LMFDB - Embedded newform 380.2.v.c.163.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(7,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("380.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.v (of order $12$, degree $4$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			163.17
Character	$\chi$	$=$	380.163
Dual form			380.2.v.c.7.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.824501 - 1.14900i) q^{2} +(-0.320669 - 1.19675i) q^{3} +(-0.640395 + 1.89470i) q^{4} +(1.11922 - 1.93580i) q^{5} +(-1.11068 + 1.35517i) q^{6} +(-1.23765 - 1.23765i) q^{7} +(2.70502 - 0.826371i) q^{8} +(1.26868 - 0.732475i) q^{9} +(-3.14704 + 0.310087i) q^{10} +0.393257i q^{11} +(2.47285 + 0.158823i) q^{12} +(0.619206 - 2.31091i) q^{13} +(-0.401613 + 2.44250i) q^{14} +(-2.67558 - 0.718683i) q^{15} +(-3.17979 - 2.42671i) q^{16} +(-0.318975 - 1.19043i) q^{17} +(-1.88764 - 0.853789i) q^{18} +(-4.15312 + 1.32349i) q^{19} +(2.95103 + 3.36027i) q^{20} +(-1.08428 + 1.87804i) q^{21} +(0.451852 - 0.324241i) q^{22} +(1.65399 + 0.443185i) q^{23} +(-1.85638 - 2.97225i) q^{24} +(-2.49468 - 4.33320i) q^{25} +(-3.16577 + 1.19388i) q^{26} +(-3.91168 - 3.91168i) q^{27} +(3.13756 - 1.55239i) q^{28} +(-1.84754 + 1.06668i) q^{29} +(1.38026 + 3.66680i) q^{30} +4.76683i q^{31} +(-0.166552 + 5.65440i) q^{32} +(0.470632 - 0.126105i) q^{33} +(-1.10481 + 1.34801i) q^{34} +(-3.78105 + 1.01064i) q^{35} +(0.575363 + 2.87285i) q^{36} +(1.95800 - 1.95800i) q^{37} +(4.94494 + 3.68071i) q^{38} -2.96415 q^{39} +(1.42783 - 6.16128i) q^{40} +(-2.87833 + 4.98541i) q^{41} +(3.05185 - 0.302602i) q^{42} +(-0.727463 - 2.71493i) q^{43} +(-0.745104 - 0.251840i) q^{44} +(0.00201292 - 3.27573i) q^{45} +(-0.854497 - 2.26584i) q^{46} +(1.56612 - 5.84485i) q^{47} +(-1.88452 + 4.58360i) q^{48} -3.93646i q^{49} +(-2.92197 + 6.43911i) q^{50} +(-1.32237 + 0.763470i) q^{51} +(3.98194 + 2.65310i) q^{52} +(-3.72343 + 13.8960i) q^{53} +(-1.26933 + 7.71969i) q^{54} +(0.761268 + 0.440142i) q^{55} +(-4.37061 - 2.32510i) q^{56} +(2.91567 + 4.54586i) q^{57} +(2.74891 + 1.24334i) q^{58} +(1.64282 - 2.84544i) q^{59} +(3.07512 - 4.60919i) q^{60} +(1.02665 + 1.77821i) q^{61} +(5.47708 - 3.93026i) q^{62} +(-2.47673 - 0.663637i) q^{63} +(6.63422 - 4.47069i) q^{64} +(-3.78043 - 3.78508i) q^{65} +(-0.532932 - 0.436781i) q^{66} +(2.61168 - 9.74692i) q^{67} +(2.45978 + 0.157984i) q^{68} -2.12153i q^{69} +(4.27870 + 3.51114i) q^{70} +(11.2466 + 6.49322i) q^{71} +(2.82651 - 3.02976i) q^{72} +(8.35948 - 2.23992i) q^{73} +(-3.86411 - 0.635366i) q^{74} +(-4.38581 + 4.37504i) q^{75} +(0.152022 - 8.71647i) q^{76} +(0.486713 - 0.486713i) q^{77} +(2.44395 + 3.40580i) q^{78} +(7.48063 - 12.9568i) q^{79} +(-8.25654 + 3.43941i) q^{80} +(-1.22954 + 2.12962i) q^{81} +(8.10142 - 0.803284i) q^{82} +(6.90293 - 6.90293i) q^{83} +(-2.86395 - 3.25708i) q^{84} +(-2.66145 - 0.714885i) q^{85} +(-2.51965 + 3.07431i) q^{86} +(1.86900 + 1.86900i) q^{87} +(0.324976 + 1.06377i) q^{88} +(7.23618 - 4.17781i) q^{89} +(-3.76546 + 2.69853i) q^{90} +(-3.62645 + 2.09373i) q^{91} +(-1.89891 + 2.85000i) q^{92} +(5.70472 - 1.52858i) q^{93} +(-8.00699 + 3.01961i) q^{94} +(-2.08626 + 9.52090i) q^{95} +(6.82034 - 1.61387i) q^{96} +(2.10029 + 7.83839i) q^{97} +(-4.52299 + 3.24562i) q^{98} +(0.288051 + 0.498919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 12 q^{6} - 36 q^{8} + 4 q^{10} - 20 q^{12} - 8 q^{13} + 8 q^{16} - 16 q^{17} + 12 q^{18} - 48 q^{20} + 40 q^{21} + 16 q^{22} - 16 q^{25} + 24 q^{26} + 8 q^{28} - 12 q^{30} - 20 q^{32} + 20 q^{33}+ \cdots + 34 q^{98}+O(q^{100}) $ 216 * q + 12 * q^6 - 36 * q^8 + 4 * q^10 - 20 * q^12 - 8 * q^13 + 8 * q^16 - 16 * q^17 + 12 * q^18 - 48 * q^20 + 40 * q^21 + 16 * q^22 - 16 * q^25 + 24 * q^26 + 8 * q^28 - 12 * q^30 - 20 * q^32 + 20 * q^33 - 56 * q^36 - 32 * q^37 - 18 * q^38 - 48 * q^41 + 54 * q^42 - 104 * q^45 - 24 * q^46 - 4 * q^48 + 8 * q^50 - 14 * q^52 - 16 * q^53 - 16 * q^56 + 12 * q^57 - 136 * q^58 + 50 * q^60 - 84 * q^61 + 42 * q^62 - 56 * q^65 + 28 * q^68 - 130 * q^70 + 80 * q^72 - 36 * q^73 + 96 * q^77 + 36 * q^78 + 6 * q^80 + 76 * q^81 - 16 * q^85 + 88 * q^86 + 104 * q^88 - 86 * q^90 + 28 * q^92 - 84 * q^93 - 128 * q^96 + 12 * q^97 + 34 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.824501	−	1.14900i	−0.583011	−	0.812465i
$2$	−0.824501	−	1.14900i	−0.583011	−	0.812465i
$3$	−0.320669	−	1.19675i	−0.185139	−	0.690947i	−0.994601	−	0.103775i	$-0.966908\pi$
$3$	−0.320669	−	1.19675i	−0.185139	−	0.690947i	0.809462	−	0.587172i	$-0.199759\pi$
$4$	−0.640395	+	1.89470i	−0.320198	+	0.947351i
$5$	1.11922	−	1.93580i	0.500532	−	0.865718i
$5$	1.11922	−	1.93580i	0.500532	−	0.865718i
$6$	−1.11068	+	1.35517i	−0.453432	+	0.553248i
$7$	−1.23765	−	1.23765i	−0.467787	−	0.467787i	0.433410	−	0.901197i	$-0.357310\pi$
$7$	−1.23765	−	1.23765i	−0.467787	−	0.467787i	−0.901197	+	0.433410i	$0.857310\pi$
$8$	2.70502	−	0.826371i	0.956368	−	0.292166i
$9$	1.26868	−	0.732475i	0.422895	−	0.244158i
$10$	−3.14704	+	0.310087i	−0.995181	+	0.0980581i
$11$			0.393257i			0.118571i	0.998241	+	0.0592857i	$0.0188823\pi$
$11$			0.393257i			0.118571i	−0.998241	+	0.0592857i	$0.981118\pi$
$12$	2.47285	+	0.158823i	0.713850	+	0.0458482i
$13$	0.619206	−	2.31091i	0.171737	−	0.640930i	−0.825348	−	0.564625i	$-0.809021\pi$
$13$	0.619206	−	2.31091i	0.171737	−	0.640930i	0.997084	−	0.0763056i	$-0.0243125\pi$
$14$	−0.401613	+	2.44250i	−0.107336	+	0.652785i
$15$	−2.67558	−	0.718683i	−0.690833	−	0.185563i
$16$	−3.17979	−	2.42671i	−0.794947	−	0.606679i
$17$	−0.318975	−	1.19043i	−0.0773628	−	0.288722i	0.916396	−	0.400273i	$-0.131085\pi$
$17$	−0.318975	−	1.19043i	−0.0773628	−	0.288722i	−0.993759	+	0.111551i	$0.964418\pi$
$18$	−1.88764	−	0.853789i	−0.444922	−	0.201240i
$19$	−4.15312	+	1.32349i	−0.952790	+	0.303629i
$19$	−4.15312	+	1.32349i	−0.952790	+	0.303629i
$20$	2.95103	+	3.36027i	0.659870	+	0.751380i
$21$	−1.08428	+	1.87804i	−0.236610	+	0.409821i
$22$	0.451852	−	0.324241i	0.0963351	−	0.0691284i
$23$	1.65399	+	0.443185i	0.344880	+	0.0924104i	0.427101	−	0.904204i	$-0.359535\pi$
$23$	1.65399	+	0.443185i	0.344880	+	0.0924104i	−0.0822212	+	0.996614i	$0.526201\pi$
$24$	−1.85638	−	2.97225i	−0.378932	−	0.606708i
$25$	−2.49468	−	4.33320i	−0.498935	−	0.866639i
$26$	−3.16577	+	1.19388i	−0.620858	+	0.234139i
$27$	−3.91168	−	3.91168i	−0.752802	−	0.752802i
$28$	3.13756	−	1.55239i	0.592942	−	0.293374i
$29$	−1.84754	+	1.06668i	−0.343080	+	0.198077i	−0.661633	−	0.749828i	$-0.730136\pi$
$29$	−1.84754	+	1.06668i	−0.343080	+	0.198077i	0.318553	+	0.947905i	$0.396803\pi$
$30$	1.38026	+	3.66680i	0.251999	+	0.669462i
$31$			4.76683i			0.856148i	0.903744	+	0.428074i	$0.140808\pi$
$31$			4.76683i			0.856148i	−0.903744	+	0.428074i	$0.859192\pi$
$32$	−0.166552	+	5.65440i	−0.0294425	+	0.999566i
$33$	0.470632	−	0.126105i	0.0819265	−	0.0219521i
$34$	−1.10481	+	1.34801i	−0.189473	+	0.231182i
$35$	−3.78105	+	1.01064i	−0.639114	+	0.170829i
$36$	0.575363	+	2.87285i	0.0958938	+	0.478808i
$37$	1.95800	−	1.95800i	0.321893	−	0.321893i	−0.527600	−	0.849493i	$-0.676908\pi$
$37$	1.95800	−	1.95800i	0.321893	−	0.321893i	0.849493	+	0.527600i	$0.176908\pi$
$38$	4.94494	+	3.68071i	0.802174	+	0.597090i
$39$	−2.96415			−0.474644
$40$	1.42783	−	6.16128i	0.225759	−	0.974183i
$41$	−2.87833	+	4.98541i	−0.449520	+	0.778591i	−0.998355	−	0.0573398i	$-0.981738\pi$
$41$	−2.87833	+	4.98541i	−0.449520	+	0.778591i	0.548835	+	0.835931i	$0.315071\pi$
$42$	3.05185	−	0.302602i	0.470911	−	0.0466925i
$43$	−0.727463	−	2.71493i	−0.110937	−	0.414023i	0.888014	−	0.459817i	$-0.152085\pi$
$43$	−0.727463	−	2.71493i	−0.110937	−	0.414023i	−0.998951	+	0.0457941i	$0.985418\pi$
$44$	−0.745104	−	0.251840i	−0.112329	−	0.0379663i
$45$	0.00201292	−	3.27573i	0.000300069	−	0.488316i
$46$	−0.854497	−	2.26584i	−0.125989	−	0.334079i
$47$	1.56612	−	5.84485i	0.228442	−	0.852559i	−0.752554	−	0.658531i	$-0.771178\pi$
$47$	1.56612	−	5.84485i	0.228442	−	0.852559i	0.980996	−	0.194028i	$-0.0621552\pi$
$48$	−1.88452	+	4.58360i	−0.272007	+	0.661586i
$49$		−	3.93646i		−	0.562351i
$50$	−2.92197	+	6.43911i	−0.413229	+	0.910627i
$51$	−1.32237	+	0.763470i	−0.185169	+	0.106907i
$52$	3.98194	+	2.65310i	0.552196	+	0.367919i
$53$	−3.72343	+	13.8960i	−0.511452	+	1.90877i	−0.106842	+	0.994276i	$0.534074\pi$
$53$	−3.72343	+	13.8960i	−0.511452	+	1.90877i	−0.404610	+	0.914489i	$0.632593\pi$
$54$	−1.26933	+	7.71969i	−0.172734	+	1.05052i
$55$	0.761268	+	0.440142i	0.102649	+	0.0593488i
$56$	−4.37061	−	2.32510i	−0.584047	−	0.310704i
$57$	2.91567	+	4.54586i	0.386190	+	0.602114i
$58$	2.74891	+	1.24334i	0.360950	+	0.163259i
$59$	1.64282	−	2.84544i	0.213876	−	0.370445i	−0.739048	−	0.673653i	$-0.764724\pi$
$59$	1.64282	−	2.84544i	0.213876	−	0.370445i	0.952924	+	0.303208i	$0.0980577\pi$
$60$	3.07512	−	4.60919i	0.396996	−	0.595044i
$61$	1.02665	+	1.77821i	0.131449	+	0.227677i	0.924235	−	0.381823i	$-0.124704\pi$
$61$	1.02665	+	1.77821i	0.131449	+	0.227677i	−0.792786	+	0.609500i	$0.791370\pi$
$62$	5.47708	−	3.93026i	0.695590	−	0.499143i
$63$	−2.47673	−	0.663637i	−0.312038	−	0.0836104i
$64$	6.63422	−	4.47069i	0.829278	−	0.558837i
$65$	−3.78043	−	3.78508i	−0.468905	−	0.469482i
$66$	−0.532932	−	0.436781i	−0.0655994	−	0.0537641i
$67$	2.61168	−	9.74692i	0.319067	−	1.19078i	−0.601075	−	0.799192i	$-0.705261\pi$
$67$	2.61168	−	9.74692i	0.319067	−	1.19078i	0.920143	−	0.391583i	$-0.128072\pi$
$68$	2.45978	+	0.157984i	0.298292	+	0.0191583i
$69$		−	2.12153i		−	0.255403i
$70$	4.27870	+	3.51114i	0.511402	+	0.419662i
$71$	11.2466	+	6.49322i	1.33472	+	0.770603i	0.986019	−	0.166630i	$-0.0532885\pi$
$71$	11.2466	+	6.49322i	1.33472	+	0.770603i	0.348704	+	0.937233i	$0.386622\pi$
$72$	2.82651	−	3.02976i	0.333108	−	0.357061i
$73$	8.35948	−	2.23992i	0.978404	−	0.262162i	0.266031	−	0.963964i	$-0.414287\pi$
$73$	8.35948	−	2.23992i	0.978404	−	0.262162i	0.712372	+	0.701802i	$0.247621\pi$
$74$	−3.86411	−	0.635366i	−0.449194	−	0.0738597i
$75$	−4.38581	+	4.37504i	−0.506429	+	0.505186i
$76$	0.152022	−	8.71647i	0.0174382	−	0.999848i
$77$	0.486713	−	0.486713i	0.0554661	−	0.0554661i
$78$	2.44395	+	3.40580i	0.276722	+	0.385631i
$79$	7.48063	−	12.9568i	0.841636	−	1.45776i	−0.0468744	−	0.998901i	$-0.514926\pi$
$79$	7.48063	−	12.9568i	0.841636	−	1.45776i	0.888511	−	0.458856i	$-0.151741\pi$
$80$	−8.25654	+	3.43941i	−0.923109	+	0.384538i
$81$	−1.22954	+	2.12962i	−0.136615	+	0.236624i
$82$	8.10142	−	0.803284i	0.894652	−	0.0887078i
$83$	6.90293	−	6.90293i	0.757695	−	0.757695i	−0.218207	−	0.975903i	$-0.570021\pi$
$83$	6.90293	−	6.90293i	0.757695	−	0.757695i	0.975903	+	0.218207i	$0.0700208\pi$
$84$	−2.86395	−	3.25708i	−0.312482	−	0.355377i
$85$	−2.66145	−	0.714885i	−0.288674	−	0.0775402i
$86$	−2.51965	+	3.07431i	−0.271701	+	0.331512i
$87$	1.86900	+	1.86900i	0.200378	+	0.200378i
$88$	0.324976	+	1.06377i	0.0346426	+	0.113398i
$89$	7.23618	−	4.17781i	0.767034	−	0.442847i	−0.0647818	−	0.997899i	$-0.520635\pi$
$89$	7.23618	−	4.17781i	0.767034	−	0.442847i	0.831815	+	0.555052i	$0.187302\pi$
$90$	−3.76546	+	2.69853i	−0.396915	+	0.284450i
$91$	−3.62645	+	2.09373i	−0.380155	+	0.219483i
$92$	−1.89891	+	2.85000i	−0.197975	+	0.297133i
$93$	5.70472	−	1.52858i	0.591552	−	0.158506i
$94$	−8.00699	+	3.01961i	−0.825858	+	0.311449i
$95$	−2.08626	+	9.52090i	−0.214045	+	0.976824i
$96$	6.82034	−	1.61387i	0.696098	−	0.164715i
$97$	2.10029	+	7.83839i	0.213252	+	0.795868i	0.986775	+	0.162099i	$0.0518263\pi$
$97$	2.10029	+	7.83839i	0.213252	+	0.795868i	−0.773522	+	0.633769i	$0.781507\pi$
$98$	−4.52299	+	3.24562i	−0.456891	+	0.327857i
$99$	0.288051	+	0.498919i	0.0289502	+	0.0501432i
$100$	9.80769	−	1.95171i	0.980769	−	0.195171i
$101$	−3.80619	−	6.59252i	−0.378730	−	0.655980i	0.612148	−	0.790744i	$-0.290306\pi$
$101$	−3.80619	−	6.59252i	−0.378730	−	0.655980i	−0.990878	+	0.134764i	$0.956973\pi$
$102$	1.96752	+	0.889917i	0.194813	+	0.0881149i
$103$	4.47585	−	4.47585i	0.441019	−	0.441019i	−0.451335	−	0.892354i	$-0.649052\pi$
$103$	4.47585	−	4.47585i	0.441019	−	0.441019i	0.892354	+	0.451335i	$0.149052\pi$
$104$	−0.234706	−	6.76274i	−0.0230148	−	0.663141i
$105$	2.42195	+	4.20090i	0.236358	+	0.409966i
$106$	19.0365	−	7.17908i	1.84899	−	0.697293i
$107$	−5.90841	−	5.90841i	−0.571187	−	0.571187i	0.361273	−	0.932460i	$-0.382342\pi$
$107$	−5.90841	−	5.90841i	−0.571187	−	0.571187i	−0.932460	+	0.361273i	$0.882342\pi$
$108$	9.91648	−	4.90644i	0.954213	−	0.472123i
$109$	−2.09300	−	1.20840i	−0.200473	−	0.115743i	0.396403	−	0.918077i	$-0.370258\pi$
$109$	−2.09300	−	1.20840i	−0.200473	−	0.115743i	−0.596876	+	0.802333i	$0.703592\pi$
$110$	−0.121944	−	1.23759i	−0.0116269	−	0.118000i
$111$	−2.97112	−	1.71538i	−0.282006	−	0.162816i
$112$	0.932039	+	6.93887i	0.0880694	+	0.655662i
$113$	8.56524	+	8.56524i	0.805750	+	0.805750i	0.983988	−	0.178237i	$-0.0570394\pi$
$113$	8.56524	+	8.56524i	0.805750	+	0.805750i	−0.178237	+	0.983988i	$0.557039\pi$
$114$	2.81921	−	7.09816i	0.264044	−	0.664804i
$115$	2.70910	−	2.70577i	0.252625	−	0.252315i
$116$	−0.837881	−	4.18363i	−0.0777953	−	0.388441i
$117$	−0.907105	−	3.38536i	−0.0838619	−	0.312977i
$118$	−4.62391	+	0.458477i	−0.425665	+	0.0422062i
$119$	−1.07855	+	1.86811i	−0.0988710	+	0.171250i
$120$	−7.83139	+	0.266976i	−0.714905	+	0.0243715i
$121$	10.8453			0.985941
$122$	1.19669	−	2.64576i	0.108343	−	0.239536i
$123$	6.88931	+	1.84598i	0.621188	+	0.166447i
$124$	−9.03172	−	3.05265i	−0.811072	−	0.274136i
$125$	−11.1803	−	0.0206108i	−0.999998	−	0.00184349i
$126$	1.27955	+	3.39293i	0.113991	+	0.302266i
$127$	−5.08318	+	18.9707i	−0.451059	+	1.68338i	0.248362	+	0.968667i	$0.420108\pi$
$127$	−5.08318	+	18.9707i	−0.451059	+	1.68338i	−0.699421	+	0.714710i	$0.746559\pi$
$128$	−10.6067	−	3.93662i	−0.937513	−	0.347951i
$129$	−3.01583	+	1.74119i	−0.265529	+	0.153303i
$130$	−1.23208	+	7.46452i	−0.108061	+	0.654682i
$131$	12.0475	+	6.95562i	1.05259	+	0.607715i	0.923374	−	0.383901i	$-0.125419\pi$
$131$	12.0475	+	6.95562i	1.05259	+	0.607715i	0.129220	+	0.991616i	$0.458753\pi$
$132$	−0.0624582	+	0.972464i	−0.00543629	+	0.0846422i
$133$	6.77810	+	3.50208i	0.587736	+	0.303669i
$134$	−13.3525	+	5.03553i	−1.15348	+	0.435004i
$135$	−11.9503	+	3.19420i	−1.02852	+	0.274913i
$136$	−1.84657	−	2.95654i	−0.158342	−	0.253521i
$137$	−8.14892	−	2.18350i	−0.696209	−	0.186549i	−0.106677	−	0.994294i	$-0.534021\pi$
$137$	−8.14892	−	2.18350i	−0.696209	−	0.186549i	−0.589532	+	0.807745i	$0.700688\pi$
$138$	−2.43764	+	1.74921i	−0.207506	+	0.148902i
$139$	1.42645	+	2.47069i	0.120990	+	0.209561i	0.920158	−	0.391546i	$-0.128060\pi$
$139$	1.42645	+	2.47069i	0.120990	+	0.209561i	−0.799168	+	0.601107i	$0.794726\pi$
$140$	0.506505	−	7.81116i	0.0428075	−	0.660164i
$141$	−7.49706			−0.631366
$142$	−1.81213	−	18.2760i	−0.152070	−	1.53369i
$143$	0.908780	+	0.243507i	0.0759960	+	0.0203631i
$144$	−5.81165	−	0.749619i	−0.484304	−	0.0624682i
$145$	−0.00293135	+	4.77033i	−0.000243435	+	0.396154i
$146$	−9.46607	−	7.75822i	−0.783417	−	0.642075i
$147$	−4.71098	+	1.26230i	−0.388555	+	0.104113i
$148$	2.45593	+	4.96372i	0.201876	+	0.408015i
$149$	1.47246	+	0.850125i	0.120629	+	0.0696449i	0.559100	−	0.829100i	$-0.311147\pi$
$149$	1.47246	+	0.850125i	0.120629	+	0.0696449i	−0.438472	+	0.898745i	$0.644480\pi$
$150$	8.64302	+	1.43206i	0.705699	+	0.116927i
$151$			10.3392i			0.841396i	0.907201	+	0.420698i	$0.138215\pi$
$151$			10.3392i			0.841396i	−0.907201	+	0.420698i	$0.861785\pi$
$152$	−10.1406	+	7.01207i	−0.822508	+	0.568754i
$153$	−1.27664	−	1.27664i	−0.103210	−	0.103210i
$154$	−0.960529	−	0.157937i	−0.0774016	−	0.0127269i
$155$	9.22765	+	5.33515i	0.741183	+	0.428529i
$156$	1.89823	−	5.61618i	0.151980	−	0.449654i
$157$	−1.01565	−	3.79046i	−0.0810576	−	0.302511i	0.913481	−	0.406882i	$-0.133384\pi$
$157$	−1.01565	−	3.79046i	−0.0810576	−	0.302511i	−0.994538	+	0.104370i	$0.966717\pi$
$158$	−21.0552	+	2.08769i	−1.67506	+	0.166088i
$159$	17.8241			1.41354
$160$	10.7594	+	6.65095i	0.850606	+	0.525804i
$161$	−1.49855	−	2.59556i	−0.118102	−	0.204559i
$162$	3.46069	−	0.343139i	0.271897	−	0.0269595i
$163$	11.5592	−	11.5592i	0.905385	−	0.905385i	−0.0905102	−	0.995896i	$-0.528850\pi$
$163$	11.5592	−	11.5592i	0.905385	−	0.905385i	0.995896	+	0.0905102i	$0.0288498\pi$
$164$	−7.60260	−	8.64621i	−0.593664	−	0.675156i
$165$	0.282627	−	1.05219i	0.0220025	−	0.0819130i
$166$	−13.6229	−	2.23998i	−1.05735	−	0.173856i
$167$	−4.54106	+	16.9474i	−0.351397	+	1.31143i	0.533561	+	0.845762i	$0.320854\pi$
$167$	−4.54106	+	16.9474i	−0.351397	+	1.31143i	−0.884958	+	0.465671i	$0.845813\pi$
$168$	−1.38105	+	5.97614i	−0.106550	+	0.461069i
$169$	6.30145	+	3.63815i	0.484727	+	0.279857i
$170$	1.37296	+	3.64742i	0.105301	+	0.279744i
$171$	−4.29957	+	4.72114i	−0.328796	+	0.361035i
$172$	5.60984	+	0.360301i	0.427746	+	0.0274727i
$173$	−14.4439	+	3.87023i	−1.09815	+	0.294248i	−0.762011	−	0.647564i	$-0.775788\pi$
$173$	−14.4439	+	3.87023i	−1.09815	+	0.294248i	−0.336139	+	0.941812i	$0.609121\pi$
$174$	0.606486	−	3.68847i	0.0459776	−	0.279623i
$175$	−2.27544	+	8.45050i	−0.172007	+	0.638798i
$176$	0.954322	−	1.25047i	0.0719348	−	0.0942580i
$177$	−3.93209	−	1.05360i	−0.295554	−	0.0791935i
$178$	−10.7665	−	4.86975i	−0.806986	−	0.365003i
$179$	1.62191			0.121227			0.0606137	−	0.998161i	$-0.480694\pi$
$179$	1.62191			0.121227			0.0606137	+	0.998161i	$0.480694\pi$
$180$	6.20523	+	2.10157i	0.462511	+	0.156642i
$181$	−5.52559	−	9.57060i	−0.410714	−	0.711377i	0.584254	−	0.811571i	$-0.301387\pi$
$181$	−5.52559	−	9.57060i	−0.410714	−	0.711377i	−0.994968	+	0.100193i	$0.968054\pi$
$182$	5.39570	+	2.44050i	0.399956	+	0.180902i
$183$	1.79887	−	1.79887i	0.132976	−	0.132976i
$184$	4.84030	−	0.167986i	0.356831	−	0.0123841i
$185$	−1.59887	−	5.98175i	−0.117551	−	0.439787i
$186$	−6.45989	−	5.29441i	−0.473662	−	0.388205i
$187$	0.468145	−	0.125439i	0.0342342	−	0.00917302i
$188$	10.0713	+	6.71035i	0.734526	+	0.489402i
$189$			9.68255i			0.704302i
$190$	12.6596	−	5.45289i	0.918425	−	0.395594i
$191$			20.0601i			1.45150i	0.687959	+	0.725750i	$0.258507\pi$
$191$			20.0601i			1.45150i	−0.687959	+	0.725750i	$0.741493\pi$
$192$	−7.47772	−	6.50592i	−0.539658	−	0.469524i
$193$	−18.7685	+	5.02899i	−1.35098	+	0.361995i	−0.860498	−	0.509454i	$-0.829847\pi$
$193$	−18.7685	+	5.02899i	−1.35098	+	0.361995i	−0.490486	+	0.871449i	$0.663181\pi$
$194$	7.27460	−	8.87599i	0.522286	−	0.637259i
$195$	−3.31755	+	5.73801i	−0.237574	+	0.410908i
$196$	7.45842	+	2.52089i	0.532744	+	0.180063i
$197$	13.8699	−	13.8699i	0.988186	−	0.988186i	−0.0117448	−	0.999931i	$-0.503739\pi$
$197$	13.8699	−	13.8699i	0.988186	−	0.988186i	0.999931	+	0.0117448i	$0.00373858\pi$
$198$	0.335758	−	0.742329i	0.0238613	−	0.0527550i
$199$	1.83501	+	3.17832i	0.130080	+	0.225305i	0.923707	−	0.383099i	$-0.125143\pi$
$199$	1.83501	+	3.17832i	0.130080	+	0.225305i	−0.793627	+	0.608404i	$0.791810\pi$
$200$	−10.3290	−	9.65984i	−0.730368	−	0.683054i
$201$	−12.5022			−0.881834
$202$	−4.43658	+	9.80885i	−0.312157	+	0.690148i
$203$	3.60677	+	0.966432i	0.253146	+	0.0678303i
$204$	−0.599709	−	2.99442i	−0.0419880	−	0.209651i
$205$	6.42929	+	11.1517i	0.449041	+	0.778867i
$206$	−8.83309	−	1.45240i	−0.615431	−	0.101194i
$207$	2.42301	−	0.649243i	0.168411	−	0.0451255i
$208$	−7.57686	+	5.84556i	−0.525361	+	0.405317i
$209$	−0.520470	−	1.63324i	−0.0360017	−	0.112974i
$210$	2.82993	−	6.24647i	0.195284	−	0.431047i
$211$	−1.57825	−	0.911203i	−0.108651	−	0.0627298i	0.444690	−	0.895685i	$-0.353314\pi$
$211$	−1.57825	−	0.911203i	−0.108651	−	0.0627298i	−0.553341	+	0.832955i	$0.686647\pi$
$212$	−23.9443	−	15.9537i	−1.64450	−	1.09571i
$213$	4.16435	−	15.5416i	0.285337	−	1.06489i
$214$	−1.91726	+	11.6602i	−0.131061	+	0.797078i
$215$	−6.06976	−	1.63039i	−0.413954	−	0.111191i
$216$	−13.8136	−	7.34865i	−0.939899	−	0.500012i
$217$	5.89965	−	5.89965i	0.400495	−	0.400495i
$218$	0.337239	+	3.40118i	0.0228407	+	0.230357i
$219$	−5.36126	−	9.28598i	−0.362281	−	0.627488i
$220$	−1.32145	+	1.16051i	−0.0890922	+	0.0782417i
$221$	−2.94849			−0.198337
$222$	0.478726	+	4.82814i	0.0321300	+	0.324043i
$223$	−7.13833	−	26.6406i	−0.478018	−	1.78399i	−0.609630	−	0.792686i	$-0.708682\pi$
$223$	−7.13833	−	26.6406i	−0.478018	−	1.78399i	0.131612	−	0.991301i	$-0.457985\pi$
$224$	7.20429	−	6.79202i	0.481357	−	0.453811i
$225$	−6.33891	−	3.67017i	−0.422594	−	0.244678i
$226$	2.77940	−	16.9035i	0.184883	−	1.12440i
$227$	−9.39918	−	9.39918i	−0.623845	−	0.623845i	0.322667	−	0.946512i	$-0.395421\pi$
$227$	−9.39918	−	9.39918i	−0.623845	−	0.623845i	−0.946512	+	0.322667i	$0.895421\pi$
$228$	−10.4802	+	2.61317i	−0.694070	+	0.173062i
$229$			21.7628i			1.43813i	0.694945	+	0.719063i	$0.255429\pi$
$229$			21.7628i			1.43813i	−0.694945	+	0.719063i	$0.744571\pi$
$230$	−5.34259	−	0.881839i	−0.352280	−	0.0581467i
$231$	−0.738550	−	0.426402i	−0.0485930	−	0.0280552i
$232$	−4.11615	+	4.41214i	−0.270239	+	0.289671i
$233$	2.65207	−	0.710620i	0.173743	−	0.0465543i	−0.170899	−	0.985289i	$-0.554667\pi$
$233$	2.65207	−	0.710620i	0.173743	−	0.0465543i	0.344642	+	0.938734i	$0.388000\pi$
$234$	−3.14187	+	3.83350i	−0.205390	+	0.250604i
$235$	−9.56164	−	9.57340i	−0.623733	−	0.624500i
$236$	4.33921	+	4.93485i	0.282458	+	0.321231i
$237$	−17.9049	−	4.79762i	−1.16305	−	0.311639i
$238$	3.03573	−	0.301003i	0.196777	−	0.0195111i
$239$	16.2040			1.04815			0.524075	−	0.851672i	$-0.324411\pi$
$239$	16.2040			1.04815			0.524075	+	0.851672i	$0.324411\pi$
$240$	6.76375	+	8.77814i	0.436598	+	0.566626i
$241$	−8.05676	−	13.9547i	−0.518981	−	0.898902i	−0.999757	−	0.0220583i	$-0.992978\pi$
$241$	−8.05676	−	13.9547i	−0.518981	−	0.898902i	0.480775	−	0.876844i	$-0.340355\pi$
$242$	−8.94200	−	12.4613i	−0.574814	−	0.801042i
$243$	−13.0874	−	3.50677i	−0.839560	−	0.224959i
$244$	−4.02664	+	0.806439i	−0.257779	+	0.0516270i
$245$	−7.62021	−	4.40578i	−0.486838	−	0.281475i
$246$	−3.55921	−	9.43782i	−0.226927	−	0.601734i
$247$	0.486822	+	10.4170i	0.0309758	+	0.662817i
$248$	3.93917	+	12.8943i	0.250138	+	0.818792i
$249$	−10.4747	−	6.04756i	−0.663806	−	0.383248i
$250$	9.19451	+	12.8632i	0.581512	+	0.813538i
$251$	21.6826	−	12.5185i	1.36860	−	0.790159i	0.377847	−	0.925868i	$-0.376665\pi$
$251$	21.6826	−	12.5185i	1.36860	−	0.790159i	0.990749	+	0.135709i	$0.0433313\pi$
$252$	2.84348	−	4.26767i	0.179122	−	0.268838i
$253$	−0.174285	+	0.650442i	−0.0109572	+	0.0408929i
$254$	25.9884	−	9.80079i	1.63066	−	0.614957i
$255$	−0.00209810	+	3.41434i	−0.000131388	+	0.213814i
$256$	4.22211	+	15.4329i	0.263882	+	0.964555i
$257$	−0.656943	−	0.176027i	−0.0409790	−	0.0109803i	0.238271	−	0.971199i	$-0.423419\pi$
$257$	−0.656943	−	0.176027i	−0.0409790	−	0.0109803i	−0.279250	+	0.960218i	$0.590086\pi$
$258$	4.48718	+	2.02957i	0.279359	+	0.126355i
$259$	−4.84663			−0.301155
$260$	9.59258	−	4.73885i	0.594906	−	0.293891i
$261$	−1.56263	+	2.70655i	−0.0967244	+	0.167531i
$262$	−1.94117	−	19.5775i	−0.119926	−	1.20950i
$263$	8.02559	+	29.9519i	0.494879	+	1.84691i	0.530705	+	0.847557i	$0.321927\pi$
$263$	8.02559	+	29.9519i	0.494879	+	1.84691i	−0.0358255	+	0.999358i	$0.511406\pi$
$264$	1.16886	−	0.730034i	0.0719382	−	0.0449305i
$265$	22.7326	+	22.7606i	1.39645	+	1.39817i
$266$	−1.56467	−	10.6755i	−0.0959359	−	0.654557i
$267$	−7.32024	−	7.32024i	−0.447991	−	0.447991i
$268$	16.7950	+	11.1902i	1.02592	+	0.683552i
$269$	14.5788	+	8.41709i	0.888887	+	0.513199i	0.873578	−	0.486684i	$-0.161794\pi$
$269$	14.5788	+	8.41709i	0.888887	+	0.513199i	0.0153085	+	0.999883i	$0.495127\pi$
$270$	13.5232	+	11.0972i	0.822993	+	0.675356i
$271$	−22.3278	−	12.8909i	−1.35631	−	0.783068i	−0.367189	−	0.930146i	$-0.619680\pi$
$271$	−22.3278	−	12.8909i	−1.35631	−	0.783068i	−0.989125	+	0.147078i	$0.953013\pi$
$272$	−1.87456	+	4.55938i	−0.113662	+	0.276453i
$273$	3.66857	+	3.66857i	0.222032	+	0.222032i
$274$	4.20996	+	11.1634i	0.254333	+	0.674405i
$275$	1.70406	−	0.981049i	0.102759	−	0.0591595i
$276$	4.01967	+	1.35862i	0.241956	+	0.0817793i
$277$	−2.27358	+	2.27358i	−0.136606	+	0.136606i	−0.772103	−	0.635497i	$-0.780795\pi$
$277$	−2.27358	+	2.27358i	−0.136606	+	0.136606i	0.635497	+	0.772103i	$0.280795\pi$
$278$	1.66270	−	3.67607i	0.0997223	−	0.220476i
$279$	3.49158	+	6.04760i	0.209036	+	0.362060i
$280$	−9.39263	+	5.85834i	−0.561317	+	0.350103i
$281$	11.1499	+	19.3122i	0.665148	+	1.15207i	0.979245	+	0.202679i	$0.0649647\pi$
$281$	11.1499	+	19.3122i	0.665148	+	1.15207i	−0.314098	+	0.949391i	$0.601702\pi$
$282$	6.18133	+	8.61411i	0.368093	+	0.512963i
$283$	−3.48430	−	13.0036i	−0.207120	−	0.772983i	−0.988793	−	0.149294i	$-0.952300\pi$
$283$	−3.48430	−	13.0036i	−0.207120	−	0.772983i	0.781673	−	0.623689i	$-0.214367\pi$
$284$	−19.5050	+	17.1507i	−1.15741	+	1.01771i
$285$	12.0632	−	0.556326i	0.714561	−	0.0329539i
$286$	−0.469501	−	1.24496i	−0.0277622	−	0.0736160i
$287$	9.73254	−	2.60783i	0.574494	−	0.153935i
$288$	3.93041	+	7.29564i	0.231601	+	0.429900i
$289$	13.4071	−	7.74056i	0.788650	−	0.455327i
$290$	5.48352	−	3.92977i	0.322003	−	0.230764i
$291$	8.70713	−	5.02706i	0.510421	−	0.294692i
$292$	−1.10940	+	17.2732i	−0.0649226	+	1.01084i
$293$	9.30632	+	9.30632i	0.543681	+	0.543681i	0.924606	−	0.380925i	$-0.124394\pi$
$293$	9.30632	+	9.30632i	0.543681	+	0.543681i	−0.380925	+	0.924606i	$0.624394\pi$
$294$	5.33459	+	4.37213i	0.311120	+	0.254988i
$295$	−3.66954	−	6.36485i	−0.213649	−	0.370576i
$296$	3.67839	−	6.91446i	0.213802	−	0.401895i
$297$	1.53829	−	1.53829i	0.0892608	−	0.0892608i
$298$	−0.237253	−	2.39278i	−0.0137437	−	0.138610i
$299$	2.04832	−	3.54779i	0.118457	−	0.205174i
$300$	−5.48074	−	11.1115i	−0.316431	−	0.641525i
$301$	−2.45978	+	4.26046i	−0.141779	+	0.245569i
$302$	11.8798	−	8.52472i	0.683605	−	0.490543i
$303$	−6.66910	+	6.66910i	−0.383130	+	0.383130i
$304$	16.4178	+	5.87002i	0.941623	+	0.336669i
$305$	4.59132	+	0.00282135i	0.262898	+	0.000161550i
$306$	−0.414266	+	2.51945i	−0.0236820	+	0.144027i
$307$	5.04658	−	1.35223i	0.288024	−	0.0771757i	−0.111914	−	0.993718i	$-0.535698\pi$
$307$	5.04658	−	1.35223i	0.288024	−	0.0771757i	0.399938	+	0.916542i	$0.369032\pi$
$308$	0.610488	+	1.23387i	0.0347858	+	0.0703060i
$309$	−6.79177	−	3.92123i	−0.386370	−	0.223071i
$310$	−1.47813	−	15.0014i	−0.0839522	−	0.852022i
$311$			10.1737i			0.576898i	0.957495	+	0.288449i	$0.0931395\pi$
$311$			10.1737i			0.576898i	−0.957495	+	0.288449i	$0.906860\pi$
$312$	−8.01807	+	2.44949i	−0.453934	+	0.138675i
$313$	6.18488	−	23.0823i	0.349590	−	1.30469i	−0.537567	−	0.843221i	$-0.680657\pi$
$313$	6.18488	−	23.0823i	0.349590	−	1.30469i	0.887157	−	0.461467i	$-0.152677\pi$
$314$	−3.51782	+	4.29222i	−0.198522	+	0.242224i
$315$	−4.05668	+	4.05170i	−0.228568	+	0.228288i
$316$	19.7588	+	22.4710i	1.11152	+	1.26409i
$317$	19.6659	+	5.26946i	1.10455	+	0.295962i	0.764614	−	0.644488i	$-0.222929\pi$
$317$	19.6659	+	5.26946i	1.10455	+	0.295962i	0.339931	+	0.940450i	$0.389596\pi$
$318$	−14.6960	−	20.4799i	−0.824111	−	1.14845i
$319$	−0.419479	−	0.726558i	−0.0234863	−	0.0406794i
$320$	−1.22921	−	17.8463i	−0.0687150	−	0.997636i
$321$	−5.17627	+	8.96556i	−0.288911	+	0.500409i
$322$	−1.74674	+	3.86187i	−0.0973420	+	0.215214i
$323$	2.90026	+	4.52184i	0.161375	+	0.251602i
$324$	−3.24761	−	3.69340i	−0.180423	−	0.205189i
$325$	−11.5583	+	3.08183i	−0.641141	+	0.170949i
$326$	−22.8121	−	3.75092i	−1.26344	−	0.207744i
$327$	−0.774991	+	2.89230i	−0.0428571	+	0.159945i
$328$	−3.66613	+	15.8642i	−0.202428	+	0.875953i
$329$	−9.17217	+	5.29555i	−0.505678	+	0.291953i
$330$	−1.44199	+	0.542795i	−0.0793791	+	0.0298799i
$331$			3.26096i			0.179238i	0.995976	+	0.0896192i	$0.0285650\pi$
$331$			3.26096i			0.179238i	−0.995976	+	0.0896192i	$0.971435\pi$
$332$	8.65840	+	17.4996i	0.475191	+	0.960416i
$333$	1.04990	−	3.91827i	0.0575340	−	0.214720i
$334$	23.2167	−	8.75553i	1.27036	−	0.479081i
$335$	−15.9451	−	15.9647i	−0.871172	−	0.872244i
$336$	8.00525	−	3.34051i	0.436722	−	0.182240i
$337$	0.0339391	+	0.126663i	0.00184878	+	0.00689975i	0.966844	−	0.255368i	$-0.0821965\pi$
$337$	0.0339391	+	0.126663i	0.00184878	+	0.00689975i	−0.964995	+	0.262267i	$0.915530\pi$
$338$	−1.01533	−	10.2400i	−0.0552268	−	0.556983i
$339$	7.50388	−	12.9971i	0.407555	−	0.705906i
$340$	3.05887	−	4.58484i	0.165891	−	0.248648i
$341$	−1.87459			−0.101515
$342$	8.96958	+	1.04761i	0.485020	+	0.0566485i
$343$	−13.5355	+	13.5355i	−0.730847	+	0.730847i
$344$	−4.21134	−	6.74277i	−0.227060	−	0.363546i
$345$	−4.10687	−	2.37447i	−0.221107	−	0.127837i
$346$	16.3559	+	13.4050i	0.879299	+	0.720658i
$347$	8.15263	−	2.18449i	0.437656	−	0.117270i	−0.0332618	−	0.999447i	$-0.510589\pi$
$347$	8.15263	−	2.18449i	0.437656	−	0.117270i	0.470918	+	0.882177i	$0.343923\pi$
$348$	−4.73810	+	2.34430i	−0.253989	+	0.125668i
$349$		−	7.11203i		−	0.380698i	−0.981716	−	0.190349i	$-0.939038\pi$
$349$		−	7.11203i		−	0.380698i	0.981716	−	0.190349i	$-0.0609620\pi$
$350$	11.5857	−	4.35297i	0.619282	−	0.232676i
$351$	−11.4617	+	6.61739i	−0.611778	+	0.353210i
$352$	−2.22363	−	0.0654977i	−0.118520	−	0.00349104i
$353$	−21.0050	−	21.0050i	−1.11798	−	1.11798i	−0.992037	−	0.125945i	$-0.959804\pi$
$353$	−21.0050	−	21.0050i	−1.11798	−	1.11798i	−0.125945	−	0.992037i	$-0.540196\pi$
$354$	2.03143	+	5.38667i	0.107969	+	0.286298i
$355$	25.1570	−	14.5038i	1.33520	−	0.769783i
$356$	3.28169	+	16.3859i	0.173929	+	0.868448i
$357$	2.58153	+	0.691719i	0.136629	+	0.0366097i
$358$	−1.33727	−	1.86357i	−0.0706768	−	0.0984929i
$359$	−9.98433	+	17.2934i	−0.526953	+	0.912709i	0.472554	+	0.881302i	$0.343332\pi$
$359$	−9.98433	+	17.2934i	−0.526953	+	0.912709i	−0.999507	+	0.0314075i	$0.990001\pi$
$360$	−2.70152	−	8.86256i	−0.142383	−	0.467098i
$361$	15.4968	−	10.9932i	0.815619	−	0.578589i
$362$	−6.44075	+	14.2399i	−0.338518	+	0.748431i
$363$	−3.47777	−	12.9792i	−0.182536	−	0.681232i
$364$	−1.64463	−	8.21185i	−0.0862023	−	0.430418i
$365$	5.02009	−	18.6893i	0.262764	−	0.978242i
$366$	−3.55006	−	0.583727i	−0.185565	−	0.0305119i
$367$	1.69556	−	6.32790i	0.0885073	−	0.330314i	−0.907448	−	0.420164i	$-0.861972\pi$
$367$	1.69556	−	6.32790i	0.0885073	−	0.330314i	0.995955	+	0.0898509i	$0.0286391\pi$
$368$	−4.18385	−	5.42299i	−0.218098	−	0.282693i
$369$			8.43322i			0.439016i
$370$	−5.55475	+	6.76905i	−0.288778	+	0.351906i
$371$	21.8067	−	12.5901i	1.13215	−	0.653644i
$372$	−0.757081	+	11.7876i	−0.0392528	+	0.611161i
$373$	−6.02713	−	6.02713i	−0.312073	−	0.312073i	0.533639	−	0.845712i	$-0.320824\pi$
$373$	−6.02713	−	6.02713i	−0.312073	−	0.312073i	−0.845712	+	0.533639i	$0.820824\pi$
$374$	−0.530116	−	0.434473i	−0.0274116	−	0.0224661i
$375$	3.56052	+	13.3867i	0.183865	+	0.691287i
$376$	−0.593628	−	17.1046i	−0.0306140	−	0.882103i
$377$	1.32099	+	4.92999i	0.0680343	+	0.253907i
$378$	11.1252	−	7.98327i	0.572220	−	0.410615i
$379$	−29.2058			−1.50020			−0.750101	−	0.661323i	$-0.769995\pi$
$379$	−29.2058			−1.50020			−0.750101	+	0.661323i	$0.769995\pi$
$380$	−16.7032	−	10.0500i	−0.856858	−	0.515552i
$381$	24.3333			1.24663
$382$	23.0491	−	16.5396i	1.17929	−	0.846239i
$383$	2.27493	+	8.49015i	0.116243	+	0.433826i	0.999377	−	0.0352954i	$-0.0112372\pi$
$383$	2.27493	+	8.49015i	0.116243	+	0.433826i	−0.883133	+	0.469122i	$0.844571\pi$
$384$	−1.30991	+	13.9560i	−0.0668458	+	0.712190i
$385$	−0.397441	−	1.48692i	−0.0202554	−	0.0757806i
$386$	21.2529	+	17.4185i	1.08175	+	0.886579i
$387$	−2.91154	−	2.91154i	−0.148002	−	0.148002i
$388$	−16.1964	−	1.04024i	−0.822249	−	0.0528103i
$389$	24.3789	−	14.0751i	1.23606	−	0.713638i	0.267772	−	0.963482i	$-0.413713\pi$
$389$	24.3789	−	14.0751i	1.23606	−	0.713638i	0.968286	+	0.249844i	$0.0803794\pi$
$390$	9.32829	−	0.919144i	0.472356	−	0.0465427i
$391$		−	2.11032i		−	0.106724i
$392$	−3.25298	−	10.6482i	−0.164300	−	0.537815i
$393$	4.46091	−	16.6483i	0.225023	−	0.839798i
$394$	−27.3722	−	4.50073i	−1.37899	−	0.226743i
$395$	−16.7094	−	28.9826i	−0.840740	−	1.45827i
$396$	−1.12977	+	0.226265i	−0.0567730	+	0.0113703i
$397$	4.13348	+	15.4264i	0.207454	+	0.774227i	0.988688	+	0.149989i	$0.0479239\pi$
$397$	4.13348	+	15.4264i	0.207454	+	0.774227i	−0.781234	+	0.624238i	$0.785409\pi$
$398$	2.13892	−	4.72895i	0.107215	−	0.237041i
$399$	2.01760	−	9.23474i	0.101007	−	0.462315i
$400$	−2.58289	+	19.8325i	−0.129144	+	0.991626i
$401$	−17.0895	+	29.5999i	−0.853409	+	1.47815i	0.0247050	+	0.999695i	$0.492135\pi$
$401$	−17.0895	+	29.5999i	−0.853409	+	1.47815i	−0.878114	+	0.478452i	$0.841198\pi$
$402$	10.3080	+	14.3650i	0.514118	+	0.716459i
$403$	11.0157	+	2.95165i	0.548731	+	0.147032i
$404$	14.9283	−	2.98978i	0.742712	−	0.148747i
$405$	2.74640	+	4.76366i	0.136470	+	0.236708i
$406$	−1.86336	−	4.94100i	−0.0924771	−	0.245218i
$407$	0.769997	+	0.769997i	0.0381673	+	0.0381673i
$408$	−2.94612	+	3.15796i	−0.145855	+	0.156343i
$409$	−7.32680	+	4.23013i	−0.362287	+	0.209166i	−0.670084	−	0.742286i	$-0.733742\pi$
$409$	−7.32680	+	4.23013i	−0.362287	+	0.209166i	0.307797	+	0.951452i	$0.400408\pi$
$410$	7.51230	−	16.5818i	0.371006	−	0.818918i
$411$			10.4524i			0.515580i
$412$	5.61409	+	11.3467i	0.276586	+	0.559013i
$413$	−5.55488	+	1.48842i	−0.273338	+	0.0732406i
$414$	−2.74375	−	2.24873i	−0.134848	−	0.110519i
$415$	−5.63680	−	21.0887i	−0.276700	−	1.03520i
$416$	12.9637	+	3.88612i	0.635596	+	0.190533i
$417$	2.49939	−	2.49939i	0.122395	−	0.122395i
$418$	−1.44746	+	1.94463i	−0.0707978	+	0.0951150i
$419$	2.35293			0.114948			0.0574741	−	0.998347i	$-0.481695\pi$
$419$	2.35293			0.114948			0.0574741	+	0.998347i	$0.481695\pi$
$420$	−9.51047	+	1.89864i	−0.464063	+	0.0926441i
$421$	8.90150	−	15.4179i	0.433833	−	0.751420i	−0.563367	−	0.826207i	$-0.690494\pi$
$421$	8.90150	−	15.4179i	0.433833	−	0.751420i	0.997200	+	0.0747865i	$0.0238275\pi$
$422$	0.254298	+	2.56470i	0.0123791	+	0.124847i
$423$	−2.29429	−	8.56241i	−0.111552	−	0.416319i
$424$	1.41134	+	40.6659i	0.0685407	+	1.97491i
$425$	−4.36263	+	4.35192i	−0.211619	+	0.211099i
$426$	−21.2908	+	8.02921i	−1.03154	+	0.389017i
$427$	0.930167	−	3.47143i	0.0450139	−	0.167994i
$428$	14.9784	−	7.41095i	0.724008	−	0.358222i
$429$		−	1.16567i		−	0.0562792i
$430$	3.13122	+	8.31840i	0.151001	+	0.401149i
$431$	25.9940	−	15.0076i	1.25209	−	0.722892i	0.280562	−	0.959836i	$-0.409479\pi$
$431$	25.9940	−	15.0076i	1.25209	−	0.722892i	0.971523	+	0.236944i	$0.0761457\pi$
$432$	2.94578	+	21.9308i	0.141729	+	1.05515i
$433$	−0.142960	+	0.533533i	−0.00687020	+	0.0256399i	−0.969276	−	0.245976i	$-0.920891\pi$
$433$	−0.142960	+	0.533533i	−0.00687020	+	0.0256399i	0.962406	+	0.271616i	$0.0875581\pi$
$434$	−11.6430	−	1.91442i	−0.558880	−	0.0918951i
$435$	5.70985	−	1.52619i	0.273766	−	0.0731752i
$436$	3.62990	−	3.19176i	0.173840	−	0.152858i
$437$	−7.45575	+	0.348434i	−0.356657	+	0.0166678i
$438$	−6.24921	+	13.8164i	−0.298599	+	0.660172i
$439$	11.1040	−	19.2326i	0.529963	−	0.917923i	−0.469426	−	0.882972i	$-0.655539\pi$
$439$	11.1040	−	19.2326i	0.529963	−	0.917923i	0.999389	−	0.0349513i	$-0.0111276\pi$
$440$	2.42296	+	0.561502i	0.115510	+	0.0267686i
$441$	−2.88336	−	4.99412i	−0.137303	−	0.237815i
$442$	2.43103	+	3.38781i	0.115632	+	0.161142i
$443$	−24.2902	−	6.50853i	−1.15406	−	0.309229i	−0.369469	−	0.929243i	$-0.620460\pi$
$443$	−24.2902	−	6.50853i	−1.15406	−	0.309229i	−0.784591	+	0.620014i	$0.787127\pi$
$444$	5.15281	−	4.53086i	0.244542	−	0.215025i
$445$	0.0114811	−	18.6837i	0.000544256	−	0.885694i
$446$	−24.7245	+	30.1671i	−1.17074	+	1.42846i
$447$	0.545218	−	2.03478i	0.0257879	−	0.0962419i
$448$	−13.7440	−	2.67768i	−0.649341	−	0.126509i
$449$			13.6049i			0.642057i	0.947070	+	0.321028i	$0.104029\pi$
$449$			13.6049i			0.642057i	−0.947070	+	0.321028i	$0.895971\pi$
$450$	1.00942	+	10.3095i	0.0475848	+	0.485993i
$451$	−1.96055	−	1.13192i	−0.0923186	−	0.0533002i
$452$	−21.7137	+	10.7434i	−1.02133	+	0.505329i
$453$	12.3735	−	3.31548i	0.581360	−	0.155775i
$454$	−3.05001	+	18.5493i	−0.143144	+	0.870560i
$455$	−0.00575380	+	9.36344i	−0.000269743	+	0.438965i
$456$	11.6435	+	9.88720i	0.545257	+	0.463011i
$457$	−11.8560	+	11.8560i	−0.554601	+	0.554601i	−0.927765	−	0.373164i	$-0.878273\pi$
$457$	−11.8560	+	11.8560i	−0.554601	+	0.554601i	0.373164	+	0.927765i	$0.378273\pi$
$458$	25.0054	−	17.9434i	1.16843	−	0.838442i
$459$	−3.40885	+	5.90431i	−0.159112	+	0.275589i
$460$	3.39174	+	6.86570i	0.158141	+	0.320115i
$461$	−19.0693	+	33.0290i	−0.888147	+	1.53832i	−0.0460826	+	0.998938i	$0.514674\pi$
$461$	−19.0693	+	33.0290i	−0.888147	+	1.53832i	−0.842064	+	0.539378i	$0.818660\pi$
$462$	0.119000	+	1.20016i	0.00553639	+	0.0558366i
$463$	−22.1937	+	22.1937i	−1.03143	+	1.03143i	−0.0319406	+	0.999490i	$0.510169\pi$
$463$	−22.1937	+	22.1937i	−1.03143	+	1.03143i	−0.999490	+	0.0319406i	$0.989831\pi$
$464$	8.46331	+	1.09164i	0.392899	+	0.0506783i
$465$	3.42584	−	12.7540i	0.158869	−	0.591455i
$466$	−3.00314	−	2.46132i	−0.139118	−	0.114018i
$467$	−11.0464	−	11.0464i	−0.511165	−	0.511165i	0.403718	−	0.914883i	$-0.367718\pi$
$467$	−11.0464	−	11.0464i	−0.511165	−	0.511165i	−0.914883	+	0.403718i	$0.867718\pi$
$468$	6.99516	+	0.449276i	0.323351	+	0.0207678i
$469$	−15.2956	+	8.83091i	−0.706284	+	0.407773i
$470$	−3.11624	+	18.8796i	−0.143741	+	0.870851i
$471$	−4.21056	+	2.43097i	−0.194012	+	0.112013i
$472$	2.09245	−	9.05454i	0.0963129	−	0.416769i
$473$	1.06766	−	0.286080i	0.0490912	−	0.0131540i
$474$	9.25020	+	24.5284i	0.424876	+	1.12663i
$475$	16.0956	+	14.6946i	0.738517	+	0.674234i
$476$	−2.84881	−	3.23987i	−0.130575	−	0.148499i
$477$	5.45463	+	20.3570i	0.249751	+	0.932082i
$478$	−13.3602	−	18.6184i	−0.611082	−	0.851584i
$479$	−7.68436	−	13.3097i	−0.351107	−	0.608136i	0.635336	−	0.772236i	$-0.280861\pi$
$479$	−7.68436	−	13.3097i	−0.351107	−	0.608136i	−0.986444	+	0.164100i	$0.947528\pi$
$480$	4.50935	−	15.0091i	0.205823	−	0.685070i
$481$	−3.31235	−	5.73716i	−0.151030	−	0.261592i
$482$	−9.39114	+	20.7629i	−0.427755	+	0.945723i
$483$	−2.62571	+	2.62571i	−0.119474	+	0.119474i
$484$	−6.94531	+	20.5487i	−0.315696	+	0.934032i
$485$	17.5243	+	4.70716i	0.795736	+	0.213741i
$486$	6.76134	+	17.9288i	0.306701	+	0.813266i
$487$	8.45803	+	8.45803i	0.383270	+	0.383270i	0.872279	−	0.489009i	$-0.162641\pi$
$487$	8.45803	+	8.45803i	0.383270	+	0.383270i	−0.489009	+	0.872279i	$0.662641\pi$
$488$	4.24657	+	3.96169i	0.192233	+	0.179337i
$489$	−17.5402	−	10.1268i	−0.793195	−	0.457951i
$490$	1.22064	+	12.3882i	0.0551431	+	0.559641i
$491$	−8.43661	−	4.87088i	−0.380739	−	0.219820i	0.297401	−	0.954753i	$-0.403880\pi$
$491$	−8.43661	−	4.87088i	−0.380739	−	0.219820i	−0.678140	+	0.734933i	$0.737214\pi$
$492$	−7.90947	+	11.8710i	−0.356586	+	0.535187i
$493$	1.85913	+	1.85913i	0.0837308	+	0.0837308i
$494$	11.5677	−	9.14817i	0.520456	−	0.411596i
$495$	1.28820		0.000791596i	0.0579004		3.55796e-5i
$496$	11.5677	−	15.1575i	0.519407	−	0.680592i
$497$	−5.88299	−	21.9556i	−0.263888	−	0.984844i
$498$	1.68775	+	17.0216i	0.0756299	+	0.762757i
$499$	−14.9260	+	25.8525i	−0.668178	+	1.15732i	0.310235	+	0.950660i	$0.399592\pi$
$499$	−14.9260	+	25.8525i	−0.668178	+	1.15732i	−0.978413	+	0.206659i	$0.933741\pi$
$500$	7.19887	−	21.1702i	0.321943	−	0.946759i
$501$	21.7381			0.971187
$502$	−32.2611	−	14.5918i	−1.43988	−	0.651264i
$503$	12.3934	+	3.32079i	0.552592	+	0.148067i	0.524301	−	0.851533i	$-0.324327\pi$
$503$	12.3934	+	3.32079i	0.552592	+	0.148067i	0.0282915	+	0.999600i	$0.490993\pi$
$504$	−7.24800	+	0.251547i	−0.322852	+	0.0112048i
$505$	−17.0218	−	0.0104598i	−0.757460	−	0.000465457i
$506$	0.891056	−	0.336037i	0.0396122	−	0.0149387i
$507$	2.33328	−	8.70793i	0.103625	−	0.386733i
$508$	−32.6886	−	21.7799i	−1.45032	−	0.966325i
$509$	−28.5296	+	16.4716i	−1.26455	+	0.730090i	−0.973952	−	0.226754i	$-0.927189\pi$
$509$	−28.5296	+	16.4716i	−1.26455	+	0.730090i	−0.290601	+	0.956844i	$0.593855\pi$
$510$	3.92480	−	2.81272i	0.173793	−	0.124549i
$511$	−13.1183	−	7.57386i	−0.580320	−	0.335048i
$512$	14.2512	−	17.5756i	0.629821	−	0.776740i
$513$	21.4227	+	11.0686i	0.945835	+	0.488690i
$514$	0.339395	+	0.899962i	0.0149701	+	0.0396956i
$515$	−3.65489	−	13.6739i	−0.161054	−	0.602542i
$516$	−1.36771	−	6.82914i	−0.0602102	−	0.300636i
$517$	2.29853	+	0.615889i	0.101089	+	0.0270867i
$518$	3.99605	+	5.56877i	0.175576	+	0.244678i
$519$	9.26344	+	16.0447i	0.406620	+	0.704286i
$520$	−13.3540	−	7.11467i	−0.585613	−	0.311999i
$521$	42.9434			1.88138			0.940692	−	0.339263i	$-0.110178\pi$
$521$	42.9434			1.88138			0.940692	+	0.339263i	$0.110178\pi$
$522$	4.39822	−	0.436098i	0.192505	−	0.0190875i
$523$	−15.3737	−	4.11936i	−0.672243	−	0.180127i	−0.0934782	−	0.995621i	$-0.529799\pi$
$523$	−15.3737	−	4.11936i	−0.672243	−	0.180127i	−0.578765	+	0.815494i	$0.696465\pi$
$524$	−20.8940	+	18.3721i	−0.912758	+	0.802587i
$525$	10.8428	+	0.0133258i	0.473220	+	0.000581585i
$526$	27.7976	−	33.9168i	1.21203	−	1.47884i
$527$	5.67458	−	1.52050i	0.247189	−	0.0662340i
$528$	−1.80253	−	0.741101i	−0.0784451	−	0.0322523i
$529$	−17.3793	−	10.0340i	−0.755623	−	0.436259i
$530$	7.40879	−	44.8859i	0.321817	−	1.94972i
$531$		−	4.81328i		−	0.208879i
$532$	−10.9761	+	10.5998i	−0.475873	+	0.459558i
$533$	9.73855	+	9.73855i	0.421823	+	0.421823i
$534$	−2.37540	+	14.4465i	−0.102793	+	0.625161i
$535$	−18.0504	+	4.82469i	−0.780385	+	0.208590i
$536$	−0.989939	−	28.5238i	−0.0427589	−	1.23204i
$537$	−0.520097	−	1.94103i	−0.0224439	−	0.0837616i
$538$	−2.34904	−	23.6909i	−0.101274	−	1.02139i
$539$	1.54804			0.0666788
$540$	1.60085	−	24.6878i	0.0688895	−	1.06239i
$541$	−21.5713	−	37.3625i	−0.927421	−	1.60634i	−0.787620	−	0.616161i	$-0.788687\pi$
$541$	−21.5713	−	37.3625i	−0.927421	−	1.60634i	−0.139801	−	0.990180i	$-0.544646\pi$
$542$	3.59760	+	36.2831i	0.154530	+	1.55849i
$543$	−9.68178	+	9.68178i	−0.415485	+	0.415485i
$544$	6.78430	−	1.60534i	0.290874	−	0.0688286i
$545$	−4.68175	+	2.69918i	−0.200544	+	0.115620i
$546$	1.19044	−	7.23992i	0.0509462	−	0.309840i
$547$	−7.36827	+	27.4988i	−0.315045	+	1.17576i	0.608903	+	0.793244i	$0.291610\pi$
$547$	−7.36827	+	27.4988i	−0.315045	+	1.17576i	−0.923948	+	0.382518i	$0.875057\pi$
$548$	9.35560	−	14.0415i	0.399651	−	0.599822i
$549$	2.60499	+	1.50399i	0.111178	+	0.0641888i
$550$	−2.53222	−	1.14909i	−0.107974	−	0.0489972i
$551$	6.26132	−	6.87524i	0.266741	−	0.292895i
$552$	−1.75317	−	5.73878i	−0.0746200	−	0.244259i
$553$	−25.2944	+	6.77760i	−1.07563	+	0.288213i
$554$	4.48691	+	0.737770i	0.190631	+	0.0313449i
$555$	−6.64597	+	3.83161i	−0.282106	+	0.162643i
$556$	−5.59470	+	1.12048i	−0.237268	+	0.0475191i
$557$	6.81409	+	1.82583i	0.288722	+	0.0773629i	0.400273	−	0.916396i	$-0.368915\pi$
$557$	6.81409	+	1.82583i	0.288722	+	0.0773629i	−0.111551	+	0.993759i	$0.535582\pi$
$558$	4.06987	−	8.99808i	0.172291	−	0.380919i
$559$	−6.72439			−0.284412
$560$	14.4755	+	5.96191i	0.611700	+	0.251937i
$561$	−0.300240	−	0.520030i	−0.0126761	−	0.0219557i
$562$	12.9966	−	28.7342i	0.548228	−	1.21208i
$563$	8.33840	−	8.33840i	0.351422	−	0.351422i	−0.509217	−	0.860638i	$-0.670065\pi$
$563$	8.33840	−	8.33840i	0.351422	−	0.351422i	0.860638	+	0.509217i	$0.170065\pi$
$564$	4.80108	−	14.2047i	0.202162	−	0.598125i
$565$	26.1671	−	6.99421i	1.10086	−	0.294249i
$566$	−12.0683	+	14.7249i	−0.507268	+	0.618935i
$567$	4.15745	−	1.11399i	0.174597	−	0.0467830i
$568$	35.7880	+	8.27040i	1.50163	+	0.347018i
$569$		−	32.9577i		−	1.38166i	−0.723018	−	0.690829i	$-0.757246\pi$
$569$		−	32.9577i		−	1.38166i	0.723018	−	0.690829i	$-0.242754\pi$
$570$	−10.5853	−	13.4019i	−0.443370	−	0.561343i
$571$		−	13.6414i		−	0.570875i	−0.958397	−	0.285437i	$-0.907861\pi$
$571$		−	13.6414i		−	0.570875i	0.958397	−	0.285437i	$-0.0921389\pi$
$572$	−1.04335	+	1.56593i	−0.0436247	+	0.0654747i
$573$	24.0070	−	6.43267i	1.00291	−	0.268729i
$574$	−11.0209	−	9.03252i	−0.460003	−	0.377010i
$575$	−2.20576	−	8.27266i	−0.0919865	−	0.344994i
$576$	5.14206	−	10.5313i	0.214252	−	0.438804i
$577$	−8.31887	+	8.31887i	−0.346319	+	0.346319i	−0.858736	−	0.512417i	$-0.828750\pi$
$577$	−8.31887	+	8.31887i	−0.346319	+	0.346319i	0.512417	+	0.858736i	$0.328750\pi$
$578$	−19.9480	−	9.02258i	−0.829729	−	0.375290i
$579$	12.0369	+	20.8486i	0.500238	+	0.866438i
$580$	−9.03647	−	3.06045i	−0.375219	−	0.127078i
$581$	−17.0868			−0.708880
$582$	−12.9551	−	5.85966i	−0.537007	−	0.242891i
$583$	−5.46471	−	1.46426i	−0.226325	−	0.0606436i
$584$	20.7615	−	12.9670i	0.859118	−	0.536580i
$585$	−7.56865	−	2.03300i	−0.312925	−	0.0840542i
$586$	3.01987	−	18.3660i	0.124750	−	0.758693i
$587$	−19.7849	+	5.30134i	−0.816610	+	0.218810i	−0.642864	−	0.765981i	$-0.722254\pi$
$587$	−19.7849	+	5.30134i	−0.816610	+	0.218810i	−0.173746	+	0.984791i	$0.555587\pi$
$588$	0.625199	−	9.73426i	0.0257828	−	0.401434i
$589$	−6.30884	−	19.7972i	−0.259951	−	0.815729i
$590$	−4.28767	+	9.46412i	−0.176521	+	0.389632i
$591$	−21.0464	−	12.1512i	−0.865735	−	0.499832i
$592$	−10.9775	+	1.47452i	−0.451174	+	0.0606023i
$593$	−1.45226	+	5.41989i	−0.0596370	+	0.222568i	−0.989312	−	0.145812i	$-0.953421\pi$
$593$	−1.45226	+	5.41989i	−0.0596370	+	0.222568i	0.929675	+	0.368380i	$0.120087\pi$
$594$	−3.03582	−	0.499172i	−0.124561	−	0.0204813i
$595$	2.40915	+	4.17871i	0.0987657	+	0.171310i
$596$	−2.55369	+	2.24546i	−0.104603	+	0.0919774i
$597$	3.21524	−	3.21524i	0.131591	−	0.131591i
$598$	−5.76525	+	0.571644i	−0.235758	+	0.0233763i
$599$	17.8129	+	30.8528i	0.727814	+	1.26061i	0.957805	+	0.287418i	$0.0927968\pi$
$599$	17.8129	+	30.8528i	0.727814	+	1.26061i	−0.229992	+	0.973193i	$0.573870\pi$
$600$	−8.24827	+	15.4589i	−0.336734	+	0.631105i
$601$	14.2551			0.581477			0.290739	−	0.956802i	$-0.406099\pi$
$601$	14.2551			0.581477			0.290739	+	0.956802i	$0.406099\pi$
$602$	6.92336	−	0.686475i	0.282175	−	0.0279786i
$603$	−3.82598	−	14.2787i	−0.155806	−	0.581475i
$604$	−19.5898	−	6.62120i	−0.797097	−	0.269413i
$605$	12.1384	−	20.9945i	0.493495	−	0.853547i
$606$	13.1615	+	2.16410i	0.534648	+	0.0879107i
$607$	22.1148	+	22.1148i	0.897613	+	0.897613i	0.995225	−	0.0976117i	$-0.0311203\pi$
$607$	22.1148	+	22.1148i	0.897613	+	0.897613i	−0.0976117	+	0.995225i	$0.531120\pi$
$608$	−6.79182	−	23.7038i	−0.275445	−	0.961317i
$609$		−	4.62633i		−	0.187468i
$610$	−3.78231	−	5.27775i	−0.153141	−	0.213690i
$611$	−12.5372	−	7.23833i	−0.507199	−	0.292831i
$612$	3.23640	−	1.60130i	0.130824	−	0.0647286i
$613$	−36.0826	+	9.66830i	−1.45736	+	0.390499i	−0.898578	−	0.438814i	$-0.855399\pi$
$613$	−36.0826	+	9.66830i	−1.45736	+	0.390499i	−0.558784	+	0.829313i	$0.688732\pi$
$614$	−5.71462	−	4.68360i	−0.230623	−	0.189015i
$615$	11.2841	−	11.2703i	0.455021	−	0.454462i
$616$	0.914361	−	1.71877i	0.0368407	−	0.0692513i
$617$	−35.4602	−	9.50153i	−1.42757	−	0.382517i	−0.539410	−	0.842043i	$-0.681353\pi$
$617$	−35.4602	−	9.50153i	−1.42757	−	0.382517i	−0.888164	+	0.459526i	$0.848019\pi$
$618$	1.09434	+	11.0368i	0.0440206	+	0.443965i
$619$	−11.4610			−0.460656			−0.230328	−	0.973113i	$-0.573980\pi$
$619$	−11.4610			−0.460656			−0.230328	+	0.973113i	$0.573980\pi$
$620$	−16.0179	+	14.0670i	−0.643293	+	0.564946i
$621$	−4.73627	−	8.20346i	−0.190060	−	0.329193i
$622$	11.6896	−	8.38823i	0.468709	−	0.336337i
$623$	−14.1265	−	3.78518i	−0.565966	−	0.151650i
$624$	9.42537	+	7.19315i	0.377317	+	0.287956i
$625$	−12.5532	+	21.6198i	−0.502127	+	0.864794i
$626$	−31.6210	+	11.9250i	−1.26383	+	0.476617i
$627$	−1.78769	+	1.14661i	−0.0713935	+	0.0457910i
$628$	7.83220	+	0.503036i	0.312539	+	0.0200733i
$629$	−2.95542	−	1.70631i	−0.117840	−	0.0680351i
$630$	8.00014	+	1.32049i	0.318733	+	0.0526096i
$631$	3.90792	−	2.25624i	0.155572	−	0.0898195i	−0.420193	−	0.907435i	$-0.638038\pi$
$631$	3.90792	−	2.25624i	0.155572	−	0.0898195i	0.575765	+	0.817615i	$0.304704\pi$
$632$	9.52807	−	41.2302i	0.379006	−	1.64005i
$633$	−0.584390	+	2.18097i	−0.0232274	+	0.0866859i
$634$	−10.1599	−	26.9407i	−0.403503	−	1.06995i
$635$	31.0343	+	31.0725i	1.23156	+	1.23307i
$636$	−11.4145	+	33.7714i	−0.452613	+	1.33912i
$637$	−9.09679	−	2.43748i	−0.360428	−	0.0965764i
$638$	−0.488954	+	1.08103i	−0.0193579	+	0.0427983i
$639$	19.0245			0.752596
$640$	−19.4918	+	16.1266i	−0.770483	+	0.637461i
$641$	17.2636	−	29.9015i	0.681873	−	1.18104i	−0.292536	−	0.956254i	$-0.594499\pi$
$641$	17.2636	−	29.9015i	0.681873	−	1.18104i	0.974409	−	0.224784i	$-0.0721675\pi$
$642$	14.5693	−	1.44459i	0.575003	−	0.0570135i
$643$	9.97158	+	37.2145i	0.393241	+	1.46760i	0.824756	+	0.565489i	$0.191313\pi$
$643$	9.97158	+	37.2145i	0.393241	+	1.46760i	−0.431515	+	0.902106i	$0.642021\pi$
$644$	5.87747	−	1.17712i	0.231605	−	0.0463849i
$645$	−0.00478498	+	7.78683i	−0.000188408	+	0.306606i
$646$	2.80432	−	7.06066i	0.110334	−	0.277798i
$647$	3.16265	+	3.16265i	0.124337	+	0.124337i	0.766537	−	0.642200i	$-0.221978\pi$
$647$	3.16265	+	3.16265i	0.124337	+	0.124337i	−0.642200	+	0.766537i	$0.721978\pi$
$648$	−1.56606	+	6.77671i	−0.0615206	+	0.266214i
$649$	1.11899	+	0.646049i	0.0439242	+	0.0253596i
$650$	13.0709	+	10.7395i	0.512682	+	0.421239i
$651$	−8.95227	−	5.16860i	−0.350867	−	0.202573i
$652$	14.4988	+	29.3037i	0.567815	+	1.14762i
$653$	−8.03029	−	8.03029i	−0.314249	−	0.314249i	0.532304	−	0.846553i	$-0.321326\pi$
$653$	−8.03029	−	8.03029i	−0.314249	−	0.314249i	−0.846553	+	0.532304i	$0.821326\pi$
$654$	3.96223	−	1.49425i	0.154936	−	0.0584296i
$655$	26.9486	−	15.5367i	1.05297	−	0.607068i
$656$	21.2507	−	8.86767i	0.829699	−	0.346225i
$657$	8.96486	−	8.96486i	0.349752	−	0.349752i
$658$	13.6470	+	6.17262i	0.532017	+	0.240634i
$659$	−0.0107699	−	0.0186540i	−0.000419536	−	0.000726658i	0.865816	−	0.500363i	$-0.166800\pi$
$659$	−0.0107699	−	0.0186540i	−0.000419536	−	0.000726658i	−0.866235	+	0.499637i	$0.833467\pi$
$660$	1.81260	+	1.20931i	0.0705552	+	0.0470724i
$661$	16.0094	+	27.7291i	0.622694	+	1.07854i	0.988982	+	0.148037i	$0.0472954\pi$
$661$	16.0094	+	27.7291i	0.622694	+	1.07854i	−0.366287	+	0.930502i	$0.619371\pi$
$662$	3.74684	−	2.68866i	0.145625	−	0.104498i
$663$	0.945490	+	3.52862i	0.0367198	+	0.137040i
$664$	12.9682	−	24.3769i	0.503262	−	0.946008i
$665$	14.3656	−	9.20147i	0.557073	−	0.356818i
$666$	−5.36773	+	2.02429i	−0.207995	+	0.0784396i
$667$	−3.52854	+	0.945471i	−0.136626	+	0.0366088i
$668$	−29.2023	−	19.4570i	−1.12987	−	0.752814i
$669$	−29.5932	+	17.0857i	−1.14414	+	0.660570i
$670$	−5.19666	+	31.4838i	−0.200764	+	1.21632i
$671$	−0.699294	+	0.403737i	−0.0269959	+	0.0155861i
$672$	−10.4386	−	6.44377i	−0.402677	−	0.248574i
$673$	10.0408	+	10.0408i	0.387044	+	0.387044i	0.873632	−	0.486588i	$-0.161759\pi$
$673$	10.0408	+	10.0408i	0.387044	+	0.387044i	−0.486588	+	0.873632i	$0.661759\pi$
$674$	0.117552	−	0.143430i	0.00452794	−	0.00552470i
$675$	−7.19169	+	26.7084i	−0.276808	+	1.02801i
$676$	−10.9286	+	9.60952i	−0.420331	+	0.369597i
$677$	−29.0068	+	29.0068i	−1.11482	+	1.11482i	−0.122333	+	0.992489i	$0.539038\pi$
$677$	−29.0068	+	29.0068i	−1.11482	+	1.11482i	−0.992489	+	0.122333i	$0.960962\pi$
$678$	−21.1206	+	2.09418i	−0.811133	+	0.0804266i
$679$	7.10174	−	12.3006i	0.272540	−	0.472053i
$680$	−7.79001	+	0.265566i	−0.298733	+	0.0101840i
$681$	−8.23448	+	14.2625i	−0.315546	+	0.546541i
$682$	1.54560	+	2.15390i	0.0591841	+	0.0824771i
$683$	30.9676	−	30.9676i	1.18494	−	1.18494i	0.206497	−	0.978447i	$-0.433794\pi$
$683$	30.9676	−	30.9676i	1.18494	−	1.18494i	0.978447	−	0.206497i	$-0.0662062\pi$
$684$	−6.19173	−	11.1698i	−0.236747	−	0.427088i
$685$	−13.3473	+	13.3309i	−0.509973	+	0.509347i
$686$	26.7123	+	4.39222i	1.01988	+	0.167696i
$687$	26.0447	−	6.97866i	0.993668	−	0.266253i
$688$	−4.27518	+	10.3982i	−0.162990	+	0.396429i
$689$	29.8069	+	17.2090i	1.13555	+	0.655610i
$690$	0.657860	+	6.67654i	0.0250443	+	0.254172i
$691$			39.7136i			1.51078i	0.655277	+	0.755388i	$0.272552\pi$
$691$			39.7136i			1.51078i	−0.655277	+	0.755388i	$0.727448\pi$
$692$	1.91687	−	29.8454i	0.0728684	−	1.13455i
$693$	0.260980	−	0.973990i	0.00991381	−	0.0369988i
$694$	−9.23183	−	7.56624i	−0.350435	−	0.287211i
$695$	6.37928	+	0.00392005i	0.241980	+	0.000148696i
$696$	6.60017	+	3.51119i	0.250179	+	0.133091i
$697$	6.85291	+	1.83623i	0.259572	+	0.0695522i
$698$	−8.17171	+	5.86388i	−0.309304	+	0.221951i
$699$	−1.70088	−	2.94600i	−0.0643331	−	0.111428i
$700$	−14.5540	−	9.72293i	−0.550089	−	0.367492i
$701$	−10.8929	+	18.8670i	−0.411419	+	0.712598i	−0.995045	−	0.0994241i	$-0.968300\pi$
$701$	−10.8929	+	18.8670i	−0.411419	+	0.712598i	0.583626	+	0.812022i	$0.301633\pi$
$702$	17.0535	+	7.71338i	0.643644	+	0.291123i
$703$	−5.54042	+	10.7232i	−0.208961	+	0.404433i
$704$	1.75813	+	2.60895i	0.0662621	+	0.0983286i
$705$	−8.39089	+	14.5128i	−0.316019	+	0.546585i
$706$	−6.81605	+	41.4533i	−0.256526	+	1.56012i
$707$	−3.44849	+	12.8699i	−0.129694	+	0.484024i
$708$	4.51435	−	6.77542i	0.169660	−	0.254636i
$709$	13.9961	−	8.08067i	0.525636	−	0.303476i	−0.213602	−	0.976921i	$-0.568519\pi$
$709$	13.9961	−	8.08067i	0.525636	−	0.303476i	0.739237	+	0.673445i	$0.235186\pi$
$710$	−37.4069	−	16.9470i	−1.40385	−	0.636009i
$711$		−	21.9175i		−	0.821970i
$712$	16.1216	−	17.2808i	0.604181	−	0.647626i
$713$	−2.11259	+	7.88428i	−0.0791170	+	0.295268i
$714$	−1.33369	−	3.53650i	−0.0499122	−	0.132350i
$715$	1.48851	−	1.48668i	0.0556671	−	0.0555988i
$716$	−1.03866	+	3.07304i	−0.0388167	+	0.114845i
$717$	−5.19612	−	19.3922i	−0.194053	−	0.724215i
$718$	28.1022	−	2.78643i	1.04876	−	0.103988i
$719$	4.25996	−	7.37846i	0.158870	−	0.275170i	−0.775592	−	0.631235i	$-0.782548\pi$
$719$	4.25996	−	7.37846i	0.158870	−	0.275170i	0.934461	+	0.356065i	$0.115882\pi$
$720$	−7.95565	+	10.4112i	−0.296490	+	0.388004i
$721$	−11.0791			−0.412605
$722$	−25.4083	−	8.74185i	−0.945598	−	0.325338i
$723$	−14.1168	+	14.1168i	−0.525010	+	0.525010i
$724$	21.6720	−	4.34038i	0.805434	−	0.161309i
$725$	9.23114	+	5.34474i	0.342836	+	0.198499i
$726$	−12.0457	+	14.6973i	−0.447057	+	0.545469i
$727$	40.9920	−	10.9838i	1.52031	−	0.407366i	0.600466	−	0.799651i	$-0.294982\pi$
$727$	40.9920	−	10.9838i	1.52031	−	0.407366i	0.919844	+	0.392285i	$0.128315\pi$
$728$	−8.07940	+	8.66036i	−0.299442	+	0.320974i
$729$			24.1642i			0.894970i
$730$	−25.6130	+	9.64127i	−0.947981	+	0.356839i
$731$	−2.99989	+	1.73199i	−0.110955	+	0.0640599i
$732$	2.25633	+	4.56030i	0.0833964	+	0.168554i
$733$	−0.361853	−	0.361853i	−0.0133654	−	0.0133654i	0.700393	−	0.713758i	$-0.253008\pi$
$733$	−0.361853	−	0.361853i	−0.0133654	−	0.0133654i	−0.713758	+	0.700393i	$0.753008\pi$
$734$	−8.66873	+	3.26917i	−0.319969	+	0.120667i
$735$	−2.82907	+	10.5323i	−0.104352	+	0.388491i
$736$	−2.78142	+	9.27850i	−0.102524	+	0.342010i
$737$	3.83304	+	1.02706i	0.141192	+	0.0378323i
$738$	9.68975	−	6.95320i	0.356685	−	0.255951i
$739$	−23.0595	+	39.9403i	−0.848259	+	1.46923i	0.0345013	+	0.999405i	$0.489016\pi$
$739$	−23.0595	+	39.9403i	−0.848259	+	1.46923i	−0.882760	+	0.469823i	$0.844318\pi$
$740$	12.3575	+	0.801308i	0.454272	+	0.0294567i
$741$	12.3105	−	3.92301i	0.452236	−	0.144116i
$742$	−32.4456	−	14.6753i	−1.19112	−	0.538746i
$743$	8.19239	+	30.5744i	0.300550	+	1.12167i	0.936709	+	0.350109i	$0.113855\pi$
$743$	8.19239	+	30.5744i	0.300550	+	1.12167i	−0.636159	+	0.771558i	$0.719478\pi$
$744$	14.1682	−	8.84904i	0.519431	−	0.324422i
$745$	3.29369	−	1.89891i	0.120671	−	0.0695708i
$746$	−1.95579	+	11.8945i	−0.0716064	+	0.435490i
$747$	3.70141	−	13.8139i	0.135428	−	0.505423i
$748$	−0.0621281	+	0.967326i	−0.00227163	+	0.0353689i
$749$			14.6250i			0.534388i
$750$	12.4457	−	15.1284i	0.454451	−	0.552411i
$751$	−11.0032	+	6.35270i	−0.401513	+	0.231813i	−0.687136	−	0.726528i	$-0.741133\pi$
$751$	−11.0032	+	6.35270i	−0.401513	+	0.231813i	0.285624	+	0.958342i	$0.407799\pi$
$752$	−19.1637	+	14.7849i	−0.698829	+	0.539148i
$753$	−21.9345	−	21.9345i	−0.799337	−	0.799337i
$754$	4.57539	−	5.58259i	0.166626	−	0.203306i
$755$	20.0148	+	11.5719i	0.728412	+	0.421146i
$756$	−18.3455	−	6.20066i	−0.667221	−	0.225516i
$757$	4.98421	+	18.6013i	0.181154	+	0.676077i	0.995421	+	0.0955864i	$0.0304726\pi$
$757$	4.98421	+	18.6013i	0.181154	+	0.676077i	−0.814267	+	0.580491i	$0.802861\pi$
$758$	24.0802	+	33.5574i	0.874634	+	1.21886i
$759$	0.834308			0.0302834
$760$	2.22444	+	27.4782i	0.0806891	+	0.996739i
$761$	3.02162			0.109534			0.0547668	−	0.998499i	$-0.482558\pi$
$761$	3.02162			0.109534			0.0547668	+	0.998499i	$0.482558\pi$
$762$	−20.0628	−	27.9589i	−0.726800	−	1.01284i
$763$	1.09483	+	4.08596i	0.0396355	+	0.147922i
$764$	−38.0079	−	12.8464i	−1.37508	−	0.464767i
$765$	−3.90017	+	1.04248i	−0.141011	+	0.0376909i
$766$	7.87949	−	9.61403i	0.284697	−	0.347369i
$767$	−5.55831	−	5.55831i	−0.200699	−	0.200699i
$768$	17.1155	−	10.0017i	0.617601	−	0.360905i
$769$	40.0036	−	23.0961i	1.44257	−	0.832867i	0.444547	−	0.895755i	$-0.353365\pi$
$769$	40.0036	−	23.0961i	1.44257	−	0.832867i	0.998021	+	0.0628884i	$0.0200312\pi$
$770$	−1.38078	+	1.68263i	−0.0497599	+	0.0606377i
$771$			0.842646i			0.0303472i
$772$	2.49079	−	38.7812i	0.0896454	−	1.39577i
$773$	2.49883	−	9.32575i	0.0898766	−	0.335424i	−0.906316	−	0.422600i	$-0.861118\pi$
$773$	2.49883	−	9.32575i	0.0898766	−	0.335424i	0.996193	+	0.0871759i	$0.0277842\pi$
$774$	−0.944785	+	5.74592i	−0.0339596	+	0.206533i
$775$	20.6556	−	11.8917i	0.741971	−	0.427162i
$776$	12.1587	+	19.4673i	0.436473	+	0.698837i
$777$	1.55417	+	5.80022i	0.0557554	+	0.208082i
$778$	−36.2727	−	16.4063i	−1.30044	−	0.588195i
$779$	5.35591	−	24.5144i	0.191895	−	0.878321i
$780$	−8.74728	−	9.96036i	−0.313203	−	0.356638i
$781$	−2.55350	+	4.42280i	−0.0913715	+	0.158260i
$782$	−2.42476	+	1.73996i	−0.0867092	+	0.0622210i
$783$	11.3995	+	3.05448i	0.407384	+	0.109158i
$784$	−9.55266	+	12.5171i	−0.341167	+	0.447040i
$785$	−8.47432	−	2.27627i	−0.302461	−	0.0812435i
$786$	−22.8069	+	8.60100i	−0.813497	+	0.306788i
$787$	2.05359	+	2.05359i	0.0732025	+	0.0732025i	0.742760	−	0.669558i	$-0.233516\pi$
$787$	2.05359	+	2.05359i	0.0732025	+	0.0732025i	−0.669558	+	0.742760i	$0.733516\pi$
$788$	17.3970	+	35.1614i	0.619744	+	1.25257i
$789$	33.2715	−	19.2093i	1.18450	−	0.683870i
$790$	−19.5241	+	43.0953i	−0.694635	+	1.53326i
$791$		−	21.2015i		−	0.753839i
$792$	1.19147	+	1.11155i	0.0423372	+	0.0394971i
$793$	4.74499	−	1.27142i	0.168500	−	0.0451493i
$794$	14.3168	−	17.4684i	0.508085	−	0.619931i
$795$	19.9492	−	34.5040i	0.707524	−	1.22373i
$796$	−7.19710	+	1.44141i	−0.255094	+	0.0510893i
$797$	10.2134	−	10.2134i	0.361777	−	0.361777i	−0.502690	−	0.864467i	$-0.667656\pi$
$797$	10.2134	−	10.2134i	0.361777	−	0.361777i	0.864467	+	0.502690i	$0.167656\pi$
$798$	−12.2742	+	5.29583i	−0.434503	+	0.187470i
$799$	−7.45744			−0.263825
$800$	24.9171	−	13.3842i	0.880953	−	0.473203i
$801$	6.12028	−	10.6006i	0.216250	−	0.374555i
$802$	48.1005	−	4.76933i	1.69849	−	0.168411i
$803$	0.880863	+	3.28742i	0.0310850	+	0.116011i
$804$	8.00632	−	23.6878i	0.282361	−	0.835406i
$805$	−6.70170	−	0.00411818i	−0.236204	−	0.000145147i
$806$	−5.69102	−	15.0907i	−0.200458	−	0.531546i
$807$	5.39821	−	20.1464i	0.190026	−	0.709186i
$808$	−15.7437	−	14.6875i	−0.553861	−	0.516706i
$809$			30.4382i			1.07015i	0.844804	+	0.535075i	$0.179717\pi$
$809$			30.4382i			1.07015i	−0.844804	+	0.535075i	$0.820283\pi$
$810$	3.20903	−	7.08326i	0.112754	−	0.248880i
$811$	3.54609	−	2.04734i	0.124520	−	0.0718917i	−0.436446	−	0.899730i	$-0.643763\pi$
$811$	3.54609	−	2.04734i	0.124520	−	0.0718917i	0.560966	+	0.827839i	$0.310430\pi$
$812$	−4.14086	+	6.21486i	−0.145316	+	0.218099i
$813$	−8.26746	+	30.8546i	−0.289952	+	1.08212i
$814$	0.249862	−	1.51959i	0.00875765	−	0.0532616i
$815$	−9.43901	−	35.3136i	−0.330634	−	1.23698i
$816$	6.05757	+	0.781339i	0.212058	+	0.0273523i
$817$	6.61441	+	10.3126i	0.231409	+	0.360793i
$818$	10.9014	+	4.93073i	0.381157	+	0.172399i
$819$	−3.06721	+	5.31256i	−0.107177	+	0.185636i
$820$	−25.2464	+	5.04011i	−0.881642	+	0.176008i
$821$	−13.6091	−	23.5717i	−0.474962	−	0.822658i	0.524627	−	0.851332i	$-0.324205\pi$
$821$	−13.6091	−	23.5717i	−0.474962	−	0.822658i	−0.999589	+	0.0286743i	$0.990871\pi$
$822$	12.0098	−	8.61804i	0.418891	−	0.300589i
$823$	37.7051	+	10.1031i	1.31432	+	0.352170i	0.846846	−	0.531838i	$-0.178498\pi$
$823$	37.7051	+	10.1031i	1.31432	+	0.352170i	0.467472	+	0.884008i	$0.345165\pi$
$824$	8.40854	−	15.8060i	0.292925	−	0.550627i
$825$	−1.72051	−	1.72475i	−0.0599006	−	0.0600480i
$826$	6.29020	+	5.15534i	0.218864	+	0.179377i
$827$	−12.1747	+	45.4365i	−0.423355	+	1.57998i	0.344134	+	0.938921i	$0.388173\pi$
$827$	−12.1747	+	45.4365i	−0.423355	+	1.57998i	−0.767489	+	0.641062i	$0.778494\pi$
$828$	−0.321561	+	5.00665i	−0.0111750	+	0.173993i
$829$		−	19.7704i		−	0.686655i	−0.939216	−	0.343328i	$-0.888446\pi$
$829$		−	19.7704i		−	0.686655i	0.939216	−	0.343328i	$-0.111554\pi$
$830$	−19.5833	+	23.8643i	−0.679746	+	0.828342i
$831$	3.44999	+	1.99185i	0.119679	+	0.0690965i
$832$	−6.22341	−	18.0994i	−0.215758	−	0.627482i
$833$	−4.68608	+	1.25563i	−0.162363	+	0.0435051i
$834$	−4.93254	−	0.811043i	−0.170800	−	0.0280841i
$835$	27.7245	+	27.7586i	0.959445	+	0.960625i
$836$	3.42781	+	0.0597838i	0.118553	+	0.00206767i
$837$	18.6463	−	18.6463i	0.644510	−	0.644510i
$838$	−1.93999	−	2.70351i	−0.0670160	−	0.0933913i
$839$	−3.97289	+	6.88124i	−0.137159	+	0.237567i	−0.926420	−	0.376491i	$-0.877131\pi$
$839$	−3.97289	+	6.88124i	−0.137159	+	0.237567i	0.789261	+	0.614058i	$0.210464\pi$
$840$	10.0229	+	9.36208i	0.345824	+	0.323022i
$841$	−12.2244	+	21.1733i	−0.421531	+	0.730113i
$842$	−25.0544	+	2.48423i	−0.863432	+	0.0856122i
$843$	19.5365	−	19.5365i	0.672874	−	0.672874i
$844$	2.73716	−	2.40678i	0.0942170	−	0.0828449i
$845$	14.0955	−	8.12648i	0.484899	−	0.279559i
$846$	−7.94655	+	9.69586i	−0.273208	+	0.333350i
$847$	−13.4227	−	13.4227i	−0.461210	−	0.461210i
$848$	45.5614	−	35.1507i	1.56458	−	1.20708i
$849$	−14.4448	+	8.33971i	−0.495744	+	0.286218i
$850$	8.59735	+	1.42449i	0.294887	+	0.0488597i
$851$	4.10626	−	2.37075i	0.140761	−	0.0812684i
$852$	26.7798	+	17.8429i	0.917461	+	0.611289i
$853$	−24.5709	+	6.58376i	−0.841293	+	0.225424i	−0.653634	−	0.756811i	$-0.726757\pi$
$853$	−24.5709	+	6.58376i	−0.841293	+	0.225424i	−0.187659	+	0.982234i	$0.560090\pi$
$854$	−4.75559	+	1.79344i	−0.162733	+	0.0613702i
$855$	4.32702	+	13.6071i	0.147981	+	0.465354i
$856$	−20.8649	−	11.0998i	−0.713147	−	0.379383i
$857$	3.52251	+	13.1462i	0.120327	+	0.449066i	0.999630	−	0.0271965i	$-0.00865799\pi$
$857$	3.52251	+	13.1462i	0.120327	+	0.449066i	−0.879303	+	0.476262i	$0.841991\pi$
$858$	−1.33936	+	0.961098i	−0.0457248	+	0.0328114i
$859$	−16.2971	−	28.2274i	−0.556049	−	0.963105i	−0.997821	−	0.0659779i	$-0.978983\pi$
$859$	−16.2971	−	28.2274i	−0.556049	−	0.963105i	0.441772	−	0.897127i	$-0.354350\pi$
$860$	6.97614	−	10.4563i	0.237884	−	0.356557i
$861$	−6.24186	−	10.8112i	−0.212722	−	0.368445i
$862$	−38.6758	−	17.4932i	−1.31730	−	0.595822i
$863$	−24.6606	+	24.6606i	−0.839458	+	0.839458i	−0.988787	−	0.149330i	$-0.952288\pi$
$863$	−24.6606	+	24.6606i	−0.839458	+	0.839458i	0.149330	+	0.988787i	$0.452288\pi$
$864$	22.7697	−	21.4667i	0.774640	−	0.730312i
$865$	−8.67395	+	32.2922i	−0.294923	+	1.09797i
$866$	0.730899	−	0.275638i	0.0248370	−	0.00936656i
$867$	−13.5628	−	13.5628i	−0.460616	−	0.460616i
$868$	7.39997	+	14.9562i	0.251171	+	0.507646i
$869$	5.09536	+	2.94181i	0.172848	+	0.0997940i
$870$	−6.46137	−	5.30227i	−0.219061	−	0.179764i
$871$	−20.9071	−	12.0707i	−0.708409	−	0.409000i
$872$	−6.66019	−	1.53913i	−0.225542	−	0.0521216i
$873$	8.40602	+	8.40602i	0.284501	+	0.284501i
$874$	6.54763	+	8.27937i	0.221477	+	0.280054i
$875$	13.8118	+	13.8628i	0.466923	+	0.468648i
$876$	21.0275	−	4.21130i	0.710453	−	0.142287i
$877$	−2.23251	−	8.33185i	−0.0753866	−	0.281346i	0.917934	−	0.396733i	$-0.129856\pi$
$877$	−2.23251	−	8.33185i	−0.0753866	−	0.281346i	−0.993321	+	0.115386i	$0.963189\pi$
$878$	−31.2535	+	3.09889i	−1.05475	+	0.104583i
$879$	8.15313	−	14.1216i	0.274998	−	0.476311i
$880$	−1.35257	−	3.24694i	−0.0455952	−	0.109454i
$881$	49.7583			1.67640			0.838200	−	0.545362i	$-0.183608\pi$
$881$	49.7583			1.67640			0.838200	+	0.545362i	$0.183608\pi$
$882$	−3.36091	+	7.43063i	−0.113168	+	0.250202i
$883$	24.2741	+	6.50424i	0.816890	+	0.218885i	0.642986	−	0.765878i	$-0.277695\pi$
$883$	24.2741	+	6.50424i	0.816890	+	0.218885i	0.173904	+	0.984763i	$0.444362\pi$
$884$	1.88820	−	5.58650i	0.0635069	−	0.187894i
$885$	−6.44046	+	6.43255i	−0.216494	+	0.216228i
$886$	12.5490	+	33.2756i	0.421591	+	1.11792i
$887$	−12.0653	+	45.0282i	−0.405112	+	1.51190i	0.398736	+	0.917066i	$0.369449\pi$
$887$	−12.0653	+	45.0282i	−0.405112	+	1.51190i	−0.803849	+	0.594834i	$0.797218\pi$
$888$	−9.45445	−	2.18487i	−0.317271	−	0.0733195i
$889$	29.7702	−	17.1878i	0.998461	−	0.576462i
$890$	−21.4770	+	15.3916i	−0.719912	+	0.515927i
$891$	−0.837488	−	0.483524i	−0.0280569	−	0.0161987i
$892$	55.0474	+	3.53551i	1.84312	+	0.118378i
$893$	1.23129	+	26.3471i	0.0412036	+	0.881672i
$894$	−2.78749	+	1.05123i	−0.0932277	+	0.0351582i
$895$	1.81528	−	3.13970i	0.0606782	−	0.104949i
$896$	8.25526	+	17.9996i	0.275789	+	0.601323i
$897$	−4.90267	−	1.31367i	−0.163695	−	0.0438620i
$898$	15.6321	−	11.2173i	0.521648	−	0.374326i
$899$	−5.08467	−	8.80691i	−0.169583	−	0.293727i
$900$	11.0133	−	9.65999i	0.367109	−	0.322000i
$901$	17.7299			0.590670
$902$	0.315897	+	3.18594i	0.0105182	+	0.106080i
$903$	5.88751	+	1.57755i	0.195924	+	0.0524977i
$904$	30.2472	+	16.0911i	1.00601	+	0.535180i
$905$	−24.7112	−	0.0151849i	−0.821428	−	0.000504765i
$906$	−14.0115	−	11.4836i	−0.465500	−	0.381516i
$907$	3.93035	−	1.05313i	0.130505	−	0.0349687i	−0.192975	−	0.981204i	$-0.561814\pi$
$907$	3.93035	−	1.05313i	0.130505	−	0.0349687i	0.323480	+	0.946235i	$0.395147\pi$
$908$	23.8278	−	11.7894i	0.790754	−	0.391247i
$909$	−9.65771	−	5.57588i	−0.320326	−	0.184940i
$910$	10.7633	−	7.71356i	0.356801	−	0.255702i
$911$			1.01001i			0.0334631i	0.999860	+	0.0167315i	$0.00532606\pi$
$911$			1.01001i			0.0334631i	−0.999860	+	0.0167315i	$0.994674\pi$
$912$	1.76030	−	21.5304i	0.0582894	−	0.712942i
$913$	2.71463	+	2.71463i	0.0898410	+	0.0898410i
$914$	23.3979	+	3.84724i	0.773932	+	0.127256i
$915$	−1.46892	−	5.49559i	−0.0485610	−	0.181679i
$916$	−41.2340	−	13.9368i	−1.36241	−	0.460484i
$917$	−6.30194	−	23.5191i	−0.208108	−	0.776671i
$918$	9.59464	−	0.951342i	0.316670	−	0.0313990i
$919$	−49.0618			−1.61840			−0.809200	−	0.587533i	$-0.800099\pi$
$919$	−49.0618			−1.61840			−0.809200	+	0.587533i	$0.800099\pi$
$920$	5.09219	−	9.55788i	0.167884	−	0.315114i
$921$	−3.23657	−	5.60591i	−0.106649	−	0.184721i
$922$	53.6730	−	5.32186i	1.76763	−	0.175266i
$923$	21.9692	−	21.9692i	0.723124	−	0.723124i
$924$	1.28087	−	1.12627i	0.0421375	−	0.0370515i
$925$	−13.3690	−	3.59982i	−0.439569	−	0.118361i
$926$	43.7993	+	7.20180i	1.43934	+	0.236666i
$927$	2.39999	−	8.95689i	0.0788261	−	0.294183i
$928$	−5.72372	−	10.6244i	−0.187890	−	0.348763i
$929$	5.35785	+	3.09335i	0.175785	+	0.101490i	0.585311	−	0.810809i	$-0.300972\pi$
$929$	5.35785	+	3.09335i	0.175785	+	0.101490i	−0.409526	+	0.912299i	$0.634306\pi$
$930$	−17.4790	+	6.57945i	−0.573159	+	0.215749i
$931$	5.20985	+	16.3486i	0.170746	+	0.535803i
$932$	−0.351960	+	5.47996i	−0.0115288	+	0.179502i
$933$	12.1754	−	3.26239i	0.398605	−	0.106806i
$934$	−3.58452	+	21.8000i	−0.117289	+	0.713318i
$935$	0.281134	−	1.04663i	0.00919405	−	0.0342285i
$936$	−5.25130	−	8.40786i	−0.171644	−	0.274819i
$937$	20.3212	+	5.44506i	0.663866	+	0.177882i	0.574990	−	0.818160i	$-0.305006\pi$
$937$	20.3212	+	5.44506i	0.663866	+	0.177882i	0.0888757	+	0.996043i	$0.471673\pi$
$938$	22.7579	+	10.2935i	0.743073	+	0.336095i
$939$	−29.6071			−0.966192
$940$	24.2620	−	11.9857i	0.791338	−	0.390930i
$941$	−19.4166	−	33.6305i	−0.632962	−	1.09632i	−0.986943	−	0.161069i	$-0.948506\pi$
$941$	−19.4166	−	33.6305i	−0.632962	−	1.09632i	0.353981	−	0.935252i	$-0.384828\pi$
$942$	6.26479	+	2.83359i	0.204118	+	0.0923233i
$943$	−6.97018	+	6.97018i	−0.226980	+	0.226980i
$944$	−12.1289	+	5.06125i	−0.394761	+	0.164730i
$945$	18.7435	+	10.8369i	0.609727	+	0.352526i
$946$	−1.20900	−	0.990871i	−0.0393078	−	0.0322160i
$947$	12.8926	−	3.45456i	0.418953	−	0.112258i	−0.0431833	−	0.999067i	$-0.513750\pi$
$947$	12.8926	−	3.45456i	0.418953	−	0.112258i	0.462136	+	0.886809i	$0.347083\pi$
$948$	20.5563	−	30.8522i	0.667637	−	1.00203i
$949$		−	20.7050i		−	0.672112i
$950$	3.61322	−	30.6096i	0.117228	−	0.993105i
$951$		−	25.2250i		−	0.817976i
$952$	−1.37375	+	5.94456i	−0.0445236	+	0.192664i
$953$	−20.8653	+	5.59083i	−0.675892	+	0.181105i	−0.580408	−	0.814326i	$-0.697107\pi$
$953$	−20.8653	+	5.59083i	−0.675892	+	0.181105i	−0.0954846	+	0.995431i	$0.530440\pi$
$954$	18.8928	−	23.0517i	0.611676	−	0.746327i
$955$	38.8325	+	22.4518i	1.25659	+	0.726522i
$956$	−10.3770	+	30.7017i	−0.335615	+	0.992965i
$957$	−0.734998	+	0.734998i	−0.0237591	+	0.0237591i
$958$	−8.95706	+	19.8032i	−0.289390	+	0.639812i
$959$	7.38308	+	12.7879i	0.238412	+	0.412942i
$960$	−20.9634	+	7.19381i	−0.676592	+	0.232179i
$961$	8.27734			0.267011
$962$	−3.86095	+	8.53619i	−0.124482	+	0.275218i
$963$	−11.8237	−	3.16814i	−0.381012	−	0.102092i
$964$	31.5995	−	6.32862i	1.01775	−	0.203831i
$965$	−11.2710	+	41.9606i	−0.362825	+	1.35076i
$966$	5.18184	+	0.852035i	0.166723	+	0.0274138i
$967$	10.3244	−	2.76643i	0.332012	−	0.0889623i	−0.0889622	−	0.996035i	$-0.528355\pi$
$967$	10.3244	−	2.76643i	0.332012	−	0.0889623i	0.420974	+	0.907073i	$0.361688\pi$
$968$	29.3368	−	8.96228i	0.942922	−	0.288059i
$969$	4.48151	−	4.92092i	0.143967	−	0.158083i
$970$	−9.04027	−	24.0164i	−0.290266	−	0.771121i
$971$	−39.7670	−	22.9595i	−1.27618	−	0.736806i	−0.300040	−	0.953927i	$-0.597000\pi$
$971$	−39.7670	−	22.9595i	−1.27618	−	0.736806i	−0.976145	+	0.217121i	$0.930333\pi$
$972$	15.0254	−	22.5511i	0.481940	−	0.723326i
$973$	1.29239	−	4.82328i	0.0414323	−	0.154627i
$974$	2.74461	−	16.6919i	0.0879428	−	0.534843i
$975$	7.39459	+	12.8442i	0.236817	+	0.411345i
$976$	1.05068	−	8.14572i	0.0336314	−	0.260738i
$977$	−27.9410	+	27.9410i	−0.893913	+	0.893913i	−0.994889	−	0.100976i	$-0.967803\pi$
$977$	−27.9410	+	27.9410i	−0.893913	+	0.893913i	0.100976	+	0.994889i	$0.467803\pi$
$978$	2.82619	+	28.5032i	0.0903717	+	0.911433i
$979$	1.64295	+	2.84568i	0.0525090	+	0.0909483i
$980$	13.2276	−	11.6166i	0.422540	−	0.371078i
$981$	−3.54048			−0.113039
$982$	1.35936	+	13.7097i	0.0433791	+	0.437494i
$983$	3.40886	+	12.7221i	0.108726	+	0.405770i	0.998741	−	0.0501601i	$-0.0159732\pi$
$983$	3.40886	+	12.7221i	0.108726	+	0.405770i	−0.890015	+	0.455931i	$0.849307\pi$
$984$	20.1612	−	0.699708i	0.642714	−	0.0223059i
$985$	−11.3259	−	42.3728i	−0.360872	−	1.35011i
$986$	0.603281	−	3.66898i	0.0192124	−	0.116844i
$987$	9.27871	+	9.27871i	0.295345	+	0.295345i
$988$	−20.0488	−	5.74860i	−0.637838	−	0.182887i
$989$		−	4.81286i		−	0.153040i
$990$	−1.06121	−	1.48079i	−0.0337276	−	0.0470627i
$991$	−32.6310	−	18.8395i	−1.03656	−	0.598457i	−0.117701	−	0.993049i	$-0.537553\pi$
$991$	−32.6310	−	18.8395i	−1.03656	−	0.598457i	−0.918856	+	0.394592i	$0.870886\pi$
$992$	−26.9536	−	0.793925i	−0.855777	−	0.0252071i
$993$	3.90257	−	1.04569i	0.123844	−	0.0331840i
$994$	−20.3764	+	24.8620i	−0.646301	+	0.788574i
$995$	8.20639	+	0.00504280i	0.260160	+	0.000159868i
$996$	18.1663	−	15.9736i	0.575620	−	0.506142i
$997$	−49.6334	−	13.2992i	−1.57191	−	0.421191i	−0.635498	−	0.772103i	$-0.719205\pi$
$997$	−49.6334	−	13.2992i	−1.57191	−	0.421191i	−0.936409	+	0.350911i	$0.885872\pi$
$998$	42.0110	−	4.16554i	1.32984	−	0.131858i
$999$	−15.3181			−0.484644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.v.c.163.17	yes	216
4.3	odd	2	inner	380.2.v.c.163.29	yes	216
5.2	odd	4	inner	380.2.v.c.87.45	yes	216
19.7	even	3	inner	380.2.v.c.83.53	yes	216
20.7	even	4	inner	380.2.v.c.87.53	yes	216
76.7	odd	6	inner	380.2.v.c.83.45	yes	216
95.7	odd	12	inner	380.2.v.c.7.29	yes	216
380.7	even	12	inner	380.2.v.c.7.17	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.v.c.7.17	✓	216	380.7	even	12	inner
380.2.v.c.7.29	yes	216	95.7	odd	12	inner
380.2.v.c.83.45	yes	216	76.7	odd	6	inner
380.2.v.c.83.53	yes	216	19.7	even	3	inner
380.2.v.c.87.45	yes	216	5.2	odd	4	inner
380.2.v.c.87.53	yes	216	20.7	even	4	inner
380.2.v.c.163.17	yes	216	1.1	even	1	trivial
380.2.v.c.163.29	yes	216	4.3	odd	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.824501 - 1.14900i) q^{2} +(-0.320669 - 1.19675i) q^{3} +(-0.640395 + 1.89470i) q^{4} +(1.11922 - 1.93580i) q^{5} +(-1.11068 + 1.35517i) q^{6} +(-1.23765 - 1.23765i) q^{7} +(2.70502 - 0.826371i) q^{8} +(1.26868 - 0.732475i) q^{9} +(-3.14704 + 0.310087i) q^{10} +0.393257i q^{11} +(2.47285 + 0.158823i) q^{12} +(0.619206 - 2.31091i) q^{13} +(-0.401613 + 2.44250i) q^{14} +(-2.67558 - 0.718683i) q^{15} +(-3.17979 - 2.42671i) q^{16} +(-0.318975 - 1.19043i) q^{17} +(-1.88764 - 0.853789i) q^{18} +(-4.15312 + 1.32349i) q^{19} +(2.95103 + 3.36027i) q^{20} +(-1.08428 + 1.87804i) q^{21} +(0.451852 - 0.324241i) q^{22} +(1.65399 + 0.443185i) q^{23} +(-1.85638 - 2.97225i) q^{24} +(-2.49468 - 4.33320i) q^{25} +(-3.16577 + 1.19388i) q^{26} +(-3.91168 - 3.91168i) q^{27} +(3.13756 - 1.55239i) q^{28} +(-1.84754 + 1.06668i) q^{29} +(1.38026 + 3.66680i) q^{30} +4.76683i q^{31} +(-0.166552 + 5.65440i) q^{32} +(0.470632 - 0.126105i) q^{33} +(-1.10481 + 1.34801i) q^{34} +(-3.78105 + 1.01064i) q^{35} +(0.575363 + 2.87285i) q^{36} +(1.95800 - 1.95800i) q^{37} +(4.94494 + 3.68071i) q^{38} -2.96415 q^{39} +(1.42783 - 6.16128i) q^{40} +(-2.87833 + 4.98541i) q^{41} +(3.05185 - 0.302602i) q^{42} +(-0.727463 - 2.71493i) q^{43} +(-0.745104 - 0.251840i) q^{44} +(0.00201292 - 3.27573i) q^{45} +(-0.854497 - 2.26584i) q^{46} +(1.56612 - 5.84485i) q^{47} +(-1.88452 + 4.58360i) q^{48} -3.93646i q^{49} +(-2.92197 + 6.43911i) q^{50} +(-1.32237 + 0.763470i) q^{51} +(3.98194 + 2.65310i) q^{52} +(-3.72343 + 13.8960i) q^{53} +(-1.26933 + 7.71969i) q^{54} +(0.761268 + 0.440142i) q^{55} +(-4.37061 - 2.32510i) q^{56} +(2.91567 + 4.54586i) q^{57} +(2.74891 + 1.24334i) q^{58} +(1.64282 - 2.84544i) q^{59} +(3.07512 - 4.60919i) q^{60} +(1.02665 + 1.77821i) q^{61} +(5.47708 - 3.93026i) q^{62} +(-2.47673 - 0.663637i) q^{63} +(6.63422 - 4.47069i) q^{64} +(-3.78043 - 3.78508i) q^{65} +(-0.532932 - 0.436781i) q^{66} +(2.61168 - 9.74692i) q^{67} +(2.45978 + 0.157984i) q^{68} -2.12153i q^{69} +(4.27870 + 3.51114i) q^{70} +(11.2466 + 6.49322i) q^{71} +(2.82651 - 3.02976i) q^{72} +(8.35948 - 2.23992i) q^{73} +(-3.86411 - 0.635366i) q^{74} +(-4.38581 + 4.37504i) q^{75} +(0.152022 - 8.71647i) q^{76} +(0.486713 - 0.486713i) q^{77} +(2.44395 + 3.40580i) q^{78} +(7.48063 - 12.9568i) q^{79} +(-8.25654 + 3.43941i) q^{80} +(-1.22954 + 2.12962i) q^{81} +(8.10142 - 0.803284i) q^{82} +(6.90293 - 6.90293i) q^{83} +(-2.86395 - 3.25708i) q^{84} +(-2.66145 - 0.714885i) q^{85} +(-2.51965 + 3.07431i) q^{86} +(1.86900 + 1.86900i) q^{87} +(0.324976 + 1.06377i) q^{88} +(7.23618 - 4.17781i) q^{89} +(-3.76546 + 2.69853i) q^{90} +(-3.62645 + 2.09373i) q^{91} +(-1.89891 + 2.85000i) q^{92} +(5.70472 - 1.52858i) q^{93} +(-8.00699 + 3.01961i) q^{94} +(-2.08626 + 9.52090i) q^{95} +(6.82034 - 1.61387i) q^{96} +(2.10029 + 7.83839i) q^{97} +(-4.52299 + 3.24562i) q^{98} +(0.288051 + 0.498919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 12 q^{6} - 36 q^{8} + 4 q^{10} - 20 q^{12} - 8 q^{13} + 8 q^{16} - 16 q^{17} + 12 q^{18} - 48 q^{20} + 40 q^{21} + 16 q^{22} - 16 q^{25} + 24 q^{26} + 8 q^{28} - 12 q^{30} - 20 q^{32} + 20 q^{33}+ \cdots + 34 q^{98}+O(q^{100}) \) 216 * q + 12 * q^6 - 36 * q^8 + 4 * q^10 - 20 * q^12 - 8 * q^13 + 8 * q^16 - 16 * q^17 + 12 * q^18 - 48 * q^20 + 40 * q^21 + 16 * q^22 - 16 * q^25 + 24 * q^26 + 8 * q^28 - 12 * q^30 - 20 * q^32 + 20 * q^33 - 56 * q^36 - 32 * q^37 - 18 * q^38 - 48 * q^41 + 54 * q^42 - 104 * q^45 - 24 * q^46 - 4 * q^48 + 8 * q^50 - 14 * q^52 - 16 * q^53 - 16 * q^56 + 12 * q^57 - 136 * q^58 + 50 * q^60 - 84 * q^61 + 42 * q^62 - 56 * q^65 + 28 * q^68 - 130 * q^70 + 80 * q^72 - 36 * q^73 + 96 * q^77 + 36 * q^78 + 6 * q^80 + 76 * q^81 - 16 * q^85 + 88 * q^86 + 104 * q^88 - 86 * q^90 + 28 * q^92 - 84 * q^93 - 128 * q^96 + 12 * q^97 + 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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