LMFDB - Embedded newform 135.2.q.a.92.6

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			92.6
Character	$\chi$	$=$	135.92
Dual form			135.2.q.a.113.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03355 + 0.0904240i) q^{2} +(1.64619 + 0.538569i) q^{3} +(-0.909563 + 0.160381i) q^{4} +(1.76770 + 1.36939i) q^{5} +(-1.75012 - 0.407783i) q^{6} +(-2.38295 + 1.66856i) q^{7} +(2.92987 - 0.785057i) q^{8} +(2.41989 + 1.77317i) q^{9} +(-1.95083 - 1.25550i) q^{10} +(-0.357163 - 0.981298i) q^{11} +(-1.58369 - 0.225845i) q^{12} +(-0.102905 + 1.17621i) q^{13} +(2.31203 - 1.94002i) q^{14} +(2.17246 + 3.20631i) q^{15} +(-1.22140 + 0.444552i) q^{16} +(5.46688 + 1.46485i) q^{17} +(-2.66142 - 1.61385i) q^{18} +(-3.77562 - 2.17985i) q^{19} +(-1.82746 - 0.962045i) q^{20} +(-4.82143 + 1.46339i) q^{21} +(0.457879 + 0.981926i) q^{22} +(2.49254 - 3.55972i) q^{23} +(5.24594 + 0.285584i) q^{24} +(1.24952 + 4.84135i) q^{25} -1.22498i q^{26} +(3.02862 + 4.22226i) q^{27} +(1.89984 - 1.89984i) q^{28} +(-5.99110 - 5.02713i) q^{29} +(-2.53528 - 3.11744i) q^{30} +(-1.88318 - 10.6800i) q^{31} +(-4.27590 + 1.99388i) q^{32} +(-0.0594626 - 1.80776i) q^{33} +(-5.78276 - 1.01966i) q^{34} +(-6.49726 - 0.313684i) q^{35} +(-2.48542 - 1.22471i) q^{36} +(1.84738 - 6.89452i) q^{37} +(4.09941 + 1.91158i) q^{38} +(-0.802872 + 1.88085i) q^{39} +(6.25419 + 2.62440i) q^{40} +(-2.34606 - 2.79593i) q^{41} +(4.85087 - 1.94846i) q^{42} +(-0.986834 + 2.11627i) q^{43} +(0.482244 + 0.835270i) q^{44} +(1.84946 + 6.44822i) q^{45} +(-2.25429 + 3.90454i) q^{46} +(-0.209148 - 0.298694i) q^{47} +(-2.25007 + 0.0740116i) q^{48} +(0.500224 - 1.37435i) q^{49} +(-1.72922 - 4.89080i) q^{50} +(8.21061 + 5.35571i) q^{51} +(-0.0950427 - 1.08634i) q^{52} +(1.16516 + 1.16516i) q^{53} +(-3.51203 - 4.09006i) q^{54} +(0.712425 - 2.22374i) q^{55} +(-5.67183 + 6.75943i) q^{56} +(-5.04139 - 5.62188i) q^{57} +(6.64669 + 4.65406i) q^{58} +(9.77378 + 3.55737i) q^{59} +(-2.49022 - 2.56792i) q^{60} +(-0.654019 + 3.70913i) q^{61} +(2.91210 + 10.8681i) q^{62} +(-8.72512 - 0.187656i) q^{63} +(6.49036 - 3.74721i) q^{64} +(-1.79260 + 1.93827i) q^{65} +(0.224923 + 1.86304i) q^{66} +(0.570007 + 0.0498691i) q^{67} +(-5.20741 - 0.455589i) q^{68} +(6.02036 - 4.51758i) q^{69} +(6.74362 - 0.263300i) q^{70} +(2.83490 - 1.63673i) q^{71} +(8.48201 + 3.29542i) q^{72} +(3.56015 + 13.2867i) q^{73} +(-1.28593 + 7.29289i) q^{74} +(-0.550446 + 8.64274i) q^{75} +(3.78377 + 1.37718i) q^{76} +(2.48846 + 1.74244i) q^{77} +(0.659736 - 2.01655i) q^{78} +(-2.43289 + 2.89941i) q^{79} +(-2.76783 - 0.886738i) q^{80} +(2.71171 + 8.58176i) q^{81} +(2.67759 + 2.67759i) q^{82} +(-0.416330 - 4.75867i) q^{83} +(4.15070 - 2.10431i) q^{84} +(7.65785 + 10.0757i) q^{85} +(0.828582 - 2.27651i) q^{86} +(-7.15504 - 11.5022i) q^{87} +(-1.81682 - 2.59468i) q^{88} +(-1.62360 + 2.81215i) q^{89} +(-2.49459 - 6.49733i) q^{90} +(-1.71736 - 2.97456i) q^{91} +(-1.69622 + 3.63755i) q^{92} +(2.65186 - 18.5956i) q^{93} +(0.243174 + 0.289803i) q^{94} +(-3.68908 - 9.02363i) q^{95} +(-8.11279 + 0.979449i) q^{96} +(-10.8407 - 5.05512i) q^{97} +(-0.392732 + 1.46570i) q^{98} +(0.875716 - 3.00794i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.03355	+	0.0904240i	−0.730831	+	0.0639395i	−0.446496	−	0.894786i	$-0.647328\pi$
$2$	−1.03355	+	0.0904240i	−0.730831	+	0.0639395i	−0.284335	+	0.958725i	$0.591773\pi$
$3$	1.64619	+	0.538569i	0.950429	+	0.310943i
$3$	1.64619	+	0.538569i	0.950429	+	0.310943i
$4$	−0.909563	+	0.160381i	−0.454782	+	0.0801903i
$5$	1.76770	+	1.36939i	0.790539	+	0.612411i
$5$	1.76770	+	1.36939i	0.790539	+	0.612411i
$6$	−1.75012	−	0.407783i	−0.714484	−	0.166477i
$7$	−2.38295	+	1.66856i	−0.900671	+	0.630657i	−0.929458	−	0.368929i	$-0.879725\pi$
$7$	−2.38295	+	1.66856i	−0.900671	+	0.630657i	0.0287865	+	0.999586i	$0.490836\pi$
$8$	2.92987	−	0.785057i	1.03587	−	0.277560i
$9$	2.41989	+	1.77317i	0.806629	+	0.591058i
$10$	−1.95083	−	1.25550i	−0.616908	−	0.397023i
$11$	−0.357163	−	0.981298i	−0.107689	−	0.295872i	0.874130	−	0.485691i	$-0.161432\pi$
$11$	−0.357163	−	0.981298i	−0.107689	−	0.295872i	−0.981819	+	0.189819i	$0.939210\pi$
$12$	−1.58369	−	0.225845i	−0.457172	−	0.0651959i
$13$	−0.102905	+	1.17621i	−0.0285408	+	0.326222i	0.968480	+	0.249091i	$0.0801317\pi$
$13$	−0.102905	+	1.17621i	−0.0285408	+	0.326222i	−0.997021	+	0.0771317i	$0.975424\pi$
$14$	2.31203	−	1.94002i	0.617915	−	0.518492i
$15$	2.17246	+	3.20631i	0.560926	+	0.827866i
$16$	−1.22140	+	0.444552i	−0.305349	+	0.111138i
$17$	5.46688	+	1.46485i	1.32591	+	0.355277i	0.851190	−	0.524858i	$-0.175882\pi$
$17$	5.46688	+	1.46485i	1.32591	+	0.355277i	0.474723	+	0.880135i	$0.342548\pi$
$18$	−2.66142	−	1.61385i	−0.627302	−	0.380388i
$19$	−3.77562	−	2.17985i	−0.866186	−	0.500093i	−0.000107079	−	1.00000i	$-0.500034\pi$
$19$	−3.77562	−	2.17985i	−0.866186	−	0.500093i	−0.866079	+	0.499907i	$0.833367\pi$
$20$	−1.82746	−	0.962045i	−0.408632	−	0.215120i
$21$	−4.82143	+	1.46339i	−1.05212	+	0.319337i
$22$	0.457879	+	0.981926i	0.0976202	+	0.209347i
$23$	2.49254	−	3.55972i	0.519731	−	0.742253i	−0.470391	−	0.882458i	$-0.655887\pi$
$23$	2.49254	−	3.55972i	0.519731	−	0.742253i	0.990123	+	0.140205i	$0.0447760\pi$
$24$	5.24594	+	0.285584i	1.07082	+	0.0582946i
$25$	1.24952	+	4.84135i	0.249905	+	0.968270i
$26$		−	1.22498i		−	0.240238i
$27$	3.02862	+	4.22226i	0.582858	+	0.812574i
$28$	1.89984	−	1.89984i	0.359036	−	0.359036i
$29$	−5.99110	−	5.02713i	−1.11252	−	0.933515i	−0.114317	−	0.993444i	$-0.536468\pi$
$29$	−5.99110	−	5.02713i	−1.11252	−	0.933515i	−0.998203	+	0.0599291i	$0.980913\pi$
$30$	−2.53528	−	3.11744i	−0.462876	−	0.569165i
$31$	−1.88318	−	10.6800i	−0.338229	−	1.91819i	−0.392678	−	0.919676i	$-0.628451\pi$
$31$	−1.88318	−	10.6800i	−0.338229	−	1.91819i	0.0544490	−	0.998517i	$-0.482660\pi$
$32$	−4.27590	+	1.99388i	−0.755879	+	0.352472i
$33$	−0.0594626	−	1.80776i	−0.0103511	−	0.314691i
$34$	−5.78276	−	1.01966i	−0.991735	−	0.174870i
$35$	−6.49726	−	0.313684i	−1.09824	−	0.0530223i
$36$	−2.48542	−	1.22471i	−0.414237	−	0.204118i
$37$	1.84738	−	6.89452i	0.303708	−	1.13345i	−0.630344	−	0.776316i	$-0.717086\pi$
$37$	1.84738	−	6.89452i	0.303708	−	1.13345i	0.934052	−	0.357137i	$-0.116247\pi$
$38$	4.09941	+	1.91158i	0.665011	+	0.310100i
$39$	−0.802872	+	1.88085i	−0.128562	+	0.301177i
$40$	6.25419	+	2.62440i	0.988874	+	0.414955i
$41$	−2.34606	−	2.79593i	−0.366393	−	0.436650i	0.551077	−	0.834454i	$-0.314217\pi$
$41$	−2.34606	−	2.79593i	−0.366393	−	0.436650i	−0.917471	+	0.397804i	$0.869772\pi$
$42$	4.85087	−	1.94846i	0.748505	−	0.300654i
$43$	−0.986834	+	2.11627i	−0.150491	+	0.322729i	−0.967072	−	0.254501i	$-0.918089\pi$
$43$	−0.986834	+	2.11627i	−0.150491	+	0.322729i	0.816582	+	0.577230i	$0.195866\pi$
$44$	0.482244	+	0.835270i	0.0727010	+	0.125922i
$45$	1.84946	+	6.44822i	0.275702	+	0.961243i
$46$	−2.25429	+	3.90454i	−0.332377	+	0.575693i
$47$	−0.209148	−	0.298694i	−0.0305073	−	0.0435690i	0.803609	−	0.595158i	$-0.202911\pi$
$47$	−0.209148	−	0.298694i	−0.0305073	−	0.0435690i	−0.834116	+	0.551589i	$0.814022\pi$
$48$	−2.25007	+	0.0740116i	−0.324770	+	0.0106826i
$49$	0.500224	−	1.37435i	0.0714605	−	0.196336i
$50$	−1.72922	−	4.89080i	−0.244549	−	0.691664i
$51$	8.21061	+	5.35571i	1.14971	+	0.749949i
$52$	−0.0950427	−	1.08634i	−0.0131800	−	0.150649i
$53$	1.16516	+	1.16516i	0.160047	+	0.160047i	0.782588	−	0.622540i	$-0.213899\pi$
$53$	1.16516	+	1.16516i	0.160047	+	0.160047i	−0.622540	+	0.782588i	$0.713899\pi$
$54$	−3.51203	−	4.09006i	−0.477927	−	0.556587i
$55$	0.712425	−	2.22374i	0.0960634	−	0.299849i
$56$	−5.67183	+	6.75943i	−0.757930	+	0.903266i
$57$	−5.04139	−	5.62188i	−0.667748	−	0.744637i
$58$	6.64669	+	4.65406i	0.872753	+	0.611108i
$59$	9.77378	+	3.55737i	1.27244	+	0.463130i	0.887924	−	0.459990i	$-0.152147\pi$
$59$	9.77378	+	3.55737i	1.27244	+	0.463130i	0.384514	+	0.923119i	$0.374369\pi$
$60$	−2.49022	−	2.56792i	−0.321486	−	0.331517i
$61$	−0.654019	+	3.70913i	−0.0837385	+	0.474905i	0.913883	+	0.405977i	$0.133069\pi$
$61$	−0.654019	+	3.70913i	−0.0837385	+	0.474905i	−0.997622	+	0.0689275i	$0.978042\pi$
$62$	2.91210	+	10.8681i	0.369837	+	1.38025i
$63$	−8.72512	−	0.187656i	−1.09926	−	0.0236425i
$64$	6.49036	−	3.74721i	0.811295	−	0.468401i
$65$	−1.79260	+	1.93827i	−0.222345	+	0.240413i
$66$	0.224923	+	1.86304i	0.0276861	+	0.229324i
$67$	0.570007	+	0.0498691i	0.0696374	+	0.00609249i	0.121921	−	0.992540i	$-0.461094\pi$
$67$	0.570007	+	0.0498691i	0.0696374	+	0.00609249i	−0.0522838	+	0.998632i	$0.516650\pi$
$68$	−5.20741	−	0.455589i	−0.631491	−	0.0552483i
$69$	6.02036	−	4.51758i	0.724766	−	0.543852i
$70$	6.74362	−	0.263300i	0.806016	−	0.0314703i
$71$	2.83490	−	1.63673i	0.336441	−	0.194244i	−0.322256	−	0.946652i	$-0.604441\pi$
$71$	2.83490	−	1.63673i	0.336441	−	0.194244i	0.658697	+	0.752408i	$0.271108\pi$
$72$	8.48201	+	3.29542i	0.999614	+	0.388369i
$73$	3.56015	+	13.2867i	0.416684	+	1.55509i	0.781439	+	0.623982i	$0.214486\pi$
$73$	3.56015	+	13.2867i	0.416684	+	1.55509i	−0.364755	+	0.931104i	$0.618847\pi$
$74$	−1.28593	+	7.29289i	−0.149487	+	0.847782i
$75$	−0.550446	+	8.64274i	−0.0635600	+	0.997978i
$76$	3.78377	+	1.37718i	0.434028	+	0.157973i
$77$	2.48846	+	1.74244i	0.283586	+	0.198569i
$78$	0.659736	−	2.01655i	0.0747004	−	0.228329i
$79$	−2.43289	+	2.89941i	−0.273722	+	0.326209i	−0.885340	−	0.464944i	$-0.846074\pi$
$79$	−2.43289	+	2.89941i	−0.273722	+	0.326209i	0.611618	+	0.791153i	$0.290519\pi$
$80$	−2.76783	−	0.886738i	−0.309453	−	0.0991403i
$81$	2.71171	+	8.58176i	0.301302	+	0.953529i
$82$	2.67759	+	2.67759i	0.295691	+	0.295691i
$83$	−0.416330	−	4.75867i	−0.0456981	−	0.522332i	−0.984200	−	0.177059i	$-0.943342\pi$
$83$	−0.416330	−	4.75867i	−0.0456981	−	0.522332i	0.938502	−	0.345273i	$-0.112214\pi$
$84$	4.15070	−	2.10431i	0.452878	−	0.229599i
$85$	7.65785	+	10.0757i	0.830611	+	1.09286i
$86$	0.828582	−	2.27651i	0.0893483	−	0.245482i
$87$	−7.15504	−	11.5022i	−0.767101	−	1.23317i
$88$	−1.81682	−	2.59468i	−0.193673	−	0.276594i
$89$	−1.62360	+	2.81215i	−0.172101	+	0.298087i	−0.939154	−	0.343496i	$-0.888389\pi$
$89$	−1.62360	+	2.81215i	−0.172101	+	0.298087i	0.767053	+	0.641583i	$0.221722\pi$
$90$	−2.49459	−	6.49733i	−0.262953	−	0.684878i
$91$	−1.71736	−	2.97456i	−0.180029	−	0.311819i
$92$	−1.69622	+	3.63755i	−0.176843	+	0.379241i
$93$	2.65186	−	18.5956i	0.274985	−	1.92828i
$94$	0.243174	+	0.289803i	0.0250815	+	0.0298909i
$95$	−3.68908	−	9.02363i	−0.378492	−	0.925805i
$96$	−8.11279	+	0.979449i	−0.828008	+	0.0999646i
$97$	−10.8407	−	5.05512i	−1.10071	−	0.513270i	−0.214581	−	0.976706i	$-0.568839\pi$
$97$	−10.8407	−	5.05512i	−1.10071	−	0.513270i	−0.886130	+	0.463436i	$0.846616\pi$
$98$	−0.392732	+	1.46570i	−0.0396719	+	0.148058i
$99$	0.875716	−	3.00794i	0.0880128	−	0.302310i
$100$	−1.91298	−	4.20312i	−0.191298	−	0.420312i
$101$	0.264044	+	0.0465580i	0.0262733	+	0.00463269i	0.186769	−	0.982404i	$-0.440198\pi$
$101$	0.264044	+	0.0465580i	0.0262733	+	0.00463269i	−0.160496	+	0.987036i	$0.551309\pi$
$102$	−8.97037	−	4.79296i	−0.888199	−	0.474574i
$103$	−11.5058	+	5.36526i	−1.13370	+	0.528655i	−0.896606	−	0.442830i	$-0.853974\pi$
$103$	−11.5058	+	5.36526i	−1.13370	+	0.528655i	−0.237099	+	0.971485i	$0.576197\pi$
$104$	0.621894	+	3.52694i	0.0609817	+	0.345845i
$105$	−10.5268	−	4.01560i	−1.02731	−	0.391883i
$106$	−1.30961	−	1.09890i	−0.127201	−	0.106734i
$107$	5.03532	−	5.03532i	0.486782	−	0.486782i	−0.420507	−	0.907289i	$-0.638148\pi$
$107$	5.03532	−	5.03532i	0.486782	−	0.486782i	0.907289	+	0.420507i	$0.138148\pi$
$108$	−3.43189	−	3.35468i	−0.330234	−	0.322804i
$109$		−	8.81333i		−	0.844164i	−0.906558	−	0.422082i	$-0.861299\pi$
$109$		−	8.81333i		−	0.844164i	0.906558	−	0.422082i	$-0.138701\pi$
$110$	−0.535249	+	2.36277i	−0.0510340	+	0.225281i
$111$	6.75432	−	10.3548i	0.641091	−	0.982830i
$112$	2.16877	−	3.09732i	0.204929	−	0.292669i
$113$	0.0274297	+	0.0588232i	0.00258037	+	0.00553362i	0.907594	−	0.419849i	$-0.137917\pi$
$113$	0.0274297	+	0.0588232i	0.00258037	+	0.00553362i	−0.905013	+	0.425383i	$0.860139\pi$
$114$	5.71888	+	5.35464i	0.535623	+	0.501508i
$115$	9.28073	−	2.87925i	0.865433	−	0.268491i
$116$	6.25554	+	3.61164i	0.580813	+	0.335332i
$117$	−2.33465	+	2.66383i	−0.215838	+	0.246271i
$118$	−10.4234	−	2.79294i	−0.959550	−	0.257111i
$119$	−15.4715	+	5.63116i	−1.41827	+	0.516208i
$120$	8.88216	+	7.68858i	0.810827	+	0.701868i
$121$	7.59111	−	6.36970i	0.690101	−	0.579063i
$122$	0.340568	−	3.89271i	0.0308336	−	0.352430i
$123$	−2.35627	−	5.86614i	−0.212457	−	0.528932i
$124$	3.42574	+	9.41215i	0.307641	+	0.845236i
$125$	−4.42093	+	10.2691i	−0.395420	+	0.918500i
$126$	9.03483	−	0.595008i	0.804887	−	0.0530076i
$127$	−16.2081	+	4.34294i	−1.43823	+	0.385374i	−0.891915	−	0.452203i	$-0.850638\pi$
$127$	−16.2081	+	4.34294i	−1.43823	+	0.385374i	−0.546320	+	0.837577i	$0.683972\pi$
$128$	1.36013	−	0.952371i	0.120219	−	0.0841785i
$129$	−2.76427	+	2.95231i	−0.243381	+	0.259936i
$130$	1.67748	−	2.16540i	0.147125	−	0.189918i
$131$	−3.72744	+	0.657248i	−0.325668	+	0.0574240i	−0.334092	−	0.942541i	$-0.608430\pi$
$131$	−3.72744	+	0.657248i	−0.325668	+	0.0574240i	0.00842419	+	0.999965i	$0.497318\pi$
$132$	0.344015	+	1.63474i	0.0299426	+	0.142285i
$133$	12.6343	−	1.10536i	1.09554	−	0.0958470i
$134$	−0.593641			−0.0512828
$135$	−0.428238	+	11.6111i	−0.0368568	+	0.999321i
$136$	17.1673			1.47208
$137$	21.5441	−	1.88486i	1.84064	−	0.161035i	0.886955	−	0.461856i	$-0.152816\pi$
$137$	21.5441	−	1.88486i	1.84064	−	0.161035i	0.953681	+	0.300821i	$0.0972608\pi$
$138$	−5.81385	+	5.21353i	−0.494908	+	0.443805i
$139$	−11.0217	+	1.94342i	−0.934847	+	0.164839i	−0.620265	−	0.784392i	$-0.712975\pi$
$139$	−11.0217	+	1.94342i	−0.934847	+	0.164839i	−0.314581	+	0.949231i	$0.601864\pi$
$140$	5.95998	−	0.756718i	0.503710	−	0.0639544i
$141$	−0.183430	−	0.604347i	−0.0154476	−	0.0508952i
$142$	−2.78201	+	1.94799i	−0.233461	+	0.163471i
$143$	1.19097	−	0.319119i	0.0995937	−	0.0266861i
$144$	−3.74391	−	1.08998i	−0.311993	−	0.0908318i
$145$	−3.70635	−	17.0906i	−0.307796	−	1.41930i
$146$	−4.88103	−	13.4105i	−0.403957	−	1.10986i
$147$	1.56365	−	1.99304i	0.128967	−	0.164383i
$148$	−0.574563	+	6.56729i	−0.0472288	+	0.539828i
$149$	−10.1272	+	8.49772i	−0.829651	+	0.696160i	−0.955211	−	0.295926i	$-0.904372\pi$
$149$	−10.1272	+	8.49772i	−0.829651	+	0.696160i	0.125560	+	0.992086i	$0.459927\pi$
$150$	−0.212597	−	8.98249i	−0.0173585	−	0.733418i
$151$	11.4353	−	4.16211i	0.930591	−	0.338708i	0.168147	−	0.985762i	$-0.446222\pi$
$151$	11.4353	−	4.16211i	0.930591	−	0.338708i	0.762444	+	0.647054i	$0.223999\pi$
$152$	−12.7734	−	3.42262i	−1.03606	−	0.277611i
$153$	10.6318	+	13.2385i	0.859531	+	1.07027i
$154$	−2.72951	−	1.57588i	−0.219950	−	0.126988i
$155$	11.2963	−	21.4579i	0.907339	−	1.72354i
$156$	0.428612	−	1.83951i	0.0343164	−	0.147279i
$157$	5.01098	+	10.7461i	0.399920	+	0.857631i	0.998403	+	0.0564955i	$0.0179927\pi$
$157$	5.01098	+	10.7461i	0.399920	+	0.857631i	−0.598483	+	0.801136i	$0.704230\pi$
$158$	2.25234	−	3.21668i	0.179187	−	0.255905i
$159$	1.29056	+	2.54560i	0.102348	+	0.201879i
$160$	−10.2889	−	2.33080i	−0.813410	−	0.184266i
$161$			12.6416i			0.996298i
$162$	−3.57869	−	8.62449i	−0.281169	−	0.677604i
$163$	−10.1170	+	10.1170i	−0.792424	+	0.792424i	−0.981888	−	0.189463i	$-0.939325\pi$
$163$	−10.1170	+	10.1170i	−0.792424	+	0.792424i	0.189463	+	0.981888i	$0.439325\pi$
$164$	2.58230	+	2.16681i	0.201644	+	0.169199i
$165$	2.37042	−	3.27700i	0.184537	−	0.255114i
$166$	0.860597	+	4.88069i	0.0667953	+	0.378815i
$167$	−19.2590	+	8.98064i	−1.49031	+	0.694943i	−0.985716	−	0.168415i	$-0.946135\pi$
$167$	−19.2590	+	8.98064i	−1.49031	+	0.694943i	−0.504593	+	0.863357i	$0.668357\pi$
$168$	−12.9773	+	8.07263i	−1.00122	+	0.622817i
$169$	11.4296	+	2.01535i	0.879201	+	0.155027i
$170$	−8.82587	−	9.72132i	−0.676913	−	0.745591i
$171$	−5.27131	−	11.9698i	−0.403107	−	0.915355i
$172$	0.558179	−	2.08315i	0.0425608	−	0.158839i
$173$	7.68830	+	3.58511i	0.584530	+	0.272571i	0.692306	−	0.721604i	$-0.256595\pi$
$173$	7.68830	+	3.58511i	0.584530	+	0.272571i	−0.107775	+	0.994175i	$0.534373\pi$
$174$	8.43518	+	11.2412i	0.639470	+	0.852191i
$175$	−11.0556	−	9.45180i	−0.835728	−	0.714489i
$176$	0.872476	+	1.03978i	0.0657653	+	0.0783761i
$177$	14.1736	+	11.1200i	1.06535	+	0.835827i
$178$	1.42378	−	3.05331i	0.106717	−	0.228856i
$179$	−6.71299	−	11.6272i	−0.501753	−	0.869061i	−0.999998	−	0.00202486i	$-0.999355\pi$
$179$	−6.71299	−	11.6272i	−0.501753	−	0.869061i	0.498245	−	0.867036i	$-0.333978\pi$
$180$	−2.71637	−	5.56844i	−0.202466	−	0.415047i
$181$	−9.97071	+	17.2698i	−0.741117	+	1.28365i	0.210870	+	0.977514i	$0.432370\pi$
$181$	−9.97071	+	17.2698i	−0.741117	+	1.28365i	−0.951987	+	0.306138i	$0.900963\pi$
$182$	2.04395	+	2.91907i	0.151508	+	0.216376i
$183$	−3.07426	+	5.75369i	−0.227256	+	0.425325i
$184$	4.50825	−	12.3863i	0.332353	−	0.913132i
$185$	12.7069	−	9.65765i	0.934232	−	0.710045i
$186$	−1.05935	+	19.4593i	−0.0776751	+	1.42683i
$187$	−0.515118	−	5.88783i	−0.0376692	−	0.430560i
$188$	0.238138	+	0.238138i	0.0173680	+	0.0173680i
$189$	−14.2622	−	5.00800i	−1.03742	−	0.364278i
$190$	4.62881	+	8.99281i	0.335809	+	0.652407i
$191$	0.583207	−	0.695039i	0.0421994	−	0.0502912i	−0.744532	−	0.667587i	$-0.767327\pi$
$191$	0.583207	−	0.695039i	0.0421994	−	0.0502912i	0.786731	+	0.617296i	$0.211772\pi$
$192$	12.7025	−	2.67312i	0.916724	−	0.192916i
$193$	−6.05638	−	4.24072i	−0.435948	−	0.305254i	0.334923	−	0.942245i	$-0.391290\pi$
$193$	−6.05638	−	4.24072i	−0.435948	−	0.305254i	−0.770871	+	0.636992i	$0.780179\pi$
$194$	11.6616	+	4.24447i	0.837252	+	0.304735i
$195$	−3.99486	+	2.22532i	−0.286078	+	0.159359i
$196$	−0.234566	+	1.33029i	−0.0167547	+	0.0950205i
$197$	−4.43194	−	16.5402i	−0.315763	−	1.17844i	−0.923277	−	0.384134i	$-0.874500\pi$
$197$	−4.43194	−	16.5402i	−0.315763	−	1.17844i	0.607515	−	0.794309i	$-0.292167\pi$
$198$	−0.633107	+	3.18805i	−0.0449930	+	0.226565i
$199$	0.887783	−	0.512562i	0.0629332	−	0.0363345i	−0.468203	−	0.883621i	$-0.655098\pi$
$199$	0.887783	−	0.512562i	0.0629332	−	0.0363345i	0.531136	+	0.847286i	$0.321765\pi$
$200$	7.46168	+	13.2036i	0.527621	+	0.933636i
$201$	0.911482	+	0.389082i	0.0642910	+	0.0274437i
$202$	−0.277113	−	0.0242442i	−0.0194976	−	0.00170582i
$203$	22.6646	+	1.98289i	1.59074	+	0.139172i
$204$	−8.32702	−	3.55453i	−0.583008	−	0.248867i
$205$	−0.318408	−	8.15504i	−0.0222386	−	0.569573i
$206$	11.4067	−	6.58568i	0.794745	−	0.458846i
$207$	12.3437	−	4.19442i	0.857945	−	0.291532i
$208$	−0.397199	−	1.48237i	−0.0275408	−	0.102784i
$209$	−0.790574	+	4.48357i	−0.0546852	+	0.310135i
$210$	11.2431	+	3.19846i	0.775847	+	0.220715i
$211$	−9.20369	−	3.34987i	−0.633608	−	0.230614i	0.00519293	−	0.999987i	$-0.498347\pi$
$211$	−9.20369	−	3.34987i	−0.633608	−	0.230614i	−0.638801	+	0.769372i	$0.720569\pi$
$212$	−1.24666	−	0.872919i	−0.0856208	−	0.0599523i
$213$	5.54827	−	1.16758i	0.380161	−	0.0800014i
$214$	−4.74895	+	5.65957i	−0.324631	+	0.386880i
$215$	−4.64244	+	2.38957i	−0.316611	+	0.162967i
$216$	12.1882	+	9.99304i	0.829301	+	0.679940i
$217$	22.3078	+	22.3078i	1.51435	+	1.51435i
$218$	0.796937	+	9.10903i	0.0539754	+	0.616942i
$219$	−1.29509	+	23.7898i	−0.0875142	+	1.60756i
$220$	−0.291352	+	2.13689i	−0.0196429	+	0.144069i
$221$	−2.28554	+	6.27947i	−0.153742	+	0.422403i
$222$	−6.04462	+	11.3129i	−0.405688	+	0.759274i
$223$	−5.62275	−	8.03011i	−0.376527	−	0.537736i	0.585507	−	0.810668i	$-0.300896\pi$
$223$	−5.62275	−	8.03011i	−0.376527	−	0.537736i	−0.962033	+	0.272932i	$0.912007\pi$
$224$	6.86234	−	11.8859i	0.458510	−	0.794162i
$225$	−5.56085	+	13.9312i	−0.370723	+	0.928743i
$226$	−0.0336690	−	0.0583165i	−0.00223963	−	0.00387916i
$227$	7.23760	−	15.5211i	0.480376	−	1.03017i	−0.505520	−	0.862815i	$-0.668699\pi$
$227$	7.23760	−	15.5211i	0.480376	−	1.03017i	0.985897	−	0.167356i	$-0.0535229\pi$
$228$	5.48710	+	4.30492i	0.363392	+	0.285100i
$229$	−11.7568	−	14.0112i	−0.776912	−	0.925888i	0.221877	−	0.975075i	$-0.428782\pi$
$229$	−11.7568	−	14.0112i	−0.776912	−	0.925888i	−0.998790	+	0.0491866i	$0.984337\pi$
$230$	−9.33176	+	3.81505i	−0.615318	+	0.251557i
$231$	3.15805	+	4.20859i	0.207785	+	0.276905i
$232$	−21.4998	−	10.0255i	−1.41153	−	0.658207i
$233$	−1.27701	+	4.76585i	−0.0836594	+	0.312221i	−0.995057	−	0.0993059i	$-0.968338\pi$
$233$	−1.27701	+	4.76585i	−0.0836594	+	0.312221i	0.911398	+	0.411527i	$0.135004\pi$
$234$	2.17210	−	2.96432i	0.141995	−	0.193783i
$235$	0.0393191	−	0.814406i	0.00256489	−	0.0531260i
$236$	−9.46041	−	1.66812i	−0.615820	−	0.108586i
$237$	−5.56654	+	3.46270i	−0.361585	+	0.224927i
$238$	15.4814	−	7.21909i	1.00351	−	0.467944i
$239$	1.04890	+	5.94858i	0.0678474	+	0.384782i	0.999756	+	0.0220886i	$0.00703161\pi$
$239$	1.04890	+	5.94858i	0.0678474	+	0.384782i	−0.931909	+	0.362693i	$0.881857\pi$
$240$	−4.07880	−	2.95041i	−0.263286	−	0.190448i
$241$	−13.1764	−	11.0563i	−0.848766	−	0.712199i	0.110751	−	0.993848i	$-0.464674\pi$
$241$	−13.1764	−	11.0563i	−0.848766	−	0.712199i	−0.959518	+	0.281649i	$0.909119\pi$
$242$	−7.26983	+	7.26983i	−0.467322	+	0.467322i
$243$	−0.157869	+	15.5877i	−0.0101273	+	0.999949i
$244$		−	3.47858i		−	0.222693i
$245$	2.76627	−	1.74444i	0.176731	−	0.111448i
$246$	2.96576	+	5.84990i	0.189090	+	0.372976i
$247$	2.95250	−	4.21661i	0.187863	−	0.268296i
$248$	−13.9019	−	29.8128i	−0.882773	−	1.89311i
$249$	1.87751	−	8.05791i	0.118983	−	0.510649i
$250$	3.64068	−	11.0134i	0.230257	−	0.696552i
$251$	−0.245642	−	0.141822i	−0.0155048	−	0.00895170i	0.492228	−	0.870467i	$-0.336183\pi$
$251$	−0.245642	−	0.141822i	−0.0155048	−	0.00895170i	−0.507732	+	0.861515i	$0.669516\pi$
$252$	7.96615	−	1.22865i	0.501820	−	0.0773980i
$253$	−4.38339	−	1.17453i	−0.275582	−	0.0738419i
$254$	16.3592	−	5.95426i	1.02647	−	0.373603i
$255$	7.17982	+	20.7108i	0.449618	+	1.29696i
$256$	−12.8018	+	10.7420i	−0.800110	+	0.671372i
$257$	−0.568503	+	6.49802i	−0.0354623	+	0.405335i	0.957630	+	0.288001i	$0.0929906\pi$
$257$	−0.568503	+	6.49802i	−0.0354623	+	0.405335i	−0.993092	+	0.117335i	$0.962565\pi$
$258$	2.59006	−	3.30132i	0.161250	−	0.205531i
$259$	7.10171	+	19.5118i	0.441279	+	1.21240i
$260$	1.31962	−	2.05048i	0.0818396	−	0.127165i
$261$	−5.58382	−	22.7884i	−0.345630	−	1.41056i
$262$	3.79307	−	1.01635i	0.234336	−	0.0627903i
$263$	−3.72625	+	2.60915i	−0.229770	+	0.160887i	−0.682792	−	0.730612i	$-0.739235\pi$
$263$	−3.72625	+	2.60915i	−0.229770	+	0.160887i	0.453022	+	0.891499i	$0.350346\pi$
$264$	−1.59341	−	5.24983i	−0.0980678	−	0.323104i
$265$	0.464091	+	3.65522i	0.0285089	+	0.224538i
$266$	−12.9583	+	2.28489i	−0.794523	+	0.140096i
$267$	−4.18728	+	3.75492i	−0.256258	+	0.229797i
$268$	−0.526455	+	0.0460589i	−0.0321584	+	0.00281349i
$269$	7.68259			0.468416			0.234208	−	0.972187i	$-0.424750\pi$
$269$	7.68259			0.468416			0.234208	+	0.972187i	$0.424750\pi$
$270$	−0.607313	−	12.0393i	−0.0369599	−	0.732691i
$271$	18.8470			1.14487			0.572437	−	0.819949i	$-0.305998\pi$
$271$	18.8470			1.14487			0.572437	+	0.819949i	$0.305998\pi$
$272$	−7.32843	+	0.641154i	−0.444351	+	0.0388757i
$273$	−1.22510	−	5.82161i	−0.0741466	−	0.352340i
$274$	−22.0965	+	3.89621i	−1.33490	+	0.235378i
$275$	4.30452	−	2.95531i	0.259573	−	0.178212i
$276$	−4.75137	+	5.07457i	−0.285999	+	0.305453i
$277$	8.10294	−	5.67374i	0.486858	−	0.340902i	−0.304235	−	0.952597i	$-0.598401\pi$
$277$	8.10294	−	5.67374i	0.486858	−	0.340902i	0.791094	+	0.611695i	$0.209512\pi$
$278$	11.2157	−	3.00525i	0.672675	−	0.180243i
$279$	14.3805	−	29.1837i	0.860937	−	1.74718i
$280$	−19.2824	+	4.18167i	−1.15234	+	0.249902i
$281$	−1.61241	−	4.43006i	−0.0961883	−	0.264275i	0.882262	−	0.470759i	$-0.156020\pi$
$281$	−1.61241	−	4.43006i	−0.0961883	−	0.264275i	−0.978450	+	0.206484i	$0.933798\pi$
$282$	0.244232	+	0.608037i	0.0145438	+	0.0362081i
$283$	0.00130413	−	0.0149063i	7.75226e−5	−	0.000886087i	−0.996156	−	0.0875988i	$-0.972081\pi$
$283$	0.00130413	−	0.0149063i	7.75226e−5	−	0.000886087i	0.996233	+	0.0867127i	$0.0276362\pi$
$284$	−2.31602	+	1.94337i	−0.137431	+	0.115318i
$285$	−1.21308	−	16.8414i	−0.0718569	−	0.997601i
$286$	−1.20207	+	0.437518i	−0.0710799	+	0.0258710i
$287$	10.2557	+	2.74801i	0.605376	+	0.162210i
$288$	−13.8827	−	2.75693i	−0.818046	−	0.162454i
$289$	13.0186	+	7.51627i	0.765798	+	0.442134i
$290$	5.37611	+	17.3289i	0.315696	+	1.01759i
$291$	−15.1234	−	14.1602i	−0.886550	−	0.830085i
$292$	−5.36910	−	11.5141i	−0.314203	−	0.673810i
$293$	−13.1517	+	18.7826i	−0.768330	+	1.09729i	0.224110	+	0.974564i	$0.428052\pi$
$293$	−13.1517	+	18.7826i	−0.768330	+	1.09729i	−0.992441	+	0.122726i	$0.960836\pi$
$294$	−1.43589	+	2.20130i	−0.0837428	+	0.128383i
$295$	12.4057	+	19.6725i	0.722286	+	1.14538i
$296$		−	21.6504i		−	1.25840i
$297$	3.06158	−	4.48001i	0.177651	−	0.259957i
$298$	9.69857	−	9.69857i	0.561823	−	0.561823i
$299$	3.93049	+	3.29807i	0.227306	+	0.190733i
$300$	−0.885462	−	7.94940i	−0.0511222	−	0.458959i
$301$	−1.17955	−	6.68957i	−0.0679882	−	0.385580i
$302$	−11.4426	+	5.33578i	−0.658448	+	0.307040i
$303$	0.409591	+	0.218849i	0.0235304	+	0.0125725i
$304$	5.58058	+	0.984008i	0.320068	+	0.0564367i
$305$	−6.23536	+	5.66101i	−0.357036	+	0.324149i
$306$	−12.1856	−	12.7213i	−0.696604	−	0.727228i
$307$	−7.06051	+	26.3502i	−0.402965	+	1.50388i	0.404814	+	0.914399i	$0.367336\pi$
$307$	−7.06051	+	26.3502i	−0.402965	+	1.50388i	−0.807779	+	0.589486i	$0.799330\pi$
$308$	−2.54286	−	1.18576i	−0.144893	−	0.0675647i
$309$	−21.8304	+	2.63556i	−1.24189	+	0.149932i
$310$	−9.73498	+	23.1993i	−0.552910	+	1.31763i
$311$	20.3862	+	24.2954i	1.15600	+	1.37766i	0.913162	+	0.407596i	$0.133633\pi$
$311$	20.3862	+	24.2954i	1.15600	+	1.37766i	0.242835	+	0.970068i	$0.421923\pi$
$312$	−0.875741	+	6.14094i	−0.0495791	+	0.347663i
$313$	4.83829	−	10.3757i	0.273476	−	0.586472i	−0.720820	−	0.693122i	$-0.756235\pi$
$313$	4.83829	−	10.3757i	0.273476	−	0.586472i	0.994297	+	0.106650i	$0.0340125\pi$
$314$	−6.15081	−	10.6535i	−0.347110	−	0.601213i
$315$	−15.1664	−	12.2798i	−0.854531	−	0.691891i
$316$	1.74786	−	3.02739i	0.0983249	−	0.170304i
$317$	−7.17947	−	10.2533i	−0.403239	−	0.575885i	0.565257	−	0.824915i	$-0.308777\pi$
$317$	−7.17947	−	10.2533i	−0.403239	−	0.575885i	−0.968496	+	0.249030i	$0.919888\pi$
$318$	−1.56404	−	2.51431i	−0.0877071	−	0.140995i
$319$	−2.79331	+	7.67456i	−0.156395	+	0.429693i
$320$	16.6044	+	2.26391i	0.928214	+	0.126556i
$321$	11.0010	−	5.57723i	0.614013	−	0.311291i
$322$	−1.14311	−	13.0658i	−0.0637028	−	0.728126i
$323$	−17.4477	−	17.4477i	−0.970816	−	0.970816i
$324$	−3.84282	−	7.37075i	−0.213490	−	0.409486i
$325$	−5.82304	+	0.971504i	−0.323004	+	0.0538893i
$326$	9.54162	−	11.3713i	0.528461	−	0.629796i
$327$	4.74658	−	14.5084i	0.262487	−	0.802318i
$328$	−9.06863	−	6.34992i	−0.500731	−	0.350616i
$329$	0.996777	+	0.362797i	0.0549541	+	0.0200017i
$330$	−2.15363	+	3.60130i	−0.118554	+	0.198245i
$331$	−4.38923	+	24.8926i	−0.241254	+	1.36822i	0.587780	+	0.809021i	$0.300002\pi$
$331$	−4.38923	+	24.8926i	−0.241254	+	1.36822i	−0.829034	+	0.559199i	$0.811109\pi$
$332$	1.14188	+	4.26154i	0.0626686	+	0.233883i
$333$	16.6956	−	13.4082i	0.914916	−	0.734767i
$334$	19.0931	−	11.0234i	1.04473	−	0.603175i
$335$	0.939311	+	0.868717i	0.0513200	+	0.0474631i
$336$	5.23832	−	3.93075i	0.285774	−	0.214440i
$337$	−1.72746	−	0.151133i	−0.0941006	−	0.00823274i	0.0400082	−	0.999199i	$-0.487262\pi$
$337$	−1.72746	−	0.151133i	−0.0941006	−	0.00823274i	−0.134109	+	0.990967i	$0.542817\pi$
$338$	−11.9953	−	1.04946i	−0.652460	−	0.0570829i
$339$	0.0134742	+	0.111607i	0.000731818	+	0.00606166i
$340$	−8.58125	−	7.93633i	−0.465384	−	0.430408i
$341$	−9.80770	+	5.66248i	−0.531117	+	0.306640i
$342$	6.53053	+	11.8948i	0.353131	+	0.643196i
$343$	−4.16923	−	15.5598i	−0.225118	−	0.840150i
$344$	−1.22990	+	6.97513i	−0.0663120	+	0.376074i
$345$	16.8285	+	0.258522i	0.906017	+	0.0139183i
$346$	−8.27043	−	3.01019i	−0.444621	−	0.161829i
$347$	8.10639	+	5.67616i	0.435174	+	0.304712i	0.770559	−	0.637369i	$-0.219977\pi$
$347$	8.10639	+	5.67616i	0.435174	+	0.304712i	−0.335385	+	0.942081i	$0.608866\pi$
$348$	8.35270	+	9.31449i	0.447752	+	0.499309i
$349$	19.9263	−	23.7472i	1.06663	−	1.27116i	0.105689	−	0.994399i	$-0.466295\pi$
$349$	19.9263	−	23.7472i	1.06663	−	1.27116i	0.960939	−	0.276759i	$-0.0892603\pi$
$350$	12.2812	+	8.76923i	0.656460	+	0.468735i
$351$	−5.27793	+	3.12781i	−0.281715	+	0.166950i
$352$	3.48379	+	3.48379i	0.185687	+	0.185687i
$353$	0.319565	+	3.65264i	0.0170087	+	0.194411i	0.999945	+	0.0104654i	$0.00333131\pi$
$353$	0.319565	+	3.65264i	0.0170087	+	0.194411i	−0.982937	+	0.183945i	$0.941113\pi$
$354$	−15.6547	−	10.2114i	−0.832037	−	0.542730i
$355$	7.25257	+	0.988845i	0.384927	+	0.0524825i
$356$	1.02575	−	2.81822i	0.0543646	−	0.149365i
$357$	−28.5018	+	0.937508i	−1.50848	+	0.0496182i
$358$	7.98960	+	11.4103i	0.422264	+	0.603055i
$359$	3.73590	−	6.47077i	0.197173	−	0.341514i	−0.750438	−	0.660941i	$-0.770157\pi$
$359$	3.73590	−	6.47077i	0.197173	−	0.341514i	0.947611	+	0.319427i	$0.103491\pi$
$360$	10.4809	+	17.4405i	0.552392	+	0.919196i
$361$	0.00352408	+	0.00610389i	0.000185478	+	0.000321258i
$362$	8.74364	−	18.7508i	0.459555	−	0.985520i
$363$	15.9269	−	6.39740i	0.835947	−	0.335777i
$364$	2.03911	+	2.43012i	0.106878	+	0.127373i
$365$	−11.9014	+	28.3621i	−0.622947	+	1.48454i
$366$	2.65713	−	6.22473i	0.138891	−	0.325372i
$367$	15.3011	+	7.13502i	0.798711	+	0.372445i	0.778733	−	0.627356i	$-0.215863\pi$
$367$	15.3011	+	7.13502i	0.798711	+	0.372445i	0.0199776	+	0.999800i	$0.493640\pi$
$368$	−1.46190	+	5.45590i	−0.0762070	+	0.284408i
$369$	−0.719542	−	10.9258i	−0.0374579	−	0.568775i
$370$	−12.2600	+	11.1307i	−0.637366	+	0.578657i
$371$	−4.72067	−	0.832381i	−0.245085	−	0.0432151i
$372$	0.570337	+	17.3392i	0.0295706	+	0.898995i
$373$	−1.92488	+	0.897584i	−0.0996663	+	0.0464752i	−0.471812	−	0.881699i	$-0.656400\pi$
$373$	−1.92488	+	0.897584i	−0.0996663	+	0.0464752i	0.372146	+	0.928174i	$0.378622\pi$
$374$	1.06480	+	6.03879i	0.0550596	+	0.312259i
$375$	−12.8083	+	14.5240i	−0.661420	+	0.750016i
$376$	−0.847268	−	0.710942i	−0.0436945	−	0.0366640i
$377$	6.52949	−	6.52949i	0.336286	−	0.336286i
$378$	15.1935	+	3.88638i	0.781470	+	0.199894i
$379$			9.60506i			0.493379i	0.969095	+	0.246689i	$0.0793427\pi$
$379$			9.60506i			0.493379i	−0.969095	+	0.246689i	$0.920657\pi$
$380$	4.80267	+	7.61591i	0.246372	+	0.390688i
$381$	−29.0206	−	1.57985i	−1.48677	−	0.0809383i
$382$	−0.539926	+	0.771094i	−0.0276250	+	0.0394526i
$383$	−0.0510389	−	0.109453i	−0.00260797	−	0.00559281i	0.904999	−	0.425413i	$-0.139871\pi$
$383$	−0.0510389	−	0.109453i	−0.00260797	−	0.00559281i	−0.907607	+	0.419820i	$0.862093\pi$
$384$	2.75195	−	0.835263i	0.140435	−	0.0426243i
$385$	2.01276	+	6.48778i	0.102580	+	0.330648i
$386$	6.64304	+	3.83536i	0.338122	+	0.195215i
$387$	−6.14055	+	3.37131i	−0.312141	+	0.171374i
$388$	10.6711	+	2.85931i	0.541742	+	0.145159i
$389$	−24.1005	+	8.77187i	−1.22194	+	0.444752i	−0.870832	−	0.491581i	$-0.836419\pi$
$389$	−24.1005	+	8.77187i	−1.22194	+	0.444752i	−0.351113	+	0.936333i	$0.614197\pi$
$390$	3.92767	−	2.66122i	0.198885	−	0.134756i
$391$	18.8409	−	15.8094i	0.952825	−	0.799515i
$392$	0.386646	−	4.41938i	0.0195286	−	0.223213i
$393$	−6.49004	−	0.925525i	−0.327379	−	0.0466866i
$394$	6.07627	+	16.6944i	0.306118	+	0.841053i
$395$	−8.27106	+	1.79370i	−0.416162	+	0.0902507i
$396$	−0.314104	+	2.87636i	−0.0157843	+	0.144543i
$397$	25.5064	−	6.83441i	1.28013	−	0.343009i	0.446225	−	0.894921i	$-0.352768\pi$
$397$	25.5064	−	6.83441i	1.28013	−	0.343009i	0.833903	+	0.551911i	$0.186101\pi$
$398$	−0.871221	+	0.610036i	−0.0436704	+	0.0305783i
$399$	21.3938	+	4.98482i	1.07103	+	0.249553i
$400$	−3.67840	−	5.35773i	−0.183920	−	0.267887i
$401$	−33.5008	+	5.90709i	−1.67295	+	0.294986i	−0.928124	−	0.372272i	$-0.878579\pi$
$401$	−33.5008	+	5.90709i	−1.67295	+	0.294986i	−0.744826	+	0.667259i	$0.767468\pi$
$402$	−0.977246	−	0.319716i	−0.0487406	−	0.0159460i
$403$	12.7558	−	1.11599i	0.635411	−	0.0555912i
$404$	−0.247631			−0.0123201
$405$	−6.95831	+	18.8834i	−0.345761	+	0.938323i
$406$	−23.6043			−1.17146
$407$	−7.42540	+	0.649638i	−0.368063	+	0.0322014i
$408$	28.2606	+	9.24574i	1.39911	+	0.457733i
$409$	33.1027	−	5.83690i	1.63682	−	0.288616i	0.721826	−	0.692075i	$-0.243303\pi$
$409$	33.1027	−	5.83690i	1.63682	−	0.288616i	0.914998	+	0.403458i	$0.132192\pi$
$410$	1.06650	+	8.39986i	0.0526708	+	0.414840i
$411$	36.4808	+	8.50012i	1.79947	+	0.419280i
$412$	9.60481	−	6.72536i	0.473195	−	0.331335i
$413$	−29.2261	+	7.83112i	−1.43812	+	0.385344i
$414$	−12.3786	+	5.45131i	−0.608373	+	0.267917i
$415$	5.78055	−	8.98202i	0.283756	−	0.440910i
$416$	−1.90522	−	5.23454i	−0.0934110	−	0.256645i
$417$	−19.1904	−	2.73669i	−0.939760	−	0.134016i
$418$	0.411677	−	4.70549i	0.0201358	−	0.230153i
$419$	23.6855	−	19.8745i	1.15711	−	0.970932i	0.157249	−	0.987559i	$-0.449737\pi$
$419$	23.6855	−	19.8745i	1.15711	−	0.970932i	0.999862	+	0.0166274i	$0.00529290\pi$
$420$	10.2188	+	1.96415i	0.498627	+	0.0958409i
$421$	−13.7828	+	5.01653i	−0.671732	+	0.244490i	−0.655293	−	0.755374i	$-0.727455\pi$
$421$	−13.7828	+	5.01653i	−0.671732	+	0.244490i	−0.0164386	+	0.999865i	$0.505233\pi$
$422$	9.81539	+	2.63003i	0.477806	+	0.128028i
$423$	0.0235220	−	1.09366i	0.00114368	−	0.0531756i
$424$	4.32849	+	2.49906i	0.210210	+	0.121365i
$425$	−0.260840	+	28.2974i	−0.0126526	+	1.37263i
$426$	−5.62885	+	1.70845i	−0.272719	+	0.0827748i
$427$	−4.63041	−	9.92994i	−0.224081	−	0.480543i
$428$	−3.77237	+	5.38751i	−0.182345	+	0.260415i
$429$	2.13243	+	0.116087i	0.102955	+	0.00560475i
$430$	4.58212	−	2.88953i	0.220970	−	0.139346i
$431$			30.3267i			1.46078i	0.683028	+	0.730392i	$0.260663\pi$
$431$			30.3267i			1.46078i	−0.683028	+	0.730392i	$0.739337\pi$
$432$	−5.57616	−	3.81067i	−0.268283	−	0.183341i
$433$	5.35178	−	5.35178i	0.257190	−	0.257190i	−0.566720	−	0.823910i	$-0.691788\pi$
$433$	5.35178	−	5.35178i	0.257190	−	0.257190i	0.823910	+	0.566720i	$0.191788\pi$
$434$	−25.0735	−	21.0391i	−1.20356	−	1.00991i
$435$	3.10312	−	30.1306i	0.148783	−	1.44465i
$436$	1.41349	+	8.01628i	0.0676938	+	0.383910i
$437$	−17.1706	+	8.00677i	−0.821380	+	0.383016i
$438$	−0.812622	−	24.7050i	−0.0388286	−	1.18045i
$439$	−9.78003	−	1.72448i	−0.466775	−	0.0823051i	−0.0646863	−	0.997906i	$-0.520605\pi$
$439$	−9.78003	−	1.72448i	−0.466775	−	0.0823051i	−0.402089	+	0.915601i	$0.631716\pi$
$440$	0.341556	−	7.07456i	0.0162830	−	0.337266i
$441$	3.64745	−	2.43880i	0.173688	−	0.116133i
$442$	1.79441	−	6.69682i	0.0853513	−	0.318535i
$443$	8.40263	+	3.91821i	0.399221	+	0.186160i	0.611851	−	0.790973i	$-0.290425\pi$
$443$	8.40263	+	3.91821i	0.399221	+	0.186160i	−0.212630	+	0.977133i	$0.568203\pi$
$444$	−4.48278	+	10.5016i	−0.212743	+	0.498382i
$445$	−6.72097	+	2.74770i	−0.318605	+	0.130253i
$446$	6.53751	+	7.79110i	0.309560	+	0.368919i
$447$	−21.2479	+	8.53468i	−1.00499	+	0.403676i
$448$	−9.21376	+	19.7590i	−0.435309	+	0.933524i
$449$	−15.0787	−	26.1171i	−0.711609	−	1.23254i	−0.964253	−	0.264984i	$-0.914633\pi$
$449$	−15.0787	−	26.1171i	−0.711609	−	1.23254i	0.252644	−	0.967559i	$-0.418700\pi$
$450$	4.48771	−	14.9014i	0.211553	−	0.702459i
$451$	−1.90571	+	3.30079i	−0.0897364	+	0.155428i
$452$	−0.0343832	−	0.0491042i	−0.00161725	−	0.00230967i
$453$	21.0663	−	0.692932i	0.989779	−	0.0325568i
$454$	−6.07695	+	16.6963i	−0.285206	+	0.783596i
$455$	1.03756	−	7.60987i	0.0486416	−	0.356756i
$456$	−19.1841	−	12.5136i	−0.898379	−	0.586004i
$457$	2.64140	+	30.1913i	0.123559	+	1.41229i	0.764462	+	0.644669i	$0.223005\pi$
$457$	2.64140	+	30.1913i	0.123559	+	1.41229i	−0.640902	+	0.767622i	$0.721440\pi$
$458$	13.4182	+	13.4182i	0.626993	+	0.626993i
$459$	10.3722	+	27.5190i	0.484131	+	1.28448i
$460$	−7.97964	+	4.10731i	−0.372052	+	0.191504i
$461$	8.35560	−	9.95782i	0.389159	−	0.463782i	−0.535524	−	0.844520i	$-0.679886\pi$
$461$	8.35560	−	9.95782i	0.389159	−	0.463782i	0.924683	+	0.380738i	$0.124330\pi$
$462$	−3.64457	−	4.06423i	−0.169561	−	0.189085i
$463$	22.5069	+	15.7595i	1.04598	+	0.732405i	0.964450	−	0.264266i	$-0.0851295\pi$
$463$	22.5069	+	15.7595i	1.04598	+	0.732405i	0.0815330	+	0.996671i	$0.474018\pi$
$464$	9.55234	+	3.47677i	0.443456	+	0.161405i
$465$	30.1524	−	29.2400i	1.39828	−	1.35597i
$466$	0.888904	−	5.04122i	0.0411777	−	0.233530i
$467$	7.76986	+	28.9975i	0.359546	+	1.34184i	0.874666	+	0.484727i	$0.161081\pi$
$467$	7.76986	+	28.9975i	0.359546	+	1.34184i	−0.515119	+	0.857118i	$0.672252\pi$
$468$	1.69628	−	2.79736i	0.0784106	−	0.129308i
$469$	−1.44151	+	0.832256i	−0.0665627	+	0.0384300i
$470$	0.0330036	+	0.845286i	0.00152234	+	0.0389901i
$471$	2.46153	+	20.3889i	0.113421	+	0.939469i
$472$	31.4287	+	2.74965i	1.44662	+	0.126563i
$473$	2.42915	+	0.212523i	0.111693	+	0.00977184i
$474$	5.44019	−	4.08223i	0.249876	−	0.187503i
$475$	5.83572	−	21.0029i	0.267761	−	0.963678i
$476$	13.1692	−	7.60323i	0.603608	−	0.348493i
$477$	0.753527	+	4.88559i	0.0345016	+	0.223696i
$478$	−1.62198	−	6.05332i	−0.0741878	−	0.276872i
$479$	1.81506	−	10.2937i	0.0829324	−	0.470333i	−0.914851	−	0.403791i	$-0.867692\pi$
$479$	1.81506	−	10.2937i	0.0829324	−	0.470333i	0.997784	−	0.0665419i	$-0.0211966\pi$
$480$	−15.6822	−	9.37823i	−0.715792	−	0.428055i
$481$	7.91931	+	2.88239i	0.361090	+	0.131426i
$482$	14.6182	+	10.2358i	0.665843	+	0.466228i
$483$	−6.80837	+	20.8105i	−0.309792	+	0.946911i
$484$	−5.88302	+	7.01111i	−0.267410	+	0.318687i
$485$	−12.2407	−	23.7812i	−0.555823	−	1.07985i
$486$	−1.24633	−	16.1249i	−0.0565348	−	0.731441i
$487$	−13.7181	−	13.7181i	−0.621625	−	0.621625i	0.324322	−	0.945947i	$-0.394864\pi$
$487$	−13.7181	−	13.7181i	−0.621625	−	0.621625i	−0.945947	+	0.324322i	$0.894864\pi$
$488$	0.995683	+	11.3807i	0.0450725	+	0.515181i
$489$	−22.1032	+	11.2058i	−0.999541	+	0.506744i
$490$	−2.70135	+	2.05311i	−0.122034	+	0.0927499i
$491$	14.3153	−	39.3310i	0.646040	−	1.77498i	0.0141799	−	0.999899i	$-0.495486\pi$
$491$	14.3153	−	39.3310i	0.646040	−	1.77498i	0.631861	−	0.775082i	$-0.282292\pi$
$492$	3.08399	+	4.95773i	0.139037	+	0.223512i
$493$	−25.3887	−	36.2588i	−1.14345	−	1.63301i
$494$	−2.67028	+	4.62506i	−0.120141	+	0.208091i
$495$	5.66706	−	4.11794i	0.254715	−	0.185088i
$496$	7.04794	+	12.2074i	0.316462	+	0.548128i
$497$	−4.02444	+	8.63045i	−0.180521	+	0.387129i
$498$	−1.21188	+	8.49803i	−0.0543056	+	0.380806i
$499$	−17.0051	−	20.2659i	−0.761253	−	0.907226i	0.236674	−	0.971589i	$-0.423943\pi$
$499$	−17.0051	−	20.2659i	−0.761253	−	0.907226i	−0.997927	+	0.0643635i	$0.979498\pi$
$500$	2.37415	−	10.0495i	0.106175	−	0.449426i
$501$	−36.5407	+	4.41153i	−1.63252	+	0.197093i
$502$	0.266708	+	0.124368i	0.0119038	+	0.00555082i
$503$	−6.58100	+	24.5606i	−0.293432	+	1.09510i	0.649023	+	0.760769i	$0.275178\pi$
$503$	−6.58100	+	24.5606i	−0.293432	+	1.09510i	−0.942455	+	0.334334i	$0.891489\pi$
$504$	−25.7108	+	6.29991i	−1.14525	+	0.280620i
$505$	0.402993	+	0.443880i	0.0179330	+	0.0197524i
$506$	4.63667	+	0.817570i	0.206125	+	0.0363454i
$507$	17.7299	+	9.47328i	0.787414	+	0.420723i
$508$	14.0458	−	6.54964i	0.623180	−	0.290593i
$509$	−5.29524	−	30.0308i	−0.234707	−	1.33109i	−0.843229	−	0.537554i	$-0.819348\pi$
$509$	−5.29524	−	30.0308i	−0.234707	−	1.33109i	0.608522	−	0.793537i	$-0.291763\pi$
$510$	−9.29347	−	20.7565i	−0.411522	−	0.919112i
$511$	−30.6533	−	25.7211i	−1.35602	−	1.13784i
$512$	9.91177	−	9.91177i	0.438043	−	0.438043i
$513$	−2.23101	−	22.5436i	−0.0985017	−	0.995323i
$514$		−	6.76745i		−	0.298499i
$515$	−27.6860	−	6.27185i	−1.21999	−	0.276371i
$516$	2.04079	−	3.12865i	0.0898408	−	0.137731i
$517$	−0.218408	+	0.311918i	−0.00960556	+	0.0137182i
$518$	−9.10432	−	19.5243i	−0.400021	−	0.857847i
$519$	10.7256	+	10.0425i	0.470800	+	0.440815i
$520$	−3.73044	+	7.08618i	−0.163591	+	0.310750i
$521$	−1.09146	−	0.630155i	−0.0478178	−	0.0276076i	0.475901	−	0.879499i	$-0.342122\pi$
$521$	−1.09146	−	0.630155i	−0.0478178	−	0.0276076i	−0.523718	+	0.851892i	$0.675456\pi$
$522$	7.83178	+	23.0480i	0.342788	+	1.00879i
$523$	−9.13037	−	2.44648i	−0.399243	−	0.106977i	0.0536101	−	0.998562i	$-0.482927\pi$
$523$	−9.13037	−	2.44648i	−0.399243	−	0.106977i	−0.452853	+	0.891585i	$0.649594\pi$
$524$	3.28493	−	1.19562i	0.143503	−	0.0522308i
$525$	−13.1093	−	21.5137i	−0.572135	−	0.938935i
$526$	3.61534	−	3.03363i	0.157636	−	0.132272i
$527$	5.34950	−	61.1451i	0.233028	−	2.66352i
$528$	0.876271	+	2.18156i	0.0381348	+	0.0949401i
$529$	1.40762	+	3.86740i	0.0612007	+	0.168148i
$530$	−0.810182	−	3.73589i	−0.0351920	−	0.162277i
$531$	17.3436	+	25.9390i	0.752649	+	1.12566i
$532$	−11.3144	+	3.03170i	−0.490544	+	0.131441i
$533$	3.53002	−	2.47175i	0.152902	−	0.107063i
$534$	3.98824	−	4.25953i	0.172588	−	0.184328i
$535$	15.7963	−	2.00560i	0.682932	−	0.0867096i
$536$	1.70920	−	0.301378i	0.0738261	−	0.0130175i
$537$	−4.78880	−	22.7561i	−0.206652	−	0.981997i
$538$	−7.94036	+	0.694691i	−0.342333	+	0.0299503i
$539$	−1.52731			−0.0657859
$540$	−1.47268	−	10.6297i	−0.0633740	−	0.457428i
$541$	−14.5318			−0.624771			−0.312385	−	0.949955i	$-0.601128\pi$
$541$	−14.5318			−0.624771			−0.312385	+	0.949955i	$0.601128\pi$
$542$	−19.4793	+	1.70422i	−0.836710	+	0.0732026i
$543$	−25.7146	+	23.0594i	−1.10352	+	0.989575i
$544$	−26.2966	+	4.63679i	−1.12746	+	0.198801i
$545$	12.0689	−	15.5793i	0.516976	−	0.667345i
$546$	1.79262	+	5.90615i	0.0767170	+	0.252760i
$547$	−11.9957	+	8.39950i	−0.512900	+	0.359136i	−0.801193	−	0.598406i	$-0.795801\pi$
$547$	−11.9957	+	8.39950i	−0.512900	+	0.359136i	0.288293	+	0.957542i	$0.406912\pi$
$548$	−19.2934	+	5.16965i	−0.824174	+	0.220837i
$549$	−8.15957	+	7.81598i	−0.348242	+	0.333578i
$550$	−4.18172	+	3.44369i	−0.178309	+	0.146840i
$551$	11.6617	+	32.0403i	0.496805	+	1.36496i
$552$	14.0923	−	17.9623i	0.599809	−	0.764524i
$553$	0.959627	−	10.9686i	0.0408075	−	0.466432i
$554$	−7.86176	+	6.59680i	−0.334014	+	0.280271i
$555$	26.1193	−	9.05479i	1.10870	−	0.384354i
$556$	9.71323	−	3.53533i	0.411933	−	0.149931i
$557$	3.61631	+	0.968988i	0.153228	+	0.0410573i	0.334618	−	0.942354i	$-0.391393\pi$
$557$	3.61631	+	0.968988i	0.153228	+	0.0410573i	−0.181390	+	0.983411i	$0.558059\pi$
$558$	−12.2241	+	31.4632i	−0.517486	+	1.33194i
$559$	−2.38763	−	1.37850i	−0.100986	−	0.0583044i
$560$	8.07518	−	2.50524i	0.341239	−	0.105866i
$561$	2.32302	−	9.96991i	0.0980778	−	0.420930i
$562$	2.06709	+	4.43289i	0.0871950	+	0.186990i
$563$	−5.55357	+	7.93132i	−0.234055	+	0.334265i	−0.918948	−	0.394378i	$-0.870960\pi$
$563$	−5.55357	+	7.93132i	−0.234055	+	0.334265i	0.684893	+	0.728644i	$0.259849\pi$
$564$	0.263767	+	0.520273i	0.0111066	+	0.0219075i
$565$	−0.0320646	+	0.141544i	−0.00134897	+	0.00595479i
$566$			0.0155243i			0.000652537i
$567$	−20.7811	−	15.9253i	−0.872723	−	0.668798i
$568$	7.02097	−	7.02097i	0.294593	−	0.294593i
$569$	29.7838	+	24.9915i	1.24860	+	1.04770i	0.996801	+	0.0799199i	$0.0254665\pi$
$569$	29.7838	+	24.9915i	1.24860	+	1.04770i	0.251799	+	0.967780i	$0.418978\pi$
$570$	2.77666	+	17.2968i	0.116301	+	0.724483i
$571$	−1.13871	−	6.45794i	−0.0476535	−	0.270256i	0.951666	−	0.307134i	$-0.0993700\pi$
$571$	−1.13871	−	6.45794i	−0.0476535	−	0.270256i	−0.999320	+	0.0368775i	$0.988259\pi$
$572$	−1.03208	+	0.481267i	−0.0431534	+	0.0201228i
$573$	1.33440	−	0.830070i	0.0557452	−	0.0346767i
$574$	−10.8483	−	1.91285i	−0.452800	−	0.0798408i
$575$	20.3484	+	7.61933i	0.848585	+	0.317748i
$576$	22.3504	+	2.44070i	0.931266	+	0.101696i
$577$	2.53716	−	9.46880i	0.105623	−	0.394191i	−0.892792	−	0.450469i	$-0.851257\pi$
$577$	2.53716	−	9.46880i	0.105623	−	0.394191i	0.998415	+	0.0562782i	$0.0179234\pi$
$578$	−14.1350	−	6.59126i	−0.587939	−	0.274160i
$579$	−7.68603	−	10.2428i	−0.319421	−	0.425677i
$580$	6.11217	+	14.9506i	0.253794	+	0.620790i
$581$	8.93223	+	10.6450i	0.370571	+	0.441630i
$582$	16.9112	+	13.2678i	0.700993	+	0.549966i
$583$	0.727218	−	1.55952i	0.0301183	−	0.0645888i
$584$	20.8616	+	36.1333i	0.863258	+	1.49521i
$585$	−7.77479	+	1.51181i	−0.321448	+	0.0625054i
$586$	11.8946	−	20.6020i	0.491360	−	0.851060i
$587$	−10.1521	−	14.4987i	−0.419023	−	0.598427i	0.553038	−	0.833156i	$-0.313469\pi$
$587$	−10.1521	−	14.4987i	−0.419023	−	0.598427i	−0.972061	+	0.234729i	$0.924580\pi$
$588$	−1.10259	+	2.06358i	−0.0454701	+	0.0851005i
$589$	−16.1708	+	44.4288i	−0.666305	+	1.83066i
$590$	−14.6008	−	19.2108i	−0.601104	−	0.790895i
$591$	1.61223	−	29.6153i	0.0663182	−	1.21821i
$592$	0.808588	+	9.24221i	0.0332328	+	0.379852i
$593$	3.34033	+	3.34033i	0.137171	+	0.137171i	0.772358	−	0.635187i	$-0.219077\pi$
$593$	3.34033	+	3.34033i	0.137171	+	0.137171i	−0.635187	+	0.772358i	$0.719077\pi$
$594$	−2.75920	+	4.90717i	−0.113211	+	0.201343i
$595$	−35.0602	−	11.2324i	−1.43733	−	0.460482i
$596$	7.84845	−	9.35341i	0.321485	−	0.383131i
$597$	1.73751	−	0.365642i	0.0711115	−	0.0149647i
$598$	−4.36059	−	3.05332i	−0.178318	−	0.124859i
$599$	18.0781	+	6.57991i	0.738653	+	0.268848i	0.683823	−	0.729648i	$-0.260316\pi$
$599$	18.0781	+	6.57991i	0.738653	+	0.268848i	0.0548301	+	0.998496i	$0.482538\pi$
$600$	5.17231	+	25.7543i	0.211159	+	1.05141i
$601$	−1.93521	+	10.9751i	−0.0789387	+	0.447684i	0.919562	+	0.392945i	$0.128544\pi$
$601$	−1.93521	+	10.9751i	−0.0789387	+	0.447684i	−0.998501	+	0.0547387i	$0.982567\pi$
$602$	1.82402	+	6.80735i	0.0743417	+	0.277447i
$603$	1.29093	+	1.13140i	0.0525706	+	0.0460741i
$604$	−9.73361	+	5.61970i	−0.396055	+	0.228662i
$605$	22.1414	−	0.864496i	0.900177	−	0.0351468i
$606$	−0.443123	−	0.189155i	−0.0180006	−	0.00768388i
$607$	18.3352	+	1.60413i	0.744204	+	0.0651094i	0.452950	−	0.891536i	$-0.350372\pi$
$607$	18.3352	+	1.60413i	0.744204	+	0.0651094i	0.291255	+	0.956646i	$0.405927\pi$
$608$	20.4905	+	1.79269i	0.831001	+	0.0727032i
$609$	36.2423	+	15.4707i	1.46861	+	0.626903i
$610$	5.93268	−	6.41477i	0.240207	−	0.259727i
$611$	0.372849	−	0.215265i	0.0150839	−	0.00870868i
$612$	−11.7935	−	10.3361i	−0.476724	−	0.417812i
$613$	−2.08262	−	7.77243i	−0.0841161	−	0.313926i	0.911029	−	0.412342i	$-0.135289\pi$
$613$	−2.08262	−	7.77243i	−0.0841161	−	0.313926i	−0.995145	+	0.0984162i	$0.968622\pi$
$614$	4.91471	−	27.8727i	0.198342	−	1.12485i
$615$	3.86789	−	13.5962i	0.155968	−	0.548253i
$616$	8.65878	+	3.15154i	0.348872	+	0.126979i
$617$	5.25082	+	3.67666i	0.211390	+	0.148017i	0.674477	−	0.738296i	$-0.264369\pi$
$617$	5.25082	+	3.67666i	0.211390	+	0.148017i	−0.463087	+	0.886313i	$0.653258\pi$
$618$	22.3245	−	4.69798i	0.898023	−	0.188980i
$619$	−17.8281	+	21.2467i	−0.716573	+	0.853979i	−0.994293	−	0.106683i	$-0.965977\pi$
$619$	−17.8281	+	21.2467i	−0.716573	+	0.853979i	0.277720	+	0.960662i	$0.410421\pi$
$620$	−6.83325	+	21.3290i	−0.274430	+	0.856595i
$621$	22.5790	−	0.256889i	0.906066	−	0.0103086i
$622$	−23.2671	−	23.2671i	−0.932926	−	0.932926i
$623$	−0.823294	−	9.41029i	−0.0329846	−	0.377015i
$624$	0.144491	−	2.65418i	0.00578427	−	0.106252i
$625$	−21.8774	+	12.0988i	−0.875095	+	0.483951i
$626$	−4.06240	+	11.1614i	−0.162366	+	0.446098i
$627$	−3.71614	+	6.95503i	−0.148409	+	0.277757i
$628$	−6.28127	−	8.97058i	−0.250650	−	0.357965i
$629$	20.1988	−	34.9854i	0.805380	−	1.39496i
$630$	16.7857	+	11.3204i	0.668757	+	0.451017i
$631$	7.53540	+	13.0517i	0.299979	+	0.519580i	0.976131	−	0.217183i	$-0.0696868\pi$
$631$	7.53540	+	13.0517i	0.299979	+	0.519580i	−0.676151	+	0.736763i	$0.736353\pi$
$632$	−4.85187	+	10.4049i	−0.192997	+	0.413883i
$633$	−13.3469	−	10.4713i	−0.530491	−	0.416198i
$634$	8.34750	+	9.94816i	0.331522	+	0.395092i
$635$	−34.5982	−	14.5182i	−1.37299	−	0.576138i
$636$	−1.58211	−	2.10840i	−0.0627347	−	0.0836036i
$637$	1.56505	+	0.729797i	0.0620097	+	0.0289156i
$638$	2.19307	−	8.18464i	0.0868244	−	0.324033i
$639$	9.76234	+	1.06606i	0.386192	+	0.0421729i
$640$	3.70847	+	0.179043i	0.146590	+	0.00707729i
$641$	28.9474	+	5.10420i	1.14335	+	0.201604i	0.713071	−	0.701091i	$-0.247304\pi$
$641$	28.9474	+	5.10420i	1.14335	+	0.201604i	0.430281	+	0.902695i	$0.358415\pi$
$642$	−10.8657	+	6.75910i	−0.428836	+	0.266761i
$643$	−19.6987	+	9.18567i	−0.776842	+	0.362248i	−0.770259	−	0.637731i	$-0.779873\pi$
$643$	−19.6987	+	9.18567i	−0.776842	+	0.362248i	−0.00658305	+	0.999978i	$0.502095\pi$
$644$	−2.02747	−	11.4983i	−0.0798935	−	0.453098i
$645$	−8.92928	+	1.43342i	−0.351590	+	0.0564408i
$646$	19.6108	+	16.4554i	0.771576	+	0.647429i
$647$	−16.4745	+	16.4745i	−0.647680	+	0.647680i	−0.952432	−	0.304752i	$-0.901426\pi$
$647$	−16.4745	+	16.4745i	−0.647680	+	0.647680i	0.304752	+	0.952432i	$0.401426\pi$
$648$	14.6822	+	23.0146i	0.576769	+	0.904100i
$649$		−	10.8616i		−	0.426353i
$650$	5.93056	−	1.53064i	0.232616	−	0.0600367i
$651$	24.7086	+	48.7372i	0.968408	+	1.91016i
$652$	7.57948	−	10.8246i	0.296835	−	0.423925i
$653$	5.62864	+	12.0707i	0.220266	+	0.472362i	0.985126	−	0.171835i	$-0.0549696\pi$
$653$	5.62864	+	12.0707i	0.220266	+	0.472362i	−0.764860	+	0.644197i	$0.777192\pi$
$654$	−3.59393	+	15.4244i	−0.140534	+	0.603142i
$655$	−7.48902	−	3.94251i	−0.292620	−	0.154047i
$656$	4.10841	+	2.37199i	0.160406	+	0.0926106i
$657$	−14.9444	+	38.4650i	−0.583036	+	1.50066i
$658$	−1.06303	−	0.284837i	−0.0414411	−	0.0111041i
$659$	−12.4761	+	4.54094i	−0.486001	+	0.176890i	−0.573387	−	0.819285i	$-0.694371\pi$
$659$	−12.4761	+	4.54094i	−0.486001	+	0.176890i	0.0873859	+	0.996175i	$0.472149\pi$
$660$	−1.63048	+	3.36081i	−0.0634664	+	0.130819i
$661$	−9.01628	+	7.56556i	−0.350693	+	0.294266i	−0.801068	−	0.598573i	$-0.795735\pi$
$661$	−9.01628	+	7.56556i	−0.350693	+	0.294266i	0.450375	+	0.892839i	$0.351290\pi$
$662$	2.28561	−	26.1246i	0.0888328	−	1.01536i
$663$	−7.14436	+	9.10628i	−0.277464	+	0.353659i
$664$	−4.95562	−	13.6155i	−0.192316	−	0.528383i
$665$	23.8474	+	15.3474i	0.924762	+	0.595148i
$666$	−16.0434	+	15.3678i	−0.621668	+	0.595490i
$667$	−32.8283	+	8.79631i	−1.27112	+	0.340595i
$668$	16.0770	−	11.2572i	0.622038	−	0.435555i
$669$	−4.93134	−	16.2473i	−0.190657	−	0.628158i
$670$	−1.04938	−	0.812928i	−0.0405410	−	0.0314061i
$671$	3.87335	−	0.682976i	0.149529	−	0.0263660i
$672$	17.6981	−	15.8707i	0.682720	−	0.612224i
$673$	11.5900	−	1.01400i	0.446763	−	0.0390867i	0.138445	−	0.990370i	$-0.455790\pi$
$673$	11.5900	−	1.01400i	0.446763	−	0.0390867i	0.308318	+	0.951283i	$0.400234\pi$
$674$	1.79908			0.0692981
$675$	−16.6571	+	19.9384i	−0.641132	+	0.767431i
$676$	−10.7192			−0.412276
$677$	5.37998	−	0.470687i	0.206769	−	0.0180900i	0.0166995	−	0.999861i	$-0.494684\pi$
$677$	5.37998	−	0.470687i	0.206769	−	0.0180900i	0.190070	+	0.981771i	$0.439129\pi$
$678$	−0.0240182	−	0.114133i	−0.000922415	−	0.00438326i
$679$	34.2678	−	6.04233i	1.31508	−	0.231883i
$680$	30.3465	+	23.5087i	1.16374	+	0.901518i
$681$	20.2736	−	21.6527i	0.776888	−	0.829734i
$682$	9.62474	−	6.73932i	0.368550	−	0.258062i
$683$	16.0348	−	4.29650i	0.613553	−	0.164401i	0.0613579	−	0.998116i	$-0.480457\pi$
$683$	16.0348	−	4.29650i	0.613553	−	0.164401i	0.552195	+	0.833715i	$0.313790\pi$
$684$	6.71432	+	10.0419i	0.256728	+	0.383962i
$685$	40.6646	+	26.1705i	1.55371	+	0.999922i
$686$	5.71610	+	15.7049i	0.218242	+	0.599614i
$687$	−11.8080	−	29.3970i	−0.450502	−	1.12157i
$688$	0.264523	−	3.02351i	0.0100848	−	0.115270i
$689$	−1.49038	+	1.25058i	−0.0567789	+	0.0476431i
$690$	−17.4165	+	1.25451i	−0.663036	+	0.0477583i
$691$	4.89099	−	1.78018i	0.186062	−	0.0677211i	−0.247309	−	0.968937i	$-0.579546\pi$
$691$	4.89099	−	1.78018i	0.186062	−	0.0677211i	0.433371	+	0.901216i	$0.357324\pi$
$692$	−7.56797	−	2.02783i	−0.287691	−	0.0770866i
$693$	2.93215	+	8.62897i	0.111383	+	0.327787i
$694$	−8.89164	−	5.13359i	−0.337522	−	0.194868i
$695$	−22.1443	−	11.6576i	−0.839982	−	0.442199i
$696$	−29.9933	−	28.0830i	−1.13689	−	1.06448i
$697$	−8.73003	−	18.7216i	−0.330674	−	0.709132i
$698$	−18.4475	+	26.3458i	−0.698248	+	0.997202i
$699$	−4.66893	+	7.15774i	−0.176595	+	0.270731i
$700$	11.5717	+	6.82390i	0.437369	+	0.257919i
$701$		−	30.8522i		−	1.16527i	−0.812733	−	0.582636i	$-0.802021\pi$
$701$		−	30.8522i		−	1.16527i	0.812733	−	0.582636i	$-0.197979\pi$
$702$	5.17218	−	3.71000i	0.195211	−	0.140025i
$703$	−22.0041	+	22.0041i	−0.829899	+	0.829899i
$704$	−5.99524	−	5.03061i	−0.225954	−	0.189598i
$705$	0.503340	−	1.31949i	0.0189569	−	0.0496949i
$706$	−0.660573	−	3.74630i	−0.0248610	−	0.140994i
$707$	−0.706888	+	0.329627i	−0.0265853	+	0.0123969i
$708$	−14.6752	−	7.84113i	−0.551529	−	0.294688i
$709$	−19.4630	−	3.43186i	−0.730949	−	0.128886i	−0.204227	−	0.978924i	$-0.565468\pi$
$709$	−19.4630	−	3.43186i	−0.730949	−	0.128886i	−0.526722	+	0.850038i	$0.676579\pi$
$710$	−7.58533	−	0.366215i	−0.284672	−	0.0137438i
$711$	−11.0285	+	2.70230i	−0.413600	+	0.101344i
$712$	−2.54923	+	9.51386i	−0.0955365	+	0.356547i
$713$	−42.7119	−	19.9169i	−1.59957	−	0.745893i
$714$	29.3733	−	3.54621i	1.09927	−	0.132714i
$715$	2.54227	+	1.06680i	0.0950756	+	0.0398959i
$716$	7.97067	+	9.49908i	0.297878	+	0.354997i
$717$	−1.47704	+	10.3574i	−0.0551610	+	0.386804i
$718$	−3.27613	+	7.02568i	−0.122264	+	0.262196i
$719$	3.29514	+	5.70736i	0.122888	+	0.212849i	0.920905	−	0.389786i	$-0.127451\pi$
$719$	3.29514	+	5.70736i	0.122888	+	0.212849i	−0.798017	+	0.602635i	$0.794118\pi$
$720$	−5.12549	−	7.05365i	−0.191016	−	0.262874i
$721$	18.4656	−	31.9834i	0.687695	−	1.19112i
$722$	−0.00419426	−	0.00599003i	−0.000156094	−	0.000222926i
$723$	−15.7363	−	25.2972i	−0.585239	−	0.940813i
$724$	6.29925	−	17.3071i	0.234110	−	0.643212i
$725$	16.8521	−	35.2866i	0.625871	−	1.31051i
$726$	−15.8828	+	8.05222i	−0.589467	+	0.298846i
$727$	1.33493	+	15.2584i	0.0495099	+	0.565901i	0.979921	+	0.199384i	$0.0638942\pi$
$727$	1.33493	+	15.2584i	0.0495099	+	0.565901i	−0.930411	+	0.366517i	$0.880550\pi$
$728$	−7.36685	−	7.36685i	−0.273034	−	0.273034i
$729$	−8.65490	+	25.5752i	−0.320552	+	0.947231i
$730$	9.73608	−	30.3898i	0.360349	−	1.12478i
$731$	−8.49492	+	10.1238i	−0.314196	+	0.374444i
$732$	1.87345	−	5.72640i	0.0692448	−	0.211654i
$733$	0.908462	+	0.636112i	0.0335548	+	0.0234953i	0.590234	−	0.807233i	$-0.299036\pi$
$733$	0.908462	+	0.636112i	0.0335548	+	0.0234953i	−0.556679	+	0.830728i	$0.687925\pi$
$734$	−16.4596	−	5.99082i	−0.607537	−	0.221125i
$735$	5.49332	−	1.38185i	0.202624	−	0.0509704i
$736$	−3.56019	+	20.1909i	−0.131230	+	0.744245i
$737$	−0.154649	−	0.577158i	−0.00569657	−	0.0212599i
$738$	1.73164	+	11.2273i	0.0637425	+	0.413283i
$739$	0.148882	−	0.0859569i	0.00547670	−	0.00316198i	−0.497259	−	0.867602i	$-0.665660\pi$
$739$	0.148882	−	0.0859569i	0.00547670	−	0.00316198i	0.502736	+	0.864440i	$0.332327\pi$
$740$	−10.0089	+	10.8222i	−0.367933	+	0.397832i
$741$	7.13131	−	5.35122i	0.261975	−	0.196582i
$742$	4.95432	+	0.433447i	0.181879	+	0.0159123i
$743$	20.1450	+	1.76246i	0.739048	+	0.0646584i	0.450462	−	0.892796i	$-0.351259\pi$
$743$	20.1450	+	1.76246i	0.739048	+	0.0646584i	0.288586	+	0.957454i	$0.406815\pi$
$744$	−6.82900	−	56.5646i	−0.250363	−	2.07376i
$745$	−29.5385	+	1.15331i	−1.08221	+	0.0422540i
$746$	1.90830	−	1.10175i	0.0698677	−	0.0403381i
$747$	7.43048	−	12.2537i	0.271867	−	0.448339i
$748$	1.41283	+	5.27274i	0.0516580	+	0.192790i
$749$	−3.59719	+	20.4007i	−0.131438	+	0.745424i
$750$	11.9248	−	16.1695i	0.435431	−	0.590426i
$751$	16.8648	+	6.13828i	0.615405	+	0.223989i	0.630867	−	0.775891i	$-0.282700\pi$
$751$	16.8648	+	6.13828i	0.615405	+	0.223989i	−0.0154616	+	0.999880i	$0.504922\pi$
$752$	0.388237	+	0.271846i	0.0141575	+	0.00991322i
$753$	−0.327993	−	0.365761i	−0.0119527	−	0.0133291i
$754$	−6.15814	+	7.33898i	−0.224266	+	0.267270i
$755$	25.9137	+	8.30206i	0.943097	+	0.302143i
$756$	13.7755	+	2.26772i	0.501011	+	0.0824761i
$757$	−19.5487	−	19.5487i	−0.710508	−	0.710508i	0.256133	−	0.966641i	$-0.417551\pi$
$757$	−19.5487	−	19.5487i	−0.710508	−	0.710508i	−0.966641	+	0.256133i	$0.917551\pi$
$758$	−0.868528	−	9.92732i	−0.0315464	−	0.360577i
$759$	−6.58334	−	4.29425i	−0.238960	−	0.155871i
$760$	−17.8926	−	23.5420i	−0.649033	−	0.853957i
$761$	0.210722	−	0.578955i	0.00763868	−	0.0209871i	−0.935815	−	0.352492i	$-0.885334\pi$
$761$	0.210722	−	0.578955i	0.00763868	−	0.0209871i	0.943453	+	0.331505i	$0.107556\pi$
$762$	30.1371	−	0.991298i	1.09175	−	0.0359110i
$763$	14.7056	+	21.0017i	0.532378	+	0.760314i
$764$	−0.418993	+	0.725717i	−0.0151586	+	0.0262555i
$765$	0.665149	+	37.9608i	0.0240485	+	1.37248i
$766$	0.0626486	+	0.108511i	0.00226359	+	0.00392064i
$767$	−5.18999	+	11.1300i	−0.187400	+	0.401880i
$768$	−26.8594	+	10.7887i	−0.969206	+	0.389303i
$769$	26.3803	+	31.4388i	0.951298	+	1.13371i	0.990914	+	0.134497i	$0.0429420\pi$
$769$	26.3803	+	31.4388i	0.951298	+	1.13371i	−0.0396163	+	0.999215i	$0.512614\pi$
$770$	−2.66695	−	6.52346i	−0.0961101	−	0.235089i
$771$	−4.43549	+	10.3908i	−0.159740	+	0.374216i
$772$	6.18879	+	2.88588i	0.222739	+	0.103865i
$773$	8.41362	−	31.4000i	0.302617	−	1.12938i	−0.632361	−	0.774674i	$-0.717914\pi$
$773$	8.41362	−	31.4000i	0.302617	−	1.12938i	0.934977	−	0.354707i	$-0.115419\pi$
$774$	6.04172	−	4.03968i	0.217165	−	0.145203i
$775$	49.3528	−	22.4621i	1.77280	−	0.806863i
$776$	−35.7306	−	6.30026i	−1.28265	−	0.226166i
$777$	1.18233	+	35.9449i	0.0424160	+	1.28952i
$778$	24.1159	−	11.2454i	0.864598	−	0.403169i
$779$	2.76312	+	15.6704i	0.0989990	+	0.561451i
$780$	3.27668	−	2.66477i	0.117324	−	0.0954141i
$781$	−2.61864	−	2.19730i	−0.0937023	−	0.0786256i
$782$	−18.0435	+	18.0435i	−0.645233	+	0.645233i
$783$	3.08106	−	40.5213i	0.110108	−	1.44811i
$784$			1.90101i			0.0678930i
$785$	−5.85771	+	25.8579i	−0.209071	+	0.922907i
$786$	6.79149	+	0.369722i	0.242244	+	0.0131875i
$787$	14.4949	−	20.7009i	0.516689	−	0.737908i	−0.473012	−	0.881056i	$-0.656833\pi$
$787$	14.4949	−	20.7009i	0.516689	−	0.737908i	0.989701	+	0.143147i	$0.0457223\pi$
$788$	6.68386	+	14.3336i	0.238103	+	0.510613i
$789$	−7.53931	+	2.28831i	−0.268407	+	0.0814661i
$790$	8.38637	−	2.60178i	0.298374	−	0.0925672i
$791$	−0.163514	−	0.0944047i	−0.00581388	−	0.00335665i
$792$	0.204330	−	9.50038i	0.00726056	−	0.337581i
$793$	−4.29541	−	1.15095i	−0.152535	−	0.0408715i
$794$	−25.7442	+	9.37011i	−0.913626	+	0.332533i
$795$	−1.20460	+	6.26713i	−0.0427229	+	0.222272i
$796$	−0.725290	+	0.608590i	−0.0257072	+	0.0215709i
$797$	0.523838	−	5.98749i	0.0185553	−	0.212088i	−0.981257	−	0.192704i	$-0.938274\pi$
$797$	0.523838	−	5.98749i	0.0185553	−	0.212088i	0.999812	−	0.0193834i	$-0.00617032\pi$
$798$	−22.5624	−	3.21755i	−0.798700	−	0.113900i
$799$	−0.705844	−	1.93929i	−0.0249710	−	0.0686072i
$800$	−14.9959	−	18.2097i	−0.530186	−	0.643811i
$801$	−8.91535	+	3.92617i	−0.315008	+	0.138724i
$802$	34.0906	−	9.13456i	1.20378	−	0.322553i
$803$	11.7666	−	8.23907i	0.415235	−	0.290750i
$804$	−0.891452	−	0.207711i	−0.0314391	−	0.00732539i
$805$	−17.3113	+	22.3466i	−0.610144	+	0.787613i
$806$	−13.0828	+	2.30686i	−0.460824	+	0.0812556i
$807$	12.6470	+	4.13760i	0.445196	+	0.145651i
$808$	0.810165	−	0.0708802i	0.0285015	−	0.00249356i
$809$	0.987575			0.0347213			0.0173607	−	0.999849i	$-0.494474\pi$
$809$	0.987575			0.0347213			0.0173607	+	0.999849i	$0.494474\pi$
$810$	5.48426	−	20.1461i	0.192697	−	0.707863i
$811$	−7.20371			−0.252957			−0.126478	−	0.991969i	$-0.540367\pi$
$811$	−7.20371			−0.252957			−0.126478	+	0.991969i	$0.540367\pi$
$812$	−20.9329	+	1.83139i	−0.734601	+	0.0642692i
$813$	31.0258	+	10.1504i	1.08812	+	0.355990i
$814$	7.61579	−	1.34287i	0.266933	−	0.0470675i
$815$	−31.7380	+	4.02966i	−1.11173	+	0.141153i
$816$	−12.4093	−	2.89140i	−0.434412	−	0.101219i
$817$	8.33907	−	5.83908i	0.291747	−	0.204284i
$818$	−33.6856	+	9.02602i	−1.17779	+	0.315587i
$819$	1.11858	−	10.2433i	0.0390865	−	0.357929i
$820$	1.59752	+	7.36646i	0.0557879	+	0.257248i
$821$	−3.24048	−	8.90315i	−0.113094	−	0.310722i	0.870214	−	0.492674i	$-0.163981\pi$
$821$	−3.24048	−	8.90315i	−0.113094	−	0.310722i	−0.983307	+	0.181952i	$0.941758\pi$
$822$	−38.4734	−	5.48657i	−1.34191	−	0.191366i
$823$	−3.23116	+	36.9323i	−0.112631	+	1.28738i	0.703992	+	0.710208i	$0.251399\pi$
$823$	−3.23116	+	36.9323i	−0.112631	+	1.28738i	−0.816623	+	0.577172i	$0.804156\pi$
$824$	−29.4986	+	24.7523i	−1.02763	+	0.862287i
$825$	8.67770	−	2.54672i	0.302119	−	0.0886653i
$826$	29.4986	−	10.7366i	1.02639	−	0.373574i
$827$	28.1808	+	7.55103i	0.979943	+	0.262575i	0.713021	−	0.701143i	$-0.247327\pi$
$827$	28.1808	+	7.55103i	0.979943	+	0.262575i	0.266923	+	0.963718i	$0.413993\pi$
$828$	−10.5547	+	5.79477i	−0.366800	+	0.201382i
$829$	16.9573	+	9.79032i	0.588952	+	0.340032i	0.764683	−	0.644407i	$-0.222896\pi$
$829$	16.9573	+	9.79032i	0.588952	+	0.340032i	−0.175731	+	0.984438i	$0.556229\pi$
$830$	−5.16230	+	9.80608i	−0.179186	+	0.340374i
$831$	16.3947	−	4.97607i	0.568725	−	0.172618i
$832$	3.73962	+	8.01964i	0.129648	+	0.278031i
$833$	4.74788	−	6.78067i	0.164504	−	0.234936i
$834$	20.0818	+	1.09323i	0.695375	+	0.0378556i
$835$	−46.3422	−	10.4981i	−1.60374	−	0.363303i
$836$		−	4.20488i		−	0.145429i
$837$	39.3904	−	40.2971i	1.36153	−	1.39287i
$838$	−22.6830	+	22.6830i	−0.783572	+	0.783572i
$839$	1.00064	+	0.839639i	0.0345460	+	0.0289876i	0.659897	−	0.751356i	$-0.270600\pi$
$839$	1.00064	+	0.839639i	0.0345460	+	0.0289876i	−0.625351	+	0.780343i	$0.715044\pi$
$840$	−33.9946	−	3.50108i	−1.17293	−	0.120799i
$841$	5.58546	+	31.6767i	0.192602	+	1.09230i
$842$	13.7916	−	6.43113i	0.475290	−	0.221631i
$843$	−0.268443	−	8.16111i	−0.00924567	−	0.281084i
$844$	8.90859	+	1.57082i	0.306646	+	0.0540700i
$845$	17.4443	+	19.2142i	0.600103	+	0.660988i
$846$	0.0745820	+	1.13248i	0.00256418	+	0.0389355i
$847$	−7.46102	+	27.8449i	−0.256364	+	0.956762i
$848$	−1.94110	−	0.905149i	−0.0666576	−	0.0310830i
$849$	0.0101749	−	0.0238362i	0.000349202	−	0.000818057i
$850$	−2.28918	−	29.2705i	−0.0785182	−	1.00397i
$851$	−19.9379	−	23.7611i	−0.683463	−	0.814519i
$852$	−4.85925	+	1.95182i	−0.166475	+	0.0668684i
$853$	−0.525925	+	1.12785i	−0.0180073	+	0.0386168i	−0.915106	−	0.403214i	$-0.867893\pi$
$853$	−0.525925	+	1.12785i	−0.0180073	+	0.0386168i	0.897098	+	0.441831i	$0.145671\pi$
$854$	5.68367	+	9.84440i	0.194491	+	0.336869i
$855$	7.07330	−	28.3776i	0.241902	−	0.970492i
$856$	10.7998	−	18.7059i	0.369131	−	0.639353i
$857$	3.01178	+	4.30127i	0.102880	+	0.146928i	0.867291	−	0.497801i	$-0.165859\pi$
$857$	3.01178	+	4.30127i	0.102880	+	0.146928i	−0.764411	+	0.644729i	$0.776970\pi$
$858$	−2.21447	+	0.0728405i	−0.0756008	+	0.00248673i
$859$	17.5440	−	48.2017i	0.598593	−	1.64462i	−0.155486	−	0.987838i	$-0.549694\pi$
$859$	17.5440	−	48.2017i	0.598593	−	1.64462i	0.754079	−	0.656783i	$-0.228083\pi$
$860$	3.83935	−	2.91802i	0.130921	−	0.0995037i
$861$	15.4029	+	10.0472i	0.524929	+	0.342407i
$862$	−2.74226	−	31.3442i	−0.0934018	−	1.06759i
$863$	−4.17796	−	4.17796i	−0.142219	−	0.142219i	0.632412	−	0.774632i	$-0.282065\pi$
$863$	−4.17796	−	4.17796i	−0.142219	−	0.142219i	−0.774632	+	0.632412i	$0.782065\pi$
$864$	−21.3688	−	12.0152i	−0.726980	−	0.408766i
$865$	8.68117	+	16.8657i	0.295169	+	0.573451i
$866$	−5.04741	+	6.01526i	−0.171518	+	0.204407i
$867$	17.3830	+	19.3846i	0.590358	+	0.658336i
$868$	−23.8681	−	16.7126i	−0.810137	−	0.567264i
$869$	3.71412	+	1.35183i	0.125993	+	0.0458577i
$870$	−0.482710	+	31.4221i	−0.0163654	+	1.06531i
$871$	−0.117313	+	0.665317i	−0.00397501	+	0.0225434i
$872$	−6.91897	−	25.8219i	−0.234306	−	0.874442i
$873$	−17.2698	−	31.4554i	−0.584494	−	1.06460i
$874$	17.0227	−	9.82804i	0.575800	−	0.332438i
$875$	−6.59982	−	31.8475i	−0.223115	−	1.07664i
$876$	−2.63745	−	21.8460i	−0.0891110	−	0.738108i
$877$	−50.0397	−	4.37791i	−1.68972	−	0.147832i	−0.798681	−	0.601754i	$-0.794469\pi$
$877$	−50.0397	−	4.37791i	−1.68972	−	0.147832i	−0.891041	+	0.453923i	$0.850024\pi$
$878$	10.2641	+	0.897992i	0.346397	+	0.0303058i
$879$	−31.7659	+	23.8366i	−1.07144	+	0.803989i
$880$	0.118412	+	3.03277i	0.00399168	+	0.102235i
$881$	−11.9474	+	6.89781i	−0.402517	+	0.232393i	−0.687569	−	0.726119i	$-0.741322\pi$
$881$	−11.9474	+	6.89781i	−0.402517	+	0.232393i	0.285053	+	0.958512i	$0.407989\pi$
$882$	−3.54930	+	2.85044i	−0.119511	+	0.0959793i
$883$	−6.38476	−	23.8282i	−0.214864	−	0.801884i	−0.986214	−	0.165473i	$-0.947085\pi$
$883$	−6.38476	−	23.8282i	−0.214864	−	0.801884i	0.771350	−	0.636411i	$-0.219582\pi$
$884$	1.07174	−	6.07813i	0.0360465	−	0.204430i
$885$	9.82712	+	39.0660i	0.330335	+	1.31319i
$886$	−9.03886	−	3.28987i	−0.303666	−	0.110526i
$887$	37.9805	+	26.5942i	1.27526	+	0.892946i	0.997701	−	0.0677631i	$-0.0215862\pi$
$887$	37.9805	+	26.5942i	1.27526	+	0.892946i	0.277558	+	0.960709i	$0.410475\pi$
$888$	11.6602	−	35.6407i	0.391291	−	1.19602i
$889$	31.3766	−	37.3932i	1.05234	−	1.25413i
$890$	6.69801	−	3.44762i	0.224518	−	0.115565i
$891$	7.45274	−	5.72609i	0.249676	−	0.191831i
$892$	6.40212	+	6.40212i	0.214359	+	0.214359i
$893$	0.138553	+	1.58366i	0.00463649	+	0.0529953i
$894$	21.1890	−	10.7423i	0.708667	−	0.359278i
$895$	4.05572	−	29.7462i	0.135568	−	0.994306i
$896$	−1.65203	+	4.53891i	−0.0551904	+	0.151634i
$897$	4.69410	+	7.54610i	0.156731	+	0.251957i
$898$	17.9463	+	25.6299i	0.598874	+	0.855281i
$899$	−42.4077	+	73.4522i	−1.41438	+	2.44977i
$900$	2.82366	−	13.5631i	0.0941220	−	0.452104i
$901$	4.66302	+	8.07658i	0.155348	+	0.269070i
$902$	1.67118	−	3.58386i	0.0556442	−	0.119329i
$903$	1.66102	−	11.6476i	0.0552754	−	0.387607i
$904$	0.126545	+	0.150811i	0.00420883	+	0.00501589i
$905$	−41.2743	+	16.8739i	−1.37200	+	0.560909i
$906$	−21.7104	+	2.62108i	−0.721280	+	0.0870794i
$907$	12.3092	+	5.73988i	0.408721	+	0.190590i	0.616095	−	0.787672i	$-0.288714\pi$
$907$	12.3092	+	5.73988i	0.408721	+	0.190590i	−0.207374	+	0.978262i	$0.566492\pi$
$908$	−4.09378	+	15.2782i	−0.135857	+	0.507024i
$909$	0.556400	+	0.580860i	0.0184546	+	0.0192659i
$910$	−0.384257	+	7.95902i	−0.0127380	+	0.263839i
$911$	−26.4310	−	4.66050i	−0.875698	−	0.154409i	−0.282308	−	0.959324i	$-0.591100\pi$
$911$	−26.4310	−	4.66050i	−0.875698	−	0.154409i	−0.593391	+	0.804915i	$0.702211\pi$
$912$	8.65675	+	4.62539i	0.286654	+	0.153162i
$913$	−4.52098	+	2.10817i	−0.149623	+	0.0697701i
$914$	−5.46005	−	30.9655i	−0.180602	−	1.02425i
$915$	−13.3134	+	5.96093i	−0.440129	+	0.197062i
$916$	12.9407	+	10.8585i	0.427573	+	0.358776i
$917$	7.78565	−	7.78565i	0.257105	−	0.257105i
$918$	−13.2085	−	27.5044i	−0.435947	−	0.907782i
$919$		−	29.6273i		−	0.977314i	−0.872476	−	0.488657i	$-0.837487\pi$
$919$		−	29.6273i		−	0.977314i	0.872476	−	0.488657i	$-0.162513\pi$
$920$	24.9310	−	15.7217i	0.821950	−	0.518330i
$921$	−25.8143	+	39.5749i	−0.850611	+	1.30404i
$922$	−7.73552	+	11.0475i	−0.254756	+	0.363829i
$923$	1.63341	+	3.50287i	0.0537645	+	0.115298i
$924$	−3.54743	−	3.32149i	−0.116702	−	0.109269i
$925$	35.6872	+	0.328957i	1.17339	+	0.0108160i
$926$	−24.6870	−	14.2531i	−0.811267	−	0.468385i
$927$	−37.3564	−	7.41852i	−1.22695	−	0.243656i
$928$	35.6409	+	9.54994i	1.16997	+	0.313492i
$929$	52.3804	−	19.0649i	1.71854	−	0.625499i	0.720832	−	0.693110i	$-0.243760\pi$
$929$	52.3804	−	19.0649i	1.71854	−	0.625499i	0.997712	+	0.0676108i	$0.0215376\pi$
$930$	−28.5201	+	32.9476i	−0.935210	+	1.08039i
$931$	−4.88454	+	4.09862i	−0.160084	+	0.134327i
$932$	0.397168	−	4.53965i	0.0130097	−	0.148701i
$933$	20.4749	+	50.9742i	0.670318	+	1.66882i
$934$	−10.6526	−	29.2678i	−0.348564	−	0.957673i
$935$	7.15218	−	11.1133i	0.233901	−	0.363444i
$936$	−4.74896	+	9.63752i	−0.155225	+	0.315012i
$937$	13.0469	−	3.49591i	0.426224	−	0.114206i	−0.0393290	−	0.999226i	$-0.512522\pi$
$937$	13.0469	−	3.49591i	0.426224	−	0.114206i	0.465553	+	0.885020i	$0.345855\pi$
$938$	1.41462	−	0.990526i	0.0461889	−	0.0323418i
$939$	13.5528	−	14.4747i	0.442279	−	0.472364i
$940$	0.0948517	+	0.747060i	0.00309372	+	0.0243664i
$941$	14.9533	−	2.63667i	0.487463	−	0.0859529i	0.0754855	−	0.997147i	$-0.475949\pi$
$941$	14.9533	−	2.63667i	0.487463	−	0.0859529i	0.411977	+	0.911194i	$0.364838\pi$
$942$	−4.38776	−	20.8504i	−0.142961	−	0.679341i
$943$	−15.8004	+	1.38235i	−0.514531	+	0.0450157i
$944$	−13.5191			−0.440009
$945$	−18.3533	−	28.3831i	−0.597032	−	0.923303i
$946$	−2.52987			−0.0822533
$947$	5.42282	−	0.474435i	0.176218	−	0.0154171i	0.00129474	−	0.999999i	$-0.499588\pi$
$947$	5.42282	−	0.474435i	0.176218	−	0.0154171i	0.174923	+	0.984582i	$0.444032\pi$
$948$	4.50777	−	4.04231i	0.146406	−	0.131288i
$949$	−15.9943	+	2.82022i	−0.519196	+	0.0915483i
$950$	−4.13235	+	22.2352i	−0.134071	+	0.721406i
$951$	−6.29665	−	20.7456i	−0.204183	−	0.672722i
$952$	−40.9087	+	28.6446i	−1.32586	+	0.928377i
$953$	45.1915	−	12.1090i	1.46390	−	0.392250i	0.563063	−	0.826414i	$-0.309623\pi$
$953$	45.1915	−	12.1090i	1.46390	−	0.392250i	0.900834	+	0.434164i	$0.142956\pi$
$954$	−1.22058	−	4.98137i	−0.0395179	−	0.161278i
$955$	1.98272	−	0.429980i	0.0641592	−	0.0139138i
$956$	−1.90807	−	5.24239i	−0.0617115	−	0.169551i
$957$	−8.73160	+	11.1294i	−0.282253	+	0.359763i
$958$	−0.945161	+	10.8032i	−0.0305367	+	0.349037i
$959$	−48.1935	+	40.4392i	−1.55625	+	1.30585i
$960$	26.1147	+	12.6694i	0.842850	+	0.408904i
$961$	−81.3865	+	29.6223i	−2.62537	+	0.955557i
$962$	−8.44566	−	2.26301i	−0.272299	−	0.0729623i
$963$	21.1134	−	3.25641i	0.680370	−	0.104936i
$964$	13.7580	+	7.94318i	0.443115	+	0.255832i
$965$	−4.89864	−	15.7899i	−0.157693	−	0.508294i
$966$	5.15504	−	22.1244i	0.165861	−	0.711840i
$967$	10.4693	+	22.4516i	0.336671	+	0.721994i	0.999645	−	0.0266490i	$-0.00848366\pi$
$967$	10.4693	+	22.4516i	0.336671	+	0.721994i	−0.662974	+	0.748643i	$0.730706\pi$
$968$	17.2404	−	24.6219i	0.554128	−	0.791377i
$969$	−19.3255	−	38.1190i	−0.620823	−	1.22456i
$970$	14.8018	+	23.4722i	0.475258	+	0.753648i
$971$		−	39.1684i		−	1.25697i	−0.777821	−	0.628486i	$-0.783675\pi$
$971$		−	39.1684i		−	1.25697i	0.777821	−	0.628486i	$-0.216325\pi$
$972$	−2.35637	−	14.2033i	−0.0755805	−	0.455570i
$973$	23.0214	−	23.0214i	0.738033	−	0.738033i
$974$	15.4188	+	12.9379i	0.494050	+	0.414557i
$975$	−10.1091	−	1.53682i	−0.323749	−	0.0492178i
$976$	−0.850083	−	4.82106i	−0.0272105	−	0.154318i
$977$	−27.2371	+	12.7009i	−0.871393	+	0.406337i	−0.806275	−	0.591540i	$-0.798520\pi$
$977$	−27.2371	+	12.7009i	−0.871393	+	0.406337i	−0.0651176	+	0.997878i	$0.520742\pi$
$978$	21.8315	−	13.5804i	0.698095	−	0.434255i
$979$	3.33945	+	0.588834i	0.106729	+	0.0188192i
$980$	−2.23633	+	2.03034i	−0.0714369	+	0.0648567i
$981$	15.6276	−	21.3273i	0.498950	−	0.680928i
$982$	−11.2391	+	41.9450i	−0.358655	+	1.33852i
$983$	53.0117	+	24.7198i	1.69081	+	0.788438i	0.997713	+	0.0675941i	$0.0215323\pi$
$983$	53.0117	+	24.7198i	1.69081	+	0.788438i	0.693098	+	0.720844i	$0.256245\pi$
$984$	−11.5088	−	15.3373i	−0.366888	−	0.488934i
$985$	14.8157	−	35.3072i	0.472069	−	1.12498i
$986$	29.5192	+	35.1796i	0.940082	+	1.12035i
$987$	1.44549	+	1.13407i	0.0460106	+	0.0360977i
$988$	−2.00922	+	4.30879i	−0.0639219	+	0.137081i
$989$	5.07361	+	8.78776i	0.161332	+	0.279434i
$990$	−5.48484	+	4.76854i	−0.174320	+	0.151554i
$991$	−6.16723	+	10.6820i	−0.195909	+	0.339324i	−0.947198	−	0.320649i	$-0.896099\pi$
$991$	−6.16723	+	10.6820i	−0.195909	+	0.339324i	0.751289	+	0.659973i	$0.229432\pi$
$992$	29.3471	+	41.9119i	0.931770	+	1.33071i
$993$	−20.6319	+	38.6140i	−0.654733	+	1.22538i
$994$	3.37907	−	9.28392i	0.107178	−	0.294468i
$995$	2.27123	+	0.309669i	0.0720029	+	0.00981716i
$996$	−0.415386	+	7.63029i	−0.0131620	+	0.241775i
$997$	2.51324	+	28.7265i	0.0795952	+	0.909777i	0.926071	+	0.377350i	$0.123165\pi$
$997$	2.51324	+	28.7265i	0.0795952	+	0.909777i	−0.846476	+	0.532427i	$0.821280\pi$
$998$	19.4082	+	19.4082i	0.614355	+	0.614355i
$999$	34.7055	−	13.0808i	1.09803	−	0.413858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.92.6	yes	192
3.2	odd	2		405.2.r.a.197.11		192
5.2	odd	4		675.2.ba.b.443.6		192
5.3	odd	4	inner	135.2.q.a.38.11	yes	192
5.4	even	2		675.2.ba.b.632.11		192
15.8	even	4		405.2.r.a.278.6		192
27.5	odd	18	inner	135.2.q.a.32.11	✓	192
27.22	even	9		405.2.r.a.287.6		192
135.32	even	36		675.2.ba.b.518.11		192
135.59	odd	18		675.2.ba.b.32.6		192
135.103	odd	36		405.2.r.a.368.11		192
135.113	even	36	inner	135.2.q.a.113.6	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.11	✓	192	27.5	odd	18	inner
135.2.q.a.38.11	yes	192	5.3	odd	4	inner
135.2.q.a.92.6	yes	192	1.1	even	1	trivial
135.2.q.a.113.6	yes	192	135.113	even	36	inner
405.2.r.a.197.11		192	3.2	odd	2
405.2.r.a.278.6		192	15.8	even	4
405.2.r.a.287.6		192	27.22	even	9
405.2.r.a.368.11		192	135.103	odd	36
675.2.ba.b.32.6		192	135.59	odd	18
675.2.ba.b.443.6		192	5.2	odd	4
675.2.ba.b.518.11		192	135.32	even	36
675.2.ba.b.632.11		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+(-1.03355 + 0.0904240i) q^{2} +(1.64619 + 0.538569i) q^{3} +(-0.909563 + 0.160381i) q^{4} +(1.76770 + 1.36939i) q^{5} +(-1.75012 - 0.407783i) q^{6} +(-2.38295 + 1.66856i) q^{7} +(2.92987 - 0.785057i) q^{8} +(2.41989 + 1.77317i) q^{9} +(-1.95083 - 1.25550i) q^{10} +(-0.357163 - 0.981298i) q^{11} +(-1.58369 - 0.225845i) q^{12} +(-0.102905 + 1.17621i) q^{13} +(2.31203 - 1.94002i) q^{14} +(2.17246 + 3.20631i) q^{15} +(-1.22140 + 0.444552i) q^{16} +(5.46688 + 1.46485i) q^{17} +(-2.66142 - 1.61385i) q^{18} +(-3.77562 - 2.17985i) q^{19} +(-1.82746 - 0.962045i) q^{20} +(-4.82143 + 1.46339i) q^{21} +(0.457879 + 0.981926i) q^{22} +(2.49254 - 3.55972i) q^{23} +(5.24594 + 0.285584i) q^{24} +(1.24952 + 4.84135i) q^{25} -1.22498i q^{26} +(3.02862 + 4.22226i) q^{27} +(1.89984 - 1.89984i) q^{28} +(-5.99110 - 5.02713i) q^{29} +(-2.53528 - 3.11744i) q^{30} +(-1.88318 - 10.6800i) q^{31} +(-4.27590 + 1.99388i) q^{32} +(-0.0594626 - 1.80776i) q^{33} +(-5.78276 - 1.01966i) q^{34} +(-6.49726 - 0.313684i) q^{35} +(-2.48542 - 1.22471i) q^{36} +(1.84738 - 6.89452i) q^{37} +(4.09941 + 1.91158i) q^{38} +(-0.802872 + 1.88085i) q^{39} +(6.25419 + 2.62440i) q^{40} +(-2.34606 - 2.79593i) q^{41} +(4.85087 - 1.94846i) q^{42} +(-0.986834 + 2.11627i) q^{43} +(0.482244 + 0.835270i) q^{44} +(1.84946 + 6.44822i) q^{45} +(-2.25429 + 3.90454i) q^{46} +(-0.209148 - 0.298694i) q^{47} +(-2.25007 + 0.0740116i) q^{48} +(0.500224 - 1.37435i) q^{49} +(-1.72922 - 4.89080i) q^{50} +(8.21061 + 5.35571i) q^{51} +(-0.0950427 - 1.08634i) q^{52} +(1.16516 + 1.16516i) q^{53} +(-3.51203 - 4.09006i) q^{54} +(0.712425 - 2.22374i) q^{55} +(-5.67183 + 6.75943i) q^{56} +(-5.04139 - 5.62188i) q^{57} +(6.64669 + 4.65406i) q^{58} +(9.77378 + 3.55737i) q^{59} +(-2.49022 - 2.56792i) q^{60} +(-0.654019 + 3.70913i) q^{61} +(2.91210 + 10.8681i) q^{62} +(-8.72512 - 0.187656i) q^{63} +(6.49036 - 3.74721i) q^{64} +(-1.79260 + 1.93827i) q^{65} +(0.224923 + 1.86304i) q^{66} +(0.570007 + 0.0498691i) q^{67} +(-5.20741 - 0.455589i) q^{68} +(6.02036 - 4.51758i) q^{69} +(6.74362 - 0.263300i) q^{70} +(2.83490 - 1.63673i) q^{71} +(8.48201 + 3.29542i) q^{72} +(3.56015 + 13.2867i) q^{73} +(-1.28593 + 7.29289i) q^{74} +(-0.550446 + 8.64274i) q^{75} +(3.78377 + 1.37718i) q^{76} +(2.48846 + 1.74244i) q^{77} +(0.659736 - 2.01655i) q^{78} +(-2.43289 + 2.89941i) q^{79} +(-2.76783 - 0.886738i) q^{80} +(2.71171 + 8.58176i) q^{81} +(2.67759 + 2.67759i) q^{82} +(-0.416330 - 4.75867i) q^{83} +(4.15070 - 2.10431i) q^{84} +(7.65785 + 10.0757i) q^{85} +(0.828582 - 2.27651i) q^{86} +(-7.15504 - 11.5022i) q^{87} +(-1.81682 - 2.59468i) q^{88} +(-1.62360 + 2.81215i) q^{89} +(-2.49459 - 6.49733i) q^{90} +(-1.71736 - 2.97456i) q^{91} +(-1.69622 + 3.63755i) q^{92} +(2.65186 - 18.5956i) q^{93} +(0.243174 + 0.289803i) q^{94} +(-3.68908 - 9.02363i) q^{95} +(-8.11279 + 0.979449i) q^{96} +(-10.8407 - 5.05512i) q^{97} +(-0.392732 + 1.46570i) q^{98} +(0.875716 - 3.00794i) 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

Related objects

Downloads

Learn more