LMFDB - Embedded newform 930.2.br.a.11.9

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			11.9
Character	$\chi$	$=$	930.11
Dual form			930.2.br.a.761.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(1.11822 - 1.32272i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.654747 + 1.60353i) q^{6} +(0.396236 + 3.76994i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.499172 - 2.95818i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(1.11822 - 1.32272i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.654747 + 1.60353i) q^{6} +(0.396236 + 3.76994i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.499172 - 2.95818i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.50186 - 1.55913i) q^{11} +(0.127184 - 1.72737i) q^{12} +(1.20728 + 5.67981i) q^{13} +(-1.54182 - 3.46298i) q^{14} +(0.307047 - 1.70462i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.94491 - 1.31116i) q^{17} +(1.38887 + 2.65914i) q^{18} +(6.45384 + 1.37181i) q^{19} +(0.406737 - 0.913545i) q^{20} +(5.42965 + 3.69151i) q^{21} +(3.81227 + 0.400685i) q^{22} +(5.27071 + 3.82939i) q^{23} +(0.412829 + 1.68213i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.90335 - 5.02875i) q^{26} +(-4.47102 - 2.64763i) 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} +(-5.97814 + 2.88853i) q^{33} +(-2.39561 + 2.15701i) q^{34} +(2.22812 + 3.06674i) q^{35} +(-2.14261 - 2.09981i) q^{36} +(-2.61824 - 1.51164i) q^{37} +(-6.56188 + 0.689681i) q^{38} +(8.86280 + 4.75438i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-4.97903 - 4.48314i) q^{41} +(-6.30464 - 1.83298i) q^{42} +(1.30393 - 6.13450i) q^{43} +(-3.74950 + 0.796981i) q^{44} +(-1.91139 - 2.31227i) q^{45} +(-6.19609 - 2.01323i) q^{46} +(10.3627 + 3.36705i) q^{47} +(-0.912432 - 1.47223i) q^{48} +(-7.20840 + 1.53219i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(1.55876 - 5.36145i) q^{51} +(4.31522 + 3.88544i) q^{52} +(0.652891 - 6.21184i) q^{53} +(5.07036 + 1.13642i) q^{54} +(-3.81227 + 0.400685i) q^{55} +(-3.28285 - 1.89535i) q^{56} +(9.03132 - 7.00264i) q^{57} +(-5.15482 - 7.09500i) q^{58} +(-3.01511 + 2.71481i) q^{59} +(-0.753543 - 1.55954i) 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} +(4.79295 - 4.59450i) q^{66} +(-2.41388 - 4.18096i) q^{67} +(1.61180 - 2.79172i) q^{68} +(10.9590 - 2.68957i) q^{69} +(-3.06674 - 2.22812i) q^{70} +(0.247791 + 0.0260439i) q^{71} +(2.68662 + 1.33494i) q^{72} +(2.26238 - 5.08138i) q^{73} +(2.95722 + 0.628577i) q^{74} +(-0.586399 - 1.62977i) q^{75} +(6.02759 - 2.68366i) q^{76} +(4.49026 - 13.8196i) q^{77} +(-9.89821 - 1.78293i) q^{78} +(0.661137 + 1.48494i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.50166 + 2.95328i) q^{81} +(6.12071 + 2.72511i) q^{82} +(1.71819 - 1.90824i) q^{83} +(6.56249 - 0.204975i) q^{84} +(1.89479 - 2.60795i) q^{85} +(0.655555 + 6.23719i) q^{86} +(14.0628 + 5.74207i) q^{87} +(3.31971 - 1.91663i) q^{88} +(-0.635760 + 0.461907i) q^{89} +(2.53237 + 1.60845i) q^{90} +(-20.9342 + 6.80192i) q^{91} +6.51496 q^{92} +(-7.12128 - 6.50287i) q^{93} -10.8960 q^{94} +(6.27509 - 2.03890i) q^{95} +(1.32272 + 1.11822i) q^{96} +(-1.23929 + 0.900398i) q^{97} +(6.38212 - 3.68472i) q^{98} +(-2.86416 + 11.1374i) 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
$3$	1.11822	−	1.32272i	0.645604	−	0.763672i
$3$	1.11822	−	1.32272i	0.645604	−	0.763672i
$4$	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
$6$	−0.654747	+	1.60353i	−0.267299	+	0.654638i
$7$	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
$9$	−0.499172	−	2.95818i	−0.166391	−	0.986060i
$10$	−0.669131	+	0.743145i	−0.211598	+	0.235003i
$11$	−3.50186	−	1.55913i	−1.05585	−	0.470095i	−0.195981	−	0.980608i	$-0.562789\pi$
$11$	−3.50186	−	1.55913i	−1.05585	−	0.470095i	−0.859870	+	0.510512i	$0.829456\pi$
$12$	0.127184	−	1.72737i	0.0367147	−	0.498650i
$13$	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
$15$	0.307047	−	1.70462i	0.0792791	−	0.440130i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.94491	−	1.31116i	0.714245	−	0.318003i	−0.0172478	−	0.999851i	$-0.505490\pi$
$17$	2.94491	−	1.31116i	0.714245	−	0.318003i	0.731493	+	0.681849i	$0.238824\pi$
$18$	1.38887	+	2.65914i	0.327359	+	0.626766i
$19$	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
$21$	5.42965	+	3.69151i	1.18485	+	0.805553i
$22$	3.81227	+	0.400685i	0.812778	+	0.0854264i
$23$	5.27071	+	3.82939i	1.09902	+	0.798484i	0.980899	−	0.194515i	$-0.0623134\pi$
$23$	5.27071	+	3.82939i	1.09902	+	0.798484i	0.118119	+	0.992999i	$0.462313\pi$
$24$	0.412829	+	1.68213i	0.0842685	+	0.343364i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.90335	−	5.02875i	−0.569394	−	0.986219i
$27$	−4.47102	−	2.64763i	−0.860449	−	0.509537i
$28$	2.53648	+	2.81704i	0.479349	+	0.532371i
$29$	2.71005	+	8.34068i	0.503244	+	1.54882i	0.803703	+	0.595030i	$0.202860\pi$
$29$	2.71005	+	8.34068i	0.503244	+	1.54882i	−0.300460	+	0.953794i	$0.597140\pi$
$30$	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
$33$	−5.97814	+	2.88853i	−1.04066	+	0.502829i
$34$	−2.39561	+	2.15701i	−0.410843	+	0.369925i
$35$	2.22812	+	3.06674i	0.376621	+	0.518374i
$36$	−2.14261	−	2.09981i	−0.357102	−	0.349969i
$37$	−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
$39$	8.86280	+	4.75438i	1.41918	+	0.761310i
$40$	−0.104528	+	0.994522i	−0.0165274	+	0.157248i
$41$	−4.97903	−	4.48314i	−0.777594	−	0.700149i	0.181452	−	0.983400i	$-0.441920\pi$
$41$	−4.97903	−	4.48314i	−0.777594	−	0.700149i	−0.959046	+	0.283251i	$0.908587\pi$
$42$	−6.30464	−	1.83298i	−0.972827	−	0.282835i
$43$	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
$45$	−1.91139	−	2.31227i	−0.284932	−	0.344693i
$46$	−6.19609	−	2.01323i	−0.913564	−	0.296835i
$47$	10.3627	+	3.36705i	1.51156	+	0.491135i	0.943364	−	0.331760i	$-0.107642\pi$
$47$	10.3627	+	3.36705i	1.51156	+	0.491135i	0.568194	+	0.822895i	$0.307642\pi$
$48$	−0.912432	−	1.47223i	−0.131698	−	0.212498i
$49$	−7.20840	+	1.53219i	−1.02977	+	0.218885i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	1.55876	−	5.36145i	0.218270	−	0.750753i
$52$	4.31522	+	3.88544i	0.598413	+	0.538814i
$53$	0.652891	−	6.21184i	0.0896815	−	0.853262i	−0.853524	−	0.521053i	$-0.825539\pi$
$53$	0.652891	−	6.21184i	0.0896815	−	0.853262i	0.943206	−	0.332209i	$-0.107794\pi$
$54$	5.07036	+	1.13642i	0.689988	+	0.154648i
$55$	−3.81227	+	0.400685i	−0.514046	+	0.0540284i
$56$	−3.28285	−	1.89535i	−0.438689	−	0.253277i
$57$	9.03132	−	7.00264i	1.19623	−	0.927522i
$58$	−5.15482	−	7.09500i	−0.676861	−	0.931619i
$59$	−3.01511	+	2.71481i	−0.392534	+	0.353439i	−0.841640	−	0.540040i	$-0.818409\pi$
$59$	−3.01511	+	2.71481i	−0.392534	+	0.353439i	0.449106	+	0.893478i	$0.351743\pi$
$60$	−0.753543	−	1.55954i	−0.0972820	−	0.201336i
$61$			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
$66$	4.79295	−	4.59450i	0.589971	−	0.565544i
$67$	−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
$69$	10.9590	−	2.68957i	1.31931	−	0.323786i
$70$	−3.06674	−	2.22812i	−0.366546	−	0.266311i
$71$	0.247791	+	0.0260439i	0.0294074	+	0.00309084i	0.119221	−	0.992868i	$-0.461960\pi$
$71$	0.247791	+	0.0260439i	0.0294074	+	0.00309084i	−0.0898134	+	0.995959i	$0.528627\pi$
$72$	2.68662	+	1.33494i	0.316622	+	0.157324i
$73$	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
$75$	−0.586399	−	1.62977i	−0.0677115	−	0.188189i
$76$	6.02759	−	2.68366i	0.691412	−	0.307837i
$77$	4.49026	−	13.8196i	0.511712	−	1.57489i
$78$	−9.89821	−	1.78293i	−1.12075	−	0.201877i
$79$	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
$81$	−8.50166	+	2.95328i	−0.944628	+	0.328142i
$82$	6.12071	+	2.72511i	0.675919	+	0.300939i
$83$	1.71819	−	1.90824i	0.188595	−	0.209456i	−0.641431	−	0.767181i	$-0.721659\pi$
$83$	1.71819	−	1.90824i	0.188595	−	0.209456i	0.830026	+	0.557725i	$0.188325\pi$
$84$	6.56249	−	0.204975i	0.716027	−	0.0223646i
$85$	1.89479	−	2.60795i	0.205519	−	0.282872i
$86$	0.655555	+	6.23719i	0.0706904	+	0.672574i
$87$	14.0628	+	5.74207i	1.50769	+	0.615614i
$88$	3.31971	−	1.91663i	0.353882	−	0.204314i
$89$	−0.635760	+	0.461907i	−0.0673904	+	0.0489620i	−0.620970	−	0.783834i	$-0.713261\pi$
$89$	−0.635760	+	0.461907i	−0.0673904	+	0.0489620i	0.553580	+	0.832796i	$0.313261\pi$
$90$	2.53237	+	1.60845i	0.266935	+	0.169546i
$91$	−20.9342	+	6.80192i	−2.19450	+	0.713035i
$92$	6.51496			0.679231
$93$	−7.12128	−	6.50287i	−0.738442	−	0.674317i
$94$	−10.8960			−1.12384
$95$	6.27509	−	2.03890i	0.643811	−	0.209187i
$96$	1.32272	+	1.11822i	0.134999	+	0.114128i
$97$	−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
$99$	−2.86416	+	11.1374i	−0.287859	+	1.11935i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−3.47758	+	4.78648i	−0.346032	+	0.476272i	−0.946191	−	0.323608i	$-0.895104\pi$
$101$	−3.47758	+	4.78648i	−0.346032	+	0.476272i	0.600159	+	0.799881i	$0.295104\pi$
$102$	0.174310	+	5.58073i	0.0172593	+	0.552574i
$103$	−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
$105$	6.54797	+	0.482115i	0.639016	+	0.0470496i
$106$	1.29863	+	6.10957i	0.126134	+	0.593414i
$107$	−6.14722	−	13.8069i	−0.594274	−	1.33476i	−0.920970	−	0.389633i	$-0.872602\pi$
$107$	−6.14722	−	13.8069i	−0.594274	−	1.33476i	0.326696	−	0.945130i	$-0.394065\pi$
$108$	−5.17337	+	0.486024i	−0.497808	+	0.0467677i
$109$	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
$111$	−4.92725	+	1.77285i	−0.467674	+	0.168272i
$112$	3.70787	+	0.788132i	0.350361	+	0.0744714i
$113$	−6.73568	+	15.1286i	−0.633640	+	1.42318i	0.256073	+	0.966657i	$0.417571\pi$
$113$	−6.73568	+	15.1286i	−0.633640	+	1.42318i	−0.889713	+	0.456520i	$0.849096\pi$
$114$	−6.42536	+	9.45074i	−0.601790	+	0.885143i
$115$	6.47927	+	0.680998i	0.604195	+	0.0635034i
$116$	7.09500	+	5.15482i	0.658754	+	0.478613i
$117$	16.1993	−	6.40655i	1.49762	−	0.592286i
$118$	2.02861	−	3.51366i	0.186749	−	0.323459i
$119$	6.10986	+	10.5826i	0.560090	+	0.970105i
$120$	1.19859	+	1.25036i	0.109416	+	0.114141i
$121$	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
$126$	−9.47449	+	6.28960i	−0.844054	+	0.560322i
$127$	−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
$129$	−6.65614	−	8.58445i	−0.586041	−	0.755818i
$130$	−5.02875	−	2.90335i	−0.441051	−	0.254641i
$131$	9.25144	−	0.972365i	0.808302	−	0.0849559i	0.308643	−	0.951178i	$-0.400125\pi$
$131$	9.25144	−	0.972365i	0.808302	−	0.0849559i	0.499659	+	0.866222i	$0.333459\pi$
$132$	−3.13858	+	5.85074i	−0.273178	+	0.509241i
$133$	−2.61438	+	24.8741i	−0.226695	+	2.15686i
$134$	3.58772	+	3.23040i	0.309932	+	0.279064i
$135$	−5.19584	−	0.0574027i	−0.447186	−	0.00494044i
$136$	−0.670225	+	3.15316i	−0.0574713	+	0.270381i
$137$	12.0272	−	2.55646i	1.02755	−	0.218413i	0.336855	−	0.941557i	$-0.390637\pi$
$137$	12.0272	−	2.55646i	1.02755	−	0.218413i	0.690698	+	0.723143i	$0.257303\pi$
$138$	−9.59153	+	5.94445i	−0.816485	+	0.506025i
$139$	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
$141$	16.0414	−	9.94186i	1.35093	−	0.837256i
$142$	−0.243711	+	0.0518024i	−0.0204518	+	0.00434716i
$143$	4.62783	−	21.7722i	0.386999	−	1.82069i
$144$	−2.96765	−	0.439388i	−0.247304	−	0.0366156i
$145$	6.51731	+	5.86821i	0.541233	+	0.487328i
$146$	−0.581415	+	5.53179i	−0.0481182	+	0.457815i
$147$	−6.03391	+	11.2480i	−0.497668	+	0.927720i
$148$	−3.00673	+	0.316020i	−0.247151	+	0.0259766i
$149$	−6.33942	−	3.66006i	−0.519345	−	0.299844i	0.217321	−	0.976100i	$-0.430268\pi$
$149$	−6.33942	−	3.66006i	−0.519345	−	0.299844i	−0.736667	+	0.676256i	$0.763601\pi$
$150$	1.06132	+	1.36879i	0.0866567	+	0.111761i
$151$	−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
$153$	−5.34866	−	8.05708i	−0.432413	−	0.651376i
$154$			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
$159$	−7.48645	−	7.80980i	−0.593714	−	0.619357i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−12.3481	+	21.3876i	−0.973169	+	1.68558i
$162$	7.17294	−	5.43589i	0.563560	−	0.427084i
$163$	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
$165$	−3.73296	+	5.49061i	−0.290610	+	0.427444i
$166$	−1.04441	+	2.34579i	−0.0810622	+	0.182069i
$167$	−10.3523	−	2.20044i	−0.801083	−	0.170275i	−0.210861	−	0.977516i	$-0.567627\pi$
$167$	−10.3523	−	2.20044i	−0.801083	−	0.170275i	−0.590222	+	0.807241i	$0.700960\pi$
$168$	−6.17796	+	2.22286i	−0.476640	+	0.171498i
$169$	−18.9266	+	8.42668i	−1.45589	+	0.648206i
$170$	−0.996149	+	3.06583i	−0.0764011	+	0.235138i
$171$	0.836476	−	19.7764i	0.0639669	−	1.51234i
$172$	−2.55087	−	5.72935i	−0.194502	−	0.436858i
$173$	4.58062	+	21.5501i	0.348258	+	1.63843i	0.708604	+	0.705607i	$0.249325\pi$
$173$	4.58062	+	21.5501i	0.348258	+	1.63843i	−0.360346	+	0.932819i	$0.617341\pi$
$174$	−15.1489	−	1.11539i	−1.14844	−	0.0845574i
$175$	3.46298	+	1.54182i	0.261777	+	0.116550i
$176$	−2.56496	+	2.84867i	−0.193341	+	0.214727i
$177$	0.219386	+	7.02390i	0.0164901	+	0.527949i
$178$	0.461907	−	0.635760i	0.0346214	−	0.0476522i
$179$	−1.91175	−	18.1891i	−0.142891	−	1.35952i	−0.797395	−	0.603458i	$-0.793789\pi$
$179$	−1.91175	−	18.1891i	−0.142891	−	1.35952i	0.654504	−	0.756059i	$-0.272878\pi$
$180$	−2.90546	−	0.747184i	−0.216560	−	0.0556918i
$181$	−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
$183$	13.2757	+	11.2232i	0.981370	+	0.829644i
$184$	−6.19609	+	2.01323i	−0.456782	+	0.148417i
$185$	−3.02329			−0.222277
$186$	8.78224	+	3.98400i	0.643945	+	0.292121i
$187$	−12.3569			−0.903629
$188$	10.3627	−	3.36705i	0.755779	−	0.245567i
$189$	8.20982	−	17.9046i	0.597176	−	1.30237i
$190$	−5.33791	+	3.87822i	−0.387253	+	0.281356i
$191$	−2.58975	+	1.49519i	−0.187388	+	0.108188i	−0.590759	−	0.806848i	$-0.701172\pi$
$191$	−2.58975	+	1.49519i	−0.187388	+	0.108188i	0.403371	+	0.915036i	$0.367838\pi$
$192$	−1.60353	−	0.654747i	−0.115725	−	0.0472523i
$193$	−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
$195$	10.0526	−	0.313986i	0.719882	−	0.0224850i
$196$	−4.93111	+	5.47656i	−0.352222	+	0.391183i
$197$	12.3527	+	5.49978i	0.880094	+	0.391843i	0.796487	−	0.604656i	$-0.206689\pi$
$197$	12.3527	+	5.49978i	0.880094	+	0.391843i	0.0836068	+	0.996499i	$0.473356\pi$
$198$	−0.717676	−	11.4774i	−0.0510030	−	0.815662i
$199$	−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
$201$	−8.22947	−	1.48235i	−0.580462	−	0.104557i
$202$	1.82827	−	5.62684i	0.128637	−	0.395903i
$203$	−30.3700	+	13.5216i	−2.13156	+	0.949030i
$204$	−1.89032	−	5.25372i	−0.132349	−	0.367834i
$205$	−6.55354	−	1.39300i	−0.457719	−	0.0972912i
$206$	2.34046	−	5.25676i	0.163068	−	0.366256i
$207$	8.69705	−	17.5032i	0.604487	−	1.21656i
$208$	5.77489	+	0.606965i	0.400417	+	0.0420855i
$209$	−20.4616	−	14.8663i	−1.41536	−	1.02832i
$210$	−6.37647	+	1.56491i	−0.440018	+	0.107989i
$211$	−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
$213$	0.311533	−	0.298635i	0.0213459	−	0.0204621i
$214$	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
$219$	−4.19141	−	8.67459i	−0.283229	−	0.586174i
$220$	−2.84867	+	2.56496i	−0.192057	+	0.172929i
$221$	11.0025	+	15.1436i	0.740106	+	1.01867i
$222$	4.13825	−	3.20869i	0.277741	−	0.215353i
$223$	−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
$225$	−2.81144	−	1.04679i	−0.187430	−	0.0697863i
$226$	1.73102	−	16.4696i	0.115146	−	1.09554i
$227$	−1.73701	−	1.56401i	−0.115290	−	0.103807i	0.609470	−	0.792809i	$-0.291382\pi$
$227$	−1.73701	−	1.56401i	−0.115290	−	0.103807i	−0.724759	+	0.689002i	$0.758049\pi$
$228$	3.19045	−	10.9737i	0.211292	−	0.726753i
$229$	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
$231$	−13.2583	−	21.3927i	−0.872335	−	1.40754i
$232$	−8.34068	−	2.71005i	−0.547592	−	0.177923i
$233$	1.61858	+	0.525910i	0.106037	+	0.0344535i	0.361555	−	0.932351i	$-0.382246\pi$
$233$	1.61858	+	0.525910i	0.106037	+	0.0344535i	−0.255518	+	0.966804i	$0.582246\pi$
$234$	−13.4267	+	11.0988i	−0.877729	+	0.725554i
$235$	10.6579	−	2.26541i	0.695245	−	0.147779i
$236$	−0.843545	+	3.96857i	−0.0549101	+	0.258332i
$237$	2.70345	+	0.785988i	0.175608	+	0.0510554i
$238$	−9.08103	−	8.17660i	−0.588636	−	0.530010i
$239$	0.228995	−	2.17874i	0.0148125	−	0.140931i	−0.984616	−	0.174731i	$-0.944094\pi$
$239$	0.228995	−	2.17874i	0.0148125	−	0.140931i	0.999429	+	0.0338002i	$0.0107610\pi$
$240$	−1.52631	−	0.818775i	−0.0985226	−	0.0528517i
$241$	−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
$243$	−5.60036	+	14.5477i	−0.359263	+	0.933236i
$244$	5.89942	+	8.11985i	0.377672	+	0.519820i
$245$	−5.47656	+	4.93111i	−0.349884	+	0.315037i
$246$	10.4489	−	5.04870i	0.666195	−	0.321893i
$247$			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	0.541025	−	0.841007i	$-0.318037\pi$
$251$	−5.57558	−	6.19231i	−0.351928	−	0.390855i	−0.892952	+	0.450152i	$0.851370\pi$
$252$	7.06718	−	8.90954i	0.445190	−	0.561248i
$253$	−12.4868	−	21.6277i	−0.785037	−	1.35972i
$254$	2.08525	−	3.61175i	0.130840	−	0.226622i
$255$	−1.33080	−	5.42253i	−0.0833379	−	0.339572i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−10.7218	−	1.12691i	−0.668807	−	0.0702944i	−0.235961	−	0.971762i	$-0.575824\pi$
$257$	−10.7218	−	1.12691i	−0.668807	−	0.0702944i	−0.432846	+	0.901468i	$0.642490\pi$
$258$	8.98311	+	6.10743i	0.559264	+	0.380232i
$259$	4.66136	−	10.4696i	0.289643	−	0.650548i
$260$	5.67981	+	1.20728i	0.352247	+	0.0748724i
$261$	23.3204	−	12.1802i	1.44350	−	0.753938i
$262$	−8.49816	+	3.78363i	−0.525018	+	0.233753i
$263$	−1.39511	+	4.29372i	−0.0860264	+	0.264762i	−0.984811	−	0.173628i	$-0.944451\pi$
$263$	−1.39511	+	4.29372i	−0.0860264	+	0.264762i	0.898785	+	0.438390i	$0.144451\pi$
$264$	1.17699	−	6.53425i	0.0724388	−	0.402156i
$265$	−2.54050	−	5.70606i	−0.156062	−	0.350521i
$266$	−5.20011	−	24.4646i	−0.318839	−	1.50002i
$267$	−0.0999463	+	1.35744i	−0.00611661	+	0.0830743i
$268$	−4.41037	−	1.96362i	−0.269406	−	0.119947i
$269$	−13.4283	+	14.9136i	−0.818735	+	0.909298i	−0.997210	−	0.0746468i	$-0.976217\pi$
$269$	−13.4283	+	14.9136i	−0.818735	+	0.909298i	0.178475	+	0.983944i	$0.442884\pi$
$270$	4.95927	−	1.55101i	0.301812	−	0.0943914i
$271$	−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
$273$	−14.4120	+	35.2961i	−0.872251	+	2.13621i
$274$	−10.6486	+	6.14795i	−0.643303	+	0.371411i
$275$	−3.10118	+	2.25314i	−0.187008	+	0.135869i
$276$	7.28515	−	8.61746i	0.438514	−	0.518710i
$277$	−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
$279$	−16.5646	+	2.14782i	−0.991698	+	0.128586i
$280$	−3.79070			−0.226538
$281$	−4.05756	+	1.31838i	−0.242053	+	0.0786479i	−0.427531	−	0.904000i	$-0.640617\pi$
$281$	−4.05756	+	1.31838i	−0.242053	+	0.0786479i	0.185478	+	0.982648i	$0.440617\pi$
$282$	−12.1841	+	14.4124i	−0.725554	+	0.858243i
$283$	−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
$285$	4.32004	−	10.5801i	0.255897	−	0.626712i
$286$	2.32666	+	22.1367i	0.137578	+	1.30897i
$287$	14.9283	−	20.5470i	0.881189	−	1.21285i
$288$	2.95818	−	0.499172i	0.174312	−	0.0294140i
$289$	−4.42187	+	4.91098i	−0.260110	+	0.288881i
$290$	−8.01171	−	3.56704i	−0.470464	−	0.209464i
$291$	−0.194826	+	2.64608i	−0.0114209	+	0.155116i
$292$	−1.15646	−	5.44072i	−0.0676767	−	0.318394i
$293$	−0.363693	−	0.816869i	−0.0212472	−	0.0477220i	0.902610	−	0.430459i	$-0.141648\pi$
$293$	−0.363693	−	0.816869i	−0.0212472	−	0.0477220i	−0.923857	+	0.382737i	$0.874982\pi$
$294$	2.26276	−	12.5621i	0.131967	−	0.732635i
$295$	−1.25375	+	3.85865i	−0.0729963	+	0.224659i
$296$	2.76191	−	1.22968i	0.160533	−	0.0714738i
$297$	11.5289	+	16.2425i	0.668976	+	0.942488i
$298$	7.16017	+	1.52194i	0.414777	+	0.0881636i
$299$	−15.3870	+	34.5598i	−0.889854	+	1.99864i
$300$	−1.43236	−	0.973832i	−0.0826973	−	0.0562242i
$301$	23.6434	+	2.48502i	1.36278	+	0.143234i
$302$	11.5536	+	8.39415i	0.664833	+	0.483029i
$303$	2.44247	+	9.95219i	0.140316	+	0.571739i
$304$	3.29901	−	5.71406i	0.189211	−	0.327724i
$305$	5.01835	+	8.69203i	0.287350	+	0.497704i
$306$	7.57665	+	6.00991i	0.433128	+	0.343564i
$307$	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	$-0.977169\pi$
$311$		−	2.52760i		−	0.143327i	0.997429	−	0.0716635i	$-0.0228308\pi$
$312$	−9.05580	+	4.37560i	−0.512683	+	0.247720i
$313$	−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
$315$	7.95977	−	8.12201i	0.448482	−	0.457623i
$316$	1.40770	+	0.812733i	0.0791891	+	0.0457198i
$317$	19.1881	−	2.01675i	1.07771	−	0.113272i	0.451000	−	0.892524i	$-0.351067\pi$
$317$	19.1881	−	2.01675i	1.07771	−	0.113272i	0.626711	+	0.779252i	$0.284401\pi$
$318$	9.53340	+	5.11412i	0.534606	+	0.286785i
$319$	3.51397	−	33.4332i	0.196745	−	1.87190i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	−25.1366	−	7.30808i	−1.40299	−	0.407897i
$322$	5.13464	−	24.1566i	0.286142	−	1.34619i
$323$	20.8046	−	4.42216i	1.15760	−	0.246056i
$324$	−5.14209	+	7.38640i	−0.285672	+	0.410356i
$325$	5.52250	+	1.79437i	0.306333	+	0.0995337i
$326$	−9.97235	−	3.24021i	−0.552317	−	0.179459i
$327$	−3.91078	−	6.31014i	−0.216267	−	0.348952i
$328$	6.55354	−	1.39300i	0.361859	−	0.0769154i
$329$	−8.58748	+	40.4009i	−0.473443	+	2.22738i
$330$	1.85356	−	6.37543i	0.102035	−	0.350956i
$331$	−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
$333$	−3.16476	+	8.49980i	−0.173428	+	0.465786i
$334$	10.5256	−	1.10628i	0.575934	−	0.0605331i
$335$	−4.18096	−	2.41388i	−0.228430	−	0.131884i
$336$	5.18869	−	4.02316i	0.283066	−	0.219482i
$337$	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
$339$	12.4789	+	25.8265i	0.677761	+	1.40270i
$340$		−	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
$345$	8.14601	−	7.80874i	0.438566	−	0.420409i
$346$	−11.0158	−	19.0799i	−0.592212	−	1.02574i
$347$	16.4142	−	28.4303i	0.881161	−	1.52622i	0.0311104	−	0.999516i	$-0.490096\pi$
$347$	16.4142	−	28.4303i	0.881161	−	1.52622i	0.850051	−	0.526700i	$-0.176571\pi$
$348$	14.7521	−	3.62048i	0.790798	−	0.194078i
$349$	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
$351$	9.64025	−	28.5910i	0.514559	−	1.52607i
$352$	1.55913	−	3.50186i	0.0831019	−	0.186650i
$353$	−12.9693	−	2.75671i	−0.690285	−	0.146725i	−0.150604	−	0.988594i	$-0.548122\pi$
$353$	−12.9693	−	2.75671i	−0.690285	−	0.146725i	−0.539681	+	0.841869i	$0.681455\pi$
$354$	−2.37915	−	6.61233i	−0.126451	−	0.351441i
$355$	0.227615	−	0.101341i	0.0120806	−	0.00537861i
$356$	−0.242839	+	0.747380i	−0.0128704	+	0.0396111i
$357$	20.8300	+	3.75203i	1.10244	+	0.198578i
$358$	7.43892	+	16.7081i	0.393159	+	0.883050i
$359$	−6.31822	−	29.7249i	−0.333463	−	1.56882i	−0.751090	−	0.660200i	$-0.770471\pi$
$359$	−6.31822	−	29.7249i	−0.333463	−	1.56882i	0.417627	−	0.908619i	$-0.362862\pi$
$360$	2.99415	−	0.187223i	0.157806	−	0.00986752i
$361$	22.4128	+	9.97884i	1.17962	+	0.525202i
$362$	13.9630	−	15.5074i	0.733877	−	0.815053i
$363$	6.39496	−	0.199742i	0.335648	−	0.0104837i
$364$	−12.9380	+	17.8077i	−0.678137	+	0.933375i
$365$	−0.581415	−	5.53179i	−0.0304326	−	0.289547i
$366$	−16.0941	−	6.57149i	−0.841254	−	0.343497i
$367$	−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
$369$	−10.7765	+	16.9667i	−0.561005	+	0.883253i
$370$	2.87532	−	0.934247i	0.149481	−	0.0485692i
$371$	23.6770			1.22925
$372$	−9.58353	−	1.07515i	−0.496883	−	0.0557440i
$373$	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
$375$	−1.32272	−	1.11822i	−0.0683049	−	0.0577446i
$376$	−8.81505	+	6.40451i	−0.454602	+	0.330287i
$377$	−44.1017	+	25.4621i	−2.27135	+	1.31137i
$378$	−2.27518	+	19.5652i	−0.117023	+	1.00633i
$379$	−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
$381$	0.225511	+	7.21999i	0.0115533	+	0.369891i
$382$	2.00096	−	2.22229i	0.102378	−	0.113702i
$383$	−14.0927	−	6.27449i	−0.720105	−	0.320611i	0.0137615	−	0.999905i	$-0.495619\pi$
$383$	−14.0927	−	6.27449i	−0.720105	−	0.320611i	−0.733866	+	0.679294i	$0.762286\pi$
$384$	1.72737	+	0.127184i	0.0881497	+	0.00649031i
$385$	−3.02112	−	14.2132i	−0.153970	−	0.724374i
$386$	10.9344	+	24.5590i	0.556546	+	1.25002i
$387$	−18.7978	−	0.795087i	−0.955548	−	0.0404165i
$388$	−0.473367	+	1.45688i	−0.0240316	+	0.0739616i
$389$	−27.1251	+	12.0769i	−1.37530	+	0.612321i	−0.955417	−	0.295259i	$-0.904594\pi$
$389$	−27.1251	+	12.0769i	−1.37530	+	0.612321i	−0.419878	+	0.907580i	$0.637927\pi$
$390$	−9.46356	+	3.40504i	−0.479206	+	0.172421i
$391$	20.5427	+	4.36649i	1.03889	+	0.220823i
$392$	2.99742	−	6.73231i	0.151393	−	0.340033i
$393$	9.05897	−	13.3244i	0.456965	−	0.672126i
$394$	−13.4476	−	1.41340i	−0.677482	−	0.0712063i
$395$	1.31503	+	0.955425i	0.0661663	+	0.0480727i
$396$	4.22926	+	10.6939i	0.212528	+	0.537387i
$397$	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
$399$	29.9780	+	31.2728i	1.50078	+	1.56560i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−7.07767	−	21.7828i	−0.353442	−	1.08778i	−0.956907	−	0.290393i	$-0.906214\pi$
$401$	−7.07767	−	21.7828i	−0.353442	−	1.08778i	0.603465	−	0.797389i	$-0.293786\pi$
$402$	8.28476	−	1.13325i	0.413206	−	0.0565215i
$403$	31.8576	−	5.50843i	1.58694	−	0.274395i
$404$			5.91641i			0.294353i
$405$	−5.88601	+	6.80844i	−0.292478	+	0.338314i
$406$	24.7052	−	22.2447i	1.22610	−	1.10398i
$407$	6.81188	+	9.37575i	0.337652	+	0.464739i
$408$	3.42129	+	4.41244i	0.169379	+	0.218449i
$409$	−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
$411$	10.0676	−	18.7673i	0.496596	−	0.925722i
$412$	−0.601482	+	5.72272i	−0.0296329	+	0.281938i
$413$	−11.4294	−	10.2911i	−0.562403	−	0.506390i
$414$	−2.86259	+	19.3341i	−0.140689	+	0.950219i
$415$	0.533873	−	2.51168i	0.0262068	−	0.123293i
$416$	−5.67981	+	1.20728i	−0.278476	+	0.0591918i
$417$	31.8123	−	19.7160i	1.55786	−	0.965497i
$418$	24.0541	+	7.81565i	1.17652	+	0.382276i
$419$	18.3640	+	5.96684i	0.897142	+	0.291499i	0.721057	−	0.692876i	$-0.243657\pi$
$419$	18.3640	+	5.96684i	0.897142	+	0.291499i	0.176085	+	0.984375i	$0.443657\pi$
$420$	5.58080	−	3.45876i	0.272315	−	0.168770i
$421$	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
$423$	4.78757	−	32.3355i	0.232780	−	1.57221i
$424$	4.64173	+	4.17943i	0.225422	+	0.202971i
$425$	0.336958	−	3.20595i	0.0163449	−	0.155511i
$426$	−0.204002	+	0.380288i	−0.00988395	+	0.0184250i
$427$	−37.8377	+	3.97690i	−1.83109	+	0.192456i
$428$	−13.0887	−	7.55676i	−0.632666	−	0.365270i
$429$	−23.6236	−	30.4674i	−1.14056	−	1.47098i
$430$	3.68632	+	5.07379i	0.177770	+	0.244680i
$431$	9.80730	−	8.83054i	0.472401	−	0.425352i	−0.398232	−	0.917285i	$-0.630376\pi$
$431$	9.80730	−	8.83054i	0.472401	−	0.425352i	0.870633	+	0.491933i	$0.163709\pi$
$432$	−3.89967	+	3.43403i	−0.187623	+	0.165220i
$433$		−	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
$438$	6.66686	+	6.95481i	0.318555	+	0.332314i
$439$	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
$441$	8.13072	+	20.5589i	0.387177	+	0.978995i
$442$	−15.1436	−	11.0025i	−0.720307	−	0.523334i
$443$	27.2032	+	2.85917i	1.29246	+	0.135843i	0.725684	−	0.688028i	$-0.241523\pi$
$443$	27.2032	+	2.85917i	1.29246	+	0.135843i	0.566777	+	0.823871i	$0.308190\pi$
$444$	−2.94417	+	4.33043i	−0.139724	+	0.205513i
$445$	−0.319631	+	0.717903i	−0.0151520	+	0.0340319i
$446$	13.4061	+	2.84956i	0.634799	+	0.134931i
$447$	−11.9301	+	4.29251i	−0.564274	+	0.203029i
$448$	3.46298	−	1.54182i	0.163610	−	0.0728441i
$449$	7.99247	−	24.5983i	0.377188	−	1.16087i	−0.564803	−	0.825226i	$-0.691048\pi$
$449$	7.99247	−	24.5983i	0.377188	−	1.16087i	0.941991	−	0.335639i	$-0.108952\pi$
$450$	2.99732	+	0.126777i	0.141295	+	0.00597631i
$451$	10.4461	+	23.4623i	0.491887	+	1.10480i
$452$	3.44308	+	16.1984i	0.161949	+	0.761910i
$453$	−24.6686	−	1.81631i	−1.15903	−	0.0853375i
$454$	2.13530	+	0.950698i	0.100215	+	0.0446185i
$455$	−14.7286	+	16.3577i	−0.690485	+	0.766862i
$456$	0.356775	+	11.4225i	0.0167075	+	0.534909i
$457$	−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
$459$	−16.6382	−	1.93481i	−0.776606	−	0.0903092i
$460$	5.64212	−	3.25748i	0.263065	−	0.151881i
$461$	−31.7223	+	23.0476i	−1.47746	+	1.07344i	−0.499092	+	0.866549i	$0.666333\pi$
$461$	−31.7223	+	23.0476i	−1.47746	+	1.07344i	−0.978365	+	0.206886i	$0.933667\pi$
$462$	19.2201	+	16.2486i	0.894202	+	0.755953i
$463$	−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
$465$	−9.41865	−	2.07101i	−0.436779	−	0.0960409i
$466$	−1.70188			−0.0788380
$467$	25.4428	−	8.26686i	1.17735	−	0.382544i	0.345969	−	0.938246i	$-0.387550\pi$
$467$	25.4428	−	8.26686i	1.17735	−	0.382544i	0.831382	+	0.555702i	$0.187550\pi$
$468$	9.33980	−	14.7047i	0.431732	−	0.679725i
$469$	14.8055	−	10.7568i	0.683653	−	0.496703i
$470$	−9.43622	+	5.44800i	−0.435260	+	0.251298i
$471$	6.05622	+	2.47285i	0.279056	+	0.113943i
$472$	−0.424096	−	4.03500i	−0.0195206	−	0.185726i
$473$	−14.1307	+	19.4492i	−0.649729	+	0.894275i
$474$	−2.81402	+	0.0878938i	−0.129252	+	0.00403710i
$475$	4.41494	−	4.90329i	0.202571	−	0.224978i
$476$	11.1633	+	4.97021i	0.511668	+	0.227809i
$477$	−18.7017	+	1.16941i	−0.856290	+	0.0535434i
$478$	0.455481	+	2.14287i	0.0208332	+	0.0980126i
$479$	−8.62513	−	19.3724i	−0.394092	−	0.885146i	−0.996230	−	0.0867535i	$-0.972351\pi$
$479$	−8.62513	−	19.3724i	−0.394092	−	0.885146i	0.602137	−	0.798392i	$-0.294316\pi$
$480$	1.70462	+	0.307047i	0.0778048	+	0.0140147i
$481$	5.42489	−	16.6961i	0.247354	−	0.761277i
$482$	7.66982	−	3.41482i	0.349351	−	0.155541i
$483$	14.4819	+	40.2491i	0.658947	+	1.83140i
$484$	3.61321	+	0.768012i	0.164237	+	0.0349096i
$485$	−0.623059	+	1.39941i	−0.0282917	+	0.0635441i
$486$	0.830765	−	15.5663i	0.0376843	−	0.706102i
$487$	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
$489$	17.6381	−	4.32874i	0.797622	−	0.195752i
$490$	3.68472	−	6.38212i	0.166459	−	0.288315i
$491$	10.3920	+	17.9996i	0.468987	+	0.812309i	0.999372	−	0.0354484i	$-0.0112859\pi$
$491$	10.3920	+	17.9996i	0.468987	+	0.812309i	−0.530385	+	0.847757i	$0.677953\pi$
$492$	−8.37732	+	8.03047i	−0.377679	+	0.362042i
$493$	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
$498$	1.93494	+	4.00458i	0.0867067	+	0.179449i
$499$	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
$501$	−14.4867	+	11.2326i	−0.647217	+	0.501834i
$502$	7.21622	+	4.16629i	0.322076	+	0.185951i
$503$	−40.9598	+	4.30504i	−1.82631	+	0.191952i	−0.954562	−	0.298011i	$-0.903677\pi$
$503$	−40.9598	+	4.30504i	−1.82631	+	0.191952i	−0.871743	+	0.489963i	$0.837010\pi$
$504$	−3.96809	+	10.6574i	−0.176753	+	0.474716i
$505$	−0.618434	+	5.88400i	−0.0275199	+	0.261835i
$506$	18.5590	+	16.7106i	0.825047	+	0.742876i
$507$	−10.0180	+	34.4575i	−0.444915	+	1.53031i
$508$	−0.867094	+	4.07936i	−0.0384711	+	0.180992i
$509$	9.09295	−	1.93277i	0.403038	−	0.0856683i	−0.00193257	−	0.999998i	$-0.500615\pi$
$509$	9.09295	−	1.93277i	0.403038	−	0.0856683i	0.404970	+	0.914330i	$0.367282\pi$
$510$	2.94132	+	4.74589i	0.130244	+	0.210152i
$511$	20.0529	+	6.51559i	0.887089	+	0.288233i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−25.2232	−	23.2208i	−1.11363	−	1.02522i
$514$	10.5453	−	2.24146i	0.465131	−	0.0988667i
$515$	−1.19637	+	5.62849i	−0.0527185	+	0.248021i
$516$	−10.4307	−	3.03258i	−0.459188	−	0.133502i
$517$	−31.0391	−	27.9478i	−1.36510	−	1.22914i
$518$	−1.19794	+	11.3976i	−0.0526343	+	0.500782i
$519$	33.6269	+	18.0389i	1.47606	+	0.791819i
$520$	−5.77489	+	0.606965i	−0.253246	+	0.0266172i
$521$	−17.9336	−	10.3540i	−0.785687	−	0.453616i	0.0527551	−	0.998607i	$-0.483200\pi$
$521$	−17.9336	−	10.3540i	−0.785687	−	0.453616i	−0.838442	+	0.544991i	$0.816533\pi$
$522$	−18.4152	+	18.7905i	−0.806009	+	0.822438i
$523$	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
$525$	5.91176	−	2.85646i	0.258011	−	0.124666i
$526$		−	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
$531$	9.53597	+	7.56407i	0.413826	+	0.328253i
$532$	12.5056	+	21.6603i	0.542185	+	0.939093i
$533$	19.4523	−	33.6924i	0.842573	−	1.45938i
$534$	−0.324419	−	1.32189i	−0.0140390	−	0.0572038i
$535$	−12.2271	−	8.88351i	−0.528623	−	0.384067i
$536$	4.80130	+	0.504637i	0.207385	+	0.0217970i
$537$	−26.1968	−	17.8107i	−1.13048	−	0.768588i
$538$	8.16248	−	18.3332i	0.351909	−	0.790402i
$539$	27.6317	+	5.87330i	1.19018	+	0.252981i
$540$	−4.23726	+	3.00760i	−0.182343	+	0.129426i
$541$	−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
$543$	−6.40724	+	35.5708i	−0.274961	+	1.52649i
$544$	1.31116	+	2.94491i	0.0562154	+	0.126262i
$545$	−0.891131	−	4.19244i	−0.0381719	−	0.179585i
$546$	2.79950	−	38.0221i	0.119808	−	1.62719i
$547$	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
$549$	29.6903	−	5.01003i	1.26715	−	0.213823i
$550$	2.25314	−	3.10118i	0.0960741	−	0.132235i
$551$	6.04844	+	57.5470i	0.257672	+	2.45159i
$552$	−4.26565	+	10.4469i	−0.181558	+	0.444651i
$553$	−5.33616	+	3.08083i	−0.226916	+	0.131010i
$554$	22.6196	−	16.4341i	0.961017	−	0.698219i
$555$	−3.38070	+	3.99896i	−0.143503	+	0.169746i
$556$	20.5506	−	6.67730i	0.871541	−	0.283181i
$557$	−30.1693			−1.27831			−0.639157	−	0.769076i	$-0.720717\pi$
$557$	−30.1693			−1.27831			−0.639157	+	0.769076i	$0.720717\pi$
$558$	15.0902	−	7.16145i	0.638818	−	0.303168i
$559$	36.4170			1.54028
$560$	3.60517	−	1.17139i	0.152346	−	0.0495003i
$561$	−13.8178	+	16.3448i	−0.583386	+	0.690076i
$562$	3.45156	−	2.50771i	0.145595	−	0.105781i
$563$	26.0865	−	15.0611i	1.09942	−	0.634748i	0.163348	−	0.986568i	$-0.447771\pi$
$563$	26.0865	−	15.0611i	1.09942	−	0.634748i	0.936068	+	0.351820i	$0.114437\pi$
$564$	7.13413	−	17.4721i	0.300401	−	0.735706i
$565$	1.73102	+	16.4696i	0.0728247	+	0.692881i
$566$	0.643179	−	0.885260i	0.0270348	−	0.0372103i
$567$	−14.5023	−	30.8805i	−0.609041	−	1.29686i
$568$	−0.166718	+	0.185159i	−0.00699532	+	0.00776909i
$569$	8.74159	+	3.89201i	0.366467	+	0.163161i	0.581705	−	0.813400i	$-0.302386\pi$
$569$	8.74159	+	3.89201i	0.366467	+	0.163161i	−0.215238	+	0.976562i	$0.569053\pi$
$570$	−0.839160	+	11.3973i	−0.0351486	+	0.477379i
$571$	−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
$573$	−0.918187	+	5.09746i	−0.0383578	+	0.212949i
$574$	−7.84827	+	24.1545i	−0.327580	+	1.00819i
$575$	5.95171	−	2.64987i	0.248203	−	0.110507i
$576$	−2.65914	+	1.38887i	−0.110798	+	0.0578695i
$577$	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
$579$	−38.5064	−	26.1797i	−1.60027	−	1.08799i
$580$	8.72186	+	0.916705i	0.362156	+	0.0380641i
$581$	7.87475	+	5.72134i	0.326700	+	0.237361i
$582$	−0.632392	−	2.57677i	−0.0262135	−	0.106811i
$583$	−11.9714	+	20.7351i	−0.495805	+	0.858760i
$584$	2.78113	+	4.81706i	0.115084	+	0.199331i
$585$	10.8257	−	13.6479i	0.447587	−	0.564270i
$586$	0.598319	+	0.664501i	0.0247163	+	0.0274503i
$587$	6.55193	+	20.1648i	0.270427	+	0.832289i	0.990393	+	0.138280i	$0.0441573\pi$
$587$	6.55193	+	20.1648i	0.270427	+	0.832289i	−0.719966	+	0.694009i	$0.755843\pi$
$588$	1.72988	+	12.6465i	0.0713391	+	0.521532i
$589$	9.00552	−	35.6153i	0.371066	−	1.46750i
$590$		−	4.05723i		−	0.167033i
$591$	21.0877	−	10.1892i	0.867432	−	0.419128i
$592$	−2.24674	+	2.02297i	−0.0923405	+	0.0831437i
$593$	−1.95779	−	2.69467i	−0.0803969	−	0.110657i	0.766924	−	0.641737i	$-0.221786\pi$
$593$	−1.95779	−	2.69467i	−0.0803969	−	0.110657i	−0.847321	+	0.531081i	$0.821786\pi$
$594$	−15.9839	−	11.8849i	−0.655826	−	0.487645i
$595$	10.5826	+	6.10986i	0.433844	+	0.250480i
$596$	−7.28003	+	0.765162i	−0.298202	+	0.0313422i
$597$	−40.1240	−	21.5242i	−1.64217	−	0.880928i
$598$	3.95435	−	37.6232i	0.161706	−	1.53853i
$599$	−28.6763	−	25.8203i	−1.17168	−	1.05499i	−0.997528	−	0.0702685i	$-0.977614\pi$
$599$	−28.6763	−	25.8203i	−1.17168	−	1.05499i	−0.174154	−	0.984718i	$-0.555719\pi$
$600$	1.66318	+	0.483546i	0.0678992	+	0.0197407i
$601$	−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
$603$	−11.1631	+	9.22769i	−0.454596	+	0.375781i
$604$	−13.5820	−	4.41307i	−0.552645	−	0.179565i
$605$	3.51314	+	1.14149i	0.142829	+	0.0464081i
$606$	−5.39832	−	8.71033i	−0.219292	−	0.353833i
$607$	−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
$609$	−16.0751	+	55.2911i	−0.651394	+	2.24051i
$610$	−7.45871	−	6.71586i	−0.301995	−	0.271917i
$611$	−6.61350	+	62.9232i	−0.267553	+	2.54560i
$612$	−9.06299	−	3.37445i	−0.366349	−	0.136404i
$613$	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
$615$	−9.17084	+	7.11081i	−0.369804	+	0.286736i
$616$	8.54098	+	11.7556i	0.344126	+	0.473648i
$617$	20.3409	−	18.3150i	0.818894	−	0.737336i	−0.148961	−	0.988843i	$-0.547593\pi$
$617$	20.3409	−	18.3150i	0.818894	−	0.737336i	0.967855	+	0.251507i	$0.0809263\pi$
$618$	−4.33607	−	8.97398i	−0.174422	−	0.360986i
$619$		−	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
$624$	7.26044	−	6.95984i	0.290650	−	0.278616i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.06324	−	3.57364i	0.0824638	−	0.142832i
$627$	−42.5445	+	10.4413i	−1.69906	+	0.416984i
$628$	3.05550	+	2.21995i	0.121928	+	0.0885856i
$629$	−9.69249	−	1.01872i	−0.386465	−	0.0406191i
$630$	−5.06035	+	10.1842i	−0.201609	+	0.405748i
$631$	−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
$633$	0.200870	+	0.558275i	0.00798388	+	0.0221894i
$634$	−17.6258	+	7.84749i	−0.700008	+	0.311664i
$635$	−1.28875	+	3.96638i	−0.0511426	+	0.157401i
$636$	−10.6471	−	1.91783i	−0.422187	−	0.0760470i
$637$	−17.4051	−	39.0925i	−0.689616	−	1.54890i
$638$	6.98945	+	32.8828i	0.276715	+	1.30184i
$639$	−0.0466477	−	0.746010i	−0.00184535	−	0.0295117i
$640$	0.913545	+	0.406737i	0.0361111	+	0.0160777i
$641$	−25.2274	+	28.0179i	−0.996424	+	1.10664i	−0.00212656	+	0.999998i	$0.500677\pi$
$641$	−25.2274	+	28.0179i	−0.996424	+	1.10664i	−0.994297	+	0.106643i	$0.965990\pi$
$642$	26.1646	−	0.817233i	1.03264	−	0.0322536i
$643$	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
$645$	−10.0566	−	4.10628i	−0.395979	−	0.161685i
$646$	−18.4199	+	10.6347i	−0.724719	+	0.418417i
$647$	0.412670	−	0.299822i	0.0162237	−	0.0117872i	−0.579644	−	0.814870i	$-0.696808\pi$
$647$	0.412670	−	0.299822i	0.0162237	−	0.0117872i	0.595868	+	0.803083i	$0.296808\pi$
$648$	2.60790	−	8.61388i	0.102448	−	0.338385i
$649$	14.7912	−	4.80597i	0.580607	−	0.188651i
$650$	−5.80670			−0.227758
$651$	21.6937	−	29.4235i	0.850244	−	1.15320i
$652$	10.4855			0.410646
$653$	−34.1949	+	11.1106i	−1.33815	+	0.434792i	−0.888690	−	0.458508i	$-0.848384\pi$
$653$	−34.1949	+	11.1106i	−1.33815	+	0.434792i	−0.449461	+	0.893300i	$0.648384\pi$
$654$	5.66931	+	4.79280i	0.221688	+	0.187413i
$655$	7.52580	−	5.46781i	0.294057	−	0.213645i
$656$	−5.80233	+	3.34997i	−0.226543	+	0.130795i
$657$	−16.1610	−	4.15604i	−0.630499	−	0.162142i
$658$	−4.31739	−	41.0773i	−0.168310	−	1.60136i
$659$	10.8518	−	14.9362i	0.422726	−	0.581833i	−0.543538	−	0.839384i	$-0.682916\pi$
$659$	10.8518	−	14.9362i	0.422726	−	0.581833i	0.966265	+	0.257552i	$0.0829158\pi$
$660$	0.207276	+	6.63618i	0.00806821	+	0.258313i
$661$	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
$663$	32.3339	+	2.38069i	1.25574	+	0.0924582i
$664$	0.533873	+	2.51168i	0.0207183	+	0.0974720i
$665$	10.1730	+	22.8488i	0.394490	+	0.886039i
$666$	0.383283	−	9.06176i	0.0148519	−	0.351136i
$667$	−17.6559	+	54.3391i	−0.683637	+	2.10402i
$668$	−9.66856	+	4.30472i	−0.374088	+	0.166555i
$669$	−22.3370	+	8.03697i	−0.863598	+	0.310727i
$670$	4.72225	+	1.00375i	0.182437	+	0.0387781i
$671$	15.6485	−	35.1471i	0.604104	−	1.35684i
$672$	−3.69151	+	5.42965i	−0.142403	+	0.209453i
$673$	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
$675$	−4.52843	+	2.54821i	−0.174299	+	0.0980805i
$676$	−10.3589	+	17.9421i	−0.398419	+	0.690081i
$677$	−22.5736	−	39.0987i	−0.867576	−	1.50269i	−0.864467	−	0.502690i	$-0.832344\pi$
$677$	−22.5736	−	39.0987i	−0.867576	−	1.50269i	−0.00310893	−	0.999995i	$-0.500990\pi$
$678$	−19.8490	−	20.7063i	−0.762295	−	0.795219i
$679$	−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	$-0.762076\pi$
$683$		−	35.5311i		−	1.35956i	0.733417	−	0.679779i	$-0.237924\pi$
$684$	−10.9475	−	16.4911i	−0.418590	−	0.630553i
$685$	9.13763	−	8.22756i	0.349131	−	0.314359i
$686$	0.823147	+	1.13296i	0.0314279	+	0.0432568i
$687$	−8.02795	−	10.3537i	−0.306285	−	0.395017i
$688$	−5.43132	−	3.13577i	−0.207067	−	0.119550i
$689$	36.0703	−	3.79114i	1.37417	−	0.144431i
$690$	−5.33428	+	9.94381i	−0.203073	+	0.378554i
$691$	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
$693$	−43.1222	−	6.38464i	−1.63808	−	0.242533i
$694$	−6.82542	+	32.1111i	−0.259089	+	1.21892i
$695$	21.1360	−	4.49260i	0.801735	−	0.170414i
$696$	−12.9113	+	8.00194i	−0.489403	+	0.303313i
$697$	−20.5409	−	6.67414i	−0.778042	−	0.252801i
$698$	−9.21122	−	2.99291i	−0.348650	−	0.113283i
$699$	2.50556	−	1.55285i	0.0947690	−	0.0587341i
$700$	3.70787	−	0.788132i	0.140144	−	0.0297886i
$701$	3.26493	−	15.3603i	0.123315	−	0.580150i	−0.872489	−	0.488634i	$-0.837495\pi$
$701$	3.26493	−	15.3603i	0.123315	−	0.580150i	0.995804	−	0.0915162i	$-0.0291713\pi$
$702$	−0.333320	+	30.1707i	−0.0125804	+	1.13872i
$703$	−14.8240	−	13.3476i	−0.559099	−	0.503415i
$704$	−0.400685	+	3.81227i	−0.0151014	+	0.143680i
$705$	8.92137	−	16.6306i	0.335998	−	0.626346i
$706$	13.1864	−	1.38595i	0.496276	−	0.0521607i
$707$	−19.4227	−	11.2137i	−0.730465	−	0.421734i
$708$	4.30603	+	5.55350i	0.161831	+	0.208713i
$709$	−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
$711$	4.06269	−	2.69700i	0.152363	−	0.101145i
$712$		−	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
$717$	−2.62580	−	2.73921i	−0.0980622	−	0.102298i
$718$	15.1945	+	26.3176i	0.567053	+	0.982164i
$719$	22.3610	−	38.7304i	0.833925	−	1.44440i	−0.0609770	−	0.998139i	$-0.519422\pi$
$719$	22.3610	−	38.7304i	0.833925	−	1.44440i	0.894902	−	0.446262i	$-0.147245\pi$
$720$	−2.78975	+	1.10330i	−0.103968	+	0.0411177i
$721$	−17.6468	−	12.8211i	−0.657200	−	0.477484i
$722$	−24.3995	−	2.56449i	−0.908056	−	0.0954405i
$723$	−8.17596	+	12.0256i	−0.304067	+	0.447237i
$724$	−8.48750	+	19.0632i	−0.315435	+	0.708480i
$725$	8.57826	+	1.82337i	0.318589	+	0.0677181i
$726$	−6.02024	+	2.16612i	−0.223432	+	0.0803921i
$727$	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
$729$	12.9801	+	23.6752i	0.480745	+	0.876861i
$730$	2.26238	+	5.08138i	0.0837343	+	0.188070i
$731$	−4.20335	−	19.7752i	−0.155466	−	0.731412i
$732$	17.3371	+	1.27650i	0.640799	+	0.0471809i
$733$	−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
$735$	0.398487	+	12.7580i	0.0146984	+	0.470586i
$736$	−3.82939	+	5.27071i	−0.141153	+	0.194281i
$737$	1.93441	+	18.4047i	0.0712549	+	0.677945i
$738$	5.00610	−	19.4665i	0.184277	−	0.716570i
$739$	−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
$741$	50.6770	+	42.8420i	1.86167	+	1.57384i
$742$	−22.5181	+	7.31659i	−0.826667	+	0.268600i
$743$	−2.08743			−0.0765803			−0.0382901	−	0.999267i	$-0.512191\pi$
$743$	−2.08743			−0.0765803			−0.0382901	+	0.999267i	$0.512191\pi$
$744$	9.44672	−	1.93894i	0.346334	−	0.0710852i
$745$	−7.32013			−0.268189
$746$	−2.38299	+	0.774281i	−0.0872475	+	0.0283484i
$747$	−6.50258	−	4.13016i	−0.237917	−	0.151115i
$748$	−9.99697	+	7.26322i	−0.365525	+	0.265570i
$749$	49.6154	−	28.6454i	1.81291	−	1.04668i
$750$	1.60353	+	0.654747i	0.0585526	+	0.0239080i
$751$	−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
$753$	−14.4254	+	0.450567i	−0.525691	+	0.0164196i
$754$	34.0750	−	37.8441i	1.24094	−	1.37820i
$755$	−13.0463	−	5.80860i	−0.474804	−	0.211397i
$756$	−3.88216	−	19.3107i	−0.141193	−	0.702324i
$757$	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
$759$	−42.5704	−	7.66805i	−1.54521	−	0.278333i
$760$	−2.03890	+	6.27509i	−0.0739587	+	0.227622i
$761$	−4.22032	+	1.87901i	−0.152987	+	0.0681140i	−0.481802	−	0.876280i	$-0.660017\pi$
$761$	−4.22032	+	1.87901i	−0.152987	+	0.0681140i	0.328815	+	0.944394i	$0.393351\pi$
$762$	−2.44557	−	6.79693i	−0.0885937	−	0.246227i
$763$	15.8923	+	3.37801i	0.575340	+	0.122292i
$764$	−1.21630	+	2.73185i	−0.0440041	+	0.0988349i
$765$	−8.66061	−	4.30331i	−0.313125	−	0.155586i
$766$	15.3419	+	1.61250i	0.554325	+	0.0582620i
$767$	−19.0597	−	13.8477i	−0.688206	−	0.500011i
$768$	−1.68213	+	0.412829i	−0.0606988	+	0.0148967i
$769$	−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
$771$	−13.4799	+	12.9218i	−0.485466	+	0.465367i
$772$	−17.9884	−	19.9781i	−0.647416	−	0.719029i
$773$	8.40902	+	25.8803i	0.302451	+	0.930850i	0.980616	+	0.195940i	$0.0627757\pi$
$773$	8.40902	+	25.8803i	0.302451	+	0.930850i	−0.678165	+	0.734910i	$0.737224\pi$
$774$	18.1235	−	5.05268i	0.651436	−	0.181615i
$775$	−4.71192	−	2.96612i	−0.169257	−	0.106546i
$776$		−	1.53185i		−	0.0549902i
$777$	−8.63590	−	17.8730i	−0.309811	−	0.641189i
$778$	22.0655	−	19.8679i	0.791087	−	0.712298i
$779$	−25.9839	−	35.7637i	−0.930969	−	1.28137i
$780$	7.94817	−	6.16279i	0.284590	−	0.220663i
$781$	−0.827124	−	0.477540i	−0.0295968	−	0.0170877i
$782$	−20.8866	+	2.19527i	−0.746903	+	0.0785027i
$783$	9.96632	−	44.4666i	0.356167	−	1.58911i
$784$	−0.770316	+	7.32907i	−0.0275113	+	0.261752i
$785$	2.80671	+	2.52717i	0.100176	+	0.0901987i
$786$	−4.49813	+	15.4716i	−0.160443	+	0.551854i
$787$	−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
$789$	4.11934	+	6.64666i	0.146652	+	0.236628i
$790$	−1.54591	−	0.502297i	−0.0550010	−	0.0178709i
$791$	−59.7028	−	19.3986i	−2.12279	−	0.689735i
$792$	−7.32685	−	8.86356i	−0.260348	−	0.314953i
$793$	−57.0065	+	12.1171i	−2.02436	+	0.430291i
$794$	−6.11088	+	28.7494i	−0.216867	+	1.02028i
$795$	−10.3884	−	3.02026i	−0.368437	−	0.107117i
$796$	−19.5360	−	17.5903i	−0.692436	−	0.623473i
$797$	1.70878	−	16.2580i	0.0605282	−	0.575887i	−0.921661	−	0.387995i	$-0.873168\pi$
$797$	1.70878	−	16.2580i	0.0605282	−	0.575887i	0.982190	−	0.187892i	$-0.0601656\pi$
$798$	−38.1747	−	20.4785i	−1.35137	−	0.724931i
$799$	34.9320	−	3.67150i	1.23580	−	0.129888i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	1.68376	+	1.65012i	0.0594926	+	0.0583042i
$802$	13.4625	+	18.5296i	0.475378	+	0.654302i
$803$	−15.8451	+	14.2670i	−0.559160	+	0.503470i
$804$	−7.52908	+	3.63792i	−0.265530	+	0.128300i
$805$			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	$0.0694274\pi$
$809$	30.9874	+	34.4150i	1.08946	+	1.20997i	0.113150	+	0.993578i	$0.463906\pi$
$810$	3.49400	−	8.29409i	0.122767	−	0.291425i
$811$	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
$813$	12.1388	+	49.4615i	0.425728	+	1.73469i
$814$	−9.37575	−	6.81188i	−0.328620	−	0.238756i
$815$	10.4281	+	1.09604i	0.365281	+	0.0383925i
$816$	−4.61736	−	3.13925i	−0.161640	−	0.109896i
$817$	16.8307	−	37.8023i	0.588831	−	1.32254i
$818$	29.8828	+	6.35178i	1.04483	+	0.222085i
$819$	30.5710	+	58.5317i	1.06824	+	2.04526i
$820$	−6.12071	+	2.72511i	−0.213744	+	0.0951651i
$821$	1.48821	−	4.58025i	0.0519391	−	0.159852i	−0.921723	−	0.387850i	$-0.873218\pi$
$821$	1.48821	−	4.58025i	0.0519391	−	0.159852i	0.973662	+	0.227998i	$0.0732179\pi$
$822$	−3.77541	+	20.9598i	−0.131683	+	0.731057i
$823$	−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
$825$	−0.487529	+	6.62149i	−0.0169736	+	0.230531i
$826$	14.0501	+	6.25551i	0.488865	+	0.217657i
$827$	−4.04237	+	4.48951i	−0.140567	+	0.156116i	−0.809318	−	0.587371i	$-0.800163\pi$
$827$	−4.04237	+	4.48951i	−0.140567	+	0.156116i	0.668750	+	0.743487i	$0.266829\pi$
$828$	−3.25208	−	19.2724i	−0.113018	−	0.669763i
$829$	−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
$831$	−18.3063	+	44.8338i	−0.635040	+	1.55527i
$832$	5.02875	−	2.90335i	0.174341	−	0.100656i
$833$	−19.2191	+	13.9635i	−0.665903	+	0.483807i
$834$	−24.1627	+	28.5816i	−0.836686	+	0.989699i
$835$	−10.0656	+	3.27050i	−0.348333	+	0.113180i
$836$	−25.2920			−0.874741
$837$	−15.6819	+	24.3121i	−0.542047	+	0.840348i
$838$	−19.3091			−0.667022
$839$	17.8439	−	5.79783i	0.616040	−	0.200163i	0.0156585	−	0.999877i	$-0.495016\pi$
$839$	17.8439	−	5.79783i	0.616040	−	0.200163i	0.600381	+	0.799714i	$0.295016\pi$
$840$	−4.23884	+	5.01404i	−0.146254	+	0.173001i
$841$	−38.7610	+	28.1615i	−1.33659	+	0.971087i
$842$	−25.0355	+	14.4542i	−0.862780	+	0.498126i
$843$	−2.79339	+	6.84124i	−0.0962095	+	0.235625i
$844$	0.0358061	+	0.340673i	0.00123250	+	0.0117264i
$845$	−12.1776	+	16.7610i	−0.418922	+	0.576597i
$846$	5.43897	+	32.2323i	0.186996	+	1.10817i
$847$	−9.36957	+	10.4060i	−0.321942	+	0.357553i
$848$	−5.70606	−	2.54050i	−0.195947	−	0.0872412i
$849$	−0.139170	+	1.89017i	−0.00477629	+	0.0648703i
$850$	0.670225	+	3.15316i	0.0229885	+	0.108153i
$851$	−8.01132	−	17.9937i	−0.274625	−	0.616817i
$852$	0.0765024	−	0.424715i	0.00262093	−	0.0145505i
$853$	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
$855$	−9.16378	−	17.5451i	−0.313395	−	0.600029i
$856$	14.7833	+	3.14228i	0.505281	+	0.107401i
$857$	6.65228	−	14.9413i	0.227237	−	0.510384i	−0.763560	−	0.645737i	$-0.776550\pi$
$857$	6.65228	−	14.9413i	0.227237	−	0.510384i	0.990797	+	0.135353i	$0.0432169\pi$
$858$	31.8823	+	21.6762i	1.08845	+	0.740012i
$859$	−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
$861$	−10.4848	−	42.7220i	−0.357323	−	1.45596i
$862$	−6.59851	+	11.4290i	−0.224746	+	0.389272i
$863$	−26.4696	−	45.8467i	−0.901036	−	1.56064i	−0.826151	−	0.563449i	$-0.809474\pi$
$863$	−26.4696	−	45.8467i	−0.901036	−	1.56064i	−0.0748854	−	0.997192i	$-0.523859\pi$
$864$	2.64763	−	4.47102i	0.0900742	−	0.152107i
$865$	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
$870$	−13.6770	+	6.60850i	−0.463695	+	0.224049i
$871$	20.8328	−	18.7579i	0.705893	−	0.635589i
$872$	2.51931	+	3.46753i	0.0853146	+	0.117425i
$873$	3.28216	+	3.21660i	0.111084	+	0.108865i
$874$	−37.2268	−	21.4929i	−1.25922	−	0.727009i
$875$	3.76994	−	0.396236i	0.127447	−	0.0133952i
$876$	−8.48971	−	4.55424i	−0.286841	−	0.153874i
$877$	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
$879$	−1.48718	−	0.432374i	−0.0501612	−	0.0145836i
$880$	−0.796981	+	3.74950i	−0.0268662	+	0.126396i
$881$	30.9973	−	6.58868i	1.04433	−	0.221978i	0.346354	−	0.938104i	$-0.387420\pi$
$881$	30.9973	−	6.58868i	1.04433	−	0.221978i	0.697971	+	0.716126i	$0.254086\pi$
$882$	−14.0858	−	17.0401i	−0.474295	−	0.573772i
$883$	−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
$885$	3.70194	+	5.97318i	0.124439	+	0.200786i
$886$	−26.7553	+	5.68701i	−0.898861	+	0.191059i
$887$	−2.17846	+	10.2488i	−0.0731454	+	0.344122i	−0.999468	−	0.0326087i	$-0.989618\pi$
$887$	−2.17846	+	10.2488i	−0.0731454	+	0.344122i	0.926323	+	0.376731i	$0.122952\pi$
$888$	1.46190	−	5.02829i	0.0490581	−	0.168738i
$889$	−11.7485	−	10.5784i	−0.394031	−	0.354787i
$890$	0.0821429	−	0.781537i	0.00275344	−	0.0261972i
$891$	34.3762	+	2.91321i	1.15165	+	0.0975962i
$892$	−13.6306	+	1.43263i	−0.456385	+	0.0479680i
$893$	62.2604	+	35.9460i	2.08346	+	1.20289i
$894$	10.0197	−	7.76902i	0.335110	−	0.259835i
$895$	−10.7502	−	14.7963i	−0.359339	−	0.494587i
$896$	−2.81704	+	2.53648i	−0.0941108	+	0.0847377i
$897$	28.5068	+	58.9981i	0.951816	+	1.96989i
$898$			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
$903$	29.7254	−	28.4947i	0.989200	−	0.948245i
$904$	−8.28015	−	14.3416i	−0.275394	−	0.476996i
$905$	−10.4337	+	18.0716i	−0.346826	+	0.600721i
$906$	24.0225	−	5.89561i	0.798095	−	0.195869i
$907$	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
$909$	15.8952	+	7.89803i	0.527210	+	0.261961i
$910$	8.95288	−	20.1085i	0.296785	−	0.666590i
$911$	−14.6567	−	3.11538i	−0.485598	−	0.103217i	−0.0413946	−	0.999143i	$-0.513180\pi$
$911$	−14.6567	−	3.11538i	−0.485598	−	0.103217i	−0.444204	+	0.895926i	$0.646513\pi$
$912$	−3.86907	−	10.7532i	−0.128118	−	0.356075i
$913$	−8.99205	+	4.00352i	−0.297593	+	0.132497i
$914$	1.24182	−	3.82193i	0.0410757	−	0.126418i
$915$	17.1087	+	3.08173i	0.565597	+	0.101879i
$916$	−3.07659	−	6.91014i	−0.101654	−	0.228318i
$917$	7.33151	+	34.4921i	0.242108	+	1.13903i
$918$	16.4218	−	3.30138i	0.541999	−	0.108962i
$919$	−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
$921$	5.84834	−	0.182669i	0.192709	−	0.00601914i
$922$	23.0476	−	31.7223i	0.759033	−	1.04472i
$923$	0.151229	+	1.43885i	0.00497776	+	0.0473602i
$924$	−23.3005	−	9.51398i	−0.766531	−	0.312987i
$925$	−2.61824	+	1.51164i	−0.0860873	+	0.0497025i
$926$	15.2048	−	11.0469i	0.499661	−	0.363025i
$927$	14.5718	+	9.25541i	0.478602	+	0.303988i
$928$	−8.34068	+	2.71005i	−0.273796	+	0.0889617i
$929$	12.1703			0.399294			0.199647	−	0.979868i	$-0.436021\pi$
$929$	12.1703			0.399294			0.199647	+	0.979868i	$0.436021\pi$
$930$	9.59764	−	0.940872i	0.314719	−	0.0308524i
$931$	−48.6237			−1.59358
$932$	1.61858	−	0.525910i	0.0530185	−	0.0172267i
$933$	−3.34330	−	2.82641i	−0.109455	−	0.0925325i
$934$	−21.6429	+	15.7245i	−0.708178	+	0.514521i
$935$	−10.7014	+	6.17847i	−0.349974	+	0.202057i
$936$	−4.33868	+	16.8712i	−0.141814	+	0.551451i
$937$	−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
$939$	0.223132	+	7.14380i	0.00728162	+	0.233129i
$940$	7.29085	−	8.09731i	0.237801	−	0.264105i
$941$	−20.9931	−	9.34673i	−0.684356	−	0.304695i	0.0349495	−	0.999389i	$-0.488873\pi$
$941$	−20.9931	−	9.34673i	−0.684356	−	0.304695i	−0.719305	+	0.694694i	$0.755540\pi$
$942$	−6.52396	−	0.480347i	−0.212562	−	0.0156506i
$943$	−9.07532	−	42.6960i	−0.295533	−	1.39037i
$944$	1.65022	+	3.70646i	0.0537102	+	0.120635i
$945$	−1.84237	−	19.6107i	−0.0599325	−	0.637937i
$946$	7.42893	−	22.8639i	0.241535	−	0.743369i
$947$	−30.5525	+	13.6029i	−0.992823	+	0.442033i	−0.837859	−	0.545887i	$-0.816193\pi$
$947$	−30.5525	+	13.6029i	−0.992823	+	0.442033i	−0.154964	+	0.987920i	$0.549526\pi$
$948$	2.64913	−	0.953172i	0.0860397	−	0.0309576i
$949$	31.5926	+	6.71522i	1.02554	+	0.217985i
$950$	−2.68366	+	6.02759i	−0.0870694	+	0.195561i
$951$	18.7889	−	27.6356i	0.609272	−	0.896147i
$952$	−12.1528	−	1.27731i	−0.393874	−	0.0413978i
$953$	40.1764	+	29.1898i	1.30144	+	0.945552i	0.999969	−	0.00792304i	$-0.00252201\pi$
$953$	40.1764	+	29.1898i	1.30144	+	0.945552i	0.301472	+	0.953475i	$0.402522\pi$
$954$	17.4250	−	6.89130i	0.564154	−	0.223114i
$955$	−1.49519	+	2.58975i	−0.0483833	+	0.0838023i
$956$	−1.09537	−	1.89724i	−0.0354269	−	0.0613611i
$957$	−40.2934	−	42.0337i	−1.30250	−	1.35876i
$958$	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
$963$	−37.7747	+	25.0766i	−1.21727	+	0.808082i
$964$	−6.23919	+	5.61779i	−0.200951	+	0.180937i
$965$	−15.8016	−	21.7490i	−0.508670	−	0.700125i
$966$	−26.2107	−	33.8041i	−0.843316	−	1.08763i
$967$	−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
$969$	17.4149	−	32.4636i	0.559446	−	1.04288i
$970$	0.160122	−	1.52346i	0.00514120	−	0.0489153i
$971$	29.7386	+	26.7767i	0.954356	+	0.859306i	0.990144	−	0.140054i	$-0.0447275\pi$
$971$	29.7386	+	26.7767i	0.954356	+	0.859306i	−0.0357882	+	0.999359i	$0.511394\pi$
$972$	4.02015	+	15.0612i	0.128946	+	0.483087i
$973$	−17.0301	+	80.1204i	−0.545960	+	2.56854i
$974$	−25.1327	+	5.34212i	−0.805304	+	0.171173i
$975$	8.54881	−	5.29822i	0.273781	−	0.169679i
$976$	9.54546	+	3.10151i	0.305543	+	0.0992769i
$977$	7.59832	+	2.46884i	0.243092	+	0.0789853i	0.428029	−	0.903765i	$-0.359208\pi$
$977$	7.59832	+	2.46884i	0.243092	+	0.0789853i	−0.184937	+	0.982750i	$0.559208\pi$
$978$	−15.4372	+	9.56735i	−0.493626	+	0.305930i
$979$	2.94652	−	0.626301i	0.0941711	−	0.0200167i
$980$	−1.53219	+	7.20840i	−0.0489441	+	0.230264i
$981$	−12.7197	−	1.88326i	−0.406107	−	0.0601279i
$982$	−15.4456	−	13.9073i	−0.492889	−	0.443799i
$983$	−5.06348	+	48.1758i	−0.161500	+	1.53657i	0.550766	+	0.834660i	$0.314336\pi$
$983$	−5.06348	+	48.1758i	−0.161500	+	1.53657i	−0.712266	+	0.701910i	$0.752331\pi$
$984$	5.48575	−	10.2262i	0.174879	−	0.325998i
$985$	13.4476	−	1.41340i	0.428478	−	0.0450348i
$986$	−24.4831	−	14.1354i	−0.779702	−	0.450161i
$987$	43.8364	+	56.5359i	1.39533	+	1.79956i
$988$	22.5197	+	30.9957i	0.716446	+	0.986103i
$989$	30.3641	−	27.3399i	0.965521	−	0.869359i
$990$	−6.36022	−	9.58087i	−0.202141	−	0.304500i
$991$		−	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
$996$	−3.07772	−	3.21065i	−0.0975213	−	0.101733i
$997$	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
$999$	7.70396	+	13.6907i	0.243742	+	0.433156i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.11822 - 1.32272i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.654747 + 1.60353i) q^{6} +(0.396236 + 3.76994i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.499172 - 2.95818i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.11822 - 1.32272i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.654747 + 1.60353i) q^{6} +(0.396236 + 3.76994i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.499172 - 2.95818i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.50186 - 1.55913i) q^{11} +(0.127184 - 1.72737i) q^{12} +(1.20728 + 5.67981i) q^{13} +(-1.54182 - 3.46298i) q^{14} +(0.307047 - 1.70462i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.94491 - 1.31116i) q^{17} +(1.38887 + 2.65914i) q^{18} +(6.45384 + 1.37181i) q^{19} +(0.406737 - 0.913545i) q^{20} +(5.42965 + 3.69151i) q^{21} +(3.81227 + 0.400685i) q^{22} +(5.27071 + 3.82939i) q^{23} +(0.412829 + 1.68213i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.90335 - 5.02875i) q^{26} +(-4.47102 - 2.64763i) 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} +(-5.97814 + 2.88853i) q^{33} +(-2.39561 + 2.15701i) q^{34} +(2.22812 + 3.06674i) q^{35} +(-2.14261 - 2.09981i) q^{36} +(-2.61824 - 1.51164i) q^{37} +(-6.56188 + 0.689681i) q^{38} +(8.86280 + 4.75438i) q^{39} +(-0.104528 + 0.994522i) q^{40} +(-4.97903 - 4.48314i) q^{41} +(-6.30464 - 1.83298i) q^{42} +(1.30393 - 6.13450i) q^{43} +(-3.74950 + 0.796981i) q^{44} +(-1.91139 - 2.31227i) q^{45} +(-6.19609 - 2.01323i) q^{46} +(10.3627 + 3.36705i) q^{47} +(-0.912432 - 1.47223i) q^{48} +(-7.20840 + 1.53219i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(1.55876 - 5.36145i) q^{51} +(4.31522 + 3.88544i) q^{52} +(0.652891 - 6.21184i) q^{53} +(5.07036 + 1.13642i) q^{54} +(-3.81227 + 0.400685i) q^{55} +(-3.28285 - 1.89535i) q^{56} +(9.03132 - 7.00264i) q^{57} +(-5.15482 - 7.09500i) q^{58} +(-3.01511 + 2.71481i) q^{59} +(-0.753543 - 1.55954i) 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} +(4.79295 - 4.59450i) q^{66} +(-2.41388 - 4.18096i) q^{67} +(1.61180 - 2.79172i) q^{68} +(10.9590 - 2.68957i) q^{69} +(-3.06674 - 2.22812i) q^{70} +(0.247791 + 0.0260439i) q^{71} +(2.68662 + 1.33494i) q^{72} +(2.26238 - 5.08138i) q^{73} +(2.95722 + 0.628577i) q^{74} +(-0.586399 - 1.62977i) q^{75} +(6.02759 - 2.68366i) q^{76} +(4.49026 - 13.8196i) q^{77} +(-9.89821 - 1.78293i) q^{78} +(0.661137 + 1.48494i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(-8.50166 + 2.95328i) q^{81} +(6.12071 + 2.72511i) q^{82} +(1.71819 - 1.90824i) q^{83} +(6.56249 - 0.204975i) q^{84} +(1.89479 - 2.60795i) q^{85} +(0.655555 + 6.23719i) q^{86} +(14.0628 + 5.74207i) q^{87} +(3.31971 - 1.91663i) q^{88} +(-0.635760 + 0.461907i) q^{89} +(2.53237 + 1.60845i) q^{90} +(-20.9342 + 6.80192i) q^{91} +6.51496 q^{92} +(-7.12128 - 6.50287i) q^{93} -10.8960 q^{94} +(6.27509 - 2.03890i) q^{95} +(1.32272 + 1.11822i) q^{96} +(-1.23929 + 0.900398i) q^{97} +(6.38212 - 3.68472i) q^{98} +(-2.86416 + 11.1374i) 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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