LMFDB - Embedded newform 475.2.u.b.24.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(24,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.24"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,6,0,-12,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			24.4
Character	$\chi$	$=$	475.24
Dual form			475.2.u.b.99.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.105338 + 0.289414i) q^{2} +(1.61894 + 0.285463i) q^{3} +(1.45942 - 1.22460i) q^{4} +(0.0879194 + 0.498616i) q^{6} +(0.0772459 - 0.0445979i) q^{7} +(1.04160 + 0.601369i) q^{8} +(-0.279590 - 0.101762i) q^{9} +(1.68341 - 2.91575i) q^{11} +(2.71230 - 1.56595i) q^{12} +(0.209636 - 0.0369645i) q^{13} +(0.0210442 + 0.0176582i) q^{14} +(0.597325 - 3.38760i) q^{16} +(0.859918 + 2.36261i) q^{17} -0.0916368i q^{18} +(-0.949628 + 4.25420i) q^{19} +(0.137788 - 0.0501507i) q^{21} +(1.02119 + 0.180063i) q^{22} +(3.83550 + 4.57098i) q^{23} +(1.51463 + 1.27092i) q^{24} +(0.0327807 + 0.0567779i) q^{26} +(-4.69462 - 2.71044i) q^{27} +(0.0581198 - 0.159683i) q^{28} +(-4.51826 - 1.64451i) q^{29} +(-4.03407 - 6.98722i) q^{31} +(3.41227 - 0.601676i) q^{32} +(3.55769 - 4.23989i) q^{33} +(-0.593190 + 0.497745i) q^{34} +(-0.532659 + 0.193872i) q^{36} +1.84372i q^{37} +(-1.33126 + 0.173294i) q^{38} +0.349941 q^{39} +(-0.523087 + 2.96657i) q^{41} +(0.0290286 + 0.0345950i) q^{42} +(-1.57346 + 1.87518i) q^{43} +(-1.11383 - 6.31683i) q^{44} +(-0.918881 + 1.59155i) q^{46} +(-2.60562 + 7.15887i) q^{47} +(1.93407 - 5.31381i) q^{48} +(-3.49602 + 6.05529i) q^{49} +(0.717721 + 4.07040i) q^{51} +(0.260681 - 0.310668i) q^{52} +(5.39920 + 6.43452i) q^{53} +(0.289917 - 1.64420i) q^{54} +0.107279 q^{56} +(-2.75181 + 6.61622i) q^{57} -1.48088i q^{58} +(9.80610 - 3.56913i) q^{59} +(-0.757296 + 0.635447i) q^{61} +(1.59726 - 1.90354i) q^{62} +(-0.0261356 + 0.00460841i) q^{63} +(-2.90628 - 5.03383i) q^{64} +(1.60184 + 0.583024i) q^{66} +(3.41324 - 9.37780i) q^{67} +(4.14824 + 2.39499i) q^{68} +(4.90462 + 8.49505i) q^{69} +(4.73200 + 3.97062i) q^{71} +(-0.230025 - 0.274133i) q^{72} +(-15.5058 - 2.73409i) q^{73} +(-0.533599 + 0.194214i) q^{74} +(3.82379 + 7.37160i) q^{76} -0.300307i q^{77} +(0.0368621 + 0.101278i) q^{78} +(0.178596 - 1.01287i) q^{79} +(-6.14281 - 5.15443i) q^{81} +(-0.913670 + 0.161105i) q^{82} +(-15.5354 + 8.96939i) q^{83} +(0.139676 - 0.241926i) q^{84} +(-0.708449 - 0.257854i) q^{86} +(-6.84536 - 3.95217i) q^{87} +(3.50689 - 2.02470i) q^{88} +(-0.113975 - 0.646383i) q^{89} +(0.0145450 - 0.0122047i) q^{91} +(11.1953 + 1.97403i) q^{92} +(-4.53634 - 12.4635i) q^{93} -2.34635 q^{94} +5.69603 q^{96} +(-5.75040 - 15.7991i) q^{97} +(-2.12075 - 0.373946i) q^{98} +(-0.767379 + 0.643907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49}+ \cdots + 186 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	0.105338	+	0.289414i	0.0744854	+	0.204647i	0.971348	−	0.237663i	$-0.0763814\pi$
$2$	0.105338	+	0.289414i	0.0744854	+	0.204647i	−0.896862	+	0.442310i	$0.854159\pi$
$3$	1.61894	+	0.285463i	0.934697	+	0.164812i	0.620198	−	0.784445i	$-0.287052\pi$
$3$	1.61894	+	0.285463i	0.934697	+	0.164812i	0.314499	+	0.949258i	$0.398163\pi$
$4$	1.45942	−	1.22460i	0.729712	−	0.612301i
$5$		0			0
$5$		0			0
$6$	0.0879194	+	0.498616i	0.0358929	+	0.203559i
$7$	0.0772459	−	0.0445979i	0.0291962	−	0.0168564i	−0.485331	−	0.874331i	$-0.661301\pi$
$7$	0.0772459	−	0.0445979i	0.0291962	−	0.0168564i	0.514527	+	0.857474i	$0.327968\pi$
$8$	1.04160	+	0.601369i	0.368262	+	0.212616i
$9$	−0.279590	−	0.101762i	−0.0931966	−	0.0339208i
$10$		0			0
$11$	1.68341	−	2.91575i	0.507567	−	0.879133i	−0.492394	−	0.870372i	$-0.663878\pi$
$11$	1.68341	−	2.91575i	0.507567	−	0.879133i	0.999962	−	0.00876033i	$-0.00278854\pi$
$12$	2.71230	−	1.56595i	0.782975	−	0.452051i
$13$	0.209636	−	0.0369645i	0.0581426	−	0.0102521i	−0.144501	−	0.989505i	$-0.546158\pi$
$13$	0.209636	−	0.0369645i	0.0581426	−	0.0102521i	0.202644	+	0.979253i	$0.435047\pi$
$14$	0.0210442	+	0.0176582i	0.00562431	+	0.00471935i
$15$		0			0
$16$	0.597325	−	3.38760i	0.149331	−	0.846899i
$17$	0.859918	+	2.36261i	0.208561	+	0.573016i	0.999230	−	0.0392271i	$-0.0124896\pi$
$17$	0.859918	+	2.36261i	0.208561	+	0.573016i	−0.790670	+	0.612243i	$0.790267\pi$
$18$		−	0.0916368i		−	0.0215990i
$19$	−0.949628	+	4.25420i	−0.217860	+	0.975980i
$19$	−0.949628	+	4.25420i	−0.217860	+	0.975980i
$20$		0			0
$21$	0.137788	−	0.0501507i	0.0300678	−	0.0109438i
$22$	1.02119	+	0.180063i	0.217718	+	0.0383896i
$23$	3.83550	+	4.57098i	0.799758	+	0.953114i	0.999643	−	0.0267049i	$-0.00850145\pi$
$23$	3.83550	+	4.57098i	0.799758	+	0.953114i	−0.199885	+	0.979819i	$0.564057\pi$
$24$	1.51463	+	1.27092i	0.309172	+	0.259426i
$25$		0			0
$26$	0.0327807	+	0.0567779i	0.00642883	+	0.0111351i
$27$	−4.69462	−	2.71044i	−0.903479	−	0.521624i
$28$	0.0581198	−	0.159683i	0.0109836	−	0.0301772i
$29$	−4.51826	−	1.64451i	−0.839019	−	0.305378i	−0.113464	−	0.993542i	$-0.536195\pi$
$29$	−4.51826	−	1.64451i	−0.839019	−	0.305378i	−0.725555	+	0.688164i	$0.758417\pi$
$30$		0			0
$31$	−4.03407	−	6.98722i	−0.724541	−	1.25494i	−0.959163	−	0.282855i	$-0.908718\pi$
$31$	−4.03407	−	6.98722i	−0.724541	−	1.25494i	0.234621	−	0.972087i	$-0.424615\pi$
$32$	3.41227	−	0.601676i	0.603210	−	0.106362i
$33$	3.55769	−	4.23989i	0.619314	−	0.738070i
$34$	−0.593190	+	0.497745i	−0.101731	+	0.0853626i
$35$		0			0
$36$	−0.532659	+	0.193872i	−0.0887765	+	0.0323120i
$37$			1.84372i			0.303106i	0.988449	+	0.151553i	$0.0484274\pi$
$37$			1.84372i			0.303106i	−0.988449	+	0.151553i	$0.951573\pi$
$38$	−1.33126	+	0.173294i	−0.215959	+	0.0281119i
$39$	0.349941			0.0560354
$40$		0			0
$41$	−0.523087	+	2.96657i	−0.0816925	+	0.463301i	0.916329	+	0.400426i	$0.131138\pi$
$41$	−0.523087	+	2.96657i	−0.0816925	+	0.463301i	−0.998021	+	0.0628748i	$0.979973\pi$
$42$	0.0290286	+	0.0345950i	0.00447922	+	0.00533812i
$43$	−1.57346	+	1.87518i	−0.239951	+	0.285962i	−0.872558	−	0.488511i	$-0.837540\pi$
$43$	−1.57346	+	1.87518i	−0.239951	+	0.285962i	0.632607	+	0.774473i	$0.281985\pi$
$44$	−1.11383	−	6.31683i	−0.167916	−	0.952298i
$45$		0			0
$46$	−0.918881	+	1.59155i	−0.135482	+	0.234661i
$47$	−2.60562	+	7.15887i	−0.380068	+	1.04423i	0.591259	+	0.806482i	$0.298631\pi$
$47$	−2.60562	+	7.15887i	−0.380068	+	1.04423i	−0.971327	+	0.237747i	$0.923591\pi$
$48$	1.93407	−	5.31381i	0.279159	−	0.766983i
$49$	−3.49602	+	6.05529i	−0.499432	+	0.865041i
$50$		0			0
$51$	0.717721	+	4.07040i	0.100501	+	0.569970i
$52$	0.260681	−	0.310668i	0.0361500	−	0.0430818i
$53$	5.39920	+	6.43452i	0.741637	+	0.883849i	0.996540	−	0.0831178i	$-0.0264878\pi$
$53$	5.39920	+	6.43452i	0.741637	+	0.883849i	−0.254902	+	0.966967i	$0.582043\pi$
$54$	0.289917	−	1.64420i	0.0394527	−	0.223747i
$55$		0			0
$56$	0.107279			0.0143358
$57$	−2.75181	+	6.61622i	−0.364486	+	0.876340i
$58$		−	1.48088i		−	0.194449i
$59$	9.80610	−	3.56913i	1.27665	−	0.464661i	0.387324	−	0.921944i	$-0.373400\pi$
$59$	9.80610	−	3.56913i	1.27665	−	0.464661i	0.889321	+	0.457283i	$0.151177\pi$
$60$		0			0
$61$	−0.757296	+	0.635447i	−0.0969618	+	0.0813606i	−0.689980	−	0.723828i	$-0.742381\pi$
$61$	−0.757296	+	0.635447i	−0.0969618	+	0.0813606i	0.593018	+	0.805189i	$0.297936\pi$
$62$	1.59726	−	1.90354i	0.202852	−	0.241750i
$63$	−0.0261356	+	0.00460841i	−0.00329277	+	0.000580605i
$64$	−2.90628	−	5.03383i	−0.363285	−	0.629228i
$65$		0			0
$66$	1.60184	+	0.583024i	0.197173	+	0.0717653i
$67$	3.41324	−	9.37780i	0.416994	−	1.14568i	−0.536403	−	0.843962i	$-0.680217\pi$
$67$	3.41324	−	9.37780i	0.416994	−	1.14568i	0.953397	−	0.301719i	$-0.0975603\pi$
$68$	4.14824	+	2.39499i	0.503048	+	0.290435i
$69$	4.90462	+	8.49505i	0.590447	+	1.02268i
$70$		0			0
$71$	4.73200	+	3.97062i	0.561585	+	0.471226i	0.878841	−	0.477114i	$-0.158317\pi$
$71$	4.73200	+	3.97062i	0.561585	+	0.471226i	−0.317256	+	0.948340i	$0.602762\pi$
$72$	−0.230025	−	0.274133i	−0.0271087	−	0.0323068i
$73$	−15.5058	−	2.73409i	−1.81482	−	0.320001i	−0.839929	−	0.542696i	$-0.817403\pi$
$73$	−15.5058	−	2.73409i	−1.81482	−	0.320001i	−0.974888	+	0.222695i	$0.928515\pi$
$74$	−0.533599	+	0.194214i	−0.0620296	+	0.0225769i
$75$		0			0
$76$	3.82379	+	7.37160i	0.438619	+	0.845580i
$77$		−	0.300307i		−	0.0342231i
$78$	0.0368621	+	0.101278i	0.00417381	+	0.0114675i
$79$	0.178596	−	1.01287i	0.0200936	−	0.113957i	−0.973111	−	0.230336i	$-0.926018\pi$
$79$	0.178596	−	1.01287i	0.0200936	−	0.113957i	0.993205	+	0.116379i	$0.0371287\pi$
$80$		0			0
$81$	−6.14281	−	5.15443i	−0.682535	−	0.572715i
$82$	−0.913670	+	0.161105i	−0.100898	+	0.0177910i
$83$	−15.5354	+	8.96939i	−1.70524	+	0.984518i	−0.764976	+	0.644059i	$0.777249\pi$
$83$	−15.5354	+	8.96939i	−1.70524	+	0.984518i	−0.940259	+	0.340459i	$0.889418\pi$
$84$	0.139676	−	0.241926i	0.0152399	−	0.0263963i
$85$		0			0
$86$	−0.708449	−	0.257854i	−0.0763940	−	0.0278052i
$87$	−6.84536	−	3.95217i	−0.733899	−	0.423717i
$88$	3.50689	−	2.02470i	0.373836	−	0.215834i
$89$	−0.113975	−	0.646383i	−0.0120813	−	0.0685164i	0.978171	−	0.207801i	$-0.0666307\pi$
$89$	−0.113975	−	0.646383i	−0.0120813	−	0.0685164i	−0.990252	+	0.139285i	$0.955520\pi$
$90$		0			0
$91$	0.0145450	−	0.0122047i	0.00152473	−	0.00127940i
$92$	11.1953	+	1.97403i	1.16719	+	0.205806i
$93$	−4.53634	−	12.4635i	−0.470397	−	1.29240i
$94$	−2.34635			−0.242008
$95$		0			0
$96$	5.69603			0.581349
$97$	−5.75040	−	15.7991i	−0.583865	−	1.60416i	−0.781518	−	0.623883i	$-0.785554\pi$
$97$	−5.75040	−	15.7991i	−0.583865	−	1.60416i	0.197653	−	0.980272i	$-0.436668\pi$
$98$	−2.12075	−	0.373946i	−0.214228	−	0.0377742i
$99$	−0.767379	+	0.643907i	−0.0771245	+	0.0647151i
$100$		0			0
$101$	0.638978	+	3.62382i	0.0635806	+	0.360584i	0.999954	+	0.00957849i	$0.00304897\pi$
$101$	0.638978	+	3.62382i	0.0635806	+	0.360584i	−0.936373	+	0.351005i	$0.885840\pi$
$102$	−1.10243	+	0.636488i	−0.109157	+	0.0630217i
$103$	−3.06071	−	1.76710i	−0.301580	−	0.174118i	0.341572	−	0.939856i	$-0.389041\pi$
$103$	−3.06071	−	1.76710i	−0.301580	−	0.174118i	−0.643153	+	0.765738i	$0.722374\pi$
$104$	0.240587	+	0.0875664i	0.0235915	+	0.00858659i
$105$		0			0
$106$	−1.29350	+	2.24041i	−0.125636	+	0.217608i
$107$	−1.63384	+	0.943300i	−0.157950	+	0.0911923i	−0.576891	−	0.816821i	$-0.695734\pi$
$107$	−1.63384	+	0.943300i	−0.157950	+	0.0911923i	0.418942	+	0.908013i	$0.362401\pi$
$108$	−10.1706	+	1.79336i	−0.978671	+	0.172566i
$109$	10.0810	+	8.45901i	0.965589	+	0.810226i	0.981853	−	0.189642i	$-0.0607327\pi$
$109$	10.0810	+	8.45901i	0.965589	+	0.810226i	−0.0162639	+	0.999868i	$0.505177\pi$
$110$		0			0
$111$	−0.526315	+	2.98488i	−0.0499556	+	0.283312i
$112$	−0.104939	−	0.288318i	−0.00991580	−	0.0272434i
$113$		−	12.3456i		−	1.16138i	−0.814125	−	0.580689i	$-0.802783\pi$
$113$		−	12.3456i		−	1.16138i	0.814125	−	0.580689i	$-0.197217\pi$
$114$	−2.20470	−	0.0994730i	−0.206489	−	0.00931650i
$115$		0			0
$116$	−8.60793	+	3.13303i	−0.799226	+	0.290895i
$117$	−0.0623737	−	0.0109982i	−0.00576645	−	0.00101678i
$118$	2.06591	+	2.46206i	0.190183	+	0.226651i
$119$	0.171793	+	0.144151i	0.0157482	+	0.0132143i
$120$		0			0
$121$	−0.167744	−	0.290542i	−0.0152495	−	0.0264129i
$122$	−0.263680	−	0.152235i	−0.0238724	−	0.0137827i
$123$	−1.69370	+	4.65339i	−0.152716	+	0.419582i
$124$	−14.4440	−	5.25718i	−1.29711	−	0.472109i
$125$		0			0
$126$	−0.00408681	−	0.00707857i	−0.000364082	−	0.000630609i
$127$	−20.8898	+	3.68344i	−1.85367	+	0.326852i	−0.985535	−	0.169473i	$-0.945793\pi$
$127$	−20.8898	+	3.68344i	−1.85367	+	0.326852i	−0.868137	+	0.496325i	$0.834682\pi$
$128$	5.60512	−	6.67993i	0.495428	−	0.590428i
$129$	−3.08264	+	2.58664i	−0.271411	+	0.227741i
$130$		0			0
$131$	−6.53156	+	2.37729i	−0.570665	+	0.207705i	−0.611204	−	0.791473i	$-0.709315\pi$
$131$	−6.53156	+	2.37729i	−0.570665	+	0.207705i	0.0405392	+	0.999178i	$0.487092\pi$
$132$		−	10.5445i		−	0.917785i
$133$	0.116374	+	0.370971i	0.0100909	+	0.0321673i
$134$	3.07361			0.265520
$135$		0			0
$136$	−0.525106	+	2.97802i	−0.0450275	+	0.255363i
$137$	13.5029	+	16.0922i	1.15363	+	1.37485i	0.914860	+	0.403772i	$0.132301\pi$
$137$	13.5029	+	16.0922i	1.15363	+	1.37485i	0.238774	+	0.971075i	$0.423254\pi$
$138$	−1.94194	+	2.31432i	−0.165309	+	0.197008i
$139$	−2.72999	−	15.4826i	−0.231555	−	1.31321i	−0.849749	−	0.527188i	$-0.823246\pi$
$139$	−2.72999	−	15.4826i	−0.231555	−	1.31321i	0.618194	−	0.786026i	$-0.287865\pi$
$140$		0			0
$141$	−6.26194	+	10.8460i	−0.527351	+	0.913398i
$142$	−0.650694	+	1.78777i	−0.0546050	+	0.150026i
$143$	0.245124	−	0.673473i	0.0204983	−	0.0563187i
$144$	−0.511736	+	0.886353i	−0.0426447	+	0.0738627i
$145$		0			0
$146$	−0.842068	−	4.77561i	−0.0696901	−	0.395232i
$147$	−7.38842	+	8.80518i	−0.609387	+	0.726239i
$148$	2.25782	+	2.69077i	0.185592	+	0.221180i
$149$	3.38951	−	19.2229i	0.277679	−	1.57480i	−0.452641	−	0.891693i	$-0.649518\pi$
$149$	3.38951	−	19.2229i	0.277679	−	1.57480i	0.730320	−	0.683105i	$-0.239371\pi$
$150$		0			0
$151$	11.2284			0.913758			0.456879	−	0.889529i	$-0.348967\pi$
$151$	11.2284			0.913758			0.456879	+	0.889529i	$0.348967\pi$
$152$	−3.54748	+	3.86010i	−0.287739	+	0.313096i
$153$		−	0.748068i		−	0.0604777i
$154$	0.0869131	−	0.0316338i	0.00700365	−	0.00254912i
$155$		0			0
$156$	0.510712	−	0.428538i	0.0408897	−	0.0343105i
$157$	−2.96506	+	3.53362i	−0.236637	+	0.282014i	−0.871274	−	0.490797i	$-0.836705\pi$
$157$	−2.96506	+	3.53362i	−0.236637	+	0.282014i	0.634636	+	0.772811i	$0.281150\pi$
$158$	0.311951	−	0.0550055i	0.0248175	−	0.00437600i
$159$	6.90418	+	11.9584i	0.547537	+	0.948362i
$160$		0			0
$161$	0.500133	+	0.182034i	0.0394160	+	0.0143463i
$162$	0.844694	−	2.32078i	0.0663654	−	0.182337i
$163$	−0.497735	−	0.287367i	−0.0389856	−	0.0225084i	0.480381	−	0.877060i	$-0.340499\pi$
$163$	−0.497735	−	0.287367i	−0.0389856	−	0.0225084i	−0.519366	+	0.854552i	$0.673832\pi$
$164$	2.86947	+	4.97007i	0.224068	+	0.388097i
$165$		0			0
$166$	−4.23234	−	3.55136i	−0.328494	−	0.275639i
$167$	2.64958	+	3.15765i	0.205031	+	0.244346i	0.858755	−	0.512387i	$-0.171239\pi$
$167$	2.64958	+	3.15765i	0.205031	+	0.244346i	−0.653724	+	0.756733i	$0.726794\pi$
$168$	0.173679	+	0.0306243i	0.0133996	+	0.00236272i
$169$	−12.1734	+	4.43076i	−0.936417	+	0.340828i
$170$		0			0
$171$	0.698424	−	1.09279i	0.0534098	−	0.0835681i
$172$			4.66355i			0.355592i
$173$	−2.20075	−	6.04652i	−0.167320	−	0.459709i	0.827487	−	0.561485i	$-0.189770\pi$
$173$	−2.20075	−	6.04652i	−0.167320	−	0.459709i	−0.994807	+	0.101776i	$0.967547\pi$
$174$	0.422737	−	2.39746i	0.0320476	−	0.181751i
$175$		0			0
$176$	−8.87186	−	7.44437i	−0.668741	−	0.561141i
$177$	16.8944	−	2.97893i	1.26986	−	0.223910i
$178$	0.175066	−	0.101075i	0.0131218	−	0.00757587i
$179$	1.91516	−	3.31715i	0.143146	−	0.247936i	−0.785534	−	0.618819i	$-0.787612\pi$
$179$	1.91516	−	3.31715i	0.143146	−	0.247936i	0.928680	+	0.370883i	$0.120945\pi$
$180$		0			0
$181$	−15.6814	−	5.70755i	−1.16559	−	0.424239i	−0.314496	−	0.949259i	$-0.601836\pi$
$181$	−15.6814	−	5.70755i	−1.16559	−	0.424239i	−0.851090	+	0.525020i	$0.824058\pi$
$182$	0.00506435	+	0.00292391i	0.000375395	+	0.000216734i
$183$	−1.40742	+	0.812572i	−0.104039	+	0.0600670i
$184$	1.24622	+	7.06769i	0.0918729	+	0.521037i
$185$		0			0
$186$	3.12926	−	2.62576i	0.229449	−	0.192530i
$187$	8.33637	+	1.46993i	0.609616	+	0.107492i
$188$	4.96407	+	13.6387i	0.362042	+	0.994703i
$189$	−0.483520			−0.0351709
$190$		0			0
$191$	7.92694			0.573573			0.286787	−	0.957994i	$-0.407413\pi$
$191$	7.92694			0.573573			0.286787	+	0.957994i	$0.407413\pi$
$192$	−3.26813	−	8.97912i	−0.235857	−	0.648012i
$193$	20.9438	+	3.69296i	1.50757	+	0.265825i	0.865533	−	0.500851i	$-0.166980\pi$
$193$	20.9438	+	3.69296i	1.50757	+	0.265825i	0.642034	+	0.766676i	$0.278091\pi$
$194$	3.96675	−	3.32850i	0.284796	−	0.238972i
$195$		0			0
$196$	2.31314	+	13.1185i	0.165224	+	0.937034i
$197$	2.50058	−	1.44371i	0.178159	−	0.102860i	−0.408268	−	0.912862i	$-0.633867\pi$
$197$	2.50058	−	1.44371i	0.178159	−	0.102860i	0.586427	+	0.810002i	$0.300534\pi$
$198$	−0.267190	−	0.154262i	−0.0189884	−	0.0109629i
$199$	10.9144	+	3.97251i	0.773701	+	0.281604i	0.698544	−	0.715568i	$-0.253832\pi$
$199$	10.9144	+	3.97251i	0.773701	+	0.281604i	0.0751574	+	0.997172i	$0.476054\pi$
$200$		0			0
$201$	8.20286	−	14.2078i	0.578585	−	1.00214i
$202$	−0.981477	+	0.566656i	−0.0690565	+	0.0398698i
$203$	−0.422359	+	0.0744732i	−0.0296438	+	0.00522700i
$204$	6.03208	+	5.06152i	0.422330	+	0.354377i
$205$		0			0
$206$	0.189015	−	1.07196i	0.0131693	−	0.0746867i
$207$	−0.607215	−	1.66831i	−0.0422043	−	0.115955i
$208$		−	0.732242i		−	0.0507719i
$209$	10.8056	+	9.93045i	0.747437	+	0.686903i
$210$		0			0
$211$	22.2708	−	8.10590i	1.53318	−	0.558033i	0.568784	−	0.822487i	$-0.307414\pi$
$211$	22.2708	−	8.10590i	1.53318	−	0.558033i	0.964398	+	0.264454i	$0.0851916\pi$
$212$	15.7595	+	2.77882i	1.08236	+	0.190850i
$213$	6.52737	+	7.77902i	0.447248	+	0.533010i
$214$	−0.445111	−	0.373492i	−0.0304272	−	0.0255314i
$215$		0			0
$216$	−3.25995	−	5.64639i	−0.221811	−	0.384188i
$217$	−0.623232	−	0.359823i	−0.0423077	−	0.0244264i
$218$	−1.38624	+	3.80866i	−0.0938879	+	0.257955i
$219$	−24.3225	−	8.85268i	−1.64356	−	0.598209i
$220$		0			0
$221$	0.267602	+	0.463501i	0.0180009	+	0.0311784i
$222$	−0.919308	+	0.162099i	−0.0616999	+	0.0108794i
$223$	−5.66673	+	6.75335i	−0.379472	+	0.452237i	−0.921648	−	0.388028i	$-0.873156\pi$
$223$	−5.66673	+	6.75335i	−0.379472	+	0.452237i	0.542175	+	0.840265i	$0.317601\pi$
$224$	0.236751	−	0.198657i	0.0158186	−	0.0132734i
$225$		0			0
$226$	3.57300	−	1.30047i	0.237672	−	0.0865057i
$227$		−	1.04512i		−	0.0693671i	−0.999398	−	0.0346835i	$-0.988958\pi$
$227$		−	1.04512i		−	0.0693671i	0.999398	−	0.0346835i	$-0.0110423\pi$
$228$	4.08618	+	13.0258i	0.270614	+	0.862651i
$229$	13.4837			0.891031			0.445515	−	0.895274i	$-0.353020\pi$
$229$	13.4837			0.891031			0.445515	+	0.895274i	$0.353020\pi$
$230$		0			0
$231$	0.0857266	−	0.486179i	0.00564039	−	0.0319883i
$232$	−3.71727	−	4.43007i	−0.244051	−	0.290848i
$233$	7.21068	−	8.59336i	0.472388	−	0.562970i	−0.476260	−	0.879305i	$-0.658008\pi$
$233$	7.21068	−	8.59336i	0.472388	−	0.562970i	0.948648	+	0.316335i	$0.102452\pi$
$234$	−0.00338731	−	0.0192104i	−0.000221435	−	0.00125582i
$235$		0			0
$236$	9.94050	−	17.2174i	0.647071	−	1.12076i
$237$	0.578273	−	1.58879i	0.0375629	−	0.103203i
$238$	−0.0236231	+	0.0649038i	−0.00153126	+	0.00420709i
$239$	−10.1645	+	17.6054i	−0.657487	+	1.13880i	0.323777	+	0.946133i	$0.395047\pi$
$239$	−10.1645	+	17.6054i	−0.657487	+	1.13880i	−0.981264	+	0.192667i	$0.938286\pi$
$240$		0			0
$241$	−0.667594	−	3.78611i	−0.0430035	−	0.243885i	0.955727	−	0.294254i	$-0.0950713\pi$
$241$	−0.667594	−	3.78611i	−0.0430035	−	0.243885i	−0.998731	+	0.0503694i	$0.983960\pi$
$242$	0.0664171	−	0.0791528i	0.00426945	−	0.00508814i
$243$	1.97995	+	2.35961i	0.127014	+	0.151369i
$244$	−0.327046	+	1.85477i	−0.0209370	+	0.118740i
$245$		0			0
$246$	−1.52517			−0.0972413
$247$	−0.0418221	+	0.926936i	−0.00266107	+	0.0589795i
$248$		−	9.70387i		−	0.616197i
$249$	−27.7114	+	10.0861i	−1.75614	+	0.639183i
$250$		0			0
$251$	−6.08068	+	5.10229i	−0.383809	+	0.322054i	−0.814196	−	0.580591i	$-0.802822\pi$
$251$	−6.08068	+	5.10229i	−0.383809	+	0.322054i	0.430387	+	0.902645i	$0.358377\pi$
$252$	−0.0324994	+	0.0387313i	−0.00204727	+	0.00243984i
$253$	19.7846	−	3.48855i	1.24385	−	0.219323i
$254$	−3.26654	−	5.65781i	−0.204961	−	0.355002i
$255$		0			0
$256$	−8.40034	−	3.05747i	−0.525021	−	0.191092i
$257$	8.28638	−	22.7666i	0.516890	−	1.42014i	−0.357038	−	0.934090i	$-0.616213\pi$
$257$	8.28638	−	22.7666i	0.516890	−	1.42014i	0.873929	−	0.486054i	$-0.161564\pi$
$258$	−1.07333	−	0.619688i	−0.0668227	−	0.0385801i
$259$	0.0822262	+	0.142420i	0.00510928	+	0.00884954i
$260$		0			0
$261$	1.09591	+	0.919578i	0.0678351	+	0.0569204i
$262$	−1.37605	−	1.63991i	−0.0850124	−	0.101314i
$263$	12.1892	+	2.14928i	0.751617	+	0.132530i	0.536316	−	0.844017i	$-0.319816\pi$
$263$	12.1892	+	2.14928i	0.751617	+	0.132530i	0.215301	+	0.976548i	$0.430927\pi$
$264$	6.25543	−	2.27679i	0.384995	−	0.140127i
$265$		0			0
$266$	−0.0951057	+	0.0727576i	−0.00583131	+	0.00446105i
$267$		−	1.07899i		−	0.0660333i
$268$	−6.50271	−	17.8660i	−0.397216	−	1.09134i
$269$	4.23334	−	24.0085i	0.258111	−	1.46382i	−0.529846	−	0.848094i	$-0.677750\pi$
$269$	4.23334	−	24.0085i	0.258111	−	1.46382i	0.787958	−	0.615729i	$-0.211138\pi$
$270$		0			0
$271$	13.3432	+	11.1963i	0.810540	+	0.680124i	0.950737	−	0.310000i	$-0.100329\pi$
$271$	13.3432	+	11.1963i	0.810540	+	0.680124i	−0.140196	+	0.990124i	$0.544773\pi$
$272$	8.51721	−	1.50181i	0.516432	−	0.0910608i
$273$	0.0270315	−	0.0156066i	0.00163602	−	0.000944557i
$274$	−3.23493	+	5.60306i	−0.195429	+	0.338494i
$275$		0			0
$276$	17.5610	+	6.39167i	1.05705	+	0.384733i
$277$	−17.9994	−	10.3920i	−1.08148	−	0.624393i	−0.150185	−	0.988658i	$-0.547987\pi$
$277$	−17.9994	−	10.3920i	−1.08148	−	0.624393i	−0.931295	+	0.364265i	$0.881320\pi$
$278$	4.19330	−	2.42100i	0.251498	−	0.145202i
$279$	0.416850	+	2.36407i	0.0249562	+	0.141533i
$280$		0			0
$281$	−4.60383	+	3.86307i	−0.274641	+	0.230452i	−0.769696	−	0.638410i	$-0.779592\pi$
$281$	−4.60383	+	3.86307i	−0.274641	+	0.230452i	0.495055	+	0.868862i	$0.335148\pi$
$282$	−3.79861	−	0.669797i	−0.226204	−	0.0398859i
$283$	3.95849	+	10.8759i	0.235308	+	0.646502i	0.999998	+	0.00210419i	$0.000669785\pi$
$283$	3.95849	+	10.8759i	0.235308	+	0.646502i	−0.764690	+	0.644398i	$0.777108\pi$
$284$	11.7684			0.698327
$285$		0			0
$286$	0.220734			0.0130523
$287$	0.0918968	+	0.252484i	0.00542450	+	0.0149037i
$288$	−1.01526	−	0.179019i	−0.0598251	−	0.0105488i
$289$	8.18031	−	6.86409i	0.481195	−	0.403770i
$290$		0			0
$291$	−4.79951	−	27.2194i	−0.281352	−	1.59563i
$292$	−25.9777	+	14.9982i	−1.52023	+	0.877706i
$293$	15.1289	+	8.73466i	0.883838	+	0.510284i	0.871922	−	0.489645i	$-0.162874\pi$
$293$	15.1289	+	8.73466i	0.883838	+	0.510284i	0.0119163	+	0.999929i	$0.496207\pi$
$294$	−3.32663	−	1.21079i	−0.194013	−	0.0706149i
$295$		0			0
$296$	−1.10876	+	1.92042i	−0.0644452	+	0.111622i
$297$	−15.8059	+	9.12556i	−0.917153	+	0.529519i
$298$	5.92042	−	1.04393i	0.342961	−	0.0604732i
$299$	0.973024	+	0.816464i	0.0562714	+	0.0472173i
$300$		0			0
$301$	−0.0379144	+	0.215023i	−0.00218535	+	0.0123937i
$302$	1.18278	+	3.24967i	0.0680616	+	0.186998i
$303$			6.04917i			0.347516i
$304$	13.8443	+	5.75810i	0.794024	+	0.330250i
$305$		0			0
$306$	0.216502	−	0.0788002i	0.0123766	−	0.00450470i
$307$	29.2028	+	5.14924i	1.66669	+	0.293883i	0.925876	−	0.377827i	$-0.123328\pi$
$307$	29.2028	+	5.14924i	1.66669	+	0.293883i	0.740815	+	0.671709i	$0.234440\pi$
$308$	−0.367756	−	0.438275i	−0.0209549	−	0.0249730i
$309$	−4.45067	−	3.73455i	−0.253190	−	0.212451i
$310$		0			0
$311$	5.81119	+	10.0653i	0.329522	+	0.570749i	0.982417	−	0.186699i	$-0.0597790\pi$
$311$	5.81119	+	10.0653i	0.329522	+	0.570749i	−0.652895	+	0.757449i	$0.726446\pi$
$312$	0.364499	+	0.210444i	0.0206357	+	0.0119140i
$313$	0.162413	−	0.446226i	0.00918012	−	0.0252222i	−0.935018	−	0.354600i	$-0.884617\pi$
$313$	0.162413	−	0.446226i	0.00918012	−	0.0252222i	0.944198	+	0.329378i	$0.106839\pi$
$314$	−1.33501	−	0.485905i	−0.0753392	−	0.0274212i
$315$		0			0
$316$	−0.979713	−	1.69691i	−0.0551132	−	0.0954588i
$317$	19.9209	−	3.51260i	1.11887	−	0.197287i	0.416526	−	0.909124i	$-0.363247\pi$
$317$	19.9209	−	3.51260i	1.11887	−	0.197287i	0.702345	+	0.711836i	$0.252136\pi$
$318$	−2.73366	+	3.25784i	−0.153296	+	0.182691i
$319$	−12.4011	+	10.4057i	−0.694327	+	0.582609i
$320$		0			0
$321$	−2.91438	+	1.06075i	−0.162665	+	0.0592051i
$322$			0.163921i			0.00913495i
$323$	−10.8676	+	1.41467i	−0.604689	+	0.0787141i
$324$	−15.2771			−0.848728
$325$		0			0
$326$	0.0307377	−	0.174322i	0.00170241	−	0.00965483i
$327$	13.9059	+	16.5724i	0.768999	+	0.916457i
$328$	−2.32886	+	2.77542i	−0.128590	+	0.153247i
$329$	0.117998	+	0.669199i	0.00650543	+	0.0368941i
$330$		0			0
$331$	3.00653	−	5.20746i	0.165254	−	0.286228i	−0.771492	−	0.636240i	$-0.780489\pi$
$331$	3.00653	−	5.20746i	0.165254	−	0.286228i	0.936745	+	0.350012i	$0.113822\pi$
$332$	−11.6889	+	32.1149i	−0.641509	+	1.76253i
$333$	0.187621	−	0.515486i	0.0102816	−	0.0282484i
$334$	−0.634767	+	1.09945i	−0.0347329	+	0.0601591i
$335$		0			0
$336$	−0.0875862	−	0.496726i	−0.00477822	−	0.0270986i
$337$	5.69981	−	6.79277i	0.310488	−	0.370026i	−0.588123	−	0.808772i	$-0.700133\pi$
$337$	5.69981	−	6.79277i	0.310488	−	0.370026i	0.898611	+	0.438746i	$0.144577\pi$
$338$	−2.56465	−	3.05643i	−0.139499	−	0.166248i
$339$	3.52422	−	19.9869i	0.191409	−	1.08554i
$340$		0			0
$341$	−27.1640			−1.47101
$342$	0.389841	+	0.0870209i	0.0210802	+	0.00470555i
$343$			1.24803i			0.0673874i
$344$	−2.76660	+	1.00696i	−0.149165	+	0.0542916i
$345$		0			0
$346$	1.51813	−	1.27386i	0.0816150	−	0.0684831i
$347$	−12.8372	+	15.2988i	−0.689139	+	0.821284i	−0.991251	−	0.131989i	$-0.957864\pi$
$347$	−12.8372	+	15.2988i	−0.689139	+	0.821284i	0.302112	+	0.953272i	$0.402308\pi$
$348$	−14.8301	+	2.61495i	−0.794977	+	0.140176i
$349$	−0.405107	−	0.701666i	−0.0216849	−	0.0375593i	0.854979	−	0.518662i	$-0.173570\pi$
$349$	−0.405107	−	0.701666i	−0.0216849	−	0.0375593i	−0.876664	+	0.481103i	$0.840236\pi$
$350$		0			0
$351$	−1.08435	−	0.394671i	−0.0578783	−	0.0210660i
$352$	3.98992	−	10.9622i	0.212663	−	0.584288i
$353$	−18.1435	−	10.4751i	−0.965681	−	0.557536i	−0.0677639	−	0.997701i	$-0.521586\pi$
$353$	−18.1435	−	10.4751i	−0.965681	−	0.557536i	−0.897917	+	0.440165i	$0.854920\pi$
$354$	2.64177	+	4.57568i	0.140408	+	0.243195i
$355$		0			0
$356$	−0.957899	−	0.803773i	−0.0507686	−	0.0425999i
$357$	0.236973	+	0.282413i	0.0125419	+	0.0149469i
$358$	1.16177	+	0.204851i	0.0614015	+	0.0108267i
$359$	24.1518	−	8.79055i	1.27469	−	0.463948i	0.386015	−	0.922493i	$-0.373851\pi$
$359$	24.1518	−	8.79055i	1.27469	−	0.463948i	0.888671	+	0.458545i	$0.151629\pi$
$360$		0			0
$361$	−17.1964	−	8.07982i	−0.905074	−	0.425253i
$362$		−	5.13963i		−	0.270133i
$363$	−0.188630	−	0.518256i	−0.00990049	−	0.0272014i
$364$	0.00628141	−	0.0356236i	0.000329235	−	0.00186719i
$365$		0			0
$366$	−0.383425	−	0.321731i	−0.0200419	−	0.0168172i
$367$	23.9170	−	4.21721i	1.24846	−	0.220137i	0.489921	−	0.871767i	$-0.337026\pi$
$367$	23.9170	−	4.21721i	1.24846	−	0.220137i	0.758537	+	0.651630i	$0.225915\pi$
$368$	17.7757	−	10.2628i	0.926621	−	0.534985i
$369$	0.448136	−	0.776194i	0.0233290	−	0.0404070i
$370$		0			0
$371$	0.704033	+	0.256247i	0.0365515	+	0.0133037i
$372$	−21.8833	−	12.6343i	−1.13460	−	0.655059i
$373$	−9.42310	+	5.44043i	−0.487910	+	0.281695i	−0.723707	−	0.690107i	$-0.757563\pi$
$373$	−9.42310	+	5.44043i	−0.487910	+	0.281695i	0.235797	+	0.971802i	$0.424230\pi$
$374$	0.452720	+	2.56750i	0.0234096	+	0.132763i
$375$		0			0
$376$	−7.01914	+	5.88976i	−0.361985	+	0.303741i
$377$	−1.00798	−	0.177734i	−0.0519135	−	0.00915375i
$378$	−0.0509331	−	0.139938i	−0.00261972	−	0.00719761i
$379$	−19.3318			−0.993008			−0.496504	−	0.868034i	$-0.665383\pi$
$379$	−19.3318			−0.993008			−0.496504	+	0.868034i	$0.665383\pi$
$380$		0			0
$381$	−34.8709			−1.78649
$382$	0.835009	+	2.29417i	0.0427228	+	0.117380i
$383$	1.02720	+	0.181124i	0.0524876	+	0.00925498i	0.199830	−	0.979831i	$-0.435961\pi$
$383$	1.02720	+	0.181124i	0.0524876	+	0.00925498i	−0.147343	+	0.989086i	$0.547072\pi$
$384$	10.9813	−	9.21437i	0.560385	−	0.470219i
$385$		0			0
$386$	1.13739	+	6.45045i	0.0578915	+	0.328319i
$387$	0.630747	−	0.364162i	0.0320627	−	0.0185114i
$388$	−27.7399	−	16.0156i	−1.40828	−	0.813070i
$389$	24.9988	+	9.09880i	1.26749	+	0.461328i	0.886275	−	0.463160i	$-0.153284\pi$
$389$	24.9988	+	9.09880i	1.26749	+	0.461328i	0.381213	+	0.924487i	$0.375507\pi$
$390$		0			0
$391$	−7.50120	+	12.9925i	−0.379352	+	0.657056i
$392$	−7.28293	+	4.20480i	−0.367843	+	0.212374i
$393$	−11.2529	+	1.98418i	−0.567632	+	0.100089i
$394$	0.681238	+	0.571627i	0.0343203	+	0.0287981i
$395$		0			0
$396$	−0.331401	+	1.87947i	−0.0166535	+	0.0944468i
$397$	1.26464	+	3.47457i	0.0634705	+	0.174384i	0.967374	−	0.253353i	$-0.0815333\pi$
$397$	1.26464	+	3.47457i	0.0634705	+	0.174384i	−0.903903	+	0.427737i	$0.859311\pi$
$398$			3.57724i			0.179311i
$399$	0.0825037	+	0.633801i	0.00413035	+	0.0317298i
$400$		0			0
$401$	19.0147	−	6.92080i	0.949551	−	0.345608i	0.179620	−	0.983736i	$-0.442513\pi$
$401$	19.0147	−	6.92080i	0.949551	−	0.345608i	0.769930	+	0.638128i	$0.220291\pi$
$402$	4.97601	+	0.877404i	0.248181	+	0.0437609i
$403$	−1.10397	−	1.31566i	−0.0549925	−	0.0655375i
$404$	5.37028	+	4.50620i	0.267181	+	0.224192i
$405$		0			0
$406$	−0.0660441	−	0.114392i	−0.00327772	−	0.00567717i
$407$	5.37583	+	3.10374i	0.266470	+	0.153847i
$408$	−1.70023	+	4.67135i	−0.0841741	+	0.231266i
$409$	11.7244	+	4.26733i	0.579733	+	0.211006i	0.615208	−	0.788365i	$-0.289072\pi$
$409$	11.7244	+	4.26733i	0.579733	+	0.211006i	−0.0354746	+	0.999371i	$0.511294\pi$
$410$		0			0
$411$	17.2668	+	29.9069i	0.851707	+	1.47520i
$412$	−6.63087	+	1.16920i	−0.326679	+	0.0576024i
$413$	0.598305	−	0.713032i	0.0294407	−	0.0350860i
$414$	0.418870	−	0.351473i	0.0205863	−	0.0172740i
$415$		0			0
$416$	0.693095	−	0.252266i	0.0339818	−	0.0123683i
$417$		−	25.8447i		−	1.26562i
$418$	−1.73577	+	4.17334i	−0.0848994	+	0.204125i
$419$	−28.9962			−1.41656			−0.708279	−	0.705933i	$-0.750528\pi$
$419$	−28.9962			−1.41656			−0.708279	+	0.705933i	$0.750528\pi$
$420$		0			0
$421$	2.53458	−	14.3743i	0.123528	−	0.700561i	−0.858644	−	0.512573i	$-0.828692\pi$
$421$	2.53458	−	14.3743i	0.123528	−	0.700561i	0.982171	−	0.187988i	$-0.0601965\pi$
$422$	4.69193	+	5.59162i	0.228399	+	0.272196i
$423$	1.45701	−	1.73639i	0.0708422	−	0.0844264i
$424$	1.75430	+	9.94912i	0.0851963	+	0.483172i
$425$		0			0
$426$	−1.56378	+	2.70854i	−0.0757653	+	0.131229i
$427$	−0.0301584	+	0.0828595i	−0.00145947	+	0.00400985i
$428$	−1.22930	+	3.37749i	−0.0594207	+	0.163257i
$429$	0.589094	−	1.02034i	0.0284417	−	0.0492625i
$430$		0			0
$431$	2.34566	+	13.3029i	0.112986	+	0.640778i	0.987727	+	0.156187i	$0.0499204\pi$
$431$	2.34566	+	13.3029i	0.112986	+	0.640778i	−0.874741	+	0.484591i	$0.838969\pi$
$432$	−11.9861	+	14.2845i	−0.576681	+	0.687261i
$433$	−24.4391	−	29.1254i	−1.17447	−	1.39968i	−0.898761	−	0.438438i	$-0.855532\pi$
$433$	−24.4391	−	29.1254i	−1.17447	−	1.39968i	−0.275709	−	0.961241i	$-0.588913\pi$
$434$	0.0384878	−	0.218275i	0.00184747	−	0.0104775i
$435$		0			0
$436$	25.0714			1.20070
$437$	−23.0881	+	11.9763i	−1.10446	+	0.572903i
$438$		−	7.97181i		−	0.380908i
$439$	−22.3525	+	8.13563i	−1.06682	+	0.388292i	−0.814988	−	0.579478i	$-0.803257\pi$
$439$	−22.3525	+	8.13563i	−1.06682	+	0.388292i	−0.251836	+	0.967770i	$0.581034\pi$
$440$		0			0
$441$	1.59365	−	1.33723i	0.0758882	−	0.0636778i
$442$	−0.105955	+	0.126272i	−0.00503977	+	0.00600616i
$443$	−19.0059	+	3.35126i	−0.902999	+	0.159223i	−0.605823	−	0.795600i	$-0.707156\pi$
$443$	−19.0059	+	3.35126i	−0.902999	+	0.159223i	−0.297176	+	0.954823i	$0.596045\pi$
$444$	2.88717	+	5.00073i	0.137019	+	0.237324i
$445$		0			0
$446$	−2.55144	−	0.928648i	−0.120814	−	0.0439727i
$447$	10.9748	−	30.1531i	0.519092	−	1.42619i
$448$	−0.448997	−	0.259228i	−0.0212131	−	0.0122474i
$449$	−13.2068	−	22.8749i	−0.623268	−	1.07953i	−0.988873	−	0.148761i	$-0.952471\pi$
$449$	−13.2068	−	22.8749i	−0.623268	−	1.07953i	0.365605	−	0.930770i	$-0.380862\pi$
$450$		0			0
$451$	7.76923	+	6.51916i	0.365839	+	0.306975i
$452$	−15.1185	−	18.0175i	−0.711113	−	0.847472i
$453$	18.1782	+	3.20531i	0.854087	+	0.150599i
$454$	0.302473	−	0.110091i	0.0141958	−	0.00516683i
$455$		0			0
$456$	−6.84509	+	5.23661i	−0.320551	+	0.245227i
$457$		−	38.4641i		−	1.79927i	−0.436638	−	0.899637i	$-0.643831\pi$
$457$		−	38.4641i		−	1.79927i	0.436638	−	0.899637i	$-0.356169\pi$
$458$	1.42035	+	3.90239i	0.0663687	+	0.182347i
$459$	2.36671	−	13.4223i	0.110469	−	0.626498i
$460$		0			0
$461$	26.0330	+	21.8442i	1.21248	+	1.01739i	0.999184	+	0.0403991i	$0.0128629\pi$
$461$	26.0330	+	21.8442i	1.21248	+	1.01739i	0.213292	+	0.976989i	$0.431582\pi$
$462$	0.149738	−	0.0264028i	0.00696642	−	0.00122837i
$463$	4.67174	−	2.69723i	0.217114	−	0.125351i	−0.387499	−	0.921870i	$-0.626661\pi$
$463$	4.67174	−	2.69723i	0.217114	−	0.125351i	0.604613	+	0.796519i	$0.293328\pi$
$464$	−8.26981	+	14.3237i	−0.383916	+	0.664963i
$465$		0			0
$466$	3.24660	+	1.18167i	0.150396	+	0.0547396i
$467$	−19.4240	−	11.2144i	−0.898834	−	0.518942i	−0.0220125	−	0.999758i	$-0.507007\pi$
$467$	−19.4240	−	11.2144i	−0.898834	−	0.518942i	−0.876822	+	0.480815i	$0.840341\pi$
$468$	−0.104498	+	0.0603320i	−0.00483043	+	0.00278885i
$469$	−0.154572	−	0.876620i	−0.00713746	−	0.0404786i
$470$		0			0
$471$	−5.80898	+	4.87431i	−0.267664	+	0.224597i
$472$	12.3604	+	2.17947i	0.568934	+	0.100318i
$473$	2.81878	+	7.74452i	0.129607	+	0.356093i
$474$	0.520734			0.0239181
$475$		0			0
$476$	0.427246			0.0195828
$477$	−0.854770	−	2.34846i	−0.0391372	−	0.107529i
$478$	−6.16597	−	1.08723i	−0.282025	−	0.0497286i
$479$	22.0166	−	18.4741i	1.00596	−	0.844104i	0.0181649	−	0.999835i	$-0.494218\pi$
$479$	22.0166	−	18.4741i	1.00596	−	0.844104i	0.987800	+	0.155731i	$0.0497732\pi$
$480$		0			0
$481$	0.0681522	+	0.386510i	0.00310747	+	0.0176233i
$482$	1.02543	−	0.592033i	0.0467071	−	0.0269664i
$483$	0.757723	+	0.437472i	0.0344776	+	0.0199057i
$484$	−0.600609	−	0.218604i	−0.0273004	−	0.00993653i
$485$		0			0
$486$	−0.474341	+	0.821582i	−0.0215165	+	0.0372677i
$487$	−29.8295	+	17.2221i	−1.35170	+	0.780406i	−0.988488	−	0.151299i	$-0.951654\pi$
$487$	−29.8295	+	17.2221i	−1.35170	+	0.780406i	−0.363215	+	0.931705i	$0.618321\pi$
$488$	−1.17094	+	0.206468i	−0.0530059	+	0.00934637i
$489$	−0.723772	−	0.607317i	−0.0327301	−	0.0274638i
$490$		0			0
$491$	−3.36638	+	19.0917i	−0.151923	+	0.861596i	0.809623	+	0.586950i	$0.199672\pi$
$491$	−3.36638	+	19.0917i	−0.151923	+	0.861596i	−0.961546	+	0.274645i	$0.911440\pi$
$492$	3.22674	+	8.86538i	0.145472	+	0.399682i
$493$		−	12.0890i		−	0.544462i
$494$	−0.272674	+	0.0855378i	−0.0122682	+	0.00384853i
$495$		0			0
$496$	−26.0796	+	9.49218i	−1.17101	+	0.426212i
$497$	0.542609	+	0.0956766i	0.0243393	+	0.00429168i
$498$	−5.83814	−	6.95763i	−0.261613	−	0.311779i
$499$	−8.63214	−	7.24323i	−0.386428	−	0.324251i	0.428792	−	0.903403i	$-0.358939\pi$
$499$	−8.63214	−	7.24323i	−0.386428	−	0.324251i	−0.815220	+	0.579152i	$0.803384\pi$
$500$		0			0
$501$	3.38813	+	5.86842i	0.151371	+	0.262181i
$502$	−2.11720	−	1.22237i	−0.0944955	−	0.0545570i
$503$	−3.62262	+	9.95307i	−0.161525	+	0.443785i	−0.993881	−	0.110455i	$-0.964769\pi$
$503$	−3.62262	+	9.95307i	−0.161525	+	0.443785i	0.832356	+	0.554241i	$0.186991\pi$
$504$	−0.0299942	−	0.0109170i	−0.00133605	−	0.000486282i
$505$		0			0
$506$	3.09371	+	5.35846i	0.137532	+	0.238213i
$507$	−20.9729	+	3.69809i	−0.931439	+	0.164238i
$508$	−25.9764	+	30.9574i	−1.15251	+	1.37351i
$509$	1.66949	−	1.40087i	0.0739990	−	0.0620925i	−0.605038	−	0.796197i	$-0.706842\pi$
$509$	1.66949	−	1.40087i	0.0739990	−	0.0620925i	0.679037	+	0.734104i	$0.262398\pi$
$510$		0			0
$511$	−1.31969	+	0.480330i	−0.0583799	+	0.0212485i
$512$		−	20.1933i		−	0.892426i
$513$	15.9889	−	17.3979i	0.705926	−	0.768137i
$514$	7.46186			0.329129
$515$		0			0
$516$	−1.33127	+	7.55002i	−0.0586060	+	0.332371i
$517$	16.4872	+	19.6487i	0.725106	+	0.864147i
$518$	−0.0325568	+	0.0387997i	−0.00143046	+	0.00170476i
$519$	−1.83684	−	10.4172i	−0.0806282	−	0.457265i
$520$		0			0
$521$	5.72367	−	9.91369i	0.250759	−	0.434327i	−0.712976	−	0.701188i	$-0.752653\pi$
$521$	5.72367	−	9.91369i	0.250759	−	0.434327i	0.963735	+	0.266862i	$0.0859866\pi$
$522$	−0.150698	+	0.414039i	−0.00659586	+	0.0181220i
$523$	3.33548	−	9.16414i	0.145850	−	0.400720i	−0.845159	−	0.534515i	$-0.820494\pi$
$523$	3.33548	−	9.16414i	0.145850	−	0.400720i	0.991009	+	0.133795i	$0.0427164\pi$
$524$	−6.62108	+	11.4680i	−0.289243	+	0.500984i
$525$		0			0
$526$	0.661953	+	3.75412i	0.0288625	+	0.163688i
$527$	13.0391	−	15.5394i	0.567991	−	0.676906i
$528$	−12.2379	−	14.5846i	−0.532588	−	0.634713i
$529$	−2.18882	+	12.4134i	−0.0951661	+	0.539714i
$530$		0			0
$531$	−3.10489			−0.134741
$532$	0.624130	+	0.398893i	0.0270595	+	0.0172942i
$533$			0.641237i			0.0277750i
$534$	0.312276	−	0.113659i	0.0135135	−	0.00491851i
$535$		0			0
$536$	9.19476	−	7.71532i	0.397153	−	0.333251i
$537$	4.04746	−	4.82357i	0.174661	−	0.208153i
$538$	7.39433	−	1.30382i	0.318792	−	0.0562117i
$539$	11.7705	+	20.3871i	0.506991	+	0.878133i
$540$		0			0
$541$	−21.4401	−	7.80354i	−0.921780	−	0.335501i	−0.162834	−	0.986654i	$-0.552063\pi$
$541$	−21.4401	−	7.80354i	−0.921780	−	0.335501i	−0.758947	+	0.651153i	$0.774286\pi$
$542$	−1.83481	+	5.04110i	−0.0788118	+	0.216534i
$543$	−23.7579	−	13.7166i	−1.01955	−	0.588638i
$544$	4.35580	+	7.54446i	0.186753	+	0.323466i
$545$		0			0
$546$	0.00736423	+	0.00617933i	0.000315160	+	0.000264451i
$547$	19.8732	+	23.6840i	0.849716	+	1.01265i	0.999713	+	0.0239661i	$0.00762938\pi$
$547$	19.8732	+	23.6840i	0.849716	+	1.01265i	−0.149996	+	0.988687i	$0.547926\pi$
$548$	39.4130	+	6.94958i	1.68364	+	0.296871i
$549$	0.276397	−	0.100600i	0.0117963	−	0.00429351i
$550$		0			0
$551$	11.2867	−	17.6599i	0.480831	−	0.752337i
$552$			11.7979i			0.502154i
$553$	−0.0313760	−	0.0862049i	−0.00133424	−	0.00366581i
$554$	1.11156	−	6.30396i	0.0472256	−	0.267830i
$555$		0			0
$556$	−22.9442	−	19.2525i	−0.973051	−	0.816486i
$557$	9.67955	−	1.70677i	0.410136	−	0.0723180i	0.0352261	−	0.999379i	$-0.488785\pi$
$557$	9.67955	−	1.70677i	0.410136	−	0.0723180i	0.374910	+	0.927061i	$0.377674\pi$
$558$	−0.640287	+	0.369670i	−0.0271055	+	0.0156494i
$559$	−0.260539	+	0.451267i	−0.0110196	+	0.0190866i
$560$		0			0
$561$	13.0765	+	4.75946i	0.552090	+	0.200944i
$562$	−1.60299	−	0.925485i	−0.0676179	−	0.0390392i
$563$	−28.9420	+	16.7096i	−1.21976	+	0.704228i	−0.964866	−	0.262742i	$-0.915373\pi$
$563$	−28.9420	+	16.7096i	−1.21976	+	0.704228i	−0.254892	+	0.966970i	$0.582040\pi$
$564$	4.14321	+	23.4973i	0.174461	+	0.989415i
$565$		0			0
$566$	−2.73065	+	2.29129i	−0.114778	+	0.0963099i
$567$	−0.704384	−	0.124202i	−0.0295814	−	0.00521599i
$568$	2.54105	+	6.98148i	0.106620	+	0.292936i
$569$	−37.6326			−1.57764			−0.788820	−	0.614624i	$-0.789308\pi$
$569$	−37.6326			−1.57764			−0.788820	+	0.614624i	$0.789308\pi$
$570$		0			0
$571$	−2.75232			−0.115181			−0.0575904	−	0.998340i	$-0.518342\pi$
$571$	−2.75232			−0.115181			−0.0575904	+	0.998340i	$0.518342\pi$
$572$	−0.466997	−	1.28306i	−0.0195261	−	0.0536476i
$573$	12.8333	+	2.26285i	0.536117	+	0.0945319i
$574$	−0.0633924	+	0.0531925i	−0.00264595	+	0.00222021i
$575$		0			0
$576$	0.300313	+	1.70316i	0.0125130	+	0.0709649i
$577$	0.0321295	−	0.0185500i	0.00133757	−	0.000772245i	−0.499331	−	0.866411i	$-0.666421\pi$
$577$	0.0321295	−	0.0185500i	0.00133757	−	0.000772245i	0.500669	+	0.865639i	$0.333088\pi$
$578$	2.84827	+	1.64445i	0.118472	+	0.0684000i
$579$	32.8526	+	11.9574i	1.36531	+	0.496932i
$580$		0			0
$581$	−0.800032	+	1.38570i	−0.0331909	+	0.0574884i
$582$	7.37210	−	4.25629i	0.305584	−	0.176429i
$583$	27.8505	−	4.91080i	1.15345	−	0.203385i
$584$	−14.5067	−	12.1725i	−0.600291	−	0.503704i
$585$		0			0
$586$	−0.934287	+	5.29861i	−0.0385951	+	0.218883i
$587$	1.23359	+	3.38927i	0.0509158	+	0.139890i	0.962544	−	0.271126i	$-0.0873961\pi$
$587$	1.23359	+	3.38927i	0.0509158	+	0.139890i	−0.911628	+	0.411016i	$0.865174\pi$
$588$			21.8984i			0.903074i
$589$	33.5559	−	10.5265i	1.38265	−	0.433736i
$590$		0			0
$591$	4.46043	−	1.62346i	0.183478	−	0.0667804i
$592$	6.24578	+	1.10130i	0.256700	+	0.0452632i
$593$	−11.4696	−	13.6689i	−0.470998	−	0.561314i	0.477281	−	0.878751i	$-0.341622\pi$
$593$	−11.4696	−	13.6689i	−0.470998	−	0.561314i	−0.948279	+	0.317437i	$0.897178\pi$
$594$	−4.30604	−	3.61319i	−0.176679	−	0.148251i
$595$		0			0
$596$	−18.5936	−	32.2051i	−0.761625	−	1.31917i
$597$	16.5358	+	9.54694i	0.676764	+	0.390730i
$598$	−0.133800	+	0.367612i	−0.00547148	+	0.0150328i
$599$	−20.6214	−	7.50558i	−0.842568	−	0.306670i	−0.115561	−	0.993300i	$-0.536867\pi$
$599$	−20.6214	−	7.50558i	−0.842568	−	0.306670i	−0.727006	+	0.686631i	$0.759089\pi$
$600$		0			0
$601$	−5.14039	−	8.90342i	−0.209681	−	0.363178i	0.741933	−	0.670474i	$-0.233909\pi$
$601$	−5.14039	−	8.90342i	−0.209681	−	0.363178i	−0.951614	+	0.307296i	$0.900576\pi$
$602$	−0.0662246	+	0.0116772i	−0.00269911	+	0.000475926i
$603$	−1.90861	+	2.27460i	−0.0777248	+	0.0926288i
$604$	16.3871	−	13.7504i	0.666780	−	0.559495i
$605$		0			0
$606$	−1.75072	+	0.637208i	−0.0711180	+	0.0258848i
$607$			32.2616i			1.30946i	0.755864	+	0.654729i	$0.227217\pi$
$607$			32.2616i			1.30946i	−0.755864	+	0.654729i	$0.772783\pi$
$608$	−0.680743	+	15.0879i	−0.0276078	+	0.611893i
$609$	−0.705034			−0.0285694
$610$		0			0
$611$	−0.281607	+	1.59707i	−0.0113926	+	0.0646107i
$612$	−0.916086	−	1.09175i	−0.0370306	−	0.0441313i
$613$	−10.5389	+	12.5598i	−0.425664	+	0.507286i	−0.935666	−	0.352887i	$-0.885200\pi$
$613$	−10.5389	+	12.5598i	−0.425664	+	0.507286i	0.510002	+	0.860173i	$0.329645\pi$
$614$	1.58591	+	8.99412i	0.0640019	+	0.362973i
$615$		0			0
$616$	0.180595	−	0.312800i	0.00727639	−	0.0126031i
$617$	−4.36994	+	12.0063i	−0.175927	+	0.483356i	−0.996046	−	0.0888371i	$-0.971685\pi$
$617$	−4.36994	+	12.0063i	−0.175927	+	0.483356i	0.820119	+	0.572193i	$0.193907\pi$
$618$	0.612008	−	1.68148i	0.0246186	−	0.0676390i
$619$	2.14103	−	3.70838i	0.0860555	−	0.149052i	−0.819785	−	0.572671i	$-0.805907\pi$
$619$	2.14103	−	3.70838i	0.0860555	−	0.149052i	0.905840	+	0.423619i	$0.139240\pi$
$620$		0			0
$621$	−5.61687	−	31.8549i	−0.225397	−	1.27829i
$622$	−2.30089	+	2.74210i	−0.0922575	+	0.109948i
$623$	−0.0376314	−	0.0448474i	−0.00150767	−	0.00179677i
$624$	0.209028	−	1.18546i	0.00836783	−	0.0474563i
$625$		0			0
$626$	0.146252			0.00584542
$627$	14.6588	+	19.1614i	0.585418	+	0.765234i
$628$			8.78807i			0.350682i
$629$	−4.35599	+	1.58545i	−0.173685	+	0.0632160i
$630$		0			0
$631$	−17.4565	+	14.6477i	−0.694933	+	0.583118i	−0.920327	−	0.391150i	$-0.872077\pi$
$631$	−17.4565	+	14.6477i	−0.694933	+	0.583118i	0.225394	+	0.974268i	$0.427633\pi$
$632$	0.795133	−	0.947603i	0.0316287	−	0.0376936i
$633$	38.3690	−	6.76550i	1.52503	−	0.268904i
$634$	3.11503	+	5.39540i	0.123714	+	0.214279i
$635$		0			0
$636$	24.7204	+	8.99749i	0.980228	+	0.356774i
$637$	−0.509061	+	1.39863i	−0.0201698	+	0.0554159i
$638$	−4.31788	−	2.49293i	−0.170946	−	0.0986959i
$639$	−0.918959	−	1.59168i	−0.0363535	−	0.0629661i
$640$		0			0
$641$	−24.0251	−	20.1595i	−0.948935	−	0.796251i	0.0301829	−	0.999544i	$-0.490391\pi$
$641$	−24.0251	−	20.1595i	−0.948935	−	0.796251i	−0.979118	+	0.203293i	$0.934835\pi$
$642$	−0.613991	−	0.731726i	−0.0242323	−	0.0288789i
$643$	10.9796	+	1.93601i	0.432995	+	0.0763487i	0.385898	−	0.922542i	$-0.373892\pi$
$643$	10.9796	+	1.93601i	0.432995	+	0.0763487i	0.0470972	+	0.998890i	$0.485003\pi$
$644$	0.952825	−	0.346800i	0.0375466	−	0.0136658i
$645$		0			0
$646$	−1.55420	−	2.99622i	−0.0611491	−	0.117885i
$647$		−	17.5536i		−	0.690102i	−0.938584	−	0.345051i	$-0.887862\pi$
$647$		−	17.5536i		−	0.690102i	0.938584	−	0.345051i	$-0.112138\pi$
$648$	−3.29865	−	9.06297i	−0.129583	−	0.356027i
$649$	6.10100	−	34.6005i	0.239485	−	1.35819i
$650$		0			0
$651$	−0.906260	−	0.760443i	−0.0355191	−	0.0298041i
$652$	−1.07832	+	0.190136i	−0.0422302	+	0.00744632i
$653$	1.81461	−	1.04766i	0.0710111	−	0.0409983i	−0.464074	−	0.885796i	$-0.653613\pi$
$653$	1.81461	−	1.04766i	0.0710111	−	0.0409983i	0.535085	+	0.844798i	$0.320280\pi$
$654$	−3.33147	+	5.77028i	−0.130271	+	0.225636i
$655$		0			0
$656$	9.73711	+	3.54402i	0.380170	+	0.138371i
$657$	4.05704	+	2.34233i	0.158280	+	0.0913831i
$658$	−0.181246	+	0.104642i	−0.00706571	+	0.00407939i
$659$	2.25744	+	12.8026i	0.0879373	+	0.498717i	0.996684	+	0.0813691i	$0.0259292\pi$
$659$	2.25744	+	12.8026i	0.0879373	+	0.498717i	−0.908747	+	0.417348i	$0.862960\pi$
$660$		0			0
$661$	29.1833	−	24.4877i	1.13510	−	0.952462i	0.135833	−	0.990732i	$-0.456629\pi$
$661$	29.1833	−	24.4877i	1.13510	−	0.952462i	0.999267	+	0.0382694i	$0.0121845\pi$
$662$	1.82382	+	0.321588i	0.0708846	+	0.0124989i
$663$	0.300920	+	0.826772i	0.0116868	+	0.0321092i
$664$	−21.5756			−0.837298
$665$		0			0
$666$	0.168953			0.00654678
$667$	−9.81278	−	26.9604i	−0.379952	−	1.04391i
$668$	7.73373	+	1.36367i	0.299227	+	0.0527618i
$669$	−11.1019	+	9.31564i	−0.429226	+	0.360163i
$670$		0			0
$671$	0.577966	+	3.27781i	0.0223121	+	0.126538i
$672$	0.439995	−	0.254031i	0.0169732	−	0.00979947i
$673$	29.4013	+	16.9749i	1.13334	+	0.654333i	0.944772	−	0.327728i	$-0.106283\pi$
$673$	29.4013	+	16.9749i	1.13334	+	0.654333i	0.188566	+	0.982061i	$0.439616\pi$
$674$	2.56633	+	0.934069i	0.0988514	+	0.0359790i
$675$		0			0
$676$	−12.3403	+	21.3740i	−0.474626	+	0.822076i
$677$	−14.3381	+	8.27810i	−0.551058	+	0.318153i	−0.749549	−	0.661949i	$-0.769729\pi$
$677$	−14.3381	+	8.27810i	−0.551058	+	0.318153i	0.198491	+	0.980103i	$0.436396\pi$
$678$	6.15572	−	1.08542i	0.236409	−	0.0416853i
$679$	−1.14880	−	0.963959i	−0.0440870	−	0.0369934i
$680$		0			0
$681$	0.298344	−	1.69199i	0.0114326	−	0.0648372i
$682$	−2.86141	−	7.86166i	−0.109569	−	0.301038i
$683$		−	5.33328i		−	0.204072i	−0.994781	−	0.102036i	$-0.967464\pi$
$683$		−	5.33328i		−	0.204072i	0.994781	−	0.102036i	$-0.0325357\pi$
$684$	−0.318942	−	2.45014i	−0.0121950	−	0.0936835i
$685$		0			0
$686$	−0.361199	+	0.131466i	−0.0137906	+	0.00501938i
$687$	21.8294	+	3.84911i	0.832844	+	0.146853i
$688$	5.41248	+	6.45035i	0.206349	+	0.245917i
$689$	1.36972	+	1.14933i	0.0521820	+	0.0437859i
$690$		0			0
$691$	7.06510	+	12.2371i	0.268769	+	0.465522i	0.968544	−	0.248842i	$-0.0800498\pi$
$691$	7.06510	+	12.2371i	0.268769	+	0.465522i	−0.699775	+	0.714363i	$0.746717\pi$
$692$	−10.6164	−	6.12940i	−0.403576	−	0.233005i
$693$	−0.0305599	+	0.0839627i	−0.00116088	+	0.00318948i
$694$	−5.77995	−	2.10373i	−0.219404	−	0.0798565i
$695$		0			0
$696$	−4.75342	−	8.23317i	−0.180178	−	0.312078i
$697$	−7.45866	+	1.31516i	−0.282517	+	0.0498153i
$698$	0.160399	−	0.191156i	0.00607119	−	0.00723536i
$699$	14.1268	−	11.8538i	0.534324	−	0.448351i
$700$		0			0
$701$	35.8607	−	13.0522i	1.35444	−	0.492976i	0.440110	−	0.897944i	$-0.354939\pi$
$701$	35.8607	−	13.0522i	1.35444	−	0.492976i	0.914331	+	0.404967i	$0.132717\pi$
$702$		−	0.355400i		−	0.0134137i
$703$	−7.84355	−	1.75085i	−0.295825	−	0.0660345i
$704$	−19.5699			−0.737567
$705$		0			0
$706$	1.12046	−	6.35442i	0.0421689	−	0.239152i
$707$	0.210973	+	0.251428i	0.00793447	+	0.00945594i
$708$	21.0080	−	25.0364i	0.789531	−	0.940926i
$709$	−5.75948	−	32.6636i	−0.216302	−	1.22671i	−0.878633	−	0.477497i	$-0.841544\pi$
$709$	−5.75948	−	32.6636i	−0.216302	−	1.22671i	0.662331	−	0.749211i	$-0.269567\pi$
$710$		0			0
$711$	−0.153005	+	0.265013i	−0.00573815	+	0.00993878i
$712$	0.269998	−	0.741814i	0.0101186	−	0.0278007i
$713$	16.4657	−	45.2392i	0.616646	−	1.69422i
$714$	−0.0567721	+	0.0983321i	−0.00212464	+	0.00367999i
$715$		0			0
$716$	−1.26716	−	7.18644i	−0.0473561	−	0.268570i
$717$	−21.4814	+	25.6006i	−0.802239	+	0.956072i
$718$	5.08822	+	6.06391i	0.189891	+	0.226303i
$719$	−7.35244	+	41.6978i	−0.274200	+	1.55506i	0.467292	+	0.884103i	$0.345230\pi$
$719$	−7.35244	+	41.6978i	−0.274200	+	1.55506i	−0.741492	+	0.670962i	$0.765881\pi$
$720$		0			0
$721$	−0.315236			−0.0117400
$722$	0.526975	−	5.82800i	0.0196120	−	0.216896i
$723$		−	6.32007i		−	0.235046i
$724$	−29.8752	+	10.8737i	−1.11030	+	0.404118i
$725$		0			0
$726$	0.130121	−	0.109184i	0.00482923	−	0.00405221i
$727$	2.70075	−	3.21863i	0.100165	−	0.119372i	−0.713633	−	0.700520i	$-0.752952\pi$
$727$	2.70075	−	3.21863i	0.100165	−	0.119372i	0.813798	+	0.581147i	$0.197396\pi$
$728$	0.0224896	−	0.00396552i	0.000833520	−	0.000146972i
$729$	14.5602	+	25.2189i	0.539265	+	0.934034i
$730$		0			0
$731$	−5.78336	−	2.10497i	−0.213905	−	0.0778551i
$732$	−1.05894	+	2.90941i	−0.0391395	+	0.107535i
$733$	14.6668	+	8.46787i	0.541730	+	0.312768i	0.745780	−	0.666193i	$-0.232077\pi$
$733$	14.6668	+	8.46787i	0.541730	+	0.312768i	−0.204050	+	0.978960i	$0.565410\pi$
$734$	3.73990	+	6.47769i	0.138042	+	0.239096i
$735$		0			0
$736$	15.8380	+	13.2897i	0.583798	+	0.489864i
$737$	−21.5975	−	25.7388i	−0.795553	−	0.948103i
$738$	0.271847	+	0.0479340i	0.0100068	+	0.00176448i
$739$	19.5893	−	7.12993i	0.720605	−	0.262279i	0.0444223	−	0.999013i	$-0.485855\pi$
$739$	19.5893	−	7.12993i	0.720605	−	0.262279i	0.676183	+	0.736734i	$0.263633\pi$
$740$		0			0
$741$	−0.332314	+	1.48872i	−0.0122079	+	0.0546894i
$742$			0.230750i			0.00847109i
$743$	15.5106	+	42.6150i	0.569028	+	1.56339i	0.806025	+	0.591881i	$0.201615\pi$
$743$	15.5106	+	42.6150i	0.569028	+	1.56339i	−0.236997	+	0.971510i	$0.576163\pi$
$744$	2.77010	−	15.7100i	0.101557	−	0.575957i
$745$		0			0
$746$	−2.56715	−	2.15410i	−0.0939901	−	0.0788671i
$747$	5.25630	−	0.926827i	0.192318	−	0.0339108i
$748$	13.9664	−	8.06349i	0.510661	−	0.294831i
$749$	−0.0841385	+	0.145732i	−0.00307435	+	0.00532494i
$750$		0			0
$751$	8.15355	+	2.96765i	0.297527	+	0.108291i	0.486471	−	0.873697i	$-0.338284\pi$
$751$	8.15355	+	2.96765i	0.297527	+	0.108291i	−0.188943	+	0.981988i	$0.560506\pi$
$752$	22.6950	+	13.1030i	0.827601	+	0.477816i
$753$	−11.3008	+	6.52451i	−0.411824	+	0.237767i
$754$	−0.0547399	−	0.310445i	−0.00199351	−	0.0113058i
$755$		0			0
$756$	−0.705661	+	0.592119i	−0.0256646	+	0.0215352i
$757$	9.92320	+	1.74973i	0.360665	+	0.0635950i	0.351045	−	0.936359i	$-0.385827\pi$
$757$	9.92320	+	1.74973i	0.360665	+	0.0635950i	0.00962040	+	0.999954i	$0.496938\pi$
$758$	−2.03638	−	5.59490i	−0.0739645	−	0.203216i
$759$	33.0259			1.19877
$760$		0			0
$761$	4.52014			0.163855			0.0819275	−	0.996638i	$-0.473892\pi$
$761$	4.52014			0.163855			0.0819275	+	0.996638i	$0.473892\pi$
$762$	−3.67324	−	10.0921i	−0.133067	−	0.365600i
$763$	1.15597	+	0.203829i	0.0418491	+	0.00737912i
$764$	11.5688	−	9.70735i	0.418543	−	0.351200i
$765$		0			0
$766$	0.0557839	+	0.316366i	0.00201556	+	0.0114308i
$767$	1.92378	−	1.11070i	0.0694637	−	0.0401049i
$768$	−12.7269	−	7.34787i	−0.459242	−	0.265143i
$769$	−37.1897	−	13.5360i	−1.34110	−	0.488119i	−0.430939	−	0.902381i	$-0.641818\pi$
$769$	−37.1897	−	13.5360i	−1.34110	−	0.488119i	−0.910158	+	0.414262i	$0.864040\pi$
$770$		0			0
$771$	19.9142	−	34.4924i	0.717193	−	1.24221i
$772$	35.0883	−	20.2582i	1.26286	−	0.729110i
$773$	−23.1416	+	4.08049i	−0.832347	+	0.146765i	−0.573554	−	0.819168i	$-0.694436\pi$
$773$	−23.1416	+	4.08049i	−0.832347	+	0.146765i	−0.258793	+	0.965933i	$0.583325\pi$
$774$	0.171835	+	0.144187i	0.00617649	+	0.00518269i
$775$		0			0
$776$	3.51146	−	19.9145i	0.126054	−	0.714888i
$777$	0.0924638	+	0.254042i	0.00331712	+	0.00911372i
$778$			8.19345i			0.293749i
$779$	−12.1237	−	5.04246i	−0.434375	−	0.180665i
$780$		0			0
$781$	19.5432	−	7.11316i	0.699312	−	0.254529i
$782$	−4.55036	−	0.802352i	−0.162721	−	0.0286920i
$783$	16.7541	+	19.9668i	0.598744	+	0.713555i
$784$	18.4246	+	15.4601i	0.658022	+	0.552146i
$785$		0			0
$786$	−1.75961	−	3.04773i	−0.0627631	−	0.108709i
$787$	−6.51669	−	3.76242i	−0.232295	−	0.134116i	0.379335	−	0.925259i	$-0.376153\pi$
$787$	−6.51669	−	3.76242i	−0.232295	−	0.134116i	−0.611630	+	0.791144i	$0.709486\pi$
$788$	1.88144	−	5.16921i	0.0670235	−	0.184145i
$789$	19.1200	+	6.95913i	0.680692	+	0.247751i
$790$		0			0
$791$	−0.550589	−	0.953649i	−0.0195767	−	0.0339078i
$792$	−1.18653	+	0.209217i	−0.0421615	+	0.00743421i
$793$	−0.135268	+	0.161206i	−0.00480349	+	0.00572458i
$794$	−0.872376	+	0.732010i	−0.0309595	+	0.0259781i
$795$		0			0
$796$	20.7935	−	7.56821i	0.737006	−	0.268248i
$797$		−	18.7858i		−	0.665426i	−0.943028	−	0.332713i	$-0.892036\pi$
$797$		−	18.7858i		−	0.665426i	0.943028	−	0.332713i	$-0.107964\pi$
$798$	−0.174740	+	0.0906412i	−0.00618574	+	0.00320866i
$799$	−19.1542			−0.677627
$800$		0			0
$801$	−0.0339113	+	0.192320i	−0.00119820	+	0.00679531i
$802$	4.00596	+	4.77411i	0.141455	+	0.168580i
$803$	−34.0746	+	40.6085i	−1.20247	+	1.43304i
$804$	−5.42742	−	30.7804i	−0.191410	−	1.08554i
$805$		0			0
$806$	0.264480	−	0.458092i	0.00931590	−	0.0161356i
$807$	13.7071	−	37.6599i	0.482512	−	1.32569i
$808$	−1.51369	+	4.15884i	−0.0532516	+	0.146308i
$809$	−9.74651	+	16.8815i	−0.342669	+	0.593520i	−0.984927	−	0.172968i	$-0.944664\pi$
$809$	−9.74651	+	16.8815i	−0.342669	+	0.593520i	0.642258	+	0.766488i	$0.277998\pi$
$810$		0			0
$811$	2.64049	+	14.9750i	0.0927201	+	0.525842i	0.995422	+	0.0955756i	$0.0304692\pi$
$811$	2.64049	+	14.9750i	0.0927201	+	0.525842i	−0.902702	+	0.430266i	$0.858420\pi$
$812$	−0.525201	+	0.625910i	−0.0184309	+	0.0219651i
$813$	18.4057	+	21.9351i	0.645517	+	0.769297i
$814$	−0.331986	+	1.88279i	−0.0116361	+	0.0659916i
$815$		0			0
$816$	14.2176			0.497715
$817$	−6.48318	−	8.47454i	−0.226818	−	0.296487i
$818$			3.84272i			0.134357i
$819$	−0.00530861	+	0.00193218i	−0.000185498	+	6.75157e-5i
$820$		0			0
$821$	−20.5043	+	17.2051i	−0.715604	+	0.600463i	−0.926165	−	0.377118i	$-0.876915\pi$
$821$	−20.5043	+	17.2051i	−0.715604	+	0.600463i	0.210562	+	0.977581i	$0.432471\pi$
$822$	−6.83664	+	8.14759i	−0.238455	+	0.284180i
$823$	27.2284	−	4.80109i	0.949121	−	0.167356i	0.322404	−	0.946602i	$-0.395509\pi$
$823$	27.2284	−	4.80109i	0.949121	−	0.167356i	0.626717	+	0.779247i	$0.284398\pi$
$824$	−2.12536	−	3.68123i	−0.0740404	−	0.128242i
$825$		0			0
$826$	0.269386	+	0.0980486i	0.00937314	+	0.00341155i
$827$	4.38543	−	12.0489i	0.152496	−	0.418980i	−0.839796	−	0.542903i	$-0.817325\pi$
$827$	4.38543	−	12.0489i	0.152496	−	0.418980i	0.992292	+	0.123923i	$0.0395474\pi$
$828$	−2.92920	−	1.69117i	−0.101797	−	0.0587724i
$829$	22.7266	+	39.3636i	0.789326	+	1.36715i	0.926380	+	0.376590i	$0.122903\pi$
$829$	22.7266	+	39.3636i	0.789326	+	1.36715i	−0.137054	+	0.990564i	$0.543763\pi$
$830$		0			0
$831$	−26.1735	−	21.9622i	−0.907949	−	0.761860i
$832$	−0.795334	−	0.947842i	−0.0275732	−	0.0328605i
$833$	−17.3126	−	3.05267i	−0.599844	−	0.105769i
$834$	7.47983	−	2.72243i	0.259005	−	0.0942702i
$835$		0			0
$836$	27.9308	+	1.26020i	0.966006	+	0.0435849i
$837$			43.7364i			1.51175i
$838$	−3.05441	−	8.39192i	−0.105513	−	0.289894i
$839$	−4.04829	+	22.9590i	−0.139762	+	0.792632i	0.831662	+	0.555282i	$0.187390\pi$
$839$	−4.04829	+	22.9590i	−0.139762	+	0.792632i	−0.971424	+	0.237350i	$0.923721\pi$
$840$		0			0
$841$	−4.50505	−	3.78019i	−0.155347	−	0.130351i
$842$	4.42712	−	0.780620i	0.152569	−	0.0269019i
$843$	−8.55610	+	4.93987i	−0.294688	+	0.170138i
$844$	22.5760	−	39.1028i	0.777098	−	1.34597i
$845$		0			0
$846$	0.656016	+	0.238770i	0.0225543	+	0.00820909i
$847$	−0.0259151	−	0.0149621i	−0.000890455	−	0.000514104i
$848$	25.0226	−	14.4468i	0.859281	−	0.496106i
$849$	3.30391	+	18.7374i	0.113390	+	0.643066i
$850$		0			0
$851$	−8.42760	+	7.07160i	−0.288894	+	0.242411i
$852$	19.0524	+	3.35945i	0.652725	+	0.115093i
$853$	−15.6588	−	43.0221i	−0.536146	−	1.47305i	−0.851643	−	0.524122i	$-0.824393\pi$
$853$	−15.6588	−	43.0221i	−0.536146	−	1.47305i	0.315497	−	0.948927i	$-0.397829\pi$
$854$	−0.0271576			−0.000929312
$855$		0			0
$856$	−2.26909			−0.0775558
$857$	−2.20568	−	6.06004i	−0.0753444	−	0.207007i	0.896303	−	0.443443i	$-0.146243\pi$
$857$	−2.20568	−	6.06004i	−0.0753444	−	0.207007i	−0.971647	+	0.236436i	$0.924021\pi$
$858$	0.357355	+	0.0630114i	0.0121999	+	0.00215117i
$859$	11.1359	−	9.34415i	0.379953	−	0.318818i	−0.432731	−	0.901523i	$-0.642450\pi$
$859$	11.1359	−	9.34415i	0.379953	−	0.318818i	0.812684	+	0.582705i	$0.198006\pi$
$860$		0			0
$861$	0.0767007	+	0.434991i	0.00261395	+	0.0148245i
$862$	−3.60296	+	2.08017i	−0.122717	+	0.0708509i
$863$	−3.95891	−	2.28568i	−0.134763	−	0.0778054i	0.431103	−	0.902303i	$-0.358125\pi$
$863$	−3.95891	−	2.28568i	−0.134763	−	0.0778054i	−0.565866	+	0.824497i	$0.691458\pi$
$864$	−17.6501	−	6.42412i	−0.600469	−	0.218553i
$865$		0			0
$866$	5.85494	−	10.1411i	0.198959	−	0.344607i
$867$	15.2029	−	8.77740i	0.516318	−	0.298096i
$868$	−1.35020	+	0.238077i	−0.0458288	+	0.00808085i
$869$	−2.65262	−	2.22581i	−0.0899841	−	0.0755056i
$870$		0			0
$871$	0.368892	−	2.09209i	0.0124994	−	0.0708879i
$872$	5.41346	+	14.8733i	0.183323	+	0.503675i
$873$			5.00244i			0.169307i
$874$	−5.89817	−	5.42048i	−0.199508	−	0.183351i
$875$		0			0
$876$	−46.3379	+	16.8656i	−1.56561	+	0.569836i
$877$	32.4562	+	5.72291i	1.09597	+	0.193249i	0.692267	−	0.721641i	$-0.256612\pi$
$877$	32.4562	+	5.72291i	1.09597	+	0.193249i	0.403702	+	0.914890i	$0.367723\pi$
$878$	−4.70913	−	5.61213i	−0.158926	−	0.189400i
$879$	21.9994	+	18.4597i	0.742020	+	0.622629i
$880$		0			0
$881$	8.12066	+	14.0654i	0.273592	+	0.473875i	0.969779	−	0.243985i	$-0.0784549\pi$
$881$	8.12066	+	14.0654i	0.273592	+	0.473875i	−0.696187	+	0.717860i	$0.745122\pi$
$882$	0.554887	+	0.320364i	0.0186840	+	0.0107872i
$883$	9.75238	−	26.7945i	0.328194	−	0.901705i	−0.660375	−	0.750936i	$-0.729603\pi$
$883$	9.75238	−	26.7945i	0.328194	−	0.901705i	0.988569	−	0.150769i	$-0.0481751\pi$
$884$	0.958150	+	0.348738i	0.0322261	+	0.0117293i
$885$		0			0
$886$	−2.97195	−	5.14757i	−0.0998447	−	0.172936i
$887$	−38.0483	+	6.70894i	−1.27754	+	0.225264i	−0.770933	−	0.636916i	$-0.780210\pi$
$887$	−38.0483	+	6.70894i	−1.27754	+	0.225264i	−0.506602	+	0.862180i	$0.669099\pi$
$888$	−2.34322	+	2.79255i	−0.0786335	+	0.0937117i
$889$	−1.44938	+	1.21617i	−0.0486106	+	0.0407891i
$890$		0			0
$891$	−25.3699	+	9.23390i	−0.849925	+	0.309347i
$892$			16.7955i			0.562355i
$893$	−27.9809	−	17.8831i	−0.936345	−	0.598435i
$894$	9.88282			0.330531
$895$		0			0
$896$	0.135062	−	0.765974i	0.00451210	−	0.0255894i
$897$	1.34220	+	1.59957i	0.0448147	+	0.0534081i
$898$	5.22913	−	6.23184i	0.174498	−	0.207959i
$899$	6.73642	+	38.2042i	0.224672	+	1.27418i
$900$		0			0
$901$	−10.5594	+	18.2893i	−0.351783	+	0.609306i
$902$	−1.06834	+	2.93524i	−0.0355719	+	0.0977329i
$903$	−0.122762	+	0.337287i	−0.00408528	+	0.0112242i
$904$	7.42428	−	12.8592i	0.246928	−	0.427691i
$905$		0			0
$906$	0.987198	+	5.59868i	0.0327975	+	0.186004i
$907$	−18.4200	+	21.9521i	−0.611627	+	0.728908i	−0.979606	−	0.200926i	$-0.935605\pi$
$907$	−18.4200	+	21.9521i	−0.611627	+	0.728908i	0.367980	+	0.929834i	$0.380049\pi$
$908$	−1.27986	−	1.52527i	−0.0424735	−	0.0506180i
$909$	0.190117	−	1.07821i	0.00630579	−	0.0357619i
$910$		0			0
$911$	−47.5952			−1.57690			−0.788450	−	0.615099i	$-0.789116\pi$
$911$	−47.5952			−1.57690			−0.788450	+	0.615099i	$0.789116\pi$
$912$	20.7694	+	13.2741i	0.687743	+	0.439548i
$913$			60.3966i			1.99884i
$914$	11.1321	−	4.05174i	0.368216	−	0.134020i
$915$		0			0
$916$	19.6785	−	16.5122i	0.650196	−	0.545579i
$917$	−0.398514	+	0.474930i	−0.0131601	+	0.0156836i
$918$	4.13391	−	0.728919i	0.136439	−	0.0240579i
$919$	−13.6098	−	23.5728i	−0.448945	−	0.777596i	0.549372	−	0.835578i	$-0.314867\pi$
$919$	−13.6098	−	23.5728i	−0.448945	−	0.777596i	−0.998318	+	0.0579814i	$0.981534\pi$
$920$		0			0
$921$	45.8077	+	16.6727i	1.50942	+	0.549383i
$922$	−3.57977	+	9.83534i	−0.117894	+	0.323910i
$923$	1.13877	+	0.657469i	0.0374830	+	0.0216408i
$924$	−0.470265	−	0.814523i	−0.0154706	−	0.0267958i
$925$		0			0
$926$	1.27273	+	1.06795i	0.0418245	+	0.0350949i
$927$	0.675919	+	0.805528i	0.0222001	+	0.0264570i
$928$	−16.4070	−	2.89300i	−0.538586	−	0.0949672i
$929$	−30.2956	+	11.0267i	−0.993967	+	0.361774i	−0.787255	−	0.616627i	$-0.788499\pi$
$929$	−30.2956	+	11.0267i	−0.993967	+	0.361774i	−0.206712	+	0.978402i	$0.566276\pi$
$930$		0			0
$931$	−22.4405	−	20.6230i	−0.735457	−	0.675893i
$932$		−	21.3716i		−	0.700049i
$933$	6.53472	+	17.9540i	0.213937	+	0.587787i
$934$	1.19953	−	6.80288i	0.0392499	−	0.222597i
$935$		0			0
$936$	−0.0583546	−	0.0489653i	−0.00190738	−	0.00160048i
$937$	−17.8964	+	3.15561i	−0.584649	+	0.103089i	−0.458146	−	0.888877i	$-0.651486\pi$
$937$	−17.8964	+	3.15561i	−0.584649	+	0.103089i	−0.126503	+	0.991966i	$0.540375\pi$
$938$	0.237424	−	0.137077i	0.00775217	−	0.00447572i
$939$	0.390318	−	0.676051i	0.0127376	−	0.0220621i
$940$		0			0
$941$	−22.1364	−	8.05700i	−0.721627	−	0.262651i	−0.0450107	−	0.998987i	$-0.514332\pi$
$941$	−22.1364	−	8.05700i	−0.721627	−	0.262651i	−0.676616	+	0.736336i	$0.736554\pi$
$942$	−2.02260	−	1.16775i	−0.0659000	−	0.0380474i
$943$	−15.5664	+	8.98729i	−0.506913	+	0.292666i
$944$	−6.23334	−	35.3510i	−0.202878	−	1.15058i
$945$		0			0
$946$	−1.94445	+	1.63159i	−0.0632195	+	0.0530475i
$947$	−8.30348	−	1.46413i	−0.269827	−	0.0475777i	0.0370976	−	0.999312i	$-0.488189\pi$
$947$	−8.30348	−	1.46413i	−0.269827	−	0.0475777i	−0.306924	+	0.951734i	$0.599300\pi$
$948$	−1.10169	−	3.02688i	−0.0357813	−	0.0983084i
$949$	−3.35164			−0.108799
$950$		0			0
$951$	33.2536			1.07832
$952$	0.0922515	+	0.253459i	0.00298989	+	0.00821465i
$953$	−49.3134	−	8.69527i	−1.59742	−	0.281668i	−0.697123	−	0.716952i	$-0.745537\pi$
$953$	−49.3134	−	8.69527i	−1.59742	−	0.281668i	−0.900293	+	0.435284i	$0.856648\pi$
$954$	0.589639	−	0.494766i	0.0190903	−	0.0160186i
$955$		0			0
$956$	6.72533	+	38.1413i	0.217513	+	1.23358i
$957$	−23.0471	+	13.3062i	−0.745007	+	0.430130i
$958$	7.66587	+	4.42589i	0.247673	+	0.142994i
$959$	1.76072	+	0.640851i	0.0568568	+	0.0206942i
$960$		0			0
$961$	−17.0475	+	29.5272i	−0.549920	+	0.952489i
$962$	−0.104683	+	0.0604385i	−0.00337510	+	0.00194862i
$963$	0.552799	−	0.0974734i	0.0178137	−	0.00314104i
$964$	−5.61078	−	4.70801i	−0.180711	−	0.151635i
$965$		0			0
$966$	−0.0467934	+	0.265378i	−0.00150555	+	0.00853841i
$967$	2.05501	+	5.64610i	0.0660847	+	0.181566i	0.968339	−	0.249637i	$-0.0803114\pi$
$967$	2.05501	+	5.64610i	0.0660847	+	0.181566i	−0.902255	+	0.431203i	$0.858089\pi$
$968$		−	0.403505i		−	0.0129692i
$969$	−17.9979	−	0.812039i	−0.578175	−	0.0260864i
$970$		0			0
$971$	−33.8031	+	12.3033i	−1.08479	+	0.394832i	−0.821689	−	0.569936i	$-0.806968\pi$
$971$	−33.8031	+	12.3033i	−1.08479	+	0.394832i	−0.263103	+	0.964768i	$0.584746\pi$
$972$	5.77917	+	1.01902i	0.185367	+	0.0326852i
$973$	−0.901371	−	1.07421i	−0.0288966	−	0.0344377i
$974$	−8.12650	−	6.81894i	−0.260390	−	0.218493i
$975$		0			0
$976$	1.70029	+	2.94498i	0.0544248	+	0.0942666i
$977$	−29.1285	−	16.8174i	−0.931905	−	0.538035i	−0.0444913	−	0.999010i	$-0.514167\pi$
$977$	−29.1285	−	16.8174i	−0.931905	−	0.538035i	−0.887413	+	0.460974i	$0.847500\pi$
$978$	0.0995253	−	0.273444i	0.00318247	−	0.00874376i
$979$	−2.07656	−	0.755805i	−0.0663671	−	0.0241556i
$980$		0			0
$981$	−1.95775	−	3.39092i	−0.0625062	−	0.108264i
$982$	−5.88002	+	1.03681i	−0.187639	+	0.0330858i
$983$	28.9508	−	34.5023i	0.923388	−	1.10045i	−0.0712938	−	0.997455i	$-0.522713\pi$
$983$	28.9508	−	34.5023i	0.923388	−	1.10045i	0.994682	−	0.102996i	$-0.0328428\pi$
$984$	−4.56257	+	3.82845i	−0.145449	+	0.122046i
$985$		0			0
$986$	3.49873	−	1.27343i	0.111422	−	0.0405544i
$987$			1.11708i			0.0355570i
$988$	1.07409	+	1.40401i	0.0341714	+	0.0446674i
$989$	−14.6064			−0.464457
$990$		0			0
$991$	−1.06445	+	6.03681i	−0.0338134	+	0.191765i	−0.997036	−	0.0769404i	$-0.975485\pi$
$991$	−1.06445	+	6.03681i	−0.0338134	+	0.191765i	0.963222	+	0.268706i	$0.0865960\pi$
$992$	−17.9694	−	21.4151i	−0.570529	−	0.679930i
$993$	6.35394	−	7.57233i	0.201636	−	0.240301i
$994$	0.0294673	+	0.167117i	0.000934645	+	0.00530064i
$995$		0			0
$996$	−28.0912	+	48.6554i	−0.890104	+	1.54171i
$997$	−15.3626	+	42.2085i	−0.486539	+	1.33676i	0.417255	+	0.908789i	$0.362992\pi$
$997$	−15.3626	+	42.2085i	−0.486539	+	1.33676i	−0.903795	+	0.427967i	$0.859230\pi$
$998$	1.18700	−	3.26125i	0.0375738	−	0.103233i
$999$	4.99729	−	8.65556i	0.158107	−	0.273850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.b.24.4		36
5.2	odd	4		475.2.l.c.176.1		18
5.3	odd	4		95.2.k.a.81.3	yes	18
5.4	even	2	inner	475.2.u.b.24.3		36
15.8	even	4		855.2.bs.c.271.1		18
19.4	even	9	inner	475.2.u.b.99.3		36
95.2	even	36		9025.2.a.cf.1.3		9
95.4	even	18	inner	475.2.u.b.99.4		36
95.17	odd	36		9025.2.a.cc.1.7		9
95.23	odd	36		95.2.k.a.61.3	✓	18
95.42	odd	36		475.2.l.c.251.1		18
95.78	even	36		1805.2.a.s.1.7		9
95.93	odd	36		1805.2.a.v.1.3		9
285.23	even	36		855.2.bs.c.631.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.3	✓	18	95.23	odd	36
95.2.k.a.81.3	yes	18	5.3	odd	4
475.2.l.c.176.1		18	5.2	odd	4
475.2.l.c.251.1		18	95.42	odd	36
475.2.u.b.24.3		36	5.4	even	2	inner
475.2.u.b.24.4		36	1.1	even	1	trivial
475.2.u.b.99.3		36	19.4	even	9	inner
475.2.u.b.99.4		36	95.4	even	18	inner
855.2.bs.c.271.1		18	15.8	even	4
855.2.bs.c.631.1		18	285.23	even	36
1805.2.a.s.1.7		9	95.78	even	36
1805.2.a.v.1.3		9	95.93	odd	36
9025.2.a.cc.1.7		9	95.17	odd	36
9025.2.a.cf.1.3		9	95.2	even	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.105338 + 0.289414i) q^{2} +(1.61894 + 0.285463i) q^{3} +(1.45942 - 1.22460i) q^{4} +(0.0879194 + 0.498616i) q^{6} +(0.0772459 - 0.0445979i) q^{7} +(1.04160 + 0.601369i) q^{8} +(-0.279590 - 0.101762i) q^{9} +(1.68341 - 2.91575i) q^{11} +(2.71230 - 1.56595i) q^{12} +(0.209636 - 0.0369645i) q^{13} +(0.0210442 + 0.0176582i) q^{14} +(0.597325 - 3.38760i) q^{16} +(0.859918 + 2.36261i) q^{17} -0.0916368i q^{18} +(-0.949628 + 4.25420i) q^{19} +(0.137788 - 0.0501507i) q^{21} +(1.02119 + 0.180063i) q^{22} +(3.83550 + 4.57098i) q^{23} +(1.51463 + 1.27092i) q^{24} +(0.0327807 + 0.0567779i) q^{26} +(-4.69462 - 2.71044i) q^{27} +(0.0581198 - 0.159683i) q^{28} +(-4.51826 - 1.64451i) q^{29} +(-4.03407 - 6.98722i) q^{31} +(3.41227 - 0.601676i) q^{32} +(3.55769 - 4.23989i) q^{33} +(-0.593190 + 0.497745i) q^{34} +(-0.532659 + 0.193872i) q^{36} +1.84372i q^{37} +(-1.33126 + 0.173294i) q^{38} +0.349941 q^{39} +(-0.523087 + 2.96657i) q^{41} +(0.0290286 + 0.0345950i) q^{42} +(-1.57346 + 1.87518i) q^{43} +(-1.11383 - 6.31683i) q^{44} +(-0.918881 + 1.59155i) q^{46} +(-2.60562 + 7.15887i) q^{47} +(1.93407 - 5.31381i) q^{48} +(-3.49602 + 6.05529i) q^{49} +(0.717721 + 4.07040i) q^{51} +(0.260681 - 0.310668i) q^{52} +(5.39920 + 6.43452i) q^{53} +(0.289917 - 1.64420i) q^{54} +0.107279 q^{56} +(-2.75181 + 6.61622i) q^{57} -1.48088i q^{58} +(9.80610 - 3.56913i) q^{59} +(-0.757296 + 0.635447i) q^{61} +(1.59726 - 1.90354i) q^{62} +(-0.0261356 + 0.00460841i) q^{63} +(-2.90628 - 5.03383i) q^{64} +(1.60184 + 0.583024i) q^{66} +(3.41324 - 9.37780i) q^{67} +(4.14824 + 2.39499i) q^{68} +(4.90462 + 8.49505i) q^{69} +(4.73200 + 3.97062i) q^{71} +(-0.230025 - 0.274133i) q^{72} +(-15.5058 - 2.73409i) q^{73} +(-0.533599 + 0.194214i) q^{74} +(3.82379 + 7.37160i) q^{76} -0.300307i q^{77} +(0.0368621 + 0.101278i) q^{78} +(0.178596 - 1.01287i) q^{79} +(-6.14281 - 5.15443i) q^{81} +(-0.913670 + 0.161105i) q^{82} +(-15.5354 + 8.96939i) q^{83} +(0.139676 - 0.241926i) q^{84} +(-0.708449 - 0.257854i) q^{86} +(-6.84536 - 3.95217i) q^{87} +(3.50689 - 2.02470i) q^{88} +(-0.113975 - 0.646383i) q^{89} +(0.0145450 - 0.0122047i) q^{91} +(11.1953 + 1.97403i) q^{92} +(-4.53634 - 12.4635i) q^{93} -2.34635 q^{94} +5.69603 q^{96} +(-5.75040 - 15.7991i) q^{97} +(-2.12075 - 0.373946i) q^{98} +(-0.767379 + 0.643907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} - 6 q^{9} + 24 q^{14} - 6 q^{16} - 42 q^{21} + 30 q^{24} + 6 q^{26} - 30 q^{29} - 36 q^{31} + 24 q^{34} + 150 q^{36} - 72 q^{39} - 60 q^{41} - 84 q^{44} + 18 q^{46} - 18 q^{49}+ \cdots + 186 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 - 6 * q^9 + 24 * q^14 - 6 * q^16 - 42 * q^21 + 30 * q^24 + 6 * q^26 - 30 * q^29 - 36 * q^31 + 24 * q^34 + 150 * q^36 - 72 * q^39 - 60 * q^41 - 84 * q^44 + 18 * q^46 - 18 * q^49 - 90 * q^51 + 132 * q^54 - 36 * q^59 - 60 * q^61 - 72 * q^64 + 78 * q^66 - 30 * q^69 - 24 * q^71 + 30 * q^74 - 66 * q^76 + 102 * q^79 + 54 * q^81 - 96 * q^84 + 126 * q^86 + 108 * q^89 + 60 * q^91 - 60 * q^94 - 132 * q^96 + 186 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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