LMFDB - Embedded newform 630.2.bz.a.517.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(13,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 6]))

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

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

chi := DirichletCharacter("630.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			517.9
Character	$\chi$	$=$	630.517
Dual form			630.2.bz.a.223.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.793555 - 1.53957i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.08313 - 0.812755i) q^{5} +(1.69250 - 0.368045i) q^{6} +(0.642660 + 2.56651i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74054 + 2.44346i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.793555 - 1.53957i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.08313 - 0.812755i) q^{5} +(1.69250 - 0.368045i) q^{6} +(0.642660 + 2.56651i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74054 + 2.44346i) q^{9} +(1.32421 - 1.80179i) q^{10} +(-0.253201 - 0.438556i) q^{11} +(-0.0825457 + 1.73008i) q^{12} +(0.803655 - 0.215339i) q^{13} +(-2.64539 - 0.0435001i) q^{14} +(0.401785 + 3.85209i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.50644 - 1.50644i) q^{17} +(-1.90972 - 2.31365i) q^{18} +0.378823 q^{19} +(1.39767 + 1.74543i) q^{20} +(3.44134 - 3.02609i) q^{21} +(0.489146 - 0.131066i) q^{22} +(0.615647 + 2.29762i) q^{23} +(-1.64977 - 0.527511i) q^{24} +(3.67886 + 3.38615i) q^{25} +0.832005i q^{26} +(5.14309 + 0.740661i) q^{27} +(0.726696 - 2.54400i) q^{28} +(1.94123 - 1.12077i) q^{29} +(-3.82482 - 0.608898i) q^{30} +(3.19169 + 1.84273i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.474259 + 0.737838i) q^{33} +(1.06521 + 1.84500i) q^{34} +(0.747201 - 5.86870i) q^{35} +(2.72909 - 1.24583i) q^{36} +(6.27123 + 6.27123i) q^{37} +(-0.0980467 + 0.365915i) q^{38} +(-0.969273 - 1.06640i) q^{39} +(-2.04770 + 0.898291i) q^{40} +(4.45935 + 2.57461i) q^{41} +(2.03229 + 4.10728i) q^{42} +(10.4368 + 2.79653i) q^{43} +0.506401i q^{44} +(5.61171 - 3.67542i) q^{45} -2.37868 q^{46} +(3.05740 + 0.819227i) q^{47} +(0.936528 - 1.45702i) q^{48} +(-6.17398 + 3.29879i) q^{49} +(-4.22293 + 2.67710i) q^{50} +(-3.51470 - 1.12382i) q^{51} +(-0.803655 - 0.215339i) q^{52} +(2.84777 - 2.84777i) q^{53} +(-2.04655 + 4.77615i) q^{54} +(0.171011 + 1.11936i) q^{55} +(2.26923 + 1.36037i) q^{56} +(-0.300617 - 0.583225i) q^{57} +(0.580152 + 2.16516i) q^{58} +(5.52845 - 9.57555i) q^{59} +(1.57809 - 3.53690i) q^{60} +(-9.87403 + 5.70077i) q^{61} +(-2.60601 + 2.60601i) q^{62} +(-7.38976 - 2.89681i) q^{63} -1.00000i q^{64} +(-1.84914 - 0.204596i) q^{65} +(-0.589950 - 0.649066i) q^{66} +(3.74752 - 1.00415i) q^{67} +(-2.05783 + 0.551394i) q^{68} +(3.04880 - 2.77112i) q^{69} +(5.47534 + 2.24067i) q^{70} -15.2959 q^{71} +(0.497041 + 2.95854i) q^{72} +(6.88933 + 6.88933i) q^{73} +(-7.68065 + 4.43443i) q^{74} +(2.29383 - 8.35095i) q^{75} +(-0.328071 - 0.189412i) q^{76} +(0.962839 - 0.931686i) q^{77} +(1.28093 - 0.660241i) q^{78} +(1.80099 - 1.03980i) q^{79} +(-0.337698 - 2.21042i) q^{80} +(-2.94103 - 8.50590i) q^{81} +(-3.64105 + 3.64105i) q^{82} +(-0.468767 + 1.74946i) q^{83} +(-4.49333 + 0.900001i) q^{84} +(-4.36247 + 1.91374i) q^{85} +(-5.40248 + 9.35738i) q^{86} +(-3.26597 - 2.09926i) q^{87} +(-0.489146 - 0.131066i) q^{88} -12.4920 q^{89} +(2.09776 + 6.37177i) q^{90} +(1.06915 + 1.92420i) q^{91} +(0.615647 - 2.29762i) q^{92} +(0.304218 - 6.37614i) q^{93} +(-1.58262 + 2.74119i) q^{94} +(-0.789138 - 0.307891i) q^{95} +(1.16498 + 1.28172i) q^{96} +(-17.6246 - 4.72251i) q^{97} +(-1.58845 - 6.81739i) q^{98} +(1.51230 + 0.144639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.793555	−	1.53957i	−0.458159	−	0.888870i
$3$	−0.793555	−	1.53957i	−0.458159	−	0.888870i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.08313	−	0.812755i	−0.931604	−	0.363475i
$5$	−2.08313	−	0.812755i	−0.931604	−	0.363475i
$6$	1.69250	−	0.368045i	0.690959	−	0.150254i
$7$	0.642660	+	2.56651i	0.242903	+	0.970051i
$7$	0.642660	+	2.56651i	0.242903	+	0.970051i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.74054	+	2.44346i	−0.580181	+	0.814488i
$10$	1.32421	−	1.80179i	0.418753	−	0.569777i
$11$	−0.253201	−	0.438556i	−0.0763429	−	0.132230i	0.825327	−	0.564656i	$-0.190991\pi$
$11$	−0.253201	−	0.438556i	−0.0763429	−	0.132230i	−0.901669	+	0.432426i	$0.857658\pi$
$12$	−0.0825457	+	1.73008i	−0.0238289	+	0.499432i
$13$	0.803655	−	0.215339i	0.222894	−	0.0597242i	−0.145644	−	0.989337i	$-0.546525\pi$
$13$	0.803655	−	0.215339i	0.222894	−	0.0597242i	0.368537	+	0.929613i	$0.379859\pi$
$14$	−2.64539	−	0.0435001i	−0.707011	−	0.0116259i
$15$	0.401785	+	3.85209i	0.103741	+	0.994604i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.50644	−	1.50644i	0.365365	−	0.365365i	−0.500419	−	0.865783i	$-0.666821\pi$
$17$	1.50644	−	1.50644i	0.365365	−	0.365365i	0.865783	+	0.500419i	$0.166821\pi$
$18$	−1.90972	−	2.31365i	−0.450125	−	0.545332i
$19$	0.378823			0.0869081			0.0434540	−	0.999055i	$-0.486164\pi$
$19$	0.378823			0.0869081			0.0434540	+	0.999055i	$0.486164\pi$
$20$	1.39767	+	1.74543i	0.312528	+	0.390290i
$21$	3.44134	−	3.02609i	0.750961	−	0.660347i
$22$	0.489146	−	0.131066i	0.104286	−	0.0279434i
$23$	0.615647	+	2.29762i	0.128371	+	0.479088i	0.999937	−	0.0111901i	$-0.00356198\pi$
$23$	0.615647	+	2.29762i	0.128371	+	0.479088i	−0.871566	+	0.490278i	$0.836895\pi$
$24$	−1.64977	−	0.527511i	−0.336757	−	0.107678i
$25$	3.67886	+	3.38615i	0.735772	+	0.677230i
$26$			0.832005i			0.163170i
$27$	5.14309	+	0.740661i	0.989789	+	0.142540i
$28$	0.726696	−	2.54400i	0.137333	−	0.480770i
$29$	1.94123	−	1.12077i	0.360477	−	0.208121i	−0.308813	−	0.951123i	$-0.599932\pi$
$29$	1.94123	−	1.12077i	0.360477	−	0.208121i	0.669290	+	0.743001i	$0.266598\pi$
$30$	−3.82482	−	0.608898i	−0.698313	−	0.111169i
$31$	3.19169	+	1.84273i	0.573245	+	0.330963i	0.758444	−	0.651738i	$-0.225960\pi$
$31$	3.19169	+	1.84273i	0.573245	+	0.330963i	−0.185199	+	0.982701i	$0.559293\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.474259	+	0.737838i	−0.0825579	+	0.128441i
$34$	1.06521	+	1.84500i	0.182682	+	0.316415i
$35$	0.747201	−	5.86870i	0.126300	−	0.991992i
$36$	2.72909	−	1.24583i	0.454848	−	0.207638i
$37$	6.27123	+	6.27123i	1.03098	+	1.03098i	0.999504	+	0.0314789i	$0.0100217\pi$
$37$	6.27123	+	6.27123i	1.03098	+	1.03098i	0.0314789	+	0.999504i	$0.489978\pi$
$38$	−0.0980467	+	0.365915i	−0.0159053	+	0.0593593i
$39$	−0.969273	−	1.06640i	−0.155208	−	0.170760i
$40$	−2.04770	+	0.898291i	−0.323770	+	0.142032i
$41$	4.45935	+	2.57461i	0.696434	+	0.402086i	0.806018	−	0.591891i	$-0.201618\pi$
$41$	4.45935	+	2.57461i	0.696434	+	0.402086i	−0.109584	+	0.993978i	$0.534952\pi$
$42$	2.03229	+	4.10728i	0.313590	+	0.633768i
$43$	10.4368	+	2.79653i	1.59160	+	0.426467i	0.942491	−	0.334231i	$-0.108477\pi$
$43$	10.4368	+	2.79653i	1.59160	+	0.426467i	0.649106	+	0.760698i	$0.275143\pi$
$44$			0.506401i			0.0763429i
$45$	5.61171	−	3.67542i	0.836545	−	0.547899i
$46$	−2.37868			−0.350717
$47$	3.05740	+	0.819227i	0.445967	+	0.119497i	0.474812	−	0.880087i	$-0.342516\pi$
$47$	3.05740	+	0.819227i	0.445967	+	0.119497i	−0.0288447	+	0.999584i	$0.509183\pi$
$48$	0.936528	−	1.45702i	0.135176	−	0.210303i
$49$	−6.17398	+	3.29879i	−0.881996	+	0.471256i
$50$	−4.22293	+	2.67710i	−0.597212	+	0.378600i
$51$	−3.51470	−	1.12382i	−0.492157	−	0.157367i
$52$	−0.803655	−	0.215339i	−0.111447	−	0.0298621i
$53$	2.84777	−	2.84777i	0.391172	−	0.391172i	−0.483933	−	0.875105i	$-0.660792\pi$
$53$	2.84777	−	2.84777i	0.391172	−	0.391172i	0.875105	+	0.483933i	$0.160792\pi$
$54$	−2.04655	+	4.77615i	−0.278501	+	0.649952i
$55$	0.171011	+	1.11936i	0.0230591	+	0.150934i
$56$	2.26923	+	1.36037i	0.303238	+	0.181787i
$57$	−0.300617	−	0.583225i	−0.0398177	−	0.0772500i
$58$	0.580152	+	2.16516i	0.0761777	+	0.284299i
$59$	5.52845	−	9.57555i	0.719743	−	1.24663i	−0.241359	−	0.970436i	$-0.577593\pi$
$59$	5.52845	−	9.57555i	0.719743	−	1.24663i	0.961102	−	0.276195i	$-0.0890736\pi$
$60$	1.57809	−	3.53690i	0.203730	−	0.456611i
$61$	−9.87403	+	5.70077i	−1.26424	+	0.729909i	−0.973892	−	0.227012i	$-0.927104\pi$
$61$	−9.87403	+	5.70077i	−1.26424	+	0.729909i	−0.290348	+	0.956921i	$0.593771\pi$
$62$	−2.60601	+	2.60601i	−0.330963	+	0.330963i
$63$	−7.38976	−	2.89681i	−0.931022	−	0.364963i
$64$		−	1.00000i		−	0.125000i
$65$	−1.84914	−	0.204596i	−0.229357	−	0.0253770i
$66$	−0.589950	−	0.649066i	−0.0726178	−	0.0798945i
$67$	3.74752	−	1.00415i	0.457833	−	0.122676i	−0.0225294	−	0.999746i	$-0.507172\pi$
$67$	3.74752	−	1.00415i	0.457833	−	0.122676i	0.480362	+	0.877070i	$0.340505\pi$
$68$	−2.05783	+	0.551394i	−0.249549	+	0.0668663i
$69$	3.04880	−	2.77112i	0.367032	−	0.333604i
$70$	5.47534	+	2.24067i	0.654429	+	0.267812i
$71$	−15.2959			−1.81529			−0.907647	−	0.419735i	$-0.862123\pi$
$71$	−15.2959			−1.81529			−0.907647	+	0.419735i	$0.862123\pi$
$72$	0.497041	+	2.95854i	0.0585768	+	0.348667i
$73$	6.88933	+	6.88933i	0.806335	+	0.806335i	0.984077	−	0.177742i	$-0.0568793\pi$
$73$	6.88933	+	6.88933i	0.806335	+	0.806335i	−0.177742	+	0.984077i	$0.556879\pi$
$74$	−7.68065	+	4.43443i	−0.892858	+	0.515492i
$75$	2.29383	−	8.35095i	0.264869	−	0.964284i
$76$	−0.328071	−	0.189412i	−0.0376323	−	0.0217270i
$77$	0.962839	−	0.931686i	0.109726	−	0.106175i
$78$	1.28093	−	0.660241i	0.145037	−	0.0747576i
$79$	1.80099	−	1.03980i	0.202627	−	0.116987i	−0.395253	−	0.918572i	$-0.629343\pi$
$79$	1.80099	−	1.03980i	0.202627	−	0.116987i	0.597880	+	0.801585i	$0.296010\pi$
$80$	−0.337698	−	2.21042i	−0.0377558	−	0.247133i
$81$	−2.94103	−	8.50590i	−0.326781	−	0.945100i
$82$	−3.64105	+	3.64105i	−0.402086	+	0.402086i
$83$	−0.468767	+	1.74946i	−0.0514538	+	0.192028i	−0.986869	−	0.161523i	$-0.948359\pi$
$83$	−0.468767	+	1.74946i	−0.0514538	+	0.192028i	0.935415	+	0.353551i	$0.115026\pi$
$84$	−4.49333	+	0.900001i	−0.490262	+	0.0981982i
$85$	−4.36247	+	1.91374i	−0.473176	+	0.207574i
$86$	−5.40248	+	9.35738i	−0.582565	+	1.00903i
$87$	−3.26597	−	2.09926i	−0.350148	−	0.225064i
$88$	−0.489146	−	0.131066i	−0.0521432	−	0.0139717i
$89$	−12.4920			−1.32415			−0.662073	−	0.749440i	$-0.730323\pi$
$89$	−12.4920			−1.32415			−0.662073	+	0.749440i	$0.730323\pi$
$90$	2.09776	+	6.37177i	0.221124	+	0.671643i
$91$	1.06915	+	1.92420i	0.112077	+	0.201711i
$92$	0.615647	−	2.29762i	0.0641856	−	0.239544i
$93$	0.304218	−	6.37614i	0.0315459	−	0.661175i
$94$	−1.58262	+	2.74119i	−0.163235	+	0.282732i
$95$	−0.789138	−	0.307891i	−0.0809639	−	0.0315889i
$96$	1.16498	+	1.28172i	0.118901	+	0.130815i
$97$	−17.6246	−	4.72251i	−1.78951	−	0.479498i	−0.797248	−	0.603652i	$-0.793712\pi$
$97$	−17.6246	−	4.72251i	−1.78951	−	0.479498i	−0.992263	+	0.124154i	$0.960378\pi$
$98$	−1.58845	−	6.81739i	−0.160457	−	0.688661i
$99$	1.51230	+	0.144639i	0.151992	+	0.0145368i
$100$	−1.49291	−	4.77192i	−0.149291	−	0.477192i
$101$	−6.06276	+	3.50034i	−0.603267	+	0.348297i	−0.770326	−	0.637650i	$-0.779906\pi$
$101$	−6.06276	+	3.50034i	−0.603267	+	0.348297i	0.167058	+	0.985947i	$0.446573\pi$
$102$	1.99520	−	3.10407i	0.197554	−	0.307349i
$103$	2.48450	−	0.665719i	0.244805	−	0.0655953i	−0.134330	−	0.990937i	$-0.542888\pi$
$103$	2.48450	−	0.665719i	0.244805	−	0.0655953i	0.379135	+	0.925341i	$0.376222\pi$
$104$	0.416002	−	0.720537i	0.0407924	−	0.0706545i
$105$	−9.62822	+	3.50677i	−0.939618	+	0.342226i
$106$	2.01368	+	3.48779i	0.195586	+	0.338765i
$107$	5.99158	+	5.99158i	0.579228	+	0.579228i	0.934691	−	0.355463i	$-0.115677\pi$
$107$	5.99158	+	5.99158i	0.579228	+	0.579228i	−0.355463	+	0.934691i	$0.615677\pi$
$108$	−4.08372	−	3.21298i	−0.392956	−	0.309169i
$109$			7.93422i			0.759960i	0.924995	+	0.379980i	$0.124069\pi$
$109$			7.93422i			0.759960i	−0.924995	+	0.379980i	$0.875931\pi$
$110$	−1.12548	−	0.124528i	−0.107310	−	0.0118733i
$111$	4.67842	−	14.6315i	0.444056	−	1.38876i
$112$	−1.90134	+	1.83982i	−0.179659	+	0.173846i
$113$	1.64582	+	6.14230i	0.154826	+	0.577819i	0.999120	+	0.0419387i	$0.0133534\pi$
$113$	1.64582	+	6.14230i	0.154826	+	0.577819i	−0.844294	+	0.535880i	$0.819980\pi$
$114$	0.641157	−	0.139424i	0.0600499	−	0.0130583i
$115$	0.584934	−	5.28662i	0.0545454	−	0.492980i
$116$	−2.24154			−0.208121
$117$	−0.872623	+	2.33851i	−0.0806740	+	0.216195i
$118$	7.81841	+	7.81841i	0.719743	+	0.719743i
$119$	4.83442	+	2.89816i	0.443170	+	0.265674i
$120$	3.00794	+	2.43973i	0.274586	+	0.222716i
$121$	5.37178	−	9.30419i	0.488344	−	0.845836i
$122$	−2.95094	−	11.0130i	−0.267165	−	0.997074i
$123$	0.425046	−	8.90858i	0.0383251	−	0.803259i
$124$	−1.84273	−	3.19169i	−0.165482	−	0.286623i
$125$	−4.91143	−	10.0438i	−0.439292	−	0.898344i
$126$	4.71071	−	6.38821i	0.419663	−	0.569107i
$127$	10.8089	+	10.8089i	0.959138	+	0.959138i	0.999197	−	0.0400595i	$-0.0127548\pi$
$127$	10.8089	+	10.8089i	0.959138	+	0.959138i	−0.0400595	+	0.999197i	$0.512755\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−3.97672	−	18.2874i	−0.350131	−	1.61011i
$130$	0.676216	−	1.73317i	0.0593081	−	0.152009i
$131$	2.44562	+	1.41198i	0.213675	+	0.123365i	0.603018	−	0.797727i	$-0.293965\pi$
$131$	2.44562	+	1.41198i	0.213675	+	0.123365i	−0.389343	+	0.921093i	$0.627298\pi$
$132$	0.779640	−	0.401857i	0.0678589	−	0.0349772i
$133$	0.243455	+	0.972255i	0.0211102	+	0.0843052i
$134$			3.87972i			0.335157i
$135$	−10.1118	−	5.72297i	−0.870281	−	0.492555i
$136$		−	2.13042i		−	0.182682i
$137$	−0.942715	+	3.51826i	−0.0805415	+	0.300585i	−0.994433	−	0.105374i	$-0.966396\pi$
$137$	−0.942715	+	3.51826i	−0.0805415	+	0.300585i	0.913891	+	0.405959i	$0.133063\pi$
$138$	1.88761	+	3.66213i	0.160684	+	0.311742i
$139$	0.324639	−	0.562291i	0.0275355	−	0.0476929i	−0.851929	−	0.523657i	$-0.824567\pi$
$139$	0.324639	−	0.562291i	0.0275355	−	0.0476929i	0.879465	+	0.475964i	$0.157901\pi$
$140$	−3.58145	+	4.70885i	−0.302688	+	0.397970i
$141$	−1.16496	−	5.35717i	−0.0981069	−	0.451155i
$142$	3.95888	−	14.7747i	0.332222	−	1.23987i
$143$	−0.297924	−	0.297924i	−0.0249137	−	0.0249137i
$144$	−2.98637	−	0.285622i	−0.248864	−	0.0238018i
$145$	−4.95474	+	0.756963i	−0.411468	+	0.0628623i
$146$	−8.43767	+	4.87149i	−0.698307	+	0.403167i
$147$	9.97810	+	6.88749i	0.822980	+	0.568070i
$148$	−2.29543	−	8.56665i	−0.188683	−	0.704175i
$149$	15.4697	+	8.93142i	1.26733	+	0.731691i	0.974481	−	0.224470i	$-0.0720649\pi$
$149$	15.4697	+	8.93142i	1.26733	+	0.731691i	0.292844	+	0.956160i	$0.405398\pi$
$150$	7.47271	+	4.37706i	0.610144	+	0.357385i
$151$	3.84861	+	6.66598i	0.313195	+	0.542470i	0.979052	−	0.203609i	$-0.0652672\pi$
$151$	3.84861	+	6.66598i	0.313195	+	0.542470i	−0.665857	+	0.746079i	$0.731934\pi$
$152$	0.267869	−	0.267869i	0.0217270	−	0.0217270i
$153$	1.05891	+	6.30294i	0.0856075	+	0.509562i
$154$	0.650738	+	1.17117i	0.0524380	+	0.0943755i
$155$	−5.15103	−	6.43270i	−0.413741	−	0.516687i
$156$	0.306216	+	1.40816i	0.0245169	+	0.112743i
$157$	−3.37300	−	12.5882i	−0.269195	−	1.00465i	−0.959633	−	0.281257i	$-0.909249\pi$
$157$	−3.37300	−	12.5882i	−0.269195	−	1.00465i	0.690438	−	0.723392i	$-0.257418\pi$
$158$	0.538240	+	2.00874i	0.0428201	+	0.159807i
$159$	−6.64420	−	2.12448i	−0.526920	−	0.168482i
$160$	2.22251	+	0.245907i	0.175704	+	0.0194407i
$161$	−5.50123	+	3.05666i	−0.433558	+	0.240898i
$162$	8.97726	−	0.639326i	0.705320	−	0.0502302i
$163$	15.7126	−	15.7126i	1.23071	−	1.23071i	0.267013	−	0.963693i	$-0.413963\pi$
$163$	15.7126	−	15.7126i	1.23071	−	1.23071i	0.963693	−	0.267013i	$-0.0860365\pi$
$164$	−2.57461	−	4.45935i	−0.201043	−	0.348217i
$165$	1.58762	−	1.15156i	0.123596	−	0.0896485i
$166$	−1.56852	−	0.905588i	−0.121741	−	0.0702872i
$167$	2.72589	+	10.1731i	0.210935	+	0.787222i	0.987558	+	0.157255i	$0.0502646\pi$
$167$	2.72589	+	10.1731i	0.210935	+	0.787222i	−0.776623	+	0.629966i	$0.783069\pi$
$168$	0.293625	−	4.57316i	0.0226536	−	0.352827i
$169$	−10.6588	+	6.15388i	−0.819911	+	0.473376i
$170$	−0.719440	−	4.70913i	−0.0551786	−	0.361174i
$171$	−0.659358	+	0.925641i	−0.0504224	+	0.0707856i
$172$	−7.64027	−	7.64027i	−0.582565	−	0.582565i
$173$	−5.54407	+	20.6907i	−0.421508	+	1.57309i	0.349926	+	0.936777i	$0.386207\pi$
$173$	−5.54407	+	20.6907i	−0.421508	+	1.57309i	−0.771433	+	0.636310i	$0.780460\pi$
$174$	2.87302	−	2.61135i	0.217803	−	0.197966i
$175$	−6.32634	+	11.6180i	−0.478226	+	0.878237i
$176$	0.253201	−	0.438556i	0.0190857	−	0.0330574i
$177$	−19.1293	−	0.912699i	−1.43785	−	0.0686027i
$178$	3.23316	−	12.0663i	0.242335	−	0.904408i
$179$		−	1.59925i		−	0.119533i	−0.998212	−	0.0597667i	$-0.980964\pi$
$179$		−	1.59925i		−	0.119533i	0.998212	−	0.0597667i	$-0.0190357\pi$
$180$	−6.69759	+	0.377149i	−0.499209	+	0.0281110i
$181$		−	16.0159i		−	1.19046i	−0.803557	−	0.595228i	$-0.797062\pi$
$181$		−	16.0159i		−	1.19046i	0.803557	−	0.595228i	$-0.202938\pi$
$182$	−2.13535	+	0.534697i	−0.158283	+	0.0396343i
$183$	16.6123	+	10.6779i	1.22802	+	0.789330i
$184$	2.05999	+	1.18934i	0.151865	+	0.0876791i
$185$	−7.96681	−	18.1607i	−0.585731	−	1.33520i
$186$	6.08014	+	1.94412i	0.445817	+	0.142550i
$187$	−1.04209	−	0.279227i	−0.0762050	−	0.0204191i
$188$	−2.23817	−	2.23817i	−0.163235	−	0.163235i
$189$	1.40435	+	13.6758i	0.102151	+	0.994769i
$190$	0.501644	−	0.682561i	0.0363930	−	0.0495182i
$191$	0.111306	+	0.192787i	0.00805379	+	0.0139496i	0.870024	−	0.493009i	$-0.164103\pi$
$191$	0.111306	+	0.192787i	0.00805379	+	0.0139496i	−0.861970	+	0.506959i	$0.830770\pi$
$192$	−1.53957	+	0.793555i	−0.111109	+	0.0572699i
$193$	2.87727	+	10.7381i	0.207110	+	0.772945i	0.988796	+	0.149273i	$0.0476933\pi$
$193$	2.87727	+	10.7381i	0.207110	+	0.772945i	−0.781686	+	0.623672i	$0.785640\pi$
$194$	9.12318	−	15.8018i	0.655006	−	1.13450i
$195$	1.15240	+	3.00923i	0.0825251	+	0.215495i
$196$	6.99622	+	0.230150i	0.499730	+	0.0164393i
$197$	−12.7854	−	12.7854i	−0.910924	−	0.910924i	0.0854209	−	0.996345i	$-0.472777\pi$
$197$	−12.7854	−	12.7854i	−0.910924	−	0.910924i	−0.996345	+	0.0854209i	$0.972777\pi$
$198$	−0.531124	+	1.42334i	−0.0377453	+	0.101152i
$199$	11.5081			0.815786			0.407893	−	0.913030i	$-0.366264\pi$
$199$	11.5081			0.815786			0.407893	+	0.913030i	$0.366264\pi$
$200$	4.99571	−	0.206977i	0.353250	−	0.0146355i
$201$	−4.51981	−	4.97272i	−0.318803	−	0.350749i
$202$	−1.81191	−	6.76213i	−0.127485	−	0.475782i
$203$	4.12401	+	4.26191i	0.289449	+	0.299127i
$204$	2.48191	+	2.73061i	0.173768	+	0.191181i
$205$	−7.19689	−	8.98761i	−0.502652	−	0.627722i
$206$			2.57214i			0.179210i
$207$	−6.68572	−	2.49480i	−0.464690	−	0.173401i
$208$	0.588316	+	0.588316i	0.0407924	+	0.0407924i
$209$	−0.0959183	−	0.166135i	−0.00663481	−	0.0114918i
$210$	−0.895314	−	10.2078i	−0.0617826	−	0.704403i
$211$	8.44542	−	14.6279i	0.581407	−	1.00703i	−0.413906	−	0.910320i	$-0.635836\pi$
$211$	8.44542	−	14.6279i	0.581407	−	1.00703i	0.995313	−	0.0967066i	$-0.0308309\pi$
$212$	−3.89013	+	1.04236i	−0.267175	+	0.0715894i
$213$	12.1382	+	23.5491i	0.831693	+	1.61356i
$214$	−7.33816	+	4.23669i	−0.501626	+	0.289614i
$215$	−19.4683	−	14.3081i	−1.32773	−	0.975804i
$216$	4.16044	−	3.11299i	0.283082	−	0.211812i
$217$	−2.67820	+	9.37577i	−0.181808	+	0.636469i
$218$	−7.66386	−	2.05353i	−0.519062	−	0.139082i
$219$	5.13953	−	16.0737i	0.347298	−	1.08616i
$220$	0.411580	−	1.05490i	0.0277487	−	0.0711213i
$221$	0.886261	−	1.53505i	0.0596164	−	0.103259i
$222$	12.9221	+	8.30593i	0.867276	+	0.557458i
$223$	5.35319	−	19.9784i	0.358476	−	1.33785i	−0.517577	−	0.855637i	$-0.673166\pi$
$223$	5.35319	−	19.9784i	0.358476	−	1.33785i	0.876053	−	0.482214i	$-0.160167\pi$
$224$	−1.28502	−	2.31273i	−0.0858593	−	0.154526i
$225$	−14.6771	+	3.09542i	−0.978476	+	0.206362i
$226$	−6.35898			−0.422993
$227$	12.8642	+	3.44696i	0.853829	+	0.228783i	0.659082	−	0.752071i	$-0.270945\pi$
$227$	12.8642	+	3.44696i	0.853829	+	0.228783i	0.194746	+	0.980854i	$0.437612\pi$
$228$	−0.0312702	+	0.655396i	−0.00207092	+	0.0434047i
$229$	−12.1375	+	21.0228i	−0.802071	+	1.38923i	0.116180	+	0.993228i	$0.462935\pi$
$229$	−12.1375	+	21.0228i	−0.802071	+	1.38923i	−0.918251	+	0.395999i	$0.870398\pi$
$230$	4.95509	+	1.93328i	0.326729	+	0.127477i
$231$	−2.19846	−	0.743012i	−0.144648	−	0.0488866i
$232$	0.580152	−	2.16516i	0.0380888	−	0.142149i
$233$	12.9577	−	12.9577i	0.848888	−	0.848888i	−0.141107	−	0.989994i	$-0.545066\pi$
$233$	12.9577	−	12.9577i	0.848888	−	0.848888i	0.989994	+	0.141107i	$0.0450661\pi$
$234$	−2.03297	−	1.44814i	−0.132900	−	0.0946678i
$235$	−5.70312	−	4.19147i	−0.372031	−	0.273421i
$236$	−9.57555	+	5.52845i	−0.623315	+	0.359871i
$237$	−3.03003	−	1.94760i	−0.196821	−	0.126511i
$238$	−4.05065	+	3.91959i	−0.262564	+	0.254069i
$239$	5.90867	+	3.41137i	0.382200	+	0.220663i	0.678775	−	0.734346i	$-0.262511\pi$
$239$	5.90867	+	3.41137i	0.382200	+	0.220663i	−0.296575	+	0.955010i	$0.595844\pi$
$240$	−3.13511	+	2.27400i	−0.202371	+	0.146786i
$241$	−7.03126	+	4.05950i	−0.452923	+	0.261495i	−0.709064	−	0.705144i	$-0.750882\pi$
$241$	−7.03126	+	4.05950i	−0.452923	+	0.261495i	0.256141	+	0.966639i	$0.417549\pi$
$242$	7.59684	+	7.59684i	0.488344	+	0.488344i
$243$	−10.7616	+	11.2778i	−0.690354	+	0.723472i
$244$	11.4015			0.729909
$245$	15.5423	−	1.85388i	0.992961	−	0.118440i
$246$	8.49501	+	2.71627i	0.541622	+	0.173183i
$247$	0.304443	−	0.0815753i	0.0193713	−	0.00519051i
$248$	3.55987	−	0.953865i	0.226052	−	0.0605705i
$249$	3.06541	−	0.666595i	0.194262	−	0.0422437i
$250$	10.9727	−	2.14455i	0.693977	−	0.135633i
$251$		−	12.9242i		−	0.815769i	−0.913034	−	0.407884i	$-0.866267\pi$
$251$		−	12.9242i		−	0.815769i	0.913034	−	0.407884i	$-0.133733\pi$
$252$	4.95131	+	6.20359i	0.311904	+	0.390789i
$253$	0.851756	−	0.851756i	0.0535494	−	0.0535494i
$254$	−13.2382	+	7.64307i	−0.830638	+	0.479569i
$255$	6.40819	+	5.19766i	0.401296	+	0.325490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.35015	+	27.4311i	0.458490	+	1.71111i	0.677620	+	0.735412i	$0.263011\pi$
$257$	7.35015	+	27.4311i	0.458490	+	1.71111i	−0.219130	+	0.975696i	$0.570322\pi$
$258$	18.6935	+	0.891904i	1.16381	+	0.0555275i
$259$	−12.0649	+	20.1255i	−0.749677	+	1.25053i
$260$	1.49910	+	1.10175i	0.0929702	+	0.0683278i
$261$	−0.640231	+	6.69406i	−0.0396293	+	0.414352i
$262$	−1.99684	+	1.99684i	−0.123365	+	0.123365i
$263$	−13.0823	−	3.50538i	−0.806686	−	0.216151i	−0.168169	−	0.985758i	$-0.553785\pi$
$263$	−13.0823	−	3.50538i	−0.806686	−	0.216151i	−0.638518	+	0.769607i	$0.720452\pi$
$264$	0.186379	+	0.857082i	0.0114708	+	0.0527498i
$265$	−8.24682	+	3.61774i	−0.506598	+	0.222236i
$266$	−1.00214	−	0.0164789i	−0.0614450	−	0.00101038i
$267$	9.91305	+	19.2322i	0.606669	+	1.17699i
$268$	−3.74752	−	1.00415i	−0.228916	−	0.0613380i
$269$	12.1645			0.741682			0.370841	−	0.928696i	$-0.379070\pi$
$269$	12.1645			0.741682			0.370841	+	0.928696i	$0.379070\pi$
$270$	8.14508	−	8.28599i	0.495694	−	0.504269i
$271$		−	8.43048i		−	0.512115i	−0.966662	−	0.256057i	$-0.917576\pi$
$271$		−	8.43048i		−	0.512115i	0.966662	−	0.256057i	$-0.0824236\pi$
$272$	2.05783	+	0.551394i	0.124774	+	0.0334332i
$273$	2.11401	−	3.17298i	0.127946	−	0.192038i
$274$	−3.15438	−	1.82118i	−0.190563	−	0.110022i
$275$	0.553528	−	2.47076i	0.0333790	−	0.148993i
$276$	−4.02590	+	0.875460i	−0.242331	+	0.0526965i
$277$	4.85286	−	18.1111i	0.291580	−	1.08819i	−0.652316	−	0.757947i	$-0.726202\pi$
$277$	4.85286	−	18.1111i	0.291580	−	1.08819i	0.943896	−	0.330244i	$-0.107131\pi$
$278$	0.459109	+	0.459109i	0.0275355	+	0.0275355i
$279$	−10.0579	+	4.59145i	−0.602151	+	0.274883i
$280$	−3.62145	−	4.67815i	−0.216423	−	0.279573i
$281$	−16.5805	−	28.7183i	−0.989111	−	1.71319i	−0.622008	−	0.783011i	$-0.713683\pi$
$281$	−16.5805	−	28.7183i	−0.989111	−	1.71319i	−0.367103	−	0.930180i	$-0.619650\pi$
$282$	5.47614	+	0.261278i	0.326100	+	0.0155589i
$283$	13.9133	−	3.72804i	0.827057	−	0.221609i	0.179628	−	0.983735i	$-0.442511\pi$
$283$	13.9133	−	3.72804i	0.827057	−	0.221609i	0.647429	+	0.762125i	$0.275844\pi$
$284$	13.2467	+	7.64797i	0.786045	+	0.453823i
$285$	0.152206	+	1.45926i	0.00901589	+	0.0864391i
$286$	0.364881	−	0.210664i	0.0215759	−	0.0124568i
$287$	−3.74192	+	13.0996i	−0.220878	+	0.773244i
$288$	1.04882	−	2.81069i	0.0618023	−	0.165621i
$289$			12.4613i			0.733018i
$290$	0.551210	−	4.98182i	0.0323682	−	0.292543i
$291$	6.71549	+	30.8819i	0.393669	+	1.81033i
$292$	−2.52167	−	9.41100i	−0.147570	−	0.550737i
$293$	10.1699	−	2.72501i	0.594130	−	0.159197i	0.0507899	−	0.998709i	$-0.483826\pi$
$293$	10.1699	−	2.72501i	0.594130	−	0.159197i	0.543340	+	0.839513i	$0.317159\pi$
$294$	−9.23532	+	7.85550i	−0.538615	+	0.458142i
$295$	−19.2991	+	15.4538i	−1.12363	+	0.899758i
$296$	8.86885			0.515492
$297$	−0.977413	−	2.44307i	−0.0567153	−	0.141761i
$298$	−12.6309	+	12.6309i	−0.731691	+	0.731691i
$299$	0.989535	+	1.71392i	0.0572263	+	0.0991188i
$300$	−6.16199	+	6.08522i	−0.355763	+	0.351330i
$301$	−0.470017	+	28.5834i	−0.0270913	+	1.64752i
$302$	−7.43494	+	1.99219i	−0.427833	+	0.114637i
$303$	10.2001	+	6.55633i	0.585983	+	0.376651i
$304$	0.189412	+	0.328071i	0.0108635	+	0.0188161i
$305$	25.2022	−	3.85028i	1.44307	−	0.220467i
$306$	−6.36224	−	0.608495i	−0.363705	−	0.0347853i
$307$	−14.8876	+	14.8876i	−0.849678	+	0.849678i	−0.990093	−	0.140415i	$-0.955156\pi$
$307$	−14.8876	+	14.8876i	−0.849678	+	0.849678i	0.140415	+	0.990093i	$0.455156\pi$
$308$	−1.29969	+	0.325444i	−0.0740565	+	0.0185439i
$309$	−2.99651	−	3.29677i	−0.170465	−	0.187547i
$310$	7.54670	−	3.31061i	0.428624	−	0.188030i
$311$	25.8518	+	14.9256i	1.46592	+	0.846351i	0.999274	−	0.0380912i	$-0.0121277\pi$
$311$	25.8518	+	14.9256i	1.46592	+	0.846351i	0.466649	+	0.884442i	$0.345461\pi$
$312$	−1.43944	−	0.0686784i	−0.0814921	−	0.00388815i
$313$	−0.570127	+	2.12774i	−0.0322255	+	0.120267i	−0.980165	−	0.198183i	$-0.936496\pi$
$313$	−0.570127	+	2.12774i	−0.0322255	+	0.120267i	0.947939	+	0.318451i	$0.103162\pi$
$314$	13.0323			0.735454
$315$	13.0394	+	12.0405i	0.734689	+	0.678404i
$316$	−2.07960			−0.116987
$317$	−8.03856	+	30.0003i	−0.451491	+	1.68499i	0.246714	+	0.969088i	$0.420649\pi$
$317$	−8.03856	+	30.0003i	−0.451491	+	1.68499i	−0.698205	+	0.715898i	$0.746018\pi$
$318$	3.77173	−	5.86795i	0.211508	−	0.329058i
$319$	−0.983040	−	0.567558i	−0.0550397	−	0.0317772i
$320$	−0.812755	+	2.08313i	−0.0454344	+	0.116450i
$321$	4.46980	−	13.9791i	0.249480	−	0.780237i
$322$	−1.52868	−	6.10490i	−0.0851900	−	0.340213i
$323$	0.570673	−	0.570673i	0.0317531	−	0.0317531i
$324$	−1.70595	+	8.83684i	−0.0947748	+	0.490936i
$325$	3.68570	+	1.92909i	0.204446	+	0.107007i
$326$	11.1105	+	19.2439i	0.615353	+	1.06582i
$327$	12.2153	−	6.29623i	0.675506	−	0.348183i
$328$	4.97376	−	1.33272i	0.274630	−	0.0735869i
$329$	−0.137689	+	8.37333i	−0.00759102	+	0.461637i
$330$	0.701411	+	1.83157i	0.0386114	+	0.100825i
$331$	−13.0184	−	22.5486i	−0.715557	−	1.23938i	−0.962744	−	0.270414i	$-0.912839\pi$
$331$	−13.0184	−	22.5486i	−0.715557	−	1.23938i	0.247187	−	0.968968i	$-0.420494\pi$
$332$	1.28069	−	1.28069i	0.0702872	−	0.0702872i
$333$	−26.2388	+	4.40818i	−1.43788	+	0.241567i
$334$	−10.5320			−0.576286
$335$	−8.62270	−	0.954052i	−0.471108	−	0.0521254i
$336$	4.34134	+	1.46724i	0.236839	+	0.0800445i
$337$	−15.8487	+	4.24664i	−0.863332	+	0.231329i	−0.663202	−	0.748440i	$-0.730803\pi$
$337$	−15.8487	+	4.24664i	−0.863332	+	0.231329i	−0.200130	+	0.979769i	$0.564136\pi$
$338$	−3.18548	−	11.8884i	−0.173268	−	0.646643i
$339$	8.15044	−	7.40811i	0.442671	−	0.402353i
$340$	4.73488	+	0.523887i	0.256785	+	0.0284118i
$341$		−	1.86632i		−	0.101067i
$342$	−0.723446	−	0.876465i	−0.0391195	−	0.0473938i
$343$	−12.4342	−	13.7256i	−0.671382	−	0.741112i
$344$	9.35738	−	5.40248i	0.504516	−	0.291282i
$345$	−8.60329	+	3.29468i	−0.463186	+	0.177379i
$346$	−18.5508	−	10.7103i	−0.997298	−	0.575790i
$347$	−11.5626	+	3.09818i	−0.620711	+	0.166319i	−0.555451	−	0.831549i	$-0.687454\pi$
$347$	−11.5626	+	3.09818i	−0.620711	+	0.166319i	−0.0652600	+	0.997868i	$0.520788\pi$
$348$	1.77878	+	3.45100i	0.0953527	+	0.184993i
$349$	8.19954	+	14.2020i	0.438911	+	0.760216i	0.997606	−	0.0691571i	$-0.0220310\pi$
$349$	8.19954	+	14.2020i	0.438911	+	0.760216i	−0.558695	+	0.829373i	$0.688698\pi$
$350$	−9.58473	−	9.11773i	−0.512325	−	0.487363i
$351$	4.29277	−	0.512271i	0.229131	−	0.0273430i
$352$	0.358080	+	0.358080i	0.0190857	+	0.0190857i
$353$	1.95004	−	7.27766i	0.103790	−	0.387351i	−0.894415	−	0.447238i	$-0.852408\pi$
$353$	1.95004	−	7.27766i	0.103790	−	0.387351i	0.998205	+	0.0598876i	$0.0190742\pi$
$354$	5.83264	−	18.2413i	0.310001	−	0.969515i
$355$	31.8634	+	12.4318i	1.69113	+	0.659814i
$356$	10.8184	+	6.24598i	0.573372	+	0.331036i
$357$	0.625545	−	9.74276i	0.0331073	−	0.515642i
$358$	1.54475	+	0.413916i	0.0816428	+	0.0218761i
$359$			29.9412i			1.58024i	0.612953	+	0.790119i	$0.289981\pi$
$359$			29.9412i			1.58024i	−0.612953	+	0.790119i	$0.710019\pi$
$360$	1.36917	−	6.56699i	0.0721614	−	0.346111i
$361$	−18.8565			−0.992447
$362$	15.4702	+	4.14523i	0.813096	+	0.217868i
$363$	−18.5872	−	0.886834i	−0.975577	−	0.0465467i
$364$	0.0361923	−	2.20098i	0.00189699	−	0.115363i
$365$	−8.75203	−	19.9507i	−0.458102	−	1.04427i
$366$	−14.6136	+	13.2826i	−0.763865	+	0.694294i
$367$	−4.29107	−	1.14979i	−0.223992	−	0.0600184i	0.145078	−	0.989420i	$-0.453657\pi$
$367$	−4.29107	−	1.14979i	−0.223992	−	0.0600184i	−0.369069	+	0.929402i	$0.620324\pi$
$368$	−1.68198	+	1.68198i	−0.0876791	+	0.0876791i
$369$	−14.0527	+	6.41505i	−0.731552	+	0.333954i
$370$	19.6039	−	2.99500i	1.01916	−	0.155702i
$371$	9.13900	+	5.47869i	0.474473	+	0.284440i
$372$	−3.45153	+	5.36979i	−0.178953	+	0.278410i
$373$	0.148226	+	0.553188i	0.00767487	+	0.0286430i	0.969657	−	0.244469i	$-0.0786137\pi$
$373$	0.148226	+	0.553188i	0.00767487	+	0.0286430i	−0.961982	+	0.273112i	$0.911947\pi$
$374$	0.539425	−	0.934311i	0.0278930	−	0.0483121i
$375$	−11.5656	+	15.5318i	−0.597246	+	0.802058i
$376$	2.74119	−	1.58262i	0.141366	−	0.0816176i
$377$	1.31873	−	1.31873i	0.0679181	−	0.0679181i
$378$	−13.5733	−	2.18307i	−0.698135	−	0.112285i
$379$		−	20.3477i		−	1.04519i	−0.852580	−	0.522597i	$-0.824963\pi$
$379$		−	20.3477i		−	1.04519i	0.852580	−	0.522597i	$-0.175037\pi$
$380$	0.529469	+	0.661210i	0.0271612	+	0.0339194i
$381$	8.06361	−	25.2186i	0.413111	−	1.29199i
$382$	−0.215026	+	0.0576160i	−0.0110017	+	0.00294789i
$383$	2.59570	−	0.695515i	0.132634	−	0.0355392i	−0.191891	−	0.981416i	$-0.561462\pi$
$383$	2.59570	−	0.695515i	0.132634	−	0.0355392i	0.324525	+	0.945877i	$0.394795\pi$
$384$	−0.368045	−	1.69250i	−0.0187817	−	0.0863698i
$385$	−2.76295	+	1.15827i	−0.140813	+	0.0590309i
$386$	−11.1169			−0.565835
$387$	−24.9989	+	20.6345i	−1.27077	+	1.04891i
$388$	12.9021	+	12.9021i	0.655006	+	0.655006i
$389$	8.34516	−	4.81808i	0.423117	−	0.244286i	−0.273293	−	0.961931i	$-0.588113\pi$
$389$	8.34516	−	4.81808i	0.423117	−	0.244286i	0.696410	+	0.717644i	$0.254780\pi$
$390$	−3.20495	+	0.334287i	−0.162289	+	0.0169273i
$391$	4.38866	+	2.53379i	0.221944	+	0.128139i
$392$	−2.03306	+	6.69826i	−0.102685	+	0.338313i
$393$	0.233106	−	4.88569i	0.0117586	−	0.246450i
$394$	15.6589	−	9.04066i	0.788883	−	0.455462i
$395$	−4.59679	+	0.702278i	−0.231290	+	0.0353354i
$396$	−1.23737	−	0.881413i	−0.0621803	−	0.0442927i
$397$	20.3478	−	20.3478i	1.02123	−	1.02123i	0.0214558	−	0.999770i	$-0.493170\pi$
$397$	20.3478	−	20.3478i	1.02123	−	1.02123i	0.999770	−	0.0214558i	$-0.00683011\pi$
$398$	−2.97851	+	11.1159i	−0.149299	+	0.557192i
$399$	1.30366	−	1.14635i	0.0652646	−	0.0573894i
$400$	−1.09306	+	4.87906i	−0.0546531	+	0.243953i
$401$	5.97433	−	10.3478i	0.298344	−	0.516747i	−0.677413	−	0.735603i	$-0.736899\pi$
$401$	5.97433	−	10.3478i	0.298344	−	0.516747i	0.975757	+	0.218856i	$0.0702324\pi$
$402$	5.97310	−	3.07877i	0.297911	−	0.153555i
$403$	2.96183	+	0.793620i	0.147539	+	0.0395330i
$404$	7.00067			0.348297
$405$	−0.786671	+	20.1092i	−0.0390900	+	0.999236i
$406$	−5.18406	+	2.88043i	−0.257281	+	0.142953i
$407$	1.16241	−	4.33817i	0.0576184	−	0.215035i
$408$	−3.27993	+	1.69061i	−0.162381	+	0.0836975i
$409$	−10.0012	+	17.3226i	−0.494528	+	0.856548i	−0.999980	−	0.00630656i	$-0.997993\pi$
$409$	−10.0012	+	17.3226i	−0.494528	+	0.856548i	0.505452	+	0.862855i	$0.331326\pi$
$410$	10.5441	−	4.62549i	0.520734	−	0.228437i
$411$	6.16470	−	1.34056i	0.304082	−	0.0661248i
$412$	−2.48450	−	0.665719i	−0.122402	−	0.0327976i
$413$	28.1287	+	8.03500i	1.38412	+	0.395377i
$414$	4.14018	−	5.81221i	0.203479	−	0.285654i
$415$	2.39838	−	3.26336i	0.117732	−	0.160192i
$416$	−0.720537	+	0.416002i	−0.0353272	+	0.0203962i
$417$	−1.12330	−	0.0535951i	−0.0550084	−	0.00262456i
$418$	0.185300	−	0.0496510i	0.00906332	−	0.00242851i
$419$	5.87726	−	10.1797i	0.287123	−	0.497311i	−0.685999	−	0.727602i	$-0.740635\pi$
$419$	5.87726	−	10.1797i	0.287123	−	0.497311i	0.973122	+	0.230291i	$0.0739679\pi$
$420$	10.0917	+	1.77716i	0.492423	+	0.0867163i
$421$	−2.95448	−	5.11731i	−0.143992	−	0.249402i	0.785004	−	0.619491i	$-0.212661\pi$
$421$	−2.95448	−	5.11731i	−0.143992	−	0.249402i	−0.928997	+	0.370088i	$0.879327\pi$
$422$	11.9436	+	11.9436i	0.581407	+	0.581407i
$423$	−7.32328	+	6.04474i	−0.356070	+	0.293905i
$424$		−	4.02736i		−	0.195586i
$425$	10.6430	−	0.440950i	0.516261	−	0.0213892i
$426$	−25.8883	+	5.62960i	−1.25429	+	0.272755i
$427$	−20.9767	−	21.6782i	−1.01514	−	1.04908i
$428$	−2.19307	−	8.18465i	−0.106006	−	0.395620i
$429$	−0.222256	+	0.695094i	−0.0107306	+	0.0335594i
$430$	18.8593	−	15.1017i	0.909478	−	0.728270i
$431$	25.4818			1.22742			0.613708	−	0.789533i	$-0.289677\pi$
$431$	25.4818			1.22742			0.613708	+	0.789533i	$0.289677\pi$
$432$	1.93012	+	4.82438i	0.0928627	+	0.232113i
$433$	−22.1764	−	22.1764i	−1.06573	−	1.06573i	−0.997682	−	0.0680463i	$-0.978323\pi$
$433$	−22.1764	−	22.1764i	−1.06573	−	1.06573i	−0.0680463	−	0.997682i	$-0.521677\pi$
$434$	−8.36313	−	5.01357i	−0.401443	−	0.240659i
$435$	5.09725	+	7.02746i	0.244394	+	0.336941i
$436$	3.96711	−	6.87123i	0.189990	−	0.329072i
$437$	0.233221	+	0.870394i	0.0111565	+	0.0416366i
$438$	14.1957	+	9.12458i	0.678299	+	0.435989i
$439$	14.8695	+	25.7546i	0.709680	+	1.22920i	0.964976	+	0.262339i	$0.0844939\pi$
$439$	14.8695	+	25.7546i	0.709680	+	1.22920i	−0.255296	+	0.966863i	$0.582173\pi$
$440$	0.912430	+	0.670584i	0.0434984	+	0.0319688i
$441$	2.68558	−	20.8276i	0.127885	−	0.991789i
$442$	1.25336	+	1.25336i	0.0596164	+	0.0596164i
$443$	−8.71507	−	2.33519i	−0.414065	−	0.110948i	0.0457714	−	0.998952i	$-0.485425\pi$
$443$	−8.71507	−	2.33519i	−0.414065	−	0.110948i	−0.459837	+	0.888003i	$0.652092\pi$
$444$	−11.3674	+	10.3321i	−0.539473	+	0.490339i
$445$	26.0224	+	10.1529i	1.23358	+	0.481294i
$446$	17.9121	+	10.3416i	0.848164	+	0.489687i
$447$	1.47450	−	30.9042i	0.0697415	−	1.46172i
$448$	2.56651	−	0.642660i	0.121256	−	0.0303628i
$449$		−	38.2841i		−	1.80674i	−0.428862	−	0.903370i	$-0.641085\pi$
$449$		−	38.2841i		−	1.80674i	0.428862	−	0.903370i	$-0.358915\pi$
$450$	0.808773	−	14.9782i	0.0381259	−	0.706078i
$451$		−	2.60757i		−	0.122786i
$452$	1.64582	−	6.14230i	0.0774130	−	0.288909i
$453$	7.20866	−	11.2150i	0.338692	−	0.526927i
$454$	−6.65901	+	11.5337i	−0.312523	+	0.541306i
$455$	−0.663267	−	4.87731i	−0.0310944	−	0.228652i
$456$	−0.624970	−	0.199834i	−0.0292669	−	0.00935807i
$457$	10.1568	−	37.9056i	0.475114	−	1.77315i	−0.145847	−	0.989307i	$-0.546591\pi$
$457$	10.1568	−	37.9056i	0.475114	−	1.77315i	0.620960	−	0.783842i	$-0.286743\pi$
$458$	−17.1651	−	17.1651i	−0.802071	−	0.802071i
$459$	8.86350	−	6.63199i	0.413713	−	0.309555i
$460$	−3.14988	+	4.28588i	−0.146864	+	0.199830i
$461$	−11.1265	+	6.42391i	−0.518215	+	0.299192i	−0.736204	−	0.676760i	$-0.763384\pi$
$461$	−11.1265	+	6.42391i	−0.518215	+	0.299192i	0.217989	+	0.975951i	$0.430050\pi$
$462$	1.28670	−	1.93124i	0.0598626	−	0.0898495i
$463$	1.64056	+	6.12265i	0.0762433	+	0.284544i	0.993512	−	0.113724i	$-0.0362781\pi$
$463$	1.64056	+	6.12265i	0.0762433	+	0.284544i	−0.917269	+	0.398268i	$0.869611\pi$
$464$	1.94123	+	1.12077i	0.0901192	+	0.0520303i
$465$	−5.81596	+	13.0351i	−0.269709	+	0.604487i
$466$	9.16248	+	15.8699i	0.424444	+	0.735158i
$467$	−2.82781	+	2.82781i	−0.130855	+	0.130855i	−0.769501	−	0.638646i	$-0.779495\pi$
$467$	−2.82781	+	2.82781i	−0.130855	+	0.130855i	0.638646	+	0.769501i	$0.279495\pi$
$468$	1.92497	−	1.58890i	0.0889816	−	0.0734467i
$469$	4.98554	+	8.97274i	0.230211	+	0.414323i
$470$	5.52473	−	4.42396i	0.254837	−	0.204062i
$471$	−16.7037	+	15.1824i	−0.769668	+	0.699568i
$472$	−2.86174	−	10.6801i	−0.131722	−	0.491593i
$473$	−1.41617	−	5.28521i	−0.0651155	−	0.243014i
$474$	2.66547	−	2.42270i	0.122429	−	0.111278i
$475$	1.39364	+	1.28275i	0.0639445	+	0.0588567i
$476$	−2.73765	−	4.92709i	−0.125480	−	0.225833i
$477$	2.00176	+	11.9151i	0.0916543	+	0.545555i
$478$	−4.82441	+	4.82441i	−0.220663	+	0.220663i
$479$	5.21109	+	9.02587i	0.238101	+	0.412402i	0.960169	−	0.279419i	$-0.0901419\pi$
$479$	5.21109	+	9.02587i	0.238101	+	0.412402i	−0.722069	+	0.691821i	$0.756809\pi$
$480$	−1.38509	−	3.61684i	−0.0632203	−	0.165085i
$481$	6.39034	+	3.68946i	0.291374	+	0.168225i
$482$	−2.10135	−	7.84235i	−0.0957139	−	0.357209i
$483$	9.07146	+	6.04390i	0.412766	+	0.275007i
$484$	−9.30419	+	5.37178i	−0.422918	+	0.244172i
$485$	32.8762	+	24.1621i	1.49283	+	1.09714i
$486$	−8.10824	−	13.3138i	−0.367797	−	0.603925i
$487$	−10.8192	−	10.8192i	−0.490265	−	0.490265i	0.418125	−	0.908390i	$-0.362687\pi$
$487$	−10.8192	−	10.8192i	−0.490265	−	0.490265i	−0.908390	+	0.418125i	$0.862687\pi$
$488$	−2.95094	+	11.0130i	−0.133583	+	0.498537i
$489$	−36.6594	−	11.7218i	−1.65780	−	0.530079i
$490$	−2.23193	+	15.4925i	−0.100828	+	0.699881i
$491$	6.17687	−	10.6987i	0.278758	−	0.482823i	−0.692318	−	0.721592i	$-0.743411\pi$
$491$	6.17687	−	10.6987i	0.278758	−	0.482823i	0.971076	+	0.238769i	$0.0767439\pi$
$492$	−4.82239	+	7.50253i	−0.217410	+	0.338240i
$493$	1.23597	−	4.61270i	0.0556652	−	0.207746i
$494$			0.315183i			0.0141808i
$495$	−3.03277	−	1.53043i	−0.136313	−	0.0687879i
$496$			3.68545i			0.165482i
$497$	−9.83009	−	39.2572i	−0.440940	−	1.76093i
$498$	−0.149505	+	3.13348i	−0.00669947	+	0.140415i
$499$	11.4061	+	6.58533i	0.510609	+	0.294800i	0.733084	−	0.680138i	$-0.238080\pi$
$499$	11.4061	+	6.58533i	0.510609	+	0.294800i	−0.222475	+	0.974938i	$0.571414\pi$
$500$	−0.768475	+	11.1539i	−0.0343672	+	0.498817i
$501$	13.4991	−	12.2696i	0.603096	−	0.548167i
$502$	12.4838	+	3.34503i	0.557181	+	0.149296i
$503$	−18.1016	−	18.1016i	−0.807112	−	0.807112i	0.177084	−	0.984196i	$-0.443334\pi$
$503$	−18.1016	−	18.1016i	−0.807112	−	0.807112i	−0.984196	+	0.177084i	$0.943334\pi$
$504$	−7.27370	+	3.17700i	−0.323996	+	0.141515i
$505$	15.4744	−	2.36412i	0.688603	−	0.105202i
$506$	0.602282	+	1.04318i	0.0267747	+	0.0463752i
$507$	17.9327	+	11.5266i	0.796419	+	0.511913i
$508$	−3.95634	−	14.7653i	−0.175534	−	0.655103i
$509$	12.0623	−	20.8925i	0.534651	−	0.926043i	−0.464529	−	0.885558i	$-0.653776\pi$
$509$	12.0623	−	20.8925i	0.534651	−	0.926043i	0.999180	−	0.0404851i	$-0.0128903\pi$
$510$	−6.67911	+	4.84458i	−0.295756	+	0.214522i
$511$	−13.2541	+	22.1090i	−0.586325	+	0.978047i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.94832	+	0.280580i	0.0860206	+	0.0123879i
$514$	−28.3988			−1.25262
$515$	−5.71660	−	0.632509i	−0.251903	−	0.0278717i
$516$	−5.69974	+	17.8257i	−0.250917	+	0.784732i
$517$	−0.414858	−	1.54827i	−0.0182454	−	0.0680928i
$518$	−16.3171	−	16.8627i	−0.716931	−	0.740903i
$519$	36.2543	−	7.88376i	1.59139	−	0.346059i
$520$	−1.45221	+	1.16286i	−0.0636835	+	0.0509950i
$521$			28.0661i			1.22960i	0.788684	+	0.614799i	$0.210763\pi$
$521$			28.0661i			1.22960i	−0.788684	+	0.614799i	$0.789237\pi$
$522$	−6.30026	−	2.35097i	−0.275755	−	0.102899i
$523$	−23.2658	−	23.2658i	−1.01734	−	1.01734i	−0.999847	−	0.0174965i	$-0.994430\pi$
$523$	−23.2658	−	23.2658i	−1.01734	−	1.01734i	−0.0174965	−	0.999847i	$-0.505570\pi$
$524$	−1.41198	−	2.44562i	−0.0616827	−	0.106837i
$525$	22.9070	+	0.520324i	0.999742	+	0.0227088i
$526$	6.77187	−	11.7292i	0.295268	−	0.511419i
$527$	7.58403	−	2.03214i	0.330366	−	0.0885212i
$528$	−0.876116	−	0.0418012i	−0.0381281	−	0.00181917i
$529$	15.0185	−	8.67095i	0.652979	−	0.376998i
$530$	−1.36003	−	8.90216i	−0.0590760	−	0.386685i
$531$	13.7750	+	30.1752i	0.597785	+	1.30949i
$532$	0.275290	−	0.963725i	0.0119353	−	0.0417828i
$533$	4.13820	+	1.10883i	0.179245	+	0.0480286i
$534$	−21.1426	+	4.59761i	−0.914929	+	0.198958i
$535$	−7.61155	−	17.3509i	−0.329076	−	0.750146i
$536$	1.93986	−	3.35994i	0.0837892	−	0.145127i
$537$	−2.46215	+	1.26909i	−0.106250	+	0.0547653i
$538$	−3.14840	+	11.7500i	−0.135737	+	0.506578i
$539$	3.00996	+	1.87238i	0.129648	+	0.0806491i
$540$	5.89555	+	10.0121i	0.253704	+	0.430853i
$541$	−29.0941			−1.25085			−0.625426	−	0.780283i	$-0.715075\pi$
$541$	−29.0941			−1.25085			−0.625426	+	0.780283i	$0.715075\pi$
$542$	8.14321	+	2.18197i	0.349781	+	0.0937235i
$543$	−24.6576	+	12.7095i	−1.05816	+	0.545418i
$544$	−1.06521	+	1.84500i	−0.0456706	+	0.0791037i
$545$	6.44857	−	16.5280i	0.276227	−	0.707982i
$546$	2.51772	+	2.86321i	0.107748	+	0.122534i
$547$	−0.312920	+	1.16783i	−0.0133795	+	0.0499330i	−0.972293	−	0.233766i	$-0.924895\pi$
$547$	−0.312920	+	1.16783i	−0.0133795	+	0.0499330i	0.958913	+	0.283699i	$0.0915617\pi$
$548$	2.57554	−	2.57554i	0.110022	−	0.110022i
$549$	3.25653	−	34.0493i	0.138985	−	1.45319i
$550$	2.24331	+	1.17415i	0.0956550	+	0.0500658i
$551$	0.735382	−	0.424573i	0.0313283	−	0.0180874i
$552$	0.196349	−	4.11531i	0.00835719	−	0.175159i
$553$	3.82608	+	3.95402i	0.162702	+	0.168142i
$554$	16.2380	+	9.37500i	0.689885	+	0.398305i
$555$	−21.6376	+	26.6770i	−0.918466	+	1.13238i
$556$	−0.562291	+	0.324639i	−0.0238464	+	0.0137678i
$557$	−10.3981	−	10.3981i	−0.440582	−	0.440582i	0.451625	−	0.892208i	$-0.350844\pi$
$557$	−10.3981	−	10.3981i	−0.440582	−	0.440582i	−0.892208	+	0.451625i	$0.850844\pi$
$558$	−1.83182	−	10.9036i	−0.0775471	−	0.461584i
$559$	8.98979			0.380227
$560$	5.45605	−	2.28726i	0.230560	−	0.0966542i
$561$	0.397065	+	1.82595i	0.0167641	+	0.0770916i
$562$	32.0311	−	8.58271i	1.35115	−	0.362040i
$563$	−8.22792	+	2.20466i	−0.346766	+	0.0929155i	−0.427998	−	0.903780i	$-0.640781\pi$
$563$	−8.22792	+	2.20466i	−0.346766	+	0.0929155i	0.0812326	+	0.996695i	$0.474114\pi$
$564$	−1.66971	+	5.22192i	−0.0703073	+	0.219883i
$565$	1.56372	−	14.1329i	0.0657862	−	0.594574i
$566$			14.4041i			0.605448i
$567$	19.9404	−	13.0146i	0.837419	−	0.546561i
$568$	−10.8159	+	10.8159i	−0.453823	+	0.453823i
$569$	−11.0015	+	6.35174i	−0.461209	+	0.266279i	−0.712552	−	0.701619i	$-0.752461\pi$
$569$	−11.0015	+	6.35174i	−0.461209	+	0.266279i	0.251344	+	0.967898i	$0.419128\pi$
$570$	−1.44893	−	0.230665i	−0.0606890	−	0.00966149i
$571$	8.84337	−	15.3172i	0.370084	−	0.641004i	−0.619494	−	0.785001i	$-0.712662\pi$
$571$	8.84337	−	15.3172i	0.370084	−	0.641004i	0.989578	+	0.143997i	$0.0459957\pi$
$572$	0.109048	+	0.406972i	0.00455952	+	0.0170164i
$573$	0.208482	−	0.324350i	0.00870945	−	0.0135499i
$574$	−11.6848	−	7.00484i	−0.487712	−	0.292376i
$575$	−5.51522	+	10.5373i	−0.230001	+	0.439436i
$576$	2.44346	+	1.74054i	0.101811	+	0.0725226i
$577$	6.59203	−	6.59203i	0.274430	−	0.274430i	−0.556451	−	0.830881i	$-0.687837\pi$
$577$	6.59203	−	6.59203i	0.274430	−	0.274430i	0.830881	+	0.556451i	$0.187837\pi$
$578$	−12.0367	−	3.22522i	−0.500660	−	0.134152i
$579$	14.2488	−	12.9510i	0.592159	−	0.538226i
$580$	4.66941	+	1.82182i	0.193887	+	0.0756469i
$581$	−4.79127	−	0.0787863i	−0.198775	−	0.00326861i
$582$	−31.5677	−	1.50616i	−1.30852	−	0.0624323i
$583$	−1.96997	−	0.527851i	−0.0815877	−	0.0218614i
$584$	9.74298			0.403167
$585$	3.71842	−	4.16219i	0.153738	−	0.172085i
$586$			10.5286i			0.434933i
$587$	−32.0404	−	8.58519i	−1.32245	−	0.354349i	−0.472553	−	0.881302i	$-0.656667\pi$
$587$	−32.0404	−	8.58519i	−1.32245	−	0.354349i	−0.849894	+	0.526954i	$0.823334\pi$
$588$	−5.19755	−	10.9538i	−0.214343	−	0.451727i
$589$	1.20909	+	0.698068i	0.0498196	+	0.0287634i
$590$	−9.93231	−	22.6412i	−0.408907	−	0.932124i
$591$	−9.53811	+	29.8300i	−0.392345	+	1.22704i
$592$	−2.29543	+	8.56665i	−0.0943415	+	0.352087i
$593$	7.81683	+	7.81683i	0.320999	+	0.320999i	0.849150	−	0.528151i	$-0.177115\pi$
$593$	7.81683	+	7.81683i	0.320999	+	0.320999i	−0.528151	+	0.849150i	$0.677115\pi$
$594$	2.61280	−	0.311795i	0.107205	−	0.0127931i
$595$	−7.71522	−	9.96644i	−0.316293	−	0.408584i
$596$	−8.93142	−	15.4697i	−0.365845	−	0.633663i
$597$	−9.13229	−	17.7175i	−0.373760	−	0.725128i
$598$	−1.91163	+	0.512221i	−0.0781725	+	0.0209463i
$599$	−29.7077	−	17.1517i	−1.21382	−	0.700800i	−0.250232	−	0.968186i	$-0.580507\pi$
$599$	−29.7077	−	17.1517i	−1.21382	−	0.700800i	−0.963590	+	0.267385i	$0.913840\pi$
$600$	−4.28303	−	7.52700i	−0.174854	−	0.307288i
$601$	−0.643356	+	0.371442i	−0.0262430	+	0.0151514i	−0.513064	−	0.858350i	$-0.671490\pi$
$601$	−0.643356	+	0.371442i	−0.0262430	+	0.0151514i	0.486821	+	0.873502i	$0.338156\pi$
$602$	−27.4878	−	7.85193i	−1.12032	−	0.320021i
$603$	−4.06913	+	10.9047i	−0.165708	+	0.444073i
$604$		−	7.69721i		−	0.313195i
$605$	−18.7521	+	15.0159i	−0.762383	+	0.610483i
$606$	−8.97292	+	8.15568i	−0.364500	+	0.331302i
$607$	−9.12704	−	34.0626i	−0.370455	−	1.38256i	−0.859873	−	0.510508i	$-0.829458\pi$
$607$	−9.12704	−	34.0626i	−0.370455	−	1.38256i	0.489418	−	0.872049i	$-0.337209\pi$
$608$	−0.365915	+	0.0980467i	−0.0148398	+	0.00397632i
$609$	3.28887	−	9.73126i	0.133272	−	0.394331i
$610$	−2.80372	+	25.3400i	−0.113519	+	1.02599i
$611$	2.63350			0.106540
$612$	2.23443	−	5.98796i	0.0903214	−	0.242049i
$613$	−21.7971	+	21.7971i	−0.880377	+	0.880377i	−0.993573	−	0.113196i	$-0.963891\pi$
$613$	−21.7971	+	21.7971i	−0.880377	+	0.880377i	0.113196	+	0.993573i	$0.463891\pi$
$614$	−10.5271	−	18.2335i	−0.424839	−	0.735842i
$615$	−8.12591	+	18.2123i	−0.327669	+	0.734389i
$616$	0.0220285	−	1.33963i	0.000887554	−	0.0539753i
$617$	−4.51518	+	1.20984i	−0.181774	+	0.0487063i	−0.348558	−	0.937287i	$-0.613329\pi$
$617$	−4.51518	+	1.20984i	−0.181774	+	0.0487063i	0.166784	+	0.985994i	$0.446662\pi$
$618$	3.95999	−	2.04113i	0.159294	−	0.0821065i
$619$	6.92195	+	11.9892i	0.278217	+	0.481886i	0.970942	−	0.239316i	$-0.0769233\pi$
$619$	6.92195	+	11.9892i	0.278217	+	0.481886i	−0.692725	+	0.721202i	$0.743590\pi$
$620$	1.24457	+	8.14640i	0.0499832	+	0.327167i
$621$	1.46457	+	12.2729i	0.0587710	+	0.492494i
$622$	−21.1079	+	21.1079i	−0.846351	+	0.846351i
$623$	−8.02809	−	32.0608i	−0.321639	−	1.28449i
$624$	0.438892	−	1.37261i	0.0175697	−	0.0549485i
$625$	2.06800	+	24.9143i	0.0827200	+	0.996573i
$626$	−1.90768	−	1.10140i	−0.0762463	−	0.0440208i
$627$	−0.179660	+	0.279510i	−0.00717495	+	0.0111626i
$628$	−3.37300	+	12.5882i	−0.134597	+	0.502324i
$629$	18.8944			0.753369
$630$	−15.0051	+	9.47882i	−0.597816	+	0.377645i
$631$	−12.9024			−0.513636			−0.256818	−	0.966460i	$-0.582674\pi$
$631$	−12.9024			−0.513636			−0.256818	+	0.966460i	$0.582674\pi$
$632$	0.538240	−	2.00874i	0.0214100	−	0.0799034i
$633$	−29.2226	−	1.39427i	−1.16149	−	0.0554171i
$634$	−26.8976	−	15.5293i	−1.06824	−	0.616748i
$635$	−13.7314	−	31.3014i	−0.544914	−	1.24216i
$636$	4.69181	+	5.16195i	0.186042	+	0.204685i
$637$	−4.25139	+	3.98059i	−0.168446	+	0.157717i
$638$	0.802649	−	0.802649i	0.0317772	−	0.0317772i
$639$	26.6232	−	37.3751i	1.05320	−	1.47853i
$640$	−1.80179	−	1.32421i	−0.0712221	−	0.0523442i
$641$	21.7691	+	37.7052i	0.859828	+	1.48927i	0.872093	+	0.489341i	$0.162763\pi$
$641$	21.7691	+	37.7052i	0.859828	+	1.48927i	−0.0122645	+	0.999925i	$0.503904\pi$
$642$	12.3459	+	7.93555i	0.487254	+	0.313191i
$643$	4.71382	−	1.26306i	0.185895	−	0.0498104i	−0.164671	−	0.986349i	$-0.552656\pi$
$643$	4.71382	−	1.26306i	0.185895	−	0.0498104i	0.350565	+	0.936538i	$0.385989\pi$
$644$	6.29253	+	0.103473i	0.247961	+	0.00407739i
$645$	−6.57913	+	41.3271i	−0.259053	+	1.62725i
$646$	0.403527	+	0.698929i	0.0158766	+	0.0274990i
$647$	−21.5220	+	21.5220i	−0.846117	+	0.846117i	−0.989646	−	0.143529i	$-0.954155\pi$
$647$	−21.5220	+	21.5220i	−0.846117	+	0.846117i	0.143529	+	0.989646i	$0.454155\pi$
$648$	−8.09420	−	3.93496i	−0.317970	−	0.154580i
$649$	−5.59923			−0.219789
$650$	−2.81729	+	3.06083i	−0.110503	+	0.120056i
$651$	16.5599	−	3.31691i	0.649035	−	0.130000i
$652$	−21.4638	+	5.75121i	−0.840588	+	0.225235i
$653$	4.28473	+	15.9908i	0.167674	+	0.625769i	0.997684	+	0.0680199i	$0.0216682\pi$
$653$	4.28473	+	15.9908i	0.167674	+	0.625769i	−0.830010	+	0.557749i	$0.811665\pi$
$654$	2.92015	+	13.4286i	0.114187	+	0.525101i
$655$	−3.94695	−	4.92903i	−0.154220	−	0.192593i
$656$			5.14922i			0.201043i
$657$	−28.8250	+	4.84266i	−1.12457	+	0.188930i
$658$	−8.05238	−	2.30017i	−0.313914	−	0.0896701i
$659$	7.56200	−	4.36592i	0.294574	−	0.170072i	−0.345429	−	0.938445i	$-0.612267\pi$
$659$	7.56200	−	4.36592i	0.294574	−	0.170072i	0.640003	+	0.768373i	$0.278933\pi$
$660$	−1.95070	+	0.203465i	−0.0759310	+	0.00791985i
$661$	−3.46958	−	2.00316i	−0.134951	−	0.0779140i	0.431005	−	0.902350i	$-0.358159\pi$
$661$	−3.46958	−	2.00316i	−0.134951	−	0.0779140i	−0.565956	+	0.824436i	$0.691493\pi$
$662$	25.1497	−	6.73883i	0.977470	−	0.261912i
$663$	−3.06661	−	0.146314i	−0.119097	−	0.00568237i
$664$	0.905588	+	1.56852i	0.0351436	+	0.0608705i
$665$	0.283057	−	2.22320i	0.0109765	−	0.0862121i
$666$	2.53314	−	26.4857i	0.0981571	−	1.02630i
$667$	3.77021	+	3.77021i	0.145983	+	0.145983i
$668$	2.72589	−	10.1731i	0.105468	−	0.393611i
$669$	−35.0061	+	7.61233i	−1.35342	+	0.294310i
$670$	3.15326	−	8.08196i	0.121821	−	0.312233i
$671$	5.00022	+	2.88688i	0.193031	+	0.111447i
$672$	−2.54087	+	3.81366i	−0.0980160	+	0.147115i
$673$	27.2705	+	7.30710i	1.05120	+	0.281668i	0.742747	−	0.669572i	$-0.233522\pi$
$673$	27.2705	+	7.30710i	1.05120	+	0.281668i	0.308452	+	0.951240i	$0.400189\pi$
$674$		−	16.4077i		−	0.632003i
$675$	16.4127	+	20.1401i	0.631726	+	0.775192i
$676$	12.3078			0.473376
$677$	14.9413	+	4.00351i	0.574241	+	0.153867i	0.534241	−	0.845332i	$-0.320598\pi$
$677$	14.9413	+	4.00351i	0.574241	+	0.153867i	0.0399999	+	0.999200i	$0.487264\pi$
$678$	5.04619	+	9.79008i	0.193798	+	0.375986i
$679$	0.793719	−	48.2688i	0.0304601	−	1.85239i
$680$	−1.73151	+	4.43795i	−0.0664004	+	0.170188i
$681$	−4.90164	−	22.5407i	−0.187831	−	0.863762i
$682$	1.80272	+	0.483039i	0.0690299	+	0.0184965i
$683$	−10.2911	+	10.2911i	−0.393776	+	0.393776i	−0.876031	−	0.482255i	$-0.839818\pi$
$683$	−10.2911	+	10.2911i	−0.393776	+	0.393776i	0.482255	+	0.876031i	$0.339818\pi$
$684$	1.03384	−	0.471950i	0.0395299	−	0.0180455i
$685$	4.82328	−	6.56279i	0.184288	−	0.250751i
$686$	16.4761	−	8.45804i	0.629060	−	0.322929i
$687$	41.9979	+	2.00380i	1.60232	+	0.0764498i
$688$	2.79653	+	10.4368i	0.106617	+	0.397899i
$689$	1.67539	−	2.90186i	0.0638273	−	0.110552i
$690$	−0.955717	−	9.16286i	−0.0363835	−	0.348824i
$691$	−29.4248	+	16.9884i	−1.11937	+	0.646270i	−0.941241	−	0.337736i	$-0.890339\pi$
$691$	−29.4248	+	16.9884i	−1.11937	+	0.646270i	−0.178132	+	0.984007i	$0.557005\pi$
$692$	15.1467	−	15.1467i	0.575790	−	0.575790i
$693$	0.600679	+	3.97430i	0.0228179	+	0.150971i
$694$		−	11.9704i		−	0.454392i
$695$	−1.13327	+	0.907473i	−0.0429874	+	0.0344224i
$696$	−3.79379	+	0.824987i	−0.143803	+	0.0312710i
$697$	10.5962	−	2.83925i	0.401360	−	0.107544i
$698$	−15.8403	+	4.24439i	−0.599564	+	0.160653i
$699$	−30.2319	−	9.66663i	−1.14348	−	0.365625i
$700$	11.2878	−	6.89830i	0.426637	−	0.260731i
$701$	−24.3767			−0.920696			−0.460348	−	0.887739i	$-0.652275\pi$
$701$	−24.3767			−0.920696			−0.460348	+	0.887739i	$0.652275\pi$
$702$	−0.616234	+	4.27908i	−0.0232582	+	0.161503i
$703$	2.37569	+	2.37569i	0.0896008	+	0.0896008i
$704$	−0.438556	+	0.253201i	−0.0165287	+	0.00954286i
$705$	−1.92732	+	12.1065i	−0.0725869	+	0.455957i
$706$	6.52497	+	3.76719i	0.245571	+	0.141780i
$707$	−12.8800	−	13.3106i	−0.484401	−	0.500598i
$708$	16.1102	+	10.3551i	0.605457	+	0.389168i
$709$	−6.51587	+	3.76194i	−0.244709	+	0.141283i	−0.617339	−	0.786697i	$-0.711789\pi$
$709$	−6.51587	+	3.76194i	−0.244709	+	0.141283i	0.372630	+	0.927980i	$0.378456\pi$
$710$	−20.2551	+	27.5601i	−0.760161	+	1.03431i
$711$	−0.593979	+	6.21046i	−0.0222760	+	0.232911i
$712$	−8.83315	+	8.83315i	−0.331036	+	0.331036i
$713$	−2.26894	+	8.46778i	−0.0849723	+	0.317121i
$714$	9.24888	+	3.12584i	0.346131	+	0.116982i
$715$	0.378475	+	0.862754i	0.0141542	+	0.0322652i
$716$	−0.799624	+	1.38499i	−0.0298833	+	0.0517595i
$717$	0.563188	−	11.8039i	0.0210327	−	0.440825i
$718$	−28.9210	−	7.74936i	−1.07932	−	0.289204i
$719$	−1.47928			−0.0551678			−0.0275839	−	0.999619i	$-0.508781\pi$
$719$	−1.47928			−0.0551678			−0.0275839	+	0.999619i	$0.508781\pi$
$720$	5.98886	+	3.02218i	0.223192	+	0.112630i
$721$	3.30527	+	5.94866i	0.123095	+	0.221540i
$722$	4.88042	−	18.2140i	0.181630	−	0.677854i
$723$	11.8296	+	7.60367i	0.439946	+	0.282784i
$724$	−8.00797	+	13.8702i	−0.297614	+	0.515482i
$725$	10.9366	+	2.45013i	0.406174	+	0.0909957i
$726$	5.66735	−	17.7244i	0.210335	−	0.657813i
$727$	35.4256	+	9.49226i	1.31386	+	0.352048i	0.846675	−	0.532110i	$-0.178601\pi$
$727$	35.4256	+	9.49226i	1.31386	+	0.352048i	0.467187	+	0.884159i	$0.345267\pi$
$728$	2.11662	+	0.604615i	0.0784470	+	0.0224085i
$729$	25.9028	+	7.61858i	0.959365	+	0.282170i
$730$	21.5361	−	3.29019i	0.797086	−	0.121775i
$731$	19.9352	−	11.5096i	0.737329	−	0.425697i
$732$	−9.04775	−	17.5535i	−0.334414	−	0.648794i
$733$	16.0151	−	4.29124i	0.591533	−	0.158501i	0.0493791	−	0.998780i	$-0.484276\pi$
$733$	16.0151	−	4.29124i	0.591533	−	0.158501i	0.542154	+	0.840279i	$0.317609\pi$
$734$	2.22122	−	3.84726i	0.0819867	−	0.142005i
$735$	−15.1878	−	22.4573i	−0.560212	−	0.828349i
$736$	−1.18934	−	2.05999i	−0.0438396	−	0.0759324i
$737$	−1.38925	−	1.38925i	−0.0511737	−	0.0511737i
$738$	−2.55937	−	15.2342i	−0.0942118	−	0.560777i
$739$		−	31.5237i		−	1.15962i	−0.814752	−	0.579809i	$-0.803127\pi$
$739$		−	31.5237i		−	1.15962i	0.814752	−	0.579809i	$-0.196873\pi$
$740$	−2.18092	+	19.7111i	−0.0801721	+	0.724593i
$741$	−0.367183	−	0.403977i	−0.0134888	−	0.0148405i
$742$	−7.65736	+	7.40960i	−0.281110	+	0.272015i
$743$	13.5908	+	50.7217i	0.498599	+	1.86080i	0.508858	+	0.860850i	$0.330068\pi$
$743$	13.5908	+	50.7217i	0.498599	+	1.86080i	−0.0102591	+	0.999947i	$0.503266\pi$
$744$	−4.29349	−	4.72372i	−0.157407	−	0.173180i
$745$	−24.9663	−	31.1784i	−0.914694	−	1.14229i
$746$	−0.572702			−0.0209681
$747$	−3.45884	−	4.19042i	−0.126552	−	0.153320i
$748$	0.762861	+	0.762861i	0.0278930	+	0.0278930i
$749$	−11.5269	+	19.2280i	−0.421184	+	0.702577i
$750$	−12.0091	−	15.1915i	−0.438512	−	0.554714i
$751$	22.9171	−	39.6935i	0.836256	−	1.44844i	−0.0567482	−	0.998389i	$-0.518073\pi$
$751$	22.9171	−	39.6935i	0.836256	−	1.44844i	0.893004	−	0.450049i	$-0.148593\pi$
$752$	0.819227	+	3.05740i	0.0298741	+	0.111492i
$753$	−19.8977	+	10.2561i	−0.725113	+	0.373752i
$754$	0.932484	+	1.61511i	0.0339591	+	0.0588188i
$755$	−2.59934	−	17.0141i	−0.0945996	−	0.619206i
$756$	5.62171	−	12.5458i	0.204459	−	0.456285i
$757$	12.5869	+	12.5869i	0.457478	+	0.457478i	0.897827	−	0.440348i	$-0.145145\pi$
$757$	12.5869	+	12.5869i	0.457478	+	0.457478i	−0.440348	+	0.897827i	$0.645145\pi$
$758$	19.6544	+	5.26638i	0.713880	+	0.191284i
$759$	−1.98725	−	0.635421i	−0.0721326	−	0.0230643i
$760$	−0.775717	+	0.340293i	−0.0281382	+	0.0123437i
$761$	4.02864	+	2.32594i	0.146038	+	0.0843152i	0.571239	−	0.820784i	$-0.306463\pi$
$761$	4.02864	+	2.32594i	0.146038	+	0.0843152i	−0.425201	+	0.905099i	$0.639796\pi$
$762$	22.2723	+	14.3159i	0.806839	+	0.518610i
$763$	−20.3633	+	5.09901i	−0.737200	+	0.184596i
$764$		−	0.222611i		−	0.00805379i
$765$	2.91690	−	13.9905i	0.105461	−	0.505826i
$766$			2.68726i			0.0970948i
$767$	2.38098	−	8.88593i	0.0859721	−	0.320852i
$768$	1.73008	+	0.0825457i	0.0624290	+	0.00297861i
$769$	−0.325569	+	0.563903i	−0.0117403	+	0.0203348i	−0.871836	−	0.489798i	$-0.837070\pi$
$769$	−0.325569	+	0.563903i	−0.0117403	+	0.0203348i	0.860096	+	0.510133i	$0.170404\pi$
$770$	−0.403699	−	2.96859i	−0.0145483	−	0.106980i
$771$	36.3994	−	33.0842i	1.31089	−	1.19150i
$772$	2.87727	−	10.7381i	0.103555	−	0.386473i
$773$	−1.12343	−	1.12343i	−0.0404070	−	0.0404070i	0.686615	−	0.727022i	$-0.259096\pi$
$773$	−1.12343	−	1.12343i	−0.0404070	−	0.0404070i	−0.727022	+	0.686615i	$0.759096\pi$
$774$	−13.4612	−	29.4877i	−0.483851	−	1.05991i
$775$	5.50205	+	17.5867i	0.197639	+	0.631732i
$776$	−15.8018	+	9.12318i	−0.567252	+	0.327503i
$777$	40.5587	+	2.60411i	1.45503	+	0.0934221i
$778$	2.49402	+	9.30782i	0.0894151	+	0.333702i
$779$	1.68931	+	0.975322i	0.0605257	+	0.0349446i
$780$	0.506606	−	3.18227i	0.0181394	−	0.113943i
$781$	3.87294	+	6.70813i	0.138585	+	0.240036i
$782$	−3.58332	+	3.58332i	−0.128139	+	0.128139i
$783$	10.8140	−	4.32642i	0.386462	−	0.154614i
$784$	−5.94383	−	3.69742i	−0.212279	−	0.132051i
$785$	−3.20473	+	28.9643i	−0.114382	+	1.03378i
$786$	4.65888	+	1.48967i	0.166177	+	0.0531348i
$787$	12.8324	+	47.8911i	0.457425	+	1.70713i	0.680860	+	0.732414i	$0.261606\pi$
$787$	12.8324	+	47.8911i	0.457425	+	1.70713i	−0.223435	+	0.974719i	$0.571727\pi$
$788$	4.67979	+	17.4652i	0.166711	+	0.622173i
$789$	4.98471	+	22.9227i	0.177460	+	0.816071i
$790$	0.511389	−	4.62192i	0.0181944	−	0.164441i
$791$	−14.7066	+	8.17144i	−0.522906	+	0.290543i
$792$	1.17164	−	0.967084i	0.0416322	−	0.0343638i
$793$	−6.70771	+	6.70771i	−0.238198	+	0.238198i
$794$	14.3881	+	24.9208i	0.510613	+	0.884407i
$795$	12.1141	+	9.82567i	0.429641	+	0.348481i
$796$	−9.96629	−	5.75404i	−0.353246	−	0.203947i
$797$	8.42815	+	31.4543i	0.298540	+	1.11417i	0.938365	+	0.345647i	$0.112340\pi$
$797$	8.42815	+	31.4543i	0.298540	+	1.11417i	−0.639824	+	0.768521i	$0.720993\pi$
$798$	0.769880	+	1.55594i	0.0272535	+	0.0550795i
$799$	5.83989	−	3.37166i	0.206600	−	0.119281i
$800$	−4.42990	−	2.31861i	−0.156621	−	0.0819752i
$801$	21.7428	−	30.5236i	0.768243	−	1.07850i
$802$	8.44898	+	8.44898i	0.298344	+	0.298344i
$803$	1.27698	−	4.76574i	0.0450635	−	0.168179i
$804$	1.42791	+	6.56641i	0.0503586	+	0.231579i
$805$	13.9441	−	1.89626i	0.491465	−	0.0668344i
$806$	−1.53316	+	2.65551i	−0.0540031	+	0.0935362i
$807$	−9.65318	−	18.7281i	−0.339808	−	0.659259i
$808$	−1.81191	+	6.76213i	−0.0637427	+	0.237891i
$809$		−	3.26923i		−	0.114940i	−0.998347	−	0.0574701i	$-0.981697\pi$
$809$		−	3.26923i		−	0.114940i	0.998347	−	0.0574701i	$-0.0183034\pi$
$810$	−19.2204	−	5.96452i	−0.675337	−	0.209572i
$811$			27.9913i			0.982907i	0.870904	+	0.491454i	$0.163534\pi$
$811$			27.9913i			0.982907i	−0.870904	+	0.491454i	$0.836466\pi$
$812$	−1.44055	−	5.75293i	−0.0505532	−	0.201888i
$813$	−12.9793	+	6.69004i	−0.455204	+	0.234630i
$814$	3.88949	+	2.24560i	0.136327	+	0.0787082i
$815$	−45.5019	+	19.9609i	−1.59386	+	0.699199i
$816$	−0.784092	−	3.60573i	−0.0274487	−	0.126226i
$817$	3.95370	+	1.05939i	0.138323	+	0.0370634i
$818$	−14.1439	−	14.1439i	−0.494528	−	0.494528i
$819$	−6.56261	−	0.736731i	−0.229316	−	0.0257435i
$820$	1.73888	+	11.3819i	0.0607244	+	0.397475i
$821$	21.3771	+	37.0262i	0.746066	+	1.29222i	0.949695	+	0.313176i	$0.101393\pi$
$821$	21.3771	+	37.0262i	0.746066	+	1.29222i	−0.203629	+	0.979048i	$0.565274\pi$
$822$	−0.300662	+	6.30160i	−0.0104868	+	0.219794i
$823$	−7.34409	−	27.4085i	−0.255999	−	0.955401i	−0.967532	−	0.252748i	$-0.918666\pi$
$823$	−7.34409	−	27.4085i	−0.255999	−	0.955401i	0.711533	−	0.702653i	$-0.248001\pi$
$824$	1.28607	−	2.22754i	0.0448024	−	0.0776000i
$825$	−4.24316	+	1.10849i	−0.147728	+	0.0385927i
$826$	−15.0415	+	25.0906i	−0.523359	+	0.873014i
$827$	−25.6489	−	25.6489i	−0.891898	−	0.891898i	0.102804	−	0.994702i	$-0.467219\pi$
$827$	−25.6489	−	25.6489i	−0.891898	−	0.891898i	−0.994702	+	0.102804i	$0.967219\pi$
$828$	4.54260	+	5.50342i	0.157866	+	0.191257i
$829$	12.9141			0.448525			0.224262	−	0.974529i	$-0.428003\pi$
$829$	12.9141			0.448525			0.224262	+	0.974529i	$0.428003\pi$
$830$	2.53142	+	3.16128i	0.0878668	+	0.109730i
$831$	−31.7343	+	6.90085i	−1.10085	+	0.239388i
$832$	−0.215339	−	0.803655i	−0.00746553	−	0.0278617i
$833$	−4.33128	+	14.2701i	−0.150070	+	0.494430i
$834$	0.342501	−	1.07116i	0.0118599	−	0.0370911i
$835$	2.58990	−	23.4075i	0.0896272	−	0.810048i
$836$			0.191837i			0.00663481i
$837$	15.0504	+	11.8413i	0.520216	+	0.409294i
$838$	8.31169	+	8.31169i	0.287123	+	0.287123i
$839$	10.6813	+	18.5005i	0.368758	+	0.638708i	0.989372	−	0.145408i	$-0.0464496\pi$
$839$	10.6813	+	18.5005i	0.368758	+	0.638708i	−0.620613	+	0.784117i	$0.713116\pi$
$840$	−4.32852	+	9.28784i	−0.149348	+	0.320461i
$841$	−11.9878	+	20.7634i	−0.413371	+	0.715980i
$842$	5.70761	−	1.52935i	0.196697	−	0.0527049i
$843$	−31.0563	+	48.3164i	−1.06963	+	1.66411i
$844$	−14.6279	+	8.44542i	−0.503513	+	0.290703i
$845$	27.2053	−	4.15631i	0.935892	−	0.142982i
$846$	−3.94336	−	8.63824i	−0.135576	−	0.296989i
$847$	27.3316	+	7.80730i	0.939124	+	0.268262i
$848$	3.89013	+	1.04236i	0.133588	+	0.0357947i
$849$	−16.7805	−	18.4620i	−0.575905	−	0.633614i
$850$	−2.32868	+	10.3945i	−0.0798731	+	0.356527i
$851$	−10.5481	+	18.2698i	−0.361583	+	0.626280i
$852$	1.26261	−	26.4632i	0.0432564	−	0.906616i
$853$	1.65282	−	6.16842i	0.0565916	−	0.211203i	−0.931840	−	0.362869i	$-0.881797\pi$
$853$	1.65282	−	6.16842i	0.0565916	−	0.211203i	0.988432	+	0.151666i	$0.0484639\pi$
$854$	26.3687	−	14.6513i	0.902317	−	0.501356i
$855$	2.12585	−	1.39233i	0.0727025	−	0.0476168i
$856$	8.47338			0.289614
$857$	22.7138	+	6.08614i	0.775888	+	0.207898i	0.624971	−	0.780648i	$-0.285111\pi$
$857$	22.7138	+	6.08614i	0.775888	+	0.207898i	0.150917	+	0.988546i	$0.451777\pi$
$858$	−0.613885	−	0.394586i	−0.0209577	−	0.0134709i
$859$	17.1443	−	29.6947i	0.584955	−	1.01317i	−0.409926	−	0.912119i	$-0.634446\pi$
$859$	17.1443	−	29.6947i	0.584955	−	1.01317i	0.994881	−	0.101053i	$-0.0322211\pi$
$860$	9.70600	+	22.1253i	0.330972	+	0.754468i
$861$	23.1371	−	4.63430i	0.788511	−	0.157937i
$862$	−6.59517	+	24.6135i	−0.224633	+	0.838340i
$863$	−21.3705	+	21.3705i	−0.727459	+	0.727459i	−0.970113	−	0.242654i	$-0.921982\pi$
$863$	−21.3705	+	21.3705i	−0.727459	+	0.727459i	0.242654	+	0.970113i	$0.421982\pi$
$864$	−5.15955	+	0.615707i	−0.175531	+	0.0209468i
$865$	28.3655	−	38.5955i	0.964456	−	1.31229i
$866$	27.1604	−	15.6811i	0.922948	−	0.532864i
$867$	19.1850	−	9.88872i	0.651557	−	0.335839i
$868$	7.00728	−	6.78055i	0.237843	−	0.230147i
$869$	−0.912022	−	0.526556i	−0.0309382	−	0.0178622i
$870$	−8.10727	+	3.10472i	−0.274862	+	0.105260i
$871$	2.79548	−	1.61397i	0.0947213	−	0.0546874i
$872$	5.61034	+	5.61034i	0.189990	+	0.189990i
$873$	42.2157	−	34.8454i	1.42878	−	1.17934i
$874$	−0.901098			−0.0304801
$875$	22.6211	−	19.0600i	0.764734	−	0.644346i
$876$	−12.4878	+	11.3504i	−0.421923	+	0.383495i
$877$	−19.8737	+	5.32514i	−0.671087	+	0.179817i	−0.578244	−	0.815864i	$-0.696262\pi$
$877$	−19.8737	+	5.32514i	−0.671087	+	0.179817i	−0.0928426	+	0.995681i	$0.529595\pi$
$878$	−28.7256	+	7.69699i	−0.969441	+	0.259761i
$879$	−12.2657	−	13.4948i	−0.413711	−	0.455167i
$880$	−0.883889	+	0.707780i	−0.0297959	+	0.0238593i
$881$		−	43.3597i		−	1.46083i	−0.683005	−	0.730413i	$-0.739327\pi$
$881$		−	43.3597i		−	1.46083i	0.683005	−	0.730413i	$-0.260673\pi$
$882$	19.4228	+	7.98465i	0.654000	+	0.268857i
$883$	1.44039	−	1.44039i	0.0484731	−	0.0484731i	−0.682455	−	0.730928i	$-0.739088\pi$
$883$	1.44039	−	1.44039i	0.0484731	−	0.0484731i	0.730928	+	0.682455i	$0.239088\pi$
$884$	−1.53505	+	0.886261i	−0.0516293	+	0.0298082i
$885$	39.1071	+	17.4487i	1.31457	+	0.586533i
$886$	4.51125	−	7.81371i	0.151558	−	0.262507i
$887$	−5.24598	−	19.5783i	−0.176143	−	0.657374i	−0.996354	−	0.0853135i	$-0.972811\pi$
$887$	−5.24598	−	19.5783i	−0.176143	−	0.657374i	0.820211	−	0.572061i	$-0.193856\pi$
$888$	−7.03792	−	13.6542i	−0.236177	−	0.458205i
$889$	−20.7948	+	34.6877i	−0.697435	+	1.16339i
$890$	−16.5420	+	22.5079i	−0.554490	+	0.754467i
$891$	−2.98565	+	3.44351i	−0.100023	+	0.115362i
$892$	−14.6252	+	14.6252i	−0.489687	+	0.489687i
$893$	1.15821	+	0.310342i	0.0387581	+	0.0103852i
$894$	29.4695	+	9.42285i	0.985609	+	0.315147i
$895$	−1.29980	+	3.33144i	−0.0434474	+	0.111358i
$896$	−0.0435001	+	2.64539i	−0.00145324	+	0.0883764i
$897$	1.85345	−	2.88355i	0.0618850	−	0.0962789i
$898$	36.9796	+	9.90866i	1.23403	+	0.330656i
$899$	8.26107			0.275522
$900$	14.2585	+	4.65785i	0.475283	+	0.155262i
$901$		−	8.57998i		−	0.285840i
$902$	2.51872	+	0.674889i	0.0838642	+	0.0224714i
$903$	44.3791	−	21.9589i	1.47684	−	0.730745i
$904$	5.50703	+	3.17949i	0.183161	+	0.105748i
$905$	−13.0170	+	33.3633i	−0.432701	+	1.10903i
$906$	8.96714	+	9.86569i	0.297913	+	0.327766i
$907$	10.5047	−	39.2041i	0.348803	−	1.30175i	−0.539303	−	0.842112i	$-0.681312\pi$
$907$	10.5047	−	39.2041i	0.348803	−	1.30175i	0.888106	−	0.459639i	$-0.152021\pi$
$908$	−9.41727	−	9.41727i	−0.312523	−	0.312523i
$909$	1.99954	−	20.9066i	0.0663207	−	0.693429i
$910$	4.88279	+	0.621675i	0.161863	+	0.0206083i
$911$	7.19230	+	12.4574i	0.238291	+	0.412733i	0.960224	−	0.279230i	$-0.0900793\pi$
$911$	7.19230	+	12.4574i	0.238291	+	0.412733i	−0.721933	+	0.691963i	$0.756746\pi$
$912$	0.354779	−	0.551954i	0.0117479	−	0.0182770i
$913$	0.885929	−	0.237384i	0.0293200	−	0.00785627i
$914$	33.9852	+	19.6214i	1.12413	+	0.649018i
$915$	−25.9271	−	35.7451i	−0.857124	−	1.18170i
$916$	21.0228	−	12.1375i	0.694614	−	0.401035i
$917$	−2.05216	+	7.18414i	−0.0677683	+	0.237241i
$918$	4.11196	+	10.2780i	0.135715	+	0.339224i
$919$		−	13.1639i		−	0.434237i	−0.976145	−	0.217118i	$-0.930334\pi$
$919$		−	13.1639i		−	0.434237i	0.976145	−	0.217118i	$-0.0696658\pi$
$920$	−3.32459	−	4.15181i	−0.109609	−	0.136881i
$921$	34.7345	+	11.1063i	1.14454	+	0.365966i
$922$	−3.32526	−	12.4101i	−0.109512	−	0.408703i
$923$	−12.2927	+	3.29381i	−0.404618	+	0.108417i
$924$	1.53242	+	1.74270i	0.0504128	+	0.0573305i
$925$	1.83565	+	44.3063i	0.0603559	+	1.45678i
$926$	−6.33863			−0.208300
$927$	−2.69771	+	7.22949i	−0.0886045	+	0.237448i
$928$	−1.58500	+	1.58500i	−0.0520303	+	0.0520303i
$929$	−24.4537	−	42.3550i	−0.802299	−	1.38962i	−0.918100	−	0.396350i	$-0.870277\pi$
$929$	−24.4537	−	42.3550i	−0.802299	−	1.38962i	0.115801	−	0.993272i	$-0.463057\pi$
$930$	−11.0856	−	8.99151i	−0.363512	−	0.294843i
$931$	−2.33885	+	1.24966i	−0.0766526	+	0.0409559i
$932$	−17.7006	+	4.74285i	−0.579801	+	0.155357i
$933$	2.46408	−	51.6449i	0.0806704	−	1.69078i
$934$	−1.99956	−	3.46335i	−0.0654277	−	0.113324i
$935$	1.94386	+	1.42863i	0.0635711	+	0.0467211i
$936$	1.03654	+	2.27061i	0.0338803	+	0.0742173i
$937$	10.4499	−	10.4499i	0.341384	−	0.341384i	−0.515503	−	0.856888i	$-0.672395\pi$
$937$	10.4499	−	10.4499i	0.341384	−	0.341384i	0.856888	+	0.515503i	$0.172395\pi$
$938$	−9.95735	+	2.49334i	−0.325119	+	0.0814105i
$939$	3.72823	−	0.810731i	0.121666	−	0.0264572i
$940$	2.84331	+	6.48148i	0.0927387	+	0.211403i
$941$	−45.5610	−	26.3047i	−1.48525	−	0.857507i	−0.485387	−	0.874299i	$-0.661321\pi$
$941$	−45.5610	−	26.3047i	−1.48525	−	0.857507i	−0.999859	+	0.0167918i	$0.994655\pi$
$942$	−10.3418	−	20.0641i	−0.336955	−	0.653723i
$943$	−3.17010	+	11.8310i	−0.103233	+	0.385269i
$944$	11.0569			0.359871
$945$	8.18965	−	29.6299i	0.266409	−	0.963860i
$946$	5.47165			0.177899
$947$	−6.47589	+	24.1683i	−0.210438	+	0.785366i	0.777285	+	0.629149i	$0.216597\pi$
$947$	−6.47589	+	24.1683i	−0.210438	+	0.785366i	−0.987723	+	0.156217i	$0.950070\pi$
$948$	1.65028	+	3.20169i	0.0535985	+	0.103986i
$949$	7.02018	+	4.05310i	0.227885	+	0.131569i
$950$	−1.59974	+	1.01415i	−0.0519025	+	0.0329034i
$951$	52.5666	−	11.4310i	1.70459	−	0.370675i
$952$	5.46776	−	1.36914i	0.177211	−	0.0443740i
$953$	8.24676	−	8.24676i	0.267139	−	0.267139i	−0.560808	−	0.827946i	$-0.689509\pi$
$953$	8.24676	−	8.24676i	0.267139	−	0.267139i	0.827946	+	0.560808i	$0.189509\pi$
$954$	−12.0272	−	1.15030i	−0.389395	−	0.0372424i
$955$	−0.0751755	−	0.492065i	−0.00243262	−	0.0159228i
$956$	−3.41137	−	5.90867i	−0.110332	−	0.191100i
$957$	−0.0936990	+	1.96385i	−0.00302886	+	0.0634821i
$958$	−10.0670	+	2.69746i	−0.325251	+	0.0871509i
$959$	−9.63550	−	0.158443i	−0.311147	−	0.00511640i
$960$	3.85209	−	0.401785i	0.124326	−	0.0129676i
$961$	−8.70872	−	15.0840i	−0.280927	−	0.486579i
$962$	−5.21769	+	5.21769i	−0.168225	+	0.168225i
$963$	−25.0688	+	4.21161i	−0.807831	+	0.135717i
$964$	8.11900			0.261495
$965$	2.73373	−	24.7074i	0.0880018	−	0.795358i
$966$	−8.18582	+	7.19808i	−0.263374	+	0.231594i
$967$	−24.6626	+	6.60833i	−0.793096	+	0.212510i	−0.632551	−	0.774519i	$-0.717992\pi$
$967$	−24.6626	+	6.60833i	−0.793096	+	0.212510i	−0.160546	+	0.987028i	$0.551325\pi$
$968$	−2.78064	−	10.3775i	−0.0893731	−	0.333545i
$969$	−1.33145	−	0.425730i	−0.0427724	−	0.0136764i
$970$	−31.8478	+	25.5023i	−1.02257	+	0.818830i
$971$		−	39.5679i		−	1.26979i	−0.772597	−	0.634897i	$-0.781043\pi$
$971$		−	39.5679i		−	1.26979i	0.772597	−	0.634897i	$-0.218957\pi$
$972$	14.9587	−	4.38610i	0.479800	−	0.140684i
$973$	1.65176	+	0.471828i	0.0529530	+	0.0151261i
$974$	13.2508	−	7.65033i	0.424582	−	0.245132i
$975$	0.0451666	−	7.20523i	0.00144649	−	0.230752i
$976$	−9.87403	−	5.70077i	−0.316060	−	0.182477i
$977$	−51.2956	+	13.7446i	−1.64109	+	0.439729i	−0.957099	−	0.289760i	$-0.906424\pi$
$977$	−51.2956	+	13.7446i	−1.64109	+	0.439729i	−0.683992	+	0.729489i	$0.739758\pi$
$978$	20.8106	−	32.3765i	0.665448	−	1.03528i
$979$	3.16297	+	5.47843i	0.101089	+	0.175091i
$980$	−14.3870	−	6.16564i	−0.459575	−	0.196954i
$981$	−19.3870	−	13.8098i	−0.618978	−	0.440914i
$982$	8.73541	+	8.73541i	0.278758	+	0.278758i
$983$	14.5523	−	54.3099i	0.464146	−	1.73222i	−0.195558	−	0.980692i	$-0.562652\pi$
$983$	14.5523	−	54.3099i	0.464146	−	1.73222i	0.659704	−	0.751525i	$-0.270682\pi$
$984$	−5.99876	−	6.59987i	−0.191234	−	0.210396i
$985$	16.2423	+	37.0251i	0.517522	+	1.17972i
$986$	4.13563	+	2.38771i	0.131705	+	0.0760401i
$987$	13.0006	−	6.43272i	0.413813	−	0.204756i
$988$	−0.304443	−	0.0815753i	−0.00968563	−	0.00259526i
$989$			25.7015i			0.817261i
$990$	2.26322	−	2.53332i	0.0719300	−	0.0805143i
$991$	52.5858			1.67044			0.835221	−	0.549914i	$-0.185339\pi$
$991$	52.5858			1.67044			0.835221	+	0.549914i	$0.185339\pi$
$992$	−3.55987	−	0.953865i	−0.113026	−	0.0302852i
$993$	−24.3842	+	37.9363i	−0.773811	+	1.20387i
$994$	40.4638	+	0.665375i	1.28343	+	0.0211044i
$995$	−23.9728	−	9.35325i	−0.759989	−	0.296518i
$996$	−2.98802	−	0.955416i	−0.0946790	−	0.0302735i
$997$	26.8307	+	7.18926i	0.849737	+	0.227686i	0.657306	−	0.753624i	$-0.271696\pi$
$997$	26.8307	+	7.18926i	0.849737	+	0.227686i	0.192431	+	0.981310i	$0.438363\pi$
$998$	−9.31307	+	9.31307i	−0.294800	+	0.294800i
$999$	27.6087	+	36.8984i	0.873499	+	1.16741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bz.a.517.9	yes	192
5.3	odd	4	inner	630.2.bz.a.13.45	yes	192
7.6	odd	2	inner	630.2.bz.a.517.16	yes	192
9.7	even	3	inner	630.2.bz.a.97.28	yes	192
35.13	even	4	inner	630.2.bz.a.13.28	✓	192
45.43	odd	12	inner	630.2.bz.a.223.16	yes	192
63.34	odd	6	inner	630.2.bz.a.97.45	yes	192
315.223	even	12	inner	630.2.bz.a.223.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bz.a.13.28	✓	192	35.13	even	4	inner
630.2.bz.a.13.45	yes	192	5.3	odd	4	inner
630.2.bz.a.97.28	yes	192	9.7	even	3	inner
630.2.bz.a.97.45	yes	192	63.34	odd	6	inner
630.2.bz.a.223.9	yes	192	315.223	even	12	inner
630.2.bz.a.223.16	yes	192	45.43	odd	12	inner
630.2.bz.a.517.9	yes	192	1.1	even	1	trivial
630.2.bz.a.517.16	yes	192	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.793555 - 1.53957i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.08313 - 0.812755i) q^{5} +(1.69250 - 0.368045i) q^{6} +(0.642660 + 2.56651i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74054 + 2.44346i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.793555 - 1.53957i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.08313 - 0.812755i) q^{5} +(1.69250 - 0.368045i) q^{6} +(0.642660 + 2.56651i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.74054 + 2.44346i) q^{9} +(1.32421 - 1.80179i) q^{10} +(-0.253201 - 0.438556i) q^{11} +(-0.0825457 + 1.73008i) q^{12} +(0.803655 - 0.215339i) q^{13} +(-2.64539 - 0.0435001i) q^{14} +(0.401785 + 3.85209i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.50644 - 1.50644i) q^{17} +(-1.90972 - 2.31365i) q^{18} +0.378823 q^{19} +(1.39767 + 1.74543i) q^{20} +(3.44134 - 3.02609i) q^{21} +(0.489146 - 0.131066i) q^{22} +(0.615647 + 2.29762i) q^{23} +(-1.64977 - 0.527511i) q^{24} +(3.67886 + 3.38615i) q^{25} +0.832005i q^{26} +(5.14309 + 0.740661i) q^{27} +(0.726696 - 2.54400i) q^{28} +(1.94123 - 1.12077i) q^{29} +(-3.82482 - 0.608898i) q^{30} +(3.19169 + 1.84273i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.474259 + 0.737838i) q^{33} +(1.06521 + 1.84500i) q^{34} +(0.747201 - 5.86870i) q^{35} +(2.72909 - 1.24583i) q^{36} +(6.27123 + 6.27123i) q^{37} +(-0.0980467 + 0.365915i) q^{38} +(-0.969273 - 1.06640i) q^{39} +(-2.04770 + 0.898291i) q^{40} +(4.45935 + 2.57461i) q^{41} +(2.03229 + 4.10728i) q^{42} +(10.4368 + 2.79653i) q^{43} +0.506401i q^{44} +(5.61171 - 3.67542i) q^{45} -2.37868 q^{46} +(3.05740 + 0.819227i) q^{47} +(0.936528 - 1.45702i) q^{48} +(-6.17398 + 3.29879i) q^{49} +(-4.22293 + 2.67710i) q^{50} +(-3.51470 - 1.12382i) q^{51} +(-0.803655 - 0.215339i) q^{52} +(2.84777 - 2.84777i) q^{53} +(-2.04655 + 4.77615i) q^{54} +(0.171011 + 1.11936i) q^{55} +(2.26923 + 1.36037i) q^{56} +(-0.300617 - 0.583225i) q^{57} +(0.580152 + 2.16516i) q^{58} +(5.52845 - 9.57555i) q^{59} +(1.57809 - 3.53690i) q^{60} +(-9.87403 + 5.70077i) q^{61} +(-2.60601 + 2.60601i) q^{62} +(-7.38976 - 2.89681i) q^{63} -1.00000i q^{64} +(-1.84914 - 0.204596i) q^{65} +(-0.589950 - 0.649066i) q^{66} +(3.74752 - 1.00415i) q^{67} +(-2.05783 + 0.551394i) q^{68} +(3.04880 - 2.77112i) q^{69} +(5.47534 + 2.24067i) q^{70} -15.2959 q^{71} +(0.497041 + 2.95854i) q^{72} +(6.88933 + 6.88933i) q^{73} +(-7.68065 + 4.43443i) q^{74} +(2.29383 - 8.35095i) q^{75} +(-0.328071 - 0.189412i) q^{76} +(0.962839 - 0.931686i) q^{77} +(1.28093 - 0.660241i) q^{78} +(1.80099 - 1.03980i) q^{79} +(-0.337698 - 2.21042i) q^{80} +(-2.94103 - 8.50590i) q^{81} +(-3.64105 + 3.64105i) q^{82} +(-0.468767 + 1.74946i) q^{83} +(-4.49333 + 0.900001i) q^{84} +(-4.36247 + 1.91374i) q^{85} +(-5.40248 + 9.35738i) q^{86} +(-3.26597 - 2.09926i) q^{87} +(-0.489146 - 0.131066i) q^{88} -12.4920 q^{89} +(2.09776 + 6.37177i) q^{90} +(1.06915 + 1.92420i) q^{91} +(0.615647 - 2.29762i) q^{92} +(0.304218 - 6.37614i) q^{93} +(-1.58262 + 2.74119i) q^{94} +(-0.789138 - 0.307891i) q^{95} +(1.16498 + 1.28172i) q^{96} +(-17.6246 - 4.72251i) q^{97} +(-1.58845 - 6.81739i) q^{98} +(1.51230 + 0.144639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

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Database

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