LMFDB - Embedded newform 231.2.s.a.8.6

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			8.6
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61087 + 1.17037i) q^{2} +(1.32659 + 1.11363i) q^{3} +(0.607116 - 1.86851i) q^{4} +(-2.20177 + 3.03048i) q^{5} +(-3.44031 - 0.241324i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(-0.0217402 - 0.0669093i) q^{8} +(0.519657 + 2.95465i) q^{9} +O(q^{10})$	\(q+(-1.61087 + 1.17037i) q^{2} +(1.32659 + 1.11363i) q^{3} +(0.607116 - 1.86851i) q^{4} +(-2.20177 + 3.03048i) q^{5} +(-3.44031 - 0.241324i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(-0.0217402 - 0.0669093i) q^{8} +(0.519657 + 2.95465i) 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} +(-6.29567 + 1.56823i) q^{15} +(3.29223 + 2.39194i) q^{16} +(3.31846 + 2.41100i) q^{17} +(-4.29513 - 4.15137i) 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} +(0.0456720 - 0.112971i) q^{24} +(-2.79092 - 8.58957i) q^{25} +(-0.565684 - 0.183802i) q^{26} +(-2.60102 + 4.49830i) q^{27} +(-1.15480 + 1.58945i) q^{28} +(2.29911 - 7.07593i) q^{29} +(8.30612 - 9.89446i) q^{30} +(-6.16968 + 4.48253i) q^{31} -7.96210 q^{32} +(-0.166111 - 5.74216i) q^{33} -8.16736 q^{34} +(3.03048 - 2.20177i) q^{35} +(5.83628 + 0.822830i) q^{36} +(-1.20809 + 3.71813i) q^{37} +(4.11194 - 5.65960i) q^{38} +(-0.0362043 + 0.516130i) q^{39} +(0.250634 + 0.0814360i) q^{40} +(2.68816 + 8.27330i) q^{41} +(3.19736 + 1.29263i) 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} +(1.70368 + 6.83944i) q^{48} +(0.809017 + 0.587785i) q^{49} +(14.5488 + 10.5703i) q^{50} +(1.71725 + 6.89393i) 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} +(-5.64173 - 2.28084i) q^{57} +(4.57787 + 14.0892i) q^{58} +(3.03813 + 0.987149i) q^{59} +(-0.891947 + 12.7156i) q^{60} +(-2.05856 + 2.83337i) q^{61} +(4.69235 - 14.4416i) q^{62} +(0.418814 - 2.97062i) q^{63} +(6.24147 - 4.53470i) q^{64} -1.11897 q^{65} +(6.98802 + 9.05547i) q^{66} +11.4951 q^{67} +(6.51966 - 4.73681i) q^{68} +(-0.877780 + 1.04563i) q^{69} +(-2.30483 + 7.09355i) q^{70} +(-9.30701 + 12.8100i) q^{71} +(0.186396 - 0.0990044i) q^{72} +(12.5288 + 4.07086i) q^{73} +(-2.40549 - 7.40335i) q^{74} +(5.86321 - 14.5029i) 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} +(-8.45991 + 3.07081i) q^{81} +(-14.0131 - 10.1811i) q^{82} +(-4.52689 - 3.28898i) q^{83} +(-3.30200 + 0.822517i) 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} +(22.0375 - 3.87591i) q^{90} +(-0.0923095 - 0.284099i) q^{91} +(1.47279 + 0.478538i) q^{92} +(-13.1765 - 0.924276i) q^{93} +(-0.294998 + 0.406030i) q^{94} +(4.06687 - 12.5165i) q^{95} +(-10.5624 - 8.86684i) q^{96} +(13.9017 - 10.1001i) q^{97} -1.99115 q^{98} +(6.17428 - 7.80245i) 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	−0.986988	−	0.160795i	$-0.948594\pi$
$2$	−1.61087	+	1.17037i	−1.13906	+	0.827574i	−0.152071	+	0.988370i	$0.548594\pi$
$3$	1.32659	+	1.11363i	0.765904	+	0.642955i
$3$	1.32659	+	1.11363i	0.765904	+	0.642955i
$4$	0.607116	−	1.86851i	0.303558	−	0.934255i
$5$	−2.20177	+	3.03048i	−0.984663	+	1.35527i	−0.0503833	+	0.998730i	$0.516044\pi$
$5$	−2.20177	+	3.03048i	−0.984663	+	1.35527i	−0.934279	+	0.356542i	$0.883956\pi$
$6$	−3.44031	−	0.241324i	−1.40450	−	0.0985200i
$7$	−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
$9$	0.519657	+	2.95465i	0.173219	+	0.984883i
$10$		−	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
$15$	−6.29567	+	1.56823i	−1.62554	+	0.404915i
$16$	3.29223	+	2.39194i	0.823057	+	0.597986i
$17$	3.31846	+	2.41100i	0.804844	+	0.584753i	0.912331	−	0.409453i	$-0.134281\pi$
$17$	3.31846	+	2.41100i	0.804844	+	0.584753i	−0.107487	+	0.994206i	$0.534281\pi$
$18$	−4.29513	−	4.15137i	−1.01237	−	0.978488i
$19$	−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	$0.0261873\pi$
$23$			0.788215i			0.164354i	−0.996618	+	0.0821771i	$0.973813\pi$
$24$	0.0456720	−	0.112971i	0.00932277	−	0.0230602i
$25$	−2.79092	−	8.58957i	−0.558184	−	1.71791i
$26$	−0.565684	−	0.183802i	−0.110940	−	0.0360465i
$27$	−2.60102	+	4.49830i	−0.500566	+	0.865698i
$28$	−1.15480	+	1.58945i	−0.218237	+	0.300378i
$29$	2.29911	−	7.07593i	0.426934	−	1.31397i	−0.474196	−	0.880419i	$-0.657261\pi$
$29$	2.29911	−	7.07593i	0.426934	−	1.31397i	0.901130	−	0.433549i	$-0.142739\pi$
$30$	8.30612	−	9.89446i	1.51648	−	1.80647i
$31$	−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
$33$	−0.166111	−	5.74216i	−0.0289162	−	0.999582i
$34$	−8.16736			−1.40069
$35$	3.03048	−	2.20177i	0.512245	−	0.372167i
$36$	5.83628	+	0.822830i	0.972714	+	0.137138i
$37$	−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
$39$	−0.0362043	+	0.516130i	−0.00579733	+	0.0826469i
$40$	0.250634	+	0.0814360i	0.0396287	+	0.0128762i
$41$	2.68816	+	8.27330i	0.419820	+	1.29207i	0.907868	+	0.419256i	$0.137709\pi$
$41$	2.68816	+	8.27330i	0.419820	+	1.29207i	−0.488049	+	0.872816i	$0.662291\pi$
$42$	3.19736	+	1.29263i	0.493363	+	0.199457i
$43$			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	−0.291481	−	0.956576i	$-0.594148\pi$
$47$	0.239719	−	0.0778895i	0.0349667	−	0.0113614i	0.326448	+	0.945215i	$0.394148\pi$
$48$	1.70368	+	6.83944i	0.245905	+	0.987188i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	14.5488	+	10.5703i	2.05751	+	1.49487i
$51$	1.71725	+	6.89393i	0.240464	+	0.965343i
$52$	0.558161	−	0.181357i	0.0774030	−	0.0251497i
$53$	4.16475	+	5.73229i	0.572072	+	0.787390i	0.992798	−	0.119798i	$-0.0382246\pi$
$53$	4.16475	+	5.73229i	0.572072	+	0.787390i	−0.420726	+	0.907188i	$0.638225\pi$
$54$	−1.07476	−	10.2903i	−0.146256	−	1.40034i
$55$	12.3629	−	1.22733i	1.66701	−	0.165494i
$56$			0.0703526i			0.00940126i
$57$	−5.64173	−	2.28084i	−0.747266	−	0.302104i
$58$	4.57787	+	14.0892i	0.601103	+	1.85001i
$59$	3.03813	+	0.987149i	0.395531	+	0.128516i	0.500028	−	0.866009i	$-0.333323\pi$
$59$	3.03813	+	0.987149i	0.395531	+	0.128516i	−0.104497	+	0.994525i	$0.533323\pi$
$60$	−0.891947	+	12.7156i	−0.115150	+	1.64158i
$61$	−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
$63$	0.418814	−	2.97062i	0.0527656	−	0.374263i
$64$	6.24147	−	4.53470i	0.780184	−	0.566837i
$65$	−1.11897			−0.138791
$66$	6.98802	+	9.05547i	0.860166	+	1.11465i
$67$	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
$69$	−0.877780	+	1.04563i	−0.105672	+	0.125880i
$70$	−2.30483	+	7.09355i	−0.275480	+	0.847841i
$71$	−9.30701	+	12.8100i	−1.10454	+	1.52027i	−0.275312	+	0.961355i	$0.588781\pi$
$71$	−9.30701	+	12.8100i	−1.10454	+	1.52027i	−0.829227	+	0.558912i	$0.811219\pi$
$72$	0.186396	−	0.0990044i	0.0219670	−	0.0116678i
$73$	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
$75$	5.86321	−	14.5029i	0.677025	−	1.67465i
$76$			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
$81$	−8.45991	+	3.07081i	−0.939990	+	0.341201i
$82$	−14.0131	−	10.1811i	−1.54748	−	1.12431i
$83$	−4.52689	−	3.28898i	−0.496891	−	0.361012i	0.310937	−	0.950430i	$-0.399357\pi$
$83$	−4.52689	−	3.28898i	−0.496891	−	0.361012i	−0.807828	+	0.589418i	$0.799357\pi$
$84$	−3.30200	+	0.822517i	−0.360278	+	0.0897440i
$85$	−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	$0.0903195\pi$
$89$			5.28218i			0.559910i	−0.960013	+	0.279955i	$0.909681\pi$
$90$	22.0375	−	3.87591i	2.32296	−	0.408557i
$91$	−0.0923095	−	0.284099i	−0.00967666	−	0.0297817i
$92$	1.47279	+	0.478538i	0.153549	+	0.0498910i
$93$	−13.1765	−	0.924276i	−1.36634	−	0.0958429i
$94$	−0.294998	+	0.406030i	−0.0304267	+	0.0418788i
$95$	4.06687	−	12.5165i	0.417252	−	1.28417i
$96$	−10.5624	−	8.86684i	−1.07802	−	0.904968i
$97$	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
$99$	6.17428	−	7.80245i	0.620539	−	0.784176i
$100$	−17.7441			−1.77441
$101$	−3.61972	+	2.62988i	−0.360176	+	0.261683i	−0.753125	−	0.657877i	$-0.771455\pi$
$101$	−3.61972	+	2.62988i	−0.360176	+	0.261683i	0.392950	+	0.919560i	$0.371455\pi$
$102$	−10.8347	−	9.09542i	−1.07280	−	0.900581i
$103$	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
$105$	6.47215	+	0.453994i	0.631617	+	0.0443053i
$106$	−13.4178	−	4.35969i	−1.30325	−	0.423451i
$107$	−2.01950	−	6.21538i	−0.195232	−	0.600863i	−0.999974	−	0.00723791i	$-0.997696\pi$
$107$	−2.01950	−	6.21538i	−0.195232	−	0.600863i	0.804741	−	0.593625i	$-0.202304\pi$
$108$	6.82600	+	7.59101i	0.656832	+	0.730446i
$109$		−	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	0.300235	−	0.953865i	$-0.402935\pi$
$113$	11.7335	−	3.81246i	1.10380	−	0.358646i	0.803563	+	0.595220i	$0.202935\pi$
$114$	11.7575	−	2.92876i	1.10119	−	0.274304i
$115$	−2.38867	−	1.73547i	−0.222745	−	0.161833i
$116$	−11.8256	−	8.59182i	−1.09798	−	0.797731i
$117$	−0.622805	+	0.644372i	−0.0575784	+	0.0595722i
$118$	−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
$123$	−5.64732	+	13.9688i	−0.509202	+	1.25953i
$124$	4.62995	+	14.2495i	0.415782	+	1.27964i
$125$	14.3628	+	4.66675i	1.28465	+	0.417407i
$126$	2.80206	+	5.27546i	0.249628	+	0.469975i
$127$	−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
$129$	−4.23002	+	5.03891i	−0.372432	+	0.443651i
$130$	1.80251	−	1.30960i	0.158091	−	0.114860i
$131$	8.94307			0.781359			0.390680	−	0.920527i	$-0.372240\pi$
$131$	8.94307			0.781359			0.390680	+	0.920527i	$0.372240\pi$
$132$	−10.8301	−	3.17578i	−0.942642	−	0.276416i
$133$	3.51337			0.304648
$134$	−18.5172	+	13.4535i	−1.59964	+	1.16221i
$135$	−7.90516	−	17.7866i	−0.680368	−	1.53082i
$136$	0.0891746	−	0.274451i	0.00764666	−	0.0235340i
$137$	1.60625	−	2.21081i	0.137231	−	0.188882i	−0.734870	−	0.678208i	$-0.762757\pi$
$137$	1.60625	−	2.21081i	0.137231	−	0.188882i	0.872101	+	0.489325i	$0.162757\pi$
$138$	0.190215	−	2.71171i	0.0161922	−	0.230836i
$139$	−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
$141$	0.404748	+	0.163631i	0.0340859	+	0.0137803i
$142$		−	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
$147$	0.418655	+	1.68069i	0.0345301	+	0.138621i
$148$	6.21391	+	4.51467i	0.510781	+	0.371104i
$149$	−0.668495	−	0.485690i	−0.0547652	−	0.0397893i	0.560066	−	0.828448i	$-0.310776\pi$
$149$	−0.668495	−	0.485690i	−0.0547652	−	0.0397893i	−0.614831	+	0.788659i	$0.710776\pi$
$150$	7.52878	+	30.2243i	0.614722	+	2.46781i
$151$	−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
$156$	0.942413	+	0.380998i	0.0754534	+	0.0305043i
$157$	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
$159$	−0.858750	+	12.2424i	−0.0681033	+	0.970882i
$160$	17.5307	−	24.1290i	1.38593	−	1.90756i
$161$	0.243572	−	0.749637i	0.0191962	−	0.0590797i
$162$	10.0339	−	14.8479i	0.788335	−	1.16656i
$163$	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
$165$	17.7672	+	12.1395i	1.38318	+	0.945062i
$166$	11.1416			0.864752
$167$	10.7849	−	7.83566i	0.834558	−	0.606342i	−0.0862875	−	0.996270i	$-0.527500\pi$
$167$	10.7849	−	7.83566i	0.834558	−	0.606342i	0.920845	+	0.389929i	$0.127500\pi$
$168$	−0.0783468	+	0.0933287i	−0.00604458	+	0.00720047i
$169$	3.98965	−	12.2789i	0.306896	−	0.944528i
$170$	17.9827	−	24.7510i	1.37921	−	1.89832i
$171$	−4.94423	−	9.30853i	−0.378095	−	0.711841i
$172$	7.09736	+	2.30607i	0.541168	+	0.175836i
$173$	0.808208	+	2.48741i	0.0614469	+	0.189114i	0.977068	−	0.212929i	$-0.0683002\pi$
$173$	0.808208	+	2.48741i	0.0614469	+	0.189114i	−0.915621	+	0.402043i	$0.868300\pi$
$174$	−9.61725	+	23.7886i	−0.729082	+	1.80341i
$175$			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	−0.622302	−	0.782777i	$-0.713802\pi$
$179$	−8.90579	+	2.89367i	−0.665650	+	0.216283i	−0.0433479	+	0.999060i	$0.513802\pi$
$180$	−15.3437	+	15.8751i	−1.14365	+	1.18326i
$181$	−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
$183$	−5.88618	+	1.46623i	−0.435119	+	0.108387i
$184$	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
$189$	3.86377	−	3.47438i	0.281048	−	0.252724i
$190$	8.09774	+	24.9223i	0.587472	+	1.80805i
$191$	7.69797	+	2.50122i	0.557005	+	0.180982i	0.573973	−	0.818874i	$-0.305401\pi$
$191$	7.69797	+	2.50122i	0.557005	+	0.180982i	−0.0169679	+	0.999856i	$0.505401\pi$
$192$	13.3298	+	0.935031i	0.961997	+	0.0674800i
$193$	−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
$195$	−1.48441	−	1.24612i	−0.106301	−	0.0892362i
$196$	1.58945	−	1.15480i	0.113532	−	0.0824859i
$197$	−17.5051			−1.24719			−0.623594	−	0.781749i	$-0.714328\pi$
$197$	−17.5051			−1.24719			−0.623594	+	0.781749i	$0.714328\pi$
$198$	−0.814245	+	19.7949i	−0.0578659	+	1.40676i
$199$	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
$201$	15.2492	+	12.8013i	1.07560	+	0.902934i
$202$	2.75298	−	8.47280i	0.193699	−	0.596144i
$203$	−4.37317	+	6.01915i	−0.306936	+	0.422461i
$204$	13.9239	+	0.976706i	0.974871	+	0.0683831i
$205$	−30.9908	−	10.0695i	−2.16449	−	0.703285i
$206$	5.96500	+	18.3584i	0.415601	+	1.27909i
$207$	−2.32890	+	0.409601i	−0.161870	+	0.0284693i
$208$			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
$213$	−26.6121	+	6.62899i	−1.82343	+	0.454211i
$214$	10.5274	+	7.64862i	0.719640	+	0.522849i
$215$	−11.5110	−	8.36322i	−0.785043	−	0.570367i
$216$	0.357525	+	0.0762385i	0.0243265	+	0.00518738i
$217$	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
$222$	5.05350	−	12.5000i	0.339169	−	0.838945i
$223$	−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
$225$	23.9289	−	12.7098i	1.59526	−	0.847322i
$226$	−14.4392	+	19.8739i	−0.960484	+	1.32199i
$227$	6.12999	−	18.8662i	0.406862	−	1.25219i	−0.512469	−	0.858706i	$-0.671269\pi$
$227$	6.12999	−	18.8662i	0.406862	−	1.25219i	0.919331	−	0.393486i	$-0.128731\pi$
$228$	−7.68695	+	9.15690i	−0.509081	+	0.606431i
$229$	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
$231$	−1.61644	+	5.51245i	−0.106354	+	0.362693i
$232$	−0.523429			−0.0343648
$233$	−9.27475	+	6.73850i	−0.607609	+	0.441454i	−0.848572	−	0.529081i	$-0.822537\pi$
$233$	−9.27475	+	6.73850i	−0.607609	+	0.441454i	0.240962	+	0.970534i	$0.422537\pi$
$234$	0.249109	−	1.76691i	0.0162847	−	0.115507i
$235$	−0.291765	+	0.897960i	−0.0190326	+	0.0585764i
$236$	3.68899	−	5.07746i	0.240133	−	0.330515i
$237$	0.318910	−	4.54639i	0.0207154	−	0.295320i
$238$	7.76762	+	2.52385i	0.503500	+	0.163597i
$239$	6.48632	+	19.9628i	0.419565	+	1.29129i	0.908103	+	0.418746i	$0.137530\pi$
$239$	6.48632	+	19.9628i	0.419565	+	1.29129i	−0.488538	+	0.872543i	$0.662470\pi$
$240$	−24.4779	−	9.89592i	−1.58004	−	0.638779i
$241$			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
$246$	−7.25156	−	29.1115i	−0.462343	−	1.85608i
$247$	−0.849075	−	0.616889i	−0.0540253	−	0.0392517i
$248$	0.434053	+	0.315358i	0.0275624	+	0.0200253i
$249$	−2.34260	−	9.40439i	−0.148456	−	0.595979i
$250$	−28.5984	+	9.29219i	−1.80872	+	0.587690i
$251$	−9.72966	−	13.3917i	−0.614131	−	0.845279i	0.382778	−	0.923840i	$-0.374967\pi$
$251$	−9.72966	−	13.3917i	−0.614131	−	0.845279i	−0.996909	+	0.0785616i	$0.974967\pi$
$252$	−5.29637	−	2.58607i	−0.333640	−	0.162907i
$253$	1.95280	−	1.73801i	0.122771	−	0.109268i
$254$		−	34.8023i		−	2.18369i
$255$	−24.6729	−	9.97476i	−1.54508	−	0.624644i
$256$	5.11431	+	15.7402i	0.319644	+	0.983764i
$257$	20.6355	+	6.70487i	1.28721	+	0.418238i	0.871112	−	0.491084i	$-0.163399\pi$
$257$	20.6355	+	6.70487i	1.28721	+	0.418238i	0.416093	+	0.909322i	$0.363399\pi$
$258$	0.916645	−	13.0677i	0.0570678	−	0.813560i
$259$	2.29793	−	3.16283i	0.142787	−	0.196529i
$260$	−0.679343	+	2.09080i	−0.0421311	+	0.129666i
$261$	22.1017	+	3.11601i	1.36806	+	0.192876i
$262$	−14.4061	+	10.4667i	−0.890014	+	0.646633i
$263$	4.58300			0.282600			0.141300	−	0.989967i	$-0.454872\pi$
$263$	4.58300			0.282600			0.141300	+	0.989967i	$0.454872\pi$
$264$	−0.380593	+	0.135950i	−0.0234239	+	0.00836713i
$265$	−26.5414			−1.63043
$266$	−5.65960	+	4.11194i	−0.347012	+	0.252119i
$267$	−5.88239	+	7.00726i	−0.359996	+	0.428837i
$268$	6.97886	−	21.4787i	0.426302	−	1.31202i
$269$	13.6550	−	18.7945i	0.832562	−	1.14592i	−0.154878	−	0.987934i	$-0.549499\pi$
$269$	13.6550	−	18.7945i	0.832562	−	1.14592i	0.987441	−	0.157990i	$-0.0505015\pi$
$270$	33.5510	+	19.3999i	2.04185	+	1.18064i
$271$	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
$273$	0.193925	−	0.479681i	0.0117369	−	0.0290316i
$274$			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
$279$	−16.4504	−	15.8999i	−0.984862	−	0.951900i
$280$	−0.213202	−	0.154900i	−0.0127413	−	0.00925707i
$281$	9.70482	+	7.05096i	0.578941	+	0.420625i	0.838342	−	0.545145i	$-0.183525\pi$
$281$	9.70482	+	7.05096i	0.578941	+	0.420625i	−0.259401	+	0.965770i	$0.583525\pi$
$282$	−0.843506	+	0.210115i	−0.0502301	+	0.0125121i
$283$	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
$288$	−4.13756	−	23.5252i	−0.243808	−	1.38624i
$289$	−0.0540569	−	0.166370i	−0.00317982	−	0.00978648i
$290$	−52.7765	−	17.1481i	−3.09915	−	1.00697i
$291$	29.6896	+	2.08260i	1.74043	+	0.122084i
$292$	15.2129	−	20.9387i	0.890266	−	1.22535i
$293$	−2.65423	+	8.16889i	−0.155062	+	0.477232i	−0.998167	−	0.0605169i	$-0.980725\pi$
$293$	−2.65423	+	8.16889i	−0.155062	+	0.477232i	0.843105	+	0.537749i	$0.180725\pi$
$294$	−2.64143	−	2.21740i	−0.154051	−	0.129321i
$295$	−9.68081	+	7.03352i	−0.563638	+	0.409507i
$296$	0.275042			0.0159865
$297$	16.8798	−	3.47475i	0.979463	−	0.201626i
$298$	1.64530			0.0953094
$299$	−0.190487	+	0.138397i	−0.0110162	+	0.00800372i
$300$	−23.5391	−	19.7604i	−1.35903	−	1.14087i
$301$	1.17377	−	3.61250i	0.0676551	−	0.208221i
$302$	10.1279	−	13.9398i	0.582795	−	0.802148i
$303$	−7.73058	−	0.542268i	−0.444110	−	0.0311525i
$304$	−13.5976	−	4.41813i	−0.779877	−	0.253397i
$305$	−4.05398	−	12.4769i	−0.232130	−	0.714423i
$306$	−4.24423	−	24.1317i	−0.242626	−	1.37952i
$307$		−	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	0.190672	−	0.981654i	$-0.438933\pi$
$311$	16.2584	−	5.28268i	0.921931	−	0.299554i	0.731259	+	0.682100i	$0.238933\pi$
$312$	0.0353210	−	0.00879833i	0.00199966	−	0.000498107i
$313$	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
$315$	8.08028	+	7.80984i	0.455272	+	0.440035i
$316$	−4.91662	+	1.59751i	−0.276582	+	0.0898668i
$317$	0.682815	+	0.939815i	0.0383507	+	0.0527853i	0.827762	−	0.561080i	$-0.189614\pi$
$317$	0.682815	+	0.939815i	0.0383507	+	0.0527853i	−0.789411	+	0.613865i	$0.789614\pi$
$318$	−12.9447	−	20.7259i	−0.725903	−	1.16225i
$319$	−22.6001	+	9.90641i	−1.26536	+	0.554652i
$320$			28.8990i			1.61550i
$321$	4.24259	−	10.4942i	0.236799	−	0.585729i
$322$	0.484987	+	1.49264i	0.0270273	+	0.0831815i
$323$	−13.7059	−	4.45333i	−0.762619	−	0.247790i
$324$	0.601689	+	17.6718i	0.0334272	+	0.981765i
$325$	1.58580	−	2.18266i	0.0879642	−	0.121072i
$326$	−11.1070	+	34.1839i	−0.615162	+	1.89327i
$327$	15.5958	−	18.5781i	0.862451	−	1.02737i
$328$	0.495120	−	0.359725i	0.0273384	−	0.0198625i
$329$	−0.252056			−0.0138963
$330$	−42.8285	+	1.23895i	−2.35763	+	0.0682022i
$331$	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
$333$	−11.6136	−	1.63734i	−0.636420	−	0.0897259i
$334$	−8.20243	+	25.2445i	−0.448817	+	1.38132i
$335$	−25.3096	+	34.8357i	−1.38281	+	1.90328i
$336$	0.493206	−	7.03116i	0.0269066	−	0.383581i
$337$	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
$339$	19.8112	+	8.00926i	1.07600	+	0.435004i
$340$			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
$345$	−1.23610	−	4.96234i	−0.0665495	−	0.267164i
$346$	−4.21310	−	3.06100i	−0.226498	−	0.164560i
$347$	−9.89554	−	7.18953i	−0.531221	−	0.385954i	0.289594	−	0.957150i	$-0.406480\pi$
$347$	−9.89554	−	7.18953i	−0.531221	−	0.385954i	−0.820814	+	0.571195i	$0.806480\pi$
$348$	−6.11959	−	24.5672i	−0.328045	−	1.31694i
$349$	−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	$0.200672\pi$
$353$			22.1511i			1.17898i	−0.807774	+	0.589492i	$0.799328\pi$
$354$	−10.2139	−	4.12927i	−0.542863	−	0.219468i
$355$	−18.3285	−	56.4094i	−0.972777	−	2.99390i
$356$	9.86980	+	3.20689i	0.523098	+	0.169965i
$357$	0.497136	−	7.08718i	0.0263112	−	0.375093i
$358$	10.9594	−	15.0844i	0.579224	−	0.797233i
$359$	5.52281	−	16.9975i	0.291483	−	0.897092i	−0.692897	−	0.721036i	$-0.743666\pi$
$359$	5.52281	−	16.9975i	0.291483	−	0.897092i	0.984380	−	0.176056i	$-0.0563339\pi$
$360$	−0.110371	+	0.782855i	−0.00581707	+	0.0412601i
$361$	−5.38498	+	3.91242i	−0.283420	+	0.205917i
$362$	6.18392			0.325019
$363$	−13.8599	+	13.0730i	−0.727455	+	0.686155i
$364$	−0.586885			−0.0307611
$365$	−39.9223	+	29.0052i	−2.08963	+	1.51820i
$366$	7.76586	−	9.25090i	0.405928	−	0.483552i
$367$	−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
$369$	−23.0478	+	12.2418i	−1.19982	+	0.637285i
$370$	27.7321	+	9.01069i	1.44172	+	0.468444i
$371$	−2.18954	−	6.73871i	−0.113675	−	0.349856i
$372$	−9.72667	+	24.0593i	−0.504304	+	1.24741i
$373$			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
$378$	−2.15773	+	10.1188i	−0.110982	+	0.520455i
$379$	−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
$381$	−29.3760	+	7.31747i	−1.50498	+	0.374885i
$382$	−15.3278	+	4.98030i	−0.784238	+	0.254814i
$383$	−8.87679	−	12.2179i	−0.453583	−	0.624303i	0.519580	−	0.854422i	$-0.326089\pi$
$383$	−8.87679	−	12.2179i	−0.453583	−	0.624303i	−0.973163	+	0.230119i	$0.926089\pi$
$384$	0.826690	−	0.516323i	0.0421868	−	0.0263485i
$385$	−12.1371	−	2.65308i	−0.618563	−	0.135214i
$386$		−	3.13178i		−	0.159403i
$387$	−11.2230	+	1.97387i	−0.570495	+	0.100337i
$388$	−10.4323	−	32.1073i	−0.529620	−	1.63000i
$389$	16.7364	+	5.43800i	0.848571	+	0.275718i	0.700848	−	0.713311i	$-0.252805\pi$
$389$	16.7364	+	5.43800i	0.848571	+	0.275718i	0.147724	+	0.989029i	$0.452805\pi$
$390$	3.84960	+	0.270033i	0.194932	+	0.0136737i
$391$	−1.90039	+	2.61566i	−0.0961067	+	0.132279i
$392$	0.0217402	−	0.0669093i	0.00109804	−	0.00337943i
$393$	11.8637	+	9.95927i	0.598447	+	0.502379i
$394$	28.1985	−	20.4874i	1.42062	−	1.03214i
$395$	9.85656			0.495937
$396$	−10.8305	−	16.2737i	−0.544251	−	0.817784i
$397$	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
$399$	4.66079	+	3.91260i	0.233331	+	0.195875i
$400$	11.3574	−	34.9546i	0.567871	−	1.74773i
$401$	−3.61909	+	4.98125i	−0.180729	+	0.248752i	−0.889764	−	0.456422i	$-0.849131\pi$
$401$	−3.61909	+	4.98125i	−0.180729	+	0.248752i	0.709035	+	0.705173i	$0.249131\pi$
$402$	−39.5468	−	2.77404i	−1.97242	−	0.138357i
$403$	−2.16658	−	0.703965i	−0.107925	−	0.0350670i
$404$	2.71637	+	8.36012i	0.135144	+	0.415932i
$405$	9.32078	−	32.3988i	0.463153	−	1.60991i
$406$		−	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
$411$	4.59285	−	1.14406i	0.226549	−	0.0564325i
$412$	−15.4089	−	11.1952i	−0.759141	−	0.551548i
$413$	−2.58439	−	1.87767i	−0.127169	−	0.0923940i
$414$	3.27218	−	3.38548i	0.160819	−	0.166387i
$415$	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	$-0.917944\pi$
$419$		−	10.4370i		−	0.509883i	0.966957	−	0.254941i	$-0.0820562\pi$
$420$	4.77764	−	11.8176i	0.233125	−	0.576642i
$421$	−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
$423$	0.354708	+	0.667811i	0.0172465	+	0.0324701i
$424$	0.293001	−	0.403281i	0.0142294	−	0.0195851i
$425$	11.4479	−	35.2330i	0.555305	−	1.70905i
$426$	35.1104	−	41.8244i	1.70110	−	2.02640i
$427$	2.83337	−	2.05856i	0.137116	−	0.0996208i
$428$	−12.8396			−0.620624
$429$	1.35854	−	1.04837i	0.0655908	−	0.0506158i
$430$	28.3308			1.36623
$431$	31.7487	−	23.0668i	1.52928	−	1.11109i	0.572647	−	0.819802i	$-0.305917\pi$
$431$	31.7487	−	23.0668i	1.52928	−	1.11109i	0.956636	−	0.291287i	$-0.0940833\pi$
$432$	−19.3228	+	8.58794i	−0.929670	+	0.413188i
$433$	−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
$435$	−3.37775	+	48.1533i	−0.161951	+	2.30877i
$436$	−26.1675	−	8.50234i	−1.25320	−	0.407188i
$437$	−0.855759	−	2.63376i	−0.0409365	−	0.125990i
$438$	−42.1207	−	17.0285i	−2.01260	−	0.813655i
$439$			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	−0.647224	−	0.762300i	$-0.724070\pi$
$443$	−15.2126	+	4.94287i	−0.722771	+	0.234843i	−0.0755470	+	0.997142i	$0.524070\pi$
$444$	3.21561	+	12.9091i	0.152606	+	0.612639i
$445$	−16.0075	−	11.6302i	−0.758830	−	0.551322i
$446$	11.0352	+	8.01752i	0.522530	+	0.379640i
$447$	−0.345937	−	1.38877i	−0.0163622	−	0.0656863i
$448$	−7.33729	+	2.38403i	−0.346654	+	0.112635i
$449$	4.54944	+	6.26176i	0.214701	+	0.295511i	0.902760	−	0.430144i	$-0.141537\pi$
$449$	4.54944	+	6.26176i	0.214701	+	0.295511i	−0.688059	+	0.725654i	$0.741537\pi$
$450$	−23.6712	+	48.4794i	−1.11587	+	2.28534i
$451$	14.5696	−	24.9025i	0.686058	−	1.17261i
$452$		−	24.2388i		−	1.14010i
$453$	−13.8958	−	5.61781i	−0.652884	−	0.263948i
$454$	12.2057	+	37.5653i	0.572842	+	1.76303i
$455$	1.06420	+	0.345780i	0.0498906	+	0.0162104i
$456$	−0.0299572	+	0.427070i	−0.00140287	+	0.0199994i
$457$	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
$459$	−19.4768	+	8.65636i	−0.909097	+	0.404044i
$460$	−4.69294	+	3.40962i	−0.218810	+	0.158974i
$461$	−16.3433			−0.761184			−0.380592	−	0.924743i	$-0.624280\pi$
$461$	−16.3433			−0.761184			−0.380592	+	0.924743i	$0.624280\pi$
$462$	−3.84770	−	10.7717i	−0.179011	−	0.501144i
$463$	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
$465$	31.8126	−	37.8960i	1.47528	−	1.75739i
$466$	7.05392	−	21.7097i	0.326766	−	1.00568i
$467$	−12.9077	+	17.7659i	−0.597296	+	0.822108i	−0.995457	−	0.0952075i	$-0.969649\pi$
$467$	−12.9077	+	17.7659i	−0.597296	+	0.822108i	0.398161	+	0.917316i	$0.369649\pi$
$468$	0.825900	+	1.55493i	0.0381772	+	0.0718765i
$469$	−10.9325	−	3.55219i	−0.504816	−	0.164025i
$470$	−0.580947	−	1.78797i	−0.0267971	−	0.0824729i
$471$	−10.0136	+	24.7691i	−0.461404	+	1.14130i
$472$		−	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
$477$	−14.7727	+	15.2842i	−0.676393	+	0.699815i
$478$	−33.8125	−	24.5662i	−1.54655	−	1.12363i
$479$	5.09714	+	3.70329i	0.232894	+	0.169207i	0.698112	−	0.715989i	$-0.254024\pi$
$479$	5.09714	+	3.70329i	0.232894	+	0.169207i	−0.465218	+	0.885196i	$0.654024\pi$
$480$	50.1268	−	12.4864i	2.28796	−	0.569924i
$481$	−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
$486$	29.8458	−	8.52297i	1.35383	−	0.386610i
$487$	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
$489$	31.1894	+	2.18781i	1.41043	+	0.0989360i
$490$	4.38405	−	6.03413i	0.198051	−	0.272594i
$491$	−7.13467	+	21.9583i	−0.321983	+	0.990962i	0.650801	+	0.759248i	$0.274433\pi$
$491$	−7.13467	+	21.9583i	−0.321983	+	0.990962i	−0.972784	+	0.231714i	$0.925567\pi$
$492$	22.6723	+	19.0328i	1.02215	+	0.858064i
$493$	24.6896	−	17.9380i	1.11196	−	0.807888i
$494$	2.08974			0.0940217
$495$	10.0508	+	35.8903i	0.451750	+	1.61315i
$496$	−31.0340			−1.39347
$497$	12.8100	−	9.30701i	0.574607	−	0.417476i
$498$	14.7802	+	12.4076i	0.662317	+	0.555996i
$499$	−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
$501$	23.0331	+	1.61567i	1.02904	+	0.0721829i
$502$	31.3465	+	10.1851i	1.39906	+	0.454583i
$503$	−2.27748	−	7.00938i	−0.101548	−	0.312533i	0.887357	−	0.461083i	$-0.152539\pi$
$503$	−2.27748	−	7.00938i	−0.101548	−	0.312533i	−0.988905	+	0.148551i	$0.952539\pi$
$504$	−0.207867	+	0.0365592i	−0.00925915	+	0.00162848i
$505$		−	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	−0.868571	−	0.495565i	$-0.834961\pi$
$509$	−28.8775	+	9.38287i	−1.27997	+	0.415888i	−0.411402	+	0.911454i	$0.634961\pi$
$510$	51.4190	−	12.8083i	2.27687	−	0.567161i
$511$	−10.6576	−	7.74323i	−0.471467	−	0.342541i
$512$	−25.7498	−	18.7083i	−1.13799	−	0.826800i
$513$	3.80732	−	17.8546i	0.168097	−	0.788300i
$514$	−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
$519$	−1.69790	+	4.19980i	−0.0745294	+	0.184351i
$520$	0.0243265	+	0.0748694i	0.00106679	+	0.00328324i
$521$	−37.3344	−	12.1307i	−1.63565	−	0.531454i	−0.660088	−	0.751188i	$-0.729481\pi$
$521$	−37.3344	−	12.1307i	−1.63565	−	0.531454i	−0.975560	+	0.219734i	$0.929481\pi$
$522$	−39.2498	+	20.8476i	−1.71792	+	0.912473i
$523$	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
$525$	−10.0579	+	11.9812i	−0.438962	+	0.522903i
$526$	−7.38262	+	5.36379i	−0.321897	+	0.233872i
$527$	−31.2812			−1.36263
$528$	13.1880	−	19.3018i	0.573936	−	0.840004i
$529$	22.3787			0.972988
$530$	42.7548	−	31.0632i	1.85715	−	1.34930i
$531$	−1.33789	+	9.48959i	−0.0580596	+	0.411813i
$532$	2.13302	−	6.56477i	0.0924783	−	0.284619i
$533$	−1.52741	+	2.10230i	−0.0661594	+	0.0910606i
$534$	1.27471	−	18.1723i	0.0551623	−	0.786394i
$535$	23.2821	+	7.56480i	1.00657	+	0.327055i
$536$	−0.249905	−	0.769130i	−0.0107943	−	0.0332214i
$537$	−15.0368	−	6.07906i	−0.648884	−	0.262331i
$538$			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
$543$	−1.30022	−	5.21974i	−0.0557977	−	0.224000i
$544$	−26.4219	−	19.1966i	−1.13283	−	0.823049i
$545$	42.4403	+	30.8347i	1.81794	+	1.32081i
$546$	0.249014	+	0.999668i	0.0106568	+	0.0427818i
$547$	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
$552$	0.0890457	+	0.0359994i	0.00379004	+	0.00153224i
$553$	0.813119	+	2.50252i	0.0345773	+	0.106418i
$554$	28.6276	+	9.30166i	1.21627	+	0.395190i
$555$	1.77488	−	25.3027i	0.0753394	−	1.07404i
$556$	−10.3560	+	14.2539i	−0.439193	+	0.604498i
$557$	−10.2472	+	31.5377i	−0.434188	+	1.33629i	0.459728	+	0.888060i	$0.347947\pi$
$557$	−10.2472	+	31.5377i	−0.434188	+	1.33629i	−0.893916	+	0.448234i	$0.852053\pi$
$558$	45.1082	+	6.35960i	1.90958	+	0.269223i
$559$	−0.917958	+	0.666936i	−0.0388255	+	0.0282084i
$560$	15.2435			0.644157
$561$	13.2931	−	19.4556i	0.561236	−	0.821416i
$562$	−23.8854			−1.00755
$563$	−3.35810	+	2.43980i	−0.141527	+	0.102825i	−0.656296	−	0.754504i	$-0.727878\pi$
$563$	−3.35810	+	2.43980i	−0.141527	+	0.102825i	0.514769	+	0.857329i	$0.327878\pi$
$564$	0.551476	−	0.656933i	0.0232213	−	0.0276619i
$565$	−14.2810	+	43.9524i	−0.600806	+	1.84909i
$566$	−11.6822	+	16.0791i	−0.491038	+	0.675856i
$567$	8.99479	−	0.306255i	0.377746	−	0.0128615i
$568$	1.05944	+	0.344234i	0.0444533	+	0.0144437i
$569$	−7.58637	−	23.3484i	−0.318037	−	0.978817i	−0.974486	−	0.224447i	$-0.927942\pi$
$569$	−7.58637	−	23.3484i	−0.318037	−	0.978817i	0.656449	−	0.754370i	$-0.272058\pi$
$570$	−17.0119	+	42.0794i	−0.712548	+	1.76251i
$571$			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
$576$	16.6419	+	16.0849i	0.693411	+	0.670204i
$577$	−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
$579$	−2.64348	+	0.658482i	−0.109859	+	0.0273656i
$580$	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
$585$	−0.581479	−	3.30616i	−0.0240412	−	0.136693i
$586$	−5.28497	−	16.2655i	−0.218320	−	0.671920i
$587$	26.6874	+	8.67127i	1.10151	+	0.357902i	0.802683	−	0.596406i	$-0.203405\pi$
$587$	26.6874	+	8.67127i	1.10151	+	0.357902i	0.298825	+	0.954308i	$0.403405\pi$
$588$	3.39456	+	0.238114i	0.139989	+	0.00981967i
$589$	15.7488	−	21.6764i	0.648919	−	0.893160i
$590$	7.36274	−	22.6602i	0.303119	−	0.932905i
$591$	−23.2220	−	19.4942i	−0.955226	−	0.801885i
$592$	−12.8709	+	9.35125i	−0.528990	+	0.384334i
$593$	−40.1746			−1.64978			−0.824888	−	0.565297i	$-0.808762\pi$
$593$	−40.1746			−1.64978			−0.824888	+	0.565297i	$0.808762\pi$
$594$	−23.1244	+	25.3529i	−0.948805	+	1.04024i
$595$	15.3650			0.629903
$596$	−1.31337	+	0.954219i	−0.0537977	+	0.0390863i
$597$	7.24428	+	6.08136i	0.296489	+	0.248894i
$598$	0.144875	−	0.445880i	0.00592439	−	0.0182334i
$599$	12.2470	−	16.8565i	0.500399	−	0.688739i	−0.481865	−	0.876246i	$-0.660040\pi$
$599$	12.2470	−	16.8565i	0.500399	−	0.688739i	0.982263	+	0.187506i	$0.0600404\pi$
$600$	−1.09784	−	0.0770091i	−0.0448192	−	0.00314388i
$601$	−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
$603$	5.97351	+	33.9640i	0.243260	+	1.38312i
$604$			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
$609$	−12.5045	+	3.11482i	−0.506707	+	0.126219i
$610$	21.1330	+	15.3540i	0.855648	+	0.621665i
$611$	0.0609142	+	0.0442567i	0.00246432	+	0.00179044i
$612$	17.3836	+	16.8018i	0.702691	+	0.679173i
$613$	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	$-0.759580\pi$
$617$		−	34.0553i		−	1.37101i	0.728066	−	0.685507i	$-0.240420\pi$
$618$	−12.5314	+	30.9968i	−0.504085	+	1.24687i
$619$	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
$621$	−3.54563	−	2.05016i	−0.142281	−	0.0822701i
$622$	−20.0076	+	27.5381i	−0.802230	+	1.10418i
$623$	1.63228	−	5.02365i	0.0653960	−	0.201268i
$624$	−1.35375	+	1.61262i	−0.0541932	+	0.0645564i
$625$	−9.23246	+	6.70777i	−0.369298	+	0.268311i
$626$	−24.4257			−0.976248
$627$	6.78927	+	19.0066i	0.271137	+	0.759051i
$628$	30.3047			1.20929
$629$	−12.9734	+	9.42575i	−0.517284	+	0.375829i
$630$	−22.1567	−	3.12377i	−0.882743	−	0.124454i
$631$	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
$633$	1.76995	−	25.2325i	0.0703492	−	1.00290i
$634$	−2.19986	−	0.714777i	−0.0873675	−	0.0283874i
$635$	−20.2321	−	62.2680i	−0.802887	−	2.47103i
$636$	22.3536	+	9.03711i	0.886378	+	0.358345i
$637$			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	−0.524800	−	0.851226i	$-0.675860\pi$
$641$	−11.3686	+	3.69389i	−0.449034	+	0.145900i	0.0757658	+	0.997126i	$0.475860\pi$
$642$	5.44779	+	21.8702i	0.215007	+	0.863148i
$643$	−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
$645$	−5.95677	−	23.9135i	−0.234548	−	0.941594i
$646$	27.2906	−	8.86724i	1.07373	−	0.348877i
$647$	4.13987	+	5.69805i	0.162755	+	0.224013i	0.882604	−	0.470118i	$-0.155789\pi$
$647$	4.13987	+	5.69805i	0.162755	+	0.224013i	−0.719848	+	0.694131i	$0.755789\pi$
$648$	0.389385	+	0.499287i	0.0152965	+	0.0196138i
$649$	−4.25343	−	9.70361i	−0.166962	−	0.380900i
$650$			5.37196i			0.210705i
$651$	12.2460	+	4.95080i	0.479957	+	0.194037i
$652$	−10.9593	−	33.7293i	−0.429200	−	1.32094i
$653$	−0.954875	−	0.310258i	−0.0373671	−	0.0121413i	0.290274	−	0.956944i	$-0.406254\pi$
$653$	−0.954875	−	0.310258i	−0.0373671	−	0.0121413i	−0.327641	+	0.944802i	$0.606254\pi$
$654$	−3.37961	+	48.1798i	−0.132153	+	1.88398i
$655$	−19.6906	+	27.1018i	−0.769375	+	1.05895i
$656$	−10.9392	+	33.6675i	−0.427105	+	1.31449i
$657$	−5.51728	+	39.1337i	−0.215250	+	1.52675i
$658$	0.406030	−	0.294998i	0.0158287	−	0.0115002i
$659$	36.4253			1.41893			0.709464	−	0.704742i	$-0.248937\pi$
$659$	36.4253			1.41893			0.709464	+	0.704742i	$0.248937\pi$
$660$	33.4696	−	25.8282i	1.30280	−	1.00536i
$661$	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
$663$	−1.36453	+	1.62546i	−0.0529940	+	0.0631278i
$664$	−0.121648	+	0.374394i	−0.00472086	+	0.0145293i
$665$	−7.73565	+	10.6472i	−0.299976	+	0.412881i
$666$	20.6243	−	10.9546i	0.799175	−	0.424482i
$667$	5.57736	+	1.81219i	0.215956	+	0.0701684i
$668$	−8.09335	−	24.9088i	−0.313141	−	0.963749i
$669$	4.44721	−	11.0003i	0.171939	−	0.425298i
$670$		−	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
$675$	45.8977	+	9.78723i	1.76660	+	0.376711i
$676$	−20.5210	−	14.9094i	−0.789270	−	0.573438i
$677$	5.86103	+	4.25829i	0.225258	+	0.163659i	0.694690	−	0.719309i	$-0.255541\pi$
$677$	5.86103	+	4.25829i	0.225258	+	0.163659i	−0.469432	+	0.882968i	$0.655541\pi$
$678$	−41.2871	+	10.2845i	−1.58562	+	0.394973i
$679$	−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	$-0.977242\pi$
$683$		−	3.73388i		−	0.142873i	0.997445	−	0.0714365i	$-0.0227583\pi$
$684$	−20.3948	+	3.58699i	−0.779815	+	0.137152i
$685$	3.16322	+	9.73540i	0.120861	+	0.371971i
$686$	1.89369	+	0.615298i	0.0723016	+	0.0234922i
$687$	5.11664	+	0.358911i	0.195212	+	0.0136933i
$688$	−9.08557	+	12.5052i	−0.346384	+	0.476757i
$689$	−0.654058	+	2.01298i	−0.0249176	+	0.0766886i
$690$	7.79897	+	6.54701i	0.296902	+	0.249240i
$691$	−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
$693$	−8.28318	+	5.51261i	−0.314652	+	0.209407i
$694$	24.3548			0.924497
$695$	27.1767	−	19.7450i	1.03087	−	0.748972i
$696$	−0.694373	−	0.582906i	−0.0263201	−	0.0220950i
$697$	−11.0264	+	33.9357i	−0.417654	+	1.28541i
$698$	12.9077	−	17.7659i	0.488564	−	0.672450i
$699$	−19.8079	−	1.38944i	−0.749205	−	0.0525536i
$700$	16.8757	+	5.48323i	0.637840	+	0.207247i
$701$	0.504912	+	1.55396i	0.0190702	+	0.0586922i	0.960139	−	0.279524i	$-0.0901766\pi$
$701$	0.504912	+	1.55396i	0.0190702	+	0.0586922i	−0.941069	+	0.338216i	$0.890177\pi$
$702$	2.29815	−	2.06654i	0.0867380	−	0.0779967i
$703$		−	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
$708$	10.5482	−	2.62752i	0.396425	−	0.0987481i
$709$	−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
$711$	5.48605	−	5.67602i	0.205743	−	0.212867i
$712$	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
$717$	−13.6266	+	33.7058i	−0.508893	+	1.25877i
$718$	10.9967	+	33.8445i	0.410394	+	1.26306i
$719$	−23.5283	−	7.64481i	−0.877457	−	0.285103i	−0.164556	−	0.986368i	$-0.552619\pi$
$719$	−23.5283	−	7.64481i	−0.877457	−	0.285103i	−0.712901	+	0.701264i	$0.752619\pi$
$720$	−21.4516	−	40.3871i	−0.799455	−	1.50514i
$721$	−5.69827	+	7.84300i	−0.212215	+	0.292089i
$722$	4.09555	−	12.6048i	0.152421	−	0.469102i
$723$	−25.4324	+	30.2957i	−0.945841	+	1.12671i
$724$	−4.93636	+	3.58648i	−0.183458	+	0.133290i
$725$	−67.1959			−2.49559
$726$	7.02629	−	37.2801i	0.260770	−	1.38359i
$727$	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
$729$	−13.4694	−	23.4003i	−0.498867	−	0.866678i
$730$	30.3629	−	93.4474i	1.12378	−	3.45864i
$731$	−9.15795	+	12.6048i	−0.338719	+	0.466207i
$732$	−0.833932	+	11.8886i	−0.0308230	+	0.439414i
$733$	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
$735$	−6.01509	−	2.43178i	−0.221870	−	0.0896975i
$736$		−	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
$741$	−0.439384	−	1.76391i	−0.0161412	−	0.0647989i
$742$	11.4138	+	8.29263i	0.419015	+	0.304432i
$743$	9.48201	+	6.88908i	0.347861	+	0.252736i	0.747971	−	0.663731i	$-0.231028\pi$
$743$	9.48201	+	6.88908i	0.347861	+	0.252736i	−0.400110	+	0.916467i	$0.631028\pi$
$744$	0.224616	+	0.901724i	0.00823483	+	0.0330588i
$745$	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
$750$	−48.2863	−	19.5212i	−1.76317	−	0.712813i
$751$	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
$753$	2.00621	−	28.6005i	0.0731102	−	1.04226i
$754$	−2.60114	+	3.58016i	−0.0947279	+	0.130382i
$755$	10.0169	−	30.8288i	0.364552	−	1.12198i
$756$	−4.14616	−	9.32883i	−0.150794	−	0.339286i
$757$	−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
$759$	4.52606	−	0.130931i	0.164285	−	0.00475250i
$760$	−0.925888			−0.0335855
$761$	4.80624	−	3.49194i	0.174226	−	0.126583i	−0.497255	−	0.867605i	$-0.665659\pi$
$761$	4.80624	−	3.49194i	0.174226	−	0.126583i	0.671481	+	0.741022i	$0.265659\pi$
$762$	38.7569	−	46.1683i	1.40402	−	1.67250i
$763$	−4.32762	+	13.3191i	−0.156671	+	0.482182i
$764$	9.34711	−	12.8652i	0.338167	−	0.465447i
$765$	−21.6225	−	40.7089i	−0.781764	−	1.47183i
$766$	28.5987	+	9.29230i	1.03331	+	0.335744i
$767$	0.294881	+	0.907550i	0.0106475	+	0.0327697i
$768$	−10.7442	+	26.5762i	−0.387699	+	0.958986i
$769$			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	−0.380146	−	0.924926i	$-0.624126\pi$
$773$	−4.00453	+	1.30115i	−0.144033	+	0.0467992i	0.236113	+	0.971726i	$0.424126\pi$
$774$	15.7686	−	16.3146i	0.566791	−	0.586417i
$775$	55.7221	+	40.4845i	2.00160	+	1.45425i
$776$	−0.978018	−	0.710571i	−0.0351088	−	0.0255080i
$777$	6.57063	−	1.63672i	0.235720	−	0.0587170i
$778$	−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
$783$	25.8497	+	28.7467i	0.923791	+	1.02732i
$784$	1.25752	+	3.87025i	0.0449114	+	0.138223i
$785$	−54.9518	−	17.8549i	−1.96131	−	0.637269i
$786$	−30.7670	−	2.15817i	−1.09742	−	0.0769795i
$787$	−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
$789$	6.07973	+	5.10376i	0.216444	+	0.181699i
$790$	−15.8777	+	11.5358i	−0.564902	+	0.410425i
$791$	−12.3374			−0.438666
$792$	−0.656286	−	0.243490i	−0.0233201	−	0.00865205i
$793$	−1.04619			−0.0371512
$794$	−15.4944	+	11.2573i	−0.549875	+	0.399508i
$795$	−35.2094	−	29.5573i	−1.24875	−	1.04829i
$796$	3.31536	−	10.2036i	0.117510	−	0.361659i
$797$	5.72593	−	7.88106i	0.202823	−	0.279162i	−0.695474	−	0.718552i	$-0.744805\pi$
$797$	5.72593	−	7.88106i	0.202823	−	0.279162i	0.898296	+	0.439390i	$0.144805\pi$
$798$	−12.0871	−	0.847860i	−0.427879	−	0.0300139i
$799$	0.983290	+	0.319490i	0.0347863	+	0.0113027i
$800$	22.2216	+	68.3911i	0.785652	+	2.41799i
$801$	−15.6070	+	2.74492i	−0.551446	+	0.0969869i
$802$		−	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
$807$	39.0447	−	9.72591i	1.37444	−	0.342368i
$808$	0.254657	+	0.185019i	0.00895879	+	0.00650894i
$809$	5.62121	+	4.08405i	0.197631	+	0.143587i	0.682200	−	0.731166i	$-0.261023\pi$
$809$	5.62121	+	4.08405i	0.197631	+	0.143587i	−0.484569	+	0.874753i	$0.661023\pi$
$810$	22.9039	+	63.0991i	0.804762	+	2.21708i
$811$	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
$816$	−10.8363	+	26.8040i	−0.379346	+	0.938326i
$817$	−4.12390	−	12.6921i	−0.144277	−	0.444039i
$818$	41.0785	+	13.3472i	1.43628	+	0.466675i
$819$	0.791445	−	0.420376i	0.0276553	−	0.0146891i
$820$	−37.6300	+	51.7932i	−1.31410	+	1.80870i
$821$	1.20533	−	3.70963i	0.0420663	−	0.129467i	−0.927818	−	0.373034i	$-0.878318\pi$
$821$	1.20533	−	3.70963i	0.0420663	−	0.129467i	0.969884	+	0.243567i	$0.0783176\pi$
$822$	−6.05952	+	7.21826i	−0.211350	+	0.251766i
$823$	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
$825$	−48.8591	+	17.4527i	−1.70106	+	0.607626i
$826$	6.36068			0.221316
$827$	19.2201	−	13.9642i	0.668347	−	0.485583i	−0.201124	−	0.979566i	$-0.564460\pi$
$827$	19.2201	−	13.9642i	0.668347	−	0.485583i	0.869471	+	0.493983i	$0.164460\pi$
$828$	−0.648567	+	4.60025i	−0.0225393	+	0.159870i
$829$	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
$831$	1.83219	−	26.1198i	0.0635581	−	0.906085i
$832$	2.19179	+	0.712157i	0.0759868	+	0.0246896i
$833$	1.26754	+	3.90108i	0.0439176	+	0.135164i
$834$	28.6733	+	11.5920i	0.992874	+	0.401399i
$835$			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	0.751433	−	0.659810i	$-0.229363\pi$
$839$	50.6080	−	16.4435i	1.74718	−	0.567693i	0.995748	+	0.0921164i	$0.0293632\pi$
$840$	−0.110329	−	0.442917i	−0.00380671	−	0.0152821i
$841$	−21.3215	−	15.4909i	−0.735223	−	0.534170i
$842$	24.0364	+	17.4635i	0.828350	+	0.601832i
$843$	5.02210	+	20.1613i	0.172970	+	0.694391i
$844$	−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
$849$	16.0284	+	6.47995i	0.550093	+	0.222391i
$850$	22.7945	+	70.1541i	0.781844	+	2.40627i
$851$	−2.93069	−	0.952239i	−0.100463	−	0.0326423i
$852$	−3.77031	+	53.7496i	−0.129169	+	1.84143i
$853$	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
$855$	39.0954	+	5.51188i	1.33703	+	0.188502i
$856$	−0.371962	+	0.270247i	−0.0127134	+	0.00923684i
$857$	46.3883			1.58460			0.792298	−	0.610135i	$-0.208885\pi$
$857$	46.3883			1.58460			0.792298	+	0.610135i	$0.208885\pi$
$858$	−0.961453	+	3.27878i	−0.0328235	+	0.111936i
$859$	−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
$861$	9.68753	−	11.5400i	0.330150	−	0.393284i
$862$	−24.1465	+	74.3153i	−0.822434	+	2.53119i
$863$	−2.78770	+	3.83693i	−0.0948943	+	0.130611i	−0.853824	−	0.520562i	$-0.825723\pi$
$863$	−2.78770	+	3.83693i	−0.0948943	+	0.130611i	0.758930	+	0.651172i	$0.225723\pi$
$864$	20.7096	−	35.8159i	0.704554	−	1.21848i
$865$	−9.31753	−	3.02745i	−0.316806	−	0.102936i
$866$	−12.4128	−	38.2028i	−0.421805	−	1.29818i
$867$	0.113564	−	0.280903i	0.00385682	−	0.00953998i
$868$		−	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
$873$	37.0665	+	35.8259i	1.25451	+	1.21252i
$874$	4.46098	+	3.24109i	0.150895	+	0.109632i
$875$	−12.2177	−	8.87669i	−0.413034	−	0.300087i
$876$	43.4992	−	10.8355i	1.46970	−	0.366097i
$877$	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	$-0.917774\pi$
$881$		−	15.1648i		−	0.510915i	0.966820	−	0.255458i	$-0.0822262\pi$
$882$	−1.03471	−	5.88314i	−0.0348406	−	0.198096i
$883$	−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
$885$	−20.6752	−	1.45028i	−0.694988	−	0.0487505i
$886$	18.7205	−	25.7666i	0.628929	−	0.865647i
$887$	−2.20110	+	6.77428i	−0.0739056	+	0.227458i	−0.981185	−	0.193071i	$-0.938155\pi$
$887$	−2.20110	+	6.77428i	−0.0739056	+	0.227458i	0.907279	+	0.420529i	$0.138155\pi$
$888$	0.364866	+	0.306295i	0.0122441	+	0.0102786i
$889$	14.1404	−	10.2736i	0.474255	−	0.344566i
$890$	39.3976			1.32061
$891$	26.2620	+	14.1882i	0.879811	+	0.475324i
$892$	−13.4588			−0.450634
$893$	−0.716438	+	0.520523i	−0.0239747	+	0.0174186i
$894$	2.18262	+	1.83225i	0.0729979	+	0.0612796i
$895$	10.8393	−	33.3600i	0.362319	−	1.11510i
$896$	−0.330766	+	0.455261i	−0.0110501	+	0.0152092i
$897$	−0.406821	−	0.0285368i	−0.0135834	−	0.000952816i
$898$	−14.6571	−	4.76239i	−0.489114	−	0.158923i
$899$	17.5333	+	53.9621i	0.584770	+	1.79974i
$900$	−9.22085	−	52.4276i	−0.307362	−	1.74759i
$901$			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
$906$	28.9593	−	7.21367i	0.962109	−	0.239658i
$907$	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
$909$	−9.65139	−	9.32837i	−0.320116	−	0.309403i
$910$	−2.11898	+	0.688499i	−0.0702436	+	0.0228235i
$911$	5.63871	+	7.76102i	0.186819	+	0.257134i	0.892145	−	0.451749i	$-0.149200\pi$
$911$	5.63871	+	7.76102i	0.186819	+	0.257134i	−0.705326	+	0.708883i	$0.749200\pi$
$912$	−13.1182	−	21.0037i	−0.434388	−	0.695504i
$913$	1.83338	+	18.4675i	0.0606759	+	0.611186i
$914$			4.96958i			0.164379i
$915$	8.51666	−	21.0663i	0.281552	−	0.696429i
$916$	−1.79788	−	5.53331i	−0.0594037	−	0.182826i
$917$	−8.50536	−	2.76356i	−0.280872	−	0.0912608i
$918$	21.2435	−	36.7392i	0.701138	−	1.21258i
$919$	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
$921$	3.16312	−	3.76799i	0.104228	−	0.124160i
$922$	26.3270	−	19.1277i	0.867033	−	0.629936i
$923$	−4.72994			−0.155688
$924$	9.31870	+	6.36704i	0.306563	+	0.209460i
$925$	35.3089			1.16095
$926$	−6.19728	+	4.50259i	−0.203655	+	0.147964i
$927$	28.7986	+	4.06019i	0.945871	+	0.133354i
$928$	−18.3058	+	56.3393i	−0.600916	+	1.84943i
$929$	13.6622	−	18.8045i	0.448244	−	0.616955i	−0.523775	−	0.851856i	$-0.675477\pi$
$929$	13.6622	−	18.8045i	0.448244	−	0.616955i	0.972019	+	0.234902i	$0.0754769\pi$
$930$	−6.89380	+	98.2781i	−0.226057	+	3.22267i
$931$	−3.34142	−	1.08569i	−0.109511	−	0.0355821i
$932$	6.96011	+	21.4210i	0.227986	+	0.701669i
$933$	27.4511	+	11.0979i	0.898710	+	0.363330i
$934$		−	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
$939$	5.13570	+	20.6173i	0.167597	+	0.672821i
$940$	1.50071	+	1.09033i	0.0489478	+	0.0355627i
$941$	29.6082	+	21.5116i	0.965201	+	0.701259i	0.954353	−	0.298682i	$-0.0965470\pi$
$941$	29.6082	+	21.5116i	0.965201	+	0.701259i	0.0108479	+	0.999941i	$0.496547\pi$
$942$	−12.8582	−	51.6195i	−0.418944	−	1.68185i
$943$	−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	$-0.700933\pi$
$947$		−	49.6861i		−	1.61458i	0.590155	−	0.807290i	$-0.299067\pi$
$948$	−8.30135	−	3.35607i	−0.269615	−	0.109000i
$949$	1.21605	+	3.74260i	0.0394745	+	0.121490i
$950$	−60.0896	−	19.5243i	−1.94956	−	0.633452i
$951$	−0.140793	+	2.00715i	−0.00456553	+	0.0650862i
$952$	−0.169620	+	0.233462i	−0.00549742	+	0.00756655i
$953$	6.04160	−	18.5941i	0.195707	−	0.602323i	−0.804261	−	0.594276i	$-0.797439\pi$
$953$	6.04160	−	18.5941i	0.195707	−	0.602323i	0.999968	−	0.00804678i	$-0.00256140\pi$
$954$	5.90874	−	41.9103i	0.191302	−	1.35690i
$955$	−24.5291	+	17.8214i	−0.793742	+	0.576688i
$956$	41.2387			1.33376
$957$	−41.0131	−	12.0265i	−1.32576	−	0.388761i
$958$	−12.5450			−0.405312
$959$	−2.21081	+	1.60625i	−0.0713908	+	0.0518684i
$960$	−32.1828	+	38.3370i	−1.03870	+	1.23732i
$961$	8.39230	−	25.8289i	0.270719	−	0.833189i
$962$	1.36680	−	1.88124i	0.0440674	−	0.0606535i
$963$	17.3148	−	9.19678i	0.557962	−	0.296362i
$964$	42.6719	+	13.8649i	1.37437	+	0.446560i
$965$	−1.82064	−	5.60336i	−0.0586085	−	0.180378i
$966$	−1.01887	+	2.52021i	−0.0327816	+	0.0810864i
$967$			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	−0.682738	−	0.730663i	$-0.739211\pi$
$971$	−25.1036	+	8.15665i	−0.805612	+	0.261759i	−0.122874	+	0.992422i	$0.539211\pi$
$972$	−18.8816	+	24.1132i	−0.605628	+	0.773430i
$973$	7.25510	+	5.27114i	0.232588	+	0.168985i
$974$	−29.7193	−	21.5923i	−0.952266	−	0.691862i
$975$	4.53438	−	1.12950i	0.145216	−	0.0361729i
$976$	−13.5545	+	4.40413i	−0.433869	+	0.140973i
$977$	9.86367	+	13.5762i	0.315567	+	0.434341i	0.937107	−	0.349042i	$-0.113493\pi$
$977$	9.86367	+	13.5762i	0.315567	+	0.434341i	−0.621540	+	0.783382i	$0.713493\pi$
$978$	−52.8027	+	32.9788i	−1.68844	+	1.05455i
$979$	13.0866	−	11.6472i	0.418248	−	0.372246i
$980$			7.35941i			0.235088i
$981$	41.3784	−	7.27753i	1.32111	−	0.232354i
$982$	−14.2062	−	43.7221i	−0.453337	−	1.39523i
$983$	−5.85629	−	1.90282i	−0.186787	−	0.0606907i	0.214130	−	0.976805i	$-0.431308\pi$
$983$	−5.85629	−	1.90282i	−0.186787	−	0.0606907i	−0.400917	+	0.916114i	$0.631308\pi$
$984$	1.05742	+	0.0741735i	0.0337093	+	0.00236457i
$985$	38.5423	−	53.0489i	1.22806	−	1.69028i
$986$	−18.7777	+	57.7917i	−0.598003	+	1.84046i
$987$	−0.334373	−	0.280697i	−0.0106432	−	0.00893468i
$988$	−1.66815	+	1.21198i	−0.0530709	+	0.0385583i
$989$	−2.99396			−0.0952024
$990$	−58.1953	−	46.0515i	−1.84957	−	1.46361i
$991$	−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
$993$	18.1919	+	15.2715i	0.577302	+	0.484628i
$994$	−9.74265	+	29.9848i	−0.309018	+	0.951060i
$995$	−12.0235	+	16.5490i	−0.381172	+	0.524638i
$996$	−18.9944	−	1.33238i	−0.601861	−	0.0422181i
$997$	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
$999$	−13.5830	−	15.1053i	−0.429747	−	0.477911i

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+(-1.61087 + 1.17037i) q^{2} +(1.32659 + 1.11363i) q^{3} +(0.607116 - 1.86851i) q^{4} +(-2.20177 + 3.03048i) q^{5} +(-3.44031 - 0.241324i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(-0.0217402 - 0.0669093i) q^{8} +(0.519657 + 2.95465i) q^{9} +O(q^{10})\)	\(q+(-1.61087 + 1.17037i) q^{2} +(1.32659 + 1.11363i) q^{3} +(0.607116 - 1.86851i) q^{4} +(-2.20177 + 3.03048i) q^{5} +(-3.44031 - 0.241324i) q^{6} +(-0.951057 - 0.309017i) q^{7} +(-0.0217402 - 0.0669093i) q^{8} +(0.519657 + 2.95465i) 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} +(-6.29567 + 1.56823i) q^{15} +(3.29223 + 2.39194i) q^{16} +(3.31846 + 2.41100i) q^{17} +(-4.29513 - 4.15137i) 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} +(0.0456720 - 0.112971i) q^{24} +(-2.79092 - 8.58957i) q^{25} +(-0.565684 - 0.183802i) q^{26} +(-2.60102 + 4.49830i) q^{27} +(-1.15480 + 1.58945i) q^{28} +(2.29911 - 7.07593i) q^{29} +(8.30612 - 9.89446i) q^{30} +(-6.16968 + 4.48253i) q^{31} -7.96210 q^{32} +(-0.166111 - 5.74216i) q^{33} -8.16736 q^{34} +(3.03048 - 2.20177i) q^{35} +(5.83628 + 0.822830i) q^{36} +(-1.20809 + 3.71813i) q^{37} +(4.11194 - 5.65960i) q^{38} +(-0.0362043 + 0.516130i) q^{39} +(0.250634 + 0.0814360i) q^{40} +(2.68816 + 8.27330i) q^{41} +(3.19736 + 1.29263i) 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} +(1.70368 + 6.83944i) q^{48} +(0.809017 + 0.587785i) q^{49} +(14.5488 + 10.5703i) q^{50} +(1.71725 + 6.89393i) 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} +(-5.64173 - 2.28084i) q^{57} +(4.57787 + 14.0892i) q^{58} +(3.03813 + 0.987149i) q^{59} +(-0.891947 + 12.7156i) q^{60} +(-2.05856 + 2.83337i) q^{61} +(4.69235 - 14.4416i) q^{62} +(0.418814 - 2.97062i) q^{63} +(6.24147 - 4.53470i) q^{64} -1.11897 q^{65} +(6.98802 + 9.05547i) q^{66} +11.4951 q^{67} +(6.51966 - 4.73681i) q^{68} +(-0.877780 + 1.04563i) q^{69} +(-2.30483 + 7.09355i) q^{70} +(-9.30701 + 12.8100i) q^{71} +(0.186396 - 0.0990044i) q^{72} +(12.5288 + 4.07086i) q^{73} +(-2.40549 - 7.40335i) q^{74} +(5.86321 - 14.5029i) 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} +(-8.45991 + 3.07081i) q^{81} +(-14.0131 - 10.1811i) q^{82} +(-4.52689 - 3.28898i) q^{83} +(-3.30200 + 0.822517i) 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} +(22.0375 - 3.87591i) q^{90} +(-0.0923095 - 0.284099i) q^{91} +(1.47279 + 0.478538i) q^{92} +(-13.1765 - 0.924276i) q^{93} +(-0.294998 + 0.406030i) q^{94} +(4.06687 - 12.5165i) q^{95} +(-10.5624 - 8.86684i) q^{96} +(13.9017 - 10.1001i) q^{97} -1.99115 q^{98} +(6.17428 - 7.80245i) 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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