LMFDB - Embedded newform 175.2.x.a.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			47.1
Character	$\chi$	$=$	175.47
Dual form			175.2.x.a.108.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.139042 + 2.65307i) q^{2} +(0.171618 - 0.138973i) q^{3} +(-5.03041 - 0.528718i) q^{4} +(-2.22928 + 0.174120i) q^{5} +(0.344844 + 0.474637i) q^{6} +(-2.47603 - 0.932359i) q^{7} +(1.27096 - 8.02453i) q^{8} +(-0.613596 + 2.88674i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{20}\right)$

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	0.293496	+	0.955960i	$0.405181\pi$
$2$	−0.139042	+	2.65307i	−0.0983173	+	1.87601i	−0.391813	+	0.920045i	$0.628152\pi$
$3$	0.171618	−	0.138973i	0.0990835	−	0.0802363i	−0.578499	−	0.815683i	$-0.696361\pi$
$3$	0.171618	−	0.138973i	0.0990835	−	0.0802363i	0.677582	+	0.735447i	$0.263028\pi$
$4$	−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	0.255421	−	0.966830i	$-0.417786\pi$
$11$	2.92528	−	0.621787i	0.882004	−	0.187476i	0.626583	+	0.779354i	$0.284453\pi$
$12$	−0.936786	+	0.608356i	−0.270427	+	0.175617i
$13$	−2.23475	+	4.38594i	−0.619808	+	1.21644i	0.341218	+	0.939984i	$0.389161\pi$
$13$	−2.23475	+	4.38594i	−0.619808	+	1.21644i	−0.961026	+	0.276458i	$0.910839\pi$
$14$	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	−0.835232	−	0.549898i	$-0.814666\pi$
$17$	−4.48584	+	1.72195i	−1.08798	+	0.417635i	−0.252744	+	0.967533i	$0.581333\pi$
$18$	−7.57342	−	2.02929i	−1.78507	−	0.478309i
$19$	0.376845	+	3.58544i	0.0864543	+	0.822557i	0.948723	+	0.316107i	$0.102376\pi$
$19$	0.376845	+	3.58544i	0.0864543	+	0.822557i	−0.862269	+	0.506450i	$0.830957\pi$
$20$	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	0.389440	−	0.921052i	$-0.372669\pi$
$23$	3.26342	+	0.171029i	0.680470	+	0.0356619i	0.291030	+	0.956714i	$0.406002\pi$
$24$	−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	−0.454201	−	0.890899i	$-0.650075\pi$
$29$	2.87272	−	3.95395i	0.533450	−	0.734231i	0.987651	+	0.156668i	$0.0500753\pi$
$30$	−0.851397	−	0.998054i	−0.155443	−	0.182219i
$31$	−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	$0.179704\pi$
$32$	−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	0.773422	−	0.633891i	$-0.218543\pi$
$37$	−0.731424	−	1.12629i	−0.120245	−	0.185162i	−0.893668	+	0.448730i	$0.851877\pi$
$38$	−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	−0.671613	−	0.740902i	$-0.734398\pi$
$41$	−4.99103	+	1.62168i	−0.779468	+	0.253264i	−0.107855	+	0.994167i	$0.534398\pi$
$42$	−0.411311	−	1.49673i	−0.0634667	−	0.230951i
$43$	−8.43891	+	8.43891i	−1.28692	+	1.28692i	−0.350276	+	0.936647i	$0.613912\pi$
$43$	−8.43891	+	8.43891i	−1.28692	+	1.28692i	−0.936647	+	0.350276i	$0.886088\pi$
$44$	−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	−0.818029	−	0.575177i	$-0.804933\pi$
$47$	1.19805	−	3.12102i	0.174753	−	0.455248i	0.992782	+	0.119929i	$0.0382666\pi$
$48$	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	0.558100	−	0.829774i	$-0.311531\pi$
$53$	−2.69056	−	3.32256i	−0.369577	−	0.456389i	−0.927677	+	0.373384i	$0.878197\pi$
$54$	−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	−0.718276	−	0.695759i	$-0.755068\pi$
$59$	0.374472	−	0.415893i	0.0487521	−	0.0541447i	0.767028	+	0.641614i	$0.221735\pi$
$60$	1.98243	−	1.51931i	0.255931	−	0.196142i
$61$	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	$0.0452320\pi$
$62$	−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	0.971122	+	0.238582i	$0.0766824\pi$
$67$	3.34846	+	8.72305i	0.409080	+	1.06569i	−0.562042	+	0.827108i	$0.689984\pi$
$68$	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	0.570218	−	0.821493i	$-0.306859\pi$
$71$	−0.293741	−	0.213415i	−0.0348607	−	0.0253278i	−0.605079	+	0.796165i	$0.706859\pi$
$72$	22.3849	+	8.59275i	2.63808	+	1.01267i
$73$	2.45523	+	1.59444i	0.287363	+	0.186615i	0.680268	−	0.732963i	$-0.261863\pi$
$73$	2.45523	+	1.59444i	0.287363	+	0.186615i	−0.392905	+	0.919579i	$0.628530\pi$
$74$	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	0.992810	−	0.119701i	$-0.0381935\pi$
$79$	2.12904	+	4.78190i	0.239536	+	0.538006i	−0.753274	+	0.657706i	$0.771527\pi$
$80$	−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	0.205545	−	0.978648i	$-0.434103\pi$
$83$	0.898387	+	0.142291i	0.0986108	+	0.0156184i	−0.106934	+	0.994266i	$0.534103\pi$
$84$	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	0.972890	−	0.231267i	$-0.0742870\pi$
$89$	6.04903	+	6.71813i	0.641196	+	0.712120i	−0.331695	+	0.943387i	$0.607620\pi$
$90$	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	−0.508583	−	0.861013i	$-0.669830\pi$
$97$	−7.15230	+	1.13281i	−0.726206	+	0.115020i	−0.217624	+	0.976033i	$0.569830\pi$
$98$	−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	−0.377467	−	0.926023i	$-0.623205\pi$
$101$	2.36935	−	1.36795i	0.235759	−	0.136116i	0.613226	+	0.789907i	$0.289871\pi$
$102$	−2.36422	−	1.53534i	−0.234092	−	0.152021i
$103$	0.623225	+	0.239234i	0.0614082	+	0.0235724i	0.388878	−	0.921289i	$-0.372863\pi$
$103$	0.623225	+	0.239234i	0.0614082	+	0.0235724i	−0.327470	+	0.944862i	$0.606196\pi$
$104$	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	−0.130327	−	0.991471i	$-0.541603\pi$
$107$	2.61232	−	0.699970i	0.252543	−	0.0676686i	0.382869	+	0.923802i	$0.374936\pi$
$108$	−2.38224	−	6.20594i	−0.229231	−	0.597167i
$109$	−3.45588	−	3.11169i	−0.331013	−	0.298046i	0.486818	−	0.873503i	$-0.338157\pi$
$109$	−3.45588	−	3.11169i	−0.331013	−	0.298046i	−0.817832	+	0.575458i	$0.804824\pi$
$110$	−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	0.991112	−	0.133026i	$-0.0424695\pi$
$113$	15.5844	+	7.94063i	1.46605	+	0.746991i	0.474941	+	0.880018i	$0.342470\pi$
$114$	−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	−0.647819	−	0.761794i	$-0.724319\pi$
$127$	−4.64631	+	2.36741i	−0.412293	+	0.210074i	0.235526	+	0.971868i	$0.424319\pi$
$128$	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	0.0603664	−	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
$133$	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	0.118858	−	0.992911i	$-0.462077\pi$
$137$	3.98957	−	0.209084i	0.340852	−	0.0178633i	0.221994	+	0.975048i	$0.428743\pi$
$138$	1.04419	+	1.60792i	0.0888877	+	0.136875i
$139$	−2.53686	+	7.80766i	−0.215174	+	0.662237i	0.783967	+	0.620802i	$0.213193\pi$
$139$	−2.53686	+	7.80766i	−0.215174	+	0.662237i	−0.999141	+	0.0414349i	$0.986807\pi$
$140$	−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	−0.998282	−	0.0585846i	$-0.981341\pi$
$149$	−18.8977	−	10.9106i	−1.54816	−	0.893830i	−0.549877	−	0.835246i	$-0.685325\pi$
$150$	2.07178	+	2.07670i	0.169160	+	0.169561i
$151$	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	$0.802124\pi$
$152$	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	−0.720703	−	0.693244i	$-0.756181\pi$
$157$	−21.1941	−	5.67894i	−1.69147	−	0.453229i	−0.970769	+	0.240016i	$0.922847\pi$
$158$	−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	−0.218973	−	0.975731i	$-0.570271\pi$
$163$	7.44756	−	4.83650i	0.583338	−	0.378824i	0.802310	+	0.596907i	$0.203604\pi$
$164$	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	0.838873	+	0.544327i	$0.183215\pi$
$167$	−1.64313	+	10.3743i	−0.127149	+	0.802786i	−0.966022	+	0.258460i	$0.916785\pi$
$168$	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	−0.691994	−	0.721903i	$-0.743268\pi$
$173$	0.942653	−	17.9869i	0.0716686	−	1.36752i	0.763663	−	0.645615i	$-0.223399\pi$
$174$	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	0.342681	−	0.939452i	$-0.388665\pi$
$179$	6.45610	+	0.678563i	0.482552	+	0.0507182i	0.139870	+	0.990170i	$0.455332\pi$
$180$	−7.81147	+	32.4525i	−0.582233	+	2.41886i
$181$	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	$0.572466\pi$
$182$	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	0.615586	−	0.788070i	$-0.288920\pi$
$191$	11.8497	+	2.51873i	0.857414	+	0.182249i	0.241828	+	0.970319i	$0.422253\pi$
$192$	−3.05929	+	1.17435i	−0.220785	+	0.0847515i
$193$	−8.29161	−	2.22173i	−0.596843	−	0.159924i	−0.0522644	−	0.998633i	$-0.516644\pi$
$193$	−8.29161	−	2.22173i	−0.596843	−	0.159924i	−0.544579	+	0.838710i	$0.683311\pi$
$194$	−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	0.999885	−	0.0151331i	$-0.00481720\pi$
$197$	0.621240	+	3.92235i	0.0442615	+	0.279456i	−0.955624	+	0.294589i	$0.904817\pi$
$198$	−23.4161	−	1.22719i	−1.66411	−	0.0872124i
$199$	6.13171	+	10.6204i	0.434666	+	0.752863i	0.997268	−	0.0738644i	$-0.0235332\pi$
$199$	6.13171	+	10.6204i	0.434666	+	0.752863i	−0.562603	+	0.826727i	$0.690200\pi$
$200$	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	0.389950	+	0.920836i	$0.372492\pi$
$211$	−6.78037	+	20.8678i	−0.466780	+	1.43660i	−0.856730	+	0.515765i	$0.827508\pi$
$212$	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	−0.411125	−	0.911579i	$-0.634864\pi$
$223$	1.26491	−	0.644506i	0.0847049	−	0.0431593i	0.495830	+	0.868420i	$0.334864\pi$
$224$	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	0.227692	−	0.973733i	$-0.426882\pi$
$227$	15.4376	−	23.7719i	1.02463	−	1.57779i	0.796939	−	0.604060i	$-0.206451\pi$
$228$	−2.53425	−	3.12954i	−0.167835	−	0.207259i
$229$	0.553987	−	0.246651i	0.0366085	−	0.0162992i	−0.388351	−	0.921512i	$-0.626955\pi$
$229$	0.553987	−	0.246651i	0.0366085	−	0.0162992i	0.424959	+	0.905212i	$0.360288\pi$
$230$	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	0.736999	−	0.675894i	$-0.236242\pi$
$233$	3.49716	+	2.83194i	0.229106	+	0.185527i	−0.507893	+	0.861420i	$0.669575\pi$
$234$	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	−0.124534	−	0.992215i	$-0.539744\pi$
$239$	−12.4990	−	4.06118i	−0.808494	−	0.262696i	−0.683960	+	0.729520i	$0.739744\pi$
$240$	−4.83024	+	2.95605i	−0.311791	+	0.190812i
$241$	−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	$0.912528\pi$
$242$	−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	$-0.764796\pi$
$251$		−	21.3400i		−	1.34697i	0.739200	−	0.673486i	$-0.235204\pi$
$252$	−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	0.872236	+	0.489085i	$0.162669\pi$
$257$	5.79368	+	21.6223i	0.361400	+	1.34876i	−0.510836	+	0.859678i	$0.670664\pi$
$258$	−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	0.691880	+	0.722012i	$0.256783\pi$
$263$	1.28540	+	24.5269i	0.0792610	+	1.51239i	−0.612619	+	0.790378i	$0.709884\pi$
$264$	−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	−0.383390	−	0.923587i	$-0.625243\pi$
$269$	−21.7527	−	9.68493i	−1.32629	−	0.590501i	−0.942897	+	0.333086i	$0.891910\pi$
$270$	6.86332	−	3.72122i	0.417688	−	0.226466i
$271$	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	$0.535171\pi$
$272$	−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	0.811581	−	0.584240i	$-0.198607\pi$
$277$	10.1183	+	6.57090i	0.607950	+	0.394807i	−0.203631	+	0.979048i	$0.565274\pi$
$278$	−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	−0.394668	−	0.918824i	$-0.629140\pi$
$281$	5.98822	−	4.35069i	0.357227	−	0.259541i	0.751895	+	0.659283i	$0.229140\pi$
$282$	1.89449	−	0.507628i	0.112815	−	0.0302288i
$283$	−9.16617	−	23.8787i	−0.544872	−	1.41944i	−0.878959	−	0.476898i	$-0.841761\pi$
$283$	−9.16617	−	23.8787i	−0.544872	−	1.41944i	0.334087	−	0.942542i	$-0.391572\pi$
$284$	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	0.646756	−	0.762697i	$-0.276125\pi$
$293$	−1.98458	−	1.98458i	−0.115941	−	0.115941i	−0.762697	+	0.646756i	$0.776125\pi$
$294$	−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	−0.0269795	−	0.999636i	$-0.508589\pi$
$307$	17.0423	−	17.0423i	0.972656	−	0.972656i	0.999636	+	0.0269795i	$0.00858889\pi$
$308$	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	0.749161	+	0.662388i	$0.230457\pi$
$311$	5.89343	+	27.7264i	0.334186	+	1.57222i	−0.414975	+	0.909833i	$0.636210\pi$
$312$	8.81953	−	0.462212i	0.499308	−	0.0261676i
$313$	11.7313	+	18.0646i	0.663091	+	1.02107i	0.996919	+	0.0784364i	$0.0249927\pi$
$313$	11.7313	+	18.0646i	0.663091	+	1.02107i	−0.333828	+	0.942634i	$0.608341\pi$
$314$	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	−0.773138	−	0.634238i	$-0.781314\pi$
$317$	0.142171	−	0.175566i	0.00798511	−	0.00986079i	0.781123	+	0.624377i	$0.214647\pi$
$318$	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	0.901099	+	0.433614i	$0.142762\pi$
$331$	1.99845	+	19.0140i	0.109845	+	1.04510i	−0.791254	+	0.611488i	$0.790571\pi$
$332$	−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	−0.909132	−	0.416507i	$-0.863254\pi$
$337$	−0.693845	+	1.36175i	−0.0377961	+	0.0741791i	0.871336	+	0.490687i	$0.163254\pi$
$338$	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	−0.118714	−	0.992929i	$-0.537877\pi$
$347$	15.4209	−	12.4876i	0.827835	−	0.670368i	0.946549	+	0.322561i	$0.104544\pi$
$348$	−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	0.120029	−	0.992770i	$-0.461701\pi$
$353$	20.9689	−	16.9803i	1.11606	−	0.903768i	0.996031	+	0.0890029i	$0.0283680\pi$
$354$	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	0.832686	+	0.553746i	$0.186802\pi$
$359$	−2.90347	+	13.6598i	−0.153239	+	0.720934i	−0.985925	+	0.167188i	$0.946531\pi$
$360$	−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	0.452317	−	0.891857i	$-0.350598\pi$
$367$	26.5370	−	10.1866i	1.38522	−	0.531737i	0.932906	+	0.360120i	$0.117264\pi$
$368$	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	0.614741	−	0.788729i	$-0.289261\pi$
$373$	22.0879	+	1.15758i	1.14367	+	0.0599372i	0.528929	+	0.848666i	$0.322594\pi$
$374$	−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	0.106747	−	0.994286i	$-0.465956\pi$
$379$	19.8453	−	27.3147i	1.01938	−	1.40306i	0.912636	−	0.408774i	$-0.134044\pi$
$380$	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	0.414725	−	0.909947i	$-0.363878\pi$
$383$	23.8477	−	29.4495i	1.21856	−	1.50480i	0.803836	−	0.594851i	$-0.202789\pi$
$384$	−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	0.993033	+	0.117836i	$0.0375958\pi$
$389$	2.63857	+	12.4135i	0.133781	+	0.629388i	−0.859252	+	0.511552i	$0.829071\pi$
$390$	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	0.448364	+	0.893851i	$0.352007\pi$
$397$	−9.62248	+	25.0674i	−0.482938	+	1.25810i	−0.931303	+	0.364246i	$0.881327\pi$
$398$	−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	−0.836185	−	0.548447i	$-0.815219\pi$
$401$	1.13896	−	1.97273i	0.0568769	−	0.0985137i	0.893062	+	0.449934i	$0.148552\pi$
$402$	−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	0.0377539	+	0.999287i	$0.487980\pi$
$409$	−19.4149	+	21.5624i	−0.960005	+	1.06619i	−0.997759	+	0.0669069i	$0.978687\pi$
$410$	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	−0.688704	−	0.725043i	$-0.741820\pi$
$419$	−4.33888	+	3.15238i	−0.211968	+	0.154004i	0.476736	+	0.879047i	$0.341820\pi$
$420$	−6.32509	+	1.91351i	−0.308633	+	0.0933698i
$421$	−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	$0.852593\pi$
$422$	−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	−0.175145	−	0.984543i	$-0.556039\pi$
$431$	−21.2587	−	9.46500i	−1.02400	−	0.455913i	−0.848853	+	0.528630i	$0.822706\pi$
$432$	3.90089	+	14.5583i	0.187682	+	0.700438i
$433$	−5.95872	−	0.943769i	−0.286358	−	0.0453546i	0.0116031	−	0.999933i	$-0.496307\pi$
$433$	−5.95872	−	0.943769i	−0.286358	−	0.0453546i	−0.297961	+	0.954578i	$0.596307\pi$
$434$	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	0.958733	+	0.284307i	$0.0917636\pi$
$439$	23.9122	+	26.5572i	1.14127	+	1.26751i	0.182535	+	0.983199i	$0.441570\pi$
$440$	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	0.965988	+	0.258586i	$0.0832567\pi$
$443$	5.44524	+	20.3219i	0.258711	+	0.965523i	−0.707277	+	0.706936i	$0.750077\pi$
$444$	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	$-0.867250\pi$
$449$		−	17.1662i		−	0.810122i	0.914290	−	0.405061i	$-0.132750\pi$
$450$	−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	0.306819	−	0.951768i	$-0.400735\pi$
$457$	22.4126	−	6.00543i	1.04842	−	0.280922i	0.741597	+	0.670845i	$0.234069\pi$
$458$	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	0.655923	−	0.754828i	$-0.272280\pi$
$461$	15.9507	+	5.18270i	0.742899	+	0.241383i	0.0869763	+	0.996210i	$0.472280\pi$
$462$	−2.13385	−	4.12261i	−0.0992756	−	0.191801i
$463$	−25.0376	−	12.7573i	−1.16360	−	0.592882i	−0.237952	−	0.971277i	$-0.576476\pi$
$463$	−25.0376	−	12.7573i	−1.16360	−	0.592882i	−0.925644	+	0.378395i	$0.876476\pi$
$464$	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	0.726429	−	0.687242i	$-0.241179\pi$
$467$	4.43522	+	3.59157i	0.205238	+	0.166198i	−0.521191	+	0.853440i	$0.674512\pi$
$468$	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	−0.854193	−	0.519957i	$-0.825948\pi$
$479$	1.95747	−	18.6240i	0.0894389	−	0.850954i	0.943632	−	0.330998i	$-0.107385\pi$
$480$	−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	0.471065	−	0.882098i	$-0.343870\pi$
$487$	22.7688	−	1.19326i	1.03175	−	0.0540719i	0.560689	+	0.828027i	$0.310536\pi$
$488$	−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	0.999071	−	0.0431034i	$-0.0137245\pi$
$491$	3.66657	+	11.2845i	0.165470	+	0.509264i	−0.833601	+	0.552368i	$0.813724\pi$
$492$	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	0.304930	−	0.952375i	$-0.401367\pi$
$499$	−8.20677	−	4.73818i	−0.367385	−	0.212110i	−0.672316	+	0.740265i	$0.734700\pi$
$500$	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	0.952650	+	0.304069i	$0.0983452\pi$
$503$	3.15307	+	19.9077i	0.140588	+	0.887640i	−0.812062	+	0.583572i	$0.801655\pi$
$504$	−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	−0.193727	−	0.981055i	$-0.562058\pi$
$509$	−17.3660	−	3.69127i	−0.769737	−	0.163613i	−0.576010	+	0.817443i	$0.695391\pi$
$510$	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	0.420115	−	0.907471i	$-0.361990\pi$
$521$	14.6625	+	1.54109i	0.642376	+	0.0675164i	0.222261	+	0.974987i	$0.428656\pi$
$522$	−29.7800	+	24.1154i	−1.30344	+	1.05550i
$523$	−0.217309	+	4.14649i	−0.00950224	+	0.181314i	0.989755	+	0.142777i	$0.0456031\pi$
$523$	−0.217309	+	4.14649i	−0.00950224	+	0.181314i	−0.999257	+	0.0385369i	$0.987730\pi$
$524$	−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	−0.477216	−	0.878786i	$-0.658354\pi$
$541$	−29.5536	−	6.28181i	−1.27061	−	0.270076i	−0.793393	+	0.608710i	$0.791687\pi$
$542$	−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	0.956472	−	0.291824i	$-0.0942622\pi$
$547$	−1.01423	−	6.40362i	−0.0433655	−	0.273799i	−0.999838	+	0.0180249i	$0.994262\pi$
$548$	−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	−0.864989	−	0.501791i	$-0.832675\pi$
$557$	3.18632	−	11.8915i	0.135009	−	0.503860i	0.999998	−	0.00206894i	$-0.000658565\pi$
$558$	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	0.127968	−	0.991778i	$-0.459155\pi$
$563$	8.51592	−	0.446300i	0.358903	−	0.0188093i	0.230936	+	0.972969i	$0.425821\pi$
$564$	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	−0.730468	−	0.682947i	$-0.760698\pi$
$569$	−31.0809	+	3.26674i	−1.30298	+	0.136949i	−0.572512	+	0.819896i	$0.694031\pi$
$570$	3.25762	−	3.42875i	0.136447	−	0.143615i
$571$	−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	$0.976772\pi$
$572$	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	−0.961224	−	0.275769i	$-0.911068\pi$
$577$	−7.64659	+	11.7747i	−0.318332	+	0.490188i	0.642892	+	0.765957i	$0.277734\pi$
$578$	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	0.776740	−	0.629822i	$-0.216872\pi$
$587$	17.5353	+	8.93468i	0.723759	+	0.368774i	−0.0529805	+	0.998596i	$0.516872\pi$
$588$	−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	−0.340647	−	0.940191i	$-0.610646\pi$
$593$	−4.03167	+	1.08028i	−0.165561	+	0.0443619i	0.175086	+	0.984553i	$0.443980\pi$
$594$	−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	−0.504750	−	0.863265i	$-0.668416\pi$
$599$	−0.232901	+	0.134465i	−0.00951606	+	0.00549410i	0.495234	+	0.868759i	$0.335082\pi$
$600$	−5.63722	−	6.97827i	−0.230139	−	0.284887i
$601$		−	10.5831i		−	0.431694i	−0.976427	−	0.215847i	$-0.930749\pi$
$601$		−	10.5831i		−	0.431694i	0.976427	−	0.215847i	$-0.0692513\pi$
$602$	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	0.959058	−	0.283209i	$-0.0913992\pi$
$607$	−0.323127	−	1.20593i	−0.0131153	−	0.0489470i	−0.972173	+	0.234262i	$0.924732\pi$
$608$	−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	0.867485	+	0.497463i	$0.165735\pi$
$613$	1.40509	+	26.8108i	0.0567512	+	1.08288i	−0.810734	+	0.585415i	$0.800932\pi$
$614$	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	−0.0297232	−	0.999558i	$-0.509463\pi$
$617$	−9.11291	−	1.44334i	−0.366872	−	0.0581068i	−0.337149	+	0.941451i	$0.609463\pi$
$618$	0.101366	+	0.378304i	0.00407755	+	0.0152176i
$619$	7.43093	+	3.30846i	0.298674	+	0.132978i	0.550602	−	0.834768i	$-0.314398\pi$
$619$	7.43093	+	3.30846i	0.298674	+	0.132978i	−0.251928	+	0.967746i	$0.581065\pi$
$620$	−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	−0.970119	−	0.242629i	$-0.921990\pi$
$631$	−26.1031	+	18.9650i	−1.03915	+	0.754985i	−0.0690289	+	0.997615i	$0.521990\pi$
$632$	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	−0.217907	−	0.975970i	$-0.569923\pi$
$641$	19.6339	−	21.8057i	0.775494	−	0.861273i	0.993401	+	0.114697i	$0.0365896\pi$
$642$	1.23308	+	0.998525i	0.0486656	+	0.0394086i
$643$	−23.5100	−	23.5100i	−0.927145	−	0.927145i	0.0703751	−	0.997521i	$-0.477580\pi$
$643$	−23.5100	−	23.5100i	−0.927145	−	0.927145i	−0.997521	+	0.0703751i	$0.977580\pi$
$644$	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	0.797639	−	0.603135i	$-0.206082\pi$
$647$	1.06439	+	1.31441i	0.0418455	+	0.0516749i	−0.755794	+	0.654810i	$0.772749\pi$
$648$	−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	−0.999875	−	0.0158035i	$-0.994969\pi$
$653$	−6.29260	+	16.3928i	−0.246249	+	0.641499i	0.753627	+	0.657303i	$0.228303\pi$
$654$	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	−0.535684	−	0.844419i	$-0.679946\pi$
$659$	−12.1353	+	3.94299i	−0.472724	+	0.153597i	0.0629598	+	0.998016i	$0.479946\pi$
$660$	4.85447	−	5.67704i	0.188960	−	0.220979i
$661$	−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	$-0.419481\pi$
$662$	−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	0.990006	+	0.141028i	$0.0450409\pi$
$673$	13.5468	+	26.5870i	0.522189	+	1.02485i	−0.467816	+	0.883826i	$0.654959\pi$
$674$	−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	−0.510362	−	0.859960i	$-0.670488\pi$
$677$	−28.8246	−	1.51063i	−1.10782	−	0.0580583i	−0.597456	+	0.801902i	$0.703822\pi$
$678$	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	−0.624782	−	0.780800i	$-0.714812\pi$
$683$	−14.8084	+	5.68441i	−0.566628	+	0.217508i	0.0581537	+	0.998308i	$0.481479\pi$
$684$	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	−0.973201	−	0.229957i	$-0.926141\pi$
$691$	0.246952	−	1.16182i	0.00939451	−	0.0441977i	0.982595	+	0.185760i	$0.0594746\pi$
$692$	−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	−0.858987	−	0.511997i	$-0.828906\pi$
$709$	3.56761	−	16.7843i	0.133985	−	0.630348i	0.992972	−	0.118351i	$-0.0377608\pi$
$710$	−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	0.853392	+	0.521269i	$0.174541\pi$
$719$	3.40612	+	32.4070i	0.127027	+	1.20858i	−0.726366	+	0.687309i	$0.758792\pi$
$720$	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	0.598446	−	0.801163i	$-0.295785\pi$
$727$	−10.8247	−	21.2447i	−0.401466	−	0.787922i	−0.999912	+	0.0132413i	$0.995785\pi$
$728$	−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	−0.243576	−	0.969882i	$-0.578321\pi$
$733$	20.4613	−	25.2676i	0.755754	−	0.933278i	0.999330	+	0.0366035i	$0.0116538\pi$
$734$	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	−0.414753	−	0.909934i	$-0.636132\pi$
$739$	−11.0359	−	51.9197i	−0.405961	−	1.90990i	0.00879226	−	0.999961i	$-0.497201\pi$
$740$	−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	−0.390001	+	0.920814i	$0.627526\pi$
$743$	−35.7302	+	35.7302i	−1.31082	+	1.31082i	−0.920814	+	0.390001i	$0.872474\pi$
$744$	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	−0.179886	−	0.983688i	$-0.557573\pi$
$751$	20.8809	−	36.1668i	0.761956	−	1.31975i	0.941841	−	0.336058i	$-0.109094\pi$
$752$	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	0.171487	−	0.985186i	$-0.445143\pi$
$757$	−22.3878	−	22.3878i	−0.813699	−	0.813699i	−0.985186	+	0.171487i	$0.945143\pi$
$758$	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	−0.950439	−	0.310912i	$-0.899366\pi$
$761$	−20.4298	+	18.3950i	−0.740578	+	0.666820i	0.209860	+	0.977731i	$0.432699\pi$
$762$	−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
$767$

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.139042 + 2.65307i) q^{2} +(0.171618 - 0.138973i) q^{3} +(-5.03041 - 0.528718i) q^{4} +(-2.22928 + 0.174120i) q^{5} +(0.344844 + 0.474637i) q^{6} +(-2.47603 - 0.932359i) q^{7} +(1.27096 - 8.02453i) q^{8} +(-0.613596 + 2.88674i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 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

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