LMFDB - Embedded newform 475.2.u.b.74.3

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			74.3
Character	$\chi$	$=$	475.74
Dual form			475.2.u.b.199.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207778 - 0.0366369i) q^{2} +(-0.0513559 + 0.0612035i) q^{3} +(-1.83756 - 0.668816i) q^{4} +(0.0129129 - 0.0108352i) q^{6} +(1.46118 - 0.843614i) q^{7} +(0.722735 + 0.417271i) q^{8} +(0.519836 + 2.94814i) q^{9} +(1.44339 - 2.50003i) q^{11} +(0.135303 - 0.0781173i) q^{12} +(-4.15627 - 4.95325i) q^{13} +(-0.334509 + 0.121751i) q^{14} +(2.86110 + 2.40075i) q^{16} +(-2.94112 - 0.518598i) q^{17} -0.631604i q^{18} +(4.34933 - 0.288668i) q^{19} +(-0.0234081 + 0.132754i) q^{21} +(-0.391499 + 0.466570i) q^{22} +(2.82424 - 7.75955i) q^{23} +(-0.0626552 + 0.0228046i) q^{24} +(0.682111 + 1.18145i) q^{26} +(-0.414708 - 0.239432i) q^{27} +(-3.24923 + 0.572926i) q^{28} +(-1.26021 - 7.14701i) q^{29} +(-2.02800 - 3.51260i) q^{31} +(-1.57939 - 1.88224i) q^{32} +(0.0788839 + 0.216732i) q^{33} +(0.592100 + 0.215507i) q^{34} +(1.01653 - 5.76504i) q^{36} -7.96989i q^{37} +(-0.914272 - 0.0993671i) q^{38} +0.516605 q^{39} +(4.17950 + 3.50702i) q^{41} +(0.00972740 - 0.0267258i) q^{42} +(1.82353 + 5.01011i) q^{43} +(-4.32437 + 3.62858i) q^{44} +(-0.871103 + 1.50879i) q^{46} +(1.62455 - 0.286452i) q^{47} +(-0.293868 + 0.0518169i) q^{48} +(-2.07663 + 3.59683i) q^{49} +(0.182783 - 0.153374i) q^{51} +(4.32457 + 11.8817i) q^{52} +(0.653921 - 1.79663i) q^{53} +(0.0773952 + 0.0649423i) q^{54} +1.40806 q^{56} +(-0.205696 + 0.281019i) q^{57} +1.53116i q^{58} +(-0.616931 + 3.49879i) q^{59} +(7.42370 + 2.70201i) q^{61} +(0.292684 + 0.804142i) q^{62} +(3.24666 + 3.86922i) q^{63} +(-3.47569 - 6.02008i) q^{64} +(-0.00844998 - 0.0479222i) q^{66} +(2.23091 - 0.393370i) q^{67} +(5.05762 + 2.92002i) q^{68} +(0.329870 + 0.571352i) q^{69} +(-9.79389 + 3.56469i) q^{71} +(-0.854469 + 2.34764i) q^{72} +(-0.907529 + 1.08155i) q^{73} +(-0.291992 + 1.65597i) q^{74} +(-8.18520 - 2.37846i) q^{76} -4.87066i q^{77} +(-0.107339 - 0.0189268i) q^{78} +(1.84675 + 1.54961i) q^{79} +(-8.40329 + 3.05855i) q^{81} +(-0.739923 - 0.881806i) q^{82} +(-9.87319 + 5.70029i) q^{83} +(0.131802 - 0.228287i) q^{84} +(-0.195335 - 1.10780i) q^{86} +(0.502142 + 0.289912i) q^{87} +(2.08638 - 1.20457i) q^{88} +(7.74938 - 6.50250i) q^{89} +(-10.2517 - 3.73131i) q^{91} +(-10.3794 + 12.3697i) q^{92} +(0.319133 + 0.0562718i) q^{93} -0.348041 q^{94} +0.196310 q^{96} +(9.71828 + 1.71360i) q^{97} +(0.563256 - 0.671262i) q^{98} +(8.12075 + 2.95571i) 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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.207778	−	0.0366369i	−0.146921	−	0.0259062i	0.0997037	−	0.995017i	$-0.468211\pi$
$2$	−0.207778	−	0.0366369i	−0.146921	−	0.0259062i	−0.246625	+	0.969111i	$0.579322\pi$
$3$	−0.0513559	+	0.0612035i	−0.0296503	+	0.0353359i	−0.780666	−	0.624949i	$-0.785120\pi$
$3$	−0.0513559	+	0.0612035i	−0.0296503	+	0.0353359i	0.751016	+	0.660285i	$0.229564\pi$
$4$	−1.83756	−	0.668816i	−0.918778	−	0.334408i
$5$		0			0
$5$		0			0
$6$	0.0129129	−	0.0108352i	0.00527169	−	0.00442347i
$7$	1.46118	−	0.843614i	0.552275	−	0.318856i	−0.197764	−	0.980250i	$-0.563368\pi$
$7$	1.46118	−	0.843614i	0.552275	−	0.318856i	0.750039	+	0.661394i	$0.230035\pi$
$8$	0.722735	+	0.417271i	0.255526	+	0.147528i
$9$	0.519836	+	2.94814i	0.173279	+	0.982712i
$10$		0			0
$11$	1.44339	−	2.50003i	0.435199	−	0.753787i	−0.562113	−	0.827061i	$-0.690011\pi$
$11$	1.44339	−	2.50003i	0.435199	−	0.753787i	0.997312	+	0.0732738i	$0.0233447\pi$
$12$	0.135303	−	0.0781173i	0.0390586	−	0.0225505i
$13$	−4.15627	−	4.95325i	−1.15274	−	1.37378i	−0.915492	−	0.402336i	$-0.868198\pi$
$13$	−4.15627	−	4.95325i	−1.15274	−	1.37378i	−0.237250	−	0.971449i	$-0.576246\pi$
$14$	−0.334509	+	0.121751i	−0.0894014	+	0.0325394i
$15$		0			0
$16$	2.86110	+	2.40075i	0.715274	+	0.600186i
$17$	−2.94112	−	0.518598i	−0.713325	−	0.125778i	−0.194803	−	0.980842i	$-0.562407\pi$
$17$	−2.94112	−	0.518598i	−0.713325	−	0.125778i	−0.518523	+	0.855064i	$0.673518\pi$
$18$		−	0.631604i		−	0.148871i
$19$	4.34933	−	0.288668i	0.997805	−	0.0662249i
$19$	4.34933	−	0.288668i	0.997805	−	0.0662249i
$20$		0			0
$21$	−0.0234081	+	0.132754i	−0.00510807	+	0.0289693i
$22$	−0.391499	+	0.466570i	−0.0834678	+	0.0994731i
$23$	2.82424	−	7.75955i	0.588896	−	1.61798i	−0.183631	−	0.982995i	$-0.558785\pi$
$23$	2.82424	−	7.75955i	0.588896	−	1.61798i	0.772527	−	0.634982i	$-0.218992\pi$
$24$	−0.0626552	+	0.0228046i	−0.0127894	+	0.00465497i
$25$		0			0
$26$	0.682111	+	1.18145i	0.133773	+	0.231702i
$27$	−0.414708	−	0.239432i	−0.0798105	−	0.0460786i
$28$	−3.24923	+	0.572926i	−0.614046	+	0.108273i
$29$	−1.26021	−	7.14701i	−0.234015	−	1.32717i	−0.844677	−	0.535276i	$-0.820208\pi$
$29$	−1.26021	−	7.14701i	−0.234015	−	1.32717i	0.610662	−	0.791891i	$-0.290903\pi$
$30$		0			0
$31$	−2.02800	−	3.51260i	−0.364240	−	0.630882i	0.624414	−	0.781094i	$-0.285338\pi$
$31$	−2.02800	−	3.51260i	−0.364240	−	0.630882i	−0.988654	+	0.150212i	$0.952005\pi$
$32$	−1.57939	−	1.88224i	−0.279199	−	0.332736i
$33$	0.0788839	+	0.216732i	0.0137319	+	0.0377281i
$34$	0.592100	+	0.215507i	0.101544	+	0.0369591i
$35$		0			0
$36$	1.01653	−	5.76504i	0.169422	−	0.960840i
$37$		−	7.96989i		−	1.31024i	−0.755524	−	0.655121i	$-0.772618\pi$
$37$		−	7.96989i		−	1.31024i	0.755524	−	0.655121i	$-0.227382\pi$
$38$	−0.914272	−	0.0993671i	−0.148315	−	0.0161195i
$39$	0.516605			0.0827230
$40$		0			0
$41$	4.17950	+	3.50702i	0.652728	+	0.547704i	0.907897	−	0.419192i	$-0.137687\pi$
$41$	4.17950	+	3.50702i	0.652728	+	0.547704i	−0.255169	+	0.966896i	$0.582131\pi$
$42$	0.00972740	−	0.0267258i	0.00150097	−	0.00412388i
$43$	1.82353	+	5.01011i	0.278086	+	0.764034i	0.997580	+	0.0695352i	$0.0221516\pi$
$43$	1.82353	+	5.01011i	0.278086	+	0.764034i	−0.719494	+	0.694499i	$0.755626\pi$
$44$	−4.32437	+	3.62858i	−0.651923	+	0.547029i
$45$		0			0
$46$	−0.871103	+	1.50879i	−0.128437	+	0.222460i
$47$	1.62455	−	0.286452i	0.236965	−	0.0417833i	−0.0539044	−	0.998546i	$-0.517167\pi$
$47$	1.62455	−	0.286452i	0.236965	−	0.0417833i	0.290869	+	0.956763i	$0.406056\pi$
$48$	−0.293868	+	0.0518169i	−0.0424162	+	0.00747912i
$49$	−2.07663	+	3.59683i	−0.296662	+	0.513833i
$50$		0			0
$51$	0.182783	−	0.153374i	0.0255948	−	0.0214766i
$52$	4.32457	+	11.8817i	0.599710	+	1.64769i
$53$	0.653921	−	1.79663i	0.0898230	−	0.246787i	−0.886644	−	0.462452i	$-0.846970\pi$
$53$	0.653921	−	1.79663i	0.0898230	−	0.246787i	0.976467	+	0.215665i	$0.0691920\pi$
$54$	0.0773952	+	0.0649423i	0.0105322	+	0.00883753i
$55$		0			0
$56$	1.40806			0.188160
$57$	−0.205696	+	0.281019i	−0.0272451	+	0.0372219i
$58$			1.53116i			0.201052i
$59$	−0.616931	+	3.49879i	−0.0803175	+	0.455503i	0.917952	+	0.396692i	$0.129842\pi$
$59$	−0.616931	+	3.49879i	−0.0803175	+	0.455503i	−0.998269	+	0.0588110i	$0.981269\pi$
$60$		0			0
$61$	7.42370	+	2.70201i	0.950508	+	0.345956i	0.770307	−	0.637673i	$-0.220103\pi$
$61$	7.42370	+	2.70201i	0.950508	+	0.345956i	0.180201	+	0.983630i	$0.442325\pi$
$62$	0.292684	+	0.804142i	0.0371709	+	0.102126i
$63$	3.24666	+	3.86922i	0.409041	+	0.487476i
$64$	−3.47569	−	6.02008i	−0.434462	−	0.752510i
$65$		0			0
$66$	−0.00844998	−	0.0479222i	−0.00104012	−	0.00589882i
$67$	2.23091	−	0.393370i	0.272550	−	0.0480578i	−0.0357028	−	0.999362i	$-0.511367\pi$
$67$	2.23091	−	0.393370i	0.272550	−	0.0480578i	0.308252	+	0.951305i	$0.400256\pi$
$68$	5.05762	+	2.92002i	0.613326	+	0.354104i
$69$	0.329870	+	0.571352i	0.0397117	+	0.0687827i
$70$		0			0
$71$	−9.79389	+	3.56469i	−1.16232	+	0.423050i	−0.849926	−	0.526902i	$-0.823354\pi$
$71$	−9.79389	+	3.56469i	−1.16232	+	0.423050i	−0.312395	+	0.949952i	$0.601131\pi$
$72$	−0.854469	+	2.34764i	−0.100700	+	0.276671i
$73$	−0.907529	+	1.08155i	−0.106218	+	0.126586i	−0.816534	−	0.577297i	$-0.804108\pi$
$73$	−0.907529	+	1.08155i	−0.106218	+	0.126586i	0.710316	+	0.703883i	$0.248552\pi$
$74$	−0.291992	+	1.65597i	−0.0339434	+	0.192503i
$75$		0			0
$76$	−8.18520	−	2.37846i	−0.938907	−	0.272828i
$77$		−	4.87066i		−	0.555063i
$78$	−0.107339	−	0.0189268i	−0.0121538	−	0.00214304i
$79$	1.84675	+	1.54961i	0.207776	+	0.174344i	0.740737	−	0.671795i	$-0.234476\pi$
$79$	1.84675	+	1.54961i	0.207776	+	0.174344i	−0.532961	+	0.846140i	$0.678921\pi$
$80$		0			0
$81$	−8.40329	+	3.05855i	−0.933699	+	0.339838i
$82$	−0.739923	−	0.881806i	−0.0817108	−	0.0973792i
$83$	−9.87319	+	5.70029i	−1.08372	+	0.625688i	−0.931898	−	0.362719i	$-0.881848\pi$
$83$	−9.87319	+	5.70029i	−1.08372	+	0.625688i	−0.151825	+	0.988407i	$0.548515\pi$
$84$	0.131802	−	0.228287i	0.0143807	−	0.0249082i
$85$		0			0
$86$	−0.195335	−	1.10780i	−0.0210635	−	0.119457i
$87$	0.502142	+	0.289912i	0.0538352	+	0.0310818i
$88$	2.08638	−	1.20457i	0.222409	−	0.128408i
$89$	7.74938	−	6.50250i	0.821433	−	0.689264i	−0.131874	−	0.991266i	$-0.542099\pi$
$89$	7.74938	−	6.50250i	0.821433	−	0.689264i	0.953307	+	0.302002i	$0.0976550\pi$
$90$		0			0
$91$	−10.2517	−	3.73131i	−1.07467	−	0.391148i
$92$	−10.3794	+	12.3697i	−1.08213	+	1.28963i
$93$	0.319133	+	0.0562718i	0.0330926	+	0.00583512i
$94$	−0.348041			−0.0358977
$95$		0			0
$96$	0.196310			0.0200358
$97$	9.71828	+	1.71360i	0.986742	+	0.173989i	0.643656	−	0.765315i	$-0.277417\pi$
$97$	9.71828	+	1.71360i	0.986742	+	0.173989i	0.343086	+	0.939304i	$0.388528\pi$
$98$	0.563256	−	0.671262i	0.0568974	−	0.0678077i
$99$	8.12075	+	2.95571i	0.816166	+	0.297060i
$100$		0			0
$101$	3.19421	−	2.68026i	0.317836	−	0.266696i	−0.469886	−	0.882727i	$-0.655705\pi$
$101$	3.19421	−	2.68026i	0.317836	−	0.266696i	0.787722	+	0.616031i	$0.211260\pi$
$102$	−0.0435976	+	0.0251711i	−0.00431680	+	0.00249231i
$103$	10.8804	+	6.28180i	1.07208	+	0.618964i	0.928748	−	0.370711i	$-0.120886\pi$
$103$	10.8804	+	6.28180i	1.07208	+	0.618964i	0.143329	+	0.989675i	$0.454219\pi$
$104$	−0.937034	−	5.31418i	−0.0918837	−	0.521098i
$105$		0			0
$106$	−0.201694	+	0.349344i	−0.0195902	+	0.0339313i
$107$	−12.9404	+	7.47116i	−1.25100	+	0.722264i	−0.971308	−	0.237826i	$-0.923565\pi$
$107$	−12.9404	+	7.47116i	−1.25100	+	0.722264i	−0.279690	+	0.960090i	$0.590232\pi$
$108$	0.601913	+	0.717332i	0.0579191	+	0.0690253i
$109$	4.89106	−	1.78020i	0.468479	−	0.170512i	−0.0969843	−	0.995286i	$-0.530920\pi$
$109$	4.89106	−	1.78020i	0.468479	−	0.170512i	0.565463	+	0.824774i	$0.308697\pi$
$110$		0			0
$111$	0.487785	+	0.409301i	0.0462985	+	0.0388491i
$112$	6.20589	+	1.09427i	0.586401	+	0.103398i
$113$			8.57064i			0.806258i	0.915143	+	0.403129i	$0.132077\pi$
$113$			8.57064i			0.806258i	−0.915143	+	0.403129i	$0.867923\pi$
$114$	0.0530349	−	0.0508536i	0.00496717	−	0.00476288i
$115$		0			0
$116$	−2.46433	+	13.9759i	−0.228807	+	1.29763i
$117$	12.4423	−	14.8281i	1.15029	−	1.37086i
$118$	0.256370	−	0.704370i	0.0236007	−	0.0648425i
$119$	−4.73500	+	1.72340i	−0.434057	+	0.157984i
$120$		0			0
$121$	1.33324	+	2.30924i	0.121204	+	0.209931i
$122$	−1.44349	−	0.833400i	−0.130688	−	0.0754525i
$123$	−0.429284	+	0.0756943i	−0.0387072	+	0.00682512i
$124$	1.37728	+	7.81096i	0.123684	+	0.701445i
$125$		0			0
$126$	−0.532830	−	0.922889i	−0.0474683	−	0.0822175i
$127$	−8.37999	−	9.98688i	−0.743604	−	0.886192i	0.253090	−	0.967443i	$-0.418553\pi$
$127$	−8.37999	−	9.98688i	−0.743604	−	0.886192i	−0.996694	+	0.0812503i	$0.974109\pi$
$128$	2.18236	+	5.99600i	0.192896	+	0.529976i
$129$	−0.400285	−	0.145692i	−0.0352431	−	0.0128274i
$130$		0			0
$131$	0.0324867	−	0.184241i	0.00283838	−	0.0160972i	−0.983356	−	0.181691i	$-0.941843\pi$
$131$	0.0324867	−	0.184241i	0.00283838	−	0.0160972i	0.986194	+	0.165594i	$0.0529541\pi$
$132$		−	0.451015i		−	0.0392558i
$133$	6.11164	−	4.09095i	0.529946	−	0.354730i
$134$	−0.477948			−0.0412884
$135$		0			0
$136$	−1.90925	−	1.60205i	−0.163717	−	0.137375i
$137$	−0.737254	+	2.02559i	−0.0629879	+	0.173058i	−0.967194	−	0.254038i	$-0.918241\pi$
$137$	−0.737254	+	2.02559i	−0.0629879	+	0.173058i	0.904206	+	0.427096i	$0.140463\pi$
$138$	−0.0476073	−	0.130800i	−0.00405260	−	0.0111344i
$139$	6.04955	−	5.07617i	0.513116	−	0.430555i	−0.349108	−	0.937082i	$-0.613515\pi$
$139$	6.04955	−	5.07617i	0.513116	−	0.430555i	0.862224	+	0.506527i	$0.169071\pi$
$140$		0			0
$141$	−0.0658982	+	0.114139i	−0.00554963	+	0.00961225i
$142$	2.16556	−	0.381846i	0.181730	−	0.0320438i
$143$	−18.3824	+	3.24131i	−1.53721	+	0.271052i
$144$	−5.59042	+	9.68290i	−0.465869	+	0.806908i
$145$		0			0
$146$	0.228189	−	0.191474i	0.0188851	−	0.0158465i
$147$	−0.113492	−	0.311815i	−0.00936063	−	0.0257181i
$148$	−5.33039	+	14.6451i	−0.438155	+	1.20382i
$149$	−13.7096	−	11.5037i	−1.12313	−	0.942421i	−0.124375	−	0.992235i	$-0.539693\pi$
$149$	−13.7096	−	11.5037i	−1.12313	−	0.942421i	−0.998759	+	0.0498141i	$0.984137\pi$
$150$		0			0
$151$	2.93984			0.239241			0.119620	−	0.992820i	$-0.461832\pi$
$151$	2.93984			0.239241			0.119620	+	0.992820i	$0.461832\pi$
$152$	3.26387	+	1.60622i	0.264735	+	0.130282i
$153$		−	8.94040i		−	0.722788i
$154$	−0.178446	+	1.01202i	−0.0143796	+	0.0815507i
$155$		0			0
$156$	−0.949291	−	0.345514i	−0.0760041	−	0.0276632i
$157$	2.31441	+	6.35878i	0.184710	+	0.507486i	0.997140	−	0.0755720i	$-0.0240783\pi$
$157$	2.31441	+	6.35878i	0.184710	+	0.507486i	−0.812431	+	0.583058i	$0.801856\pi$
$158$	−0.326942	−	0.389634i	−0.0260101	−	0.0309976i
$159$	0.0763776	+	0.132290i	0.00605714	+	0.0104913i
$160$		0			0
$161$	−2.41933	−	13.7207i	−0.190670	−	1.08134i
$162$	1.85808	−	0.327629i	0.145984	−	0.0257410i
$163$	0.786207	+	0.453917i	0.0615805	+	0.0355535i	0.530474	−	0.847701i	$-0.322014\pi$
$163$	0.786207	+	0.453917i	0.0615805	+	0.0355535i	−0.468894	+	0.883255i	$0.655347\pi$
$164$	−5.33452	−	9.23965i	−0.416556	−	0.721496i
$165$		0			0
$166$	2.26028	−	0.822673i	0.175431	−	0.0638518i
$167$	−4.88117	+	13.4109i	−0.377716	+	1.03777i	0.594585	+	0.804033i	$0.297317\pi$
$167$	−4.88117	+	13.4109i	−0.377716	+	1.03777i	−0.972301	+	0.233733i	$0.924906\pi$
$168$	−0.0723123	+	0.0861785i	−0.00557902	+	0.00664881i
$169$	−5.00268	+	28.3716i	−0.384822	+	2.18243i
$170$		0			0
$171$	3.11197	+	12.6724i	0.237978	+	0.969080i
$172$		−	10.4260i		−	0.794971i
$173$	13.8636	+	2.44452i	1.05403	+	0.185854i	0.673705	−	0.739000i	$-0.264702\pi$
$173$	13.8636	+	2.44452i	1.05403	+	0.185854i	0.380323	+	0.924854i	$0.375813\pi$
$174$	−0.0937127	−	0.0786343i	−0.00710434	−	0.00596125i
$175$		0			0
$176$	10.1316	−	3.68761i	0.763699	−	0.277964i
$177$	−0.182455	−	0.217442i	−0.0137142	−	0.0163439i
$178$	−1.84839	+	1.06717i	−0.138542	+	0.0799875i
$179$	7.87488	−	13.6397i	0.588596	−	1.01948i	−0.405821	−	0.913953i	$-0.633014\pi$
$179$	7.87488	−	13.6397i	0.588596	−	1.01948i	0.994417	−	0.105525i	$-0.0336524\pi$
$180$		0			0
$181$	0.791542	+	4.48906i	0.0588348	+	0.333669i	0.999991	−	0.00430380i	$-0.00136995\pi$
$181$	0.791542	+	4.48906i	0.0588348	+	0.333669i	−0.941156	+	0.337973i	$0.890259\pi$
$182$	1.99338	+	1.15088i	0.147759	+	0.0853087i
$183$	−0.546623	+	0.315593i	−0.0404075	+	0.0233293i
$184$	5.27902	−	4.42962i	0.389174	−	0.326556i
$185$		0			0
$186$	−0.0642474	−	0.0233841i	−0.00471085	−	0.00171461i
$187$	−5.54169	+	6.60433i	−0.405249	+	0.482956i
$188$	−3.17678	−	0.560153i	−0.231691	−	0.0408533i
$189$	−0.807951			−0.0587698
$190$		0			0
$191$	−9.95887			−0.720599			−0.360299	−	0.932837i	$-0.617325\pi$
$191$	−9.95887			−0.720599			−0.360299	+	0.932837i	$0.617325\pi$
$192$	0.546947	+	0.0964416i	0.0394725	+	0.00696007i
$193$	13.7564	−	16.3943i	0.990210	−	1.18009i	0.00656365	−	0.999978i	$-0.497911\pi$
$193$	13.7564	−	16.3943i	0.990210	−	1.18009i	0.983647	−	0.180108i	$-0.0576448\pi$
$194$	−1.95647	−	0.712096i	−0.140466	−	0.0511255i
$195$		0			0
$196$	6.22154	−	5.22049i	0.444396	−	0.372892i
$197$	−1.18364	+	0.683372i	−0.0843305	+	0.0486883i	−0.541572	−	0.840654i	$-0.682171\pi$
$197$	−1.18364	+	0.683372i	−0.0843305	+	0.0486883i	0.457242	+	0.889342i	$0.348837\pi$
$198$	−1.57903	−	0.911652i	−0.112217	−	0.0647883i
$199$	3.11454	+	17.6634i	0.220784	+	1.25213i	0.870583	+	0.492022i	$0.163742\pi$
$199$	3.11454	+	17.6634i	0.220784	+	1.25213i	−0.649799	+	0.760106i	$0.725147\pi$
$200$		0			0
$201$	−0.0904949	+	0.156742i	−0.00638302	+	0.0110557i
$202$	−0.761885	+	0.439874i	−0.0536060	+	0.0309495i
$203$	−7.87072	−	9.37996i	−0.552416	−	0.658344i
$204$	−0.438453	+	0.159584i	−0.0306979	+	0.0111731i
$205$		0			0
$206$	−2.03057	−	1.70385i	−0.141476	−	0.118713i
$207$	24.3443	+	4.29257i	1.69205	+	0.298354i
$208$		−	24.1499i		−	1.67449i
$209$	5.55611	−	11.2901i	0.384324	−	0.780953i
$210$		0			0
$211$	3.60629	−	20.4523i	0.248267	−	1.40799i	−0.564513	−	0.825424i	$-0.690936\pi$
$211$	3.60629	−	20.4523i	0.248267	−	1.40799i	0.812781	−	0.582570i	$-0.197953\pi$
$212$	−2.40323	+	2.86406i	−0.165055	+	0.196705i
$213$	0.284802	−	0.782488i	0.0195143	−	0.0536152i
$214$	2.96246	−	1.07825i	0.202510	−	0.0737075i
$215$		0			0
$216$	−0.199816	−	0.346091i	−0.0135957	−	0.0235485i
$217$	−5.92656	−	3.42170i	−0.402321	−	0.232280i
$218$	−1.08148	+	0.190694i	−0.0732469	+	0.0129154i
$219$	−0.0195878	−	0.111088i	−0.00132362	−	0.00750662i
$220$		0			0
$221$	9.65533	+	16.7235i	0.649488	+	1.12495i
$222$	−0.0863557	−	0.102915i	−0.00579582	−	0.00690719i
$223$	−0.666925	−	1.83236i	−0.0446606	−	0.122704i	0.915357	−	0.402642i	$-0.131908\pi$
$223$	−0.666925	−	1.83236i	−0.0446606	−	0.122704i	−0.960018	+	0.279938i	$0.909686\pi$
$224$	−3.89565	−	1.41790i	−0.260289	−	0.0947375i
$225$		0			0
$226$	0.314002	−	1.78079i	0.0208871	−	0.118457i
$227$		−	12.6099i		−	0.836950i	−0.908228	−	0.418475i	$-0.862565\pi$
$227$		−	12.6099i		−	0.836950i	0.908228	−	0.418475i	$-0.137435\pi$
$228$	0.565928	−	0.378815i	0.0374795	−	0.0250877i
$229$	6.12765			0.404926			0.202463	−	0.979290i	$-0.435105\pi$
$229$	6.12765			0.404926			0.202463	+	0.979290i	$0.435105\pi$
$230$		0			0
$231$	0.298102	+	0.250137i	0.0196136	+	0.0164578i
$232$	2.07145	−	5.69125i	0.135997	−	0.373649i
$233$	−2.25977	−	6.20868i	−0.148043	−	0.406744i	0.843400	−	0.537286i	$-0.180550\pi$
$233$	−2.25977	−	6.20868i	−0.148043	−	0.406744i	−0.991443	+	0.130542i	$0.958328\pi$
$234$	−3.12849	+	2.62512i	−0.204516	+	0.171609i
$235$		0			0
$236$	3.47369	−	6.01660i	0.226118	−	0.391648i
$237$	−0.189683	+	0.0334462i	−0.0123212	+	0.00217256i
$238$	1.04697	−	0.184609i	0.0678650	−	0.0119664i
$239$	−1.10191	+	1.90856i	−0.0712766	+	0.123455i	−0.899461	−	0.437001i	$-0.856041\pi$
$239$	−1.10191	+	1.90856i	−0.0712766	+	0.123455i	0.828184	+	0.560456i	$0.189374\pi$
$240$		0			0
$241$	−0.0956409	+	0.0802523i	−0.00616077	+	0.00516950i	−0.645863	−	0.763453i	$-0.723502\pi$
$241$	−0.0956409	+	0.0802523i	−0.00616077	+	0.00516950i	0.639702	+	0.768623i	$0.279058\pi$
$242$	−0.192415	−	0.528656i	−0.0123689	−	0.0339833i
$243$	0.735707	−	2.02134i	0.0471956	−	0.129669i
$244$	−11.8343	−	9.93017i	−0.757615	−	0.635714i
$245$		0			0
$246$	0.0919690			0.00586373
$247$	−19.5068	−	20.3435i	−1.24119	−	1.29443i
$248$		−	3.38491i		−	0.214942i
$249$	0.158168	−	0.897017i	0.0100235	−	0.0568462i
$250$		0			0
$251$	−3.49264	−	1.27122i	−0.220453	−	0.0802385i	0.229432	−	0.973325i	$-0.426313\pi$
$251$	−3.49264	−	1.27122i	−0.220453	−	0.0802385i	−0.449886	+	0.893086i	$0.648535\pi$
$252$	−3.37813	−	9.28133i	−0.212802	−	0.584669i
$253$	−15.3226	−	18.2608i	−0.963323	−	1.14804i
$254$	1.37529	+	2.38207i	0.0862935	+	0.149465i
$255$		0			0
$256$	2.18042	+	12.3658i	0.136276	+	0.772861i
$257$	−26.5659	+	4.68428i	−1.65713	+	0.292198i	−0.922423	−	0.386182i	$-0.873794\pi$
$257$	−26.5659	+	4.68428i	−1.65713	+	0.292198i	−0.734712	+	0.678379i	$0.762683\pi$
$258$	0.0778328	+	0.0449368i	0.00484566	+	0.00279764i
$259$	−6.72351	−	11.6455i	−0.417779	−	0.723614i
$260$		0			0
$261$	20.4153	−	7.43055i	1.26367	−	0.459940i
$262$	−0.0135001	+	0.0370911i	−0.000834036	+	0.00229150i
$263$	−13.2902	+	15.8386i	−0.819508	+	0.976652i	−0.999976	−	0.00692932i	$-0.997794\pi$
$263$	−13.2902	+	15.8386i	−0.819508	+	0.976652i	0.180468	+	0.983581i	$0.442239\pi$
$264$	−0.0334238	+	0.189556i	−0.00205709	+	0.0116663i
$265$		0			0
$266$	−1.41975	+	0.626099i	−0.0870502	+	0.0383886i
$267$			0.808231i			0.0494629i
$268$	−4.36252	−	0.769230i	−0.266483	−	0.0469882i
$269$	10.5139	+	8.82218i	0.641042	+	0.537898i	0.904338	−	0.426817i	$-0.140365\pi$
$269$	10.5139	+	8.82218i	0.641042	+	0.537898i	−0.263296	+	0.964715i	$0.584810\pi$
$270$		0			0
$271$	5.05880	−	1.84125i	0.307300	−	0.111848i	−0.183767	−	0.982970i	$-0.558829\pi$
$271$	5.05880	−	1.84125i	0.307300	−	0.111848i	0.491067	+	0.871122i	$0.336607\pi$
$272$	−7.16979	−	8.54463i	−0.434733	−	0.518094i
$273$	0.754854	−	0.435815i	0.0456859	−	0.0263767i
$274$	0.227397	−	0.393863i	0.0137375	−	0.0237941i
$275$		0			0
$276$	−0.224026	−	1.27051i	−0.0134848	−	0.0764759i
$277$	19.7441	+	11.3993i	1.18631	+	0.684916i	0.957466	−	0.288547i	$-0.0931723\pi$
$277$	19.7441	+	11.3993i	1.18631	+	0.684916i	0.228843	+	0.973463i	$0.426506\pi$
$278$	−1.44294	+	0.833082i	−0.0865418	+	0.0499649i
$279$	9.30140	−	7.80481i	0.556861	−	0.467261i
$280$		0			0
$281$	16.1900	+	5.89267i	0.965814	+	0.351528i	0.776309	−	0.630352i	$-0.217090\pi$
$281$	16.1900	+	5.89267i	0.965814	+	0.351528i	0.189505	+	0.981880i	$0.439312\pi$
$282$	0.0178739	−	0.0213013i	0.00106438	−	0.00126848i
$283$	16.0512	+	2.83026i	0.954146	+	0.168242i	0.628986	−	0.777417i	$-0.283470\pi$
$283$	16.0512	+	2.83026i	0.954146	+	0.168242i	0.325161	+	0.945659i	$0.394582\pi$
$284$	20.3809			1.20939
$285$		0			0
$286$	3.93821			0.232871
$287$	9.06558	+	1.59851i	0.535124	+	0.0943568i
$288$	4.72807	−	5.63470i	0.278604	−	0.332028i
$289$	−7.59356	−	2.76383i	−0.446680	−	0.162578i
$290$		0			0
$291$	−0.603969	+	0.506790i	−0.0354053	+	0.0297086i
$292$	2.39099	−	1.38044i	0.139922	−	0.0807841i
$293$	−21.9002	−	12.6441i	−1.27942	−	0.738675i	−0.302681	−	0.953092i	$-0.597882\pi$
$293$	−21.9002	−	12.6441i	−1.27942	−	0.738675i	−0.976742	+	0.214416i	$0.931215\pi$
$294$	0.0121571	+	0.0689465i	0.000709018	+	0.00402104i
$295$		0			0
$296$	3.32561	−	5.76012i	0.193297	−	0.334800i
$297$	−1.19717	+	0.691187i	−0.0694669	+	0.0401067i
$298$	2.42710	+	2.89250i	0.140598	+	0.167558i
$299$	−50.1733	+	18.2616i	−2.90160	+	1.05609i
$300$		0			0
$301$	6.89110	+	5.78232i	0.397197	+	0.333287i
$302$	−0.610834	−	0.107707i	−0.0351496	−	0.00619782i
$303$			0.333144i			0.0191386i
$304$	13.1369	+	9.61573i	0.753451	+	0.551500i
$305$		0			0
$306$	−0.327549	+	1.85762i	−0.0187247	+	0.106193i
$307$	11.0746	−	13.1982i	0.632059	−	0.753259i	−0.351035	−	0.936362i	$-0.614170\pi$
$307$	11.0746	−	13.1982i	0.632059	−	0.753259i	0.983094	+	0.183104i	$0.0586145\pi$
$308$	−3.25757	+	8.95011i	−0.185617	+	0.509980i
$309$	−0.943241	+	0.343312i	−0.0536591	+	0.0195303i
$310$		0			0
$311$	−12.4862	−	21.6267i	−0.708028	−	1.22634i	−0.965588	−	0.260078i	$-0.916252\pi$
$311$	−12.4862	−	21.6267i	−0.708028	−	1.22634i	0.257560	−	0.966262i	$-0.417082\pi$
$312$	0.373369	+	0.215565i	0.0211378	+	0.0122039i
$313$	16.6071	−	2.92827i	0.938687	−	0.165516i	0.316684	−	0.948531i	$-0.397430\pi$
$313$	16.6071	−	2.92827i	0.938687	−	0.165516i	0.622002	+	0.783015i	$0.286319\pi$
$314$	−0.247917	−	1.40601i	−0.0139908	−	0.0793457i
$315$		0			0
$316$	−2.35710	−	4.08263i	−0.132598	−	0.229666i
$317$	−15.5048	−	18.4779i	−0.870834	−	1.03782i	−0.998939	−	0.0460593i	$-0.985334\pi$
$317$	−15.5048	−	18.4779i	−0.870834	−	1.03782i	0.128104	−	0.991761i	$-0.459111\pi$
$318$	−0.0110229	−	0.0302852i	−0.000618134	−	0.00169831i
$319$	−19.6867	−	7.16538i	−1.10224	−	0.401184i
$320$		0			0
$321$	0.207305	−	1.17569i	0.0115707	−	0.0656205i
$322$			2.93950i			0.163812i
$323$	−12.9416	−	1.40655i	−0.720089	−	0.0782624i
$324$	17.4871			0.971506
$325$		0			0
$326$	−0.146727	−	0.123118i	−0.00812644	−	0.00681889i
$327$	−0.142230	+	0.390774i	−0.00786534	+	0.0216099i
$328$	1.55729	+	4.27863i	0.0859872	+	0.236248i
$329$	2.13211	−	1.78905i	0.117547	−	0.0986335i
$330$		0			0
$331$	−7.77017	+	13.4583i	−0.427087	+	0.739736i	−0.996613	−	0.0822371i	$-0.973794\pi$
$331$	−7.77017	+	13.4583i	−0.427087	+	0.739736i	0.569526	+	0.821973i	$0.307127\pi$
$332$	21.9550	−	3.87126i	1.20494	−	0.212463i
$333$	23.4963	−	4.14304i	1.28759	−	0.227037i
$334$	1.50553	−	2.60766i	0.0823792	−	0.142685i
$335$		0			0
$336$	−0.385681	+	0.323625i	−0.0210406	+	0.0176552i
$337$	3.76416	+	10.3419i	0.205047	+	0.563361i	0.999004	−	0.0446119i	$-0.0142051\pi$
$337$	3.76416	+	10.3419i	0.205047	+	0.563361i	−0.793958	+	0.607973i	$0.791983\pi$
$338$	2.07890	−	5.71172i	0.113077	−	0.310677i
$339$	−0.524554	−	0.440153i	−0.0284898	−	0.0239058i
$340$		0			0
$341$	−11.7088			−0.634067
$342$	−0.182324	−	2.74705i	−0.00985894	−	0.148544i
$343$			18.8181i			1.01608i
$344$	−0.772645	+	4.38189i	−0.0416582	+	0.236255i
$345$		0			0
$346$	−2.79099	−	1.01584i	−0.150045	−	0.0546118i
$347$	10.4212	+	28.6321i	0.559441	+	1.53705i	0.820451	+	0.571716i	$0.193722\pi$
$347$	10.4212	+	28.6321i	0.559441	+	1.53705i	−0.261010	+	0.965336i	$0.584056\pi$
$348$	−0.728816	−	0.868569i	−0.0390686	−	0.0465602i
$349$	2.80872	+	4.86485i	0.150347	+	0.260409i	0.931355	−	0.364112i	$-0.118627\pi$
$349$	2.80872	+	4.86485i	0.150347	+	0.260409i	−0.781008	+	0.624521i	$0.785294\pi$
$350$		0			0
$351$	0.537673	+	3.04929i	0.0286988	+	0.162759i
$352$	−6.98532	+	1.23170i	−0.372319	+	0.0656499i
$353$	6.48321	+	3.74308i	0.345067	+	0.199224i	0.662510	−	0.749053i	$-0.269491\pi$
$353$	6.48321	+	3.74308i	0.345067	+	0.199224i	−0.317444	+	0.948277i	$0.602824\pi$
$354$	0.0299438	+	0.0518642i	0.00159150	+	0.00275655i
$355$		0			0
$356$	−18.5889	+	6.76581i	−0.985210	+	0.358587i
$357$	0.137692	−	0.378305i	0.00728743	−	0.0200220i
$358$	−2.13594	+	2.54552i	−0.112888	+	0.134535i
$359$	4.42550	−	25.0982i	0.233569	−	1.32463i	−0.612038	−	0.790828i	$-0.709650\pi$
$359$	4.42550	−	25.0982i	0.233569	−	1.32463i	0.845607	−	0.533806i	$-0.179239\pi$
$360$		0			0
$361$	18.8333	−	2.51102i	0.991229	−	0.132159i
$362$		−	0.961728i		−	0.0505473i
$363$	−0.209803	−	0.0369940i	−0.0110118	−	0.00194168i
$364$	16.3425	+	13.7130i	0.856580	+	0.718756i
$365$		0			0
$366$	0.125139	−	0.0455468i	0.00654111	−	0.00238077i
$367$	21.5117	+	25.6366i	1.12290	+	1.33822i	0.934432	+	0.356141i	$0.115908\pi$
$367$	21.5117	+	25.6366i	1.12290	+	1.33822i	0.188468	+	0.982079i	$0.439648\pi$
$368$	26.7091	−	15.4205i	1.39231	−	0.803850i
$369$	−8.16651	+	14.1448i	−0.425132	+	0.736350i
$370$		0			0
$371$	−0.560167	−	3.17686i	−0.0290824	−	0.164935i
$372$	−0.548790	−	0.316844i	−0.0284534	−	0.0164276i
$373$	−9.07481	+	5.23935i	−0.469876	+	0.271283i	−0.716188	−	0.697908i	$-0.754115\pi$
$373$	−9.07481	+	5.23935i	−0.469876	+	0.271283i	0.246312	+	0.969191i	$0.420781\pi$
$374$	1.39341	−	1.16921i	0.0720513	−	0.0604582i
$375$		0			0
$376$	1.29365	+	0.470849i	0.0667148	+	0.0242822i
$377$	−30.1632	+	35.9471i	−1.55348	+	1.85137i
$378$	0.167875	+	0.0296008i	0.00863454	+	0.00152250i
$379$	14.2962			0.734344			0.367172	−	0.930153i	$-0.380326\pi$
$379$	14.2962			0.734344			0.367172	+	0.930153i	$0.380326\pi$
$380$		0			0
$381$	1.04159			0.0533625
$382$	2.06924	+	0.364862i	0.105871	+	0.0186680i
$383$	−23.7712	+	28.3295i	−1.21465	+	1.44757i	−0.356408	+	0.934331i	$0.615999\pi$
$383$	−23.7712	+	28.3295i	−1.21465	+	1.44757i	−0.858246	+	0.513238i	$0.828446\pi$
$384$	−0.479053	−	0.174361i	−0.0244466	−	0.00889783i
$385$		0			0
$386$	−3.45893	+	2.90238i	−0.176055	+	0.147727i
$387$	−13.8225	+	7.98045i	−0.702639	+	0.405669i
$388$	−16.7118	−	9.64857i	−0.848413	−	0.489832i
$389$	2.88385	+	16.3551i	0.146217	+	0.829237i	0.966382	+	0.257110i	$0.0827704\pi$
$389$	2.88385	+	16.3551i	0.146217	+	0.829237i	−0.820165	+	0.572127i	$0.806119\pi$
$390$		0			0
$391$	−12.3305	+	21.3571i	−0.623581	+	1.08007i
$392$	−3.00171	+	1.73304i	−0.151609	+	0.0875316i
$393$	0.00960783	+	0.0114502i	0.000484651	+	0.000577584i
$394$	0.270970	−	0.0986252i	0.0136513	−	0.00496866i
$395$		0			0
$396$	−12.9455	−	10.8626i	−0.650536	−	0.545865i
$397$	26.2337	+	4.62570i	1.31663	+	0.232157i	0.787464	−	0.616361i	$-0.211394\pi$
$397$	26.2337	+	4.62570i	1.31663	+	0.232157i	0.529166	+	0.848518i	$0.322505\pi$
$398$		−	3.78419i		−	0.189684i
$399$	−0.0634878	+	0.584148i	−0.00317836	+	0.0292440i
$400$		0			0
$401$	0.224832	−	1.27508i	0.0112276	−	0.0636747i	−0.978679	−	0.205395i	$-0.934152\pi$
$401$	0.224832	−	1.27508i	0.0112276	−	0.0636747i	0.989907	+	0.141720i	$0.0452633\pi$
$402$	0.0245454	−	0.0292521i	0.00122421	−	0.00145896i
$403$	−8.96988	+	24.6445i	−0.446821	+	1.22763i
$404$	−7.66215	+	2.78879i	−0.381206	+	0.138748i
$405$		0			0
$406$	1.29171	+	2.23731i	0.0641066	+	0.111036i
$407$	−19.9250	−	11.5037i	−0.987643	−	0.570216i
$408$	0.196102	−	0.0345782i	0.00970852	−	0.00171187i
$409$	−4.69402	−	26.6211i	−0.232104	−	1.31633i	−0.848627	−	0.528992i	$-0.822570\pi$
$409$	−4.69402	−	26.6211i	−0.232104	−	1.31633i	0.616522	−	0.787337i	$-0.288541\pi$
$410$		0			0
$411$	−0.0861109	−	0.149148i	−0.00424754	−	0.00735695i
$412$	−15.7920	−	18.8201i	−0.778015	−	0.927202i
$413$	2.05018	+	5.63282i	0.100883	+	0.277173i
$414$	−4.90096	−	1.78380i	−0.240869	−	0.0876692i
$415$		0			0
$416$	−2.75884	+	15.6462i	−0.135263	+	0.767117i
$417$			0.630945i			0.0308975i
$418$	−1.56807	+	2.14228i	−0.0766970	+	0.104782i
$419$	4.15498			0.202984			0.101492	−	0.994836i	$-0.467638\pi$
$419$	4.15498			0.202984			0.101492	+	0.994836i	$0.467638\pi$
$420$		0			0
$421$	−20.2274	−	16.9728i	−0.985822	−	0.827203i	−0.000864321	−	1.00000i	$-0.500275\pi$
$421$	−20.2274	−	16.9728i	−0.985822	−	0.827203i	−0.984957	+	0.172797i	$0.944720\pi$
$422$	−1.49862	+	4.11742i	−0.0729516	+	0.200433i
$423$	1.68900	+	4.64049i	0.0821219	+	0.225628i
$424$	1.22230	−	1.02563i	0.0593599	−	0.0498089i
$425$		0			0
$426$	−0.0878437	+	0.152150i	−0.00425604	+	0.00737168i
$427$	13.1268	−	2.31461i	0.635252	−	0.112012i
$428$	28.7756	−	5.07391i	1.39092	−	0.245257i
$429$	0.745664	−	1.29153i	0.0360010	−	0.0623555i
$430$		0			0
$431$	−7.44700	+	6.24878i	−0.358710	+	0.300993i	−0.804276	−	0.594256i	$-0.797447\pi$
$431$	−7.44700	+	6.24878i	−0.358710	+	0.300993i	0.445567	+	0.895249i	$0.353002\pi$
$432$	−0.611705	−	1.68064i	−0.0294306	−	0.0808600i
$433$	−0.225679	+	0.620049i	−0.0108455	+	0.0297976i	−0.944997	−	0.327078i	$-0.893936\pi$
$433$	−0.225679	+	0.620049i	−0.0108455	+	0.0297976i	0.934152	+	0.356876i	$0.116158\pi$
$434$	1.10605	+	0.928086i	0.0530921	+	0.0445496i
$435$		0			0
$436$	−10.1782			−0.487449
$437$	10.0436	−	34.5641i	0.480452	−	1.65342i
$438$			0.0237993i			0.00113717i
$439$	−4.72146	+	26.7767i	−0.225343	+	1.27798i	0.636686	+	0.771123i	$0.280305\pi$
$439$	−4.72146	+	26.7767i	−0.225343	+	1.27798i	−0.862029	+	0.506860i	$0.830806\pi$
$440$		0			0
$441$	−11.6835	−	4.25243i	−0.556355	−	0.202497i
$442$	−1.39347	−	3.82853i	−0.0662806	−	0.182104i
$443$	24.2897	+	28.9473i	1.15404	+	1.37533i	0.914572	+	0.404424i	$0.132528\pi$
$443$	24.2897	+	28.9473i	1.15404	+	1.37533i	0.239466	+	0.970905i	$0.423028\pi$
$444$	−0.622586	−	1.07835i	−0.0295466	−	0.0511763i
$445$		0			0
$446$	0.0714405	+	0.405159i	0.00338280	+	0.0191848i
$447$	1.40814	−	0.248292i	0.0666025	−	0.0117438i
$448$	−10.1572	−	5.86429i	−0.479885	−	0.277062i
$449$	−8.27496	−	14.3327i	−0.390520	−	0.676400i	0.601998	−	0.798497i	$-0.294371\pi$
$449$	−8.27496	−	14.3327i	−0.390520	−	0.676400i	−0.992518	+	0.122097i	$0.961038\pi$
$450$		0			0
$451$	14.8003	−	5.38687i	0.696919	−	0.253658i
$452$	5.73218	−	15.7490i	0.269619	−	0.740772i
$453$	−0.150978	+	0.179928i	−0.00709356	+	0.00845377i
$454$	−0.461989	+	2.62007i	−0.0216822	+	0.122966i
$455$		0			0
$456$	−0.265925	+	0.117271i	−0.0124531	+	0.00549173i
$457$		−	11.4492i		−	0.535571i	−0.963479	−	0.267785i	$-0.913708\pi$
$457$		−	11.4492i		−	0.535571i	0.963479	−	0.267785i	$-0.0862918\pi$
$458$	−1.27319	−	0.224498i	−0.0594923	−	0.0104901i
$459$	1.09553	+	0.919262i	0.0511352	+	0.0429075i
$460$		0			0
$461$	10.1108	−	3.68002i	0.470905	−	0.171396i	−0.0956571	−	0.995414i	$-0.530495\pi$
$461$	10.1108	−	3.68002i	0.470905	−	0.171396i	0.566562	+	0.824019i	$0.308273\pi$
$462$	−0.0527748	−	0.0628946i	−0.00245531	−	0.00292612i
$463$	14.7988	−	8.54409i	0.687758	−	0.397078i	−0.115013	−	0.993364i	$-0.536691\pi$
$463$	14.7988	−	8.54409i	0.687758	−	0.397078i	0.802772	+	0.596286i	$0.203358\pi$
$464$	13.5526	−	23.4737i	0.629162	−	1.08974i
$465$		0			0
$466$	0.242065	+	1.37282i	0.0112134	+	0.0635946i
$467$	27.5880	+	15.9280i	1.27662	+	0.737058i	0.976226	−	0.216756i	$-0.0695478\pi$
$467$	27.5880	+	15.9280i	1.27662	+	0.737058i	0.300396	+	0.953815i	$0.402881\pi$
$468$	−32.7807	+	18.9259i	−1.51529	+	0.874851i
$469$	2.92792	−	2.45682i	0.135199	−	0.113445i
$470$		0			0
$471$	−0.508038	−	0.184911i	−0.0234092	−	0.00852024i
$472$	−1.90582	+	2.27127i	−0.0877225	+	0.104544i
$473$	15.1575	+	2.67267i	0.696941	+	0.122890i
$474$	0.0406374			0.00186654
$475$		0			0
$476$	9.85346			0.451633
$477$	5.63665	+	0.993894i	0.258085	+	0.0455073i
$478$	0.298877	−	0.356187i	0.0136703	−	0.0162916i
$479$	−3.61807	−	1.31687i	−0.165314	−	0.0601693i	0.258038	−	0.966135i	$-0.416924\pi$
$479$	−3.61807	−	1.31687i	−0.165314	−	0.0601693i	−0.423351	+	0.905966i	$0.639146\pi$
$480$		0			0
$481$	−39.4769	+	33.1250i	−1.79999	+	1.51037i
$482$	0.0228123	−	0.0131707i	0.00103907	−	0.000599909i
$483$	0.964000	+	0.556566i	0.0438635	+	0.0253246i
$484$	−0.905448	−	5.13505i	−0.0411567	−	0.233411i
$485$		0			0
$486$	−0.226919	+	0.393036i	−0.0102933	+	0.0178285i
$487$	−30.6638	+	17.7037i	−1.38951	+	0.802233i	−0.993260	−	0.115910i	$-0.963022\pi$
$487$	−30.6638	+	17.7037i	−1.38951	+	0.802233i	−0.396249	+	0.918143i	$0.629688\pi$
$488$	4.23790	+	5.05053i	0.191841	+	0.228627i
$489$	−0.0681576	+	0.0248074i	−0.00308220	+	0.00112183i
$490$		0			0
$491$	15.5179	+	13.0210i	0.700311	+	0.587631i	0.921862	−	0.387518i	$-0.126667\pi$
$491$	15.5179	+	13.0210i	0.700311	+	0.587631i	−0.221551	+	0.975149i	$0.571112\pi$
$492$	0.839458	+	0.148019i	0.0378457	+	0.00667322i
$493$			21.6737i			0.976136i
$494$	3.30777	+	4.94162i	0.148824	+	0.222334i
$495$		0			0
$496$	2.63055	−	14.9186i	0.118115	−	0.669866i
$497$	−11.3034	+	13.4709i	−0.507029	+	0.604253i
$498$	−0.0657279	+	0.180586i	−0.00294534	+	0.00809225i
$499$	0.553880	−	0.201596i	0.0247951	−	0.00902467i	−0.329593	−	0.944123i	$-0.606911\pi$
$499$	0.553880	−	0.201596i	0.0247951	−	0.00902467i	0.354388	+	0.935099i	$0.384689\pi$
$500$		0			0
$501$	−0.570118	−	0.987473i	−0.0254710	−	0.0441170i
$502$	0.679121	+	0.392091i	0.0303107	+	0.0174999i
$503$	11.1776	−	1.97091i	0.498385	−	0.0878787i	0.0811953	−	0.996698i	$-0.474126\pi$
$503$	11.1776	−	1.97091i	0.498385	−	0.0878787i	0.417190	+	0.908820i	$0.363015\pi$
$504$	0.731962	+	4.15116i	0.0326042	+	0.184908i
$505$		0			0
$506$	2.51468	+	4.35556i	0.111791	+	0.193628i
$507$	−1.47953	−	1.76323i	−0.0657080	−	0.0783078i
$508$	8.71931	+	23.9561i	0.386857	+	1.06288i
$509$	11.1499	+	4.05822i	0.494209	+	0.179877i	0.577088	−	0.816682i	$-0.304189\pi$
$509$	11.1499	+	4.05822i	0.494209	+	0.179877i	−0.0828785	+	0.996560i	$0.526411\pi$
$510$		0			0
$511$	−0.413654	+	2.34595i	−0.0182990	+	0.103779i
$512$		−	15.4108i		−	0.681069i
$513$	−1.87282	−	0.921654i	−0.0826869	−	0.0406920i
$514$	5.69143			0.251038
$515$		0			0
$516$	0.638105	+	0.535434i	0.0280910	+	0.0235712i
$517$	1.62872	−	4.47488i	0.0716312	−	0.196805i
$518$	0.970346	+	2.66600i	0.0426346	+	0.117137i
$519$	−0.861589	+	0.722959i	−0.0378196	+	0.0317344i
$520$		0			0
$521$	12.2611	−	21.2368i	0.537166	−	0.930400i	−0.461889	−	0.886938i	$-0.652828\pi$
$521$	12.2611	−	21.2368i	0.537166	−	0.930400i	0.999055	−	0.0434617i	$-0.0138386\pi$
$522$	−4.51408	+	0.795955i	−0.197576	+	0.0348380i
$523$	−20.9112	+	3.68721i	−0.914382	+	0.161230i	−0.610993	−	0.791636i	$-0.709230\pi$
$523$	−20.9112	+	3.68721i	−0.914382	+	0.161230i	−0.303390	+	0.952867i	$0.598118\pi$
$524$	−0.182919	+	0.316826i	−0.00799087	+	0.0138406i
$525$		0			0
$526$	3.34169	−	2.80401i	0.145705	−	0.122261i
$527$	4.14296	+	11.3827i	0.180470	+	0.495838i
$528$	−0.294623	+	0.809471i	−0.0128218	+	0.0352277i
$529$	−34.6152	−	29.0456i	−1.50501	−	1.26285i
$530$		0			0
$531$	−10.6356			−0.461546
$532$	−13.9666	+	3.42979i	−0.605528	+	0.148700i
$533$		−	35.2782i		−	1.52807i
$534$	0.0296111	−	0.167933i	0.00128140	−	0.00726717i
$535$		0			0
$536$	1.77650	+	0.646594i	0.0767332	+	0.0279286i
$537$	0.430376	+	1.18245i	0.0185721	+	0.0510264i
$538$	−1.86134	−	2.21825i	−0.0802479	−	0.0956357i
$539$	5.99478	+	10.3833i	0.258214	+	0.447239i
$540$		0			0
$541$	2.57449	+	14.6006i	0.110686	+	0.627730i	0.988796	+	0.149272i	$0.0476930\pi$
$541$	2.57449	+	14.6006i	0.110686	+	0.627730i	−0.878110	+	0.478458i	$0.841196\pi$
$542$	−1.11857	+	0.197233i	−0.0480465	+	0.00847190i
$543$	−0.315396	−	0.182094i	−0.0135350	−	0.00781441i
$544$	3.66903	+	6.35495i	0.157308	+	0.272466i
$545$		0			0
$546$	−0.172809	+	0.0628974i	−0.00739555	+	0.00269176i
$547$	−2.72298	+	7.48131i	−0.116426	+	0.319878i	−0.984195	−	0.177091i	$-0.943331\pi$
$547$	−2.72298	+	7.48131i	−0.116426	+	0.319878i	0.867769	+	0.496969i	$0.165554\pi$
$548$	2.70949	−	3.22905i	0.115744	−	0.137938i
$549$	−4.10678	+	23.2907i	−0.175273	+	0.994022i
$550$		0			0
$551$	−7.54419	−	30.7209i	−0.321393	−	1.30876i
$552$			0.550581i			0.0234343i
$553$	4.00571	+	0.706315i	0.170340	+	0.0300355i
$554$	−3.68476	−	3.09188i	−0.156551	−	0.131362i
$555$		0			0
$556$	−14.5114	+	5.28172i	−0.615421	+	0.223995i
$557$	5.20994	+	6.20896i	0.220752	+	0.263082i	0.865042	−	0.501699i	$-0.167292\pi$
$557$	5.20994	+	6.20896i	0.220752	+	0.263082i	−0.644290	+	0.764781i	$0.722847\pi$
$558$	−2.21857	+	1.28089i	−0.0939197	+	0.0542246i
$559$	17.2372	−	29.8558i	0.729057	−	1.26276i
$560$		0			0
$561$	−0.119610	−	0.678342i	−0.00504994	−	0.0286396i
$562$	−3.14804	−	1.81752i	−0.132792	−	0.0766675i
$563$	7.18648	−	4.14912i	0.302874	−	0.174864i	−0.340859	−	0.940114i	$-0.610718\pi$
$563$	7.18648	−	4.14912i	0.302874	−	0.174864i	0.643733	+	0.765250i	$0.277385\pi$
$564$	0.197430	−	0.165663i	0.00831329	−	0.00697568i
$565$		0			0
$566$	−3.23141	−	1.17614i	−0.135826	−	0.0494367i
$567$	−9.69850	+	11.5582i	−0.407299	+	0.485400i
$568$	−8.56583	−	1.51039i	−0.359414	−	0.0633745i
$569$	7.28643			0.305463			0.152732	−	0.988268i	$-0.451193\pi$
$569$	7.28643			0.305463			0.152732	+	0.988268i	$0.451193\pi$
$570$		0			0
$571$	−20.6974			−0.866159			−0.433080	−	0.901356i	$-0.642573\pi$
$571$	−20.6974			−0.866159			−0.433080	+	0.901356i	$0.642573\pi$
$572$	35.9465	+	6.33834i	1.50300	+	0.265019i
$573$	0.511446	−	0.609518i	0.0213660	−	0.0254630i
$574$	−1.82507	−	0.664270i	−0.0761768	−	0.0277261i
$575$		0			0
$576$	15.9412	−	13.3763i	0.664218	−	0.557345i
$577$	−12.6361	+	7.29547i	−0.526049	+	0.303715i	−0.739406	−	0.673260i	$-0.764894\pi$
$577$	−12.6361	+	7.29547i	−0.526049	+	0.303715i	0.213357	+	0.976974i	$0.431560\pi$
$578$	1.47652	+	0.852469i	0.0614151	+	0.0354580i
$579$	0.296914	+	1.68389i	0.0123393	+	0.0699799i
$580$		0			0
$581$	−9.61769	+	16.6583i	−0.399009	+	0.691104i
$582$	0.144059	−	0.0831724i	0.00597143	−	0.00344761i
$583$	−3.54777	−	4.22807i	−0.146934	−	0.175109i
$584$	−1.10720	+	0.402989i	−0.0458164	+	0.0166758i
$585$		0			0
$586$	4.08715	+	3.42952i	0.168838	+	0.141672i
$587$	10.3481	+	1.82464i	0.427110	+	0.0753110i	0.383071	−	0.923719i	$-0.374866\pi$
$587$	10.3481	+	1.82464i	0.427110	+	0.0753110i	0.0440388	+	0.999030i	$0.485977\pi$
$588$			0.648883i			0.0267595i
$589$	−9.83443	−	14.6920i	−0.405220	−	0.605375i
$590$		0			0
$591$	0.0189618	−	0.107538i	0.000779985	−	0.00442352i
$592$	19.1337	−	22.8026i	0.786389	−	0.937183i
$593$	8.31653	−	22.8495i	0.341519	−	0.938316i	−0.643435	−	0.765501i	$-0.722491\pi$
$593$	8.31653	−	22.8495i	0.341519	−	0.938316i	0.984954	−	0.172815i	$-0.0552864\pi$
$594$	0.274069	−	0.0997530i	0.0112452	−	0.00409292i
$595$		0			0
$596$	17.4983	+	30.3079i	0.716757	+	1.24146i
$597$	−1.24101	−	0.716500i	−0.0507913	−	0.0293244i
$598$	11.0940	−	1.95617i	0.453666	−	0.0799936i
$599$	6.58292	+	37.3336i	0.268971	+	1.52541i	0.757484	+	0.652854i	$0.226428\pi$
$599$	6.58292	+	37.3336i	0.268971	+	1.52541i	−0.488513	+	0.872557i	$0.662461\pi$
$600$		0			0
$601$	−12.9738	−	22.4713i	−0.529213	−	0.916623i	−0.999420	−	0.0340669i	$-0.989154\pi$
$601$	−12.9738	−	22.4713i	−0.529213	−	0.916623i	0.470207	−	0.882556i	$-0.344179\pi$
$602$	−1.21998	−	1.45391i	−0.0497225	−	0.0592569i
$603$	2.31942	+	6.37255i	0.0944541	+	0.259510i
$604$	−5.40211	−	1.96621i	−0.219809	−	0.0800039i
$605$		0			0
$606$	0.0122054	−	0.0692202i	0.000495810	−	0.00281188i
$607$			11.5300i			0.467988i	0.972238	+	0.233994i	$0.0751796\pi$
$607$			11.5300i			0.467988i	−0.972238	+	0.233994i	$0.924820\pi$
$608$	−7.41261	−	7.73056i	−0.300621	−	0.313516i
$609$	0.978294			0.0396425
$610$		0			0
$611$	−8.17093	−	6.85623i	−0.330561	−	0.277373i
$612$	−5.97948	+	16.4285i	−0.241706	+	0.664082i
$613$	−7.74954	−	21.2917i	−0.313001	−	0.859963i	−0.992047	−	0.125868i	$-0.959829\pi$
$613$	−7.74954	−	21.2917i	−0.313001	−	0.859963i	0.679046	−	0.734096i	$-0.262394\pi$
$614$	−2.78459	+	2.33655i	−0.112377	+	0.0942956i
$615$		0			0
$616$	2.03239	−	3.52020i	0.0818872	−	0.141833i
$617$	5.88595	−	1.03785i	0.236959	−	0.0417823i	−0.0539072	−	0.998546i	$-0.517168\pi$
$617$	5.88595	−	1.03785i	0.236959	−	0.0417823i	0.290867	+	0.956764i	$0.406056\pi$
$618$	0.208563	−	0.0367753i	0.00838963	−	0.00147932i
$619$	−17.1031	+	29.6234i	−0.687431	+	1.19067i	0.285235	+	0.958458i	$0.407928\pi$
$619$	−17.1031	+	29.6234i	−0.687431	+	1.19067i	−0.972666	+	0.232208i	$0.925405\pi$
$620$		0			0
$621$	−3.02912	+	2.54173i	−0.121554	+	0.101996i
$622$	1.80203	+	4.95103i	0.0722547	+	0.198518i
$623$	5.83766	−	16.0388i	0.233881	−	0.642582i
$624$	1.47806	+	1.24024i	0.0591697	+	0.0496492i
$625$		0			0
$626$	−3.55787			−0.142201
$627$	0.405656	+	0.919866i	0.0162003	+	0.0367359i
$628$		−	13.2325i		−	0.528035i
$629$	−4.13317	+	23.4404i	−0.164800	+	0.934629i
$630$		0			0
$631$	13.3916	+	4.87414i	0.533111	+	0.194036i	0.594527	−	0.804076i	$-0.297339\pi$
$631$	13.3916	+	4.87414i	0.533111	+	0.194036i	−0.0614161	+	0.998112i	$0.519562\pi$
$632$	0.688105	+	1.89055i	0.0273713	+	0.0752021i
$633$	1.06655	+	1.27106i	0.0423915	+	0.0505202i
$634$	2.54458	+	4.40735i	0.101058	+	0.175038i
$635$		0			0
$636$	−0.0518706	−	0.294173i	−0.00205680	−	0.0116647i
$637$	26.4471	−	4.66333i	1.04787	−	0.184768i
$638$	3.82795	+	2.21007i	0.151550	+	0.0874975i
$639$	−15.6004	−	27.0207i	−0.617142	−	1.06892i
$640$		0			0
$641$	37.3475	−	13.5934i	1.47514	−	0.536906i	0.525647	−	0.850703i	$-0.323823\pi$
$641$	37.3475	−	13.5934i	1.47514	−	0.536906i	0.949490	+	0.313797i	$0.101601\pi$
$642$	−0.0861471	+	0.236687i	−0.00339996	+	0.00934130i
$643$	−10.2245	+	12.1851i	−0.403214	+	0.480532i	−0.928997	−	0.370087i	$-0.879328\pi$
$643$	−10.2245	+	12.1851i	−0.403214	+	0.480532i	0.525783	+	0.850619i	$0.323772\pi$
$644$	−4.73096	+	26.8306i	−0.186426	+	1.05727i
$645$		0			0
$646$	2.63745	+	0.766390i	0.103769	+	0.0301532i
$647$		−	18.8549i		−	0.741262i	−0.928780	−	0.370631i	$-0.879142\pi$
$647$		−	18.8549i		−	0.741262i	0.928780	−	0.370631i	$-0.120858\pi$
$648$	−7.34960	−	1.29593i	−0.288719	−	0.0509090i
$649$	7.85659	+	6.59246i	0.308398	+	0.258777i
$650$		0			0
$651$	0.513784	−	0.187002i	0.0201368	−	0.00732919i
$652$	−1.14111	−	1.35993i	−0.0446894	−	0.0532588i
$653$	−36.8279	+	21.2626i	−1.44119	+	0.832070i	−0.997929	−	0.0643232i	$-0.979511\pi$
$653$	−36.8279	+	21.2626i	−1.44119	+	0.832070i	−0.443259	+	0.896394i	$0.646178\pi$
$654$	0.0438691	−	0.0759835i	0.00171542	−	0.00297119i
$655$		0			0
$656$	3.53850	+	20.0678i	0.138155	+	0.783517i
$657$	−3.66032	−	2.11329i	−0.142803	−	0.0824473i
$658$	−0.508551	+	0.293612i	−0.0198254	+	0.0114462i
$659$	35.1057	−	29.4572i	1.36752	−	1.14749i	0.393945	−	0.919134i	$-0.371110\pi$
$659$	35.1057	−	29.4572i	1.36752	−	1.14749i	0.973578	−	0.228354i	$-0.0733344\pi$
$660$		0			0
$661$	43.3834	+	15.7903i	1.68742	+	0.614170i	0.994296	−	0.106652i	$-0.0340131\pi$
$661$	43.3834	+	15.7903i	1.68742	+	0.614170i	0.693121	+	0.720822i	$0.256235\pi$
$662$	2.10754	−	2.51167i	0.0819120	−	0.0976189i
$663$	−1.51940	−	0.267910i	−0.0590084	−	0.0104048i
$664$	−9.51427			−0.369225
$665$		0			0
$666$	−5.03382			−0.195056
$667$	−59.0167	−	10.4062i	−2.28514	−	0.402931i
$668$	17.9388	−	21.3787i	0.694074	−	0.827166i
$669$	0.146397	+	0.0532843i	0.00566005	+	0.00206009i
$670$		0			0
$671$	17.4704	−	14.6594i	0.674437	−	0.565920i
$672$	0.286845	−	0.165610i	0.0110653	−	0.00638855i
$673$	−4.75292	−	2.74410i	−0.183212	−	0.105777i	0.405589	−	0.914056i	$-0.367066\pi$
$673$	−4.75292	−	2.74410i	−0.183212	−	0.105777i	−0.588801	+	0.808278i	$0.700400\pi$
$674$	−0.403213	−	2.28674i	−0.0155312	−	0.0880818i
$675$		0			0
$676$	28.1681	−	48.7885i	1.08339	−	1.87648i
$677$	25.4878	−	14.7154i	0.979574	−	0.565557i	0.0774324	−	0.996998i	$-0.475328\pi$
$677$	25.4878	−	14.7154i	0.979574	−	0.565557i	0.902141	+	0.431440i	$0.141994\pi$
$678$	0.0928650	+	0.110672i	0.00356646	+	0.00425034i
$679$	15.6458	−	5.69460i	0.600430	−	0.218539i
$680$		0			0
$681$	0.771771	+	0.647593i	0.0295743	+	0.0248158i
$682$	2.43284	+	0.428975i	0.0931581	+	0.0164263i
$683$		−	27.4543i		−	1.05051i	−0.850945	−	0.525254i	$-0.823970\pi$
$683$		−	27.4543i		−	1.05051i	0.850945	−	0.525254i	$-0.176030\pi$
$684$	2.75705	−	25.3675i	0.105419	−	0.969951i
$685$		0			0
$686$	0.689437	−	3.90999i	0.0263228	−	0.149284i
$687$	−0.314690	+	0.375033i	−0.0120062	+	0.0143084i
$688$	−6.81069	+	18.7122i	−0.259655	+	0.713397i
$689$	−11.6170	+	4.22826i	−0.442574	+	0.161084i
$690$		0			0
$691$	−1.71390	−	2.96856i	−0.0651997	−	0.112929i	0.831583	−	0.555401i	$-0.187435\pi$
$691$	−1.71390	−	2.96856i	−0.0651997	−	0.112929i	−0.896783	+	0.442471i	$0.854102\pi$
$692$	−23.8402	−	13.7641i	−0.906267	−	0.523233i
$693$	14.3594	−	2.53195i	0.545468	−	0.0961806i
$694$	−1.11631	−	6.33094i	−0.0423747	−	0.240319i
$695$		0			0
$696$	0.241944	+	0.419059i	0.00917085	+	0.0158844i
$697$	−10.4737	−	12.4820i	−0.396718	−	0.472790i
$698$	−0.405358	−	1.11371i	−0.0153430	−	0.0421546i
$699$	0.496045	+	0.180546i	0.0187622	+	0.00682887i
$700$		0			0
$701$	−0.566267	+	3.21146i	−0.0213876	+	0.121295i	−0.993632	−	0.112671i	$-0.964059\pi$
$701$	−0.566267	+	3.21146i	−0.0213876	+	0.121295i	0.972245	+	0.233966i	$0.0751705\pi$
$702$		−	0.653276i		−	0.0246563i
$703$	−2.30065	−	34.6637i	−0.0867707	−	1.30737i
$704$	−20.0672			−0.756309
$705$		0			0
$706$	−1.20994	−	1.01526i	−0.0455365	−	0.0382097i
$707$	2.40622	−	6.61103i	0.0904952	−	0.248634i
$708$	0.189843	+	0.521590i	0.00713474	+	0.0196025i
$709$	13.1285	−	11.0161i	0.493052	−	0.413720i	−0.362067	−	0.932152i	$-0.617929\pi$
$709$	13.1285	−	11.0161i	0.493052	−	0.413720i	0.855118	+	0.518433i	$0.173484\pi$
$710$		0			0
$711$	−3.60845	+	6.25001i	−0.135327	+	0.234394i
$712$	8.31406	−	1.46599i	0.311583	−	0.0549404i
$713$	−32.9838	+	5.81593i	−1.23525	+	0.217808i
$714$	−0.0424693	+	0.0735590i	−0.00158937	+	0.00275288i
$715$		0			0
$716$	−23.5930	+	19.7968i	−0.881710	+	0.739843i
$717$	−0.0602213	−	0.165457i	−0.00224900	−	0.00617909i
$718$	−1.83904	+	5.05273i	−0.0686325	+	0.188566i
$719$	−4.76900	−	4.00167i	−0.177854	−	0.149237i	0.549515	−	0.835484i	$-0.314813\pi$
$719$	−4.76900	−	4.00167i	−0.177854	−	0.149237i	−0.727369	+	0.686247i	$0.759257\pi$
$720$		0			0
$721$	21.1977			0.789442
$722$	−4.00516	−	0.168259i	−0.149056	−	0.00626197i
$723$		−	0.00997498i		−	0.000370974i
$724$	1.54785	−	8.77829i	0.0575253	−	0.326242i
$725$		0			0
$726$	0.0422373	+	0.0153731i	0.00156757	+	0.000570549i
$727$	−14.4739	−	39.7667i	−0.536807	−	1.47487i	−0.850825	−	0.525449i	$-0.823897\pi$
$727$	−14.4739	−	39.7667i	−0.536807	−	1.47487i	0.314017	−	0.949417i	$-0.398325\pi$
$728$	−5.85229	−	6.97449i	−0.216900	−	0.258492i
$729$	−13.3280	−	23.0847i	−0.493628	−	0.854989i
$730$		0			0
$731$	−2.76498	−	15.6810i	−0.102266	−	0.579982i
$732$	1.21552	−	0.214330i	0.0449270	−	0.00792185i
$733$	19.7134	+	11.3815i	0.728129	+	0.420386i	0.817737	−	0.575591i	$-0.195228\pi$
$733$	19.7134	+	11.3815i	0.728129	+	0.420386i	−0.0896082	+	0.995977i	$0.528561\pi$
$734$	−3.53041	−	6.11485i	−0.130310	−	0.225703i
$735$		0			0
$736$	−19.0659	+	6.93941i	−0.702778	+	0.255790i
$737$	2.23665	−	6.14514i	0.0823879	−	0.226359i
$738$	2.21505	−	2.63979i	0.0815370	−	0.0971720i
$739$	−3.11567	+	17.6698i	−0.114612	+	0.649996i	0.872330	+	0.488918i	$0.162608\pi$
$739$	−3.11567	+	17.6698i	−0.114612	+	0.649996i	−0.986942	+	0.161078i	$0.948503\pi$
$740$		0			0
$741$	2.24689	−	0.149127i	0.0825414	−	0.00547833i
$742$			0.680606i			0.0249858i
$743$	−17.0676	−	3.00948i	−0.626150	−	0.110407i	−0.148435	−	0.988922i	$-0.547424\pi$
$743$	−17.0676	−	3.00948i	−0.626150	−	0.110407i	−0.477715	+	0.878515i	$0.658535\pi$
$744$	0.207168	+	0.173835i	0.00759516	+	0.00637310i
$745$		0			0
$746$	2.07750	−	0.756149i	0.0760628	−	0.0276846i
$747$	−21.9377	−	26.1443i	−0.802658	−	0.956570i
$748$	14.6002	−	8.42945i	0.533838	−	0.308211i
$749$	−12.6055	+	21.8334i	−0.460597	+	0.797777i
$750$		0			0
$751$	−0.379642	−	2.15305i	−0.0138533	−	0.0785661i	0.977097	−	0.212793i	$-0.0682560\pi$
$751$	−0.379642	−	2.15305i	−0.0138533	−	0.0785661i	−0.990951	+	0.134227i	$0.957145\pi$
$752$	5.33569	+	3.08056i	0.194573	+	0.112337i
$753$	0.257170	−	0.148477i	0.00937181	−	0.00541081i
$754$	7.58424	−	6.36394i	0.276202	−	0.231761i
$755$		0			0
$756$	1.48466	+	0.540370i	0.0539964	+	0.0196531i
$757$	−10.0523	+	11.9799i	−0.365358	+	0.435417i	−0.917136	−	0.398574i	$-0.869505\pi$
$757$	−10.0523	+	11.9799i	−0.365358	+	0.435417i	0.551778	+	0.833991i	$0.313950\pi$
$758$	−2.97043	−	0.523767i	−0.107891	−	0.0190241i
$759$	1.90453			0.0691299
$760$		0			0
$761$	26.2993			0.953349			0.476675	−	0.879080i	$-0.341842\pi$
$761$	26.2993			0.953349			0.476675	+	0.879080i	$0.341842\pi$
$762$	−0.216421	−	0.0381608i	−0.00784009	−	0.00138242i
$763$	5.64493	−	6.72737i	0.204360	−	0.243547i
$764$	18.3000	+	6.66065i	0.662070	+	0.240974i
$765$		0			0
$766$	5.97705	−	5.01534i	0.215960	−	0.181212i
$767$	19.8945	−	11.4861i	0.718349	−	0.414739i
$768$	−0.868806	−	0.501605i	−0.0313503	−	0.0181001i
$769$	−0.0147166	−	0.0834622i	−0.000530695	−	0.00300972i	0.984541	−	0.175153i	$-0.0560420\pi$
$769$	−0.0147166	−	0.0834622i	−0.000530695	−	0.00300972i	−0.985072	+	0.172143i	$0.944931\pi$
$770$		0			0
$771$	1.07762	−	1.86649i	0.0388095	−	0.0672200i
$772$	−36.2430	+	20.9249i	−1.30441	+	0.753104i
$773$	−0.00737611	−	0.00879051i	−0.000265300	−	0.000316173i	0.765912	−	0.642946i	$-0.222288\pi$
$773$	−0.00737611	−	0.00879051i	−0.000265300	−	0.000316173i	−0.766177	+	0.642630i	$0.777843\pi$
$774$	3.16440	−	1.15175i	0.113742	−	0.0413987i
$775$		0			0
$776$	6.30871	+	5.29364i	0.226470	+	0.190030i
$777$	1.05803	+	0.186560i	0.0379568	+	0.00669281i
$778$		−	3.50389i		−	0.125621i
$779$	19.1904	+	14.0467i	0.687567	+	0.503275i
$780$		0			0
$781$	−5.22461	+	29.6302i	−0.186951	+	1.06025i
$782$	3.34447	−	3.98578i	0.119598	−	0.142531i
$783$	−1.18860	+	3.26566i	−0.0424771	+	0.116705i
$784$	−14.5765	+	5.30542i	−0.520590	+	0.189479i
$785$		0			0
$786$	−0.00157680	−	0.00273110i	−5.62426e−5	−	9.74150e-5i
$787$	26.0733	+	15.0534i	0.929411	+	0.536596i	0.886625	−	0.462488i	$-0.153043\pi$
$787$	26.0733	+	15.0534i	0.929411	+	0.536596i	0.0427861	+	0.999084i	$0.486377\pi$
$788$	2.63205	−	0.464101i	0.0937628	−	0.0165329i
$789$	−0.286851	−	1.62681i	−0.0102122	−	0.0579161i
$790$		0			0
$791$	7.23031	+	12.5233i	0.257080	+	0.445276i
$792$	4.63582	+	5.52475i	0.164727	+	0.196314i
$793$	−17.4712	−	48.0017i	−0.620421	−	1.70459i
$794$	−5.28131	−	1.92224i	−0.187427	−	0.0682178i
$795$		0			0
$796$	6.09044	−	34.5406i	0.215870	−	1.22426i
$797$		−	38.2339i		−	1.35432i	−0.735838	−	0.677158i	$-0.763211\pi$
$797$		−	38.2339i		−	1.35432i	0.735838	−	0.677158i	$-0.236789\pi$
$798$	0.0345928	−	0.119047i	0.00122457	−	0.00421423i
$799$	−4.92654			−0.174288
$800$		0			0
$801$	23.1987	+	19.4660i	0.819685	+	0.687798i
$802$	−0.0934304	+	0.256698i	−0.00329914	+	0.00906431i
$803$	1.39399	+	3.82995i	0.0491927	+	0.135156i
$804$	0.271121	−	0.227497i	0.00956169	−	0.00802321i
$805$		0			0
$806$	2.76665	−	4.79197i	0.0974509	−	0.168790i
$807$	−1.07990	+	0.190415i	−0.0380142	+	0.00670292i
$808$	3.42697	−	0.604267i	0.120560	−	0.0212580i
$809$	1.85001	−	3.20432i	0.0650431	−	0.112658i	−0.831670	−	0.555270i	$-0.812615\pi$
$809$	1.85001	−	3.20432i	0.0650431	−	0.112658i	0.896713	+	0.442612i	$0.145948\pi$
$810$		0			0
$811$	31.3508	−	26.3064i	1.10088	−	0.923744i	0.103392	−	0.994641i	$-0.467030\pi$
$811$	31.3508	−	26.3064i	1.10088	−	0.923744i	0.997484	+	0.0708964i	$0.0225860\pi$
$812$	8.18942	+	22.5002i	0.287392	+	0.789604i
$813$	−0.147108	+	0.404175i	−0.00515929	+	0.0141750i
$814$	3.71851	+	3.12020i	0.130334	+	0.109363i
$815$		0			0
$816$	0.891172			0.0311973
$817$	9.37739	+	21.2642i	0.328073	+	0.743940i
$818$			5.70327i			0.199410i
$819$	5.67122	−	32.1631i	0.198168	−	1.12387i
$820$		0			0
$821$	−16.3884	−	5.96489i	−0.571959	−	0.208176i	0.0398170	−	0.999207i	$-0.487323\pi$
$821$	−16.3884	−	5.96489i	−0.571959	−	0.208176i	−0.611776	+	0.791031i	$0.709545\pi$
$822$	0.0124276	+	0.0341447i	0.000433464	+	0.00119093i
$823$	−4.18116	−	4.98291i	−0.145746	−	0.173693i	0.688233	−	0.725490i	$-0.258387\pi$
$823$	−4.18116	−	4.98291i	−0.145746	−	0.173693i	−0.833979	+	0.551797i	$0.813942\pi$
$824$	5.24243	+	9.08016i	0.182629	+	0.316322i
$825$		0			0
$826$	−0.219613	−	1.24549i	−0.00764133	−	0.0433361i
$827$	1.59761	−	0.281701i	0.0555542	−	0.00979571i	−0.145802	−	0.989314i	$-0.546576\pi$
$827$	1.59761	−	0.281701i	0.0555542	−	0.00979571i	0.201356	+	0.979518i	$0.435465\pi$
$828$	−41.8632	−	24.1697i	−1.45485	−	0.839955i
$829$	16.3252	+	28.2760i	0.566996	+	0.982066i	0.996861	+	0.0791727i	$0.0252279\pi$
$829$	16.3252	+	28.2760i	0.566996	+	0.982066i	−0.429865	+	0.902893i	$0.641439\pi$
$830$		0			0
$831$	−1.71165	+	0.622990i	−0.0593765	+	0.0216113i
$832$	−15.3730	+	42.2371i	−0.532964	+	1.46431i
$833$	7.97292	−	9.50176i	0.276245	−	0.329216i
$834$	0.0231159	−	0.131097i	0.000800437	−	0.00453951i
$835$		0			0
$836$	−17.7607	+	17.0302i	−0.614265	+	0.589001i
$837$			1.94227i			0.0671347i
$838$	−0.863314	−	0.152226i	−0.0298227	−	0.00525854i
$839$	8.85542	+	7.43058i	0.305723	+	0.256532i	0.782722	−	0.622372i	$-0.213831\pi$
$839$	8.85542	+	7.43058i	0.305723	+	0.256532i	−0.476999	+	0.878904i	$0.658275\pi$
$840$		0			0
$841$	−22.2406	+	8.09491i	−0.766916	+	0.279135i
$842$	3.58098	+	4.26764i	0.123409	+	0.147073i
$843$	−1.19210	+	0.688261i	−0.0410582	+	0.0237050i
$844$	−20.3056	+	35.1703i	−0.698947	+	1.21061i
$845$		0			0
$846$	−0.180924	−	1.02607i	−0.00622030	−	0.0352771i
$847$	3.89622	+	2.24948i	0.133876	+	0.0772931i
$848$	6.18419	−	3.57044i	0.212366	−	0.122610i
$849$	−0.997547	+	0.837041i	−0.0342357	+	0.0287272i
$850$		0			0
$851$	−61.8427	−	22.5089i	−2.11994	−	0.771596i
$852$	−1.04668	+	1.24739i	−0.0358587	+	0.0427347i
$853$	46.9892	+	8.28547i	1.60888	+	0.283689i	0.904609	−	0.426242i	$-0.140163\pi$
$853$	46.9892	+	8.28547i	1.60888	+	0.283689i	0.704271	+	0.709931i	$0.251274\pi$
$854$	−2.81227			−0.0962339
$855$		0			0
$856$	−12.4700			−0.426216
$857$	37.9503	+	6.69167i	1.29636	+	0.228583i	0.778913	−	0.627132i	$-0.215772\pi$
$857$	37.9503	+	6.69167i	1.29636	+	0.228583i	0.517447	+	0.855716i	$0.326883\pi$
$858$	−0.202250	+	0.241033i	−0.00690471	+	0.00822872i
$859$	18.0347	+	6.56408i	0.615335	+	0.223964i	0.630836	−	0.775916i	$-0.282712\pi$
$859$	18.0347	+	6.56408i	0.615335	+	0.223964i	−0.0155009	+	0.999880i	$0.504934\pi$
$860$		0			0
$861$	−0.563405	+	0.472753i	−0.0192008	+	0.0161114i
$862$	1.77626	−	1.02553i	0.0604997	−	0.0349295i
$863$	7.93967	+	4.58397i	0.270269	+	0.156040i	0.629010	−	0.777397i	$-0.283460\pi$
$863$	7.93967	+	4.58397i	0.270269	+	0.156040i	−0.358741	+	0.933437i	$0.616794\pi$
$864$	0.204316	+	1.15873i	0.00695097	+	0.0394209i
$865$		0			0
$866$	0.0696079	−	0.120564i	0.00236537	−	0.00409695i
$867$	0.559130	−	0.322814i	0.0189890	−	0.0109633i
$868$	8.60190	+	10.2513i	0.291967	+	0.347953i
$869$	6.53965	−	2.38024i	0.221842	−	0.0807440i
$870$		0			0
$871$	−11.2207	−	9.41533i	−0.380201	−	0.319026i
$872$	4.27777	+	0.754286i	0.144864	+	0.0255434i
$873$			29.5416i			0.999832i
$874$	−3.35317	+	6.81370i	−0.113423	+	0.230477i
$875$		0			0
$876$	−0.0383037	+	0.217231i	−0.00129416	+	0.00733955i
$877$	−2.33325	+	2.78066i	−0.0787882	+	0.0938961i	−0.803999	−	0.594631i	$-0.797298\pi$
$877$	−2.33325	+	2.78066i	−0.0787882	+	0.0938961i	0.725210	+	0.688527i	$0.241743\pi$
$878$	1.96203	−	5.39064i	0.0662154	−	0.181925i
$879$	1.89857	−	0.691022i	0.0640370	−	0.0233076i
$880$		0			0
$881$	4.17191	+	7.22596i	0.140555	+	0.243449i	0.927706	−	0.373312i	$-0.121778\pi$
$881$	4.17191	+	7.22596i	0.140555	+	0.243449i	−0.787151	+	0.616761i	$0.788445\pi$
$882$	2.27177	+	1.31161i	0.0764946	+	0.0441642i
$883$	−27.7836	+	4.89899i	−0.934991	+	0.164864i	−0.620331	−	0.784340i	$-0.713002\pi$
$883$	−27.7836	+	4.89899i	−0.934991	+	0.164864i	−0.314660	+	0.949204i	$0.601891\pi$
$884$	−6.55725	−	37.1880i	−0.220544	−	1.25077i
$885$		0			0
$886$	−3.98633	−	6.90452i	−0.133923	−	0.231962i
$887$	5.68349	+	6.77332i	0.190833	+	0.227426i	0.852974	−	0.521953i	$-0.174796\pi$
$887$	5.68349	+	6.77332i	0.190833	+	0.227426i	−0.662141	+	0.749379i	$0.730352\pi$
$888$	0.181750	+	0.499355i	0.00609914	+	0.0167573i
$889$	−20.6698	−	7.52318i	−0.693242	−	0.252319i
$890$		0			0
$891$	−4.48278	+	25.4231i	−0.150179	+	0.851707i
$892$			3.81312i			0.127673i
$893$	6.98301	−	1.71483i	0.233678	−	0.0573846i
$894$	−0.301677			−0.0100896
$895$		0			0
$896$	8.24714	+	6.92017i	0.275517	+	0.231187i
$897$	1.45902	−	4.00862i	0.0487152	−	0.133844i
$898$	1.19425	+	3.28118i	0.0398528	+	0.109495i
$899$	−22.5489	+	18.9208i	−0.752048	+	0.631043i
$900$		0			0
$901$	−2.85499	+	4.94498i	−0.0951134	+	0.164741i
$902$	−3.27254	+	0.577037i	−0.108964	+	0.0192132i
$903$	−0.707797	+	0.124804i	−0.0235540	+	0.00415321i
$904$	−3.57628	+	6.19431i	−0.118945	+	0.206020i
$905$		0			0
$906$	0.0379619	−	0.0318539i	0.00126120	−	0.00105827i
$907$	1.44651	+	3.97425i	0.0480305	+	0.131963i	0.961389	−	0.275195i	$-0.0887423\pi$
$907$	1.44651	+	3.97425i	0.0480305	+	0.131963i	−0.913358	+	0.407157i	$0.866520\pi$
$908$	−8.43371	+	23.1714i	−0.279882	+	0.768971i
$909$	9.56225	+	8.02368i	0.317160	+	0.266129i
$910$		0			0
$911$	10.1182			0.335231			0.167616	−	0.985852i	$-0.446393\pi$
$911$	10.1182			0.335231			0.167616	+	0.985852i	$0.446393\pi$
$912$	−1.26317	+	0.310199i	−0.0418278	+	0.0102717i
$913$			32.9110i			1.08920i
$914$	−0.419463	+	2.37890i	−0.0138746	+	0.0786869i
$915$		0			0
$916$	−11.2599	−	4.09826i	−0.372037	−	0.135410i
$917$	−0.107959	−	0.296616i	−0.00356513	−	0.00979513i
$918$	−0.193949	−	0.231140i	−0.00640128	−	0.00762875i
$919$	−23.9378	−	41.4616i	−0.789637	−	1.36769i	−0.926190	−	0.377058i	$-0.876936\pi$
$919$	−23.9378	−	41.4616i	−0.789637	−	1.36769i	0.136553	−	0.990633i	$-0.456398\pi$
$920$		0			0
$921$	0.239030	+	1.35561i	0.00787630	+	0.0446687i
$922$	−2.23562	+	0.394201i	−0.0736263	+	0.0129823i
$923$	58.3629	+	33.6958i	1.92104	+	1.10911i
$924$	−0.380483	−	0.659016i	−0.0125170	−	0.0216800i
$925$		0			0
$926$	−3.38790	+	1.23309i	−0.111333	+	0.0405220i
$927$	−12.8636	+	35.3424i	−0.422496	+	1.16080i
$928$	−11.4620	+	13.6599i	−0.376259	+	0.448408i
$929$	3.75604	−	21.3015i	0.123232	−	0.698881i	−0.859111	−	0.511789i	$-0.828983\pi$
$929$	3.75604	−	21.3015i	0.123232	−	0.698881i	0.982342	−	0.187092i	$-0.0599061\pi$
$930$		0			0
$931$	−7.99367	+	16.2433i	−0.261982	+	0.532351i
$932$			12.9202i			0.423214i
$933$	1.96487	+	0.346460i	0.0643271	+	0.0113426i
$934$	−5.14864	−	4.32023i	−0.168469	−	0.141362i
$935$		0			0
$936$	15.1798	−	5.52501i	0.496168	−	0.180591i
$937$	−23.1939	−	27.6414i	−0.757712	−	0.903006i	0.239989	−	0.970776i	$-0.422856\pi$
$937$	−23.1939	−	27.6414i	−0.757712	−	0.903006i	−0.997701	+	0.0677696i	$0.978412\pi$
$938$	−0.698368	+	0.403203i	−0.0228025	+	0.0131651i
$939$	−0.673649	+	1.16679i	−0.0219837	+	0.0380769i
$940$		0			0
$941$	−8.41858	−	47.7441i	−0.274438	−	1.55641i	−0.740742	−	0.671789i	$-0.765526\pi$
$941$	−8.41858	−	47.7441i	−0.274438	−	1.55641i	0.466305	−	0.884624i	$-0.345585\pi$
$942$	0.0987847	+	0.0570334i	0.00321858	+	0.00185825i
$943$	39.0168	−	22.5264i	1.27056	−	0.733559i
$944$	−10.1648	+	8.52928i	−0.330836	+	0.277604i
$945$		0			0
$946$	−3.05148	−	1.11065i	−0.0992120	−	0.0361102i
$947$	22.6328	−	26.9727i	0.735466	−	0.876495i	−0.260569	−	0.965455i	$-0.583910\pi$
$947$	22.6328	−	26.9727i	0.735466	−	0.876495i	0.996035	+	0.0889606i	$0.0283545\pi$
$948$	0.370922	+	0.0654036i	0.0120470	+	0.00212421i
$949$	9.12913			0.296344
$950$		0			0
$951$	1.92717			0.0624928
$952$	−4.14128	−	0.730219i	−0.134220	−	0.0236665i
$953$	−28.6643	+	34.1607i	−0.928527	+	1.10657i	0.0655452	+	0.997850i	$0.479121\pi$
$953$	−28.6643	+	34.1607i	−0.928527	+	1.10657i	−0.994072	+	0.108725i	$0.965323\pi$
$954$	−1.13476	−	0.413019i	−0.0367392	−	0.0133720i
$955$		0			0
$956$	3.30130	−	2.77012i	0.106772	−	0.0895920i
$957$	1.44957	−	0.836912i	0.0468581	−	0.0270535i
$958$	0.703510	+	0.406172i	0.0227294	+	0.0131228i
$959$	0.631553	+	3.58171i	0.0203939	+	0.115660i
$960$		0			0
$961$	7.27442	−	12.5997i	0.234659	−	0.406441i
$962$	9.41604	−	5.43635i	0.303585	−	0.175275i
$963$	−28.7529	−	34.2664i	−0.926549	−	1.10422i
$964$	0.229419	−	0.0835019i	0.00738910	−	0.00268941i
$965$		0			0
$966$	−0.179908	−	0.150960i	−0.00578843	−	0.00485707i
$967$	−2.66419	−	0.469769i	−0.0856746	−	0.0151067i	0.130647	−	0.991429i	$-0.458295\pi$
$967$	−2.66419	−	0.469769i	−0.0856746	−	0.0151067i	−0.216321	+	0.976322i	$0.569406\pi$
$968$			2.22529i			0.0715236i
$969$	0.750712	−	0.719836i	0.0241163	−	0.0231245i
$970$		0			0
$971$	−1.24026	+	7.03387i	−0.0398019	+	0.225728i	−0.998220	−	0.0596403i	$-0.981005\pi$
$971$	−1.24026	+	7.03387i	−0.0398019	+	0.225728i	0.958418	+	0.285368i	$0.0921158\pi$
$972$	−2.70380	+	3.22227i	−0.0867246	+	0.103354i
$973$	4.55716	−	12.5207i	0.146096	−	0.401395i
$974$	7.01988	−	2.55503i	0.224932	−	0.0818684i
$975$		0			0
$976$	14.7531	+	25.5531i	0.472235	+	0.817935i
$977$	−25.0272	−	14.4495i	−0.800692	−	0.462280i	0.0430210	−	0.999074i	$-0.486302\pi$
$977$	−25.0272	−	14.4495i	−0.800692	−	0.462280i	−0.843713	+	0.536794i	$0.819635\pi$
$978$	0.0150705	−	0.00265734i	0.000481903	−	8.49725e-5i
$979$	−5.07105	−	28.7593i	−0.162071	−	0.919152i
$980$		0			0
$981$	7.79083	+	13.4941i	0.248742	+	0.430834i
$982$	−2.74722	−	3.27402i	−0.0876675	−	0.104478i
$983$	−3.53684	−	9.71738i	−0.112808	−	0.309936i	0.870423	−	0.492305i	$-0.163846\pi$
$983$	−3.53684	−	9.71738i	−0.112808	−	0.309936i	−0.983230	+	0.182369i	$0.941623\pi$
$984$	−0.341843	−	0.124421i	−0.0108976	−	0.00396639i
$985$		0			0
$986$	0.794059	−	4.50333i	0.0252880	−	0.143415i
$987$			0.222371i			0.00707814i
$988$	22.2388	+	50.4289i	0.707511	+	1.60436i
$989$	44.0262			1.39995
$990$		0			0
$991$	24.2226	+	20.3251i	0.769455	+	0.645650i	0.940569	−	0.339602i	$-0.110292\pi$
$991$	24.2226	+	20.3251i	0.769455	+	0.645650i	−0.171114	+	0.985251i	$0.554737\pi$
$992$	−3.40856	+	9.36494i	−0.108222	+	0.297337i
$993$	−0.424653	−	1.16673i	−0.0134760	−	0.0370249i
$994$	2.84214	−	2.38484i	0.0901473	−	0.0756426i
$995$		0			0
$996$	−0.890582	+	1.54253i	−0.0282192	+	0.0488771i
$997$	7.75758	−	1.36787i	0.245685	−	0.0433209i	−0.0494495	−	0.998777i	$-0.515747\pi$
$997$	7.75758	−	1.36787i	0.245685	−	0.0433209i	0.295134	+	0.955456i	$0.404636\pi$
$998$	−0.122470	+	0.0215948i	−0.00387672	+	0.000683571i
$999$	−1.90824	+	3.30518i	−0.0603742	+	0.104571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.b.74.3		36
5.2	odd	4		95.2.k.a.36.2	✓	18
5.3	odd	4		475.2.l.c.226.2		18
5.4	even	2	inner	475.2.u.b.74.4		36
15.2	even	4		855.2.bs.c.226.2		18
19.9	even	9	inner	475.2.u.b.199.4		36
95.3	even	36		9025.2.a.cf.1.4		9
95.9	even	18	inner	475.2.u.b.199.3		36
95.22	even	36		1805.2.a.s.1.6		9
95.28	odd	36		475.2.l.c.351.2		18
95.47	odd	36		95.2.k.a.66.2	yes	18
95.73	odd	36		9025.2.a.cc.1.6		9
95.92	odd	36		1805.2.a.v.1.4		9
285.47	even	36		855.2.bs.c.541.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.2	✓	18	5.2	odd	4
95.2.k.a.66.2	yes	18	95.47	odd	36
475.2.l.c.226.2		18	5.3	odd	4
475.2.l.c.351.2		18	95.28	odd	36
475.2.u.b.74.3		36	1.1	even	1	trivial
475.2.u.b.74.4		36	5.4	even	2	inner
475.2.u.b.199.3		36	95.9	even	18	inner
475.2.u.b.199.4		36	19.9	even	9	inner
855.2.bs.c.226.2		18	15.2	even	4
855.2.bs.c.541.2		18	285.47	even	36
1805.2.a.s.1.6		9	95.22	even	36
1805.2.a.v.1.4		9	95.92	odd	36
9025.2.a.cc.1.6		9	95.73	odd	36
9025.2.a.cf.1.4		9	95.3	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+(-0.207778 - 0.0366369i) q^{2} +(-0.0513559 + 0.0612035i) q^{3} +(-1.83756 - 0.668816i) q^{4} +(0.0129129 - 0.0108352i) q^{6} +(1.46118 - 0.843614i) q^{7} +(0.722735 + 0.417271i) q^{8} +(0.519836 + 2.94814i) q^{9} +(1.44339 - 2.50003i) q^{11} +(0.135303 - 0.0781173i) q^{12} +(-4.15627 - 4.95325i) q^{13} +(-0.334509 + 0.121751i) q^{14} +(2.86110 + 2.40075i) q^{16} +(-2.94112 - 0.518598i) q^{17} -0.631604i q^{18} +(4.34933 - 0.288668i) q^{19} +(-0.0234081 + 0.132754i) q^{21} +(-0.391499 + 0.466570i) q^{22} +(2.82424 - 7.75955i) q^{23} +(-0.0626552 + 0.0228046i) q^{24} +(0.682111 + 1.18145i) q^{26} +(-0.414708 - 0.239432i) q^{27} +(-3.24923 + 0.572926i) q^{28} +(-1.26021 - 7.14701i) q^{29} +(-2.02800 - 3.51260i) q^{31} +(-1.57939 - 1.88224i) q^{32} +(0.0788839 + 0.216732i) q^{33} +(0.592100 + 0.215507i) q^{34} +(1.01653 - 5.76504i) q^{36} -7.96989i q^{37} +(-0.914272 - 0.0993671i) q^{38} +0.516605 q^{39} +(4.17950 + 3.50702i) q^{41} +(0.00972740 - 0.0267258i) q^{42} +(1.82353 + 5.01011i) q^{43} +(-4.32437 + 3.62858i) q^{44} +(-0.871103 + 1.50879i) q^{46} +(1.62455 - 0.286452i) q^{47} +(-0.293868 + 0.0518169i) q^{48} +(-2.07663 + 3.59683i) q^{49} +(0.182783 - 0.153374i) q^{51} +(4.32457 + 11.8817i) q^{52} +(0.653921 - 1.79663i) q^{53} +(0.0773952 + 0.0649423i) q^{54} +1.40806 q^{56} +(-0.205696 + 0.281019i) q^{57} +1.53116i q^{58} +(-0.616931 + 3.49879i) q^{59} +(7.42370 + 2.70201i) q^{61} +(0.292684 + 0.804142i) q^{62} +(3.24666 + 3.86922i) q^{63} +(-3.47569 - 6.02008i) q^{64} +(-0.00844998 - 0.0479222i) q^{66} +(2.23091 - 0.393370i) q^{67} +(5.05762 + 2.92002i) q^{68} +(0.329870 + 0.571352i) q^{69} +(-9.79389 + 3.56469i) q^{71} +(-0.854469 + 2.34764i) q^{72} +(-0.907529 + 1.08155i) q^{73} +(-0.291992 + 1.65597i) q^{74} +(-8.18520 - 2.37846i) q^{76} -4.87066i q^{77} +(-0.107339 - 0.0189268i) q^{78} +(1.84675 + 1.54961i) q^{79} +(-8.40329 + 3.05855i) q^{81} +(-0.739923 - 0.881806i) q^{82} +(-9.87319 + 5.70029i) q^{83} +(0.131802 - 0.228287i) q^{84} +(-0.195335 - 1.10780i) q^{86} +(0.502142 + 0.289912i) q^{87} +(2.08638 - 1.20457i) q^{88} +(7.74938 - 6.50250i) q^{89} +(-10.2517 - 3.73131i) q^{91} +(-10.3794 + 12.3697i) q^{92} +(0.319133 + 0.0562718i) q^{93} -0.348041 q^{94} +0.196310 q^{96} +(9.71828 + 1.71360i) q^{97} +(0.563256 - 0.671262i) q^{98} +(8.12075 + 2.95571i) 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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