LMFDB - Embedded newform 975.2.bn.d.257.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.12
Character	$\chi$	$=$	975.257
Dual form			975.2.bn.d.368.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0288234 + 0.107570i) q^{2} +(-1.51684 + 0.836177i) q^{3} +(1.72131 + 0.993799i) q^{4} +(-0.0462274 - 0.187269i) q^{6} +(1.03453 + 3.86093i) q^{7} +(-0.314011 + 0.314011i) q^{8} +(1.60161 - 2.53670i) q^{9} +(2.60494 + 4.51189i) q^{11} +(-3.44195 - 0.0681144i) q^{12} +(3.33885 - 1.36091i) q^{13} -0.445140 q^{14} +(1.96287 + 3.39979i) q^{16} +(-0.878092 - 3.27708i) q^{17} +(0.226709 + 0.245402i) q^{18} +(0.210416 - 0.364452i) q^{19} +(-4.79764 - 4.99136i) q^{21} +(-0.560429 + 0.150166i) q^{22} +(0.705071 - 2.63136i) q^{23} +(0.213736 - 0.738874i) q^{24} +(0.0501565 + 0.398387i) q^{26} +(-0.308267 + 5.18700i) q^{27} +(-2.05624 + 7.67398i) q^{28} +(-2.52506 - 4.37354i) q^{29} +4.23553i q^{31} +(-1.28019 + 0.343025i) q^{32} +(-7.72402 - 4.66563i) q^{33} +0.377826 q^{34} +(5.27784 - 2.77476i) q^{36} +(5.74223 + 1.53863i) q^{37} +(0.0331393 + 0.0331393i) q^{38} +(-3.92655 + 4.85615i) q^{39} +(-0.973131 - 1.68551i) q^{41} +(0.675207 - 0.372216i) q^{42} +(0.242554 + 0.905224i) q^{43} +10.3551i q^{44} +(0.262734 + 0.151689i) q^{46} +(1.29449 + 1.29449i) q^{47} +(-5.82019 - 3.51564i) q^{48} +(-7.77434 + 4.48852i) q^{49} +(4.07215 + 4.23657i) q^{51} +(7.09967 + 0.975600i) q^{52} +(-2.45762 - 2.45762i) q^{53} +(-0.549082 - 0.182667i) q^{54} +(-1.53723 - 0.887520i) q^{56} +(-0.0144218 + 0.728761i) q^{57} +(0.543244 - 0.145562i) q^{58} +(-7.83433 - 4.52315i) q^{59} +(2.65934 - 4.60611i) q^{61} +(-0.455618 - 0.122082i) q^{62} +(11.4509 + 3.55942i) q^{63} +7.70388i q^{64} +(0.724516 - 0.696396i) q^{66} +(-7.41523 - 1.98691i) q^{67} +(1.74529 - 6.51352i) q^{68} +(1.13080 + 4.58092i) q^{69} +(-6.09876 + 10.5634i) q^{71} +(0.293626 + 1.29948i) q^{72} +(-1.29733 - 1.29733i) q^{73} +(-0.331021 + 0.573345i) q^{74} +(0.724384 - 0.418223i) q^{76} +(-14.7252 + 14.7252i) q^{77} +(-0.409202 - 0.562351i) q^{78} -2.49102i q^{79} +(-3.86966 - 8.12562i) q^{81} +(0.209360 - 0.0560979i) q^{82} +(-9.55183 + 9.55183i) q^{83} +(-3.29782 - 13.3596i) q^{84} -0.104367 q^{86} +(7.48717 + 4.52256i) q^{87} +(-2.23476 - 0.598803i) q^{88} +(3.74597 - 2.16273i) q^{89} +(8.70853 + 11.4832i) q^{91} +(3.82869 - 3.82869i) q^{92} +(-3.54166 - 6.42463i) q^{93} +(-0.176560 + 0.101937i) q^{94} +(1.65501 - 1.59078i) q^{96} +(0.740590 + 2.76392i) q^{97} +(-0.258749 - 0.965663i) q^{98} +(15.6174 + 0.618364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.0288234	+	0.107570i	−0.0203812	+	0.0760637i	−0.975367	−	0.220586i	$-0.929203\pi$
$2$	−0.0288234	+	0.107570i	−0.0203812	+	0.0760637i	0.954986	+	0.296650i	$0.0958695\pi$
$3$	−1.51684	+	0.836177i	−0.875749	+	0.482767i
$3$	−1.51684	+	0.836177i	−0.875749	+	0.482767i
$4$	1.72131	+	0.993799i	0.860655	+	0.496899i
$5$		0			0
$5$		0			0
$6$	−0.0462274	−	0.187269i	−0.0188723	−	0.0764521i
$7$	1.03453	+	3.86093i	0.391017	+	1.45929i	0.828460	+	0.560048i	$0.189217\pi$
$7$	1.03453	+	3.86093i	0.391017	+	1.45929i	−0.437443	+	0.899246i	$0.644116\pi$
$8$	−0.314011	+	0.314011i	−0.111020	+	0.111020i
$9$	1.60161	−	2.53670i	0.533872	−	0.845566i
$10$		0			0
$11$	2.60494	+	4.51189i	0.785419	+	1.36039i	0.928748	+	0.370711i	$0.120886\pi$
$11$	2.60494	+	4.51189i	0.785419	+	1.36039i	−0.143329	+	0.989675i	$0.545781\pi$
$12$	−3.44195	−	0.0681144i	−0.993604	−	0.0196629i
$13$	3.33885	−	1.36091i	0.926031	−	0.377448i
$13$	3.33885	−	1.36091i	0.926031	−	0.377448i
$14$	−0.445140			−0.118969
$15$		0			0
$16$	1.96287	+	3.39979i	0.490718	+	0.849948i
$17$	−0.878092	−	3.27708i	−0.212969	−	0.794809i	−0.986872	−	0.161506i	$-0.948365\pi$
$17$	−0.878092	−	3.27708i	−0.212969	−	0.794809i	0.773903	−	0.633304i	$-0.218302\pi$
$18$	0.226709	+	0.245402i	0.0534359	+	0.0578419i
$19$	0.210416	−	0.364452i	0.0482728	−	0.0836110i	−0.840879	−	0.541223i	$-0.817962\pi$
$19$	0.210416	−	0.364452i	0.0482728	−	0.0836110i	0.889152	+	0.457612i	$0.151295\pi$
$20$		0			0
$21$	−4.79764	−	4.99136i	−1.04693	−	1.08920i
$22$	−0.560429	+	0.150166i	−0.119484	+	0.0320156i
$23$	0.705071	−	2.63136i	0.147017	−	0.548676i	−0.852640	−	0.522499i	$-0.825000\pi$
$23$	0.705071	−	2.63136i	0.147017	−	0.548676i	0.999657	−	0.0261774i	$-0.00833348\pi$
$24$	0.213736	−	0.738874i	0.0436287	−	0.150822i
$25$		0			0
$26$	0.0501565	+	0.398387i	0.00983649	+	0.0781302i
$27$	−0.308267	+	5.18700i	−0.0593259	+	0.998239i
$28$	−2.05624	+	7.67398i	−0.388592	+	1.45024i
$29$	−2.52506	−	4.37354i	−0.468892	−	0.812146i	0.530475	−	0.847700i	$-0.322013\pi$
$29$	−2.52506	−	4.37354i	−0.468892	−	0.812146i	−0.999368	+	0.0355548i	$0.988680\pi$
$30$		0			0
$31$			4.23553i			0.760724i	0.924838	+	0.380362i	$0.124201\pi$
$31$			4.23553i			0.760724i	−0.924838	+	0.380362i	$0.875799\pi$
$32$	−1.28019	+	0.343025i	−0.226307	+	0.0606389i
$33$	−7.72402	−	4.66563i	−1.34458	−	0.812181i
$34$	0.377826			0.0647967
$35$		0			0
$36$	5.27784	−	2.77476i	0.879640	−	0.462460i
$37$	5.74223	+	1.53863i	0.944017	+	0.252949i	0.697822	−	0.716272i	$-0.254153\pi$
$37$	5.74223	+	1.53863i	0.944017	+	0.252949i	0.246195	+	0.969220i	$0.420820\pi$
$38$	0.0331393	+	0.0331393i	0.00537590	+	0.00537590i
$39$	−3.92655	+	4.85615i	−0.628751	+	0.777607i
$40$		0			0
$41$	−0.973131	−	1.68551i	−0.151978	−	0.263233i	0.779977	−	0.625808i	$-0.215231\pi$
$41$	−0.973131	−	1.68551i	−0.151978	−	0.263233i	−0.931954	+	0.362576i	$0.881897\pi$
$42$	0.675207	−	0.372216i	0.104187	−	0.0574342i
$43$	0.242554	+	0.905224i	0.0369892	+	0.138045i	0.981951	−	0.189135i	$-0.0605683\pi$
$43$	0.242554	+	0.905224i	0.0369892	+	0.138045i	−0.944962	+	0.327180i	$0.893902\pi$
$44$			10.3551i			1.56110i
$45$		0			0
$46$	0.262734	+	0.151689i	0.0387380	+	0.0223654i
$47$	1.29449	+	1.29449i	0.188821	+	0.188821i	0.795186	−	0.606365i	$-0.207373\pi$
$47$	1.29449	+	1.29449i	0.188821	+	0.188821i	−0.606365	+	0.795186i	$0.707373\pi$
$48$	−5.82019	−	3.51564i	−0.840072	−	0.507438i
$49$	−7.77434	+	4.48852i	−1.11062	+	0.641217i
$50$		0			0
$51$	4.07215	+	4.23657i	0.570215	+	0.593239i
$52$	7.09967	+	0.975600i	0.984547	+	0.135291i
$53$	−2.45762	−	2.45762i	−0.337580	−	0.337580i	0.517876	−	0.855456i	$-0.326723\pi$
$53$	−2.45762	−	2.45762i	−0.337580	−	0.337580i	−0.855456	+	0.517876i	$0.826723\pi$
$54$	−0.549082	−	0.182667i	−0.0747206	−	0.0248579i
$55$		0			0
$56$	−1.53723	−	0.887520i	−0.205421	−	0.118600i
$57$	−0.0144218	+	0.728761i	−0.00191022	+	0.0965268i
$58$	0.543244	−	0.145562i	0.0713314	−	0.0191132i
$59$	−7.83433	−	4.52315i	−1.01994	−	0.588865i	−0.105856	−	0.994381i	$-0.533758\pi$
$59$	−7.83433	−	4.52315i	−1.01994	−	0.588865i	−0.914088	+	0.405517i	$0.867092\pi$
$60$		0			0
$61$	2.65934	−	4.60611i	0.340493	−	0.589752i	−0.644031	−	0.764999i	$-0.722739\pi$
$61$	2.65934	−	4.60611i	0.340493	−	0.589752i	0.984524	+	0.175248i	$0.0560726\pi$
$62$	−0.455618	−	0.122082i	−0.0578635	−	0.0155045i
$63$	11.4509	+	3.55942i	1.44268	+	0.448445i
$64$			7.70388i			0.962986i
$65$		0			0
$66$	0.724516	−	0.696396i	0.0891817	−	0.0857205i
$67$	−7.41523	−	1.98691i	−0.905915	−	0.242739i	−0.224360	−	0.974506i	$-0.572029\pi$
$67$	−7.41523	−	1.98691i	−0.905915	−	0.242739i	−0.681555	+	0.731767i	$0.738696\pi$
$68$	1.74529	−	6.51352i	0.211648	−	0.789881i
$69$	1.13080	+	4.58092i	0.136133	+	0.551478i
$70$		0			0
$71$	−6.09876	+	10.5634i	−0.723789	+	1.25364i	0.235681	+	0.971830i	$0.424268\pi$
$71$	−6.09876	+	10.5634i	−0.723789	+	1.25364i	−0.959470	+	0.281809i	$0.909065\pi$
$72$	0.293626	+	1.29948i	0.0346042	+	0.153145i
$73$	−1.29733	−	1.29733i	−0.151841	−	0.151841i	0.627099	−	0.778940i	$-0.284242\pi$
$73$	−1.29733	−	1.29733i	−0.151841	−	0.151841i	−0.778940	+	0.627099i	$0.784242\pi$
$74$	−0.331021	+	0.573345i	−0.0384804	+	0.0666500i
$75$		0			0
$76$	0.724384	−	0.418223i	0.0830925	−	0.0479735i
$77$	−14.7252	+	14.7252i	−1.67809	+	1.67809i
$78$	−0.409202	−	0.562351i	−0.0463330	−	0.0636737i
$79$		−	2.49102i		−	0.280262i	−0.990133	−	0.140131i	$-0.955248\pi$
$79$		−	2.49102i		−	0.280262i	0.990133	−	0.140131i	$-0.0447523\pi$
$80$		0			0
$81$	−3.86966	−	8.12562i	−0.429962	−	0.902847i
$82$	0.209360	−	0.0560979i	0.0231200	−	0.00619497i
$83$	−9.55183	+	9.55183i	−1.04845	+	1.04845i	−0.0496844	+	0.998765i	$0.515822\pi$
$83$	−9.55183	+	9.55183i	−1.04845	+	1.04845i	−0.998765	+	0.0496844i	$0.984178\pi$
$84$	−3.29782	−	13.3596i	−0.359822	−	1.45765i
$85$		0			0
$86$	−0.104367			−0.0112541
$87$	7.48717	+	4.52256i	0.802709	+	0.484870i
$88$	−2.23476	−	0.598803i	−0.238227	−	0.0638326i
$89$	3.74597	−	2.16273i	0.397072	−	0.229249i	−0.288148	−	0.957586i	$-0.593040\pi$
$89$	3.74597	−	2.16273i	0.397072	−	0.229249i	0.685220	+	0.728336i	$0.259706\pi$
$90$		0			0
$91$	8.70853	+	11.4832i	0.912901	+	1.20376i
$92$	3.82869	−	3.82869i	0.399168	−	0.399168i
$93$	−3.54166	−	6.42463i	−0.367253	−	0.666203i
$94$	−0.176560	+	0.101937i	−0.0182108	+	0.0105140i
$95$		0			0
$96$	1.65501	−	1.59078i	0.168914	−	0.162358i
$97$	0.740590	+	2.76392i	0.0751955	+	0.280633i	0.993278	−	0.115757i	$-0.0369294\pi$
$97$	0.740590	+	2.76392i	0.0751955	+	0.280633i	−0.918082	+	0.396390i	$0.870263\pi$
$98$	−0.258749	−	0.965663i	−0.0261376	−	0.0975467i
$99$	15.6174	+	0.618364i	1.56961	+	0.0621479i
$100$		0			0
$101$	2.39453	−	1.38248i	0.238265	−	0.137562i	−0.376114	−	0.926573i	$-0.622740\pi$
$101$	2.39453	−	1.38248i	0.238265	−	0.137562i	0.614379	+	0.789011i	$0.289407\pi$
$102$	−0.573103	+	0.315930i	−0.0567456	+	0.0312817i
$103$	−0.0455864	+	0.0455864i	−0.00449176	+	0.00449176i	−0.709349	−	0.704857i	$-0.751011\pi$
$103$	−0.0455864	+	0.0455864i	−0.00449176	+	0.00449176i	0.704857	+	0.709349i	$0.251011\pi$
$104$	−0.621096	+	1.47578i	−0.0609035	+	0.144712i
$105$		0			0
$106$	0.335204	−	0.193530i	0.0325579	−	0.0187973i
$107$	16.4075	+	4.39639i	1.58618	+	0.425015i	0.940831	−	0.338875i	$-0.110046\pi$
$107$	16.4075	+	4.39639i	1.58618	+	0.425015i	0.645346	+	0.763890i	$0.276713\pi$
$108$	−5.68546	+	8.62208i	−0.547083	+	0.829660i
$109$	4.73152			0.453198			0.226599	−	0.973988i	$-0.427239\pi$
$109$	4.73152			0.453198			0.226599	+	0.973988i	$0.427239\pi$
$110$		0			0
$111$	−9.99662	+	2.46767i	−0.948837	+	0.234221i
$112$	−11.0957	+	11.0957i	−1.04845	+	1.04845i
$113$	2.72351	−	0.729762i	0.256206	−	0.0686502i	−0.128430	−	0.991719i	$-0.540994\pi$
$113$	2.72351	−	0.729762i	0.256206	−	0.0686502i	0.384636	+	0.923068i	$0.374327\pi$
$114$	−0.0779774	−	0.0225567i	−0.00730325	−	0.00211263i
$115$		0			0
$116$		−	10.0376i		−	0.931970i
$117$	1.89534	−	10.6493i	0.175224	−	0.984529i
$118$	0.712369	−	0.712369i	0.0655789	−	0.0655789i
$119$	11.7442	−	6.78050i	1.07659	−	0.621567i
$120$		0			0
$121$	−8.07143	+	13.9801i	−0.733766	+	1.27092i
$122$	0.418829	+	0.418829i	0.0379190	+	0.0379190i
$123$	2.88547	+	1.74294i	0.260174	+	0.157156i
$124$	−4.20927	+	7.29067i	−0.378003	+	0.654721i
$125$		0			0
$126$	−0.712943	+	1.12919i	−0.0635140	+	0.100596i
$127$	−0.468909	+	1.74999i	−0.0416089	+	0.155287i	−0.983605	−	0.180338i	$-0.942281\pi$
$127$	−0.468909	+	1.74999i	−0.0416089	+	0.155287i	0.941996	+	0.335625i	$0.108947\pi$
$128$	−3.38909	−	0.908103i	−0.299556	−	0.0802657i
$129$	−1.12484	−	1.17026i	−0.0990370	−	0.103036i
$130$		0			0
$131$		−	20.2873i		−	1.77251i	−0.463200	−	0.886254i	$-0.653299\pi$
$131$		−	20.2873i		−	1.77251i	0.463200	−	0.886254i	$-0.346701\pi$
$132$	−8.65874	−	15.7071i	−0.753647	−	1.36713i
$133$	1.62481	+	0.435365i	0.140889	+	0.0377510i
$134$	0.427464	−	0.740390i	0.0369273	−	0.0639599i
$135$		0			0
$136$	1.30477	+	0.753310i	0.111883	+	0.0645958i
$137$	−12.9118	+	3.45972i	−1.10313	+	0.295584i	−0.764040	−	0.645169i	$-0.776787\pi$
$137$	−12.9118	+	3.45972i	−1.10313	+	0.295584i	−0.339093	+	0.940753i	$0.610120\pi$
$138$	−0.525365	−	0.0103967i	−0.0447220	−	0.000885026i
$139$	−17.9438	−	10.3598i	−1.52197	−	0.878710i	−0.999663	−	0.0259523i	$-0.991738\pi$
$139$	−17.9438	−	10.3598i	−1.52197	−	0.878710i	−0.522307	−	0.852758i	$-0.674928\pi$
$140$		0			0
$141$	−3.04596	−	0.881112i	−0.256516	−	0.0742030i
$142$	−0.960517	−	0.960517i	−0.0806048	−	0.0806048i
$143$	14.8378	+	11.5194i	1.24080	+	0.963304i
$144$	11.7680	+	0.465948i	0.980667	+	0.0388290i
$145$		0			0
$146$	0.176948	−	0.102161i	0.0146443	−	0.00845490i
$147$	8.03924	−	13.3091i	0.663066	−	1.09772i
$148$	8.35507	+	8.35507i	0.686783	+	0.686783i
$149$	7.82540	+	4.51800i	0.641082	+	0.370129i	0.785031	−	0.619456i	$-0.212647\pi$
$149$	7.82540	+	4.51800i	0.641082	+	0.370129i	−0.143949	+	0.989585i	$0.545980\pi$
$150$		0			0
$151$		−	11.7129i		−	0.953180i	−0.879126	−	0.476590i	$-0.841873\pi$
$151$		−	11.7129i		−	0.953180i	0.879126	−	0.476590i	$-0.158127\pi$
$152$	0.0483689	+	0.180515i	0.00392323	+	0.0146417i
$153$	−9.71933	−	3.02117i	−0.785761	−	0.244247i
$154$	−1.15956	−	2.00842i	−0.0934403	−	0.161843i
$155$		0			0
$156$	−11.5848	+	4.45675i	−0.927530	+	0.356826i
$157$	−11.2708	−	11.2708i	−0.899508	−	0.899508i	0.0958846	−	0.995392i	$-0.469432\pi$
$157$	−11.2708	−	11.2708i	−0.899508	−	0.899508i	−0.995392	+	0.0958846i	$0.969432\pi$
$158$	0.267960	+	0.0717997i	0.0213177	+	0.00571207i
$159$	5.78282	+	1.67281i	0.458608	+	0.132663i
$160$		0			0
$161$	10.8889			0.858167
$162$	0.985613	−	0.182053i	0.0774370	−	0.0143034i
$163$	12.3808	−	3.31744i	0.969742	−	0.259842i	0.261023	−	0.965333i	$-0.415940\pi$
$163$	12.3808	−	3.31744i	0.969742	−	0.259842i	0.708719	+	0.705491i	$0.249273\pi$
$164$		−	3.86839i		−	0.302070i
$165$		0			0
$166$	−0.752177	−	1.30281i	−0.0583803	−	0.101118i
$167$	5.83706	−	21.7842i	0.451685	−	1.68571i	−0.245968	−	0.969278i	$-0.579106\pi$
$167$	5.83706	−	21.7842i	0.451685	−	1.68571i	0.697654	−	0.716435i	$-0.254227\pi$
$168$	3.07386	+	0.0608301i	0.237153	+	0.00469315i
$169$	9.29585	−	9.08774i	0.715066	−	0.699057i
$170$		0			0
$171$	−0.587498	−	1.11747i	−0.0449271	−	0.0854554i
$172$	−0.482100	+	1.79922i	−0.0367598	+	0.137189i
$173$	3.49516	−	0.936524i	0.265732	−	0.0712026i	−0.123493	−	0.992345i	$-0.539410\pi$
$173$	3.49516	−	0.936524i	0.265732	−	0.0712026i	0.389225	+	0.921143i	$0.372743\pi$
$174$	−0.702299	+	0.675042i	−0.0532412	+	0.0511748i
$175$		0			0
$176$	−10.2263	+	17.7125i	−0.770838	+	1.33513i
$177$	15.6656	+	0.310014i	1.17750	+	0.0233021i
$178$	0.124675	+	0.465292i	0.00934476	+	0.0348751i
$179$	2.91155	+	5.04296i	0.217620	+	0.376928i	0.954080	−	0.299553i	$-0.0968374\pi$
$179$	2.91155	+	5.04296i	0.217620	+	0.376928i	−0.736460	+	0.676481i	$0.763504\pi$
$180$		0			0
$181$	9.95426			0.739894			0.369947	−	0.929053i	$-0.379376\pi$
$181$	9.95426			0.739894			0.369947	+	0.929053i	$0.379376\pi$
$182$	−1.48626	+	0.605795i	−0.110169	+	0.0449045i
$183$	−0.182270	+	9.21041i	−0.0134738	+	0.680853i
$184$	0.604876	+	1.04768i	0.0445921	+	0.0772357i
$185$		0			0
$186$	0.793182	−	0.195798i	0.0581590	−	0.0143566i
$187$	12.4985	−	12.4985i	0.913978	−	0.913978i
$188$	0.941755	+	3.51468i	0.0686846	+	0.256334i
$189$	−20.3456	+	4.17593i	−1.47992	+	0.303754i
$190$		0			0
$191$	19.8105	+	11.4376i	1.43343	+	0.827594i	0.997381	−	0.0723271i	$-0.0230425\pi$
$191$	19.8105	+	11.4376i	1.43343	+	0.827594i	0.436053	+	0.899921i	$0.356376\pi$
$192$	−6.44181	−	11.6856i	−0.464898	−	0.843333i
$193$	4.42994	−	16.5328i	0.318874	−	1.19005i	−0.601454	−	0.798908i	$-0.705412\pi$
$193$	4.42994	−	16.5328i	0.318874	−	1.19005i	0.920328	−	0.391147i	$-0.127922\pi$
$194$	−0.318662			−0.0228786
$195$		0			0
$196$	−17.8427			−1.27448
$197$	−0.382929	+	1.42911i	−0.0272826	+	0.101820i	−0.978225	−	0.207549i	$-0.933451\pi$
$197$	−0.382929	+	1.42911i	−0.0272826	+	0.101820i	0.950942	+	0.309369i	$0.100118\pi$
$198$	−0.516664	+	1.66215i	−0.0367177	+	0.118124i
$199$	−20.6928	−	11.9470i	−1.46687	−	0.846899i	−0.467558	−	0.883962i	$-0.654866\pi$
$199$	−20.6928	−	11.9470i	−1.46687	−	0.846899i	−0.999313	+	0.0370636i	$0.988200\pi$
$200$		0			0
$201$	12.9091	−	3.18663i	0.910540	−	0.224768i
$202$	0.0796957	+	0.297429i	0.00560737	+	0.0209270i
$203$	14.2737	−	14.2737i	1.00181	−	1.00181i
$204$	2.79913	+	11.3394i	0.195978	+	0.793914i
$205$		0			0
$206$	−0.00358979	−	0.00621770i	−0.000250113	−	0.000433208i
$207$	−5.54571	−	6.00297i	−0.385453	−	0.417236i
$208$	11.1805	+	8.68011i	0.775231	+	0.601857i
$209$	2.19249			0.151658
$210$		0			0
$211$	1.53923	+	2.66603i	0.105965	+	0.183537i	0.914132	−	0.405416i	$-0.132873\pi$
$211$	1.53923	+	2.66603i	0.105965	+	0.183537i	−0.808167	+	0.588953i	$0.799540\pi$
$212$	−1.78795	−	6.67270i	−0.122797	−	0.458283i
$213$	0.418005	−	21.1226i	0.0286413	−	1.44730i
$214$	−0.945842	+	1.63825i	−0.0646565	+	0.111988i
$215$		0			0
$216$	−1.53198	−	1.72558i	−0.104238	−	0.117411i
$217$	−16.3531	+	4.38180i	−1.11012	+	0.297456i
$218$	−0.136379	+	0.508972i	−0.00923672	+	0.0344719i
$219$	3.05264	+	0.883046i	0.206279	+	0.0596707i
$220$		0			0
$221$	−7.39163	−	9.74669i	−0.497215	−	0.655633i
$222$	0.0226880	−	1.14647i	0.00152272	−	0.0769458i
$223$	1.49616	−	5.58375i	0.100190	−	0.373916i	−0.897565	−	0.440883i	$-0.854666\pi$
$223$	1.49616	−	5.58375i	0.100190	−	0.373916i	0.997755	+	0.0669668i	$0.0213322\pi$
$224$	−2.64879	−	4.58784i	−0.176980	−	0.306538i
$225$		0			0
$226$			0.314003i			0.0208872i
$227$	14.1812	−	3.79984i	0.941238	−	0.252204i	0.244598	−	0.969625i	$-0.421344\pi$
$227$	14.1812	−	3.79984i	0.941238	−	0.252204i	0.696640	+	0.717421i	$0.254677\pi$
$228$	−0.749066	+	1.24009i	−0.0496081	+	0.0821271i
$229$	3.60574			0.238274			0.119137	−	0.992878i	$-0.461987\pi$
$229$	3.60574			0.238274			0.119137	+	0.992878i	$0.461987\pi$
$230$		0			0
$231$	10.0229	−	34.6486i	0.659459	−	2.27971i
$232$	2.16624	+	0.580442i	0.142220	+	0.0381079i
$233$	−7.88221	−	7.88221i	−0.516381	−	0.516381i	0.400093	−	0.916474i	$-0.368978\pi$
$233$	−7.88221	−	7.88221i	−0.516381	−	0.516381i	−0.916474	+	0.400093i	$0.868978\pi$
$234$	1.09092	+	0.510831i	0.0713156	+	0.0333941i
$235$		0			0
$236$	−8.99021	−	15.5715i	−0.585213	−	1.01362i
$237$	2.08294	+	3.77848i	0.135301	+	0.245439i
$238$	0.390874	+	1.45876i	0.0253366	+	0.0945575i
$239$		−	0.0947772i		−	0.00613063i	−0.999995	−	0.00306532i	$-0.999024\pi$
$239$		−	0.0947772i		−	0.00613063i	0.999995	−	0.00306532i	$-0.000975722\pi$
$240$		0			0
$241$	9.34499	+	5.39533i	0.601964	+	0.347544i	0.769814	−	0.638269i	$-0.220349\pi$
$241$	9.34499	+	5.39533i	0.601964	+	0.347544i	−0.167850	+	0.985813i	$0.553682\pi$
$242$	−1.27120	−	1.27120i	−0.0817159	−	0.0817159i
$243$	12.6641	+	9.08955i	0.812404	+	0.583095i
$244$	9.15509	−	5.28569i	0.586095	−	0.338382i
$245$		0			0
$246$	−0.270658	+	0.260154i	−0.0172565	+	0.0165868i
$247$	0.206563	−	1.50321i	0.0131433	−	0.0956468i
$248$	−1.33000	−	1.33000i	−0.0844554	−	0.0844554i
$249$	6.50158	−	22.4756i	0.412021	−	1.42434i
$250$		0			0
$251$	−18.5242	−	10.6949i	−1.16923	−	0.675058i	−0.215735	−	0.976452i	$-0.569215\pi$
$251$	−18.5242	−	10.6949i	−1.16923	−	0.675058i	−0.953500	+	0.301394i	$0.902548\pi$
$252$	16.1733	+	17.5068i	1.01882	+	1.10282i
$253$	13.7091	−	3.67333i	0.861882	−	0.230941i
$254$	−0.174732	−	0.100881i	−0.0109636	−	0.00632986i
$255$		0			0
$256$	−7.50851	+	13.0051i	−0.469282	+	0.812821i
$257$	15.6729	+	4.19954i	0.977648	+	0.261960i	0.712054	−	0.702125i	$-0.247765\pi$
$257$	15.6729	+	4.19954i	0.977648	+	0.261960i	0.265594	+	0.964085i	$0.414432\pi$
$258$	0.158307	−	0.0872689i	0.00985579	−	0.00543313i
$259$			23.7621i			1.47651i
$260$		0			0
$261$	−15.1385	−	0.599402i	−0.937051	−	0.0371021i
$262$	2.18231	+	0.584748i	0.134824	+	0.0361259i
$263$	−5.94046	+	22.1701i	−0.366304	+	1.36707i	0.499340	+	0.866406i	$0.333576\pi$
$263$	−5.94046	+	22.1701i	−0.366304	+	1.36707i	−0.865644	+	0.500660i	$0.833091\pi$
$264$	3.89049	−	0.960370i	0.239443	−	0.0591067i
$265$		0			0
$266$	−0.0936648	+	0.162232i	−0.00574296	+	0.00994709i
$267$	−3.87361	+	6.41282i	−0.237061	+	0.392458i
$268$	−10.7893	−	10.7893i	−0.659063	−	0.659063i
$269$	1.73455	−	3.00433i	0.105758	−	0.183177i	−0.808290	−	0.588785i	$-0.799607\pi$
$269$	1.73455	−	3.00433i	0.105758	−	0.183177i	0.914047	+	0.405607i	$0.132940\pi$
$270$		0			0
$271$	10.2881	−	5.93984i	0.624958	−	0.360819i	−0.153839	−	0.988096i	$-0.549164\pi$
$271$	10.2881	−	5.93984i	0.624958	−	0.360819i	0.778797	+	0.627277i	$0.215830\pi$
$272$	9.41782	−	9.41782i	0.571039	−	0.571039i
$273$	−22.8114	−	10.1363i	−1.38061	−	0.613475i
$274$		−	1.48865i		−	0.0899328i
$275$		0			0
$276$	−2.60605	+	9.00897i	−0.156866	+	0.542276i
$277$	−16.6029	+	4.44872i	−0.997570	+	0.267298i	−0.720427	−	0.693531i	$-0.756054\pi$
$277$	−16.6029	+	4.44872i	−0.997570	+	0.267298i	−0.277143	+	0.960829i	$0.589387\pi$
$278$	1.63161	−	1.63161i	0.0978575	−	0.0978575i
$279$	10.7443	+	6.78369i	0.643242	+	0.406129i
$280$		0			0
$281$	22.1387			1.32068			0.660341	−	0.750966i	$-0.270412\pi$
$281$	22.1387			1.32068			0.660341	+	0.750966i	$0.270412\pi$
$282$	0.182576	−	0.302258i	0.0108723	−	0.0179992i
$283$	−2.73331	−	0.732387i	−0.162478	−	0.0435359i	0.176663	−	0.984271i	$-0.443470\pi$
$283$	−2.73331	−	0.732387i	−0.162478	−	0.0435359i	−0.339141	+	0.940736i	$0.610136\pi$
$284$	−20.9957	+	12.1219i	−1.24587	+	0.719301i
$285$		0			0
$286$	−1.66682	+	1.26408i	−0.0985614	+	0.0747464i
$287$	5.50091	−	5.50091i	0.324708	−	0.324708i
$288$	−1.18022	+	3.79684i	−0.0695449	+	0.223731i
$289$	4.75421	−	2.74484i	0.279659	−	0.161461i
$290$		0			0
$291$	−3.43448	−	3.57316i	−0.201333	−	0.209462i
$292$	−0.943823	−	3.52240i	−0.0552331	−	0.206133i
$293$	2.04676	+	7.63862i	0.119573	+	0.446253i	0.999588	−	0.0286927i	$-0.00913443\pi$
$293$	2.04676	+	7.63862i	0.119573	+	0.446253i	−0.880015	+	0.474946i	$0.842468\pi$
$294$	1.19995	+	1.24840i	0.0699823	+	0.0728080i
$295$		0			0
$296$	−2.28627	+	1.31998i	−0.132887	+	0.0767222i
$297$	−24.2062	+	12.1210i	−1.40459	+	0.703329i
$298$	−0.711557	+	0.711557i	−0.0412194	+	0.0412194i
$299$	−1.22691	−	9.74525i	−0.0709543	−	0.563583i
$300$		0			0
$301$	−3.24408	+	1.87297i	−0.186985	+	0.107956i
$302$	1.25996	+	0.337605i	0.0725024	+	0.0194270i
$303$	−2.47612	+	4.09926i	−0.142250	+	0.235496i
$304$	1.65208			0.0947533
$305$		0			0
$306$	0.605132	−	0.958431i	0.0345931	−	0.0547899i
$307$	10.6962	−	10.6962i	0.610465	−	0.610465i	−0.332602	−	0.943067i	$-0.607927\pi$
$307$	10.6962	−	10.6962i	0.610465	−	0.610465i	0.943067	+	0.332602i	$0.107927\pi$
$308$	−39.9805	+	10.7127i	−2.27810	+	0.610415i
$309$	0.0310290	−	0.107266i	0.00176518	−	0.00610213i
$310$		0			0
$311$			12.0194i			0.681560i	0.940143	+	0.340780i	$0.110691\pi$
$311$			12.0194i			0.681560i	−0.940143	+	0.340780i	$0.889309\pi$
$312$	−0.291908	−	2.75787i	−0.0165260	−	0.156133i
$313$	−16.5079	+	16.5079i	−0.933082	+	0.933082i	−0.997897	−	0.0648148i	$-0.979354\pi$
$313$	−16.5079	+	16.5079i	−0.933082	+	0.933082i	0.0648148	+	0.997897i	$0.479354\pi$
$314$	1.53727	−	0.887541i	0.0867530	−	0.0500869i
$315$		0			0
$316$	2.47557	−	4.28782i	0.139262	−	0.241209i
$317$	0.778692	+	0.778692i	0.0437357	+	0.0437357i	0.728636	−	0.684901i	$-0.240154\pi$
$317$	0.778692	+	0.778692i	0.0437357	+	0.0437357i	−0.684901	+	0.728636i	$0.740154\pi$
$318$	−0.346626	+	0.573844i	−0.0194378	+	0.0321796i
$319$	13.1553	−	22.7856i	0.736554	−	1.27575i
$320$		0			0
$321$	−28.5638	+	7.05100i	−1.59428	+	0.393548i
$322$	−0.313855	+	1.17132i	−0.0174905	+	0.0652753i
$323$	−1.37910	−	0.369530i	−0.0767354	−	0.0205612i
$324$	1.41435	−	17.8324i	0.0785748	−	0.990688i
$325$		0			0
$326$			1.42743i			0.0790581i
$327$	−7.17697	+	3.95639i	−0.396887	+	0.218789i
$328$	0.834844	+	0.223696i	0.0460965	+	0.0123515i
$329$	−3.65874	+	6.33712i	−0.201713	+	0.349377i
$330$		0			0
$331$	−24.3850	−	14.0787i	−1.34032	−	0.773834i	−0.353466	−	0.935448i	$-0.614997\pi$
$331$	−24.3850	−	14.0787i	−1.34032	−	0.773834i	−0.986854	+	0.161614i	$0.948330\pi$
$332$	−25.9343	+	6.94906i	−1.42333	+	0.381379i
$333$	13.0999	−	12.1020i	0.717868	−	0.663186i
$334$	2.17509	+	1.25579i	0.119016	+	0.0687138i
$335$		0			0
$336$	7.55244	−	26.1084i	0.412019	−	1.42433i
$337$	17.9435	+	17.9435i	0.977446	+	0.977446i	0.999751	−	0.0223051i	$-0.00710052\pi$
$337$	17.9435	+	17.9435i	0.977446	+	0.977446i	−0.0223051	+	0.999751i	$0.507101\pi$
$338$	0.709634	+	1.26190i	0.0385990	+	0.0686382i
$339$	−3.52092	+	3.38427i	−0.191230	+	0.183808i
$340$		0			0
$341$	−19.1103	+	11.0333i	−1.03488	+	0.597487i
$342$	0.137141	−	0.0309880i	0.00741572	−	0.00167564i
$343$	−5.58789	−	5.58789i	−0.301717	−	0.301717i
$344$	−0.360415	−	0.208086i	−0.0194323	−	0.0112192i
$345$		0			0
$346$			0.402969i			0.0216637i
$347$	−0.129801	−	0.484424i	−0.00696808	−	0.0260052i	0.962354	−	0.271798i	$-0.0876183\pi$
$347$	−0.129801	−	0.484424i	−0.00696808	−	0.0260052i	−0.969322	+	0.245793i	$0.920952\pi$
$348$	8.39323	+	15.2255i	0.449924	+	0.816171i
$349$	4.63210	+	8.02304i	0.247951	+	0.429463i	0.962957	−	0.269655i	$-0.0869095\pi$
$349$	4.63210	+	8.02304i	0.247951	+	0.429463i	−0.715006	+	0.699118i	$0.753576\pi$
$350$		0			0
$351$	6.02978	+	17.7381i	0.321846	+	0.946792i
$352$	−4.88250	−	4.88250i	−0.260238	−	0.260238i
$353$	20.4549	+	5.48087i	1.08870	+	0.291717i	0.758157	−	0.652072i	$-0.226100\pi$
$353$	20.4549	+	5.48087i	1.08870	+	0.291717i	0.330547	+	0.943790i	$0.392767\pi$
$354$	−0.484884	+	1.67622i	−0.0257713	+	0.0890900i
$355$		0			0
$356$	8.59729			0.455656
$357$	−12.1443	+	20.1052i	−0.642747	+	1.06408i
$358$	−0.626394	+	0.167842i	−0.0331059	+	0.00887071i
$359$			17.7610i			0.937391i	0.883360	+	0.468695i	$0.155276\pi$
$359$			17.7610i			0.937391i	−0.883360	+	0.468695i	$0.844724\pi$
$360$		0			0
$361$	9.41145	+	16.3011i	0.495339	+	0.857953i
$362$	−0.286915	+	1.07078i	−0.0150799	+	0.0562791i
$363$	0.553211	−	27.9548i	0.0290361	−	1.46724i
$364$	3.57812	+	28.4206i	0.187544	+	1.48964i
$365$		0			0
$366$	−0.985514	−	0.285082i	−0.0515136	−	0.0149015i
$367$	0.292041	−	1.08991i	0.0152444	−	0.0568929i	−0.957885	−	0.287153i	$-0.907291\pi$
$367$	0.292041	−	1.08991i	0.0152444	−	0.0568929i	0.973129	+	0.230260i	$0.0739578\pi$
$368$	10.3300	−	2.76792i	0.538490	−	0.144288i
$369$	−5.83421	−	0.231003i	−0.303717	−	0.0120255i
$370$		0			0
$371$	6.94621	−	12.0312i	0.360629	−	0.624628i
$372$	0.288501	−	14.5785i	0.0149581	−	0.755859i
$373$	4.61559	+	17.2256i	0.238986	+	0.891908i	0.976311	+	0.216370i	$0.0694218\pi$
$373$	4.61559	+	17.2256i	0.238986	+	0.891908i	−0.737325	+	0.675538i	$0.763912\pi$
$374$	0.984215	+	1.70471i	0.0508926	+	0.0881485i
$375$		0			0
$376$	−0.812968			−0.0419256
$377$	−14.3828	−	11.1662i	−0.740752	−	0.575089i
$378$	0.137222	−	2.30894i	0.00705793	−	0.118759i
$379$	−5.17481	−	8.96303i	−0.265812	−	0.460400i	0.701964	−	0.712212i	$-0.252307\pi$
$379$	−5.17481	−	8.96303i	−0.265812	−	0.460400i	−0.967776	+	0.251813i	$0.918973\pi$
$380$		0			0
$381$	−0.752043	−	3.04655i	−0.0385283	−	0.156079i
$382$	−1.80135	+	1.80135i	−0.0921650	+	0.0921650i
$383$	−4.29989	−	16.0474i	−0.219714	−	0.819985i	−0.984454	−	0.175645i	$-0.943799\pi$
$383$	−4.29989	−	16.0474i	−0.219714	−	0.819985i	0.764739	−	0.644340i	$-0.222868\pi$
$384$	5.90004	−	1.45643i	0.301085	−	0.0743231i
$385$		0			0
$386$	1.65075	+	0.953061i	0.0840210	+	0.0485095i
$387$	2.68476	+	0.834534i	0.136474	+	0.0424218i
$388$	−1.47199	+	5.49356i	−0.0747292	+	0.278893i
$389$	−24.1762			−1.22578			−0.612891	−	0.790167i	$-0.709994\pi$
$389$	−24.1762			−1.22578			−0.612891	+	0.790167i	$0.709994\pi$
$390$		0			0
$391$	−9.24230			−0.467403
$392$	1.03179	−	3.85068i	0.0521130	−	0.194488i
$393$	16.9638	+	30.7726i	0.855709	+	1.55227i
$394$	−0.142693	−	0.0823836i	−0.00718875	−	0.00415043i
$395$		0			0
$396$	26.2679	+	16.5850i	1.32001	+	0.833425i
$397$	−2.21309	−	8.25936i	−0.111072	−	0.414525i	0.887891	−	0.460053i	$-0.152170\pi$
$397$	−2.21309	−	8.25936i	−0.111072	−	0.414525i	−0.998963	+	0.0455279i	$0.985503\pi$
$398$	1.88158	−	1.88158i	0.0943149	−	0.0943149i
$399$	−2.82861	+	0.698246i	−0.141608	+	0.0349560i
$400$		0			0
$401$	13.7400	+	23.7983i	0.686142	+	1.18843i	0.973076	+	0.230482i	$0.0740304\pi$
$401$	13.7400	+	23.7983i	0.686142	+	1.18843i	−0.286935	+	0.957950i	$0.592636\pi$
$402$	−0.0292982	+	1.48049i	−0.00146126	+	0.0738401i
$403$	5.76418	+	14.1418i	0.287134	+	0.704454i
$404$	5.49564			0.273418
$405$		0			0
$406$	1.12401	+	1.94684i	0.0557835	+	0.0966199i
$407$	8.01606	+	29.9163i	0.397341	+	1.48290i
$408$	−2.60903	−	0.0516315i	−0.129166	−	0.00255614i
$409$	−18.6648	+	32.3284i	−0.922916	+	1.59854i	−0.128038	+	0.991769i	$0.540868\pi$
$409$	−18.6648	+	32.3284i	−0.922916	+	1.59854i	−0.794878	+	0.606769i	$0.792465\pi$
$410$		0			0
$411$	16.6923	−	16.0444i	0.823369	−	0.791414i
$412$	−0.123772	+	0.0331646i	−0.00609781	+	0.00163390i
$413$	9.35870	−	34.9272i	0.460512	−	1.71865i
$414$	0.805588	−	0.423528i	0.0395925	−	0.0208153i
$415$		0			0
$416$	−3.80753	+	2.88753i	−0.186680	+	0.141573i
$417$	35.8805	+	0.710057i	1.75708	+	0.0347717i
$418$	−0.0631949	+	0.235847i	−0.00309097	+	0.0115356i
$419$	14.8413	+	25.7059i	0.725046	+	1.25582i	0.958955	+	0.283558i	$0.0915150\pi$
$419$	14.8413	+	25.7059i	0.725046	+	1.25582i	−0.233909	+	0.972259i	$0.575152\pi$
$420$		0			0
$421$		−	21.3437i		−	1.04023i	−0.854097	−	0.520114i	$-0.825889\pi$
$421$		−	21.3437i		−	1.04023i	0.854097	−	0.520114i	$-0.174111\pi$
$422$	−0.331151	+	0.0887317i	−0.0161202	+	0.00431939i
$423$	5.35700	−	1.21045i	0.260466	−	0.0588543i
$424$	1.54344			0.0749561
$425$		0			0
$426$	2.26011	+	0.653789i	0.109503	+	0.0316762i
$427$	20.5350	+	5.50234i	0.993760	+	0.266277i
$428$	23.8734	+	23.8734i	1.15396	+	1.15396i
$429$	−32.1388	−	5.06614i	−1.55168	−	0.244596i
$430$		0			0
$431$	1.45407	+	2.51852i	0.0700400	+	0.121313i	0.898919	−	0.438116i	$-0.144354\pi$
$431$	1.45407	+	2.51852i	0.0700400	+	0.121313i	−0.828879	+	0.559429i	$0.811021\pi$
$432$	−18.2398	+	9.13337i	−0.877563	+	0.439429i
$433$	−6.84446	−	25.5439i	−0.328924	−	1.22756i	−0.910308	−	0.413932i	$-0.864155\pi$
$433$	−6.84446	−	25.5439i	−0.328924	−	1.22756i	0.581384	−	0.813629i	$-0.302511\pi$
$434$		−	1.88541i		−	0.0905024i
$435$		0			0
$436$	8.14442	+	4.70218i	0.390047	+	0.225194i
$437$	−0.810645	−	0.810645i	−0.0387784	−	0.0387784i
$438$	−0.182977	+	0.302922i	−0.00874299	+	0.0144742i
$439$	23.2175	−	13.4046i	1.10811	−	0.639768i	0.169771	−	0.985484i	$-0.445697\pi$
$439$	23.2175	−	13.4046i	1.10811	−	0.639768i	0.938339	+	0.345716i	$0.112364\pi$
$440$		0			0
$441$	−1.06549	+	26.9100i	−0.0507376	+	1.28143i
$442$	1.26151	−	0.514187i	0.0600037	−	0.0244574i
$443$	−19.3624	−	19.3624i	−0.919937	−	0.919937i	0.0770872	−	0.997024i	$-0.475438\pi$
$443$	−19.3624	−	19.3624i	−0.919937	−	0.919937i	−0.997024	+	0.0770872i	$0.975438\pi$
$444$	−19.6596	−	5.68700i	−0.933006	−	0.269893i
$445$		0			0
$446$	0.557522	+	0.321885i	0.0263994	+	0.0152417i
$447$	−15.6477	−	0.309661i	−0.740113	−	0.0146465i
$448$	−29.7442	+	7.96992i	−1.40528	+	0.376543i
$449$	−3.02917	−	1.74889i	−0.142956	−	0.0825354i	0.426816	−	0.904338i	$-0.359635\pi$
$449$	−3.02917	−	1.74889i	−0.142956	−	0.0825354i	−0.569772	+	0.821803i	$0.692968\pi$
$450$		0			0
$451$	5.06990	−	8.78132i	0.238732	−	0.413496i
$452$	5.41324	+	1.45047i	0.254617	+	0.0682245i
$453$	9.79404	+	17.7666i	0.460164	+	0.834746i
$454$			1.63500i			0.0767343i
$455$		0			0
$456$	−0.224311	−	0.233368i	−0.0105043	−	0.0109284i
$457$	33.6949	+	9.02853i	1.57618	+	0.422337i	0.937742	−	0.347334i	$-0.112913\pi$
$457$	33.6949	+	9.02853i	1.57618	+	0.422337i	0.638441	+	0.769671i	$0.279580\pi$
$458$	−0.103930	+	0.387870i	−0.00485631	+	0.0181240i
$459$	17.2689	−	3.54445i	0.806044	−	0.165441i
$460$		0			0
$461$	−5.43399	+	9.41194i	−0.253086	+	0.438358i	−0.964374	−	0.264543i	$-0.914779\pi$
$461$	−5.43399	+	9.41194i	−0.253086	+	0.438358i	0.711288	+	0.702901i	$0.248112\pi$
$462$	3.43827	+	2.07686i	0.159963	+	0.0966242i
$463$	−6.69797	−	6.69797i	−0.311281	−	0.311281i	0.534125	−	0.845406i	$-0.320641\pi$
$463$	−6.69797	−	6.69797i	−0.311281	−	0.311281i	−0.845406	+	0.534125i	$0.820641\pi$
$464$	9.91274	−	17.1694i	0.460188	−	0.797068i
$465$		0			0
$466$	1.07508	−	0.620700i	0.0498023	−	0.0287534i
$467$	−4.56632	+	4.56632i	−0.211304	+	0.211304i	−0.804821	−	0.593517i	$-0.797739\pi$
$467$	−4.56632	+	4.56632i	−0.211304	+	0.211304i	0.593517	+	0.804821i	$0.297739\pi$
$468$	13.8457	−	16.4472i	0.640019	−	0.760271i
$469$		−	30.6852i		−	1.41691i
$470$		0			0
$471$	26.5204	+	7.67163i	1.22200	+	0.353490i
$472$	3.88039	−	1.03975i	0.178609	−	0.0478582i
$473$	−3.45243	+	3.45243i	−0.158743	+	0.158743i
$474$	−0.466490	+	0.115153i	−0.0214266	+	0.00528917i
$475$		0			0
$476$	26.9538			1.23543
$477$	−10.1704	+	2.29808i	−0.465670	+	0.105222i
$478$	0.0101952	+	0.00273180i	0.000466319	+	0.000124950i
$479$	13.8170	−	7.97728i	0.631317	−	0.364491i	−0.149945	−	0.988694i	$-0.547910\pi$
$479$	13.8170	−	7.97728i	0.631317	−	0.364491i	0.781262	+	0.624203i	$0.214576\pi$
$480$		0			0
$481$	21.2664	−	2.67741i	0.969664	−	0.122079i
$482$	−0.849732	+	0.849732i	−0.0387042	+	0.0387042i
$483$	−16.5168	+	9.10506i	−0.751538	+	0.414295i
$484$	−27.7869	+	16.0427i	−1.26304	+	0.729216i
$485$		0			0
$486$	−1.34279	+	1.10029i	−0.0609102	+	0.0499103i
$487$	−8.49708	−	31.7115i	−0.385040	−	1.43699i	−0.838104	−	0.545510i	$-0.816336\pi$
$487$	−8.49708	−	31.7115i	−0.385040	−	1.43699i	0.453065	−	0.891478i	$-0.350331\pi$
$488$	0.611308	+	2.28143i	0.0276726	+	0.103276i
$489$	−16.0058	+	15.3846i	−0.723807	+	0.695716i
$490$		0			0
$491$	−25.2561	+	14.5816i	−1.13979	+	0.658058i	−0.946379	−	0.323059i	$-0.895289\pi$
$491$	−25.2561	+	14.5816i	−1.13979	+	0.658058i	−0.193412	+	0.981118i	$0.561955\pi$
$492$	3.23466	+	5.86773i	0.145830	+	0.264538i
$493$	−12.1152	+	12.1152i	−0.545642	+	0.545642i
$494$	0.155747	+	0.0655476i	0.00700738	+	0.00294913i
$495$		0			0
$496$	−14.3999	+	8.31380i	−0.646576	+	0.373301i
$497$	−47.0937	−	12.6187i	−2.11244	−	0.566027i
$498$	2.23031	+	1.34720i	0.0999427	+	0.0603695i
$499$	16.7557			0.750087			0.375044	−	0.927007i	$-0.377628\pi$
$499$	16.7557			0.750087			0.375044	+	0.927007i	$0.377628\pi$
$500$		0			0
$501$	9.36157	+	37.9240i	0.418244	+	1.69432i
$502$	1.68439	−	1.68439i	0.0751778	−	0.0751778i
$503$	8.90077	−	2.38495i	0.396866	−	0.106340i	−0.0548660	−	0.998494i	$-0.517473\pi$
$503$	8.90077	−	2.38495i	0.396866	−	0.106340i	0.451732	+	0.892154i	$0.350806\pi$
$504$	−4.71342	+	2.47802i	−0.209952	+	0.110380i
$505$		0			0
$506$			1.58057i			0.0702648i
$507$	−6.50137	+	21.5576i	−0.288736	+	0.957409i
$508$	−2.54628	+	2.54628i	−0.112973	+	0.112973i
$509$	−0.476859	+	0.275315i	−0.0211364	+	0.0122031i	−0.510531	−	0.859859i	$-0.670551\pi$
$509$	−0.476859	+	0.275315i	−0.0211364	+	0.0122031i	0.489395	+	0.872062i	$0.337218\pi$
$510$		0			0
$511$	3.66677	−	6.35104i	0.162208	−	0.280953i
$512$	−6.14451	−	6.14451i	−0.271552	−	0.271552i
$513$	1.82555	+	1.20378i	0.0805999	+	0.0531481i
$514$	−0.903491	+	1.56489i	−0.0398513	+	0.0690245i
$515$		0			0
$516$	−0.773199	−	3.13225i	−0.0340382	−	0.137890i
$517$	−2.46852	+	9.21266i	−0.108566	+	0.405172i
$518$	−2.55610	−	0.684904i	−0.112308	−	0.0300930i
$519$	−4.51850	+	4.34313i	−0.198340	+	0.190642i
$520$		0			0
$521$		−	32.2002i		−	1.41072i	−0.708852	−	0.705358i	$-0.750786\pi$
$521$		−	32.2002i		−	1.41072i	0.708852	−	0.705358i	$-0.249214\pi$
$522$	0.500821	−	1.61118i	0.0219204	−	0.0705194i
$523$	−13.6311	−	3.65245i	−0.596048	−	0.159711i	−0.0518323	−	0.998656i	$-0.516506\pi$
$523$	−13.6311	−	3.65245i	−0.596048	−	0.159711i	−0.544216	+	0.838945i	$0.683173\pi$
$524$	20.1615	−	34.9207i	0.880758	−	1.52552i
$525$		0			0
$526$	−2.21362	−	1.27803i	−0.0965184	−	0.0557249i
$527$	13.8802	−	3.71919i	0.604631	−	0.162010i
$528$	0.700906	−	35.4181i	0.0305030	−	1.54137i
$529$	13.4917	+	7.78941i	0.586594	+	0.338670i
$530$		0			0
$531$	−24.0215	+	12.6290i	−1.04244	+	0.548051i
$532$	2.36413	+	2.36413i	0.102498	+	0.102498i
$533$	−5.54297	−	4.30333i	−0.240093	−	0.186398i
$534$	−0.578179	−	0.601524i	−0.0250202	−	0.0260305i
$535$		0			0
$536$	2.95238	−	1.70456i	0.127523	−	0.0736256i
$537$	−8.63317	−	5.21479i	−0.372549	−	0.225035i
$538$	0.273182	+	0.273182i	0.0117777	+	0.0117777i
$539$	−40.5034	−	23.3846i	−1.74460	−	1.00725i
$540$		0			0
$541$		−	22.8149i		−	0.980890i	−0.871472	−	0.490445i	$-0.836834\pi$
$541$		−	22.8149i		−	0.980890i	0.871472	−	0.490445i	$-0.163166\pi$
$542$	0.342412	+	1.27790i	0.0147079	+	0.0548905i
$543$	−15.0990	+	8.32353i	−0.647961	+	0.357197i
$544$	2.24824	+	3.89407i	0.0963927	+	0.166957i
$545$		0			0
$546$	1.74786	−	2.16167i	0.0748017	−	0.0925109i
$547$	−10.0470	−	10.0470i	−0.429577	−	0.429577i	0.458907	−	0.888484i	$-0.348241\pi$
$547$	−10.0470	−	10.0470i	−0.429577	−	0.429577i	−0.888484	+	0.458907i	$0.848241\pi$
$548$	−25.6636	−	6.87653i	−1.09629	−	0.293751i
$549$	−7.42506	−	14.1231i	−0.316894	−	0.602761i
$550$		0			0
$551$	−2.12526			−0.0905391
$552$	−1.79354	−	1.08337i	−0.0763383	−	0.0461115i
$553$	9.61765	−	2.57704i	0.408984	−	0.109587i
$554$		−	1.91420i		−	0.0813267i
$555$		0			0
$556$	−20.5912	−	35.6650i	−0.873261	−	1.51253i
$557$	−6.81604	+	25.4378i	−0.288805	+	1.07783i	0.657209	+	0.753708i	$0.271737\pi$
$557$	−6.81604	+	25.4378i	−0.288805	+	1.07783i	−0.946014	+	0.324126i	$0.894930\pi$
$558$	−1.03941	+	0.960235i	−0.0440017	+	0.0406500i
$559$	2.04178	+	2.69231i	0.0863581	+	0.113873i
$560$		0			0
$561$	−8.50725	+	29.4091i	−0.359176	+	1.24165i
$562$	−0.638111	+	2.38146i	−0.0269171	+	0.100456i
$563$	−18.9045	+	5.06546i	−0.796732	+	0.213484i	−0.634149	−	0.773211i	$-0.718649\pi$
$563$	−18.9045	+	5.06546i	−0.796732	+	0.213484i	−0.162583	+	0.986695i	$0.551983\pi$
$564$	−4.36739	−	4.54374i	−0.183900	−	0.191326i
$565$		0			0
$566$	0.157566	−	0.272913i	0.00662300	−	0.0114714i
$567$	27.3692	−	23.3467i	1.14940	−	0.980470i
$568$	−1.40193	−	5.23209i	−0.0588239	−	0.219534i
$569$	−2.45559	−	4.25321i	−0.102944	−	0.178304i	0.809952	−	0.586495i	$-0.199493\pi$
$569$	−2.45559	−	4.25321i	−0.102944	−	0.178304i	−0.912896	+	0.408192i	$0.866159\pi$
$570$		0			0
$571$	−17.2440			−0.721639			−0.360819	−	0.932636i	$-0.617503\pi$
$571$	−17.2440			−0.721639			−0.360819	+	0.932636i	$0.617503\pi$
$572$	14.0924	+	34.5743i	0.589233	+	1.44562i
$573$	−39.6132	−	0.783925i	−1.65486	−	0.0327489i
$574$	0.433180	+	0.750289i	0.0180806	+	0.0313165i
$575$		0			0
$576$	19.5424	+	12.3387i	0.814267	+	0.514111i
$577$	−16.3463	+	16.3463i	−0.680507	+	0.680507i	−0.960114	−	0.279607i	$-0.909796\pi$
$577$	−16.3463	+	16.3463i	−0.680507	+	0.680507i	0.279607	+	0.960114i	$0.409796\pi$
$578$	0.158231	+	0.590527i	0.00658156	+	0.0245627i
$579$	7.10481	+	28.7818i	0.295266	+	1.19613i
$580$		0			0
$581$	−46.7606	−	26.9973i	−1.93996	−	1.12003i
$582$	0.483360	−	0.266458i	0.0200359	−	0.0110450i
$583$	4.68655	−	17.4905i	0.194097	−	0.724381i
$584$	0.814753			0.0337147
$585$		0			0
$586$	−0.880683			−0.0363807
$587$	0.347066	−	1.29527i	0.0143250	−	0.0534615i	−0.958393	−	0.285451i	$-0.907857\pi$
$587$	0.347066	−	1.29527i	0.0143250	−	0.0534615i	0.972718	+	0.231989i	$0.0745234\pi$
$588$	27.0646	−	14.9197i	1.11613	−	0.615278i
$589$	1.54365	+	0.891226i	0.0636049	+	0.0367223i
$590$		0			0
$591$	−0.614148	−	2.48793i	−0.0252627	−	0.102340i
$592$	6.04025	+	22.5425i	0.248253	+	0.926491i
$593$	−16.7430	+	16.7430i	−0.687552	+	0.687552i	−0.961690	−	0.274138i	$-0.911607\pi$
$593$	−16.7430	+	16.7430i	−0.687552	+	0.687552i	0.274138	+	0.961690i	$0.411607\pi$
$594$	−0.606152	−	2.95323i	−0.0248707	−	0.121173i
$595$		0			0
$596$	8.97996	+	15.5537i	0.367834	+	0.637106i
$597$	41.3774	+	0.818839i	1.69347	+	0.0335129i
$598$	1.08366	+	0.148912i	0.0443143	+	0.00608945i
$599$	29.1006			1.18902			0.594509	−	0.804089i	$-0.297347\pi$
$599$	29.1006			1.18902			0.594509	+	0.804089i	$0.297347\pi$
$600$		0			0
$601$	15.9418	+	27.6120i	0.650280	+	1.12632i	0.983055	+	0.183311i	$0.0586816\pi$
$601$	15.9418	+	27.6120i	0.650280	+	1.12632i	−0.332775	+	0.943006i	$0.607985\pi$
$602$	−0.107971	−	0.402952i	−0.00440055	−	0.0164231i
$603$	−16.9165	+	15.6279i	−0.688894	+	0.636419i
$604$	11.6402	−	20.1615i	0.473635	−	0.820359i
$605$		0			0
$606$	−0.369589	−	0.384512i	−0.0150135	−	0.0156197i
$607$	14.1691	−	3.79661i	0.575107	−	0.154100i	0.0404693	−	0.999181i	$-0.487115\pi$
$607$	14.1691	−	3.79661i	0.575107	−	0.154100i	0.534638	+	0.845081i	$0.320448\pi$
$608$	−0.144356	+	0.538745i	−0.00585442	+	0.0218490i
$609$	−9.71556	+	33.5862i	−0.393695	+	1.36098i
$610$		0			0
$611$	6.08379	+	2.56042i	0.246124	+	0.103584i
$612$	−13.7275	−	14.8594i	−0.554903	−	0.600657i
$613$	−5.37967	+	20.0772i	−0.217283	+	0.810911i	0.768067	+	0.640369i	$0.221219\pi$
$613$	−5.37967	+	20.0772i	−0.217283	+	0.810911i	−0.985350	+	0.170542i	$0.945448\pi$
$614$	0.842294	+	1.45890i	0.0339922	+	0.0588762i
$615$		0			0
$616$		−	9.24775i		−	0.372602i
$617$	−39.2451	+	10.5157i	−1.57995	+	0.423345i	−0.938909	−	0.344164i	$-0.888162\pi$
$617$	−39.2451	+	10.5157i	−1.57995	+	0.423345i	−0.641037	+	0.767510i	$0.721496\pi$
$618$	0.0106442	+	0.00642956i	0.000428174	+	0.000258635i
$619$	21.9052			0.880445			0.440222	−	0.897889i	$-0.354900\pi$
$619$	21.9052			0.880445			0.440222	+	0.897889i	$0.354900\pi$
$620$		0			0
$621$	13.4315	+	4.46836i	0.538988	+	0.179309i
$622$	−1.29293	−	0.346441i	−0.0518420	−	0.0138910i
$623$	12.2255	+	12.2255i	0.489804	+	0.489804i
$624$	−24.2172	−	3.81743i	−0.969464	−	0.152820i
$625$		0			0
$626$	−1.29995	−	2.25158i	−0.0519564	−	0.0899911i
$627$	−3.32566	+	1.83331i	−0.132814	+	0.0732153i
$628$	−8.19964	−	30.6015i	−0.327201	−	1.22113i
$629$		−	20.1688i		−	0.804183i
$630$		0			0
$631$	16.2845	+	9.40185i	0.648275	+	0.374282i	0.787795	−	0.615937i	$-0.211223\pi$
$631$	16.2845	+	9.40185i	0.648275	+	0.374282i	−0.139520	+	0.990219i	$0.544556\pi$
$632$	0.782208	+	0.782208i	0.0311146	+	0.0311146i
$633$	−4.56404	−	2.75687i	−0.181404	−	0.109576i
$634$	−0.106209	+	0.0613196i	−0.00421809	+	0.00243531i
$635$		0			0
$636$	8.29159	+	8.62639i	0.328783	+	0.342059i
$637$	−19.8489	+	25.5667i	−0.786442	+	1.01299i
$638$	2.07188	+	2.07188i	0.0820264	+	0.0820264i
$639$	17.0282	+	32.3891i	0.673624	+	1.28129i
$640$		0			0
$641$	−18.6204	−	10.7505i	−0.735461	−	0.424619i	0.0849557	−	0.996385i	$-0.472925\pi$
$641$	−18.6204	−	10.7505i	−0.735461	−	0.424619i	−0.820417	+	0.571766i	$0.806258\pi$
$642$	0.0648275	−	3.27585i	0.00255854	−	0.129288i
$643$	−2.64106	+	0.707671i	−0.104153	+	0.0279078i	−0.310519	−	0.950567i	$-0.600503\pi$
$643$	−2.64106	+	0.707671i	−0.104153	+	0.0279078i	0.206366	+	0.978475i	$0.433836\pi$
$644$	18.7432	+	10.8214i	0.738585	+	0.426422i
$645$		0			0
$646$	0.0795009	−	0.137700i	0.00312792	−	0.00541772i
$647$	39.8449	+	10.6764i	1.56647	+	0.419733i	0.934703	−	0.355429i	$-0.115665\pi$
$647$	39.8449	+	10.6764i	1.56647	+	0.419733i	0.631762	+	0.775162i	$0.282332\pi$
$648$	3.76665	+	1.33642i	0.147968	+	0.0524995i
$649$		−	47.1302i		−	1.85002i
$650$		0			0
$651$	21.1411	−	20.3206i	0.828585	−	0.796426i
$652$	24.6081	+	6.59373i	0.963729	+	0.258230i
$653$	4.49795	−	16.7866i	0.176018	−	0.656909i	−0.820358	−	0.571851i	$-0.806226\pi$
$653$	4.49795	−	16.7866i	0.176018	−	0.656909i	0.996376	−	0.0850584i	$-0.0271077\pi$
$654$	−0.218726	−	0.886066i	−0.00855286	−	0.0346479i
$655$		0			0
$656$	3.82026	−	6.61688i	0.149156	−	0.258346i
$657$	−5.36876	+	1.21311i	−0.209455	+	0.0473280i
$658$	−0.576229	−	0.576229i	−0.0224638	−	0.0224638i
$659$	−9.34358	+	16.1835i	−0.363974	+	0.630422i	−0.988611	−	0.150494i	$-0.951914\pi$
$659$	−9.34358	+	16.1835i	−0.363974	+	0.630422i	0.624637	+	0.780915i	$0.285247\pi$
$660$		0			0
$661$	36.7989	−	21.2459i	1.43131	−	0.826368i	0.434091	−	0.900869i	$-0.357070\pi$
$661$	36.7989	−	21.2459i	1.43131	−	0.826368i	0.997221	+	0.0745005i	$0.0237362\pi$
$662$	2.21731	−	2.21731i	0.0861780	−	0.0861780i
$663$	19.3619	+	8.60347i	0.751953	+	0.334131i
$664$		−	5.99876i		−	0.232797i
$665$		0			0
$666$	0.924235	+	1.75798i	0.0358134	+	0.0681203i
$667$	−13.2887	+	3.56070i	−0.514540	+	0.137871i
$668$	31.6965	−	31.6965i	1.22638	−	1.22638i
$669$	2.39957	+	9.72072i	0.0927727	+	0.375825i
$670$		0			0
$671$	27.7097			1.06972
$672$	7.85405	+	4.74417i	0.302977	+	0.183010i
$673$	0.980547	+	0.262737i	0.0377973	+	0.0101278i	0.277668	−	0.960677i	$-0.410438\pi$
$673$	0.980547	+	0.262737i	0.0377973	+	0.0101278i	−0.239871	+	0.970805i	$0.577105\pi$
$674$	−2.44738	+	1.41300i	−0.0942697	+	0.0544267i
$675$		0			0
$676$	25.0324	−	6.40462i	0.962786	−	0.246331i
$677$	−2.15255	+	2.15255i	−0.0827291	+	0.0827291i	−0.747260	−	0.664531i	$-0.768631\pi$
$677$	−2.15255	+	2.15255i	−0.0827291	+	0.0827291i	0.664531	+	0.747260i	$0.268631\pi$
$678$	−0.262562	−	0.476293i	−0.0100836	−	0.0182919i
$679$	−9.90513	+	5.71873i	−0.380124	+	0.219465i
$680$		0			0
$681$	−18.3333	+	17.6217i	−0.702532	+	0.675266i
$682$	−0.636035	−	2.37371i	−0.0243550	−	0.0908942i
$683$	8.32509	+	31.0697i	0.318551	+	1.18885i	0.920638	+	0.390418i	$0.127669\pi$
$683$	8.32509	+	31.0697i	0.318551	+	1.18885i	−0.602087	+	0.798430i	$0.705664\pi$
$684$	0.0992783	−	2.50737i	0.00379600	−	0.0958718i
$685$		0			0
$686$	0.762153	−	0.440029i	0.0290991	−	0.0168004i
$687$	−5.46933	+	3.01504i	−0.208668	+	0.115031i
$688$	−2.60147	+	2.60147i	−0.0991802	+	0.0991802i
$689$	−11.5502	−	4.86103i	−0.440028	−	0.185190i
$690$		0			0
$691$	−15.5777	+	8.99379i	−0.592603	+	0.342140i	−0.766126	−	0.642690i	$-0.777818\pi$
$691$	−15.5777	+	8.99379i	−0.592603	+	0.342140i	0.173523	+	0.984830i	$0.444485\pi$
$692$	6.94696	+	1.86143i	0.264084	+	0.0707611i
$693$	13.7693	+	60.9374i	0.523051	+	2.31482i
$694$	0.0558510			0.00212007
$695$		0			0
$696$	−3.77119	+	0.930921i	−0.142947	+	0.0352865i
$697$	−4.66906	+	4.66906i	−0.176853	+	0.176853i
$698$	−0.996554	+	0.267026i	−0.0377201	+	0.0101071i
$699$	18.5470	+	5.36514i	0.701512	+	0.202928i
$700$		0			0
$701$			36.5117i			1.37903i	0.724272	+	0.689515i	$0.242176\pi$
$701$			36.5117i			1.37903i	−0.724272	+	0.689515i	$0.757824\pi$
$702$	−2.08190	+	0.137352i	−0.0785761	+	0.00518402i
$703$	1.76901	−	1.76901i	0.0667196	−	0.0667196i
$704$	−34.7591	+	20.0682i	−1.31003	+	0.756347i
$705$		0			0
$706$	−1.17916	+	2.04236i	−0.0443782	+	0.0768653i
$707$	7.81490	+	7.81490i	0.293909	+	0.293909i
$708$	26.6573	+	16.1021i	1.00184	+	0.605153i
$709$	−17.1761	+	29.7499i	−0.645063	+	1.11728i	0.339224	+	0.940706i	$0.389836\pi$
$709$	−17.1761	+	29.7499i	−0.645063	+	1.11728i	−0.984287	+	0.176577i	$0.943498\pi$
$710$		0			0
$711$	−6.31896	−	3.98965i	−0.236980	−	0.149624i
$712$	−0.497153	+	1.85540i	−0.0186316	+	0.0695340i
$713$	11.1452	+	2.98635i	0.417391	+	0.111840i
$714$	−1.81268	−	1.88587i	−0.0678377	−	0.0705769i
$715$		0			0
$716$			11.5740i			0.432540i
$717$	0.0792506	+	0.143762i	0.00295967	+	0.00536889i
$718$	−1.91056	−	0.511933i	−0.0713014	−	0.0191052i
$719$	−5.50044	+	9.52704i	−0.205132	+	0.355299i	−0.950175	−	0.311718i	$-0.899096\pi$
$719$	−5.50044	+	9.52704i	−0.205132	+	0.355299i	0.745043	+	0.667016i	$0.232429\pi$
$720$		0			0
$721$	−0.223167	−	0.128845i	−0.00831116	−	0.00479845i
$722$	−2.02479	+	0.542540i	−0.0753547	+	0.0201912i
$723$	−18.6863	−	0.369793i	−0.694952	−	0.0137528i
$724$	17.1344	+	9.89253i	0.636794	+	0.367653i
$725$		0			0
$726$	2.99116	+	0.865260i	0.111012	+	0.0321128i
$727$	−13.9424	−	13.9424i	−0.517094	−	0.517094i	0.399597	−	0.916691i	$-0.369150\pi$
$727$	−13.9424	−	13.9424i	−0.517094	−	0.517094i	−0.916691	+	0.399597i	$0.869150\pi$
$728$	−6.34042	−	0.871268i	−0.234991	−	0.0322913i
$729$	−26.8099	−	3.19796i	−0.992961	−	0.118443i
$730$		0			0
$731$	2.75351	−	1.58974i	0.101842	−	0.0587986i
$732$	−9.46704	+	15.6728i	−0.349912	+	0.579285i
$733$	−10.0007	−	10.0007i	−0.369383	−	0.369383i	0.497869	−	0.867252i	$-0.334116\pi$
$733$	−10.0007	−	10.0007i	−0.369383	−	0.369383i	−0.867252	+	0.497869i	$0.834116\pi$
$734$	0.108825	+	0.0628299i	0.00401679	+	0.00231909i
$735$		0			0
$736$			3.61049i			0.133084i
$737$	−10.3515	−	38.6325i	−0.381304	−	1.42305i
$738$	0.193011	−	0.620930i	0.00710483	−	0.0228568i
$739$	−5.27257	−	9.13236i	−0.193955	−	0.335939i	0.752603	−	0.658475i	$-0.228798\pi$
$739$	−5.27257	−	9.13236i	−0.193955	−	0.335939i	−0.946557	+	0.322536i	$0.895465\pi$
$740$		0			0
$741$	0.943625	+	2.45285i	0.0346649	+	0.0901077i
$742$	1.09399	+	1.09399i	0.0401615	+	0.0401615i
$743$	−33.1343	−	8.87832i	−1.21558	−	0.325714i	−0.406632	−	0.913592i	$-0.633297\pi$
$743$	−33.1343	−	8.87832i	−1.21558	−	0.325714i	−0.808949	+	0.587878i	$0.799963\pi$
$744$	3.12953	+	0.905286i	0.114734	+	0.0331894i
$745$		0			0
$746$	−1.98600			−0.0727127
$747$	8.93174	+	39.5284i	0.326795	+	1.44627i
$748$	33.9347	−	9.09277i	1.24077	−	0.332465i
$749$			67.8966i			2.48089i
$750$		0			0
$751$	−7.98474	−	13.8300i	−0.291367	−	0.504663i	0.682766	−	0.730637i	$-0.260777\pi$
$751$	−7.98474	−	13.8300i	−0.291367	−	0.504663i	−0.974133	+	0.225974i	$0.927444\pi$
$752$	−1.86008	+	6.94191i	−0.0678301	+	0.253145i
$753$	37.0411	+	0.733024i	1.34985	+	0.0267129i
$754$	1.61571	−	1.22531i	0.0588408	−	0.0446233i
$755$		0			0
$756$	−39.1710	−	13.0313i	−1.42464	−	0.473945i
$757$	10.9112	−	40.7211i	0.396574	−	1.48003i	−0.422510	−	0.906358i	$-0.638851\pi$
$757$	10.9112	−	40.7211i	0.396574	−	1.48003i	0.819083	−	0.573675i	$-0.194483\pi$
$758$	1.11331	−	0.298311i	0.0404373	−	0.0108351i
$759$	−17.7229	+	17.0351i	−0.643301	+	0.618334i
$760$		0			0
$761$	2.02411	−	3.50585i	0.0733738	−	0.127087i	−0.827004	−	0.562196i	$-0.809957\pi$
$761$	2.02411	−	3.50585i	0.0733738	−	0.127087i	0.900378	+	0.435109i	$0.143290\pi$
$762$	0.349395	+	0.00691435i	0.0126572	+	0.000250480i
$763$	4.89492	+	18.2681i	0.177208	+	0.661349i
$764$	22.7333	+	39.3752i	0.822462	+	1.42455i
$765$		0			0
$766$	1.85016			0.0668492
$767$	−32.3133	−	4.44032i	−1.16676	−	0.160331i
$768$	0.514629	−	26.0052i	0.0185701	−	0.938381i
$769$	−9.59863	−	16.6253i	−0.346135	−	0.599524i	0.639424	−	0.768854i	$-0.279173\pi$
$769$	−9.59863	−	16.6253i	−0.346135	−	0.599524i	−0.985559	+	0.169330i	$0.945840\pi$
$770$		0			0
$771$	−27.2848	+	6.73528i	−0.982640	+	0.242565i
$772$	24.0556	−	24.0556i	0.865778	−	0.865778i
$773$	0.891235	+	3.32613i	0.0320555	+	0.119633i	0.980100	−	0.198506i	$-0.0636089\pi$
$773$	0.891235	+	3.32613i	0.0320555	+	0.119633i	−0.948044	+	0.318139i	$0.896942\pi$
$774$	−0.167155	+	0.264746i	−0.00600826	+	0.00951611i
$775$		0			0
$776$	−1.10045	−	0.635348i	−0.0395040	−	0.0228077i
$777$	−19.8693	−	36.0433i	−0.712808	−	1.29305i
$778$	0.696840	−	2.60064i	0.0249829	−	0.0932375i
$779$	−0.819051			−0.0293455
$780$		0			0
$781$	−63.5476			−2.27391
$782$	0.266394	−	0.994197i	0.00952624	−	0.0355524i
$783$	23.4639	−	11.7493i	0.838533	−	0.419885i
$784$	−30.5200	−	17.6208i	−1.09000	−	0.629313i
$785$		0			0
$786$	−3.79917	+	0.937828i	−0.135512	+	0.0334512i
$787$	−8.97719	−	33.5033i	−0.320002	−	1.19426i	−0.919241	−	0.393694i	$-0.871197\pi$
$787$	−8.97719	−	33.5033i	−0.320002	−	1.19426i	0.599239	−	0.800570i	$-0.295470\pi$
$788$	−2.07939	+	2.07939i	−0.0740752	+	0.0740752i
$789$	−9.52740	−	38.5958i	−0.339184	−	1.37405i
$790$		0			0
$791$	5.63512	+	9.76031i	0.200362	+	0.347037i
$792$	−5.09821	+	4.70987i	−0.181157	+	0.167358i
$793$	2.61064	−	18.9982i	0.0927065	−	0.674647i
$794$	0.952251			0.0337941
$795$		0			0
$796$	−23.7458	−	41.1289i	−0.841647	−	1.45778i
$797$	−7.97400	−	29.7594i	−0.282454	−	1.05413i	−0.950680	−	0.310173i	$-0.899613\pi$
$797$	−7.97400	−	29.7594i	−0.282454	−	1.05413i	0.668226	−	0.743958i	$-0.267054\pi$
$798$	0.00641973	−	0.324401i	0.000227256	−	0.0114837i
$799$	3.10547	−	5.37883i	0.109864	−	0.190289i
$800$		0			0
$801$	0.513392	−	12.9662i	0.0181398	−	0.458140i
$802$	−2.95603	+	0.792066i	−0.104381	+	0.0279688i
$803$	2.47394	−	9.23288i	0.0873036	−	0.325821i
$804$	25.3875	+	7.34391i	0.895348	+	0.259000i
$805$		0			0
$806$	−1.68738	+	0.212439i	−0.0594355	+	0.00748286i
$807$	−0.118885	+	6.00749i	−0.00418496	+	0.211474i
$808$	−0.317795	+	1.18603i	−0.0111800	+	0.0417242i
$809$	−18.8982	−	32.7327i	−0.664427	−	1.15082i	−0.979440	−	0.201734i	$-0.935342\pi$
$809$	−18.8982	−	32.7327i	−0.664427	−	1.15082i	0.315013	−	0.949087i	$-0.397991\pi$
$810$		0			0
$811$		−	11.6051i		−	0.407512i	−0.979022	−	0.203756i	$-0.934685\pi$
$811$		−	11.6051i		−	0.407512i	0.979022	−	0.203756i	$-0.0653148\pi$
$812$	38.7545	−	10.3842i	1.36002	−	0.364416i
$813$	−10.6387	+	17.6125i	−0.373114	+	0.617696i
$814$	−3.44916			−0.120893
$815$		0			0
$816$	−6.41037	+	22.1603i	−0.224408	+	0.775766i
$817$	0.380948	+	0.102075i	0.0133277	+	0.00357114i
$818$	−2.93960	−	2.93960i	−0.102781	−	0.102781i
$819$	43.0770	−	3.69928i	1.50523	−	0.129263i
$820$		0			0
$821$	−21.9513	−	38.0208i	−0.766107	−	1.32694i	−0.939659	−	0.342111i	$-0.888858\pi$
$821$	−21.9513	−	38.0208i	−0.766107	−	1.32694i	0.173553	−	0.984825i	$-0.444475\pi$
$822$	1.24478	+	2.25805i	0.0434166	+	0.0787585i
$823$	11.4601	+	42.7695i	0.399472	+	1.49085i	0.814027	+	0.580827i	$0.197271\pi$
$823$	11.4601	+	42.7695i	0.399472	+	1.49085i	−0.414554	+	0.910025i	$0.636063\pi$
$824$		−	0.0286293i		−	0.000997349i
$825$		0			0
$826$	3.48738	+	2.01344i	0.121341	+	0.0700565i
$827$	6.22326	+	6.22326i	0.216404	+	0.216404i	0.806981	−	0.590577i	$-0.201100\pi$
$827$	6.22326	+	6.22326i	0.216404	+	0.216404i	−0.590577	+	0.806981i	$0.701100\pi$
$828$	−3.58014	−	15.8443i	−0.124418	−	0.550628i
$829$	34.6858	−	20.0259i	1.20469	−	0.695527i	0.243094	−	0.970003i	$-0.421838\pi$
$829$	34.6858	−	20.0259i	1.20469	−	0.695527i	0.961594	+	0.274475i	$0.0885042\pi$
$830$		0			0
$831$	21.4640	−	20.6310i	0.744578	−	0.715680i
$832$	10.4843	+	25.7221i	0.363477	+	0.891754i
$833$	21.5358	+	21.5358i	0.746172	+	0.746172i
$834$	−1.11058	+	3.83921i	−0.0384562	+	0.132941i
$835$		0			0
$836$	3.77395	+	2.17889i	0.130525	+	0.0753586i
$837$	−21.9697	−	1.30567i	−0.759384	−	0.0451307i
$838$	−3.19297	+	0.855555i	−0.110299	+	0.0295546i
$839$	−3.62533	−	2.09309i	−0.125160	−	0.0722614i	0.436113	−	0.899892i	$-0.356355\pi$
$839$	−3.62533	−	2.09309i	−0.125160	−	0.0722614i	−0.561273	+	0.827631i	$0.689688\pi$
$840$		0			0
$841$	1.74811	−	3.02782i	0.0602797	−	0.104407i
$842$	2.29595	+	0.615198i	0.0791236	+	0.0212011i
$843$	−33.5808	+	18.5119i	−1.15659	+	0.637582i
$844$			6.11875i			0.210616i
$845$		0			0
$846$	−0.0241979	+	0.611144i	−0.000831942	+	0.0210116i
$847$	−62.3264	−	16.7003i	−2.14156	−	0.573830i
$848$	3.53140	−	13.1794i	0.121269	−	0.452582i
$849$	4.75840	−	1.17461i	0.163308	−	0.0403126i
$850$		0			0
$851$	8.09736	−	14.0250i	0.277574	−	0.480772i
$852$	21.7111	−	35.9431i	0.743810	−	1.23139i
$853$	1.57958	+	1.57958i	0.0540837	+	0.0540837i	0.733631	−	0.679548i	$-0.237824\pi$
$853$	1.57958	+	1.57958i	0.0540837	+	0.0540837i	−0.679548	+	0.733631i	$0.737824\pi$
$854$	−1.18378	+	2.05036i	−0.0405081	+	0.0701620i
$855$		0			0
$856$	−6.53267	+	3.77164i	−0.223282	+	0.128912i
$857$	31.1740	−	31.1740i	1.06488	−	1.06488i	0.0671414	−	0.997743i	$-0.478612\pi$
$857$	31.1740	−	31.1740i	1.06488	−	1.06488i	0.997743	−	0.0671414i	$-0.0213879\pi$
$858$	1.47132	−	3.31116i	0.0502299	−	0.113041i
$859$			17.7932i			0.607095i	0.952816	+	0.303547i	$0.0981711\pi$
$859$			17.7932i			0.607095i	−0.952816	+	0.303547i	$0.901829\pi$
$860$		0			0
$861$	−3.74427	+	12.9437i	−0.127604	+	0.441121i
$862$	−0.312829	+	0.0838223i	−0.0106550	+	0.00285500i
$863$	4.49895	−	4.49895i	0.153146	−	0.153146i	−0.626375	−	0.779522i	$-0.715462\pi$
$863$	4.49895	−	4.49895i	0.153146	−	0.153146i	0.779522	+	0.626375i	$0.215462\pi$
$864$	−1.38463	−	6.74608i	−0.0471062	−	0.229506i
$865$		0			0
$866$	2.94505			0.100077
$867$	−4.91620	+	8.13885i	−0.166963	+	0.276410i
$868$	−32.5034	−	8.70925i	−1.10324	−	0.295611i
$869$	11.2392	−	6.48896i	0.381264	−	0.220123i
$870$		0			0
$871$	−27.4624	+	3.45747i	−0.930526	+	0.117152i
$872$	−1.48575	+	1.48575i	−0.0503139	+	0.0503139i
$873$	8.19736	+	2.54808i	0.277439	+	0.0862395i
$874$	0.110567	−	0.0638359i	0.00373998	−	0.00215928i
$875$		0			0
$876$	4.37698	+	4.55371i	0.147884	+	0.153856i
$877$	−1.58848	−	5.92830i	−0.0536393	−	0.200184i	0.933906	−	0.357518i	$-0.116377\pi$
$877$	−1.58848	−	5.92830i	−0.0536393	−	0.200184i	−0.987546	+	0.157334i	$0.949710\pi$
$878$	0.772733	+	2.88388i	0.0260785	+	0.0973262i
$879$	−9.49185	−	9.87511i	−0.320152	−	0.333079i
$880$		0			0
$881$	36.9093	−	21.3096i	1.24350	−	0.717938i	0.273699	−	0.961815i	$-0.411753\pi$
$881$	36.9093	−	21.3096i	1.24350	−	0.717938i	0.969806	+	0.243878i	$0.0784195\pi$
$882$	−2.86401	−	0.890253i	−0.0964362	−	0.0299764i
$883$	13.2826	−	13.2826i	0.446996	−	0.446996i	−0.447358	−	0.894355i	$-0.647635\pi$
$883$	13.2826	−	13.2826i	0.446996	−	0.446996i	0.894355	+	0.447358i	$0.147635\pi$
$884$	−3.03704	−	24.1229i	−0.102147	−	0.811340i
$885$		0			0
$886$	2.64092	−	1.52473i	0.0887233	−	0.0512244i
$887$	−0.0708297	−	0.0189788i	−0.00237823	−	0.000637244i	0.257630	−	0.966244i	$-0.417059\pi$
$887$	−0.0708297	−	0.0189788i	−0.00237823	−	0.000637244i	−0.260008	+	0.965606i	$0.583725\pi$
$888$	2.36417	−	3.91393i	0.0793364	−	0.131343i
$889$	−7.24169			−0.242879
$890$		0			0
$891$	26.5817	−	38.6262i	0.890519	−	1.29403i
$892$	8.12449	−	8.12449i	0.272028	−	0.272028i
$893$	0.744161	−	0.199397i	0.0249024	−	0.00667257i
$894$	0.484331	−	1.67431i	0.0161985	−	0.0559972i
$895$		0			0
$896$		−	14.0245i		−	0.468525i
$897$	10.0098	+	13.7561i	0.334217	+	0.459302i
$898$	0.275440	−	0.275440i	0.00919156	−	0.00919156i
$899$	18.5243	−	10.6950i	0.617819	−	0.356698i
$900$		0			0
$901$	−5.89581	+	10.2118i	−0.196418	+	0.340206i
$902$	0.798478	+	0.798478i	0.0265864	+	0.0265864i
$903$	3.35462	−	5.55362i	0.111635	−	0.184813i
$904$	−0.626059	+	1.08437i	−0.0208224	+	0.0360655i
$905$		0			0
$906$	−2.19345	+	0.541456i	−0.0728726	+	0.0179887i
$907$	3.44596	−	12.8605i	0.114421	−	0.427026i	−0.884822	−	0.465930i	$-0.845720\pi$
$907$	3.44596	−	12.8605i	0.114421	−	0.427026i	0.999243	+	0.0389038i	$0.0123866\pi$
$908$	28.1865	+	7.55255i	0.935401	+	0.250640i
$909$	0.328176	−	8.28841i	0.0108849	−	0.274909i
$910$		0			0
$911$			26.2784i			0.870641i	0.900276	+	0.435321i	$0.143365\pi$
$911$			26.2784i			0.870641i	−0.900276	+	0.435321i	$0.856635\pi$
$912$	−2.50594	+	1.38143i	−0.0829801	+	0.0457438i
$913$	−67.9787	−	18.2148i	−2.24977	−	0.602823i
$914$	−1.94240	+	3.36434i	−0.0642490	+	0.111283i
$915$		0			0
$916$	6.20659	+	3.58338i	0.205072	+	0.118398i
$917$	78.3277	−	20.9879i	2.58661	−	0.693080i
$918$	−0.116471	+	1.95979i	−0.00384412	+	0.0646826i
$919$	−12.6380	−	7.29655i	−0.416889	−	0.240691i	0.276856	−	0.960911i	$-0.410707\pi$
$919$	−12.6380	−	7.29655i	−0.416889	−	0.240691i	−0.693746	+	0.720220i	$0.744041\pi$
$920$		0			0
$921$	−7.28052	+	25.1684i	−0.239901	+	0.829326i
$922$	−0.855820	−	0.855820i	−0.0281849	−	0.0281849i
$923$	−5.98707	+	43.5693i	−0.197067	+	1.43410i
$924$	51.6863	−	49.6803i	1.70035	−	1.63436i
$925$		0			0
$926$	0.913562	−	0.527445i	0.0300215	−	0.0173329i
$927$	0.0426271	+	0.188651i	0.00140006	+	0.00619611i
$928$	4.73279	+	4.73279i	0.155361	+	0.155361i
$929$	38.3045	+	22.1151i	1.25673	+	0.725573i	0.972437	−	0.233165i	$-0.0749082\pi$
$929$	38.3045	+	22.1151i	1.25673	+	0.725573i	0.284292	+	0.958738i	$0.408242\pi$
$930$		0			0
$931$			3.77783i			0.123813i
$932$	−5.73440	−	21.4011i	−0.187836	−	0.701015i
$933$	−10.0504	−	18.2316i	−0.329035	−	0.596875i
$934$	−0.359584	−	0.622817i	−0.0117659	−	0.0203792i
$935$		0			0
$936$	2.74884	+	3.93916i	0.0898488	+	0.128755i
$937$	−22.4956	−	22.4956i	−0.734898	−	0.734898i	0.236688	−	0.971586i	$-0.423938\pi$
$937$	−22.4956	−	22.4956i	−0.734898	−	0.734898i	−0.971586	+	0.236688i	$0.923938\pi$
$938$	3.30082	+	0.884452i	0.107776	+	0.0288784i
$939$	11.2363	−	38.8434i	0.366684	−	1.26761i
$940$		0			0
$941$	37.4186			1.21981			0.609905	−	0.792474i	$-0.291207\pi$
$941$	37.4186			1.21981			0.609905	+	0.792474i	$0.291207\pi$
$942$	−1.58965	+	2.63169i	−0.0517935	+	0.0857450i
$943$	−5.12131	+	1.37225i	−0.166773	+	0.0446867i
$944$		−	35.5135i		−	1.15586i
$945$		0			0
$946$	−0.271869	−	0.470890i	−0.00883921	−	0.0153100i
$947$	0.895335	−	3.34143i	0.0290945	−	0.108582i	−0.949852	−	0.312701i	$-0.898766\pi$
$947$	0.895335	−	3.34143i	0.0290945	−	0.108582i	0.978946	+	0.204119i	$0.0654329\pi$
$948$	−0.169674	+	8.57396i	−0.00551077	+	0.278469i
$949$	−6.09715	−	2.56605i	−0.197922	−	0.0832974i
$950$		0			0
$951$	−1.83228	−	0.530028i	−0.0594157	−	0.0171873i
$952$	−1.55865	+	5.81695i	−0.0505161	+	0.188529i
$953$	−28.6007	+	7.66352i	−0.926466	+	0.248246i	−0.690347	−	0.723478i	$-0.742542\pi$
$953$	−28.6007	+	7.66352i	−0.926466	+	0.248246i	−0.236119	+	0.971724i	$0.575876\pi$
$954$	0.0459404	−	1.16027i	0.00148737	−	0.0375652i
$955$		0			0
$956$	0.0941895	−	0.163141i	0.00304631	−	0.00527636i
$957$	−0.901655	+	45.5623i	−0.0291464	+	1.47282i
$958$	0.459864	+	1.71624i	0.0148575	+	0.0554491i
$959$	−26.7155	−	46.2725i	−0.862687	−	1.49422i
$960$		0			0
$961$	13.0603			0.421299
$962$	−0.324959	+	2.36480i	−0.0104771	+	0.0762443i
$963$	37.4309	−	34.5797i	1.20619	−	1.11431i
$964$	10.7238	+	18.5741i	0.345389	+	0.598231i
$965$		0			0
$966$	−0.503366	−	2.03915i	−0.0161955	−	0.0656086i
$967$	−18.5880	+	18.5880i	−0.597750	+	0.597750i	−0.939713	−	0.341963i	$-0.888908\pi$
$967$	−18.5880	+	18.5880i	−0.597750	+	0.597750i	0.341963	+	0.939713i	$0.388908\pi$
$968$	−1.85540	−	6.92443i	−0.0596347	−	0.222560i
$969$	2.40087	−	0.592657i	0.0771272	−	0.0190389i
$970$		0			0
$971$	−6.10879	−	3.52691i	−0.196040	−	0.113184i	0.398767	−	0.917052i	$-0.369438\pi$
$971$	−6.10879	−	3.52691i	−0.196040	−	0.113184i	−0.594807	+	0.803868i	$0.702772\pi$
$972$	12.7657	+	28.2315i	0.409460	+	0.905527i
$973$	21.4352	−	79.9972i	0.687180	−	2.56459i
$974$	3.65614			0.117150
$975$		0			0
$976$	20.8797			0.668344
$977$	5.28126	−	19.7099i	0.168963	−	0.630577i	−0.828539	−	0.559932i	$-0.810827\pi$
$977$	5.28126	−	19.7099i	0.168963	−	0.630577i	0.997501	−	0.0706455i	$-0.0225059\pi$
$978$	−1.19359	−	2.16519i	−0.0381667	−	0.0692350i
$979$	19.5160	+	11.2676i	0.623735	+	0.360114i
$980$		0			0
$981$	7.57808	−	12.0024i	0.241949	−	0.383208i
$982$	−0.840582	−	3.13710i	−0.0268241	−	0.100109i
$983$	30.8727	−	30.8727i	0.984687	−	0.984687i	−0.0151975	−	0.999885i	$-0.504838\pi$
$983$	30.8727	−	30.8727i	0.984687	−	0.984687i	0.999885	+	0.0151975i	$0.00483769\pi$
$984$	−1.45337	+	0.358767i	−0.0463319	+	0.0114371i
$985$		0			0
$986$	−0.954036	−	1.65244i	−0.0303827	−	0.0526244i
$987$	0.250768	−	12.6718i	0.00798203	−	0.403347i
$988$	1.84945	−	2.38221i	0.0588387	−	0.0757880i
$989$	2.55299			0.0811803
$990$		0			0
$991$	−6.36105	−	11.0177i	−0.202065	−	0.349988i	0.747128	−	0.664680i	$-0.231432\pi$
$991$	−6.36105	−	11.0177i	−0.202065	−	0.349988i	−0.949194	+	0.314692i	$0.898099\pi$
$992$	−1.45290	−	5.42228i	−0.0461295	−	0.172158i
$993$	48.7604	+	0.964945i	1.54736	+	0.0306216i
$994$	2.71480	−	4.70218i	0.0861083	−	0.149144i
$995$		0			0
$996$	33.5275	−	32.2263i	1.06236	−	1.02113i
$997$	8.75218	−	2.34514i	0.277184	−	0.0742713i	−0.117549	−	0.993067i	$-0.537504\pi$
$997$	8.75218	−	2.34514i	0.277184	−	0.0742713i	0.394733	+	0.918796i	$0.370837\pi$
$998$	−0.482956	+	1.80241i	−0.0152877	+	0.0570544i
$999$	−9.75099	+	29.3106i	−0.308508	+	0.927348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.257.12		96
3.2	odd	2	inner	975.2.bn.d.257.13		96
5.2	odd	4		195.2.bf.a.23.12	yes	96
5.3	odd	4	inner	975.2.bn.d.218.13		96
5.4	even	2		195.2.bf.a.62.13	yes	96
13.4	even	6	inner	975.2.bn.d.407.12		96
15.2	even	4		195.2.bf.a.23.13	yes	96
15.8	even	4	inner	975.2.bn.d.218.12		96
15.14	odd	2		195.2.bf.a.62.12	yes	96
39.17	odd	6	inner	975.2.bn.d.407.13		96
65.4	even	6		195.2.bf.a.17.13	yes	96
65.17	odd	12		195.2.bf.a.173.12	yes	96
65.43	odd	12	inner	975.2.bn.d.368.13		96
195.17	even	12		195.2.bf.a.173.13	yes	96
195.134	odd	6		195.2.bf.a.17.12	✓	96
195.173	even	12	inner	975.2.bn.d.368.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.12	✓	96	195.134	odd	6
195.2.bf.a.17.13	yes	96	65.4	even	6
195.2.bf.a.23.12	yes	96	5.2	odd	4
195.2.bf.a.23.13	yes	96	15.2	even	4
195.2.bf.a.62.12	yes	96	15.14	odd	2
195.2.bf.a.62.13	yes	96	5.4	even	2
195.2.bf.a.173.12	yes	96	65.17	odd	12
195.2.bf.a.173.13	yes	96	195.17	even	12
975.2.bn.d.218.12		96	15.8	even	4	inner
975.2.bn.d.218.13		96	5.3	odd	4	inner
975.2.bn.d.257.12		96	1.1	even	1	trivial
975.2.bn.d.257.13		96	3.2	odd	2	inner
975.2.bn.d.368.12		96	195.173	even	12	inner
975.2.bn.d.368.13		96	65.43	odd	12	inner
975.2.bn.d.407.12		96	13.4	even	6	inner
975.2.bn.d.407.13		96	39.17	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0288234 + 0.107570i) q^{2} +(-1.51684 + 0.836177i) q^{3} +(1.72131 + 0.993799i) q^{4} +(-0.0462274 - 0.187269i) q^{6} +(1.03453 + 3.86093i) q^{7} +(-0.314011 + 0.314011i) q^{8} +(1.60161 - 2.53670i) q^{9} +(2.60494 + 4.51189i) q^{11} +(-3.44195 - 0.0681144i) q^{12} +(3.33885 - 1.36091i) q^{13} -0.445140 q^{14} +(1.96287 + 3.39979i) q^{16} +(-0.878092 - 3.27708i) q^{17} +(0.226709 + 0.245402i) q^{18} +(0.210416 - 0.364452i) q^{19} +(-4.79764 - 4.99136i) q^{21} +(-0.560429 + 0.150166i) q^{22} +(0.705071 - 2.63136i) q^{23} +(0.213736 - 0.738874i) q^{24} +(0.0501565 + 0.398387i) q^{26} +(-0.308267 + 5.18700i) q^{27} +(-2.05624 + 7.67398i) q^{28} +(-2.52506 - 4.37354i) q^{29} +4.23553i q^{31} +(-1.28019 + 0.343025i) q^{32} +(-7.72402 - 4.66563i) q^{33} +0.377826 q^{34} +(5.27784 - 2.77476i) q^{36} +(5.74223 + 1.53863i) q^{37} +(0.0331393 + 0.0331393i) q^{38} +(-3.92655 + 4.85615i) q^{39} +(-0.973131 - 1.68551i) q^{41} +(0.675207 - 0.372216i) q^{42} +(0.242554 + 0.905224i) q^{43} +10.3551i q^{44} +(0.262734 + 0.151689i) q^{46} +(1.29449 + 1.29449i) q^{47} +(-5.82019 - 3.51564i) q^{48} +(-7.77434 + 4.48852i) q^{49} +(4.07215 + 4.23657i) q^{51} +(7.09967 + 0.975600i) q^{52} +(-2.45762 - 2.45762i) q^{53} +(-0.549082 - 0.182667i) q^{54} +(-1.53723 - 0.887520i) q^{56} +(-0.0144218 + 0.728761i) q^{57} +(0.543244 - 0.145562i) q^{58} +(-7.83433 - 4.52315i) q^{59} +(2.65934 - 4.60611i) q^{61} +(-0.455618 - 0.122082i) q^{62} +(11.4509 + 3.55942i) q^{63} +7.70388i q^{64} +(0.724516 - 0.696396i) q^{66} +(-7.41523 - 1.98691i) q^{67} +(1.74529 - 6.51352i) q^{68} +(1.13080 + 4.58092i) q^{69} +(-6.09876 + 10.5634i) q^{71} +(0.293626 + 1.29948i) q^{72} +(-1.29733 - 1.29733i) q^{73} +(-0.331021 + 0.573345i) q^{74} +(0.724384 - 0.418223i) q^{76} +(-14.7252 + 14.7252i) q^{77} +(-0.409202 - 0.562351i) q^{78} -2.49102i q^{79} +(-3.86966 - 8.12562i) q^{81} +(0.209360 - 0.0560979i) q^{82} +(-9.55183 + 9.55183i) q^{83} +(-3.29782 - 13.3596i) q^{84} -0.104367 q^{86} +(7.48717 + 4.52256i) q^{87} +(-2.23476 - 0.598803i) q^{88} +(3.74597 - 2.16273i) q^{89} +(8.70853 + 11.4832i) q^{91} +(3.82869 - 3.82869i) q^{92} +(-3.54166 - 6.42463i) q^{93} +(-0.176560 + 0.101937i) q^{94} +(1.65501 - 1.59078i) q^{96} +(0.740590 + 2.76392i) q^{97} +(-0.258749 - 0.965663i) q^{98} +(15.6174 + 0.618364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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