LMFDB - Embedded newform 195.2.bf.a.17.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(17,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.12
Character	$\chi$	$=$	195.17
Dual form			195.2.bf.a.23.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.107570 + 0.0288234i) q^{2} +(0.836177 - 1.51684i) q^{3} +(-1.72131 + 0.993799i) q^{4} +(-1.90035 - 1.17843i) q^{5} +(-0.0462274 + 0.187269i) q^{6} +(-3.86093 - 1.03453i) q^{7} +(0.314011 - 0.314011i) q^{8} +(-1.60161 - 2.53670i) q^{9} +(0.238387 + 0.0719893i) q^{10} +(2.60494 - 4.51189i) q^{11} +(0.0681144 + 3.44195i) q^{12} +(-1.36091 + 3.33885i) q^{13} +0.445140 q^{14} +(-3.37651 + 1.89715i) q^{15} +(1.96287 - 3.39979i) q^{16} +(3.27708 + 0.878092i) q^{17} +(0.245402 + 0.226709i) q^{18} +(-0.210416 - 0.364452i) q^{19} +(4.44220 + 0.139875i) q^{20} +(-4.79764 + 4.99136i) q^{21} +(-0.150166 + 0.560429i) q^{22} +(-2.63136 + 0.705071i) q^{23} +(-0.213736 - 0.738874i) q^{24} +(2.22263 + 4.47883i) q^{25} +(0.0501565 - 0.398387i) q^{26} +(-5.18700 + 0.308267i) q^{27} +(7.67398 - 2.05624i) q^{28} +(2.52506 - 4.37354i) q^{29} +(0.308530 - 0.301399i) q^{30} -4.23553i q^{31} +(-0.343025 + 1.28019i) q^{32} +(-4.66563 - 7.72402i) q^{33} -0.377826 q^{34} +(6.11798 + 6.51579i) q^{35} +(5.27784 + 2.77476i) q^{36} +(-1.53863 - 5.74223i) q^{37} +(0.0331393 + 0.0331393i) q^{38} +(3.92655 + 4.85615i) q^{39} +(-0.966769 + 0.226691i) q^{40} +(-0.973131 + 1.68551i) q^{41} +(0.372216 - 0.675207i) q^{42} +(0.905224 + 0.242554i) q^{43} +10.3551i q^{44} +(0.0543123 + 6.70798i) q^{45} +(0.262734 - 0.151689i) q^{46} +(-1.29449 - 1.29449i) q^{47} +(-3.51564 - 5.82019i) q^{48} +(7.77434 + 4.48852i) q^{49} +(-0.368184 - 0.417726i) q^{50} +(4.07215 - 4.23657i) q^{51} +(-0.975600 - 7.09967i) q^{52} +(-2.45762 - 2.45762i) q^{53} +(0.549082 - 0.182667i) q^{54} +(-10.2672 + 5.50442i) q^{55} +(-1.53723 + 0.887520i) q^{56} +(-0.728761 + 0.0144218i) q^{57} +(-0.145562 + 0.543244i) q^{58} +(7.83433 - 4.52315i) q^{59} +(3.92664 - 6.62116i) q^{60} +(2.65934 + 4.60611i) q^{61} +(0.122082 + 0.455618i) q^{62} +(3.55942 + 11.4509i) q^{63} +7.70388i q^{64} +(6.52079 - 4.74124i) q^{65} +(0.724516 + 0.696396i) q^{66} +(1.98691 + 7.41523i) q^{67} +(-6.51352 + 1.74529i) q^{68} +(-1.13080 + 4.58092i) q^{69} +(-0.845920 - 0.524565i) q^{70} +(-6.09876 - 10.5634i) q^{71} +(-1.29948 - 0.293626i) q^{72} +(-1.29733 - 1.29733i) q^{73} +(0.331021 + 0.573345i) q^{74} +(8.65219 + 0.373728i) q^{75} +(0.724384 + 0.418223i) q^{76} +(-14.7252 + 14.7252i) q^{77} +(-0.562351 - 0.409202i) q^{78} -2.49102i q^{79} +(-7.73653 + 4.14768i) q^{80} +(-3.86966 + 8.12562i) q^{81} +(0.0560979 - 0.209360i) q^{82} +(9.55183 - 9.55183i) q^{83} +(3.29782 - 13.3596i) q^{84} +(-5.19282 - 5.53048i) q^{85} -0.104367 q^{86} +(-4.52256 - 7.48717i) q^{87} +(-0.598803 - 2.23476i) q^{88} +(-3.74597 - 2.16273i) q^{89} +(-0.199189 - 0.720015i) q^{90} +(8.70853 - 11.4832i) q^{91} +(3.82869 - 3.82869i) q^{92} +(-6.42463 - 3.54166i) q^{93} +(0.176560 + 0.101937i) q^{94} +(-0.0296156 + 0.940545i) q^{95} +(1.65501 + 1.59078i) q^{96} +(-2.76392 - 0.740590i) q^{97} +(-0.965663 - 0.258749i) 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} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.107570	+	0.0288234i	−0.0760637	+	0.0203812i	−0.296650	−	0.954986i	$-0.595870\pi$
$2$	−0.107570	+	0.0288234i	−0.0760637	+	0.0203812i	0.220586	+	0.975367i	$0.429203\pi$
$3$	0.836177	−	1.51684i	0.482767	−	0.875749i
$3$	0.836177	−	1.51684i	0.482767	−	0.875749i
$4$	−1.72131	+	0.993799i	−0.860655	+	0.496899i
$5$	−1.90035	−	1.17843i	−0.849860	−	0.527008i
$5$	−1.90035	−	1.17843i	−0.849860	−	0.527008i
$6$	−0.0462274	+	0.187269i	−0.0188723	+	0.0764521i
$7$	−3.86093	−	1.03453i	−1.45929	−	0.391017i	−0.560048	−	0.828460i	$-0.689217\pi$
$7$	−3.86093	−	1.03453i	−1.45929	−	0.391017i	−0.899246	+	0.437443i	$0.855884\pi$
$8$	0.314011	−	0.314011i	0.111020	−	0.111020i
$9$	−1.60161	−	2.53670i	−0.533872	−	0.845566i
$10$	0.238387	+	0.0719893i	0.0753846	+	0.0227650i
$11$	2.60494	−	4.51189i	0.785419	−	1.36039i	−0.143329	−	0.989675i	$-0.545781\pi$
$11$	2.60494	−	4.51189i	0.785419	−	1.36039i	0.928748	−	0.370711i	$-0.120886\pi$
$12$	0.0681144	+	3.44195i	0.0196629	+	0.993604i
$13$	−1.36091	+	3.33885i	−0.377448	+	0.926031i
$13$	−1.36091	+	3.33885i	−0.377448	+	0.926031i
$14$	0.445140			0.118969
$15$	−3.37651	+	1.89715i	−0.871811	+	0.489842i
$16$	1.96287	−	3.39979i	0.490718	−	0.849948i
$17$	3.27708	+	0.878092i	0.794809	+	0.212969i	0.633304	−	0.773903i	$-0.281698\pi$
$17$	3.27708	+	0.878092i	0.794809	+	0.212969i	0.161506	+	0.986872i	$0.448365\pi$
$18$	0.245402	+	0.226709i	0.0578419	+	0.0534359i
$19$	−0.210416	−	0.364452i	−0.0482728	−	0.0836110i	0.840879	−	0.541223i	$-0.182038\pi$
$19$	−0.210416	−	0.364452i	−0.0482728	−	0.0836110i	−0.889152	+	0.457612i	$0.848705\pi$
$20$	4.44220	+	0.139875i	0.993307	+	0.0312770i
$21$	−4.79764	+	4.99136i	−1.04693	+	1.08920i
$22$	−0.150166	+	0.560429i	−0.0320156	+	0.119484i
$23$	−2.63136	+	0.705071i	−0.548676	+	0.147017i	−0.522499	−	0.852640i	$-0.675000\pi$
$23$	−2.63136	+	0.705071i	−0.548676	+	0.147017i	−0.0261774	+	0.999657i	$0.508333\pi$
$24$	−0.213736	−	0.738874i	−0.0436287	−	0.150822i
$25$	2.22263	+	4.47883i	0.444525	+	0.895766i
$26$	0.0501565	−	0.398387i	0.00983649	−	0.0781302i
$27$	−5.18700	+	0.308267i	−0.998239	+	0.0593259i
$28$	7.67398	−	2.05624i	1.45024	−	0.388592i
$29$	2.52506	−	4.37354i	0.468892	−	0.812146i	−0.530475	−	0.847700i	$-0.677987\pi$
$29$	2.52506	−	4.37354i	0.468892	−	0.812146i	0.999368	+	0.0355548i	$0.0113198\pi$
$30$	0.308530	−	0.301399i	0.0563296	−	0.0550278i
$31$		−	4.23553i		−	0.760724i	−0.924838	−	0.380362i	$-0.875799\pi$
$31$		−	4.23553i		−	0.760724i	0.924838	−	0.380362i	$-0.124201\pi$
$32$	−0.343025	+	1.28019i	−0.0606389	+	0.226307i
$33$	−4.66563	−	7.72402i	−0.812181	−	1.34458i
$34$	−0.377826			−0.0647967
$35$	6.11798	+	6.51579i	1.03413	+	1.10137i
$36$	5.27784	+	2.77476i	0.879640	+	0.462460i
$37$	−1.53863	−	5.74223i	−0.252949	−	0.944017i	−0.969220	−	0.246195i	$-0.920820\pi$
$37$	−1.53863	−	5.74223i	−0.252949	−	0.944017i	0.716272	−	0.697822i	$-0.245847\pi$
$38$	0.0331393	+	0.0331393i	0.00537590	+	0.00537590i
$39$	3.92655	+	4.85615i	0.628751	+	0.777607i
$40$	−0.966769	+	0.226691i	−0.152860	+	0.0358430i
$41$	−0.973131	+	1.68551i	−0.151978	+	0.263233i	−0.931954	−	0.362576i	$-0.881897\pi$
$41$	−0.973131	+	1.68551i	−0.151978	+	0.263233i	0.779977	+	0.625808i	$0.215231\pi$
$42$	0.372216	−	0.675207i	0.0574342	−	0.104187i
$43$	0.905224	+	0.242554i	0.138045	+	0.0369892i	0.327180	−	0.944962i	$-0.393902\pi$
$43$	0.905224	+	0.242554i	0.138045	+	0.0369892i	−0.189135	+	0.981951i	$0.560568\pi$
$44$			10.3551i			1.56110i
$45$	0.0543123	+	6.70798i	0.00809640	+	0.999967i
$46$	0.262734	−	0.151689i	0.0387380	−	0.0223654i
$47$	−1.29449	−	1.29449i	−0.188821	−	0.188821i	0.606365	−	0.795186i	$-0.292627\pi$
$47$	−1.29449	−	1.29449i	−0.188821	−	0.188821i	−0.795186	+	0.606365i	$0.792627\pi$
$48$	−3.51564	−	5.82019i	−0.507438	−	0.840072i
$49$	7.77434	+	4.48852i	1.11062	+	0.641217i
$50$	−0.368184	−	0.417726i	−0.0520690	−	0.0590754i
$51$	4.07215	−	4.23657i	0.570215	−	0.593239i
$52$	−0.975600	−	7.09967i	−0.135291	−	0.984547i
$53$	−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
$55$	−10.2672	+	5.50442i	−1.38443	+	0.742216i
$56$	−1.53723	+	0.887520i	−0.205421	+	0.118600i
$57$	−0.728761	+	0.0144218i	−0.0965268	+	0.00191022i
$58$	−0.145562	+	0.543244i	−0.0191132	+	0.0713314i
$59$	7.83433	−	4.52315i	1.01994	−	0.588865i	0.105856	−	0.994381i	$-0.466242\pi$
$59$	7.83433	−	4.52315i	1.01994	−	0.588865i	0.914088	+	0.405517i	$0.132908\pi$
$60$	3.92664	−	6.62116i	0.506927	−	0.854787i
$61$	2.65934	+	4.60611i	0.340493	+	0.589752i	0.984524	−	0.175248i	$-0.0560726\pi$
$61$	2.65934	+	4.60611i	0.340493	+	0.589752i	−0.644031	+	0.764999i	$0.722739\pi$
$62$	0.122082	+	0.455618i	0.0155045	+	0.0578635i
$63$	3.55942	+	11.4509i	0.448445	+	1.44268i
$64$			7.70388i			0.962986i
$65$	6.52079	−	4.74124i	0.808804	−	0.588078i
$66$	0.724516	+	0.696396i	0.0891817	+	0.0857205i
$67$	1.98691	+	7.41523i	0.242739	+	0.905915i	0.974506	+	0.224360i	$0.0720292\pi$
$67$	1.98691	+	7.41523i	0.242739	+	0.905915i	−0.731767	+	0.681555i	$0.761304\pi$
$68$	−6.51352	+	1.74529i	−0.789881	+	0.211648i
$69$	−1.13080	+	4.58092i	−0.136133	+	0.551478i
$70$	−0.845920	−	0.524565i	−0.101107	−	0.0626975i
$71$	−6.09876	−	10.5634i	−0.723789	−	1.25364i	−0.959470	−	0.281809i	$-0.909065\pi$
$71$	−6.09876	−	10.5634i	−0.723789	−	1.25364i	0.235681	−	0.971830i	$-0.424268\pi$
$72$	−1.29948	−	0.293626i	−0.153145	−	0.0346042i
$73$	−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
$75$	8.65219	+	0.373728i	0.999068	+	0.0431544i
$76$	0.724384	+	0.418223i	0.0830925	+	0.0479735i
$77$	−14.7252	+	14.7252i	−1.67809	+	1.67809i
$78$	−0.562351	−	0.409202i	−0.0636737	−	0.0463330i
$79$		−	2.49102i		−	0.280262i	−0.990133	−	0.140131i	$-0.955248\pi$
$79$		−	2.49102i		−	0.280262i	0.990133	−	0.140131i	$-0.0447523\pi$
$80$	−7.73653	+	4.14768i	−0.864971	+	0.463725i
$81$	−3.86966	+	8.12562i	−0.429962	+	0.902847i
$82$	0.0560979	−	0.209360i	0.00619497	−	0.0231200i
$83$	9.55183	−	9.55183i	1.04845	−	1.04845i	0.0496844	−	0.998765i	$-0.484178\pi$
$83$	9.55183	−	9.55183i	1.04845	−	1.04845i	0.998765	−	0.0496844i	$-0.0158216\pi$
$84$	3.29782	−	13.3596i	0.359822	−	1.45765i
$85$	−5.19282	−	5.53048i	−0.563241	−	0.599864i
$86$	−0.104367			−0.0112541
$87$	−4.52256	−	7.48717i	−0.484870	−	0.802709i
$88$	−0.598803	−	2.23476i	−0.0638326	−	0.238227i
$89$	−3.74597	−	2.16273i	−0.397072	−	0.229249i	0.288148	−	0.957586i	$-0.406960\pi$
$89$	−3.74597	−	2.16273i	−0.397072	−	0.229249i	−0.685220	+	0.728336i	$0.740294\pi$
$90$	−0.199189	−	0.720015i	−0.0209964	−	0.0758962i
$91$	8.70853	−	11.4832i	0.912901	−	1.20376i
$92$	3.82869	−	3.82869i	0.399168	−	0.399168i
$93$	−6.42463	−	3.54166i	−0.666203	−	0.367253i
$94$	0.176560	+	0.101937i	0.0182108	+	0.0105140i
$95$	−0.0296156	+	0.940545i	−0.00303850	+	0.0964978i
$96$	1.65501	+	1.59078i	0.168914	+	0.162358i
$97$	−2.76392	−	0.740590i	−0.280633	−	0.0751955i	0.115757	−	0.993278i	$-0.463071\pi$
$97$	−2.76392	−	0.740590i	−0.280633	−	0.0751955i	−0.396390	+	0.918082i	$0.629737\pi$
$98$	−0.965663	−	0.258749i	−0.0975467	−	0.0261376i
$99$	−15.6174	+	0.618364i	−1.56961	+	0.0621479i
$100$	−8.27689	−	5.50062i	−0.827689	−	0.550062i
$101$	2.39453	+	1.38248i	0.238265	+	0.137562i	0.614379	−	0.789011i	$-0.289407\pi$
$101$	2.39453	+	1.38248i	0.238265	+	0.137562i	−0.376114	+	0.926573i	$0.622740\pi$
$102$	−0.315930	+	0.573103i	−0.0312817	+	0.0567456i
$103$	0.0455864	−	0.0455864i	0.00449176	−	0.00449176i	−0.704857	−	0.709349i	$-0.748989\pi$
$103$	0.0455864	−	0.0455864i	0.00449176	−	0.00449176i	0.709349	+	0.704857i	$0.248989\pi$
$104$	0.621096	+	1.47578i	0.0609035	+	0.144712i
$105$	14.9991	−	3.83165i	1.46377	−	0.373931i
$106$	0.335204	+	0.193530i	0.0325579	+	0.0187973i
$107$	−4.39639	−	16.4075i	−0.425015	−	1.58618i	−0.763890	−	0.645346i	$-0.776713\pi$
$107$	−4.39639	−	16.4075i	−0.425015	−	1.58618i	0.338875	−	0.940831i	$-0.389954\pi$
$108$	8.62208	−	5.68546i	0.829660	−	0.547083i
$109$	−4.73152			−0.453198			−0.226599	−	0.973988i	$-0.572761\pi$
$109$	−4.73152			−0.453198			−0.226599	+	0.973988i	$0.572761\pi$
$110$	0.945792	−	0.888048i	0.0901777	−	0.0846721i
$111$	−9.99662	−	2.46767i	−0.948837	−	0.234221i
$112$	−11.0957	+	11.0957i	−1.04845	+	1.04845i
$113$	−0.729762	+	2.72351i	−0.0686502	+	0.256206i	−0.991719	−	0.128430i	$-0.959006\pi$
$113$	−0.729762	+	2.72351i	−0.0686502	+	0.256206i	0.923068	+	0.384636i	$0.125673\pi$
$114$	0.0779774	−	0.0225567i	0.00730325	−	0.00211263i
$115$	5.83137	+	1.76098i	0.543778	+	0.164213i
$116$			10.0376i			0.931970i
$117$	10.6493	−	1.89534i	0.984529	−	0.175224i
$118$	−0.712369	+	0.712369i	−0.0655789	+	0.0655789i
$119$	−11.7442	−	6.78050i	−1.07659	−	0.621567i
$120$	−0.464536	+	1.65599i	−0.0424061	+	0.151170i
$121$	−8.07143	−	13.9801i	−0.733766	−	1.27092i
$122$	−0.418829	−	0.418829i	−0.0379190	−	0.0379190i
$123$	1.74294	+	2.88547i	0.157156	+	0.260174i
$124$	4.20927	+	7.29067i	0.378003	+	0.654721i
$125$	1.05421	−	11.1305i	0.0942918	−	0.995545i
$126$	−0.712943	−	1.12919i	−0.0635140	−	0.100596i
$127$	−1.74999	+	0.468909i	−0.155287	+	0.0416089i	−0.335625	−	0.941996i	$-0.608947\pi$
$127$	−1.74999	+	0.468909i	−0.155287	+	0.0416089i	0.180338	+	0.983605i	$0.442281\pi$
$128$	−0.908103	−	3.38909i	−0.0802657	−	0.299556i
$129$	1.12484	−	1.17026i	0.0990370	−	0.103036i
$130$	−0.564785	+	0.697968i	−0.0495349	+	0.0612158i
$131$			20.2873i			1.77251i	0.463200	+	0.886254i	$0.346701\pi$
$131$			20.2873i			1.77251i	−0.463200	+	0.886254i	$0.653299\pi$
$132$	15.7071	+	8.65874i	1.36713	+	0.753647i
$133$	0.435365	+	1.62481i	0.0377510	+	0.140889i
$134$	−0.427464	−	0.740390i	−0.0369273	−	0.0639599i
$135$	10.2204	+	5.52668i	0.879629	+	0.475661i
$136$	1.30477	−	0.753310i	0.111883	−	0.0645958i
$137$	−3.45972	+	12.9118i	−0.295584	+	1.10313i	0.645169	+	0.764040i	$0.276787\pi$
$137$	−3.45972	+	12.9118i	−0.295584	+	1.10313i	−0.940753	+	0.339093i	$0.889880\pi$
$138$	−0.0103967	−	0.525365i	−0.000885026	−	0.0447220i
$139$	17.9438	−	10.3598i	1.52197	−	0.878710i	0.522307	−	0.852758i	$-0.325072\pi$
$139$	17.9438	−	10.3598i	1.52197	−	0.878710i	0.999663	−	0.0259523i	$-0.00826180\pi$
$140$	−17.0063	−	5.13565i	−1.43730	−	0.434042i
$141$	−3.04596	+	0.881112i	−0.256516	+	0.0742030i
$142$	0.960517	+	0.960517i	0.0806048	+	0.0806048i
$143$	11.5194	+	14.8378i	0.963304	+	1.24080i
$144$	−11.7680	+	0.465948i	−0.980667	+	0.0388290i
$145$	−9.95238	+	5.33563i	−0.826500	+	0.443100i
$146$	0.176948	+	0.102161i	0.0146443	+	0.00845490i
$147$	13.3091	−	8.03924i	1.09772	−	0.663066i
$148$	8.35507	+	8.35507i	0.686783	+	0.686783i
$149$	−7.82540	+	4.51800i	−0.641082	+	0.370129i	−0.785031	−	0.619456i	$-0.787353\pi$
$149$	−7.82540	+	4.51800i	−0.641082	+	0.370129i	0.143949	+	0.989585i	$0.454020\pi$
$150$	−0.941491	+	0.209183i	−0.0768724	+	0.0170797i
$151$			11.7129i			0.953180i	0.879126	+	0.476590i	$0.158127\pi$
$151$			11.7129i			0.953180i	−0.879126	+	0.476590i	$0.841873\pi$
$152$	−0.180515	−	0.0483689i	−0.0146417	−	0.00392323i
$153$	−3.02117	−	9.71933i	−0.244247	−	0.785761i
$154$	1.15956	−	2.00842i	0.0934403	−	0.161843i
$155$	−4.99126	+	8.04898i	−0.400908	+	0.646509i
$156$	−11.5848	−	4.45675i	−0.927530	−	0.356826i
$157$	11.2708	+	11.2708i	0.899508	+	0.899508i	0.995392	−	0.0958846i	$-0.0305680\pi$
$157$	11.2708	+	11.2708i	0.899508	+	0.899508i	−0.0958846	+	0.995392i	$0.530568\pi$
$158$	0.0717997	+	0.267960i	0.00571207	+	0.0213177i
$159$	−5.78282	+	1.67281i	−0.458608	+	0.132663i
$160$	2.16047	−	2.02857i	0.170800	−	0.160372i
$161$	10.8889			0.858167
$162$	0.182053	−	0.985613i	0.0143034	−	0.0774370i
$163$	−3.31744	+	12.3808i	−0.259842	+	0.969742i	0.705491	+	0.708719i	$0.250727\pi$
$163$	−3.31744	+	12.3808i	−0.259842	+	0.969742i	−0.965333	+	0.261023i	$0.915940\pi$
$164$		−	3.86839i		−	0.302070i
$165$	−0.235882	+	20.1764i	−0.0183634	+	1.57073i
$166$	−0.752177	+	1.30281i	−0.0583803	+	0.101118i
$167$	21.7842	−	5.83706i	1.68571	−	0.451685i	0.716435	−	0.697654i	$-0.245773\pi$
$167$	21.7842	−	5.83706i	1.68571	−	0.451685i	0.969278	+	0.245968i	$0.0791059\pi$
$168$	0.0608301	+	3.07386i	0.00469315	+	0.237153i
$169$	−9.29585	−	9.08774i	−0.715066	−	0.699057i
$170$	0.718001	+	0.445240i	0.0550682	+	0.0341484i
$171$	−0.587498	+	1.11747i	−0.0449271	+	0.0854554i
$172$	−1.79922	+	0.482100i	−0.137189	+	0.0367598i
$173$	−0.936524	+	3.49516i	−0.0712026	+	0.265732i	−0.992345	−	0.123493i	$-0.960590\pi$
$173$	−0.936524	+	3.49516i	−0.0712026	+	0.265732i	0.921143	+	0.389225i	$0.127257\pi$
$174$	0.702299	+	0.675042i	0.0532412	+	0.0511748i
$175$	−3.94790	−	19.5918i	−0.298433	−	1.48100i
$176$	−10.2263	−	17.7125i	−0.770838	−	1.33513i
$177$	−0.310014	−	15.6656i	−0.0233021	−	1.17750i
$178$	0.465292	+	0.124675i	0.0348751	+	0.00934476i
$179$	−2.91155	+	5.04296i	−0.217620	+	0.376928i	−0.954080	−	0.299553i	$-0.903163\pi$
$179$	−2.91155	+	5.04296i	−0.217620	+	0.376928i	0.736460	+	0.676481i	$0.236496\pi$
$180$	−6.75988	−	11.4925i	−0.503851	−	0.856604i
$181$	9.95426			0.739894			0.369947	−	0.929053i	$-0.379376\pi$
$181$	9.95426			0.739894			0.369947	+	0.929053i	$0.379376\pi$
$182$	−0.605795	+	1.48626i	−0.0449045	+	0.110169i
$183$	9.21041	−	0.182270i	0.680853	−	0.0134738i
$184$	−0.604876	+	1.04768i	−0.0445921	+	0.0772357i
$185$	−3.84287	+	12.7254i	−0.282533	+	0.935588i
$186$	0.793182	+	0.195798i	0.0581590	+	0.0143566i
$187$	12.4985	−	12.4985i	0.913978	−	0.913978i
$188$	3.51468	+	0.941755i	0.256334	+	0.0686846i
$189$	20.3456	+	4.17593i	1.47992	+	0.303754i
$190$	−0.0239239	−	0.102028i	−0.00173562	−	0.00740191i
$191$	19.8105	−	11.4376i	1.43343	−	0.827594i	0.436053	−	0.899921i	$-0.356376\pi$
$191$	19.8105	−	11.4376i	1.43343	−	0.827594i	0.997381	+	0.0723271i	$0.0230425\pi$
$192$	11.6856	+	6.44181i	0.843333	+	0.464898i
$193$	−16.5328	+	4.42994i	−1.19005	+	0.318874i	−0.798908	−	0.601454i	$-0.794588\pi$
$193$	−16.5328	+	4.42994i	−1.19005	+	0.318874i	−0.391147	+	0.920328i	$0.627922\pi$
$194$	0.318662			0.0228786
$195$	−1.73918	−	13.8555i	−0.124545	−	0.992214i
$196$	−17.8427			−1.27448
$197$	−1.42911	+	0.382929i	−0.101820	+	0.0272826i	−0.309369	−	0.950942i	$-0.600118\pi$
$197$	−1.42911	+	0.382929i	−0.101820	+	0.0272826i	0.207549	+	0.978225i	$0.433451\pi$
$198$	1.66215	−	0.516664i	0.118124	−	0.0367177i
$199$	20.6928	−	11.9470i	1.46687	−	0.846899i	0.467558	−	0.883962i	$-0.345134\pi$
$199$	20.6928	−	11.9470i	1.46687	−	0.846899i	0.999313	+	0.0370636i	$0.0118004\pi$
$200$	2.10433	+	0.708474i	0.148799	+	0.0500967i
$201$	12.9091	+	3.18663i	0.910540	+	0.224768i
$202$	−0.297429	−	0.0796957i	−0.0209270	−	0.00560737i
$203$	−14.2737	+	14.2737i	−1.00181	+	1.00181i
$204$	−2.79913	+	11.3394i	−0.195978	+	0.793914i
$205$	3.83554	−	2.05629i	0.267885	−	0.143618i
$206$	−0.00358979	+	0.00621770i	−0.000250113	+	0.000433208i
$207$	6.00297	+	5.54571i	0.417236	+	0.385453i
$208$	8.68011	+	11.1805i	0.601857	+	0.775231i
$209$	−2.19249			−0.151658
$210$	−1.50302	+	0.844498i	−0.103718	+	0.0582759i
$211$	1.53923	−	2.66603i	0.105965	−	0.183537i	−0.808167	−	0.588953i	$-0.799540\pi$
$211$	1.53923	−	2.66603i	0.105965	−	0.183537i	0.914132	+	0.405416i	$0.132873\pi$
$212$	6.67270	+	1.78795i	0.458283	+	0.122797i
$213$	−21.1226	+	0.418005i	−1.44730	+	0.0286413i
$214$	0.945842	+	1.63825i	0.0646565	+	0.111988i
$215$	−1.43441	−	1.52768i	−0.0978257	−	0.104187i
$216$	−1.53198	+	1.72558i	−0.104238	+	0.117411i
$217$	−4.38180	+	16.3531i	−0.297456	+	1.11012i
$218$	0.508972	−	0.136379i	0.0344719	−	0.00923672i
$219$	−3.05264	+	0.883046i	−0.206279	+	0.0596707i
$220$	12.2028	−	19.6784i	0.822711	−	1.32671i
$221$	−7.39163	+	9.74669i	−0.497215	+	0.655633i
$222$	1.14647	−	0.0226880i	0.0769458	−	0.00152272i
$223$	−5.58375	+	1.49616i	−0.373916	+	0.100190i	−0.440883	−	0.897565i	$-0.645334\pi$
$223$	−5.58375	+	1.49616i	−0.373916	+	0.100190i	0.0669668	+	0.997755i	$0.478668\pi$
$224$	2.64879	−	4.58784i	0.176980	−	0.306538i
$225$	7.80165	−	12.8115i	0.520110	−	0.854099i
$226$		−	0.314003i		−	0.0208872i
$227$	3.79984	−	14.1812i	0.252204	−	0.941238i	−0.717421	−	0.696640i	$-0.754677\pi$
$227$	3.79984	−	14.1812i	0.252204	−	0.941238i	0.969625	−	0.244598i	$-0.0786560\pi$
$228$	1.24009	−	0.749066i	0.0821271	−	0.0496081i
$229$	−3.60574			−0.238274			−0.119137	−	0.992878i	$-0.538013\pi$
$229$	−3.60574			−0.238274			−0.119137	+	0.992878i	$0.538013\pi$
$230$	−0.678040	−	0.0213499i	−0.0447086	−	0.00140777i
$231$	10.0229	+	34.6486i	0.659459	+	2.27971i
$232$	−0.580442	−	2.16624i	−0.0381079	−	0.142220i
$233$	−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
$235$	0.934517	+	3.98544i	0.0609612	+	0.259981i
$236$	−8.99021	+	15.5715i	−0.585213	+	1.01362i
$237$	−3.77848	−	2.08294i	−0.245439	−	0.135301i
$238$	1.45876	+	0.390874i	0.0945575	+	0.0253366i
$239$		−	0.0947772i		−	0.00613063i	−0.999995	−	0.00306532i	$-0.999024\pi$
$239$		−	0.0947772i		−	0.00613063i	0.999995	−	0.00306532i	$-0.000975722\pi$
$240$	−0.177741	+	15.2033i	−0.0114731	+	0.981368i
$241$	9.34499	−	5.39533i	0.601964	−	0.347544i	−0.167850	−	0.985813i	$-0.553682\pi$
$241$	9.34499	−	5.39533i	0.601964	−	0.347544i	0.769814	+	0.638269i	$0.220349\pi$
$242$	1.27120	+	1.27120i	0.0817159	+	0.0817159i
$243$	9.08955	+	12.6641i	0.583095	+	0.812404i
$244$	−9.15509	−	5.28569i	−0.586095	−	0.338382i
$245$	−9.48455	−	17.6912i	−0.605946	−	1.13025i
$246$	−0.270658	−	0.260154i	−0.0172565	−	0.0165868i
$247$	1.50321	−	0.206563i	0.0956468	−	0.0131433i
$248$	−1.33000	−	1.33000i	−0.0844554	−	0.0844554i
$249$	−6.50158	−	22.4756i	−0.412021	−	1.42434i
$250$	0.207417	+	1.22770i	0.0131182	+	0.0776466i
$251$	−18.5242	+	10.6949i	−1.16923	+	0.675058i	−0.953500	−	0.301394i	$-0.902548\pi$
$251$	−18.5242	+	10.6949i	−1.16923	+	0.675058i	−0.215735	+	0.976452i	$0.569215\pi$
$252$	−17.5068	−	16.1733i	−1.10282	−	1.01882i
$253$	−3.67333	+	13.7091i	−0.230941	+	0.861882i
$254$	0.174732	−	0.100881i	0.0109636	−	0.00632986i
$255$	−12.7310	+	3.25223i	−0.797245	+	0.203662i
$256$	−7.50851	−	13.0051i	−0.469282	−	0.812821i
$257$	−4.19954	−	15.6729i	−0.261960	−	0.977648i	−0.964085	−	0.265594i	$-0.914432\pi$
$257$	−4.19954	−	15.6729i	−0.261960	−	0.977648i	0.702125	−	0.712054i	$-0.252235\pi$
$258$	−0.0872689	+	0.158307i	−0.00543313	+	0.00985579i
$259$			23.7621i			1.47651i
$260$	−6.51245	+	14.6415i	−0.403885	+	0.908027i
$261$	−15.1385	+	0.599402i	−0.937051	+	0.0371021i
$262$	−0.584748	−	2.18231i	−0.0361259	−	0.134824i
$263$	22.1701	−	5.94046i	1.36707	−	0.366304i	0.500660	−	0.865644i	$-0.333091\pi$
$263$	22.1701	−	5.94046i	1.36707	−	0.366304i	0.866406	+	0.499340i	$0.166424\pi$
$264$	−3.89049	−	0.960370i	−0.239443	−	0.0591067i
$265$	1.77420	+	7.56645i	0.108988	+	0.464803i
$266$	−0.0936648	−	0.162232i	−0.00574296	−	0.00994709i
$267$	−6.41282	+	3.87361i	−0.392458	+	0.237061i
$268$	−10.7893	−	10.7893i	−0.659063	−	0.659063i
$269$	−1.73455	−	3.00433i	−0.105758	−	0.183177i	0.808290	−	0.588785i	$-0.200393\pi$
$269$	−1.73455	−	3.00433i	−0.105758	−	0.183177i	−0.914047	+	0.405607i	$0.867060\pi$
$270$	−1.25871	−	0.299922i	−0.0766024	−	0.0182526i
$271$	10.2881	+	5.93984i	0.624958	+	0.360819i	0.778797	−	0.627277i	$-0.215830\pi$
$271$	10.2881	+	5.93984i	0.624958	+	0.360819i	−0.153839	+	0.988096i	$0.549164\pi$
$272$	9.41782	−	9.41782i	0.571039	−	0.571039i
$273$	−10.1363	−	22.8114i	−0.613475	−	1.38061i
$274$		−	1.48865i		−	0.0899328i
$275$	25.9978	+	1.63885i	1.56773	+	0.0988264i
$276$	−2.60605	−	9.00897i	−0.156866	−	0.542276i
$277$	−4.44872	+	16.6029i	−0.267298	+	0.997570i	0.693531	+	0.720427i	$0.256054\pi$
$277$	−4.44872	+	16.6029i	−0.267298	+	0.997570i	−0.960829	+	0.277143i	$0.910613\pi$
$278$	−1.63161	+	1.63161i	−0.0978575	+	0.0978575i
$279$	−10.7443	+	6.78369i	−0.643242	+	0.406129i
$280$	3.96714	+	0.124917i	0.237082	+	0.00746519i
$281$	22.1387			1.32068			0.660341	−	0.750966i	$-0.270412\pi$
$281$	22.1387			1.32068			0.660341	+	0.750966i	$0.270412\pi$
$282$	0.302258	−	0.182576i	0.0179992	−	0.0108723i
$283$	−0.732387	−	2.73331i	−0.0435359	−	0.162478i	0.940736	−	0.339141i	$-0.110136\pi$
$283$	−0.732387	−	2.73331i	−0.0435359	−	0.162478i	−0.984271	+	0.176663i	$0.943470\pi$
$284$	20.9957	+	12.1219i	1.24587	+	0.719301i
$285$	1.40189	+	0.831384i	0.0830410	+	0.0492470i
$286$	−1.66682	−	1.26408i	−0.0985614	−	0.0747464i
$287$	5.50091	−	5.50091i	0.324708	−	0.324708i
$288$	3.79684	−	1.18022i	0.223731	−	0.0695449i
$289$	−4.75421	−	2.74484i	−0.279659	−	0.161461i
$290$	0.916790	−	0.860817i	0.0538358	−	0.0505489i
$291$	−3.43448	+	3.57316i	−0.201333	+	0.209462i
$292$	3.52240	+	0.943823i	0.206133	+	0.0552331i
$293$	7.63862	+	2.04676i	0.446253	+	0.119573i	0.474946	−	0.880015i	$-0.342468\pi$
$293$	7.63862	+	2.04676i	0.446253	+	0.119573i	−0.0286927	+	0.999588i	$0.509134\pi$
$294$	−1.19995	+	1.24840i	−0.0699823	+	0.0728080i
$295$	−20.2181	−	0.636624i	−1.17715	−	0.0370657i
$296$	−2.28627	−	1.31998i	−0.132887	−	0.0767222i
$297$	−12.1210	+	24.2062i	−0.703329	+	1.40459i
$298$	0.711557	−	0.711557i	0.0412194	−	0.0412194i
$299$	1.22691	−	9.74525i	0.0709543	−	0.563583i
$300$	−15.2645	+	7.95523i	−0.881297	+	0.459296i
$301$	−3.24408	−	1.87297i	−0.186985	−	0.107956i
$302$	−0.337605	−	1.25996i	−0.0194270	−	0.0725024i
$303$	4.09926	−	2.47612i	0.235496	−	0.142250i
$304$	−1.65208			−0.0947533
$305$	0.374296	−	11.8870i	0.0214321	−	0.680649i
$306$	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	$0.107927\pi$
$308$	10.7127	−	39.9805i	0.610415	−	2.27810i
$309$	−0.0310290	−	0.107266i	−0.00176518	−	0.00610213i
$310$	0.304913	−	1.00970i	0.0173179	−	0.0573469i
$311$		−	12.0194i		−	0.681560i	−0.940143	−	0.340780i	$-0.889309\pi$
$311$		−	12.0194i		−	0.681560i	0.940143	−	0.340780i	$-0.110691\pi$
$312$	2.75787	+	0.291908i	0.156133	+	0.0165260i
$313$	16.5079	−	16.5079i	0.933082	−	0.933082i	−0.0648148	−	0.997897i	$-0.520646\pi$
$313$	16.5079	−	16.5079i	0.933082	−	0.933082i	0.997897	+	0.0648148i	$0.0206457\pi$
$314$	−1.53727	−	0.887541i	−0.0867530	−	0.0500869i
$315$	6.72993	−	25.9552i	0.379189	−	1.46241i
$316$	2.47557	+	4.28782i	0.139262	+	0.241209i
$317$	−0.778692	−	0.778692i	−0.0437357	−	0.0437357i	0.684901	−	0.728636i	$-0.259846\pi$
$317$	−0.778692	−	0.778692i	−0.0437357	−	0.0437357i	−0.728636	+	0.684901i	$0.759846\pi$
$318$	0.573844	−	0.346626i	0.0321796	−	0.0194378i
$319$	−13.1553	−	22.7856i	−0.736554	−	1.27575i
$320$	9.07846	−	14.6400i	0.507501	−	0.818403i
$321$	−28.5638	−	7.05100i	−1.59428	−	0.393548i
$322$	−1.17132	+	0.313855i	−0.0652753	+	0.0174905i
$323$	−0.369530	−	1.37910i	−0.0205612	−	0.0767354i
$324$	−1.41435	−	17.8324i	−0.0785748	−	0.990688i
$325$	−17.9789	+	1.32573i	−0.997292	+	0.0735385i
$326$		−	1.42743i		−	0.0790581i
$327$	−3.95639	+	7.17697i	−0.218789	+	0.396887i
$328$	0.223696	+	0.834844i	0.0123515	+	0.0460965i
$329$	3.65874	+	6.33712i	0.201713	+	0.349377i
$330$	−0.556178	−	2.17718i	−0.0306166	−	0.119850i
$331$	−24.3850	+	14.0787i	−1.34032	+	0.773834i	−0.986854	−	0.161614i	$-0.948330\pi$
$331$	−24.3850	+	14.0787i	−1.34032	+	0.773834i	−0.353466	+	0.935448i	$0.614997\pi$
$332$	−6.94906	+	25.9343i	−0.381379	+	1.42333i
$333$	−12.1020	+	13.0999i	−0.663186	+	0.717868i
$334$	−2.17509	+	1.25579i	−0.119016	+	0.0687138i
$335$	4.96249	−	16.4329i	0.271130	−	0.897826i
$336$	7.55244	+	26.1084i	0.412019	+	1.42433i
$337$	−17.9435	−	17.9435i	−0.977446	−	0.977446i	0.0223051	−	0.999751i	$-0.492899\pi$
$337$	−17.9435	−	17.9435i	−0.977446	−	0.977446i	−0.999751	+	0.0223051i	$0.992899\pi$
$338$	1.26190	+	0.709634i	0.0686382	+	0.0385990i
$339$	3.52092	+	3.38427i	0.191230	+	0.183808i
$340$	14.4346	+	4.35904i	0.782828	+	0.236402i
$341$	−19.1103	−	11.0333i	−1.03488	−	0.597487i
$342$	0.0309880	−	0.137141i	0.00167564	−	0.00741572i
$343$	−5.58789	−	5.58789i	−0.301717	−	0.301717i
$344$	0.360415	−	0.208086i	0.0194323	−	0.0112192i
$345$	7.54719	−	7.37276i	0.406327	−	0.396936i
$346$		−	0.402969i		−	0.0216637i
$347$	0.484424	+	0.129801i	0.0260052	+	0.00696808i	0.271798	−	0.962354i	$-0.412382\pi$
$347$	0.484424	+	0.129801i	0.0260052	+	0.00696808i	−0.245793	+	0.969322i	$0.579048\pi$
$348$	15.2255	+	8.39323i	0.816171	+	0.449924i
$349$	−4.63210	+	8.02304i	−0.247951	+	0.429463i	−0.962957	−	0.269655i	$-0.913090\pi$
$349$	−4.63210	+	8.02304i	−0.247951	+	0.429463i	0.715006	+	0.699118i	$0.246424\pi$
$350$	0.989380	+	1.99371i	0.0528846	+	0.106568i
$351$	6.02978	−	17.7381i	0.321846	−	0.946792i
$352$	4.88250	+	4.88250i	0.260238	+	0.260238i
$353$	5.48087	+	20.4549i	0.291717	+	1.08870i	0.943790	+	0.330547i	$0.107233\pi$
$353$	5.48087	+	20.4549i	0.291717	+	1.08870i	−0.652072	+	0.758157i	$0.726100\pi$
$354$	0.484884	+	1.67622i	0.0257713	+	0.0890900i
$355$	−0.858387	+	27.2610i	−0.0455584	+	1.44686i
$356$	8.59729			0.455656
$357$	−20.1052	+	12.1443i	−1.06408	+	0.642747i
$358$	0.167842	−	0.626394i	0.00887071	−	0.0331059i
$359$			17.7610i			0.937391i	0.883360	+	0.468695i	$0.155276\pi$
$359$			17.7610i			0.937391i	−0.883360	+	0.468695i	$0.844724\pi$
$360$	2.12344	+	2.08933i	0.111915	+	0.110117i
$361$	9.41145	−	16.3011i	0.495339	−	0.857953i
$362$	−1.07078	+	0.286915i	−0.0562791	+	0.0150799i
$363$	−27.9548	+	0.553211i	−1.46724	+	0.0290361i
$364$	−3.57812	+	28.4206i	−0.187544	+	1.48964i
$365$	0.936569	+	3.99419i	0.0490223	+	0.209065i
$366$	−0.985514	+	0.285082i	−0.0515136	+	0.0149015i
$367$	1.08991	−	0.292041i	0.0568929	−	0.0152444i	−0.230260	−	0.973129i	$-0.573958\pi$
$367$	1.08991	−	0.292041i	0.0568929	−	0.0152444i	0.287153	+	0.957885i	$0.407291\pi$
$368$	−2.76792	+	10.3300i	−0.144288	+	0.538490i
$369$	5.83421	−	0.231003i	0.303717	−	0.0120255i
$370$	0.0465905	−	1.47964i	0.00242212	−	0.0769227i
$371$	6.94621	+	12.0312i	0.360629	+	0.624628i
$372$	14.5785	−	0.288501i	0.755859	−	0.0149581i
$373$	17.2256	+	4.61559i	0.891908	+	0.238986i	0.675538	−	0.737325i	$-0.263912\pi$
$373$	17.2256	+	4.61559i	0.891908	+	0.238986i	0.216370	+	0.976311i	$0.430578\pi$
$374$	−0.984215	+	1.70471i	−0.0508926	+	0.0881485i
$375$	−16.0017	−	10.9062i	−0.826326	−	0.563192i
$376$	−0.812968			−0.0419256
$377$	11.1662	+	14.3828i	0.575089	+	0.740752i
$378$	−2.30894	+	0.137222i	−0.118759	+	0.00705793i
$379$	5.17481	−	8.96303i	0.265812	−	0.460400i	−0.701964	−	0.712212i	$-0.747693\pi$
$379$	5.17481	−	8.96303i	0.265812	−	0.460400i	0.967776	+	0.251813i	$0.0810267\pi$
$380$	−0.883734	−	1.64840i	−0.0453346	−	0.0845612i
$381$	−0.752043	+	3.04655i	−0.0385283	+	0.156079i
$382$	−1.80135	+	1.80135i	−0.0921650	+	0.0921650i
$383$	−16.0474	−	4.29989i	−0.819985	−	0.219714i	−0.175645	−	0.984454i	$-0.556201\pi$
$383$	−16.0474	−	4.29989i	−0.819985	−	0.219714i	−0.644340	+	0.764739i	$0.722868\pi$
$384$	−5.90004	−	1.45643i	−0.301085	−	0.0743231i
$385$	45.3355	−	10.6304i	2.31051	−	0.541776i
$386$	1.65075	−	0.953061i	0.0840210	−	0.0485095i
$387$	−0.834534	−	2.68476i	−0.0424218	−	0.136474i
$388$	5.49356	−	1.47199i	0.278893	−	0.0747292i
$389$	24.1762			1.22578			0.612891	−	0.790167i	$-0.290006\pi$
$389$	24.1762			1.22578			0.612891	+	0.790167i	$0.290006\pi$
$390$	0.586447	+	1.44031i	0.0296959	+	0.0729331i
$391$	−9.24230			−0.467403
$392$	3.85068	−	1.03179i	0.194488	−	0.0521130i
$393$	30.7726	+	16.9638i	1.55227	+	0.855709i
$394$	0.142693	−	0.0823836i	0.00718875	−	0.00415043i
$395$	−2.93548	+	4.73380i	−0.147700	+	0.238183i
$396$	26.2679	−	16.5850i	1.32001	−	0.833425i
$397$	8.25936	+	2.21309i	0.414525	+	0.111072i	0.460053	−	0.887891i	$-0.347830\pi$
$397$	8.25936	+	2.21309i	0.414525	+	0.111072i	−0.0455279	+	0.998963i	$0.514497\pi$
$398$	−1.88158	+	1.88158i	−0.0943149	+	0.0943149i
$399$	2.82861	+	0.698246i	0.141608	+	0.0349560i
$400$	19.5898	+	1.23490i	0.979491	+	0.0617452i
$401$	13.7400	−	23.7983i	0.686142	−	1.18843i	−0.286935	−	0.957950i	$-0.592636\pi$
$401$	13.7400	−	23.7983i	0.686142	−	1.18843i	0.973076	−	0.230482i	$-0.0740304\pi$
$402$	−1.48049	+	0.0292982i	−0.0738401	+	0.00146126i
$403$	14.1418	+	5.76418i	0.704454	+	0.287134i
$404$	−5.49564			−0.273418
$405$	16.9291	−	10.8814i	0.841215	−	0.540700i
$406$	1.12401	−	1.94684i	0.0557835	−	0.0966199i
$407$	−29.9163	−	8.01606i	−1.48290	−	0.397341i
$408$	−0.0516315	−	2.60903i	−0.00255614	−	0.129166i
$409$	18.6648	+	32.3284i	0.922916	+	1.59854i	0.794878	+	0.606769i	$0.207535\pi$
$409$	18.6648	+	32.3284i	0.922916	+	1.59854i	0.128038	+	0.991769i	$0.459132\pi$
$410$	−0.353321	+	0.331749i	−0.0174493	+	0.0163839i
$411$	16.6923	+	16.0444i	0.823369	+	0.791414i
$412$	−0.0331646	+	0.123772i	−0.00163390	+	0.00609781i
$413$	−34.9272	+	9.35870i	−1.71865	+	0.460512i
$414$	−0.805588	−	0.423528i	−0.0395925	−	0.0208153i
$415$	−29.4079	+	6.89565i	−1.44358	+	0.338494i
$416$	−3.80753	−	2.88753i	−0.186680	−	0.141573i
$417$	−0.710057	−	35.8805i	−0.0347717	−	1.75708i
$418$	0.235847	−	0.0631949i	0.0115356	−	0.00309097i
$419$	−14.8413	+	25.7059i	−0.725046	+	1.25582i	0.233909	+	0.972259i	$0.424848\pi$
$419$	−14.8413	+	25.7059i	−0.725046	+	1.25582i	−0.958955	+	0.283558i	$0.908485\pi$
$420$	−22.0103	+	21.5016i	−1.07399	+	1.04917i
$421$			21.3437i			1.04023i	0.854097	+	0.520114i	$0.174111\pi$
$421$			21.3437i			1.04023i	−0.854097	+	0.520114i	$0.825889\pi$
$422$	−0.0887317	+	0.331151i	−0.00431939	+	0.0161202i
$423$	−1.21045	+	5.35700i	−0.0588543	+	0.260466i
$424$	−1.54344			−0.0749561
$425$	3.35090	+	16.6292i	0.162543	+	0.806633i
$426$	2.26011	−	0.653789i	0.109503	−	0.0316762i
$427$	−5.50234	−	20.5350i	−0.266277	−	0.993760i
$428$	23.8734	+	23.8734i	1.15396	+	1.15396i
$429$	32.1388	−	5.06614i	1.55168	−	0.244596i
$430$	0.198332	+	0.122988i	0.00956444	+	0.00593102i
$431$	1.45407	−	2.51852i	0.0700400	−	0.121313i	−0.828879	−	0.559429i	$-0.811021\pi$
$431$	1.45407	−	2.51852i	0.0700400	−	0.121313i	0.898919	+	0.438116i	$0.144354\pi$
$432$	−9.13337	+	18.2398i	−0.439429	+	0.877563i
$433$	−25.5439	−	6.84446i	−1.22756	−	0.328924i	−0.413932	−	0.910308i	$-0.635845\pi$
$433$	−25.5439	−	6.84446i	−1.22756	−	0.328924i	−0.813629	+	0.581384i	$0.802511\pi$
$434$		−	1.88541i		−	0.0905024i
$435$	−0.228649	+	19.5577i	−0.0109629	+	0.937721i
$436$	8.14442	−	4.70218i	0.390047	−	0.225194i
$437$	0.810645	+	0.810645i	0.0387784	+	0.0387784i
$438$	0.302922	−	0.182977i	0.0144742	−	0.00874299i
$439$	−23.2175	−	13.4046i	−1.10811	−	0.639768i	−0.169771	−	0.985484i	$-0.554303\pi$
$439$	−23.2175	−	13.4046i	−1.10811	−	0.639768i	−0.938339	+	0.345716i	$0.887636\pi$
$440$	−1.49557	+	4.95247i	−0.0712985	+	0.236100i
$441$	−1.06549	−	26.9100i	−0.0507376	−	1.28143i
$442$	0.514187	−	1.26151i	0.0244574	−	0.0600037i
$443$	−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
$445$	4.57001	+	8.52429i	0.216639	+	0.404090i
$446$	0.557522	−	0.321885i	0.0263994	−	0.0152417i
$447$	0.309661	+	15.6477i	0.0146465	+	0.740113i
$448$	7.96992	−	29.7442i	0.376543	−	1.40528i
$449$	3.02917	−	1.74889i	0.142956	−	0.0825354i	−0.426816	−	0.904338i	$-0.640365\pi$
$449$	3.02917	−	1.74889i	0.142956	−	0.0825354i	0.569772	+	0.821803i	$0.307032\pi$
$450$	−0.469956	+	1.60301i	−0.0221539	+	0.0755664i
$451$	5.06990	+	8.78132i	0.238732	+	0.413496i
$452$	−1.45047	−	5.41324i	−0.0682245	−	0.254617i
$453$	17.7666	+	9.79404i	0.834746	+	0.460164i
$454$			1.63500i			0.0767343i
$455$	−30.0813	+	11.5596i	−1.41023	+	0.541924i
$456$	−0.224311	+	0.233368i	−0.0105043	+	0.0109284i
$457$	−9.02853	−	33.6949i	−0.422337	−	1.57618i	−0.769671	−	0.638441i	$-0.779580\pi$
$457$	−9.02853	−	33.6949i	−0.422337	−	1.57618i	0.347334	−	0.937742i	$-0.387087\pi$
$458$	0.387870	−	0.103930i	0.0181240	−	0.00485631i
$459$	−17.2689	−	3.54445i	−0.806044	−	0.165441i
$460$	−11.7877	+	2.76400i	−0.549602	+	0.128872i
$461$	−5.43399	−	9.41194i	−0.253086	−	0.438358i	0.711288	−	0.702901i	$-0.248112\pi$
$461$	−5.43399	−	9.41194i	−0.253086	−	0.438358i	−0.964374	+	0.264543i	$0.914779\pi$
$462$	−2.07686	−	3.43827i	−0.0966242	−	0.159963i
$463$	−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
$465$	8.03544	+	14.3013i	0.372635	+	0.663208i
$466$	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	$0.297739\pi$
$468$	−16.4472	+	13.8457i	−0.760271	+	0.640019i
$469$		−	30.6852i		−	1.41691i
$470$	−0.215400	−	0.401779i	−0.00993567	−	0.0185327i
$471$	26.5204	−	7.67163i	1.22200	−	0.353490i
$472$	1.03975	−	3.88039i	0.0478582	−	0.178609i
$473$	3.45243	−	3.45243i	0.158743	−	0.158743i
$474$	0.466490	+	0.115153i	0.0214266	+	0.00528917i
$475$	1.16464	−	1.75246i	0.0534374	−	0.0804084i
$476$	26.9538			1.23543
$477$	−2.29808	+	10.1704i	−0.105222	+	0.465670i
$478$	0.00273180	+	0.0101952i	0.000124950	+	0.000466319i
$479$	−13.8170	−	7.97728i	−0.631317	−	0.364491i	0.149945	−	0.988694i	$-0.452090\pi$
$479$	−13.8170	−	7.97728i	−0.631317	−	0.364491i	−0.781262	+	0.624203i	$0.785424\pi$
$480$	−1.27048	−	4.97334i	−0.0579892	−	0.227001i
$481$	21.2664	+	2.67741i	0.969664	+	0.122079i
$482$	−0.849732	+	0.849732i	−0.0387042	+	0.0387042i
$483$	9.10506	−	16.5168i	0.414295	−	0.751538i
$484$	27.7869	+	16.0427i	1.26304	+	0.729216i
$485$	4.37967	+	4.66445i	0.198871	+	0.211802i
$486$	−1.34279	−	1.10029i	−0.0609102	−	0.0499103i
$487$	31.7115	+	8.49708i	1.43699	+	0.385040i	0.891478	−	0.453065i	$-0.149669\pi$
$487$	31.7115	+	8.49708i	1.43699	+	0.385040i	0.545510	+	0.838104i	$0.316336\pi$
$488$	2.28143	+	0.611308i	0.103276	+	0.0276726i
$489$	16.0058	+	15.3846i	0.723807	+	0.695716i
$490$	1.53018	+	1.62967i	0.0691263	+	0.0736211i
$491$	−25.2561	−	14.5816i	−1.13979	−	0.658058i	−0.193412	−	0.981118i	$-0.561955\pi$
$491$	−25.2561	−	14.5816i	−1.13979	−	0.658058i	−0.946379	+	0.323059i	$0.895289\pi$
$492$	−5.86773	−	3.23466i	−0.264538	−	0.145830i
$493$	12.1152	−	12.1152i	0.545642	−	0.545642i
$494$	−0.155747	+	0.0655476i	−0.00700738	+	0.00294913i
$495$	30.4072	+	17.2288i	1.36670	+	0.774379i
$496$	−14.3999	−	8.31380i	−0.646576	−	0.373301i
$497$	12.6187	+	47.0937i	0.566027	+	2.11244i
$498$	1.34720	+	2.23031i	0.0603695	+	0.0999427i
$499$	−16.7557			−0.750087			−0.375044	−	0.927007i	$-0.622372\pi$
$499$	−16.7557			−0.750087			−0.375044	+	0.927007i	$0.622372\pi$
$500$	9.24688	+	20.2068i	0.413533	+	0.903674i
$501$	9.36157	−	37.9240i	0.418244	−	1.69432i
$502$	1.68439	−	1.68439i	0.0751778	−	0.0751778i
$503$	−2.38495	+	8.90077i	−0.106340	+	0.396866i	−0.998494	−	0.0548660i	$-0.982527\pi$
$503$	−2.38495	+	8.90077i	−0.106340	+	0.396866i	0.892154	+	0.451732i	$0.149194\pi$
$504$	4.71342	+	2.47802i	0.209952	+	0.110380i
$505$	−2.92128	−	5.44898i	−0.129995	−	0.242476i
$506$		−	1.58057i		−	0.0702648i
$507$	−21.5576	+	6.50137i	−0.957409	+	0.288736i
$508$	2.54628	−	2.54628i	0.112973	−	0.112973i
$509$	0.476859	+	0.275315i	0.0211364	+	0.0122031i	0.510531	−	0.859859i	$-0.329449\pi$
$509$	0.476859	+	0.275315i	0.0211364	+	0.0122031i	−0.489395	+	0.872062i	$0.662782\pi$
$510$	1.27574	−	0.716793i	0.0564905	−	0.0317401i
$511$	3.66677	+	6.35104i	0.162208	+	0.280953i
$512$	6.14451	+	6.14451i	0.271552	+	0.271552i
$513$	1.20378	+	1.82555i	0.0531481	+	0.0805999i
$514$	0.903491	+	1.56489i	0.0398513	+	0.0690245i
$515$	−0.140350	+	0.0329097i	−0.00618457	+	0.00145018i
$516$	−0.773199	+	3.13225i	−0.0340382	+	0.137890i
$517$	−9.21266	+	2.46852i	−0.405172	+	0.108566i
$518$	−0.684904	−	2.55610i	−0.0300930	−	0.112308i
$519$	4.51850	+	4.34313i	0.198340	+	0.190642i
$520$	0.558797	−	3.53640i	0.0245049	−	0.155081i
$521$			32.2002i			1.41072i	0.708852	+	0.705358i	$0.249214\pi$
$521$			32.2002i			1.41072i	−0.708852	+	0.705358i	$0.750786\pi$
$522$	1.61118	−	0.500821i	0.0705194	−	0.0219204i
$523$	−3.65245	−	13.6311i	−0.159711	−	0.596048i	−0.998656	−	0.0518323i	$-0.983494\pi$
$523$	−3.65245	−	13.6311i	−0.159711	−	0.596048i	0.838945	−	0.544216i	$-0.183173\pi$
$524$	−20.1615	−	34.9207i	−0.880758	−	1.52552i
$525$	−33.0188	−	10.3939i	−1.44106	−	0.453627i
$526$	−2.21362	+	1.27803i	−0.0965184	+	0.0557249i
$527$	3.71919	−	13.8802i	0.162010	−	0.604631i
$528$	−35.4181	+	0.700906i	−1.54137	+	0.0305030i
$529$	−13.4917	+	7.78941i	−0.586594	+	0.338670i
$530$	−0.408942	−	0.762787i	−0.0177633	−	0.0331333i
$531$	−24.0215	−	12.6290i	−1.04244	−	0.548051i
$532$	−2.36413	−	2.36413i	−0.102498	−	0.102498i
$533$	−4.30333	−	5.54297i	−0.186398	−	0.240093i
$534$	0.578179	−	0.601524i	0.0250202	−	0.0260305i
$535$	−10.9804	+	36.3608i	−0.474725	+	1.57202i
$536$	2.95238	+	1.70456i	0.127523	+	0.0736256i
$537$	5.21479	+	8.63317i	0.225035	+	0.372549i
$538$	0.273182	+	0.273182i	0.0117777	+	0.0117777i
$539$	40.5034	−	23.3846i	1.74460	−	1.00725i
$540$	−23.0848	+	0.643851i	−0.993413	+	0.0277069i
$541$			22.8149i			0.980890i	0.871472	+	0.490445i	$0.163166\pi$
$541$			22.8149i			0.980890i	−0.871472	+	0.490445i	$0.836834\pi$
$542$	−1.27790	−	0.342412i	−0.0548905	−	0.0147079i
$543$	8.32353	−	15.0990i	0.357197	−	0.647961i
$544$	−2.24824	+	3.89407i	−0.0963927	+	0.166957i
$545$	8.99153	+	5.57575i	0.385155	+	0.238839i
$546$	1.74786	+	2.16167i	0.0748017	+	0.0925109i
$547$	10.0470	+	10.0470i	0.429577	+	0.429577i	0.888484	−	0.458907i	$-0.151759\pi$
$547$	10.0470	+	10.0470i	0.429577	+	0.429577i	−0.458907	+	0.888484i	$0.651759\pi$
$548$	−6.87653	−	25.6636i	−0.293751	−	1.09629i
$549$	7.42506	−	14.1231i	0.316894	−	0.602761i
$550$	−2.84383	+	0.573053i	−0.121261	+	0.0244351i
$551$	−2.12526			−0.0905391
$552$	1.08337	+	1.79354i	0.0461115	+	0.0763383i
$553$	−2.57704	+	9.61765i	−0.109587	+	0.408984i
$554$		−	1.91420i		−	0.0813267i
$555$	16.0891	+	16.4697i	0.682942	+	0.699100i
$556$	−20.5912	+	35.6650i	−0.873261	+	1.51253i
$557$	−25.4378	+	6.81604i	−1.07783	+	0.288805i	−0.753708	−	0.657209i	$-0.771737\pi$
$557$	−25.4378	+	6.81604i	−1.07783	+	0.288805i	−0.324126	+	0.946014i	$0.605070\pi$
$558$	0.960235	−	1.03941i	0.0406500	−	0.0440017i
$559$	−2.04178	+	2.69231i	−0.0863581	+	0.113873i
$560$	34.1611	−	8.01020i	1.44357	−	0.338493i
$561$	−8.50725	−	29.4091i	−0.359176	−	1.24165i
$562$	−2.38146	+	0.638111i	−0.100456	+	0.0269171i
$563$	5.06546	−	18.9045i	0.213484	−	0.796732i	−0.773211	−	0.634149i	$-0.781351\pi$
$563$	5.06546	−	18.9045i	0.213484	−	0.796732i	0.986695	−	0.162583i	$-0.0519826\pi$
$564$	4.36739	−	4.54374i	0.183900	−	0.191326i
$565$	4.59625	−	4.31564i	0.193366	−	0.181560i
$566$	0.157566	+	0.272913i	0.00662300	+	0.0114714i
$567$	23.3467	−	27.3692i	0.980470	−	1.14940i
$568$	−5.23209	−	1.40193i	−0.219534	−	0.0588239i
$569$	2.45559	−	4.25321i	0.102944	−	0.178304i	−0.809952	−	0.586495i	$-0.800507\pi$
$569$	2.45559	−	4.25321i	0.102944	−	0.178304i	0.912896	+	0.408192i	$0.133841\pi$
$570$	−0.174765	−	0.0490250i	−0.00732012	−	0.00205343i
$571$	−17.2440			−0.721639			−0.360819	−	0.932636i	$-0.617503\pi$
$571$	−17.2440			−0.721639			−0.360819	+	0.932636i	$0.617503\pi$
$572$	−34.5743	−	14.0924i	−1.44562	−	0.589233i
$573$	−0.783925	−	39.6132i	−0.0327489	−	1.65486i
$574$	−0.433180	+	0.750289i	−0.0180806	+	0.0313165i
$575$	−9.00642	−	10.2183i	−0.375594	−	0.426133i
$576$	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	$0.409796\pi$
$578$	0.590527	+	0.158231i	0.0245627	+	0.00658156i
$579$	−7.10481	+	28.7818i	−0.295266	+	1.19613i
$580$	11.8286	−	19.0749i	0.491155	−	0.792044i
$581$	−46.7606	+	26.9973i	−1.93996	+	1.12003i
$582$	0.266458	−	0.483360i	0.0110450	−	0.0200359i
$583$	−17.4905	+	4.68655i	−0.724381	+	0.194097i
$584$	−0.814753			−0.0337147
$585$	−22.4709	−	8.94761i	−0.929056	−	0.369938i
$586$	−0.880683			−0.0363807
$587$	1.29527	−	0.347066i	0.0534615	−	0.0143250i	−0.231989	−	0.972718i	$-0.574523\pi$
$587$	1.29527	−	0.347066i	0.0534615	−	0.0143250i	0.285451	+	0.958393i	$0.407857\pi$
$588$	−14.9197	+	27.0646i	−0.615278	+	1.11613i
$589$	−1.54365	+	0.891226i	−0.0636049	+	0.0367223i
$590$	2.19322	−	0.514273i	0.0902935	−	0.0211723i
$591$	−0.614148	+	2.48793i	−0.0252627	+	0.102340i
$592$	−22.5425	−	6.04025i	−0.926491	−	0.248253i
$593$	16.7430	−	16.7430i	0.687552	−	0.687552i	−0.274138	−	0.961690i	$-0.588393\pi$
$593$	16.7430	−	16.7430i	0.687552	−	0.687552i	0.961690	+	0.274138i	$0.0883925\pi$
$594$	0.606152	−	2.95323i	0.0248707	−	0.121173i
$595$	14.3277	+	26.7249i	0.587377	+	1.09562i
$596$	8.97996	−	15.5537i	0.367834	−	0.637106i
$597$	−0.818839	−	41.3774i	−0.0335129	−	1.69347i
$598$	0.148912	+	1.08366i	0.00608945	+	0.0443143i
$599$	−29.1006			−1.18902			−0.594509	−	0.804089i	$-0.702653\pi$
$599$	−29.1006			−1.18902			−0.594509	+	0.804089i	$0.702653\pi$
$600$	2.83424	−	2.59953i	0.115707	−	0.106125i
$601$	15.9418	−	27.6120i	0.650280	−	1.12632i	−0.332775	−	0.943006i	$-0.607985\pi$
$601$	15.9418	−	27.6120i	0.650280	−	1.12632i	0.983055	−	0.183311i	$-0.0586816\pi$
$602$	0.402952	+	0.107971i	0.0164231	+	0.00440055i
$603$	15.6279	−	16.9165i	0.636419	−	0.688894i
$604$	−11.6402	−	20.1615i	−0.473635	−	0.820359i
$605$	−1.13604	+	36.0786i	−0.0461864	+	1.46681i
$606$	−0.369589	+	0.384512i	−0.0150135	+	0.0156197i
$607$	3.79661	−	14.1691i	0.154100	−	0.575107i	−0.845081	−	0.534638i	$-0.820448\pi$
$607$	3.79661	−	14.1691i	0.154100	−	0.575107i	0.999181	−	0.0404693i	$-0.0128853\pi$
$608$	0.538745	−	0.144356i	0.0218490	−	0.00585442i
$609$	9.71556	+	33.5862i	0.393695	+	1.36098i
$610$	0.302361	+	1.28948i	0.0122422	+	0.0522095i
$611$	6.08379	−	2.56042i	0.246124	−	0.103584i
$612$	14.8594	+	13.7275i	0.600657	+	0.554903i
$613$	20.0772	−	5.37967i	0.810911	−	0.217283i	0.170542	−	0.985350i	$-0.445448\pi$
$613$	20.0772	−	5.37967i	0.810911	−	0.217283i	0.640369	+	0.768067i	$0.278781\pi$
$614$	−0.842294	+	1.45890i	−0.0339922	+	0.0588762i
$615$	0.0881186	−	7.53733i	0.00355329	−	0.303934i
$616$			9.24775i			0.372602i
$617$	−10.5157	+	39.2451i	−0.423345	+	1.57995i	0.344164	+	0.938909i	$0.388162\pi$
$617$	−10.5157	+	39.2451i	−0.423345	+	1.57995i	−0.767510	+	0.641037i	$0.778504\pi$
$618$	0.00642956	+	0.0106442i	0.000258635	+	0.000428174i
$619$	−21.9052			−0.880445			−0.440222	−	0.897889i	$-0.645100\pi$
$619$	−21.9052			−0.880445			−0.440222	+	0.897889i	$0.645100\pi$
$620$	0.592445	−	18.8151i	0.0237932	−	0.755632i
$621$	13.4315	−	4.46836i	0.538988	−	0.179309i
$622$	0.346441	+	1.29293i	0.0138910	+	0.0518420i
$623$	12.2255	+	12.2255i	0.489804	+	0.489804i
$624$	24.2172	−	3.81743i	0.969464	−	0.152820i
$625$	−15.1199	+	19.9095i	−0.604795	+	0.796381i
$626$	−1.29995	+	2.25158i	−0.0519564	+	0.0899911i
$627$	−1.83331	+	3.32566i	−0.0732153	+	0.132814i
$628$	−30.6015	−	8.19964i	−1.22113	−	0.327201i
$629$		−	20.1688i		−	0.804183i
$630$	0.0241766	+	2.98599i	0.000963219	+	0.118965i
$631$	16.2845	−	9.40185i	0.648275	−	0.374282i	−0.139520	−	0.990219i	$-0.544556\pi$
$631$	16.2845	−	9.40185i	0.648275	−	0.374282i	0.787795	+	0.615937i	$0.211223\pi$
$632$	−0.782208	−	0.782208i	−0.0311146	−	0.0311146i
$633$	−2.75687	−	4.56404i	−0.109576	−	0.181404i
$634$	0.106209	+	0.0613196i	0.00421809	+	0.00243531i
$635$	3.87816	+	1.17115i	0.153900	+	0.0464755i
$636$	8.29159	−	8.62639i	0.328783	−	0.342059i
$637$	−25.5667	+	19.8489i	−1.01299	+	0.786442i
$638$	2.07188	+	2.07188i	0.0820264	+	0.0820264i
$639$	−17.0282	+	32.3891i	−0.673624	+	1.28129i
$640$	−2.26808	+	7.51056i	−0.0896536	+	0.296881i
$641$	−18.6204	+	10.7505i	−0.735461	+	0.424619i	−0.820417	−	0.571766i	$-0.806258\pi$
$641$	−18.6204	+	10.7505i	−0.735461	+	0.424619i	0.0849557	+	0.996385i	$0.472925\pi$
$642$	3.27585	−	0.0648275i	0.129288	−	0.00255854i
$643$	0.707671	−	2.64106i	0.0279078	−	0.104153i	−0.950567	−	0.310519i	$-0.899497\pi$
$643$	0.707671	−	2.64106i	0.0279078	−	0.104153i	0.978475	+	0.206366i	$0.0661637\pi$
$644$	−18.7432	+	10.8214i	−0.738585	+	0.426422i
$645$	−3.51666	+	0.898359i	−0.138468	+	0.0353728i
$646$	0.0795009	+	0.137700i	0.00312792	+	0.00541772i
$647$	−10.6764	−	39.8449i	−0.419733	−	1.56647i	−0.775162	−	0.631762i	$-0.782332\pi$
$647$	−10.6764	−	39.8449i	−0.419733	−	1.56647i	0.355429	−	0.934703i	$-0.384335\pi$
$648$	1.33642	+	3.76665i	0.0524995	+	0.147968i
$649$		−	47.1302i		−	1.85002i
$650$	1.89579	−	0.660824i	0.0743590	−	0.0259196i
$651$	21.1411	+	20.3206i	0.828585	+	0.796426i
$652$	−6.59373	−	24.6081i	−0.258230	−	0.963729i
$653$	−16.7866	+	4.49795i	−0.656909	+	0.176018i	−0.571851	−	0.820358i	$-0.693774\pi$
$653$	−16.7866	+	4.49795i	−0.656909	+	0.176018i	−0.0850584	+	0.996376i	$0.527108\pi$
$654$	0.218726	−	0.886066i	0.00855286	−	0.0346479i
$655$	23.9070	−	38.5528i	0.934126	−	1.50638i
$656$	3.82026	+	6.61688i	0.149156	+	0.258346i
$657$	−1.21311	+	5.36876i	−0.0473280	+	0.209455i
$658$	−0.576229	−	0.576229i	−0.0224638	−	0.0224638i
$659$	9.34358	+	16.1835i	0.363974	+	0.630422i	0.988611	−	0.150494i	$-0.0480863\pi$
$659$	9.34358	+	16.1835i	0.363974	+	0.630422i	−0.624637	+	0.780915i	$0.714753\pi$
$660$	−19.6453	−	34.9643i	−0.764691	−	1.36098i
$661$	36.7989	+	21.2459i	1.43131	+	0.826368i	0.997221	−	0.0745005i	$-0.0237362\pi$
$661$	36.7989	+	21.2459i	1.43131	+	0.826368i	0.434091	+	0.900869i	$0.357070\pi$
$662$	2.21731	−	2.21731i	0.0861780	−	0.0861780i
$663$	8.60347	+	19.3619i	0.334131	+	0.751953i
$664$		−	5.99876i		−	0.232797i
$665$	1.08737	−	3.60074i	0.0421663	−	0.139631i
$666$	0.924235	−	1.75798i	0.0358134	−	0.0681203i
$667$	−3.56070	+	13.2887i	−0.137871	+	0.514540i
$668$	−31.6965	+	31.6965i	−1.22638	+	1.22638i
$669$	−2.39957	+	9.72072i	−0.0927727	+	0.375825i
$670$	−0.0601646	+	1.91073i	−0.00232436	+	0.0738180i
$671$	27.7097			1.06972
$672$	−4.74417	−	7.85405i	−0.183010	−	0.302977i
$673$	0.262737	+	0.980547i	0.0101278	+	0.0377973i	0.970805	−	0.239871i	$-0.0771051\pi$
$673$	0.262737	+	0.980547i	0.0101278	+	0.0377973i	−0.960677	+	0.277668i	$0.910438\pi$
$674$	2.44738	+	1.41300i	0.0942697	+	0.0544267i
$675$	−12.9094	−	22.5465i	−0.496884	−	0.867817i
$676$	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	$0.268631\pi$
$678$	−0.476293	−	0.262562i	−0.0182919	−	0.0100836i
$679$	9.90513	+	5.71873i	0.380124	+	0.219465i
$680$	−3.36724	−	0.106027i	−0.129128	−	0.00406594i
$681$	−18.3333	−	17.6217i	−0.702532	−	0.675266i
$682$	2.37371	+	0.636035i	0.0908942	+	0.0243550i
$683$	31.0697	+	8.32509i	1.18885	+	0.318551i	0.798430	−	0.602087i	$-0.205664\pi$
$683$	31.0697	+	8.32509i	1.18885	+	0.318551i	0.390418	+	0.920638i	$0.372331\pi$
$684$	−0.0992783	−	2.50737i	−0.00379600	−	0.0958718i
$685$	21.7903	−	20.4599i	0.832565	−	0.781734i
$686$	0.762153	+	0.440029i	0.0290991	+	0.0168004i
$687$	−3.01504	+	5.46933i	−0.115031	+	0.208668i
$688$	2.60147	−	2.60147i	0.0991802	−	0.0991802i
$689$	11.5502	−	4.86103i	0.440028	−	0.185190i
$690$	−0.599346	+	1.01063i	−0.0228167	+	0.0384739i
$691$	−15.5777	−	8.99379i	−0.592603	−	0.342140i	0.173523	−	0.984830i	$-0.444485\pi$
$691$	−15.5777	−	8.99379i	−0.592603	−	0.342140i	−0.766126	+	0.642690i	$0.777818\pi$
$692$	−1.86143	−	6.94696i	−0.0707611	−	0.264084i
$693$	60.9374	+	13.7693i	2.31482	+	0.523051i
$694$	−0.0558510			−0.00212007
$695$	−46.3076	−	1.45812i	−1.75655	−	0.0553098i
$696$	−3.77119	−	0.930921i	−0.142947	−	0.0352865i
$697$	−4.66906	+	4.66906i	−0.176853	+	0.176853i
$698$	0.267026	−	0.996554i	0.0101071	−	0.0377201i
$699$	−18.5470	+	5.36514i	−0.701512	+	0.202928i
$700$	26.2659	+	29.8002i	0.992758	+	1.12634i
$701$		−	36.5117i		−	1.37903i	−0.724272	−	0.689515i	$-0.757824\pi$
$701$		−	36.5117i		−	1.37903i	0.724272	−	0.689515i	$-0.242176\pi$
$702$	−0.137352	+	2.08190i	−0.00518402	+	0.0785761i
$703$	−1.76901	+	1.76901i	−0.0667196	+	0.0667196i
$704$	34.7591	+	20.0682i	1.31003	+	0.756347i
$705$	6.82670	+	1.91502i	0.257108	+	0.0721237i
$706$	−1.17916	−	2.04236i	−0.0443782	−	0.0768653i
$707$	−7.81490	−	7.81490i	−0.293909	−	0.293909i
$708$	16.1021	+	26.6573i	0.605153	+	1.00184i
$709$	17.1761	+	29.7499i	0.645063	+	1.11728i	0.984287	+	0.176577i	$0.0565023\pi$
$709$	17.1761	+	29.7499i	0.645063	+	1.11728i	−0.339224	+	0.940706i	$0.610164\pi$
$710$	−0.693416	−	2.95721i	−0.0260235	−	0.110982i
$711$	−6.31896	+	3.98965i	−0.236980	+	0.149624i
$712$	−1.85540	+	0.497153i	−0.0695340	+	0.0186316i
$713$	2.98635	+	11.1452i	0.111840	+	0.417391i
$714$	1.81268	−	1.88587i	0.0678377	−	0.0705769i
$715$	−4.40569	−	41.7717i	−0.164764	−	1.56217i
$716$		−	11.5740i		−	0.432540i
$717$	−0.143762	−	0.0792506i	−0.00536889	−	0.00295967i
$718$	−0.511933	−	1.91056i	−0.0191052	−	0.0713014i
$719$	5.50044	+	9.52704i	0.205132	+	0.355299i	0.950175	−	0.311718i	$-0.100904\pi$
$719$	5.50044	+	9.52704i	0.205132	+	0.355299i	−0.745043	+	0.667016i	$0.767571\pi$
$720$	22.9124	+	12.9823i	0.853893	+	0.483820i
$721$	−0.223167	+	0.128845i	−0.00831116	+	0.00479845i
$722$	−0.542540	+	2.02479i	−0.0201912	+	0.0753547i
$723$	−0.369793	−	18.6863i	−0.0137528	−	0.694952i
$724$	−17.1344	+	9.89253i	−0.636794	+	0.367653i
$725$	25.2006	+	1.58860i	0.935927	+	0.0589990i
$726$	2.99116	−	0.865260i	0.111012	−	0.0321128i
$727$	13.9424	+	13.9424i	0.517094	+	0.517094i	0.916691	−	0.399597i	$-0.130850\pi$
$727$	13.9424	+	13.9424i	0.517094	+	0.517094i	−0.399597	+	0.916691i	$0.630850\pi$
$728$	−0.871268	−	6.34042i	−0.0322913	−	0.234991i
$729$	26.8099	−	3.19796i	0.992961	−	0.118443i
$730$	−0.215873	−	0.402661i	−0.00798982	−	0.0149031i
$731$	2.75351	+	1.58974i	0.101842	+	0.0587986i
$732$	−15.6728	+	9.46704i	−0.579285	+	0.349912i
$733$	−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
$735$	−34.7655	−	0.406443i	−1.28235	−	0.0149919i
$736$		−	3.61049i		−	0.133084i
$737$	38.6325	+	10.3515i	1.42305	+	0.381304i
$738$	−0.620930	+	0.193011i	−0.0228568	+	0.00710483i
$739$	5.27257	−	9.13236i	0.193955	−	0.335939i	−0.752603	−	0.658475i	$-0.771202\pi$
$739$	5.27257	−	9.13236i	0.193955	−	0.335939i	0.946557	+	0.322536i	$0.104535\pi$
$740$	−6.03169	−	25.7234i	−0.221729	−	0.945610i
$741$	0.943625	−	2.45285i	0.0346649	−	0.0901077i
$742$	−1.09399	−	1.09399i	−0.0401615	−	0.0401615i
$743$	−8.87832	−	33.1343i	−0.325714	−	1.21558i	−0.913592	−	0.406632i	$-0.866703\pi$
$743$	−8.87832	−	33.1343i	−0.325714	−	1.21558i	0.587878	−	0.808949i	$-0.299963\pi$
$744$	−3.12953	+	0.905286i	−0.114734	+	0.0331894i
$745$	20.1951	+	0.635898i	0.739891	+	0.0232975i
$746$	−1.98600			−0.0727127
$747$	−39.5284	−	8.93174i	−1.44627	−	0.326795i
$748$	−9.09277	+	33.9347i	−0.332465	+	1.24077i
$749$			67.8966i			2.48089i
$750$	2.03566	+	0.711957i	0.0743320	+	0.0259970i
$751$	−7.98474	+	13.8300i	−0.291367	+	0.504663i	−0.974133	−	0.225974i	$-0.927444\pi$
$751$	−7.98474	+	13.8300i	−0.291367	+	0.504663i	0.682766	+	0.730637i	$0.260777\pi$
$752$	−6.94191	+	1.86008i	−0.253145	+	0.0678301i
$753$	0.733024	+	37.0411i	0.0267129	+	1.34985i
$754$	−1.61571	−	1.22531i	−0.0588408	−	0.0446233i
$755$	13.8028	−	22.2585i	0.502334	−	0.810070i
$756$	−39.1710	+	13.0313i	−1.42464	+	0.473945i
$757$	40.7211	−	10.9112i	1.48003	−	0.396574i	0.573675	−	0.819083i	$-0.305517\pi$
$757$	40.7211	−	10.9112i	1.48003	−	0.396574i	0.906358	+	0.422510i	$0.138851\pi$
$758$	−0.298311	+	1.11331i	−0.0108351	+	0.0404373i
$759$	17.7229	+	17.0351i	0.643301	+	0.618334i
$760$	0.286042	+	0.304641i	0.0103758	+	0.0110505i
$761$	2.02411	+	3.50585i	0.0733738	+	0.127087i	0.900378	−	0.435109i	$-0.143290\pi$
$761$	2.02411	+	3.50585i	0.0733738	+	0.127087i	−0.827004	+	0.562196i	$0.809957\pi$
$762$	−0.00691435	−	0.349395i	−0.000250480	−	0.0126572i
$763$	18.2681	+	4.89492i	0.661349	+	0.177208i
$764$	−22.7333	+	39.3752i	−0.822462	+	1.42455i
$765$	−5.71224	+	22.0303i	−0.206526	+	0.796508i
$766$	1.85016			0.0668492
$767$	4.44032	+	32.3133i	0.160331	+	1.16676i
$768$	−26.0052	+	0.514629i	−0.938381	+	0.0185701i
$769$	9.59863	−	16.6253i	0.346135	−	0.599524i	−0.639424	−	0.768854i	$-0.720827\pi$
$769$	9.59863	−	16.6253i	0.346135	−	0.599524i	0.985559	+	0.169330i	$0.0541605\pi$
$770$	−4.57035	+	2.45024i	−0.164704	+	0.0883005i
$771$	−27.2848	−	6.73528i	−0.982640	−	0.242565i
$772$	24.0556	−	24.0556i	0.865778	−	0.865778i
$773$	3.32613	+	0.891235i	0.119633	+	0.0320555i	0.318139	−	0.948044i	$-0.396942\pi$
$773$	3.32613	+	0.891235i	0.119633	+	0.0320555i	−0.198506	+	0.980100i	$0.563609\pi$
$774$	0.167155	+	0.264746i	0.00600826	+	0.00951611i
$775$	18.9702	−	9.41400i	0.681431	−	0.338161i
$776$	−1.10045	+	0.635348i	−0.0395040	+	0.0228077i
$777$	36.0433	+	19.8693i	1.29305	+	0.712808i
$778$	−2.60064	+	0.696840i	−0.0932375	+	0.0249829i
$779$	0.819051			0.0293455
$780$	16.7633	+	22.1212i	0.600221	+	0.792068i
$781$	−63.5476			−2.27391
$782$	0.994197	−	0.266394i	0.0355524	−	0.00952624i
$783$	−11.7493	+	23.4639i	−0.419885	+	0.838533i
$784$	30.5200	−	17.6208i	1.09000	−	0.629313i
$785$	−8.13661	−	34.7002i	−0.290408	−	1.23850i
$786$	−3.79917	−	0.937828i	−0.135512	−	0.0334512i
$787$	33.5033	+	8.97719i	1.19426	+	0.320002i	0.800570	−	0.599239i	$-0.204530\pi$
$787$	33.5033	+	8.97719i	1.19426	+	0.320002i	0.393694	+	0.919241i	$0.371197\pi$
$788$	2.07939	−	2.07939i	0.0740752	−	0.0740752i
$789$	9.52740	−	38.5958i	0.339184	−	1.37405i
$790$	0.179327	−	0.593827i	0.00638016	−	0.0211274i
$791$	5.63512	−	9.76031i	0.200362	−	0.347037i
$792$	−4.70987	+	5.09821i	−0.167358	+	0.181157i
$793$	−18.9982	+	2.61064i	−0.674647	+	0.0927065i
$794$	−0.952251			−0.0337941
$795$	12.9606	+	3.63571i	0.459667	+	0.128945i
$796$	−23.7458	+	41.1289i	−0.841647	+	1.45778i
$797$	29.7594	+	7.97400i	1.05413	+	0.282454i	0.743958	−	0.668226i	$-0.232946\pi$
$797$	29.7594	+	7.97400i	1.05413	+	0.282454i	0.310173	+	0.950680i	$0.399613\pi$
$798$	−0.324401	+	0.00641973i	−0.0114837	+	0.000227256i
$799$	−3.10547	−	5.37883i	−0.109864	−	0.190289i
$800$	−6.49616	+	1.30903i	−0.229674	+	0.0462810i
$801$	0.513392	+	12.9662i	0.0181398	+	0.458140i
$802$	−0.792066	+	2.95603i	−0.0279688	+	0.104381i
$803$	−9.23288	+	2.47394i	−0.325821	+	0.0873036i
$804$	−25.3875	+	7.34391i	−0.895348	+	0.259000i
$805$	−20.6927	−	12.8318i	−0.729322	−	0.452261i
$806$	−1.68738	−	0.212439i	−0.0594355	−	0.00748286i
$807$	−6.00749	+	0.118885i	−0.211474	+	0.00418496i
$808$	1.18603	−	0.317795i	0.0417242	−	0.0111800i
$809$	18.8982	−	32.7327i	0.664427	−	1.15082i	−0.315013	−	0.949087i	$-0.602009\pi$
$809$	18.8982	−	32.7327i	0.664427	−	1.15082i	0.979440	−	0.201734i	$-0.0646576\pi$
$810$	−1.50743	+	1.65847i	−0.0529659	+	0.0582727i
$811$			11.6051i			0.407512i	0.979022	+	0.203756i	$0.0653148\pi$
$811$			11.6051i			0.407512i	−0.979022	+	0.203756i	$0.934685\pi$
$812$	10.3842	−	38.7545i	0.364416	−	1.36002i
$813$	17.6125	−	10.6387i	0.617696	−	0.373114i
$814$	3.44916			0.120893
$815$	20.8942	−	19.6185i	0.731891	−	0.687207i
$816$	−6.41037	−	22.1603i	−0.224408	−	0.775766i
$817$	−0.102075	−	0.380948i	−0.00357114	−	0.0133277i
$818$	−2.93960	−	2.93960i	−0.102781	−	0.102781i
$819$	−43.0770	−	3.69928i	−1.50523	−	0.129263i
$820$	−4.55861	+	7.35127i	−0.159193	+	0.256717i
$821$	−21.9513	+	38.0208i	−0.766107	+	1.32694i	0.173553	+	0.984825i	$0.444475\pi$
$821$	−21.9513	+	38.0208i	−0.766107	+	1.32694i	−0.939659	+	0.342111i	$0.888858\pi$
$822$	−2.25805	−	1.24478i	−0.0787585	−	0.0434166i
$823$	42.7695	+	11.4601i	1.49085	+	0.399472i	0.910025	−	0.414554i	$-0.136063\pi$
$823$	42.7695	+	11.4601i	1.49085	+	0.399472i	0.580827	+	0.814027i	$0.302729\pi$
$824$		−	0.0286293i		−	0.000997349i
$825$	24.2246	−	38.0642i	0.843394	−	1.32522i
$826$	3.48738	−	2.01344i	0.121341	−	0.0700565i
$827$	−6.22326	−	6.22326i	−0.216404	−	0.216404i	0.590577	−	0.806981i	$-0.298900\pi$
$827$	−6.22326	−	6.22326i	−0.216404	−	0.216404i	−0.806981	+	0.590577i	$0.798900\pi$
$828$	−15.8443	−	3.58014i	−0.550628	−	0.124418i
$829$	−34.6858	−	20.0259i	−1.20469	−	0.695527i	−0.243094	−	0.970003i	$-0.578162\pi$
$829$	−34.6858	−	20.0259i	−1.20469	−	0.695527i	−0.961594	+	0.274475i	$0.911496\pi$
$830$	2.96466	−	1.58940i	0.102905	−	0.0551690i
$831$	21.4640	+	20.6310i	0.744578	+	0.715680i
$832$	−25.7221	−	10.4843i	−0.891754	−	0.363477i
$833$	21.5358	+	21.5358i	0.746172	+	0.746172i
$834$	1.11058	+	3.83921i	0.0384562	+	0.132941i
$835$	−48.2761	−	14.5786i	−1.67066	−	0.504515i
$836$	3.77395	−	2.17889i	0.130525	−	0.0753586i
$837$	1.30567	+	21.9697i	0.0451307	+	0.759384i
$838$	0.855555	−	3.19297i	0.0295546	−	0.110299i
$839$	3.62533	−	2.09309i	0.125160	−	0.0722614i	−0.436113	−	0.899892i	$-0.643645\pi$
$839$	3.62533	−	2.09309i	0.125160	−	0.0722614i	0.561273	+	0.827631i	$0.310312\pi$
$840$	3.50672	−	5.91308i	0.120993	−	0.204021i
$841$	1.74811	+	3.02782i	0.0602797	+	0.104407i
$842$	−0.615198	−	2.29595i	−0.0212011	−	0.0791236i
$843$	18.5119	−	33.5808i	0.637582	−	1.15659i
$844$			6.11875i			0.210616i
$845$	6.95610	+	28.2243i	0.239297	+	0.970946i
$846$	−0.0241979	−	0.611144i	−0.000831942	−	0.0210116i
$847$	16.7003	+	62.3264i	0.573830	+	2.14156i
$848$	−13.1794	+	3.53140i	−0.452582	+	0.121269i
$849$	−4.75840	−	1.17461i	−0.163308	−	0.0403126i
$850$	−0.839767	−	1.69222i	−0.0288038	−	0.0580427i
$851$	8.09736	+	14.0250i	0.277574	+	0.480772i
$852$	35.9431	−	21.7111i	1.23139	−	0.743810i
$853$	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
$855$	2.43331	−	1.43126i	0.0832174	−	0.0489482i
$856$	−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	$-0.0213879\pi$
$858$	−3.31116	+	1.47132i	−0.113041	+	0.0502299i
$859$			17.7932i			0.607095i	0.952816	+	0.303547i	$0.0981711\pi$
$859$			17.7932i			0.607095i	−0.952816	+	0.303547i	$0.901829\pi$
$860$	3.98726	+	1.20409i	0.135964	+	0.0410592i
$861$	−3.74427	−	12.9437i	−0.127604	−	0.441121i
$862$	−0.0838223	+	0.312829i	−0.00285500	+	0.0106550i
$863$	−4.49895	+	4.49895i	−0.153146	+	0.153146i	−0.779522	−	0.626375i	$-0.784538\pi$
$863$	−4.49895	+	4.49895i	−0.153146	+	0.153146i	0.626375	+	0.779522i	$0.284538\pi$
$864$	1.38463	−	6.74608i	0.0471062	−	0.229506i
$865$	5.89850	−	5.53838i	0.200555	−	0.188311i
$866$	2.94505			0.100077
$867$	−8.13885	+	4.91620i	−0.276410	+	0.166963i
$868$	−8.70925	−	32.5034i	−0.295611	−	1.10324i
$869$	−11.2392	−	6.48896i	−0.381264	−	0.220123i
$870$	−0.539124	−	2.11042i	−0.0182780	−	0.0715500i
$871$	−27.4624	−	3.45747i	−0.930526	−	0.117152i
$872$	−1.48575	+	1.48575i	−0.0503139	+	0.0503139i
$873$	2.54808	+	8.19736i	0.0862395	+	0.277439i
$874$	−0.110567	−	0.0638359i	−0.00373998	−	0.00215928i
$875$	−15.5851	+	41.8836i	−0.526874	+	1.41592i
$876$	4.37698	−	4.55371i	0.147884	−	0.153856i
$877$	5.92830	+	1.58848i	0.200184	+	0.0536393i	0.357518	−	0.933906i	$-0.383623\pi$
$877$	5.92830	+	1.58848i	0.200184	+	0.0536393i	−0.157334	+	0.987546i	$0.550290\pi$
$878$	2.88388	+	0.772733i	0.0973262	+	0.0260785i
$879$	9.49185	−	9.87511i	0.320152	−	0.333079i
$880$	−1.43933	+	45.7108i	−0.0485199	+	1.54091i
$881$	36.9093	+	21.3096i	1.24350	+	0.717938i	0.969806	−	0.243878i	$-0.0784195\pi$
$881$	36.9093	+	21.3096i	1.24350	+	0.717938i	0.273699	+	0.961815i	$0.411753\pi$
$882$	0.890253	+	2.86401i	0.0299764	+	0.0964362i
$883$	−13.2826	+	13.2826i	−0.446996	+	0.446996i	−0.894355	−	0.447358i	$-0.852365\pi$
$883$	−13.2826	+	13.2826i	−0.446996	+	0.446996i	0.447358	+	0.894355i	$0.352365\pi$
$884$	3.03704	−	24.1229i	0.102147	−	0.811340i
$885$	−17.8716	+	30.1354i	−0.600748	+	1.01299i
$886$	2.64092	+	1.52473i	0.0887233	+	0.0512244i
$887$	0.0189788	+	0.0708297i	0.000637244	+	0.00237823i	0.966244	−	0.257630i	$-0.0829415\pi$
$887$	0.0189788	+	0.0708297i	0.000637244	+	0.00237823i	−0.965606	+	0.260008i	$0.916275\pi$
$888$	−3.91393	+	2.36417i	−0.131343	+	0.0793364i
$889$	7.24169			0.242879
$890$	−0.737296	−	0.785237i	−0.0247142	−	0.0263212i
$891$	26.5817	+	38.6262i	0.890519	+	1.29403i
$892$	8.12449	−	8.12449i	0.272028	−	0.272028i
$893$	−0.199397	+	0.744161i	−0.00667257	+	0.0249024i
$894$	−0.484331	−	1.67431i	−0.0161985	−	0.0559972i
$895$	11.4757	−	6.15231i	0.383591	−	0.205649i
$896$			14.0245i			0.468525i
$897$	−13.7561	−	10.0098i	−0.459302	−	0.334217i
$898$	−0.275440	+	0.275440i	−0.00919156	+	0.00919156i
$899$	−18.5243	−	10.6950i	−0.617819	−	0.356698i
$900$	−0.697013	+	29.8058i	−0.0232338	+	0.993527i
$901$	−5.89581	−	10.2118i	−0.196418	−	0.340206i
$902$	−0.798478	−	0.798478i	−0.0265864	−	0.0265864i
$903$	−5.55362	+	3.35462i	−0.184813	+	0.111635i
$904$	0.626059	+	1.08437i	0.0208224	+	0.0360655i
$905$	−18.9165	−	11.7304i	−0.628807	−	0.389930i
$906$	−2.19345	−	0.541456i	−0.0728726	−	0.0179887i
$907$	12.8605	−	3.44596i	0.427026	−	0.114421i	−0.0389038	−	0.999243i	$-0.512387\pi$
$907$	12.8605	−	3.44596i	0.427026	−	0.114421i	0.465930	+	0.884822i	$0.345720\pi$
$908$	7.55255	+	28.1865i	0.250640	+	0.935401i
$909$	−0.328176	−	8.28841i	−0.0108849	−	0.274909i
$910$	2.90266	−	2.11052i	0.0962224	−	0.0699630i
$911$		−	26.2784i		−	0.870641i	−0.900276	−	0.435321i	$-0.856635\pi$
$911$		−	26.2784i		−	0.870641i	0.900276	−	0.435321i	$-0.143365\pi$
$912$	−1.38143	+	2.50594i	−0.0457438	+	0.0829801i
$913$	−18.2148	−	67.9787i	−0.602823	−	2.24977i
$914$	1.94240	+	3.36434i	0.0642490	+	0.111283i
$915$	−17.7178	−	10.5074i	−0.585731	−	0.347364i
$916$	6.20659	−	3.58338i	0.205072	−	0.118398i
$917$	20.9879	−	78.3277i	0.693080	−	2.58661i
$918$	1.95979	−	0.116471i	0.0646826	−	0.00384412i
$919$	12.6380	−	7.29655i	0.416889	−	0.240691i	−0.276856	−	0.960911i	$-0.589293\pi$
$919$	12.6380	−	7.29655i	0.416889	−	0.240691i	0.693746	+	0.720220i	$0.255959\pi$
$920$	2.38408	−	1.27815i	0.0786009	−	0.0421392i
$921$	−7.28052	−	25.1684i	−0.239901	−	0.829326i
$922$	0.855820	+	0.855820i	0.0281849	+	0.0281849i
$923$	43.5693	−	5.98707i	1.43410	−	0.197067i
$924$	−51.6863	−	49.6803i	−1.70035	−	1.63436i
$925$	22.2987	−	19.6541i	0.733177	−	0.646222i
$926$	0.913562	+	0.527445i	0.0300215	+	0.0173329i
$927$	−0.188651	−	0.0426271i	−0.00619611	−	0.00140006i
$928$	4.73279	+	4.73279i	0.155361	+	0.155361i
$929$	−38.3045	+	22.1151i	−1.25673	+	0.725573i	−0.972437	−	0.233165i	$-0.925092\pi$
$929$	−38.3045	+	22.1151i	−1.25673	+	0.725573i	−0.284292	+	0.958738i	$0.591758\pi$
$930$	−1.27659	−	1.30679i	−0.0418610	−	0.0428513i
$931$		−	3.77783i		−	0.123813i
$932$	21.4011	+	5.73440i	0.701015	+	0.187836i
$933$	−18.2316	−	10.0504i	−0.596875	−	0.329035i
$934$	0.359584	−	0.622817i	0.0117659	−	0.0203792i
$935$	−38.4799	+	9.02288i	−1.25843	+	0.295080i
$936$	2.74884	−	3.93916i	0.0898488	−	0.128755i
$937$	22.4956	+	22.4956i	0.734898	+	0.734898i	0.971586	−	0.236688i	$-0.0760619\pi$
$937$	22.4956	+	22.4956i	0.734898	+	0.734898i	−0.236688	+	0.971586i	$0.576062\pi$
$938$	0.884452	+	3.30082i	0.0288784	+	0.107776i
$939$	−11.2363	−	38.8434i	−0.366684	−	1.26761i
$940$	−5.56932	−	5.93145i	−0.181651	−	0.193463i
$941$	37.4186			1.21981			0.609905	−	0.792474i	$-0.291207\pi$
$941$	37.4186			1.21981			0.609905	+	0.792474i	$0.291207\pi$
$942$	−2.63169	+	1.58965i	−0.0857450	+	0.0517935i
$943$	1.37225	−	5.12131i	0.0446867	−	0.166773i
$944$		−	35.5135i		−	1.15586i
$945$	−33.7426	−	31.9114i	−1.09765	−	1.03808i
$946$	−0.271869	+	0.470890i	−0.00883921	+	0.0153100i
$947$	3.34143	−	0.895335i	0.108582	−	0.0290945i	−0.204119	−	0.978946i	$-0.565433\pi$
$947$	3.34143	−	0.895335i	0.108582	−	0.0290945i	0.312701	+	0.949852i	$0.398766\pi$
$948$	8.57396	−	0.169674i	0.278469	−	0.00551077i
$949$	6.09715	−	2.56605i	0.197922	−	0.0832974i
$950$	−0.0747691	+	0.222082i	−0.00242583	+	0.00720528i
$951$	−1.83228	+	0.530028i	−0.0594157	+	0.0171873i
$952$	−5.81695	+	1.55865i	−0.188529	+	0.0505161i
$953$	7.66352	−	28.6007i	0.248246	−	0.926466i	−0.723478	−	0.690347i	$-0.757458\pi$
$953$	7.66352	−	28.6007i	0.248246	−	0.926466i	0.971724	−	0.236119i	$-0.0758756\pi$
$954$	−0.0459404	−	1.16027i	−0.00148737	−	0.0375652i
$955$	−51.1250	−	1.60981i	−1.65437	−	0.0520923i
$956$	0.0941895	+	0.163141i	0.00304631	+	0.00527636i
$957$	−45.5623	+	0.901655i	−1.47282	+	0.0291464i
$958$	1.71624	+	0.459864i	0.0554491	+	0.0148575i
$959$	26.7155	−	46.2725i	0.862687	−	1.49422i
$960$	−14.6154	−	26.0122i	−0.471711	−	0.839542i
$961$	13.0603			0.421299
$962$	−2.36480	+	0.324959i	−0.0762443	+	0.0104771i
$963$	−34.5797	+	37.4309i	−1.11431	+	1.20619i
$964$	−10.7238	+	18.5741i	−0.345389	+	0.598231i
$965$	36.6383	+	11.0642i	1.17943	+	0.356170i
$966$	−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	$0.388908\pi$
$968$	−6.92443	−	1.85540i	−0.222560	−	0.0596347i
$969$	−2.40087	−	0.592657i	−0.0771272	−	0.0190389i
$970$	−0.605568	−	0.375519i	−0.0194436	−	0.0120572i
$971$	−6.10879	+	3.52691i	−0.196040	+	0.113184i	−0.594807	−	0.803868i	$-0.702772\pi$
$971$	−6.10879	+	3.52691i	−0.196040	+	0.113184i	0.398767	+	0.917052i	$0.369438\pi$
$972$	−28.2315	−	12.7657i	−0.905527	−	0.409460i
$973$	−79.9972	+	21.4352i	−2.56459	+	0.687180i
$974$	−3.65614			−0.117150
$975$	−13.0227	+	28.3798i	−0.417059	+	0.908879i
$976$	20.8797			0.668344
$977$	19.7099	−	5.28126i	0.630577	−	0.168963i	0.0706455	−	0.997501i	$-0.477494\pi$
$977$	19.7099	−	5.28126i	0.630577	−	0.168963i	0.559932	+	0.828539i	$0.310827\pi$
$978$	−2.16519	−	1.19359i	−0.0692350	−	0.0381667i
$979$	−19.5160	+	11.2676i	−0.623735	+	0.360114i
$980$	33.9074	+	21.0263i	1.08313	+	0.671662i
$981$	7.57808	+	12.0024i	0.241949	+	0.383208i
$982$	3.13710	+	0.840582i	0.100109	+	0.0268241i
$983$	−30.8727	+	30.8727i	−0.984687	+	0.984687i	−0.999885	−	0.0151975i	$-0.995162\pi$
$983$	−30.8727	+	30.8727i	−0.984687	+	0.984687i	0.0151975	+	0.999885i	$0.495162\pi$
$984$	1.45337	+	0.358767i	0.0463319	+	0.0114371i
$985$	3.16706	+	0.956404i	0.100911	+	0.0304736i
$986$	−0.954036	+	1.65244i	−0.0303827	+	0.0526244i
$987$	12.6718	−	0.250768i	0.403347	−	0.00798203i
$988$	−2.38221	+	1.84945i	−0.0757880	+	0.0588387i
$989$	−2.55299			−0.0811803
$990$	−3.76750	−	0.976876i	−0.119739	−	0.0310471i
$991$	−6.36105	+	11.0177i	−0.202065	+	0.349988i	−0.949194	−	0.314692i	$-0.898099\pi$
$991$	−6.36105	+	11.0177i	−0.202065	+	0.349988i	0.747128	+	0.664680i	$0.231432\pi$
$992$	5.42228	+	1.45290i	0.172158	+	0.0461295i
$993$	0.964945	+	48.7604i	0.0306216	+	1.54736i
$994$	−2.71480	−	4.70218i	−0.0861083	−	0.149144i
$995$	−53.4020	−	1.68151i	−1.69296	−	0.0533075i
$996$	33.5275	+	32.2263i	1.06236	+	1.02113i
$997$	2.34514	−	8.75218i	0.0742713	−	0.277184i	−0.918796	−	0.394733i	$-0.870837\pi$
$997$	2.34514	−	8.75218i	0.0742713	−	0.277184i	0.993067	+	0.117549i	$0.0375037\pi$
$998$	1.80241	−	0.482956i	0.0570544	−	0.0152877i
$999$	9.75099	+	29.3106i	0.308508	+	0.927348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bf.a.17.12	✓	96
3.2	odd	2	inner	195.2.bf.a.17.13	yes	96
5.2	odd	4		975.2.bn.d.368.12		96
5.3	odd	4	inner	195.2.bf.a.173.13	yes	96
5.4	even	2		975.2.bn.d.407.13		96
13.10	even	6	inner	195.2.bf.a.62.12	yes	96
15.2	even	4		975.2.bn.d.368.13		96
15.8	even	4	inner	195.2.bf.a.173.12	yes	96
15.14	odd	2		975.2.bn.d.407.12		96
39.23	odd	6	inner	195.2.bf.a.62.13	yes	96
65.23	odd	12	inner	195.2.bf.a.23.13	yes	96
65.49	even	6		975.2.bn.d.257.13		96
65.62	odd	12		975.2.bn.d.218.12		96
195.23	even	12	inner	195.2.bf.a.23.12	yes	96
195.62	even	12		975.2.bn.d.218.13		96
195.179	odd	6		975.2.bn.d.257.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.12	✓	96	1.1	even	1	trivial
195.2.bf.a.17.13	yes	96	3.2	odd	2	inner
195.2.bf.a.23.12	yes	96	195.23	even	12	inner
195.2.bf.a.23.13	yes	96	65.23	odd	12	inner
195.2.bf.a.62.12	yes	96	13.10	even	6	inner
195.2.bf.a.62.13	yes	96	39.23	odd	6	inner
195.2.bf.a.173.12	yes	96	15.8	even	4	inner
195.2.bf.a.173.13	yes	96	5.3	odd	4	inner
975.2.bn.d.218.12		96	65.62	odd	12
975.2.bn.d.218.13		96	195.62	even	12
975.2.bn.d.257.12		96	195.179	odd	6
975.2.bn.d.257.13		96	65.49	even	6
975.2.bn.d.368.12		96	5.2	odd	4
975.2.bn.d.368.13		96	15.2	even	4
975.2.bn.d.407.12		96	15.14	odd	2
975.2.bn.d.407.13		96	5.4	even	2

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.107570 + 0.0288234i) q^{2} +(0.836177 - 1.51684i) q^{3} +(-1.72131 + 0.993799i) q^{4} +(-1.90035 - 1.17843i) q^{5} +(-0.0462274 + 0.187269i) q^{6} +(-3.86093 - 1.03453i) q^{7} +(0.314011 - 0.314011i) q^{8} +(-1.60161 - 2.53670i) q^{9} +(0.238387 + 0.0719893i) q^{10} +(2.60494 - 4.51189i) q^{11} +(0.0681144 + 3.44195i) q^{12} +(-1.36091 + 3.33885i) q^{13} +0.445140 q^{14} +(-3.37651 + 1.89715i) q^{15} +(1.96287 - 3.39979i) q^{16} +(3.27708 + 0.878092i) q^{17} +(0.245402 + 0.226709i) q^{18} +(-0.210416 - 0.364452i) q^{19} +(4.44220 + 0.139875i) q^{20} +(-4.79764 + 4.99136i) q^{21} +(-0.150166 + 0.560429i) q^{22} +(-2.63136 + 0.705071i) q^{23} +(-0.213736 - 0.738874i) q^{24} +(2.22263 + 4.47883i) q^{25} +(0.0501565 - 0.398387i) q^{26} +(-5.18700 + 0.308267i) q^{27} +(7.67398 - 2.05624i) q^{28} +(2.52506 - 4.37354i) q^{29} +(0.308530 - 0.301399i) q^{30} -4.23553i q^{31} +(-0.343025 + 1.28019i) q^{32} +(-4.66563 - 7.72402i) q^{33} -0.377826 q^{34} +(6.11798 + 6.51579i) q^{35} +(5.27784 + 2.77476i) q^{36} +(-1.53863 - 5.74223i) q^{37} +(0.0331393 + 0.0331393i) q^{38} +(3.92655 + 4.85615i) q^{39} +(-0.966769 + 0.226691i) q^{40} +(-0.973131 + 1.68551i) q^{41} +(0.372216 - 0.675207i) q^{42} +(0.905224 + 0.242554i) q^{43} +10.3551i q^{44} +(0.0543123 + 6.70798i) q^{45} +(0.262734 - 0.151689i) q^{46} +(-1.29449 - 1.29449i) q^{47} +(-3.51564 - 5.82019i) q^{48} +(7.77434 + 4.48852i) q^{49} +(-0.368184 - 0.417726i) q^{50} +(4.07215 - 4.23657i) q^{51} +(-0.975600 - 7.09967i) q^{52} +(-2.45762 - 2.45762i) q^{53} +(0.549082 - 0.182667i) q^{54} +(-10.2672 + 5.50442i) q^{55} +(-1.53723 + 0.887520i) q^{56} +(-0.728761 + 0.0144218i) q^{57} +(-0.145562 + 0.543244i) q^{58} +(7.83433 - 4.52315i) q^{59} +(3.92664 - 6.62116i) q^{60} +(2.65934 + 4.60611i) q^{61} +(0.122082 + 0.455618i) q^{62} +(3.55942 + 11.4509i) q^{63} +7.70388i q^{64} +(6.52079 - 4.74124i) q^{65} +(0.724516 + 0.696396i) q^{66} +(1.98691 + 7.41523i) q^{67} +(-6.51352 + 1.74529i) q^{68} +(-1.13080 + 4.58092i) q^{69} +(-0.845920 - 0.524565i) q^{70} +(-6.09876 - 10.5634i) q^{71} +(-1.29948 - 0.293626i) q^{72} +(-1.29733 - 1.29733i) q^{73} +(0.331021 + 0.573345i) q^{74} +(8.65219 + 0.373728i) q^{75} +(0.724384 + 0.418223i) q^{76} +(-14.7252 + 14.7252i) q^{77} +(-0.562351 - 0.409202i) q^{78} -2.49102i q^{79} +(-7.73653 + 4.14768i) q^{80} +(-3.86966 + 8.12562i) q^{81} +(0.0560979 - 0.209360i) q^{82} +(9.55183 - 9.55183i) q^{83} +(3.29782 - 13.3596i) q^{84} +(-5.19282 - 5.53048i) q^{85} -0.104367 q^{86} +(-4.52256 - 7.48717i) q^{87} +(-0.598803 - 2.23476i) q^{88} +(-3.74597 - 2.16273i) q^{89} +(-0.199189 - 0.720015i) q^{90} +(8.70853 - 11.4832i) q^{91} +(3.82869 - 3.82869i) q^{92} +(-6.42463 - 3.54166i) q^{93} +(0.176560 + 0.101937i) q^{94} +(-0.0296156 + 0.940545i) q^{95} +(1.65501 + 1.59078i) q^{96} +(-2.76392 - 0.740590i) q^{97} +(-0.965663 - 0.258749i) q^{98} +(-15.6174 + 0.618364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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