LMFDB - Embedded newform 930.2.r.a.119.15

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			119.15
Character	$\chi$	$=$	930.119
Dual form			930.2.r.a.719.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.337599 + 1.69883i) q^{3} +1.00000 q^{4} +(-1.95677 - 1.08215i) q^{5} +(0.337599 - 1.69883i) q^{6} +(4.20156 + 2.42577i) q^{7} -1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.337599 + 1.69883i) q^{3} +1.00000 q^{4} +(-1.95677 - 1.08215i) q^{5} +(0.337599 - 1.69883i) q^{6} +(4.20156 + 2.42577i) q^{7} -1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +(1.95677 + 1.08215i) q^{10} +(-0.613210 - 1.06211i) q^{11} +(-0.337599 + 1.69883i) q^{12} +(0.733571 + 1.27058i) q^{13} +(-4.20156 - 2.42577i) q^{14} +(2.49899 - 2.95889i) q^{15} +1.00000 q^{16} +(3.27327 + 1.88983i) q^{17} +(2.77205 + 1.14705i) q^{18} +(2.65459 - 4.59788i) q^{19} +(-1.95677 - 1.08215i) q^{20} +(-5.53941 + 6.31880i) q^{21} +(0.613210 + 1.06211i) q^{22} +6.72188i q^{23} +(0.337599 - 1.69883i) 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} +(-2.49899 + 2.95889i) 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} +(-2.77205 - 1.14705i) 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} +(5.53941 - 6.31880i) q^{42} +(1.37011 - 2.37311i) q^{43} +(-0.613210 - 1.06211i) q^{44} +(4.18301 + 5.24428i) q^{45} -6.72188i q^{46} -5.00458 q^{47} +(-0.337599 + 1.69883i) q^{48} +(8.26872 + 14.3218i) q^{49} +(-2.65791 - 4.23503i) q^{50} +(-4.31555 + 4.92274i) 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} +(6.91483 + 6.06193i) q^{57} -5.15742 q^{58} +(12.1296 + 7.00301i) q^{59} +(2.49899 - 2.95889i) 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} +(-11.4193 - 2.26930i) q^{69} +(5.59645 + 9.29338i) q^{70} +(-4.89947 + 2.82871i) q^{71} +(2.77205 + 1.14705i) q^{72} +(-0.218186 - 0.377910i) q^{73} +(1.72299 - 2.98431i) q^{74} +(-8.09191 + 3.08561i) 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} +(6.36857 + 6.35935i) q^{81} +(1.44137 - 0.832174i) q^{82} +(-2.21035 + 1.27615i) q^{83} +(-5.53941 + 6.31880i) q^{84} +(-4.35998 - 7.24012i) q^{85} +(-1.37011 + 2.37311i) q^{86} +(-1.74114 + 8.76158i) q^{87} +(0.613210 + 1.06211i) q^{88} -12.3868 q^{89} +(-4.18301 - 5.24428i) q^{90} +7.11789i q^{91} +6.72188i q^{92} +(0.971197 - 9.59462i) q^{93} +5.00458 q^{94} +(-10.1700 + 6.12435i) q^{95} +(0.337599 - 1.69883i) q^{96} +14.0563i q^{97} +(-8.26872 - 14.3218i) q^{98} +(0.481561 + 3.64761i) 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} + 5 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} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 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 + 5 * 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 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * 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
$3$	−0.337599	+	1.69883i	−0.194913	+	0.980821i
$3$	−0.337599	+	1.69883i	−0.194913	+	0.980821i
$4$	1.00000			0.500000
$5$	−1.95677	−	1.08215i	−0.875095	−	0.483951i
$5$	−1.95677	−	1.08215i	−0.875095	−	0.483951i
$6$	0.337599	−	1.69883i	0.137824	−	0.693545i
$7$	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
$9$	−2.77205	−	1.14705i	−0.924018	−	0.382349i
$10$	1.95677	+	1.08215i	0.618786	+	0.342205i
$11$	−0.613210	−	1.06211i	−0.184890	−	0.320239i	0.758650	−	0.651499i	$-0.225860\pi$
$11$	−0.613210	−	1.06211i	−0.184890	−	0.320239i	−0.943539	+	0.331260i	$0.892526\pi$
$12$	−0.337599	+	1.69883i	−0.0974563	+	0.490410i
$13$	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
$15$	2.49899	−	2.95889i	0.645236	−	0.763983i
$16$	1.00000			0.250000
$17$	3.27327	+	1.88983i	0.793886	+	0.458350i	0.841329	−	0.540524i	$-0.181774\pi$
$17$	3.27327	+	1.88983i	0.793886	+	0.458350i	−0.0474430	+	0.998874i	$0.515107\pi$
$18$	2.77205	+	1.14705i	0.653379	+	0.270361i
$19$	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
$21$	−5.53941	+	6.31880i	−1.20880	+	1.37887i
$22$	0.613210	+	1.06211i	0.130737	+	0.226443i
$23$			6.72188i			1.40161i	0.713353	+	0.700805i	$0.247176\pi$
$23$			6.72188i			1.40161i	−0.713353	+	0.700805i	$0.752824\pi$
$24$	0.337599	−	1.69883i	0.0689120	−	0.346772i
$25$	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	$-0.341052\pi$
$29$	5.15742			0.957708			0.478854	+	0.877895i	$0.341052\pi$
$30$	−2.49899	+	2.95889i	−0.456251	+	0.540218i
$31$	−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
$36$	−2.77205	−	1.14705i	−0.462009	−	0.191174i
$37$	−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	−0.608311	−	0.793699i	$-0.708153\pi$
$41$	−1.44137	+	0.832174i	−0.225104	+	0.129964i	0.383207	+	0.923662i	$0.374819\pi$
$42$	5.53941	−	6.31880i	0.854750	−	0.975012i
$43$	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
$45$	4.18301	+	5.24428i	0.623566	+	0.781771i
$46$		−	6.72188i		−	0.991088i
$47$	−5.00458			−0.729994			−0.364997	−	0.931009i	$-0.618930\pi$
$47$	−5.00458			−0.729994			−0.364997	+	0.931009i	$0.618930\pi$
$48$	−0.337599	+	1.69883i	−0.0487282	+	0.245205i
$49$	8.26872	+	14.3218i	1.18125	+	2.04598i
$50$	−2.65791	−	4.23503i	−0.375886	−	0.598924i
$51$	−4.31555	+	4.92274i	−0.604298	+	0.689321i
$52$	0.733571	+	1.27058i	0.101728	+	0.176198i
$53$	3.13635	−	1.81077i	0.430811	−	0.248729i	−0.268881	−	0.963173i	$-0.586654\pi$
$53$	3.13635	−	1.81077i	0.430811	−	0.248729i	0.699692	+	0.714445i	$0.253321\pi$
$54$	−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
$57$	6.91483	+	6.06193i	0.915892	+	0.802922i
$58$	−5.15742			−0.677202
$59$	12.1296	+	7.00301i	1.57914	+	0.911714i	0.994980	+	0.100072i	$0.0319074\pi$
$59$	12.1296	+	7.00301i	1.57914	+	0.911714i	0.584155	+	0.811642i	$0.301426\pi$
$60$	2.49899	−	2.95889i	0.322618	−	0.381992i
$61$			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
$69$	−11.4193	−	2.26930i	−1.37473	−	0.273191i
$70$	5.59645	+	9.29338i	0.668904	+	1.11077i
$71$	−4.89947	+	2.82871i	−0.581461	+	0.335706i	−0.761714	−	0.647914i	$-0.775642\pi$
$71$	−4.89947	+	2.82871i	−0.581461	+	0.335706i	0.180253	+	0.983620i	$0.442308\pi$
$72$	2.77205	+	1.14705i	0.326690	+	0.135181i
$73$	−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
$75$	−8.09191	+	3.08561i	−0.934373	+	0.356295i
$76$	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
$81$	6.36857	+	6.35935i	0.707619	+	0.706594i
$82$	1.44137	−	0.832174i	0.159172	−	0.0918983i
$83$	−2.21035	+	1.27615i	−0.242618	+	0.140075i	−0.616379	−	0.787449i	$-0.711401\pi$
$83$	−2.21035	+	1.27615i	−0.242618	+	0.140075i	0.373761	+	0.927525i	$0.378068\pi$
$84$	−5.53941	+	6.31880i	−0.604400	+	0.689437i
$85$	−4.35998	−	7.24012i	−0.472906	−	0.785302i
$86$	−1.37011	+	2.37311i	−0.147743	+	0.255899i
$87$	−1.74114	+	8.76158i	−0.186669	+	0.939340i
$88$	0.613210	+	1.06211i	0.0653685	+	0.113221i
$89$	−12.3868			−1.31300			−0.656501	−	0.754325i	$-0.727964\pi$
$89$	−12.3868			−1.31300			−0.656501	+	0.754325i	$0.727964\pi$
$90$	−4.18301	−	5.24428i	−0.440927	−	0.552796i
$91$			7.11789i			0.746158i
$92$			6.72188i			0.700805i
$93$	0.971197	−	9.59462i	0.100708	−	0.994916i
$94$	5.00458			0.516184
$95$	−10.1700	+	6.12435i	−1.04342	+	0.628345i
$96$	0.337599	−	1.69883i	0.0344560	−	0.173386i
$97$			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
$99$	0.481561	+	3.64761i	0.0483987	+	0.366599i
$100$	2.65791	+	4.23503i	0.265791	+	0.423503i
$101$			8.98721i			0.894261i	0.894469	+	0.447130i	$0.147554\pi$
$101$			8.98721i			0.894261i	−0.894469	+	0.447130i	$0.852446\pi$
$102$	4.31555	−	4.92274i	0.427303	−	0.487424i
$103$	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
$105$	17.6772	−	6.36999i	1.72512	−	0.621647i
$106$	−3.13635	+	1.81077i	−0.304629	+	0.175878i
$107$	−2.90858	+	5.03780i	−0.281183	+	0.487023i	−0.971676	−	0.236316i	$-0.924060\pi$
$107$	−2.90858	+	5.03780i	−0.281183	+	0.487023i	0.690494	+	0.723338i	$0.257393\pi$
$108$	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
$111$	−4.48816	−	3.93457i	−0.425997	−	0.373453i
$112$	4.20156	+	2.42577i	0.397010	+	0.229214i
$113$	5.92849	+	10.2684i	0.557705	+	0.965974i	0.997688	+	0.0679674i	$0.0216514\pi$
$113$	5.92849	+	10.2684i	0.557705	+	0.965974i	−0.439982	+	0.898006i	$0.645015\pi$
$114$	−6.91483	−	6.06193i	−0.647634	−	0.567752i
$115$	7.27407	−	13.1532i	0.678310	−	1.22654i
$116$	5.15742			0.478854
$117$	−0.576082	−	4.36356i	−0.0532588	−	0.403411i
$118$	−12.1296	−	7.00301i	−1.11662	−	0.644679i
$119$	9.16857	+	15.8804i	0.840481	+	1.45576i
$120$	−2.49899	+	2.95889i	−0.228125	+	0.270109i
$121$	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
$129$	3.56896	+	3.12875i	0.314229	+	0.275471i
$130$	0.0604740	+	3.28007i	0.00530392	+	0.287681i
$131$	6.31523	+	3.64610i	0.551765	+	0.318561i	0.749833	−	0.661627i	$-0.230134\pi$
$131$	6.31523	+	3.64610i	0.551765	+	0.318561i	−0.198069	+	0.980188i	$0.563467\pi$
$132$	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
$135$	−10.3213	+	5.33576i	−0.888318	+	0.459229i
$136$	−3.27327	−	1.88983i	−0.280681	−	0.162051i
$137$	10.3598	−	5.98123i	0.885097	−	0.511011i	0.0127612	−	0.999919i	$-0.495938\pi$
$137$	10.3598	−	5.98123i	0.885097	−	0.511011i	0.872336	+	0.488908i	$0.162605\pi$
$138$	11.4193	+	2.26930i	0.972079	+	0.193176i
$139$		−	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
$141$	1.68954	−	8.50194i	0.142285	−	0.715993i
$142$	4.89947	−	2.82871i	0.411155	−	0.237380i
$143$	0.899666	−	1.55827i	0.0752339	−	0.130309i
$144$	−2.77205	−	1.14705i	−0.231005	−	0.0955872i
$145$	−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	0.925917	−	0.377726i	$-0.123294\pi$
$149$	12.9604	+	7.48268i	1.06176	+	0.613005i	0.135838	+	0.990731i	$0.456627\pi$
$150$	8.09191	−	3.08561i	0.660702	−	0.251939i
$151$			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
$162$	−6.36857	−	6.35935i	−0.500362	−	0.499638i
$163$			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
$165$	−4.67508	−	0.839781i	−0.363955	−	0.0653769i
$166$	2.21035	−	1.27615i	0.171557	−	0.0990483i
$167$	13.9138	+	8.03314i	1.07668	+	0.621623i	0.929999	−	0.367561i	$-0.119807\pi$
$167$	13.9138	+	8.03314i	1.07668	+	0.621623i	0.146683	+	0.989184i	$0.453140\pi$
$168$	5.53941	−	6.31880i	0.427375	−	0.487506i
$169$	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	$-0.812792\pi$
$173$	−11.7912	−	20.4229i	−0.896467	−	1.55273i	−0.0644877	−	0.997919i	$-0.520541\pi$
$174$	1.74114	−	8.76158i	0.131995	−	0.664213i
$175$	0.894165	+	24.2412i	0.0675925	+	1.83246i
$176$	−0.613210	−	1.06211i	−0.0462225	−	0.0800597i
$177$	−15.9919	+	18.2419i	−1.20202	+	1.37114i
$178$	12.3868			0.928432
$179$	12.3901	−	21.4603i	0.926079	−	1.60402i	0.136263	−	0.990673i	$-0.456491\pi$
$179$	12.3901	−	21.4603i	0.926079	−	1.60402i	0.789816	−	0.613344i	$-0.210176\pi$
$180$	4.18301	+	5.24428i	0.311783	+	0.390886i
$181$	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
$183$	−12.2103	−	2.42648i	−0.902611	−	0.179371i
$184$		−	6.72188i		−	0.495544i
$185$	6.60097	−	3.97508i	0.485313	−	0.292254i
$186$	−0.971197	+	9.59462i	−0.0712116	+	0.703512i
$187$		−	4.63544i		−	0.338977i
$188$	−5.00458			−0.364997
$189$	22.6035	−	11.1621i	1.64416	−	0.811922i
$190$	10.1700	−	6.12435i	0.737810	−	0.444307i
$191$	−5.66215	+	3.26904i	−0.409699	+	0.236540i	−0.690660	−	0.723179i	$-0.742680\pi$
$191$	−5.66215	+	3.26904i	−0.409699	+	0.236540i	0.280961	+	0.959719i	$0.409347\pi$
$192$	−0.337599	+	1.69883i	−0.0243641	+	0.122603i
$193$	−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
$195$	5.59270	+	1.00461i	0.400502	+	0.0719418i
$196$	8.26872	+	14.3218i	0.590623	+	1.02299i
$197$	−6.28191	+	3.62687i	−0.447568	+	0.258403i	−0.706802	−	0.707411i	$-0.749863\pi$
$197$	−6.28191	+	3.62687i	−0.447568	+	0.258403i	0.259235	+	0.965814i	$0.416530\pi$
$198$	−0.481561	−	3.64761i	−0.0342231	−	0.259225i
$199$	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
$204$	−4.31555	+	4.92274i	−0.302149	+	0.344661i
$205$	3.72096	−	0.0686027i	0.259883	−	0.00479142i
$206$	−2.37364	+	1.37042i	−0.165379	+	0.0954817i
$207$	7.71031	−	18.6334i	0.535904	−	1.29511i
$208$	0.733571	+	1.27058i	0.0508640	+	0.0880990i
$209$	−6.51128			−0.450395
$210$	−17.6772	+	6.36999i	−1.21985	+	0.439571i
$211$	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
$222$	4.48816	+	3.93457i	0.301225	+	0.264071i
$223$	−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
$225$	−2.51010	−	14.7885i	−0.167340	−	0.985899i
$226$	−5.92849	−	10.2684i	−0.394357	−	0.683047i
$227$	−5.80110	−	10.0478i	−0.385033	−	0.666896i	0.606741	−	0.794900i	$-0.292476\pi$
$227$	−5.80110	−	10.0478i	−0.385033	−	0.666896i	−0.991774	+	0.128003i	$0.959143\pi$
$228$	6.91483	+	6.06193i	0.457946	+	0.401461i
$229$	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
$231$	10.1081	+	2.00872i	0.665064	+	0.132164i
$232$	−5.15742			−0.338601
$233$	11.5244			0.754991			0.377496	−	0.926011i	$-0.376785\pi$
$233$	11.5244			0.754991			0.377496	+	0.926011i	$0.376785\pi$
$234$	0.576082	+	4.36356i	0.0376596	+	0.285255i
$235$	9.79283	+	5.41570i	0.638814	+	0.353281i
$236$	12.1296	+	7.00301i	0.789568	+	0.455857i
$237$	5.79807	−	6.61385i	0.376625	−	0.429616i
$238$	−9.16857	−	15.8804i	−0.594310	−	1.02937i
$239$	−3.13030	−	5.42184i	−0.202482	−	0.350710i	0.746845	−	0.664998i	$-0.231568\pi$
$239$	−3.13030	−	5.42184i	−0.202482	−	0.350710i	−0.949328	+	0.314288i	$0.898234\pi$
$240$	2.49899	−	2.95889i	0.161309	−	0.190996i
$241$	−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
$243$	−12.9535	+	8.67222i	−0.830966	+	0.556323i
$244$			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	−0.969054	−	0.246850i	$-0.920604\pi$
$251$	−4.28946	+	7.42956i	−0.270748	+	0.468949i	0.698306	+	0.715800i	$0.253938\pi$
$252$	−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
$255$	13.7717	−	4.96262i	0.862416	−	0.310771i
$256$	1.00000			0.0625000
$257$	−2.27123	−	3.93388i	−0.141675	−	0.245389i	0.786452	−	0.617651i	$-0.211916\pi$
$257$	−2.27123	−	3.93388i	−0.141675	−	0.245389i	−0.928128	+	0.372262i	$0.878582\pi$
$258$	−3.56896	−	3.12875i	−0.222194	−	0.194788i
$259$	−14.4785	+	8.35916i	−0.899650	+	0.519413i
$260$	−0.0604740	−	3.28007i	−0.00375044	−	0.203421i
$261$	−14.2966	−	5.91579i	−0.884939	−	0.366178i
$262$	−6.31523	−	3.64610i	−0.390156	−	0.225257i
$263$			12.1422i			0.748718i	0.927284	+	0.374359i	$0.122137\pi$
$263$			12.1422i			0.748718i	−0.927284	+	0.374359i	$0.877863\pi$
$264$	−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
$267$	4.18178	−	21.0431i	0.255921	−	1.28782i
$268$	−12.5793	+	7.26264i	−0.768401	+	0.443637i
$269$	−10.7295	−	18.5841i	−0.654192	−	1.13309i	−0.982096	−	0.188383i	$-0.939675\pi$
$269$	−10.7295	−	18.5841i	−0.654192	−	1.13309i	0.327904	−	0.944711i	$-0.393658\pi$
$270$	10.3213	−	5.33576i	0.628136	−	0.324724i
$271$			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
$273$	−12.0921	−	2.40299i	−0.731847	−	0.145436i
$274$	−10.3598	+	5.98123i	−0.625858	+	0.361339i
$275$	2.86822	−	5.41997i	0.172960	−	0.326836i
$276$	−11.4193	−	2.26930i	−0.687364	−	0.136596i
$277$	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
$279$	15.9718	+	4.88903i	0.956205	+	0.292699i
$280$	5.59645	+	9.29338i	0.334452	+	0.555386i
$281$		−	14.7922i		−	0.882428i	−0.897402	−	0.441214i	$-0.854548\pi$
$281$		−	14.7922i		−	0.882428i	0.897402	−	0.441214i	$-0.145452\pi$
$282$	−1.68954	+	8.50194i	−0.100611	+	0.506283i
$283$		−	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
$285$	−6.97085	−	19.3447i	−0.412918	−	1.14588i
$286$	−0.899666	+	1.55827i	−0.0531984	+	0.0921423i
$287$	−8.07465			−0.476632
$288$	2.77205	+	1.14705i	0.163345	+	0.0675904i
$289$	−1.35712	−	2.35059i	−0.0798303	−	0.138270i
$290$	10.0919	+	5.58108i	0.592616	+	0.327732i
$291$	−23.8792	−	4.74538i	−1.39982	−	0.278179i
$292$	−0.218186	−	0.377910i	−0.0127684	−	0.0221155i
$293$	8.93490	−	15.4757i	0.521982	−	0.904100i	−0.477691	−	0.878528i	$-0.658526\pi$
$293$	8.93490	−	15.4757i	0.521982	−	0.904100i	0.999673	−	0.0255719i	$-0.00814068\pi$
$294$	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
$297$	−6.35925	−	0.413338i	−0.369001	−	0.0239843i
$298$	−12.9604	−	7.48268i	−0.750775	−	0.433460i
$299$	−8.54070	+	4.93098i	−0.493922	+	0.285166i
$300$	−8.09191	+	3.08561i	−0.467187	+	0.178148i
$301$	11.5132	−	6.64716i	0.663611	−	0.383136i
$302$		−	6.74649i		−	0.388217i
$303$	−15.2678	−	3.03407i	−0.877109	−	0.174303i
$304$	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	$0.149756\pi$
$311$			15.9884i			0.906617i	−0.891354	+	0.453308i	$0.850244\pi$
$312$	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
$315$	4.85372	+	32.1811i	0.273476	+	1.81320i
$316$	−4.39774	−	2.53904i	−0.247392	−	0.142832i
$317$	4.61995	−	8.00199i	0.259482	−	0.449437i	−0.706621	−	0.707592i	$-0.749781\pi$
$317$	4.61995	−	8.00199i	0.259482	−	0.449437i	0.966103	+	0.258156i	$0.0831147\pi$
$318$	−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
$321$	−7.57644	−	6.64193i	−0.422876	−	0.370717i
$322$	16.3057	−	28.2424i	0.908683	−	1.57389i
$323$	17.3784	−	10.0334i	0.966959	−	0.558274i
$324$	6.36857	+	6.35935i	0.353809	+	0.353297i
$325$	−3.43119	+	6.48379i	−0.190328	+	0.359656i
$326$		−	8.61619i		−	0.477207i
$327$	3.45801	−	17.4011i	0.191228	−	0.962281i
$328$	1.44137	−	0.832174i	0.0795862	−	0.0459491i
$329$	−21.0270	−	12.1400i	−1.15926	−	0.669298i
$330$	4.67508	+	0.839781i	0.257355	+	0.0462284i
$331$	−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
$336$	−5.53941	+	6.31880i	−0.302200	+	0.344719i
$337$	−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
$345$	19.8893	+	16.7979i	1.07081	+	0.904369i
$346$	11.7912	+	20.4229i	0.633898	+	1.09794i
$347$	−20.8204	−	12.0207i	−1.11770	−	0.645304i	−0.176886	−	0.984231i	$-0.556603\pi$
$347$	−20.8204	−	12.0207i	−1.11770	−	0.645304i	−0.940812	+	0.338927i	$0.889936\pi$
$348$	−1.74114	+	8.76158i	−0.0933347	+	0.469670i
$349$	−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
$351$	7.60744	+	0.494467i	0.406055	+	0.0263927i
$352$	0.613210	+	1.06211i	0.0326842	+	0.0566107i
$353$	27.1647	+	15.6835i	1.44583	+	0.834751i	0.998229	−	0.0594826i	$-0.0189451\pi$
$353$	27.1647	+	15.6835i	1.44583	+	0.834751i	0.447601	+	0.894233i	$0.352278\pi$
$354$	15.9919	−	18.2419i	0.849958	−	0.969545i
$355$	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	−0.867836	−	0.496851i	$-0.834490\pi$
$359$	−16.5120	+	9.53319i	−0.871468	+	0.503142i	−0.00363226	+	0.999993i	$0.501156\pi$
$360$	−4.18301	−	5.24428i	−0.220464	−	0.276398i
$361$	−4.59366	−	7.95645i	−0.241771	−	0.418760i
$362$	−22.3120	+	12.8818i	−1.17269	+	0.677055i
$363$	12.3677	+	10.8423i	0.649138	+	0.569071i
$364$			7.11789i			0.373079i
$365$	0.0179868	+	0.975594i	0.000941473	+	0.0510649i
$366$	12.2103	+	2.42648i	0.638242	+	0.126834i
$367$	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
$369$	4.95009	−	0.653516i	0.257692	−	0.0340207i
$370$	−6.60097	+	3.97508i	−0.343168	+	0.206655i
$371$	17.5701			0.912193
$372$	0.971197	−	9.59462i	0.0503542	−	0.497458i
$373$			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
$375$	19.1731	+	2.71881i	0.990095	+	0.140399i
$376$	5.00458			0.258092
$377$	3.78333	+	6.55292i	0.194851	+	0.337492i
$378$	−22.6035	+	11.1621i	−1.16260	+	0.574116i
$379$	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
$381$	8.82194	+	7.73381i	0.451962	+	0.396215i
$382$	5.66215	−	3.26904i	0.289701	−	0.167259i
$383$	−28.3694	+	16.3791i	−1.44961	+	0.836931i	−0.998458	−	0.0555180i	$-0.982319\pi$
$383$	−28.3694	+	16.3791i	−1.44961	+	0.836931i	−0.451149	+	0.892449i	$0.648986\pi$
$384$	0.337599	−	1.69883i	0.0172280	−	0.0866931i
$385$	−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	−0.646259	−	0.763118i	$-0.723667\pi$
$389$	6.66148	−	11.5380i	0.337750	−	0.585001i	0.984009	+	0.178117i	$0.0570007\pi$
$390$	−5.59270	−	1.00461i	−0.283197	−	0.0508705i
$391$	−12.7032	+	22.0026i	−0.642428	+	1.11272i
$392$	−8.26872	−	14.3218i	−0.417633	−	0.723362i
$393$	−8.32613	+	9.49760i	−0.419997	+	0.479090i
$394$	6.28191	−	3.62687i	0.316478	−	0.182719i
$395$	5.85777	+	9.72733i	0.294736	+	0.489435i
$396$	0.481561	+	3.64761i	0.0241994	+	0.183299i
$397$	−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	$-0.433088\pi$
$401$	8.35710			0.417334			0.208667	+	0.977987i	$0.433088\pi$
$402$	8.09126	+	23.8219i	0.403555	+	1.18813i
$403$	−4.73890	−	6.65360i	−0.236062	−	0.331439i
$404$			8.98721i			0.447130i
$405$	−5.58009	−	19.3355i	−0.277277	−	0.960790i
$406$	−21.6692	−	12.5107i	−1.07542	−	0.620896i
$407$	4.22623			0.209486
$408$	4.31555	−	4.92274i	0.213651	−	0.243712i
$409$	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
$414$	−7.71031	+	18.6334i	−0.378941	+	0.915783i
$415$	5.70614	−	0.105203i	0.280103	−	0.00516421i
$416$	−0.733571	−	1.27058i	−0.0359663	−	0.0622954i
$417$	39.4999	+	7.84959i	1.93432	+	0.384396i
$418$	6.51128			0.318477
$419$			4.07196i			0.198928i	0.995041	+	0.0994641i	$0.0317128\pi$
$419$			4.07196i			0.198928i	−0.995041	+	0.0994641i	$0.968287\pi$
$420$	17.6772	−	6.36999i	0.862561	−	0.310824i
$421$	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
$423$	13.8730	+	5.74049i	0.674527	+	0.279112i
$424$	−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
$429$	2.34351	+	2.05445i	0.113146	+	0.0991898i
$430$	5.24905	−	3.16097i	0.253132	−	0.152435i
$431$	5.46905	+	3.15756i	0.263435	+	0.152094i	0.625900	−	0.779903i	$-0.284732\pi$
$431$	5.46905	+	3.15756i	0.263435	+	0.152094i	−0.362465	+	0.931997i	$0.618065\pi$
$432$	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
$435$	12.8883	−	15.2602i	0.617948	−	0.731673i
$436$	−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
$441$	−6.49352	−	49.1855i	−0.309215	−	2.34217i
$442$		−	5.54528i		−	0.263762i
$443$	−0.372788	−	0.645688i	−0.0177117	−	0.0306775i	0.857034	−	0.515260i	$-0.172305\pi$
$443$	−0.372788	−	0.645688i	−0.0177117	−	0.0306775i	−0.874745	+	0.484583i	$0.838971\pi$
$444$	−4.48816	−	3.93457i	−0.212999	−	0.186726i
$445$	24.2382	+	13.4044i	1.14900	+	0.635428i
$446$	1.55000	−	2.68467i	0.0733945	−	0.127123i
$447$	−17.0872	+	19.4914i	−0.808197	+	0.921909i
$448$	4.20156	+	2.42577i	0.198505	+	0.114607i
$449$	0.467690			0.0220717			0.0110358	−	0.999939i	$-0.496487\pi$
$449$	0.467690			0.0220717			0.0110358	+	0.999939i	$0.496487\pi$
$450$	2.51010	+	14.7885i	0.118327	+	0.697136i
$451$	1.76772	+	1.02060i	0.0832389	+	0.0480580i
$452$	5.92849	+	10.2684i	0.278853	+	0.482987i
$453$	−11.4612	−	2.27761i	−0.538492	−	0.107011i
$454$	5.80110	+	10.0478i	0.272259	+	0.471567i
$455$	7.70261	−	13.9281i	0.361104	−	0.652959i
$456$	−6.91483	−	6.06193i	−0.323817	−	0.283876i
$457$	−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
$459$	17.6095	−	8.69596i	0.821943	−	0.405893i
$460$	7.27407	−	13.1532i	0.339155	−	0.613271i
$461$	−20.3780			−0.949098			−0.474549	−	0.880229i	$-0.657389\pi$
$461$	−20.3780			−0.949098			−0.474549	+	0.880229i	$0.657389\pi$
$462$	−10.1081	−	2.00872i	−0.470271	−	0.0934542i
$463$	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
$465$	−12.2832	+	17.7235i	−0.569620	+	0.821908i
$466$	−11.5244			−0.533860
$467$	−14.5915			−0.675212			−0.337606	−	0.941287i	$-0.609617\pi$
$467$	−14.5915			−0.675212			−0.337606	+	0.941287i	$0.609617\pi$
$468$	−0.576082	−	4.36356i	−0.0266294	−	0.201706i
$469$	−70.4700			−3.25400
$470$	−9.79283	−	5.41570i	−0.451710	−	0.249808i
$471$	−14.5225	−	2.88596i	−0.669160	−	0.132978i
$472$	−12.1296	−	7.00301i	−0.558309	−	0.322340i
$473$	−3.36067			−0.154524
$474$	−5.79807	+	6.61385i	−0.266314	+	0.303784i
$475$	26.5278	−	0.978509i	1.21718	−	0.0448971i
$476$	9.16857	+	15.8804i	0.420241	+	0.727878i
$477$	−10.7712	+	1.42202i	−0.493178	+	0.0651099i
$478$	3.13030	+	5.42184i	0.143177	+	0.247989i
$479$	2.09151	+	1.20753i	0.0955635	+	0.0551736i	0.547020	−	0.837119i	$-0.315762\pi$
$479$	2.09151	+	1.20753i	0.0955635	+	0.0551736i	−0.451457	+	0.892293i	$0.649095\pi$
$480$	−2.49899	+	2.95889i	−0.114063	+	0.135054i
$481$	−5.05575			−0.230522
$482$	16.5387	+	9.54864i	0.753318	+	0.434929i
$483$	−42.4742	−	37.2353i	−1.93264	−	1.69426i
$484$	4.74795	−	8.22368i	0.215816	−	0.373804i
$485$	15.2109	−	27.5049i	0.690694	−	1.24893i
$486$	12.9535	−	8.67222i	0.587582	−	0.393380i
$487$	−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
$489$	−14.6375	−	2.90882i	−0.661929	−	0.131541i
$490$	0.681656	+	36.9726i	0.0307941	+	1.67025i
$491$	−16.5114	−	28.5986i	−0.745149	−	1.29064i	−0.950125	−	0.311869i	$-0.899045\pi$
$491$	−16.5114	−	28.5986i	−0.745149	−	1.29064i	0.204976	−	0.978767i	$-0.434288\pi$
$492$	−0.927120	−	2.72958i	−0.0417978	−	0.123059i
$493$	16.8816	+	9.74662i	0.760311	+	0.438966i
$494$	−7.78931			−0.350457
$495$	3.00495	−	7.65867i	0.135062	−	0.344231i
$496$	−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
$501$	−18.3442	+	20.9252i	−0.819559	+	0.934870i
$502$	4.28946	−	7.42956i	0.191448	−	0.331597i
$503$	3.33345	−	5.77370i	0.148631	−	0.257436i	−0.782091	−	0.623165i	$-0.785847\pi$
$503$	3.33345	−	5.77370i	0.148631	−	0.257436i	0.930722	+	0.365728i	$0.119180\pi$
$504$	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
$507$	14.1281	+	12.3855i	0.627452	+	0.550060i
$508$	3.38672	−	5.86597i	0.150261	−	0.260260i
$509$	14.4408	+	25.0122i	0.640077	+	1.10865i	0.985415	+	0.170168i	$0.0544310\pi$
$509$	14.4408	+	25.0122i	0.640077	+	1.10865i	−0.345338	+	0.938478i	$0.612236\pi$
$510$	−13.7717	+	4.96262i	−0.609820	+	0.219748i
$511$		−	2.11708i		−	0.0936541i
$512$	−1.00000			−0.0441942
$513$	−12.2150	−	24.7356i	−0.539304	−	1.09211i
$514$	2.27123	+	3.93388i	0.100180	+	0.173516i
$515$	−6.12766	+	0.112974i	−0.270017	+	0.00497825i
$516$	3.56896	+	3.12875i	0.157115	+	0.137736i
$517$	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	0.933980	−	0.357326i	$-0.116311\pi$
$521$	24.9143	+	14.3843i	1.09152	+	0.630187i	0.157537	+	0.987513i	$0.449645\pi$
$522$	14.2966	+	5.91579i	0.625747	+	0.258927i
$523$	−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
$525$	−41.4836	−	6.66477i	−1.81049	−	0.290874i
$526$		−	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
$534$	−4.18178	+	21.0431i	−0.180963	+	0.910625i
$535$	11.1431	−	6.71032i	0.481757	−	0.290112i
$536$	12.5793	−	7.26264i	0.543342	−	0.313698i
$537$	32.2745	+	28.2936i	1.39275	+	1.22096i
$538$	10.7295	+	18.5841i	0.462584	+	0.801218i
$539$	10.1409	−	17.5646i	0.436801	−	0.756561i
$540$	−10.3213	+	5.33576i	−0.444159	+	0.229614i
$541$	−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
$546$	12.0921	+	2.40299i	0.517494	+	0.102839i
$547$	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
$549$	8.24436	−	19.9240i	0.351861	−	0.850338i
$550$	−2.86822	+	5.41997i	−0.122301	+	0.231108i
$551$	13.6908	−	23.7132i	0.583248	−	1.01021i
$552$	11.4193	+	2.26930i	0.486040	+	0.0965878i
$553$	−12.3182	−	21.3358i	−0.523825	−	0.907292i
$554$	−10.5269			−0.447244
$555$	4.52452	+	12.5559i	0.192055	+	0.532969i
$556$		−	23.2512i		−	0.986072i
$557$		−	45.6098i		−	1.93255i	−0.257517	−	0.966274i	$-0.582904\pi$
$557$		−	45.6098i		−	1.93255i	0.257517	−	0.966274i	$-0.417096\pi$
$558$	−15.9718	−	4.88903i	−0.676139	−	0.206969i
$559$	4.02030			0.170041
$560$	−5.59645	−	9.29338i	−0.236493	−	0.392717i
$561$	7.87484	+	1.56492i	0.332476	+	0.0660710i
$562$			14.7922i			0.623971i
$563$	−7.54847	−	13.0743i	−0.318130	−	0.551017i	0.661968	−	0.749532i	$-0.269722\pi$
$563$	−7.54847	−	13.0743i	−0.318130	−	0.551017i	−0.980098	+	0.198515i	$0.936388\pi$
$564$	1.68954	−	8.50194i	0.0711425	−	0.357996i
$565$	−0.488732	−	26.5085i	−0.0205611	−	1.11522i
$566$			20.3465i			0.855226i
$567$	11.3316	+	42.1679i	0.475882	+	1.77088i
$568$	4.89947	−	2.82871i	0.205577	−	0.118690i
$569$	−12.7540	−	22.0905i	−0.534674	−	0.926082i	−0.999179	−	0.0405119i	$-0.987101\pi$
$569$	−12.7540	−	22.0905i	−0.534674	−	0.926082i	0.464505	−	0.885570i	$-0.346232\pi$
$570$	6.97085	+	19.3447i	0.291977	+	0.810260i
$571$	−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
$576$	−2.77205	−	1.14705i	−0.115502	−	0.0477936i
$577$	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
$579$	13.1210	−	14.9671i	0.545290	−	0.622011i
$580$	−10.0919	−	5.58108i	−0.419043	−	0.231742i
$581$	−12.3826			−0.513716
$582$	23.8792	+	4.74538i	0.989825	+	0.196702i
$583$	−3.84649	−	2.22077i	−0.159305	−	0.0919749i
$584$	0.218186	+	0.377910i	0.00902862	+	0.0156380i
$585$	−3.59476	+	9.16190i	−0.148625	+	0.378798i
$586$	−8.93490	+	15.4757i	−0.369097	+	0.639295i
$587$		−	0.191388i		−	0.00789944i	−0.999992	−	0.00394972i	$-0.998743\pi$
$587$		−	0.191388i		−	0.00789944i	0.999992	−	0.00394972i	$-0.00125724\pi$
$588$	−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	$-0.411895\pi$
$593$	13.3090			0.546537			0.273268	+	0.961938i	$0.411895\pi$
$594$	6.35925	+	0.413338i	0.260923	+	0.0169594i
$595$	−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	−0.879633	−	0.475653i	$-0.842212\pi$
$599$	−22.2111	+	12.8236i	−0.907521	+	0.523958i	−0.0278885	+	0.999611i	$0.508878\pi$
$600$	8.09191	−	3.08561i	0.330351	−	0.125969i
$601$	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
$603$	43.2010	−	5.70344i	1.75928	−	0.232262i
$604$			6.74649i			0.274511i
$605$	−18.1899	+	10.9539i	−0.739524	+	0.445339i
$606$	15.2678	+	3.03407i	0.620210	+	0.123251i
$607$	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
$609$	−28.5691	+	32.5887i	−1.15768	+	1.32056i
$610$	−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
$615$	−1.13965	+	6.34445i	−0.0459551	+	0.255833i
$616$			5.95003i			0.239734i
$617$	−6.88123	+	11.9186i	−0.277028	+	0.479826i	−0.970645	−	0.240518i	$-0.922683\pi$
$617$	−6.88123	+	11.9186i	−0.277028	+	0.479826i	0.693617	+	0.720344i	$0.256016\pi$
$618$	−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
$627$	2.19820	−	11.0616i	0.0877876	−	0.441756i
$628$			8.54850i			0.341122i
$629$	−11.2797	+	6.51231i	−0.449749	+	0.259663i
$630$	−4.85372	−	32.1811i	−0.193377	−	1.28213i
$631$	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
$633$	8.29771	+	7.27424i	0.329804	+	0.289125i
$634$	−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
$639$	16.8263	−	2.22142i	0.665637	−	0.0878781i
$640$	1.95677	+	1.08215i	0.0773482	+	0.0427756i
$641$	−18.9148	−	32.7615i	−0.747091	−	1.29400i	−0.949211	−	0.314640i	$-0.898116\pi$
$641$	−18.9148	−	32.7615i	−0.747091	−	1.29400i	0.202120	−	0.979361i	$-0.435217\pi$
$642$	7.57644	+	6.64193i	0.299018	+	0.262136i
$643$	−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
$645$	−3.59787	−	9.98439i	−0.141666	−	0.393135i
$646$	−17.3784	+	10.0334i	−0.683743	+	0.394759i
$647$		−	23.7433i		−	0.933445i	−0.884404	−	0.466723i	$-0.845435\pi$
$647$		−	23.7433i		−	0.933445i	0.884404	−	0.466723i	$-0.154565\pi$
$648$	−6.36857	−	6.35935i	−0.250181	−	0.249819i
$649$		−	17.1773i		−	0.674267i
$650$	3.43119	−	6.48379i	0.134582	−	0.254315i
$651$	27.3549	−	37.9565i	1.07212	−	1.48763i
$652$			8.61619i			0.337436i
$653$	28.2082			1.10387			0.551936	−	0.833886i	$-0.313889\pi$
$653$	28.2082			1.10387			0.551936	+	0.833886i	$0.313889\pi$
$654$	−3.45801	+	17.4011i	−0.135219	+	0.680436i
$655$	−8.41185	−	13.9686i	−0.328678	−	0.545799i
$656$	−1.44137	+	0.832174i	−0.0562760	+	0.0324909i
$657$	0.171344	+	1.29786i	0.00668478	+	0.0506342i
$658$	21.0270	+	12.1400i	0.819720	+	0.473265i
$659$		−	40.5424i		−	1.57931i	−0.613554	−	0.789653i	$-0.710261\pi$
$659$		−	40.5424i		−	1.57931i	0.613554	−	0.789653i	$-0.289739\pi$
$660$	−4.67508	−	0.839781i	−0.181977	−	0.0326884i
$661$	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
$663$	−9.42050	−	1.87208i	−0.365862	−	0.0727056i
$664$	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
$669$	−4.03753	−	3.53952i	−0.156100	−	0.136846i
$670$	−32.4740	+	0.598717i	−1.25458	+	0.0231304i
$671$	7.63389	−	4.40743i	0.294703	−	0.170147i
$672$	5.53941	−	6.31880i	0.213688	−	0.243753i
$673$	−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
$675$	25.9706	+	0.728330i	0.999607	+	0.0280334i
$676$	5.42375	−	9.39421i	0.208606	−	0.361316i
$677$	11.7145	−	6.76337i	0.450225	−	0.259938i	−0.257700	−	0.966225i	$-0.582965\pi$
$677$	11.7145	−	6.76337i	0.450225	−	0.259938i	0.707925	+	0.706287i	$0.249631\pi$
$678$	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	$-0.325677\pi$
$683$	27.2154			1.04137			0.520685	+	0.853749i	$0.325677\pi$
$684$	−12.6326	+	9.70063i	−0.483021	+	0.370913i
$685$	−26.7443	+	0.493080i	−1.02185	+	0.0188396i
$686$		−	46.2713i		−	1.76664i
$687$	−26.2650	+	29.9604i	−1.00207	+	1.14306i
$688$	1.37011	−	2.37311i	0.0522351	−	0.0904739i
$689$	4.60147	+	2.65666i	0.175302	+	0.101211i
$690$	−19.8893	−	16.7979i	−0.757174	−	0.639486i
$691$	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
$693$	−6.82496	+	16.4938i	−0.259259	+	0.626548i
$694$	20.8204	+	12.0207i	0.790332	+	0.456299i
$695$	−25.1613	+	45.4974i	−0.954421	+	1.72581i
$696$	1.74114	−	8.76158i	0.0659976	−	0.332107i
$697$	−6.29066			−0.238276
$698$	0.217399			0.00822866
$699$	−3.89064	+	19.5781i	−0.147157	+	0.740511i
$700$	0.894165	+	24.2412i	0.0337963	+	0.916232i
$701$	16.1244	+	9.30943i	0.609011	+	0.351612i	0.772578	−	0.634920i	$-0.218967\pi$
$701$	16.1244	+	9.30943i	0.609011	+	0.351612i	−0.163568	+	0.986532i	$0.552300\pi$
$702$	−7.60744	−	0.494467i	−0.287124	−	0.0186625i
$703$	9.14766	+	15.8442i	0.345011	+	0.597576i
$704$	−0.613210	−	1.06211i	−0.0231112	−	0.0400298i
$705$	−12.5064	+	14.8080i	−0.471018	+	0.557703i
$706$	−27.1647	−	15.6835i	−1.02236	−	0.590258i
$707$	−21.8009	+	37.7603i	−0.819907	+	1.42012i
$708$	−15.9919	+	18.2419i	−0.601011	+	0.685572i
$709$		−	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	−0.984108	−	0.177573i	$-0.943176\pi$
$719$	−9.07047	+	15.7105i	−0.338272	+	0.585903i	0.645836	+	0.763476i	$0.276509\pi$
$720$	4.18301	+	5.24428i	0.155891	+	0.195443i
$721$	13.2973			0.495217
$722$	4.59366	+	7.95645i	0.170958	+	0.296108i
$723$	21.8050	−	24.8729i	0.810936	−	0.925033i
$724$	22.3120	−	12.8818i	0.829219	−	0.478750i
$725$	13.7080	+	21.8418i	0.509101	+	0.811185i
$726$	−12.3677	−	10.8423i	−0.459010	−	0.402394i
$727$	−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
$732$	−12.2103	−	2.42648i	−0.451305	−	0.0896853i
$733$	−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
$735$	63.0402	+	11.3239i	2.32527	+	0.417687i
$736$		−	6.72188i		−	0.247772i
$737$	15.4275	+	8.90706i	0.568278	+	0.328096i
$738$	−4.95009	+	0.653516i	−0.182215	+	0.0240563i
$739$	−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
$741$	−2.62966	+	13.2327i	−0.0966030	+	0.486116i
$742$	−17.5701			−0.645018
$743$			41.0727i			1.50681i	0.657557	+	0.753405i	$0.271590\pi$
$743$			41.0727i			1.50681i	−0.657557	+	0.753405i	$0.728410\pi$
$744$	−0.971197	+	9.59462i	−0.0356058	+	0.351756i
$745$	−17.2631	−	28.6669i	−0.632473	−	1.05028i
$746$		−	13.9912i		−	0.512255i
$747$	7.59102	−	1.00217i	0.277741	−	0.0366676i
$748$		−	4.63544i		−	0.169489i
$749$	−24.4411	+	14.1111i	−0.893058	+	0.515607i
$750$	−19.1731	−	2.71881i	−0.700103	−	0.0992770i
$751$	−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
$753$	−11.1734	−	9.79527i	−0.407183	−	0.356960i
$754$	−3.78333	−	6.55292i	−0.137781	−	0.238643i
$755$	7.30070	−	13.2013i	0.265700	−	0.480446i
$756$	22.6035	−	11.1621i	0.822082	−	0.405961i
$757$	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	−0.517313	−	0.855796i	$-0.673068\pi$
$761$	13.3099	−	23.0535i	0.482485	−	0.835689i	0.999798	+	0.0201077i	$0.00640091\pi$
$762$	−8.82194	−	7.73381i	−0.319585	−	0.280166i
$763$	−43.0364	−	24.8471i	−1.55802	−	0.899525i
$764$	−5.66215	+	3.26904i	−0.204849	+	0.118270i
$765$	3.78135	+	25.0711i	0.136715	+	0.906448i
$766$	28.3694	−	16.3791i	1.02503	−	0.591799i
$767$			20.5488i			0.741974i
$768$	−0.337599	+	1.69883i	−0.0121820	+	0.0613013i
$769$	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	$-0.989143\pi$
$773$		−	1.89621i		−	0.0682018i	0.999418	−	0.0341009i	$-0.0108568\pi$
$774$	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
$780$	5.59270	+	1.00461i	0.200251	+	0.0359709i
$781$	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
$786$	8.32613	−	9.49760i	0.296983	−	0.338768i
$787$	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
$789$	−20.6275	−	4.09918i	−0.734359	−	0.145935i
$790$	−5.85777	−	9.72733i	−0.208410	−	0.346083i
$791$			57.5246i			2.04534i
$792$	−0.481561	−	3.64761i	−0.0171115	−	0.129612i
$793$	−9.13226	+	5.27251i	−0.324296	+	0.187232i
$794$	18.2024	+	10.5092i	0.645981	+	0.372957i
$795$	2.47982	−	13.8052i	0.0879502	−	0.489621i
$796$	16.6477	−	9.61156i	0.590063	−	0.340673i
$797$	35.9670	−	20.7656i	1.27402	−	0.735554i	0.298275	−	0.954480i	$-0.403589\pi$
$797$	35.9670	−	20.7656i	1.27402	−	0.735554i	0.975742	+	0.218926i	$0.0702553\pi$
$798$	−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
$801$	34.3370	+	14.2083i	1.21324	+	0.502024i
$802$	−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	−0.687766	−	0.725932i	$-0.741409\pi$
$809$	8.10033	−	14.0302i	0.284792	−	0.493275i	0.972559	+	0.232657i	$0.0747420\pi$
$810$	5.58009	+	19.3355i	0.196064	+	0.679381i
$811$	−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
$813$	−20.6013	−	4.09398i	−0.722521	−	0.143582i
$814$	−4.22623			−0.148129
$815$	9.32399	−	16.8599i	0.326605	−	0.590578i
$816$	−4.31555	+	4.92274i	−0.151074	+	0.172330i
$817$	−7.27417	−	12.5992i	−0.254491	−	0.440792i
$818$	−25.3153	−	14.6158i	−0.885130	−	0.511030i
$819$	8.16455	−	19.7312i	0.285293	−	0.689464i
$820$	3.72096	−	0.0686027i	0.129942	−	0.00239571i
$821$	−0.813290			−0.0283840			−0.0141920	−	0.999899i	$-0.504518\pi$
$821$	−0.813290			−0.0283840			−0.0141920	+	0.999899i	$0.504518\pi$
$822$	−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
$825$	8.23930	+	6.70239i	0.286856	+	0.233347i
$826$	−33.9754	−	58.8471i	−1.18215	−	2.04755i
$827$	15.5522	−	8.97904i	0.540801	−	0.312232i	−0.204602	−	0.978845i	$-0.565590\pi$
$827$	15.5522	−	8.97904i	0.540801	−	0.312232i	0.745404	+	0.666613i	$0.232257\pi$
$828$	7.71031	−	18.6334i	0.267952	−	0.647556i
$829$		−	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
$831$	−3.55386	+	17.8834i	−0.123282	+	0.620367i
$832$	0.733571	+	1.27058i	0.0254320	+	0.0440495i
$833$			62.5058i			2.16570i
$834$	−39.4999	−	7.84959i	−1.36777	−	0.271809i
$835$	−18.5331	−	30.7758i	−0.641364	−	1.06504i
$836$	−6.51128			−0.225197
$837$	−13.6977	+	25.4828i	−0.473461	+	0.880815i
$838$		−	4.07196i		−	0.140663i
$839$			23.1387i			0.798837i	0.916769	+	0.399418i	$0.130788\pi$
$839$			23.1387i			0.798837i	−0.916769	+	0.399418i	$0.869212\pi$
$840$	−17.6772	+	6.36999i	−0.609923	+	0.219785i
$841$	−2.40107			−0.0827955
$842$	−3.85212	−	6.67207i	−0.132753	−	0.229935i
$843$	25.1294	+	4.99383i	0.865504	+	0.171996i
$844$	3.18547	−	5.51739i	0.109648	−	0.189916i
$845$	−20.7790	+	12.5130i	−0.714818	+	0.430461i
$846$	−13.8730	−	5.74049i	−0.476963	−	0.197362i
$847$	39.8975	−	23.0348i	1.37090	−	0.791487i
$848$	3.13635	−	1.81077i	0.107703	−	0.0621822i
$849$	34.5652	+	6.86894i	1.18627	+	0.235741i
$850$	−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
$855$	35.2167	−	5.31156i	1.20439	−	0.181651i
$856$	2.90858	−	5.03780i	0.0994131	−	0.172188i
$857$	−24.6728	−	42.7345i	−0.842806	−	1.45978i	−0.887513	−	0.460783i	$-0.847569\pi$
$857$	−24.6728	−	42.7345i	−0.842806	−	1.45978i	0.0447063	−	0.999000i	$-0.485765\pi$
$858$	−2.34351	−	2.05445i	−0.0800060	−	0.0701378i
$859$	−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
$861$	2.72599	−	13.7175i	0.0929016	−	0.467490i
$862$	−5.46905	−	3.15756i	−0.186277	−	0.107547i
$863$	−35.6756	+	20.5973i	−1.21441	+	0.701141i	−0.963717	−	0.266925i	$-0.913992\pi$
$863$	−35.6756	+	20.5973i	−1.21441	+	0.701141i	−0.250695	+	0.968066i	$0.580659\pi$
$864$	−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
$870$	−12.8883	+	15.2602i	−0.436955	+	0.517371i
$871$	−18.4556	−	10.6553i	−0.625343	−	0.361042i
$872$	10.2430			0.346871
$873$	16.1232	−	38.9647i	0.545687	−	1.31876i
$874$	−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
$879$	23.2742	+	20.4035i	0.785019	+	0.688192i
$880$	0.0505518	+	2.74189i	0.00170410	+	0.0924293i
$881$	−5.42379	−	9.39429i	−0.182732	−	0.316502i	0.760078	−	0.649832i	$-0.225161\pi$
$881$	−5.42379	−	9.39429i	−0.182732	−	0.316502i	−0.942810	+	0.333331i	$0.891827\pi$
$882$	6.49352	+	49.1855i	0.218648	+	1.65616i
$883$	−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
$885$	51.0328	−	18.3897i	1.71545	−	0.618162i
$886$	0.372788	+	0.645688i	0.0125241	+	0.0216923i
$887$	21.2710	−	36.8424i	0.714210	−	1.23705i	−0.249054	−	0.968490i	$-0.580120\pi$
$887$	21.2710	−	36.8424i	0.714210	−	1.23705i	0.963264	−	0.268558i	$-0.0865470\pi$
$888$	4.48816	+	3.93457i	0.150613	+	0.132036i
$889$	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
$894$	17.0872	−	19.4914i	0.571482	−	0.651888i
$895$	−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
$900$	−2.51010	−	14.7885i	−0.0836702	−	0.492950i
$901$	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
$906$	11.4612	+	2.27761i	0.380771	+	0.0756684i
$907$			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
$909$	10.3087	−	24.9130i	0.341920	−	0.826313i
$910$	−7.70261	+	13.9281i	−0.255339	+	0.461712i
$911$	20.2395	−	35.0559i	0.670566	−	1.16145i	−0.307178	−	0.951652i	$-0.599385\pi$
$911$	20.2395	−	35.0559i	0.670566	−	1.16145i	0.977744	−	0.209802i	$-0.0672818\pi$
$912$	6.91483	+	6.06193i	0.228973	+	0.200731i
$913$	2.71082	+	1.56510i	0.0897152	+	0.0517971i
$914$	20.1181			0.665448
$915$	21.2669	+	17.9614i	0.703064	+	0.593786i
$916$	19.9216	+	11.5017i	0.658227	+	0.380027i
$917$	17.6892	+	30.6386i	0.584149	+	1.01178i
$918$	−17.6095	+	8.69596i	−0.581202	+	0.287010i
$919$	−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
$921$	−36.5814	+	41.7283i	−1.20540	+	1.37500i
$922$	20.3780			0.671114
$923$	−7.18822	−	4.15012i	−0.236603	−	0.136603i
$924$	10.1081	+	2.00872i	0.332532	+	0.0660821i
$925$	−17.2182	+	0.635113i	−0.566131	+	0.0208824i
$926$	−1.03856			−0.0341293
$927$	−8.15178	+	1.07621i	−0.267740	+	0.0353473i
$928$	−5.15742			−0.169300
$929$	50.0428			1.64185			0.820925	−	0.571036i	$-0.193458\pi$
$929$	50.0428			1.64185			0.820925	+	0.571036i	$0.193458\pi$
$930$	12.2832	−	17.7235i	0.402782	−	0.581177i
$931$	87.8001			2.87753
$932$	11.5244			0.377496
$933$	−27.1615	−	5.39765i	−0.889229	−	0.176711i
$934$	14.5915			0.477447
$935$	−5.01623	+	9.07051i	−0.164048	+	0.296637i
$936$	0.576082	+	4.36356i	0.0188298	+	0.142627i
$937$	−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
$939$	−7.70065	−	6.75082i	−0.251301	−	0.220305i
$940$	9.79283	+	5.41570i	0.319407	+	0.176641i
$941$	13.8129	+	23.9246i	0.450287	+	0.779919i	0.998404	−	0.0564823i	$-0.0179884\pi$
$941$	13.8129	+	23.9246i	0.450287	+	0.779919i	−0.548117	+	0.836402i	$0.684655\pi$
$942$	14.5225	+	2.88596i	0.473167	+	0.0940297i
$943$	−5.59378	−	9.68871i	−0.182158	−	0.315508i
$944$	12.1296	+	7.00301i	0.394784	+	0.227929i
$945$	−56.3089	−	2.61866i	−1.83173	−	0.0851852i
$946$	3.36067			0.109265
$947$	−33.7051	−	19.4596i	−1.09527	−	0.632353i	−0.160293	−	0.987069i	$-0.551244\pi$
$947$	−33.7051	−	19.4596i	−1.09527	−	0.632353i	−0.934974	+	0.354717i	$0.884577\pi$
$948$	5.79807	−	6.61385i	0.188313	−	0.214808i
$949$	0.320110	−	0.554447i	0.0103912	−	0.0179981i
$950$	−26.5278	+	0.978509i	−0.860676	+	0.0317470i
$951$	12.0343	+	10.5500i	0.390240	+	0.342107i
$952$	−9.16857	−	15.8804i	−0.297155	−	0.514687i
$953$			8.83785i			0.286286i	0.989702	+	0.143143i	$0.0457209\pi$
$953$			8.83785i			0.286286i	−0.989702	+	0.143143i	$0.954279\pi$
$954$	10.7712	−	1.42202i	0.348730	−	0.0460396i
$955$	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
$960$	2.49899	−	2.95889i	0.0806545	−	0.0954979i
$961$	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
$966$	42.4742	+	37.2353i	1.36659	+	1.19803i
$967$	−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	−0.938979	−	0.343973i	$-0.888227\pi$
$971$	−34.6066	+	19.9801i	−1.11058	+	0.641193i	−0.171600	+	0.985167i	$0.554894\pi$
$972$	−12.9535	+	8.67222i	−0.415483	+	0.278161i
$973$	56.4021	−	97.6914i	1.80817	−	3.13184i
$974$	16.9348	+	29.3319i	0.542625	+	0.939854i
$975$	−9.85650	−	8.01792i	−0.315661	−	0.256779i
$976$			7.18747i			0.230065i
$977$	−47.1033			−1.50697			−0.753485	−	0.657466i	$-0.771628\pi$
$977$	−47.1033			−1.50697			−0.753485	+	0.657466i	$0.771628\pi$
$978$	14.6375	+	2.90882i	0.468054	+	0.0930137i
$979$	7.59573	+	13.1562i	0.242761	+	0.420474i
$980$	−0.681656	−	36.9726i	−0.0217747	−	1.18104i
$981$	28.3941	+	11.7492i	0.906552	+	0.375122i
$982$	16.5114	+	28.5986i	0.526900	+	0.912617i
$983$	−20.5691	+	11.8756i	−0.656052	+	0.378772i	−0.790771	−	0.612112i	$-0.790320\pi$
$983$	−20.5691	+	11.8756i	−0.656052	+	0.378772i	0.134719	+	0.990884i	$0.456987\pi$
$984$	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
$987$	27.7225	−	31.6230i	0.882416	−	1.00657i
$988$	7.78931			0.247811
$989$	15.9518	+	9.20975i	0.507236	+	0.292853i
$990$	−3.00495	+	7.65867i	−0.0955035	+	0.243408i
$991$		−	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
$999$	7.92828	+	16.0550i	0.250840	+	0.507957i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.337599 + 1.69883i) q^{3} +1.00000 q^{4} +(-1.95677 - 1.08215i) q^{5} +(0.337599 - 1.69883i) q^{6} +(4.20156 + 2.42577i) q^{7} -1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.337599 + 1.69883i) q^{3} +1.00000 q^{4} +(-1.95677 - 1.08215i) q^{5} +(0.337599 - 1.69883i) q^{6} +(4.20156 + 2.42577i) q^{7} -1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +(1.95677 + 1.08215i) q^{10} +(-0.613210 - 1.06211i) q^{11} +(-0.337599 + 1.69883i) q^{12} +(0.733571 + 1.27058i) q^{13} +(-4.20156 - 2.42577i) q^{14} +(2.49899 - 2.95889i) q^{15} +1.00000 q^{16} +(3.27327 + 1.88983i) q^{17} +(2.77205 + 1.14705i) q^{18} +(2.65459 - 4.59788i) q^{19} +(-1.95677 - 1.08215i) q^{20} +(-5.53941 + 6.31880i) q^{21} +(0.613210 + 1.06211i) q^{22} +6.72188i q^{23} +(0.337599 - 1.69883i) 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} +(-2.49899 + 2.95889i) 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} +(-2.77205 - 1.14705i) 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} +(5.53941 - 6.31880i) q^{42} +(1.37011 - 2.37311i) q^{43} +(-0.613210 - 1.06211i) q^{44} +(4.18301 + 5.24428i) q^{45} -6.72188i q^{46} -5.00458 q^{47} +(-0.337599 + 1.69883i) q^{48} +(8.26872 + 14.3218i) q^{49} +(-2.65791 - 4.23503i) q^{50} +(-4.31555 + 4.92274i) 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} +(6.91483 + 6.06193i) q^{57} -5.15742 q^{58} +(12.1296 + 7.00301i) q^{59} +(2.49899 - 2.95889i) 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} +(-11.4193 - 2.26930i) q^{69} +(5.59645 + 9.29338i) q^{70} +(-4.89947 + 2.82871i) q^{71} +(2.77205 + 1.14705i) q^{72} +(-0.218186 - 0.377910i) q^{73} +(1.72299 - 2.98431i) q^{74} +(-8.09191 + 3.08561i) 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} +(6.36857 + 6.35935i) q^{81} +(1.44137 - 0.832174i) q^{82} +(-2.21035 + 1.27615i) q^{83} +(-5.53941 + 6.31880i) q^{84} +(-4.35998 - 7.24012i) q^{85} +(-1.37011 + 2.37311i) q^{86} +(-1.74114 + 8.76158i) q^{87} +(0.613210 + 1.06211i) q^{88} -12.3868 q^{89} +(-4.18301 - 5.24428i) q^{90} +7.11789i q^{91} +6.72188i q^{92} +(0.971197 - 9.59462i) q^{93} +5.00458 q^{94} +(-10.1700 + 6.12435i) q^{95} +(0.337599 - 1.69883i) q^{96} +14.0563i q^{97} +(-8.26872 - 14.3218i) q^{98} +(0.481561 + 3.64761i) 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	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) \) 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 + 5 * 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 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

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