LMFDB - Embedded newform 930.2.bj.b.277.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(277,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("930.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bj (of order $20$, 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:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			277.7
Character	$\chi$	$=$	930.277
Dual form			930.2.bj.b.883.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.61098 - 1.55073i) q^{5} +1.00000i q^{6} +(-1.36477 + 2.67852i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.61098 - 1.55073i) q^{5} +1.00000i q^{6} +(-1.36477 + 2.67852i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-1.78365 - 1.34855i) q^{10} +(2.11928 - 0.688597i) q^{11} +(0.987688 - 0.156434i) q^{12} +(-6.87689 - 1.08919i) q^{13} +(2.85904 + 0.928958i) q^{14} +(-1.83373 + 1.27962i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.917097 - 1.79990i) q^{17} +(0.156434 - 0.987688i) q^{18} +(-1.13393 + 1.56073i) q^{19} +(-1.05293 + 1.97265i) q^{20} +(1.76698 - 2.43204i) q^{21} +(-1.01165 - 1.98547i) q^{22} +(-1.82777 + 0.931295i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(0.190487 - 4.99637i) q^{25} +6.96261i q^{26} +(-0.891007 - 0.453990i) q^{27} +(0.470269 - 2.96916i) q^{28} +(-6.04997 - 4.39556i) q^{29} +(1.55073 + 1.61098i) q^{30} +(-5.47453 - 1.01466i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.20091 + 0.348590i) q^{33} +(-1.63428 + 1.18737i) q^{34} +(1.95504 + 6.43142i) q^{35} -1.00000 q^{36} +(-3.18538 + 3.18538i) q^{37} +(1.71890 + 0.875822i) q^{38} +(6.62183 + 2.15156i) q^{39} +(2.11308 + 0.731374i) q^{40} +(3.47851 + 2.52729i) q^{41} +(-2.67852 - 1.36477i) q^{42} +(-0.712853 - 4.50078i) q^{43} +(-1.80277 + 1.30979i) q^{44} +(2.01133 - 0.977011i) q^{45} +(1.20575 + 1.65958i) q^{46} +(-5.31061 - 0.841118i) q^{47} +(-0.891007 + 0.453990i) q^{48} +(-1.19736 - 1.64803i) q^{49} +(-4.96466 + 0.593463i) q^{50} +(0.624239 + 1.92121i) q^{51} +(6.87689 - 1.08919i) q^{52} +(-7.30852 + 3.72388i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(2.34629 - 4.39575i) q^{55} -3.00617 q^{56} +(1.36413 - 1.36413i) q^{57} +(-3.39502 + 6.66310i) q^{58} +(0.288245 + 0.396735i) q^{59} +(1.34855 - 1.78365i) q^{60} -4.20268i q^{61} +(-0.145760 + 5.56586i) q^{62} +(-2.12569 + 2.12569i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-12.7675 + 8.90952i) q^{65} +(0.688597 + 2.11928i) q^{66} +(10.6362 + 10.6362i) q^{67} +(1.42841 + 1.42841i) q^{68} +(1.95095 - 0.633903i) q^{69} +(6.04641 - 2.93706i) q^{70} +(-3.24666 + 9.99219i) q^{71} +(0.156434 + 0.987688i) q^{72} +(-3.55590 + 6.97884i) q^{73} +(3.64446 + 2.64786i) q^{74} +(-0.969746 + 4.90506i) q^{75} +(0.596145 - 1.83474i) q^{76} +(-1.04792 + 6.61633i) q^{77} +(1.08919 - 6.87689i) q^{78} +(0.181602 - 0.558913i) q^{79} +(0.391812 - 2.20147i) q^{80} +(0.809017 + 0.587785i) q^{81} +(1.95201 - 3.83104i) q^{82} +(-0.666589 - 4.20867i) q^{83} +(-0.928958 + 2.85904i) q^{84} +(-4.26858 - 1.47743i) q^{85} +(-4.33385 + 1.40815i) q^{86} +(5.28787 + 5.28787i) q^{87} +(1.57568 + 1.57568i) q^{88} +(-2.89504 - 8.91003i) q^{89} +(-1.27962 - 1.83373i) q^{90} +(12.3028 - 16.9334i) q^{91} +(1.45053 - 1.45053i) q^{92} +(5.24840 + 1.85857i) q^{93} +5.37681i q^{94} +(0.593521 + 4.27272i) q^{95} +(0.587785 + 0.809017i) q^{96} +(-0.812745 + 1.59510i) q^{97} +(-1.44043 + 1.44043i) q^{98} +2.22835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{7}+O(q^{10}) $ 128 * q + 4 * q^7	$ 128 q + 4 q^{7} - 4 q^{10} - 4 q^{15} + 32 q^{16} + 12 q^{17} + 40 q^{19} + 40 q^{21} + 4 q^{22} + 32 q^{24} - 8 q^{25} - 4 q^{28} - 8 q^{29} + 20 q^{31} + 4 q^{33} + 24 q^{35} - 128 q^{36} - 64 q^{37} - 16 q^{38} - 24 q^{41} + 16 q^{42} - 24 q^{43} + 8 q^{44} + 20 q^{46} - 12 q^{47} + 100 q^{49} - 24 q^{50} + 64 q^{53} + 32 q^{54} + 68 q^{55} - 16 q^{57} + 40 q^{58} + 8 q^{62} - 4 q^{63} + 84 q^{65} - 12 q^{66} - 32 q^{67} - 8 q^{68} + 88 q^{70} + 24 q^{71} + 20 q^{73} + 16 q^{74} - 24 q^{75} - 24 q^{76} + 60 q^{77} + 56 q^{79} + 32 q^{81} - 16 q^{82} + 8 q^{83} - 68 q^{85} - 20 q^{87} + 4 q^{88} - 136 q^{89} - 40 q^{91} + 48 q^{93} - 92 q^{95} + 64 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) $ 128 * q + 4 * q^7 - 4 * q^10 - 4 * q^15 + 32 * q^16 + 12 * q^17 + 40 * q^19 + 40 * q^21 + 4 * q^22 + 32 * q^24 - 8 * q^25 - 4 * q^28 - 8 * q^29 + 20 * q^31 + 4 * q^33 + 24 * q^35 - 128 * q^36 - 64 * q^37 - 16 * q^38 - 24 * q^41 + 16 * q^42 - 24 * q^43 + 8 * q^44 + 20 * q^46 - 12 * q^47 + 100 * q^49 - 24 * q^50 + 64 * q^53 + 32 * q^54 + 68 * q^55 - 16 * q^57 + 40 * q^58 + 8 * q^62 - 4 * q^63 + 84 * q^65 - 12 * q^66 - 32 * q^67 - 8 * q^68 + 88 * q^70 + 24 * q^71 + 20 * q^73 + 16 * q^74 - 24 * q^75 - 24 * q^76 + 60 * q^77 + 56 * q^79 + 32 * q^81 - 16 * q^82 + 8 * q^83 - 68 * q^85 - 20 * q^87 + 4 * q^88 - 136 * q^89 - 40 * q^91 + 48 * q^93 - 92 * q^95 + 64 * q^97 - 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	1.61098	−	1.55073i	0.720450	−	0.693507i
$5$	1.61098	−	1.55073i	0.720450	−	0.693507i
$6$			1.00000i			0.408248i
$7$	−1.36477	+	2.67852i	−0.515836	+	1.01239i	0.475336	+	0.879804i	$0.342326\pi$
$7$	−1.36477	+	2.67852i	−0.515836	+	1.01239i	−0.991172	+	0.132581i	$0.957674\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	−1.78365	−	1.34855i	−0.564039	−	0.426450i
$11$	2.11928	−	0.688597i	0.638988	−	0.207620i	0.0284358	−	0.999596i	$-0.490947\pi$
$11$	2.11928	−	0.688597i	0.638988	−	0.207620i	0.610553	+	0.791976i	$0.290947\pi$
$12$	0.987688	−	0.156434i	0.285121	−	0.0451587i
$13$	−6.87689	−	1.08919i	−1.90731	−	0.302087i	−0.912940	−	0.408094i	$-0.866194\pi$
$13$	−6.87689	−	1.08919i	−1.90731	−	0.302087i	−0.994365	+	0.106006i	$0.966194\pi$
$14$	2.85904	+	0.928958i	0.764111	+	0.248275i
$15$	−1.83373	+	1.27962i	−0.473467	+	0.330397i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.917097	−	1.79990i	−0.222429	−	0.436541i	0.752644	−	0.658428i	$-0.228778\pi$
$17$	−0.917097	−	1.79990i	−0.222429	−	0.436541i	−0.975072	+	0.221887i	$0.928778\pi$
$18$	0.156434	−	0.987688i	0.0368720	−	0.232800i
$19$	−1.13393	+	1.56073i	−0.260142	+	0.358055i	−0.919031	−	0.394185i	$-0.871027\pi$
$19$	−1.13393	+	1.56073i	−0.260142	+	0.358055i	0.658889	+	0.752241i	$0.271027\pi$
$20$	−1.05293	+	1.97265i	−0.235442	+	0.441098i
$21$	1.76698	−	2.43204i	0.385588	−	0.530716i
$22$	−1.01165	−	1.98547i	−0.215684	−	0.423304i
$23$	−1.82777	+	0.931295i	−0.381116	+	0.194188i	−0.634044	−	0.773297i	$-0.718606\pi$
$23$	−1.82777	+	0.931295i	−0.381116	+	0.194188i	0.252928	+	0.967485i	$0.418606\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	0.190487	−	4.99637i	0.0380974	−	0.999274i
$26$			6.96261i			1.36548i
$27$	−0.891007	−	0.453990i	−0.171474	−	0.0873705i
$28$	0.470269	−	2.96916i	0.0888725	−	0.561119i
$29$	−6.04997	−	4.39556i	−1.12345	−	0.816235i	−0.138723	−	0.990331i	$-0.544300\pi$
$29$	−6.04997	−	4.39556i	−1.12345	−	0.816235i	−0.984729	+	0.174096i	$0.944300\pi$
$30$	1.55073	+	1.61098i	0.283123	+	0.294123i
$31$	−5.47453	−	1.01466i	−0.983254	−	0.182238i
$31$	−5.47453	−	1.01466i	−0.983254	−	0.182238i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.20091	+	0.348590i	−0.383130	+	0.0606818i
$34$	−1.63428	+	1.18737i	−0.280277	+	0.203633i
$35$	1.95504	+	6.43142i	0.330462	+	1.08711i
$36$	−1.00000			−0.166667
$37$	−3.18538	+	3.18538i	−0.523673	+	0.523673i	−0.918679	−	0.395006i	$-0.870743\pi$
$37$	−3.18538	+	3.18538i	−0.523673	+	0.523673i	0.395006	+	0.918679i	$0.370743\pi$
$38$	1.71890	+	0.875822i	0.278842	+	0.142077i
$39$	6.62183	+	2.15156i	1.06034	+	0.344526i
$40$	2.11308	+	0.731374i	0.334107	+	0.115640i
$41$	3.47851	+	2.52729i	0.543252	+	0.394696i	0.825291	−	0.564707i	$-0.191011\pi$
$41$	3.47851	+	2.52729i	0.543252	+	0.394696i	−0.282039	+	0.959403i	$0.591011\pi$
$42$	−2.67852	−	1.36477i	−0.413305	−	0.210589i
$43$	−0.712853	−	4.50078i	−0.108709	−	0.686362i	−0.980505	−	0.196493i	$-0.937045\pi$
$43$	−0.712853	−	4.50078i	−0.108709	−	0.686362i	0.871796	−	0.489869i	$-0.162955\pi$
$44$	−1.80277	+	1.30979i	−0.271778	+	0.197458i
$45$	2.01133	−	0.977011i	0.299831	−	0.145644i
$46$	1.20575	+	1.65958i	0.177779	+	0.244692i
$47$	−5.31061	−	0.841118i	−0.774633	−	0.122690i	−0.243412	−	0.969923i	$-0.578267\pi$
$47$	−5.31061	−	0.841118i	−0.774633	−	0.122690i	−0.531221	+	0.847233i	$0.678267\pi$
$48$	−0.891007	+	0.453990i	−0.128606	+	0.0655279i
$49$	−1.19736	−	1.64803i	−0.171052	−	0.235433i
$50$	−4.96466	+	0.593463i	−0.702108	+	0.0839283i
$51$	0.624239	+	1.92121i	0.0874109	+	0.269023i
$52$	6.87689	−	1.08919i	0.953653	−	0.151044i
$53$	−7.30852	+	3.72388i	−1.00390	+	0.511514i	−0.877045	−	0.480407i	$-0.840489\pi$
$53$	−7.30852	+	3.72388i	−1.00390	+	0.511514i	−0.126857	+	0.991921i	$0.540489\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	2.34629	−	4.39575i	0.316374	−	0.592723i
$56$	−3.00617			−0.401717
$57$	1.36413	−	1.36413i	0.180683	−	0.180683i
$58$	−3.39502	+	6.66310i	−0.445788	+	0.874909i
$59$	0.288245	+	0.396735i	0.0375263	+	0.0516505i	0.827368	−	0.561660i	$-0.189837\pi$
$59$	0.288245	+	0.396735i	0.0375263	+	0.0516505i	−0.789842	+	0.613311i	$0.789837\pi$
$60$	1.34855	−	1.78365i	0.174098	−	0.230268i
$61$		−	4.20268i		−	0.538098i	−0.963127	−	0.269049i	$-0.913291\pi$
$61$		−	4.20268i		−	0.538098i	0.963127	−	0.269049i	$-0.0867093\pi$
$62$	−0.145760	+	5.56586i	−0.0185116	+	0.706864i
$63$	−2.12569	+	2.12569i	−0.267811	+	0.267811i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−12.7675	+	8.90952i	−1.58362	+	1.10509i
$66$	0.688597	+	2.11928i	0.0847605	+	0.260866i
$67$	10.6362	+	10.6362i	1.29942	+	1.29942i	0.928777	+	0.370639i	$0.120861\pi$
$67$	10.6362	+	10.6362i	1.29942	+	1.29942i	0.370639	+	0.928777i	$0.379139\pi$
$68$	1.42841	+	1.42841i	0.173220	+	0.173220i
$69$	1.95095	−	0.633903i	0.234867	−	0.0763129i
$70$	6.04641	−	2.93706i	0.722684	−	0.351046i
$71$	−3.24666	+	9.99219i	−0.385308	+	1.18585i	0.550949	+	0.834539i	$0.314266\pi$
$71$	−3.24666	+	9.99219i	−0.385308	+	1.18585i	−0.936257	+	0.351316i	$0.885734\pi$
$72$	0.156434	+	0.987688i	0.0184360	+	0.116400i
$73$	−3.55590	+	6.97884i	−0.416186	+	0.816812i	0.583802	+	0.811896i	$0.301565\pi$
$73$	−3.55590	+	6.97884i	−0.416186	+	0.816812i	−0.999988	+	0.00491537i	$0.998435\pi$
$74$	3.64446	+	2.64786i	0.423660	+	0.307807i
$75$	−0.969746	+	4.90506i	−0.111977	+	0.566387i
$76$	0.596145	−	1.83474i	0.0683825	−	0.210460i
$77$	−1.04792	+	6.61633i	−0.119422	+	0.754000i
$78$	1.08919	−	6.87689i	0.123327	−	0.778654i
$79$	0.181602	−	0.558913i	0.0204318	−	0.0628826i	−0.940321	−	0.340289i	$-0.889475\pi$
$79$	0.181602	−	0.558913i	0.0204318	−	0.0628826i	0.960753	+	0.277407i	$0.0894750\pi$
$80$	0.391812	−	2.20147i	0.0438059	−	0.246132i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	1.95201	−	3.83104i	0.215564	−	0.423067i
$83$	−0.666589	−	4.20867i	−0.0731676	−	0.461962i	−0.996884	−	0.0788845i	$-0.974864\pi$
$83$	−0.666589	−	4.20867i	−0.0731676	−	0.461962i	0.923716	−	0.383078i	$-0.125136\pi$
$84$	−0.928958	+	2.85904i	−0.101358	+	0.311947i
$85$	−4.26858	−	1.47743i	−0.462993	−	0.160250i
$86$	−4.33385	+	1.40815i	−0.467331	+	0.151845i
$87$	5.28787	+	5.28787i	0.566919	+	0.566919i
$88$	1.57568	+	1.57568i	0.167968	+	0.167968i
$89$	−2.89504	−	8.91003i	−0.306874	−	0.944461i	−0.978971	−	0.203998i	$-0.934606\pi$
$89$	−2.89504	−	8.91003i	−0.306874	−	0.944461i	0.672097	−	0.740463i	$-0.265394\pi$
$90$	−1.27962	−	1.83373i	−0.134884	−	0.193292i
$91$	12.3028	−	16.9334i	1.28969	−	1.77510i
$92$	1.45053	−	1.45053i	0.151228	−	0.151228i
$93$	5.24840	+	1.85857i	0.544234	+	0.192725i
$94$			5.37681i			0.554576i
$95$	0.593521	+	4.27272i	0.0608940	+	0.438372i
$96$	0.587785	+	0.809017i	0.0599906	+	0.0825700i
$97$	−0.812745	+	1.59510i	−0.0825217	+	0.161958i	−0.928580	−	0.371133i	$-0.878970\pi$
$97$	−0.812745	+	1.59510i	−0.0825217	+	0.161958i	0.846058	+	0.533091i	$0.178970\pi$
$98$	−1.44043	+	1.44043i	−0.145505	+	0.145505i
$99$	2.22835			0.223957
$100$	1.36280	+	4.81069i	0.136280	+	0.481069i
$101$	−2.57514	+	7.92546i	−0.256236	+	0.788613i	0.737348	+	0.675513i	$0.236078\pi$
$101$	−2.57514	+	7.92546i	−0.256236	+	0.788613i	−0.993584	+	0.113099i	$0.963922\pi$
$102$	1.79990	−	0.917097i	0.178217	−	0.0908061i
$103$	−14.5866	+	2.31029i	−1.43726	+	0.227640i	−0.825947	−	0.563748i	$-0.809359\pi$
$103$	−14.5866	+	2.31029i	−1.43726	+	0.227640i	−0.611314	+	0.791388i	$0.709359\pi$
$104$	−2.15156	−	6.62183i	−0.210978	−	0.649324i
$105$	−0.924871	−	6.65808i	−0.0902581	−	0.649762i
$106$	4.82133	+	6.63600i	0.468289	+	0.644545i
$107$	9.51922	−	4.85029i	0.920258	−	0.468895i	0.0713595	−	0.997451i	$-0.477266\pi$
$107$	9.51922	−	4.85029i	0.920258	−	0.468895i	0.848899	+	0.528556i	$0.177266\pi$
$108$	0.987688	+	0.156434i	0.0950404	+	0.0150529i
$109$	−11.3689	−	15.6480i	−1.08894	−	1.49880i	−0.849277	−	0.527947i	$-0.822962\pi$
$109$	−11.3689	−	15.6480i	−1.08894	−	1.49880i	−0.239667	−	0.970855i	$-0.577038\pi$
$110$	−4.70867	−	1.62976i	−0.448954	−	0.155391i
$111$	3.64446	−	2.64786i	0.345917	−	0.251324i
$112$	0.470269	+	2.96916i	0.0444362	+	0.280559i
$113$	−1.82214	−	0.928429i	−0.171413	−	0.0873392i	0.366179	−	0.930544i	$-0.380666\pi$
$113$	−1.82214	−	0.928429i	−0.171413	−	0.0873392i	−0.537592	+	0.843205i	$0.680666\pi$
$114$	−1.56073	−	1.13393i	−0.146175	−	0.106203i
$115$	−1.50031	+	4.33466i	−0.139904	+	0.404210i
$116$	7.11217	+	2.31088i	0.660348	+	0.214560i
$117$	−6.20373	−	3.16096i	−0.573535	−	0.292231i
$118$	0.346759	−	0.346759i	0.0319218	−	0.0319218i
$119$	6.07271			0.556684
$120$	−1.97265	−	1.05293i	−0.180077	−	0.0961187i
$121$	−4.88198	+	3.54697i	−0.443817	+	0.322452i
$122$	−4.15094	+	0.657444i	−0.375808	+	0.0595221i
$123$	−3.04033	−	3.04033i	−0.274137	−	0.274137i
$124$	5.52013	−	0.726726i	0.495723	−	0.0652619i
$125$	−7.44114	−	8.34443i	−0.665556	−	0.746348i
$126$	2.43204	+	1.76698i	0.216664	+	0.157415i
$127$	0.297204	−	1.87647i	0.0263726	−	0.166510i	−0.970987	−	0.239133i	$-0.923137\pi$
$127$	0.297204	−	1.87647i	0.0263726	−	0.166510i	0.997359	+	0.0726228i	$0.0231369\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$			4.55688i			0.401211i
$130$	10.7971	+	11.2166i	0.946969	+	0.983760i
$131$	2.69612	+	8.29781i	0.235561	+	0.724983i	0.997046	+	0.0768008i	$0.0244705\pi$
$131$	2.69612	+	8.29781i	0.235561	+	0.724983i	−0.761485	+	0.648182i	$0.775529\pi$
$132$	1.98547	−	1.01165i	0.172813	−	0.0880527i
$133$	−2.63287	−	5.16731i	−0.228299	−	0.448062i
$134$	8.84136	−	12.1691i	0.763778	−	1.05125i
$135$	−2.13941	+	0.650341i	−0.184131	+	0.0559724i
$136$	1.18737	−	1.63428i	0.101816	−	0.140138i
$137$	0.115563	−	0.729639i	0.00987325	−	0.0623373i	−0.982260	−	0.187525i	$-0.939953\pi$
$137$	0.115563	−	0.729639i	0.00987325	−	0.0623373i	0.992133	+	0.125188i	$0.0399534\pi$
$138$	−0.931295	−	1.82777i	−0.0792771	−	0.155590i
$139$	10.8138	−	7.85667i	0.917213	−	0.666394i	−0.0256159	−	0.999672i	$-0.508155\pi$
$139$	10.8138	−	7.85667i	0.917213	−	0.666394i	0.942829	+	0.333278i	$0.108155\pi$
$140$	−3.84677	−	5.51251i	−0.325111	−	0.465892i
$141$	5.11365	+	1.66153i	0.430647	+	0.139926i
$142$	10.3771	+	1.64356i	0.870824	+	0.137925i
$143$	−15.3241	+	2.42710i	−1.28147	+	0.202964i
$144$	0.951057	−	0.309017i	0.0792547	−	0.0257514i
$145$	−16.5627	+	2.30072i	−1.37546	+	0.191064i
$146$	7.44919	+	2.42039i	0.616499	+	0.200313i
$147$	0.924812	+	1.81505i	0.0762772	+	0.149703i
$148$	2.04514	−	4.01381i	0.168109	−	0.329933i
$149$		−	13.6539i		−	1.11857i	−0.828974	−	0.559287i	$-0.811075\pi$
$149$		−	13.6539i		−	1.11857i	0.828974	−	0.559287i	$-0.188925\pi$
$150$	4.99637	+	0.190487i	0.407952	+	0.0155532i
$151$	21.3385	−	6.93329i	1.73650	−	0.564223i	0.742137	−	0.670248i	$-0.233812\pi$
$151$	21.3385	−	6.93329i	1.73650	−	0.564223i	0.994363	+	0.106025i	$0.0338123\pi$
$152$	−1.90541	−	0.301788i	−0.154549	−	0.0244782i
$153$	−0.316010	−	1.99521i	−0.0255479	−	0.161303i
$154$	6.69880			0.539805
$155$	−10.3928	+	6.85492i	−0.834769	+	0.550600i
$156$	−6.96261			−0.557455
$157$	−3.58586	−	22.6402i	−0.286183	−	1.80689i	−0.542238	−	0.840225i	$-0.682423\pi$
$157$	−3.58586	−	22.6402i	−0.286183	−	1.80689i	0.256056	−	0.966662i	$-0.417577\pi$
$158$	−0.580440	−	0.0919327i	−0.0461773	−	0.00731377i
$159$	7.80108	−	2.53472i	0.618666	−	0.201017i
$160$	−2.23566	−	0.0426019i	−0.176745	−	0.00336798i
$161$		−	6.16672i		−	0.486006i
$162$	0.453990	−	0.891007i	0.0356689	−	0.0700041i
$163$	−3.82578	−	7.50851i	−0.299658	−	0.588112i	0.691256	−	0.722610i	$-0.257058\pi$
$163$	−3.82578	−	7.50851i	−0.299658	−	0.588112i	−0.990914	+	0.134498i	$0.957058\pi$
$164$	−4.08923	−	1.32867i	−0.319316	−	0.103752i
$165$	−3.00505	+	3.97459i	−0.233943	+	0.309421i
$166$	−4.05258	+	1.31676i	−0.314541	+	0.102201i
$167$	3.80739	−	0.603031i	0.294625	−	0.0466640i	−0.00737235	−	0.999973i	$-0.502347\pi$
$167$	3.80739	−	0.603031i	0.294625	−	0.0466640i	0.301997	+	0.953309i	$0.402347\pi$
$168$	2.96916	+	0.470269i	0.229076	+	0.0362820i
$169$	33.7415	+	10.9633i	2.59550	+	0.843329i
$170$	−0.791492	+	4.44715i	−0.0607046	+	0.341081i
$171$	−1.56073	+	1.13393i	−0.119352	+	0.0867141i
$172$	2.06878	+	4.06021i	0.157743	+	0.309588i
$173$	0.116294	−	0.734250i	0.00884165	−	0.0558240i	−0.982873	−	0.184284i	$-0.941003\pi$
$173$	0.116294	−	0.734250i	0.00884165	−	0.0558240i	0.991715	+	0.128460i	$0.0410034\pi$
$174$	4.39556	−	6.04997i	0.333227	−	0.458647i
$175$	13.1229	+	7.32914i	0.991998	+	0.554031i
$176$	1.30979	−	1.80277i	0.0987291	−	0.135889i
$177$	−0.222633	−	0.436942i	−0.0167341	−	0.0328426i
$178$	−8.34744	+	4.25324i	−0.625667	+	0.318793i
$179$	5.41589	+	16.6684i	0.404803	+	1.24585i	0.921060	+	0.389421i	$0.127325\pi$
$179$	5.41589	+	16.6684i	0.404803	+	1.24585i	−0.516257	+	0.856434i	$0.672675\pi$
$180$	−1.61098	+	1.55073i	−0.120075	+	0.115584i
$181$		−	1.59466i		−	0.118530i	−0.998242	−	0.0592652i	$-0.981124\pi$
$181$		−	1.59466i		−	0.118530i	0.998242	−	0.0592652i	$-0.0188758\pi$
$182$	−18.6495	−	9.50239i	−1.38239	−	0.704364i
$183$	−0.657444	+	4.15094i	−0.0485996	+	0.306846i
$184$	−1.65958	−	1.20575i	−0.122346	−	0.0888894i
$185$	−0.191913	+	10.0712i	−0.0141097	+	0.740451i
$186$	1.01466	−	5.47453i	0.0743983	−	0.401412i
$187$	−3.18300	−	3.18300i	−0.232764	−	0.232764i
$188$	5.31061	−	0.841118i	0.387316	−	0.0613449i
$189$	2.43204	−	1.76698i	0.176905	−	0.128529i
$190$	4.12727	−	1.25461i	0.299423	−	0.0910193i
$191$	10.5929			0.766472			0.383236	−	0.923650i	$-0.374810\pi$
$191$	10.5929			0.766472			0.383236	+	0.923650i	$0.374810\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	7.99514	+	4.07373i	0.575503	+	0.293233i	0.717415	−	0.696646i	$-0.245325\pi$
$193$	7.99514	+	4.07373i	0.575503	+	0.293233i	−0.141912	+	0.989879i	$0.545325\pi$
$194$	1.70260	+	0.553210i	0.122240	+	0.0397181i
$195$	14.0041	−	6.80254i	1.00285	−	0.487140i
$196$	1.64803	+	1.19736i	0.117716	+	0.0855259i
$197$	−2.30563	−	1.17478i	−0.164269	−	0.0836993i	0.369923	−	0.929062i	$-0.379384\pi$
$197$	−2.30563	−	1.17478i	−0.164269	−	0.0836993i	−0.534192	+	0.845363i	$0.679384\pi$
$198$	−0.348590	−	2.20091i	−0.0247732	−	0.156412i
$199$	10.1054	−	7.34197i	0.716349	−	0.520458i	−0.168866	−	0.985639i	$-0.554011\pi$
$199$	10.1054	−	7.34197i	0.716349	−	0.520458i	0.885216	+	0.465181i	$0.154011\pi$
$200$	4.53828	−	2.09858i	0.320905	−	0.148392i
$201$	−8.84136	−	12.1691i	−0.623622	−	0.858342i
$202$	8.23072	+	1.30362i	0.579112	+	0.0917223i
$203$	20.0304	−	10.2060i	1.40586	−	0.716322i
$204$	−1.18737	−	1.63428i	−0.0831328	−	0.114422i
$205$	9.52293	−	1.32283i	0.665110	−	0.0923902i
$206$	4.56370	+	14.0456i	0.317968	+	0.978604i
$207$	−2.02610	+	0.320902i	−0.140823	+	0.0223042i
$208$	−6.20373	+	3.16096i	−0.430151	+	0.219173i
$209$	−1.32842	+	4.08845i	−0.0918886	+	0.282804i
$210$	−6.43142	+	1.95504i	−0.443810	+	0.134910i
$211$	4.30010			0.296031			0.148016	−	0.988985i	$-0.452711\pi$
$211$	4.30010			0.296031			0.148016	+	0.988985i	$0.452711\pi$
$212$	5.80007	−	5.80007i	0.398351	−	0.398351i
$213$	4.76981	−	9.36128i	0.326822	−	0.641424i
$214$	−6.27971	−	8.64327i	−0.429272	−	0.590842i
$215$	−8.12787	−	6.14520i	−0.554316	−	0.419099i
$216$		−	1.00000i		−	0.0680414i
$217$	10.1893	−	13.2789i	0.691693	−	0.901427i
$218$	−13.6768	+	13.6768i	−0.926311	+	0.926311i
$219$	4.60385	−	6.33666i	0.311099	−	0.428192i
$220$	−0.873094	+	4.90565i	−0.0588640	+	0.330739i
$221$	4.34633	+	13.3766i	0.292366	+	0.899810i
$222$	−3.18538	−	3.18538i	−0.213789	−	0.213789i
$223$	−4.36783	−	4.36783i	−0.292491	−	0.292491i	0.545572	−	0.838064i	$-0.316312\pi$
$223$	−4.36783	−	4.36783i	−0.292491	−	0.292491i	−0.838064	+	0.545572i	$0.816312\pi$
$224$	2.85904	−	0.928958i	0.191028	−	0.0620686i
$225$	1.72513	−	4.69297i	0.115008	−	0.312864i
$226$	−0.631952	+	1.94495i	−0.0420368	+	0.129376i
$227$	−3.97850	−	25.1193i	−0.264062	−	1.66722i	−0.661766	−	0.749710i	$-0.730193\pi$
$227$	−3.97850	−	25.1193i	−0.264062	−	1.66722i	0.397704	−	0.917514i	$-0.369807\pi$
$228$	−0.875822	+	1.71890i	−0.0580028	+	0.113837i
$229$	−20.4482	−	14.8565i	−1.35126	−	0.981745i	−0.998948	−	0.0458615i	$-0.985397\pi$
$229$	−20.4482	−	14.8565i	−1.35126	−	0.981745i	−0.352309	−	0.935884i	$-0.614603\pi$
$230$	4.51600	+	0.803745i	0.297776	+	0.0529973i
$231$	2.07004	−	6.37094i	0.136199	−	0.419177i
$232$	1.16984	−	7.38611i	0.0768041	−	0.484922i
$233$	−0.602923	+	3.80671i	−0.0394988	+	0.249386i	−0.999535	−	0.0304900i	$-0.990293\pi$
$233$	−0.602923	+	3.80671i	−0.0394988	+	0.249386i	0.960036	+	0.279876i	$0.0902932\pi$
$234$	−2.15156	+	6.62183i	−0.140652	+	0.432883i
$235$	−9.85962	+	6.88029i	−0.643170	+	0.448821i
$236$	−0.396735	−	0.288245i	−0.0258253	−	0.0187632i
$237$	−0.266799	+	0.523623i	−0.0173305	+	0.0340129i
$238$	−0.949981	−	5.99794i	−0.0615781	−	0.388789i
$239$	−5.00801	+	15.4131i	−0.323941	+	0.996988i	0.647975	+	0.761661i	$0.275616\pi$
$239$	−5.00801	+	15.4131i	−0.323941	+	0.996988i	−0.971916	+	0.235327i	$0.924384\pi$
$240$	−0.731374	+	2.11308i	−0.0472100	+	0.136398i
$241$	−14.5541	+	4.72890i	−0.937510	+	0.304615i	−0.737630	−	0.675205i	$-0.764055\pi$
$241$	−14.5541	+	4.72890i	−0.937510	+	0.304615i	−0.199880	+	0.979820i	$0.564055\pi$
$242$	4.26701	+	4.26701i	0.274294	+	0.274294i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	1.29870	+	3.99698i	0.0831407	+	0.255881i
$245$	−4.48456	−	0.798150i	−0.286508	−	0.0509919i
$246$	−2.52729	+	3.47851i	−0.161134	+	0.221782i
$247$	9.49787	−	9.49787i	0.604335	−	0.604335i
$248$	−1.58132	−	5.33849i	−0.100414	−	0.338994i
$249$			4.26114i			0.270039i
$250$	−7.07764	+	8.65488i	−0.447629	+	0.547383i
$251$	−3.71172	−	5.10874i	−0.234282	−	0.322461i	0.675647	−	0.737225i	$-0.263864\pi$
$251$	−3.71172	−	5.10874i	−0.234282	−	0.322461i	−0.909929	+	0.414764i	$0.863864\pi$
$252$	1.36477	−	2.67852i	0.0859727	−	0.168731i
$253$	−3.23228	+	3.23228i	−0.203211	+	0.203211i
$254$	−1.89986			−0.119208
$255$	3.98491	+	2.12700i	0.249545	+	0.133198i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−7.05825	+	3.59636i	−0.440282	+	0.224335i	−0.660057	−	0.751216i	$-0.729468\pi$
$257$	−7.05825	+	3.59636i	−0.440282	+	0.224335i	0.219775	+	0.975551i	$0.429468\pi$
$258$	4.50078	−	0.712853i	0.280206	−	0.0443803i
$259$	−4.18478	−	12.8794i	−0.260029	−	0.800288i
$260$	9.38946	−	12.4188i	0.582310	−	0.770184i
$261$	−4.39556	−	6.04997i	−0.272078	−	0.374484i
$262$	7.77388	−	3.96099i	0.480272	−	0.244711i
$263$	4.41598	+	0.699422i	0.272301	+	0.0431282i	0.291091	−	0.956695i	$-0.405982\pi$
$263$	4.41598	+	0.699422i	0.272301	+	0.0431282i	−0.0187907	+	0.999823i	$0.505982\pi$
$264$	−1.30979	−	1.80277i	−0.0806120	−	0.110953i
$265$	−5.99913	+	17.3326i	−0.368524	+	1.06473i
$266$	−4.69182	+	3.40880i	−0.287674	+	0.209007i
$267$	1.46556	+	9.25321i	0.0896911	+	0.566287i
$268$	−13.4024	−	6.82885i	−0.818680	−	0.417138i
$269$	23.0503	+	16.7470i	1.40540	+	1.02108i	0.993971	+	0.109640i	$0.0349697\pi$
$269$	23.0503	+	16.7470i	1.40540	+	1.02108i	0.411428	+	0.911442i	$0.365030\pi$
$270$	0.977011	+	2.01133i	0.0594590	+	0.122406i
$271$	−15.7139	−	5.10575i	−0.954551	−	0.310152i	−0.209987	−	0.977704i	$-0.567342\pi$
$271$	−15.7139	−	5.10575i	−0.954551	−	0.310152i	−0.744563	+	0.667552i	$0.767342\pi$
$272$	−1.79990	−	0.917097i	−0.109135	−	0.0556072i
$273$	−14.8003	+	14.8003i	−0.895756	+	0.895756i
$274$	−0.738734			−0.0446285
$275$	−3.03679	−	10.7199i	−0.183125	−	0.646434i
$276$	−1.65958	+	1.20575i	−0.0998949	+	0.0725779i
$277$	−2.00998	+	0.318350i	−0.120768	+	0.0191278i	−0.216526	−	0.976277i	$-0.569473\pi$
$277$	−2.00998	+	0.318350i	−0.120768	+	0.0191278i	0.0957578	+	0.995405i	$0.469473\pi$
$278$	−9.45159	−	9.45159i	−0.566869	−	0.566869i
$279$	−4.89304	−	2.65672i	−0.292939	−	0.159054i
$280$	−4.84287	+	4.66176i	−0.289417	+	0.278593i
$281$	−22.3993	−	16.2741i	−1.33623	−	0.970829i	−0.999574	−	0.0292025i	$-0.990703\pi$
$281$	−22.3993	−	16.2741i	−1.33623	−	0.970829i	−0.336658	−	0.941627i	$-0.609297\pi$
$282$	0.841118	−	5.31061i	0.0500879	−	0.316242i
$283$	−10.7402	−	5.47241i	−0.638439	−	0.325301i	0.104635	−	0.994511i	$-0.466633\pi$
$283$	−10.7402	−	5.47241i	−0.638439	−	0.325301i	−0.743073	+	0.669210i	$0.766633\pi$
$284$		−	10.5064i		−	0.623441i
$285$	0.0821861	−	4.31296i	0.00486828	−	0.255478i
$286$	4.79443	+	14.7558i	0.283501	+	0.872526i
$287$	−11.5168	+	5.86808i	−0.679813	+	0.346382i
$288$	−0.453990	−	0.891007i	−0.0267516	−	0.0525031i
$289$	7.59376	−	10.4519i	0.446692	−	0.614819i
$290$	4.86336	+	15.9989i	0.285587	+	0.939485i
$291$	1.05227	−	1.44832i	0.0616850	−	0.0849021i
$292$	1.22528	−	7.73611i	0.0717040	−	0.452721i
$293$	12.5964	+	24.7219i	0.735892	+	1.44427i	0.889879	+	0.456197i	$0.150789\pi$
$293$	12.5964	+	24.7219i	0.735892	+	1.44427i	−0.153987	+	0.988073i	$0.549211\pi$
$294$	1.64803	−	1.19736i	0.0961149	−	0.0698316i
$295$	1.07958	+	0.192141i	0.0628558	+	0.0111869i
$296$	−4.28433	−	1.39206i	−0.249021	−	0.0809119i
$297$	−2.20091	−	0.348590i	−0.127710	−	0.0202273i
$298$	−13.4858	+	2.13594i	−0.781213	+	0.123732i
$299$	13.5837	−	4.41362i	0.785567	−	0.255246i
$300$	−0.593463	−	4.96466i	−0.0342636	−	0.286635i
$301$	13.0283	+	4.23315i	0.750939	+	0.243995i
$302$	−10.1860	−	19.9912i	−0.586139	−	1.15036i
$303$	3.78325	−	7.42504i	0.217342	−	0.426558i
$304$			1.92916i			0.110645i
$305$	−6.51721	−	6.77041i	−0.373174	−	0.387673i
$306$	−1.92121	+	0.624239i	−0.109828	+	0.0356854i
$307$	−26.1311	−	4.13876i	−1.49138	−	0.236211i	−0.643109	−	0.765775i	$-0.722356\pi$
$307$	−26.1311	−	4.13876i	−1.49138	−	0.236211i	−0.848270	+	0.529564i	$0.822356\pi$
$308$	−1.04792	−	6.61633i	−0.0597110	−	0.377000i
$309$	14.7684			0.840147
$310$	8.39631	+	9.19249i	0.476878	+	0.522099i
$311$	−13.4437			−0.762319			−0.381160	−	0.924509i	$-0.624475\pi$
$311$	−13.4437			−0.762319			−0.381160	+	0.924509i	$0.624475\pi$
$312$	1.08919	+	6.87689i	0.0616634	+	0.389327i
$313$	29.9624	+	4.74558i	1.69358	+	0.268236i	0.927312	−	0.374290i	$-0.122113\pi$
$313$	29.9624	+	4.74558i	1.69358	+	0.268236i	0.766264	+	0.642526i	$0.222113\pi$
$314$	−21.8005	+	7.08342i	−1.23028	+	0.399741i
$315$	−0.128069	+	6.72079i	−0.00721585	+	0.378673i
$316$			0.587675i			0.0330593i
$317$	7.53056	−	14.7796i	0.422958	−	0.830102i	−0.576953	−	0.816777i	$-0.695758\pi$
$317$	7.53056	−	14.7796i	0.422958	−	0.830102i	0.999911	−	0.0133250i	$-0.00424161\pi$
$318$	−3.72388	−	7.30852i	−0.208825	−	0.409841i
$319$	−15.8484	−	5.14945i	−0.887339	−	0.288314i
$320$	0.307657	+	2.21480i	0.0171986	+	0.123811i
$321$	−10.1608	+	3.30144i	−0.567119	+	0.184268i
$322$	−6.09080	+	0.964688i	−0.339427	+	0.0537599i
$323$	3.84909	+	0.609636i	0.214169	+	0.0339210i
$324$	−0.951057	−	0.309017i	−0.0528365	−	0.0171676i
$325$	−6.75196	+	34.1520i	−0.374532	+	1.89441i
$326$	−6.81758	+	4.95327i	−0.377591	+	0.274336i
$327$	8.78106	+	17.2338i	0.485594	+	0.953031i
$328$	−0.672617	+	4.24674i	−0.0371391	+	0.234487i
$329$	9.50074	−	13.0766i	0.523793	−	0.720939i
$330$	4.39575	+	2.34629i	0.241978	+	0.129159i
$331$	−1.83098	+	2.52013i	−0.100640	+	0.138519i	−0.856367	−	0.516368i	$-0.827284\pi$
$331$	−1.83098	+	2.52013i	−0.100640	+	0.138519i	0.755727	+	0.654887i	$0.227284\pi$
$332$	1.93452	+	3.79670i	0.106170	+	0.208371i
$333$	−4.01381	+	2.04514i	−0.219956	+	0.112073i
$334$	−1.19121	−	3.66618i	−0.0651803	−	0.200604i
$335$	33.6284	+	0.640810i	1.83732	+	0.0350112i
$336$		−	3.00617i		−	0.164000i
$337$	1.62211	+	0.826507i	0.0883620	+	0.0450227i	0.497613	−	0.867399i	$-0.334210\pi$
$337$	1.62211	+	0.826507i	0.0883620	+	0.0450227i	−0.409251	+	0.912422i	$0.634210\pi$
$338$	5.54997	−	35.0411i	0.301879	−	1.90599i
$339$	1.65447	+	1.20204i	0.0898586	+	0.0652861i
$340$	4.51622	+	0.0860592i	0.244926	+	0.00466722i
$341$	−12.3008	+	1.61940i	−0.666124	+	0.0876953i
$342$	1.36413	+	1.36413i	0.0737635	+	0.0737635i
$343$	−14.7357	+	2.33391i	−0.795655	+	0.126019i
$344$	3.68659	−	2.67847i	0.198768	−	0.144413i
$345$	2.15993	−	4.04660i	0.116287	−	0.217862i
$346$	−0.743402			−0.0399655
$347$	9.12468	−	9.12468i	0.489838	−	0.489838i	−0.418417	−	0.908255i	$-0.637415\pi$
$347$	9.12468	−	9.12468i	0.489838	−	0.489838i	0.908255	+	0.418417i	$0.137415\pi$
$348$	−6.66310	−	3.39502i	−0.357180	−	0.181992i
$349$	16.2293	+	5.27322i	0.868734	+	0.282269i	0.709272	−	0.704935i	$-0.249024\pi$
$349$	16.2293	+	5.27322i	0.868734	+	0.282269i	0.159462	+	0.987204i	$0.449024\pi$
$350$	5.18603	−	14.1079i	0.277205	−	0.754097i
$351$	5.63287	+	4.09252i	0.300660	+	0.218442i
$352$	−1.98547	−	1.01165i	−0.105826	−	0.0539211i
$353$	−1.35583	−	8.56038i	−0.0721636	−	0.455623i	−0.997139	−	0.0755951i	$-0.975914\pi$
$353$	−1.35583	−	8.56038i	−0.0721636	−	0.455623i	0.924975	−	0.380028i	$-0.124086\pi$
$354$	−0.396735	+	0.288245i	−0.0210862	+	0.0153200i
$355$	10.2649	+	21.1319i	0.544803	+	1.12156i
$356$	5.50670	+	7.57932i	0.291854	+	0.401703i
$357$	−5.99794	−	0.949981i	−0.317445	−	0.0502783i
$358$	15.6159	−	7.95672i	0.825329	−	0.420526i
$359$	15.1780	+	20.8907i	0.801064	+	1.10257i	0.992641	+	0.121092i	$0.0386396\pi$
$359$	15.1780	+	20.8907i	0.801064	+	1.10257i	−0.191578	+	0.981477i	$0.561360\pi$
$360$	1.78365	+	1.34855i	0.0940065	+	0.0710751i
$361$	4.72126	+	14.5305i	0.248487	+	0.764766i
$362$	−1.57503	+	0.249461i	−0.0827818	+	0.0131114i
$363$	5.37675	−	2.73959i	0.282206	−	0.143791i
$364$	−6.46797	+	19.9064i	−0.339014	+	1.04338i
$365$	5.09382	+	16.7570i	0.266623	+	0.877100i
$366$	4.20268			0.219677
$367$	−22.8697	+	22.8697i	−1.19379	+	1.19379i	−0.217795	+	0.975994i	$0.569887\pi$
$367$	−22.8697	+	22.8697i	−1.19379	+	1.19379i	−0.975994	+	0.217795i	$0.930113\pi$
$368$	−0.931295	+	1.82777i	−0.0485471	+	0.0952790i
$369$	2.52729	+	3.47851i	0.131565	+	0.181084i
$370$	9.97725	−	1.38594i	0.518693	−	0.0720514i
$371$		−	24.6583i		−	1.28019i
$372$	−5.56586	−	0.145760i	−0.288576	−	0.00755732i
$373$	8.97098	−	8.97098i	0.464500	−	0.464500i	−0.435627	−	0.900127i	$-0.643473\pi$
$373$	8.97098	−	8.97098i	0.464500	−	0.464500i	0.900127	+	0.435627i	$0.143473\pi$
$374$	−2.64588	+	3.64174i	−0.136815	+	0.188310i
$375$	6.04417	+	9.40574i	0.312120	+	0.485710i
$376$	−1.66153	−	5.11365i	−0.0856867	−	0.263716i
$377$	36.8174	+	36.8174i	1.89619	+	1.89619i
$378$	−2.12569	−	2.12569i	−0.109333	−	0.109333i
$379$	−32.7344	+	10.6361i	−1.68145	+	0.546338i	−0.985193	−	0.171450i	$-0.945155\pi$
$379$	−32.7344	+	10.6361i	−1.68145	+	0.546338i	−0.696262	+	0.717788i	$0.745155\pi$
$380$	−1.88481	−	3.88019i	−0.0966890	−	0.199049i
$381$	−0.587089	+	1.80688i	−0.0300775	+	0.0925690i
$382$	−1.65709	−	10.4624i	−0.0847840	−	0.535305i
$383$	11.9674	−	23.4874i	0.611507	−	1.20015i	−0.352884	−	0.935667i	$-0.614799\pi$
$383$	11.9674	−	23.4874i	0.611507	−	1.20015i	0.964390	−	0.264482i	$-0.0852011\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	8.57194	+	12.2838i	0.436867	+	0.626040i
$386$	2.77286	−	8.53398i	0.141135	−	0.434368i
$387$	0.712853	−	4.50078i	0.0362364	−	0.228787i
$388$	0.280053	−	1.76818i	0.0142175	−	0.0897659i
$389$	4.17119	−	12.8376i	0.211488	−	0.650893i	−0.787896	−	0.615808i	$-0.788830\pi$
$389$	4.17119	−	12.8376i	0.211488	−	0.650893i	0.999384	−	0.0350850i	$-0.0111702\pi$
$390$	−8.90952	−	12.7675i	−0.451151	−	0.646510i
$391$	3.35248	+	2.43572i	0.169542	+	0.123180i
$392$	0.924812	−	1.81505i	0.0467101	−	0.0916737i
$393$	−1.36486	−	8.61742i	−0.0688483	−	0.434691i
$394$	−0.799633	+	2.46102i	−0.0402849	+	0.123984i
$395$	−0.574165	−	1.18201i	−0.0288894	−	0.0594733i
$396$	−2.11928	+	0.688597i	−0.106498	+	0.0346033i
$397$	14.8683	+	14.8683i	0.746221	+	0.746221i	0.973767	−	0.227547i	$-0.0730704\pi$
$397$	14.8683	+	14.8683i	0.746221	+	0.746221i	−0.227547	+	0.973767i	$0.573070\pi$
$398$	−8.83240	−	8.83240i	−0.442728	−	0.442728i
$399$	1.79211	+	5.51556i	0.0897179	+	0.276123i
$400$	−2.78269	−	4.15411i	−0.139134	−	0.207706i
$401$	−17.3675	+	23.9043i	−0.867291	+	1.19372i	0.112490	+	0.993653i	$0.464117\pi$
$401$	−17.3675	+	23.9043i	−0.867291	+	1.19372i	−0.979781	+	0.200071i	$0.935883\pi$
$402$	−10.6362	+	10.6362i	−0.530484	+	0.530484i
$403$	36.5426	+	12.9405i	1.82031	+	0.644612i
$404$		−	8.33332i		−	0.414598i
$405$	2.21480	−	0.307657i	0.110054	−	0.0152876i
$406$	−13.2138	−	18.1873i	−0.655791	−	0.902619i
$407$	−4.55728	+	8.94417i	−0.225896	+	0.443346i
$408$	−1.42841	+	1.42841i	−0.0707169	+	0.0707169i
$409$	−10.0425			−0.496569			−0.248284	−	0.968687i	$-0.579867\pi$
$409$	−10.0425			−0.496569			−0.248284	+	0.968687i	$0.579867\pi$
$410$	−2.79625	−	9.19875i	−0.138097	−	0.454294i
$411$	−0.228281	+	0.702578i	−0.0112603	+	0.0346556i
$412$	13.1588	−	6.70473i	0.648286	−	0.330318i
$413$	−1.45605	+	0.230616i	−0.0716477	+	0.0113479i
$414$	0.633903	+	1.95095i	0.0311546	+	0.0958841i
$415$	−7.60037	−	5.74638i	−0.373087	−	0.282079i
$416$	4.09252	+	5.63287i	0.200652	+	0.276174i
$417$	−11.9097	+	6.06829i	−0.583220	+	0.297166i
$418$	4.24592	+	0.672488i	0.207675	+	0.0328925i
$419$	21.4850	+	29.5716i	1.04961	+	1.44467i	0.889145	+	0.457625i	$0.151300\pi$
$419$	21.4850	+	29.5716i	1.04961	+	1.44467i	0.160466	+	0.987041i	$0.448700\pi$
$420$	2.93706	+	6.04641i	0.143314	+	0.295034i
$421$	1.49234	−	1.08425i	0.0727320	−	0.0528429i	−0.550825	−	0.834621i	$-0.685687\pi$
$421$	1.49234	−	1.08425i	0.0727320	−	0.0528429i	0.623557	+	0.781778i	$0.285687\pi$
$422$	−0.672684	−	4.24716i	−0.0327457	−	0.206748i
$423$	−4.79077	−	2.44102i	−0.232935	−	0.118686i
$424$	−6.63600	−	4.82133i	−0.322272	−	0.234145i
$425$	−9.16768	+	4.23930i	−0.444698	+	0.205636i
$426$	−9.99219	−	3.24666i	−0.484123	−	0.157301i
$427$	11.2570	+	5.73570i	0.544762	+	0.277570i
$428$	−7.55450	+	7.55450i	−0.365160	+	0.365160i
$429$	15.5151			0.749077
$430$	−4.79807	+	8.98913i	−0.231383	+	0.433494i
$431$	−2.95138	+	2.14430i	−0.142163	+	0.103288i	−0.656594	−	0.754245i	$-0.728003\pi$
$431$	−2.95138	+	2.14430i	−0.142163	+	0.103288i	0.514431	+	0.857532i	$0.328003\pi$
$432$	−0.987688	+	0.156434i	−0.0475202	+	0.00752646i
$433$	2.89662	+	2.89662i	0.139203	+	0.139203i	0.773274	−	0.634072i	$-0.218618\pi$
$433$	2.89662	+	2.89662i	0.139203	+	0.139203i	−0.634072	+	0.773274i	$0.718618\pi$
$434$	−14.7093	−	7.98656i	−0.706070	−	0.383367i
$435$	16.7187	+	0.318585i	0.801599	+	0.0152750i
$436$	15.6480	+	11.3689i	0.749401	+	0.544472i
$437$	0.619073	−	3.90867i	0.0296143	−	0.186977i
$438$	−6.97884	−	3.55590i	−0.333462	−	0.169907i
$439$		−	24.2123i		−	1.15559i	−0.816182	−	0.577795i	$-0.803913\pi$
$439$		−	24.2123i		−	1.15559i	0.816182	−	0.577795i	$-0.196087\pi$
$440$	4.98183	+	0.0949319i	0.237500	+	0.00452570i
$441$	−0.629491	−	1.93737i	−0.0299757	−	0.0922558i
$442$	12.5320	−	6.38539i	0.596088	−	0.303722i
$443$	10.3757	+	20.3634i	0.492963	+	0.967494i	0.994734	+	0.102494i	$0.0326821\pi$
$443$	10.3757	+	20.3634i	0.492963	+	0.967494i	−0.501771	+	0.865001i	$0.667318\pi$
$444$	−2.64786	+	3.64446i	−0.125662	+	0.172959i
$445$	−18.4809	−	9.86441i	−0.876077	−	0.467618i
$446$	−3.63078	+	4.99733i	−0.171922	+	0.236631i
$447$	−2.13594	+	13.4858i	−0.101027	+	0.637858i
$448$	−1.36477	−	2.67852i	−0.0644795	−	0.126548i
$449$	−30.8155	+	22.3887i	−1.45427	+	1.05659i	−0.469462	+	0.882953i	$0.655552\pi$
$449$	−30.8155	+	22.3887i	−1.45427	+	1.05659i	−0.984810	+	0.173638i	$0.944448\pi$
$450$	−4.90506	−	0.969746i	−0.231227	−	0.0457143i
$451$	9.11224	+	2.96075i	0.429078	+	0.139416i
$452$	2.01986	+	0.319915i	0.0950063	+	0.0150475i
$453$	−22.1604	+	3.50986i	−1.04119	+	0.164908i
$454$	−24.1876	+	7.85904i	−1.13518	+	0.368843i
$455$	−6.43951	−	46.3576i	−0.301889	−	2.17328i
$456$	1.83474	+	0.596145i	0.0859198	+	0.0279170i
$457$	−12.0845	−	23.7172i	−0.565289	−	1.10944i	−0.979908	−	0.199448i	$-0.936085\pi$
$457$	−12.0845	−	23.7172i	−0.565289	−	1.10944i	0.414619	−	0.909995i	$-0.363915\pi$
$458$	−11.4748	+	22.5205i	−0.536182	+	1.05232i
$459$			2.02008i			0.0942893i
$460$	0.0873915	−	4.58613i	0.00407465	−	0.213829i
$461$	39.2709	−	12.7599i	1.82903	−	0.594287i	0.829676	−	0.558245i	$-0.188525\pi$
$461$	39.2709	−	12.7599i	1.82903	−	0.594287i	0.999350	−	0.0360417i	$-0.0114749\pi$
$462$	−6.61633	−	1.04792i	−0.307819	−	0.0487538i
$463$	3.01876	+	19.0597i	0.140294	+	0.885780i	0.952970	+	0.303065i	$0.0980098\pi$
$463$	3.01876	+	19.0597i	0.140294	+	0.885780i	−0.812676	+	0.582715i	$0.801990\pi$
$464$	−7.47818			−0.347166
$465$	11.3372	−	5.14473i	0.525749	−	0.238581i
$466$	3.85416			0.178540
$467$	2.66721	+	16.8401i	0.123424	+	0.779266i	0.969299	+	0.245886i	$0.0790788\pi$
$467$	2.66721	+	16.8401i	0.123424	+	0.779266i	−0.845875	+	0.533381i	$0.820921\pi$
$468$	6.87689	+	1.08919i	0.317884	+	0.0503479i
$469$	−43.0052	+	13.9732i	−1.98580	+	0.645224i
$470$	8.33797	+	8.66191i	0.384602	+	0.399544i
$471$			22.9224i			1.05621i
$472$	−0.222633	+	0.436942i	−0.0102475	+	0.0201119i
$473$	−4.60996	−	9.04756i	−0.211966	−	0.416007i
$474$	0.558913	+	0.181602i	0.0256717	+	0.00834124i
$475$	7.58197	+	5.96286i	0.347885	+	0.273595i
$476$	−5.77549	+	1.87657i	−0.264719	+	0.0860125i
$477$	−8.10155	+	1.28316i	−0.370945	+	0.0587519i
$478$	16.0067	+	2.53522i	0.732131	+	0.115958i
$479$	15.5553	+	5.05423i	0.710741	+	0.230934i	0.642004	−	0.766701i	$-0.278103\pi$
$479$	15.5553	+	5.05423i	0.710741	+	0.230934i	0.0687369	+	0.997635i	$0.478103\pi$
$480$	2.20147	+	0.391812i	0.100483	+	0.0178837i
$481$	25.3750	−	18.4360i	1.15700	−	0.840609i
$482$	6.94744	+	13.6351i	0.316447	+	0.621063i
$483$	−0.964688	+	6.09080i	−0.0438948	+	0.277141i
$484$	3.54697	−	4.88198i	0.161226	−	0.221908i
$485$	1.16426	+	3.83002i	0.0528661	+	0.173912i
$486$	−0.587785	+	0.809017i	−0.0266625	+	0.0366978i
$487$	6.76112	+	13.2695i	0.306376	+	0.601296i	0.991939	−	0.126717i	$-0.0404440\pi$
$487$	6.76112	+	13.2695i	0.306376	+	0.601296i	−0.685563	+	0.728013i	$0.740444\pi$
$488$	3.74461	−	1.90798i	0.169511	−	0.0863700i
$489$	2.60409	+	8.01455i	0.117761	+	0.362431i
$490$	−0.0867832	+	4.55421i	−0.00392047	+	0.205738i
$491$		−	8.41214i		−	0.379635i	−0.981819	−	0.189817i	$-0.939210\pi$
$491$		−	8.41214i		−	0.379635i	0.981819	−	0.189817i	$-0.0607896\pi$
$492$	3.83104	+	1.95201i	0.172717	+	0.0880035i
$493$	−2.36318	+	14.9205i	−0.106432	+	0.671987i
$494$	−10.8667	−	7.89514i	−0.488917	−	0.355219i
$495$	3.58982	−	3.45556i	0.161350	−	0.155316i
$496$	−5.02539	+	2.39697i	−0.225647	+	0.107627i
$497$	−22.3333	−	22.3333i	−1.00179	−	1.00179i
$498$	4.20867	−	0.666589i	0.188595	−	0.0298705i
$499$	4.17012	−	3.02977i	0.186680	−	0.135631i	−0.490520	−	0.871430i	$-0.663193\pi$
$499$	4.17012	−	3.02977i	0.186680	−	0.135631i	0.677200	+	0.735799i	$0.263193\pi$
$500$	9.65551	+	5.63658i	0.431808	+	0.252076i
$501$	−3.85485			−0.172222
$502$	−4.46521	+	4.46521i	−0.199292	+	0.199292i
$503$	12.7849	+	6.51423i	0.570050	+	0.290455i	0.715160	−	0.698960i	$-0.246354\pi$
$503$	12.7849	+	6.51423i	0.570050	+	0.290455i	−0.145110	+	0.989416i	$0.546354\pi$
$504$	−2.85904	−	0.928958i	−0.127352	−	0.0413791i
$505$	8.14174	+	16.7611i	0.362303	+	0.745857i
$506$	3.69812	+	2.68684i	0.164401	+	0.119445i
$507$	−31.6111	−	16.1066i	−1.40390	−	0.715321i
$508$	0.297204	+	1.87647i	0.0131863	+	0.0832549i
$509$	13.6749	−	9.93543i	0.606131	−	0.440380i	−0.241919	−	0.970297i	$-0.577777\pi$
$509$	13.6749	−	9.93543i	0.606131	−	0.440380i	0.848050	+	0.529916i	$0.177777\pi$
$510$	1.47743	−	4.26858i	0.0654219	−	0.189016i
$511$	−13.8400	−	19.0491i	−0.612244	−	0.842682i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	1.71890	−	0.875822i	0.0758912	−	0.0386685i
$514$	4.65623	+	6.40876i	0.205378	+	0.282678i
$515$	−19.9160	+	26.3417i	−0.877605	+	1.16075i
$516$	−1.40815	−	4.33385i	−0.0619905	−	0.190787i
$517$	−11.8339	+	1.87430i	−0.520454	+	0.0824318i
$518$	−12.0662	+	6.14804i	−0.530159	+	0.270129i
$519$	−0.229724	+	0.707017i	−0.0100838	+	0.0310346i
$520$	−13.7348	−	7.33112i	−0.602310	−	0.321491i
$521$	−27.9524			−1.22461			−0.612307	−	0.790620i	$-0.709759\pi$
$521$	−27.9524			−1.22461			−0.612307	+	0.790620i	$0.709759\pi$
$522$	−5.28787	+	5.28787i	−0.231444	+	0.231444i
$523$	−19.0391	+	37.3663i	−0.832521	+	1.63391i	−0.0606280	+	0.998160i	$0.519310\pi$
$523$	−19.0391	+	37.3663i	−0.832521	+	1.63391i	−0.771893	+	0.635753i	$0.780690\pi$
$524$	−5.12833	−	7.05854i	−0.224032	−	0.308354i
$525$	−11.8148	−	9.29178i	−0.515641	−	0.405526i
$526$		−	4.47102i		−	0.194946i
$527$	3.19439	+	10.7842i	0.139150	+	0.469766i
$528$	−1.57568	+	1.57568i	−0.0685727	+	0.0685727i
$529$	−11.0456	+	15.2030i	−0.480245	+	0.661000i
$530$	18.0577	+	3.21385i	0.784375	+	0.139601i
$531$	0.151539	+	0.466390i	0.00657625	+	0.0202396i
$532$	4.10080	+	4.10080i	0.177792	+	0.177792i
$533$	−21.1686	−	21.1686i	−0.916915	−	0.916915i
$534$	8.91003	−	2.89504i	0.385575	−	0.125281i
$535$	7.81377	−	22.5754i	0.337819	−	0.976021i
$536$	−4.64818	+	14.3056i	−0.200771	+	0.617909i
$537$	−2.74170	−	17.3104i	−0.118313	−	0.746999i
$538$	12.9350	−	25.3863i	0.557666	−	1.09448i
$539$	−3.67238	−	2.66814i	−0.158181	−	0.114925i
$540$	1.83373	−	1.27962i	0.0789111	−	0.0550662i
$541$	1.69658	−	5.22153i	0.0729416	−	0.224491i	−0.907939	−	0.419103i	$-0.862345\pi$
$541$	1.69658	−	5.22153i	0.0729416	−	0.224491i	0.980880	+	0.194612i	$0.0623447\pi$
$542$	−2.58470	+	16.3191i	−0.111022	+	0.700967i
$543$	−0.249461	+	1.57503i	−0.0107054	+	0.0675911i
$544$	−0.624239	+	1.92121i	−0.0267640	+	0.0823712i
$545$	−42.5808	−	7.57840i	−1.82396	−	0.324623i
$546$	16.9334	+	12.3028i	0.724682	+	0.526512i
$547$	12.9197	−	25.3564i	0.552408	−	1.08416i	−0.430932	−	0.902384i	$-0.641815\pi$
$547$	12.9197	−	25.3564i	0.552408	−	1.08416i	0.983340	−	0.181777i	$-0.0581849\pi$
$548$	0.115563	+	0.729639i	0.00493663	+	0.0311686i
$549$	1.29870	−	3.99698i	0.0554271	−	0.170587i
$550$	−10.1129	+	4.67637i	−0.431214	+	0.199401i
$551$	13.7205	−	4.45808i	0.584515	−	0.189920i
$552$	1.45053	+	1.45053i	0.0617385	+	0.0617385i
$553$	1.24921	+	1.24921i	0.0531219	+	0.0531219i
$554$	0.628861	+	1.93544i	0.0267178	+	0.0822288i
$555$	1.76504	−	9.91721i	0.0749217	−	0.420962i
$556$	−7.85667	+	10.8138i	−0.333197	+	0.458606i
$557$	28.3357	−	28.3357i	1.20062	−	1.20062i	0.226642	−	0.973978i	$-0.427225\pi$
$557$	28.3357	−	28.3357i	1.20062	−	1.20062i	0.973978	−	0.226642i	$-0.0727749\pi$
$558$	−1.85857	+	5.24840i	−0.0786796	+	0.222183i
$559$			31.7278i			1.34194i
$560$	5.36195	+	4.05399i	0.226584	+	0.171312i
$561$	2.64588	+	3.64174i	0.111709	+	0.153754i
$562$	−12.5697	+	24.6694i	−0.530220	+	1.04062i
$563$	9.96989	−	9.96989i	0.420181	−	0.420181i	−0.465085	−	0.885266i	$-0.653976\pi$
$563$	9.96989	−	9.96989i	0.420181	−	0.420181i	0.885266	+	0.465085i	$0.153976\pi$
$564$	−5.37681			−0.226405
$565$	−4.37517	+	1.32997i	−0.184065	+	0.0559524i
$566$	−3.72489	+	11.4640i	−0.156569	+	0.481870i
$567$	−2.67852	+	1.36477i	−0.112487	+	0.0573151i
$568$	−10.3771	+	1.64356i	−0.435412	+	0.0689625i
$569$	−9.73564	−	29.9632i	−0.408139	−	1.25612i	−0.918245	−	0.396012i	$-0.870394\pi$
$569$	−9.73564	−	29.9632i	−0.408139	−	1.25612i	0.510106	−	0.860111i	$-0.329606\pi$
$570$	−4.27272	+	0.593521i	−0.178964	+	0.0248599i
$571$	−22.3190	−	30.7194i	−0.934020	−	1.28557i	−0.958271	−	0.285862i	$-0.907720\pi$
$571$	−22.3190	−	30.7194i	−0.934020	−	1.28557i	0.0242511	−	0.999706i	$-0.492280\pi$
$572$	13.8241	−	7.04371i	0.578013	−	0.294513i
$573$	−10.4624	−	1.65709i	−0.437075	−	0.0692258i
$574$	7.59746	+	10.4570i	0.317112	+	0.436467i
$575$	4.30493	+	9.30961i	0.179528	+	0.388237i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−0.164646	−	1.03954i	−0.00685432	−	0.0432765i	0.984024	−	0.178035i	$-0.0569741\pi$
$577$	−0.164646	−	1.03954i	−0.00685432	−	0.0432765i	−0.990878	+	0.134759i	$0.956974\pi$
$578$	−11.5112	−	5.86523i	−0.478801	−	0.243961i
$579$	−7.25944	−	5.27429i	−0.301692	−	0.219192i
$580$	15.0411	−	7.30626i	0.624547	−	0.303376i
$581$	12.1828	+	3.95842i	0.505426	+	0.164223i
$582$	−1.59510	−	0.812745i	−0.0661191	−	0.0336894i
$583$	−12.9246	+	12.9246i	−0.535281	+	0.535281i
$584$	−7.83254			−0.324113
$585$	−14.8958	+	4.52807i	−0.615867	+	0.187213i
$586$	22.4470	−	16.3087i	0.927278	−	0.673707i
$587$	−26.6666	+	4.22357i	−1.10065	+	0.174325i	−0.680225	−	0.733003i	$-0.738118\pi$
$587$	−26.6666	+	4.22357i	−1.10065	+	0.174325i	−0.420422	+	0.907329i	$0.638118\pi$
$588$	−1.44043	−	1.44043i	−0.0594023	−	0.0594023i
$589$	7.79136	−	7.39369i	0.321037	−	0.304652i
$590$	0.0208916	−	1.09635i	0.000860094	−	0.0451360i
$591$	2.09347	+	1.52099i	0.0861137	+	0.0625653i
$592$	−0.704707	+	4.44934i	−0.0289633	+	0.182867i
$593$	−37.8125	−	19.2664i	−1.55277	−	0.791177i	−0.553638	−	0.832757i	$-0.686761\pi$
$593$	−37.8125	−	19.2664i	−1.55277	−	0.791177i	−0.999135	+	0.0415800i	$0.986761\pi$
$594$			2.22835i			0.0914302i
$595$	9.78299	−	9.41712i	0.401063	−	0.386064i
$596$	4.21929	+	12.9857i	0.172829	+	0.531913i
$597$	−11.1295	+	5.67075i	−0.455499	+	0.232088i
$598$	−6.48424	−	12.7260i	−0.265160	−	0.520406i
$599$	−10.0977	+	13.8983i	−0.412582	+	0.567871i	−0.963846	−	0.266460i	$-0.914146\pi$
$599$	−10.0977	+	13.8983i	−0.412582	+	0.567871i	0.551264	+	0.834331i	$0.314146\pi$
$600$	−4.81069	+	1.36280i	−0.196396	+	0.0556361i
$601$	7.61885	−	10.4864i	0.310779	−	0.427751i	−0.624845	−	0.780749i	$-0.714838\pi$
$601$	7.61885	−	10.4864i	0.310779	−	0.427751i	0.935624	+	0.352998i	$0.114838\pi$
$602$	2.14296	−	13.5301i	0.0873405	−	0.551446i
$603$	6.82885	+	13.4024i	0.278092	+	0.545787i
$604$	−18.1516	+	13.1879i	−0.738578	+	0.536608i
$605$	−2.36438	+	13.2847i	−0.0961255	+	0.540100i
$606$	−7.92546	−	2.57514i	−0.321950	−	0.104608i
$607$	−21.1910	−	3.35633i	−0.860117	−	0.136229i	−0.289232	−	0.957259i	$-0.593400\pi$
$607$	−21.1910	−	3.35633i	−0.860117	−	0.136229i	−0.570885	+	0.821030i	$0.693400\pi$
$608$	1.90541	−	0.301788i	0.0772747	−	0.0122391i
$609$	−21.3804	+	6.94692i	−0.866378	+	0.281503i
$610$	−5.66754	+	7.49610i	−0.229472	+	0.303508i
$611$	35.6043	+	11.5686i	1.44040	+	0.468014i
$612$	0.917097	+	1.79990i	0.0370715	+	0.0727568i
$613$	−9.58662	+	18.8148i	−0.387200	+	0.759923i	−0.999529	−	0.0306800i	$-0.990233\pi$
$613$	−9.58662	+	18.8148i	−0.387200	+	0.759923i	0.612329	+	0.790603i	$0.290233\pi$
$614$			26.4568i			1.06771i
$615$	−9.61262	−	0.183174i	−0.387618	−	0.00738630i
$616$	−6.37094	+	2.07004i	−0.256692	+	0.0834044i
$617$	36.7425	+	5.81944i	1.47920	+	0.234282i	0.843279	−	0.537476i	$-0.180622\pi$
$617$	36.7425	+	5.81944i	1.47920	+	0.234282i	0.635917	+	0.771757i	$0.280622\pi$
$618$	−2.31029	−	14.5866i	−0.0929335	−	0.586759i
$619$	−23.8670			−0.959296			−0.479648	−	0.877461i	$-0.659236\pi$
$619$	−23.8670			−0.959296			−0.479648	+	0.877461i	$0.659236\pi$
$620$	7.76585	−	9.73096i	0.311884	−	0.390805i
$621$	2.05135			0.0823179
$622$	2.10305	+	13.2781i	0.0843246	+	0.532405i
$623$	27.8168	+	4.40574i	1.11445	+	0.176512i
$624$	6.62183	−	2.15156i	0.265086	−	0.0861315i
$625$	−24.9274	−	1.90349i	−0.997097	−	0.0761394i
$626$		−	30.3359i		−	1.21247i
$627$	1.95164	−	3.83030i	0.0779409	−	0.152968i
$628$	10.4066	+	20.4240i	0.415267	+	0.815008i
$629$	8.65468	+	2.81208i	0.345085	+	0.112125i
$630$	6.65808	−	0.924871i	0.265264	−	0.0368477i
$631$	−12.1853	+	3.95923i	−0.485087	+	0.157614i	−0.541343	−	0.840802i	$-0.682084\pi$
$631$	−12.1853	+	3.95923i	−0.485087	+	0.157614i	0.0562556	+	0.998416i	$0.482084\pi$
$632$	0.580440	−	0.0919327i	0.0230887	−	0.00365689i
$633$	−4.24716	−	0.672684i	−0.168809	−	0.0267368i
$634$	−15.7756	−	5.12581i	−0.626530	−	0.203572i
$635$	−2.43111	−	3.48383i	−0.0964755	−	0.138252i
$636$	−6.63600	+	4.82133i	−0.263134	+	0.191178i
$637$	6.43911	+	12.6375i	0.255127	+	0.500714i
$638$	−2.60682	+	16.4588i	−0.103205	+	0.651611i
$639$	−6.17551	+	8.49987i	−0.244300	+	0.336249i
$640$	2.13941	−	0.650341i	0.0845674	−	0.0257070i
$641$	15.7415	−	21.6663i	0.621752	−	0.855769i	−0.375727	−	0.926731i	$-0.622607\pi$
$641$	15.7415	−	21.6663i	0.621752	−	0.855769i	0.997479	+	0.0709619i	$0.0226069\pi$
$642$	4.85029	+	9.51922i	0.191426	+	0.375694i
$643$	7.09021	−	3.61264i	0.279611	−	0.142469i	−0.308562	−	0.951204i	$-0.599848\pi$
$643$	7.09021	−	3.61264i	0.279611	−	0.142469i	0.588172	+	0.808736i	$0.299848\pi$
$644$	1.90562	+	5.86490i	0.0750920	+	0.231109i
$645$	7.06648	+	7.34103i	0.278242	+	0.289053i
$646$		−	3.89707i		−	0.153328i
$647$	0.258293	+	0.131607i	0.0101545	+	0.00517400i	0.459060	−	0.888405i	$-0.348186\pi$
$647$	0.258293	+	0.131607i	0.0101545	+	0.00517400i	−0.448906	+	0.893579i	$0.648186\pi$
$648$	−0.156434	+	0.987688i	−0.00614533	+	0.0388001i
$649$	0.884064	+	0.642310i	0.0347026	+	0.0252129i
$650$	34.7878	+	1.32629i	1.36449	+	0.0520212i
$651$	−12.1411	+	11.5214i	−0.475847	+	0.451560i
$652$	5.95879	+	5.95879i	0.233364	+	0.233364i
$653$	4.99512	−	0.791150i	0.195474	−	0.0309601i	−0.0579296	−	0.998321i	$-0.518450\pi$
$653$	4.99512	−	0.791150i	0.195474	−	0.0309601i	0.253404	+	0.967361i	$0.418450\pi$
$654$	15.6480	−	11.3689i	0.611884	−	0.444559i
$655$	17.2110	+	9.18662i	0.672491	+	0.358951i
$656$	4.29968			0.167874
$657$	−5.53844	+	5.53844i	−0.216075	+	0.216075i
$658$	−14.4019	−	7.33813i	−0.561444	−	0.286070i
$659$	24.9864	+	8.11856i	0.973330	+	0.316254i	0.752160	−	0.658981i	$-0.229012\pi$
$659$	24.9864	+	8.11856i	0.973330	+	0.316254i	0.221171	+	0.975235i	$0.429012\pi$
$660$	1.62976	−	4.70867i	0.0634382	−	0.183285i
$661$	−0.393398	−	0.285820i	−0.0153014	−	0.0111171i	0.580108	−	0.814539i	$-0.303010\pi$
$661$	−0.393398	−	0.285820i	−0.0153014	−	0.0111171i	−0.595410	+	0.803422i	$0.703010\pi$
$662$	2.77553	+	1.41420i	0.107874	+	0.0549645i
$663$	−2.20025	−	13.8919i	−0.0854508	−	0.539515i
$664$	3.44733	−	2.50463i	0.133782	−	0.0971986i
$665$	−12.2546	−	4.24153i	−0.475212	−	0.164480i
$666$	2.64786	+	3.64446i	0.102602	+	0.141220i
$667$	15.1515	+	2.39976i	0.586669	+	0.0929192i
$668$	−3.43470	+	1.75007i	−0.132892	+	0.0677121i
$669$	3.63078	+	4.99733i	0.140374	+	0.193208i
$670$	−4.62773	−	33.3147i	−0.178785	−	1.28706i
$671$	−2.89395	−	8.90667i	−0.111720	−	0.343838i
$672$	−2.96916	+	0.470269i	−0.114538	+	0.0181410i
$673$	31.1030	−	15.8477i	1.19893	−	0.610886i	0.263591	−	0.964635i	$-0.415093\pi$
$673$	31.1030	−	15.8477i	1.19893	−	0.610886i	0.935340	+	0.353749i	$0.115093\pi$
$674$	0.562577	−	1.73143i	0.0216697	−	0.0666923i
$675$	−2.43803	+	4.36532i	−0.0938398	+	0.168021i
$676$	−35.4779			−1.36454
$677$	11.9263	−	11.9263i	0.458364	−	0.458364i	−0.439754	−	0.898118i	$-0.644934\pi$
$677$	11.9263	−	11.9263i	0.458364	−	0.458364i	0.898118	+	0.439754i	$0.144934\pi$
$678$	0.928429	−	1.82214i	0.0356561	−	0.0699790i
$679$	−3.16330	−	4.35391i	−0.121396	−	0.167088i
$680$	−0.621492	−	4.47408i	−0.0238331	−	0.171573i
$681$			25.4324i			0.974571i
$682$	3.52373	+	11.8960i	0.134930	+	0.455522i
$683$	−12.0309	+	12.0309i	−0.460351	+	0.460351i	−0.898770	−	0.438420i	$-0.855538\pi$
$683$	−12.0309	+	12.0309i	−0.460351	+	0.460351i	0.438420	+	0.898770i	$0.355538\pi$
$684$	1.13393	−	1.56073i	0.0433571	−	0.0596759i
$685$	−0.945301	−	1.35464i	−0.0361181	−	0.0517581i
$686$	4.61035	+	14.1892i	0.176024	+	0.541746i
$687$	17.8724	+	17.8724i	0.681875	+	0.681875i
$688$	−3.22220	−	3.22220i	−0.122845	−	0.122845i
$689$	54.3159	−	17.6483i	2.06927	−	0.672346i
$690$	−4.33466	−	1.50031i	−0.165018	−	0.0571157i
$691$	−3.07332	+	9.45871i	−0.116915	+	0.359826i	−0.992342	−	0.123524i	$-0.960580\pi$
$691$	−3.07332	+	9.45871i	−0.116915	+	0.359826i	0.875427	+	0.483351i	$0.160580\pi$
$692$	0.116294	+	0.734250i	0.00442082	+	0.0279120i
$693$	−3.04119	+	5.96867i	−0.115525	+	0.226731i
$694$	−10.4398	−	7.58492i	−0.396288	−	0.287920i
$695$	5.23718	−	29.4261i	0.198658	−	1.11620i
$696$	−2.31088	+	7.11217i	−0.0875938	+	0.269586i
$697$	1.35874	−	8.57875i	0.0514660	−	0.324943i
$698$	2.66947	−	16.8544i	0.101041	−	0.637948i
$699$	1.19100	−	3.66552i	0.0450477	−	0.138643i
$700$	−14.7455	−	2.91522i	−0.557326	−	0.110185i
$701$	0.414603	+	0.301227i	0.0156593	+	0.0113772i	0.595587	−	0.803291i	$-0.296919\pi$
$701$	0.414603	+	0.301227i	0.0156593	+	0.0113772i	−0.579928	+	0.814668i	$0.696919\pi$
$702$	3.16096	−	6.20373i	0.119303	−	0.234145i
$703$	−1.35950	−	8.58352i	−0.0512744	−	0.323734i
$704$	−0.688597	+	2.11928i	−0.0259525	+	0.0798736i
$705$	10.8145	−	5.25320i	0.407299	−	0.197847i
$706$	−8.24289	+	2.67828i	−0.310225	+	0.100798i
$707$	−17.7140	−	17.7140i	−0.666204	−	0.666204i
$708$	0.346759	+	0.346759i	0.0130320	+	0.0130320i
$709$	−15.0388	−	46.2845i	−0.564792	−	1.73825i	−0.668568	−	0.743651i	$-0.733092\pi$
$709$	−15.0388	−	46.2845i	−0.564792	−	1.73825i	0.103775	−	0.994601i	$-0.466908\pi$
$710$	19.2659	−	13.4443i	0.723037	−	0.504554i
$711$	0.345427	−	0.475439i	0.0129545	−	0.0178304i
$712$	6.62457	−	6.62457i	0.248266	−	0.248266i
$713$	10.9511	−	3.24384i	0.410123	−	0.121483i
$714$			6.07271i			0.227265i
$715$	−20.9230	+	27.6735i	−0.782475	+	1.03493i
$716$	−10.3016	−	14.1790i	−0.384990	−	0.529894i
$717$	7.35749	−	14.4399i	0.274770	−	0.539267i
$718$	18.2591	−	18.2591i	0.681425	−	0.681425i
$719$	−36.9575			−1.37828			−0.689141	−	0.724628i	$-0.742012\pi$
$719$	−36.9575			−1.37828			−0.689141	+	0.724628i	$0.742012\pi$
$720$	1.05293	−	1.97265i	0.0392403	−	0.0735163i
$721$	13.7193	−	42.2235i	0.510932	−	1.57249i
$722$	13.6131	−	6.93621i	0.506627	−	0.258139i
$723$	15.1146	−	2.39392i	0.562120	−	0.0890310i
$724$	0.492778	+	1.51662i	0.0183140	+	0.0563646i
$725$	−23.1143	+	29.3906i	−0.858443	+	1.09154i
$726$	−3.54697	−	4.88198i	−0.131640	−	0.181187i
$727$	39.8362	−	20.2976i	1.47744	−	0.752795i	0.484887	−	0.874577i	$-0.338861\pi$
$727$	39.8362	−	20.2976i	1.47744	−	0.752795i	0.992557	+	0.121782i	$0.0388608\pi$
$728$	20.6731	+	3.27430i	0.766196	+	0.121354i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	15.7538	−	7.65247i	0.583075	−	0.283231i
$731$	−7.44722	+	5.41072i	−0.275445	+	0.200123i
$732$	−0.657444	−	4.15094i	−0.0242998	−	0.153423i
$733$	16.5772	+	8.44653i	0.612295	+	0.311980i	0.732498	−	0.680770i	$-0.238355\pi$
$733$	16.5772	+	8.44653i	0.612295	+	0.311980i	−0.120203	+	0.992749i	$0.538355\pi$
$734$	26.1658	+	19.0105i	0.965796	+	0.701692i
$735$	4.30449	+	1.48986i	0.158774	+	0.0549545i
$736$	1.95095	+	0.633903i	0.0719131	+	0.0233660i
$737$	29.8651	+	15.2170i	1.10010	+	0.560527i
$738$	3.04033	−	3.04033i	0.111916	−	0.111916i
$739$	−1.09485			−0.0402746			−0.0201373	−	0.999797i	$-0.506410\pi$
$739$	−1.09485			−0.0402746			−0.0201373	+	0.999797i	$0.506410\pi$
$740$	−2.92966	−	9.63761i	−0.107696	−	0.354286i
$741$	−10.8667	+	7.89514i	−0.399199	+	0.290035i
$742$	−24.3547	+	3.85740i	−0.894088	+	0.141610i
$743$	17.7262	+	17.7262i	0.650311	+	0.650311i	0.953068	−	0.302757i	$-0.0979069\pi$
$743$	17.7262	+	17.7262i	0.650311	+	0.650311i	−0.302757	+	0.953068i	$0.597907\pi$
$744$	0.726726	+	5.52013i	0.0266431	+	0.202378i
$745$	−21.1735	−	21.9961i	−0.775738	−	0.805876i
$746$	−10.2639	−	7.45716i	−0.375788	−	0.273026i
$747$	0.666589	−	4.20867i	0.0243892	−	0.153987i
$748$	4.01081	+	2.04361i	0.146650	+	0.0747218i
$749$			32.1170i			1.17353i
$750$	8.34443	−	7.44114i	0.304695	−	0.271712i
$751$	−0.120312	−	0.370281i	−0.00439024	−	0.0135118i	0.948837	−	0.315765i	$-0.102261\pi$
$751$	−0.120312	−	0.370281i	−0.00439024	−	0.0135118i	−0.953228	+	0.302253i	$0.902261\pi$
$752$	−4.79077	+	2.44102i	−0.174702	+	0.0890149i
$753$	2.86684	+	5.62649i	0.104473	+	0.205041i
$754$	30.6046	−	42.1236i	1.11455	−	1.53405i
$755$	23.6241	−	44.2595i	0.859770	−	1.61077i
$756$	−1.76698	+	2.43204i	−0.0642646	+	0.0884526i
$757$	1.07969	−	6.81693i	0.0392422	−	0.247765i	−0.960267	−	0.279082i	$-0.909970\pi$
$757$	1.07969	−	6.81693i	0.0392422	−	0.247765i	0.999510	+	0.0313164i	$0.00996995\pi$
$758$	15.6259	+	30.6676i	0.567558	+	1.11390i
$759$	3.69812	−	2.68684i	0.134233	−	0.0975262i
$760$	−3.53757	+	2.46860i	−0.128321	+	0.0895457i
$761$	−44.7694	−	14.5465i	−1.62289	−	0.527308i	−0.650267	−	0.759705i	$-0.725343\pi$
$761$	−44.7694	−	14.5465i	−1.62289	−	0.527308i	−0.972621	+	0.232397i	$0.925343\pi$
$762$	1.87647	+	0.297204i	0.0679774	+	0.0107666i
$763$	57.4293	−	9.09591i	2.07908	−	0.329294i
$764$	−10.0744	+	3.27337i	−0.364479	+	0.118426i
$765$	−3.60311	−	2.72419i	−0.130271	−	0.0984933i
$766$	−25.0703	−	8.14585i	−0.905828	−	0.294321i
$767$	−1.55011	−	3.04226i	−0.0559711	−	0.109850i
$768$	−0.453990	+	0.891007i	−0.0163820	+	0.0321514i
$769$		−	41.8985i		−	1.51090i	−0.655206	−	0.755450i	$-0.727418\pi$
$769$		−	41.8985i		−	1.51090i	0.655206	−	0.755450i	$-0.272582\pi$
$770$	10.7916	−	10.3880i	0.388902	−	0.374358i
$771$	7.53395	−	2.44793i	0.271328	−	0.0881600i
$772$	−8.86268	−	1.40371i	−0.318975	−	0.0505207i
$773$	−1.73050	−	10.9259i	−0.0622417	−	0.392979i	−0.999067	−	0.0431818i	$-0.986251\pi$
$773$	−1.73050	−	10.9259i	−0.0622417	−	0.392979i	0.936825	−	0.349797i	$-0.113749\pi$
$774$	−4.55688			−0.163794
$775$	−6.11243	+	27.1595i	−0.219565	+	0.975598i
$776$	−1.79022			−0.0642653
$777$	2.11847	+	13.3755i	0.0759997	+	0.479843i
$778$	−13.3321	−	2.11159i	−0.477978	−	0.0757043i
$779$	−7.88881	+	2.56323i	−0.282646	+	0.0918372i
$780$	−11.2166	+	10.7971i	−0.401619	+	0.386599i
$781$			23.4119i			0.837745i
$782$	1.88129	−	3.69224i	0.0672748	−	0.132034i
$783$	3.39502	+	6.66310i	0.121328	+	0.238120i
$784$	−1.93737	−	0.629491i	−0.0691919	−	0.0224818i
$785$	−40.8856	−	30.9122i	−1.45927	−	1.10330i
$786$	−8.29781	+	2.69612i	−0.295973	+	0.0961675i
$787$	−24.3387	+	3.85487i	−0.867581	+	0.137411i	−0.574330	−	0.818624i	$-0.694737\pi$
$787$	−24.3387	+	3.85487i	−0.867581	+	0.137411i	−0.293251	+	0.956035i	$0.594737\pi$
$788$	2.55581	+	0.404800i	0.0910469	+	0.0144204i
$789$	−4.25219	−	1.38162i	−0.151382	−	0.0491870i
$790$	−1.07764	+	0.752003i	−0.0383406	+	0.0267551i
$791$	4.97363	−	3.61355i	0.176842	−	0.128483i
$792$	1.01165	+	1.98547i	0.0359474	+	0.0705507i
$793$	−4.57752	+	28.9013i	−0.162553	+	1.02632i
$794$	12.3594	−	17.0112i	0.438618	−	0.603705i
$795$	8.63668	−	16.1807i	0.306312	−	0.573871i
$796$	−7.34197	+	10.1054i	−0.260229	+	0.358175i
$797$	1.44447	+	2.83493i	0.0511657	+	0.100418i	0.915174	−	0.403060i	$-0.132053\pi$
$797$	1.44447	+	2.83493i	0.0511657	+	0.100418i	−0.864008	+	0.503478i	$0.832053\pi$
$798$	5.16731	−	2.63287i	0.182921	−	0.0932027i
$799$	3.35642	+	10.3300i	0.118741	+	0.365449i
$800$	−3.66766	+	3.39827i	−0.129671	+	0.120147i
$801$		−	9.36856i		−	0.331022i
$802$	26.3269	+	13.4142i	0.929635	+	0.473672i
$803$	−2.73035	+	17.2387i	−0.0963519	+	0.608342i
$804$	12.1691	+	8.84136i	0.429171	+	0.311811i
$805$	−9.56290	−	9.93444i	−0.337048	−	0.350143i
$806$	7.06466	−	38.1170i	0.248842	−	1.34261i
$807$	−20.1467	−	20.1467i	−0.709196	−	0.709196i
$808$	−8.23072	+	1.30362i	−0.289556	+	0.0458611i
$809$	19.5968	−	14.2379i	0.688985	−	0.500577i	−0.187341	−	0.982295i	$-0.559987\pi$
$809$	19.5968	−	14.2379i	0.688985	−	0.500577i	0.876326	+	0.481718i	$0.159987\pi$
$810$	−0.650341	−	2.13941i	−0.0228506	−	0.0751711i
$811$	−12.7451			−0.447541			−0.223770	−	0.974642i	$-0.571837\pi$
$811$	−12.7451			−0.447541			−0.223770	+	0.974642i	$0.571837\pi$
$812$	−15.8963	+	15.8963i	−0.557849	+	0.557849i
$813$	14.7217	+	7.50108i	0.516313	+	0.263075i
$814$	9.54697	+	3.10200i	0.334621	+	0.108725i
$815$	−17.8069	−	6.16329i	−0.623748	−	0.215891i
$816$	1.63428	+	1.18737i	0.0572112	+	0.0415664i
$817$	7.83282	+	3.99102i	0.274036	+	0.139628i
$818$	1.57099	+	9.91884i	0.0549284	+	0.346804i
$819$	16.9334	−	12.3028i	0.591700	−	0.429895i
$820$	−8.64807	+	4.20083i	−0.302004	+	0.146699i
$821$	22.6159	+	31.1281i	0.789301	+	1.08638i	0.994195	+	0.107595i	$0.0343151\pi$
$821$	22.6159	+	31.1281i	0.789301	+	1.08638i	−0.204894	+	0.978784i	$0.565685\pi$
$822$	0.729639	+	0.115563i	0.0254491	+	0.00403074i
$823$	−33.7958	+	17.2198i	−1.17805	+	0.600245i	−0.929661	−	0.368416i	$-0.879900\pi$
$823$	−33.7958	+	17.2198i	−1.17805	+	0.600245i	−0.248386	+	0.968661i	$0.579900\pi$
$824$	−8.68067	−	11.9479i	−0.302405	−	0.416225i
$825$	1.32244	+	11.0630i	0.0460415	+	0.385164i
$826$	0.455554	+	1.40205i	0.0158507	+	0.0487835i
$827$	−26.6899	+	4.22726i	−0.928099	+	0.146996i	−0.602143	−	0.798388i	$-0.705686\pi$
$827$	−26.6899	+	4.22726i	−0.928099	+	0.146996i	−0.325956	+	0.945385i	$0.605686\pi$
$828$	1.82777	−	0.931295i	0.0635193	−	0.0323647i
$829$	0.0972505	−	0.299306i	0.00337765	−	0.0103953i	−0.949353	−	0.314210i	$-0.898260\pi$
$829$	0.0972505	−	0.299306i	0.00337765	−	0.0103953i	0.952731	+	0.303815i	$0.0982604\pi$
$830$	−4.48667	+	8.40572i	−0.155735	+	0.291767i
$831$	2.03504			0.0705947
$832$	4.92331	−	4.92331i	0.170685	−	0.170685i
$833$	−1.86819	+	3.66654i	−0.0647291	+	0.127038i
$834$	7.85667	+	10.8138i	0.272054	+	0.374451i
$835$	5.19848	−	6.87570i	0.179901	−	0.237943i
$836$		−	4.29885i		−	0.148679i
$837$	4.41720	+	3.38945i	0.152681	+	0.117157i
$838$	25.8465	−	25.8465i	0.892853	−	0.892853i
$839$	−26.1239	+	35.9564i	−0.901896	+	1.24135i	0.0679633	+	0.997688i	$0.478350\pi$
$839$	−26.1239	+	35.9564i	−0.901896	+	1.24135i	−0.969859	+	0.243666i	$0.921650\pi$
$840$	5.51251	−	3.84677i	0.190200	−	0.132726i
$841$	8.31971	+	25.6054i	0.286886	+	0.882946i
$842$	−1.30435	−	1.30435i	−0.0449508	−	0.0449508i
$843$	19.5777	+	19.5777i	0.674293	+	0.674293i
$844$	−4.08964	+	1.32880i	−0.140771	+	0.0457393i
$845$	71.3578	−	34.6623i	2.45478	−	1.19242i
$846$	−1.66153	+	5.11365i	−0.0571244	+	0.175811i
$847$	−2.83782	−	17.9173i	−0.0975087	−	0.615646i
$848$	−3.72388	+	7.30852i	−0.127878	+	0.250976i
$849$	9.75190	+	7.08517i	0.334684	+	0.243162i
$850$	5.62125	+	8.39164i	0.192807	+	0.287831i
$851$	2.85561	−	8.78866i	0.0978890	−	0.301271i
$852$	−1.64356	+	10.3771i	−0.0563076	+	0.355512i
$853$	7.32293	−	46.2351i	0.250732	−	1.58306i	−0.465403	−	0.885099i	$-0.654090\pi$
$853$	7.32293	−	46.2351i	0.250732	−	1.58306i	0.716135	−	0.697962i	$-0.245910\pi$
$854$	3.90411	−	12.0156i	0.133596	−	0.411166i
$855$	−0.755870	+	4.24700i	−0.0258502	+	0.145244i
$856$	8.64327	+	6.27971i	0.295421	+	0.214636i
$857$	−23.8509	+	46.8101i	−0.814732	+	1.59900i	−0.0140577	+	0.999901i	$0.504475\pi$
$857$	−23.8509	+	46.8101i	−0.814732	+	1.59900i	−0.800674	+	0.599100i	$0.795525\pi$
$858$	−2.42710	−	15.3241i	−0.0828598	−	0.523156i
$859$	−12.4253	+	38.2412i	−0.423946	+	1.30477i	0.480053	+	0.877239i	$0.340617\pi$
$859$	−12.4253	+	38.2412i	−0.423946	+	1.30477i	−0.904000	+	0.427533i	$0.859383\pi$
$860$	9.62904	+	3.33279i	0.328347	+	0.113647i
$861$	12.2929	−	3.99422i	0.418942	−	0.136123i
$862$	2.57960	+	2.57960i	0.0878616	+	0.0878616i
$863$	−26.3516	−	26.3516i	−0.897019	−	0.897019i	0.0981525	−	0.995171i	$-0.468707\pi$
$863$	−26.3516	−	26.3516i	−0.897019	−	0.897019i	−0.995171	+	0.0981525i	$0.968707\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−0.951275	−	1.36320i	−0.0323443	−	0.0463501i
$866$	2.40783	−	3.31409i	0.0818214	−	0.112617i
$867$	−9.13531	+	9.13531i	−0.310251	+	0.310251i
$868$	−5.58718	+	15.7776i	−0.189641	+	0.535527i
$869$		−	1.30955i		−	0.0444233i
$870$	−2.30072	−	16.5627i	−0.0780015	−	0.561527i
$871$	−61.5590	−	84.7286i	−2.08585	−	2.87092i
$872$	8.78106	−	17.2338i	0.297364	−	0.583610i
$873$	−1.26588	+	1.26588i	−0.0428435	+	0.0428435i
$874$	−3.95740			−0.133861
$875$	32.5062	−	8.54299i	1.09891	−	0.288806i
$876$	−2.42039	+	7.44919i	−0.0817773	+	0.251685i
$877$	−21.2821	+	10.8438i	−0.718647	+	0.366169i	−0.774760	−	0.632256i	$-0.782129\pi$
$877$	−21.2821	+	10.8438i	−0.718647	+	0.366169i	0.0561130	+	0.998424i	$0.482129\pi$
$878$	−23.9142	+	3.78764i	−0.807065	+	0.127827i
$879$	−8.57400	−	26.3881i	−0.289194	−	0.890048i
$880$	−0.685567	−	4.93535i	−0.0231105	−	0.166371i
$881$	−10.0574	−	13.8429i	−0.338844	−	0.466378i	0.605260	−	0.796028i	$-0.293069\pi$
$881$	−10.0574	−	13.8429i	−0.338844	−	0.466378i	−0.944103	+	0.329650i	$0.893069\pi$
$882$	−1.81505	+	0.924812i	−0.0611158	+	0.0311401i
$883$	7.80877	+	1.23679i	0.262786	+	0.0416212i	0.286437	−	0.958099i	$-0.407529\pi$
$883$	7.80877	+	1.23679i	0.262786	+	0.0416212i	−0.0236511	+	0.999720i	$0.507529\pi$
$884$	−8.26721	−	11.3788i	−0.278057	−	0.382712i
$885$	−1.03624	−	0.358660i	−0.0348327	−	0.0120562i
$886$	18.4896	−	13.4335i	0.621169	−	0.451306i
$887$	−3.83593	−	24.2191i	−0.128798	−	0.813198i	−0.964513	−	0.264035i	$-0.914947\pi$
$887$	−3.83593	−	24.2191i	−0.128798	−	0.813198i	0.835715	−	0.549163i	$-0.185053\pi$
$888$	4.01381	+	2.04514i	0.134695	+	0.0686304i
$889$	4.62055	+	3.35702i	0.154968	+	0.112591i
$890$	−6.85192	+	19.7965i	−0.229677	+	0.663579i
$891$	2.11928	+	0.688597i	0.0709987	+	0.0230689i
$892$	5.50379	+	2.80432i	0.184280	+	0.0938955i
$893$	7.33464	−	7.33464i	0.245445	−	0.245445i
$894$	13.6539			0.456656
$895$	34.5730	+	18.4538i	1.15565	+	0.616843i
$896$	−2.43204	+	1.76698i	−0.0812489	+	0.0590308i
$897$	−14.1069	+	2.23432i	−0.471016	+	0.0746017i
$898$	26.9337	+	26.9337i	0.898789	+	0.898789i
$899$	28.6608	+	30.2023i	0.955890	+	1.00730i
$900$	−0.190487	+	4.99637i	−0.00634956	+	0.166546i
$901$	13.4052	+	9.73948i	0.446593	+	0.324469i
$902$	1.49883	−	9.46321i	0.0499054	−	0.315091i
$903$	−12.2057	−	6.21911i	−0.406180	−	0.206959i
$904$		−	2.04504i		−	0.0680170i
$905$	−2.47289	−	2.56897i	−0.0822017	−	0.0853953i
$906$	6.93329	+	21.3385i	0.230343	+	0.708923i
$907$	−20.7783	+	10.5871i	−0.689934	+	0.351539i	−0.763551	−	0.645748i	$-0.776546\pi$
$907$	−20.7783	+	10.5871i	−0.689934	+	0.351539i	0.0736171	+	0.997287i	$0.476546\pi$
$908$	11.5461	+	22.6604i	0.383169	+	0.752012i
$909$	−4.89820	+	6.74180i	−0.162463	+	0.223611i
$910$	−44.7795	+	13.6122i	−1.48443	+	0.451239i
$911$	−6.07211	+	8.35754i	−0.201178	+	0.276898i	−0.897671	−	0.440665i	$-0.854743\pi$
$911$	−6.07211	+	8.35754i	−0.201178	+	0.276898i	0.696493	+	0.717563i	$0.254743\pi$
$912$	0.301788	−	1.90541i	0.00999319	−	0.0630945i
$913$	−4.31077	−	8.46037i	−0.142666	−	0.279997i
$914$	−21.5347	+	15.6459i	−0.712306	+	0.517521i
$915$	5.37785	+	7.70657i	0.177786	+	0.254771i
$916$	24.0383	+	7.81053i	0.794249	+	0.258067i
$917$	−25.9054	−	4.10302i	−0.855473	−	0.135494i
$918$	1.99521	−	0.316010i	0.0658517	−	0.0104299i
$919$	−48.7510	+	15.8402i	−1.60815	+	0.522519i	−0.969104	−	0.246651i	$-0.920670\pi$
$919$	−48.7510	+	15.8402i	−1.60815	+	0.522519i	−0.639044	+	0.769170i	$0.720670\pi$
$920$	−4.54334	+	0.631113i	−0.149789	+	0.0208072i
$921$	25.1619	+	8.17560i	0.829113	+	0.269395i
$922$	−18.7461	−	36.7913i	−0.617370	−	1.21166i
$923$	33.2103	−	65.1789i	1.09313	−	2.14539i
$924$			6.69880i			0.220374i
$925$	15.3086	+	16.5221i	0.503342	+	0.543243i
$926$	18.3528	−	5.96319i	0.603111	−	0.195963i
$927$	−14.5866	−	2.31029i	−0.479087	−	0.0758799i
$928$	1.16984	+	7.38611i	0.0384020	+	0.242461i
$929$	−34.2160			−1.12259			−0.561295	−	0.827616i	$-0.689697\pi$
$929$	−34.2160			−1.12259			−0.561295	+	0.827616i	$0.689697\pi$
$930$	−6.85492	−	10.3928i	−0.224782	−	0.340793i
$931$	3.92985			0.128796
$932$	−0.602923	−	3.80671i	−0.0197494	−	0.124693i
$933$	13.2781	+	2.10305i	0.434707	+	0.0688508i
$934$	16.2155	−	5.26874i	0.530588	−	0.172398i
$935$	−10.0637	−	0.191770i	−0.329118	−	0.00627155i
$936$		−	6.96261i		−	0.227580i
$937$	7.24517	−	14.2194i	0.236689	−	0.464529i	−0.741856	−	0.670559i	$-0.766054\pi$
$937$	7.24517	−	14.2194i	0.236689	−	0.464529i	0.978546	+	0.206030i	$0.0660544\pi$
$938$	20.5287	+	40.2898i	0.670286	+	1.31551i
$939$	−28.8512	−	9.37431i	−0.941522	−	0.305919i
$940$	7.25092	−	9.59034i	0.236499	−	0.312802i
$941$	−45.4361	+	14.7631i	−1.48117	+	0.481262i	−0.934463	−	0.356059i	$-0.884120\pi$
$941$	−45.4361	+	14.7631i	−1.48117	+	0.481262i	−0.546710	+	0.837322i	$0.684120\pi$
$942$	22.6402	−	3.58586i	0.737658	−	0.116834i
$943$	−8.71156	−	1.37978i	−0.283687	−	0.0449317i
$944$	0.466390	+	0.151539i	0.0151797	+	0.00493219i
$945$	1.17785	−	6.61801i	0.0383156	−	0.215284i
$946$	−8.21502	+	5.96856i	−0.267093	+	0.194055i
$947$	3.64432	+	7.15239i	0.118425	+	0.232421i	0.942608	−	0.333902i	$-0.108365\pi$
$947$	3.64432	+	7.15239i	0.118425	+	0.232421i	−0.824183	+	0.566323i	$0.808365\pi$
$948$	0.0919327	−	0.580440i	0.00298583	−	0.0188518i
$949$	32.0548	−	44.1197i	1.04054	−	1.43218i
$950$	4.70336	−	8.42142i	0.152597	−	0.273227i
$951$	−9.74988	+	13.4196i	−0.316161	+	0.435159i
$952$	2.75695	+	5.41082i	0.0893533	+	0.175366i
$953$	16.2595	−	8.28463i	0.526697	−	0.268365i	−0.170359	−	0.985382i	$-0.554493\pi$
$953$	16.2595	−	8.28463i	0.526697	−	0.268365i	0.697056	+	0.717017i	$0.254493\pi$
$954$	2.53472	+	7.80108i	0.0820647	+	0.252569i
$955$	17.0648	−	16.4266i	0.552205	−	0.531553i
$956$		−	16.2063i		−	0.524148i
$957$	14.8477	+	7.56529i	0.479959	+	0.244551i
$958$	2.55862	−	16.1545i	0.0826652	−	0.521927i
$959$	1.79663	+	1.30533i	0.0580163	+	0.0421513i
$960$	0.0426019	−	2.23566i	0.00137497	−	0.0721557i
$961$	28.9409	+	11.1095i	0.933579	+	0.358372i
$962$	−22.1785	−	22.1785i	−0.715065	−	0.715065i
$963$	10.5521	−	1.67129i	0.340038	−	0.0538567i
$964$	12.3804	−	8.99491i	0.398747	−	0.289706i
$965$	19.1972	−	5.83561i	0.617980	−	0.187855i
$966$	6.16672			0.198411
$967$	30.7330	−	30.7330i	0.988306	−	0.988306i	−0.0116264	−	0.999932i	$-0.503701\pi$
$967$	30.7330	−	30.7330i	0.988306	−	0.988306i	0.999932	+	0.0116264i	$0.00370088\pi$
$968$	−5.37675	−	2.73959i	−0.172815	−	0.0880538i
$969$	−3.70633	−	1.20426i	−0.119065	−	0.0386864i
$970$	3.60073	−	1.74907i	0.115613	−	0.0561592i
$971$	42.1304	+	30.6095i	1.35203	+	0.982306i	0.998908	+	0.0467281i	$0.0148794\pi$
$971$	42.1304	+	30.6095i	1.35203	+	0.982306i	0.353121	+	0.935578i	$0.385121\pi$
$972$	0.891007	+	0.453990i	0.0285790	+	0.0145618i
$973$	6.28588	+	39.6875i	0.201516	+	1.27232i
$974$	12.0484	−	8.75368i	0.386056	−	0.280486i
$975$	12.0114	−	32.6753i	0.384672	−	1.04645i
$976$	−2.47027	−	3.40004i	−0.0790715	−	0.108833i
$977$	−4.65613	−	0.737459i	−0.148963	−	0.0235934i	0.0815076	−	0.996673i	$-0.474027\pi$
$977$	−4.65613	−	0.737459i	−0.148963	−	0.0235934i	−0.230470	+	0.973079i	$0.574027\pi$
$978$	7.50851	−	3.82578i	0.240096	−	0.122335i
$979$	−12.2708	−	16.8894i	−0.392178	−	0.539786i
$980$	4.51172	−	0.626721i	0.144121	−	0.0200199i
$981$	−5.97699	−	18.3953i	−0.190831	−	0.587316i
$982$	−8.30857	+	1.31595i	−0.265137	+	0.0419936i
$983$	−8.81909	+	4.49355i	−0.281285	+	0.143322i	−0.588942	−	0.808176i	$-0.700455\pi$
$983$	−8.81909	+	4.49355i	−0.281285	+	0.143322i	0.307656	+	0.951498i	$0.400455\pi$
$984$	1.32867	−	4.08923i	0.0423565	−	0.130360i
$985$	−5.53607	+	1.68287i	−0.176394	+	0.0536205i
$986$	15.1065			0.481089
$987$	−11.4294	+	11.4294i	−0.363802	+	0.363802i
$988$	−6.09801	+	11.9680i	−0.194004	+	0.380753i
$989$	5.49448	+	7.56251i	0.174714	+	0.240474i
$990$	−3.97459	−	3.00505i	−0.126321	−	0.0955067i
$991$		−	13.6460i		−	0.433480i	−0.976229	−	0.216740i	$-0.930458\pi$
$991$		−	13.6460i		−	0.433480i	0.976229	−	0.216740i	$-0.0695423\pi$
$992$	3.15361	+	4.58855i	0.100127	+	0.145687i
$993$	2.20267	−	2.20267i	0.0698997	−	0.0698997i
$994$	−18.5647	+	25.5521i	−0.588835	+	0.810462i
$995$	4.89408	−	27.4984i	0.155153	−	0.871757i
$996$	−1.31676	−	4.05258i	−0.0417232	−	0.128411i
$997$	12.8345	+	12.8345i	0.406473	+	0.406473i	0.880507	−	0.474033i	$-0.157202\pi$
$997$	12.8345	+	12.8345i	0.406473	+	0.406473i	−0.474033	+	0.880507i	$0.657202\pi$
$998$	−3.64482	−	3.64482i	−0.115375	−	0.115375i
$999$	4.28433	−	1.39206i	0.135550	−	0.0440429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bj.b.277.7	yes	128
5.3	odd	4		930.2.bj.a.463.7	✓	128
31.15	odd	10		930.2.bj.a.697.7	yes	128
155.108	even	20	inner	930.2.bj.b.883.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bj.a.463.7	✓	128	5.3	odd	4
930.2.bj.a.697.7	yes	128	31.15	odd	10
930.2.bj.b.277.7	yes	128	1.1	even	1	trivial
930.2.bj.b.883.7	yes	128	155.108	even	20	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.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.61098 - 1.55073i) q^{5} +1.00000i q^{6} +(-1.36477 + 2.67852i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.61098 - 1.55073i) q^{5} +1.00000i q^{6} +(-1.36477 + 2.67852i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +(-1.78365 - 1.34855i) q^{10} +(2.11928 - 0.688597i) q^{11} +(0.987688 - 0.156434i) q^{12} +(-6.87689 - 1.08919i) q^{13} +(2.85904 + 0.928958i) q^{14} +(-1.83373 + 1.27962i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.917097 - 1.79990i) q^{17} +(0.156434 - 0.987688i) q^{18} +(-1.13393 + 1.56073i) q^{19} +(-1.05293 + 1.97265i) q^{20} +(1.76698 - 2.43204i) q^{21} +(-1.01165 - 1.98547i) q^{22} +(-1.82777 + 0.931295i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(0.190487 - 4.99637i) q^{25} +6.96261i q^{26} +(-0.891007 - 0.453990i) q^{27} +(0.470269 - 2.96916i) q^{28} +(-6.04997 - 4.39556i) q^{29} +(1.55073 + 1.61098i) q^{30} +(-5.47453 - 1.01466i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.20091 + 0.348590i) q^{33} +(-1.63428 + 1.18737i) q^{34} +(1.95504 + 6.43142i) q^{35} -1.00000 q^{36} +(-3.18538 + 3.18538i) q^{37} +(1.71890 + 0.875822i) q^{38} +(6.62183 + 2.15156i) q^{39} +(2.11308 + 0.731374i) q^{40} +(3.47851 + 2.52729i) q^{41} +(-2.67852 - 1.36477i) q^{42} +(-0.712853 - 4.50078i) q^{43} +(-1.80277 + 1.30979i) q^{44} +(2.01133 - 0.977011i) q^{45} +(1.20575 + 1.65958i) q^{46} +(-5.31061 - 0.841118i) q^{47} +(-0.891007 + 0.453990i) q^{48} +(-1.19736 - 1.64803i) q^{49} +(-4.96466 + 0.593463i) q^{50} +(0.624239 + 1.92121i) q^{51} +(6.87689 - 1.08919i) q^{52} +(-7.30852 + 3.72388i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(2.34629 - 4.39575i) q^{55} -3.00617 q^{56} +(1.36413 - 1.36413i) q^{57} +(-3.39502 + 6.66310i) q^{58} +(0.288245 + 0.396735i) q^{59} +(1.34855 - 1.78365i) q^{60} -4.20268i q^{61} +(-0.145760 + 5.56586i) q^{62} +(-2.12569 + 2.12569i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-12.7675 + 8.90952i) q^{65} +(0.688597 + 2.11928i) q^{66} +(10.6362 + 10.6362i) q^{67} +(1.42841 + 1.42841i) q^{68} +(1.95095 - 0.633903i) q^{69} +(6.04641 - 2.93706i) q^{70} +(-3.24666 + 9.99219i) q^{71} +(0.156434 + 0.987688i) q^{72} +(-3.55590 + 6.97884i) q^{73} +(3.64446 + 2.64786i) q^{74} +(-0.969746 + 4.90506i) q^{75} +(0.596145 - 1.83474i) q^{76} +(-1.04792 + 6.61633i) q^{77} +(1.08919 - 6.87689i) q^{78} +(0.181602 - 0.558913i) q^{79} +(0.391812 - 2.20147i) q^{80} +(0.809017 + 0.587785i) q^{81} +(1.95201 - 3.83104i) q^{82} +(-0.666589 - 4.20867i) q^{83} +(-0.928958 + 2.85904i) q^{84} +(-4.26858 - 1.47743i) q^{85} +(-4.33385 + 1.40815i) q^{86} +(5.28787 + 5.28787i) q^{87} +(1.57568 + 1.57568i) q^{88} +(-2.89504 - 8.91003i) q^{89} +(-1.27962 - 1.83373i) q^{90} +(12.3028 - 16.9334i) q^{91} +(1.45053 - 1.45053i) q^{92} +(5.24840 + 1.85857i) q^{93} +5.37681i q^{94} +(0.593521 + 4.27272i) q^{95} +(0.587785 + 0.809017i) q^{96} +(-0.812745 + 1.59510i) q^{97} +(-1.44043 + 1.44043i) q^{98} +2.22835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{7}+O(q^{10}) \) 128 * q + 4 * q^7	\( 128 q + 4 q^{7} - 4 q^{10} - 4 q^{15} + 32 q^{16} + 12 q^{17} + 40 q^{19} + 40 q^{21} + 4 q^{22} + 32 q^{24} - 8 q^{25} - 4 q^{28} - 8 q^{29} + 20 q^{31} + 4 q^{33} + 24 q^{35} - 128 q^{36} - 64 q^{37} - 16 q^{38} - 24 q^{41} + 16 q^{42} - 24 q^{43} + 8 q^{44} + 20 q^{46} - 12 q^{47} + 100 q^{49} - 24 q^{50} + 64 q^{53} + 32 q^{54} + 68 q^{55} - 16 q^{57} + 40 q^{58} + 8 q^{62} - 4 q^{63} + 84 q^{65} - 12 q^{66} - 32 q^{67} - 8 q^{68} + 88 q^{70} + 24 q^{71} + 20 q^{73} + 16 q^{74} - 24 q^{75} - 24 q^{76} + 60 q^{77} + 56 q^{79} + 32 q^{81} - 16 q^{82} + 8 q^{83} - 68 q^{85} - 20 q^{87} + 4 q^{88} - 136 q^{89} - 40 q^{91} + 48 q^{93} - 92 q^{95} + 64 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 128 * q + 4 * q^7 - 4 * q^10 - 4 * q^15 + 32 * q^16 + 12 * q^17 + 40 * q^19 + 40 * q^21 + 4 * q^22 + 32 * q^24 - 8 * q^25 - 4 * q^28 - 8 * q^29 + 20 * q^31 + 4 * q^33 + 24 * q^35 - 128 * q^36 - 64 * q^37 - 16 * q^38 - 24 * q^41 + 16 * q^42 - 24 * q^43 + 8 * q^44 + 20 * q^46 - 12 * q^47 + 100 * q^49 - 24 * q^50 + 64 * q^53 + 32 * q^54 + 68 * q^55 - 16 * q^57 + 40 * q^58 + 8 * q^62 - 4 * q^63 + 84 * q^65 - 12 * q^66 - 32 * q^67 - 8 * q^68 + 88 * q^70 + 24 * q^71 + 20 * q^73 + 16 * q^74 - 24 * q^75 - 24 * q^76 + 60 * q^77 + 56 * q^79 + 32 * q^81 - 16 * q^82 + 8 * q^83 - 68 * q^85 - 20 * q^87 + 4 * q^88 - 136 * q^89 - 40 * q^91 + 48 * q^93 - 92 * q^95 + 64 * q^97 - 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more