LMFDB - Embedded newform 230.2.l.a.83.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			83.4
Character	$\chi$	$=$	230.83
Dual form			230.2.l.a.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.479249 + 0.877679i) q^{2} +(0.0160392 - 0.224257i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(-1.80481 + 1.32009i) q^{5} +(0.189139 + 0.121552i) q^{6} +(3.97650 - 1.48316i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(2.91943 + 0.419751i) q^{9} +O(q^{10})$	\(q+(-0.479249 + 0.877679i) q^{2} +(0.0160392 - 0.224257i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(-1.80481 + 1.32009i) q^{5} +(0.189139 + 0.121552i) q^{6} +(3.97650 - 1.48316i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(2.91943 + 0.419751i) q^{9} +(-0.293662 - 2.21670i) q^{10} +(-0.850780 + 2.89749i) q^{11} +(-0.197328 + 0.107749i) q^{12} +(-2.04842 + 5.49203i) q^{13} +(-0.603997 + 4.20089i) q^{14} +(0.267092 + 0.425915i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(0.313276 + 1.44011i) q^{17} +(-1.76754 + 2.36116i) q^{18} +(4.78140 - 3.07282i) q^{19} +(2.08629 + 0.804611i) q^{20} +(-0.268828 - 0.915545i) q^{21} +(-2.13533 - 2.13533i) q^{22} +(-2.36877 + 4.17000i) q^{23} -0.224830i q^{24} +(1.51471 - 4.76504i) q^{25} +(-3.83854 - 4.42991i) q^{26} +(0.284330 - 1.30704i) q^{27} +(-3.39757 - 2.54339i) q^{28} +(3.42485 - 5.32917i) q^{29} +(-0.501820 + 0.0303016i) q^{30} +(1.79209 - 2.06819i) q^{31} +(-0.599278 - 0.800541i) q^{32} +(0.636136 + 0.237266i) q^{33} +(-1.41409 - 0.415214i) q^{34} +(-5.21894 + 7.92617i) q^{35} +(-1.22525 - 2.68292i) q^{36} +(-5.02392 + 3.76086i) q^{37} +(0.405468 + 5.66918i) q^{38} +(1.19877 + 0.547460i) q^{39} +(-1.70604 + 1.44548i) q^{40} +(-0.610534 - 4.24636i) q^{41} +(0.932390 + 0.202829i) q^{42} +(2.13268 + 0.152532i) q^{43} +(2.89749 - 0.850780i) q^{44} +(-5.82314 + 3.09635i) q^{45} +(-2.52469 - 4.07749i) q^{46} +(1.03690 - 1.03690i) q^{47} +(0.197328 + 0.107749i) q^{48} +(8.32253 - 7.21151i) q^{49} +(3.45626 + 3.61307i) q^{50} +(0.327979 - 0.0471562i) q^{51} +(5.72765 - 1.24598i) q^{52} +(-2.92896 - 7.85285i) q^{53} +(1.01090 + 0.875950i) q^{54} +(-2.28946 - 6.35254i) q^{55} +(3.86056 - 1.76306i) q^{56} +(-0.612411 - 1.12155i) q^{57} +(3.03595 + 5.55992i) q^{58} +(-9.55015 + 4.36141i) q^{59} +(0.213902 - 0.454959i) q^{60} +(-8.07789 - 6.99953i) q^{61} +(0.956345 + 2.56406i) q^{62} +(12.2317 - 2.66084i) q^{63} +(0.989821 - 0.142315i) q^{64} +(-3.55297 - 12.6162i) q^{65} +(-0.513111 + 0.444614i) q^{66} +(-3.85770 - 2.10646i) q^{67} +(1.04213 - 1.04213i) q^{68} +(0.897158 + 0.598097i) q^{69} +(-4.45546 - 8.37916i) q^{70} +(7.76304 - 2.27943i) q^{71} +(2.94194 + 0.210411i) q^{72} +(-5.59835 - 1.21785i) q^{73} +(-0.893119 - 6.21178i) q^{74} +(-1.04430 - 0.416112i) q^{75} +(-5.17004 - 2.36108i) q^{76} +(0.914309 + 12.7837i) q^{77} +(-1.05500 + 0.789766i) q^{78} +(4.78369 + 10.4748i) q^{79} +(-0.451051 - 2.19010i) q^{80} +(8.20138 + 2.40814i) q^{81} +(4.01954 + 1.49921i) q^{82} +(-0.282133 - 0.376886i) q^{83} +(-0.624866 + 0.721134i) q^{84} +(-2.46648 - 2.18557i) q^{85} +(-1.15596 + 1.79871i) q^{86} +(-1.14017 - 0.853521i) q^{87} +(-0.641908 + 2.95080i) q^{88} +(-6.58045 - 7.59424i) q^{89} +(0.0731368 - 6.59477i) q^{90} +24.8772i q^{91} +(4.78868 - 0.261733i) q^{92} +(-0.435061 - 0.435061i) q^{93} +(0.413134 + 1.40701i) q^{94} +(-4.57314 + 11.8578i) q^{95} +(-0.189139 + 0.121552i) q^{96} +(7.75416 - 10.3583i) q^{97} +(2.34083 + 10.7606i) q^{98} +(-3.70002 + 8.10191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.479249	+	0.877679i	−0.338880	+	0.620613i
$2$	−0.479249	+	0.877679i	−0.338880	+	0.620613i
$3$	0.0160392	−	0.224257i	0.00926021	−	0.129475i	−0.990719	−	0.135926i	$-0.956599\pi$
$3$	0.0160392	−	0.224257i	0.00926021	−	0.129475i	0.999979	+	0.00645144i	$0.00205357\pi$
$4$	−0.540641	−	0.841254i	−0.270320	−	0.420627i
$5$	−1.80481	+	1.32009i	−0.807138	+	0.590363i
$5$	−1.80481	+	1.32009i	−0.807138	+	0.590363i
$6$	0.189139	+	0.121552i	0.0772155	+	0.0496234i
$7$	3.97650	−	1.48316i	1.50297	−	0.560581i	0.542771	−	0.839881i	$-0.317375\pi$
$7$	3.97650	−	1.48316i	1.50297	−	0.560581i	0.960204	+	0.279300i	$0.0901024\pi$
$8$	0.997452	−	0.0713392i	0.352653	−	0.0252222i
$9$	2.91943	+	0.419751i	0.973144	+	0.139917i
$10$	−0.293662	−	2.21670i	−0.0928640	−	0.700982i
$11$	−0.850780	+	2.89749i	−0.256520	+	0.873626i	0.726036	+	0.687657i	$0.241361\pi$
$11$	−0.850780	+	2.89749i	−0.256520	+	0.873626i	−0.982556	+	0.185969i	$0.940457\pi$
$12$	−0.197328	+	0.107749i	−0.0569637	+	0.0311046i
$13$	−2.04842	+	5.49203i	−0.568130	+	1.52322i	0.261671	+	0.965157i	$0.415727\pi$
$13$	−2.04842	+	5.49203i	−0.568130	+	1.52322i	−0.829801	+	0.558059i	$0.811546\pi$
$14$	−0.603997	+	4.20089i	−0.161425	+	1.12274i
$15$	0.267092	+	0.425915i	0.0689628	+	0.109971i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	0.313276	+	1.44011i	0.0759807	+	0.349277i	0.999405	−	0.0345041i	$-0.0109852\pi$
$17$	0.313276	+	1.44011i	0.0759807	+	0.349277i	−0.923424	+	0.383782i	$0.874622\pi$
$18$	−1.76754	+	2.36116i	−0.416613	+	0.556530i
$19$	4.78140	−	3.07282i	1.09693	−	0.704953i	0.138522	−	0.990359i	$-0.455765\pi$
$19$	4.78140	−	3.07282i	1.09693	−	0.704953i	0.958407	+	0.285406i	$0.0921286\pi$
$20$	2.08629	+	0.804611i	0.466508	+	0.179916i
$21$	−0.268828	−	0.915545i	−0.0586631	−	0.199788i
$22$	−2.13533	−	2.13533i	−0.455254	−	0.455254i
$23$	−2.36877	+	4.17000i	−0.493924	+	0.869505i
$23$	−2.36877	+	4.17000i	−0.493924	+	0.869505i
$24$		−	0.224830i		−	0.0458931i
$25$	1.51471	−	4.76504i	0.302942	−	0.953009i
$26$	−3.83854	−	4.42991i	−0.752799	−	0.868777i
$27$	0.284330	−	1.30704i	0.0547193	−	0.251541i
$28$	−3.39757	−	2.54339i	−0.642080	−	0.480655i
$29$	3.42485	−	5.32917i	0.635979	−	0.989602i	−0.362363	−	0.932037i	$-0.618030\pi$
$29$	3.42485	−	5.32917i	0.635979	−	0.989602i	0.998342	−	0.0575653i	$-0.0183337\pi$
$30$	−0.501820	+	0.0303016i	−0.0916194	+	0.00553229i
$31$	1.79209	−	2.06819i	0.321870	−	0.371457i	−0.571638	−	0.820506i	$-0.693692\pi$
$31$	1.79209	−	2.06819i	0.321870	−	0.371457i	0.893507	+	0.449049i	$0.148237\pi$
$32$	−0.599278	−	0.800541i	−0.105938	−	0.141517i
$33$	0.636136	+	0.237266i	0.110737	+	0.0413028i
$34$	−1.41409	−	0.415214i	−0.242514	−	0.0712086i
$35$	−5.21894	+	7.92617i	−0.882161	+	1.33977i
$36$	−1.22525	−	2.68292i	−0.204208	−	0.447153i
$37$	−5.02392	+	3.76086i	−0.825927	+	0.618282i	−0.926350	−	0.376663i	$-0.877071\pi$
$37$	−5.02392	+	3.76086i	−0.825927	+	0.618282i	0.100423	+	0.994945i	$0.467980\pi$
$38$	0.405468	+	5.66918i	0.0657755	+	0.919662i
$39$	1.19877	+	0.547460i	0.191957	+	0.0876638i
$40$	−1.70604	+	1.44548i	−0.269749	+	0.228551i
$41$	−0.610534	−	4.24636i	−0.0953494	−	0.663170i	−0.980304	−	0.197493i	$-0.936720\pi$
$41$	−0.610534	−	4.24636i	−0.0953494	−	0.663170i	0.884955	−	0.465677i	$-0.154189\pi$
$42$	0.932390	+	0.202829i	0.143871	+	0.0312972i
$43$	2.13268	+	0.152532i	0.325231	+	0.0232610i	0.233000	−	0.972477i	$-0.425146\pi$
$43$	2.13268	+	0.152532i	0.325231	+	0.0232610i	0.0922307	+	0.995738i	$0.470600\pi$
$44$	2.89749	−	0.850780i	0.436813	−	0.128260i
$45$	−5.82314	+	3.09635i	−0.868063	+	0.461576i
$46$	−2.52469	−	4.07749i	−0.372245	−	0.601193i
$47$	1.03690	−	1.03690i	0.151248	−	0.151248i	−0.627427	−	0.778675i	$-0.715892\pi$
$47$	1.03690	−	1.03690i	0.151248	−	0.151248i	0.778675	+	0.627427i	$0.215892\pi$
$48$	0.197328	+	0.107749i	0.0284819	+	0.0155523i
$49$	8.32253	−	7.21151i	1.18893	−	1.03022i
$50$	3.45626	+	3.61307i	0.488788	+	0.510966i
$51$	0.327979	−	0.0471562i	0.0459262	−	0.00660319i
$52$	5.72765	−	1.24598i	0.794283	−	0.172786i
$53$	−2.92896	−	7.85285i	−0.402324	−	1.07867i	−0.967316	−	0.253575i	$-0.918393\pi$
$53$	−2.92896	−	7.85285i	−0.402324	−	1.07867i	0.564992	−	0.825097i	$-0.308879\pi$
$54$	1.01090	+	0.875950i	0.137566	+	0.119202i
$55$	−2.28946	−	6.35254i	−0.308710	−	0.856577i
$56$	3.86056	−	1.76306i	0.515889	−	0.235599i
$57$	−0.612411	−	1.12155i	−0.0811158	−	0.148552i
$58$	3.03595	+	5.55992i	0.398639	+	0.730053i
$59$	−9.55015	+	4.36141i	−1.24332	+	0.567807i	−0.924925	−	0.380150i	$-0.875872\pi$
$59$	−9.55015	+	4.36141i	−1.24332	+	0.567807i	−0.318399	+	0.947957i	$0.603145\pi$
$60$	0.213902	−	0.454959i	0.0276146	−	0.0587350i
$61$	−8.07789	−	6.99953i	−1.03427	−	0.896198i	−0.0395887	−	0.999216i	$-0.512605\pi$
$61$	−8.07789	−	6.99953i	−1.03427	−	0.896198i	−0.994680	+	0.103018i	$0.967150\pi$
$62$	0.956345	+	2.56406i	0.121456	+	0.325636i
$63$	12.2317	−	2.66084i	1.54104	−	0.335234i
$64$	0.989821	−	0.142315i	0.123728	−	0.0177894i
$65$	−3.55297	−	12.6162i	−0.440692	−	1.56485i
$66$	−0.513111	+	0.444614i	−0.0631596	+	0.0547281i
$67$	−3.85770	−	2.10646i	−0.471293	−	0.257346i	0.226006	−	0.974126i	$-0.427433\pi$
$67$	−3.85770	−	2.10646i	−0.471293	−	0.257346i	−0.697299	+	0.716780i	$0.745615\pi$
$68$	1.04213	−	1.04213i	0.126376	−	0.126376i
$69$	0.897158	+	0.598097i	0.108005	+	0.0720024i
$70$	−4.45546	−	8.37916i	−0.532529	−	1.00150i
$71$	7.76304	−	2.27943i	0.921303	−	0.270519i	0.213512	−	0.976940i	$-0.431510\pi$
$71$	7.76304	−	2.27943i	0.921303	−	0.270519i	0.707791	+	0.706421i	$0.249692\pi$
$72$	2.94194	+	0.210411i	0.346711	+	0.0247972i
$73$	−5.59835	−	1.21785i	−0.655238	−	0.142538i	−0.127357	−	0.991857i	$-0.540649\pi$
$73$	−5.59835	−	1.21785i	−0.655238	−	0.142538i	−0.527880	+	0.849319i	$0.677013\pi$
$74$	−0.893119	−	6.21178i	−0.103823	−	0.722105i
$75$	−1.04430	−	0.416112i	−0.120585	−	0.0480484i
$76$	−5.17004	−	2.36108i	−0.593044	−	0.270834i
$77$	0.914309	+	12.7837i	0.104195	+	1.45684i
$78$	−1.05500	+	0.789766i	−0.119456	+	0.0894234i
$79$	4.78369	+	10.4748i	0.538207	+	1.17851i	0.962075	+	0.272785i	$0.0879449\pi$
$79$	4.78369	+	10.4748i	0.538207	+	1.17851i	−0.423868	+	0.905724i	$0.639328\pi$
$80$	−0.451051	−	2.19010i	−0.0504291	−	0.244861i
$81$	8.20138	+	2.40814i	0.911265	+	0.267571i
$82$	4.01954	+	1.49921i	0.443884	+	0.165560i
$83$	−0.282133	−	0.376886i	−0.0309681	−	0.0413686i	0.784790	−	0.619762i	$-0.212771\pi$
$83$	−0.282133	−	0.376886i	−0.0309681	−	0.0413686i	−0.815758	+	0.578393i	$0.803680\pi$
$84$	−0.624866	+	0.721134i	−0.0681784	+	0.0786821i
$85$	−2.46648	−	2.18557i	−0.267527	−	0.237059i
$86$	−1.15596	+	1.79871i	−0.124650	+	0.193960i
$87$	−1.14017	−	0.853521i	−0.122239	−	0.0915071i
$88$	−0.641908	+	2.95080i	−0.0684276	+	0.314557i
$89$	−6.58045	−	7.59424i	−0.697526	−	0.804988i	0.290890	−	0.956757i	$-0.406049\pi$
$89$	−6.58045	−	7.59424i	−0.697526	−	0.804988i	−0.988416	+	0.151768i	$0.951503\pi$
$90$	0.0731368	−	6.59477i	0.00770929	−	0.695150i
$91$			24.8772i			2.60784i
$92$	4.78868	−	0.261733i	0.499255	−	0.0272876i
$93$	−0.435061	−	0.435061i	−0.0451137	−	0.0451137i
$94$	0.413134	+	1.40701i	0.0426115	+	0.145121i
$95$	−4.57314	+	11.8578i	−0.469194	+	1.21658i
$96$	−0.189139	+	0.121552i	−0.0193039	+	0.0124059i
$97$	7.75416	−	10.3583i	0.787316	−	1.05173i	−0.209941	−	0.977714i	$-0.567327\pi$
$97$	7.75416	−	10.3583i	0.787316	−	1.05173i	0.997257	−	0.0740165i	$-0.0235817\pi$
$98$	2.34083	+	10.7606i	0.236460	+	1.08699i
$99$	−3.70002	+	8.10191i	−0.371866	+	0.814272i
$100$	−4.82753	+	1.30192i	−0.482753	+	0.130192i
$101$	0.246966	−	1.71769i	0.0245741	−	0.170916i	−0.973838	−	0.227242i	$-0.927029\pi$
$101$	0.246966	−	1.71769i	0.0245741	−	0.170916i	0.998412	+	0.0563252i	$0.0179384\pi$
$102$	−0.115795	+	0.310459i	−0.0114655	+	0.0307401i
$103$	−16.0513	+	8.76469i	−1.58159	+	0.863611i	−0.582890	+	0.812551i	$0.698078\pi$
$103$	−16.0513	+	8.76469i	−1.58159	+	0.863611i	−0.998696	+	0.0510594i	$0.983740\pi$
$104$	−1.65141	+	5.62417i	−0.161934	+	0.551496i
$105$	1.69379	+	1.29751i	0.165297	+	0.126624i
$106$	8.29598	+	1.19278i	0.805777	+	0.115853i
$107$	10.2847	−	0.735579i	0.994264	−	0.0711111i	0.435285	−	0.900293i	$-0.356648\pi$
$107$	10.2847	−	0.735579i	0.994264	−	0.0711111i	0.558979	+	0.829182i	$0.311193\pi$
$108$	−1.25328	+	0.467448i	−0.120597	+	0.0449802i
$109$	−7.61007	−	4.89069i	−0.728912	−	0.468443i	0.122815	−	0.992430i	$-0.460808\pi$
$109$	−7.61007	−	4.89069i	−0.728912	−	0.468443i	−0.851727	+	0.523986i	$0.824444\pi$
$110$	6.67271	+	1.03504i	0.636218	+	0.0986875i
$111$	0.762819	+	1.18697i	0.0724035	+	0.112662i
$112$	−0.302770	+	4.23328i	−0.0286091	+	0.400007i
$113$	−4.27466	+	7.82845i	−0.402126	+	0.736439i	−0.997766	−	0.0668130i	$-0.978717\pi$
$113$	−4.27466	+	7.82845i	−0.402126	+	0.736439i	0.595639	+	0.803252i	$0.296899\pi$
$114$	1.27785			0.119682
$115$	−1.22959	−	10.6531i	−0.114660	−	0.993405i
$116$	−6.33480			−0.588171
$117$	−8.28551	+	15.1738i	−0.765996	+	1.40282i
$118$	0.748984	−	10.4722i	0.0689496	−	0.964041i
$119$	3.38165	+	5.26195i	0.309995	+	0.482362i
$120$	0.296796	+	0.405776i	0.0270936	+	0.0370421i
$121$	1.58216	+	1.01679i	0.143833	+	0.0924357i
$122$	10.0147	−	3.73528i	0.906685	−	0.338176i
$123$	−0.962067	+	0.0688084i	−0.0867466	+	0.00620424i
$124$	−2.70875	−	0.389459i	−0.243253	−	0.0349745i
$125$	3.55652	+	10.5996i	0.318105	+	0.948055i
$126$	−3.52665	+	12.0107i	−0.314179	+	1.07000i
$127$	5.81234	−	3.17378i	0.515761	−	0.281627i	−0.200214	−	0.979752i	$-0.564164\pi$
$127$	5.81234	−	3.17378i	0.515761	−	0.281627i	0.715976	+	0.698125i	$0.245982\pi$
$128$	−0.349464	+	0.936950i	−0.0308886	+	0.0828154i
$129$	0.0684128	−	0.475822i	0.00602341	−	0.0418938i
$130$	12.7757	+	2.92794i	1.12051	+	0.256797i
$131$	−0.106677	+	0.233590i	−0.00932041	+	0.0204088i	−0.914235	−	0.405184i	$-0.867207\pi$
$131$	−0.106677	+	0.233590i	−0.00932041	+	0.0204088i	0.904915	+	0.425593i	$0.139935\pi$
$132$	−0.144320	−	0.663428i	−0.0125614	−	0.0577440i
$133$	14.4558	−	19.3106i	1.25347	−	1.67444i
$134$	3.69760	−	2.37630i	0.319424	−	0.205281i
$135$	1.21226	+	2.73431i	0.104334	+	0.235332i
$136$	0.415214	+	1.41409i	0.0356043	+	0.121257i
$137$	−9.64576	−	9.64576i	−0.824093	−	0.824093i	0.162599	−	0.986692i	$-0.448012\pi$
$137$	−9.64576	−	9.64576i	−0.824093	−	0.824093i	−0.986692	+	0.162599i	$0.948012\pi$
$138$	−0.954899	+	0.500779i	−0.0812864	+	0.0426291i
$139$		−	13.8204i		−	1.17223i	−0.810227	−	0.586116i	$-0.800656\pi$
$139$		−	13.8204i		−	1.17223i	0.810227	−	0.586116i	$-0.199344\pi$
$140$	9.48949	+	0.105240i	0.802008	+	0.00889436i
$141$	−0.215902	−	0.249164i	−0.0181822	−	0.0209834i
$142$	−1.71982	+	7.90587i	−0.144324	+	0.663446i
$143$	−14.1704	−	10.6078i	−1.18499	−	0.887069i
$144$	−1.59459	+	2.48124i	−0.132883	+	0.206770i
$145$	0.853778	+	14.1393i	0.0709024	+	1.17420i
$146$	3.75188	−	4.32990i	0.310508	−	0.358345i
$147$	−1.48374	−	1.98205i	−0.122377	−	0.163477i
$148$	5.87997	+	2.19312i	0.483331	+	0.180273i
$149$	14.1555	+	4.15644i	1.15967	+	0.340509i	0.804303	−	0.594219i	$-0.202539\pi$
$149$	14.1555	+	4.15644i	1.15967	+	0.340509i	0.355364	+	0.934728i	$0.384357\pi$
$150$	0.865691	−	0.717138i	0.0706834	−	0.0585540i
$151$	−5.07415	−	11.1108i	−0.412929	−	0.904188i	−0.995794	−	0.0916192i	$-0.970796\pi$
$151$	−5.07415	−	11.1108i	−0.412929	−	0.904188i	0.582865	−	0.812569i	$-0.301932\pi$
$152$	4.55000	−	3.40609i	0.369054	−	0.276270i
$153$	0.310102	+	4.33579i	0.0250703	+	0.350528i
$154$	−11.6582	−	5.32411i	−0.939442	−	0.429029i
$155$	−0.504200	+	6.09843i	−0.0404983	+	0.489837i
$156$	−0.187552	−	1.30445i	−0.0150161	−	0.104440i
$157$	−10.0517	−	2.18662i	−0.802216	−	0.174511i	−0.207277	−	0.978282i	$-0.566460\pi$
$157$	−10.0517	−	2.18662i	−0.802216	−	0.174511i	−0.594939	+	0.803771i	$0.702824\pi$
$158$	−11.4861	−	0.821503i	−0.913786	−	0.0653553i
$159$	−1.80803	+	0.530886i	−0.143386	+	0.0421020i
$160$	2.13837	+	0.653727i	0.169053	+	0.0516816i
$161$	−3.23466	+	20.0953i	−0.254927	+	1.58373i
$162$	−6.04408	+	6.04408i	−0.474868	+	0.474868i
$163$	18.5453	+	10.1265i	1.45258	+	0.793170i	0.995363	−	0.0961850i	$-0.0306640\pi$
$163$	18.5453	+	10.1265i	1.45258	+	0.793170i	0.457218	+	0.889355i	$0.348846\pi$
$164$	−3.24218	+	2.80937i	−0.253172	+	0.219375i
$165$	−1.46132	+	0.411536i	−0.113764	+	0.0320381i
$166$	0.465997	−	0.0670002i	0.0361684	−	0.00520023i
$167$	−1.44270	+	0.313840i	−0.111639	+	0.0242857i	−0.268038	−	0.963408i	$-0.586375\pi$
$167$	−1.44270	+	0.313840i	−0.111639	+	0.0242857i	0.156398	+	0.987694i	$0.450012\pi$
$168$	−0.333457	−	0.894034i	−0.0257268	−	0.0689762i
$169$	−16.1417	−	13.9868i	−1.24167	−	1.07591i
$170$	3.10029	−	1.11734i	0.237781	−	0.0856964i
$171$	15.2488	−	6.96389i	1.16610	−	0.532542i
$172$	−1.02470	−	1.87659i	−0.0781324	−	0.143089i
$173$	7.45550	+	13.6537i	0.566831	+	1.03807i	0.991173	+	0.132571i	$0.0423234\pi$
$173$	7.45550	+	13.6537i	0.566831	+	1.03807i	−0.424343	+	0.905502i	$0.639495\pi$
$174$	1.29554	−	0.591655i	0.0982149	−	0.0448532i
$175$	−1.04406	−	21.1947i	−0.0789235	−	1.60217i
$176$	−2.28222	−	1.97756i	−0.172029	−	0.149064i
$177$	0.824898	+	2.21164i	0.0620032	+	0.166237i
$178$	9.81898	−	2.13599i	0.735964	−	0.160099i
$179$	15.2734	−	2.19599i	1.14159	−	0.164136i	0.454526	−	0.890733i	$-0.349809\pi$
$179$	15.2734	−	2.19599i	1.14159	−	0.164136i	0.687063	+	0.726598i	$0.258900\pi$
$180$	5.75304	+	3.22473i	0.428806	+	0.240357i
$181$	−8.40074	+	7.27928i	−0.624422	+	0.541065i	−0.908579	−	0.417713i	$-0.862832\pi$
$181$	−8.40074	+	7.27928i	−0.624422	+	0.541065i	0.284157	+	0.958778i	$0.408286\pi$
$182$	−21.8342	−	11.9224i	−1.61846	−	0.883745i
$183$	−1.69925	+	1.69925i	−0.125613	+	0.125613i
$184$	−2.06525	+	4.32836i	−0.152253	+	0.319091i
$185$	4.10256	−	13.4197i	0.301626	−	0.986636i
$186$	0.590347	−	0.173341i	0.0432863	−	0.0127100i
$187$	−4.43923	−	0.317500i	−0.324629	−	0.0232179i
$188$	−1.43289	−	0.311707i	−0.104504	−	0.0227336i
$189$	−0.807914	−	5.61916i	−0.0587671	−	0.408734i
$190$	−8.21563	−	9.69656i	−0.596025	−	0.703463i
$191$	0.433670	+	0.198050i	0.0313793	+	0.0143304i	0.431043	−	0.902331i	$-0.358146\pi$
$191$	0.433670	+	0.198050i	0.0313793	+	0.0143304i	−0.399664	+	0.916662i	$0.630873\pi$
$192$	−0.0160392	−	0.224257i	−0.00115753	−	0.0161843i
$193$	14.4214	−	10.7957i	1.03807	−	0.777091i	0.0627835	−	0.998027i	$-0.480002\pi$
$193$	14.4214	−	10.7957i	1.03807	−	0.777091i	0.975288	+	0.220936i	$0.0709113\pi$
$194$	5.37513	+	11.7699i	0.385912	+	0.845029i
$195$	−2.88626	+	0.594424i	−0.206689	+	0.0425676i
$196$	−10.5662	−	3.10252i	−0.754729	−	0.221609i
$197$	3.91720	+	1.46104i	0.279089	+	0.104095i	0.485111	−	0.874453i	$-0.338779\pi$
$197$	3.91720	+	1.46104i	0.279089	+	0.104095i	−0.206022	+	0.978547i	$0.566052\pi$
$198$	−5.33765	−	7.13026i	−0.379330	−	0.506725i
$199$	−8.68408	+	10.0220i	−0.615598	+	0.710438i	−0.974865	−	0.222797i	$-0.928481\pi$
$199$	−8.68408	+	10.0220i	−0.615598	+	0.710438i	0.359267	+	0.933235i	$0.383027\pi$
$200$	1.17092	−	4.86096i	0.0827964	−	0.343722i
$201$	−0.534263	+	0.831330i	−0.0376840	+	0.0586375i
$202$	1.38922	+	1.03996i	0.0977453	+	0.0731712i
$203$	5.71491	−	26.2710i	0.401108	−	1.84386i
$204$	−0.216989	−	0.250419i	−0.0151923	−	0.0175328i
$205$	6.70749	+	6.85793i	0.468471	+	0.478978i
$206$		−	18.2884i		−	1.27421i
$207$	−8.66583	+	11.1797i	−0.602317	+	0.777045i
$208$	−4.14478	−	4.14478i	−0.287389	−	0.287389i
$209$	4.83555	+	16.4684i	0.334482	+	1.13914i
$210$	−1.95054	+	0.864772i	−0.134600	+	0.0596750i
$211$	11.9933	−	7.70761i	0.825651	−	0.530614i	−0.0582421	−	0.998302i	$-0.518550\pi$
$211$	11.9933	−	7.70761i	0.825651	−	0.530614i	0.883893	+	0.467689i	$0.154913\pi$
$212$	−5.02272	+	6.70957i	−0.344962	+	0.460815i
$213$	−0.386666	−	1.77747i	−0.0264939	−	0.121791i
$214$	−4.28335	+	9.37923i	−0.292804	+	0.641151i
$215$	−4.05045	+	2.54004i	−0.276239	+	0.173230i
$216$	0.190362	−	1.32400i	0.0129525	−	0.0900866i
$217$	4.05881	−	10.8821i	0.275530	−	0.738725i
$218$	7.93957	−	4.33534i	0.537736	−	0.293626i
$219$	−0.362903	+	1.23593i	−0.0245227	+	0.0835167i
$220$	−4.10633	+	5.36046i	−0.276848	+	0.361402i
$221$	−8.55084	−	1.22943i	−0.575192	−	0.0827001i
$222$	−1.40736	+	0.100656i	−0.0944557	+	0.00675560i
$223$	−4.54583	+	1.69551i	−0.304411	+	0.113540i	−0.497028	−	0.867734i	$-0.665575\pi$
$223$	−4.54583	+	1.69551i	−0.304411	+	0.113540i	0.192617	+	0.981274i	$0.438303\pi$
$224$	−3.57035	−	2.29453i	−0.238554	−	0.153310i
$225$	6.42223	−	13.2754i	0.428149	−	0.885028i
$226$	−4.82224	−	7.50356i	−0.320771	−	0.499129i
$227$	1.66030	−	23.2140i	0.110198	−	1.54077i	−0.578478	−	0.815698i	$-0.696353\pi$
$227$	1.66030	−	23.2140i	0.110198	−	1.54077i	0.688676	−	0.725069i	$-0.258192\pi$
$228$	−0.612411	+	1.12155i	−0.0405579	+	0.0742762i
$229$	−0.636089			−0.0420340			−0.0210170	−	0.999779i	$-0.506690\pi$
$229$	−0.636089			−0.0420340			−0.0210170	+	0.999779i	$0.506690\pi$
$230$	9.93926	+	4.02629i	0.655376	+	0.265486i
$231$	2.88150			0.189589
$232$	3.03595	−	5.55992i	0.199320	−	0.365027i
$233$	1.28326	−	17.9423i	0.0840691	−	1.17544i	−0.763879	−	0.645360i	$-0.776708\pi$
$233$	1.28326	−	17.9423i	0.0840691	−	1.17544i	0.847948	−	0.530079i	$-0.177838\pi$
$234$	−9.34689	−	14.5440i	−0.611025	−	0.950774i
$235$	−0.502611	+	3.24023i	−0.0327867	+	0.211369i
$236$	8.83225	+	5.67614i	0.574930	+	0.369485i
$237$	2.42578	−	0.904767i	0.157571	−	0.0587710i
$238$	−6.23895	+	0.446219i	−0.404411	+	0.0289241i
$239$	−8.36634	−	1.20290i	−0.541174	−	0.0778090i	−0.133693	−	0.991023i	$-0.542684\pi$
$239$	−8.36634	−	1.20290i	−0.541174	−	0.0778090i	−0.407481	+	0.913214i	$0.633593\pi$
$240$	−0.498380	+	0.0660238i	−0.0321703	+	0.00426182i
$241$	−3.95621	+	13.4736i	−0.254842	+	0.867912i	0.728330	+	0.685227i	$0.240297\pi$
$241$	−3.95621	+	13.4736i	−0.254842	+	0.867912i	−0.983172	+	0.182685i	$0.941521\pi$
$242$	−1.65067	+	0.901332i	−0.106109	+	0.0579398i
$243$	2.07393	−	5.56042i	0.133043	−	0.356701i
$244$	−1.52114	+	10.5798i	−0.0973813	+	0.677302i
$245$	−5.50076	+	24.0020i	−0.351431	+	1.53343i
$246$	0.400678	−	0.877362i	0.0255463	−	0.0559386i
$247$	7.08170	+	32.5540i	0.450598	+	2.07136i
$248$	1.63999	−	2.19076i	0.104139	−	0.139114i
$249$	−0.0890444	+	0.0572253i	−0.00564296	+	0.00362651i
$250$	−11.0075	−	1.95835i	−0.696175	−	0.123857i
$251$	0.649447	+	2.21181i	0.0409928	+	0.139609i	0.977447	−	0.211182i	$-0.0677312\pi$
$251$	0.649447	+	2.21181i	0.0409928	+	0.139609i	−0.936454	+	0.350790i	$0.885913\pi$
$252$	−8.85137	−	8.85137i	−0.557584	−	0.557584i
$253$	−10.0672	−	10.4113i	−0.632922	−	0.654550i
$254$			6.62239i			0.415526i
$255$	−0.529690	+	0.518070i	−0.0331705	+	0.0324428i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	3.35786	−	15.4359i	0.209458	−	0.962862i	−0.745589	−	0.666406i	$-0.767832\pi$
$257$	3.35786	−	15.4359i	0.209458	−	0.962862i	0.955047	−	0.296456i	$-0.0958047\pi$
$258$	0.384832	+	0.288082i	0.0239586	+	0.0179352i
$259$	−14.3997	+	22.4063i	−0.894752	+	1.39226i
$260$	−8.69255	+	9.80979i	−0.539089	+	0.608377i
$261$	12.2355	−	14.1206i	0.757361	−	0.874041i
$262$	−0.153892	−	0.205576i	−0.00950749	−	0.0127005i
$263$	−11.6117	−	4.33095i	−0.716009	−	0.267058i	−0.0350568	−	0.999385i	$-0.511161\pi$
$263$	−11.6117	−	4.33095i	−0.716009	−	0.267058i	−0.680952	+	0.732328i	$0.738434\pi$
$264$	0.651442	+	0.191281i	0.0400935	+	0.0117725i
$265$	15.6527	+	10.3064i	0.961539	+	0.633120i
$266$	10.0206	+	21.9421i	0.614404	+	1.34536i
$267$	−1.80860	+	1.35390i	−0.110685	+	0.0828576i
$268$	0.313560	+	4.38415i	0.0191537	+	0.267804i
$269$	−11.3264	−	5.17260i	−0.690584	−	0.315379i	0.0390305	−	0.999238i	$-0.487573\pi$
$269$	−11.3264	−	5.17260i	−0.690584	−	0.315379i	−0.729614	+	0.683859i	$0.760300\pi$
$270$	−2.98082	−	0.246446i	−0.181407	−	0.0149982i
$271$	0.839048	+	5.83571i	0.0509685	+	0.354494i	0.999307	+	0.0372325i	$0.0118542\pi$
$271$	0.839048	+	5.83571i	0.0509685	+	0.354494i	−0.948338	+	0.317262i	$0.897237\pi$
$272$	−1.44011	−	0.313276i	−0.0873194	−	0.0189952i
$273$	5.57888	+	0.399009i	0.337649	+	0.0241491i
$274$	13.0886	−	3.84316i	0.790712	−	0.232174i
$275$	12.5180	+	8.44287i	0.754863	+	0.509124i
$276$	0.0181110	−	1.07809i	0.00109015	−	0.0648935i
$277$	−4.36140	+	4.36140i	−0.262051	+	0.262051i	−0.825887	−	0.563836i	$-0.809325\pi$
$277$	−4.36140	+	4.36140i	−0.262051	+	0.262051i	0.563836	+	0.825887i	$0.309325\pi$
$278$	12.1299	+	6.62342i	0.727502	+	0.397246i
$279$	6.10002	−	5.28570i	0.365199	−	0.316446i
$280$	−4.64019	+	8.27829i	−0.277305	+	0.494722i
$281$	−27.7915	+	3.99581i	−1.65790	+	0.238370i	−0.906722	−	0.421729i	$-0.861423\pi$
$281$	−27.7915	+	3.99581i	−1.65790	+	0.238370i	−0.751178	+	0.660099i	$0.770514\pi$
$282$	0.322157	−	0.0700809i	0.0191841	−	0.00417326i
$283$	−1.30311	−	3.49378i	−0.0774620	−	0.207684i	0.892447	−	0.451153i	$-0.148987\pi$
$283$	−1.30311	−	3.49378i	−0.0774620	−	0.207684i	−0.969909	+	0.243469i	$0.921714\pi$
$284$	−6.11460	−	5.29833i	−0.362835	−	0.314398i
$285$	2.58583	+	1.21574i	0.153171	+	0.0720145i
$286$	16.1014	−	7.35325i	0.952094	−	0.434807i
$287$	−8.72580	−	15.9801i	−0.515068	−	0.943276i
$288$	−1.41352	−	2.58867i	−0.0832926	−	0.152539i
$289$	13.4880	−	6.15975i	0.793410	−	0.362338i
$290$	−12.8189	−	6.02690i	−0.752753	−	0.353912i
$291$	−2.19856	−	1.90506i	−0.128882	−	0.111677i
$292$	2.00218	+	5.36805i	0.117169	+	0.314141i
$293$	−13.3607	+	2.90644i	−0.780539	+	0.169796i	−0.585145	−	0.810929i	$-0.698962\pi$
$293$	−13.3607	+	2.90644i	−0.780539	+	0.169796i	−0.195394	+	0.980725i	$0.562599\pi$
$294$	2.45069	−	0.352356i	0.142927	−	0.0205498i
$295$	11.4788	−	20.4786i	0.668321	−	1.19231i
$296$	−4.74282	+	4.10968i	−0.275671	+	0.238870i
$297$	3.54525	+	1.93585i	0.205716	+	0.112329i
$298$	−10.4321	+	10.4321i	−0.604313	+	0.604313i
$299$	−18.0495	−	21.5513i	−1.04383	−	1.24634i
$300$	0.214535	+	1.10349i	0.0123862	+	0.0637098i
$301$	8.70683	−	2.55656i	0.501853	−	0.147357i
$302$	12.1835	+	0.871384i	0.701084	+	0.0501425i
$303$	−0.381242	−	0.0829341i	−0.0219018	−	0.00476444i
$304$	0.808869	+	5.62581i	0.0463918	+	0.322662i
$305$	23.8191	+	1.96930i	1.36388	+	0.112762i
$306$	−3.95405	−	1.80575i	−0.226038	−	0.103228i
$307$	1.04823	+	14.6562i	0.0598257	+	0.836472i	0.935445	+	0.353471i	$0.114999\pi$
$307$	1.04823	+	14.6562i	0.0598257	+	0.836472i	−0.875620	+	0.483001i	$0.839547\pi$
$308$	10.2600	−	7.68056i	0.584619	−	0.437640i
$309$	1.70809	+	3.74020i	0.0971699	+	0.212772i
$310$	−5.11082	−	3.36519i	−0.290275	−	0.191130i
$311$	20.7030	+	6.07895i	1.17396	+	0.344706i	0.809842	−	0.586648i	$-0.199553\pi$
$311$	20.7030	+	6.07895i	1.17396	+	0.344706i	0.364117	+	0.931353i	$0.381371\pi$
$312$	1.23477	+	0.460546i	0.0699052	+	0.0260733i
$313$	13.5796	+	18.1402i	0.767564	+	1.02535i	0.998626	+	0.0524068i	$0.0166893\pi$
$313$	13.5796	+	18.1402i	0.767564	+	1.02535i	−0.231061	+	0.972939i	$0.574220\pi$
$314$	6.73643	−	7.77426i	0.380159	−	0.438727i
$315$	−18.5633	+	20.9492i	−1.04593	+	1.18036i
$316$	6.22572	−	9.68741i	0.350224	−	0.544960i
$317$	−17.9811	−	13.4604i	−1.00992	−	0.756014i	−0.0399375	−	0.999202i	$-0.512716\pi$
$317$	−17.9811	−	13.4604i	−1.00992	−	0.756014i	−0.969979	+	0.243188i	$0.921807\pi$
$318$	0.400550	−	1.84130i	0.0224617	−	0.103255i
$319$	12.5274	+	14.4574i	0.701402	+	0.809461i
$320$	−1.59858	+	1.56351i	−0.0893631	+	0.0874027i
$321$		−	2.31822i		−	0.129390i
$322$	−16.0870	−	12.4696i	−0.896493	−	0.694905i
$323$	5.92309	+	5.92309i	0.329570	+	0.329570i
$324$	−2.40814	−	8.20138i	−0.133786	−	0.455632i
$325$	23.0670	+	18.0797i	1.27953	+	1.00288i
$326$	−17.7757	+	11.4237i	−0.984502	+	0.632701i
$327$	−1.21883	+	1.62817i	−0.0674014	+	0.0900378i
$328$	−0.911910	−	4.19198i	−0.0503518	−	0.231464i
$329$	2.58536	−	5.66114i	0.142535	−	0.312109i
$330$	0.339140	−	1.47980i	0.0186690	−	0.0814603i
$331$	0.0430398	−	0.299348i	0.00236568	−	0.0164537i	−0.988604	−	0.150537i	$-0.951900\pi$
$331$	0.0430398	−	0.299348i	0.00236568	−	0.0164537i	0.990970	+	0.134083i	$0.0428089\pi$
$332$	−0.164524	+	0.441106i	−0.00902942	+	0.0242088i
$333$	−16.2456	+	8.87077i	−0.890254	+	0.486115i
$334$	0.415961	−	1.41663i	0.0227604	−	0.0775148i
$335$	9.74317	−	1.29074i	0.532326	−	0.0705209i
$336$	0.944484	+	0.135796i	0.0515258	+	0.00740830i
$337$	−17.8317	+	1.27535i	−0.971354	+	0.0694726i	−0.547988	−	0.836486i	$-0.684606\pi$
$337$	−17.8317	+	1.27535i	−0.971354	+	0.0694726i	−0.423366	+	0.905959i	$0.639152\pi$
$338$	20.0118	−	7.46403i	1.08850	−	0.405989i
$339$	1.68702	+	1.08418i	0.0916264	+	0.0588847i
$340$	−0.505142	+	3.25655i	−0.0273952	+	0.176611i
$341$	4.46788	+	6.95215i	0.241949	+	0.376480i
$342$	−1.19591	+	16.7210i	−0.0646673	+	0.904166i
$343$	8.16089	−	14.9456i	0.440647	−	0.806984i
$344$	2.13813			0.115280
$345$	−2.40875	+	0.104877i	−0.129683	+	0.00564639i
$346$	−15.5566			−0.836329
$347$	9.01289	−	16.5059i	0.483837	−	0.886082i	−0.515733	−	0.856750i	$-0.672480\pi$
$347$	9.01289	−	16.5059i	0.483837	−	0.886082i	0.999570	−	0.0293320i	$-0.00933800\pi$
$348$	−0.101605	+	1.42062i	−0.00544659	+	0.0761533i
$349$	18.7709	+	29.2081i	1.00478	+	1.56347i	0.813190	+	0.581998i	$0.197729\pi$
$349$	18.7709	+	29.2081i	1.00478	+	1.56347i	0.191593	+	0.981474i	$0.438635\pi$
$350$	19.1025	+	9.24121i	1.02107	+	0.493963i
$351$	6.59590	+	4.23893i	0.352063	+	0.226257i
$352$	2.82941	−	1.05532i	0.150808	−	0.0562486i
$353$	−6.03442	+	0.431590i	−0.321180	+	0.0229712i	−0.230998	−	0.972954i	$-0.574199\pi$
$353$	−6.03442	+	0.431590i	−0.321180	+	0.0229712i	−0.0901814	+	0.995925i	$0.528745\pi$
$354$	−2.33644	−	0.335929i	−0.124180	−	0.0178544i
$355$	−11.0018	+	14.3619i	−0.583914	+	0.762250i
$356$	−2.83102	+	9.64158i	−0.150044	+	0.511003i
$357$	1.23427	−	0.673960i	0.0653243	−	0.0356698i
$358$	−5.39240	+	14.4576i	−0.284997	+	0.764107i
$359$	−0.514662	+	3.57955i	−0.0271628	+	0.188922i	−0.998885	−	0.0472045i	$-0.984969\pi$
$359$	−0.514662	+	3.57955i	−0.0271628	+	0.188922i	0.971722	+	0.236126i	$0.0758778\pi$
$360$	−5.58741	+	3.50387i	−0.294483	+	0.184670i
$361$	5.52668	−	12.1017i	0.290878	−	0.636934i
$362$	−2.36283	−	10.8617i	−0.124187	−	0.570880i
$363$	0.253399	−	0.338502i	0.0133000	−	0.0177667i
$364$	20.9280	−	13.4496i	1.09693	−	0.704952i
$365$	11.7117	−	5.19235i	0.613016	−	0.271780i
$366$	−0.677034	−	2.30577i	−0.0353891	−	0.120524i
$367$	13.4097	+	13.4097i	0.699980	+	0.699980i	0.964406	−	0.264426i	$-0.0851826\pi$
$367$	13.4097	+	13.4097i	0.699980	+	0.699980i	−0.264426	+	0.964406i	$0.585183\pi$
$368$	−2.80914	−	3.88699i	−0.146437	−	0.202624i
$369$		−	12.6532i		−	0.658700i
$370$	9.81203	+	10.0321i	0.510103	+	0.521544i
$371$	−23.2940	−	26.8827i	−1.20937	−	1.39568i
$372$	−0.130785	+	0.601209i	−0.00678088	+	0.0311712i
$373$	20.6232	+	15.4383i	1.06783	+	0.799366i	0.980442	−	0.196809i	$-0.0630578\pi$
$373$	20.6232	+	15.4383i	1.06783	+	0.799366i	0.0873858	+	0.996175i	$0.472149\pi$
$374$	2.40616	−	3.74406i	0.124420	−	0.193601i
$375$	2.43407	−	0.627566i	0.125695	−	0.0324074i
$376$	0.960291	−	1.10823i	0.0495232	−	0.0571528i
$377$	22.2525	+	29.7258i	1.14606	+	1.53096i
$378$	5.31901	+	1.98389i	0.273580	+	0.102040i
$379$	−14.4353	−	4.23858i	−0.741490	−	0.217721i	−0.110894	−	0.993832i	$-0.535371\pi$
$379$	−14.4353	−	4.23858i	−0.741490	−	0.217721i	−0.630596	+	0.776111i	$0.717190\pi$
$380$	12.4478	−	2.56362i	0.638559	−	0.131511i
$381$	−0.618515	−	1.35436i	−0.0316875	−	0.0693860i
$382$	−0.381661	+	0.285708i	−0.0195275	+	0.0146181i
$383$	−0.839642	−	11.7397i	−0.0429037	−	0.599872i	−0.972740	−	0.231899i	$-0.925506\pi$
$383$	−0.839642	−	11.7397i	−0.0429037	−	0.599872i	0.929836	−	0.367974i	$-0.119948\pi$
$384$	0.204512	+	0.0933976i	0.0104365	+	0.00476617i
$385$	−18.5258	−	21.8653i	−0.944164	−	1.11436i
$386$	2.56373	+	17.8311i	0.130490	+	0.907581i
$387$	6.16219	+	1.34050i	0.313242	+	0.0681416i
$388$	−12.9062	−	0.923070i	−0.655213	−	0.0468618i
$389$	21.7646	−	6.39066i	1.10351	−	0.324019i	0.321263	−	0.946990i	$-0.395893\pi$
$389$	21.7646	−	6.39066i	1.10351	−	0.324019i	0.782245	+	0.622971i	$0.214075\pi$
$390$	0.861522	−	2.81808i	0.0436249	−	0.142699i
$391$	−6.74733	−	2.10493i	−0.341227	−	0.106451i
$392$	7.78686	−	7.78686i	0.393296	−	0.393296i
$393$	0.0506731	+	0.0276696i	0.00255612	+	0.00139575i
$394$	−3.15964	+	2.73784i	−0.159180	+	0.137930i
$395$	−22.4614	−	12.5902i	−1.13016	−	0.633482i
$396$	8.81614	−	1.26757i	0.443028	−	0.0636978i
$397$	−20.8157	+	4.52817i	−1.04471	+	0.227262i	−0.701998	−	0.712179i	$-0.747708\pi$
$397$	−20.8157	+	4.52817i	−1.04471	+	0.227262i	−0.342710	+	0.939441i	$0.611345\pi$
$398$	−4.63423	−	12.4249i	−0.232293	−	0.622802i
$399$	−4.09868	−	3.55153i	−0.205191	−	0.177799i
$400$	3.70520	+	3.35730i	0.185260	+	0.167865i
$401$	−8.25340	+	3.76920i	−0.412155	+	0.188225i	−0.610692	−	0.791869i	$-0.709108\pi$
$401$	−8.25340	+	3.76920i	−0.412155	+	0.188225i	0.198536	+	0.980094i	$0.436381\pi$
$402$	−0.473596	−	0.867326i	−0.0236208	−	0.0432583i
$403$	7.68759	+	14.0788i	0.382946	+	0.701313i
$404$	−1.57853	+	0.720891i	−0.0785349	+	0.0358657i
$405$	−17.9809	+	6.48033i	−0.893480	+	0.322010i
$406$	20.3187	+	17.6062i	1.00840	+	0.873782i
$407$	−6.62281	−	17.7564i	−0.328280	−	0.880154i
$408$	0.323779	−	0.0704338i	0.0160294	−	0.00348699i
$409$	−22.7524	+	3.27130i	−1.12503	+	0.161755i	−0.679616	−	0.733568i	$-0.737854\pi$
$409$	−22.7524	+	3.27130i	−1.12503	+	0.161755i	−0.445417	+	0.895323i	$0.646945\pi$
$410$	−9.23362	+	2.60036i	−0.456016	+	0.128423i
$411$	−2.31784	+	2.00842i	−0.114330	+	0.0990679i
$412$	16.0513	+	8.76469i	0.790793	+	0.431805i
$413$	−31.5075	+	31.5075i	−1.55038	+	1.55038i
$414$	−5.65913	−	12.9637i	−0.278131	−	0.637131i
$415$	1.00672	+	0.307767i	0.0494181	+	0.0151077i
$416$	5.62417	−	1.65141i	0.275748	−	0.0809669i
$417$	−3.09932	−	0.221668i	−0.151774	−	0.0108551i
$418$	−16.7714	−	3.64839i	−0.820314	−	0.178448i
$419$	0.998722	+	6.94626i	0.0487908	+	0.339347i	0.999566	+	0.0294653i	$0.00938044\pi$
$419$	0.998722	+	6.94626i	0.0487908	+	0.339347i	−0.950775	+	0.309882i	$0.899710\pi$
$420$	0.175804	−	2.12639i	0.00857836	−	0.103757i
$421$	−4.14762	−	1.89416i	−0.202143	−	0.0923155i	0.311771	−	0.950157i	$-0.399078\pi$
$421$	−4.14762	−	1.89416i	−0.202143	−	0.0923155i	−0.513914	+	0.857842i	$0.671805\pi$
$422$	1.01704	+	14.2201i	0.0495088	+	0.692224i
$423$	3.46241	−	2.59193i	0.168348	−	0.126024i
$424$	−3.48171	−	7.62389i	−0.169087	−	0.370249i
$425$	7.33670	+	0.688573i	0.355882	+	0.0334007i
$426$	1.74536	+	0.512484i	0.0845630	+	0.0248299i
$427$	−42.5031	−	15.8528i	−2.05687	−	0.767173i
$428$	−6.17916	−	8.25439i	−0.298681	−	0.398991i
$429$	−2.60615	+	3.00766i	−0.125826	+	0.145211i
$430$	−0.288168	−	4.77231i	−0.0138967	−	0.230141i
$431$	−7.35787	+	11.4491i	−0.354416	+	0.551483i	−0.971988	−	0.235032i	$-0.924480\pi$
$431$	−7.35787	+	11.4491i	−0.354416	+	0.551483i	0.617571	+	0.786515i	$0.288117\pi$
$432$	1.07081	+	0.801601i	0.0515196	+	0.0385671i
$433$	−2.06009	+	9.47007i	−0.0990015	+	0.455103i	0.900782	+	0.434273i	$0.142995\pi$
$433$	−2.06009	+	9.47007i	−0.0990015	+	0.455103i	−0.999783	+	0.0208300i	$0.993369\pi$
$434$	7.60581	+	8.77757i	0.365090	+	0.421337i
$435$	3.18452	+	0.0353167i	0.152686	+	0.00169331i
$436$			9.04610i			0.433230i
$437$	1.48760	+	27.2173i	0.0711617	+	1.30198i
$438$	−0.910833	−	0.910833i	−0.0435213	−	0.0435213i
$439$	−5.02868	−	17.1261i	−0.240006	−	0.817384i	−0.988103	−	0.153795i	$-0.950850\pi$
$439$	−5.02868	−	17.1261i	−0.240006	−	0.817384i	0.748097	−	0.663589i	$-0.230968\pi$
$440$	−2.73681	−	6.17303i	−0.130472	−	0.294288i
$441$	27.3241	−	17.5601i	1.30115	−	0.836196i
$442$	5.17702	−	6.91570i	0.246246	−	0.328946i
$443$	−3.95656	−	18.1880i	−0.187982	−	0.864138i	−0.970422	−	0.241413i	$-0.922389\pi$
$443$	−3.95656	−	18.1880i	−0.187982	−	0.864138i	0.782441	−	0.622725i	$-0.213974\pi$
$444$	0.586131	−	1.28345i	0.0278165	−	0.0609097i
$445$	21.9016	+	5.01940i	1.03823	+	0.237942i
$446$	0.690474	−	4.80235i	0.0326949	−	0.227398i
$447$	1.15915	−	3.10781i	0.0548261	−	0.146994i
$448$	3.72495	−	2.03398i	0.175987	−	0.0960963i
$449$	−7.56267	+	25.7561i	−0.356905	+	1.21551i	0.564019	+	0.825762i	$0.309254\pi$
$449$	−7.56267	+	25.7561i	−0.356905	+	1.21551i	−0.920924	+	0.389743i	$0.872564\pi$
$450$	8.57371	+	11.9989i	0.404168	+	0.565633i
$451$	12.8232	+	1.84370i	0.603822	+	0.0868164i
$452$	8.89677	−	0.636309i	0.418469	−	0.0299295i
$453$	−2.57307	+	0.959705i	−0.120893	+	0.0450909i
$454$	19.5787	+	12.5825i	0.918876	+	0.590526i
$455$	−32.8402	−	44.8987i	−1.53957	−	2.10488i
$456$	−0.690860	−	1.07500i	−0.0323525	−	0.0503415i
$457$	−0.897191	+	12.5444i	−0.0419688	+	0.586801i	0.932340	+	0.361583i	$0.117764\pi$
$457$	−0.897191	+	12.5444i	−0.0419688	+	0.586801i	−0.974309	+	0.225217i	$0.927691\pi$
$458$	0.304845	−	0.558282i	0.0142445	−	0.0260868i
$459$	1.97136			0.0920151
$460$	−8.29718	+	6.79389i	−0.386858	+	0.316767i
$461$	−17.9112			−0.834208			−0.417104	−	0.908859i	$-0.636955\pi$
$461$	−17.9112			−0.834208			−0.417104	+	0.908859i	$0.636955\pi$
$462$	−1.38095	+	2.52903i	−0.0642478	+	0.117661i
$463$	−0.639316	+	8.93881i	−0.0297115	+	0.415422i	0.960730	+	0.277486i	$0.0895012\pi$
$463$	−0.639316	+	8.93881i	−0.0297115	+	0.415422i	−0.990441	+	0.137936i	$0.955953\pi$
$464$	3.42485	+	5.32917i	0.158995	+	0.247401i
$465$	1.35953	+	0.210884i	0.0630465	+	0.00977950i
$466$	15.1326	+	9.72512i	0.701003	+	0.450507i
$467$	37.0654	−	13.8247i	1.71518	−	0.639731i	0.716839	−	0.697239i	$-0.245588\pi$
$467$	37.0654	−	13.8247i	1.71518	−	0.639731i	0.998345	+	0.0575081i	$0.0183155\pi$
$468$	17.2445	−	1.23335i	0.797127	−	0.0570116i
$469$	−18.4644	−	2.65477i	−0.852605	−	0.122586i
$470$	−2.60301	−	1.99401i	−0.120068	−	0.0919768i
$471$	−0.651586	+	2.21910i	−0.0300235	+	0.102251i
$472$	−9.21468	+	5.03159i	−0.424140	+	0.231598i
$473$	−2.25640	+	6.04965i	−0.103750	+	0.278163i
$474$	−0.368455	+	2.56266i	−0.0169237	+	0.117707i
$475$	−7.39967	−	27.4380i	−0.339520	−	1.25894i
$476$	2.59837	−	5.68965i	0.119096	−	0.260785i
$477$	−5.25466	−	24.1553i	−0.240594	−	1.10599i
$478$	5.06532	−	6.76648i	0.231682	−	0.309491i
$479$	−19.8287	+	12.7431i	−0.905995	+	0.582248i	−0.908562	−	0.417749i	$-0.862819\pi$
$479$	−19.8287	+	12.7431i	−0.905995	+	0.582248i	0.00256735	+	0.999997i	$0.499183\pi$
$480$	0.180900	−	0.469059i	0.00825693	−	0.0214095i
$481$	−10.3637	−	35.2954i	−0.472542	−	1.60933i
$482$	−9.92950	−	9.92950i	−0.452276	−	0.452276i
$483$	4.45462	+	1.04770i	0.202692	+	0.0476722i
$484$		−	1.88072i		−	0.0854872i
$485$	−0.320849	+	28.9311i	−0.0145690	+	1.31369i
$486$	3.88633	+	4.48507i	0.176288	+	0.203447i
$487$	3.92866	−	18.0597i	0.178024	−	0.818365i	−0.798335	−	0.602213i	$-0.794286\pi$
$487$	3.92866	−	18.0597i	0.178024	−	0.818365i	0.976360	−	0.216152i	$-0.0693506\pi$
$488$	−8.55665	−	6.40543i	−0.387341	−	0.289960i
$489$	2.56839	−	3.99649i	0.116147	−	0.180728i
$490$	−18.4298	−	16.3308i	−0.832573	−	0.737751i
$491$	−15.4434	+	17.8226i	−0.696950	+	0.804323i	−0.988337	−	0.152282i	$-0.951338\pi$
$491$	−15.4434	+	17.8226i	−0.696950	+	0.804323i	0.291387	+	0.956605i	$0.405883\pi$
$492$	0.578018	+	0.772141i	0.0260591	+	0.0348108i
$493$	8.74751	+	3.26265i	0.393968	+	0.146942i
$494$	−31.9659	−	9.38603i	−1.43821	−	0.422298i
$495$	−4.01742	−	19.5068i	−0.180570	−	0.876766i
$496$	1.13683	+	2.48930i	0.0510450	+	0.111773i
$497$	27.4889	−	20.5780i	1.23305	−	0.923048i
$498$	−0.00755106	−	0.105578i	−0.000338371	−	0.00473104i
$499$	22.8385	+	10.4300i	1.02239	+	0.466910i	0.854806	−	0.518947i	$-0.173676\pi$
$499$	22.8385	+	10.4300i	1.02239	+	0.466910i	0.167585	+	0.985858i	$0.446403\pi$
$500$	6.99413	−	8.72251i	0.312787	−	0.390082i
$501$	0.0472410	+	0.328569i	0.00211057	+	0.0146794i
$502$	−2.25251	−	0.490004i	−0.100534	−	0.0218699i
$503$	6.49258	+	0.464358i	0.289490	+	0.0207047i	0.215329	−	0.976542i	$-0.430918\pi$
$503$	6.49258	+	0.464358i	0.289490	+	0.0207047i	0.0741608	+	0.997246i	$0.476372\pi$
$504$	12.0107	−	3.52665i	0.534998	−	0.157090i
$505$	1.82178	+	3.42613i	0.0810681	+	0.152461i
$506$	13.9625	−	3.84622i	0.620707	−	0.170985i
$507$	−3.39554	+	3.39554i	−0.150801	+	0.150801i
$508$	−5.81234	−	3.17378i	−0.257881	−	0.140814i
$509$	13.7776	−	11.9384i	0.610683	−	0.529160i	−0.293691	−	0.955900i	$-0.594884\pi$
$509$	13.7776	−	11.9384i	0.610683	−	0.529160i	0.904374	+	0.426740i	$0.140338\pi$
$510$	−0.200846	−	0.713182i	−0.00889361	−	0.0315802i
$511$	−24.0681	+	3.46047i	−1.06471	+	0.153082i
$512$	0.977147	−	0.212565i	0.0431842	−	0.00939415i
$513$	−2.65681	−	7.12319i	−0.117301	−	0.314497i
$514$	11.9385	+	10.3447i	0.526583	+	0.456287i
$515$	17.3995	−	37.0079i	0.766713	−	1.63076i
$516$	−0.437273	+	0.199696i	−0.0192499	+	0.00879113i
$517$	2.12224	+	3.88660i	0.0933362	+	0.170932i
$518$	−12.7645	−	23.3765i	−0.560841	−	1.02710i
$519$	3.18152	−	1.45295i	0.139653	−	0.0637775i
$520$	−4.44395	−	12.3306i	−0.194880	−	0.540733i
$521$	−12.4715	−	10.8066i	−0.546387	−	0.473447i	0.337383	−	0.941367i	$-0.390458\pi$
$521$	−12.4715	−	10.8066i	−0.546387	−	0.473447i	−0.883771	+	0.467920i	$0.845004\pi$
$522$	6.52945	+	17.5061i	0.285786	+	0.766223i
$523$	−18.8457	+	4.09964i	−0.824067	+	0.179265i	−0.604777	−	0.796395i	$-0.706738\pi$
$523$	−18.8457	+	4.09964i	−0.824067	+	0.179265i	−0.219290	+	0.975660i	$0.570374\pi$
$524$	0.254182	−	0.0365459i	0.0111040	−	0.00159651i
$525$	−4.76981	−	0.105808i	−0.208172	−	0.00461786i
$526$	9.36608	−	8.11576i	0.408381	−	0.353864i
$527$	3.53983	+	1.93290i	0.154198	+	0.0841982i
$528$	−0.480086	+	0.480086i	−0.0208930	+	0.0208930i
$529$	−11.7778	−	19.7556i	−0.512079	−	0.858938i
$530$	−16.5473	+	8.79871i	−0.718769	+	0.382192i
$531$	−29.7117	+	8.72414i	−1.28938	+	0.378596i
$532$	−24.0605	−	1.72084i	−1.04315	−	0.0746079i
$533$	24.5718	+	5.34526i	1.06432	+	0.231529i
$534$	−0.321522	−	2.23623i	−0.0139136	−	0.0967712i
$535$	−17.5910	+	14.9044i	−0.760526	+	0.644373i
$536$	−3.99815	−	1.82589i	−0.172694	−	0.0788665i
$537$	−0.247492	−	3.46039i	−0.0106801	−	0.149327i
$538$	9.96805	−	7.46199i	0.429753	−	0.321709i
$539$	13.8147	+	30.2499i	0.595039	+	1.30295i
$540$	1.64486	−	2.49810i	0.0707833	−	0.107501i
$541$	3.38355	+	0.993499i	0.145470	+	0.0427139i	0.353657	−	0.935375i	$-0.384938\pi$
$541$	3.38355	+	0.993499i	0.145470	+	0.0427139i	−0.208187	+	0.978089i	$0.566756\pi$
$542$	−5.52399	−	2.06034i	−0.237276	−	0.0884993i
$543$	1.49769	+	2.00068i	0.0642719	+	0.0858572i
$544$	0.965126	−	1.11382i	0.0413794	−	0.0477544i
$545$	20.1909	−	1.21920i	0.864884	−	0.0522246i
$546$	−3.02387	+	4.70524i	−0.129410	+	0.201366i
$547$	34.4056	+	25.7557i	1.47108	+	1.10124i	0.972085	+	0.234629i	$0.0753877\pi$
$547$	34.4056	+	25.7557i	1.47108	+	1.10124i	0.498993	+	0.866606i	$0.333703\pi$
$548$	−2.89964	+	13.3294i	−0.123866	+	0.569405i
$549$	−20.6448	−	23.8254i	−0.881098	−	1.01684i
$550$	−13.4094	+	6.94054i	−0.571777	+	0.295946i
$551$		−	36.0048i		−	1.53386i
$552$	0.937539	+	0.532570i	0.0399043	+	0.0226677i
$553$	34.5581	+	34.5581i	1.46956	+	1.46956i
$554$	−1.73771	−	5.91810i	−0.0738283	−	0.251436i
$555$	−2.94365	−	1.13527i	−0.124951	−	0.0481894i
$556$	−11.6265	+	7.47188i	−0.493072	+	0.316878i
$557$	−3.75275	+	5.01309i	−0.159009	+	0.212412i	−0.872970	−	0.487775i	$-0.837809\pi$
$557$	−3.75275	+	5.01309i	−0.159009	+	0.212412i	0.713960	+	0.700186i	$0.246900\pi$
$558$	1.71572	+	7.88702i	0.0726321	+	0.333884i
$559$	−5.20635	+	11.4003i	−0.220205	+	0.482182i
$560$	−5.04187	−	8.03996i	−0.213058	−	0.339750i
$561$	−0.142403	+	0.990434i	−0.00601226	+	0.0418162i
$562$	9.81200	−	26.3070i	0.413894	−	1.10969i
$563$	−20.8820	+	11.4024i	−0.880070	+	0.480554i	−0.854699	−	0.519124i	$-0.826258\pi$
$563$	−20.8820	+	11.4024i	−0.880070	+	0.480554i	−0.0253705	+	0.999678i	$0.508077\pi$
$564$	−0.0928847	+	0.316336i	−0.00391115	+	0.0133202i
$565$	−2.61931	−	19.7719i	−0.110195	−	0.831808i
$566$	3.69093	+	0.530676i	0.155142	+	0.0223060i
$567$	36.1844	−	2.58796i	1.51960	−	0.108684i
$568$	7.58065	−	2.82744i	0.318077	−	0.118637i
$569$	−0.378590	−	0.243305i	−0.0158713	−	0.0101999i	0.532681	−	0.846316i	$-0.321185\pi$
$569$	−0.378590	−	0.243305i	−0.0158713	−	0.0101999i	−0.548552	+	0.836116i	$0.684821\pi$
$570$	−2.30629	+	1.68689i	−0.0965999	+	0.0706559i
$571$	−5.18400	−	8.06646i	−0.216944	−	0.337571i	0.715676	−	0.698433i	$-0.246119\pi$
$571$	−5.18400	−	8.06646i	−0.216944	−	0.337571i	−0.932619	+	0.360862i	$0.882483\pi$
$572$	−1.26277	+	17.6559i	−0.0527992	+	0.738229i
$573$	0.0513698	−	0.0940768i	0.00214601	−	0.00393012i
$574$	18.2072			0.759956
$575$	16.2822	+	17.6037i	0.679016	+	0.734124i
$576$	2.94945			0.122894
$577$	3.29705	−	6.03810i	0.137258	−	0.251369i	−0.800004	−	0.599994i	$-0.795169\pi$
$577$	3.29705	−	6.03810i	0.137258	−	0.251369i	0.937262	+	0.348625i	$0.113351\pi$
$578$	−1.05781	+	14.7902i	−0.0439992	+	0.615190i
$579$	−2.18970	−	3.40724i	−0.0910008	−	0.141600i
$580$	11.4331	−	8.36252i	0.474735	−	0.347235i
$581$	−1.68088	−	1.08024i	−0.0697348	−	0.0448158i
$582$	2.72569	−	1.01663i	0.112983	−	0.0421406i
$583$	25.2455	−	1.80559i	1.04556	−	0.0747800i
$584$	−5.67097	−	0.815362i	−0.234666	−	0.0337399i
$585$	−5.07698	−	38.3235i	−0.209907	−	1.58448i
$586$	3.85217	−	13.1193i	0.159132	−	0.541953i
$587$	−13.6135	+	7.43355i	−0.561890	+	0.306815i	−0.734978	−	0.678091i	$-0.762807\pi$
$587$	−13.6135	+	7.43355i	−0.561890	+	0.306815i	0.173088	+	0.984906i	$0.444626\pi$
$588$	−0.865234	+	2.31978i	−0.0356816	+	0.0956662i
$589$	2.21355	−	15.3956i	0.0912079	−	0.634365i
$590$	12.4724	+	19.8890i	0.513483	+	0.818819i
$591$	0.390476	−	0.855024i	0.0160621	−	0.0351710i
$592$	−1.33399	−	6.13224i	−0.0548265	−	0.252033i
$593$	−20.0355	+	26.7643i	−0.822760	+	1.09908i	0.170748	+	0.985315i	$0.445381\pi$
$593$	−20.0355	+	26.7643i	−0.822760	+	1.09908i	−0.993508	+	0.113763i	$0.963709\pi$
$594$	−3.39811	+	2.18383i	−0.139426	+	0.0896038i
$595$	−13.0495	−	5.03275i	−0.534978	−	0.206323i
$596$	−4.15644	−	14.1555i	−0.170255	−	0.579834i
$597$	2.10821	+	2.10821i	0.0862832	+	0.0862832i
$598$	27.5654	−	5.51326i	1.12723	−	0.225454i
$599$			32.4892i			1.32747i	0.747968	+	0.663735i	$0.231030\pi$
$599$			32.4892i			1.32747i	−0.747968	+	0.663735i	$0.768970\pi$
$600$	−1.07132	−	0.340552i	−0.0437366	−	0.0139030i
$601$	−1.65841	−	1.91391i	−0.0676479	−	0.0780699i	0.720917	−	0.693022i	$-0.243721\pi$
$601$	−1.65841	−	1.91391i	−0.0676479	−	0.0780699i	−0.788565	+	0.614952i	$0.789175\pi$
$602$	−1.92890	+	8.86703i	−0.0786163	+	0.361393i
$603$	−10.3781	−	7.76895i	−0.422629	−	0.316376i
$604$	−6.60375	+	10.2756i	−0.268703	+	0.418109i
$605$	−4.19777	+	0.253475i	−0.170663	+	0.0103052i
$606$	0.255499	−	0.294862i	0.0103790	−	0.0119780i
$607$	16.9849	+	22.6891i	0.689395	+	0.920923i	0.999557	−	0.0297603i	$-0.00947439\pi$
$607$	16.9849	+	22.6891i	0.689395	+	0.920923i	−0.310163	+	0.950684i	$0.600383\pi$
$608$	−5.32530	−	1.98624i	−0.215970	−	0.0805525i
$609$	−5.79979	−	1.70297i	−0.235019	−	0.0690079i
$610$	−13.1437	+	19.9618i	−0.532173	+	0.808228i
$611$	3.57070	+	7.81874i	0.144455	+	0.316312i
$612$	3.47985	−	2.60498i	0.140664	−	0.105300i
$613$	−0.151619	−	2.11992i	−0.00612385	−	0.0856226i	0.993471	−	0.114085i	$-0.0363935\pi$
$613$	−0.151619	−	2.11992i	−0.00612385	−	0.0856226i	−0.999595	+	0.0284621i	$0.990939\pi$
$614$	−13.3658	−	6.10395i	−0.539399	−	0.246335i
$615$	1.64552	−	1.39420i	0.0663537	−	0.0562197i
$616$	1.82396	+	12.6859i	0.0734894	+	0.511130i
$617$	−4.31442	−	0.938545i	−0.173692	−	0.0377844i	0.124878	−	0.992172i	$-0.460146\pi$
$617$	−4.31442	−	0.938545i	−0.173692	−	0.0377844i	−0.298570	+	0.954388i	$0.596510\pi$
$618$	−4.10129	−	0.293330i	−0.164978	−	0.0117995i
$619$	10.8700	−	3.19171i	0.436900	−	0.128286i	−0.0558834	−	0.998437i	$-0.517798\pi$
$619$	10.8700	−	3.19171i	0.436900	−	0.128286i	0.492784	+	0.870152i	$0.335979\pi$
$620$	5.40291	−	2.87290i	0.216986	−	0.115378i
$621$	4.77686	+	4.28175i	0.191689	+	0.171821i
$622$	−15.2573	+	15.2573i	−0.611760	+	0.611760i
$623$	−37.4306	−	20.4386i	−1.49962	−	0.818857i
$624$	−0.995975	+	0.863017i	−0.0398709	+	0.0345483i
$625$	−20.4113	−	14.4353i	−0.816452	−	0.577414i
$626$	−22.4293	+	3.22485i	−0.896455	+	0.128891i
$627$	3.77070	−	0.820265i	0.150587	−	0.0327582i
$628$	3.59488	+	9.63823i	0.143451	+	0.384607i
$629$	−6.98992	−	6.05680i	−0.278706	−	0.241500i
$630$	−9.49025	−	26.3326i	−0.378101	−	1.04911i
$631$	17.5141	−	7.99843i	0.697226	−	0.318412i	−0.0350836	−	0.999384i	$-0.511170\pi$
$631$	17.5141	−	7.99843i	0.697226	−	0.318412i	0.732309	+	0.680972i	$0.238442\pi$
$632$	5.51877	+	10.1069i	0.219525	+	0.402030i
$633$	−1.53612	−	2.81320i	−0.0610553	−	0.111815i
$634$	20.4314	−	9.33069i	0.811433	−	0.370569i
$635$	−6.30051	+	13.4009i	−0.250028	+	0.531798i
$636$	1.42411	+	1.23399i	0.0564695	+	0.0489311i
$637$	22.5578	+	60.4799i	0.893773	+	2.39630i
$638$	−18.6927	+	4.06636i	−0.740053	+	0.160989i
$639$	23.6204	−	3.39611i	0.934411	−	0.134348i
$640$	−0.606142	−	2.15235i	−0.0239599	−	0.0850789i
$641$	23.8736	−	20.6866i	0.942949	−	0.817070i	−0.0403281	−	0.999186i	$-0.512840\pi$
$641$	23.8736	−	20.6866i	0.942949	−	0.817070i	0.983277	+	0.182117i	$0.0582948\pi$
$642$	2.03465	+	1.11100i	0.0803014	+	0.0438479i
$643$	−18.8496	+	18.8496i	−0.743354	+	0.743354i	−0.973222	−	0.229868i	$-0.926171\pi$
$643$	−18.8496	+	18.8496i	−0.743354	+	0.743354i	0.229868	+	0.973222i	$0.426171\pi$
$644$	18.6540	−	8.14315i	0.735071	−	0.320885i
$645$	0.504656	+	0.949081i	0.0198708	+	0.0373700i
$646$	−8.03721	+	2.35994i	−0.316220	+	0.0928505i
$647$	−2.33035	−	0.166670i	−0.0916155	−	0.00655247i	0.0254562	−	0.999676i	$-0.491896\pi$
$647$	−2.33035	−	0.166670i	−0.0916155	−	0.00655247i	−0.117072	+	0.993123i	$0.537351\pi$
$648$	8.35228	+	1.81693i	0.328109	+	0.0713756i
$649$	−4.51206	−	31.3821i	−0.177114	−	1.23185i
$650$	−26.9230	+	11.5808i	−1.05601	+	0.454235i
$651$	−2.37528	−	1.08476i	−0.0930947	−	0.0425149i
$652$	−1.50739	−	21.0761i	−0.0590341	−	0.825405i
$653$	20.2231	−	15.1388i	0.791390	−	0.592427i	−0.125257	−	0.992124i	$-0.539976\pi$
$653$	20.2231	−	15.1388i	0.791390	−	0.592427i	0.916647	+	0.399697i	$0.130885\pi$
$654$	−0.844884	−	1.85004i	−0.0330376	−	0.0723422i
$655$	−0.115828	−	0.562410i	−0.00452578	−	0.0219752i
$656$	4.11625	+	1.20864i	0.160712	+	0.0471894i
$657$	−15.8328	−	5.90533i	−0.617697	−	0.230389i
$658$	3.72964	+	4.98221i	0.145396	+	0.194227i
$659$	12.6866	−	14.6412i	0.494201	−	0.570339i	−0.452782	−	0.891621i	$-0.649568\pi$
$659$	12.6866	−	14.6412i	0.494201	−	0.570339i	0.946983	+	0.321283i	$0.104114\pi$
$660$	1.13626	+	1.00685i	0.0442287	+	0.0391915i
$661$	−0.0335207	+	0.0521592i	−0.00130380	+	0.00202876i	−0.841905	−	0.539626i	$-0.818566\pi$
$661$	−0.0335207	+	0.0521592i	−0.00130380	+	0.00202876i	0.840601	+	0.541655i	$0.182202\pi$
$662$	0.242105	+	0.181237i	0.00940967	+	0.00704399i
$663$	−0.412855	+	1.89787i	−0.0160340	+	0.0737070i
$664$	−0.308301	−	0.355799i	−0.0119644	−	0.0138077i
$665$	−0.598146	+	53.9350i	−0.0231951	+	2.09151i
$666$		−	18.5097i		−	0.717238i
$667$	14.1100	+	26.9052i	0.546340	+	1.04177i
$668$	1.04400	+	1.04400i	0.0403936	+	0.0403936i
$669$	0.307318	+	1.04663i	0.0118816	+	0.0404650i
$670$	−3.53654	+	9.16996i	−0.136629	+	0.354266i
$671$	27.1536	−	17.4506i	1.04825	−	0.673671i
$672$	−0.571829	+	0.763874i	−0.0220588	+	0.0294671i
$673$	0.156901	+	0.721264i	0.00604810	+	0.0278027i	0.980072	−	0.198642i	$-0.0636532\pi$
$673$	0.156901	+	0.721264i	0.00604810	+	0.0278027i	−0.974024	+	0.226445i	$0.927290\pi$
$674$	7.42647	−	16.2617i	0.286057	−	0.626378i
$675$	−5.79744	−	3.33464i	−0.223144	−	0.128350i
$676$	−3.03963	+	21.1411i	−0.116909	+	0.813119i
$677$	−1.70651	+	4.57533i	−0.0655864	+	0.175844i	−0.965609	−	0.260000i	$-0.916277\pi$
$677$	−1.70651	+	4.57533i	−0.0655864	+	0.175844i	0.900022	+	0.435844i	$0.143550\pi$
$678$	−1.76007	+	0.961070i	−0.0675950	+	0.0369097i
$679$	15.4713	−	52.6906i	0.593736	−	2.02208i
$680$	−2.61611	−	2.00405i	−0.100323	−	0.0768518i
$681$	−5.17927	−	0.744666i	−0.198470	−	0.0285357i
$682$	−8.24298	+	0.589550i	−0.315640	+	0.0225750i
$683$	0.879438	−	0.328013i	0.0336508	−	0.0125511i	−0.332582	−	0.943074i	$-0.607920\pi$
$683$	0.879438	−	0.328013i	0.0336508	−	0.0125511i	0.366233	+	0.930523i	$0.380647\pi$
$684$	−14.1025	−	9.06313i	−0.539223	−	0.346537i
$685$	30.1421	+	4.67552i	1.15167	+	0.178642i
$686$	9.20630	+	14.3253i	0.351498	+	0.546942i
$687$	−0.0102023	+	0.142647i	−0.000389243	+	0.00544233i
$688$	−1.02470	+	1.87659i	−0.0390662	+	0.0715444i
$689$	49.1279			1.87162
$690$	1.06234	−	2.16437i	0.0404426	−	0.0823961i
$691$	49.9682			1.90088			0.950439	−	0.310911i	$-0.100634\pi$
$691$	49.9682			1.90088			0.950439	+	0.310911i	$0.100634\pi$
$692$	7.45550	−	13.6537i	0.283415	−	0.519037i
$693$	−2.69671	+	37.7049i	−0.102440	+	1.43229i
$694$	10.1674	+	15.8208i	0.385951	+	0.600551i
$695$	18.2442	+	24.9433i	0.692043	+	0.946153i
$696$	−1.19816	−	0.770008i	−0.0454160	−	0.0291871i
$697$	5.92395	−	2.20952i	0.224386	−	0.0836915i
$698$	−34.6313	+	2.47688i	−1.31081	+	0.0937511i
$699$	−4.00310	−	0.575559i	−0.151411	−	0.0217696i
$700$	−17.2657	+	12.3371i	−0.652582	+	0.466297i
$701$	−5.75276	+	19.5921i	−0.217279	+	0.739983i	0.776648	+	0.629935i	$0.216919\pi$
$701$	−5.75276	+	19.5921i	−0.217279	+	0.739983i	−0.993926	+	0.110048i	$0.964900\pi$
$702$	−6.88150	+	3.75758i	−0.259725	+	0.141821i
$703$	−12.4649	+	33.4198i	−0.470124	+	1.26045i
$704$	−0.429764	+	2.98908i	−0.0161974	+	0.112655i
$705$	0.718582	+	0.164684i	0.0270634	+	0.00620237i
$706$	2.51319	−	5.50312i	0.0945852	−	0.207113i
$707$	−1.56554	−	7.19668i	−0.0588782	−	0.270659i
$708$	1.41457	−	1.88965i	0.0531630	−	0.0710174i
$709$	−42.0369	+	27.0155i	−1.57873	+	1.01459i	−0.602428	+	0.798173i	$0.705800\pi$
$709$	−42.0369	+	27.0155i	−1.57873	+	1.01459i	−0.976301	+	0.216415i	$0.930564\pi$
$710$	−7.33253	−	16.5390i	−0.275185	−	0.620696i
$711$	9.56884	+	32.5885i	0.358860	+	1.22216i
$712$	−7.10545	−	7.10545i	−0.266288	−	0.266288i
$713$	4.37928	+	12.3721i	0.164005	+	0.463339i
$714$			1.40628i			0.0526288i
$715$	39.5782	+	0.438926i	1.48014	+	0.0164149i
$716$	−10.1048	−	11.6616i	−0.377635	−	0.435814i
$717$	−0.403947	+	1.85691i	−0.0150857	+	0.0693478i
$718$	−2.89505	−	2.16720i	−0.108042	−	0.0808793i
$719$	−23.0848	+	35.9207i	−0.860918	+	1.33961i	0.0785258	+	0.996912i	$0.474979\pi$
$719$	−23.0848	+	35.9207i	−0.860918	+	1.33961i	−0.939444	+	0.342703i	$0.888658\pi$
$720$	−0.397515	−	6.58318i	−0.0148145	−	0.245341i
$721$	−50.8287	+	58.6594i	−1.89296	+	2.18459i
$722$	7.97279	+	10.6504i	0.296716	+	0.396367i
$723$	2.95809	+	1.10331i	0.110013	+	0.0410326i
$724$	10.6655	+	3.13167i	0.396380	+	0.116388i
$725$	−20.2061	−	24.3917i	−0.750435	−	0.905886i
$726$	0.175654	+	0.384630i	0.00651915	+	0.0142749i
$727$	1.97018	−	1.47486i	0.0730699	−	0.0546994i	−0.562118	−	0.827057i	$-0.690013\pi$
$727$	1.97018	−	1.47486i	0.0730699	−	0.0546994i	0.635188	+	0.772357i	$0.280923\pi$
$728$	1.77472	+	24.8138i	0.0657755	+	0.919661i
$729$	22.1119	+	10.0982i	0.818958	+	0.374006i
$730$	−1.05558	+	12.7675i	−0.0390688	+	0.472547i
$731$	0.448455	+	3.11908i	0.0165867	+	0.115363i
$732$	2.34819	+	0.510818i	0.0867916	+	0.0188804i
$733$	0.131669	+	0.00941717i	0.00486331	+	0.000347831i	0.0737706	−	0.997275i	$-0.476497\pi$
$733$	0.131669	+	0.00941717i	0.00486331	+	0.000347831i	−0.0689073	+	0.997623i	$0.521951\pi$
$734$	−18.1960	+	5.34282i	−0.671626	+	0.197207i
$735$	5.29437	+	1.61855i	0.195286	+	0.0597013i
$736$	4.75781	−	0.602687i	0.175375	−	0.0222153i
$737$	9.38552	−	9.38552i	0.345720	−	0.345720i
$738$	11.1055	+	6.06404i	0.408798	+	0.223220i
$739$	−13.4447	+	11.6499i	−0.494570	+	0.428547i	−0.866098	−	0.499875i	$-0.833379\pi$
$739$	−13.4447	+	11.6499i	−0.494570	+	0.428547i	0.371528	+	0.928422i	$0.378834\pi$
$740$	−13.5074	+	3.80394i	−0.496541	+	0.139836i
$741$	7.41405	−	1.06598i	0.272362	−	0.0391597i
$742$	34.7580	−	7.56115i	1.27601	−	0.277579i
$743$	8.77249	+	23.5200i	0.321831	+	0.862863i	0.992626	+	0.121220i	$0.0386806\pi$
$743$	8.77249	+	23.5200i	0.321831	+	0.862863i	−0.670794	+	0.741643i	$0.734047\pi$
$744$	−0.464990	−	0.402916i	−0.0170473	−	0.0147716i
$745$	−31.0350	+	11.1850i	−1.13704	+	0.409787i
$746$	−23.4335	+	10.7017i	−0.857962	+	0.391818i
$747$	−0.665470	−	1.21872i	−0.0243483	−	0.0445906i
$748$	2.13293	+	3.90617i	0.0779877	+	0.142824i
$749$	39.8063	−	18.1789i	1.45449	−	0.664243i
$750$	−0.615725	+	2.43709i	−0.0224831	+	0.0889901i
$751$	−29.3836	−	25.4611i	−1.07222	−	0.929087i	−0.0745474	−	0.997217i	$-0.523751\pi$
$751$	−29.3836	−	25.4611i	−1.07222	−	0.929087i	−0.997676	+	0.0681302i	$0.978297\pi$
$752$	0.512456	+	1.37395i	0.0186873	+	0.0501027i
$753$	0.506431	−	0.110167i	0.0184554	−	0.00401472i
$754$	−36.7542	+	5.28445i	−1.33851	+	0.192448i
$755$	23.8253	+	13.3547i	0.867090	+	0.486026i
$756$	−4.29035	+	3.71761i	−0.156038	+	0.135208i
$757$	−10.3839	−	5.67003i	−0.377409	−	0.206081i	0.279336	−	0.960193i	$-0.409886\pi$
$757$	−10.3839	−	5.67003i	−0.377409	−	0.206081i	−0.656745	+	0.754112i	$0.728067\pi$
$758$	10.6382	−	10.6382i	0.386397	−	0.386397i
$759$	−2.49626	+	2.09066i	−0.0906086	+	0.0758861i
$760$	−3.71556	+	12.1538i	−0.134778	+	0.440864i
$761$	−6.63294	+	1.94761i	−0.240444	+	0.0706007i	−0.399734	−	0.916631i	$-0.630898\pi$
$761$	−6.63294	+	1.94761i	−0.240444	+	0.0706007i	0.159290	+	0.987232i	$0.449079\pi$
$762$	1.48512	+	0.106218i	0.0538001	+	0.00384786i
$763$	−37.5151	−	8.16090i	−1.35814	−	0.295445i
$764$	−0.0678491	−	0.471901i	−0.00245469	−	0.0170728i
$765$	−6.28332	−	7.41594i	−0.227174	−	0.268124i
$766$	10.7061	+	4.88932i	0.386828	+	0.176658i
$767$	−4.39025	−	61.3838i	−0.158523	−	2.21644i
$768$	−0.179985	+	0.134735i	−0.00649466	+	0.00486184i
$769$	0.758068	+	1.65994i	0.0273366	+	0.0598588i	0.922808	−	0.385261i	$-0.125888\pi$
$769$	0.758068	+	1.65994i	0.0273366	+	0.0598588i	−0.895471	+	0.445120i	$0.853161\pi$
$770$	28.0692	−	5.78084i	1.01154	−	0.208327i
$771$	−3.40774	−	1.00060i	−0.122727	−	0.0360358i
$772$	−16.8787	−	6.29542i	−0.607477	−	0.226577i
$773$	−27.5155	−	36.7564i	−0.989664	−	1.32204i	−0.946409	−	0.322972i	$-0.895318\pi$
$773$	−27.5155	−	36.7564i	−0.989664	−	1.32204i	−0.0432551	−	0.999064i	$-0.513773\pi$
$774$	−4.12975	+	4.76599i	−0.148441	+	0.171310i
$775$	−7.14050	−	11.6721i	−0.256494	−	0.419275i
$776$	6.99545	−	10.8851i	0.251122	−	0.390753i
$777$	4.79381	+	3.58860i	0.171977	+	0.128740i
$778$	−4.82171	+	22.1650i	−0.172867	+	0.794655i
$779$	−15.9675	−	18.4275i	−0.572095	−	0.660233i
$780$	2.06049	+	2.10670i	0.0737774	+	0.0754321i
$781$			24.4326i			0.874268i
$782$	5.08110	−	4.91321i	0.181700	−	0.175696i
$783$	−5.99167	−	5.99167i	−0.214125	−	0.214125i
$784$	3.10252	+	10.5662i	0.110804	+	0.377365i
$785$	21.0281	−	9.32277i	0.750524	−	0.332744i
$786$	−0.0485701	+	0.0312141i	−0.00173244	+	0.00111337i
$787$	14.8378	−	19.8210i	0.528912	−	0.706544i	−0.453921	−	0.891042i	$-0.649975\pi$
$787$	14.8378	−	19.8210i	0.528912	−	0.706544i	0.982833	+	0.184498i	$0.0590660\pi$
$788$	−0.888693	−	4.08525i	−0.0316584	−	0.145531i
$789$	−1.15749	+	2.53454i	−0.0412076	+	0.0902320i
$790$	21.8148	−	13.6801i	0.776134	−	0.486715i
$791$	−5.38735	+	37.4698i	−0.191552	+	1.33227i
$792$	−3.11261	+	8.34522i	−0.110602	+	0.296535i
$793$	54.9886	−	30.0261i	1.95270	−	1.06626i
$794$	6.00160	−	20.4396i	0.212989	−	0.725374i
$795$	2.56234	−	3.34492i	0.0908770	−	0.118632i
$796$	13.1260	+	1.88723i	0.465238	+	0.0668912i
$797$	−13.5655	+	0.970221i	−0.480513	+	0.0343670i	−0.309495	−	0.950901i	$-0.600160\pi$
$797$	−13.5655	+	0.970221i	−0.480513	+	0.0343670i	−0.171018	+	0.985268i	$0.554706\pi$
$798$	5.08139	−	1.89526i	0.179879	−	0.0670914i
$799$	1.81809	+	1.16842i	0.0643195	+	0.0413356i
$800$	−4.72235	+	1.64300i	−0.166960	+	0.0580886i
$801$	−16.0235	−	24.9330i	−0.566162	−	0.880965i
$802$	0.647285	−	9.05022i	0.0228564	−	0.319575i
$803$	8.29167	−	15.1851i	0.292607	−	0.535869i
$804$	0.988204			0.0348513
$805$	−20.6896	−	40.5383i	−0.729214	−	1.42879i
$806$	−16.0409			−0.565017
$807$	−1.34166	+	2.45706i	−0.0472285	+	0.0864926i
$808$	0.123799	−	1.73093i	0.00435522	−	0.0608939i
$809$	25.5823	+	39.8068i	0.899426	+	1.39953i	0.916654	+	0.399683i	$0.130880\pi$
$809$	25.5823	+	39.8068i	0.899426	+	1.39953i	−0.0172276	+	0.999852i	$0.505484\pi$
$810$	2.92970	−	18.8872i	0.102939	−	0.663628i
$811$	−6.61161	−	4.24903i	−0.232165	−	0.149203i	0.419386	−	0.907808i	$-0.362245\pi$
$811$	−6.61161	−	4.24903i	−0.232165	−	0.149203i	−0.651552	+	0.758604i	$0.725882\pi$
$812$	−25.1903	+	9.39550i	−0.884007	+	0.329717i
$813$	1.32215	−	0.0945623i	0.0463700	−	0.00331645i
$814$	18.7584	+	2.69705i	0.657482	+	0.0945317i
$815$	−46.8388	+	6.20506i	−1.64069	+	0.217354i
$816$	−0.0933524	+	0.317929i	−0.00326799	+	0.0111297i
$817$	10.6659	−	5.82403i	0.373153	−	0.203757i
$818$	8.03291	−	21.5371i	0.280864	−	0.753026i
$819$	−10.4422	+	72.6272i	−0.364881	+	2.53780i
$820$	2.14292	−	9.35037i	0.0748339	−	0.326529i
$821$	19.0072	−	41.6200i	0.663357	−	1.45255i	−0.216004	−	0.976392i	$-0.569303\pi$
$821$	19.0072	−	41.6200i	0.663357	−	1.45255i	0.879361	−	0.476156i	$-0.157970\pi$
$822$	−0.651925	−	2.99685i	−0.0227385	−	0.104527i
$823$	17.7508	−	23.7122i	0.618753	−	0.826557i	−0.376238	−	0.926523i	$-0.622783\pi$
$823$	17.7508	−	23.7122i	0.618753	−	0.826557i	0.994991	+	0.0999663i	$0.0318735\pi$
$824$	−15.3852	+	9.88745i	−0.535968	+	0.344446i
$825$	2.09415	−	2.67183i	0.0729089	−	0.0930210i
$826$	−12.5535	−	42.7534i	−0.436793	−	1.48758i
$827$	−10.6633	−	10.6633i	−0.370799	−	0.370799i	0.496969	−	0.867768i	$-0.334446\pi$
$827$	−10.6633	−	10.6633i	−0.370799	−	0.370799i	−0.867768	+	0.496969i	$0.834446\pi$
$828$	14.0901	+	1.24594i	0.489665	+	0.0432995i
$829$		−	46.7260i		−	1.62286i	−0.584448	−	0.811431i	$-0.698689\pi$
$829$		−	46.7260i		−	1.62286i	0.584448	−	0.811431i	$-0.301311\pi$
$830$	−0.752592	+	0.736082i	−0.0261228	+	0.0255498i
$831$	0.908119	+	1.04803i	0.0315023	+	0.0363556i
$832$	−1.24598	+	5.72765i	−0.0431964	+	0.198571i
$833$	12.9926	+	9.72615i	0.450167	+	0.336991i
$834$	1.67990	−	2.61397i	0.0581702	−	0.0905145i
$835$	2.18951	−	2.47092i	0.0757710	−	0.0855097i
$836$	11.2398	−	12.9714i	0.388736	−	0.448625i
$837$	−2.19367	−	2.93039i	−0.0758242	−	0.101289i
$838$	−6.57523	−	2.45243i	−0.227137	−	0.0847179i
$839$	39.6610	+	11.6455i	1.36925	+	0.402048i	0.882014	−	0.471223i	$-0.156187\pi$
$839$	39.6610	+	11.6455i	1.36925	+	0.402048i	0.487235	+	0.873271i	$0.338005\pi$
$840$	1.78204	+	1.17337i	0.0614861	+	0.0404852i
$841$	−4.62343	−	10.1239i	−0.159429	−	0.349100i
$842$	3.65021	−	2.73251i	0.125794	−	0.0941685i
$843$	0.450336	+	6.29651i	0.0155104	+	0.216863i
$844$	−12.9681	−	5.92234i	−0.446381	−	0.203855i
$845$	47.5966	+	3.93515i	1.63737	+	0.135373i
$846$	0.615524	+	4.28107i	0.0211622	+	0.147186i
$847$	7.79952	+	1.69668i	0.267995	+	0.0582987i
$848$	8.35994	+	0.597915i	0.287081	+	0.0205325i
$849$	−0.804405	+	0.236195i	−0.0276071	+	0.00810618i
$850$	−4.12045	+	6.10927i	−0.141330	+	0.209546i
$851$	−3.78226	−	29.8584i	−0.129654	−	1.02353i
$852$	−1.28626	+	1.28626i	−0.0440665	+	0.0440665i
$853$	−49.7540	−	27.1677i	−1.70355	−	0.930206i	−0.967353	−	0.253434i	$-0.918440\pi$
$853$	−49.7540	−	27.1677i	−1.70355	−	0.930206i	−0.736192	−	0.676772i	$-0.763378\pi$
$854$	34.2833	−	29.7066i	1.17315	−	1.01654i
$855$	−18.3283	+	32.6983i	−0.626813	+	1.11826i
$856$	10.2061	−	1.46741i	0.348836	−	0.0501550i
$857$	−7.39440	+	1.60855i	−0.252588	+	0.0549471i	−0.337076	−	0.941477i	$-0.609438\pi$
$857$	−7.39440	+	1.60855i	−0.252588	+	0.0549471i	0.0844884	+	0.996424i	$0.473074\pi$
$858$	−1.39076	−	3.72878i	−0.0474799	−	0.127299i
$859$	1.48111	+	1.28339i	0.0505349	+	0.0437887i	0.679762	−	0.733433i	$-0.262083\pi$
$859$	1.48111	+	1.28339i	0.0505349	+	0.0437887i	−0.629227	+	0.777221i	$0.716628\pi$
$860$	4.32666	+	2.03421i	0.147538	+	0.0693658i
$861$	−3.72360	+	1.70051i	−0.126900	+	0.0579533i
$862$	−6.52236	−	11.9448i	−0.222152	−	0.406842i
$863$	−3.33625	−	6.10989i	−0.113567	−	0.207983i	0.814713	−	0.579865i	$-0.196895\pi$
$863$	−3.33625	−	6.10989i	−0.113567	−	0.207983i	−0.928280	+	0.371881i	$0.878713\pi$
$864$	−1.21674	+	0.555664i	−0.0413942	+	0.0189041i
$865$	−31.4800	−	14.8005i	−1.07035	−	0.503232i
$866$	−7.32439	−	6.34662i	−0.248893	−	0.215667i
$867$	−1.16503	−	3.12357i	−0.0395665	−	0.106082i
$868$	−11.3490	+	2.46882i	−0.385209	+	0.0837971i
$869$	−34.4206	+	4.94893i	−1.16764	+	0.167881i
$870$	−1.55718	+	2.77806i	−0.0527932	+	0.0941852i
$871$	19.4710	−	16.8717i	0.659749	−	0.571676i
$872$	−7.93957	−	4.33534i	−0.268868	−	0.146813i
$873$	26.9857	−	26.9857i	0.913326	−	0.913326i
$874$	−24.6009	−	11.7382i	−0.832139	−	0.397051i
$875$	29.8634	+	36.8743i	1.00957	+	1.24658i
$876$	1.23593	−	0.362903i	0.0417584	−	0.0122614i
$877$	−52.7657	−	3.77388i	−1.78177	−	0.127435i	−0.858802	−	0.512308i	$-0.828791\pi$
$877$	−52.7657	−	3.77388i	−1.78177	−	0.127435i	−0.922969	+	0.384873i	$0.874245\pi$
$878$	17.4412	+	3.79410i	0.588612	+	0.128045i
$879$	0.437494	+	3.04284i	0.0147563	+	0.102632i
$880$	6.72955	+	0.556380i	0.226853	+	0.0187556i
$881$	40.6738	+	18.5751i	1.37034	+	0.625811i	0.958407	−	0.285405i	$-0.0921281\pi$
$881$	40.6738	+	18.5751i	1.37034	+	0.625811i	0.411929	+	0.911216i	$0.364855\pi$
$882$	2.31711	+	32.3975i	0.0780212	+	1.09088i
$883$	−20.1204	+	15.0619i	−0.677105	+	0.506874i	−0.881602	−	0.471993i	$-0.843535\pi$
$883$	−20.1204	+	15.0619i	−0.677105	+	0.506874i	0.204498	+	0.978867i	$0.434444\pi$
$884$	3.58868	+	7.85811i	0.120700	+	0.264297i
$885$	−4.40836	−	2.90266i	−0.148185	−	0.0975717i
$886$	17.8594	+	5.24399i	0.599998	+	0.176175i
$887$	−1.79174	−	0.668283i	−0.0601606	−	0.0224387i	0.319204	−	0.947686i	$-0.396585\pi$
$887$	−1.79174	−	0.668283i	−0.0601606	−	0.0224387i	−0.379364	+	0.925247i	$0.623857\pi$
$888$	0.845552	+	1.12953i	0.0283749	+	0.0379044i
$889$	18.4055	−	21.2411i	0.617302	−	0.712404i
$890$	−14.9017	+	16.8170i	−0.499507	+	0.563708i
$891$	−13.9551	+	21.7146i	−0.467515	+	0.727468i
$892$	3.88401	+	2.90754i	0.130046	+	0.0973515i
$893$	1.77164	−	8.14408i	0.0592855	−	0.272531i
$894$	2.17214	+	2.50678i	0.0726471	+	0.0838392i
$895$	−24.6668	+	24.1257i	−0.824520	+	0.806433i
$896$			4.24409i			0.141785i
$897$	−5.12253	+	3.70207i	−0.171036	+	0.123608i
$898$	−18.9812	−	18.9812i	−0.633410	−	0.633410i
$899$	−4.88407	−	16.6336i	−0.162893	−	0.554762i
$900$	−14.6401	+	1.77451i	−0.488004	+	0.0591503i
$901$	10.3914	−	6.67813i	0.346187	−	0.222481i
$902$	−7.76369	+	10.3711i	−0.258503	+	0.345319i
$903$	−0.433675	−	1.99357i	−0.0144318	−	0.0663419i
$904$	−3.70529	+	8.11346i	−0.123236	+	0.269850i
$905$	5.55245	−	24.2275i	0.184570	−	0.805349i
$906$	0.390827	−	2.71826i	0.0129844	−	0.0903083i
$907$	3.62408	−	9.71653i	0.120336	−	0.322632i	−0.862790	−	0.505562i	$-0.831285\pi$
$907$	3.62408	−	9.71653i	0.120336	−	0.322632i	0.983126	+	0.182930i	$0.0585580\pi$
$908$	−20.4265	+	11.1537i	−0.677877	+	0.370149i
$909$	1.44200	−	4.91101i	0.0478282	−	0.162888i
$910$	55.1453	−	7.30548i	1.82805	−	0.242174i
$911$	16.5997	+	2.38667i	0.549972	+	0.0790740i	0.411698	−	0.911320i	$-0.364936\pi$
$911$	16.5997	+	2.38667i	0.549972	+	0.0790740i	0.138273	+	0.990394i	$0.455845\pi$
$912$	1.27460	−	0.0911611i	0.0422062	−	0.00301865i
$913$	1.33206	−	0.496832i	0.0440847	−	0.0164427i
$914$	−10.5799	−	6.79932i	−0.349954	−	0.224901i
$915$	0.823667	−	5.31001i	0.0272296	−	0.175544i
$916$	0.343896	+	0.535112i	0.0113626	+	0.0176806i
$917$	−0.0777501	+	1.08709i	−0.00256753	+	0.0358988i
$918$	−0.944771	+	1.73022i	−0.0311821	+	0.0571058i
$919$	25.5261			0.842030			0.421015	−	0.907054i	$-0.361674\pi$
$919$	25.5261			0.842030			0.421015	+	0.907054i	$0.361674\pi$
$920$	−1.98644	−	10.5382i	−0.0654909	−	0.347435i
$921$	3.30356			0.108856
$922$	8.58393	−	15.7203i	0.282697	−	0.517720i
$923$	−3.38326	+	47.3041i	−0.111361	+	1.55703i
$924$	−1.55785	−	2.42407i	−0.0512497	−	0.0797460i
$925$	10.3109	+	29.6358i	0.339019	+	0.974420i
$926$	−7.53901	−	4.84503i	−0.247747	−	0.159218i
$927$	−50.5397	+	18.8504i	−1.65994	+	0.619127i
$928$	−6.31866	+	0.451919i	−0.207420	+	0.0148350i
$929$	−39.8653	−	5.73177i	−1.30794	−	0.188053i	−0.547140	−	0.837041i	$-0.684283\pi$
$929$	−39.8653	−	5.73177i	−1.30794	−	0.188053i	−0.760799	+	0.648988i	$0.775193\pi$
$930$	−0.836640	+	1.09216i	−0.0274345	+	0.0358134i
$931$	17.6337	−	60.0548i	0.577920	−	1.96822i
$932$	−15.7878	+	8.62079i	−0.517147	+	0.282383i
$933$	1.69530	−	4.54529i	0.0555018	−	0.148806i
$934$	−5.62993	+	39.1570i	−0.184217	+	1.28126i
$935$	8.43112	−	5.28716i	0.275727	−	0.172909i
$936$	−7.18192	+	15.7262i	−0.234748	+	0.514027i
$937$	−3.91494	−	17.9967i	−0.127896	−	0.587926i	−0.995828	−	0.0912449i	$-0.970915\pi$
$937$	−3.91494	−	17.9967i	−0.127896	−	0.587926i	0.867933	−	0.496681i	$-0.165448\pi$
$938$	11.1791	−	14.9335i	0.365009	−	0.487596i
$939$	4.28587	−	2.75436i	0.139864	−	0.0898852i
$940$	2.99759	−	1.32898i	0.0977705	−	0.0433465i
$941$	−4.06915	−	13.8582i	−0.132650	−	0.451766i	0.866200	−	0.499697i	$-0.166555\pi$
$941$	−4.06915	−	13.8582i	−0.132650	−	0.451766i	−0.998851	+	0.0479313i	$0.984737\pi$
$942$	−1.63538	−	1.63538i	−0.0532837	−	0.0532837i
$943$	19.1535	+	7.51273i	0.623725	+	0.244648i
$944$		−	10.4989i		−	0.341711i
$945$	8.87595	+	9.07503i	0.288735	+	0.295211i
$946$	−4.22828	−	4.87969i	−0.137473	−	0.158652i
$947$	3.77450	−	17.3511i	0.122655	−	0.563835i	−0.874268	−	0.485444i	$-0.838658\pi$
$947$	3.77450	−	17.3511i	0.122655	−	0.563835i	0.996923	−	0.0783913i	$-0.0249784\pi$
$948$	−2.07261	−	1.55154i	−0.0673153	−	0.0503916i
$949$	18.1563	−	28.2517i	0.589377	−	0.917088i
$950$	27.6281	+	6.65510i	0.896373	+	0.215920i
$951$	−3.30700	+	3.81648i	−0.107237	+	0.123758i
$952$	3.74842	+	5.00730i	0.121487	+	0.162287i
$953$	−34.3479	−	12.8111i	−1.11264	−	0.414993i	−0.275124	−	0.961409i	$-0.588719\pi$
$953$	−34.3479	−	12.8111i	−1.11264	−	0.414993i	−0.837514	+	0.546416i	$0.815992\pi$
$954$	23.7189	+	6.96449i	0.767927	+	0.225484i
$955$	−1.04414	+	0.215040i	−0.0337875	+	0.00695853i
$956$	3.51124	+	7.68855i	0.113562	+	0.248666i
$957$	3.44310	−	2.57748i	0.111300	−	0.0833180i
$958$	−1.68149	−	23.5103i	−0.0543265	−	0.759584i
$959$	−52.6625	−	24.0502i	−1.70056	−	0.776621i
$960$	0.324987	+	0.383569i	0.0104889	+	0.0123796i
$961$	3.34596	+	23.2717i	0.107934	+	0.750700i
$962$	35.9448	+	7.81931i	1.15891	+	0.252105i
$963$	30.3343	+	2.16956i	0.977511	+	0.0699129i
$964$	13.4736	−	3.95621i	0.433956	−	0.127421i
$965$	−11.7766	+	38.5217i	−0.379101	+	1.24006i
$966$	−3.05442	+	3.40761i	−0.0982743	+	0.109638i
$967$	−28.9418	+	28.9418i	−0.930706	+	0.930706i	−0.997750	−	0.0670441i	$-0.978643\pi$
$967$	−28.9418	+	28.9418i	−0.930706	+	0.930706i	0.0670441	+	0.997750i	$0.478643\pi$
$968$	1.65067	+	0.901332i	0.0530544	+	0.0289699i
$969$	1.42329	−	1.23329i	0.0457228	−	0.0396190i
$970$	−25.2384	−	14.1468i	−0.810358	−	0.454226i
$971$	21.2763	−	3.05907i	0.682789	−	0.0981703i	0.207813	−	0.978169i	$-0.433366\pi$
$971$	21.2763	−	3.05907i	0.682789	−	0.0981703i	0.474977	+	0.879998i	$0.342457\pi$
$972$	−5.79897	+	1.26149i	−0.186002	+	0.0404623i
$973$	−20.4978	−	54.9568i	−0.657131	−	1.76184i
$974$	13.9678	+	12.1032i	0.447559	+	0.387812i
$975$	4.42446	−	4.88295i	0.141696	−	0.156380i
$976$	9.72268	−	4.44020i	0.311215	−	0.142127i
$977$	2.09656	+	3.83956i	0.0670749	+	0.122838i	0.909065	−	0.416655i	$-0.136798\pi$
$977$	2.09656	+	3.83956i	0.0670749	+	0.122838i	−0.841990	+	0.539493i	$0.818616\pi$
$978$	2.27674	+	4.16954i	0.0728021	+	0.133327i
$979$	27.6028	−	12.6058i	0.882188	−	0.402882i
$980$	23.1657	−	8.34890i	0.740000	−	0.266696i
$981$	−20.1642	−	17.4724i	−0.643793	−	0.557850i
$982$	−8.24130	−	22.0958i	−0.262991	−	0.705105i
$983$	49.7752	−	10.8279i	1.58758	−	0.345358i	0.669832	−	0.742513i	$-0.266366\pi$
$983$	49.7752	−	10.8279i	1.58758	−	0.345358i	0.917752	+	0.397155i	$0.130002\pi$
$984$	−0.954707	+	0.137266i	−0.0304349	+	0.00437588i
$985$	−8.99853	+	2.53416i	−0.286717	+	0.0807450i
$986$	−7.05579	+	6.11388i	−0.224702	+	0.194706i
$987$	−1.22808	−	0.670584i	−0.0390903	−	0.0213449i
$988$	23.5575	−	23.5575i	0.749466	−	0.749466i
$989$	−5.68790	+	8.53197i	−0.180865	+	0.271301i
$990$	19.0461	+	5.82261i	0.605324	+	0.185055i
$991$	−49.3161	+	14.4805i	−1.56658	+	0.459989i	−0.946003	−	0.324157i	$-0.894919\pi$
$991$	−49.3161	+	14.4805i	−1.56658	+	0.459989i	−0.620576	+	0.784146i	$0.713101\pi$
$992$	−2.72963	−	0.195227i	−0.0866659	−	0.00619847i
$993$	−0.0664405	−	0.0144532i	−0.00210843	−	0.000458660i
$994$	4.88680	+	33.9884i	0.155000	+	1.07805i
$995$	2.44324	−	29.5516i	0.0774559	−	0.936848i
$996$	0.0962820	+	0.0439705i	0.00305081	+	0.00139326i
$997$	0.585079	+	8.18047i	0.0185296	+	0.259078i	0.998270	+	0.0588041i	$0.0187287\pi$
$997$	0.585079	+	8.18047i	0.0185296	+	0.259078i	−0.979740	+	0.200274i	$0.935817\pi$
$998$	−20.0995	+	15.0463i	−0.636239	+	0.476282i
$999$	3.48716	+	7.63581i	0.110329	+	0.241586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.83.4	yes	240
5.2	odd	4	inner	230.2.l.a.37.3	✓	240
23.5	odd	22	inner	230.2.l.a.143.3	yes	240
115.97	even	44	inner	230.2.l.a.97.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.37.3	✓	240	5.2	odd	4	inner
230.2.l.a.83.4	yes	240	1.1	even	1	trivial
230.2.l.a.97.4	yes	240	115.97	even	44	inner
230.2.l.a.143.3	yes	240	23.5	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.479249 + 0.877679i) q^{2} +(0.0160392 - 0.224257i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(-1.80481 + 1.32009i) q^{5} +(0.189139 + 0.121552i) q^{6} +(3.97650 - 1.48316i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(2.91943 + 0.419751i) q^{9} +O(q^{10})\)	\(q+(-0.479249 + 0.877679i) q^{2} +(0.0160392 - 0.224257i) q^{3} +(-0.540641 - 0.841254i) q^{4} +(-1.80481 + 1.32009i) q^{5} +(0.189139 + 0.121552i) q^{6} +(3.97650 - 1.48316i) q^{7} +(0.997452 - 0.0713392i) q^{8} +(2.91943 + 0.419751i) q^{9} +(-0.293662 - 2.21670i) q^{10} +(-0.850780 + 2.89749i) q^{11} +(-0.197328 + 0.107749i) q^{12} +(-2.04842 + 5.49203i) q^{13} +(-0.603997 + 4.20089i) q^{14} +(0.267092 + 0.425915i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(0.313276 + 1.44011i) q^{17} +(-1.76754 + 2.36116i) q^{18} +(4.78140 - 3.07282i) q^{19} +(2.08629 + 0.804611i) q^{20} +(-0.268828 - 0.915545i) q^{21} +(-2.13533 - 2.13533i) q^{22} +(-2.36877 + 4.17000i) q^{23} -0.224830i q^{24} +(1.51471 - 4.76504i) q^{25} +(-3.83854 - 4.42991i) q^{26} +(0.284330 - 1.30704i) q^{27} +(-3.39757 - 2.54339i) q^{28} +(3.42485 - 5.32917i) q^{29} +(-0.501820 + 0.0303016i) q^{30} +(1.79209 - 2.06819i) q^{31} +(-0.599278 - 0.800541i) q^{32} +(0.636136 + 0.237266i) q^{33} +(-1.41409 - 0.415214i) q^{34} +(-5.21894 + 7.92617i) q^{35} +(-1.22525 - 2.68292i) q^{36} +(-5.02392 + 3.76086i) q^{37} +(0.405468 + 5.66918i) q^{38} +(1.19877 + 0.547460i) q^{39} +(-1.70604 + 1.44548i) q^{40} +(-0.610534 - 4.24636i) q^{41} +(0.932390 + 0.202829i) q^{42} +(2.13268 + 0.152532i) q^{43} +(2.89749 - 0.850780i) q^{44} +(-5.82314 + 3.09635i) q^{45} +(-2.52469 - 4.07749i) q^{46} +(1.03690 - 1.03690i) q^{47} +(0.197328 + 0.107749i) q^{48} +(8.32253 - 7.21151i) q^{49} +(3.45626 + 3.61307i) q^{50} +(0.327979 - 0.0471562i) q^{51} +(5.72765 - 1.24598i) q^{52} +(-2.92896 - 7.85285i) q^{53} +(1.01090 + 0.875950i) q^{54} +(-2.28946 - 6.35254i) q^{55} +(3.86056 - 1.76306i) q^{56} +(-0.612411 - 1.12155i) q^{57} +(3.03595 + 5.55992i) q^{58} +(-9.55015 + 4.36141i) q^{59} +(0.213902 - 0.454959i) q^{60} +(-8.07789 - 6.99953i) q^{61} +(0.956345 + 2.56406i) q^{62} +(12.2317 - 2.66084i) q^{63} +(0.989821 - 0.142315i) q^{64} +(-3.55297 - 12.6162i) q^{65} +(-0.513111 + 0.444614i) q^{66} +(-3.85770 - 2.10646i) q^{67} +(1.04213 - 1.04213i) q^{68} +(0.897158 + 0.598097i) q^{69} +(-4.45546 - 8.37916i) q^{70} +(7.76304 - 2.27943i) q^{71} +(2.94194 + 0.210411i) q^{72} +(-5.59835 - 1.21785i) q^{73} +(-0.893119 - 6.21178i) q^{74} +(-1.04430 - 0.416112i) q^{75} +(-5.17004 - 2.36108i) q^{76} +(0.914309 + 12.7837i) q^{77} +(-1.05500 + 0.789766i) q^{78} +(4.78369 + 10.4748i) q^{79} +(-0.451051 - 2.19010i) q^{80} +(8.20138 + 2.40814i) q^{81} +(4.01954 + 1.49921i) q^{82} +(-0.282133 - 0.376886i) q^{83} +(-0.624866 + 0.721134i) q^{84} +(-2.46648 - 2.18557i) q^{85} +(-1.15596 + 1.79871i) q^{86} +(-1.14017 - 0.853521i) q^{87} +(-0.641908 + 2.95080i) q^{88} +(-6.58045 - 7.59424i) q^{89} +(0.0731368 - 6.59477i) q^{90} +24.8772i q^{91} +(4.78868 - 0.261733i) q^{92} +(-0.435061 - 0.435061i) q^{93} +(0.413134 + 1.40701i) q^{94} +(-4.57314 + 11.8578i) q^{95} +(-0.189139 + 0.121552i) q^{96} +(7.75416 - 10.3583i) q^{97} +(2.34083 + 10.7606i) q^{98} +(-3.70002 + 8.10191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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