LMFDB - Embedded newform 936.2.bk.c.277.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(277,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4, 1]))

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

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

chi := DirichletCharacter("936.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.bk (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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$160$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.14
Character	$\chi$	$=$	936.277
Dual form			936.2.bk.c.517.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36380 + 0.374231i) q^{2} +(-1.67788 + 0.429783i) q^{3} +(1.71990 - 1.02075i) q^{4} +(-1.29210 - 2.23799i) q^{5} +(2.12746 - 1.21405i) q^{6} -1.30034i q^{7} +(-1.96361 + 2.03574i) q^{8} +(2.63057 - 1.44225i) q^{9} +(2.59969 + 2.56862i) q^{10} +(-3.23663 - 5.60601i) q^{11} +(-2.44709 + 2.45189i) q^{12} +(-3.36381 + 1.29798i) q^{13} +(0.486627 + 1.77340i) q^{14} +(3.12984 + 3.19975i) q^{15} +(1.91613 - 3.51119i) q^{16} +(-2.70603 - 4.68698i) q^{17} +(-3.04784 + 2.95138i) q^{18} +(0.939139 + 1.62664i) q^{19} +(-4.50672 - 2.53020i) q^{20} +(0.558864 + 2.18181i) q^{21} +(6.51206 + 6.43423i) q^{22} +3.26888 q^{23} +(2.41977 - 4.25966i) q^{24} +(-0.839052 + 1.45328i) q^{25} +(4.10183 - 3.02903i) q^{26} +(-3.79393 + 3.55050i) q^{27} +(-1.32732 - 2.23646i) q^{28} +(6.35820 - 3.67091i) q^{29} +(-5.46592 - 3.19254i) q^{30} +(-4.79360 + 2.76759i) q^{31} +(-1.29923 + 5.50563i) q^{32} +(7.84006 + 8.01517i) q^{33} +(5.44449 + 5.37943i) q^{34} +(-2.91014 + 1.68017i) q^{35} +(3.05215 - 5.16569i) q^{36} +(1.93131 - 3.34512i) q^{37} +(-1.88953 - 1.86695i) q^{38} +(5.08623 - 3.62357i) q^{39} +(7.09314 + 1.76414i) q^{40} +6.06334i q^{41} +(-1.57868 - 2.76642i) q^{42} +8.47246i q^{43} +(-11.2890 - 6.33800i) q^{44} +(-6.62670 - 4.02365i) q^{45} +(-4.45810 + 1.22331i) q^{46} +(-2.30419 - 1.33032i) q^{47} +(-1.70599 + 6.71488i) q^{48} +5.30912 q^{49} +(0.600438 - 2.29598i) q^{50} +(6.55478 + 6.70119i) q^{51} +(-4.46052 + 5.66602i) q^{52} -0.775873i q^{53} +(3.84546 - 6.26198i) q^{54} +(-8.36411 + 14.4871i) q^{55} +(2.64715 + 2.55336i) q^{56} +(-2.27486 - 2.32568i) q^{57} +(-7.29755 + 7.38582i) q^{58} +(-4.03487 + 6.98861i) q^{59} +(8.64918 + 2.30847i) q^{60} -12.0836i q^{61} +(5.50180 - 5.56835i) q^{62} +(-1.87542 - 3.42064i) q^{63} +(-0.288489 - 7.99480i) q^{64} +(7.25125 + 5.85104i) q^{65} +(-13.6918 - 7.99711i) q^{66} -13.0810 q^{67} +(-9.43835 - 5.29897i) q^{68} +(-5.48479 + 1.40491i) q^{69} +(3.34008 - 3.38048i) q^{70} +(-4.07336 + 2.35176i) q^{71} +(-2.22936 + 8.18718i) q^{72} +5.80347i q^{73} +(-1.38207 + 5.28483i) q^{74} +(0.783234 - 2.79905i) q^{75} +(3.27562 + 1.83903i) q^{76} +(-7.28971 + 4.20872i) q^{77} +(-5.58055 + 6.84525i) q^{78} +(3.46837 - 6.00740i) q^{79} +(-10.3338 + 0.248534i) q^{80} +(4.83982 - 7.58789i) q^{81} +(-2.26909 - 8.26918i) q^{82} +(-4.16832 + 7.21974i) q^{83} +(3.18828 + 3.18205i) q^{84} +(-6.99293 + 12.1121i) q^{85} +(-3.17065 - 11.5547i) q^{86} +(-9.09061 + 8.89200i) q^{87} +(17.7679 + 4.41906i) q^{88} +(-8.28219 - 4.78173i) q^{89} +(10.5433 + 3.00754i) q^{90} +(1.68782 + 4.37410i) q^{91} +(5.62215 - 3.33671i) q^{92} +(6.85364 - 6.70390i) q^{93} +(3.64030 + 0.951998i) q^{94} +(2.42692 - 4.20356i) q^{95} +(-0.186280 - 9.79619i) q^{96} -0.486805i q^{97} +(-7.24058 + 1.98683i) q^{98} +(-16.5995 - 10.0790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 3 q^{2} + q^{4} - 3 q^{6} + 10 q^{9} + 8 q^{10} - 7 q^{12} + 2 q^{14} + 24 q^{15} - 15 q^{16} + 8 q^{17} - 6 q^{18} + q^{22} + 20 q^{23} + 12 q^{24} - 144 q^{25} - 20 q^{26} - 6 q^{28} + 7 q^{30}+ \cdots - 99 q^{98}+O(q^{100}) $ 320 * q - 3 * q^2 + q^4 - 3 * q^6 + 10 * q^9 + 8 * q^10 - 7 * q^12 + 2 * q^14 + 24 * q^15 - 15 * q^16 + 8 * q^17 - 6 * q^18 + q^22 + 20 * q^23 + 12 * q^24 - 144 * q^25 - 20 * q^26 - 6 * q^28 + 7 * q^30 + 12 * q^31 - 3 * q^32 + 18 * q^33 - 30 * q^34 + 39 * q^36 - 10 * q^38 + 44 * q^39 - 28 * q^40 + 10 * q^42 - 30 * q^46 - 12 * q^47 - 8 * q^48 - 316 * q^49 - 56 * q^52 + 36 * q^54 + 14 * q^55 + 52 * q^56 + 36 * q^57 - 3 * q^58 + 3 * q^60 - q^62 - 42 * q^63 - 26 * q^64 + 66 * q^65 + 50 * q^66 - 12 * q^68 + 3 * q^70 - 48 * q^71 + 21 * q^72 + 26 * q^74 + 35 * q^78 + 32 * q^79 - 48 * q^80 + 34 * q^81 - 23 * q^82 + 120 * q^84 + 42 * q^86 - 2 * q^87 + 13 * q^88 - 72 * q^89 + 109 * q^90 - 28 * q^92 + 130 * q^94 + 112 * q^95 - 15 * q^96 - 99 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−1.36380	+	0.374231i	−0.964352	+	0.264621i
$2$	−1.36380	+	0.374231i	−0.964352	+	0.264621i
$3$	−1.67788	+	0.429783i	−0.968725	+	0.248136i
$3$	−1.67788	+	0.429783i	−0.968725	+	0.248136i
$4$	1.71990	−	1.02075i	0.859951	−	0.510376i
$5$	−1.29210	−	2.23799i	−0.577845	−	1.00086i	−0.995726	−	0.0923556i	$-0.970560\pi$
$5$	−1.29210	−	2.23799i	−0.577845	−	1.00086i	0.417881	−	0.908502i	$-0.362773\pi$
$6$	2.12746	−	1.21405i	0.868531	−	0.495635i
$7$		−	1.30034i		−	0.491482i	−0.969336	−	0.245741i	$-0.920969\pi$
$7$		−	1.30034i		−	0.491482i	0.969336	−	0.245741i	$-0.0790313\pi$
$8$	−1.96361	+	2.03574i	−0.694240	+	0.719743i
$9$	2.63057	−	1.44225i	0.876857	−	0.480750i
$10$	2.59969	+	2.56862i	0.822094	+	0.812269i
$11$	−3.23663	−	5.60601i	−0.975881	−	1.69028i	−0.676995	−	0.735987i	$-0.736718\pi$
$11$	−3.23663	−	5.60601i	−0.975881	−	1.69028i	−0.298886	−	0.954289i	$-0.596615\pi$
$12$	−2.44709	+	2.45189i	−0.706414	+	0.707799i
$13$	−3.36381	+	1.29798i	−0.932954	+	0.359995i
$13$	−3.36381	+	1.29798i	−0.932954	+	0.359995i
$14$	0.486627	+	1.77340i	0.130056	+	0.473962i
$15$	3.12984	+	3.19975i	0.808122	+	0.826172i
$16$	1.91613	−	3.51119i	0.479033	−	0.877797i
$17$	−2.70603	−	4.68698i	−0.656308	−	1.13676i	−0.981564	−	0.191133i	$-0.938784\pi$
$17$	−2.70603	−	4.68698i	−0.656308	−	1.13676i	0.325256	−	0.945626i	$-0.394550\pi$
$18$	−3.04784	+	2.95138i	−0.718383	+	0.695648i
$19$	0.939139	+	1.62664i	0.215453	+	0.373176i	0.953413	−	0.301669i	$-0.0975438\pi$
$19$	0.939139	+	1.62664i	0.215453	+	0.373176i	−0.737959	+	0.674845i	$0.764210\pi$
$20$	−4.50672	−	2.53020i	−1.00773	−	0.565771i
$21$	0.558864	+	2.18181i	0.121954	+	0.476111i
$22$	6.51206	+	6.43423i	1.38838	+	1.37178i
$23$	3.26888			0.681608			0.340804	−	0.940134i	$-0.389301\pi$
$23$	3.26888			0.681608			0.340804	+	0.940134i	$0.389301\pi$
$24$	2.41977	−	4.25966i	0.493934	−	0.869499i
$25$	−0.839052	+	1.45328i	−0.167810	+	0.290656i
$26$	4.10183	−	3.02903i	0.804434	−	0.594042i
$27$	−3.79393	+	3.55050i	−0.730143	+	0.683295i
$28$	−1.32732	−	2.23646i	−0.250840	−	0.422651i
$29$	6.35820	−	3.67091i	1.18069	−	0.681670i	0.224514	−	0.974471i	$-0.427921\pi$
$29$	6.35820	−	3.67091i	1.18069	−	0.681670i	0.956174	+	0.292800i	$0.0945872\pi$
$30$	−5.46592	−	3.19254i	−0.997937	−	0.582875i
$31$	−4.79360	+	2.76759i	−0.860957	+	0.497074i	−0.864333	−	0.502921i	$-0.832259\pi$
$31$	−4.79360	+	2.76759i	−0.860957	+	0.497074i	0.00337580	+	0.999994i	$0.498925\pi$
$32$	−1.29923	+	5.50563i	−0.229673	+	0.973268i
$33$	7.84006	+	8.01517i	1.36478	+	1.39526i
$34$	5.44449	+	5.37943i	0.933723	+	0.922564i
$35$	−2.91014	+	1.68017i	−0.491903	+	0.284001i
$36$	3.05215	−	5.16569i	0.508691	−	0.860949i
$37$	1.93131	−	3.34512i	0.317505	−	0.549934i	−0.662462	−	0.749095i	$-0.730488\pi$
$37$	1.93131	−	3.34512i	0.317505	−	0.549934i	0.979967	+	0.199161i	$0.0638218\pi$
$38$	−1.88953	−	1.86695i	−0.306523	−	0.302860i
$39$	5.08623	−	3.62357i	0.814449	−	0.580236i
$40$	7.09314	+	1.76414i	1.12152	+	0.278935i
$41$			6.06334i			0.946934i	0.880811	+	0.473467i	$0.156998\pi$
$41$			6.06334i			0.946934i	−0.880811	+	0.473467i	$0.843002\pi$
$42$	−1.57868	−	2.76642i	−0.243596	−	0.426867i
$43$			8.47246i			1.29204i	0.763321	+	0.646019i	$0.223567\pi$
$43$			8.47246i			1.29204i	−0.763321	+	0.646019i	$0.776433\pi$
$44$	−11.2890	−	6.33800i	−1.70189	−	0.955489i
$45$	−6.62670	−	4.02365i	−0.987851	−	0.599810i
$46$	−4.45810	+	1.22331i	−0.657311	+	0.180368i
$47$	−2.30419	−	1.33032i	−0.336100	−	0.194048i	0.322446	−	0.946588i	$-0.395495\pi$
$47$	−2.30419	−	1.33032i	−0.336100	−	0.194048i	−0.658546	+	0.752540i	$0.728828\pi$
$48$	−1.70599	+	6.71488i	−0.246239	+	0.969209i
$49$	5.30912			0.758446
$50$	0.600438	−	2.29598i	0.0849147	−	0.324701i
$51$	6.55478	+	6.70119i	0.917853	+	0.938354i
$52$	−4.46052	+	5.66602i	−0.618562	+	0.785736i
$53$		−	0.775873i		−	0.106574i	−0.998579	−	0.0532872i	$-0.983030\pi$
$53$		−	0.775873i		−	0.106574i	0.998579	−	0.0532872i	$-0.0169699\pi$
$54$	3.84546	−	6.26198i	0.523301	−	0.852148i
$55$	−8.36411	+	14.4871i	−1.12782	+	1.95344i
$56$	2.64715	+	2.55336i	0.353741	+	0.341206i
$57$	−2.27486	−	2.32568i	−0.301313	−	0.308043i
$58$	−7.29755	+	7.38582i	−0.958215	+	0.969805i
$59$	−4.03487	+	6.98861i	−0.525296	+	0.909839i	0.474270	+	0.880379i	$0.342712\pi$
$59$	−4.03487	+	6.98861i	−0.525296	+	0.909839i	−0.999566	+	0.0294597i	$0.990621\pi$
$60$	8.64918	+	2.30847i	1.11660	+	0.298022i
$61$		−	12.0836i		−	1.54714i	−0.633708	−	0.773572i	$-0.718468\pi$
$61$		−	12.0836i		−	1.54714i	0.633708	−	0.773572i	$-0.281532\pi$
$62$	5.50180	−	5.56835i	0.698730	−	0.707181i
$63$	−1.87542	−	3.42064i	−0.236280	−	0.430960i
$64$	−0.288489	−	7.99480i	−0.0360611	−	0.999350i
$65$	7.25125	+	5.85104i	0.899407	+	0.725733i
$66$	−13.6918	−	7.99711i	−1.68534	−	0.984376i
$67$	−13.0810			−1.59810			−0.799048	−	0.601267i	$-0.794663\pi$
$67$	−13.0810			−1.59810			−0.799048	+	0.601267i	$0.794663\pi$
$68$	−9.43835	−	5.29897i	−1.14457	−	0.642594i
$69$	−5.48479	+	1.40491i	−0.660291	+	0.169131i
$70$	3.34008	−	3.38048i	0.399216	−	0.404045i
$71$	−4.07336	+	2.35176i	−0.483419	+	0.279102i	−0.721840	−	0.692060i	$-0.756703\pi$
$71$	−4.07336	+	2.35176i	−0.483419	+	0.279102i	0.238421	+	0.971162i	$0.423370\pi$
$72$	−2.22936	+	8.18718i	−0.262733	+	0.964869i
$73$			5.80347i			0.679245i	0.940562	+	0.339623i	$0.110299\pi$
$73$			5.80347i			0.679245i	−0.940562	+	0.339623i	$0.889701\pi$
$74$	−1.38207	+	5.28483i	−0.160662	+	0.614349i
$75$	0.783234	−	2.79905i	0.0904401	−	0.323206i
$76$	3.27562	+	1.83903i	0.375739	+	0.210951i
$77$	−7.28971	+	4.20872i	−0.830740	+	0.479628i
$78$	−5.58055	+	6.84525i	−0.631873	+	0.775072i
$79$	3.46837	−	6.00740i	0.390223	−	0.675885i	−0.602256	−	0.798303i	$-0.705731\pi$
$79$	3.46837	−	6.00740i	0.390223	−	0.675885i	0.992479	+	0.122418i	$0.0390647\pi$
$80$	−10.3338	+	0.248534i	−1.15536	+	0.0277870i
$81$	4.83982	−	7.58789i	0.537758	−	0.843099i
$82$	−2.26909	−	8.26918i	−0.250579	−	0.913178i
$83$	−4.16832	+	7.21974i	−0.457532	+	0.792469i	−0.998830	−	0.0483617i	$-0.984600\pi$
$83$	−4.16832	+	7.21974i	−0.457532	+	0.792469i	0.541297	+	0.840831i	$0.317933\pi$
$84$	3.18828	+	3.18205i	0.347870	+	0.347190i
$85$	−6.99293	+	12.1121i	−0.758490	+	1.31374i
$86$	−3.17065	−	11.5547i	−0.341900	−	1.24598i
$87$	−9.09061	+	8.89200i	−0.974615	+	0.953322i
$88$	17.7679	+	4.41906i	1.89406	+	0.471073i
$89$	−8.28219	−	4.78173i	−0.877911	−	0.506862i	−0.00794179	−	0.999968i	$-0.502528\pi$
$89$	−8.28219	−	4.78173i	−0.877911	−	0.506862i	−0.869969	+	0.493106i	$0.835861\pi$
$90$	10.5433	+	3.00754i	1.11136	+	0.317022i
$91$	1.68782	+	4.37410i	0.176931	+	0.458530i
$92$	5.62215	−	3.33671i	0.586150	−	0.347876i
$93$	6.85364	−	6.70390i	0.710689	−	0.695162i
$94$	3.64030	+	0.951998i	0.375468	+	0.0981911i
$95$	2.42692	−	4.20356i	0.248997	−	0.431276i
$96$	−0.186280	−	9.79619i	−0.0190121	−	0.999819i
$97$		−	0.486805i		−	0.0494275i	−0.999695	−	0.0247138i	$-0.992133\pi$
$97$		−	0.486805i		−	0.0494275i	0.999695	−	0.0247138i	$-0.00786744\pi$
$98$	−7.24058	+	1.98683i	−0.731409	+	0.200701i
$99$	−16.5995	−	10.0790i	−1.66831	−	1.01298i
$100$	0.0403506	+	3.35597i	0.00403506	+	0.335597i
$101$	−5.34248	+	3.08448i	−0.531597	+	0.306918i	−0.741667	−	0.670769i	$-0.765964\pi$
$101$	−5.34248	+	3.08448i	−0.531597	+	0.306918i	0.210069	+	0.977686i	$0.432631\pi$
$102$	−11.4472	−	6.68609i	−1.13344	−	0.662021i
$103$	−1.50651	−	2.60935i	−0.148441	−	0.257107i	0.782210	−	0.623014i	$-0.214092\pi$
$103$	−1.50651	−	2.60935i	−0.148441	−	0.257107i	−0.930651	+	0.365907i	$0.880759\pi$
$104$	3.96286	−	9.39658i	0.388590	−	0.921411i
$105$	4.16076	−	4.06986i	0.406049	−	0.397177i
$106$	0.290355	+	1.05814i	0.0282018	+	0.102775i
$107$	−2.62070	−	1.51306i	−0.253353	−	0.146273i	0.367946	−	0.929847i	$-0.380061\pi$
$107$	−2.62070	−	1.51306i	−0.253353	−	0.146273i	−0.621299	+	0.783574i	$0.713395\pi$
$108$	−2.90101	+	9.97918i	−0.279150	+	0.960247i
$109$	19.2395			1.84281			0.921403	−	0.388609i	$-0.127044\pi$
$109$	19.2395			1.84281			0.921403	+	0.388609i	$0.127044\pi$
$110$	5.98548	−	22.8876i	0.570693	−	2.18225i
$111$	−1.80282	+	6.44276i	−0.171117	+	0.611519i
$112$	−4.56573	−	2.49162i	−0.431421	−	0.235436i
$113$	−4.13615	+	7.16403i	−0.389097	+	0.673935i	−0.992328	−	0.123631i	$-0.960546\pi$
$113$	−4.13615	+	7.16403i	−0.389097	+	0.673935i	0.603232	+	0.797566i	$0.293879\pi$
$114$	3.97280	+	2.32043i	0.372087	+	0.217329i
$115$	−4.22372	−	7.31570i	−0.393864	−	0.682193i
$116$	7.18840	−	12.8037i	0.667426	−	1.18880i
$117$	−6.97674	+	8.26590i	−0.645000	+	0.764183i
$118$	2.88741	−	11.0410i	0.265808	−	1.01641i
$119$	−6.09466	+	3.51875i	−0.558697	+	0.322564i
$120$	−12.6596	+	0.0884956i	−1.15566	+	0.00807851i
$121$	−15.4516	+	26.7629i	−1.40469	+	2.43299i
$122$	4.52205	+	16.4796i	0.409407	+	1.49199i
$123$	−2.60592	−	10.1736i	−0.234968	−	0.917319i
$124$	−5.41951	+	9.65306i	−0.486687	+	0.866871i
$125$	−8.58445			−0.767817
$126$	3.83780	+	3.96323i	0.341898	+	0.353072i
$127$	−2.48206	+	4.29906i	−0.220247	+	0.381480i	−0.954883	−	0.296982i	$-0.904020\pi$
$127$	−2.48206	+	4.29906i	−0.220247	+	0.381480i	0.734636	+	0.678462i	$0.237353\pi$
$128$	3.38534	+	10.7953i	0.299224	+	0.954183i
$129$	−3.64132	−	14.2158i	−0.320601	−	1.25163i
$130$	−12.0789	−	5.26601i	−1.05939	−	0.461860i
$131$	4.10310	−	2.36893i	0.358490	−	0.206974i	−0.309928	−	0.950760i	$-0.600305\pi$
$131$	4.10310	−	2.36893i	0.358490	−	0.206974i	0.668418	+	0.743786i	$0.266972\pi$
$132$	21.6656	+	5.78257i	1.88575	+	0.503308i
$133$	2.11518	−	1.22120i	0.183409	−	0.105891i
$134$	17.8399	−	4.89530i	1.54113	−	0.422890i
$135$	12.8481	+	3.90315i	1.10579	+	0.335930i
$136$	14.8551	+	3.69461i	1.27381	+	0.316811i
$137$			6.63460i			0.566833i	0.958997	+	0.283416i	$0.0914678\pi$
$137$			6.63460i			0.566833i	−0.958997	+	0.283416i	$0.908532\pi$
$138$	6.95440	−	3.96859i	0.591998	−	0.337829i
$139$	4.34998	+	2.51146i	0.368960	+	0.213019i	0.673004	−	0.739639i	$-0.265004\pi$
$139$	4.34998	+	2.51146i	0.368960	+	0.213019i	−0.304044	+	0.952658i	$0.598337\pi$
$140$	−3.29012	+	5.86026i	−0.278066	+	0.495282i
$141$	4.43791	+	1.24182i	0.373739	+	0.104580i
$142$	4.67515	−	4.73170i	0.392330	−	0.397076i
$143$	18.1639	+	14.6565i	1.51894	+	1.22564i
$144$	−0.0234906	−	12.0000i	−0.00195755	−	0.999998i
$145$	−16.4309	−	9.48637i	−1.36451	−	0.787800i
$146$	−2.17184	−	7.91478i	−0.179743	−	0.655032i
$147$	−8.90807	+	2.28177i	−0.734725	+	0.188197i
$148$	−0.0928778	−	7.72466i	−0.00763451	−	0.634963i
$149$	1.43168	−	2.47974i	0.117287	−	0.203148i	−0.801404	−	0.598123i	$-0.795913\pi$
$149$	1.43168	−	2.47974i	0.117287	−	0.203148i	0.918692	+	0.394975i	$0.129247\pi$
$150$	−0.0206869	+	4.11045i	−0.00168907	+	0.335617i
$151$	−11.6205	−	6.70909i	−0.945662	−	0.545978i	−0.0539311	−	0.998545i	$-0.517175\pi$
$151$	−11.6205	−	6.70909i	−0.945662	−	0.545978i	−0.891731	+	0.452567i	$0.850508\pi$
$152$	−5.15551	−	1.28223i	−0.418167	−	0.104003i
$153$	−13.8782	−	8.42666i	−1.12199	−	0.681255i
$154$	8.36668	−	8.46789i	0.674207	−	0.682362i
$155$	12.3876	+	7.15201i	0.995000	+	0.574463i
$156$	5.04906	−	11.4240i	0.404248	−	0.914649i
$157$	10.2591	−	5.92309i	0.818765	−	0.472714i	−0.0312255	−	0.999512i	$-0.509941\pi$
$157$	10.2591	−	5.92309i	0.818765	−	0.472714i	0.849990	+	0.526798i	$0.176608\pi$
$158$	−2.48202	+	9.49086i	−0.197459	+	0.755053i
$159$	0.333457	+	1.30182i	0.0264449	+	0.103241i
$160$	14.0003	−	4.20618i	1.10682	−	0.332528i
$161$		−	4.25065i		−	0.334998i
$162$	−3.76093	+	12.1596i	−0.295486	+	0.955347i
$163$	8.37296	+	14.5024i	0.655821	+	1.13591i	0.981687	+	0.190499i	$0.0610105\pi$
$163$	8.37296	+	14.5024i	0.655821	+	1.13591i	−0.325867	+	0.945416i	$0.605656\pi$
$164$	6.18916	+	10.4284i	0.483292	+	0.814318i
$165$	7.80769	−	27.9023i	0.607828	−	2.17219i
$166$	2.98291	−	11.4062i	0.231519	−	0.885293i
$167$			7.22113i			0.558788i	0.960177	+	0.279394i	$0.0901336\pi$
$167$			7.22113i			0.558788i	−0.960177	+	0.279394i	$0.909866\pi$
$168$	−5.53900	−	3.14652i	−0.427343	−	0.242760i
$169$	9.63049	−	8.73234i	0.740807	−	0.671718i
$170$	5.00424	−	19.1355i	0.383807	−	1.46762i
$171$	4.81649	+	2.92451i	0.368326	+	0.223643i
$172$	8.64827	+	14.5718i	0.659425	+	1.11109i
$173$			9.25265i			0.703466i	0.936100	+	0.351733i	$0.114407\pi$
$173$			9.25265i			0.703466i	−0.936100	+	0.351733i	$0.885593\pi$
$174$	9.07012	−	15.5289i	0.687604	−	1.17724i
$175$	1.88976	+	1.09105i	0.142852	+	0.0824758i
$176$	−25.8856	+	0.622563i	−1.95120	+	0.0469274i
$177$	3.76645	−	13.4602i	0.283104	−	1.01173i
$178$	13.0847	+	3.42187i	0.980742	+	0.256480i
$179$	7.89214	+	4.55653i	0.589887	+	0.340571i	0.765053	−	0.643968i	$-0.222713\pi$
$179$	7.89214	+	4.55653i	0.589887	+	0.340571i	−0.175166	+	0.984539i	$0.556046\pi$
$180$	−15.5044	−	0.156064i	−1.15563	−	0.0116323i
$181$			7.29845i			0.542489i	0.962510	+	0.271245i	$0.0874352\pi$
$181$			7.29845i			0.542489i	−0.962510	+	0.271245i	$0.912565\pi$
$182$	−3.93877	−	5.33376i	−0.291961	−	0.395365i
$183$	5.19332	+	20.2748i	0.383902	+	1.49876i
$184$	−6.41880	+	6.65459i	−0.473200	+	0.490583i
$185$	−9.98177			−0.733874
$186$	−6.83819	+	11.7076i	−0.501400	+	0.858444i
$187$	−17.5168	+	30.3401i	−1.28096	+	2.21868i
$188$	−5.32091	+	0.0639762i	−0.388067	+	0.00466594i
$189$	4.61686	+	4.93340i	0.335827	+	0.358852i
$190$	−1.73674	+	6.64104i	−0.125996	+	0.481792i
$191$	−3.18218			−0.230254			−0.115127	−	0.993351i	$-0.536728\pi$
$191$	−3.18218			−0.230254			−0.115127	+	0.993351i	$0.536728\pi$
$192$	3.92008	+	13.2903i	0.282907	+	0.959147i
$193$		−	14.6378i		−	1.05365i	−0.849973	−	0.526826i	$-0.823382\pi$
$193$		−	14.6378i		−	1.05365i	0.849973	−	0.526826i	$-0.176618\pi$
$194$	0.182177	+	0.663904i	0.0130796	+	0.0476656i
$195$	−14.6814	−	6.70089i	−1.05136	−	0.479860i
$196$	9.13117	−	5.41929i	0.652226	−	0.387092i
$197$	7.48399	−	12.9626i	0.533212	−	0.923550i	−0.466036	−	0.884766i	$-0.654318\pi$
$197$	7.48399	−	12.9626i	0.533212	−	0.923550i	0.999248	−	0.0387843i	$-0.0123485\pi$
$198$	26.4102	+	7.53369i	1.87689	+	0.535396i
$199$	−2.29103	−	3.96817i	−0.162407	−	0.281296i	0.773325	−	0.634010i	$-0.218592\pi$
$199$	−2.29103	−	3.96817i	−0.162407	−	0.281296i	−0.935731	+	0.352714i	$0.885259\pi$
$200$	−1.31094	−	4.56177i	−0.0926972	−	0.322566i
$201$	21.9483	−	5.62199i	1.54812	−	0.396545i
$202$	6.13177	−	6.20594i	0.431430	−	0.436649i
$203$	−4.77342	−	8.26781i	−0.335029	−	0.580287i
$204$	18.1138	+	4.83459i	1.26822	+	0.338489i
$205$	13.5697	−	7.83445i	0.947746	−	0.547182i
$206$	3.03108	+	2.99486i	0.211185	+	0.208661i
$207$	8.59902	−	4.71455i	0.597673	−	0.327684i
$208$	−1.88806	+	14.2981i	−0.130913	+	0.991394i
$209$	6.07929	−	10.5296i	0.420513	−	0.728351i
$210$	−4.15138	+	7.10755i	−0.286473	+	0.490468i
$211$			5.65966i			0.389627i	0.980840	+	0.194814i	$0.0624102\pi$
$211$			5.65966i			0.389627i	−0.980840	+	0.194814i	$0.937590\pi$
$212$	−0.791973	−	1.33443i	−0.0543930	−	0.0916487i
$213$	5.82387	−	5.69663i	0.399045	−	0.390327i
$214$	4.14035	+	1.08277i	0.283029	+	0.0740166i
$215$	18.9612	−	10.9473i	1.29315	−	0.746598i
$216$	0.221888	−	14.6953i	0.0150975	−	0.999886i
$217$	3.59880	+	6.23331i	0.244303	+	0.423145i
$218$	−26.2388	+	7.19999i	−1.77711	+	0.487645i
$219$	−2.49424	−	9.73754i	−0.168545	−	0.658002i
$220$	0.402236	+	33.4540i	0.0271188	+	2.25547i
$221$	15.1862	+	12.2538i	1.02153	+	0.824277i
$222$	0.0476164	−	9.46130i	0.00319580	−	0.635001i
$223$	24.4421	−	14.1116i	1.63676	−	0.944985i	0.654824	−	0.755781i	$-0.272743\pi$
$223$	24.4421	−	14.1116i	1.63676	−	0.944985i	0.981938	−	0.189204i	$-0.0605908\pi$
$224$	7.15919	+	1.68944i	0.478343	+	0.112880i
$225$	−0.111191	+	5.03309i	−0.00741272	+	0.335539i
$226$	2.95989	−	11.3182i	0.196889	−	0.752874i
$227$	29.8264			1.97965			0.989825	−	0.142293i	$-0.0454474\pi$
$227$	29.8264			1.97965			0.989825	+	0.142293i	$0.0454474\pi$
$228$	−6.28648	−	1.67787i	−0.416333	−	0.111119i
$229$	−0.362816	−	0.628416i	−0.0239755	−	0.0415269i	0.853789	−	0.520620i	$-0.174299\pi$
$229$	−0.362816	−	0.628416i	−0.0239755	−	0.0415269i	−0.877764	+	0.479093i	$0.840966\pi$
$230$	8.49807	+	8.39651i	0.560346	+	0.553650i
$231$	10.4224	−	10.1947i	0.685746	−	0.670764i
$232$	−5.01199	+	20.1519i	−0.329053	+	1.32304i
$233$	−23.5383			−1.54205			−0.771024	−	0.636806i	$-0.780255\pi$
$233$	−23.5383			−1.54205			−0.771024	+	0.636806i	$0.780255\pi$
$234$	6.42153	−	13.8839i	0.419788	−	0.907622i
$235$			6.87565i			0.448518i
$236$	0.194040	+	16.1383i	0.0126309	+	1.05052i
$237$	−3.23764	+	11.5704i	−0.210307	+	0.751575i
$238$	6.99508	−	7.07969i	0.453423	−	0.458908i
$239$	15.0107	−	8.66644i	0.970962	−	0.560585i	0.0714327	−	0.997445i	$-0.477243\pi$
$239$	15.0107	−	8.66644i	0.970962	−	0.560585i	0.899529	+	0.436860i	$0.143910\pi$
$240$	17.2321	−	4.85832i	1.11233	−	0.313603i
$241$		−	21.0901i		−	1.35853i	−0.733892	−	0.679266i	$-0.762298\pi$
$241$		−	21.0901i		−	1.35853i	0.733892	−	0.679266i	$-0.237702\pi$
$242$	11.0574	−	42.2817i	0.710794	−	2.71797i
$243$	−4.85950	+	14.8117i	−0.311737	+	0.950169i
$244$	−12.3343	−	20.7826i	−0.789625	−	1.33047i
$245$	−6.85992	−	11.8817i	−0.438264	−	0.759096i
$246$	7.36122	+	12.8995i	0.469334	+	0.822442i
$247$	−5.27043	−	4.25272i	−0.335350	−	0.270594i
$248$	3.77866	−	15.1930i	0.239945	−	0.964756i
$249$	3.89102	−	13.9053i	0.246583	−	0.881215i
$250$	11.7075	−	3.21256i	0.740446	−	0.203180i
$251$	−12.6790	+	7.32021i	−0.800290	+	0.462048i	−0.843573	−	0.537015i	$-0.819552\pi$
$251$	−12.6790	+	7.32021i	−0.800290	+	0.462048i	0.0432824	+	0.999063i	$0.486218\pi$
$252$	−6.71715	−	3.96883i	−0.423141	−	0.250013i
$253$	−10.5802	−	18.3254i	−0.665169	−	1.15211i
$254$	1.77620	−	6.79192i	0.111449	−	0.426163i
$255$	6.52772	−	23.3281i	0.408782	−	1.46086i
$256$	−8.65687	−	13.4558i	−0.541055	−	0.840987i
$257$	5.55811			0.346705			0.173353	−	0.984860i	$-0.444540\pi$
$257$	5.55811			0.346705			0.173353	+	0.984860i	$0.444540\pi$
$258$	10.2860	+	18.0248i	0.640379	+	1.12217i
$259$	−4.34979	−	2.51135i	−0.270283	−	0.156048i
$260$	18.4439	+	2.66150i	1.14384	+	0.165059i
$261$	11.4313	−	18.8267i	0.707581	−	1.16534i
$262$	−4.70929	+	4.76625i	−0.290941	+	0.294460i
$263$	−9.83880	−	17.0413i	−0.606686	−	1.05081i	−0.991783	−	0.127935i	$-0.959165\pi$
$263$	−9.83880	−	17.0413i	−0.606686	−	1.05081i	0.385096	−	0.922876i	$-0.374168\pi$
$264$	−31.7116	+	0.221676i	−1.95171	+	0.0136432i
$265$	−1.73639	+	1.00251i	−0.106666	+	0.0615835i
$266$	−2.42767	+	2.45704i	−0.148850	+	0.150650i
$267$	15.9516	+	4.46362i	0.976225	+	0.273169i
$268$	−22.4980	+	13.3524i	−1.37429	+	0.815630i
$269$	−21.8270	+	12.6018i	−1.33082	+	0.768348i	−0.985425	−	0.170110i	$-0.945588\pi$
$269$	−21.8270	+	12.6018i	−1.33082	+	0.768348i	−0.345393	+	0.938458i	$0.612254\pi$
$270$	−18.9830	−	0.514964i	−1.15527	−	0.0313397i
$271$	−25.6629	−	14.8165i	−1.55891	−	0.900039i	−0.997361	−	0.0725966i	$-0.976871\pi$
$271$	−25.6629	−	14.8165i	−1.55891	−	0.900039i	−0.561551	−	0.827442i	$-0.689795\pi$
$272$	−21.6420	+	0.520502i	−1.31224	+	0.0315600i
$273$	−4.71187	−	6.61382i	−0.285175	−	0.400287i
$274$	−2.48287	−	9.04828i	−0.149996	−	0.546626i
$275$	10.8628			0.655053
$276$	−7.99924	+	8.01492i	−0.481498	+	0.482441i
$277$			12.5855i			0.756190i	0.925767	+	0.378095i	$0.123421\pi$
$277$			12.5855i			0.756190i	−0.925767	+	0.378095i	$0.876579\pi$
$278$	−6.87237	−	1.79724i	−0.412177	−	0.107791i
$279$	−8.61836	+	14.1939i	−0.515968	+	0.849768i
$280$	2.29398	−	9.22349i	0.137092	−	0.551209i
$281$	4.30070	+	2.48301i	0.256558	+	0.148124i	0.622764	−	0.782410i	$-0.286010\pi$
$281$	4.30070	+	2.48301i	0.256558	+	0.148124i	−0.366205	+	0.930534i	$0.619343\pi$
$282$	−6.51714	−	0.0327991i	−0.388090	−	0.00195316i
$283$		−	15.7139i		−	0.934097i	−0.884232	−	0.467048i	$-0.845317\pi$
$283$		−	15.7139i		−	0.934097i	0.884232	−	0.467048i	$-0.154683\pi$
$284$	−4.60523	+	8.20268i	−0.273270	+	0.486740i
$285$	−2.26547	+	8.09612i	−0.134195	+	0.479573i
$286$	−30.2569	−	13.1910i	−1.78913	−	0.780002i
$287$	7.88439			0.465401
$288$	4.52279	+	16.3568i	0.266508	+	0.963833i
$289$	−6.14519	+	10.6438i	−0.361482	+	0.626104i
$290$	25.9585	+	6.78858i	1.52434	+	0.398639i
$291$	0.209221	+	0.816801i	0.0122647	+	0.0478817i
$292$	5.92390	+	9.98141i	0.346670	+	0.584118i
$293$	−3.33150	+	5.77033i	−0.194628	+	0.337106i	−0.946779	−	0.321885i	$-0.895683\pi$
$293$	−3.33150	+	5.77033i	−0.194628	+	0.337106i	0.752150	+	0.658992i	$0.229017\pi$
$294$	11.2949	−	6.44555i	0.658733	−	0.375912i
$295$	20.8539			1.21416
$296$	3.01747	+	10.5001i	0.175387	+	0.610308i
$297$	32.1837	+	9.77716i	1.86749	+	0.567328i
$298$	−1.02453	+	3.91764i	−0.0593493	+	0.226943i
$299$	−10.9959	+	4.24294i	−0.635909	+	0.245376i
$300$	−1.51004	−	5.61357i	−0.0871824	−	0.324100i
$301$	11.0171			0.635013
$302$	18.3588	+	4.80112i	1.05643	+	0.276273i
$303$	7.63840	−	7.47151i	0.438814	−	0.429227i
$304$	7.51094	−	0.180642i	0.430782	−	0.0103605i
$305$	−27.0429	+	15.6132i	−1.54847	+	0.894010i
$306$	22.0806	+	6.29864i	1.26227	+	0.360069i
$307$	−5.22014			−0.297929			−0.148965	−	0.988843i	$-0.547594\pi$
$307$	−5.22014			−0.297929			−0.148965	+	0.988843i	$0.547594\pi$
$308$	−8.24155	+	14.6796i	−0.469606	+	0.836446i
$309$	3.64920	+	3.73071i	0.207596	+	0.212233i
$310$	−19.5708	−	5.11808i	−1.11155	−	0.290687i
$311$	2.10841	+	3.65187i	0.119557	+	0.207079i	0.919592	−	0.392874i	$-0.128519\pi$
$311$	2.10841	+	3.65187i	0.119557	+	0.207079i	−0.800035	+	0.599953i	$0.795186\pi$
$312$	−2.61071	+	17.4695i	−0.147802	+	0.989017i
$313$	−15.8487	+	27.4507i	−0.895819	+	1.55160i	−0.0630319	+	0.998012i	$0.520077\pi$
$313$	−15.8487	+	27.4507i	−0.895819	+	1.55160i	−0.832787	+	0.553593i	$0.813256\pi$
$314$	−11.7748	+	11.9172i	−0.664488	+	0.672525i
$315$	−5.23210	+	8.61696i	−0.294796	+	0.485511i
$316$	−0.166796	−	13.8725i	−0.00938304	−	0.780389i
$317$	16.0732	−	27.8397i	0.902763	−	1.56363i	0.0788718	−	0.996885i	$-0.474868\pi$
$317$	16.0732	−	27.8397i	0.902763	−	1.56363i	0.823892	−	0.566747i	$-0.191798\pi$
$318$	−0.941951	−	1.65064i	−0.0528220	−	0.0925631i
$319$	−41.1583	−	23.7628i	−2.30442	−	1.33046i
$320$	−17.5195	+	10.9757i	−0.979369	+	0.613562i
$321$	5.04752	+	1.41241i	0.281725	+	0.0788328i
$322$	1.59072	+	5.79704i	0.0886475	+	0.323056i
$323$	5.08267	−	8.80345i	0.282807	−	0.489837i
$324$	0.578668	−	17.9907i	0.0321482	−	0.999483i
$325$	0.936084	−	5.97764i	0.0519246	−	0.331580i
$326$	−16.8463	−	16.6449i	−0.933029	−	0.921878i
$327$	−32.2815	+	8.26880i	−1.78517	+	0.457266i
$328$	−12.3434	−	11.9060i	−0.681550	−	0.657400i
$329$	−1.72987	+	2.99623i	−0.0953709	+	0.165187i
$330$	−0.206217	+	40.9751i	−0.0113519	+	2.25561i
$331$	−8.67836			−0.477006			−0.238503	−	0.971142i	$-0.576657\pi$
$331$	−8.67836			−0.477006			−0.238503	+	0.971142i	$0.576657\pi$
$332$	0.200457	+	16.6721i	0.0110015	+	0.914999i
$333$	0.255936	−	11.5850i	0.0140252	−	0.634854i
$334$	−2.70237	−	9.84819i	−0.147867	−	0.538869i
$335$	16.9020	+	29.2751i	0.923453	+	1.59947i
$336$	8.73162	+	2.21837i	0.476349	+	0.121022i
$337$	4.19269	+	7.26195i	0.228390	+	0.395584i	0.957331	−	0.288993i	$-0.0933204\pi$
$337$	4.19269	+	7.26195i	0.228390	+	0.395584i	−0.728941	+	0.684577i	$0.759987\pi$
$338$	−9.86616	+	15.5132i	−0.536648	+	0.843806i
$339$	3.86100	−	13.7980i	0.209700	−	0.749407i
$340$	0.336295	+	27.9697i	0.0182381	+	1.51687i
$341$	31.0303	+	17.9153i	1.68038	+	0.970170i
$342$	−7.66317	−	2.18597i	−0.414377	−	0.118204i
$343$		−	16.0060i		−	0.864244i
$344$	−17.2477	−	16.6366i	−0.929936	−	0.896984i
$345$	10.2311	+	10.4596i	0.550823	+	0.563126i
$346$	−3.46262	−	12.6188i	−0.186152	−	0.678389i
$347$	−8.23985	−	4.75728i	−0.442338	−	0.255384i	0.262251	−	0.965000i	$-0.415535\pi$
$347$	−8.23985	−	4.75728i	−0.442338	−	0.255384i	−0.704589	+	0.709616i	$0.748869\pi$
$348$	−6.55844	+	24.5726i	−0.351569	+	1.31723i
$349$	10.6617	+	18.4666i	0.570707	+	0.988494i	0.996494	+	0.0836702i	$0.0266642\pi$
$349$	10.6617	+	18.4666i	0.570707	+	0.988494i	−0.425786	+	0.904824i	$0.640002\pi$
$350$	−2.98556	−	0.780772i	−0.159585	−	0.0417340i
$351$	8.15360	−	16.8677i	0.435207	−	0.900331i
$352$	35.0698	−	10.5362i	1.86923	−	0.561583i
$353$	−19.5467	+	11.2853i	−1.04037	+	0.600656i	−0.919937	−	0.392066i	$-0.871760\pi$
$353$	−19.5467	+	11.2853i	−1.04037	+	0.600656i	−0.120429	+	0.992722i	$0.538427\pi$
$354$	−0.0994799	+	19.7665i	−0.00528730	+	1.05058i
$355$	10.5264	+	6.07741i	0.558683	+	0.322556i
$356$	−19.1255	+	0.229957i	−1.01365	+	0.0121877i
$357$	8.71382	−	8.52344i	0.461184	−	0.451108i
$358$	−12.4685	−	3.26072i	−0.658981	−	0.172334i
$359$			25.1861i			1.32927i	0.747167	+	0.664636i	$0.231413\pi$
$359$			25.1861i			1.32927i	−0.747167	+	0.664636i	$0.768587\pi$
$360$	21.2034	−	5.58939i	1.11751	−	0.294587i
$361$	7.73604	−	13.3992i	0.407160	−	0.705222i
$362$	−2.73130	−	9.95362i	−0.143554	−	0.523151i
$363$	14.4237	−	51.5458i	0.757046	−	2.70545i
$364$	7.36775	+	5.80018i	0.386175	+	0.304012i
$365$	12.9881	−	7.49868i	0.679828	−	0.392499i
$366$	−14.6701	−	25.7073i	−0.766819	−	1.34374i
$367$	9.62345	+	16.6683i	0.502340	+	0.870079i	0.999996	+	0.00270419i	$0.000860770\pi$
$367$	9.62345	+	16.6683i	0.502340	+	0.870079i	−0.497656	+	0.867374i	$0.665806\pi$
$368$	6.26360	−	11.4776i	0.326513	−	0.598314i
$369$	8.74486	+	15.9500i	0.455239	+	0.830326i
$370$	13.6131	−	3.73548i	0.707713	−	0.194199i
$371$	−1.00890			−0.0523793
$372$	4.94457	−	18.5259i	0.256364	−	0.960524i
$373$	−2.18849	−	1.26353i	−0.113316	−	0.0654229i	0.442271	−	0.896881i	$-0.354173\pi$
$373$	−2.18849	−	1.26353i	−0.113316	−	0.0654229i	−0.555587	+	0.831459i	$0.687506\pi$
$374$	12.5353	−	47.9331i	0.648185	−	2.47856i
$375$	14.4037	−	3.68946i	0.743803	−	0.190523i
$376$	7.23272	−	2.07850i	0.372999	−	0.107190i
$377$	−16.6230	+	20.6011i	−0.856129	+	1.06101i
$378$	−8.14270	−	5.00040i	−0.418815	−	0.257193i
$379$	−0.946561	+	1.63949i	−0.0486216	+	0.0842151i	−0.889312	−	0.457301i	$-0.848816\pi$
$379$	−0.946561	+	1.63949i	−0.0486216	+	0.0842151i	0.840690	+	0.541516i	$0.182150\pi$
$380$	−0.116713	−	9.70700i	−0.00598723	−	0.497959i
$381$	2.31694	−	8.28006i	0.118701	−	0.424200i
$382$	4.33986	−	1.19087i	0.222046	−	0.0609301i
$383$	8.47922	+	4.89548i	0.433268	+	0.250147i	0.700738	−	0.713419i	$-0.252854\pi$
$383$	8.47922	+	4.89548i	0.433268	+	0.250147i	−0.267470	+	0.963566i	$0.586188\pi$
$384$	−10.3199	−	16.6583i	−0.526633	−	0.850093i
$385$	18.8381	+	10.8762i	0.960079	+	0.554302i
$386$	5.47791	+	19.9630i	0.278818	+	1.01609i
$387$	12.2194	+	22.2874i	0.621148	+	1.13293i
$388$	−0.496907	−	0.837257i	−0.0252266	−	0.0425053i
$389$	10.0373	+	5.79502i	0.508910	+	0.293819i	0.732385	−	0.680890i	$-0.238407\pi$
$389$	10.0373	+	5.79502i	0.508910	+	0.293819i	−0.223475	+	0.974710i	$0.571740\pi$
$390$	22.5302	+	3.64443i	1.14086	+	0.184543i
$391$	−8.84568	−	15.3212i	−0.447345	−	0.774825i
$392$	−10.4250	+	10.8080i	−0.526543	+	0.545886i
$393$	−5.86640	+	5.73823i	−0.295921	+	0.289455i
$394$	−5.35565	+	20.4792i	−0.269814	+	1.03173i
$395$	−17.9260			−0.901953
$396$	−38.8376	−	0.390930i	−1.95166	−	0.0196450i
$397$	−12.8586	−	22.2718i	−0.645355	−	1.11779i	−0.984219	−	0.176952i	$-0.943376\pi$
$397$	−12.8586	−	22.2718i	−0.645355	−	1.11779i	0.338865	−	0.940835i	$-0.389957\pi$
$398$	4.60951	+	4.55442i	0.231054	+	0.228293i
$399$	−3.02417	+	2.95809i	−0.151398	+	0.148090i
$400$	3.49501	+	5.73075i	0.174750	+	0.286538i
$401$			7.18562i			0.358833i	0.983773	+	0.179416i	$0.0574210\pi$
$401$			7.18562i			0.358833i	−0.983773	+	0.179416i	$0.942579\pi$
$402$	−27.8292	+	15.8810i	−1.38800	+	0.792073i
$403$	12.5325	−	15.5317i	0.624289	−	0.773687i
$404$	−6.04006	+	10.7584i	−0.300504	+	0.535249i
$405$	−23.2351	−	1.02712i	−1.15456	−	0.0510381i
$406$	9.60406	+	9.48928i	0.476642	+	0.470945i
$407$	−25.0037			−1.23939
$408$	−26.5129	+	0.185335i	−1.31258	+	0.00917546i
$409$	23.2680	+	13.4338i	1.15053	+	0.664259i	0.949017	−	0.315226i	$-0.102080\pi$
$409$	23.2680	+	13.4338i	1.15053	+	0.664259i	0.201514	+	0.979486i	$0.435414\pi$
$410$	−15.5744	+	15.7628i	−0.769166	+	0.778469i
$411$	−2.85144	−	11.1321i	−0.140651	−	0.549105i
$412$	−5.25455	−	2.95006i	−0.258873	−	0.145339i
$413$	9.08756	+	5.24670i	0.447169	+	0.258173i
$414$	−9.96302	+	9.64772i	−0.489656	+	0.474159i
$415$	21.5436			1.05753
$416$	−2.77585	−	20.2063i	−0.136097	−	0.990695i
$417$	−8.37813	−	2.34438i	−0.410279	−	0.114805i
$418$	−4.35043	+	16.6354i	−0.212786	+	0.813664i
$419$			18.3474i			0.896329i	0.893951	+	0.448165i	$0.147922\pi$
$419$			18.3474i			0.896329i	−0.893951	+	0.448165i	$0.852078\pi$
$420$	3.00179	−	11.2469i	0.146472	−	0.548791i
$421$	−9.00621	+	15.5992i	−0.438936	+	0.760259i	−0.997608	−	0.0691294i	$-0.977978\pi$
$421$	−9.00621	+	15.5992i	−0.438936	+	0.760259i	0.558672	+	0.829389i	$0.311311\pi$
$422$	−2.11802	−	7.71865i	−0.103104	−	0.375738i
$423$	−7.97999	−	0.176294i	−0.388001	−	0.00857170i
$424$	1.57948	+	1.52351i	0.0767062	+	0.0739882i
$425$	9.08200			0.440542
$426$	−5.81074	+	9.94854i	−0.281531	+	0.482008i
$427$	−15.7128			−0.760393
$428$	−6.05182	+	0.0727643i	−0.292526	+	0.00351719i
$429$	−36.7760	−	16.7853i	−1.77556	−	0.810402i
$430$	−21.7625	+	22.0258i	−1.04948	+	1.06218i
$431$	−10.7237	−	6.19133i	−0.516542	−	0.298226i	0.218977	−	0.975730i	$-0.429728\pi$
$431$	−10.7237	−	6.19133i	−0.516542	−	0.298226i	−0.735519	+	0.677504i	$0.763062\pi$
$432$	5.19681	+	20.1244i	0.250031	+	0.968238i
$433$	−18.2783	−	31.6589i	−0.878398	−	1.52143i	−0.853099	−	0.521750i	$-0.825279\pi$
$433$	−18.2783	−	31.6589i	−0.878398	−	1.52143i	−0.0252993	−	0.999680i	$-0.508054\pi$
$434$	−7.24074	−	7.15421i	−0.347567	−	0.343413i
$435$	31.6461	+	8.85528i	1.51732	+	0.424578i
$436$	33.0900	−	19.6387i	1.58472	−	0.940523i
$437$	3.06993	+	5.31728i	0.146855	+	0.254360i
$438$	7.04573	+	12.3466i	0.336658	+	0.589945i
$439$	−18.9768	−	32.8688i	−0.905713	−	1.56874i	−0.819957	−	0.572425i	$-0.806003\pi$
$439$	−18.9768	−	32.8688i	−0.905713	−	1.56874i	−0.0857561	−	0.996316i	$-0.527331\pi$
$440$	−13.0681	−	45.4741i	−0.622997	−	2.16789i
$441$	13.9660	−	7.65708i	0.665049	−	0.364623i
$442$	−25.2967	−	11.0285i	−1.20324	−	0.524574i
$443$	−9.45782	−	5.46048i	−0.449355	−	0.259435i	0.258203	−	0.966091i	$-0.416870\pi$
$443$	−9.45782	−	5.46048i	−0.449355	−	0.259435i	−0.707558	+	0.706656i	$0.750203\pi$
$444$	3.47577	+	12.9212i	0.164953	+	0.613211i
$445$			24.7139i			1.17155i
$446$	−28.0531	+	28.3924i	−1.32835	+	1.34442i
$447$	−1.33643	+	4.77601i	−0.0632111	+	0.225898i
$448$	−10.3959	+	0.375133i	−0.491162	+	0.0177234i
$449$	−29.3882	+	16.9673i	−1.38692	+	0.800737i	−0.992967	−	0.118395i	$-0.962225\pi$
$449$	−29.3882	+	16.9673i	−1.38692	+	0.800737i	−0.393950	+	0.919132i	$0.628892\pi$
$450$	−1.73189	−	6.90574i	−0.0816422	−	0.325540i
$451$	33.9911	−	19.6248i	1.60058	−	0.924095i
$452$	0.198911	+	16.5434i	0.00935596	+	0.778137i
$453$	22.3813	+	6.26277i	1.05156	+	0.294250i
$454$	−40.6773	+	11.1620i	−1.90908	+	0.523857i
$455$	7.60834	−	9.42909i	0.356684	−	0.442042i
$456$	9.20142	−	0.0643213i	0.430896	−	0.00301212i
$457$	−7.13346	+	4.11851i	−0.333689	+	0.192656i	−0.657478	−	0.753474i	$-0.728377\pi$
$457$	−7.13346	+	4.11851i	−0.333689	+	0.192656i	0.323789	+	0.946129i	$0.395043\pi$
$458$	0.729981	+	0.721257i	0.0341098	+	0.0337021i
$459$	26.9076	+	8.17432i	1.25594	+	0.381545i
$460$	−14.7319	−	8.27093i	−0.686879	−	0.385634i
$461$	−13.7318			−0.639553			−0.319777	−	0.947493i	$-0.603608\pi$
$461$	−13.7318			−0.639553			−0.319777	+	0.947493i	$0.603608\pi$
$462$	−10.3989	+	17.8040i	−0.483803	+	0.828316i
$463$	−20.1239	+	11.6185i	−0.935236	+	0.539959i	−0.888464	−	0.458947i	$-0.848227\pi$
$463$	−20.1239	+	11.6185i	−0.935236	+	0.539959i	−0.0467722	+	0.998906i	$0.514894\pi$
$464$	−0.706095	−	29.3588i	−0.0327796	−	1.36295i
$465$	−23.8588	−	6.67622i	−1.10643	−	0.309602i
$466$	32.1016	−	8.80877i	1.48708	−	0.408058i
$467$		−	16.3231i		−	0.755343i	−0.925940	−	0.377672i	$-0.876725\pi$
$467$		−	16.3231i		−	0.755343i	0.925940	−	0.377672i	$-0.123275\pi$
$468$	−3.56189	+	21.3381i	−0.164648	+	0.986352i
$469$			17.0097i			0.785436i
$470$	−2.57308	−	9.37702i	−0.118687	−	0.432530i
$471$	−14.6679	+	14.3474i	−0.675861	+	0.661095i
$472$	−6.30409	−	21.9368i	−0.290169	−	1.00973i
$473$	47.4967	−	27.4222i	2.18390	−	1.26088i
$474$	0.0855128	−	16.9913i	0.00392773	−	0.780435i
$475$	−3.15195			−0.144621
$476$	−6.89045	+	12.2731i	−0.315823	+	0.562534i
$477$	−1.11900	−	2.04099i	−0.0512357	−	0.0934505i
$478$	−17.2284	+	17.4368i	−0.788007	+	0.797539i
$479$	24.6273	−	14.2186i	1.12525	−	0.649663i	0.182514	−	0.983203i	$-0.441577\pi$
$479$	24.6273	−	14.2186i	1.12525	−	0.649663i	0.942736	+	0.333540i	$0.108243\pi$
$480$	−21.6830	+	13.0746i	−0.989691	+	0.596769i
$481$	−2.15465	+	13.7592i	−0.0982435	+	0.627363i
$482$	7.89255	+	28.7627i	0.359496	+	1.31010i
$483$	1.82686	+	7.13209i	0.0831250	+	0.324521i
$484$	0.743077	+	61.8018i	0.0337762	+	2.80917i
$485$	−1.08946	+	0.629001i	−0.0494699	+	0.0285615i
$486$	1.08440	−	22.0187i	0.0491896	−	0.998789i
$487$	1.54591	−	0.892532i	0.0700519	−	0.0404445i	−0.464565	−	0.885539i	$-0.653789\pi$
$487$	1.54591	−	0.892532i	0.0700519	−	0.0404445i	0.534617	+	0.845095i	$0.320456\pi$
$488$	24.5991	+	23.7274i	1.11355	+	1.07409i
$489$	−20.2817	−	20.7347i	−0.917171	−	0.937657i
$490$	13.8021	+	13.6371i	0.623514	+	0.616062i
$491$		−	11.0112i		−	0.496926i	−0.968641	−	0.248463i	$-0.920075\pi$
$491$		−	11.0112i		−	0.496926i	0.968641	−	0.248463i	$-0.0799255\pi$
$492$	−14.8666	−	14.8375i	−0.670239	−	0.668928i
$493$	−34.4109	−	19.8672i	−1.54979	−	0.894772i
$494$	8.77931	+	3.82750i	0.395000	+	0.172207i
$495$	−1.10841	+	50.1724i	−0.0498192	+	2.25508i
$496$	0.532343	+	22.1343i	0.0239029	+	0.993860i
$497$	3.05808	+	5.29675i	0.137174	+	0.237592i
$498$	−0.102770	+	20.4203i	−0.00460523	+	0.915053i
$499$	−20.8469	−	36.1079i	−0.933236	−	1.61641i	−0.777750	−	0.628573i	$-0.783639\pi$
$499$	−20.8469	−	36.1079i	−0.933236	−	1.61641i	−0.155485	−	0.987838i	$-0.549694\pi$
$500$	−14.7644	+	8.76259i	−0.660285	+	0.391875i
$501$	−3.10352	−	12.1162i	−0.138655	−	0.541312i
$502$	14.5522	−	14.7282i	0.649494	−	0.657350i
$503$	5.86829	+	10.1642i	0.261654	+	0.453198i	0.966682	−	0.255982i	$-0.0823987\pi$
$503$	5.86829	+	10.1642i	0.261654	+	0.453198i	−0.705027	+	0.709180i	$0.749065\pi$
$504$	10.6461	+	2.89892i	0.474215	+	0.129128i
$505$	13.8061	+	7.97094i	0.614362	+	0.354702i
$506$	21.2871	+	21.0327i	0.946329	+	0.935019i
$507$	−12.4058	+	18.7909i	−0.550961	+	0.834531i
$508$	0.119364	+	9.92753i	0.00529593	+	0.440463i
$509$	29.8048			1.32107			0.660537	−	0.750794i	$-0.270329\pi$
$509$	29.8048			1.32107			0.660537	+	0.750794i	$0.270329\pi$
$510$	−0.172411	+	34.2578i	−0.00763448	+	1.51696i
$511$	7.54648			0.333837
$512$	16.8418	+	15.1114i	0.744310	+	0.667834i
$513$	−9.33841	−	2.83693i	−0.412301	−	0.125254i
$514$	−7.58015	+	2.08001i	−0.334346	+	0.0917455i
$515$	−3.89313	+	6.74310i	−0.171552	+	0.297136i
$516$	−20.7735	−	20.7329i	−0.914502	−	0.912714i
$517$			17.2231i			0.757470i
$518$	6.87207	+	1.79716i	0.301941	+	0.0789626i
$519$	−3.97663	−	15.5248i	−0.174555	−	0.681465i
$520$	−26.1498	+	3.27252i	−1.14675	+	0.143510i
$521$	12.9981			0.569457			0.284729	−	0.958608i	$-0.408097\pi$
$521$	12.9981			0.569457			0.284729	+	0.958608i	$0.408097\pi$
$522$	−8.54452	+	29.9538i	−0.373983	+	1.31104i
$523$	−14.6589	−	8.46331i	−0.640988	−	0.370075i	0.144007	−	0.989577i	$-0.454001\pi$
$523$	−14.6589	−	8.46331i	−0.640988	−	0.370075i	−0.784995	+	0.619502i	$0.787335\pi$
$524$	4.63885	−	8.26258i	0.202649	−	0.360952i
$525$	−3.63971	−	1.01847i	−0.158850	−	0.0444497i
$526$	19.7955	+	19.5589i	0.863126	+	0.852811i
$527$	25.9433	+	14.9784i	1.13011	+	0.652467i
$528$	43.1654	−	12.1698i	1.87853	−	0.529622i
$529$	−12.3144			−0.535410
$530$	1.99292	−	2.01703i	0.0865671	−	0.0876142i
$531$	−0.534699	+	24.2033i	−0.0232040	+	1.05034i
$532$	2.39136	−	4.25941i	0.103679	−	0.184669i
$533$	−7.87010	−	20.3959i	−0.340892	−	0.883446i
$534$	−23.4253	−	0.117894i	−1.01371	−	0.00510175i
$535$			7.82013i			0.338094i
$536$	25.6859	−	26.6295i	1.10946	−	1.15022i
$537$	−15.2004	−	4.25341i	−0.655946	−	0.183548i
$538$	25.0517	−	25.3547i	1.08006	−	1.09312i
$539$	−17.1837	−	29.7630i	−0.740153	−	1.28198i
$540$	26.0817	−	6.40169i	1.12238	−	0.275485i
$541$	−36.1291			−1.55331			−0.776655	−	0.629927i	$-0.783085\pi$
$541$	−36.1291			−1.55331			−0.776655	+	0.629927i	$0.783085\pi$
$542$	40.5439	+	10.6029i	1.74151	+	0.455433i
$543$	−3.13675	−	12.2459i	−0.134611	−	0.525523i
$544$	29.3205	−	8.80895i	1.25711	−	0.377681i
$545$	−24.8593	−	43.0576i	−1.06486	−	1.84439i
$546$	8.90114	+	7.25661i	0.380934	+	0.310554i
$547$	8.53773	+	4.92926i	0.365047	+	0.210760i	0.671292	−	0.741193i	$-0.265739\pi$
$547$	8.53773	+	4.92926i	0.365047	+	0.210760i	−0.306245	+	0.951953i	$0.599073\pi$
$548$	6.77228	+	11.4109i	0.289298	+	0.487448i
$549$	−17.4276	−	31.7867i	−0.743790	−	1.35662i
$550$	−14.8147	+	4.06520i	−0.631702	+	0.173341i
$551$	11.9425	+	6.89498i	0.508766	+	0.293736i
$552$	7.90994	−	13.9243i	0.336670	−	0.592658i
$553$	−7.81165	−	4.51006i	−0.332185	−	0.191787i
$554$	−4.70988	−	17.1641i	−0.200104	−	0.729233i
$555$	16.7482	−	4.29000i	0.710923	−	0.182100i
$556$	10.0451	−	0.120778i	0.426008	−	0.00512212i
$557$	−5.79247	+	10.0329i	−0.245435	+	0.425106i	−0.962254	−	0.272154i	$-0.912264\pi$
$557$	−5.79247	+	10.0329i	−0.245435	+	0.425106i	0.716819	+	0.697259i	$0.245597\pi$
$558$	6.44193	−	22.5829i	0.272709	−	0.956012i
$559$	−10.9971	−	28.4998i	−0.465127	−	1.20541i
$560$	0.323179	+	13.4375i	0.0136568	+	0.567837i
$561$	16.3515	−	58.4355i	0.690362	−	2.46715i
$562$	−6.79451	−	1.77688i	−0.286609	−	0.0749530i
$563$	25.4510	+	14.6941i	1.07263	+	0.619284i	0.928899	−	0.370333i	$-0.120756\pi$
$563$	25.4510	+	14.6941i	1.07263	+	0.619284i	0.143732	+	0.989617i	$0.454090\pi$
$564$	8.90036	−	2.39418i	0.374773	−	0.100813i
$565$	21.3773			0.899351
$566$	5.88064	+	21.4307i	0.247182	+	0.900798i
$567$	−9.86683	−	6.29341i	−0.414368	−	0.264298i
$568$	3.21092	−	12.9102i	0.134727	−	0.541701i
$569$	−0.441484	−	0.764674i	−0.0185080	−	0.0320568i	0.856623	−	0.515943i	$-0.172558\pi$
$569$	−0.441484	−	0.764674i	−0.0185080	−	0.0320568i	−0.875131	+	0.483886i	$0.839225\pi$
$570$	0.0598359	−	11.8893i	0.00250625	−	0.497988i
$571$	−11.2871	+	6.51659i	−0.472349	+	0.272711i	−0.717223	−	0.696844i	$-0.754587\pi$
$571$	−11.2871	+	6.51659i	−0.472349	+	0.272711i	0.244873	+	0.969555i	$0.421254\pi$
$572$	46.2008	+	6.66688i	1.93175	+	0.278756i
$573$	5.33932	−	1.36765i	0.223053	−	0.0571343i
$574$	−10.7527	+	2.95058i	−0.448811	+	0.123155i
$575$	−2.74276	+	4.75060i	−0.114381	+	0.198114i
$576$	−12.2894	−	20.6148i	−0.512058	−	0.858951i
$577$			13.7113i			0.570809i	0.958407	+	0.285404i	$0.0921279\pi$
$577$			13.7113i			0.570809i	−0.958407	+	0.285404i	$0.907872\pi$
$578$	4.39758	−	16.8157i	0.182915	−	0.699441i
$579$	6.29108	+	24.5605i	0.261449	+	1.02070i
$580$	−37.9427	+	0.456206i	−1.57549	+	0.0189429i
$581$	9.38811	+	5.42023i	0.389484	+	0.224869i
$582$	−0.591007	−	1.03566i	−0.0244980	−	0.0429293i
$583$	−4.34955	+	2.51121i	−0.180140	+	0.104004i
$584$	−11.8144	−	11.3957i	−0.488882	−	0.471559i
$585$	27.5136	+	4.93346i	1.13755	+	0.203974i
$586$	2.38407	−	9.11633i	0.0984850	−	0.376592i
$587$	−22.3897	−	38.7800i	−0.924120	−	1.60062i	−0.792970	−	0.609261i	$-0.791466\pi$
$587$	−22.3897	−	38.7800i	−0.924120	−	1.60062i	−0.131150	−	0.991363i	$-0.541867\pi$
$588$	−12.9919	+	13.0174i	−0.535777	+	0.536827i
$589$	−9.00372	−	5.19830i	−0.370992	−	0.214192i
$590$	−28.4405	+	7.80415i	−1.17088	+	0.321292i
$591$	−6.98611	+	24.9663i	−0.287370	+	1.02698i
$592$	−8.04470	−	13.1909i	−0.330635	−	0.542141i
$593$		−	41.8951i		−	1.72043i	−0.509934	−	0.860214i	$-0.670330\pi$
$593$		−	41.8951i		−	1.72043i	0.509934	−	0.860214i	$-0.329670\pi$
$594$	−47.5511	−	1.28995i	−1.95104	−	0.0529274i
$595$	15.7498	+	9.09318i	0.645681	+	0.372784i
$596$	−0.0688503	−	5.72629i	−0.00282022	−	0.234558i
$597$	5.54952	+	5.67348i	0.227127	+	0.232200i
$598$	13.4084	−	9.90153i	0.548309	−	0.404904i
$599$	5.56381	+	9.63680i	0.227331	+	0.393749i	0.957016	−	0.290034i	$-0.0936667\pi$
$599$	5.56381	+	9.63680i	0.227331	+	0.393749i	−0.729685	+	0.683783i	$0.760333\pi$
$600$	4.16017	+	7.09069i	0.169838	+	0.289476i
$601$	3.21521	+	5.56890i	0.131151	+	0.227160i	0.924121	−	0.382101i	$-0.124799\pi$
$601$	3.21521	+	5.56890i	0.131151	+	0.227160i	−0.792970	+	0.609261i	$0.791466\pi$
$602$	−15.0251	+	4.12292i	−0.612376	+	0.168038i
$603$	−34.4105	+	18.8661i	−1.40130	+	0.768286i
$604$	−26.8344	+	0.322645i	−1.09188	+	0.0131282i
$605$	79.8600			3.24677
$606$	−7.62118	+	13.0482i	−0.309589	+	0.530046i
$607$	6.44187	−	11.1576i	0.261467	−	0.452875i	−0.705165	−	0.709044i	$-0.749127\pi$
$607$	6.44187	−	11.1576i	0.261467	−	0.452875i	0.966632	+	0.256169i	$0.0824603\pi$
$608$	−10.1758	+	3.05718i	−0.412684	+	0.123985i
$609$	11.5626	+	11.8209i	0.468540	+	0.479006i
$610$	31.0382	−	31.4136i	1.25670	−	1.27190i
$611$	9.47759	+	1.48417i	0.383422	+	0.0600430i
$612$	−32.4707	−	0.326842i	−1.31255	−	0.0132118i
$613$	−6.92597	+	11.9961i	−0.279737	+	0.484519i	−0.971319	−	0.237779i	$-0.923581\pi$
$613$	−6.92597	+	11.9961i	−0.279737	+	0.484519i	0.691582	+	0.722298i	$0.256914\pi$
$614$	7.11923	−	1.95354i	0.287309	−	0.0788383i
$615$	−19.4012	+	18.9773i	−0.782331	+	0.765238i
$616$	5.74628	−	23.1042i	0.231524	−	0.930897i
$617$	26.0075	+	15.0155i	1.04702	+	0.604500i	0.921815	−	0.387631i	$-0.126706\pi$
$617$	26.0075	+	15.0155i	1.04702	+	0.604500i	0.125209	+	0.992130i	$0.460040\pi$
$618$	−6.37293	−	3.72230i	−0.256357	−	0.149733i
$619$	−10.4182	+	18.0449i	−0.418744	+	0.725285i	−0.995813	−	0.0914096i	$-0.970863\pi$
$619$	−10.4182	+	18.0449i	−0.418744	+	0.725285i	0.577070	+	0.816695i	$0.304196\pi$
$620$	28.6060	−	0.343945i	1.14884	−	0.0138132i
$621$	−12.4019	+	11.6062i	−0.497671	+	0.465739i
$622$	−4.24209	−	4.19140i	−0.170092	−	0.168060i
$623$	−6.21787	+	10.7697i	−0.249114	+	0.431477i
$624$	−2.97715	−	24.8019i	−0.119181	−	0.992873i
$625$	15.2872	+	26.4783i	0.611490	+	1.05913i
$626$	11.3415	−	43.3683i	0.453298	−	1.73335i
$627$	−5.67487	+	20.2803i	−0.226632	+	0.809916i
$628$	11.5986	−	20.6591i	0.462836	−	0.824389i
$629$	−20.9047			−0.833524
$630$	3.91082	−	13.7098i	0.155811	−	0.546213i
$631$	−18.8407	+	10.8777i	−0.750038	+	0.433035i	−0.825708	−	0.564098i	$-0.809224\pi$
$631$	−18.8407	+	10.8777i	−0.750038	+	0.433035i	0.0756698	+	0.997133i	$0.475891\pi$
$632$	5.41899	+	18.8569i	0.215556	+	0.750087i
$633$	−2.43243	−	9.49624i	−0.0966804	−	0.377442i
$634$	−11.5022	+	43.9829i	−0.456812	+	1.74678i
$635$	12.8283			0.509076
$636$	1.90235	+	1.89863i	0.0754331	+	0.0752856i
$637$	−17.8589	+	6.89114i	−0.707595	+	0.273037i
$638$	65.0244	+	17.0050i	2.57434	+	0.673233i
$639$	−7.32345	+	12.0613i	−0.289711	+	0.477137i
$640$	19.7856	−	21.5250i	0.782096	−	0.850851i
$641$	−21.9343			−0.866354			−0.433177	−	0.901309i	$-0.642607\pi$
$641$	−21.9343			−0.866354			−0.433177	+	0.901309i	$0.642607\pi$
$642$	−7.41237	−	0.0373046i	−0.292543	−	0.00147230i
$643$	−11.7764	+	20.3972i	−0.464414	+	0.804389i	−0.999175	−	0.0406148i	$-0.987068\pi$
$643$	−11.7764	+	20.3972i	−0.464414	+	0.804389i	0.534761	+	0.845003i	$0.320402\pi$
$644$	−4.33886	−	7.31071i	−0.170975	−	0.288082i
$645$	−27.1097	+	26.5175i	−1.06745	+	1.04412i
$646$	−3.63723	+	13.9082i	−0.143105	+	0.547212i
$647$	13.4046	−	23.2174i	0.526988	−	0.912769i	−0.472518	−	0.881321i	$-0.656655\pi$
$647$	13.4046	−	23.2174i	0.526988	−	0.912769i	0.999505	−	0.0314481i	$-0.0100119\pi$
$648$	5.94348	+	24.7523i	0.233482	+	0.972361i
$649$	52.2376			2.05051
$650$	0.960385	+	8.50262i	0.0376694	+	0.333500i
$651$	−8.71734	−	8.91205i	−0.341659	−	0.349291i
$652$	29.2040	+	16.3960i	1.14372	+	0.642116i
$653$			9.78185i			0.382794i	0.981513	+	0.191397i	$0.0613017\pi$
$653$			9.78185i			0.382794i	−0.981513	+	0.191397i	$0.938698\pi$
$654$	40.9311	−	23.3577i	1.60053	−	0.913359i
$655$	−10.6033	−	6.12179i	−0.414303	−	0.239198i
$656$	21.2895	+	11.6182i	0.831216	+	0.453613i
$657$	8.37007	+	15.2665i	0.326547	+	0.595601i
$658$	1.23792	−	4.73362i	0.0482592	−	0.184536i
$659$		−	12.2056i		−	0.475462i	−0.971331	−	0.237731i	$-0.923596\pi$
$659$		−	12.2056i		−	0.475462i	0.971331	−	0.237731i	$-0.0764036\pi$
$660$	−15.0529	−	55.9590i	−0.585933	−	2.17820i
$661$	6.02514			0.234351			0.117175	−	0.993111i	$-0.462616\pi$
$661$	6.02514			0.234351			0.117175	+	0.993111i	$0.462616\pi$
$662$	11.8355	−	3.24771i	0.460002	−	0.126226i
$663$	−30.7471	−	14.0336i	−1.19412	−	0.545019i
$664$	−6.51258	−	22.6624i	−0.252737	−	0.879470i
$665$	−5.46605	−	3.15582i	−0.211964	−	0.122378i
$666$	3.98642	+	15.8954i	0.154471	+	0.615935i
$667$	20.7842	−	11.9998i	0.804767	−	0.464632i
$668$	7.37098	+	12.4196i	0.285192	+	0.480531i
$669$	−34.9460	+	34.1825i	−1.35109	+	1.32157i
$670$	−34.0065	−	33.6001i	−1.31379	−	1.29808i
$671$	−67.7407	+	39.1101i	−2.61510	+	1.50983i
$672$	−12.7384	+	0.242227i	−0.491393	+	0.00934409i
$673$	−7.07909	−	12.2613i	−0.272879	−	0.472640i	0.696719	−	0.717344i	$-0.254643\pi$
$673$	−7.07909	−	12.2613i	−0.272879	−	0.472640i	−0.969598	+	0.244704i	$0.921309\pi$
$674$	−8.43564	−	8.33482i	−0.324929	−	0.321045i
$675$	−1.97657	−	8.49271i	−0.0760783	−	0.326885i
$676$	7.64996	−	24.8491i	0.294229	−	0.955735i
$677$	0.702181	+	0.405404i	0.0269870	+	0.0155810i	0.513433	−	0.858130i	$-0.328374\pi$
$677$	0.702181	+	0.405404i	0.0269870	+	0.0155810i	−0.486446	+	0.873711i	$0.661707\pi$
$678$	−0.101977	+	20.2627i	−0.00391640	+	0.778183i
$679$	−0.633011			−0.0242927
$680$	−10.9258	−	38.0192i	−0.418983	−	1.45797i
$681$	−50.0452	+	12.8189i	−1.91774	+	0.491221i
$682$	−49.0236	−	12.8205i	−1.87721	−	0.490921i
$683$	−4.48198	−	7.76302i	−0.171498	−	0.297044i	0.767446	−	0.641114i	$-0.221527\pi$
$683$	−4.48198	−	7.76302i	−0.171498	−	0.297044i	−0.938944	+	0.344070i	$0.888194\pi$
$684$	11.2691	+	0.113432i	0.430885	+	0.00433718i
$685$	14.8481	−	8.57258i	0.567319	−	0.327542i
$686$	5.98994	+	21.8290i	0.228697	+	0.833436i
$687$	0.878845	+	0.898474i	0.0335300	+	0.0342789i
$688$	29.7484	+	16.2343i	1.13415	+	0.618929i
$689$	1.00707	+	2.60989i	0.0383663	+	0.0994289i
$690$	−17.8674	−	10.4360i	−0.680202	−	0.397292i
$691$	−6.69178	−	11.5905i	−0.254567	−	0.440923i	0.710211	−	0.703989i	$-0.248600\pi$
$691$	−6.69178	−	11.5905i	−0.254567	−	0.440923i	−0.964778	+	0.263066i	$0.915266\pi$
$692$	9.44465	+	15.9137i	0.359032	+	0.604946i
$693$	−13.1061	+	21.5849i	−0.497859	+	0.819944i
$694$	13.0178	+	3.40438i	0.494150	+	0.129228i
$695$		−	12.9802i		−	0.492369i
$696$	−0.251419	−	35.9665i	−0.00953003	−	1.36331i
$697$	28.4187	−	16.4076i	1.07644	−	0.621481i
$698$	−21.4512	−	21.1948i	−0.811939	−	0.802236i
$699$	39.4946	−	10.1164i	1.49382	−	0.382637i
$700$	4.36389	−	0.0524695i	0.164940	−	0.00198316i
$701$			19.5053i			0.736706i	0.929686	+	0.368353i	$0.120078\pi$
$701$			19.5053i			0.736706i	−0.929686	+	0.368353i	$0.879922\pi$
$702$	−4.80747	+	26.0555i	−0.181446	+	0.983401i
$703$	7.25505			0.273630
$704$	−43.8852	+	27.4935i	−1.65399	+	1.03620i
$705$	−2.95504	−	11.5365i	−0.111293	−	0.434491i
$706$	22.4345	−	22.7059i	0.844334	−	0.854547i
$707$	4.01088	+	6.94704i	0.150845	+	0.261270i
$708$	−7.26156	−	26.9948i	−0.272906	−	1.01453i
$709$	42.8061			1.60762			0.803809	−	0.594888i	$-0.202803\pi$
$709$	42.8061			1.60762			0.803809	+	0.594888i	$0.202803\pi$
$710$	−16.6302	−	4.34908i	−0.624122	−	0.163218i
$711$	0.459627	−	20.8052i	0.0172374	−	0.780255i
$712$	25.9973	−	7.47097i	0.974292	−	0.279986i
$713$	−15.6697	+	9.04691i	−0.586835	+	0.338810i
$714$	−8.69418	+	14.8852i	−0.325371	+	0.557066i
$715$	9.33137	−	59.5883i	0.348974	−	2.22848i
$716$	18.2248	−	0.219127i	0.681093	−	0.00818915i
$717$	−21.4615	+	20.9926i	−0.801494	+	0.783983i
$718$	−9.42541	−	34.3488i	−0.351753	−	1.28189i
$719$	0.336249	+	0.582400i	0.0125400	+	0.0217199i	0.872227	−	0.489101i	$-0.162675\pi$
$719$	0.336249	+	0.582400i	0.0125400	+	0.0217199i	−0.859687	+	0.510821i	$0.829342\pi$
$720$	−26.8254	+	15.5578i	−0.999724	+	0.579803i
$721$	−3.39304	+	1.95897i	−0.126364	+	0.0729560i
$722$	−5.53602	+	21.1689i	−0.206029	+	0.787825i
$723$	9.06417	+	35.3867i	0.337100	+	1.31604i
$724$	7.44990	+	12.5526i	0.276873	+	0.466514i
$725$			12.3203i			0.457566i
$726$	−0.380959	+	75.6960i	−0.0141387	+	2.80934i
$727$	−21.3458	+	36.9720i	−0.791672	+	1.37122i	0.133259	+	0.991081i	$0.457456\pi$
$727$	−21.3458	+	36.9720i	−0.791672	+	1.37122i	−0.924931	+	0.380135i	$0.875877\pi$
$728$	−12.2187	−	5.15306i	−0.452857	−	0.190985i
$729$	1.78785	−	26.9407i	0.0662166	−	0.997805i
$730$	−14.9069	+	15.0872i	−0.551730	+	0.558404i
$731$	39.7102	−	22.9267i	1.46874	−	0.847975i
$732$	29.6276	+	29.5696i	1.09507	+	1.09292i
$733$	−13.0642	−	22.6279i	−0.482539	−	0.835782i	0.517260	−	0.855828i	$-0.326952\pi$
$733$	−13.0642	−	22.6279i	−0.482539	−	0.835782i	−0.999799	+	0.0200466i	$0.993619\pi$
$734$	−19.3623	−	19.1309i	−0.714674	−	0.706133i
$735$	16.6167	+	16.9879i	0.612916	+	0.626606i
$736$	−4.24702	+	17.9972i	−0.156547	+	0.663387i
$737$	42.3383	+	73.3321i	1.55955	+	2.70122i
$738$	−17.8952	−	18.4801i	−0.658733	−	0.680261i
$739$	23.7722	−	41.1747i	0.874476	−	1.51464i	0.0171552	−	0.999853i	$-0.494539\pi$
$739$	23.7722	−	41.1747i	0.874476	−	1.51464i	0.857320	−	0.514783i	$-0.172128\pi$
$740$	−17.1677	+	10.1889i	−0.631096	+	0.374552i
$741$	10.6709	+	4.87041i	0.392006	+	0.178919i
$742$	1.37593	−	0.377560i	0.0505122	−	0.0138607i
$743$		−	33.3375i		−	1.22303i	−0.791231	−	0.611517i	$-0.790560\pi$
$743$		−	33.3375i		−	1.22303i	0.791231	−	0.611517i	$-0.209440\pi$
$744$	0.189551	+	27.1161i	0.00694929	+	0.994123i
$745$	−7.39948			−0.271096
$746$	3.45751	+	0.904197i	0.126589	+	0.0331050i
$747$	−0.552383	+	25.0038i	−0.0202107	+	0.914842i
$748$	0.842397	+	70.0623i	0.0308011	+	2.56173i
$749$	−1.96750	+	3.40780i	−0.0718907	+	0.124518i
$750$	−18.2631	+	10.4220i	−0.666872	+	0.380557i
$751$	−34.0494			−1.24248			−0.621241	−	0.783620i	$-0.713371\pi$
$751$	−34.0494			−1.24248			−0.621241	+	0.783620i	$0.713371\pi$
$752$	−9.08614	+	5.54136i	−0.331338	+	0.202073i
$753$	18.1277	−	17.7317i	0.660611	−	0.646178i
$754$	14.9609	−	34.3166i	0.544845	−	1.24974i
$755$			34.6753i			1.26196i
$756$	12.9763	+	3.77230i	0.471944	+	0.137197i
$757$	−8.06852	−	4.65836i	−0.293255	−	0.169311i	0.346154	−	0.938178i	$-0.387488\pi$
$757$	−8.06852	−	4.65836i	−0.293255	−	0.169311i	−0.639409	+	0.768867i	$0.720821\pi$
$758$	0.677373	−	2.59017i	0.0246033	−	0.0940793i
$759$	25.6282	+	26.2006i	0.930244	+	0.951022i
$760$	3.79183	+	13.1947i	0.137544	+	0.478623i
$761$	−11.1285	−	6.42502i	−0.403406	−	0.232907i	0.284546	−	0.958662i	$-0.408157\pi$
$761$	−11.1285	−	6.42502i	−0.403406	−	0.232907i	−0.687953	+	0.725756i	$0.741490\pi$
$762$	−0.0611953	+	12.1594i	−0.00221687	+	0.440489i
$763$		−	25.0178i		−	0.905705i
$764$	−5.47304	+	3.24821i	−0.198008	+	0.117516i
$765$	−0.926699	+	41.9473i	−0.0335049	+	1.51661i
$766$	−13.3960	−	3.50327i	−0.484017	−	0.126578i
$767$	4.50148	−	28.7456i	0.162539	−	1.03794i
$768$	20.3083	+	18.8567i	0.732812	+	0.680431i
$769$		−	4.93866i		−	0.178093i	−0.996027	−	0.0890463i	$-0.971618\pi$
$769$		−	4.93866i		−	0.178093i	0.996027	−	0.0890463i	$-0.0283819\pi$
$770$	−29.7616	−	7.78315i	−1.07253	−	0.280485i
$771$	−9.32585	+	2.38878i	−0.335862	+	0.0860299i
$772$	−14.9416	−	25.1756i	−0.537758	−	0.906089i
$773$	−14.8833	−	25.7786i	−0.535315	−	0.927193i	−0.999148	−	0.0412705i	$-0.986859\pi$
$773$	−14.8833	−	25.7786i	−0.535315	−	0.927193i	0.463833	−	0.885923i	$-0.346474\pi$
$774$	−25.0055	−	25.8227i	−0.898803	−	0.928178i
$775$		−	9.28861i		−	0.333657i
$776$	0.991009	+	0.955894i	0.0355751	+	0.0343146i
$777$	8.37777	+	2.34428i	0.300551	+	0.0841007i
$778$	−15.8575	−	4.14700i	−0.568519	−	0.148677i
$779$	−9.86284	+	5.69432i	−0.353373	+	0.204020i
$780$	−32.0906	+	3.46121i	−1.14903	+	0.123931i
$781$	26.3679	+	15.2235i	0.943519	+	0.544741i
$782$	17.7974	+	17.5847i	0.636433	+	0.628827i
$783$	−11.0890	+	36.5020i	−0.396289	+	1.30447i
$784$	10.1730	−	18.6413i	0.363321	−	0.665761i
$785$	−26.5116	−	15.3065i	−0.946239	−	0.546311i
$786$	5.85317	−	10.0212i	0.208776	−	0.357444i
$787$	−10.7851	+	18.6803i	−0.384447	+	0.665882i	−0.991692	−	0.128632i	$-0.958941\pi$
$787$	−10.7851	+	18.6803i	−0.384447	+	0.665882i	0.607245	+	0.794515i	$0.292275\pi$
$788$	−0.359910	−	29.9338i	−0.0128213	−	1.06635i
$789$	23.8324	+	24.3647i	0.848456	+	0.867407i
$790$	24.4474	−	6.70844i	0.869801	−	0.238676i
$791$	9.31567	+	5.37840i	0.331227	+	0.191234i
$792$	53.1131	−	14.0011i	1.88729	−	0.497507i
$793$	15.6843	+	40.6469i	0.556965	+	1.44341i
$794$	25.8713	+	25.5621i	0.918139	+	0.907167i
$795$	2.48260	−	2.42836i	0.0880487	−	0.0861250i
$796$	−7.99086	−	4.48630i	−0.283229	−	0.159013i
$797$	−47.5546	−	27.4556i	−1.68447	−	0.972529i	−0.958626	−	0.284668i	$-0.908117\pi$
$797$	−47.5546	−	27.4556i	−1.68447	−	0.972529i	−0.725843	−	0.687861i	$-0.758550\pi$
$798$	3.01735	−	5.16599i	0.106813	−	0.182874i
$799$			14.3996i			0.509420i
$800$	−6.91112	−	6.50766i	−0.244345	−	0.230081i
$801$	−28.6834	−	0.633672i	−1.01348	−	0.0223897i
$802$	−2.68908	−	9.79976i	−0.0949547	−	0.346041i
$803$	32.5343	−	18.7837i	1.14811	−	0.662863i
$804$	32.0104	−	32.0731i	1.12892	−	1.13113i
$805$	−9.51289	+	5.49227i	−0.335285	+	0.193577i
$806$	−11.2794	+	25.8721i	−0.397301	+	0.911307i
$807$	31.2071	−	30.5253i	1.09854	−	1.07454i
$808$	4.21133	−	16.9326i	0.148154	−	0.595688i
$809$	15.5586	−	26.9483i	0.547011	−	0.947451i	−0.451466	−	0.892288i	$-0.649099\pi$
$809$	15.5586	−	26.9483i	0.547011	−	0.947451i	0.998477	−	0.0551626i	$-0.0175677\pi$
$810$	32.0725	−	7.29451i	1.12691	−	0.256303i
$811$	2.10641			0.0739661			0.0369830	−	0.999316i	$-0.488225\pi$
$811$	2.10641			0.0739661			0.0369830	+	0.999316i	$0.488225\pi$
$812$	−16.6492	−	9.34735i	−0.584273	−	0.328028i
$813$	49.4273	+	13.8308i	1.73349	+	0.485068i
$814$	34.1001	−	9.35715i	1.19521	−	0.327968i
$815$	21.6374	−	37.4771i	0.757926	−	1.31277i
$816$	36.0890	−	10.1747i	1.26337	−	0.356186i
$817$	−13.7816	+	7.95681i	−0.482157	+	0.278374i
$818$	−36.7603	−	9.61342i	−1.28529	−	0.336125i
$819$	10.7485	+	9.07213i	0.375582	+	0.317006i
$820$	15.3415	−	27.3257i	0.535748	−	0.954256i
$821$	−18.1541	−	31.4438i	−0.633581	−	1.09740i	−0.986814	−	0.161859i	$-0.948251\pi$
$821$	−18.1541	−	31.4438i	−0.633581	−	1.09740i	0.353232	−	0.935536i	$-0.385082\pi$
$822$	8.05476	+	14.1148i	0.280942	+	0.492311i
$823$	15.1901	−	26.3101i	0.529495	−	0.917112i	−0.469914	−	0.882712i	$-0.655715\pi$
$823$	15.1901	−	26.3101i	0.529495	−	0.917112i	0.999408	−	0.0343992i	$-0.0109518\pi$
$824$	8.27017	+	2.05688i	0.288105	+	0.0716548i
$825$	−18.2265	+	4.66866i	−0.634566	+	0.162542i
$826$	−14.3571	−	3.75461i	−0.499547	−	0.130640i
$827$	18.2942			0.636153			0.318076	−	0.948065i	$-0.396963\pi$
$827$	18.2942			0.636153			0.318076	+	0.948065i	$0.396963\pi$
$828$	9.97710	−	16.8860i	0.346728	−	0.586830i
$829$	−30.0649	−	17.3580i	−1.04420	−	0.602868i	−0.123179	−	0.992384i	$-0.539309\pi$
$829$	−30.0649	−	17.3580i	−1.04420	−	0.602868i	−0.921020	+	0.389516i	$0.872642\pi$
$830$	−29.3811	+	8.06226i	−1.01983	+	0.279845i
$831$	−5.40904	−	21.1170i	−0.187638	−	0.732540i
$832$	11.3475	+	26.5186i	0.393404	+	0.919365i
$833$	−14.3666	−	24.8837i	−0.497774	−	0.862170i
$834$	12.3034	+	0.0619201i	0.426033	+	0.00214412i
$835$	16.1608	−	9.33044i	0.559267	−	0.322893i
$836$	−0.292357	−	24.3154i	−0.0101114	−	0.840966i
$837$	8.36028	−	27.5198i	0.288973	−	0.951222i
$838$	−6.86616	−	25.0222i	−0.237188	−	0.864377i
$839$			36.4884i			1.25972i	0.776709	+	0.629859i	$0.216887\pi$
$839$			36.4884i			1.25972i	−0.776709	+	0.629859i	$0.783113\pi$
$840$	0.115074	+	16.4618i	0.00397044	+	0.567987i
$841$	12.4511	−	21.5660i	0.429349	−	0.743654i
$842$	6.44497	−	24.6446i	0.222108	−	0.849310i
$843$	−8.28322	−	2.31783i	−0.285289	−	0.0798302i
$844$	5.77711	+	9.73407i	0.198856	+	0.335061i
$845$	−31.9864	−	10.2698i	−1.10037	−	0.353293i
$846$	10.9491	−	2.74593i	0.376438	−	0.0944070i
$847$	34.8009	+	20.0923i	1.19577	+	0.690379i
$848$	−2.72423	−	1.48667i	−0.0935506	−	0.0510526i
$849$	6.75359	+	26.3661i	0.231783	+	0.904883i
$850$	−12.3860	+	3.39876i	−0.424838	+	0.116577i
$851$	6.31320	−	10.9348i	0.216414	−	0.374840i
$852$	4.20165	−	15.7424i	0.143946	−	0.539325i
$853$	9.39257	−	16.2684i	0.321595	−	0.557020i	−0.659222	−	0.751948i	$-0.729114\pi$
$853$	9.39257	−	16.2684i	0.321595	−	0.557020i	0.980817	+	0.194929i	$0.0624476\pi$
$854$	21.4291	−	5.88019i	0.733287	−	0.201216i
$855$	0.321615	−	14.5580i	0.0109990	−	0.497873i
$856$	8.22624	−	2.36401i	0.281167	−	0.0808002i
$857$	−5.27092	+	9.12950i	−0.180051	+	0.311858i	−0.941898	−	0.335900i	$-0.890960\pi$
$857$	−5.27092	+	9.12950i	−0.180051	+	0.311858i	0.761847	+	0.647758i	$0.224293\pi$
$858$	56.4367	+	9.12908i	1.92672	+	0.311662i
$859$	7.73474	−	4.46566i	0.263906	−	0.152366i	−0.362209	−	0.932097i	$-0.617977\pi$
$859$	7.73474	−	4.46566i	0.263906	−	0.152366i	0.626115	+	0.779731i	$0.284644\pi$
$860$	21.4370	−	38.1830i	0.730997	−	1.30203i
$861$	−13.2291	+	3.38858i	−0.450846	+	0.115483i
$862$	16.9420	+	4.43060i	0.577046	+	0.150907i
$863$		−	30.7552i		−	1.04692i	−0.852051	−	0.523459i	$-0.824641\pi$
$863$		−	30.7552i		−	1.04692i	0.852051	−	0.523459i	$-0.175359\pi$
$864$	−14.6186	−	25.5009i	−0.497334	−	0.867559i
$865$	20.7073	−	11.9554i	0.704069	−	0.406494i
$866$	36.7756	+	36.3361i	1.24969	+	1.23475i
$867$	5.73638	−	20.5001i	0.194818	−	0.696220i
$868$	12.5523	+	7.04720i	0.426051	+	0.239198i
$869$	−44.9034			−1.52324
$870$	−46.4729	−	0.233887i	−1.57558	−	0.00792950i
$871$	44.0020	−	16.9789i	1.49095	−	0.575307i
$872$	−37.7787	+	39.1666i	−1.27935	+	1.32635i
$873$	−0.702095	−	1.28057i	−0.0237623	−	0.0433409i
$874$	−6.17666	−	6.10284i	−0.208929	−	0.206432i
$875$			11.1627i			0.377368i
$876$	−14.2295	−	14.2016i	−0.480769	−	0.479829i
$877$	−15.6560	+	27.1170i	−0.528666	+	0.915676i	0.470776	+	0.882253i	$0.343974\pi$
$877$	−15.6560	+	27.1170i	−0.528666	+	0.915676i	−0.999441	+	0.0334226i	$0.989359\pi$
$878$	38.1811	+	37.7248i	1.28855	+	1.27315i
$879$	3.10987	−	11.1138i	0.104893	−	0.374858i
$880$	34.8401	+	57.1271i	1.17446	+	1.92575i
$881$	−10.5496	+	18.2724i	−0.355424	+	0.615612i	−0.987190	−	0.159547i	$-0.948997\pi$
$881$	−10.5496	+	18.2724i	−0.355424	+	0.615612i	0.631767	+	0.775159i	$0.282330\pi$
$882$	−16.1813	+	15.6692i	−0.544854	+	0.527611i
$883$			30.1532i			1.01474i	0.861729	+	0.507369i	$0.169382\pi$
$883$			30.1532i			1.01474i	−0.861729	+	0.507369i	$0.830618\pi$
$884$	38.6268	+	5.57394i	1.29916	+	0.187472i
$885$	−34.9903	+	8.96265i	−1.17619	+	0.301276i
$886$	14.9421	+	3.90759i	0.501988	+	0.131278i
$887$	−6.19457			−0.207993			−0.103997	−	0.994578i	$-0.533163\pi$
$887$	−6.19457			−0.207993			−0.103997	+	0.994578i	$0.533163\pi$
$888$	−9.57575	−	16.3211i	−0.321341	−	0.547701i
$889$	5.59023	+	3.22752i	0.187490	+	0.108248i
$890$	−9.24870	−	33.7048i	−0.310017	−	1.12979i
$891$	−58.2025	−	2.57287i	−1.94986	−	0.0861945i
$892$	27.6335	−	49.2199i	0.925239	−	1.64801i
$893$		−	4.99743i		−	0.167233i
$894$	0.0352980	−	7.01366i	0.00118054	−	0.234572i
$895$		−	23.5500i		−	0.787190i
$896$	14.0376	−	4.40209i	0.468964	−	0.147063i
$897$	16.6263	−	11.8450i	0.555135	−	0.395493i
$898$	33.7300	−	34.1380i	1.12558	−	1.13920i
$899$	−20.3191	+	35.1938i	−0.677681	+	1.17378i
$900$	4.94629	+	8.76992i	0.164876	+	0.292331i
$901$	−3.63650	+	2.09953i	−0.121149	+	0.0699456i
$902$	−39.0129	+	39.4848i	−1.29899	+	1.31470i
$903$	−18.4853	+	4.73495i	−0.615153	+	0.157569i
$904$	−6.46233	−	22.4875i	−0.214934	−	0.747923i
$905$	16.3338	−	9.43033i	0.542954	−	0.313475i
$906$	−32.8673	−	0.165413i	−1.09194	−	0.00549547i
$907$	−36.3286	+	20.9743i	−1.20627	+	0.696441i	−0.961943	−	0.273252i	$-0.911901\pi$
$907$	−36.3286	+	20.9743i	−1.20627	+	0.696441i	−0.244328	+	0.969693i	$0.578567\pi$
$908$	51.2986	−	30.4454i	1.70240	−	1.01037i
$909$	−9.60519	+	15.8192i	−0.318584	+	0.524689i
$910$	−6.84760	+	15.7067i	−0.226996	+	0.520671i
$911$	−1.92995	+	3.34276i	−0.0639419	+	0.110751i	−0.896224	−	0.443601i	$-0.853701\pi$
$911$	−1.92995	+	3.34276i	−0.0639419	+	0.110751i	0.832282	+	0.554352i	$0.187034\pi$
$912$	−12.5248	+	3.53117i	−0.414738	+	0.116929i
$913$	53.9653			1.78599
$914$	8.18735	−	8.28638i	0.270813	−	0.274089i
$915$	38.6644	−	37.8197i	1.27821	−	1.25028i
$916$	−1.26546	−	0.710469i	−0.0418121	−	0.0234746i
$917$	−3.08041	−	5.33543i	−0.101724	−	0.176191i
$918$	−39.7557	−	1.07848i	−1.31213	−	0.0355952i
$919$	8.49660	+	14.7165i	0.280277	+	0.485454i	0.971453	−	0.237232i	$-0.0762403\pi$
$919$	8.49660	+	14.7165i	0.280277	+	0.485454i	−0.691176	+	0.722687i	$0.742907\pi$
$920$	23.1866	+	5.76676i	0.764440	+	0.190125i
$921$	8.75878	−	2.24353i	0.288612	−	0.0739268i
$922$	18.7274	−	5.13885i	0.616755	−	0.169239i
$923$	10.6495	−	13.1980i	0.350532	−	0.434418i
$924$	7.51930	−	28.1727i	0.247367	−	0.926813i
$925$	3.24093	+	5.61346i	0.106561	+	0.184569i
$926$	23.0969	−	23.3763i	0.759013	−	0.768194i
$927$	−7.72633	−	4.69133i	−0.253766	−	0.154083i
$928$	11.9499	+	39.7753i	0.392275	+	1.30569i
$929$			42.6510i			1.39933i	0.714469	+	0.699667i	$0.246668\pi$
$929$			42.6510i			1.39933i	−0.714469	+	0.699667i	$0.753332\pi$
$930$	35.0371	+	0.176333i	1.14891	+	0.00578219i
$931$	4.98600	+	8.63600i	0.163410	+	0.283034i
$932$	−40.4837	+	24.0268i	−1.32609	+	0.787024i
$933$	−5.10718	−	5.22125i	−0.167201	−	0.170936i
$934$	6.10861	+	22.2615i	0.199880	+	0.728417i
$935$	90.5341			2.96078
$936$	−3.12766	−	30.4338i	−0.102231	−	0.994761i
$937$	−0.0656941			−0.00214613			−0.00107307	−	0.999999i	$-0.500342\pi$
$937$	−0.0656941			−0.00214613			−0.00107307	+	0.999999i	$0.500342\pi$
$938$	−6.36555	−	23.1979i	−0.207843	−	0.757437i
$939$	14.7943	−	52.8705i	0.482794	−	1.72536i
$940$	7.01833	+	11.8255i	0.228913	+	0.385704i
$941$	16.0145	+	27.7380i	0.522058	+	0.904232i	0.999671	+	0.0256610i	$0.00816906\pi$
$941$	16.0145	+	27.7380i	0.522058	+	0.904232i	−0.477612	+	0.878571i	$0.658498\pi$
$942$	14.6348	−	25.0562i	0.476829	−	0.816376i
$943$			19.8203i			0.645438i
$944$	16.8070	+	27.5583i	0.547020	+	0.896946i
$945$	5.07542	−	16.7069i	0.165104	−	0.543476i
$946$	−54.5138	+	55.1732i	−1.77240	+	1.79383i
$947$	−18.2475	−	31.6055i	−0.592963	−	1.02704i	−0.993831	−	0.110906i	$-0.964625\pi$
$947$	−18.2475	−	31.6055i	−0.592963	−	1.02704i	0.400868	−	0.916136i	$-0.368709\pi$
$948$	6.24203	+	23.2047i	0.202732	+	0.753654i
$949$	−7.53280	−	19.5218i	−0.244525	−	0.633705i
$950$	4.29863	−	1.17955i	0.139466	−	0.0382698i
$951$	−15.0040	+	53.6197i	−0.486537	+	1.73874i
$952$	4.80425	−	19.3166i	0.155707	−	0.626055i
$953$	10.8158	+	18.7335i	0.350359	+	0.606839i	0.986312	−	0.164888i	$-0.0527264\pi$
$953$	10.8158	+	18.7335i	0.350359	+	0.606839i	−0.635954	+	0.771727i	$0.719393\pi$
$954$	2.28990	+	2.36474i	0.0741382	+	0.0765612i
$955$	4.11170	+	7.12167i	0.133051	+	0.230452i
$956$	16.9707	−	30.2276i	0.548871	−	0.977632i
$957$	79.2716	+	22.1819i	2.56249	+	0.717040i
$958$	−28.2657	+	28.6076i	−0.913223	+	0.924269i
$959$	8.62723			0.278588
$960$	24.6784	−	25.9455i	0.796493	−	0.837389i
$961$	−0.180905	+	0.313336i	−0.00583563	+	0.0101076i
$962$	−2.21059	−	19.5711i	−0.0712721	−	0.630997i
$963$	−9.07617	−	0.200510i	−0.292475	−	0.00646136i
$964$	−21.5277	−	36.2729i	−0.693362	−	1.16827i
$965$	−32.7592	+	18.9135i	−1.05456	+	0.608848i
$966$	−5.16052	−	9.04308i	−0.166037	−	0.290956i
$967$	20.4923	−	11.8312i	0.658988	−	0.380467i	−0.132903	−	0.991129i	$-0.542430\pi$
$967$	20.4923	−	11.8312i	0.658988	−	0.380467i	0.791891	+	0.610662i	$0.209097\pi$
$968$	−24.1415	−	84.0073i	−0.775939	−	2.70010i
$969$	−4.74455	+	16.9556i	−0.152417	+	0.544692i
$970$	1.25042	−	1.26554i	0.0401485	−	0.0406341i
$971$	29.6885	−	17.1406i	0.952748	−	0.550069i	0.0588143	−	0.998269i	$-0.481268\pi$
$971$	29.6885	−	17.1406i	0.952748	−	0.550069i	0.893933	+	0.448200i	$0.147935\pi$
$972$	6.76117	+	30.4350i	0.216865	+	0.976202i
$973$	3.26575	−	5.65644i	0.104695	−	0.181337i
$974$	−1.77430	+	1.79576i	−0.0568523	+	0.0575400i
$975$	0.998455	+	10.4321i	0.0319761	+	0.334094i
$976$	−42.4277	−	23.1537i	−1.35808	−	0.741133i
$977$		−	16.0453i		−	0.513333i	−0.966500	−	0.256667i	$-0.917376\pi$
$977$		−	16.0453i		−	0.513333i	0.966500	−	0.256667i	$-0.0826242\pi$
$978$	35.4198	+	20.6880i	1.13260	+	0.661529i
$979$			61.9068i			1.97855i
$980$	−23.9267	−	13.4331i	−0.764310	−	0.429106i
$981$	50.6108	−	27.7481i	1.61588	−	0.885930i
$982$	4.12071	+	15.0170i	0.131497	+	0.479212i
$983$	4.87488	+	2.81451i	0.155485	+	0.0897691i	0.575724	−	0.817644i	$-0.304720\pi$
$983$	4.87488	+	2.81451i	0.155485	+	0.0897691i	−0.420239	+	0.907413i	$0.638054\pi$
$984$	25.8278	+	14.6719i	0.823359	+	0.467723i
$985$	−38.6803			−1.23246
$986$	54.3645	+	14.2172i	1.73132	+	0.452769i
$987$	1.61479	−	5.77078i	0.0513994	−	0.183686i
$988$	−13.4056	−	1.93446i	−0.426489	−	0.0615433i
$989$			27.6954i			0.880664i
$990$	−17.2644	−	68.8400i	−0.548699	−	2.18788i
$991$	−1.44165	+	2.49701i	−0.0457955	+	0.0793201i	−0.888015	−	0.459815i	$-0.847916\pi$
$991$	−1.44165	+	2.49701i	−0.0457955	+	0.0793201i	0.842219	+	0.539135i	$0.181249\pi$
$992$	−9.00934	−	29.9876i	−0.286047	−	0.952106i
$993$	14.5613	−	3.72981i	0.462087	−	0.118362i
$994$	−6.15281	−	6.07928i	−0.195155	−	0.192823i
$995$	−5.92048	+	10.2546i	−0.187692	+	0.325092i
$996$	−7.50172	−	27.8876i	−0.237701	−	0.883653i
$997$			26.9566i			0.853724i	0.904317	+	0.426862i	$0.140381\pi$
$997$			26.9566i			0.853724i	−0.904317	+	0.426862i	$0.859619\pi$
$998$	41.9437	+	41.4424i	1.32770	+	1.31184i
$999$	4.54961	+	19.5483i	0.143943	+	0.618480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.bk.c.277.14	✓	320
8.5	even	2	inner	936.2.bk.c.277.42	yes	320
9.4	even	3		936.2.ca.c.589.95	yes	320
13.10	even	6		936.2.ca.c.205.66	yes	320
72.13	even	6		936.2.ca.c.589.66	yes	320
104.101	even	6		936.2.ca.c.205.95	yes	320
117.49	even	6	inner	936.2.bk.c.517.42	yes	320
936.517	even	6	inner	936.2.bk.c.517.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.bk.c.277.14	✓	320	1.1	even	1	trivial
936.2.bk.c.277.42	yes	320	8.5	even	2	inner
936.2.bk.c.517.14	yes	320	936.517	even	6	inner
936.2.bk.c.517.42	yes	320	117.49	even	6	inner
936.2.ca.c.205.66	yes	320	13.10	even	6
936.2.ca.c.205.95	yes	320	104.101	even	6
936.2.ca.c.589.66	yes	320	72.13	even	6
936.2.ca.c.589.95	yes	320	9.4	even	3

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36380 + 0.374231i) q^{2} +(-1.67788 + 0.429783i) q^{3} +(1.71990 - 1.02075i) q^{4} +(-1.29210 - 2.23799i) q^{5} +(2.12746 - 1.21405i) q^{6} -1.30034i q^{7} +(-1.96361 + 2.03574i) q^{8} +(2.63057 - 1.44225i) q^{9} +(2.59969 + 2.56862i) q^{10} +(-3.23663 - 5.60601i) q^{11} +(-2.44709 + 2.45189i) q^{12} +(-3.36381 + 1.29798i) q^{13} +(0.486627 + 1.77340i) q^{14} +(3.12984 + 3.19975i) q^{15} +(1.91613 - 3.51119i) q^{16} +(-2.70603 - 4.68698i) q^{17} +(-3.04784 + 2.95138i) q^{18} +(0.939139 + 1.62664i) q^{19} +(-4.50672 - 2.53020i) q^{20} +(0.558864 + 2.18181i) q^{21} +(6.51206 + 6.43423i) q^{22} +3.26888 q^{23} +(2.41977 - 4.25966i) q^{24} +(-0.839052 + 1.45328i) q^{25} +(4.10183 - 3.02903i) q^{26} +(-3.79393 + 3.55050i) q^{27} +(-1.32732 - 2.23646i) q^{28} +(6.35820 - 3.67091i) q^{29} +(-5.46592 - 3.19254i) q^{30} +(-4.79360 + 2.76759i) q^{31} +(-1.29923 + 5.50563i) q^{32} +(7.84006 + 8.01517i) q^{33} +(5.44449 + 5.37943i) q^{34} +(-2.91014 + 1.68017i) q^{35} +(3.05215 - 5.16569i) q^{36} +(1.93131 - 3.34512i) q^{37} +(-1.88953 - 1.86695i) q^{38} +(5.08623 - 3.62357i) q^{39} +(7.09314 + 1.76414i) q^{40} +6.06334i q^{41} +(-1.57868 - 2.76642i) q^{42} +8.47246i q^{43} +(-11.2890 - 6.33800i) q^{44} +(-6.62670 - 4.02365i) q^{45} +(-4.45810 + 1.22331i) q^{46} +(-2.30419 - 1.33032i) q^{47} +(-1.70599 + 6.71488i) q^{48} +5.30912 q^{49} +(0.600438 - 2.29598i) q^{50} +(6.55478 + 6.70119i) q^{51} +(-4.46052 + 5.66602i) q^{52} -0.775873i q^{53} +(3.84546 - 6.26198i) q^{54} +(-8.36411 + 14.4871i) q^{55} +(2.64715 + 2.55336i) q^{56} +(-2.27486 - 2.32568i) q^{57} +(-7.29755 + 7.38582i) q^{58} +(-4.03487 + 6.98861i) q^{59} +(8.64918 + 2.30847i) q^{60} -12.0836i q^{61} +(5.50180 - 5.56835i) q^{62} +(-1.87542 - 3.42064i) q^{63} +(-0.288489 - 7.99480i) q^{64} +(7.25125 + 5.85104i) q^{65} +(-13.6918 - 7.99711i) q^{66} -13.0810 q^{67} +(-9.43835 - 5.29897i) q^{68} +(-5.48479 + 1.40491i) q^{69} +(3.34008 - 3.38048i) q^{70} +(-4.07336 + 2.35176i) q^{71} +(-2.22936 + 8.18718i) q^{72} +5.80347i q^{73} +(-1.38207 + 5.28483i) q^{74} +(0.783234 - 2.79905i) q^{75} +(3.27562 + 1.83903i) q^{76} +(-7.28971 + 4.20872i) q^{77} +(-5.58055 + 6.84525i) q^{78} +(3.46837 - 6.00740i) q^{79} +(-10.3338 + 0.248534i) q^{80} +(4.83982 - 7.58789i) q^{81} +(-2.26909 - 8.26918i) q^{82} +(-4.16832 + 7.21974i) q^{83} +(3.18828 + 3.18205i) q^{84} +(-6.99293 + 12.1121i) q^{85} +(-3.17065 - 11.5547i) q^{86} +(-9.09061 + 8.89200i) q^{87} +(17.7679 + 4.41906i) q^{88} +(-8.28219 - 4.78173i) q^{89} +(10.5433 + 3.00754i) q^{90} +(1.68782 + 4.37410i) q^{91} +(5.62215 - 3.33671i) q^{92} +(6.85364 - 6.70390i) q^{93} +(3.64030 + 0.951998i) q^{94} +(2.42692 - 4.20356i) q^{95} +(-0.186280 - 9.79619i) q^{96} -0.486805i q^{97} +(-7.24058 + 1.98683i) q^{98} +(-16.5995 - 10.0790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 3 q^{2} + q^{4} - 3 q^{6} + 10 q^{9} + 8 q^{10} - 7 q^{12} + 2 q^{14} + 24 q^{15} - 15 q^{16} + 8 q^{17} - 6 q^{18} + q^{22} + 20 q^{23} + 12 q^{24} - 144 q^{25} - 20 q^{26} - 6 q^{28} + 7 q^{30}+ \cdots - 99 q^{98}+O(q^{100}) \) 320 * q - 3 * q^2 + q^4 - 3 * q^6 + 10 * q^9 + 8 * q^10 - 7 * q^12 + 2 * q^14 + 24 * q^15 - 15 * q^16 + 8 * q^17 - 6 * q^18 + q^22 + 20 * q^23 + 12 * q^24 - 144 * q^25 - 20 * q^26 - 6 * q^28 + 7 * q^30 + 12 * q^31 - 3 * q^32 + 18 * q^33 - 30 * q^34 + 39 * q^36 - 10 * q^38 + 44 * q^39 - 28 * q^40 + 10 * q^42 - 30 * q^46 - 12 * q^47 - 8 * q^48 - 316 * q^49 - 56 * q^52 + 36 * q^54 + 14 * q^55 + 52 * q^56 + 36 * q^57 - 3 * q^58 + 3 * q^60 - q^62 - 42 * q^63 - 26 * q^64 + 66 * q^65 + 50 * q^66 - 12 * q^68 + 3 * q^70 - 48 * q^71 + 21 * q^72 + 26 * q^74 + 35 * q^78 + 32 * q^79 - 48 * q^80 + 34 * q^81 - 23 * q^82 + 120 * q^84 + 42 * q^86 - 2 * q^87 + 13 * q^88 - 72 * q^89 + 109 * q^90 - 28 * q^92 + 130 * q^94 + 112 * q^95 - 15 * q^96 - 99 * q^98

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