LMFDB - Embedded newform 930.2.br.b.11.1

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			11.1
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-1.72275 + 0.179283i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.58303 - 0.702867i) q^{6} +(-0.113415 - 1.07907i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.93571 - 0.617720i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.72275 + 0.179283i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.58303 - 0.702867i) q^{6} +(-0.113415 - 1.07907i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.93571 - 0.617720i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-2.56206 - 1.14070i) q^{11} +(-1.28835 + 1.15765i) q^{12} +(1.02862 + 4.83927i) q^{13} +(0.441316 + 0.991212i) q^{14} +(1.40230 - 1.01664i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.58997 + 0.707901i) q^{17} +(-2.60114 + 1.49467i) q^{18} +(1.90535 + 0.404995i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.388846 + 1.83864i) q^{21} +(2.78916 + 0.293153i) q^{22} +(-4.13404 - 3.00356i) q^{23} +(0.867562 - 1.49911i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.47369 - 4.28455i) q^{26} +(-4.94675 + 1.59050i) q^{27} +(-0.726018 - 0.806325i) q^{28} +(-0.677305 - 2.08453i) q^{29} +(-1.01951 + 1.40021i) q^{30} +(0.859116 - 5.50108i) q^{31} +1.00000i q^{32} +(4.61829 + 1.50581i) q^{33} +(1.29340 - 1.16458i) q^{34} +(0.637757 + 0.877797i) q^{35} +(2.01196 - 2.22532i) q^{36} +(2.45281 + 1.41613i) q^{37} +(-1.93725 + 0.203613i) q^{38} +(-2.63965 - 8.15242i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-0.267518 - 0.240874i) q^{41} +(-0.937984 - 1.62849i) q^{42} +(-0.350040 + 1.64681i) q^{43} +(-2.74324 + 0.583094i) q^{44} +(-2.23354 + 2.00282i) q^{45} +(4.85986 + 1.57906i) q^{46} +(4.18402 + 1.35947i) q^{47} +(-0.361849 + 1.69383i) q^{48} +(5.69550 - 1.21062i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(2.61220 - 1.50459i) q^{51} +(3.67662 + 3.31044i) q^{52} +(0.556631 - 5.29599i) q^{53} +(4.21314 - 3.04128i) q^{54} +(2.78916 - 0.293153i) q^{55} +(0.939652 + 0.542509i) q^{56} +(-3.35505 - 0.356106i) q^{57} +(1.28831 + 1.77321i) q^{58} +(8.37326 - 7.53932i) q^{59} +(0.536921 - 1.64673i) q^{60} +2.17337i q^{61} +(0.882860 + 5.49732i) q^{62} +(-0.999520 - 3.09779i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.31044 - 3.67662i) q^{65} +(-4.85758 - 0.00497752i) q^{66} +(0.967850 + 1.67637i) q^{67} +(-0.870221 + 1.50727i) q^{68} +(7.66039 + 4.43320i) q^{69} +(-0.877797 - 0.637757i) q^{70} +(9.83673 + 1.03388i) q^{71} +(-1.22582 + 2.73813i) q^{72} +(5.48528 - 12.3201i) q^{73} +(-2.77037 - 0.588861i) q^{74} +(-0.706110 + 1.58158i) q^{75} +(1.77951 - 0.792289i) q^{76} +(-0.940326 + 2.89403i) q^{77} +(5.02969 + 6.93771i) q^{78} +(-6.34492 - 14.2509i) q^{79} +(0.207912 + 0.978148i) q^{80} +(8.23684 - 3.62690i) q^{81} +(0.328859 + 0.146417i) q^{82} +(8.96001 - 9.95110i) q^{83} +(1.39531 + 1.25893i) q^{84} +(1.02301 - 1.40805i) q^{85} +(-0.175984 - 1.67438i) q^{86} +(1.54055 + 3.46969i) q^{87} +(2.42879 - 1.40226i) q^{88} +(5.49395 - 3.99159i) q^{89} +(1.50532 - 2.59500i) q^{90} +(5.10526 - 1.65880i) q^{91} -5.10996 q^{92} +(-0.493787 + 9.63100i) q^{93} -4.39934 q^{94} +(-1.85258 + 0.601940i) q^{95} +(-0.179283 - 1.72275i) q^{96} +(-5.71138 + 4.14956i) q^{97} +(-5.04264 + 2.91137i) q^{98} +(-8.22612 - 1.76614i) 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} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 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 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * 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
$3$	−1.72275	+	0.179283i	−0.994628	+	0.103509i
$3$	−1.72275	+	0.179283i	−0.994628	+	0.103509i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	1.58303	−	0.702867i	0.646269	−	0.286944i
$7$	−0.113415	−	1.07907i	−0.0428669	−	0.407851i	−0.994823	−	0.101618i	$-0.967598\pi$
$7$	−0.113415	−	1.07907i	−0.0428669	−	0.407851i	0.951957	−	0.306233i	$-0.0990687\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	2.93571	−	0.617720i	0.978572	−	0.205907i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−2.56206	−	1.14070i	−0.772491	−	0.343935i	−0.0176510	−	0.999844i	$-0.505619\pi$
$11$	−2.56206	−	1.14070i	−0.772491	−	0.343935i	−0.754840	+	0.655909i	$0.772285\pi$
$12$	−1.28835	+	1.15765i	−0.371915	+	0.334184i
$13$	1.02862	+	4.83927i	0.285287	+	1.34217i	0.854274	+	0.519824i	$0.174002\pi$
$13$	1.02862	+	4.83927i	0.285287	+	1.34217i	−0.568986	+	0.822347i	$0.692664\pi$
$14$	0.441316	+	0.991212i	0.117947	+	0.264913i
$15$	1.40230	−	1.01664i	0.362073	−	0.262495i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.58997	+	0.707901i	−0.385625	+	0.171691i	−0.590387	−	0.807121i	$-0.701025\pi$
$17$	−1.58997	+	0.707901i	−0.385625	+	0.171691i	0.204762	+	0.978812i	$0.434358\pi$
$18$	−2.60114	+	1.49467i	−0.613096	+	0.352298i
$19$	1.90535	+	0.404995i	0.437117	+	0.0929122i	0.421214	−	0.906961i	$-0.361604\pi$
$19$	1.90535	+	0.404995i	0.437117	+	0.0929122i	0.0159036	+	0.999874i	$0.494938\pi$
$20$	−0.406737	+	0.913545i	−0.0909491	+	0.204275i
$21$	0.388846	+	1.83864i	0.0848531	+	0.401223i
$22$	2.78916	+	0.293153i	0.594652	+	0.0625004i
$23$	−4.13404	−	3.00356i	−0.862007	−	0.626285i	0.0664232	−	0.997792i	$-0.478841\pi$
$23$	−4.13404	−	3.00356i	−0.862007	−	0.626285i	−0.928430	+	0.371507i	$0.878841\pi$
$24$	0.867562	−	1.49911i	0.177090	−	0.306005i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.47369	−	4.28455i	−0.485130	−	0.840270i
$27$	−4.94675	+	1.59050i	−0.952002	+	0.306092i
$28$	−0.726018	−	0.806325i	−0.137205	−	0.152381i
$29$	−0.677305	−	2.08453i	−0.125772	−	0.387087i	0.868269	−	0.496094i	$-0.165233\pi$
$29$	−0.677305	−	2.08453i	−0.125772	−	0.387087i	−0.994041	+	0.109007i	$0.965233\pi$
$30$	−1.01951	+	1.40021i	−0.186136	+	0.255643i
$31$	0.859116	−	5.50108i	0.154302	−	0.988024i
$31$	0.859116	−	5.50108i	0.154302	−	0.988024i
$32$			1.00000i			0.176777i
$33$	4.61829	+	1.50581i	0.803942	+	0.262128i
$34$	1.29340	−	1.16458i	0.221816	−	0.199724i
$35$	0.637757	+	0.877797i	0.107801	+	0.148375i
$36$	2.01196	−	2.22532i	0.335326	−	0.370886i
$37$	2.45281	+	1.41613i	0.403240	+	0.232811i	0.687881	−	0.725824i	$-0.258541\pi$
$37$	2.45281	+	1.41613i	0.403240	+	0.232811i	−0.284641	+	0.958634i	$0.591874\pi$
$38$	−1.93725	+	0.203613i	−0.314263	+	0.0330304i
$39$	−2.63965	−	8.15242i	−0.422682	−	1.30543i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	−0.267518	−	0.240874i	−0.0417792	−	0.0376182i	0.647977	−	0.761660i	$-0.275615\pi$
$41$	−0.267518	−	0.240874i	−0.0417792	−	0.0376182i	−0.689756	+	0.724042i	$0.742282\pi$
$42$	−0.937984	−	1.62849i	−0.144734	−	0.251281i
$43$	−0.350040	+	1.64681i	−0.0533806	+	0.251136i	−0.996745	−	0.0806234i	$-0.974309\pi$
$43$	−0.350040	+	1.64681i	−0.0533806	+	0.251136i	0.943364	+	0.331759i	$0.107642\pi$
$44$	−2.74324	+	0.583094i	−0.413559	+	0.0879047i
$45$	−2.23354	+	2.00282i	−0.332957	+	0.298563i
$46$	4.85986	+	1.57906i	0.716547	+	0.232820i
$47$	4.18402	+	1.35947i	0.610302	+	0.198299i	0.597830	−	0.801623i	$-0.296030\pi$
$47$	4.18402	+	1.35947i	0.610302	+	0.198299i	0.0124720	+	0.999922i	$0.496030\pi$
$48$	−0.361849	+	1.69383i	−0.0522285	+	0.244484i
$49$	5.69550	−	1.21062i	0.813642	−	0.172945i
$50$	−0.207912	+	0.978148i	−0.0294032	+	0.138331i
$51$	2.61220	−	1.50459i	0.365782	−	0.210685i
$52$	3.67662	+	3.31044i	0.509855	+	0.459076i
$53$	0.556631	−	5.29599i	0.0764592	−	0.727461i	−0.887391	−	0.461017i	$-0.847485\pi$
$53$	0.556631	−	5.29599i	0.0764592	−	0.727461i	0.963850	−	0.266444i	$-0.0858486\pi$
$54$	4.21314	−	3.04128i	0.573336	−	0.413866i
$55$	2.78916	−	0.293153i	0.376091	−	0.0395287i
$56$	0.939652	+	0.542509i	0.125566	+	0.0724958i
$57$	−3.35505	−	0.356106i	−0.444387	−	0.0471674i
$58$	1.28831	+	1.77321i	0.169163	+	0.232833i
$59$	8.37326	−	7.53932i	1.09011	−	0.981536i	0.0902095	−	0.995923i	$-0.471246\pi$
$59$	8.37326	−	7.53932i	1.09011	−	0.981536i	0.999897	+	0.0143869i	$0.00457966\pi$
$60$	0.536921	−	1.64673i	0.0693162	−	0.212592i
$61$			2.17337i			0.278271i	0.990273	+	0.139136i	$0.0444324\pi$
$61$			2.17337i			0.278271i	−0.990273	+	0.139136i	$0.955568\pi$
$62$	0.882860	+	5.49732i	0.112123	+	0.698161i
$63$	−0.999520	−	3.09779i	−0.125928	−	0.390285i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−3.31044	−	3.67662i	−0.410610	−	0.456028i
$66$	−4.85758	−	0.00497752i	−0.597927	−	0.000612690i
$67$	0.967850	+	1.67637i	0.118242	+	0.204801i	0.919071	−	0.394092i	$-0.128941\pi$
$67$	0.967850	+	1.67637i	0.118242	+	0.204801i	−0.800829	+	0.598893i	$0.795608\pi$
$68$	−0.870221	+	1.50727i	−0.105530	+	0.182783i
$69$	7.66039	+	4.43320i	0.922203	+	0.533695i
$70$	−0.877797	−	0.637757i	−0.104917	−	0.0762265i
$71$	9.83673	+	1.03388i	1.16741	+	0.122699i	0.668334	−	0.743862i	$-0.267008\pi$
$71$	9.83673	+	1.03388i	1.16741	+	0.122699i	0.499072	+	0.866561i	$0.333674\pi$
$72$	−1.22582	+	2.73813i	−0.144465	+	0.322692i
$73$	5.48528	−	12.3201i	0.642004	−	1.44196i	−0.240024	−	0.970767i	$-0.577155\pi$
$73$	5.48528	−	12.3201i	0.642004	−	1.44196i	0.882028	−	0.471197i	$-0.156178\pi$
$74$	−2.77037	−	0.588861i	−0.322049	−	0.0684537i
$75$	−0.706110	+	1.58158i	−0.0815345	+	0.182626i
$76$	1.77951	−	0.792289i	0.204124	−	0.0908818i
$77$	−0.940326	+	2.89403i	−0.107160	+	0.329805i
$78$	5.02969	+	6.93771i	0.569500	+	0.785541i
$79$	−6.34492	−	14.2509i	−0.713859	−	1.60335i	−0.794970	−	0.606649i	$-0.792513\pi$
$79$	−6.34492	−	14.2509i	−0.713859	−	1.60335i	0.0811108	−	0.996705i	$-0.474153\pi$
$80$	0.207912	+	0.978148i	0.0232452	+	0.109360i
$81$	8.23684	−	3.62690i	0.915205	−	0.402989i
$82$	0.328859	+	0.146417i	0.0363164	+	0.0161691i
$83$	8.96001	−	9.95110i	0.983489	−	1.09228i	−0.0122372	−	0.999925i	$-0.503895\pi$
$83$	8.96001	−	9.95110i	0.983489	−	1.09228i	0.995727	−	0.0923505i	$-0.0294380\pi$
$84$	1.39531	+	1.25893i	0.152240	+	0.137361i
$85$	1.02301	−	1.40805i	0.110961	−	0.152724i
$86$	−0.175984	−	1.67438i	−0.0189768	−	0.180553i
$87$	1.54055	+	3.46969i	0.165164	+	0.371990i
$88$	2.42879	−	1.40226i	0.258910	−	0.149482i
$89$	5.49395	−	3.99159i	0.582358	−	0.423108i	−0.257216	−	0.966354i	$-0.582805\pi$
$89$	5.49395	−	3.99159i	0.582358	−	0.423108i	0.839573	+	0.543246i	$0.182805\pi$
$90$	1.50532	−	2.59500i	0.158675	−	0.273537i
$91$	5.10526	−	1.65880i	0.535177	−	0.173889i
$92$	−5.10996			−0.532750
$93$	−0.493787	+	9.63100i	−0.0512033	+	0.998688i
$94$	−4.39934			−0.453757
$95$	−1.85258	+	0.601940i	−0.190071	+	0.0617577i
$96$	−0.179283	−	1.72275i	−0.0182980	−	0.175827i
$97$	−5.71138	+	4.14956i	−0.579903	+	0.421324i	−0.838689	−	0.544611i	$-0.816677\pi$
$97$	−5.71138	+	4.14956i	−0.579903	+	0.421324i	0.258786	+	0.965935i	$0.416677\pi$
$98$	−5.04264	+	2.91137i	−0.509383	+	0.294093i
$99$	−8.22612	−	1.76614i	−0.826756	−	0.177504i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−2.22301	+	3.05971i	−0.221198	+	0.304452i	−0.905165	−	0.425060i	$-0.860253\pi$
$101$	−2.22301	+	3.05971i	−0.221198	+	0.304452i	0.683968	+	0.729512i	$0.260253\pi$
$102$	−2.01941	+	2.23817i	−0.199951	+	0.221611i
$103$	8.12338	−	9.02192i	0.800420	−	0.888957i	−0.195360	−	0.980732i	$-0.562587\pi$
$103$	8.12338	−	9.02192i	0.800420	−	0.888957i	0.995780	+	0.0917750i	$0.0292541\pi$
$104$	−4.51965	−	2.01228i	−0.443189	−	0.197320i
$105$	−1.25607	−	1.39788i	−0.122580	−	0.136419i
$106$	1.10716	+	5.20880i	0.107537	+	0.505923i
$107$	0.518603	+	1.16480i	0.0501353	+	0.112606i	0.936876	−	0.349661i	$-0.113703\pi$
$107$	0.518603	+	1.16480i	0.0501353	+	0.112606i	−0.886741	+	0.462266i	$0.847036\pi$
$108$	−3.06713	+	4.19437i	−0.295135	+	0.403603i
$109$	3.02851	−	9.32081i	0.290079	−	0.892771i	−0.694751	−	0.719250i	$-0.744486\pi$
$109$	3.02851	−	9.32081i	0.290079	−	0.892771i	0.984830	−	0.173521i	$-0.0555145\pi$
$110$	−2.56206	+	1.14070i	−0.244283	+	0.108762i
$111$	−4.47946	−	1.99989i	−0.425172	−	0.189821i
$112$	−1.06131	−	0.225588i	−0.100284	−	0.0213160i
$113$	−5.22443	+	11.7343i	−0.491473	+	1.10387i	0.482230	+	0.876044i	$0.339827\pi$
$113$	−5.22443	+	11.7343i	−0.491473	+	1.10387i	−0.973703	+	0.227821i	$0.926840\pi$
$114$	3.30088	−	0.698090i	0.309156	−	0.0653821i
$115$	5.08196	+	0.534136i	0.473895	+	0.0498084i
$116$	−1.77321	−	1.28831i	−0.164638	−	0.119617i
$117$	6.00904	+	13.5713i	0.555536	+	1.25467i
$118$	−5.63367	+	9.75780i	−0.518621	+	0.898278i
$119$	0.944204	+	1.63541i	0.0865551	+	0.149918i
$120$	−0.00177482	+	1.73205i	−0.000162018	+	0.158114i
$121$	−2.09748	−	2.32948i	−0.190680	−	0.211771i
$122$	−0.671608	−	2.06700i	−0.0608045	−	0.187137i
$123$	0.504050	+	0.367004i	0.0454487	+	0.0330916i
$124$	−2.53842	−	4.95545i	−0.227956	−	0.445012i
$125$			1.00000i			0.0894427i
$126$	1.90787	+	2.63731i	0.169967	+	0.234950i
$127$	2.48363	−	2.23627i	0.220387	−	0.198437i	−0.551540	−	0.834148i	$-0.685960\pi$
$127$	2.48363	−	2.23627i	0.220387	−	0.198437i	0.771927	+	0.635711i	$0.219293\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	0.307785	−	2.89979i	0.0270989	−	0.255312i
$130$	4.28455	+	2.47369i	0.375780	+	0.216957i
$131$	8.72067	−	0.916579i	0.761928	−	0.0800819i	0.284409	−	0.958703i	$-0.408203\pi$
$131$	8.72067	−	0.916579i	0.761928	−	0.0800819i	0.477519	+	0.878621i	$0.341536\pi$
$132$	4.62137	−	1.49634i	0.402239	−	0.130240i
$133$	0.220923	−	2.10195i	0.0191565	−	0.182262i
$134$	−1.43851	−	1.29524i	−0.124268	−	0.111891i
$135$	3.48876	−	3.85079i	0.300265	−	0.331423i
$136$	0.361858	−	1.70241i	0.0310291	−	0.145980i
$137$	−6.54191	+	1.39053i	−0.558914	+	0.118801i	−0.478703	−	0.877977i	$-0.658893\pi$
$137$	−6.54191	+	1.39053i	−0.558914	+	0.118801i	−0.0802110	+	0.996778i	$0.525559\pi$
$138$	−8.65540	−	1.84903i	−0.736797	−	0.157400i
$139$	−12.3210	−	4.00333i	−1.04505	−	0.339558i	−0.264327	−	0.964433i	$-0.585150\pi$
$139$	−12.3210	−	4.00333i	−1.04505	−	0.339558i	−0.780725	+	0.624875i	$0.785150\pi$
$140$	1.03191	+	0.335289i	0.0872125	+	0.0283371i
$141$	−7.45173	−	1.59190i	−0.627549	−	0.134062i
$142$	−9.67478	+	2.05644i	−0.811889	+	0.172572i
$143$	2.88479	−	13.5718i	0.241238	−	1.13494i
$144$	0.319699	−	2.98292i	0.0266416	−	0.248576i
$145$	1.62883	+	1.46660i	0.135267	+	0.121795i
$146$	−1.40968	+	13.4122i	−0.116666	+	1.11000i
$147$	−9.59486	+	3.10669i	−0.791371	+	0.256236i
$148$	2.81675	−	0.296052i	0.231535	−	0.0243353i
$149$	13.9398	+	8.04813i	1.14199	+	0.659329i	0.946923	−	0.321461i	$-0.104174\pi$
$149$	13.9398	+	8.04813i	1.14199	+	0.659329i	0.195068	+	0.980790i	$0.437507\pi$
$150$	0.182814	−	1.72238i	0.0149267	−	0.140631i
$151$	−5.36846	−	7.38905i	−0.436879	−	0.601312i	0.532636	−	0.846344i	$-0.321201\pi$
$151$	−5.36846	−	7.38905i	−0.436879	−	0.601312i	−0.969515	+	0.245032i	$0.921201\pi$
$152$	−1.44758	+	1.30341i	−0.117415	+	0.105721i
$153$	−4.23042	+	3.06035i	−0.342009	+	0.247415i
$154$		−	3.04296i		−	0.245209i
$155$	2.00653	+	5.19364i	0.161168	+	0.417163i
$156$	−6.92739	−	5.04390i	−0.554635	−	0.403835i
$157$	5.24115	+	16.1306i	0.418289	+	1.28736i	0.909276	+	0.416195i	$0.136636\pi$
$157$	5.24115	+	16.1306i	0.418289	+	1.28736i	−0.490986	+	0.871167i	$0.663364\pi$
$158$	10.4382	+	11.5927i	0.830415	+	0.922269i
$159$	−0.00945119	+	9.22345i	−0.000749528	+	0.731467i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−2.77219	+	4.80158i	−0.218480	+	0.378418i
$162$	−6.71293	+	5.99471i	−0.527418	+	0.470989i
$163$	−11.5080	−	8.36106i	−0.901377	−	0.654889i	0.0374423	−	0.999299i	$-0.488079\pi$
$163$	−11.5080	−	8.36106i	−0.901377	−	0.654889i	−0.938819	+	0.344410i	$0.888079\pi$
$164$	−0.358009	−	0.0376282i	−0.0279558	−	0.00293827i
$165$	−4.75247	+	1.00508i	−0.369979	+	0.0782453i
$166$	−5.44642	+	12.2329i	−0.422724	+	0.949454i
$167$	9.78410	+	2.07968i	0.757117	+	0.160930i	0.570268	−	0.821459i	$-0.306839\pi$
$167$	9.78410	+	2.07968i	0.757117	+	0.160930i	0.186849	+	0.982389i	$0.440173\pi$
$168$	−1.71605	−	0.766141i	−0.132396	−	0.0591091i
$169$	−10.4843	+	4.66793i	−0.806488	+	0.359072i
$170$	−0.537826	+	1.65526i	−0.0412494	+	0.126952i
$171$	5.84374	+	0.0119761i	0.446882	+	0.000915833i
$172$	0.684782	+	1.53804i	0.0522141	+	0.117275i
$173$	−3.30095	−	15.5298i	−0.250967	−	1.18071i	−0.905391	−	0.424578i	$-0.860422\pi$
$173$	−3.30095	−	15.5298i	−0.250967	−	1.18071i	0.654424	−	0.756127i	$-0.272911\pi$
$174$	−2.53734	−	2.82381i	−0.192355	−	0.214073i
$175$	−0.991212	−	0.441316i	−0.0749286	−	0.0333604i
$176$	−1.87659	+	2.08417i	−0.141454	+	0.157100i
$177$	−13.0733	+	14.4895i	−0.982652	+	1.08910i
$178$	−3.99159	+	5.49395i	−0.299182	+	0.411789i
$179$	2.74109	+	26.0797i	0.204878	+	1.94929i	0.300283	+	0.953850i	$0.402919\pi$
$179$	2.74109	+	26.0797i	0.204878	+	1.94929i	−0.0954047	+	0.995439i	$0.530415\pi$
$180$	−0.629748	+	2.93316i	−0.0469386	+	0.218625i
$181$	8.18523	−	4.72575i	0.608404	−	0.351262i	−0.163937	−	0.986471i	$-0.552419\pi$
$181$	8.18523	−	4.72575i	0.608404	−	0.351262i	0.772340	+	0.635209i	$0.219086\pi$
$182$	−4.34279	+	3.15522i	−0.321909	+	0.233881i
$183$	−0.389649	−	3.74416i	−0.0288037	−	0.276777i
$184$	4.85986	−	1.57906i	0.358273	−	0.116410i
$185$	−2.83226			−0.208232
$186$	−2.50652	−	9.31221i	−0.183787	−	0.682805i
$187$	4.88111			0.356942
$188$	4.18402	−	1.35947i	0.305151	−	0.0991495i
$189$	2.27730	+	5.15752i	0.165649	+	0.375154i
$190$	1.57590	−	1.14496i	0.114328	−	0.0830639i
$191$	−5.63445	+	3.25305i	−0.407694	+	0.235382i	−0.689799	−	0.724001i	$-0.742301\pi$
$191$	−5.63445	+	3.25305i	−0.407694	+	0.235382i	0.282104	+	0.959384i	$0.408968\pi$
$192$	0.702867	+	1.58303i	0.0507250	+	0.114245i
$193$	−1.15411	−	10.9807i	−0.0830749	−	0.790405i	−0.954165	−	0.299281i	$-0.903253\pi$
$193$	−1.15411	−	10.9807i	−0.0830749	−	0.790405i	0.871090	−	0.491123i	$-0.163414\pi$
$194$	4.14956	−	5.71138i	0.297921	−	0.410053i
$195$	6.36221	+	5.74038i	0.455607	+	0.411077i
$196$	3.89617	−	4.32714i	0.278298	−	0.309081i
$197$	−19.6057	−	8.72900i	−1.39685	−	0.621916i	−0.436240	−	0.899830i	$-0.643690\pi$
$197$	−19.6057	−	8.72900i	−1.39685	−	0.621916i	−0.960606	+	0.277915i	$0.910357\pi$
$198$	8.36927	−	0.862309i	0.594778	−	0.0612816i
$199$	−0.723398	−	3.40332i	−0.0512803	−	0.241255i	0.945041	−	0.326952i	$-0.106022\pi$
$199$	−0.723398	−	3.40332i	−0.0512803	−	0.241255i	−0.996321	+	0.0856971i	$0.972688\pi$
$200$	0.406737	+	0.913545i	0.0287606	+	0.0645974i
$201$	−1.96791	−	2.71443i	−0.138805	−	0.191461i
$202$	1.16870	−	3.59690i	0.0822297	−	0.253077i
$203$	−2.17254	+	0.967279i	−0.152483	+	0.0678896i
$204$	1.22894	−	2.75265i	0.0860432	−	0.192724i
$205$	0.352114	+	0.0748442i	0.0245927	+	0.00522734i
$206$	−4.93786	+	11.0906i	−0.344037	+	0.772720i
$207$	−13.9917	−	6.26391i	−0.972492	−	0.435372i
$208$	4.92028	+	0.517142i	0.341160	+	0.0358573i
$209$	−4.41965	−	3.21106i	−0.305713	−	0.222114i
$210$	1.62656	+	0.941320i	0.112243	+	0.0649572i
$211$	−5.90668	+	10.2307i	−0.406633	+	0.704308i	−0.994510	−	0.104642i	$-0.966630\pi$
$211$	−5.90668	+	10.2307i	−0.406633	+	0.704308i	0.587877	+	0.808950i	$0.299964\pi$
$212$	−2.66258	−	4.61173i	−0.182867	−	0.316735i
$213$	−17.1316	−	0.0175546i	−1.17384	−	0.00120282i
$214$	−0.853164	−	0.947535i	−0.0583211	−	0.0647722i
$215$	−0.520261	−	1.60120i	−0.0354815	−	0.109201i
$216$	1.62088	−	4.93688i	0.110287	−	0.335912i
$217$	−6.03351	−	0.303143i	−0.409581	−	0.0205787i
$218$			9.80048i			0.663772i
$219$	−7.24096	+	22.2079i	−0.489299	+	1.50067i
$220$	2.08417	−	1.87659i	0.140515	−	0.126520i
$221$	−5.06119	−	6.96614i	−0.340453	−	0.468593i
$222$	4.87822	+	0.517776i	0.327405	+	0.0347509i
$223$	−19.6581	−	11.3496i	−1.31640	−	0.760025i	−0.333254	−	0.942837i	$-0.608147\pi$
$223$	−19.6581	−	11.3496i	−1.31640	−	0.760025i	−0.983148	+	0.182812i	$0.941480\pi$
$224$	1.07907	−	0.113415i	0.0720986	−	0.00757787i
$225$	0.932896	−	2.85126i	0.0621931	−	0.190084i
$226$	1.34264	−	12.7744i	0.0893111	−	0.849739i
$227$	−11.1638	−	10.0519i	−0.740969	−	0.667171i	0.209564	−	0.977795i	$-0.432795\pi$
$227$	−11.1638	−	10.0519i	−0.740969	−	0.667171i	−0.950533	+	0.310624i	$0.899462\pi$
$228$	−2.92360	+	1.68395i	−0.193620	+	0.111522i
$229$	−4.47148	+	21.0367i	−0.295484	+	1.39014i	0.540480	+	0.841357i	$0.318243\pi$
$229$	−4.47148	+	21.0367i	−0.295484	+	1.39014i	−0.835964	+	0.548785i	$0.815091\pi$
$230$	−4.99829	+	1.06242i	−0.329578	+	0.0700539i
$231$	1.10109	−	5.15426i	0.0724466	−	0.339125i
$232$	2.08453	+	0.677305i	0.136856	+	0.0444672i
$233$	15.7270	+	5.11001i	1.03031	+	0.334768i	0.774913	−	0.632068i	$-0.217794\pi$
$233$	15.7270	+	5.11001i	1.03031	+	0.334768i	0.255397	+	0.966836i	$0.417794\pi$
$234$	−9.90870	−	11.0502i	−0.647752	−	0.722373i
$235$	−4.30320	+	0.914673i	−0.280710	+	0.0596667i
$236$	2.34261	−	11.0211i	0.152491	−	0.717414i
$237$	13.4856	+	23.4132i	0.875987	+	1.52085i
$238$	−1.40336	−	1.26359i	−0.0909664	−	0.0819065i
$239$	−0.171834	+	1.63489i	−0.0111150	+	0.105752i	−0.998673	−	0.0515046i	$-0.983598\pi$
$239$	−0.171834	+	1.63489i	−0.0111150	+	0.105752i	0.987558	+	0.157257i	$0.0502650\pi$
$240$	−0.533545	−	1.64783i	−0.0344402	−	0.106367i
$241$	5.82709	−	0.612452i	0.375356	−	0.0394515i	0.0850275	−	0.996379i	$-0.472902\pi$
$241$	5.82709	−	0.612452i	0.375356	−	0.0394515i	0.290328	+	0.956927i	$0.406236\pi$
$242$	2.71467	+	1.56732i	0.174506	+	0.100751i
$243$	−13.5398	+	7.72496i	−0.868576	+	0.495556i
$244$	1.27747	+	1.75829i	0.0817819	+	0.112563i
$245$	−4.32714	+	3.89617i	−0.276451	+	0.248917i
$246$	−0.592790	−	0.193281i	−0.0377949	−	0.0123232i
$247$			9.63708i			0.613193i
$248$	3.94549	+	3.92850i	0.250539	+	0.249460i
$249$	−13.6518	+	18.7496i	−0.865146	+	1.18821i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	4.26731	+	4.73932i	0.269350	+	0.299143i	0.862612	−	0.505866i	$-0.168827\pi$
$251$	4.26731	+	4.73932i	0.269350	+	0.299143i	−0.593262	+	0.805009i	$0.702160\pi$
$252$	−2.62947	−	1.91866i	−0.165641	−	0.120864i
$253$	7.16550	+	12.4110i	0.450491	+	0.780274i
$254$	−1.67103	+	2.89430i	−0.104850	+	0.181605i
$255$	−1.50994	+	2.60912i	−0.0945561	+	0.163389i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−21.3550	−	2.24450i	−1.33209	−	0.140008i	−0.588420	−	0.808555i	$-0.700250\pi$
$257$	−21.3550	−	2.24450i	−1.33209	−	0.140008i	−0.743670	+	0.668547i	$0.766917\pi$
$258$	0.603364	+	2.85298i	0.0375638	+	0.177619i
$259$	1.24992	−	2.80737i	0.0776665	−	0.174442i
$260$	−4.83927	−	1.02862i	−0.300119	−	0.0637922i
$261$	−3.27603	−	5.70120i	−0.202781	−	0.352895i
$262$	−8.01061	+	3.56655i	−0.494897	+	0.220342i
$263$	6.72329	−	20.6922i	0.414576	−	1.27593i	−0.498053	−	0.867146i	$-0.665952\pi$
$263$	6.72329	−	20.6922i	0.414576	−	1.27593i	0.912630	−	0.408788i	$-0.134048\pi$
$264$	−3.93279	+	2.85119i	−0.242047	+	0.175478i
$265$	2.16594	+	4.86478i	0.133053	+	0.298841i
$266$	0.439426	+	2.06734i	0.0269430	+	0.126757i
$267$	−8.74906	+	7.86147i	−0.535434	+	0.481114i
$268$	1.76835	+	0.787320i	0.108019	+	0.0480932i
$269$	15.0429	−	16.7068i	0.917181	−	1.01863i	−0.0825761	−	0.996585i	$-0.526315\pi$
$269$	15.0429	−	16.7068i	0.917181	−	1.01863i	0.999757	−	0.0220477i	$-0.00701857\pi$
$270$	−2.12805	+	4.74040i	−0.129509	+	0.288492i
$271$	−15.5909	+	21.4591i	−0.947082	+	1.30355i	0.00572905	+	0.999984i	$0.498176\pi$
$271$	−15.5909	+	21.4591i	−0.947082	+	1.30355i	−0.952811	+	0.303563i	$0.901824\pi$
$272$	0.181926	+	1.73091i	0.0110309	+	0.104952i
$273$	−8.49768	+	3.77298i	−0.514303	+	0.228351i
$274$	5.79203	−	3.34403i	0.349910	−	0.202020i
$275$	−2.26891	+	1.64846i	−0.136820	+	0.0994058i
$276$	8.80316	−	0.916130i	0.529888	−	0.0551446i
$277$	16.9181	−	5.49703i	1.01651	−	0.330285i	0.247067	−	0.968998i	$-0.420533\pi$
$277$	16.9181	−	5.49703i	1.01651	−	0.330285i	0.769445	+	0.638713i	$0.220533\pi$
$278$	12.9551			0.776992
$279$	−0.876008	−	16.6803i	−0.0524453	−	0.998624i
$280$	−1.08502			−0.0648422
$281$	−0.545324	+	0.177186i	−0.0325313	+	0.0105701i	−0.325237	−	0.945632i	$-0.605444\pi$
$281$	−0.545324	+	0.177186i	−0.0325313	+	0.0105701i	0.292706	+	0.956202i	$0.405444\pi$
$282$	7.57894	−	0.788728i	0.451320	−	0.0469681i
$283$	22.5931	−	16.4149i	1.34302	−	0.975762i	0.343695	−	0.939081i	$-0.388321\pi$
$283$	22.5931	−	16.4149i	1.34302	−	0.975762i	0.999327	−	0.0366809i	$-0.0116785\pi$
$284$	8.56578	−	4.94546i	0.508286	−	0.293459i
$285$	3.08361	−	1.36913i	0.182657	−	0.0811001i
$286$	1.45034	+	13.7990i	0.0857603	+	0.815955i
$287$	−0.229580	+	0.315990i	−0.0135517	+	0.0186523i
$288$	0.617720	+	2.93571i	0.0363995	+	0.172989i
$289$	−9.34833	+	10.3824i	−0.549902	+	0.610728i
$290$	−2.00231	−	0.891487i	−0.117580	−	0.0523499i
$291$	9.09532	−	8.17260i	0.533177	−	0.479086i
$292$	−2.80391	−	13.1914i	−0.164087	−	0.771967i
$293$	6.04617	+	13.5799i	0.353221	+	0.793347i	0.999541	+	0.0302813i	$0.00964030\pi$
$293$	6.04617	+	13.5799i	0.353221	+	0.793347i	−0.646320	+	0.763066i	$0.723693\pi$
$294$	8.16523	−	5.91961i	0.476206	−	0.345239i
$295$	−3.48180	+	10.7159i	−0.202718	+	0.623902i
$296$	−2.58740	+	1.15199i	−0.150390	+	0.0669578i
$297$	14.4882	+	1.56781i	0.840689	+	0.0909737i
$298$	−15.7445	−	3.34660i	−0.912056	−	0.193863i
$299$	10.2827	−	23.0952i	0.594662	−	1.33563i
$300$	0.358377	+	1.69457i	0.0206909	+	0.0978360i
$301$	1.81673	+	0.190946i	0.104714	+	0.0110059i
$302$	7.38905	+	5.36846i	0.425192	+	0.308920i
$303$	3.28113	−	5.66965i	0.188496	−	0.325713i
$304$	0.973959	−	1.68695i	0.0558604	−	0.0967530i
$305$	−1.08668	−	1.88219i	−0.0622233	−	0.107774i
$306$	3.07767	−	4.21784i	0.175939	−	0.241118i
$307$	5.33919	+	5.92977i	0.304723	+	0.338430i	0.875985	−	0.482338i	$-0.160212\pi$
$307$	5.33919	+	5.92977i	0.304723	+	0.338430i	−0.571262	+	0.820768i	$0.693546\pi$
$308$	0.940326	+	2.89403i	0.0535801	+	0.164902i
$309$	−12.3770	+	16.9989i	−0.704105	+	0.967033i
$310$	−3.51324	−	4.31939i	−0.199539	−	0.245325i
$311$		−	1.63084i		−	0.0924767i	−0.998930	−	0.0462384i	$-0.985277\pi$
$311$		−	1.63084i		−	0.0924767i	0.998930	−	0.0462384i	$-0.0147234\pi$
$312$	8.14699	+	2.65635i	0.461232	+	0.150386i
$313$	8.87925	−	7.99491i	0.501885	−	0.451899i	−0.378885	−	0.925444i	$-0.623692\pi$
$313$	8.87925	−	7.99491i	0.501885	−	0.451899i	0.880770	+	0.473545i	$0.157026\pi$
$314$	−9.96926	−	13.7215i	−0.562598	−	0.774349i
$315$	2.41451	+	2.18301i	0.136042	+	0.122999i
$316$	−13.5096	−	7.79979i	−0.759976	−	0.438772i
$317$	15.7851	−	1.65908i	0.886580	−	0.0931833i	0.349719	−	0.936854i	$-0.386277\pi$
$317$	15.7851	−	1.65908i	0.886580	−	0.0931833i	0.536860	+	0.843671i	$0.319610\pi$
$318$	−2.84122	−	8.77495i	−0.159327	−	0.492075i
$319$	−0.642534	+	6.11330i	−0.0359750	+	0.342279i
$320$	0.743145	+	0.669131i	0.0415431	+	0.0374055i
$321$	−1.10225	−	1.91368i	−0.0615217	−	0.106811i
$322$	1.15274	−	5.42323i	0.0642399	−	0.302225i
$323$	−3.31615	+	0.704870i	−0.184516	+	0.0392200i
$324$	4.53191	−	7.77572i	0.251773	−	0.431984i
$325$	4.70524	+	1.52882i	0.261000	+	0.0848039i
$326$	13.5285	+	4.39567i	0.749273	+	0.243454i
$327$	−3.54630	+	16.6004i	−0.196111	+	0.918002i
$328$	0.352114	−	0.0748442i	0.0194423	−	0.00413258i
$329$	0.992436	−	4.66905i	0.0547148	−	0.257413i
$330$	4.20928	−	2.42448i	0.231713	−	0.133463i
$331$	−4.94172	−	4.44955i	−0.271622	−	0.244569i	0.522051	−	0.852914i	$-0.325167\pi$
$331$	−4.94172	−	4.44955i	−0.271622	−	0.244569i	−0.793673	+	0.608345i	$0.791834\pi$
$332$	1.39969	−	13.3172i	0.0768181	−	0.730875i
$333$	8.07553	+	2.64221i	0.442536	+	0.144792i
$334$	−9.94789	+	1.04557i	−0.544324	+	0.0572108i
$335$	−1.67637	−	0.967850i	−0.0915896	−	0.0528793i
$336$	1.86881	+	0.198356i	0.101952	+	0.0108212i
$337$	3.31825	+	4.56717i	0.180756	+	0.248790i	0.889774	−	0.456400i	$-0.150862\pi$
$337$	3.31825	+	4.56717i	0.180756	+	0.248790i	−0.709018	+	0.705190i	$0.750862\pi$
$338$	8.52874	−	7.67931i	0.463902	−	0.417699i
$339$	6.89661	−	21.1518i	0.374572	−	1.14881i
$340$		−	1.74044i		−	0.0943887i
$341$	−8.47622	+	13.1141i	−0.459013	+	0.710170i
$342$	−5.56143	+	1.79443i	−0.300728	+	0.0970314i
$343$	−4.29932	−	13.2319i	−0.232141	−	0.714458i
$344$	−1.12655	−	1.25116i	−0.0607394	−	0.0674579i
$345$	−8.85070	−	0.00906924i	−0.476506	−	0.000488271i
$346$	7.93835	+	13.7496i	0.426768	+	0.739185i
$347$	−1.02223	+	1.77056i	−0.0548764	+	0.0950487i	−0.892159	−	0.451722i	$-0.850810\pi$
$347$	−1.02223	+	1.77056i	−0.0548764	+	0.0950487i	0.837282	+	0.546771i	$0.184143\pi$
$348$	3.28576	+	1.90153i	0.176135	+	0.101932i
$349$	−0.0904382	−	0.0657072i	−0.00484104	−	0.00351722i	0.585362	−	0.810772i	$-0.300952\pi$
$349$	−0.0904382	−	0.0657072i	−0.00484104	−	0.00351722i	−0.590203	+	0.807255i	$0.700952\pi$
$350$	1.07907	+	0.113415i	0.0576789	+	0.00606230i
$351$	−12.7852	−	22.3026i	−0.682422	−	1.19043i
$352$	1.14070	−	2.56206i	0.0607997	−	0.136558i
$353$	22.5622	+	4.79575i	1.20087	+	0.255252i	0.764564	−	0.644548i	$-0.222954\pi$
$353$	22.5622	+	4.79575i	1.20087	+	0.255252i	0.436302	+	0.899800i	$0.356288\pi$
$354$	7.95597	−	17.8202i	0.422855	−	0.947135i
$355$	−9.03580	+	4.02300i	−0.479571	+	0.213519i
$356$	2.09850	−	6.45853i	0.111220	−	0.342301i
$357$	−1.91983	−	2.64812i	−0.101608	−	0.140153i
$358$	−10.6660	−	23.9562i	−0.563716	−	1.26613i
$359$	−3.33381	−	15.6843i	−0.175952	−	0.827787i	−0.974240	−	0.225512i	$-0.927594\pi$
$359$	−3.33381	−	15.6843i	−0.175952	−	0.827787i	0.798289	−	0.602275i	$-0.205739\pi$
$360$	−0.307470	−	2.98420i	−0.0162051	−	0.157281i
$361$	−13.8910	−	6.18468i	−0.731106	−	0.325510i
$362$	−6.32428	+	7.02383i	−0.332397	+	0.369164i
$363$	4.03106	+	3.63707i	0.211576	+	0.190897i
$364$	3.15522	−	4.34279i	0.165379	−	0.227624i
$365$	1.40968	+	13.4122i	0.0737860	+	0.702027i
$366$	1.52759	+	3.44050i	0.0798483	+	0.179838i
$367$	7.58642	−	4.38002i	0.396008	−	0.228635i	−0.288752	−	0.957404i	$-0.593240\pi$
$367$	7.58642	−	4.38002i	0.396008	−	0.228635i	0.684760	+	0.728769i	$0.259907\pi$
$368$	−4.13404	+	3.00356i	−0.215502	+	0.156571i
$369$	−0.934148	−	0.541886i	−0.0486298	−	0.0282095i
$370$	2.69364	−	0.875218i	0.140036	−	0.0455004i
$371$	−5.77790			−0.299973
$372$	5.26148	+	8.08188i	0.272795	+	0.419026i
$373$	14.7122			0.761766			0.380883	−	0.924623i	$-0.375620\pi$
$373$	14.7122			0.761766			0.380883	+	0.924623i	$0.375620\pi$
$374$	−4.64221	+	1.50835i	−0.240043	+	0.0779948i
$375$	−0.179283	−	1.72275i	−0.00925816	−	0.0889623i
$376$	−3.55914	+	2.58586i	−0.183549	+	0.133356i
$377$	9.39090	−	5.42184i	0.483656	−	0.279239i
$378$	−3.75960	−	4.20136i	−0.193373	−	0.216095i
$379$	0.414328	+	3.94207i	0.0212826	+	0.202490i	0.999996	−	0.00274017i	$-0.000872223\pi$
$379$	0.414328	+	3.94207i	0.0212826	+	0.202490i	−0.978714	+	0.205231i	$0.934206\pi$
$380$	−1.14496	+	1.57590i	−0.0587351	+	0.0808419i
$381$	−3.87774	+	4.29780i	−0.198663	+	0.220183i
$382$	4.35343	−	4.83498i	0.222741	−	0.247379i
$383$	−24.8097	−	11.0460i	−1.26771	−	0.564423i	−0.340955	−	0.940080i	$-0.610750\pi$
$383$	−24.8097	−	11.0460i	−1.26771	−	0.564423i	−0.926759	+	0.375657i	$0.877417\pi$
$384$	−1.15765	−	1.28835i	−0.0590760	−	0.0657459i
$385$	−0.632667	−	2.97646i	−0.0322437	−	0.151695i
$386$	4.49083	+	10.0866i	0.228577	+	0.513393i
$387$	−0.0103510	+	5.05079i	−0.000526171	+	0.256746i
$388$	−2.18155	+	6.71413i	−0.110752	+	0.340858i
$389$	−8.00756	+	3.56520i	−0.405999	+	0.180763i	−0.599567	−	0.800324i	$-0.704661\pi$
$389$	−8.00756	+	3.56520i	−0.405999	+	0.180763i	0.193568	+	0.981087i	$0.437994\pi$
$390$	−7.82470	−	3.49339i	−0.396219	−	0.176895i
$391$	8.69923	+	1.84908i	0.439939	+	0.0935119i
$392$	−2.36832	+	5.31934i	−0.119618	+	0.268667i
$393$	−14.8592	+	3.14250i	−0.749546	+	0.158518i
$394$	21.3435	+	2.24329i	1.07527	+	0.113015i
$395$	12.6203	+	9.16920i	0.634997	+	0.461353i
$396$	−7.69318	+	3.40635i	−0.386597	+	0.171176i
$397$	−14.7542	+	25.5550i	−0.740490	+	1.28257i	0.211782	+	0.977317i	$0.432073\pi$
$397$	−14.7542	+	25.5550i	−0.740490	+	1.28257i	−0.952272	+	0.305250i	$0.901260\pi$
$398$	1.73968	+	3.01321i	0.0872021	+	0.151038i
$399$	−0.00375112	+	3.66073i	−0.000187791	+	0.183266i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	0.313174	+	0.963850i	0.0156392	+	0.0481324i	0.958572	−	0.284852i	$-0.0919444\pi$
$401$	0.313174	+	0.963850i	0.0156392	+	0.0481324i	−0.942932	+	0.332984i	$0.891944\pi$
$402$	2.71040	+	1.97346i	0.135182	+	0.0984275i
$403$	27.5049	−	1.50102i	1.37012	−	0.0747711i
$404$			3.78201i			0.188162i
$405$	−5.31987	+	7.25941i	−0.264346	+	0.360723i
$406$	1.76731	−	1.59129i	0.0877099	−	0.0789744i
$407$	−4.66887	−	6.42615i	−0.231427	−	0.318532i
$408$	−0.318176	+	2.99769i	−0.0157521	+	0.148408i
$409$	4.27001	+	2.46529i	0.211139	+	0.121901i	0.601840	−	0.798616i	$-0.294434\pi$
$409$	4.27001	+	2.46529i	0.211139	+	0.121901i	−0.390702	+	0.920517i	$0.627768\pi$
$410$	−0.358009	+	0.0376282i	−0.0176808	+	0.00185833i
$411$	11.0208	−	3.56838i	0.543614	−	0.176015i
$412$	1.26900	−	12.0737i	0.0625190	−	0.594828i
$413$	−9.08513	−	8.18029i	−0.447050	−	0.402526i
$414$	15.2426	+	1.63365i	0.749132	+	0.0802895i
$415$	−2.78405	+	13.0979i	−0.136664	+	0.642951i
$416$	−4.83927	+	1.02862i	−0.237265	+	0.0504321i
$417$	21.9437	+	4.68778i	1.07459	+	0.229561i
$418$	5.19561	+	1.68816i	0.254126	+	0.0825704i
$419$	23.6581	+	7.68698i	1.15577	+	0.375533i	0.823315	−	0.567585i	$-0.192122\pi$
$419$	23.6581	+	7.68698i	1.15577	+	0.375533i	0.332458	+	0.943118i	$0.392122\pi$
$420$	−1.83784	−	0.392613i	−0.0896772	−	0.0191575i
$421$	14.4470	−	3.07081i	0.704104	−	0.149662i	0.158074	−	0.987427i	$-0.449472\pi$
$421$	14.4470	−	3.07081i	0.704104	−	0.149662i	0.546030	+	0.837765i	$0.316138\pi$
$422$	2.45614	−	11.5552i	0.119563	−	0.562499i
$423$	13.1229	+	1.40646i	0.638055	+	0.0683846i
$424$	3.95737	+	3.56323i	0.192187	+	0.173046i
$425$	−0.181926	+	1.73091i	−0.00882469	+	0.0839613i
$426$	16.2985	−	5.27725i	0.789665	−	0.255683i
$427$	2.34522	−	0.246493i	0.113493	−	0.0119286i
$428$	1.10421	+	0.637517i	0.0533741	+	0.0308156i
$429$	−2.53655	+	23.8981i	−0.122466	+	1.15381i
$430$	0.989595	+	1.36206i	0.0477225	+	0.0656844i
$431$	−13.4771	+	12.1349i	−0.649171	+	0.584517i	−0.926517	−	0.376254i	$-0.877212\pi$
$431$	−13.4771	+	12.1349i	−0.649171	+	0.584517i	0.277345	+	0.960770i	$0.410545\pi$
$432$	−0.0159733	+	5.19613i	−0.000768517	+	0.249999i
$433$		−	8.16389i		−	0.392331i	−0.980571	−	0.196166i	$-0.937151\pi$
$433$		−	8.16389i		−	0.392331i	0.980571	−	0.196166i	$-0.0628490\pi$
$434$	5.83188	−	1.57615i	0.279939	−	0.0756576i
$435$	−3.06900	−	2.23456i	−0.147147	−	0.107139i
$436$	−3.02851	−	9.32081i	−0.145039	−	0.446386i
$437$	−6.66037	−	7.39709i	−0.318609	−	0.353851i
$438$	0.0239353	−	23.3586i	0.00114367	−	1.11612i
$439$	−2.29185	−	3.96959i	−0.109384	−	0.189458i	0.806137	−	0.591729i	$-0.201554\pi$
$439$	−2.29185	−	3.96959i	−0.109384	−	0.189458i	−0.915521	+	0.402271i	$0.868221\pi$
$440$	−1.40226	+	2.42879i	−0.0668503	+	0.115788i
$441$	15.9725	−	7.07224i	0.760597	−	0.336774i
$442$	6.96614	+	5.06119i	0.331345	+	0.240736i
$443$	4.47518	+	0.470360i	0.212622	+	0.0223475i	0.210241	−	0.977650i	$-0.432575\pi$
$443$	4.47518	+	0.470360i	0.212622	+	0.0223475i	0.00238159	+	0.999997i	$0.499242\pi$
$444$	−4.79947	+	1.01502i	−0.227773	+	0.0481707i
$445$	−2.76211	+	6.20379i	−0.130936	+	0.294088i
$446$	22.2032	+	4.71943i	1.05135	+	0.223471i
$447$	−25.4576	−	11.3657i	−1.20410	−	0.537580i
$448$	−0.991212	+	0.441316i	−0.0468304	+	0.0208502i
$449$	−0.686178	+	2.11184i	−0.0323827	+	0.0996638i	−0.965941	−	0.258761i	$-0.916686\pi$
$449$	−0.686178	+	2.11184i	−0.0323827	+	0.0996638i	0.933559	+	0.358424i	$0.116686\pi$
$450$	−0.00614814	+	2.99999i	−0.000289826	+	0.141421i
$451$	0.410631	+	0.922293i	0.0193359	+	0.0434291i
$452$	2.67057	+	12.5640i	0.125613	+	0.590963i
$453$	10.5732	+	11.7670i	0.496773	+	0.552861i
$454$	13.7236	+	6.11016i	0.644083	+	0.286764i
$455$	−3.59189	+	3.98919i	−0.168390	+	0.187016i
$456$	2.26014	−	2.50498i	0.105841	−	0.117306i
$457$	−9.91273	+	13.6437i	−0.463698	+	0.638225i	−0.975270	−	0.221015i	$-0.929063\pi$
$457$	−9.91273	+	13.6437i	−0.463698	+	0.638225i	0.511573	+	0.859240i	$0.329063\pi$
$458$	−2.24805	−	21.3888i	−0.105045	−	0.999434i
$459$	6.73927	−	6.03066i	0.314562	−	0.281487i
$460$	4.42535	−	2.55498i	0.206333	−	0.119126i
$461$	−6.56002	+	4.76613i	−0.305531	+	0.221981i	−0.729976	−	0.683472i	$-0.760469\pi$
$461$	−6.56002	+	4.76613i	−0.305531	+	0.221981i	0.424446	+	0.905453i	$0.360469\pi$
$462$	0.545552	+	5.24225i	0.0253814	+	0.243892i
$463$	35.9129	−	11.6688i	1.66902	−	0.542296i	0.686284	−	0.727334i	$-0.259241\pi$
$463$	35.9129	−	11.6688i	1.66902	−	0.542296i	0.982731	+	0.185038i	$0.0592407\pi$
$464$	−2.19180			−0.101752
$465$	−4.38787	−	8.58758i	−0.203483	−	0.398240i
$466$	−16.5364			−0.766032
$467$	15.8957	−	5.16483i	0.735566	−	0.239000i	0.0828070	−	0.996566i	$-0.473612\pi$
$467$	15.8957	−	5.16483i	0.735566	−	0.239000i	0.652759	+	0.757566i	$0.273612\pi$
$468$	12.8384	+	7.44739i	0.593457	+	0.344256i
$469$	1.69915	−	1.23451i	0.0784596	−	0.0570042i
$470$	3.80994	−	2.19967i	0.175739	−	0.101463i
$471$	−11.9211	−	26.8493i	−0.549296	−	1.23715i
$472$	1.17776	+	11.2056i	0.0542107	+	0.515780i
$473$	2.77535	−	3.81993i	0.127611	−	0.175641i
$474$	−20.0607	−	18.1000i	−0.921418	−	0.831360i
$475$	1.30341	−	1.44758i	0.0598046	−	0.0664197i
$476$	1.72515	+	0.768085i	0.0790720	+	0.0352051i
$477$	−1.63733	−	15.8914i	−0.0749682	−	0.727616i
$478$	−0.341784	−	1.60797i	−0.0156329	−	0.0735468i
$479$	−7.56381	−	16.9886i	−0.345599	−	0.776229i	−0.999802	−	0.0199093i	$-0.993662\pi$
$479$	−7.56381	−	16.9886i	−0.345599	−	0.776229i	0.654203	−	0.756319i	$-0.273004\pi$
$480$	1.01664	+	1.40230i	0.0464029	+	0.0640060i
$481$	−4.33003	+	13.3265i	−0.197432	+	0.607635i
$482$	−5.35263	+	2.38315i	−0.243806	+	0.108549i
$483$	3.91495	−	8.76892i	0.178136	−	0.399000i
$484$	−3.06613	−	0.651726i	−0.139370	−	0.0296239i
$485$	2.87142	−	6.44931i	0.130384	−	0.292848i
$486$	10.4899	−	11.5309i	0.475833	−	0.523052i
$487$	1.00228	+	0.105344i	0.0454176	+	0.00477358i	0.127210	−	0.991876i	$-0.459398\pi$
$487$	1.00228	+	0.105344i	0.0454176	+	0.00477358i	−0.0817924	+	0.996649i	$0.526064\pi$
$488$	−1.75829	−	1.27747i	−0.0795941	−	0.0578285i
$489$	21.3244	+	12.3408i	0.964322	+	0.558070i
$490$	2.91137	−	5.04264i	0.131522	−	0.227803i
$491$	13.0997	+	22.6894i	0.591182	+	1.02396i	0.994074	+	0.108710i	$0.0346718\pi$
$491$	13.0997	+	22.6894i	0.591182	+	1.02396i	−0.402892	+	0.915248i	$0.631995\pi$
$492$	0.623504		0.000638900i	0.0281097		2.88038e-5i
$493$	2.55254	+	2.83488i	0.114960	+	0.127677i
$494$	−2.97802	−	9.16541i	−0.133988	−	0.412371i
$495$	8.00710	−	2.58353i	0.359892	−	0.116121i
$496$	−4.96636	−	2.51700i	−0.222996	−	0.113016i
$497$		−	10.7318i		−	0.481388i
$498$	7.18966	−	22.0506i	0.322176	−	0.988110i
$499$	−2.63585	+	2.37333i	−0.117997	+	0.106245i	−0.726017	−	0.687677i	$-0.758631\pi$
$499$	−2.63585	+	2.37333i	−0.117997	+	0.106245i	0.608020	+	0.793922i	$0.291964\pi$
$500$	0.587785	+	0.809017i	0.0262866	+	0.0361803i
$501$	−17.2284	−	1.82863i	−0.769708	−	0.0816970i
$502$	−5.52298	−	3.18869i	−0.246503	−	0.142318i
$503$	3.78395	−	0.397709i	0.168718	−	0.0177330i	−0.0197927	−	0.999804i	$-0.506301\pi$
$503$	3.78395	−	0.397709i	0.168718	−	0.0177330i	0.188511	+	0.982071i	$0.439634\pi$
$504$	3.09367	+	1.01221i	0.137803	+	0.0450873i
$505$	0.395327	−	3.76129i	0.0175918	−	0.167375i
$506$	−10.6500	−	9.58931i	−0.473451	−	0.426297i
$507$	17.2250	−	9.92133i	0.764989	−	0.440622i
$508$	0.694852	−	3.26902i	0.0308291	−	0.145039i
$509$	2.63097	−	0.559230i	0.116616	−	0.0247874i	−0.149234	−	0.988802i	$-0.547681\pi$
$509$	2.63097	−	0.559230i	0.116616	−	0.0247874i	0.265850	+	0.964014i	$0.414347\pi$
$510$	0.629778	−	2.94801i	0.0278870	−	0.130540i
$511$	−13.9165	−	4.52173i	−0.615628	−	0.200030i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−10.0694	+	1.02705i	−0.444576	+	0.0453455i
$514$	21.0034	−	4.46442i	0.926422	−	0.196917i
$515$	−2.52409	+	11.8749i	−0.111225	+	0.523271i
$516$	−1.45545	−	2.52689i	−0.0640727	−	0.111240i
$517$	−9.16896	−	8.25577i	−0.403250	−	0.363088i
$518$	−0.321222	+	3.05622i	−0.0141137	+	0.134283i
$519$	8.47094	+	26.1620i	0.371833	+	1.14839i
$520$	4.92028	−	0.517142i	0.215768	−	0.0226782i
$521$	6.74136	+	3.89213i	0.295345	+	0.170517i	0.640350	−	0.768084i	$-0.278789\pi$
$521$	6.74136	+	3.89213i	0.295345	+	0.170517i	−0.345005	+	0.938601i	$0.612123\pi$
$522$	4.87746	+	4.40981i	0.213480	+	0.193012i
$523$	−18.3331	−	25.2333i	−0.801650	−	1.10338i	−0.992559	−	0.121768i	$-0.961143\pi$
$523$	−18.3331	−	25.2333i	−0.801650	−	1.10338i	0.190909	−	0.981608i	$-0.438857\pi$
$524$	6.51642	−	5.86741i	0.284671	−	0.256319i
$525$	1.78673	+	0.582568i	0.0779792	+	0.0254254i
$526$			21.7570i			0.948652i
$527$	2.52825	+	9.35474i	0.110132	+	0.407499i
$528$	2.85924	−	3.92694i	0.124432	−	0.170898i
$529$	0.961551	+	2.95935i	0.0418066	+	0.128667i
$530$	−3.56323	−	3.95737i	−0.154777	−	0.171897i
$531$	19.9243	−	27.3056i	0.864642	−	1.18496i
$532$	−1.05676	−	1.83037i	−0.0458164	−	0.0793564i
$533$	0.890480	−	1.54236i	0.0385710	−	0.0668069i
$534$	5.89153	−	10.1803i	0.254951	−	0.440545i
$535$	−1.03152	−	0.749446i	−0.0445967	−	0.0324014i
$536$	−1.92510	−	0.202336i	−0.0831515	−	0.00873958i
$537$	−9.39786	−	44.4373i	−0.405548	−	1.91761i
$538$	−9.14394	+	20.5376i	−0.394223	+	0.885440i
$539$	−15.9732	−	3.39520i	−0.688013	−	0.146242i
$540$	0.559029	−	5.16599i	0.0240568	−	0.222309i
$541$	−0.457481	+	0.203684i	−0.0196686	+	0.00875704i	−0.416547	−	0.909114i	$-0.636760\pi$
$541$	−0.457481	+	0.203684i	−0.0196686	+	0.00875704i	0.396879	+	0.917871i	$0.370093\pi$
$542$	8.19664	−	25.2267i	0.352076	−	1.08358i
$543$	−13.2538	+	9.60874i	−0.568777	+	0.412351i
$544$	−0.707901	−	1.58997i	−0.0303510	−	0.0681695i
$545$	2.03763	+	9.58631i	0.0872826	+	0.410632i
$546$	6.91586	−	6.21425i	0.295971	−	0.265945i
$547$	−18.9537	−	8.43872i	−0.810400	−	0.360814i	−0.0406620	−	0.999173i	$-0.512947\pi$
$547$	−18.9537	−	8.43872i	−0.810400	−	0.360814i	−0.769738	+	0.638359i	$0.779613\pi$
$548$	−4.47519	+	4.97020i	−0.191171	+	0.212316i
$549$	1.34253	+	6.38039i	0.0572979	+	0.272308i
$550$	1.64846	−	2.26891i	0.0702905	−	0.0967466i
$551$	−0.446279	−	4.24606i	−0.0190121	−	0.180888i
$552$	−8.08920	+	3.59162i	−0.344299	+	0.152869i
$553$	−14.6582	+	8.46290i	−0.623329	+	0.359879i
$554$	−14.3914	+	10.4560i	−0.611433	+	0.444232i
$555$	4.87927	−	0.507778i	0.207114	−	0.0215540i
$556$	−12.3210	+	4.00333i	−0.522526	+	0.169779i
$557$	4.13618			0.175256			0.0876278	−	0.996153i	$-0.472071\pi$
$557$	4.13618			0.175256			0.0876278	+	0.996153i	$0.472071\pi$
$558$	5.98763	+	15.5932i	0.253477	+	0.660113i
$559$	−8.32940			−0.352296
$560$	1.03191	−	0.335289i	0.0436063	−	0.0141685i
$561$	−8.40892	+	0.875103i	−0.355025	+	0.0369469i
$562$	0.463880	−	0.337029i	0.0195676	−	0.0142167i
$563$	−17.7173	+	10.2291i	−0.746695	+	0.431104i	−0.824498	−	0.565864i	$-0.808543\pi$
$563$	−17.7173	+	10.2291i	−0.746695	+	0.431104i	0.0778036	+	0.996969i	$0.475209\pi$
$564$	−6.96427	+	3.09215i	−0.293249	+	0.130203i
$565$	−1.34264	−	12.7744i	−0.0564853	−	0.537422i
$566$	−16.4149	+	22.5931i	−0.689968	+	0.949660i
$567$	−4.84787	−	8.47681i	−0.203592	−	0.355993i
$568$	−6.61831	+	7.35038i	−0.277698	+	0.308415i
$569$	1.72660	+	0.768730i	0.0723827	+	0.0322268i	0.442609	−	0.896715i	$-0.354053\pi$
$569$	1.72660	+	0.768730i	0.0723827	+	0.0322268i	−0.370226	+	0.928942i	$0.620720\pi$
$570$	−2.50960	+	2.25500i	−0.105116	+	0.0944517i
$571$	7.23443	+	34.0353i	0.302752	+	1.42433i	0.821891	+	0.569645i	$0.192919\pi$
$571$	7.23443	+	34.0353i	0.302752	+	1.42433i	−0.519139	+	0.854690i	$0.673747\pi$
$572$	−5.64349	−	12.6755i	−0.235966	−	0.529989i
$573$	9.12351	−	6.61435i	0.381140	−	0.276318i
$574$	0.120697	−	0.371468i	0.00503781	−	0.0155048i
$575$	−4.66818	+	2.07841i	−0.194676	+	0.0866755i
$576$	−1.49467	−	2.60114i	−0.0622780	−	0.108381i
$577$	35.3759	+	7.51938i	1.47272	+	0.313036i	0.873214	−	0.487336i	$-0.162031\pi$
$577$	35.3759	+	7.51938i	1.47272	+	0.313036i	0.599503	+	0.800372i	$0.295365\pi$
$578$	5.68246	−	12.7630i	0.236359	−	0.530872i
$579$	3.95689	+	18.7100i	0.164443	+	0.777560i
$580$	2.17980	+	0.229106i	0.0905111	+	0.00951310i
$581$	−11.7542	−	8.53991i	−0.487645	−	0.354295i
$582$	−6.12469	+	10.5832i	−0.253876	+	0.438688i
$583$	−7.46728	+	12.9337i	−0.309263	+	0.535660i
$584$	6.74304	+	11.6793i	0.279029	+	0.483292i
$585$	−11.9896	−	8.74858i	−0.495710	−	0.361709i
$586$	−9.94668	−	11.0469i	−0.410893	−	0.456343i
$587$	−4.48366	−	13.7993i	−0.185060	−	0.569557i	0.814889	−	0.579617i	$-0.196798\pi$
$587$	−4.48366	−	13.7993i	−0.185060	−	0.569557i	−0.999949	+	0.0100599i	$0.996798\pi$
$588$	−5.93634	+	8.15308i	−0.244810	+	0.336227i
$589$	3.86483	−	10.1336i	0.159247	−	0.417546i
$590$		−	11.2673i		−	0.463869i
$591$	35.3406	+	11.5229i	1.45372	+	0.473989i
$592$	2.10478	−	1.89515i	0.0865060	−	0.0778904i
$593$	−20.9768	−	28.8721i	−0.861415	−	1.18564i	−0.981230	−	0.192840i	$-0.938230\pi$
$593$	−20.9768	−	28.8721i	−0.861415	−	1.18564i	0.119815	−	0.992796i	$-0.461770\pi$
$594$	−14.2635	+	2.98601i	−0.585240	+	0.122518i
$595$	−1.63541	−	0.944204i	−0.0670453	−	0.0387086i
$596$	16.0081	−	1.68252i	0.655717	−	0.0689186i
$597$	1.85639	+	5.73337i	0.0759770	+	0.234651i
$598$	−2.64257	+	25.1424i	−0.108063	+	1.02815i
$599$	−25.2394	−	22.7256i	−1.03125	−	0.928545i	−0.0337688	−	0.999430i	$-0.510751\pi$
$599$	−25.2394	−	22.7256i	−1.03125	−	0.928545i	−0.997484	+	0.0708851i	$0.977418\pi$
$600$	−0.864488	−	1.50089i	−0.0352926	−	0.0612734i
$601$	5.94082	−	27.9493i	0.242331	−	1.14008i	−0.673711	−	0.738995i	$-0.735301\pi$
$601$	5.94082	−	27.9493i	0.242331	−	1.14008i	0.916042	−	0.401083i	$-0.131366\pi$
$602$	−1.78682	+	0.379799i	−0.0728252	+	0.0154795i
$603$	3.87686	+	4.32347i	0.157878	+	0.176065i
$604$	−8.68634	−	2.82236i	−0.353442	−	0.114840i
$605$	2.98121	+	0.968654i	0.121203	+	0.0393814i
$606$	−1.36852	+	6.40608i	−0.0555922	+	0.260229i
$607$	13.1165	−	2.78800i	0.532383	−	0.113161i	0.0661266	−	0.997811i	$-0.478936\pi$
$607$	13.1165	−	2.78800i	0.532383	−	0.113161i	0.466256	+	0.884650i	$0.345603\pi$
$608$	−0.404995	+	1.90535i	−0.0164247	+	0.0772722i
$609$	3.56933	−	2.05588i	0.144636	−	0.0833084i
$610$	1.61513	+	1.45427i	0.0653946	+	0.0588815i
$611$	−2.27508	+	21.6459i	−0.0920399	+	0.875701i
$612$	−1.62365	+	4.96246i	−0.0656322	+	0.200595i
$613$	−26.2377	+	2.75769i	−1.05973	+	0.111382i	−0.618322	−	0.785925i	$-0.712187\pi$
$613$	−26.2377	+	2.75769i	−1.05973	+	0.111382i	−0.441407	+	0.897307i	$0.645521\pi$
$614$	−6.91027	−	3.98964i	−0.278876	−	0.161009i
$615$	−0.620022	−	0.0658093i	−0.0250017	−	0.00265369i
$616$	−1.78861	−	2.46181i	−0.0720650	−	0.0991890i
$617$	25.4085	−	22.8780i	1.02291	−	0.921032i	0.0260056	−	0.999662i	$-0.491721\pi$
$617$	25.4085	−	22.8780i	1.02291	−	0.921032i	0.996904	+	0.0786300i	$0.0250546\pi$
$618$	6.51832	−	19.9916i	0.262205	−	0.804181i
$619$			14.6854i			0.590258i	0.955457	+	0.295129i	$0.0953626\pi$
$619$			14.6854i			0.590258i	−0.955457	+	0.295129i	$0.904637\pi$
$620$	4.67606	+	3.02233i	0.187795	+	0.121380i
$621$	25.2272	+	8.28264i	1.01233	+	0.332371i
$622$	0.503959	+	1.55103i	0.0202069	+	0.0621905i
$623$	−4.93032	−	5.47567i	−0.197529	−	0.219378i
$624$	−8.56910	−	0.00878069i	−0.343039	−	0.000351509i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.97410	+	10.3474i	−0.238773	+	0.413567i
$627$	8.18963	+	4.73948i	0.327062	+	0.189277i
$628$	13.7215	+	9.96926i	0.547548	+	0.397817i
$629$	−4.90238	−	0.515261i	−0.195471	−	0.0205448i
$630$	−2.97092	−	1.33004i	−0.118364	−	0.0529901i
$631$	−19.0814	+	42.8575i	−0.759618	+	1.70613i	−0.0529380	+	0.998598i	$0.516859\pi$
$631$	−19.0814	+	42.8575i	−0.759618	+	1.70613i	−0.706680	+	0.707533i	$0.749808\pi$
$632$	15.2587	+	3.24333i	0.606958	+	0.129013i
$633$	8.34153	−	18.6838i	0.331546	−	0.742615i
$634$	−14.4998	+	6.45574i	−0.575862	+	0.256390i
$635$	−1.03275	+	3.17848i	−0.0409835	+	0.126134i
$636$	5.41376	+	7.46749i	0.214670	+	0.296105i
$637$	11.7170	+	26.3168i	0.464244	+	1.04271i
$638$	−1.27803	−	6.01265i	−0.0505976	−	0.238043i
$639$	29.5165	−	3.04116i	1.16765	−	0.120307i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−19.4832	+	21.6383i	−0.769540	+	0.854661i	−0.992761	−	0.120107i	$-0.961676\pi$
$641$	−19.4832	+	21.6383i	−0.769540	+	0.854661i	0.223221	+	0.974768i	$0.428343\pi$
$642$	1.63966	+	1.47940i	0.0647124	+	0.0583875i
$643$	−20.0333	+	27.5735i	−0.790037	+	1.08739i	0.204066	+	0.978957i	$0.434584\pi$
$643$	−20.0333	+	27.5735i	−0.790037	+	1.08739i	−0.994103	+	0.108436i	$0.965416\pi$
$644$	0.579546	+	5.51402i	0.0228373	+	0.217283i
$645$	1.18335	+	2.66519i	0.0465942	+	0.104942i
$646$	2.93603	−	1.69512i	0.115517	−	0.0666935i
$647$	16.4963	−	11.9853i	0.648537	−	0.471189i	−0.214236	−	0.976782i	$-0.568726\pi$
$647$	16.4963	−	11.9853i	0.648537	−	0.471189i	0.862772	+	0.505593i	$0.168726\pi$
$648$	−1.90727	+	8.79558i	−0.0749247	+	0.345523i
$649$	−30.0530	+	9.76480i	−1.17968	+	0.383302i
$650$	−4.94738			−0.194052
$651$	10.4486	−	0.559469i	0.409511	−	0.0219273i
$652$	−14.2247			−0.557082
$653$	−11.2157	+	3.64421i	−0.438906	+	0.142609i	−0.520131	−	0.854087i	$-0.674117\pi$
$653$	−11.2157	+	3.64421i	−0.438906	+	0.142609i	0.0812250	+	0.996696i	$0.474117\pi$
$654$	−1.75706	−	16.8837i	−0.0687066	−	0.660206i
$655$	−7.09403	+	5.15411i	−0.277187	+	0.201388i
$656$	−0.311752	+	0.179990i	−0.0121719	+	0.00702744i
$657$	8.49283	−	39.5568i	0.331337	−	1.54326i
$658$	0.498951	+	4.74721i	0.0194512	+	0.185065i
$659$	11.4444	−	15.7518i	0.445810	−	0.613604i	−0.525681	−	0.850682i	$-0.676190\pi$
$659$	11.4444	−	15.7518i	0.445810	−	0.613604i	0.971491	+	0.237077i	$0.0761895\pi$
$660$	−3.25405	+	3.60655i	−0.126664	+	0.140385i
$661$	23.5186	−	26.1201i	0.914769	−	1.01595i	−0.0850395	−	0.996378i	$-0.527102\pi$
$661$	23.5186	−	26.1201i	0.914769	−	1.01595i	0.999808	−	0.0195761i	$-0.00623167\pi$
$662$	6.07484	+	2.70469i	0.236105	+	0.105121i
$663$	9.96807	+	11.0935i	0.387128	+	0.430836i
$664$	2.78405	+	13.0979i	0.108042	+	0.508298i
$665$	0.859648	+	1.93080i	0.0333357	+	0.0748732i
$666$	−8.49677	−	0.0174132i	−0.329243	−	0.000674746i
$667$	−3.46100	+	10.6519i	−0.134010	+	0.412441i
$668$	9.13791	−	4.06846i	0.353556	−	0.157413i
$669$	35.9007	+	16.0281i	1.38800	+	0.619683i
$670$	1.89340	+	0.402455i	0.0731485	+	0.0155482i
$671$	2.47917	−	5.56830i	0.0957073	−	0.214962i
$672$	−1.83864	+	0.388846i	−0.0709270	+	0.0150000i
$673$	32.8783	+	3.45564i	1.26736	+	0.133205i	0.714244	−	0.699897i	$-0.246771\pi$
$673$	32.8783	+	3.45564i	1.26736	+	0.133205i	0.553119	+	0.833102i	$0.313437\pi$
$674$	−4.56717	−	3.31825i	−0.175921	−	0.127814i
$675$	−1.09596	+	5.07926i	−0.0421835	+	0.195501i
$676$	−5.73827	+	9.93898i	−0.220703	+	0.382268i
$677$	−24.1819	−	41.8844i	−0.929388	−	1.60975i	−0.784348	−	0.620321i	$-0.787002\pi$
$677$	−24.1819	−	41.8844i	−0.929388	−	1.60975i	−0.145040	−	0.989426i	$-0.546331\pi$
$678$	−0.0227971	+	22.2477i	−0.000875516	+	0.854419i
$679$	5.12544	+	5.69237i	0.196696	+	0.218453i
$680$	0.537826	+	1.65526i	0.0206247	+	0.0634762i
$681$	21.0346	+	15.3155i	0.806047	+	0.586890i
$682$	4.00887	−	15.0916i	0.153508	−	0.577886i
$683$			33.7863i			1.29280i	0.763000	+	0.646399i	$0.223726\pi$
$683$			33.7863i			1.29280i	−0.763000	+	0.646399i	$0.776274\pi$
$684$	4.73472	−	3.42518i	0.181037	−	0.130965i
$685$	4.97020	−	4.47519i	0.189902	−	0.170988i
$686$	8.17779	+	11.2558i	0.312230	+	0.429747i
$687$	3.93170	−	37.0425i	0.150004	−	1.41326i
$688$	1.45804	+	0.841800i	0.0555872	+	0.0320933i
$689$	26.2013	−	2.75387i	0.998189	−	0.104914i
$690$	8.42032	−	2.72639i	0.320556	−	0.103792i
$691$	3.59410	−	34.1955i	0.136726	−	1.30086i	−0.683977	−	0.729504i	$-0.739751\pi$
$691$	3.59410	−	34.1955i	0.136726	−	1.30086i	0.820703	−	0.571356i	$-0.193582\pi$
$692$	−11.7987	−	10.6236i	−0.448519	−	0.403848i
$693$	−0.972832	+	9.07689i	−0.0369548	+	0.344803i
$694$	0.425069	−	1.99979i	0.0161354	−	0.0759110i
$695$	12.6720	−	2.69351i	0.480675	−	0.102171i
$696$	−3.71255	−	0.793103i	−0.140724	−	0.0300625i
$697$	0.595861	+	0.193607i	0.0225698	+	0.00733338i
$698$	0.106316	+	0.0345443i	0.00402414	+	0.00130752i
$699$	−28.0098	−	5.98367i	−1.05943	−	0.226323i
$700$	−1.06131	+	0.225588i	−0.0401136	+	0.00852642i
$701$	2.72702	−	12.8296i	0.102998	−	0.484568i	−0.896167	−	0.443717i	$-0.853660\pi$
$701$	2.72702	−	12.8296i	0.102998	−	0.484568i	0.999165	−	0.0408516i	$-0.0130071\pi$
$702$	19.0513	+	17.2602i	0.719045	+	0.651445i
$703$	4.09994	+	3.69160i	0.154632	+	0.139231i
$704$	−0.293153	+	2.78916i	−0.0110486	+	0.105121i
$705$	7.24934	−	2.34724i	0.273026	−	0.0884023i
$706$	−22.9399	+	2.41108i	−0.863355	+	0.0907423i
$707$	3.55377	+	2.05177i	0.133653	+	0.0771648i
$708$	−2.05982	+	19.4066i	−0.0774129	+	0.729344i
$709$	−19.1273	−	26.3264i	−0.718340	−	0.988710i	−0.999577	−	0.0290721i	$-0.990745\pi$
$709$	−19.1273	−	26.3264i	−0.718340	−	0.988710i	0.281237	−	0.959638i	$-0.409255\pi$
$710$	7.35038	−	6.61831i	0.275855	−	0.248381i
$711$	−27.4300	−	37.9173i	−1.02870	−	1.42201i
$712$			6.79090i			0.254500i
$713$	−20.0744	+	20.1613i	−0.751794	+	0.755047i
$714$	2.64418	+	1.92525i	0.0989558	+	0.0720507i
$715$	4.28763	+	13.1960i	0.160348	+	0.493501i
$716$	17.5469	+	19.4878i	0.655757	+	0.728292i
$717$	0.00291761	−	2.84730i	0.000108960	−	0.106334i
$718$	8.01736	+	13.8865i	0.299205	+	0.518239i
$719$	−7.06188	+	12.2315i	−0.263364	+	0.456159i	−0.967134	−	0.254269i	$-0.918165\pi$
$719$	−7.06188	+	12.2315i	−0.263364	+	0.456159i	0.703770	+	0.710428i	$0.251499\pi$
$720$	1.21459	+	2.74313i	0.0452651	+	0.102230i
$721$	−10.6566	−	7.74250i	−0.396874	−	0.288346i
$722$	15.1223	+	1.58942i	0.562794	+	0.0591521i
$723$	−9.92880	+	2.09980i	−0.369256	+	0.0780924i
$724$	3.84427	−	8.63437i	0.142871	−	0.320894i
$725$	−2.14391	−	0.455702i	−0.0796227	−	0.0169243i
$726$	−4.95768	−	2.21339i	−0.183997	−	0.0821467i
$727$	−26.7278	+	11.9000i	−0.991279	+	0.441346i	−0.837309	−	0.546730i	$-0.815872\pi$
$727$	−26.7278	+	11.9000i	−0.991279	+	0.441346i	−0.153970	+	0.988076i	$0.549206\pi$
$728$	−1.65880	+	5.10526i	−0.0614792	+	0.189214i
$729$	21.9406	−	15.7356i	0.812615	−	0.582800i
$730$	−5.48528	−	12.3201i	−0.203019	−	0.455989i
$731$	−0.609224	−	2.86617i	−0.0225330	−	0.106009i
$732$	−2.51600	−	2.80006i	−0.0929939	−	0.103493i
$733$	−6.10586	−	2.71850i	−0.225525	−	0.100410i	0.290864	−	0.956765i	$-0.406057\pi$
$733$	−6.10586	−	2.71850i	−0.225525	−	0.100410i	−0.516389	+	0.856354i	$0.672724\pi$
$734$	−5.86161	+	6.50998i	−0.216356	+	0.240288i
$735$	6.75604	−	7.48790i	0.249200	−	0.276195i
$736$	3.00356	−	4.13404i	0.110713	−	0.152383i
$737$	−0.567456	−	5.39898i	−0.0209025	−	0.198874i
$738$	1.05588	+	0.226697i	0.0388675	+	0.00834483i
$739$	20.4177	−	11.7881i	0.751076	−	0.433634i	−0.0750067	−	0.997183i	$-0.523898\pi$
$739$	20.4177	−	11.7881i	0.751076	−	0.433634i	0.826082	+	0.563549i	$0.190564\pi$
$740$	−2.29135	+	1.66476i	−0.0842317	+	0.0611979i
$741$	−1.72777	−	16.6023i	−0.0634712	−	0.609899i
$742$	5.49511	−	1.78547i	0.201732	−	0.0655466i
$743$	−14.7228			−0.540127			−0.270064	−	0.962842i	$-0.587045\pi$
$743$	−14.7228			−0.540127			−0.270064	+	0.962842i	$0.587045\pi$
$744$	−7.50140	−	6.06044i	−0.275015	−	0.222187i
$745$	−16.0963			−0.589721
$746$	−13.9921	+	4.54630i	−0.512287	+	0.166452i
$747$	20.1571	−	34.7484i	0.737508	−	1.27138i
$748$	3.94890	−	2.86905i	0.144386	−	0.104903i
$749$	1.19809	−	0.691717i	0.0437772	−	0.0252748i
$750$	0.702867	+	1.58303i	0.0256651	+	0.0578040i
$751$	4.63143	+	44.0651i	0.169003	+	1.60796i	0.669901	+	0.742451i	$0.266337\pi$
$751$	4.63143	+	44.0651i	0.169003	+	1.60796i	−0.500897	+	0.865507i	$0.666997\pi$
$752$	2.58586	−	3.55914i	0.0942968	−	0.129788i
$753$	−8.20117	−	7.39960i	−0.298867	−	0.269656i
$754$	−7.25584	+	8.05843i	−0.264242	+	0.293471i
$755$	8.34374	+	3.71487i	0.303660	+	0.135198i
$756$	4.87389	+	2.83395i	0.177262	+	0.103070i
$757$	−8.60153	−	40.4670i	−0.312628	−	1.47080i	−0.801264	−	0.598311i	$-0.795839\pi$
$757$	−8.60153	−	40.4670i	−0.312628	−	1.47080i	0.488636	−	0.872488i	$-0.337495\pi$
$758$	−1.61222	−	3.62110i	−0.0585583	−	0.131524i
$759$	−14.5694	−	20.0964i	−0.528837	−	0.729453i
$760$	0.601940	−	1.85258i	0.0218346	−	0.0672001i
$761$	−29.3063	+	13.0480i	−1.06235	+	0.472990i	−0.862092	−	0.506752i	$-0.830846\pi$
$761$	−29.3063	+	13.0480i	−1.06235	+	0.472990i	−0.200262	+	0.979742i	$0.564179\pi$
$762$	2.35986	−	5.28574i	0.0854886	−	0.191482i
$763$	−10.4013	−	2.21087i	−0.376553	−	0.0800388i
$764$	−2.64627	+	5.94362i	−0.0957387	+	0.215033i
$765$	2.13347	−	4.76555i	0.0771359	−	0.172299i
$766$	27.0088	+	2.83874i	0.975867	+	0.102568i
$767$	45.0977	+	32.7654i	1.62838	+	1.18309i
$768$	1.49911	+	0.867562i	0.0540945	+	0.0313054i
$769$	−26.7784	+	46.3816i	−0.965654	+	1.67256i	−0.257807	+	0.966196i	$0.583000\pi$
$769$	−26.7784	+	46.3816i	−0.965654	+	1.67256i	−0.707847	+	0.706366i	$0.750333\pi$
$770$	1.52148	+	2.63528i	0.0548303	+	0.0949689i
$771$	37.1917	+	0.0381100i	1.33943	+	0.00137250i
$772$	−7.38796	−	8.20516i	−0.265899	−	0.295310i
$773$	6.87899	+	21.1714i	0.247420	+	0.761481i	0.995229	+	0.0975666i	$0.0311059\pi$
$773$	6.87899	+	21.1714i	0.247420	+	0.761481i	−0.747809	+	0.663914i	$0.768894\pi$
$774$	−1.55093	−	4.80678i	−0.0557472	−	0.172776i
$775$	−4.33452	−	3.49456i	−0.155701	−	0.125528i
$776$		−	7.05965i		−	0.253427i
$777$	−1.64999	+	5.06049i	−0.0591929	+	0.181544i
$778$	6.51394	−	5.86517i	0.233536	−	0.210277i
$779$	−0.412162	−	0.567293i	−0.0147672	−	0.0203254i
$780$	8.52124	+	0.904448i	0.305110	+	0.0323844i
$781$	−24.0230	−	13.8697i	−0.859609	−	0.496296i
$782$	−8.84486	+	0.929632i	−0.316291	+	0.0332436i
$783$	6.66590	+	9.23439i	0.238220	+	0.330010i
$784$	0.608642	−	5.79084i	0.0217372	−	0.206816i
$785$	−12.6043	−	11.3489i	−0.449866	−	0.405061i
$786$	13.1608	−	7.58044i	0.469431	−	0.270385i
$787$	−2.83663	+	13.3453i	−0.101115	+	0.475708i	0.898230	+	0.439525i	$0.144853\pi$
$787$	−2.83663	+	13.3453i	−0.101115	+	0.475708i	−0.999345	+	0.0361828i	$0.988480\pi$
$788$	−20.9921	+	4.46201i	−0.747812	+	0.158952i
$789$	−7.87277	+	36.8528i	−0.280278	+	1.31199i
$790$	−14.8361	−	4.82053i	−0.527844	−	0.171507i
$791$	13.2546	+	4.30670i	0.471281	+	0.153128i
$792$	6.26403	−	5.61696i	0.222583	−	0.199590i
$793$	−10.5175	+	2.23556i	−0.373488	+	0.0793872i
$794$	6.13513	−	28.8635i	0.217727	−	1.02433i
$795$	−4.60354	−	7.99247i	−0.163271	−	0.283464i
$796$	−2.58566	−	2.32814i	−0.0916464	−	0.0825188i
$797$	3.50578	−	33.3553i	0.124181	−	1.18150i	−0.737963	−	0.674841i	$-0.764212\pi$
$797$	3.50578	−	33.3553i	0.124181	−	1.18150i	0.862144	−	0.506663i	$-0.169121\pi$
$798$	−1.12766	−	3.48272i	−0.0399187	−	0.123287i
$799$	−7.61484	+	0.800352i	−0.269394	+	0.0283144i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	13.6630	−	15.1119i	0.482758	−	0.533953i
$802$	−0.595692	−	0.819900i	−0.0210346	−	0.0289517i
$803$	−28.1073	+	25.3079i	−0.991884	+	0.893097i
$804$	−3.18757	−	1.03932i	−0.112417	−	0.0366539i
$805$		−	5.54439i		−	0.195414i
$806$	−25.6949	+	9.92704i	−0.905064	+	0.349665i
$807$	−22.9198	+	31.4786i	−0.806816	+	1.10810i
$808$	−1.16870	−	3.59690i	−0.0411149	−	0.126539i
$809$	21.3388	+	23.6992i	0.750233	+	0.833218i	0.990503	−	0.137488i	$-0.0439029\pi$
$809$	21.3388	+	23.6992i	0.750233	+	0.833218i	−0.240271	+	0.970706i	$0.577236\pi$
$810$	2.81621	−	8.54804i	0.0989516	−	0.300347i
$811$	−13.9954	−	24.2407i	−0.491444	−	0.851206i	0.508507	−	0.861058i	$-0.330197\pi$
$811$	−13.9954	−	24.2407i	−0.491444	−	0.851206i	−0.999951	+	0.00985161i	$0.996864\pi$
$812$	−1.18907	+	2.05953i	−0.0417283	+	0.0722755i
$813$	23.0120	−	39.7638i	0.807066	−	1.39458i
$814$	6.42615	+	4.66887i	0.225236	+	0.163644i
$815$	14.1468	+	1.48688i	0.495539	+	0.0520833i
$816$	−0.623735	−	2.94930i	−0.0218351	−	0.103246i
$817$	−1.33390	+	2.99598i	−0.0466672	+	0.104816i
$818$	−4.82284	−	1.02513i	−0.168627	−	0.0358427i
$819$	13.9629	−	8.02339i	0.487904	−	0.280360i
$820$	0.328859	−	0.146417i	0.0114842	−	0.00511311i
$821$	−11.4323	+	35.1849i	−0.398989	+	1.22796i	0.526822	+	0.849976i	$0.323383\pi$
$821$	−11.4323	+	35.1849i	−0.398989	+	1.22796i	−0.925811	+	0.377987i	$0.876617\pi$
$822$	−9.37868	+	6.79934i	−0.327119	+	0.237154i
$823$	14.2072	+	31.9100i	0.495233	+	1.11231i	0.972362	+	0.233478i	$0.0750108\pi$
$823$	14.2072	+	31.9100i	0.495233	+	1.11231i	−0.477129	+	0.878833i	$0.658323\pi$
$824$	2.52409	+	11.8749i	0.0879308	+	0.413682i
$825$	3.61322	−	3.24666i	0.125796	−	0.113034i
$826$	11.1683	+	4.97246i	0.388596	+	0.173014i
$827$	−15.3405	+	17.0373i	−0.533440	+	0.592445i	−0.948274	−	0.317452i	$-0.897173\pi$
$827$	−15.3405	+	17.0373i	−0.533440	+	0.592445i	0.414834	+	0.909897i	$0.363840\pi$
$828$	−15.0014	+	3.15652i	−0.521334	+	0.109697i
$829$	24.0543	−	33.1080i	0.835442	−	1.14989i	−0.151444	−	0.988466i	$-0.548392\pi$
$829$	24.0543	−	33.1080i	0.835442	−	1.14989i	0.986886	−	0.161421i	$-0.0516078\pi$
$830$	−1.39969	−	13.3172i	−0.0485840	−	0.462246i
$831$	−28.1601	+	12.5031i	−0.976864	+	0.433729i
$832$	4.28455	−	2.47369i	0.148540	−	0.0857597i
$833$	−8.19869	+	5.95669i	−0.284068	+	0.206387i
$834$	−22.3183	+	2.32263i	−0.772819	+	0.0804260i
$835$	−9.51312	+	3.09100i	−0.329215	+	0.106968i
$836$	−5.46299			−0.188941
$837$	4.49964	+	28.5789i	0.155530	+	0.987831i
$838$	−24.8756			−0.859313
$839$	−39.7746	+	12.9236i	−1.37317	+	0.446171i	−0.900419	−	0.435024i	$-0.856740\pi$
$839$	−39.7746	+	12.9236i	−1.37317	+	0.446171i	−0.472754	+	0.881195i	$0.656740\pi$
$840$	1.86921	−	0.194526i	0.0644939	−	0.00671177i
$841$	19.5750	−	14.2220i	0.674999	−	0.490416i
$842$	−12.7910	+	7.38488i	−0.440807	+	0.254500i
$843$	0.907689	−	0.403015i	0.0312625	−	0.0138806i
$844$	1.23483	+	11.7486i	0.0425047	+	0.404405i
$845$	6.74574	−	9.28472i	0.232061	−	0.319404i
$846$	−12.9152	+	2.71756i	−0.444034	+	0.0934316i
$847$	−2.27580	+	2.52753i	−0.0781974	+	0.0868470i
$848$	−4.86478	−	2.16594i	−0.167057	−	0.0743787i
$849$	−35.9793	+	32.3292i	−1.23481	+	1.10954i
$850$	−0.361858	−	1.70241i	−0.0124116	−	0.0583921i
$851$	−5.88659	−	13.2215i	−0.201790	−	0.453227i
$852$	−13.8700	+	10.0555i	−0.475180	+	0.344495i
$853$	−14.0868	+	43.3547i	−0.482323	+	1.48444i	0.353497	+	0.935436i	$0.384992\pi$
$853$	−14.0868	+	43.3547i	−0.482323	+	1.48444i	−0.835821	+	0.549003i	$0.815008\pi$
$854$	−2.15427	+	0.959142i	−0.0737176	+	0.0328212i
$855$	−5.06682	+	2.91150i	−0.173281	+	0.0995711i
$856$	−1.24717	−	0.265095i	−0.0426274	−	0.00906074i
$857$	14.5907	−	32.7713i	0.498410	−	1.11945i	−0.472789	−	0.881176i	$-0.656753\pi$
$857$	14.5907	−	32.7713i	0.498410	−	1.11945i	0.971199	−	0.238271i	$-0.0765806\pi$
$858$	−4.97250	−	23.5122i	−0.169759	−	0.802695i
$859$	31.1115	+	3.26995i	1.06151	+	0.111569i	0.619153	−	0.785270i	$-0.287476\pi$
$859$	31.1115	+	3.26995i	1.06151	+	0.111569i	0.442356	+	0.896839i	$0.354143\pi$
$860$	−1.36206	−	0.989595i	−0.0464459	−	0.0337449i
$861$	0.338857	−	0.585531i	0.0115482	−	0.0199548i
$862$	9.06765	−	15.7056i	0.308845	−	0.534936i
$863$	19.7831	+	34.2653i	0.673424	+	1.16640i	0.976927	+	0.213574i	$0.0685105\pi$
$863$	19.7831	+	34.2653i	0.673424	+	1.16640i	−0.303503	+	0.952831i	$0.598156\pi$
$864$	−1.59050	−	4.94675i	−0.0541099	−	0.168292i
$865$	10.6236	+	11.7987i	0.361213	+	0.401168i
$866$	2.52278	+	7.76432i	0.0857275	+	0.263842i
$867$	14.2434	−	19.5622i	0.483732	−	0.664367i
$868$	−5.05939	+	3.30116i	−0.171727	+	0.112049i
$869$			43.7494i			1.48410i
$870$	3.60931	+	1.17683i	0.122367	+	0.0398981i
$871$	−7.11683	+	6.40802i	−0.241145	+	0.217128i
$872$	5.76057	+	7.92875i	0.195078	+	0.268501i
$873$	−14.2037	+	15.7100i	−0.480723	+	0.531702i
$874$	8.62022	+	4.97689i	0.291583	+	0.168346i
$875$	1.07907	−	0.113415i	0.0364793	−	0.00383413i
$876$	7.19543	+	22.2227i	0.243111	+	0.750836i
$877$	−4.18683	+	39.8350i	−0.141379	+	1.34513i	0.661927	+	0.749568i	$0.269739\pi$
$877$	−4.18683	+	39.8350i	−0.141379	+	1.34513i	−0.803307	+	0.595566i	$0.796928\pi$
$878$	3.40635	+	3.06709i	0.114959	+	0.103509i
$879$	−12.8507	−	22.3108i	−0.433443	−	0.752524i
$880$	0.583094	−	2.74324i	0.0196561	−	0.0924746i
$881$	28.0145	−	5.95467i	0.943833	−	0.200618i	0.289803	−	0.957086i	$-0.406410\pi$
$881$	28.0145	−	5.95467i	0.943833	−	0.200618i	0.654030	+	0.756469i	$0.273077\pi$
$882$	−13.0053	+	11.6619i	−0.437913	+	0.392676i
$883$	−29.8618	−	9.70267i	−1.00493	−	0.326521i	−0.240095	−	0.970749i	$-0.577179\pi$
$883$	−29.8618	−	9.70267i	−1.00493	−	0.326521i	−0.764833	+	0.644228i	$0.777179\pi$
$884$	−8.18919	−	2.66083i	−0.275432	−	0.0894933i
$885$	4.07708	−	19.0850i	0.137050	−	0.641534i
$886$	−4.40150	+	0.935567i	−0.147871	+	0.0314310i
$887$	−3.22444	+	15.1698i	−0.108266	+	0.509352i	0.890278	+	0.455417i	$0.150510\pi$
$887$	−3.22444	+	15.1698i	−0.108266	+	0.509352i	−0.998544	+	0.0539354i	$0.982823\pi$
$888$	4.25091	−	2.44846i	0.142651	−	0.0821649i
$889$	−2.69478	−	2.42639i	−0.0903801	−	0.0813786i
$890$	0.709842	−	6.75370i	0.0237940	−	0.226384i
$891$	−25.2405	−	0.103456i	−0.845589	−	0.00346589i
$892$	−22.5748	+	2.37271i	−0.755861	+	0.0794442i
$893$	7.42144	+	4.28477i	0.248349	+	0.143384i
$894$	27.7238	+	2.94262i	0.927223	+	0.0984158i
$895$	−15.4137	−	21.2151i	−0.515223	−	0.709144i
$896$	0.806325	−	0.726018i	0.0269374	−	0.0242546i
$897$	−13.5738	+	41.6308i	−0.453217	+	1.39001i
$898$		−	2.22052i		−	0.0740997i
$899$	−12.0491	+	1.93506i	−0.401858	+	0.0645377i
$900$	−0.921202	−	2.85506i	−0.0307067	−	0.0951688i
$901$	2.86401	+	8.81452i	0.0954141	+	0.293654i
$902$	−0.675538	−	0.750260i	−0.0224929	−	0.0249809i
$903$	−3.16399	−	0.00324212i	−0.105291	−	0.000107891i
$904$	−6.42237	−	11.1239i	−0.213605	−	0.369974i
$905$	−4.72575	+	8.18523i	−0.157089	+	0.272086i
$906$	−13.6919	−	7.92376i	−0.454884	−	0.263249i
$907$	−33.7651	−	24.5318i	−1.12115	−	0.814564i	−0.136768	−	0.990603i	$-0.543671\pi$
$907$	−33.7651	−	24.5318i	−1.12115	−	0.814564i	−0.984383	+	0.176039i	$0.943671\pi$
$908$	−14.9401	−	1.57027i	−0.495805	−	0.0521112i
$909$	−4.63607	+	10.3556i	−0.153769	+	0.343474i
$910$	2.18336	−	4.90390i	0.0723776	−	0.162563i
$911$	20.9363	+	4.45014i	0.693649	+	0.147440i	0.541228	−	0.840876i	$-0.317960\pi$
$911$	20.9363	+	4.45014i	0.693649	+	0.147440i	0.152421	+	0.988316i	$0.451293\pi$
$912$	−1.37544	+	3.08080i	−0.0455455	+	0.102015i
$913$	−34.3074	+	15.2746i	−1.13541	+	0.505516i
$914$	5.21143	−	16.0391i	0.172379	−	0.530527i
$915$	2.20953	+	3.04772i	0.0730447	+	0.100754i
$916$	8.74753	+	19.6473i	0.289027	+	0.649165i
$917$	−1.97811	−	9.30628i	−0.0653230	−	0.307321i
$918$	−4.54585	+	7.81805i	−0.150036	+	0.258034i
$919$	−40.3252	−	17.9540i	−1.33021	−	0.592246i	−0.386274	−	0.922384i	$-0.626238\pi$
$919$	−40.3252	−	17.9540i	−1.33021	−	0.592246i	−0.943933	+	0.330138i	$0.892905\pi$
$920$	−3.41923	+	3.79744i	−0.112729	+	0.125198i
$921$	−10.2612	−	9.25826i	−0.338117	−	0.305070i
$922$	4.76613	−	6.56002i	0.156964	−	0.216043i
$923$	5.11501	+	48.6660i	0.168362	+	1.60186i
$924$	−2.13880	−	4.81709i	−0.0703612	−	0.158471i
$925$	2.45281	−	1.41613i	0.0806480	−	0.0465621i
$926$	−30.5494	+	22.1954i	−1.00391	+	0.729387i
$927$	18.2749	−	31.5038i	0.600226	−	1.03472i
$928$	2.08453	−	0.677305i	0.0684280	−	0.0222336i
$929$	−32.2565			−1.05830			−0.529150	−	0.848528i	$-0.677489\pi$
$929$	−32.2565			−1.05830			−0.529150	+	0.848528i	$0.677489\pi$
$930$	6.82682	+	6.81135i	0.223860	+	0.223353i
$931$	11.3422			0.371726
$932$	15.7270	−	5.11001i	0.515155	−	0.167384i
$933$	0.292383	+	2.80953i	0.00957220	+	0.0919800i
$934$	−13.5217	+	9.82409i	−0.442444	+	0.321454i
$935$	−4.22717	+	2.44056i	−0.138243	+	0.0798147i
$936$	−14.5114	−	3.11560i	−0.474321	−	0.101837i
$937$	−1.36887	−	13.0239i	−0.0447190	−	0.425473i	−0.993862	−	0.110628i	$-0.964714\pi$
$937$	−1.36887	−	13.0239i	−0.0447190	−	0.425473i	0.949143	−	0.314846i	$-0.101953\pi$
$938$	−1.23451	+	1.69915i	−0.0403081	+	0.0554793i
$939$	−13.8633	+	15.3651i	−0.452413	+	0.501421i
$940$	−2.94373	+	3.26934i	−0.0960139	+	0.106634i
$941$	−45.4533	−	20.2371i	−1.48174	−	0.659711i	−0.502897	−	0.864346i	$-0.667732\pi$
$941$	−45.4533	−	20.2371i	−1.48174	−	0.659711i	−0.978838	+	0.204636i	$0.934399\pi$
$942$	19.6345	+	21.8514i	0.639728	+	0.711956i
$943$	0.382450	+	1.79929i	0.0124543	+	0.0585929i
$944$	−4.58284	−	10.2932i	−0.149159	−	0.335016i
$945$	−4.55096	−	3.32789i	−0.148043	−	0.108256i
$946$	−1.45909	+	4.49060i	−0.0474390	+	0.146002i
$947$	−45.6791	+	20.3377i	−1.48437	+	0.660885i	−0.979341	−	0.202216i	$-0.935186\pi$
$947$	−45.6791	+	20.3377i	−1.48437	+	0.660885i	−0.505031	+	0.863101i	$0.668519\pi$
$948$	24.6720	+	11.0150i	0.801311	+	0.357751i
$949$	65.2627	+	13.8720i	2.11852	+	0.450305i
$950$	−0.792289	+	1.77951i	−0.0257053	+	0.0577350i
$951$	−26.8963	+	5.68818i	−0.872172	+	0.184452i
$952$	−1.87806	−	0.197392i	−0.0608684	−	0.00639753i
$953$	−6.79690	−	4.93824i	−0.220173	−	0.159965i	0.472231	−	0.881475i	$-0.343449\pi$
$953$	−6.79690	−	4.93824i	−0.220173	−	0.159965i	−0.692405	+	0.721509i	$0.743449\pi$
$954$	6.46790	+	14.6076i	0.209406	+	0.472939i
$955$	3.25305	−	5.63445i	0.105266	−	0.182326i
$956$	0.821946	+	1.42365i	0.0265836	+	0.0460442i
$957$	0.0109097	−	10.6469i	0.000352662	−	0.344164i
$958$	12.4434	+	13.8198i	0.402027	+	0.446496i
$959$	2.24243	+	6.90150i	0.0724119	+	0.222861i
$960$	−1.40021	−	1.01951i	−0.0451917	−	0.0329045i
$961$	−29.5238	−	9.45214i	−0.952382	−	0.304908i
$962$		−	14.0123i		−	0.451774i
$963$	2.24199	+	3.09917i	0.0722472	+	0.0998695i
$964$	4.35422	−	3.92056i	0.140240	−	0.126273i
$965$	6.48982	+	8.93247i	0.208915	+	0.287546i
$966$	−1.01359	+	9.54952i	−0.0326117	+	0.307251i
$967$	−29.2570	−	16.8915i	−0.940841	−	0.543195i	−0.0506171	−	0.998718i	$-0.516119\pi$
$967$	−29.2570	−	16.8915i	−0.940841	−	0.543195i	−0.890224	+	0.455523i	$0.849452\pi$
$968$	3.11746	−	0.327658i	0.100199	−	0.0105313i
$969$	5.58652	−	1.80884i	0.179465	−	0.0581084i
$970$	−0.737935	+	7.02098i	−0.0236937	+	0.225430i
$971$	33.6709	+	30.3174i	1.08055	+	0.972931i	0.999717	−	0.0237970i	$-0.00757552\pi$
$971$	33.6709	+	30.3174i	1.08055	+	0.972931i	0.0808323	+	0.996728i	$0.474242\pi$
$972$	−6.41328	+	14.2081i	−0.205706	+	0.455725i
$973$	−2.92250	+	13.7493i	−0.0936911	+	0.440782i
$974$	−0.985777	+	0.209533i	−0.0315863	+	0.00671388i
$975$	−8.38002	−	1.79021i	−0.268376	−	0.0573325i
$976$	2.06700	+	0.671608i	0.0661629	+	0.0214976i
$977$	27.3012	+	8.87071i	0.873444	+	0.283799i	0.711232	−	0.702957i	$-0.248137\pi$
$977$	27.3012	+	8.87071i	0.873444	+	0.283799i	0.162211	+	0.986756i	$0.448137\pi$
$978$	−24.0942	−	5.14719i	−0.770448	−	0.164589i
$979$	−18.6291	+	3.95973i	−0.595388	+	0.126554i
$980$	−1.21062	+	5.69550i	−0.0386717	+	0.181936i
$981$	3.13320	−	29.2340i	0.100036	−	0.933370i
$982$	−19.4700	−	17.5308i	−0.621312	−	0.559432i
$983$	6.42601	−	61.1394i	0.204958	−	1.95004i	−0.0934931	−	0.995620i	$-0.529803\pi$
$983$	6.42601	−	61.1394i	0.204958	−	1.95004i	0.298451	−	0.954425i	$-0.403530\pi$
$984$	−0.593185	+	0.192066i	−0.0189101	+	0.00612283i
$985$	21.3435	−	2.24329i	0.680061	−	0.0714773i
$986$	−3.30363	−	1.90735i	−0.105209	−	0.0607425i
$987$	−0.872634	+	8.22151i	−0.0277763	+	0.261694i
$988$	5.66454	+	7.79656i	0.180213	+	0.248042i
$989$	6.39336	−	5.75661i	0.203297	−	0.183050i
$990$	−6.81685	+	4.93142i	−0.216654	+	0.156731i
$991$			11.6788i			0.370990i	0.982645	+	0.185495i	$0.0593889\pi$
$991$			11.6788i			0.370990i	−0.982645	+	0.185495i	$0.940611\pi$
$992$	5.50108	+	0.859116i	0.174660	+	0.0272770i
$993$	9.31107	+	6.77948i	0.295478	+	0.215140i
$994$	3.31631	+	10.2066i	0.105187	+	0.323732i
$995$	2.32814	+	2.58566i	0.0738071	+	0.0819710i
$996$	−0.0237657	+	23.1931i	−0.000753046	+	0.734901i
$997$	−22.1905	−	38.4350i	−0.702779	−	1.21725i	−0.967487	−	0.252921i	$-0.918609\pi$
$997$	−22.1905	−	38.4350i	−0.702779	−	1.21725i	0.264708	−	0.964329i	$-0.414724\pi$
$998$	1.77344	−	3.07169i	0.0561373	−	0.0972326i
$999$	−14.3858	−	3.10405i	−0.455147	−	0.0982077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.b.11.1	✓	176
3.2	odd	2	inner	930.2.br.b.11.17	yes	176
31.17	odd	30	inner	930.2.br.b.761.17	yes	176
93.17	even	30	inner	930.2.br.b.761.1	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.b.11.1	✓	176	1.1	even	1	trivial
930.2.br.b.11.17	yes	176	3.2	odd	2	inner
930.2.br.b.761.1	yes	176	93.17	even	30	inner
930.2.br.b.761.17	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.72275 + 0.179283i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.58303 - 0.702867i) q^{6} +(-0.113415 - 1.07907i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.93571 - 0.617720i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.72275 + 0.179283i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.58303 - 0.702867i) q^{6} +(-0.113415 - 1.07907i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.93571 - 0.617720i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-2.56206 - 1.14070i) q^{11} +(-1.28835 + 1.15765i) q^{12} +(1.02862 + 4.83927i) q^{13} +(0.441316 + 0.991212i) q^{14} +(1.40230 - 1.01664i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.58997 + 0.707901i) q^{17} +(-2.60114 + 1.49467i) q^{18} +(1.90535 + 0.404995i) q^{19} +(-0.406737 + 0.913545i) q^{20} +(0.388846 + 1.83864i) q^{21} +(2.78916 + 0.293153i) q^{22} +(-4.13404 - 3.00356i) q^{23} +(0.867562 - 1.49911i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.47369 - 4.28455i) q^{26} +(-4.94675 + 1.59050i) q^{27} +(-0.726018 - 0.806325i) q^{28} +(-0.677305 - 2.08453i) q^{29} +(-1.01951 + 1.40021i) q^{30} +(0.859116 - 5.50108i) q^{31} +1.00000i q^{32} +(4.61829 + 1.50581i) q^{33} +(1.29340 - 1.16458i) q^{34} +(0.637757 + 0.877797i) q^{35} +(2.01196 - 2.22532i) q^{36} +(2.45281 + 1.41613i) q^{37} +(-1.93725 + 0.203613i) q^{38} +(-2.63965 - 8.15242i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-0.267518 - 0.240874i) q^{41} +(-0.937984 - 1.62849i) q^{42} +(-0.350040 + 1.64681i) q^{43} +(-2.74324 + 0.583094i) q^{44} +(-2.23354 + 2.00282i) q^{45} +(4.85986 + 1.57906i) q^{46} +(4.18402 + 1.35947i) q^{47} +(-0.361849 + 1.69383i) q^{48} +(5.69550 - 1.21062i) q^{49} +(-0.207912 + 0.978148i) q^{50} +(2.61220 - 1.50459i) q^{51} +(3.67662 + 3.31044i) q^{52} +(0.556631 - 5.29599i) q^{53} +(4.21314 - 3.04128i) q^{54} +(2.78916 - 0.293153i) q^{55} +(0.939652 + 0.542509i) q^{56} +(-3.35505 - 0.356106i) q^{57} +(1.28831 + 1.77321i) q^{58} +(8.37326 - 7.53932i) q^{59} +(0.536921 - 1.64673i) q^{60} +2.17337i q^{61} +(0.882860 + 5.49732i) q^{62} +(-0.999520 - 3.09779i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-3.31044 - 3.67662i) q^{65} +(-4.85758 - 0.00497752i) q^{66} +(0.967850 + 1.67637i) q^{67} +(-0.870221 + 1.50727i) q^{68} +(7.66039 + 4.43320i) q^{69} +(-0.877797 - 0.637757i) q^{70} +(9.83673 + 1.03388i) q^{71} +(-1.22582 + 2.73813i) q^{72} +(5.48528 - 12.3201i) q^{73} +(-2.77037 - 0.588861i) q^{74} +(-0.706110 + 1.58158i) q^{75} +(1.77951 - 0.792289i) q^{76} +(-0.940326 + 2.89403i) q^{77} +(5.02969 + 6.93771i) q^{78} +(-6.34492 - 14.2509i) q^{79} +(0.207912 + 0.978148i) q^{80} +(8.23684 - 3.62690i) q^{81} +(0.328859 + 0.146417i) q^{82} +(8.96001 - 9.95110i) q^{83} +(1.39531 + 1.25893i) q^{84} +(1.02301 - 1.40805i) q^{85} +(-0.175984 - 1.67438i) q^{86} +(1.54055 + 3.46969i) q^{87} +(2.42879 - 1.40226i) q^{88} +(5.49395 - 3.99159i) q^{89} +(1.50532 - 2.59500i) q^{90} +(5.10526 - 1.65880i) q^{91} -5.10996 q^{92} +(-0.493787 + 9.63100i) q^{93} -4.39934 q^{94} +(-1.85258 + 0.601940i) q^{95} +(-0.179283 - 1.72275i) q^{96} +(-5.71138 + 4.14956i) q^{97} +(-5.04264 + 2.91137i) q^{98} +(-8.22612 - 1.76614i) 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	\( 176 q + 44 q^{4} + 4 q^{7} + 4 q^{9} + 22 q^{10} + 38 q^{13} - 44 q^{16} + 4 q^{18} + 8 q^{19} - 42 q^{21} + 4 q^{22} + 88 q^{25} + 30 q^{27} + 36 q^{28} + 32 q^{31} - 70 q^{33} + 14 q^{34} - 4 q^{36} + 42 q^{37} + 58 q^{39} - 22 q^{40} - 12 q^{42} - 46 q^{43} + 16 q^{45} + 10 q^{46} + 38 q^{49} + 38 q^{51} + 2 q^{52} + 4 q^{55} + 78 q^{57} - 40 q^{58} + 16 q^{63} + 44 q^{64} + 34 q^{66} - 76 q^{67} + 148 q^{69} - 8 q^{70} - 4 q^{72} - 52 q^{73} + 12 q^{76} + 60 q^{78} + 8 q^{79} - 108 q^{81} - 40 q^{82} - 8 q^{84} + 28 q^{87} + 6 q^{88} + 24 q^{90} - 20 q^{91} - 28 q^{93} - 20 q^{94} - 112 q^{97} - 132 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 + 4 * q^9 + 22 * q^10 + 38 * q^13 - 44 * q^16 + 4 * q^18 + 8 * q^19 - 42 * q^21 + 4 * q^22 + 88 * q^25 + 30 * q^27 + 36 * q^28 + 32 * q^31 - 70 * q^33 + 14 * q^34 - 4 * q^36 + 42 * q^37 + 58 * q^39 - 22 * q^40 - 12 * q^42 - 46 * q^43 + 16 * q^45 + 10 * q^46 + 38 * q^49 + 38 * q^51 + 2 * q^52 + 4 * q^55 + 78 * q^57 - 40 * q^58 + 16 * q^63 + 44 * q^64 + 34 * q^66 - 76 * q^67 + 148 * q^69 - 8 * q^70 - 4 * q^72 - 52 * q^73 + 12 * q^76 + 60 * q^78 + 8 * q^79 - 108 * q^81 - 40 * q^82 - 8 * q^84 + 28 * q^87 + 6 * q^88 + 24 * q^90 - 20 * q^91 - 28 * q^93 - 20 * q^94 - 112 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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