534386i	0.999829	−	0.0184733i	$-0.00588057\pi$
$884$	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	0.572289	−	0.820052i	$-0.306056\pi$
$887$	9.29073	+	4.33234i	0.311952	+	0.145466i	−0.260336	+	0.965518i	$0.583833\pi$
$888$	−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	0.951283	+	0.308321i	$0.0997669\pi$
$907$	−1.17717	+	13.4551i	−0.0390872	+	0.446769i	−0.990370	+	0.138448i	$0.955789\pi$
$908$	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	−0.830090	−	0.557629i	$-0.811711\pi$
$911$	4.95701	−	13.6193i	0.164233	−	0.451227i	0.994323	+	0.106403i	$0.0339332\pi$
$912$	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	$0.0621340\pi$
$919$			11.7599i			0.387925i	−0.981009	+	0.193962i	$0.937866\pi$
$920$	−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	−0.182433	+	0.983218i	$0.558397\pi$
$929$	−36.0388	+	30.2401i	−1.18239	+	0.992146i	−0.999960	+	0.00892776i	$0.997158\pi$
$930$	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	0.801147	−	0.598468i	$-0.204224\pi$
$937$	36.6017	+	9.80740i	1.19573	+	0.320394i	0.394580	+	0.918862i	$0.370890\pi$
$938$	−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	0.862364	−	0.506289i	$-0.168983\pi$
$941$	−3.79401	−	10.4240i	−0.123681	−	0.339811i	−0.986045	+	0.166477i	$0.946761\pi$
$942$	−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	−0.939558	−	0.342391i	$-0.888763\pi$
$947$	−9.12331	+	13.0294i	−0.296468	+	0.423400i	0.643090	+	0.765791i	$0.277652\pi$
$948$	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	−0.362638	−	0.931930i	$-0.618124\pi$
$953$	−35.2746	−	9.45180i	−1.14266	−	0.306174i	−0.780019	+	0.625756i	$0.784790\pi$
$954$	−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	−0.118487	−	0.992956i	$-0.537804\pi$
$967$	−1.95128	+	0.170714i	−0.0627488	+	0.00548981i	0.0557381	+	0.998445i	$0.482249\pi$
$968$	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	$-0.854281\pi$
$971$		−	27.5442i		−	0.883934i	0.897031	−	0.441967i	$-0.145719\pi$
$972$	−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	0.895123	+	0.445819i	$0.147088\pi$
$977$	2.84484	+	32.5167i	0.0910146	+	1.04030i	−0.804108	+	0.594483i	$0.797357\pi$
$978$	−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	−0.811915	−	0.583775i	$-0.801575\pi$
$983$	2.79155	−	31.9076i	0.0890367	−	1.01769i	0.900952	−	0.433919i	$-0.142870\pi$
$984$	−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	0.931362	+	0.364094i	$0.118621\pi$
$991$	24.5859	+	42.5840i	0.780995	+	1.35272i	−0.150367	+	0.988630i	$0.548046\pi$
$992$	−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	0.905031	−	0.425347i	$-0.139848\pi$
$997$	25.7299	+	18.0163i	0.814874	+	0.570581i	−0.0901563	+	0.995928i	$0.528737\pi$
$998$	−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.68.6	yes	192
3.2	odd	2		405.2.r.a.233.11		192
5.2	odd	4	inner	135.2.q.a.122.6	yes	192
5.3	odd	4		675.2.ba.b.257.11		192
5.4	even	2		675.2.ba.b.68.11		192
15.2	even	4		405.2.r.a.152.11		192
27.2	odd	18	inner	135.2.q.a.83.6	yes	192
27.25	even	9		405.2.r.a.8.11		192
135.2	even	36	inner	135.2.q.a.2.6	✓	192
135.29	odd	18		675.2.ba.b.218.11		192
135.52	odd	36		405.2.r.a.332.11		192
135.83	even	36		675.2.ba.b.407.11		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.6	✓	192	135.2	even	36	inner
135.2.q.a.68.6	yes	192	1.1	even	1	trivial
135.2.q.a.83.6	yes	192	27.2	odd	18	inner
135.2.q.a.122.6	yes	192	5.2	odd	4	inner
405.2.r.a.8.11		192	27.25	even	9
405.2.r.a.152.11		192	15.2	even	4
405.2.r.a.233.11		192	3.2	odd	2
405.2.r.a.332.11		192	135.52	odd	36
675.2.ba.b.68.11		192	5.4	even	2
675.2.ba.b.218.11		192	135.29	odd	18
675.2.ba.b.257.11		192	5.3	odd	4
675.2.ba.b.407.11		192	135.83	even	36

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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