LMFDB - Embedded newform 930.2.bn.b.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (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:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.97807 + 1.04271i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93366 + 1.74107i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.97807 + 1.04271i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93366 + 1.74107i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(2.00625 - 0.987398i) q^{10} +(0.677493 + 0.144006i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(-1.38792 + 0.145877i) q^{13} +(2.54513 - 0.540984i) q^{14} +(1.75712 - 1.38294i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.17916 - 5.54750i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(0.475813 - 4.52706i) q^{19} +(0.380423 - 2.20347i) q^{20} +(2.37704 - 1.05833i) q^{21} +(0.514724 - 0.463459i) q^{22} +(5.65227 + 1.83653i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(2.82550 + 4.12511i) q^{25} +(-0.697784 + 1.20860i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.05833 - 2.37704i) q^{28} +(7.10863 + 5.16472i) q^{29} +(-0.0860174 - 2.23441i) q^{30} +(2.99954 + 4.69071i) q^{31} +1.00000i q^{32} +(0.407117 - 0.560349i) q^{33} +(-5.18112 - 2.30678i) q^{34} +(2.00946 + 5.46021i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(9.50405 - 5.48717i) q^{37} +(-3.38279 - 3.04588i) q^{38} +(-0.431254 + 1.32726i) q^{39} +(-1.55904 - 1.60294i) q^{40} +(-5.05596 + 2.25106i) q^{41} +(0.540984 - 2.54513i) q^{42} +(-8.62869 - 0.906912i) q^{43} +(-0.0723994 - 0.688835i) q^{44} +(-0.548698 - 2.16770i) q^{45} +(4.80811 - 3.49329i) q^{46} +(-7.65033 - 10.5298i) q^{47} +(0.207912 + 0.978148i) q^{48} +(-0.0240043 - 0.228386i) q^{49} +(4.99807 + 0.138804i) q^{50} +(-5.54750 - 1.17916i) q^{51} +(0.567628 + 1.27491i) q^{52} +(0.438422 - 0.394757i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.18997 + 0.991284i) q^{55} +(-1.30100 - 2.25339i) q^{56} +(-3.94214 - 2.27600i) q^{57} +(8.35669 - 2.71525i) q^{58} +(2.32422 + 1.03481i) q^{59} +(-1.85824 - 1.24377i) q^{60} -14.2000 q^{61} +(5.55795 + 0.330452i) q^{62} -2.60199i q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.89751 - 1.15865i) q^{65} +(-0.214034 - 0.658729i) q^{66} +(-3.18752 - 1.84032i) q^{67} +(-4.91161 + 2.83572i) q^{68} +(3.97674 - 4.41662i) q^{69} +(5.59853 + 1.58374i) q^{70} +(5.85946 + 6.50759i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-3.16453 + 14.8879i) q^{73} +(1.14713 - 10.9142i) q^{74} +(4.91771 - 0.903387i) q^{75} +(-4.45252 + 0.946413i) q^{76} +(1.05931 + 1.45802i) q^{77} +(0.820294 + 1.12904i) q^{78} +(-0.621428 + 0.132089i) q^{79} +(-2.21318 + 0.319106i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-1.15067 + 5.41350i) q^{82} +(-3.52397 - 7.91496i) q^{83} +(-1.74107 - 1.93366i) q^{84} +(3.45200 - 12.2029i) q^{85} +(-5.80553 + 6.44769i) q^{86} +(7.60954 - 4.39337i) q^{87} +(-0.599834 - 0.346314i) q^{88} +(1.81833 + 5.59625i) q^{89} +(-2.07622 - 0.830237i) q^{90} +(-2.93775 - 2.13440i) q^{91} -5.94315i q^{92} +(5.50520 - 0.832332i) q^{93} -13.0155 q^{94} +(5.66161 - 8.45869i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-13.6733 + 4.44273i) q^{97} +(-0.198877 - 0.114822i) q^{98} +(-0.346314 - 0.599834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$3$	0.406737	−	0.913545i	0.234830	−	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.97807	+	1.04271i	0.884618	+	0.466316i
$5$	1.97807	+	1.04271i	0.884618	+	0.466316i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.93366	+	1.74107i	0.730853	+	0.658063i	0.948071	−	0.318060i	$-0.103031\pi$
$7$	1.93366	+	1.74107i	0.730853	+	0.658063i	−0.217217	+	0.976123i	$0.569698\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	2.00625	−	0.987398i	0.634432	−	0.312243i
$11$	0.677493	+	0.144006i	0.204272	+	0.0434193i	0.308911	−	0.951091i	$-0.400035\pi$
$11$	0.677493	+	0.144006i	0.204272	+	0.0434193i	−0.104639	+	0.994510i	$0.533369\pi$
$12$	−0.994522	−	0.104528i	−0.287094	−	0.0301748i
$13$	−1.38792	+	0.145877i	−0.384940	+	0.0404589i	−0.295022	−	0.955490i	$-0.595327\pi$
$13$	−1.38792	+	0.145877i	−0.384940	+	0.0404589i	−0.0899179	+	0.995949i	$0.528660\pi$
$14$	2.54513	−	0.540984i	0.680215	−	0.144584i
$15$	1.75712	−	1.38294i	0.453686	−	0.357075i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.17916	−	5.54750i	−0.285988	−	1.34547i	−0.853066	−	0.521803i	$-0.825260\pi$
$17$	−1.17916	−	5.54750i	−0.285988	−	1.34547i	0.567078	−	0.823664i	$-0.308074\pi$
$18$	−0.994522	+	0.104528i	−0.234411	+	0.0246376i
$19$	0.475813	−	4.52706i	0.109159	−	1.03858i	−0.793602	−	0.608437i	$-0.791797\pi$
$19$	0.475813	−	4.52706i	0.109159	−	1.03858i	0.902761	−	0.430142i	$-0.141536\pi$
$20$	0.380423	−	2.20347i	0.0850651	−	0.492711i
$21$	2.37704	−	1.05833i	0.518712	−	0.230945i
$22$	0.514724	−	0.463459i	0.109739	−	0.0988098i
$23$	5.65227	+	1.83653i	1.17858	+	0.382944i	0.831839	−	0.555017i	$-0.187288\pi$
$23$	5.65227	+	1.83653i	1.17858	+	0.382944i	0.346741	+	0.937961i	$0.387288\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	2.82550	+	4.12511i	0.565100	+	0.825023i
$26$	−0.697784	+	1.20860i	−0.136847	+	0.237025i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	1.05833	−	2.37704i	0.200005	−	0.449218i
$29$	7.10863	+	5.16472i	1.32004	+	0.959064i	0.999932	+	0.0116827i	$0.00371879\pi$
$29$	7.10863	+	5.16472i	1.32004	+	0.959064i	0.320107	+	0.947381i	$0.396281\pi$
$30$	−0.0860174	−	2.23441i	−0.0157046	−	0.407946i
$31$	2.99954	+	4.69071i	0.538733	+	0.842476i
$31$	2.99954	+	4.69071i	0.538733	+	0.842476i
$32$			1.00000i			0.176777i
$33$	0.407117	−	0.560349i	0.0708700	−	0.0975442i
$34$	−5.18112	−	2.30678i	−0.888554	−	0.395610i
$35$	2.00946	+	5.46021i	0.339661	+	0.922943i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	9.50405	−	5.48717i	1.56246	−	0.902085i	0.565448	−	0.824784i	$-0.308703\pi$
$37$	9.50405	−	5.48717i	1.56246	−	0.902085i	0.997008	−	0.0773010i	$-0.0246302\pi$
$38$	−3.38279	−	3.04588i	−0.548761	−	0.494107i
$39$	−0.431254	+	1.32726i	−0.0690559	+	0.212532i
$40$	−1.55904	−	1.60294i	−0.246505	−	0.253446i
$41$	−5.05596	+	2.25106i	−0.789608	+	0.351556i	−0.761597	−	0.648051i	$-0.775584\pi$
$41$	−5.05596	+	2.25106i	−0.789608	+	0.351556i	−0.0280116	+	0.999608i	$0.508918\pi$
$42$	0.540984	−	2.54513i	0.0834757	−	0.392722i
$43$	−8.62869	−	0.906912i	−1.31586	−	0.138303i	−0.579546	−	0.814939i	$-0.696770\pi$
$43$	−8.62869	−	0.906912i	−1.31586	−	0.138303i	−0.736317	+	0.676636i	$0.763437\pi$
$44$	−0.0723994	−	0.688835i	−0.0109146	−	0.103846i
$45$	−0.548698	−	2.16770i	−0.0817951	−	0.323142i
$46$	4.80811	−	3.49329i	0.708917	−	0.515058i
$47$	−7.65033	−	10.5298i	−1.11592	−	1.53593i	−0.812400	−	0.583100i	$-0.801840\pi$
$47$	−7.65033	−	10.5298i	−1.11592	−	1.53593i	−0.303515	−	0.952827i	$-0.598160\pi$
$48$	0.207912	+	0.978148i	0.0300095	+	0.141183i
$49$	−0.0240043	−	0.228386i	−0.00342919	−	0.0326265i
$50$	4.99807	+	0.138804i	0.706834	+	0.0196299i
$51$	−5.54750	−	1.17916i	−0.776806	−	0.165115i
$52$	0.567628	+	1.27491i	0.0787159	+	0.176799i
$53$	0.438422	−	0.394757i	0.0602219	−	0.0542240i	−0.638470	−	0.769647i	$-0.720432\pi$
$53$	0.438422	−	0.394757i	0.0602219	−	0.0542240i	0.698692	+	0.715423i	$0.253766\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	1.18997	+	0.991284i	0.160456	+	0.133665i
$56$	−1.30100	−	2.25339i	−0.173853	−	0.301122i
$57$	−3.94214	−	2.27600i	−0.522150	−	0.301463i
$58$	8.35669	−	2.71525i	1.09729	−	0.356530i
$59$	2.32422	+	1.03481i	0.302588	+	0.134721i	0.552414	−	0.833570i	$-0.313707\pi$
$59$	2.32422	+	1.03481i	0.302588	+	0.134721i	−0.249826	+	0.968291i	$0.580373\pi$
$60$	−1.85824	−	1.24377i	−0.239897	−	0.160569i
$61$	−14.2000			−1.81812			−0.909061	−	0.416664i	$-0.863199\pi$
$61$	−14.2000			−1.81812			−0.909061	+	0.416664i	$0.863199\pi$
$62$	5.55795	+	0.330452i	0.705860	+	0.0419674i
$63$		−	2.60199i		−	0.327820i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−2.89751	−	1.15865i	−0.359392	−	0.143713i
$66$	−0.214034	−	0.658729i	−0.0263458	−	0.0810840i
$67$	−3.18752	−	1.84032i	−0.389417	−	0.224830i	0.292490	−	0.956269i	$-0.405516\pi$
$67$	−3.18752	−	1.84032i	−0.389417	−	0.224830i	−0.681908	+	0.731438i	$0.738849\pi$
$68$	−4.91161	+	2.83572i	−0.595620	+	0.343881i
$69$	3.97674	−	4.41662i	0.478743	−	0.531698i
$70$	5.59853	+	1.58374i	0.669152	+	0.189293i
$71$	5.85946	+	6.50759i	0.695391	+	0.772309i	0.982635	−	0.185548i	$-0.0594060\pi$
$71$	5.85946	+	6.50759i	0.695391	+	0.772309i	−0.287245	+	0.957857i	$0.592739\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	−3.16453	+	14.8879i	−0.370380	+	1.74250i	0.259439	+	0.965759i	$0.416462\pi$
$73$	−3.16453	+	14.8879i	−0.370380	+	1.74250i	−0.629819	+	0.776742i	$0.716871\pi$
$74$	1.14713	−	10.9142i	0.133351	−	1.26875i
$75$	4.91771	−	0.903387i	0.567848	−	0.104314i
$76$	−4.45252	+	0.946413i	−0.510739	+	0.108561i
$77$	1.05931	+	1.45802i	0.120720	+	0.166157i
$78$	0.820294	+	1.12904i	0.0928800	+	0.127838i
$79$	−0.621428	+	0.132089i	−0.0699161	+	0.0148611i	−0.242737	−	0.970092i	$-0.578045\pi$
$79$	−0.621428	+	0.132089i	−0.0699161	+	0.0148611i	0.172821	+	0.984953i	$0.444712\pi$
$80$	−2.21318	+	0.319106i	−0.247441	+	0.0356771i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−1.15067	+	5.41350i	−0.127071	+	0.597821i
$83$	−3.52397	−	7.91496i	−0.386806	−	0.868780i	−0.997064	−	0.0765771i	$-0.975601\pi$
$83$	−3.52397	−	7.91496i	−0.386806	−	0.868780i	0.610258	−	0.792203i	$-0.291066\pi$
$84$	−1.74107	−	1.93366i	−0.189966	−	0.210979i
$85$	3.45200	−	12.2029i	0.374422	−	1.32359i
$86$	−5.80553	+	6.44769i	−0.626026	+	0.695272i
$87$	7.60954	−	4.39337i	0.815829	−	0.471019i
$88$	−0.599834	−	0.346314i	−0.0639425	−	0.0369172i
$89$	1.81833	+	5.59625i	0.192743	+	0.593201i	0.999996	+	0.00299516i	$0.000953389\pi$
$89$	1.81833	+	5.59625i	0.192743	+	0.593201i	−0.807253	+	0.590206i	$0.799047\pi$
$90$	−2.07622	−	0.830237i	−0.218853	−	0.0875146i
$91$	−2.93775	−	2.13440i	−0.307959	−	0.223746i
$92$		−	5.94315i		−	0.619616i
$93$	5.50520	−	0.832332i	0.570863	−	0.0863088i
$94$	−13.0155			−1.34245
$95$	5.66161	−	8.45869i	0.580869	−	0.867843i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−13.6733	+	4.44273i	−1.38832	+	0.451091i	−0.905394	−	0.424572i	$-0.860425\pi$
$97$	−13.6733	+	4.44273i	−1.38832	+	0.451091i	−0.482922	+	0.875663i	$0.660425\pi$
$98$	−0.198877	−	0.114822i	−0.0200896	−	0.0115988i
$99$	−0.346314	−	0.599834i	−0.0348059	−	0.0602856i
$100$	3.05009	−	3.96194i	0.305009	−	0.396194i
$101$	−5.48325	+	16.8757i	−0.545603	+	1.67919i	0.173947	+	0.984755i	$0.444348\pi$
$101$	−5.48325	+	16.8757i	−0.545603	+	1.67919i	−0.719551	+	0.694440i	$0.755652\pi$
$102$	−4.21470	+	3.79493i	−0.417317	+	0.375754i
$103$	−4.72799	−	10.6192i	−0.465863	−	1.04635i	−0.981834	−	0.189739i	$-0.939236\pi$
$103$	−4.72799	−	10.6192i	−0.465863	−	1.04635i	0.515972	−	0.856606i	$-0.327431\pi$
$104$	1.36507	+	0.290155i	0.133856	+	0.0284520i
$105$	5.80547	+	0.385130i	0.566556	+	0.0375848i
$106$	−0.0616671	−	0.586723i	−0.00598964	−	0.0569876i
$107$	2.82035	+	13.2687i	0.272653	+	1.28273i	0.874854	+	0.484387i	$0.160957\pi$
$107$	2.82035	+	13.2687i	0.272653	+	1.28273i	−0.602200	+	0.798345i	$0.705709\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	−6.75156	+	4.90529i	−0.646682	+	0.469842i	−0.862139	−	0.506671i	$-0.830876\pi$
$109$	−6.75156	+	4.90529i	−0.646682	+	0.469842i	0.215457	+	0.976513i	$0.430876\pi$
$110$	1.50141	−	0.380044i	0.143154	−	0.0362358i
$111$	−1.14713	−	10.9142i	−0.108881	−	1.03593i
$112$	−2.58774	−	0.271982i	−0.244518	−	0.0256999i
$113$	1.16832	−	5.49651i	0.109906	−	0.517068i	−0.888409	−	0.459052i	$-0.848189\pi$
$113$	1.16832	−	5.49651i	0.109906	−	0.517068i	0.998316	−	0.0580161i	$-0.0184775\pi$
$114$	−4.15845	+	1.85146i	−0.389475	+	0.173405i
$115$	9.26559	+	9.52648i	0.864021	+	0.888349i
$116$	2.71525	−	8.35669i	0.252105	−	0.775899i
$117$	1.03711	+	0.933817i	0.0958807	+	0.0863314i
$118$	2.20332	−	1.27209i	0.202832	−	0.117105i
$119$	7.37851	−	12.7800i	0.676387	−	1.17154i
$120$	−2.09847	+	0.772279i	−0.191563	+	0.0704991i
$121$	−9.61074	−	4.27898i	−0.873704	−	0.388998i
$122$	−8.34654	+	11.4880i	−0.755660	+	1.04008i
$123$			5.53444i			0.499023i
$124$	3.53422	−	4.30224i	0.317382	−	0.386353i
$125$	1.28772	+	11.1059i	0.115177	+	0.993345i
$126$	−2.10505	−	1.52941i	−0.187533	−	0.136251i
$127$	−0.964409	+	2.16610i	−0.0855775	+	0.192210i	−0.951265	−	0.308375i	$-0.900215\pi$
$127$	−0.964409	+	2.16610i	−0.0855775	+	0.192210i	0.865688	+	0.500585i	$0.166882\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−4.33811	+	7.51383i	−0.381949	+	0.661556i
$130$	−2.64048	+	1.66310i	−0.231586	+	0.145863i
$131$	−1.13736	+	1.26317i	−0.0993719	+	0.110364i	−0.790779	−	0.612102i	$-0.790324\pi$
$131$	−1.13736	+	1.26317i	−0.0993719	+	0.110364i	0.691407	+	0.722465i	$0.256991\pi$
$132$	−0.658729	−	0.214034i	−0.0573350	−	0.0186293i
$133$	8.80199	−	7.92535i	0.763229	−	0.687215i
$134$	−3.36242	+	1.49705i	−0.290469	+	0.129325i
$135$	−2.20347	−	0.380423i	−0.189644	−	0.0327416i
$136$	−0.592827	+	5.64037i	−0.0508345	+	0.483658i
$137$	5.24656	−	0.551436i	0.448244	−	0.0471123i	0.122282	−	0.992495i	$-0.460979\pi$
$137$	5.24656	−	0.551436i	0.448244	−	0.0471123i	0.325962	+	0.945383i	$0.394312\pi$
$138$	−1.23565	−	5.81328i	−0.105185	−	0.494859i
$139$	10.6674	−	7.75028i	0.904793	−	0.657371i	−0.0348997	−	0.999391i	$-0.511111\pi$
$139$	10.6674	−	7.75028i	0.904793	−	0.657371i	0.939693	+	0.342020i	$0.111111\pi$
$140$	4.57201	−	3.59841i	0.386405	−	0.304121i
$141$	−12.7311	+	2.70608i	−1.07215	+	0.227893i
$142$	8.70886	−	0.915338i	0.730831	−	0.0768135i
$143$	−0.961315	−	0.101038i	−0.0803892	−	0.00844925i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	8.67602	+	17.6284i	0.720504	+	1.46396i
$146$	10.1845	+	11.3111i	0.842878	+	0.936111i
$147$	−0.218404	−	0.0709638i	−0.0180137	−	0.00585300i
$148$	−8.15552	−	7.34326i	−0.670379	−	0.603612i
$149$	10.7596	+	18.6361i	0.881457	+	1.52673i	0.849721	+	0.527233i	$0.176770\pi$
$149$	10.7596	+	18.6361i	0.881457	+	1.52673i	0.0317365	+	0.999496i	$0.489896\pi$
$150$	2.15970	−	4.50951i	0.176339	−	0.368200i
$151$	4.17956	+	12.8634i	0.340128	+	1.04681i	0.964141	+	0.265392i	$0.0855015\pi$
$151$	4.17956	+	12.8634i	0.340128	+	1.04681i	−0.624012	+	0.781414i	$0.714499\pi$
$152$	−1.85146	+	4.15845i	−0.150173	+	0.337295i
$153$	−3.33359	+	4.58829i	−0.269505	+	0.370941i
$154$	1.80221			0.145227
$155$	1.04223	+	12.4062i	0.0837136	+	0.996490i
$156$	1.39557			0.111735
$157$	0.194160	−	0.267239i	0.0154957	−	0.0213280i	−0.801199	−	0.598398i	$-0.795804\pi$
$157$	0.194160	−	0.267239i	0.0154957	−	0.0213280i	0.816695	+	0.577070i	$0.195804\pi$
$158$	−0.258404	+	0.580385i	−0.0205575	+	0.0461730i
$159$	−0.182306	−	0.561080i	−0.0144578	−	0.0444966i
$160$	−1.04271	+	1.97807i	−0.0824337	+	0.156380i
$161$	7.73201	+	13.3922i	0.609368	+	1.05546i
$162$	0.743145	+	0.669131i	0.0583870	+	0.0525719i
$163$	−22.1159	−	7.18589i	−1.73225	−	0.562843i	−0.738480	−	0.674276i	$-0.764456\pi$
$163$	−22.1159	−	7.18589i	−1.73225	−	0.562843i	−0.993772	+	0.111433i	$0.964456\pi$
$164$	3.70326	+	4.11289i	0.289176	+	0.321163i
$165$	1.38959	−	0.683901i	0.108179	−	0.0532416i
$166$	−8.47467	−	1.80135i	−0.657762	−	0.139812i
$167$	10.9750	+	1.15352i	0.849274	+	0.0892623i	0.519158	−	0.854678i	$-0.326245\pi$
$167$	10.9750	+	1.15352i	0.849274	+	0.0892623i	0.330116	+	0.943940i	$0.392912\pi$
$168$	−2.58774	+	0.271982i	−0.199648	+	0.0209839i
$169$	−10.8109	+	2.29792i	−0.831605	+	0.176763i
$170$	−7.84328	−	9.96538i	−0.601552	−	0.764310i
$171$	−3.68264	+	2.67559i	−0.281619	+	0.204608i
$172$	1.80389	+	8.48663i	0.137545	+	0.647099i
$173$	−3.67505	+	0.386263i	−0.279409	+	0.0293670i	−0.243196	−	0.969977i	$-0.578196\pi$
$173$	−3.67505	+	0.386263i	−0.279409	+	0.0293670i	−0.0362124	+	0.999344i	$0.511529\pi$
$174$	0.918465	−	8.73861i	0.0696286	−	0.662472i
$175$	−1.71858	+	12.8959i	−0.129912	+	0.974842i
$176$	−0.632748	+	0.281718i	−0.0476952	+	0.0212353i
$177$	1.89069	−	1.70239i	0.142113	−	0.127959i
$178$	5.59625	+	1.81833i	0.419456	+	0.136290i
$179$	13.0109	−	14.4501i	0.972482	−	1.08005i	−0.0242851	−	0.999705i	$-0.507731\pi$
$179$	13.0109	−	14.4501i	0.972482	−	1.08005i	0.996767	−	0.0803456i	$-0.0256024\pi$
$180$	−1.89205	+	1.19170i	−0.141025	+	0.0888241i
$181$	2.33850	−	4.05039i	0.173819	−	0.301063i	−0.765933	−	0.642920i	$-0.777723\pi$
$181$	2.33850	−	4.05039i	0.173819	−	0.301063i	0.939752	+	0.341857i	$0.111056\pi$
$182$	−3.45353	+	1.12212i	−0.255993	+	0.0831770i
$183$	−5.77565	+	12.9723i	−0.426949	+	0.958942i
$184$	−4.80811	−	3.49329i	−0.354458	−	0.257529i
$185$	24.5212	−	0.943984i	1.80283	−	0.0694031i
$186$	2.56250	−	4.94303i	0.187892	−	0.362441i
$187$		−	3.92820i		−	0.287258i
$188$	−7.65033	+	10.5298i	−0.557958	+	0.767963i
$189$	−2.37704	−	1.05833i	−0.172904	−	0.0769818i
$190$	−3.51541	−	9.55223i	−0.255035	−	0.692992i
$191$	−3.10023	+	5.36975i	−0.224325	+	0.388542i	−0.956117	−	0.292986i	$-0.905351\pi$
$191$	−3.10023	+	5.36975i	−0.224325	+	0.388542i	0.731792	+	0.681528i	$0.238684\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−14.2428	−	12.8243i	−1.02522	−	0.923111i	−0.0281484	−	0.999604i	$-0.508961\pi$
$193$	−14.2428	−	12.8243i	−1.02522	−	0.923111i	−0.997070	+	0.0764928i	$0.975628\pi$
$194$	−4.44273	+	13.6733i	−0.318970	+	0.981688i
$195$	−2.23700	+	2.17574i	−0.160195	+	0.155808i
$196$	−0.209790	+	0.0934045i	−0.0149850	+	0.00667175i
$197$	1.63308	−	7.68304i	0.116352	−	0.547394i	−0.880899	−	0.473304i	$-0.843061\pi$
$197$	1.63308	−	7.68304i	0.116352	−	0.547394i	0.997252	−	0.0740904i	$-0.0236053\pi$
$198$	−0.688835	−	0.0723994i	−0.0489533	−	0.00514520i
$199$	−2.54615	−	24.2250i	−0.180492	−	1.71727i	−0.592066	−	0.805889i	$-0.701688\pi$
$199$	−2.54615	−	24.2250i	−0.180492	−	1.71727i	0.411574	−	0.911376i	$-0.364979\pi$
$200$	−1.41248	−	4.79634i	−0.0998773	−	0.339153i
$201$	−2.97769	+	2.16342i	−0.210030	+	0.152596i
$202$	10.4298	+	14.3553i	0.733835	+	1.01004i
$203$	4.75349	+	22.3634i	0.333630	+	1.56960i
$204$	0.592827	+	5.64037i	0.0415062	+	0.394905i
$205$	−12.3482	−	0.819172i	−0.862438	−	0.0572134i
$206$	−11.3702	−	2.41681i	−0.792199	−	0.168387i
$207$	−2.41730	−	5.42934i	−0.168014	−	0.377365i
$208$	1.03711	−	0.933817i	0.0719106	−	0.0647486i
$209$	0.974282	−	2.99853i	0.0673925	−	0.207413i
$210$	3.72394	−	4.47035i	0.256977	−	0.308483i
$211$	1.75156	+	3.03380i	0.120583	+	0.208855i	0.919998	−	0.391924i	$-0.128190\pi$
$211$	1.75156	+	3.03380i	0.120583	+	0.208855i	−0.799415	+	0.600779i	$0.794857\pi$
$212$	−0.510916	−	0.294977i	−0.0350898	−	0.0202591i
$213$	8.32824	−	2.70601i	0.570642	−	0.185413i
$214$	12.3923	+	5.51743i	0.847124	+	0.377164i
$215$	−16.1225	−	10.7912i	−1.09954	−	0.735953i
$216$	1.00000			0.0680414
$217$	−2.36678	+	14.2926i	−0.160668	+	0.970247i
$218$			8.34539i			0.565221i
$219$	12.3137	+	8.94641i	0.832081	+	0.604542i
$220$	0.575046	−	1.43805i	0.0387696	−	0.0969535i
$221$	2.44583	+	7.52749i	0.164524	+	0.506354i
$222$	−9.50405	−	5.48717i	−0.637870	−	0.368274i
$223$	5.68109	−	3.27998i	0.380434	−	0.219644i	−0.297573	−	0.954699i	$-0.596177\pi$
$223$	5.68109	−	3.27998i	0.380434	−	0.219644i	0.678007	+	0.735055i	$0.262844\pi$
$224$	−1.74107	+	1.93366i	−0.116330	+	0.129198i
$225$	1.17493	−	4.85999i	0.0783286	−	0.324000i
$226$	−3.76005	−	4.17596i	−0.250115	−	0.277780i
$227$	−4.75874	−	10.6883i	−0.315848	−	0.709407i	0.683949	−	0.729530i	$-0.260261\pi$
$227$	−4.75874	−	10.6883i	−0.315848	−	0.709407i	−0.999798	+	0.0201227i	$0.993594\pi$
$228$	−0.946413	+	4.45252i	−0.0626777	+	0.294875i
$229$	−1.08173	+	10.2919i	−0.0714826	+	0.680111i	0.898837	+	0.438284i	$0.144413\pi$
$229$	−1.08173	+	10.2919i	−0.0714826	+	0.680111i	−0.970319	+	0.241827i	$0.922253\pi$
$230$	13.1533	−	1.89649i	0.867300	−	0.125051i
$231$	1.76283	−	0.374701i	0.115986	−	0.0246535i
$232$	−5.16472	−	7.10863i	−0.339080	−	0.466704i
$233$	14.2912	+	19.6702i	0.936250	+	1.28864i	0.957371	+	0.288860i	$0.0932763\pi$
$233$	14.2912	+	19.6702i	0.936250	+	1.28864i	−0.0211217	+	0.999777i	$0.506724\pi$
$234$	1.36507	−	0.290155i	0.0892375	−	0.0189680i
$235$	−4.15333	−	28.8057i	−0.270933	−	1.87908i
$236$	0.265939	−	2.53024i	0.0173111	−	0.164704i
$237$	−0.132089	+	0.621428i	−0.00858008	+	0.0403661i
$238$	−6.00222	−	13.4812i	−0.389066	−	0.873857i
$239$	−8.45251	−	9.38746i	−0.546747	−	0.607224i	0.404921	−	0.914352i	$-0.367299\pi$
$239$	−8.45251	−	9.38746i	−0.546747	−	0.607224i	−0.951668	+	0.307127i	$0.900632\pi$
$240$	−0.608664	+	2.15163i	−0.0392891	+	0.138887i
$241$	−7.25726	+	8.06001i	−0.467481	+	0.519191i	−0.930070	−	0.367382i	$-0.880254\pi$
$241$	−7.25726	+	8.06001i	−0.467481	+	0.519191i	0.462589	+	0.886573i	$0.346921\pi$
$242$	−9.11082	+	5.26013i	−0.585665	+	0.338134i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.38804	+	13.5050i	0.280915	+	0.864568i
$245$	0.190659	−	0.476792i	0.0121807	−	0.0304611i
$246$	4.47745	+	3.25306i	0.285472	+	0.207408i
$247$			6.35262i			0.404207i
$248$	−1.40322	−	5.38804i	−0.0891047	−	0.342141i
$249$	−8.66400			−0.549059
$250$	9.74179	+	5.48612i	0.616125	+	0.346973i
$251$	2.80602	+	1.24932i	0.177114	+	0.0788564i	0.493378	−	0.869815i	$-0.335762\pi$
$251$	2.80602	+	1.24932i	0.177114	+	0.0788564i	−0.316264	+	0.948671i	$0.602429\pi$
$252$	−2.47464	+	0.804059i	−0.155888	+	0.0506510i
$253$	3.56490	+	2.05820i	0.224124	+	0.129398i
$254$	1.18554	+	2.05342i	0.0743877	+	0.128843i
$255$	−9.74381	−	8.11691i	−0.610181	−	0.508300i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−10.8164	+	9.73909i	−0.674706	+	0.607508i	−0.933565	−	0.358407i	$-0.883320\pi$
$257$	−10.8164	+	9.73909i	−0.674706	+	0.607508i	0.258860	+	0.965915i	$0.416653\pi$
$258$	3.52894	+	7.92612i	0.219702	+	0.493459i
$259$	27.9311	+	5.93694i	1.73555	+	0.368904i
$260$	−0.206563	+	3.11374i	−0.0128105	+	0.193106i
$261$	−0.918465	−	8.73861i	−0.0568515	−	0.540906i
$262$	0.353400	+	1.66262i	0.0218332	+	0.102717i
$263$	9.81265	+	13.5060i	0.605074	+	0.832813i	0.996161	−	0.0875407i	$-0.0279008\pi$
$263$	9.81265	+	13.5060i	0.605074	+	0.832813i	−0.391087	+	0.920354i	$0.627901\pi$
$264$	−0.560349	+	0.407117i	−0.0344871	+	0.0250563i
$265$	1.27885	−	0.323707i	0.0785589	−	0.0198852i
$266$	−1.23806	−	11.7794i	−0.0759104	−	0.722239i
$267$	5.85201	+	0.615071i	0.358137	+	0.0376417i
$268$	−0.765246	+	3.60020i	−0.0467448	+	0.219917i
$269$	16.7172	−	7.44297i	1.01927	−	0.453806i	0.172068	−	0.985085i	$-0.444955\pi$
$269$	16.7172	−	7.44297i	1.01927	−	0.453806i	0.847197	+	0.531279i	$0.178288\pi$
$270$	−1.60294	+	1.55904i	−0.0975515	+	0.0948800i
$271$	−1.63959	+	5.04614i	−0.0995980	+	0.306531i	−0.988425	−	0.151712i	$-0.951521\pi$
$271$	−1.63959	+	5.04614i	−0.0995980	+	0.306531i	0.888827	+	0.458244i	$0.151521\pi$
$272$	4.21470	+	3.79493i	0.255554	+	0.230102i
$273$	−3.14476	+	1.81563i	−0.190329	+	0.109887i
$274$	2.63773	−	4.56868i	0.159351	−	0.276004i
$275$	1.32022	+	3.20162i	0.0796121	+	0.193065i
$276$	−5.42934	−	2.41730i	−0.326808	−	0.145504i
$277$	−5.93198	+	8.16467i	−0.356418	+	0.490568i	−0.949146	−	0.314835i	$-0.898051\pi$
$277$	−5.93198	+	8.16467i	−0.356418	+	0.490568i	0.592728	+	0.805403i	$0.298051\pi$
$278$		−	13.1856i		−	0.790818i
$279$	1.47879	−	5.36779i	0.0885330	−	0.321361i
$280$	−0.223816	−	5.81392i	−0.0133756	−	0.347448i
$281$	−11.3985	−	8.28147i	−0.679976	−	0.494031i	0.193374	−	0.981125i	$-0.438057\pi$
$281$	−11.3985	−	8.28147i	−0.679976	−	0.494031i	−0.873350	+	0.487094i	$0.838057\pi$
$282$	−5.29389	+	11.8903i	−0.315247	+	0.708056i
$283$	−8.74348	+	2.84093i	−0.519746	+	0.168876i	−0.557130	−	0.830425i	$-0.688097\pi$
$283$	−8.74348	+	2.84093i	−0.519746	+	0.168876i	0.0373842	+	0.999301i	$0.488097\pi$
$284$	4.37842	−	7.58364i	0.259811	−	0.450006i
$285$	−5.42461	−	8.61260i	−0.321326	−	0.510166i
$286$	−0.646789	+	0.718332i	−0.0382454	+	0.0424758i
$287$	−13.6957	−	4.45002i	−0.808434	−	0.262676i
$288$	0.743145	−	0.669131i	0.0437902	−	0.0394289i
$289$	−13.8541	+	6.16824i	−0.814947	+	0.362838i
$290$	19.3613	+	3.34268i	1.13694	+	0.196289i
$291$	−1.50280	+	14.2982i	−0.0880960	+	0.838177i
$292$	15.1372	−	1.59098i	0.885835	−	0.0931051i
$293$	−3.39212	−	15.9587i	−0.198170	−	0.932316i	−0.959009	−	0.283375i	$-0.908546\pi$
$293$	−3.39212	−	15.9587i	−0.198170	−	0.932316i	0.760839	−	0.648940i	$-0.224788\pi$
$294$	−0.185786	+	0.134981i	−0.0108352	+	0.00787227i
$295$	3.51845	+	4.47042i	0.204852	+	0.260278i
$296$	−10.7345	+	2.28169i	−0.623931	+	0.132621i
$297$	−0.688835	+	0.0723994i	−0.0399702	+	0.00420104i
$298$	21.4012	+	2.24936i	1.23974	+	0.130302i
$299$	−8.11282	−	1.72443i	−0.469176	−	0.0997265i
$300$	−2.37883	−	4.39786i	−0.137342	−	0.253911i
$301$	−15.1059	−	16.7768i	−0.870691	−	0.967001i
$302$	12.8634	+	4.17956i	0.740204	+	0.240507i
$303$	13.1865	+	11.8732i	0.757544	+	0.682095i
$304$	2.27600	+	3.94214i	0.130537	+	0.226097i
$305$	−28.0885	−	14.8065i	−1.60834	−	0.847818i
$306$	1.75257	+	5.39386i	0.100188	+	0.308346i
$307$	13.4111	−	30.1219i	0.765415	−	1.71915i	0.0733582	−	0.997306i	$-0.476628\pi$
$307$	13.4111	−	30.1219i	0.765415	−	1.71915i	0.692056	−	0.721844i	$-0.256705\pi$
$308$	1.05931	−	1.45802i	0.0603601	−	0.0830785i
$309$	−11.6242			−0.661278
$310$	10.6494	+	6.44900i	0.604847	+	0.366279i
$311$	−7.97289			−0.452101			−0.226050	−	0.974116i	$-0.572581\pi$
$311$	−7.97289			−0.452101			−0.226050	+	0.974116i	$0.572581\pi$
$312$	0.820294	−	1.12904i	0.0464400	−	0.0639192i
$313$	−7.80195	+	17.5235i	−0.440992	+	0.990485i	0.547163	+	0.837026i	$0.315708\pi$
$313$	−7.80195	+	17.5235i	−0.440992	+	0.990485i	−0.988155	+	0.153459i	$0.950959\pi$
$314$	−0.102076	−	0.314158i	−0.00576049	−	0.0177290i
$315$	2.71313	−	5.14691i	0.152868	−	0.289996i
$316$	0.317655	+	0.550195i	0.0178695	+	0.0309509i
$317$	2.65073	+	2.38673i	0.148880	+	0.134052i	0.740205	−	0.672381i	$-0.234728\pi$
$317$	2.65073	+	2.38673i	0.148880	+	0.134052i	−0.591325	+	0.806433i	$0.701395\pi$
$318$	−0.561080	−	0.182306i	−0.0314638	−	0.0102232i
$319$	4.07230	+	4.52274i	0.228005	+	0.253225i
$320$	0.987398	+	2.00625i	0.0551972	+	0.112153i
$321$	13.2687	+	2.82035i	0.740586	+	0.157416i
$322$	15.3793	+	1.61643i	0.857055	+	0.0900801i
$323$	−25.6749	+	2.69854i	−1.42859	+	0.150151i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	−4.52333	−	5.31316i	−0.250909	−	0.294721i
$326$	−18.8129	+	13.6684i	−1.04195	+	0.757022i
$327$	1.73510	+	8.16302i	0.0959514	+	0.451416i
$328$	5.50412	−	0.578506i	0.303914	−	0.0319427i
$329$	3.53999	−	33.6808i	0.195166	−	1.85688i
$330$	0.263492	−	1.52619i	0.0145047	−	0.0840138i
$331$	−1.56998	+	0.698999i	−0.0862938	+	0.0384205i	−0.449430	−	0.893316i	$-0.648373\pi$
$331$	−1.56998	+	0.698999i	−0.0862938	+	0.0384205i	0.363136	+	0.931736i	$0.381706\pi$
$332$	−6.43861	+	5.79735i	−0.353365	+	0.318171i
$333$	−10.4372	−	3.39126i	−0.571956	−	0.185840i
$334$	7.38419	−	8.20097i	0.404045	−	0.448737i
$335$	−4.38621	−	6.96394i	−0.239644	−	0.380480i
$336$	−1.30100	+	2.25339i	−0.0709751	+	0.122933i
$337$	25.7853	−	8.37815i	1.40461	−	0.456387i	0.493934	−	0.869499i	$-0.335558\pi$
$337$	25.7853	−	8.37815i	1.40461	−	0.456387i	0.910680	+	0.413112i	$0.135558\pi$
$338$	−4.49541	+	10.0969i	−0.244518	+	0.549197i
$339$	−4.54611	−	3.30294i	−0.246911	−	0.179391i
$340$	−12.6723	+	0.487842i	−0.687254	+	0.0264570i
$341$	1.35668	+	3.60988i	0.0734683	+	0.195486i
$342$			4.55199i			0.246144i
$343$	11.0571	−	15.2188i	0.597027	−	0.821738i
$344$	7.92612	+	3.52894i	0.427348	+	0.190268i
$345$	12.4715	−	4.58977i	0.671445	−	0.247105i
$346$	−1.84765	+	3.20022i	−0.0993300	+	0.172045i
$347$	7.36616	−	4.25285i	0.395436	−	0.228305i	−0.289077	−	0.957306i	$-0.593348\pi$
$347$	7.36616	−	4.25285i	0.395436	−	0.228305i	0.684513	+	0.729001i	$0.260015\pi$
$348$	−6.52982	−	5.87948i	−0.350035	−	0.315173i
$349$	−2.50449	+	7.70804i	−0.134062	+	0.412602i	−0.995443	−	0.0953584i	$-0.969600\pi$
$349$	−2.50449	+	7.70804i	−0.134062	+	0.412602i	0.861381	+	0.507960i	$0.169600\pi$
$350$	9.42289	+	8.97040i	0.503674	+	0.479488i
$351$	1.27491	−	0.567628i	0.0680499	−	0.0302978i
$352$	−0.144006	+	0.677493i	−0.00767553	+	0.0361105i
$353$	23.1366	+	2.43175i	1.23143	+	0.129429i	0.697804	−	0.716289i	$-0.254161\pi$
$353$	23.1366	+	2.43175i	1.23143	+	0.129429i	0.533631	+	0.845718i	$0.320827\pi$
$354$	−0.265939	−	2.53024i	−0.0141345	−	0.134481i
$355$	4.80486	+	18.9822i	0.255015	+	1.00747i
$356$	4.76045	−	3.45867i	0.252303	−	0.183309i
$357$	−8.67396	−	11.9387i	−0.459075	−	0.631862i
$358$	−4.04274	−	19.0196i	−0.213666	−	1.00522i
$359$	0.472830	+	4.49867i	0.0249550	+	0.237431i	0.999888	+	0.0149344i	$0.00475395\pi$
$359$	0.472830	+	4.49867i	0.0249550	+	0.237431i	−0.974933	+	0.222497i	$0.928579\pi$
$360$	−0.148014	+	2.23116i	−0.00780100	+	0.117593i
$361$	−1.68305	−	0.357743i	−0.0885816	−	0.0188286i
$362$	−1.90230	−	4.27264i	−0.0999829	−	0.224565i
$363$	−7.81808	+	7.03943i	−0.410343	+	0.369474i
$364$	−1.12212	+	3.45353i	−0.0588150	+	0.181014i
$365$	−21.7835	+	26.1496i	−1.14020	+	1.36873i
$366$	7.09999	+	12.2975i	0.371122	+	0.642803i
$367$	−2.04466	−	1.18049i	−0.106730	−	0.0616208i	0.445685	−	0.895190i	$-0.352960\pi$
$367$	−2.04466	−	1.18049i	−0.106730	−	0.0616208i	−0.552415	+	0.833569i	$0.686294\pi$
$368$	−5.65227	+	1.83653i	−0.294645	+	0.0957359i
$369$	5.05596	+	2.25106i	0.263203	+	0.117185i
$370$	13.6495	−	20.3929i	0.709603	−	1.06018i
$371$	1.53506			0.0796962
$372$	−2.49280	−	4.97855i	−0.129245	−	0.258126i
$373$			1.52880i			0.0791582i	0.999216	+	0.0395791i	$0.0126017\pi$
$373$			1.52880i			0.0791582i	−0.999216	+	0.0395791i	$0.987398\pi$
$374$	−3.17798	−	2.30894i	−0.164329	−	0.119392i
$375$	10.6695	+	3.34080i	0.550973	+	0.172518i
$376$	4.02202	+	12.3785i	0.207420	+	0.638372i
$377$	−10.6196	−	6.13125i	−0.546939	−	0.315775i
$378$	−2.25339	+	1.30100i	−0.115902	+	0.0669160i
$379$	−15.5814	+	17.3049i	−0.800363	+	0.888893i	−0.995775	−	0.0918279i	$-0.970729\pi$
$379$	−15.5814	+	17.3049i	−0.800363	+	0.888893i	0.195412	+	0.980721i	$0.437396\pi$
$380$	−9.79422	−	2.77064i	−0.502433	−	0.142131i
$381$	1.58657	+	1.76206i	0.0812824	+	0.0902732i
$382$	2.52195	+	5.66440i	0.129034	+	0.289816i
$383$	−5.53607	+	26.0452i	−0.282880	+	1.33085i	0.575488	+	0.817810i	$0.304812\pi$
$383$	−5.53607	+	26.0452i	−0.282880	+	1.33085i	−0.858368	+	0.513035i	$0.828521\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	0.575097	+	3.98863i	0.0293097	+	0.203279i
$386$	−18.7468	+	3.98475i	−0.954185	+	0.202818i
$387$	5.09976	+	7.01921i	0.259235	+	0.356807i
$388$	8.45058	+	11.6312i	0.429013	+	0.590486i
$389$	−21.7713	+	4.62763i	−1.10385	+	0.234630i	−0.723576	−	0.690245i	$-0.757503\pi$
$389$	−21.7713	+	4.62763i	−1.10385	+	0.234630i	−0.380271	+	0.924875i	$0.624169\pi$
$390$	0.445334	+	3.08864i	0.0225504	+	0.156400i
$391$	3.52326	−	33.5215i	0.178179	−	1.69526i
$392$	−0.0477456	+	0.224626i	−0.00241152	+	0.0113453i
$393$	0.691356	+	1.55281i	0.0348743	+	0.0783289i
$394$	−5.25581	−	5.83717i	−0.264784	−	0.294072i
$395$	−1.36696	−	0.386691i	−0.0687791	−	0.0194565i
$396$	−0.463459	+	0.514724i	−0.0232897	+	0.0258658i
$397$	−0.786378	+	0.454015i	−0.0394672	+	0.0227864i	−0.519604	−	0.854407i	$-0.673920\pi$
$397$	−0.786378	+	0.454015i	−0.0394672	+	0.0227864i	0.480137	+	0.877194i	$0.340587\pi$
$398$	−21.0950	−	12.1792i	−1.05740	−	0.610489i
$399$	−3.66007	−	11.2645i	−0.183233	−	0.563933i
$400$	−4.71056	−	1.67650i	−0.235528	−	0.0838250i
$401$	−23.0563	−	16.7514i	−1.15138	−	0.836524i	−0.162714	−	0.986673i	$-0.552025\pi$
$401$	−23.0563	−	16.7514i	−1.15138	−	0.836524i	−0.988663	+	0.150149i	$0.952025\pi$
$402$			3.68063i			0.183573i
$403$	−4.84739	−	6.07278i	−0.241466	−	0.302507i
$404$	17.7442			0.882805
$405$	−1.24377	+	1.85824i	−0.0618032	+	0.0923366i
$406$	20.8864	+	9.29923i	1.03658	+	0.461513i
$407$	7.22911	−	2.34888i	0.358334	−	0.116430i
$408$	4.91161	+	2.83572i	0.243161	+	0.140389i
$409$	8.22290	+	14.2425i	0.406596	+	0.704246i	0.994506	−	0.104681i	$-0.0333822\pi$
$409$	8.22290	+	14.2425i	0.406596	+	0.704246i	−0.587909	+	0.808927i	$0.700049\pi$
$410$	−7.92083	+	9.50844i	−0.391182	+	0.469588i
$411$	1.63021	−	5.01726i	0.0804122	−	0.247483i
$412$	−8.63847	+	7.77811i	−0.425587	+	0.383200i
$413$	2.69256	+	6.04760i	0.132492	+	0.297583i
$414$	−5.81328	−	1.23565i	−0.285707	−	0.0607289i
$415$	1.28239	−	19.3308i	0.0629500	−	0.948912i
$416$	−0.145877	−	1.38792i	−0.00715219	−	0.0680485i
$417$	−2.74143	−	12.8974i	−0.134249	−	0.631590i
$418$	−1.85319	−	2.55070i	−0.0906427	−	0.124759i
$419$	11.0755	−	8.04684i	0.541075	−	0.393114i	−0.283409	−	0.958999i	$-0.591465\pi$
$419$	11.0755	−	8.04684i	0.541075	−	0.393114i	0.824484	+	0.565885i	$0.191465\pi$
$420$	−1.42771	−	5.64034i	−0.0696650	−	0.275220i
$421$	1.41794	+	13.4908i	0.0691060	+	0.657500i	0.973168	+	0.230098i	$0.0739046\pi$
$421$	1.41794	+	13.4908i	0.0691060	+	0.657500i	−0.904061	+	0.427402i	$0.859429\pi$
$422$	3.48394	+	0.366177i	0.169595	+	0.0178252i
$423$	−2.70608	+	12.7311i	−0.131574	+	0.619007i
$424$	−0.538951	+	0.239956i	−0.0261738	+	0.0116533i
$425$	19.5524	−	20.5386i	0.948429	−	0.996269i
$426$	2.70601	−	8.32824i	0.131107	−	0.403505i
$427$	−27.4579	−	24.7232i	−1.32878	−	1.19644i
$428$	11.7477	−	6.78256i	0.567848	−	0.327847i
$429$	−0.483305	+	0.837109i	−0.0233342	+	0.0404160i
$430$	−18.2068	+	6.70047i	−0.878011	+	0.323125i
$431$	−4.71324	−	2.09847i	−0.227029	−	0.101080i	0.290070	−	0.957005i	$-0.406321\pi$
$431$	−4.71324	−	2.09847i	−0.227029	−	0.101080i	−0.517099	+	0.855926i	$0.672988\pi$
$432$	0.587785	−	0.809017i	0.0282798	−	0.0389238i
$433$		−	35.0453i		−	1.68417i	−0.539344	−	0.842085i	$-0.681328\pi$
$433$		−	35.0453i		−	1.68417i	0.539344	−	0.842085i	$-0.318672\pi$
$434$	10.1718	+	10.3158i	0.488263	+	0.495173i
$435$	19.6332	−	0.755813i	0.941341	−	0.0362385i
$436$	6.75156	+	4.90529i	0.323341	+	0.234921i
$437$	11.0035	−	24.7143i	0.526370	−	1.18225i
$438$	14.4756	−	4.70341i	0.691671	−	0.224737i
$439$	5.03065	−	8.71334i	0.240100	−	0.415865i	−0.720643	−	0.693307i	$-0.756153\pi$
$439$	5.03065	−	8.71334i	0.240100	−	0.415865i	0.960743	+	0.277442i	$0.0894865\pi$
$440$	−0.825406	−	1.31049i	−0.0393497	−	0.0624751i
$441$	−0.153662	+	0.170659i	−0.00731722	+	0.00812660i
$442$	7.52749	+	2.44583i	0.358046	+	0.116336i
$443$	15.9504	−	14.3618i	0.757825	−	0.682348i	−0.196706	−	0.980463i	$-0.563024\pi$
$443$	15.9504	−	14.3618i	0.757825	−	0.682348i	0.954530	+	0.298114i	$0.0963576\pi$
$444$	−10.0256	+	4.46366i	−0.475792	+	0.211836i
$445$	−2.23850	+	12.9657i	−0.106115	+	0.614635i
$446$	0.685703	−	6.52403i	0.0324690	−	0.308922i
$447$	21.4012	−	2.24936i	1.01224	−	0.106391i
$448$	0.540984	+	2.54513i	0.0255591	+	0.120246i
$449$	−1.95197	+	1.41819i	−0.0921193	+	0.0669286i	−0.632892	−	0.774240i	$-0.718132\pi$
$449$	−1.95197	+	1.41819i	−0.0921193	+	0.0669286i	0.540772	+	0.841169i	$0.318132\pi$
$450$	−3.24121	−	3.80717i	−0.152792	−	0.179472i
$451$	−3.74954	+	0.796990i	−0.176559	+	0.0375288i
$452$	−5.58852	+	0.587377i	−0.262862	+	0.0276279i
$453$	13.4513	+	1.41378i	0.631995	+	0.0664254i
$454$	−11.4441	−	2.43252i	−0.537099	−	0.114164i
$455$	−3.58549	−	7.28521i	−0.168091	−	0.341536i
$456$	3.04588	+	3.38279i	0.142636	+	0.158414i
$457$	11.8422	+	3.84778i	0.553957	+	0.179991i	0.572600	−	0.819835i	$-0.305935\pi$
$457$	11.8422	+	3.84778i	0.553957	+	0.179991i	−0.0186434	+	0.999826i	$0.505935\pi$
$458$	7.69054	+	6.92459i	0.359355	+	0.323565i
$459$	2.83572	+	4.91161i	0.132360	+	0.229254i
$460$	6.19700	−	11.7559i	0.288937	−	0.548124i
$461$	7.22647	+	22.2408i	0.336570	+	1.03586i	0.965943	+	0.258753i	$0.0833117\pi$
$461$	7.22647	+	22.2408i	0.336570	+	1.03586i	−0.629373	+	0.777103i	$0.716688\pi$
$462$	0.733026	−	1.64640i	0.0341035	−	0.0765977i
$463$	17.0025	−	23.4019i	0.790171	−	1.08758i	−0.203916	−	0.978988i	$-0.565367\pi$
$463$	17.0025	−	23.4019i	0.790171	−	1.08758i	0.994087	−	0.108589i	$-0.0346332\pi$
$464$	−8.78674			−0.407914
$465$	11.7575	+	4.09394i	0.545243	+	0.189852i
$466$	24.3137			1.12631
$467$	10.6970	−	14.7232i	0.495000	−	0.681309i	−0.486300	−	0.873792i	$-0.661654\pi$
$467$	10.6970	−	14.7232i	0.495000	−	0.681309i	0.981300	+	0.192482i	$0.0616539\pi$
$468$	0.567628	−	1.27491i	0.0262386	−	0.0589329i
$469$	−2.95945	−	9.10824i	−0.136654	−	0.420579i
$470$	−25.7456	−	13.5715i	−1.18756	−	0.626005i
$471$	−0.165163	−	0.286070i	−0.00761029	−	0.0131814i
$472$	−1.89069	−	1.70239i	−0.0870261	−	0.0783587i
$473$	−5.71528	−	1.85701i	−0.262789	−	0.0853853i
$474$	0.425106	+	0.472128i	0.0195258	+	0.0216856i
$475$	20.0190	−	10.8284i	0.918536	−	0.496842i
$476$	−14.4345	−	3.06816i	−0.661606	−	0.140629i
$477$	−0.586723	−	0.0616671i	−0.0268642	−	0.00282354i
$478$	−12.5629	+	1.32041i	−0.574612	+	0.0603942i
$479$	−7.28072	+	1.54756i	−0.332664	+	0.0707100i	−0.371216	−	0.928547i	$-0.621059\pi$
$479$	−7.28072	+	1.54756i	−0.332664	+	0.0707100i	0.0385514	+	0.999257i	$0.487726\pi$
$480$	1.38294	+	1.75712i	0.0631225	+	0.0802011i
$481$	−12.3904	+	9.00218i	−0.564955	+	0.410464i
$482$	2.25497	+	10.6088i	0.102711	+	0.483218i
$483$	15.3793	−	1.61643i	0.699782	−	0.0735501i
$484$	−1.09967	+	10.4626i	−0.0499849	+	0.475574i
$485$	−31.6793	−	5.46933i	−1.43848	−	0.248350i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−13.3940	+	12.0600i	−0.606939	+	0.546490i	−0.914266	−	0.405114i	$-0.867232\pi$
$487$	−13.3940	+	12.0600i	−0.606939	+	0.546490i	0.307328	+	0.951604i	$0.400565\pi$
$488$	13.5050	+	4.38804i	0.611342	+	0.198637i
$489$	−15.5600	+	17.2811i	−0.703647	+	0.781479i
$490$	−0.273666	−	0.434497i	−0.0123630	−	0.0196286i
$491$	9.32779	−	16.1562i	0.420957	−	0.729120i	−0.575076	−	0.818100i	$-0.695027\pi$
$491$	9.32779	−	16.1562i	0.420957	−	0.729120i	0.996033	+	0.0889803i	$0.0283608\pi$
$492$	5.26356	−	1.71024i	0.237300	−	0.0771034i
$493$	20.2691	−	45.5251i	0.912874	−	2.05035i
$494$	5.13937	+	3.73397i	0.231231	+	0.167999i
$495$	−0.0595781	−	1.54762i	−0.00267784	−	0.0695603i
$496$	−5.18381	−	2.03178i	−0.232760	−	0.0912296i
$497$			22.7852i			1.02206i
$498$	−5.09257	+	7.00933i	−0.228204	+	0.314095i
$499$	−12.5957	−	5.60795i	−0.563859	−	0.251046i	0.104954	−	0.994477i	$-0.466531\pi$
$499$	−12.5957	−	5.60795i	−0.563859	−	0.251046i	−0.668813	+	0.743431i	$0.733197\pi$
$500$	10.1644	−	4.65661i	0.454568	−	0.208250i
$501$	5.51775	−	9.55702i	0.246515	−	0.426976i
$502$	2.66006	−	1.53578i	0.118724	−	0.0685454i
$503$	16.3234	+	14.6977i	0.727826	+	0.655337i	0.947324	−	0.320275i	$-0.103775\pi$
$503$	16.3234	+	14.6977i	0.727826	+	0.655337i	−0.219499	+	0.975613i	$0.570442\pi$
$504$	−0.804059	+	2.47464i	−0.0358157	+	0.110229i
$505$	−28.4427	+	27.6638i	−1.26569	+	1.23102i
$506$	3.76051	−	1.67429i	0.167175	−	0.0744312i
$507$	−2.29792	+	10.8109i	−0.102054	+	0.480128i
$508$	2.35810	+	0.247846i	0.104624	+	0.0109964i
$509$	−1.63424	−	15.5487i	−0.0724363	−	0.689186i	−0.969133	−	0.246540i	$-0.920706\pi$
$509$	−1.63424	−	15.5487i	−0.0724363	−	0.689186i	0.896696	−	0.442646i	$-0.145960\pi$
$510$	−12.2940	+	3.11191i	−0.544387	+	0.137798i
$511$	−32.0401	+	23.2785i	−1.41737	+	1.02978i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	0.946413	+	4.45252i	0.0417851	+	0.196584i
$514$	1.52139	+	14.4751i	0.0671059	+	0.638470i
$515$	1.72054	−	25.9355i	0.0758161	−	1.14286i
$516$	8.48663	+	1.80389i	0.373603	+	0.0794118i
$517$	−3.66670	−	8.23555i	−0.161261	−	0.362199i
$518$	21.2206	−	19.1071i	0.932379	−	0.839518i
$519$	−1.14191	+	3.51443i	−0.0501242	+	0.154266i
$520$	2.39765	+	1.99732i	0.105144	+	0.0875884i
$521$	−4.59771	−	7.96347i	−0.201430	−	0.348886i	0.747560	−	0.664195i	$-0.231225\pi$
$521$	−4.59771	−	7.96347i	−0.201430	−	0.348886i	−0.948989	+	0.315308i	$0.897892\pi$
$522$	−7.60954	−	4.39337i	−0.333061	−	0.192293i
$523$	−37.6158	+	12.2221i	−1.64482	+	0.534436i	−0.977609	−	0.210429i	$-0.932514\pi$
$523$	−37.6158	+	12.2221i	−1.64482	+	0.534436i	−0.667215	+	0.744865i	$0.732514\pi$
$524$	1.55281	+	0.691356i	0.0678348	+	0.0302020i
$525$	11.0820	+	6.81525i	0.483659	+	0.297442i
$526$	16.6943			0.727905
$527$	22.4848	−	22.1710i	0.979453	−	0.965786i
$528$			0.692629i			0.0301428i
$529$	9.96790	+	7.24210i	0.433387	+	0.314874i
$530$	0.489802	−	1.22488i	0.0212756	−	0.0532053i
$531$	−0.786193	−	2.41965i	−0.0341179	−	0.105004i
$532$	−10.2574	−	5.92212i	−0.444715	−	0.256757i
$533$	6.68890	−	3.86184i	0.289729	−	0.167275i
$534$	3.93733	−	4.37284i	0.170385	−	0.189231i
$535$	−8.25660	+	29.1872i	−0.356964	+	1.26187i
$536$	2.46282	+	2.73524i	0.106378	+	0.118144i
$537$	−7.90880	−	17.7635i	−0.341290	−	0.766550i
$538$	3.80463	−	17.8994i	0.164029	−	0.771696i
$539$	0.0166261	−	0.158187i	0.000716136	−	0.00681358i
$540$	0.319106	+	2.21318i	0.0137321	+	0.0952402i
$541$	19.4143	−	4.12664i	0.834687	−	0.177418i	0.229306	−	0.973354i	$-0.426354\pi$
$541$	19.4143	−	4.12664i	0.834687	−	0.177418i	0.605381	+	0.795936i	$0.293021\pi$
$542$	3.11869	+	4.29250i	0.133959	+	0.184379i
$543$	−2.74907	−	3.78377i	−0.117974	−	0.162377i
$544$	5.54750	−	1.17916i	0.237847	−	0.0505560i
$545$	−18.4699	+	2.66306i	−0.791161	+	0.114073i
$546$	−0.379569	+	3.61136i	−0.0162441	+	0.154552i
$547$	−0.270950	+	1.27472i	−0.0115850	+	0.0545030i	−0.983560	−	0.180579i	$-0.942203\pi$
$547$	−0.270950	+	1.27472i	−0.0115850	+	0.0545030i	0.971975	+	0.235083i	$0.0755360\pi$
$548$	−2.14572	−	4.81937i	−0.0916608	−	0.205873i
$549$	9.50164	+	10.5526i	0.405520	+	0.450376i
$550$	3.36617	+	0.813790i	0.143534	+	0.0347001i
$551$	26.7634	−	29.7237i	1.14016	−	1.26627i
$552$	−5.14692	+	2.97157i	−0.219067	+	0.126479i
$553$	−1.43160	−	0.826537i	−0.0608780	−	0.0351479i
$554$	3.11863	+	9.59815i	0.132498	+	0.407786i
$555$	9.11129	−	22.7852i	0.386753	−	0.967177i
$556$	−10.6674	−	7.75028i	−0.452396	−	0.328685i
$557$		−	10.9800i		−	0.465237i	−0.972568	−	0.232618i	$-0.925271\pi$
$557$		−	10.9800i		−	0.465237i	0.972568	−	0.232618i	$-0.0747293\pi$
$558$	−3.47342	−	4.35148i	−0.147042	−	0.184213i
$559$	12.1083			0.512125
$560$	−4.83512	−	3.23627i	−0.204321	−	0.136757i
$561$	−3.58859	−	1.59774i	−0.151510	−	0.0674568i
$562$	−13.3997	+	4.35383i	−0.565232	+	0.183655i
$563$	11.2856	+	6.51575i	0.475632	+	0.274606i	0.718594	−	0.695430i	$-0.244786\pi$
$563$	11.2856	+	6.51575i	0.475632	+	0.274606i	−0.242963	+	0.970036i	$0.578119\pi$
$564$	6.50776	+	11.2718i	0.274026	+	0.474627i
$565$	8.04229	−	9.65424i	0.338342	−	0.406157i
$566$	−2.84093	+	8.74348i	−0.119413	+	0.367516i
$567$	−1.93366	+	1.74107i	−0.0812059	+	0.0731181i
$568$	−3.56172	−	7.99976i	−0.149447	−	0.335663i
$569$	−25.4605	−	5.41179i	−1.06736	−	0.226874i	−0.359440	−	0.933168i	$-0.617032\pi$
$569$	−25.4605	−	5.41179i	−1.06736	−	0.226874i	−0.707918	+	0.706294i	$0.750366\pi$
$570$	−10.1562	−	0.673757i	−0.425398	−	0.0282206i
$571$	−0.0480876	−	0.457523i	−0.00201240	−	0.0191467i	0.993470	−	0.114097i	$-0.0363975\pi$
$571$	−0.0480876	−	0.457523i	−0.00201240	−	0.0191467i	−0.995482	+	0.0949503i	$0.969731\pi$
$572$	0.200970	+	0.945488i	0.00840296	+	0.0395328i
$573$	3.64454	+	5.01628i	0.152253	+	0.209558i
$574$	−11.6503	+	8.46443i	−0.486274	+	0.353299i
$575$	8.39457	+	28.5054i	0.350078	+	1.18876i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−20.7934	−	2.18548i	−0.865641	−	0.0909825i	−0.338710	−	0.940891i	$-0.609991\pi$
$577$	−20.7934	−	2.18548i	−0.865641	−	0.0909825i	−0.526931	+	0.849908i	$0.676657\pi$
$578$	−3.15302	+	14.8338i	−0.131148	+	0.617005i
$579$	−17.5086	+	7.79534i	−0.727633	+	0.323963i
$580$	14.0846	−	13.6989i	0.584831	−	0.568814i
$581$	6.96637	−	21.4403i	0.289014	−	0.889493i
$582$	10.6842	+	9.62008i	0.442874	+	0.398765i
$583$	0.353875	−	0.204310i	0.0146560	−	0.00846165i
$584$	7.61027	−	13.1814i	0.314915	−	0.545449i
$585$	1.07777	+	2.92856i	0.0445602	+	0.121081i
$586$	−14.9047	−	6.63599i	−0.615706	−	0.274130i
$587$	9.93058	−	13.6683i	0.409879	−	0.564150i	−0.553310	−	0.832975i	$-0.686636\pi$
$587$	9.93058	−	13.6683i	0.409879	−	0.564150i	0.963189	+	0.268826i	$0.0866356\pi$
$588$			0.229644i			0.00947035i
$589$	22.6623	−	11.3472i	0.933785	−	0.467553i
$590$	5.68474	−	0.218843i	0.234037	−	0.00900964i
$591$	−6.35457	−	4.61687i	−0.261392	−	0.189913i
$592$	−4.46366	+	10.0256i	−0.183455	+	0.412048i
$593$	−16.5820	+	5.38781i	−0.680940	+	0.221251i	−0.629007	−	0.777400i	$-0.716538\pi$
$593$	−16.5820	+	5.38781i	−0.680940	+	0.221251i	−0.0519332	+	0.998651i	$0.516538\pi$
$594$	−0.346314	+	0.599834i	−0.0142095	+	0.0246115i
$595$	27.9210	−	17.5859i	1.14465	−	0.720953i
$596$	14.3991	−	15.9918i	0.589810	−	0.655051i
$597$	−23.1663	−	7.52718i	−0.948132	−	0.308067i
$598$	−6.16369	+	5.54981i	−0.252052	+	0.226949i
$599$	−19.8724	+	8.84776i	−0.811964	+	0.361510i	−0.770348	−	0.637624i	$-0.779917\pi$
$599$	−19.8724	+	8.84776i	−0.811964	+	0.361510i	−0.0416165	+	0.999134i	$0.513251\pi$
$600$	−4.95618	−	0.660485i	−0.202335	−	0.0269642i
$601$	0.121973	−	1.16050i	0.00497539	−	0.0473377i	−0.991753	−	0.128168i	$-0.959090\pi$
$601$	0.121973	−	1.16050i	0.00497539	−	0.0473377i	0.996728	+	0.0808300i	$0.0257571\pi$
$602$	−22.4518	+	2.35978i	−0.915066	+	0.0961774i
$603$	0.765246	+	3.60020i	0.0311632	+	0.146611i
$604$	10.9422	−	7.95000i	0.445233	−	0.323481i
$605$	−14.5489	−	18.4854i	−0.591499	−	0.751536i
$606$	17.3564	−	3.68922i	0.705056	−	0.149864i
$607$	−34.4685	+	3.62279i	−1.39903	+	0.147044i	−0.773819	−	0.633407i	$-0.781656\pi$
$607$	−34.4685	+	3.62279i	−1.39903	+	0.147044i	−0.625216	+	0.780452i	$0.714989\pi$
$608$	4.52706	+	0.475813i	0.183596	+	0.0192968i
$609$	22.3634	+	4.75349i	0.906211	+	0.192621i
$610$	−28.4887	+	14.0210i	−1.15348	+	0.567695i
$611$	12.1541	+	13.4985i	0.491703	+	0.546091i
$612$	5.39386	+	1.75257i	0.218034	+	0.0708435i
$613$	24.7930	+	22.3238i	1.00138	+	0.901648i	0.995154	−	0.0983325i	$-0.0313509\pi$
$613$	24.7930	+	22.3238i	1.00138	+	0.901648i	0.00622810	+	0.999981i	$0.498018\pi$
$614$	−16.4863	−	28.5551i	−0.665332	−	1.15239i
$615$	−5.77083	+	10.9475i	−0.232702	+	0.441445i
$616$	−0.556915	−	1.71401i	−0.0224387	−	0.0690593i
$617$	8.46305	−	19.0083i	0.340710	−	0.765246i	−0.659202	−	0.751966i	$-0.729106\pi$
$617$	8.46305	−	19.0083i	0.340710	−	0.765246i	0.999912	−	0.0132806i	$-0.00422746\pi$
$618$	−6.83254	+	9.40418i	−0.274845	+	0.378292i
$619$	28.1871			1.13293			0.566467	−	0.824084i	$-0.308310\pi$
$619$	28.1871			1.13293			0.566467	+	0.824084i	$0.308310\pi$
$620$	11.4769	−	4.82494i	0.460925	−	0.193774i
$621$	−5.94315			−0.238490
$622$	−4.68635	+	6.45020i	−0.187905	+	0.258630i
$623$	−6.22744	+	13.9871i	−0.249497	+	0.560380i
$624$	−0.431254	−	1.32726i	−0.0172640	−	0.0531331i
$625$	−9.03312	+	23.3110i	−0.361325	+	0.932440i
$626$	9.59091	+	16.6120i	0.383330	+	0.663947i
$627$	−2.34302	−	2.10966i	−0.0935712	−	0.0842518i
$628$	−0.314158	−	0.102076i	−0.0125363	−	0.00407328i
$629$	−41.6468	−	46.2535i	−1.66057	−	1.84425i
$630$	−2.56920	−	5.22025i	−0.102359	−	0.207980i
$631$	4.44186	+	0.944146i	0.176828	+	0.0375858i	0.295474	−	0.955351i	$-0.404522\pi$
$631$	4.44186	+	0.944146i	0.176828	+	0.0375858i	−0.118647	+	0.992937i	$0.537856\pi$
$632$	0.631831	+	0.0664081i	0.0251329	+	0.00264157i
$633$	3.48394	−	0.366177i	0.138474	−	0.0145542i
$634$	3.48896	−	0.741602i	0.138564	−	0.0294528i
$635$	−4.16628	+	3.27909i	−0.165334	+	0.130127i
$636$	−0.477284	+	0.346767i	−0.0189255	+	0.0137502i
$637$	0.0666322	+	0.313480i	0.00264007	+	0.0124205i
$638$	6.05261	−	0.636155i	0.239625	−	0.0251856i
$639$	0.915338	−	8.70886i	0.0362102	−	0.344517i
$640$	2.20347	+	0.380423i	0.0870998	+	0.0150375i
$641$	−22.9699	+	10.2269i	−0.907257	+	0.403937i	−0.806677	−	0.590992i	$-0.798736\pi$
$641$	−22.9699	+	10.2269i	−0.907257	+	0.403937i	−0.100580	+	0.994929i	$0.532070\pi$
$642$	10.0808	−	9.07683i	0.397859	−	0.358234i
$643$	41.4839	+	13.4789i	1.63597	+	0.531558i	0.975632	−	0.219413i	$-0.0704143\pi$
$643$	41.4839	+	13.4789i	1.63597	+	0.531558i	0.660335	+	0.750971i	$0.270414\pi$
$644$	10.3474	−	11.4920i	0.407746	−	0.452848i
$645$	−16.4158	+	10.3395i	−0.646373	+	0.407116i
$646$	−12.9082	+	22.3576i	−0.507865	+	0.879648i
$647$	17.5338	−	5.69707i	0.689324	−	0.223975i	0.0566508	−	0.998394i	$-0.481958\pi$
$647$	17.5338	−	5.69707i	0.689324	−	0.223975i	0.632673	+	0.774419i	$0.281958\pi$
$648$	0.406737	−	0.913545i	0.0159781	−	0.0358875i
$649$	1.42563	+	1.03578i	0.0559607	+	0.0406578i
$650$	−6.95719	+	0.536452i	−0.272883	+	0.0210414i
$651$	12.0943	+	7.97550i	0.474013	+	0.312585i
$652$			23.2540i			0.910699i
$653$	28.4708	−	39.1867i	1.11415	−	1.53350i	0.298993	−	0.954255i	$-0.403349\pi$
$653$	28.4708	−	39.1867i	1.11415	−	1.53350i	0.815157	−	0.579240i	$-0.196651\pi$
$654$	7.62389	+	3.39437i	0.298118	+	0.132731i
$655$	−3.56690	+	1.31269i	−0.139370	+	0.0512911i
$656$	2.76722	−	4.79296i	0.108042	−	0.187134i
$657$	13.1814	−	7.61027i	0.514254	−	0.296905i
$658$	−25.1675	−	22.6610i	−0.981133	−	0.883416i
$659$	3.75292	−	11.5503i	0.146193	−	0.449936i	−0.850969	−	0.525215i	$-0.823985\pi$
$659$	3.75292	−	11.5503i	0.146193	−	0.449936i	0.997163	+	0.0752790i	$0.0239847\pi$
$660$	−1.07983	−	1.11024i	−0.0420325	−	0.0432160i
$661$	10.3445	−	4.60569i	0.402356	−	0.179141i	−0.195573	−	0.980689i	$-0.562657\pi$
$661$	10.3445	−	4.60569i	0.402356	−	0.179141i	0.597930	+	0.801548i	$0.295990\pi$
$662$	−0.357308	+	1.68100i	−0.0138872	+	0.0653340i
$663$	7.87151	+	0.827329i	0.305704	+	0.0321308i
$664$	0.905635	+	8.61654i	0.0351455	+	0.334387i
$665$	25.6748	−	6.49892i	0.995626	−	0.252017i
$666$	−8.87842	+	6.45055i	−0.344032	+	0.249954i
$667$	30.6947	+	42.2476i	1.18850	+	1.63583i
$668$	−2.29441	−	10.7943i	−0.0887733	−	0.417646i
$669$	−0.685703	−	6.52403i	−0.0265108	−	0.252233i
$670$	−8.21209	−	0.544783i	−0.317261	−	0.0210468i
$671$	−9.62039	−	2.04488i	−0.371391	−	0.0789416i
$672$	1.05833	+	2.37704i	0.0408258	+	0.0916962i
$673$	5.12940	−	4.61853i	0.197724	−	0.178031i	−0.564321	−	0.825555i	$-0.690862\pi$
$673$	5.12940	−	4.61853i	0.197724	−	0.178031i	0.762045	+	0.647524i	$0.224195\pi$
$674$	8.37815	−	25.7853i	0.322714	−	0.993212i
$675$	−3.96194	−	3.05009i	−0.152495	−	0.117398i
$676$	5.52620	+	9.57165i	0.212546	+	0.368140i
$677$	−30.8683	−	17.8218i	−1.18637	−	0.684949i	−0.228888	−	0.973453i	$-0.573509\pi$
$677$	−30.8683	−	17.8218i	−1.18637	−	0.684949i	−0.957479	+	0.288504i	$0.906842\pi$
$678$	−5.34427	+	1.73646i	−0.205246	+	0.0666884i
$679$	−34.1746	−	15.2155i	−1.31150	−	0.583918i
$680$	−7.05394	+	10.5389i	−0.270506	+	0.404148i
$681$	−11.6998			−0.448337
$682$	3.71789	+	1.02425i	0.142365	+	0.0392207i
$683$		−	23.8764i		−	0.913604i	−0.889568	−	0.456802i	$-0.848995\pi$
$683$		−	23.8764i		−	0.913604i	0.889568	−	0.456802i	$-0.151005\pi$
$684$	3.68264	+	2.67559i	0.140809	+	0.102304i
$685$	10.9530	+	4.37988i	0.418494	+	0.167347i
$686$	−5.81306	−	17.8908i	−0.221944	−	0.683073i
$687$	8.96219	+	5.17432i	0.341929	+	0.197413i
$688$	7.51383	−	4.33811i	0.286462	−	0.165389i
$689$	−0.550910	+	0.611847i	−0.0209880	+	0.0233095i
$690$	3.61738	−	12.7875i	0.137711	−	0.486811i
$691$	6.41657	+	7.12632i	0.244098	+	0.271098i	0.852727	−	0.522357i	$-0.174947\pi$
$691$	6.41657	+	7.12632i	0.244098	+	0.271098i	−0.608629	+	0.793455i	$0.708280\pi$
$692$	1.50301	+	3.37582i	0.0571359	+	0.128329i
$693$	0.374701	−	1.76283i	0.0142337	−	0.0669644i
$694$	0.889088	−	8.45911i	0.0337493	−	0.321103i
$695$	29.1821	−	4.20759i	1.10694	−	0.159603i
$696$	−8.59473	+	1.82687i	−0.325782	+	0.0692472i
$697$	18.4495	+	25.3936i	0.698826	+	0.961851i
$698$	4.76383	+	6.55685i	0.180314	+	0.248180i
$699$	23.7824	−	5.05510i	0.899532	−	0.191201i
$700$	12.7958	−	2.35060i	0.483637	−	0.0888445i
$701$	−1.10679	+	10.5304i	−0.0418028	+	0.397727i	0.953535	+	0.301281i	$0.0974143\pi$
$701$	−1.10679	+	10.5304i	−0.0418028	+	0.397727i	−0.995338	+	0.0964463i	$0.969252\pi$
$702$	0.290155	−	1.36507i	0.0109512	−	0.0515213i
$703$	−20.3186	−	45.6363i	−0.766329	−	1.72120i
$704$	0.463459	+	0.514724i	0.0174673	+	0.0193994i
$705$	−28.0046	−	7.92208i	−1.05472	−	0.298363i
$706$	15.5667	−	17.2885i	0.585859	−	0.650662i
$707$	−39.9845	+	23.0851i	−1.50377	+	0.868203i
$708$	−2.20332	−	1.27209i	−0.0828059	−	0.0478080i
$709$	7.58181	+	23.3344i	0.284741	+	0.876342i	0.986476	+	0.163904i	$0.0524088\pi$
$709$	7.58181	+	23.3344i	0.284741	+	0.876342i	−0.701736	+	0.712438i	$0.747591\pi$
$710$	18.1811	+	7.27024i	0.682326	+	0.272847i
$711$	0.513977	+	0.373426i	0.0192757	+	0.0140046i
$712$		−	5.88424i		−	0.220521i
$713$	8.33956	+	32.0219i	0.312319	+	1.19923i
$714$	−14.7570			−0.552268
$715$	−1.79619	−	1.20224i	−0.0671738	−	0.0449611i
$716$	−17.7635	−	7.90880i	−0.663851	−	0.295566i
$717$	−12.0138	+	3.90353i	−0.448664	+	0.145780i
$718$	3.91743	+	2.26173i	0.146197	+	0.0844069i
$719$	−5.53602	−	9.58867i	−0.206459	−	0.357597i	0.744138	−	0.668026i	$-0.232861\pi$
$719$	−5.53602	−	9.58867i	−0.206459	−	0.357597i	−0.950597	+	0.310429i	$0.899527\pi$
$720$	1.71805	+	1.43119i	0.0640279	+	0.0533373i
$721$	9.34655	−	28.7657i	0.348084	−	1.07129i
$722$	−1.27869	+	1.15134i	−0.0475880	+	0.0428484i
$723$	4.41139	+	9.90814i	0.164061	+	0.368488i
$724$	−4.57479	−	0.972401i	−0.170021	−	0.0361390i
$725$	−1.21964	+	43.9168i	−0.0452963	+	1.63103i
$726$	1.09967	+	10.4626i	0.0408125	+	0.388305i
$727$	−5.54842	−	26.1033i	−0.205779	−	0.968116i	−0.952866	−	0.303390i	$-0.901882\pi$
$727$	−5.54842	−	26.1033i	−0.205779	−	0.968116i	0.747087	−	0.664726i	$-0.231452\pi$
$728$	2.13440	+	2.93775i	0.0791060	+	0.108880i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	8.35149	+	32.9936i	0.309102	+	1.22115i
$731$	5.14350	+	48.9371i	0.190239	+	1.81000i
$732$	14.1222	+	1.48430i	0.521971	+	0.0548614i
$733$	−8.97575	+	42.2276i	−0.331527	+	1.55971i	0.424659	+	0.905353i	$0.360394\pi$
$733$	−8.97575	+	42.2276i	−0.331527	+	1.55971i	−0.756186	+	0.654357i	$0.772939\pi$
$734$	−2.15685	+	0.960294i	−0.0796110	+	0.0354451i
$735$	−0.358023	−	0.368104i	−0.0132059	−	0.0135777i
$736$	−1.83653	+	5.65227i	−0.0676955	+	0.208345i
$737$	−1.89451	−	1.70582i	−0.0697851	−	0.0628348i
$738$	4.79296	−	2.76722i	0.176431	−	0.101863i
$739$	13.6377	−	23.6212i	0.501672	−	0.868922i	−0.498326	−	0.866990i	$-0.666052\pi$
$739$	13.6377	−	23.6212i	0.501672	−	0.868922i	0.999998	−	0.00193182i	$-0.000614918\pi$
$740$	−8.47525	−	23.0293i	−0.311556	−	0.846575i
$741$	5.80340	+	2.58384i	0.213193	+	0.0949198i
$742$	0.902284	−	1.24189i	0.0331239	−	0.0455911i
$743$		−	4.22363i		−	0.154950i	−0.996994	−	0.0774750i	$-0.975314\pi$
$743$		−	4.22363i		−	0.154950i	0.996994	−	0.0774750i	$-0.0246858\pi$
$744$	−5.49296	−	0.909605i	−0.201382	−	0.0333477i
$745$	1.85102	+	48.0826i	0.0678161	+	1.76161i
$746$	1.23682	+	0.898606i	0.0452834	+	0.0329003i
$747$	−3.52397	+	7.91496i	−0.128935	+	0.289593i
$748$	−3.73594	+	1.21388i	−0.136600	+	0.0443839i
$749$	−17.6482	+	30.5675i	−0.644849	+	1.11691i
$750$	8.97416	−	6.66816i	0.327690	−	0.243487i
$751$	29.9083	−	33.2165i	1.09137	−	1.21209i	0.115597	−	0.993296i	$-0.463122\pi$
$751$	29.9083	−	33.2165i	1.09137	−	1.21209i	0.975772	−	0.218792i	$-0.0702116\pi$
$752$	12.3785	+	4.02202i	0.451397	+	0.146668i
$753$	2.28262	−	2.05528i	0.0831833	−	0.0748986i
$754$	−11.2023	+	4.98761i	−0.407965	+	0.181638i
$755$	−5.14535	+	29.8027i	−0.187259	+	1.08463i
$756$	−0.271982	+	2.58774i	−0.00989189	+	0.0941151i
$757$	12.9221	−	1.35817i	0.469663	−	0.0493635i	0.133259	−	0.991081i	$-0.457456\pi$
$757$	12.9221	−	1.35817i	0.469663	−	0.0493635i	0.336404	+	0.941718i	$0.390789\pi$
$758$	4.84144	+	22.7772i	0.175849	+	0.827305i
$759$	3.33023	−	2.41956i	0.120880	−	0.0878243i
$760$	−7.99839	+	6.29516i	−0.290132	+	0.228349i
$761$	−1.32986	+	0.282669i	−0.0482072	+	0.0102468i	−0.231952	−	0.972727i	$-0.574511\pi$
$761$	−1.32986	+	0.282669i	−0.0482072	+	0.0102468i	0.183745	+	0.982974i	$0.441178\pi$
$762$	2.35810	−	0.247846i	0.0854250	−	0.00897853i
$763$	−21.5957	−	2.26980i	−0.781815	−	0.0821721i
$764$	6.06496	+	1.28915i	0.219423	+	0.0466397i
$765$	−11.3783	+	5.59997i	−0.411384	+	0.202467i
$766$	17.8170	+	19.7877i	0.643753	+	0.714960i
$767$	−3.37679	−	1.09719i	−0.121929	−	0.0396171i
$768$	−0.743145	−	0.669131i	−0.0268159	−	0.0241452i
$769$	11.8474	+	20.5203i	0.427228	+	0.739981i	0.996626	−	0.0820811i	$-0.0261567\pi$
$769$	11.8474	+	20.5203i	0.427228	+	0.739981i	−0.569397	+	0.822063i	$0.692823\pi$
$770$	3.56490	+	1.87919i	0.128470	+	0.0677214i
$771$	4.49769	+	13.8425i	0.161980	+	0.498525i
$772$	−7.79534	+	17.5086i	−0.280560	+	0.630149i
$773$	−20.2918	+	27.9292i	−0.729844	+	1.00454i	0.269295	+	0.963058i	$0.413209\pi$
$773$	−20.2918	+	27.9292i	−0.729844	+	1.00454i	−0.999139	+	0.0414862i	$0.986791\pi$
$774$	8.67622			0.311860
$775$	−10.8745	+	25.6270i	−0.390624	+	0.920550i
$776$	14.3770			0.516104
$777$	16.7843	−	23.1016i	0.602132	−	0.828764i
$778$	−9.05300	+	20.3334i	−0.324566	+	0.728987i
$779$	7.78498	+	23.9597i	0.278926	+	0.858446i
$780$	2.76053	+	1.45518i	0.0988427	+	0.0521037i
$781$	3.03262	+	5.25265i	0.108516	+	0.187955i
$782$	−25.0486	−	22.5538i	−0.895735	−	0.806524i
$783$	−8.35669	−	2.71525i	−0.298644	−	0.0970352i
$784$	0.153662	+	0.170659i	0.00548792	+	0.00609495i
$785$	0.662715	−	0.326162i	0.0236533	−	0.0116412i
$786$	1.66262	+	0.353400i	0.0593036	+	0.0126054i
$787$	−19.3314	−	2.03181i	−0.689091	−	0.0724263i	−0.246490	−	0.969145i	$-0.579277\pi$
$787$	−19.3314	−	2.03181i	−0.689091	−	0.0724263i	−0.442600	+	0.896719i	$0.645944\pi$
$788$	−7.81166	+	0.821038i	−0.278279	+	0.0292483i
$789$	16.3295	−	3.47094i	0.581345	−	0.123569i
$790$	−1.11632	+	0.878600i	−0.0397168	+	0.0312592i
$791$	11.8289	−	8.59423i	0.420589	−	0.305576i
$792$	0.144006	+	0.677493i	0.00511702	+	0.0240737i
$793$	19.7085	−	2.07144i	0.699868	−	0.0735591i
$794$	−0.0949151	+	0.903057i	−0.00336841	+	0.0320483i
$795$	0.224432	−	1.29995i	0.00795979	−	0.0461044i
$796$	−22.2526	+	9.90747i	−0.788721	+	0.351161i
$797$	−21.9600	+	19.7729i	−0.777864	+	0.700392i	−0.959106	−	0.283046i	$-0.908655\pi$
$797$	−21.9600	+	19.7729i	−0.777864	+	0.700392i	0.181242	+	0.983439i	$0.441988\pi$
$798$	−11.2645	−	3.66007i	−0.398761	−	0.129565i
$799$	−49.3930	+	54.8565i	−1.74740	+	1.94068i
$800$	−4.12511	+	2.82550i	−0.145845	+	0.0998965i
$801$	2.94212	−	5.09590i	0.103955	−	0.180055i
$802$	−27.1043	+	8.80673i	−0.957087	+	0.310976i
$803$	−4.28789	+	9.63077i	−0.151316	+	0.339862i
$804$	2.97769	+	2.16342i	0.105015	+	0.0762980i
$805$	1.33017	+	34.5530i	0.0468825	+	1.21783i
$806$	−7.76221	+	0.352133i	−0.273412	+	0.0124034i
$807$		−	18.2992i		−	0.644164i
$808$	10.4298	−	14.3553i	0.366918	−	0.505019i
$809$	11.1835	+	4.97923i	0.393192	+	0.175060i	0.593803	−	0.804611i	$-0.297626\pi$
$809$	11.1835	+	4.97923i	0.393192	+	0.175060i	−0.200611	+	0.979671i	$0.564293\pi$
$810$	0.772279	+	2.09847i	0.0271351	+	0.0737328i
$811$	25.2040	−	43.6547i	0.885034	−	1.53292i	0.0393588	−	0.999225i	$-0.487468\pi$
$811$	25.2040	−	43.6547i	0.885034	−	1.53292i	0.845675	−	0.533698i	$-0.179198\pi$
$812$	19.8000	−	11.4315i	0.694842	−	0.401167i
$813$	3.94300	+	3.55029i	0.138287	+	0.124514i
$814$	2.34888	−	7.22911i	0.0823282	−	0.253380i
$815$	−36.2539	−	37.2747i	−1.26992	−	1.30568i
$816$	5.18112	−	2.30678i	0.181375	−	0.0807535i
$817$	−8.21129	+	38.6311i	−0.287277	+	1.35153i
$818$	16.3557	+	1.71905i	0.571864	+	0.0601053i
$819$	0.379569	+	3.61136i	0.0132632	+	0.126191i
$820$	3.03674	+	11.9970i	0.106047	+	0.418954i
$821$	32.4564	−	23.5810i	1.13274	−	0.822982i	0.146646	−	0.989189i	$-0.453152\pi$
$821$	32.4564	−	23.5810i	1.13274	−	0.822982i	0.986091	+	0.166207i	$0.0531520\pi$
$822$	−3.10084	−	4.26794i	−0.108154	−	0.148861i
$823$	2.70504	+	12.7262i	0.0942916	+	0.443607i	0.999814	+	0.0193077i	$0.00614623\pi$
$823$	2.70504	+	12.7262i	0.0942916	+	0.443607i	−0.905522	+	0.424299i	$0.860520\pi$
$824$	1.21506	+	11.5605i	0.0423286	+	0.402730i
$825$	3.46181	+	0.0961400i	0.120525	+	0.00334716i
$826$	6.47526	+	1.37636i	0.225303	+	0.0478897i
$827$	4.25671	+	9.56073i	0.148020	+	0.332459i	0.972305	−	0.233717i	$-0.0750889\pi$
$827$	4.25671	+	9.56073i	0.148020	+	0.332459i	−0.824284	+	0.566176i	$0.808422\pi$
$828$	−4.41662	+	3.97674i	−0.153488	+	0.138201i
$829$	1.68332	−	5.18074i	0.0584643	−	0.179935i	−0.917559	−	0.397599i	$-0.869844\pi$
$829$	1.68332	−	5.18074i	0.0584643	−	0.179935i	0.976024	+	0.217664i	$0.0698437\pi$
$830$	−14.8852	−	12.3998i	−0.516672	−	0.430405i
$831$	5.04605	+	8.74001i	0.175045	+	0.303188i
$832$	−1.20860	−	0.697784i	−0.0419006	−	0.0241913i
$833$	−1.23867	+	0.402467i	−0.0429172	+	0.0139447i
$834$	−12.0456	−	5.36305i	−0.417106	−	0.185707i
$835$	20.5066	+	13.7256i	0.709659	+	0.474993i
$836$	−3.15284			−0.109043
$837$	−4.30224	−	3.53422i	−0.148707	−	0.122161i
$838$		−	13.6901i		−	0.472917i
$839$	−3.10218	−	2.25387i	−0.107099	−	0.0778122i	0.532947	−	0.846149i	$-0.321085\pi$
$839$	−3.10218	−	2.25387i	−0.107099	−	0.0778122i	−0.640046	+	0.768337i	$0.721085\pi$
$840$	−5.40232	−	2.16027i	−0.186398	−	0.0745363i
$841$	14.8967	+	45.8475i	0.513681	+	1.58095i
$842$	11.7477	+	6.78254i	0.404853	+	0.233742i
$843$	−12.2017	+	7.04464i	−0.420248	+	0.242630i
$844$	2.34405	−	2.60333i	0.0806855	−	0.0896104i
$845$	−23.7807	−	6.72719i	−0.818081	−	0.231423i
$846$	8.70909	+	9.67242i	0.299425	+	0.332545i
$847$	−11.1339	−	25.0071i	−0.382564	−	0.859253i
$848$	−0.122659	+	0.577063i	−0.00421211	+	0.0198164i
$849$	−0.960976	+	9.14307i	−0.0329806	+	0.313789i
$850$	−5.12350	−	27.8905i	−0.175735	−	0.956636i
$851$	63.7968	−	13.5604i	2.18693	−	0.464846i
$852$	−5.14714	−	7.08443i	−0.176338	−	0.242708i
$853$	13.4906	+	18.5682i	0.461910	+	0.635764i	0.974903	−	0.222628i	$-0.0714636\pi$
$853$	13.4906	+	18.5682i	0.461910	+	0.635764i	−0.512994	+	0.858392i	$0.671464\pi$
$854$	−36.1408	+	7.68197i	−1.23671	+	0.262872i
$855$	−10.0744	+	1.45257i	−0.344537	+	0.0496768i
$856$	1.41794	−	13.4908i	0.0484642	−	0.461106i
$857$	1.46427	−	6.88886i	0.0500186	−	0.235319i	−0.946036	−	0.324061i	$-0.894952\pi$
$857$	1.46427	−	6.88886i	0.0500186	−	0.235319i	0.996055	+	0.0887426i	$0.0282849\pi$
$858$	0.393156	+	0.883043i	0.0134221	+	0.0301466i
$859$	−10.4000	−	11.5504i	−0.354844	−	0.394094i	0.539123	−	0.842227i	$-0.318756\pi$
$859$	−10.4000	−	11.5504i	−0.354844	−	0.394094i	−0.893967	+	0.448133i	$0.852089\pi$
$860$	−5.28091	+	18.6681i	−0.180077	+	0.636575i
$861$	−9.63585	+	10.7017i	−0.328389	+	0.364713i
$862$	−4.46807	+	2.57964i	−0.152183	+	0.0878629i
$863$	−28.9918	−	16.7384i	−0.986892	−	0.569782i	−0.0825483	−	0.996587i	$-0.526306\pi$
$863$	−28.9918	−	16.7384i	−0.986892	−	0.569782i	−0.904344	+	0.426805i	$0.859639\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−7.67225	−	3.06797i	−0.260864	−	0.104314i
$866$	−28.3523	−	20.5991i	−0.963449	−	0.699987i
$867$			15.1652i			0.515037i
$868$	14.3245	−	2.16572i	0.486204	−	0.0735094i
$869$	−0.440035			−0.0149272
$870$	10.9286	−	16.3279i	0.370516	−	0.553566i
$871$	4.69249	+	2.08923i	0.158999	+	0.0707909i
$872$	7.93693	−	2.57887i	0.268778	−	0.0873314i
$873$	12.4508	+	7.18849i	0.421397	+	0.243294i
$874$	−13.5266	−	23.4287i	−0.457544	−	0.792489i
$875$	−16.8462	+	23.7171i	−0.569507	+	0.801783i
$876$	4.70341	−	14.4756i	0.158913	−	0.489085i
$877$	−5.96895	+	5.37447i	−0.201557	+	0.181483i	−0.763728	−	0.645538i	$-0.776633\pi$
$877$	−5.96895	+	5.37447i	−0.201557	+	0.181483i	0.562171	+	0.827021i	$0.309966\pi$
$878$	−4.09230	−	9.19146i	−0.138108	−	0.310197i
$879$	−15.9587	−	3.39212i	−0.538273	−	0.114413i
$880$	−1.54537	−	0.102518i	−0.0520944	−	0.00345590i
$881$	−3.84973	−	36.6278i	−0.129701	−	1.23402i	−0.844833	−	0.535031i	$-0.820300\pi$
$881$	−3.84973	−	36.6278i	−0.129701	−	1.23402i	0.715132	−	0.698990i	$-0.246367\pi$
$882$	0.0477456	+	0.224626i	0.00160768	+	0.00756353i
$883$	−8.93378	−	12.2963i	−0.300646	−	0.413803i	0.631790	−	0.775140i	$-0.282321\pi$
$883$	−8.93378	−	12.2963i	−0.300646	−	0.413803i	−0.932435	+	0.361337i	$0.882321\pi$
$884$	6.40327	−	4.65225i	0.215365	−	0.156472i
$885$	5.51501	−	1.39598i	0.185385	−	0.0469255i
$886$	−2.24353	−	21.3458i	−0.0753728	−	0.717125i
$887$	−11.3420	−	1.19210i	−0.380829	−	0.0400267i	−0.0878197	−	0.996136i	$-0.527990\pi$
$887$	−11.3420	−	1.19210i	−0.380829	−	0.0400267i	−0.293009	+	0.956110i	$0.594657\pi$
$888$	−2.28169	+	10.7345i	−0.0765686	+	0.360227i
$889$	−5.63617	+	2.50938i	−0.189031	+	0.0841620i
$890$	9.17375	+	9.43206i	0.307505	+	0.316163i
$891$	−0.214034	+	0.658729i	−0.00717041	+	0.0220683i
$892$	−4.87500	−	4.38947i	−0.163227	−	0.146970i
$893$	−51.3091	+	29.6233i	−1.71699	+	0.991306i
$894$	10.7596	−	18.6361i	0.359853	−	0.623285i
$895$	40.8038	−	15.0166i	1.36392	−	0.501949i
$896$	2.37704	+	1.05833i	0.0794112	+	0.0353562i
$897$	−4.87513	+	6.71004i	−0.162776	+	0.224042i
$898$			2.41277i			0.0805152i
$899$	−2.90359	+	48.8363i	−0.0968402	+	1.62878i
$900$	−4.98520	+	0.384397i	−0.166173	+	0.0128132i
$901$	−2.70688	−	1.96667i	−0.0901794	−	0.0655191i
$902$	−1.55915	+	3.50190i	−0.0519140	+	0.116601i
$903$	−21.4705	+	6.97620i	−0.714495	+	0.232153i
$904$	−2.80965	+	4.86646i	−0.0934476	+	0.161856i
$905$	8.84910	−	5.57357i	0.294154	−	0.185272i
$906$	9.05023	−	10.0513i	0.300674	−	0.333932i
$907$	40.6395	+	13.2046i	1.34941	+	0.438451i	0.892495	−	0.451058i	$-0.148953\pi$
$907$	40.6395	+	13.2046i	1.34941	+	0.438451i	0.456918	+	0.889509i	$0.348953\pi$
$908$	−8.69464	+	7.82869i	−0.288542	+	0.259804i
$909$	16.2101	−	7.21720i	0.537655	−	0.239379i
$910$	−8.00136	−	1.38141i	−0.265242	−	0.0457934i
$911$	2.17665	−	20.7094i	0.0721156	−	0.686134i	−0.897419	−	0.441179i	$-0.854560\pi$
$911$	2.17665	−	20.7094i	0.0721156	−	0.686134i	0.969535	−	0.244955i	$-0.0787731\pi$
$912$	4.52706	−	0.475813i	0.149906	−	0.0157557i
$913$	−1.24767	−	5.86980i	−0.0412917	−	0.194262i
$914$	10.0736	−	7.31891i	0.333206	−	0.242088i
$915$	−24.9510	+	19.6378i	−0.824856	+	0.649205i
$916$	10.1225	−	2.15160i	0.334457	−	0.0710910i
$917$	−4.39854	+	0.462305i	−0.145252	+	0.0152667i
$918$	5.64037	+	0.592827i	0.186160	+	0.0195662i
$919$	−17.3529	−	3.68847i	−0.572419	−	0.121671i	−0.0873974	−	0.996174i	$-0.527855\pi$
$919$	−17.3529	−	3.68847i	−0.572419	−	0.121671i	−0.485022	+	0.874502i	$0.661188\pi$
$920$	−5.86825	−	11.9234i	−0.193471	−	0.393104i
$921$	−22.0629	−	24.5034i	−0.726999	−	0.807414i
$922$	22.2408	+	7.22647i	0.732461	+	0.237991i
$923$	−9.08179	−	8.17728i	−0.298931	−	0.269158i
$924$	−0.901107	−	1.56076i	−0.0296442	−	0.0513453i
$925$	49.4889	+	23.7013i	1.62718	+	0.779294i
$926$	−8.93872	−	27.5106i	−0.293745	−	0.904053i
$927$	−4.72799	+	10.6192i	−0.155288	+	0.348782i
$928$	−5.16472	+	7.10863i	−0.169540	+	0.233352i
$929$	29.1472			0.956289			0.478145	−	0.878281i	$-0.341309\pi$
$929$	29.1472			0.956289			0.478145	+	0.878281i	$0.341309\pi$
$930$	10.2230	−	7.10569i	0.335224	−	0.233005i
$931$	−1.04534			−0.0342595
$932$	14.2912	−	19.6702i	0.468125	−	0.644319i
$933$	−3.24287	+	7.28360i	−0.106167	+	0.238454i
$934$	−5.62377	−	17.3082i	−0.184015	−	0.566341i
$935$	4.09599	−	7.77024i	0.133953	−	0.254114i
$936$	−0.697784	−	1.20860i	−0.0228078	−	0.0395042i
$937$	−15.3614	−	13.8314i	−0.501834	−	0.451853i	0.378919	−	0.925430i	$-0.376296\pi$
$937$	−15.3614	−	13.8314i	−0.501834	−	0.451853i	−0.880752	+	0.473577i	$0.842963\pi$
$938$	−9.10824	−	2.95945i	−0.297394	−	0.0966293i
$939$	12.8351	+	14.2549i	0.418859	+	0.465190i
$940$	−26.1124	+	12.8515i	−0.851693	+	0.419170i
$941$	35.3806	+	7.52038i	1.15338	+	0.245158i	0.744621	−	0.667487i	$-0.232630\pi$
$941$	35.3806	+	7.52038i	1.15338	+	0.245158i	0.408754	+	0.912645i	$0.365963\pi$
$942$	−0.328516	−	0.0345284i	−0.0107036	−	0.00112500i
$943$	−32.7118	+	3.43815i	−1.06524	+	0.111961i
$944$	−2.48858	+	0.528964i	−0.0809964	+	0.0172163i
$945$	−3.59841	−	4.57201i	−0.117056	−	0.148727i
$946$	−4.86171	+	3.53224i	−0.158068	+	0.114843i
$947$	3.86980	+	18.2060i	0.125751	+	0.591614i	0.995223	+	0.0976307i	$0.0311264\pi$
$947$	3.86980	+	18.2060i	0.125751	+	0.591614i	−0.869471	+	0.493984i	$0.835540\pi$
$948$	0.631831	−	0.0664081i	0.0205209	−	0.00215683i
$949$	2.22032	−	21.1249i	0.0720746	−	0.685744i
$950$	3.00652	−	22.5605i	0.0975445	−	0.731960i
$951$	3.25853	−	1.45079i	0.105665	−	0.0470451i
$952$	−10.9666	+	9.87438i	−0.355430	+	0.320030i
$953$	−1.10577	−	0.359287i	−0.0358194	−	0.0116384i	0.291052	−	0.956707i	$-0.405995\pi$
$953$	−1.10577	−	0.359287i	−0.0358194	−	0.0116384i	−0.326872	+	0.945069i	$0.605995\pi$
$954$	−0.394757	+	0.438422i	−0.0127807	+	0.0141944i
$955$	−11.7316	+	7.38908i	−0.379625	+	0.239105i
$956$	−6.31604	+	10.9397i	−0.204275	+	0.353815i
$957$	5.78808	−	1.88066i	0.187102	−	0.0607932i
$958$	−3.02749	+	6.79986i	−0.0978138	+	0.219693i
$959$	11.1051	+	8.06835i	0.358604	+	0.260541i
$960$	2.23441	−	0.0860174i	0.0721154	−	0.00277620i
$961$	−13.0055	+	28.1399i	−0.419533	+	0.907740i
$962$			15.3154i			0.493789i
$963$	7.97338	−	10.9744i	0.256938	−	0.353645i
$964$	9.90814	+	4.41139i	0.319120	+	0.142081i
$965$	−14.8012	−	40.2184i	−0.476466	−	1.29468i
$966$	7.73201	−	13.3922i	0.248773	−	0.430888i
$967$	34.2286	−	19.7619i	1.10072	−	0.635500i	0.164308	−	0.986409i	$-0.447461\pi$
$967$	34.2286	−	19.7619i	1.10072	−	0.635500i	0.936409	+	0.350909i	$0.114127\pi$
$968$	7.81808	+	7.03943i	0.251283	+	0.226256i
$969$	−7.97769	+	24.5528i	−0.256280	+	0.788750i
$970$	−23.0454	+	22.4143i	−0.739943	+	0.719679i
$971$	−5.01871	+	2.23447i	−0.161058	+	0.0717077i	−0.485682	−	0.874135i	$-0.661429\pi$
$971$	−5.01871	+	2.23447i	−0.161058	+	0.0717077i	0.324624	+	0.945843i	$0.394762\pi$
$972$	0.207912	−	0.978148i	0.00666877	−	0.0313741i
$973$	34.1208	+	3.58624i	1.09386	+	0.114970i
$974$	1.88395	+	17.9246i	0.0603658	+	0.574342i
$975$	−6.69362	+	1.97121i	−0.214367	+	0.0631292i
$976$	11.4880	−	8.34654i	0.367723	−	0.267166i
$977$	−18.9259	−	26.0493i	−0.605493	−	0.833390i	0.390704	−	0.920516i	$-0.372232\pi$
$977$	−18.9259	−	26.0493i	−0.605493	−	0.833390i	−0.996197	+	0.0871265i	$0.972232\pi$
$978$	4.83479	+	22.7459i	0.154599	+	0.727333i
$979$	0.426016	+	4.05327i	0.0136155	+	0.129543i
$980$	−0.512373	−	0.0339904i	−0.0163672	−	0.00108578i
$981$	8.16302	+	1.73510i	0.260625	+	0.0553976i
$982$	−7.58791	−	17.0427i	−0.242140	−	0.543855i
$983$	−38.7134	+	34.8577i	−1.23477	+	1.11179i	−0.244935	+	0.969540i	$0.578767\pi$
$983$	−38.7134	+	34.8577i	−1.23477	+	1.11179i	−0.989831	+	0.142249i	$0.954567\pi$
$984$	1.71024	−	5.26356i	0.0545203	−	0.167796i
$985$	11.2416	−	13.4947i	0.358186	−	0.429978i
$986$	−24.9167	−	43.1570i	−0.793510	−	1.37440i
$987$	−29.3291	−	16.9331i	−0.933554	−	0.538988i
$988$	6.04170	−	1.96307i	0.192212	−	0.0624535i
$989$	−47.1061	−	20.9730i	−1.49789	−	0.666903i
$990$	−1.28707	−	0.861468i	−0.0409057	−	0.0273792i
$991$	−38.8085			−1.23279			−0.616396	−	0.787436i	$-0.711408\pi$
$991$	−38.8085			−1.23279			−0.616396	+	0.787436i	$0.711408\pi$
$992$	−4.69071	+	2.99954i	−0.148930	+	0.0952355i
$993$			1.71856i			0.0545367i
$994$	18.4336	+	13.3928i	0.584679	+	0.424794i
$995$	20.2233	−	50.5736i	0.641121	−	1.60329i
$996$	2.67732	+	8.23996i	0.0848343	+	0.261093i
$997$	−41.6935	−	24.0717i	−1.32045	−	0.762360i	−0.336646	−	0.941631i	$-0.609293\pi$
$997$	−41.6935	−	24.0717i	−1.32045	−	0.762360i	−0.983800	+	0.179272i	$0.942626\pi$
$998$	−11.9405	+	6.89383i	−0.377969	+	0.218220i
$999$	−7.34326	+	8.15552i	−0.232331	+	0.258029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.16	yes	144
5.4	even	2	inner	930.2.bn.b.19.1	✓	144
31.18	even	15	inner	930.2.bn.b.49.1	yes	144
155.49	even	30	inner	930.2.bn.b.49.16	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.1	✓	144	5.4	even	2	inner
930.2.bn.b.19.16	yes	144	1.1	even	1	trivial
930.2.bn.b.49.1	yes	144	31.18	even	15	inner
930.2.bn.b.49.16	yes	144	155.49	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.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.97807 + 1.04271i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93366 + 1.74107i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.97807 + 1.04271i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.93366 + 1.74107i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(2.00625 - 0.987398i) q^{10} +(0.677493 + 0.144006i) q^{11} +(-0.994522 - 0.104528i) q^{12} +(-1.38792 + 0.145877i) q^{13} +(2.54513 - 0.540984i) q^{14} +(1.75712 - 1.38294i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.17916 - 5.54750i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(0.475813 - 4.52706i) q^{19} +(0.380423 - 2.20347i) q^{20} +(2.37704 - 1.05833i) q^{21} +(0.514724 - 0.463459i) q^{22} +(5.65227 + 1.83653i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(2.82550 + 4.12511i) q^{25} +(-0.697784 + 1.20860i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(1.05833 - 2.37704i) q^{28} +(7.10863 + 5.16472i) q^{29} +(-0.0860174 - 2.23441i) q^{30} +(2.99954 + 4.69071i) q^{31} +1.00000i q^{32} +(0.407117 - 0.560349i) q^{33} +(-5.18112 - 2.30678i) q^{34} +(2.00946 + 5.46021i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(9.50405 - 5.48717i) q^{37} +(-3.38279 - 3.04588i) q^{38} +(-0.431254 + 1.32726i) q^{39} +(-1.55904 - 1.60294i) q^{40} +(-5.05596 + 2.25106i) q^{41} +(0.540984 - 2.54513i) q^{42} +(-8.62869 - 0.906912i) q^{43} +(-0.0723994 - 0.688835i) q^{44} +(-0.548698 - 2.16770i) q^{45} +(4.80811 - 3.49329i) q^{46} +(-7.65033 - 10.5298i) q^{47} +(0.207912 + 0.978148i) q^{48} +(-0.0240043 - 0.228386i) q^{49} +(4.99807 + 0.138804i) q^{50} +(-5.54750 - 1.17916i) q^{51} +(0.567628 + 1.27491i) q^{52} +(0.438422 - 0.394757i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.18997 + 0.991284i) q^{55} +(-1.30100 - 2.25339i) q^{56} +(-3.94214 - 2.27600i) q^{57} +(8.35669 - 2.71525i) q^{58} +(2.32422 + 1.03481i) q^{59} +(-1.85824 - 1.24377i) q^{60} -14.2000 q^{61} +(5.55795 + 0.330452i) q^{62} -2.60199i q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.89751 - 1.15865i) q^{65} +(-0.214034 - 0.658729i) q^{66} +(-3.18752 - 1.84032i) q^{67} +(-4.91161 + 2.83572i) q^{68} +(3.97674 - 4.41662i) q^{69} +(5.59853 + 1.58374i) q^{70} +(5.85946 + 6.50759i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-3.16453 + 14.8879i) q^{73} +(1.14713 - 10.9142i) q^{74} +(4.91771 - 0.903387i) q^{75} +(-4.45252 + 0.946413i) q^{76} +(1.05931 + 1.45802i) q^{77} +(0.820294 + 1.12904i) q^{78} +(-0.621428 + 0.132089i) q^{79} +(-2.21318 + 0.319106i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-1.15067 + 5.41350i) q^{82} +(-3.52397 - 7.91496i) q^{83} +(-1.74107 - 1.93366i) q^{84} +(3.45200 - 12.2029i) q^{85} +(-5.80553 + 6.44769i) q^{86} +(7.60954 - 4.39337i) q^{87} +(-0.599834 - 0.346314i) q^{88} +(1.81833 + 5.59625i) q^{89} +(-2.07622 - 0.830237i) q^{90} +(-2.93775 - 2.13440i) q^{91} -5.94315i q^{92} +(5.50520 - 0.832332i) q^{93} -13.0155 q^{94} +(5.66161 - 8.45869i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-13.6733 + 4.44273i) q^{97} +(-0.198877 - 0.114822i) q^{98} +(-0.346314 - 0.599834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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