LMFDB - Embedded newform 930.2.r.b.119.18

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			119.18
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.337599 - 1.69883i) q^{3} +1.00000 q^{4} +(-0.0412189 + 2.23569i) q^{5} +(0.337599 - 1.69883i) q^{6} +(-4.20156 - 2.42577i) q^{7} +1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.337599 - 1.69883i) q^{3} +1.00000 q^{4} +(-0.0412189 + 2.23569i) q^{5} +(0.337599 - 1.69883i) q^{6} +(-4.20156 - 2.42577i) q^{7} +1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +(-0.0412189 + 2.23569i) 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} +(3.78414 + 0.824789i) q^{15} +1.00000 q^{16} +(-3.27327 - 1.88983i) q^{17} +(-2.77205 - 1.14705i) q^{18} +(2.65459 - 4.59788i) q^{19} +(-0.0412189 + 2.23569i) q^{20} +(-5.53941 + 6.31880i) q^{21} +(-0.613210 - 1.06211i) q^{22} -6.72188i q^{23} +(0.337599 - 1.69883i) q^{24} +(-4.99660 - 0.184305i) 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} +(-2.77205 - 1.14705i) q^{36} +(1.72299 - 2.98431i) q^{37} +(2.65459 - 4.59788i) q^{38} +(-2.40616 + 0.817266i) q^{39} +(-0.0412189 + 2.23569i) 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} +(2.67870 - 6.15017i) q^{45} -6.72188i q^{46} +5.00458 q^{47} +(0.337599 - 1.69883i) q^{48} +(8.26872 + 14.3218i) q^{49} +(-4.99660 - 0.184305i) 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} +(2.39983 - 1.32717i) q^{55} +(-4.20156 - 2.42577i) q^{56} +(-6.91483 - 6.06193i) 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} +(2.87086 - 1.58766i) 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} +(-1.99995 + 8.42616i) q^{75} +(2.65459 - 4.59788i) q^{76} +5.95003i q^{77} +(-2.40616 + 0.817266i) q^{78} +(-4.39774 - 2.53904i) q^{79} +(-0.0412189 + 2.23569i) 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} +(2.67870 - 6.15017i) 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} + 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
$3$	0.337599	−	1.69883i	0.194913	−	0.980821i
$3$	0.337599	−	1.69883i	0.194913	−	0.980821i
$4$	1.00000			0.500000
$5$	−0.0412189	+	2.23569i	−0.0184337	+	0.999830i
$5$	−0.0412189	+	2.23569i	−0.0184337	+	0.999830i
$6$	0.337599	−	1.69883i	0.137824	−	0.693545i
$7$	−4.20156	−	2.42577i	−1.58804	−	0.916855i	−0.993630	−	0.112692i	$-0.964053\pi$
$7$	−4.20156	−	2.42577i	−1.58804	−	0.916855i	−0.594409	−	0.804163i	$-0.702614\pi$
$8$	1.00000			0.353553
$9$	−2.77205	−	1.14705i	−0.924018	−	0.382349i
$10$	−0.0412189	+	2.23569i	−0.0130346	+	0.706987i
$11$	−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	0.746184	−	0.665740i	$-0.231884\pi$
$13$	−0.733571	−	1.27058i	−0.203456	−	0.352396i	−0.949640	+	0.313344i	$0.898551\pi$
$14$	−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	$0.818226\pi$
$18$	−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	$-0.0417639\pi$
$20$	−0.0412189	+	2.23569i	−0.00921683	+	0.499915i
$21$	−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	$-0.752824\pi$
$23$		−	6.72188i		−	1.40161i	0.713353	−	0.700805i	$-0.247176\pi$
$24$	0.337599	−	1.69883i	0.0689120	−	0.346772i
$25$	−4.99660	−	0.184305i	−0.999320	−	0.0368611i
$26$	−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	$0.341052\pi$
$30$	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
$36$	−2.77205	−	1.14705i	−0.462009	−	0.191174i
$37$	1.72299	−	2.98431i	0.283258	−	0.490617i	−0.688927	−	0.724831i	$-0.741918\pi$
$37$	1.72299	−	2.98431i	0.283258	−	0.490617i	0.972185	+	0.234213i	$0.0752514\pi$
$38$	2.65459	−	4.59788i	0.430631	−	0.745874i
$39$	−2.40616	+	0.817266i	−0.385293	+	0.130867i
$40$	−0.0412189	+	2.23569i	−0.00651729	+	0.353493i
$41$	−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	−0.951381	−	0.308016i	$-0.900335\pi$
$43$	−1.37011	+	2.37311i	−0.208940	+	0.361896i	0.742441	+	0.669912i	$0.233668\pi$
$44$	−0.613210	−	1.06211i	−0.0924450	−	0.160119i
$45$	2.67870	−	6.15017i	0.399317	−	0.916813i
$46$		−	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	$0.381070\pi$
$48$	0.337599	−	1.69883i	0.0487282	−	0.245205i
$49$	8.26872	+	14.3218i	1.18125	+	2.04598i
$50$	−4.99660	−	0.184305i	−0.706626	−	0.0260647i
$51$	−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	−0.699692	−	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
$55$	2.39983	−	1.32717i	0.323593	−	0.178955i
$56$	−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	$0.301426\pi$
$60$	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
$65$	2.87086	−	1.58766i	0.356086	−	0.196925i
$66$	−2.01137	+	0.683174i	−0.247582	+	0.0840928i
$67$	12.5793	−	7.26264i	1.53680	−	0.887273i	0.537779	−	0.843086i	$-0.319264\pi$
$67$	12.5793	−	7.26264i	1.53680	−	0.887273i	0.999023	−	0.0441870i	$-0.0140697\pi$
$68$	−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	0.878511	−	0.477721i	$-0.158537\pi$
$73$	0.218186	+	0.377910i	0.0255368	+	0.0442310i	−0.852975	+	0.521952i	$0.825204\pi$
$74$	1.72299	−	2.98431i	0.200294	−	0.346919i
$75$	−1.99995	+	8.42616i	−0.230934	+	0.972969i
$76$	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	$0.758881\pi$
$80$	−0.0412189	+	2.23569i	−0.00460842	+	0.249958i
$81$	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	−0.373761	−	0.927525i	$-0.621932\pi$
$83$	2.21035	−	1.27615i	0.242618	−	0.140075i	0.616379	+	0.787449i	$0.288599\pi$
$84$	−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	$0.727964\pi$
$90$	2.67870	−	6.15017i	0.282360	−	0.648285i
$91$			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	$-0.747064\pi$
$97$		−	14.0563i		−	1.42720i	0.700555	−	0.713599i	$-0.252936\pi$
$98$	8.26872	+	14.3218i	0.835267	+	1.44672i
$99$	0.481561	+	3.64761i	0.0483987	+	0.366599i
$100$	−4.99660	−	0.184305i	−0.499660	−	0.0184305i
$101$			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	−0.612361	−	0.790578i	$-0.709780\pi$
$103$	−2.37364	+	1.37042i	−0.233881	+	0.135031i	0.378480	+	0.925609i	$0.376447\pi$
$104$	−0.733571	−	1.27058i	−0.0719325	−	0.124591i
$105$	−13.8985	−	12.6449i	−1.35636	−	1.23401i
$106$	−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	$0.663204\pi$
$110$	2.39983	−	1.32717i	0.228814	−	0.126541i
$111$	−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	$-0.978349\pi$
$113$	−5.92849	−	10.2684i	−0.557705	−	0.965974i	0.439982	−	0.898006i	$-0.354985\pi$
$114$	−6.91483	−	6.06193i	−0.647634	−	0.567752i
$115$	15.0280	+	0.277069i	1.40137	+	0.0258368i
$116$	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
$120$	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	−0.976254	−	0.216627i	$-0.930494\pi$
$127$	−3.38672	+	5.86597i	−0.300523	+	0.520521i	0.675732	+	0.737148i	$0.263828\pi$
$128$	1.00000			0.0883883
$129$	3.56896	+	3.12875i	0.314229	+	0.275471i
$130$	2.87086	−	1.58766i	0.251791	−	0.139247i
$131$	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
$135$	−9.54377	−	6.62695i	−0.821397	−	0.570357i
$136$	−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	$0.504062\pi$
$138$	−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
$145$	−0.212583	+	11.5304i	−0.0176541	+	0.957545i
$146$	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	$0.456627\pi$
$150$	−1.99995	+	8.42616i	−0.163295	+	0.687993i
$151$			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
$155$	−0.955887	−	12.4131i	−0.0767787	−	0.997048i
$156$	−2.40616	+	0.817266i	−0.192647	+	0.0654336i
$157$		−	8.54850i		−	0.682245i	−0.940019	−	0.341122i	$-0.889193\pi$
$157$		−	8.54850i		−	0.682245i	0.940019	−	0.341122i	$-0.110807\pi$
$158$	−4.39774	−	2.53904i	−0.349866	−	0.201995i
$159$	2.01737	+	5.93944i	0.159988	+	0.471029i
$160$	−0.0412189	+	2.23569i	−0.00325864	+	0.176747i
$161$	−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	$-0.890440\pi$
$163$		−	8.61619i		−	0.674872i	0.941348	−	0.337436i	$-0.109560\pi$
$164$	−1.44137	+	0.832174i	−0.112552	+	0.0649819i
$165$	−1.44446	−	4.52495i	−0.112451	−	0.352267i
$166$	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	$0.880193\pi$
$168$	−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	$0.187208\pi$
$173$	11.7912	+	20.4229i	0.896467	+	1.55273i	0.0644877	+	0.997919i	$0.479459\pi$
$174$	1.74114	−	8.76158i	0.131995	−	0.664213i
$175$	20.5464	+	12.8950i	1.55316	+	0.974769i
$176$	−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	$-0.210176\pi$
$180$	2.67870	−	6.15017i	0.199658	−	0.458406i
$181$	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	0.813413	−	0.581686i	$-0.197607\pi$
$193$	9.95206	+	5.74583i	0.716365	+	0.413594i	−0.0970482	+	0.995280i	$0.530940\pi$
$194$		−	14.0563i		−	1.00918i
$195$	−1.72797	−	5.41310i	−0.123743	−	0.387640i
$196$	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	$0.250137\pi$
$198$	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	$0.0947285\pi$
$200$	−4.99660	−	0.184305i	−0.353313	−	0.0130324i
$201$	−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
$205$	−1.80107	−	3.25675i	−0.125792	−	0.227461i
$206$	−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
$210$	−13.8985	−	12.6449i	−0.959090	−	0.872578i
$211$	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
$220$	2.39983	−	1.32717i	0.161796	−	0.0894777i
$221$			5.54528i			0.373016i
$222$	−4.48816	−	3.93457i	−0.301225	−	0.264071i
$223$	1.55000	−	2.68467i	0.103795	−	0.179779i	−0.809450	−	0.587189i	$-0.800235\pi$
$223$	1.55000	−	2.68467i	0.103795	−	0.179779i	0.913245	+	0.407410i	$0.133568\pi$
$224$	−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	$0.707524\pi$
$228$	−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	$0.391839\pi$
$230$	15.0280	+	0.277069i	0.990919	+	0.0182694i
$231$	10.1081	+	2.00872i	0.665064	+	0.132164i
$232$	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	$0.623215\pi$
$234$	0.576082	+	4.36356i	0.0376596	+	0.285255i
$235$	−0.206284	+	11.1887i	−0.0134565	+	0.729870i
$236$	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	$0.898234\pi$
$240$	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
$243$	12.9535	−	8.67222i	0.830966	−	0.556323i
$244$			7.18747i			0.460130i
$245$	−32.3600	+	17.8959i	−2.06740	+	1.14333i
$246$	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
$255$	−10.8278	−	9.85113i	−0.678065	−	0.616902i
$256$	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	$0.788084\pi$
$258$	3.56896	+	3.12875i	0.222194	+	0.194788i
$259$	−14.4785	+	8.35916i	−0.899650	+	0.519413i
$260$	2.87086	−	1.58766i	0.178043	−	0.0984627i
$261$	−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	$-0.877863\pi$
$263$		−	12.1422i		−	0.748718i	0.927284	−	0.374359i	$-0.122137\pi$
$264$	−2.01137	+	0.683174i	−0.123791	+	0.0420464i
$265$	−3.91905	−	7.08654i	−0.240745	−	0.435323i
$266$	−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	$-0.393658\pi$
$270$	−9.54377	−	6.62695i	−0.580815	−	0.403303i
$271$			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	$-0.602424\pi$
$277$	−10.5269			−0.632498			−0.316249	+	0.948676i	$0.602424\pi$
$278$		−	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	$0.206721\pi$
$283$			20.3465i			1.20947i	−0.796426	+	0.604736i	$0.793279\pi$
$284$	−4.89947	+	2.82871i	−0.290730	+	0.167853i
$285$	13.8376	−	15.2095i	0.819669	−	0.900936i
$286$	−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
$290$	−0.212583	+	11.5304i	−0.0124833	+	0.677087i
$291$	−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	$0.341474\pi$
$293$	−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
$297$	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
$300$	−1.99995	+	8.42616i	−0.115467	+	0.486485i
$301$	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
$305$	−16.0689	−	0.296260i	−0.920104	−	0.0169638i
$306$	6.90598	+	8.99330i	0.394788	+	0.514113i
$307$	−27.7464	−	16.0194i	−1.58357	−	0.914275i	−0.994332	−	0.106316i	$-0.966094\pi$
$307$	−27.7464	−	16.0194i	−1.58357	−	0.914275i	−0.589239	−	0.807959i	$-0.700572\pi$
$308$			5.95003i			0.339034i
$309$	1.52677	+	4.49506i	0.0868552	+	0.255715i
$310$	−0.955887	−	12.4131i	−0.0542907	−	0.705020i
$311$			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	−0.770301	−	0.637681i	$-0.779894\pi$
$313$	2.95626	−	5.12039i	0.167098	−	0.289421i	0.937398	+	0.348259i	$0.113227\pi$
$314$		−	8.54850i		−	0.482420i
$315$	−26.1736	+	19.3424i	−1.47472	+	1.08982i
$316$	−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
$320$	−0.0412189	+	2.23569i	−0.00230421	+	0.124979i
$321$	−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
$330$	−1.44446	−	4.52495i	−0.0795147	−	0.249090i
$331$	−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
$335$	15.7185	+	28.4227i	0.858793	+	1.55290i
$336$	−5.53941	+	6.31880i	−0.302200	+	0.344719i
$337$	9.11905			0.496746			0.248373	−	0.968664i	$-0.420104\pi$
$337$	9.11905			0.496746			0.248373	+	0.968664i	$0.420104\pi$
$338$	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	$0.443397\pi$
$348$	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	$0.501852\pi$
$350$	20.5464	+	12.8950i	1.09825	+	0.689265i
$351$	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	−0.447601	−	0.894233i	$-0.647722\pi$
$353$	−27.1647	−	15.6835i	−1.44583	−	0.834751i	−0.998229	+	0.0594826i	$0.981055\pi$
$354$	15.9919	−	18.2419i	0.849958	−	0.969545i
$355$	−6.12217	−	11.0703i	−0.324931	−	0.587550i
$356$	−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	$0.501156\pi$
$360$	2.67870	−	6.15017i	0.141180	−	0.324142i
$361$	−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
$365$	−0.853882	+	0.472220i	−0.0446942	+	0.0247171i
$366$	12.2103	+	2.42648i	0.638242	+	0.126834i
$367$	−4.44107	−	7.69216i	−0.231822	−	0.401528i	0.726522	−	0.687143i	$-0.241135\pi$
$367$	−4.44107	−	7.69216i	−0.231822	−	0.401528i	−0.958344	+	0.285615i	$0.907802\pi$
$368$		−	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	$-0.882019\pi$
$373$		−	13.9912i		−	0.724438i	0.932093	−	0.362219i	$-0.117981\pi$
$374$			4.63544i			0.239693i
$375$	−18.7558	−	4.81858i	−0.968547	−	0.248830i
$376$	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	0.451149	−	0.892449i	$-0.351014\pi$
$383$	28.3694	−	16.3791i	1.44961	−	0.836931i	0.998458	+	0.0555180i	$0.0176810\pi$
$384$	0.337599	−	1.69883i	0.0172280	−	0.0866931i
$385$	−13.3024	−	0.245254i	−0.677954	−	0.0124993i
$386$	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	$0.0570007\pi$
$390$	−1.72797	−	5.41310i	−0.0874993	−	0.274103i
$391$	−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	0.881573	−	0.472047i	$-0.156485\pi$
$397$	18.2024	+	10.5092i	0.913555	+	0.527441i	0.0319815	+	0.999488i	$0.489818\pi$
$398$	16.6477	−	9.61156i	0.834474	−	0.481784i
$399$	14.3482	+	42.2433i	0.718309	+	2.11481i
$400$	−4.99660	−	0.184305i	−0.249830	−	0.00921527i
$401$	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
$405$	−14.4800	+	13.9760i	−0.719518	+	0.694473i
$406$	−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	$0.409565\pi$
$410$	−1.80107	−	3.25675i	−0.0889485	−	0.160839i
$411$	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
$415$	2.76196	+	4.99426i	0.135579	+	0.245159i
$416$	−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	$0.968287\pi$
$420$	−13.8985	−	12.6449i	−0.678179	−	0.617006i
$421$	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
$425$	16.0069	+	10.0460i	0.776451	+	0.487302i
$426$	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	$-0.656116\pi$
$433$	−19.6028			−0.942052			−0.471026	+	0.882119i	$0.656116\pi$
$434$	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	$-0.385714\pi$
$440$	2.39983	−	1.32717i	0.114407	−	0.0632703i
$441$	−6.49352	−	49.1855i	−0.309215	−	2.34217i
$442$			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	$0.827695\pi$
$444$	−4.48816	−	3.93457i	−0.212999	−	0.186726i
$445$	0.510572	−	27.6931i	0.0242034	−	1.31278i
$446$	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	$0.496487\pi$
$450$	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
$453$	11.4612	+	2.27761i	0.538492	+	0.107011i
$454$	5.80110	+	10.0478i	0.272259	+	0.471567i
$455$	−15.9134	−	0.293392i	−0.746031	−	0.0137544i
$456$	−6.91483	−	6.06193i	−0.323817	−	0.283876i
$457$	20.1181			0.941085			0.470543	−	0.882377i	$-0.344058\pi$
$457$	20.1181			0.941085			0.470543	+	0.882377i	$0.344058\pi$
$458$	19.9216	+	11.5017i	0.930873	+	0.537440i
$459$	17.6095	−	8.69596i	0.821943	−	0.405893i
$460$	15.0280	+	0.277069i	0.700686	+	0.0129184i
$461$	−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	$-0.507683\pi$
$463$	−1.03856			−0.0482662			−0.0241331	+	0.999709i	$0.507683\pi$
$464$	5.15742			0.239427
$465$	−21.4106	−	2.56677i	−0.992891	−	0.119031i
$466$	−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	$0.390383\pi$
$468$	0.576082	+	4.36356i	0.0266294	+	0.201706i
$469$	−70.4700			−3.25400
$470$	−0.206284	+	11.1887i	−0.00951516	+	0.516096i
$471$	−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
$475$	−14.1113	+	22.4845i	−0.647472	+	1.03166i
$476$	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	$0.649095\pi$
$480$	3.78414	+	0.824789i	0.172722	+	0.0376463i
$481$	−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
$485$	31.4254	+	0.579384i	1.42695	+	0.0263085i
$486$	12.9535	−	8.67222i	0.587582	−	0.393380i
$487$	16.9348	+	29.3319i	0.767387	+	1.32915i	0.938975	+	0.343985i	$0.111777\pi$
$487$	16.9348	+	29.3319i	0.767387	+	1.32915i	−0.171588	+	0.985169i	$0.554890\pi$
$488$			7.18747i			0.325361i
$489$	−14.6375	−	2.90882i	−0.661929	−	0.131541i
$490$	−32.3600	+	17.8959i	−1.46188	+	0.808456i
$491$	−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
$495$	−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
$501$	−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	−0.930722	−	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
$505$	−20.0926	−	0.370443i	−0.894109	−	0.0164845i
$506$	−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	$0.612236\pi$
$510$	−10.8278	−	9.85113i	−0.479464	−	0.436215i
$511$		−	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
$515$	−2.96599	−	5.36320i	−0.130697	−	0.236331i
$516$	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
$520$	2.87086	−	1.58766i	0.125896	−	0.0696236i
$521$	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	$-0.461107\pi$
$523$	5.57472			0.243765			0.121883	+	0.992545i	$0.461107\pi$
$524$	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
$530$	−3.91905	−	7.08654i	−0.170232	−	0.307820i
$531$	−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
$540$	−9.54377	−	6.62695i	−0.410699	−	0.285178i
$541$	−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
$545$	0.422204	−	22.9001i	0.0180852	−	0.980931i
$546$	12.0921	+	2.40299i	0.517494	+	0.102839i
$547$	−10.2933	+	5.94282i	−0.440108	+	0.254097i	−0.703644	−	0.710553i	$-0.748445\pi$
$547$	−10.2933	+	5.94282i	−0.440108	+	0.254097i	0.263535	+	0.964650i	$0.415111\pi$
$548$	−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
$555$	8.98147	−	9.87194i	0.381242	−	0.419041i
$556$		−	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	$0.582904\pi$
$558$	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	0.980098	−	0.198515i	$-0.0636118\pi$
$563$	7.54847	+	13.0743i	0.318130	+	0.551017i	−0.661968	+	0.749532i	$0.730278\pi$
$564$	1.68954	−	8.50194i	0.0711425	−	0.357996i
$565$	23.2014	−	12.8310i	0.976090	−	0.539804i
$566$			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	$-0.346232\pi$
$570$	13.8376	−	15.2095i	0.579594	−	0.637058i
$571$	−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
$575$	−1.23888	+	33.5866i	−0.0516648	+	1.40066i
$576$	−2.77205	−	1.14705i	−0.115502	−	0.0477936i
$577$	−7.13962	−	4.12206i	−0.297226	−	0.171604i	0.343970	−	0.938981i	$-0.388228\pi$
$577$	−7.13962	−	4.12206i	−0.297226	−	0.171604i	−0.641196	+	0.767377i	$0.721562\pi$
$578$	−1.35712	−	2.35059i	−0.0564486	−	0.0977718i
$579$	13.1210	−	14.9671i	0.545290	−	0.622011i
$580$	−0.212583	+	11.5304i	−0.00882704	+	0.478773i
$581$	−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
$585$	−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	$0.588105\pi$
$594$	6.35925	+	0.413338i	0.260923	+	0.0169594i
$595$	−35.8816	+	19.8435i	−1.47100	+	0.813503i
$596$	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	$0.508878\pi$
$600$	−1.99995	+	8.42616i	−0.0816476	+	0.343997i
$601$	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	−0.999632	−	0.0271209i	$-0.991366\pi$
$607$	−36.3638	+	20.9946i	−1.47596	+	0.852146i	−0.476329	+	0.879267i	$0.658033\pi$
$608$	2.65459	−	4.59788i	0.107658	−	0.186469i
$609$	−28.5691	+	32.5887i	−1.15768	+	1.32056i
$610$	−16.0689	−	0.296260i	−0.650612	−	0.0119952i
$611$	−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	−0.991928	−	0.126805i	$-0.959528\pi$
$613$	−9.56057	+	16.5594i	−0.386148	+	0.668828i	0.605780	+	0.795632i	$0.292861\pi$
$614$	−27.7464	−	16.0194i	−1.11975	−	0.646490i
$615$	−6.14071	+	1.96024i	−0.247617	+	0.0790445i
$616$			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	$-0.0404945\pi$
$620$	−0.955887	−	12.4131i	−0.0383893	−	0.498524i
$621$	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
$625$	24.9321	+	1.84180i	0.997283	+	0.0736720i
$626$	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
$630$	−26.1736	+	19.3424i	−1.04278	+	0.770619i
$631$	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
$640$	−0.0412189	+	2.23569i	−0.00162932	+	0.0883733i
$641$	−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	$-0.338647\pi$
$643$	24.6208			0.970949			0.485475	+	0.874251i	$0.338647\pi$
$644$	−16.3057	+	28.2424i	−0.642536	+	1.11291i
$645$	−7.14202	+	7.85012i	−0.281217	+	0.309098i
$646$	−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	$0.845435\pi$
$648$	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	$-0.686111\pi$
$653$	−28.2082			−1.10387			−0.551936	+	0.833886i	$0.686111\pi$
$654$	−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	$-0.289739\pi$
$660$	−1.44446	−	4.52495i	−0.0562254	−	0.176133i
$661$	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
$665$	−27.8736	−	50.4019i	−1.08089	−	1.95450i
$666$	−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
$670$	15.7185	+	28.4227i	0.607259	+	1.09806i
$671$	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	$0.165604\pi$
$673$	22.4232	+	38.8381i	0.864351	+	1.49710i	−0.00333889	+	0.999994i	$0.501063\pi$
$674$	9.11905			0.351253
$675$	15.2092	−	21.0637i	0.585401	−	0.810744i
$676$	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
$685$	−12.9451	−	23.4078i	−0.494608	−	0.894366i
$686$		−	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
$690$	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
$693$	6.82496	−	16.4938i	0.259259	−	0.626548i
$694$	20.8204	+	12.0207i	0.790332	+	0.456299i
$695$	51.9825	+	0.958391i	1.97181	+	0.0363539i
$696$	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
$700$	20.5464	+	12.8950i	0.776582	+	0.487384i
$701$	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
$705$	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
$708$	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	$-0.405398\pi$
$710$	−6.12217	−	11.0703i	−0.229761	−	0.415461i
$711$	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	$0.276509\pi$
$720$	2.67870	−	6.15017i	0.0998292	−	0.229203i
$721$	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
$725$	−25.7696	−	0.950539i	−0.957057	−	0.0353021i
$726$	−12.3677	−	10.8423i	−0.459010	−	0.402394i
$727$	27.6084	+	15.9397i	1.02394	+	0.591171i	0.915242	−	0.402904i	$-0.131999\pi$
$727$	27.6084	+	15.9397i	1.02394	+	0.591171i	0.108696	+	0.994075i	$0.465332\pi$
$728$			7.11789i			0.263807i
$729$	−10.3596	−	24.9335i	−0.383687	−	0.923463i
$730$	−0.853882	+	0.472220i	−0.0316036	+	0.0174776i
$731$	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	−0.311226	−	0.950336i	$-0.600740\pi$
$733$	9.64309	−	5.56744i	0.356175	−	0.205638i	0.667402	+	0.744698i	$0.267406\pi$
$734$	−4.44107	−	7.69216i	−0.163923	−	0.283923i
$735$	19.4775	+	61.0158i	0.718438	+	2.25060i
$736$		−	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	$-0.728410\pi$
$743$		−	41.0727i		−	1.50681i	0.657557	−	0.753405i	$-0.271590\pi$
$744$	−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
$750$	−18.7558	−	4.81858i	−0.684866	−	0.175950i
$751$	−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
$755$	−15.0831	−	0.278083i	−0.548928	−	0.0101205i
$756$	22.6035	−	11.1621i	0.822082	−	0.405961i
$757$	−14.7301	−	25.5133i	−0.535374	−	0.927295i	−0.999145	−	0.0413402i	$-0.986837\pi$
$757$	−14.7301	−	25.5133i	−0.535374	−	0.927295i	0.463771	−	0.885955i	$-0.346496\pi$
$758$	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
$765$	−20.3909	+	15.0689i	−0.737233	+	0.544818i
$766$	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	$0.125842\pi$
$770$	−13.3024	−	0.245254i	−0.479386	−	0.00883834i
$771$	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
$775$	27.7913	−	1.62541i	0.998294	−	0.0583864i
$776$		−	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
$780$	−1.72797	−	5.41310i	−0.0618713	−	0.193820i
$781$	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
$785$	19.1118	+	0.352360i	0.682129	+	0.0125763i
$786$	8.32613	−	9.49760i	0.296983	−	0.338768i
$787$	−11.6044	+	20.0994i	−0.413652	+	0.716466i	−0.995286	−	0.0969848i	$-0.969080\pi$
$787$	−11.6044	+	20.0994i	−0.413652	+	0.716466i	0.581634	+	0.813450i	$0.302413\pi$
$788$	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
$795$	−13.3619	+	4.26539i	−0.473898	+	0.151278i
$796$	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
$800$	−4.99660	−	0.184305i	−0.176657	−	0.00651618i
$801$	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	$0.0747420\pi$
$810$	−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
$813$	20.6013	+	4.09398i	0.722521	+	0.143582i
$814$	−4.22623			−0.148129
$815$	19.2631	+	0.355150i	0.674758	+	0.0124404i
$816$	−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
$820$	−1.80107	−	3.25675i	−0.0628961	−	0.113731i
$821$	−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	−0.762857	−	0.646568i	$-0.776204\pi$
$823$	5.12126	−	8.87028i	0.178516	−	0.309198i	0.941372	+	0.337369i	$0.109537\pi$
$824$	−2.37364	+	1.37042i	−0.0826895	+	0.0477408i
$825$	10.1759	−	3.04284i	0.354280	−	0.105938i
$826$	−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	$0.434410\pi$
$828$	−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	$-0.0579602\pi$
$830$	2.76196	+	4.99426i	0.0958691	+	0.173353i
$831$	−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	$0.869212\pi$
$840$	−13.8985	−	12.6449i	−0.479545	−	0.436289i
$841$	−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
$850$	16.0069	+	10.0460i	0.549034	+	0.344575i
$851$	−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	$-0.965924\pi$
$853$		−	6.24127i		−	0.213697i	0.994275	−	0.106848i	$-0.0340760\pi$
$854$	17.4351	−	30.1985i	0.596618	−	1.03337i
$855$	−21.1669	−	28.6425i	−0.723892	−	0.979552i
$856$	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	$0.514235\pi$
$858$	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	0.250695	−	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
$865$	−46.1453	+	25.5196i	−1.56899	+	0.867692i
$866$	−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
$873$	−16.1232	+	38.9647i	−0.545687	+	1.31876i
$874$	−30.9064	−	17.8438i	−1.04542	−	0.603576i
$875$	−29.6760	+	45.4039i	−1.00323	+	1.53493i
$876$	0.715665	−	0.243080i	0.0241801	−	0.00821291i
$877$	21.2480	−	12.2675i	0.717492	−	0.414244i	−0.0963366	−	0.995349i	$-0.530713\pi$
$877$	21.2480	−	12.2675i	0.717492	−	0.414244i	0.813829	+	0.581104i	$0.197379\pi$
$878$	−13.3071	−	23.0486i	−0.449094	−	0.777854i
$879$	23.2742	+	20.4035i	0.785019	+	0.688192i
$880$	2.39983	−	1.32717i	0.0808981	−	0.0447388i
$881$	−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	$-0.341315\pi$
$883$	28.4156			0.956260			0.478130	+	0.878289i	$0.341315\pi$
$884$			5.54528i			0.186508i
$885$	40.1240	+	36.5047i	1.34875	+	1.22709i
$886$	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	$0.913453\pi$
$888$	−4.48816	−	3.93457i	−0.150613	−	0.132036i
$889$	28.4590	−	16.4308i	0.954484	−	0.551072i
$890$	0.510572	−	27.6931i	0.0171144	−	0.928274i
$891$	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
$900$	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
$905$	27.8801	+	50.4137i	0.926766	+	1.67581i
$906$	11.4612	+	2.27761i	0.380771	+	0.0756684i
$907$		−	34.0991i		−	1.13224i	−0.824322	−	0.566122i	$-0.808443\pi$
$907$		−	34.0991i		−	1.13224i	0.824322	−	0.566122i	$-0.191557\pi$
$908$	5.80110	+	10.0478i	0.192516	+	0.333448i
$909$	10.3087	−	24.9130i	0.341920	−	0.826313i
$910$	−15.9134	−	0.293392i	−0.527524	−	0.00972585i
$911$	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
$915$	−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
$918$	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	$0.921497\pi$
$920$	15.0280	+	0.277069i	0.495460	+	0.00913469i
$921$	−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
$925$	−9.15913	+	14.5939i	−0.301150	+	0.479843i
$926$	−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	$0.193458\pi$
$930$	−21.4106	−	2.56677i	−0.702080	−	0.0841678i
$931$	87.8001			2.87753
$932$	−11.5244			−0.377496
$933$	27.1615	+	5.39765i	0.889229	+	0.176711i
$934$	14.5915			0.477447
$935$	−10.3634	−	0.191068i	−0.338920	−	0.00624860i
$936$	0.576082	+	4.36356i	0.0188298	+	0.142627i
$937$	7.21427	+	4.16516i	0.235680	+	0.136070i	0.613190	−	0.789936i	$-0.289886\pi$
$937$	7.21427	+	4.16516i	0.235680	+	0.136070i	−0.377510	+	0.926006i	$0.623219\pi$
$938$	−70.4700			−2.30093
$939$	−7.70065	−	6.75082i	−0.251301	−	0.220305i
$940$	−0.206284	+	11.1887i	−0.00672823	+	0.364935i
$941$	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
$945$	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	$0.448756\pi$
$948$	−5.79807	+	6.61385i	−0.188313	+	0.214808i
$949$	0.320110	−	0.554447i	0.0103912	−	0.0179981i
$950$	−14.1113	+	22.4845i	−0.457832	+	0.729494i
$951$	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	$-0.954279\pi$
$953$		−	8.83785i		−	0.286286i	0.989702	−	0.143143i	$-0.0457209\pi$
$954$	10.7712	−	1.42202i	0.348730	−	0.0460396i
$955$	−7.07518	−	12.7935i	−0.228947	−	0.413990i
$956$	−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
$966$	42.4742	+	37.2353i	1.36659	+	1.19803i
$967$	11.7705	−	20.3872i	0.378515	−	0.655607i	−0.612331	−	0.790601i	$-0.709768\pi$
$967$	11.7705	−	20.3872i	0.378515	−	0.655607i	0.990846	+	0.134994i	$0.0431015\pi$
$968$	4.74795	−	8.22368i	0.152605	−	0.264319i
$969$	11.1782	+	32.9102i	0.359094	+	1.05723i
$970$	31.4254	+	0.579384i	1.00901	+	0.0186029i
$971$	−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
$975$	12.1732	−	3.64009i	0.389855	−	0.116576i
$976$			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	$0.228372\pi$
$978$	−14.6375	−	2.90882i	−0.468054	−	0.0930137i
$979$	7.59573	+	13.1562i	0.242761	+	0.420474i
$980$	−32.3600	+	17.8959i	−1.03370	+	0.571665i
$981$	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	−0.134719	−	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
$985$	7.84961	+	14.1939i	0.250109	+	0.452255i
$986$	−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
$990$	−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
$995$	20.8023	+	37.6153i	0.659476	+	1.19248i
$996$	−1.42175	−	4.18584i	−0.0450498	−	0.132634i
$997$	−34.1845	+	19.7364i	−1.08263	+	0.625059i	−0.931606	−	0.363470i	$-0.881592\pi$
$997$	−34.1845	+	19.7364i	−1.08263	+	0.625059i	−0.151029	+	0.988529i	$0.548259\pi$
$998$	−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.b.119.18	yes	64
3.2	odd	2		930.2.r.a.119.26	yes	64
5.4	even	2		930.2.r.a.119.15	✓	64
15.14	odd	2	inner	930.2.r.b.119.7	yes	64
31.6	odd	6	inner	930.2.r.b.719.7	yes	64
93.68	even	6		930.2.r.a.719.15	yes	64
155.99	odd	6		930.2.r.a.719.26	yes	64
465.254	even	6	inner	930.2.r.b.719.18	yes	64

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.337599 - 1.69883i) q^{3} +1.00000 q^{4} +(-0.0412189 + 2.23569i) q^{5} +(0.337599 - 1.69883i) q^{6} +(-4.20156 - 2.42577i) q^{7} +1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.337599 - 1.69883i) q^{3} +1.00000 q^{4} +(-0.0412189 + 2.23569i) q^{5} +(0.337599 - 1.69883i) q^{6} +(-4.20156 - 2.42577i) q^{7} +1.00000 q^{8} +(-2.77205 - 1.14705i) q^{9} +(-0.0412189 + 2.23569i) 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} +(3.78414 + 0.824789i) q^{15} +1.00000 q^{16} +(-3.27327 - 1.88983i) q^{17} +(-2.77205 - 1.14705i) q^{18} +(2.65459 - 4.59788i) q^{19} +(-0.0412189 + 2.23569i) q^{20} +(-5.53941 + 6.31880i) q^{21} +(-0.613210 - 1.06211i) q^{22} -6.72188i q^{23} +(0.337599 - 1.69883i) q^{24} +(-4.99660 - 0.184305i) 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} +(-2.77205 - 1.14705i) q^{36} +(1.72299 - 2.98431i) q^{37} +(2.65459 - 4.59788i) q^{38} +(-2.40616 + 0.817266i) q^{39} +(-0.0412189 + 2.23569i) 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} +(2.67870 - 6.15017i) q^{45} -6.72188i q^{46} +5.00458 q^{47} +(0.337599 - 1.69883i) q^{48} +(8.26872 + 14.3218i) q^{49} +(-4.99660 - 0.184305i) 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} +(2.39983 - 1.32717i) q^{55} +(-4.20156 - 2.42577i) q^{56} +(-6.91483 - 6.06193i) 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} +(2.87086 - 1.58766i) 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} +(-1.99995 + 8.42616i) q^{75} +(2.65459 - 4.59788i) q^{76} +5.95003i q^{77} +(-2.40616 + 0.817266i) q^{78} +(-4.39774 - 2.53904i) q^{79} +(-0.0412189 + 2.23569i) 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} +(2.67870 - 6.15017i) 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	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 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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