LMFDB - Embedded newform 231.2.s.a.8.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(8,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("231.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.s (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.19
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61087 - 1.17037i) q^{2} +(-0.418655 + 1.68069i) q^{3} +(0.607116 - 1.86851i) q^{4} +(2.20177 - 3.03048i) q^{5} +(1.29263 + 3.19736i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(0.0217402 + 0.0669093i) q^{8} +(-2.64946 - 1.40726i) q^{9} +O(q^{10})$	\(q+(1.61087 - 1.17037i) q^{2} +(-0.418655 + 1.68069i) q^{3} +(0.607116 - 1.86851i) q^{4} +(2.20177 - 3.03048i) q^{5} +(1.29263 + 3.19736i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(0.0217402 + 0.0669093i) q^{8} +(-2.64946 - 1.40726i) q^{9} -7.45860i q^{10} +(2.20500 + 2.47749i) q^{11} +(2.88622 + 1.80264i) q^{12} +(0.175583 + 0.241669i) q^{13} +(-1.89369 + 0.615298i) q^{14} +(4.17152 + 4.96923i) q^{15} +(3.29223 + 2.39194i) q^{16} +(-3.31846 - 2.41100i) q^{17} +(-5.91495 + 0.833920i) q^{18} +(-3.34142 + 1.08569i) q^{19} +(-4.32575 - 5.95388i) q^{20} +(0.917527 - 1.46906i) q^{21} +(6.45155 + 1.41026i) q^{22} -0.788215i q^{23} +(-0.121556 + 0.00852662i) q^{24} +(-2.79092 - 8.58957i) q^{25} +(0.565684 + 0.183802i) q^{26} +(3.47438 - 3.86377i) q^{27} +(-1.15480 + 1.58945i) q^{28} +(-2.29911 + 7.07593i) q^{29} +(12.5356 + 3.12258i) q^{30} +(-6.16968 + 4.48253i) q^{31} +7.96210 q^{32} +(-5.08704 + 2.66871i) q^{33} -8.16736 q^{34} +(-3.03048 + 2.20177i) q^{35} +(-4.23801 + 4.09617i) q^{36} +(-1.20809 + 3.71813i) q^{37} +(-4.11194 + 5.65960i) q^{38} +(-0.479681 + 0.193925i) q^{39} +(0.250634 + 0.0814360i) q^{40} +(-2.68816 - 8.27330i) q^{41} +(-0.241324 - 3.44031i) q^{42} +3.79840i q^{43} +(5.96791 - 2.61594i) q^{44} +(-10.0982 + 4.93066i) q^{45} +(-0.922501 - 1.26971i) q^{46} +(-0.239719 + 0.0778895i) q^{47} +(-5.39843 + 4.53182i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-14.5488 - 10.5703i) q^{50} +(5.44144 - 4.56793i) q^{51} +(0.558161 - 0.181357i) q^{52} +(-4.16475 - 5.73229i) q^{53} +(1.07476 - 10.2903i) q^{54} +(12.3629 - 1.22733i) q^{55} -0.0703526i q^{56} +(-0.425815 - 6.07043i) q^{57} +(4.57787 + 14.0892i) q^{58} +(-3.03813 - 0.987149i) q^{59} +(11.8176 - 4.77764i) q^{60} +(-2.05856 + 2.83337i) q^{61} +(-4.69235 + 14.4416i) q^{62} +(2.08492 + 2.15711i) q^{63} +(6.24147 - 4.53470i) q^{64} +1.11897 q^{65} +(-5.07119 + 10.2527i) q^{66} +11.4951 q^{67} +(-6.51966 + 4.73681i) q^{68} +(1.32475 + 0.329990i) q^{69} +(-2.30483 + 7.09355i) q^{70} +(9.30701 - 12.8100i) q^{71} +(0.0365592 - 0.207867i) q^{72} +(12.5288 + 4.07086i) q^{73} +(2.40549 + 7.40335i) q^{74} +(15.6049 - 1.09462i) q^{75} +6.90261i q^{76} +(-1.33149 - 3.03762i) q^{77} +(-0.545740 + 0.873791i) q^{78} +(-1.54664 - 2.12877i) q^{79} +(14.4975 - 4.71051i) q^{80} +(5.03924 + 7.45695i) q^{81} +(-14.0131 - 10.1811i) q^{82} +(4.52689 + 3.28898i) q^{83} +(-2.18791 - 2.60630i) q^{84} +(-14.6130 + 4.74804i) q^{85} +(4.44553 + 6.11874i) q^{86} +(-10.9299 - 6.82647i) q^{87} +(-0.117830 + 0.201396i) q^{88} -5.28218i q^{89} +(-10.4962 + 19.7612i) q^{90} +(-0.0923095 - 0.284099i) q^{91} +(-1.47279 - 0.478538i) q^{92} +(-4.95080 - 12.2460i) q^{93} +(-0.294998 + 0.406030i) q^{94} +(-4.06687 + 12.5165i) q^{95} +(-3.33337 + 13.3818i) q^{96} +(13.9017 - 10.1001i) q^{97} +1.99115 q^{98} +(-2.35558 - 9.66702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	1.61087	−	1.17037i	1.13906	−	0.827574i	0.152071	−	0.988370i	$-0.451406\pi$
$2$	1.61087	−	1.17037i	1.13906	−	0.827574i	0.986988	+	0.160795i	$0.0514059\pi$
$3$	−0.418655	+	1.68069i	−0.241710	+	0.970348i
$3$	−0.418655	+	1.68069i	−0.241710	+	0.970348i
$4$	0.607116	−	1.86851i	0.303558	−	0.934255i
$5$	2.20177	−	3.03048i	0.984663	−	1.35527i	0.0503833	−	0.998730i	$-0.483956\pi$
$5$	2.20177	−	3.03048i	0.984663	−	1.35527i	0.934279	−	0.356542i	$-0.116044\pi$
$6$	1.29263	+	3.19736i	0.527713	+	1.30532i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$7$	−0.951057	−	0.309017i	−0.359466	−	0.116797i
$8$	0.0217402	+	0.0669093i	0.00768630	+	0.0236560i
$9$	−2.64946	−	1.40726i	−0.883152	−	0.469087i
$10$		−	7.45860i		−	2.35862i
$11$	2.20500	+	2.47749i	0.664833	+	0.746992i
$11$	2.20500	+	2.47749i	0.664833	+	0.746992i
$12$	2.88622	+	1.80264i	0.833180	+	0.520376i
$13$	0.175583	+	0.241669i	0.0486980	+	0.0670270i	0.832672	−	0.553767i	$-0.186810\pi$
$13$	0.175583	+	0.241669i	0.0486980	+	0.0670270i	−0.783974	+	0.620794i	$0.786810\pi$
$14$	−1.89369	+	0.615298i	−0.506111	+	0.164445i
$15$	4.17152	+	4.96923i	1.07708	+	1.28305i
$16$	3.29223	+	2.39194i	0.823057	+	0.597986i
$17$	−3.31846	−	2.41100i	−0.804844	−	0.584753i	0.107487	−	0.994206i	$-0.465719\pi$
$17$	−3.31846	−	2.41100i	−0.804844	−	0.584753i	−0.912331	+	0.409453i	$0.865719\pi$
$18$	−5.91495	+	0.833920i	−1.39417	+	0.196557i
$19$	−3.34142	+	1.08569i	−0.766574	+	0.249075i	−0.666098	−	0.745865i	$-0.732037\pi$
$19$	−3.34142	+	1.08569i	−0.766574	+	0.249075i	−0.100476	+	0.994939i	$0.532037\pi$
$20$	−4.32575	−	5.95388i	−0.967267	−	1.33133i
$21$	0.917527	−	1.46906i	0.200221	−	0.320576i
$22$	6.45155	+	1.41026i	1.37548	+	0.300669i
$23$		−	0.788215i		−	0.164354i	−0.996618	−	0.0821771i	$-0.973813\pi$
$23$		−	0.788215i		−	0.164354i	0.996618	−	0.0821771i	$-0.0261873\pi$
$24$	−0.121556	+	0.00852662i	−0.0248124	+	0.00174049i
$25$	−2.79092	−	8.58957i	−0.558184	−	1.71791i
$26$	0.565684	+	0.183802i	0.110940	+	0.0360465i
$27$	3.47438	−	3.86377i	0.668645	−	0.743582i
$28$	−1.15480	+	1.58945i	−0.218237	+	0.300378i
$29$	−2.29911	+	7.07593i	−0.426934	+	1.31397i	0.474196	+	0.880419i	$0.342739\pi$
$29$	−2.29911	+	7.07593i	−0.426934	+	1.31397i	−0.901130	+	0.433549i	$0.857261\pi$
$30$	12.5356	+	3.12258i	2.28868	+	0.570102i
$31$	−6.16968	+	4.48253i	−1.10811	+	0.805087i	−0.982365	−	0.186976i	$-0.940131\pi$
$31$	−6.16968	+	4.48253i	−1.10811	+	0.805087i	−0.125743	+	0.992063i	$0.540131\pi$
$32$	7.96210			1.40751
$33$	−5.08704	+	2.66871i	−0.885540	+	0.464564i
$34$	−8.16736			−1.40069
$35$	−3.03048	+	2.20177i	−0.512245	+	0.372167i
$36$	−4.23801	+	4.09617i	−0.706334	+	0.682694i
$37$	−1.20809	+	3.71813i	−0.198610	+	0.611257i	0.801306	+	0.598255i	$0.204139\pi$
$37$	−1.20809	+	3.71813i	−0.198610	+	0.611257i	−0.999915	+	0.0130025i	$0.995861\pi$
$38$	−4.11194	+	5.65960i	−0.667044	+	0.918108i
$39$	−0.479681	+	0.193925i	−0.0768104	+	0.0310529i
$40$	0.250634	+	0.0814360i	0.0396287	+	0.0128762i
$41$	−2.68816	−	8.27330i	−0.419820	−	1.29207i	−0.907868	−	0.419256i	$-0.862291\pi$
$41$	−2.68816	−	8.27330i	−0.419820	−	1.29207i	0.488049	−	0.872816i	$-0.337709\pi$
$42$	−0.241324	−	3.44031i	−0.0372370	−	0.530852i
$43$			3.79840i			0.579251i	0.957140	+	0.289626i	$0.0935308\pi$
$43$			3.79840i			0.579251i	−0.957140	+	0.289626i	$0.906469\pi$
$44$	5.96791	−	2.61594i	0.899696	−	0.394368i
$45$	−10.0982	+	4.93066i	−1.50535	+	0.735019i
$46$	−0.922501	−	1.26971i	−0.136015	−	0.187209i
$47$	−0.239719	+	0.0778895i	−0.0349667	+	0.0113614i	−0.326448	−	0.945215i	$-0.605852\pi$
$47$	−0.239719	+	0.0778895i	−0.0349667	+	0.0113614i	0.291481	+	0.956576i	$0.405852\pi$
$48$	−5.39843	+	4.53182i	−0.779196	+	0.654113i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−14.5488	−	10.5703i	−2.05751	−	1.49487i
$51$	5.44144	−	4.56793i	0.761954	−	0.639638i
$52$	0.558161	−	0.181357i	0.0774030	−	0.0251497i
$53$	−4.16475	−	5.73229i	−0.572072	−	0.787390i	0.420726	−	0.907188i	$-0.361775\pi$
$53$	−4.16475	−	5.73229i	−0.572072	−	0.787390i	−0.992798	+	0.119798i	$0.961775\pi$
$54$	1.07476	−	10.2903i	0.146256	−	1.40034i
$55$	12.3629	−	1.22733i	1.66701	−	0.165494i
$56$		−	0.0703526i		−	0.00940126i
$57$	−0.425815	−	6.07043i	−0.0564006	−	0.804048i
$58$	4.57787	+	14.0892i	0.601103	+	1.85001i
$59$	−3.03813	−	0.987149i	−0.395531	−	0.128516i	0.104497	−	0.994525i	$-0.466677\pi$
$59$	−3.03813	−	0.987149i	−0.395531	−	0.128516i	−0.500028	+	0.866009i	$0.666677\pi$
$60$	11.8176	−	4.77764i	1.52565	−	0.616790i
$61$	−2.05856	+	2.83337i	−0.263572	+	0.362776i	−0.920207	−	0.391433i	$-0.871979\pi$
$61$	−2.05856	+	2.83337i	−0.263572	+	0.362776i	0.656635	+	0.754209i	$0.271979\pi$
$62$	−4.69235	+	14.4416i	−0.595929	+	1.83408i
$63$	2.08492	+	2.15711i	0.262675	+	0.271770i
$64$	6.24147	−	4.53470i	0.780184	−	0.566837i
$65$	1.11897			0.138791
$66$	−5.07119	+	10.2527i	−0.624221	+	1.26202i
$67$	11.4951			1.40435			0.702176	−	0.712004i	$-0.252212\pi$
$67$	11.4951			1.40435			0.702176	+	0.712004i	$0.252212\pi$
$68$	−6.51966	+	4.73681i	−0.790625	+	0.574423i
$69$	1.32475	+	0.329990i	0.159481	+	0.0397261i
$70$	−2.30483	+	7.09355i	−0.275480	+	0.847841i
$71$	9.30701	−	12.8100i	1.10454	−	1.52027i	0.275312	−	0.961355i	$-0.411219\pi$
$71$	9.30701	−	12.8100i	1.10454	−	1.52027i	0.829227	−	0.558912i	$-0.188781\pi$
$72$	0.0365592	−	0.207867i	0.00430854	−	0.0244974i
$73$	12.5288	+	4.07086i	1.46639	+	0.476458i	0.930014	−	0.367523i	$-0.119794\pi$
$73$	12.5288	+	4.07086i	1.46639	+	0.476458i	0.536373	+	0.843981i	$0.319794\pi$
$74$	2.40549	+	7.40335i	0.279633	+	0.860622i
$75$	15.6049	−	1.09462i	1.80189	−	0.126395i
$76$			6.90261i			0.791784i
$77$	−1.33149	−	3.03762i	−0.151738	−	0.346169i
$78$	−0.545740	+	0.873791i	−0.0617929	+	0.0989373i
$79$	−1.54664	−	2.12877i	−0.174011	−	0.239506i	0.713099	−	0.701063i	$-0.247291\pi$
$79$	−1.54664	−	2.12877i	−0.174011	−	0.239506i	−0.887110	+	0.461557i	$0.847291\pi$
$80$	14.4975	−	4.71051i	1.62087	−	0.526652i
$81$	5.03924	+	7.45695i	0.559915	+	0.828550i
$82$	−14.0131	−	10.1811i	−1.54748	−	1.12431i
$83$	4.52689	+	3.28898i	0.496891	+	0.361012i	0.807828	−	0.589418i	$-0.200643\pi$
$83$	4.52689	+	3.28898i	0.496891	+	0.361012i	−0.310937	+	0.950430i	$0.600643\pi$
$84$	−2.18791	−	2.60630i	−0.238721	−	0.284370i
$85$	−14.6130	+	4.74804i	−1.58500	+	0.514997i
$86$	4.44553	+	6.11874i	0.479374	+	0.659801i
$87$	−10.9299	−	6.82647i	−1.17181	−	0.731875i
$88$	−0.117830	+	0.201396i	−0.0125608	+	0.0214689i
$89$		−	5.28218i		−	0.559910i	−0.960013	−	0.279955i	$-0.909681\pi$
$89$		−	5.28218i		−	0.559910i	0.960013	−	0.279955i	$-0.0903195\pi$
$90$	−10.4962	+	19.7612i	−1.10640	+	2.08302i
$91$	−0.0923095	−	0.284099i	−0.00967666	−	0.0297817i
$92$	−1.47279	−	0.478538i	−0.153549	−	0.0498910i
$93$	−4.95080	−	12.2460i	−0.513374	−	1.26985i
$94$	−0.294998	+	0.406030i	−0.0304267	+	0.0418788i
$95$	−4.06687	+	12.5165i	−0.417252	+	1.28417i
$96$	−3.33337	+	13.3818i	−0.340211	+	1.36578i
$97$	13.9017	−	10.1001i	1.41150	−	1.02551i	0.418397	−	0.908264i	$-0.362592\pi$
$97$	13.9017	−	10.1001i	1.41150	−	1.02551i	0.993102	−	0.117250i	$-0.0374078\pi$
$98$	1.99115			0.201136
$99$	−2.35558	−	9.66702i	−0.236744	−	0.971572i
$100$	−17.7441			−1.77441
$101$	3.61972	−	2.62988i	0.360176	−	0.261683i	−0.392950	−	0.919560i	$-0.628545\pi$
$101$	3.61972	−	2.62988i	0.360176	−	0.261683i	0.753125	+	0.657877i	$0.228545\pi$
$102$	3.41930	−	13.7268i	0.338562	−	1.35916i
$103$	2.99576	−	9.22000i	0.295181	−	0.908474i	−0.687980	−	0.725730i	$-0.741502\pi$
$103$	2.99576	−	9.22000i	0.295181	−	0.908474i	0.983161	−	0.182744i	$-0.0584978\pi$
$104$	−0.0123527	+	0.0170021i	−0.00121128	+	0.00166719i
$105$	−2.43178	−	6.01509i	−0.237317	−	0.587013i
$106$	−13.4178	−	4.35969i	−1.30325	−	0.423451i
$107$	2.01950	+	6.21538i	0.195232	+	0.600863i	0.999974	+	0.00723791i	$0.00230392\pi$
$107$	2.01950	+	6.21538i	0.195232	+	0.600863i	−0.804741	+	0.593625i	$0.797696\pi$
$108$	−5.11013	−	8.83766i	−0.491723	−	0.850405i
$109$		−	14.0045i		−	1.34139i	−0.741735	−	0.670693i	$-0.765997\pi$
$109$		−	14.0045i		−	1.34139i	0.741735	−	0.670693i	$-0.234003\pi$
$110$	18.4786	−	16.4462i	1.76187	−	1.56808i
$111$	−5.74326	−	3.58705i	−0.545127	−	0.340468i
$112$	−2.39194	−	3.29223i	−0.226017	−	0.311086i
$113$	−11.7335	+	3.81246i	−1.10380	+	0.358646i	−0.803563	−	0.595220i	$-0.797065\pi$
$113$	−11.7335	+	3.81246i	−1.10380	+	0.358646i	−0.300235	+	0.953865i	$0.597065\pi$
$114$	−7.79056	−	9.28032i	−0.729653	−	0.869182i
$115$	−2.38867	−	1.73547i	−0.222745	−	0.161833i
$116$	11.8256	+	8.59182i	1.09798	+	0.797731i
$117$	−0.125108	−	0.887383i	−0.0115662	−	0.0820386i
$118$	−6.04937	+	1.96556i	−0.556889	+	0.180944i
$119$	2.41100	+	3.31846i	0.221016	+	0.304202i
$120$	−0.241798	+	0.387145i	−0.0220730	+	0.0353414i
$121$	−1.27594	+	10.9257i	−0.115995	+	0.993250i
$122$			6.97347i			0.631348i
$123$	15.0303	−	1.05431i	1.35523	−	0.0950640i
$124$	4.62995	+	14.2495i	0.415782	+	1.27964i
$125$	−14.3628	−	4.66675i	−1.28465	−	0.417407i
$126$	5.88314	+	1.03471i	0.524112	+	0.0921796i
$127$	−10.2736	+	14.1404i	−0.911637	+	1.25476i	0.0549680	+	0.998488i	$0.482494\pi$
$127$	−10.2736	+	14.1404i	−0.911637	+	1.25476i	−0.966605	+	0.256272i	$0.917506\pi$
$128$	−0.173894	+	0.535191i	−0.0153702	+	0.0473046i
$129$	−6.38395	−	1.59022i	−0.562076	−	0.140011i
$130$	1.80251	−	1.30960i	0.158091	−	0.114860i
$131$	−8.94307			−0.781359			−0.390680	−	0.920527i	$-0.627760\pi$
$131$	−8.94307			−0.781359			−0.390680	+	0.920527i	$0.627760\pi$
$132$	1.89810	+	11.1254i	0.165208	+	0.968342i
$133$	3.51337			0.304648
$134$	18.5172	−	13.4535i	1.59964	−	1.16221i
$135$	−4.05927	−	19.0362i	−0.349367	−	1.63837i
$136$	0.0891746	−	0.274451i	0.00764666	−	0.0235340i
$137$	−1.60625	+	2.21081i	−0.137231	+	0.188882i	−0.872101	−	0.489325i	$-0.837243\pi$
$137$	−1.60625	+	2.21081i	−0.137231	+	0.188882i	0.734870	+	0.678208i	$0.237243\pi$
$138$	2.52021	−	1.01887i	0.214534	−	0.0867319i
$139$	−8.52888	−	2.77120i	−0.723410	−	0.235050i	−0.0759089	−	0.997115i	$-0.524186\pi$
$139$	−8.52888	−	2.77120i	−0.723410	−	0.235050i	−0.647501	+	0.762065i	$0.724186\pi$
$140$	2.27418	+	6.99921i	0.192203	+	0.591541i
$141$	−0.0305487	−	0.435503i	−0.00257267	−	0.0366760i
$142$		−	31.5279i		−	2.64576i
$143$	−0.211573	+	0.967887i	−0.0176927	+	0.0809388i
$144$	−5.35653	−	10.9704i	−0.446377	−	0.914197i
$145$	16.3814	+	22.5470i	1.36040	+	1.87243i
$146$	24.9467	−	8.10568i	2.06460	−	0.670831i
$147$	−1.32659	+	1.11363i	−0.109415	+	0.0918506i
$148$	6.21391	+	4.51467i	0.510781	+	0.371104i
$149$	0.668495	+	0.485690i	0.0547652	+	0.0397893i	0.614831	−	0.788659i	$-0.289224\pi$
$149$	0.668495	+	0.485690i	0.0547652	+	0.0397893i	−0.560066	+	0.828448i	$0.689224\pi$
$150$	23.8563	−	20.0267i	1.94786	−	1.63517i
$151$	−8.23006	+	2.67411i	−0.669753	+	0.217616i	−0.624104	−	0.781342i	$-0.714536\pi$
$151$	−8.23006	+	2.67411i	−0.669753	+	0.217616i	−0.0456494	+	0.998958i	$0.514536\pi$
$152$	−0.145286	−	0.199969i	−0.0117842	−	0.0162196i
$153$	5.39920	+	11.0578i	0.436500	+	0.893968i
$154$	−5.69999	−	3.33488i	−0.459319	−	0.268732i
$155$			28.5666i			2.29453i
$156$	0.0711294	+	1.01402i	0.00569491	+	0.0811868i
$157$	4.76655	+	14.6699i	0.380412	+	1.17079i	0.939754	+	0.341851i	$0.111054\pi$
$157$	4.76655	+	14.6699i	0.380412	+	1.17079i	−0.559342	+	0.828937i	$0.688946\pi$
$158$	−4.98289	−	1.61904i	−0.396417	−	0.128804i
$159$	11.3778	−	4.59981i	0.902318	−	0.364789i
$160$	17.5307	−	24.1290i	1.38593	−	1.90756i
$161$	−0.243572	+	0.749637i	−0.0191962	+	0.0590797i
$162$	16.8449	+	6.11443i	1.32346	+	0.480395i
$163$	14.6039	−	10.6104i	1.14387	−	0.831069i	0.156215	−	0.987723i	$-0.450071\pi$
$163$	14.6039	−	10.6104i	1.14387	−	0.831069i	0.987654	+	0.156654i	$0.0500706\pi$
$164$	−17.0908			−1.33456
$165$	−3.11302	+	21.2921i	−0.242348	+	1.65759i
$166$	11.1416			0.864752
$167$	−10.7849	+	7.83566i	−0.834558	+	0.606342i	−0.920845	−	0.389929i	$-0.872500\pi$
$167$	−10.7849	+	7.83566i	−0.834558	+	0.606342i	0.0862875	+	0.996270i	$0.472500\pi$
$168$	0.118241	+	0.0294535i	0.00912250	+	0.00227238i
$169$	3.98965	−	12.2789i	0.306896	−	0.944528i
$170$	−17.9827	+	24.7510i	−1.37921	+	1.89832i
$171$	10.3808	+	1.82575i	0.793839	+	0.139618i
$172$	7.09736	+	2.30607i	0.541168	+	0.175836i
$173$	−0.808208	−	2.48741i	−0.0614469	−	0.189114i	0.915621	−	0.402043i	$-0.131700\pi$
$173$	−0.808208	−	2.48741i	−0.0614469	−	0.189114i	−0.977068	+	0.212929i	$0.931700\pi$
$174$	−25.5962	+	1.79547i	−1.94044	+	0.136114i
$175$			9.03161i			0.682726i
$176$	1.33334	+	13.4307i	0.100504	+	1.01238i
$177$	2.93102	−	4.69289i	0.220309	−	0.352739i
$178$	−6.18209	−	8.50891i	−0.463367	−	0.637770i
$179$	8.90579	−	2.89367i	0.665650	−	0.216283i	0.0433479	−	0.999060i	$-0.486198\pi$
$179$	8.90579	−	2.89367i	0.665650	−	0.216283i	0.622302	+	0.782777i	$0.286198\pi$
$180$	3.08222	+	21.8620i	0.229735	+	1.62950i
$181$	−2.51257	−	1.82549i	−0.186758	−	0.135687i	0.490478	−	0.871454i	$-0.336822\pi$
$181$	−2.51257	−	1.82549i	−0.186758	−	0.135687i	−0.677236	+	0.735766i	$0.736822\pi$
$182$	−0.481199	−	0.349612i	−0.0356689	−	0.0259149i
$183$	−3.90019	−	4.64601i	−0.288311	−	0.343443i
$184$	0.0527389	−	0.0171359i	0.00388797	−	0.00126328i
$185$	8.60778	+	11.8476i	0.632856	+	0.871052i
$186$	−22.3074	−	13.9324i	−1.63566	−	1.02158i
$187$	−1.34396	−	13.5377i	−0.0982803	−	0.989975i
$188$			0.495206i			0.0361166i
$189$	−4.49830	+	2.60102i	−0.327203	+	0.189196i
$190$	8.09774	+	24.9223i	0.587472	+	1.80805i
$191$	−7.69797	−	2.50122i	−0.557005	−	0.180982i	0.0169679	−	0.999856i	$-0.494599\pi$
$191$	−7.69797	−	2.50122i	−0.557005	−	0.180982i	−0.573973	+	0.818874i	$0.694599\pi$
$192$	5.00841	+	12.3885i	0.361451	+	0.894061i
$193$	−0.924500	+	1.27246i	−0.0665469	+	0.0915940i	−0.840993	−	0.541046i	$-0.818029\pi$
$193$	−0.924500	+	1.27246i	−0.0665469	+	0.0915940i	0.774446	+	0.632640i	$0.218029\pi$
$194$	10.5729	−	32.5401i	0.759091	−	2.33624i
$195$	−0.468461	+	1.88064i	−0.0335472	+	0.134676i
$196$	1.58945	−	1.15480i	0.113532	−	0.0824859i
$197$	17.5051			1.24719			0.623594	−	0.781749i	$-0.285672\pi$
$197$	17.5051			1.24719			0.623594	+	0.781749i	$0.285672\pi$
$198$	−15.1085	−	12.8154i	−1.07371	−	0.910754i
$199$	5.46085			0.387109			0.193555	−	0.981090i	$-0.437998\pi$
$199$	5.46085			0.387109			0.193555	+	0.981090i	$0.437998\pi$
$200$	0.514047	−	0.373477i	0.0363486	−	0.0264088i
$201$	−4.81248	+	19.3198i	−0.339446	+	1.36271i
$202$	2.75298	−	8.47280i	0.193699	−	0.596144i
$203$	4.37317	−	6.01915i	0.306936	−	0.422461i
$204$	−5.23164	−	12.9406i	−0.366288	−	0.906026i
$205$	−30.9908	−	10.0695i	−2.16449	−	0.703285i
$206$	−5.96500	−	18.3584i	−0.415601	−	1.27909i
$207$	−1.10922	+	2.08834i	−0.0770964	+	0.145150i
$208$			1.21562i			0.0842878i
$209$	−10.0576	−	5.88439i	−0.695700	−	0.407031i
$210$	−10.9571	−	6.84346i	−0.756115	−	0.472244i
$211$	−8.58388	−	11.8147i	−0.590938	−	0.813357i	0.403903	−	0.914802i	$-0.367653\pi$
$211$	−8.58388	−	11.8147i	−0.590938	−	0.813357i	−0.994841	+	0.101445i	$0.967653\pi$
$212$	−13.2393	+	4.30171i	−0.909280	+	0.295443i
$213$	17.6332	+	21.0052i	1.20821	+	1.43925i
$214$	10.5274	+	7.64862i	0.719640	+	0.522849i
$215$	11.5110	+	8.36322i	0.785043	+	0.570367i
$216$	0.334055	+	0.148469i	0.0227296	+	0.0101021i
$217$	7.25289	−	2.35661i	0.492358	−	0.159977i
$218$	−16.3904	−	22.5594i	−1.11010	−	1.52792i
$219$	−12.0871	+	19.3528i	−0.816771	+	1.30774i
$220$	5.21243	−	23.8453i	0.351422	−	1.60765i
$221$		−	1.22530i		−	0.0824226i
$222$	−13.4498	+	0.943449i	−0.902693	+	0.0633202i
$223$	−2.11690	−	6.51515i	−0.141758	−	0.436286i	0.854822	−	0.518922i	$-0.173666\pi$
$223$	−2.11690	−	6.51515i	−0.141758	−	0.436286i	−0.996580	+	0.0826352i	$0.973666\pi$
$224$	−7.57241	−	2.46043i	−0.505953	−	0.164394i
$225$	−4.69334	+	26.6852i	−0.312889	+	1.77902i
$226$	−14.4392	+	19.8739i	−0.960484	+	1.32199i
$227$	−6.12999	+	18.8662i	−0.406862	+	1.25219i	0.512469	+	0.858706i	$0.328731\pi$
$227$	−6.12999	+	18.8662i	−0.406862	+	1.25219i	−0.919331	+	0.393486i	$0.871269\pi$
$228$	−11.6012	−	2.88981i	−0.768306	−	0.191382i
$229$	2.39578	−	1.74064i	0.158318	−	0.115025i	−0.505806	−	0.862647i	$-0.668805\pi$
$229$	2.39578	−	1.74064i	0.158318	−	0.115025i	0.664124	+	0.747623i	$0.268805\pi$
$230$	−5.87898			−0.387648
$231$	5.66274	−	0.966117i	0.372581	−	0.0635658i
$232$	−0.523429			−0.0343648
$233$	9.27475	−	6.73850i	0.607609	−	0.441454i	−0.240962	−	0.970534i	$-0.577463\pi$
$233$	9.27475	−	6.73850i	0.607609	−	0.441454i	0.848572	+	0.529081i	$0.177463\pi$
$234$	−1.24010	−	1.28304i	−0.0810677	−	0.0838749i
$235$	−0.291765	+	0.897960i	−0.0190326	+	0.0585764i
$236$	−3.68899	+	5.07746i	−0.240133	+	0.330515i
$237$	4.22532	−	1.70821i	0.274464	−	0.110960i
$238$	7.76762	+	2.52385i	0.503500	+	0.163597i
$239$	−6.48632	−	19.9628i	−0.419565	−	1.29129i	−0.908103	−	0.418746i	$-0.862470\pi$
$239$	−6.48632	−	19.9628i	−0.419565	−	1.29129i	0.488538	−	0.872543i	$-0.337530\pi$
$240$	1.84749	+	26.3379i	0.119255	+	1.70010i
$241$			22.8374i			1.47109i	0.677478	+	0.735543i	$0.263073\pi$
$241$			22.8374i			1.47109i	−0.677478	+	0.735543i	$0.736927\pi$
$242$	10.7318	+	19.0933i	0.689863	+	1.22736i
$243$	−14.6425	+	5.34752i	−0.939319	+	0.343044i
$244$	4.04439	+	5.56663i	0.258916	+	0.356367i
$245$	3.56254	−	1.15754i	0.227603	−	0.0739525i
$246$	22.9779	−	19.2893i	1.46502	−	1.22984i
$247$	−0.849075	−	0.616889i	−0.0540253	−	0.0392517i
$248$	−0.434053	−	0.315358i	−0.0275624	−	0.0200253i
$249$	−7.42297	+	6.23137i	−0.470411	+	0.394897i
$250$	−28.5984	+	9.29219i	−1.80872	+	0.587690i
$251$	9.72966	+	13.3917i	0.614131	+	0.845279i	0.996909	−	0.0785616i	$-0.0250327\pi$
$251$	9.72966	+	13.3917i	0.614131	+	0.845279i	−0.382778	+	0.923840i	$0.625033\pi$
$252$	5.29637	−	2.58607i	0.333640	−	0.162907i
$253$	1.95280	−	1.73801i	0.122771	−	0.109268i
$254$			34.8023i			2.18369i
$255$	−1.86221	−	26.5477i	−0.116616	−	1.66248i
$256$	5.11431	+	15.7402i	0.319644	+	0.983764i
$257$	−20.6355	−	6.70487i	−1.28721	−	0.418238i	−0.416093	−	0.909322i	$-0.636601\pi$
$257$	−20.6355	−	6.70487i	−1.28721	−	0.418238i	−0.871112	+	0.491084i	$0.836601\pi$
$258$	−12.1449	+	4.90992i	−0.756107	+	0.305679i
$259$	2.29793	−	3.16283i	0.142787	−	0.196529i
$260$	0.679343	−	2.09080i	0.0421311	−	0.129666i
$261$	16.0491	−	15.5119i	0.993413	−	0.960165i
$262$	−14.4061	+	10.4667i	−0.890014	+	0.646633i
$263$	−4.58300			−0.282600			−0.141300	−	0.989967i	$-0.545128\pi$
$263$	−4.58300			−0.282600			−0.141300	+	0.989967i	$0.545128\pi$
$264$	−0.289155	−	0.282352i	−0.0177962	−	0.0173776i
$265$	−26.5414			−1.63043
$266$	5.65960	−	4.11194i	0.347012	−	0.252119i
$267$	8.87772	+	2.21141i	0.543307	+	0.135336i
$268$	6.97886	−	21.4787i	0.426302	−	1.31202i
$269$	−13.6550	+	18.7945i	−0.832562	+	1.14592i	0.154878	+	0.987934i	$0.450501\pi$
$269$	−13.6550	+	18.7945i	−0.832562	+	1.14592i	−0.987441	+	0.157990i	$0.949499\pi$
$270$	−28.8183	−	25.9140i	−1.75382	−	1.57708i
$271$	9.55954	+	3.10608i	0.580701	+	0.188681i	0.584615	−	0.811311i	$-0.301246\pi$
$271$	9.55954	+	3.10608i	0.580701	+	0.188681i	−0.00391360	+	0.999992i	$0.501246\pi$
$272$	−5.15814	−	15.8751i	−0.312758	−	0.962570i
$273$	0.516130	−	0.0362043i	0.0312376	−	0.00219119i
$274$			5.44123i			0.328717i
$275$	15.1266	−	25.8545i	0.912170	−	1.55909i
$276$	1.42086	−	2.27496i	0.0855260	−	0.136937i
$277$	−8.88574	−	12.2302i	−0.533892	−	0.734840i	0.453825	−	0.891091i	$-0.350059\pi$
$277$	−8.88574	−	12.2302i	−0.533892	−	0.734840i	−0.987717	+	0.156251i	$0.950059\pi$
$278$	−16.9822	+	5.51787i	−1.01853	+	0.330940i
$279$	22.6544	−	3.19394i	1.35628	−	0.191216i
$280$	−0.213202	−	0.154900i	−0.0127413	−	0.00925707i
$281$	−9.70482	−	7.05096i	−0.578941	−	0.420625i	0.259401	−	0.965770i	$-0.416475\pi$
$281$	−9.70482	−	7.05096i	−0.578941	−	0.420625i	−0.838342	+	0.545145i	$0.816475\pi$
$282$	−0.558909	−	0.665787i	−0.0332825	−	0.0396470i
$283$	9.49310	−	3.08449i	0.564306	−	0.183354i	−0.0129517	−	0.999916i	$-0.504123\pi$
$283$	9.49310	−	3.08449i	0.564306	−	0.183354i	0.577258	+	0.816562i	$0.304123\pi$
$284$	−18.2852	−	25.1674i	−1.08503	−	1.49341i
$285$	−19.3339	−	12.0753i	−1.14524	−	0.715278i
$286$	0.791965	+	1.80676i	0.0468299	+	0.106836i
$287$			8.69906i			0.513489i
$288$	−21.0952	−	11.2047i	−1.24305	−	0.660246i
$289$	−0.0540569	−	0.166370i	−0.00317982	−	0.00978648i
$290$	52.7765	+	17.1481i	3.09915	+	1.00697i
$291$	11.1552	+	27.5929i	0.653932	+	1.61752i
$292$	15.2129	−	20.9387i	0.890266	−	1.22535i
$293$	2.65423	−	8.16889i	0.155062	−	0.477232i	−0.843105	−	0.537749i	$-0.819275\pi$
$293$	2.65423	−	8.16889i	0.155062	−	0.477232i	0.998167	+	0.0605169i	$0.0192749\pi$
$294$	−0.833603	+	3.34651i	−0.0486167	+	0.195172i
$295$	−9.68081	+	7.03352i	−0.563638	+	0.409507i
$296$	−0.275042			−0.0159865
$297$	17.2335	+	0.0881443i	0.999987	+	0.00511465i
$298$	1.64530			0.0953094
$299$	0.190487	−	0.138397i	0.0110162	−	0.00800372i
$300$	7.42866	−	29.8224i	0.428894	−	1.72180i
$301$	1.17377	−	3.61250i	0.0676551	−	0.208221i
$302$	−10.1279	+	13.9398i	−0.582795	+	0.802148i
$303$	2.90461	+	7.18465i	0.166865	+	0.412747i
$304$	−13.5976	−	4.41813i	−0.779877	−	0.253397i
$305$	4.05398	+	12.4769i	0.232130	+	0.714423i
$306$	21.6391	+	11.4936i	1.23702	+	0.657045i
$307$		−	2.84037i		−	0.162108i	−0.996710	−	0.0810542i	$-0.974171\pi$
$307$		−	2.84037i		−	0.162108i	0.996710	−	0.0810542i	$-0.0258287\pi$
$308$	−6.48419	+	0.643721i	−0.369471	+	0.0366794i
$309$	14.2418	+	8.89495i	0.810188	+	0.506016i
$310$	33.4334	+	46.0172i	1.89889	+	2.61360i
$311$	−16.2584	+	5.28268i	−0.921931	+	0.299554i	−0.731259	−	0.682100i	$-0.761067\pi$
$311$	−16.2584	+	5.28268i	−0.921931	+	0.299554i	−0.190672	+	0.981654i	$0.561067\pi$
$312$	−0.0234037	−	0.0278791i	−0.00132498	−	0.00157835i
$313$	9.92434	+	7.21045i	0.560957	+	0.407559i	0.831809	−	0.555062i	$-0.187305\pi$
$313$	9.92434	+	7.21045i	0.560957	+	0.407559i	−0.270852	+	0.962621i	$0.587305\pi$
$314$	24.8475	+	18.0528i	1.40223	+	1.01878i
$315$	11.1276	−	1.56883i	0.626969	−	0.0883934i
$316$	−4.91662	+	1.59751i	−0.276582	+	0.0898668i
$317$	−0.682815	−	0.939815i	−0.0383507	−	0.0527853i	0.789411	−	0.613865i	$-0.210386\pi$
$317$	−0.682815	−	0.939815i	−0.0383507	−	0.0527853i	−0.827762	+	0.561080i	$0.810386\pi$
$318$	12.9447	−	20.7259i	0.725903	−	1.16225i
$319$	−22.6001	+	9.90641i	−1.26536	+	0.554652i
$320$		−	28.8990i		−	1.61550i
$321$	−11.2916	+	0.792059i	−0.630237	+	0.0442084i
$322$	0.484987	+	1.49264i	0.0270273	+	0.0831815i
$323$	13.7059	+	4.45333i	0.762619	+	0.247790i
$324$	16.9928	−	4.88864i	0.944043	−	0.271591i
$325$	1.58580	−	2.18266i	0.0879642	−	0.121072i
$326$	11.1070	−	34.1839i	0.615162	−	1.89327i
$327$	23.5372	+	5.86305i	1.30161	+	0.324227i
$328$	0.495120	−	0.359725i	0.0273384	−	0.0198625i
$329$	0.252056			0.0138963
$330$	19.9049	+	37.9422i	1.09573	+	2.08865i
$331$	13.7133			0.753752			0.376876	−	0.926264i	$-0.376998\pi$
$331$	13.7133			0.753752			0.376876	+	0.926264i	$0.376998\pi$
$332$	8.89383	−	6.46175i	0.488113	−	0.354635i
$333$	8.43317	−	8.15093i	0.462135	−	0.446668i
$334$	−8.20243	+	25.2445i	−0.448817	+	1.38132i
$335$	25.3096	−	34.8357i	1.38281	−	1.90328i
$336$	6.53462	−	2.64182i	0.356493	−	0.144123i
$337$	17.6519	+	5.73546i	0.961562	+	0.312430i	0.747405	−	0.664369i	$-0.231300\pi$
$337$	17.6519	+	5.73546i	0.961562	+	0.312430i	0.214157	+	0.976799i	$0.431300\pi$
$338$	−7.94397	−	24.4490i	−0.432095	−	1.32985i
$339$	−1.49527	−	21.3166i	−0.0812118	−	1.15776i
$340$			30.1871i			1.63712i
$341$	−24.7096	−	5.40135i	−1.33810	−	0.292499i
$342$	18.8589	−	9.20829i	1.01977	−	0.497927i
$343$	−0.587785	−	0.809017i	−0.0317374	−	0.0436828i
$344$	−0.254149	+	0.0825779i	−0.0137028	+	0.00445230i
$345$	3.91682	−	3.28806i	0.210875	−	0.177023i
$346$	−4.21310	−	3.06100i	−0.226498	−	0.164560i
$347$	9.89554	+	7.18953i	0.531221	+	0.385954i	0.820814	−	0.571195i	$-0.193520\pi$
$347$	9.89554	+	7.18953i	0.531221	+	0.385954i	−0.289594	+	0.957150i	$0.593520\pi$
$348$	−19.3911	+	16.2782i	−1.03947	+	0.872605i
$349$	−10.4890	+	3.40807i	−0.561462	+	0.182430i	−0.575979	−	0.817465i	$-0.695379\pi$
$349$	−10.4890	+	3.40807i	−0.561462	+	0.182430i	0.0145169	+	0.999895i	$0.495379\pi$
$350$	10.5703	+	14.5488i	0.565006	+	0.777664i
$351$	1.54380	+	0.161239i	0.0824017	+	0.00860631i
$352$	17.5564	+	19.7261i	0.935762	+	1.05140i
$353$		−	22.1511i		−	1.17898i	−0.807774	−	0.589492i	$-0.799328\pi$
$353$		−	22.1511i		−	1.17898i	0.807774	−	0.589492i	$-0.200672\pi$
$354$	−0.770904	−	10.9900i	−0.0409731	−	0.584113i
$355$	−18.3285	−	56.4094i	−0.972777	−	2.99390i
$356$	−9.86980	−	3.20689i	−0.523098	−	0.169965i
$357$	−6.58668	+	2.66286i	−0.348604	+	0.140934i
$358$	10.9594	−	15.0844i	0.579224	−	0.797233i
$359$	−5.52281	+	16.9975i	−0.291483	+	0.897092i	0.692897	+	0.721036i	$0.256334\pi$
$359$	−5.52281	+	16.9975i	−0.291483	+	0.897092i	−0.984380	+	0.176056i	$0.943666\pi$
$360$	−0.549443	−	0.568469i	−0.0289582	−	0.0299609i
$361$	−5.38498	+	3.91242i	−0.283420	+	0.205917i
$362$	−6.18392			−0.325019
$363$	−17.8286	−	6.71859i	−0.935761	−	0.352634i
$364$	−0.586885			−0.0307611
$365$	39.9223	−	29.0052i	2.08963	−	1.51820i
$366$	−11.7203	−	2.91948i	−0.612628	−	0.152603i
$367$	−8.41347	+	25.8940i	−0.439180	+	1.35166i	0.449563	+	0.893249i	$0.351580\pi$
$367$	−8.41347	+	25.8940i	−0.439180	+	1.35166i	−0.888742	+	0.458407i	$0.848420\pi$
$368$	1.88537	−	2.59498i	0.0982815	−	0.135273i
$369$	−4.52053	+	25.7027i	−0.235329	+	1.33803i
$370$	27.7321	+	9.01069i	1.44172	+	0.468444i
$371$	2.18954	+	6.73871i	0.113675	+	0.349856i
$372$	−25.8874	+	1.81589i	−1.34220	+	0.0941497i
$373$			19.0242i			0.985036i	0.870302	+	0.492518i	$0.163923\pi$
$373$			19.0242i			0.985036i	−0.870302	+	0.492518i	$0.836077\pi$
$374$	−18.0090	−	20.2346i	−0.931225	−	1.04631i
$375$	13.8564	−	22.1857i	0.715543	−	1.14566i
$376$	−0.0104231	−	0.0143461i	−0.000537529	−	0.000739845i
$377$	−2.11372	+	0.686790i	−0.108862	+	0.0353715i
$378$	−4.20204	+	9.45457i	−0.216130	+	0.486291i
$379$	−7.80914	−	5.67367i	−0.401128	−	0.291437i	0.368872	−	0.929480i	$-0.379744\pi$
$379$	−7.80914	−	5.67367i	−0.401128	−	0.291437i	−0.770000	+	0.638043i	$0.779744\pi$
$380$	20.9182	+	15.1980i	1.07308	+	0.779640i
$381$	−19.4646	−	23.1868i	−0.997203	−	1.18789i
$382$	−15.3278	+	4.98030i	−0.784238	+	0.254814i
$383$	8.87679	+	12.2179i	0.453583	+	0.624303i	0.973163	−	0.230119i	$-0.0739115\pi$
$383$	8.87679	+	12.2179i	0.453583	+	0.624303i	−0.519580	+	0.854422i	$0.673911\pi$
$384$	−0.826690	−	0.516323i	−0.0421868	−	0.0263485i
$385$	−12.1371	−	2.65308i	−0.618563	−	0.135214i
$386$			3.13178i			0.159403i
$387$	5.34534	−	10.0637i	0.271719	−	0.511567i
$388$	−10.4323	−	32.1073i	−0.529620	−	1.63000i
$389$	−16.7364	−	5.43800i	−0.848571	−	0.275718i	−0.147724	−	0.989029i	$-0.547195\pi$
$389$	−16.7364	−	5.43800i	−0.848571	−	0.275718i	−0.700848	+	0.713311i	$0.747195\pi$
$390$	1.44641	+	3.57774i	0.0732418	+	0.181166i
$391$	−1.90039	+	2.61566i	−0.0961067	+	0.132279i
$392$	−0.0217402	+	0.0669093i	−0.00109804	+	0.00337943i
$393$	3.74406	−	15.0305i	0.188863	−	0.758191i
$394$	28.1985	−	20.4874i	1.42062	−	1.03214i
$395$	−9.85656			−0.495937
$396$	−19.4930	−	1.46758i	−0.979561	−	0.0737488i
$397$	9.61863			0.482745			0.241373	−	0.970433i	$-0.422402\pi$
$397$	9.61863			0.482745			0.241373	+	0.970433i	$0.422402\pi$
$398$	8.79672	−	6.39119i	0.440940	−	0.320362i
$399$	−1.47089	+	5.90490i	−0.0736366	+	0.295615i
$400$	11.3574	−	34.9546i	0.567871	−	1.74773i
$401$	3.61909	−	4.98125i	0.180729	−	0.248752i	−0.709035	−	0.705173i	$-0.750869\pi$
$401$	3.61909	−	4.98125i	0.180729	−	0.248752i	0.889764	+	0.456422i	$0.150869\pi$
$402$	14.8589	+	36.7540i	0.741095	+	1.83312i
$403$	−2.16658	−	0.703965i	−0.107925	−	0.0350670i
$404$	−2.71637	−	8.36012i	−0.135144	−	0.415932i
$405$	33.6934	+	1.14719i	1.67424	+	0.0570045i
$406$		−	14.8143i		−	0.735221i
$407$	−11.8755	+	5.20544i	−0.588647	+	0.258024i
$408$	0.423935	+	0.264775i	0.0209879	+	0.0131083i
$409$	−12.7504	−	17.5494i	−0.630467	−	0.867763i	0.367596	−	0.929986i	$-0.380181\pi$
$409$	−12.7504	−	17.5494i	−0.630467	−	0.867763i	−0.998062	+	0.0622228i	$0.980181\pi$
$410$	−61.7072	+	20.0499i	−3.04750	+	0.990193i
$411$	−3.04323	−	3.62518i	−0.150111	−	0.178817i
$412$	−15.4089	−	11.1952i	−0.759141	−	0.551548i
$413$	2.58439	+	1.87767i	0.127169	+	0.0923940i
$414$	0.657309	+	4.66225i	0.0323050	+	0.229137i
$415$	19.9344	−	6.47707i	0.978540	−	0.317947i
$416$	1.39801	+	1.92420i	0.0685431	+	0.0943415i
$417$	8.22819	−	13.1742i	0.402936	−	0.645146i
$418$	−23.0884	+	2.29212i	−1.12929	+	0.112111i
$419$			10.4370i			0.509883i	0.966957	+	0.254941i	$0.0820562\pi$
$419$			10.4370i			0.509883i	−0.966957	+	0.254941i	$0.917944\pi$
$420$	−12.7156	+	0.891947i	−0.620459	+	0.0435226i
$421$	−4.61096	−	14.1911i	−0.224724	−	0.691631i	−0.998319	−	0.0579504i	$-0.981543\pi$
$421$	−4.61096	−	14.1911i	−0.224724	−	0.691631i	0.773595	−	0.633680i	$-0.218457\pi$
$422$	−27.6550	−	8.98567i	−1.34623	−	0.437416i
$423$	0.744737	+	0.130983i	0.0362103	+	0.00636859i
$424$	0.293001	−	0.403281i	0.0142294	−	0.0195851i
$425$	−11.4479	+	35.2330i	−0.555305	+	1.70905i
$426$	52.9887	+	13.1993i	2.56731	+	0.639508i
$427$	2.83337	−	2.05856i	0.137116	−	0.0996208i
$428$	12.8396			0.620624
$429$	−1.53814	−	0.760800i	−0.0742623	−	0.0367318i
$430$	28.3308			1.36623
$431$	−31.7487	+	23.0668i	−1.52928	+	1.11109i	−0.572647	+	0.819802i	$0.694083\pi$
$431$	−31.7487	+	23.0668i	−1.52928	+	1.11109i	−0.956636	+	0.291287i	$0.905917\pi$
$432$	20.6804	−	4.40988i	0.994984	−	0.212170i
$433$	−6.23401	+	19.1863i	−0.299587	+	0.922035i	0.682054	+	0.731301i	$0.261087\pi$
$433$	−6.23401	+	19.1863i	−0.299587	+	0.922035i	−0.981642	+	0.190734i	$0.938913\pi$
$434$	8.92539	−	12.2847i	0.428432	−	0.589686i
$435$	−44.7527	+	18.0926i	−2.14573	+	0.867475i
$436$	−26.1675	−	8.50234i	−1.25320	−	0.407188i
$437$	0.855759	+	2.63376i	0.0409365	+	0.125990i
$438$	3.17910	+	45.3212i	0.151903	+	2.16553i
$439$			34.3647i			1.64014i	0.572265	+	0.820068i	$0.306065\pi$
$439$			34.3647i			1.64014i	−0.572265	+	0.820068i	$0.693935\pi$
$440$	0.350891	+	0.800511i	0.0167281	+	0.0381629i
$441$	−1.31629	−	2.69581i	−0.0626804	−	0.128372i
$442$	−1.43405	−	1.97380i	−0.0682108	−	0.0938841i
$443$	15.2126	−	4.94287i	0.722771	−	0.234843i	0.0755470	−	0.997142i	$-0.475930\pi$
$443$	15.2126	−	4.94287i	0.722771	−	0.234843i	0.647224	+	0.762300i	$0.275930\pi$
$444$	−10.1893	+	8.55359i	−0.483561	+	0.405936i
$445$	−16.0075	−	11.6302i	−0.758830	−	0.551322i
$446$	−11.0352	−	8.01752i	−0.522530	−	0.379640i
$447$	−1.09616	+	0.920198i	−0.0518468	+	0.0435239i
$448$	−7.33729	+	2.38403i	−0.346654	+	0.112635i
$449$	−4.54944	−	6.26176i	−0.214701	−	0.295511i	0.688059	−	0.725654i	$-0.258463\pi$
$449$	−4.54944	−	6.26176i	−0.214701	−	0.295511i	−0.902760	+	0.430144i	$0.858463\pi$
$450$	23.6712	+	48.4794i	1.11587	+	2.28534i
$451$	14.5696	−	24.9025i	0.686058	−	1.17261i
$452$			24.2388i			1.14010i
$453$	−1.04880	−	14.9517i	−0.0492770	−	0.702494i
$454$	12.2057	+	37.5653i	0.572842	+	1.76303i
$455$	−1.06420	−	0.345780i	−0.0498906	−	0.0162104i
$456$	0.396911	−	0.160463i	0.0185870	−	0.00751437i
$457$	1.46702	−	2.01917i	0.0686241	−	0.0944530i	−0.773325	−	0.634009i	$-0.781408\pi$
$457$	1.46702	−	2.01917i	0.0686241	−	0.0944530i	0.841949	+	0.539556i	$0.181408\pi$
$458$	1.82211	−	5.60789i	0.0851418	−	0.262040i
$459$	−20.8451	+	4.44501i	−0.972967	+	0.207475i
$460$	−4.69294	+	3.40962i	−0.218810	+	0.158974i
$461$	16.3433			0.761184			0.380592	−	0.924743i	$-0.375720\pi$
$461$	16.3433			0.761184			0.380592	+	0.924743i	$0.375720\pi$
$462$	7.99124	−	8.18377i	0.371786	−	0.380744i
$463$	3.84716			0.178793			0.0893964	−	0.995996i	$-0.471506\pi$
$463$	3.84716			0.178793			0.0893964	+	0.995996i	$0.471506\pi$
$464$	−24.4944	+	17.7962i	−1.13713	+	0.826170i
$465$	−48.0117	−	11.9595i	−2.22649	−	0.554611i
$466$	7.05392	−	21.7097i	0.326766	−	1.00568i
$467$	12.9077	−	17.7659i	0.597296	−	0.822108i	−0.398161	−	0.917316i	$-0.630351\pi$
$467$	12.9077	−	17.7659i	0.597296	−	0.822108i	0.995457	+	0.0952075i	$0.0303515\pi$
$468$	−1.73404	−	0.304979i	−0.0801560	−	0.0140976i
$469$	−10.9325	−	3.55219i	−0.504816	−	0.164025i
$470$	0.580947	+	1.78797i	0.0267971	+	0.0824729i
$471$	−26.6512	+	1.86947i	−1.22802	+	0.0861406i
$472$		−	0.224740i		−	0.0103445i
$473$	−9.41052	+	8.37549i	−0.432696	+	0.385105i
$474$	4.80722	−	7.69689i	0.220803	−	0.353530i
$475$	18.6513	+	25.6713i	0.855779	+	1.17788i
$476$	7.66432	−	2.49029i	0.351294	−	0.114142i
$477$	2.96750	+	21.0483i	0.135873	+	0.963737i
$478$	−33.8125	−	24.5662i	−1.54655	−	1.12363i
$479$	−5.09714	−	3.70329i	−0.232894	−	0.169207i	0.465218	−	0.885196i	$-0.345976\pi$
$479$	−5.09714	−	3.70329i	−0.232894	−	0.169207i	−0.698112	+	0.715989i	$0.745976\pi$
$480$	33.2141	+	39.5655i	1.51601	+	1.80591i
$481$	−1.11068	+	0.360882i	−0.0506426	+	0.0164548i
$482$	26.7281	+	36.7881i	1.21743	+	1.67565i
$483$	−1.15794	−	0.723209i	−0.0526880	−	0.0329071i
$484$	19.6402	+	9.01731i	0.892737	+	0.409878i
$485$		−	64.3669i		−	2.92275i
$486$	−17.3287	+	25.7513i	−0.786045	+	1.16810i
$487$	5.70111	+	17.5462i	0.258342	+	0.795094i	0.993153	+	0.116823i	$0.0372709\pi$
$487$	5.70111	+	17.5462i	0.258342	+	0.795094i	−0.734811	+	0.678272i	$0.762729\pi$
$488$	−0.234332	−	0.0761391i	−0.0106077	−	0.00344666i
$489$	11.7188	+	28.9868i	0.529942	+	1.31083i
$490$	4.38405	−	6.03413i	0.198051	−	0.272594i
$491$	7.13467	−	21.9583i	0.321983	−	0.990962i	−0.650801	−	0.759248i	$-0.725567\pi$
$491$	7.13467	−	21.9583i	0.321983	−	0.990962i	0.972784	−	0.231714i	$-0.0744332\pi$
$492$	7.15513	−	28.7243i	0.322578	−	1.29499i
$493$	24.6896	−	17.9380i	1.11196	−	0.807888i
$494$	−2.08974			−0.0940217
$495$	−34.4822	−	14.1461i	−1.54986	−	0.635818i
$496$	−31.0340			−1.39347
$497$	−12.8100	+	9.30701i	−0.574607	+	0.417476i
$498$	−4.66446	+	18.7255i	−0.209020	+	0.839111i
$499$	−1.53845	+	4.73486i	−0.0688705	+	0.211962i	−0.979568	−	0.201112i	$-0.935545\pi$
$499$	−1.53845	+	4.73486i	−0.0688705	+	0.211962i	0.910698	+	0.413073i	$0.135545\pi$
$500$	−17.4397	+	24.0037i	−0.779929	+	1.07348i
$501$	−8.65420	−	21.4065i	−0.386641	−	0.956371i
$502$	31.3465	+	10.1851i	1.39906	+	0.454583i
$503$	2.27748	+	7.00938i	0.101548	+	0.312533i	0.988905	−	0.148551i	$-0.0474609\pi$
$503$	2.27748	+	7.00938i	0.101548	+	0.312533i	−0.887357	+	0.461083i	$0.847461\pi$
$504$	−0.0990044	+	0.186396i	−0.00441001	+	0.00830274i
$505$		−	16.7599i		−	0.745805i
$506$	1.11159	−	5.08521i	0.0494163	−	0.226065i
$507$	18.9667	+	11.8460i	0.842342	+	0.526098i
$508$	20.1843	+	27.7812i	0.895531	+	1.23259i
$509$	28.8775	−	9.38287i	1.27997	−	0.415888i	0.411402	−	0.911454i	$-0.365039\pi$
$509$	28.8775	−	9.38287i	1.27997	−	0.415888i	0.868571	+	0.495565i	$0.165039\pi$
$510$	−34.0703	−	40.5855i	−1.50866	−	1.79716i
$511$	−10.6576	−	7.74323i	−0.471467	−	0.342541i
$512$	25.7498	+	18.7083i	1.13799	+	0.826800i
$513$	−7.41449	+	16.6826i	−0.327358	+	0.736553i
$514$	−41.0883	+	13.3504i	−1.81233	+	0.588860i
$515$	−21.3450	−	29.3789i	−0.940575	−	1.29459i
$516$	−6.84714	+	10.9630i	−0.301428	+	0.482620i
$517$	−0.721552	−	0.422156i	−0.0317338	−	0.0185664i
$518$		−	7.78434i		−	0.342024i
$519$	4.51893	−	0.316984i	0.198359	−	0.0139141i
$520$	0.0243265	+	0.0748694i	0.00106679	+	0.00328324i
$521$	37.3344	+	12.1307i	1.63565	+	0.531454i	0.975560	−	0.219734i	$-0.0705188\pi$
$521$	37.3344	+	12.1307i	1.63565	+	0.531454i	0.660088	+	0.751188i	$0.270519\pi$
$522$	7.69835	−	43.7710i	0.336948	−	1.91581i
$523$	6.41393	−	8.82802i	0.280462	−	0.386022i	−0.645425	−	0.763824i	$-0.723320\pi$
$523$	6.41393	−	8.82802i	0.280462	−	0.386022i	0.925887	+	0.377801i	$0.123320\pi$
$524$	−5.42948	+	16.7102i	−0.237188	+	0.729989i
$525$	−15.1794	−	3.78113i	−0.662482	−	0.165022i
$526$	−7.38262	+	5.36379i	−0.321897	+	0.233872i
$527$	31.2812			1.36263
$528$	−23.1311	−	3.38189i	−1.00665	−	0.147178i
$529$	22.3787			0.972988
$530$	−42.7548	+	31.0632i	−1.85715	+	1.34930i
$531$	6.66022	+	6.89085i	0.289029	+	0.299037i
$532$	2.13302	−	6.56477i	0.0924783	−	0.284619i
$533$	1.52741	−	2.10230i	0.0661594	−	0.0910606i
$534$	16.8890	−	6.82789i	0.730860	−	0.295472i
$535$	23.2821	+	7.56480i	1.00657	+	0.327055i
$536$	0.249905	+	0.769130i	0.0107943	+	0.0332214i
$537$	1.13491	+	16.1793i	0.0489751	+	0.698190i
$538$			46.2570i			1.99428i
$539$	0.327649	+	3.30040i	0.0141128	+	0.142158i
$540$	−38.0337	−	3.97237i	−1.63671	−	0.170943i
$541$	−2.11365	−	2.90919i	−0.0908728	−	0.125076i	0.761160	−	0.648564i	$-0.224630\pi$
$541$	−2.11365	−	2.90919i	−0.0908728	−	0.125076i	−0.852033	+	0.523489i	$0.824630\pi$
$542$	19.0345	−	6.18467i	0.817600	−	0.265654i
$543$	4.11998	−	3.45861i	0.176805	−	0.148423i
$544$	−26.4219	−	19.1966i	−1.13283	−	0.823049i
$545$	−42.4403	−	30.8347i	−1.81794	−	1.32081i
$546$	0.789046	−	0.662382i	0.0337681	−	0.0283473i
$547$	4.66921	−	1.51712i	0.199641	−	0.0648673i	−0.207490	−	0.978237i	$-0.566529\pi$
$547$	4.66921	−	1.51712i	0.199641	−	0.0648673i	0.407131	+	0.913370i	$0.366529\pi$
$548$	3.15574	+	4.34351i	0.134807	+	0.185545i
$549$	9.44136	−	4.60995i	0.402947	−	0.196748i
$550$	−5.89220	−	59.3520i	−0.251244	−	2.53078i
$551$		−	26.1398i		−	1.11359i
$552$	0.00672081	+	0.0958120i	0.000286057	+	0.00407803i
$553$	0.813119	+	2.50252i	0.0345773	+	0.106418i
$554$	−28.6276	−	9.30166i	−1.21627	−	0.395190i
$555$	−23.5158	+	9.50698i	−0.998192	+	0.403549i
$556$	−10.3560	+	14.2539i	−0.439193	+	0.604498i
$557$	10.2472	−	31.5377i	0.434188	−	1.33629i	−0.459728	−	0.888060i	$-0.652053\pi$
$557$	10.2472	−	31.5377i	0.434188	−	1.33629i	0.893916	−	0.448234i	$-0.147947\pi$
$558$	32.7552	−	31.6590i	1.38664	−	1.34023i
$559$	−0.917958	+	0.666936i	−0.0388255	+	0.0282084i
$560$	−15.2435			−0.644157
$561$	23.3154	+	3.40884i	0.984376	+	0.143921i
$562$	−23.8854			−1.00755
$563$	3.35810	−	2.43980i	0.141527	−	0.102825i	−0.514769	−	0.857329i	$-0.672122\pi$
$563$	3.35810	−	2.43980i	0.141527	−	0.102825i	0.656296	+	0.754504i	$0.272122\pi$
$564$	−0.832289	−	0.207320i	−0.0350457	−	0.00872976i
$565$	−14.2810	+	43.9524i	−0.600806	+	1.84909i
$566$	11.6822	−	16.0791i	0.491038	−	0.675856i
$567$	−2.48828	−	8.64919i	−0.104498	−	0.363232i
$568$	1.05944	+	0.344234i	0.0444533	+	0.0144437i
$569$	7.58637	+	23.3484i	0.318037	+	0.978817i	0.974486	+	0.224447i	$0.0720576\pi$
$569$	7.58637	+	23.3484i	0.318037	+	0.978817i	−0.656449	+	0.754370i	$0.727942\pi$
$570$	−45.2769	+	3.17598i	−1.89644	+	0.133027i
$571$			15.8878i			0.664885i	0.943124	+	0.332442i	$0.107873\pi$
$571$			15.8878i			0.664885i	−0.943124	+	0.332442i	$0.892127\pi$
$572$	1.68006	+	0.982946i	0.0702467	+	0.0410990i
$573$	7.42658	−	11.8908i	0.310250	−	0.496744i
$574$	10.1811	+	14.0131i	0.424951	+	0.584894i
$575$	−6.77043	+	2.19985i	−0.282346	+	0.0917399i
$576$	−22.9180	+	3.23110i	−0.954917	+	0.134629i
$577$	−4.37044	−	3.17531i	−0.181944	−	0.132190i	0.493085	−	0.869981i	$-0.335869\pi$
$577$	−4.37044	−	3.17531i	−0.181944	−	0.132190i	−0.675029	+	0.737791i	$0.735869\pi$
$578$	−0.281793	−	0.204734i	−0.0117210	−	0.00851583i
$579$	−1.75158	−	2.08652i	−0.0727930	−	0.0867130i
$580$	52.0747	−	16.9201i	2.16228	−	0.702568i
$581$	−3.28898	−	4.52689i	−0.136450	−	0.187807i
$582$	50.2635	+	31.3929i	2.08349	+	1.30128i
$583$	5.01842	−	22.9578i	0.207842	−	0.950816i
$584$			0.926795i			0.0383511i
$585$	−2.96466	−	1.57468i	−0.122573	−	0.0651050i
$586$	−5.28497	−	16.2655i	−0.218320	−	0.671920i
$587$	−26.6874	−	8.67127i	−1.10151	−	0.357902i	−0.298825	−	0.954308i	$-0.596595\pi$
$587$	−26.6874	−	8.67127i	−1.10151	−	0.357902i	−0.802683	+	0.596406i	$0.796595\pi$
$588$	1.27544	+	3.15484i	0.0525982	+	0.130103i
$589$	15.7488	−	21.6764i	0.648919	−	0.893160i
$590$	−7.36274	+	22.6602i	−0.303119	+	0.932905i
$591$	−7.32860	+	29.4207i	−0.301458	+	1.21021i
$592$	−12.8709	+	9.35125i	−0.528990	+	0.384334i
$593$	40.1746			1.64978			0.824888	−	0.565297i	$-0.191238\pi$
$593$	40.1746			1.64978			0.824888	+	0.565297i	$0.191238\pi$
$594$	27.8641	−	20.0275i	1.14328	−	0.821738i
$595$	15.3650			0.629903
$596$	1.31337	−	0.954219i	0.0537977	−	0.0390863i
$597$	−2.28621	+	9.17800i	−0.0935683	+	0.375631i
$598$	0.144875	−	0.445880i	0.00592439	−	0.0182334i
$599$	−12.2470	+	16.8565i	−0.500399	+	0.688739i	−0.982263	−	0.187506i	$-0.939960\pi$
$599$	−12.2470	+	16.8565i	−0.500399	+	0.688739i	0.481865	+	0.876246i	$0.339960\pi$
$600$	0.412492	+	1.02031i	0.0168399	+	0.0416541i
$601$	−44.1389	−	14.3416i	−1.80046	−	0.585006i	−0.800565	−	0.599246i	$-0.795467\pi$
$601$	−44.1389	−	14.3416i	−1.80046	−	0.585006i	−0.999899	+	0.0142404i	$0.995467\pi$
$602$	−2.33715	−	7.19301i	−0.0952552	−	0.293165i
$603$	−30.4558	−	16.1766i	−1.24026	−	0.658763i
$604$			17.0014i			0.691779i
$605$	30.3009	+	27.9227i	1.23191	+	1.13522i
$606$	13.0876	+	8.17409i	0.531649	+	0.332050i
$607$	−7.22839	−	9.94902i	−0.293391	−	0.403818i	0.636721	−	0.771095i	$-0.280290\pi$
$607$	−7.22839	−	9.94902i	−0.293391	−	0.403818i	−0.930112	+	0.367276i	$0.880290\pi$
$608$	−26.6047	+	8.64439i	−1.07896	+	0.350576i
$609$	8.28549	+	9.86990i	0.335745	+	0.399948i
$610$	21.1330	+	15.3540i	0.855648	+	0.621665i
$611$	−0.0609142	−	0.0442567i	−0.00246432	−	0.00179044i
$612$	23.9395	−	3.37512i	0.967696	−	0.136431i
$613$	30.3954	−	9.87607i	1.22766	−	0.398891i	0.377793	−	0.925890i	$-0.376683\pi$
$613$	30.3954	−	9.87607i	1.22766	−	0.398891i	0.849866	+	0.526999i	$0.176683\pi$
$614$	−3.32427	−	4.57547i	−0.134157	−	0.184651i
$615$	29.8982	−	47.8703i	1.20561	−	1.93032i
$616$	0.174298	−	0.155128i	0.00702267	−	0.00625027i
$617$			34.0553i			1.37101i	0.728066	+	0.685507i	$0.240420\pi$
$617$			34.0553i			1.37101i	−0.728066	+	0.685507i	$0.759580\pi$
$618$	33.3521	−	2.33951i	1.34162	−	0.0941088i
$619$	10.1879	+	31.3551i	0.409486	+	1.26027i	0.917091	+	0.398678i	$0.130531\pi$
$619$	10.1879	+	31.3551i	0.409486	+	1.26027i	−0.507605	+	0.861590i	$0.669469\pi$
$620$	53.3770	+	17.3432i	2.14367	+	0.696521i
$621$	−3.04548	−	2.73856i	−0.122211	−	0.109895i
$622$	−20.0076	+	27.5381i	−0.802230	+	1.10418i
$623$	−1.63228	+	5.02365i	−0.0653960	+	0.201268i
$624$	−2.04308	−	0.508923i	−0.0817885	−	0.0203732i
$625$	−9.23246	+	6.70777i	−0.369298	+	0.268311i
$626$	24.4257			0.976248
$627$	14.1005	−	14.4402i	0.563120	−	0.576688i
$628$	30.3047			1.20929
$629$	12.9734	−	9.42575i	0.517284	−	0.375829i
$630$	16.0890	−	15.5505i	0.641002	−	0.619549i
$631$	12.5113	−	38.5058i	0.498067	−	1.53289i	−0.314055	−	0.949405i	$-0.601688\pi$
$631$	12.5113	−	38.5058i	0.498067	−	1.53289i	0.812122	−	0.583488i	$-0.198312\pi$
$632$	0.108810	−	0.149765i	0.00432825	−	0.00595732i
$633$	23.4505	−	9.48058i	0.932076	−	0.376819i
$634$	−2.19986	−	0.714777i	−0.0873675	−	0.0283874i
$635$	20.2321	+	62.2680i	0.802887	+	2.47103i
$636$	−1.68716	−	24.0522i	−0.0669001	−	0.953730i
$637$			0.298720i			0.0118357i
$638$	−24.8118	+	42.4084i	−0.982307	+	1.67896i
$639$	−42.6855	+	20.8422i	−1.68861	+	0.824503i
$640$	1.23901	+	1.70535i	0.0489762	+	0.0674099i
$641$	11.3686	−	3.69389i	0.449034	−	0.145900i	−0.0757658	−	0.997126i	$-0.524140\pi$
$641$	11.3686	−	3.69389i	0.449034	−	0.145900i	0.524800	+	0.851226i	$0.324140\pi$
$642$	−17.2623	+	14.4912i	−0.681290	+	0.571924i
$643$	−7.68605	−	5.58425i	−0.303108	−	0.220221i	0.425825	−	0.904805i	$-0.359984\pi$
$643$	−7.68605	−	5.58425i	−0.303108	−	0.220221i	−0.728934	+	0.684584i	$0.759984\pi$
$644$	1.25283	+	0.910233i	0.0493683	+	0.0358682i
$645$	−18.8751	+	15.8451i	−0.743208	+	0.623902i
$646$	27.2906	−	8.86724i	1.07373	−	0.348877i
$647$	−4.13987	−	5.69805i	−0.162755	−	0.224013i	0.719848	−	0.694131i	$-0.244211\pi$
$647$	−4.13987	−	5.69805i	−0.162755	−	0.224013i	−0.882604	+	0.470118i	$0.844211\pi$
$648$	−0.389385	+	0.499287i	−0.0152965	+	0.0196138i
$649$	−4.25343	−	9.70361i	−0.166962	−	0.380900i
$650$		−	5.37196i		−	0.210705i
$651$	0.924276	+	13.1765i	0.0362252	+	0.516427i
$652$	−10.9593	−	33.7293i	−0.429200	−	1.32094i
$653$	0.954875	+	0.310258i	0.0373671	+	0.0121413i	0.327641	−	0.944802i	$-0.393746\pi$
$653$	0.954875	+	0.310258i	0.0373671	+	0.0121413i	−0.290274	+	0.956944i	$0.593746\pi$
$654$	44.7774	−	18.1026i	1.75093	−	0.707867i
$655$	−19.6906	+	27.1018i	−0.769375	+	1.05895i
$656$	10.9392	−	33.6675i	0.427105	−	1.31449i
$657$	−27.4658	−	28.4169i	−1.07154	−	1.10865i
$658$	0.406030	−	0.294998i	0.0158287	−	0.0115002i
$659$	−36.4253			−1.41893			−0.709464	−	0.704742i	$-0.751063\pi$
$659$	−36.4253			−1.41893			−0.709464	+	0.704742i	$0.751063\pi$
$660$	37.8945	+	18.7435i	1.47504	+	0.729588i
$661$	24.5113			0.953380			0.476690	−	0.879071i	$-0.341836\pi$
$661$	24.5113			0.953380			0.476690	+	0.879071i	$0.341836\pi$
$662$	22.0904	−	16.0496i	0.858567	−	0.623786i
$663$	2.05935	+	0.512978i	0.0799786	+	0.0199224i
$664$	−0.121648	+	0.374394i	−0.00472086	+	0.0145293i
$665$	7.73565	−	10.6472i	0.299976	−	0.412881i
$666$	4.04519	−	23.0000i	0.156748	−	0.891232i
$667$	5.57736	+	1.81219i	0.215956	+	0.0701684i
$668$	8.09335	+	24.9088i	0.313141	+	0.963749i
$669$	11.8362	−	0.830260i	0.457614	−	0.0320997i
$670$		−	85.7374i		−	3.31233i
$671$	−11.5588	+	1.14750i	−0.446222	+	0.0442989i
$672$	7.30544	−	11.6968i	0.281814	−	0.451215i
$673$	15.7288	+	21.6489i	0.606301	+	0.834502i	0.996267	−	0.0863272i	$-0.0275130\pi$
$673$	15.7288	+	21.6489i	0.606301	+	0.834502i	−0.389965	+	0.920830i	$0.627513\pi$
$674$	35.1476	−	11.4201i	1.35383	−	0.439887i
$675$	−42.8848	−	19.0600i	−1.65064	−	0.733618i
$676$	−20.5210	−	14.9094i	−0.789270	−	0.573438i
$677$	−5.86103	−	4.25829i	−0.225258	−	0.163659i	0.469432	−	0.882968i	$-0.344459\pi$
$677$	−5.86103	−	4.25829i	−0.225258	−	0.163659i	−0.694690	+	0.719309i	$0.744459\pi$
$678$	−27.3569	−	32.5882i	−1.05063	−	1.25154i
$679$	−16.3424	+	5.30996i	−0.627163	+	0.203778i
$680$	−0.635376	−	0.874521i	−0.0243656	−	0.0335363i
$681$	−29.1419	−	18.2010i	−1.11672	−	0.697465i
$682$	−46.1256	+	20.2184i	−1.76624	+	0.774203i
$683$			3.73388i			0.142873i	0.997445	+	0.0714365i	$0.0227583\pi$
$683$			3.73388i			0.142873i	−0.997445	+	0.0714365i	$0.977242\pi$
$684$	9.71377	−	18.2882i	0.371415	−	0.699266i
$685$	3.16322	+	9.73540i	0.120861	+	0.371971i
$686$	−1.89369	−	0.615298i	−0.0723016	−	0.0234922i
$687$	1.92247	+	4.75530i	0.0733469	+	0.181426i
$688$	−9.08557	+	12.5052i	−0.346384	+	0.476757i
$689$	0.654058	−	2.01298i	0.0249176	−	0.0766886i
$690$	2.46126	−	9.88076i	0.0936987	−	0.376154i
$691$	−26.2005	+	19.0358i	−0.996714	+	0.724155i	−0.961381	−	0.275220i	$-0.911249\pi$
$691$	−26.2005	+	19.0358i	−0.996714	+	0.724155i	−0.0353329	+	0.999376i	$0.511249\pi$
$692$	−5.13842			−0.195334
$693$	−0.746987	+	9.92179i	−0.0283757	+	0.376898i
$694$	24.3548			0.924497
$695$	−27.1767	+	19.7450i	−1.03087	+	0.748972i
$696$	0.219136	−	0.879723i	0.00830633	−	0.0333458i
$697$	−11.0264	+	33.9357i	−0.417654	+	1.28541i
$698$	−12.9077	+	17.7659i	−0.488564	+	0.672450i
$699$	7.44243	+	18.4091i	0.281499	+	0.696297i
$700$	16.8757	+	5.48323i	0.637840	+	0.207247i
$701$	−0.504912	−	1.55396i	−0.0190702	−	0.0586922i	0.941069	−	0.338216i	$-0.109823\pi$
$701$	−0.504912	−	1.55396i	−0.0190702	−	0.0586922i	−0.960139	+	0.279524i	$0.909823\pi$
$702$	2.67557	−	1.54707i	0.100983	−	0.0583905i
$703$		−	13.7355i		−	0.518042i
$704$	24.9971	+	5.46420i	0.942115	+	0.205940i
$705$	−1.38705	−	0.866302i	−0.0522392	−	0.0326268i
$706$	−25.9249	−	35.6826i	−0.975697	−	1.34293i
$707$	−4.25524	+	1.38261i	−0.160035	+	0.0519984i
$708$	−6.98924	−	8.32577i	−0.262672	−	0.312902i
$709$	−29.9472	−	21.7579i	−1.12469	−	0.817135i	−0.139777	−	0.990183i	$-0.544638\pi$
$709$	−29.9472	−	21.7579i	−1.12469	−	0.817135i	−0.984913	+	0.173048i	$0.944638\pi$
$710$	−95.5446	−	69.4172i	−3.58573	−	2.60518i
$711$	1.10203	+	7.81662i	0.0413293	+	0.293146i
$712$	0.353427	−	0.114835i	0.0132452	−	0.00430364i
$713$	3.53320	+	4.86303i	0.132319	+	0.182122i
$714$	−7.49377	+	11.9984i	−0.280447	+	0.449027i
$715$	2.46733	+	2.77224i	0.0922727	+	0.103676i
$716$		−	18.3973i		−	0.687541i
$717$	36.2669	−	2.54397i	1.35441	−	0.0950064i
$718$	10.9967	+	33.8445i	0.410394	+	1.26306i
$719$	23.5283	+	7.64481i	0.877457	+	0.285103i	0.712901	−	0.701264i	$-0.247381\pi$
$719$	23.5283	+	7.64481i	0.877457	+	0.285103i	0.164556	+	0.986368i	$0.447381\pi$
$720$	−45.0393	−	7.92141i	−1.67852	−	0.295214i
$721$	−5.69827	+	7.84300i	−0.212215	+	0.292089i
$722$	−4.09555	+	12.6048i	−0.152421	+	0.469102i
$723$	−38.3826	−	9.56098i	−1.42747	−	0.355577i
$724$	−4.93636	+	3.58648i	−0.183458	+	0.133290i
$725$	67.1959			2.49559
$726$	−36.5829	+	10.0433i	−1.35772	+	0.372741i
$727$	1.33028			0.0493372			0.0246686	−	0.999696i	$-0.492147\pi$
$727$	1.33028			0.0493372			0.0246686	+	0.999696i	$0.492147\pi$
$728$	0.0170021	−	0.0123527i	0.000630139	−	0.000457822i
$729$	−2.85738	−	26.8484i	−0.105829	−	0.994384i
$730$	30.3629	−	93.4474i	1.12378	−	3.45864i
$731$	9.15795	−	12.6048i	0.338719	−	0.466207i
$732$	−11.0490	+	4.46688i	−0.408382	+	0.165101i
$733$	8.35538	+	2.71483i	0.308613	+	0.100274i	0.459229	−	0.888318i	$-0.348126\pi$
$733$	8.35538	+	2.71483i	0.308613	+	0.100274i	−0.150616	+	0.988592i	$0.548126\pi$
$734$	16.7525	+	51.5588i	0.618345	+	1.90307i
$735$	0.453994	+	6.47215i	0.0167458	+	0.238729i
$736$		−	6.27585i		−	0.231331i
$737$	25.3467	+	28.4791i	0.933659	+	1.04904i
$738$	22.7996	+	46.6944i	0.839264	+	1.71884i
$739$	−21.1340	−	29.0884i	−0.777427	−	1.07004i	−0.995561	−	0.0941172i	$-0.969997\pi$
$739$	−21.1340	−	29.0884i	−0.777427	−	1.07004i	0.218135	−	0.975919i	$-0.430003\pi$
$740$	27.3633	−	8.89086i	1.00589	−	0.326835i
$741$	1.39227	−	1.16877i	0.0511463	−	0.0429359i
$742$	11.4138	+	8.29263i	0.419015	+	0.304432i
$743$	−9.48201	−	6.88908i	−0.347861	−	0.252736i	0.400110	−	0.916467i	$-0.368972\pi$
$743$	−9.48201	−	6.88908i	−0.347861	−	0.252736i	−0.747971	+	0.663731i	$0.768972\pi$
$744$	0.711738	−	0.597484i	0.0260936	−	0.0219048i
$745$	2.94375	−	0.956482i	0.107851	−	0.0350428i
$746$	22.2653	+	30.6455i	0.815190	+	1.12201i
$747$	−7.36535	−	15.0845i	−0.269484	−	0.551914i
$748$	−26.1113	−	5.70774i	−0.954723	−	0.208696i
$749$		−	6.53524i		−	0.238792i
$750$	−3.64445	−	51.9554i	−0.133077	−	1.89714i
$751$	1.62734	+	5.00843i	0.0593824	+	0.182760i	0.976348	−	0.216207i	$-0.0693686\pi$
$751$	1.62734	+	5.00843i	0.0593824	+	0.182760i	−0.916965	+	0.398967i	$0.869369\pi$
$752$	−0.975518	−	0.316965i	−0.0355735	−	0.0115585i
$753$	−26.5808	+	10.7461i	−0.968657	+	0.391608i
$754$	−2.60114	+	3.58016i	−0.0947279	+	0.130382i
$755$	−10.0169	+	30.8288i	−0.364552	+	1.12198i
$756$	2.12904	+	9.98424i	0.0774324	+	0.363123i
$757$	−41.9131	+	30.4516i	−1.52336	+	1.10678i	−0.563566	+	0.826071i	$0.690571\pi$
$757$	−41.9131	+	30.4516i	−1.52336	+	1.10678i	−0.959792	+	0.280713i	$0.909429\pi$
$758$	−19.2198			−0.698094
$759$	2.10352	+	4.00968i	0.0763530	+	0.145542i
$760$	−0.925888			−0.0335855
$761$	−4.80624	+	3.49194i	−0.174226	+	0.126583i	−0.671481	−	0.741022i	$-0.734341\pi$
$761$	−4.80624	+	3.49194i	−0.174226	+	0.126583i	0.497255	+	0.867605i	$0.334341\pi$
$762$	−58.4920	−	14.5702i	−2.11894	−	0.527821i
$763$	−4.32762	+	13.3191i	−0.156671	+	0.482182i
$764$	−9.34711	+	12.8652i	−0.338167	+	0.465447i
$765$	45.3982	+	7.98452i	1.64137	+	0.288681i
$766$	28.5987	+	9.29230i	1.03331	+	0.335744i
$767$	−0.294881	−	0.907550i	−0.0106475	−	0.0327697i
$768$	−28.5956	+	2.00586i	−1.03186	+	0.0723803i
$769$			24.7849i			0.893767i	0.894592	+	0.446883i	$0.147466\pi$
$769$			24.7849i			0.893767i	−0.894592	+	0.446883i	$0.852534\pi$
$770$	−22.6564	+	9.93107i	−0.816479	+	0.357891i
$771$	19.9080	−	31.8749i	0.716968	−	1.14795i
$772$	1.81633	+	2.49997i	0.0653713	+	0.0899759i
$773$	4.00453	−	1.30115i	0.144033	−	0.0467992i	−0.236113	−	0.971726i	$-0.575874\pi$
$773$	4.00453	−	1.30115i	0.144033	−	0.0467992i	0.380146	+	0.924926i	$0.375874\pi$
$774$	−3.16757	−	22.4674i	−0.113856	−	0.807573i
$775$	55.7221	+	40.4845i	2.00160	+	1.45425i
$776$	0.978018	+	0.710571i	0.0351088	+	0.0255080i
$777$	4.35371	+	5.18625i	0.156188	+	0.186056i
$778$	−33.3247	+	10.8279i	−1.19475	+	0.388198i
$779$	17.9645	+	24.7260i	0.643645	+	0.885902i
$780$	3.22959	+	2.01709i	0.115638	+	0.0722235i
$781$	52.2586	−	5.18801i	1.86996	−	0.185641i
$782$			6.43764i			0.230209i
$783$	19.3518	+	33.4677i	0.691576	+	1.19604i
$784$	1.25752	+	3.87025i	0.0449114	+	0.138223i
$785$	54.9518	+	17.8549i	1.96131	+	0.637269i
$786$	−11.5601	−	28.5942i	−0.412334	−	1.01992i
$787$	−24.4481	+	33.6499i	−0.871480	+	1.19949i	0.107229	+	0.994234i	$0.465802\pi$
$787$	−24.4481	+	33.6499i	−0.871480	+	1.19949i	−0.978709	+	0.205255i	$0.934198\pi$
$788$	10.6276	−	32.7085i	0.378593	−	1.16519i
$789$	1.91869	−	7.70261i	0.0683073	−	0.274220i
$790$	−15.8777	+	11.5358i	−0.564902	+	0.410425i
$791$	12.3374			0.438666
$792$	0.595603	−	0.367772i	0.0211638	−	0.0130682i
$793$	−1.04619			−0.0371512
$794$	15.4944	−	11.2573i	0.549875	−	0.399508i
$795$	11.1117	−	44.6079i	0.394091	−	1.58208i
$796$	3.31536	−	10.2036i	0.117510	−	0.361659i
$797$	−5.72593	+	7.88106i	−0.202823	+	0.279162i	−0.898296	−	0.439390i	$-0.855195\pi$
$797$	−5.72593	+	7.88106i	−0.202823	+	0.279162i	0.695474	+	0.718552i	$0.255195\pi$
$798$	4.54149	+	11.2335i	0.160767	+	0.397662i
$799$	0.983290	+	0.319490i	0.0347863	+	0.0113027i
$800$	−22.2216	−	68.3911i	−0.785652	−	2.41799i
$801$	−7.43340	+	13.9949i	−0.262646	+	0.494485i
$802$		−	12.2598i		−	0.432909i
$803$	17.5405	+	40.0163i	0.618992	+	1.41214i
$804$	33.1774	+	20.7215i	1.17008	+	0.730791i
$805$	1.73547	+	2.38867i	0.0611673	+	0.0841896i
$806$	−4.31398	+	1.40170i	−0.151954	+	0.0493727i
$807$	−25.8711	−	30.8184i	−0.910706	−	1.08486i
$808$	0.254657	+	0.185019i	0.00895879	+	0.00650894i
$809$	−5.62121	−	4.08405i	−0.197631	−	0.143587i	0.484569	−	0.874753i	$-0.338977\pi$
$809$	−5.62121	−	4.08405i	−0.197631	−	0.143587i	−0.682200	+	0.731166i	$0.738977\pi$
$810$	55.6184	−	37.5856i	1.95423	−	1.32063i
$811$	11.4259	−	3.71249i	0.401217	−	0.130363i	−0.101456	−	0.994840i	$-0.532350\pi$
$811$	11.4259	−	3.71249i	0.401217	−	0.130363i	0.502673	+	0.864477i	$0.332350\pi$
$812$	−8.59182	−	11.8256i	−0.301514	−	0.414998i
$813$	−9.22252	+	14.7663i	−0.323448	+	0.517876i
$814$	−13.0376	+	22.2840i	−0.456969	+	0.781053i
$815$		−	67.6186i		−	2.36858i
$816$	28.8407	−	2.02305i	1.00963	−	0.0708210i
$817$	−4.12390	−	12.6921i	−0.144277	−	0.444039i
$818$	−41.0785	−	13.3472i	−1.43628	−	0.466675i
$819$	−0.155232	+	0.882612i	−0.00542424	+	0.0308410i
$820$	−37.6300	+	51.7932i	−1.31410	+	1.80870i
$821$	−1.20533	+	3.70963i	−0.0420663	+	0.129467i	−0.969884	−	0.243567i	$-0.921682\pi$
$821$	−1.20533	+	3.70963i	−0.0420663	+	0.129467i	0.927818	+	0.373034i	$0.121682\pi$
$822$	−9.14504	−	2.27800i	−0.318970	−	0.0794543i
$823$	36.3545	−	26.4131i	1.26724	−	0.920703i	0.268150	−	0.963377i	$-0.413588\pi$
$823$	36.3545	−	26.4131i	1.26724	−	0.920703i	0.999089	+	0.0426743i	$0.0135878\pi$
$824$	0.682032			0.0237597
$825$	37.1206	+	36.2473i	1.29237	+	1.26197i
$826$	6.36068			0.221316
$827$	−19.2201	+	13.9642i	−0.668347	+	0.485583i	−0.869471	−	0.493983i	$-0.835540\pi$
$827$	−19.2201	+	13.9642i	−0.668347	+	0.485583i	0.201124	+	0.979566i	$0.435540\pi$
$828$	3.22866	+	3.34046i	0.112204	+	0.116089i
$829$	11.3740	−	35.0056i	0.395035	−	1.21579i	−0.533899	−	0.845548i	$-0.679274\pi$
$829$	11.3740	−	35.0056i	0.395035	−	1.21579i	0.928934	−	0.370245i	$-0.120726\pi$
$830$	24.5312	−	33.7643i	0.851489	−	1.17197i
$831$	24.2752	−	9.81398i	0.842098	−	0.340443i
$832$	2.19179	+	0.712157i	0.0759868	+	0.0246896i
$833$	−1.26754	−	3.90108i	−0.0439176	−	0.135164i
$834$	−2.16414	−	30.8520i	−0.0749380	−	1.06832i
$835$			49.9356i			1.72809i
$836$	−17.1012	+	15.2203i	−0.591456	+	0.526404i
$837$	−4.11634	+	39.4122i	−0.142282	+	1.36229i
$838$	12.2152	+	16.8127i	0.421966	+	0.580786i
$839$	−50.6080	+	16.4435i	−1.74718	+	0.567693i	−0.995748	−	0.0921164i	$-0.970637\pi$
$839$	−50.6080	+	16.4435i	−1.74718	+	0.567693i	−0.751433	+	0.659810i	$0.770637\pi$
$840$	0.349598	−	0.293478i	0.0120623	−	0.0101259i
$841$	−21.3215	−	15.4909i	−0.735223	−	0.534170i
$842$	−24.0364	−	17.4635i	−0.828350	−	0.601832i
$843$	15.9135	−	13.3589i	0.548089	−	0.460105i
$844$	−27.2873	+	8.86617i	−0.939266	+	0.305186i
$845$	−28.4266	−	39.1258i	−0.977904	−	1.34597i
$846$	1.35297	−	0.660619i	0.0465162	−	0.0227126i
$847$	4.58974	−	9.99672i	0.157705	−	0.343491i
$848$		−	28.8338i		−	0.990158i
$849$	1.20976	+	17.2463i	0.0415188	+	0.591892i
$850$	22.7945	+	70.1541i	0.781844	+	2.40627i
$851$	2.93069	+	0.952239i	0.100463	+	0.0326423i
$852$	49.9538	−	20.1953i	1.71139	−	0.691880i
$853$	10.8266	−	14.9016i	0.370697	−	0.510220i	−0.582393	−	0.812907i	$-0.697884\pi$
$853$	10.8266	−	14.9016i	0.370697	−	0.510220i	0.953090	+	0.302687i	$0.0978836\pi$
$854$	2.15492	−	6.63216i	0.0737398	−	0.226948i
$855$	28.3890	−	27.4389i	0.970885	−	0.938390i
$856$	−0.371962	+	0.270247i	−0.0127134	+	0.00923684i
$857$	−46.3883			−1.58460			−0.792298	−	0.610135i	$-0.791115\pi$
$857$	−46.3883			−1.58460			−0.792298	+	0.610135i	$0.791115\pi$
$858$	−3.36817	+	0.574641i	−0.114987	+	0.0196179i
$859$	−33.4756			−1.14217			−0.571087	−	0.820890i	$-0.693478\pi$
$859$	−33.4756			−1.14217			−0.571087	+	0.820890i	$0.693478\pi$
$860$	22.6153	−	16.4310i	0.771174	−	0.560291i
$861$	−14.6204	−	3.64190i	−0.498264	−	0.124116i
$862$	−24.1465	+	74.3153i	−0.822434	+	2.53119i
$863$	2.78770	−	3.83693i	0.0948943	−	0.130611i	−0.758930	−	0.651172i	$-0.774277\pi$
$863$	2.78770	−	3.83693i	0.0948943	−	0.130611i	0.853824	+	0.520562i	$0.174277\pi$
$864$	27.6634	−	30.7637i	0.941127	−	1.04660i
$865$	−9.31753	−	3.02745i	−0.316806	−	0.102936i
$866$	12.4128	+	38.2028i	0.421805	+	1.29818i
$867$	0.302248	−	0.0212014i	0.0102649	−	0.000720039i
$868$		−	14.9828i		−	0.508551i
$869$	1.86367	−	8.52574i	0.0632206	−	0.289216i
$870$	−50.9159	+	81.5220i	−1.72621	+	2.76386i
$871$	2.01835	+	2.77802i	0.0683891	+	0.0941295i
$872$	0.937031	−	0.304460i	0.0317319	−	0.0103103i
$873$	−51.0454	+	7.19665i	−1.72762	+	0.243570i
$874$	4.46098	+	3.24109i	0.150895	+	0.109632i
$875$	12.2177	+	8.87669i	0.413034	+	0.300087i
$876$	28.8226	+	34.3343i	0.973826	+	1.16005i
$877$	16.8853	−	5.48636i	0.570175	−	0.185261i	−0.00971910	−	0.999953i	$-0.503094\pi$
$877$	16.8853	−	5.48636i	0.570175	−	0.185261i	0.579895	+	0.814692i	$0.303094\pi$
$878$	40.2193	+	55.3571i	1.35734	+	1.86821i
$879$	12.6182	+	7.88090i	0.425601	+	0.265816i
$880$	43.6372	+	25.5307i	1.47101	+	0.860640i
$881$			15.1648i			0.510915i	0.966820	+	0.255458i	$0.0822262\pi$
$881$			15.1648i			0.510915i	−0.966820	+	0.255458i	$0.917774\pi$
$882$	−5.27546	−	2.80206i	−0.177634	−	0.0943503i
$883$	−7.02959	−	21.6348i	−0.236564	−	0.728070i	−0.996910	−	0.0785517i	$-0.974970\pi$
$883$	−7.02959	−	21.6348i	−0.236564	−	0.728070i	0.760346	−	0.649519i	$-0.225030\pi$
$884$	−2.28948	−	0.743899i	−0.0770037	−	0.0250200i
$885$	−7.76827	−	19.2151i	−0.261127	−	0.645908i
$886$	18.7205	−	25.7666i	0.628929	−	0.865647i
$887$	2.20110	−	6.77428i	0.0739056	−	0.227458i	−0.907279	−	0.420529i	$-0.861845\pi$
$887$	2.20110	−	6.77428i	0.0739056	−	0.227458i	0.981185	+	0.193071i	$0.0618446\pi$
$888$	0.115148	−	0.462261i	0.00386410	−	0.0155125i
$889$	14.1404	−	10.2736i	0.474255	−	0.344566i
$890$	−39.3976			−1.32061
$891$	−7.36301	+	28.9273i	−0.246670	+	0.969099i
$892$	−13.4588			−0.450634
$893$	0.716438	−	0.520523i	0.0239747	−	0.0174186i
$894$	−0.688811	+	2.76524i	−0.0230373	+	0.0924833i
$895$	10.8393	−	33.3600i	0.362319	−	1.11510i
$896$	0.330766	−	0.455261i	0.0110501	−	0.0152092i
$897$	0.152855	+	0.378092i	0.00510367	+	0.0126241i
$898$	−14.6571	−	4.76239i	−0.489114	−	0.158923i
$899$	−17.5333	−	53.9621i	−0.584770	−	1.79974i
$900$	47.0122	+	24.9706i	1.56707	+	0.832353i
$901$			29.0635i			0.968247i
$902$	−5.67525	−	57.1666i	−0.188965	−	1.90344i
$903$	5.58009	+	3.48514i	0.185694	+	0.115978i
$904$	−0.510178	−	0.702199i	−0.0169683	−	0.0233548i
$905$	−11.0642	+	3.59498i	−0.367787	+	0.119501i
$906$	−19.1885	−	22.8579i	−0.637495	−	0.759401i
$907$	23.6320	+	17.1696i	0.784686	+	0.570108i	0.906382	−	0.422460i	$-0.138833\pi$
$907$	23.6320	+	17.1696i	0.784686	+	0.570108i	−0.121696	+	0.992567i	$0.538833\pi$
$908$	31.5300	+	22.9079i	1.04636	+	0.760225i
$909$	−13.2912	+	1.87387i	−0.440842	+	0.0621522i
$910$	−2.11898	+	0.688499i	−0.0702436	+	0.0228235i
$911$	−5.63871	−	7.76102i	−0.186819	−	0.257134i	0.705326	−	0.708883i	$-0.250800\pi$
$911$	−5.63871	−	7.76102i	−0.186819	−	0.257134i	−0.892145	+	0.451749i	$0.850800\pi$
$912$	13.1182	−	21.0037i	0.434388	−	0.695504i
$913$	1.83338	+	18.4675i	0.0606759	+	0.611186i
$914$		−	4.96958i		−	0.164379i
$915$	−22.6670	+	1.58999i	−0.749348	+	0.0525636i
$916$	−1.79788	−	5.53331i	−0.0594037	−	0.182826i
$917$	8.50536	+	2.76356i	0.280872	+	0.0912608i
$918$	−28.3765	+	31.5568i	−0.936564	+	1.04153i
$919$	7.72730	−	10.6357i	0.254900	−	0.350840i	−0.662320	−	0.749221i	$-0.730428\pi$
$919$	7.72730	−	10.6357i	0.254900	−	0.350840i	0.917220	+	0.398381i	$0.130428\pi$
$920$	0.0641891	−	0.197554i	0.00211625	−	0.00651315i
$921$	4.77379	+	1.18913i	0.157302	+	0.0391833i
$922$	26.3270	−	19.1277i	0.867033	−	0.629936i
$923$	4.72994			0.155688
$924$	1.63274	−	11.1674i	0.0537132	−	0.367381i
$925$	35.3089			1.16095
$926$	6.19728	−	4.50259i	0.203655	−	0.147964i
$927$	−20.9121	+	20.2122i	−0.686843	+	0.663855i
$928$	−18.3058	+	56.3393i	−0.600916	+	1.84943i
$929$	−13.6622	+	18.8045i	−0.448244	+	0.616955i	−0.972019	−	0.234902i	$-0.924523\pi$
$929$	−13.6622	+	18.8045i	−0.448244	+	0.616955i	0.523775	+	0.851856i	$0.324523\pi$
$930$	−91.3378	+	36.9260i	−2.99508	+	1.21085i
$931$	−3.34142	−	1.08569i	−0.109511	−	0.0355821i
$932$	−6.96011	−	21.4210i	−0.227986	−	0.701669i
$933$	−2.07190	−	29.5370i	−0.0678310	−	0.966999i
$934$		−	43.7253i		−	1.43074i
$935$	−43.9849	−	25.7341i	−1.43846	−	0.841595i
$936$	0.0566543	−	0.0276627i	0.00185181	−	0.000904185i
$937$	−9.18416	−	12.6409i	−0.300033	−	0.412961i	0.632207	−	0.774799i	$-0.282149\pi$
$937$	−9.18416	−	12.6409i	−0.300033	−	0.412961i	−0.932241	+	0.361839i	$0.882149\pi$
$938$	−21.7682	+	7.07292i	−0.710758	+	0.230939i
$939$	−16.2734	+	13.6611i	−0.531063	+	0.445812i
$940$	1.50071	+	1.09033i	0.0489478	+	0.0355627i
$941$	−29.6082	−	21.5116i	−0.965201	−	0.701259i	−0.0108479	−	0.999941i	$-0.503453\pi$
$941$	−29.6082	−	21.5116i	−0.965201	−	0.701259i	−0.954353	+	0.298682i	$0.903453\pi$
$942$	−40.7437	+	34.2031i	−1.32750	+	1.11440i
$943$	−6.52114	+	2.11885i	−0.212357	+	0.0689991i
$944$	−7.64102	−	10.5170i	−0.248694	−	0.342298i
$945$	−2.02190	+	19.3589i	−0.0657725	+	0.629744i
$946$	−5.35675	+	24.5056i	−0.174163	+	0.796746i
$947$			49.6861i			1.61458i	0.590155	+	0.807290i	$0.299067\pi$
$947$			49.6861i			1.61458i	−0.590155	+	0.807290i	$0.700933\pi$
$948$	−0.626552	−	8.93214i	−0.0203495	−	0.290102i
$949$	1.21605	+	3.74260i	0.0394745	+	0.121490i
$950$	60.0896	+	19.5243i	1.94956	+	0.633452i
$951$	1.86540	−	0.754145i	0.0604899	−	0.0244548i
$952$	−0.169620	+	0.233462i	−0.00549742	+	0.00756655i
$953$	−6.04160	+	18.5941i	−0.195707	+	0.602323i	0.804261	+	0.594276i	$0.202561\pi$
$953$	−6.04160	+	18.5941i	−0.195707	+	0.602323i	−0.999968	+	0.00804678i	$0.997439\pi$
$954$	29.4145	+	30.4331i	0.952331	+	0.985308i
$955$	−24.5291	+	17.8214i	−0.793742	+	0.576688i
$956$	−41.2387			−1.33376
$957$	−7.18798	−	42.1312i	−0.232355	−	1.36191i
$958$	−12.5450			−0.405312
$959$	2.21081	−	1.60625i	0.0713908	−	0.0518684i
$960$	48.5704	+	12.0987i	1.56760	+	0.390484i
$961$	8.39230	−	25.8289i	0.270719	−	0.833189i
$962$	−1.36680	+	1.88124i	−0.0440674	+	0.0606535i
$963$	3.39608	−	19.3093i	0.109437	−	0.622235i
$964$	42.6719	+	13.8649i	1.37437	+	0.446560i
$965$	1.82064	+	5.60336i	0.0586085	+	0.180378i
$966$	−2.71171	+	0.190215i	−0.0872478	+	0.00612007i
$967$			4.24279i			0.136439i	0.997670	+	0.0682194i	$0.0217318\pi$
$967$			4.24279i			0.136439i	−0.997670	+	0.0682194i	$0.978268\pi$
$968$	−0.758773	+	0.152155i	−0.0243879	+	0.00489044i
$969$	−13.2227	+	21.1711i	−0.424776	+	0.680113i
$970$	−75.3329	−	103.687i	−2.41879	−	3.32918i
$971$	25.1036	−	8.15665i	0.805612	−	0.261759i	0.122874	−	0.992422i	$-0.460789\pi$
$971$	25.1036	−	8.15665i	0.805612	−	0.261759i	0.682738	+	0.730663i	$0.260789\pi$
$972$	1.10219	+	30.6063i	0.0353526	+	0.981697i
$973$	7.25510	+	5.27114i	0.232588	+	0.168985i
$974$	29.7193	+	21.5923i	0.952266	+	0.691862i
$975$	3.00449	+	3.57902i	0.0962205	+	0.114620i
$976$	−13.5545	+	4.40413i	−0.433869	+	0.140973i
$977$	−9.86367	−	13.5762i	−0.315567	−	0.434341i	0.621540	−	0.783382i	$-0.286507\pi$
$977$	−9.86367	−	13.5762i	−0.315567	−	0.434341i	−0.937107	+	0.349042i	$0.886507\pi$
$978$	52.8027	+	32.9788i	1.68844	+	1.05455i
$979$	13.0866	−	11.6472i	0.418248	−	0.372246i
$980$		−	7.35941i		−	0.235088i
$981$	−19.7080	+	37.1043i	−0.629227	+	1.18465i
$982$	−14.2062	−	43.7221i	−0.453337	−	1.39523i
$983$	5.85629	+	1.90282i	0.186787	+	0.0606907i	0.400917	−	0.916114i	$-0.368692\pi$
$983$	5.85629	+	1.90282i	0.186787	+	0.0606907i	−0.214130	+	0.976805i	$0.568692\pi$
$984$	0.397304	+	0.982745i	0.0126656	+	0.0313288i
$985$	38.5423	−	53.0489i	1.22806	−	1.69028i
$986$	18.7777	−	57.7917i	0.598003	−	1.84046i
$987$	−0.105524	+	0.423628i	−0.00335888	+	0.0134842i
$988$	−1.66815	+	1.21198i	−0.0530709	+	0.0385583i
$989$	2.99396			0.0952024
$990$	−72.1024	+	17.5693i	−2.29156	+	0.558389i
$991$	−60.7161			−1.92871			−0.964355	−	0.264613i	$-0.914756\pi$
$991$	−60.7161			−1.92871			−0.964355	+	0.264613i	$0.914756\pi$
$992$	−49.1236	+	35.6904i	−1.55968	+	1.13317i
$993$	−5.74114	+	23.0479i	−0.182190	+	0.731402i
$994$	−9.74265	+	29.9848i	−0.309018	+	0.951060i
$995$	12.0235	−	16.5490i	0.381172	−	0.524638i
$996$	7.13677	+	17.6530i	0.226137	+	0.559358i
$997$	16.6793	+	5.41942i	0.528238	+	0.171635i	0.560981	−	0.827829i	$-0.310424\pi$
$997$	16.6793	+	5.41942i	0.528238	+	0.171635i	−0.0327427	+	0.999464i	$0.510424\pi$
$998$	3.06328	+	9.42781i	0.0969665	+	0.298432i
$999$	10.1686	+	17.5860i	0.321721	+	0.556396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.s.a.8.19	yes	96
3.2	odd	2	inner	231.2.s.a.8.6	✓	96
11.7	odd	10	inner	231.2.s.a.29.6	yes	96
33.29	even	10	inner	231.2.s.a.29.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.s.a.8.6	✓	96	3.2	odd	2	inner
231.2.s.a.8.19	yes	96	1.1	even	1	trivial
231.2.s.a.29.6	yes	96	11.7	odd	10	inner
231.2.s.a.29.19	yes	96	33.29	even	10	inner

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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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61087 - 1.17037i) q^{2} +(-0.418655 + 1.68069i) q^{3} +(0.607116 - 1.86851i) q^{4} +(2.20177 - 3.03048i) q^{5} +(1.29263 + 3.19736i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(0.0217402 + 0.0669093i) q^{8} +(-2.64946 - 1.40726i) q^{9} +O(q^{10})\)	\(q+(1.61087 - 1.17037i) q^{2} +(-0.418655 + 1.68069i) q^{3} +(0.607116 - 1.86851i) q^{4} +(2.20177 - 3.03048i) q^{5} +(1.29263 + 3.19736i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(0.0217402 + 0.0669093i) q^{8} +(-2.64946 - 1.40726i) q^{9} -7.45860i q^{10} +(2.20500 + 2.47749i) q^{11} +(2.88622 + 1.80264i) q^{12} +(0.175583 + 0.241669i) q^{13} +(-1.89369 + 0.615298i) q^{14} +(4.17152 + 4.96923i) q^{15} +(3.29223 + 2.39194i) q^{16} +(-3.31846 - 2.41100i) q^{17} +(-5.91495 + 0.833920i) q^{18} +(-3.34142 + 1.08569i) q^{19} +(-4.32575 - 5.95388i) q^{20} +(0.917527 - 1.46906i) q^{21} +(6.45155 + 1.41026i) q^{22} -0.788215i q^{23} +(-0.121556 + 0.00852662i) q^{24} +(-2.79092 - 8.58957i) q^{25} +(0.565684 + 0.183802i) q^{26} +(3.47438 - 3.86377i) q^{27} +(-1.15480 + 1.58945i) q^{28} +(-2.29911 + 7.07593i) q^{29} +(12.5356 + 3.12258i) q^{30} +(-6.16968 + 4.48253i) q^{31} +7.96210 q^{32} +(-5.08704 + 2.66871i) q^{33} -8.16736 q^{34} +(-3.03048 + 2.20177i) q^{35} +(-4.23801 + 4.09617i) q^{36} +(-1.20809 + 3.71813i) q^{37} +(-4.11194 + 5.65960i) q^{38} +(-0.479681 + 0.193925i) q^{39} +(0.250634 + 0.0814360i) q^{40} +(-2.68816 - 8.27330i) q^{41} +(-0.241324 - 3.44031i) q^{42} +3.79840i q^{43} +(5.96791 - 2.61594i) q^{44} +(-10.0982 + 4.93066i) q^{45} +(-0.922501 - 1.26971i) q^{46} +(-0.239719 + 0.0778895i) q^{47} +(-5.39843 + 4.53182i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-14.5488 - 10.5703i) q^{50} +(5.44144 - 4.56793i) q^{51} +(0.558161 - 0.181357i) q^{52} +(-4.16475 - 5.73229i) q^{53} +(1.07476 - 10.2903i) q^{54} +(12.3629 - 1.22733i) q^{55} -0.0703526i q^{56} +(-0.425815 - 6.07043i) q^{57} +(4.57787 + 14.0892i) q^{58} +(-3.03813 - 0.987149i) q^{59} +(11.8176 - 4.77764i) q^{60} +(-2.05856 + 2.83337i) q^{61} +(-4.69235 + 14.4416i) q^{62} +(2.08492 + 2.15711i) q^{63} +(6.24147 - 4.53470i) q^{64} +1.11897 q^{65} +(-5.07119 + 10.2527i) q^{66} +11.4951 q^{67} +(-6.51966 + 4.73681i) q^{68} +(1.32475 + 0.329990i) q^{69} +(-2.30483 + 7.09355i) q^{70} +(9.30701 - 12.8100i) q^{71} +(0.0365592 - 0.207867i) q^{72} +(12.5288 + 4.07086i) q^{73} +(2.40549 + 7.40335i) q^{74} +(15.6049 - 1.09462i) q^{75} +6.90261i q^{76} +(-1.33149 - 3.03762i) q^{77} +(-0.545740 + 0.873791i) q^{78} +(-1.54664 - 2.12877i) q^{79} +(14.4975 - 4.71051i) q^{80} +(5.03924 + 7.45695i) q^{81} +(-14.0131 - 10.1811i) q^{82} +(4.52689 + 3.28898i) q^{83} +(-2.18791 - 2.60630i) q^{84} +(-14.6130 + 4.74804i) q^{85} +(4.44553 + 6.11874i) q^{86} +(-10.9299 - 6.82647i) q^{87} +(-0.117830 + 0.201396i) q^{88} -5.28218i q^{89} +(-10.4962 + 19.7612i) q^{90} +(-0.0923095 - 0.284099i) q^{91} +(-1.47279 - 0.478538i) q^{92} +(-4.95080 - 12.2460i) q^{93} +(-0.294998 + 0.406030i) q^{94} +(-4.06687 + 12.5165i) q^{95} +(-3.33337 + 13.3818i) q^{96} +(13.9017 - 10.1001i) q^{97} +1.99115 q^{98} +(-2.35558 - 9.66702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

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