LMFDB - Embedded newform 875.2.bb.b.243.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			243.18
Character	$\chi$	$=$	875.243
Dual form			875.2.bb.b.857.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.65307 + 0.139042i) q^{2} +(0.138973 + 0.171618i) q^{3} +(5.03041 + 0.528718i) q^{4} +(0.344844 + 0.474637i) q^{6} +(-0.932359 + 2.47603i) q^{7} +(8.02453 + 1.27096i) q^{8} +(0.613596 - 2.88674i) q^{9} +(2.92528 - 0.621787i) q^{11} +(0.608356 + 0.936786i) q^{12} +(-4.38594 - 2.23475i) q^{13} +(-2.81788 + 6.43944i) q^{14} +(11.2177 + 2.38441i) q^{16} +(1.72195 + 4.48584i) q^{17} +(2.02929 - 7.57342i) q^{18} +(-0.376845 - 3.58544i) q^{19} +(-0.554503 + 0.184092i) q^{21} +(7.84742 - 1.24291i) q^{22} +(-0.171029 + 3.26342i) q^{23} +(0.897076 + 1.55378i) q^{24} +(-11.3255 - 6.53878i) q^{26} +(1.17097 - 0.596641i) q^{27} +(-5.99927 + 11.9625i) q^{28} +(-2.87272 + 3.95395i) q^{29} +(-0.657478 + 1.47672i) q^{31} +(13.7345 + 3.68016i) q^{32} +(0.513245 + 0.415617i) q^{33} +(3.94475 + 12.1407i) q^{34} +(4.61291 - 14.1971i) q^{36} +(-1.12629 + 0.731424i) q^{37} +(-0.501272 - 9.56484i) q^{38} +(-0.226006 - 1.06328i) q^{39} +(-4.99103 + 1.62168i) q^{41} +(-1.49673 + 0.411311i) q^{42} +(-8.43891 - 8.43891i) q^{43} +(15.0441 - 1.58120i) q^{44} +(-0.907502 + 8.63431i) q^{46} +(-3.12102 - 1.19805i) q^{47} +(1.14976 + 2.25653i) q^{48} +(-5.26142 - 4.61709i) q^{49} +(-0.530544 + 0.918929i) q^{51} +(-20.8816 - 13.5606i) q^{52} +(3.32256 - 2.69056i) q^{53} +(3.18964 - 1.42012i) q^{54} +(-10.6287 + 18.6840i) q^{56} +(0.562954 - 0.562954i) q^{57} +(-8.17129 + 10.0907i) q^{58} +(-0.374472 + 0.415893i) q^{59} +(7.43964 - 6.69868i) q^{61} +(-1.94966 + 3.82643i) q^{62} +(6.57556 + 4.21076i) q^{63} +(14.1129 + 4.58555i) q^{64} +(1.30389 + 1.17403i) q^{66} +(8.72305 - 3.34846i) q^{67} +(6.29039 + 23.4761i) q^{68} +(-0.583829 + 0.424177i) q^{69} +(-0.293741 - 0.213415i) q^{71} +(8.59275 - 22.3849i) q^{72} +(-1.59444 + 2.45523i) q^{73} +(-3.08984 + 1.78392i) q^{74} -18.2355i q^{76} +(-1.18785 + 7.82279i) q^{77} +(-0.451771 - 2.85237i) q^{78} +(-2.12904 - 4.78190i) q^{79} +(-7.82313 - 3.48308i) q^{81} +(-13.4670 + 3.60848i) q^{82} +(-0.142291 + 0.898387i) q^{83} +(-2.88671 + 0.632885i) q^{84} +(-21.2157 - 23.5624i) q^{86} +(-1.07780 + 0.0564851i) q^{87} +(24.2642 - 1.27163i) q^{88} +(-6.04903 - 6.71813i) q^{89} +(9.62257 - 8.77612i) q^{91} +(-2.58577 + 16.3259i) q^{92} +(-0.344803 + 0.0923897i) q^{93} +(-8.11372 - 3.61246i) q^{94} +(1.27715 + 2.86853i) q^{96} +(1.13281 + 7.15230i) q^{97} +(-13.3169 - 12.9810i) q^{98} -8.82604i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.65307	+	0.139042i	1.87601	+	0.0983173i	0.955960	−	0.293496i	$-0.0948187\pi$
$2$	2.65307	+	0.139042i	1.87601	+	0.0983173i	0.920045	+	0.391813i	$0.128152\pi$
$3$	0.138973	+	0.171618i	0.0802363	+	0.0990835i	0.815683	−	0.578499i	$-0.196361\pi$
$3$	0.138973	+	0.171618i	0.0802363	+	0.0990835i	−0.735447	+	0.677582i	$0.763028\pi$
$4$	5.03041	+	0.528718i	2.51521	+	0.264359i
$5$		0			0
$5$		0			0
$6$	0.344844	+	0.474637i	0.140782	+	0.193770i
$7$	−0.932359	+	2.47603i	−0.352398	+	0.935850i
$7$	−0.932359	+	2.47603i	−0.352398	+	0.935850i
$8$	8.02453	+	1.27096i	2.83710	+	0.449352i
$9$	0.613596	−	2.88674i	0.204532	−	0.962247i
$10$		0			0
$11$	2.92528	−	0.621787i	0.882004	−	0.187476i	0.255421	−	0.966830i	$-0.417786\pi$
$11$	2.92528	−	0.621787i	0.882004	−	0.187476i	0.626583	+	0.779354i	$0.284453\pi$
$12$	0.608356	+	0.936786i	0.175617	+	0.270427i
$13$	−4.38594	−	2.23475i	−1.21644	−	0.619808i	−0.276458	−	0.961026i	$-0.589161\pi$
$13$	−4.38594	−	2.23475i	−1.21644	−	0.619808i	−0.939984	+	0.341218i	$0.889161\pi$
$14$	−2.81788	+	6.43944i	−0.753111	+	1.72101i
$15$		0			0
$16$	11.2177	+	2.38441i	2.80444	+	0.596102i
$17$	1.72195	+	4.48584i	0.417635	+	1.08798i	0.967533	+	0.252744i	$0.0813331\pi$
$17$	1.72195	+	4.48584i	0.417635	+	1.08798i	−0.549898	+	0.835232i	$0.685334\pi$
$18$	2.02929	−	7.57342i	0.478309	−	1.78507i
$19$	−0.376845	−	3.58544i	−0.0864543	−	0.822557i	−0.948723	−	0.316107i	$-0.897624\pi$
$19$	−0.376845	−	3.58544i	−0.0864543	−	0.822557i	0.862269	−	0.506450i	$-0.169043\pi$
$20$		0			0
$21$	−0.554503	+	0.184092i	−0.121002	+	0.0401722i
$22$	7.84742	−	1.24291i	1.67308	−	0.264989i
$23$	−0.171029	+	3.26342i	−0.0356619	+	0.680470i	0.921052	+	0.389440i	$0.127331\pi$
$23$	−0.171029	+	3.26342i	−0.0356619	+	0.680470i	−0.956714	+	0.291030i	$0.906002\pi$
$24$	0.897076	+	1.55378i	0.183115	+	0.317164i
$25$		0			0
$26$	−11.3255	−	6.53878i	−2.22111	−	1.28236i
$27$	1.17097	−	0.596641i	0.225354	−	0.114824i
$28$	−5.99927	+	11.9625i	−1.13376	+	2.26070i
$29$	−2.87272	+	3.95395i	−0.533450	+	0.734231i	−0.987651	−	0.156668i	$-0.949925\pi$
$29$	−2.87272	+	3.95395i	−0.533450	+	0.734231i	0.454201	+	0.890899i	$0.349925\pi$
$30$		0			0
$31$	−0.657478	+	1.47672i	−0.118087	+	0.265227i	−0.962912	−	0.269815i	$-0.913037\pi$
$31$	−0.657478	+	1.47672i	−0.118087	+	0.265227i	0.844826	+	0.535042i	$0.179704\pi$
$32$	13.7345	+	3.68016i	2.42794	+	0.650566i
$33$	0.513245	+	0.415617i	0.0893445	+	0.0723497i
$34$	3.94475	+	12.1407i	0.676518	+	2.08211i
$35$		0			0
$36$	4.61291	−	14.1971i	0.768819	−	2.36618i
$37$	−1.12629	+	0.731424i	−0.185162	+	0.120245i	−0.633891	−	0.773422i	$-0.718543\pi$
$37$	−1.12629	+	0.731424i	−0.185162	+	0.120245i	0.448730	+	0.893668i	$0.351877\pi$
$38$	−0.501272	−	9.56484i	−0.0813171	−	1.55162i
$39$	−0.226006	−	1.06328i	−0.0361900	−	0.170260i
$40$		0			0
$41$	−4.99103	+	1.62168i	−0.779468	+	0.253264i	−0.671613	−	0.740902i	$-0.734398\pi$
$41$	−4.99103	+	1.62168i	−0.779468	+	0.253264i	−0.107855	+	0.994167i	$0.534398\pi$
$42$	−1.49673	+	0.411311i	−0.230951	+	0.0634667i
$43$	−8.43891	−	8.43891i	−1.28692	−	1.28692i	−0.936647	−	0.350276i	$-0.886088\pi$
$43$	−8.43891	−	8.43891i	−1.28692	−	1.28692i	−0.350276	−	0.936647i	$-0.613912\pi$
$44$	15.0441	−	1.58120i	2.26798	−	0.238375i
$45$		0			0
$46$	−0.907502	+	8.63431i	−0.133804	+	1.27306i
$47$	−3.12102	−	1.19805i	−0.455248	−	0.174753i	0.119929	−	0.992782i	$-0.461733\pi$
$47$	−3.12102	−	1.19805i	−0.455248	−	0.174753i	−0.575177	+	0.818029i	$0.695067\pi$
$48$	1.14976	+	2.25653i	0.165954	+	0.325703i
$49$	−5.26142	−	4.61709i	−0.751631	−	0.659584i
$50$		0			0
$51$	−0.530544	+	0.918929i	−0.0742910	+	0.128676i
$52$	−20.8816	−	13.5606i	−2.89575	−	1.88052i
$53$	3.32256	−	2.69056i	0.456389	−	0.369577i	−0.373384	−	0.927677i	$-0.621803\pi$
$53$	3.32256	−	2.69056i	0.456389	−	0.369577i	0.829774	+	0.558100i	$0.188469\pi$
$54$	3.18964	−	1.42012i	0.434055	−	0.193254i
$55$		0			0
$56$	−10.6287	+	18.6840i	−1.42032	+	2.49675i
$57$	0.562954	−	0.562954i	0.0745651	−	0.0745651i
$58$	−8.17129	+	10.0907i	−1.07294	+	1.32497i
$59$	−0.374472	+	0.415893i	−0.0487521	+	0.0541447i	−0.767028	−	0.641614i	$-0.778265\pi$
$59$	−0.374472	+	0.415893i	−0.0487521	+	0.0541447i	0.718276	+	0.695759i	$0.244932\pi$
$60$		0			0
$61$	7.43964	−	6.69868i	0.952549	−	0.857679i	−0.0373720	−	0.999301i	$-0.511899\pi$
$61$	7.43964	−	6.69868i	0.952549	−	0.857679i	0.989921	+	0.141623i	$0.0452320\pi$
$62$	−1.94966	+	3.82643i	−0.247607	+	0.485957i
$63$	6.57556	+	4.21076i	0.828443	+	0.530506i
$64$	14.1129	+	4.58555i	1.76411	+	0.573194i
$65$		0			0
$66$	1.30389	+	1.17403i	0.160497	+	0.144513i
$67$	8.72305	−	3.34846i	1.06569	−	0.409080i	0.238582	−	0.971122i	$-0.423318\pi$
$67$	8.72305	−	3.34846i	1.06569	−	0.409080i	0.827108	+	0.562042i	$0.189984\pi$
$68$	6.29039	+	23.4761i	0.762822	+	2.84689i
$69$	−0.583829	+	0.424177i	−0.0702848	+	0.0510649i
$70$		0			0
$71$	−0.293741	−	0.213415i	−0.0348607	−	0.0253278i	0.570218	−	0.821493i	$-0.306859\pi$
$71$	−0.293741	−	0.213415i	−0.0348607	−	0.0253278i	−0.605079	+	0.796165i	$0.706859\pi$
$72$	8.59275	−	22.3849i	1.01267	−	2.63808i
$73$	−1.59444	+	2.45523i	−0.186615	+	0.287363i	−0.919579	−	0.392905i	$-0.871470\pi$
$73$	−1.59444	+	2.45523i	−0.186615	+	0.287363i	0.732963	+	0.680268i	$0.238137\pi$
$74$	−3.08984	+	1.78392i	−0.359186	+	0.207376i
$75$		0			0
$76$		−	18.2355i		−	2.09176i
$77$	−1.18785	+	7.82279i	−0.135368	+	0.891490i
$78$	−0.451771	−	2.85237i	−0.0511530	−	0.322968i
$79$	−2.12904	−	4.78190i	−0.239536	−	0.538006i	0.753274	−	0.657706i	$-0.228473\pi$
$79$	−2.12904	−	4.78190i	−0.239536	−	0.538006i	−0.992810	+	0.119701i	$0.961807\pi$
$80$		0			0
$81$	−7.82313	−	3.48308i	−0.869237	−	0.387009i
$82$	−13.4670	+	3.60848i	−1.48719	+	0.398490i
$83$	−0.142291	+	0.898387i	−0.0156184	+	0.0986108i	−0.994266	−	0.106934i	$-0.965897\pi$
$83$	−0.142291	+	0.898387i	−0.0156184	+	0.0986108i	0.978648	+	0.205545i	$0.0658966\pi$
$84$	−2.88671	+	0.632885i	−0.314966	+	0.0690534i
$85$		0			0
$86$	−21.2157	−	23.5624i	−2.28775	−	2.54080i
$87$	−1.07780	+	0.0564851i	−0.115552	+	0.00605584i
$88$	24.2642	−	1.27163i	2.58658	−	0.135557i
$89$	−6.04903	−	6.71813i	−0.641196	−	0.712120i	0.331695	−	0.943387i	$-0.392380\pi$
$89$	−6.04903	−	6.71813i	−0.641196	−	0.712120i	−0.972890	+	0.231267i	$0.925713\pi$
$90$		0			0
$91$	9.62257	−	8.77612i	1.00872	−	0.919988i
$92$	−2.58577	+	16.3259i	−0.269585	+	1.70210i
$93$	−0.344803	+	0.0923897i	−0.0357544	+	0.00958037i
$94$	−8.11372	−	3.61246i	−0.836866	−	0.372597i
$95$		0			0
$96$	1.27715	+	2.86853i	0.130349	+	0.292768i
$97$	1.13281	+	7.15230i	0.115020	+	0.726206i	0.976033	+	0.217624i	$0.0698305\pi$
$97$	1.13281	+	7.15230i	0.115020	+	0.726206i	−0.861013	+	0.508583i	$0.830170\pi$
$98$	−13.3169	−	12.9810i	−1.34521	−	1.31128i
$99$		−	8.82604i		−	0.887051i
$100$		0			0
$101$	2.36935	−	1.36795i	0.235759	−	0.136116i	−0.377467	−	0.926023i	$-0.623205\pi$
$101$	2.36935	−	1.36795i	0.235759	−	0.136116i	0.613226	+	0.789907i	$0.289871\pi$
$102$	−1.53534	+	2.36422i	−0.152021	+	0.234092i
$103$	−0.239234	+	0.623225i	−0.0235724	+	0.0614082i	−0.944862	−	0.327470i	$-0.893804\pi$
$103$	−0.239234	+	0.623225i	−0.0235724	+	0.0614082i	0.921289	+	0.388878i	$0.127137\pi$
$104$	−32.3548	−	23.5072i	−3.17265	−	2.30507i
$105$		0			0
$106$	9.18910	−	6.67627i	0.892524	−	0.648457i
$107$	−0.699970	−	2.61232i	−0.0676686	−	0.252543i	0.923802	−	0.382869i	$-0.125064\pi$
$107$	−0.699970	−	2.61232i	−0.0676686	−	0.252543i	−0.991471	+	0.130327i	$0.958397\pi$
$108$	6.20594	−	2.38224i	0.597167	−	0.229231i
$109$	3.45588	+	3.11169i	0.331013	+	0.298046i	0.817832	−	0.575458i	$-0.195176\pi$
$109$	3.45588	+	3.11169i	0.331013	+	0.298046i	−0.486818	+	0.873503i	$0.661843\pi$
$110$		0			0
$111$	−0.282050	−	0.0916436i	−0.0267710	−	0.00869843i
$112$	−16.3628	+	25.5523i	−1.54614	+	2.41447i
$113$	−7.94063	+	15.5844i	−0.746991	+	1.46605i	0.133026	+	0.991112i	$0.457530\pi$
$113$	−7.94063	+	15.5844i	−0.746991	+	1.46605i	−0.880018	+	0.474941i	$0.842470\pi$
$114$	1.57183	−	1.41528i	0.147216	−	0.132554i
$115$		0			0
$116$	−16.5415	+	18.3712i	−1.53584	+	1.70572i
$117$	−9.14234	+	11.2899i	−0.845210	+	1.04375i
$118$	−1.05133	+	1.05133i	−0.0967825	+	0.0967825i
$119$	−12.7125	+	0.0811892i	−1.16536	+	0.00744260i
$120$		0			0
$121$	−1.87838	+	0.836308i	−0.170762	+	0.0760280i
$122$	20.6693	−	16.7377i	1.87131	−	1.51536i
$123$	−0.971930	−	0.631178i	−0.0876359	−	0.0569114i
$124$	−4.08816	+	7.08089i	−0.367127	+	0.635883i
$125$		0			0
$126$	16.8600	+	12.0857i	1.50200	+	1.07668i
$127$	2.36741	+	4.64631i	0.210074	+	0.412293i	0.971868	−	0.235526i	$-0.0756813\pi$
$127$	2.36741	+	4.64631i	0.210074	+	0.412293i	−0.761794	+	0.647819i	$0.775681\pi$
$128$	10.2557	+	3.93679i	0.906483	+	0.347966i
$129$	0.275484	−	2.62105i	0.0242550	−	0.230771i
$130$		0			0
$131$	3.74207	−	0.393308i	0.326946	−	0.0343634i	0.0603664	−	0.998176i	$-0.480773\pi$
$131$	3.74207	−	0.393308i	0.326946	−	0.0343634i	0.266580	+	0.963813i	$0.414106\pi$
$132$	2.36209	+	2.36209i	0.205594	+	0.205594i
$133$	9.22901	+	2.40984i	0.800257	+	0.208960i
$134$	23.6085	−	7.67085i	2.03946	−	0.662661i
$135$		0			0
$136$	8.11653	+	38.1853i	0.695987	+	3.27436i
$137$	−0.209084	−	3.98957i	−0.0178633	−	0.340852i	−0.992911	−	0.118858i	$-0.962077\pi$
$137$	−0.209084	−	3.98957i	−0.0178633	−	0.340852i	0.975048	−	0.221994i	$-0.0712566\pi$
$138$	−1.60792	+	1.04419i	−0.136875	+	0.0888877i
$139$	2.53686	−	7.80766i	0.215174	−	0.662237i	−0.783967	−	0.620802i	$-0.786807\pi$
$139$	2.53686	−	7.80766i	0.215174	−	0.662237i	0.999141	−	0.0414349i	$-0.0131929\pi$
$140$		0			0
$141$	−0.228132	−	0.702119i	−0.0192122	−	0.0591291i
$142$	−0.749643	−	0.607049i	−0.0629086	−	0.0509424i
$143$	−14.2196	−	3.81014i	−1.18911	−	0.318620i
$144$	13.7663	−	30.9197i	1.14719	−	2.57664i
$145$		0			0
$146$	−4.57155	+	6.29220i	−0.378344	+	0.520746i
$147$	0.0611781	−	1.54460i	0.00504589	−	0.127397i
$148$	−6.05244	+	3.08387i	−0.497508	+	0.253493i
$149$	18.8977	+	10.9106i	1.54816	+	0.893830i	0.998282	+	0.0585846i	$0.0186588\pi$
$149$	18.8977	+	10.9106i	1.54816	+	0.893830i	0.549877	+	0.835246i	$0.314675\pi$
$150$		0			0
$151$	1.20290	+	2.08349i	0.0978908	+	0.169552i	0.910811	−	0.412823i	$-0.135457\pi$
$151$	1.20290	+	2.08349i	0.0978908	+	0.169552i	−0.812921	+	0.582375i	$0.802124\pi$
$152$	1.53295	−	29.2505i	0.124339	−	2.37253i
$153$	14.0060	−	2.21834i	1.13232	−	0.179342i
$154$	−4.23913	+	20.5893i	−0.341599	+	1.65913i
$155$		0			0
$156$	−0.574732	−	5.46821i	−0.0460154	−	0.437807i
$157$	−5.67894	+	21.1941i	−0.453229	+	1.69147i	0.240016	+	0.970769i	$0.422847\pi$
$157$	−5.67894	+	21.1941i	−0.453229	+	1.69147i	−0.693244	+	0.720703i	$0.743819\pi$
$158$	−4.98361	−	12.9827i	−0.396475	−	1.03285i
$159$	0.923495	+	0.196295i	0.0732379	+	0.0155672i
$160$		0			0
$161$	−7.92085	−	3.46615i	−0.624251	−	0.273171i
$162$	−20.2710	−	10.3286i	−1.59264	−	0.811492i
$163$	4.83650	+	7.44756i	0.378824	+	0.583338i	0.975731	−	0.218973i	$-0.0702706\pi$
$163$	4.83650	+	7.44756i	0.378824	+	0.583338i	−0.596907	+	0.802310i	$0.703604\pi$
$164$	−25.9644	+	5.51889i	−2.02748	+	0.430953i
$165$		0			0
$166$	−0.502420	+	2.36370i	−0.0389954	+	0.183459i
$167$	10.3743	+	1.64313i	0.802786	+	0.127149i	0.544327	−	0.838873i	$-0.316785\pi$
$167$	10.3743	+	1.64313i	0.802786	+	0.127149i	0.258460	+	0.966022i	$0.416785\pi$
$168$	−4.68360	+	0.772502i	−0.361347	+	0.0595999i
$169$	6.60118	+	9.08574i	0.507783	+	0.698903i
$170$		0			0
$171$	−10.5815	−	1.11216i	−0.809186	−	0.0850489i
$172$	−37.9894	−	46.9130i	−2.89667	−	3.57709i
$173$	17.9869	+	0.942653i	1.36752	+	0.0716686i	0.721903	−	0.691994i	$-0.243268\pi$
$173$	17.9869	+	0.942653i	1.36752	+	0.0716686i	0.645615	+	0.763663i	$0.276601\pi$
$174$	−2.86733			−0.217372
$175$		0			0
$176$	34.2976			2.58528
$177$	−0.123416	−	0.00646797i	−0.00927653	−	0.000486162i
$178$	−15.1144	−	18.6647i	−1.13287	−	1.39898i
$179$	−6.45610	−	0.678563i	−0.482552	−	0.0507182i	−0.139870	−	0.990170i	$-0.544668\pi$
$179$	−6.45610	−	0.678563i	−0.482552	−	0.0507182i	−0.342681	+	0.939452i	$0.611335\pi$
$180$		0			0
$181$	10.3669	+	14.2688i	0.770563	+	1.06059i	0.996261	+	0.0863916i	$0.0275336\pi$
$181$	10.3669	+	14.2688i	0.770563	+	1.06059i	−0.225698	+	0.974197i	$0.572466\pi$
$182$	26.7496	−	21.9457i	1.98281	−	1.62673i
$183$	2.18352	+	0.345836i	0.161411	+	0.0255650i
$184$	−5.52010	+	25.9700i	−0.406947	+	1.91454i
$185$		0			0
$186$	−0.927634	+	0.197175i	−0.0680174	+	0.0144575i
$187$	7.82642	+	12.0516i	0.572325	+	0.881303i
$188$	−15.0666	−	7.67682i	−1.09885	−	0.559890i
$189$	0.385532	+	3.45565i	0.0280433	+	0.251361i
$190$		0			0
$191$	11.8497	+	2.51873i	0.857414	+	0.182249i	0.615586	−	0.788070i	$-0.288920\pi$
$191$	11.8497	+	2.51873i	0.857414	+	0.182249i	0.241828	+	0.970319i	$0.422253\pi$
$192$	1.17435	+	3.05929i	0.0847515	+	0.220785i
$193$	2.22173	−	8.29161i	0.159924	−	0.596843i	−0.838710	−	0.544579i	$-0.816689\pi$
$193$	2.22173	−	8.29161i	0.159924	−	0.596843i	0.998633	−	0.0522644i	$-0.0166439\pi$
$194$	2.01097	+	19.1331i	0.144379	+	1.37368i
$195$		0			0
$196$	−24.0260	−	26.0077i	−1.71614	−	1.85769i
$197$	3.92235	−	0.621240i	0.279456	−	0.0442615i	−0.0151331	−	0.999885i	$-0.504817\pi$
$197$	3.92235	−	0.621240i	0.279456	−	0.0442615i	0.294589	+	0.955624i	$0.404817\pi$
$198$	1.22719	−	23.4161i	0.0872124	−	1.66411i
$199$	−6.13171	−	10.6204i	−0.434666	−	0.752863i	0.562603	−	0.826727i	$-0.309800\pi$
$199$	−6.13171	−	10.6204i	−0.434666	−	0.752863i	−0.997268	+	0.0738644i	$0.976467\pi$
$200$		0			0
$201$	1.78693	+	1.03168i	0.126040	+	0.0727693i
$202$	6.47626	−	3.29982i	0.455668	−	0.232174i
$203$	−7.11169	−	10.7994i	−0.499143	−	0.757971i
$204$	−3.15471	+	4.34209i	−0.220874	+	0.304007i
$205$		0			0
$206$	−0.721358	+	1.62020i	−0.0502594	+	0.112885i
$207$	9.31571	+	2.49614i	0.647487	+	0.173494i
$208$	−43.8719	−	35.5267i	−3.04197	−	2.46334i
$209$	−3.33176	−	10.2541i	−0.230463	−	0.709291i
$210$		0			0
$211$	−6.78037	+	20.8678i	−0.466780	+	1.43660i	0.389950	+	0.920836i	$0.372492\pi$
$211$	−6.78037	+	20.8678i	−0.466780	+	1.43660i	−0.856730	+	0.515765i	$0.827508\pi$
$212$	18.1364	−	11.7779i	1.24561	−	0.808912i
$213$	−0.00419630	−	0.0800702i	−0.000287526	−	0.00548632i
$214$	−1.49385	−	7.02801i	−0.102117	−	0.480425i
$215$		0			0
$216$	10.1548	−	3.29950i	0.690948	−	0.224503i
$217$	−3.04339	−	3.00477i	−0.206599	−	0.203977i
$218$	8.73604	+	8.73604i	0.591679	+	0.591679i
$219$	−0.642945	+	0.0675763i	−0.0434462	+	0.00456638i
$220$		0			0
$221$	2.47234	−	23.5228i	0.166308	−	1.58231i
$222$	−0.735557	−	0.282354i	−0.0493674	−	0.0189504i
$223$	0.644506	+	1.26491i	0.0431593	+	0.0847049i	0.911579	−	0.411125i	$-0.134864\pi$
$223$	0.644506	+	1.26491i	0.0431593	+	0.0847049i	−0.868420	+	0.495830i	$0.834864\pi$
$224$	−21.9177	+	30.5758i	−1.46444	+	2.04293i
$225$		0			0
$226$	−23.2339	+	40.2423i	−1.54550	+	2.67688i
$227$	−23.7719	−	15.4376i	−1.57779	−	1.02463i	−0.973733	−	0.227692i	$-0.926882\pi$
$227$	−23.7719	−	15.4376i	−1.57779	−	1.02463i	−0.604060	−	0.796939i	$-0.706451\pi$
$228$	3.12954	−	2.53425i	0.207259	−	0.167835i
$229$	−0.553987	+	0.246651i	−0.0366085	+	0.0162992i	−0.424959	−	0.905212i	$-0.639712\pi$
$229$	−0.553987	+	0.246651i	−0.0366085	+	0.0162992i	0.388351	+	0.921512i	$0.373045\pi$
$230$		0			0
$231$	−1.50761	+	0.883303i	−0.0991933	+	0.0581171i
$232$	−28.0775	+	28.0775i	−1.84338	+	1.84338i
$233$	−2.83194	+	3.49716i	−0.185527	+	0.229106i	−0.861420	−	0.507893i	$-0.830425\pi$
$233$	−2.83194	+	3.49716i	−0.185527	+	0.229106i	0.675894	+	0.736999i	$0.263758\pi$
$234$	−25.8251	+	28.6816i	−1.68824	+	1.87498i
$235$		0			0
$236$	−2.10364	+	1.89412i	−0.136935	+	0.123297i
$237$	0.524779	−	1.02994i	0.0340881	−	0.0669016i
$238$	−33.7386	−	1.55217i	−2.18695	−	0.100612i
$239$	12.4990	+	4.06118i	0.808494	+	0.262696i	0.683960	−	0.729520i	$-0.260256\pi$
$239$	12.4990	+	4.06118i	0.808494	+	0.262696i	0.124534	+	0.992215i	$0.460256\pi$
$240$		0			0
$241$	−12.3140	−	11.0876i	−0.793216	−	0.714215i	0.169263	−	0.985571i	$-0.445861\pi$
$241$	−12.3140	−	11.0876i	−0.793216	−	0.714215i	−0.962479	+	0.271356i	$0.912528\pi$
$242$	−5.09975	+	1.95761i	−0.327824	+	0.125840i
$243$	−1.50988	−	5.63495i	−0.0968588	−	0.361482i
$244$	40.9662	−	29.7637i	2.62259	−	1.90542i
$245$		0			0
$246$	−2.49084	−	1.80970i	−0.158810	−	0.115382i
$247$	−6.35975	+	16.5677i	−0.404661	+	1.05418i
$248$	−7.15280	+	11.0144i	−0.454203	+	0.699412i
$249$	−0.173954	+	0.100432i	−0.0110239	+	0.00636464i
$250$		0			0
$251$		−	21.3400i		−	1.34697i	−0.739200	−	0.673486i	$-0.764796\pi$
$251$		−	21.3400i		−	1.34697i	0.739200	−	0.673486i	$-0.235204\pi$
$252$	30.8515	+	24.6585i	1.94346	+	1.55334i
$253$	1.52885	+	9.65275i	0.0961177	+	0.606863i
$254$	5.63488	+	12.6562i	0.353564	+	0.794118i
$255$		0			0
$256$	−0.450797	−	0.200708i	−0.0281748	−	0.0125442i
$257$	21.6223	−	5.79368i	1.34876	−	0.361400i	0.489085	−	0.872236i	$-0.337331\pi$
$257$	21.6223	−	5.79368i	1.34876	−	0.361400i	0.859678	+	0.510836i	$0.170664\pi$
$258$	1.09531	−	6.91553i	0.0681912	−	0.430542i
$259$	−0.760915	−	3.47068i	−0.0472810	−	0.215658i
$260$		0			0
$261$	9.65136	+	10.7189i	0.597404	+	0.663485i
$262$	9.98267	−	0.523170i	0.616731	−	0.0323215i
$263$	−24.5269	+	1.28540i	−1.51239	+	0.0792610i	−0.790378	−	0.612619i	$-0.790116\pi$
$263$	−24.5269	+	1.28540i	−1.51239	+	0.0792610i	−0.722012	+	0.691880i	$0.756783\pi$
$264$	3.59031	+	3.98745i	0.220969	+	0.245410i
$265$		0			0
$266$	24.1502	+	7.67670i	1.48074	+	0.470689i
$267$	0.312296	−	1.97176i	0.0191122	−	0.120670i
$268$	45.6509	−	12.2321i	2.78857	−	0.747196i
$269$	21.7527	+	9.68493i	1.32629	+	0.590501i	0.942897	−	0.333086i	$-0.108090\pi$
$269$	21.7527	+	9.68493i	1.32629	+	0.590501i	0.383390	+	0.923587i	$0.374757\pi$
$270$		0			0
$271$	11.5585	+	25.9608i	0.702129	+	1.57701i	0.812397	+	0.583105i	$0.198162\pi$
$271$	11.5585	+	25.9608i	0.702129	+	1.57701i	−0.110268	+	0.993902i	$0.535171\pi$
$272$	8.62037	+	54.4269i	0.522687	+	3.30011i
$273$	2.84342	+	0.431757i	0.172092	+	0.0261311i
$274$		−	10.6137i		−	0.641196i
$275$		0			0
$276$	−3.16117	+	1.82510i	−0.190280	+	0.109858i
$277$	6.57090	−	10.1183i	0.394807	−	0.607950i	−0.584240	−	0.811581i	$-0.698607\pi$
$277$	6.57090	−	10.1183i	0.394807	−	0.607950i	0.979048	+	0.203631i	$0.0652742\pi$
$278$	7.81606	−	20.3615i	0.468776	−	1.22120i
$279$	3.85948	+	2.80408i	0.231061	+	0.167876i
$280$		0			0
$281$	5.98822	−	4.35069i	0.357227	−	0.259541i	−0.394668	−	0.918824i	$-0.629140\pi$
$281$	5.98822	−	4.35069i	0.357227	−	0.259541i	0.751895	+	0.659283i	$0.229140\pi$
$282$	−0.507628	−	1.89449i	−0.0302288	−	0.112815i
$283$	23.8787	−	9.16617i	1.41944	−	0.544872i	0.476898	−	0.878959i	$-0.341761\pi$
$283$	23.8787	−	9.16617i	1.41944	−	0.544872i	0.942542	+	0.334087i	$0.108428\pi$
$284$	−1.36480	−	1.22887i	−0.0809862	−	0.0729203i
$285$		0			0
$286$	−37.1959	−	12.0857i	−2.19944	−	0.714642i
$287$	0.638097	−	13.8699i	0.0376657	−	0.818715i
$288$	19.0511	−	37.3899i	1.12260	−	2.20322i
$289$	−4.52417	+	4.07358i	−0.266128	+	0.239623i
$290$		0			0
$291$	−1.07003	+	1.18839i	−0.0627263	+	0.0696647i
$292$	−9.31883	+	11.5078i	−0.545343	+	0.673443i
$293$	1.98458	−	1.98458i	0.115941	−	0.115941i	−0.646756	−	0.762697i	$-0.723875\pi$
$293$	1.98458	−	1.98458i	0.115941	−	0.115941i	0.762697	+	0.646756i	$0.223875\pi$
$294$	0.377074	−	4.08944i	0.0219914	−	0.238501i
$295$		0			0
$296$	−9.96759	+	4.43786i	−0.579354	+	0.257945i
$297$	3.05444	−	2.47344i	0.177237	−	0.143523i
$298$	48.6199	+	31.5741i	2.81648	+	1.82904i
$299$	8.04305	−	13.9310i	0.465141	−	0.805649i
$300$		0			0
$301$	28.7631	−	13.0269i	1.65788	−	0.750857i
$302$	2.90170	+	5.69490i	0.166974	+	0.327705i
$303$	0.564040	+	0.216515i	0.0324033	+	0.0124384i
$304$	4.32180	−	41.1192i	0.247872	−	2.35835i
$305$		0			0
$306$	37.4675	−	3.93799i	2.14187	−	0.225120i
$307$	−17.0423	−	17.0423i	−0.972656	−	0.972656i	0.0269795	−	0.999636i	$-0.491411\pi$
$307$	−17.0423	−	17.0423i	−0.972656	−	0.972656i	−0.999636	+	0.0269795i	$0.991411\pi$
$308$	−10.1114	+	38.7238i	−0.576151	+	2.20650i
$309$	−0.140204	+	0.0455549i	−0.00797590	+	0.00259153i
$310$		0			0
$311$	5.89343	+	27.7264i	0.334186	+	1.57222i	0.749161	+	0.662388i	$0.230457\pi$
$311$	5.89343	+	27.7264i	0.334186	+	1.57222i	−0.414975	+	0.909833i	$0.636210\pi$
$312$	−0.462212	−	8.81953i	−0.0261676	−	0.499308i
$313$	−18.0646	+	11.7313i	−1.02107	+	0.663091i	−0.942634	−	0.333828i	$-0.891659\pi$
$313$	−18.0646	+	11.7313i	−1.02107	+	0.663091i	−0.0784364	+	0.996919i	$0.524993\pi$
$314$	−18.0135	+	55.4398i	−1.01656	+	3.12865i
$315$		0			0
$316$	−8.18167	−	25.1806i	−0.460255	−	1.41652i
$317$	−0.175566	−	0.142171i	−0.00986079	−	0.00798511i	0.624377	−	0.781123i	$-0.285353\pi$
$317$	−0.175566	−	0.142171i	−0.00986079	−	0.00798511i	−0.634238	+	0.773138i	$0.718686\pi$
$318$	2.42281	+	0.649189i	0.135864	+	0.0364047i
$319$	−5.94497	+	13.3526i	−0.332855	+	0.747603i
$320$		0			0
$321$	0.351044	−	0.483170i	0.0195934	−	0.0269679i
$322$	−20.5327	−	10.2973i	−1.14424	−	0.573844i
$323$	15.4348	−	7.86443i	0.858816	−	0.437589i
$324$	−37.5120	−	21.6576i	−2.08400	−	1.20320i
$325$		0			0
$326$	11.7961	+	20.4314i	0.653323	+	1.13159i
$327$	−0.0537458	+	1.02553i	−0.00297215	+	0.0567120i
$328$	−42.1118	+	6.66985i	−2.32523	+	0.368281i
$329$	5.87631	−	6.61072i	0.323972	−	0.364461i
$330$		0			0
$331$	1.99845	+	19.0140i	0.109845	+	1.04510i	0.901099	+	0.433614i	$0.142762\pi$
$331$	1.99845	+	19.0140i	0.109845	+	1.04510i	−0.791254	+	0.611488i	$0.790571\pi$
$332$	−1.19077	+	4.44403i	−0.0653522	+	0.243898i
$333$	1.42034	+	3.70012i	0.0778343	+	0.202765i
$334$	27.2953	+	5.80179i	1.49353	+	0.317460i
$335$		0			0
$336$	−6.65923	+	0.742941i	−0.363291	+	0.0405308i
$337$	1.36175	+	0.693845i	0.0741791	+	0.0377961i	0.490687	−	0.871336i	$-0.336746\pi$
$337$	1.36175	+	0.693845i	0.0741791	+	0.0377961i	−0.416507	+	0.909132i	$0.636746\pi$
$338$	16.2501	+	25.0230i	0.883889	+	1.36107i
$339$	−3.77809	+	0.803057i	−0.205198	+	0.0436161i
$340$		0			0
$341$	−1.00510	+	4.72863i	−0.0544292	+	0.256069i
$342$	−27.9188	−	4.42190i	−1.50968	−	0.239109i
$343$	16.3376	−	8.72262i	0.882145	−	0.470977i
$344$	−56.9928	−	78.4438i	−3.07284	−	4.22941i
$345$		0			0
$346$	47.5894	+	5.00185i	2.55842	+	0.268901i
$347$	−12.4876	−	15.4209i	−0.670368	−	0.827835i	0.322561	−	0.946549i	$-0.395456\pi$
$347$	−12.4876	−	15.4209i	−0.670368	−	0.827835i	−0.992929	+	0.118714i	$0.962123\pi$
$348$	−5.45164	−	0.285708i	−0.292239	−	0.0153156i
$349$	−7.02028			−0.375787			−0.187894	−	0.982189i	$-0.560166\pi$
$349$	−7.02028			−0.375787			−0.187894	+	0.982189i	$0.560166\pi$
$350$		0			0
$351$	−6.46917			−0.345299
$352$	42.4656	+	2.22553i	2.26342	+	0.118621i
$353$	16.9803	+	20.9689i	0.903768	+	1.11606i	0.992770	+	0.120029i	$0.0382986\pi$
$353$	16.9803	+	20.9689i	0.903768	+	1.11606i	−0.0890029	+	0.996031i	$0.528368\pi$
$354$	−0.326533	−	0.0343200i	−0.0173550	−	0.00182409i
$355$		0			0
$356$	−26.8771	−	36.9932i	−1.42448	−	1.96063i
$357$	−1.78064	−	2.17041i	−0.0942413	−	0.114870i
$358$	−17.0341	−	2.69794i	−0.900283	−	0.142591i
$359$	2.90347	−	13.6598i	0.153239	−	0.720934i	−0.832686	−	0.553746i	$-0.813198\pi$
$359$	2.90347	−	13.6598i	0.153239	−	0.720934i	0.985925	−	0.167188i	$-0.0534688\pi$
$360$		0			0
$361$	5.87140	−	1.24800i	0.309021	−	0.0656845i
$362$	25.5201	+	39.2975i	1.34131	+	2.06543i
$363$	−0.404570	−	0.206138i	−0.0212344	−	0.0108195i
$364$	53.0456	−	39.0599i	2.78035	−	2.04730i
$365$		0			0
$366$	5.74496	+	1.22113i	0.300294	+	0.0638295i
$367$	−10.1866	−	26.5370i	−0.531737	−	1.38522i	−0.891857	−	0.452317i	$-0.850598\pi$
$367$	−10.1866	−	26.5370i	−0.531737	−	1.38522i	0.360120	−	0.932906i	$-0.382736\pi$
$368$	−9.69987	+	36.2004i	−0.505641	+	1.88708i
$369$	1.61891	+	15.4029i	0.0842770	+	0.801842i
$370$		0			0
$371$	3.56408	+	10.7353i	0.185038	+	0.557350i
$372$	−1.78335	+	0.282455i	−0.0924624	+	0.0146446i
$373$	−1.15758	+	22.0879i	−0.0599372	+	1.14367i	0.788729	+	0.614741i	$0.210739\pi$
$373$	−1.15758	+	22.0879i	−0.0599372	+	1.14367i	−0.848666	+	0.528929i	$0.822594\pi$
$374$	19.0884	+	33.0620i	0.987037	+	1.70960i
$375$		0			0
$376$	−23.5221	−	13.5805i	−1.21306	−	0.700359i
$377$	21.4357	−	10.9220i	1.10399	−	0.562512i
$378$	0.542364	+	9.22169i	0.0278962	+	0.474312i
$379$	−19.8453	+	27.3147i	−1.01938	+	1.40306i	−0.106747	+	0.994286i	$0.534044\pi$
$379$	−19.8453	+	27.3147i	−1.01938	+	1.40306i	−0.912636	+	0.408774i	$0.865956\pi$
$380$		0			0
$381$	−0.468382	+	1.05200i	−0.0239959	+	0.0538957i
$382$	31.0879	+	8.32997i	1.59059	+	0.426199i
$383$	29.4495	+	23.8477i	1.50480	+	1.21856i	0.909947	+	0.414725i	$0.136122\pi$
$383$	29.4495	+	23.8477i	1.50480	+	1.21856i	0.594851	+	0.803836i	$0.297211\pi$
$384$	0.749644	+	2.30717i	0.0382551	+	0.117737i
$385$		0			0
$386$	7.04729	−	21.6893i	0.358698	−	1.10396i
$387$	−29.5391	+	19.1829i	−1.50155	+	0.975121i
$388$	1.91697	+	36.5780i	0.0973195	+	1.85697i
$389$	−2.63857	−	12.4135i	−0.133781	−	0.629388i	−0.993033	−	0.117836i	$-0.962404\pi$
$389$	−2.63857	−	12.4135i	−0.133781	−	0.629388i	0.859252	−	0.511552i	$-0.170929\pi$
$390$		0			0
$391$	−14.9337	+	4.85225i	−0.755229	+	0.245389i
$392$	−36.3522	−	43.7370i	−1.83606	−	2.20905i
$393$	0.587546	+	0.587546i	0.0296378	+	0.0296378i
$394$	10.4927	−	1.10282i	0.528613	−	0.0555594i
$395$		0			0
$396$	4.66649	−	44.3987i	0.234500	−	2.23112i
$397$	25.0674	+	9.62248i	1.25810	+	0.482938i	0.893851	−	0.448364i	$-0.147993\pi$
$397$	25.0674	+	9.62248i	1.25810	+	0.482938i	0.364246	+	0.931303i	$0.381327\pi$
$398$	−14.7912	−	29.0294i	−0.741416	−	1.45511i
$399$	0.869015	+	1.91877i	0.0435052	+	0.0960584i
$400$		0			0
$401$	1.13896	−	1.97273i	0.0568769	−	0.0985137i	−0.836185	−	0.548447i	$-0.815219\pi$
$401$	1.13896	−	1.97273i	0.0568769	−	0.0985137i	0.893062	+	0.449934i	$0.148552\pi$
$402$	4.59740	+	2.98559i	0.229297	+	0.148907i
$403$	6.18376	−	5.00751i	0.308035	−	0.249442i
$404$	12.6421	−	5.62861i	0.628967	−	0.280034i
$405$		0			0
$406$	−17.3663	−	29.6405i	−0.861873	−	1.47103i
$407$	−2.83993	+	2.83993i	−0.140770	+	0.140770i
$408$	−5.42529	+	6.69967i	−0.268592	+	0.331683i
$409$	19.4149	−	21.5624i	0.960005	−	1.06619i	−0.0377539	−	0.999287i	$-0.512020\pi$
$409$	19.4149	−	21.5624i	0.960005	−	1.06619i	0.997759	−	0.0669069i	$-0.0213130\pi$
$410$		0			0
$411$	0.655623	−	0.590326i	0.0323395	−	0.0291186i
$412$	−1.53295	+	3.00859i	−0.0755233	+	0.148223i
$413$	−0.680620	−	1.31496i	−0.0334911	−	0.0647051i
$414$	24.3682	+	7.91770i	1.19763	+	0.389134i
$415$		0			0
$416$	−52.0146	−	46.8342i	−2.55023	−	2.29624i
$417$	1.69249	−	0.649685i	0.0828815	−	0.0318152i
$418$	−7.41365	−	27.6681i	−0.362613	−	1.35329i
$419$	4.33888	−	3.15238i	0.211968	−	0.154004i	−0.476736	−	0.879047i	$-0.658180\pi$
$419$	4.33888	−	3.15238i	0.211968	−	0.154004i	0.688704	+	0.725043i	$0.258180\pi$
$420$		0			0
$421$	−15.3126	−	11.1253i	−0.746290	−	0.542212i	0.148385	−	0.988930i	$-0.452593\pi$
$421$	−15.3126	−	11.1253i	−0.746290	−	0.542212i	−0.894675	+	0.446718i	$0.852593\pi$
$422$	−20.8903	+	54.4211i	−1.01692	+	2.64918i
$423$	−5.37350	+	8.27447i	−0.261269	+	0.402318i
$424$	30.0816	−	17.3676i	1.46089	−	0.843446i
$425$		0			0
$426$		−	0.213016i		−	0.0103206i
$427$	9.64971	+	24.6663i	0.466982	+	1.19369i
$428$	−2.13996	−	13.5112i	−0.103439	−	0.653086i
$429$	−1.32226	−	2.96985i	−0.0638394	−	0.143386i
$430$		0			0
$431$	−21.2587	−	9.46500i	−1.02400	−	0.455913i	−0.175145	−	0.984543i	$-0.556039\pi$
$431$	−21.2587	−	9.46500i	−1.02400	−	0.455913i	−0.848853	+	0.528630i	$0.822706\pi$
$432$	14.5583	−	3.90089i	0.700438	−	0.187682i
$433$	0.943769	−	5.95872i	0.0453546	−	0.286358i	−0.954578	−	0.297961i	$-0.903693\pi$
$433$	0.943769	−	5.95872i	0.0453546	−	0.286358i	0.999933	+	0.0116031i	$0.00369347\pi$
$434$	−7.65655	−	8.39502i	−0.367526	−	0.402974i
$435$		0			0
$436$	15.7393	+	17.4803i	0.753776	+	0.837153i
$437$	11.7653	−	0.616591i	0.562809	−	0.0294956i
$438$	−1.71518	+	0.0898886i	−0.0819543	+	0.00429504i
$439$	−23.9122	−	26.5572i	−1.14127	−	1.26751i	−0.958733	−	0.284307i	$-0.908236\pi$
$439$	−23.9122	−	26.5572i	−1.14127	−	1.26751i	−0.182535	−	0.983199i	$-0.558430\pi$
$440$		0			0
$441$	−16.5567	+	12.3553i	−0.788416	+	0.588349i
$442$	9.82995	−	62.0638i	0.467563	−	2.95208i
$443$	−20.3219	+	5.44524i	−0.965523	+	0.258711i	−0.706936	−	0.707277i	$-0.749923\pi$
$443$	−20.3219	+	5.44524i	−0.965523	+	0.258711i	−0.258586	+	0.965988i	$0.583257\pi$
$444$	−1.37038	−	0.610130i	−0.0650351	−	0.0289555i
$445$		0			0
$446$	1.53404	+	3.44552i	0.0726391	+	0.163150i
$447$	0.753824	+	4.75946i	0.0356547	+	0.225115i
$448$	−24.5122	+	30.6685i	−1.15809	+	1.44895i
$449$			17.1662i			0.810122i	0.914290	+	0.405061i	$0.132750\pi$
$449$			17.1662i			0.810122i	−0.914290	+	0.405061i	$0.867250\pi$
$450$		0			0
$451$	−13.5918	+	7.84723i	−0.640013	+	0.369512i
$452$	−48.1844	+	74.1974i	−2.26640	+	3.48995i
$453$	−0.190392	+	0.495989i	−0.00894541	+	0.0233036i
$454$	−60.9220	−	44.2624i	−2.85921	−	2.07734i
$455$		0			0
$456$	5.23294	−	3.80195i	0.245055	−	0.178043i
$457$	−6.00543	−	22.4126i	−0.280922	−	1.04842i	−0.951768	−	0.306819i	$-0.900735\pi$
$457$	−6.00543	−	22.4126i	−0.280922	−	1.04842i	0.670845	−	0.741597i	$-0.265931\pi$
$458$	−1.50406	+	0.577355i	−0.0702802	+	0.0269780i
$459$	4.69280	+	4.22542i	0.219041	+	0.197226i
$460$		0			0
$461$	15.9507	+	5.18270i	0.742899	+	0.241383i	0.655923	−	0.754828i	$-0.272280\pi$
$461$	15.9507	+	5.18270i	0.742899	+	0.241383i	0.0869763	+	0.996210i	$0.472280\pi$
$462$	−4.12261	+	2.13385i	−0.191801	+	0.0992756i
$463$	12.7573	−	25.0376i	0.592882	−	1.16360i	−0.378395	−	0.925644i	$-0.623524\pi$
$463$	12.7573	−	25.0376i	0.592882	−	1.16360i	0.971277	−	0.237952i	$-0.0764760\pi$
$464$	−41.6532	+	37.5047i	−1.93370	+	1.74111i
$465$		0			0
$466$	−7.99959	+	8.88445i	−0.370574	+	0.411564i
$467$	3.59157	−	4.43522i	0.166198	−	0.205238i	−0.687242	−	0.726429i	$-0.741179\pi$
$467$	3.59157	−	4.43522i	0.166198	−	0.205238i	0.853440	+	0.521191i	$0.174512\pi$
$468$	−51.9589	+	51.9589i	−2.40180	+	2.40180i
$469$	0.157878	+	24.7205i	0.00729015	+	1.14149i
$470$		0			0
$471$	−4.42650	+	1.97081i	−0.203962	+	0.0908099i
$472$	−3.53354	+	2.86141i	−0.162645	+	0.131707i
$473$	−29.9334	−	19.4390i	−1.37634	−	0.893804i
$474$	1.53548	−	2.65953i	0.0705270	−	0.122156i
$475$		0			0
$476$	−63.9922	−	6.31293i	−2.93308	−	0.289353i
$477$	−5.72824	−	11.2423i	−0.262278	−	0.514750i
$478$	32.5961	+	12.5125i	1.49091	+	0.572308i
$479$	−1.95747	+	18.6240i	−0.0894389	+	0.850954i	0.854193	+	0.519957i	$0.174052\pi$
$479$	−1.95747	+	18.6240i	−0.0894389	+	0.850954i	−0.943632	+	0.330998i	$0.892615\pi$
$480$		0			0
$481$	6.57441	−	0.690999i	0.299767	−	0.0315068i
$482$	−31.1284	−	31.1284i	−1.41786	−	1.41786i
$483$	−0.505935	−	1.84106i	−0.0230208	−	0.0837712i
$484$	−9.89119	+	3.21384i	−0.449599	+	0.146084i
$485$		0			0
$486$	−3.22233	−	15.1599i	−0.146168	−	0.687665i
$487$	−1.19326	−	22.7688i	−0.0540719	−	1.03175i	−0.882098	−	0.471065i	$-0.843870\pi$
$487$	−1.19326	−	22.7688i	−0.0540719	−	1.03175i	0.828027	−	0.560689i	$-0.189464\pi$
$488$	68.2134	−	44.2983i	3.08787	−	2.00529i
$489$	−0.605988	+	1.86504i	−0.0274037	+	0.0843400i
$490$		0			0
$491$	3.66657	+	11.2845i	0.165470	+	0.509264i	0.999071	−	0.0431034i	$-0.0137245\pi$
$491$	3.66657	+	11.2845i	0.165470	+	0.509264i	−0.833601	+	0.552368i	$0.813724\pi$
$492$	−4.55549	−	3.68897i	−0.205377	−	0.166311i
$493$	−22.6835	−	6.07802i	−1.02161	−	0.273740i
$494$	−19.1765	+	43.0711i	−0.862790	+	1.93786i
$495$		0			0
$496$	−10.8965	+	14.9978i	−0.489268	+	0.673420i
$497$	0.802294	−	0.528331i	0.0359878	−	0.0236989i
$498$	−0.475476	+	0.242267i	−0.0213066	+	0.0108563i
$499$	8.20677	+	4.73818i	0.367385	+	0.212110i	0.672316	−	0.740265i	$-0.265300\pi$
$499$	8.20677	+	4.73818i	0.367385	+	0.212110i	−0.304930	+	0.952375i	$0.598633\pi$
$500$		0			0
$501$	1.15976	+	2.00876i	0.0518142	+	0.0897449i
$502$	2.96715	−	56.6167i	0.132431	−	2.52693i
$503$	−19.9077	+	3.15307i	−0.887640	+	0.140588i	−0.583572	−	0.812062i	$-0.698345\pi$
$503$	−19.9077	+	3.15307i	−0.887640	+	0.140588i	−0.304069	+	0.952650i	$0.598345\pi$
$504$	47.4140	+	42.1466i	2.11199	+	1.87736i
$505$		0			0
$506$	2.71400	+	25.8220i	0.120652	+	1.14793i
$507$	−0.641887	+	2.39556i	−0.0285072	+	0.106390i
$508$	9.45248	+	24.6245i	0.419386	+	1.09254i
$509$	17.3660	+	3.69127i	0.769737	+	0.163613i	0.576010	−	0.817443i	$-0.304609\pi$
$509$	17.3660	+	3.69127i	0.769737	+	0.163613i	0.193727	+	0.981055i	$0.437942\pi$
$510$		0			0
$511$	−4.59261	−	6.23703i	−0.203165	−	0.275910i
$512$	−20.7441	−	10.5696i	−0.916768	−	0.467117i
$513$	−2.58050	−	3.97362i	−0.113932	−	0.175440i
$514$	58.1711	−	12.3647i	2.56582	−	0.545382i
$515$		0			0
$516$	2.77159	−	13.0393i	0.122013	−	0.574024i
$517$	−9.87478	−	1.56401i	−0.434292	−	0.0687852i
$518$	−1.53619	−	9.31377i	−0.0674965	−	0.409224i
$519$	2.33792	+	3.21787i	0.102623	+	0.141249i
$520$		0			0
$521$	14.6625	+	1.54109i	0.642376	+	0.0675164i	0.420115	−	0.907471i	$-0.361990\pi$
$521$	14.6625	+	1.54109i	0.642376	+	0.0675164i	0.222261	+	0.974987i	$0.428656\pi$
$522$	24.1154	+	29.7800i	1.05550	+	1.30344i
$523$	−4.14649	−	0.217309i	−0.181314	−	0.00950224i	−0.0385369	−	0.999257i	$-0.512270\pi$
$523$	−4.14649	−	0.217309i	−0.181314	−	0.00950224i	−0.142777	+	0.989755i	$0.545603\pi$
$524$	19.0321			0.831422
$525$		0			0
$526$	−65.2502			−2.84504
$527$	−7.75647	−	0.406500i	−0.337877	−	0.0177074i
$528$	4.76645	+	5.88608i	0.207433	+	0.256159i
$529$	12.2533	+	1.28788i	0.532754	+	0.0559947i
$530$		0			0
$531$	0.970802	+	1.33619i	0.0421292	+	0.0579859i
$532$	45.1516	+	17.0020i	1.95757	+	0.737132i
$533$	25.5144	+	4.04109i	1.10515	+	0.175039i
$534$	1.10270	−	5.18780i	0.0477185	−	0.224498i
$535$		0			0
$536$	74.2541	−	15.7832i	3.20729	−	0.681730i
$537$	−0.780772	−	1.20228i	−0.0336928	−	0.0518824i
$538$	56.3649	+	28.7194i	2.43006	+	1.23818i
$539$	−18.2619	−	10.2348i	−0.786597	−	0.440843i
$540$		0			0
$541$	−29.5536	−	6.28181i	−1.27061	−	0.270076i	−0.477216	−	0.878786i	$-0.658354\pi$
$541$	−29.5536	−	6.28181i	−1.27061	−	0.270076i	−0.793393	+	0.608710i	$0.791687\pi$
$542$	27.0559	+	70.4830i	1.16215	+	3.02750i
$543$	−1.00806	+	3.76211i	−0.0432598	+	0.161448i
$544$	7.14162	+	67.9480i	0.306194	+	2.91324i
$545$		0			0
$546$	7.48376	+	1.54084i	0.320275	+	0.0659417i
$547$	−6.40362	+	1.01423i	−0.273799	+	0.0433655i	−0.291824	−	0.956472i	$-0.594262\pi$
$547$	−6.40362	+	1.01423i	−0.273799	+	0.0433655i	0.0180249	+	0.999838i	$0.494262\pi$
$548$	1.05757	−	20.1797i	0.0451773	−	0.862035i
$549$	−14.7724	−	25.5866i	−0.630472	−	1.09201i
$550$		0			0
$551$	15.2593	+	8.80994i	0.650066	+	0.375316i
$552$	−5.22406	+	2.66179i	−0.222351	+	0.113293i
$553$	13.8251	−	0.813112i	0.587905	−	0.0345770i
$554$	18.8399	−	25.9310i	0.800433	−	1.10170i
$555$		0			0
$556$	16.8895	−	37.9345i	0.716275	−	1.60878i
$557$	−11.8915	−	3.18632i	−0.503860	−	0.135009i	−0.00206894	−	0.999998i	$-0.500659\pi$
$557$	−11.8915	−	3.18632i	−0.503860	−	0.135009i	−0.501791	+	0.864989i	$0.667325\pi$
$558$	9.84960	+	7.97605i	0.416967	+	0.337653i
$559$	18.1537	+	55.8715i	0.767821	+	2.36311i
$560$		0			0
$561$	−0.980610	+	3.01801i	−0.0414014	+	0.127420i
$562$	16.4921	−	10.7101i	0.695677	−	0.451778i
$563$	0.446300	+	8.51592i	0.0188093	+	0.358903i	0.991778	+	0.127968i	$0.0408453\pi$
$563$	0.446300	+	8.51592i	0.0188093	+	0.358903i	−0.972969	+	0.230936i	$0.925821\pi$
$564$	−0.776378	−	3.65257i	−0.0326914	−	0.153801i
$565$		0			0
$566$	64.6263	−	20.9984i	2.71645	−	0.882627i
$567$	15.9182	−	16.1228i	0.668500	−	0.677094i
$568$	−2.08589	−	2.08589i	−0.0875221	−	0.0875221i
$569$	31.0809	−	3.26674i	1.30298	−	0.136949i	0.572512	−	0.819896i	$-0.305969\pi$
$569$	31.0809	−	3.26674i	1.30298	−	0.136949i	0.730468	+	0.682947i	$0.239302\pi$
$570$		0			0
$571$	−0.883002	+	8.40120i	−0.0369525	+	0.351579i	0.960386	+	0.278672i	$0.0898943\pi$
$571$	−0.883002	+	8.40120i	−0.0369525	+	0.351579i	−0.997339	+	0.0729071i	$0.976772\pi$
$572$	−69.5161	−	26.6847i	−2.90662	−	1.11575i
$573$	1.21453	+	2.38365i	0.0507378	+	0.0995786i
$574$	3.62141	−	36.7092i	0.151155	−	1.53221i
$575$		0			0
$576$	21.8969	−	37.9266i	0.912372	−	1.58027i
$577$	11.7747	+	7.64659i	0.490188	+	0.318332i	0.765957	−	0.642892i	$-0.222266\pi$
$577$	11.7747	+	7.64659i	0.490188	+	0.318332i	−0.275769	+	0.961224i	$0.588932\pi$
$578$	−12.5694	+	10.1785i	−0.522816	+	0.423368i
$579$	1.73175	−	0.771024i	0.0719690	−	0.0320427i
$580$		0			0
$581$	−2.09177	−	1.18993i	−0.0867811	−	0.0493668i
$582$	−3.00411	+	3.00411i	−0.124524	+	0.124524i
$583$	8.04646	−	9.93656i	0.333251	−	0.411530i
$584$	−15.9151	+	17.6756i	−0.658573	+	0.731420i
$585$		0			0
$586$	5.54118	−	4.98931i	0.228904	−	0.206106i
$587$	8.93468	−	17.5353i	0.368774	−	0.723759i	−0.629822	−	0.776740i	$-0.716872\pi$
$587$	8.93468	−	17.5353i	0.368774	−	0.723759i	0.998596	+	0.0529805i	$0.0168721\pi$
$588$	1.12441	−	7.73765i	0.0463699	−	0.319095i
$589$	5.54247	+	1.80086i	0.228373	+	0.0742030i
$590$		0			0
$591$	0.651718	+	0.586810i	0.0268081	+	0.0241381i
$592$	−14.3785	+	5.51939i	−0.590953	+	0.226845i
$593$	−1.08028	−	4.03167i	−0.0443619	−	0.165561i	0.940191	−	0.340647i	$-0.110646\pi$
$593$	−1.08028	−	4.03167i	−0.0443619	−	0.165561i	−0.984553	+	0.175086i	$0.943980\pi$
$594$	8.44756	−	6.13751i	0.346608	−	0.251825i
$595$		0			0
$596$	89.2946	+	64.8763i	3.65765	+	2.65744i
$597$	0.970511	−	2.52827i	0.0397204	−	0.103475i
$598$	23.2758	−	35.8415i	0.951817	−	1.46567i
$599$	0.232901	−	0.134465i	0.00951606	−	0.00549410i	−0.495234	−	0.868759i	$-0.664918\pi$
$599$	0.232901	−	0.134465i	0.00951606	−	0.00549410i	0.504750	+	0.863265i	$0.331584\pi$
$600$		0			0
$601$		−	10.5831i		−	0.431694i	−0.976427	−	0.215847i	$-0.930749\pi$
$601$		−	10.5831i		−	0.431694i	0.976427	−	0.215847i	$-0.0692513\pi$
$602$	78.1218	−	30.5620i	3.18401	−	1.24561i
$603$	−4.31373	−	27.2358i	−0.175669	−	1.10913i
$604$	4.94952	+	11.1168i	0.201393	+	0.452336i
$605$		0			0
$606$	1.46633	+	0.652854i	0.0595658	+	0.0265204i
$607$	−1.20593	+	0.323127i	−0.0489470	+	0.0131153i	−0.283209	−	0.959058i	$-0.591399\pi$
$607$	−1.20593	+	0.323127i	−0.0489470	+	0.0131153i	0.234262	+	0.972173i	$0.424732\pi$
$608$	8.01920	−	50.6313i	0.325222	−	2.05337i
$609$	0.865037	−	2.72132i	0.0350531	−	0.110274i
$610$		0			0
$611$	11.0113	+	12.2293i	0.445469	+	0.494743i
$612$	71.6291	−	3.75392i	2.89543	−	0.151743i
$613$	−26.8108	+	1.40509i	−1.08288	+	0.0567512i	−0.585415	−	0.810734i	$-0.699068\pi$
$613$	−26.8108	+	1.40509i	−1.08288	+	0.0567512i	−0.497463	+	0.867485i	$0.665735\pi$
$614$	−42.8449	−	47.5841i	−1.72908	−	1.92034i
$615$		0			0
$616$	−19.4744	+	61.2645i	−0.784644	+	2.46842i
$617$	−1.44334	+	9.11291i	−0.0581068	+	0.366872i	0.941451	+	0.337149i	$0.109463\pi$
$617$	−1.44334	+	9.11291i	−0.0581068	+	0.366872i	−0.999558	+	0.0297232i	$0.990537\pi$
$618$	−0.378304	+	0.101366i	−0.0152176	+	0.00407755i
$619$	−7.43093	−	3.30846i	−0.298674	−	0.132978i	0.251928	−	0.967746i	$-0.418935\pi$
$619$	−7.43093	−	3.30846i	−0.298674	−	0.132978i	−0.550602	+	0.834768i	$0.685602\pi$
$620$		0			0
$621$	1.74682	+	3.92342i	0.0700975	+	0.157442i
$622$	11.7806	+	74.3796i	0.472358	+	2.98235i
$623$	22.2741	−	8.71385i	0.892394	−	0.349113i
$624$		−	12.4665i		−	0.499058i
$625$		0			0
$626$	−49.5578	+	28.6122i	−1.98073	+	1.14357i
$627$	1.29676	−	1.99683i	0.0517876	−	0.0797459i
$628$	−39.7731	+	103.612i	−1.58712	+	4.13459i
$629$	−5.22048	−	3.79290i	−0.208154	−	0.151233i
$630$		0			0
$631$	−26.1031	+	18.9650i	−1.03915	+	0.754985i	−0.970119	−	0.242629i	$-0.921990\pi$
$631$	−26.1031	+	18.9650i	−1.03915	+	0.754985i	−0.0690289	+	0.997615i	$0.521990\pi$
$632$	−11.0069	−	41.0784i	−0.437832	−	1.63401i
$633$	−4.52358	+	1.73644i	−0.179796	+	0.0690173i
$634$	−0.446023	−	0.401601i	−0.0177138	−	0.0159496i
$635$		0			0
$636$	4.54178	+	1.47571i	0.180093	+	0.0585158i
$637$	12.7582	+	32.0082i	0.505499	+	1.26821i
$638$	−17.6290	+	34.5989i	−0.697939	+	1.36978i
$639$	−0.796314	+	0.717004i	−0.0315017	+	0.0283642i
$640$		0			0
$641$	19.6339	−	21.8057i	0.775494	−	0.861273i	−0.217907	−	0.975970i	$-0.569923\pi$
$641$	19.6339	−	21.8057i	0.775494	−	0.861273i	0.993401	+	0.114697i	$0.0365896\pi$
$642$	0.998525	−	1.23308i	0.0394086	−	0.0486656i
$643$	23.5100	−	23.5100i	0.927145	−	0.927145i	−0.0703751	−	0.997521i	$-0.522420\pi$
$643$	23.5100	−	23.5100i	0.927145	−	0.927145i	0.997521	+	0.0703751i	$0.0224196\pi$
$644$	−38.0126	−	21.6241i	−1.49790	−	0.852107i
$645$		0			0
$646$	42.0432	−	18.7188i	1.65417	−	0.736482i
$647$	1.31441	−	1.06439i	0.0516749	−	0.0418455i	−0.603135	−	0.797639i	$-0.706082\pi$
$647$	1.31441	−	1.06439i	0.0516749	−	0.0418455i	0.654810	+	0.755794i	$0.272749\pi$
$648$	−58.3501	−	37.8930i	−2.29221	−	1.48858i
$649$	−0.836837	+	1.44944i	−0.0328487	+	0.0568956i
$650$		0			0
$651$	0.0927208	−	0.939882i	0.00363401	−	0.0368369i
$652$	20.3919	+	40.0214i	0.798610	+	1.56736i
$653$	−16.3928	−	6.29260i	−0.641499	−	0.246249i	0.0158035	−	0.999875i	$-0.494969\pi$
$653$	−16.3928	−	6.29260i	−0.641499	−	0.246249i	−0.657303	+	0.753627i	$0.728303\pi$
$654$	−0.285183	+	2.71334i	−0.0111515	+	0.106100i
$655$		0			0
$656$	−59.8549	+	6.29100i	−2.33694	+	0.245622i
$657$	6.10926	+	6.10926i	0.238345	+	0.238345i
$658$	16.5094	−	16.7217i	0.643605	−	0.651879i
$659$	12.1353	−	3.94299i	0.472724	−	0.153597i	−0.0629598	−	0.998016i	$-0.520054\pi$
$659$	12.1353	−	3.94299i	0.472724	−	0.153597i	0.535684	+	0.844419i	$0.320054\pi$
$660$		0			0
$661$	−9.56810	−	45.0144i	−0.372156	−	1.75086i	−0.622424	−	0.782680i	$-0.713852\pi$
$661$	−9.56810	−	45.0144i	−0.372156	−	1.75086i	0.250268	−	0.968177i	$-0.419481\pi$
$662$	2.65829	+	50.7233i	0.103318	+	1.97142i
$663$	4.38051	−	2.84474i	0.170125	−	0.110480i
$664$	−2.28363	+	7.02829i	−0.0886220	+	0.272751i
$665$		0			0
$666$	3.25380	+	10.0142i	0.126082	+	0.388041i
$667$	−12.4121	−	10.0511i	−0.480598	−	0.389181i
$668$	51.3182	+	13.7507i	1.98556	+	0.532029i
$669$	−0.127513	+	0.286398i	−0.00492992	+	0.0110728i
$670$		0			0
$671$	17.5979	−	24.2214i	0.679358	−	0.935056i
$672$	−8.29333	+	0.487764i	−0.319922	+	0.0188159i
$673$	−26.5870	+	13.5468i	−1.02485	+	0.522189i	−0.883826	−	0.467816i	$-0.845041\pi$
$673$	−26.5870	+	13.5468i	−1.02485	+	0.522189i	−0.141028	+	0.990006i	$0.545041\pi$
$674$	3.51634	+	2.03016i	0.135444	+	0.0781988i
$675$		0			0
$676$	28.4029	+	49.1952i	1.09242	+	1.89212i
$677$	−1.51063	+	28.8246i	−0.0580583	+	1.10782i	0.801902	+	0.597456i	$0.203822\pi$
$677$	−1.51063	+	28.8246i	−0.0580583	+	1.10782i	−0.859960	+	0.510362i	$0.829512\pi$
$678$	−10.1352	+	1.60526i	−0.389240	+	0.0616495i
$679$	−18.7655	−	3.86364i	−0.720153	−	0.148273i
$680$		0			0
$681$	−0.654283	−	6.22509i	−0.0250722	−	0.238546i
$682$	−3.32408	+	12.4056i	−0.127286	+	0.475036i
$683$	−5.68441	−	14.8084i	−0.217508	−	0.566628i	0.780800	−	0.624782i	$-0.214812\pi$
$683$	−5.68441	−	14.8084i	−0.217508	−	0.566628i	−0.998308	+	0.0581537i	$0.981479\pi$
$684$	−52.6412	−	11.1892i	−2.01279	−	0.427831i
$685$		0			0
$686$	44.5575	−	20.8701i	1.70121	−	0.796826i
$687$	−0.119319	−	0.0607961i	−0.00455231	−	0.00231952i
$688$	−74.5438	−	114.787i	−2.84196	−	4.37623i
$689$	−20.5853	+	4.37554i	−0.784238	+	0.166695i
$690$		0			0
$691$	0.246952	−	1.16182i	0.00939451	−	0.0441977i	−0.973201	−	0.229957i	$-0.926141\pi$
$691$	0.246952	−	1.16182i	0.00939451	−	0.0441977i	0.982595	+	0.185760i	$0.0594746\pi$
$692$	89.9831	+	14.2519i	3.42064	+	0.541777i
$693$	21.8535	+	8.22904i	0.830147	+	0.312595i
$694$	−30.9863	−	42.6489i	−1.17622	−	1.61893i
$695$		0			0
$696$	−8.72062	−	0.916574i	−0.330554	−	0.0347427i
$697$	−15.8689	−	19.5965i	−0.601079	−	0.742270i
$698$	−18.6253	−	0.976112i	−0.704979	−	0.0369464i
$699$	−0.993738			−0.0375866
$700$		0			0
$701$	8.69736			0.328495			0.164247	−	0.986419i	$-0.447480\pi$
$701$	8.69736			0.328495			0.164247	+	0.986419i	$0.447480\pi$
$702$	−17.1632	−	0.899484i	−0.647782	−	0.0339488i
$703$	3.04692	+	3.76263i	0.114917	+	0.141910i
$704$	44.1353	+	4.63881i	1.66341	+	0.174832i
$705$		0			0
$706$	42.1343	+	57.9929i	1.58574	+	2.18259i
$707$	1.17798	+	7.14199i	0.0443027	+	0.268602i
$708$	−0.617415	−	0.0977889i	−0.0232039	−	0.00367513i
$709$	−3.56761	+	16.7843i	−0.133985	+	0.630348i	0.858987	+	0.511997i	$0.171094\pi$
$709$	−3.56761	+	16.7843i	−0.133985	+	0.630348i	−0.992972	+	0.118351i	$0.962239\pi$
$710$		0			0
$711$	−15.1105	+	3.21183i	−0.566687	+	0.120453i
$712$	−40.0021	−	61.5979i	−1.49914	−	2.30848i
$713$	−4.70671	−	2.39819i	−0.176268	−	0.0898129i
$714$	−4.42238	−	6.00584i	−0.165503	−	0.224763i
$715$		0			0
$716$	−32.1181	−	6.82691i	−1.20031	−	0.255134i
$717$	1.04006	+	2.70945i	0.0388417	+	0.101186i
$718$	9.60239	−	35.8366i	0.358358	−	1.33741i
$719$	−3.40612	−	32.4070i	−0.127027	−	1.20858i	−0.853392	−	0.521269i	$-0.825459\pi$
$719$	−3.40612	−	32.4070i	−0.127027	−	1.20858i	0.726366	−	0.687309i	$-0.241208\pi$
$720$		0			0
$721$	−1.32007	−	1.17342i	−0.0491620	−	0.0437004i
$722$	15.7508	−	2.49468i	0.586183	−	0.0928423i
$723$	0.191508	−	3.65419i	0.00712225	−	0.135901i
$724$	44.6055	+	77.2589i	1.65775	+	2.87131i
$725$		0			0
$726$	−1.04469	−	0.603152i	−0.0387721	−	0.0223851i
$727$	−21.2447	+	10.8247i	−0.787922	+	0.401466i	−0.801163	−	0.598446i	$-0.795785\pi$
$727$	−21.2447	+	10.8247i	−0.787922	+	0.401466i	0.0132413	+	0.999912i	$0.495785\pi$
$728$	88.3707	−	58.1943i	3.27524	−	2.15683i
$729$	−14.3432	+	19.7418i	−0.531231	+	0.731177i
$730$		0			0
$731$	23.3242	−	52.3870i	0.862677	−	1.93760i
$732$	10.8012	+	2.89417i	0.399223	+	0.106972i
$733$	25.2676	+	20.4613i	0.933278	+	0.755754i	0.969882	−	0.243576i	$-0.0783205\pi$
$733$	25.2676	+	20.4613i	0.933278	+	0.755754i	−0.0366035	+	0.999330i	$0.511654\pi$
$734$	−23.3361	−	71.8210i	−0.861350	−	2.65096i
$735$		0			0
$736$	−14.3589	+	44.1921i	−0.529276	+	1.62894i
$737$	23.4353	−	15.2191i	0.863250	−	0.560601i
$738$	2.15344	+	41.0900i	0.0792691	+	1.51254i
$739$	11.0359	+	51.9197i	0.405961	+	1.90990i	0.414753	+	0.909934i	$0.363868\pi$
$739$	11.0359	+	51.9197i	0.405961	+	1.90990i	−0.00879226	+	0.999961i	$0.502799\pi$
$740$		0			0
$741$	−3.72715	+	1.21102i	−0.136920	+	0.0444881i
$742$	7.96309	+	28.9771i	0.292334	+	1.06378i
$743$	−35.7302	−	35.7302i	−1.31082	−	1.31082i	−0.920814	−	0.390001i	$-0.872474\pi$
$743$	−35.7302	−	35.7302i	−1.31082	−	1.31082i	−0.390001	−	0.920814i	$-0.627526\pi$
$744$	−2.88431	+	0.303153i	−0.105744	+	0.0111141i
$745$		0			0
$746$	−6.14228	+	58.4399i	−0.224885	+	2.13964i
$747$	2.50610	+	0.962003i	0.0916936	+	0.0351979i
$748$	32.9982	+	64.7627i	1.20653	+	2.36796i
$749$	7.12080	+	0.702478i	0.260189	+	0.0256680i
$750$		0			0
$751$	20.8809	−	36.1668i	0.761956	−	1.31975i	−0.179886	−	0.983688i	$-0.557573\pi$
$751$	20.8809	−	36.1668i	0.761956	−	1.31975i	0.941841	−	0.336058i	$-0.109094\pi$
$752$	−32.1542	−	20.8812i	−1.17254	−	0.761459i
$753$	3.66233	−	2.96570i	0.133463	−	0.108076i
$754$	58.3890	−	25.9964i	2.12640	−	0.946735i
$755$		0			0
$756$	0.112321	+	17.5872i	0.00408509	+	0.639639i
$757$	−22.3878	+	22.3878i	−0.813699	+	0.813699i	−0.985186	−	0.171487i	$-0.945143\pi$
$757$	−22.3878	+	22.3878i	−0.813699	+	0.813699i	0.171487	+	0.985186i	$0.445143\pi$
$758$	−56.4488	+	69.7084i	−2.05031	+	2.53192i
$759$	−1.44411	+	1.60385i	−0.0524180	+	0.0582161i
$760$		0			0
$761$	−20.4298	+	18.3950i	−0.740578	+	0.666820i	−0.950439	−	0.310912i	$-0.899366\pi$
$761$	−20.4298	+	18.3950i	−0.740578	+	0.666820i	0.209860	+	0.977731i	$0.432699\pi$
$762$	−1.38892	+	2.72591i	−0.0503154	+	0.0987494i
$763$	−10.9267	+	5.65564i	−0.395575	+	0.204748i
$764$	58.2772	+	18.9354i	2.10839	+	0.685059i
$765$		0			0
$766$	74.8157	+	67.3644i	2.70320	+	2.43397i
$767$	2.57183	−	0.987233i	0.0928634	−	0.0356469i
$768$	−0.0282037	−	0.105258i	−0.00101771	−	0.00379816i
$769$	−23.0581	+	16.7527i	−0.831495	+	0.604117i	−0.919982	−	0.391961i	$-0.871797\pi$
$769$	−23.0581	+	16.7527i	−0.831495	+	0.604117i	0.0884867	+	0.996077i	$0.471797\pi$
$770$		0			0
$771$	3.99922	+	2.90561i	0.144029	+	0.104643i
$772$	15.5602	−	40.5356i	0.560022	−	1.45891i
$773$	−14.3483	+	22.0944i	−0.516072	+	0.794681i	−0.996608	−	0.0822942i	$-0.973775\pi$
$773$	−14.3483	+	22.0944i	−0.516072	+	0.794681i	0.480536	+	0.876975i	$0.340442\pi$
$774$	−81.0365	+	46.7864i	−2.91280	+	1.68170i
$775$		0			0
$776$			58.8336i			2.11200i
$777$	0.489884	−	0.612919i	0.0175745	−	0.0219883i
$778$	−5.27432	−	33.3007i	−0.189093	−	1.19389i
$779$	7.69531	+	17.2839i	0.275713	+	0.619261i
$780$		0			0
$781$	−0.991973	−	0.441655i	−0.0354956	−	0.0158037i
$782$	−40.2948	+	10.7970i	−1.44094	+	0.386098i
$783$	−1.00478	+	6.34396i	−0.0359081	+	0.226715i
$784$	−48.0122	−	64.3387i	−1.71472	−	2.29781i
$785$		0			0
$786$	1.47711	+	1.64050i	0.0526868	+	0.0585146i
$787$	−36.8769	+	1.93264i	−1.31452	+	0.0688911i	−0.696662	−	0.717399i	$-0.745332\pi$
$787$	−36.8769	+	1.93264i	−1.31452	+	0.0688911i	−0.617857	+	0.786290i	$0.711999\pi$
$788$	20.0595	−	1.05127i	0.714591	−	0.0374501i
$789$	−3.62917	−	4.03061i	−0.129202	−	0.143493i
$790$		0			0
$791$	−31.1838	−	34.1914i	−1.10877	−	1.21571i
$792$	11.2176	−	70.8248i	0.398598	−	2.51665i
$793$	−47.5997	+	12.7543i	−1.69032	+	0.452919i
$794$	65.1677	+	29.0145i	2.31272	+	1.02969i
$795$		0			0
$796$	−25.2298	−	56.6672i	−0.894248	−	2.00851i
$797$	−2.57517	−	16.2590i	−0.0912170	−	0.575922i	−0.990387	−	0.138323i	$-0.955829\pi$
$797$	−2.57517	−	16.2590i	−0.0912170	−	0.575922i	0.899170	−	0.437599i	$-0.144171\pi$
$798$	2.03877	+	5.21145i	0.0721717	+	0.184483i
$799$		−	16.0634i		−	0.568282i
$800$		0			0
$801$	−23.1052	+	13.3398i	−0.816381	+	0.471338i
$802$	3.29603	−	5.07544i	0.116387	−	0.179220i
$803$	−3.13756	+	8.17362i	−0.110722	+	0.288441i
$804$	8.44351	+	6.13457i	0.297780	+	0.216350i
$805$		0			0
$806$	17.1022	−	12.4255i	0.602400	−	0.437669i
$807$	1.36094	+	5.07910i	0.0479074	+	0.178793i
$808$	20.7515	−	7.96576i	0.730036	−	0.280235i
$809$	14.2895	+	12.8663i	0.502393	+	0.452356i	0.880942	−	0.473225i	$-0.156910\pi$
$809$	14.2895	+	12.8663i	0.502393	+	0.452356i	−0.378549	+	0.925581i	$0.623577\pi$
$810$		0			0
$811$	6.38309	+	2.07399i	0.224141	+	0.0728277i	0.418934	−	0.908017i	$-0.362404\pi$
$811$	6.38309	+	2.07399i	0.224141	+	0.0728277i	−0.194794	+	0.980844i	$0.562404\pi$
$812$	−30.0649	−	58.0857i	−1.05507	−	2.03841i
$813$	−2.84901	+	5.59150i	−0.0999192	+	0.196103i
$814$	−7.92941	+	7.13968i	−0.277926	+	0.250245i
$815$		0			0
$816$	−8.14261	+	9.04329i	−0.285048	+	0.316578i
$817$	−27.0771	+	33.4374i	−0.947308	+	1.16983i
$818$	54.5072	−	54.5072i	1.90580	−	1.90580i
$819$	−19.4300	−	33.1629i	−0.678940	−	1.15880i
$820$		0			0
$821$	−41.4237	+	18.4430i	−1.44570	+	0.643666i	−0.971562	−	0.236785i	$-0.923906\pi$
$821$	−41.4237	+	18.4430i	−1.44570	+	0.643666i	−0.474136	+	0.880452i	$0.657240\pi$
$822$	1.82150	−	1.47502i	0.0635320	−	0.0514472i
$823$	8.27427	+	5.37337i	0.288423	+	0.187304i	0.680738	−	0.732527i	$-0.261659\pi$
$823$	8.27427	+	5.37337i	0.288423	+	0.187304i	−0.392315	+	0.919831i	$0.628326\pi$
$824$	−2.71183	+	4.69703i	−0.0944711	+	0.163629i
$825$		0			0
$826$	−1.62290	−	3.58333i	−0.0564679	−	0.124680i
$827$	−8.32384	−	16.3365i	−0.289448	−	0.568074i	0.699797	−	0.714342i	$-0.253274\pi$
$827$	−8.32384	−	16.3365i	−0.289448	−	0.568074i	−0.989245	+	0.146268i	$0.953274\pi$
$828$	45.5421	+	17.4820i	1.58270	+	0.607541i
$829$	2.48022	−	23.5977i	0.0861416	−	0.819583i	−0.863100	−	0.505034i	$-0.831480\pi$
$829$	2.48022	−	23.5977i	0.0861416	−	0.819583i	0.949241	−	0.314549i	$-0.101853\pi$
$830$		0			0
$831$	2.64966	−	0.278491i	0.0919157	−	0.00966073i
$832$	−51.6507	−	51.6507i	−1.79067	−	1.79067i
$833$	11.6516	−	31.5523i	0.403704	−	1.09322i
$834$	4.58063	−	1.48834i	0.158614	−	0.0515368i
$835$		0			0
$836$	−11.3386	−	53.3439i	−0.392154	−	1.84494i
$837$	0.111182	+	2.12148i	0.00384301	+	0.0733291i
$838$	11.9497	−	7.76021i	0.412795	−	0.268072i
$839$	−4.66811	+	14.3670i	−0.161161	+	0.496003i	−0.998733	−	0.0503242i	$-0.983975\pi$
$839$	−4.66811	+	14.3670i	−0.161161	+	0.496003i	0.837572	+	0.546327i	$0.183975\pi$
$840$		0			0
$841$	1.58024	+	4.86346i	0.0544909	+	0.167706i
$842$	−39.0785	−	31.6452i	−1.34674	−	1.09056i
$843$	1.57886	+	0.423054i	0.0543788	+	0.0145707i
$844$	−45.1413	+	101.389i	−1.55383	+	3.48995i
$845$		0			0
$846$	−15.4068	+	21.2056i	−0.529696	+	0.729064i
$847$	−0.319398	−	5.43065i	−0.0109747	−	0.186599i
$848$	43.6871	−	22.2597i	1.50022	−	0.764401i
$849$	4.89158	+	2.82415i	0.167878	+	0.0969247i
$850$		0			0
$851$	−2.19432	−	3.80067i	−0.0752202	−	0.130285i
$852$	0.0212254	−	0.405005i	0.000727171	−	0.0138752i
$853$	−24.6553	+	3.90501i	−0.844180	+	0.133705i	−0.563520	−	0.826102i	$-0.690553\pi$
$853$	−24.6553	+	3.90501i	−0.844180	+	0.133705i	−0.280660	+	0.959807i	$0.590553\pi$
$854$	22.1717	+	66.7833i	0.758701	+	2.28528i
$855$		0			0
$856$	−2.29677	−	21.8523i	−0.0785019	−	0.746896i
$857$	12.2346	−	45.6601i	0.417926	−	1.55972i	−0.360977	−	0.932575i	$-0.617557\pi$
$857$	12.2346	−	45.6601i	0.417926	−	1.55972i	0.778903	−	0.627145i	$-0.215777\pi$
$858$	−3.09512	−	8.06307i	−0.105666	−	0.275269i
$859$	−41.2291	−	8.76352i	−1.40672	−	0.299007i	−0.558874	−	0.829252i	$-0.688767\pi$
$859$	−41.2291	−	8.76352i	−1.40672	−	0.299007i	−0.847845	+	0.530245i	$0.822100\pi$
$860$		0			0
$861$	2.46900	−	1.81804i	0.0841433	−	0.0619586i
$862$	−55.0849	−	28.0672i	−1.87620	−	0.955972i
$863$	−23.6069	−	36.3514i	−0.803587	−	1.23742i	−0.967982	−	0.251021i	$-0.919234\pi$
$863$	−23.6069	−	36.3514i	−0.803587	−	1.23742i	0.164394	−	0.986395i	$-0.447433\pi$
$864$	18.2785	−	3.88522i	0.621848	−	0.132178i
$865$		0			0
$866$	3.33240	−	15.6777i	0.113239	−	0.532750i
$867$	−1.32784	−	0.210309i	−0.0450958	−	0.00714247i
$868$	−13.7209	−	16.7243i	−0.465716	−	0.567660i
$869$	−9.20135	−	12.6646i	−0.312134	−	0.429616i
$870$		0			0
$871$	−45.7418	−	4.80765i	−1.54990	−	0.162901i
$872$	23.7770	+	29.3621i	0.805190	+	0.994326i
$873$	21.3419	+	1.11848i	0.722316	+	0.0378550i
$874$	31.2998			1.05873
$875$		0			0
$876$	−3.27001			−0.110483
$877$	4.31254	+	0.226010i	0.145624	+	0.00763183i	0.125009	−	0.992156i	$-0.460104\pi$
$877$	4.31254	+	0.226010i	0.145624	+	0.00763183i	0.0206153	+	0.999787i	$0.493437\pi$
$878$	−59.7483	−	73.7830i	−2.01641	−	2.49006i
$879$	0.616394	+	0.0647856i	0.0207905	+	0.00218517i
$880$		0			0
$881$	−6.93297	−	9.54241i	−0.233578	−	0.321492i	0.676098	−	0.736812i	$-0.263670\pi$
$881$	−6.93297	−	9.54241i	−0.233578	−	0.321492i	−0.909675	+	0.415320i	$0.863670\pi$
$882$	−45.6441	+	30.4775i	−1.53692	+	1.02623i
$883$	−19.7520	−	3.12841i	−0.664708	−	0.105279i	−0.185042	−	0.982731i	$-0.559242\pi$
$883$	−19.7520	−	3.12841i	−0.664708	−	0.105279i	−0.479666	+	0.877451i	$0.659242\pi$
$884$	24.8738	−	117.022i	0.836597	−	3.93588i
$885$		0			0
$886$	−54.6726	+	11.6210i	−1.83676	+	0.390416i
$887$	−0.228041	−	0.351152i	−0.00765687	−	0.0117905i	0.834821	−	0.550521i	$-0.185571\pi$
$887$	−0.228041	−	0.351152i	−0.00765687	−	0.0117905i	−0.842478	+	0.538730i	$0.818904\pi$
$888$	−2.14684	−	1.09387i	−0.0720434	−	0.0367079i
$889$	−13.7117	+	1.52975i	−0.459874	+	0.0513062i
$890$		0			0
$891$	−25.0506	−	5.32466i	−0.839225	−	0.178383i
$892$	2.57335	+	6.70380i	0.0861621	+	0.224460i
$893$	−3.11939	+	11.6417i	−0.104387	+	0.389576i
$894$	1.33819	+	12.7320i	0.0447557	+	0.425822i
$895$		0			0
$896$	−19.3096	+	21.7229i	−0.645088	+	0.725710i
$897$	3.50857	−	0.555703i	0.117148	−	0.0185544i
$898$	−2.38681	+	45.5431i	−0.0796490	+	1.51979i
$899$	−3.95014	−	6.84184i	−0.131744	−	0.228188i
$900$		0			0
$901$	17.7907	+	10.2715i	0.592695	+	0.342192i
$902$	−37.1511	+	18.9294i	−1.23700	+	0.630281i
$903$	6.23294	+	3.12586i	0.207419	+	0.104022i
$904$	−83.5269	+	114.965i	−2.77806	+	3.82368i
$905$		0			0
$906$	−0.574087	+	1.28942i	−0.0190728	+	0.0428381i
$907$	47.3268	+	12.6812i	1.57146	+	0.421072i	0.936270	−	0.351282i	$-0.114254\pi$
$907$	47.3268	+	12.6812i	1.57146	+	0.421072i	0.635192	+	0.772354i	$0.280921\pi$
$908$	−111.420	−	90.2262i	−3.69761	−	2.99426i
$909$	−2.49508	−	7.67907i	−0.0827566	−	0.254699i
$910$		0			0
$911$	1.87294	−	5.76433i	0.0620534	−	0.190981i	−0.915224	−	0.402946i	$-0.867986\pi$
$911$	1.87294	−	5.76433i	0.0620534	−	0.190981i	0.977277	+	0.211965i	$0.0679863\pi$
$912$	7.65739	−	4.97277i	0.253562	−	0.164665i
$913$	0.142366	+	2.71651i	0.00471163	+	0.0899032i
$914$	−12.8166	−	60.2972i	−0.423934	−	1.99445i
$915$		0			0
$916$	−2.91719	+	0.947853i	−0.0963868	+	0.0313180i
$917$	−2.51511	+	9.63217i	−0.0830563	+	0.318082i
$918$	11.8628	+	11.8628i	0.391532	+	0.391532i
$919$	−2.98351	+	0.313580i	−0.0984170	+	0.0103440i	−0.153609	−	0.988132i	$-0.549090\pi$
$919$	−2.98351	+	0.313580i	−0.0984170	+	0.0103440i	0.0551920	+	0.998476i	$0.482423\pi$
$920$		0			0
$921$	0.556337	−	5.29319i	0.0183319	−	0.174417i
$922$	41.5978	+	15.9679i	1.36995	+	0.525875i
$923$	0.811402	+	1.59247i	0.0267076	+	0.0524167i
$924$	−8.05091	+	3.64628i	−0.264856	+	0.119954i
$925$		0			0
$926$	37.3273	−	64.6527i	1.22665	−	2.12462i
$927$	1.65230	+	1.07301i	0.0542686	+	0.0352424i
$928$	−54.0066	+	43.7337i	−1.77285	+	1.43563i
$929$	26.8993	−	11.9763i	0.882536	−	0.392930i	0.0851274	−	0.996370i	$-0.472870\pi$
$929$	26.8993	−	11.9763i	0.882536	−	0.392930i	0.797409	+	0.603440i	$0.206204\pi$
$930$		0			0
$931$	−14.5716	+	20.6044i	−0.477564	+	0.675283i
$932$	−16.0948	+	16.0948i	−0.527204	+	0.527204i
$933$	−3.93932	+	4.86465i	−0.128967	+	0.159261i
$934$	10.1454	−	11.2676i	0.331967	−	0.368687i
$935$		0			0
$936$	−87.7119	+	78.9762i	−2.86695	+	2.58142i
$937$	5.60030	−	10.9912i	0.182954	−	0.359067i	−0.781255	−	0.624213i	$-0.785420\pi$
$937$	5.60030	−	10.9912i	0.182954	−	0.359067i	0.964208	+	0.265145i	$0.0854199\pi$
$938$	−3.01831	+	65.6071i	−0.0985513	+	2.14215i
$939$	−4.52379	−	1.46987i	−0.147628	−	0.0479673i
$940$		0			0
$941$	−14.2139	−	12.7982i	−0.463359	−	0.417210i	0.404103	−	0.914713i	$-0.367584\pi$
$941$	−14.2139	−	12.7982i	−0.463359	−	0.417210i	−0.867462	+	0.497503i	$0.834250\pi$
$942$	−12.0178	+	4.61322i	−0.391563	+	0.150307i
$943$	−4.43863	−	16.5652i	−0.144542	−	0.539436i
$944$	−5.19239	+	3.77249i	−0.168998	+	0.122784i
$945$		0			0
$946$	−76.7125	−	55.7349i	−2.49414	−	1.81210i
$947$	5.94548	−	15.4885i	0.193202	−	0.503309i	−0.802422	−	0.596757i	$-0.796456\pi$
$947$	5.94548	−	15.4885i	0.193202	−	0.503309i	0.995624	+	0.0934481i	$0.0297889\pi$
$948$	3.18440	−	4.90355i	0.103425	−	0.159260i
$949$	12.4800	−	7.20530i	0.405116	−	0.233894i
$950$		0			0
$951$		−	0.0498883i		−	0.00161774i
$952$	−102.115	−	15.5056i	−3.30957	−	0.502540i
$953$	−1.04982	−	6.62829i	−0.0340069	−	0.214711i	0.964833	−	0.262863i	$-0.0846668\pi$
$953$	−1.04982	−	6.62829i	−0.0340069	−	0.214711i	−0.998840	+	0.0481520i	$0.984667\pi$
$954$	−13.6343	−	30.6231i	−0.441426	−	0.991460i
$955$		0			0
$956$	60.7280	+	27.0379i	1.96408	+	0.874467i
$957$	−3.11774	+	0.835396i	−0.100782	+	0.0270045i
$958$	−7.78282	+	49.1388i	−0.251451	+	1.58760i
$959$	10.0732	+	3.20201i	0.325281	+	0.103398i
$960$		0			0
$961$	18.9946	+	21.0957i	0.612730	+	0.680505i
$962$	17.5385	−	0.919152i	0.565463	−	0.0296346i
$963$	−7.97060	+	0.417722i	−0.256849	+	0.0134609i
$964$	−56.0825	−	62.2859i	−1.80629	−	2.00609i
$965$		0			0
$966$	−1.08630	−	4.95481i	−0.0349510	−	0.159418i
$967$	0.497917	−	3.14373i	0.0160119	−	0.101095i	−0.978388	−	0.206777i	$-0.933702\pi$
$967$	0.497917	−	3.14373i	0.0160119	−	0.101095i	0.994400	+	0.105682i	$0.0337025\pi$
$968$	−16.1360	+	4.32363i	−0.518631	+	0.138967i
$969$	3.49470	+	1.55594i	0.112266	+	0.0499841i
$970$		0			0
$971$	−19.0985	−	42.8958i	−0.612899	−	1.37659i	−0.907127	−	0.420858i	$-0.861729\pi$
$971$	−19.0985	−	42.8958i	−0.612899	−	1.37659i	0.294228	−	0.955735i	$-0.404937\pi$
$972$	−4.61602	−	29.1444i	−0.148059	−	0.934808i
$973$	16.9667	+	13.5609i	0.543927	+	0.434742i
$974$		−	60.5732i		−	1.94089i
$975$		0			0
$976$	99.4284	−	57.4050i	3.18263	−	1.83749i
$977$	6.45000	−	9.93213i	0.206354	−	0.317757i	−0.720307	−	0.693655i	$-0.755999\pi$
$977$	6.45000	−	9.93213i	0.206354	−	0.317757i	0.926661	+	0.375898i	$0.122666\pi$
$978$	−1.86705	+	4.86383i	−0.0597016	+	0.155528i
$979$	−21.8723	−	15.8912i	−0.699042	−	0.507884i
$980$		0			0
$981$	11.1032	−	8.06691i	0.354496	−	0.257557i
$982$	8.15865	+	30.4485i	0.260353	+	0.971651i
$983$	−39.6310	+	15.2129i	−1.26403	+	0.485217i	−0.895775	−	0.444507i	$-0.853379\pi$
$983$	−39.6310	+	15.2129i	−1.26403	+	0.485217i	−0.368258	+	0.929724i	$0.620046\pi$
$984$	−6.99707	−	6.30019i	−0.223059	−	0.200843i
$985$		0			0
$986$	−59.3358	−	19.2794i	−1.88964	−	0.613980i
$987$	1.95117	+	0.0897651i	0.0621064	+	0.00285725i
$988$	−40.7518	+	79.9799i	−1.29649	+	2.54450i
$989$	28.9830	−	26.0964i	0.921606	−	0.829818i
$990$		0			0
$991$	28.8511	−	32.0424i	0.916484	−	1.01786i	−0.0832882	−	0.996526i	$-0.526542\pi$
$991$	28.8511	−	32.0424i	0.916484	−	1.01786i	0.999772	−	0.0213333i	$-0.00679112\pi$
$992$	−14.4647	+	17.8624i	−0.459255	+	0.567133i
$993$	−2.98540	+	2.98540i	−0.0947388	+	0.0947388i
$994$	2.20200	−	1.29015i	0.0698433	−	0.0409210i
$995$		0			0
$996$	−0.928160	+	0.413243i	−0.0294099	+	0.0130941i
$997$	−26.2140	+	21.2277i	−0.830205	+	0.672287i	−0.947129	−	0.320854i	$-0.896030\pi$
$997$	−26.2140	+	21.2277i	−0.830205	+	0.672287i	0.116923	+	0.993141i	$0.462697\pi$
$998$	21.1143	+	13.7118i	0.668363	+	0.434040i
$999$	−0.882464	+	1.52847i	−0.0279199	+	0.0483587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.243.18		288
5.2	odd	4		175.2.x.a.47.1	yes	288
5.3	odd	4		875.2.bb.c.257.18		288
5.4	even	2		875.2.bb.a.243.1		288
7.3	odd	6	inner	875.2.bb.b.493.1		288
25.6	even	5		175.2.x.a.33.1	✓	288
25.8	odd	20		875.2.bb.a.607.18		288
25.17	odd	20	inner	875.2.bb.b.607.1		288
25.19	even	10		875.2.bb.c.768.18		288
35.3	even	12		875.2.bb.c.507.18		288
35.17	even	12		175.2.x.a.122.1	yes	288
35.24	odd	6		875.2.bb.a.493.18		288
175.17	even	60	inner	875.2.bb.b.857.18		288
175.31	odd	30		175.2.x.a.108.1	yes	288
175.94	odd	30		875.2.bb.c.143.18		288
175.108	even	60		875.2.bb.a.857.1		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.1	✓	288	25.6	even	5
175.2.x.a.47.1	yes	288	5.2	odd	4
175.2.x.a.108.1	yes	288	175.31	odd	30
175.2.x.a.122.1	yes	288	35.17	even	12
875.2.bb.a.243.1		288	5.4	even	2
875.2.bb.a.493.18		288	35.24	odd	6
875.2.bb.a.607.18		288	25.8	odd	20
875.2.bb.a.857.1		288	175.108	even	60
875.2.bb.b.243.18		288	1.1	even	1	trivial
875.2.bb.b.493.1		288	7.3	odd	6	inner
875.2.bb.b.607.1		288	25.17	odd	20	inner
875.2.bb.b.857.18		288	175.17	even	60	inner
875.2.bb.c.143.18		288	175.94	odd	30
875.2.bb.c.257.18		288	5.3	odd	4
875.2.bb.c.507.18		288	35.3	even	12
875.2.bb.c.768.18		288	25.19	even	10

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.65307 + 0.139042i) q^{2} +(0.138973 + 0.171618i) q^{3} +(5.03041 + 0.528718i) q^{4} +(0.344844 + 0.474637i) q^{6} +(-0.932359 + 2.47603i) q^{7} +(8.02453 + 1.27096i) q^{8} +(0.613596 - 2.88674i) q^{9} +(2.92528 - 0.621787i) q^{11} +(0.608356 + 0.936786i) q^{12} +(-4.38594 - 2.23475i) q^{13} +(-2.81788 + 6.43944i) q^{14} +(11.2177 + 2.38441i) q^{16} +(1.72195 + 4.48584i) q^{17} +(2.02929 - 7.57342i) q^{18} +(-0.376845 - 3.58544i) q^{19} +(-0.554503 + 0.184092i) q^{21} +(7.84742 - 1.24291i) q^{22} +(-0.171029 + 3.26342i) q^{23} +(0.897076 + 1.55378i) q^{24} +(-11.3255 - 6.53878i) q^{26} +(1.17097 - 0.596641i) q^{27} +(-5.99927 + 11.9625i) q^{28} +(-2.87272 + 3.95395i) q^{29} +(-0.657478 + 1.47672i) q^{31} +(13.7345 + 3.68016i) q^{32} +(0.513245 + 0.415617i) q^{33} +(3.94475 + 12.1407i) q^{34} +(4.61291 - 14.1971i) q^{36} +(-1.12629 + 0.731424i) q^{37} +(-0.501272 - 9.56484i) q^{38} +(-0.226006 - 1.06328i) q^{39} +(-4.99103 + 1.62168i) q^{41} +(-1.49673 + 0.411311i) q^{42} +(-8.43891 - 8.43891i) q^{43} +(15.0441 - 1.58120i) q^{44} +(-0.907502 + 8.63431i) q^{46} +(-3.12102 - 1.19805i) q^{47} +(1.14976 + 2.25653i) q^{48} +(-5.26142 - 4.61709i) q^{49} +(-0.530544 + 0.918929i) q^{51} +(-20.8816 - 13.5606i) q^{52} +(3.32256 - 2.69056i) q^{53} +(3.18964 - 1.42012i) q^{54} +(-10.6287 + 18.6840i) q^{56} +(0.562954 - 0.562954i) q^{57} +(-8.17129 + 10.0907i) q^{58} +(-0.374472 + 0.415893i) q^{59} +(7.43964 - 6.69868i) q^{61} +(-1.94966 + 3.82643i) q^{62} +(6.57556 + 4.21076i) q^{63} +(14.1129 + 4.58555i) q^{64} +(1.30389 + 1.17403i) q^{66} +(8.72305 - 3.34846i) q^{67} +(6.29039 + 23.4761i) q^{68} +(-0.583829 + 0.424177i) q^{69} +(-0.293741 - 0.213415i) q^{71} +(8.59275 - 22.3849i) q^{72} +(-1.59444 + 2.45523i) q^{73} +(-3.08984 + 1.78392i) q^{74} -18.2355i q^{76} +(-1.18785 + 7.82279i) q^{77} +(-0.451771 - 2.85237i) q^{78} +(-2.12904 - 4.78190i) q^{79} +(-7.82313 - 3.48308i) q^{81} +(-13.4670 + 3.60848i) q^{82} +(-0.142291 + 0.898387i) q^{83} +(-2.88671 + 0.632885i) q^{84} +(-21.2157 - 23.5624i) q^{86} +(-1.07780 + 0.0564851i) q^{87} +(24.2642 - 1.27163i) q^{88} +(-6.04903 - 6.71813i) q^{89} +(9.62257 - 8.77612i) q^{91} +(-2.58577 + 16.3259i) q^{92} +(-0.344803 + 0.0923897i) q^{93} +(-8.11372 - 3.61246i) q^{94} +(1.27715 + 2.86853i) q^{96} +(1.13281 + 7.15230i) q^{97} +(-13.3169 - 12.9810i) q^{98} -8.82604i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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