LMFDB - Embedded newform 125.2.h.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	125.4
Dual form			125.2.h.a.94.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.69510 - 0.169561i) q^{2} +(2.45880 + 1.15702i) q^{3} +(5.25058 + 0.663302i) q^{4} +(1.42401 - 1.72400i) q^{5} +(-6.43051 - 3.53521i) q^{6} +(-0.679948 + 0.935868i) q^{7} +(-8.73317 - 1.66594i) q^{8} +(2.79471 + 3.37822i) q^{9} +O(q^{10})$	\(q+(-2.69510 - 0.169561i) q^{2} +(2.45880 + 1.15702i) q^{3} +(5.25058 + 0.663302i) q^{4} +(1.42401 - 1.72400i) q^{5} +(-6.43051 - 3.53521i) q^{6} +(-0.679948 + 0.935868i) q^{7} +(-8.73317 - 1.66594i) q^{8} +(2.79471 + 3.37822i) q^{9} +(-4.13018 + 4.40490i) q^{10} +(0.198843 - 3.16052i) q^{11} +(12.1427 + 7.70596i) q^{12} +(-0.669023 + 0.553464i) q^{13} +(1.99121 - 2.40697i) q^{14} +(5.49607 - 2.59136i) q^{15} +(13.0022 + 3.33840i) q^{16} +(-0.00124451 - 0.00985132i) q^{17} +(-6.95920 - 9.57852i) q^{18} +(1.13763 + 2.41759i) q^{19} +(8.62043 - 8.10746i) q^{20} +(-2.75467 + 1.51440i) q^{21} +(-1.07180 + 8.48420i) q^{22} +(-2.91674 + 7.36684i) q^{23} +(-19.5456 - 14.2007i) q^{24} +(-0.944368 - 4.91001i) q^{25} +(1.89693 - 1.37820i) q^{26} +(0.935558 + 3.64376i) q^{27} +(-4.19089 + 4.46284i) q^{28} +(-0.0827079 - 0.0776679i) q^{29} +(-15.2518 + 6.05204i) q^{30} +(-4.77298 + 0.602967i) q^{31} +(-17.5651 - 5.70725i) q^{32} +(4.14571 - 7.54101i) q^{33} +(0.00168368 + 0.0267613i) q^{34} +(0.645184 + 2.50492i) q^{35} +(12.4331 + 19.5914i) q^{36} +(2.08871 - 8.13500i) q^{37} +(-2.65610 - 6.70855i) q^{38} +(-2.28536 + 0.586781i) q^{39} +(-15.3082 + 12.6837i) q^{40} +(-5.27442 + 2.08829i) q^{41} +(7.68090 - 3.61436i) q^{42} +(3.29763 - 1.07147i) q^{43} +(3.14042 - 16.4627i) q^{44} +(9.80377 - 0.00744791i) q^{45} +(9.11002 - 19.3598i) q^{46} +(-5.02789 + 0.959122i) q^{47} +(28.1072 + 23.2523i) q^{48} +(1.74960 + 5.38471i) q^{49} +(1.71262 + 13.3931i) q^{50} +(0.00833819 - 0.0256623i) q^{51} +(-3.87987 + 2.46224i) q^{52} +(-2.92345 - 5.31774i) q^{53} +(-1.90358 - 9.97892i) q^{54} +(-5.16559 - 4.84343i) q^{55} +(7.49720 - 7.04034i) q^{56} +7.26064i q^{57} +(0.209737 + 0.223347i) q^{58} +(-1.11039 + 1.74969i) q^{59} +(30.5764 - 9.96056i) q^{60} +(-9.42206 - 3.73046i) q^{61} +(12.9659 - 0.815745i) q^{62} +(-5.06183 + 0.318463i) q^{63} +(21.4095 + 8.47662i) q^{64} +(0.00147498 + 1.94154i) q^{65} +(-12.4518 + 19.6208i) q^{66} +(-5.85531 - 6.23527i) q^{67} -0.0525506i q^{68} +(-15.6953 + 14.7388i) q^{69} +(-1.31410 - 6.86041i) q^{70} +(1.84361 + 9.66456i) q^{71} +(-18.7787 - 34.1584i) q^{72} +(2.41458 - 1.53234i) q^{73} +(-7.00867 + 21.5705i) q^{74} +(3.35898 - 13.1654i) q^{75} +(4.36964 + 13.4484i) q^{76} +(2.82263 + 2.33508i) q^{77} +(6.25877 - 1.19392i) q^{78} +(0.889148 - 1.88954i) q^{79} +(24.2707 - 17.6619i) q^{80} +(0.549093 - 2.87845i) q^{81} +(14.5692 - 4.73382i) q^{82} +(13.7986 - 6.49314i) q^{83} +(-15.4681 + 6.12427i) q^{84} +(-0.0187559 - 0.0118829i) q^{85} +(-9.06912 + 2.32855i) q^{86} +(-0.113498 - 0.286664i) q^{87} +(-7.00177 + 27.2701i) q^{88} +(0.705163 + 1.11116i) q^{89} +(-26.4234 - 1.64227i) q^{90} +(-0.0630684 - 1.00244i) q^{91} +(-20.2010 + 36.7455i) q^{92} +(-12.4334 - 4.03987i) q^{93} +(13.7133 - 1.73239i) q^{94} +(5.78794 + 1.48141i) q^{95} +(-36.5856 - 34.3562i) q^{96} +(4.80808 - 5.12008i) q^{97} +(-3.80230 - 14.8090i) q^{98} +(11.2327 - 8.16100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{50}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.69510	−	0.169561i	−1.90572	−	0.119898i	−0.934186	−	0.356786i	$-0.883872\pi$
$2$	−2.69510	−	0.169561i	−1.90572	−	0.119898i	−0.971537	+	0.236888i	$0.923872\pi$
$3$	2.45880	+	1.15702i	1.41959	+	0.668007i	0.973857	−	0.227161i	$-0.0729443\pi$
$3$	2.45880	+	1.15702i	1.41959	+	0.668007i	0.445730	+	0.895168i	$0.352944\pi$
$4$	5.25058	+	0.663302i	2.62529	+	0.331651i
$5$	1.42401	−	1.72400i	0.636838	−	0.770997i
$5$	1.42401	−	1.72400i	0.636838	−	0.770997i
$6$	−6.43051	−	3.53521i	−2.62525	−	1.44324i
$7$	−0.679948	+	0.935868i	−0.256996	+	0.353725i	−0.917946	−	0.396705i	$-0.870154\pi$
$7$	−0.679948	+	0.935868i	−0.256996	+	0.353725i	0.660950	+	0.750430i	$0.270154\pi$
$8$	−8.73317	−	1.66594i	−3.08764	−	0.588999i
$9$	2.79471	+	3.37822i	0.931570	+	1.12607i
$10$	−4.13018	+	4.40490i	−1.30608	+	1.39295i
$11$	0.198843	−	3.16052i	0.0599535	−	0.952933i	−0.846971	−	0.531639i	$-0.821576\pi$
$11$	0.198843	−	3.16052i	0.0599535	−	0.952933i	0.906924	−	0.421294i	$-0.138424\pi$
$12$	12.1427	+	7.70596i	3.50528	+	2.22452i
$13$	−0.669023	+	0.553464i	−0.185554	+	0.153503i	−0.725563	−	0.688156i	$-0.758421\pi$
$13$	−0.669023	+	0.553464i	−0.185554	+	0.153503i	0.540010	+	0.841659i	$0.318421\pi$
$14$	1.99121	−	2.40697i	0.532175	−	0.643289i
$15$	5.49607	−	2.59136i	1.41908	−	0.669085i
$16$	13.0022	+	3.33840i	3.25055	+	0.834599i
$17$	−0.00124451	−	0.00985132i	−0.000301838	−	0.00238930i	0.991963	−	0.126528i	$-0.0403833\pi$
$17$	−0.00124451	−	0.00985132i	−0.000301838	−	0.00238930i	−0.992265	+	0.124138i	$0.960383\pi$
$18$	−6.95920	−	9.57852i	−1.64030	−	2.25768i
$19$	1.13763	+	2.41759i	0.260991	+	0.554634i	0.991778	−	0.127972i	$-0.0408467\pi$
$19$	1.13763	+	2.41759i	0.260991	+	0.554634i	−0.730787	+	0.682606i	$0.760847\pi$
$20$	8.62043	−	8.10746i	1.92759	−	1.81288i
$21$	−2.75467	+	1.51440i	−0.601119	+	0.330468i
$22$	−1.07180	+	8.48420i	−0.228509	+	1.80884i
$23$	−2.91674	+	7.36684i	−0.608182	+	1.53609i	0.219923	+	0.975517i	$0.429420\pi$
$23$	−2.91674	+	7.36684i	−0.608182	+	1.53609i	−0.828104	+	0.560574i	$0.810580\pi$
$24$	−19.5456	−	14.2007i	−3.98972	−	2.89870i
$25$	−0.944368	−	4.91001i	−0.188874	−	0.982001i
$26$	1.89693	−	1.37820i	0.372018	−	0.270287i
$27$	0.935558	+	3.64376i	0.180048	+	0.701241i
$28$	−4.19089	+	4.46284i	−0.792003	+	0.843397i
$29$	−0.0827079	−	0.0776679i	−0.0153585	−	0.0144226i	0.676830	−	0.736139i	$-0.263353\pi$
$29$	−0.0827079	−	0.0776679i	−0.0153585	−	0.0144226i	−0.692188	+	0.721717i	$0.743353\pi$
$30$	−15.2518	+	6.05204i	−2.78459	+	1.10495i
$31$	−4.77298	+	0.602967i	−0.857252	+	0.108296i	−0.541659	−	0.840598i	$-0.682204\pi$
$31$	−4.77298	+	0.602967i	−0.857252	+	0.108296i	−0.315593	+	0.948895i	$0.602204\pi$
$32$	−17.5651	−	5.70725i	−3.10510	−	1.00891i
$33$	4.14571	−	7.54101i	0.721675	−	1.31272i
$34$	0.00168368	+	0.0267613i	0.000288749	+	0.00458953i
$35$	0.645184	+	2.50492i	0.109056	+	0.423409i
$36$	12.4331	+	19.5914i	2.07218	+	3.26523i
$37$	2.08871	−	8.13500i	0.343382	−	1.33738i	−0.529026	−	0.848606i	$-0.677442\pi$
$37$	2.08871	−	8.13500i	0.343382	−	1.33738i	0.872408	−	0.488779i	$-0.162558\pi$
$38$	−2.65610	−	6.70855i	−0.430877	−	1.08827i
$39$	−2.28536	+	0.586781i	−0.365951	+	0.0939601i
$40$	−15.3082	+	12.6837i	−2.42045	+	2.00547i
$41$	−5.27442	+	2.08829i	−0.823727	+	0.326136i	−0.741900	−	0.670510i	$-0.766075\pi$
$41$	−5.27442	+	2.08829i	−0.823727	+	0.326136i	−0.0818264	+	0.996647i	$0.526075\pi$
$42$	7.68090	−	3.61436i	1.18519	−	0.557708i
$43$	3.29763	−	1.07147i	0.502884	−	0.163397i	−0.0465796	−	0.998915i	$-0.514832\pi$
$43$	3.29763	−	1.07147i	0.502884	−	0.163397i	0.549464	+	0.835518i	$0.314832\pi$
$44$	3.14042	−	16.4627i	0.473437	−	2.48184i
$45$	9.80377	−	0.00744791i	1.46146	−	0.00111027i
$46$	9.11002	−	19.3598i	1.34320	−	2.85444i
$47$	−5.02789	+	0.959122i	−0.733394	+	0.139902i	−0.540532	−	0.841324i	$-0.681777\pi$
$47$	−5.02789	+	0.959122i	−0.733394	+	0.139902i	−0.192862	+	0.981226i	$0.561777\pi$
$48$	28.1072	+	23.2523i	4.05692	+	3.35617i
$49$	1.74960	+	5.38471i	0.249943	+	0.769245i
$50$	1.71262	+	13.3931i	0.242201	+	1.89407i
$51$	0.00833819	−	0.0256623i	0.00116758	−	0.00359344i
$52$	−3.87987	+	2.46224i	−0.538041	+	0.341451i
$53$	−2.92345	−	5.31774i	−0.401567	−	0.730448i	0.595787	−	0.803142i	$-0.296840\pi$
$53$	−2.92345	−	5.31774i	−0.401567	−	0.730448i	−0.997354	+	0.0726943i	$0.976840\pi$
$54$	−1.90358	−	9.97892i	−0.259044	−	1.35796i
$55$	−5.16559	−	4.84343i	−0.696528	−	0.653088i
$56$	7.49720	−	7.04034i	1.00186	−	0.940806i
$57$			7.26064i			0.961695i
$58$	0.209737	+	0.223347i	0.0275398	+	0.0293269i
$59$	−1.11039	+	1.74969i	−0.144560	+	0.227790i	−0.908891	−	0.417034i	$-0.863070\pi$
$59$	−1.11039	+	1.74969i	−0.144560	+	0.227790i	0.764331	+	0.644825i	$0.223070\pi$
$60$	30.5764	−	9.96056i	3.94740	−	1.28590i
$61$	−9.42206	−	3.73046i	−1.20637	−	0.477636i	−0.323040	−	0.946385i	$-0.604705\pi$
$61$	−9.42206	−	3.73046i	−1.20637	−	0.477636i	−0.883331	+	0.468749i	$0.844705\pi$
$62$	12.9659	−	0.815745i	1.64667	−	0.103600i
$63$	−5.06183	+	0.318463i	−0.637731	+	0.0401226i
$64$	21.4095	+	8.47662i	2.67619	+	1.05958i
$65$	0.00147498	+	1.94154i	0.000182949	+	0.240818i
$66$	−12.4518	+	19.6208i	−1.53271	+	2.41516i
$67$	−5.85531	−	6.23527i	−0.715339	−	0.761759i	0.263882	−	0.964555i	$-0.414997\pi$
$67$	−5.85531	−	6.23527i	−0.715339	−	0.761759i	−0.979221	+	0.202796i	$0.934997\pi$
$68$		−	0.0525506i		−	0.00637270i
$69$	−15.6953	+	14.7388i	−1.88949	+	1.77435i
$70$	−1.31410	−	6.86041i	−0.157064	−	0.819976i
$71$	1.84361	+	9.66456i	0.218797	+	1.14697i	0.906896	+	0.421355i	$0.138445\pi$
$71$	1.84361	+	9.66456i	0.218797	+	1.14697i	−0.688099	+	0.725617i	$0.741555\pi$
$72$	−18.7787	−	34.1584i	−2.21310	−	4.02561i
$73$	2.41458	−	1.53234i	0.282606	−	0.179347i	−0.386967	−	0.922094i	$-0.626477\pi$
$73$	2.41458	−	1.53234i	0.282606	−	0.179347i	0.669573	+	0.742747i	$0.266477\pi$
$74$	−7.00867	+	21.5705i	−0.814741	+	2.50751i
$75$	3.35898	−	13.1654i	0.387861	−	1.52021i
$76$	4.36964	+	13.4484i	0.501232	+	1.54263i
$77$	2.82263	+	2.33508i	0.321668	+	0.266107i
$78$	6.25877	−	1.19392i	0.708666	−	0.135185i
$79$	0.889148	−	1.88954i	0.100037	−	0.212589i	−0.848543	−	0.529126i	$-0.822520\pi$
$79$	0.889148	−	1.88954i	0.100037	−	0.212589i	0.948580	+	0.316536i	$0.102520\pi$
$80$	24.2707	−	17.6619i	2.71355	−	1.97466i
$81$	0.549093	−	2.87845i	0.0610103	−	0.319827i
$82$	14.5692	−	4.73382i	1.60890	−	0.522763i
$83$	13.7986	−	6.49314i	1.51460	−	0.712714i	0.524279	−	0.851546i	$-0.324335\pi$
$83$	13.7986	−	6.49314i	1.51460	−	0.712714i	0.990316	+	0.138832i	$0.0443348\pi$
$84$	−15.4681	+	6.12427i	−1.68771	+	0.668213i
$85$	−0.0187559	−	0.0118829i	−0.00203436	−	0.00128888i
$86$	−9.06912	+	2.32855i	−0.977948	+	0.251094i
$87$	−0.113498	−	0.286664i	−0.0121683	−	0.0307337i
$88$	−7.00177	+	27.2701i	−0.746392	+	2.90700i
$89$	0.705163	+	1.11116i	0.0747471	+	0.117783i	0.879645	−	0.475631i	$-0.157780\pi$
$89$	0.705163	+	1.11116i	0.0747471	+	0.117783i	−0.804898	+	0.593413i	$0.797780\pi$
$90$	−26.4234	−	1.64227i	−2.78527	−	0.173110i
$91$	−0.0630684	−	1.00244i	−0.00661137	−	0.105085i
$92$	−20.2010	+	36.7455i	−2.10610	+	3.83098i
$93$	−12.4334	−	4.03987i	−1.28929	−	0.418915i
$94$	13.7133	−	1.73239i	1.41442	−	0.178683i
$95$	5.78794	+	1.48141i	0.593830	+	0.151989i
$96$	−36.5856	−	34.3562i	−3.73401	−	3.50647i
$97$	4.80808	−	5.12008i	0.488186	−	0.519865i	−0.436958	−	0.899482i	$-0.643944\pi$
$97$	4.80808	−	5.12008i	0.488186	−	0.519865i	0.925144	+	0.379617i	$0.123944\pi$
$98$	−3.80230	−	14.8090i	−0.384091	−	1.49593i
$99$	11.2327	−	8.16100i	1.12892	−	0.820211i
$100$	−1.70166	−	26.4068i	−0.170166	−	2.64068i
$101$	−1.93911	−	1.40884i	−0.192948	−	0.140185i	0.487117	−	0.873337i	$-0.338049\pi$
$101$	−1.93911	−	1.40884i	−0.192948	−	0.140185i	−0.680065	+	0.733152i	$0.738049\pi$
$102$	−0.0268236	+	0.0677487i	−0.00265593	+	0.00670812i
$103$	−1.88344	+	14.9090i	−0.185581	+	1.46902i	0.574131	+	0.818763i	$0.305340\pi$
$103$	−1.88344	+	14.9090i	−0.185581	+	1.46902i	−0.759712	+	0.650260i	$0.774660\pi$
$104$	6.76473	−	3.71894i	0.663336	−	0.364672i
$105$	−1.31187	+	6.90559i	−0.128026	+	0.673916i
$106$	6.97731	+	14.8275i	0.677697	+	1.44018i
$107$	−1.53755	−	2.11626i	−0.148641	−	0.204587i	0.728203	−	0.685361i	$-0.240356\pi$
$107$	−1.53755	−	2.11626i	−0.148641	−	0.204587i	−0.876844	+	0.480774i	$0.840356\pi$
$108$	2.49531	+	19.7524i	0.240111	+	1.90067i
$109$	−15.4027	−	3.95475i	−1.47531	−	0.378796i	−0.576490	−	0.817104i	$-0.695578\pi$
$109$	−15.4027	−	3.95475i	−1.47531	−	0.378796i	−0.898825	+	0.438308i	$0.855578\pi$
$110$	13.1005	+	13.9294i	1.24909	+	1.32812i
$111$	14.5481	−	17.5856i	1.38084	−	1.66915i
$112$	−11.9651	+	9.89841i	−1.13060	+	0.935311i
$113$	−6.25485	−	3.96945i	−0.588407	−	0.373414i	0.208042	−	0.978120i	$-0.433291\pi$
$113$	−6.25485	−	3.96945i	−0.588407	−	0.373414i	−0.796449	+	0.604705i	$0.793291\pi$
$114$	1.23112	−	19.5681i	0.115305	−	1.83272i
$115$	8.54697	+	15.5189i	0.797009	+	1.44715i
$116$	−0.382747	−	0.462662i	−0.0355372	−	0.0429571i
$117$	−3.73945	−	0.713338i	−0.345712	−	0.0659481i
$118$	3.28929	−	4.52731i	0.302803	−	0.416773i
$119$	0.0100657	+	0.00553369i	0.000922725	+	0.000507272i
$120$	−52.3152	+	13.4746i	−4.77570	+	1.23006i
$121$	0.963907	+	0.121770i	0.0876279	+	0.0110700i
$122$	24.7608	+	11.6516i	2.24174	+	1.05488i
$123$	−15.3849	−	0.967938i	−1.38721	−	0.0872760i
$124$	−25.4609			−2.28645
$125$	−9.80966	−	5.36383i	−0.877402	−	0.479755i
$126$	13.6961			1.22015
$127$	16.9238	+	1.06476i	1.50175	+	0.0944818i	0.792236	−	0.610214i	$-0.208917\pi$
$127$	16.9238	+	1.06476i	1.50175	+	0.0944818i	0.709509	+	0.704696i	$0.248917\pi$
$128$	−22.8408	−	10.7481i	−2.01886	−	0.950005i
$129$	9.34791	+	1.18092i	0.823038	+	0.103974i
$130$	0.325234	−	5.23288i	0.0285249	−	0.458954i
$131$	15.7784	+	8.67426i	1.37857	+	0.757873i	0.986762	−	0.162175i	$-0.0518509\pi$
$131$	15.7784	+	8.67426i	1.37857	+	0.757873i	0.391805	+	0.920048i	$0.371851\pi$
$132$	26.7693	−	36.8448i	2.32997	−	3.20693i
$133$	−3.03608	−	0.579164i	−0.263262	−	0.0502198i
$134$	14.7234	+	17.7975i	1.27191	+	1.53747i
$135$	7.61409	+	3.57586i	0.655317	+	0.307761i
$136$	−0.00554319	+	0.0881065i	−0.000475325	+	0.00755507i
$137$	10.6111	+	6.73401i	0.906567	+	0.575325i	0.905346	−	0.424674i	$-0.139611\pi$
$137$	10.6111	+	6.73401i	0.906567	+	0.575325i	0.00122115	+	0.999999i	$0.499611\pi$
$138$	44.7994	−	37.0613i	3.81358	−	3.15487i
$139$	7.21872	−	8.72593i	0.612284	−	0.740124i	−0.369687	−	0.929156i	$-0.620535\pi$
$139$	7.21872	−	8.72593i	0.612284	−	0.740124i	0.981971	+	0.189032i	$0.0605351\pi$
$140$	1.72607	+	13.5802i	0.145879	+	1.14774i
$141$	−13.4723	−	3.45910i	−1.13457	−	0.291308i
$142$	−3.32999	−	26.3596i	−0.279446	−	2.21204i
$143$	1.61620	+	2.22451i	0.135154	+	0.186023i
$144$	25.0595	+	53.2542i	2.08829	+	4.43785i
$145$	−0.251677	+	0.0319885i	−0.0209006	+	0.00265650i
$146$	−6.76737	+	3.72039i	−0.560072	+	0.307902i
$147$	−1.92832	+	15.2642i	−0.159045	+	1.25897i
$148$	16.3629	−	41.3280i	1.34502	−	3.39714i
$149$	14.4368	+	10.4890i	1.18271	+	0.859290i	0.992475	−	0.122448i	$-0.0390746\pi$
$149$	14.4368	+	10.4890i	1.18271	+	0.859290i	0.190236	+	0.981738i	$0.439075\pi$
$150$	−11.2851	+	34.9124i	−0.921425	+	2.85059i
$151$	2.07935	−	1.51074i	0.169215	−	0.122942i	−0.499954	−	0.866052i	$-0.666650\pi$
$151$	2.07935	−	1.51074i	0.169215	−	0.122942i	0.669170	+	0.743110i	$0.266650\pi$
$152$	−5.90758	−	23.0085i	−0.479168	−	1.86623i
$153$	0.0298019	−	0.0317358i	0.00240934	−	0.00256569i
$154$	−7.21133	−	6.77189i	−0.581105	−	0.545694i
$155$	−5.75727	+	9.08726i	−0.462435	+	0.729906i
$156$	−12.3887	+	1.56505i	−0.991888	+	0.125305i
$157$	−7.98951	−	2.59595i	−0.637633	−	0.207179i	−0.0276794	−	0.999617i	$-0.508812\pi$
$157$	−7.98951	−	2.59595i	−0.637633	−	0.207179i	−0.609953	+	0.792437i	$0.708812\pi$
$158$	−2.71674	+	4.94172i	−0.216132	+	0.393142i
$159$	−1.03543	−	16.4577i	−0.0821152	−	1.30518i
$160$	−34.8523	+	22.1551i	−2.75532	+	1.75151i
$161$	−4.91116	−	7.73875i	−0.387054	−	0.609899i
$162$	−1.96793	+	7.66459i	−0.154615	+	0.602187i
$163$	7.72305	+	19.5062i	0.604916	+	1.52784i	0.832466	+	0.554076i	$0.186928\pi$
$163$	7.72305	+	19.5062i	0.604916	+	1.52784i	−0.227550	+	0.973766i	$0.573072\pi$
$164$	−29.0790	+	7.46621i	−2.27068	+	0.583013i
$165$	−7.09718	−	17.8857i	−0.552515	−	1.39240i
$166$	−38.2896	+	15.1599i	−2.97185	+	1.17664i
$167$	−17.1214	+	8.05672i	−1.32489	+	0.623448i	−0.952475	−	0.304617i	$-0.901472\pi$
$167$	−17.1214	+	8.05672i	−1.32489	+	0.623448i	−0.372419	+	0.928065i	$0.621472\pi$
$168$	26.5799	−	8.63634i	2.05069	−	0.666308i
$169$	−2.29469	+	12.0292i	−0.176514	+	0.925321i
$170$	0.0485341	+	0.0352058i	0.00372240	+	0.00270016i
$171$	−4.98782	+	10.5997i	−0.381428	+	0.810576i
$172$	18.0252	−	3.43849i	1.37441	−	0.262182i
$173$	−0.0250570	−	0.0207290i	−0.00190505	−	0.00157600i	0.636471	−	0.771301i	$-0.280394\pi$
$173$	−0.0250570	−	0.0207290i	−0.00190505	−	0.00157600i	−0.638376	+	0.769725i	$0.720394\pi$
$174$	0.257282	+	0.791834i	0.0195045	+	0.0600288i
$175$	5.23724	+	2.45475i	0.395898	+	0.185561i
$176$	13.1365	−	40.4299i	0.990198	−	3.04752i
$177$	−4.75465	+	3.01739i	−0.357381	+	0.226801i
$178$	−1.71207	−	3.11425i	−0.128325	−	0.233423i
$179$	0.498654	+	2.61404i	0.0372711	+	0.195382i	0.996053	−	0.0887613i	$-0.0282908\pi$
$179$	0.498654	+	2.61404i	0.0372711	+	0.195382i	−0.958782	+	0.284143i	$0.908291\pi$
$180$	51.4804	+	6.46376i	3.83712	+	0.481780i
$181$	−0.421541	+	0.395854i	−0.0313329	+	0.0294236i	−0.700055	−	0.714088i	$-0.746841\pi$
$181$	−0.421541	+	0.395854i	−0.0313329	+	0.0294236i	0.668723	+	0.743512i	$0.266841\pi$
$182$			2.71238i			0.201055i
$183$	−18.8507	−	20.0740i	−1.39348	−	1.48391i
$184$	37.7451	−	59.4767i	2.78260	−	4.38468i
$185$	−11.0504	−	15.1853i	−0.812441	−	1.11644i
$186$	32.8243	+	12.9961i	2.40680	+	0.952918i
$187$	−0.0313828	+	0.00197444i	−0.00229494	+	0.000144385i
$188$	−27.0355	+	1.70093i	−1.97177	+	0.124053i
$189$	−4.04621	−	1.60201i	−0.294318	−	0.116529i
$190$	−15.3479	−	4.97395i	−1.11345	−	0.360848i
$191$	10.6200	−	16.7345i	0.768439	−	1.21087i	−0.204288	−	0.978911i	$-0.565488\pi$
$191$	10.6200	−	16.7345i	0.768439	−	1.21087i	0.972727	−	0.231955i	$-0.0745121\pi$
$192$	42.8340	+	45.6136i	3.09128	+	3.29188i
$193$			3.08227i			0.221866i	0.993828	+	0.110933i	$0.0353840\pi$
$193$			3.08227i			0.221866i	−0.993828	+	0.110933i	$0.964616\pi$
$194$	−13.8264	+	12.9839i	−0.992678	+	0.932187i
$195$	−2.24277	+	4.77555i	−0.160608	+	0.341984i
$196$	5.61472	+	29.4334i	0.401051	+	2.10238i
$197$	−2.66155	−	4.84134i	−0.189628	−	0.344931i	0.764354	−	0.644797i	$-0.223058\pi$
$197$	−2.66155	−	4.84134i	−0.189628	−	0.344931i	−0.953981	+	0.299866i	$0.903058\pi$
$198$	−31.6569	+	20.0901i	−2.24976	+	1.42774i
$199$	3.40027	−	10.4649i	0.241038	−	0.741840i	−0.755224	−	0.655466i	$-0.772472\pi$
$199$	3.40027	−	10.4649i	0.241038	−	0.741840i	0.996263	−	0.0863737i	$-0.0275279\pi$
$200$	0.0675421	+	44.4532i	0.00477595	+	3.14331i
$201$	−7.18267	−	22.1060i	−0.506626	−	1.55924i
$202$	4.98720	+	4.12577i	0.350898	+	0.290288i
$203$	0.128924	−	0.0245936i	0.00904869	−	0.00172613i
$204$	0.0608022	−	0.129211i	0.00425701	−	0.00904660i
$205$	−3.91063	+	12.0669i	−0.273131	+	0.842787i
$206$	7.60404	−	39.8617i	0.529798	−	2.77730i
$207$	−33.0382	+	10.7348i	−2.29632	+	0.746119i
$208$	−10.5464	+	4.96278i	−0.731264	+	0.344107i
$209$	7.86707	−	3.11479i	0.544176	−	0.215455i
$210$	4.70655	−	18.3888i	0.324783	−	1.26895i
$211$	−4.36230	+	1.12005i	−0.300313	+	0.0771073i	−0.395840	−	0.918320i	$-0.629546\pi$
$211$	−4.36230	+	1.12005i	−0.300313	+	0.0771073i	0.0955268	+	0.995427i	$0.469546\pi$
$212$	−11.8226	−	29.8604i	−0.811976	−	2.05082i
$213$	−6.64904	+	25.8963i	−0.455584	+	1.77438i
$214$	3.78503	+	5.96425i	0.258739	+	0.407707i
$215$	2.84866	−	7.21090i	0.194277	−	0.491780i
$216$	−2.10010	−	33.3801i	−0.142894	−	2.27123i
$217$	2.68108	−	4.87687i	0.182004	−	0.331063i
$218$	40.8413	+	13.2702i	2.76612	+	0.898768i
$219$	7.70993	−	0.973990i	0.520989	−	0.0658162i
$220$	−23.9097	−	28.8572i	−1.61199	−	1.94555i
$221$	0.00628495	+	0.00590197i	0.000422772	+	0.000397009i
$222$	−42.1904	+	44.9282i	−2.83163	+	3.01538i
$223$	4.74220	+	18.4697i	0.317561	+	1.23682i	0.904249	+	0.427006i	$0.140432\pi$
$223$	4.74220	+	18.4697i	0.317561	+	1.23682i	−0.586687	+	0.809814i	$0.699568\pi$
$224$	17.2846	−	12.5580i	1.15488	−	0.839067i
$225$	13.9479	−	16.9123i	0.929858	−	1.12749i
$226$	16.1844	+	11.7586i	1.07657	+	0.782173i
$227$	6.50309	−	16.4249i	0.431626	−	1.09016i	−0.537428	−	0.843310i	$-0.680604\pi$
$227$	6.50309	−	16.4249i	0.431626	−	1.09016i	0.969053	−	0.246852i	$-0.0793961\pi$
$228$	−4.81600	+	38.1226i	−0.318947	+	2.52473i
$229$	9.57009	−	5.26120i	0.632409	−	0.347670i	−0.133093	−	0.991104i	$-0.542491\pi$
$229$	9.57009	−	5.26120i	0.632409	−	0.347670i	0.765502	+	0.643434i	$0.222491\pi$
$230$	−20.4035	−	43.2743i	−1.34537	−	2.85342i
$231$	4.23853	+	9.00733i	0.278875	+	0.592639i
$232$	0.592912	+	0.816074i	0.0389266	+	0.0535779i
$233$	2.81859	+	22.3114i	0.184652	+	1.46167i	0.763275	+	0.646074i	$0.223590\pi$
$233$	2.81859	+	22.3114i	0.184652	+	1.46167i	−0.578623	+	0.815595i	$0.696410\pi$
$234$	9.95723	+	2.55658i	0.650924	+	0.167129i
$235$	−5.50626	+	10.0339i	−0.359189	+	0.654540i
$236$	−6.99075	+	8.45037i	−0.455059	+	0.550072i
$237$	4.37247	−	3.61722i	0.284022	−	0.234964i
$238$	−0.0261899	−	0.0166206i	−0.00169764	−	0.00107735i
$239$	−0.210227	+	3.34147i	−0.0135985	+	0.216142i	0.985359	+	0.170492i	$0.0545357\pi$
$239$	−0.210227	+	3.34147i	−0.0135985	+	0.216142i	−0.998958	+	0.0456495i	$0.985464\pi$
$240$	80.1119	−	15.3453i	5.17120	−	0.990532i
$241$	−1.29077	−	1.56028i	−0.0831460	−	0.100506i	0.727300	−	0.686320i	$-0.240775\pi$
$241$	−1.29077	−	1.56028i	−0.0831460	−	0.100506i	−0.810446	+	0.585814i	$0.800775\pi$
$242$	−2.57718	−	0.491623i	−0.165667	−	0.0316027i
$243$	11.3142	−	15.5726i	0.725805	−	0.998985i
$244$	−46.9969	−	25.8367i	−3.00867	−	1.65403i
$245$	11.7747	+	4.65159i	0.752259	+	0.297179i
$246$	41.2998	+	5.21738i	2.63318	+	0.332648i
$247$	−2.09915	−	0.987787i	−0.133566	−	0.0628514i
$248$	42.6877	+	2.68569i	2.71067	+	0.170541i
$249$	41.4407			2.62620
$250$	25.5285	+	16.1194i	1.61456	+	1.01948i
$251$	1.17033			0.0738705			0.0369352	−	0.999318i	$-0.488240\pi$
$251$	1.17033			0.0738705			0.0369352	+	0.999318i	$0.488240\pi$
$252$	−26.7888	−	1.68541i	−1.68753	−	0.106171i
$253$	22.7031	+	10.6833i	1.42733	+	0.671650i
$254$	−45.4308	−	5.73925i	−2.85058	−	0.360112i
$255$	−0.0323682	−	0.0509186i	−0.00202697	−	0.00318864i
$256$	19.3793	+	10.6538i	1.21120	+	0.665865i
$257$	−2.27267	+	3.12806i	−0.141765	+	0.195123i	−0.873995	−	0.485934i	$-0.838479\pi$
$257$	−2.27267	+	3.12806i	−0.141765	+	0.195123i	0.732230	+	0.681057i	$0.238479\pi$
$258$	−24.9933	−	4.76773i	−1.55602	−	0.296826i
$259$	6.19307	+	7.48613i	0.384819	+	0.465166i
$260$	−1.28008	+	10.1952i	−0.0793873	+	0.632278i
$261$	0.0312349	−	0.496465i	0.00193339	−	0.0307304i
$262$	−41.0536	−	26.0534i	−2.53630	−	1.60958i
$263$	3.40819	−	2.81950i	0.210158	−	0.173858i	−0.526390	−	0.850243i	$-0.676455\pi$
$263$	3.40819	−	2.81950i	0.210158	−	0.173858i	0.736548	+	0.676386i	$0.236455\pi$
$264$	−48.7680	+	58.9504i	−3.00147	+	3.62815i
$265$	−13.3308	−	2.53250i	−0.818907	−	0.155570i
$266$	8.08434	+	2.07571i	0.495683	+	0.127270i
$267$	0.448217	+	3.54800i	0.0274304	+	0.217134i
$268$	−26.6079	−	36.6226i	−1.62533	−	2.23708i
$269$	−5.46224	−	11.6078i	−0.333038	−	0.707743i	0.666239	−	0.745738i	$-0.267903\pi$
$269$	−5.46224	−	11.6078i	−0.333038	−	0.707743i	−0.999278	+	0.0379951i	$0.987903\pi$
$270$	−19.9144	−	10.9283i	−1.21195	−	0.665078i
$271$	8.33874	−	4.58426i	0.506543	−	0.278474i	−0.207922	−	0.978145i	$-0.566670\pi$
$271$	8.33874	−	4.58426i	0.506543	−	0.278474i	0.714465	+	0.699671i	$0.246670\pi$
$272$	0.0167062	−	0.132243i	0.00101296	−	0.00801844i
$273$	1.00478	−	2.53778i	0.0608119	−	0.153593i
$274$	−27.4561	−	19.9481i	−1.65869	−	1.20511i
$275$	−15.7060	+	2.00837i	−0.947105	+	0.121109i
$276$	−92.1855	+	66.9767i	−5.54891	+	4.03152i
$277$	−4.38365	−	17.0732i	−0.263388	−	1.02583i	−0.953322	−	0.301956i	$-0.902360\pi$
$277$	−4.38365	−	17.0732i	−0.263388	−	1.02583i	0.689934	−	0.723872i	$-0.257640\pi$
$278$	−20.9347	+	22.2932i	−1.25558	+	1.33706i
$279$	−15.3760	−	14.4391i	−0.920540	−	0.864444i
$280$	−1.46144	−	22.9507i	−0.0873380	−	1.37157i
$281$	−12.1365	+	1.53320i	−0.724004	+	0.0914629i	−0.478694	−	0.877982i	$-0.658890\pi$
$281$	−12.1365	+	1.53320i	−0.724004	+	0.0914629i	−0.245310	+	0.969445i	$0.578890\pi$
$282$	35.7226	+	11.6070i	2.12725	+	0.691186i
$283$	−5.99843	+	10.9111i	−0.356570	+	0.648598i	−0.992376	−	0.123251i	$-0.960668\pi$
$283$	−5.99843	+	10.9111i	−0.356570	+	0.648598i	0.635806	+	0.771849i	$0.280668\pi$
$284$	3.26951	+	51.9674i	0.194010	+	3.08370i
$285$	12.5174	+	10.3393i	0.741464	+	0.612444i
$286$	−3.97864	−	6.26933i	−0.235262	−	0.370713i
$287$	1.63197	−	6.35610i	0.0963321	−	0.375189i
$288$	−29.8090	−	75.2890i	−1.75651	−	4.43645i
$289$	16.4658	−	4.22770i	0.968578	−	0.248688i
$290$	0.683718	−	0.0435374i	0.0401493	−	0.00255660i
$291$	17.7461	−	7.02619i	1.04030	−	0.411882i
$292$	13.6944	−	6.44408i	0.801403	−	0.377111i
$293$	21.3454	−	6.93555i	1.24701	−	0.405179i	0.390164	−	0.920745i	$-0.372418\pi$
$293$	21.3454	−	6.93555i	1.24701	−	0.405179i	0.856850	+	0.515566i	$0.172418\pi$
$294$	7.78524	−	40.8117i	0.454044	−	2.38018i
$295$	1.43526	+	4.40590i	0.0835643	+	0.256521i
$296$	−31.7935	+	67.5646i	−1.84796	+	3.92711i
$297$	11.7022	−	2.23231i	0.679030	−	0.129532i
$298$	−37.1302	−	30.7167i	−2.15089	−	1.77937i
$299$	−2.12591	−	6.54289i	−0.122945	−	0.378385i
$300$	26.3692	−	66.8978i	1.52243	−	3.86234i
$301$	−1.23947	+	3.81469i	−0.0714417	+	0.219875i
$302$	−5.86023	+	3.71901i	−0.337218	+	0.214005i
$303$	−3.13781	−	5.70765i	−0.180262	−	0.327896i
$304$	6.72084	+	35.2319i	0.385467	+	2.02069i
$305$	−19.8485	+	10.9314i	−1.13652	+	0.625932i
$306$	−0.0857003	+	0.0804779i	−0.00489916	+	0.00460062i
$307$			3.95388i			0.225660i	0.993614	+	0.112830i	$0.0359915\pi$
$307$			3.95388i			0.225660i	−0.993614	+	0.112830i	$0.964009\pi$
$308$	13.2716	+	14.1328i	0.756218	+	0.805290i
$309$	−21.8810	+	34.4789i	−1.24477	+	1.96144i
$310$	17.0573	−	23.5149i	0.968788	−	1.33555i
$311$	12.8127	+	5.07292i	0.726543	+	0.287659i	0.702136	−	0.712043i	$-0.252230\pi$
$311$	12.8127	+	5.07292i	0.726543	+	0.287659i	0.0244076	+	0.999702i	$0.492230\pi$
$312$	20.9360	−	1.31718i	1.18527	−	0.0745707i
$313$	−31.7780	+	1.99930i	−1.79620	+	0.113007i	−0.925485	−	0.378784i	$-0.876342\pi$
$313$	−31.7780	+	1.99930i	−1.79620	+	0.113007i	−0.870713	+	0.491792i	$0.836342\pi$
$314$	21.0924	+	8.35106i	1.19031	+	0.471277i
$315$	−6.65908	+	9.18010i	−0.375197	+	0.517240i
$316$	5.92188	−	9.33139i	0.333132	−	0.524932i
$317$	9.03773	+	9.62421i	0.507610	+	0.540549i	0.930818	−	0.365483i	$-0.119096\pi$
$317$	9.03773	+	9.62421i	0.507610	+	0.540549i	−0.423208	+	0.906032i	$0.639096\pi$
$318$			44.5308i			2.49716i
$319$	−0.261917	+	0.245956i	−0.0146645	+	0.0137709i
$320$	45.1012	−	24.8392i	2.52123	−	1.38855i
$321$	−1.33197	−	6.98244i	−0.0743434	−	0.389722i
$322$	11.9239	+	21.6894i	0.664491	+	1.20871i
$323$	0.0224007	−	0.0142159i	0.00124641	−	0.000790995i
$324$	4.79234	−	14.7493i	0.266241	−	0.819405i
$325$	3.34931	+	2.76223i	0.185787	+	0.153221i
$326$	−17.5069	−	53.8806i	−0.969617	−	2.98417i
$327$	−33.2965	−	27.5452i	−1.84130	−	1.52325i
$328$	49.5414	−	9.45053i	2.73547	−	0.521818i
$329$	2.52109	−	5.35760i	0.138992	−	0.295374i
$330$	16.0949	+	49.4072i	0.885994	+	2.71978i
$331$	−4.47038	+	23.4346i	−0.245714	+	1.28808i	0.618830	+	0.785525i	$0.287607\pi$
$331$	−4.47038	+	23.4346i	−0.245714	+	1.28808i	−0.864545	+	0.502556i	$0.832393\pi$
$332$	76.7577	−	24.9401i	4.21262	−	1.36876i
$333$	33.3192	−	15.6788i	1.82588	−	0.859194i
$334$	47.5100	−	18.8105i	2.59963	−	1.02927i
$335$	−19.0877	+	1.21545i	−1.04287	+	0.0664073i
$336$	−40.8725	+	10.4943i	−2.22978	+	0.572509i
$337$	5.98000	+	15.1038i	0.325752	+	0.822755i	0.996694	+	0.0812452i	$0.0258897\pi$
$337$	5.98000	+	15.1038i	0.325752	+	0.822755i	−0.670943	+	0.741509i	$0.734110\pi$
$338$	8.22409	−	32.0307i	0.447332	−	1.74224i
$339$	−10.7867	−	16.9971i	−0.585851	−	0.923154i
$340$	−0.0905974	−	0.0748328i	−0.00491333	−	0.00405838i
$341$	0.956617	+	15.2050i	0.0518037	+	0.823397i
$342$	15.2400	−	27.7214i	0.824082	−	1.49900i
$343$	−13.9303	−	4.52622i	−0.752164	−	0.244393i
$344$	−30.5838	+	3.86363i	−1.64897	+	0.208313i
$345$	3.05950	+	48.0469i	0.164718	+	2.58676i
$346$	0.0640164	+	0.0601154i	0.00344154	+	0.00323182i
$347$	6.18869	−	6.59028i	0.332226	−	0.353785i	−0.541068	−	0.840979i	$-0.681980\pi$
$347$	6.18869	−	6.59028i	0.332226	−	0.353785i	0.873294	+	0.487194i	$0.161980\pi$
$348$	−0.405788	−	1.58044i	−0.0217525	−	0.0847204i
$349$	−26.8288	+	19.4923i	−1.43611	+	1.04340i	−0.447276	+	0.894396i	$0.647606\pi$
$349$	−26.8288	+	19.4923i	−1.43611	+	1.04340i	−0.988837	+	0.149001i	$0.952394\pi$
$350$	−13.6987	−	7.50382i	−0.732224	−	0.401096i
$351$	−2.64260	−	1.91996i	−0.141051	−	0.102480i
$352$	−21.5306	+	54.3801i	−1.14758	+	2.89847i
$353$	3.60201	−	28.5128i	0.191716	−	1.51759i	−0.543302	−	0.839537i	$-0.682826\pi$
$353$	3.60201	−	28.5128i	0.191716	−	1.51759i	0.735018	−	0.678048i	$-0.237174\pi$
$354$	13.3259	−	7.32597i	0.708263	−	0.389371i
$355$	19.2871	+	10.5841i	1.02365	+	0.561744i
$356$	2.96548	+	6.30196i	0.157170	+	0.334003i
$357$	0.0183470	+	0.0252525i	0.000971027	+	0.00133650i
$358$	−0.900683	−	7.12964i	−0.0476025	−	0.376813i
$359$	−11.8771	−	3.04953i	−0.626852	−	0.160948i	−0.0781163	−	0.996944i	$-0.524891\pi$
$359$	−11.8771	−	3.04953i	−0.626852	−	0.160948i	−0.548735	+	0.835996i	$0.684891\pi$
$360$	−85.6304	−	16.2675i	−4.51312	−	0.857370i
$361$	7.56050	−	9.13908i	0.397921	−	0.481004i
$362$	1.20322	−	0.995388i	0.0632397	−	0.0523164i
$363$	2.22916	+	1.41467i	0.117001	+	0.0742508i
$364$	0.333778	−	5.30524i	0.0174947	−	0.278070i
$365$	0.796641	−	6.34483i	0.0416981	−	0.332103i
$366$	47.4008	+	57.2977i	2.47768	+	2.99500i
$367$	13.9023	+	2.65201i	0.725696	+	0.138434i	0.536976	−	0.843597i	$-0.319566\pi$
$367$	13.9023	+	2.65201i	0.725696	+	0.138434i	0.188719	+	0.982031i	$0.439566\pi$
$368$	−62.5174	+	86.0478i	−3.25894	+	4.48555i
$369$	−21.7952	−	11.9820i	−1.13461	−	0.623759i
$370$	27.2071	+	42.7996i	1.41443	+	2.22504i
$371$	6.96450	+	0.879822i	0.361579	+	0.0456781i
$372$	−62.6031	−	29.4588i	−3.24582	−	1.52737i
$373$	34.2993	+	2.15793i	1.77595	+	0.111733i	0.916638	−	0.399718i	$-0.130892\pi$
$373$	34.2993	+	2.15793i	1.77595	+	0.111733i	0.859312	+	0.511451i	$0.170892\pi$
$374$	0.0849145			0.00439082
$375$	−17.9139	−	24.5385i	−0.925069	−	1.26717i
$376$	45.5073			2.34686
$377$	0.0983198	+	0.00618576i	0.00506373	+	0.000318583i
$378$	10.6333	+	5.00365i	0.546917	+	0.257360i
$379$	−24.8702	−	3.14184i	−1.27750	−	0.161386i	−0.542847	−	0.839831i	$-0.682654\pi$
$379$	−24.8702	−	3.14184i	−1.27750	−	0.161386i	−0.734650	+	0.678446i	$0.762654\pi$
$380$	29.4074	+	11.6174i	1.50857	+	0.595960i
$381$	40.3803	+	22.1992i	2.06874	+	1.13730i
$382$	−31.4596	+	43.3004i	−1.60961	+	2.21544i
$383$	−23.7078	−	4.52251i	−1.21141	−	0.231089i	−0.458190	−	0.888854i	$-0.651502\pi$
$383$	−23.7078	−	4.52251i	−1.21141	−	0.231089i	−0.753223	+	0.657765i	$0.771502\pi$
$384$	−43.7252	−	52.8547i	−2.23134	−	2.69723i
$385$	8.04515	−	1.54103i	0.410019	−	0.0785381i
$386$	0.522633	−	8.30701i	0.0266013	−	0.422816i
$387$	12.8356	+	8.14570i	0.652468	+	0.414069i
$388$	28.6413	−	23.6942i	1.45404	−	1.20289i
$389$	12.9862	−	15.6976i	0.658426	−	0.795900i	−0.330580	−	0.943778i	$-0.607244\pi$
$389$	12.9862	−	15.6976i	0.658426	−	0.795900i	0.989006	+	0.147878i	$0.0472443\pi$
$390$	6.85425	−	12.4903i	0.347078	−	0.632471i
$391$	0.0762030	+	0.0195656i	0.00385375	+	0.000989475i
$392$	−6.30893	−	49.9403i	−0.318649	−	2.52237i
$393$	28.7596	+	39.5842i	1.45073	+	1.99676i
$394$	6.35224	+	13.4992i	0.320021	+	0.680079i
$395$	−1.99141	−	4.22362i	−0.100198	−	0.212513i
$396$	64.3911	−	35.3993i	3.23578	−	1.77888i
$397$	3.80898	−	30.1512i	0.191167	−	1.51325i	−0.546143	−	0.837692i	$-0.683905\pi$
$397$	3.80898	−	30.1512i	0.191167	−	1.51325i	0.737311	−	0.675554i	$-0.236095\pi$
$398$	−10.9385	+	27.6275i	−0.548298	+	1.38484i
$399$	−6.79500	−	4.93686i	−0.340176	−	0.247152i
$400$	4.11269	−	66.9935i	0.205635	−	3.34968i
$401$	5.73755	−	4.16858i	0.286520	−	0.208169i	−0.435236	−	0.900316i	$-0.643335\pi$
$401$	5.73755	−	4.16858i	0.286520	−	0.208169i	0.721756	+	0.692147i	$0.243335\pi$
$402$	15.6097	+	60.7957i	0.778540	+	3.03221i
$403$	2.85951	−	3.04507i	0.142442	−	0.151686i
$404$	−9.24695	−	8.68346i	−0.460053	−	0.432018i
$405$	−4.18053	−	5.04559i	−0.207732	−	0.250717i
$406$	−0.351633	+	0.0444216i	−0.0174513	+	0.00220461i
$407$	−25.2955	−	8.21901i	−1.25385	−	0.407401i
$408$	−0.115571	+	0.210222i	−0.00572161	+	0.0104076i
$409$	−0.597370	−	9.49493i	−0.0295381	−	0.469494i	−0.984795	−	0.173718i	$-0.944422\pi$
$409$	−0.597370	−	9.49493i	−0.0295381	−	0.469494i	0.955257	−	0.295776i	$-0.0955781\pi$
$410$	12.5856	−	31.8583i	0.621560	−	1.57337i
$411$	18.2991	+	28.8348i	0.902630	+	1.42232i
$412$	−19.7783	+	77.0314i	−0.974406	+	3.79506i
$413$	−0.882475	−	2.22888i	−0.0434237	−	0.109676i
$414$	90.8615	−	23.3293i	4.46560	−	1.14657i
$415$	8.45524	−	33.0352i	0.415052	−	1.62163i
$416$	14.9102	−	5.90338i	0.731034	−	0.289437i
$417$	27.8455	−	13.1031i	1.36360	−	0.641660i
$418$	−21.7307	+	7.06072i	−1.06288	+	0.345351i
$419$	−0.0225629	+	0.118279i	−0.00110227	+	0.00577829i	−0.982834	−	0.184491i	$-0.940936\pi$
$419$	−0.0225629	+	0.118279i	−0.00110227	+	0.00577829i	0.981732	+	0.190270i	$0.0609362\pi$
$420$	−11.4686	+	35.3882i	−0.559610	+	1.72677i
$421$	3.46315	−	7.35957i	0.168784	−	0.358684i	−0.802484	−	0.596674i	$-0.796489\pi$
$421$	3.46315	−	7.35957i	0.168784	−	0.358684i	0.971268	+	0.237990i	$0.0764886\pi$
$422$	11.9467	−	2.27896i	0.581558	−	0.110938i
$423$	−17.2916	−	14.3049i	−0.840748	−	0.695527i
$424$	16.6720	+	51.3111i	0.809662	+	2.49188i
$425$	−0.0471948	+	0.0154138i	−0.00228928	+	0.000747681i
$426$	22.3108	−	68.6656i	1.08096	−	3.32686i
$427$	9.89773	−	6.28129i	0.478985	−	0.303973i
$428$	−6.66933	−	12.1315i	−0.322374	−	0.586397i
$429$	1.40010	+	7.33961i	0.0675977	+	0.354360i
$430$	−8.90012	+	18.9511i	−0.429202	+	0.913902i
$431$	−28.1766	+	26.4596i	−1.35722	+	1.27451i	−0.428594	+	0.903497i	$0.640991\pi$
$431$	−28.1766	+	26.4596i	−1.35722	+	1.27451i	−0.928626	+	0.371017i	$0.879009\pi$
$432$			50.5001i			2.42969i
$433$	−14.6334	−	15.5830i	−0.703238	−	0.748873i	0.273835	−	0.961777i	$-0.411708\pi$
$433$	−14.6334	−	15.5830i	−0.703238	−	0.748873i	−0.977073	+	0.212904i	$0.931708\pi$
$434$	−8.05270	+	12.6890i	−0.386542	+	0.609093i
$435$	−0.655834	−	0.212543i	−0.0314448	−	0.0101906i
$436$	−78.2501	−	30.9814i	−3.74750	−	1.48374i
$437$	−21.1282	+	1.32927i	−1.01070	+	0.0635878i
$438$	−20.9442	+	1.31770i	−1.00075	+	0.0629619i
$439$	−5.18040	−	2.05106i	−0.247247	−	0.0978920i	0.241233	−	0.970467i	$-0.422448\pi$
$439$	−5.18040	−	2.05106i	−0.247247	−	0.0978920i	−0.488480	+	0.872575i	$0.662448\pi$
$440$	37.0431	+	50.9041i	1.76596	+	2.42676i
$441$	−13.3011	+	20.9592i	−0.633387	+	0.998059i
$442$	−0.0159378	−	0.0169721i	−0.000758085	−	0.000807279i
$443$		−	7.03208i		−	0.334104i	−0.985948	−	0.167052i	$-0.946575\pi$
$443$		−	7.03208i		−	0.334104i	0.985948	−	0.167052i	$-0.0534248\pi$
$444$	88.0505	−	82.6849i	4.17869	−	3.92405i
$445$	2.91980	+	0.366603i	0.138412	+	0.0173787i
$446$	−9.64897	−	50.5817i	−0.456892	−	2.39511i
$447$	23.3613	+	42.4940i	1.10495	+	2.00990i
$448$	−22.4904	+	14.2728i	−1.06257	+	0.674327i
$449$	−0.163627	+	0.503593i	−0.00772205	+	0.0237660i	−0.954843	−	0.297110i	$-0.903977\pi$
$449$	−0.163627	+	0.503593i	−0.00772205	+	0.0237660i	0.947121	+	0.320876i	$0.103977\pi$
$450$	−40.4586	+	43.2154i	−1.90723	+	2.03719i
$451$	5.55131	+	17.0852i	0.261401	+	0.804509i
$452$	−30.2086	−	24.9908i	−1.42090	−	1.17547i
$453$	6.86067	−	1.30874i	0.322342	−	0.0614901i
$454$	−20.3115	+	43.1642i	−0.953267	+	2.02580i
$455$	−1.81803	−	1.31876i	−0.0852304	−	0.0618246i
$456$	12.0958	−	63.4084i	0.566438	−	2.96937i
$457$	16.5399	−	5.37412i	0.773702	−	0.251391i	0.104553	−	0.994519i	$-0.466659\pi$
$457$	16.5399	−	5.37412i	0.773702	−	0.251391i	0.669149	+	0.743128i	$0.266659\pi$
$458$	−26.6844	+	12.5567i	−1.24688	+	0.586738i
$459$	0.0347315	−	0.0137512i	0.00162113	−	0.000641850i
$460$	34.5828	+	87.1526i	1.61243	+	4.06351i
$461$	18.3433	−	4.70976i	0.854332	−	0.219355i	0.203968	−	0.978978i	$-0.434616\pi$
$461$	18.3433	−	4.70976i	0.854332	−	0.219355i	0.650364	+	0.759622i	$0.274616\pi$
$462$	−9.89596	−	24.9943i	−0.460402	−	1.16284i
$463$	−3.11631	+	12.1372i	−0.144827	+	0.564065i	0.854199	+	0.519946i	$0.174048\pi$
$463$	−3.11631	+	12.1372i	−0.144827	+	0.564065i	−0.999026	+	0.0441189i	$0.985952\pi$
$464$	−0.816098	−	1.28596i	−0.0378864	−	0.0596994i
$465$	−24.6701	+	15.6824i	−1.14405	+	0.727256i
$466$	−3.81322	−	60.6094i	−0.176644	−	2.80768i
$467$	−2.70315	+	4.91701i	−0.125087	+	0.227532i	−0.931434	−	0.363911i	$-0.881441\pi$
$467$	−2.70315	+	4.91701i	−0.125087	+	0.227532i	0.806347	+	0.591443i	$0.201441\pi$
$468$	−19.1611	−	6.22582i	−0.885723	−	0.287789i
$469$	9.81669	−	1.24014i	0.453293	−	0.0572642i
$470$	16.5413	−	26.1087i	0.762992	−	1.20431i
$471$	−16.6410	−	15.6270i	−0.766778	−	0.720052i
$472$	12.6121	−	13.4305i	0.580518	−	0.618189i
$473$	−2.73068	−	10.6353i	−0.125557	−	0.489011i
$474$	−12.3976	+	9.00737i	−0.569440	+	0.413722i
$475$	10.7961	−	7.86889i	0.495357	−	0.361049i
$476$	0.0491805	+	0.0357317i	0.00225418	+	0.00163776i
$477$	9.79432	−	24.7376i	0.448451	−	1.13266i
$478$	1.13317	−	8.96994i	0.0518299	−	0.410276i
$479$	−11.8980	+	6.54097i	−0.543633	+	0.298865i	−0.729808	−	0.683652i	$-0.760391\pi$
$479$	−11.8980	+	6.54097i	−0.543633	+	0.298865i	0.186176	+	0.982516i	$0.440391\pi$
$480$	−111.329	+	14.1500i	−5.08143	+	0.645857i
$481$	3.10503	+	6.59852i	0.141577	+	0.300867i
$482$	3.21420	+	4.42396i	0.146403	+	0.201506i
$483$	−3.12164	−	24.7103i	−0.142040	−	1.12436i
$484$	4.98030	+	1.27872i	0.226377	+	0.0581238i
$485$	−1.98026	−	15.5802i	−0.0899191	−	0.707460i
$486$	−33.1334	+	40.0513i	−1.50296	+	1.81677i
$487$	2.20319	−	1.82264i	0.0998363	−	0.0825918i	−0.586167	−	0.810190i	$-0.699364\pi$
$487$	2.20319	−	1.82264i	0.0998363	−	0.0825918i	0.686003	+	0.727599i	$0.259364\pi$
$488$	76.0697	+	48.2753i	3.44351	+	2.18532i
$489$	−3.57969	+	56.8975i	−0.161879	+	2.57299i
$490$	−30.9453	−	14.5330i	−1.39797	−	0.656536i
$491$	−26.7348	−	32.3169i	−1.20653	−	1.45844i	−0.852119	−	0.523348i	$-0.824683\pi$
$491$	−26.7348	−	32.3169i	−1.20653	−	1.45844i	−0.354407	−	0.935091i	$-0.615317\pi$
$492$	−80.1378	−	15.2871i	−3.61289	−	0.689196i
$493$	−0.000662200	0	0.000911441i	−2.98240e−5	0	4.10492e-5i
$494$	5.48994	+	3.01812i	0.247004	+	0.135792i
$495$	1.92587	−	30.9865i	0.0865615	−	1.39274i
$496$	−64.0721	−	8.09419i	−2.87692	−	0.363440i
$497$	−10.2983	−	4.84602i	−0.461943	−	0.217374i
$498$	−111.687	−	7.02674i	−5.00480	−	0.314876i
$499$	−10.0775			−0.451131			−0.225566	−	0.974228i	$-0.572423\pi$
$499$	−10.0775			−0.451131			−0.225566	+	0.974228i	$0.572423\pi$
$500$	−47.9485	−	34.6700i	−2.14432	−	1.55049i
$501$	−51.4199			−2.29727
$502$	−3.15415	−	0.198442i	−0.140777	−	0.00885692i
$503$	−3.26604	−	1.53688i	−0.145626	−	0.0685262i	0.351586	−	0.936156i	$-0.385643\pi$
$503$	−3.26604	−	1.53688i	−0.145626	−	0.0685262i	−0.497211	+	0.867630i	$0.665643\pi$
$504$	44.7364	+	5.65152i	1.99272	+	0.251739i
$505$	−5.19017	+	1.33681i	−0.230959	+	0.0594873i
$506$	−59.3756	−	32.6420i	−2.63957	−	1.45111i
$507$	−19.5602	+	26.9223i	−0.868698	+	1.19566i
$508$	88.1536	+	16.8162i	3.91118	+	0.746098i
$509$	14.7011	+	17.7705i	0.651613	+	0.787665i	0.988065	−	0.154035i	$-0.0492270\pi$
$509$	14.7011	+	17.7705i	0.651613	+	0.787665i	−0.336452	+	0.941701i	$0.609227\pi$
$510$	0.0786017	+	0.142719i	0.00348054	+	0.00631970i
$511$	−0.207722	+	3.30165i	−0.00918908	+	0.146056i
$512$	−7.79529	−	4.94704i	−0.344506	−	0.218630i
$513$	−7.74480	+	6.40706i	−0.341941	+	0.282878i
$514$	6.65546	−	8.04507i	0.293560	−	0.354853i
$515$	23.0210	+	24.4776i	1.01443	+	1.07861i
$516$	48.2986	+	12.4010i	2.12623	+	0.545923i
$517$	2.03156	+	16.0815i	0.0893480	+	0.707263i
$518$	−15.4216	−	21.2260i	−0.677585	−	0.932616i
$519$	−0.0376263	−	0.0799599i	−0.00165161	−	0.00350985i
$520$	3.22161	−	16.9582i	0.141277	−	0.743668i
$521$	22.6847	−	12.4710i	0.993836	−	0.546366i	0.100108	−	0.994977i	$-0.468081\pi$
$521$	22.6847	−	12.4710i	0.993836	−	0.546366i	0.893727	+	0.448611i	$0.148081\pi$
$522$	−0.168362	+	1.33273i	−0.00736902	+	0.0583318i
$523$	−2.18560	+	5.52019i	−0.0955695	+	0.241381i	−0.969695	−	0.244320i	$-0.921435\pi$
$523$	−2.18560	+	5.52019i	−0.0955695	+	0.241381i	0.874125	+	0.485700i	$0.161435\pi$
$524$	77.0922	+	56.0107i	3.36779	+	2.44684i
$525$	10.0371	+	12.0953i	0.438056	+	0.527883i
$526$	−9.66349	+	7.02093i	−0.421348	+	0.306127i
$527$	0.0118801	+	0.0462697i	0.000517503	+	0.00201554i
$528$	79.0782	−	84.2097i	3.44144	−	3.66476i
$529$	−28.9966	−	27.2297i	−1.26072	−	1.18390i
$530$	35.4985	+	9.08573i	1.54196	+	0.394659i
$531$	−9.01406	+	1.13874i	−0.391177	+	0.0494171i
$532$	−15.5570	−	5.05478i	−0.674483	−	0.219153i
$533$	2.37292	−	4.31632i	0.102782	−	0.186960i
$534$	−0.606385	−	9.63821i	−0.0262408	−	0.417086i
$535$	−5.83794	−	0.362840i	−0.252396	−	0.0156869i
$536$	40.7478	+	64.2082i	1.76004	+	2.77337i
$537$	−1.79841	+	7.00433i	−0.0776070	+	0.302259i
$538$	12.7530	+	32.2105i	0.549822	+	1.38869i
$539$	17.3664	−	4.45893i	0.748023	−	0.192060i
$540$	37.6065	+	23.8258i	1.61833	+	1.02530i
$541$	0.589591	−	0.233436i	0.0253485	−	0.0100362i	−0.355416	−	0.934708i	$-0.615661\pi$
$541$	0.589591	−	0.233436i	0.0253485	−	0.0100362i	0.380765	+	0.924672i	$0.375661\pi$
$542$	−23.2511	+	10.9411i	−0.998718	+	0.469961i
$543$	−1.49450	+	0.485591i	−0.0641349	+	0.0208387i
$544$	−0.0343640	+	0.180142i	−0.00147334	+	0.00772354i
$545$	−28.7517	+	20.9227i	−1.23159	+	0.896231i
$546$	−3.13828	+	6.66919i	−0.134306	+	0.285415i
$547$	−8.57741	+	1.63623i	−0.366744	+	0.0699601i	−0.367459	−	0.930040i	$-0.619772\pi$
$547$	−8.57741	+	1.63623i	−0.366744	+	0.0699601i	0.000715488		1.00000i	$0.499772\pi$
$548$	51.2477	+	42.3958i	2.18919	+	1.81106i
$549$	−13.7296	−	42.2554i	−0.585965	−	1.80341i
$550$	42.6697	−	2.74964i	1.81944	−	0.117245i
$551$	0.0936782	−	0.288312i	0.00399082	−	0.0122825i
$552$	161.623	−	102.569i	6.87914	−	4.36564i
$553$	1.16378	+	2.11691i	0.0494891	+	0.0900203i
$554$	8.91942	+	46.7572i	0.378950	+	1.98652i
$555$	−9.60096	−	50.1231i	−0.407538	−	2.12761i
$556$	43.6904	−	41.0280i	1.85289	−	1.73998i
$557$		−	5.92873i		−	0.251208i	−0.992080	−	0.125604i	$-0.959913\pi$
$557$		−	5.92873i		−	0.251208i	0.992080	−	0.125604i	$-0.0400869\pi$
$558$	38.9917	+	41.5219i	1.65065	+	1.75776i
$559$	−1.61317	+	2.54195i	−0.0682299	+	0.107513i
$560$	0.0263793	+	34.7234i	0.00111473	+	1.46733i
$561$	−0.0794483	−	0.0314558i	−0.00335431	−	0.00132807i
$562$	32.9691	−	2.07424i	1.39072	−	0.0874965i
$563$	−7.80617	+	0.491123i	−0.328991	+	0.0206984i	−0.226427	−	0.974028i	$-0.572705\pi$
$563$	−7.80617	+	0.491123i	−0.328991	+	0.0206984i	−0.102564	+	0.994726i	$0.532705\pi$
$564$	−68.4429	−	27.0985i	−2.88197	−	1.14105i
$565$	−15.7503	+	5.13083i	−0.662622	+	0.215855i
$566$	18.0165	−	28.3894i	0.757289	−	1.19330i
$567$	2.32049	+	2.47107i	0.0974515	+	0.103775i
$568$		−	87.4736i		−	3.67031i
$569$	−2.88955	+	2.71347i	−0.121136	+	0.113754i	−0.742748	−	0.669571i	$-0.766478\pi$
$569$	−2.88955	+	2.71347i	−0.121136	+	0.113754i	0.621612	+	0.783325i	$0.286478\pi$
$570$	−31.9824	−	29.9878i	−1.33959	−	1.25605i
$571$	5.36849	+	28.1426i	0.224664	+	1.17773i	0.898542	+	0.438888i	$0.144627\pi$
$571$	5.36849	+	28.1426i	0.224664	+	1.17773i	−0.673878	+	0.738843i	$0.735373\pi$
$572$	7.01048	+	12.7520i	0.293123	+	0.533188i
$573$	45.4747	−	28.8591i	1.89973	−	1.20561i
$574$	−5.47607	+	16.8536i	−0.228567	+	0.703456i
$575$	38.9257	+	7.36419i	1.62331	+	0.307108i
$576$	31.1974	+	96.0158i	1.29989	+	4.00066i
$577$	−6.62948	−	5.48438i	−0.275989	−	0.228318i	0.489124	−	0.872214i	$-0.337317\pi$
$577$	−6.62948	−	5.48438i	−0.275989	−	0.228318i	−0.765112	+	0.643897i	$0.777317\pi$
$578$	−45.0939	+	8.60212i	−1.87566	+	0.357801i
$579$	−3.56625	+	7.57867i	−0.148208	+	0.314959i
$580$	−1.34267	+	0.00102002i	−0.0557512	+	4.23541e-5i
$581$	−3.30562	+	17.3287i	−0.137140	+	0.718915i
$582$	−49.0189	+	15.9272i	−2.03190	+	0.660204i
$583$	−17.3881	+	8.18224i	−0.720143	+	0.338874i
$584$	−23.6398	+	9.35965i	−0.978221	+	0.387305i
$585$	−6.55482	+	5.43101i	−0.271009	+	0.224545i
$586$	−58.7041	+	15.0726i	−2.42504	+	0.622645i
$587$	12.8696	+	32.5049i	0.531185	+	1.34162i	0.909408	+	0.415906i	$0.136535\pi$
$587$	12.8696	+	32.5049i	0.531185	+	1.34162i	−0.378222	+	0.925715i	$0.623465\pi$
$588$	−20.2496	+	78.8670i	−0.835080	+	3.25242i
$589$	−6.88763	−	10.8532i	−0.283800	−	0.447197i
$590$	−3.12111	−	12.1177i	−0.128494	−	0.498877i
$591$	−0.942672	−	14.9833i	−0.0387763	−	0.616332i
$592$	54.3157	−	98.7998i	2.23236	−	4.06065i
$593$	−15.2818	−	4.96535i	−0.627548	−	0.203903i	−0.0220592	−	0.999757i	$-0.507022\pi$
$593$	−15.2818	−	4.96535i	−0.627548	−	0.203903i	−0.605488	+	0.795854i	$0.707022\pi$
$594$	−31.9171	+	4.03207i	−1.30957	+	0.165438i
$595$	0.0238739	−	0.00947331i	0.000978732	−	0.000388368i
$596$	68.8444	+	64.6492i	2.81997	+	2.64813i
$597$	20.4687	−	21.7970i	0.837729	−	0.892091i
$598$	4.62013	+	17.9942i	0.188931	+	0.735838i
$599$	35.1529	−	25.5401i	1.43631	−	1.04354i	0.447510	−	0.894279i	$-0.352311\pi$
$599$	35.1529	−	25.5401i	1.43631	−	1.04354i	0.988798	−	0.149260i	$-0.0476890\pi$
$600$	−51.2672	+	109.379i	−2.09298	+	4.46540i
$601$	−26.3530	−	19.1466i	−1.07496	−	0.781006i	−0.0981643	−	0.995170i	$-0.531297\pi$
$601$	−26.3530	−	19.1466i	−1.07496	−	0.781006i	−0.976798	+	0.214165i	$0.931297\pi$
$602$	3.98731	−	10.0708i	0.162511	−	0.410455i
$603$	4.70025	−	37.2063i	0.191409	−	1.51516i
$604$	11.9199	−	6.55302i	0.485013	−	0.266638i
$605$	1.58255	−	1.48838i	0.0643397	−	0.0605111i
$606$	7.48890	+	15.9147i	0.304216	+	0.646492i
$607$	−1.59428	−	2.19434i	−0.0647100	−	0.0890657i	0.775435	−	0.631427i	$-0.217530\pi$
$607$	−1.59428	−	2.19434i	−0.0647100	−	0.0890657i	−0.840145	+	0.542361i	$0.817530\pi$
$608$	−6.18485	−	48.9581i	−0.250829	−	1.98551i
$609$	0.345453	+	0.0886973i	0.0139985	+	0.00359420i
$610$	55.3471	−	26.0958i	2.24094	−	1.05659i
$611$	2.83294	−	3.42443i	0.114608	−	0.138538i
$612$	0.177528	−	0.146864i	0.00717613	−	0.00593661i
$613$	6.66488	+	4.22966i	0.269192	+	0.170835i	0.663571	−	0.748114i	$-0.269040\pi$
$613$	6.66488	+	4.22966i	0.269192	+	0.170835i	−0.394379	+	0.918948i	$0.629040\pi$
$614$	0.670424	−	10.6561i	0.0270561	−	0.430045i
$615$	−23.5771	+	25.1453i	−0.950720	+	1.01396i
$616$	−20.7604	−	25.0950i	−0.836460	−	1.01111i
$617$	−15.4769	−	2.95238i	−0.623078	−	0.118859i	−0.133832	−	0.991004i	$-0.542728\pi$
$617$	−15.4769	−	2.95238i	−0.623078	−	0.118859i	−0.489247	+	0.872146i	$0.662728\pi$
$618$	64.8177	−	89.2139i	2.60735	−	3.58871i
$619$	22.7602	+	12.5125i	0.914809	+	0.502921i	0.868323	−	0.495998i	$-0.165198\pi$
$619$	22.7602	+	12.5125i	0.914809	+	0.502921i	0.0464857	+	0.998919i	$0.485198\pi$
$620$	−36.2566	+	43.8946i	−1.45610	+	1.76285i
$621$	−29.5717	−	3.73578i	−1.18667	−	0.149912i
$622$	−33.6714	−	15.8446i	−1.35010	−	0.635309i
$623$	−1.51937	−	0.0955908i	−0.0608724	−	0.00382976i
$624$	−31.6736			−1.26796
$625$	−23.2163	+	9.27371i	−0.928654	+	0.370948i
$626$	85.9838			3.43660
$627$	22.9474	+	1.44373i	0.916431	+	0.0576569i
$628$	−40.2277	−	18.9297i	−1.60526	−	0.755378i
$629$	−0.0827399	−	0.0104525i	−0.00329905	−	0.000416768i
$630$	19.5035	−	23.6122i	0.777037	−	0.940731i
$631$	−32.9343	−	18.1058i	−1.31109	−	0.720780i	−0.335851	−	0.941915i	$-0.609024\pi$
$631$	−32.9343	−	18.1058i	−1.31109	−	0.720780i	−0.975243	+	0.221135i	$0.929024\pi$
$632$	−10.9129	+	15.0204i	−0.434093	+	0.597478i
$633$	−12.0219	−	2.29330i	−0.477828	−	0.0911507i
$634$	−22.7257	−	27.4706i	−0.902553	−	1.09100i
$635$	25.9354	−	27.6605i	1.02921	−	1.09767i
$636$	5.47984	−	87.0995i	0.217290	−	3.45372i
$637$	−4.15076	−	2.63415i	−0.164459	−	0.104369i
$638$	0.747597	−	0.618466i	0.0295976	−	0.0244853i
$639$	−27.4967	+	33.2378i	−1.08775	+	1.31487i
$640$	−51.0554	+	24.0722i	−2.01814	+	0.951538i
$641$	16.3176	+	4.18965i	0.644507	+	0.165481i	0.556776	−	0.830663i	$-0.312038\pi$
$641$	16.3176	+	4.18965i	0.644507	+	0.165481i	0.0877314	+	0.996144i	$0.472038\pi$
$642$	2.40585	+	19.0442i	0.0949511	+	0.751616i
$643$	27.4326	+	37.7577i	1.08183	+	1.48902i	0.857485	+	0.514509i	$0.172026\pi$
$643$	27.4326	+	37.7577i	1.08183	+	1.48902i	0.224350	+	0.974509i	$0.427974\pi$
$644$	−20.6533	−	43.8905i	−0.813854	−	1.72953i
$645$	15.3475	−	14.4342i	0.604306	−	0.568345i
$646$	−0.0627826	+	0.0345150i	−0.00247015	+	0.00135797i
$647$	−1.78859	+	14.1581i	−0.0703167	+	0.556614i	0.917121	+	0.398608i	$0.130507\pi$
$647$	−1.78859	+	14.1581i	−0.0703167	+	0.556614i	−0.987438	+	0.158006i	$0.949493\pi$
$648$	−9.59065	+	24.2232i	−0.376756	+	0.951577i
$649$	5.30914	+	3.85732i	0.208402	+	0.151413i
$650$	−8.55837	−	8.01241i	−0.335687	−	0.314272i
$651$	12.2349	−	8.88915i	0.479522	−	0.348393i
$652$	27.6120	+	107.542i	1.08137	+	4.21165i
$653$	−23.2607	+	24.7702i	−0.910263	+	0.969332i	−0.999644	−	0.0266658i	$-0.991511\pi$
$653$	−23.2607	+	24.7702i	−0.910263	+	0.969332i	0.0893813	+	0.995997i	$0.471511\pi$
$654$	85.0667	+	79.8829i	3.32637	+	3.12367i
$655$	37.4231	−	14.8498i	1.46224	−	0.580228i
$656$	−75.5506	+	9.54426i	−2.94976	+	0.372641i
$657$	11.9247	+	3.87456i	0.465225	+	0.151161i
$658$	−7.70304	+	14.0118i	−0.300296	+	0.546236i
$659$	−2.73480	−	43.4685i	−0.106533	−	1.69329i	−0.581706	−	0.813399i	$-0.697615\pi$
$659$	−2.73480	−	43.4685i	−0.106533	−	1.69329i	0.475173	−	0.879892i	$-0.342385\pi$
$660$	−25.4007	−	98.6179i	−0.988719	−	3.83870i
$661$	7.50250	+	11.8221i	0.291814	+	0.459825i	0.958329	−	0.285667i	$-0.0922150\pi$
$661$	7.50250	+	11.8221i	0.291814	+	0.459825i	−0.666516	+	0.745491i	$0.732215\pi$
$662$	16.0217	−	62.4005i	0.622702	−	2.42526i
$663$	0.00862472	+	0.0217836i	0.000334956	+	0.000846003i
$664$	−131.323	+	33.7180i	−5.09632	+	1.30851i
$665$	−5.32190	+	4.40947i	−0.206375	+	0.170992i
$666$	−92.4570	+	36.6063i	−3.58264	+	1.41847i
$667$	0.813404	−	0.382759i	0.0314951	−	0.0148205i
$668$	−95.2413	+	30.9458i	−3.68500	+	1.19733i
$669$	−9.70969	+	50.9000i	−0.375398	+	1.96791i
$670$	51.6492	−	0.0392379i	1.99538	−	0.00151589i
$671$	−13.6637	+	29.0368i	−0.527481	+	1.12095i
$672$	57.0292	−	10.8789i	2.19995	−	0.419663i
$673$	−23.5355	−	19.4703i	−0.907229	−	0.750525i	0.0616404	−	0.998098i	$-0.480367\pi$
$673$	−23.5355	−	19.4703i	−0.907229	−	0.750525i	−0.968869	+	0.247574i	$0.920367\pi$
$674$	−13.5557	−	41.7201i	−0.522146	−	1.60700i
$675$	17.0074	−	8.03464i	0.654613	−	0.309253i
$676$	−20.0274	+	61.6381i	−0.770285	+	2.37069i
$677$	−34.5675	+	21.9372i	−1.32854	+	0.843115i	−0.995024	−	0.0996308i	$-0.968234\pi$
$677$	−34.5675	+	21.9372i	−1.32854	+	0.843115i	−0.333512	+	0.942746i	$0.608234\pi$
$678$	26.1891	+	47.6378i	1.00579	+	1.82952i
$679$	1.52248	+	7.98112i	0.0584274	+	0.306287i
$680$	0.144002	+	0.135021i	0.00552224	+	0.00517784i
$681$	34.9938	−	32.8614i	1.34097	−	1.25925i
$682$		−	41.1412i		−	1.57538i
$683$	−31.7139	−	33.7719i	−1.21350	−	1.29225i	−0.944271	−	0.329170i	$-0.893231\pi$
$683$	−31.7139	−	33.7719i	−1.21350	−	1.29225i	−0.269229	−	0.963076i	$-0.586769\pi$
$684$	−33.2197	+	52.3459i	−1.27019	+	2.00149i
$685$	26.7198	−	8.70424i	1.02091	−	0.332572i
$686$	36.7760	+	14.5606i	1.40411	+	0.555928i
$687$	29.6182	−	1.86342i	1.13001	−	0.0710939i
$688$	46.4534	−	2.92260i	1.77102	−	0.111423i
$689$	4.89903	+	1.93967i	0.186638	+	0.0738954i
$690$	−0.0987685	−	130.010i	−0.00376005	−	4.94940i
$691$	−11.9039	+	18.7575i	−0.452844	+	0.713568i	−0.991664	−	0.128853i	$-0.958870\pi$
$691$	−11.9039	+	18.7575i	−0.452844	+	0.713568i	0.538820	+	0.842421i	$0.318870\pi$
$692$	−0.117814	−	0.125460i	−0.00447863	−	0.00476926i
$693$			16.0613i			0.610120i
$694$	−17.7966	+	16.7121i	−0.675549	+	0.634383i
$695$	−4.76397	−	24.8709i	−0.180708	−	0.943408i
$696$	0.513635	+	2.69257i	0.0194693	+	0.102062i
$697$	0.0271365	+	0.0493611i	0.00102787	+	0.00186969i
$698$	75.6114	−	47.9845i	2.86193	−	1.81624i
$699$	−18.8845	+	58.1204i	−0.714276	+	2.19831i
$700$	25.8703	+	16.3627i	0.977806	+	0.618453i
$701$	15.7014	+	48.3241i	0.593035	+	1.82518i	0.564272	+	0.825589i	$0.309157\pi$
$701$	15.7014	+	48.3241i	0.593035	+	1.82518i	0.0287634	+	0.999586i	$0.490843\pi$
$702$	6.79651	+	5.62256i	0.256518	+	0.212210i
$703$	22.0433	−	4.20499i	0.831379	−	0.158594i
$704$	31.0477	−	65.9797i	1.17015	−	2.48670i
$705$	−25.1482	+	18.3005i	−0.947137	+	0.689235i
$706$	−14.5424	+	76.2342i	−0.547312	+	2.86911i
$707$	2.63698	−	0.856808i	0.0991740	−	0.0322236i
$708$	−26.9661	+	12.6893i	−1.01345	+	0.476893i
$709$	−11.0840	+	4.38846i	−0.416267	+	0.164812i	−0.566916	−	0.823775i	$-0.691864\pi$
$709$	−11.0840	+	4.38846i	−0.416267	+	0.164812i	0.150649	+	0.988587i	$0.451864\pi$
$710$	−50.1859	−	31.7955i	−1.88344	−	1.19326i
$711$	8.86819	−	2.27696i	0.332583	−	0.0853928i
$712$	−4.30718	−	10.8787i	−0.161418	−	0.407696i
$713$	9.47956	−	36.9204i	0.355012	−	1.38268i
$714$	−0.0451652	−	0.0711689i	−0.00169026	−	0.00266343i
$715$	6.13656	+	0.381400i	0.229494	+	0.0142635i
$716$	0.884326	+	14.0560i	0.0330488	+	0.525296i
$717$	−4.38306	+	7.97275i	−0.163688	+	0.297748i
$718$	31.4930	+	10.2327i	1.17531	+	0.381881i
$719$	11.0179	−	1.39188i	0.410898	−	0.0519085i	0.0828325	−	0.996563i	$-0.473603\pi$
$719$	11.0179	−	1.39188i	0.410898	−	0.0519085i	0.328065	+	0.944655i	$0.393603\pi$
$720$	127.495	+	32.6320i	4.75147	+	1.21612i
$721$	−12.6722	−	11.9000i	−0.471937	−	0.443178i
$722$	−21.9259	+	23.3488i	−0.815999	+	0.868951i
$723$	−1.36847	−	5.32985i	−0.0508941	−	0.198219i
$724$	−2.47591	+	1.79885i	−0.0920163	+	0.0668538i
$725$	−0.303243	+	0.479444i	−0.0112622	+	0.0178061i
$726$	−5.76794	−	4.19065i	−0.214068	−	0.155530i
$727$	2.79072	−	7.04856i	0.103502	−	0.261417i	−0.868792	−	0.495177i	$-0.835103\pi$
$727$	2.79072	−	7.04856i	0.103502	−	0.261417i	0.972294	+	0.233760i	$0.0751032\pi$
$728$	−1.11923	+	8.85958i	−0.0414813	+	0.328358i
$729$	38.1335	−	20.9641i	1.41235	−	0.776447i
$730$	−3.22286	+	16.9649i	−0.119284	+	0.627898i
$731$	−0.0146593	−	0.0311526i	−0.000542193	−	0.00115222i
$732$	−85.6620	−	117.904i	−3.16616	−	4.35784i
$733$	3.32192	+	26.2957i	0.122698	+	0.971254i	0.926484	+	0.376335i	$0.122816\pi$
$733$	3.32192	+	26.2957i	0.122698	+	0.971254i	−0.803786	+	0.594919i	$0.797184\pi$
$734$	−37.0185	−	9.50473i	−1.36638	−	0.350826i
$735$	23.5696	+	25.0609i	0.869378	+	0.924386i
$736$	93.2772	−	112.753i	3.43824	−	4.15612i
$737$	−20.8710	+	17.2660i	−0.768793	+	0.636000i
$738$	56.7085	+	35.9883i	2.08747	+	1.32475i
$739$	1.77401	−	28.1971i	0.0652581	−	1.03725i	−0.820065	−	0.572271i	$-0.806063\pi$
$739$	1.77401	−	28.1971i	0.0652581	−	1.03725i	0.885323	−	0.464977i	$-0.153937\pi$
$740$	−47.9485	−	87.0613i	−1.76262	−	3.20044i
$741$	−4.01850	−	4.85753i	−0.147623	−	0.178446i
$742$	−18.6208	−	3.55212i	−0.683593	−	0.130402i
$743$	9.11754	−	12.5492i	0.334490	−	0.460386i	−0.608332	−	0.793683i	$-0.708161\pi$
$743$	9.11754	−	12.5492i	0.334490	−	0.460386i	0.942822	+	0.333297i	$0.108161\pi$
$744$	101.853	+	55.9942i	3.73412	+	2.05285i
$745$	38.6413	−	9.95269i	1.41571	−	0.364638i
$746$	−92.0741	−	11.6317i	−3.37107	−	0.425866i
$747$	60.4984	+	28.4684i	2.21352	+	1.04160i
$748$	−0.166087	−	0.0104493i	−0.00607276	−	0.000382065i
$749$	3.02600			0.110568
$750$	44.1189	+	69.1713i	1.61099	+	2.52578i
$751$	−33.3764			−1.21792			−0.608962	−	0.793200i	$-0.708414\pi$
$751$	−33.3764			−1.21792			−0.608962	+	0.793200i	$0.708414\pi$
$752$	−68.5756	−	4.31441i	−2.50069	−	0.157330i
$753$	2.87760	+	1.35410i	0.104866	+	0.0493460i
$754$	−0.263933	−	0.0333425i	−0.00961187	−	0.00121426i
$755$	0.356512	−	5.73613i	0.0129748	−	0.208759i
$756$	−20.1823	−	11.0953i	−0.734024	−	0.403533i
$757$	18.1000	−	24.9125i	0.657857	−	0.905462i	−0.341552	−	0.939863i	$-0.610952\pi$
$757$	18.1000	−	24.9125i	0.657857	−	0.905462i	0.999408	+	0.0344012i	$0.0109524\pi$
$758$	66.4950	+	12.6846i	2.41521	+	0.460725i
$759$	43.4615	+	52.5359i	1.57755	+	1.90693i
$760$	−48.0792	−	22.5797i	−1.74401	−	0.819053i
$761$	1.18878	−	18.8952i	0.0430934	−	0.684950i	−0.915880	−	0.401453i	$-0.868505\pi$
$761$	1.18878	−	18.8952i	0.0430934	−	0.684950i	0.958973	−	0.283497i	$-0.0914946\pi$
$762$	−105.065	−	66.6761i	−3.80609	−	2.41542i
$763$	14.1742	−	11.7259i	0.513140	−	0.424506i
$764$	66.8614	−	80.8215i	2.41896	−	2.92402i
$765$	−0.0122743	−	0.0965708i	−0.000443777	−	0.00349152i
$766$	63.1281	+	16.2085i	2.28091	+	0.585639i
$767$	−0.225516	−	1.78514i	−0.00814291	−	0.0644578i
$768$	35.3229	+	48.6178i	1.27461	+	1.75435i
$769$	−5.81976	−	12.3676i	−0.209866	−	0.445988i	0.771985	−	0.635640i	$-0.219264\pi$
$769$	−5.81976	−	12.3676i	−0.209866	−	0.445988i	−0.981851	+	0.189653i	$0.939264\pi$
$770$	−21.9438	+	2.78908i	−0.790799	+	0.100512i
$771$	−9.20726	+	5.06173i	−0.331591	+	0.182294i
$772$	−2.04447	+	16.1837i	−0.0735823	+	0.582464i
$773$	−11.4928	+	29.0275i	−0.413368	+	1.04405i	0.562715	+	0.826651i	$0.309757\pi$
$773$	−11.4928	+	29.0275i	−0.413368	+	1.04405i	−0.976083	+	0.217397i	$0.930243\pi$
$774$	−33.2119	−	24.1299i	−1.19378	−	0.867330i
$775$	7.46802	+	22.8659i	0.268259	+	0.821369i
$776$	−50.5195	+	36.7046i	−1.81354	+	1.31762i
$777$	6.56588	+	25.5724i	0.235549	+	0.917405i
$778$	−37.6608	+	40.1046i	−1.35020	+	1.43782i
$779$	−11.0490	−	10.3757i	−0.395872	−	0.371748i
$780$	−14.9435	+	23.5868i	−0.535063	+	0.844542i
$781$	30.9116	−	3.90505i	1.10611	−	0.139734i
$782$	−0.202057	−	0.0656523i	−0.00722554	−	0.00234772i
$783$	0.205625	−	0.374030i	0.00734843	−	0.0133668i
$784$	4.77232	+	75.8539i	0.170440	+	2.70907i
$785$	−15.8526	+	10.0773i	−0.565804	+	0.359673i
$786$	−70.7981	−	111.560i	−2.52528	−	3.97921i
$787$	−6.46426	+	25.1766i	−0.230426	+	0.897450i	0.743157	+	0.669117i	$0.233328\pi$
$787$	−6.46426	+	25.1766i	−0.230426	+	0.897450i	−0.973583	+	0.228333i	$0.926672\pi$
$788$	−10.7634	−	27.1853i	−0.383430	−	0.968435i
$789$	11.6423	−	2.98923i	0.414476	−	0.106419i
$790$	4.65087	+	11.7207i	0.165471	+	0.417005i
$791$	7.96786	−	3.15470i	0.283304	−	0.112168i
$792$	−111.692	+	52.5585i	−3.96882	+	1.86758i
$793$	8.36825	−	2.71901i	0.297165	−	0.0965548i
$794$	−15.3781	+	80.6146i	−0.545747	+	2.86091i
$795$	−29.8477	−	21.6510i	−1.05859	−	0.767881i
$796$	24.7948	−	52.6916i	0.878828	−	1.86760i
$797$	26.7317	−	5.09934i	0.946885	−	0.180628i	0.309262	−	0.950977i	$-0.399918\pi$
$797$	26.7317	−	5.09934i	0.946885	−	0.180628i	0.637623	+	0.770349i	$0.279918\pi$
$798$	17.4761	+	14.4575i	0.618647	+	0.511790i
$799$	0.0157059	+	0.0483377i	0.000555634	+	0.00171007i
$800$	−11.4347	+	91.6346i	−0.404278	+	3.23977i
$801$	−1.78302	+	5.48756i	−0.0629998	+	0.193893i
$802$	−16.1701	+	10.2619i	−0.570986	+	0.362359i
$803$	−4.36288	−	7.93604i	−0.153963	−	0.280057i
$804$	−23.0502	−	120.833i	−0.812918	−	4.26147i
$805$	−20.3352	−	2.55324i	−0.716721	−	0.0899898i
$806$	−8.22299	+	7.72190i	−0.289643	+	0.271992i
$807$		−	34.8613i		−	1.22717i
$808$	14.5875	+	15.5341i	0.513186	+	0.546488i
$809$	10.7222	−	16.8955i	0.376974	−	0.594016i	−0.601878	−	0.798588i	$-0.705581\pi$
$809$	10.7222	−	16.8955i	0.376974	−	0.594016i	0.978851	+	0.204573i	$0.0655805\pi$
$810$	10.4114	+	14.3072i	0.365820	+	0.502704i
$811$	−9.20615	−	3.64497i	−0.323272	−	0.127992i	0.200883	−	0.979615i	$-0.435619\pi$
$811$	−9.20615	−	3.64497i	−0.323272	−	0.127992i	−0.524155	+	0.851623i	$0.675619\pi$
$812$	0.693239	−	0.0436149i	0.0243279	−	0.00153058i
$813$	25.8074	−	1.62366i	0.905104	−	0.0569443i
$814$	66.7803	+	26.4402i	2.34065	+	0.926728i
$815$	44.6264	+	14.4625i	1.56320	+	0.506601i
$816$	0.194086	−	0.305830i	0.00679436	−	0.0107062i
$817$	6.34186	+	6.75340i	0.221874	+	0.236271i
$818$			25.6911i			0.898267i
$819$	3.21022	−	3.01460i	0.112174	−	0.105339i
$820$	−28.5371	+	60.7642i	−0.996558	+	2.12198i
$821$	−5.31776	−	27.8767i	−0.185591	−	0.972902i	−0.946173	−	0.323660i	$-0.895086\pi$
$821$	−5.31776	−	27.8767i	−0.185591	−	0.972902i	0.760582	−	0.649242i	$-0.224914\pi$
$822$	−44.4287	−	80.8156i	−1.54963	−	2.81877i
$823$	−11.1681	+	7.08752i	−0.389297	+	0.247055i	−0.716042	−	0.698057i	$-0.754048\pi$
$823$	−11.1681	+	7.08752i	−0.389297	+	0.247055i	0.326745	+	0.945113i	$0.394048\pi$
$824$	41.2858	−	127.065i	1.43826	−	4.42651i
$825$	−40.9415	−	13.2340i	−1.42540	−	0.460747i
$826$	2.00043	+	6.15668i	0.0696037	+	0.214218i
$827$	7.32816	+	6.06238i	0.254825	+	0.210810i	0.756061	−	0.654501i	$-0.227121\pi$
$827$	7.32816	+	6.06238i	0.254825	+	0.210810i	−0.501236	+	0.865311i	$0.667121\pi$
$828$	−180.590	+	34.4494i	−6.27595	+	1.19720i
$829$	18.3760	−	39.0509i	0.638224	−	1.35629i	−0.279911	−	0.960026i	$-0.590305\pi$
$829$	18.3760	−	39.0509i	0.638224	−	1.35629i	0.918135	−	0.396268i	$-0.129695\pi$
$830$	−28.3892	+	87.5994i	−0.985404	+	3.04062i
$831$	8.97555	−	47.0515i	0.311358	−	1.63220i
$832$	−19.0149	+	6.17833i	−0.659225	+	0.214195i
$833$	0.0508691	−	0.0239372i	0.00176251	−	0.000829375i
$834$	−77.2680	+	30.5926i	−2.67557	+	1.05933i
$835$	−10.4913	+	40.9902i	−0.363067	+	1.41853i
$836$	43.3727	−	11.1362i	1.50008	−	0.385154i
$837$	−6.66246	−	16.8275i	−0.230288	−	0.581642i
$838$	0.0808646	−	0.314947i	0.00279342	−	0.0108797i
$839$	2.17548	+	3.42801i	0.0751059	+	0.118348i	0.879805	−	0.475335i	$-0.157673\pi$
$839$	2.17548	+	3.42801i	0.0751059	+	0.118348i	−0.804699	+	0.593683i	$0.797673\pi$
$840$	22.9611	−	58.1221i	0.792234	−	2.00540i
$841$	−1.82012	−	28.9299i	−0.0627626	−	0.997584i
$842$	−10.5814	+	19.2476i	−0.364660	+	0.663315i
$843$	−31.6152	−	10.2724i	−1.08888	−	0.353800i
$844$	−23.6475	+	2.98738i	−0.813981	+	0.102830i
$845$	17.4707	+	21.0858i	0.601009	+	0.725372i
$846$	44.1771	+	41.4851i	1.51884	+	1.42629i
$847$	−0.769367	+	0.819293i	−0.0264358	+	0.0281512i
$848$	−20.2586	−	78.9020i	−0.695683	−	2.70950i
$849$	−27.3733	+	19.8879i	−0.939450	+	0.682550i
$850$	0.129808	−	0.0335394i	0.00445238	−	0.00115039i
$851$	53.8370	+	39.1148i	1.84551	+	1.34084i
$852$	−52.0884	+	131.560i	−1.78452	+	4.50718i
$853$	−0.882260	+	6.98381i	−0.0302080	+	0.239121i	−0.999988	−	0.00485930i	$-0.998453\pi$
$853$	−0.882260	+	6.98381i	−0.0302080	+	0.239121i	0.969780	+	0.243980i	$0.0784532\pi$
$854$	−27.7404	+	15.2504i	−0.949258	+	0.521859i
$855$	11.1711	+	23.6931i	0.382044	+	0.810286i
$856$	9.90216	+	21.0432i	0.338449	+	0.719240i
$857$	22.9665	+	31.6107i	0.784522	+	1.07980i	0.994769	+	0.102153i	$0.0325732\pi$
$857$	22.9665	+	31.6107i	0.784522	+	1.07980i	−0.210247	+	0.977648i	$0.567427\pi$
$858$	−2.52891	−	20.0184i	−0.0863355	−	0.683416i
$859$	−48.5003	−	12.4528i	−1.65481	−	0.424883i	−0.698118	−	0.715983i	$-0.745979\pi$
$859$	−48.5003	−	12.4528i	−1.65481	−	0.424883i	−0.956693	+	0.291100i	$0.905979\pi$
$860$	19.7401	−	35.9719i	0.673133	−	1.22663i
$861$	11.3668	−	13.7401i	0.387380	−	0.468262i
$862$	80.4253	−	66.5336i	2.73930	−	2.26614i
$863$	−28.2295	−	17.9150i	−0.960943	−	0.609833i	−0.0398624	−	0.999205i	$-0.512692\pi$
$863$	−28.2295	−	17.9150i	−0.960943	−	0.609833i	−0.921080	+	0.389372i	$0.872692\pi$
$864$	4.36266	−	69.3425i	0.148421	−	2.35908i
$865$	−0.0714184	+	0.0136800i	−0.00242830	+	0.000465135i
$866$	36.7963	+	44.4791i	1.25039	+	1.51146i
$867$	45.3776	+	8.65625i	1.54111	+	0.293982i
$868$	17.3121	−	23.8280i	0.587610	−	0.808775i
$869$	−5.79512	−	3.18589i	−0.196586	−	0.108074i
$870$	1.73150	+	0.684027i	0.0587033	+	0.0231907i
$871$	7.36833	+	0.930836i	0.249666	+	0.0315402i
$872$	127.926	+	60.1976i	4.33213	+	2.03855i
$873$	30.7339	+	1.93362i	1.04019	+	0.0654430i
$874$	57.1680			1.93374
$875$	11.6899	−	5.53342i	0.395191	−	0.187064i
$876$	41.1276			1.38957
$877$	41.6261	+	2.61889i	1.40561	+	0.0884338i	0.747389	−	0.664387i	$-0.231307\pi$
$877$	41.6261	+	2.61889i	1.40561	+	0.0884338i	0.658226	+	0.752821i	$0.271307\pi$
$878$	13.6139	+	6.40622i	0.459447	+	0.216199i
$879$	60.5087	+	7.64402i	2.04091	+	0.257826i
$880$	−50.9947	−	80.2200i	−1.71903	−	2.70422i
$881$	15.4225	+	8.47860i	0.519598	+	0.285651i	0.719894	−	0.694084i	$-0.244190\pi$
$881$	15.4225	+	8.47860i	0.519598	+	0.285651i	−0.200296	+	0.979735i	$0.564190\pi$
$882$	39.4018	−	54.2319i	1.32673	−	1.82608i
$883$	−11.5895	−	2.21081i	−0.390017	−	0.0743997i	−0.0113568	−	0.999936i	$-0.503615\pi$
$883$	−11.5895	−	2.21081i	−0.390017	−	0.0743997i	−0.378660	+	0.925536i	$0.623615\pi$
$884$	0.0290849	+	0.0351576i	0.000978230	+	0.00118248i
$885$	−1.56870	+	12.4938i	−0.0527311	+	0.419976i
$886$	−1.19237	+	18.9522i	−0.0400584	+	0.636710i
$887$	2.29899	+	1.45899i	0.0771926	+	0.0489879i	0.573863	−	0.818951i	$-0.305444\pi$
$887$	2.29899	+	1.45899i	0.0771926	+	0.0489879i	−0.496670	+	0.867939i	$0.665444\pi$
$888$	−156.347	+	129.342i	−5.24668	+	4.34043i
$889$	−12.5038	+	15.1145i	−0.419364	+	0.506923i
$890$	−7.80699	−	1.48312i	−0.261691	−	0.0497142i
$891$	−8.98821	−	2.30778i	−0.301116	−	0.0773135i
$892$	12.6483	+	100.122i	0.423498	+	3.35233i
$893$	−8.03867	−	11.0643i	−0.269004	−	0.370252i
$894$	−55.7556	−	118.487i	−1.86475	−	3.96279i
$895$	5.21669	+	2.86274i	0.174375	+	0.0956909i
$896$	25.5894	−	14.0679i	0.854880	−	0.469975i
$897$	2.34308	−	18.5474i	0.0782330	−	0.619278i
$898$	0.526381	−	1.32949i	0.0175656	−	0.0443656i
$899$	0.441594	+	0.320837i	0.0147280	+	0.0107005i
$900$	84.4524	−	79.5479i	2.81508	−	2.65160i
$901$	−0.0487485	+	0.0354179i	−0.00162405	+	0.00117994i
$902$	−12.0643	−	46.9875i	−0.401699	−	1.56451i
$903$	−7.46128	+	7.94545i	−0.248296	+	0.264408i
$904$	48.0118	+	45.0861i	1.59685	+	1.49954i
$905$	0.0821718	+	1.29044i	0.00273148	+	0.0428957i
$906$	−18.7121	+	2.36389i	−0.621668	+	0.0785349i
$907$	24.0243	+	7.80597i	0.797714	+	0.259193i	0.679386	−	0.733781i	$-0.262246\pi$
$907$	24.0243	+	7.80597i	0.797714	+	0.259193i	0.118329	+	0.992974i	$0.462246\pi$
$908$	45.0397	−	81.9269i	1.49470	−	2.71884i
$909$	−0.659852	−	10.4880i	−0.0218859	−	0.347866i
$910$	4.67615	+	3.86247i	0.155013	+	0.128040i
$911$	−6.26764	−	9.87623i	−0.207656	−	0.327214i	0.724497	−	0.689278i	$-0.242072\pi$
$911$	−6.26764	−	9.87623i	−0.207656	−	0.327214i	−0.932153	+	0.362064i	$0.882072\pi$
$912$	−24.2389	+	94.4042i	−0.802630	+	3.12604i
$913$	−17.7779	−	44.9019i	−0.588364	−	1.48604i
$914$	−45.4878	+	11.6793i	−1.50460	+	0.386316i
$915$	−61.4512	+	3.91306i	−2.03152	+	0.129362i
$916$	53.7383	−	21.2765i	1.77556	−	0.702995i
$917$	−18.8465	+	8.86848i	−0.622365	+	0.292863i
$918$	−0.0959365	+	0.0311717i	−0.00316638	+	0.00102882i
$919$	−2.03890	+	10.6883i	−0.0672570	+	0.352573i	−0.999968	−	0.00805238i	$-0.997437\pi$
$919$	−2.03890	+	10.6883i	−0.0672570	+	0.352573i	0.932711	+	0.360626i	$0.117437\pi$
$920$	−48.7885	−	149.768i	−1.60851	−	4.93771i
$921$	−4.57472	+	9.72178i	−0.150742	+	0.320343i
$922$	−50.2356	+	9.58295i	−1.65442	+	0.315598i
$923$	−6.58240	−	5.44544i	−0.216662	−	0.179239i
$924$	16.2801	+	50.1051i	0.535578	+	1.64834i
$925$	−41.9154	−	2.57316i	−1.37817	−	0.0846050i
$926$	10.4568	−	32.1826i	0.343631	−	1.05759i
$927$	−55.6294	+	35.3035i	−1.82711	+	1.15952i
$928$	1.00950	+	1.83628i	0.0331386	+	0.0602789i
$929$	−3.87093	−	20.2921i	−0.127001	−	0.665764i	−0.987664	−	0.156588i	$-0.949950\pi$
$929$	−3.87093	−	20.2921i	−0.127001	−	0.665764i	0.860663	−	0.509175i	$-0.170050\pi$
$930$	69.1476	−	38.0826i	2.26744	−	1.24878i
$931$	−11.0276	+	10.3556i	−0.361416	+	0.339393i
$932$			119.017i			3.89854i
$933$	25.6344	+	27.2979i	0.839233	+	0.893692i
$934$	8.11899	−	12.7935i	0.265661	−	0.418615i
$935$	−0.0412856	+	0.0569156i	−0.00135018	+	0.00186134i
$936$	31.4689	+	12.4594i	1.02859	+	0.407248i
$937$	−41.3334	+	2.60048i	−1.35030	+	0.0849539i	−0.721394	−	0.692525i	$-0.756498\pi$
$937$	−41.3334	+	2.60048i	−1.35030	+	0.0849539i	−0.628909	+	0.777479i	$0.716498\pi$
$938$	−26.6672	+	1.67776i	−0.870716	+	0.0547808i
$939$	−80.4488	−	31.8519i	−2.62535	−	1.03945i
$940$	−35.5666	+	49.0315i	−1.16005	+	1.59923i
$941$	−27.7681	+	43.7555i	−0.905214	+	1.42639i	−0.000674659		1.00000i	$0.500215\pi$
$941$	−27.7681	+	43.7555i	−0.905214	+	1.42639i	−0.904540	+	0.426390i	$0.859785\pi$
$942$	42.1995	+	44.9379i	1.37493	+	1.46415i
$943$		−	44.9468i		−	1.46367i
$944$	−20.2786	+	19.0429i	−0.660013	+	0.619794i
$945$	−8.52372	+	4.69439i	−0.277277	+	0.152709i
$946$	5.55611	+	29.1262i	0.180645	+	0.946973i
$947$	−23.0061	−	41.8480i	−0.747598	−	1.35988i	−0.926608	−	0.376029i	$-0.877289\pi$
$947$	−23.0061	−	41.8480i	−0.747598	−	1.35988i	0.179010	−	0.983847i	$-0.442711\pi$
$948$	25.3573	−	16.0922i	0.823567	−	0.522652i
$949$	−0.767316	+	2.36156i	−0.0249081	+	0.0766594i
$950$	−30.4307	+	19.3768i	−0.987303	+	0.628668i
$951$	11.0865	+	34.1208i	0.359505	+	1.10644i
$952$	−0.0786870	−	0.0650956i	−0.00255026	−	0.00210976i
$953$	21.9964	−	4.19604i	0.712534	−	0.135923i	0.181645	−	0.983364i	$-0.441858\pi$
$953$	21.9964	−	4.19604i	0.712534	−	0.135923i	0.530889	+	0.847441i	$0.321858\pi$
$954$	−30.5912	+	65.0096i	−0.990427	+	2.10476i
$955$	−13.7272	−	42.1391i	−0.444203	−	1.36359i
$956$	−3.32022	+	17.4052i	−0.107384	+	0.562924i
$957$	−0.928577	+	0.301713i	−0.0300166	+	0.00975300i
$958$	33.1753	−	15.6111i	1.07185	−	0.504373i
$959$	−13.5171	+	5.35182i	−0.436491	+	0.172819i
$960$	139.634	−	8.89154i	4.50667	−	0.286973i
$961$	−7.60832	+	1.95348i	−0.245430	+	0.0630156i
$962$	−7.24951	−	18.3102i	−0.233734	−	0.590343i
$963$	2.85219	−	11.1085i	0.0919105	−	0.357968i
$964$	−5.74237	−	9.04853i	−0.184949	−	0.291433i
$965$	5.31383	+	4.38919i	0.171058	+	0.141293i
$966$	4.22322	+	67.1261i	0.135880	+	2.15975i
$967$	19.5675	−	35.5931i	0.629247	−	1.14460i	−0.348994	−	0.937125i	$-0.613477\pi$
$967$	19.5675	−	35.5931i	0.629247	−	1.14460i	0.978241	−	0.207471i	$-0.0665233\pi$
$968$	−8.21510	−	2.66925i	−0.264043	−	0.0857929i
$969$	0.0715269	−	0.00903595i	0.00229777	−	0.000290276i
$970$	2.69521	+	42.3260i	0.0865379	+	1.35900i
$971$	−13.9333	−	13.0842i	−0.447140	−	0.419892i	0.427988	−	0.903785i	$-0.359223\pi$
$971$	−13.9333	−	13.0842i	−0.447140	−	0.419892i	−0.875128	+	0.483892i	$0.839223\pi$
$972$	69.7354	−	74.2606i	2.23676	−	2.38191i
$973$	3.25797	+	12.6890i	0.104446	+	0.406789i
$974$	−6.24688	+	4.53862i	−0.200163	+	0.145427i
$975$	5.03932	+	10.6670i	0.161387	+	0.341617i
$976$	−110.054	−	79.9587i	−3.52273	−	2.55942i
$977$	9.57611	−	24.1865i	0.306367	−	0.773794i	−0.692272	−	0.721637i	$-0.743390\pi$
$977$	9.57611	−	24.1865i	0.306367	−	0.773794i	0.998639	−	0.0521576i	$-0.0166098\pi$
$978$	19.2952	−	152.737i	0.616993	−	4.88400i
$979$	3.65206	−	2.00773i	0.116720	−	0.0641675i
$980$	58.7386	+	32.2337i	1.87634	+	1.02967i
$981$	−29.6861	−	63.0863i	−0.947805	−	2.01419i
$982$	66.5733	+	91.6303i	2.12444	+	2.92404i
$983$	−0.952877	−	7.54279i	−0.0303920	−	0.240578i	0.969599	−	0.244698i	$-0.0786887\pi$
$983$	−0.952877	−	7.54279i	−0.0303920	−	0.240578i	−0.999992	+	0.00411970i	$0.998689\pi$
$984$	132.747	+	34.0836i	4.23181	+	1.08654i
$985$	−12.1366	−	2.30562i	−0.386703	−	0.0734631i
$986$	0.00193924	−	0.00234414i	6.17580e−5	−	7.46526e-5i
$987$	12.3977	−	10.2563i	0.394624	−	0.326461i
$988$	−10.3666	−	6.57882i	−0.329804	−	0.209300i
$989$	−1.72501	+	27.4183i	−0.0548522	+	0.871851i
$990$	−10.4445	+	83.1851i	−0.331949	+	2.64380i
$991$	3.15938	+	3.81903i	0.100361	+	0.121316i	0.818302	−	0.574788i	$-0.194915\pi$
$991$	3.15938	+	3.81903i	0.100361	+	0.121316i	−0.717941	+	0.696103i	$0.754915\pi$
$992$	87.2792	+	16.6494i	2.77112	+	0.528619i
$993$	−38.1061	+	52.4485i	−1.20926	+	1.66440i
$994$	26.9333	+	14.8067i	0.854272	+	0.469640i
$995$	−13.1996	−	20.7643i	−0.418454	−	0.658272i
$996$	217.588	+	27.4877i	6.89453	+	0.870982i
$997$	−31.9963	−	15.0563i	−1.01333	−	0.476839i	−0.153901	−	0.988086i	$-0.549184\pi$
$997$	−31.9963	−	15.0563i	−1.01333	−	0.476839i	−0.859434	+	0.511247i	$0.829184\pi$
$998$	27.1599	+	1.70875i	0.859731	+	0.0540897i
$999$	31.5960			0.999655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.4.1	✓	240
5.2	odd	4		625.2.g.b.226.24		480
5.3	odd	4		625.2.g.b.226.1		480
5.4	even	2		625.2.h.a.399.12		240
125.17	odd	100		625.2.g.b.401.24		480
125.31	even	25		625.2.h.a.224.12		240
125.94	even	50	inner	125.2.h.a.94.1	yes	240
125.108	odd	100		625.2.g.b.401.1		480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.4.1	✓	240	1.1	even	1	trivial
125.2.h.a.94.1	yes	240	125.94	even	50	inner
625.2.g.b.226.1		480	5.3	odd	4
625.2.g.b.226.24		480	5.2	odd	4
625.2.g.b.401.1		480	125.108	odd	100
625.2.g.b.401.24		480	125.17	odd	100
625.2.h.a.224.12		240	125.31	even	25
625.2.h.a.399.12		240	5.4	even	2

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.69510 - 0.169561i) q^{2} +(2.45880 + 1.15702i) q^{3} +(5.25058 + 0.663302i) q^{4} +(1.42401 - 1.72400i) q^{5} +(-6.43051 - 3.53521i) q^{6} +(-0.679948 + 0.935868i) q^{7} +(-8.73317 - 1.66594i) q^{8} +(2.79471 + 3.37822i) q^{9} +O(q^{10})\)	\(q+(-2.69510 - 0.169561i) q^{2} +(2.45880 + 1.15702i) q^{3} +(5.25058 + 0.663302i) q^{4} +(1.42401 - 1.72400i) q^{5} +(-6.43051 - 3.53521i) q^{6} +(-0.679948 + 0.935868i) q^{7} +(-8.73317 - 1.66594i) q^{8} +(2.79471 + 3.37822i) q^{9} +(-4.13018 + 4.40490i) q^{10} +(0.198843 - 3.16052i) q^{11} +(12.1427 + 7.70596i) q^{12} +(-0.669023 + 0.553464i) q^{13} +(1.99121 - 2.40697i) q^{14} +(5.49607 - 2.59136i) q^{15} +(13.0022 + 3.33840i) q^{16} +(-0.00124451 - 0.00985132i) q^{17} +(-6.95920 - 9.57852i) q^{18} +(1.13763 + 2.41759i) q^{19} +(8.62043 - 8.10746i) q^{20} +(-2.75467 + 1.51440i) q^{21} +(-1.07180 + 8.48420i) q^{22} +(-2.91674 + 7.36684i) q^{23} +(-19.5456 - 14.2007i) q^{24} +(-0.944368 - 4.91001i) q^{25} +(1.89693 - 1.37820i) q^{26} +(0.935558 + 3.64376i) q^{27} +(-4.19089 + 4.46284i) q^{28} +(-0.0827079 - 0.0776679i) q^{29} +(-15.2518 + 6.05204i) q^{30} +(-4.77298 + 0.602967i) q^{31} +(-17.5651 - 5.70725i) q^{32} +(4.14571 - 7.54101i) q^{33} +(0.00168368 + 0.0267613i) q^{34} +(0.645184 + 2.50492i) q^{35} +(12.4331 + 19.5914i) q^{36} +(2.08871 - 8.13500i) q^{37} +(-2.65610 - 6.70855i) q^{38} +(-2.28536 + 0.586781i) q^{39} +(-15.3082 + 12.6837i) q^{40} +(-5.27442 + 2.08829i) q^{41} +(7.68090 - 3.61436i) q^{42} +(3.29763 - 1.07147i) q^{43} +(3.14042 - 16.4627i) q^{44} +(9.80377 - 0.00744791i) q^{45} +(9.11002 - 19.3598i) q^{46} +(-5.02789 + 0.959122i) q^{47} +(28.1072 + 23.2523i) q^{48} +(1.74960 + 5.38471i) q^{49} +(1.71262 + 13.3931i) q^{50} +(0.00833819 - 0.0256623i) q^{51} +(-3.87987 + 2.46224i) q^{52} +(-2.92345 - 5.31774i) q^{53} +(-1.90358 - 9.97892i) q^{54} +(-5.16559 - 4.84343i) q^{55} +(7.49720 - 7.04034i) q^{56} +7.26064i q^{57} +(0.209737 + 0.223347i) q^{58} +(-1.11039 + 1.74969i) q^{59} +(30.5764 - 9.96056i) q^{60} +(-9.42206 - 3.73046i) q^{61} +(12.9659 - 0.815745i) q^{62} +(-5.06183 + 0.318463i) q^{63} +(21.4095 + 8.47662i) q^{64} +(0.00147498 + 1.94154i) q^{65} +(-12.4518 + 19.6208i) q^{66} +(-5.85531 - 6.23527i) q^{67} -0.0525506i q^{68} +(-15.6953 + 14.7388i) q^{69} +(-1.31410 - 6.86041i) q^{70} +(1.84361 + 9.66456i) q^{71} +(-18.7787 - 34.1584i) q^{72} +(2.41458 - 1.53234i) q^{73} +(-7.00867 + 21.5705i) q^{74} +(3.35898 - 13.1654i) q^{75} +(4.36964 + 13.4484i) q^{76} +(2.82263 + 2.33508i) q^{77} +(6.25877 - 1.19392i) q^{78} +(0.889148 - 1.88954i) q^{79} +(24.2707 - 17.6619i) q^{80} +(0.549093 - 2.87845i) q^{81} +(14.5692 - 4.73382i) q^{82} +(13.7986 - 6.49314i) q^{83} +(-15.4681 + 6.12427i) q^{84} +(-0.0187559 - 0.0118829i) q^{85} +(-9.06912 + 2.32855i) q^{86} +(-0.113498 - 0.286664i) q^{87} +(-7.00177 + 27.2701i) q^{88} +(0.705163 + 1.11116i) q^{89} +(-26.4234 - 1.64227i) q^{90} +(-0.0630684 - 1.00244i) q^{91} +(-20.2010 + 36.7455i) q^{92} +(-12.4334 - 4.03987i) q^{93} +(13.7133 - 1.73239i) q^{94} +(5.78794 + 1.48141i) q^{95} +(-36.5856 - 34.3562i) q^{96} +(4.80808 - 5.12008i) q^{97} +(-3.80230 - 14.8090i) q^{98} +(11.2327 - 8.16100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

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