LMFDB - Embedded newform 175.2.x.a.108.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			108.1
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.139042 - 2.65307i) q^{2} +(0.171618 + 0.138973i) q^{3} +(-5.03041 + 0.528718i) q^{4} +(-2.22928 - 0.174120i) q^{5} +(0.344844 - 0.474637i) q^{6} +(-2.47603 + 0.932359i) q^{7} +(1.27096 + 8.02453i) q^{8} +(-0.613596 - 2.88674i) q^{9} +(-0.151991 + 5.93865i) q^{10} +(2.92528 + 0.621787i) q^{11} +(-0.936786 - 0.608356i) q^{12} +(-2.23475 - 4.38594i) q^{13} +(2.81788 + 6.43944i) q^{14} +(-0.358386 - 0.339692i) q^{15} +(11.2177 - 2.38441i) q^{16} +(-4.48584 - 1.72195i) q^{17} +(-7.57342 + 2.02929i) q^{18} +(0.376845 - 3.58544i) q^{19} +(11.3063 - 0.302763i) q^{20} +(-0.554503 - 0.184092i) q^{21} +(1.24291 - 7.84742i) q^{22} +(3.26342 - 0.171029i) q^{23} +(-0.897076 + 1.55378i) q^{24} +(4.93936 + 0.776324i) q^{25} +(-11.3255 + 6.53878i) q^{26} +(0.596641 - 1.17097i) q^{27} +(11.9625 - 5.99927i) q^{28} +(2.87272 + 3.95395i) q^{29} +(-0.851397 + 0.998054i) q^{30} +(-0.657478 - 1.47672i) q^{31} +(-3.68016 - 13.7345i) q^{32} +(0.415617 + 0.513245i) q^{33} +(-3.94475 + 12.1407i) q^{34} +(5.68209 - 1.64736i) q^{35} +(4.61291 + 14.1971i) q^{36} +(-0.731424 + 1.12629i) q^{37} +(-9.56484 - 0.501272i) q^{38} +(0.226006 - 1.06328i) q^{39} +(-1.43609 - 18.1102i) q^{40} +(-4.99103 - 1.62168i) q^{41} +(-0.411311 + 1.49673i) q^{42} +(-8.43891 - 8.43891i) q^{43} +(-15.0441 - 1.58120i) q^{44} +(0.865237 + 6.54219i) q^{45} +(-0.907502 - 8.63431i) q^{46} +(1.19805 + 3.12102i) q^{47} +(2.25653 + 1.14976i) q^{48} +(5.26142 - 4.61709i) q^{49} +(1.37287 - 13.2124i) q^{50} +(-0.530544 - 0.918929i) q^{51} +(13.5606 + 20.8816i) q^{52} +(-2.69056 + 3.32256i) q^{53} +(-3.18964 - 1.42012i) q^{54} +(-6.41299 - 1.89548i) q^{55} +(-10.6287 - 18.6840i) q^{56} +(0.562954 - 0.562954i) q^{57} +(10.0907 - 8.17129i) q^{58} +(0.374472 + 0.415893i) q^{59} +(1.98243 + 1.51931i) q^{60} +(7.43964 + 6.69868i) q^{61} +(-3.82643 + 1.94966i) q^{62} +(4.21076 + 6.57556i) q^{63} +(-14.1129 + 4.58555i) q^{64} +(4.21820 + 10.1666i) q^{65} +(1.30389 - 1.17403i) q^{66} +(3.34846 - 8.72305i) q^{67} +(23.4761 + 6.29039i) q^{68} +(0.583829 + 0.424177i) q^{69} +(-5.16061 - 14.8460i) q^{70} +(-0.293741 + 0.213415i) q^{71} +(22.3849 - 8.59275i) q^{72} +(2.45523 - 1.59444i) q^{73} +(3.08984 + 1.78392i) q^{74} +(0.739794 + 0.819671i) q^{75} +18.2355i q^{76} +(-7.82279 + 1.18785i) q^{77} +(-2.85237 - 0.451771i) q^{78} +(2.12904 - 4.78190i) q^{79} +(-25.4227 + 3.36227i) q^{80} +(-7.82313 + 3.48308i) q^{81} +(-3.60848 + 13.4670i) q^{82} +(0.898387 - 0.142291i) q^{83} +(2.88671 + 0.632885i) q^{84} +(9.70036 + 4.61979i) q^{85} +(-21.2157 + 23.5624i) q^{86} +(-0.0564851 + 1.07780i) q^{87} +(-1.27163 + 24.2642i) q^{88} +(6.04903 - 6.71813i) q^{89} +(17.2366 - 3.20517i) q^{90} +(9.62257 + 8.77612i) q^{91} +(-16.3259 + 2.58577i) q^{92} +(0.0923897 - 0.344803i) q^{93} +(8.11372 - 3.61246i) q^{94} +(-1.46439 + 7.92734i) q^{95} +(1.27715 - 2.86853i) q^{96} +(-7.15230 - 1.13281i) q^{97} +(-12.9810 - 13.3169i) q^{98} -8.82604i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.139042	−	2.65307i	−0.0983173	−	1.87601i	−0.391813	−	0.920045i	$-0.628152\pi$
$2$	−0.139042	−	2.65307i	−0.0983173	−	1.87601i	0.293496	−	0.955960i	$-0.405181\pi$
$3$	0.171618	+	0.138973i	0.0990835	+	0.0802363i	0.677582	−	0.735447i	$-0.263028\pi$
$3$	0.171618	+	0.138973i	0.0990835	+	0.0802363i	−0.578499	+	0.815683i	$0.696361\pi$
$4$	−5.03041	+	0.528718i	−2.51521	+	0.264359i
$5$	−2.22928	−	0.174120i	−0.996964	−	0.0778689i
$5$	−2.22928	−	0.174120i	−0.996964	−	0.0778689i
$6$	0.344844	−	0.474637i	0.140782	−	0.193770i
$7$	−2.47603	+	0.932359i	−0.935850	+	0.352398i
$7$	−2.47603	+	0.932359i	−0.935850	+	0.352398i
$8$	1.27096	+	8.02453i	0.449352	+	2.83710i
$9$	−0.613596	−	2.88674i	−0.204532	−	0.962247i
$10$	−0.151991	+	5.93865i	−0.0480636	+	1.87796i
$11$	2.92528	+	0.621787i	0.882004	+	0.187476i	0.626583	−	0.779354i	$-0.284453\pi$
$11$	2.92528	+	0.621787i	0.882004	+	0.187476i	0.255421	+	0.966830i	$0.417786\pi$
$12$	−0.936786	−	0.608356i	−0.270427	−	0.175617i
$13$	−2.23475	−	4.38594i	−0.619808	−	1.21644i	−0.961026	−	0.276458i	$-0.910839\pi$
$13$	−2.23475	−	4.38594i	−0.619808	−	1.21644i	0.341218	−	0.939984i	$-0.389161\pi$
$14$	2.81788	+	6.43944i	0.753111	+	1.72101i
$15$	−0.358386	−	0.339692i	−0.0925348	−	0.0877082i
$16$	11.2177	−	2.38441i	2.80444	−	0.596102i
$17$	−4.48584	−	1.72195i	−1.08798	−	0.417635i	−0.252744	−	0.967533i	$-0.581333\pi$
$17$	−4.48584	−	1.72195i	−1.08798	−	0.417635i	−0.835232	+	0.549898i	$0.814666\pi$
$18$	−7.57342	+	2.02929i	−1.78507	+	0.478309i
$19$	0.376845	−	3.58544i	0.0864543	−	0.822557i	−0.862269	−	0.506450i	$-0.830957\pi$
$19$	0.376845	−	3.58544i	0.0864543	−	0.822557i	0.948723	−	0.316107i	$-0.102376\pi$
$20$	11.3063	−	0.302763i	2.52816	−	0.0676999i
$21$	−0.554503	−	0.184092i	−0.121002	−	0.0401722i
$22$	1.24291	−	7.84742i	0.264989	−	1.67308i
$23$	3.26342	−	0.171029i	0.680470	−	0.0356619i	0.291030	−	0.956714i	$-0.406002\pi$
$23$	3.26342	−	0.171029i	0.680470	−	0.0356619i	0.389440	+	0.921052i	$0.372669\pi$
$24$	−0.897076	+	1.55378i	−0.183115	+	0.317164i
$25$	4.93936	+	0.776324i	0.987873	+	0.155265i
$26$	−11.3255	+	6.53878i	−2.22111	+	1.28236i
$27$	0.596641	−	1.17097i	0.114824	−	0.225354i
$28$	11.9625	−	5.99927i	2.26070	−	1.13376i
$29$	2.87272	+	3.95395i	0.533450	+	0.734231i	0.987651	−	0.156668i	$-0.0500753\pi$
$29$	2.87272	+	3.95395i	0.533450	+	0.734231i	−0.454201	+	0.890899i	$0.650075\pi$
$30$	−0.851397	+	0.998054i	−0.155443	+	0.182219i
$31$	−0.657478	−	1.47672i	−0.118087	−	0.265227i	0.844826	−	0.535042i	$-0.179704\pi$
$31$	−0.657478	−	1.47672i	−0.118087	−	0.265227i	−0.962912	+	0.269815i	$0.913037\pi$
$32$	−3.68016	−	13.7345i	−0.650566	−	2.42794i
$33$	0.415617	+	0.513245i	0.0723497	+	0.0893445i
$34$	−3.94475	+	12.1407i	−0.676518	+	2.08211i
$35$	5.68209	−	1.64736i	0.960449	−	0.278455i
$36$	4.61291	+	14.1971i	0.768819	+	2.36618i
$37$	−0.731424	+	1.12629i	−0.120245	+	0.185162i	−0.893668	−	0.448730i	$-0.851877\pi$
$37$	−0.731424	+	1.12629i	−0.120245	+	0.185162i	0.773422	+	0.633891i	$0.218543\pi$
$38$	−9.56484	−	0.501272i	−1.55162	−	0.0813171i
$39$	0.226006	−	1.06328i	0.0361900	−	0.170260i
$40$	−1.43609	−	18.1102i	−0.227066	−	2.86347i
$41$	−4.99103	−	1.62168i	−0.779468	−	0.253264i	−0.107855	−	0.994167i	$-0.534398\pi$
$41$	−4.99103	−	1.62168i	−0.779468	−	0.253264i	−0.671613	+	0.740902i	$0.734398\pi$
$42$	−0.411311	+	1.49673i	−0.0634667	+	0.230951i
$43$	−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
$45$	0.865237	+	6.54219i	0.128982	+	0.975252i
$46$	−0.907502	−	8.63431i	−0.133804	−	1.27306i
$47$	1.19805	+	3.12102i	0.174753	+	0.455248i	0.992782	−	0.119929i	$-0.0382666\pi$
$47$	1.19805	+	3.12102i	0.174753	+	0.455248i	−0.818029	+	0.575177i	$0.804933\pi$
$48$	2.25653	+	1.14976i	0.325703	+	0.165954i
$49$	5.26142	−	4.61709i	0.751631	−	0.659584i
$50$	1.37287	−	13.2124i	0.194153	−	1.86852i
$51$	−0.530544	−	0.918929i	−0.0742910	−	0.128676i
$52$	13.5606	+	20.8816i	1.88052	+	2.89575i
$53$	−2.69056	+	3.32256i	−0.369577	+	0.456389i	−0.927677	−	0.373384i	$-0.878197\pi$
$53$	−2.69056	+	3.32256i	−0.369577	+	0.456389i	0.558100	+	0.829774i	$0.311531\pi$
$54$	−3.18964	−	1.42012i	−0.434055	−	0.193254i
$55$	−6.41299	−	1.89548i	−0.864727	−	0.255587i
$56$	−10.6287	−	18.6840i	−1.42032	−	2.49675i
$57$	0.562954	−	0.562954i	0.0745651	−	0.0745651i
$58$	10.0907	−	8.17129i	1.32497	−	1.07294i
$59$	0.374472	+	0.415893i	0.0487521	+	0.0541447i	0.767028	−	0.641614i	$-0.221735\pi$
$59$	0.374472	+	0.415893i	0.0487521	+	0.0541447i	−0.718276	+	0.695759i	$0.755068\pi$
$60$	1.98243	+	1.51931i	0.255931	+	0.196142i
$61$	7.43964	+	6.69868i	0.952549	+	0.857679i	0.989921	−	0.141623i	$-0.0452320\pi$
$61$	7.43964	+	6.69868i	0.952549	+	0.857679i	−0.0373720	+	0.999301i	$0.511899\pi$
$62$	−3.82643	+	1.94966i	−0.485957	+	0.247607i
$63$	4.21076	+	6.57556i	0.530506	+	0.828443i
$64$	−14.1129	+	4.58555i	−1.76411	+	0.573194i
$65$	4.21820	+	10.1666i	0.523203	+	1.26101i
$66$	1.30389	−	1.17403i	0.160497	−	0.144513i
$67$	3.34846	−	8.72305i	0.409080	−	1.06569i	−0.562042	−	0.827108i	$-0.689984\pi$
$67$	3.34846	−	8.72305i	0.409080	−	1.06569i	0.971122	−	0.238582i	$-0.0766824\pi$
$68$	23.4761	+	6.29039i	2.84689	+	0.762822i
$69$	0.583829	+	0.424177i	0.0702848	+	0.0510649i
$70$	−5.16061	−	14.8460i	−0.616811	−	1.77443i
$71$	−0.293741	+	0.213415i	−0.0348607	+	0.0253278i	−0.605079	−	0.796165i	$-0.706859\pi$
$71$	−0.293741	+	0.213415i	−0.0348607	+	0.0253278i	0.570218	+	0.821493i	$0.306859\pi$
$72$	22.3849	−	8.59275i	2.63808	−	1.01267i
$73$	2.45523	−	1.59444i	0.287363	−	0.186615i	−0.392905	−	0.919579i	$-0.628530\pi$
$73$	2.45523	−	1.59444i	0.287363	−	0.186615i	0.680268	+	0.732963i	$0.261863\pi$
$74$	3.08984	+	1.78392i	0.359186	+	0.207376i
$75$	0.739794	+	0.819671i	0.0854241	+	0.0946474i
$76$			18.2355i			2.09176i
$77$	−7.82279	+	1.18785i	−0.891490	+	0.135368i
$78$	−2.85237	−	0.451771i	−0.322968	−	0.0511530i
$79$	2.12904	−	4.78190i	0.239536	−	0.538006i	−0.753274	−	0.657706i	$-0.771527\pi$
$79$	2.12904	−	4.78190i	0.239536	−	0.538006i	0.992810	+	0.119701i	$0.0381935\pi$
$80$	−25.4227	+	3.36227i	−2.84234	+	0.375913i
$81$	−7.82313	+	3.48308i	−0.869237	+	0.387009i
$82$	−3.60848	+	13.4670i	−0.398490	+	1.48719i
$83$	0.898387	−	0.142291i	0.0986108	−	0.0156184i	−0.106934	−	0.994266i	$-0.534103\pi$
$83$	0.898387	−	0.142291i	0.0986108	−	0.0156184i	0.205545	+	0.978648i	$0.434103\pi$
$84$	2.88671	+	0.632885i	0.314966	+	0.0690534i
$85$	9.70036	+	4.61979i	1.05215	+	0.501086i
$86$	−21.2157	+	23.5624i	−2.28775	+	2.54080i
$87$	−0.0564851	+	1.07780i	−0.00605584	+	0.115552i
$88$	−1.27163	+	24.2642i	−0.135557	+	2.58658i
$89$	6.04903	−	6.71813i	0.641196	−	0.712120i	−0.331695	−	0.943387i	$-0.607620\pi$
$89$	6.04903	−	6.71813i	0.641196	−	0.712120i	0.972890	+	0.231267i	$0.0742870\pi$
$90$	17.2366	−	3.20517i	1.81690	−	0.337855i
$91$	9.62257	+	8.77612i	1.00872	+	0.919988i
$92$	−16.3259	+	2.58577i	−1.70210	+	0.269585i
$93$	0.0923897	−	0.344803i	0.00958037	−	0.0357544i
$94$	8.11372	−	3.61246i	0.836866	−	0.372597i
$95$	−1.46439	+	7.92734i	−0.150243	+	0.813328i
$96$	1.27715	−	2.86853i	0.130349	−	0.292768i
$97$	−7.15230	−	1.13281i	−0.726206	−	0.115020i	−0.217624	−	0.976033i	$-0.569830\pi$
$97$	−7.15230	−	1.13281i	−0.726206	−	0.115020i	−0.508583	+	0.861013i	$0.669830\pi$
$98$	−12.9810	−	13.3169i	−1.31128	−	1.34521i
$99$		−	8.82604i		−	0.887051i
$100$	−25.2575	−	1.29370i	−2.52575	−	0.129370i
$101$	2.36935	+	1.36795i	0.235759	+	0.136116i	0.613226	−	0.789907i	$-0.289871\pi$
$101$	2.36935	+	1.36795i	0.235759	+	0.136116i	−0.377467	+	0.926023i	$0.623205\pi$
$102$	−2.36422	+	1.53534i	−0.234092	+	0.152021i
$103$	0.623225	−	0.239234i	0.0614082	−	0.0235724i	−0.327470	−	0.944862i	$-0.606196\pi$
$103$	0.623225	−	0.239234i	0.0614082	−	0.0235724i	0.388878	+	0.921289i	$0.372863\pi$
$104$	32.3548	−	23.5072i	3.17265	−	2.30507i
$105$	1.20409	+	0.506943i	0.117507	+	0.0494726i
$106$	9.18910	+	6.67627i	0.892524	+	0.648457i
$107$	2.61232	+	0.699970i	0.252543	+	0.0676686i	0.382869	−	0.923802i	$-0.374936\pi$
$107$	2.61232	+	0.699970i	0.252543	+	0.0676686i	−0.130327	+	0.991471i	$0.541603\pi$
$108$	−2.38224	+	6.20594i	−0.229231	+	0.597167i
$109$	−3.45588	+	3.11169i	−0.331013	+	0.298046i	−0.817832	−	0.575458i	$-0.804824\pi$
$109$	−3.45588	+	3.11169i	−0.331013	+	0.298046i	0.486818	+	0.873503i	$0.338157\pi$
$110$	−4.13719	+	17.2777i	−0.394465	+	1.64736i
$111$	−0.282050	+	0.0916436i	−0.0267710	+	0.00869843i
$112$	−25.5523	+	16.3628i	−2.41447	+	1.54614i
$113$	15.5844	−	7.94063i	1.46605	−	0.746991i	0.474941	−	0.880018i	$-0.342470\pi$
$113$	15.5844	−	7.94063i	1.46605	−	0.746991i	0.991112	+	0.133026i	$0.0424695\pi$
$114$	−1.57183	−	1.41528i	−0.147216	−	0.132554i
$115$	−7.30485	−	0.186957i	−0.681181	−	0.0174338i
$116$	−16.5415	−	18.3712i	−1.53584	−	1.70572i
$117$	−11.2899	+	9.14234i	−1.04375	+	0.845210i
$118$	1.05133	−	1.05133i	0.0967825	−	0.0967825i
$119$	12.7125	+	0.0811892i	1.16536	+	0.00744260i
$120$	2.27038	−	3.30761i	0.207256	−	0.301942i
$121$	−1.87838	−	0.836308i	−0.170762	−	0.0760280i
$122$	16.7377	−	20.6693i	1.51536	−	1.87131i
$123$	−0.631178	−	0.971930i	−0.0569114	−	0.0876359i
$124$	4.08816	+	7.08089i	0.367127	+	0.635883i
$125$	−10.8760	−	2.59069i	−0.972783	−	0.231718i
$126$	16.8600	−	12.0857i	1.50200	−	1.07668i
$127$	−4.64631	−	2.36741i	−0.412293	−	0.210074i	0.235526	−	0.971868i	$-0.424319\pi$
$127$	−4.64631	−	2.36741i	−0.412293	−	0.210074i	−0.647819	+	0.761794i	$0.724319\pi$
$128$	3.93679	+	10.2557i	0.347966	+	0.906483i
$129$	−0.275484	−	2.62105i	−0.0242550	−	0.230771i
$130$	26.3862	−	12.6048i	2.31422	−	1.10551i
$131$	3.74207	+	0.393308i	0.326946	+	0.0343634i	0.266580	−	0.963813i	$-0.414106\pi$
$131$	3.74207	+	0.393308i	0.326946	+	0.0343634i	0.0603664	+	0.998176i	$0.480773\pi$
$132$	−2.36209	−	2.36209i	−0.205594	−	0.205594i
$133$	2.40984	+	9.22901i	0.208960	+	0.800257i
$134$	−23.6085	−	7.67085i	−2.03946	−	0.662661i
$135$	−1.53397	+	2.50654i	−0.132023	+	0.215729i
$136$	8.11653	−	38.1853i	0.695987	−	3.27436i
$137$	3.98957	+	0.209084i	0.340852	+	0.0178633i	0.221994	−	0.975048i	$-0.428743\pi$
$137$	3.98957	+	0.209084i	0.340852	+	0.0178633i	0.118858	+	0.992911i	$0.462077\pi$
$138$	1.04419	−	1.60792i	0.0888877	−	0.136875i
$139$	−2.53686	−	7.80766i	−0.215174	−	0.662237i	−0.999141	−	0.0414349i	$-0.986807\pi$
$139$	−2.53686	−	7.80766i	−0.215174	−	0.662237i	0.783967	−	0.620802i	$-0.213193\pi$
$140$	−27.7123	+	11.2911i	−2.34212	+	0.954275i
$141$	−0.228132	+	0.702119i	−0.0192122	+	0.0591291i
$142$	0.607049	+	0.749643i	0.0509424	+	0.0629086i
$143$	−3.81014	−	14.2196i	−0.318620	−	1.18911i
$144$	−13.7663	−	30.9197i	−1.14719	−	2.57664i
$145$	−5.71562	−	9.31466i	−0.474656	−	0.773541i
$146$	−4.57155	−	6.29220i	−0.378344	−	0.520746i
$147$	1.54460	−	0.0611781i	0.127397	−	0.00504589i
$148$	3.08387	−	6.05244i	0.253493	−	0.497508i
$149$	−18.8977	+	10.9106i	−1.54816	+	0.893830i	−0.549877	+	0.835246i	$0.685325\pi$
$149$	−18.8977	+	10.9106i	−1.54816	+	0.893830i	−0.998282	+	0.0585846i	$0.981341\pi$
$150$	2.07178	−	2.07670i	0.169160	−	0.169561i
$151$	1.20290	−	2.08349i	0.0978908	−	0.169552i	−0.812921	−	0.582375i	$-0.802124\pi$
$151$	1.20290	−	2.08349i	0.0978908	−	0.169552i	0.910811	+	0.412823i	$0.135457\pi$
$152$	29.2505	−	1.53295i	2.37253	−	0.124339i
$153$	−2.21834	+	14.0060i	−0.179342	+	1.13232i
$154$	4.23913	+	20.5893i	0.341599	+	1.65913i
$155$	1.20858	+	3.40650i	0.0970751	+	0.273617i
$156$	−0.574732	+	5.46821i	−0.0460154	+	0.437807i
$157$	−21.1941	+	5.67894i	−1.69147	+	0.453229i	−0.970769	−	0.240016i	$-0.922847\pi$
$157$	−21.1941	+	5.67894i	−1.69147	+	0.453229i	−0.720703	+	0.693244i	$0.756181\pi$
$158$	−12.9827	−	4.98361i	−1.03285	−	0.396475i
$159$	−0.923495	+	0.196295i	−0.0732379	+	0.0155672i
$160$	5.81264	+	31.2589i	0.459529	+	2.47123i
$161$	−7.92085	+	3.46615i	−0.624251	+	0.273171i
$162$	10.3286	+	20.2710i	0.811492	+	1.59264i
$163$	7.44756	+	4.83650i	0.583338	+	0.378824i	0.802310	−	0.596907i	$-0.203604\pi$
$163$	7.44756	+	4.83650i	0.583338	+	0.378824i	−0.218973	+	0.975731i	$0.570271\pi$
$164$	25.9644	+	5.51889i	2.02748	+	0.430953i
$165$	−0.837161	−	1.21653i	−0.0651729	−	0.0947070i
$166$	−0.502420	−	2.36370i	−0.0389954	−	0.183459i
$167$	−1.64313	−	10.3743i	−0.127149	−	0.802786i	−0.966022	−	0.258460i	$-0.916785\pi$
$167$	−1.64313	−	10.3743i	−0.127149	−	0.802786i	0.838873	−	0.544327i	$-0.183215\pi$
$168$	0.772502	−	4.68360i	0.0595999	−	0.361347i
$169$	−6.60118	+	9.08574i	−0.507783	+	0.698903i
$170$	10.9079	−	26.3781i	0.836595	−	2.02311i
$171$	−10.5815	+	1.11216i	−0.809186	+	0.0850489i
$172$	46.9130	+	37.9894i	3.57709	+	2.89667i
$173$	0.942653	+	17.9869i	0.0716686	+	1.36752i	0.763663	+	0.645615i	$0.223399\pi$
$173$	0.942653	+	17.9869i	0.0716686	+	1.36752i	−0.691994	+	0.721903i	$0.743268\pi$
$174$	2.86733			0.217372
$175$	−12.9538	+	2.68306i	−0.979216	+	0.202820i
$176$	34.2976			2.58528
$177$	0.00646797	+	0.123416i	0.000486162	+	0.00927653i
$178$	−18.6647	−	15.1144i	−1.39898	−	1.13287i
$179$	6.45610	−	0.678563i	0.482552	−	0.0507182i	0.139870	−	0.990170i	$-0.455332\pi$
$179$	6.45610	−	0.678563i	0.482552	−	0.0507182i	0.342681	+	0.939452i	$0.388665\pi$
$180$	−7.81147	−	32.4525i	−0.582233	−	2.41886i
$181$	10.3669	−	14.2688i	0.770563	−	1.06059i	−0.225698	−	0.974197i	$-0.572466\pi$
$181$	10.3669	−	14.2688i	0.770563	−	1.06059i	0.996261	−	0.0863916i	$-0.0275336\pi$
$182$	21.9457	−	26.7496i	1.62673	−	1.98281i
$183$	0.345836	+	2.18352i	0.0255650	+	0.161411i
$184$	5.52010	+	25.9700i	0.406947	+	1.91454i
$185$	1.82666	−	2.38347i	0.134299	−	0.175236i
$186$	−0.927634	−	0.197175i	−0.0680174	−	0.0144575i
$187$	−12.0516	−	7.82642i	−0.881303	−	0.572325i
$188$	−7.67682	−	15.0666i	−0.559890	−	1.09885i
$189$	−0.385532	+	3.45565i	−0.0280433	+	0.251361i
$190$	21.2354	+	2.78291i	1.54058	+	0.201893i
$191$	11.8497	−	2.51873i	0.857414	−	0.182249i	0.241828	−	0.970319i	$-0.422253\pi$
$191$	11.8497	−	2.51873i	0.857414	−	0.182249i	0.615586	+	0.788070i	$0.288920\pi$
$192$	−3.05929	−	1.17435i	−0.220785	−	0.0847515i
$193$	−8.29161	+	2.22173i	−0.596843	+	0.159924i	−0.544579	−	0.838710i	$-0.683311\pi$
$193$	−8.29161	+	2.22173i	−0.596843	+	0.159924i	−0.0522644	+	0.998633i	$0.516644\pi$
$194$	−2.01097	+	19.1331i	−0.144379	+	1.37368i
$195$	−0.688969	+	2.33099i	−0.0493381	+	0.166925i
$196$	−24.0260	+	26.0077i	−1.71614	+	1.85769i
$197$	0.621240	−	3.92235i	0.0442615	−	0.279456i	−0.955624	−	0.294589i	$-0.904817\pi$
$197$	0.621240	−	3.92235i	0.0442615	−	0.279456i	0.999885	+	0.0151331i	$0.00481720\pi$
$198$	−23.4161	+	1.22719i	−1.66411	+	0.0872124i
$199$	6.13171	−	10.6204i	0.434666	−	0.752863i	−0.562603	−	0.826727i	$-0.690200\pi$
$199$	6.13171	−	10.6204i	0.434666	−	0.752863i	0.997268	+	0.0738644i	$0.0235332\pi$
$200$	0.0481015	+	40.6227i	0.00340129	+	2.87246i
$201$	1.78693	−	1.03168i	0.126040	−	0.0727693i
$202$	3.29982	−	6.47626i	0.232174	−	0.455668i
$203$	−10.7994	−	7.11169i	−0.757971	−	0.499143i
$204$	3.15471	+	4.34209i	0.220874	+	0.304007i
$205$	10.8440	+	4.48422i	0.757380	+	0.313192i
$206$	−0.721358	−	1.62020i	−0.0502594	−	0.112885i
$207$	−2.49614	−	9.31571i	−0.173494	−	0.647487i
$208$	−35.5267	−	43.8719i	−2.46334	−	3.04197i
$209$	3.33176	−	10.2541i	0.230463	−	0.709291i
$210$	1.17754	−	3.26502i	0.0812579	−	0.225308i
$211$	−6.78037	−	20.8678i	−0.466780	−	1.43660i	−0.856730	−	0.515765i	$-0.827508\pi$
$211$	−6.78037	−	20.8678i	−0.466780	−	1.43660i	0.389950	−	0.920836i	$-0.372492\pi$
$212$	11.7779	−	18.1364i	0.808912	−	1.24561i
$213$	−0.0800702	−	0.00419630i	−0.00548632	−	0.000287526i
$214$	1.49385	−	7.02801i	0.102117	−	0.480425i
$215$	17.3433	+	20.2821i	1.18280	+	1.38323i
$216$	10.1548	+	3.29950i	0.690948	+	0.224503i
$217$	3.00477	+	3.04339i	0.203977	+	0.206599i
$218$	8.73604	+	8.73604i	0.591679	+	0.591679i
$219$	0.642945	+	0.0675763i	0.0434462	+	0.00456638i
$220$	33.2622	+	6.14441i	2.24253	+	0.414256i
$221$	2.47234	+	23.5228i	0.166308	+	1.58231i
$222$	0.282354	+	0.735557i	0.0189504	+	0.0493674i
$223$	1.26491	+	0.644506i	0.0847049	+	0.0431593i	0.495830	−	0.868420i	$-0.334864\pi$
$223$	1.26491	+	0.644506i	0.0847049	+	0.0431593i	−0.411125	+	0.911579i	$0.634864\pi$
$224$	21.9177	+	30.5758i	1.46444	+	2.04293i
$225$	−0.789727	−	14.7350i	−0.0526484	−	0.982335i
$226$	−23.2339	−	40.2423i	−1.54550	−	2.67688i
$227$	15.4376	+	23.7719i	1.02463	+	1.57779i	0.796939	+	0.604060i	$0.206451\pi$
$227$	15.4376	+	23.7719i	1.02463	+	1.57779i	0.227692	+	0.973733i	$0.426882\pi$
$228$	−2.53425	+	3.12954i	−0.167835	+	0.207259i
$229$	0.553987	+	0.246651i	0.0366085	+	0.0162992i	0.424959	−	0.905212i	$-0.360288\pi$
$229$	0.553987	+	0.246651i	0.0366085	+	0.0162992i	−0.388351	+	0.921512i	$0.626955\pi$
$230$	0.519669	+	19.4063i	0.0342660	+	1.27961i
$231$	−1.50761	−	0.883303i	−0.0991933	−	0.0581171i
$232$	−28.0775	+	28.0775i	−1.84338	+	1.84338i
$233$	3.49716	−	2.83194i	0.229106	−	0.185527i	−0.507893	−	0.861420i	$-0.669575\pi$
$233$	3.49716	−	2.83194i	0.229106	−	0.185527i	0.736999	+	0.675894i	$0.236242\pi$
$234$	25.8251	+	28.6816i	1.68824	+	1.87498i
$235$	−2.12735	−	7.16623i	−0.138773	−	0.467473i
$236$	−2.10364	−	1.89412i	−0.136935	−	0.123297i
$237$	1.02994	−	0.524779i	0.0669016	−	0.0340881i
$238$	−1.55217	−	33.7386i	−0.100612	−	2.18695i
$239$	−12.4990	+	4.06118i	−0.808494	+	0.262696i	−0.683960	−	0.729520i	$-0.739744\pi$
$239$	−12.4990	+	4.06118i	−0.808494	+	0.262696i	−0.124534	+	0.992215i	$0.539744\pi$
$240$	−4.83024	−	2.95605i	−0.311791	−	0.190812i
$241$	−12.3140	+	11.0876i	−0.793216	+	0.714215i	−0.962479	−	0.271356i	$-0.912528\pi$
$241$	−12.3140	+	11.0876i	−0.793216	+	0.714215i	0.169263	+	0.985571i	$0.445861\pi$
$242$	−1.95761	+	5.09975i	−0.125840	+	0.327824i
$243$	−5.63495	−	1.50988i	−0.361482	−	0.0968588i
$244$	−40.9662	−	29.7637i	−2.62259	−	1.90542i
$245$	−12.5331	+	9.37666i	−0.800710	+	0.599053i
$246$	−2.49084	+	1.80970i	−0.158810	+	0.115382i
$247$	−16.5677	+	6.35975i	−1.05418	+	0.404661i
$248$	11.0144	−	7.15280i	0.699412	−	0.454203i
$249$	0.173954	+	0.100432i	0.0110239	+	0.00636464i
$250$	−5.36105	+	29.2151i	−0.339063	+	1.84773i
$251$			21.3400i			1.34697i	0.739200	+	0.673486i	$0.235204\pi$
$251$			21.3400i			1.34697i	−0.739200	+	0.673486i	$0.764796\pi$
$252$	−24.6585	−	30.8515i	−1.55334	−	1.94346i
$253$	9.65275	+	1.52885i	0.606863	+	0.0961177i
$254$	−5.63488	+	12.6562i	−0.353564	+	0.794118i
$255$	1.02273	+	2.14093i	0.0640456	+	0.134070i
$256$	−0.450797	+	0.200708i	−0.0281748	+	0.0125442i
$257$	5.79368	−	21.6223i	0.361400	−	1.34876i	−0.510836	−	0.859678i	$-0.670664\pi$
$257$	5.79368	−	21.6223i	0.361400	−	1.34876i	0.872236	−	0.489085i	$-0.162669\pi$
$258$	−6.91553	+	1.09531i	−0.430542	+	0.0681912i
$259$	0.760915	−	3.47068i	0.0472810	−	0.215658i
$260$	−26.5945	−	48.9120i	−1.64932	−	3.03339i
$261$	9.65136	−	10.7189i	0.597404	−	0.663485i
$262$	0.523170	−	9.98267i	0.0323215	−	0.616731i
$263$	1.28540	−	24.5269i	0.0792610	−	1.51239i	−0.612619	−	0.790378i	$-0.709884\pi$
$263$	1.28540	−	24.5269i	0.0792610	−	1.51239i	0.691880	−	0.722012i	$-0.256783\pi$
$264$	−3.59031	+	3.98745i	−0.220969	+	0.245410i
$265$	6.57653	−	6.93844i	0.403993	−	0.426225i
$266$	24.1502	−	7.67670i	1.48074	−	0.470689i
$267$	1.97176	−	0.312296i	0.120670	−	0.0191122i
$268$	−12.2321	+	45.6509i	−0.747196	+	2.78857i
$269$	−21.7527	+	9.68493i	−1.32629	+	0.590501i	−0.942897	−	0.333086i	$-0.891910\pi$
$269$	−21.7527	+	9.68493i	−1.32629	+	0.590501i	−0.383390	+	0.923587i	$0.625243\pi$
$270$	6.86332	+	3.72122i	0.417688	+	0.226466i
$271$	11.5585	−	25.9608i	0.702129	−	1.57701i	−0.110268	−	0.993902i	$-0.535171\pi$
$271$	11.5585	−	25.9608i	0.702129	−	1.57701i	0.812397	−	0.583105i	$-0.198162\pi$
$272$	−54.4269	−	8.62037i	−3.30011	−	0.522687i
$273$	0.431757	+	2.84342i	0.0261311	+	0.172092i
$274$		−	10.6137i		−	0.641196i
$275$	13.9663	+	5.34219i	0.842199	+	0.322146i
$276$	−3.16117	−	1.82510i	−0.190280	−	0.109858i
$277$	10.1183	−	6.57090i	0.607950	−	0.394807i	−0.203631	−	0.979048i	$-0.565274\pi$
$277$	10.1183	−	6.57090i	0.607950	−	0.394807i	0.811581	+	0.584240i	$0.198607\pi$
$278$	−20.3615	+	7.81606i	−1.22120	+	0.468776i
$279$	−3.85948	+	2.80408i	−0.231061	+	0.167876i
$280$	20.4410	+	43.5024i	1.22158	+	2.59977i
$281$	5.98822	+	4.35069i	0.357227	+	0.259541i	0.751895	−	0.659283i	$-0.229140\pi$
$281$	5.98822	+	4.35069i	0.357227	+	0.259541i	−0.394668	+	0.918824i	$0.629140\pi$
$282$	1.89449	+	0.507628i	0.112815	+	0.0302288i
$283$	−9.16617	+	23.8787i	−0.544872	+	1.41944i	0.334087	+	0.942542i	$0.391572\pi$
$283$	−9.16617	+	23.8787i	−0.544872	+	1.41944i	−0.878959	+	0.476898i	$0.841761\pi$
$284$	1.36480	−	1.22887i	0.0809862	−	0.0729203i
$285$	−1.35300	+	1.15696i	−0.0801450	+	0.0685324i
$286$	−37.1959	+	12.0857i	−2.19944	+	0.714642i
$287$	13.8699	−	0.638097i	0.818715	−	0.0376657i
$288$	−37.3899	+	19.0511i	−2.20322	+	1.12260i
$289$	4.52417	+	4.07358i	0.266128	+	0.239623i
$290$	−23.9178	+	16.4591i	−1.40450	+	0.966510i
$291$	−1.07003	−	1.18839i	−0.0627263	−	0.0696647i
$292$	−11.5078	+	9.31883i	−0.673443	+	0.545343i
$293$	−1.98458	+	1.98458i	−0.115941	+	0.115941i	−0.762697	−	0.646756i	$-0.776125\pi$
$293$	−1.98458	+	1.98458i	−0.115941	+	0.115941i	0.646756	+	0.762697i	$0.276125\pi$
$294$	−0.377074	−	4.08944i	−0.0219914	−	0.238501i
$295$	−0.762387	−	0.992345i	−0.0443879	−	0.0577765i
$296$	−9.96759	−	4.43786i	−0.579354	−	0.257945i
$297$	2.47344	−	3.05444i	0.143523	−	0.177237i
$298$	31.5741	+	48.6199i	1.82904	+	2.81648i
$299$	−8.04305	−	13.9310i	−0.465141	−	0.805649i
$300$	−4.15485	−	3.73214i	−0.239880	−	0.215475i
$301$	28.7631	+	13.0269i	1.65788	+	0.750857i
$302$	−5.69490	−	2.90170i	−0.327705	−	0.166974i
$303$	0.216515	+	0.564040i	0.0124384	+	0.0324033i
$304$	−4.32180	−	41.1192i	−0.247872	−	2.35835i
$305$	−15.4187	−	16.2286i	−0.882870	−	0.929248i
$306$	37.4675	+	3.93799i	2.14187	+	0.225120i
$307$	17.0423	+	17.0423i	0.972656	+	0.972656i	0.999636	−	0.0269795i	$-0.00858889\pi$
$307$	17.0423	+	17.0423i	0.972656	+	0.972656i	−0.0269795	+	0.999636i	$0.508589\pi$
$308$	38.7238	−	10.1114i	2.20650	−	0.576151i
$309$	0.140204	+	0.0455549i	0.00797590	+	0.00259153i
$310$	8.86965	−	3.68008i	0.503762	−	0.209015i
$311$	5.89343	−	27.7264i	0.334186	−	1.57222i	−0.414975	−	0.909833i	$-0.636210\pi$
$311$	5.89343	−	27.7264i	0.334186	−	1.57222i	0.749161	−	0.662388i	$-0.230457\pi$
$312$	8.81953	+	0.462212i	0.499308	+	0.0261676i
$313$	11.7313	−	18.0646i	0.663091	−	1.02107i	−0.333828	−	0.942634i	$-0.608341\pi$
$313$	11.7313	−	18.0646i	0.663091	−	1.02107i	0.996919	−	0.0784364i	$-0.0249927\pi$
$314$	18.0135	+	55.4398i	1.01656	+	3.12865i
$315$	−8.24202	−	15.3919i	−0.464385	−	0.867237i
$316$	−8.18167	+	25.1806i	−0.460255	+	1.41652i
$317$	0.142171	+	0.175566i	0.00798511	+	0.00986079i	0.781123	−	0.624377i	$-0.214647\pi$
$317$	0.142171	+	0.175566i	0.00798511	+	0.00986079i	−0.773138	+	0.634238i	$0.781314\pi$
$318$	0.649189	+	2.42281i	0.0364047	+	0.135864i
$319$	5.94497	+	13.3526i	0.332855	+	0.747603i
$320$	32.2600	−	7.76514i	1.80339	−	0.434085i
$321$	0.351044	+	0.483170i	0.0195934	+	0.0269679i
$322$	10.2973	+	20.5327i	0.573844	+	1.14424i
$323$	−7.86443	+	15.4348i	−0.437589	+	0.858816i
$324$	37.5120	−	21.6576i	2.08400	−	1.20320i
$325$	−7.63333	−	23.3987i	−0.423421	−	1.29792i
$326$	11.7961	−	20.4314i	0.653323	−	1.13159i
$327$	−1.02553	+	0.0537458i	−0.0567120	+	0.00297215i
$328$	6.66985	−	42.1118i	0.368281	−	2.32523i
$329$	−5.87631	−	6.61072i	−0.323972	−	0.364461i
$330$	−3.11115	+	2.39020i	−0.171263	+	0.131576i
$331$	1.99845	−	19.0140i	0.109845	−	1.04510i	−0.791254	−	0.611488i	$-0.790571\pi$
$331$	1.99845	−	19.0140i	0.109845	−	1.04510i	0.901099	−	0.433614i	$-0.142762\pi$
$332$	−4.44403	+	1.19077i	−0.243898	+	0.0653522i
$333$	3.70012	+	1.42034i	0.202765	+	0.0778343i
$334$	−27.2953	+	5.80179i	−1.49353	+	0.317460i
$335$	−8.98352	+	18.8631i	−0.490822	+	1.03060i
$336$	−6.65923	−	0.742941i	−0.363291	−	0.0405308i
$337$	−0.693845	−	1.36175i	−0.0377961	−	0.0741791i	0.871336	−	0.490687i	$-0.163254\pi$
$337$	−0.693845	−	1.36175i	−0.0377961	−	0.0741791i	−0.909132	+	0.416507i	$0.863254\pi$
$338$	25.0230	+	16.2501i	1.36107	+	0.883889i
$339$	3.77809	+	0.803057i	0.205198	+	0.0436161i
$340$	−51.2394	−	18.1107i	−2.77885	−	0.982190i
$341$	−1.00510	−	4.72863i	−0.0544292	−	0.256069i
$342$	4.42190	+	27.9188i	0.239109	+	1.50968i
$343$	−8.72262	+	16.3376i	−0.470977	+	0.882145i
$344$	56.9928	−	78.4438i	3.07284	−	4.22941i
$345$	−1.22766	−	1.04726i	−0.0660950	−	0.0563828i
$346$	47.5894	−	5.00185i	2.55842	−	0.268901i
$347$	15.4209	+	12.4876i	0.827835	+	0.670368i	0.946549	−	0.322561i	$-0.104544\pi$
$347$	15.4209	+	12.4876i	0.827835	+	0.670368i	−0.118714	+	0.992929i	$0.537877\pi$
$348$	−0.285708	−	5.45164i	−0.0153156	−	0.292239i
$349$	7.02028			0.375787			0.187894	−	0.982189i	$-0.439834\pi$
$349$	7.02028			0.375787			0.187894	+	0.982189i	$0.439834\pi$
$350$	8.91947	+	33.9943i	0.476766	+	1.81707i
$351$	−6.46917			−0.345299
$352$	−2.22553	−	42.4656i	−0.118621	−	2.26342i
$353$	20.9689	+	16.9803i	1.11606	+	0.903768i	0.996031	−	0.0890029i	$-0.0283680\pi$
$353$	20.9689	+	16.9803i	1.11606	+	0.903768i	0.120029	+	0.992770i	$0.461701\pi$
$354$	0.326533	−	0.0343200i	0.0173550	−	0.00182409i
$355$	0.691991	−	0.424616i	0.0367271	−	0.0225363i
$356$	−26.8771	+	36.9932i	−1.42448	+	1.96063i
$357$	2.17041	+	1.78064i	0.114870	+	0.0942413i
$358$	−2.69794	−	17.0341i	−0.142591	−	0.900283i
$359$	−2.90347	−	13.6598i	−0.153239	−	0.720934i	−0.985925	−	0.167188i	$-0.946531\pi$
$359$	−2.90347	−	13.6598i	−0.153239	−	0.720934i	0.832686	−	0.553746i	$-0.186802\pi$
$360$	−51.3983	+	15.2580i	−2.70893	+	0.804166i
$361$	5.87140	+	1.24800i	0.309021	+	0.0656845i
$362$	−39.2975	−	25.5201i	−2.06543	−	1.34131i
$363$	−0.206138	−	0.404570i	−0.0108195	−	0.0212344i
$364$	−53.0456	−	39.0599i	−2.78035	−	2.04730i
$365$	−5.75101	+	3.12695i	−0.301022	+	0.163672i
$366$	5.74496	−	1.22113i	0.300294	−	0.0638295i
$367$	26.5370	+	10.1866i	1.38522	+	0.531737i	0.932906	−	0.360120i	$-0.117264\pi$
$367$	26.5370	+	10.1866i	1.38522	+	0.531737i	0.452317	+	0.891857i	$0.350598\pi$
$368$	36.2004	−	9.69987i	1.88708	−	0.505641i
$369$	−1.61891	+	15.4029i	−0.0842770	+	0.801842i
$370$	−6.57749	−	4.51485i	−0.341948	−	0.234716i
$371$	3.56408	−	10.7353i	0.185038	−	0.557350i
$372$	−0.282455	+	1.78335i	−0.0146446	+	0.0924624i
$373$	22.0879	−	1.15758i	1.14367	−	0.0599372i	0.528929	−	0.848666i	$-0.322594\pi$
$373$	22.0879	−	1.15758i	1.14367	−	0.0599372i	0.614741	+	0.788729i	$0.289261\pi$
$374$	−19.0884	+	33.0620i	−0.987037	+	1.70960i
$375$	−1.50649	−	1.95609i	−0.0777946	−	0.101012i
$376$	−23.5221	+	13.5805i	−1.21306	+	0.700359i
$377$	10.9220	−	21.4357i	0.562512	−	1.10399i
$378$	9.22169	+	0.542364i	0.474312	+	0.0278962i
$379$	19.8453	+	27.3147i	1.01938	+	1.40306i	0.912636	+	0.408774i	$0.134044\pi$
$379$	19.8453	+	27.3147i	1.01938	+	1.40306i	0.106747	+	0.994286i	$0.465956\pi$
$380$	3.17517	−	40.6520i	0.162883	−	2.08541i
$381$	−0.468382	−	1.05200i	−0.0239959	−	0.0538957i
$382$	−8.32997	−	31.0879i	−0.426199	−	1.59059i
$383$	23.8477	+	29.4495i	1.21856	+	1.50480i	0.803836	+	0.594851i	$0.202789\pi$
$383$	23.8477	+	29.4495i	1.21856	+	1.50480i	0.414725	+	0.909947i	$0.363878\pi$
$384$	−0.749644	+	2.30717i	−0.0382551	+	0.117737i
$385$	17.6460	−	1.28593i	0.899324	−	0.0655373i
$386$	7.04729	+	21.6893i	0.358698	+	1.10396i
$387$	−19.1829	+	29.5391i	−0.975121	+	1.50155i
$388$	36.5780	+	1.91697i	1.85697	+	0.0973195i
$389$	2.63857	−	12.4135i	0.133781	−	0.629388i	−0.859252	−	0.511552i	$-0.829071\pi$
$389$	2.63857	−	12.4135i	0.133781	−	0.629388i	0.993033	−	0.117836i	$-0.0375958\pi$
$390$	6.28007	+	1.50378i	0.318004	+	0.0761468i
$391$	−14.9337	−	4.85225i	−0.755229	−	0.245389i
$392$	43.7370	+	36.3522i	2.20905	+	1.83606i
$393$	0.587546	+	0.587546i	0.0296378	+	0.0296378i
$394$	−10.4927	−	1.10282i	−0.528613	−	0.0555594i
$395$	−5.57884	+	10.2895i	−0.280702	+	0.517720i
$396$	4.66649	+	44.3987i	0.234500	+	2.23112i
$397$	−9.62248	−	25.0674i	−0.482938	−	1.25810i	−0.931303	−	0.364246i	$-0.881327\pi$
$397$	−9.62248	−	25.0674i	−0.482938	−	1.25810i	0.448364	−	0.893851i	$-0.352007\pi$
$398$	−29.0294	−	14.7912i	−1.45511	−	0.741416i
$399$	−0.869015	+	1.91877i	−0.0435052	+	0.0960584i
$400$	57.2596	−	3.06884i	2.86298	−	0.153442i
$401$	1.13896	+	1.97273i	0.0568769	+	0.0985137i	0.893062	−	0.449934i	$-0.148552\pi$
$401$	1.13896	+	1.97273i	0.0568769	+	0.0985137i	−0.836185	+	0.548447i	$0.815219\pi$
$402$	−2.98559	−	4.59740i	−0.148907	−	0.229297i
$403$	−5.00751	+	6.18376i	−0.249442	+	0.308035i
$404$	−12.6421	−	5.62861i	−0.628967	−	0.280034i
$405$	18.0464	−	6.40260i	0.896733	−	0.318148i
$406$	−17.3663	+	29.6405i	−0.861873	+	1.47103i
$407$	−2.83993	+	2.83993i	−0.140770	+	0.140770i
$408$	6.69967	−	5.42529i	0.331683	−	0.268592i
$409$	−19.4149	−	21.5624i	−0.960005	−	1.06619i	−0.997759	−	0.0669069i	$-0.978687\pi$
$409$	−19.4149	−	21.5624i	−0.960005	−	1.06619i	0.0377539	−	0.999287i	$-0.487980\pi$
$410$	10.3892	−	29.3935i	0.513086	−	1.45164i
$411$	0.655623	+	0.590326i	0.0323395	+	0.0291186i
$412$	−3.00859	+	1.53295i	−0.148223	+	0.0755233i
$413$	−1.31496	−	0.680620i	−0.0647051	−	0.0334911i
$414$	−24.3682	+	7.91770i	−1.19763	+	0.389134i
$415$	−2.02753	+	0.160778i	−0.0995276	+	0.00789229i
$416$	−52.0146	+	46.8342i	−2.55023	+	2.29624i
$417$	0.649685	−	1.69249i	0.0318152	−	0.0828815i
$418$	−27.6681	−	7.41365i	−1.35329	−	0.362613i
$419$	−4.33888	−	3.15238i	−0.211968	−	0.154004i	0.476736	−	0.879047i	$-0.341820\pi$
$419$	−4.33888	−	3.15238i	−0.211968	−	0.154004i	−0.688704	+	0.725043i	$0.741820\pi$
$420$	−6.32509	−	1.91351i	−0.308633	−	0.0933698i
$421$	−15.3126	+	11.1253i	−0.746290	+	0.542212i	−0.894675	−	0.446718i	$-0.852593\pi$
$421$	−15.3126	+	11.1253i	−0.746290	+	0.542212i	0.148385	+	0.988930i	$0.452593\pi$
$422$	−54.4211	+	20.8903i	−2.64918	+	1.01692i
$423$	8.27447	−	5.37350i	0.402318	−	0.261269i
$424$	−30.0816	−	17.3676i	−1.46089	−	0.843446i
$425$	−20.8204	−	11.9878i	−1.00994	−	0.581494i
$426$			0.213016i			0.0103206i
$427$	−24.6663	−	9.64971i	−1.19369	−	0.466982i
$428$	−13.5112	−	2.13996i	−0.653086	−	0.103439i
$429$	1.32226	−	2.96985i	0.0638394	−	0.143386i
$430$	51.3984	−	48.8331i	2.47865	−	2.35494i
$431$	−21.2587	+	9.46500i	−1.02400	+	0.455913i	−0.848853	−	0.528630i	$-0.822706\pi$
$431$	−21.2587	+	9.46500i	−1.02400	+	0.455913i	−0.175145	+	0.984543i	$0.556039\pi$
$432$	3.90089	−	14.5583i	0.187682	−	0.700438i
$433$	−5.95872	+	0.943769i	−0.286358	+	0.0453546i	−0.297961	−	0.954578i	$-0.596307\pi$
$433$	−5.95872	+	0.943769i	−0.286358	+	0.0453546i	0.0116031	+	0.999933i	$0.496307\pi$
$434$	7.65655	−	8.39502i	0.367526	−	0.402974i
$435$	0.313587	−	2.39288i	0.0150354	−	0.114730i
$436$	15.7393	−	17.4803i	0.753776	−	0.837153i
$437$	0.616591	−	11.7653i	0.0294956	−	0.562809i
$438$	0.0898886	−	1.71518i	0.00429504	−	0.0819543i
$439$	23.9122	−	26.5572i	1.14127	−	1.26751i	0.182535	−	0.983199i	$-0.441570\pi$
$439$	23.9122	−	26.5572i	1.14127	−	1.26751i	0.958733	−	0.284307i	$-0.0917636\pi$
$440$	7.05971	−	53.8703i	0.336559	−	2.56817i
$441$	−16.5567	−	12.3553i	−0.788416	−	0.588349i
$442$	62.0638	−	9.82995i	2.95208	−	0.467563i
$443$	5.44524	−	20.3219i	0.258711	−	0.965523i	−0.707277	−	0.706936i	$-0.750077\pi$
$443$	5.44524	−	20.3219i	0.258711	−	0.965523i	0.965988	−	0.258586i	$-0.0832567\pi$
$444$	1.37038	−	0.610130i	0.0650351	−	0.0289555i
$445$	−14.6547	+	13.9233i	−0.694701	+	0.660029i
$446$	1.53404	−	3.44552i	0.0726391	−	0.163150i
$447$	−4.75946	−	0.753824i	−0.225115	−	0.0356547i
$448$	30.6685	−	24.5122i	1.44895	−	1.15809i
$449$			17.1662i			0.810122i	0.914290	+	0.405061i	$0.132750\pi$
$449$			17.1662i			0.810122i	−0.914290	+	0.405061i	$0.867250\pi$
$450$	−38.9833	+	4.14398i	−1.83769	+	0.195349i
$451$	−13.5918	−	7.84723i	−0.640013	−	0.369512i
$452$	−74.1974	+	48.1844i	−3.48995	+	2.26640i
$453$	0.495989	−	0.190392i	0.0233036	−	0.00894541i
$454$	60.9220	−	44.2624i	2.85921	−	2.07734i
$455$	−19.9233	−	21.2399i	−0.934018	−	0.995742i
$456$	5.23294	+	3.80195i	0.245055	+	0.178043i
$457$	22.4126	+	6.00543i	1.04842	+	0.280922i	0.741597	−	0.670845i	$-0.234069\pi$
$457$	22.4126	+	6.00543i	1.04842	+	0.280922i	0.306819	+	0.951768i	$0.400735\pi$
$458$	0.577355	−	1.50406i	0.0269780	−	0.0702802i
$459$	−4.69280	+	4.22542i	−0.219041	+	0.197226i
$460$	36.8453	−	2.92174i	1.71792	−	0.136227i
$461$	15.9507	−	5.18270i	0.742899	−	0.241383i	0.0869763	−	0.996210i	$-0.472280\pi$
$461$	15.9507	−	5.18270i	0.742899	−	0.241383i	0.655923	+	0.754828i	$0.272280\pi$
$462$	−2.13385	+	4.12261i	−0.0992756	+	0.191801i
$463$	−25.0376	+	12.7573i	−1.16360	+	0.592882i	−0.925644	−	0.378395i	$-0.876476\pi$
$463$	−25.0376	+	12.7573i	−1.16360	+	0.592882i	−0.237952	+	0.971277i	$0.576476\pi$
$464$	41.6532	+	37.5047i	1.93370	+	1.74111i
$465$	−0.266000	+	0.752575i	−0.0123354	+	0.0348999i
$466$	−7.99959	−	8.88445i	−0.370574	−	0.411564i
$467$	4.43522	−	3.59157i	0.205238	−	0.166198i	−0.521191	−	0.853440i	$-0.674512\pi$
$467$	4.43522	−	3.59157i	0.205238	−	0.166198i	0.726429	+	0.687242i	$0.241179\pi$
$468$	51.9589	−	51.9589i	2.40180	−	2.40180i
$469$	−0.157878	+	24.7205i	−0.00729015	+	1.14149i
$470$	−18.7167	+	6.64042i	−0.863339	+	0.306300i
$471$	−4.42650	−	1.97081i	−0.203962	−	0.0908099i
$472$	−2.86141	+	3.53354i	−0.131707	+	0.162645i
$473$	−19.4390	−	29.9334i	−0.893804	−	1.37634i
$474$	−1.53548	−	2.65953i	−0.0705270	−	0.122156i
$475$	4.64484	−	17.4173i	0.213120	−	0.799159i
$476$	−63.9922	+	6.31293i	−2.93308	+	0.289353i
$477$	11.2423	+	5.72824i	0.514750	+	0.262278i
$478$	12.5125	+	32.5961i	0.572308	+	1.49091i
$479$	1.95747	+	18.6240i	0.0894389	+	0.850954i	0.943632	+	0.330998i	$0.107385\pi$
$479$	1.95747	+	18.6240i	0.0894389	+	0.850954i	−0.854193	+	0.519957i	$0.825948\pi$
$480$	−3.34660	+	6.17238i	−0.152751	+	0.281729i
$481$	6.57441	+	0.690999i	0.299767	+	0.0315068i
$482$	31.1284	+	31.1284i	1.41786	+	1.41786i
$483$	−1.84106	−	0.505935i	−0.0837712	−	0.0230208i
$484$	9.89119	+	3.21384i	0.449599	+	0.146084i
$485$	15.7472	+	3.77072i	0.715045	+	0.171219i
$486$	−3.22233	+	15.1599i	−0.146168	+	0.687665i
$487$	22.7688	+	1.19326i	1.03175	+	0.0540719i	0.560689	−	0.828027i	$-0.310536\pi$
$487$	22.7688	+	1.19326i	1.03175	+	0.0540719i	0.471065	+	0.882098i	$0.343870\pi$
$488$	−44.2983	+	68.2134i	−2.00529	+	3.08787i
$489$	0.605988	+	1.86504i	0.0274037	+	0.0843400i
$490$	26.6196	+	31.9474i	1.20255	+	1.44324i
$491$	3.66657	−	11.2845i	0.165470	−	0.509264i	−0.833601	−	0.552368i	$-0.813724\pi$
$491$	3.66657	−	11.2845i	0.165470	−	0.509264i	0.999071	+	0.0431034i	$0.0137245\pi$
$492$	3.68897	+	4.55549i	0.166311	+	0.205377i
$493$	−6.07802	−	22.6835i	−0.273740	−	1.02161i
$494$	19.1765	+	43.0711i	0.862790	+	1.93786i
$495$	−1.53679	+	19.6757i	−0.0690736	+	0.884357i
$496$	−10.8965	−	14.9978i	−0.489268	−	0.673420i
$497$	0.528331	−	0.802294i	0.0236989	−	0.0359878i
$498$	0.242267	−	0.475476i	0.0108563	−	0.0213066i
$499$	−8.20677	+	4.73818i	−0.367385	+	0.212110i	−0.672316	−	0.740265i	$-0.734700\pi$
$499$	−8.20677	+	4.73818i	−0.367385	+	0.212110i	0.304930	+	0.952375i	$0.401367\pi$
$500$	56.0807	+	7.28186i	2.50801	+	0.325655i
$501$	1.15976	−	2.00876i	0.0518142	−	0.0897449i
$502$	56.6167	−	2.96715i	2.52693	−	0.132431i
$503$	3.15307	−	19.9077i	0.140588	−	0.887640i	−0.812062	−	0.583572i	$-0.801655\pi$
$503$	3.15307	−	19.9077i	0.140588	−	0.887640i	0.952650	−	0.304069i	$-0.0983452\pi$
$504$	−47.4140	+	42.1466i	−2.11199	+	1.87736i
$505$	−5.04376	−	3.46208i	−0.224444	−	0.154061i
$506$	2.71400	−	25.8220i	0.120652	−	1.14793i
$507$	−2.39556	+	0.641887i	−0.106390	+	0.0285072i
$508$	24.6245	+	9.45248i	1.09254	+	0.419386i
$509$	−17.3660	+	3.69127i	−0.769737	+	0.163613i	−0.576010	−	0.817443i	$-0.695391\pi$
$509$	−17.3660	+	3.69127i	−0.769737	+	0.163613i	−0.193727	+	0.981055i	$0.562058\pi$
$510$	5.53783	−	3.01105i	0.245219	−	0.133331i
$511$	−4.59261	+	6.23703i	−0.203165	+	0.275910i
$512$	10.5696	+	20.7441i	0.467117	+	0.916768i
$513$	−3.97362	−	2.58050i	−0.175440	−	0.113932i
$514$	−58.1711	−	12.3647i	−2.56582	−	0.545382i
$515$	−1.43100	+	0.424803i	−0.0630573	+	0.0187190i
$516$	2.77159	+	13.0393i	0.122013	+	0.574024i
$517$	1.56401	+	9.87478i	0.0687852	+	0.434292i
$518$	−9.31377	−	1.53619i	−0.409224	−	0.0674965i
$519$	−2.33792	+	3.21787i	−0.102623	+	0.141249i
$520$	−76.2210	+	46.7704i	−3.34251	+	2.05102i
$521$	14.6625	−	1.54109i	0.642376	−	0.0675164i	0.222261	−	0.974987i	$-0.428656\pi$
$521$	14.6625	−	1.54109i	0.642376	−	0.0675164i	0.420115	+	0.907471i	$0.361990\pi$
$522$	−29.7800	−	24.1154i	−1.30344	−	1.05550i
$523$	−0.217309	−	4.14649i	−0.00950224	−	0.181314i	−0.999257	−	0.0385369i	$-0.987730\pi$
$523$	−0.217309	−	4.14649i	−0.00950224	−	0.181314i	0.989755	−	0.142777i	$-0.0456031\pi$
$524$	−19.0321			−0.831422
$525$	−2.59598	−	1.33977i	−0.113298	−	0.0584725i
$526$	−65.2502			−2.84504
$527$	0.406500	+	7.75647i	0.0177074	+	0.337877i
$528$	5.88608	+	4.76645i	0.256159	+	0.207433i
$529$	−12.2533	+	1.28788i	−0.532754	+	0.0559947i
$530$	−19.3226	−	16.4833i	−0.839320	−	0.715988i
$531$	0.970802	−	1.33619i	0.0421292	−	0.0579859i
$532$	−17.0020	−	45.1516i	−0.737132	−	1.95757i
$533$	4.04109	+	25.5144i	0.175039	+	1.10515i
$534$	−1.10270	−	5.18780i	−0.0477185	−	0.224498i
$535$	−5.70172	−	2.01529i	−0.246507	−	0.0871284i
$536$	74.2541	+	15.7832i	3.20729	+	0.681730i
$537$	1.20228	+	0.780772i	0.0518824	+	0.0336928i
$538$	28.7194	+	56.3649i	1.23818	+	2.43006i
$539$	18.2619	−	10.2348i	0.786597	−	0.440843i
$540$	6.39125	−	13.4200i	0.275036	−	0.577504i
$541$	−29.5536	+	6.28181i	−1.27061	+	0.270076i	−0.793393	−	0.608710i	$-0.791687\pi$
$541$	−29.5536	+	6.28181i	−1.27061	+	0.270076i	−0.477216	+	0.878786i	$0.658354\pi$
$542$	−70.4830	−	27.0559i	−3.02750	−	1.16215i
$543$	3.76211	−	1.00806i	0.161448	−	0.0432598i
$544$	−7.14162	+	67.9480i	−0.306194	+	2.91324i
$545$	8.24592	−	6.33508i	0.353217	−	0.271365i
$546$	7.48376	−	1.54084i	0.320275	−	0.0659417i
$547$	−1.01423	+	6.40362i	−0.0433655	+	0.273799i	−0.999838	−	0.0180249i	$-0.994262\pi$
$547$	−1.01423	+	6.40362i	−0.0433655	+	0.273799i	0.956472	+	0.291824i	$0.0942622\pi$
$548$	−20.1797	+	1.05757i	−0.862035	+	0.0451773i
$549$	14.7724	−	25.5866i	0.630472	−	1.09201i
$550$	12.2313	−	37.7964i	0.521546	−	1.61164i
$551$	15.2593	−	8.80994i	0.650066	−	0.375316i
$552$	−2.66179	+	5.22406i	−0.113293	+	0.222351i
$553$	−0.813112	+	13.8251i	−0.0345770	+	0.587905i
$554$	−18.8399	−	25.9310i	−0.800433	−	1.10170i
$555$	0.644725	−	0.155189i	0.0273671	−	0.00658739i
$556$	16.8895	+	37.9345i	0.716275	+	1.60878i
$557$	3.18632	+	11.8915i	0.135009	+	0.503860i	0.999998	+	0.00206894i	$0.000658565\pi$
$557$	3.18632	+	11.8915i	0.135009	+	0.503860i	−0.864989	+	0.501791i	$0.832675\pi$
$558$	7.97605	+	9.84960i	0.337653	+	0.416967i
$559$	−18.1537	+	55.8715i	−0.767821	+	2.36311i
$560$	59.8123	−	32.0281i	2.52753	−	1.35343i
$561$	−0.980610	−	3.01801i	−0.0414014	−	0.127420i
$562$	10.7101	−	16.4921i	0.451778	−	0.695677i
$563$	8.51592	+	0.446300i	0.358903	+	0.0188093i	0.230936	−	0.972969i	$-0.425821\pi$
$563$	8.51592	+	0.446300i	0.358903	+	0.0188093i	0.127968	+	0.991778i	$0.459155\pi$
$564$	0.776378	−	3.65257i	0.0326914	−	0.153801i
$565$	−36.1245	+	14.9883i	−1.51977	+	0.630563i
$566$	64.6263	+	20.9984i	2.71645	+	0.882627i
$567$	16.1228	−	15.9182i	0.677094	−	0.668500i
$568$	−2.08589	−	2.08589i	−0.0875221	−	0.0875221i
$569$	−31.0809	−	3.26674i	−1.30298	−	0.136949i	−0.572512	−	0.819896i	$-0.694031\pi$
$569$	−31.0809	−	3.26674i	−1.30298	−	0.136949i	−0.730468	+	0.682947i	$0.760698\pi$
$570$	3.25762	+	3.42875i	0.136447	+	0.143615i
$571$	−0.883002	−	8.40120i	−0.0369525	−	0.351579i	−0.997339	−	0.0729071i	$-0.976772\pi$
$571$	−0.883002	−	8.40120i	−0.0369525	−	0.351579i	0.960386	−	0.278672i	$-0.0898943\pi$
$572$	26.6847	+	69.5161i	1.11575	+	2.90662i
$573$	2.38365	+	1.21453i	0.0995786	+	0.0507378i
$574$	−3.62141	−	36.7092i	−0.151155	−	1.53221i
$575$	16.2520	+	1.68870i	0.677755	+	0.0704236i
$576$	21.8969	+	37.9266i	0.912372	+	1.58027i
$577$	−7.64659	−	11.7747i	−0.318332	−	0.490188i	0.642892	−	0.765957i	$-0.277734\pi$
$577$	−7.64659	−	11.7747i	−0.318332	−	0.490188i	−0.961224	+	0.275769i	$0.911068\pi$
$578$	10.1785	−	12.5694i	0.423368	−	0.522816i
$579$	−1.73175	−	0.771024i	−0.0719690	−	0.0320427i
$580$	33.6768	+	43.8347i	1.39835	+	1.82014i
$581$	−2.09177	+	1.18993i	−0.0867811	+	0.0493668i
$582$	−3.00411	+	3.00411i	−0.124524	+	0.124524i
$583$	−9.93656	+	8.04646i	−0.411530	+	0.333251i
$584$	15.9151	+	17.6756i	0.658573	+	0.731420i
$585$	26.7601	−	18.4150i	1.10639	−	0.761368i
$586$	5.54118	+	4.98931i	0.228904	+	0.206106i
$587$	17.5353	−	8.93468i	0.723759	−	0.368774i	−0.0529805	−	0.998596i	$-0.516872\pi$
$587$	17.5353	−	8.93468i	0.723759	−	0.368774i	0.776740	+	0.629822i	$0.216872\pi$
$588$	−7.73765	+	1.12441i	−0.319095	+	0.0463699i
$589$	−5.54247	+	1.80086i	−0.228373	+	0.0742030i
$590$	−2.52676	+	2.16064i	−0.104025	+	0.0889523i
$591$	0.651718	−	0.586810i	0.0268081	−	0.0241381i
$592$	−5.51939	+	14.3785i	−0.226845	+	0.590953i
$593$	−4.03167	−	1.08028i	−0.165561	−	0.0443619i	0.175086	−	0.984553i	$-0.443980\pi$
$593$	−4.03167	−	1.08028i	−0.165561	−	0.0443619i	−0.340647	+	0.940191i	$0.610646\pi$
$594$	−8.44756	−	6.13751i	−0.346608	−	0.251825i
$595$	−28.3256	−	2.39450i	−1.16124	−	0.0981650i
$596$	89.2946	−	64.8763i	3.65765	−	2.65744i
$597$	2.52827	−	0.970511i	0.103475	−	0.0397204i
$598$	−35.8415	+	23.2758i	−1.46567	+	0.951817i
$599$	−0.232901	−	0.134465i	−0.00951606	−	0.00549410i	0.495234	−	0.868759i	$-0.335082\pi$
$599$	−0.232901	−	0.134465i	−0.00951606	−	0.00549410i	−0.504750	+	0.863265i	$0.668416\pi$
$600$	−5.63722	+	6.97827i	−0.230139	+	0.284887i
$601$			10.5831i			0.431694i	0.976427	+	0.215847i	$0.0692513\pi$
$601$			10.5831i			0.431694i	−0.976427	+	0.215847i	$0.930749\pi$
$602$	30.5620	−	78.1218i	1.24561	−	3.18401i
$603$	−27.2358	−	4.31373i	−1.10913	−	0.175669i
$604$	−4.94952	+	11.1168i	−0.201393	+	0.452336i
$605$	4.04181	+	2.19143i	0.164323	+	0.0890941i
$606$	1.46633	−	0.652854i	0.0595658	−	0.0265204i
$607$	−0.323127	+	1.20593i	−0.0131153	+	0.0489470i	−0.972173	−	0.234262i	$-0.924732\pi$
$607$	−0.323127	+	1.20593i	−0.0131153	+	0.0489470i	0.959058	+	0.283209i	$0.0913992\pi$
$608$	−50.6313	+	8.01920i	−2.05337	+	0.325222i
$609$	−0.865037	−	2.72132i	−0.0350531	−	0.110274i
$610$	−40.9119	+	43.1633i	−1.65647	+	1.74763i
$611$	11.0113	−	12.2293i	0.445469	−	0.494743i
$612$	3.75392	−	71.6291i	0.151743	−	2.89543i
$613$	1.40509	−	26.8108i	0.0567512	−	1.08288i	−0.810734	−	0.585415i	$-0.800932\pi$
$613$	1.40509	−	26.8108i	0.0567512	−	1.08288i	0.867485	−	0.497463i	$-0.165735\pi$
$614$	42.8449	−	47.5841i	1.72908	−	1.92034i
$615$	1.23784	+	2.27660i	0.0499145	+	0.0918015i
$616$	−19.4744	−	61.2645i	−0.784644	−	2.46842i
$617$	−9.11291	+	1.44334i	−0.366872	+	0.0581068i	−0.337149	−	0.941451i	$-0.609463\pi$
$617$	−9.11291	+	1.44334i	−0.366872	+	0.0581068i	−0.0297232	+	0.999558i	$0.509463\pi$
$618$	0.101366	−	0.378304i	0.00407755	−	0.0152176i
$619$	7.43093	−	3.30846i	0.298674	−	0.132978i	−0.251928	−	0.967746i	$-0.581065\pi$
$619$	7.43093	−	3.30846i	0.298674	−	0.132978i	0.550602	+	0.834768i	$0.314398\pi$
$620$	−7.88071	−	16.4971i	−0.316497	−	0.662540i
$621$	1.74682	−	3.92342i	0.0700975	−	0.157442i
$622$	−74.3796	−	11.7806i	−2.98235	−	0.472358i
$623$	−8.71385	+	22.2741i	−0.349113	+	0.892394i
$624$		−	12.4665i		−	0.499058i
$625$	23.7946	+	7.66910i	0.951786	+	0.306764i
$626$	−49.5578	−	28.6122i	−1.98073	−	1.14357i
$627$	1.99683	−	1.29676i	0.0797459	−	0.0517876i
$628$	103.612	−	39.7731i	4.13459	−	1.58712i
$629$	5.22048	−	3.79290i	0.208154	−	0.151233i
$630$	−39.6899	+	24.0068i	−1.58128	+	0.956453i
$631$	−26.1031	−	18.9650i	−1.03915	−	0.754985i	−0.0690289	−	0.997615i	$-0.521990\pi$
$631$	−26.1031	−	18.9650i	−1.03915	−	0.754985i	−0.970119	+	0.242629i	$0.921990\pi$
$632$	41.0784	+	11.0069i	1.63401	+	0.437832i
$633$	1.73644	−	4.52358i	0.0690173	−	0.179796i
$634$	0.446023	−	0.401601i	0.0177138	−	0.0159496i
$635$	9.94570	+	6.08664i	0.394683	+	0.241541i
$636$	4.54178	−	1.47571i	0.180093	−	0.0585158i
$637$	−32.0082	−	12.7582i	−1.26821	−	0.505499i
$638$	34.5989	−	17.6290i	1.36978	−	0.697939i
$639$	0.796314	+	0.717004i	0.0315017	+	0.0283642i
$640$	−6.99048	−	23.5483i	−0.276323	−	0.930827i
$641$	19.6339	+	21.8057i	0.775494	+	0.861273i	0.993401	−	0.114697i	$-0.0365896\pi$
$641$	19.6339	+	21.8057i	0.775494	+	0.861273i	−0.217907	+	0.975970i	$0.569923\pi$
$642$	1.23308	−	0.998525i	0.0486656	−	0.0394086i
$643$	−23.5100	+	23.5100i	−0.927145	+	0.927145i	−0.997521	−	0.0703751i	$-0.977580\pi$
$643$	−23.5100	+	23.5100i	−0.927145	+	0.927145i	0.0703751	+	0.997521i	$0.477580\pi$
$644$	38.0126	−	21.6241i	1.49790	−	0.852107i
$645$	0.157752	+	5.89102i	0.00621148	+	0.231959i
$646$	42.0432	+	18.7188i	1.65417	+	0.736482i
$647$	1.06439	−	1.31441i	0.0418455	−	0.0516749i	−0.755794	−	0.654810i	$-0.772749\pi$
$647$	1.06439	−	1.31441i	0.0418455	−	0.0516749i	0.797639	+	0.603135i	$0.206082\pi$
$648$	−37.8930	−	58.3501i	−1.48858	−	2.29221i
$649$	0.836837	+	1.44944i	0.0328487	+	0.0568956i
$650$	−61.0170	+	23.5052i	−2.39328	+	0.921948i
$651$	0.0927208	+	0.939882i	0.00363401	+	0.0368369i
$652$	−40.0214	−	20.3919i	−1.56736	−	0.798610i
$653$	−6.29260	−	16.3928i	−0.246249	−	0.641499i	0.753627	−	0.657303i	$-0.228303\pi$
$653$	−6.29260	−	16.3928i	−0.246249	−	0.641499i	−0.999875	+	0.0158035i	$0.994969\pi$
$654$	0.285183	+	2.71334i	0.0111515	+	0.106100i
$655$	−8.27364	−	1.52836i	−0.323278	−	0.0597180i
$656$	−59.8549	−	6.29100i	−2.33694	−	0.245622i
$657$	−6.10926	−	6.10926i	−0.238345	−	0.238345i
$658$	−16.7217	+	16.5094i	−0.651879	+	0.643605i
$659$	−12.1353	−	3.94299i	−0.472724	−	0.153597i	0.0629598	−	0.998016i	$-0.479946\pi$
$659$	−12.1353	−	3.94299i	−0.472724	−	0.153597i	−0.535684	+	0.844419i	$0.679946\pi$
$660$	4.85447	+	5.67704i	0.188960	+	0.220979i
$661$	−9.56810	+	45.0144i	−0.372156	+	1.75086i	0.250268	+	0.968177i	$0.419481\pi$
$661$	−9.56810	+	45.0144i	−0.372156	+	1.75086i	−0.622424	+	0.782680i	$0.713852\pi$
$662$	−50.7233	−	2.65829i	−1.97142	−	0.103318i
$663$	−2.84474	+	4.38051i	−0.110480	+	0.170125i
$664$	2.28363	+	7.02829i	0.0886220	+	0.272751i
$665$	−3.76525	−	20.9936i	−0.146010	−	0.814098i
$666$	3.25380	−	10.0142i	0.126082	−	0.388041i
$667$	10.0511	+	12.4121i	0.389181	+	0.480598i
$668$	13.7507	+	51.3182i	0.532029	+	1.98556i
$669$	0.127513	+	0.286398i	0.00492992	+	0.0110728i
$670$	51.2942	+	21.2112i	1.98167	+	0.819459i
$671$	17.5979	+	24.2214i	0.679358	+	0.935056i
$672$	−0.487764	+	8.29333i	−0.0188159	+	0.319922i
$673$	13.5468	−	26.5870i	0.522189	−	1.02485i	−0.467816	−	0.883826i	$-0.654959\pi$
$673$	13.5468	−	26.5870i	0.522189	−	1.02485i	0.990006	−	0.141028i	$-0.0450409\pi$
$674$	−3.51634	+	2.03016i	−0.135444	+	0.0781988i
$675$	3.85608	−	5.32068i	0.148421	−	0.204793i
$676$	28.4029	−	49.1952i	1.09242	−	1.89212i
$677$	−28.8246	+	1.51063i	−1.10782	+	0.0580583i	−0.597456	−	0.801902i	$-0.703822\pi$
$677$	−28.8246	+	1.51063i	−1.10782	+	0.0580583i	−0.510362	+	0.859960i	$0.670488\pi$
$678$	1.60526	−	10.1352i	0.0616495	−	0.389240i
$679$	18.7655	−	3.86364i	0.720153	−	0.148273i
$680$	−24.7428	+	83.7124i	−0.948844	+	3.21022i
$681$	−0.654283	+	6.22509i	−0.0250722	+	0.238546i
$682$	−12.4056	+	3.32408i	−0.475036	+	0.127286i
$683$	−14.8084	−	5.68441i	−0.566628	−	0.217508i	0.0581537	−	0.998308i	$-0.481479\pi$
$683$	−14.8084	−	5.68441i	−0.566628	−	0.217508i	−0.624782	+	0.780800i	$0.714812\pi$
$684$	52.6412	−	11.1892i	2.01279	−	0.427831i
$685$	−8.85745	−	1.16077i	−0.338426	−	0.0443508i
$686$	44.5575	+	20.8701i	1.70121	+	0.796826i
$687$	0.0607961	+	0.119319i	0.00231952	+	0.00455231i
$688$	−114.787	−	74.5438i	−4.37623	−	2.84196i
$689$	20.5853	+	4.37554i	0.784238	+	0.166695i
$690$	−2.60777	+	3.40268i	−0.0992762	+	0.129538i
$691$	0.246952	+	1.16182i	0.00939451	+	0.0441977i	0.982595	−	0.185760i	$-0.0594746\pi$
$691$	0.246952	+	1.16182i	0.00939451	+	0.0441977i	−0.973201	+	0.229957i	$0.926141\pi$
$692$	−14.2519	−	89.9831i	−0.541777	−	3.42064i
$693$	8.22904	+	21.8535i	0.312595	+	0.830147i
$694$	30.9863	−	42.6489i	1.17622	−	1.61893i
$695$	4.29590	+	17.8472i	0.162953	+	0.676981i
$696$	−8.72062	+	0.916574i	−0.330554	+	0.0347427i
$697$	19.5965	+	15.8689i	0.742270	+	0.601079i
$698$	−0.976112	−	18.6253i	−0.0369464	−	0.704979i
$699$	0.993738			0.0375866
$700$	63.7444	−	20.3458i	2.40931	−	0.768999i
$701$	8.69736			0.328495			0.164247	−	0.986419i	$-0.447480\pi$
$701$	8.69736			0.328495			0.164247	+	0.986419i	$0.447480\pi$
$702$	0.899484	+	17.1632i	0.0339488	+	0.647782i
$703$	3.76263	+	3.04692i	0.141910	+	0.114917i
$704$	−44.1353	+	4.63881i	−1.66341	+	0.174832i
$705$	0.630824	−	1.52550i	0.0237582	−	0.0574536i
$706$	42.1343	−	57.9929i	1.58574	−	2.18259i
$707$	−7.14199	−	1.17798i	−0.268602	−	0.0443027i
$708$	−0.0977889	−	0.617415i	−0.00367513	−	0.0232039i
$709$	3.56761	+	16.7843i	0.133985	+	0.630348i	0.992972	+	0.118351i	$0.0377608\pi$
$709$	3.56761	+	16.7843i	0.133985	+	0.630348i	−0.858987	+	0.511997i	$0.828906\pi$
$710$	−1.22275	−	1.77686i	−0.0458891	−	0.0666844i
$711$	−15.1105	−	3.21183i	−0.566687	−	0.120453i
$712$	61.5979	+	40.0021i	2.30848	+	1.49914i
$713$	−2.39819	−	4.70671i	−0.0898129	−	0.176268i
$714$	4.42238	−	6.00584i	0.165503	−	0.224763i
$715$	6.01794	+	32.3629i	0.225058	+	1.21031i
$716$	−32.1181	+	6.82691i	−1.20031	+	0.255134i
$717$	−2.70945	−	1.04006i	−0.101186	−	0.0388417i
$718$	−35.8366	+	9.60239i	−1.33741	+	0.358358i
$719$	3.40612	−	32.4070i	0.127027	−	1.20858i	−0.726366	−	0.687309i	$-0.758792\pi$
$719$	3.40612	−	32.4070i	0.127027	−	1.20858i	0.853392	−	0.521269i	$-0.174541\pi$
$720$	25.3052	+	71.3256i	0.943071	+	2.65815i
$721$	−1.32007	+	1.17342i	−0.0491620	+	0.0437004i
$722$	2.49468	−	15.7508i	0.0928423	−	0.586183i
$723$	−3.65419	+	0.191508i	−0.135901	+	0.00712225i
$724$	−44.6055	+	77.2589i	−1.65775	+	2.87131i
$725$	11.1198	+	21.7602i	0.412981	+	0.808153i
$726$	−1.04469	+	0.603152i	−0.0387721	+	0.0223851i
$727$	−10.8247	+	21.2447i	−0.401466	+	0.787922i	−0.999912	−	0.0132413i	$-0.995785\pi$
$727$	−10.8247	+	21.2447i	−0.401466	+	0.787922i	0.598446	+	0.801163i	$0.295785\pi$
$728$	−58.1943	+	88.3707i	−2.15683	+	3.27524i
$729$	14.3432	+	19.7418i	0.531231	+	0.731177i
$730$	9.09566	+	14.8231i	0.336646	+	0.548626i
$731$	23.3242	+	52.3870i	0.862677	+	1.93760i
$732$	−2.89417	−	10.8012i	−0.106972	−	0.399223i
$733$	20.4613	+	25.2676i	0.755754	+	0.933278i	0.999330	−	0.0366035i	$-0.0116538\pi$
$733$	20.4613	+	25.2676i	0.755754	+	0.933278i	−0.243576	+	0.969882i	$0.578321\pi$
$734$	23.3361	−	71.8210i	0.861350	−	2.65096i
$735$	−3.45400	−	0.132563i	−0.127403	−	0.00488968i
$736$	−14.3589	−	44.1921i	−0.529276	−	1.62894i
$737$	15.2191	−	23.4353i	0.560601	−	0.863250i
$738$	41.0900	+	2.15344i	1.51254	+	0.0792691i
$739$	−11.0359	+	51.9197i	−0.405961	+	1.90990i	0.00879226	+	0.999961i	$0.497201\pi$
$739$	−11.0359	+	51.9197i	−0.405961	+	1.90990i	−0.414753	+	0.909934i	$0.636132\pi$
$740$	−7.92867	+	12.9556i	−0.291464	+	0.476258i
$741$	−3.72715	−	1.21102i	−0.136920	−	0.0444881i
$742$	−28.9771	−	7.96309i	−1.06378	−	0.292334i
$743$	−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
$745$	44.0280	−	21.0323i	1.61306	−	0.770563i
$746$	−6.14228	−	58.4399i	−0.224885	−	2.13964i
$747$	−0.962003	−	2.50610i	−0.0351979	−	0.0916936i
$748$	64.7627	+	32.9982i	2.36796	+	1.20653i
$749$	−7.12080	+	0.702478i	−0.260189	+	0.0256680i
$750$	−4.98018	+	4.26879i	−0.181850	+	0.155874i
$751$	20.8809	+	36.1668i	0.761956	+	1.31975i	0.941841	+	0.336058i	$0.109094\pi$
$751$	20.8809	+	36.1668i	0.761956	+	1.31975i	−0.179886	+	0.983688i	$0.557573\pi$
$752$	20.8812	+	32.1542i	0.761459	+	1.17254i
$753$	−2.96570	+	3.66233i	−0.108076	+	0.133463i
$754$	−58.3890	−	25.9964i	−2.12640	−	0.946735i
$755$	−3.04438	+	4.43523i	−0.110796	+	0.161414i
$756$	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	$0.445143\pi$
$758$	69.7084	−	56.4488i	2.53192	−	2.05031i
$759$	1.44411	+	1.60385i	0.0524180	+	0.0582161i
$760$	−65.4743	−	1.67572i	−2.37500	−	0.0607846i
$761$	−20.4298	−	18.3950i	−0.740578	−	0.666820i	0.209860	−	0.977731i	$-0.432699\pi$
$761$	−20.4298	−	18.3950i	−0.740578	−	0.666820i	−0.950439	+	0.310912i	$0.899366\pi$
$762$	−2.72591	+	1.38892i	−0.0987494	+	0.0503154i
$763$	5.65564	−	10.9267i	0.204748	−	0.395575i
$764$	−58.2772	+	18.9354i	−2.10839	+	0.685059i
$765$	7.38403	−	30.8371i	0.266970	−	1.11492i
$766$	74.8157	−	67.3644i	2.70320	−	2.43397i
$767$	0.987233	−	2.57183i	0.0356469	−	0.0928634i
$768$	−0.105258	−	0.0282037i	−0.00379816	−	0.00101771i
$769$	23.0581	+	16.7527i	0.831495	+	0.604117i	0.919982	−	0.391961i	$-0.128203\pi$
$769$	23.0581	+	16.7527i	0.831495	+	0.604117i	−0.0884867	+	0.996077i	$0.528203\pi$
$770$	−5.86521	−	46.6373i	−0.211367	−	1.68069i
$771$	3.99922	−	2.90561i	0.144029	−	0.104643i
$772$	40.5356	−	15.5602i	1.45891	−	0.560022i
$773$	22.0944	−	14.3483i	0.794681	−	0.516072i	−0.0822942	−	0.996608i	$-0.526225\pi$
$773$	22.0944	−	14.3483i	0.794681	−	0.516072i	0.876975	+	0.480536i	$0.159558\pi$
$774$	81.0365	+	46.7864i	2.91280	+	1.68170i
$775$	−2.10111	−	7.80447i	−0.0754741	−	0.280345i
$776$		−	58.8336i		−	2.11200i
$777$	0.612919	−	0.489884i	0.0219883	−	0.0175745i
$778$	−33.3007	−	5.27432i	−1.19389	−	0.189093i
$779$	−7.69531	+	17.2839i	−0.275713	+	0.619261i
$780$	2.23336	−	12.0901i	0.0799672	−	0.432895i
$781$	−0.991973	+	0.441655i	−0.0354956	+	0.0158037i
$782$	−10.7970	+	40.2948i	−0.386098	+	1.44094i
$783$	6.34396	−	1.00478i	0.226715	−	0.0359081i
$784$	48.0122	−	64.3387i	1.71472	−	2.29781i
$785$	48.2363	−	8.96962i	1.72163	−	0.320139i
$786$	1.47711	−	1.64050i	0.0526868	−	0.0585146i
$787$	−1.93264	+	36.8769i	−0.0688911	+	1.31452i	0.717399	+	0.696662i	$0.245332\pi$
$787$	−1.93264	+	36.8769i	−0.0688911	+	1.31452i	−0.786290	+	0.617857i	$0.788001\pi$
$788$	−1.05127	+	20.0595i	−0.0374501	+	0.714591i
$789$	3.62917	−	4.03061i	0.129202	−	0.143493i
$790$	28.0744	+	13.3704i	0.998843	+	0.475698i
$791$	−31.1838	+	34.1914i	−1.10877	+	1.21571i
$792$	70.8248	−	11.2176i	2.51665	−	0.398598i
$793$	12.7543	−	47.5997i	0.452919	−	1.69032i
$794$	−65.1677	+	29.0145i	−2.31272	+	1.02969i
$795$	2.09291	−	0.276797i	0.0742278	−	0.00981698i
$796$	−25.2298	+	56.6672i	−0.894248	+	2.00851i
$797$	16.2590	+	2.57517i	0.575922	+	0.0912170i	0.437599	−	0.899170i	$-0.355829\pi$
$797$	16.2590	+	2.57517i	0.575922	+	0.0912170i	0.138323	+	0.990387i	$0.455829\pi$
$798$	5.21145	+	2.03877i	0.184483	+	0.0721717i
$799$		−	16.0634i		−	0.568282i
$800$	−7.51519	−	70.6968i	−0.265702	−	2.49951i
$801$	−23.1052	−	13.3398i	−0.816381	−	0.471338i
$802$	5.07544	−	3.29603i	0.179220	−	0.116387i
$803$	8.17362	−	3.13756i	0.288441	−	0.110722i
$804$	−8.44351	+	6.13457i	−0.297780	+	0.216350i
$805$	18.2613	−	6.34783i	0.643627	−	0.223732i
$806$	17.1022	+	12.4255i	0.602400	+	0.437669i
$807$	−5.07910	−	1.36094i	−0.178793	−	0.0479074i
$808$	−7.96576	+	20.7515i	−0.280235	+	0.730036i
$809$	−14.2895	+	12.8663i	−0.502393	+	0.452356i	−0.880942	−	0.473225i	$-0.843090\pi$
$809$	−14.2895	+	12.8663i	−0.502393	+	0.452356i	0.378549	+	0.925581i	$0.376423\pi$
$810$	−19.4957	−	46.9882i	−0.685011	−	1.65100i
$811$	6.38309	−	2.07399i	0.224141	−	0.0728277i	−0.194794	−	0.980844i	$-0.562404\pi$
$811$	6.38309	−	2.07399i	0.224141	−	0.0728277i	0.418934	+	0.908017i	$0.362404\pi$
$812$	58.0857	+	30.0649i	2.03841	+	1.05507i
$813$	5.59150	−	2.84901i	0.196103	−	0.0999192i
$814$	7.92941	+	7.13968i	0.277926	+	0.250245i
$815$	−15.7605	−	12.0787i	−0.552068	−	0.423097i
$816$	−8.14261	−	9.04329i	−0.285048	−	0.316578i
$817$	−33.4374	+	27.0771i	−1.16983	+	0.947308i
$818$	−54.5072	+	54.5072i	−1.90580	+	1.90580i
$819$	19.4300	−	33.1629i	0.678940	−	1.15880i
$820$	−56.9208	−	16.8241i	−1.98776	−	0.587522i
$821$	−41.4237	−	18.4430i	−1.44570	−	0.643666i	−0.474136	−	0.880452i	$-0.657240\pi$
$821$	−41.4237	−	18.4430i	−1.44570	−	0.643666i	−0.971562	+	0.236785i	$0.923906\pi$
$822$	1.47502	−	1.82150i	0.0514472	−	0.0635320i
$823$	5.37337	+	8.27427i	0.187304	+	0.288423i	0.919831	−	0.392315i	$-0.128326\pi$
$823$	5.37337	+	8.27427i	0.187304	+	0.288423i	−0.732527	+	0.680738i	$0.761659\pi$
$824$	2.71183	+	4.69703i	0.0944711	+	0.163629i
$825$	1.65444	+	2.85776i	0.0576003	+	0.0994943i
$826$	−1.62290	+	3.58333i	−0.0564679	+	0.124680i
$827$	16.3365	+	8.32384i	0.568074	+	0.289448i	0.714342	−	0.699797i	$-0.246726\pi$
$827$	16.3365	+	8.32384i	0.568074	+	0.289448i	−0.146268	+	0.989245i	$0.546726\pi$
$828$	17.4820	+	45.5421i	0.607541	+	1.58270i
$829$	−2.48022	−	23.5977i	−0.0861416	−	0.819583i	−0.949241	−	0.314549i	$-0.898147\pi$
$829$	−2.48022	−	23.5977i	−0.0861416	−	0.819583i	0.863100	−	0.505034i	$-0.168520\pi$
$830$	0.708467	+	5.35683i	0.0245912	+	0.185938i
$831$	2.64966	+	0.278491i	0.0919157	+	0.00966073i
$832$	51.6507	+	51.6507i	1.79067	+	1.79067i
$833$	−31.5523	+	11.6516i	−1.09322	+	0.403704i
$834$	−4.58063	−	1.48834i	−0.158614	−	0.0515368i
$835$	1.85661	+	23.4133i	0.0642507	+	0.810250i
$836$	−11.3386	+	53.3439i	−0.392154	+	1.84494i
$837$	−2.12148	−	0.111182i	−0.0733291	−	0.00384301i
$838$	−7.76021	+	11.9497i	−0.268072	+	0.412795i
$839$	4.66811	+	14.3670i	0.161161	+	0.496003i	0.998733	−	0.0503242i	$-0.0160255\pi$
$839$	4.66811	+	14.3670i	0.161161	+	0.496003i	−0.837572	+	0.546327i	$0.816025\pi$
$840$	−2.53763	+	10.3065i	−0.0875566	+	0.355609i
$841$	1.58024	−	4.86346i	0.0544909	−	0.167706i
$842$	31.6452	+	39.0785i	1.09056	+	1.34674i
$843$	0.423054	+	1.57886i	0.0145707	+	0.0543788i
$844$	45.1413	+	101.389i	1.55383	+	3.48995i
$845$	16.2979	−	19.1053i	0.560664	−	0.657241i
$846$	−15.4068	−	21.2056i	−0.529696	−	0.729064i
$847$	5.43065	+	0.319398i	0.186599	+	0.0109747i
$848$	−22.2597	+	43.6871i	−0.764401	+	1.50022i
$849$	−4.89158	+	2.82415i	−0.167878	+	0.0969247i
$850$	−28.9096	+	56.9048i	−0.991592	+	1.95182i
$851$	−2.19432	+	3.80067i	−0.0752202	+	0.130285i
$852$	0.405005	−	0.0212254i	0.0138752	−	0.000727171i
$853$	3.90501	−	24.6553i	0.133705	−	0.844180i	−0.826102	−	0.563520i	$-0.809447\pi$
$853$	3.90501	−	24.6553i	0.133705	−	0.844180i	0.959807	−	0.280660i	$-0.0905533\pi$
$854$	−22.1717	+	66.7833i	−0.758701	+	2.28528i
$855$	23.7827	−	0.636863i	0.813352	−	0.0217803i
$856$	−2.29677	+	21.8523i	−0.0785019	+	0.746896i
$857$	45.6601	−	12.2346i	1.55972	−	0.417926i	0.627145	−	0.778903i	$-0.284223\pi$
$857$	45.6601	−	12.2346i	1.55972	−	0.417926i	0.932575	+	0.360977i	$0.117557\pi$
$858$	−8.06307	−	3.09512i	−0.275269	−	0.105666i
$859$	41.2291	−	8.76352i	1.40672	−	0.299007i	0.558874	−	0.829252i	$-0.311233\pi$
$859$	41.2291	−	8.76352i	1.40672	−	0.299007i	0.847845	+	0.530245i	$0.177900\pi$
$860$	−97.9675	−	92.8575i	−3.34066	−	3.16641i
$861$	2.46900	+	1.81804i	0.0841433	+	0.0619586i
$862$	28.0672	+	55.0849i	0.955972	+	1.87620i
$863$	−36.3514	−	23.6069i	−1.23742	−	0.803587i	−0.251021	−	0.967982i	$-0.580766\pi$
$863$	−36.3514	−	23.6069i	−1.23742	−	0.803587i	−0.986395	+	0.164394i	$0.947433\pi$
$864$	−18.2785	−	3.88522i	−0.621848	−	0.132178i
$865$	1.03044	−	40.2619i	0.0350361	−	1.36895i
$866$	3.33240	+	15.6777i	0.113239	+	0.532750i
$867$	0.210309	+	1.32784i	0.00714247	+	0.0450958i
$868$	−16.7243	−	13.7209i	−0.567660	−	0.465716i
$869$	9.20135	−	12.6646i	0.312134	−	0.429616i
$870$	−6.39208	−	0.499260i	−0.216712	−	0.0169265i
$871$	−45.7418	+	4.80765i	−1.54990	+	0.162901i
$872$	−29.3621	−	23.7770i	−0.994326	−	0.805190i
$873$	1.11848	+	21.3419i	0.0378550	+	0.722316i
$874$	−31.2998			−1.05873
$875$	29.3448	−	3.72577i	0.992036	−	0.125954i
$876$	−3.27001			−0.110483
$877$	−0.226010	−	4.31254i	−0.00763183	−	0.145624i	−0.999787	−	0.0206153i	$-0.993437\pi$
$877$	−0.226010	−	4.31254i	−0.00763183	−	0.145624i	0.992156	−	0.125009i	$-0.0398959\pi$
$878$	−73.7830	−	59.7483i	−2.49006	−	2.01641i
$879$	−0.616394	+	0.0647856i	−0.0207905	+	0.00218517i
$880$	−76.4589	−	5.97190i	−2.57743	−	0.201313i
$881$	−6.93297	+	9.54241i	−0.233578	+	0.321492i	−0.909675	−	0.415320i	$-0.863670\pi$
$881$	−6.93297	+	9.54241i	−0.233578	+	0.321492i	0.676098	+	0.736812i	$0.263670\pi$
$882$	−30.4775	+	45.6441i	−1.02623	+	1.53692i
$883$	−3.12841	−	19.7520i	−0.105279	−	0.664708i	−0.982731	−	0.185042i	$-0.940758\pi$
$883$	−3.12841	−	19.7520i	−0.105279	−	0.664708i	0.877451	−	0.479666i	$-0.159242\pi$
$884$	−24.8738	−	117.022i	−0.836597	−	3.93588i
$885$	0.00707033	−	0.276255i	0.000237667	−	0.00928622i
$886$	−54.6726	−	11.6210i	−1.83676	−	0.390416i
$887$	0.351152	+	0.228041i	0.0117905	+	0.00765687i	0.550521	−	0.834821i	$-0.314429\pi$
$887$	0.351152	+	0.228041i	0.0117905	+	0.00765687i	−0.538730	+	0.842478i	$0.681096\pi$
$888$	−1.09387	−	2.14684i	−0.0367079	−	0.0720434i
$889$	13.7117	+	1.52975i	0.459874	+	0.0513062i
$890$	38.9772	+	36.9441i	1.30652	+	1.23837i
$891$	−25.0506	+	5.32466i	−0.839225	+	0.178383i
$892$	−6.70380	−	2.57335i	−0.224460	−	0.0861621i
$893$	11.6417	−	3.11939i	0.389576	−	0.104387i
$894$	−1.33819	+	12.7320i	−0.0447557	+	0.425822i
$895$	−14.5106	+	0.388570i	−0.485036	+	0.0129885i
$896$	−19.3096	−	21.7229i	−0.645088	−	0.725710i
$897$	0.555703	−	3.50857i	0.0185544	−	0.117148i
$898$	45.5431	−	2.38681i	1.51979	−	0.0796490i
$899$	3.95014	−	6.84184i	0.131744	−	0.228188i
$900$	11.7633	+	73.7057i	0.392111	+	2.45686i
$901$	17.7907	−	10.2715i	0.592695	−	0.342192i
$902$	−18.9294	+	37.1511i	−0.630281	+	1.23700i
$903$	3.12586	+	6.23294i	0.104022	+	0.207419i
$904$	83.5269	+	114.965i	2.77806	+	3.82368i
$905$	−25.5951	+	30.0040i	−0.850810	+	0.997366i
$906$	−0.574087	−	1.28942i	−0.0190728	−	0.0428381i
$907$	−12.6812	−	47.3268i	−0.421072	−	1.57146i	−0.772354	−	0.635192i	$-0.780921\pi$
$907$	−12.6812	−	47.3268i	−0.421072	−	1.57146i	0.351282	−	0.936270i	$-0.385746\pi$
$908$	−90.2262	−	111.420i	−2.99426	−	3.69761i
$909$	2.49508	−	7.67907i	0.0827566	−	0.254699i
$910$	−53.5808	+	55.8111i	−1.77619	+	1.85012i
$911$	1.87294	+	5.76433i	0.0620534	+	0.190981i	0.977277	−	0.211965i	$-0.0679863\pi$
$911$	1.87294	+	5.76433i	0.0620534	+	0.190981i	−0.915224	+	0.402946i	$0.867986\pi$
$912$	4.97277	−	7.65739i	0.164665	−	0.253562i
$913$	2.71651	+	0.142366i	0.0899032	+	0.00471163i
$914$	12.8166	−	60.2972i	0.423934	−	1.99445i
$915$	−0.390770	−	4.92790i	−0.0129185	−	0.162911i
$916$	−2.91719	−	0.947853i	−0.0963868	−	0.0313180i
$917$	−9.63217	+	2.51511i	−0.318082	+	0.0830563i
$918$	11.8628	+	11.8628i	0.391532	+	0.391532i
$919$	2.98351	+	0.313580i	0.0984170	+	0.0103440i	0.153609	−	0.988132i	$-0.450910\pi$
$919$	2.98351	+	0.313580i	0.0984170	+	0.0103440i	−0.0551920	+	0.998476i	$0.517577\pi$
$920$	−7.78394	−	58.8556i	−0.256629	−	1.94041i
$921$	0.556337	+	5.29319i	0.0183319	+	0.174417i
$922$	−15.9679	−	41.5978i	−0.525875	−	1.36995i
$923$	1.59247	+	0.811402i	0.0524167	+	0.0267076i
$924$	8.05091	+	3.64628i	0.264856	+	0.119954i
$925$	−4.48714	+	4.99536i	−0.147536	+	0.164246i
$926$	37.3273	+	64.6527i	1.22665	+	2.12462i
$927$	−1.07301	−	1.65230i	−0.0352424	−	0.0542686i
$928$	43.7337	−	54.0066i	1.43563	−	1.77285i
$929$	−26.8993	−	11.9763i	−0.882536	−	0.392930i	−0.0851274	−	0.996370i	$-0.527130\pi$
$929$	−26.8993	−	11.9763i	−0.882536	−	0.392930i	−0.797409	+	0.603440i	$0.793796\pi$
$930$	2.03362	+	0.601077i	0.0666851	+	0.0197101i
$931$	−14.5716	−	20.6044i	−0.477564	−	0.675283i
$932$	−16.0948	+	16.0948i	−0.527204	+	0.527204i
$933$	4.86465	−	3.93932i	0.159261	−	0.128967i
$934$	−10.1454	−	11.2676i	−0.331967	−	0.368687i
$935$	25.5037	+	19.5457i	0.834060	+	0.639213i
$936$	−87.7119	−	78.9762i	−2.86695	−	2.58142i
$937$	10.9912	−	5.60030i	0.359067	−	0.182954i	−0.265145	−	0.964208i	$-0.585420\pi$
$937$	10.9912	−	5.60030i	0.359067	−	0.182954i	0.624213	+	0.781255i	$0.285420\pi$
$938$	65.6071	−	3.01831i	2.14215	−	0.0985513i
$939$	4.52379	−	1.46987i	0.147628	−	0.0479673i
$940$	14.4904	+	34.9243i	0.472624	+	1.13911i
$941$	−14.2139	+	12.7982i	−0.463359	+	0.417210i	−0.867462	−	0.497503i	$-0.834250\pi$
$941$	−14.2139	+	12.7982i	−0.463359	+	0.417210i	0.404103	+	0.914713i	$0.367584\pi$
$942$	−4.61322	+	12.0178i	−0.150307	+	0.391563i
$943$	−16.5652	−	4.43863i	−0.539436	−	0.144542i
$944$	5.19239	+	3.77249i	0.168998	+	0.122784i
$945$	1.46115	−	7.63647i	0.0475314	−	0.248414i
$946$	−76.7125	+	55.7349i	−2.49414	+	1.81210i
$947$	15.4885	−	5.94548i	0.503309	−	0.193202i	−0.0934481	−	0.995624i	$-0.529789\pi$
$947$	15.4885	−	5.94548i	0.503309	−	0.193202i	0.596757	+	0.802422i	$0.296456\pi$
$948$	−4.90355	+	3.18440i	−0.159260	+	0.103425i
$949$	−12.4800	−	7.20530i	−0.405116	−	0.233894i
$950$	−46.8551	−	9.90138i	−1.52018	−	0.321243i
$951$			0.0498883i			0.00161774i
$952$	15.5056	+	102.115i	0.502540	+	3.30957i
$953$	−6.62829	−	1.04982i	−0.214711	−	0.0340069i	0.0481520	−	0.998840i	$-0.484667\pi$
$953$	−6.62829	−	1.04982i	−0.214711	−	0.0340069i	−0.262863	+	0.964833i	$0.584667\pi$
$954$	13.6343	−	30.6231i	0.441426	−	0.991460i
$955$	−26.8548	+	3.55168i	−0.869002	+	0.114930i
$956$	60.7280	−	27.0379i	1.96408	−	0.874467i
$957$	−0.835396	+	3.11774i	−0.0270045	+	0.100782i
$958$	49.1388	−	7.78282i	1.58760	−	0.251451i
$959$	−10.0732	+	3.20201i	−0.325281	+	0.103398i
$960$	6.61553	+	3.15064i	0.213515	+	0.101686i
$961$	18.9946	−	21.0957i	0.612730	−	0.680505i
$962$	0.919152	−	17.5385i	0.0296346	−	0.565463i
$963$	0.417722	−	7.97060i	0.0134609	−	0.256849i
$964$	56.0825	−	62.2859i	1.80629	−	2.00609i
$965$	18.8712	−	3.50912i	0.607484	−	0.112963i
$966$	−1.08630	+	4.95481i	−0.0349510	+	0.159418i
$967$	3.14373	−	0.497917i	0.101095	−	0.0160119i	−0.105682	−	0.994400i	$-0.533702\pi$
$967$	3.14373	−	0.497917i	0.101095	−	0.0160119i	0.206777	+	0.978388i	$0.433702\pi$
$968$	4.32363	−	16.1360i	0.138967	−	0.518631i
$969$	−3.49470	+	1.55594i	−0.112266	+	0.0499841i
$970$	7.81446	−	42.3028i	0.250907	−	1.35826i
$971$	−19.0985	+	42.8958i	−0.612899	+	1.37659i	0.294228	+	0.955735i	$0.404937\pi$
$971$	−19.0985	+	42.8958i	−0.612899	+	1.37659i	−0.907127	+	0.420858i	$0.861729\pi$
$972$	29.1444	+	4.61602i	0.934808	+	0.148059i
$973$	13.5609	+	16.9667i	0.434742	+	0.543927i
$974$		−	60.5732i		−	1.94089i
$975$	1.94177	−	5.07645i	0.0621865	−	0.162577i
$976$	99.4284	+	57.4050i	3.18263	+	1.83749i
$977$	9.93213	−	6.45000i	0.317757	−	0.206354i	−0.375898	−	0.926661i	$-0.622666\pi$
$977$	9.93213	−	6.45000i	0.317757	−	0.206354i	0.693655	+	0.720307i	$0.255999\pi$
$978$	4.86383	−	1.86705i	0.155528	−	0.0597016i
$979$	21.8723	−	15.8912i	0.699042	−	0.507884i
$980$	58.0890	−	53.7949i	1.85559	−	1.71842i
$981$	11.1032	+	8.06691i	0.354496	+	0.257557i
$982$	−30.4485	−	8.15865i	−0.971651	−	0.260353i
$983$	15.2129	−	39.6310i	0.485217	−	1.26403i	−0.444507	−	0.895775i	$-0.646621\pi$
$983$	15.2129	−	39.6310i	0.485217	−	1.26403i	0.929724	−	0.368258i	$-0.120046\pi$
$984$	6.99707	−	6.30019i	0.223059	−	0.200843i
$985$	−2.06788	+	8.63585i	−0.0658880	+	0.275161i
$986$	−59.3358	+	19.2794i	−1.88964	+	0.613980i
$987$	−0.0897651	−	1.95117i	−0.00285725	−	0.0621064i
$988$	79.9799	−	40.7518i	2.54450	−	1.29649i
$989$	−28.9830	−	26.0964i	−0.921606	−	0.829818i
$990$	52.4148	+	1.34148i	1.66585	+	0.0426349i
$991$	28.8511	+	32.0424i	0.916484	+	1.01786i	0.999772	+	0.0213333i	$0.00679112\pi$
$991$	28.8511	+	32.0424i	0.916484	+	1.01786i	−0.0832882	+	0.996526i	$0.526542\pi$
$992$	−17.8624	+	14.4647i	−0.567133	+	0.459255i
$993$	2.98540	−	2.98540i	0.0947388	−	0.0947388i
$994$	−2.20200	−	1.29015i	−0.0698433	−	0.0409210i
$995$	−15.5185	+	22.6083i	−0.491970	+	0.716730i
$996$	−0.928160	−	0.413243i	−0.0294099	−	0.0130941i
$997$	−21.2277	+	26.2140i	−0.672287	+	0.830205i	−0.993141	−	0.116923i	$-0.962697\pi$
$997$	−21.2277	+	26.2140i	−0.672287	+	0.830205i	0.320854	+	0.947129i	$0.396030\pi$
$998$	13.7118	+	21.1143i	0.434040	+	0.668363i
$999$	0.882464	+	1.52847i	0.0279199	+	0.0483587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.1	yes	288
5.2	odd	4		875.2.bb.b.857.18		288
5.3	odd	4		875.2.bb.a.857.1		288
5.4	even	2		875.2.bb.c.143.18		288
7.5	odd	6	inner	175.2.x.a.33.1	✓	288
25.3	odd	20		875.2.bb.c.507.18		288
25.4	even	10		875.2.bb.a.493.18		288
25.21	even	5		875.2.bb.b.493.1		288
25.22	odd	20	inner	175.2.x.a.122.1	yes	288
35.12	even	12		875.2.bb.b.607.1		288
35.19	odd	6		875.2.bb.c.768.18		288
35.33	even	12		875.2.bb.a.607.18		288
175.47	even	60	inner	175.2.x.a.47.1	yes	288
175.54	odd	30		875.2.bb.a.243.1		288
175.96	odd	30		875.2.bb.b.243.18		288
175.103	even	60		875.2.bb.c.257.18		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.1	✓	288	7.5	odd	6	inner
175.2.x.a.47.1	yes	288	175.47	even	60	inner
175.2.x.a.108.1	yes	288	1.1	even	1	trivial
175.2.x.a.122.1	yes	288	25.22	odd	20	inner
875.2.bb.a.243.1		288	175.54	odd	30
875.2.bb.a.493.18		288	25.4	even	10
875.2.bb.a.607.18		288	35.33	even	12
875.2.bb.a.857.1		288	5.3	odd	4
875.2.bb.b.243.18		288	175.96	odd	30
875.2.bb.b.493.1		288	25.21	even	5
875.2.bb.b.607.1		288	35.12	even	12
875.2.bb.b.857.18		288	5.2	odd	4
875.2.bb.c.143.18		288	5.4	even	2
875.2.bb.c.257.18		288	175.103	even	60
875.2.bb.c.507.18		288	25.3	odd	20
875.2.bb.c.768.18		288	35.19	odd	6

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.139042 - 2.65307i) q^{2} +(0.171618 + 0.138973i) q^{3} +(-5.03041 + 0.528718i) q^{4} +(-2.22928 - 0.174120i) q^{5} +(0.344844 - 0.474637i) q^{6} +(-2.47603 + 0.932359i) q^{7} +(1.27096 + 8.02453i) q^{8} +(-0.613596 - 2.88674i) q^{9} +(-0.151991 + 5.93865i) q^{10} +(2.92528 + 0.621787i) q^{11} +(-0.936786 - 0.608356i) q^{12} +(-2.23475 - 4.38594i) q^{13} +(2.81788 + 6.43944i) q^{14} +(-0.358386 - 0.339692i) q^{15} +(11.2177 - 2.38441i) q^{16} +(-4.48584 - 1.72195i) q^{17} +(-7.57342 + 2.02929i) q^{18} +(0.376845 - 3.58544i) q^{19} +(11.3063 - 0.302763i) q^{20} +(-0.554503 - 0.184092i) q^{21} +(1.24291 - 7.84742i) q^{22} +(3.26342 - 0.171029i) q^{23} +(-0.897076 + 1.55378i) q^{24} +(4.93936 + 0.776324i) q^{25} +(-11.3255 + 6.53878i) q^{26} +(0.596641 - 1.17097i) q^{27} +(11.9625 - 5.99927i) q^{28} +(2.87272 + 3.95395i) q^{29} +(-0.851397 + 0.998054i) q^{30} +(-0.657478 - 1.47672i) q^{31} +(-3.68016 - 13.7345i) q^{32} +(0.415617 + 0.513245i) q^{33} +(-3.94475 + 12.1407i) q^{34} +(5.68209 - 1.64736i) q^{35} +(4.61291 + 14.1971i) q^{36} +(-0.731424 + 1.12629i) q^{37} +(-9.56484 - 0.501272i) q^{38} +(0.226006 - 1.06328i) q^{39} +(-1.43609 - 18.1102i) q^{40} +(-4.99103 - 1.62168i) q^{41} +(-0.411311 + 1.49673i) q^{42} +(-8.43891 - 8.43891i) q^{43} +(-15.0441 - 1.58120i) q^{44} +(0.865237 + 6.54219i) q^{45} +(-0.907502 - 8.63431i) q^{46} +(1.19805 + 3.12102i) q^{47} +(2.25653 + 1.14976i) q^{48} +(5.26142 - 4.61709i) q^{49} +(1.37287 - 13.2124i) q^{50} +(-0.530544 - 0.918929i) q^{51} +(13.5606 + 20.8816i) q^{52} +(-2.69056 + 3.32256i) q^{53} +(-3.18964 - 1.42012i) q^{54} +(-6.41299 - 1.89548i) q^{55} +(-10.6287 - 18.6840i) q^{56} +(0.562954 - 0.562954i) q^{57} +(10.0907 - 8.17129i) q^{58} +(0.374472 + 0.415893i) q^{59} +(1.98243 + 1.51931i) q^{60} +(7.43964 + 6.69868i) q^{61} +(-3.82643 + 1.94966i) q^{62} +(4.21076 + 6.57556i) q^{63} +(-14.1129 + 4.58555i) q^{64} +(4.21820 + 10.1666i) q^{65} +(1.30389 - 1.17403i) q^{66} +(3.34846 - 8.72305i) q^{67} +(23.4761 + 6.29039i) q^{68} +(0.583829 + 0.424177i) q^{69} +(-5.16061 - 14.8460i) q^{70} +(-0.293741 + 0.213415i) q^{71} +(22.3849 - 8.59275i) q^{72} +(2.45523 - 1.59444i) q^{73} +(3.08984 + 1.78392i) q^{74} +(0.739794 + 0.819671i) q^{75} +18.2355i q^{76} +(-7.82279 + 1.18785i) q^{77} +(-2.85237 - 0.451771i) q^{78} +(2.12904 - 4.78190i) q^{79} +(-25.4227 + 3.36227i) q^{80} +(-7.82313 + 3.48308i) q^{81} +(-3.60848 + 13.4670i) q^{82} +(0.898387 - 0.142291i) q^{83} +(2.88671 + 0.632885i) q^{84} +(9.70036 + 4.61979i) q^{85} +(-21.2157 + 23.5624i) q^{86} +(-0.0564851 + 1.07780i) q^{87} +(-1.27163 + 24.2642i) q^{88} +(6.04903 - 6.71813i) q^{89} +(17.2366 - 3.20517i) q^{90} +(9.62257 + 8.77612i) q^{91} +(-16.3259 + 2.58577i) q^{92} +(0.0923897 - 0.344803i) q^{93} +(8.11372 - 3.61246i) q^{94} +(-1.46439 + 7.92734i) q^{95} +(1.27715 - 2.86853i) q^{96} +(-7.15230 - 1.13281i) q^{97} +(-12.9810 - 13.3169i) q^{98} -8.82604i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more