LMFDB - Embedded newform 627.2.s.a.94.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [627,2,Mod(94,627)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("627.94"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 9, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.s (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			94.13
Character	$\chi$	$=$	627.94
Dual form			627.2.s.a.607.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.347788 - 1.07038i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.593275 - 0.431039i) q^{4} +(1.10843 - 3.41140i) q^{5} +(1.07038 + 0.347788i) q^{6} +(0.927280 + 1.27629i) q^{7} +(-2.48875 - 1.80818i) q^{8} +(-0.309017 - 0.951057i) q^{9} -4.03699 q^{10} +(-1.99207 - 2.65173i) q^{11} +0.733328i q^{12} +(-0.655482 - 2.01737i) q^{13} +(1.04362 - 1.43642i) q^{14} +(2.10836 + 2.90191i) q^{15} +(-0.616666 + 1.89790i) q^{16} +(-0.561413 - 0.182414i) q^{17} +(-0.910521 + 0.661532i) q^{18} +(-0.693386 + 4.30340i) q^{19} +(-0.812843 - 2.50167i) q^{20} -1.57758 q^{21} +(-2.14554 + 3.05451i) q^{22} +3.06632 q^{23} +(2.92570 - 0.950618i) q^{24} +(-6.36393 - 4.62366i) q^{25} +(-1.93138 + 1.40323i) q^{26} +(0.951057 + 0.309017i) q^{27} +(1.10026 + 0.357497i) q^{28} +(-0.100498 + 0.0730163i) q^{29} +(2.37289 - 3.26600i) q^{30} +(3.13956 - 1.02011i) q^{31} -3.90658 q^{32} +(3.31620 - 0.0529726i) q^{33} +0.664367i q^{34} +(5.38176 - 1.74864i) q^{35} +(-0.593275 - 0.431039i) q^{36} +(0.732770 + 1.00857i) q^{37} +(4.84742 - 0.754482i) q^{38} +(2.01737 + 0.655482i) q^{39} +(-8.92704 + 6.48587i) q^{40} +(-4.25561 - 3.09188i) q^{41} +(0.548664 + 1.68861i) q^{42} +0.00853166i q^{43} +(-2.32484 - 0.714542i) q^{44} -3.58695 q^{45} +(-1.06643 - 3.28214i) q^{46} +(2.96364 + 2.15321i) q^{47} +(-1.17297 - 1.61445i) q^{48} +(1.39405 - 4.29044i) q^{49} +(-2.73578 + 8.41988i) q^{50} +(0.477566 - 0.346972i) q^{51} +(-1.25844 - 0.914314i) q^{52} +(-2.63016 + 0.854590i) q^{53} -1.12547i q^{54} +(-11.2542 + 3.85649i) q^{55} -4.85306i q^{56} +(-3.07396 - 3.09043i) q^{57} +(0.113107 + 0.0821773i) q^{58} +(-4.74520 - 6.53120i) q^{59} +(2.50167 + 0.812843i) q^{60} +(-9.81677 - 3.18966i) q^{61} +(-2.18381 - 3.00575i) q^{62} +(0.927280 - 1.27629i) q^{63} +(2.59199 + 7.97734i) q^{64} -7.60859 q^{65} +(-1.21004 - 3.53118i) q^{66} -11.8404i q^{67} +(-0.411700 + 0.133769i) q^{68} +(-1.80234 + 2.48071i) q^{69} +(-3.74342 - 5.15238i) q^{70} +(10.6057 + 3.44600i) q^{71} +(-0.950618 + 2.92570i) q^{72} +(7.76996 + 10.6944i) q^{73} +(0.824707 - 1.13511i) q^{74} +(7.48124 - 2.43080i) q^{75} +(1.44356 + 2.85197i) q^{76} +(1.53717 - 5.00135i) q^{77} -2.38732i q^{78} +(-4.30687 - 13.2552i) q^{79} +(5.79097 + 4.20739i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.82944 + 5.63044i) q^{82} +(6.97337 + 2.26578i) q^{83} +(-0.935940 + 0.680000i) q^{84} +(-1.24457 + 1.71301i) q^{85} +(0.00913212 - 0.00296721i) q^{86} -0.124223i q^{87} +(0.162958 + 10.2015i) q^{88} -0.496364i q^{89} +(1.24750 + 3.83941i) q^{90} +(1.96693 - 2.70725i) q^{91} +(1.81917 - 1.32171i) q^{92} +(-1.02011 + 3.13956i) q^{93} +(1.27404 - 3.92109i) q^{94} +(13.9120 + 7.13543i) q^{95} +(2.29623 - 3.16049i) q^{96} +(0.160599 - 0.0521817i) q^{97} -5.07724 q^{98} +(-1.90636 + 2.71400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 40 q^{4} + 4 q^{5} - 10 q^{7} + 40 q^{9} + 10 q^{11} - 40 q^{16} - 50 q^{17} + 76 q^{20} + 16 q^{23} - 80 q^{25} - 68 q^{26} - 40 q^{35} + 40 q^{36} - 62 q^{38} + 8 q^{42} + 40 q^{44} - 4 q^{45}+ \cdots - 10 q^{99}+O(q^{100}) $ 160 * q - 40 * q^4 + 4 * q^5 - 10 * q^7 + 40 * q^9 + 10 * q^11 - 40 * q^16 - 50 * q^17 + 76 * q^20 + 16 * q^23 - 80 * q^25 - 68 * q^26 - 40 * q^35 + 40 * q^36 - 62 * q^38 + 8 * q^42 + 40 * q^44 - 4 * q^45 + 20 * q^47 + 110 * q^49 - 18 * q^55 - 20 * q^57 - 24 * q^58 + 10 * q^61 + 120 * q^62 - 10 * q^63 - 136 * q^64 - 12 * q^66 + 160 * q^68 + 20 * q^73 - 100 * q^74 + 90 * q^77 - 156 * q^80 - 40 * q^81 + 68 * q^82 - 200 * q^83 + 30 * q^85 - 84 * q^92 - 96 * q^93 - 60 * q^95 + 100 * q^96 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$-1$

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 $

$2$	−0.347788	−	1.07038i	−0.245923	−	0.756874i	−0.995483	−	0.0949374i	$-0.969735\pi$
$2$	−0.347788	−	1.07038i	−0.245923	−	0.756874i	0.749560	−	0.661936i	$-0.230265\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	0.593275	−	0.431039i	0.296637	−	0.215520i
$5$	1.10843	−	3.41140i	0.495705	−	1.52562i	−0.320150	−	0.947367i	$-0.603733\pi$
$5$	1.10843	−	3.41140i	0.495705	−	1.52562i	0.815855	−	0.578256i	$-0.196267\pi$
$6$	1.07038	+	0.347788i	0.436981	+	0.141984i
$7$	0.927280	+	1.27629i	0.350479	+	0.482393i	0.947465	−	0.319859i	$-0.103635\pi$
$7$	0.927280	+	1.27629i	0.350479	+	0.482393i	−0.596987	+	0.802251i	$0.703635\pi$
$8$	−2.48875	−	1.80818i	−0.879906	−	0.639289i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	−4.03699			−1.27661
$11$	−1.99207	−	2.65173i	−0.600632	−	0.799526i
$11$	−1.99207	−	2.65173i	−0.600632	−	0.799526i
$12$			0.733328i			0.211694i
$13$	−0.655482	−	2.01737i	−0.181798	−	0.559517i	0.818081	−	0.575104i	$-0.195038\pi$
$13$	−0.655482	−	2.01737i	−0.181798	−	0.559517i	−0.999879	+	0.0155871i	$0.995038\pi$
$14$	1.04362	−	1.43642i	0.278919	−	0.383900i
$15$	2.10836	+	2.90191i	0.544376	+	0.749269i
$16$	−0.616666	+	1.89790i	−0.154167	+	0.474476i
$17$	−0.561413	−	0.182414i	−0.136163	−	0.0442419i	0.240143	−	0.970738i	$-0.422806\pi$
$17$	−0.561413	−	0.182414i	−0.136163	−	0.0442419i	−0.376306	+	0.926496i	$0.622806\pi$
$18$	−0.910521	+	0.661532i	−0.214612	+	0.155925i
$19$	−0.693386	+	4.30340i	−0.159074	+	0.987267i
$19$	−0.693386	+	4.30340i	−0.159074	+	0.987267i
$20$	−0.812843	−	2.50167i	−0.181757	−	0.559391i
$21$	−1.57758			−0.344257
$22$	−2.14554	+	3.05451i	−0.457431	+	0.651224i
$23$	3.06632			0.639373			0.319686	−	0.947523i	$-0.396422\pi$
$23$	3.06632			0.639373			0.319686	+	0.947523i	$0.396422\pi$
$24$	2.92570	−	0.950618i	0.597207	−	0.194044i
$25$	−6.36393	−	4.62366i	−1.27279	−	0.924733i
$26$	−1.93138	+	1.40323i	−0.378775	+	0.275196i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	1.10026	+	0.357497i	0.207930	+	0.0675606i
$29$	−0.100498	+	0.0730163i	−0.0186621	+	0.0135588i	−0.597077	−	0.802184i	$-0.703671\pi$
$29$	−0.100498	+	0.0730163i	−0.0186621	+	0.0135588i	0.578415	+	0.815743i	$0.303671\pi$
$30$	2.37289	−	3.26600i	0.433228	−	0.596287i
$31$	3.13956	−	1.02011i	0.563882	−	0.183217i	−0.0131849	−	0.999913i	$-0.504197\pi$
$31$	3.13956	−	1.02011i	0.563882	−	0.183217i	0.577067	+	0.816697i	$0.304197\pi$
$32$	−3.90658			−0.690593
$33$	3.31620	−	0.0529726i	0.577277	−	0.00922135i
$34$			0.664367i			0.113938i
$35$	5.38176	−	1.74864i	0.909683	−	0.295574i
$36$	−0.593275	−	0.431039i	−0.0988791	−	0.0718399i
$37$	0.732770	+	1.00857i	0.120467	+	0.165808i	0.864991	−	0.501787i	$-0.167324\pi$
$37$	0.732770	+	1.00857i	0.120467	+	0.165808i	−0.744525	+	0.667595i	$0.767324\pi$
$38$	4.84742	−	0.754482i	0.786356	−	0.122393i
$39$	2.01737	+	0.655482i	0.323037	+	0.104961i
$40$	−8.92704	+	6.48587i	−1.41149	+	1.02551i
$41$	−4.25561	−	3.09188i	−0.664614	−	0.482871i	0.203604	−	0.979053i	$-0.434735\pi$
$41$	−4.25561	−	3.09188i	−0.664614	−	0.482871i	−0.868218	+	0.496183i	$0.834735\pi$
$42$	0.548664	+	1.68861i	0.0846607	+	0.260559i
$43$			0.00853166i			0.00130107i	1.00000		0.000650533i	$0.000207071\pi$
$43$			0.00853166i			0.00130107i	−1.00000		0.000650533i	$0.999793\pi$
$44$	−2.32484	−	0.714542i	−0.350483	−	0.107721i
$45$	−3.58695			−0.534712
$46$	−1.06643	−	3.28214i	−0.157237	−	0.483925i
$47$	2.96364	+	2.15321i	0.432292	+	0.314078i	0.782565	−	0.622569i	$-0.213911\pi$
$47$	2.96364	+	2.15321i	0.432292	+	0.314078i	−0.350273	+	0.936648i	$0.613911\pi$
$48$	−1.17297	−	1.61445i	−0.169304	−	0.233026i
$49$	1.39405	−	4.29044i	0.199150	−	0.612920i
$50$	−2.73578	+	8.41988i	−0.386898	+	1.19075i
$51$	0.477566	−	0.346972i	0.0668727	−	0.0485858i
$52$	−1.25844	−	0.914314i	−0.174515	−	0.126792i
$53$	−2.63016	+	0.854590i	−0.361280	+	0.117387i	−0.484032	−	0.875050i	$-0.660828\pi$
$53$	−2.63016	+	0.854590i	−0.361280	+	0.117387i	0.122752	+	0.992437i	$0.460828\pi$
$54$		−	1.12547i		−	0.153156i
$55$	−11.2542	+	3.85649i	−1.51751	+	0.520009i
$56$		−	4.85306i		−	0.648518i
$57$	−3.07396	−	3.09043i	−0.407156	−	0.409338i
$58$	0.113107	+	0.0821773i	0.0148517	+	0.0107904i
$59$	−4.74520	−	6.53120i	−0.617772	−	0.850290i	0.379416	−	0.925226i	$-0.376125\pi$
$59$	−4.74520	−	6.53120i	−0.617772	−	0.850290i	−0.997188	+	0.0749359i	$0.976125\pi$
$60$	2.50167	+	0.812843i	0.322965	+	0.104938i
$61$	−9.81677	−	3.18966i	−1.25691	−	0.408394i	−0.396516	−	0.918028i	$-0.629781\pi$
$61$	−9.81677	−	3.18966i	−1.25691	−	0.408394i	−0.860392	+	0.509633i	$0.829781\pi$
$62$	−2.18381	−	3.00575i	−0.277344	−	0.381731i
$63$	0.927280	−	1.27629i	0.116826	−	0.160798i
$64$	2.59199	+	7.97734i	0.323999	+	0.997167i
$65$	−7.60859			−0.943729
$66$	−1.21004	−	3.53118i	−0.148945	−	0.434658i
$67$		−	11.8404i		−	1.44654i	−0.690568	−	0.723268i	$-0.742639\pi$
$67$		−	11.8404i		−	1.44654i	0.690568	−	0.723268i	$-0.257361\pi$
$68$	−0.411700	+	0.133769i	−0.0499259	+	0.0162219i
$69$	−1.80234	+	2.48071i	−0.216976	+	0.298642i
$70$	−3.74342	−	5.15238i	−0.447424	−	0.615827i
$71$	10.6057	+	3.44600i	1.25866	+	0.408965i	0.861018	−	0.508575i	$-0.169827\pi$
$71$	10.6057	+	3.44600i	1.25866	+	0.408965i	0.397645	+	0.917539i	$0.369827\pi$
$72$	−0.950618	+	2.92570i	−0.112031	+	0.344797i
$73$	7.76996	+	10.6944i	0.909405	+	1.25169i	0.967369	+	0.253370i	$0.0815390\pi$
$73$	7.76996	+	10.6944i	0.909405	+	1.25169i	−0.0579646	+	0.998319i	$0.518461\pi$
$74$	0.824707	−	1.13511i	0.0958702	−	0.131954i
$75$	7.48124	−	2.43080i	0.863860	−	0.280685i
$76$	1.44356	+	2.85197i	0.165588	+	0.327144i
$77$	1.53717	−	5.00135i	0.175177	−	0.569957i
$78$		−	2.38732i		−	0.270311i
$79$	−4.30687	−	13.2552i	−0.484560	−	1.49132i	−0.832617	−	0.553849i	$-0.813158\pi$
$79$	−4.30687	−	13.2552i	−0.484560	−	1.49132i	0.348057	−	0.937474i	$-0.386842\pi$
$80$	5.79097	+	4.20739i	0.647450	+	0.470400i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−1.82944	+	5.63044i	−0.202028	+	0.621778i
$83$	6.97337	+	2.26578i	0.765426	+	0.248702i	0.665606	−	0.746303i	$-0.268173\pi$
$83$	6.97337	+	2.26578i	0.765426	+	0.248702i	0.0998204	+	0.995005i	$0.468173\pi$
$84$	−0.935940	+	0.680000i	−0.102119	+	0.0741941i
$85$	−1.24457	+	1.71301i	−0.134993	+	0.185802i
$86$	0.00913212	−	0.00296721i	0.000984742	−	0.000319962i
$87$		−	0.124223i		−	0.0133181i
$88$	0.162958	+	10.2015i	0.0173714	+	1.08749i
$89$		−	0.496364i		−	0.0526145i	−0.999654	−	0.0263072i	$-0.991625\pi$
$89$		−	0.496364i		−	0.0526145i	0.999654	−	0.0263072i	$-0.00837482\pi$
$90$	1.24750	+	3.83941i	0.131498	+	0.404709i
$91$	1.96693	−	2.70725i	0.206190	−	0.283797i
$92$	1.81917	−	1.32171i	0.189662	−	0.137797i
$93$	−1.02011	+	3.13956i	−0.105780	+	0.325558i
$94$	1.27404	−	3.92109i	0.131407	−	0.404429i
$95$	13.9120	+	7.13543i	1.42734	+	0.732079i
$96$	2.29623	−	3.16049i	0.234358	−	0.322566i
$97$	0.160599	−	0.0521817i	0.0163063	−	0.00529825i	−0.300852	−	0.953671i	$-0.597271\pi$
$97$	0.160599	−	0.0521817i	0.0163063	−	0.00529825i	0.317159	+	0.948372i	$0.397271\pi$
$98$	−5.07724			−0.512878
$99$	−1.90636	+	2.71400i	−0.191596	+	0.272767i
$100$	−5.76854			−0.576854
$101$	7.82398	−	2.54217i	0.778515	−	0.252955i	0.107309	−	0.994226i	$-0.465777\pi$
$101$	7.82398	−	2.54217i	0.778515	−	0.252955i	0.671206	+	0.741271i	$0.265777\pi$
$102$	−0.537484	−	0.390505i	−0.0532189	−	0.0386658i
$103$	8.11014	+	11.1626i	0.799116	+	1.09989i	0.992913	+	0.118847i	$0.0379197\pi$
$103$	8.11014	+	11.1626i	0.799116	+	1.09989i	−0.193797	+	0.981042i	$0.562080\pi$
$104$	−2.01644	+	6.20595i	−0.197728	+	0.608544i
$105$	−1.74864	+	5.38176i	−0.170650	+	0.525206i
$106$	1.82947	+	2.51805i	0.177694	+	0.244575i
$107$	11.9773	+	8.70205i	1.15789	+	0.841259i	0.989510	−	0.144463i	$-0.0461453\pi$
$107$	11.9773	+	8.70205i	1.15789	+	0.841259i	0.168383	+	0.985722i	$0.446145\pi$
$108$	0.697436	−	0.226611i	0.0671108	−	0.0218056i
$109$	8.16882			0.782431			0.391216	−	0.920299i	$-0.372055\pi$
$109$	8.16882			0.782431			0.391216	+	0.920299i	$0.372055\pi$
$110$	8.04197	+	10.7050i	0.766772	+	1.02068i
$111$	−1.24666			−0.118328
$112$	−2.99410	+	0.972842i	−0.282916	+	0.0919249i
$113$	1.55097	−	2.13473i	0.145903	−	0.200819i	−0.729810	−	0.683650i	$-0.760392\pi$
$113$	1.55097	−	2.13473i	0.145903	−	0.200819i	0.875713	+	0.482831i	$0.160392\pi$
$114$	−2.23886	+	4.36512i	−0.209688	+	0.408831i
$115$	3.39881	−	10.4605i	0.316940	−	0.975442i
$116$	−0.0281502	+	0.0866375i	−0.00261368	+	0.00804409i
$117$	−1.71607	+	1.24680i	−0.158651	+	0.115267i
$118$	−5.34055	+	7.35064i	−0.491638	+	0.676681i
$119$	−0.287773	−	0.885675i	−0.0263801	−	0.0811897i
$120$		−	11.0344i		−	1.00730i
$121$	−3.06331	+	10.5649i	−0.278483	+	0.960441i
$122$			11.6170i			1.05175i
$123$	5.00277	−	1.62550i	0.451084	−	0.146566i
$124$	1.42292	−	1.95848i	0.127782	−	0.175877i
$125$	−8.31758	+	6.04307i	−0.743947	+	0.540509i
$126$	−1.68861	−	0.548664i	−0.150434	−	0.0488789i
$127$	−1.30501	+	4.01640i	−0.115801	+	0.356398i	−0.992113	−	0.125345i	$-0.959996\pi$
$127$	−1.30501	+	4.01640i	−0.115801	+	0.356398i	0.876312	+	0.481743i	$0.159996\pi$
$128$	1.31635	−	0.956382i	0.116350	−	0.0845330i
$129$	−0.00690226	−	0.00501478i	−0.000607710	−	0.000441527i
$130$	2.64618	+	8.14409i	0.232085	+	0.714284i
$131$		−	8.20683i		−	0.717034i	−0.933523	−	0.358517i	$-0.883283\pi$
$131$		−	8.20683i		−	0.717034i	0.933523	−	0.358517i	$-0.116717\pi$
$132$	1.94459	−	1.46084i	0.169254	−	0.127150i
$133$	−6.13535	+	3.10549i	−0.532002	+	0.269280i
$134$	−12.6737	+	4.11795i	−1.09484	+	0.355737i
$135$	2.10836	−	2.90191i	0.181459	−	0.249756i
$136$	1.06738	+	1.46912i	0.0915270	+	0.125976i
$137$	4.34180	−	13.3627i	0.370945	−	1.14165i	−0.575229	−	0.817993i	$-0.695087\pi$
$137$	4.34180	−	13.3627i	0.370945	−	1.14165i	0.946174	−	0.323659i	$-0.104913\pi$
$138$	3.28214	+	1.06643i	0.279394	+	0.0907806i
$139$	2.41870	+	3.32906i	0.205152	+	0.282367i	0.899178	−	0.437582i	$-0.144165\pi$
$139$	2.41870	+	3.32906i	0.205152	+	0.282367i	−0.694027	+	0.719949i	$0.744165\pi$
$140$	2.43913	−	3.35717i	0.206144	−	0.283733i
$141$	−3.48397	+	1.13201i	−0.293403	+	0.0953325i
$142$		−	12.5506i		−	1.05322i
$143$	−4.04374	+	5.75689i	−0.338154	+	0.481416i
$144$	1.99557			0.166298
$145$	0.137692	+	0.423773i	0.0114347	+	0.0351925i
$146$	8.74482	−	12.0362i	0.723726	−	0.996124i
$147$	2.65164	+	3.64966i	0.218703	+	0.301019i
$148$	0.869467	+	0.282507i	0.0714698	+	0.0232219i
$149$	−1.96516	−	0.638519i	−0.160992	−	0.0523095i	0.227412	−	0.973799i	$-0.426974\pi$
$149$	−1.96516	−	0.638519i	−0.160992	−	0.0523095i	−0.388404	+	0.921489i	$0.626974\pi$
$150$	−5.20377	−	7.16238i	−0.424886	−	0.584806i
$151$	17.5430	+	12.7458i	1.42763	+	1.03724i	0.990451	+	0.137862i	$0.0440230\pi$
$151$	17.5430	+	12.7458i	1.42763	+	1.03724i	0.437181	+	0.899374i	$0.355977\pi$
$152$	9.50699	−	9.45631i	0.771119	−	0.767008i
$153$			0.590304i			0.0477233i
$154$	−5.88796	+	0.0940537i	−0.474466	+	0.00757906i
$155$		−	11.8410i		−	0.951093i
$156$	1.47939	−	0.480683i	0.118446	−	0.0384854i
$157$	6.93101	+	5.03567i	0.553155	+	0.401890i	0.828947	−	0.559327i	$-0.188940\pi$
$157$	6.93101	+	5.03567i	0.553155	+	0.401890i	−0.275793	+	0.961217i	$0.588940\pi$
$158$	−12.6902	+	9.21997i	−1.00958	+	0.733502i
$159$	0.854590	−	2.63016i	0.0677734	−	0.208585i
$160$	−4.33017	+	13.3269i	−0.342330	+	1.05358i
$161$	2.84334	+	3.91352i	0.224087	+	0.308429i
$162$	0.910521	+	0.661532i	0.0715373	+	0.0519749i
$163$	4.44121	+	13.6686i	0.347863	+	1.07061i	0.960033	+	0.279885i	$0.0902964\pi$
$163$	4.44121	+	13.6686i	0.347863	+	1.07061i	−0.612171	+	0.790725i	$0.709704\pi$
$164$	−3.85747			−0.301218
$165$	3.49507	−	11.3716i	0.272091	−	0.885278i
$166$		−	8.25217i		−	0.640493i
$167$	−1.36322	−	4.19557i	−0.105489	−	0.324663i	0.884356	−	0.466814i	$-0.154598\pi$
$167$	−1.36322	−	4.19557i	−0.105489	−	0.324663i	−0.989845	+	0.142151i	$0.954598\pi$
$168$	3.92621	+	2.85256i	0.302914	+	0.220080i
$169$	6.87711	−	4.99652i	0.529009	−	0.384347i
$170$	2.26642	+	0.736404i	0.173826	+	0.0564796i
$171$	4.30704	−	0.670374i	0.329368	−	0.0512648i
$172$	0.00367748	+	0.00506162i	0.000280405	+	0.000385945i
$173$	15.4348	+	11.2140i	1.17348	+	0.852586i	0.991422	−	0.130701i	$-0.0417227\pi$
$173$	15.4348	+	11.2140i	1.17348	+	0.852586i	0.182062	+	0.983287i	$0.441723\pi$
$174$	−0.132966	+	0.0432032i	−0.0100801	+	0.00327523i
$175$		−	12.4097i		−	0.938081i
$176$	6.26117	−	2.14553i	0.471953	−	0.161725i
$177$	8.07301			0.606805
$178$	−0.531299	+	0.172629i	−0.0398225	+	0.0129391i
$179$	9.87366	−	13.5899i	0.737992	−	1.01576i	−0.260739	−	0.965409i	$-0.583966\pi$
$179$	9.87366	−	13.5899i	0.737992	−	1.01576i	0.998732	−	0.0503500i	$-0.0160337\pi$
$180$	−2.12805	+	1.54612i	−0.158615	+	0.115241i
$181$	−18.6791	−	6.06920i	−1.38840	−	0.451120i	−0.482981	−	0.875631i	$-0.660446\pi$
$181$	−18.6791	−	6.06920i	−1.38840	−	0.451120i	−0.905423	+	0.424511i	$0.860446\pi$
$182$	−3.58186	−	1.16382i	−0.265505	−	0.0862679i
$183$	8.35064	−	6.06710i	0.617297	−	0.448493i
$184$	−7.63132	−	5.54448i	−0.562588	−	0.408744i
$185$	4.25286	−	1.38184i	0.312676	−	0.101595i
$186$	3.71531			0.272420
$187$	0.634661	+	1.85210i	0.0464110	+	0.135439i
$188$	2.68637			0.195924
$189$	0.487500	+	1.50037i	0.0354604	+	0.109136i
$190$	2.79919	−	17.3728i	0.203075	−	1.26035i
$191$	−20.4196	+	14.8357i	−1.47751	+	1.07347i	−0.499161	+	0.866509i	$0.666358\pi$
$191$	−20.4196	+	14.8357i	−1.47751	+	1.07347i	−0.978349	+	0.206964i	$0.933642\pi$
$192$	−7.97734	−	2.59199i	−0.575715	−	0.187061i
$193$	4.08153	−	12.5617i	0.293795	−	0.904208i	−0.689828	−	0.723973i	$-0.742314\pi$
$193$	4.08153	−	12.5617i	0.293795	−	0.904208i	0.983624	−	0.180235i	$-0.0576859\pi$
$194$	−0.111709	−	0.153754i	−0.00802021	−	0.0110389i
$195$	4.47222	−	6.15548i	0.320262	−	0.440803i
$196$	−1.02229	−	3.14630i	−0.0730210	−	0.224736i
$197$		−	6.75131i		−	0.481011i	−0.970648	−	0.240506i	$-0.922687\pi$
$197$		−	6.75131i		−	0.481011i	0.970648	−	0.240506i	$-0.0773132\pi$
$198$	3.56802	+	1.09663i	0.253568	+	0.0779344i
$199$	13.3098			0.943505			0.471752	−	0.881731i	$-0.343622\pi$
$199$	13.3098			0.943505			0.471752	+	0.881731i	$0.343622\pi$
$200$	7.47780	+	23.0143i	0.528760	+	1.62736i
$201$	9.57909	+	6.95961i	0.675657	+	0.490893i
$202$	−5.44217	−	7.49051i	−0.382910	−	0.527030i
$203$	−0.186380	−	0.0605586i	−0.0130813	−	0.00425038i
$204$	0.133769	−	0.411700i	0.00936573	−	0.0288247i
$205$	−15.2647	+	11.0904i	−1.06613	+	0.774590i
$206$	9.12768	−	12.5632i	0.635955	−	0.875318i
$207$	−0.947546	−	2.91625i	−0.0658590	−	0.202693i
$208$	4.23298			0.293504
$209$	12.7927	−	6.73400i	0.884890	−	0.465800i
$210$	6.36869			0.439481
$211$	−2.51793	−	7.74940i	−0.173342	−	0.533491i	0.826212	−	0.563359i	$-0.190491\pi$
$211$	−2.51793	−	7.74940i	−0.173342	−	0.533491i	−0.999554	+	0.0298682i	$0.990491\pi$
$212$	−1.19204	+	1.64071i	−0.0818699	+	0.112684i
$213$	−9.02174	+	6.55467i	−0.618159	+	0.449119i
$214$	5.14893	−	15.8468i	0.351974	−	1.08326i
$215$	0.0291049	+	0.00945674i	0.00198494	+	0.000644945i
$216$	−1.80818	−	2.48875i	−0.123031	−	0.169338i
$217$	4.21321	+	3.06107i	0.286011	+	0.207799i
$218$	−2.84102	−	8.74375i	−0.192418	−	0.592202i
$219$	−13.2190			−0.893260
$220$	−5.01451	+	7.13894i	−0.338078	+	0.481307i
$221$			1.25214i			0.0842283i
$222$	0.433574	+	1.33440i	0.0290996	+	0.0895593i
$223$	10.0832	−	13.8783i	0.675221	−	0.929361i	−0.324644	−	0.945836i	$-0.605244\pi$
$223$	10.0832	−	13.8783i	0.675221	−	0.929361i	0.999864	+	0.0164750i	$0.00524439\pi$
$224$	−3.62249	−	4.98593i	−0.242038	−	0.333137i
$225$	−2.43080	+	7.48124i	−0.162054	+	0.498750i
$226$	−2.82438	−	0.917698i	−0.187875	−	0.0610444i
$227$	−17.9159	+	13.0167i	−1.18912	+	0.863947i	−0.993171	−	0.116667i	$-0.962779\pi$
$227$	−17.9159	+	13.0167i	−1.18912	+	0.863947i	−0.195949	+	0.980614i	$0.562779\pi$
$228$	−3.15580	−	0.508479i	−0.208998	−	0.0336748i
$229$	−3.26191	−	10.0391i	−0.215553	−	0.663405i	−0.999114	−	0.0420893i	$-0.986599\pi$
$229$	−3.26191	−	10.0391i	−0.215553	−	0.663405i	0.783561	−	0.621315i	$-0.213401\pi$
$230$	−12.3787			−0.816229
$231$	3.14266	+	4.18332i	0.206772	+	0.275242i
$232$	0.382142			0.0250889
$233$	−21.0691	+	6.84578i	−1.38029	+	0.448482i	−0.902763	−	0.430138i	$-0.858465\pi$
$233$	−21.0691	+	6.84578i	−1.38029	+	0.448482i	−0.477522	+	0.878620i	$0.658465\pi$
$234$	1.93138	+	1.40323i	0.126258	+	0.0917321i
$235$	10.6305	−	7.72348i	0.693454	−	0.503824i
$236$	−5.63041	−	1.82943i	−0.366508	−	0.119086i
$237$	13.2552	+	4.30687i	0.861016	+	0.279761i
$238$	−0.847926	+	0.616054i	−0.0549629	+	0.0399329i
$239$	−9.28836	+	12.7843i	−0.600814	+	0.826950i	−0.995783	−	0.0917451i	$-0.970755\pi$
$239$	−9.28836	+	12.7843i	−0.600814	+	0.826950i	0.394969	+	0.918695i	$0.370755\pi$
$240$	−6.80770	+	2.21195i	−0.439435	+	0.142781i
$241$	21.4801			1.38366			0.691829	−	0.722062i	$-0.256805\pi$
$241$	21.4801			1.38366			0.691829	+	0.722062i	$0.256805\pi$
$242$	12.3738	−	0.395416i	0.795418	−	0.0254183i
$243$		−	1.00000i		−	0.0641500i
$244$	−7.19891	+	2.33907i	−0.460863	+	0.149743i
$245$	−13.0912	−	9.51130i	−0.836365	−	0.607655i
$246$	−3.47980	−	4.78954i	−0.221864	−	0.305370i
$247$	9.13602	−	1.42199i	0.581311	−	0.0904788i
$248$	−9.65813	−	3.13812i	−0.613292	−	0.199271i
$249$	−5.93190	+	4.30978i	−0.375919	+	0.273121i
$250$	9.36115	+	6.80127i	0.592051	+	0.430150i
$251$	−7.46789	−	22.9838i	−0.471369	−	1.45072i	−0.850793	−	0.525501i	$-0.823878\pi$
$251$	−7.46789	−	22.9838i	−0.471369	−	1.45072i	0.379424	−	0.925223i	$-0.376122\pi$
$252$		−	1.15689i		−	0.0728769i
$253$	−6.10833	−	8.13106i	−0.384028	−	0.511195i
$254$	4.75295			0.298227
$255$	−0.654311	−	2.01376i	−0.0409745	−	0.126107i
$256$	12.0904	+	8.78416i	0.755647	+	0.549010i
$257$	15.2911	+	21.0464i	0.953834	+	1.31284i	0.949803	+	0.312849i	$0.101283\pi$
$257$	15.2911	+	21.0464i	0.953834	+	1.31284i	0.00403139	+	0.999992i	$0.498717\pi$
$258$	−0.00296721	+	0.00913212i	−0.000184730	+	0.000568541i
$259$	−0.607747	+	1.87045i	−0.0377636	+	0.116224i
$260$	−4.51398	+	3.27960i	−0.279945	+	0.203392i
$261$	0.100498	+	0.0730163i	0.00622069	+	0.00451960i
$262$	−8.78443	+	2.85424i	−0.542704	+	0.176335i
$263$			21.9979i			1.35645i	0.734856	+	0.678223i	$0.237250\pi$
$263$			21.9979i			1.35645i	−0.734856	+	0.678223i	$0.762750\pi$
$264$	−8.34899	−	5.86447i	−0.513845	−	0.360933i
$265$			9.91976i			0.609366i
$266$	5.45786	+	5.48711i	0.334643	+	0.336436i
$267$	0.401567	+	0.291755i	0.0245755	+	0.0178551i
$268$	−5.10368	−	7.02461i	−0.311757	−	0.429096i
$269$	−26.2751	−	8.53730i	−1.60202	−	0.520528i	−0.634415	−	0.772993i	$-0.718759\pi$
$269$	−26.2751	−	8.53730i	−1.60202	−	0.520528i	−0.967606	+	0.252465i	$0.918759\pi$
$270$	−3.83941	−	1.24750i	−0.233659	−	0.0759204i
$271$	8.46413	+	11.6499i	0.514159	+	0.707680i	0.984614	−	0.174745i	$-0.0559100\pi$
$271$	8.46413	+	11.6499i	0.514159	+	0.707680i	−0.470454	+	0.882424i	$0.655910\pi$
$272$	0.692409	−	0.953019i	0.0419835	−	0.0577853i
$273$	1.03408	+	3.18256i	0.0625852	+	0.192617i
$274$	−15.8132			−0.955310
$275$	0.416696	+	26.0861i	0.0251277	+	1.57305i
$276$			2.24862i			0.135351i
$277$	−4.88933	+	1.58864i	−0.293771	+	0.0954521i	−0.452195	−	0.891919i	$-0.649359\pi$
$277$	−4.88933	+	1.58864i	−0.293771	+	0.0954521i	0.158424	+	0.987371i	$0.449359\pi$
$278$	2.72217	−	3.74674i	0.163265	−	0.224715i
$279$	−1.94036	−	2.67067i	−0.116166	−	0.159889i
$280$	−16.5557	−	5.37928i	−0.989394	−	0.321473i
$281$	−5.87959	+	18.0955i	−0.350747	+	1.07949i	0.607688	+	0.794176i	$0.292097\pi$
$281$	−5.87959	+	18.0955i	−0.350747	+	1.07949i	−0.958435	+	0.285312i	$0.907903\pi$
$282$	2.42337	+	3.33548i	0.144309	+	0.198625i
$283$	−3.97971	+	5.47760i	−0.236569	+	0.325610i	−0.910751	−	0.412956i	$-0.864496\pi$
$283$	−3.97971	+	5.47760i	−0.236569	+	0.325610i	0.674182	+	0.738565i	$0.264496\pi$
$284$	7.77744	−	2.52704i	0.461506	−	0.149953i
$285$	−13.9500	+	7.06096i	−0.826324	+	0.418255i
$286$	7.56843	+	2.32616i	0.447531	+	0.137549i
$287$		−	8.29843i		−	0.489841i
$288$	1.20720	+	3.71538i	0.0711349	+	0.218931i
$289$	−13.4714	−	9.78753i	−0.792434	−	0.575737i
$290$	0.405711	−	0.294766i	0.0238242	−	0.0173093i
$291$	−0.0521817	+	0.160599i	−0.00305894	+	0.00941446i
$292$	9.21944	+	2.99558i	0.539527	+	0.175303i
$293$	−20.7270	+	15.0590i	−1.21088	+	0.879759i	−0.995311	−	0.0967287i	$-0.969162\pi$
$293$	−20.7270	+	15.0590i	−1.21088	+	0.879759i	−0.215573	+	0.976488i	$0.569162\pi$
$294$	2.98432	−	4.10757i	0.174049	−	0.239558i
$295$	−27.5402	+	8.94837i	−1.60345	+	0.520994i
$296$		−	3.83506i		−	0.222909i
$297$	−1.07514	−	3.13753i	−0.0623861	−	0.182058i
$298$			2.32554i			0.134715i
$299$	−2.00992	−	6.18590i	−0.116237	−	0.357740i
$300$	3.39066	−	4.66684i	0.195760	−	0.269440i
$301$	−0.0108889	+	0.00791123i	−0.000627624	+	0.000455996i
$302$	7.54157	−	23.2106i	0.433968	−	1.33562i
$303$	−2.54217	+	7.82398i	−0.146044	+	0.449476i
$304$	−7.73985	−	3.96974i	−0.443911	−	0.227680i
$305$	−21.7624	+	29.9534i	−1.24611	+	1.71512i
$306$	0.631851	−	0.205301i	0.0361205	−	0.0117363i
$307$	6.59725			0.376525			0.188262	−	0.982119i	$-0.439714\pi$
$307$	6.59725			0.376525			0.188262	+	0.982119i	$0.439714\pi$
$308$	−1.24382	−	3.62976i	−0.0708730	−	0.206825i
$309$	−13.7978			−0.784929
$310$	−12.6744	+	4.11816i	−0.719858	+	0.233896i
$311$	20.7036	+	15.0420i	1.17399	+	0.852955i	0.991481	−	0.130249i	$-0.0415776\pi$
$311$	20.7036	+	15.0420i	1.17399	+	0.852955i	0.182511	+	0.983204i	$0.441578\pi$
$312$	−3.83549	−	5.27910i	−0.217142	−	0.298870i
$313$	2.57051	−	7.91121i	0.145294	−	0.447168i	−0.851755	−	0.523940i	$-0.824461\pi$
$313$	2.57051	−	7.91121i	0.145294	−	0.447168i	0.997049	+	0.0767723i	$0.0244614\pi$
$314$	2.97957	−	9.17016i	0.168147	−	0.517502i
$315$	−3.32611	−	4.57800i	−0.187405	−	0.257941i
$316$	−8.26865	−	6.00753i	−0.465148	−	0.337950i
$317$	1.11004	−	0.360673i	0.0623460	−	0.0202574i	−0.277678	−	0.960674i	$-0.589565\pi$
$317$	1.11004	−	0.360673i	0.0623460	−	0.0202574i	0.340024	+	0.940417i	$0.389565\pi$
$318$	−3.11249			−0.174540
$319$	0.393819	+	0.121041i	0.0220496	+	0.00677697i
$320$	30.0869			1.68191
$321$	−14.0802	+	4.57494i	−0.785881	+	0.255348i
$322$	3.20008	−	4.40453i	0.178334	−	0.245455i
$323$	1.17428	−	2.28950i	0.0653384	−	0.127391i
$324$	−0.226611	+	0.697436i	−0.0125895	+	0.0387465i
$325$	−5.15618	+	15.8691i	−0.286013	+	0.880259i
$326$	13.0861	−	9.50758i	0.724770	−	0.526576i
$327$	−4.80151	+	6.60872i	−0.265524	+	0.365463i
$328$	5.00046	+	15.3898i	0.276104	+	0.849762i
$329$			5.77910i			0.318612i
$330$	−13.3875	+	0.213850i	−0.736957	+	0.0117721i
$331$			27.6357i			1.51900i	0.650510	+	0.759498i	$0.274555\pi$
$331$			27.6357i			1.51900i	−0.650510	+	0.759498i	$0.725445\pi$
$332$	5.11376	−	1.66156i	0.280654	−	0.0911901i
$333$	0.732770	−	1.00857i	0.0401555	−	0.0552693i
$334$	−4.01674	+	2.91833i	−0.219786	+	0.159684i
$335$	−40.3923	−	13.1243i	−2.20687	−	0.717055i
$336$	0.972842	−	2.99410i	0.0530729	−	0.163342i
$337$	19.2009	−	13.9503i	1.04594	−	0.759921i	0.0745046	−	0.997221i	$-0.476262\pi$
$337$	19.2009	−	13.9503i	1.04594	−	0.759921i	0.971436	+	0.237300i	$0.0762625\pi$
$338$	−7.73995	−	5.62340i	−0.420998	−	0.305873i
$339$	0.815394	+	2.50953i	0.0442861	+	0.136299i
$340$			1.55274i			0.0842094i
$341$	−8.95928	−	6.29314i	−0.485172	−	0.340793i
$342$	−2.21549	−	4.37703i	−0.119800	−	0.236683i
$343$	17.2711	−	5.61172i	0.932552	−	0.303005i
$344$	0.0154268	−	0.0212332i	0.000831757	−	0.00114482i
$345$	6.46491	+	8.89819i	0.348059	+	0.479062i
$346$	6.63525	−	20.4212i	0.356713	−	1.09785i
$347$	8.91739	+	2.89743i	0.478710	+	0.155542i	0.538426	−	0.842673i	$-0.319019\pi$
$347$	8.91739	+	2.89743i	0.478710	+	0.155542i	−0.0597153	+	0.998215i	$0.519019\pi$
$348$	−0.0535449	−	0.0736982i	−0.00287031	−	0.00395064i
$349$	4.11522	−	5.66411i	0.220283	−	0.303193i	−0.684545	−	0.728970i	$-0.739999\pi$
$349$	4.11522	−	5.66411i	0.220283	−	0.303193i	0.904828	+	0.425777i	$0.139999\pi$
$350$	−13.2831	+	4.31593i	−0.710009	+	0.230696i
$351$		−	2.12118i		−	0.113220i
$352$	7.78218	+	10.3592i	0.414792	+	0.552147i
$353$	−2.66239			−0.141705			−0.0708525	−	0.997487i	$-0.522572\pi$
$353$	−2.66239			−0.141705			−0.0708525	+	0.997487i	$0.522572\pi$
$354$	−2.80770	−	8.64120i	−0.149227	−	0.459274i
$355$	23.5113	−	32.3606i	1.24785	−	1.71752i
$356$	−0.213952	−	0.294480i	−0.0113395	−	0.0156074i
$357$	0.885675	+	0.287773i	0.0468749	+	0.0152306i
$358$	−17.9803	−	5.84217i	−0.950291	−	0.308768i
$359$	−12.1171	−	16.6777i	−0.639515	−	0.880217i	0.359075	−	0.933309i	$-0.383092\pi$
$359$	−12.1171	−	16.6777i	−0.639515	−	0.880217i	−0.998590	+	0.0530921i	$0.983092\pi$
$360$	8.92704	+	6.48587i	0.470496	+	0.341836i
$361$	−18.0384	−	5.96783i	−0.949391	−	0.314096i
$362$			22.1045i			1.16179i
$363$	−6.74658	−	8.68814i	−0.354103	−	0.456009i
$364$		−	2.45397i		−	0.128623i
$365$	45.0954	−	14.6524i	2.36040	−	0.766941i
$366$	−9.39836	−	6.82831i	−0.491260	−	0.356921i
$367$	27.8031	−	20.2001i	1.45131	−	1.05444i	0.465786	−	0.884897i	$-0.345772\pi$
$367$	27.8031	−	20.2001i	1.45131	−	1.05444i	0.985523	−	0.169541i	$-0.0542284\pi$
$368$	−1.89090	+	5.81959i	−0.0985700	+	0.303367i
$369$	−1.62550	+	5.00277i	−0.0846200	+	0.260434i
$370$	−2.95819	−	4.07159i	−0.153789	−	0.211672i
$371$	−3.52960	−	2.56440i	−0.183247	−	0.133137i
$372$	0.748072	+	2.30233i	0.0387857	+	0.119370i
$373$	6.00111			0.310726			0.155363	−	0.987857i	$-0.450345\pi$
$373$	6.00111			0.310726			0.155363	+	0.987857i	$0.450345\pi$
$374$	1.76172	−	1.32347i	0.0910964	−	0.0684348i
$375$		−	10.2811i		−	0.530913i
$376$	−3.48237	−	10.7176i	−0.179589	−	0.552719i
$377$	0.213175	+	0.154881i	0.0109791	+	0.00797678i
$378$	1.43642	−	1.04362i	0.0738815	−	0.0536781i
$379$	−34.1648	−	11.1008i	−1.75493	−	0.570211i	−0.758273	−	0.651937i	$-0.773957\pi$
$379$	−34.1648	−	11.1008i	−1.75493	−	0.570211i	−0.996655	+	0.0817267i	$0.973957\pi$
$380$	11.3293	−	1.76336i	0.581181	−	0.0904585i
$381$	−2.48227	−	3.41656i	−0.127171	−	0.175036i
$382$	22.9815	+	16.6971i	1.17584	+	0.854296i
$383$	13.2744	−	4.31311i	0.678289	−	0.220389i	0.0504428	−	0.998727i	$-0.483937\pi$
$383$	13.2744	−	4.31311i	0.678289	−	0.220389i	0.627846	+	0.778338i	$0.283937\pi$
$384$			1.62709i			0.0830323i
$385$	−15.3578	−	10.7875i	−0.782704	−	0.549784i
$386$	−14.8653			−0.756622
$387$	0.00811409	−	0.00263643i	0.000412462	−	0.000134017i
$388$	0.0727868	−	0.100182i	0.00369519	−	0.00508599i
$389$	−11.5645	+	8.40212i	−0.586345	+	0.426004i	−0.841006	−	0.541026i	$-0.818036\pi$
$389$	−11.5645	+	8.40212i	−0.586345	+	0.426004i	0.254661	+	0.967030i	$0.418036\pi$
$390$	−8.14409	−	2.64618i	−0.412392	−	0.133994i
$391$	−1.72147	−	0.559341i	−0.0870587	−	0.0282871i
$392$	−11.2273	+	8.15714i	−0.567066	+	0.411998i
$393$	6.63946	+	4.82385i	0.334917	+	0.243331i
$394$	−7.22648	+	2.34802i	−0.364065	+	0.118292i
$395$	−49.9925			−2.51540
$396$	0.0388463	+	2.43186i	0.00195210	+	0.122206i
$397$	6.00432			0.301348			0.150674	−	0.988583i	$-0.451856\pi$
$397$	6.00432			0.301348			0.150674	+	0.988583i	$0.451856\pi$
$398$	−4.62898	−	14.2465i	−0.232030	−	0.714114i
$399$	1.09387	−	6.78896i	0.0547621	−	0.339873i
$400$	12.6997	−	9.22686i	0.634984	−	0.461343i
$401$	30.4052	+	9.87926i	1.51836	+	0.493347i	0.945311	−	0.326171i	$-0.105759\pi$
$401$	30.4052	+	9.87926i	1.51836	+	0.493347i	0.573054	+	0.819518i	$0.305759\pi$
$402$	4.11795	−	12.6737i	0.205385	−	0.632109i
$403$	−4.11586	−	5.66499i	−0.205025	−	0.282193i
$404$	3.54600	−	4.88065i	0.176420	−	0.242821i
$405$	1.10843	+	3.41140i	0.0550783	+	0.169514i
$406$			0.220559i			0.0109462i
$407$	1.21473	−	3.95225i	0.0602117	−	0.195906i
$408$	−1.81593			−0.0899021
$409$	6.04455	+	18.6032i	0.298884	+	0.919870i	0.981889	+	0.189456i	$0.0606725\pi$
$409$	6.04455	+	18.6032i	0.298884	+	0.919870i	−0.683005	+	0.730413i	$0.739327\pi$
$410$	17.1799	+	12.4819i	0.848453	+	0.616437i
$411$	8.25860	+	11.3670i	0.407366	+	0.560692i
$412$	9.62308	+	3.12673i	0.474095	+	0.154043i
$413$	3.93559	−	12.1125i	0.193658	−	0.596017i
$414$	−2.79195	+	2.02847i	−0.137217	+	0.0996939i
$415$	15.4590	−	21.2775i	0.758851	−	1.04447i
$416$	2.56069	+	7.88100i	0.125548	+	0.386398i
$417$	−4.11494			−0.201510
$418$	−11.6571	−	11.3511i	−0.570167	−	0.555199i
$419$	10.9300			0.533967			0.266983	−	0.963701i	$-0.413973\pi$
$419$	10.9300			0.533967			0.266983	+	0.963701i	$0.413973\pi$
$420$	1.28233	+	3.94659i	0.0625711	+	0.192574i
$421$	−5.68851	+	7.82957i	−0.277241	+	0.381590i	−0.924818	−	0.380411i	$-0.875783\pi$
$421$	−5.68851	+	7.82957i	−0.277241	+	0.381590i	0.647576	+	0.762001i	$0.275783\pi$
$422$	−7.41911	+	5.39030i	−0.361156	+	0.262396i
$423$	1.13201	−	3.48397i	0.0550402	−	0.169396i
$424$	8.09106	+	2.62894i	0.392937	+	0.127673i
$425$	2.72937	+	3.75665i	0.132394	+	0.182224i
$426$	10.1536	+	7.37706i	0.491946	+	0.357420i
$427$	−5.03195	−	15.4868i	−0.243513	−	0.749457i
$428$	10.8568			0.524782
$429$	−2.28058	−	6.65527i	−0.110107	−	0.321319i
$430$		−	0.0344422i		−	0.00166095i
$431$	−11.3313	−	34.8743i	−0.545811	−	1.67983i	−0.719053	−	0.694955i	$-0.755424\pi$
$431$	−11.3313	−	34.8743i	−0.545811	−	1.67983i	0.173242	−	0.984879i	$-0.444576\pi$
$432$	−1.17297	+	1.61445i	−0.0564345	+	0.0776754i
$433$	18.4643	+	25.4139i	0.887338	+	1.22132i	0.974334	+	0.225107i	$0.0722731\pi$
$433$	18.4643	+	25.4139i	0.887338	+	1.22132i	−0.0869965	+	0.996209i	$0.527727\pi$
$434$	1.81121	−	5.57434i	0.0869410	−	0.267577i
$435$	−0.423773	−	0.137692i	−0.0203184	−	0.00660184i
$436$	4.84636	−	3.52108i	0.232098	−	0.168629i
$437$	−2.12615	+	13.1956i	−0.101707	+	0.631232i
$438$	4.59742	+	14.1494i	0.219673	+	0.676085i
$439$	−7.81827			−0.373146			−0.186573	−	0.982441i	$-0.559738\pi$
$439$	−7.81827			−0.373146			−0.186573	+	0.982441i	$0.559738\pi$
$440$	34.9821	+	10.7518i	1.66770	+	0.512570i
$441$	−4.51123			−0.214821
$442$	1.34027	−	0.435481i	0.0637502	−	0.0207137i
$443$	−22.2822	−	16.1890i	−1.05866	−	0.769162i	−0.0848209	−	0.996396i	$-0.527032\pi$
$443$	−22.2822	−	16.1890i	−1.05866	−	0.769162i	−0.973840	+	0.227234i	$0.927032\pi$
$444$	−0.739613	+	0.537360i	−0.0351005	+	0.0255020i
$445$	−1.69329	−	0.550185i	−0.0802698	−	0.0260813i
$446$	−18.3619	−	5.96615i	−0.869462	−	0.282505i
$447$	1.67166	−	1.21454i	0.0790670	−	0.0574456i
$448$	−7.77790	+	10.7054i	−0.367471	+	0.505781i
$449$	1.32346	−	0.430018i	0.0624579	−	0.0202938i	−0.277621	−	0.960691i	$-0.589546\pi$
$449$	1.32346	−	0.430018i	0.0624579	−	0.0202938i	0.340079	+	0.940397i	$0.389546\pi$
$450$	8.85319			0.417343
$451$	0.278648	+	17.4440i	0.0131210	+	0.821404i
$452$		−	1.93501i		−	0.0910153i
$453$	−20.6231	+	6.70084i	−0.968957	+	0.314833i
$454$	20.1637	+	14.6498i	0.946331	+	0.687550i
$455$	−7.05529	−	9.71078i	−0.330757	−	0.455248i
$456$	2.06225	+	13.2496i	0.0965736	+	0.620469i
$457$	−14.8604	−	4.82843i	−0.695139	−	0.225864i	−0.0599276	−	0.998203i	$-0.519087\pi$
$457$	−14.8604	−	4.82843i	−0.695139	−	0.225864i	−0.635211	+	0.772338i	$0.719087\pi$
$458$	−9.61125	+	6.98298i	−0.449104	+	0.326293i
$459$	−0.477566	−	0.346972i	−0.0222909	−	0.0161953i
$460$	−2.49244	−	7.67094i	−0.116211	−	0.357659i
$461$		−	32.4788i		−	1.51269i	−0.654175	−	0.756344i	$-0.726984\pi$
$461$		−	32.4788i		−	1.51269i	0.654175	−	0.756344i	$-0.273016\pi$
$462$	3.38477	−	4.81875i	0.157474	−	0.224188i
$463$	−13.6099			−0.632507			−0.316254	−	0.948675i	$-0.602425\pi$
$463$	−13.6099			−0.632507			−0.316254	+	0.948675i	$0.602425\pi$
$464$	−0.0766040	−	0.235763i	−0.00355625	−	0.0109450i
$465$	9.57958	+	6.95998i	0.444243	+	0.322761i
$466$	14.6552	+	20.1711i	0.678888	+	0.934410i
$467$	5.59517	−	17.2202i	0.258914	−	0.796855i	−0.734119	−	0.679020i	$-0.762405\pi$
$467$	5.59517	−	17.2202i	0.258914	−	0.796855i	0.993033	−	0.117834i	$-0.0375952\pi$
$468$	−0.480683	+	1.47939i	−0.0222196	+	0.0683848i
$469$	15.1118	−	10.9794i	0.697798	−	0.506980i
$470$	−11.9642	−	8.69250i	−0.551868	−	0.400955i
$471$	−8.14789	+	2.64741i	−0.375435	+	0.121986i
$472$			24.8347i			1.14311i
$473$	0.0226236	−	0.0169957i	0.00104024	−	0.000781461i
$474$		−	15.6860i		−	0.720480i
$475$	24.3101	−	24.1805i	1.11542	−	1.10948i
$476$	−0.552489	−	0.401407i	−0.0253233	−	0.0183985i
$477$	1.62553	+	2.23734i	0.0744277	+	0.102441i
$478$	16.9145	+	5.49585i	0.773650	+	0.251374i
$479$	−3.57427	−	1.16135i	−0.163312	−	0.0530634i	0.226220	−	0.974076i	$-0.427363\pi$
$479$	−3.57427	−	1.16135i	−0.163312	−	0.0530634i	−0.389532	+	0.921013i	$0.627363\pi$
$480$	−8.23648	−	11.3365i	−0.375942	−	0.517440i
$481$	1.55434	−	2.13936i	0.0708718	−	0.0975466i
$482$	−7.47053	−	22.9919i	−0.340273	−	1.04725i
$483$	−4.83738			−0.220108
$484$	2.73648	+	7.58827i	0.124386	+	0.344921i
$485$		−	0.605706i		−	0.0275037i
$486$	−1.07038	+	0.347788i	−0.0485535	+	0.0157760i
$487$	−1.12323	+	1.54600i	−0.0508985	+	0.0700558i	−0.833708	−	0.552206i	$-0.813786\pi$
$487$	−1.12323	+	1.54600i	−0.0508985	+	0.0700558i	0.782809	+	0.622262i	$0.213786\pi$
$488$	18.6640	+	25.6888i	0.844879	+	1.16288i
$489$	−13.6686	−	4.44121i	−0.618117	−	0.200839i
$490$	−5.62776	+	17.3205i	−0.254236	+	0.782459i
$491$	−15.3005	−	21.0593i	−0.690501	−	0.950392i	0.309499	−	0.950900i	$-0.399839\pi$
$491$	−15.3005	−	21.0593i	−0.690501	−	0.950392i	−1.00000		0.000507216i	$0.999839\pi$
$492$	2.26736	−	3.12076i	0.102221	−	0.140695i
$493$	0.0697403	−	0.0226600i	0.00314094	−	0.00102055i
$494$	−4.69947	−	9.28448i	−0.211439	−	0.417728i
$495$	7.14547	+	9.51163i	0.321165	+	0.427516i
$496$			6.58766i			0.295795i
$497$	5.43634	+	16.7313i	0.243853	+	0.750503i
$498$	6.67615	+	4.85050i	0.299165	+	0.217356i
$499$	13.5412	−	9.83829i	0.606190	−	0.440423i	−0.241881	−	0.970306i	$-0.577764\pi$
$499$	13.5412	−	9.83829i	0.606190	−	0.440423i	0.848070	+	0.529883i	$0.177764\pi$
$500$	−2.32981	+	7.17041i	−0.104192	+	0.320670i
$501$	4.19557	+	1.36322i	0.187444	+	0.0609043i
$502$	−22.0042	+	15.9870i	−0.982095	+	0.713534i
$503$	−17.9303	+	24.6790i	−0.799473	+	1.10038i	0.193390	+	0.981122i	$0.438052\pi$
$503$	−17.9303	+	24.6790i	−0.799473	+	1.10038i	−0.992863	+	0.119259i	$0.961948\pi$
$504$	−4.61554	+	1.49968i	−0.205592	+	0.0668010i
$505$		−	29.5085i		−	1.31311i
$506$	−6.57892	+	9.36613i	−0.292469	+	0.416375i
$507$			8.50058i			0.377524i
$508$	0.956999	+	2.94534i	0.0424600	+	0.130678i
$509$	−23.5273	+	32.3825i	−1.04283	+	1.43533i	−0.147962	+	0.988993i	$0.547271\pi$
$509$	−23.5273	+	32.3825i	−1.04283	+	1.43533i	−0.894866	+	0.446336i	$0.852729\pi$
$510$	−1.92793	+	1.40072i	−0.0853703	+	0.0620251i
$511$	−6.44428	+	19.8335i	−0.285078	+	0.877381i
$512$	6.20312	−	19.0912i	0.274142	−	0.843721i
$513$	−1.98927	+	3.87850i	−0.0878285	+	0.171240i
$514$	17.2096	−	23.6870i	0.759084	−	1.04479i
$515$	47.0697	−	15.2939i	2.07414	−	0.673929i
$516$	−0.00625650			−0.000275427
$517$	−0.194053	−	12.1481i	−0.00853443	−	0.534274i
$518$	2.21347			0.0972541
$519$	−18.1447	+	5.89556i	−0.796462	+	0.258786i
$520$	18.9359	+	13.7577i	0.830394	+	0.603316i
$521$	4.65411	+	6.40584i	0.203900	+	0.280645i	0.898705	−	0.438554i	$-0.144509\pi$
$521$	4.65411	+	6.40584i	0.203900	+	0.280645i	−0.694805	+	0.719199i	$0.744509\pi$
$522$	0.0432032	−	0.132966i	0.00189095	−	0.00581975i
$523$	−6.37395	+	19.6170i	−0.278713	+	0.857792i	0.709499	+	0.704706i	$0.248921\pi$
$523$	−6.37395	+	19.6170i	−0.278713	+	0.857792i	−0.988213	+	0.153086i	$0.951079\pi$
$524$	−3.53747	−	4.86890i	−0.154535	−	0.212699i
$525$	10.0396	+	7.29421i	0.438165	+	0.318345i
$526$	23.5461	−	7.65059i	1.02666	−	0.333582i
$527$	−1.94867			−0.0848856
$528$	−1.94445	+	6.32650i	−0.0846215	+	0.275326i
$529$	−13.5977			−0.591202
$530$	10.6179	−	3.44997i	0.461213	−	0.149857i
$531$	−4.74520	+	6.53120i	−0.205924	+	0.283430i
$532$	−2.30136	+	4.48698i	−0.0997765	+	0.194535i
$533$	−3.44798	+	10.6118i	−0.149349	+	0.459648i
$534$	0.172629	−	0.531299i	0.00747040	−	0.0229915i
$535$	42.9622	−	31.2139i	1.85742	−	1.34949i
$536$	−21.4096	+	29.4678i	−0.924755	+	1.27282i
$537$	5.19089	+	15.9759i	0.224004	+	0.689412i
$538$			31.0935i			1.34054i
$539$	−14.1541	+	4.85022i	−0.609661	+	0.208914i
$540$		−	2.63041i		−	0.113195i
$541$	9.85147	−	3.20094i	0.423548	−	0.137619i	−0.0894847	−	0.995988i	$-0.528522\pi$
$541$	9.85147	−	3.20094i	0.423548	−	0.137619i	0.513033	+	0.858369i	$0.328522\pi$
$542$	9.52609	−	13.1115i	0.409180	−	0.563189i
$543$	15.8894	−	11.5443i	0.681878	−	0.495413i
$544$	2.19320	+	0.712615i	0.0940329	+	0.0305531i
$545$	9.05457	−	27.8671i	0.387855	−	1.19370i
$546$	3.04691	−	2.21371i	0.130396	−	0.0947381i
$547$	−0.884297	−	0.642479i	−0.0378098	−	0.0274704i	0.568720	−	0.822531i	$-0.307439\pi$
$547$	−0.884297	−	0.642479i	−0.0378098	−	0.0274704i	−0.606530	+	0.795061i	$0.707439\pi$
$548$	−3.18396	−	9.79923i	−0.136012	−	0.418602i
$549$			10.3220i			0.440530i
$550$	27.7771	−	9.51844i	1.18442	−	0.405868i
$551$	−0.244534	−	0.483113i	−0.0104175	−	0.0205813i
$552$	8.97115	−	2.91490i	0.381838	−	0.124067i
$553$	12.9238	−	17.7881i	0.549575	−	0.756425i
$554$	3.40090	+	4.68093i	0.144490	+	0.198874i
$555$	−1.38184	+	4.25286i	−0.0586557	+	0.180524i
$556$	2.86991	+	0.932491i	0.121711	+	0.0395464i
$557$	−4.04565	−	5.56836i	−0.171420	−	0.235939i	0.714660	−	0.699472i	$-0.246581\pi$
$557$	−4.04565	−	5.56836i	−0.171420	−	0.235939i	−0.886080	+	0.463533i	$0.846581\pi$
$558$	−2.18381	+	3.00575i	−0.0924478	+	0.127244i
$559$	0.0172115	−	0.00559235i	0.000727968	−	0.000236531i
$560$			11.2924i			0.477191i
$561$	−1.87142	−	0.575182i	−0.0790115	−	0.0242842i
$562$	21.4140			0.903293
$563$	−0.168751	−	0.519362i	−0.00711201	−	0.0218885i	0.947438	−	0.319941i	$-0.103663\pi$
$563$	−0.168751	−	0.519362i	−0.00711201	−	0.0218885i	−0.954550	+	0.298052i	$0.903663\pi$
$564$	−1.57901	+	2.17332i	−0.0664883	+	0.0915134i
$565$	−5.56327	−	7.65718i	−0.234048	−	0.322140i
$566$	7.24721	+	2.35476i	0.304623	+	0.0989781i
$567$	−1.50037	−	0.487500i	−0.0630096	−	0.0204731i
$568$	−20.1639	−	27.7533i	−0.846059	−	1.16450i
$569$	−12.9662	−	9.42051i	−0.543572	−	0.394928i	0.281838	−	0.959462i	$-0.409056\pi$
$569$	−12.9662	−	9.42051i	−0.543572	−	0.394928i	−0.825410	+	0.564534i	$0.809056\pi$
$570$	12.4096	+	12.4761i	0.519779	+	0.522565i
$571$		−	19.8437i		−	0.830432i	−0.909723	−	0.415216i	$-0.863706\pi$
$571$		−	19.8437i		−	0.830432i	0.909723	−	0.415216i	$-0.136294\pi$
$572$	0.0824002	+	5.15843i	0.00344532	+	0.215685i
$573$		−	25.2400i		−	1.05442i
$574$	−8.88248	+	2.88609i	−0.370748	+	0.120463i
$575$	−19.5139	−	14.1777i	−0.813784	−	0.591249i
$576$	6.78593	−	4.93027i	0.282747	−	0.205428i
$577$	−12.8010	+	39.3973i	−0.532911	+	1.64013i	0.215208	+	0.976568i	$0.430957\pi$
$577$	−12.8010	+	39.3973i	−0.532911	+	1.64013i	−0.748120	+	0.663564i	$0.769043\pi$
$578$	−5.79120	+	17.8235i	−0.240882	+	0.741360i
$579$	7.76353	+	10.6856i	0.322641	+	0.444078i
$580$	0.264352	+	0.192063i	0.0109766	+	0.00797499i
$581$	3.57446	+	11.0011i	0.148294	+	0.456401i
$582$	0.190050			0.00787783
$583$	7.50560	+	5.27205i	0.310850	+	0.218346i
$584$		−	40.6653i		−	1.68274i
$585$	2.35118	+	7.23620i	0.0972095	+	0.299180i
$586$	23.3275	+	16.9484i	0.963651	+	0.700133i
$587$	2.01033	−	1.46059i	0.0829750	−	0.0602849i	−0.545524	−	0.838095i	$-0.683669\pi$
$587$	2.01033	−	1.46059i	0.0829750	−	0.0602849i	0.628499	+	0.777810i	$0.283669\pi$
$588$	3.14630	+	1.02229i	0.129751	+	0.0421587i
$589$	2.21299	+	14.2181i	0.0911848	+	0.585847i
$590$	19.1563	+	26.3664i	0.788653	+	1.08549i
$591$	5.46193	+	3.96832i	0.224674	+	0.163235i
$592$	−2.36605	+	0.768775i	−0.0972439	+	0.0315964i
$593$			1.36639i			0.0561108i	0.999606	+	0.0280554i	$0.00893148\pi$
$593$			1.36639i			0.0561108i	−0.999606	+	0.0280554i	$0.991069\pi$
$594$	−2.98443	+	2.24201i	−0.122453	+	0.0919906i
$595$	−3.34037			−0.136942
$596$	−1.44111	+	0.468244i	−0.0590300	+	0.0191800i
$597$	−7.82329	+	10.7678i	−0.320186	+	0.440698i
$598$	−5.92224	+	4.30276i	−0.242179	+	0.175953i
$599$	−20.2330	−	6.57410i	−0.826698	−	0.268610i	−0.135044	−	0.990840i	$-0.543118\pi$
$599$	−20.2330	−	6.57410i	−0.826698	−	0.268610i	−0.691654	+	0.722229i	$0.743118\pi$
$600$	−23.0143	−	7.47780i	−0.939555	−	0.305280i
$601$	−6.50054	+	4.72292i	−0.265163	+	0.192652i	−0.712420	−	0.701753i	$-0.752401\pi$
$601$	−6.50054	+	4.72292i	−0.265163	+	0.192652i	0.447257	+	0.894405i	$0.352401\pi$
$602$	0.0122551	+	0.00890382i	0.000499479	+	0.000362892i
$603$	−11.2609	+	3.65889i	−0.458579	+	0.149001i
$604$	15.9018			0.647034
$605$	32.6454	+	22.1606i	1.32723	+	0.900955i
$606$	9.25878			0.376112
$607$	−6.61745	−	20.3664i	−0.268594	−	0.826648i	−0.990844	−	0.135015i	$-0.956892\pi$
$607$	−6.61745	−	20.3664i	−0.268594	−	0.826648i	0.722249	−	0.691633i	$-0.243108\pi$
$608$	2.70877	−	16.8116i	0.109855	−	0.681799i
$609$	0.158544	−	0.115189i	0.00642455	−	0.00466771i
$610$	39.6302	+	12.8766i	1.60458	+	0.521360i
$611$	2.40120	−	7.39014i	0.0971423	−	0.298973i
$612$	0.254444	+	0.350213i	0.0102853	+	0.0141565i
$613$	15.5032	−	21.3384i	0.626170	−	0.861849i	−0.371614	−	0.928387i	$-0.621196\pi$
$613$	15.5032	−	21.3384i	0.626170	−	0.861849i	0.997784	+	0.0665385i	$0.0211955\pi$
$614$	−2.29444	−	7.06157i	−0.0925962	−	0.284982i
$615$		−	18.8682i		−	0.760838i
$616$	−12.8690	+	9.66764i	−0.518507	+	0.389520i
$617$	0.737970			0.0297096			0.0148548	−	0.999890i	$-0.495271\pi$
$617$	0.737970			0.0297096			0.0148548	+	0.999890i	$0.495271\pi$
$618$	4.79870	+	14.7689i	0.193032	+	0.594092i
$619$	34.3234	+	24.9374i	1.37957	+	1.00232i	0.996920	+	0.0784262i	$0.0249895\pi$
$619$	34.3234	+	24.9374i	1.37957	+	1.00232i	0.382653	+	0.923892i	$0.375011\pi$
$620$	−5.10394	−	7.02498i	−0.204979	−	0.282130i
$621$	2.91625	+	0.947546i	0.117025	+	0.0380237i
$622$	8.90025	−	27.3921i	0.356867	−	1.09833i
$623$	0.633505	−	0.460268i	0.0253808	−	0.0184403i
$624$	−2.48808	+	3.42455i	−0.0996030	+	0.137092i
$625$	−0.758146	−	2.33333i	−0.0303258	−	0.0933334i
$626$	−9.36200			−0.374181
$627$	−2.07144	+	14.3077i	−0.0827255	+	0.571393i
$628$	6.28256			0.250702
$629$	−0.227409	−	0.699892i	−0.00906738	−	0.0279065i
$630$	−3.74342	+	5.15238i	−0.149141	+	0.205276i
$631$	−28.3407	+	20.5907i	−1.12822	+	0.819703i	−0.985435	−	0.170050i	$-0.945607\pi$
$631$	−28.3407	+	20.5907i	−1.12822	+	0.819703i	−0.142789	+	0.989753i	$0.545607\pi$
$632$	−13.2491	+	40.7764i	−0.527019	+	1.62200i
$633$	7.74940	+	2.51793i	0.308011	+	0.100079i
$634$	−0.772116	−	1.06273i	−0.0306646	−	0.0422063i
$635$	12.2550	+	8.90380i	0.486326	+	0.353337i
$636$	−0.626694	−	1.92877i	−0.0248501	−	0.0764806i
$637$	−9.56916			−0.379144
$638$	−0.00740602	−	0.463633i	−0.000293207	−	0.0183554i
$639$		−	11.1515i		−	0.441146i
$640$	−1.80352	−	5.55067i	−0.0712904	−	0.219409i
$641$	−0.280779	+	0.386459i	−0.0110901	+	0.0152642i	−0.814526	−	0.580127i	$-0.803003\pi$
$641$	−0.280779	+	0.386459i	−0.0110901	+	0.0152642i	0.803436	+	0.595391i	$0.203003\pi$
$642$	9.79386	+	13.4801i	0.386533	+	0.532017i
$643$	−0.133731	+	0.411582i	−0.00527384	+	0.0162312i	−0.953659	−	0.300890i	$-0.902716\pi$
$643$	−0.133731	+	0.411582i	−0.00527384	+	0.0162312i	0.948385	+	0.317121i	$0.102716\pi$
$644$	3.37376	+	1.09620i	0.132945	+	0.0431964i
$645$	−0.0247581	+	0.0179878i	−0.000974848	+	0.000708269i
$646$	−2.85903	−	0.460663i	−0.112487	−	0.0181245i
$647$	−6.71614	−	20.6702i	−0.264039	−	0.812628i	−0.991913	−	0.126917i	$-0.959492\pi$
$647$	−6.71614	−	20.6702i	−0.264039	−	0.812628i	0.727875	−	0.685710i	$-0.240508\pi$
$648$	3.07627			0.120847
$649$	−7.86620	+	25.5936i	−0.308775	+	1.00464i
$650$	18.7792			0.736582
$651$	−4.95292	+	1.60930i	−0.194120	+	0.0630735i
$652$	8.52658	+	6.19492i	0.333927	+	0.242612i
$653$	10.7392	−	7.80250i	0.420258	−	0.305335i	−0.357484	−	0.933919i	$-0.616365\pi$
$653$	10.7392	−	7.80250i	0.420258	−	0.305335i	0.777742	+	0.628584i	$0.216365\pi$
$654$	8.74375	+	2.84102i	0.341908	+	0.111093i
$655$	−27.9967	−	9.09669i	−1.09392	−	0.355437i
$656$	8.49238	−	6.17008i	0.331572	−	0.240901i
$657$	7.76996	−	10.6944i	0.303135	−	0.417229i
$658$	6.18584	−	2.00990i	0.241149	−	0.0783541i
$659$	11.5900			0.451483			0.225741	−	0.974187i	$-0.427520\pi$
$659$	11.5900			0.451483			0.225741	+	0.974187i	$0.427520\pi$
$660$	−2.82807	−	8.25299i	−0.110082	−	0.321247i
$661$			22.4236i			0.872176i	0.899904	+	0.436088i	$0.143636\pi$
$661$			22.4236i			0.872176i	−0.899904	+	0.436088i	$0.856364\pi$
$662$	29.5807	−	9.61136i	1.14969	−	0.373556i
$663$	−1.01301	−	0.735992i	−0.0393419	−	0.0285836i
$664$	−13.2580	−	18.2481i	−0.514511	−	0.708164i
$665$	3.79345	+	24.3723i	0.147104	+	0.945118i
$666$	−1.33440	−	0.433574i	−0.0517071	−	0.0168007i
$667$	−0.308161	+	0.223892i	−0.0119320	+	0.00866912i
$668$	−2.61722	−	1.90152i	−0.101263	−	0.0735721i
$669$	5.30105	+	16.3150i	0.204950	+	0.630772i
$670$			47.7996i			1.84666i
$671$	11.0976	+	32.3854i	0.428417	+	1.25023i
$672$	6.16295			0.237741
$673$	−6.82590	−	21.0080i	−0.263119	−	0.809797i	−0.992121	−	0.125285i	$-0.960015\pi$
$673$	−6.82590	−	21.0080i	−0.263119	−	0.809797i	0.729002	−	0.684512i	$-0.239985\pi$
$674$	−21.6100	−	15.7006i	−0.832385	−	0.604763i
$675$	−4.62366	−	6.36393i	−0.177965	−	0.244948i
$676$	1.92632	−	5.92861i	0.0740893	−	0.228024i
$677$	−2.43433	+	7.49209i	−0.0935588	+	0.287944i	−0.986875	−	0.161484i	$-0.948372\pi$
$677$	−2.43433	+	7.49209i	−0.0935588	+	0.287944i	0.893317	+	0.449428i	$0.148372\pi$
$678$	2.40256	−	1.74557i	0.0922699	−	0.0670380i
$679$	0.215519	+	0.156584i	0.00827086	+	0.00600913i
$680$	6.19487	−	2.01283i	0.237562	−	0.0771887i
$681$		−	22.1453i		−	0.848609i
$682$	−3.62014	+	11.7785i	−0.138622	+	0.451023i
$683$			35.4612i			1.35689i	0.734653	+	0.678443i	$0.237345\pi$
$683$			35.4612i			1.35689i	−0.734653	+	0.678443i	$0.762655\pi$
$684$	2.26630	−	2.25422i	0.0866542	−	0.0861922i
$685$	−40.7729	−	29.6232i	−1.55785	−	1.13184i
$686$	−12.0134	−	16.5350i	−0.458672	−	0.631308i
$687$	10.0391	+	3.26191i	0.383017	+	0.124450i
$688$	−0.0161923	−	0.00526119i	−0.000617324	−	0.000200581i
$689$	3.44804	+	4.74582i	0.131360	+	0.180801i
$690$	7.27604	−	10.0146i	0.276994	−	0.381249i
$691$	14.0116	+	43.1232i	0.533025	+	1.64048i	0.747877	+	0.663837i	$0.231073\pi$
$691$	14.0116	+	43.1232i	0.533025	+	1.64048i	−0.214852	+	0.976647i	$0.568927\pi$
$692$	13.9907			0.531848
$693$	−5.23158	+	0.0835687i	−0.198731	+	0.00317451i
$694$		−	10.5527i		−	0.400575i
$695$	14.0377	−	4.56113i	0.532481	−	0.173013i
$696$	−0.224618	+	0.309160i	−0.00851411	+	0.0117187i
$697$	1.82515	+	2.51210i	0.0691325	+	0.0951527i
$698$	−7.49398	−	2.43494i	−0.283652	−	0.0921640i
$699$	6.84578	−	21.0691i	0.258931	−	0.796908i
$700$	−5.34905	−	7.36233i	−0.202175	−	0.278270i
$701$	2.09558	−	2.88432i	0.0791489	−	0.108939i	−0.767607	−	0.640921i	$-0.778553\pi$
$701$	2.09558	−	2.88432i	0.0791489	−	0.108939i	0.846756	+	0.531982i	$0.178553\pi$
$702$	−2.27048	+	0.737722i	−0.0856936	+	0.0278435i
$703$	−4.84837	+	2.45407i	−0.182860	+	0.0925570i
$704$	15.9903	−	22.7647i	0.602657	−	0.857976i
$705$			13.1400i			0.494880i
$706$	0.925949	+	2.84978i	0.0348485	+	0.107253i
$707$	10.4996	+	7.62838i	0.394877	+	0.286895i
$708$	4.78951	−	3.47978i	0.180001	−	0.130778i
$709$	−4.76372	+	14.6612i	−0.178905	+	0.550614i	−0.999790	−	0.0204798i	$-0.993481\pi$
$709$	−4.76372	+	14.6612i	−0.178905	+	0.550614i	0.820885	+	0.571093i	$0.193481\pi$
$710$	−42.8151	−	13.9115i	−1.60682	−	0.522088i
$711$	−11.2755	+	8.19214i	−0.422865	+	0.307229i
$712$	−0.897517	+	1.23533i	−0.0336359	+	0.0462958i
$713$	9.62692	−	3.12798i	0.360531	−	0.117144i
$714$		−	1.04809i		−	0.0392239i
$715$	15.1568	+	20.1759i	0.566834	+	0.754536i
$716$		−	12.3185i		−	0.460364i
$717$	−4.88318	−	15.0289i	−0.182366	−	0.561264i
$718$	−13.6373	+	18.7702i	−0.508941	+	0.700498i
$719$	−20.5464	+	14.9279i	−0.766253	+	0.556715i	−0.900822	−	0.434189i	$-0.857035\pi$
$719$	−20.5464	+	14.9279i	−0.766253	+	0.556715i	0.134569	+	0.990904i	$0.457035\pi$
$720$	2.21195	−	6.80770i	0.0824347	−	0.253708i
$721$	−6.72642	+	20.7018i	−0.250505	+	0.770975i
$722$	−0.114298	+	21.3835i	−0.00425374	+	0.795813i
$723$	−12.6257	+	17.3778i	−0.469555	+	0.646287i
$724$	−13.6979	+	4.45071i	−0.509078	+	0.165409i
$725$	0.977167			0.0362911
$726$	−6.95324	+	10.2430i	−0.258059	+	0.380155i
$727$	−39.4881			−1.46453			−0.732267	−	0.681018i	$-0.761538\pi$
$727$	−39.4881			−1.46453			−0.732267	+	0.681018i	$0.761538\pi$
$728$	−9.79040	+	3.18109i	−0.362856	+	0.117899i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−31.3673	−	43.1733i	−1.16095	−	1.59792i
$731$	0.00155629	−	0.00478978i	5.75616e−5	−	0.000177156i
$732$	2.33907	−	7.19891i	0.0864544	−	0.266079i
$733$	−8.10938	−	11.1616i	−0.299527	−	0.412263i	0.632552	−	0.774518i	$-0.282007\pi$
$733$	−8.10938	−	11.1616i	−0.299527	−	0.412263i	−0.932079	+	0.362254i	$0.882007\pi$
$734$	−31.2914	−	22.7345i	−1.15499	−	0.839147i
$735$	15.3896	−	5.00039i	0.567654	−	0.184442i
$736$	−11.9788			−0.441546
$737$	−31.3975	+	23.5869i	−1.15654	+	0.868835i
$738$	5.92020			0.217925
$739$	−25.3166	+	8.22586i	−0.931286	+	0.302593i	−0.735088	−	0.677971i	$-0.762859\pi$
$739$	−25.3166	+	8.22586i	−0.931286	+	0.302593i	−0.196198	+	0.980564i	$0.562859\pi$
$740$	1.92749	−	2.65296i	0.0708558	−	0.0975247i
$741$	−4.21961	+	8.22702i	−0.155011	+	0.302227i
$742$	−1.51734	+	4.66988i	−0.0557032	+	0.171437i
$743$	−15.0156	+	46.2134i	−0.550870	+	1.69540i	0.155738	+	0.987798i	$0.450224\pi$
$743$	−15.0156	+	46.2134i	−0.550870	+	1.69540i	−0.706608	+	0.707605i	$0.749776\pi$
$744$	8.21570	−	5.96906i	0.301202	−	0.218836i
$745$	−4.35648	+	5.99619i	−0.159609	+	0.219683i
$746$	−2.08712	−	6.42348i	−0.0764147	−	0.235180i
$747$		−	7.33223i		−	0.268272i
$748$	1.17485	+	0.825237i	0.0429569	+	0.0301737i
$749$			23.3558i			0.853403i
$750$	−11.0047	+	3.57564i	−0.401834	+	0.130564i
$751$	−26.4260	+	36.3723i	−0.964300	+	1.32725i	−0.0194261	+	0.999811i	$0.506184\pi$
$751$	−26.4260	+	36.3723i	−0.964300	+	1.32725i	−0.944874	+	0.327434i	$0.893816\pi$
$752$	−5.91417	+	4.29690i	−0.215668	+	0.156692i
$753$	22.9838	+	7.46789i	0.837576	+	0.272145i
$754$	0.0916419	−	0.282045i	0.00333740	−	0.0102715i
$755$	62.9261	−	45.7185i	2.29011	−	1.66387i
$756$	0.935940	+	0.680000i	0.0340398	+	0.0247314i
$757$	−10.2494	−	31.5445i	−0.372522	−	1.14650i	−0.945136	−	0.326678i	$-0.894071\pi$
$757$	−10.2494	−	31.5445i	−0.372522	−	1.14650i	0.572614	−	0.819825i	$-0.305929\pi$
$758$			40.4301i			1.46849i
$759$	10.1686	−	0.162431i	0.369095	−	0.00589588i
$760$	−21.7214	−	42.9138i	−0.787918	−	1.55665i
$761$	26.0958	−	8.47904i	0.945972	−	0.307365i	0.204894	−	0.978784i	$-0.434315\pi$
$761$	26.0958	−	8.47904i	0.945972	−	0.307365i	0.741078	+	0.671419i	$0.234315\pi$
$762$	−2.79371	+	3.84522i	−0.101206	+	0.139297i
$763$	7.57478	+	10.4258i	0.274226	+	0.377439i
$764$	−5.71965	+	17.6033i	−0.206930	+	0.636865i
$765$	2.01376	+	0.654311i	0.0728077	+	0.0236567i
$766$	−9.23333	−	12.7086i	−0.333614	−	0.459180i
$767$	−10.0654	+	13.8539i	−0.363442	+	0.500235i
$768$	−14.2131	+	4.61811i	−0.512870	+	0.166642i
$769$		−	23.9621i		−	0.864097i	−0.901850	−	0.432049i	$-0.857791\pi$
$769$		−	23.9621i		−	0.864097i	0.901850	−	0.432049i	$-0.142209\pi$
$770$	−6.20554	+	20.1904i	−0.223632	+	0.727613i
$771$	−26.0148			−0.936901
$772$	−2.99310	−	9.21182i	−0.107724	−	0.331541i
$773$	2.93501	−	4.03969i	0.105565	−	0.145298i	−0.752966	−	0.658059i	$-0.771378\pi$
$773$	2.93501	−	4.03969i	0.105565	−	0.145298i	0.858531	+	0.512762i	$0.171378\pi$
$774$	−0.00564396	−	0.00776825i	−0.000202868	−	0.000279224i
$775$	−24.6966	−	8.02441i	−0.887128	−	0.288245i
$776$	−0.494044	−	0.160525i	−0.0177352	−	0.00576250i
$777$	−1.15600	−	1.59110i	−0.0414714	−	0.0570805i
$778$	13.0155	+	9.45629i	0.466627	+	0.339025i
$779$	16.2564	−	16.1697i	0.582445	−	0.579340i
$780$		−	5.57959i		−	0.199781i
$781$	−11.9894	−	34.9880i	−0.429016	−	1.25197i
$782$			2.03717i			0.0728489i
$783$	−0.118143	+	0.0383870i	−0.00422208	+	0.00137184i
$784$	7.28318	+	5.29154i	0.260113	+	0.188984i
$785$	24.8612	−	18.0627i	0.887335	−	0.644686i
$786$	2.85424	−	8.78443i	0.101807	−	0.313330i
$787$	1.53199	−	4.71499i	0.0546097	−	0.168071i	−0.920032	−	0.391844i	$-0.871837\pi$
$787$	1.53199	−	4.71499i	0.0546097	−	0.168071i	0.974641	+	0.223773i	$0.0718373\pi$
$788$	−2.91008	−	4.00538i	−0.103667	−	0.142686i
$789$	−17.7967	−	12.9300i	−0.633578	−	0.460321i
$790$	17.3868	+	53.5110i	0.618594	+	1.90384i
$791$	4.16272			0.148009
$792$	9.65186	−	3.30742i	0.342964	−	0.117524i
$793$			21.8948i			0.777506i
$794$	−2.08823	−	6.42691i	−0.0741085	−	0.228083i
$795$	−8.02525	−	5.83069i	−0.284626	−	0.206793i
$796$	7.89635	−	5.73703i	0.279879	−	0.203344i
$797$	31.4563	+	10.2208i	1.11424	+	0.362039i	0.807567	−	0.589776i	$-0.200784\pi$
$797$	31.4563	+	10.2208i	1.11424	+	0.362039i	0.306673	+	0.951815i	$0.400784\pi$
$798$	−7.64721	+	1.19026i	−0.270708	+	0.0421347i
$799$	−1.27105	−	1.74945i	−0.0449665	−	0.0618911i
$800$	24.8612	+	18.0627i	0.878976	+	0.638613i
$801$	−0.472070	+	0.153385i	−0.0166798	+	0.00541959i
$802$		−	35.9811i		−	1.27054i
$803$	12.8804	−	41.9079i	0.454540	−	1.47890i
$804$	8.68290			0.306222
$805$	16.5022	−	5.36190i	0.581627	−	0.188982i
$806$	−4.63225	+	6.37575i	−0.163164	+	0.224576i
$807$	22.3509	−	16.2389i	0.786790	−	0.571636i
$808$	−24.0686	−	7.82038i	−0.846732	−	0.275120i
$809$	−7.37582	−	2.39655i	−0.259320	−	0.0842582i	0.176472	−	0.984306i	$-0.443532\pi$
$809$	−7.37582	−	2.39655i	−0.259320	−	0.0842582i	−0.435792	+	0.900048i	$0.643532\pi$
$810$	3.26600	−	2.37289i	0.114755	−	0.0833747i
$811$	19.0221	+	13.8203i	0.667955	+	0.485298i	0.869340	−	0.494214i	$-0.164544\pi$
$811$	19.0221	+	13.8203i	0.667955	+	0.485298i	−0.201385	+	0.979512i	$0.564544\pi$
$812$	−0.136678	+	0.0444093i	−0.00479645	+	0.00155846i
$813$	−14.4000			−0.505031
$814$	−4.65288	+	0.0743246i	−0.163083	+	0.00260508i
$815$	51.5519			1.80579
$816$	0.364021	+	1.12034i	0.0127433	+	0.0392198i
$817$	−0.0367151	−	0.00591573i	−0.00128450	−	0.000206965i
$818$	17.8103	−	12.9399i	0.622723	−	0.452434i
$819$	−3.18256	−	1.03408i	−0.111208	−	0.0361336i
$820$	−4.27573	+	13.1593i	−0.149315	+	0.459544i
$821$	13.6262	+	18.7548i	0.475557	+	0.654548i	0.977643	−	0.210270i	$-0.0674342\pi$
$821$	13.6262	+	18.7548i	0.475557	+	0.654548i	−0.502087	+	0.864817i	$0.667434\pi$
$822$	9.29476	−	12.7931i	0.324192	−	0.446212i
$823$	−3.48243	−	10.7178i	−0.121390	−	0.373600i	0.871836	−	0.489798i	$-0.162929\pi$
$823$	−3.48243	−	10.7178i	−0.121390	−	0.373600i	−0.993226	+	0.116198i	$0.962929\pi$
$824$		−	42.4457i		−	1.47866i
$825$	−21.3490	−	14.9959i	−0.743276	−	0.522090i
$826$	−14.3337			−0.498735
$827$	15.1755	+	46.7053i	0.527703	+	1.62410i	0.758909	+	0.651197i	$0.225733\pi$
$827$	15.1755	+	46.7053i	0.527703	+	1.62410i	−0.231206	+	0.972905i	$0.574267\pi$
$828$	−1.81917	−	1.32171i	−0.0632206	−	0.0459325i
$829$	7.11425	+	9.79193i	0.247088	+	0.340088i	0.914489	−	0.404611i	$-0.132593\pi$
$829$	7.11425	+	9.79193i	0.247088	+	0.340088i	−0.667401	+	0.744699i	$0.732593\pi$
$830$	−28.1514	−	9.14695i	−0.977150	−	0.317495i
$831$	1.58864	−	4.88933i	0.0551093	−	0.169609i
$832$	14.3942	−	10.4580i	0.499029	−	0.362566i
$833$	−1.56527	+	2.15441i	−0.0542335	+	0.0746460i
$834$	1.43113	+	4.40456i	0.0495559	+	0.152517i
$835$	−15.8238			−0.547605
$836$	4.68697	−	9.50927i	0.162102	−	0.328885i
$837$	3.30113			0.114104
$838$	−3.80133	−	11.6993i	−0.131315	−	0.404146i
$839$	21.1857	−	29.1596i	0.731412	−	1.00670i	−0.267655	−	0.963515i	$-0.586249\pi$
$839$	21.1857	−	29.1596i	0.731412	−	1.00670i	0.999067	−	0.0431874i	$-0.0137512\pi$
$840$	14.0831	−	10.2320i	0.485914	−	0.353038i
$841$	−8.95672	+	27.5660i	−0.308853	+	0.950550i
$842$	10.3590	+	3.36585i	0.356995	+	0.115995i
$843$	−11.1836	−	15.3930i	−0.385185	−	0.530162i
$844$	−4.83412	−	3.51220i	−0.166397	−	0.120895i
$845$	−9.42230	−	28.9988i	−0.324137	−	0.997591i
$846$	−4.12288			−0.141747
$847$	−16.3244	+	5.88690i	−0.560912	+	0.202276i
$848$		−	5.51878i		−	0.189516i
$849$	−2.09226	−	6.43931i	−0.0718061	−	0.220996i
$850$	3.07181	−	4.22798i	0.105362	−	0.145019i
$851$	2.24691	+	3.09261i	0.0770231	+	0.106013i
$852$	−2.52704	+	7.77744i	−0.0865751	+	0.266451i
$853$	42.0441	+	13.6609i	1.43956	+	0.467742i	0.921761	−	0.387759i	$-0.126751\pi$
$853$	42.0441	+	13.6609i	1.43956	+	0.467742i	0.517801	+	0.855501i	$0.326751\pi$
$854$	−14.8267	+	10.7722i	−0.507359	+	0.368618i
$855$	2.48714	−	15.4361i	0.0850585	−	0.527903i
$856$	−14.0737	−	43.3145i	−0.481030	−	1.48046i
$857$	−20.3697			−0.695815			−0.347907	−	0.937529i	$-0.613108\pi$
$857$	−20.3697			−0.695815			−0.347907	+	0.937529i	$0.613108\pi$
$858$	−6.33052	+	4.75571i	−0.216120	+	0.162357i
$859$	25.7651			0.879094			0.439547	−	0.898220i	$-0.355139\pi$
$859$	25.7651			0.879094			0.439547	+	0.898220i	$0.355139\pi$
$860$	0.0213434	−	0.00693489i	0.000727804	−	0.000236478i
$861$	6.71357	+	4.87770i	0.228798	+	0.166231i
$862$	−33.3879	+	24.2577i	−1.13719	+	0.826220i
$863$	37.1298	+	12.0642i	1.26391	+	0.410671i	0.862888	−	0.505396i	$-0.168653\pi$
$863$	37.1298	+	12.0642i	1.26391	+	0.410671i	0.401027	+	0.916066i	$0.368653\pi$
$864$	−3.71538	−	1.20720i	−0.126400	−	0.0410698i
$865$	55.3638	−	40.2242i	1.88243	−	1.36766i
$866$	20.7809	−	28.6025i	0.706165	−	0.971952i
$867$	15.8366	−	5.14561i	0.537838	−	0.174754i
$868$	3.81903			0.129626
$869$	−26.5695	+	37.8259i	−0.901309	+	1.28315i
$870$			0.501487i			0.0170020i
$871$	−23.8864	+	7.76117i	−0.809360	+	0.262977i
$872$	−20.3302	−	14.7707i	−0.688466	−	0.500200i
$873$	−0.0992555	−	0.136613i	−0.00335929	−	0.00462366i
$874$	14.8638	−	2.31349i	0.502775	−	0.0782549i
$875$	−15.4254	−	5.01203i	−0.521475	−	0.169438i
$876$	−7.84252	+	5.69793i	−0.264974	+	0.192515i
$877$	−39.0016	−	28.3363i	−1.31699	−	0.956850i	−0.999964	−	0.00843400i	$-0.997315\pi$
$877$	−39.0016	−	28.3363i	−1.31699	−	0.956850i	−0.317027	−	0.948416i	$-0.602685\pi$
$878$	2.71910	+	8.36853i	0.0917652	+	0.282424i
$879$		−	25.6200i		−	0.864140i
$880$	−0.379180	−	23.7375i	−0.0127822	−	0.800191i
$881$	−21.8692			−0.736792			−0.368396	−	0.929669i	$-0.620093\pi$
$881$	−21.8692			−0.736792			−0.368396	+	0.929669i	$0.620093\pi$
$882$	1.56895	+	4.82874i	0.0528294	+	0.162592i
$883$	27.2712	+	19.8137i	0.917749	+	0.666784i	0.942963	−	0.332898i	$-0.108027\pi$
$883$	27.2712	+	19.8137i	0.917749	+	0.666784i	−0.0252137	+	0.999682i	$0.508027\pi$
$884$	0.539723	+	0.742865i	0.0181529	+	0.0249853i
$885$	8.94837	−	27.5402i	0.300796	−	0.925755i
$886$	−9.57890	+	29.4808i	−0.321809	+	0.990428i
$887$	−37.9580	+	27.5781i	−1.27450	+	0.925981i	−0.999372	−	0.0354250i	$-0.988722\pi$
$887$	−37.9580	+	27.5781i	−1.27450	+	0.925981i	−0.275132	+	0.961407i	$0.588722\pi$
$888$	3.10263	+	2.25419i	0.104118	+	0.0756458i
$889$	−6.33621	+	2.05876i	−0.212510	+	0.0690486i
$890$			2.00382i			0.0671681i
$891$	3.17026	+	0.974383i	0.106208	+	0.0326430i
$892$		−	12.5799i		−	0.421207i
$893$	−11.3211	+	11.2607i	−0.378845	+	0.376826i
$894$	−1.88140	−	1.36692i	−0.0629234	−	0.0457166i
$895$	−35.4164	−	48.7465i	−1.18384	−	1.62941i
$896$	2.44124	+	0.793208i	0.0815562	+	0.0264992i
$897$	6.18590	+	2.00992i	0.206541	+	0.0671093i
$898$	−0.920566	−	1.26705i	−0.0307197	−	0.0422820i
$899$	−0.241037	+	0.331759i	−0.00803902	+	0.0110648i
$900$	1.78258	+	5.48620i	0.0594192	+	0.182873i
$901$	1.63249			0.0543862
$902$	18.5748	−	6.36506i	0.618472	−	0.211933i
$903$		−	0.0134594i		−	0.000447901i
$904$	−7.71997	+	2.50837i	−0.256762	+	0.0834271i
$905$	−41.4089	+	56.9944i	−1.37648	+	1.89456i
$906$	14.3449	+	19.7441i	0.476578	+	0.655953i
$907$	−29.5151	−	9.59005i	−0.980034	−	0.318432i	−0.225174	−	0.974319i	$-0.572295\pi$
$907$	−29.5151	−	9.59005i	−0.980034	−	0.318432i	−0.754860	+	0.655886i	$0.772295\pi$
$908$	−5.01836	+	15.4449i	−0.166540	+	0.512558i
$909$	−4.83549	−	6.65548i	−0.160383	−	0.220748i
$910$	−7.94049	+	10.9291i	−0.263225	+	0.362297i
$911$	18.0865	−	5.87666i	0.599233	−	0.194703i	0.00633467	−	0.999980i	$-0.497984\pi$
$911$	18.0865	−	5.87666i	0.599233	−	0.194703i	0.592898	+	0.805277i	$0.297984\pi$
$912$	7.76095	−	3.92831i	0.256991	−	0.130079i
$913$	−7.88319	−	23.0051i	−0.260896	−	0.761356i
$914$			17.5855i			0.581678i
$915$	−11.4412	−	35.2123i	−0.378233	−	1.16408i
$916$	−6.26247	−	4.54995i	−0.206918	−	0.150335i
$917$	10.4743	−	7.61003i	0.345892	−	0.251305i
$918$	−0.205301	+	0.631851i	−0.00677593	+	0.0208542i
$919$	33.7008	+	10.9501i	1.11169	+	0.361209i	0.806590	−	0.591112i	$-0.201311\pi$
$919$	33.7008	+	10.9501i	1.11169	+	0.361209i	0.305098	+	0.952321i	$0.401311\pi$
$920$	−27.3732	+	19.8878i	−0.902468	+	0.655681i
$921$	−3.87777	+	5.33729i	−0.127777	+	0.175870i
$922$	−34.7647	+	11.2957i	−1.14491	+	0.372005i
$923$		−	23.6543i		−	0.778592i
$924$	3.66763	+	1.12725i	0.120656	+	0.0370838i
$925$		−	9.80655i		−	0.322437i
$926$	4.73337	+	14.5678i	0.155548	+	0.478728i
$927$	8.11014	−	11.1626i	0.266372	−	0.366629i
$928$	0.392605	−	0.285244i	0.0128879	−	0.00936360i
$929$	0.511984	−	1.57573i	0.0167977	−	0.0516979i	−0.942306	−	0.334752i	$-0.891348\pi$
$929$	0.511984	−	1.57573i	0.0167977	−	0.0516979i	0.959104	+	0.283054i	$0.0913475\pi$
$930$	4.11816	−	12.6744i	0.135040	−	0.415610i
$931$	17.4968	+	8.97407i	0.573436	+	0.294113i
$932$	−9.54899	+	13.1431i	−0.312787	+	0.430515i
$933$	−24.3385	+	7.90806i	−0.796807	+	0.258898i
$934$	−20.3781			−0.666791
$935$	7.02171	−	0.112164i	0.229634	−	0.00366816i
$936$	6.52532			0.213287
$937$	−3.48340	+	1.13182i	−0.113798	+	0.0369751i	−0.365362	−	0.930865i	$-0.619055\pi$
$937$	−3.48340	+	1.13182i	−0.113798	+	0.0369751i	0.251565	+	0.967840i	$0.419055\pi$
$938$	−17.0078	−	12.3569i	−0.555325	−	0.403467i
$939$	4.88940	+	6.72968i	0.159559	+	0.219615i
$940$	2.97766	−	9.16429i	0.0971205	−	0.298906i
$941$	14.7751	−	45.4730i	0.481654	−	1.48238i	−0.355116	−	0.934822i	$-0.615559\pi$
$941$	14.7751	−	45.4730i	0.481654	−	1.48238i	0.836770	−	0.547555i	$-0.184441\pi$
$942$	5.66747	+	7.80061i	0.184656	+	0.254158i
$943$	−13.0491	−	9.48071i	−0.424936	−	0.308734i
$944$	15.3218	−	4.97835i	0.498682	−	0.162032i
$945$	5.65872			0.184078
$946$	−0.0260601	−	0.0183050i	−0.000847286	−	0.000595147i
$947$	−30.2853			−0.984139			−0.492069	−	0.870556i	$-0.663759\pi$
$947$	−30.2853			−0.984139			−0.492069	+	0.870556i	$0.663759\pi$
$948$	9.72038	−	3.15834i	0.315703	−	0.102578i
$949$	16.4815	−	22.6849i	0.535012	−	0.736382i
$950$	−34.3371	−	17.6114i	−1.11404	−	0.571389i
$951$	−0.360673	+	1.11004i	−0.0116956	+	0.0359955i
$952$	−0.885267	+	2.72457i	−0.0286917	+	0.0883039i
$953$	14.8836	−	10.8136i	0.482128	−	0.350286i	−0.320021	−	0.947410i	$-0.603690\pi$
$953$	14.8836	−	10.8136i	0.482128	−	0.350286i	0.802149	+	0.597124i	$0.203690\pi$
$954$	1.82947	−	2.51805i	0.0592314	−	0.0815250i
$955$	27.9768	+	86.1036i	0.905307	+	2.78625i
$956$			11.5883i			0.374791i
$957$	−0.329405	+	0.247461i	−0.0106482	+	0.00799926i
$958$			4.22973i			0.136656i
$959$	21.0807	−	6.84955i	0.680733	−	0.221183i
$960$	−17.6846	+	24.3408i	−0.570769	+	0.785597i
$961$	−16.2633	+	11.8160i	−0.524622	+	0.381160i
$962$	−2.83052	−	0.919690i	−0.0912595	−	0.0296520i
$963$	4.57494	−	14.0802i	0.147425	−	0.453729i
$964$	12.7436	−	9.25878i	0.410444	−	0.298205i
$965$	−38.3287	−	27.8474i	−1.23385	−	0.896441i
$966$	1.68238	+	5.17784i	0.0541298	+	0.166594i
$967$			13.9050i			0.447153i	0.974686	+	0.223577i	$0.0717733\pi$
$967$			13.9050i			0.447153i	−0.974686	+	0.223577i	$0.928227\pi$
$968$	26.7270	−	20.7543i	0.859039	−	0.667067i
$969$	1.16202	+	2.29574i	0.0373295	+	0.0737499i
$970$	−0.648336	+	0.210657i	−0.0208168	+	0.00676379i
$971$	34.4311	−	47.3904i	1.10495	−	1.52083i	0.276291	−	0.961074i	$-0.410895\pi$
$971$	34.4311	−	47.3904i	1.10495	−	1.52083i	0.828657	−	0.559756i	$-0.189105\pi$
$972$	−0.431039	−	0.593275i	−0.0138256	−	0.0190293i
$973$	−2.00603	+	6.17394i	−0.0643105	+	0.197927i
$974$	2.04545	+	0.664608i	0.0655405	+	0.0212954i
$975$	−9.80764	−	13.4991i	−0.314096	−	0.432316i
$976$	12.1073	−	16.6643i	0.387547	−	0.533412i
$977$	−30.6948	+	9.97334i	−0.982013	+	0.319075i	−0.755656	−	0.654969i	$-0.772682\pi$
$977$	−30.6948	+	9.97334i	−0.982013	+	0.319075i	−0.226357	+	0.974044i	$0.572682\pi$
$978$			16.1753i			0.517228i
$979$	−1.31622	+	0.988792i	−0.0420666	+	0.0316019i
$980$	−11.8664			−0.379059
$981$	−2.52431	−	7.76901i	−0.0805949	−	0.248046i
$982$	−17.2201	+	23.7015i	−0.549517	+	0.756345i
$983$	31.7673	+	43.7239i	1.01322	+	1.39458i	0.916850	+	0.399231i	$0.130723\pi$
$983$	31.7673	+	43.7239i	1.01322	+	1.39458i	0.0963686	+	0.995346i	$0.469277\pi$
$984$	−15.3898	−	5.00046i	−0.490610	−	0.159409i
$985$	−23.0314	−	7.48336i	−0.733842	−	0.238440i
$986$	−0.0485096	−	0.0667678i	−0.00154486	−	0.00212632i
$987$	−4.67539	−	3.39687i	−0.148819	−	0.108124i
$988$	4.80724	−	4.78161i	0.152939	−	0.152123i
$989$			0.0261608i			0.000831866i
$990$	7.69596	−	10.9564i	0.244594	−	0.348217i
$991$		−	49.9577i		−	1.58696i	−0.608597	−	0.793479i	$-0.708267\pi$
$991$		−	49.9577i		−	1.58696i	0.608597	−	0.793479i	$-0.291733\pi$
$992$	−12.2650	+	3.98513i	−0.389413	+	0.126528i
$993$	−22.3577	−	16.2439i	−0.709502	−	0.515483i
$994$	16.0182	−	11.6379i	0.508067	−	0.369132i
$995$	14.7529	−	45.4049i	0.467700	−	1.43943i
$996$	−1.66156	+	5.11376i	−0.0526486	+	0.162036i
$997$	−29.8935	−	41.1449i	−0.946736	−	1.30307i	−0.952962	−	0.303090i	$-0.901982\pi$
$997$	−29.8935	−	41.1449i	−0.946736	−	1.30307i	0.00622583	−	0.999981i	$-0.498018\pi$
$998$	−15.2402	−	11.0727i	−0.482420	−	0.350499i
$999$	0.385240	+	1.18565i	0.0121884	+	0.0375122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.s.a.94.13	✓	160
11.2	odd	10	inner	627.2.s.a.607.28	yes	160
19.18	odd	2	inner	627.2.s.a.94.28	yes	160
209.189	even	10	inner	627.2.s.a.607.13	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.s.a.94.13	✓	160	1.1	even	1	trivial
627.2.s.a.94.28	yes	160	19.18	odd	2	inner
627.2.s.a.607.13	yes	160	209.189	even	10	inner
627.2.s.a.607.28	yes	160	11.2	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.347788 - 1.07038i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.593275 - 0.431039i) q^{4} +(1.10843 - 3.41140i) q^{5} +(1.07038 + 0.347788i) q^{6} +(0.927280 + 1.27629i) q^{7} +(-2.48875 - 1.80818i) q^{8} +(-0.309017 - 0.951057i) q^{9} -4.03699 q^{10} +(-1.99207 - 2.65173i) q^{11} +0.733328i q^{12} +(-0.655482 - 2.01737i) q^{13} +(1.04362 - 1.43642i) q^{14} +(2.10836 + 2.90191i) q^{15} +(-0.616666 + 1.89790i) q^{16} +(-0.561413 - 0.182414i) q^{17} +(-0.910521 + 0.661532i) q^{18} +(-0.693386 + 4.30340i) q^{19} +(-0.812843 - 2.50167i) q^{20} -1.57758 q^{21} +(-2.14554 + 3.05451i) q^{22} +3.06632 q^{23} +(2.92570 - 0.950618i) q^{24} +(-6.36393 - 4.62366i) q^{25} +(-1.93138 + 1.40323i) q^{26} +(0.951057 + 0.309017i) q^{27} +(1.10026 + 0.357497i) q^{28} +(-0.100498 + 0.0730163i) q^{29} +(2.37289 - 3.26600i) q^{30} +(3.13956 - 1.02011i) q^{31} -3.90658 q^{32} +(3.31620 - 0.0529726i) q^{33} +0.664367i q^{34} +(5.38176 - 1.74864i) q^{35} +(-0.593275 - 0.431039i) q^{36} +(0.732770 + 1.00857i) q^{37} +(4.84742 - 0.754482i) q^{38} +(2.01737 + 0.655482i) q^{39} +(-8.92704 + 6.48587i) q^{40} +(-4.25561 - 3.09188i) q^{41} +(0.548664 + 1.68861i) q^{42} +0.00853166i q^{43} +(-2.32484 - 0.714542i) q^{44} -3.58695 q^{45} +(-1.06643 - 3.28214i) q^{46} +(2.96364 + 2.15321i) q^{47} +(-1.17297 - 1.61445i) q^{48} +(1.39405 - 4.29044i) q^{49} +(-2.73578 + 8.41988i) q^{50} +(0.477566 - 0.346972i) q^{51} +(-1.25844 - 0.914314i) q^{52} +(-2.63016 + 0.854590i) q^{53} -1.12547i q^{54} +(-11.2542 + 3.85649i) q^{55} -4.85306i q^{56} +(-3.07396 - 3.09043i) q^{57} +(0.113107 + 0.0821773i) q^{58} +(-4.74520 - 6.53120i) q^{59} +(2.50167 + 0.812843i) q^{60} +(-9.81677 - 3.18966i) q^{61} +(-2.18381 - 3.00575i) q^{62} +(0.927280 - 1.27629i) q^{63} +(2.59199 + 7.97734i) q^{64} -7.60859 q^{65} +(-1.21004 - 3.53118i) q^{66} -11.8404i q^{67} +(-0.411700 + 0.133769i) q^{68} +(-1.80234 + 2.48071i) q^{69} +(-3.74342 - 5.15238i) q^{70} +(10.6057 + 3.44600i) q^{71} +(-0.950618 + 2.92570i) q^{72} +(7.76996 + 10.6944i) q^{73} +(0.824707 - 1.13511i) q^{74} +(7.48124 - 2.43080i) q^{75} +(1.44356 + 2.85197i) q^{76} +(1.53717 - 5.00135i) q^{77} -2.38732i q^{78} +(-4.30687 - 13.2552i) q^{79} +(5.79097 + 4.20739i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.82944 + 5.63044i) q^{82} +(6.97337 + 2.26578i) q^{83} +(-0.935940 + 0.680000i) q^{84} +(-1.24457 + 1.71301i) q^{85} +(0.00913212 - 0.00296721i) q^{86} -0.124223i q^{87} +(0.162958 + 10.2015i) q^{88} -0.496364i q^{89} +(1.24750 + 3.83941i) q^{90} +(1.96693 - 2.70725i) q^{91} +(1.81917 - 1.32171i) q^{92} +(-1.02011 + 3.13956i) q^{93} +(1.27404 - 3.92109i) q^{94} +(13.9120 + 7.13543i) q^{95} +(2.29623 - 3.16049i) q^{96} +(0.160599 - 0.0521817i) q^{97} -5.07724 q^{98} +(-1.90636 + 2.71400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 40 q^{4} + 4 q^{5} - 10 q^{7} + 40 q^{9} + 10 q^{11} - 40 q^{16} - 50 q^{17} + 76 q^{20} + 16 q^{23} - 80 q^{25} - 68 q^{26} - 40 q^{35} + 40 q^{36} - 62 q^{38} + 8 q^{42} + 40 q^{44} - 4 q^{45}+ \cdots - 10 q^{99}+O(q^{100}) \) 160 * q - 40 * q^4 + 4 * q^5 - 10 * q^7 + 40 * q^9 + 10 * q^11 - 40 * q^16 - 50 * q^17 + 76 * q^20 + 16 * q^23 - 80 * q^25 - 68 * q^26 - 40 * q^35 + 40 * q^36 - 62 * q^38 + 8 * q^42 + 40 * q^44 - 4 * q^45 + 20 * q^47 + 110 * q^49 - 18 * q^55 - 20 * q^57 - 24 * q^58 + 10 * q^61 + 120 * q^62 - 10 * q^63 - 136 * q^64 - 12 * q^66 + 160 * q^68 + 20 * q^73 - 100 * q^74 + 90 * q^77 - 156 * q^80 - 40 * q^81 + 68 * q^82 - 200 * q^83 + 30 * q^85 - 84 * q^92 - 96 * q^93 - 60 * q^95 + 100 * q^96 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more