LMFDB - Embedded newform 570.2.bh.a.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.a.553.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.180509 - 2.22877i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.19282 + 0.587565i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.180509 - 2.22877i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.19282 + 0.587565i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-1.42623 + 1.72217i) q^{10} +(2.60269 + 4.50800i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-0.614723 - 7.02631i) q^{13} +(2.13327 + 0.776446i) q^{14} +(0.374072 - 2.20456i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(3.90635 - 5.57885i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(2.04226 - 3.85087i) q^{19} +(2.15610 - 0.592661i) q^{20} +(-2.23569 + 0.394212i) q^{21} +(0.453680 - 5.18558i) q^{22} +(-2.49399 + 5.34838i) q^{23} +(0.342020 - 0.939693i) q^{24} +(-4.93483 - 0.804627i) q^{25} +(-3.52658 + 6.10821i) q^{26} +(0.965926 + 0.258819i) q^{27} +(-1.30212 - 1.85962i) q^{28} +(1.13913 - 6.46033i) q^{29} +(-1.57090 + 1.59131i) q^{30} +(-3.39714 - 1.96134i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(2.19989 + 4.71769i) q^{33} +(-6.39980 + 2.32934i) q^{34} +(0.913722 + 4.99336i) q^{35} +(0.173648 + 0.984808i) q^{36} +(4.05456 - 4.05456i) q^{37} +(-3.88169 + 1.98306i) q^{38} -7.05315i q^{39} +(-2.10611 - 0.751207i) q^{40} +(3.58637 + 4.27407i) q^{41} +(2.05748 + 0.959418i) q^{42} +(4.39877 - 2.05118i) q^{43} +(-3.34596 + 3.98756i) q^{44} +(0.564789 - 2.16357i) q^{45} +(5.11066 - 2.95064i) q^{46} +(-1.70077 + 1.19089i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(-1.59894 + 0.923151i) q^{49} +(3.58086 + 3.48962i) q^{50} +(4.37772 - 5.21716i) q^{51} +(6.39233 - 2.98079i) q^{52} +(-0.746107 - 0.347915i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(10.5171 - 4.98707i) q^{55} +2.27018i q^{56} +(2.37011 - 3.65822i) q^{57} +(-4.63862 + 4.63862i) q^{58} +(-0.410354 - 2.32724i) q^{59} +(2.19955 - 0.402490i) q^{60} +(-3.87117 + 1.40899i) q^{61} +(1.65780 + 3.55516i) q^{62} +(-2.26154 + 0.197859i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-15.7710 + 0.101761i) q^{65} +(0.903906 - 5.12631i) q^{66} +(1.85826 + 2.65387i) q^{67} +(6.57846 + 1.76269i) q^{68} +(-2.95064 + 5.11066i) q^{69} +(2.11559 - 4.61441i) q^{70} +(0.604107 - 1.65977i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.0176494 + 0.201734i) q^{73} +(-5.64690 + 0.995700i) q^{74} +(-4.84593 - 1.23166i) q^{75} +(4.31713 + 0.602020i) q^{76} +(-8.35599 - 8.35599i) q^{77} +(-4.04552 + 5.77760i) q^{78} +(-6.04895 + 5.07567i) q^{79} +(1.29435 + 1.82337i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.486277 - 5.55817i) q^{82} +(-1.89533 - 7.07347i) q^{83} +(-1.13509 - 1.96603i) q^{84} +(-11.7288 - 9.71340i) q^{85} +(-4.77977 - 0.842803i) q^{86} +(1.69785 - 6.33647i) q^{87} +(5.02802 - 1.34725i) q^{88} +(8.87439 + 7.44650i) q^{89} +(-1.70362 + 1.44834i) q^{90} +(5.47639 + 15.0463i) q^{91} +(-5.87883 - 0.514331i) q^{92} +(-3.21327 - 2.24996i) q^{93} +2.07626 q^{94} +(-8.21405 - 5.24684i) q^{95} +1.00000 q^{96} +(4.64536 + 3.25272i) q^{97} +(1.83928 + 0.160916i) q^{98} +(1.78035 + 4.89147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q - 12 * q^5 + 12 * q^7	$ 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	0.180509	−	2.22877i	0.0807262	−	0.996736i
$5$	0.180509	−	2.22877i	0.0807262	−	0.996736i
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	−2.19282	+	0.587565i	−0.828809	+	0.222079i	−0.648194	−	0.761475i	$-0.724475\pi$
$7$	−2.19282	+	0.587565i	−0.828809	+	0.222079i	−0.180615	+	0.983554i	$0.557809\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	−1.42623	+	1.72217i	−0.451015	+	0.544597i
$11$	2.60269	+	4.50800i	0.784742	+	1.35921i	0.929153	+	0.369695i	$0.120538\pi$
$11$	2.60269	+	4.50800i	0.784742	+	1.35921i	−0.144411	+	0.989518i	$0.546129\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	−0.614723	−	7.02631i	−0.170493	−	1.94875i	−0.292609	−	0.956232i	$-0.594523\pi$
$13$	−0.614723	−	7.02631i	−0.170493	−	1.94875i	0.122116	−	0.992516i	$-0.461032\pi$
$14$	2.13327	+	0.776446i	0.570140	+	0.207514i
$15$	0.374072	−	2.20456i	0.0965851	−	0.569214i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	3.90635	−	5.57885i	0.947430	−	1.35307i	0.0118600	−	0.999930i	$-0.496225\pi$
$17$	3.90635	−	5.57885i	0.947430	−	1.35307i	0.935570	−	0.353141i	$-0.114886\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	2.04226	−	3.85087i	0.468526	−	0.883450i
$19$	2.04226	−	3.85087i	0.468526	−	0.883450i
$20$	2.15610	−	0.592661i	0.482118	−	0.132523i
$21$	−2.23569	+	0.394212i	−0.487867	+	0.0860241i
$22$	0.453680	−	5.18558i	0.0967248	−	1.10557i
$23$	−2.49399	+	5.34838i	−0.520033	+	1.11521i	0.454454	+	0.890770i	$0.349834\pi$
$23$	−2.49399	+	5.34838i	−0.520033	+	1.11521i	−0.974487	+	0.224444i	$0.927943\pi$
$24$	0.342020	−	0.939693i	0.0698146	−	0.191814i
$25$	−4.93483	−	0.804627i	−0.986967	−	0.160925i
$26$	−3.52658	+	6.10821i	−0.691618	+	1.19792i
$27$	0.965926	+	0.258819i	0.185893	+	0.0498097i
$28$	−1.30212	−	1.85962i	−0.246077	−	0.351435i
$29$	1.13913	−	6.46033i	0.211531	−	1.19965i	−0.675294	−	0.737549i	$-0.735983\pi$
$29$	1.13913	−	6.46033i	0.211531	−	1.19965i	0.886825	−	0.462105i	$-0.152906\pi$
$30$	−1.57090	+	1.59131i	−0.286807	+	0.290532i
$31$	−3.39714	−	1.96134i	−0.610145	−	0.352267i	0.162877	−	0.986646i	$-0.447923\pi$
$31$	−3.39714	−	1.96134i	−0.610145	−	0.352267i	−0.773022	+	0.634379i	$0.781256\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	2.19989	+	4.71769i	0.382952	+	0.821244i
$34$	−6.39980	+	2.32934i	−1.09756	+	0.399478i
$35$	0.913722	+	4.99336i	0.154447	+	0.844031i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	4.05456	−	4.05456i	0.666565	−	0.666565i	−0.290354	−	0.956919i	$-0.593773\pi$
$37$	4.05456	−	4.05456i	0.666565	−	0.666565i	0.956919	+	0.290354i	$0.0937732\pi$
$38$	−3.88169	+	1.98306i	−0.629693	+	0.321694i
$39$		−	7.05315i		−	1.12941i
$40$	−2.10611	−	0.751207i	−0.333005	−	0.118776i
$41$	3.58637	+	4.27407i	0.560097	+	0.667498i	0.969567	−	0.244826i	$-0.0787308\pi$
$41$	3.58637	+	4.27407i	0.560097	+	0.667498i	−0.409470	+	0.912324i	$0.634286\pi$
$42$	2.05748	+	0.959418i	0.317476	+	0.148041i
$43$	4.39877	−	2.05118i	0.670806	−	0.312802i	−0.0572097	−	0.998362i	$-0.518220\pi$
$43$	4.39877	−	2.05118i	0.670806	−	0.312802i	0.728016	+	0.685560i	$0.240443\pi$
$44$	−3.34596	+	3.98756i	−0.504422	+	0.601147i
$45$	0.564789	−	2.16357i	0.0841937	−	0.322525i
$46$	5.11066	−	2.95064i	0.753526	−	0.435048i
$47$	−1.70077	+	1.19089i	−0.248083	+	0.173709i	−0.691004	−	0.722851i	$-0.742831\pi$
$47$	−1.70077	+	1.19089i	−0.248083	+	0.173709i	0.442921	+	0.896561i	$0.353942\pi$
$48$	−0.819152	+	0.573576i	−0.118234	+	0.0827886i
$49$	−1.59894	+	0.923151i	−0.228421	+	0.131879i
$50$	3.58086	+	3.48962i	0.506411	+	0.493506i
$51$	4.37772	−	5.21716i	0.613003	−	0.730549i
$52$	6.39233	−	2.98079i	0.886456	−	0.413361i
$53$	−0.746107	−	0.347915i	−0.102486	−	0.0477898i	0.370699	−	0.928753i	$-0.379118\pi$
$53$	−0.746107	−	0.347915i	−0.102486	−	0.0477898i	−0.473185	+	0.880963i	$0.656896\pi$
$54$	−0.642788	−	0.766044i	−0.0874723	−	0.104245i
$55$	10.5171	−	4.98707i	1.41813	−	0.672457i
$56$			2.27018i			0.303365i
$57$	2.37011	−	3.65822i	0.313929	−	0.484543i
$58$	−4.63862	+	4.63862i	−0.609080	+	0.609080i
$59$	−0.410354	−	2.32724i	−0.0534236	−	0.302980i	0.946375	−	0.323071i	$-0.104715\pi$
$59$	−0.410354	−	2.32724i	−0.0534236	−	0.302980i	−0.999798	+	0.0200913i	$0.993604\pi$
$60$	2.19955	−	0.402490i	0.283960	−	0.0519612i
$61$	−3.87117	+	1.40899i	−0.495653	+	0.180403i	−0.577738	−	0.816223i	$-0.696064\pi$
$61$	−3.87117	+	1.40899i	−0.495653	+	0.180403i	0.0820850	+	0.996625i	$0.473842\pi$
$62$	1.65780	+	3.55516i	0.210540	+	0.451505i
$63$	−2.26154	+	0.197859i	−0.284927	+	0.0249279i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−15.7710	+	0.101761i	−1.95615	+	0.0126219i
$66$	0.903906	−	5.12631i	0.111263	−	0.631005i
$67$	1.85826	+	2.65387i	0.227023	+	0.324222i	0.916462	−	0.400121i	$-0.131032\pi$
$67$	1.85826	+	2.65387i	0.227023	+	0.324222i	−0.689439	+	0.724343i	$0.742143\pi$
$68$	6.57846	+	1.76269i	0.797755	+	0.213758i
$69$	−2.95064	+	5.11066i	−0.355215	+	0.615251i
$70$	2.11559	−	4.61441i	0.252862	−	0.551527i
$71$	0.604107	−	1.65977i	0.0716944	−	0.196979i	−0.898670	−	0.438626i	$-0.855465\pi$
$71$	0.604107	−	1.65977i	0.0716944	−	0.196979i	0.970364	+	0.241647i	$0.0776876\pi$
$72$	0.422618	−	0.906308i	0.0498060	−	0.106809i
$73$	−0.0176494	+	0.201734i	−0.00206571	+	0.0236112i	−0.997158	−	0.0753440i	$-0.975995\pi$
$73$	−0.0176494	+	0.201734i	−0.00206571	+	0.0236112i	0.995092	+	0.0989552i	$0.0315501\pi$
$74$	−5.64690	+	0.995700i	−0.656438	+	0.115748i
$75$	−4.84593	−	1.23166i	−0.559559	−	0.142220i
$76$	4.31713	+	0.602020i	0.495208	+	0.0690564i
$77$	−8.35599	−	8.35599i	−0.952253	−	0.952253i
$78$	−4.04552	+	5.77760i	−0.458065	+	0.654185i
$79$	−6.04895	+	5.07567i	−0.680560	+	0.571058i	−0.916170	−	0.400790i	$-0.868736\pi$
$79$	−6.04895	+	5.07567i	−0.680560	+	0.571058i	0.235610	+	0.971848i	$0.424291\pi$
$80$	1.29435	+	1.82337i	0.144712	+	0.203859i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	−0.486277	−	5.55817i	−0.0537003	−	0.613797i
$83$	−1.89533	−	7.07347i	−0.208040	−	0.776414i	−0.988502	−	0.151211i	$-0.951683\pi$
$83$	−1.89533	−	7.07347i	−0.208040	−	0.776414i	0.780462	−	0.625203i	$-0.214984\pi$
$84$	−1.13509	−	1.96603i	−0.123848	−	0.214511i
$85$	−11.7288	−	9.71340i	−1.27217	−	1.05357i
$86$	−4.77977	−	0.842803i	−0.515416	−	0.0908818i
$87$	1.69785	−	6.33647i	0.182029	−	0.679341i
$88$	5.02802	−	1.34725i	0.535989	−	0.143618i
$89$	8.87439	+	7.44650i	0.940684	+	0.789327i	0.977704	−	0.209987i	$-0.0673422\pi$
$89$	8.87439	+	7.44650i	0.940684	+	0.789327i	−0.0370203	+	0.999315i	$0.511787\pi$
$90$	−1.70362	+	1.44834i	−0.179577	+	0.152668i
$91$	5.47639	+	15.0463i	0.574082	+	1.57728i
$92$	−5.87883	−	0.514331i	−0.612910	−	0.0536227i
$93$	−3.21327	−	2.24996i	−0.333201	−	0.233310i
$94$	2.07626			0.214150
$95$	−8.21405	−	5.24684i	−0.842744	−	0.538314i
$96$	1.00000			0.102062
$97$	4.64536	+	3.25272i	0.471665	+	0.330263i	0.785124	−	0.619338i	$-0.212599\pi$
$97$	4.64536	+	3.25272i	0.471665	+	0.330263i	−0.313459	+	0.949602i	$0.601488\pi$
$98$	1.83928	+	0.160916i	0.185795	+	0.0162550i
$99$	1.78035	+	4.89147i	0.178932	+	0.491611i
$100$	−0.931710	−	4.91242i	−0.0931710	−	0.491242i
$101$	13.7849	+	11.5669i	1.37165	+	1.15095i	0.972188	+	0.234200i	$0.0752471\pi$
$101$	13.7849	+	11.5669i	1.37165	+	1.15095i	0.399461	+	0.916750i	$0.369197\pi$
$102$	−6.57846	+	1.76269i	−0.651364	+	0.174533i
$103$	1.94847	−	7.27181i	0.191989	−	0.716512i	−0.801037	−	0.598615i	$-0.795718\pi$
$103$	1.94847	−	7.27181i	0.191989	−	0.716512i	0.993026	−	0.117897i	$-0.0376154\pi$
$104$	−6.94600	−	1.22477i	−0.681111	−	0.120098i
$105$	0.475046	+	5.05399i	0.0463597	+	0.493219i
$106$	0.411619	+	0.712945i	0.0399800	+	0.0692473i
$107$	1.25763	+	4.69355i	0.121580	+	0.453743i	0.999695	−	0.0247073i	$-0.00786539\pi$
$107$	1.25763	+	4.69355i	0.121580	+	0.453743i	−0.878115	+	0.478450i	$0.841199\pi$
$108$	0.0871557	+	0.996195i	0.00838657	+	0.0958589i
$109$	3.08106	+	1.12141i	0.295112	+	0.107412i	0.485333	−	0.874329i	$-0.338698\pi$
$109$	3.08106	+	1.12141i	0.295112	+	0.107412i	−0.190221	+	0.981741i	$0.560921\pi$
$110$	−11.4756	−	1.94719i	−1.09415	−	0.185658i
$111$	4.39250	−	3.68575i	0.416918	−	0.349836i
$112$	1.30212	−	1.85962i	0.123039	−	0.175717i
$113$	8.08485	+	8.08485i	0.760559	+	0.760559i	0.976423	−	0.215864i	$-0.0692569\pi$
$113$	8.08485	+	8.08485i	0.760559	+	0.760559i	−0.215864	+	0.976423i	$0.569257\pi$
$114$	−4.03975	+	1.63720i	−0.378357	+	0.153338i
$115$	11.4701	+	6.52396i	1.06959	+	0.608363i
$116$	6.46033	−	1.13913i	0.599827	−	0.105766i
$117$	0.614723	−	7.02631i	0.0568311	−	0.649583i
$118$	−0.998705	+	2.14173i	−0.0919382	+	0.197162i
$119$	−5.28800	+	14.5287i	−0.484750	+	1.33184i
$120$	−2.03262	−	0.931907i	−0.185552	−	0.0850711i
$121$	−8.04804	+	13.9396i	−0.731640	+	1.26724i
$122$	3.97924	+	1.06623i	0.360264	+	0.0965323i
$123$	3.20021	+	4.57038i	0.288554	+	0.412097i
$124$	0.681167	−	3.86309i	0.0611706	−	0.346916i
$125$	−2.68411	+	10.8534i	−0.240074	+	0.970755i
$126$	1.96603	+	1.13509i	0.175148	+	0.101122i
$127$	−15.5949	+	1.36438i	−1.38383	+	0.121069i	−0.754616	−	0.656167i	$-0.772177\pi$
$127$	−15.5949	+	1.36438i	−1.38383	+	0.121069i	−0.629209	+	0.777236i	$0.716621\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	4.56080	−	1.66000i	0.401556	−	0.146155i
$130$	12.9772	+	8.96251i	1.13818	+	0.786064i
$131$	1.74396	+	9.89051i	0.152371	+	0.864138i	0.961150	+	0.276026i	$0.0890175\pi$
$131$	1.74396	+	9.89051i	0.152371	+	0.864138i	−0.808779	+	0.588112i	$0.799871\pi$
$132$	−3.68077	+	3.68077i	−0.320370	+	0.320370i
$133$	−2.21567	+	9.64422i	−0.192123	+	0.836260i
$134$		−	3.23978i		−	0.279874i
$135$	0.751207	−	2.10611i	0.0646536	−	0.181265i
$136$	−4.37772	−	5.21716i	−0.375386	−	0.447368i
$137$	11.1137	+	5.18241i	0.949508	+	0.442763i	0.834749	−	0.550630i	$-0.185613\pi$
$137$	11.1137	+	5.18241i	0.949508	+	0.442763i	0.114759	+	0.993393i	$0.463390\pi$
$138$	5.34838	−	2.49399i	0.455284	−	0.212303i
$139$	5.63659	−	6.71742i	0.478089	−	0.569764i	−0.472058	−	0.881568i	$-0.656489\pi$
$139$	5.63659	−	6.71742i	0.478089	−	0.569764i	0.950147	+	0.311803i	$0.100933\pi$
$140$	−4.37971	+	2.56645i	−0.370153	+	0.216904i
$141$	−1.79809	+	1.03813i	−0.151427	+	0.0874262i
$142$	−1.44686	+	1.01310i	−0.121418	+	0.0850178i
$143$	30.0747	−	21.0585i	2.51497	−	1.76100i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	−14.1930	−	3.70501i	−1.17866	−	0.307684i
$146$	0.130167	−	0.155128i	0.0107727	−	0.0128384i
$147$	−1.67332	+	0.780281i	−0.138013	+	0.0643565i
$148$	5.19678	+	2.42330i	0.427172	+	0.199194i
$149$	4.18098	+	4.98270i	0.342519	+	0.408198i	0.909614	−	0.415454i	$-0.136377\pi$
$149$	4.18098	+	4.98270i	0.342519	+	0.408198i	−0.567095	+	0.823652i	$0.691933\pi$
$150$	3.26310	+	3.78843i	0.266431	+	0.309324i
$151$			21.9753i			1.78832i	0.447745	+	0.894161i	$0.352227\pi$
$151$			21.9753i			1.78832i	−0.447745	+	0.894161i	$0.647773\pi$
$152$	−3.19108	−	2.96935i	−0.258831	−	0.240846i
$153$	4.81577	−	4.81577i	0.389332	−	0.389332i
$154$	2.05203	+	11.6376i	0.165357	+	0.937786i
$155$	−4.98459	+	7.21741i	−0.400372	+	0.579716i
$156$	6.62779	−	2.41232i	0.530648	−	0.193140i
$157$	−1.82585	−	3.91554i	−0.145718	−	0.312494i	0.819879	−	0.572537i	$-0.194041\pi$
$157$	−1.82585	−	3.91554i	−0.145718	−	0.312494i	−0.965597	+	0.260043i	$0.916263\pi$
$158$	7.86629	−	0.688212i	0.625809	−	0.0547512i
$159$	−0.712945	−	0.411619i	−0.0565402	−	0.0326435i
$160$	−0.0144278	−	2.23602i	−0.00114062	−	0.176773i
$161$	2.32636	−	13.1934i	0.183343	−	1.03979i
$162$	−0.573576	−	0.819152i	−0.0450644	−	0.0643587i
$163$	−17.7818	−	4.76463i	−1.39278	−	0.373195i	−0.517034	−	0.855965i	$-0.672964\pi$
$163$	−17.7818	−	4.76463i	−1.39278	−	0.373195i	−0.875747	+	0.482770i	$0.839631\pi$
$164$	−2.78970	+	4.83190i	−0.217839	+	0.377308i
$165$	10.9117	−	4.05147i	0.849478	−	0.315406i
$166$	−2.50461	+	6.88136i	−0.194396	+	0.534097i
$167$	−5.81790	+	12.4765i	−0.450203	+	0.965463i	0.541948	+	0.840412i	$0.317687\pi$
$167$	−5.81790	+	12.4765i	−0.450203	+	0.965463i	−0.992150	+	0.125051i	$0.960091\pi$
$168$	−0.197859	+	2.26154i	−0.0152651	+	0.174481i
$169$	−36.1887	+	6.38104i	−2.78374	+	0.490849i
$170$	4.03633	+	14.6841i	0.309572	+	1.12622i
$171$	2.67993	−	3.43773i	0.204939	−	0.262890i
$172$	3.43195	+	3.43195i	0.261684	+	0.261684i
$173$	−7.61350	+	10.8732i	−0.578843	+	0.826674i	−0.996643	−	0.0818649i	$-0.973912\pi$
$173$	−7.61350	+	10.8732i	−0.578843	+	0.826674i	0.417800	+	0.908539i	$0.362801\pi$
$174$	−5.02525	+	4.21668i	−0.380963	+	0.319666i
$175$	11.2940	−	1.13513i	0.853744	−	0.0858078i
$176$	−4.89147	−	1.78035i	−0.368708	−	0.134199i
$177$	−0.205961	−	2.35414i	−0.0154810	−	0.176948i
$178$	−2.99834	−	11.1900i	−0.224735	−	0.838723i
$179$	−6.00736	−	10.4051i	−0.449011	−	0.777711i	0.549310	−	0.835618i	$-0.314890\pi$
$179$	−6.00736	−	10.4051i	−0.449011	−	0.777711i	−0.998322	+	0.0579077i	$0.981557\pi$
$180$	2.22626	−	0.209255i	0.165935	−	0.0155969i
$181$	−1.42809	−	0.251810i	−0.106149	−	0.0187169i	0.120321	−	0.992735i	$-0.461607\pi$
$181$	−1.42809	−	0.251810i	−0.106149	−	0.0187169i	−0.226470	+	0.974018i	$0.572719\pi$
$182$	4.14418	−	15.4663i	0.307187	−	1.14644i
$183$	−3.97924	+	1.06623i	−0.294154	+	0.0788183i
$184$	4.52064	+	3.79327i	0.333266	+	0.279644i
$185$	−8.30479	−	9.76856i	−0.610580	−	0.718199i
$186$	1.34164	+	3.68612i	0.0983736	+	0.270279i
$187$	35.3165	+	3.08979i	2.58260	+	0.225948i
$188$	−1.70077	−	1.19089i	−0.124041	−	0.0868547i
$189$	−2.27018			−0.165131
$190$	3.71909	+	9.00935i	0.269811	+	0.653607i
$191$	14.2702			1.03256			0.516279	−	0.856420i	$-0.327317\pi$
$191$	14.2702			1.03256			0.516279	+	0.856420i	$0.327317\pi$
$192$	−0.819152	−	0.573576i	−0.0591172	−	0.0413943i
$193$	15.8072	+	1.38295i	1.13783	+	0.0995469i	0.640458	−	0.767993i	$-0.278744\pi$
$193$	15.8072	+	1.38295i	1.13783	+	0.0995469i	0.497368	+	0.867540i	$0.334300\pi$
$194$	−1.93958	−	5.32894i	−0.139253	−	0.382596i
$195$	−15.7199	−	1.27316i	−1.12572	−	0.0911728i
$196$	−1.41435	−	1.18678i	−0.101025	−	0.0847700i
$197$	−0.123287	+	0.0330346i	−0.00878383	+	0.00235362i	−0.263208	−	0.964739i	$-0.584781\pi$
$197$	−0.123287	+	0.0330346i	−0.00878383	+	0.00235362i	0.254424	+	0.967093i	$0.418114\pi$
$198$	1.34725	−	5.02802i	0.0957452	−	0.357326i
$199$	−10.8520	−	1.91350i	−0.769277	−	0.135644i	−0.224783	−	0.974409i	$-0.572167\pi$
$199$	−10.8520	−	1.91350i	−0.769277	−	0.135644i	−0.544494	+	0.838764i	$0.683278\pi$
$200$	−2.05444	+	4.55843i	−0.145271	+	0.322330i
$201$	1.61989	+	2.80573i	0.114258	+	0.197901i
$202$	−4.65743	−	17.3818i	−0.327695	−	1.22298i
$203$	1.29795	+	14.8357i	0.0910985	+	1.04126i
$204$	6.39980	+	2.32934i	0.448075	+	0.163086i
$205$	10.1733	−	7.22169i	0.710534	−	0.504385i
$206$	−5.76703	+	4.83912i	−0.401808	+	0.337157i
$207$	−3.38484	+	4.83405i	−0.235262	+	0.335990i
$208$	4.98733	+	4.98733i	0.345809	+	0.345809i
$209$	22.6751	−	0.816137i	1.56847	−	0.0564534i
$210$	2.50972	−	4.41246i	0.173187	−	0.304489i
$211$	12.4732	−	2.19937i	0.858692	−	0.151411i	0.273069	−	0.961994i	$-0.411961\pi$
$211$	12.4732	−	2.19937i	0.858692	−	0.151411i	0.585623	+	0.810584i	$0.300850\pi$
$212$	0.0717499	−	0.820105i	0.00492780	−	0.0563250i
$213$	0.746467	−	1.60080i	0.0511471	−	0.109685i
$214$	1.66192	−	4.56608i	0.113606	−	0.312131i
$215$	−3.77759	−	10.1741i	−0.257630	−	0.693868i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	8.60174	+	2.30483i	0.583924	+	0.156462i
$218$	−1.88064	−	2.68583i	−0.127373	−	0.181907i
$219$	−0.0351646	+	0.199428i	−0.00237620	+	0.0134761i
$220$	8.28338	+	8.17717i	0.558465	+	0.551304i
$221$	−41.6001	−	24.0178i	−2.79832	−	1.61561i
$222$	−5.71219	+	0.499752i	−0.383377	+	0.0335411i
$223$	8.90753	+	19.1023i	0.596492	+	1.27918i	0.940365	+	0.340166i	$0.110483\pi$
$223$	8.90753	+	19.1023i	0.596492	+	1.27918i	−0.343873	+	0.939016i	$0.611739\pi$
$224$	−2.13327	+	0.776446i	−0.142535	+	0.0518785i
$225$	−4.72014	−	1.64933i	−0.314676	−	0.109955i
$226$	−1.98544	−	11.2600i	−0.132070	−	0.749004i
$227$	8.83965	−	8.83965i	0.586708	−	0.586708i	−0.350030	−	0.936738i	$-0.613829\pi$
$227$	8.83965	−	8.83965i	0.586708	−	0.586708i	0.936738	+	0.350030i	$0.113829\pi$
$228$	4.24823	+	0.975991i	0.281346	+	0.0646366i
$229$		−	9.44449i		−	0.624109i	−0.950064	−	0.312055i	$-0.898983\pi$
$229$		−	9.44449i		−	0.624109i	0.950064	−	0.312055i	$-0.101017\pi$
$230$	−5.65378	−	11.9231i	−0.372799	−	0.786186i
$231$	−7.59592	−	9.05246i	−0.499775	−	0.595608i
$232$	−5.94538	−	2.77237i	−0.390333	−	0.182015i
$233$	−22.1023	+	10.3065i	−1.44797	+	0.675201i	−0.978215	−	0.207595i	$-0.933437\pi$
$233$	−22.1023	+	10.3065i	−1.44797	+	0.675201i	−0.469758	+	0.882795i	$0.655659\pi$
$234$	−4.53368	+	5.40303i	−0.296376	+	0.353207i
$235$	2.34722	+	4.00559i	0.153116	+	0.261296i
$236$	2.04654	−	1.18157i	0.133218	−	0.0769135i
$237$	−6.46830	+	4.52916i	−0.420162	+	0.294200i
$238$	12.6650	−	8.86811i	0.820948	−	0.574834i
$239$	−14.0745	+	8.12593i	−0.910405	+	0.525623i	−0.880562	−	0.473932i	$-0.842834\pi$
$239$	−14.0745	+	8.12593i	−0.910405	+	0.525623i	−0.0298439	+	0.999555i	$0.509501\pi$
$240$	1.13051	+	1.92924i	0.0729738	+	0.124532i
$241$	−10.2895	+	12.2625i	−0.662804	+	0.789899i	−0.987785	−	0.155821i	$-0.950198\pi$
$241$	−10.2895	+	12.2625i	−0.662804	+	0.789899i	0.324981	+	0.945720i	$0.394642\pi$
$242$	14.5880	−	6.80250i	0.937752	−	0.437281i
$243$	0.906308	+	0.422618i	0.0581397	+	0.0271110i
$244$	−2.64804	−	3.15581i	−0.169523	−	0.202030i
$245$	1.76887	+	3.73032i	0.113009	+	0.238321i
$246$		−	5.57940i		−	0.355730i
$247$	−28.3128	−	11.9823i	−1.80150	−	0.762417i
$248$	−2.77376	+	2.77376i	−0.176134	+	0.176134i
$249$	−1.27162	−	7.21174i	−0.0805859	−	0.457026i
$250$	8.42393	−	7.35101i	0.532776	−	0.464919i
$251$	−7.33322	+	2.66908i	−0.462869	+	0.168471i	−0.562919	−	0.826512i	$-0.690322\pi$
$251$	−7.33322	+	2.66908i	−0.462869	+	0.168471i	0.100050	+	0.994982i	$0.468100\pi$
$252$	−0.959418	−	2.05748i	−0.0604376	−	0.129609i
$253$	−30.6016	+	2.67729i	−1.92391	+	0.168320i
$254$	13.5572	+	7.82725i	0.850654	+	0.491125i
$255$	−10.8376	−	10.6987i	−0.678679	−	0.669977i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.05065	+	2.92864i	0.127916	+	0.182683i	0.878002	−	0.478658i	$-0.158876\pi$
$257$	2.05065	+	2.92864i	0.127916	+	0.182683i	−0.750085	+	0.661341i	$0.769988\pi$
$258$	−4.68813	−	1.25618i	−0.291870	−	0.0782064i
$259$	−6.50860	+	11.2732i	−0.404425	+	0.700484i
$260$	−5.48962	−	14.7851i	−0.340452	−	0.916932i
$261$	2.24365	−	6.16438i	0.138878	−	0.381566i
$262$	4.24439	−	9.10213i	0.262219	−	0.562331i
$263$	0.599500	−	6.85232i	0.0369667	−	0.422532i	−0.955052	−	0.296439i	$-0.904201\pi$
$263$	0.599500	−	6.85232i	0.0369667	−	0.422532i	0.992018	−	0.126093i	$-0.0402437\pi$
$264$	5.12631	−	0.903906i	0.315502	−	0.0556316i
$265$	−0.910102	+	1.60010i	−0.0559071	+	0.0982933i
$266$	7.34667	−	6.62923i	0.450453	−	0.406464i
$267$	8.19162	+	8.19162i	0.501319	+	0.501319i
$268$	−1.85826	+	2.65387i	−0.113511	+	0.162111i
$269$	20.2765	−	17.0140i	1.23628	−	1.03736i	0.238475	−	0.971149i	$-0.423353\pi$
$269$	20.2765	−	17.0140i	1.23628	−	1.03736i	0.997805	−	0.0662138i	$-0.0210919\pi$
$270$	−1.82337	+	1.29435i	−0.110967	+	0.0787715i
$271$	13.7211	+	4.99407i	0.833497	+	0.303368i	0.723294	−	0.690541i	$-0.242627\pi$
$271$	13.7211	+	4.99407i	0.833497	+	0.303368i	0.110204	+	0.993909i	$0.464850\pi$
$272$	0.593576	+	6.78461i	0.0359908	+	0.411377i
$273$	4.14418	+	15.4663i	0.250817	+	0.936063i
$274$	−6.13131	−	10.6197i	−0.370406	−	0.641562i
$275$	−9.21661	−	24.3404i	−0.555782	−	1.46778i
$276$	−5.81163	−	1.02475i	−0.349819	−	0.0616825i
$277$	−3.45117	+	12.8800i	−0.207361	+	0.773881i	0.781356	+	0.624086i	$0.214528\pi$
$277$	−3.45117	+	12.8800i	−0.207361	+	0.773881i	−0.988717	+	0.149796i	$0.952138\pi$
$278$	−8.47018	+	2.26958i	−0.508007	+	0.136120i
$279$	−3.00495	−	2.52145i	−0.179902	−	0.150955i
$280$	5.05970	+	0.409788i	0.302375	+	0.0244895i
$281$	−4.98591	−	13.6987i	−0.297434	−	0.817194i	−0.994927	−	0.100602i	$-0.967923\pi$
$281$	−4.98591	−	13.6987i	−0.297434	−	0.817194i	0.697492	−	0.716592i	$-0.254299\pi$
$282$	2.06836	+	0.180958i	0.123169	+	0.0107759i
$283$	3.52344	+	2.46714i	0.209447	+	0.146656i	0.673593	−	0.739102i	$-0.264750\pi$
$283$	3.52344	+	2.46714i	0.209447	+	0.146656i	−0.464146	+	0.885758i	$0.653639\pi$
$284$	1.76629			0.104810
$285$	−7.72550	−	5.94278i	−0.457619	−	0.352020i
$286$	−36.7144			−2.17097
$287$	−10.3756	−	7.26505i	−0.612450	−	0.428842i
$288$	0.996195	+	0.0871557i	0.0587013	+	0.00513570i
$289$	−10.0496	−	27.6112i	−0.591156	−	1.62419i
$290$	9.50110	+	11.1757i	0.557924	+	0.656261i
$291$	4.34419	+	3.64521i	0.254661	+	0.213686i
$292$	−0.195604	+	0.0524121i	−0.0114469	+	0.00306718i
$293$	6.42466	−	23.9771i	0.375332	−	1.40076i	−0.477526	−	0.878618i	$-0.658466\pi$
$293$	6.42466	−	23.9771i	0.375332	−	1.40076i	0.852859	−	0.522142i	$-0.174867\pi$
$294$	1.81825	+	0.320607i	0.106043	+	0.0186982i
$295$	−5.26094	+	0.494498i	−0.306304	+	0.0287908i
$296$	−2.86700	−	4.96580i	−0.166641	−	0.288631i
$297$	1.34725	+	5.02802i	0.0781756	+	0.291755i
$298$	−0.566900	−	6.47970i	−0.0328396	−	0.375359i
$299$	39.1125	+	14.2358i	2.26193	+	0.823276i
$300$	−0.500019	−	4.97494i	−0.0288686	−	0.287228i
$301$	−8.44052	+	7.08244i	−0.486503	+	0.408225i
$302$	12.6045	−	18.0011i	0.725308	−	1.03585i
$303$	12.7243	+	12.7243i	0.730993	+	0.730993i
$304$	0.910830	+	4.26267i	0.0522397	+	0.244481i
$305$	2.44154	+	8.88229i	0.139802	+	0.508598i
$306$	−6.70705	+	1.18263i	−0.383417	+	0.0676067i
$307$	1.47327	−	16.8396i	0.0840841	−	0.961085i	−0.830588	−	0.556888i	$-0.811995\pi$
$307$	1.47327	−	16.8396i	0.0840841	−	0.961085i	0.914672	−	0.404198i	$-0.132449\pi$
$308$	4.99414	−	10.7100i	0.284568	−	0.610257i
$309$	2.57484	−	7.07431i	0.146478	−	0.402444i
$310$	8.22288	−	3.05311i	0.467028	−	0.173405i
$311$	3.66526	−	6.34842i	0.207838	−	0.359986i	−0.743195	−	0.669075i	$-0.766691\pi$
$311$	3.66526	−	6.34842i	0.207838	−	0.359986i	0.951033	+	0.309089i	$0.100024\pi$
$312$	−6.81282	−	1.82549i	−0.385700	−	0.103348i
$313$	−5.14531	−	7.34826i	−0.290830	−	0.415348i	0.646975	−	0.762511i	$-0.276034\pi$
$313$	−5.14531	−	7.34826i	−0.290830	−	0.415348i	−0.937805	+	0.347163i	$0.887145\pi$
$314$	−0.750215	+	4.25468i	−0.0423371	+	0.240106i
$315$	0.0327536	+	5.07616i	0.00184546	+	0.286009i
$316$	−6.83843	−	3.94817i	−0.384692	−	0.222102i
$317$	0.0662511	−	0.00579622i	0.00372103	−	0.000325548i	−0.0852951	−	0.996356i	$-0.527183\pi$
$317$	0.0662511	−	0.00579622i	0.00372103	−	0.000325548i	0.0890161	+	0.996030i	$0.471628\pi$
$318$	0.347915	+	0.746107i	0.0195101	+	0.0418396i
$319$	32.0880	−	11.6791i	1.79658	−	0.653903i
$320$	−1.27071	+	1.83992i	−0.0710349	+	0.102854i
$321$	0.843778	+	4.78530i	0.0470951	+	0.267090i
$322$	−9.47307	+	9.47307i	−0.527914	+	0.527914i
$323$	−13.5056	−	26.4363i	−0.751474	−	1.47096i
$324$			1.00000i			0.0555556i
$325$	−2.62001	+	35.1683i	−0.145332	+	1.95079i
$326$	11.8332	+	14.1022i	0.655378	+	0.781049i
$327$	2.97159	+	1.38568i	0.164330	+	0.0766281i
$328$	5.05666	−	2.35796i	0.279207	−	0.130196i
$329$	3.02976	−	3.61073i	0.167036	−	0.199066i
$330$	−11.2622	−	2.93995i	−0.619964	−	0.161839i
$331$	23.1327	−	13.3557i	1.27149	−	0.734095i	0.296221	−	0.955119i	$-0.404273\pi$
$331$	23.1327	−	13.3557i	1.27149	−	0.734095i	0.975268	+	0.221025i	$0.0709402\pi$
$332$	5.99865	−	4.20030i	0.329219	−	0.230521i
$333$	4.69702	−	3.28889i	0.257395	−	0.180230i
$334$	11.9220	−	6.88317i	0.652342	−	0.376630i
$335$	6.25031	−	3.66259i	0.341491	−	0.200109i
$336$	1.45924	−	1.73906i	0.0796081	−	0.0948733i
$337$	−2.65730	+	1.23912i	−0.144752	+	0.0674991i	−0.493645	−	0.869664i	$-0.664336\pi$
$337$	−2.65730	+	1.23912i	−0.144752	+	0.0674991i	0.348892	+	0.937163i	$0.386558\pi$
$338$	33.3040	+	15.5299i	1.81150	+	0.844717i
$339$	7.34945	+	8.75873i	0.399167	+	0.475709i
$340$	5.11611	−	14.3437i	0.277460	−	0.777896i
$341$		−	20.4191i		−	1.10576i
$342$	−4.16707	+	1.27888i	−0.225329	+	0.0691539i
$343$	14.2006	−	14.2006i	0.766760	−	0.766760i
$344$	−0.842803	−	4.77977i	−0.0454409	−	0.257708i
$345$	10.8579	+	7.49882i	0.584568	+	0.403723i
$346$	12.4732	−	4.53988i	0.670565	−	0.244066i
$347$	−1.34984	−	2.89474i	−0.0724631	−	0.155398i	0.866740	−	0.498761i	$-0.166211\pi$
$347$	−1.34984	−	2.89474i	−0.0724631	−	0.155398i	−0.939203	+	0.343364i	$0.888434\pi$
$348$	6.53503	−	0.571741i	0.350315	−	0.0306486i
$349$	27.9867	+	16.1582i	1.49810	+	0.864926i	0.999998	−	0.00219469i	$-0.000698592\pi$
$349$	27.9867	+	16.1582i	1.49810	+	0.864926i	0.498098	+	0.867121i	$0.334032\pi$
$350$	−9.90257	−	5.54812i	−0.529315	−	0.296559i
$351$	1.22477	−	6.94600i	0.0653732	−	0.370750i
$352$	2.98569	+	4.26401i	0.159138	+	0.227272i
$353$	−28.7400	−	7.70087i	−1.52968	−	0.409876i	−0.606764	−	0.794882i	$-0.707533\pi$
$353$	−28.7400	−	7.70087i	−1.52968	−	0.409876i	−0.922914	+	0.385006i	$0.874199\pi$
$354$	−1.18157	+	2.04654i	−0.0627996	+	0.108772i
$355$	−3.59020	−	1.64602i	−0.190548	−	0.0873617i
$356$	−3.96220	+	10.8861i	−0.209996	+	0.576960i
$357$	−6.53413	+	14.0125i	−0.345823	+	0.741620i
$358$	−1.04715	+	11.9690i	−0.0553437	+	0.632582i
$359$	13.5466	−	2.38863i	0.714961	−	0.126067i	0.195677	−	0.980668i	$-0.437310\pi$
$359$	13.5466	−	2.38863i	0.714961	−	0.126067i	0.519284	+	0.854601i	$0.326199\pi$
$360$	−1.94367	−	1.10552i	−0.102440	−	0.0582658i
$361$	−10.6584	−	15.7289i	−0.560967	−	0.827838i
$362$	1.02539	+	1.02539i	0.0538931	+	0.0538931i
$363$	−9.23233	+	13.1851i	−0.484572	+	0.692040i
$364$	−12.2658	+	10.2922i	−0.642904	+	0.539460i
$365$	0.446433	+	0.0757514i	0.0233674	+	0.00396501i
$366$	3.87117	+	1.40899i	0.202349	+	0.0736491i
$367$	−2.10104	−	24.0150i	−0.109673	−	1.25357i	−0.829138	−	0.559044i	$-0.811168\pi$
$367$	−2.10104	−	24.0150i	−0.109673	−	1.25357i	0.719465	−	0.694529i	$-0.244387\pi$
$368$	−1.52736	−	5.70020i	−0.0796194	−	0.297144i
$369$	2.78970	+	4.83190i	0.145226	+	0.251539i
$370$	1.19987	+	12.7654i	0.0623783	+	0.663640i
$371$	1.84050	+	0.324530i	0.0955541	+	0.0168488i
$372$	1.01526	−	3.78902i	0.0526390	−	0.196452i
$373$	28.8663	−	7.73470i	1.49464	−	0.400488i	0.583340	−	0.812228i	$-0.301746\pi$
$373$	28.8663	−	7.73470i	1.49464	−	0.400488i	0.911301	+	0.411741i	$0.135079\pi$
$374$	−27.1574	−	22.7877i	−1.40427	−	1.17833i
$375$	−3.61983	+	10.5781i	−0.186927	+	0.546252i
$376$	0.710122	+	1.95104i	0.0366217	+	0.100617i
$377$	−46.0926	−	4.03258i	−2.37389	−	0.207688i
$378$	1.85962	+	1.30212i	0.0956485	+	0.0669738i
$379$	−17.1050			−0.878625			−0.439312	−	0.898334i	$-0.644778\pi$
$379$	−17.1050			−0.878625			−0.439312	+	0.898334i	$0.644778\pi$
$380$	2.12105	−	9.51321i	0.108807	−	0.488017i
$381$	−15.6545			−0.802004
$382$	−11.6895	−	8.18507i	−0.598086	−	0.418785i
$383$	−10.6406	−	0.930932i	−0.543709	−	0.0475684i	−0.188007	−	0.982168i	$-0.560203\pi$
$383$	−10.6406	−	0.930932i	−0.543709	−	0.0475684i	−0.355702	+	0.934599i	$0.615758\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	−20.1319	+	17.1152i	−1.02602	+	0.872273i
$386$	−12.1553	−	10.1995i	−0.618687	−	0.519140i
$387$	4.68813	−	1.25618i	0.238311	−	0.0638552i
$388$	−1.46775	+	5.47771i	−0.0745136	+	0.278088i
$389$	−28.0264	−	4.94181i	−1.42099	−	0.250560i	−0.590253	−	0.807218i	$-0.700972\pi$
$389$	−28.0264	−	4.94181i	−1.42099	−	0.250560i	−0.830741	+	0.556659i	$0.812083\pi$
$390$	12.1467	+	10.0594i	0.615072	+	0.509380i
$391$	20.0954	+	34.8063i	1.01627	+	1.76023i
$392$	0.477858	+	1.78339i	0.0241355	+	0.0900749i
$393$	0.875313	+	10.0049i	0.0441537	+	0.504679i
$394$	0.119939	+	0.0436541i	0.00604242	+	0.00219926i
$395$	10.2206	+	14.3979i	0.514255	+	0.724438i
$396$	−3.98756	+	3.34596i	−0.200382	+	0.168141i
$397$	−17.3817	+	24.8236i	−0.872361	+	1.24586i	0.0957669	+	0.995404i	$0.469470\pi$
$397$	−17.3817	+	24.8236i	−0.872361	+	1.24586i	−0.968128	+	0.250457i	$0.919419\pi$
$398$	7.79189	+	7.79189i	0.390572	+	0.390572i
$399$	−3.04779	+	9.41442i	−0.152580	+	0.471310i
$400$	4.29751	−	2.55567i	0.214875	−	0.127783i
$401$	11.1177	−	1.96035i	0.555192	−	0.0978954i	0.110989	−	0.993822i	$-0.464598\pi$
$401$	11.1177	−	1.96035i	0.555192	−	0.0978954i	0.444203	+	0.895926i	$0.353487\pi$
$402$	0.282366	−	3.22745i	0.0140831	−	0.160971i
$403$	−11.6927	+	25.0751i	−0.582455	+	1.24908i
$404$	−6.15462	+	16.9097i	−0.306204	+	0.841288i
$405$	0.931907	−	2.03262i	0.0463069	−	0.101002i
$406$	7.44617	−	12.8971i	0.369547	−	0.640075i
$407$	28.8307	+	7.72516i	1.42909	+	0.382922i
$408$	−3.90635	−	5.57885i	−0.193393	−	0.276194i
$409$	3.32173	−	18.8384i	0.164249	−	0.931501i	−0.785587	−	0.618751i	$-0.787639\pi$
$409$	3.32173	−	18.8384i	0.164249	−	0.931501i	0.949836	−	0.312750i	$-0.101250\pi$
$410$	−12.4757	+	0.0804984i	−0.616129	+	0.00397553i
$411$	10.6197	+	6.13131i	0.523833	+	0.302435i
$412$	7.49968	−	0.656137i	0.369483	−	0.0323256i
$413$	2.26723	+	4.86210i	0.111563	+	0.239248i
$414$	5.54539	−	2.01836i	0.272541	−	0.0991969i
$415$	−16.1073	+	2.94743i	−0.790675	+	0.144684i
$416$	−1.22477	−	6.94600i	−0.0600491	−	0.340556i
$417$	6.20060	−	6.20060i	0.303645	−	0.303645i
$418$	−19.0425	−	12.3374i	−0.931397	−	0.603440i
$419$			32.4315i			1.58438i	0.610273	+	0.792191i	$0.291060\pi$
$419$			32.4315i			1.58438i	−0.610273	+	0.792191i	$0.708940\pi$
$420$	−4.58672	+	2.17496i	−0.223809	+	0.106127i
$421$	−0.497269	−	0.592622i	−0.0242354	−	0.0288826i	0.753791	−	0.657115i	$-0.228223\pi$
$421$	−0.497269	−	0.592622i	−0.0242354	−	0.0288826i	−0.778026	+	0.628232i	$0.783779\pi$
$422$	−11.4790	−	5.35273i	−0.558787	−	0.260567i
$423$	−1.88173	+	0.877464i	−0.0914927	+	0.0426638i
$424$	−0.529167	+	0.630637i	−0.0256986	+	0.0306264i
$425$	−23.7661	+	24.3875i	−1.15283	+	1.18297i
$426$	−1.52965	+	0.883146i	−0.0741120	+	0.0427886i
$427$	7.66091	−	5.36423i	0.370738	−	0.259593i
$428$	−3.98036	+	2.78708i	−0.192398	+	0.134719i
$429$	31.7956	−	18.3572i	1.53511	−	0.886294i
$430$	−2.74121	+	10.5009i	−0.132193	+	0.506397i
$431$	15.5855	−	18.5741i	0.750727	−	0.894682i	−0.246496	−	0.969144i	$-0.579279\pi$
$431$	15.5855	−	18.5741i	0.750727	−	0.894682i	0.997224	+	0.0744615i	$0.0237238\pi$
$432$	−0.906308	+	0.422618i	−0.0436048	+	0.0203332i
$433$	−2.44742	−	1.14125i	−0.117616	−	0.0548450i	0.362920	−	0.931820i	$-0.381780\pi$
$433$	−2.44742	−	1.14125i	−0.117616	−	0.0548450i	−0.480535	+	0.876975i	$0.659558\pi$
$434$	−5.72414	−	6.82176i	−0.274767	−	0.327455i
$435$	−13.8161	−	4.92791i	−0.662429	−	0.236275i
$436$			3.27879i			0.157026i
$437$	15.5025	+	20.5268i	0.741587	+	0.981930i
$438$	0.143192	−	0.143192i	0.00684200	−	0.00684200i
$439$	−1.10458	−	6.26441i	−0.0527189	−	0.298984i	0.947036	−	0.321128i	$-0.104062\pi$
$439$	−1.10458	−	6.26441i	−0.0527189	−	0.298984i	−0.999755	+	0.0221439i	$0.992951\pi$
$440$	−2.09512	−	11.4495i	−0.0998807	−	0.545833i
$441$	−1.73496	+	0.631473i	−0.0826170	+	0.0300701i
$442$	20.3007	+	43.5351i	0.965608	+	2.07075i
$443$	−30.5134	+	2.66958i	−1.44974	+	0.126835i	−0.784653	−	0.619935i	$-0.787159\pi$
$443$	−30.5134	+	2.66958i	−1.44974	+	0.126835i	−0.665082	+	0.746770i	$0.731603\pi$
$444$	4.96580	+	2.86700i	0.235666	+	0.136062i
$445$	18.1984	−	18.4348i	0.862689	−	0.873894i
$446$	3.65999	−	20.7568i	0.173305	−	0.982863i
$447$	3.73080	+	5.32813i	0.176461	+	0.252012i
$448$	2.19282	+	0.587565i	0.103601	+	0.0277598i
$449$	−1.28508	+	2.22583i	−0.0606468	+	0.105043i	−0.894755	−	0.446558i	$-0.852650\pi$
$449$	−1.28508	+	2.22583i	−0.0606468	+	0.105043i	0.834108	+	0.551601i	$0.185983\pi$
$450$	2.92050	+	4.05841i	0.137674	+	0.191315i
$451$	−9.93328	+	27.2915i	−0.467740	+	1.28510i
$452$	−4.83209	+	10.3625i	−0.227283	+	0.487409i
$453$	−1.91527	+	21.8917i	−0.0899873	+	1.02856i
$454$	−12.3112	+	2.17080i	−0.577795	+	0.101881i
$455$	34.5232	−	9.48962i	1.61847	−	0.444880i
$456$	−2.92014	−	3.23617i	−0.136748	−	0.151547i
$457$	10.2087	+	10.2087i	0.477544	+	0.477544i	0.904345	−	0.426801i	$-0.140360\pi$
$457$	10.2087	+	10.2087i	0.477544	+	0.477544i	−0.426801	+	0.904345i	$0.640360\pi$
$458$	−5.41714	+	7.73647i	−0.253126	+	0.361502i
$459$	5.21716	−	4.37772i	0.243516	−	0.204334i
$460$	−2.20751	+	13.0097i	−0.102926	+	0.606581i
$461$	16.6093	+	6.04530i	0.773574	+	0.281558i	0.698490	−	0.715620i	$-0.253856\pi$
$461$	16.6093	+	6.04530i	0.773574	+	0.281558i	0.0750833	+	0.997177i	$0.476078\pi$
$462$	1.02993	+	11.7722i	0.0479168	+	0.547691i
$463$	−4.06954	−	15.1877i	−0.189128	−	0.705834i	−0.993709	−	0.111992i	$-0.964277\pi$
$463$	−4.06954	−	15.1877i	−0.189128	−	0.705834i	0.804581	−	0.593842i	$-0.202390\pi$
$464$	3.28000	+	5.68112i	0.152270	+	0.263740i
$465$	−5.59466	+	6.75551i	−0.259446	+	0.313279i
$466$	24.0167	+	4.23480i	1.11255	+	0.196173i
$467$	−0.674714	+	2.51807i	−0.0312220	+	0.116522i	−0.979778	−	0.200087i	$-0.935878\pi$
$467$	−0.674714	+	2.51807i	−0.0312220	+	0.116522i	0.948556	+	0.316609i	$0.102544\pi$
$468$	6.81282	−	1.82549i	0.314923	−	0.0843833i
$469$	−5.63416	−	4.72762i	−0.260161	−	0.218301i
$470$	0.374784	−	4.62750i	0.0172875	−	0.213451i
$471$	−1.47764	−	4.05977i	−0.0680859	−	0.187064i
$472$	−2.35414	−	0.205961i	−0.108358	−	0.00948012i
$473$	20.6954	+	14.4911i	0.951575	+	0.666300i
$474$	7.89634			0.362691
$475$	−13.1767	+	17.3601i	−0.604589	+	0.796538i
$476$	−15.4611			−0.708657
$477$	−0.674357	−	0.472190i	−0.0308767	−	0.0216201i
$478$	16.1900	+	1.41644i	0.740514	+	0.0647866i
$479$	−1.40876	−	3.87055i	−0.0643681	−	0.176850i	0.903339	−	0.428927i	$-0.141108\pi$
$479$	−1.40876	−	3.87055i	−0.0643681	−	0.176850i	−0.967707	+	0.252078i	$0.918886\pi$
$480$	0.180509	−	2.22877i	0.00823908	−	0.101729i
$481$	−30.9810	−	25.9961i	−1.41261	−	1.18532i
$482$	15.4621	−	4.14307i	0.704282	−	0.188712i
$483$	3.46739	−	12.9405i	0.157771	−	0.588811i
$484$	−15.8515	−	2.79506i	−0.720525	−	0.127048i
$485$	8.08809	−	9.76630i	0.367261	−	0.443465i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	8.79026	+	32.8057i	0.398325	+	1.48657i	0.816043	+	0.577992i	$0.196163\pi$
$487$	8.79026	+	32.8057i	0.398325	+	1.48657i	−0.417718	+	0.908577i	$0.637170\pi$
$488$	0.359048	+	4.10394i	0.0162533	+	0.185777i
$489$	−17.2989	−	6.29629i	−0.782284	−	0.284728i
$490$	0.690651	−	4.07028i	0.0312004	−	0.183876i
$491$	14.5392	−	12.1998i	0.656144	−	0.550570i	−0.252784	−	0.967523i	$-0.581346\pi$
$491$	14.5392	−	12.1998i	0.656144	−	0.550570i	0.908928	+	0.416952i	$0.136902\pi$
$492$	−3.20021	+	4.57038i	−0.144277	+	0.206049i
$493$	−31.5914	−	31.5914i	−1.42281	−	1.42281i
$494$	16.3197	+	26.0549i	0.734259	+	1.17227i
$495$	11.2233	−	3.08503i	0.504451	−	0.138662i
$496$	3.86309	−	0.681167i	0.173458	−	0.0305853i
$497$	−0.349477	+	3.99453i	−0.0156762	+	0.179179i
$498$	−3.09483	+	6.63689i	−0.138683	+	0.297406i
$499$	−6.22823	+	17.1119i	−0.278814	+	0.766034i	0.718684	+	0.695337i	$0.244745\pi$
$499$	−6.22823	+	17.1119i	−0.278814	+	0.766034i	−0.997498	+	0.0706975i	$0.977477\pi$
$500$	−11.1168	+	1.18983i	−0.497161	+	0.0532108i
$501$	−6.88317	+	11.9220i	−0.307517	+	0.532635i
$502$	7.53794	+	2.01979i	0.336435	+	0.0901475i
$503$	7.45970	+	10.6536i	0.332612	+	0.475019i	0.950270	−	0.311428i	$-0.100807\pi$
$503$	7.45970	+	10.6536i	0.332612	+	0.475019i	−0.617658	+	0.786447i	$0.711918\pi$
$504$	−0.394212	+	2.23569i	−0.0175596	+	0.0995854i
$505$	28.2683	−	28.6355i	1.25792	−	1.27426i
$506$	26.6030	+	15.3592i	1.18265	+	0.682801i
$507$	−36.6071	+	3.20271i	−1.62578	+	0.142237i
$508$	−6.61587	−	14.1878i	−0.293532	−	0.629481i
$509$	31.5844	−	11.4958i	1.39995	−	0.509542i	0.471790	−	0.881711i	$-0.343608\pi$
$509$	31.5844	−	11.4958i	1.39995	−	0.509542i	0.928165	+	0.372169i	$0.121386\pi$
$510$	2.74116	+	14.9801i	0.121381	+	0.663328i
$511$	−0.0798297	−	0.452737i	−0.00353146	−	0.0200279i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.96935	−	3.19108i	0.131100	−	0.140890i
$514$		−	3.57521i		−	0.157696i
$515$	−15.8555	−	5.65533i	−0.698675	−	0.249204i
$516$	3.11977	+	3.71800i	0.137340	+	0.163676i
$517$	−9.79513	−	4.56754i	−0.430789	−	0.200880i
$518$	11.7976	−	5.50131i	0.518357	−	0.241714i
$519$	−8.53219	+	10.1683i	−0.374521	+	0.446337i
$520$	−3.98354	+	15.2599i	−0.174690	+	0.669193i
$521$	2.28823	−	1.32111i	0.100249	−	0.0578788i	−0.449037	−	0.893513i	$-0.648233\pi$
$521$	2.28823	−	1.32111i	0.100249	−	0.0578788i	0.549286	+	0.835634i	$0.314900\pi$
$522$	−5.37363	+	3.76266i	−0.235198	+	0.164687i
$523$	−1.89500	+	1.32689i	−0.0828626	+	0.0580210i	−0.614274	−	0.789093i	$-0.710551\pi$
$523$	−1.89500	+	1.32689i	−0.0828626	+	0.0580210i	0.531411	+	0.847114i	$0.321662\pi$
$524$	−8.69757	+	5.02154i	−0.379955	+	0.219367i
$525$	11.3499	−	0.146476i	0.495352	−	0.00639272i
$526$	−4.42141	+	5.26923i	−0.192783	+	0.229749i
$527$	−24.2125	+	11.2905i	−1.05471	+	0.491820i
$528$	−4.71769	−	2.19989i	−0.205311	−	0.0957380i
$529$	−7.60105	−	9.05858i	−0.330480	−	0.393851i
$530$	1.66329	−	0.788711i	0.0722487	−	0.0342594i
$531$		−	2.36314i		−	0.102551i
$532$	−9.82041	+	1.21647i	−0.425769	+	0.0527406i
$533$	27.8263	−	27.8263i	1.20529	−	1.20529i
$534$	−2.01166	−	11.4087i	−0.0870531	−	0.493703i
$535$	10.6879	−	1.95575i	0.462077	−	0.0845543i
$536$	3.04440	−	1.10807i	0.131498	−	0.0478613i
$537$	−5.07764	−	10.8890i	−0.219116	−	0.469897i
$538$	−26.3684	+	2.30693i	−1.13682	+	0.0994590i
$539$	−8.32313	−	4.80536i	−0.358503	−	0.206982i
$540$	2.23602	−	0.0144278i	0.0962230	−	0.000620873i
$541$	−3.92979	+	22.2870i	−0.168955	+	0.958192i	0.775937	+	0.630810i	$0.217277\pi$
$541$	−3.92979	+	22.2870i	−0.168955	+	0.958192i	−0.944892	+	0.327381i	$0.893834\pi$
$542$	−8.37519	−	11.9610i	−0.359745	−	0.513769i
$543$	−1.40070	−	0.375318i	−0.0601100	−	0.0161064i
$544$	3.40526	−	5.89808i	0.145999	−	0.252878i
$545$	3.05553	−	6.66454i	0.130885	−	0.285478i
$546$	5.47639	−	15.0463i	0.234368	−	0.643920i
$547$	−2.75348	+	5.90485i	−0.117730	+	0.252473i	−0.956338	−	0.292262i	$-0.905592\pi$
$547$	−2.75348	+	5.90485i	−0.117730	+	0.252473i	0.838608	+	0.544735i	$0.183370\pi$
$548$	−1.06876	+	12.2160i	−0.0456551	+	0.521840i
$549$	−4.05703	+	0.715364i	−0.173150	+	0.0305310i
$550$	−6.41129	+	25.2249i	−0.273378	+	1.07559i
$551$	−22.5515	−	17.5803i	−0.960726	−	0.748946i
$552$	4.17284	+	4.17284i	0.177608	+	0.177608i
$553$	10.2820	−	14.6842i	0.437234	−	0.624435i
$554$	10.2147	−	8.57113i	0.433980	−	0.364152i
$555$	−7.42180	−	10.4552i	−0.315038	−	0.443798i
$556$	8.24014	+	2.99916i	0.349460	+	0.127193i
$557$	2.13399	+	24.3917i	0.0904202	+	1.03351i	0.896896	+	0.442241i	$0.145816\pi$
$557$	2.13399	+	24.3917i	0.0904202	+	1.03351i	−0.806476	+	0.591267i	$0.798628\pi$
$558$	1.01526	+	3.78902i	0.0429796	+	0.160402i
$559$	−17.1163	−	29.6462i	−0.723941	−	1.25390i
$560$	−3.90962	−	3.23780i	−0.165212	−	0.136822i
$561$	34.9128	+	6.15607i	1.47402	+	0.259910i
$562$	−3.77302	+	14.0811i	−0.159155	+	0.593975i
$563$	−37.8236	+	10.1348i	−1.59407	+	0.427131i	−0.943246	−	0.332094i	$-0.892245\pi$
$563$	−37.8236	+	10.1348i	−1.59407	+	0.427131i	−0.650828	+	0.759225i	$0.725578\pi$
$564$	−1.59051	−	1.33459i	−0.0669724	−	0.0561965i
$565$	19.4787	−	16.5599i	0.819474	−	0.696680i
$566$	−1.47114	−	4.04193i	−0.0618367	−	0.169895i
$567$	−2.26154	−	0.197859i	−0.0949756	−	0.00830929i
$568$	−1.44686	−	1.01310i	−0.0607090	−	0.0425089i
$569$	23.8049			0.997953			0.498976	−	0.866616i	$-0.333709\pi$
$569$	23.8049			0.997953			0.498976	+	0.866616i	$0.333709\pi$
$570$	2.91973	+	9.29920i	0.122294	+	0.389501i
$571$	−12.1784			−0.509650			−0.254825	−	0.966987i	$-0.582018\pi$
$571$	−12.1784			−0.509650			−0.254825	+	0.966987i	$0.582018\pi$
$572$	30.0747	+	21.0585i	1.25749	+	0.880501i
$573$	14.2159	+	1.24373i	0.593879	+	0.0519577i
$574$	4.33210	+	11.9024i	0.180819	+	0.496795i
$575$	16.6109	−	24.3866i	0.692721	−	1.01699i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	46.2167	−	12.3837i	1.92403	−	0.515541i	0.938739	−	0.344629i	$-0.111995\pi$
$577$	46.2167	−	12.3837i	1.92403	−	0.515541i	0.985286	−	0.170912i	$-0.0546715\pi$
$578$	−7.60493	+	28.3820i	−0.316323	+	1.18054i
$579$	15.6265	+	2.75537i	0.649415	+	0.114509i
$580$	−1.37271	−	14.6042i	−0.0569988	−	0.606407i
$581$	8.31224	+	14.3972i	0.344850	+	0.597298i
$582$	−1.46775	−	5.47771i	−0.0608401	−	0.227058i
$583$	−0.373486	−	4.26897i	−0.0154682	−	0.176803i
$584$	0.190292	+	0.0692607i	0.00787435	+	0.00286603i
$585$	−15.5491	−	2.63839i	−0.642875	−	0.109084i
$586$	−19.0155	+	15.9559i	−0.785523	+	0.659132i
$587$	−23.1205	+	33.0195i	−0.954286	+	1.36286i	−0.0225420	+	0.999746i	$0.507176\pi$
$587$	−23.1205	+	33.0195i	−0.954286	+	1.36286i	−0.931744	+	0.363116i	$0.881713\pi$
$588$	−1.30553	−	1.30553i	−0.0538393	−	0.0538393i
$589$	−14.4907	+	9.07638i	−0.597079	+	0.373986i
$590$	4.59315	+	2.61248i	0.189097	+	0.107554i
$591$	−0.125697	+	0.0221638i	−0.00517048	+	0.000911695i
$592$	−0.499752	+	5.71219i	−0.0205397	+	0.234769i
$593$	3.64191	−	7.81010i	0.149555	−	0.320722i	−0.817230	−	0.576311i	$-0.804492\pi$
$593$	3.64191	−	7.81010i	0.149555	−	0.320722i	0.966786	+	0.255589i	$0.0822694\pi$
$594$	1.78035	−	4.89147i	0.0730486	−	0.200699i
$595$	31.4265	+	14.4083i	1.28836	+	0.590683i
$596$	−3.25222	+	5.63302i	−0.133216	+	0.230737i
$597$	−10.6439	−	2.85203i	−0.435627	−	0.116726i
$598$	−23.8738	−	34.0953i	−0.976271	−	1.39426i
$599$	2.15775	−	12.2372i	0.0881632	−	0.499998i	−0.908466	−	0.417959i	$-0.862746\pi$
$599$	2.15775	−	12.2372i	0.0881632	−	0.499998i	0.996629	−	0.0820394i	$-0.0261433\pi$
$600$	−2.44391	+	4.36203i	−0.0997724	+	0.178079i
$601$	−24.3706	−	14.0704i	−0.994098	−	0.573943i	−0.0876012	−	0.996156i	$-0.527920\pi$
$601$	−24.3706	−	14.0704i	−0.994098	−	0.573943i	−0.906497	+	0.422213i	$0.861253\pi$
$602$	10.9764	−	0.960309i	0.447364	−	0.0391393i
$603$	1.36919	+	2.93624i	0.0557577	+	0.119573i
$604$	−20.6500	+	7.51599i	−0.840237	+	0.305821i
$605$	29.6155	+	20.4535i	1.20404	+	0.831552i
$606$	−3.12478	−	17.7215i	−0.126936	−	0.719888i
$607$	7.12658	−	7.12658i	0.289259	−	0.289259i	−0.547528	−	0.836787i	$-0.684431\pi$
$607$	7.12658	−	7.12658i	0.289259	−	0.289259i	0.836787	+	0.547528i	$0.184431\pi$
$608$	1.69886	−	4.01421i	0.0688979	−	0.162798i
$609$			14.8923i			0.603468i
$610$	3.09468	−	8.67635i	0.125300	−	0.351295i
$611$	9.41308	+	11.2181i	0.380812	+	0.453835i
$612$	6.17243	+	2.87825i	0.249506	+	0.116346i
$613$	−16.1641	+	7.53746i	−0.652863	+	0.304435i	−0.720685	−	0.693262i	$-0.756173\pi$
$613$	−16.1641	+	7.53746i	−0.652863	+	0.304435i	0.0678220	+	0.997697i	$0.478395\pi$
$614$	−10.8656	+	12.9491i	−0.438501	+	0.522585i
$615$	10.7640	−	6.30755i	0.434046	−	0.254345i
$616$	−10.2340	+	5.90857i	−0.412338	+	0.238063i
$617$	−5.06539	+	3.54683i	−0.203925	+	0.142790i	−0.671078	−	0.741387i	$-0.734169\pi$
$617$	−5.06539	+	3.54683i	−0.203925	+	0.142790i	0.467153	+	0.884176i	$0.345280\pi$
$618$	−6.16685	+	4.31807i	−0.248067	+	0.173698i
$619$	22.8849	−	13.2126i	0.919823	−	0.531060i	0.0362446	−	0.999343i	$-0.488460\pi$
$619$	22.8849	−	13.2126i	0.919823	−	0.531060i	0.883579	+	0.468283i	$0.155127\pi$
$620$	−8.48698	−	2.21549i	−0.340845	−	0.0889761i
$621$	−3.79327	+	4.52064i	−0.152219	+	0.181407i
$622$	−6.64371	+	3.09801i	−0.266388	+	0.124219i
$623$	−23.8353	−	11.1146i	−0.954940	−	0.445296i
$624$	4.53368	+	5.40303i	0.181492	+	0.216294i
$625$	23.7052	+	7.94140i	0.948206	+	0.317656i
$626$			8.97057i			0.358536i
$627$	22.6599	+	1.16323i	0.904950	+	0.0464550i
$628$	3.05493	−	3.05493i	0.121905	−	0.121905i
$629$	−6.78124	−	38.4583i	−0.270386	−	1.53343i
$630$	2.88474	−	4.17693i	0.114931	−	0.166413i
$631$	6.33768	−	2.30673i	0.252299	−	0.0918294i	−0.212775	−	0.977101i	$-0.568250\pi$
$631$	6.33768	−	2.30673i	0.252299	−	0.0918294i	0.465074	+	0.885272i	$0.346028\pi$
$632$	3.33714	+	7.15652i	0.132744	+	0.284671i
$633$	12.6174	−	1.10388i	0.501498	−	0.0438754i
$634$	−0.0575943	−	0.0332521i	−0.00228736	−	0.00132061i
$635$	0.225860	+	35.0038i	0.00896297	+	1.38908i
$636$	0.142954	−	0.810731i	0.00566848	−	0.0321476i
$637$	7.46925	+	10.6672i	0.295943	+	0.422650i
$638$	−32.9838	−	8.83798i	−1.30584	−	0.349899i
$639$	0.883146	−	1.52965i	0.0349367	−	0.0605122i
$640$	2.09624	−	0.778322i	0.0828611	−	0.0307659i
$641$	−13.4958	+	37.0794i	−0.533051	+	1.46455i	0.322370	+	0.946614i	$0.395521\pi$
$641$	−13.4958	+	37.0794i	−0.533051	+	1.46455i	−0.855421	+	0.517933i	$0.826702\pi$
$642$	2.05355	−	4.40386i	0.0810473	−	0.173807i
$643$	−3.82752	+	43.7488i	−0.150943	+	1.72528i	0.422779	+	0.906233i	$0.361055\pi$
$643$	−3.82752	+	43.7488i	−0.150943	+	1.72528i	−0.573722	+	0.819050i	$0.694501\pi$
$644$	13.1934	−	2.32636i	0.519894	−	0.0916713i
$645$	−2.87648	−	10.4646i	−0.113261	−	0.412044i
$646$	−4.10007	+	29.4019i	−0.161315	+	1.15680i
$647$	−24.2285	−	24.2285i	−0.952522	−	0.952522i	0.0464007	−	0.998923i	$-0.485225\pi$
$647$	−24.2285	−	24.2285i	−0.952522	−	0.952522i	−0.998923	+	0.0464007i	$0.985225\pi$
$648$	0.573576	−	0.819152i	0.0225322	−	0.0321793i
$649$	9.42315	−	7.90696i	0.369891	−	0.310375i
$650$	22.3179	−	27.3054i	0.875380	−	1.07101i
$651$	8.36813	+	3.04575i	0.327973	+	0.119372i
$652$	−1.60446	−	18.3391i	−0.0628355	−	0.718213i
$653$	4.64043	+	17.3183i	0.181594	+	0.677718i	0.995334	+	0.0964891i	$0.0307613\pi$
$653$	4.64043	+	17.3183i	0.181594	+	0.677718i	−0.813740	+	0.581229i	$0.802572\pi$
$654$	−1.63940	−	2.83952i	−0.0641055	−	0.111034i
$655$	22.3585	−	2.10157i	0.873618	−	0.0821150i
$656$	−5.49464	−	0.968853i	−0.214530	−	0.0378274i
$657$	−0.0524121	+	0.195604i	−0.00204479	+	0.00763126i
$658$	−4.55286	+	1.21994i	−0.177489	+	0.0475580i
$659$	−30.2191	−	25.3568i	−1.17717	−	0.987761i	−0.999994	−	0.00358194i	$-0.998860\pi$
$659$	−30.2191	−	25.3568i	−1.17717	−	0.987761i	−0.177175	−	0.984179i	$-0.556696\pi$
$660$	7.53917	+	8.86799i	0.293462	+	0.345186i
$661$	−12.8365	−	35.2681i	−0.499283	−	1.37177i	−0.891969	−	0.452096i	$-0.850676\pi$
$661$	−12.8365	−	35.2681i	−0.499283	−	1.37177i	0.392687	−	0.919672i	$-0.371546\pi$
$662$	−26.6097	−	2.32805i	−1.03422	−	0.0904822i
$663$	−39.3485	−	27.5521i	−1.52817	−	1.07004i
$664$	−7.32300			−0.284187
$665$	21.0948	+	6.67910i	0.818022	+	0.259004i
$666$	−5.73401			−0.222188
$667$	31.7113	+	22.2045i	1.22787	+	0.859762i
$668$	−13.7139	−	1.19981i	−0.530608	−	0.0464222i
$669$	7.20876	+	19.8059i	0.278707	+	0.765741i
$670$	−7.22073	−	0.584810i	−0.278961	−	0.0225932i
$671$	−16.4272	−	13.7841i	−0.634165	−	0.532128i
$672$	−2.19282	+	0.587565i	−0.0845899	+	0.0226658i
$673$	5.27625	−	19.6912i	0.203385	−	0.759042i	−0.786551	−	0.617525i	$-0.788135\pi$
$673$	5.27625	−	19.6912i	0.203385	−	0.759042i	0.989936	−	0.141517i	$-0.0451979\pi$
$674$	2.88746	+	0.509138i	0.111221	+	0.0196112i
$675$	−4.55843	−	2.05444i	−0.175454	−	0.0790754i
$676$	−18.3735	−	31.8238i	−0.706672	−	1.22399i
$677$	7.62028	+	28.4393i	0.292871	+	1.09301i	0.942893	+	0.333095i	$0.108093\pi$
$677$	7.62028	+	28.4393i	0.292871	+	1.09301i	−0.650022	+	0.759915i	$0.725240\pi$
$678$	−0.996513	−	11.3902i	−0.0382709	−	0.437438i
$679$	−12.0976	−	4.40318i	−0.464264	−	0.168978i
$680$	−12.4181	+	8.81518i	−0.476211	+	0.338047i
$681$	9.57644	−	8.03558i	0.366970	−	0.307924i
$682$	−11.7119	+	16.7263i	−0.448472	+	0.640485i
$683$	30.7464	+	30.7464i	1.17648	+	1.17648i	0.980635	+	0.195844i	$0.0627446\pi$
$683$	30.7464	+	30.7464i	1.17648	+	1.17648i	0.195844	+	0.980635i	$0.437255\pi$
$684$	4.14700	+	1.34253i	0.158564	+	0.0513331i
$685$	13.5565	−	23.8344i	0.517968	−	0.910667i
$686$	−19.7776	+	3.48732i	−0.755111	+	0.133146i
$687$	0.823142	−	9.40855i	0.0314048	−	0.358959i
$688$	−2.05118	+	4.39877i	−0.0782005	+	0.167702i
$689$	−1.98591	+	5.45625i	−0.0756572	+	0.207867i
$690$	−4.59310	−	12.3705i	−0.174856	−	0.470937i
$691$	−6.42547	+	11.1292i	−0.244436	+	0.423376i	−0.961973	−	0.273145i	$-0.911936\pi$
$691$	−6.42547	+	11.1292i	−0.244436	+	0.423376i	0.717537	+	0.696521i	$0.245270\pi$
$692$	−12.8214	−	3.43549i	−0.487398	−	0.130598i
$693$	−6.77804	−	9.68004i	−0.257476	−	0.367714i
$694$	−0.554630	+	3.14546i	−0.0210535	+	0.119400i
$695$	−13.9541	−	13.7752i	−0.529310	−	0.522524i
$696$	−5.68112	−	3.28000i	−0.215342	−	0.124328i
$697$	37.8540	−	3.31180i	1.43382	−	0.125443i
$698$	−13.6575	−	29.2885i	−0.516942	−	1.10859i
$699$	−22.9165	+	8.34093i	−0.866782	+	0.315483i
$700$	4.92944	+	10.2246i	0.186315	+	0.386455i
$701$	−3.23466	−	18.3447i	−0.122171	−	0.692869i	−0.982948	−	0.183885i	$-0.941133\pi$
$701$	−3.23466	−	18.3447i	−0.122171	−	0.692869i	0.860776	−	0.508983i	$-0.169979\pi$
$702$	−4.98733	+	4.98733i	−0.188235	+	0.188235i
$703$	−7.33311	−	23.8940i	−0.276574	−	0.901179i
$704$		−	5.20539i		−	0.196186i
$705$	1.98918	+	4.19492i	0.0749168	+	0.157990i
$706$	19.1254	+	22.7928i	0.719795	+	0.857818i
$707$	−37.0241	−	17.2646i	−1.39244	−	0.649304i
$708$	2.14173	−	0.998705i	0.0804911	−	0.0375336i
$709$	−29.0632	+	34.6362i	−1.09149	+	1.30079i	−0.141011	+	0.990008i	$0.545035\pi$
$709$	−29.0632	+	34.6362i	−1.09149	+	1.30079i	−0.950481	+	0.310782i	$0.899409\pi$
$710$	1.99680	+	3.40760i	0.0749387	+	0.127885i
$711$	−6.83843	+	3.94817i	−0.256461	+	0.148068i
$712$	9.48963	−	6.64471i	0.355639	−	0.249021i
$713$	18.9624	−	13.2776i	0.710149	−	0.497251i
$714$	13.3897	−	7.73054i	0.501096	−	0.289308i
$715$	−41.5058	−	70.8308i	−1.55223	−	2.64892i
$716$	7.72292	−	9.20382i	0.288619	−	0.343963i
$717$	−14.7292	+	6.86833i	−0.550072	+	0.256503i
$718$	−12.4668	−	5.81335i	−0.465256	−	0.216952i
$719$	5.47970	+	6.53046i	0.204358	+	0.243545i	0.858483	−	0.512842i	$-0.171407\pi$
$719$	5.47970	+	6.53046i	0.204358	+	0.243545i	−0.654125	+	0.756387i	$0.726963\pi$
$720$	0.958060	+	2.02043i	0.0357048	+	0.0752968i
$721$			17.0906i			0.636488i
$722$	−0.290919	+	18.9978i	−0.0108269	+	0.707024i
$723$	−11.3191	+	11.3191i	−0.420961	+	0.420961i
$724$	−0.251810	−	1.42809i	−0.00935844	−	0.0530744i
$725$	−10.8196	+	30.9641i	−0.401829	+	1.14998i
$726$	15.1254	−	5.50518i	0.561355	−	0.204317i
$727$	−4.54484	−	9.74644i	−0.168559	−	0.361475i	0.803824	−	0.594867i	$-0.202795\pi$
$727$	−4.54484	−	9.74644i	−0.168559	−	0.361475i	−0.972383	+	0.233392i	$0.925018\pi$
$728$	15.9510	−	1.39553i	0.591182	−	0.0517217i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	−0.322247	−	0.318115i	−0.0119269	−	0.0117740i
$731$	5.73993	−	32.5527i	0.212299	−	1.20401i
$732$	−2.36291	−	3.37459i	−0.0873358	−	0.124728i
$733$	3.41381	+	0.914727i	0.126092	+	0.0337862i	0.321313	−	0.946973i	$-0.395876\pi$
$733$	3.41381	+	0.914727i	0.126092	+	0.0337862i	−0.195221	+	0.980759i	$0.562542\pi$
$734$	−12.0534	+	20.8770i	−0.444898	+	0.770586i
$735$	1.43702	+	3.87029i	0.0530052	+	0.142758i
$736$	−2.01836	+	5.54539i	−0.0743976	+	0.204406i
$737$	−7.12717	+	15.2843i	−0.262533	+	0.563003i
$738$	0.486277	−	5.55817i	0.0179001	−	0.204599i
$739$	47.5044	−	8.37630i	1.74748	−	0.308127i	0.793625	−	0.608407i	$-0.208191\pi$
$739$	47.5044	−	8.37630i	1.74748	−	0.308127i	0.953851	+	0.300280i	$0.0970802\pi$
$740$	6.33904	−	11.1450i	0.233028	−	0.409698i
$741$	−27.1608	−	14.4044i	−0.997775	−	0.529157i
$742$	−1.32151	−	1.32151i	−0.0485141	−	0.0485141i
$743$	14.6420	−	20.9110i	0.537164	−	0.767150i	−0.455214	−	0.890382i	$-0.650437\pi$
$743$	14.6420	−	20.9110i	0.537164	−	0.767150i	0.992378	+	0.123232i	$0.0393261\pi$
$744$	−3.00495	+	2.52145i	−0.110167	+	0.0924409i
$745$	11.8600	−	8.41902i	0.434516	−	0.308449i
$746$	−28.0823	−	10.2211i	−1.02817	−	0.374222i
$747$	−0.638241	−	7.29513i	−0.0233520	−	0.266915i
$748$	9.17550	+	34.2434i	0.335490	+	1.25206i
$749$	−5.51553	−	9.55318i	−0.201533	−	0.349066i
$750$	9.03256	−	6.58885i	0.329822	−	0.240591i
$751$	7.43306	+	1.31065i	0.271236	+	0.0478263i	0.307612	−	0.951512i	$-0.400470\pi$
$751$	7.43306	+	1.31065i	0.271236	+	0.0478263i	−0.0363757	+	0.999338i	$0.511581\pi$
$752$	0.537375	−	2.00551i	0.0195960	−	0.0731334i
$753$	−7.53794	+	2.01979i	−0.274698	+	0.0736051i
$754$	35.4438	+	29.7409i	1.29079	+	1.08310i
$755$	48.9778	+	3.96674i	1.78249	+	0.144364i
$756$	−0.776446	−	2.13327i	−0.0282391	−	0.0775862i
$757$	−13.0491	−	1.14165i	−0.474277	−	0.0414939i	−0.152488	−	0.988305i	$-0.548729\pi$
$757$	−13.0491	−	1.14165i	−0.474277	−	0.0414939i	−0.321789	+	0.946811i	$0.604284\pi$
$758$	14.0116	+	9.81103i	0.508924	+	0.356353i
$759$	−30.7185			−1.11501
$760$	−7.19401	+	6.57618i	−0.260954	+	0.238543i
$761$	6.86631			0.248904			0.124452	−	0.992226i	$-0.460283\pi$
$761$	6.86631			0.248904			0.124452	+	0.992226i	$0.460283\pi$
$762$	12.8234	+	8.97905i	0.464543	+	0.325277i
$763$	−7.41511	−	0.648738i	−0.268445	−	0.0234859i
$764$	4.88071	+	13.4096i	0.176578	+	0.485144i
$765$	−9.86394	−	11.6025i	−0.356632	−	0.419490i
$766$	8.18231	+	6.86577i	0.295639	+	0.248070i
$767$	−16.0996	+	4.31388i	−0.581324	+	0.155765i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	18.6361	+	3.28604i	0.672034	+	0.118498i	0.499245	−	0.866461i	$-0.333611\pi$
$769$	18.6361	+	3.28604i	0.672034	+	0.118498i	0.172790	+	0.984959i	$0.444722\pi$
$770$	26.3080	−	2.47280i	0.948074	−	0.0891134i
$771$	1.78760	+	3.09622i	0.0643790	+	0.111508i
$772$	4.10683	+	15.3269i	0.147808	+	0.551627i
$773$	1.65835	+	18.9550i	0.0596468	+	0.681766i	0.965880	+	0.258989i	$0.0833892\pi$
$773$	1.65835	+	18.9550i	0.0596468	+	0.681766i	−0.906234	+	0.422777i	$0.861055\pi$
$774$	−4.56080	−	1.66000i	−0.163935	−	0.0596674i
$775$	15.1862	+	12.4123i	0.545504	+	0.445864i
$776$	4.34419	−	3.64521i	0.155947	−	0.130855i
$777$	−7.46636	+	10.6631i	−0.267854	+	0.382535i
$778$	20.1234	+	20.1234i	0.721458	+	0.721458i
$779$	23.7832	−	5.08189i	0.852121	−	0.182078i
$780$	−4.18013	−	15.2073i	−0.149673	−	0.544508i
$781$	9.05456	−	1.59656i	0.323998	−	0.0571295i
$782$	3.50286	−	40.0379i	0.125262	−	1.43175i
$783$	2.77237	−	5.94538i	0.0990766	−	0.212470i
$784$	0.631473	−	1.73496i	0.0225526	−	0.0619627i
$785$	−9.05642	+	3.36260i	−0.323237	+	0.120016i
$786$	5.02154	−	8.69757i	0.179113	−	0.310232i
$787$	−29.8591	−	8.00073i	−1.06436	−	0.285195i	−0.316188	−	0.948697i	$-0.602403\pi$
$787$	−29.8591	−	8.00073i	−1.06436	−	0.285195i	−0.748175	+	0.663502i	$0.769070\pi$
$788$	−0.0732090	−	0.104553i	−0.00260796	−	0.00372456i
$789$	1.19444	−	6.77399i	0.0425231	−	0.241160i
$790$	−0.113927	−	17.6564i	−0.00405333	−	0.628186i
$791$	−22.4790	−	12.9783i	−0.799262	−	0.461454i
$792$	5.18558	−	0.453680i	0.184262	−	0.0161208i
$793$	12.2797	+	26.3339i	0.436065	+	0.935145i
$794$	28.4765	−	10.3646i	1.01059	−	0.367825i
$795$	−1.04610	+	1.51469i	−0.0371012	+	0.0537205i
$796$	−1.91350	−	10.8520i	−0.0678222	−	0.384639i
$797$	14.5904	−	14.5904i	0.516819	−	0.516819i	−0.399789	−	0.916607i	$-0.630917\pi$
$797$	14.5904	−	14.5904i	0.516819	−	0.516819i	0.916607	+	0.399789i	$0.130917\pi$
$798$	7.89649	−	5.96370i	0.279533	−	0.211113i
$799$			14.1404i			0.500251i
$800$	−4.98618	−	0.371466i	−0.176288	−	0.0131333i
$801$	7.44650	+	8.87439i	0.263109	+	0.313561i
$802$	−10.2315	−	4.77103i	−0.361287	−	0.168471i
$803$	−0.955353	+	0.445489i	−0.0337137	+	0.0157209i
$804$	−2.08249	+	2.48182i	−0.0734438	+	0.0875269i
$805$	−28.9852	−	7.56645i	−1.02159	−	0.266682i
$806$	23.9606	−	13.8336i	0.843975	−	0.487269i
$807$	21.6822	−	15.1821i	0.763250	−	0.534434i
$808$	14.7406	−	10.3215i	0.518572	−	0.363108i
$809$	−20.8443	+	12.0345i	−0.732847	+	0.423109i	−0.819463	−	0.573133i	$-0.805728\pi$
$809$	−20.8443	+	12.0345i	−0.732847	+	0.423109i	0.0866161	+	0.996242i	$0.472395\pi$
$810$	−1.92924	+	1.13051i	−0.0677865	+	0.0397219i
$811$	3.34069	−	3.98128i	0.117308	−	0.139802i	−0.704195	−	0.710007i	$-0.748692\pi$
$811$	3.34069	−	3.98128i	0.117308	−	0.139802i	0.821502	+	0.570205i	$0.193136\pi$
$812$	−13.4970	+	6.29378i	−0.473653	+	0.220868i
$813$	13.2336	+	6.17094i	0.464124	+	0.216424i
$814$	−19.1858	−	22.8647i	−0.672461	−	0.801407i
$815$	−13.8291	+	38.7716i	−0.484411	+	1.35811i
$816$			6.81052i			0.238416i
$817$	1.08460	−	21.1281i	0.0379453	−	0.739180i
$818$	−13.5263	+	13.5263i	−0.472936	+	0.472936i
$819$	2.78044	+	15.7686i	0.0971563	+	0.551001i
$820$	10.2656	+	7.08981i	0.358492	+	0.247587i
$821$	37.0386	−	13.4809i	1.29266	−	0.470488i	0.398058	−	0.917360i	$-0.369684\pi$
$821$	37.0386	−	13.4809i	1.29266	−	0.470488i	0.894598	+	0.446872i	$0.147462\pi$
$822$	−5.18241	−	11.1137i	−0.180757	−	0.387635i
$823$	21.5167	−	1.88246i	0.750023	−	0.0656185i	0.294267	−	0.955723i	$-0.404924\pi$
$823$	21.5167	−	1.88246i	0.750023	−	0.0656185i	0.455756	+	0.890105i	$0.349369\pi$
$824$	−6.51972	−	3.76416i	−0.227125	−	0.131131i
$825$	−7.06013	−	25.0511i	−0.245802	−	0.872167i
$826$	0.931576	−	5.28323i	0.0324137	−	0.183827i
$827$	1.29686	+	1.85211i	0.0450962	+	0.0644040i	0.841067	−	0.540931i	$-0.181928\pi$
$827$	1.29686	+	1.85211i	0.0450962	+	0.0644040i	−0.795971	+	0.605335i	$0.793039\pi$
$828$	−5.70020	−	1.52736i	−0.198096	−	0.0530796i
$829$	−25.0490	+	43.3861i	−0.869986	+	1.50686i	−0.00797659	+	0.999968i	$0.502539\pi$
$829$	−25.0490	+	43.3861i	−0.869986	+	1.50686i	−0.862010	+	0.506892i	$0.830794\pi$
$830$	14.8849	+	6.82435i	0.516662	+	0.236877i
$831$	−4.56060	+	12.5302i	−0.158206	+	0.434666i
$832$	−2.98079	+	6.39233i	−0.103340	+	0.221614i
$833$	−1.09592	+	12.5264i	−0.0379714	+	0.434015i
$834$	−8.63575	+	1.52272i	−0.299032	+	0.0527273i
$835$	26.7571	+	15.2189i	0.925969	+	0.526672i
$836$	8.52225	+	21.0285i	0.294748	+	0.727285i
$837$	−2.77376	−	2.77376i	−0.0958750	−	0.0958750i
$838$	18.6019	−	26.5663i	0.642593	−	0.917718i
$839$	1.26676	−	1.06294i	0.0437335	−	0.0366967i	−0.620659	−	0.784081i	$-0.713135\pi$
$839$	1.26676	−	1.06294i	0.0437335	−	0.0366967i	0.664392	+	0.747384i	$0.268690\pi$
$840$	5.00473	+	0.849210i	0.172680	+	0.0293005i
$841$	−13.1872	−	4.79976i	−0.454732	−	0.165509i
$842$	0.0674249	+	0.770670i	0.00232361	+	0.0265590i
$843$	−3.77302	−	14.0811i	−0.129950	−	0.484979i
$844$	6.33282	+	10.9688i	0.217985	+	0.377560i
$845$	7.68948	+	81.8080i	0.264526	+	2.81428i
$846$	2.04471	+	0.360538i	0.0702987	+	0.0123956i
$847$	9.45749	−	35.2958i	0.324963	−	1.21278i
$848$	0.795187	−	0.213070i	0.0273068	−	0.00731684i
$849$	3.29501	+	2.76484i	0.113084	+	0.0948891i
$850$	33.4562	−	6.34543i	1.14754	−	0.217646i
$851$	11.5733	+	31.7973i	0.396727	+	1.09000i
$852$	1.75957	+	0.153942i	0.0602819	+	0.00527398i
$853$	−2.83876	−	1.98772i	−0.0971974	−	0.0680583i	0.523967	−	0.851738i	$-0.324451\pi$
$853$	−2.83876	−	1.98772i	−0.0971974	−	0.0680583i	−0.621165	+	0.783680i	$0.713340\pi$
$854$	−9.35225			−0.320027
$855$	−7.17816	−	6.59348i	−0.245488	−	0.225492i
$856$	4.85912			0.166081
$857$	4.97926	+	3.48652i	0.170088	+	0.119097i	0.655521	−	0.755177i	$-0.272449\pi$
$857$	4.97926	+	3.48652i	0.170088	+	0.119097i	−0.485433	+	0.874274i	$0.661338\pi$
$858$	−36.5747	−	3.19987i	−1.24864	−	0.109242i
$859$	−15.3809	−	42.2587i	−0.524790	−	1.44185i	−0.865131	−	0.501546i	$-0.832765\pi$
$859$	−15.3809	−	42.2587i	−0.524790	−	1.44185i	0.340342	−	0.940302i	$-0.389457\pi$
$860$	8.26852	−	7.02952i	0.281954	−	0.239705i
$861$	−9.70289	−	8.14169i	−0.330674	−	0.277468i
$862$	−23.4206	+	6.27552i	−0.797707	+	0.213745i
$863$	−7.59984	+	28.3630i	−0.258702	+	0.965488i	0.707292	+	0.706922i	$0.249917\pi$
$863$	−7.59984	+	28.3630i	−0.258702	+	0.965488i	−0.965994	+	0.258566i	$0.916750\pi$
$864$	0.984808	+	0.173648i	0.0335038	+	0.00590763i
$865$	22.8596	+	18.9314i	0.777248	+	0.643689i
$866$	1.35021	+	2.33864i	0.0458822	+	0.0794702i
$867$	−7.60493	−	28.3820i	−0.258277	−	0.963903i
$868$	0.776137	+	8.87129i	0.0263438	+	0.301111i
$869$	−38.6247	−	14.0582i	−1.31025	−	0.476893i
$870$	8.49092	+	11.9613i	0.287869	+	0.405525i
$871$	17.5046	−	14.6881i	0.593122	−	0.497688i
$872$	1.88064	−	2.68583i	0.0636864	−	0.0909537i
$873$	4.00996	+	4.00996i	0.135717	+	0.135717i
$874$	−0.925244	−	25.7064i	−0.0312969	−	0.869534i
$875$	−0.491277	−	25.3766i	−0.0166082	−	0.857885i
$876$	−0.199428	+	0.0351646i	−0.00673805	+	0.00118810i
$877$	0.235396	−	2.69059i	0.00794877	−	0.0908548i	−0.991184	−	0.132492i	$-0.957702\pi$
$877$	0.235396	−	2.69059i	0.00794877	−	0.0908548i	0.999133	+	0.0416377i	$0.0132575\pi$
$878$	−2.68830	+	5.76507i	−0.0907256	+	0.194562i
$879$	8.48995	−	23.3260i	0.286359	−	0.786765i
$880$	−4.85094	+	10.5806i	−0.163525	+	0.356671i
$881$	13.4506	−	23.2972i	0.453163	−	0.784901i	−0.545418	−	0.838164i	$-0.683629\pi$
$881$	13.4506	−	23.2972i	0.453163	−	0.784901i	0.998580	+	0.0532634i	$0.0169623\pi$
$882$	1.78339	+	0.477858i	0.0600499	+	0.0160903i
$883$	−15.9266	−	22.7456i	−0.535974	−	0.765450i	0.456259	−	0.889847i	$-0.349189\pi$
$883$	−15.9266	−	22.7456i	−0.535974	−	0.765450i	−0.992233	+	0.124397i	$0.960300\pi$
$884$	8.34130	−	47.3059i	0.280548	−	1.59107i
$885$	−5.28402	+	0.0340948i	−0.177621	+	0.00114608i
$886$	26.5263	+	15.3150i	0.891169	+	0.514517i
$887$	−39.7768	+	3.48001i	−1.33557	+	0.116847i	−0.732461	−	0.680809i	$-0.761628\pi$
$887$	−39.7768	+	3.48001i	−1.33557	+	0.116847i	−0.603112	+	0.797657i	$0.706073\pi$
$888$	−2.42330	−	5.19678i	−0.0813205	−	0.174392i
$889$	33.3952	−	12.1549i	1.12004	−	0.407661i
$890$	−25.4811	+	4.66272i	−0.854128	+	0.156295i
$891$	0.903906	+	5.12631i	0.0302820	+	0.171738i
$892$	−14.9037	+	14.9037i	−0.499013	+	0.499013i
$893$	1.11256	+	8.98155i	0.0372303	+	0.300556i
$894$		−	6.50445i		−	0.217541i
$895$	−24.2749	+	11.5108i	−0.811419	+	0.384764i
$896$	−1.45924	−	1.73906i	−0.0487498	−	0.0580978i
$897$	37.7229	+	17.5905i	1.25953	+	0.587329i
$898$	2.32936	−	1.08620i	0.0777317	−	0.0362469i
$899$	−16.5407	+	19.7125i	−0.551664	+	0.657447i
$900$	−0.0645217	−	4.99958i	−0.00215072	−	0.166653i
$901$	−4.85553	+	2.80334i	−0.161761	+	0.0933928i
$902$	23.7906	−	16.6584i	0.792141	−	0.554663i
$903$	−9.02567	+	6.31985i	−0.300356	+	0.210311i
$904$	9.90188	−	5.71686i	0.329332	−	0.190140i
$905$	−0.819009	+	3.13742i	−0.0272248	+	0.104291i
$906$	14.1254	−	16.8340i	0.469286	−	0.559274i
$907$	18.8115	−	8.77196i	0.624626	−	0.291268i	−0.0844196	−	0.996430i	$-0.526904\pi$
$907$	18.8115	−	8.77196i	0.624626	−	0.291268i	0.709046	+	0.705162i	$0.249126\pi$
$908$	11.3299	+	5.28321i	0.375996	+	0.175330i
$909$	11.5669	+	13.7849i	0.383650	+	0.457216i
$910$	−33.7228	−	12.0282i	−1.11790	−	0.398732i
$911$			8.74111i			0.289606i	0.989461	+	0.144803i	$0.0462548\pi$
$911$			8.74111i			0.289606i	−0.989461	+	0.144803i	$0.953745\pi$
$912$	0.535848	+	4.32584i	0.0177437	+	0.143243i
$913$	26.9542	−	26.9542i	0.892055	−	0.892055i
$914$	−2.50701	−	14.2180i	−0.0829246	−	0.470289i
$915$	1.65810	+	9.06128i	0.0548152	+	0.299557i
$916$	8.87492	−	3.23021i	0.293236	−	0.106729i
$917$	−9.63552	−	20.6634i	−0.318193	−	0.682367i
$918$	−6.78461	+	0.593576i	−0.223925	+	0.0195909i
$919$	33.1126	+	19.1176i	1.09228	+	0.630631i	0.934184	−	0.356792i	$-0.116130\pi$
$919$	33.1126	+	19.1176i	1.09228	+	0.630631i	0.158100	+	0.987423i	$0.449463\pi$
$920$	9.27035	−	9.39076i	0.305634	−	0.309604i
$921$	2.93533	−	16.6471i	0.0967225	−	0.548540i
$922$	−10.1381	−	14.4787i	−0.333881	−	0.476832i
$923$	−12.0334	−	3.22435i	−0.396085	−	0.106131i
$924$	5.90857	−	10.2340i	0.194378	−	0.336672i
$925$	−23.2710	+	16.7461i	−0.765144	+	0.550610i
$926$	−5.37776	+	14.7753i	−0.176724	+	0.485545i
$927$	3.18161	−	6.82298i	0.104498	−	0.224096i
$928$	0.571741	−	6.53503i	0.0187683	−	0.214523i
$929$	21.8521	−	3.85311i	0.716944	−	0.126417i	0.196736	−	0.980456i	$-0.436966\pi$
$929$	21.8521	−	3.85311i	0.716944	−	0.126417i	0.520208	+	0.854040i	$0.325855\pi$
$930$	8.45768	−	2.32482i	0.277338	−	0.0762339i
$931$	0.289476	+	8.04264i	0.00948720	+	0.263587i
$932$	−17.2444	−	17.2444i	−0.564859	−	0.564859i
$933$	4.20461	−	6.00481i	0.137653	−	0.196589i
$934$	1.99700	−	1.67568i	0.0653438	−	0.0548299i
$935$	13.2614	−	78.1547i	0.433694	−	2.55593i
$936$	−6.62779	−	2.41232i	−0.216636	−	0.0788491i
$937$	−2.39942	−	27.4254i	−0.0783855	−	0.895950i	−0.928980	−	0.370129i	$-0.879314\pi$
$937$	−2.39942	−	27.4254i	−0.0783855	−	0.895950i	0.850595	−	0.525821i	$-0.176242\pi$
$938$	1.90358	+	7.10426i	0.0621541	+	0.231962i
$939$	−4.48529	−	7.76874i	−0.146372	−	0.253523i
$940$	−2.96123	+	3.57566i	−0.0965847	+	0.116625i
$941$	−31.4276	−	5.54153i	−1.02451	−	0.180649i	−0.363947	−	0.931420i	$-0.618571\pi$
$941$	−31.4276	−	5.54153i	−1.02451	−	0.180649i	−0.660563	+	0.750771i	$0.729682\pi$
$942$	−1.11818	+	4.17311i	−0.0364323	+	0.135967i
$943$	−31.8037	+	8.52178i	−1.03567	+	0.277507i
$944$	1.81027	+	1.51899i	0.0589192	+	0.0494391i
$945$	−0.409788	+	5.05970i	−0.0133304	+	0.164592i
$946$	−8.64093	−	23.7408i	−0.280941	−	0.771879i
$947$	−6.38661	−	0.558756i	−0.207537	−	0.0181571i	−0.0170868	−	0.999854i	$-0.505439\pi$
$947$	−6.38661	−	0.558756i	−0.207537	−	0.0181571i	−0.190450	+	0.981697i	$0.560995\pi$
$948$	−6.46830	−	4.52916i	−0.210081	−	0.147100i
$949$	1.42830			0.0463644
$950$	20.7511	−	6.66274i	0.673254	−	0.216168i
$951$	0.0665042			0.00215655
$952$	12.6650	+	8.86811i	0.410474	+	0.287417i
$953$	−34.6399	−	3.03060i	−1.12210	−	0.0981708i	−0.489030	−	0.872267i	$-0.662649\pi$
$953$	−34.6399	−	3.03060i	−1.12210	−	0.0981708i	−0.633068	+	0.774096i	$0.718205\pi$
$954$	0.281564	+	0.773590i	0.00911597	+	0.0250459i
$955$	2.57591	−	31.8051i	0.0833545	−	1.02919i
$956$	−12.4496	−	10.4465i	−0.402650	−	0.337864i
$957$	32.9838	−	8.83798i	1.06621	−	0.285691i
$958$	−1.06606	+	3.97860i	−0.0344429	+	0.128543i
$959$	−27.4154	−	4.83407i	−0.885289	−	0.156100i
$960$	−1.42623	+	1.72217i	−0.0460315	+	0.0555827i
$961$	−7.80628	−	13.5209i	−0.251816	−	0.436157i
$962$	10.4674	+	39.0648i	0.337482	+	1.25950i
$963$	0.423500	+	4.84063i	0.0136471	+	0.155987i
$964$	−15.0422	−	5.47492i	−0.484477	−	0.176335i
$965$	5.93562	−	34.9809i	0.191074	−	1.12608i
$966$	−10.2627	+	8.61139i	−0.330196	+	0.277067i
$967$	29.9179	−	42.7272i	0.962094	−	1.37401i	0.0349173	−	0.999390i	$-0.488883\pi$
$967$	29.9179	−	42.7272i	0.962094	−	1.37401i	0.927177	−	0.374623i	$-0.122228\pi$
$968$	11.3816	+	11.3816i	0.365820	+	0.365820i
$969$	−11.1502	−	27.5128i	−0.358195	−	0.883839i
$970$	−12.2271	+	3.36095i	−0.392588	+	0.107913i
$971$	−5.80992	+	1.02445i	−0.186449	+	0.0328760i	−0.266093	−	0.963947i	$-0.585733\pi$
$971$	−5.80992	+	1.02445i	−0.186449	+	0.0328760i	0.0796438	+	0.996823i	$0.474622\pi$
$972$	−0.0871557	+	0.996195i	−0.00279552	+	0.0319530i
$973$	−8.41311	+	18.0420i	−0.269712	+	0.578399i
$974$	11.6160	−	31.9147i	0.372201	−	1.02261i
$975$	−5.67516	+	34.8061i	−0.181750	+	1.11469i
$976$	2.05981	−	3.56769i	0.0659328	−	0.114199i
$977$	47.1369	+	12.6303i	1.50804	+	0.404079i	0.915785	−	0.401669i	$-0.131570\pi$
$977$	47.1369	+	12.6303i	1.50804	+	0.404079i	0.592258	+	0.805748i	$0.298237\pi$
$978$	10.5590	+	15.0799i	0.337641	+	0.482201i
$979$	−10.4715	+	59.3867i	−0.334670	+	1.89801i
$980$	−2.90036	+	2.93804i	−0.0926487	+	0.0938521i
$981$	2.83952	+	1.63940i	0.0906588	+	0.0523419i
$982$	−18.9073	+	1.65418i	−0.603357	+	0.0527869i
$983$	16.4915	+	35.3662i	0.525999	+	1.12801i	0.972431	+	0.233191i	$0.0749166\pi$
$983$	16.4915	+	35.3662i	0.525999	+	1.12801i	−0.446432	+	0.894817i	$0.647306\pi$
$984$	5.24292	−	1.90827i	0.167138	−	0.0608334i
$985$	0.0513721	+	0.280741i	0.00163685	+	0.00894516i
$986$	7.75808	+	43.9982i	0.247068	+	1.40119i
$987$	3.33293	−	3.33293i	0.106088	−	0.106088i
$988$	1.57615	−	30.7035i	0.0501439	−	0.976810i
$989$			28.6419i			0.910760i
$990$	−10.9631	−	3.91032i	−0.348431	−	0.124278i
$991$	−16.7348	−	19.9438i	−0.531600	−	0.633536i	0.431683	−	0.902026i	$-0.357920\pi$
$991$	−16.7348	−	19.9438i	−0.531600	−	0.633536i	−0.963283	+	0.268489i	$0.913476\pi$
$992$	−3.55516	−	1.65780i	−0.112876	−	0.0526351i
$993$	24.2087	−	11.2887i	0.768240	−	0.358236i
$994$	2.57745	−	3.07168i	0.0817516	−	0.0974278i
$995$	−6.22364	+	23.8412i	−0.197303	+	0.755817i
$996$	6.34190	−	3.66150i	0.200951	−	0.116019i
$997$	−40.4291	+	28.3087i	−1.28040	+	0.896547i	−0.998029	−	0.0627577i	$-0.980010\pi$
$997$	−40.4291	+	28.3087i	−1.28040	+	0.896547i	−0.282373	+	0.959305i	$0.591122\pi$
$998$	14.9169	−	10.4449i	0.472185	−	0.330627i
$999$	4.96580	−	2.86700i	0.157111	−	0.0907080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.67.4	✓	120
5.3	odd	4	inner	570.2.bh.a.523.3	yes	120
19.2	odd	18	inner	570.2.bh.a.97.3	yes	120
95.78	even	36	inner	570.2.bh.a.553.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.67.4	✓	120	1.1	even	1	trivial
570.2.bh.a.97.3	yes	120	19.2	odd	18	inner
570.2.bh.a.523.3	yes	120	5.3	odd	4	inner
570.2.bh.a.553.4	yes	120	95.78	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.180509 - 2.22877i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.19282 + 0.587565i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(0.180509 - 2.22877i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.19282 + 0.587565i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-1.42623 + 1.72217i) q^{10} +(2.60269 + 4.50800i) q^{11} +(0.258819 + 0.965926i) q^{12} +(-0.614723 - 7.02631i) q^{13} +(2.13327 + 0.776446i) q^{14} +(0.374072 - 2.20456i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(3.90635 - 5.57885i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(2.04226 - 3.85087i) q^{19} +(2.15610 - 0.592661i) q^{20} +(-2.23569 + 0.394212i) q^{21} +(0.453680 - 5.18558i) q^{22} +(-2.49399 + 5.34838i) q^{23} +(0.342020 - 0.939693i) q^{24} +(-4.93483 - 0.804627i) q^{25} +(-3.52658 + 6.10821i) q^{26} +(0.965926 + 0.258819i) q^{27} +(-1.30212 - 1.85962i) q^{28} +(1.13913 - 6.46033i) q^{29} +(-1.57090 + 1.59131i) q^{30} +(-3.39714 - 1.96134i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(2.19989 + 4.71769i) q^{33} +(-6.39980 + 2.32934i) q^{34} +(0.913722 + 4.99336i) q^{35} +(0.173648 + 0.984808i) q^{36} +(4.05456 - 4.05456i) q^{37} +(-3.88169 + 1.98306i) q^{38} -7.05315i q^{39} +(-2.10611 - 0.751207i) q^{40} +(3.58637 + 4.27407i) q^{41} +(2.05748 + 0.959418i) q^{42} +(4.39877 - 2.05118i) q^{43} +(-3.34596 + 3.98756i) q^{44} +(0.564789 - 2.16357i) q^{45} +(5.11066 - 2.95064i) q^{46} +(-1.70077 + 1.19089i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(-1.59894 + 0.923151i) q^{49} +(3.58086 + 3.48962i) q^{50} +(4.37772 - 5.21716i) q^{51} +(6.39233 - 2.98079i) q^{52} +(-0.746107 - 0.347915i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(10.5171 - 4.98707i) q^{55} +2.27018i q^{56} +(2.37011 - 3.65822i) q^{57} +(-4.63862 + 4.63862i) q^{58} +(-0.410354 - 2.32724i) q^{59} +(2.19955 - 0.402490i) q^{60} +(-3.87117 + 1.40899i) q^{61} +(1.65780 + 3.55516i) q^{62} +(-2.26154 + 0.197859i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-15.7710 + 0.101761i) q^{65} +(0.903906 - 5.12631i) q^{66} +(1.85826 + 2.65387i) q^{67} +(6.57846 + 1.76269i) q^{68} +(-2.95064 + 5.11066i) q^{69} +(2.11559 - 4.61441i) q^{70} +(0.604107 - 1.65977i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.0176494 + 0.201734i) q^{73} +(-5.64690 + 0.995700i) q^{74} +(-4.84593 - 1.23166i) q^{75} +(4.31713 + 0.602020i) q^{76} +(-8.35599 - 8.35599i) q^{77} +(-4.04552 + 5.77760i) q^{78} +(-6.04895 + 5.07567i) q^{79} +(1.29435 + 1.82337i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.486277 - 5.55817i) q^{82} +(-1.89533 - 7.07347i) q^{83} +(-1.13509 - 1.96603i) q^{84} +(-11.7288 - 9.71340i) q^{85} +(-4.77977 - 0.842803i) q^{86} +(1.69785 - 6.33647i) q^{87} +(5.02802 - 1.34725i) q^{88} +(8.87439 + 7.44650i) q^{89} +(-1.70362 + 1.44834i) q^{90} +(5.47639 + 15.0463i) q^{91} +(-5.87883 - 0.514331i) q^{92} +(-3.21327 - 2.24996i) q^{93} +2.07626 q^{94} +(-8.21405 - 5.24684i) q^{95} +1.00000 q^{96} +(4.64536 + 3.25272i) q^{97} +(1.83928 + 0.160916i) q^{98} +(1.78035 + 4.89147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q - 12 * q^5 + 12 * q^7	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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