LMFDB - Embedded newform 966.2.s.a.97.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			97.11
Character	$\chi$	$=$	966.97
Dual form			966.2.s.a.727.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.126102 + 0.877058i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.49385 - 0.883586i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.126102 + 0.877058i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.49385 - 0.883586i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(0.368090 - 0.806004i) q^{10} +(-0.964515 - 3.28484i) q^{11} +(0.281733 + 0.959493i) q^{12} +(4.25048 + 1.94113i) q^{13} +(-2.64176 + 0.145197i) q^{14} +(-0.669652 + 0.580257i) q^{15} +(0.415415 + 0.909632i) q^{16} +(3.13323 - 2.01361i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-1.89160 - 1.21566i) q^{19} +(-0.580257 + 0.669652i) q^{20} +(2.46335 + 0.965353i) q^{21} +3.42351i q^{22} +(-3.88983 - 2.80521i) q^{23} -1.00000i q^{24} +(4.04414 + 1.18747i) q^{25} +(-3.53143 - 3.06000i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(2.57566 + 0.604956i) q^{28} +(4.84907 - 3.11631i) q^{29} +(0.806004 - 0.368090i) q^{30} +(-0.664410 + 0.575715i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(1.42218 - 3.11414i) q^{33} +(-3.57361 + 1.04931i) q^{34} +(0.460477 + 2.29867i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(-3.36929 + 0.484431i) q^{37} +(1.47249 + 1.69934i) q^{38} +(1.94113 + 4.25048i) q^{39} +(0.745415 - 0.479049i) q^{40} +(3.73926 + 0.537625i) q^{41} +(-2.09160 - 1.62026i) q^{42} +(0.231881 + 0.200926i) q^{43} +(0.964515 - 3.28484i) q^{44} -0.886077 q^{45} +(2.94194 + 3.78748i) q^{46} +3.46317i q^{47} +(-0.281733 + 0.959493i) q^{48} +(5.43855 - 4.40706i) q^{49} +(-3.54577 - 2.27873i) q^{50} +(3.68657 + 0.530049i) q^{51} +(2.52628 + 3.93097i) q^{52} +(-9.13631 + 4.17241i) q^{53} +(0.755750 - 0.654861i) q^{54} +(3.00262 - 0.431711i) q^{55} +(-2.30089 - 1.30610i) q^{56} +(-0.633489 - 2.15747i) q^{57} +(-5.53062 + 1.62394i) q^{58} +(9.72355 + 4.44060i) q^{59} +(-0.877058 + 0.126102i) q^{60} +(5.41747 + 6.25210i) q^{61} +(0.799694 - 0.365208i) q^{62} +(1.22950 + 2.34272i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-2.23848 + 3.48314i) q^{65} +(-2.24192 + 2.58732i) q^{66} +(-2.17715 + 7.41469i) q^{67} +3.72448 q^{68} +(-1.10271 - 4.66734i) q^{69} +(0.205785 - 2.33529i) q^{70} +(-4.38966 - 1.28892i) q^{71} +(0.654861 - 0.755750i) q^{72} +(6.72425 - 10.4631i) q^{73} +(3.36929 + 0.484431i) q^{74} +(2.27873 + 3.54577i) q^{75} +(-0.934080 - 2.04535i) q^{76} +(-5.30779 - 7.33965i) q^{77} +(-0.665001 - 4.62519i) q^{78} +(6.68301 + 3.05203i) q^{79} +(-0.850184 + 0.249637i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.43633 - 1.56932i) q^{82} +(-0.727988 - 5.06327i) q^{83} +(1.55039 + 2.14389i) q^{84} +(1.37094 + 3.00195i) q^{85} +(-0.165881 - 0.258115i) q^{86} +(5.70544 + 0.820318i) q^{87} +(-1.85089 + 2.88004i) q^{88} +(-8.05982 + 9.30153i) q^{89} +(0.850184 + 0.249637i) q^{90} +(12.3152 + 1.08521i) q^{91} +(-1.75572 - 4.46290i) q^{92} -0.879141 q^{93} +(0.975687 - 3.32289i) q^{94} +(1.30473 - 1.50574i) q^{95} +(0.540641 - 0.841254i) q^{96} +(-1.17133 + 8.14677i) q^{97} +(-6.45986 + 2.69633i) q^{98} +(3.11414 - 1.42218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$3$	0.755750	+	0.654861i	0.436332	+	0.378084i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	−0.126102	+	0.877058i	−0.0563945	+	0.392232i	0.942001	+	0.335610i	$0.108942\pi$
$5$	−0.126102	+	0.877058i	−0.0563945	+	0.392232i	−0.998396	+	0.0566226i	$0.981967\pi$
$6$	−0.540641	−	0.841254i	−0.220716	−	0.343440i
$7$	2.49385	−	0.883586i	0.942586	−	0.333964i
$7$	2.49385	−	0.883586i	0.942586	−	0.333964i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	0.368090	−	0.806004i	0.116400	−	0.254881i
$11$	−0.964515	−	3.28484i	−0.290812	−	0.990415i	−0.967231	−	0.253898i	$-0.918287\pi$
$11$	−0.964515	−	3.28484i	−0.290812	−	0.990415i	0.676419	−	0.736517i	$-0.263531\pi$
$12$	0.281733	+	0.959493i	0.0813292	+	0.276982i
$13$	4.25048	+	1.94113i	1.17887	+	0.538372i	0.905835	−	0.423631i	$-0.139245\pi$
$13$	4.25048	+	1.94113i	1.17887	+	0.538372i	0.273036	+	0.962004i	$0.411972\pi$
$14$	−2.64176	+	0.145197i	−0.706041	+	0.0388055i
$15$	−0.669652	+	0.580257i	−0.172903	+	0.149822i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	3.13323	−	2.01361i	0.759921	−	0.488371i	−0.102394	−	0.994744i	$-0.532650\pi$
$17$	3.13323	−	2.01361i	0.759921	−	0.488371i	0.862315	+	0.506372i	$0.169014\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	−1.89160	−	1.21566i	−0.433962	−	0.278891i	0.305367	−	0.952235i	$-0.401221\pi$
$19$	−1.89160	−	1.21566i	−0.433962	−	0.278891i	−0.739329	+	0.673344i	$0.764857\pi$
$20$	−0.580257	+	0.669652i	−0.129749	+	0.149739i
$21$	2.46335	+	0.965353i	0.537547	+	0.210657i
$22$			3.42351i			0.729895i
$23$	−3.88983	−	2.80521i	−0.811085	−	0.584928i
$23$	−3.88983	−	2.80521i	−0.811085	−	0.584928i
$24$		−	1.00000i		−	0.204124i
$25$	4.04414	+	1.18747i	0.808827	+	0.237493i
$26$	−3.53143	−	3.06000i	−0.692570	−	0.600115i
$27$	−0.540641	+	0.841254i	−0.104046	+	0.161899i
$28$	2.57566	+	0.604956i	0.486754	+	0.114326i
$29$	4.84907	−	3.11631i	0.900450	−	0.578684i	−0.00647334	−	0.999979i	$-0.502061\pi$
$29$	4.84907	−	3.11631i	0.900450	−	0.578684i	0.906924	+	0.421295i	$0.138424\pi$
$30$	0.806004	−	0.368090i	0.147155	−	0.0672037i
$31$	−0.664410	+	0.575715i	−0.119332	+	0.103401i	−0.712482	−	0.701690i	$-0.752429\pi$
$31$	−0.664410	+	0.575715i	−0.119332	+	0.103401i	0.593151	+	0.805091i	$0.297884\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	1.42218	−	3.11414i	0.247569	−	0.542101i
$34$	−3.57361	+	1.04931i	−0.612870	+	0.179955i
$35$	0.460477	+	2.29867i	0.0778349	+	0.388546i
$36$	−0.415415	+	0.909632i	−0.0692358	+	0.151605i
$37$	−3.36929	+	0.484431i	−0.553908	+	0.0796400i	−0.413585	−	0.910466i	$-0.635723\pi$
$37$	−3.36929	+	0.484431i	−0.553908	+	0.0796400i	−0.140324	+	0.990106i	$0.544814\pi$
$38$	1.47249	+	1.69934i	0.238869	+	0.275669i
$39$	1.94113	+	4.25048i	0.310829	+	0.680622i
$40$	0.745415	−	0.479049i	0.117860	−	0.0757443i
$41$	3.73926	+	0.537625i	0.583974	+	0.0839628i	0.427969	−	0.903793i	$-0.359229\pi$
$41$	3.73926	+	0.537625i	0.583974	+	0.0839628i	0.156005	+	0.987756i	$0.450138\pi$
$42$	−2.09160	−	1.62026i	−0.322740	−	0.250011i
$43$	0.231881	+	0.200926i	0.0353615	+	0.0306409i	0.672362	−	0.740222i	$-0.265280\pi$
$43$	0.231881	+	0.200926i	0.0353615	+	0.0306409i	−0.637001	+	0.770863i	$0.719825\pi$
$44$	0.964515	−	3.28484i	0.145406	−	0.495208i
$45$	−0.886077			−0.132089
$46$	2.94194	+	3.78748i	0.433766	+	0.558433i
$47$			3.46317i			0.505155i	0.967577	+	0.252577i	$0.0812783\pi$
$47$			3.46317i			0.505155i	−0.967577	+	0.252577i	$0.918722\pi$
$48$	−0.281733	+	0.959493i	−0.0406646	+	0.138491i
$49$	5.43855	−	4.40706i	0.776936	−	0.629580i
$50$	−3.54577	−	2.27873i	−0.501448	−	0.322261i
$51$	3.68657	+	0.530049i	0.516223	+	0.0742217i
$52$	2.52628	+	3.93097i	0.350332	+	0.545127i
$53$	−9.13631	+	4.17241i	−1.25497	+	0.573125i	−0.928236	−	0.371992i	$-0.878675\pi$
$53$	−9.13631	+	4.17241i	−1.25497	+	0.573125i	−0.326733	+	0.945117i	$0.605948\pi$
$54$	0.755750	−	0.654861i	0.102844	−	0.0891153i
$55$	3.00262	−	0.431711i	0.404873	−	0.0582119i
$56$	−2.30089	−	1.30610i	−0.307470	−	0.174535i
$57$	−0.633489	−	2.15747i	−0.0839077	−	0.285763i
$58$	−5.53062	+	1.62394i	−0.726206	+	0.213233i
$59$	9.72355	+	4.44060i	1.26590	+	0.578117i	0.931303	−	0.364245i	$-0.118673\pi$
$59$	9.72355	+	4.44060i	1.26590	+	0.578117i	0.334596	+	0.942362i	$0.391400\pi$
$60$	−0.877058	+	0.126102i	−0.113228	+	0.0162797i
$61$	5.41747	+	6.25210i	0.693636	+	0.800499i	0.987878	−	0.155232i	$-0.0496125\pi$
$61$	5.41747	+	6.25210i	0.693636	+	0.800499i	−0.294242	+	0.955731i	$0.595067\pi$
$62$	0.799694	−	0.365208i	0.101561	−	0.0463815i
$63$	1.22950	+	2.34272i	0.154903	+	0.295155i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−2.23848	+	3.48314i	−0.277649	+	0.432030i
$66$	−2.24192	+	2.58732i	−0.275962	+	0.318477i
$67$	−2.17715	+	7.41469i	−0.265981	+	0.905849i	0.712874	+	0.701293i	$0.247393\pi$
$67$	−2.17715	+	7.41469i	−0.265981	+	0.905849i	−0.978855	+	0.204556i	$0.934425\pi$
$68$	3.72448			0.451660
$69$	−1.10271	−	4.66734i	−0.132751	−	0.561881i
$70$	0.205785	−	2.33529i	0.0245960	−	0.279120i
$71$	−4.38966	−	1.28892i	−0.520957	−	0.152967i	0.0106736	−	0.999943i	$-0.496602\pi$
$71$	−4.38966	−	1.28892i	−0.520957	−	0.152967i	−0.531631	+	0.846976i	$0.678421\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	6.72425	−	10.4631i	0.787014	−	1.22462i	−0.183368	−	0.983044i	$-0.558700\pi$
$73$	6.72425	−	10.4631i	0.787014	−	1.22462i	0.970382	−	0.241574i	$-0.0776636\pi$
$74$	3.36929	+	0.484431i	0.391672	+	0.0563140i
$75$	2.27873	+	3.54577i	0.263125	+	0.409431i
$76$	−0.934080	−	2.04535i	−0.107146	−	0.234618i
$77$	−5.30779	−	7.33965i	−0.604879	−	0.836430i
$78$	−0.665001	−	4.62519i	−0.0752966	−	0.523699i
$79$	6.68301	+	3.05203i	0.751897	+	0.343380i	0.754224	−	0.656617i	$-0.228013\pi$
$79$	6.68301	+	3.05203i	0.751897	+	0.343380i	−0.00232670	+	0.999997i	$0.500741\pi$
$80$	−0.850184	+	0.249637i	−0.0950535	+	0.0279102i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−3.43633	−	1.56932i	−0.379479	−	0.173302i
$83$	−0.727988	−	5.06327i	−0.0799070	−	0.555766i	−0.989968	−	0.141291i	$-0.954875\pi$
$83$	−0.727988	−	5.06327i	−0.0799070	−	0.555766i	0.910061	−	0.414474i	$-0.136035\pi$
$84$	1.55039	+	2.14389i	0.169162	+	0.233918i
$85$	1.37094	+	3.00195i	0.148700	+	0.325607i
$86$	−0.165881	−	0.258115i	−0.0178874	−	0.0278333i
$87$	5.70544	+	0.820318i	0.611687	+	0.0879473i
$88$	−1.85089	+	2.88004i	−0.197306	+	0.307013i
$89$	−8.05982	+	9.30153i	−0.854339	+	0.985960i	−0.999994	−	0.00337520i	$-0.998926\pi$
$89$	−8.05982	+	9.30153i	−0.854339	+	0.985960i	0.145655	+	0.989335i	$0.453471\pi$
$90$	0.850184	+	0.249637i	0.0896173	+	0.0263140i
$91$	12.3152	+	1.08521i	1.29098	+	0.113761i
$92$	−1.75572	−	4.46290i	−0.183046	−	0.465289i
$93$	−0.879141			−0.0911626
$94$	0.975687	−	3.32289i	0.100634	−	0.342729i
$95$	1.30473	−	1.50574i	0.133863	−	0.154486i
$96$	0.540641	−	0.841254i	0.0551789	−	0.0858601i
$97$	−1.17133	+	8.14677i	−0.118930	+	0.827179i	0.839807	+	0.542886i	$0.182668\pi$
$97$	−1.17133	+	8.14677i	−0.118930	+	0.827179i	−0.958737	+	0.284294i	$0.908241\pi$
$98$	−6.45986	+	2.69633i	−0.652545	+	0.272370i
$99$	3.11414	−	1.42218i	0.312982	−	0.142934i
$100$	2.76015	+	3.18538i	0.276015	+	0.318538i
$101$	18.8291	−	2.70722i	1.87357	−	0.269379i	0.890825	−	0.454347i	$-0.150127\pi$
$101$	18.8291	−	2.70722i	1.87357	−	0.269379i	0.982744	+	0.184968i	$0.0592183\pi$
$102$	−3.38791	−	1.54721i	−0.335453	−	0.153196i
$103$	0.0874233	−	0.0256698i	0.00861407	−	0.00252932i	−0.277423	−	0.960748i	$-0.589480\pi$
$103$	0.0874233	−	0.0256698i	0.00861407	−	0.00252932i	0.286037	+	0.958219i	$0.407662\pi$
$104$	−1.31647	−	4.48347i	−0.129090	−	0.439640i
$105$	−1.15730	+	2.03877i	−0.112941	+	0.198963i
$106$	9.94173	−	1.42940i	0.965626	−	0.138836i
$107$	−0.894323	+	0.774935i	−0.0864575	+	0.0749158i	−0.697017	−	0.717054i	$-0.745490\pi$
$107$	−0.894323	+	0.774935i	−0.0864575	+	0.0749158i	0.610560	+	0.791970i	$0.290944\pi$
$108$	−0.909632	+	0.415415i	−0.0875294	+	0.0399733i
$109$	−8.55444	−	13.3110i	−0.819366	−	1.27496i	−0.958616	−	0.284702i	$-0.908105\pi$
$109$	−8.55444	−	13.3110i	−0.819366	−	1.27496i	0.139250	−	0.990257i	$-0.455531\pi$
$110$	−3.00262	−	0.431711i	−0.286288	−	0.0411620i
$111$	−2.86358	−	1.84031i	−0.271799	−	0.174674i
$112$	1.83972	+	1.90143i	0.173837	+	0.179668i
$113$	2.19195	−	7.46509i	0.206201	−	0.702257i	−0.789836	−	0.613318i	$-0.789834\pi$
$113$	2.19195	−	7.46509i	0.206201	−	0.702257i	0.996037	−	0.0889387i	$-0.0283475\pi$
$114$			2.24855i			0.210596i
$115$	2.95085	−	3.05786i	0.275168	−	0.285147i
$116$	5.76411			0.535184
$117$	−1.31647	+	4.48347i	−0.121707	+	0.414497i
$118$	−8.07862	−	7.00016i	−0.743697	−	0.644417i
$119$	6.03461	−	7.79011i	0.553192	−	0.714118i
$120$	0.877058	+	0.126102i	0.0800641	+	0.0115115i
$121$	−0.606064	+	0.389494i	−0.0550967	+	0.0354085i
$122$	−3.43661	−	7.52512i	−0.311136	−	0.681292i
$123$	2.47388	+	2.85500i	0.223062	+	0.257427i
$124$	−0.870192	+	0.125115i	−0.0781456	+	0.0112356i
$125$	−3.39190	+	7.42722i	−0.303380	+	0.664311i
$126$	−0.519681	−	2.59421i	−0.0462969	−	0.231111i
$127$	1.78843	−	0.525130i	0.158697	−	0.0465978i	−0.201419	−	0.979505i	$-0.564555\pi$
$127$	1.78843	−	0.525130i	0.158697	−	0.0465978i	0.360116	+	0.932907i	$0.382737\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	0.0436654	+	0.303699i	0.00384452	+	0.0267392i
$130$	3.12912	−	2.71139i	0.274442	−	0.237805i
$131$	−20.5166	+	9.36960i	−1.79254	+	0.818626i	−0.825329	+	0.564653i	$0.809010\pi$
$131$	−20.5166	+	9.36960i	−1.79254	+	0.818626i	−0.967211	+	0.253973i	$0.918263\pi$
$132$	2.88004	−	1.85089i	0.250675	−	0.161099i
$133$	−5.79149	−	1.36027i	−0.502186	−	0.117950i
$134$	4.17792	−	6.50097i	0.360917	−	0.561598i
$135$	−0.669652	−	0.580257i	−0.0576345	−	0.0499406i
$136$	−3.57361	−	1.04931i	−0.306435	−	0.0899774i
$137$			8.53890i			0.729527i	0.931100	+	0.364764i	$0.118850\pi$
$137$			8.53890i			0.729527i	−0.931100	+	0.364764i	$0.881150\pi$
$138$	−0.256896	+	4.78895i	−0.0218685	+	0.407662i
$139$		−	8.62650i		−	0.731690i	−0.930676	−	0.365845i	$-0.880780\pi$
$139$		−	8.62650i		−	0.731690i	0.930676	−	0.365845i	$-0.119220\pi$
$140$	−0.855377	+	2.18272i	−0.0722925	+	0.184473i
$141$	−2.26789	+	2.61729i	−0.190991	+	0.220415i
$142$	3.84872	+	2.47342i	0.322977	+	0.207565i
$143$	2.27664	−	15.8344i	0.190382	−	1.32414i
$144$	−0.841254	+	0.540641i	−0.0701045	+	0.0450534i
$145$	2.12171	+	4.64589i	0.176198	+	0.385820i
$146$	−9.39968	+	8.14487i	−0.777923	+	0.674074i
$147$	6.99619	+	0.230860i	0.577036	+	0.0190410i
$148$	−3.09633	−	1.41405i	−0.254517	−	0.116234i
$149$	−2.27083	−	7.73375i	−0.186034	−	0.633574i	−0.998706	−	0.0508525i	$-0.983806\pi$
$149$	−2.27083	−	7.73375i	−0.186034	−	0.633574i	0.812672	−	0.582721i	$-0.198012\pi$
$150$	−1.18747	−	4.04414i	−0.0969562	−	0.330202i
$151$	1.65877	−	3.63221i	0.134989	−	0.295585i	−0.830051	−	0.557688i	$-0.811689\pi$
$151$	1.65877	−	3.63221i	0.134989	−	0.295585i	0.965040	+	0.262103i	$0.0844159\pi$
$152$	0.320002	+	2.22566i	0.0259556	+	0.180525i
$153$	2.43902	+	2.81478i	0.197183	+	0.227561i
$154$	3.02497	+	8.53771i	0.243759	+	0.687989i
$155$	−0.421152	−	0.655325i	−0.0338277	−	0.0526370i
$156$	−0.665001	+	4.62519i	−0.0532427	+	0.370311i
$157$	15.3488	+	9.86409i	1.22497	+	0.787240i	0.983100	−	0.183069i	$-0.0586031\pi$
$157$	15.3488	+	9.86409i	1.22497	+	0.787240i	0.241869	+	0.970309i	$0.422239\pi$
$158$	−5.55244	−	4.81122i	−0.441729	−	0.382760i
$159$	−9.63711	−	2.82971i	−0.764273	−	0.224411i
$160$	0.886077			0.0700505
$161$	−12.1793	−	3.55878i	−0.959863	−	0.280471i
$162$	1.00000			0.0785674
$163$	0.222824	+	0.0654270i	0.0174529	+	0.00512464i	0.290447	−	0.956891i	$-0.406196\pi$
$163$	0.222824	+	0.0654270i	0.0174529	+	0.00512464i	−0.272994	+	0.962016i	$0.588014\pi$
$164$	2.85500	+	2.47388i	0.222938	+	0.193177i
$165$	2.55194	+	1.64003i	0.198668	+	0.127676i
$166$	−0.727988	+	5.06327i	−0.0565028	+	0.392986i
$167$	−3.82010	−	5.94419i	−0.295608	−	0.459975i	0.661401	−	0.750032i	$-0.269962\pi$
$167$	−3.82010	−	5.94419i	−0.295608	−	0.459975i	−0.957009	+	0.290057i	$0.906326\pi$
$168$	−0.883586	−	2.49385i	−0.0681702	−	0.192405i
$169$	5.78541	+	6.67672i	0.445032	+	0.513594i
$170$	−0.469664	−	3.26659i	−0.0360216	−	0.250536i
$171$	0.934080	−	2.04535i	0.0714309	−	0.156412i
$172$	0.0864418	+	0.294394i	0.00659113	+	0.0224473i
$173$	0.379155	+	1.29128i	0.0288266	+	0.0981744i	0.972650	−	0.232276i	$-0.0746174\pi$
$173$	0.379155	+	1.29128i	0.0288266	+	0.0981744i	−0.943823	+	0.330451i	$0.892799\pi$
$174$	−5.24321	−	2.39450i	−0.397487	−	0.181526i
$175$	11.1347	−	0.611986i	0.841703	−	0.0462618i
$176$	2.58732	−	2.24192i	0.195026	−	0.168991i
$177$	4.44060	+	9.72355i	0.333776	+	0.730867i
$178$	10.3539	−	6.65404i	0.776057	−	0.498741i
$179$	−0.262744	+	1.82742i	−0.0196384	+	0.136588i	−0.997282	−	0.0736817i	$-0.976525\pi$
$179$	−0.262744	+	1.82742i	−0.0196384	+	0.136588i	0.977643	+	0.210270i	$0.0674342\pi$
$180$	−0.745415	−	0.479049i	−0.0555600	−	0.0357062i
$181$	−11.7383	+	13.5467i	−0.872502	+	1.00692i	0.127385	+	0.991853i	$0.459342\pi$
$181$	−11.7383	+	13.5467i	−0.872502	+	1.00692i	−0.999886	+	0.0150673i	$0.995204\pi$
$182$	−11.5106	−	4.51085i	−0.853223	−	0.334366i
$183$			8.27271i			0.611536i
$184$	0.427257	+	4.77676i	0.0314978	+	0.352148i
$185$		−	3.01615i		−	0.221752i
$186$	0.843529	+	0.247683i	0.0618506	+	0.0181610i
$187$	−9.63642	−	8.35000i	−0.704685	−	0.610613i
$188$	−1.87233	+	2.91340i	−0.136554	+	0.212482i
$189$	−0.604956	+	2.57566i	−0.0440040	+	0.187352i
$190$	−1.67610	+	1.07716i	−0.121597	+	0.0781457i
$191$	−16.6294	+	7.59440i	−1.20326	+	0.549511i	−0.913206	−	0.407498i	$-0.866401\pi$
$191$	−16.6294	+	7.59440i	−1.20326	+	0.549511i	−0.290056	+	0.957010i	$0.593674\pi$
$192$	−0.755750	+	0.654861i	−0.0545415	+	0.0472605i
$193$	0.102686	+	0.714197i	0.00739150	+	0.0514090i	0.993183	−	0.116562i	$-0.0371875\pi$
$193$	0.102686	+	0.714197i	0.00739150	+	0.0514090i	−0.985792	+	0.167971i	$0.946278\pi$
$194$	3.41909	−	7.48677i	0.245477	−	0.537519i
$195$	−3.97270	+	1.16649i	−0.284491	+	0.0835340i
$196$	6.95784	−	0.767152i	0.496988	−	0.0547966i
$197$	4.66838	−	10.2223i	0.332608	−	0.728310i	−0.667255	−	0.744829i	$-0.732531\pi$
$197$	4.66838	−	10.2223i	0.332608	−	0.728310i	0.999864	+	0.0165186i	$0.00525829\pi$
$198$	−3.38866	+	0.487216i	−0.240822	+	0.0346250i
$199$	−15.6128	−	18.0182i	−1.10676	−	1.27727i	−0.957487	−	0.288478i	$-0.906851\pi$
$199$	−15.6128	−	18.0182i	−1.10676	−	1.27727i	−0.149277	−	0.988795i	$-0.547695\pi$
$200$	−1.75092	−	3.83398i	−0.123809	−	0.271103i
$201$	−6.50097	+	4.17792i	−0.458543	+	0.294688i
$202$	−18.8291	−	2.70722i	−1.32481	−	0.190479i
$203$	9.33932	−	12.0562i	0.655492	−	0.846178i
$204$	2.81478	+	2.43902i	0.197074	+	0.170765i
$205$	−0.943056	+	3.21175i	−0.0658659	+	0.224319i
$206$	−0.0911141			−0.00634822
$207$	2.22308	−	4.24946i	0.154515	−	0.295358i
$208$			4.67275i			0.323997i
$209$	−2.16876	+	7.38611i	−0.150016	+	0.510908i
$210$	1.68481	−	1.63013i	0.116263	−	0.112490i
$211$	−13.0888	−	8.41164i	−0.901068	−	0.579081i	0.00603889	−	0.999982i	$-0.498078\pi$
$211$	−13.0888	−	8.41164i	−0.901068	−	0.579081i	−0.907107	+	0.420901i	$0.861714\pi$
$212$	−9.94173	−	1.42940i	−0.682801	−	0.0981719i
$213$	−2.47342	−	3.84872i	−0.169476	−	0.263710i
$214$	1.07642	−	0.491585i	0.0735826	−	0.0336041i
$215$	−0.205464	+	0.178036i	−0.0140125	+	0.0121419i
$216$	0.989821	−	0.142315i	0.0673488	−	0.00968330i
$217$	−1.14824	+	2.02281i	−0.0779479	+	0.137317i
$218$	4.45779	+	15.1818i	0.301920	+	1.02824i
$219$	11.9338	−	3.50407i	0.806408	−	0.236783i
$220$	2.75936	+	1.26016i	0.186036	+	0.0849599i
$221$	17.2264	−	2.47679i	1.15877	−	0.166607i
$222$	2.22911	+	2.57253i	0.149608	+	0.172657i
$223$	−9.75917	+	4.45686i	−0.653522	+	0.298454i	−0.714448	−	0.699689i	$-0.753322\pi$
$223$	−9.75917	+	4.45686i	−0.653522	+	0.298454i	0.0609257	+	0.998142i	$0.480595\pi$
$224$	−1.22950	−	2.34272i	−0.0821497	−	0.156529i
$225$	−0.599838	+	4.17197i	−0.0399892	+	0.278131i
$226$	−4.20632	+	6.54516i	−0.279800	+	0.435378i
$227$	−11.8582	+	13.6850i	−0.787053	+	0.908308i	−0.997598	−	0.0692764i	$-0.977931\pi$
$227$	−11.8582	+	13.6850i	−0.787053	+	0.908308i	0.210544	+	0.977584i	$0.432476\pi$
$228$	0.633489	−	2.15747i	0.0419538	−	0.142882i
$229$	−20.3324			−1.34360			−0.671802	−	0.740731i	$-0.734480\pi$
$229$	−20.3324			−1.34360			−0.671802	+	0.740731i	$0.734480\pi$
$230$	−3.69282	+	2.10265i	−0.243497	+	0.138644i
$231$	0.795087	−	9.02280i	0.0523129	−	0.593656i
$232$	−5.53062	−	1.62394i	−0.363103	−	0.106617i
$233$	10.4747	−	12.0884i	0.686218	−	0.791938i	−0.300603	−	0.953749i	$-0.597188\pi$
$233$	10.4747	−	12.0884i	0.686218	−	0.791938i	0.986822	+	0.161811i	$0.0517335\pi$
$234$	2.52628	−	3.93097i	0.165148	−	0.256975i
$235$	−3.03740	−	0.436712i	−0.198138	−	0.0284879i
$236$	5.77920	+	8.99262i	0.376194	+	0.585370i
$237$	3.05203	+	6.68301i	0.198250	+	0.434108i
$238$	−7.98489	+	5.77441i	−0.517584	+	0.374299i
$239$	2.26048	+	15.7220i	0.146219	+	1.01697i	0.922337	+	0.386386i	$0.126277\pi$
$239$	2.26048	+	15.7220i	0.146219	+	1.01697i	−0.776119	+	0.630587i	$0.782814\pi$
$240$	−0.806004	−	0.368090i	−0.0520273	−	0.0237601i
$241$	−13.5607	+	3.98178i	−0.873522	+	0.256489i	−0.687613	−	0.726078i	$-0.741341\pi$
$241$	−13.5607	+	3.98178i	−0.873522	+	0.256489i	−0.185909	+	0.982567i	$0.559523\pi$
$242$	0.691247	−	0.202968i	0.0444350	−	0.0130473i
$243$	−0.909632	−	0.415415i	−0.0583529	−	0.0266489i
$244$	1.17733	+	8.18850i	0.0753708	+	0.524215i
$245$	3.17943	+	5.32566i	0.203127	+	0.340244i
$246$	−1.56932	−	3.43633i	−0.100056	−	0.219092i
$247$	−5.68045	−	8.83896i	−0.361439	−	0.562410i
$248$	0.870192	+	0.125115i	0.0552573	+	0.00794479i
$249$	2.76556	−	4.30329i	0.175260	−	0.272710i
$250$	5.34699	−	6.17076i	0.338173	−	0.390273i
$251$	−19.3386	−	5.67832i	−1.22064	−	0.358412i	−0.392930	−	0.919568i	$-0.628539\pi$
$251$	−19.3386	−	5.67832i	−1.22064	−	0.358412i	−0.827710	+	0.561156i	$0.810357\pi$
$252$	−0.232243	+	2.63554i	−0.0146299	+	0.166023i
$253$	−5.46287	+	15.4831i	−0.343448	+	0.973415i
$254$	−1.86393			−0.116954
$255$	−0.929767	+	3.16650i	−0.0582243	+	0.198294i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	2.57464	−	4.00622i	0.160602	−	0.249901i	−0.751621	−	0.659595i	$-0.770728\pi$
$257$	2.57464	−	4.00622i	0.160602	−	0.249901i	0.912223	+	0.409693i	$0.134364\pi$
$258$	0.0436654	−	0.303699i	0.00271849	−	0.0189075i
$259$	−7.97446	+	4.18516i	−0.495509	+	0.260053i
$260$	−3.76625	+	1.71999i	−0.233573	+	0.106669i
$261$	3.77469	+	4.35622i	0.233647	+	0.269643i
$262$	22.3252	−	3.20988i	1.37926	−	0.198307i
$263$	2.42487	+	1.10740i	0.149524	+	0.0682854i	0.488772	−	0.872412i	$-0.337445\pi$
$263$	2.42487	+	1.10740i	0.149524	+	0.0682854i	−0.339248	+	0.940697i	$0.610172\pi$
$264$	−3.28484	+	0.964515i	−0.202168	+	0.0593618i
$265$	−2.50734	−	8.53922i	−0.154025	−	0.524560i
$266$	5.17367	+	2.93682i	0.317218	+	0.180068i
$267$	−12.1824	+	1.75157i	−0.745552	+	0.107194i
$268$	−5.84022	+	5.06058i	−0.356748	+	0.309124i
$269$	−8.05118	+	3.67685i	−0.490889	+	0.224181i	−0.645451	−	0.763802i	$-0.723331\pi$
$269$	−8.05118	+	3.67685i	−0.490889	+	0.224181i	0.154562	+	0.987983i	$0.450603\pi$
$270$	0.479049	+	0.745415i	0.0291540	+	0.0453645i
$271$	−25.8923	−	3.72275i	−1.57285	−	0.226141i	−0.700002	−	0.714141i	$-0.746818\pi$
$271$	−25.8923	−	3.72275i	−1.57285	−	0.226141i	−0.872844	+	0.488000i	$0.837727\pi$
$272$	3.13323	+	2.01361i	0.189980	+	0.122093i
$273$	8.59655	+	8.88489i	0.520287	+	0.537738i
$274$	2.40569	−	8.19301i	0.145333	−	0.494958i
$275$		−	14.4296i		−	0.870141i
$276$	1.59569	−	4.52258i	0.0960494	−	0.272228i
$277$	−18.5551			−1.11487			−0.557433	−	0.830222i	$-0.688214\pi$
$277$	−18.5551			−1.11487			−0.557433	+	0.830222i	$0.688214\pi$
$278$	−2.43036	+	8.27706i	−0.145764	+	0.496425i
$279$	−0.664410	−	0.575715i	−0.0397772	−	0.0344671i
$280$	1.43567	−	1.85331i	0.0857977	−	0.110757i
$281$	−7.40551	−	1.06475i	−0.441775	−	0.0635177i	−0.0821618	−	0.996619i	$-0.526182\pi$
$281$	−7.40551	−	1.06475i	−0.441775	−	0.0635177i	−0.359614	+	0.933101i	$0.617092\pi$
$282$	2.91340	−	1.87233i	0.173491	−	0.111496i
$283$	4.02295	+	8.80902i	0.239139	+	0.523642i	0.990707	−	0.136014i	$-0.0434292\pi$
$283$	4.02295	+	8.80902i	0.239139	+	0.523642i	−0.751568	+	0.659656i	$0.770702\pi$
$284$	−2.99598	−	3.45754i	−0.177779	−	0.205167i
$285$	1.97211	−	0.283546i	0.116817	−	0.0167958i
$286$	−6.64548	+	14.5516i	−0.392955	+	0.860452i
$287$	9.80018	−	1.96321i	0.578487	−	0.115884i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−1.29952	+	2.84554i	−0.0764421	+	0.167385i
$290$	−0.726864	−	5.05545i	−0.0426830	−	0.296866i
$291$	−6.22023	+	5.38986i	−0.364637	+	0.315959i
$292$	11.3136	−	5.16675i	0.662079	−	0.302361i
$293$	−23.7807	+	15.2829i	−1.38928	+	0.892837i	−0.999605	−	0.0281153i	$-0.991049\pi$
$293$	−23.7807	+	15.2829i	−1.38928	+	0.892837i	−0.389676	+	0.920952i	$0.627413\pi$
$294$	−6.64776	−	2.19256i	−0.387705	−	0.127873i
$295$	−5.12082	+	7.96815i	−0.298146	+	0.463924i
$296$	2.57253	+	2.22911i	0.149525	+	0.129564i
$297$	3.28484	+	0.964515i	0.190605	+	0.0559668i
$298$			8.06025i			0.466918i
$299$	−11.0884	−	19.4742i	−0.641256	−	1.12622i
$300$			4.21487i			0.243346i
$301$	0.755811	+	0.296192i	0.0435642	+	0.0170722i
$302$	−2.61489	+	3.01775i	−0.150470	+	0.173652i
$303$	16.0030	+	10.2845i	0.919346	+	0.590828i
$304$	0.320002	−	2.22566i	0.0183534	−	0.127650i
$305$	−6.16660	+	3.96304i	−0.353099	+	0.226923i
$306$	−1.54721	−	3.38791i	−0.0884479	−	0.193674i
$307$	−6.57023	+	5.69314i	−0.374983	+	0.324925i	−0.821880	−	0.569661i	$-0.807075\pi$
$307$	−6.57023	+	5.69314i	−0.374983	+	0.324925i	0.446897	+	0.894586i	$0.352529\pi$
$308$	−0.497083	−	9.04411i	−0.0283239	−	0.515336i
$309$	0.0828803	+	0.0378501i	0.00471489	+	0.00215322i
$310$	0.219466	+	0.747432i	0.0124648	+	0.0424513i
$311$	−6.39702	−	21.7862i	−0.362742	−	1.23538i	−0.915593	−	0.402105i	$-0.868279\pi$
$311$	−6.39702	−	21.7862i	−0.362742	−	1.23538i	0.552852	−	0.833280i	$-0.313540\pi$
$312$	1.94113	−	4.25048i	0.109895	−	0.240636i
$313$	−3.94483	−	27.4369i	−0.222975	−	1.55082i	−0.726696	−	0.686959i	$-0.758945\pi$
$313$	−3.94483	−	27.4369i	−0.222975	−	1.55082i	0.503722	−	0.863866i	$-0.331964\pi$
$314$	−11.9481	−	13.7888i	−0.674268	−	0.778146i
$315$	−2.20974	+	0.782925i	−0.124505	+	0.0441128i
$316$	3.97205	+	6.18064i	0.223445	+	0.347688i
$317$	−4.62256	+	32.1506i	−0.259629	+	1.80576i	0.275838	+	0.961204i	$0.411045\pi$
$317$	−4.62256	+	32.1506i	−0.259629	+	1.80576i	−0.535467	+	0.844556i	$0.679865\pi$
$318$	8.44952	+	5.43018i	0.473826	+	0.304509i
$319$	−14.9136	−	12.9227i	−0.835000	−	0.723531i
$320$	−0.850184	−	0.249637i	−0.0475268	−	0.0139551i
$321$	−1.18336			−0.0660487
$322$	10.6833	+	6.84592i	0.595358	+	0.381508i
$323$	−8.37467			−0.465979
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	14.8845	+	12.8975i	0.825643	+	0.715424i
$326$	−0.195365	−	0.125553i	−0.0108203	−	0.00695376i
$327$	2.25182	−	15.6617i	0.124526	−	0.866095i
$328$	−2.04239	−	3.17801i	−0.112772	−	0.175476i
$329$	3.06001	+	8.63661i	0.168704	+	0.476152i
$330$	−1.98652	−	2.29256i	−0.109354	−	0.126201i
$331$	−3.90240	−	27.1418i	−0.214496	−	1.49185i	−0.757896	−	0.652376i	$-0.773773\pi$
$331$	−3.90240	−	27.1418i	−0.214496	−	1.49185i	0.543400	−	0.839474i	$-0.317137\pi$
$332$	2.12499	−	4.65307i	0.116624	−	0.255370i
$333$	−0.959001	−	3.26606i	−0.0525529	−	0.178979i
$334$	1.99069	+	6.77965i	0.108925	+	0.370966i
$335$	−6.22857	−	2.84449i	−0.340303	−	0.155411i
$336$	0.145197	+	2.64176i	0.00792114	+	0.144120i
$337$	11.2713	−	9.76666i	0.613988	−	0.532024i	−0.291404	−	0.956600i	$-0.594122\pi$
$337$	11.2713	−	9.76666i	0.613988	−	0.532024i	0.905392	+	0.424576i	$0.139577\pi$
$338$	−3.67001	−	8.03621i	−0.199622	−	0.437112i
$339$	6.54516	−	4.20632i	0.355484	−	0.228456i
$340$	−0.469664	+	3.26659i	−0.0254711	+	0.177155i
$341$	2.53196	+	1.62719i	0.137113	+	0.0881174i
$342$	−1.47249	+	1.69934i	−0.0796229	+	0.0918897i
$343$	9.66890	−	15.7960i	0.522071	−	0.852902i
$344$		−	0.306822i		−	0.0165428i
$345$	4.23258	−	0.378582i	0.227874	−	0.0203822i
$346$		−	1.34580i		−	0.0723505i
$347$	27.7185	+	8.13889i	1.48801	+	0.436919i	0.921905	−	0.387416i	$-0.126632\pi$
$347$	27.7185	+	8.13889i	1.48801	+	0.436919i	0.566103	+	0.824334i	$0.308450\pi$
$348$	4.35622	+	3.77469i	0.233518	+	0.202344i
$349$	0.587910	−	0.914805i	0.0314701	−	0.0489684i	−0.825162	−	0.564896i	$-0.808916\pi$
$349$	0.587910	−	0.914805i	0.0314701	−	0.0489684i	0.856632	+	0.515928i	$0.172553\pi$
$350$	−10.8561	−	2.54981i	−0.580281	−	0.136293i
$351$	−3.93097	+	2.52628i	−0.209819	+	0.134843i
$352$	−3.11414	+	1.42218i	−0.165984	+	0.0758023i
$353$	10.6813	−	9.25539i	0.568508	−	0.492615i	−0.322521	−	0.946562i	$-0.604530\pi$
$353$	10.6813	−	9.25539i	0.568508	−	0.492615i	0.891028	+	0.453948i	$0.149985\pi$
$354$	−1.52128	−	10.5807i	−0.0808552	−	0.562360i
$355$	1.68400	−	3.68745i	0.0893776	−	0.195710i
$356$	−11.8091	+	3.46748i	−0.625883	+	0.183776i
$357$	9.66209	−	1.93554i	0.511372	−	0.102440i
$358$	0.766945	−	1.67938i	0.0405343	−	0.0887578i
$359$	18.1614	−	2.61122i	0.958522	−	0.137815i	0.354741	−	0.934965i	$-0.384569\pi$
$359$	18.1614	−	2.61122i	0.958522	−	0.137815i	0.603781	+	0.797150i	$0.293660\pi$
$360$	0.580257	+	0.669652i	0.0305822	+	0.0352938i
$361$	−5.79256	−	12.6839i	−0.304872	−	0.667576i
$362$	15.0794	−	9.69093i	0.792555	−	0.509344i
$363$	−0.713097	−	0.102528i	−0.0374279	−	0.00538132i
$364$	9.77350	+	7.57104i	0.512271	+	0.396830i
$365$	8.32884	+	7.21698i	0.435951	+	0.377754i
$366$	2.33069	−	7.93761i	0.121827	−	0.414905i
$367$	26.6728			1.39231			0.696153	−	0.717893i	$-0.254893\pi$
$367$	26.6728			1.39231			0.696153	+	0.717893i	$0.254893\pi$
$368$	0.935820	−	4.70364i	0.0487830	−	0.245194i
$369$			3.77771i			0.196660i
$370$	−0.849748	+	2.89398i	−0.0441763	+	0.150451i
$371$	−19.0979	+	18.4781i	−0.991512	+	0.959334i
$372$	−0.739580	−	0.475299i	−0.0383454	−	0.0246431i
$373$	−2.12876	−	0.306070i	−0.110223	−	0.0158477i	0.0869825	−	0.996210i	$-0.472278\pi$
$373$	−2.12876	−	0.306070i	−0.110223	−	0.0158477i	−0.197206	+	0.980362i	$0.563187\pi$
$374$	6.89361	+	10.7267i	0.356460	+	0.554662i
$375$	−7.42722	+	3.39190i	−0.383540	+	0.175157i
$376$	2.61729	−	2.26789i	0.134976	−	0.116958i
$377$	26.6601	−	3.83314i	1.37306	−	0.197417i
$378$	1.30610	−	2.30089i	0.0671784	−	0.118345i
$379$	−1.45459	−	4.95388i	−0.0747173	−	0.254464i	0.913661	−	0.406477i	$-0.133243\pi$
$379$	−1.45459	−	4.95388i	−0.0747173	−	0.254464i	−0.988379	+	0.152013i	$0.951425\pi$
$380$	1.91168	−	0.561320i	0.0980671	−	0.0287951i
$381$	1.69549	+	0.774305i	0.0868627	+	0.0396689i
$382$	18.0954	−	2.60173i	0.925841	−	0.133116i
$383$	−2.74559	−	3.16858i	−0.140293	−	0.161907i	0.681255	−	0.732046i	$-0.261435\pi$
$383$	−2.74559	−	3.16858i	−0.140293	−	0.161907i	−0.821548	+	0.570140i	$0.806889\pi$
$384$	0.909632	−	0.415415i	0.0464195	−	0.0211991i
$385$	7.10662	−	3.72969i	0.362187	−	0.190083i
$386$	0.102686	−	0.714197i	0.00522658	−	0.0363517i
$387$	−0.165881	+	0.258115i	−0.00843219	+	0.0131207i
$388$	−5.38986	+	6.22023i	−0.273629	+	0.315785i
$389$	0.533510	−	1.81697i	0.0270500	−	0.0921239i	−0.944862	−	0.327470i	$-0.893804\pi$
$389$	0.533510	−	1.81697i	0.0270500	−	0.0921239i	0.971912	+	0.235346i	$0.0756223\pi$
$390$	4.14041			0.209658
$391$	−17.8363	−	0.956806i	−0.902023	−	0.0483878i
$392$	−6.89213	−	1.22417i	−0.348105	−	0.0618300i
$393$	−21.6412	−	6.35442i	−1.09165	−	0.320538i
$394$	−7.35924	+	8.49301i	−0.370753	+	0.427872i
$395$	−3.51954	+	5.47652i	−0.177087	+	0.275554i
$396$	3.38866	+	0.487216i	0.170287	+	0.0244835i
$397$	12.1096	+	18.8429i	0.607764	+	0.945700i	0.999670	+	0.0256943i	$0.00817964\pi$
$397$	12.1096	+	18.8429i	0.607764	+	0.945700i	−0.391906	+	0.920005i	$0.628184\pi$
$398$	9.90409	+	21.6869i	0.496447	+	1.08707i
$399$	−3.48613	−	4.82065i	−0.174525	−	0.241334i
$400$	0.599838	+	4.17197i	0.0299919	+	0.208598i
$401$	−0.915928	−	0.418290i	−0.0457392	−	0.0208884i	0.392414	−	0.919789i	$-0.371640\pi$
$401$	−0.915928	−	0.418290i	−0.0457392	−	0.0208884i	−0.438153	+	0.898900i	$0.644367\pi$
$402$	7.41469	−	2.17715i	0.369811	−	0.108586i
$403$	−3.94160	+	1.15736i	−0.196345	+	0.0576521i
$404$	17.3037	+	7.90234i	0.860892	+	0.393156i
$405$	−0.126102	−	0.877058i	−0.00626605	−	0.0435814i
$406$	−12.3576	+	8.93663i	−0.613299	+	0.443517i
$407$	4.84101	+	10.6003i	0.239960	+	0.525439i
$408$	−2.01361	−	3.13323i	−0.0996884	−	0.155118i
$409$	2.88460	+	0.414743i	0.142634	+	0.0205077i	0.213262	−	0.976995i	$-0.431591\pi$
$409$	2.88460	+	0.414743i	0.142634	+	0.0205077i	−0.0706278	+	0.997503i	$0.522500\pi$
$410$	1.80971	−	2.81596i	0.0893752	−	0.139071i
$411$	−5.59179	+	6.45327i	−0.275823	+	0.318316i
$412$	0.0874233	+	0.0256698i	0.00430704	+	0.00126466i
$413$	28.1727	+	2.48257i	1.38629	+	0.122159i
$414$	−3.33024	+	3.45101i	−0.163672	+	0.169608i
$415$	4.53258			0.222495
$416$	1.31647	−	4.48347i	0.0645450	−	0.219820i
$417$	5.64915	−	6.51947i	0.276640	−	0.319260i
$418$	4.16181	−	6.47591i	0.203561	−	0.316747i
$419$	1.01835	−	7.08275i	0.0497494	−	0.346015i	−0.949710	−	0.313132i	$-0.898622\pi$
$419$	1.01835	−	7.08275i	0.0497494	−	0.346015i	0.999459	−	0.0328834i	$-0.0104690\pi$
$420$	−2.07583	+	1.08944i	−0.101290	+	0.0531590i
$421$	31.1835	−	14.2410i	1.51979	−	0.694065i	0.531557	−	0.847023i	$-0.321607\pi$
$421$	31.1835	−	14.2410i	1.51979	−	0.694065i	0.988233	+	0.152958i	$0.0488799\pi$
$422$	10.1887	+	11.7584i	0.495980	+	0.572392i
$423$	−3.42792	+	0.492860i	−0.166671	+	0.0239637i
$424$	9.13631	+	4.17241i	0.443698	+	0.202630i
$425$	15.0623	−	4.42269i	0.730629	−	0.214532i
$426$	1.28892	+	4.38966i	0.0624485	+	0.212680i
$427$	19.0346	+	10.8050i	0.921150	+	0.522889i
$428$	−1.17131	+	0.168410i	−0.0566176	+	0.00814038i
$429$	12.0899	−	10.4759i	0.583705	−	0.505783i
$430$	0.247300	−	0.112938i	0.0119259	−	0.00544636i
$431$	18.7076	+	29.1096i	0.901113	+	1.40216i	0.915524	+	0.402262i	$0.131776\pi$
$431$	18.7076	+	29.1096i	0.901113	+	1.40216i	−0.0144119	+	0.999896i	$0.504588\pi$
$432$	−0.989821	−	0.142315i	−0.0476228	−	0.00684713i
$433$	18.1388	+	11.6571i	0.871695	+	0.560204i	0.898271	−	0.439443i	$-0.144824\pi$
$433$	18.1388	+	11.6571i	0.871695	+	0.560204i	−0.0265761	+	0.999647i	$0.508460\pi$
$434$	1.67162	−	1.61737i	0.0802405	−	0.0776364i
$435$	−1.43893	+	4.90055i	−0.0689915	+	0.234964i
$436$		−	15.8228i		−	0.757773i
$437$	3.94782	+	10.0350i	0.188850	+	0.480041i
$438$	−12.4376			−0.594290
$439$	−7.62517	+	25.9689i	−0.363929	+	1.23943i	0.550552	+	0.834801i	$0.314417\pi$
$439$	−7.62517	+	25.9689i	−0.363929	+	1.23943i	−0.914481	+	0.404628i	$0.867401\pi$
$440$	−2.29256	−	1.98652i	−0.109294	−	0.0947034i
$441$	5.13619	+	4.75600i	0.244580	+	0.226476i
$442$	−17.2264	−	2.47679i	−0.819377	−	0.117809i
$443$	7.69153	−	4.94304i	0.365435	−	0.234851i	−0.345017	−	0.938597i	$-0.612127\pi$
$443$	7.69153	−	4.94304i	0.365435	−	0.234851i	0.710452	+	0.703745i	$0.248490\pi$
$444$	−1.41405	−	3.09633i	−0.0671077	−	0.146945i
$445$	−7.14162	−	8.24187i	−0.338545	−	0.390702i
$446$	10.6195	−	1.52685i	0.502848	−	0.0722986i
$447$	3.34835	−	7.33186i	0.158371	−	0.346785i
$448$	0.519681	+	2.59421i	0.0245526	+	0.122565i
$449$	3.58585	−	1.05290i	0.169227	−	0.0496894i	−0.196022	−	0.980600i	$-0.562802\pi$
$449$	3.58585	−	1.05290i	0.169227	−	0.0496894i	0.365248	+	0.930910i	$0.380984\pi$
$450$	1.75092	−	3.83398i	0.0825391	−	0.180735i
$451$	−1.84056	−	12.8014i	−0.0866688	−	0.602794i
$452$	5.87992	−	5.09498i	0.276568	−	0.239648i
$453$	3.63221	−	1.65877i	0.170656	−	0.0779360i
$454$	15.2333	−	9.78987i	0.714936	−	0.459461i
$455$	−2.50477	+	10.6643i	−0.117425	+	0.499950i
$456$	−1.21566	+	1.89160i	−0.0569283	+	0.0885822i
$457$	−18.9283	−	16.4015i	−0.885428	−	0.767228i	0.0880243	−	0.996118i	$-0.471945\pi$
$457$	−18.9283	−	16.4015i	−0.885428	−	0.767228i	−0.973452	+	0.228891i	$0.926490\pi$
$458$	19.5088	+	5.72831i	0.911587	+	0.267666i
$459$			3.72448i			0.173844i
$460$	4.13562	−	0.977087i	0.192824	−	0.0455569i
$461$			10.1422i			0.472370i	0.971708	+	0.236185i	$0.0758971\pi$
$461$			10.1422i			0.472370i	−0.971708	+	0.236185i	$0.924103\pi$
$462$	−3.30490	+	8.43331i	−0.153758	+	0.392353i
$463$	15.1186	−	17.4477i	0.702619	−	0.810865i	−0.286485	−	0.958085i	$-0.592487\pi$
$463$	15.1186	−	17.4477i	0.702619	−	0.810865i	0.989104	+	0.147219i	$0.0470323\pi$
$464$	4.84907	+	3.11631i	0.225113	+	0.144671i
$465$	0.110861	−	0.771057i	0.00514107	−	0.0357569i
$466$	−13.4561	+	8.64769i	−0.623340	+	0.400597i
$467$	−2.65834	−	5.82095i	−0.123013	−	0.269361i	0.838100	−	0.545517i	$-0.183667\pi$
$467$	−2.65834	−	5.82095i	−0.123013	−	0.269361i	−0.961113	+	0.276156i	$0.910939\pi$
$468$	−3.53143	+	3.06000i	−0.163240	+	0.141448i
$469$	1.12204	+	20.4148i	0.0518110	+	0.942669i
$470$	2.79133	+	1.27476i	0.128754	+	0.0588001i
$471$	5.14026	+	17.5061i	0.236851	+	0.806640i
$472$	−3.01159	−	10.2565i	−0.138620	−	0.472096i
$473$	0.436356	−	0.955486i	0.0200637	−	0.0439333i
$474$	−1.04558	−	7.27215i	−0.0480250	−	0.334021i
$475$	−6.20633	−	7.16249i	−0.284766	−	0.328637i
$476$	9.28829	−	3.29090i	0.425728	−	0.150838i
$477$	−5.43018	−	8.44952i	−0.248631	−	0.386877i
$478$	2.26048	−	15.7220i	0.103392	−	0.719108i
$479$	19.1085	+	12.2803i	0.873092	+	0.561102i	0.898697	−	0.438570i	$-0.144515\pi$
$479$	19.1085	+	12.2803i	0.873092	+	0.561102i	−0.0256054	+	0.999672i	$0.508151\pi$
$480$	0.669652	+	0.580257i	0.0305653	+	0.0264850i
$481$	−15.2615	−	4.48117i	−0.695862	−	0.204324i
$482$	14.1332			0.643750
$483$	−6.87399	−	10.6653i	−0.312777	−	0.485287i
$484$	−0.720430			−0.0327468
$485$	−6.99748	−	2.05465i	−0.317739	−	0.0932967i
$486$	0.755750	+	0.654861i	0.0342815	+	0.0297051i
$487$	−36.2271	−	23.2817i	−1.64161	−	1.05500i	−0.939286	−	0.343134i	$-0.888512\pi$
$487$	−36.2271	−	23.2817i	−1.64161	−	1.05500i	−0.702319	−	0.711862i	$-0.747852\pi$
$488$	1.17733	−	8.18850i	0.0532952	−	0.370676i
$489$	0.125553	+	0.195365i	0.00567772	+	0.00883471i
$490$	−1.55023	−	6.00568i	−0.0700324	−	0.271309i
$491$	5.06816	+	5.84897i	0.228723	+	0.263960i	0.858498	−	0.512817i	$-0.171398\pi$
$491$	5.06816	+	5.84897i	0.228723	+	0.263960i	−0.629775	+	0.776778i	$0.716853\pi$
$492$	0.537625	+	3.73926i	0.0242380	+	0.168579i
$493$	8.91826	−	19.5283i	0.401658	−	0.879509i
$494$	2.96013	+	10.0813i	0.133183	+	0.453579i
$495$	0.854634	+	2.91062i	0.0384129	+	0.130822i
$496$	−0.799694	−	0.365208i	−0.0359073	−	0.0163983i
$497$	−12.0860	+	0.664273i	−0.542132	+	0.0297967i
$498$	−3.86591	+	3.34983i	−0.173236	+	0.150109i
$499$	−5.09410	−	11.1545i	−0.228043	−	0.499345i	0.760675	−	0.649133i	$-0.224868\pi$
$499$	−5.09410	−	11.1545i	−0.228043	−	0.499345i	−0.988718	+	0.149788i	$0.952141\pi$
$500$	−6.86890	+	4.41438i	−0.307187	+	0.197417i
$501$	1.00558	−	6.99395i	0.0449259	−	0.312467i
$502$	16.9555	+	10.8966i	0.756759	+	0.486340i
$503$	−1.17102	+	1.35143i	−0.0522132	+	0.0602573i	−0.781255	−	0.624212i	$-0.785420\pi$
$503$	−1.17102	+	1.35143i	−0.0522132	+	0.0602573i	0.729042	+	0.684469i	$0.239966\pi$
$504$	0.965353	−	2.46335i	0.0430002	−	0.109726i
$505$			16.8556i			0.750066i
$506$	9.60368	−	13.3169i	0.426936	−	0.592007i
$507$			8.83457i			0.392357i
$508$	1.78843	+	0.525130i	0.0793487	+	0.0232989i
$509$	14.5929	+	12.6448i	0.646819	+	0.560472i	0.915280	−	0.402819i	$-0.131969\pi$
$509$	14.5929	+	12.6448i	0.646819	+	0.560472i	−0.268461	+	0.963291i	$0.586515\pi$
$510$	1.78421	−	2.77629i	0.0790062	−	0.122936i
$511$	7.52417	−	32.0349i	0.332850	−	1.41714i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	2.04535	−	0.934080i	0.0903044	−	0.0412406i
$514$	−3.59903	+	3.11858i	−0.158747	+	0.137555i
$515$	0.0114897	+	0.0799123i	0.000506295	+	0.00352136i
$516$	−0.127459	+	0.279095i	−0.00561105	+	0.0122865i
$517$	11.3759	−	3.34028i	0.500313	−	0.146905i
$518$	8.83054	−	1.76896i	0.387992	−	0.0777238i
$519$	−0.559064	+	1.22418i	−0.0245402	+	0.0537355i
$520$	4.09827	−	0.589242i	0.179721	−	0.0258400i
$521$	−18.4315	−	21.2711i	−0.807499	−	0.931903i	0.191269	−	0.981538i	$-0.438740\pi$
$521$	−18.4315	−	21.2711i	−0.807499	−	0.931903i	−0.998767	+	0.0496345i	$0.984194\pi$
$522$	−2.39450	−	5.24321i	−0.104804	−	0.229489i
$523$	−1.34477	+	0.864234i	−0.0588029	+	0.0377903i	−0.569712	−	0.821844i	$-0.692945\pi$
$523$	−1.34477	+	0.864234i	−0.0588029	+	0.0377903i	0.510909	+	0.859635i	$0.329309\pi$
$524$	−22.3252	−	3.20988i	−0.975281	−	0.140224i
$525$	8.81580	+	6.82916i	0.384753	+	0.298049i
$526$	−2.01466	−	1.74571i	−0.0878433	−	0.0761166i
$527$	−0.922489	+	3.14171i	−0.0401843	+	0.136855i
$528$	3.42351			0.148989
$529$	7.26154	+	21.8236i	0.315719	+	0.948853i
$530$			8.89972i			0.386579i
$531$	−3.01159	+	10.2565i	−0.130692	+	0.445096i
$532$	−4.13670	−	4.27545i	−0.179349	−	0.185364i
$533$	14.8501	+	9.54355i	0.643227	+	0.413377i
$534$	12.1824	+	1.75157i	0.527185	+	0.0757977i
$535$	−0.566887	−	0.882094i	−0.0245087	−	0.0381362i
$536$	7.02938	−	3.21021i	0.303623	−	0.138660i
$537$	−1.39528	+	1.20901i	−0.0602106	+	0.0521728i
$538$	8.76094	−	1.25963i	0.377711	−	0.0543066i
$539$	−19.7220	−	13.6141i	−0.849488	−	0.586399i
$540$	−0.249637	−	0.850184i	−0.0107427	−	0.0365861i
$541$	−28.2896	+	8.30657i	−1.21626	+	0.357127i	−0.826050	−	0.563597i	$-0.809417\pi$
$541$	−28.2896	+	8.30657i	−1.21626	+	0.357127i	−0.390214	+	0.920724i	$0.627599\pi$
$542$	23.7947	+	10.8667i	1.02207	+	0.466763i
$543$	−17.7424	+	2.55098i	−0.761401	+	0.109473i
$544$	−2.43902	−	2.81478i	−0.104572	−	0.120683i
$545$	12.7532	−	5.82420i	0.546288	−	0.249481i
$546$	−5.74516	−	10.9469i	−0.245870	−	0.468485i
$547$	5.23010	−	36.3761i	0.223623	−	1.55533i	−0.500548	−	0.865709i	$-0.666868\pi$
$547$	5.23010	−	36.3761i	0.223623	−	1.55533i	0.724170	−	0.689621i	$-0.242223\pi$
$548$	−4.61648	+	7.18338i	−0.197206	+	0.306859i
$549$	−5.41747	+	6.25210i	−0.231212	+	0.266833i
$550$	−4.06530	+	13.8451i	−0.173345	+	0.590359i
$551$	−12.9609			−0.552151
$552$	−2.80521	+	3.88983i	−0.119398	+	0.165562i
$553$	19.3631	+	1.70628i	0.823404	+	0.0725582i
$554$	17.8035	+	5.22757i	0.756396	+	0.222098i
$555$	1.97516	−	2.27946i	0.0838408	−	0.0967575i
$556$	4.66384	−	7.25707i	0.197791	−	0.307768i
$557$	40.4181	+	5.81125i	1.71257	+	0.246230i	0.927672	−	0.373395i	$-0.121806\pi$
$557$	40.4181	+	5.81125i	1.71257	+	0.246230i	0.784898	+	0.619625i	$0.212715\pi$
$558$	0.475299	+	0.739580i	0.0201210	+	0.0313089i
$559$	0.595582	+	1.30414i	0.0251904	+	0.0551593i
$560$	−1.89965	+	1.37377i	−0.0802751	+	0.0580523i
$561$	−1.81463	−	12.6210i	−0.0766137	−	0.532860i
$562$	6.80556	+	3.10799i	0.287075	+	0.131103i
$563$	2.65744	−	0.780294i	0.111998	−	0.0328855i	−0.225253	−	0.974300i	$-0.572321\pi$
$563$	2.65744	−	0.780294i	0.111998	−	0.0328855i	0.337251	+	0.941415i	$0.390503\pi$
$564$	−3.32289	+	0.975687i	−0.139919	+	0.0410838i
$565$	6.27091	+	2.86383i	0.263819	+	0.120482i
$566$	−1.37820	−	9.58559i	−0.0579301	−	0.402912i
$567$	−2.14389	+	1.55039i	−0.0900351	+	0.0651104i
$568$	1.90052	+	4.16155i	0.0797439	+	0.174615i
$569$	−13.3317	−	20.7446i	−0.558895	−	0.869658i	0.440713	−	0.897648i	$-0.354726\pi$
$569$	−13.3317	−	20.7446i	−0.558895	−	0.869658i	−0.999608	+	0.0279900i	$0.991089\pi$
$570$	−1.97211	−	0.283546i	−0.0826024	−	0.0118764i
$571$	5.71187	−	8.88784i	0.239034	−	0.371945i	−0.700923	−	0.713237i	$-0.747228\pi$
$571$	5.71187	−	8.88784i	0.239034	−	0.371945i	0.939957	+	0.341293i	$0.110865\pi$
$572$	10.4759	−	12.0899i	0.438021	−	0.505503i
$573$	−17.5409	−	5.15049i	−0.732784	−	0.215165i
$574$	−9.95631	−	0.877348i	−0.415568	−	0.0366198i
$575$	−12.3999	−	15.9637i	−0.517112	−	0.665733i
$576$	−1.00000			−0.0416667
$577$	−5.56005	+	18.9358i	−0.231468	+	0.788307i	0.759063	+	0.651017i	$0.225657\pi$
$577$	−5.56005	+	18.9358i	−0.231468	+	0.788307i	−0.990531	+	0.137290i	$0.956161\pi$
$578$	2.04856	−	2.36416i	0.0852088	−	0.0983361i
$579$	−0.390095	+	0.606999i	−0.0162118	+	0.0252260i
$580$	−0.726864	+	5.05545i	−0.0301814	+	0.209916i
$581$	−6.28932	−	11.9838i	−0.260925	−	0.497171i
$582$	7.48677	−	3.41909i	0.310337	−	0.141726i
$583$	22.5178	+	25.9869i	0.932592	+	1.07627i
$584$	−12.3110	+	1.77005i	−0.509431	+	0.0732452i
$585$	−3.76625	−	1.71999i	−0.155715	−	0.0711128i
$586$	27.1231	−	7.96405i	1.12044	−	0.328992i
$587$	0.923728	+	3.14593i	0.0381264	+	0.129846i	0.976357	−	0.216164i	$-0.0693545\pi$
$587$	0.923728	+	3.14593i	0.0381264	+	0.129846i	−0.938231	+	0.346010i	$0.887536\pi$
$588$	5.76076	+	3.97664i	0.237570	+	0.163994i
$589$	1.95667	−	0.281326i	0.0806231	−	0.0115919i
$590$	7.15828	−	6.20268i	0.294702	−	0.255360i
$591$	10.2223	−	4.66838i	0.420490	−	0.192031i
$592$	−1.84031	−	2.86358i	−0.0756362	−	0.117692i
$593$	−41.7604	−	6.00423i	−1.71489	−	0.246564i	−0.786348	−	0.617784i	$-0.788031\pi$
$593$	−41.7604	−	6.00423i	−1.71489	−	0.246564i	−0.928545	+	0.371220i	$0.878940\pi$
$594$	−2.88004	−	1.85089i	−0.118170	−	0.0759429i
$595$	6.07140	+	6.27505i	0.248903	+	0.257252i
$596$	2.27083	−	7.73375i	0.0930170	−	0.316787i
$597$		−	23.8414i		−	0.975765i
$598$	5.15269	+	21.8093i	0.210709	+	0.891848i
$599$	15.8902			0.649256			0.324628	−	0.945842i	$-0.394761\pi$
$599$	15.8902			0.649256			0.324628	+	0.945842i	$0.394761\pi$
$600$	1.18747	−	4.04414i	0.0484781	−	0.165101i
$601$	7.20109	+	6.23978i	0.293738	+	0.254526i	0.789245	−	0.614078i	$-0.210472\pi$
$601$	7.20109	+	6.23978i	0.293738	+	0.254526i	−0.495507	+	0.868604i	$0.665018\pi$
$602$	−0.641748	−	0.497130i	−0.0261557	−	0.0202615i
$603$	−7.64906	−	1.09977i	−0.311494	−	0.0447861i
$604$	3.35917	−	2.15881i	0.136683	−	0.0878407i
$605$	−0.265183	−	0.580669i	−0.0107812	−	0.0236076i
$606$	−12.4573	−	14.3764i	−0.506042	−	0.584003i
$607$	28.4118	−	4.08500i	1.15320	−	0.165805i	0.460925	−	0.887439i	$-0.347518\pi$
$607$	28.4118	−	4.08500i	1.15320	−	0.165805i	0.692275	+	0.721634i	$0.256609\pi$
$608$	−0.934080	+	2.04535i	−0.0378820	+	0.0829499i
$609$	14.9533	−	2.99550i	0.605939	−	0.121384i
$610$	7.03333	−	2.06517i	0.284771	−	0.0836163i
$611$	−6.72246	+	14.7201i	−0.271961	+	0.595513i
$612$	0.530049	+	3.68657i	0.0214260	+	0.149021i
$613$	−34.8657	+	30.2113i	−1.40821	+	1.22022i	−0.466184	+	0.884688i	$0.654372\pi$
$613$	−34.8657	+	30.2113i	−1.40821	+	1.22022i	−0.942028	+	0.335535i	$0.891083\pi$
$614$	7.90804	−	3.61148i	0.319142	−	0.145747i
$615$	−2.81596	+	1.80971i	−0.113551	+	0.0729746i
$616$	−2.07107	+	8.81780i	−0.0834459	+	0.355279i
$617$	7.42027	−	11.5462i	0.298729	−	0.464831i	−0.659147	−	0.752014i	$-0.729083\pi$
$617$	7.42027	−	11.5462i	0.298729	−	0.464831i	0.957876	+	0.287183i	$0.0927189\pi$
$618$	−0.0688594	−	0.0596670i	−0.00276993	−	0.00240016i
$619$	−31.1439	−	9.14466i	−1.25178	−	0.367555i	−0.412349	−	0.911026i	$-0.635292\pi$
$619$	−31.1439	−	9.14466i	−1.25178	−	0.367555i	−0.839428	+	0.543471i	$0.817110\pi$
$620$		−	0.778986i		−	0.0312848i
$621$	4.46290	−	1.75572i	0.179090	−	0.0704546i
$622$			22.7060i			0.910428i
$623$	−11.8813	+	30.3181i	−0.476013	+	1.21467i
$624$	−3.06000	+	3.53143i	−0.122498	+	0.141370i
$625$	11.6425	+	7.48217i	0.465700	+	0.299287i
$626$	−3.94483	+	27.4369i	−0.157667	+	1.09660i
$627$	−6.47591	+	4.16181i	−0.258623	+	0.166207i
$628$	7.57932	+	16.5964i	0.302448	+	0.662268i
$629$	−9.58133	+	8.30227i	−0.382033	+	0.331033i
$630$	2.34081	−	0.128656i	0.0932599	−	0.00512576i
$631$	4.22901	+	1.93132i	0.168354	+	0.0768848i	0.497810	−	0.867286i	$-0.334138\pi$
$631$	4.22901	+	1.93132i	0.168354	+	0.0768848i	−0.329455	+	0.944171i	$0.606865\pi$
$632$	−2.06987	−	7.04933i	−0.0823351	−	0.280407i
$633$	−4.38338	−	14.9284i	−0.174224	−	0.593351i
$634$	13.4932	−	29.5460i	0.535883	−	1.17342i
$635$	0.235045	+	1.63478i	0.00932749	+	0.0648741i
$636$	−6.57740	−	7.59072i	−0.260811	−	0.300992i
$637$	31.6711	−	8.17519i	1.25486	−	0.323913i
$638$	10.6687	+	16.6009i	0.422379	+	0.657234i
$639$	0.651088	−	4.52842i	0.0257566	−	0.179141i
$640$	0.745415	+	0.479049i	0.0294651	+	0.0189361i
$641$	−3.80054	−	3.29318i	−0.150112	−	0.130073i	0.576567	−	0.817050i	$-0.304392\pi$
$641$	−3.80054	−	3.29318i	−0.150112	−	0.130073i	−0.726679	+	0.686977i	$0.758937\pi$
$642$	1.13542	+	0.333391i	0.0448116	+	0.0131579i
$643$	−28.0424			−1.10588			−0.552942	−	0.833219i	$-0.686495\pi$
$643$	−28.0424			−1.10588			−0.552942	+	0.833219i	$0.686495\pi$
$644$	−8.32185	−	9.57846i	−0.327927	−	0.377444i
$645$	−0.271868			−0.0107048
$646$	8.03544	+	2.35942i	0.316150	+	0.0928301i
$647$	29.7293	+	25.7606i	1.16878	+	1.01275i	0.999631	+	0.0271630i	$0.00864732\pi$
$647$	29.7293	+	25.7606i	1.16878	+	1.01275i	0.169149	+	0.985591i	$0.445898\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	5.20812	−	36.2233i	0.204437	−	1.42189i
$650$	−10.6479	−	16.5685i	−0.417646	−	0.649870i
$651$	−2.19244	+	0.776797i	−0.0859286	+	0.0304451i
$652$	0.152079	+	0.175508i	0.00595587	+	0.00687344i
$653$	−3.31227	−	23.0373i	−0.129619	−	0.901520i	−0.946037	−	0.324059i	$-0.894952\pi$
$653$	−3.31227	−	23.0373i	−0.129619	−	0.901520i	0.816418	−	0.577461i	$-0.195957\pi$
$654$	−6.57302	+	14.3929i	−0.257025	+	0.562807i
$655$	−5.63050	−	19.1757i	−0.220002	−	0.749258i
$656$	1.06430	+	3.62469i	0.0415541	+	0.141520i
$657$	11.3136	+	5.16675i	0.441386	+	0.201574i
$658$	−0.502841	−	9.14887i	−0.0196028	−	0.356660i
$659$	−23.5846	+	20.4362i	−0.918727	+	0.796082i	−0.979369	−	0.202078i	$-0.935231\pi$
$659$	−23.5846	+	20.4362i	−0.918727	+	0.796082i	0.0606420	+	0.998160i	$0.480685\pi$
$660$	1.26016	+	2.75936i	0.0490516	+	0.107408i
$661$	−18.5503	+	11.9215i	−0.721521	+	0.463694i	−0.849166	−	0.528126i	$-0.822895\pi$
$661$	−18.5503	+	11.9215i	−0.721521	+	0.463694i	0.127644	+	0.991820i	$0.459258\pi$
$662$	−3.90240	+	27.1418i	−0.151671	+	1.05490i
$663$	14.6408	+	9.40908i	0.568602	+	0.365418i
$664$	−3.34983	+	3.86591i	−0.129999	+	0.150026i
$665$	1.92335	−	4.90794i	0.0745845	−	0.190322i
$666$			3.40394i			0.131900i
$667$	−27.6040	−	1.48078i	−1.06883	−	0.0573360i
$668$		−	7.06587i		−	0.273387i
$669$	−10.2941	−	3.02262i	−0.397993	−	0.116861i
$670$	5.17488	+	4.48406i	0.199923	+	0.173234i
$671$	15.3119	−	23.8257i	0.591108	−	0.919783i
$672$	0.604956	−	2.57566i	0.0233367	−	0.0993583i
$673$	−11.8336	+	7.60498i	−0.456151	+	0.293151i	−0.748468	−	0.663171i	$-0.769210\pi$
$673$	−11.8336	+	7.60498i	−0.456151	+	0.293151i	0.292317	+	0.956322i	$0.405574\pi$
$674$	−13.5663	+	6.19554i	−0.522556	+	0.238643i
$675$	−3.18538	+	2.76015i	−0.122606	+	0.106238i
$676$	1.25729	+	8.74464i	0.0483573	+	0.336332i
$677$	−3.78431	+	8.28648i	−0.145443	+	0.318475i	−0.968307	−	0.249763i	$-0.919647\pi$
$677$	−3.78431	+	8.28648i	−0.145443	+	0.318475i	0.822864	+	0.568238i	$0.192375\pi$
$678$	−7.46509	+	2.19195i	−0.286695	+	0.0841813i
$679$	4.27726	+	21.3518i	0.164146	+	0.819406i
$680$	1.37094	−	3.00195i	0.0525733	−	0.115119i
$681$	−17.9236	+	2.57702i	−0.686833	+	0.0987517i
$682$	−1.97097	−	2.27462i	−0.0754722	−	0.0870995i
$683$	13.4363	+	29.4215i	0.514127	+	1.12578i	0.971616	+	0.236566i	$0.0760218\pi$
$683$	13.4363	+	29.4215i	0.514127	+	1.12578i	−0.457488	+	0.889216i	$0.651251\pi$
$684$	1.89160	−	1.21566i	0.0723271	−	0.0464818i
$685$	−7.48911	−	1.07677i	−0.286144	−	0.0411413i
$686$	−13.7275	+	12.4321i	−0.524117	+	0.474659i
$687$	−15.3662	−	13.3149i	−0.586258	−	0.507995i
$688$	−0.0864418	+	0.294394i	−0.00329556	+	0.0112237i
$689$	−46.9329			−1.78800
$690$	−4.16779	−	0.829208i	−0.158665	−	0.0315674i
$691$			1.77135i			0.0673852i	0.999432	+	0.0336926i	$0.0107267\pi$
$691$			1.77135i			0.0673852i	−0.999432	+	0.0336926i	$0.989273\pi$
$692$	−0.379155	+	1.29128i	−0.0144133	+	0.0490872i
$693$	6.50956	−	6.29830i	0.247278	−	0.239253i
$694$	−24.3027	−	15.6184i	−0.922519	−	0.592867i
$695$	7.56594	+	1.08782i	0.286992	+	0.0412633i
$696$	−3.11631	−	4.84907i	−0.118123	−	0.183804i
$697$	12.7985	−	5.84490i	0.484779	−	0.221391i
$698$	−0.821826	+	0.712116i	−0.0311066	+	0.0269540i
$699$	15.8325	−	2.27636i	0.598838	−	0.0860999i
$700$	9.69796	+	5.50503i	0.366548	+	0.208071i
$701$	4.79179	+	16.3193i	0.180983	+	0.616373i	0.999143	+	0.0413823i	$0.0131762\pi$
$701$	4.79179	+	16.3193i	0.180983	+	0.616373i	−0.818160	+	0.574991i	$0.805006\pi$
$702$	4.48347	−	1.31647i	0.169218	−	0.0496868i
$703$	6.96225	+	3.17955i	0.262586	+	0.119919i
$704$	3.38866	−	0.487216i	0.127715	−	0.0183627i
$705$	−2.00953	−	2.31912i	−0.0756832	−	0.0873430i
$706$	−12.8562	+	5.87121i	−0.483848	+	0.220966i
$707$	44.5649	−	23.3886i	1.67604	−	0.879618i
$708$	−1.52128	+	10.5807i	−0.0571732	+	0.397649i
$709$	−11.1046	+	17.2790i	−0.417040	+	0.648928i	−0.984684	−	0.174347i	$-0.944219\pi$
$709$	−11.1046	+	17.2790i	−0.417040	+	0.648928i	0.567644	+	0.823274i	$0.307855\pi$
$710$	−2.65467	+	3.06365i	−0.0996278	+	0.114977i
$711$	−2.06987	+	7.04933i	−0.0776262	+	0.264371i
$712$	12.3077			0.461250
$713$	4.19945	−	0.375619i	0.157270	−	0.0140670i
$714$	−9.81602	−	0.864986i	−0.367355	−	0.0323713i
$715$	13.6006	+	3.99349i	0.508633	+	0.149348i
$716$	−1.20901	+	1.39528i	−0.0451829	+	0.0521439i
$717$	−8.58737	+	13.3622i	−0.320701	+	0.499021i
$718$	−18.1614	−	2.61122i	−0.677777	−	0.0974497i
$719$	−8.25329	−	12.8424i	−0.307796	−	0.478940i	0.652552	−	0.757744i	$-0.273698\pi$
$719$	−8.25329	−	12.8424i	−0.307796	−	0.478940i	−0.960348	+	0.278804i	$0.910062\pi$
$720$	−0.368090	−	0.806004i	−0.0137179	−	0.0300380i
$721$	0.195339	−	0.141263i	0.00727480	−	0.00526089i
$722$	1.98444	+	13.8021i	0.0738533	+	0.513661i
$723$	−12.8560	−	5.87114i	−0.478120	−	0.218350i
$724$	−17.1988	+	5.05003i	−0.639189	+	0.187683i
$725$	23.3108	−	6.84468i	0.865742	−	0.254205i
$726$	0.655326	+	0.299277i	0.0243214	+	0.0111072i
$727$	2.77581	+	19.3062i	0.102949	+	0.716027i	0.974282	+	0.225334i	$0.0723473\pi$
$727$	2.77581	+	19.3062i	0.102949	+	0.716027i	−0.871332	+	0.490693i	$0.836744\pi$
$728$	−7.24459	−	10.0179i	−0.268503	−	0.371287i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	−5.95820	−	9.27115i	−0.220523	−	0.343141i
$731$	1.13112	+	0.162631i	0.0418361	+	0.00601512i
$732$	−4.47256	+	6.95945i	−0.165311	+	0.257229i
$733$	−33.8086	+	39.0172i	−1.24875	+	1.44113i	−0.396468	+	0.918049i	$0.629764\pi$
$733$	−33.8086	+	39.0172i	−1.24875	+	1.44113i	−0.852281	+	0.523084i	$0.824781\pi$
$734$	−25.5923	−	7.51458i	−0.944630	−	0.277368i
$735$	−1.08471	+	6.10695i	−0.0400101	+	0.225258i
$736$	−2.22308	+	4.24946i	−0.0819439	+	0.156637i
$737$	26.4559			0.974517
$738$	1.06430	−	3.62469i	0.0391776	−	0.133427i
$739$	12.0005	−	13.8493i	0.441445	−	0.509455i	−0.490805	−	0.871270i	$-0.663297\pi$
$739$	12.0005	−	13.8493i	0.441445	−	0.509455i	0.932250	+	0.361814i	$0.117843\pi$
$740$	1.63065	−	2.53735i	0.0599441	−	0.0932748i
$741$	1.49529	−	10.3999i	0.0549307	−	0.382052i
$742$	23.5302	−	12.3491i	0.863819	−	0.453350i
$743$	−6.40178	+	2.92360i	−0.234859	+	0.107256i	−0.529368	−	0.848392i	$-0.677571\pi$
$743$	−6.40178	+	2.92360i	−0.234859	+	0.107256i	0.294510	+	0.955649i	$0.404844\pi$
$744$	0.575715	+	0.664410i	0.0211067	+	0.0243585i
$745$	7.06930	−	1.01641i	0.258999	−	0.0372385i
$746$	1.95630	+	0.893414i	0.0716254	+	0.0327102i
$747$	4.90813	−	1.44116i	0.179579	−	0.0527291i
$748$	−3.59232	−	12.2343i	−0.131348	−	0.447331i
$749$	−1.54558	+	2.72278i	−0.0564744	+	0.0994883i
$750$	8.08197	−	1.16201i	0.295112	−	0.0424307i
$751$	21.2599	−	18.4218i	0.775786	−	0.672222i	−0.174132	−	0.984722i	$-0.555712\pi$
$751$	21.2599	−	18.4218i	0.775786	−	0.672222i	0.949918	+	0.312500i	$0.101166\pi$
$752$	−3.15021	+	1.43865i	−0.114876	+	0.0524622i
$753$	−10.8966	−	16.9555i	−0.397095	−	0.617891i
$754$	−26.6601	−	3.83314i	−0.970902	−	0.139595i
$755$	2.97648	+	1.91287i	0.108325	+	0.0696165i
$756$	−1.90143	+	1.83972i	−0.0691543	+	0.0669100i
$757$	−11.9786	+	40.7953i	−0.435368	+	1.48273i	0.391418	+	0.920213i	$0.371985\pi$
$757$	−11.9786	+	40.7953i	−0.435368	+	1.48273i	−0.826787	+	0.562516i	$0.809834\pi$
$758$			5.16302i			0.187529i
$759$	−14.2678	+	8.12394i	−0.517890	+	0.294880i
$760$	−1.99239			−0.0722714
$761$	−9.24117	+	31.4725i	−0.334992	+	1.14088i	0.604013	+	0.796975i	$0.293568\pi$
$761$	−9.24117	+	31.4725i	−0.334992	+	1.14088i	−0.939005	+	0.343904i	$0.888251\pi$
$762$	−1.40867	−	1.22062i	−0.0510306	−	0.0442183i
$763$	−33.0948	−	25.6369i	−1.19811	−	0.928119i
$764$	−18.0954	−	2.60173i	−0.654668	−	0.0941271i
$765$	−2.77629	+	1.78421i	−0.100377	+	0.0645083i
$766$	1.74168	+	3.81375i	0.0629295	+	0.137796i
$767$	32.7100	+	37.7493i	1.18109	+	1.36305i
$768$	−0.989821	+	0.142315i	−0.0357171	+	0.00513534i
$769$	16.9550	−	37.1263i	0.611414	−	1.33881i	−0.310189	−	0.950675i	$-0.600392\pi$
$769$	16.9550	−	37.1263i	0.611414	−	1.33881i	0.921603	−	0.388134i	$-0.126880\pi$
$770$	−7.86952	+	1.57645i	−0.283598	+	0.0568113i
$771$	4.56930	−	1.34167i	0.164559	−	0.0483190i
$772$	−0.299739	+	0.656337i	−0.0107878	+	0.0236221i
$773$	−3.34578	−	23.2704i	−0.120339	−	0.836978i	−0.957172	−	0.289519i	$-0.906505\pi$
$773$	−3.34578	−	23.2704i	−0.120339	−	0.836978i	0.836833	−	0.547458i	$-0.184405\pi$
$774$	0.231881	−	0.200926i	0.00833479	−	0.00722213i
$775$	−3.37061	+	1.53930i	−0.121076	+	0.0552934i
$776$	6.92398	−	4.44977i	0.248556	−	0.159737i
$777$	−8.76739	−	2.05923i	−0.314529	−	0.0738745i
$778$	−1.02380	+	1.59306i	−0.0367049	+	0.0571140i
$779$	−6.41961	−	5.56263i	−0.230006	−	0.199302i
$780$	−3.97270	−	1.16649i	−0.142245	−	0.0417670i
$781$			15.6625i			0.560449i
$782$	16.8443	+	5.94313i	0.602350	+	0.212526i
$783$			5.76411i			0.205992i
$784$	6.26806	+	3.11632i	0.223859	+	0.111297i
$785$	−10.5869	+	12.2179i	−0.377862	+	0.436076i
$786$	18.9743	+	12.1940i	0.676791	+	0.434947i
$787$	4.50614	−	31.3409i	0.160626	−	1.11718i	−0.736830	−	0.676078i	$-0.763678\pi$
$787$	4.50614	−	31.3409i	0.160626	−	1.11718i	0.897456	−	0.441103i	$-0.145413\pi$
$788$	9.45390	−	6.07565i	0.336781	−	0.216436i
$789$	1.10740	+	2.42487i	0.0394246	+	0.0863278i
$790$	4.91989	−	4.26311i	0.175042	−	0.151675i
$791$	−1.12967	−	20.5536i	−0.0401664	−	0.730801i
$792$	−3.11414	−	1.42218i	−0.110656	−	0.0505349i
$793$	10.8907	+	37.0904i	0.386741	+	1.31712i
$794$	−6.31043	−	21.4913i	−0.223949	−	0.762699i
$795$	3.69708	−	8.09547i	0.131122	−	0.287117i
$796$	−3.39299	−	23.5988i	−0.120261	−	0.836436i
$797$	29.5897	+	34.1484i	1.04812	+	1.20960i	0.977245	+	0.212112i	$0.0680342\pi$
$797$	29.5897	+	34.1484i	1.04812	+	1.20960i	0.0708765	+	0.997485i	$0.477420\pi$
$798$	1.98679	+	5.60753i	0.0703314	+	0.198505i
$799$	6.97346	+	10.8509i	0.246703	+	0.383878i
$800$	0.599838	−	4.17197i	0.0212075	−	0.147501i
$801$	−10.3539	−	6.65404i	−0.365837	−	0.235109i
$802$	0.760980	+	0.659393i	0.0268711	+	0.0232840i
$803$	−40.8553	−	11.9962i	−1.44175	−	0.423337i
$804$	−7.72772			−0.272536
$805$	4.65708	−	10.2332i	0.164141	−	0.360672i
$806$	4.10800			0.144698
$807$	−8.49250	−	2.49362i	−0.298950	−	0.0877797i
$808$	−14.3764	−	12.4573i	−0.505762	−	0.438245i
$809$	29.7082	+	19.0923i	1.04448	+	0.671249i	0.946092	−	0.323899i	$-0.104994\pi$
$809$	29.7082	+	19.0923i	1.04448	+	0.671249i	0.0983922	+	0.995148i	$0.468630\pi$
$810$	−0.126102	+	0.877058i	−0.00443077	+	0.0308167i
$811$	−23.5123	−	36.5859i	−0.825629	−	1.28470i	−0.956038	−	0.293243i	$-0.905265\pi$
$811$	−23.5123	−	36.5859i	−0.825629	−	1.28470i	0.130409	−	0.991460i	$-0.458371\pi$
$812$	14.3748	−	5.09309i	0.504457	−	0.178732i
$813$	−17.1302	−	19.7693i	−0.600783	−	0.693341i
$814$	−1.65846	−	11.5348i	−0.0581288	−	0.404295i
$815$	−0.0854817	+	0.187179i	−0.00299429	+	0.00655659i
$816$	1.04931	+	3.57361i	0.0367331	+	0.125102i
$817$	−0.194369	−	0.661958i	−0.00680009	−	0.0231590i
$818$	−2.65091	−	1.21063i	−0.0926868	−	0.0423286i
$819$	0.678469	+	12.3443i	0.0237076	+	0.431345i
$820$	−2.52975	+	2.19204i	−0.0883428	+	0.0765495i
$821$	1.66867	+	3.65387i	0.0582369	+	0.127521i	0.936513	−	0.350633i	$-0.114033\pi$
$821$	1.66867	+	3.65387i	0.0582369	+	0.127521i	−0.878276	+	0.478154i	$0.841306\pi$
$822$	7.18338	−	4.61648i	0.250549	−	0.161018i
$823$	3.60254	−	25.0562i	0.125577	−	0.873405i	−0.825489	−	0.564418i	$-0.809101\pi$
$823$	3.60254	−	25.0562i	0.125577	−	0.873405i	0.951066	−	0.308988i	$-0.0999902\pi$
$824$	−0.0766500	−	0.0492600i	−0.00267023	−	0.00171605i
$825$	9.44941	−	10.9052i	0.328986	−	0.379670i
$826$	−26.3321	−	10.3192i	−0.916211	−	0.359050i
$827$			2.07995i			0.0723269i	0.999346	+	0.0361635i	$0.0115137\pi$
$827$			2.07995i			0.0723269i	−0.999346	+	0.0361635i	$0.988486\pi$
$828$	4.16761	−	2.37298i	0.144834	−	0.0824669i
$829$			25.1172i			0.872356i	0.899860	+	0.436178i	$0.143668\pi$
$829$			25.1172i			0.872356i	−0.899860	+	0.436178i	$0.856332\pi$
$830$	−4.34898	−	1.27697i	−0.150955	−	0.0443244i
$831$	−14.0230	−	12.1510i	−0.486452	−	0.421513i
$832$	−2.52628	+	3.93097i	−0.0875829	+	0.136282i
$833$	8.16616	−	24.7594i	0.282941	−	0.857864i
$834$	−7.25707	+	4.66384i	−0.251292	+	0.161495i
$835$	5.69512	−	2.60087i	0.197088	−	0.0900069i
$836$	−5.81770	+	5.04107i	−0.201210	+	0.174349i
$837$	−0.125115	−	0.870192i	−0.00432460	−	0.0300782i
$838$	−2.97254	+	6.50895i	−0.102685	+	0.224848i
$839$	−0.0830973	+	0.0243996i	−0.00286884	+	0.000842367i	−0.283167	−	0.959071i	$-0.591385\pi$
$839$	−0.0830973	+	0.0243996i	−0.00286884	+	0.000842367i	0.280298	+	0.959913i	$0.409567\pi$
$840$	2.29867	−	0.460477i	0.0793117	−	0.0158880i
$841$	1.75509	−	3.84312i	0.0605204	−	0.132521i
$842$	−33.9325	+	4.87875i	−1.16939	+	0.168133i
$843$	−4.89944	−	5.65426i	−0.168746	−	0.194743i
$844$	−6.46330	−	14.1526i	−0.222476	−	0.487154i
$845$	−6.58542	+	4.23219i	−0.226545	+	0.145592i
$846$	3.42792	+	0.492860i	0.117854	+	0.0169449i
$847$	−1.16728	+	1.50685i	−0.0401082	+	0.0517759i
$848$	−7.59072	−	6.57740i	−0.260666	−	0.225869i
$849$	−2.72834	+	9.29189i	−0.0936365	+	0.318897i
$850$	−15.6982			−0.538444
$851$	14.4649	+	7.56723i	0.495851	+	0.259401i
$852$		−	4.57498i		−	0.156736i
$853$	−14.5209	+	49.4538i	−0.497188	+	1.69327i	0.202892	+	0.979201i	$0.434966\pi$
$853$	−14.5209	+	49.4538i	−0.497188	+	1.69327i	−0.700080	+	0.714065i	$0.746852\pi$
$854$	−15.2195	−	15.7300i	−0.520800	−	0.538268i
$855$	1.67610	+	1.07716i	0.0573214	+	0.0368383i
$856$	1.17131	+	0.168410i	0.0400347	+	0.00575612i
$857$	−7.82064	−	12.1692i	−0.267148	−	0.415691i	0.681599	−	0.731725i	$-0.261285\pi$
$857$	−7.82064	−	12.1692i	−0.267148	−	0.415691i	−0.948748	+	0.316035i	$0.897648\pi$
$858$	−14.5516	+	6.64548i	−0.496782	+	0.226873i
$859$	0.932178	−	0.807737i	0.0318055	−	0.0275596i	−0.638813	−	0.769362i	$-0.720574\pi$
$859$	0.932178	−	0.807737i	0.0318055	−	0.0275596i	0.670618	+	0.741802i	$0.266029\pi$
$860$	−0.269101	+	0.0386909i	−0.00917627	+	0.00131935i
$861$	8.69211	+	4.93406i	0.296226	+	0.168152i
$862$	−9.74868	−	33.2010i	−0.332041	−	1.13083i
$863$	−36.6634	+	10.7654i	−1.24804	+	0.366457i	−0.838029	−	0.545625i	$-0.816292\pi$
$863$	−36.6634	+	10.7654i	−1.24804	+	0.366457i	−0.410008	+	0.912082i	$0.634474\pi$
$864$	0.909632	+	0.415415i	0.0309463	+	0.0141327i
$865$	−1.18034	+	0.169707i	−0.0401328	+	0.00577023i
$866$	−14.1199	−	16.2952i	−0.479812	−	0.553733i
$867$	−2.84554	+	1.29952i	−0.0966397	+	0.0441339i
$868$	−2.05958	+	1.08091i	−0.0699066	+	0.0366884i
$869$	3.57955	−	24.8963i	0.121428	−	0.844549i
$870$	2.76129	−	4.29665i	0.0936165	−	0.145670i
$871$	−23.6468	+	27.2899i	−0.801242	+	0.924682i
$872$	−4.45779	+	15.1818i	−0.150960	+	0.514122i
$873$	−8.23055			−0.278562
$874$	−0.960706	−	10.7408i	−0.0324964	−	0.363312i
$875$	−1.89628	+	21.5194i	−0.0641061	+	0.727488i
$876$	11.9338	+	3.50407i	0.403204	+	0.118391i
$877$	25.9388	−	29.9350i	0.875893	−	1.01083i	−0.123935	−	0.992290i	$-0.539552\pi$
$877$	25.9388	−	29.9350i	0.875893	−	1.01083i	0.999828	−	0.0185437i	$-0.00590297\pi$
$878$	14.6326	−	22.7687i	0.493826	−	0.768408i
$879$	−27.9804	−	4.02297i	−0.943755	−	0.135692i
$880$	1.64003	+	2.55194i	0.0552854	+	0.0860258i
$881$	12.1561	+	26.6182i	0.409550	+	0.896789i	0.996212	+	0.0869574i	$0.0277144\pi$
$881$	12.1561	+	26.6182i	0.409550	+	0.896789i	−0.586662	+	0.809832i	$0.699558\pi$
$882$	−3.58822	−	6.01038i	−0.120821	−	0.202380i
$883$	6.96284	+	48.4276i	0.234318	+	1.62972i	0.679076	+	0.734068i	$0.262381\pi$
$883$	6.96284	+	48.4276i	0.234318	+	1.62972i	−0.444758	+	0.895651i	$0.646710\pi$
$884$	15.8308	+	7.22970i	0.532449	+	0.243161i
$885$	−9.08808	+	2.66850i	−0.305493	+	0.0897007i
$886$	−8.77258	+	2.57586i	−0.294721	+	0.0865378i
$887$	17.1584	+	7.83596i	0.576122	+	0.263106i	0.682096	−	0.731263i	$-0.261069\pi$
$887$	17.1584	+	7.83596i	0.576122	+	0.263106i	−0.105974	+	0.994369i	$0.533796\pi$
$888$	0.484431	+	3.36929i	0.0162564	+	0.113066i
$889$	3.99607	−	2.88983i	0.134024	−	0.0969217i
$890$	4.53033	+	9.92004i	0.151857	+	0.332521i
$891$	1.85089	+	2.88004i	0.0620071	+	0.0964850i
$892$	−10.6195	−	1.52685i	−0.355567	−	0.0511228i
$893$	4.21002	−	6.55092i	0.140883	−	0.219218i
$894$	−5.27834	+	6.09153i	−0.176534	+	0.203731i
$895$	−1.56962	−	0.460883i	−0.0524667	−	0.0154056i
$896$	0.232243	−	2.63554i	0.00775870	−	0.0880472i
$897$	4.37285	−	21.9789i	0.146005	−	0.733855i
$898$	−3.73723			−0.124713
$899$	−1.42767	+	4.86219i	−0.0476154	+	0.162163i
$900$	−2.76015	+	3.18538i	−0.0920051	+	0.106179i
$901$	−20.2246	+	31.4701i	−0.673779	+	1.04842i
$902$	−1.84056	+	12.8014i	−0.0612841	+	0.426240i
$903$	0.377239	+	0.718798i	0.0125537	+	0.0239201i
$904$	−7.07716	+	3.23203i	−0.235383	+	0.107496i
$905$	−10.4010	−	12.0034i	−0.345742	−	0.399008i
$906$	−3.95241	+	0.568271i	−0.131310	+	0.0188795i
$907$	−9.08915	−	4.15088i	−0.301800	−	0.137828i	0.258759	−	0.965942i	$-0.416686\pi$
$907$	−9.08915	−	4.15088i	−0.301800	−	0.137828i	−0.560559	+	0.828114i	$0.689414\pi$
$908$	−17.3744	+	5.10159i	−0.576590	+	0.169302i
$909$	5.35933	+	18.2522i	0.177758	+	0.605387i
$910$	5.40779	−	9.52665i	0.179266	−	0.315805i
$911$	−33.1703	+	4.76917i	−1.09898	+	0.158010i	−0.667861	−	0.744286i	$-0.732790\pi$
$911$	−33.1703	+	4.76917i	−1.09898	+	0.158010i	−0.431119	+	0.902295i	$0.641881\pi$
$912$	1.69934	−	1.47249i	0.0562707	−	0.0487589i
$913$	−15.9298	+	7.27491i	−0.527201	+	0.240764i
$914$	13.5407	+	21.0698i	0.447888	+	0.696927i
$915$	−7.25564	−	1.04320i	−0.239864	−	0.0344873i
$916$	−17.1047	−	10.9925i	−0.565156	−	0.363204i
$917$	−42.8863	+	41.4945i	−1.41623	+	1.37027i
$918$	1.04931	−	3.57361i	0.0346323	−	0.117947i
$919$			32.5181i			1.07267i	0.844004	+	0.536337i	$0.180192\pi$
$919$			32.5181i			1.07267i	−0.844004	+	0.536337i	$0.819808\pi$
$920$	−4.24337	−	0.227630i	−0.139900	−	0.00750474i
$921$	−8.69366			−0.286466
$922$	2.85739	−	9.73138i	0.0941032	−	0.320486i
$923$	−16.1562	−	13.9994i	−0.531788	−	0.460797i
$924$	5.54696	−	7.16060i	0.182482	−	0.235567i
$925$	−14.2011	−	2.04181i	−0.466930	−	0.0671344i
$926$	−19.4217	+	12.4816i	−0.638238	+	0.410171i
$927$	0.0378501	+	0.0828803i	0.00124316	+	0.00272214i
$928$	−3.77469	−	4.35622i	−0.123910	−	0.143000i
$929$	38.8816	−	5.59033i	1.27566	−	0.183413i	0.529005	−	0.848619i	$-0.322565\pi$
$929$	38.8816	−	5.59033i	1.27566	−	0.183413i	0.746660	+	0.665206i	$0.231656\pi$
$930$	−0.323602	+	0.708591i	−0.0106113	+	0.0232356i
$931$	−15.6450	+	1.72498i	−0.512745	+	0.0565339i
$932$	15.3473	−	4.50639i	0.502719	−	0.147612i
$933$	9.43241	−	20.6541i	0.308803	−	0.676185i
$934$	0.910706	+	6.33410i	0.0297992	+	0.207258i
$935$	8.53860	−	7.39874i	0.279242	−	0.241965i
$936$	4.25048	−	1.94113i	0.138931	−	0.0634478i
$937$	30.3427	−	19.5001i	0.991252	−	0.637039i	0.0587762	−	0.998271i	$-0.481280\pi$
$937$	30.3427	−	19.5001i	0.991252	−	0.637039i	0.932476	+	0.361232i	$0.117644\pi$
$938$	4.67493	−	19.9040i	0.152642	−	0.649888i
$939$	14.9860	−	23.3187i	0.489051	−	0.760978i
$940$	−2.31912	−	2.00953i	−0.0756413	−	0.0655435i
$941$	−12.6582	−	3.71679i	−0.412647	−	0.121164i	0.0688185	−	0.997629i	$-0.478077\pi$
$941$	−12.6582	−	3.71679i	−0.412647	−	0.121164i	−0.481465	+	0.876465i	$0.659895\pi$
$942$		−	18.2452i		−	0.594460i
$943$	−13.0369	−	12.5807i	−0.424541	−	0.409684i
$944$			10.6895i			0.347915i
$945$	−2.18272	−	0.855377i	−0.0710038	−	0.0278254i
$946$	−0.687872	+	0.793847i	−0.0223647	+	0.0258102i
$947$	−10.9460	−	7.03459i	−0.355698	−	0.228594i	0.350572	−	0.936536i	$-0.385987\pi$
$947$	−10.9460	−	7.03459i	−0.355698	−	0.228594i	−0.706270	+	0.707942i	$0.749624\pi$
$948$	−1.04558	+	7.27215i	−0.0339588	+	0.236189i
$949$	48.8916	−	31.4207i	1.58709	−	1.01996i
$950$	3.93702	+	8.62088i	0.127734	+	0.279698i
$951$	−24.5477	+	21.2707i	−0.796014	+	0.689750i
$952$	−9.83920	+	0.540783i	−0.318890	+	0.0175269i
$953$	−13.9283	−	6.36083i	−0.451181	−	0.206047i	0.176847	−	0.984238i	$-0.443410\pi$
$953$	−13.9283	−	6.36083i	−0.451181	−	0.206047i	−0.628028	+	0.778191i	$0.716138\pi$
$954$	2.82971	+	9.63711i	0.0916153	+	0.312013i
$955$	−4.56373	−	15.5426i	−0.147679	−	0.502948i
$956$	−6.59832	+	14.4483i	−0.213405	+	0.467292i
$957$	−2.80837	−	19.5326i	−0.0907816	−	0.631400i
$958$	−14.8747	−	17.1664i	−0.480581	−	0.554620i
$959$	7.54486	+	21.2947i	0.243636	+	0.687642i
$960$	−0.479049	−	0.745415i	−0.0154612	−	0.0240582i
$961$	−4.30177	+	29.9194i	−0.138767	+	0.965143i
$962$	13.3808	+	8.59930i	0.431413	+	0.277252i
$963$	−0.894323	−	0.774935i	−0.0288192	−	0.0249719i
$964$	−13.5607	−	3.98178i	−0.436761	−	0.128245i
$965$	−0.639341			−0.0205811
$966$	3.59079	+	12.1699i	0.115532	+	0.391560i
$967$	38.1591			1.22711			0.613556	−	0.789651i	$-0.289738\pi$
$967$	38.1591			1.22711			0.613556	+	0.789651i	$0.289738\pi$
$968$	0.691247	+	0.202968i	0.0222175	+	0.00652365i
$969$	−6.32916	−	5.48424i	−0.203322	−	0.176179i
$970$	6.13518	+	3.94284i	0.196989	+	0.126597i
$971$	3.32131	−	23.1002i	0.106586	−	0.741321i	−0.864507	−	0.502620i	$-0.832369\pi$
$971$	3.32131	−	23.1002i	0.106586	−	0.741321i	0.971093	−	0.238701i	$-0.0767214\pi$
$972$	−0.540641	−	0.841254i	−0.0173411	−	0.0269832i
$973$	−7.62225	−	21.5132i	−0.244358	−	0.689680i
$974$	28.2004	+	32.5450i	0.903599	+	1.04281i
$975$	2.80289	+	19.4945i	0.0897644	+	0.624325i
$976$	−3.43661	+	7.52512i	−0.110003	+	0.240873i
$977$	−11.5116	−	39.2049i	−0.368289	−	1.25428i	−0.910315	−	0.413915i	$-0.864161\pi$
$977$	−11.5116	−	39.2049i	−0.368289	−	1.25428i	0.542026	−	0.840361i	$-0.317657\pi$
$978$	−0.0654270	−	0.222824i	−0.00209212	−	0.00712512i
$979$	38.3278	+	17.5037i	1.22496	+	0.559421i
$980$	−0.204559	+	6.19916i	−0.00653441	+	0.198025i
$981$	11.9581	−	10.3617i	0.381791	−	0.330824i
$982$	−3.21502	−	7.03992i	−0.102595	−	0.224653i
$983$	−29.6491	+	19.0543i	−0.945660	+	0.607739i	−0.919994	−	0.391932i	$-0.871807\pi$
$983$	−29.6491	+	19.0543i	−0.945660	+	0.607739i	−0.0256657	+	0.999671i	$0.508171\pi$
$984$	0.537625	−	3.73926i	0.0171388	−	0.119203i
$985$	8.37688	+	5.38349i	0.266909	+	0.171532i
$986$	−14.0588	+	16.2247i	−0.447722	+	0.516699i
$987$	−3.34318	+	8.53099i	−0.106415	+	0.271545i
$988$		−	10.5069i		−	0.334269i
$989$	−0.338337	−	1.43204i	−0.0107585	−	0.0455363i
$990$		−	3.03349i		−	0.0964108i
$991$	−27.6988	−	8.13312i	−0.879883	−	0.258357i	−0.189569	−	0.981867i	$-0.560709\pi$
$991$	−27.6988	−	8.13312i	−0.879883	−	0.258357i	−0.690313	+	0.723510i	$0.742527\pi$
$992$	0.664410	+	0.575715i	0.0210950	+	0.0182790i
$993$	14.8249	−	23.0679i	0.470453	−	0.732039i
$994$	11.7836	+	2.76766i	0.373753	+	0.0877849i
$995$	17.7718	−	11.4212i	0.563403	−	0.362077i
$996$	4.65307	−	2.12499i	0.147438	−	0.0673328i
$997$	−33.7919	+	29.2809i	−1.07020	+	0.927334i	−0.997545	−	0.0700229i	$-0.977693\pi$
$997$	−33.7919	+	29.2809i	−1.07020	+	0.927334i	−0.0726553	+	0.997357i	$0.523147\pi$
$998$	1.74516	+	12.1379i	0.0552421	+	0.384217i
$999$	1.41405	−	3.09633i	0.0447385	−	0.0979636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.97.11	yes	160
7.6	odd	2	inner	966.2.s.a.97.6	✓	160
23.14	odd	22	inner	966.2.s.a.727.6	yes	160
161.83	even	22	inner	966.2.s.a.727.11	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.6	✓	160	7.6	odd	2	inner
966.2.s.a.97.11	yes	160	1.1	even	1	trivial
966.2.s.a.727.6	yes	160	23.14	odd	22	inner
966.2.s.a.727.11	yes	160	161.83	even	22	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.126102 + 0.877058i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.49385 - 0.883586i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(0.755750 + 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.126102 + 0.877058i) q^{5} +(-0.540641 - 0.841254i) q^{6} +(2.49385 - 0.883586i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(0.368090 - 0.806004i) q^{10} +(-0.964515 - 3.28484i) q^{11} +(0.281733 + 0.959493i) q^{12} +(4.25048 + 1.94113i) q^{13} +(-2.64176 + 0.145197i) q^{14} +(-0.669652 + 0.580257i) q^{15} +(0.415415 + 0.909632i) q^{16} +(3.13323 - 2.01361i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-1.89160 - 1.21566i) q^{19} +(-0.580257 + 0.669652i) q^{20} +(2.46335 + 0.965353i) q^{21} +3.42351i q^{22} +(-3.88983 - 2.80521i) q^{23} -1.00000i q^{24} +(4.04414 + 1.18747i) q^{25} +(-3.53143 - 3.06000i) q^{26} +(-0.540641 + 0.841254i) q^{27} +(2.57566 + 0.604956i) q^{28} +(4.84907 - 3.11631i) q^{29} +(0.806004 - 0.368090i) q^{30} +(-0.664410 + 0.575715i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(1.42218 - 3.11414i) q^{33} +(-3.57361 + 1.04931i) q^{34} +(0.460477 + 2.29867i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(-3.36929 + 0.484431i) q^{37} +(1.47249 + 1.69934i) q^{38} +(1.94113 + 4.25048i) q^{39} +(0.745415 - 0.479049i) q^{40} +(3.73926 + 0.537625i) q^{41} +(-2.09160 - 1.62026i) q^{42} +(0.231881 + 0.200926i) q^{43} +(0.964515 - 3.28484i) q^{44} -0.886077 q^{45} +(2.94194 + 3.78748i) q^{46} +3.46317i q^{47} +(-0.281733 + 0.959493i) q^{48} +(5.43855 - 4.40706i) q^{49} +(-3.54577 - 2.27873i) q^{50} +(3.68657 + 0.530049i) q^{51} +(2.52628 + 3.93097i) q^{52} +(-9.13631 + 4.17241i) q^{53} +(0.755750 - 0.654861i) q^{54} +(3.00262 - 0.431711i) q^{55} +(-2.30089 - 1.30610i) q^{56} +(-0.633489 - 2.15747i) q^{57} +(-5.53062 + 1.62394i) q^{58} +(9.72355 + 4.44060i) q^{59} +(-0.877058 + 0.126102i) q^{60} +(5.41747 + 6.25210i) q^{61} +(0.799694 - 0.365208i) q^{62} +(1.22950 + 2.34272i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-2.23848 + 3.48314i) q^{65} +(-2.24192 + 2.58732i) q^{66} +(-2.17715 + 7.41469i) q^{67} +3.72448 q^{68} +(-1.10271 - 4.66734i) q^{69} +(0.205785 - 2.33529i) q^{70} +(-4.38966 - 1.28892i) q^{71} +(0.654861 - 0.755750i) q^{72} +(6.72425 - 10.4631i) q^{73} +(3.36929 + 0.484431i) q^{74} +(2.27873 + 3.54577i) q^{75} +(-0.934080 - 2.04535i) q^{76} +(-5.30779 - 7.33965i) q^{77} +(-0.665001 - 4.62519i) q^{78} +(6.68301 + 3.05203i) q^{79} +(-0.850184 + 0.249637i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.43633 - 1.56932i) q^{82} +(-0.727988 - 5.06327i) q^{83} +(1.55039 + 2.14389i) q^{84} +(1.37094 + 3.00195i) q^{85} +(-0.165881 - 0.258115i) q^{86} +(5.70544 + 0.820318i) q^{87} +(-1.85089 + 2.88004i) q^{88} +(-8.05982 + 9.30153i) q^{89} +(0.850184 + 0.249637i) q^{90} +(12.3152 + 1.08521i) q^{91} +(-1.75572 - 4.46290i) q^{92} -0.879141 q^{93} +(0.975687 - 3.32289i) q^{94} +(1.30473 - 1.50574i) q^{95} +(0.540641 - 0.841254i) q^{96} +(-1.17133 + 8.14677i) q^{97} +(-6.45986 + 2.69633i) q^{98} +(3.11414 - 1.42218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more