LMFDB - Embedded newform 930.2.r.b.119.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (of order $6$, degree $2$, 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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.7
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.30243 + 1.14178i) q^{3} +1.00000 q^{4} +(1.95677 + 1.08215i) q^{5} +(-1.30243 + 1.14178i) q^{6} +(4.20156 + 2.42577i) q^{7} +1.00000 q^{8} +(0.392656 - 2.97419i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.30243 + 1.14178i) q^{3} +1.00000 q^{4} +(1.95677 + 1.08215i) q^{5} +(-1.30243 + 1.14178i) q^{6} +(4.20156 + 2.42577i) q^{7} +1.00000 q^{8} +(0.392656 - 2.97419i) q^{9} +(1.95677 + 1.08215i) q^{10} +(0.613210 + 1.06211i) q^{11} +(-1.30243 + 1.14178i) q^{12} +(0.733571 + 1.27058i) q^{13} +(4.20156 + 2.42577i) q^{14} +(-3.78414 + 0.824789i) q^{15} +1.00000 q^{16} +(-3.27327 - 1.88983i) q^{17} +(0.392656 - 2.97419i) q^{18} +(2.65459 - 4.59788i) q^{19} +(1.95677 + 1.08215i) q^{20} +(-8.24195 + 1.63787i) q^{21} +(0.613210 + 1.06211i) q^{22} -6.72188i q^{23} +(-1.30243 + 1.14178i) q^{24} +(2.65791 + 4.23503i) q^{25} +(0.733571 + 1.27058i) q^{26} +(2.88448 + 4.32201i) q^{27} +(4.20156 + 2.42577i) q^{28} -5.15742 q^{29} +(-3.78414 + 0.824789i) q^{30} +(-5.54251 + 0.529744i) q^{31} +1.00000 q^{32} +(-2.01137 - 0.683174i) q^{33} +(-3.27327 - 1.88983i) q^{34} +(5.59645 + 9.29338i) q^{35} +(0.392656 - 2.97419i) q^{36} +(-1.72299 + 2.98431i) q^{37} +(2.65459 - 4.59788i) q^{38} +(-2.40616 - 0.817266i) q^{39} +(1.95677 + 1.08215i) q^{40} +(1.44137 - 0.832174i) q^{41} +(-8.24195 + 1.63787i) q^{42} +(1.37011 - 2.37311i) q^{43} +(0.613210 + 1.06211i) q^{44} +(3.98685 - 5.39491i) q^{45} -6.72188i q^{46} +5.00458 q^{47} +(-1.30243 + 1.14178i) q^{48} +(8.26872 + 14.3218i) q^{49} +(2.65791 + 4.23503i) q^{50} +(6.42099 - 1.27601i) q^{51} +(0.733571 + 1.27058i) q^{52} +(-3.13635 + 1.81077i) q^{53} +(2.88448 + 4.32201i) q^{54} +(0.0505518 + 2.74189i) q^{55} +(4.20156 + 2.42577i) q^{56} +(1.79237 + 9.01939i) q^{57} -5.15742 q^{58} +(-12.1296 - 7.00301i) q^{59} +(-3.78414 + 0.824789i) q^{60} +7.18747i q^{61} +(-5.54251 + 0.529744i) q^{62} +(8.86447 - 11.5437i) q^{63} +1.00000 q^{64} +(0.0604740 + 3.28007i) q^{65} +(-2.01137 - 0.683174i) q^{66} +(-12.5793 + 7.26264i) q^{67} +(-3.27327 - 1.88983i) q^{68} +(7.67494 + 8.75479i) q^{69} +(5.59645 + 9.29338i) q^{70} +(4.89947 - 2.82871i) q^{71} +(0.392656 - 2.97419i) q^{72} +(-0.218186 - 0.377910i) q^{73} +(-1.72299 + 2.98431i) q^{74} +(-8.29725 - 2.48107i) q^{75} +(2.65459 - 4.59788i) q^{76} +5.95003i q^{77} +(-2.40616 - 0.817266i) q^{78} +(-4.39774 - 2.53904i) q^{79} +(1.95677 + 1.08215i) q^{80} +(-8.69164 - 2.33567i) q^{81} +(1.44137 - 0.832174i) q^{82} +(2.21035 - 1.27615i) q^{83} +(-8.24195 + 1.63787i) q^{84} +(-4.35998 - 7.24012i) q^{85} +(1.37011 - 2.37311i) q^{86} +(6.71718 - 5.88866i) q^{87} +(0.613210 + 1.06211i) q^{88} +12.3868 q^{89} +(3.98685 - 5.39491i) q^{90} +7.11789i q^{91} -6.72188i q^{92} +(6.61388 - 7.01830i) q^{93} +5.00458 q^{94} +(10.1700 - 6.12435i) q^{95} +(-1.30243 + 1.14178i) q^{96} +14.0563i q^{97} +(8.26872 + 14.3218i) q^{98} +(3.39971 - 1.40676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.30243	+	1.14178i	−0.751959	+	0.659210i
$3$	−1.30243	+	1.14178i	−0.751959	+	0.659210i
$4$	1.00000			0.500000
$5$	1.95677	+	1.08215i	0.875095	+	0.483951i
$5$	1.95677	+	1.08215i	0.875095	+	0.483951i
$6$	−1.30243	+	1.14178i	−0.531715	+	0.466132i
$7$	4.20156	+	2.42577i	1.58804	+	0.916855i	0.993630	+	0.112692i	$0.0359474\pi$
$7$	4.20156	+	2.42577i	1.58804	+	0.916855i	0.594409	+	0.804163i	$0.297386\pi$
$8$	1.00000			0.353553
$9$	0.392656	−	2.97419i	0.130885	−	0.991398i
$10$	1.95677	+	1.08215i	0.618786	+	0.342205i
$11$	0.613210	+	1.06211i	0.184890	+	0.320239i	0.943539	−	0.331260i	$-0.107474\pi$
$11$	0.613210	+	1.06211i	0.184890	+	0.320239i	−0.758650	+	0.651499i	$0.774140\pi$
$12$	−1.30243	+	1.14178i	−0.375980	+	0.329605i
$13$	0.733571	+	1.27058i	0.203456	+	0.352396i	0.949640	−	0.313344i	$-0.101449\pi$
$13$	0.733571	+	1.27058i	0.203456	+	0.352396i	−0.746184	+	0.665740i	$0.768116\pi$
$14$	4.20156	+	2.42577i	1.12291	+	0.648314i
$15$	−3.78414	+	0.824789i	−0.977061	+	0.212960i
$16$	1.00000			0.250000
$17$	−3.27327	−	1.88983i	−0.793886	−	0.458350i	0.0474430	−	0.998874i	$-0.484893\pi$
$17$	−3.27327	−	1.88983i	−0.793886	−	0.458350i	−0.841329	+	0.540524i	$0.818226\pi$
$18$	0.392656	−	2.97419i	0.0925499	−	0.701024i
$19$	2.65459	−	4.59788i	0.609004	−	1.05483i	−0.382401	−	0.923996i	$-0.624903\pi$
$19$	2.65459	−	4.59788i	0.609004	−	1.05483i	0.991405	−	0.130829i	$-0.0417639\pi$
$20$	1.95677	+	1.08215i	0.437548	+	0.241976i
$21$	−8.24195	+	1.63787i	−1.79854	+	0.357413i
$22$	0.613210	+	1.06211i	0.130737	+	0.226443i
$23$		−	6.72188i		−	1.40161i	−0.713353	−	0.700805i	$-0.752824\pi$
$23$		−	6.72188i		−	1.40161i	0.713353	−	0.700805i	$-0.247176\pi$
$24$	−1.30243	+	1.14178i	−0.265858	+	0.233066i
$25$	2.65791	+	4.23503i	0.531583	+	0.847006i
$26$	0.733571	+	1.27058i	0.143865	+	0.249182i
$27$	2.88448	+	4.32201i	0.555118	+	0.831771i
$28$	4.20156	+	2.42577i	0.794020	+	0.458427i
$29$	−5.15742			−0.957708			−0.478854	−	0.877895i	$-0.658948\pi$
$29$	−5.15742			−0.957708			−0.478854	+	0.877895i	$0.658948\pi$
$30$	−3.78414	+	0.824789i	−0.690886	+	0.150585i
$31$	−5.54251	+	0.529744i	−0.995463	+	0.0951449i
$31$	−5.54251	+	0.529744i	−0.995463	+	0.0951449i
$32$	1.00000			0.176777
$33$	−2.01137	−	0.683174i	−0.350134	−	0.118925i
$34$	−3.27327	−	1.88983i	−0.561362	−	0.324102i
$35$	5.59645	+	9.29338i	0.945972	+	1.57087i
$36$	0.392656	−	2.97419i	0.0654426	−	0.495699i
$37$	−1.72299	+	2.98431i	−0.283258	+	0.490617i	−0.972185	−	0.234213i	$-0.924749\pi$
$37$	−1.72299	+	2.98431i	−0.283258	+	0.490617i	0.688927	+	0.724831i	$0.258082\pi$
$38$	2.65459	−	4.59788i	0.430631	−	0.745874i
$39$	−2.40616	−	0.817266i	−0.385293	−	0.130867i
$40$	1.95677	+	1.08215i	0.309393	+	0.171103i
$41$	1.44137	−	0.832174i	0.225104	−	0.129964i	−0.383207	−	0.923662i	$-0.625181\pi$
$41$	1.44137	−	0.832174i	0.225104	−	0.129964i	0.608311	+	0.793699i	$0.291847\pi$
$42$	−8.24195	+	1.63787i	−1.27176	+	0.252729i
$43$	1.37011	−	2.37311i	0.208940	−	0.361896i	−0.742441	−	0.669912i	$-0.766332\pi$
$43$	1.37011	−	2.37311i	0.208940	−	0.361896i	0.951381	+	0.308016i	$0.0996652\pi$
$44$	0.613210	+	1.06211i	0.0924450	+	0.160119i
$45$	3.98685	−	5.39491i	0.594325	−	0.804225i
$46$		−	6.72188i		−	0.991088i
$47$	5.00458			0.729994			0.364997	−	0.931009i	$-0.381070\pi$
$47$	5.00458			0.729994			0.364997	+	0.931009i	$0.381070\pi$
$48$	−1.30243	+	1.14178i	−0.187990	+	0.164802i
$49$	8.26872	+	14.3218i	1.18125	+	2.04598i
$50$	2.65791	+	4.23503i	0.375886	+	0.598924i
$51$	6.42099	−	1.27601i	0.899118	−	0.178677i
$52$	0.733571	+	1.27058i	0.101728	+	0.176198i
$53$	−3.13635	+	1.81077i	−0.430811	+	0.248729i	−0.699692	−	0.714445i	$-0.746679\pi$
$53$	−3.13635	+	1.81077i	−0.430811	+	0.248729i	0.268881	+	0.963173i	$0.413346\pi$
$54$	2.88448	+	4.32201i	0.392528	+	0.588151i
$55$	0.0505518	+	2.74189i	0.00681640	+	0.369717i
$56$	4.20156	+	2.42577i	0.561457	+	0.324157i
$57$	1.79237	+	9.01939i	0.237405	+	1.19465i
$58$	−5.15742			−0.677202
$59$	−12.1296	−	7.00301i	−1.57914	−	0.911714i	−0.994980	−	0.100072i	$-0.968093\pi$
$59$	−12.1296	−	7.00301i	−1.57914	−	0.911714i	−0.584155	−	0.811642i	$-0.698574\pi$
$60$	−3.78414	+	0.824789i	−0.488530	+	0.106480i
$61$			7.18747i			0.920261i	0.887851	+	0.460130i	$0.152197\pi$
$61$			7.18747i			0.920261i	−0.887851	+	0.460130i	$0.847803\pi$
$62$	−5.54251	+	0.529744i	−0.703899	+	0.0672776i
$63$	8.86447	−	11.5437i	1.11682	−	1.45438i
$64$	1.00000			0.125000
$65$	0.0604740	+	3.28007i	0.00750088	+	0.406843i
$66$	−2.01137	−	0.683174i	−0.247582	−	0.0840928i
$67$	−12.5793	+	7.26264i	−1.53680	+	0.887273i	−0.537779	+	0.843086i	$0.680736\pi$
$67$	−12.5793	+	7.26264i	−1.53680	+	0.887273i	−0.999023	+	0.0441870i	$0.985930\pi$
$68$	−3.27327	−	1.88983i	−0.396943	−	0.229175i
$69$	7.67494	+	8.75479i	0.923955	+	1.05395i
$70$	5.59645	+	9.29338i	0.668904	+	1.11077i
$71$	4.89947	−	2.82871i	0.581461	−	0.335706i	−0.180253	−	0.983620i	$-0.557692\pi$
$71$	4.89947	−	2.82871i	0.581461	−	0.335706i	0.761714	+	0.647914i	$0.224358\pi$
$72$	0.392656	−	2.97419i	0.0462749	−	0.350512i
$73$	−0.218186	−	0.377910i	−0.0255368	−	0.0442310i	0.852975	−	0.521952i	$-0.174796\pi$
$73$	−0.218186	−	0.377910i	−0.0255368	−	0.0442310i	−0.878511	+	0.477721i	$0.841463\pi$
$74$	−1.72299	+	2.98431i	−0.200294	+	0.346919i
$75$	−8.29725	−	2.48107i	−0.958083	−	0.286490i
$76$	2.65459	−	4.59788i	0.304502	−	0.527413i
$77$			5.95003i			0.678069i
$78$	−2.40616	−	0.817266i	−0.272444	−	0.0925371i
$79$	−4.39774	−	2.53904i	−0.494785	−	0.285664i	0.231773	−	0.972770i	$-0.425548\pi$
$79$	−4.39774	−	2.53904i	−0.494785	−	0.285664i	−0.726557	+	0.687106i	$0.758881\pi$
$80$	1.95677	+	1.08215i	0.218774	+	0.120988i
$81$	−8.69164	−	2.33567i	−0.965738	−	0.259519i
$82$	1.44137	−	0.832174i	0.159172	−	0.0918983i
$83$	2.21035	−	1.27615i	0.242618	−	0.140075i	−0.373761	−	0.927525i	$-0.621932\pi$
$83$	2.21035	−	1.27615i	0.242618	−	0.140075i	0.616379	+	0.787449i	$0.288599\pi$
$84$	−8.24195	+	1.63787i	−0.899270	+	0.178707i
$85$	−4.35998	−	7.24012i	−0.472906	−	0.785302i
$86$	1.37011	−	2.37311i	0.147743	−	0.255899i
$87$	6.71718	−	5.88866i	0.720157	−	0.631330i
$88$	0.613210	+	1.06211i	0.0653685	+	0.113221i
$89$	12.3868			1.31300			0.656501	−	0.754325i	$-0.272036\pi$
$89$	12.3868			1.31300			0.656501	+	0.754325i	$0.272036\pi$
$90$	3.98685	−	5.39491i	0.420251	−	0.568673i
$91$			7.11789i			0.746158i
$92$		−	6.72188i		−	0.700805i
$93$	6.61388	−	7.01830i	0.685827	−	0.727764i
$94$	5.00458			0.516184
$95$	10.1700	−	6.12435i	1.04342	−	0.628345i
$96$	−1.30243	+	1.14178i	−0.132929	+	0.116533i
$97$			14.0563i			1.42720i	0.700555	+	0.713599i	$0.252936\pi$
$97$			14.0563i			1.42720i	−0.700555	+	0.713599i	$0.747064\pi$
$98$	8.26872	+	14.3218i	0.835267	+	1.44672i
$99$	3.39971	−	1.40676i	0.341683	−	0.141385i
$100$	2.65791	+	4.23503i	0.265791	+	0.423503i
$101$		−	8.98721i		−	0.894261i	−0.894469	−	0.447130i	$-0.852446\pi$
$101$		−	8.98721i		−	0.894261i	0.894469	−	0.447130i	$-0.147554\pi$
$102$	6.42099	−	1.27601i	0.635773	−	0.126343i
$103$	2.37364	−	1.37042i	0.233881	−	0.135031i	−0.378480	−	0.925609i	$-0.623553\pi$
$103$	2.37364	−	1.37042i	0.233881	−	0.135031i	0.612361	+	0.790578i	$0.290220\pi$
$104$	0.733571	+	1.27058i	0.0719325	+	0.124591i
$105$	−17.9000	−	5.71406i	−1.74686	−	0.557635i
$106$	−3.13635	+	1.81077i	−0.304629	+	0.175878i
$107$	2.90858	−	5.03780i	0.281183	−	0.487023i	−0.690494	−	0.723338i	$-0.742607\pi$
$107$	2.90858	−	5.03780i	0.281183	−	0.487023i	0.971676	+	0.236316i	$0.0759400\pi$
$108$	2.88448	+	4.32201i	0.277559	+	0.415886i
$109$	−10.2430			−0.981098			−0.490549	−	0.871414i	$-0.663204\pi$
$109$	−10.2430			−0.981098			−0.490549	+	0.871414i	$0.663204\pi$
$110$	0.0505518	+	2.74189i	0.00481992	+	0.261429i
$111$	−1.16336	−	5.85414i	−0.110421	−	0.555651i
$112$	4.20156	+	2.42577i	0.397010	+	0.229214i
$113$	−5.92849	−	10.2684i	−0.557705	−	0.965974i	−0.997688	−	0.0679674i	$-0.978349\pi$
$113$	−5.92849	−	10.2684i	−0.557705	−	0.965974i	0.439982	−	0.898006i	$-0.354985\pi$
$114$	1.79237	+	9.01939i	0.167871	+	0.844743i
$115$	7.27407	−	13.1532i	0.678310	−	1.22654i
$116$	−5.15742			−0.478854
$117$	4.06700	−	1.68288i	0.375994	−	0.155582i
$118$	−12.1296	−	7.00301i	−1.11662	−	0.644679i
$119$	−9.16857	−	15.8804i	−0.840481	−	1.45576i
$120$	−3.78414	+	0.824789i	−0.345443	+	0.0752926i
$121$	4.74795	−	8.22368i	0.431631	−	0.747608i
$122$			7.18747i			0.650723i
$123$	−0.927120	+	2.72958i	−0.0835956	+	0.246118i
$124$	−5.54251	+	0.529744i	−0.497732	+	0.0475724i
$125$	0.618004	+	11.1632i	0.0552760	+	0.998471i
$126$	8.86447	−	11.5437i	0.789710	−	1.02840i
$127$	3.38672	−	5.86597i	0.300523	−	0.520521i	−0.675732	−	0.737148i	$-0.736172\pi$
$127$	3.38672	−	5.86597i	0.300523	−	0.520521i	0.976254	+	0.216627i	$0.0695055\pi$
$128$	1.00000			0.0883883
$129$	0.925098	+	4.65519i	0.0814503	+	0.409866i
$130$	0.0604740	+	3.28007i	0.00530392	+	0.287681i
$131$	−6.31523	−	3.64610i	−0.551765	−	0.318561i	0.198069	−	0.980188i	$-0.436533\pi$
$131$	−6.31523	−	3.64610i	−0.551765	−	0.318561i	−0.749833	+	0.661627i	$0.769866\pi$
$132$	−2.01137	−	0.683174i	−0.175067	−	0.0594626i
$133$	22.3068	−	12.8788i	1.93424	−	1.11674i
$134$	−12.5793	+	7.26264i	−1.08668	+	0.627397i
$135$	0.967217	+	11.5786i	0.0832448	+	0.996529i
$136$	−3.27327	−	1.88983i	−0.280681	−	0.162051i
$137$	−10.3598	+	5.98123i	−0.885097	+	0.511011i	−0.872336	−	0.488908i	$-0.837395\pi$
$137$	−10.3598	+	5.98123i	−0.885097	+	0.511011i	−0.0127612	+	0.999919i	$0.504062\pi$
$138$	7.67494	+	8.75479i	0.653335	+	0.745257i
$139$		−	23.2512i		−	1.97214i	−0.166319	−	0.986072i	$-0.553188\pi$
$139$		−	23.2512i		−	1.97214i	0.166319	−	0.986072i	$-0.446812\pi$
$140$	5.59645	+	9.29338i	0.472986	+	0.785434i
$141$	−6.51813	+	5.71416i	−0.548926	+	0.481219i
$142$	4.89947	−	2.82871i	0.411155	−	0.237380i
$143$	−0.899666	+	1.55827i	−0.0752339	+	0.130309i
$144$	0.392656	−	2.97419i	0.0327213	−	0.247849i
$145$	−10.0919	−	5.58108i	−0.838086	−	0.463484i
$146$	−0.218186	−	0.377910i	−0.0180572	−	0.0312761i
$147$	−27.1219	−	9.21212i	−2.23698	−	0.759803i
$148$	−1.72299	+	2.98431i	−0.141629	+	0.245309i
$149$	−12.9604	−	7.48268i	−1.06176	−	0.613005i	−0.135838	−	0.990731i	$-0.543373\pi$
$149$	−12.9604	−	7.48268i	−1.06176	−	0.613005i	−0.925917	+	0.377726i	$0.876706\pi$
$150$	−8.29725	−	2.48107i	−0.677467	−	0.202579i
$151$			6.74649i			0.549022i	0.961584	+	0.274511i	$0.0885159\pi$
$151$			6.74649i			0.549022i	−0.961584	+	0.274511i	$0.911484\pi$
$152$	2.65459	−	4.59788i	0.215315	−	0.372937i
$153$	−6.90598	+	8.99330i	−0.558315	+	0.727065i
$154$			5.95003i			0.479467i
$155$	−11.4187	−	4.96122i	−0.917171	−	0.398495i
$156$	−2.40616	−	0.817266i	−0.192647	−	0.0654336i
$157$			8.54850i			0.682245i	0.940019	+	0.341122i	$0.110807\pi$
$157$			8.54850i			0.682245i	−0.940019	+	0.341122i	$0.889193\pi$
$158$	−4.39774	−	2.53904i	−0.349866	−	0.201995i
$159$	2.01737	−	5.93944i	0.159988	−	0.471029i
$160$	1.95677	+	1.08215i	0.154696	+	0.0855513i
$161$	16.3057	−	28.2424i	1.28507	−	2.22581i
$162$	−8.69164	−	2.33567i	−0.682880	−	0.183507i
$163$			8.61619i			0.674872i	0.941348	+	0.337436i	$0.109560\pi$
$163$			8.61619i			0.674872i	−0.941348	+	0.337436i	$0.890440\pi$
$164$	1.44137	−	0.832174i	0.112552	−	0.0649819i
$165$	−3.19649	−	3.51341i	−0.248847	−	0.273519i
$166$	2.21035	−	1.27615i	0.171557	−	0.0990483i
$167$	−13.9138	−	8.03314i	−1.07668	−	0.621623i	−0.146683	−	0.989184i	$-0.546860\pi$
$167$	−13.9138	−	8.03314i	−1.07668	−	0.621623i	−0.929999	+	0.367561i	$0.880193\pi$
$168$	−8.24195	+	1.63787i	−0.635880	+	0.126365i
$169$	5.42375	−	9.39421i	0.417211	−	0.722631i
$170$	−4.35998	−	7.24012i	−0.334395	−	0.555292i
$171$	−12.6326	−	9.70063i	−0.966042	−	0.741826i
$172$	1.37011	−	2.37311i	0.104470	−	0.180948i
$173$	11.7912	+	20.4229i	0.896467	+	1.55273i	0.831979	+	0.554807i	$0.187208\pi$
$173$	11.7912	+	20.4229i	0.896467	+	1.55273i	0.0644877	+	0.997919i	$0.479459\pi$
$174$	6.71718	−	5.88866i	0.509228	−	0.446418i
$175$	0.894165	+	24.2412i	0.0675925	+	1.83246i
$176$	0.613210	+	1.06211i	0.0462225	+	0.0800597i
$177$	23.7939	−	4.72841i	1.78846	−	0.355409i
$178$	12.3868			0.928432
$179$	−12.3901	+	21.4603i	−0.926079	+	1.60402i	−0.136263	+	0.990673i	$0.543509\pi$
$179$	−12.3901	+	21.4603i	−0.926079	+	1.60402i	−0.789816	+	0.613344i	$0.789824\pi$
$180$	3.98685	−	5.39491i	0.297162	−	0.402113i
$181$	22.3120	−	12.8818i	1.65844	−	0.957500i	0.685002	−	0.728541i	$-0.259801\pi$
$181$	22.3120	−	12.8818i	1.65844	−	0.957500i	0.973436	−	0.228959i	$-0.0735322\pi$
$182$			7.11789i			0.527613i
$183$	−8.20654	−	9.36118i	−0.606645	−	0.691999i
$184$		−	6.72188i		−	0.495544i
$185$	−6.60097	+	3.97508i	−0.485313	+	0.292254i
$186$	6.61388	−	7.01830i	0.484953	−	0.514607i
$187$		−	4.63544i		−	0.338977i
$188$	5.00458			0.364997
$189$	1.63510	+	25.1563i	0.118936	+	1.82985i
$190$	10.1700	−	6.12435i	0.737810	−	0.444307i
$191$	5.66215	−	3.26904i	0.409699	−	0.236540i	−0.280961	−	0.959719i	$-0.590653\pi$
$191$	5.66215	−	3.26904i	0.409699	−	0.236540i	0.690660	+	0.723179i	$0.257320\pi$
$192$	−1.30243	+	1.14178i	−0.0939949	+	0.0824012i
$193$	−9.95206	−	5.74583i	−0.716365	−	0.413594i	0.0970482	−	0.995280i	$-0.469060\pi$
$193$	−9.95206	−	5.74583i	−0.716365	−	0.413594i	−0.813413	+	0.581686i	$0.802393\pi$
$194$			14.0563i			1.00918i
$195$	−3.82390	−	4.20302i	−0.273835	−	0.300984i
$196$	8.26872	+	14.3218i	0.590623	+	1.02299i
$197$	6.28191	−	3.62687i	0.447568	−	0.258403i	−0.259235	−	0.965814i	$-0.583470\pi$
$197$	6.28191	−	3.62687i	0.447568	−	0.258403i	0.706802	+	0.707411i	$0.250137\pi$
$198$	3.39971	−	1.40676i	0.241607	−	0.0999742i
$199$	16.6477	−	9.61156i	1.18013	−	0.681345i	0.224082	−	0.974570i	$-0.428062\pi$
$199$	16.6477	−	9.61156i	1.18013	−	0.681345i	0.956043	+	0.293225i	$0.0947285\pi$
$200$	2.65791	+	4.23503i	0.187943	+	0.299462i
$201$	8.09126	−	23.8219i	0.570713	−	1.68027i
$202$		−	8.98721i		−	0.632338i
$203$	−21.6692	−	12.5107i	−1.52088	−	0.878079i
$204$	6.42099	−	1.27601i	0.449559	−	0.0893383i
$205$	3.72096	−	0.0686027i	0.259883	−	0.00479142i
$206$	2.37364	−	1.37042i	0.165379	−	0.0954817i
$207$	−19.9922	−	2.63939i	−1.38955	−	0.183450i
$208$	0.733571	+	1.27058i	0.0508640	+	0.0880990i
$209$	6.51128			0.450395
$210$	−17.9000	−	5.71406i	−1.23522	−	0.394307i
$211$	3.18547	−	5.51739i	0.219297	−	0.379833i	−0.735297	−	0.677746i	$-0.762957\pi$
$211$	3.18547	−	5.51739i	0.219297	−	0.379833i	0.954593	+	0.297913i	$0.0962904\pi$
$212$	−3.13635	+	1.81077i	−0.215405	+	0.124364i
$213$	−3.15145	+	9.27835i	−0.215934	+	0.635742i
$214$	2.90858	−	5.03780i	0.198826	−	0.344377i
$215$	5.24905	−	3.16097i	0.357982	−	0.215576i
$216$	2.88448	+	4.32201i	0.196264	+	0.294076i
$217$	−24.5722	−	11.2191i	−1.66807	−	0.761602i
$218$	−10.2430			−0.693741
$219$	0.715665	+	0.243080i	0.0483601	+	0.0164258i
$220$	0.0505518	+	2.74189i	0.00340820	+	0.184859i
$221$		−	5.54528i		−	0.373016i
$222$	−1.16336	−	5.85414i	−0.0780796	−	0.392904i
$223$	−1.55000	+	2.68467i	−0.103795	+	0.179779i	−0.913245	−	0.407410i	$-0.866432\pi$
$223$	−1.55000	+	2.68467i	−0.103795	+	0.179779i	0.809450	+	0.587189i	$0.199765\pi$
$224$	4.20156	+	2.42577i	0.280728	+	0.162079i
$225$	13.6394	−	6.24224i	0.909296	−	0.416149i
$226$	−5.92849	−	10.2684i	−0.394357	−	0.683047i
$227$	5.80110	+	10.0478i	0.385033	+	0.666896i	0.991774	−	0.128003i	$-0.0408568\pi$
$227$	5.80110	+	10.0478i	0.385033	+	0.666896i	−0.606741	+	0.794900i	$0.707524\pi$
$228$	1.79237	+	9.01939i	0.118703	+	0.597324i
$229$	19.9216	+	11.5017i	1.31645	+	0.760055i	0.983156	−	0.182767i	$-0.0585053\pi$
$229$	19.9216	+	11.5017i	1.31645	+	0.760055i	0.333297	+	0.942822i	$0.391839\pi$
$230$	7.27407	−	13.1532i	0.479638	−	0.867296i
$231$	−6.79365	−	7.74951i	−0.446990	−	0.509880i
$232$	−5.15742			−0.338601
$233$	−11.5244			−0.754991			−0.377496	−	0.926011i	$-0.623215\pi$
$233$	−11.5244			−0.754991			−0.377496	+	0.926011i	$0.623215\pi$
$234$	4.06700	−	1.68288i	0.265868	−	0.110013i
$235$	9.79283	+	5.41570i	0.638814	+	0.353281i
$236$	−12.1296	−	7.00301i	−0.789568	−	0.455857i
$237$	8.62679	−	1.71435i	0.560371	−	0.111359i
$238$	−9.16857	−	15.8804i	−0.594310	−	1.02937i
$239$	3.13030	+	5.42184i	0.202482	+	0.350710i	0.949328	−	0.314288i	$-0.101766\pi$
$239$	3.13030	+	5.42184i	0.202482	+	0.350710i	−0.746845	+	0.664998i	$0.768432\pi$
$240$	−3.78414	+	0.824789i	−0.244265	+	0.0532399i
$241$	−16.5387	−	9.54864i	−1.06535	−	0.615082i	−0.138445	−	0.990370i	$-0.544210\pi$
$241$	−16.5387	−	9.54864i	−1.06535	−	0.615082i	−0.926908	+	0.375288i	$0.877544\pi$
$242$	4.74795	−	8.22368i	0.305210	−	0.528638i
$243$	13.9871	−	6.88194i	0.897273	−	0.441476i
$244$			7.18747i			0.460130i
$245$	0.681656	+	36.9726i	0.0435494	+	2.36209i
$246$	−0.927120	+	2.72958i	−0.0591110	+	0.174032i
$247$	7.78931			0.495622
$248$	−5.54251	+	0.529744i	−0.351949	+	0.0336388i
$249$	−1.42175	+	4.18584i	−0.0900996	+	0.265267i
$250$	0.618004	+	11.1632i	0.0390860	+	0.706026i
$251$	4.28946	−	7.42956i	0.270748	−	0.468949i	−0.698306	−	0.715800i	$-0.746062\pi$
$251$	4.28946	−	7.42956i	0.270748	−	0.468949i	0.969054	+	0.246850i	$0.0793956\pi$
$252$	8.86447	−	11.5437i	0.558409	−	0.727188i
$253$	7.13939	−	4.12193i	0.448850	−	0.259143i
$254$	3.38672	−	5.86597i	0.212502	−	0.368064i
$255$	13.9452	+	4.45161i	0.873285	+	0.278770i
$256$	1.00000			0.0625000
$257$	2.27123	+	3.93388i	0.141675	+	0.245389i	0.928128	−	0.372262i	$-0.121418\pi$
$257$	2.27123	+	3.93388i	0.141675	+	0.245389i	−0.786452	+	0.617651i	$0.788084\pi$
$258$	0.925098	+	4.65519i	0.0575941	+	0.289819i
$259$	−14.4785	+	8.35916i	−0.899650	+	0.519413i
$260$	0.0604740	+	3.28007i	0.00375044	+	0.203421i
$261$	−2.02509	+	15.3391i	−0.125350	+	0.949469i
$262$	−6.31523	−	3.64610i	−0.390156	−	0.225257i
$263$		−	12.1422i		−	0.748718i	−0.927284	−	0.374359i	$-0.877863\pi$
$263$		−	12.1422i		−	0.748718i	0.927284	−	0.374359i	$-0.122137\pi$
$264$	−2.01137	−	0.683174i	−0.123791	−	0.0420464i
$265$	−8.09664	+	0.149276i	−0.497373	+	0.00916997i
$266$	22.3068	−	12.8788i	1.36772	−	0.789652i
$267$	−16.1330	+	14.1431i	−0.987323	+	0.865543i
$268$	−12.5793	+	7.26264i	−0.768401	+	0.443637i
$269$	10.7295	+	18.5841i	0.654192	+	1.13309i	0.982096	+	0.188383i	$0.0603245\pi$
$269$	10.7295	+	18.5841i	0.654192	+	1.13309i	−0.327904	+	0.944711i	$0.606342\pi$
$270$	0.967217	+	11.5786i	0.0588630	+	0.704653i
$271$			12.1268i			0.736649i	0.929697	+	0.368325i	$0.120068\pi$
$271$			12.1268i			0.736649i	−0.929697	+	0.368325i	$0.879932\pi$
$272$	−3.27327	−	1.88983i	−0.198471	−	0.114588i
$273$	−8.12710	−	9.27057i	−0.491875	−	0.561080i
$274$	−10.3598	+	5.98123i	−0.625858	+	0.361339i
$275$	−2.86822	+	5.41997i	−0.172960	+	0.326836i
$276$	7.67494	+	8.75479i	0.461977	+	0.526977i
$277$	10.5269			0.632498			0.316249	−	0.948676i	$-0.397576\pi$
$277$	10.5269			0.632498			0.316249	+	0.948676i	$0.397576\pi$
$278$		−	23.2512i		−	1.39452i
$279$	−0.600736	+	16.6925i	−0.0359651	+	0.999353i
$280$	5.59645	+	9.29338i	0.334452	+	0.555386i
$281$			14.7922i			0.882428i	0.897402	+	0.441214i	$0.145452\pi$
$281$			14.7922i			0.882428i	−0.897402	+	0.441214i	$0.854548\pi$
$282$	−6.51813	+	5.71416i	−0.388149	+	0.340273i
$283$		−	20.3465i		−	1.20947i	−0.796426	−	0.604736i	$-0.793279\pi$
$283$		−	20.3465i		−	1.20947i	0.796426	−	0.604736i	$-0.206721\pi$
$284$	4.89947	−	2.82871i	0.290730	−	0.167853i
$285$	−6.25305	+	19.5885i	−0.370399	+	1.16032i
$286$	−0.899666	+	1.55827i	−0.0531984	+	0.0921423i
$287$	8.07465			0.476632
$288$	0.392656	−	2.97419i	0.0231375	−	0.175256i
$289$	−1.35712	−	2.35059i	−0.0798303	−	0.138270i
$290$	−10.0919	−	5.58108i	−0.592616	−	0.327732i
$291$	−16.0492	−	18.3073i	−0.940822	−	1.07319i
$292$	−0.218186	−	0.377910i	−0.0127684	−	0.0221155i
$293$	−8.93490	+	15.4757i	−0.521982	+	0.904100i	0.477691	+	0.878528i	$0.341474\pi$
$293$	−8.93490	+	15.4757i	−0.521982	+	0.904100i	−0.999673	+	0.0255719i	$0.991859\pi$
$294$	−27.1219	−	9.21212i	−1.58178	−	0.537262i
$295$	−16.1565	−	26.8293i	−0.940669	−	1.56206i
$296$	−1.72299	+	2.98431i	−0.100147	+	0.173459i
$297$	−2.82166	+	5.71394i	−0.163730	+	0.331557i
$298$	−12.9604	−	7.48268i	−0.750775	−	0.433460i
$299$	8.54070	−	4.93098i	0.493922	−	0.285166i
$300$	−8.29725	−	2.48107i	−0.479042	−	0.143245i
$301$	11.5132	−	6.64716i	0.663611	−	0.383136i
$302$			6.74649i			0.388217i
$303$	10.2615	+	11.7052i	0.589505	+	0.672448i
$304$	2.65459	−	4.59788i	0.152251	−	0.263706i
$305$	−7.77790	+	14.0642i	−0.445361	+	0.805316i
$306$	−6.90598	+	8.99330i	−0.394788	+	0.514113i
$307$	27.7464	+	16.0194i	1.58357	+	0.914275i	0.994332	+	0.106316i	$0.0339056\pi$
$307$	27.7464	+	16.0194i	1.58357	+	0.914275i	0.589239	+	0.807959i	$0.299428\pi$
$308$			5.95003i			0.339034i
$309$	−1.52677	+	4.49506i	−0.0868552	+	0.255715i
$310$	−11.4187	−	4.96122i	−0.648538	−	0.281778i
$311$		−	15.9884i		−	0.906617i	−0.891354	−	0.453308i	$-0.850244\pi$
$311$		−	15.9884i		−	0.906617i	0.891354	−	0.453308i	$-0.149756\pi$
$312$	−2.40616	−	0.817266i	−0.136222	−	0.0462686i
$313$	−2.95626	+	5.12039i	−0.167098	+	0.289421i	−0.937398	−	0.348259i	$-0.886773\pi$
$313$	−2.95626	+	5.12039i	−0.167098	+	0.289421i	0.770301	+	0.637681i	$0.220106\pi$
$314$			8.54850i			0.482420i
$315$	29.8378	−	12.9958i	1.68117	−	0.732231i
$316$	−4.39774	−	2.53904i	−0.247392	−	0.142832i
$317$	−4.61995	+	8.00199i	−0.259482	+	0.449437i	−0.966103	−	0.258156i	$-0.916885\pi$
$317$	−4.61995	+	8.00199i	−0.259482	+	0.449437i	0.706621	+	0.707592i	$0.250219\pi$
$318$	2.01737	−	5.93944i	0.113128	−	0.333067i
$319$	−3.16258	−	5.47775i	−0.177071	−	0.306695i
$320$	1.95677	+	1.08215i	0.109387	+	0.0604939i
$321$	1.96386	+	9.88236i	0.109612	+	0.551579i
$322$	16.3057	−	28.2424i	0.908683	−	1.57389i
$323$	−17.3784	+	10.0334i	−0.966959	+	0.558274i
$324$	−8.69164	−	2.33567i	−0.482869	−	0.129759i
$325$	−3.43119	+	6.48379i	−0.190328	+	0.359656i
$326$			8.61619i			0.477207i
$327$	13.3408	−	11.6953i	0.737746	−	0.646749i
$328$	1.44137	−	0.832174i	0.0795862	−	0.0459491i
$329$	21.0270	+	12.1400i	1.15926	+	0.669298i
$330$	−3.19649	−	3.51341i	−0.175961	−	0.193407i
$331$	−9.28774	+	5.36228i	−0.510500	+	0.294737i	−0.733039	−	0.680186i	$-0.761899\pi$
$331$	−9.28774	+	5.36228i	−0.510500	+	0.294737i	0.222539	+	0.974924i	$0.428566\pi$
$332$	2.21035	−	1.27615i	0.121309	−	0.0700377i
$333$	8.19937	+	6.29632i	0.449323	+	0.345036i
$334$	−13.9138	−	8.03314i	−0.761329	−	0.439554i
$335$	−32.4740	+	0.598717i	−1.77424	+	0.0327114i
$336$	−8.24195	+	1.63787i	−0.449635	+	0.0893533i
$337$	−9.11905			−0.496746			−0.248373	−	0.968664i	$-0.579896\pi$
$337$	−9.11905			−0.496746			−0.248373	+	0.968664i	$0.579896\pi$
$338$	5.42375	−	9.39421i	0.295013	−	0.510978i
$339$	19.4458	+	6.60489i	1.05615	+	0.358728i
$340$	−4.35998	−	7.24012i	−0.236453	−	0.392651i
$341$	−3.96137	−	5.56192i	−0.214520	−	0.301195i
$342$	−12.6326	−	9.70063i	−0.683095	−	0.524550i
$343$			46.2713i			2.49841i
$344$	1.37011	−	2.37311i	0.0738716	−	0.127949i
$345$	5.54414	+	25.4366i	0.298486	+	1.36946i
$346$	11.7912	+	20.4229i	0.633898	+	1.09794i
$347$	20.8204	+	12.0207i	1.11770	+	0.645304i	0.940812	−	0.338927i	$-0.110064\pi$
$347$	20.8204	+	12.0207i	1.11770	+	0.645304i	0.176886	+	0.984231i	$0.443397\pi$
$348$	6.71718	−	5.88866i	0.360079	−	0.315665i
$349$	−0.217399			−0.0116371			−0.00581854	−	0.999983i	$-0.501852\pi$
$349$	−0.217399			−0.0116371			−0.00581854	+	0.999983i	$0.501852\pi$
$350$	0.894165	+	24.2412i	0.0477951	+	1.29575i
$351$	−3.37550	+	6.83547i	−0.180171	+	0.364850i
$352$	0.613210	+	1.06211i	0.0326842	+	0.0566107i
$353$	−27.1647	−	15.6835i	−1.44583	−	0.834751i	−0.447601	−	0.894233i	$-0.647722\pi$
$353$	−27.1647	−	15.6835i	−1.44583	−	0.834751i	−0.998229	+	0.0594826i	$0.981055\pi$
$354$	23.7939	−	4.72841i	1.26463	−	0.251312i
$355$	12.6482	−	0.233193i	0.671299	−	0.0123766i
$356$	12.3868			0.656501
$357$	30.0735	+	10.2146i	1.59166	+	0.540616i
$358$	−12.3901	+	21.4603i	−0.654837	+	1.13421i
$359$	16.5120	−	9.53319i	0.871468	−	0.503142i	0.00363226	−	0.999993i	$-0.498844\pi$
$359$	16.5120	−	9.53319i	0.871468	−	0.503142i	0.867836	+	0.496851i	$0.165510\pi$
$360$	3.98685	−	5.39491i	0.210126	−	0.284336i
$361$	−4.59366	−	7.95645i	−0.241771	−	0.418760i
$362$	22.3120	−	12.8818i	1.17269	−	0.677055i
$363$	3.20580	+	16.1319i	0.168261	+	0.846706i
$364$			7.11789i			0.373079i
$365$	−0.0179868	−	0.975594i	−0.000941473	−	0.0510649i
$366$	−8.20654	−	9.36118i	−0.428963	−	0.489317i
$367$	4.44107	+	7.69216i	0.231822	+	0.401528i	0.958344	−	0.285615i	$-0.0921979\pi$
$367$	4.44107	+	7.69216i	0.231822	+	0.401528i	−0.726522	+	0.687143i	$0.758865\pi$
$368$		−	6.72188i		−	0.350402i
$369$	−1.90908	−	4.61366i	−0.0993830	−	0.240178i
$370$	−6.60097	+	3.97508i	−0.343168	+	0.206655i
$371$	−17.5701			−0.912193
$372$	6.61388	−	7.01830i	0.342914	−	0.363882i
$373$			13.9912i			0.724438i	0.932093	+	0.362219i	$0.117981\pi$
$373$			13.9912i			0.724438i	−0.932093	+	0.362219i	$0.882019\pi$
$374$		−	4.63544i		−	0.239693i
$375$	−13.5509	−	13.8337i	−0.699767	−	0.714371i
$376$	5.00458			0.258092
$377$	−3.78333	−	6.55292i	−0.194851	−	0.337492i
$378$	1.63510	+	25.1563i	0.0841006	+	1.29390i
$379$	6.08547	−	10.5403i	0.312589	−	0.541421i	−0.666333	−	0.745655i	$-0.732137\pi$
$379$	6.08547	−	10.5403i	0.312589	−	0.541421i	0.978922	+	0.204234i	$0.0654703\pi$
$380$	10.1700	−	6.12435i	0.521710	−	0.314172i
$381$	2.28670	+	11.5069i	0.117151	+	0.589518i
$382$	5.66215	−	3.26904i	0.289701	−	0.167259i
$383$	28.3694	−	16.3791i	1.44961	−	0.836931i	0.451149	−	0.892449i	$-0.351014\pi$
$383$	28.3694	−	16.3791i	1.44961	−	0.836931i	0.998458	+	0.0555180i	$0.0176810\pi$
$384$	−1.30243	+	1.14178i	−0.0664644	+	0.0582665i
$385$	−6.43881	+	11.6429i	−0.328152	+	0.593375i
$386$	−9.95206	−	5.74583i	−0.506547	−	0.292455i
$387$	−6.52010	−	5.00680i	−0.331435	−	0.254510i
$388$			14.0563i			0.713599i
$389$	−6.66148	+	11.5380i	−0.337750	+	0.585001i	−0.984009	−	0.178117i	$-0.942999\pi$
$389$	−6.66148	+	11.5380i	−0.337750	+	0.585001i	0.646259	+	0.763118i	$0.276333\pi$
$390$	−3.82390	−	4.20302i	−0.193631	−	0.212828i
$391$	−12.7032	+	22.0026i	−0.642428	+	1.11272i
$392$	8.26872	+	14.3218i	0.417633	+	0.723362i
$393$	12.3882	−	2.46184i	0.624903	−	0.124183i
$394$	6.28191	−	3.62687i	0.316478	−	0.182719i
$395$	−5.85777	−	9.72733i	−0.294736	−	0.489435i
$396$	3.39971	−	1.40676i	0.170842	−	0.0706924i
$397$	−18.2024	−	10.5092i	−0.913555	−	0.527441i	−0.0319815	−	0.999488i	$-0.510182\pi$
$397$	−18.2024	−	10.5092i	−0.913555	−	0.527441i	−0.881573	+	0.472047i	$0.843515\pi$
$398$	16.6477	−	9.61156i	0.834474	−	0.481784i
$399$	−14.3482	+	42.2433i	−0.718309	+	2.11481i
$400$	2.65791	+	4.23503i	0.132896	+	0.211752i
$401$	−8.35710			−0.417334			−0.208667	−	0.977987i	$-0.566912\pi$
$401$	−8.35710			−0.417334			−0.208667	+	0.977987i	$0.566912\pi$
$402$	8.09126	−	23.8219i	0.403555	−	1.18813i
$403$	−4.73890	−	6.65360i	−0.236062	−	0.331439i
$404$		−	8.98721i		−	0.447130i
$405$	−14.4800	−	13.9760i	−0.719518	−	0.694473i
$406$	−21.6692	−	12.5107i	−1.07542	−	0.620896i
$407$	−4.22623			−0.209486
$408$	6.42099	−	1.27601i	0.317886	−	0.0631717i
$409$	25.3153	+	14.6158i	1.25176	+	0.722706i	0.971460	−	0.237205i	$-0.0762314\pi$
$409$	25.3153	+	14.6158i	1.25176	+	0.722706i	0.280304	+	0.959911i	$0.409565\pi$
$410$	3.72096	−	0.0686027i	0.183765	−	0.00338805i
$411$	6.66365	−	19.6188i	0.328693	−	0.967724i
$412$	2.37364	−	1.37042i	0.116941	−	0.0675157i
$413$	−33.9754	−	58.8471i	−1.67182	−	2.89568i
$414$	−19.9922	−	2.63939i	−0.982562	−	0.129719i
$415$	5.70614	−	0.105203i	0.280103	−	0.00516421i
$416$	0.733571	+	1.27058i	0.0359663	+	0.0622954i
$417$	26.5479	+	30.2831i	1.30006	+	1.48297i
$418$	6.51128			0.318477
$419$		−	4.07196i		−	0.198928i	−0.995041	−	0.0994641i	$-0.968287\pi$
$419$		−	4.07196i		−	0.198928i	0.995041	−	0.0994641i	$-0.0317128\pi$
$420$	−17.9000	−	5.71406i	−0.873432	−	0.278817i
$421$	3.85212	+	6.67207i	0.187741	+	0.325177i	0.944497	−	0.328521i	$-0.106550\pi$
$421$	3.85212	+	6.67207i	0.187741	+	0.325177i	−0.756756	+	0.653698i	$0.773217\pi$
$422$	3.18547	−	5.51739i	0.155066	−	0.268582i
$423$	1.96508	−	14.8846i	0.0955454	−	0.723714i
$424$	−3.13635	+	1.81077i	−0.152315	+	0.0879389i
$425$	−0.696610	−	18.8854i	−0.0337906	−	0.916077i
$426$	−3.15145	+	9.27835i	−0.152688	+	0.449537i
$427$	−17.4351	+	30.1985i	−0.843746	+	1.46141i
$428$	2.90858	−	5.03780i	0.140591	−	0.243511i
$429$	−0.607452	−	3.05676i	−0.0293281	−	0.147582i
$430$	5.24905	−	3.16097i	0.253132	−	0.152435i
$431$	−5.46905	−	3.15756i	−0.263435	−	0.152094i	0.362465	−	0.931997i	$-0.381935\pi$
$431$	−5.46905	−	3.15756i	−0.263435	−	0.152094i	−0.625900	+	0.779903i	$0.715268\pi$
$432$	2.88448	+	4.32201i	0.138780	+	0.207943i
$433$	19.6028			0.942052			0.471026	−	0.882119i	$-0.343884\pi$
$433$	19.6028			0.942052			0.471026	+	0.882119i	$0.343884\pi$
$434$	−24.5722	−	11.2191i	−1.17950	−	0.538534i
$435$	19.5164	−	4.25378i	0.935739	−	0.203953i
$436$	−10.2430			−0.490549
$437$	−30.9064	−	17.8438i	−1.47845	−	0.853586i
$438$	0.715665	+	0.243080i	0.0341958	+	0.0116148i
$439$	−13.3071	−	23.0486i	−0.635115	−	1.10005i	−0.986491	−	0.163817i	$-0.947619\pi$
$439$	−13.3071	−	23.0486i	−0.635115	−	1.10005i	0.351376	−	0.936234i	$-0.385714\pi$
$440$	0.0505518	+	2.74189i	0.00240996	+	0.130715i
$441$	45.8427	−	18.9692i	2.18298	−	0.903296i
$442$		−	5.54528i		−	0.263762i
$443$	0.372788	+	0.645688i	0.0177117	+	0.0306775i	0.874745	−	0.484583i	$-0.161029\pi$
$443$	0.372788	+	0.645688i	0.0177117	+	0.0306775i	−0.857034	+	0.515260i	$0.827695\pi$
$444$	−1.16336	−	5.85414i	−0.0552106	−	0.277825i
$445$	24.2382	+	13.4044i	1.14900	+	0.635428i
$446$	−1.55000	+	2.68467i	−0.0733945	+	0.127123i
$447$	25.4236	−	5.05228i	1.20250	−	0.238965i
$448$	4.20156	+	2.42577i	0.198505	+	0.114607i
$449$	−0.467690			−0.0220717			−0.0110358	−	0.999939i	$-0.503513\pi$
$449$	−0.467690			−0.0220717			−0.0110358	+	0.999939i	$0.503513\pi$
$450$	13.6394	−	6.24224i	0.642970	−	0.294262i
$451$	1.76772	+	1.02060i	0.0832389	+	0.0480580i
$452$	−5.92849	−	10.2684i	−0.278853	−	0.482987i
$453$	−7.70304	−	8.78684i	−0.361920	−	0.412842i
$454$	5.80110	+	10.0478i	0.272259	+	0.471567i
$455$	−7.70261	+	13.9281i	−0.361104	+	0.652959i
$456$	1.79237	+	9.01939i	0.0839354	+	0.422372i
$457$	−20.1181			−0.941085			−0.470543	−	0.882377i	$-0.655942\pi$
$457$	−20.1181			−0.941085			−0.470543	+	0.882377i	$0.655942\pi$
$458$	19.9216	+	11.5017i	0.930873	+	0.537440i
$459$	−1.27385	−	19.5983i	−0.0594581	−	0.914770i
$460$	7.27407	−	13.1532i	0.339155	−	0.613271i
$461$	20.3780			0.949098			0.474549	−	0.880229i	$-0.342611\pi$
$461$	20.3780			0.949098			0.474549	+	0.880229i	$0.342611\pi$
$462$	−6.79365	−	7.74951i	−0.316069	−	0.360540i
$463$	1.03856			0.0482662			0.0241331	−	0.999709i	$-0.492317\pi$
$463$	1.03856			0.0482662			0.0241331	+	0.999709i	$0.492317\pi$
$464$	−5.15742			−0.239427
$465$	20.5367	−	6.57603i	0.952366	−	0.304956i
$466$	−11.5244			−0.533860
$467$	14.5915			0.675212			0.337606	−	0.941287i	$-0.390383\pi$
$467$	14.5915			0.675212			0.337606	+	0.941287i	$0.390383\pi$
$468$	4.06700	−	1.68288i	0.187997	−	0.0777911i
$469$	−70.4700			−3.25400
$470$	9.79283	+	5.41570i	0.451710	+	0.249808i
$471$	−9.76055	−	11.1338i	−0.449742	−	0.513020i
$472$	−12.1296	−	7.00301i	−0.558309	−	0.322340i
$473$	3.36067			0.154524
$474$	8.62679	−	1.71435i	0.396242	−	0.0787428i
$475$	26.5278	−	0.978509i	1.21718	−	0.0448971i
$476$	−9.16857	−	15.8804i	−0.420241	−	0.727878i
$477$	4.15408	+	10.0391i	0.190202	+	0.459660i
$478$	3.13030	+	5.42184i	0.143177	+	0.247989i
$479$	−2.09151	−	1.20753i	−0.0955635	−	0.0551736i	0.451457	−	0.892293i	$-0.350905\pi$
$479$	−2.09151	−	1.20753i	−0.0955635	−	0.0551736i	−0.547020	+	0.837119i	$0.684238\pi$
$480$	−3.78414	+	0.824789i	−0.172722	+	0.0376463i
$481$	−5.05575			−0.230522
$482$	−16.5387	−	9.54864i	−0.753318	−	0.434929i
$483$	11.0096	+	55.4014i	0.500954	+	2.52085i
$484$	4.74795	−	8.22368i	0.215816	−	0.373804i
$485$	−15.2109	+	27.5049i	−0.690694	+	1.24893i
$486$	13.9871	−	6.88194i	0.634468	−	0.312171i
$487$	−16.9348	−	29.3319i	−0.767387	−	1.32915i	−0.938975	−	0.343985i	$-0.888223\pi$
$487$	−16.9348	−	29.3319i	−0.767387	−	1.32915i	0.171588	−	0.985169i	$-0.445110\pi$
$488$			7.18747i			0.325361i
$489$	−9.83784	−	11.2220i	−0.444882	−	0.507477i
$490$	0.681656	+	36.9726i	0.0307941	+	1.67025i
$491$	16.5114	+	28.5986i	0.745149	+	1.29064i	0.950125	+	0.311869i	$0.100955\pi$
$491$	16.5114	+	28.5986i	0.745149	+	1.29064i	−0.204976	+	0.978767i	$0.565712\pi$
$492$	−0.927120	+	2.72958i	−0.0417978	+	0.123059i
$493$	16.8816	+	9.74662i	0.760311	+	0.438966i
$494$	7.78931			0.350457
$495$	8.17477	+	0.926270i	0.367429	+	0.0416328i
$496$	−5.54251	+	0.529744i	−0.248866	+	0.0237862i
$497$	27.4472			1.23118
$498$	−1.42175	+	4.18584i	−0.0637101	+	0.187572i
$499$	−8.05303	−	4.64942i	−0.360503	−	0.208137i	0.308798	−	0.951128i	$-0.400073\pi$
$499$	−8.05303	−	4.64942i	−0.360503	−	0.208137i	−0.669301	+	0.742991i	$0.733407\pi$
$500$	0.618004	+	11.1632i	0.0276380	+	0.499236i
$501$	27.2939	−	5.42395i	1.21940	−	0.242324i
$502$	4.28946	−	7.42956i	0.191448	−	0.331597i
$503$	−3.33345	+	5.77370i	−0.148631	+	0.257436i	−0.930722	−	0.365728i	$-0.880820\pi$
$503$	−3.33345	+	5.77370i	−0.148631	+	0.257436i	0.782091	+	0.623165i	$0.214153\pi$
$504$	8.86447	−	11.5437i	0.394855	−	0.514199i
$505$	9.72549	−	17.5859i	0.432778	−	0.782563i
$506$	7.13939	−	4.12193i	0.317385	−	0.183242i
$507$	3.66210	+	18.4281i	0.162640	+	0.818419i
$508$	3.38672	−	5.86597i	0.150261	−	0.260260i
$509$	−14.4408	−	25.0122i	−0.640077	−	1.10865i	−0.985415	−	0.170168i	$-0.945569\pi$
$509$	−14.4408	−	25.0122i	−0.640077	−	1.10865i	0.345338	−	0.938478i	$-0.387764\pi$
$510$	13.9452	+	4.45161i	0.617506	+	0.197120i
$511$		−	2.11708i		−	0.0936541i
$512$	1.00000			0.0441942
$513$	27.5292	−	1.78934i	1.21544	−	0.0790012i
$514$	2.27123	+	3.93388i	0.100180	+	0.173516i
$515$	6.12766	−	0.112974i	0.270017	−	0.00497825i
$516$	0.925098	+	4.65519i	0.0407252	+	0.204933i
$517$	3.06886	+	5.31543i	0.134968	+	0.233772i
$518$	−14.4785	+	8.35916i	−0.636149	+	0.367281i
$519$	−38.6758	−	13.1365i	−1.69768	−	0.576627i
$520$	0.0604740	+	3.28007i	0.00265196	+	0.143841i
$521$	−24.9143	−	14.3843i	−1.09152	−	0.630187i	−0.157537	−	0.987513i	$-0.550355\pi$
$521$	−24.9143	−	14.3843i	−1.09152	−	0.630187i	−0.933980	+	0.357326i	$0.883689\pi$
$522$	−2.02509	+	15.3391i	−0.0886357	+	0.671376i
$523$	−5.57472			−0.243765			−0.121883	−	0.992545i	$-0.538893\pi$
$523$	−5.57472			−0.243765			−0.121883	+	0.992545i	$0.538893\pi$
$524$	−6.31523	−	3.64610i	−0.275882	−	0.159281i
$525$	−28.8428	−	30.5516i	−1.25880	−	1.33338i
$526$		−	12.1422i		−	0.529424i
$527$	19.1433	+	8.74037i	0.833894	+	0.380737i
$528$	−2.01137	−	0.683174i	−0.0875335	−	0.0297313i
$529$	−22.1837			−0.964509
$530$	−8.09664	+	0.149276i	−0.351696	+	0.00648415i
$531$	−25.5910	+	33.3259i	−1.11056	+	1.44622i
$532$	22.3068	−	12.8788i	0.967122	−	0.558368i
$533$	2.11469	+	1.22092i	0.0915974	+	0.0528838i
$534$	−16.1330	+	14.1431i	−0.698143	+	0.612031i
$535$	11.1431	−	6.71032i	0.481757	−	0.290112i
$536$	−12.5793	+	7.26264i	−0.543342	+	0.313698i
$537$	−8.36576	−	42.0974i	−0.361009	−	1.81664i
$538$	10.7295	+	18.5841i	0.462584	+	0.801218i
$539$	−10.1409	+	17.5646i	−0.436801	+	0.756561i
$540$	0.967217	+	11.5786i	0.0416224	+	0.498265i
$541$	−2.79788	+	4.84607i	−0.120290	+	0.208349i	−0.919882	−	0.392195i	$-0.871716\pi$
$541$	−2.79788	+	4.84607i	−0.120290	+	0.208349i	0.799592	+	0.600544i	$0.205049\pi$
$542$			12.1268i			0.520890i
$543$	−14.3516	+	42.2532i	−0.615885	+	1.81326i
$544$	−3.27327	−	1.88983i	−0.140340	−	0.0810256i
$545$	−20.0431	−	11.0844i	−0.858554	−	0.474803i
$546$	−8.12710	−	9.27057i	−0.347808	−	0.396744i
$547$	10.2933	−	5.94282i	0.440108	−	0.254097i	−0.263535	−	0.964650i	$-0.584889\pi$
$547$	10.2933	−	5.94282i	0.440108	−	0.254097i	0.703644	+	0.710553i	$0.251555\pi$
$548$	−10.3598	+	5.98123i	−0.442548	+	0.255505i
$549$	21.3769	+	2.82220i	0.912344	+	0.120449i
$550$	−2.86822	+	5.41997i	−0.122301	+	0.231108i
$551$	−13.6908	+	23.7132i	−0.583248	+	1.01021i
$552$	7.67494	+	8.75479i	0.326667	+	0.372629i
$553$	−12.3182	−	21.3358i	−0.523825	−	0.907292i
$554$	10.5269			0.447244
$555$	4.05862	−	12.7142i	0.172279	−	0.539686i
$556$		−	23.2512i		−	0.986072i
$557$			45.6098i			1.93255i	0.257517	+	0.966274i	$0.417096\pi$
$557$			45.6098i			1.93255i	−0.257517	+	0.966274i	$0.582904\pi$
$558$	−0.600736	+	16.6925i	−0.0254312	+	0.706649i
$559$	4.02030			0.170041
$560$	5.59645	+	9.29338i	0.236493	+	0.392717i
$561$	5.29268	+	6.03735i	0.223457	+	0.254897i
$562$			14.7922i			0.623971i
$563$	7.54847	+	13.0743i	0.318130	+	0.551017i	0.980098	−	0.198515i	$-0.0636118\pi$
$563$	7.54847	+	13.0743i	0.318130	+	0.551017i	−0.661968	+	0.749532i	$0.730278\pi$
$564$	−6.51813	+	5.71416i	−0.274463	+	0.240609i
$565$	−0.488732	−	26.5085i	−0.0205611	−	1.11522i
$566$		−	20.3465i		−	0.855226i
$567$	−30.8526	−	30.8974i	−1.29569	−	1.29757i
$568$	4.89947	−	2.82871i	0.205577	−	0.118690i
$569$	12.7540	+	22.0905i	0.534674	+	0.926082i	0.999179	+	0.0405119i	$0.0128989\pi$
$569$	12.7540	+	22.0905i	0.534674	+	0.926082i	−0.464505	+	0.885570i	$0.653768\pi$
$570$	−6.25305	+	19.5885i	−0.261911	+	0.820472i
$571$	−18.8839	+	10.9026i	−0.790267	+	0.456261i	−0.840057	−	0.542499i	$-0.817478\pi$
$571$	−18.8839	+	10.9026i	−0.790267	+	0.456261i	0.0497894	+	0.998760i	$0.484145\pi$
$572$	−0.899666	+	1.55827i	−0.0376169	+	0.0651545i
$573$	−3.64202	+	10.7227i	−0.152148	+	0.447946i
$574$	8.07465			0.337030
$575$	28.4674	−	17.8662i	1.18717	−	0.745072i
$576$	0.392656	−	2.97419i	0.0163607	−	0.123925i
$577$	7.13962	+	4.12206i	0.297226	+	0.171604i	0.641196	−	0.767377i	$-0.278438\pi$
$577$	7.13962	+	4.12206i	0.297226	+	0.171604i	−0.343970	+	0.938981i	$0.611772\pi$
$578$	−1.35712	−	2.35059i	−0.0564486	−	0.0977718i
$579$	19.5224	−	3.87957i	0.811322	−	0.161229i
$580$	−10.0919	−	5.58108i	−0.419043	−	0.231742i
$581$	12.3826			0.513716
$582$	−16.0492	−	18.3073i	−0.665262	−	0.758863i
$583$	−3.84649	−	2.22077i	−0.159305	−	0.0919749i
$584$	−0.218186	−	0.377910i	−0.00902862	−	0.0156380i
$585$	9.77931	+	1.10808i	0.404325	+	0.0458134i
$586$	−8.93490	+	15.4757i	−0.369097	+	0.639295i
$587$			0.191388i			0.00789944i	0.999992	+	0.00394972i	$0.00125724\pi$
$587$			0.191388i			0.00789944i	−0.999992	+	0.00394972i	$0.998743\pi$
$588$	−27.1219	−	9.21212i	−1.11849	−	0.379902i
$589$	−12.2774	+	26.8900i	−0.505880	+	1.10798i
$590$	−16.1565	−	26.8293i	−0.665153	−	1.10454i
$591$	−4.04067	+	11.8963i	−0.166211	+	0.489350i
$592$	−1.72299	+	2.98431i	−0.0708145	+	0.122654i
$593$	−13.3090			−0.546537			−0.273268	−	0.961938i	$-0.588105\pi$
$593$	−13.3090			−0.546537			−0.273268	+	0.961938i	$0.588105\pi$
$594$	−2.82166	+	5.71394i	−0.115774	+	0.234446i
$595$	−0.755837	−	40.9961i	−0.0309863	−	1.68068i
$596$	−12.9604	−	7.48268i	−0.530878	−	0.306502i
$597$	−10.7082	+	31.5265i	−0.438256	+	1.29029i
$598$	8.54070	−	4.93098i	0.349255	−	0.201643i
$599$	22.2111	−	12.8236i	0.907521	−	0.523958i	0.0278885	−	0.999611i	$-0.491122\pi$
$599$	22.2111	−	12.8236i	0.907521	−	0.523958i	0.879633	+	0.475653i	$0.157788\pi$
$600$	−8.29725	−	2.48107i	−0.338734	−	0.101289i
$601$	12.8659	+	7.42814i	0.524812	+	0.303000i	0.738901	−	0.673814i	$-0.235345\pi$
$601$	12.8659	+	7.42814i	0.524812	+	0.303000i	−0.214089	+	0.976814i	$0.568678\pi$
$602$	11.5132	−	6.64716i	0.469244	−	0.270918i
$603$	16.6612	+	40.2649i	0.678496	+	1.63971i
$604$			6.74649i			0.274511i
$605$	18.1899	−	10.9539i	0.739524	−	0.445339i
$606$	10.2615	+	11.7052i	0.416843	+	0.475492i
$607$	36.3638	−	20.9946i	1.47596	−	0.852146i	0.476329	−	0.879267i	$-0.341967\pi$
$607$	36.3638	−	20.9946i	1.47596	−	0.852146i	0.999632	+	0.0271209i	$0.00863391\pi$
$608$	2.65459	−	4.59788i	0.107658	−	0.186469i
$609$	42.5071	−	8.44719i	1.72248	−	0.342298i
$610$	−7.77790	+	14.0642i	−0.314918	+	0.569444i
$611$	3.67122	+	6.35873i	0.148522	+	0.257247i
$612$	−6.90598	+	8.99330i	−0.279158	+	0.363533i
$613$	9.56057	−	16.5594i	0.386148	−	0.668828i	−0.605780	−	0.795632i	$-0.707139\pi$
$613$	9.56057	−	16.5594i	0.386148	−	0.668828i	0.991928	+	0.126805i	$0.0404721\pi$
$614$	27.7464	+	16.0194i	1.11975	+	0.646490i
$615$	−4.76797	+	4.33789i	−0.192263	+	0.174921i
$616$			5.95003i			0.239734i
$617$	6.88123	−	11.9186i	0.277028	−	0.479826i	−0.693617	−	0.720344i	$-0.743984\pi$
$617$	6.88123	−	11.9186i	0.277028	−	0.479826i	0.970645	+	0.240518i	$0.0773173\pi$
$618$	−1.52677	+	4.49506i	−0.0614159	+	0.180818i
$619$		−	6.31319i		−	0.253748i	−0.991919	−	0.126874i	$-0.959506\pi$
$619$		−	6.31319i		−	0.253748i	0.991919	−	0.126874i	$-0.0404945\pi$
$620$	−11.4187	−	4.96122i	−0.458585	−	0.199247i
$621$	29.0521	−	19.3891i	1.16582	−	0.778059i
$622$		−	15.9884i		−	0.641075i
$623$	52.0440	+	30.0476i	2.08510	+	1.20383i
$624$	−2.40616	−	0.817266i	−0.0963233	−	0.0327168i
$625$	−10.8710	+	22.5127i	−0.434839	+	0.900508i
$626$	−2.95626	+	5.12039i	−0.118156	+	0.204652i
$627$	−8.48050	+	7.43448i	−0.338678	+	0.296905i
$628$			8.54850i			0.341122i
$629$	11.2797	−	6.51231i	0.449749	−	0.259663i
$630$	29.8378	−	12.9958i	1.18877	−	0.517766i
$631$	9.96964	−	5.75597i	0.396885	−	0.229142i	−0.288254	−	0.957554i	$-0.593075\pi$
$631$	9.96964	−	5.75597i	0.396885	−	0.229142i	0.685139	+	0.728412i	$0.259741\pi$
$632$	−4.39774	−	2.53904i	−0.174933	−	0.100998i
$633$	2.15082	+	10.8231i	0.0854874	+	0.430181i
$634$	−4.61995	+	8.00199i	−0.183482	+	0.317800i
$635$	12.9749	−	7.81344i	0.514893	−	0.310067i
$636$	2.01737	−	5.93944i	0.0799939	−	0.235514i
$637$	−12.1314	+	21.0122i	−0.480663	+	0.832532i
$638$	−3.16258	−	5.47775i	−0.125208	−	0.216866i
$639$	−6.48933	−	15.6827i	−0.256714	−	0.620398i
$640$	1.95677	+	1.08215i	0.0773482	+	0.0427756i
$641$	18.9148	+	32.7615i	0.747091	+	1.29400i	0.949211	+	0.314640i	$0.101884\pi$
$641$	18.9148	+	32.7615i	0.747091	+	1.29400i	−0.202120	+	0.979361i	$0.564783\pi$
$642$	1.96386	+	9.88236i	0.0775075	+	0.390025i
$643$	−24.6208			−0.970949			−0.485475	−	0.874251i	$-0.661353\pi$
$643$	−24.6208			−0.970949			−0.485475	+	0.874251i	$0.661353\pi$
$644$	16.3057	−	28.2424i	0.642536	−	1.11291i
$645$	−3.22739	+	10.1102i	−0.127078	+	0.398090i
$646$	−17.3784	+	10.0334i	−0.683743	+	0.394759i
$647$			23.7433i			0.933445i	0.884404	+	0.466723i	$0.154565\pi$
$647$			23.7433i			0.933445i	−0.884404	+	0.466723i	$0.845435\pi$
$648$	−8.69164	−	2.33567i	−0.341440	−	0.0917537i
$649$		−	17.1773i		−	0.674267i
$650$	−3.43119	+	6.48379i	−0.134582	+	0.254315i
$651$	44.8134	−	13.4440i	1.75637	−	0.526914i
$652$			8.61619i			0.337436i
$653$	−28.2082			−1.10387			−0.551936	−	0.833886i	$-0.686111\pi$
$653$	−28.2082			−1.10387			−0.551936	+	0.833886i	$0.686111\pi$
$654$	13.3408	−	11.6953i	0.521665	−	0.457321i
$655$	−8.41185	−	13.9686i	−0.328678	−	0.545799i
$656$	1.44137	−	0.832174i	0.0562760	−	0.0324909i
$657$	−1.20965	+	0.500540i	−0.0471929	+	0.0195279i
$658$	21.0270	+	12.1400i	0.819720	+	0.473265i
$659$			40.5424i			1.57931i	0.613554	+	0.789653i	$0.289739\pi$
$659$			40.5424i			1.57931i	−0.613554	+	0.789653i	$0.710261\pi$
$660$	−3.19649	−	3.51341i	−0.124423	−	0.136759i
$661$	25.2605	+	43.7525i	0.982520	+	1.70177i	0.652476	+	0.757810i	$0.273730\pi$
$661$	25.2605	+	43.7525i	0.982520	+	1.70177i	0.330044	+	0.943965i	$0.392936\pi$
$662$	−9.28774	+	5.36228i	−0.360978	+	0.208411i
$663$	6.33152	+	7.22235i	0.245896	+	0.280493i
$664$	2.21035	−	1.27615i	0.0857784	−	0.0495242i
$665$	57.5861	−	1.06170i	2.23309	−	0.0411711i
$666$	8.19937	+	6.29632i	0.317719	+	0.243977i
$667$			34.6675i			1.34233i
$668$	−13.9138	−	8.03314i	−0.538341	−	0.310811i
$669$	−1.04655	−	5.26636i	−0.0404621	−	0.203609i
$670$	−32.4740	+	0.598717i	−1.25458	+	0.0231304i
$671$	−7.63389	+	4.40743i	−0.294703	+	0.170147i
$672$	−8.24195	+	1.63787i	−0.317940	+	0.0631823i
$673$	−22.4232	−	38.8381i	−0.864351	−	1.49710i	−0.867690	−	0.497106i	$-0.834396\pi$
$673$	−22.4232	−	38.8381i	−0.864351	−	1.49710i	0.00333889	−	0.999994i	$-0.498937\pi$
$674$	−9.11905			−0.351253
$675$	−10.6372	+	23.7034i	−0.409424	+	0.912344i
$676$	5.42375	−	9.39421i	0.208606	−	0.361316i
$677$	−11.7145	+	6.76337i	−0.450225	+	0.259938i	−0.707925	−	0.706287i	$-0.750369\pi$
$677$	−11.7145	+	6.76337i	−0.450225	+	0.259938i	0.257700	+	0.966225i	$0.417035\pi$
$678$	19.4458	+	6.60489i	0.746811	+	0.253659i
$679$	−34.0973	+	59.0582i	−1.30853	+	2.26645i
$680$	−4.35998	−	7.24012i	−0.167198	−	0.277646i
$681$	−19.0280	−	6.46297i	−0.729153	−	0.247661i
$682$	−3.96137	−	5.56192i	−0.151689	−	0.212977i
$683$	−27.2154			−1.04137			−0.520685	−	0.853749i	$-0.674323\pi$
$683$	−27.2154			−1.04137			−0.520685	+	0.853749i	$0.674323\pi$
$684$	−12.6326	−	9.70063i	−0.483021	−	0.370913i
$685$	−26.7443	+	0.493080i	−1.02185	+	0.0188396i
$686$			46.2713i			1.76664i
$687$	−39.0790	+	7.76593i	−1.49096	+	0.296289i
$688$	1.37011	−	2.37311i	0.0522351	−	0.0904739i
$689$	−4.60147	−	2.65666i	−0.175302	−	0.101211i
$690$	5.54414	+	25.4366i	0.211062	+	0.968353i
$691$	16.8946	+	29.2622i	0.642700	+	1.11319i	0.984828	+	0.173535i	$0.0555190\pi$
$691$	16.8946	+	29.2622i	0.642700	+	1.11319i	−0.342128	+	0.939653i	$0.611148\pi$
$692$	11.7912	+	20.4229i	0.448233	+	0.776363i
$693$	17.6965	+	2.33631i	0.672236	+	0.0887492i
$694$	20.8204	+	12.0207i	0.790332	+	0.456299i
$695$	25.1613	−	45.4974i	0.954421	−	1.72581i
$696$	6.71718	−	5.88866i	0.254614	−	0.223209i
$697$	−6.29066			−0.238276
$698$	−0.217399			−0.00822866
$699$	15.0098	−	13.1584i	0.567723	−	0.497698i
$700$	0.894165	+	24.2412i	0.0337963	+	0.916232i
$701$	−16.1244	−	9.30943i	−0.609011	−	0.351612i	0.163568	−	0.986532i	$-0.447700\pi$
$701$	−16.1244	−	9.30943i	−0.609011	−	0.351612i	−0.772578	+	0.634920i	$0.781033\pi$
$702$	−3.37550	+	6.83547i	−0.127400	+	0.257988i
$703$	9.14766	+	15.8442i	0.345011	+	0.597576i
$704$	0.613210	+	1.06211i	0.0231112	+	0.0400298i
$705$	−18.9381	+	4.12773i	−0.713248	+	0.155459i
$706$	−27.1647	−	15.6835i	−1.02236	−	0.590258i
$707$	21.8009	−	37.7603i	0.819907	−	1.42012i
$708$	23.7939	−	4.72841i	0.894228	−	0.177705i
$709$		−	50.9195i		−	1.91232i	−0.292844	−	0.956160i	$-0.594602\pi$
$709$		−	50.9195i		−	1.91232i	0.292844	−	0.956160i	$-0.405398\pi$
$710$	12.6482	−	0.233193i	0.474680	−	0.00875158i
$711$	−9.27839	+	12.0828i	−0.347967	+	0.453139i
$712$	12.3868			0.464216
$713$	3.56088	+	37.2561i	0.133356	+	1.39525i
$714$	30.0735	+	10.2146i	1.12547	+	0.382273i
$715$	−3.44672	+	2.07560i	−0.128900	+	0.0776232i
$716$	−12.3901	+	21.4603i	−0.463040	+	0.802008i
$717$	−10.2676	−	3.48745i	−0.383450	−	0.130241i
$718$	16.5120	−	9.53319i	0.616221	−	0.355775i
$719$	9.07047	−	15.7105i	0.338272	−	0.585903i	−0.645836	−	0.763476i	$-0.723491\pi$
$719$	9.07047	−	15.7105i	0.338272	−	0.585903i	0.984108	+	0.177573i	$0.0568244\pi$
$720$	3.98685	−	5.39491i	0.148581	−	0.201056i
$721$	13.2973			0.495217
$722$	−4.59366	−	7.95645i	−0.170958	−	0.296108i
$723$	32.4430	−	6.44722i	1.20657	−	0.239775i
$724$	22.3120	−	12.8818i	0.829219	−	0.478750i
$725$	−13.7080	−	21.8418i	−0.509101	−	0.811185i
$726$	3.20580	+	16.1319i	0.118978	+	0.598712i
$727$	−27.6084	−	15.9397i	−1.02394	−	0.591171i	−0.108696	−	0.994075i	$-0.534668\pi$
$727$	−27.6084	−	15.9397i	−1.02394	−	0.591171i	−0.915242	+	0.402904i	$0.868001\pi$
$728$			7.11789i			0.263807i
$729$	−10.3596	+	24.9335i	−0.383687	+	0.923463i
$730$	−0.0179868	−	0.975594i	−0.000665722	−	0.0361083i
$731$	−8.96952	+	5.17856i	−0.331750	+	0.191536i
$732$	−8.20654	−	9.36118i	−0.303322	−	0.345999i
$733$	−9.64309	+	5.56744i	−0.356175	+	0.205638i	−0.667402	−	0.744698i	$-0.732594\pi$
$733$	−9.64309	+	5.56744i	−0.356175	+	0.205638i	0.311226	+	0.950336i	$0.399260\pi$
$734$	4.44107	+	7.69216i	0.163923	+	0.283923i
$735$	−43.1025	−	47.3759i	−1.58986	−	1.74749i
$736$		−	6.72188i		−	0.247772i
$737$	−15.4275	−	8.90706i	−0.568278	−	0.328096i
$738$	−1.90908	−	4.61366i	−0.0702744	−	0.169831i
$739$	−11.6080	+	6.70189i	−0.427008	+	0.246533i	−0.698071	−	0.716028i	$-0.745958\pi$
$739$	−11.6080	+	6.70189i	−0.427008	+	0.246533i	0.271063	+	0.962562i	$0.412625\pi$
$740$	−6.60097	+	3.97508i	−0.242656	+	0.146127i
$741$	−10.1450	+	8.89371i	−0.372687	+	0.326719i
$742$	−17.5701			−0.645018
$743$		−	41.0727i		−	1.50681i	−0.657557	−	0.753405i	$-0.728410\pi$
$743$		−	41.0727i		−	1.50681i	0.657557	−	0.753405i	$-0.271590\pi$
$744$	6.61388	−	7.01830i	0.242477	−	0.257303i
$745$	−17.2631	−	28.6669i	−0.632473	−	1.05028i
$746$			13.9912i			0.512255i
$747$	−2.92760	−	7.07511i	−0.107115	−	0.258865i
$748$		−	4.63544i		−	0.169489i
$749$	24.4411	−	14.1111i	0.893058	−	0.515607i
$750$	−13.5509	−	13.8337i	−0.494810	−	0.505137i
$751$	−15.7647	+	27.3052i	−0.575262	+	0.996382i	0.420752	+	0.907176i	$0.361766\pi$
$751$	−15.7647	+	27.3052i	−0.575262	+	0.996382i	−0.996013	+	0.0892063i	$0.971567\pi$
$752$	5.00458			0.182498
$753$	2.89623	+	14.5741i	0.105544	+	0.531111i
$754$	−3.78333	−	6.55292i	−0.137781	−	0.238643i
$755$	−7.30070	+	13.2013i	−0.265700	+	0.480446i
$756$	1.63510	+	25.1563i	0.0594681	+	0.914924i
$757$	14.7301	+	25.5133i	0.535374	+	0.927295i	0.999145	+	0.0413402i	$0.0131628\pi$
$757$	14.7301	+	25.5133i	0.535374	+	0.927295i	−0.463771	+	0.885955i	$0.653504\pi$
$758$	6.08547	−	10.5403i	0.221034	−	0.382842i
$759$	−4.59221	+	13.5202i	−0.166687	+	0.490751i
$760$	10.1700	−	6.12435i	0.368905	−	0.222153i
$761$	−13.3099	+	23.0535i	−0.482485	+	0.835689i	−0.999798	−	0.0201077i	$-0.993599\pi$
$761$	−13.3099	+	23.0535i	−0.482485	+	0.835689i	0.517313	+	0.855796i	$0.326932\pi$
$762$	2.28670	+	11.5069i	0.0828386	+	0.416852i
$763$	−43.0364	−	24.8471i	−1.55802	−	0.899525i
$764$	5.66215	−	3.26904i	0.204849	−	0.118270i
$765$	−23.2455	+	10.1245i	−0.840443	+	0.366054i
$766$	28.3694	−	16.3791i	1.02503	−	0.591799i
$767$		−	20.5488i		−	0.741974i
$768$	−1.30243	+	1.14178i	−0.0469975	+	0.0412006i
$769$	3.54686	−	6.14334i	0.127903	−	0.221535i	−0.794961	−	0.606661i	$-0.792509\pi$
$769$	3.54686	−	6.14334i	0.127903	−	0.221535i	0.922864	+	0.385126i	$0.125842\pi$
$770$	−6.43881	+	11.6429i	−0.232039	+	0.419579i
$771$	−7.44977	−	2.53036i	−0.268297	−	0.0911287i
$772$	−9.95206	−	5.74583i	−0.358183	−	0.206797i
$773$			1.89621i			0.0682018i	0.999418	+	0.0341009i	$0.0108568\pi$
$773$			1.89621i			0.0682018i	−0.999418	+	0.0341009i	$0.989143\pi$
$774$	−6.52010	−	5.00680i	−0.234360	−	0.179966i
$775$	−16.9750	−	22.0647i	−0.609760	−	0.792586i
$776$			14.0563i			0.504590i
$777$	9.31289	−	27.4186i	0.334098	−	0.983635i
$778$	−6.66148	+	11.5380i	−0.238826	+	0.413658i
$779$		−	8.83631i		−	0.316594i
$780$	−3.82390	−	4.20302i	−0.136917	−	0.150492i
$781$	6.00882	+	3.46919i	0.215012	+	0.124137i
$782$	−12.7032	+	22.0026i	−0.454265	+	0.786810i
$783$	−14.8765	−	22.2904i	−0.531641	−	0.796594i
$784$	8.26872	+	14.3218i	0.295311	+	0.511494i
$785$	−9.25074	+	16.7275i	−0.330173	+	0.597029i
$786$	12.3882	−	2.46184i	0.441873	−	0.0878109i
$787$	11.6044	−	20.0994i	0.413652	−	0.716466i	−0.581634	−	0.813450i	$-0.697587\pi$
$787$	11.6044	−	20.0994i	0.413652	−	0.716466i	0.995286	+	0.0969848i	$0.0309198\pi$
$788$	6.28191	−	3.62687i	0.223784	−	0.129202i
$789$	13.8637	+	15.8143i	0.493562	+	0.563006i
$790$	−5.85777	−	9.72733i	−0.208410	−	0.346083i
$791$		−	57.5246i		−	2.04534i
$792$	3.39971	−	1.40676i	0.120803	−	0.0499871i
$793$	−9.13226	+	5.27251i	−0.324296	+	0.187232i
$794$	−18.2024	−	10.5092i	−0.645981	−	0.372957i
$795$	10.3749	−	9.43905i	0.367959	−	0.334768i
$796$	16.6477	−	9.61156i	0.590063	−	0.340673i
$797$	−35.9670	+	20.7656i	−1.27402	+	0.735554i	−0.975742	−	0.218926i	$-0.929745\pi$
$797$	−35.9670	+	20.7656i	−1.27402	+	0.735554i	−0.298275	+	0.954480i	$0.596411\pi$
$798$	−14.3482	+	42.2433i	−0.507921	+	1.49540i
$799$	−16.3814	−	9.45779i	−0.579532	−	0.334593i
$800$	2.65791	+	4.23503i	0.0939715	+	0.149731i
$801$	4.86376	−	36.8408i	0.171853	−	1.30171i
$802$	−8.35710			−0.295100
$803$	0.267588	−	0.463477i	0.00944299	−	0.0163557i
$804$	8.09126	−	23.8219i	0.285357	−	0.840134i
$805$	62.4690	−	37.6187i	2.20174	−	1.32588i
$806$	−4.73890	−	6.65360i	−0.166921	−	0.234363i
$807$	−35.1936	−	11.9537i	−1.23887	−	0.420791i
$808$		−	8.98721i		−	0.316169i
$809$	−8.10033	+	14.0302i	−0.284792	+	0.493275i	−0.972559	−	0.232657i	$-0.925258\pi$
$809$	−8.10033	+	14.0302i	−0.284792	+	0.493275i	0.687766	+	0.725932i	$0.258591\pi$
$810$	−14.4800	−	13.9760i	−0.508776	−	0.491067i
$811$	−21.9137	−	37.9556i	−0.769493	−	1.33280i	−0.937838	−	0.347072i	$-0.887176\pi$
$811$	−21.9137	−	37.9556i	−0.769493	−	1.33280i	0.168346	−	0.985728i	$-0.446157\pi$
$812$	−21.6692	−	12.5107i	−0.760439	−	0.439040i
$813$	−13.8462	−	15.7943i	−0.485606	−	0.553930i
$814$	−4.22623			−0.148129
$815$	−9.32399	+	16.8599i	−0.326605	+	0.590578i
$816$	6.42099	−	1.27601i	0.224780	−	0.0446691i
$817$	−7.27417	−	12.5992i	−0.254491	−	0.440792i
$818$	25.3153	+	14.6158i	0.885130	+	0.511030i
$819$	21.1700	+	2.79488i	0.739739	+	0.0976611i
$820$	3.72096	−	0.0686027i	0.129942	−	0.00239571i
$821$	0.813290			0.0283840			0.0141920	−	0.999899i	$-0.495482\pi$
$821$	0.813290			0.0283840			0.0141920	+	0.999899i	$0.495482\pi$
$822$	6.66365	−	19.6188i	0.232421	−	0.684284i
$823$	−5.12126	+	8.87028i	−0.178516	+	0.309198i	−0.941372	−	0.337369i	$-0.890463\pi$
$823$	−5.12126	+	8.87028i	−0.178516	+	0.309198i	0.762857	+	0.646568i	$0.223796\pi$
$824$	2.37364	−	1.37042i	0.0826895	−	0.0477408i
$825$	−2.45278	−	10.3340i	−0.0853949	−	0.359784i
$826$	−33.9754	−	58.8471i	−1.18215	−	2.04755i
$827$	−15.5522	+	8.97904i	−0.540801	+	0.312232i	−0.745404	−	0.666613i	$-0.767743\pi$
$827$	−15.5522	+	8.97904i	−0.540801	+	0.312232i	0.204602	+	0.978845i	$0.434410\pi$
$828$	−19.9922	−	2.63939i	−0.694776	−	0.0917250i
$829$		−	10.4276i		−	0.362165i	−0.983468	−	0.181083i	$-0.942040\pi$
$829$		−	10.4276i		−	0.362165i	0.983468	−	0.181083i	$-0.0579602\pi$
$830$	5.70614	−	0.105203i	0.198063	−	0.00365165i
$831$	−13.7105	+	12.0194i	−0.475613	+	0.416949i
$832$	0.733571	+	1.27058i	0.0254320	+	0.0440495i
$833$		−	62.5058i		−	2.16570i
$834$	26.5479	+	30.2831i	0.919279	+	1.04862i
$835$	−18.5331	−	30.7758i	−0.641364	−	1.06504i
$836$	6.51128			0.225197
$837$	−18.2768	−	22.4267i	−0.631739	−	0.775181i
$838$		−	4.07196i		−	0.140663i
$839$		−	23.1387i		−	0.798837i	−0.916769	−	0.399418i	$-0.869212\pi$
$839$		−	23.1387i		−	0.798837i	0.916769	−	0.399418i	$-0.130788\pi$
$840$	−17.9000	−	5.71406i	−0.617610	−	0.197154i
$841$	−2.40107			−0.0827955
$842$	3.85212	+	6.67207i	0.132753	+	0.229935i
$843$	−16.8895	−	19.2658i	−0.581705	−	0.663550i
$844$	3.18547	−	5.51739i	0.109648	−	0.189916i
$845$	20.7790	−	12.5130i	0.714818	−	0.430461i
$846$	1.96508	−	14.8846i	0.0675608	−	0.511743i
$847$	39.8975	−	23.0348i	1.37090	−	0.791487i
$848$	−3.13635	+	1.81077i	−0.107703	+	0.0621822i
$849$	23.2313	+	26.4999i	0.797295	+	0.909473i
$850$	−0.696610	−	18.8854i	−0.0238935	−	0.647764i
$851$	20.0602	+	11.5818i	0.687654	+	0.397017i
$852$	−3.15145	+	9.27835i	−0.107967	+	0.317871i
$853$			6.24127i			0.213697i	0.994275	+	0.106848i	$0.0340760\pi$
$853$			6.24127i			0.213697i	−0.994275	+	0.106848i	$0.965924\pi$
$854$	−17.4351	+	30.1985i	−0.596618	+	1.03337i
$855$	−14.2217	−	32.6523i	−0.486371	−	1.11669i
$856$	2.90858	−	5.03780i	0.0994131	−	0.172188i
$857$	24.6728	+	42.7345i	0.842806	+	1.45978i	0.887513	+	0.460783i	$0.152431\pi$
$857$	24.6728	+	42.7345i	0.842806	+	1.45978i	−0.0447063	+	0.999000i	$0.514235\pi$
$858$	−0.607452	−	3.05676i	−0.0207381	−	0.104356i
$859$	−7.11320	+	4.10681i	−0.242699	+	0.140123i	−0.616417	−	0.787420i	$-0.711416\pi$
$859$	−7.11320	+	4.10681i	−0.242699	+	0.140123i	0.373717	+	0.927543i	$0.378083\pi$
$860$	5.24905	−	3.16097i	0.178991	−	0.107788i
$861$	−10.5167	+	9.21951i	−0.358408	+	0.314200i
$862$	−5.46905	−	3.15756i	−0.186277	−	0.107547i
$863$	35.6756	−	20.5973i	1.21441	−	0.701141i	0.250695	−	0.968066i	$-0.419341\pi$
$863$	35.6756	−	20.5973i	1.21441	−	0.701141i	0.963717	+	0.266925i	$0.0860075\pi$
$864$	2.88448	+	4.32201i	0.0981320	+	0.147038i
$865$	0.972040	+	52.7228i	0.0330503	+	1.79263i
$866$	19.6028			0.666131
$867$	4.45142	+	1.51195i	0.151178	+	0.0513486i
$868$	−24.5722	−	11.2191i	−0.834034	−	0.380801i
$869$		−	6.22786i		−	0.211266i
$870$	19.5164	−	4.25378i	0.661667	−	0.144217i
$871$	−18.4556	−	10.6553i	−0.625343	−	0.361042i
$872$	−10.2430			−0.346871
$873$	41.8060	+	5.51927i	1.41492	+	0.186799i
$874$	−30.9064	−	17.8438i	−1.04542	−	0.603576i
$875$	−24.4829	+	48.4021i	−0.827673	+	1.63629i
$876$	0.715665	+	0.243080i	0.0241801	+	0.00821291i
$877$	−21.2480	+	12.2675i	−0.717492	+	0.414244i	−0.813829	−	0.581104i	$-0.802621\pi$
$877$	−21.2480	+	12.2675i	−0.717492	+	0.414244i	0.0963366	+	0.995349i	$0.469287\pi$
$878$	−13.3071	−	23.0486i	−0.449094	−	0.777854i
$879$	−6.03282	−	30.3578i	−0.203482	−	1.02394i
$880$	0.0505518	+	2.74189i	0.00170410	+	0.0924293i
$881$	5.42379	+	9.39429i	0.182732	+	0.316502i	0.942810	−	0.333331i	$-0.108173\pi$
$881$	5.42379	+	9.39429i	0.182732	+	0.316502i	−0.760078	+	0.649832i	$0.774839\pi$
$882$	45.8427	−	18.9692i	1.54360	−	0.638726i
$883$	−28.4156			−0.956260			−0.478130	−	0.878289i	$-0.658685\pi$
$883$	−28.4156			−0.956260			−0.478130	+	0.878289i	$0.658685\pi$
$884$		−	5.54528i		−	0.186508i
$885$	51.6760	+	16.4960i	1.73707	+	0.554508i
$886$	0.372788	+	0.645688i	0.0125241	+	0.0216923i
$887$	−21.2710	+	36.8424i	−0.714210	+	1.23705i	0.249054	+	0.968490i	$0.419880\pi$
$887$	−21.2710	+	36.8424i	−0.714210	+	1.23705i	−0.963264	+	0.268558i	$0.913453\pi$
$888$	−1.16336	−	5.85414i	−0.0390398	−	0.196452i
$889$	28.4590	−	16.4308i	0.954484	−	0.551072i
$890$	24.2382	+	13.4044i	0.812466	+	0.449316i
$891$	−2.84907	−	10.6638i	−0.0954473	−	0.357249i
$892$	−1.55000	+	2.68467i	−0.0518977	+	0.0898895i
$893$	13.2851	−	23.0105i	0.444569	−	0.770016i
$894$	25.4236	−	5.05228i	0.850293	−	0.168974i
$895$	−47.4678	+	28.5850i	−1.58667	+	0.955490i
$896$	4.20156	+	2.42577i	0.140364	+	0.0810393i
$897$	−5.49357	+	16.1739i	−0.183425	+	0.540031i
$898$	−0.467690			−0.0156070
$899$	28.5850	−	2.73211i	0.953363	−	0.0911210i
$900$	13.6394	−	6.24224i	0.454648	−	0.208075i
$901$	13.6882			0.456019
$902$	1.76772	+	1.02060i	0.0588588	+	0.0339821i
$903$	−7.40556	+	21.8031i	−0.246442	+	0.725562i
$904$	−5.92849	−	10.2684i	−0.197179	−	0.341523i
$905$	57.5996	−	1.06195i	1.91467	−	0.0353005i
$906$	−7.70304	−	8.78684i	−0.255916	−	0.291923i
$907$			34.0991i			1.13224i	0.824322	+	0.566122i	$0.191557\pi$
$907$			34.0991i			1.13224i	−0.824322	+	0.566122i	$0.808443\pi$
$908$	5.80110	+	10.0478i	0.192516	+	0.333448i
$909$	−26.7297	−	3.52888i	−0.886568	−	0.117046i
$910$	−7.70261	+	13.9281i	−0.255339	+	0.461712i
$911$	−20.2395	+	35.0559i	−0.670566	+	1.16145i	0.307178	+	0.951652i	$0.400615\pi$
$911$	−20.2395	+	35.0559i	−0.670566	+	1.16145i	−0.977744	+	0.209802i	$0.932718\pi$
$912$	1.79237	+	9.01939i	0.0593513	+	0.298662i
$913$	2.71082	+	1.56510i	0.0897152	+	0.0517971i
$914$	−20.1181			−0.665448
$915$	−5.92815	−	27.1984i	−0.195978	−	0.899151i
$916$	19.9216	+	11.5017i	0.658227	+	0.380027i
$917$	−17.6892	−	30.6386i	−0.584149	−	1.01178i
$918$	−1.27385	−	19.5983i	−0.0420432	−	0.646840i
$919$	−8.28952	−	14.3579i	−0.273446	−	0.473622i	0.696296	−	0.717755i	$-0.254830\pi$
$919$	−8.28952	−	14.3579i	−0.273446	−	0.473622i	−0.969742	+	0.244133i	$0.921497\pi$
$920$	7.27407	−	13.1532i	0.239819	−	0.433648i
$921$	−54.4285	+	10.8163i	−1.79348	+	0.356408i
$922$	20.3780			0.671114
$923$	7.18822	+	4.15012i	0.236603	+	0.136603i
$924$	−6.79365	−	7.74951i	−0.223495	−	0.254940i
$925$	−17.2182	+	0.635113i	−0.566131	+	0.0208824i
$926$	1.03856			0.0341293
$927$	−3.14387	−	7.59776i	−0.103258	−	0.249543i
$928$	−5.15742			−0.169300
$929$	−50.0428			−1.64185			−0.820925	−	0.571036i	$-0.806542\pi$
$929$	−50.0428			−1.64185			−0.820925	+	0.571036i	$0.806542\pi$
$930$	20.5367	−	6.57603i	0.673425	−	0.215636i
$931$	87.8001			2.87753
$932$	−11.5244			−0.377496
$933$	18.2553	+	20.8238i	0.597651	+	0.681739i
$934$	14.5915			0.477447
$935$	5.01623	−	9.07051i	0.164048	−	0.296637i
$936$	4.06700	−	1.68288i	0.132934	−	0.0550066i
$937$	−7.21427	−	4.16516i	−0.235680	−	0.136070i	0.377510	−	0.926006i	$-0.376781\pi$
$937$	−7.21427	−	4.16516i	−0.235680	−	0.136070i	−0.613190	+	0.789936i	$0.710114\pi$
$938$	−70.4700			−2.30093
$939$	−1.99606	−	10.0444i	−0.0651389	−	0.327785i
$940$	9.79283	+	5.41570i	0.319407	+	0.176641i
$941$	−13.8129	−	23.9246i	−0.450287	−	0.779919i	0.548117	−	0.836402i	$-0.315345\pi$
$941$	−13.8129	−	23.9246i	−0.450287	−	0.779919i	−0.998404	+	0.0564823i	$0.982012\pi$
$942$	−9.76055	−	11.1338i	−0.318016	−	0.362760i
$943$	−5.59378	−	9.68871i	−0.182158	−	0.315508i
$944$	−12.1296	−	7.00301i	−0.394784	−	0.227929i
$945$	−24.0233	+	50.9945i	−0.781477	+	1.65885i
$946$	3.36067			0.109265
$947$	33.7051	+	19.4596i	1.09527	+	0.632353i	0.934974	−	0.354717i	$-0.115423\pi$
$947$	33.7051	+	19.4596i	1.09527	+	0.632353i	0.160293	+	0.987069i	$0.448756\pi$
$948$	8.62679	−	1.71435i	0.280185	−	0.0556796i
$949$	0.320110	−	0.554447i	0.0103912	−	0.0179981i
$950$	26.5278	−	0.978509i	0.860676	−	0.0317470i
$951$	−3.11938	−	15.6970i	−0.101153	−	0.509011i
$952$	−9.16857	−	15.8804i	−0.297155	−	0.514687i
$953$		−	8.83785i		−	0.286286i	−0.989702	−	0.143143i	$-0.954279\pi$
$953$		−	8.83785i		−	0.286286i	0.989702	−	0.143143i	$-0.0457209\pi$
$954$	4.15408	+	10.0391i	0.134493	+	0.325028i
$955$	14.6171	−	0.269493i	0.472999	−	0.00872059i
$956$	3.13030	+	5.42184i	0.101241	+	0.175355i
$957$	10.3735	+	3.52341i	0.335326	+	0.113896i
$958$	−2.09151	−	1.20753i	−0.0675736	−	0.0390137i
$959$	−58.0363			−1.87409
$960$	−3.78414	+	0.824789i	−0.122133	+	0.0266200i
$961$	30.4387	−	5.87222i	0.981895	−	0.189427i
$962$	−5.05575			−0.163004
$963$	−13.8413	−	10.6288i	−0.446030	−	0.342508i
$964$	−16.5387	−	9.54864i	−0.532676	−	0.307541i
$965$	−13.2561	−	22.0129i	−0.426729	−	0.708619i
$966$	11.0096	+	55.4014i	0.354228	+	1.78251i
$967$	−11.7705	+	20.3872i	−0.378515	+	0.655607i	−0.990846	−	0.134994i	$-0.956899\pi$
$967$	−11.7705	+	20.3872i	−0.378515	+	0.655607i	0.612331	+	0.790601i	$0.290232\pi$
$968$	4.74795	−	8.22368i	0.152605	−	0.264319i
$969$	11.1782	−	32.9102i	0.359094	−	1.05723i
$970$	−15.2109	+	27.5049i	−0.488394	+	0.883129i
$971$	34.6066	−	19.9801i	1.11058	−	0.641193i	0.171600	−	0.985167i	$-0.445106\pi$
$971$	34.6066	−	19.9801i	1.11058	−	0.641193i	0.938979	+	0.343973i	$0.111773\pi$
$972$	13.9871	−	6.88194i	0.448636	−	0.220738i
$973$	56.4021	−	97.6914i	1.80817	−	3.13184i
$974$	−16.9348	−	29.3319i	−0.542625	−	0.939854i
$975$	−2.93421	−	12.3624i	−0.0939699	−	0.395913i
$976$			7.18747i			0.230065i
$977$	47.1033			1.50697			0.753485	−	0.657466i	$-0.228372\pi$
$977$	47.1033			1.50697			0.753485	+	0.657466i	$0.228372\pi$
$978$	−9.83784	−	11.2220i	−0.314579	−	0.358840i
$979$	7.59573	+	13.1562i	0.242761	+	0.420474i
$980$	0.681656	+	36.9726i	0.0217747	+	1.18104i
$981$	−4.02196	+	30.4646i	−0.128411	+	0.972658i
$982$	16.5114	+	28.5986i	0.526900	+	0.912617i
$983$	20.5691	−	11.8756i	0.656052	−	0.378772i	−0.134719	−	0.990884i	$-0.543013\pi$
$983$	20.5691	−	11.8756i	0.656052	−	0.378772i	0.790771	+	0.612112i	$0.209680\pi$
$984$	−0.927120	+	2.72958i	−0.0295555	+	0.0870159i
$985$	16.2171	−	0.298991i	0.516719	−	0.00952665i
$986$	16.8816	+	9.74662i	0.537621	+	0.310396i
$987$	−41.2475	+	8.19688i	−1.31292	+	0.260909i
$988$	7.78931			0.247811
$989$	−15.9518	−	9.20975i	−0.507236	−	0.292853i
$990$	8.17477	+	0.926270i	0.259811	+	0.0294388i
$991$		−	34.1967i		−	1.08629i	−0.839638	−	0.543146i	$-0.817233\pi$
$991$		−	34.1967i		−	1.08629i	0.839638	−	0.543146i	$-0.182767\pi$
$992$	−5.54251	+	0.529744i	−0.175975	+	0.0168194i
$993$	5.97408	−	17.5886i	0.189582	−	0.558157i
$994$	27.4472			0.870573
$995$	42.9769	−	0.792357i	1.36246	−	0.0251194i
$996$	−1.42175	+	4.18584i	−0.0450498	+	0.132634i
$997$	34.1845	−	19.7364i	1.08263	−	0.625059i	0.151029	−	0.988529i	$-0.451741\pi$
$997$	34.1845	−	19.7364i	1.08263	−	0.625059i	0.931606	+	0.363470i	$0.118408\pi$
$998$	−8.05303	−	4.64942i	−0.254914	−	0.147175i
$999$	−17.8682	+	1.16139i	−0.565323	+	0.0367448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.b.119.7	yes	64
3.2	odd	2		930.2.r.a.119.15	✓	64
5.4	even	2		930.2.r.a.119.26	yes	64
15.14	odd	2	inner	930.2.r.b.119.18	yes	64
31.6	odd	6	inner	930.2.r.b.719.18	yes	64
93.68	even	6		930.2.r.a.719.26	yes	64
155.99	odd	6		930.2.r.a.719.15	yes	64
465.254	even	6	inner	930.2.r.b.719.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.15	✓	64	3.2	odd	2
930.2.r.a.119.26	yes	64	5.4	even	2
930.2.r.a.719.15	yes	64	155.99	odd	6
930.2.r.a.719.26	yes	64	93.68	even	6
930.2.r.b.119.7	yes	64	1.1	even	1	trivial
930.2.r.b.119.18	yes	64	15.14	odd	2	inner
930.2.r.b.719.7	yes	64	465.254	even	6	inner
930.2.r.b.719.18	yes	64	31.6	odd	6	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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.30243 + 1.14178i) q^{3} +1.00000 q^{4} +(1.95677 + 1.08215i) q^{5} +(-1.30243 + 1.14178i) q^{6} +(4.20156 + 2.42577i) q^{7} +1.00000 q^{8} +(0.392656 - 2.97419i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.30243 + 1.14178i) q^{3} +1.00000 q^{4} +(1.95677 + 1.08215i) q^{5} +(-1.30243 + 1.14178i) q^{6} +(4.20156 + 2.42577i) q^{7} +1.00000 q^{8} +(0.392656 - 2.97419i) q^{9} +(1.95677 + 1.08215i) q^{10} +(0.613210 + 1.06211i) q^{11} +(-1.30243 + 1.14178i) q^{12} +(0.733571 + 1.27058i) q^{13} +(4.20156 + 2.42577i) q^{14} +(-3.78414 + 0.824789i) q^{15} +1.00000 q^{16} +(-3.27327 - 1.88983i) q^{17} +(0.392656 - 2.97419i) q^{18} +(2.65459 - 4.59788i) q^{19} +(1.95677 + 1.08215i) q^{20} +(-8.24195 + 1.63787i) q^{21} +(0.613210 + 1.06211i) q^{22} -6.72188i q^{23} +(-1.30243 + 1.14178i) q^{24} +(2.65791 + 4.23503i) q^{25} +(0.733571 + 1.27058i) q^{26} +(2.88448 + 4.32201i) q^{27} +(4.20156 + 2.42577i) q^{28} -5.15742 q^{29} +(-3.78414 + 0.824789i) q^{30} +(-5.54251 + 0.529744i) q^{31} +1.00000 q^{32} +(-2.01137 - 0.683174i) q^{33} +(-3.27327 - 1.88983i) q^{34} +(5.59645 + 9.29338i) q^{35} +(0.392656 - 2.97419i) q^{36} +(-1.72299 + 2.98431i) q^{37} +(2.65459 - 4.59788i) q^{38} +(-2.40616 - 0.817266i) q^{39} +(1.95677 + 1.08215i) q^{40} +(1.44137 - 0.832174i) q^{41} +(-8.24195 + 1.63787i) q^{42} +(1.37011 - 2.37311i) q^{43} +(0.613210 + 1.06211i) q^{44} +(3.98685 - 5.39491i) q^{45} -6.72188i q^{46} +5.00458 q^{47} +(-1.30243 + 1.14178i) q^{48} +(8.26872 + 14.3218i) q^{49} +(2.65791 + 4.23503i) q^{50} +(6.42099 - 1.27601i) q^{51} +(0.733571 + 1.27058i) q^{52} +(-3.13635 + 1.81077i) q^{53} +(2.88448 + 4.32201i) q^{54} +(0.0505518 + 2.74189i) q^{55} +(4.20156 + 2.42577i) q^{56} +(1.79237 + 9.01939i) q^{57} -5.15742 q^{58} +(-12.1296 - 7.00301i) q^{59} +(-3.78414 + 0.824789i) q^{60} +7.18747i q^{61} +(-5.54251 + 0.529744i) q^{62} +(8.86447 - 11.5437i) q^{63} +1.00000 q^{64} +(0.0604740 + 3.28007i) q^{65} +(-2.01137 - 0.683174i) q^{66} +(-12.5793 + 7.26264i) q^{67} +(-3.27327 - 1.88983i) q^{68} +(7.67494 + 8.75479i) q^{69} +(5.59645 + 9.29338i) q^{70} +(4.89947 - 2.82871i) q^{71} +(0.392656 - 2.97419i) q^{72} +(-0.218186 - 0.377910i) q^{73} +(-1.72299 + 2.98431i) q^{74} +(-8.29725 - 2.48107i) q^{75} +(2.65459 - 4.59788i) q^{76} +5.95003i q^{77} +(-2.40616 - 0.817266i) q^{78} +(-4.39774 - 2.53904i) q^{79} +(1.95677 + 1.08215i) q^{80} +(-8.69164 - 2.33567i) q^{81} +(1.44137 - 0.832174i) q^{82} +(2.21035 - 1.27615i) q^{83} +(-8.24195 + 1.63787i) q^{84} +(-4.35998 - 7.24012i) q^{85} +(1.37011 - 2.37311i) q^{86} +(6.71718 - 5.88866i) q^{87} +(0.613210 + 1.06211i) q^{88} +12.3868 q^{89} +(3.98685 - 5.39491i) q^{90} +7.11789i q^{91} -6.72188i q^{92} +(6.61388 - 7.01830i) q^{93} +5.00458 q^{94} +(10.1700 - 6.12435i) q^{95} +(-1.30243 + 1.14178i) q^{96} +14.0563i q^{97} +(8.26872 + 14.3218i) q^{98} +(3.39971 - 1.40676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

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