LMFDB - Embedded newform 260.2.j.a.31.10

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			31.10
Character	$\chi$	$=$	260.31
Dual form			260.2.j.a.151.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.714871 + 1.22023i) q^{2} -1.31885i q^{3} +(-0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.60930 + 0.942808i) q^{6} +(-3.16584 + 3.16584i) q^{7} +(2.82791 + 0.0538847i) q^{8} +1.26063 q^{9} +O(q^{10})$	\(q+(-0.714871 + 1.22023i) q^{2} -1.31885i q^{3} +(-0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.60930 + 0.942808i) q^{6} +(-3.16584 + 3.16584i) q^{7} +(2.82791 + 0.0538847i) 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} +(-0.901189 + 1.53826i) q^{18} +(3.64223 + 3.64223i) q^{19} +(1.92512 + 0.542133i) q^{20} +(4.17527 + 4.17527i) q^{21} +(-0.581758 - 2.22764i) q^{22} -3.14629 q^{23} +(0.0710659 - 3.72960i) q^{24} -1.00000i q^{25} +(-5.09659 - 0.157334i) q^{26} -5.61914i q^{27} +(8.61910 + 2.42722i) q^{28} -5.51361 q^{29} +(-1.80461 + 0.471282i) q^{30} +(-4.30677 - 4.30677i) q^{31} +(-2.67147 - 4.98631i) q^{32} +(1.51823 + 1.51823i) q^{33} +(-6.24880 - 3.66085i) 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} +(3.13412 + 0.882598i) q^{44} +(-0.891402 + 0.891402i) q^{45} +(2.24919 - 3.83920i) q^{46} +(-5.08030 + 5.08030i) q^{47} +(4.50016 + 2.75290i) q^{48} -13.0451i q^{49} +(1.22023 + 0.714871i) q^{50} +6.75384 q^{51} +(3.83539 - 6.10654i) q^{52} -8.73922 q^{53} +(6.85664 + 4.01696i) q^{54} -1.62801i q^{55} +(-9.12331 + 8.78213i) q^{56} +(4.80356 - 4.80356i) q^{57} +(3.94151 - 6.72786i) q^{58} +(-0.898987 + 0.898987i) q^{59} +(0.714993 - 2.53895i) 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} +(5.46318 + 3.20060i) q^{70} +(7.03030 + 7.03030i) q^{71} +(3.56496 + 0.0679288i) q^{72} +(-5.90818 - 5.90818i) q^{73} +(-6.95202 + 1.81555i) q^{74} -1.31885 q^{75} +(2.79247 - 9.91610i) q^{76} -7.28888i q^{77} +(-0.207500 + 6.72164i) q^{78} -10.3997i q^{79} +(-0.936803 - 3.88875i) q^{80} -3.62891 q^{81} +(2.00289 + 7.66939i) q^{82} +(2.46310 + 2.46310i) q^{83} +(3.20115 - 11.3673i) q^{84} +(-3.62110 - 3.62110i) q^{85} +(-2.71884 + 4.64085i) 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} +(-6.57620 + 3.52327i) q^{96} +(-0.451121 + 0.451121i) q^{97} +(15.9180 + 9.32553i) 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 $

$2$	−0.714871	+	1.22023i	−0.505490	+	0.862833i
$2$	−0.714871	+	1.22023i	−0.505490	+	0.862833i
$3$		−	1.31885i		−	0.761439i	−0.924691	−	0.380719i	$-0.875676\pi$
$3$		−	1.31885i		−	0.761439i	0.924691	−	0.380719i	$-0.124324\pi$
$4$	−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
$6$	1.60930	+	0.942808i	0.656994	+	0.384900i
$7$	−3.16584	+	3.16584i	−1.19657	+	1.19657i	−0.221389	+	0.975186i	$0.571059\pi$
$7$	−3.16584	+	3.16584i	−1.19657	+	1.19657i	−0.975186	+	0.221389i	$0.928941\pi$
$8$	2.82791	+	0.0538847i	0.999819	+	0.0190511i
$9$	1.26063			0.420211
$10$	−0.357343	−	1.36832i	−0.113002	−	0.432702i
$11$	−1.15118	+	1.15118i	−0.347093	+	0.347093i	−0.859026	−	0.511933i	$-0.828930\pi$
$11$	−1.15118	+	1.15118i	−0.347093	+	0.347093i	0.511933	+	0.859026i	$0.328930\pi$
$12$	−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	$0.786721\pi$
$18$	−0.901189	+	1.53826i	−0.212412	+	0.362572i
$19$	3.64223	+	3.64223i	0.835586	+	0.835586i	0.988274	−	0.152688i	$-0.0487931\pi$
$19$	3.64223	+	3.64223i	0.835586	+	0.835586i	−0.152688	+	0.988274i	$0.548793\pi$
$20$	1.92512	+	0.542133i	0.430470	+	0.121225i
$21$	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	$-0.606383\pi$
$23$	−3.14629			−0.656047			−0.328024	+	0.944669i	$0.606383\pi$
$24$	0.0710659	−	3.72960i	0.0145063	−	0.761301i
$25$		−	1.00000i		−	0.200000i
$26$	−5.09659	−	0.157334i	−0.999524	−	0.0308558i
$27$		−	5.61914i		−	1.08140i
$28$	8.61910	+	2.42722i	1.62886	+	0.458702i
$29$	−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	0.205201	−	0.978720i	$-0.434215\pi$
$31$	−4.30677	−	4.30677i	−0.773519	−	0.773519i	−0.978720	+	0.205201i	$0.934215\pi$
$32$	−2.67147	−	4.98631i	−0.472253	−	0.881463i
$33$	1.51823	+	1.51823i	0.264290	+	0.264290i
$34$	−6.24880	−	3.66085i	−1.07166	−	0.627831i
$35$		−	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	$-0.406346\pi$
$43$	3.80326			0.579991			0.289996	+	0.957028i	$0.406346\pi$
$44$	3.13412	+	0.882598i	0.472486	+	0.133057i
$45$	−0.891402	+	0.891402i	−0.132882	+	0.132882i
$46$	2.24919	−	3.83920i	0.331625	−	0.566059i
$47$	−5.08030	+	5.08030i	−0.741038	+	0.741038i	−0.972778	−	0.231740i	$-0.925558\pi$
$47$	−5.08030	+	5.08030i	−0.741038	+	0.741038i	0.231740	+	0.972778i	$0.425558\pi$
$48$	4.50016	+	2.75290i	0.649542	+	0.397346i
$49$		−	13.0451i		−	1.86358i
$50$	1.22023	+	0.714871i	0.172567	+	0.101098i
$51$	6.75384			0.945727
$52$	3.83539	−	6.10654i	0.531872	−	0.846824i
$53$	−8.73922			−1.20042			−0.600212	−	0.799841i	$-0.704917\pi$
$53$	−8.73922			−1.20042			−0.600212	+	0.799841i	$0.704917\pi$
$54$	6.85664	+	4.01696i	0.933070	+	0.546639i
$55$		−	1.62801i		−	0.219521i
$56$	−9.12331	+	8.78213i	−1.21915	+	1.17356i
$57$	4.80356	−	4.80356i	0.636248	−	0.636248i
$58$	3.94151	−	6.72786i	0.517546	−	0.883412i
$59$	−0.898987	+	0.898987i	−0.117038	+	0.117038i	−0.763200	−	0.646162i	$-0.776373\pi$
$59$	−0.898987	+	0.898987i	−0.117038	+	0.117038i	0.646162	+	0.763200i	$0.276373\pi$
$60$	0.714993	−	2.53895i	0.0923052	−	0.327777i
$61$	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	$0.107166\pi$
$67$	10.4298	+	10.4298i	1.27421	+	1.27421i	0.330348	+	0.943859i	$0.392834\pi$
$68$	8.93416	−	5.00793i	1.08343	−	0.607301i
$69$			4.14949i			0.499540i
$70$	5.46318	+	3.20060i	0.652975	+	0.382545i
$71$	7.03030	+	7.03030i	0.834343	+	0.834343i	0.988108	−	0.153764i	$-0.0491396\pi$
$71$	7.03030	+	7.03030i	0.834343	+	0.834343i	−0.153764	+	0.988108i	$0.549140\pi$
$72$	3.56496	+	0.0679288i	0.420135	+	0.00800549i
$73$	−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
$76$	2.79247	−	9.91610i	0.320319	−	1.13745i
$77$		−	7.28888i		−	0.830645i
$78$	−0.207500	+	6.72164i	−0.0234948	+	0.761076i
$79$		−	10.3997i		−	1.17005i	−0.811014	−	0.585026i	$-0.801084\pi$
$79$		−	10.3997i		−	1.17005i	0.811014	−	0.585026i	$-0.198916\pi$
$80$	−0.936803	−	3.88875i	−0.104738	−	0.434776i
$81$	−3.62891			−0.403212
$82$	2.00289	+	7.66939i	0.221182	+	0.846943i
$83$	2.46310	+	2.46310i	0.270360	+	0.270360i	0.829245	−	0.558885i	$-0.188771\pi$
$83$	2.46310	+	2.46310i	0.270360	+	0.270360i	−0.558885	+	0.829245i	$0.688771\pi$
$84$	3.20115	−	11.3673i	0.349274	−	1.24027i
$85$	−3.62110	−	3.62110i	−0.392763	−	0.392763i
$86$	−2.71884	+	4.64085i	−0.293180	+	0.500435i
$87$			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
$96$	−6.57620	+	3.52327i	−0.671180	+	0.359592i
$97$	−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	$0.260311\pi$
$98$	15.9180	+	9.32553i	1.60796	+	0.942021i
$99$	−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	$0.963955\pi$
$102$	−4.82812	+	8.24123i	−0.478055	+	0.816004i
$103$	5.39362			0.531449			0.265724	−	0.964049i	$-0.414389\pi$
$103$	5.39362			0.531449			0.265724	+	0.964049i	$0.414389\pi$
$104$	4.70957	+	9.04544i	0.461812	+	0.886978i
$105$	−5.90472			−0.576242
$106$	6.24741	−	10.6639i	0.606802	−	1.03577i
$107$		−	16.2845i		−	1.57428i	−0.616773	−	0.787141i	$-0.711560\pi$
$107$		−	16.2845i		−	1.57428i	0.616773	−	0.787141i	$-0.288440\pi$
$108$	−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	$0.245915\pi$
$110$	1.98655	+	1.16382i	0.189410	+	0.110966i
$111$	4.73809	−	4.73809i	0.449719	−	0.449719i
$112$	−4.19423	−	17.4106i	−0.396317	−	1.64515i
$113$	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
$122$	−7.63795	+	13.0374i	−0.691507	+	1.18035i
$123$	−5.22701	−	5.22701i	−0.471303	−	0.471303i
$124$	−3.30197	+	11.7253i	−0.296525	+	1.05297i
$125$	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	$-0.346813\pi$
$127$	10.4330			0.925775			0.462887	+	0.886417i	$0.346813\pi$
$128$	−6.08669	+	9.53688i	−0.537993	+	0.842949i
$129$		−	5.01593i		−	0.441628i
$130$	3.71509	−	3.49258i	0.325835	−	0.306320i
$131$			13.5871i			1.18711i	0.804793	+	0.593555i	$0.202276\pi$
$131$			13.5871i			1.18711i	−0.804793	+	0.593555i	$0.797724\pi$
$132$	1.16402	−	4.13343i	0.101315	−	0.359769i
$133$	−23.0615			−1.99968
$134$	−20.1828	+	5.27081i	−1.74353	+	0.455329i
$135$	3.97333	+	3.97333i	0.341970	+	0.341970i
$136$	−0.275944	+	14.4818i	−0.0236620	+	1.24180i
$137$	−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	$-0.513928\pi$
$138$	−5.06333	−	2.96635i	−0.431019	−	0.252512i
$139$			12.6107i			1.06962i	0.844972	+	0.534811i	$0.179617\pi$
$139$			12.6107i			1.06962i	−0.844972	+	0.534811i	$0.820383\pi$
$140$	−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
$148$	2.75441	−	9.78094i	0.226411	−	0.803988i
$149$	−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	$0.270035\pi$
$150$	0.942808	−	1.60930i	0.0769799	−	0.131399i
$151$	2.55542	−	2.55542i	0.207957	−	0.207957i	−0.595441	−	0.803399i	$-0.703023\pi$
$151$	2.55542	−	2.55542i	0.207957	−	0.207957i	0.803399	+	0.595441i	$0.203023\pi$
$152$	10.1037	+	10.4962i	0.819515	+	0.851353i
$153$			6.45570i			0.521913i
$154$	8.89411	+	5.21061i	0.716708	+	0.419883i
$155$	6.09069			0.489216
$156$	−8.05361	−	5.05830i	−0.644805	−	0.404988i
$157$	13.7276			1.09558			0.547792	−	0.836614i	$-0.315468\pi$
$157$	13.7276			1.09558			0.547792	+	0.836614i	$0.315468\pi$
$158$	12.6900	+	7.43441i	1.00956	+	0.591450i
$159$			11.5257i			0.914050i
$160$	5.41486	+	1.63684i	0.428083	+	0.129404i
$161$	9.96066	−	9.96066i	0.785010	−	0.785010i
$162$	2.59420	−	4.42810i	0.203820	−	0.347904i
$163$	−9.01274	+	9.01274i	−0.705933	+	0.705933i	−0.965677	−	0.259745i	$-0.916362\pi$
$163$	−9.01274	+	9.01274i	−0.705933	+	0.705933i	0.259745	+	0.965677i	$0.416362\pi$
$164$	−10.7902	−	3.03863i	−0.842575	−	0.237277i
$165$	−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	$-0.293622\pi$
$167$	18.1043	−	18.1043i	1.40095	−	1.40095i	0.797078	−	0.603876i	$-0.206378\pi$
$168$	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	$0.949287\pi$
$174$	−8.87305	−	5.19827i	−0.672664	−	0.394080i
$175$	3.16584	+	3.16584i	0.239315	+	0.239315i
$176$	−1.52512	−	6.33093i	−0.114961	−	0.477212i
$177$	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	$-0.336829\pi$
$179$	13.1238			0.980918			0.490459	+	0.871464i	$0.336829\pi$
$180$	2.42687	+	0.683431i	0.180888	+	0.0509399i
$181$		−	15.1357i		−	1.12503i	−0.826788	−	0.562514i	$-0.809834\pi$
$181$		−	15.1357i		−	1.12503i	0.826788	−	0.562514i	$-0.190166\pi$
$182$	16.6331	−	15.6369i	1.23293	−	1.15908i
$183$		−	14.0911i		−	1.04164i
$184$	−8.89745	−	0.169537i	−0.655928	−	0.0124984i
$185$	−5.08069			−0.373540
$186$	−2.87043	−	10.9913i	−0.210470	−	0.805925i
$187$	−5.89518	−	5.89518i	−0.431098	−	0.431098i
$188$	13.8313	+	3.89503i	1.00875	+	0.284074i
$189$	17.7893	+	17.7893i	1.29398	+	1.29398i
$190$	3.68222	−	6.28528i	0.267137	−	0.455982i
$191$			7.36234i			0.532720i	0.963874	+	0.266360i	$0.0858210\pi$
$191$			7.36234i			0.532720i	−0.963874	+	0.266360i	$0.914179\pi$
$192$	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	$-0.343750\pi$
$199$	13.2997			0.942792			0.471396	+	0.881922i	$0.343750\pi$
$200$	0.0538847	−	2.82791i	0.00381022	−	0.199964i
$201$	13.7554	−	13.7554i	0.970231	−	0.970231i
$202$	−2.77141	−	1.62363i	−0.194996	−	0.114238i
$203$	17.4552	−	17.4552i	1.22511	−	1.22511i
$204$	−6.60472	−	11.7828i	−0.462423	−	0.824963i
$205$			5.60496i			0.391467i
$206$	−3.85574	+	6.58145i	−0.268642	+	0.458552i
$207$	−3.96632			−0.275678
$208$	−14.4042	−	0.719556i	−0.998755	−	0.0498922i
$209$	−8.38571			−0.580052
$210$	4.22111	−	7.20512i	0.291284	−	0.497200i
$211$			12.5743i			0.865649i	0.901478	+	0.432825i	$0.142483\pi$
$211$			12.5743i			0.865649i	−0.901478	+	0.432825i	$0.857517\pi$
$212$	8.54626	+	15.2466i	0.586960	+	1.04714i
$213$	9.27192	−	9.27192i	0.635301	−	0.635301i
$214$	19.8708	+	11.6413i	1.35834	+	0.795783i
$215$	−2.68931	+	2.68931i	−0.183409	+	0.183409i
$216$	0.302786	−	15.8904i	0.0206020	−	1.08121i
$217$	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	0.244692	−	0.969601i	$-0.421313\pi$
$223$	−10.8252	−	10.8252i	−0.724908	−	0.724908i	−0.969601	+	0.244692i	$0.921313\pi$
$224$	24.2433	+	7.32842i	1.61982	+	0.489650i
$225$		−	1.26063i		−	0.0840422i
$226$	−1.39505	+	2.38124i	−0.0927971	+	0.158398i
$227$	−0.955202	−	0.955202i	−0.0633990	−	0.0633990i	0.674696	−	0.738095i	$-0.264275\pi$
$227$	−0.955202	−	0.955202i	−0.0633990	−	0.0633990i	−0.738095	+	0.674696i	$0.764275\pi$
$228$	−13.0779	−	3.68285i	−0.866102	−	0.243903i
$229$	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
$232$	−15.5920	−	0.297099i	−1.02366	−	0.0195055i
$233$		−	15.2378i		−	0.998258i	−0.866528	−	0.499129i	$-0.833653\pi$
$233$		−	15.2378i		−	0.998258i	0.866528	−	0.499129i	$-0.166347\pi$
$234$	−6.42493	−	0.198341i	−0.420011	−	0.0129659i
$235$		−	7.18463i		−	0.468674i
$236$	2.44752	+	0.689246i	0.159320	+	0.0448661i
$237$	−13.7156			−0.890924
$238$	31.3724	−	8.19302i	2.03357	−	0.531074i
$239$	8.88863	+	8.88863i	0.574958	+	0.574958i	0.933510	−	0.358552i	$-0.116729\pi$
$239$	8.88863	+	8.88863i	0.574958	+	0.574958i	−0.358552	+	0.933510i	$0.616729\pi$
$240$	−5.12869	+	1.23550i	−0.331055	+	0.0797514i
$241$	−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	$0.821214\pi$
$242$	−10.1884	−	5.96887i	−0.654936	−	0.383694i
$243$		−	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	$-0.531078\pi$
$251$	−3.08877			−0.194962			−0.0974808	+	0.995237i	$0.531078\pi$
$252$	10.8655	+	3.05984i	0.684463	+	0.192752i
$253$	3.62194	−	3.62194i	0.227709	−	0.227709i
$254$	−7.45821	+	12.7306i	−0.467970	+	0.798789i
$255$	−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	$-0.197777\pi$
$258$	6.12058	+	3.58574i	0.381051	+	0.223238i
$259$	−22.7471			−1.41344
$260$	1.60595	+	7.03000i	0.0995966	+	0.435982i
$261$	−6.95063			−0.430233
$262$	−16.5794	−	9.71302i	−1.02428	−	0.600072i
$263$			16.3459i			1.00793i	0.863724	+	0.503966i	$0.168126\pi$
$263$			16.3459i			1.00793i	−0.863724	+	0.503966i	$0.831874\pi$
$264$	4.21162	+	4.37523i	0.259207	+	0.269277i
$265$	6.17956	−	6.17956i	0.379607	−	0.379607i
$266$	16.4860	−	28.1403i	1.01082	−	1.72539i
$267$	−3.00494	+	3.00494i	−0.183899	+	0.183899i
$268$	7.99647	−	28.3956i	0.488462	−	1.73454i
$269$	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	−0.577750	−	0.816214i	$-0.696069\pi$
$271$	3.92561	−	3.92561i	0.238464	−	0.238464i	0.816214	+	0.577750i	$0.196069\pi$
$272$	−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	$0.874073\pi$
$278$	−15.3879	−	9.01499i	−0.922905	−	0.540683i
$279$	−5.42926	−	5.42926i	−0.325041	−	0.325041i
$280$	0.241251	−	12.6611i	0.0144175	−	0.756643i
$281$	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	$-0.239959\pi$
$283$	24.5292			1.45811			0.729056	+	0.684454i	$0.239959\pi$
$284$	5.39008	−	19.1402i	0.319842	−	1.13576i
$285$			6.79327i			0.402398i
$286$	6.04820	−	5.68596i	0.357637	−	0.336218i
$287$			25.0944i			1.48127i
$288$	−3.36774	−	6.28590i	−0.198446	−	0.370400i
$289$	−9.22467			−0.542628
$290$	1.97025	+	7.54439i	0.115697	+	0.443022i
$291$	0.594961	+	0.594961i	0.0348772	+	0.0348772i
$292$	−4.52975	+	16.0852i	−0.265084	+	0.941316i
$293$	−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	$0.984882\pi$
$294$	12.2990	−	20.9934i	0.717292	−	1.22436i
$295$		−	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
$304$	−20.0306	+	4.82538i	−1.14883	+	0.276754i
$305$	−7.55500	+	7.55500i	−0.432598	+	0.432598i
$306$	−7.87744	−	4.61499i	−0.450323	−	0.263821i
$307$	6.71827	−	6.71827i	0.383432	−	0.383432i	−0.488905	−	0.872337i	$-0.662604\pi$
$307$	6.71827	−	6.71827i	0.383432	−	0.383432i	0.872337	+	0.488905i	$0.162604\pi$
$308$	−12.7163	+	7.12794i	−0.724577	+	0.406152i
$309$		−	7.11338i		−	0.404666i
$310$	−4.35406	+	7.43204i	−0.247294	+	0.422112i
$311$	−8.21407			−0.465777			−0.232889	−	0.972503i	$-0.574818\pi$
$311$	−8.21407			−0.465777			−0.232889	+	0.972503i	$0.574818\pi$
$312$	11.9296	−	6.21122i	0.675380	−	0.351641i
$313$	17.6085			0.995289			0.497644	−	0.867381i	$-0.334198\pi$
$313$	17.6085			0.995289			0.497644	+	0.867381i	$0.334198\pi$
$314$	−9.81348	+	16.7509i	−0.553807	+	0.945306i
$315$		−	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	$0.133847\pi$
$318$	−14.0640	−	8.23940i	−0.788672	−	0.462043i
$319$	6.34713	−	6.34713i	0.355371	−	0.355371i
$320$	−5.86825	+	5.43725i	−0.328045	+	0.303951i
$321$	−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
$330$	1.53490	−	2.61996i	0.0844935	−	0.144224i
$331$	−10.5088	−	10.5088i	−0.577616	−	0.577616i	0.356630	−	0.934246i	$-0.383926\pi$
$331$	−10.5088	−	10.5088i	−0.577616	−	0.577616i	−0.934246	+	0.356630i	$0.883926\pi$
$332$	1.88844	−	6.70587i	0.103642	−	0.368033i
$333$	4.52893	+	4.52893i	0.248184	+	0.248184i
$334$	9.14918	+	35.0337i	0.500621	+	1.91696i
$335$	−14.7500			−0.805880
$336$	−22.9620	+	5.53156i	−1.25268	+	0.301771i
$337$			22.5861i			1.23034i	0.788393	+	0.615172i	$0.210913\pi$
$337$			22.5861i			1.23034i	−0.788393	+	0.615172i	$0.789087\pi$
$338$	−8.29716	−	16.4060i	−0.451306	−	0.892369i
$339$		−	2.57369i		−	0.139784i
$340$	−2.77627	+	9.85855i	−0.150564	+	0.534655i
$341$	9.91571			0.536966
$342$	−8.88505	+	2.32037i	−0.480448	+	0.125471i
$343$	19.1377	+	19.1377i	1.03334	+	1.03334i
$344$	10.7553	+	0.204937i	0.579886	+	0.0110495i
$345$	−2.93413	−	2.93413i	−0.157968	−	0.157968i
$346$	−5.09238	−	2.98337i	−0.273768	−	0.160387i
$347$		−	4.76733i		−	0.255924i	−0.991779	−	0.127962i	$-0.959156\pi$
$347$		−	4.76733i		−	0.255924i	0.991779	−	0.127962i	$-0.0408435\pi$
$348$	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
$356$	−1.74687	+	6.20316i	−0.0925840	+	0.328767i
$357$	−21.3816	+	21.3816i	−1.13163	+	1.13163i
$358$	−9.38181	+	16.0140i	−0.495844	+	0.846368i
$359$	−2.57511	+	2.57511i	−0.135909	+	0.135909i	−0.771788	−	0.635879i	$-0.780638\pi$
$359$	−2.57511	+	2.57511i	−0.135909	+	0.135909i	0.635879	+	0.771788i	$0.280638\pi$
$360$	−2.56884	+	2.47277i	−0.135390	+	0.130327i
$361$			7.53175i			0.396408i
$362$	18.4690	+	10.8201i	0.970710	+	0.568690i
$363$	11.0119			0.577973
$364$	7.19010	+	31.4745i	0.376864	+	1.64971i
$365$	8.35543			0.437343
$366$	17.1944	+	10.0733i	0.898765	+	0.526541i
$367$		−	33.7688i		−	1.76272i	−0.472449	−	0.881358i	$-0.656630\pi$
$367$		−	33.7688i		−	1.76272i	0.472449	−	0.881358i	$-0.343370\pi$
$368$	6.56740	−	10.7357i	0.342349	−	0.559639i
$369$	4.99627	−	4.99627i	0.260095	−	0.260095i
$370$	3.63203	−	6.19960i	0.188820	−	0.322302i
$371$	27.6670	−	27.6670i	1.43640	−	1.43640i
$372$	15.4640	+	4.35480i	0.801769	+	0.225786i
$373$	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	0.636446	−	0.771321i	$-0.280404\pi$
$379$	−2.62573	−	2.62573i	−0.134875	−	0.134875i	−0.771321	+	0.636446i	$0.780404\pi$
$380$	5.03717	+	8.98632i	0.258401	+	0.460988i
$381$		−	13.7595i		−	0.704921i
$382$	−8.98375	−	5.26312i	−0.459648	−	0.269285i
$383$	4.82603	+	4.82603i	0.246598	+	0.246598i	0.819573	−	0.572975i	$-0.194211\pi$
$383$	4.82603	+	4.82603i	0.246598	+	0.246598i	−0.572975	+	0.819573i	$0.694211\pi$
$384$	12.5777	+	8.02744i	0.641854	+	0.409649i
$385$	5.15402	+	5.15402i	0.262673	+	0.262673i
$386$	13.6890	−	3.57494i	0.696753	−	0.181960i
$387$	4.79451			0.243719
$388$	1.22819	+	0.345871i	0.0623519	+	0.0175589i
$389$			10.1698i			0.515632i	0.966194	+	0.257816i	$0.0830028\pi$
$389$			10.1698i			0.515632i	−0.966194	+	0.257816i	$0.916997\pi$
$390$	−4.60620	−	4.89964i	−0.233244	−	0.248103i
$391$		−	16.1122i		−	0.814828i
$392$	0.702930	−	36.8903i	0.0355033	−	1.86324i
$393$	17.9194			0.903912
$394$	−4.65951	−	17.8420i	−0.234743	−	0.898867i
$395$	7.35367	+	7.35367i	0.370003	+	0.370003i
$396$	3.95097	+	1.11263i	0.198544	+	0.0559119i
$397$	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	$0.695226\pi$
$398$	−9.50758	+	16.2287i	−0.476572	+	0.813472i
$399$			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
$408$	19.0993	+	0.363929i	0.945555	+	0.0180172i
$409$	−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	$0.332883\pi$
$410$	−6.83934	−	4.00682i	−0.337771	−	0.197883i
$411$	−16.0972	+	16.0972i	−0.794018	+	0.794018i
$412$	−5.27453	−	9.40977i	−0.259857	−	0.463586i
$413$		−	5.69210i		−	0.280090i
$414$	2.83540	−	4.83982i	0.139353	−	0.237864i
$415$	−3.48335			−0.170991
$416$	11.1752	−	17.0621i	0.547909	−	0.836538i
$417$	16.6316			0.814452
$418$	5.99470	−	10.2325i	0.293210	−	0.500488i
$419$		−	6.39826i		−	0.312576i	−0.987712	−	0.156288i	$-0.950047\pi$
$419$		−	6.39826i		−	0.312576i	0.987712	−	0.156288i	$-0.0499527\pi$
$420$	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	$0.305374\pi$
$422$	−15.3435	−	8.98899i	−0.746911	−	0.437577i
$423$	−6.40439	+	6.40439i	−0.311392	+	0.311392i
$424$	−24.7138	−	0.470910i	−1.20021	−	0.0228694i
$425$	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	0.821856	−	0.569695i	$-0.192939\pi$
$431$	5.23501	+	5.23501i	0.252162	+	0.252162i	−0.569695	+	0.821856i	$0.692939\pi$
$432$	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	$-0.121719\pi$
$434$	−19.4939	+	33.2745i	−0.935735	+	1.59723i
$435$	−5.14181	−	5.14181i	−0.246531	−	0.246531i
$436$	−0.515906	−	0.145284i	−0.0247074	−	0.00695785i
$437$	−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	$-0.633926\pi$
$439$	−17.1154			−0.816874			−0.408437	+	0.912786i	$0.633926\pi$
$440$	0.0877248	−	4.60387i	0.00418212	−	0.219481i
$441$		−	16.4450i		−	0.783097i
$442$	0.805709	−	26.0997i	0.0383236	−	1.24143i
$443$			25.3075i			1.20239i	0.799101	+	0.601197i	$0.205309\pi$
$443$			25.3075i			1.20239i	−0.799101	+	0.601197i	$0.794691\pi$
$444$	−12.8996	−	3.63265i	−0.612188	−	0.172398i
$445$	3.22222			0.152748
$446$	20.9478	−	5.47061i	0.991908	−	0.259041i
$447$	1.43207	+	1.43207i	0.0677347	+	0.0677347i
$448$	−26.2732	+	24.3435i	−1.24129	+	1.15012i
$449$	−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	$0.798778\pi$
$450$	1.53826	+	0.901189i	0.0725143	+	0.0424825i
$451$			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
$460$	−6.05700	−	1.70571i	−0.282409	−	0.0795291i
$461$	−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	$0.293236\pi$
$462$	6.87201	−	11.7300i	0.319715	−	0.545729i
$463$	−28.1044	+	28.1044i	−1.30612	+	1.30612i	−0.381931	+	0.924191i	$0.624741\pi$
$463$	−28.1044	+	28.1044i	−1.30612	+	1.30612i	−0.924191	+	0.381931i	$0.875259\pi$
$464$	11.5088	−	18.8134i	0.534282	−	0.873392i
$465$		−	8.03272i		−	0.372508i
$466$	18.5936	+	10.8930i	0.861330	+	0.504609i
$467$	22.7594			1.05318			0.526590	−	0.850120i	$-0.323470\pi$
$467$	22.7594			1.05318			0.526590	+	0.850120i	$0.323470\pi$
$468$	4.83501	−	7.69810i	0.223499	−	0.355845i
$469$	−66.0384			−3.04937
$470$	8.76690	+	5.13608i	0.404387	+	0.236910i
$471$		−	18.1047i		−	0.834220i
$472$	−2.59070	+	2.49382i	−0.119247	+	0.114787i
$473$	−4.37822	+	4.37822i	−0.201311	+	0.201311i
$474$	9.80488	−	16.7362i	0.450353	−	0.768718i
$475$	3.64223	−	3.64223i	0.167117	−	0.167117i
$476$	−12.4298	+	44.1384i	−0.569720	+	2.02308i
$477$	−11.0169			−0.504431
$478$	−17.2004	+	4.49195i	−0.786727	+	0.205457i
$479$	11.1803	−	11.1803i	0.510840	−	0.510840i	−0.403944	−	0.914784i	$-0.632361\pi$
$479$	11.1803	−	11.1803i	0.510840	−	0.510840i	0.914784	+	0.403944i	$0.132361\pi$
$480$	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
$486$	14.7299	+	8.62951i	0.668162	+	0.391442i
$487$	−18.0398	−	18.0398i	−0.817459	−	0.817459i	0.168280	−	0.985739i	$-0.446179\pi$
$487$	−18.0398	−	18.0398i	−0.817459	−	0.817459i	−0.985739	+	0.168280i	$0.946179\pi$
$488$	30.2145	+	0.575725i	1.36775	+	0.0260618i
$489$	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	$-0.588344\pi$
$491$	−12.1425			−0.547983			−0.273991	+	0.961732i	$0.588344\pi$
$492$	−4.00751	+	14.2307i	−0.180672	+	0.641569i
$493$		−	28.2352i		−	1.27165i
$494$	−17.9899	−	19.1360i	−0.809405	−	0.860971i
$495$		−	2.05232i		−	0.0922450i
$496$	23.6852	−	5.70578i	1.06350	−	0.256197i
$497$	−44.5136			−1.99671
$498$	1.64164	+	6.28610i	0.0735636	+	0.281687i
$499$	−16.5596	−	16.5596i	−0.741311	−	0.741311i	0.231519	−	0.972830i	$-0.425630\pi$
$499$	−16.5596	−	16.5596i	−0.741311	−	0.741311i	−0.972830	+	0.231519i	$0.925630\pi$
$500$	0.542133	−	1.92512i	0.0242449	−	0.0860940i
$501$	−23.8769	−	23.8769i	−1.06674	−	1.06674i
$502$	2.20807	−	3.76901i	0.0985511	−	0.168219i
$503$		−	33.5270i		−	1.49490i	−0.664320	−	0.747448i	$-0.731279\pi$
$503$		−	33.5270i		−	1.49490i	0.664320	−	0.747448i	$-0.268721\pi$
$504$	−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
$512$	22.5905	+	1.29261i	0.998367	+	0.0571257i
$513$	20.4662	−	20.4662i	0.903606	−	0.903606i
$514$	22.7747	+	13.3425i	1.00455	+	0.588513i
$515$	−3.81386	+	3.81386i	−0.168059	+	0.168059i
$516$	−8.75085	+	4.90518i	−0.385235	+	0.215938i
$517$		−	11.6966i		−	0.514418i
$518$	16.2612	−	27.7567i	0.714478	−	1.21956i
$519$	5.50395			0.241597
$520$	−9.72626	−	3.06592i	−0.426525	−	0.134449i
$521$	23.9342			1.04858			0.524288	−	0.851541i	$-0.324331\pi$
$521$	23.9342			1.04858			0.524288	+	0.851541i	$0.324331\pi$
$522$	4.96880	−	8.48136i	0.217478	−	0.371219i
$523$		−	15.8127i		−	0.691441i	−0.938337	−	0.345721i	$-0.887634\pi$
$523$		−	15.8127i		−	0.691441i	0.938337	−	0.345721i	$-0.112366\pi$
$524$	23.7042	−	13.2871i	1.03552	−	0.580450i
$525$	4.17527	−	4.17527i	0.182224	−	0.182224i
$526$	−19.9458	−	11.6852i	−0.869676	−	0.509499i
$527$	22.0550	−	22.0550i	0.960730	−	0.960730i
$528$	−8.34955	+	2.01141i	−0.363368	+	0.0875355i
$529$	−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
$538$	−15.1222	+	25.8124i	−0.651963	+	1.11285i
$539$	15.0172	+	15.0172i	0.646836	+	0.646836i
$540$	3.04632	−	10.8175i	0.131093	−	0.465512i
$541$	−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
$544$	25.5349	−	13.6806i	1.09480	−	0.586550i
$545$			0.267986i			0.0114793i
$546$	−20.6227	−	21.9366i	−0.882571	−	0.938798i
$547$			34.2390i			1.46395i	0.681330	+	0.731977i	$0.261402\pi$
$547$			34.2390i			1.46395i	−0.681330	+	0.731977i	$0.738598\pi$
$548$	−9.35785	+	33.2299i	−0.399748	+	1.41951i
$549$	13.4691			0.574846
$550$	−2.22764	+	0.581758i	−0.0949870	+	0.0248062i
$551$	−20.0818	−	20.0818i	−0.855515	−	0.855515i
$552$	−0.223594	+	11.7344i	−0.00951680	+	0.499449i
$553$	32.9236	+	32.9236i	1.40006	+	1.40006i
$554$	−15.6528	−	9.17019i	−0.665024	−	0.389604i
$555$			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	$-0.652338\pi$
$563$	−21.8541			−0.921043			−0.460521	+	0.887649i	$0.652338\pi$
$564$	5.13696	−	18.2414i	0.216305	−	0.768102i
$565$	−1.37990	+	1.37990i	−0.0580526	+	0.0580526i
$566$	−17.5352	+	29.9313i	−0.737061	+	1.25811i
$567$	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	$-0.129227\pi$
$570$	−8.28934	−	4.85631i	−0.347202	−	0.203408i
$571$	−13.5630			−0.567592			−0.283796	−	0.958885i	$-0.591594\pi$
$571$	−13.5630			−0.567592			−0.283796	+	0.958885i	$0.591594\pi$
$572$	2.61450	+	11.4449i	0.109318	+	0.478536i
$573$	9.70983			0.405634
$574$	−30.6209	−	17.9392i	−1.27809	−	0.748769i
$575$			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	$0.0343105\pi$
$578$	6.59444	−	11.2562i	0.274293	−	0.468197i
$579$	−9.32963	+	9.32963i	−0.387726	+	0.387726i
$580$	−10.6144	−	2.98911i	−0.440737	−	0.124116i
$581$	−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	0.659771	−	0.751467i	$-0.270653\pi$
$587$	−2.22161	−	2.22161i	−0.0916957	−	0.0916957i	−0.751467	+	0.659771i	$0.770653\pi$
$588$	16.8246	+	30.0152i	0.693836	+	1.23781i
$589$		−	31.3725i		−	1.29268i
$590$	1.55135	+	0.908858i	0.0638681	+	0.0374171i
$591$	12.1601	+	12.1601i	0.500198	+	0.500198i
$592$	−19.7575	+	4.75960i	−0.812030	+	0.195618i
$593$	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
$596$	2.95626	+	0.832512i	0.121093	+	0.0341010i
$597$		−	17.5403i		−	0.717878i
$598$	16.0354	+	0.495019i	0.655735	+	0.0202428i
$599$			10.9689i			0.448178i	0.974569	+	0.224089i	$0.0719406\pi$
$599$			10.9689i			0.448178i	−0.974569	+	0.224089i	$0.928059\pi$
$600$	−3.72960	−	0.0710659i	−0.152260	−	0.00290125i
$601$	−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
$604$	−6.95722	−	1.95922i	−0.283085	−	0.0797196i
$605$	−5.90405	−	5.90405i	−0.240034	−	0.240034i
$606$	−2.14133	+	3.65508i	−0.0869854	+	0.148478i
$607$			8.03050i			0.325948i	0.986630	+	0.162974i	$0.0521086\pi$
$607$			8.03050i			0.325948i	−0.986630	+	0.162974i	$0.947891\pi$
$608$	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
$616$	0.392759	−	20.6123i	0.0158247	−	0.830494i
$617$	−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	$0.926816\pi$
$618$	8.67995	+	5.08514i	0.349159	+	0.204554i
$619$	14.7740	−	14.7740i	0.593815	−	0.593815i	−0.344844	−	0.938660i	$-0.612068\pi$
$619$	14.7740	−	14.7740i	0.593815	−	0.593815i	0.938660	+	0.344844i	$0.112068\pi$
$620$	−5.95621	−	10.6259i	−0.239207	−	0.426746i
$621$			17.6795i			0.709452i
$622$	5.87200	−	10.0231i	0.235446	−	0.401888i
$623$	14.4264			0.577982
$624$	−0.948987	+	18.9970i	−0.0379899	+	0.760491i
$625$	−1.00000			−0.0400000
$626$	−12.5878	+	21.4864i	−0.503108	+	0.858768i
$627$			11.0595i			0.441674i
$628$	−13.4245	−	23.9494i	−0.535697	−	0.955685i
$629$	−18.3977	+	18.3977i	−0.733563	+	0.733563i
$630$	6.88706	+	4.03478i	0.274387	+	0.160749i
$631$	−10.6634	+	10.6634i	−0.424502	+	0.424502i	−0.886750	−	0.462249i	$-0.847043\pi$
$631$	−10.6634	+	10.6634i	−0.424502	+	0.424502i	0.462249	+	0.886750i	$0.347043\pi$
$632$	0.560383	−	29.4093i	0.0222908	−	1.16984i
$633$	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	$0.717781\pi$
$642$	15.3531	−	26.2067i	0.605940	−	1.03429i
$643$	1.12070	+	1.12070i	0.0441961	+	0.0441961i	0.728859	−	0.684663i	$-0.240051\pi$
$643$	1.12070	+	1.12070i	0.0441961	+	0.0441961i	−0.684663	+	0.728859i	$0.740051\pi$
$644$	−27.1182	−	7.63676i	−1.06861	−	0.300930i
$645$	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	$-0.549352\pi$
$647$	−7.85583			−0.308845			−0.154422	+	0.988005i	$0.549352\pi$
$648$	−10.2622	−	0.195543i	−0.403139	−	0.00768164i
$649$		−	2.06979i		−	0.0812462i
$650$	−0.157334	+	5.09659i	−0.00617115	+	0.199905i
$651$		−	35.9639i		−	1.40953i
$652$	24.5375	+	6.91000i	0.960962	+	0.270616i
$653$	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
$656$	5.25074	+	21.7963i	0.205007	+	0.851003i
$657$	−7.44804	−	7.44804i	−0.290576	−	0.290576i
$658$	39.2509	+	22.9951i	1.53016	+	0.896443i
$659$		−	32.2931i		−	1.25796i	−0.777422	−	0.628980i	$-0.783473\pi$
$659$		−	32.2931i		−	1.25796i	0.777422	−	0.628980i	$-0.216527\pi$
$660$	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
$668$	−49.2896	−	13.8804i	−1.90707	−	0.537050i
$669$	−14.2768	+	14.2768i	−0.551973	+	0.551973i
$670$	10.5444	−	17.9984i	0.407364	−	0.695339i
$671$	−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	$0.816938\pi$
$674$	−27.5602	−	16.1461i	−1.06158	−	0.621926i
$675$	−5.61914			−0.216281
$676$	25.9505	+	1.60374i	0.998096	+	0.0616821i
$677$	25.9332			0.996695			0.498347	−	0.866977i	$-0.333940\pi$
$677$	25.9332			0.996695			0.498347	+	0.866977i	$0.333940\pi$
$678$	3.14050	+	1.83986i	0.120610	+	0.0706593i
$679$		−	2.85635i		−	0.109617i
$680$	−10.0450	−	10.4353i	−0.385209	−	0.400174i
$681$	−1.25977	+	1.25977i	−0.0482744	+	0.0482744i
$682$	−7.08845	+	12.0994i	−0.271431	+	0.463312i
$683$	−0.268824	+	0.268824i	−0.0102863	+	0.0102863i	−0.712231	−	0.701945i	$-0.752315\pi$
$683$	−0.268824	+	0.268824i	−0.0102863	+	0.0102863i	0.701945	+	0.712231i	$0.252315\pi$
$684$	3.52028	−	12.5006i	0.134601	−	0.477971i
$685$	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	0.999727	−	0.0233799i	$-0.00744274\pi$
$691$	25.6651	+	25.6651i	0.976347	+	0.976347i	−0.0233799	+	0.999727i	$0.507443\pi$
$692$	7.28078	−	4.08115i	0.276774	−	0.155142i
$693$		−	9.18860i		−	0.349046i
$694$	5.81724	+	3.40802i	0.220819	+	0.129367i
$695$	−8.91708	−	8.91708i	−0.338244	−	0.338244i
$696$	−0.391829	+	20.5635i	−0.0148523	+	0.779458i
$697$	20.2961	+	20.2961i	0.768769	+	0.768769i
$698$	−38.5201	+	10.0597i	−1.45801	+	0.380764i
$699$	−20.0963			−0.760113
$700$	2.42722	−	8.61910i	0.0917404	−	0.325771i
$701$		−	23.7249i		−	0.896075i	−0.894015	−	0.448038i	$-0.852123\pi$
$701$		−	23.7249i		−	0.896075i	0.894015	−	0.448038i	$-0.147877\pi$
$702$	−0.884082	+	28.6385i	−0.0333675	+	1.08089i
$703$			26.1701i			0.987024i
$704$	−9.55357	+	8.85189i	−0.360064	+	0.333618i
$705$	−9.47546			−0.356866
$706$	−7.16454	−	27.4342i	−0.269641	−	1.03250i
$707$	−7.19033	−	7.19033i	−0.270420	−	0.270420i
$708$	0.909013	−	3.22792i	0.0341628	−	0.121313i
$709$	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	$0.521164\pi$
$710$	7.10749	−	12.1319i	0.266739	−	0.455304i
$711$		−	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	$-0.641662\pi$
$719$	−23.0868			−0.860993			−0.430496	+	0.902592i	$0.641662\pi$
$720$	−1.18096	−	4.90229i	−0.0440119	−	0.182698i
$721$	−17.0753	+	17.0753i	−0.635918	+	0.635918i
$722$	−9.19046	−	5.38422i	−0.342034	−	0.200380i
$723$	−6.42400	+	6.42400i	−0.238911	+	0.238911i
$724$	−26.4059	+	14.8015i	−0.981368	+	0.550093i
$725$			5.51361i			0.204770i
$726$	−7.87205	+	13.4370i	−0.292159	+	0.498694i
$727$	−25.5175			−0.946390			−0.473195	−	0.880958i	$-0.656899\pi$
$727$	−25.5175			−0.946390			−0.473195	+	0.880958i	$0.656899\pi$
$728$	−43.5461	−	13.7266i	−1.61393	−	0.508743i
$729$	−26.8071			−0.992857
$730$	−5.97305	+	10.1955i	−0.221072	+	0.377354i
$731$			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	$0.316647\pi$
$734$	41.2057	+	24.1403i	1.52093	+	0.891035i
$735$	12.1654	−	12.1654i	0.448728	−	0.448728i
$736$	8.40522	+	15.6884i	0.309820	+	0.578282i
$737$	−24.0132			−0.884537
$738$	2.52491	+	9.66828i	0.0929432	+	0.355894i
$739$	17.3469	−	17.3469i	0.638117	−	0.638117i	−0.311974	−	0.950091i	$-0.600990\pi$
$739$	17.3469	−	17.3469i	0.638117	−	0.638117i	0.950091	+	0.311974i	$0.100990\pi$
$740$	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	0.675951	−	0.736947i	$-0.263733\pi$
$743$	−1.66264	−	1.66264i	−0.0609964	−	0.0609964i	−0.736947	+	0.675951i	$0.763733\pi$
$744$	−16.3686	+	15.7565i	−0.600101	+	0.577660i
$745$		−	1.53562i		−	0.0562608i
$746$	−9.92583	+	16.9426i	−0.363410	+	0.620314i
$747$	3.10506	+	3.10506i	0.113608	+	0.113608i
$748$	−4.51979	+	16.0498i	−0.165260	+	0.586839i
$749$	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	$-0.642306\pi$
$751$	−23.6951			−0.864646			−0.432323	+	0.901719i	$0.642306\pi$
$752$	−6.73058	−	27.9393i	−0.245439	−	1.01884i
$753$			4.07363i			0.148451i
$754$	28.1006	+	0.867478i	1.02336	+	0.0315917i
$755$			3.61391i			0.131524i
$756$	13.6389	−	48.4319i	0.496042	−	1.76145i
$757$	−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
$760$	−14.5663	−	0.277555i	−0.528375	−	0.0100680i
$761$	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	$0.646657\pi$
$762$	16.7898	+	9.83627i	0.608229	+	0.356330i
$763$			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
$772$	−5.42363	+	19.2594i	−0.195201	+	0.693160i
$773$	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	$0.228157\pi$
$774$	−3.42745	+	5.85040i	−0.123197	+	0.210288i
$775$	−4.30677	+	4.30677i	−0.154704	+	0.154704i
$776$	−1.30004	+	1.25142i	−0.0466687	+	0.0449234i
$777$			30.0000i			1.07625i
$778$	−12.4095	−	7.27012i	−0.444904	−	0.260647i
$779$	28.8706			1.03440
$780$	9.27152	−	2.11800i	0.331974	−	0.0758367i
$781$	−16.1862			−0.579189
$782$	19.6606	+	11.5181i	0.703060	+	0.411887i
$783$			30.9817i			1.10720i
$784$	44.5122	+	27.2295i	1.58972	+	0.972484i
$785$	−9.70690	+	9.70690i	−0.346454	+	0.346454i
$786$	−12.8100	+	21.8657i	−0.456918	+	0.779925i
$787$	11.0812	−	11.0812i	0.395004	−	0.395004i	−0.481463	−	0.876467i	$-0.659894\pi$
$787$	11.0812	−	11.0812i	0.395004	−	0.395004i	0.876467	+	0.481463i	$0.159894\pi$
$788$	25.1023	+	7.06905i	0.894232	+	0.251825i
$789$	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	$0.752663\pi$
$798$	−37.1128	−	21.7425i	−1.31378	−	0.769677i
$799$	−26.0162	−	26.0162i	−0.920388	−	0.920388i
$800$	−4.98631	+	2.67147i	−0.176293	+	0.0944506i
$801$	−2.87229	−	2.87229i	−0.101487	−	0.101487i
$802$	26.0212	−	6.79555i	0.918842	−	0.239959i
$803$	13.6027			0.480030
$804$	−37.4495	−	10.5462i	−1.32074	−	0.371934i
$805$			14.0865i			0.496484i
$806$	21.2723	+	22.6275i	0.749283	+	0.797018i
$807$		−	27.8986i		−	0.982077i
$808$	−0.122384	+	6.42282i	−0.00430546	+	0.225954i
$809$	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	$0.101544\pi$
$811$	35.9727	+	35.9727i	1.26317	+	1.26317i	0.313626	+	0.949546i	$0.398456\pi$
$812$	−47.5223	−	13.3828i	−1.66771	−	0.469642i
$813$	−5.17729	−	5.17729i	−0.181575	−	0.181575i
$814$	5.91299	−	10.0930i	0.207250	−	0.353760i
$815$		−	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	$-0.694423\pi$
$823$	−32.9063			−1.14704			−0.573520	+	0.819192i	$0.694423\pi$
$824$	15.2527	+	0.290634i	0.531353	+	0.0101247i
$825$	1.51823	−	1.51823i	0.0528580	−	0.0528580i
$826$	6.94567	+	4.06911i	0.241671	+	0.141583i
$827$	5.90778	−	5.90778i	0.205434	−	0.205434i	−0.596890	−	0.802323i	$-0.703597\pi$
$827$	5.90778	−	5.90778i	0.205434	−	0.205434i	0.802323	+	0.596890i	$0.203597\pi$
$828$	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	$-0.428431\pi$
$830$	2.49014	−	4.25049i	0.0864342	−	0.147537i
$831$	16.9179			0.586876
$832$	12.8309	+	25.8335i	0.444830	+	0.895615i
$833$	66.8038			2.31462
$834$	−11.8894	+	20.2943i	−0.411697	+	0.702736i
$835$			25.6034i			0.886041i
$836$	8.20056	+	14.6298i	0.283622	+	0.505983i
$837$	−24.2003	+	24.2003i	−0.836486	+	0.836486i
$838$	7.80735	+	4.57393i	0.269700	+	0.158004i
$839$	−29.0414	+	29.0414i	−1.00262	+	1.00262i	−0.00262283	+	0.999997i	$0.500835\pi$
$839$	−29.0414	+	29.0414i	−1.00262	+	1.00262i	−0.999997	+	0.00262283i	$0.999165\pi$
$840$	−16.6980	−	0.318174i	−0.576137	−	0.0109781i
$841$	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
$850$	−3.66085	+	6.24880i	−0.125566	+	0.214332i
$851$	−11.3033	−	11.3033i	−0.387473	−	0.387473i
$852$	−25.2431	−	7.10871i	−0.864814	−	0.243540i
$853$	−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
$856$	0.877486	−	46.0512i	0.0299918	−	1.57400i
$857$			31.1973i			1.06568i	0.846216	+	0.532840i	$0.178875\pi$
$857$			31.1973i			1.06568i	−0.846216	+	0.532840i	$0.821125\pi$
$858$	−7.49893	−	7.97667i	−0.256009	−	0.272319i
$859$		−	33.0567i		−	1.12788i	−0.825815	−	0.563940i	$-0.809285\pi$
$859$		−	33.0567i		−	1.12788i	0.825815	−	0.563940i	$-0.190715\pi$
$860$	7.32173	+	2.06187i	0.249669	+	0.0703092i
$861$	33.0957			1.12790
$862$	−10.1303	+	2.64556i	−0.345038	+	0.0901081i
$863$	−28.9412	−	28.9412i	−0.985169	−	0.985169i	0.0147222	−	0.999892i	$-0.495314\pi$
$863$	−28.9412	−	28.9412i	−0.985169	−	0.985169i	−0.999892	+	0.0147222i	$0.995314\pi$
$864$	−28.0188	+	15.0113i	−0.953217	+	0.510696i
$865$	−2.95097	−	2.95097i	−0.100336	−	0.100336i
$866$	18.9490	+	11.1013i	0.643913	+	0.377236i
$867$			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
$876$	21.2140	+	5.97407i	0.716754	+	0.201845i
$877$	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	$-0.0308937\pi$
$878$	12.2353	−	20.8847i	0.412922	−	0.704826i
$879$	−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	$0.700511\pi$
$882$	20.0667	+	11.7561i	0.675682	+	0.395848i
$883$	5.54312			0.186541			0.0932704	−	0.995641i	$-0.470268\pi$
$883$	5.54312			0.186541			0.0932704	+	0.995641i	$0.470268\pi$
$884$	31.2716	+	19.6410i	1.05178	+	0.660599i
$885$	−1.67673			−0.0563628
$886$	−30.8809	−	18.0916i	−1.03746	−	0.607798i
$887$			42.2799i			1.41962i	0.704394	+	0.709810i	$0.251219\pi$
$887$			42.2799i			1.41962i	−0.704394	+	0.709810i	$0.748781\pi$
$888$	13.6542	−	13.1436i	0.458205	−	0.441070i
$889$	−33.0290	+	33.0290i	−1.10776	+	1.10776i
$890$	−2.30347	+	3.93185i	−0.0772124	+	0.131796i
$891$	4.17752	−	4.17752i	0.139952	−	0.139952i
$892$	−8.29959	+	29.4719i	−0.277891	+	0.986793i
$893$	−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
$902$	−11.1345	−	6.52314i	−0.370739	−	0.217197i
$903$	15.8796	+	15.8796i	0.528441	+	0.528441i
$904$	5.51858	+	0.105154i	0.183545	+	0.00349738i
$905$	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	$-0.701189\pi$
$907$	−35.5858			−1.18161			−0.590804	+	0.806815i	$0.701189\pi$
$908$	−0.732346	+	2.60057i	−0.0243037	+	0.0863029i
$909$			2.86318i			0.0949656i
$910$	−0.704412	+	22.8183i	−0.0233510	+	0.756420i
$911$			50.3196i			1.66716i	0.552396	+	0.833582i	$0.313714\pi$
$911$			50.3196i			1.66716i	−0.552396	+	0.833582i	$0.686286\pi$
$912$	6.36395	+	26.4173i	0.210731	+	0.874765i
$913$	−5.67093			−0.187680
$914$	−7.08661	−	27.1357i	−0.234404	−	0.897571i
$915$	9.96391	+	9.96391i	0.329397	+	0.329397i
$916$	10.2179	−	36.2840i	0.337610	−	1.19886i
$917$	−43.0146	−	43.0146i	−1.42047	−	1.42047i
$918$	−20.5708	+	35.1129i	−0.678939	+	1.15890i
$919$		−	17.7610i		−	0.585882i	−0.956131	−	0.292941i	$-0.905366\pi$
$919$		−	17.7610i		−	0.585882i	0.956131	−	0.292941i	$-0.0946339\pi$
$920$	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
$928$	14.7294	+	27.4925i	0.483517	+	0.902487i
$929$	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	$0.0968082\pi$
$930$	9.80176	+	5.74235i	0.321412	+	0.188299i
$931$	47.5132	−	47.5132i	1.55718	−	1.55718i
$932$	−26.5840	+	14.9013i	−0.870787	+	0.488109i
$933$			10.8331i			0.354661i
$934$	−16.2700	+	27.7717i	−0.532371	+	0.908717i
$935$	8.33704			0.272650
$936$	5.93704	+	11.4030i	0.194058	+	0.372718i
$937$	33.5601			1.09636			0.548181	−	0.836360i	$-0.315321\pi$
$937$	33.5601			1.09636			0.548181	+	0.836360i	$0.315321\pi$
$938$	47.2089	−	80.5820i	1.54142	−	2.63109i
$939$		−	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	$0.0794891\pi$
$942$	22.0919	+	12.9425i	0.719793	+	0.421690i
$943$	−12.4697	+	12.4697i	−0.406070	+	0.406070i
$944$	−1.19101	−	4.94401i	−0.0387642	−	0.160914i
$945$	−25.1578			−0.818385
$946$	−2.21257	−	8.47229i	−0.0719370	−	0.275458i
$947$	−0.674394	+	0.674394i	−0.0219149	+	0.0219149i	−0.717979	−	0.696064i	$-0.754933\pi$
$947$	−0.674394	+	0.674394i	−0.0219149	+	0.0219149i	0.696064	+	0.717979i	$0.254933\pi$
$948$	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	$0.803985\pi$
$954$	7.87569	−	13.4432i	0.254985	−	0.435240i
$955$	−5.20596	−	5.20596i	−0.168461	−	0.168461i
$956$	6.81484	−	24.1996i	0.220408	−	0.782670i
$957$	−8.37092	−	8.37092i	−0.270594	−	0.270594i
$958$	5.65006	+	21.6350i	0.182545	+	0.698994i
$959$	77.2812			2.49554
$960$	7.17092	+	7.73934i	0.231440	+	0.249786i
$961$			6.09655i			0.196663i
$962$	−17.7447	−	18.8752i	−0.572113	−	0.608561i
$963$		−	20.5288i		−	0.661530i
$964$	−3.73449	+	13.2612i	−0.120280	+	0.427115i
$965$	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	$0.0929060\pi$
$967$	38.7294	+	38.7294i	1.24545	+	1.24545i	0.287746	+	0.957707i	$0.407094\pi$
$968$	−0.449915	+	23.6119i	−0.0144608	+	0.758915i
$969$	24.5991	+	24.5991i	0.790236	+	0.790236i
$970$	0.778483	+	0.456074i	0.0249956	+	0.0146436i
$971$			6.78979i			0.217895i	0.994048	+	0.108947i	$0.0347480\pi$
$971$			6.78979i			0.217895i	−0.994048	+	0.108947i	$0.965252\pi$
$972$	−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
$980$	7.07216	−	25.1133i	0.225912	−	0.802216i
$981$	0.238883	−	0.238883i	0.00762695	−	0.00762695i
$982$	8.68031	−	14.8166i	0.277000	−	0.472817i
$983$	3.97472	−	3.97472i	0.126774	−	0.126774i	−0.640873	−	0.767647i	$-0.721427\pi$
$983$	3.97472	−	3.97472i	0.126774	−	0.126774i	0.767647	+	0.640873i	$0.221427\pi$
$984$	−14.4999	−	15.0632i	−0.462239	−	0.480197i
$985$		−	13.0393i		−	0.415467i
$986$	34.4534	+	20.1845i	1.09722	+	0.642806i
$987$	−42.4232			−1.35035
$988$	36.2108	−	8.27207i	1.15202	−	0.263169i
$989$	−11.9662			−0.380502
$990$	2.50430	+	1.46714i	0.0795920	+	0.0466289i
$991$		−	29.3559i		−	0.932522i	−0.884647	−	0.466261i	$-0.845601\pi$
$991$		−	29.3559i		−	0.932522i	0.884647	−	0.466261i	$-0.154399\pi$
$992$	−9.96949	+	32.9803i	−0.316532	+	1.04712i
$993$	−13.8595	+	13.8595i	−0.439819	+	0.439819i
$994$	31.8215	−	54.3168i	1.00932	−	1.72282i
$995$	−9.40432	+	9.40432i	−0.298137	+	0.298137i
$996$	−8.84404	−	2.49057i	−0.280234	−	0.0789167i
$997$	−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.31.10	yes	56
4.3	odd	2	inner	260.2.j.a.31.5	✓	56
13.8	odd	4	inner	260.2.j.a.151.5	yes	56
52.47	even	4	inner	260.2.j.a.151.10	yes	56

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

\(f(q)\)	\(=\)	\(q+(-0.714871 + 1.22023i) q^{2} -1.31885i q^{3} +(-0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.60930 + 0.942808i) q^{6} +(-3.16584 + 3.16584i) q^{7} +(2.82791 + 0.0538847i) q^{8} +1.26063 q^{9} +O(q^{10})\)	\(q+(-0.714871 + 1.22023i) q^{2} -1.31885i q^{3} +(-0.977920 - 1.74461i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.60930 + 0.942808i) q^{6} +(-3.16584 + 3.16584i) q^{7} +(2.82791 + 0.0538847i) 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} +(-0.901189 + 1.53826i) q^{18} +(3.64223 + 3.64223i) q^{19} +(1.92512 + 0.542133i) q^{20} +(4.17527 + 4.17527i) q^{21} +(-0.581758 - 2.22764i) q^{22} -3.14629 q^{23} +(0.0710659 - 3.72960i) q^{24} -1.00000i q^{25} +(-5.09659 - 0.157334i) q^{26} -5.61914i q^{27} +(8.61910 + 2.42722i) q^{28} -5.51361 q^{29} +(-1.80461 + 0.471282i) q^{30} +(-4.30677 - 4.30677i) q^{31} +(-2.67147 - 4.98631i) q^{32} +(1.51823 + 1.51823i) q^{33} +(-6.24880 - 3.66085i) 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} +(3.13412 + 0.882598i) q^{44} +(-0.891402 + 0.891402i) q^{45} +(2.24919 - 3.83920i) q^{46} +(-5.08030 + 5.08030i) q^{47} +(4.50016 + 2.75290i) q^{48} -13.0451i q^{49} +(1.22023 + 0.714871i) q^{50} +6.75384 q^{51} +(3.83539 - 6.10654i) q^{52} -8.73922 q^{53} +(6.85664 + 4.01696i) q^{54} -1.62801i q^{55} +(-9.12331 + 8.78213i) q^{56} +(4.80356 - 4.80356i) q^{57} +(3.94151 - 6.72786i) q^{58} +(-0.898987 + 0.898987i) q^{59} +(0.714993 - 2.53895i) 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} +(5.46318 + 3.20060i) q^{70} +(7.03030 + 7.03030i) q^{71} +(3.56496 + 0.0679288i) q^{72} +(-5.90818 - 5.90818i) q^{73} +(-6.95202 + 1.81555i) q^{74} -1.31885 q^{75} +(2.79247 - 9.91610i) q^{76} -7.28888i q^{77} +(-0.207500 + 6.72164i) q^{78} -10.3997i q^{79} +(-0.936803 - 3.88875i) q^{80} -3.62891 q^{81} +(2.00289 + 7.66939i) q^{82} +(2.46310 + 2.46310i) q^{83} +(3.20115 - 11.3673i) q^{84} +(-3.62110 - 3.62110i) q^{85} +(-2.71884 + 4.64085i) 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} +(-6.57620 + 3.52327i) q^{96} +(-0.451121 + 0.451121i) q^{97} +(15.9180 + 9.32553i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more