LMFDB - Embedded newform 966.2.s.a.727.6

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			727.6
Character	$\chi$	$=$	966.727
Dual form			966.2.s.a.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.126102 + 0.877058i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.30089 + 1.30610i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(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} +(2.30089 + 1.30610i) 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} +(-2.57566 - 0.604956i) 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} +(-2.59421 + 0.519681i) 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} +(2.64176 - 0.145197i) 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} +(-0.855377 + 2.18272i) 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} +(2.34272 - 1.22950i) 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} +(3.58822 + 6.01038i) 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} +(-2.49385 + 0.883586i) 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} +(1.62026 - 2.09160i) 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} +(-6.50956 + 6.29830i) 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} +(-1.90143 + 1.83972i) 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} +(-5.13619 - 4.75600i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{21}{22}\right)$

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	0.998396	+	0.0566226i	$0.0180332\pi$
$5$	0.126102	+	0.877058i	0.0563945	+	0.392232i	−0.942001	+	0.335610i	$0.891058\pi$
$6$	0.540641	−	0.841254i	0.220716	−	0.343440i
$7$	2.30089	+	1.30610i	0.869656	+	0.493659i
$7$	2.30089	+	1.30610i	0.869656	+	0.493659i
$8$	−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	0.676419	+	0.736517i	$0.263531\pi$
$11$	−0.964515	+	3.28484i	−0.290812	+	0.990415i	−0.967231	+	0.253898i	$0.918287\pi$
$12$	−0.281733	+	0.959493i	−0.0813292	+	0.276982i
$13$	−4.25048	+	1.94113i	−1.17887	+	0.538372i	−0.905835	−	0.423631i	$-0.860755\pi$
$13$	−4.25048	+	1.94113i	−1.17887	+	0.538372i	−0.273036	+	0.962004i	$0.588028\pi$
$14$	−2.57566	−	0.604956i	−0.688374	−	0.161681i
$15$	−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	$-0.467350\pi$
$17$	−3.13323	−	2.01361i	−0.759921	−	0.488371i	−0.862315	+	0.506372i	$0.830986\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	1.89160	−	1.21566i	0.433962	−	0.278891i	−0.305367	−	0.952235i	$-0.598779\pi$
$19$	1.89160	−	1.21566i	0.433962	−	0.278891i	0.739329	+	0.673344i	$0.235143\pi$
$20$	0.580257	+	0.669652i	0.129749	+	0.149739i
$21$	−2.59421	+	0.519681i	−0.566103	+	0.113404i
$22$		−	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
$28$	2.64176	−	0.145197i	0.499246	−	0.0274396i
$29$	4.84907	+	3.11631i	0.900450	+	0.578684i	0.906924	−	0.421295i	$-0.138424\pi$
$29$	4.84907	+	3.11631i	0.900450	+	0.578684i	−0.00647334	+	0.999979i	$0.502061\pi$
$30$	0.806004	+	0.368090i	0.147155	+	0.0672037i
$31$	0.664410	+	0.575715i	0.119332	+	0.103401i	0.712482	−	0.701690i	$-0.247571\pi$
$31$	0.664410	+	0.575715i	0.119332	+	0.103401i	−0.593151	+	0.805091i	$0.702116\pi$
$32$	−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
$35$	−0.855377	+	2.18272i	−0.144585	+	0.368947i
$36$	−0.415415	−	0.909632i	−0.0692358	−	0.151605i
$37$	−3.36929	−	0.484431i	−0.553908	−	0.0796400i	−0.140324	−	0.990106i	$-0.544814\pi$
$37$	−3.36929	−	0.484431i	−0.553908	−	0.0796400i	−0.413585	+	0.910466i	$0.635723\pi$
$38$	−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	$-0.640771\pi$
$41$	−3.73926	+	0.537625i	−0.583974	+	0.0839628i	−0.156005	+	0.987756i	$0.549862\pi$
$42$	2.34272	−	1.22950i	0.361489	−	0.189717i
$43$	0.231881	−	0.200926i	0.0353615	−	0.0306409i	−0.637001	−	0.770863i	$-0.719825\pi$
$43$	0.231881	−	0.200926i	0.0353615	−	0.0306409i	0.672362	+	0.740222i	$0.265280\pi$
$44$	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
$49$	3.58822	+	6.01038i	0.512602	+	0.858626i
$50$	−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	−0.326733	−	0.945117i	$-0.605948\pi$
$53$	−9.13631	−	4.17241i	−1.25497	−	0.573125i	−0.928236	+	0.371992i	$0.878675\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	−3.00262	−	0.431711i	−0.404873	−	0.0582119i
$56$	−2.49385	+	0.883586i	−0.333254	+	0.118074i
$57$	−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	$-0.881327\pi$
$59$	−9.72355	+	4.44060i	−1.26590	+	0.578117i	−0.334596	+	0.942362i	$0.608600\pi$
$60$	−0.877058	−	0.126102i	−0.113228	−	0.0162797i
$61$	−5.41747	+	6.25210i	−0.693636	+	0.800499i	−0.987878	−	0.155232i	$-0.950387\pi$
$61$	−5.41747	+	6.25210i	−0.693636	+	0.800499i	0.294242	+	0.955731i	$0.404933\pi$
$62$	−0.799694	−	0.365208i	−0.101561	−	0.0463815i
$63$	1.62026	−	2.09160i	0.204133	−	0.263516i
$64$	−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	−0.978855	−	0.204556i	$-0.934425\pi$
$67$	−2.17715	−	7.41469i	−0.265981	−	0.905849i	0.712874	−	0.701293i	$-0.247393\pi$
$68$	−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	−0.531631	−	0.846976i	$-0.678421\pi$
$71$	−4.38966	+	1.28892i	−0.520957	+	0.152967i	0.0106736	+	0.999943i	$0.496602\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	−6.72425	−	10.4631i	−0.787014	−	1.22462i	−0.970382	−	0.241574i	$-0.922336\pi$
$73$	−6.72425	−	10.4631i	−0.787014	−	1.22462i	0.183368	−	0.983044i	$-0.441300\pi$
$74$	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
$77$	−6.50956	+	6.29830i	−0.741833	+	0.717758i
$78$	−0.665001	+	4.62519i	−0.0752966	+	0.523699i
$79$	6.68301	−	3.05203i	0.751897	−	0.343380i	−0.00232670	−	0.999997i	$-0.500741\pi$
$79$	6.68301	−	3.05203i	0.751897	−	0.343380i	0.754224	+	0.656617i	$0.228013\pi$
$80$	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	−0.910061	−	0.414474i	$-0.863965\pi$
$83$	0.727988	−	5.06327i	0.0799070	−	0.555766i	0.989968	−	0.141291i	$-0.0451254\pi$
$84$	−1.90143	+	1.83972i	−0.207463	+	0.200730i
$85$	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	$-0.00107436\pi$
$89$	8.05982	+	9.30153i	0.854339	+	0.985960i	−0.145655	+	0.989335i	$0.546529\pi$
$90$	−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	0.958737	+	0.284294i	$0.0917592\pi$
$97$	1.17133	+	8.14677i	0.118930	+	0.827179i	−0.839807	+	0.542886i	$0.817332\pi$
$98$	−5.13619	−	4.75600i	−0.518833	−	0.480429i
$99$	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	$-0.849873\pi$
$101$	−18.8291	−	2.70722i	−1.87357	−	0.269379i	−0.982744	+	0.184968i	$0.940782\pi$
$102$	−3.38791	+	1.54721i	−0.335453	+	0.153196i
$103$	−0.0874233	−	0.0256698i	−0.00861407	−	0.00252932i	0.277423	−	0.960748i	$-0.410520\pi$
$103$	−0.0874233	−	0.0256698i	−0.00861407	−	0.00252932i	−0.286037	+	0.958219i	$0.592338\pi$
$104$	1.31647	−	4.48347i	0.129090	−	0.439640i
$105$	−0.782925	−	2.20974i	−0.0764057	−	0.215649i
$106$	9.94173	+	1.42940i	0.965626	+	0.138836i
$107$	−0.894323	−	0.774935i	−0.0864575	−	0.0749158i	0.610560	−	0.791970i	$-0.290944\pi$
$107$	−0.894323	−	0.774935i	−0.0864575	−	0.0749158i	−0.697017	+	0.717054i	$0.745490\pi$
$108$	0.909632	+	0.415415i	0.0875294	+	0.0399733i
$109$	−8.55444	+	13.3110i	−0.819366	+	1.27496i	0.139250	+	0.990257i	$0.455531\pi$
$109$	−8.55444	+	13.3110i	−0.819366	+	1.27496i	−0.958616	+	0.284702i	$0.908105\pi$
$110$	3.00262	−	0.431711i	0.286288	−	0.0411620i
$111$	2.86358	−	1.84031i	0.271799	−	0.174674i
$112$	2.14389	−	1.55039i	0.202579	−	0.146498i
$113$	2.19195	+	7.46509i	0.206201	+	0.702257i	0.996037	+	0.0889387i	$0.0283475\pi$
$113$	2.19195	+	7.46509i	0.206201	+	0.702257i	−0.789836	+	0.613318i	$0.789834\pi$
$114$		−	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
$119$	−4.57927	−	8.72540i	−0.419781	−	0.799857i
$120$	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
$126$	−0.965353	+	2.46335i	−0.0860005	+	0.219453i
$127$	1.78843	+	0.525130i	0.158697	+	0.0465978i	0.360116	−	0.932907i	$-0.382737\pi$
$127$	1.78843	+	0.525130i	0.158697	+	0.0465978i	−0.201419	+	0.979505i	$0.564555\pi$
$128$	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	0.967211	+	0.253973i	$0.0817374\pi$
$131$	20.5166	+	9.36960i	1.79254	+	0.818626i	0.825329	+	0.564653i	$0.190990\pi$
$132$	−2.88004	−	1.85089i	−0.250675	−	0.161099i
$133$	5.94013	−	0.326482i	0.515075	−	0.0283096i
$134$	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	$-0.881150\pi$
$137$		−	8.53890i		−	0.729527i	0.931100	−	0.364764i	$-0.118850\pi$
$138$	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	$-0.119220\pi$
$140$	0.460477	+	2.29867i	0.0389175	+	0.194273i
$141$	−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
$147$	−6.64776	−	2.19256i	−0.548298	−	0.180840i
$148$	−3.09633	+	1.41405i	−0.254517	+	0.116234i
$149$	−2.27083	+	7.73375i	−0.186034	+	0.633574i	0.812672	+	0.582721i	$0.198012\pi$
$149$	−2.27083	+	7.73375i	−0.186034	+	0.633574i	−0.998706	+	0.0508525i	$0.983806\pi$
$150$	1.18747	−	4.04414i	0.0969562	−	0.330202i
$151$	1.65877	+	3.63221i	0.134989	+	0.295585i	0.965040	−	0.262103i	$-0.0844159\pi$
$151$	1.65877	+	3.63221i	0.134989	+	0.295585i	−0.830051	+	0.557688i	$0.811689\pi$
$152$	−0.320002	+	2.22566i	−0.0259556	+	0.180525i
$153$	−2.43902	+	2.81478i	−0.197183	+	0.227561i
$154$	4.47144	−	7.87713i	0.360319	−	0.634757i
$155$	−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	$-0.941397\pi$
$157$	−15.3488	+	9.86409i	−1.22497	+	0.787240i	−0.241869	+	0.970309i	$0.577761\pi$
$158$	−5.55244	+	4.81122i	−0.441729	+	0.382760i
$159$	9.63711	−	2.82971i	0.764273	−	0.224411i
$160$	−0.886077			−0.0700505
$161$	−12.6140	+	1.37400i	−0.994120	+	0.108286i
$162$	1.00000			0.0785674
$163$	0.222824	−	0.0654270i	0.0174529	−	0.00512464i	−0.272994	−	0.962016i	$-0.588014\pi$
$163$	0.222824	−	0.0654270i	0.0174529	−	0.00512464i	0.290447	+	0.956891i	$0.406196\pi$
$164$	−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	$-0.730038\pi$
$167$	3.82010	−	5.94419i	0.295608	−	0.459975i	0.957009	+	0.290057i	$0.0936743\pi$
$168$	1.30610	−	2.30089i	0.100768	−	0.177518i
$169$	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	$-0.925383\pi$
$173$	−0.379155	+	1.29128i	−0.0288266	+	0.0981744i	0.943823	+	0.330451i	$0.107201\pi$
$174$	5.24321	−	2.39450i	0.397487	−	0.181526i
$175$	10.8561	+	2.54981i	0.820642	+	0.192747i
$176$	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	0.977643	−	0.210270i	$-0.0674342\pi$
$179$	−0.262744	−	1.82742i	−0.0196384	−	0.136588i	−0.997282	+	0.0736817i	$0.976525\pi$
$180$	0.745415	−	0.479049i	0.0555600	−	0.0357062i
$181$	11.7383	+	13.5467i	0.872502	+	1.00692i	0.999886	+	0.0150673i	$0.00479626\pi$
$181$	11.7383	+	13.5467i	0.872502	+	1.00692i	−0.127385	+	0.991853i	$0.540658\pi$
$182$	12.1221	−	2.42834i	0.898549	−	0.180000i
$183$		−	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
$189$	0.145197	+	2.64176i	0.0105615	+	0.192160i
$190$	−1.67610	−	1.07716i	−0.121597	−	0.0781457i
$191$	−16.6294	−	7.59440i	−1.20326	−	0.549511i	−0.290056	−	0.957010i	$-0.593674\pi$
$191$	−16.6294	−	7.59440i	−1.20326	−	0.549511i	−0.913206	+	0.407498i	$0.866401\pi$
$192$	0.755750	+	0.654861i	0.0545415	+	0.0472605i
$193$	0.102686	−	0.714197i	0.00739150	−	0.0514090i	−0.985792	−	0.167971i	$-0.946278\pi$
$193$	0.102686	−	0.714197i	0.00739150	−	0.0514090i	0.993183	+	0.116562i	$0.0371875\pi$
$194$	−3.41909	−	7.48677i	−0.245477	−	0.537519i
$195$	3.97270	+	1.16649i	0.284491	+	0.0835340i
$196$	6.26806	+	3.11632i	0.447718	+	0.222594i
$197$	4.66838	+	10.2223i	0.332608	+	0.728310i	0.999864	−	0.0165186i	$-0.00525829\pi$
$197$	4.66838	+	10.2223i	0.332608	+	0.728310i	−0.667255	+	0.744829i	$0.732531\pi$
$198$	−3.38866	−	0.487216i	−0.240822	−	0.0346250i
$199$	15.6128	−	18.0182i	1.10676	−	1.27727i	0.149277	−	0.988795i	$-0.452305\pi$
$199$	15.6128	−	18.0182i	1.10676	−	1.27727i	0.957487	−	0.288478i	$-0.0931491\pi$
$200$	−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
$203$	7.08699	+	13.5037i	0.497409	+	0.947771i
$204$	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
$210$	1.37377	+	1.89965i	0.0947989	+	0.131089i
$211$	−13.0888	+	8.41164i	−0.901068	+	0.579081i	−0.907107	−	0.420901i	$-0.861714\pi$
$211$	−13.0888	+	8.41164i	−0.901068	+	0.579081i	0.00603889	+	0.999982i	$0.498078\pi$
$212$	−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
$217$	0.776797	+	2.19244i	0.0527324	+	0.148833i
$218$	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	$-0.246678\pi$
$223$	9.75917	+	4.45686i	0.653522	+	0.298454i	−0.0609257	+	0.998142i	$0.519405\pi$
$224$	−1.62026	+	2.09160i	−0.108258	+	0.139751i
$225$	−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	$-0.0220691\pi$
$227$	11.8582	+	13.6850i	0.787053	+	0.908308i	−0.210544	+	0.977584i	$0.567524\pi$
$228$	0.633489	+	2.15747i	0.0419538	+	0.142882i
$229$	20.3324			1.34360			0.671802	−	0.740731i	$-0.265520\pi$
$229$	20.3324			1.34360			0.671802	+	0.740731i	$0.265520\pi$
$230$	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	0.986822	−	0.161811i	$-0.0517335\pi$
$233$	10.4747	+	12.0884i	0.686218	+	0.791938i	−0.300603	+	0.953749i	$0.597188\pi$
$234$	−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
$238$	6.85200	+	7.08184i	0.444149	+	0.459047i
$239$	2.26048	−	15.7220i	0.146219	−	1.01697i	−0.776119	−	0.630587i	$-0.782814\pi$
$239$	2.26048	−	15.7220i	0.146219	−	1.01697i	0.922337	−	0.386386i	$-0.126277\pi$
$240$	−0.806004	+	0.368090i	−0.0520273	+	0.0237601i
$241$	13.5607	+	3.98178i	0.873522	+	0.256489i	0.687613	−	0.726078i	$-0.258659\pi$
$241$	13.5607	+	3.98178i	0.873522	+	0.256489i	0.185909	+	0.982567i	$0.440477\pi$
$242$	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
$245$	−4.81897	+	3.90499i	−0.307873	+	0.249481i
$246$	−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	$-0.371461\pi$
$251$	19.3386	−	5.67832i	1.22064	−	0.358412i	0.827710	+	0.561156i	$0.189643\pi$
$252$	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	$-0.229272\pi$
$257$	−2.57464	−	4.00622i	−0.160602	−	0.249901i	−0.912223	+	0.409693i	$0.865636\pi$
$258$	−0.0436654	−	0.303699i	−0.00271849	−	0.0189075i
$259$	−7.11967	−	5.51525i	−0.442395	−	0.342701i
$260$	−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	−0.339248	−	0.940697i	$-0.610172\pi$
$263$	2.42487	−	1.10740i	0.149524	−	0.0682854i	0.488772	+	0.872412i	$0.337445\pi$
$264$	3.28484	+	0.964515i	0.202168	+	0.0593618i
$265$	2.50734	−	8.53922i	0.154025	−	0.524560i
$266$	−5.60753	+	1.98679i	−0.343820	+	0.121818i
$267$	−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	$-0.276669\pi$
$269$	8.05118	+	3.67685i	0.490889	+	0.224181i	−0.154562	+	0.987983i	$0.549397\pi$
$270$	0.479049	−	0.745415i	0.0291540	−	0.0453645i
$271$	25.8923	−	3.72275i	1.57285	−	0.226141i	0.700002	−	0.714141i	$-0.253182\pi$
$271$	25.8923	−	3.72275i	1.57285	−	0.226141i	0.872844	+	0.488000i	$0.162273\pi$
$272$	−3.13323	+	2.01361i	−0.189980	+	0.122093i
$273$	10.0179	−	7.24459i	0.606309	−	0.438463i
$274$	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
$280$	−1.08944	−	2.07583i	−0.0651062	−	0.124054i
$281$	−7.40551	+	1.06475i	−0.441775	+	0.0635177i	−0.359614	−	0.933101i	$-0.617092\pi$
$281$	−7.40551	+	1.06475i	−0.441775	+	0.0635177i	−0.0821618	+	0.996619i	$0.526182\pi$
$282$	2.91340	+	1.87233i	0.173491	+	0.111496i
$283$	−4.02295	+	8.80902i	−0.239139	+	0.523642i	−0.990707	−	0.136014i	$-0.956571\pi$
$283$	−4.02295	+	8.80902i	−0.239139	+	0.523642i	0.751568	+	0.659656i	$0.229298\pi$
$284$	−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
$287$	−9.30583	−	3.64683i	−0.549306	−	0.215265i
$288$	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	$-0.00895055\pi$
$293$	23.7807	+	15.2829i	1.38928	+	0.892837i	0.389676	+	0.920952i	$0.372587\pi$
$294$	6.99619	+	0.230860i	0.408026	+	0.0134640i
$295$	−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
$301$	0.795962	−	0.159450i	0.0458785	−	0.00919053i
$302$	−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	$-0.192925\pi$
$307$	6.57023	+	5.69314i	0.374983	+	0.324925i	−0.446897	+	0.894586i	$0.647471\pi$
$308$	−2.07107	+	8.81780i	−0.118010	+	0.502441i
$309$	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	−0.552852	−	0.833280i	$-0.686460\pi$
$311$	6.39702	−	21.7862i	0.362742	−	1.23538i	0.915593	−	0.402105i	$-0.131721\pi$
$312$	1.94113	+	4.25048i	0.109895	+	0.240636i
$313$	3.94483	−	27.4369i	0.222975	−	1.55082i	−0.503722	−	0.863866i	$-0.668036\pi$
$313$	3.94483	−	27.4369i	0.222975	−	1.55082i	0.726696	−	0.686959i	$-0.241055\pi$
$314$	11.9481	−	13.7888i	0.674268	−	0.778146i
$315$	2.03877	+	1.15730i	0.114872	+	0.0652066i
$316$	3.97205	−	6.18064i	0.223445	−	0.347688i
$317$	−4.62256	−	32.1506i	−0.259629	−	1.80576i	−0.535467	−	0.844556i	$-0.679865\pi$
$317$	−4.62256	−	32.1506i	−0.259629	−	1.80576i	0.275838	−	0.961204i	$-0.411045\pi$
$318$	−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
$322$	11.7159	−	4.87211i	0.652902	−	0.271512i
$323$	−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
$329$	−4.52324	+	7.96838i	−0.249374	+	0.439311i
$330$	−1.98652	+	2.29256i	−0.109354	+	0.126201i
$331$	−3.90240	+	27.1418i	−0.214496	+	1.49185i	0.543400	+	0.839474i	$0.317137\pi$
$331$	−3.90240	+	27.1418i	−0.214496	+	1.49185i	−0.757896	+	0.652376i	$0.773773\pi$
$332$	−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
$336$	−0.604956	+	2.57566i	−0.0330030	+	0.140514i
$337$	11.2713	+	9.76666i	0.613988	+	0.532024i	0.905392	−	0.424576i	$-0.139577\pi$
$337$	11.2713	+	9.76666i	0.613988	+	0.532024i	−0.291404	+	0.956600i	$0.594122\pi$
$338$	−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
$343$	0.405948	+	18.5158i	0.0219192	+	0.999760i
$344$			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	0.566103	−	0.824334i	$-0.308450\pi$
$347$	27.7185	−	8.13889i	1.48801	−	0.436919i	0.921905	+	0.387416i	$0.126632\pi$
$348$	−4.35622	+	3.77469i	−0.233518	+	0.202344i
$349$	−0.587910	−	0.914805i	−0.0314701	−	0.0489684i	0.825162	−	0.564896i	$-0.191084\pi$
$349$	−0.587910	−	0.914805i	−0.0314701	−	0.0489684i	−0.856632	+	0.515928i	$0.827447\pi$
$350$	−11.1347	+	0.611986i	−0.595174	+	0.0327120i
$351$	−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	$-0.395470\pi$
$353$	−10.6813	−	9.25539i	−0.568508	−	0.492615i	−0.891028	+	0.453948i	$0.850015\pi$
$354$	−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
$357$	9.17470	+	3.59544i	0.485577	+	0.190291i
$358$	0.766945	+	1.67938i	0.0405343	+	0.0887578i
$359$	18.1614	+	2.61122i	0.958522	+	0.137815i	0.603781	−	0.797150i	$-0.293660\pi$
$359$	18.1614	+	2.61122i	0.958522	+	0.137815i	0.354741	+	0.934965i	$0.384569\pi$
$360$	−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
$364$	−10.9469	+	5.74516i	−0.573775	+	0.301128i
$365$	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	$-0.745107\pi$
$367$	−26.6728			−1.39231			−0.696153	+	0.717893i	$0.745107\pi$
$368$	0.935820	+	4.70364i	0.0487830	+	0.245194i
$369$			3.77771i			0.196660i
$370$	0.849748	+	2.89398i	0.0441763	+	0.150451i
$371$	−15.5721	−	21.5332i	−0.808463	−	1.11795i
$372$	−0.739580	+	0.475299i	−0.0383454	+	0.0246431i
$373$	−2.12876	+	0.306070i	−0.110223	+	0.0158477i	−0.197206	−	0.980362i	$-0.563187\pi$
$373$	−2.12876	+	0.306070i	−0.110223	+	0.0158477i	0.0869825	+	0.996210i	$0.472278\pi$
$374$	−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
$378$	−0.883586	−	2.49385i	−0.0454468	−	0.128270i
$379$	−1.45459	+	4.95388i	−0.0747173	+	0.254464i	−0.988379	−	0.152013i	$-0.951425\pi$
$379$	−1.45459	+	4.95388i	−0.0747173	+	0.254464i	0.913661	+	0.406477i	$0.133243\pi$
$380$	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	$-0.738565\pi$
$383$	2.74559	−	3.16858i	0.140293	−	0.161907i	0.821548	+	0.570140i	$0.193111\pi$
$384$	−0.909632	−	0.415415i	−0.0464195	−	0.0211991i
$385$	−6.34484	−	4.91503i	−0.323363	−	0.250493i
$386$	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	0.971912	−	0.235346i	$-0.0756223\pi$
$389$	0.533510	+	1.81697i	0.0270500	+	0.0921239i	−0.944862	+	0.327470i	$0.893804\pi$
$390$	−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	0.391906	+	0.920005i	$0.371816\pi$
$397$	−12.1096	+	18.8429i	−0.607764	+	0.945700i	−0.999670	+	0.0256943i	$0.991820\pi$
$398$	−9.90409	+	21.6869i	−0.496447	+	1.08707i
$399$	−4.27545	+	4.13670i	−0.214040	+	0.207094i
$400$	0.599838	−	4.17197i	0.0299919	−	0.208598i
$401$	−0.915928	+	0.418290i	−0.0457392	+	0.0208884i	−0.438153	−	0.898900i	$-0.644367\pi$
$401$	−0.915928	+	0.418290i	−0.0457392	+	0.0208884i	0.392414	+	0.919789i	$0.371640\pi$
$402$	−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
$406$	−10.6043	−	10.9600i	−0.526285	−	0.543937i
$407$	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	$-0.568409\pi$
$409$	−2.88460	+	0.414743i	−0.142634	+	0.0205077i	0.0706278	+	0.997503i	$0.477500\pi$
$410$	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	−0.999459	−	0.0328834i	$-0.989531\pi$
$419$	−1.01835	−	7.08275i	−0.0497494	−	0.346015i	0.949710	−	0.313132i	$-0.101378\pi$
$420$	−1.85331	−	1.43567i	−0.0904325	−	0.0700535i
$421$	31.1835	+	14.2410i	1.51979	+	0.694065i	0.988233	−	0.152958i	$-0.0488799\pi$
$421$	31.1835	+	14.2410i	1.51979	+	0.694065i	0.531557	+	0.847023i	$0.321607\pi$
$422$	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
$427$	−20.6309	+	7.30965i	−0.998398	+	0.353739i
$428$	−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	−0.0144119	−	0.999896i	$-0.504588\pi$
$431$	18.7076	−	29.1096i	0.901113	−	1.40216i	0.915524	−	0.402262i	$-0.131776\pi$
$432$	0.989821	−	0.142315i	0.0476228	−	0.00684713i
$433$	−18.1388	+	11.6571i	−0.871695	+	0.560204i	−0.898271	−	0.439443i	$-0.855176\pi$
$433$	−18.1388	+	11.6571i	−0.871695	+	0.560204i	0.0265761	+	0.999647i	$0.491540\pi$
$434$	−1.36301	−	1.88478i	−0.0654267	−	0.0904725i
$435$	−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	0.914481	+	0.404628i	$0.132599\pi$
$439$	7.62517	+	25.9689i	0.363929	+	1.23943i	−0.550552	+	0.834801i	$0.685583\pi$
$440$	2.29256	−	1.98652i	0.109294	−	0.0947034i
$441$	6.45986	−	2.69633i	0.307613	−	0.128396i
$442$	−17.2264	+	2.47679i	−0.819377	+	0.117809i
$443$	7.69153	+	4.94304i	0.365435	+	0.234851i	0.710452	−	0.703745i	$-0.248490\pi$
$443$	7.69153	+	4.94304i	0.365435	+	0.234851i	−0.345017	+	0.938597i	$0.612127\pi$
$444$	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
$448$	0.965353	−	2.46335i	0.0456086	−	0.116382i
$449$	3.58585	+	1.05290i	0.169227	+	0.0496894i	0.365248	−	0.930910i	$-0.380984\pi$
$449$	3.58585	+	1.05290i	0.169227	+	0.0496894i	−0.196022	+	0.980600i	$0.562802\pi$
$450$	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
$455$	−0.601175	−	10.9380i	−0.0281835	−	0.512781i
$456$	−1.21566	−	1.89160i	−0.0569283	−	0.0885822i
$457$	−18.9283	+	16.4015i	−0.885428	+	0.767228i	−0.973452	−	0.228891i	$-0.926490\pi$
$457$	−18.9283	+	16.4015i	−0.885428	+	0.767228i	0.0880243	+	0.996118i	$0.471945\pi$
$458$	−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	$0.924103\pi$
$462$	1.77913	+	8.88131i	0.0827728	+	0.413196i
$463$	15.1186	+	17.4477i	0.702619	+	0.810865i	0.989104	−	0.147219i	$-0.0470323\pi$
$463$	15.1186	+	17.4477i	0.702619	+	0.810865i	−0.286485	+	0.958085i	$0.592487\pi$
$464$	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	$-0.816333\pi$
$467$	2.65834	−	5.82095i	0.123013	−	0.269361i	0.961113	+	0.276156i	$0.0890606\pi$
$468$	3.53143	+	3.06000i	0.163240	+	0.141448i
$469$	4.67493	−	19.9040i	0.215868	−	0.919081i
$470$	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
$476$	−8.56963	−	4.86454i	−0.392789	−	0.222966i
$477$	−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	$-0.855485\pi$
$479$	−19.1085	+	12.2803i	−0.873092	+	0.561102i	0.0256054	+	0.999672i	$0.491849\pi$
$480$	0.669652	−	0.580257i	0.0305653	−	0.0264850i
$481$	15.2615	−	4.48117i	0.695862	−	0.204324i
$482$	−14.1332			−0.643750
$483$	8.63322	−	9.29879i	0.392825	−	0.423110i
$484$	−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	−0.702319	+	0.711862i	$0.747852\pi$
$487$	−36.2271	+	23.2817i	−1.64161	+	1.05500i	−0.939286	+	0.343134i	$0.888512\pi$
$488$	−1.17733	−	8.18850i	−0.0532952	−	0.370676i
$489$	−0.125553	+	0.195365i	−0.00567772	+	0.00883471i
$490$	3.52361	−	5.10447i	0.159180	−	0.230597i
$491$	5.06816	−	5.84897i	0.228723	−	0.263960i	−0.629775	−	0.776778i	$-0.716853\pi$
$491$	5.06816	−	5.84897i	0.228723	−	0.263960i	0.858498	+	0.512817i	$0.171398\pi$
$492$	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
$497$	−11.7836	−	2.76766i	−0.528567	−	0.124147i
$498$	−3.86591	−	3.34983i	−0.173236	−	0.150109i
$499$	−5.09410	+	11.1545i	−0.228043	+	0.499345i	−0.988718	−	0.149788i	$-0.952141\pi$
$499$	−5.09410	+	11.1545i	−0.228043	+	0.499345i	0.760675	+	0.649133i	$0.224868\pi$
$500$	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	$-0.214580\pi$
$503$	1.17102	+	1.35143i	0.0522132	+	0.0602573i	−0.729042	+	0.684469i	$0.760034\pi$
$504$	0.519681	+	2.59421i	0.0231484	+	0.115555i
$505$		−	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	$-0.868031\pi$
$509$	−14.5929	+	12.6448i	−0.646819	+	0.560472i	0.268461	+	0.963291i	$0.413485\pi$
$510$	−1.78421	−	2.77629i	−0.0790062	−	0.122936i
$511$	−1.80590	−	32.8571i	−0.0798881	−	1.45351i
$512$	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
$518$	8.38510	+	3.28600i	0.368420	+	0.144379i
$519$	−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	$-0.561260\pi$
$521$	18.4315	−	21.2711i	0.807499	−	0.931903i	0.998767	+	0.0496345i	$0.0158056\pi$
$522$	−2.39450	+	5.24321i	−0.104804	+	0.229489i
$523$	1.34477	+	0.864234i	0.0588029	+	0.0377903i	0.569712	−	0.821844i	$-0.307055\pi$
$523$	1.34477	+	0.864234i	0.0588029	+	0.0377903i	−0.510909	+	0.859635i	$0.670691\pi$
$524$	22.3252	−	3.20988i	0.975281	−	0.140224i
$525$	−9.87424	+	5.18220i	−0.430947	+	0.226170i
$526$	−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
$532$	4.82065	−	3.48613i	0.209002	−	0.151143i
$533$	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
$539$	−23.2040	+	5.98959i	−0.999467	+	0.257990i
$540$	−0.249637	+	0.850184i	−0.0107427	+	0.0365861i
$541$	−28.2896	−	8.30657i	−1.21626	−	0.357127i	−0.390214	−	0.920724i	$-0.627599\pi$
$541$	−28.2896	−	8.30657i	−1.21626	−	0.357127i	−0.826050	+	0.563597i	$0.809417\pi$
$542$	−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
$546$	−7.57104	+	9.77350i	−0.324011	+	0.418267i
$547$	5.23010	+	36.3761i	0.223623	+	1.55533i	0.724170	+	0.689621i	$0.242223\pi$
$547$	5.23010	+	36.3761i	0.223623	+	1.55533i	−0.500548	+	0.865709i	$0.666868\pi$
$548$	−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	0.784898	−	0.619625i	$-0.212715\pi$
$557$	40.4181	−	5.81125i	1.71257	−	0.246230i	0.927672	+	0.373395i	$0.121806\pi$
$558$	−0.475299	+	0.739580i	−0.0201210	+	0.0313089i
$559$	−0.595582	+	1.30414i	−0.0251904	+	0.0551593i
$560$	1.63013	+	1.68481i	0.0688857	+	0.0711963i
$561$	−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	$-0.427679\pi$
$563$	−2.65744	−	0.780294i	−0.111998	−	0.0328855i	−0.337251	+	0.941415i	$0.609497\pi$
$564$	−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
$567$	−1.83972	−	1.90143i	−0.0772610	−	0.0798525i
$568$	1.90052	−	4.16155i	0.0797439	−	0.174615i
$569$	−13.3317	+	20.7446i	−0.558895	+	0.869658i	−0.999608	−	0.0279900i	$-0.991089\pi$
$569$	−13.3317	+	20.7446i	−0.558895	+	0.869658i	0.440713	+	0.897648i	$0.354726\pi$
$570$	1.97211	−	0.283546i	0.0826024	−	0.0118764i
$571$	5.71187	+	8.88784i	0.239034	+	0.371945i	0.939957	−	0.341293i	$-0.110865\pi$
$571$	5.71187	+	8.88784i	0.239034	+	0.371945i	−0.700923	+	0.713237i	$0.747228\pi$
$572$	−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	0.990531	+	0.137290i	$0.0438392\pi$
$577$	5.56005	+	18.9358i	0.231468	+	0.788307i	−0.759063	+	0.651017i	$0.774343\pi$
$578$	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
$581$	8.28814	−	10.6992i	0.343850	−	0.443878i
$582$	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	$-0.930646\pi$
$587$	−0.923728	+	3.14593i	−0.0381264	+	0.129846i	0.938231	+	0.346010i	$0.112464\pi$
$588$	−6.77784	+	1.74955i	−0.279513	+	0.0721501i
$589$	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	$-0.211969\pi$
$593$	41.7604	−	6.00423i	1.71489	−	0.246564i	0.928545	+	0.371220i	$0.121060\pi$
$594$	2.88004	−	1.85089i	0.118170	−	0.0759429i
$595$	7.07523	−	5.11657i	0.290056	−	0.209759i
$596$	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	$-0.789528\pi$
$601$	−7.20109	+	6.23978i	−0.293738	+	0.254526i	0.495507	+	0.868604i	$0.334982\pi$
$602$	−0.718798	+	0.377239i	−0.0292960	+	0.0153751i
$603$	−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	$-0.652482\pi$
$607$	−28.4118	−	4.08500i	−1.15320	−	0.165805i	−0.692275	+	0.721634i	$0.743391\pi$
$608$	0.934080	+	2.04535i	0.0378820	+	0.0829499i
$609$	−14.1990	−	5.56440i	−0.575373	−	0.225481i
$610$	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	−0.942028	−	0.335535i	$-0.891083\pi$
$613$	−34.8657	−	30.2113i	−1.40821	−	1.22022i	−0.466184	−	0.884688i	$-0.654372\pi$
$614$	−7.90804	−	3.61148i	−0.319142	−	0.145747i
$615$	2.81596	+	1.80971i	0.113551	+	0.0729746i
$616$	−0.497083	−	9.04411i	−0.0200281	−	0.364398i
$617$	7.42027	+	11.5462i	0.298729	+	0.464831i	0.957876	−	0.287183i	$-0.0927189\pi$
$617$	7.42027	+	11.5462i	0.298729	+	0.464831i	−0.659147	+	0.752014i	$0.729083\pi$
$618$	−0.0688594	+	0.0596670i	−0.00276993	+	0.00240016i
$619$	31.1439	−	9.14466i	1.25178	−	0.367555i	0.412349	−	0.911026i	$-0.364708\pi$
$619$	31.1439	−	9.14466i	1.25178	−	0.367555i	0.839428	+	0.543471i	$0.182890\pi$
$620$			0.778986i			0.0312848i
$621$	−4.46290	−	1.75572i	−0.179090	−	0.0704546i
$622$			22.7060i			0.910428i
$623$	6.39608	+	31.9287i	0.256253	+	1.27920i
$624$	−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
$630$	−2.28223	−	0.536037i	−0.0909263	−	0.0213562i
$631$	4.22901	−	1.93132i	0.168354	−	0.0768848i	−0.329455	−	0.944171i	$-0.606865\pi$
$631$	4.22901	−	1.93132i	0.168354	−	0.0768848i	0.497810	+	0.867286i	$0.334138\pi$
$632$	−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
$637$	−26.9186	−	18.5818i	−1.06655	−	0.736239i
$638$	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	−0.726679	−	0.686977i	$-0.758937\pi$
$641$	−3.80054	+	3.29318i	−0.150112	+	0.130073i	0.576567	+	0.817050i	$0.304392\pi$
$642$	−1.13542	+	0.333391i	−0.0448116	+	0.0131579i
$643$	28.0424			1.10588			0.552942	−	0.833219i	$-0.313505\pi$
$643$	28.0424			1.10588			0.552942	+	0.833219i	$0.313505\pi$
$644$	−9.86870	+	7.97551i	−0.388881	+	0.314279i
$645$	−0.271868			−0.0107048
$646$	8.03544	−	2.35942i	0.316150	−	0.0928301i
$647$	−29.7293	+	25.7606i	−1.16878	+	1.01275i	−0.169149	+	0.985591i	$0.554102\pi$
$647$	−29.7293	+	25.7606i	−1.16878	+	1.01275i	−0.999631	+	0.0271630i	$0.991353\pi$
$648$	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
$651$	−2.02281	−	1.14824i	−0.0792801	−	0.0450032i
$652$	0.152079	−	0.175508i	0.00595587	−	0.00687344i
$653$	−3.31227	+	23.0373i	−0.129619	+	0.901520i	0.816418	+	0.577461i	$0.195957\pi$
$653$	−3.31227	+	23.0373i	−0.129619	+	0.901520i	−0.946037	+	0.324059i	$0.894952\pi$
$654$	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
$658$	2.09506	−	8.91995i	0.0816740	−	0.347736i
$659$	−23.5846	−	20.4362i	−0.918727	−	0.796082i	0.0606420	−	0.998160i	$-0.480685\pi$
$659$	−23.5846	−	20.4362i	−0.918727	−	0.796082i	−0.979369	+	0.202078i	$0.935231\pi$
$660$	1.26016	−	2.75936i	0.0490516	−	0.107408i
$661$	18.5503	+	11.9215i	0.721521	+	0.463694i	0.849166	−	0.528126i	$-0.177105\pi$
$661$	18.5503	+	11.9215i	0.721521	+	0.463694i	−0.127644	+	0.991820i	$0.540742\pi$
$662$	−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
$665$	1.03541	+	5.16867i	0.0401513	+	0.200432i
$666$		−	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
$672$	−0.145197	−	2.64176i	−0.00560109	−	0.101908i
$673$	−11.8336	−	7.60498i	−0.456151	−	0.293151i	0.292317	−	0.956322i	$-0.405574\pi$
$673$	−11.8336	−	7.60498i	−0.456151	−	0.293151i	−0.748468	+	0.663171i	$0.769210\pi$
$674$	−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	$-0.0803526\pi$
$677$	3.78431	+	8.28648i	0.145443	+	0.318475i	−0.822864	+	0.568238i	$0.807625\pi$
$678$	7.46509	+	2.19195i	0.286695	+	0.0841813i
$679$	−7.94538	+	20.2747i	−0.304916	+	0.778072i
$680$	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	−0.457488	−	0.889216i	$-0.651251\pi$
$683$	13.4363	−	29.4215i	0.514127	−	1.12578i	0.971616	−	0.236566i	$-0.0760218\pi$
$684$	−1.89160	−	1.21566i	−0.0723271	−	0.0464818i
$685$	7.48911	−	1.07677i	0.286144	−	0.0411413i
$686$	−5.60601	−	17.6514i	−0.214038	−	0.673934i
$687$	−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
$693$	5.30779	+	7.33965i	0.201626	+	0.278810i
$694$	−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
$700$	10.5112	−	3.72420i	0.397287	−	0.140762i
$701$	4.79179	−	16.3193i	0.180983	−	0.616373i	−0.818160	−	0.574991i	$-0.805006\pi$
$701$	4.79179	−	16.3193i	0.180983	−	0.616373i	0.999143	−	0.0413823i	$-0.0131762\pi$
$702$	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
$707$	−39.7879	−	30.8217i	−1.49638	−	1.15917i
$708$	−1.52128	−	10.5807i	−0.0571732	−	0.397649i
$709$	−11.1046	−	17.2790i	−0.417040	−	0.648928i	0.567644	−	0.823274i	$-0.307855\pi$
$709$	−11.1046	−	17.2790i	−0.417040	−	0.648928i	−0.984684	+	0.174347i	$0.944219\pi$
$710$	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	$-0.726302\pi$
$719$	8.25329	−	12.8424i	0.307796	−	0.478940i	0.960348	+	0.278804i	$0.0899380\pi$
$720$	0.368090	−	0.806004i	0.0137179	−	0.0300380i
$721$	−0.167624	−	0.173247i	−0.00624266	−	0.00645205i
$722$	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	0.871332	+	0.490693i	$0.163256\pi$
$727$	−2.77581	+	19.3062i	−0.102949	+	0.716027i	−0.974282	+	0.225334i	$0.927653\pi$
$728$	8.88489	−	8.59655i	0.329296	−	0.318609i
$729$	−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	0.852281	+	0.523084i	$0.175219\pi$
$733$	33.8086	+	39.0172i	1.24875	+	1.44113i	0.396468	+	0.918049i	$0.370236\pi$
$734$	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	0.932250	−	0.361814i	$-0.117843\pi$
$739$	12.0005	+	13.8493i	0.441445	+	0.509455i	−0.490805	+	0.871270i	$0.663297\pi$
$740$	−1.63065	−	2.53735i	−0.0599441	−	0.0932748i
$741$	−1.49529	−	10.3999i	−0.0549307	−	0.382052i
$742$	21.0079	+	16.2738i	0.771225	+	0.597429i
$743$	−6.40178	−	2.92360i	−0.234859	−	0.107256i	0.294510	−	0.955649i	$-0.404844\pi$
$743$	−6.40178	−	2.92360i	−0.234859	−	0.107256i	−0.529368	+	0.848392i	$0.677571\pi$
$744$	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
$749$	−1.04560	−	2.95112i	−0.0382054	−	0.107831i
$750$	8.08197	+	1.16201i	0.295112	+	0.0424307i
$751$	21.2599	+	18.4218i	0.775786	+	0.672222i	0.949918	−	0.312500i	$-0.101166\pi$
$751$	21.2599	+	18.4218i	0.775786	+	0.672222i	−0.174132	+	0.984722i	$0.555712\pi$
$752$	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
$756$	1.55039	+	2.14389i	0.0563872	+	0.0779727i
$757$	−11.9786	−	40.7953i	−0.435368	−	1.48273i	−0.826787	−	0.562516i	$-0.809834\pi$
$757$	−11.9786	−	40.7953i	−0.435368	−	1.48273i	0.391418	−	0.920213i	$-0.371985\pi$
$758$		−	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	0.939005	+	0.343904i	$0.111749\pi$
$761$	9.24117	+	31.4725i	0.334992	+	1.14088i	−0.604013	+	0.796975i	$0.706432\pi$
$762$	1.40867	−	1.22062i	0.0510306	−	0.0442183i
$763$	−37.0683	+	19.4542i	−1.34196	+	0.704288i
$764$	−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	−0.921603	−	0.388134i	$-0.873120\pi$
$769$	−16.9550	−	37.1263i	−0.611414	−	1.33881i	0.310189	−	0.950675i	$-0.399608\pi$
$770$	7.47256	+	2.92839i	0.269292	+	0.105532i
$771$	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	−0.836833	−	0.547458i	$-0.815595\pi$
$773$	3.34578	−	23.2704i	0.120339	−	0.836978i	0.957172	−	0.289519i	$-0.0934955\pi$
$774$	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
$777$	8.99241	−	0.494242i	0.322601	−	0.0177308i
$778$	−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
$784$	6.95784	−	0.767152i	0.248494	−	0.0273983i
$785$	−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	−0.897456	−	0.441103i	$-0.854587\pi$
$787$	−4.50614	−	31.3409i	−0.160626	−	1.11718i	0.736830	−	0.676078i	$-0.236322\pi$
$788$	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
$791$	−4.70670	+	20.0393i	−0.167351	+	0.712515i
$792$	−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	−0.0708765	+	0.997485i	$0.522580\pi$
$797$	−29.5897	+	34.1484i	−1.04812	+	1.20960i	−0.977245	+	0.212112i	$0.931966\pi$
$798$	2.93682	−	5.17367i	0.103962	−	0.183146i
$799$	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
$805$	−2.79572	−	10.8899i	−0.0985363	−	0.383819i
$806$	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	0.0983922	−	0.995148i	$-0.468630\pi$
$809$	29.7082	−	19.0923i	1.04448	−	0.671249i	0.946092	+	0.323899i	$0.104994\pi$
$810$	0.126102	+	0.877058i	0.00443077	+	0.0308167i
$811$	23.5123	−	36.5859i	0.825629	−	1.28470i	−0.130409	−	0.991460i	$-0.541629\pi$
$811$	23.5123	−	36.5859i	0.825629	−	1.28470i	0.956038	−	0.293243i	$-0.0947345\pi$
$812$	13.2626	+	7.52849i	0.465426	+	0.264198i
$813$	−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
$819$	−2.82680	+	12.0354i	−0.0987765	+	0.420551i
$820$	−2.52975	−	2.19204i	−0.0883428	−	0.0765495i
$821$	1.66867	−	3.65387i	0.0582369	−	0.127521i	−0.878276	−	0.478154i	$-0.841306\pi$
$821$	1.66867	−	3.65387i	0.0582369	−	0.127521i	0.936513	+	0.350633i	$0.114033\pi$
$822$	−7.18338	−	4.61648i	−0.250549	−	0.161018i
$823$	3.60254	+	25.0562i	0.125577	+	0.873405i	0.951066	+	0.308988i	$0.0999902\pi$
$823$	3.60254	+	25.0562i	0.125577	+	0.873405i	−0.825489	+	0.564418i	$0.809101\pi$
$824$	0.0766500	−	0.0492600i	0.00267023	−	0.00171605i
$825$	−9.44941	−	10.9052i	−0.328986	−	0.379670i
$826$	27.7309	−	5.55516i	0.964883	−	0.193289i
$827$		−	2.07995i		−	0.0723269i	−0.999346	−	0.0361635i	$-0.988486\pi$
$827$		−	2.07995i		−	0.0723269i	0.999346	−	0.0361635i	$-0.0115137\pi$
$828$	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
$833$	0.859833	−	26.0572i	0.0297914	−	0.902828i
$834$	−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	$-0.408615\pi$
$839$	0.0830973	+	0.0243996i	0.00286884	+	0.000842367i	−0.280298	+	0.959913i	$0.590433\pi$
$840$	2.18272	+	0.855377i	0.0753109	+	0.0295133i
$841$	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
$847$	−0.885771	−	1.68776i	−0.0304355	−	0.0579922i
$848$	−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	0.700080	+	0.714065i	$0.253148\pi$
$853$	14.5209	+	49.4538i	0.497188	+	1.69327i	−0.202892	+	0.979201i	$0.565034\pi$
$854$	17.7358	−	12.8259i	0.606907	−	0.438895i
$855$	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	$-0.738715\pi$
$857$	7.82064	−	12.1692i	0.267148	−	0.415691i	0.948748	+	0.316035i	$0.102352\pi$
$858$	−14.5516	−	6.64548i	−0.496782	−	0.226873i
$859$	−0.932178	−	0.807737i	−0.0318055	−	0.0275596i	0.638813	−	0.769362i	$-0.279426\pi$
$859$	−0.932178	−	0.807737i	−0.0318055	−	0.0275596i	−0.670618	+	0.741802i	$0.733971\pi$
$860$	0.269101	+	0.0386909i	0.00917627	+	0.00131935i
$861$	9.42104	−	3.33794i	0.321068	−	0.113757i
$862$	−9.74868	+	33.2010i	−0.332041	+	1.13083i
$863$	−36.6634	−	10.7654i	−1.24804	−	0.366457i	−0.410008	−	0.912082i	$-0.634474\pi$
$863$	−36.6634	−	10.7654i	−1.24804	−	0.366457i	−0.838029	+	0.545625i	$0.816292\pi$
$864$	−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
$868$	1.83881	+	1.42443i	0.0624132	+	0.0483484i
$869$	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	0.999828	+	0.0185437i	$0.00590297\pi$
$877$	25.9388	+	29.9350i	0.875893	+	1.01083i	−0.123935	+	0.992290i	$0.539552\pi$
$878$	−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	0.586662	+	0.809832i	$0.300442\pi$
$881$	−12.1561	+	26.6182i	−0.409550	+	0.896789i	−0.996212	+	0.0869574i	$0.972286\pi$
$882$	−5.43855	+	4.40706i	−0.183126	+	0.148393i
$883$	6.96284	−	48.4276i	0.234318	−	1.62972i	−0.444758	−	0.895651i	$-0.646710\pi$
$883$	6.96284	−	48.4276i	0.234318	−	1.62972i	0.679076	−	0.734068i	$-0.262381\pi$
$884$	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	$-0.738931\pi$
$887$	−17.1584	+	7.83596i	−0.576122	+	0.263106i	0.105974	+	0.994369i	$0.466204\pi$
$888$	−0.484431	+	3.36929i	−0.0162564	+	0.113066i
$889$	3.42911	+	3.54413i	0.115009	+	0.118866i
$890$	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
$903$	−0.497130	+	0.641748i	−0.0165435	+	0.0213560i
$904$	−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	−0.560559	−	0.828114i	$-0.689414\pi$
$907$	−9.08915	+	4.15088i	−0.301800	+	0.137828i	0.258759	+	0.965942i	$0.416686\pi$
$908$	17.3744	+	5.10159i	0.576590	+	0.169302i
$909$	−5.35933	+	18.2522i	−0.177758	+	0.605387i
$910$	3.65841	+	10.3256i	0.121275	+	0.342289i
$911$	−33.1703	−	4.76917i	−1.09898	−	0.158010i	−0.431119	−	0.902295i	$-0.641881\pi$
$911$	−33.1703	−	4.76917i	−1.09898	−	0.158010i	−0.667861	+	0.744286i	$0.732790\pi$
$912$	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
$917$	34.9688	+	48.3551i	1.15477	+	1.59683i
$918$	1.04931	+	3.57361i	0.0346323	+	0.117947i
$919$		−	32.5181i		−	1.07267i	−0.844004	−	0.536337i	$-0.819808\pi$
$919$		−	32.5181i		−	1.07267i	0.844004	−	0.536337i	$-0.180192\pi$
$920$	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
$924$	−4.20922	−	8.02032i	−0.138473	−	0.263849i
$925$	−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	$-0.677435\pi$
$929$	−38.8816	−	5.59033i	−1.27566	−	0.183413i	−0.746660	+	0.665206i	$0.768344\pi$
$930$	0.323602	+	0.708591i	0.0106113	+	0.0232356i
$931$	14.0940	+	7.00719i	0.461913	+	0.229651i
$932$	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	$-0.518720\pi$
$937$	−30.3427	−	19.5001i	−0.991252	−	0.637039i	−0.932476	+	0.361232i	$0.882356\pi$
$938$	1.12204	+	20.4148i	0.0366359	+	0.666567i
$939$	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	$-0.521923\pi$
$941$	12.6582	−	3.71679i	0.412647	−	0.121164i	0.481465	+	0.876465i	$0.340105\pi$
$942$			18.2452i			0.594460i
$943$	13.0369	−	12.5807i	0.424541	−	0.409684i
$944$			10.6895i			0.347915i
$945$	−2.29867	+	0.460477i	−0.0747757	+	0.0149793i
$946$	−0.687872	−	0.793847i	−0.0223647	−	0.0258102i
$947$	−10.9460	+	7.03459i	−0.355698	+	0.228594i	−0.706270	−	0.707942i	$-0.749624\pi$
$947$	−10.9460	+	7.03459i	−0.355698	+	0.228594i	0.350572	+	0.936536i	$0.385987\pi$
$948$	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
$952$	9.59300	+	2.25315i	0.310911	+	0.0730249i
$953$	−13.9283	+	6.36083i	−0.451181	+	0.206047i	−0.628028	−	0.778191i	$-0.716138\pi$
$953$	−13.9283	+	6.36083i	−0.451181	+	0.206047i	0.176847	+	0.984238i	$0.443410\pi$
$954$	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
$959$	11.1526	−	19.6471i	0.360138	−	0.634438i
$960$	−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
$966$	−5.66374	+	11.3544i	−0.182228	+	0.365321i
$967$	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	−0.971093	−	0.238701i	$-0.923279\pi$
$971$	−3.32131	−	23.1002i	−0.106586	−	0.741321i	0.864507	−	0.502620i	$-0.167631\pi$
$972$	0.540641	−	0.841254i	0.0173411	−	0.0269832i
$973$	11.2671	−	19.8486i	0.361205	−	0.636318i
$974$	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	0.542026	+	0.840361i	$0.317657\pi$
$977$	−11.5116	+	39.2049i	−0.368289	+	1.25428i	−0.910315	+	0.413915i	$0.864161\pi$
$978$	0.0654270	−	0.222824i	0.00209212	−	0.00712512i
$979$	−38.3278	+	17.5037i	−1.22496	+	0.559421i
$980$	−1.94278	+	5.89042i	−0.0620598	+	0.188163i
$981$	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	$-0.128193\pi$
$983$	29.6491	+	19.0543i	0.945660	+	0.607739i	0.0256657	+	0.999671i	$0.491829\pi$
$984$	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
$987$	−1.79974	−	8.98419i	−0.0572865	−	0.285970i
$988$			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	−0.690313	−	0.723510i	$-0.742527\pi$
$991$	−27.6988	+	8.13312i	−0.879883	+	0.258357i	−0.189569	+	0.981867i	$0.560709\pi$
$992$	−0.664410	+	0.575715i	−0.0210950	+	0.0182790i
$993$	−14.8249	−	23.0679i	−0.470453	−	0.732039i
$994$	12.0860	−	0.664273i	0.383345	−	0.0210695i
$995$	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	$-0.0223072\pi$
$997$	33.7919	+	29.2809i	1.07020	+	0.927334i	0.0726553	+	0.997357i	$0.476853\pi$
$998$	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.727.6	yes	160
7.6	odd	2	inner	966.2.s.a.727.11	yes	160
23.5	odd	22	inner	966.2.s.a.97.11	yes	160
161.97	even	22	inner	966.2.s.a.97.6	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.6	✓	160	161.97	even	22	inner
966.2.s.a.97.11	yes	160	23.5	odd	22	inner
966.2.s.a.727.6	yes	160	1.1	even	1	trivial
966.2.s.a.727.11	yes	160	7.6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.126102 + 0.877058i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.30089 + 1.30610i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(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} +(2.30089 + 1.30610i) 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} +(-2.57566 - 0.604956i) 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} +(-2.59421 + 0.519681i) 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} +(2.64176 - 0.145197i) 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} +(-0.855377 + 2.18272i) 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} +(2.34272 - 1.22950i) 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} +(3.58822 + 6.01038i) 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} +(-2.49385 + 0.883586i) 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} +(1.62026 - 2.09160i) 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} +(-6.50956 + 6.29830i) 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} +(-1.90143 + 1.83972i) 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} +(-5.13619 - 4.75600i) 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

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