LMFDB - Embedded newform 538.2.d.b.21.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(5,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(134))

chi = DirichletCharacter(H, H._module([104]))

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

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

chi := DirichletCharacter("538.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.d (of order $67$, degree $66$, 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:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$792$
Relative dimension:	$12$ over $\Q(\zeta_{67})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{67}]$

Embedding invariants

Embedding label			21.8
Character	$\chi$	$=$	538.21
Dual form			538.2.d.b.205.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0702762 + 0.997528i) q^{2} +(1.38143 + 0.262179i) q^{3} +(-0.990123 + 0.140205i) q^{4} +(1.40783 + 2.62461i) q^{5} +(-0.164449 + 1.39644i) q^{6} +(3.20066 + 0.764442i) q^{7} +(-0.209440 - 0.977821i) q^{8} +(-0.951795 - 0.374779i) q^{9} +(-2.51919 + 1.58880i) q^{10} +(1.81390 - 0.918877i) q^{11} +(-1.40454 - 0.0659064i) q^{12} +(-0.642654 + 0.405309i) q^{13} +(-0.537622 + 3.24646i) q^{14} +(1.25670 + 3.99482i) q^{15} +(0.960685 - 0.277640i) q^{16} +(-1.43102 - 0.724920i) q^{17} +(0.306964 - 0.975780i) q^{18} +(0.000188652 - 0.00804521i) q^{19} +(-1.76191 - 2.40131i) q^{20} +(4.22105 + 1.89516i) q^{21} +(1.04408 + 1.74484i) q^{22} +(2.02835 + 0.384957i) q^{23} +(-0.0329623 - 1.40570i) q^{24} +(-2.14095 + 3.22458i) q^{25} +(-0.449470 - 0.612581i) q^{26} +(-4.78451 - 3.01750i) q^{27} +(-3.27622 - 0.308144i) q^{28} +(-5.63877 - 8.49279i) q^{29} +(-3.89662 + 1.53433i) q^{30} +(-0.417370 + 0.568832i) q^{31} +(0.344467 + 0.938798i) q^{32} +(2.74668 - 0.793796i) q^{33} +(0.622561 - 1.47843i) q^{34} +(2.49963 + 9.47670i) q^{35} +(0.994940 + 0.237631i) q^{36} +(-0.00525575 + 0.00538043i) q^{37} +(0.00803858 - 0.000377201i) q^{38} +(-0.994042 + 0.391414i) q^{39} +(2.27155 - 1.92631i) q^{40} +(-0.556885 + 7.90464i) q^{41} +(-1.59384 + 4.34380i) q^{42} +(3.96912 + 5.97807i) q^{43} +(-1.66715 + 1.16412i) q^{44} +(-0.356320 - 3.02572i) q^{45} +(-0.241461 + 2.05039i) q^{46} +(-3.57436 - 4.42103i) q^{47} +(1.39991 - 0.131668i) q^{48} +(3.41534 + 1.73013i) q^{49} +(-3.36706 - 1.90905i) q^{50} +(-1.78679 - 1.37661i) q^{51} +(0.579480 - 0.491409i) q^{52} +(-1.30625 + 3.56002i) q^{53} +(2.67380 - 4.98474i) q^{54} +(4.96537 + 3.46716i) q^{55} +(0.0771420 - 3.28977i) q^{56} +(0.00236989 - 0.0110644i) q^{57} +(8.07552 - 6.22167i) q^{58} +(-1.38258 + 0.195778i) q^{59} +(-1.80438 - 3.77916i) q^{60} +(4.35981 - 4.90337i) q^{61} +(-0.596757 - 0.376363i) q^{62} +(-2.75987 - 1.92713i) q^{63} +(-0.912270 + 0.409590i) q^{64} +(-1.96853 - 1.11611i) q^{65} +(0.984859 + 2.68410i) q^{66} +(1.68971 + 0.239270i) q^{67} +(1.51852 + 0.517124i) q^{68} +(2.70109 + 1.06358i) q^{69} +(-9.27760 + 3.15943i) q^{70} +(-0.507377 - 3.06383i) q^{71} +(-0.167123 + 1.00918i) q^{72} +(6.24937 + 2.12819i) q^{73} +(-0.00573648 - 0.00486463i) q^{74} +(-3.80298 + 3.89320i) q^{75} +(0.000941189 + 0.00799219i) q^{76} +(6.50809 - 1.55439i) q^{77} +(-0.460304 - 0.964078i) q^{78} +(-1.53721 - 2.56895i) q^{79} +(2.08118 + 2.13056i) q^{80} +(-3.57342 - 3.33053i) q^{81} -7.92423 q^{82} +(-4.39121 - 4.09273i) q^{83} +(-4.44507 - 1.28463i) q^{84} +(-0.112003 - 4.77645i) q^{85} +(-5.68435 + 4.37943i) q^{86} +(-5.56291 - 13.2105i) q^{87} +(-1.27840 - 1.58122i) q^{88} +(-4.10321 - 15.5563i) q^{89} +(2.99320 - 0.568075i) q^{90} +(-2.36675 + 0.805982i) q^{91} +(-2.06229 - 0.0967705i) q^{92} +(-0.725701 + 0.676374i) q^{93} +(4.15890 - 3.87622i) q^{94} +(0.0213812 - 0.0108312i) q^{95} +(0.229723 + 1.38719i) q^{96} +(4.08371 + 4.59285i) q^{97} +(-1.48584 + 3.52849i) q^{98} +(-2.07084 + 0.194772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 792 q - 12 q^{2} - 5 q^{3} - 12 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 12 q^{8} - 23 q^{9} - 9 q^{10} - 11 q^{11} - 5 q^{12} - 13 q^{13} - 8 q^{14} - 26 q^{15} - 12 q^{16} - 18 q^{17} - 23 q^{18} - 17 q^{19}+ \cdots - 123 q^{99}+O(q^{100}) $ 792 * q - 12 * q^2 - 5 * q^3 - 12 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 12 * q^8 - 23 * q^9 - 9 * q^10 - 11 * q^11 - 5 * q^12 - 13 * q^13 - 8 * q^14 - 26 * q^15 - 12 * q^16 - 18 * q^17 - 23 * q^18 - 17 * q^19 - 9 * q^20 + 179 * q^21 - 11 * q^22 - 26 * q^23 - 5 * q^24 - 55 * q^25 - 13 * q^26 + 169 * q^27 - 8 * q^28 - 33 * q^29 + 41 * q^30 - 40 * q^31 - 12 * q^32 - 54 * q^33 - 18 * q^34 - 58 * q^35 - 23 * q^36 + 154 * q^37 - 17 * q^38 - 44 * q^39 - 9 * q^40 + 88 * q^41 - 22 * q^42 - 23 * q^43 + 56 * q^44 - 85 * q^45 - 26 * q^46 + 167 * q^47 - 5 * q^48 - 64 * q^49 - 55 * q^50 - 38 * q^51 - 13 * q^52 + 61 * q^53 - 32 * q^54 - 40 * q^55 - 8 * q^56 - 68 * q^57 - 33 * q^58 - 53 * q^59 + 108 * q^60 + 12 * q^61 - 40 * q^62 - 88 * q^63 - 12 * q^64 - 84 * q^65 - 54 * q^66 - 61 * q^67 - 18 * q^68 - 60 * q^69 - 58 * q^70 - 100 * q^71 - 23 * q^72 + 15 * q^73 - 47 * q^74 - 81 * q^75 - 17 * q^76 - 98 * q^77 - 44 * q^78 - 3 * q^79 - 9 * q^80 + 148 * q^81 + 222 * q^82 + 120 * q^83 + 246 * q^84 + 26 * q^85 - 23 * q^86 - 146 * q^87 - 11 * q^88 - 102 * q^89 - 85 * q^90 - 80 * q^91 - 26 * q^92 + 12 * q^93 - 34 * q^94 - 78 * q^95 - 5 * q^96 - 90 * q^97 - 64 * q^98 - 123 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{32}{67}\right)$

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 $

$2$	0.0702762	+	0.997528i	0.0496928	+	0.705359i
$2$	0.0702762	+	0.997528i	0.0496928	+	0.705359i
$3$	1.38143	+	0.262179i	0.797567	+	0.151369i	0.569192	−	0.822204i	$-0.307256\pi$
$3$	1.38143	+	0.262179i	0.797567	+	0.151369i	0.228374	+	0.973573i	$0.426659\pi$
$4$	−0.990123	+	0.140205i	−0.495061	+	0.0701024i
$5$	1.40783	+	2.62461i	0.629603	+	1.17376i	0.972171	+	0.234271i	$0.0752702\pi$
$5$	1.40783	+	2.62461i	0.629603	+	1.17376i	−0.342569	+	0.939493i	$0.611297\pi$
$6$	−0.164449	+	1.39644i	−0.0671361	+	0.570092i
$7$	3.20066	+	0.764442i	1.20973	+	0.288932i	0.786788	−	0.617223i	$-0.211742\pi$
$7$	3.20066	+	0.764442i	1.20973	+	0.288932i	0.422946	+	0.906155i	$0.360996\pi$
$8$	−0.209440	−	0.977821i	−0.0740483	−	0.345712i
$9$	−0.951795	−	0.374779i	−0.317265	−	0.124926i
$10$	−2.51919	+	1.58880i	−0.796637	+	0.502423i
$11$	1.81390	−	0.918877i	0.546911	−	0.277052i	−0.156689	−	0.987648i	$-0.550082\pi$
$11$	1.81390	−	0.918877i	0.546911	−	0.277052i	0.703600	+	0.710596i	$0.251575\pi$
$12$	−1.40454	−	0.0659064i	−0.405456	−	0.0190255i
$13$	−0.642654	+	0.405309i	−0.178240	+	0.112412i	−0.619600	−	0.784918i	$-0.712705\pi$
$13$	−0.642654	+	0.405309i	−0.178240	+	0.112412i	0.441360	+	0.897330i	$0.354496\pi$
$14$	−0.537622	+	3.24646i	−0.143686	+	0.867654i
$15$	1.25670	+	3.99482i	0.324479	+	1.03146i
$16$	0.960685	−	0.277640i	0.240171	−	0.0694100i
$17$	−1.43102	−	0.724920i	−0.347073	−	0.175819i	0.269730	−	0.962936i	$-0.413065\pi$
$17$	−1.43102	−	0.724920i	−0.347073	−	0.175819i	−0.616804	+	0.787117i	$0.711573\pi$
$18$	0.306964	−	0.975780i	0.0723521	−	0.229994i
$19$	0.000188652	−	0.00804521i	4.32798e−5	−	0.00184570i	−0.999703	−	0.0243654i	$-0.992243\pi$
$19$	0.000188652	−	0.00804521i	4.32798e−5	−	0.00184570i	0.999746	+	0.0225197i	$0.00716885\pi$
$20$	−1.76191	−	2.40131i	−0.393976	−	0.536948i
$21$	4.22105	+	1.89516i	0.921108	+	0.413559i
$22$	1.04408	+	1.74484i	0.222598	+	0.372001i
$23$	2.02835	+	0.384957i	0.422940	+	0.0802692i	0.393560	−	0.919299i	$-0.371244\pi$
$23$	2.02835	+	0.384957i	0.422940	+	0.0802692i	0.0293807	+	0.999568i	$0.490647\pi$
$24$	−0.0329623	−	1.40570i	−0.00672839	−	0.286937i
$25$	−2.14095	+	3.22458i	−0.428190	+	0.644915i
$26$	−0.449470	−	0.612581i	−0.0881483	−	0.120137i
$27$	−4.78451	−	3.01750i	−0.920780	−	0.580717i
$28$	−3.27622	−	0.308144i	−0.619147	−	0.0582338i
$29$	−5.63877	−	8.49279i	−1.04709	−	1.57707i	−0.792354	−	0.610061i	$-0.791145\pi$
$29$	−5.63877	−	8.49279i	−1.04709	−	1.57707i	−0.254739	−	0.967010i	$-0.581989\pi$
$30$	−3.89662	+	1.53433i	−0.711423	+	0.280130i
$31$	−0.417370	+	0.568832i	−0.0749618	+	0.102165i	−0.842113	−	0.539301i	$-0.818689\pi$
$31$	−0.417370	+	0.568832i	−0.0749618	+	0.102165i	0.767151	+	0.641466i	$0.221674\pi$
$32$	0.344467	+	0.938798i	0.0608937	+	0.165958i
$33$	2.74668	−	0.793796i	0.478135	−	0.138182i
$34$	0.622561	−	1.47843i	0.106768	−	0.253548i
$35$	2.49963	+	9.47670i	0.422514	+	1.60185i
$36$	0.994940	+	0.237631i	0.165823	+	0.0396051i
$37$	−0.00525575	+	0.00538043i	−0.000864039	+	0.000884538i	−0.715779	−	0.698327i	$-0.753928\pi$
$37$	−0.00525575	+	0.00538043i	−0.000864039	+	0.000884538i	0.714915	+	0.699212i	$0.246465\pi$
$38$	0.00803858		0.000377201i	0.00130403		6.11901e-5i
$39$	−0.994042	+	0.391414i	−0.159174	+	0.0626764i
$40$	2.27155	−	1.92631i	0.359163	−	0.304576i
$41$	−0.556885	+	7.90464i	−0.0869708	+	1.23450i	0.740138	+	0.672455i	$0.234760\pi$
$41$	−0.556885	+	7.90464i	−0.0869708	+	1.23450i	−0.827108	+	0.562042i	$0.810016\pi$
$42$	−1.59384	+	4.34380i	−0.245935	+	0.670262i
$43$	3.96912	+	5.97807i	0.605286	+	0.911646i	0.999974	−	0.00716852i	$-0.00228183\pi$
$43$	3.96912	+	5.97807i	0.605286	+	0.911646i	−0.394689	+	0.918815i	$0.629148\pi$
$44$	−1.66715	+	1.16412i	−0.251333	+	0.175498i
$45$	−0.356320	−	3.02572i	−0.0531170	−	0.451048i
$46$	−0.241461	+	2.05039i	−0.0356015	+	0.302313i
$47$	−3.57436	−	4.42103i	−0.521374	−	0.644873i	0.446953	−	0.894557i	$-0.352509\pi$
$47$	−3.57436	−	4.42103i	−0.521374	−	0.644873i	−0.968327	+	0.249684i	$0.919673\pi$
$48$	1.39991	−	0.131668i	0.202059	−	0.0190046i
$49$	3.41534	+	1.73013i	0.487906	+	0.247161i
$50$	−3.36706	−	1.90905i	−0.476174	−	0.269980i
$51$	−1.78679	−	1.37661i	−0.250201	−	0.192764i
$52$	0.579480	−	0.491409i	0.0803594	−	0.0681461i
$53$	−1.30625	+	3.56002i	−0.179428	+	0.489007i	−0.996114	−	0.0880756i	$-0.971928\pi$
$53$	−1.30625	+	3.56002i	−0.179428	+	0.489007i	0.816686	+	0.577082i	$0.195809\pi$
$54$	2.67380	−	4.98474i	0.363858	−	0.678337i
$55$	4.96537	+	3.46716i	0.669530	+	0.467512i
$56$	0.0771420	−	3.28977i	0.0103085	−	0.439615i
$57$	0.00236989	−	0.0110644i	0.000313900	−	0.00146552i
$58$	8.07552	−	6.22167i	1.06037	−	0.816945i
$59$	−1.38258	+	0.195778i	−0.179997	+	0.0254882i	−0.229623	−	0.973280i	$-0.573749\pi$
$59$	−1.38258	+	0.195778i	−0.179997	+	0.0254882i	0.0496261	+	0.998768i	$0.484197\pi$
$60$	−1.80438	−	3.77916i	−0.232945	−	0.487888i
$61$	4.35981	−	4.90337i	0.558217	−	0.627812i	−0.399081	−	0.916916i	$-0.630671\pi$
$61$	4.35981	−	4.90337i	0.558217	−	0.627812i	0.957298	+	0.289104i	$0.0933573\pi$
$62$	−0.596757	−	0.376363i	−0.0757882	−	0.0477981i
$63$	−2.75987	−	1.92713i	−0.347711	−	0.242796i
$64$	−0.912270	+	0.409590i	−0.114034	+	0.0511988i
$65$	−1.96853	−	1.11611i	−0.244166	−	0.138437i
$66$	0.984859	+	2.68410i	0.121228	+	0.330390i
$67$	1.68971	+	0.239270i	0.206431	+	0.0292314i	0.242657	−	0.970112i	$-0.421981\pi$
$67$	1.68971	+	0.239270i	0.206431	+	0.0292314i	−0.0362253	+	0.999344i	$0.511533\pi$
$68$	1.51852	+	0.517124i	0.184148	+	0.0627105i
$69$	2.70109	+	1.06358i	0.325173	+	0.128040i
$70$	−9.27760	+	3.15943i	−1.10889	+	0.377624i
$71$	−0.507377	−	3.06383i	−0.0602146	−	0.363609i	−0.999775	−	0.0212254i	$-0.993243\pi$
$71$	−0.507377	−	3.06383i	−0.0602146	−	0.363609i	0.939560	−	0.342384i	$-0.111234\pi$
$72$	−0.167123	+	1.00918i	−0.0196956	+	0.118933i
$73$	6.24937	+	2.12819i	0.731433	+	0.249085i	0.663051	−	0.748574i	$-0.269261\pi$
$73$	6.24937	+	2.12819i	0.731433	+	0.249085i	0.0683820	+	0.997659i	$0.478216\pi$
$74$	−0.00573648	−	0.00486463i	−0.000666853	−	0.000565502i
$75$	−3.80298	+	3.89320i	−0.439130	+	0.449548i
$76$	0.000941189		0.00799219i	0.000107962		0.000916767i
$77$	6.50809	−	1.55439i	0.741666	−	0.177139i
$78$	−0.460304	−	0.964078i	−0.0521192	−	0.109160i
$79$	−1.53721	−	2.56895i	−0.172950	−	0.289029i	0.759374	−	0.650655i	$-0.225506\pi$
$79$	−1.53721	−	2.56895i	−0.172950	−	0.289029i	−0.932323	+	0.361625i	$0.882222\pi$
$80$	2.08118	+	2.13056i	0.232683	+	0.238204i
$81$	−3.57342	−	3.33053i	−0.397047	−	0.370059i
$82$	−7.92423			−0.875085
$83$	−4.39121	−	4.09273i	−0.481998	−	0.449236i	0.402747	−	0.915311i	$-0.368056\pi$
$83$	−4.39121	−	4.09273i	−0.481998	−	0.449236i	−0.884745	+	0.466076i	$0.845668\pi$
$84$	−4.44507	−	1.28463i	−0.484997	−	0.140165i
$85$	−0.112003	−	4.77645i	−0.0121484	−	0.518078i
$86$	−5.68435	+	4.37943i	−0.612959	+	0.472246i
$87$	−5.56291	−	13.2105i	−0.596407	−	1.41632i
$88$	−1.27840	−	1.58122i	−0.136278	−	0.168559i
$89$	−4.10321	−	15.5563i	−0.434939	−	1.64896i	−0.722627	−	0.691238i	$-0.757066\pi$
$89$	−4.10321	−	15.5563i	−0.434939	−	1.64896i	0.287688	−	0.957724i	$-0.407114\pi$
$90$	2.99320	−	0.568075i	0.315511	−	0.0598804i
$91$	−2.36675	+	0.805982i	−0.248103	+	0.0844899i
$92$	−2.06229	−	0.0967705i	−0.215008	−	0.0100890i
$93$	−0.725701	+	0.676374i	−0.0752517	+	0.0701367i
$94$	4.15890	−	3.87622i	0.428958	−	0.399801i
$95$	0.0213812	−	0.0108312i	0.00219366	−	0.00111126i
$96$	0.229723	+	1.38719i	0.0234460	+	0.141580i
$97$	4.08371	+	4.59285i	0.414638	+	0.466333i	0.917327	−	0.398135i	$-0.130342\pi$
$97$	4.08371	+	4.59285i	0.414638	+	0.466333i	−0.502689	+	0.864468i	$0.667656\pi$
$98$	−1.48584	+	3.52849i	−0.150092	+	0.356431i
$99$	−2.07084	+	0.194772i	−0.208127	+	0.0195753i
$100$	1.66770	−	3.49290i	0.166770	−	0.349290i
$101$	1.21467	−	5.67097i	0.120864	−	0.564282i	−0.875800	−	0.482673i	$-0.839666\pi$
$101$	1.21467	−	5.67097i	0.120864	−	0.564282i	0.996664	−	0.0816088i	$-0.0260058\pi$
$102$	1.24763	−	1.87912i	0.123534	−	0.186060i
$103$	2.33794	−	2.89173i	0.230364	−	0.284930i	−0.649294	−	0.760537i	$-0.724936\pi$
$103$	2.33794	−	2.89173i	0.230364	−	0.284930i	0.879658	+	0.475607i	$0.157771\pi$
$104$	0.530917	+	0.543513i	0.0520607	+	0.0532958i
$105$	0.968460	+	13.7467i	0.0945121	+	1.34154i
$106$	−3.64302	−	1.05284i	−0.353841	−	0.102261i
$107$	−5.81185	+	7.18851i	−0.561852	+	0.694940i	−0.976616	−	0.214989i	$-0.931028\pi$
$107$	−5.81185	+	7.18851i	−0.561852	+	0.694940i	0.414764	+	0.909929i	$0.363864\pi$
$108$	5.16032	+	2.31688i	0.496552	+	0.222942i
$109$	6.30084	−	7.08639i	0.603511	−	0.678753i	−0.364053	−	0.931378i	$-0.618607\pi$
$109$	6.30084	−	7.08639i	0.603511	−	0.678753i	0.967564	+	0.252625i	$0.0812940\pi$
$110$	−3.10964	+	5.19675i	−0.296493	+	0.495491i
$111$	−0.00867106	+	0.00605472i	−0.000823020	+	0.000574689i
$112$	3.28706	−	0.154242i	0.310598	−	0.0145745i
$113$	12.3805	−	7.01949i	1.16466	−	0.660338i	0.215929	−	0.976409i	$-0.430722\pi$
$113$	12.3805	−	7.01949i	1.16466	−	0.660338i	0.948735	+	0.316071i	$0.102364\pi$
$114$	0.0112036	+	0.00158647i	0.00104931	+	0.000148586i
$115$	1.84522	+	5.86559i	0.172067	+	0.546969i
$116$	6.77380	+	7.61832i	0.628932	+	0.707343i
$117$	0.763576	−	0.144918i	0.0705927	−	0.0133977i
$118$	−0.292457	−	1.36540i	−0.0269228	−	0.125696i
$119$	−4.02604	−	3.41415i	−0.369067	−	0.312975i
$120$	3.64301	−	2.06550i	0.332560	−	0.188554i
$121$	−4.06140	+	5.53527i	−0.369218	+	0.503206i
$122$	5.19763	+	4.00444i	0.470572	+	0.362545i
$123$	−2.84172	+	10.7737i	−0.256230	+	0.971430i
$124$	0.333494	−	0.621731i	0.0299487	−	0.0558331i
$125$	3.34897	+	0.314987i	0.299541	+	0.0281733i
$126$	1.72841	−	2.88848i	0.153979	−	0.257326i
$127$	−1.04768	+	0.250227i	−0.0929664	+	0.0222040i	−0.278523	−	0.960430i	$-0.589845\pi$
$127$	−1.04768	+	0.250227i	−0.0929664	+	0.0222040i	0.185557	+	0.982634i	$0.440591\pi$
$128$	−0.472689	−	0.881230i	−0.0417802	−	0.0778904i
$129$	3.91573	+	9.29888i	0.344761	+	0.818720i
$130$	0.975011	−	2.04210i	0.0855141	−	0.179104i
$131$	−1.12379	+	3.57231i	−0.0981859	+	0.312114i	−0.990154	−	0.139984i	$-0.955295\pi$
$131$	−1.12379	+	3.57231i	−0.0981859	+	0.312114i	0.891968	+	0.452099i	$0.149325\pi$
$132$	−2.60825	+	1.17105i	−0.227019	+	0.101927i
$133$	0.00675391	−	0.0256057i	0.000585638	−	0.00222030i
$134$	−0.119931	+	1.70235i	−0.0103605	+	0.147061i
$135$	1.18396	−	16.8056i	0.101899	−	1.44640i
$136$	−0.409129	+	1.55111i	−0.0350826	+	0.133007i
$137$	2.29610	−	1.03090i	0.196169	−	0.0880757i	−0.309132	−	0.951019i	$-0.600038\pi$
$137$	2.29610	−	1.03090i	0.196169	−	0.0880757i	0.505300	+	0.862943i	$0.331382\pi$
$138$	−0.871129	+	2.76915i	−0.0741554	+	0.235726i
$139$	7.43471	−	15.5715i	0.630604	−	1.32076i	−0.299722	−	0.954026i	$-0.596894\pi$
$139$	7.43471	−	15.5715i	0.630604	−	1.32076i	0.930326	−	0.366733i	$-0.119524\pi$
$140$	−3.80361	−	9.03263i	−0.321464	−	0.763397i
$141$	−3.77862	−	7.04444i	−0.318217	−	0.593249i
$142$	3.02060	−	0.721437i	0.253483	−	0.0605416i
$143$	−0.793280	+	1.32571i	−0.0663374	+	0.110861i
$144$	−1.01843	−	0.0957881i	−0.0848691	−	0.00798234i
$145$	14.3518	−	26.7560i	1.19186	−	2.22197i
$146$	−1.68374	+	6.38348i	−0.139347	+	0.528300i
$147$	4.26444	+	3.28548i	0.351725	+	0.270982i
$148$	0.00444947	−	0.00606417i	0.000365744	−	0.000498472i
$149$	−16.8589	+	9.55862i	−1.38114	+	0.783073i	−0.990505	−	0.137474i	$-0.956102\pi$
$149$	−16.8589	+	9.55862i	−1.38114	+	0.783073i	−0.390632	+	0.920547i	$0.627743\pi$
$150$	−4.15083	−	3.51998i	−0.338914	−	0.287405i
$151$	−3.46832	−	16.1927i	−0.282248	−	1.31774i	−0.863636	−	0.504116i	$-0.831818\pi$
$151$	−3.46832	−	16.1927i	−0.282248	−	1.31774i	0.581388	−	0.813627i	$-0.302510\pi$
$152$	−0.00790629	+	0.00150052i	−0.000641285	+	0.000121708i
$153$	1.09035	+	1.22629i	0.0881499	+	0.0991399i
$154$	2.00791	+	6.38277i	0.161802	+	0.514338i
$155$	−2.08055	−	0.294614i	−0.167114	−	0.0236639i
$156$	0.929346	−	0.526918i	0.0744072	−	0.0421872i
$157$	14.3074	−	0.671359i	1.14186	−	0.0535803i	0.532467	−	0.846451i	$-0.321265\pi$
$157$	14.3074	−	0.671359i	1.14186	−	0.0535803i	0.609390	+	0.792871i	$0.291414\pi$
$158$	2.45457	−	1.71395i	0.195275	−	0.136354i
$159$	−2.73786	+	4.57544i	−0.217126	+	0.362856i
$160$	−1.97903	+	2.22577i	−0.156456	+	0.175962i
$161$	6.19777	+	2.78267i	0.488453	+	0.219305i
$162$	3.07117	−	3.79865i	0.241294	−	0.298450i
$163$	7.30347	+	2.11072i	0.572052	+	0.165324i	0.551075	−	0.834456i	$-0.314218\pi$
$163$	7.30347	+	2.11072i	0.572052	+	0.165324i	0.0209770	+	0.999780i	$0.493322\pi$
$164$	−0.556885	−	7.90464i	−0.0434854	−	0.617249i
$165$	5.95027	+	6.09144i	0.463228	+	0.474218i
$166$	3.77402	−	4.66798i	0.292921	−	0.362305i
$167$	0.366140	−	0.551460i	0.0283328	−	0.0426732i	−0.818655	−	0.574286i	$-0.805280\pi$
$167$	0.366140	−	0.551460i	0.0283328	−	0.0426732i	0.846987	+	0.531613i	$0.178414\pi$
$168$	0.969075	−	4.52436i	0.0747657	−	0.349062i
$169$	−5.35250	+	11.2105i	−0.411731	+	0.862344i
$170$	4.75677	−	0.447396i	0.364827	−	0.0343137i
$171$	−0.00319473	+	0.00758669i	−0.000244307	+	0.000580169i
$172$	−4.76807	−	5.36253i	−0.363562	−	0.408889i
$173$	−0.00205442	−	0.0124057i	−0.000156194	−	0.000943189i	0.986485	−	0.163849i	$-0.0523910\pi$
$173$	−0.00205442	−	0.0124057i	−0.000156194	−	0.000943189i	−0.986642	+	0.162906i	$0.947913\pi$
$174$	12.7869	−	6.47755i	0.969374	−	0.491061i
$175$	−9.31745	+	8.68412i	−0.704333	+	0.656458i
$176$	1.48747	−	1.38636i	0.112122	−	0.104501i
$177$	−1.96126	−	0.0920300i	−0.147418	−	0.00691740i
$178$	15.2295	−	5.18630i	1.14150	−	0.388730i
$179$	−0.181148	+	0.0343797i	−0.0135396	+	0.00256966i	−0.193225	−	0.981154i	$-0.561895\pi$
$179$	−0.181148	+	0.0343797i	−0.0135396	+	0.00256966i	0.179686	+	0.983724i	$0.442492\pi$
$180$	0.777021	+	2.94588i	0.0579158	+	0.219573i
$181$	15.7201	+	19.4437i	1.16846	+	1.44524i	0.871530	+	0.490342i	$0.163128\pi$
$181$	15.7201	+	19.4437i	1.16846	+	1.44524i	0.296934	+	0.954898i	$0.404036\pi$
$182$	−0.970316	−	2.30426i	−0.0719246	−	0.170803i
$183$	7.30832	−	5.63059i	0.540246	−	0.416225i
$184$	−0.0483985	−	2.06399i	−0.00356799	−	0.152159i
$185$	−0.0215208	−	0.00621955i	−0.00158224	−	0.000457270i
$186$	−0.725701	−	0.676374i	−0.0532110	−	0.0495941i
$187$	−3.26184			−0.238529
$188$	4.15890	+	3.87622i	0.303319	+	0.282702i
$189$	−13.0069	−	13.3154i	−0.946111	−	0.968556i
$190$	0.0123070	+	0.0205671i	0.000892843	+	0.00149210i
$191$	−9.45387	−	19.8005i	−0.684058	−	1.43272i	−0.890835	−	0.454328i	$-0.849879\pi$
$191$	−9.45387	−	19.8005i	−0.684058	−	1.43272i	0.206777	−	0.978388i	$-0.433703\pi$
$192$	−1.36762	+	0.326641i	−0.0986994	+	0.0235733i
$193$	−1.71305	−	14.5466i	−0.123308	−	1.04708i	−0.905588	−	0.424158i	$-0.860570\pi$
$193$	−1.71305	−	14.5466i	−0.123308	−	1.04708i	0.782280	−	0.622927i	$-0.214057\pi$
$194$	−4.29450	+	4.39639i	−0.308327	+	0.315642i
$195$	−2.42676	−	2.05793i	−0.173784	−	0.147372i
$196$	−3.62418	−	1.23419i	−0.258870	−	0.0881567i
$197$	−3.79677	+	22.9270i	−0.270508	+	1.63348i	0.418138	+	0.908384i	$0.362683\pi$
$197$	−3.79677	+	22.9270i	−0.270508	+	1.63348i	−0.688646	+	0.725097i	$0.741795\pi$
$198$	−0.339821	−	2.05203i	−0.0241500	−	0.145831i
$199$	−19.2758	+	6.56425i	−1.36642	+	0.465327i	−0.906340	−	0.422549i	$-0.861135\pi$
$199$	−19.2758	+	6.56425i	−1.36642	+	0.465327i	−0.460083	+	0.887876i	$0.652180\pi$
$200$	3.60146	+	1.41811i	0.254662	+	0.100276i
$201$	2.27148	+	0.773540i	0.160218	+	0.0545613i
$202$	5.74231	+	0.813131i	0.404027	+	0.0572117i
$203$	−11.5555	−	31.4930i	−0.811038	−	2.21038i
$204$	1.96215	+	1.11249i	0.137378	+	0.0778901i
$205$	−21.5306	+	9.66682i	−1.50377	+	0.675160i
$206$	3.04888	+	2.12894i	0.212426	+	0.148330i
$207$	−1.78630	−	1.12658i	−0.124156	−	0.0783030i
$208$	−0.504858	+	0.567801i	−0.0350056	+	0.0393699i
$209$	−0.00705037	−	0.0147665i	−0.000487684	−	0.00102142i
$210$	−13.6447	+	1.93213i	−0.941571	+	0.133330i
$211$	10.7777	−	8.30355i	0.741970	−	0.571640i	−0.168260	−	0.985743i	$-0.553815\pi$
$211$	10.7777	−	8.30355i	0.741970	−	0.571640i	0.910230	+	0.414102i	$0.135904\pi$
$212$	0.794220	−	3.70800i	0.0545472	−	0.254667i
$213$	0.102366	−	4.36547i	0.00701401	−	0.299117i
$214$	−7.57917	−	5.29230i	−0.518102	−	0.361774i
$215$	−10.1023	+	18.8335i	−0.688968	+	1.28444i
$216$	−1.94850	+	5.31038i	−0.132579	+	0.361326i
$217$	−1.77070	+	1.50158i	−0.120203	+	0.101934i
$218$	7.51167	+	5.78726i	0.508754	+	0.391962i
$219$	8.07508	+	4.57838i	0.545663	+	0.309378i
$220$	−5.40244	−	2.73674i	−0.364232	−	0.184511i
$221$	1.21347	−	0.114132i	0.0816267	−	0.00767738i
$222$	−0.00664912	−	0.00822412i	−0.000446260	−	0.000551967i
$223$	−1.85127	+	15.7203i	−0.123970	+	1.05271i	0.780199	+	0.625532i	$0.215118\pi$
$223$	−1.85127	+	15.7203i	−0.123970	+	1.05271i	−0.904169	+	0.427175i	$0.859509\pi$
$224$	0.384862	+	3.26810i	0.0257147	+	0.218359i
$225$	3.24625	−	2.26675i	0.216417	−	0.151117i
$226$	7.87219	+	11.8566i	0.523650	+	0.788692i
$227$	−5.39047	+	14.6910i	−0.357778	+	0.975077i	0.623388	+	0.781913i	$0.285756\pi$
$227$	−5.39047	+	14.6910i	−0.357778	+	0.975077i	−0.981166	+	0.193165i	$0.938125\pi$
$228$	−0.000795200		0.0112874i	−5.26634e−5		0.000747525i
$229$	−6.87402	+	5.82929i	−0.454248	+	0.385210i	−0.844550	−	0.535477i	$-0.820132\pi$
$229$	−6.87402	+	5.82929i	−0.454248	+	0.385210i	0.390302	+	0.920687i	$0.372371\pi$
$230$	−5.72142	+	2.25287i	−0.377259	+	0.148550i
$231$	9.39798	−	0.440989i	0.618342	−	0.0290150i
$232$	−7.12344	+	7.29244i	−0.467677	+	0.478772i
$233$	−4.85798	−	1.16028i	−0.318257	−	0.0760122i	0.0700469	−	0.997544i	$-0.477685\pi$
$233$	−4.85798	−	1.16028i	−0.318257	−	0.0760122i	−0.388304	+	0.921531i	$0.626939\pi$
$234$	0.198221	+	0.751504i	0.0129581	+	0.0491274i
$235$	6.57139	−	15.6054i	0.428670	−	1.01798i
$236$	1.34148	−	0.387689i	0.0873226	−	0.0252364i
$237$	−1.45002	−	3.95184i	−0.0941890	−	0.256699i
$238$	3.12278	−	4.25602i	0.202420	−	0.275877i
$239$	−25.9462	+	10.2166i	−1.67832	+	0.660855i	−0.997438	−	0.0715383i	$-0.977209\pi$
$239$	−25.9462	+	10.2166i	−1.67832	+	0.660855i	−0.680882	+	0.732393i	$0.738403\pi$
$240$	2.31641	+	3.48885i	0.149524	+	0.225204i
$241$	−7.03128	−	0.661326i	−0.452925	−	0.0425997i	−0.135276	−	0.990808i	$-0.543192\pi$
$241$	−7.03128	−	0.661326i	−0.452925	−	0.0425997i	−0.317649	+	0.948208i	$0.602893\pi$
$242$	−5.80700	−	3.66236i	−0.373288	−	0.235425i
$243$	5.97559	+	8.14411i	0.383334	+	0.522445i
$244$	−3.62927	+	5.46620i	−0.232340	+	0.349938i
$245$	0.267312	+	11.3997i	0.0170779	+	0.728300i
$246$	−10.9467	−	2.07757i	−0.697939	−	0.132461i
$247$	0.00313956	+	0.00524675i	0.000199765	+	0.000333843i
$248$	0.643630	+	0.288977i	0.0408706	+	0.0183500i
$249$	−4.99311	−	6.80509i	−0.316425	−	0.431255i
$250$	−0.0788550	+	3.36283i	−0.00498723	+	0.212684i
$251$	−7.90235	+	25.1201i	−0.498792	+	1.58556i	0.281118	+	0.959673i	$0.409295\pi$
$251$	−7.90235	+	25.1201i	−0.498792	+	1.58556i	−0.779910	+	0.625892i	$0.784735\pi$
$252$	3.00280	+	1.52115i	0.189159	+	0.0958233i
$253$	4.03295	−	1.16553i	0.253549	−	0.0732763i
$254$	−0.323235	−	1.02750i	−0.0202816	−	0.0644713i
$255$	1.09756	−	6.62767i	0.0687318	−	0.415041i
$256$	0.845832	−	0.533449i	0.0528645	−	0.0333406i
$257$	26.3070	+	1.23443i	1.64099	+	0.0770014i	0.847227	−	0.531231i	$-0.178270\pi$
$257$	26.3070	+	1.23443i	1.64099	+	0.0770014i	0.793759	+	0.608232i	$0.208121\pi$
$258$	−9.00070	+	4.55954i	−0.560359	+	0.283864i
$259$	−0.0209349	+	0.0132032i	−0.00130083	+	0.000820407i
$260$	2.10557	+	0.829089i	0.130582	+	0.0514179i
$261$	2.18404	+	10.1967i	0.135188	+	0.631159i
$262$	−3.64246	−	0.869962i	−0.225032	−	0.0537464i
$263$	−3.13042	+	26.5822i	−0.193030	+	1.63913i	0.464408	+	0.885622i	$0.346267\pi$
$263$	−3.13042	+	26.5822i	−0.193030	+	1.63913i	−0.657437	+	0.753509i	$0.728360\pi$
$264$	−1.35146	−	2.51951i	−0.0831763	−	0.155065i
$265$	−11.1827	+	1.58351i	−0.686947	+	0.0972741i
$266$	0.0260171	+	0.00493774i	0.00159521	+	0.000302752i
$267$	−1.58976	−	22.5656i	−0.0972915	−	1.38099i
$268$	−1.70657			−0.104245
$269$	10.0530	+	12.9591i	0.612941	+	0.790128i
$269$	10.0530	+	12.9591i	0.612941	+	0.790128i
$270$	16.8473			1.02529
$271$	−0.636214	−	9.03066i	−0.0386472	−	0.548574i	−0.978400	−	0.206720i	$-0.933721\pi$
$271$	−0.636214	−	9.03066i	−0.0386472	−	0.548574i	0.939753	−	0.341854i	$-0.111055\pi$
$272$	−1.57603	−	0.299112i	−0.0955607	−	0.0181363i
$273$	−3.48080	+	0.492894i	−0.210668	+	0.0298313i
$274$	1.18971	+	2.21797i	0.0718731	+	0.133993i
$275$	−0.920478	+	7.81632i	−0.0555069	+	0.471342i
$276$	−2.82353	−	0.674369i	−0.169956	−	0.0405923i
$277$	−0.305125	−	1.42455i	−0.0183332	−	0.0855928i	0.967718	−	0.252036i	$-0.0811001\pi$
$277$	−0.305125	−	1.42455i	−0.0183332	−	0.0855928i	−0.986051	+	0.166443i	$0.946772\pi$
$278$	16.0555	+	6.32202i	0.962946	+	0.379169i
$279$	0.610437	−	0.384990i	0.0365459	−	0.0230488i
$280$	8.74299	−	4.42899i	0.522494	−	0.264683i
$281$	13.0363	+	0.611711i	0.777678	+	0.0364916i	0.432014	−	0.901867i	$-0.357803\pi$
$281$	13.0363	+	0.611711i	0.777678	+	0.0364916i	0.345664	+	0.938358i	$0.387654\pi$
$282$	6.76148	−	4.26433i	0.402640	−	0.253937i
$283$	−3.23301	+	19.5227i	−0.192183	+	1.16051i	0.701789	+	0.712384i	$0.252385\pi$
$283$	−3.23301	+	19.5227i	−0.192183	+	1.16051i	−0.893972	+	0.448122i	$0.852093\pi$
$284$	0.931929	+	2.96243i	0.0552998	+	0.175788i
$285$	0.0323762	−	0.00935679i	0.00191780	−	0.000554248i
$286$	−1.37818	−	0.698153i	−0.0814935	−	0.0412827i
$287$	−7.82504	+	24.8743i	−0.461898	+	1.46829i
$288$	0.0239800	−	1.02264i	0.00141303	−	0.0602598i
$289$	−8.53442	−	11.6315i	−0.502025	−	0.684208i
$290$	27.6985	+	12.4360i	1.62651	+	0.730270i
$291$	4.43720	+	7.41534i	0.260113	+	0.434695i
$292$	−6.48602	−	1.23097i	−0.379566	−	0.0720372i
$293$	−0.751599	−	32.0525i	−0.0439089	−	1.87253i	−0.372471	−	0.928044i	$-0.621489\pi$
$293$	−0.751599	−	32.0525i	−0.0439089	−	1.87253i	0.328562	−	0.944482i	$-0.393436\pi$
$294$	−2.97767	+	4.48479i	−0.173661	+	0.261558i
$295$	−2.46029	−	3.35312i	−0.143244	−	0.195226i
$296$	0.00636187	+	0.00401230i	0.000369776	+	0.000233210i
$297$	−11.4513	−	1.07705i	−0.664474	−	0.0624969i
$298$	−10.7198	−	16.1455i	−0.620980	−	0.935284i
$299$	−1.45955	+	0.574714i	−0.0844082	+	0.0332366i
$300$	3.21957	−	4.38794i	0.185882	−	0.253338i
$301$	8.13391	+	22.1679i	0.468831	+	1.27774i
$302$	15.9089	−	4.59771i	0.915455	−	0.264568i
$303$	3.16478	−	7.51556i	0.181812	−	0.431758i
$304$	−0.00205244	−	0.00778129i	−0.000117715	−	0.000446288i
$305$	19.0073	+	4.53970i	1.08836	+	0.259942i
$306$	−1.14663	+	1.17384i	−0.0655487	+	0.0671038i
$307$	−26.0248	+	1.22118i	−1.48531	+	0.0696966i	−0.774003	−	0.633181i	$-0.781749\pi$
$307$	−26.0248	+	1.22118i	−1.48531	+	0.0696966i	−0.711310	+	0.702878i	$0.751898\pi$
$308$	−6.22588	+	2.45150i	−0.354752	+	0.139687i
$309$	3.98784	−	3.38175i	0.226860	−	0.192381i
$310$	0.147672	−	2.09611i	0.00838720	−	0.119051i
$311$	−8.81627	+	24.0276i	−0.499925	+	1.36248i	0.395991	+	0.918254i	$0.370401\pi$
$311$	−8.81627	+	24.0276i	−0.499925	+	1.36248i	−0.895916	+	0.444224i	$0.853480\pi$
$312$	0.590926	+	0.890018i	0.0334546	+	0.0503874i
$313$	4.88679	−	3.41229i	0.276217	−	0.192874i	−0.426220	−	0.904620i	$-0.640155\pi$
$313$	4.88679	−	3.41229i	0.276217	−	0.192874i	0.702437	+	0.711746i	$0.252095\pi$
$314$	1.67517	+	14.2249i	0.0945354	+	0.802756i
$315$	1.17253	−	9.95668i	0.0660648	−	0.560996i
$316$	1.88221	+	2.32805i	0.105882	+	0.130963i
$317$	−23.0175	+	2.16491i	−1.29279	+	0.121593i	−0.717617	−	0.696438i	$-0.754767\pi$
$317$	−23.0175	+	2.16491i	−1.29279	+	0.121593i	−0.575174	+	0.818031i	$0.695066\pi$
$318$	−4.75653	−	2.40954i	−0.266733	−	0.135120i
$319$	−18.0320	−	10.2237i	−1.00960	−	0.572419i
$320$	−2.35934	−	1.81772i	−0.131891	−	0.101614i
$321$	−9.91331	+	8.40665i	−0.553307	+	0.469214i
$322$	−2.34024	+	6.37800i	−0.130416	+	0.355432i
$323$	−0.00610210	+	0.0113761i	−0.000339530	+	0.000632983i
$324$	4.00508	+	2.79662i	0.222505	+	0.155368i
$325$	0.0689409	−	2.94003i	0.00382415	−	0.163084i
$326$	−1.59224	+	7.43375i	−0.0881860	+	0.411717i
$327$	10.5620	−	8.13738i	0.584082	−	0.449998i
$328$	7.84596	−	1.11102i	0.433221	−	0.0613456i
$329$	−8.06068	−	16.8826i	−0.444399	−	0.930767i
$330$	−5.65822	+	6.36365i	−0.311475	+	0.350307i
$331$	−2.87531	−	1.81340i	−0.158041	−	0.0996735i	0.452096	−	0.891970i	$-0.350677\pi$
$331$	−2.87531	−	1.81340i	−0.158041	−	0.0996735i	−0.610137	+	0.792296i	$0.708886\pi$
$332$	4.92166	+	3.43664i	0.270111	+	0.188610i
$333$	0.00701887	−	0.00315133i	0.000384632	−	0.000172692i
$334$	0.575827	+	0.326481i	0.0315079	+	0.0178642i
$335$	1.75085	+	4.77170i	0.0956590	+	0.260706i
$336$	4.58127	+	0.648724i	0.249929	+	0.0353908i
$337$	5.07995	+	1.72995i	0.276722	+	0.0942362i	0.457264	−	0.889331i	$-0.348830\pi$
$337$	5.07995	+	1.72995i	0.276722	+	0.0942362i	−0.180541	+	0.983567i	$0.557785\pi$
$338$	−11.5589	−	4.55144i	−0.628722	−	0.247566i
$339$	18.9432	−	6.45099i	1.02885	−	0.350369i
$340$	0.780578	+	4.71356i	0.0423328	+	0.255629i
$341$	−0.234380	+	1.41532i	−0.0126924	+	0.0766436i
$342$	−0.00779245	−	0.00265367i	−0.000421367	−	0.000143494i
$343$	−7.95951	−	6.74980i	−0.429773	−	0.364455i
$344$	5.01419	−	5.13314i	0.270347	−	0.276760i
$345$	1.01120	+	8.58666i	0.0544409	+	0.462290i
$346$	0.0122307	−	0.00292116i	0.000657524	−	0.000157043i
$347$	6.60437	+	13.8324i	0.354541	+	0.742564i	0.999770	−	0.0214247i	$-0.00682021\pi$
$347$	6.60437	+	13.8324i	0.354541	+	0.742564i	−0.645229	+	0.763989i	$0.723238\pi$
$348$	7.36015	+	12.3001i	0.394545	+	0.659354i
$349$	15.1212	+	15.4799i	0.809417	+	0.828619i	0.987863	−	0.155331i	$-0.0496443\pi$
$349$	15.1212	+	15.4799i	0.809417	+	0.828619i	−0.178446	+	0.983950i	$0.557107\pi$
$350$	−9.31745	−	8.68412i	−0.498038	−	0.464186i
$351$	4.29780			0.229400
$352$	1.48747	+	1.38636i	0.0792824	+	0.0738934i
$353$	−16.1015	−	4.65336i	−0.856995	−	0.247673i	−0.180005	−	0.983666i	$-0.557611\pi$
$353$	−16.1015	−	4.65336i	−0.856995	−	0.247673i	−0.676990	+	0.735992i	$0.736716\pi$
$354$	−0.0460276	−	1.96288i	−0.00244634	−	0.104326i
$355$	7.32706	−	5.64503i	0.388880	−	0.299607i
$356$	6.24375	+	14.8273i	0.330918	+	0.785847i
$357$	−4.66656	−	5.77194i	−0.246981	−	0.305484i
$358$	−0.0470251	−	0.178284i	−0.00248535	−	0.00942258i
$359$	−22.8837	+	4.34306i	−1.20776	+	0.229218i	−0.750956	−	0.660352i	$-0.770407\pi$
$359$	−22.8837	+	4.34306i	−1.20776	+	0.229218i	−0.456799	+	0.889570i	$0.651004\pi$
$360$	−2.88399	+	0.982125i	−0.152000	+	0.0517626i
$361$	18.9791	+	0.890570i	0.998897	+	0.0468721i
$362$	−18.2909	+	17.0476i	−0.961348	+	0.896004i
$363$	−7.06175	+	6.58175i	−0.370646	+	0.345453i
$364$	2.23037	−	1.12985i	0.116903	−	0.0592203i
$365$	3.21241	+	19.3983i	0.168145	+	1.01535i
$366$	6.13027	+	6.89455i	0.320434	+	0.360384i
$367$	8.11304	−	19.2664i	0.423497	−	1.00570i	−0.560603	−	0.828085i	$-0.689431\pi$
$367$	8.11304	−	19.2664i	0.423497	−	1.00570i	0.984100	−	0.177615i	$-0.0568381\pi$
$368$	2.05549	−	0.193328i	0.107150	−	0.0100779i
$369$	3.49253	−	7.31489i	0.181814	−	0.380798i
$370$	0.00469177	−	0.0219047i	0.000243914	−	0.00113877i
$371$	−6.90230	+	10.3959i	−0.358350	+	0.539726i
$372$	0.623702	−	0.771440i	0.0323375	−	0.0399973i
$373$	−6.28772	−	6.43689i	−0.325566	−	0.333290i	0.532883	−	0.846189i	$-0.321109\pi$
$373$	−6.28772	−	6.43689i	−0.325566	−	0.333290i	−0.858449	+	0.512899i	$0.828571\pi$
$374$	−0.229230	−	3.25378i	−0.0118532	−	0.168249i
$375$	4.54377	+	1.31316i	0.234639	+	0.0678113i
$376$	−3.57436	+	4.42103i	−0.184334	+	0.227997i
$377$	7.06598	+	3.17248i	0.363916	+	0.163391i
$378$	12.3685	−	13.9105i	0.636165	−	0.715478i
$379$	6.09040	−	10.1781i	0.312843	−	0.522815i	−0.660898	−	0.750476i	$-0.729824\pi$
$379$	6.09040	−	10.1781i	0.312843	−	0.522815i	0.973740	+	0.227661i	$0.0731078\pi$
$380$	−0.0196514	+	0.0137219i	−0.00100810	+	0.000703921i
$381$	−1.51289	+	0.0709908i	−0.0775079	+	0.00363697i
$382$	19.0872	−	10.8220i	0.976586	−	0.553702i
$383$	−12.4900	−	1.76863i	−0.638210	−	0.0903729i	−0.186381	−	0.982477i	$-0.559676\pi$
$383$	−12.4900	−	1.76863i	−0.638210	−	0.0903729i	−0.451829	+	0.892105i	$0.649228\pi$
$384$	−0.421945	−	1.34128i	−0.0215323	−	0.0684470i
$385$	13.2420	+	14.8929i	0.674874	+	0.759013i
$386$	14.3902	−	2.73110i	0.732442	−	0.139009i
$387$	−1.53734	−	7.17744i	−0.0781474	−	0.364850i
$388$	−4.68732	−	3.97492i	−0.237962	−	0.201796i
$389$	21.9400	−	12.4395i	1.11240	−	0.630707i	0.176972	−	0.984216i	$-0.443370\pi$
$389$	21.9400	−	12.4395i	1.11240	−	0.630707i	0.935431	+	0.353509i	$0.115012\pi$
$390$	1.88230	−	2.56538i	0.0953140	−	0.129903i
$391$	−2.62355	−	2.02127i	−0.132678	−	0.102220i
$392$	0.976448	−	3.70196i	0.0493181	−	0.186977i
$393$	−2.48902	+	4.64025i	−0.125554	+	0.234070i
$394$	−23.1371	−	2.17616i	−1.16563	−	0.109633i
$395$	4.57836	−	7.65124i	0.230362	−	0.384976i
$396$	2.02307	−	0.483190i	0.101663	−	0.0242812i
$397$	−9.47267	−	17.6598i	−0.475420	−	0.886322i	−0.999402	−	0.0345922i	$-0.988987\pi$
$397$	−9.47267	−	17.6598i	−0.475420	−	0.886322i	0.523982	−	0.851730i	$-0.324446\pi$
$398$	−7.90265	−	18.7668i	−0.396124	−	0.940695i
$399$	0.0160433	−	0.0336017i	0.000803170	−	0.00168219i
$400$	−1.16151	+	3.69222i	−0.0580754	+	0.184611i
$401$	−2.78306	+	1.24954i	−0.138979	+	0.0623989i	−0.477890	−	0.878420i	$-0.658598\pi$
$401$	−2.78306	+	1.24954i	−0.138979	+	0.0623989i	0.338911	+	0.940819i	$0.389942\pi$
$402$	−0.611996	+	2.32023i	−0.0305236	+	0.115723i
$403$	0.0376716	−	0.534726i	0.00187656	−	0.0266366i
$404$	−0.407573	+	5.78525i	−0.0202775	+	0.287827i
$405$	3.71057	−	14.0677i	0.184380	−	0.699030i
$406$	30.6031	−	13.7401i	1.51880	−	0.681912i
$407$	−0.00458943	+	0.0145889i	−0.000227490	+	0.000723147i
$408$	−0.971850	+	2.03548i	−0.0481138	+	0.100771i
$409$	11.4356	+	27.1566i	0.565452	+	1.34281i	0.914076	+	0.405544i	$0.132918\pi$
$409$	11.4356	+	27.1566i	0.565452	+	1.34281i	−0.348623	+	0.937263i	$0.613351\pi$
$410$	−11.1560	−	20.7981i	−0.550956	−	1.02714i
$411$	3.44217	−	0.822125i	0.169790	−	0.0405524i
$412$	−1.90941	+	3.19096i	−0.0940698	+	0.157207i
$413$	−4.57483	−	0.430284i	−0.225113	−	0.0211729i
$414$	0.998264	−	1.86106i	0.0490620	−	0.0914659i
$415$	4.55975	−	17.2871i	0.223829	−	0.848592i
$416$	−0.601876	−	0.463707i	−0.0295094	−	0.0227351i
$417$	14.3530	−	19.5617i	0.702871	−	0.957940i
$418$	0.0142346	−	0.00807067i	0.000696235	−	0.000394749i
$419$	−15.1530	−	12.8500i	−0.740270	−	0.627762i	0.195365	−	0.980731i	$-0.437411\pi$
$419$	−15.1530	−	12.8500i	−0.740270	−	0.627762i	−0.935635	+	0.352969i	$0.885172\pi$
$420$	−2.88625	−	13.4751i	−0.140835	−	0.657519i
$421$	−12.2138	+	2.31803i	−0.595262	+	0.112974i	−0.475329	−	0.879808i	$-0.657671\pi$
$421$	−12.2138	+	2.31803i	−0.595262	+	0.112974i	−0.119933	+	0.992782i	$0.538268\pi$
$422$	9.04044	+	10.1675i	0.440082	+	0.494948i
$423$	1.74515	+	5.54751i	0.0848522	+	0.269729i
$424$	3.75465	+	0.531672i	0.182342	+	0.0258203i
$425$	5.40130	−	3.06241i	0.262002	−	0.148549i
$426$	4.36187	−	0.204676i	0.211334	−	0.00991658i
$427$	17.7026	−	12.3612i	0.856689	−	0.598199i
$428$	4.74657	−	7.93236i	0.229434	−	0.383425i
$429$	−1.44343	+	1.62339i	−0.0696895	+	0.0783780i
$430$	−19.4969	−	8.75372i	−0.940226	−	0.422142i
$431$	−9.28013	+	11.4783i	−0.447008	+	0.552892i	−0.950345	−	0.311198i	$-0.899270\pi$
$431$	−9.28013	+	11.4783i	−0.447008	+	0.552892i	0.503337	+	0.864090i	$0.332106\pi$
$432$	−5.43419	−	1.57049i	−0.261452	−	0.0755603i
$433$	0.417954	+	5.93261i	0.0200856	+	0.285103i	0.997332	+	0.0729965i	$0.0232562\pi$
$433$	0.417954	+	5.93261i	0.0200856	+	0.285103i	−0.977247	+	0.212106i	$0.931968\pi$
$434$	−1.62231	−	1.66079i	−0.0778732	−	0.0797206i
$435$	26.8409	−	33.1987i	1.28692	−	1.59176i
$436$	−5.24506	+	7.89980i	−0.251193	+	0.378332i
$437$	0.00347972	−	0.0162459i	0.000166457	−	0.000777146i
$438$	−3.99958	+	8.37686i	−0.191107	+	0.400262i
$439$	28.0735	−	2.64044i	1.33987	−	0.126022i	0.600667	−	0.799500i	$-0.294902\pi$
$439$	28.0735	−	2.64044i	1.33987	−	0.126022i	0.739207	+	0.673478i	$0.235200\pi$
$440$	2.35031	−	5.58141i	0.112047	−	0.266083i
$441$	−2.60229	−	2.92673i	−0.123919	−	0.139368i
$442$	0.199128	+	1.20245i	0.00947156	+	0.0571946i
$443$	−26.2488	+	13.2970i	−1.24712	+	0.631760i	−0.946721	−	0.322055i	$-0.895627\pi$
$443$	−26.2488	+	13.2970i	−1.24712	+	0.631760i	−0.300397	+	0.953814i	$0.597119\pi$
$444$	0.00773651	−	0.00721064i	0.000367158	−	0.000342202i
$445$	35.0526	−	32.6700i	1.66165	−	1.54871i
$446$	−15.8115	−	0.741936i	−0.748696	−	0.0351317i
$447$	−25.7954	+	8.78448i	−1.22008	+	0.415492i
$448$	−3.23297	+	0.613580i	−0.152743	+	0.0289889i
$449$	−5.62498	−	21.3257i	−0.265459	−	1.00642i	−0.958400	−	0.285427i	$-0.907864\pi$
$449$	−5.62498	−	21.3257i	−0.265459	−	1.00642i	0.692941	−	0.720994i	$-0.256315\pi$
$450$	2.48928	+	3.07892i	0.117346	+	0.145142i
$451$	6.25326	+	14.8499i	0.294455	+	0.699256i
$452$	−11.2741	+	8.68596i	−0.530289	+	0.408553i
$453$	−0.545854	−	23.2783i	−0.0256465	−	1.09371i
$454$	−15.0335	−	4.34472i	−0.705558	−	0.203908i
$455$	−5.44738	−	5.07712i	−0.255377	−	0.238019i
$456$	−0.0113154			−0.000529890
$457$	−18.3408	−	17.0941i	−0.857947	−	0.799631i	0.123303	−	0.992369i	$-0.460651\pi$
$457$	−18.3408	−	17.0941i	−0.857947	−	0.799631i	−0.981250	+	0.192738i	$0.938263\pi$
$458$	−6.29796	−	6.44737i	−0.294284	−	0.301266i
$459$	4.65929	+	7.78649i	0.217477	+	0.363442i
$460$	−2.64937	−	5.54895i	−0.123528	−	0.258721i
$461$	4.20262	−	1.00375i	0.195736	−	0.0467493i	−0.133259	−	0.991081i	$-0.542544\pi$
$461$	4.20262	−	1.00375i	0.195736	−	0.0467493i	0.328994	+	0.944332i	$0.393290\pi$
$462$	1.10035	+	9.34375i	0.0511931	+	0.434711i
$463$	−17.2737	+	17.6835i	−0.802779	+	0.821824i	−0.986943	−	0.161071i	$-0.948505\pi$
$463$	−17.2737	+	17.6835i	−0.802779	+	0.821824i	0.184164	+	0.982896i	$0.441042\pi$
$464$	−7.77502	−	6.59335i	−0.360946	−	0.306088i
$465$	−2.79689	−	0.952464i	−0.129703	−	0.0441694i
$466$	0.816007	−	4.92751i	0.0378008	−	0.228262i
$467$	−3.03862	−	18.3489i	−0.140611	−	0.849086i	−0.960851	−	0.277067i	$-0.910638\pi$
$467$	−3.03862	−	18.3489i	−0.140611	−	0.849086i	0.820240	−	0.572020i	$-0.193840\pi$
$468$	−0.735716	+	0.250544i	−0.0340085	+	0.0115814i
$469$	5.22528	+	2.05751i	0.241281	+	0.0950069i
$470$	16.0286	+	5.45845i	0.739345	+	0.251780i
$471$	19.9407	+	2.82367i	0.918818	+	0.130108i
$472$	0.481004	+	1.31091i	0.0221400	+	0.0603397i
$473$	12.6927	+	7.19647i	0.583611	+	0.330894i
$474$	3.84017	−	1.72416i	0.176385	−	0.0791931i
$475$	0.0255385	+	0.0178327i	0.00117179	+	0.000818221i
$476$	4.46496	+	2.81596i	0.204651	+	0.129069i
$477$	2.57751	−	2.89886i	0.118016	−	0.132730i
$478$	−12.0147	−	25.1641i	−0.549540	−	1.15098i
$479$	7.74666	−	1.09695i	0.353954	−	0.0501211i	0.0390300	−	0.999238i	$-0.487573\pi$
$479$	7.74666	−	1.09695i	0.353954	−	0.0501211i	0.314924	+	0.949117i	$0.398021\pi$
$480$	−3.31744	+	2.55587i	−0.151420	+	0.116659i
$481$	0.00119689	−	0.00558796i	5.45734e−5	−	0.000254789i
$482$	0.165559	−	7.06038i	0.00754100	−	0.321591i
$483$	7.83221	+	5.46898i	0.356378	+	0.248847i
$484$	3.24521	−	6.05002i	0.147510	−	0.275001i
$485$	−6.30526	+	17.1841i	−0.286307	+	0.780292i
$486$	−7.70404	+	6.53315i	−0.349462	+	0.296350i
$487$	20.4945	+	15.7897i	0.928696	+	0.715500i	0.958811	−	0.284046i	$-0.0916768\pi$
$487$	20.4945	+	15.7897i	0.928696	+	0.715500i	−0.0301148	+	0.999546i	$0.509587\pi$
$488$	−5.70774	−	3.23616i	−0.258377	−	0.146494i
$489$	9.53582	+	4.83062i	0.431225	+	0.218448i
$490$	−11.3527	+	1.06778i	−0.512864	+	0.0482373i
$491$	13.4649	+	16.6543i	0.607661	+	0.751600i	0.984635	−	0.174624i	$-0.0558711\pi$
$491$	13.4649	+	16.6543i	0.607661	+	0.751600i	−0.376974	+	0.926224i	$0.623035\pi$
$492$	1.30313	−	11.0657i	0.0587498	−	0.498880i
$493$	1.91260	+	16.2410i	0.0861391	+	0.731458i
$494$	−0.00501314	+	0.00350052i	−0.000225552	+	0.000157496i
$495$	−3.42660	−	5.16094i	−0.154014	−	0.231967i
$496$	−0.243030	+	0.662347i	−0.0109124	+	0.0297403i
$497$	0.718179	−	10.1941i	0.0322147	−	0.457269i
$498$	6.43737	−	5.45900i	0.288466	−	0.244624i
$499$	−2.13232	+	0.839623i	−0.0954558	+	0.0375867i	−0.413626	−	0.910447i	$-0.635738\pi$
$499$	−2.13232	+	0.839623i	−0.0954558	+	0.0375867i	0.318170	+	0.948034i	$0.396932\pi$
$500$	−3.36005	+	0.157667i	−0.150266	+	0.00705107i
$501$	0.650377	−	0.665807i	0.0290567	−	0.0297460i
$502$	−25.6133	−	6.11746i	−1.14318	−	0.273036i
$503$	−5.10547	−	19.3561i	−0.227642	−	0.863046i	−0.979119	−	0.203287i	$-0.934837\pi$
$503$	−5.10547	−	19.3561i	−0.227642	−	0.863046i	0.751477	−	0.659759i	$-0.229342\pi$
$504$	−1.30636	+	3.10228i	−0.0581900	+	0.138187i
$505$	16.5942	−	4.79574i	0.738430	−	0.213408i
$506$	1.44607	+	3.94107i	0.0642856	+	0.175202i
$507$	−10.3332	+	14.0831i	−0.458915	+	0.625454i
$508$	1.00225	−	0.394645i	0.0444675	−	0.0175095i
$509$	−0.622301	−	0.937274i	−0.0275830	−	0.0415439i	0.819044	−	0.573731i	$-0.194505\pi$
$509$	−0.622301	−	0.937274i	−0.0275830	−	0.0415439i	−0.846627	+	0.532187i	$0.821370\pi$
$510$	6.68842	+	0.629078i	0.296168	+	0.0278560i
$511$	18.3752	+	11.5889i	0.812871	+	0.512661i
$512$	0.591572	+	0.806252i	0.0261440	+	0.0356316i
$513$	−0.0251790	+	0.0379231i	−0.00111168	+	0.00167435i
$514$	0.617383	+	26.3287i	0.0272316	+	1.16131i
$515$	10.8811	+	2.06511i	0.479479	+	0.0909995i
$516$	−5.18080	−	8.65802i	−0.228072	−	0.381148i
$517$	−10.5459	−	4.73490i	−0.463809	−	0.208241i
$518$	−0.0146418	−	0.0199552i	−0.000643323	−	0.000876782i
$519$	0.000414489	−	0.0176762i	1.81941e−5	−	0.000775899i
$520$	−0.679068	+	2.15863i	−0.0297791	+	0.0946622i
$521$	24.5194	+	12.4209i	1.07421	+	0.544171i	0.897917	−	0.440166i	$-0.145080\pi$
$521$	24.5194	+	12.4209i	1.07421	+	0.544171i	0.176298	+	0.984337i	$0.443588\pi$
$522$	−10.0180	+	2.89522i	−0.438476	+	0.126720i
$523$	1.74452	+	5.54551i	0.0762827	+	0.242488i	0.984317	−	0.176407i	$-0.0564474\pi$
$523$	1.74452	+	5.54551i	0.0762827	+	0.242488i	−0.908035	+	0.418895i	$0.862418\pi$
$524$	0.611833	−	3.69459i	0.0267280	−	0.161399i
$525$	−15.1482	+	9.55364i	−0.661120	+	0.416955i
$526$	−26.7365	−	1.25458i	−1.16577	−	0.0547023i
$527$	1.00962	−	0.511450i	0.0439799	−	0.0222791i
$528$	2.41830	−	1.52518i	0.105243	−	0.0663747i
$529$	−17.4347	−	6.86508i	−0.758030	−	0.298482i
$530$	−2.36547	−	11.0437i	−0.102749	−	0.479710i
$531$	1.38931	+	0.331821i	0.0602908	+	0.0143998i
$532$	−0.00309715	+	0.0262997i	−0.000134278	+	0.00114024i
$533$	−2.84594	−	5.30566i	−0.123271	−	0.229814i
$534$	22.3981	−	3.17165i	0.969261	−	0.137251i
$535$	−27.0492	−	5.13362i	−1.16944	−	0.221946i
$536$	−0.119931	−	1.70235i	−0.00518024	−	0.0735304i
$537$	−0.259256			−0.0111877
$538$	−12.2205	+	10.9388i	−0.526865	+	0.471607i
$539$	7.78487			0.335318
$540$	1.18396	+	16.8056i	0.0509497	+	0.723199i
$541$	−8.95031	−	1.69867i	−0.384804	−	0.0730313i	−0.00955237	−	0.999954i	$-0.503041\pi$
$541$	−8.95031	−	1.69867i	−0.384804	−	0.0730313i	−0.375251	+	0.926923i	$0.622444\pi$
$542$	8.96363	−	1.26928i	0.385021	−	0.0545203i
$543$	16.6184	+	30.9815i	0.713163	+	1.32954i
$544$	0.187615	−	1.59315i	0.00804393	−	0.0683058i
$545$	27.4696	+	6.56081i	1.17667	+	0.281034i
$546$	−0.736292	−	3.43756i	−0.0315104	−	0.147114i
$547$	11.1994	+	4.40988i	0.478852	+	0.188553i	0.593469	−	0.804857i	$-0.297758\pi$
$547$	11.1994	+	4.40988i	0.478852	+	0.188553i	−0.114617	+	0.993410i	$0.536564\pi$
$548$	−2.12888	+	1.34264i	−0.0909412	+	0.0573548i
$549$	−5.98733	+	3.03304i	−0.255533	+	0.129447i
$550$	−7.86169	−	0.368901i	−0.335223	−	0.0157300i
$551$	−0.0693900	+	0.0437629i	−0.00295611	+	0.00186436i
$552$	0.474275	−	2.86394i	0.0201865	−	0.121897i
$553$	−2.95627	−	9.39743i	−0.125713	−	0.399619i
$554$	1.39958	−	0.404482i	0.0594626	−	0.0171848i
$555$	−0.0280987	−	0.0142341i	−0.00119272	−	0.000604206i
$556$	−5.17807	+	16.4601i	−0.219599	+	0.698064i
$557$	0.469247	−	20.0114i	0.0198826	−	0.847910i	−0.895439	−	0.445185i	$-0.853138\pi$
$557$	0.469247	−	20.0114i	0.0198826	−	0.847910i	0.915321	−	0.402725i	$-0.131937\pi$
$558$	0.426938	+	0.581872i	0.0180737	+	0.0246326i
$559$	−4.97374	−	2.23311i	−0.210367	−	0.0944503i
$560$	5.03246	+	8.41013i	0.212660	+	0.355393i
$561$	−4.50599	−	0.855185i	−0.190243	−	0.0361059i
$562$	0.305940	+	13.0470i	0.0129053	+	0.550355i
$563$	−0.650743	+	0.980112i	−0.0274256	+	0.0413068i	−0.846551	−	0.532308i	$-0.821325\pi$
$563$	−0.650743	+	0.980112i	−0.0274256	+	0.0413068i	0.819125	+	0.573615i	$0.194459\pi$
$564$	4.72896	+	6.44508i	0.199125	+	0.271387i
$565$	35.8532	+	22.6119i	1.50836	+	0.951290i
$566$	−19.7017	−	1.85304i	−0.828123	−	0.0778890i
$567$	−8.89130	−	13.3916i	−0.373399	−	0.562393i
$568$	−2.88961	+	1.13781i	−0.121245	+	0.0477416i
$569$	−5.14749	+	7.01550i	−0.215794	+	0.294105i	−0.900625	−	0.434597i	$-0.856891\pi$
$569$	−5.14749	+	7.01550i	−0.215794	+	0.294105i	0.684831	+	0.728702i	$0.259876\pi$
$570$	0.0116089	+	0.0316386i	0.000486245	+	0.00132520i
$571$	24.6659	−	7.12850i	1.03224	−	0.298318i	0.281948	−	0.959430i	$-0.409019\pi$
$571$	24.6659	−	7.12850i	1.03224	−	0.298318i	0.750288	+	0.661111i	$0.229915\pi$
$572$	0.599574	−	1.42384i	0.0250694	−	0.0595336i
$573$	−7.86854	−	29.8316i	−0.328713	−	1.24623i
$574$	−25.3627	−	6.05762i	−1.05862	−	0.252840i
$575$	−5.58392	+	5.71639i	−0.232866	+	0.238390i
$576$	1.02180	−	0.0479468i	0.0425750	−	0.00199778i
$577$	27.3197	−	10.7574i	1.13733	−	0.447836i	0.278675	−	0.960386i	$-0.410105\pi$
$577$	27.3197	−	10.7574i	1.13733	−	0.447836i	0.858658	+	0.512550i	$0.171299\pi$
$578$	11.0030	−	9.33074i	0.457665	−	0.388107i
$579$	1.44734	−	20.5441i	0.0601495	−	0.853785i
$580$	−10.4588	+	28.5040i	−0.434276	+	1.18356i
$581$	−10.9261	−	16.4563i	−0.453291	−	0.682721i
$582$	−7.08518	+	4.94735i	−0.293690	+	0.205074i
$583$	0.901811	+	7.65781i	0.0373492	+	0.317154i
$584$	0.772116	−	6.55649i	0.0319504	−	0.271310i
$585$	1.45534	+	1.80007i	0.0601710	+	0.0744239i
$586$	31.9204	−	3.00227i	1.31862	−	0.124023i
$587$	27.2480	+	13.8032i	1.12464	+	0.569718i	0.913135	−	0.407658i	$-0.133654\pi$
$587$	27.2480	+	13.8032i	1.12464	+	0.569718i	0.211510	+	0.977376i	$0.432162\pi$
$588$	−4.68296	−	2.65513i	−0.193122	−	0.109496i
$589$	0.00449763	+	0.00346514i	0.000185322	+	0.000142779i
$590$	3.17193	−	2.68985i	0.130586	−	0.110739i
$591$	−11.2559	+	30.6765i	−0.463007	+	1.26186i
$592$	−0.00355529	+	0.00662811i	−0.000146122	+	0.000272413i
$593$	−14.2118	−	9.92366i	−0.583609	−	0.407516i	0.243218	−	0.969972i	$-0.421797\pi$
$593$	−14.2118	−	9.92366i	−0.583609	−	0.407516i	−0.826827	+	0.562456i	$0.809857\pi$
$594$	0.269633	−	11.4987i	0.0110632	−	0.471798i
$595$	3.29283	−	15.3734i	0.134993	−	0.630247i
$596$	15.3522	−	11.8279i	0.628852	−	0.484490i
$597$	−28.3491	+	4.01433i	−1.16025	+	0.164295i
$598$	−0.675865	−	1.41556i	−0.0276382	−	0.0578864i
$599$	0.558983	−	0.628674i	0.0228394	−	0.0256869i	−0.735784	−	0.677217i	$-0.763186\pi$
$599$	0.558983	−	0.628674i	0.0228394	−	0.0256869i	0.758623	+	0.651530i	$0.225872\pi$
$600$	4.60335	+	2.90324i	0.187931	+	0.118524i
$601$	17.7381	+	12.3860i	0.723554	+	0.505234i	0.875538	−	0.483148i	$-0.160507\pi$
$601$	17.7381	+	12.3860i	0.723554	+	0.505234i	−0.151985	+	0.988383i	$0.548567\pi$
$602$	−21.5415	+	9.67168i	−0.877965	+	0.394188i
$603$	−1.51859	−	0.861005i	−0.0618417	−	0.0350628i
$604$	5.70436	+	15.5465i	0.232107	+	0.632577i
$605$	−20.2457	−	2.86687i	−0.823106	−	0.116555i
$606$	7.71939	+	2.62879i	0.313579	+	0.106787i
$607$	−23.2672	−	9.16168i	−0.944385	−	0.371861i	−0.156496	−	0.987679i	$-0.550020\pi$
$607$	−23.2672	−	9.16168i	−0.944385	−	0.371861i	−0.787889	+	0.615818i	$0.788826\pi$
$608$	0.00761781	−	0.00259420i	0.000308943	−	0.000105209i
$609$	−7.70629	−	46.5349i	−0.312275	−	1.88569i
$610$	−3.19271	+	19.2794i	−0.129269	+	0.780599i
$611$	4.08896	+	1.39247i	0.165422	+	0.0563333i
$612$	−1.25152	−	1.06131i	−0.0505895	−	0.0429008i
$613$	−2.75697	+	2.82238i	−0.111353	+	0.113995i	−0.768749	−	0.639550i	$-0.779121\pi$
$613$	−2.75697	+	2.82238i	−0.111353	+	0.113995i	0.657396	+	0.753545i	$0.271658\pi$
$614$	−3.04709	−	25.8746i	−0.122970	−	1.04422i
$615$	−32.2774	+	7.70912i	−1.30155	+	0.310862i
$616$	−2.88297	−	6.03820i	−0.116158	−	0.243286i
$617$	−18.3346	−	30.6403i	−0.738123	−	1.23353i	−0.965672	−	0.259765i	$-0.916355\pi$
$617$	−18.3346	−	30.6403i	−0.738123	−	1.23353i	0.227549	−	0.973767i	$-0.426929\pi$
$618$	3.65364	+	3.74032i	0.146971	+	0.150458i
$619$	10.5164	+	9.80161i	0.422691	+	0.393960i	0.864079	−	0.503356i	$-0.167902\pi$
$619$	10.5164	+	9.80161i	0.422691	+	0.393960i	−0.441388	+	0.897316i	$0.645514\pi$
$620$	2.10131			0.0843906
$621$	−8.54306	−	7.96237i	−0.342821	−	0.319519i
$622$	−24.5877	−	7.10590i	−0.985878	−	0.284921i
$623$	−1.24109	−	52.9270i	−0.0497230	−	2.12047i
$624$	−0.846290	+	0.652012i	−0.0338787	+	0.0261014i
$625$	11.3988	+	27.0693i	0.455953	+	1.08277i
$626$	3.74728	+	4.63490i	0.149771	+	0.185248i
$627$	−0.00586808	−	0.0222473i	−0.000234349	−	0.000888474i
$628$	−14.0720	+	2.67070i	−0.561533	+	0.106572i
$629$	0.0114215	−	0.00388951i	0.000455404	−	0.000155085i
$630$	10.0145	+	0.469917i	0.398986	+	0.0187219i
$631$	−25.4453	+	23.7157i	−1.01296	+	0.944109i	−0.998443	−	0.0557856i	$-0.982234\pi$
$631$	−25.4453	+	23.7157i	−1.01296	+	0.944109i	−0.0145190	+	0.999895i	$0.504622\pi$
$632$	−2.19002	+	2.04116i	−0.0871143	+	0.0811930i
$633$	17.0657	−	8.64505i	0.678299	−	0.343610i
$634$	−3.77713	−	22.8084i	−0.150009	−	0.905839i
$635$	−2.13171	−	2.39747i	−0.0845942	−	0.0951409i
$636$	2.06932	−	4.91410i	0.0820537	−	0.194857i
$637$	−2.89612	+	0.272394i	−0.114749	+	0.0107926i
$638$	8.93123	−	18.7059i	0.353591	−	0.740573i
$639$	−0.665339	+	3.10629i	−0.0263204	+	0.122883i
$640$	1.64742	−	2.48125i	0.0651200	−	0.0980800i
$641$	−11.4905	+	14.2123i	−0.453849	+	0.561354i	−0.952142	−	0.305655i	$-0.901125\pi$
$641$	−11.4905	+	14.2123i	−0.453849	+	0.561354i	0.498293	+	0.867009i	$0.333960\pi$
$642$	−9.08254	−	9.29801i	−0.358459	−	0.366963i
$643$	0.227771	+	3.23307i	0.00898241	+	0.127500i	0.999980	−	0.00638260i	$-0.00203166\pi$
$643$	0.227771	+	3.23307i	0.00898241	+	0.127500i	−0.990997	+	0.133882i	$0.957256\pi$
$644$	−6.52670	−	1.88623i	−0.257188	−	0.0743278i
$645$	−18.8933	+	23.3686i	−0.743922	+	0.920136i
$646$	−0.0117768	−	0.00528755i	−0.000463352	−	0.000208036i
$647$	28.1057	−	31.6097i	1.10495	−	1.24271i	0.137267	−	0.990534i	$-0.456168\pi$
$647$	28.1057	−	31.6097i	1.10495	−	1.24271i	0.967682	−	0.252173i	$-0.0811452\pi$
$648$	−2.50825	+	4.19172i	−0.0985332	+	0.164666i
$649$	−2.32797	+	1.62554i	−0.0913807	+	0.0638082i
$650$	2.93761	−	0.137844i	0.115222	−	0.00540668i
$651$	−2.83977	+	1.61008i	−0.111299	+	0.0631041i
$652$	−7.52726	−	1.06589i	−0.294790	−	0.0417434i
$653$	11.1232	+	35.3587i	0.435286	+	1.38369i	0.874376	+	0.485250i	$0.161271\pi$
$653$	11.1232	+	35.3587i	0.435286	+	1.38369i	−0.439089	+	0.898443i	$0.644699\pi$
$654$	8.85952	+	9.96407i	0.346435	+	0.389626i
$655$	−10.9581	+	2.07971i	−0.428167	+	0.0812611i
$656$	1.65965	+	7.74849i	0.0647986	+	0.302528i
$657$	−5.15052	−	4.36773i	−0.200941	−	0.170401i
$658$	16.2744	−	9.22719i	0.634441	−	0.359713i
$659$	15.3308	−	20.8943i	0.597203	−	0.813926i	−0.397404	−	0.917644i	$-0.630089\pi$
$659$	15.3308	−	20.8943i	0.597203	−	0.813926i	0.994607	+	0.103718i	$0.0330739\pi$
$660$	−6.74555	−	5.19701i	−0.262570	−	0.202293i
$661$	−3.35522	+	12.7205i	−0.130503	+	0.494769i	0.869497	+	0.493939i	$0.164443\pi$
$661$	−3.35522	+	12.7205i	−0.130503	+	0.494769i	−1.00000		0.000830326i	$0.999736\pi$
$662$	1.60685	−	2.99564i	0.0624520	−	0.116429i
$663$	1.70624	+	0.160480i	0.0662648	+	0.00623252i
$664$	−3.08227	+	5.15101i	−0.119615	+	0.199898i
$665$	0.0767136	−	0.0183222i	0.00297482	−	0.000710505i
$666$	0.00363680	+	0.00678005i	0.000140923	+	0.000262722i
$667$	−8.16803	−	19.3970i	−0.316268	−	0.751056i
$668$	−0.285207	+	0.597347i	−0.0110350	+	0.0231121i
$669$	−6.67892	+	21.2310i	−0.258222	+	0.820839i
$670$	−4.63686	+	2.08186i	−0.179138	+	0.0804291i
$671$	3.40267	−	12.9003i	0.131358	−	0.498012i
$672$	−0.325166	+	4.61554i	−0.0125436	+	0.178048i
$673$	0.588810	−	8.35780i	0.0226970	−	0.322170i	−0.973087	−	0.230439i	$-0.925984\pi$
$673$	0.588810	−	8.35780i	0.0226970	−	0.322170i	0.995784	−	0.0917310i	$-0.0292400\pi$
$674$	−1.36867	+	5.18896i	−0.0527192	+	0.199871i
$675$	19.9735	−	8.96771i	0.768782	−	0.345167i
$676$	3.72787	−	11.8502i	0.143380	−	0.455777i
$677$	19.0467	−	39.8921i	0.732024	−	1.53318i	−0.110116	−	0.993919i	$-0.535122\pi$
$677$	19.0467	−	39.8921i	0.732024	−	1.53318i	0.842140	−	0.539259i	$-0.181296\pi$
$678$	7.76629	+	18.4430i	0.298263	+	0.708299i
$679$	9.55960	+	17.8219i	0.366864	+	0.683941i
$680$	−4.64705	+	1.10990i	−0.178206	+	0.0425627i
$681$	−11.2982	+	18.8813i	−0.432949	+	0.723533i
$682$	−1.42829	−	0.134337i	−0.0546920	−	0.00514404i
$683$	17.3743	−	32.3908i	0.664810	−	1.23940i	−0.294123	−	0.955768i	$-0.595027\pi$
$683$	17.3743	−	32.3908i	0.664810	−	1.23940i	0.958933	−	0.283633i	$-0.0915398\pi$
$684$	0.00209949	−	0.00795967i	8.02759e−5	−	0.000304346i
$685$	5.93824	+	4.57503i	0.226888	+	0.174803i
$686$	6.17375	−	8.41418i	0.235715	−	0.321255i
$687$	−11.0243	+	6.25051i	−0.420602	+	0.238472i
$688$	5.47283	+	4.64105i	0.208650	+	0.176938i
$689$	−0.603439	−	2.81730i	−0.0229892	−	0.107331i
$690$	−8.49437	+	1.61213i	−0.323375	+	0.0613729i
$691$	11.9646	+	13.4563i	0.455155	+	0.511901i	0.929694	−	0.368334i	$-0.120072\pi$
$691$	11.9646	+	13.4563i	0.455155	+	0.511901i	−0.474539	+	0.880235i	$0.657385\pi$
$692$	0.00377346	+	0.0119951i	0.000143446	+	0.000455987i
$693$	−6.77693	−	0.959637i	−0.257434	−	0.0364536i
$694$	−13.3341	+	7.56013i	−0.506156	+	0.286979i
$695$	51.3361	−	2.40889i	1.94729	−	0.0913743i
$696$	−11.7524	+	8.20635i	−0.445475	+	0.311061i
$697$	6.52715	−	10.9080i	0.247233	−	0.413170i
$698$	−14.3790	+	16.1716i	−0.544251	+	0.612105i
$699$	−6.40674	−	2.87649i	−0.242325	−	0.108799i
$700$	8.00786	−	9.90470i	0.302669	−	0.374362i
$701$	−39.1929	−	11.3268i	−1.48030	−	0.427809i	−0.563149	−	0.826356i	$-0.690410\pi$
$701$	−39.1929	−	11.3268i	−1.48030	−	0.427809i	−0.917148	+	0.398547i	$0.869515\pi$
$702$	0.302033	+	4.28718i	0.0113995	+	0.161809i
$703$	4.22952e−5	0	4.32986e-5i	1.59519e−6	0	1.63304e-6i
$704$	−1.27840	+	1.58122i	−0.0481816	+	0.0595945i
$705$	13.1693	−	19.8348i	0.495984	−	0.747023i
$706$	3.51031	−	16.3887i	0.132112	−	0.616797i
$707$	8.22286	−	17.2223i	0.309252	−	0.647710i
$708$	1.95479	−	0.183858i	0.0734656	−	0.00690979i
$709$	−8.44406	+	20.0525i	−0.317123	+	0.753088i	0.682628	+	0.730766i	$0.260837\pi$
$709$	−8.44406	+	20.0525i	−0.317123	+	0.753088i	−0.999751	+	0.0223217i	$0.992894\pi$
$710$	6.14599	+	6.91224i	0.230655	+	0.259412i
$711$	0.500323	+	3.02123i	0.0187636	+	0.113305i
$712$	−14.3519	+	7.27032i	−0.537860	+	0.272467i
$713$	−1.06555	+	0.993121i	−0.0399051	+	0.0371927i
$714$	5.42972	−	5.06066i	0.203202	−	0.189390i
$715$	−4.59628	−	0.215675i	−0.171891	−	0.00806580i
$716$	0.174538	−	0.0594379i	0.00652279	−	0.00222130i
$717$	−38.5213	+	7.31090i	−1.43860	+	0.273031i
$718$	−5.94050	−	22.5219i	−0.221698	−	0.840510i
$719$	−2.65375	−	3.28235i	−0.0989682	−	0.122411i	0.725741	−	0.687968i	$-0.241497\pi$
$719$	−2.65375	−	3.28235i	−0.0989682	−	0.122411i	−0.824709	+	0.565557i	$0.808661\pi$
$720$	−1.18237	−	2.80784i	−0.0440644	−	0.104642i
$721$	9.69349	−	7.46821i	0.361004	−	0.278131i
$722$	0.445407	+	18.9947i	0.0165763	+	0.706910i
$723$	−9.53981	−	2.75703i	−0.354790	−	0.102535i
$724$	−18.2909	−	17.0476i	−0.679776	−	0.633570i
$725$	39.4580			1.46543
$726$	−7.06175	−	6.58175i	−0.262086	−	0.244272i
$727$	−19.7860	−	20.2554i	−0.733821	−	0.751231i	0.241887	−	0.970304i	$-0.422234\pi$
$727$	−19.7860	−	20.2554i	−0.733821	−	0.751231i	−0.975708	+	0.219074i	$0.929696\pi$
$728$	1.28380	+	2.14545i	0.0475808	+	0.0795158i
$729$	12.4337	+	26.0417i	0.460509	+	0.964507i
$730$	−19.1246	+	4.56771i	−0.707833	+	0.169058i
$731$	−1.34628	−	11.4320i	−0.0497938	−	0.422829i
$732$	−6.44669	+	6.59963i	−0.238277	+	0.243929i
$733$	−1.00593	−	0.853049i	−0.0371550	−	0.0315081i	0.628001	−	0.778213i	$-0.283874\pi$
$733$	−1.00593	−	0.853049i	−0.0371550	−	0.0315081i	−0.665156	+	0.746705i	$0.731635\pi$
$734$	19.7889	+	6.73901i	0.730423	+	0.248741i
$735$	−2.61949	+	15.8179i	−0.0966212	+	0.583453i
$736$	0.337302	+	2.03682i	0.0124331	+	0.0750781i
$737$	3.28483	−	1.11863i	0.120998	−	0.0412052i
$738$	7.54225	+	2.96984i	0.277634	+	0.109321i
$739$	12.9810	+	4.42061i	0.477514	+	0.162615i	0.550699	−	0.834704i	$-0.314361\pi$
$739$	12.9810	+	4.42061i	0.477514	+	0.162615i	−0.0731850	+	0.997318i	$0.523316\pi$
$740$	0.0221802	+	0.00314080i	0.000815361	+	0.000115458i
$741$	0.00296148	+	0.00807112i	0.000108793	+	0.000296500i
$742$	−10.8552	−	6.15466i	−0.398508	−	0.225945i
$743$	9.52784	−	4.27781i	0.349543	−	0.156937i	−0.227232	−	0.973841i	$-0.572968\pi$
$743$	9.52784	−	4.27781i	0.349543	−	0.156937i	0.576775	+	0.816903i	$0.304311\pi$
$744$	0.813364	+	0.567946i	0.0298194	+	0.0208219i
$745$	−48.8223	−	30.7912i	−1.78871	−	1.12810i
$746$	5.97910	−	6.72454i	0.218910	−	0.246203i
$747$	2.64567	+	5.54118i	0.0967998	+	0.202741i
$748$	3.22962	−	0.457326i	0.118087	−	0.0167215i
$749$	−24.0969	+	18.5651i	−0.880482	+	0.678355i
$750$	−0.990594	+	4.62482i	−0.0361714	+	0.168875i
$751$	−1.01692	+	43.3674i	−0.0371080	+	1.58250i	0.592491	+	0.805577i	$0.298145\pi$
$751$	−1.01692	+	43.3674i	−0.0371080	+	1.58250i	−0.629599	+	0.776920i	$0.716781\pi$
$752$	−4.66129	−	3.25483i	−0.169980	−	0.118691i
$753$	−17.5025	+	32.6297i	−0.637825	+	1.18909i
$754$	−2.66807	+	7.27146i	−0.0971652	+	0.264811i
$755$	37.6168	−	31.8996i	1.36901	−	1.16095i
$756$	14.7453	+	11.3603i	0.536281	+	0.413170i
$757$	44.9931	+	25.5101i	1.63530	+	0.927180i	0.986019	+	0.166634i	$0.0532899\pi$
$757$	44.9931	+	25.5101i	1.63530	+	0.927180i	0.649285	+	0.760545i	$0.275068\pi$
$758$	10.5810	+	5.36006i	0.384318	+	0.194686i
$759$	5.87680	−	0.552741i	0.213314	−	0.0200632i
$760$	−0.0150690	−	0.0186385i	−0.000546612	−	0.000676089i
$761$	−1.56720	+	13.3081i	−0.0568111	+	0.482417i	0.934995	+	0.354662i	$0.115404\pi$
$761$	−1.56720	+	13.3081i	−0.0568111	+	0.482417i	−0.991806	+	0.127755i	$0.959223\pi$
$762$	−0.177136	−	1.50416i	−0.00641695	−	0.0544901i
$763$	25.5839	−	17.8645i	0.926201	−	0.646737i
$764$	12.1366	+	18.2795i	0.439087	+	0.661328i
$765$	−1.68351	+	4.58818i	−0.0608673	+	0.165886i
$766$	0.886508	−	12.5834i	0.0320308	−	0.454658i
$767$	0.809170	−	0.686190i	0.0292175	−	0.0247769i
$768$	1.30831	−	0.515162i	0.0472097	−	0.0185893i
$769$	−31.8436	+	1.49422i	−1.14831	+	0.0538830i	−0.612510	−	0.790463i	$-0.709840\pi$
$769$	−31.8436	+	1.49422i	−1.14831	+	0.0538830i	−0.535798	+	0.844346i	$0.679989\pi$
$770$	−13.9255	+	14.2559i	−0.501840	+	0.513746i
$771$	36.0176	+	8.60241i	1.29714	+	0.309808i
$772$	3.73563	+	14.1627i	0.134448	+	0.509727i
$773$	−0.746435	+	1.77260i	−0.0268474	+	0.0637558i	−0.934493	−	0.355982i	$-0.884147\pi$
$773$	−0.746435	+	1.77260i	−0.0268474	+	0.0637558i	0.907646	+	0.419738i	$0.137878\pi$
$774$	7.05166	−	2.03794i	0.253467	−	0.0732523i
$775$	−0.940674	−	2.56368i	−0.0337900	−	0.0920901i
$776$	3.63569	−	4.95507i	0.130514	−	0.177877i
$777$	−0.0323816	+	0.0127506i	−0.00116168	+	0.000457424i
$778$	13.9506	+	21.0116i	0.500153	+	0.753302i
$779$	0.0634894	+	0.00597148i	0.00227475	+	0.000213951i
$780$	2.69132	+	1.69736i	0.0963647	+	0.0607753i
$781$	−3.73561	−	5.09126i	−0.133671	−	0.182179i
$782$	1.83190	−	2.75911i	0.0655087	−	0.0986655i
$783$	1.35181	+	57.6488i	0.0483097	+	2.06020i
$784$	3.76142	+	0.713875i	0.134337	+	0.0254955i
$785$	21.9045	+	36.6063i	0.781807	+	1.30654i
$786$	−4.80370	−	2.15676i	−0.171342	−	0.0769292i
$787$	−24.8240	−	33.8325i	−0.884879	−	1.20600i	−0.977635	−	0.210310i	$-0.932553\pi$
$787$	−24.8240	−	33.8325i	−0.884879	−	1.20600i	0.0927563	−	0.995689i	$-0.470432\pi$
$788$	0.544788	−	23.2329i	0.0194073	−	0.827636i
$789$	−11.2937	+	35.9007i	−0.402068	+	1.27810i
$790$	7.95408	+	4.02934i	0.282993	+	0.143358i
$791$	44.9919	−	13.0027i	1.59973	−	0.462324i
$792$	0.624169	+	1.98412i	0.0221789	+	0.0705025i
$793$	−0.814472	+	4.91824i	−0.0289228	+	0.174652i
$794$	16.9505	−	10.6903i	0.601550	−	0.379385i
$795$	−15.8632	−	0.744363i	−0.562610	−	0.0263998i
$796$	18.1650	−	9.20197i	0.643842	−	0.326155i
$797$	−35.9573	+	22.6775i	−1.27367	+	0.803280i	−0.987911	−	0.155021i	$-0.950455\pi$
$797$	−35.9573	+	22.6775i	−1.27367	+	0.803280i	−0.285762	+	0.958301i	$0.592247\pi$
$798$	0.0346461	+	0.0136422i	0.00122646	+	0.000482930i
$799$	1.91009	+	8.91771i	0.0675741	+	0.315486i
$800$	−3.76471	−	0.899161i	−0.133103	−	0.0317902i
$801$	−1.92475	+	16.3442i	−0.0680077	+	0.577494i
$802$	−1.44203	−	2.68837i	−0.0509198	−	0.0949295i
$803$	13.2913	−	1.88209i	0.469039	−	0.0664175i
$804$	−2.35750	−	0.447427i	−0.0831427	−	0.0157795i
$805$	1.42199	+	20.1843i	0.0501186	+	0.711403i
$806$	0.536051			0.0188816
$807$	10.4899	+	20.5377i	0.369261	+	0.722960i
$808$	−5.79959			−0.204029
$809$	2.86536	+	40.6721i	0.100741	+	1.42995i	0.745977	+	0.665972i	$0.231983\pi$
$809$	2.86536	+	40.6721i	0.100741	+	1.42995i	−0.645236	+	0.763983i	$0.723241\pi$
$810$	14.2937	+	2.71278i	0.502229	+	0.0953172i
$811$	53.1313	−	7.52358i	1.86569	−	0.264189i	0.885852	−	0.463968i	$-0.153575\pi$
$811$	53.1313	−	7.52358i	1.86569	−	0.264189i	0.979841	+	0.199779i	$0.0640224\pi$
$812$	15.8568	+	29.5618i	0.556466	+	1.03742i
$813$	1.48877	−	12.6420i	0.0522133	−	0.443374i
$814$	−0.0148754	−	0.00355283i	−0.000521383	−	0.000124527i
$815$	4.74225	+	22.1403i	0.166114	+	0.775542i
$816$	−2.09874	−	0.826402i	−0.0734707	−	0.0289298i
$817$	0.0488436	−	0.0308047i	0.00170882	−	0.00107772i
$818$	−26.2858	+	13.3158i	−0.919061	+	0.465574i
$819$	2.55473	+	0.119878i	0.0892694	+	0.00418886i
$820$	19.9626	−	12.5900i	0.697126	−	0.439663i
$821$	4.16632	−	25.1586i	0.145406	−	0.878040i	−0.810795	−	0.585330i	$-0.800965\pi$
$821$	4.16632	−	25.1586i	0.145406	−	0.878040i	0.956201	−	0.292711i	$-0.0945573\pi$
$822$	1.06199	+	3.37588i	0.0370413	+	0.117747i
$823$	−54.2865	+	15.6889i	−1.89231	+	0.546881i	−0.898049	+	0.439895i	$0.855016\pi$
$823$	−54.2865	+	15.6889i	−1.89231	+	0.546881i	−0.994260	+	0.106987i	$0.965880\pi$
$824$	−3.31725	−	1.68044i	−0.115562	−	0.0585409i
$825$	−3.32085	+	10.5563i	−0.115617	+	0.367525i
$826$	0.107719	−	4.59375i	0.00374802	−	0.159837i
$827$	28.1188	+	38.3230i	0.977786	+	1.33262i	0.942845	+	0.333233i	$0.108140\pi$
$827$	28.1188	+	38.3230i	0.977786	+	1.33262i	0.0349418	+	0.999389i	$0.488875\pi$
$828$	1.92661	+	0.865008i	0.0669543	+	0.0300611i
$829$	−8.31102	−	13.8892i	−0.288654	−	0.482390i	0.679183	−	0.733969i	$-0.262334\pi$
$829$	−8.31102	−	13.8892i	−0.288654	−	0.482390i	−0.967837	+	0.251578i	$0.919050\pi$
$830$	17.5648	+	3.33360i	0.609684	+	0.115711i
$831$	−0.0480213	−	2.04790i	−0.00166584	−	0.0710410i
$832$	0.420263	−	0.632976i	0.0145700	−	0.0219445i
$833$	−3.63322	−	4.95170i	−0.125884	−	0.171566i
$834$	20.5220	+	12.9428i	0.710619	+	0.448173i
$835$	1.96283	+	0.184614i	0.0679267	+	0.00638883i
$836$	0.00905107	+	0.0136322i	0.000313038	+	0.000471479i
$837$	3.71336	−	1.46217i	0.128352	−	0.0505401i
$838$	11.7533	−	16.0185i	0.406011	−	0.553351i
$839$	4.22318	+	11.5097i	0.145800	+	0.397360i	0.990434	−	0.137985i	$-0.0440625\pi$
$839$	4.22318	+	11.5097i	0.145800	+	0.397360i	−0.844634	+	0.535344i	$0.820182\pi$
$840$	13.2390	−	3.82609i	0.456788	−	0.132013i
$841$	−29.0771	+	69.0507i	−1.00266	+	2.38106i
$842$	−3.17063	−	12.0207i	−0.109267	−	0.414259i
$843$	17.8482	+	4.26286i	0.614726	+	0.146821i
$844$	−9.50708	+	9.73263i	−0.327247	+	0.335011i
$845$	−36.9586	+	1.73424i	−1.27141	+	0.0596597i
$846$	−5.41115	+	2.13069i	−0.186039	+	0.0732548i
$847$	−17.2305	+	14.6118i	−0.592048	+	0.502067i
$848$	−0.266495	+	3.78273i	−0.00915147	+	0.129899i
$849$	−9.58462	+	26.1216i	−0.328943	+	0.896491i
$850$	3.43443	+	5.17273i	0.117800	+	0.177423i
$851$	−0.0127317	+	0.00889016i	−0.000436438	+	0.000304751i
$852$	0.510706	+	4.33671i	0.0174965	+	0.148573i
$853$	0.823421	−	6.99215i	0.0281934	−	0.239407i	−0.971800	−	0.235806i	$-0.924227\pi$
$853$	0.823421	−	6.99215i	0.0281934	−	0.239407i	0.999994	−	0.00360073i	$-0.00114615\pi$
$854$	13.5747	+	16.7901i	0.464516	+	0.574547i
$855$	−0.0244098	+	0.00229586i	−0.000834797	+	7.85167e-5i
$856$	8.24631	+	4.17738i	0.281853	+	0.142780i
$857$	−44.5001	−	25.2305i	−1.52009	−	0.861858i	−0.999970	−	0.00776783i	$-0.997527\pi$
$857$	−44.5001	−	25.2305i	−1.52009	−	0.861858i	−0.520124	−	0.854091i	$-0.674114\pi$
$858$	−1.72081	−	1.32578i	−0.0587476	−	0.0452613i
$859$	−8.78426	+	7.44920i	−0.299715	+	0.254163i	−0.784020	−	0.620736i	$-0.786834\pi$
$859$	−8.78426	+	7.44920i	−0.299715	+	0.254163i	0.484305	+	0.874899i	$0.339073\pi$
$860$	7.36191	−	20.0639i	0.251039	−	0.684174i
$861$	−17.3312	+	32.3105i	−0.590647	+	1.10114i
$862$	−12.1021	−	8.45053i	−0.412200	−	0.287826i
$863$	−0.507532	+	21.6441i	−0.0172766	+	0.736773i	0.920739	+	0.390180i	$0.127587\pi$
$863$	−0.507532	+	21.6441i	−0.0172766	+	0.736773i	−0.938015	+	0.346594i	$0.887338\pi$
$864$	1.18471	−	5.53112i	0.0403048	−	0.188173i
$865$	0.0296679	−	0.0228572i	0.00100874	−	0.000777169i
$866$	−5.88857	+	0.833842i	−0.200102	+	0.0283351i
$867$	−8.74013	−	18.3056i	−0.296830	−	0.621692i
$868$	1.54268	−	1.73501i	0.0523619	−	0.0588900i
$869$	−5.14890	−	3.24731i	−0.174664	−	0.110157i
$870$	35.0029	+	24.4414i	1.18671	+	0.828642i
$871$	−1.18288	+	0.531089i	−0.0400803	+	0.0179953i
$872$	−8.24887	−	4.67692i	−0.279342	−	0.158381i
$873$	−2.16556	−	5.90194i	−0.0732930	−	0.199750i
$874$	0.0164503	+	0.00232941i	0.000556438	+	7.87936e-5i
$875$	10.4781	+	3.56826i	0.354225	+	0.120629i
$876$	−8.63723	−	3.40099i	−0.291825	−	0.114909i
$877$	16.7408	−	5.70099i	0.565298	−	0.192509i	−0.0250099	−	0.999687i	$-0.507962\pi$
$877$	16.7408	−	5.70099i	0.565298	−	0.192509i	0.590307	+	0.807178i	$0.299006\pi$
$878$	4.60681	+	27.8185i	0.155472	+	0.938829i
$879$	7.36520	−	44.4752i	0.248422	−	1.50011i
$880$	5.73278	+	1.95226i	0.193252	+	0.0658108i
$881$	1.89488	+	1.60689i	0.0638401	+	0.0541375i	0.678123	−	0.734948i	$-0.262794\pi$
$881$	1.89488	+	1.60689i	0.0638401	+	0.0541375i	−0.614283	+	0.789086i	$0.710555\pi$
$882$	2.73661	−	2.80154i	0.0921466	−	0.0943327i
$883$	1.58336	+	13.4453i	0.0532844	+	0.452469i	0.993668	+	0.112354i	$0.0358392\pi$
$883$	1.58336	+	13.4453i	0.0532844	+	0.452469i	−0.940384	+	0.340115i	$0.889534\pi$
$884$	−1.18548	+	0.283139i	−0.0398720	+	0.00952300i
$885$	−2.51959	−	5.27712i	−0.0846951	−	0.177389i
$886$	−15.1088	−	25.2494i	−0.507590	−	0.848271i
$887$	−35.8096	−	36.6591i	−1.20237	−	1.23089i	−0.965803	−	0.259277i	$-0.916516\pi$
$887$	−35.8096	−	36.6591i	−1.20237	−	1.23089i	−0.236565	−	0.971616i	$-0.576022\pi$
$888$	0.00773651	+	0.00721064i	0.000259620	+	0.000241973i
$889$	−3.54454			−0.118880
$890$	35.0526	+	32.6700i	1.17497	+	1.09510i
$891$	−9.54218	−	2.75771i	−0.319675	−	0.0923868i
$892$	−0.371070	−	15.8245i	−0.0124243	−	0.529845i
$893$	−0.0362424	+	0.0279224i	−0.00121281	+	0.000934389i
$894$	−10.5756	−	25.1143i	−0.353700	−	0.839948i
$895$	−0.345259	−	0.427042i	−0.0115407	−	0.0142744i
$896$	−0.839264	−	3.18186i	−0.0280378	−	0.106298i
$897$	−2.16694	+	0.411261i	−0.0723521	+	0.0137316i
$898$	20.8777	−	7.10976i	0.696697	−	0.237256i
$899$	7.18442	+	0.337121i	0.239614	+	0.0112436i
$900$	−2.89637	+	2.69950i	−0.0965458	+	0.0899834i
$901$	4.45001	−	4.14754i	0.148251	−	0.138174i
$902$	−14.3738	+	7.28140i	−0.478594	+	0.242444i
$903$	5.42445	+	32.7558i	0.180514	+	1.09005i
$904$	−9.45679	−	10.6358i	−0.314528	−	0.353742i
$905$	−28.9010	+	68.6327i	−0.960703	+	2.28143i
$906$	23.1824	−	2.18042i	0.770184	−	0.0724395i
$907$	7.40200	−	15.5030i	0.245779	−	0.514769i	−0.742044	−	0.670352i	$-0.766143\pi$
$907$	7.40200	−	15.5030i	0.245779	−	0.514769i	0.987823	+	0.155582i	$0.0497254\pi$
$908$	3.27748	−	15.3017i	0.108767	−	0.507804i
$909$	−3.28147	+	4.94237i	−0.108840	+	0.163928i
$910$	4.68174	−	5.79072i	0.155198	−	0.191960i
$911$	−19.7616	−	20.2304i	−0.654731	−	0.670264i	0.304621	−	0.952474i	$-0.401470\pi$
$911$	−19.7616	−	20.2304i	−0.654731	−	0.670264i	−0.959353	+	0.282209i	$0.908933\pi$
$912$	−0.000795200	−	0.0112874i	−2.63317e−5	−	0.000373763i
$913$	−11.7259	−	3.38882i	−0.388072	−	0.112154i
$914$	15.7630	−	19.4968i	0.521392	−	0.644896i
$915$	25.0670	+	11.2546i	0.828690	+	0.372065i
$916$	5.98883	−	6.73548i	0.197877	−	0.222547i
$917$	−6.32769	+	10.5747i	−0.208959	+	0.349206i
$918$	−7.43980	+	5.19498i	−0.245550	+	0.171460i
$919$	−28.3274	+	1.32923i	−0.934434	+	0.0438472i	−0.508646	−	0.860976i	$-0.669854\pi$
$919$	−28.3274	+	1.32923i	−0.934434	+	0.0438472i	−0.425788	+	0.904823i	$0.640003\pi$
$920$	5.34904	−	3.03278i	0.176353	−	0.0999879i
$921$	−36.2715	−	5.13618i	−1.19519	−	0.169243i
$922$	1.29661	+	4.12169i	0.0427017	+	0.135741i
$923$	1.56786	+	1.76334i	0.0516069	+	0.0580409i
$924$	−9.24332	+	1.75428i	−0.304083	+	0.0577114i
$925$	−0.00609732	−	0.0284668i	−0.000200479	−	0.000935982i
$926$	−18.8538	−	15.9883i	−0.619573	−	0.525408i
$927$	−3.30900	+	1.87612i	−0.108682	+	0.0616200i
$928$	6.03065	−	8.21915i	0.197966	−	0.269807i
$929$	−8.64537	−	6.66070i	−0.283645	−	0.218531i	0.458627	−	0.888629i	$-0.348341\pi$
$929$	−8.64537	−	6.66070i	−0.283645	−	0.218531i	−0.742272	+	0.670098i	$0.766252\pi$
$930$	0.753554	−	2.85691i	0.0247100	−	0.0936817i
$931$	0.0145636	−	0.0271508i	0.000477302	−	0.000889830i
$932$	4.97267	+	0.467703i	0.162885	+	0.0153201i
$933$	−18.4785	+	30.8809i	−0.604960	+	1.01099i
$934$	18.0900	−	4.32060i	0.591923	−	0.141374i
$935$	−4.59213	−	8.56107i	−0.150179	−	0.279977i
$936$	−0.301628	−	0.716290i	−0.00985900	−	0.0234127i
$937$	3.63795	−	7.61945i	0.118846	−	0.248917i	−0.834370	−	0.551205i	$-0.814168\pi$
$937$	3.63795	−	7.61945i	0.118846	−	0.248917i	0.953217	+	0.302288i	$0.0977505\pi$
$938$	−1.68521	+	5.35696i	−0.0550240	+	0.174911i
$939$	7.64536	−	3.43261i	0.249497	−	0.112019i
$940$	−4.31853	+	16.3726i	−0.140855	+	0.534015i
$941$	3.80554	−	54.0173i	0.124057	−	1.76091i	−0.406860	−	0.913491i	$-0.633376\pi$
$941$	3.80554	−	54.0173i	0.124057	−	1.76091i	0.530917	−	0.847424i	$-0.321848\pi$
$942$	−1.41533	+	20.0898i	−0.0461141	+	0.654561i
$943$	−4.17251	+	15.8190i	−0.135876	+	0.515138i
$944$	−1.27387	+	0.571941i	−0.0414609	+	0.0186151i
$945$	16.6364	−	52.8840i	0.541182	−	1.72032i
$946$	−6.28668	+	13.1671i	−0.204398	+	0.428098i
$947$	17.7012	+	42.0360i	0.575213	+	1.36599i	0.906400	+	0.422421i	$0.138820\pi$
$947$	17.7012	+	42.0360i	0.575213	+	1.36599i	−0.331187	+	0.943565i	$0.607449\pi$
$948$	1.98976	+	3.70950i	0.0646246	+	0.120479i
$949$	−4.87875	+	1.16524i	−0.158371	+	0.0378252i
$950$	−0.0159939	+	0.0267286i	−0.000518910	+	0.000867189i
$951$	−32.3646	−	3.04404i	−1.04949	−	0.0987098i
$952$	−2.49522	+	4.65181i	−0.0808704	+	0.150766i
$953$	6.79169	−	25.7490i	0.220004	−	0.834090i	−0.762366	−	0.647146i	$-0.775962\pi$
$953$	6.79169	−	25.7490i	0.220004	−	0.834090i	0.982370	−	0.186944i	$-0.0598585\pi$
$954$	3.07283	+	2.36742i	0.0994865	+	0.0766479i
$955$	38.6593	−	52.6886i	1.25099	−	1.70496i
$956$	24.2575	−	13.7534i	0.784543	−	0.444818i
$957$	−22.2294	−	18.8509i	−0.718575	−	0.609364i
$958$	1.63865	+	7.65042i	0.0529423	+	0.247174i
$959$	8.13708	−	1.54432i	0.262760	−	0.0498688i
$960$	−2.78269	−	3.12962i	−0.0898109	−	0.101008i
$961$	9.15325	+	29.0965i	0.295266	+	0.938596i
$962$	0.00565825		0.000801229i	0.000182429		2.58327e-5i
$963$	8.22579	−	4.66383i	0.265072	−	0.150290i
$964$	7.05455	−	0.331027i	0.227212	−	0.0106617i
$965$	35.7674	−	24.9753i	1.15139	−	0.803982i
$966$	−4.90504	+	8.19718i	−0.157817	+	0.263740i
$967$	−11.5146	+	12.9502i	−0.370285	+	0.416449i	−0.902861	−	0.429933i	$-0.858537\pi$
$967$	−11.5146	+	12.9502i	−0.370285	+	0.416449i	0.532576	+	0.846382i	$0.321224\pi$
$968$	6.26313	+	2.81202i	0.201305	+	0.0903816i
$969$	−0.0114122	+	0.0141154i	−0.000366612	+	0.000453452i
$970$	−17.5848	−	5.08203i	−0.564613	−	0.163174i
$971$	−0.954493	−	13.5484i	−0.0306311	−	0.434790i	−0.988866	−	0.148808i	$-0.952456\pi$
$971$	−0.954493	−	13.5484i	−0.0306311	−	0.434790i	0.958235	−	0.285982i	$-0.0923198\pi$
$972$	−7.05841	−	7.22586i	−0.226399	−	0.231770i
$973$	35.6995	−	44.1557i	1.14447	−	1.41557i
$974$	−14.3104	+	21.5535i	−0.458535	+	0.690619i
$975$	0.866051	−	4.04336i	0.0277358	−	0.129491i
$976$	2.82704	−	5.92105i	0.0904912	−	0.189528i
$977$	−28.9685	+	2.72463i	−0.926785	+	0.0871686i	−0.546273	−	0.837607i	$-0.683954\pi$
$977$	−28.9685	+	2.72463i	−0.926785	+	0.0871686i	−0.380512	+	0.924776i	$0.624252\pi$
$978$	−4.14853	+	9.85172i	−0.132655	+	0.315023i
$979$	−21.7371	−	24.4472i	−0.694722	−	0.781335i
$980$	−1.86296	−	11.2496i	−0.0595102	−	0.359356i
$981$	−8.65294	+	4.38337i	−0.276267	+	0.139950i
$982$	−15.6669	+	14.6020i	−0.499951	+	0.465968i
$983$	30.6955	−	28.6090i	0.979033	−	0.912486i	−0.0171434	−	0.999853i	$-0.505457\pi$
$983$	30.6955	−	28.6090i	0.979033	−	0.912486i	0.996176	+	0.0873669i	$0.0278452\pi$
$984$	11.1299	+	0.522258i	0.354808	+	0.0166490i
$985$	−65.5198	+	22.3124i	−2.08763	+	0.710931i
$986$	−16.0664	+	3.04923i	−0.511660	+	0.0971071i
$987$	−6.70898	−	25.4354i	−0.213549	−	0.809617i
$988$	−0.00384417	−	0.00475474i	−0.000122299	−	0.000151268i
$989$	5.74947	+	13.6536i	0.182823	+	0.434158i
$990$	4.90737	−	3.78082i	0.155967	−	0.120162i
$991$	0.00535357	+	0.228307i	0.000170062	+	0.00725240i	0.999804	−	0.0198162i	$-0.00630811\pi$
$991$	0.00535357	+	0.228307i	0.000170062	+	0.00725240i	−0.999634	+	0.0270686i	$0.991383\pi$
$992$	−0.677789	−	0.195882i	−0.0215198	−	0.00621927i
$993$	−3.49659	−	3.25892i	−0.110961	−	0.103419i
$994$	10.2194			0.324139
$995$	−44.3657	−	41.3501i	−1.40649	−	1.31089i
$996$	5.89790	+	6.03782i	0.186882	+	0.191316i
$997$	−4.77630	−	7.98204i	−0.151267	−	0.252794i	0.773111	−	0.634270i	$-0.218699\pi$
$997$	−4.77630	−	7.98204i	−0.151267	−	0.252794i	−0.924379	+	0.381476i	$0.875416\pi$
$998$	−0.987399	−	2.06804i	−0.0312556	−	0.0654628i
$999$	0.0413816	−	0.00988355i	0.00130926	−	0.000312702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.d.b.21.8	✓	792
269.205	even	67	inner	538.2.d.b.205.8	yes	792

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.d.b.21.8	✓	792	1.1	even	1	trivial
538.2.d.b.205.8	yes	792	269.205	even	67	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.d (of order \(67\), degree \(66\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0702762 + 0.997528i) q^{2} +(1.38143 + 0.262179i) q^{3} +(-0.990123 + 0.140205i) q^{4} +(1.40783 + 2.62461i) q^{5} +(-0.164449 + 1.39644i) q^{6} +(3.20066 + 0.764442i) q^{7} +(-0.209440 - 0.977821i) q^{8} +(-0.951795 - 0.374779i) q^{9} +(-2.51919 + 1.58880i) q^{10} +(1.81390 - 0.918877i) q^{11} +(-1.40454 - 0.0659064i) q^{12} +(-0.642654 + 0.405309i) q^{13} +(-0.537622 + 3.24646i) q^{14} +(1.25670 + 3.99482i) q^{15} +(0.960685 - 0.277640i) q^{16} +(-1.43102 - 0.724920i) q^{17} +(0.306964 - 0.975780i) q^{18} +(0.000188652 - 0.00804521i) q^{19} +(-1.76191 - 2.40131i) q^{20} +(4.22105 + 1.89516i) q^{21} +(1.04408 + 1.74484i) q^{22} +(2.02835 + 0.384957i) q^{23} +(-0.0329623 - 1.40570i) q^{24} +(-2.14095 + 3.22458i) q^{25} +(-0.449470 - 0.612581i) q^{26} +(-4.78451 - 3.01750i) q^{27} +(-3.27622 - 0.308144i) q^{28} +(-5.63877 - 8.49279i) q^{29} +(-3.89662 + 1.53433i) q^{30} +(-0.417370 + 0.568832i) q^{31} +(0.344467 + 0.938798i) q^{32} +(2.74668 - 0.793796i) q^{33} +(0.622561 - 1.47843i) q^{34} +(2.49963 + 9.47670i) q^{35} +(0.994940 + 0.237631i) q^{36} +(-0.00525575 + 0.00538043i) q^{37} +(0.00803858 - 0.000377201i) q^{38} +(-0.994042 + 0.391414i) q^{39} +(2.27155 - 1.92631i) q^{40} +(-0.556885 + 7.90464i) q^{41} +(-1.59384 + 4.34380i) q^{42} +(3.96912 + 5.97807i) q^{43} +(-1.66715 + 1.16412i) q^{44} +(-0.356320 - 3.02572i) q^{45} +(-0.241461 + 2.05039i) q^{46} +(-3.57436 - 4.42103i) q^{47} +(1.39991 - 0.131668i) q^{48} +(3.41534 + 1.73013i) q^{49} +(-3.36706 - 1.90905i) q^{50} +(-1.78679 - 1.37661i) q^{51} +(0.579480 - 0.491409i) q^{52} +(-1.30625 + 3.56002i) q^{53} +(2.67380 - 4.98474i) q^{54} +(4.96537 + 3.46716i) q^{55} +(0.0771420 - 3.28977i) q^{56} +(0.00236989 - 0.0110644i) q^{57} +(8.07552 - 6.22167i) q^{58} +(-1.38258 + 0.195778i) q^{59} +(-1.80438 - 3.77916i) q^{60} +(4.35981 - 4.90337i) q^{61} +(-0.596757 - 0.376363i) q^{62} +(-2.75987 - 1.92713i) q^{63} +(-0.912270 + 0.409590i) q^{64} +(-1.96853 - 1.11611i) q^{65} +(0.984859 + 2.68410i) q^{66} +(1.68971 + 0.239270i) q^{67} +(1.51852 + 0.517124i) q^{68} +(2.70109 + 1.06358i) q^{69} +(-9.27760 + 3.15943i) q^{70} +(-0.507377 - 3.06383i) q^{71} +(-0.167123 + 1.00918i) q^{72} +(6.24937 + 2.12819i) q^{73} +(-0.00573648 - 0.00486463i) q^{74} +(-3.80298 + 3.89320i) q^{75} +(0.000941189 + 0.00799219i) q^{76} +(6.50809 - 1.55439i) q^{77} +(-0.460304 - 0.964078i) q^{78} +(-1.53721 - 2.56895i) q^{79} +(2.08118 + 2.13056i) q^{80} +(-3.57342 - 3.33053i) q^{81} -7.92423 q^{82} +(-4.39121 - 4.09273i) q^{83} +(-4.44507 - 1.28463i) q^{84} +(-0.112003 - 4.77645i) q^{85} +(-5.68435 + 4.37943i) q^{86} +(-5.56291 - 13.2105i) q^{87} +(-1.27840 - 1.58122i) q^{88} +(-4.10321 - 15.5563i) q^{89} +(2.99320 - 0.568075i) q^{90} +(-2.36675 + 0.805982i) q^{91} +(-2.06229 - 0.0967705i) q^{92} +(-0.725701 + 0.676374i) q^{93} +(4.15890 - 3.87622i) q^{94} +(0.0213812 - 0.0108312i) q^{95} +(0.229723 + 1.38719i) q^{96} +(4.08371 + 4.59285i) q^{97} +(-1.48584 + 3.52849i) q^{98} +(-2.07084 + 0.194772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 792 q - 12 q^{2} - 5 q^{3} - 12 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 12 q^{8} - 23 q^{9} - 9 q^{10} - 11 q^{11} - 5 q^{12} - 13 q^{13} - 8 q^{14} - 26 q^{15} - 12 q^{16} - 18 q^{17} - 23 q^{18} - 17 q^{19}+ \cdots - 123 q^{99}+O(q^{100}) \) 792 * q - 12 * q^2 - 5 * q^3 - 12 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 12 * q^8 - 23 * q^9 - 9 * q^10 - 11 * q^11 - 5 * q^12 - 13 * q^13 - 8 * q^14 - 26 * q^15 - 12 * q^16 - 18 * q^17 - 23 * q^18 - 17 * q^19 - 9 * q^20 + 179 * q^21 - 11 * q^22 - 26 * q^23 - 5 * q^24 - 55 * q^25 - 13 * q^26 + 169 * q^27 - 8 * q^28 - 33 * q^29 + 41 * q^30 - 40 * q^31 - 12 * q^32 - 54 * q^33 - 18 * q^34 - 58 * q^35 - 23 * q^36 + 154 * q^37 - 17 * q^38 - 44 * q^39 - 9 * q^40 + 88 * q^41 - 22 * q^42 - 23 * q^43 + 56 * q^44 - 85 * q^45 - 26 * q^46 + 167 * q^47 - 5 * q^48 - 64 * q^49 - 55 * q^50 - 38 * q^51 - 13 * q^52 + 61 * q^53 - 32 * q^54 - 40 * q^55 - 8 * q^56 - 68 * q^57 - 33 * q^58 - 53 * q^59 + 108 * q^60 + 12 * q^61 - 40 * q^62 - 88 * q^63 - 12 * q^64 - 84 * q^65 - 54 * q^66 - 61 * q^67 - 18 * q^68 - 60 * q^69 - 58 * q^70 - 100 * q^71 - 23 * q^72 + 15 * q^73 - 47 * q^74 - 81 * q^75 - 17 * q^76 - 98 * q^77 - 44 * q^78 - 3 * q^79 - 9 * q^80 + 148 * q^81 + 222 * q^82 + 120 * q^83 + 246 * q^84 + 26 * q^85 - 23 * q^86 - 146 * q^87 - 11 * q^88 - 102 * q^89 - 85 * q^90 - 80 * q^91 - 26 * q^92 + 12 * q^93 - 34 * q^94 - 78 * q^95 - 5 * q^96 - 90 * q^97 - 64 * q^98 - 123 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more