LMFDB - Embedded newform 930.2.br.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(1.43236 - 0.973832i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.06132 - 1.36879i) q^{6} +(0.396236 + 3.76994i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.10330 - 2.78975i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(1.43236 - 0.973832i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.06132 - 1.36879i) q^{6} +(0.396236 + 3.76994i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.10330 - 2.78975i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(3.50186 + 1.55913i) q^{11} +(0.586399 - 1.62977i) q^{12} +(1.20728 + 5.67981i) q^{13} +(1.54182 + 3.46298i) q^{14} +(-0.753543 + 1.55954i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.94491 + 1.31116i) q^{17} +(0.187223 - 2.99415i) q^{18} +(6.45384 + 1.37181i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(4.23884 + 5.01404i) q^{21} +(3.81227 + 0.400685i) q^{22} +(-5.27071 - 3.82939i) q^{23} +(0.0540730 - 1.73121i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.90335 + 5.02875i) q^{26} +(-1.13642 - 5.07036i) q^{27} +(2.53648 + 2.81704i) q^{28} +(-2.71005 - 8.34068i) q^{29} +(-0.234737 + 1.71607i) q^{30} +(0.212774 - 5.56370i) q^{31} -1.00000i q^{32} +(6.53425 - 1.17699i) q^{33} +(-2.39561 + 2.15701i) q^{34} +(-2.22812 - 3.06674i) q^{35} +(-0.747184 - 2.90546i) q^{36} +(-2.61824 - 1.51164i) q^{37} +(6.56188 - 0.689681i) q^{38} +(7.26044 + 6.95984i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(4.97903 + 4.48314i) q^{41} +(5.58080 + 3.45876i) q^{42} +(1.30393 - 6.13450i) q^{43} +(3.74950 - 0.796981i) q^{44} +(0.439388 + 2.96765i) q^{45} +(-6.19609 - 2.01323i) q^{46} +(-10.3627 - 3.36705i) q^{47} +(-0.483546 - 1.66318i) q^{48} +(-7.20840 + 1.53219i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-2.94132 + 4.74589i) q^{51} +(4.31522 + 3.88544i) q^{52} +(-0.652891 + 6.21184i) q^{53} +(-2.64763 - 4.47102i) q^{54} +(-3.81227 + 0.400685i) q^{55} +(3.28285 + 1.89535i) q^{56} +(10.5801 - 4.32004i) q^{57} +(-5.15482 - 7.09500i) q^{58} +(3.01511 - 2.71481i) q^{59} +(0.307047 + 1.70462i) q^{60} +10.0367i q^{61} +(-1.51692 - 5.35714i) q^{62} +(10.9544 + 3.05398i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.88544 - 4.31522i) q^{65} +(5.85074 - 3.13858i) q^{66} +(-2.41388 - 4.18096i) q^{67} +(-1.61180 + 2.79172i) q^{68} +(-11.2787 - 0.352283i) q^{69} +(-3.06674 - 2.22812i) q^{70} +(-0.247791 - 0.0260439i) q^{71} +(-1.60845 - 2.53237i) q^{72} +(2.26238 - 5.08138i) q^{73} +(-2.95722 - 0.628577i) q^{74} +(-0.127184 - 1.72737i) q^{75} +(6.02759 - 2.68366i) q^{76} +(-4.49026 + 13.8196i) q^{77} +(9.05580 + 4.37560i) q^{78} +(0.661137 + 1.48494i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-6.56544 - 6.15589i) q^{81} +(6.12071 + 2.72511i) q^{82} +(-1.71819 + 1.90824i) q^{83} +(6.37647 + 1.56491i) q^{84} +(1.89479 - 2.60795i) q^{85} +(-0.655555 - 6.23719i) q^{86} +(-12.0042 - 9.30771i) q^{87} +(3.31971 - 1.91663i) q^{88} +(0.635760 - 0.461907i) q^{89} +(1.33494 + 2.68662i) q^{90} +(-20.9342 + 6.80192i) q^{91} -6.51496 q^{92} +(-5.11334 - 8.17642i) q^{93} -10.8960 q^{94} +(-6.27509 + 2.03890i) q^{95} +(-0.973832 - 1.43236i) q^{96} +(-1.23929 + 0.900398i) q^{97} +(-6.38212 + 3.68472i) q^{98} +(8.21321 - 8.04914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	1.43236	−	0.973832i	0.826973	−	0.562242i
$3$	1.43236	−	0.973832i	0.826973	−	0.562242i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	1.06132	−	1.36879i	0.433284	−	0.558807i
$7$	0.396236	+	3.76994i	0.149763	+	1.42490i	0.768774	+	0.639520i	$0.220867\pi$
$7$	0.396236	+	3.76994i	0.149763	+	1.42490i	−0.619011	+	0.785382i	$0.712466\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	1.10330	−	2.78975i	0.367768	−	0.929918i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	3.50186	+	1.55913i	1.05585	+	0.470095i	0.859870	−	0.510512i	$-0.170544\pi$
$11$	3.50186	+	1.55913i	1.05585	+	0.470095i	0.195981	+	0.980608i	$0.437211\pi$
$12$	0.586399	−	1.62977i	0.169279	−	0.470473i
$13$	1.20728	+	5.67981i	0.334839	+	1.57530i	0.747405	+	0.664368i	$0.231299\pi$
$13$	1.20728	+	5.67981i	0.334839	+	1.57530i	−0.412566	+	0.910928i	$0.635367\pi$
$14$	1.54182	+	3.46298i	0.412068	+	0.925520i
$15$	−0.753543	+	1.55954i	−0.194564	+	0.402672i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.94491	+	1.31116i	−0.714245	+	0.318003i	−0.731493	−	0.681849i	$-0.761176\pi$
$17$	−2.94491	+	1.31116i	−0.714245	+	0.318003i	0.0172478	+	0.999851i	$0.494510\pi$
$18$	0.187223	−	2.99415i	0.0441289	−	0.705728i
$19$	6.45384	+	1.37181i	1.48061	+	0.314714i	0.876196	−	0.481955i	$-0.160073\pi$
$19$	6.45384	+	1.37181i	1.48061	+	0.314714i	0.604416	+	0.796669i	$0.293406\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	4.23884	+	5.01404i	0.924990	+	1.09415i
$22$	3.81227	+	0.400685i	0.812778	+	0.0854264i
$23$	−5.27071	−	3.82939i	−1.09902	−	0.798484i	−0.118119	−	0.992999i	$-0.537687\pi$
$23$	−5.27071	−	3.82939i	−1.09902	−	0.798484i	−0.980899	+	0.194515i	$0.937687\pi$
$24$	0.0540730	−	1.73121i	0.0110376	−	0.353381i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.90335	+	5.02875i	0.569394	+	0.986219i
$27$	−1.13642	−	5.07036i	−0.218705	−	0.975791i
$28$	2.53648	+	2.81704i	0.479349	+	0.532371i
$29$	−2.71005	−	8.34068i	−0.503244	−	1.54882i	−0.803703	−	0.595030i	$-0.797140\pi$
$29$	−2.71005	−	8.34068i	−0.503244	−	1.54882i	0.300460	−	0.953794i	$-0.402860\pi$
$30$	−0.234737	+	1.71607i	−0.0428569	+	0.313310i
$31$	0.212774	−	5.56370i	0.0382153	−	0.999270i
$31$	0.212774	−	5.56370i	0.0382153	−	0.999270i
$32$		−	1.00000i		−	0.176777i
$33$	6.53425	−	1.17699i	1.13747	−	0.204888i
$34$	−2.39561	+	2.15701i	−0.410843	+	0.369925i
$35$	−2.22812	−	3.06674i	−0.376621	−	0.518374i
$36$	−0.747184	−	2.90546i	−0.124531	−	0.484244i
$37$	−2.61824	−	1.51164i	−0.430437	−	0.248513i	0.269096	−	0.963113i	$-0.413275\pi$
$37$	−2.61824	−	1.51164i	−0.430437	−	0.248513i	−0.699533	+	0.714601i	$0.746608\pi$
$38$	6.56188	−	0.689681i	1.06448	−	0.111881i
$39$	7.26044	+	6.95984i	1.16260	+	1.11447i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	4.97903	+	4.48314i	0.777594	+	0.700149i	0.959046	−	0.283251i	$-0.0914129\pi$
$41$	4.97903	+	4.48314i	0.777594	+	0.700149i	−0.181452	+	0.983400i	$0.558080\pi$
$42$	5.58080	+	3.45876i	0.861136	+	0.533698i
$43$	1.30393	−	6.13450i	0.198847	−	0.935503i	−0.759635	−	0.650350i	$-0.774622\pi$
$43$	1.30393	−	6.13450i	0.198847	−	0.935503i	0.958482	−	0.285153i	$-0.0920443\pi$
$44$	3.74950	−	0.796981i	0.565258	−	0.120149i
$45$	0.439388	+	2.96765i	0.0655000	+	0.442391i
$46$	−6.19609	−	2.01323i	−0.913564	−	0.296835i
$47$	−10.3627	−	3.36705i	−1.51156	−	0.491135i	−0.568194	−	0.822895i	$-0.692358\pi$
$47$	−10.3627	−	3.36705i	−1.51156	−	0.491135i	−0.943364	+	0.331760i	$0.892358\pi$
$48$	−0.483546	−	1.66318i	−0.0697938	−	0.240060i
$49$	−7.20840	+	1.53219i	−1.02977	+	0.218885i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	−2.94132	+	4.74589i	−0.411867	+	0.664558i
$52$	4.31522	+	3.88544i	0.598413	+	0.538814i
$53$	−0.652891	+	6.21184i	−0.0896815	+	0.853262i	0.853524	+	0.521053i	$0.174461\pi$
$53$	−0.652891	+	6.21184i	−0.0896815	+	0.853262i	−0.943206	+	0.332209i	$0.892206\pi$
$54$	−2.64763	−	4.47102i	−0.360297	−	0.608429i
$55$	−3.81227	+	0.400685i	−0.514046	+	0.0540284i
$56$	3.28285	+	1.89535i	0.438689	+	0.253277i
$57$	10.5801	−	4.32004i	1.40137	−	0.572203i
$58$	−5.15482	−	7.09500i	−0.676861	−	0.931619i
$59$	3.01511	−	2.71481i	0.392534	−	0.353439i	−0.449106	−	0.893478i	$-0.648257\pi$
$59$	3.01511	−	2.71481i	0.392534	−	0.353439i	0.841640	+	0.540040i	$0.181591\pi$
$60$	0.307047	+	1.70462i	0.0396396	+	0.220065i
$61$			10.0367i			1.28507i	0.766258	+	0.642533i	$0.222117\pi$
$61$			10.0367i			1.28507i	−0.766258	+	0.642533i	$0.777883\pi$
$62$	−1.51692	−	5.35714i	−0.192649	−	0.680358i
$63$	10.9544	+	3.05398i	1.38012	+	0.384766i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−3.88544	−	4.31522i	−0.481930	−	0.535237i
$66$	5.85074	−	3.13858i	0.720176	−	0.386333i
$67$	−2.41388	−	4.18096i	−0.294902	−	0.510785i	0.680060	−	0.733156i	$-0.261954\pi$
$67$	−2.41388	−	4.18096i	−0.294902	−	0.510785i	−0.974962	+	0.222371i	$0.928620\pi$
$68$	−1.61180	+	2.79172i	−0.195460	+	0.338546i
$69$	−11.2787	−	0.352283i	−1.35780	−	0.0424099i
$70$	−3.06674	−	2.22812i	−0.366546	−	0.266311i
$71$	−0.247791	−	0.0260439i	−0.0294074	−	0.00309084i	0.0898134	−	0.995959i	$-0.471373\pi$
$71$	−0.247791	−	0.0260439i	−0.0294074	−	0.00309084i	−0.119221	+	0.992868i	$0.538040\pi$
$72$	−1.60845	−	2.53237i	−0.189558	−	0.298442i
$73$	2.26238	−	5.08138i	0.264791	−	0.594731i	−0.731398	−	0.681951i	$-0.761132\pi$
$73$	2.26238	−	5.08138i	0.264791	−	0.594731i	0.996189	+	0.0872203i	$0.0277984\pi$
$74$	−2.95722	−	0.628577i	−0.343770	−	0.0730706i
$75$	−0.127184	−	1.72737i	−0.0146859	−	0.199460i
$76$	6.02759	−	2.68366i	0.691412	−	0.307837i
$77$	−4.49026	+	13.8196i	−0.511712	+	1.57489i
$78$	9.05580	+	4.37560i	1.02537	+	0.495439i
$79$	0.661137	+	1.48494i	0.0743837	+	0.167069i	0.946910	−	0.321498i	$-0.104186\pi$
$79$	0.661137	+	1.48494i	0.0743837	+	0.167069i	−0.872526	+	0.488567i	$0.837520\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	−6.56544	−	6.15589i	−0.729494	−	0.683988i
$82$	6.12071	+	2.72511i	0.675919	+	0.300939i
$83$	−1.71819	+	1.90824i	−0.188595	+	0.209456i	−0.830026	−	0.557725i	$-0.811675\pi$
$83$	−1.71819	+	1.90824i	−0.188595	+	0.209456i	0.641431	+	0.767181i	$0.278341\pi$
$84$	6.37647	+	1.56491i	0.695730	+	0.170746i
$85$	1.89479	−	2.60795i	0.205519	−	0.282872i
$86$	−0.655555	−	6.23719i	−0.0706904	−	0.672574i
$87$	−12.0042	−	9.30771i	−1.28698	−	0.997891i
$88$	3.31971	−	1.91663i	0.353882	−	0.204314i
$89$	0.635760	−	0.461907i	0.0673904	−	0.0489620i	−0.553580	−	0.832796i	$-0.686739\pi$
$89$	0.635760	−	0.461907i	0.0673904	−	0.0489620i	0.620970	+	0.783834i	$0.286739\pi$
$90$	1.33494	+	2.68662i	0.140715	+	0.283195i
$91$	−20.9342	+	6.80192i	−2.19450	+	0.713035i
$92$	−6.51496			−0.679231
$93$	−5.11334	−	8.17642i	−0.530228	−	0.847855i
$94$	−10.8960			−1.12384
$95$	−6.27509	+	2.03890i	−0.643811	+	0.209187i
$96$	−0.973832	−	1.43236i	−0.0993913	−	0.146190i
$97$	−1.23929	+	0.900398i	−0.125831	+	0.0914216i	−0.648921	−	0.760856i	$-0.724779\pi$
$97$	−1.23929	+	0.900398i	−0.125831	+	0.0914216i	0.523090	+	0.852278i	$0.324779\pi$
$98$	−6.38212	+	3.68472i	−0.644691	+	0.372213i
$99$	8.21321	−	8.04914i	0.825458	−	0.808969i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	3.47758	−	4.78648i	0.346032	−	0.476272i	−0.600159	−	0.799881i	$-0.704896\pi$
$101$	3.47758	−	4.78648i	0.346032	−	0.476272i	0.946191	+	0.323608i	$0.104896\pi$
$102$	−1.33080	+	5.42253i	−0.131769	+	0.536911i
$103$	−3.85034	+	4.27623i	−0.379385	+	0.421350i	−0.902350	−	0.431005i	$-0.858159\pi$
$103$	−3.85034	+	4.27623i	−0.379385	+	0.421350i	0.522965	+	0.852354i	$0.324826\pi$
$104$	5.30468	+	2.36180i	0.520167	+	0.231593i
$105$	−6.17796	−	2.22286i	−0.602907	−	0.216929i
$106$	1.29863	+	6.10957i	0.126134	+	0.593414i
$107$	6.14722	+	13.8069i	0.594274	+	1.33476i	0.920970	+	0.389633i	$0.127398\pi$
$107$	6.14722	+	13.8069i	0.594274	+	1.33476i	−0.326696	+	0.945130i	$0.605935\pi$
$108$	−3.89967	−	3.43403i	−0.375246	−	0.330440i
$109$	1.32448	−	4.07633i	0.126862	−	0.390441i	−0.867374	−	0.497657i	$-0.834194\pi$
$109$	1.32448	−	4.07633i	0.126862	−	0.390441i	0.994236	+	0.107216i	$0.0341937\pi$
$110$	−3.50186	+	1.55913i	−0.333890	+	0.148657i
$111$	−5.22235	+	0.384513i	−0.495684	+	0.0364963i
$112$	3.70787	+	0.788132i	0.350361	+	0.0744714i
$113$	6.73568	−	15.1286i	0.633640	−	1.42318i	−0.256073	−	0.966657i	$-0.582429\pi$
$113$	6.73568	−	15.1286i	0.633640	−	1.42318i	0.889713	−	0.456520i	$-0.150904\pi$
$114$	8.72733	−	7.37804i	0.817389	−	0.691016i
$115$	6.47927	+	0.680998i	0.604195	+	0.0635034i
$116$	−7.09500	−	5.15482i	−0.658754	−	0.478613i
$117$	17.1773	+	2.89854i	1.58804	+	0.267970i
$118$	2.02861	−	3.51366i	0.186749	−	0.323459i
$119$	−6.10986	−	10.5826i	−0.560090	−	0.970105i
$120$	0.818775	+	1.52631i	0.0747436	+	0.139332i
$121$	2.47172	+	2.74513i	0.224702	+	0.249557i
$122$	3.10151	+	9.54546i	0.280797	+	0.864205i
$123$	11.4976	+	1.57273i	1.03670	+	0.141808i
$124$	−3.09812	−	4.62619i	−0.278220	−	0.415444i
$125$			1.00000i			0.0894427i
$126$	11.3620	−	0.480573i	1.01220	−	0.0428129i
$127$	−3.09928	+	2.79061i	−0.275017	+	0.247626i	−0.795084	−	0.606499i	$-0.792573\pi$
$127$	−3.09928	+	2.79061i	−0.275017	+	0.247626i	0.520068	+	0.854125i	$0.325907\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−4.10628	−	10.0566i	−0.361538	−	0.885435i
$130$	−5.02875	−	2.90335i	−0.441051	−	0.254641i
$131$	−9.25144	+	0.972365i	−0.808302	+	0.0849559i	−0.499659	−	0.866222i	$-0.666541\pi$
$131$	−9.25144	+	0.972365i	−0.808302	+	0.0849559i	−0.308643	+	0.951178i	$0.599875\pi$
$132$	4.59450	−	4.79295i	0.399900	−	0.417172i
$133$	−2.61438	+	24.8741i	−0.226695	+	2.15686i
$134$	−3.58772	−	3.23040i	−0.309932	−	0.279064i
$135$	3.51935	+	3.82285i	0.302898	+	0.329018i
$136$	−0.670225	+	3.15316i	−0.0574713	+	0.270381i
$137$	−12.0272	+	2.55646i	−1.02755	+	0.218413i	−0.690698	−	0.723143i	$-0.742697\pi$
$137$	−12.0272	+	2.55646i	−1.02755	+	0.218413i	−0.336855	+	0.941557i	$0.609363\pi$
$138$	−10.8356	+	3.15028i	−0.922385	+	0.268170i
$139$	20.5506	+	6.67730i	1.74308	+	0.566361i	0.995235	−	0.0975099i	$-0.0310878\pi$
$139$	20.5506	+	6.67730i	1.74308	+	0.566361i	0.747847	+	0.663871i	$0.231088\pi$
$140$	−3.60517	−	1.17139i	−0.304693	−	0.0990007i
$141$	−18.1221	+	5.26872i	−1.52615	+	0.443706i
$142$	−0.243711	+	0.0518024i	−0.0204518	+	0.00434716i
$143$	−4.62783	+	21.7722i	−0.386999	+	1.82069i
$144$	−2.31227	−	1.91139i	−0.192689	−	0.159282i
$145$	6.51731	+	5.86821i	0.541233	+	0.487328i
$146$	0.581415	−	5.53179i	0.0481182	−	0.457815i
$147$	−8.83291	+	9.21441i	−0.728526	+	0.759992i
$148$	−3.00673	+	0.316020i	−0.247151	+	0.0259766i
$149$	6.33942	+	3.66006i	0.519345	+	0.299844i	0.736667	−	0.676256i	$-0.236399\pi$
$149$	6.33942	+	3.66006i	0.519345	+	0.299844i	−0.217321	+	0.976100i	$0.569732\pi$
$150$	−0.654747	−	1.60353i	−0.0534599	−	0.130928i
$151$	−8.39415	−	11.5536i	−0.683106	−	0.940215i	0.316860	−	0.948472i	$-0.397372\pi$
$151$	−8.39415	−	11.5536i	−0.683106	−	0.940215i	−0.999966	+	0.00825726i	$0.997372\pi$
$152$	4.90329	−	4.41494i	0.397709	−	0.358099i
$153$	0.408678	+	9.66217i	0.0330397	+	0.781141i
$154$			14.5308i			1.17092i
$155$	2.59758	+	4.92469i	0.208643	+	0.395561i
$156$	9.96471	+	1.36305i	0.797815	+	0.109131i
$157$	1.16710	+	3.59195i	0.0931444	+	0.286669i	0.986766	−	0.162153i	$-0.0518438\pi$
$157$	1.16710	+	3.59195i	0.0931444	+	0.286669i	−0.893621	+	0.448822i	$0.851844\pi$
$158$	1.08765	+	1.20796i	0.0865287	+	0.0960999i
$159$	5.11412	+	9.53340i	0.405576	+	0.756047i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	12.3481	−	21.3876i	0.973169	−	1.68558i
$162$	−8.14638	−	3.82576i	−0.640040	−	0.300580i
$163$	8.48299	+	6.16325i	0.664439	+	0.482743i	0.868159	−	0.496286i	$-0.165303\pi$
$163$	8.48299	+	6.16325i	0.664439	+	0.482743i	−0.203720	+	0.979029i	$0.565303\pi$
$164$	6.66325	+	0.700335i	0.520312	+	0.0546870i
$165$	−5.07033	+	4.28643i	−0.394725	+	0.333698i
$166$	−1.04441	+	2.34579i	−0.0810622	+	0.182069i
$167$	10.3523	+	2.20044i	0.801083	+	0.170275i	0.590222	−	0.807241i	$-0.299040\pi$
$167$	10.3523	+	2.20044i	0.801083	+	0.170275i	0.210861	+	0.977516i	$0.432373\pi$
$168$	6.54797	−	0.482115i	0.505187	−	0.0371960i
$169$	−18.9266	+	8.42668i	−1.45589	+	0.648206i
$170$	0.996149	−	3.06583i	0.0764011	−	0.235138i
$171$	10.9475	−	16.4911i	0.837180	−	1.26111i
$172$	−2.55087	−	5.72935i	−0.194502	−	0.436858i
$173$	−4.58062	−	21.5501i	−0.348258	−	1.63843i	−0.708604	−	0.705607i	$-0.750675\pi$
$173$	−4.58062	−	21.5501i	−0.348258	−	1.63843i	0.360346	−	0.932819i	$-0.382659\pi$
$174$	−14.2929	−	5.14266i	−1.08354	−	0.389864i
$175$	3.46298	+	1.54182i	0.261777	+	0.116550i
$176$	2.56496	−	2.84867i	0.193341	−	0.214727i
$177$	1.67494	−	6.82480i	0.125896	−	0.512983i
$178$	0.461907	−	0.635760i	0.0346214	−	0.0476522i
$179$	1.91175	+	18.1891i	0.142891	+	1.35952i	0.797395	+	0.603458i	$0.206211\pi$
$179$	1.91175	+	18.1891i	0.142891	+	1.35952i	−0.654504	+	0.756059i	$0.727122\pi$
$180$	2.09981	+	2.14261i	0.156511	+	0.159701i
$181$	−18.0716	+	10.4337i	−1.34325	+	0.775527i	−0.987283	−	0.158970i	$-0.949183\pi$
$181$	−18.0716	+	10.4337i	−1.34325	+	0.775527i	−0.355969	+	0.934498i	$0.615849\pi$
$182$	−17.8077	+	12.9380i	−1.31999	+	0.959030i
$183$	9.77405	+	14.3761i	0.722518	+	1.06272i
$184$	−6.19609	+	2.01323i	−0.456782	+	0.148417i
$185$	3.02329			0.222277
$186$	−7.38972	−	6.19613i	−0.541841	−	0.454322i
$187$	−12.3569			−0.903629
$188$	−10.3627	+	3.36705i	−0.755779	+	0.245567i
$189$	18.6646	−	6.29331i	1.35765	−	0.457771i
$190$	−5.33791	+	3.87822i	−0.387253	+	0.281356i
$191$	2.58975	−	1.49519i	0.187388	−	0.108188i	−0.403371	−	0.915036i	$-0.632162\pi$
$191$	2.58975	−	1.49519i	0.187388	−	0.108188i	0.590759	+	0.806848i	$0.298828\pi$
$192$	−1.36879	−	1.06132i	−0.0987841	−	0.0765944i
$193$	−2.81006	−	26.7360i	−0.202273	−	1.92450i	−0.352438	−	0.935835i	$-0.614647\pi$
$193$	−2.81006	−	26.7360i	−0.202273	−	1.92450i	0.150165	−	0.988661i	$-0.452019\pi$
$194$	−0.900398	+	1.23929i	−0.0646448	+	0.0889760i
$195$	−9.76764	−	2.39718i	−0.699475	−	0.171665i
$196$	−4.93111	+	5.47656i	−0.352222	+	0.391183i
$197$	−12.3527	−	5.49978i	−0.880094	−	0.391843i	−0.0836068	−	0.996499i	$-0.526644\pi$
$197$	−12.3527	−	5.49978i	−0.880094	−	0.391843i	−0.796487	+	0.604656i	$0.793311\pi$
$198$	5.32390	−	10.1932i	0.378353	−	0.724400i
$199$	−5.46565	−	25.7139i	−0.387450	−	1.82281i	−0.548853	−	0.835919i	$-0.684935\pi$
$199$	−5.46565	−	25.7139i	−0.387450	−	1.82281i	0.161403	−	0.986889i	$-0.448398\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	−7.52908	−	3.63792i	−0.531061	−	0.256599i
$202$	1.82827	−	5.62684i	0.128637	−	0.395903i
$203$	30.3700	−	13.5216i	2.13156	−	0.949030i
$204$	0.409990	+	5.56837i	0.0287050	+	0.389864i
$205$	−6.55354	−	1.39300i	−0.457719	−	0.0972912i
$206$	−2.34046	+	5.25676i	−0.163068	+	0.366256i
$207$	−16.4983	+	10.4790i	−1.14671	+	0.728340i
$208$	5.77489	+	0.606965i	0.400417	+	0.0420855i
$209$	20.4616	+	14.8663i	1.41536	+	1.02832i
$210$	−6.56249	−	0.204975i	−0.452855	−	0.0141446i
$211$	−0.171275	+	0.296656i	−0.0117910	+	0.0204227i	−0.871861	−	0.489754i	$-0.837087\pi$
$211$	−0.171275	+	0.296656i	−0.0117910	+	0.0204227i	0.860070	+	0.510177i	$0.170420\pi$
$212$	3.12303	+	5.40925i	0.214491	+	0.371509i
$213$	−0.380288	+	0.204002i	−0.0260569	+	0.0139780i
$214$	10.1129	+	11.2315i	0.691305	+	0.767772i
$215$	1.93802	+	5.96460i	0.132172	+	0.406782i
$216$	−4.76998	−	2.06090i	−0.324556	−	0.140226i
$217$	21.0591	−	1.40240i	1.42959	−	0.0952009i
$218$		−	4.28610i		−	0.290292i
$219$	−1.70788	−	9.48154i	−0.115408	−	0.640703i
$220$	−2.84867	+	2.56496i	−0.192057	+	0.172929i
$221$	−11.0025	−	15.1436i	−0.740106	−	1.01867i
$222$	−4.84793	+	1.97949i	−0.325372	+	0.132855i
$223$	−11.8694	−	6.85282i	−0.794836	−	0.458899i	0.0468261	−	0.998903i	$-0.485089\pi$
$223$	−11.8694	−	6.85282i	−0.794836	−	0.458899i	−0.841662	+	0.540004i	$0.818423\pi$
$224$	3.76994	−	0.396236i	0.251890	−	0.0264747i
$225$	−1.86435	−	2.35037i	−0.124290	−	0.156691i
$226$	1.73102	−	16.4696i	0.115146	−	1.09554i
$227$	1.73701	+	1.56401i	0.115290	+	0.103807i	0.724759	−	0.689002i	$-0.241951\pi$
$227$	1.73701	+	1.56401i	0.115290	+	0.103807i	−0.609470	+	0.792809i	$0.708618\pi$
$228$	6.02025	−	9.71382i	0.398701	−	0.643314i
$229$	1.57266	−	7.39880i	0.103925	−	0.488926i	−0.895144	−	0.445777i	$-0.852927\pi$
$229$	1.57266	−	7.39880i	0.103925	−	0.488926i	0.999069	−	0.0431496i	$-0.0137392\pi$
$230$	6.37259	−	1.35454i	0.420196	−	0.0893154i
$231$	7.02630	+	24.1674i	0.462296	+	1.59010i
$232$	−8.34068	−	2.71005i	−0.547592	−	0.177923i
$233$	−1.61858	−	0.525910i	−0.106037	−	0.0344535i	0.255518	−	0.966804i	$-0.417754\pi$
$233$	−1.61858	−	0.525910i	−0.106037	−	0.0344535i	−0.361555	+	0.932351i	$0.617754\pi$
$234$	17.2322	−	2.55139i	1.12651	−	0.166790i
$235$	10.6579	−	2.26541i	0.695245	−	0.147779i
$236$	0.843545	−	3.96857i	0.0549101	−	0.258332i
$237$	2.39306	+	1.48313i	0.155446	+	0.0963395i
$238$	−9.08103	−	8.17660i	−0.588636	−	0.530010i
$239$	−0.228995	+	2.17874i	−0.0148125	+	0.140931i	−0.999429	−	0.0338002i	$-0.989239\pi$
$239$	−0.228995	+	2.17874i	−0.0148125	+	0.140931i	0.984616	+	0.174731i	$0.0559057\pi$
$240$	1.25036	+	1.19859i	0.0807101	+	0.0773685i
$241$	−8.34967	+	0.877586i	−0.537850	+	0.0565303i	−0.369559	−	0.929207i	$-0.620491\pi$
$241$	−8.34967	+	0.877586i	−0.537850	+	0.0565303i	−0.168290	+	0.985737i	$0.553825\pi$
$242$	3.19904	+	1.84697i	0.205642	+	0.118727i
$243$	−15.3989	−	2.42381i	−0.987838	−	0.155487i
$244$	5.89942	+	8.11985i	0.377672	+	0.519820i
$245$	5.47656	−	4.93111i	0.349884	−	0.315037i
$246$	11.4209	−	2.05720i	0.728167	−	0.131162i
$247$			38.3127i			2.43778i
$248$	−4.37606	−	3.44240i	−0.277880	−	0.218592i
$249$	−0.602755	+	4.40651i	−0.0381981	+	0.279251i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	5.57558	+	6.19231i	0.351928	+	0.390855i	0.892952	−	0.450152i	$-0.148630\pi$
$251$	5.57558	+	6.19231i	0.351928	+	0.390855i	−0.541025	+	0.841007i	$0.681963\pi$
$252$	10.6574	−	3.96809i	0.671350	−	0.249966i
$253$	−12.4868	−	21.6277i	−0.785037	−	1.35972i
$254$	−2.08525	+	3.61175i	−0.130840	+	0.226622i
$255$	0.174310	−	5.58073i	0.0109157	−	0.349479i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	10.7218	+	1.12691i	0.668807	+	0.0702944i	0.432846	−	0.901468i	$-0.357510\pi$
$257$	10.7218	+	1.12691i	0.668807	+	0.0702944i	0.235961	+	0.971762i	$0.424176\pi$
$258$	−7.01297	−	8.29550i	−0.436608	−	0.516455i
$259$	4.66136	−	10.4696i	0.289643	−	0.650548i
$260$	−5.67981	−	1.20728i	−0.352247	−	0.0748724i
$261$	−26.2584	−	1.64193i	−1.62536	−	0.101633i
$262$	−8.49816	+	3.78363i	−0.525018	+	0.233753i
$263$	1.39511	−	4.29372i	0.0860264	−	0.264762i	−0.898785	−	0.438390i	$-0.855549\pi$
$263$	1.39511	−	4.29372i	0.0860264	−	0.264762i	0.984811	+	0.173628i	$0.0555489\pi$
$264$	2.88853	−	5.97814i	0.177777	−	0.367929i
$265$	−2.54050	−	5.70606i	−0.156062	−	0.350521i
$266$	5.20011	+	24.4646i	0.318839	+	1.50002i
$267$	0.460817	−	1.28074i	0.0282015	−	0.0783800i
$268$	−4.41037	−	1.96362i	−0.269406	−	0.119947i
$269$	13.4283	−	14.9136i	0.818735	−	0.909298i	−0.178475	−	0.983944i	$-0.557116\pi$
$269$	13.4283	−	14.9136i	0.818735	−	0.909298i	0.997210	+	0.0746468i	$0.0237829\pi$
$270$	4.52843	+	2.54821i	0.275591	+	0.155079i
$271$	−17.2832	+	23.7883i	−1.04988	+	1.44504i	−0.160971	+	0.986959i	$0.551463\pi$
$271$	−17.2832	+	23.7883i	−1.04988	+	1.44504i	−0.888911	+	0.458080i	$0.848537\pi$
$272$	0.336958	+	3.20595i	0.0204311	+	0.194389i
$273$	−23.3613	+	30.1291i	−1.41389	+	1.82350i
$274$	−10.6486	+	6.14795i	−0.643303	+	0.371411i
$275$	3.10118	−	2.25314i	0.187008	−	0.135869i
$276$	−9.33175	+	6.34447i	−0.561706	+	0.381892i
$277$	−26.5910	+	8.63994i	−1.59770	+	0.519123i	−0.966537	−	0.256528i	$-0.917421\pi$
$277$	−26.5910	+	8.63994i	−1.59770	+	0.519123i	−0.631161	+	0.775652i	$0.717421\pi$
$278$	21.6082			1.29597
$279$	−15.2866	−	6.73203i	−0.915184	−	0.403036i
$280$	−3.79070			−0.226538
$281$	4.05756	−	1.31838i	0.242053	−	0.0786479i	−0.185478	−	0.982648i	$-0.559383\pi$
$281$	4.05756	−	1.31838i	0.242053	−	0.0786479i	0.427531	+	0.904000i	$0.359383\pi$
$282$	−15.6070	+	10.6109i	−0.929382	+	0.631868i
$283$	−0.885260	+	0.643179i	−0.0526233	+	0.0382330i	−0.613786	−	0.789472i	$-0.710354\pi$
$283$	−0.885260	+	0.643179i	−0.0526233	+	0.0382330i	0.561163	+	0.827706i	$0.310354\pi$
$284$	−0.215775	+	0.124578i	−0.0128039	+	0.00739233i
$285$	−7.00264	+	9.03132i	−0.414800	+	0.534969i
$286$	2.32666	+	22.1367i	0.137578	+	1.30897i
$287$	−14.9283	+	20.5470i	−0.881189	+	1.21285i
$288$	−2.78975	−	1.10330i	−0.164388	−	0.0650128i
$289$	−4.42187	+	4.91098i	−0.260110	+	0.288881i
$290$	8.01171	+	3.56704i	0.470464	+	0.209464i
$291$	−0.898274	+	2.49656i	−0.0526578	+	0.146351i
$292$	−1.15646	−	5.44072i	−0.0676767	−	0.318394i
$293$	0.363693	+	0.816869i	0.0212472	+	0.0477220i	0.923857	−	0.382737i	$-0.125018\pi$
$293$	0.363693	+	0.816869i	0.0212472	+	0.0477220i	−0.902610	+	0.430459i	$0.858352\pi$
$294$	−5.55319	+	11.4929i	−0.323869	+	0.670282i
$295$	−1.25375	+	3.85865i	−0.0729963	+	0.224659i
$296$	−2.76191	+	1.22968i	−0.160533	+	0.0714738i
$297$	3.92575	−	19.5275i	0.227795	−	1.13310i
$298$	7.16017	+	1.52194i	0.414777	+	0.0881636i
$299$	15.3870	−	34.5598i	0.889854	−	1.99864i
$300$	−1.11822	−	1.32272i	−0.0645604	−	0.0763672i
$301$	23.6434	+	2.48502i	1.36278	+	0.143234i
$302$	−11.5536	−	8.39415i	−0.664833	−	0.483029i
$303$	0.319918	−	10.2425i	0.0183788	−	0.588418i
$304$	3.29901	−	5.71406i	0.189211	−	0.327724i
$305$	−5.01835	−	8.69203i	−0.287350	−	0.497704i
$306$	3.37445	+	9.06299i	0.192905	+	0.518096i
$307$	2.26045	+	2.51048i	0.129011	+	0.143281i	0.804189	−	0.594374i	$-0.202600\pi$
$307$	2.26045	+	2.51048i	0.129011	+	0.143281i	−0.675178	+	0.737655i	$0.735933\pi$
$308$	4.49026	+	13.8196i	0.255856	+	0.787444i
$309$	−1.35073	+	9.87468i	−0.0768405	+	0.561751i
$310$	3.99226	+	3.88096i	0.226745	+	0.220424i
$311$			2.52760i			0.143327i	0.997429	+	0.0716635i	$0.0228308\pi$
$311$			2.52760i			0.143327i	−0.997429	+	0.0716635i	$0.977169\pi$
$312$	9.89821	−	1.78293i	0.560376	−	0.100938i
$313$	−3.06658	+	2.76116i	−0.173333	+	0.156070i	−0.751231	−	0.660039i	$-0.770540\pi$
$313$	−3.06658	+	2.76116i	−0.173333	+	0.156070i	0.577898	+	0.816109i	$0.303873\pi$
$314$	2.21995	+	3.05550i	0.125279	+	0.172432i
$315$	−11.0138	+	2.83235i	−0.620555	+	0.159585i
$316$	1.40770	+	0.812733i	0.0791891	+	0.0457198i
$317$	−19.1881	+	2.01675i	−1.07771	+	0.113272i	−0.626711	−	0.779252i	$-0.715599\pi$
$317$	−19.1881	+	2.01675i	−1.07771	+	0.113272i	−0.451000	+	0.892524i	$0.648933\pi$
$318$	7.80980	+	7.48645i	0.437952	+	0.419819i
$319$	3.51397	−	33.4332i	0.196745	−	1.87190i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	22.2506	+	13.7901i	1.24191	+	0.769686i
$322$	5.13464	−	24.1566i	0.286142	−	1.34619i
$323$	−20.8046	+	4.42216i	−1.15760	+	0.246056i
$324$	−8.92990	−	1.12115i	−0.496105	−	0.0622860i
$325$	5.52250	+	1.79437i	0.306333	+	0.0995337i
$326$	9.97235	+	3.24021i	0.552317	+	0.179459i
$327$	−2.07253	−	7.12858i	−0.114611	−	0.394212i
$328$	6.55354	−	1.39300i	0.361859	−	0.0769154i
$329$	8.58748	−	40.4009i	0.473443	−	2.22738i
$330$	−3.49759	+	5.64346i	−0.192536	+	0.310662i
$331$	−11.6819	−	10.5184i	−0.642096	−	0.578146i	0.282419	−	0.959291i	$-0.408863\pi$
$331$	−11.6819	−	10.5184i	−0.642096	−	0.578146i	−0.924515	+	0.381145i	$0.875530\pi$
$332$	−0.268407	+	2.55372i	−0.0147307	+	0.140154i
$333$	−7.10583	+	5.63645i	−0.389397	+	0.308876i
$334$	10.5256	−	1.10628i	0.575934	−	0.0605331i
$335$	4.18096	+	2.41388i	0.228430	+	0.131884i
$336$	6.07850	−	2.48195i	0.331610	−	0.135402i
$337$	4.33257	+	5.96328i	0.236010	+	0.324840i	0.910551	−	0.413398i	$-0.135658\pi$
$337$	4.33257	+	5.96328i	0.236010	+	0.324840i	−0.674540	+	0.738238i	$0.735658\pi$
$338$	−15.3963	+	13.8629i	−0.837449	+	0.754042i
$339$	−5.08479	−	28.2290i	−0.276168	−	1.53319i
$340$		−	3.22360i		−	0.174825i
$341$	9.41963	−	19.1516i	0.510102	−	1.03712i
$342$	5.31570	−	19.0669i	0.287440	−	1.03102i
$343$	−0.432754	−	1.33188i	−0.0233665	−	0.0719147i
$344$	−4.19649	−	4.66067i	−0.226259	−	0.251286i
$345$	9.94381	−	5.33428i	0.535357	−	0.287188i
$346$	−11.0158	−	19.0799i	−0.592212	−	1.02574i
$347$	−16.4142	+	28.4303i	−0.881161	+	1.52622i	−0.0311104	+	0.999516i	$0.509904\pi$
$347$	−16.4142	+	28.4303i	−0.881161	+	1.52622i	−0.850051	+	0.526700i	$0.823429\pi$
$348$	−15.1825	−	0.474215i	−0.813868	−	0.0254206i
$349$	7.83553	+	5.69285i	0.419426	+	0.304731i	0.777407	−	0.628998i	$-0.216535\pi$
$349$	7.83553	+	5.69285i	0.419426	+	0.304731i	−0.357981	+	0.933729i	$0.616535\pi$
$350$	3.76994	+	0.396236i	0.201512	+	0.0211797i
$351$	27.4267	−	12.5760i	1.46393	−	0.671258i
$352$	1.55913	−	3.50186i	0.0831019	−	0.186650i
$353$	12.9693	+	2.75671i	0.690285	+	0.146725i	0.539681	−	0.841869i	$-0.318545\pi$
$353$	12.9693	+	2.75671i	0.690285	+	0.146725i	0.150604	+	0.988594i	$0.451878\pi$
$354$	−0.516013	−	7.00835i	−0.0274258	−	0.372490i
$355$	0.227615	−	0.101341i	0.0120806	−	0.00537861i
$356$	0.242839	−	0.747380i	0.0128704	−	0.0396111i
$357$	−19.0572	−	9.20810i	−1.00861	−	0.487344i
$358$	7.43892	+	16.7081i	0.393159	+	0.883050i
$359$	6.31822	+	29.7249i	0.333463	+	1.56882i	0.751090	+	0.660200i	$0.229529\pi$
$359$	6.31822	+	29.7249i	0.333463	+	1.56882i	−0.417627	+	0.908619i	$0.637138\pi$
$360$	2.65914	+	1.38887i	0.140149	+	0.0731998i
$361$	22.4128	+	9.97884i	1.17962	+	0.525202i
$362$	−13.9630	+	15.5074i	−0.733877	+	0.815053i
$363$	6.21368	+	1.52496i	0.326134	+	0.0800398i
$364$	−12.9380	+	17.8077i	−0.678137	+	0.933375i
$365$	0.581415	+	5.53179i	0.0304326	+	0.289547i
$366$	13.7381	+	10.6522i	0.718104	+	0.556798i
$367$	−5.02321	+	2.90015i	−0.262210	+	0.151387i	−0.625342	−	0.780351i	$-0.715041\pi$
$367$	−5.02321	+	2.90015i	−0.262210	+	0.151387i	0.363133	+	0.931737i	$0.381707\pi$
$368$	−5.27071	+	3.82939i	−0.274755	+	0.199621i
$369$	18.0002	−	8.94400i	0.937055	−	0.465606i
$370$	2.87532	−	0.934247i	0.149481	−	0.0485692i
$371$	−23.6770			−1.22925
$372$	−8.94275	−	3.60932i	−0.463660	−	0.187134i
$373$	2.50562			0.129736			0.0648682	−	0.997894i	$-0.479337\pi$
$373$	2.50562			0.129736			0.0648682	+	0.997894i	$0.479337\pi$
$374$	−11.7521	+	3.81850i	−0.607689	+	0.197450i
$375$	0.973832	+	1.43236i	0.0502885	+	0.0739667i
$376$	−8.81505	+	6.40451i	−0.454602	+	0.330287i
$377$	44.1017	−	25.4621i	2.27135	−	1.31137i
$378$	15.8064	−	11.7530i	0.812993	−	0.604508i
$379$	−1.61390	−	15.3552i	−0.0829003	−	0.788744i	−0.954437	−	0.298413i	$-0.903543\pi$
$379$	−1.61390	−	15.3552i	−0.0829003	−	0.788744i	0.871536	−	0.490331i	$-0.163124\pi$
$380$	−3.87822	+	5.33791i	−0.198949	+	0.273829i
$381$	−1.72170	+	7.01533i	−0.0882055	+	0.359406i
$382$	2.00096	−	2.22229i	0.102378	−	0.113702i
$383$	14.0927	+	6.27449i	0.720105	+	0.320611i	0.733866	−	0.679294i	$-0.237714\pi$
$383$	14.0927	+	6.27449i	0.720105	+	0.320611i	−0.0137615	+	0.999905i	$0.504381\pi$
$384$	−1.62977	−	0.586399i	−0.0831686	−	0.0299245i
$385$	−3.02112	−	14.2132i	−0.153970	−	0.724374i
$386$	−10.9344	−	24.5590i	−0.556546	−	1.25002i
$387$	−15.6751	−	10.4059i	−0.796811	−	0.528959i
$388$	−0.473367	+	1.45688i	−0.0240316	+	0.0739616i
$389$	27.1251	−	12.0769i	1.37530	−	0.612321i	0.419878	−	0.907580i	$-0.362073\pi$
$389$	27.1251	−	12.0769i	1.37530	−	0.612321i	0.955417	+	0.295259i	$0.0954061\pi$
$390$	−10.0303	+	0.738517i	−0.507906	+	0.0373963i
$391$	20.5427	+	4.36649i	1.03889	+	0.220823i
$392$	−2.99742	+	6.73231i	−0.151393	+	0.340033i
$393$	−12.3045	+	10.4021i	−0.620678	+	0.524717i
$394$	−13.4476	−	1.41340i	−0.677482	−	0.0712063i
$395$	−1.31503	−	0.955425i	−0.0661663	−	0.0480727i
$396$	1.91346	−	11.3395i	0.0961549	−	0.569831i
$397$	14.6958	−	25.4539i	0.737563	−	1.27750i	−0.216026	−	0.976388i	$-0.569310\pi$
$397$	14.6958	−	25.4539i	0.737563	−	1.27750i	0.953590	−	0.301109i	$-0.0973570\pi$
$398$	−13.1442	−	22.7664i	−0.658857	−	1.14117i
$399$	20.4785	+	38.1747i	1.02521	+	1.91112i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	7.07767	+	21.7828i	0.353442	+	1.08778i	0.956907	+	0.290393i	$0.0937862\pi$
$401$	7.07767	+	21.7828i	0.353442	+	1.08778i	−0.603465	+	0.797389i	$0.706214\pi$
$402$	−8.28476	−	1.13325i	−0.413206	−	0.0565215i
$403$	31.8576	−	5.50843i	1.58694	−	0.274395i
$404$		−	5.91641i		−	0.294353i
$405$	8.76378	+	2.04843i	0.435476	+	0.101788i
$406$	24.7052	−	22.2447i	1.22610	−	1.10398i
$407$	−6.81188	−	9.37575i	−0.337652	−	0.464739i
$408$	2.11065	+	5.16914i	0.104493	+	0.255911i
$409$	−26.4574	−	15.2752i	−1.30823	−	0.755309i	−0.326433	−	0.945220i	$-0.605847\pi$
$409$	−26.4574	−	15.2752i	−1.30823	−	0.755309i	−0.981801	+	0.189911i	$0.939180\pi$
$410$	−6.66325	+	0.700335i	−0.329074	+	0.0345871i
$411$	−14.7377	+	15.3742i	−0.726957	+	0.758355i
$412$	−0.601482	+	5.72272i	−0.0296329	+	0.281938i
$413$	11.4294	+	10.2911i	0.562403	+	0.506390i
$414$	−12.4526	+	15.0644i	−0.612011	+	0.740373i
$415$	0.533873	−	2.51168i	0.0262068	−	0.123293i
$416$	5.67981	−	1.20728i	0.278476	−	0.0591918i
$417$	35.9384	−	10.4486i	1.75991	−	0.511668i
$418$	24.0541	+	7.81565i	1.17652	+	0.382276i
$419$	−18.3640	−	5.96684i	−0.897142	−	0.291499i	−0.176085	−	0.984375i	$-0.556343\pi$
$419$	−18.3640	−	5.96684i	−0.897142	−	0.291499i	−0.721057	+	0.692876i	$0.756343\pi$
$420$	−6.30464	+	1.83298i	−0.307635	+	0.0894402i
$421$	28.2768	−	6.01041i	1.37813	−	0.292930i	0.541498	−	0.840702i	$-0.317857\pi$
$421$	28.2768	−	6.01041i	1.37813	−	0.292930i	0.836627	+	0.547773i	$0.184524\pi$
$422$	−0.0712199	+	0.335064i	−0.00346693	+	0.0163106i
$423$	−20.8265	+	25.1945i	−1.01262	+	1.22500i
$424$	4.64173	+	4.17943i	0.225422	+	0.202971i
$425$	−0.336958	+	3.20595i	−0.0163449	+	0.155511i
$426$	−0.298635	+	0.311533i	−0.0144689	+	0.0150938i
$427$	−37.8377	+	3.97690i	−1.83109	+	0.192456i
$428$	13.0887	+	7.55676i	0.632666	+	0.365270i
$429$	14.5738	+	35.6924i	0.703628	+	1.72324i
$430$	3.68632	+	5.07379i	0.177770	+	0.244680i
$431$	−9.80730	+	8.83054i	−0.472401	+	0.425352i	−0.870633	−	0.491933i	$-0.836291\pi$
$431$	−9.80730	+	8.83054i	−0.472401	+	0.425352i	0.398232	+	0.917285i	$0.369624\pi$
$432$	−5.17337	−	0.486024i	−0.248904	−	0.0233839i
$433$		−	2.20724i		−	0.106073i	−0.998593	−	0.0530366i	$-0.983110\pi$
$433$		−	2.20724i		−	0.106073i	0.998593	−	0.0530366i	$-0.0168900\pi$
$434$	19.5950	−	7.84138i	0.940592	−	0.376398i
$435$	15.0498	+	2.05862i	0.721582	+	0.0987034i
$436$	−1.32448	−	4.07633i	−0.0634310	−	0.195221i
$437$	−28.7631	−	31.9447i	−1.37593	−	1.52812i
$438$	−4.55424	−	8.48971i	−0.217610	−	0.405654i
$439$	12.1059	+	20.9680i	0.577783	+	1.00075i	0.995733	+	0.0922794i	$0.0294153\pi$
$439$	12.1059	+	20.9680i	0.577783	+	1.00075i	−0.417950	+	0.908470i	$0.637251\pi$
$440$	−1.91663	+	3.31971i	−0.0913719	+	0.158261i
$441$	−3.67861	+	21.8001i	−0.175172	+	1.03810i
$442$	−15.1436	−	11.0025i	−0.720307	−	0.523334i
$443$	−27.2032	−	2.85917i	−1.29246	−	0.135843i	−0.566777	−	0.823871i	$-0.691810\pi$
$443$	−27.2032	−	2.85917i	−1.29246	−	0.135843i	−0.725684	+	0.688028i	$0.758477\pi$
$444$	−3.99896	+	3.38070i	−0.189782	+	0.160441i
$445$	−0.319631	+	0.717903i	−0.0151520	+	0.0340319i
$446$	−13.4061	−	2.84956i	−0.634799	−	0.134931i
$447$	12.6446	−	0.931000i	0.598069	−	0.0440348i
$448$	3.46298	−	1.54182i	0.163610	−	0.0728441i
$449$	−7.99247	+	24.5983i	−0.377188	+	1.16087i	0.564803	+	0.825226i	$0.308952\pi$
$449$	−7.99247	+	24.5983i	−0.377188	+	1.16087i	−0.941991	+	0.335639i	$0.891048\pi$
$450$	−2.49940	−	1.65922i	−0.117823	−	0.0782162i
$451$	10.4461	+	23.4623i	0.491887	+	1.10480i
$452$	−3.44308	−	16.1984i	−0.161949	−	0.761910i
$453$	−23.2747	−	8.37435i	−1.09354	−	0.393461i
$454$	2.13530	+	0.950698i	0.100215	+	0.0446185i
$455$	14.7286	−	16.3577i	0.690485	−	0.766862i
$456$	2.72386	−	11.0988i	0.127556	−	0.519747i
$457$	−2.36208	+	3.25113i	−0.110494	+	0.152081i	−0.860682	−	0.509143i	$-0.829963\pi$
$457$	−2.36208	+	3.25113i	−0.110494	+	0.152081i	0.750189	+	0.661224i	$0.229963\pi$
$458$	−0.790663	−	7.52266i	−0.0369453	−	0.351511i
$459$	9.99471	+	13.4417i	0.466513	+	0.627406i
$460$	5.64212	−	3.25748i	0.263065	−	0.151881i
$461$	31.7223	−	23.0476i	1.47746	−	1.07344i	0.499092	−	0.866549i	$-0.333667\pi$
$461$	31.7223	−	23.0476i	1.47746	−	1.07344i	0.978365	−	0.206886i	$-0.0663329\pi$
$462$	14.1505	+	20.8133i	0.658342	+	0.968322i
$463$	−17.8743	+	5.80772i	−0.830691	+	0.269908i	−0.693336	−	0.720614i	$-0.743860\pi$
$463$	−17.8743	+	5.80772i	−0.830691	+	0.269908i	−0.137354	+	0.990522i	$0.543860\pi$
$464$	−8.76991			−0.407133
$465$	8.51649	+	4.52432i	0.394943	+	0.209810i
$466$	−1.70188			−0.0788380
$467$	−25.4428	+	8.26686i	−1.17735	+	0.382544i	−0.831382	−	0.555702i	$-0.812450\pi$
$467$	−25.4428	+	8.26686i	−1.17735	+	0.382544i	−0.345969	+	0.938246i	$0.612450\pi$
$468$	15.6004	−	7.75158i	0.721130	−	0.358317i
$469$	14.8055	−	10.7568i	0.683653	−	0.496703i
$470$	9.43622	−	5.44800i	0.435260	−	0.251298i
$471$	5.16966	+	4.00841i	0.238205	+	0.184698i
$472$	−0.424096	−	4.03500i	−0.0195206	−	0.185726i
$473$	14.1307	−	19.4492i	0.649729	−	0.894275i
$474$	2.73425	+	0.671040i	0.125588	+	0.0308219i
$475$	4.41494	−	4.90329i	0.202571	−	0.224978i
$476$	−11.1633	−	4.97021i	−0.511668	−	0.227809i
$477$	16.6092	+	8.67496i	0.760482	+	0.397199i
$478$	0.455481	+	2.14287i	0.0208332	+	0.0980126i
$479$	8.62513	+	19.3724i	0.394092	+	0.885146i	0.996230	+	0.0867535i	$0.0276493\pi$
$479$	8.62513	+	19.3724i	0.394092	+	0.885146i	−0.602137	+	0.798392i	$0.705684\pi$
$480$	1.55954	+	0.753543i	0.0711830	+	0.0343944i
$481$	5.42489	−	16.6961i	0.247354	−	0.761277i
$482$	−7.66982	+	3.41482i	−0.349351	+	0.155541i
$483$	−3.14096	−	42.6597i	−0.142919	−	1.94108i
$484$	3.61321	+	0.768012i	0.164237	+	0.0349096i
$485$	0.623059	−	1.39941i	0.0282917	−	0.0635441i
$486$	−15.3942	+	2.45334i	−0.698295	+	0.111286i
$487$	25.5534	+	2.68577i	1.15794	+	0.121704i	0.663958	−	0.747770i	$-0.268876\pi$
$487$	25.5534	+	2.68577i	1.15794	+	0.121704i	0.493978	+	0.869474i	$0.335542\pi$
$488$	8.11985	+	5.89942i	0.367568	+	0.267054i
$489$	18.1526	+	0.566985i	0.820891	+	0.0256399i
$490$	3.68472	−	6.38212i	0.166459	−	0.288315i
$491$	−10.3920	−	17.9996i	−0.468987	−	0.812309i	0.530385	−	0.847757i	$-0.322047\pi$
$491$	−10.3920	−	17.9996i	−0.468987	−	0.812309i	−0.999372	+	0.0354484i	$0.988714\pi$
$492$	10.2262	−	5.48575i	0.461031	−	0.247317i
$493$	18.9168	+	21.0092i	0.851970	+	0.946208i
$494$	11.8393	+	36.4376i	0.532675	+	1.63940i
$495$	−3.08827	+	11.0774i	−0.138808	+	0.497890i
$496$	−5.22564	−	1.92164i	−0.234638	−	0.0862840i
$497$		−	0.944475i		−	0.0423655i
$498$	0.788431	+	4.37710i	0.0353304	+	0.196142i
$499$	4.45339	−	4.00985i	0.199361	−	0.179506i	−0.563403	−	0.826182i	$-0.690508\pi$
$499$	4.45339	−	4.00985i	0.199361	−	0.179506i	0.762764	+	0.646676i	$0.223842\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	16.9710	−	6.92955i	0.758210	−	0.309589i
$502$	7.21622	+	4.16629i	0.322076	+	0.185951i
$503$	40.9598	−	4.30504i	1.82631	−	0.191952i	0.871743	−	0.489963i	$-0.162990\pi$
$503$	40.9598	−	4.30504i	1.82631	−	0.191952i	0.954562	+	0.298011i	$0.0963232\pi$
$504$	8.90954	−	7.06718i	0.396862	−	0.314797i
$505$	−0.618434	+	5.88400i	−0.0275199	+	0.261835i
$506$	−18.5590	−	16.7106i	−0.825047	−	0.742876i
$507$	−18.9036	+	30.5014i	−0.839536	+	1.35461i
$508$	−0.867094	+	4.07936i	−0.0384711	+	0.180992i
$509$	−9.09295	+	1.93277i	−0.403038	+	0.0856683i	−0.404970	−	0.914330i	$-0.632718\pi$
$509$	−9.09295	+	1.93277i	−0.403038	+	0.0856683i	0.00193257	+	0.999998i	$0.499385\pi$
$510$	−1.55876	−	5.36145i	−0.0690231	−	0.237409i
$511$	20.0529	+	6.51559i	0.887089	+	0.288233i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−0.378744	−	34.2822i	−0.0167220	−	1.51360i
$514$	10.5453	−	2.24146i	0.465131	−	0.0988667i
$515$	1.19637	−	5.62849i	0.0527185	−	0.248021i
$516$	−9.23318	−	5.72236i	−0.406468	−	0.251913i
$517$	−31.0391	−	27.9478i	−1.36510	−	1.22914i
$518$	1.19794	−	11.3976i	0.0526343	−	0.500782i
$519$	−27.5473	−	26.4068i	−1.20919	−	1.15913i
$520$	−5.77489	+	0.606965i	−0.253246	+	0.0266172i
$521$	17.9336	+	10.3540i	0.785687	+	0.453616i	0.838442	−	0.544991i	$-0.183467\pi$
$521$	17.9336	+	10.3540i	0.785687	+	0.453616i	−0.0527551	+	0.998607i	$0.516800\pi$
$522$	−25.4806	+	6.55274i	−1.11526	+	0.286805i
$523$	3.02719	+	4.16657i	0.132370	+	0.182191i	0.870057	−	0.492951i	$-0.164082\pi$
$523$	3.02719	+	4.16657i	0.132370	+	0.182191i	−0.737687	+	0.675143i	$0.764082\pi$
$524$	−6.91303	+	6.22452i	−0.301997	+	0.271919i
$525$	6.46170	−	1.16392i	0.282012	−	0.0507978i
$526$		−	4.51468i		−	0.196850i
$527$	6.66829	+	16.6636i	0.290475	+	0.725876i
$528$	0.899810	−	6.57816i	0.0391592	−	0.286277i
$529$	6.00872	+	18.4930i	0.261249	+	0.804041i
$530$	−4.17943	−	4.64173i	−0.181543	−	0.201624i
$531$	−4.24708	−	11.4067i	−0.184308	−	0.495007i
$532$	12.5056	+	21.6603i	0.542185	+	0.939093i
$533$	−19.4523	+	33.6924i	−0.842573	+	1.45938i
$534$	0.0424928	−	1.36046i	0.00183885	−	0.0588727i
$535$	−12.2271	−	8.88351i	−0.528623	−	0.384067i
$536$	−4.80130	−	0.504637i	−0.207385	−	0.0217970i
$537$	20.4514	+	24.1916i	0.882544	+	1.04394i
$538$	8.16248	−	18.3332i	0.351909	−	0.790402i
$539$	−27.6317	−	5.87330i	−1.19018	−	0.252981i
$540$	5.09423	+	1.02413i	0.219221	+	0.0440714i
$541$	−8.89548	+	3.96052i	−0.382447	+	0.170276i	−0.588950	−	0.808170i	$-0.700458\pi$
$541$	−8.89548	+	3.96052i	−0.382447	+	0.170276i	0.206503	+	0.978446i	$0.433792\pi$
$542$	−9.08634	+	27.9649i	−0.390292	+	1.20119i
$543$	−15.7244	+	32.5435i	−0.674799	+	1.39657i
$544$	1.31116	+	2.94491i	0.0562154	+	0.126262i
$545$	0.891131	+	4.19244i	0.0381719	+	0.179585i
$546$	−12.9075	+	35.8736i	−0.552390	+	1.53525i
$547$	37.5364	+	16.7123i	1.60494	+	0.714566i	0.996851	−	0.0793009i	$-0.0252688\pi$
$547$	37.5364	+	16.7123i	1.60494	+	0.714566i	0.608091	+	0.793867i	$0.291935\pi$
$548$	−8.22756	+	9.13763i	−0.351464	+	0.390340i
$549$	27.9999	+	11.0735i	1.19501	+	0.472606i
$550$	2.25314	−	3.10118i	0.0960741	−	0.132235i
$551$	−6.04844	−	57.5470i	−0.257672	−	2.45159i
$552$	−6.91448	+	8.91762i	−0.294300	+	0.379559i
$553$	−5.33616	+	3.08083i	−0.226916	+	0.131010i
$554$	−22.6196	+	16.4341i	−0.961017	+	0.698219i
$555$	4.33043	−	2.94417i	0.183817	−	0.124973i
$556$	20.5506	−	6.67730i	0.871541	−	0.283181i
$557$	30.1693			1.27831			0.639157	−	0.769076i	$-0.279283\pi$
$557$	30.1693			1.27831			0.639157	+	0.769076i	$0.279283\pi$
$558$	−16.6187	−	1.67873i	−0.703527	−	0.0710662i
$559$	36.4170			1.54028
$560$	−3.60517	+	1.17139i	−0.152346	+	0.0495003i
$561$	−17.6996	+	12.0336i	−0.747276	+	0.508058i
$562$	3.45156	−	2.50771i	0.145595	−	0.105781i
$563$	−26.0865	+	15.0611i	−1.09942	+	0.634748i	−0.936068	−	0.351820i	$-0.885563\pi$
$563$	−26.0865	+	15.0611i	−1.09942	+	0.634748i	−0.163348	+	0.986568i	$0.552229\pi$
$564$	−11.5642	+	14.9144i	−0.486940	+	0.628008i
$565$	1.73102	+	16.4696i	0.0728247	+	0.692881i
$566$	−0.643179	+	0.885260i	−0.0270348	+	0.0372103i
$567$	20.6059	−	27.1905i	0.865364	−	1.14189i
$568$	−0.166718	+	0.185159i	−0.00699532	+	0.00776909i
$569$	−8.74159	−	3.89201i	−0.366467	−	0.163161i	0.215238	−	0.976562i	$-0.430947\pi$
$569$	−8.74159	−	3.89201i	−0.366467	−	0.163161i	−0.581705	+	0.813400i	$0.697614\pi$
$570$	−3.86907	+	10.7532i	−0.162058	+	0.450403i
$571$	−2.28339	−	10.7425i	−0.0955571	−	0.449561i	−0.999748	−	0.0224330i	$-0.992859\pi$
$571$	−2.28339	−	10.7425i	−0.0955571	−	0.449561i	0.904191	−	0.427128i	$-0.140475\pi$
$572$	9.05340	+	20.3343i	0.378542	+	0.850219i
$573$	2.25338	−	4.66363i	0.0941364	−	0.194826i
$574$	−7.84827	+	24.1545i	−0.327580	+	1.00819i
$575$	−5.95171	+	2.64987i	−0.248203	+	0.110507i
$576$	−2.99415	−	0.187223i	−0.124756	−	0.00780096i
$577$	27.3387	+	5.81101i	1.13812	+	0.241916i	0.738167	−	0.674618i	$-0.235692\pi$
$577$	27.3387	+	5.81101i	1.13812	+	0.241916i	0.399957	+	0.916534i	$0.369025\pi$
$578$	−2.68787	+	6.03705i	−0.111801	+	0.251108i
$579$	−30.0613	−	35.5590i	−1.24931	−	1.47778i
$580$	8.72186	+	0.916705i	0.362156	+	0.0380641i
$581$	−7.87475	−	5.72134i	−0.326700	−	0.237361i
$582$	−0.0828317	+	2.65195i	−0.00343348	+	0.109927i
$583$	−11.9714	+	20.7351i	−0.495805	+	0.858760i
$584$	−2.78113	−	4.81706i	−0.115084	−	0.199331i
$585$	−16.3252	+	6.07842i	−0.674965	+	0.251312i
$586$	0.598319	+	0.664501i	0.0247163	+	0.0274503i
$587$	−6.55193	−	20.1648i	−0.270427	−	0.832289i	−0.990393	−	0.138280i	$-0.955843\pi$
$587$	−6.55193	−	20.1648i	−0.270427	−	0.832289i	0.719966	−	0.694009i	$-0.244157\pi$
$588$	−1.72988	+	12.6465i	−0.0713391	+	0.521532i
$589$	9.00552	−	35.6153i	0.371066	−	1.46750i
$590$			4.05723i			0.167033i
$591$	−23.0494	+	4.15180i	−0.948124	+	0.170782i
$592$	−2.24674	+	2.02297i	−0.0923405	+	0.0831437i
$593$	1.95779	+	2.69467i	0.0803969	+	0.110657i	0.847321	−	0.531081i	$-0.178214\pi$
$593$	1.95779	+	2.69467i	0.0803969	+	0.110657i	−0.766924	+	0.641737i	$0.778214\pi$
$594$	−2.30073	−	19.7849i	−0.0944001	−	0.811785i
$595$	10.5826	+	6.10986i	0.433844	+	0.250480i
$596$	7.28003	−	0.765162i	0.298202	−	0.0313422i
$597$	−32.8698	−	31.5089i	−1.34527	−	1.28957i
$598$	3.95435	−	37.6232i	0.161706	−	1.53853i
$599$	28.6763	+	25.8203i	1.17168	+	1.05499i	0.997528	+	0.0702685i	$0.0223856\pi$
$599$	28.6763	+	25.8203i	1.17168	+	1.05499i	0.174154	+	0.984718i	$0.444281\pi$
$600$	−1.47223	−	0.912432i	−0.0601036	−	0.0372499i
$601$	−1.38410	+	6.51169i	−0.0564587	+	0.265617i	−0.997319	−	0.0731777i	$-0.976686\pi$
$601$	−1.38410	+	6.51169i	−0.0564587	+	0.265617i	0.940860	+	0.338795i	$0.110019\pi$
$602$	23.2541	−	4.94281i	0.947765	−	0.201454i
$603$	−14.3271	+	2.12125i	−0.583443	+	0.0863841i
$604$	−13.5820	−	4.41307i	−0.552645	−	0.179565i
$605$	−3.51314	−	1.14149i	−0.142829	−	0.0464081i
$606$	−2.86086	−	9.84009i	−0.116214	−	0.399726i
$607$	−6.36079	+	1.35203i	−0.258177	+	0.0548771i	−0.335182	−	0.942154i	$-0.608798\pi$
$607$	−6.36079	+	1.35203i	−0.258177	+	0.0548771i	0.0770048	+	0.997031i	$0.475464\pi$
$608$	1.37181	−	6.45384i	0.0556341	−	0.261738i
$609$	30.3330	−	48.9431i	1.22915	−	1.98327i
$610$	−7.45871	−	6.71586i	−0.301995	−	0.271917i
$611$	6.61350	−	62.9232i	0.267553	−	2.54560i
$612$	6.00991	+	7.57665i	0.242936	+	0.306268i
$613$	22.0026	−	2.31257i	0.888678	−	0.0934038i	0.350823	−	0.936442i	$-0.385902\pi$
$613$	22.0026	−	2.31257i	0.888678	−	0.0934038i	0.537854	+	0.843038i	$0.319235\pi$
$614$	2.92560	+	1.68909i	0.118068	+	0.0681663i
$615$	−10.7436	+	4.38677i	−0.433222	+	0.176892i
$616$	8.54098	+	11.7556i	0.344126	+	0.473648i
$617$	−20.3409	+	18.3150i	−0.818894	+	0.737336i	−0.967855	−	0.251507i	$-0.919074\pi$
$617$	−20.3409	+	18.3150i	−0.818894	+	0.737336i	0.148961	+	0.988843i	$0.452407\pi$
$618$	1.76682	+	9.80878i	0.0710719	+	0.394567i
$619$		−	15.3993i		−	0.618949i	−0.950908	−	0.309475i	$-0.899847\pi$
$619$		−	15.3993i		−	0.618949i	0.950908	−	0.309475i	$-0.100153\pi$
$620$	4.99615	+	2.45734i	0.200650	+	0.0986891i
$621$	−13.4266	+	31.0762i	−0.538793	+	1.24705i
$622$	0.781071	+	2.40389i	0.0313181	+	0.0963872i
$623$	1.99327	+	2.21375i	0.0798587	+	0.0886921i
$624$	8.86280	−	4.75438i	0.354796	−	0.190328i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.06324	+	3.57364i	−0.0824638	+	0.142832i
$627$	43.7856	+	1.36761i	1.74863	+	0.0546172i
$628$	3.05550	+	2.21995i	0.121928	+	0.0885856i
$629$	9.69249	+	1.01872i	0.386465	+	0.0406191i
$630$	−9.59945	+	6.09716i	−0.382451	+	0.242917i
$631$	−0.658428	+	1.47885i	−0.0262116	+	0.0588723i	−0.926177	−	0.377089i	$-0.876925\pi$
$631$	−0.658428	+	1.47885i	−0.0262116	+	0.0588723i	0.899965	+	0.435962i	$0.143592\pi$
$632$	1.58995	+	0.337954i	0.0632447	+	0.0134431i
$633$	0.0435666	+	0.591711i	0.00173162	+	0.0235184i
$634$	−17.6258	+	7.84749i	−0.700008	+	0.311664i
$635$	1.28875	−	3.96638i	0.0511426	−	0.157401i
$636$	9.74100	+	4.70668i	0.386256	+	0.186632i
$637$	−17.4051	−	39.0925i	−0.689616	−	1.54890i
$638$	−6.98945	−	32.8828i	−0.276715	−	1.30184i
$639$	−0.346044	+	0.662541i	−0.0136893	+	0.0262097i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	25.2274	−	28.0179i	0.996424	−	1.10664i	0.00212656	−	0.999998i	$-0.499323\pi$
$641$	25.2274	−	28.0179i	0.996424	−	1.10664i	0.994297	−	0.106643i	$-0.0340102\pi$
$642$	25.4230	+	6.23931i	1.00336	+	0.246246i
$643$	3.04245	−	4.18757i	0.119982	−	0.165142i	−0.744801	−	0.667287i	$-0.767456\pi$
$643$	3.04245	−	4.18757i	0.119982	−	0.165142i	0.864783	+	0.502145i	$0.167456\pi$
$644$	−2.58146	−	24.5610i	−0.101724	−	0.967838i
$645$	8.58445	+	6.65614i	0.338012	+	0.262085i
$646$	−18.4199	+	10.6347i	−0.724719	+	0.418417i
$647$	−0.412670	+	0.299822i	−0.0162237	+	0.0117872i	−0.595868	−	0.803083i	$-0.703192\pi$
$647$	−0.412670	+	0.299822i	−0.0162237	+	0.0117872i	0.579644	+	0.814870i	$0.303192\pi$
$648$	−8.83929	+	1.69321i	−0.347240	+	0.0665157i
$649$	14.7912	−	4.80597i	0.580607	−	0.188651i
$650$	5.80670			0.227758
$651$	28.7985	−	22.5168i	1.12870	−	0.882501i
$652$	10.4855			0.410646
$653$	34.1949	−	11.1106i	1.33815	−	0.434792i	0.449461	−	0.893300i	$-0.351616\pi$
$653$	34.1949	−	11.1106i	1.33815	−	0.434792i	0.888690	+	0.458508i	$0.151616\pi$
$654$	−4.17394	−	6.13924i	−0.163214	−	0.240063i
$655$	7.52580	−	5.46781i	0.294057	−	0.213645i
$656$	5.80233	−	3.34997i	0.226543	−	0.130795i
$657$	−11.6797	−	11.9178i	−0.455669	−	0.464957i
$658$	−4.31739	−	41.0773i	−0.168310	−	1.60136i
$659$	−10.8518	+	14.9362i	−0.422726	+	0.581833i	−0.966265	−	0.257552i	$-0.917084\pi$
$659$	−10.8518	+	14.9362i	−0.422726	+	0.581833i	0.543538	+	0.839384i	$0.317084\pi$
$660$	−1.58249	+	6.44806i	−0.0615982	+	0.250991i
$661$	11.4718	−	12.7408i	0.446202	−	0.495558i	−0.477520	−	0.878621i	$-0.658464\pi$
$661$	11.4718	−	12.7408i	0.446202	−	0.495558i	0.923722	+	0.383063i	$0.125131\pi$
$662$	−14.3605	−	6.39372i	−0.558138	−	0.248499i
$663$	−30.5068	−	10.9765i	−1.18479	−	0.426292i
$664$	0.533873	+	2.51168i	0.0207183	+	0.0974720i
$665$	−10.1730	−	22.8488i	−0.394490	−	0.886039i
$666$	−5.01629	+	7.55641i	−0.194377	+	0.292805i
$667$	−17.6559	+	54.3391i	−0.683637	+	2.10402i
$668$	9.66856	−	4.30472i	0.374088	−	0.166555i
$669$	−23.6748	+	1.74313i	−0.915320	+	0.0673934i
$670$	4.72225	+	1.00375i	0.182437	+	0.0387781i
$671$	−15.6485	+	35.1471i	−0.604104	+	1.35684i
$672$	5.01404	−	4.23884i	0.193421	−	0.163517i
$673$	23.9167	+	2.51375i	0.921921	+	0.0968978i	0.553583	−	0.832794i	$-0.313260\pi$
$673$	23.9167	+	2.51375i	0.921921	+	0.0968978i	0.368338	+	0.929692i	$0.379927\pi$
$674$	5.96328	+	4.33257i	0.229697	+	0.166884i
$675$	−4.95927	−	1.55101i	−0.190882	−	0.0596983i
$676$	−10.3589	+	17.9421i	−0.398419	+	0.690081i
$677$	22.5736	+	39.0987i	0.867576	+	1.50269i	0.864467	+	0.502690i	$0.167656\pi$
$677$	22.5736	+	39.0987i	0.867576	+	1.50269i	0.00310893	+	0.999995i	$0.499010\pi$
$678$	−13.5592	−	25.2761i	−0.520736	−	0.970722i
$679$	−3.88550	−	4.31528i	−0.149112	−	0.165605i
$680$	−0.996149	−	3.06583i	−0.0382006	−	0.117569i
$681$	4.01111	+	0.548670i	0.153706	+	0.0210251i
$682$	3.04044	−	21.1250i	0.116425	−	0.808920i
$683$			35.5311i			1.35956i	0.733417	+	0.679779i	$0.237924\pi$
$683$			35.5311i			1.35956i	−0.733417	+	0.679779i	$0.762076\pi$
$684$	−0.836476	−	19.7764i	−0.0319835	−	0.756169i
$685$	9.13763	−	8.22756i	0.349131	−	0.314359i
$686$	−0.823147	−	1.13296i	−0.0314279	−	0.0432568i
$687$	−4.95257	−	12.1292i	−0.188952	−	0.462760i
$688$	−5.43132	−	3.13577i	−0.207067	−	0.119550i
$689$	−36.0703	+	3.79114i	−1.37417	+	0.144431i
$690$	7.80874	−	8.14601i	0.297274	−	0.310113i
$691$	4.77507	−	45.4318i	0.181652	−	1.72831i	−0.401427	−	0.915891i	$-0.631486\pi$
$691$	4.77507	−	45.4318i	0.181652	−	1.72831i	0.583080	−	0.812415i	$-0.301848\pi$
$692$	−16.3726	−	14.7420i	−0.622395	−	0.560407i
$693$	33.5991	+	27.7739i	1.27633	+	1.05504i
$694$	−6.82542	+	32.1111i	−0.259089	+	1.21892i
$695$	−21.1360	+	4.49260i	−0.801735	+	0.170414i
$696$	−14.5860	+	4.24065i	−0.552880	+	0.160741i
$697$	−20.5409	−	6.67414i	−0.778042	−	0.252801i
$698$	9.21122	+	2.99291i	0.348650	+	0.113283i
$699$	−2.83054	+	0.822936i	−0.107061	+	0.0311263i
$700$	3.70787	−	0.788132i	0.140144	−	0.0297886i
$701$	−3.26493	+	15.3603i	−0.123315	+	0.580150i	0.872489	+	0.488634i	$0.162505\pi$
$701$	−3.26493	+	15.3603i	−0.123315	+	0.580150i	−0.995804	+	0.0915162i	$0.970829\pi$
$702$	22.1981	−	20.4358i	0.837815	−	0.771300i
$703$	−14.8240	−	13.3476i	−0.559099	−	0.503415i
$704$	0.400685	−	3.81227i	0.0151014	−	0.143680i
$705$	13.0598	−	13.6239i	0.491861	−	0.513105i
$706$	13.1864	−	1.38595i	0.496276	−	0.0521607i
$707$	19.4227	+	11.2137i	0.730465	+	0.421734i
$708$	−2.65646	−	6.50588i	−0.0998358	−	0.244506i
$709$	−8.45075	−	11.6315i	−0.317375	−	0.436829i	0.620289	−	0.784374i	$-0.287015\pi$
$709$	−8.45075	−	11.6315i	−0.317375	−	0.436829i	−0.937663	+	0.347545i	$0.887015\pi$
$710$	0.185159	−	0.166718i	0.00694888	−	0.00625680i
$711$	4.87204	−	0.206071i	0.182716	−	0.00772828i
$712$		−	0.785842i		−	0.0294507i
$713$	−22.4271	+	28.5098i	−0.839900	+	1.06770i
$714$	−20.9699	−	2.86842i	−0.784780	−	0.107348i
$715$	−6.87830	−	21.1692i	−0.257234	−	0.791684i
$716$	12.2379	+	13.5916i	0.457352	+	0.507941i
$717$	1.79373	+	3.34374i	0.0669879	+	0.124874i
$718$	15.1945	+	26.3176i	0.567053	+	0.982164i
$719$	−22.3610	+	38.7304i	−0.833925	+	1.44440i	0.0609770	+	0.998139i	$0.480578\pi$
$719$	−22.3610	+	38.7304i	−0.833925	+	1.44440i	−0.894902	+	0.446262i	$0.852755\pi$
$720$	2.95818	+	0.499172i	0.110245	+	0.0186030i
$721$	−17.6468	−	12.8211i	−0.657200	−	0.477484i
$722$	24.3995	+	2.56449i	0.908056	+	0.0954405i
$723$	−11.1051	+	9.38819i	−0.413003	+	0.349151i
$724$	−8.48750	+	19.0632i	−0.315435	+	0.708480i
$725$	−8.57826	−	1.82337i	−0.318589	−	0.0677181i
$726$	6.38081	−	0.469807i	0.236814	−	0.0174362i
$727$	21.7359	−	9.67744i	0.806140	−	0.358917i	0.0380638	−	0.999275i	$-0.487881\pi$
$727$	21.7359	−	9.67744i	0.806140	−	0.358917i	0.768076	+	0.640359i	$0.221214\pi$
$728$	−6.80192	+	20.9342i	−0.252096	+	0.775872i
$729$	−24.4171	+	11.5241i	−0.904336	+	0.426820i
$730$	2.26238	+	5.08138i	0.0837343	+	0.188070i
$731$	4.20335	+	19.7752i	0.155466	+	0.731412i
$732$	16.3575	+	5.88550i	0.604589	+	0.217534i
$733$	−12.9441	−	5.76310i	−0.478103	−	0.212865i	0.153513	−	0.988147i	$-0.450941\pi$
$733$	−12.9441	−	5.76310i	−0.478103	−	0.212865i	−0.631616	+	0.775282i	$0.717608\pi$
$734$	−3.88116	+	4.31047i	−0.143256	+	0.159102i
$735$	3.04232	−	12.3964i	0.112218	−	0.457247i
$736$	−3.82939	+	5.27071i	−0.141153	+	0.194281i
$737$	−1.93441	−	18.4047i	−0.0712549	−	0.677945i
$738$	14.3554	−	14.0686i	0.528429	−	0.517874i
$739$	−13.4084	+	7.74137i	−0.493237	+	0.284771i	−0.725917	−	0.687783i	$-0.758584\pi$
$739$	−13.4084	+	7.74137i	−0.493237	+	0.284771i	0.232679	+	0.972554i	$0.425251\pi$
$740$	2.44589	−	1.77704i	0.0899127	−	0.0653254i
$741$	37.3102	+	54.8776i	1.37062	+	2.01598i
$742$	−22.5181	+	7.31659i	−0.826667	+	0.268600i
$743$	2.08743			0.0765803			0.0382901	−	0.999267i	$-0.487809\pi$
$743$	2.08743			0.0765803			0.0382901	+	0.999267i	$0.487809\pi$
$744$	−9.62040	−	0.669201i	−0.352701	−	0.0245341i
$745$	−7.32013			−0.268189
$746$	2.38299	−	0.774281i	0.0872475	−	0.0283484i
$747$	3.42783	+	6.89868i	0.125418	+	0.252410i
$748$	−9.99697	+	7.26322i	−0.365525	+	0.265570i
$749$	−49.6154	+	28.6454i	−1.81291	+	1.04668i
$750$	1.36879	+	1.06132i	0.0499812	+	0.0387541i
$751$	−4.00682	−	38.1224i	−0.146211	−	1.39110i	−0.783937	−	0.620841i	$-0.786791\pi$
$751$	−4.00682	−	38.1224i	−0.146211	−	1.39110i	0.637726	−	0.770264i	$-0.279875\pi$
$752$	−6.40451	+	8.81505i	−0.233548	+	0.321452i
$753$	14.0165	+	3.43993i	0.510790	+	0.125358i
$754$	34.0750	−	37.8441i	1.24094	−	1.37820i
$755$	13.0463	+	5.80860i	0.474804	+	0.211397i
$756$	11.4009	−	16.0622i	0.414647	−	0.584176i
$757$	11.0936	+	52.1913i	0.403204	+	1.89693i	0.440749	+	0.897631i	$0.354713\pi$
$757$	11.0936	+	52.1913i	0.403204	+	1.89693i	−0.0375447	+	0.999295i	$0.511954\pi$
$758$	−6.27993	−	14.1049i	−0.228097	−	0.512315i
$759$	−38.9473	−	18.8187i	−1.41370	−	0.683074i
$760$	−2.03890	+	6.27509i	−0.0739587	+	0.227622i
$761$	4.22032	−	1.87901i	0.152987	−	0.0681140i	−0.328815	−	0.944394i	$-0.606649\pi$
$761$	4.22032	−	1.87901i	0.152987	−	0.0681140i	0.481802	+	0.876280i	$0.339983\pi$
$762$	0.530418	+	7.20401i	0.0192150	+	0.260974i
$763$	15.8923	+	3.37801i	0.575340	+	0.122292i
$764$	1.21630	−	2.73185i	0.0440041	−	0.0988349i
$765$	−5.18501	−	8.16335i	−0.187465	−	0.295147i
$766$	15.3419	+	1.61250i	0.554325	+	0.0582620i
$767$	19.0597	+	13.8477i	0.688206	+	0.500011i
$768$	−1.73121	−	0.0540730i	−0.0624695	−	0.00195119i
$769$	−21.8864	+	37.9083i	−0.789242	+	1.36701i	0.137190	+	0.990545i	$0.456193\pi$
$769$	−21.8864	+	37.9083i	−0.789242	+	1.36701i	−0.926432	+	0.376463i	$0.877140\pi$
$770$	−7.26539	−	12.5840i	−0.261826	−	0.453497i
$771$	16.4549	−	8.82708i	0.592607	−	0.317900i
$772$	−17.9884	−	19.9781i	−0.647416	−	0.719029i
$773$	−8.40902	−	25.8803i	−0.302451	−	0.930850i	−0.980616	−	0.195940i	$-0.937224\pi$
$773$	−8.40902	−	25.8803i	−0.302451	−	0.930850i	0.678165	−	0.734910i	$-0.262776\pi$
$774$	−18.1235	−	5.05268i	−0.651436	−	0.181615i
$775$	−4.71192	−	2.96612i	−0.169257	−	0.106546i
$776$			1.53185i			0.0549902i
$777$	−3.51887	−	19.5356i	−0.126239	−	0.700835i
$778$	22.0655	−	19.8679i	0.791087	−	0.712298i
$779$	25.9839	+	35.7637i	0.930969	+	1.28137i
$780$	−9.31121	+	3.80192i	−0.333395	+	0.136131i
$781$	−0.827124	−	0.477540i	−0.0295968	−	0.0170877i
$782$	20.8866	−	2.19527i	0.746903	−	0.0785027i
$783$	−39.2105	+	23.2195i	−1.40127	+	0.829796i
$784$	−0.770316	+	7.32907i	−0.0275113	+	0.261752i
$785$	−2.80671	−	2.52717i	−0.100176	−	0.0901987i
$786$	−8.48780	+	13.6953i	−0.302750	+	0.488495i
$787$	−2.20673	+	10.3818i	−0.0786613	+	0.370072i	−0.999817	−	0.0191215i	$-0.993913\pi$
$787$	−2.20673	+	10.3818i	−0.0786613	+	0.370072i	0.921156	+	0.389194i	$0.127246\pi$
$788$	−13.2262	+	2.81132i	−0.471165	+	0.100149i
$789$	−2.18306	−	7.50875i	−0.0777189	−	0.267319i
$790$	−1.54591	−	0.502297i	−0.0550010	−	0.0178709i
$791$	59.7028	+	19.3986i	2.12279	+	0.689735i
$792$	−1.68429	−	11.3758i	−0.0598486	−	0.404221i
$793$	−57.0065	+	12.1171i	−2.02436	+	0.430291i
$794$	6.11088	−	28.7494i	0.216867	−	1.02028i
$795$	−9.19565	−	5.69910i	−0.326136	−	0.202126i
$796$	−19.5360	−	17.5903i	−0.692436	−	0.623473i
$797$	−1.70878	+	16.2580i	−0.0605282	+	0.575887i	0.921661	+	0.387995i	$0.126832\pi$
$797$	−1.70878	+	16.2580i	−0.0605282	+	0.575887i	−0.982190	+	0.187892i	$0.939834\pi$
$798$	31.2728	+	29.9780i	1.10705	+	1.06121i
$799$	34.9320	−	3.67150i	1.23580	−	0.129888i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−0.587169	−	2.28324i	−0.0207466	−	0.0806742i
$802$	13.4625	+	18.5296i	0.475378	+	0.654302i
$803$	15.8451	−	14.2670i	0.559160	−	0.503470i
$804$	−8.22947	+	1.48235i	−0.290231	+	0.0522783i
$805$			24.6963i			0.870429i
$806$	28.5962	−	15.0834i	1.00726	−	0.531289i
$807$	4.71076	−	34.4385i	0.165826	−	1.21229i
$808$	−1.82827	−	5.62684i	−0.0643184	−	0.197952i
$809$	−30.9874	−	34.4150i	−1.08946	−	1.20997i	−0.976308	−	0.216387i	$-0.930573\pi$
$809$	−30.9874	−	34.4150i	−1.08946	−	1.20997i	−0.113150	−	0.993578i	$-0.536094\pi$
$810$	8.96786	−	0.759981i	0.315098	−	0.0267030i
$811$	13.4207	+	23.2453i	0.471263	+	0.816251i	0.999460	−	0.0328707i	$-0.0104650\pi$
$811$	13.4207	+	23.2453i	0.471263	+	0.816251i	−0.528197	+	0.849122i	$0.677132\pi$
$812$	16.6221	−	28.7902i	0.583320	−	1.01034i
$813$	−1.58996	+	50.9044i	−0.0557624	+	1.78530i
$814$	−9.37575	−	6.81188i	−0.328620	−	0.238756i
$815$	−10.4281	−	1.09604i	−0.365281	−	0.0383925i
$816$	3.60470	+	4.26392i	0.126190	+	0.149267i
$817$	16.8307	−	37.8023i	0.588831	−	1.32254i
$818$	−29.8828	−	6.35178i	−1.04483	−	0.222085i
$819$	−4.12106	+	65.9057i	−0.144001	+	2.30293i
$820$	−6.12071	+	2.72511i	−0.213744	+	0.0951651i
$821$	−1.48821	+	4.58025i	−0.0519391	+	0.159852i	−0.973662	−	0.227998i	$-0.926782\pi$
$821$	−1.48821	+	4.58025i	−0.0519391	+	0.159852i	0.921723	+	0.387850i	$0.126782\pi$
$822$	−9.26549	+	19.1760i	−0.323171	+	0.668839i
$823$	−5.58860	−	12.5522i	−0.194806	−	0.437542i	0.789560	−	0.613673i	$-0.210309\pi$
$823$	−5.58860	−	12.5522i	−0.194806	−	0.437542i	−0.984367	+	0.176130i	$0.943642\pi$
$824$	1.19637	+	5.62849i	0.0416776	+	0.196078i
$825$	2.24782	−	6.24733i	0.0782591	−	0.217504i
$826$	14.0501	+	6.25551i	0.488865	+	0.217657i
$827$	4.04237	−	4.48951i	0.140567	−	0.156116i	−0.668750	−	0.743487i	$-0.733171\pi$
$827$	4.04237	−	4.48951i	0.140567	−	0.156116i	0.809318	+	0.587371i	$0.199837\pi$
$828$	−7.18797	+	18.1751i	−0.249799	+	0.631629i
$829$	−2.98602	+	4.10991i	−0.103709	+	0.142743i	−0.857717	−	0.514122i	$-0.828118\pi$
$829$	−2.98602	+	4.10991i	−0.103709	+	0.142743i	0.754008	+	0.656865i	$0.228118\pi$
$830$	−0.268407	−	2.55372i	−0.00931654	−	0.0886410i
$831$	−29.6740	+	38.2706i	−1.02938	+	1.32759i
$832$	5.02875	−	2.90335i	0.174341	−	0.100656i
$833$	19.2191	−	13.9635i	0.665903	−	0.483807i
$834$	30.9507	−	21.0428i	1.07174	−	0.728651i
$835$	−10.0656	+	3.27050i	−0.348333	+	0.113180i
$836$	25.2920			0.874741
$837$	−28.4517	+	5.24388i	−0.983436	+	0.181255i
$838$	−19.3091			−0.667022
$839$	−17.8439	+	5.79783i	−0.616040	+	0.200163i	−0.600381	−	0.799714i	$-0.704984\pi$
$839$	−17.8439	+	5.79783i	−0.616040	+	0.200163i	−0.0156585	+	0.999877i	$0.504984\pi$
$840$	−5.42965	+	3.69151i	−0.187341	+	0.127369i
$841$	−38.7610	+	28.1615i	−1.33659	+	0.971087i
$842$	25.0355	−	14.4542i	0.862780	−	0.498126i
$843$	4.52800	−	5.83977i	0.155952	−	0.201132i
$844$	0.0358061	+	0.340673i	0.00123250	+	0.0117264i
$845$	12.1776	−	16.7610i	0.418922	−	0.576597i
$846$	−12.0216	+	30.3972i	−0.413311	+	1.04508i
$847$	−9.36957	+	10.4060i	−0.321942	+	0.357553i
$848$	5.70606	+	2.54050i	0.195947	+	0.0872412i
$849$	−0.641662	+	1.78336i	−0.0220218	+	0.0612047i
$850$	0.670225	+	3.15316i	0.0229885	+	0.108153i
$851$	8.01132	+	17.9937i	0.274625	+	0.616817i
$852$	−0.187750	+	0.388569i	−0.00643219	+	0.0133121i
$853$	11.5366	−	35.5059i	0.395004	−	1.21570i	−0.533954	−	0.845513i	$-0.679295\pi$
$853$	11.5366	−	35.5059i	0.395004	−	1.21570i	0.928958	−	0.370184i	$-0.120705\pi$
$854$	−34.7569	+	15.4748i	−1.18936	+	0.529535i
$855$	−1.23530	+	19.7555i	−0.0422464	+	0.675623i
$856$	14.7833	+	3.14228i	0.505281	+	0.107401i
$857$	−6.65228	+	14.9413i	−0.227237	+	0.510384i	−0.990797	−	0.135353i	$-0.956783\pi$
$857$	−6.65228	+	14.9413i	−0.227237	+	0.510384i	0.763560	+	0.645737i	$0.223450\pi$
$858$	24.8900	+	29.4419i	0.849732	+	1.00513i
$859$	−17.1195	−	1.79933i	−0.584110	−	0.0613924i	−0.192135	−	0.981368i	$-0.561541\pi$
$859$	−17.1195	−	1.79933i	−0.584110	−	0.0613924i	−0.391975	+	0.919976i	$0.628208\pi$
$860$	5.07379	+	3.68632i	0.173015	+	0.125703i
$861$	−1.37332	+	43.9684i	−0.0468026	+	1.49844i
$862$	−6.59851	+	11.4290i	−0.224746	+	0.389272i
$863$	26.4696	+	45.8467i	0.901036	+	1.56064i	0.826151	+	0.563449i	$0.190526\pi$
$863$	26.4696	+	45.8467i	0.901036	+	1.56064i	0.0748854	+	0.997192i	$0.476141\pi$
$864$	−5.07036	+	1.13642i	−0.172497	+	0.0386619i
$865$	14.7420	+	16.3726i	0.501243	+	0.556687i
$866$	−0.682074	−	2.09921i	−0.0231778	−	0.0713340i
$867$	−1.55123	+	11.3404i	−0.0526826	+	0.385141i
$868$	16.2129	−	13.5128i	0.550300	−	0.458654i
$869$			6.23085i			0.211367i
$870$	14.9493	−	2.69277i	0.506830	−	0.0912935i
$871$	20.8328	−	18.7579i	0.705893	−	0.635589i
$872$	−2.51931	−	3.46753i	−0.0853146	−	0.117425i
$873$	1.14457	+	4.45073i	0.0387379	+	0.150634i
$874$	−37.2268	−	21.4929i	−1.25922	−	0.727009i
$875$	−3.76994	+	0.396236i	−0.127447	+	0.0133952i
$876$	−6.95481	−	6.66686i	−0.234981	−	0.225252i
$877$	4.05946	−	38.6231i	0.137078	−	1.30421i	−0.682349	−	0.731027i	$-0.739041\pi$
$877$	4.05946	−	38.6231i	0.137078	−	1.30421i	0.819427	−	0.573184i	$-0.194292\pi$
$878$	17.9929	+	16.2008i	0.607230	+	0.546752i
$879$	1.31643	+	0.815873i	0.0444022	+	0.0275187i
$880$	−0.796981	+	3.74950i	−0.0268662	+	0.126396i
$881$	−30.9973	+	6.58868i	−1.04433	+	0.221978i	−0.697971	−	0.716126i	$-0.745914\pi$
$881$	−30.9973	+	6.58868i	−1.04433	+	0.221978i	−0.346354	+	0.938104i	$0.612580\pi$
$882$	3.23804	+	21.8699i	0.109030	+	0.736398i
$883$	−50.5572	−	16.4270i	−1.70138	−	0.552813i	−0.712523	−	0.701649i	$-0.752447\pi$
$883$	−50.5572	−	16.4270i	−1.70138	−	0.552813i	−0.988862	+	0.148836i	$0.952447\pi$
$884$	−17.8024	−	5.78434i	−0.598758	−	0.194548i
$885$	1.96186	+	6.74792i	0.0659470	+	0.226829i
$886$	−26.7553	+	5.68701i	−0.898861	+	0.191059i
$887$	2.17846	−	10.2488i	0.0731454	−	0.344122i	−0.926323	−	0.376731i	$-0.877048\pi$
$887$	2.17846	−	10.2488i	0.0731454	−	0.344122i	0.999468	+	0.0326087i	$0.0103815\pi$
$888$	−2.75854	+	4.45098i	−0.0925707	+	0.149365i
$889$	−11.7485	−	10.5784i	−0.394031	−	0.354787i
$890$	−0.0821429	+	0.781537i	−0.00275344	+	0.0261972i
$891$	−13.3935	−	31.7935i	−0.448697	−	1.06512i
$892$	−13.6306	+	1.43263i	−0.456385	+	0.0479680i
$893$	−62.2604	−	35.9460i	−2.08346	−	1.20289i
$894$	11.7380	−	4.79283i	0.392579	−	0.160296i
$895$	−10.7502	−	14.7963i	−0.359339	−	0.494587i
$896$	2.81704	−	2.53648i	0.0941108	−	0.0847377i
$897$	−11.6157	−	64.4864i	−0.387837	−	2.15314i
$898$			25.8642i			0.863099i
$899$	−46.9816	+	13.3032i	−1.56692	+	0.443687i
$900$	−2.88980	−	0.805651i	−0.0963266	−	0.0268550i
$901$	−6.22200	−	19.1494i	−0.207285	−	0.637958i
$902$	17.1851	+	19.0860i	0.572200	+	0.635493i
$903$	36.2858	−	19.4652i	1.20751	−	0.647762i
$904$	−8.28015	−	14.3416i	−0.275394	−	0.476996i
$905$	10.4337	−	18.0716i	0.346826	−	0.600721i
$906$	−24.7233	−	0.772215i	−0.821378	−	0.0256551i
$907$	38.3572	+	27.8681i	1.27363	+	0.925346i	0.999341	−	0.0363009i	$-0.0115575\pi$
$907$	38.3572	+	27.8681i	1.27363	+	0.925346i	0.274289	+	0.961647i	$0.411557\pi$
$908$	2.32458	+	0.244323i	0.0771438	+	0.00810814i
$909$	−9.51627	−	14.9825i	−0.315635	−	0.496939i
$910$	8.95288	−	20.1085i	0.296785	−	0.666590i
$911$	14.6567	+	3.11538i	0.485598	+	0.103217i	0.444204	−	0.895926i	$-0.353487\pi$
$911$	14.6567	+	3.11538i	0.485598	+	0.103217i	0.0413946	+	0.999143i	$0.486820\pi$
$912$	−0.839160	−	11.3973i	−0.0277874	−	0.377401i
$913$	−8.99205	+	4.00352i	−0.297593	+	0.132497i
$914$	−1.24182	+	3.82193i	−0.0410757	+	0.126418i
$915$	−15.6526	−	7.56308i	−0.517460	−	0.250028i
$916$	−3.07659	−	6.91014i	−0.101654	−	0.228318i
$917$	−7.33151	−	34.4921i	−0.242108	−	1.13903i
$918$	13.6592	+	9.69530i	0.450822	+	0.319993i
$919$	−7.57961	−	3.37466i	−0.250028	−	0.111320i	0.277896	−	0.960611i	$-0.410363\pi$
$919$	−7.57961	−	3.37466i	−0.250028	−	0.111320i	−0.527924	+	0.849291i	$0.677030\pi$
$920$	4.35936	−	4.84156i	0.143724	−	0.159621i
$921$	5.68256	+	1.39462i	0.187247	+	0.0459542i
$922$	23.0476	−	31.7223i	0.759033	−	1.04472i
$923$	−0.151229	−	1.43885i	−0.00497776	−	0.0473602i
$924$	19.8896	+	15.4219i	0.654320	+	0.507342i
$925$	−2.61824	+	1.51164i	−0.0860873	+	0.0497025i
$926$	−15.2048	+	11.0469i	−0.499661	+	0.363025i
$927$	7.68154	+	15.4595i	0.252295	+	0.507756i
$928$	−8.34068	+	2.71005i	−0.273796	+	0.0889617i
$929$	−12.1703			−0.399294			−0.199647	−	0.979868i	$-0.563979\pi$
$929$	−12.1703			−0.399294			−0.199647	+	0.979868i	$0.563979\pi$
$930$	9.49775	+	1.67114i	0.311444	+	0.0547989i
$931$	−48.6237			−1.59358
$932$	−1.61858	+	0.525910i	−0.0530185	+	0.0172267i
$933$	2.46146	+	3.62043i	0.0805845	+	0.118528i
$934$	−21.6429	+	15.7245i	−0.708178	+	0.514521i
$935$	10.7014	−	6.17847i	0.349974	−	0.202057i
$936$	12.4415	−	12.1930i	0.406663	−	0.398540i
$937$	−0.302640	−	2.87943i	−0.00988681	−	0.0940667i	0.988466	−	0.151445i	$-0.0483926\pi$
$937$	−0.302640	−	2.87943i	−0.00988681	−	0.0940667i	−0.998353	+	0.0573781i	$0.981726\pi$
$938$	10.7568	−	14.8055i	0.351222	−	0.483416i
$939$	−1.70354	+	6.94130i	−0.0555928	+	0.226521i
$940$	7.29085	−	8.09731i	0.237801	−	0.264105i
$941$	20.9931	+	9.34673i	0.684356	+	0.304695i	0.719305	−	0.694694i	$-0.244460\pi$
$941$	20.9931	+	9.34673i	0.684356	+	0.304695i	−0.0349495	+	0.999389i	$0.511127\pi$
$942$	6.15531	+	2.21471i	0.200551	+	0.0721592i
$943$	−9.07532	−	42.6960i	−0.295533	−	1.39037i
$944$	−1.65022	−	3.70646i	−0.0537102	−	0.120635i
$945$	−13.0174	+	14.7825i	−0.423456	+	0.480874i
$946$	7.42893	−	22.8639i	0.241535	−	0.743369i
$947$	30.5525	−	13.6029i	0.992823	−	0.442033i	0.154964	−	0.987920i	$-0.450474\pi$
$947$	30.5525	−	13.6029i	0.992823	−	0.442033i	0.837859	+	0.545887i	$0.183807\pi$
$948$	2.80779	−	0.206733i	0.0911928	−	0.00671437i
$949$	31.5926	+	6.71522i	1.02554	+	0.217985i
$950$	2.68366	−	6.02759i	0.0870694	−	0.195561i
$951$	−25.5203	+	21.5747i	−0.827551	+	0.699607i
$952$	−12.1528	−	1.27731i	−0.393874	−	0.0413978i
$953$	−40.1764	−	29.1898i	−1.30144	−	0.945552i	−0.301472	−	0.953475i	$-0.597478\pi$
$953$	−40.1764	−	29.1898i	−1.30144	−	0.945552i	−0.999969	+	0.00792304i	$0.997478\pi$
$954$	18.4770	+	3.11786i	0.598214	+	0.100944i
$955$	−1.49519	+	2.58975i	−0.0483833	+	0.0838023i
$956$	1.09537	+	1.89724i	0.0354269	+	0.0613611i
$957$	−27.5251	−	51.3104i	−0.889759	−	1.65863i
$958$	14.1894	+	15.7589i	0.458438	+	0.509147i
$959$	−14.4033	−	44.3288i	−0.465107	−	1.43145i
$960$	1.71607	+	0.234737i	0.0553859	+	0.00757611i
$961$	−30.9095	−	2.36762i	−0.997079	−	0.0763747i
$962$		−	17.5553i		−	0.566006i
$963$	45.3001	−	1.91604i	1.45977	−	0.0617436i
$964$	−6.23919	+	5.61779i	−0.200951	+	0.180937i
$965$	15.8016	+	21.7490i	0.508670	+	0.700125i
$966$	−16.1698	−	39.6012i	−0.520255	−	1.27415i
$967$	−10.0648	−	5.81093i	−0.323663	−	0.186867i	0.329361	−	0.944204i	$-0.393167\pi$
$967$	−10.0648	−	5.81093i	−0.323663	−	0.186867i	−0.653024	+	0.757337i	$0.726500\pi$
$968$	3.67370	−	0.386121i	0.118077	−	0.0124104i
$969$	−25.4933	+	26.5943i	−0.818961	+	0.854333i
$970$	0.160122	−	1.52346i	0.00514120	−	0.0489153i
$971$	−29.7386	−	26.7767i	−0.954356	−	0.859306i	0.0357882	−	0.999359i	$-0.488606\pi$
$971$	−29.7386	−	26.7767i	−0.954356	−	0.859306i	−0.990144	+	0.140054i	$0.955272\pi$
$972$	−13.8826	+	7.09033i	−0.445285	+	0.227422i
$973$	−17.0301	+	80.1204i	−0.545960	+	2.56854i
$974$	25.1327	−	5.34212i	0.805304	−	0.171173i
$975$	9.65762	−	2.80781i	0.309291	−	0.0899217i
$976$	9.54546	+	3.10151i	0.305543	+	0.0992769i
$977$	−7.59832	−	2.46884i	−0.243092	−	0.0789853i	0.184937	−	0.982750i	$-0.440792\pi$
$977$	−7.59832	−	2.46884i	−0.243092	−	0.0789853i	−0.428029	+	0.903765i	$0.640792\pi$
$978$	17.4394	−	5.07024i	0.557651	−	0.162128i
$979$	2.94652	−	0.626301i	0.0941711	−	0.0200167i
$980$	1.53219	−	7.20840i	0.0489441	−	0.230264i
$981$	−9.91064	−	8.19240i	−0.316423	−	0.261563i
$982$	−15.4456	−	13.9073i	−0.492889	−	0.443799i
$983$	5.06348	−	48.1758i	0.161500	−	1.53657i	−0.550766	−	0.834660i	$-0.685664\pi$
$983$	5.06348	−	48.1758i	0.161500	−	1.53657i	0.712266	−	0.701910i	$-0.247669\pi$
$984$	8.03047	−	8.37732i	0.256002	−	0.267059i
$985$	13.4476	−	1.41340i	0.428478	−	0.0450348i
$986$	24.4831	+	14.1354i	0.779702	+	0.450161i
$987$	−27.0434	−	66.2314i	−0.860800	−	2.10817i
$988$	22.5197	+	30.9957i	0.716446	+	0.986103i
$989$	−30.3641	+	27.3399i	−0.965521	+	0.869359i
$990$	0.485969	+	11.4895i	0.0154451	+	0.365161i
$991$		−	33.0901i		−	1.05114i	−0.850750	−	0.525570i	$-0.823852\pi$
$991$		−	33.0901i		−	1.05114i	0.850750	−	0.525570i	$-0.176148\pi$
$992$	−5.56370	−	0.212774i	−0.176648	−	0.00675557i
$993$	−26.9759	−	3.68997i	−0.856054	−	0.117098i
$994$	−0.291859	−	0.898249i	−0.00925720	−	0.0284907i
$995$	17.5903	+	19.5360i	0.557651	+	0.619334i
$996$	2.10244	+	3.91923i	0.0666184	+	0.124186i
$997$	3.17006	+	5.49070i	0.100397	+	0.173892i	0.911848	−	0.410528i	$-0.134655\pi$
$997$	3.17006	+	5.49070i	0.100397	+	0.173892i	−0.811451	+	0.584420i	$0.801322\pi$
$998$	2.99631	−	5.18977i	0.0948467	−	0.164279i
$999$	−4.68914	+	14.9933i	−0.148358	+	0.474367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.11.20	yes	176
3.2	odd	2	inner	930.2.br.a.11.9	✓	176
31.17	odd	30	inner	930.2.br.a.761.9	yes	176
93.17	even	30	inner	930.2.br.a.761.20	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.9	✓	176	3.2	odd	2	inner
930.2.br.a.11.20	yes	176	1.1	even	1	trivial
930.2.br.a.761.9	yes	176	31.17	odd	30	inner
930.2.br.a.761.20	yes	176	93.17	even	30	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.43236 - 0.973832i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.06132 - 1.36879i) q^{6} +(0.396236 + 3.76994i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.10330 - 2.78975i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.43236 - 0.973832i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.06132 - 1.36879i) q^{6} +(0.396236 + 3.76994i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.10330 - 2.78975i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(3.50186 + 1.55913i) q^{11} +(0.586399 - 1.62977i) q^{12} +(1.20728 + 5.67981i) q^{13} +(1.54182 + 3.46298i) q^{14} +(-0.753543 + 1.55954i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.94491 + 1.31116i) q^{17} +(0.187223 - 2.99415i) q^{18} +(6.45384 + 1.37181i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(4.23884 + 5.01404i) q^{21} +(3.81227 + 0.400685i) q^{22} +(-5.27071 - 3.82939i) q^{23} +(0.0540730 - 1.73121i) q^{24} +(0.500000 - 0.866025i) q^{25} +(2.90335 + 5.02875i) q^{26} +(-1.13642 - 5.07036i) q^{27} +(2.53648 + 2.81704i) q^{28} +(-2.71005 - 8.34068i) q^{29} +(-0.234737 + 1.71607i) q^{30} +(0.212774 - 5.56370i) q^{31} -1.00000i q^{32} +(6.53425 - 1.17699i) q^{33} +(-2.39561 + 2.15701i) q^{34} +(-2.22812 - 3.06674i) q^{35} +(-0.747184 - 2.90546i) q^{36} +(-2.61824 - 1.51164i) q^{37} +(6.56188 - 0.689681i) q^{38} +(7.26044 + 6.95984i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(4.97903 + 4.48314i) q^{41} +(5.58080 + 3.45876i) q^{42} +(1.30393 - 6.13450i) q^{43} +(3.74950 - 0.796981i) q^{44} +(0.439388 + 2.96765i) q^{45} +(-6.19609 - 2.01323i) q^{46} +(-10.3627 - 3.36705i) q^{47} +(-0.483546 - 1.66318i) q^{48} +(-7.20840 + 1.53219i) q^{49} +(0.207912 - 0.978148i) q^{50} +(-2.94132 + 4.74589i) q^{51} +(4.31522 + 3.88544i) q^{52} +(-0.652891 + 6.21184i) q^{53} +(-2.64763 - 4.47102i) q^{54} +(-3.81227 + 0.400685i) q^{55} +(3.28285 + 1.89535i) q^{56} +(10.5801 - 4.32004i) q^{57} +(-5.15482 - 7.09500i) q^{58} +(3.01511 - 2.71481i) q^{59} +(0.307047 + 1.70462i) q^{60} +10.0367i q^{61} +(-1.51692 - 5.35714i) q^{62} +(10.9544 + 3.05398i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.88544 - 4.31522i) q^{65} +(5.85074 - 3.13858i) q^{66} +(-2.41388 - 4.18096i) q^{67} +(-1.61180 + 2.79172i) q^{68} +(-11.2787 - 0.352283i) q^{69} +(-3.06674 - 2.22812i) q^{70} +(-0.247791 - 0.0260439i) q^{71} +(-1.60845 - 2.53237i) q^{72} +(2.26238 - 5.08138i) q^{73} +(-2.95722 - 0.628577i) q^{74} +(-0.127184 - 1.72737i) q^{75} +(6.02759 - 2.68366i) q^{76} +(-4.49026 + 13.8196i) q^{77} +(9.05580 + 4.37560i) q^{78} +(0.661137 + 1.48494i) q^{79} +(0.207912 + 0.978148i) q^{80} +(-6.56544 - 6.15589i) q^{81} +(6.12071 + 2.72511i) q^{82} +(-1.71819 + 1.90824i) q^{83} +(6.37647 + 1.56491i) q^{84} +(1.89479 - 2.60795i) q^{85} +(-0.655555 - 6.23719i) q^{86} +(-12.0042 - 9.30771i) q^{87} +(3.31971 - 1.91663i) q^{88} +(0.635760 - 0.461907i) q^{89} +(1.33494 + 2.68662i) q^{90} +(-20.9342 + 6.80192i) q^{91} -6.51496 q^{92} +(-5.11334 - 8.17642i) q^{93} -10.8960 q^{94} +(-6.27509 + 2.03890i) q^{95} +(-0.973832 - 1.43236i) q^{96} +(-1.23929 + 0.900398i) q^{97} +(-6.38212 + 3.68472i) q^{98} +(8.21321 - 8.04914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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