LMFDB - Embedded newform 260.2.j.a.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(31,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("260.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.j (of order $4$, degree $2$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.5
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22023 + 0.714871i) q^{2} +1.31885i q^{3} +(0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.942808 - 1.60930i) q^{6} +(3.16584 - 3.16584i) q^{7} +(0.0538847 + 2.82791i) q^{8} +1.26063 q^{9} +O(q^{10})$	\(q+(-1.22023 + 0.714871i) q^{2} +1.31885i q^{3} +(0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.942808 - 1.60930i) q^{6} +(3.16584 - 3.16584i) q^{7} +(0.0538847 + 2.82791i) q^{8} +1.26063 q^{9} +(0.357343 - 1.36832i) q^{10} +(1.15118 - 1.15118i) q^{11} +(2.30088 + 1.28973i) q^{12} +(1.72571 + 3.16574i) q^{13} +(-1.59989 + 6.12621i) q^{14} +(-0.932568 - 0.932568i) q^{15} +(-2.08734 - 3.41218i) q^{16} +5.12100i q^{17} +(-1.53826 + 0.901189i) q^{18} +(-3.64223 - 3.64223i) q^{19} +(0.542133 + 1.92512i) q^{20} +(4.17527 + 4.17527i) q^{21} +(-0.581758 + 2.22764i) q^{22} +3.14629 q^{23} +(-3.72960 + 0.0710659i) q^{24} -1.00000i q^{25} +(-4.36886 - 2.62927i) q^{26} +5.61914i q^{27} +(-2.42722 - 8.61910i) q^{28} -5.51361 q^{29} +(1.80461 + 0.471282i) q^{30} +(4.30677 + 4.30677i) q^{31} +(4.98631 + 2.67147i) q^{32} +(1.51823 + 1.51823i) q^{33} +(-3.66085 - 6.24880i) q^{34} +4.47717i q^{35} +(1.23280 - 2.19931i) q^{36} +(3.59259 + 3.59259i) q^{37} +(7.04809 + 1.84064i) q^{38} +(-4.17514 + 2.27595i) q^{39} +(-2.03774 - 1.96153i) q^{40} +(3.96330 - 3.96330i) q^{41} +(-8.07956 - 2.11001i) q^{42} -3.80326 q^{43} +(-0.882598 - 3.13412i) q^{44} +(-0.891402 + 0.891402i) q^{45} +(-3.83920 + 2.24919i) q^{46} +(5.08030 - 5.08030i) q^{47} +(4.50016 - 2.75290i) q^{48} -13.0451i q^{49} +(0.714871 + 1.22023i) q^{50} -6.75384 q^{51} +(7.21060 + 0.0851495i) q^{52} -8.73922 q^{53} +(-4.01696 - 6.85664i) q^{54} +1.62801i q^{55} +(9.12331 + 8.78213i) q^{56} +(4.80356 - 4.80356i) q^{57} +(6.72786 - 3.94151i) q^{58} +(0.898987 - 0.898987i) q^{59} +(-2.53895 + 0.714993i) q^{60} +10.6844 q^{61} +(-8.33403 - 2.17647i) q^{62} +(3.99096 - 3.99096i) q^{63} +(-7.99419 + 0.304763i) q^{64} +(-3.45878 - 1.01826i) q^{65} +(-2.93793 - 0.767251i) q^{66} +(-10.4298 - 10.4298i) q^{67} +(8.93416 + 5.00793i) q^{68} +4.14949i q^{69} +(-3.20060 - 5.46318i) q^{70} +(-7.03030 - 7.03030i) q^{71} +(0.0679288 + 3.56496i) q^{72} +(-5.90818 - 5.90818i) q^{73} +(-6.95202 - 1.81555i) q^{74} +1.31885 q^{75} +(-9.91610 + 2.79247i) q^{76} -7.28888i q^{77} +(3.46762 - 5.76187i) q^{78} +10.3997i q^{79} +(3.88875 + 0.936803i) q^{80} -3.62891 q^{81} +(-2.00289 + 7.66939i) q^{82} +(-2.46310 - 2.46310i) q^{83} +(11.3673 - 3.20115i) q^{84} +(-3.62110 - 3.62110i) q^{85} +(4.64085 - 2.71884i) q^{86} -7.27162i q^{87} +(3.31746 + 3.19340i) q^{88} +(-2.27845 - 2.27845i) q^{89} +(0.450478 - 1.72495i) q^{90} +(15.4855 + 4.55891i) q^{91} +(3.07682 - 5.48906i) q^{92} +(-5.67999 + 5.67999i) q^{93} +(-2.56738 + 9.83089i) q^{94} +5.15090 q^{95} +(-3.52327 + 6.57620i) q^{96} +(-0.451121 + 0.451121i) q^{97} +(9.32553 + 15.9180i) q^{98} +(1.45121 - 1.45121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	$ 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) $ 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.22023	+	0.714871i	−0.862833	+	0.505490i
$2$	−1.22023	+	0.714871i	−0.862833	+	0.505490i
$3$			1.31885i			0.761439i	0.924691	+	0.380719i	$0.124324\pi$
$3$			1.31885i			0.761439i	−0.924691	+	0.380719i	$0.875676\pi$
$4$	0.977920	−	1.74461i	0.488960	−	0.872306i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.942808	−	1.60930i	−0.384900	−	0.656994i
$7$	3.16584	−	3.16584i	1.19657	−	1.19657i	0.221389	−	0.975186i	$-0.428941\pi$
$7$	3.16584	−	3.16584i	1.19657	−	1.19657i	0.975186	−	0.221389i	$-0.0710590\pi$
$8$	0.0538847	+	2.82791i	0.0190511	+	0.999819i
$9$	1.26063			0.420211
$10$	0.357343	−	1.36832i	0.113002	−	0.432702i
$11$	1.15118	−	1.15118i	0.347093	−	0.347093i	−0.511933	−	0.859026i	$-0.671070\pi$
$11$	1.15118	−	1.15118i	0.347093	−	0.347093i	0.859026	+	0.511933i	$0.171070\pi$
$12$	2.30088	+	1.28973i	0.664208	+	0.372313i
$13$	1.72571	+	3.16574i	0.478626	+	0.878019i
$13$	1.72571	+	3.16574i	0.478626	+	0.878019i
$14$	−1.59989	+	6.12621i	−0.427587	+	1.63730i
$15$	−0.932568	−	0.932568i	−0.240788	−	0.240788i
$16$	−2.08734	−	3.41218i	−0.521836	−	0.853046i
$17$			5.12100i			1.24203i	0.783800	+	0.621013i	$0.213279\pi$
$17$			5.12100i			1.24203i	−0.783800	+	0.621013i	$0.786721\pi$
$18$	−1.53826	+	0.901189i	−0.362572	+	0.212412i
$19$	−3.64223	−	3.64223i	−0.835586	−	0.835586i	0.152688	−	0.988274i	$-0.451207\pi$
$19$	−3.64223	−	3.64223i	−0.835586	−	0.835586i	−0.988274	+	0.152688i	$0.951207\pi$
$20$	0.542133	+	1.92512i	0.121225	+	0.430470i
$21$	4.17527	+	4.17527i	0.911118	+	0.911118i
$22$	−0.581758	+	2.22764i	−0.124031	+	0.474935i
$23$	3.14629			0.656047			0.328024	−	0.944669i	$-0.393617\pi$
$23$	3.14629			0.656047			0.328024	+	0.944669i	$0.393617\pi$
$24$	−3.72960	+	0.0710659i	−0.761301	+	0.0145063i
$25$		−	1.00000i		−	0.200000i
$26$	−4.36886	−	2.62927i	−0.856804	−	0.515643i
$27$			5.61914i			1.08140i
$28$	−2.42722	−	8.61910i	−0.458702	−	1.62886i
$29$	−5.51361			−1.02385			−0.511925	−	0.859030i	$-0.671068\pi$
$29$	−5.51361			−1.02385			−0.511925	+	0.859030i	$0.671068\pi$
$30$	1.80461	+	0.471282i	0.329476	+	0.0860439i
$31$	4.30677	+	4.30677i	0.773519	+	0.773519i	0.978720	−	0.205201i	$-0.0657848\pi$
$31$	4.30677	+	4.30677i	0.773519	+	0.773519i	−0.205201	+	0.978720i	$0.565785\pi$
$32$	4.98631	+	2.67147i	0.881463	+	0.472253i
$33$	1.51823	+	1.51823i	0.264290	+	0.264290i
$34$	−3.66085	−	6.24880i	−0.627831	−	1.07166i
$35$			4.47717i			0.756780i
$36$	1.23280	−	2.19931i	0.205466	−	0.366552i
$37$	3.59259	+	3.59259i	0.590618	+	0.590618i	0.937798	−	0.347180i	$-0.112861\pi$
$37$	3.59259	+	3.59259i	0.590618	+	0.590618i	−0.347180	+	0.937798i	$0.612861\pi$
$38$	7.04809	+	1.84064i	1.14335	+	0.298591i
$39$	−4.17514	+	2.27595i	−0.668558	+	0.364444i
$40$	−2.03774	−	1.96153i	−0.322195	−	0.310146i
$41$	3.96330	−	3.96330i	0.618964	−	0.618964i	−0.326302	−	0.945266i	$-0.605802\pi$
$41$	3.96330	−	3.96330i	0.618964	−	0.618964i	0.945266	+	0.326302i	$0.105802\pi$
$42$	−8.07956	−	2.11001i	−1.24670	−	0.325582i
$43$	−3.80326			−0.579991			−0.289996	−	0.957028i	$-0.593654\pi$
$43$	−3.80326			−0.579991			−0.289996	+	0.957028i	$0.593654\pi$
$44$	−0.882598	−	3.13412i	−0.133057	−	0.472486i
$45$	−0.891402	+	0.891402i	−0.132882	+	0.132882i
$46$	−3.83920	+	2.24919i	−0.566059	+	0.331625i
$47$	5.08030	−	5.08030i	0.741038	−	0.741038i	−0.231740	−	0.972778i	$-0.574442\pi$
$47$	5.08030	−	5.08030i	0.741038	−	0.741038i	0.972778	+	0.231740i	$0.0744418\pi$
$48$	4.50016	−	2.75290i	0.649542	−	0.397346i
$49$		−	13.0451i		−	1.86358i
$50$	0.714871	+	1.22023i	0.101098	+	0.172567i
$51$	−6.75384			−0.945727
$52$	7.21060	+	0.0851495i	0.999930	+	0.0118081i
$53$	−8.73922			−1.20042			−0.600212	−	0.799841i	$-0.704917\pi$
$53$	−8.73922			−1.20042			−0.600212	+	0.799841i	$0.704917\pi$
$54$	−4.01696	−	6.85664i	−0.546639	−	0.933070i
$55$			1.62801i			0.219521i
$56$	9.12331	+	8.78213i	1.21915	+	1.17356i
$57$	4.80356	−	4.80356i	0.636248	−	0.636248i
$58$	6.72786	−	3.94151i	0.883412	−	0.517546i
$59$	0.898987	−	0.898987i	0.117038	−	0.117038i	−0.646162	−	0.763200i	$-0.723627\pi$
$59$	0.898987	−	0.898987i	0.117038	−	0.117038i	0.763200	+	0.646162i	$0.223627\pi$
$60$	−2.53895	+	0.714993i	−0.327777	+	0.0923052i
$61$	10.6844			1.36799			0.683997	−	0.729485i	$-0.260240\pi$
$61$	10.6844			1.36799			0.683997	+	0.729485i	$0.260240\pi$
$62$	−8.33403	−	2.17647i	−1.05842	−	0.276411i
$63$	3.99096	−	3.99096i	0.502814	−	0.502814i
$64$	−7.99419	+	0.304763i	−0.999274	+	0.0380953i
$65$	−3.45878	−	1.01826i	−0.429009	−	0.126299i
$66$	−2.93793	−	0.767251i	−0.361634	−	0.0944421i
$67$	−10.4298	−	10.4298i	−1.27421	−	1.27421i	−0.943859	−	0.330348i	$-0.892834\pi$
$67$	−10.4298	−	10.4298i	−1.27421	−	1.27421i	−0.330348	−	0.943859i	$-0.607166\pi$
$68$	8.93416	+	5.00793i	1.08343	+	0.607301i
$69$			4.14949i			0.499540i
$70$	−3.20060	−	5.46318i	−0.382545	−	0.652975i
$71$	−7.03030	−	7.03030i	−0.834343	−	0.834343i	0.153764	−	0.988108i	$-0.450860\pi$
$71$	−7.03030	−	7.03030i	−0.834343	−	0.834343i	−0.988108	+	0.153764i	$0.950860\pi$
$72$	0.0679288	+	3.56496i	0.00800549	+	0.420135i
$73$	−5.90818	−	5.90818i	−0.691500	−	0.691500i	0.271062	−	0.962562i	$-0.412625\pi$
$73$	−5.90818	−	5.90818i	−0.691500	−	0.691500i	−0.962562	+	0.271062i	$0.912625\pi$
$74$	−6.95202	−	1.81555i	−0.808156	−	0.211053i
$75$	1.31885			0.152288
$76$	−9.91610	+	2.79247i	−1.13745	+	0.320319i
$77$		−	7.28888i		−	0.830645i
$78$	3.46762	−	5.76187i	0.392631	−	0.652404i
$79$			10.3997i			1.17005i	0.811014	+	0.585026i	$0.198916\pi$
$79$			10.3997i			1.17005i	−0.811014	+	0.585026i	$0.801084\pi$
$80$	3.88875	+	0.936803i	0.434776	+	0.104738i
$81$	−3.62891			−0.403212
$82$	−2.00289	+	7.66939i	−0.221182	+	0.846943i
$83$	−2.46310	−	2.46310i	−0.270360	−	0.270360i	0.558885	−	0.829245i	$-0.311229\pi$
$83$	−2.46310	−	2.46310i	−0.270360	−	0.270360i	−0.829245	+	0.558885i	$0.811229\pi$
$84$	11.3673	−	3.20115i	1.24027	−	0.349274i
$85$	−3.62110	−	3.62110i	−0.392763	−	0.392763i
$86$	4.64085	−	2.71884i	0.500435	−	0.293180i
$87$		−	7.27162i		−	0.779600i
$88$	3.31746	+	3.19340i	0.353642	+	0.340417i
$89$	−2.27845	−	2.27845i	−0.241515	−	0.241515i	0.575961	−	0.817477i	$-0.304628\pi$
$89$	−2.27845	−	2.27845i	−0.241515	−	0.241515i	−0.817477	+	0.575961i	$0.804628\pi$
$90$	0.450478	−	1.72495i	0.0474845	−	0.181826i
$91$	15.4855	+	4.55891i	1.62333	+	0.477904i
$92$	3.07682	−	5.48906i	0.320781	−	0.572274i
$93$	−5.67999	+	5.67999i	−0.588987	+	0.588987i
$94$	−2.56738	+	9.83089i	−0.264805	+	1.01398i
$95$	5.15090			0.528471
$96$	−3.52327	+	6.57620i	−0.359592	+	0.671180i
$97$	−0.451121	+	0.451121i	−0.0458044	+	0.0458044i	−0.729638	−	0.683834i	$-0.760311\pi$
$97$	−0.451121	+	0.451121i	−0.0458044	+	0.0458044i	0.683834	+	0.729638i	$0.260311\pi$
$98$	9.32553	+	15.9180i	0.942021	+	1.60796i
$99$	1.45121	−	1.45121i	0.145852	−	0.145852i
$100$	−1.74461	−	0.977920i	−0.174461	−	0.0977920i
$101$			2.27122i			0.225995i	0.993595	+	0.112998i	$0.0360452\pi$
$101$			2.27122i			0.225995i	−0.993595	+	0.112998i	$0.963955\pi$
$102$	8.24123	−	4.82812i	0.816004	−	0.478055i
$103$	−5.39362			−0.531449			−0.265724	−	0.964049i	$-0.585611\pi$
$103$	−5.39362			−0.531449			−0.265724	+	0.964049i	$0.585611\pi$
$104$	−8.85946	+	5.05074i	−0.868741	+	0.495266i
$105$	−5.90472			−0.576242
$106$	10.6639	−	6.24741i	1.03577	−	0.606802i
$107$			16.2845i			1.57428i	0.616773	+	0.787141i	$0.288440\pi$
$107$			16.2845i			1.57428i	−0.616773	+	0.787141i	$0.711560\pi$
$108$	9.80322	+	5.49507i	0.943315	+	0.528763i
$109$	0.189495	−	0.189495i	0.0181503	−	0.0181503i	−0.697973	−	0.716124i	$-0.745915\pi$
$109$	0.189495	−	0.189495i	0.0181503	−	0.0181503i	0.716124	+	0.697973i	$0.245915\pi$
$110$	−1.16382	−	1.98655i	−0.110966	−	0.189410i
$111$	−4.73809	+	4.73809i	−0.449719	+	0.449719i
$112$	−17.4106	−	4.19423i	−1.64515	−	0.396317i
$113$	1.95147			0.183579			0.0917893	−	0.995778i	$-0.470741\pi$
$113$	1.95147			0.183579			0.0917893	+	0.995778i	$0.470741\pi$
$114$	−2.42752	+	9.29538i	−0.227358	+	0.870592i
$115$	−2.22477	+	2.22477i	−0.207460	+	0.207460i
$116$	−5.39187	+	9.61910i	−0.500622	+	0.893111i
$117$	2.17549	+	3.99084i	0.201124	+	0.368953i
$118$	−0.454311	+	1.73963i	−0.0418227	+	0.160146i
$119$	16.2123	+	16.2123i	1.48618	+	1.48618i
$120$	2.58697	−	2.68747i	0.236157	−	0.245332i
$121$			8.34958i			0.759053i
$122$	−13.0374	+	7.63795i	−1.18035	+	0.691507i
$123$	5.22701	+	5.22701i	0.471303	+	0.471303i
$124$	11.7253	−	3.30197i	1.05297	−	0.296525i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−2.01687	+	7.72290i	−0.179677	+	0.688011i
$127$	−10.4330			−0.925775			−0.462887	−	0.886417i	$-0.653187\pi$
$127$	−10.4330			−0.925775			−0.462887	+	0.886417i	$0.653187\pi$
$128$	9.53688	−	6.08669i	0.842949	−	0.537993i
$129$		−	5.01593i		−	0.441628i
$130$	4.94843	−	1.23007i	0.434006	−	0.107884i
$131$		−	13.5871i		−	1.18711i	−0.804793	−	0.593555i	$-0.797724\pi$
$131$		−	13.5871i		−	1.18711i	0.804793	−	0.593555i	$-0.202276\pi$
$132$	4.13343	−	1.16402i	0.359769	−	0.101315i
$133$	−23.0615			−1.99968
$134$	20.1828	+	5.27081i	1.74353	+	0.455329i
$135$	−3.97333	−	3.97333i	−0.341970	−	0.341970i
$136$	−14.4818	+	0.275944i	−1.24180	+	0.0236620i
$137$	−12.2055	−	12.2055i	−1.04279	−	1.04279i	−0.999043	−	0.0437428i	$-0.986072\pi$
$137$	−12.2055	−	12.2055i	−1.04279	−	1.04279i	−0.0437428	−	0.999043i	$-0.513928\pi$
$138$	−2.96635	−	5.06333i	−0.252512	−	0.431019i
$139$		−	12.6107i		−	1.06962i	−0.844972	−	0.534811i	$-0.820383\pi$
$139$		−	12.6107i		−	1.06962i	0.844972	−	0.534811i	$-0.179617\pi$
$140$	7.81093	+	4.37832i	0.660144	+	0.370035i
$141$	6.70016	+	6.70016i	0.564255	+	0.564255i
$142$	13.6043	+	3.55283i	1.14165	+	0.298147i
$143$	5.63093	+	1.65773i	0.470882	+	0.138627i
$144$	−2.63137	−	4.30151i	−0.219281	−	0.358459i
$145$	3.89871	−	3.89871i	0.323770	−	0.323770i
$146$	11.4329	+	2.98575i	0.946195	+	0.247103i
$147$	17.2045			1.41900
$148$	9.78094	−	2.75441i	0.803988	−	0.226411i
$149$	−1.08585	+	1.08585i	−0.0889562	+	0.0889562i	−0.750185	−	0.661228i	$-0.770035\pi$
$149$	−1.08585	+	1.08585i	−0.0889562	+	0.0889562i	0.661228	+	0.750185i	$0.270035\pi$
$150$	−1.60930	+	0.942808i	−0.131399	+	0.0769799i
$151$	−2.55542	+	2.55542i	−0.207957	+	0.207957i	−0.803399	−	0.595441i	$-0.796977\pi$
$151$	−2.55542	+	2.55542i	−0.207957	+	0.207957i	0.595441	+	0.803399i	$0.296977\pi$
$152$	10.1037	−	10.4962i	0.819515	−	0.851353i
$153$			6.45570i			0.521913i
$154$	5.21061	+	8.89411i	0.419883	+	0.716708i
$155$	−6.09069			−0.489216
$156$	−0.112299	+	9.50971i	−0.00899116	+	0.761386i
$157$	13.7276			1.09558			0.547792	−	0.836614i	$-0.315468\pi$
$157$	13.7276			1.09558			0.547792	+	0.836614i	$0.315468\pi$
$158$	−7.43441	−	12.6900i	−0.591450	−	1.00956i
$159$		−	11.5257i		−	0.914050i
$160$	−5.41486	+	1.63684i	−0.428083	+	0.129404i
$161$	9.96066	−	9.96066i	0.785010	−	0.785010i
$162$	4.42810	−	2.59420i	0.347904	−	0.203820i
$163$	9.01274	−	9.01274i	0.705933	−	0.705933i	−0.259745	−	0.965677i	$-0.583638\pi$
$163$	9.01274	−	9.01274i	0.705933	−	0.705933i	0.965677	+	0.259745i	$0.0836384\pi$
$164$	−3.03863	−	10.7902i	−0.237277	−	0.842575i
$165$	−2.14710			−0.167152
$166$	4.76635	+	1.24475i	0.369940	+	0.0966113i
$167$	−18.1043	+	18.1043i	−1.40095	+	1.40095i	−0.603876	+	0.797078i	$0.706378\pi$
$167$	−18.1043	+	18.1043i	−1.40095	+	1.40095i	−0.797078	+	0.603876i	$0.793622\pi$
$168$	−11.5823	+	12.0323i	−0.893595	+	0.928311i
$169$	−7.04385	+	10.9263i	−0.541835	+	0.840485i
$170$	7.00718	+	1.82995i	0.537426	+	0.140351i
$171$	−4.59152	−	4.59152i	−0.351122	−	0.351122i
$172$	−3.71928	+	6.63521i	−0.283593	+	0.505930i
$173$			4.17330i			0.317290i	0.987336	+	0.158645i	$0.0507125\pi$
$173$			4.17330i			0.317290i	−0.987336	+	0.158645i	$0.949287\pi$
$174$	5.19827	+	8.87305i	0.394080	+	0.672664i
$175$	−3.16584	−	3.16584i	−0.239315	−	0.239315i
$176$	−6.33093	−	1.52512i	−0.477212	−	0.114961i
$177$	1.18563	+	1.18563i	0.0891174	+	0.0891174i
$178$	4.40903	+	1.15144i	0.330471	+	0.0863038i
$179$	−13.1238			−0.980918			−0.490459	−	0.871464i	$-0.663171\pi$
$179$	−13.1238			−0.980918			−0.490459	+	0.871464i	$0.663171\pi$
$180$	0.683431	+	2.42687i	0.0509399	+	0.180888i
$181$		−	15.1357i		−	1.12503i	−0.826788	−	0.562514i	$-0.809834\pi$
$181$		−	15.1357i		−	1.12503i	0.826788	−	0.562514i	$-0.190166\pi$
$182$	−22.1550	+	5.50724i	−1.64223	+	0.408224i
$183$			14.0911i			1.04164i
$184$	0.169537	+	8.89745i	0.0124984	+	0.655928i
$185$	−5.08069			−0.373540
$186$	2.87043	−	10.9913i	0.210470	−	0.805925i
$187$	5.89518	+	5.89518i	0.431098	+	0.431098i
$188$	−3.89503	−	13.8313i	−0.284074	−	1.00875i
$189$	17.7893	+	17.7893i	1.29398	+	1.29398i
$190$	−6.28528	+	3.68222i	−0.455982	+	0.267137i
$191$		−	7.36234i		−	0.532720i	−0.963874	−	0.266360i	$-0.914179\pi$
$191$		−	7.36234i		−	0.532720i	0.963874	−	0.266360i	$-0.0858210\pi$
$192$	−0.401936	−	10.5431i	−0.0290073	−	0.760886i
$193$	−7.07406	−	7.07406i	−0.509202	−	0.509202i	0.405079	−	0.914282i	$-0.367244\pi$
$193$	−7.07406	−	7.07406i	−0.509202	−	0.509202i	−0.914282	+	0.405079i	$0.867244\pi$
$194$	0.227978	−	0.872964i	0.0163679	−	0.0626751i
$195$	1.34293	−	4.56161i	0.0961692	−	0.326664i
$196$	−22.7586	−	12.7570i	−1.62561	−	0.911217i
$197$	−9.22020	+	9.22020i	−0.656912	+	0.656912i	−0.954648	−	0.297736i	$-0.903768\pi$
$197$	−9.22020	+	9.22020i	−0.656912	+	0.656912i	0.297736	+	0.954648i	$0.403768\pi$
$198$	−0.733383	+	2.80824i	−0.0521192	+	0.199573i
$199$	−13.2997			−0.942792			−0.471396	−	0.881922i	$-0.656250\pi$
$199$	−13.2997			−0.942792			−0.471396	+	0.881922i	$0.656250\pi$
$200$	2.82791	−	0.0538847i	0.199964	−	0.00381022i
$201$	13.7554	−	13.7554i	0.970231	−	0.970231i
$202$	−1.62363	−	2.77141i	−0.114238	−	0.194996i
$203$	−17.4552	+	17.4552i	−1.22511	+	1.22511i
$204$	−6.60472	+	11.7828i	−0.462423	+	0.824963i
$205$			5.60496i			0.391467i
$206$	6.58145	−	3.85574i	0.458552	−	0.268642i
$207$	3.96632			0.275678
$208$	7.19994	−	12.4964i	0.499226	−	0.866472i
$209$	−8.38571			−0.580052
$210$	7.20512	−	4.22111i	0.497200	−	0.291284i
$211$		−	12.5743i		−	0.865649i	−0.901478	−	0.432825i	$-0.857517\pi$
$211$		−	12.5743i		−	0.865649i	0.901478	−	0.432825i	$-0.142483\pi$
$212$	−8.54626	+	15.2466i	−0.586960	+	1.04714i
$213$	9.27192	−	9.27192i	0.635301	−	0.635301i
$214$	−11.6413	−	19.8708i	−0.795783	−	1.35834i
$215$	2.68931	−	2.68931i	0.183409	−	0.183409i
$216$	−15.8904	+	0.302786i	−1.08121	+	0.0206020i
$217$	27.2691			1.85115
$218$	−0.0957629	+	0.366691i	−0.00648588	+	0.0248355i
$219$	7.79201	−	7.79201i	0.526535	−	0.526535i
$220$	2.84025	+	1.59206i	0.191489	+	0.107337i
$221$	−16.2118	+	8.83736i	−1.09052	+	0.594465i
$222$	2.39444	−	9.16867i	0.160704	−	0.615361i
$223$	10.8252	+	10.8252i	0.724908	+	0.724908i	0.969601	−	0.244692i	$-0.0786870\pi$
$223$	10.8252	+	10.8252i	0.724908	+	0.724908i	−0.244692	+	0.969601i	$0.578687\pi$
$224$	24.2433	−	7.32842i	1.61982	−	0.489650i
$225$		−	1.26063i		−	0.0840422i
$226$	−2.38124	+	1.39505i	−0.158398	+	0.0927971i
$227$	0.955202	+	0.955202i	0.0633990	+	0.0633990i	0.738095	−	0.674696i	$-0.235725\pi$
$227$	0.955202	+	0.955202i	0.0633990	+	0.0633990i	−0.674696	+	0.738095i	$0.735725\pi$
$228$	−3.68285	−	13.0779i	−0.243903	−	0.866102i
$229$	13.3273	+	13.3273i	0.880691	+	0.880691i	0.993605	−	0.112913i	$-0.0360183\pi$
$229$	13.3273	+	13.3273i	0.880691	+	0.880691i	−0.112913	+	0.993605i	$0.536018\pi$
$230$	1.12431	−	4.30514i	0.0741345	−	0.283873i
$231$	9.61295			0.632485
$232$	−0.297099	−	15.5920i	−0.0195055	−	1.02366i
$233$		−	15.2378i		−	0.998258i	−0.866528	−	0.499129i	$-0.833653\pi$
$233$		−	15.2378i		−	0.998258i	0.866528	−	0.499129i	$-0.166347\pi$
$234$	−5.50752	−	3.31455i	−0.360038	−	0.216679i
$235$			7.18463i			0.468674i
$236$	−0.689246	−	2.44752i	−0.0448661	−	0.159320i
$237$	−13.7156			−0.890924
$238$	−31.3724	−	8.19302i	−2.03357	−	0.531074i
$239$	−8.88863	−	8.88863i	−0.574958	−	0.574958i	0.358552	−	0.933510i	$-0.383271\pi$
$239$	−8.88863	−	8.88863i	−0.574958	−	0.574958i	−0.933510	+	0.358552i	$0.883271\pi$
$240$	−1.23550	+	5.12869i	−0.0797514	+	0.331055i
$241$	−4.87091	−	4.87091i	−0.313763	−	0.313763i	0.532603	−	0.846365i	$-0.321214\pi$
$241$	−4.87091	−	4.87091i	−0.313763	−	0.313763i	−0.846365	+	0.532603i	$0.821214\pi$
$242$	−5.96887	−	10.1884i	−0.383694	−	0.654936i
$243$			12.0714i			0.774382i
$244$	10.4485	−	18.6401i	0.668895	−	1.19331i
$245$	9.22426	+	9.22426i	0.589316	+	0.589316i
$246$	−10.1148	−	2.64152i	−0.644895	−	0.168417i
$247$	5.24494	−	17.8158i	0.333727	−	1.13359i
$248$	−11.9471	+	12.4112i	−0.758642	+	0.788115i
$249$	3.24846	−	3.24846i	0.205863	−	0.205863i
$250$	−1.36832	−	0.357343i	−0.0865403	−	0.0226003i
$251$	3.08877			0.194962			0.0974808	−	0.995237i	$-0.468922\pi$
$251$	3.08877			0.194962			0.0974808	+	0.995237i	$0.468922\pi$
$252$	−3.05984	−	10.8655i	−0.192752	−	0.684463i
$253$	3.62194	−	3.62194i	0.227709	−	0.227709i
$254$	12.7306	−	7.45821i	0.798789	−	0.467970i
$255$	4.77569	−	4.77569i	0.299065	−	0.299065i
$256$	−7.28599	+	14.2448i	−0.455374	+	0.890300i
$257$		−	18.6642i		−	1.16424i	−0.813102	−	0.582122i	$-0.802223\pi$
$257$		−	18.6642i		−	1.16424i	0.813102	−	0.582122i	$-0.197777\pi$
$258$	3.58574	+	6.12058i	0.223238	+	0.381051i
$259$	22.7471			1.41344
$260$	−5.15887	+	5.03845i	−0.319940	+	0.312472i
$261$	−6.95063			−0.430233
$262$	9.71302	+	16.5794i	0.600072	+	1.02428i
$263$		−	16.3459i		−	1.00793i	−0.863724	−	0.503966i	$-0.831874\pi$
$263$		−	16.3459i		−	1.00793i	0.863724	−	0.503966i	$-0.168126\pi$
$264$	−4.21162	+	4.37523i	−0.259207	+	0.269277i
$265$	6.17956	−	6.17956i	0.379607	−	0.379607i
$266$	28.1403	−	16.4860i	1.72539	−	1.01082i
$267$	3.00494	−	3.00494i	0.183899	−	0.183899i
$268$	−28.3956	+	7.99647i	−1.73454	+	0.488462i
$269$	21.1537			1.28976			0.644882	−	0.764282i	$-0.276906\pi$
$269$	21.1537			1.28976			0.644882	+	0.764282i	$0.276906\pi$
$270$	7.68879	+	2.00796i	0.467925	+	0.122200i
$271$	−3.92561	+	3.92561i	−0.238464	+	0.238464i	−0.816214	−	0.577750i	$-0.803931\pi$
$271$	−3.92561	+	3.92561i	−0.238464	+	0.238464i	0.577750	+	0.816214i	$0.303931\pi$
$272$	17.4738	−	10.6893i	1.05950	−	0.648134i
$273$	−6.01252	+	20.4231i	−0.363895	+	1.23606i
$274$	23.6189	+	6.16816i	1.42687	+	0.372632i
$275$	−1.15118	−	1.15118i	−0.0694186	−	0.0694186i
$276$	7.23925	+	4.05787i	0.435752	+	0.244255i
$277$			12.8278i			0.770745i	0.922761	+	0.385373i	$0.125927\pi$
$277$			12.8278i			0.770745i	−0.922761	+	0.385373i	$0.874073\pi$
$278$	9.01499	+	15.3879i	0.540683	+	0.922905i
$279$	5.42926	+	5.42926i	0.325041	+	0.325041i
$280$	−12.6611	+	0.241251i	−0.756643	+	0.0144175i
$281$	18.6392	+	18.6392i	1.11192	+	1.11192i	0.992891	+	0.119028i	$0.0379779\pi$
$281$	18.6392	+	18.6392i	1.11192	+	1.11192i	0.119028	+	0.992891i	$0.462022\pi$
$282$	−12.9655	−	3.38599i	−0.772083	−	0.201633i
$283$	−24.5292			−1.45811			−0.729056	−	0.684454i	$-0.760041\pi$
$283$	−24.5292			−1.45811			−0.729056	+	0.684454i	$0.760041\pi$
$284$	−19.1402	+	5.39008i	−1.13576	+	0.319842i
$285$			6.79327i			0.402398i
$286$	−8.05609	+	2.00257i	−0.476366	+	0.118414i
$287$		−	25.0944i		−	1.48127i
$288$	6.28590	+	3.36774i	0.370400	+	0.198446i
$289$	−9.22467			−0.542628
$290$	−1.97025	+	7.54439i	−0.115697	+	0.443022i
$291$	−0.594961	−	0.594961i	−0.0348772	−	0.0348772i
$292$	−16.0852	+	4.52975i	−0.941316	+	0.265084i
$293$	−16.2853	−	16.2853i	−0.951395	−	0.951395i	0.0474777	−	0.998872i	$-0.484882\pi$
$293$	−16.2853	−	16.2853i	−0.951395	−	0.951395i	−0.998872	+	0.0474777i	$0.984882\pi$
$294$	−20.9934	+	12.2990i	−1.22436	+	0.717292i
$295$			1.27136i			0.0740214i
$296$	−9.96594	+	10.3531i	−0.579259	+	0.601763i
$297$	6.46862	+	6.46862i	0.375348	+	0.375348i
$298$	0.548743	−	2.10123i	0.0317879	−	0.121721i
$299$	5.42959	+	9.96035i	0.314001	+	0.576022i
$300$	1.28973	−	2.30088i	0.0744627	−	0.132842i
$301$	−12.0405	+	12.0405i	−0.694003	+	0.694003i
$302$	1.29141	−	4.94500i	0.0743121	−	0.284553i
$303$	−2.99540			−0.172081
$304$	−4.82538	+	20.0306i	−0.276754	+	1.14883i
$305$	−7.55500	+	7.55500i	−0.432598	+	0.432598i
$306$	−4.61499	−	7.87744i	−0.263821	−	0.450323i
$307$	−6.71827	+	6.71827i	−0.383432	+	0.383432i	−0.872337	−	0.488905i	$-0.837396\pi$
$307$	−6.71827	+	6.71827i	−0.383432	+	0.383432i	0.488905	+	0.872337i	$0.337396\pi$
$308$	−12.7163	−	7.12794i	−0.724577	−	0.406152i
$309$		−	7.11338i		−	0.404666i
$310$	7.43204	−	4.35406i	0.422112	−	0.247294i
$311$	8.21407			0.465777			0.232889	−	0.972503i	$-0.425182\pi$
$311$	8.21407			0.465777			0.232889	+	0.972503i	$0.425182\pi$
$312$	−6.66118	−	11.6843i	−0.377115	−	0.661493i
$313$	17.6085			0.995289			0.497644	−	0.867381i	$-0.334198\pi$
$313$	17.6085			0.995289			0.497644	+	0.867381i	$0.334198\pi$
$314$	−16.7509	+	9.81348i	−0.945306	+	0.553807i
$315$			5.64407i			0.318007i
$316$	18.1434	+	10.1700i	1.02064	+	0.572109i
$317$	8.98553	−	8.98553i	0.504678	−	0.504678i	−0.408210	−	0.912888i	$-0.633847\pi$
$317$	8.98553	−	8.98553i	0.504678	−	0.504678i	0.912888	+	0.408210i	$0.133847\pi$
$318$	8.23940	+	14.0640i	0.462043	+	0.788672i
$319$	−6.34713	+	6.34713i	−0.355371	+	0.355371i
$320$	5.43725	−	5.86825i	0.303951	−	0.328045i
$321$	−21.4768			−1.19872
$322$	−5.03371	+	19.2749i	−0.280518	+	1.07415i
$323$	18.6519	−	18.6519i	1.03782	−	1.03782i
$324$	−3.54878	+	6.33104i	−0.197155	+	0.351724i
$325$	3.16574	−	1.72571i	0.175604	−	0.0957252i
$326$	−4.55467	+	17.4406i	−0.252260	+	0.965943i
$327$	0.249915	+	0.249915i	0.0138203	+	0.0138203i
$328$	11.4214	+	10.9943i	0.630644	+	0.607060i
$329$		−	32.1668i		−	1.77341i
$330$	2.61996	−	1.53490i	0.144224	−	0.0844935i
$331$	10.5088	+	10.5088i	0.577616	+	0.577616i	0.934246	−	0.356630i	$-0.116074\pi$
$331$	10.5088	+	10.5088i	0.577616	+	0.577616i	−0.356630	+	0.934246i	$0.616074\pi$
$332$	−6.70587	+	1.88844i	−0.368033	+	0.103642i
$333$	4.52893	+	4.52893i	0.248184	+	0.248184i
$334$	9.14918	−	35.0337i	0.500621	−	1.91696i
$335$	14.7500			0.805880
$336$	5.53156	−	22.9620i	0.301771	−	1.25268i
$337$			22.5861i			1.23034i	0.788393	+	0.615172i	$0.210913\pi$
$337$			22.5861i			1.23034i	−0.788393	+	0.615172i	$0.789087\pi$
$338$	0.784223	−	18.3680i	0.0426561	−	0.999090i
$339$			2.57369i			0.139784i
$340$	−9.85855	+	2.77627i	−0.534655	+	0.150564i
$341$	9.91571			0.536966
$342$	8.88505	+	2.32037i	0.480448	+	0.125471i
$343$	−19.1377	−	19.1377i	−1.03334	−	1.03334i
$344$	−0.204937	−	10.7553i	−0.0110495	−	0.579886i
$345$	−2.93413	−	2.93413i	−0.157968	−	0.157968i
$346$	−2.98337	−	5.09238i	−0.160387	−	0.273768i
$347$			4.76733i			0.255924i	0.991779	+	0.127962i	$0.0408435\pi$
$347$			4.76733i			0.255924i	−0.991779	+	0.127962i	$0.959156\pi$
$348$	−12.6862	−	7.11107i	−0.680050	−	0.381193i
$349$	19.9060	+	19.9060i	1.06554	+	1.06554i	0.997696	+	0.0678468i	$0.0216129\pi$
$349$	19.9060	+	19.9060i	1.06554	+	1.06554i	0.0678468	+	0.997696i	$0.478387\pi$
$350$	6.12621	+	1.59989i	0.327460	+	0.0855175i
$351$	−17.7887	+	9.69700i	−0.949493	+	0.517588i
$352$	8.81545	−	2.66479i	0.469865	−	0.142034i
$353$	−14.1771	+	14.1771i	−0.754573	+	0.754573i	−0.975329	−	0.220756i	$-0.929147\pi$
$353$	−14.1771	+	14.1771i	−0.754573	+	0.754573i	0.220756	+	0.975329i	$0.429147\pi$
$354$	−2.29431	−	0.599169i	−0.121941	−	0.0318455i
$355$	9.94235			0.527685
$356$	−6.20316	+	1.74687i	−0.328767	+	0.0925840i
$357$	−21.3816	+	21.3816i	−1.13163	+	1.13163i
$358$	16.0140	−	9.38181i	0.846368	−	0.495844i
$359$	2.57511	−	2.57511i	0.135909	−	0.135909i	−0.635879	−	0.771788i	$-0.719362\pi$
$359$	2.57511	−	2.57511i	0.135909	−	0.135909i	0.771788	+	0.635879i	$0.219362\pi$
$360$	−2.56884	−	2.47277i	−0.135390	−	0.130327i
$361$			7.53175i			0.396408i
$362$	10.8201	+	18.4690i	0.568690	+	0.970710i
$363$	−11.0119			−0.577973
$364$	23.0972	−	22.5580i	1.21062	−	1.18236i
$365$	8.35543			0.437343
$366$	−10.0733	−	17.1944i	−0.526541	−	0.898765i
$367$			33.7688i			1.76272i	0.472449	+	0.881358i	$0.343370\pi$
$367$			33.7688i			1.76272i	−0.472449	+	0.881358i	$0.656630\pi$
$368$	−6.56740	−	10.7357i	−0.342349	−	0.559639i
$369$	4.99627	−	4.99627i	0.260095	−	0.260095i
$370$	6.19960	−	3.63203i	0.322302	−	0.188820i
$371$	−27.6670	+	27.6670i	−1.43640	+	1.43640i
$372$	4.35480	+	15.4640i	0.225786	+	0.801769i
$373$	13.8848			0.718927			0.359464	−	0.933159i	$-0.382960\pi$
$373$	13.8848			0.718927			0.359464	+	0.933159i	$0.382960\pi$
$374$	−11.4078	−	2.97918i	−0.589881	−	0.154050i
$375$	−0.932568	+	0.932568i	−0.0481576	+	0.0481576i
$376$	14.6404	+	14.0929i	0.755021	+	0.726786i
$377$	−9.51488	−	17.4547i	−0.490041	−	0.898960i
$378$	−34.4240	−	8.98998i	−1.77058	−	0.462394i
$379$	2.62573	+	2.62573i	0.134875	+	0.134875i	0.771321	−	0.636446i	$-0.219596\pi$
$379$	2.62573	+	2.62573i	0.134875	+	0.134875i	−0.636446	+	0.771321i	$0.719596\pi$
$380$	5.03717	−	8.98632i	0.258401	−	0.460988i
$381$		−	13.7595i		−	0.704921i
$382$	5.26312	+	8.98375i	0.269285	+	0.459648i
$383$	−4.82603	−	4.82603i	−0.246598	−	0.246598i	0.572975	−	0.819573i	$-0.305789\pi$
$383$	−4.82603	−	4.82603i	−0.246598	−	0.246598i	−0.819573	+	0.572975i	$0.805789\pi$
$384$	8.02744	+	12.5777i	0.409649	+	0.641854i
$385$	5.15402	+	5.15402i	0.262673	+	0.262673i
$386$	13.6890	+	3.57494i	0.696753	+	0.181960i
$387$	−4.79451			−0.243719
$388$	0.345871	+	1.22819i	0.0175589	+	0.0623519i
$389$			10.1698i			0.515632i	0.966194	+	0.257816i	$0.0830028\pi$
$389$			10.1698i			0.515632i	−0.966194	+	0.257816i	$0.916997\pi$
$390$	1.62228	+	6.52624i	0.0821474	+	0.330469i
$391$			16.1122i			0.814828i
$392$	36.8903	−	0.702930i	1.86324	−	0.0355033i
$393$	17.9194			0.903912
$394$	4.65951	−	17.8420i	0.234743	−	0.898867i
$395$	−7.35367	−	7.35367i	−0.370003	−	0.370003i
$396$	−1.11263	−	3.95097i	−0.0559119	−	0.198544i
$397$	4.82489	+	4.82489i	0.242154	+	0.242154i	0.817741	−	0.575587i	$-0.195226\pi$
$397$	4.82489	+	4.82489i	0.242154	+	0.242154i	−0.575587	+	0.817741i	$0.695226\pi$
$398$	16.2287	−	9.50758i	0.813472	−	0.476572i
$399$		−	30.4146i		−	1.52264i
$400$	−3.41218	+	2.08734i	−0.170609	+	0.104367i
$401$	−13.4470	−	13.4470i	−0.671510	−	0.671510i	0.286554	−	0.958064i	$-0.407490\pi$
$401$	−13.4470	−	13.4470i	−0.671510	−	0.671510i	−0.958064	+	0.286554i	$0.907490\pi$
$402$	−6.95142	+	26.6181i	−0.346705	+	1.32759i
$403$	−6.20189	+	21.0664i	−0.308938	+	1.04939i
$404$	3.96240	+	2.22108i	0.197137	+	0.110503i
$405$	2.56603	−	2.56603i	0.127507	−	0.127507i
$406$	8.82113	−	33.7775i	0.437786	−	1.67635i
$407$	8.27141			0.409999
$408$	−0.363929	−	19.0993i	−0.0180172	−	0.945555i
$409$	−7.36333	+	7.36333i	−0.364093	+	0.364093i	−0.865317	−	0.501224i	$-0.832883\pi$
$409$	−7.36333	+	7.36333i	−0.364093	+	0.364093i	0.501224	+	0.865317i	$0.332883\pi$
$410$	−4.00682	−	6.83934i	−0.197883	−	0.337771i
$411$	16.0972	−	16.0972i	0.794018	−	0.794018i
$412$	−5.27453	+	9.40977i	−0.259857	+	0.463586i
$413$		−	5.69210i		−	0.280090i
$414$	−4.83982	+	2.83540i	−0.237864	+	0.139353i
$415$	3.48335			0.170991
$416$	0.147746	+	20.3955i	0.00724383	+	0.999974i
$417$	16.6316			0.814452
$418$	10.2325	−	5.99470i	0.500488	−	0.293210i
$419$			6.39826i			0.312576i	0.987712	+	0.156288i	$0.0499527\pi$
$419$			6.39826i			0.312576i	−0.987712	+	0.156288i	$0.950047\pi$
$420$	−5.77435	+	10.3015i	−0.281759	+	0.502659i
$421$	−5.02248	+	5.02248i	−0.244781	+	0.244781i	−0.818824	−	0.574044i	$-0.805374\pi$
$421$	−5.02248	+	5.02248i	−0.244781	+	0.244781i	0.574044	+	0.818824i	$0.305374\pi$
$422$	8.98899	+	15.3435i	0.437577	+	0.746911i
$423$	6.40439	−	6.40439i	0.311392	−	0.311392i
$424$	−0.470910	−	24.7138i	−0.0228694	−	1.20021i
$425$	5.12100			0.248405
$426$	−4.68565	+	17.9421i	−0.227020	+	0.869297i
$427$	33.8250	−	33.8250i	1.63691	−	1.63691i
$428$	28.4101	+	15.9249i	1.37326	+	0.769761i
$429$	−2.18630	+	7.42635i	−0.105556	+	0.358548i
$430$	−1.35907	+	5.20408i	−0.0655400	+	0.250963i
$431$	−5.23501	−	5.23501i	−0.252162	−	0.252162i	0.569695	−	0.821856i	$-0.307061\pi$
$431$	−5.23501	−	5.23501i	−0.252162	−	0.252162i	−0.821856	+	0.569695i	$0.807061\pi$
$432$	19.1735	−	11.7291i	0.922487	−	0.564315i
$433$		−	15.5290i		−	0.746278i	−0.927775	−	0.373139i	$-0.878281\pi$
$433$		−	15.5290i		−	0.746278i	0.927775	−	0.373139i	$-0.121719\pi$
$434$	−33.2745	+	19.4939i	−1.59723	+	0.935735i
$435$	5.14181	+	5.14181i	0.246531	+	0.246531i
$436$	−0.145284	−	0.515906i	−0.00695785	−	0.0247074i
$437$	−11.4595	−	11.4595i	−0.548184	−	0.548184i
$438$	−3.93776	+	15.0783i	−0.188154	+	0.720470i
$439$	17.1154			0.816874			0.408437	−	0.912786i	$-0.366074\pi$
$439$	17.1154			0.816874			0.408437	+	0.912786i	$0.366074\pi$
$440$	−4.60387	+	0.0877248i	−0.219481	+	0.00418212i
$441$		−	16.4450i		−	0.783097i
$442$	13.4645	−	22.3729i	0.640442	−	1.06417i
$443$		−	25.3075i		−	1.20239i	−0.799101	−	0.601197i	$-0.794691\pi$
$443$		−	25.3075i		−	1.20239i	0.799101	−	0.601197i	$-0.205309\pi$
$444$	3.63265	+	12.8996i	0.172398	+	0.612188i
$445$	3.22222			0.152748
$446$	−20.9478	−	5.47061i	−0.991908	−	0.259041i
$447$	−1.43207	−	1.43207i	−0.0677347	−	0.0677347i
$448$	−24.3435	+	26.2732i	−1.15012	+	1.24129i
$449$	−4.57419	−	4.57419i	−0.215869	−	0.215869i	0.590886	−	0.806755i	$-0.298778\pi$
$449$	−4.57419	−	4.57419i	−0.215869	−	0.215869i	−0.806755	+	0.590886i	$0.798778\pi$
$450$	0.901189	+	1.53826i	0.0424825	+	0.0725143i
$451$		−	9.12493i		−	0.429676i
$452$	1.90838	−	3.40455i	0.0897626	−	0.160137i
$453$	−3.37022	−	3.37022i	−0.158347	−	0.158347i
$454$	−1.84841	−	0.482720i	−0.0867502	−	0.0226552i
$455$	−14.1736	+	7.72630i	−0.664467	+	0.362214i
$456$	13.8429	+	13.3252i	0.648253	+	0.624011i
$457$	−14.0229	+	14.0229i	−0.655964	+	0.655964i	−0.954423	−	0.298458i	$-0.903528\pi$
$457$	−14.0229	+	14.0229i	−0.655964	+	0.655964i	0.298458	+	0.954423i	$0.403528\pi$
$458$	−25.7896	−	6.73506i	−1.20507	−	0.314709i
$459$	−28.7756			−1.34313
$460$	1.70571	+	6.05700i	0.0795291	+	0.282409i
$461$	−4.11173	+	4.11173i	−0.191502	+	0.191502i	−0.796345	−	0.604843i	$-0.793236\pi$
$461$	−4.11173	+	4.11173i	−0.191502	+	0.191502i	0.604843	+	0.796345i	$0.293236\pi$
$462$	−11.7300	+	6.87201i	−0.545729	+	0.319715i
$463$	28.1044	−	28.1044i	1.30612	−	1.30612i	0.381931	−	0.924191i	$-0.375259\pi$
$463$	28.1044	−	28.1044i	1.30612	−	1.30612i	0.924191	−	0.381931i	$-0.124741\pi$
$464$	11.5088	+	18.8134i	0.534282	+	0.873392i
$465$		−	8.03272i		−	0.372508i
$466$	10.8930	+	18.5936i	0.504609	+	0.861330i
$467$	−22.7594			−1.05318			−0.526590	−	0.850120i	$-0.676530\pi$
$467$	−22.7594			−1.05318			−0.526590	+	0.850120i	$0.676530\pi$
$468$	9.08992	+	0.107342i	0.420182	+	0.00496190i
$469$	−66.0384			−3.04937
$470$	−5.13608	−	8.76690i	−0.236910	−	0.404387i
$471$			18.1047i			0.834220i
$472$	2.59070	+	2.49382i	0.119247	+	0.114787i
$473$	−4.37822	+	4.37822i	−0.201311	+	0.201311i
$474$	16.7362	−	9.80488i	0.768718	−	0.450353i
$475$	−3.64223	+	3.64223i	−0.167117	+	0.167117i
$476$	44.1384	−	12.4298i	2.02308	−	0.569720i
$477$	−11.0169			−0.504431
$478$	17.2004	+	4.49195i	0.786727	+	0.205457i
$479$	−11.1803	+	11.1803i	−0.510840	+	0.510840i	−0.914784	−	0.403944i	$-0.867639\pi$
$479$	−11.1803	+	11.1803i	−0.510840	+	0.510840i	0.403944	+	0.914784i	$0.367639\pi$
$480$	−2.15875	−	7.14140i	−0.0985329	−	0.325959i
$481$	−5.17345	+	17.5730i	−0.235889	+	0.801259i
$482$	9.42569	+	2.46156i	0.429328	+	0.112121i
$483$	13.1366	+	13.1366i	0.597737	+	0.597737i
$484$	14.5668	+	8.16523i	0.662127	+	0.371147i
$485$		−	0.637981i		−	0.0289692i
$486$	−8.62951	−	14.7299i	−0.391442	−	0.668162i
$487$	18.0398	+	18.0398i	0.817459	+	0.817459i	0.985739	−	0.168280i	$-0.0538212\pi$
$487$	18.0398	+	18.0398i	0.817459	+	0.817459i	−0.168280	+	0.985739i	$0.553821\pi$
$488$	0.575725	+	30.2145i	0.0260618	+	1.36775i
$489$	11.8865	+	11.8865i	0.537525	+	0.537525i
$490$	−17.8499	−	4.66156i	−0.806374	−	0.210588i
$491$	12.1425			0.547983			0.273991	−	0.961732i	$-0.411656\pi$
$491$	12.1425			0.547983			0.273991	+	0.961732i	$0.411656\pi$
$492$	14.2307	−	4.00751i	0.641569	−	0.180672i
$493$		−	28.2352i		−	1.27165i
$494$	6.33597	+	25.4888i	0.285069	+	1.14680i
$495$			2.05232i			0.0922450i
$496$	5.70578	−	23.6852i	0.256197	−	1.06350i
$497$	−44.5136			−1.99671
$498$	−1.64164	+	6.28610i	−0.0735636	+	0.281687i
$499$	16.5596	+	16.5596i	0.741311	+	0.741311i	0.972830	−	0.231519i	$-0.0743697\pi$
$499$	16.5596	+	16.5596i	0.741311	+	0.741311i	−0.231519	+	0.972830i	$0.574370\pi$
$500$	1.92512	−	0.542133i	0.0860940	−	0.0242449i
$501$	−23.8769	−	23.8769i	−1.06674	−	1.06674i
$502$	−3.76901	+	2.20807i	−0.168219	+	0.0985511i
$503$			33.5270i			1.49490i	0.664320	+	0.747448i	$0.268721\pi$
$503$			33.5270i			1.49490i	−0.664320	+	0.747448i	$0.731279\pi$
$504$	11.5011	+	11.0710i	0.512301	+	0.493143i
$505$	−1.60600	−	1.60600i	−0.0714659	−	0.0714659i
$506$	−1.83038	+	7.00882i	−0.0813703	+	0.311580i
$507$	−14.4102	−	9.28979i	−0.639978	−	0.412574i
$508$	−10.2026	+	18.2015i	−0.452667	+	0.807559i
$509$	14.1742	−	14.1742i	0.628262	−	0.628262i	−0.319368	−	0.947631i	$-0.603471\pi$
$509$	14.1742	−	14.1742i	0.628262	−	0.628262i	0.947631	+	0.319368i	$0.103471\pi$
$510$	−2.41344	+	9.24143i	−0.106869	+	0.409217i
$511$	−37.4087			−1.65486
$512$	−1.29261	−	22.5905i	−0.0571257	−	0.998367i
$513$	20.4662	−	20.4662i	0.903606	−	0.903606i
$514$	13.3425	+	22.7747i	0.588513	+	1.00455i
$515$	3.81386	−	3.81386i	0.168059	−	0.168059i
$516$	−8.75085	−	4.90518i	−0.385235	−	0.215938i
$517$		−	11.6966i		−	0.514418i
$518$	−27.7567	+	16.2612i	−1.21956	+	0.714478i
$519$	−5.50395			−0.241597
$520$	2.69317	−	9.83600i	0.118103	−	0.431337i
$521$	23.9342			1.04858			0.524288	−	0.851541i	$-0.324331\pi$
$521$	23.9342			1.04858			0.524288	+	0.851541i	$0.324331\pi$
$522$	8.48136	−	4.96880i	0.371219	−	0.217478i
$523$			15.8127i			0.691441i	0.938337	+	0.345721i	$0.112366\pi$
$523$			15.8127i			0.691441i	−0.938337	+	0.345721i	$0.887634\pi$
$524$	−23.7042	−	13.2871i	−1.03552	−	0.580450i
$525$	4.17527	−	4.17527i	0.182224	−	0.182224i
$526$	11.6852	+	19.9458i	0.509499	+	0.869676i
$527$	−22.0550	+	22.0550i	−0.960730	+	0.960730i
$528$	2.01141	−	8.34955i	0.0875355	−	0.363368i
$529$	−13.1008			−0.569602
$530$	−3.12290	+	11.9581i	−0.135650	+	0.519425i
$531$	1.13329	−	1.13329i	0.0491807	−	0.0491807i
$532$	−22.5523	+	40.2333i	−0.977765	+	1.74433i
$533$	19.3863	+	5.70729i	0.839715	+	0.247210i
$534$	−1.51857	+	5.81486i	−0.0657151	+	0.251633i
$535$	−11.5149	−	11.5149i	−0.497832	−	0.497832i
$536$	28.9327	−	30.0567i	1.24970	−	1.29825i
$537$		−	17.3083i		−	0.746909i
$538$	−25.8124	+	15.1222i	−1.11285	+	0.651963i
$539$	−15.0172	−	15.0172i	−0.646836	−	0.646836i
$540$	−10.8175	+	3.04632i	−0.465512	+	0.131093i
$541$	−21.1871	−	21.1871i	−0.910906	−	0.910906i	0.0854374	−	0.996344i	$-0.472771\pi$
$541$	−21.1871	−	21.1871i	−0.910906	−	0.910906i	−0.996344	+	0.0854374i	$0.972771\pi$
$542$	1.98384	−	7.59644i	0.0852133	−	0.326295i
$543$	19.9617			0.856640
$544$	−13.6806	+	25.5349i	−0.586550	+	1.09480i
$545$			0.267986i			0.0114793i
$546$	−7.26323	−	29.2191i	−0.310838	−	1.25046i
$547$		−	34.2390i		−	1.46395i	−0.681330	−	0.731977i	$-0.738598\pi$
$547$		−	34.2390i		−	1.46395i	0.681330	−	0.731977i	$-0.261402\pi$
$548$	−33.2299	+	9.35785i	−1.41951	+	0.399748i
$549$	13.4691			0.574846
$550$	2.22764	+	0.581758i	0.0949870	+	0.0248062i
$551$	20.0818	+	20.0818i	0.855515	+	0.855515i
$552$	−11.7344	+	0.223594i	−0.499449	+	0.00951680i
$553$	32.9236	+	32.9236i	1.40006	+	1.40006i
$554$	−9.17019	−	15.6528i	−0.389604	−	0.665024i
$555$		−	6.70067i		−	0.284428i
$556$	−22.0007	−	12.3322i	−0.933038	−	0.523003i
$557$	−10.4107	−	10.4107i	−0.441117	−	0.441117i	0.451271	−	0.892387i	$-0.350971\pi$
$557$	−10.4107	−	10.4107i	−0.441117	−	0.441117i	−0.892387	+	0.451271i	$0.850971\pi$
$558$	−10.5062	−	2.74372i	−0.444761	−	0.116151i
$559$	−6.56332	−	12.0401i	−0.277599	−	0.509243i
$560$	15.2769	−	9.34540i	0.645568	−	0.394915i
$561$	−7.77486	+	7.77486i	−0.328255	+	0.328255i
$562$	−36.0686	−	9.41947i	−1.52146	−	0.397336i
$563$	21.8541			0.921043			0.460521	−	0.887649i	$-0.347662\pi$
$563$	21.8541			0.921043			0.460521	+	0.887649i	$0.347662\pi$
$564$	18.2414	−	5.13696i	0.768102	−	0.216305i
$565$	−1.37990	+	1.37990i	−0.0580526	+	0.0580526i
$566$	29.9313	−	17.5352i	1.25811	−	0.737061i
$567$	−11.4885	+	11.4885i	−0.482473	+	0.482473i
$568$	19.5023	−	20.2599i	0.818297	−	0.850087i
$569$		−	18.8406i		−	0.789838i	−0.918716	−	0.394919i	$-0.870773\pi$
$569$		−	18.8406i		−	0.789838i	0.918716	−	0.394919i	$-0.129227\pi$
$570$	−4.85631	−	8.28934i	−0.203408	−	0.347202i
$571$	13.5630			0.567592			0.283796	−	0.958885i	$-0.408406\pi$
$571$	13.5630			0.567592			0.283796	+	0.958885i	$0.408406\pi$
$572$	8.39870	−	8.20265i	0.351167	−	0.342970i
$573$	9.70983			0.405634
$574$	17.9392	+	30.6209i	0.748769	+	1.27809i
$575$		−	3.14629i		−	0.131209i
$576$	−10.0777	+	0.384194i	−0.419906	+	0.0160081i
$577$	21.2972	−	21.2972i	0.886615	−	0.886615i	−0.107581	−	0.994196i	$-0.534311\pi$
$577$	21.2972	−	21.2972i	0.886615	−	0.886615i	0.994196	+	0.107581i	$0.0343105\pi$
$578$	11.2562	−	6.59444i	0.468197	−	0.274293i
$579$	9.32963	−	9.32963i	0.387726	−	0.387726i
$580$	−2.98911	−	10.6144i	−0.124116	−	0.440737i
$581$	−15.5956			−0.647013
$582$	1.15131	+	0.300669i	0.0477233	+	0.0124631i
$583$	−10.0604	+	10.0604i	−0.416659	+	0.416659i
$584$	16.3895	−	17.0262i	0.678201	−	0.704548i
$585$	−4.36025	−	1.28365i	−0.180274	−	0.0530723i
$586$	31.5136	+	8.22990i	1.30181	+	0.339974i
$587$	2.22161	+	2.22161i	0.0916957	+	0.0916957i	0.751467	−	0.659771i	$-0.229347\pi$
$587$	2.22161	+	2.22161i	0.0916957	+	0.0916957i	−0.659771	+	0.751467i	$0.729347\pi$
$588$	16.8246	−	30.0152i	0.693836	−	1.23781i
$589$		−	31.3725i		−	1.29268i
$590$	−0.908858	−	1.55135i	−0.0374171	−	0.0638681i
$591$	−12.1601	−	12.1601i	−0.500198	−	0.500198i
$592$	4.75960	−	19.7575i	0.195618	−	0.812030i
$593$	21.3821	+	21.3821i	0.878059	+	0.878059i	0.993334	−	0.115274i	$-0.0367747\pi$
$593$	21.3821	+	21.3821i	0.878059	+	0.878059i	−0.115274	+	0.993334i	$0.536775\pi$
$594$	−12.5174	−	3.26898i	−0.513596	−	0.134128i
$595$	−22.9276			−0.939940
$596$	0.832512	+	2.95626i	0.0341010	+	0.121093i
$597$		−	17.5403i		−	0.717878i
$598$	−13.7457	−	8.27247i	−0.562104	−	0.338286i
$599$		−	10.9689i		−	0.448178i	−0.974569	−	0.224089i	$-0.928059\pi$
$599$		−	10.9689i		−	0.448178i	0.974569	−	0.224089i	$-0.0719406\pi$
$600$	0.0710659	+	3.72960i	0.00290125	+	0.152260i
$601$	−7.98288			−0.325628			−0.162814	−	0.986657i	$-0.552057\pi$
$601$	−7.98288			−0.325628			−0.162814	+	0.986657i	$0.552057\pi$
$602$	6.08477	−	23.2996i	0.247997	−	0.949619i
$603$	−13.1482	−	13.1482i	−0.535436	−	0.535436i
$604$	1.95922	+	6.95722i	0.0797196	+	0.283085i
$605$	−5.90405	−	5.90405i	−0.240034	−	0.240034i
$606$	3.65508	−	2.14133i	0.148478	−	0.0869854i
$607$		−	8.03050i		−	0.325948i	−0.986630	−	0.162974i	$-0.947891\pi$
$607$		−	8.03050i		−	0.325948i	0.986630	−	0.162974i	$-0.0521086\pi$
$608$	−8.43120	−	27.8914i	−0.341930	−	1.13115i
$609$	−23.0208	−	23.0208i	−0.932849	−	0.932849i
$610$	3.81799	−	14.6197i	0.154586	−	0.591933i
$611$	24.8500	+	7.31580i	1.00533	+	0.295966i
$612$	11.2627	+	6.31316i	0.455268	+	0.255194i
$613$	−16.8379	+	16.8379i	−0.680078	+	0.680078i	−0.960018	−	0.279939i	$-0.909686\pi$
$613$	−16.8379	+	16.8379i	−0.680078	+	0.680078i	0.279939	+	0.960018i	$0.409686\pi$
$614$	3.39514	−	13.0005i	0.137017	−	0.524659i
$615$	−7.39211			−0.298078
$616$	20.6123	−	0.392759i	0.830494	−	0.0158247i
$617$	−29.8466	+	29.8466i	−1.20158	+	1.20158i	−0.227894	+	0.973686i	$0.573184\pi$
$617$	−29.8466	+	29.8466i	−1.20158	+	1.20158i	−0.973686	+	0.227894i	$0.926816\pi$
$618$	5.08514	+	8.67995i	0.204554	+	0.349159i
$619$	−14.7740	+	14.7740i	−0.593815	+	0.593815i	−0.938660	−	0.344844i	$-0.887932\pi$
$619$	−14.7740	+	14.7740i	−0.593815	+	0.593815i	0.344844	+	0.938660i	$0.387932\pi$
$620$	−5.95621	+	10.6259i	−0.239207	+	0.426746i
$621$			17.6795i			0.709452i
$622$	−10.0231	+	5.87200i	−0.401888	+	0.235446i
$623$	−14.4264			−0.577982
$624$	16.4809	+	9.49565i	0.659765	+	0.380130i
$625$	−1.00000			−0.0400000
$626$	−21.4864	+	12.5878i	−0.858768	+	0.503108i
$627$		−	11.0595i		−	0.441674i
$628$	13.4245	−	23.9494i	0.535697	−	0.955685i
$629$	−18.3977	+	18.3977i	−0.733563	+	0.733563i
$630$	−4.03478	−	6.88706i	−0.160749	−	0.274387i
$631$	10.6634	−	10.6634i	0.424502	−	0.424502i	−0.462249	−	0.886750i	$-0.652957\pi$
$631$	10.6634	−	10.6634i	0.424502	−	0.424502i	0.886750	+	0.462249i	$0.152957\pi$
$632$	−29.4093	+	0.560383i	−1.16984	+	0.0222908i
$633$	16.5836			0.659139
$634$	−4.54092	+	17.3879i	−0.180343	+	0.690562i
$635$	7.37721	−	7.37721i	0.292756	−	0.292756i
$636$	−20.1079	−	11.2712i	−0.797331	−	0.446934i
$637$	41.2973	−	22.5120i	1.63626	−	0.891958i
$638$	3.20758	−	12.2823i	0.126989	−	0.486263i
$639$	−8.86263	−	8.86263i	−0.350600	−	0.350600i
$640$	−2.43965	+	11.0475i	−0.0964358	+	0.436692i
$641$			39.2397i			1.54987i	0.632038	+	0.774937i	$0.282219\pi$
$641$			39.2397i			1.54987i	−0.632038	+	0.774937i	$0.717781\pi$
$642$	26.2067	−	15.3531i	1.03429	−	0.605940i
$643$	−1.12070	−	1.12070i	−0.0441961	−	0.0441961i	0.684663	−	0.728859i	$-0.259949\pi$
$643$	−1.12070	−	1.12070i	−0.0441961	−	0.0441961i	−0.728859	+	0.684663i	$0.759949\pi$
$644$	−7.63676	−	27.1182i	−0.300930	−	1.06861i
$645$	3.54680	+	3.54680i	0.139655	+	0.139655i
$646$	−9.42590	+	36.0933i	−0.370857	+	1.42007i
$647$	7.85583			0.308845			0.154422	−	0.988005i	$-0.450648\pi$
$647$	7.85583			0.308845			0.154422	+	0.988005i	$0.450648\pi$
$648$	−0.195543	−	10.2622i	−0.00768164	−	0.403139i
$649$		−	2.06979i		−	0.0812462i
$650$	−2.62927	+	4.36886i	−0.103129	+	0.171361i
$651$			35.9639i			1.40953i
$652$	−6.91000	−	24.5375i	−0.270616	−	0.960962i
$653$	40.0654			1.56788			0.783940	−	0.620836i	$-0.213207\pi$
$653$	40.0654			1.56788			0.783940	+	0.620836i	$0.213207\pi$
$654$	−0.483611	−	0.126297i	−0.0189107	−	0.00493860i
$655$	9.60753	+	9.60753i	0.375397	+	0.375397i
$656$	−21.7963	−	5.25074i	−0.851003	−	0.205007i
$657$	−7.44804	−	7.44804i	−0.290576	−	0.290576i
$658$	22.9951	+	39.2509i	0.896443	+	1.53016i
$659$			32.2931i			1.25796i	0.777422	+	0.628980i	$0.216527\pi$
$659$			32.2931i			1.25796i	−0.777422	+	0.628980i	$0.783473\pi$
$660$	−2.09969	+	3.74586i	−0.0817305	+	0.145807i
$661$	−7.34291	−	7.34291i	−0.285606	−	0.285606i	0.549734	−	0.835340i	$-0.314729\pi$
$661$	−7.34291	−	7.34291i	−0.285606	−	0.285606i	−0.835340	+	0.549734i	$0.814729\pi$
$662$	−20.3356	−	5.31071i	−0.790364	−	0.206407i
$663$	−11.6552	−	21.3809i	−0.452649	−	0.830366i
$664$	6.83271	−	7.09816i	0.265161	−	0.275462i
$665$	16.3069	−	16.3069i	0.632355	−	0.632355i
$666$	−8.76394	−	2.28874i	−0.339596	−	0.0886868i
$667$	−17.3474			−0.671695
$668$	13.8804	+	49.2896i	0.537050	+	1.90707i
$669$	−14.2768	+	14.2768i	−0.551973	+	0.551973i
$670$	−17.9984	+	10.5444i	−0.695339	+	0.407364i
$671$	12.2996	−	12.2996i	0.474821	−	0.474821i
$672$	9.66509	+	31.9733i	0.372839	+	1.23340i
$673$			28.2213i			1.08785i	0.839134	+	0.543925i	$0.183062\pi$
$673$			28.2213i			1.08785i	−0.839134	+	0.543925i	$0.816938\pi$
$674$	−16.1461	−	27.5602i	−0.621926	−	1.06158i
$675$	5.61914			0.216281
$676$	12.1738	+	22.9738i	0.468225	+	0.883609i
$677$	25.9332			0.996695			0.498347	−	0.866977i	$-0.333940\pi$
$677$	25.9332			0.996695			0.498347	+	0.866977i	$0.333940\pi$
$678$	−1.83986	−	3.14050i	−0.0706593	−	0.120610i
$679$			2.85635i			0.109617i
$680$	10.0450	−	10.4353i	0.385209	−	0.400174i
$681$	−1.25977	+	1.25977i	−0.0482744	+	0.0482744i
$682$	−12.0994	+	7.08845i	−0.463312	+	0.271431i
$683$	0.268824	−	0.268824i	0.0102863	−	0.0102863i	−0.701945	−	0.712231i	$-0.747685\pi$
$683$	0.268824	−	0.268824i	0.0102863	−	0.0102863i	0.712231	+	0.701945i	$0.247685\pi$
$684$	−12.5006	+	3.52028i	−0.477971	+	0.134601i
$685$	17.2612			0.659516
$686$	37.0334	+	9.67141i	1.41394	+	0.369256i
$687$	−17.5767	+	17.5767i	−0.670593	+	0.670593i
$688$	7.93870	+	12.9774i	0.302660	+	0.494759i
$689$	−15.0814	−	27.6661i	−0.574554	−	1.05400i
$690$	5.67784	+	1.48279i	0.216152	+	0.0564489i
$691$	−25.6651	−	25.6651i	−0.976347	−	0.976347i	0.0233799	−	0.999727i	$-0.492557\pi$
$691$	−25.6651	−	25.6651i	−0.976347	−	0.976347i	−0.999727	+	0.0233799i	$0.992557\pi$
$692$	7.28078	+	4.08115i	0.276774	+	0.155142i
$693$		−	9.18860i		−	0.349046i
$694$	−3.40802	−	5.81724i	−0.129367	−	0.220819i
$695$	8.91708	+	8.91708i	0.338244	+	0.338244i
$696$	20.5635	−	0.391829i	0.779458	−	0.0148523i
$697$	20.2961	+	20.2961i	0.768769	+	0.768769i
$698$	−38.5201	−	10.0597i	−1.45801	−	0.380764i
$699$	20.0963			0.760113
$700$	−8.61910	+	2.42722i	−0.325771	+	0.0917404i
$701$		−	23.7249i		−	0.896075i	−0.894015	−	0.448038i	$-0.852123\pi$
$701$		−	23.7249i		−	0.896075i	0.894015	−	0.448038i	$-0.147877\pi$
$702$	14.7743	−	24.5492i	0.557618	−	0.926551i
$703$		−	26.1701i		−	0.987024i
$704$	−8.85189	+	9.55357i	−0.333618	+	0.360064i
$705$	−9.47546			−0.356866
$706$	7.16454	−	27.4342i	0.269641	−	1.03250i
$707$	7.19033	+	7.19033i	0.270420	+	0.270420i
$708$	3.22792	−	0.909013i	0.121313	−	0.0341628i
$709$	24.7992	+	24.7992i	0.931352	+	0.931352i	0.997791	−	0.0664387i	$-0.0211637\pi$
$709$	24.7992	+	24.7992i	0.931352	+	0.931352i	−0.0664387	+	0.997791i	$0.521164\pi$
$710$	−12.1319	+	7.10749i	−0.455304	+	0.266739i
$711$			13.1101i			0.491669i
$712$	6.32049	−	6.56604i	0.236870	−	0.246073i
$713$	13.5504	+	13.5504i	0.507465	+	0.507465i
$714$	10.8054	−	41.3755i	0.404381	−	1.54844i
$715$	−5.15386	+	2.80947i	−0.192743	+	0.105068i
$716$	−12.8340	+	22.8959i	−0.479630	+	0.855661i
$717$	11.7228	−	11.7228i	0.437795	−	0.437795i
$718$	−1.30135	+	4.98309i	−0.0485661	+	0.185967i
$719$	23.0868			0.860993			0.430496	−	0.902592i	$-0.358338\pi$
$719$	23.0868			0.860993			0.430496	+	0.902592i	$0.358338\pi$
$720$	4.90229	+	1.18096i	0.182698	+	0.0440119i
$721$	−17.0753	+	17.0753i	−0.635918	+	0.635918i
$722$	−5.38422	−	9.19046i	−0.200380	−	0.342034i
$723$	6.42400	−	6.42400i	0.238911	−	0.238911i
$724$	−26.4059	−	14.8015i	−0.981368	−	0.550093i
$725$			5.51361i			0.204770i
$726$	13.4370	−	7.87205i	0.498694	−	0.292159i
$727$	25.5175			0.946390			0.473195	−	0.880958i	$-0.343101\pi$
$727$	25.5175			0.946390			0.473195	+	0.880958i	$0.343101\pi$
$728$	−12.0578	+	44.0375i	−0.446891	+	1.63214i
$729$	−26.8071			−0.992857
$730$	−10.1955	+	5.97305i	−0.377354	+	0.221072i
$731$		−	19.4765i		−	0.720364i
$732$	24.5835	+	13.7800i	0.908633	+	0.509323i
$733$	−7.95833	+	7.95833i	−0.293948	+	0.293948i	−0.838638	−	0.544690i	$-0.816647\pi$
$733$	−7.95833	+	7.95833i	−0.293948	+	0.293948i	0.544690	+	0.838638i	$0.316647\pi$
$734$	−24.1403	−	41.2057i	−0.891035	−	1.52093i
$735$	−12.1654	+	12.1654i	−0.448728	+	0.448728i
$736$	15.6884	+	8.40522i	0.578282	+	0.309820i
$737$	−24.0132			−0.884537
$738$	−2.52491	+	9.66828i	−0.0929432	+	0.355894i
$739$	−17.3469	+	17.3469i	−0.638117	+	0.638117i	−0.950091	−	0.311974i	$-0.899010\pi$
$739$	−17.3469	+	17.3469i	−0.638117	+	0.638117i	0.311974	+	0.950091i	$0.399010\pi$
$740$	−4.96851	+	8.86383i	−0.182646	+	0.325841i
$741$	23.4964	+	6.91729i	0.863162	+	0.254113i
$742$	13.9817	−	53.5383i	0.513286	−	1.96545i
$743$	1.66264	+	1.66264i	0.0609964	+	0.0609964i	0.736947	−	0.675951i	$-0.236267\pi$
$743$	1.66264	+	1.66264i	0.0609964	+	0.0609964i	−0.675951	+	0.736947i	$0.736267\pi$
$744$	−16.3686	−	15.7565i	−0.600101	−	0.577660i
$745$		−	1.53562i		−	0.0562608i
$746$	−16.9426	+	9.92583i	−0.620314	+	0.363410i
$747$	−3.10506	−	3.10506i	−0.113608	−	0.113608i
$748$	16.0498	−	4.51979i	0.586839	−	0.165260i
$749$	51.5541	+	51.5541i	1.88375	+	1.88375i
$750$	0.471282	−	1.80461i	0.0172088	−	0.0658952i
$751$	23.6951			0.864646			0.432323	−	0.901719i	$-0.357694\pi$
$751$	23.6951			0.864646			0.432323	+	0.901719i	$0.357694\pi$
$752$	−27.9393	−	6.73058i	−1.01884	−	0.245439i
$753$			4.07363i			0.148451i
$754$	24.0882	+	14.4968i	0.877239	+	0.527941i
$755$		−	3.61391i		−	0.131524i
$756$	48.4319	−	13.6389i	1.76145	−	0.496042i
$757$	−11.4607			−0.416547			−0.208273	−	0.978071i	$-0.566784\pi$
$757$	−11.4607			−0.416547			−0.208273	+	0.978071i	$0.566784\pi$
$758$	−5.08104	−	1.32693i	−0.184552	−	0.0481964i
$759$	4.77680	+	4.77680i	0.173387	+	0.173387i
$760$	0.277555	+	14.5663i	0.0100680	+	0.528375i
$761$	12.4446	+	12.4446i	0.451117	+	0.451117i	0.895725	−	0.444608i	$-0.146657\pi$
$761$	12.4446	+	12.4446i	0.451117	+	0.451117i	−0.444608	+	0.895725i	$0.646657\pi$
$762$	9.83627	+	16.7898i	0.356330	+	0.608229i
$763$		−	1.19982i		−	0.0434364i
$764$	−12.8444	−	7.19978i	−0.464695	−	0.260479i
$765$	−4.56487	−	4.56487i	−0.165043	−	0.165043i
$766$	9.33884	+	2.43888i	0.337426	+	0.0881202i
$767$	4.39735	+	1.29457i	0.158779	+	0.0467443i
$768$	−18.7868	−	9.60913i	−0.677909	−	0.346740i
$769$	−18.9433	+	18.9433i	−0.683113	+	0.683113i	−0.960700	−	0.277587i	$-0.910465\pi$
$769$	−18.9433	+	18.9433i	−0.683113	+	0.683113i	0.277587	+	0.960700i	$0.410465\pi$
$770$	−9.97354	−	2.60463i	−0.359421	−	0.0938643i
$771$	24.6154			0.886500
$772$	−19.2594	+	5.42363i	−0.693160	+	0.195201i
$773$	2.69603	−	2.69603i	0.0969694	−	0.0969694i	−0.656958	−	0.753927i	$-0.728157\pi$
$773$	2.69603	−	2.69603i	0.0969694	−	0.0969694i	0.753927	+	0.656958i	$0.228157\pi$
$774$	5.85040	−	3.42745i	0.210288	−	0.123197i
$775$	4.30677	−	4.30677i	0.154704	−	0.154704i
$776$	−1.30004	−	1.25142i	−0.0466687	−	0.0449234i
$777$			30.0000i			1.07625i
$778$	−7.27012	−	12.4095i	−0.260647	−	0.444904i
$779$	−28.8706			−1.03440
$780$	−6.64497	−	6.80378i	−0.237928	−	0.243615i
$781$	−16.1862			−0.579189
$782$	−11.5181	−	19.6606i	−0.411887	−	0.703060i
$783$		−	30.9817i		−	1.10720i
$784$	−44.5122	+	27.2295i	−1.58972	+	0.972484i
$785$	−9.70690	+	9.70690i	−0.346454	+	0.346454i
$786$	−21.8657	+	12.8100i	−0.779925	+	0.456918i
$787$	−11.0812	+	11.0812i	−0.395004	+	0.395004i	−0.876467	−	0.481463i	$-0.840106\pi$
$787$	−11.0812	+	11.0812i	−0.395004	+	0.395004i	0.481463	+	0.876467i	$0.340106\pi$
$788$	7.06905	+	25.1023i	0.251825	+	0.894232i
$789$	21.5578			0.767478
$790$	14.2301	+	3.71624i	0.506284	+	0.132218i
$791$	6.17803	−	6.17803i	0.219665	−	0.219665i
$792$	4.18210	+	4.02570i	0.148604	+	0.143047i
$793$	18.4381	+	33.8240i	0.654757	+	1.20113i
$794$	−9.33664	−	2.43830i	−0.331345	−	0.0865321i
$795$	8.14992	+	8.14992i	0.289048	+	0.289048i
$796$	−13.0061	+	23.2029i	−0.460988	+	0.822403i
$797$			39.5895i			1.40233i	0.712998	+	0.701166i	$0.247337\pi$
$797$			39.5895i			1.40233i	−0.712998	+	0.701166i	$0.752663\pi$
$798$	21.7425	+	37.1128i	0.769677	+	1.31378i
$799$	26.0162	+	26.0162i	0.920388	+	0.920388i
$800$	2.67147	−	4.98631i	0.0944506	−	0.176293i
$801$	−2.87229	−	2.87229i	−0.101487	−	0.101487i
$802$	26.0212	+	6.79555i	0.918842	+	0.239959i
$803$	−13.6027			−0.480030
$804$	−10.5462	−	37.4495i	−0.371934	−	1.32074i
$805$			14.0865i			0.496484i
$806$	−7.49199	−	30.1393i	−0.263894	−	1.06161i
$807$			27.8986i			0.982077i
$808$	−6.42282	+	0.122384i	−0.225954	+	0.00430546i
$809$	4.29089			0.150860			0.0754298	−	0.997151i	$-0.475967\pi$
$809$	4.29089			0.150860			0.0754298	+	0.997151i	$0.475967\pi$
$810$	−1.29676	+	4.96552i	−0.0455636	+	0.174470i
$811$	−35.9727	−	35.9727i	−1.26317	−	1.26317i	−0.949546	−	0.313626i	$-0.898456\pi$
$811$	−35.9727	−	35.9727i	−1.26317	−	1.26317i	−0.313626	−	0.949546i	$-0.601544\pi$
$812$	13.3828	+	47.5223i	0.469642	+	1.66771i
$813$	−5.17729	−	5.17729i	−0.181575	−	0.181575i
$814$	−10.0930	+	5.91299i	−0.353760	+	0.207250i
$815$			12.7459i			0.446471i
$816$	14.0976	+	23.0453i	0.493514	+	0.806748i
$817$	13.8524	+	13.8524i	0.484632	+	0.484632i
$818$	3.72113	−	14.2488i	0.130106	−	0.498197i
$819$	19.5216	+	5.74711i	0.682139	+	0.200820i
$820$	9.77848	+	5.48120i	0.341479	+	0.191412i
$821$	−12.6441	+	12.6441i	−0.441283	+	0.441283i	−0.892443	−	0.451160i	$-0.851010\pi$
$821$	−12.6441	+	12.6441i	−0.441283	+	0.441283i	0.451160	+	0.892443i	$0.351010\pi$
$822$	−8.13488	+	31.1497i	−0.283736	+	1.08647i
$823$	32.9063			1.14704			0.573520	−	0.819192i	$-0.305577\pi$
$823$	32.9063			1.14704			0.573520	+	0.819192i	$0.305577\pi$
$824$	−0.290634	−	15.2527i	−0.0101247	−	0.531353i
$825$	1.51823	−	1.51823i	0.0528580	−	0.0528580i
$826$	4.06911	+	6.94567i	0.141583	+	0.241671i
$827$	−5.90778	+	5.90778i	−0.205434	+	0.205434i	−0.802323	−	0.596890i	$-0.796403\pi$
$827$	−5.90778	+	5.90778i	−0.205434	+	0.205434i	0.596890	+	0.802323i	$0.296403\pi$
$828$	3.87874	−	6.91969i	0.134796	−	0.240476i
$829$		−	56.1353i		−	1.94966i	−0.222950	−	0.974830i	$-0.571569\pi$
$829$		−	56.1353i		−	1.94966i	0.222950	−	0.974830i	$-0.428431\pi$
$830$	−4.25049	+	2.49014i	−0.147537	+	0.0864342i
$831$	−16.9179			−0.586876
$832$	−14.7605	−	24.7816i	−0.511727	−	0.859148i
$833$	66.8038			2.31462
$834$	−20.2943	+	11.8894i	−0.702736	+	0.411697i
$835$		−	25.6034i		−	0.886041i
$836$	−8.20056	+	14.6298i	−0.283622	+	0.505983i
$837$	−24.2003	+	24.2003i	−0.836486	+	0.836486i
$838$	−4.57393	−	7.80735i	−0.158004	−	0.269700i
$839$	29.0414	−	29.0414i	1.00262	−	1.00262i	0.00262283	−	0.999997i	$-0.499165\pi$
$839$	29.0414	−	29.0414i	1.00262	−	1.00262i	0.999997	−	0.00262283i	$-0.000834873\pi$
$840$	−0.318174	−	16.6980i	−0.0109781	−	0.576137i
$841$	1.39984			0.0482704
$842$	2.53815	−	9.71900i	0.0874706	−	0.334939i
$843$	−24.5823	+	24.5823i	−0.846658	+	0.846658i
$844$	−21.9373	−	12.2966i	−0.755111	−	0.423268i
$845$	−2.74531	−	12.7068i	−0.0944415	−	0.437128i
$846$	−3.23652	+	12.3931i	−0.111274	+	0.426085i
$847$	26.4334	+	26.4334i	0.908264	+	0.908264i
$848$	18.2418	+	29.8198i	0.626425	+	1.02402i
$849$		−	32.3504i		−	1.11026i
$850$	−6.24880	+	3.66085i	−0.214332	+	0.125566i
$851$	11.3033	+	11.3033i	0.387473	+	0.387473i
$852$	−7.10871	−	25.2431i	−0.243540	−	0.864814i
$853$	−40.0582	−	40.0582i	−1.37157	−	1.37157i	−0.858123	−	0.513444i	$-0.828369\pi$
$853$	−40.0582	−	40.0582i	−1.37157	−	1.37157i	−0.513444	−	0.858123i	$-0.671631\pi$
$854$	−17.0938	+	65.4548i	−0.584937	+	2.23982i
$855$	6.49339			0.222069
$856$	−46.0512	+	0.877486i	−1.57400	+	0.0299918i
$857$			31.1973i			1.06568i	0.846216	+	0.532840i	$0.178875\pi$
$857$			31.1973i			1.06568i	−0.846216	+	0.532840i	$0.821125\pi$
$858$	−2.64109	−	10.6248i	−0.0901653	−	0.362724i
$859$			33.0567i			1.12788i	0.825815	+	0.563940i	$0.190715\pi$
$859$			33.0567i			1.12788i	−0.825815	+	0.563940i	$0.809285\pi$
$860$	−2.06187	−	7.32173i	−0.0703092	−	0.249669i
$861$	33.0957			1.12790
$862$	10.1303	+	2.64556i	0.345038	+	0.0901081i
$863$	28.9412	+	28.9412i	0.985169	+	0.985169i	0.999892	−	0.0147222i	$-0.00468638\pi$
$863$	28.9412	+	28.9412i	0.985169	+	0.985169i	−0.0147222	+	0.999892i	$0.504686\pi$
$864$	−15.0113	+	28.0188i	−0.510696	+	0.953217i
$865$	−2.95097	−	2.95097i	−0.100336	−	0.100336i
$866$	11.1013	+	18.9490i	0.377236	+	0.643913i
$867$		−	12.1660i		−	0.413178i
$868$	26.6670	−	47.5740i	0.905137	−	1.61477i
$869$	11.9718	+	11.9718i	0.406117	+	0.406117i
$870$	−9.94992	−	2.59846i	−0.337334	−	0.0880961i
$871$	15.0193	−	51.0171i	0.508910	−	1.72865i
$872$	0.546086	+	0.525664i	0.0184928	+	0.0178012i
$873$	−0.568697	+	0.568697i	−0.0192475	+	0.0192475i
$874$	22.1754	+	5.79118i	0.750092	+	0.195890i
$875$	4.47717			0.151356
$876$	−5.97407	−	21.2140i	−0.201845	−	0.716754i
$877$	32.3445	−	32.3445i	1.09220	−	1.09220i	0.0969030	−	0.995294i	$-0.469106\pi$
$877$	32.3445	−	32.3445i	1.09220	−	1.09220i	0.995294	−	0.0969030i	$-0.0308937\pi$
$878$	−20.8847	+	12.2353i	−0.704826	+	0.412922i
$879$	21.4778	−	21.4778i	0.724429	−	0.724429i
$880$	5.55507	−	3.39822i	0.187261	−	0.114554i
$881$			47.9699i			1.61615i	0.589082	+	0.808073i	$0.299489\pi$
$881$			47.9699i			1.61615i	−0.589082	+	0.808073i	$0.700511\pi$
$882$	11.7561	+	20.0667i	0.395848	+	0.675682i
$883$	−5.54312			−0.186541			−0.0932704	−	0.995641i	$-0.529732\pi$
$883$	−5.54312			−0.186541			−0.0932704	+	0.995641i	$0.529732\pi$
$884$	−0.436051	+	36.9255i	−0.0146660	+	1.24194i
$885$	−1.67673			−0.0563628
$886$	18.0916	+	30.8809i	0.607798	+	1.03746i
$887$		−	42.2799i		−	1.41962i	−0.704394	−	0.709810i	$-0.748781\pi$
$887$		−	42.2799i		−	1.41962i	0.704394	−	0.709810i	$-0.251219\pi$
$888$	−13.6542	−	13.1436i	−0.458205	−	0.441070i
$889$	−33.0290	+	33.0290i	−1.10776	+	1.10776i
$890$	−3.93185	+	2.30347i	−0.131796	+	0.0772124i
$891$	−4.17752	+	4.17752i	−0.139952	+	0.139952i
$892$	29.4719	−	8.29959i	0.986793	−	0.277891i
$893$	−37.0073			−1.23840
$894$	2.77120	+	0.723711i	0.0926829	+	0.0242045i
$895$	9.27992	−	9.27992i	0.310194	−	0.310194i
$896$	10.9227	−	49.4617i	0.364903	−	1.65240i
$897$	−13.1362	+	7.16082i	−0.438606	+	0.239093i
$898$	8.85152	+	2.31161i	0.295379	+	0.0771394i
$899$	−23.7458	−	23.7458i	−0.791968	−	0.791968i
$900$	−2.19931	−	1.23280i	−0.0733105	−	0.0410933i
$901$		−	44.7536i		−	1.49096i
$902$	6.52314	+	11.1345i	0.217197	+	0.370739i
$903$	−15.8796	−	15.8796i	−0.528441	−	0.528441i
$904$	0.105154	+	5.51858i	0.00349738	+	0.183545i
$905$	10.7026	+	10.7026i	0.355765	+	0.355765i
$906$	6.52172	+	1.70317i	0.216670	+	0.0565841i
$907$	35.5858			1.18161			0.590804	−	0.806815i	$-0.298811\pi$
$907$	35.5858			1.18161			0.590804	+	0.806815i	$0.298811\pi$
$908$	2.60057	−	0.732346i	0.0863029	−	0.0243037i
$909$			2.86318i			0.0949656i
$910$	11.7717	−	19.5601i	0.390228	−	0.648412i
$911$		−	50.3196i		−	1.66716i	−0.552396	−	0.833582i	$-0.686286\pi$
$911$		−	50.3196i		−	1.66716i	0.552396	−	0.833582i	$-0.313714\pi$
$912$	−26.4173	−	6.36395i	−0.874765	−	0.210731i
$913$	−5.67093			−0.187680
$914$	7.08661	−	27.1357i	0.234404	−	0.897571i
$915$	−9.96391	−	9.96391i	−0.329397	−	0.329397i
$916$	36.2840	−	10.2179i	1.19886	−	0.337610i
$917$	−43.0146	−	43.0146i	−1.42047	−	1.42047i
$918$	35.1129	−	20.5708i	1.15890	−	0.678939i
$919$			17.7610i			0.585882i	0.956131	+	0.292941i	$0.0946339\pi$
$919$			17.7610i			0.585882i	−0.956131	+	0.292941i	$0.905366\pi$
$920$	−6.41132	−	6.17156i	−0.211375	−	0.203470i
$921$	−8.86040	−	8.86040i	−0.291960	−	0.291960i
$922$	2.07790	−	7.95661i	0.0684320	−	0.262037i
$923$	10.1239	−	34.3884i	0.333231	−	1.13191i
$924$	9.40069	−	16.7709i	0.309260	−	0.551721i
$925$	3.59259	−	3.59259i	0.118124	−	0.118124i
$926$	−14.2028	+	54.3848i	−0.466733	+	1.78720i
$927$	−6.79937			−0.223321
$928$	−27.4925	−	14.7294i	−0.902487	−	0.483517i
$929$	19.9532	−	19.9532i	0.654642	−	0.654642i	−0.299465	−	0.954107i	$-0.596808\pi$
$929$	19.9532	−	19.9532i	0.654642	−	0.654642i	0.954107	+	0.299465i	$0.0968082\pi$
$930$	5.74235	+	9.80176i	0.188299	+	0.321412i
$931$	−47.5132	+	47.5132i	−1.55718	+	1.55718i
$932$	−26.5840	−	14.9013i	−0.870787	−	0.488109i
$933$			10.8331i			0.354661i
$934$	27.7717	−	16.2700i	0.908717	−	0.532371i
$935$	−8.33704			−0.272650
$936$	−11.1685	+	6.36713i	−0.365055	+	0.208116i
$937$	33.5601			1.09636			0.548181	−	0.836360i	$-0.315321\pi$
$937$	33.5601			1.09636			0.548181	+	0.836360i	$0.315321\pi$
$938$	80.5820	−	47.2089i	2.63109	−	1.54142i
$939$			23.2229i			0.757852i
$940$	12.5344	+	7.02600i	0.408827	+	0.229163i
$941$	22.1432	−	22.1432i	0.721846	−	0.721846i	−0.247135	−	0.968981i	$-0.579489\pi$
$941$	22.1432	−	22.1432i	0.721846	−	0.721846i	0.968981	+	0.247135i	$0.0794891\pi$
$942$	−12.9425	−	22.0919i	−0.421690	−	0.719793i
$943$	12.4697	−	12.4697i	0.406070	−	0.406070i
$944$	−4.94401	−	1.19101i	−0.160914	−	0.0387642i
$945$	−25.1578			−0.818385
$946$	2.21257	−	8.47229i	0.0719370	−	0.275458i
$947$	0.674394	−	0.674394i	0.0219149	−	0.0219149i	−0.696064	−	0.717979i	$-0.745067\pi$
$947$	0.674394	−	0.674394i	0.0219149	−	0.0219149i	0.717979	+	0.696064i	$0.245067\pi$
$948$	−13.4128	+	23.9284i	−0.435626	+	0.777158i
$949$	8.50797	−	28.8996i	0.276180	−	0.938120i
$950$	1.84064	−	7.04809i	0.0597181	−	0.228670i
$951$	11.8506	+	11.8506i	0.384281	+	0.384281i
$952$	−44.9733	+	46.7205i	−1.45759	+	1.51422i
$953$			35.6625i			1.15522i	0.816312	+	0.577611i	$0.196015\pi$
$953$			35.6625i			1.15522i	−0.816312	+	0.577611i	$0.803985\pi$
$954$	13.4432	−	7.87569i	0.435240	−	0.254985i
$955$	5.20596	+	5.20596i	0.168461	+	0.168461i
$956$	−24.1996	+	6.81484i	−0.782670	+	0.220408i
$957$	−8.37092	−	8.37092i	−0.270594	−	0.270594i
$958$	5.65006	−	21.6350i	0.182545	−	0.698994i
$959$	−77.2812			−2.49554
$960$	7.73934	+	7.17092i	0.249786	+	0.231440i
$961$			6.09655i			0.196663i
$962$	−6.24961	−	25.1414i	−0.201496	−	0.810591i
$963$			20.5288i			0.661530i
$964$	−13.2612	+	3.73449i	−0.427115	+	0.120280i
$965$	10.0042			0.322048
$966$	−25.4207	−	6.63871i	−0.817897	−	0.213597i
$967$	−38.7294	−	38.7294i	−1.24545	−	1.24545i	−0.957707	−	0.287746i	$-0.907094\pi$
$967$	−38.7294	−	38.7294i	−1.24545	−	1.24545i	−0.287746	−	0.957707i	$-0.592906\pi$
$968$	−23.6119	+	0.449915i	−0.758915	+	0.0144608i
$969$	24.5991	+	24.5991i	0.790236	+	0.790236i
$970$	0.456074	+	0.778483i	0.0146436	+	0.0249956i
$971$		−	6.78979i		−	0.217895i	−0.994048	−	0.108947i	$-0.965252\pi$
$971$		−	6.78979i		−	0.217895i	0.994048	−	0.108947i	$-0.0347480\pi$
$972$	21.0600	+	11.8049i	0.675499	+	0.378642i
$973$	−39.9233	−	39.9233i	−1.27988	−	1.27988i
$974$	−34.9087	−	9.11655i	−1.11855	−	0.292113i
$975$	2.27595	+	4.17514i	0.0728889	+	0.133712i
$976$	−22.3020	−	36.4571i	−0.713869	−	1.16696i
$977$	36.5076	−	36.5076i	1.16798	−	1.16798i	0.185300	−	0.982682i	$-0.440674\pi$
$977$	36.5076	−	36.5076i	1.16798	−	1.16798i	0.982682	−	0.185300i	$-0.0593257\pi$
$978$	−23.0015	−	6.00693i	−0.735507	−	0.192081i
$979$	−5.24580			−0.167657
$980$	25.1133	−	7.07216i	0.802216	−	0.225912i
$981$	0.238883	−	0.238883i	0.00762695	−	0.00762695i
$982$	−14.8166	+	8.68031i	−0.472817	+	0.277000i
$983$	−3.97472	+	3.97472i	−0.126774	+	0.126774i	−0.767647	−	0.640873i	$-0.778573\pi$
$983$	−3.97472	+	3.97472i	−0.126774	+	0.126774i	0.640873	+	0.767647i	$0.278573\pi$
$984$	−14.4999	+	15.0632i	−0.462239	+	0.480197i
$985$		−	13.0393i		−	0.415467i
$986$	20.1845	+	34.4534i	0.642806	+	1.09722i
$987$	42.4232			1.35035
$988$	−25.9526	−	26.5728i	−0.825661	−	0.845394i
$989$	−11.9662			−0.380502
$990$	−1.46714	−	2.50430i	−0.0466289	−	0.0795920i
$991$			29.3559i			0.932522i	0.884647	+	0.466261i	$0.154399\pi$
$991$			29.3559i			0.932522i	−0.884647	+	0.466261i	$0.845601\pi$
$992$	9.96949	+	32.9803i	0.316532	+	1.04712i
$993$	−13.8595	+	13.8595i	−0.439819	+	0.439819i
$994$	54.3168	−	31.8215i	1.72282	−	1.00932i
$995$	9.40432	−	9.40432i	0.298137	−	0.298137i
$996$	−2.49057	−	8.84404i	−0.0789167	−	0.280234i
$997$	−27.3795			−0.867118			−0.433559	−	0.901125i	$-0.642742\pi$
$997$	−27.3795			−0.867118			−0.433559	+	0.901125i	$0.642742\pi$
$998$	−32.0445	−	8.36856i	−1.01435	−	0.264902i
$999$	−20.1873	+	20.1873i	−0.638696	+	0.638696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.j.a.31.5	✓	56
4.3	odd	2	inner	260.2.j.a.31.10	yes	56
13.8	odd	4	inner	260.2.j.a.151.10	yes	56
52.47	even	4	inner	260.2.j.a.151.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.j.a.31.5	✓	56	1.1	even	1	trivial
260.2.j.a.31.10	yes	56	4.3	odd	2	inner
260.2.j.a.151.5	yes	56	52.47	even	4	inner
260.2.j.a.151.10	yes	56	13.8	odd	4	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22023 + 0.714871i) q^{2} +1.31885i q^{3} +(0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.942808 - 1.60930i) q^{6} +(3.16584 - 3.16584i) q^{7} +(0.0538847 + 2.82791i) q^{8} +1.26063 q^{9} +O(q^{10})\)	\(q+(-1.22023 + 0.714871i) q^{2} +1.31885i q^{3} +(0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.942808 - 1.60930i) q^{6} +(3.16584 - 3.16584i) q^{7} +(0.0538847 + 2.82791i) q^{8} +1.26063 q^{9} +(0.357343 - 1.36832i) q^{10} +(1.15118 - 1.15118i) q^{11} +(2.30088 + 1.28973i) q^{12} +(1.72571 + 3.16574i) q^{13} +(-1.59989 + 6.12621i) q^{14} +(-0.932568 - 0.932568i) q^{15} +(-2.08734 - 3.41218i) q^{16} +5.12100i q^{17} +(-1.53826 + 0.901189i) q^{18} +(-3.64223 - 3.64223i) q^{19} +(0.542133 + 1.92512i) q^{20} +(4.17527 + 4.17527i) q^{21} +(-0.581758 + 2.22764i) q^{22} +3.14629 q^{23} +(-3.72960 + 0.0710659i) q^{24} -1.00000i q^{25} +(-4.36886 - 2.62927i) q^{26} +5.61914i q^{27} +(-2.42722 - 8.61910i) q^{28} -5.51361 q^{29} +(1.80461 + 0.471282i) q^{30} +(4.30677 + 4.30677i) q^{31} +(4.98631 + 2.67147i) q^{32} +(1.51823 + 1.51823i) q^{33} +(-3.66085 - 6.24880i) q^{34} +4.47717i q^{35} +(1.23280 - 2.19931i) q^{36} +(3.59259 + 3.59259i) q^{37} +(7.04809 + 1.84064i) q^{38} +(-4.17514 + 2.27595i) q^{39} +(-2.03774 - 1.96153i) q^{40} +(3.96330 - 3.96330i) q^{41} +(-8.07956 - 2.11001i) q^{42} -3.80326 q^{43} +(-0.882598 - 3.13412i) q^{44} +(-0.891402 + 0.891402i) q^{45} +(-3.83920 + 2.24919i) q^{46} +(5.08030 - 5.08030i) q^{47} +(4.50016 - 2.75290i) q^{48} -13.0451i q^{49} +(0.714871 + 1.22023i) q^{50} -6.75384 q^{51} +(7.21060 + 0.0851495i) q^{52} -8.73922 q^{53} +(-4.01696 - 6.85664i) q^{54} +1.62801i q^{55} +(9.12331 + 8.78213i) q^{56} +(4.80356 - 4.80356i) q^{57} +(6.72786 - 3.94151i) q^{58} +(0.898987 - 0.898987i) q^{59} +(-2.53895 + 0.714993i) q^{60} +10.6844 q^{61} +(-8.33403 - 2.17647i) q^{62} +(3.99096 - 3.99096i) q^{63} +(-7.99419 + 0.304763i) q^{64} +(-3.45878 - 1.01826i) q^{65} +(-2.93793 - 0.767251i) q^{66} +(-10.4298 - 10.4298i) q^{67} +(8.93416 + 5.00793i) q^{68} +4.14949i q^{69} +(-3.20060 - 5.46318i) q^{70} +(-7.03030 - 7.03030i) q^{71} +(0.0679288 + 3.56496i) q^{72} +(-5.90818 - 5.90818i) q^{73} +(-6.95202 - 1.81555i) q^{74} +1.31885 q^{75} +(-9.91610 + 2.79247i) q^{76} -7.28888i q^{77} +(3.46762 - 5.76187i) q^{78} +10.3997i q^{79} +(3.88875 + 0.936803i) q^{80} -3.62891 q^{81} +(-2.00289 + 7.66939i) q^{82} +(-2.46310 - 2.46310i) q^{83} +(11.3673 - 3.20115i) q^{84} +(-3.62110 - 3.62110i) q^{85} +(4.64085 - 2.71884i) q^{86} -7.27162i q^{87} +(3.31746 + 3.19340i) q^{88} +(-2.27845 - 2.27845i) q^{89} +(0.450478 - 1.72495i) q^{90} +(15.4855 + 4.55891i) q^{91} +(3.07682 - 5.48906i) q^{92} +(-5.67999 + 5.67999i) q^{93} +(-2.56738 + 9.83089i) q^{94} +5.15090 q^{95} +(-3.52327 + 6.57620i) q^{96} +(-0.451121 + 0.451121i) q^{97} +(9.32553 + 15.9180i) q^{98} +(1.45121 - 1.45121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9}+O(q^{10}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9	\( 56 q - 12 q^{6} + 12 q^{8} - 56 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 40 q^{24} - 16 q^{26} - 44 q^{28} + 40 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{41} + 8 q^{42} + 28 q^{44} - 12 q^{46} + 104 q^{48} + 56 q^{52} - 16 q^{53} + 20 q^{54} - 48 q^{57} - 4 q^{58} + 16 q^{61} - 8 q^{65} + 64 q^{66} + 24 q^{68} - 8 q^{70} - 32 q^{72} + 48 q^{73} - 136 q^{74} - 88 q^{76} + 52 q^{78} - 32 q^{80} + 56 q^{81} - 20 q^{84} - 64 q^{86} - 8 q^{89} - 88 q^{92} - 48 q^{93} - 16 q^{94} - 4 q^{96} - 32 q^{97} + 16 q^{98}+O(q^{100}) \) 56 * q - 12 * q^6 + 12 * q^8 - 56 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 40 * q^24 - 16 * q^26 - 44 * q^28 + 40 * q^32 - 4 * q^34 + 16 * q^37 + 8 * q^41 + 8 * q^42 + 28 * q^44 - 12 * q^46 + 104 * q^48 + 56 * q^52 - 16 * q^53 + 20 * q^54 - 48 * q^57 - 4 * q^58 + 16 * q^61 - 8 * q^65 + 64 * q^66 + 24 * q^68 - 8 * q^70 - 32 * q^72 + 48 * q^73 - 136 * q^74 - 88 * q^76 + 52 * q^78 - 32 * q^80 + 56 * q^81 - 20 * q^84 - 64 * q^86 - 8 * q^89 - 88 * q^92 - 48 * q^93 - 16 * q^94 - 4 * q^96 - 32 * q^97 + 16 * q^98

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