LMFDB - Embedded newform 260.2.p.d.103.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(103,260)]

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, 3, 2]))

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

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

chi := DirichletCharacter("260.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.p (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:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			103.9
Character	$\chi$	$=$	260.103
Dual form			260.2.p.d.207.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.885485 + 1.10269i) q^{2} +(1.59124 - 1.59124i) q^{3} +(-0.431834 - 1.95282i) q^{4} +(0.349775 - 2.20854i) q^{5} +(0.345619 + 3.16365i) q^{6} +(-1.15539 + 1.15539i) q^{7} +(2.53573 + 1.25302i) q^{8} -2.06407i q^{9} +O(q^{10})$	\(q+(-0.885485 + 1.10269i) q^{2} +(1.59124 - 1.59124i) q^{3} +(-0.431834 - 1.95282i) q^{4} +(0.349775 - 2.20854i) q^{5} +(0.345619 + 3.16365i) q^{6} +(-1.15539 + 1.15539i) q^{7} +(2.53573 + 1.25302i) q^{8} -2.06407i q^{9} +(2.12561 + 2.34132i) q^{10} -1.00150 q^{11} +(-3.79455 - 2.42026i) q^{12} +(1.28460 - 3.36895i) q^{13} +(-0.250952 - 2.29711i) q^{14} +(-2.95774 - 4.07089i) q^{15} +(-3.62704 + 1.68659i) q^{16} +(3.12166 - 3.12166i) q^{17} +(2.27602 + 1.82770i) q^{18} -5.00790i q^{19} +(-4.46394 + 0.270674i) q^{20} +3.67700i q^{21} +(0.886815 - 1.10434i) q^{22} +(-1.24973 + 1.24973i) q^{23} +(6.02880 - 2.04110i) q^{24} +(-4.75531 - 1.54499i) q^{25} +(2.57740 + 4.39966i) q^{26} +(1.48928 + 1.48928i) q^{27} +(2.75521 + 1.75734i) q^{28} +8.31301i q^{29} +(7.10795 + 0.343252i) q^{30} +0.288879 q^{31} +(1.35191 - 5.49294i) q^{32} +(-1.59363 + 1.59363i) q^{33} +(0.678029 + 6.20640i) q^{34} +(2.14760 + 2.95585i) q^{35} +(-4.03077 + 0.891335i) q^{36} +(3.74705 + 3.74705i) q^{37} +(5.52214 + 4.43442i) q^{38} +(-3.31670 - 7.40489i) q^{39} +(3.65428 - 5.16200i) q^{40} +5.64607i q^{41} +(-4.05458 - 3.25593i) q^{42} +(7.56234 - 7.56234i) q^{43} +(0.432483 + 1.95576i) q^{44} +(-4.55859 - 0.721961i) q^{45} +(-0.271444 - 2.48468i) q^{46} +(-3.67990 + 3.67990i) q^{47} +(-3.08772 + 8.45524i) q^{48} +4.33015i q^{49} +(5.91439 - 3.87556i) q^{50} -9.93461i q^{51} +(-7.13369 - 1.05376i) q^{52} +(5.06483 + 5.06483i) q^{53} +(-2.96095 + 0.323475i) q^{54} +(-0.350301 + 2.21186i) q^{55} +(-4.37749 + 1.48204i) q^{56} +(-7.96876 - 7.96876i) q^{57} +(-9.16664 - 7.36105i) q^{58} +13.0878i q^{59} +(-6.67248 + 7.53389i) q^{60} -7.36625 q^{61} +(-0.255798 + 0.318543i) q^{62} +(2.38481 + 2.38481i) q^{63} +(4.85989 + 6.35464i) q^{64} +(-6.99114 - 4.01546i) q^{65} +(-0.346138 - 3.16841i) q^{66} +(4.73121 - 4.73121i) q^{67} +(-7.44409 - 4.74802i) q^{68} +3.97725i q^{69} +(-5.16105 - 0.249234i) q^{70} -4.14895 q^{71} +(2.58632 - 5.23393i) q^{72} +(6.49166 - 6.49166i) q^{73} +(-7.44977 + 0.813864i) q^{74} +(-10.0253 + 5.10839i) q^{75} +(-9.77955 + 2.16258i) q^{76} +(1.15713 - 1.15713i) q^{77} +(11.1022 + 2.89964i) q^{78} -13.9090 q^{79} +(2.45626 + 8.60040i) q^{80} +10.9318 q^{81} +(-6.22585 - 4.99951i) q^{82} +(1.78063 + 1.78063i) q^{83} +(7.18053 - 1.58785i) q^{84} +(-5.80244 - 7.98620i) q^{85} +(1.64255 + 15.0352i) q^{86} +(13.2280 + 13.2280i) q^{87} +(-2.53954 - 1.25490i) q^{88} +12.4897 q^{89} +(4.83266 - 4.38741i) q^{90} +(2.40824 + 5.37666i) q^{91} +(2.98019 + 1.90083i) q^{92} +(0.459675 - 0.459675i) q^{93} +(-0.799279 - 7.31627i) q^{94} +(-11.0602 - 1.75164i) q^{95} +(-6.58935 - 10.8918i) q^{96} +(2.03795 + 2.03795i) q^{97} +(-4.77479 - 3.83428i) q^{98} +2.06717i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) $ 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.885485	+	1.10269i	−0.626132	+	0.779717i
$2$	−0.885485	+	1.10269i	−0.626132	+	0.779717i
$3$	1.59124	−	1.59124i	0.918701	−	0.918701i	−0.0782339	−	0.996935i	$-0.524928\pi$
$3$	1.59124	−	1.59124i	0.918701	−	0.918701i	0.996935	+	0.0782339i	$0.0249281\pi$
$4$	−0.431834	−	1.95282i	−0.215917	−	0.976412i
$5$	0.349775	−	2.20854i	0.156424	−	0.987690i
$5$	0.349775	−	2.20854i	0.156424	−	0.987690i
$6$	0.345619	+	3.16365i	0.141098	+	1.29156i
$7$	−1.15539	+	1.15539i	−0.436696	+	0.436696i	−0.890899	−	0.454202i	$-0.849924\pi$
$7$	−1.15539	+	1.15539i	−0.436696	+	0.436696i	0.454202	+	0.890899i	$0.349924\pi$
$8$	2.53573	+	1.25302i	0.896517	+	0.443009i
$9$		−	2.06407i		−	0.688024i
$10$	2.12561	+	2.34132i	0.672176	+	0.740391i
$11$	−1.00150			−0.301964			−0.150982	−	0.988536i	$-0.548244\pi$
$11$	−1.00150			−0.301964			−0.150982	+	0.988536i	$0.548244\pi$
$12$	−3.79455	−	2.42026i	−1.09539	−	0.698668i
$13$	1.28460	−	3.36895i	0.356283	−	0.934378i
$13$	1.28460	−	3.36895i	0.356283	−	0.934378i
$14$	−0.250952	−	2.29711i	−0.0670698	−	0.613929i
$15$	−2.95774	−	4.07089i	−0.763685	−	1.05110i
$16$	−3.62704	+	1.68659i	−0.906760	+	0.421647i
$17$	3.12166	−	3.12166i	0.757114	−	0.757114i	−0.218682	−	0.975796i	$-0.570176\pi$
$17$	3.12166	−	3.12166i	0.757114	−	0.757114i	0.975796	+	0.218682i	$0.0701758\pi$
$18$	2.27602	+	1.82770i	0.536464	+	0.430794i
$19$		−	5.00790i		−	1.14889i	−0.818543	−	0.574446i	$-0.805218\pi$
$19$		−	5.00790i		−	1.14889i	0.818543	−	0.574446i	$-0.194782\pi$
$20$	−4.46394	+	0.270674i	−0.998167	+	0.0605244i
$21$			3.67700i			0.802387i
$22$	0.886815	−	1.10434i	0.189070	−	0.235447i
$23$	−1.24973	+	1.24973i	−0.260588	+	0.260588i	−0.825293	−	0.564705i	$-0.808990\pi$
$23$	−1.24973	+	1.24973i	−0.260588	+	0.260588i	0.564705	+	0.825293i	$0.308990\pi$
$24$	6.02880	−	2.04110i	1.23062	−	0.416639i
$25$	−4.75531	−	1.54499i	−0.951063	−	0.308997i
$26$	2.57740	+	4.39966i	0.505470	+	0.862844i
$27$	1.48928	+	1.48928i	0.286613	+	0.286613i
$28$	2.75521	+	1.75734i	0.520686	+	0.332105i
$29$			8.31301i			1.54369i	0.635812	+	0.771844i	$0.280665\pi$
$29$			8.31301i			1.54369i	−0.635812	+	0.771844i	$0.719335\pi$
$30$	7.10795	+	0.343252i	1.29773	+	0.0626690i
$31$	0.288879			0.0518842			0.0259421	−	0.999663i	$-0.491741\pi$
$31$	0.288879			0.0518842			0.0259421	+	0.999663i	$0.491741\pi$
$32$	1.35191	−	5.49294i	0.238986	−	0.971023i
$33$	−1.59363	+	1.59363i	−0.277415	+	0.277415i
$34$	0.678029	+	6.20640i	0.116281	+	1.06439i
$35$	2.14760	+	2.95585i	0.363011	+	0.499631i
$36$	−4.03077	+	0.891335i	−0.671794	+	0.148556i
$37$	3.74705	+	3.74705i	0.616011	+	0.616011i	0.944506	−	0.328495i	$-0.106541\pi$
$37$	3.74705	+	3.74705i	0.616011	+	0.616011i	−0.328495	+	0.944506i	$0.606541\pi$
$38$	5.52214	+	4.43442i	0.895810	+	0.719358i
$39$	−3.31670	−	7.40489i	−0.531097	−	1.18573i
$40$	3.65428	−	5.16200i	0.577792	−	0.816184i
$41$			5.64607i			0.881769i	0.897564	+	0.440884i	$0.145335\pi$
$41$			5.64607i			0.881769i	−0.897564	+	0.440884i	$0.854665\pi$
$42$	−4.05458	−	3.25593i	−0.625635	−	0.502400i
$43$	7.56234	−	7.56234i	1.15325	−	1.15325i	0.167349	−	0.985898i	$-0.446479\pi$
$43$	7.56234	−	7.56234i	1.15325	−	1.15325i	0.985898	−	0.167349i	$-0.0535206\pi$
$44$	0.432483	+	1.95576i	0.0651992	+	0.294842i
$45$	−4.55859	−	0.721961i	−0.679554	−	0.107624i
$46$	−0.271444	−	2.48468i	−0.0400222	−	0.366347i
$47$	−3.67990	+	3.67990i	−0.536768	+	0.536768i	−0.922578	−	0.385810i	$-0.873922\pi$
$47$	−3.67990	+	3.67990i	−0.536768	+	0.536768i	0.385810	+	0.922578i	$0.373922\pi$
$48$	−3.08772	+	8.45524i	−0.445673	+	1.22041i
$49$			4.33015i			0.618592i
$50$	5.91439	−	3.87556i	0.836422	−	0.548087i
$51$		−	9.93461i		−	1.39112i
$52$	−7.13369	−	1.05376i	−0.989265	−	0.146131i
$53$	5.06483	+	5.06483i	0.695708	+	0.695708i	0.963482	−	0.267774i	$-0.0862881\pi$
$53$	5.06483	+	5.06483i	0.695708	+	0.695708i	−0.267774	+	0.963482i	$0.586288\pi$
$54$	−2.96095	+	0.323475i	−0.402935	+	0.0440193i
$55$	−0.350301	+	2.21186i	−0.0472345	+	0.298247i
$56$	−4.37749	+	1.48204i	−0.584966	+	0.198045i
$57$	−7.96876	−	7.96876i	−1.05549	−	1.05549i
$58$	−9.16664	−	7.36105i	−1.20364	−	0.966553i
$59$			13.0878i			1.70389i	0.523630	+	0.851946i	$0.324577\pi$
$59$			13.0878i			1.70389i	−0.523630	+	0.851946i	$0.675423\pi$
$60$	−6.67248	+	7.53389i	−0.861413	+	0.972621i
$61$	−7.36625			−0.943152			−0.471576	−	0.881826i	$-0.656315\pi$
$61$	−7.36625			−0.943152			−0.471576	+	0.881826i	$0.656315\pi$
$62$	−0.255798	+	0.318543i	−0.0324864	+	0.0404550i
$63$	2.38481	+	2.38481i	0.300457	+	0.300457i
$64$	4.85989	+	6.35464i	0.607486	+	0.794330i
$65$	−6.99114	−	4.01546i	−0.867145	−	0.498056i
$66$	−0.346138	−	3.16841i	−0.0426067	−	0.390004i
$67$	4.73121	−	4.73121i	0.578009	−	0.578009i	−0.356346	−	0.934354i	$-0.615977\pi$
$67$	4.73121	−	4.73121i	0.578009	−	0.578009i	0.934354	+	0.356346i	$0.115977\pi$
$68$	−7.44409	−	4.74802i	−0.902729	−	0.575781i
$69$			3.97725i			0.478804i
$70$	−5.16105	−	0.249234i	−0.616863	−	0.0297892i
$71$	−4.14895			−0.492390			−0.246195	−	0.969220i	$-0.579180\pi$
$71$	−4.14895			−0.492390			−0.246195	+	0.969220i	$0.579180\pi$
$72$	2.58632	−	5.23393i	0.304801	−	0.616825i
$73$	6.49166	−	6.49166i	0.759792	−	0.759792i	−0.216493	−	0.976284i	$-0.569462\pi$
$73$	6.49166	−	6.49166i	0.759792	−	0.759792i	0.976284	+	0.216493i	$0.0694618\pi$
$74$	−7.44977	+	0.813864i	−0.866018	+	0.0946098i
$75$	−10.0253	+	5.10839i	−1.15762	+	0.589867i
$76$	−9.77955	+	2.16258i	−1.12179	+	0.248065i
$77$	1.15713	−	1.15713i	0.131867	−	0.131867i
$78$	11.1022	+	2.89964i	1.25707	+	0.328320i
$79$	−13.9090			−1.56489			−0.782443	−	0.622723i	$-0.786026\pi$
$79$	−13.9090			−1.56489			−0.782443	+	0.622723i	$0.786026\pi$
$80$	2.45626	+	8.60040i	0.274618	+	0.961553i
$81$	10.9318			1.21465
$82$	−6.22585	−	4.99951i	−0.687530	−	0.552104i
$83$	1.78063	+	1.78063i	0.195449	+	0.195449i	0.798046	−	0.602597i	$-0.205867\pi$
$83$	1.78063	+	1.78063i	0.195449	+	0.195449i	−0.602597	+	0.798046i	$0.705867\pi$
$84$	7.18053	−	1.58785i	0.783460	−	0.173249i
$85$	−5.80244	−	7.98620i	−0.629363	−	0.866225i
$86$	1.64255	+	15.0352i	0.177121	+	1.62129i
$87$	13.2280	+	13.2280i	1.41819	+	1.41819i
$88$	−2.53954	−	1.25490i	−0.270716	−	0.133773i
$89$	12.4897			1.32390			0.661951	−	0.749547i	$-0.269729\pi$
$89$	12.4897			1.32390			0.661951	+	0.749547i	$0.269729\pi$
$90$	4.83266	−	4.38741i	0.509407	−	0.462473i
$91$	2.40824	+	5.37666i	0.252452	+	0.563627i
$92$	2.98019	+	1.90083i	0.310706	+	0.198176i
$93$	0.459675	−	0.459675i	0.0476661	−	0.0476661i
$94$	−0.799279	−	7.31627i	−0.0824394	−	0.754615i
$95$	−11.0602	−	1.75164i	−1.13475	−	0.179714i
$96$	−6.58935	−	10.8918i	−0.672523	−	1.11164i
$97$	2.03795	+	2.03795i	0.206923	+	0.206923i	0.802958	−	0.596035i	$-0.203258\pi$
$97$	2.03795	+	2.03795i	0.206923	+	0.206923i	−0.596035	+	0.802958i	$0.703258\pi$
$98$	−4.77479	−	3.83428i	−0.482327	−	0.387321i
$99$			2.06717i			0.207759i
$100$	−0.963580	+	9.95347i	−0.0963580	+	0.995347i
$101$	3.87660			0.385736			0.192868	−	0.981225i	$-0.438221\pi$
$101$	3.87660			0.385736			0.192868	+	0.981225i	$0.438221\pi$
$102$	10.9548	+	8.79694i	1.08468	+	0.871027i
$103$	−0.0173781	+	0.0173781i	−0.00171232	+	0.00171232i	−0.707962	−	0.706250i	$-0.750385\pi$
$103$	−0.0173781	+	0.0173781i	−0.00171232	+	0.00171232i	0.706250	+	0.707962i	$0.250385\pi$
$104$	7.47875	−	6.93313i	0.733351	−	0.679850i
$105$	8.12081	+	1.28612i	0.792510	+	0.125513i
$106$	−10.0697	+	1.10009i	−0.978060	+	0.106850i
$107$	6.11504	+	6.11504i	0.591163	+	0.591163i	0.937946	−	0.346782i	$-0.112726\pi$
$107$	6.11504	+	6.11504i	0.591163	+	0.591163i	−0.346782	+	0.937946i	$0.612726\pi$
$108$	2.26519	−	3.55143i	0.217968	−	0.341737i
$109$	−4.74580			−0.454565			−0.227283	−	0.973829i	$-0.572984\pi$
$109$	−4.74580			−0.454565			−0.227283	+	0.973829i	$0.572984\pi$
$110$	−2.12880	−	2.34484i	−0.202973	−	0.223572i
$111$	11.9249			1.13186
$112$	2.24198	−	6.13931i	0.211847	−	0.580111i
$113$	−6.72237	−	6.72237i	−0.632387	−	0.632387i	0.316279	−	0.948666i	$-0.397566\pi$
$113$	−6.72237	−	6.72237i	−0.632387	−	0.632387i	−0.948666	+	0.316279i	$0.897566\pi$
$114$	15.8433	−	1.73083i	1.48386	−	0.162107i
$115$	2.32296	+	3.19722i	0.216618	+	0.298142i
$116$	16.2338	−	3.58984i	1.50727	−	0.333308i
$117$	−6.95375	−	2.65150i	−0.642874	−	0.245131i
$118$	−14.4318	−	11.5891i	−1.32855	−	1.06686i
$119$			7.21347i			0.661258i
$120$	−2.39914	−	14.0288i	−0.219010	−	1.28065i
$121$	−9.99699			−0.908817
$122$	6.52270	−	8.12266i	0.590538	−	0.735391i
$123$	8.98424	+	8.98424i	0.810082	+	0.810082i
$124$	−0.124748	−	0.564130i	−0.0112027	−	0.0506604i
$125$	−5.07546	+	9.96191i	−0.453963	+	0.891021i
$126$	−4.74140	+	0.517984i	−0.422398	+	0.0461456i
$127$	−2.66972	−	2.66972i	−0.236899	−	0.236899i	0.578666	−	0.815565i	$-0.303574\pi$
$127$	−2.66972	−	2.66972i	−0.236899	−	0.236899i	−0.815565	+	0.578666i	$0.803574\pi$
$128$	−11.3105	−	0.268006i	−0.999719	−	0.0236886i
$129$		−	24.0670i		−	2.11898i
$130$	10.6183	−	4.15341i	0.931290	−	0.364278i
$131$		−	18.7764i		−	1.64050i	−0.572005	−	0.820250i	$-0.693834\pi$
$131$		−	18.7764i		−	1.64050i	0.572005	−	0.820250i	$-0.306166\pi$
$132$	3.80026	+	2.42389i	0.330770	+	0.210973i
$133$	5.78608	+	5.78608i	0.501717	+	0.501717i
$134$	1.02762	+	9.40644i	0.0887732	+	0.812593i
$135$	3.81006	−	2.76823i	0.327918	−	0.238252i
$136$	11.8272	−	4.00420i	1.01417	−	0.343357i
$137$	−0.875109	−	0.875109i	−0.0747656	−	0.0747656i	0.668735	−	0.743501i	$-0.266836\pi$
$137$	−0.875109	−	0.875109i	−0.0747656	−	0.0747656i	−0.743501	+	0.668735i	$0.766836\pi$
$138$	−4.38565	−	3.52179i	−0.373332	−	0.299795i
$139$	8.67356			0.735681			0.367841	−	0.929889i	$-0.380097\pi$
$139$	8.67356			0.735681			0.367841	+	0.929889i	$0.380097\pi$
$140$	4.84486	−	5.47032i	0.409465	−	0.462327i
$141$			11.7112i			0.986259i
$142$	3.67384	−	4.57499i	0.308301	−	0.383925i
$143$	−1.28653	+	3.37401i	−0.107585	+	0.282149i
$144$	3.48124	+	7.48647i	0.290103	+	0.623872i
$145$	18.3596	+	2.90768i	1.52468	+	0.241470i
$146$	1.41000	+	12.9065i	0.116692	+	1.06815i
$147$	6.89029	+	6.89029i	0.568302	+	0.568302i
$148$	5.69922	−	8.93542i	0.468473	−	0.734487i
$149$	5.04127			0.412997			0.206499	−	0.978447i	$-0.433793\pi$
$149$	5.04127			0.412997			0.206499	+	0.978447i	$0.433793\pi$
$150$	3.24427	−	15.5781i	0.264893	−	1.27195i
$151$	12.6118			1.02634			0.513168	−	0.858288i	$-0.328472\pi$
$151$	12.6118			1.02634			0.513168	+	0.858288i	$0.328472\pi$
$152$	6.27499	−	12.6987i	0.508969	−	1.03000i
$153$	−6.44333	−	6.44333i	−0.520912	−	0.520912i
$154$	0.251330	+	2.30057i	0.0202527	+	0.185385i
$155$	0.101043	−	0.638002i	0.00811595	−	0.0512456i
$156$	−13.0282	+	9.67461i	−1.04309	+	0.774589i
$157$	−8.48528	+	8.48528i	−0.677199	+	0.677199i	−0.959365	−	0.282167i	$-0.908947\pi$
$157$	−8.48528	+	8.48528i	−0.677199	+	0.677199i	0.282167	+	0.959365i	$0.408947\pi$
$158$	12.3162	−	15.3373i	0.979825	−	1.22017i
$159$	16.1187			1.27829
$160$	−11.6585	−	4.90704i	−0.921686	−	0.387936i
$161$		−	2.88786i		−	0.227595i
$162$	−9.67996	+	12.0544i	−0.760530	+	0.947081i
$163$	−7.33086	−	7.33086i	−0.574198	−	0.574198i	0.359101	−	0.933299i	$-0.383083\pi$
$163$	−7.33086	−	7.33086i	−0.574198	−	0.574198i	−0.933299	+	0.359101i	$0.883083\pi$
$164$	11.0258	−	2.43816i	0.860969	−	0.190389i
$165$	2.96218	+	4.07701i	0.230606	+	0.317395i
$166$	−3.54019	+	0.386755i	−0.274772	+	0.0300180i
$167$	−13.5670	+	13.5670i	−1.04985	+	1.04985i	−0.0511560	+	0.998691i	$0.516291\pi$
$167$	−13.5670	+	13.5670i	−1.04985	+	1.04985i	−0.998691	+	0.0511560i	$0.983709\pi$
$168$	−4.60735	+	9.32389i	−0.355465	+	0.719354i
$169$	−9.69963	−	8.65547i	−0.746125	−	0.665806i
$170$	13.9442	+	0.673387i	1.06947	+	0.0516464i
$171$	−10.3367			−0.790464
$172$	−18.0336	−	11.5022i	−1.37505	−	0.877038i
$173$	1.85755	+	1.85755i	0.141227	+	0.141227i	0.774186	−	0.632959i	$-0.218160\pi$
$173$	1.85755	+	1.85755i	0.141227	+	0.141227i	−0.632959	+	0.774186i	$0.718160\pi$
$174$	−26.2995	+	2.87313i	−1.99376	+	0.217812i
$175$	7.27931	−	3.70918i	0.550264	−	0.280388i
$176$	3.63249	−	1.68912i	0.273809	−	0.127323i
$177$	20.8258	+	20.8258i	1.56537	+	1.56537i
$178$	−11.0594	+	13.7722i	−0.828938	+	1.03227i
$179$	−24.8021			−1.85379			−0.926896	−	0.375318i	$-0.877534\pi$
$179$	−24.8021			−1.85379			−0.926896	+	0.375318i	$0.877534\pi$
$180$	0.558689	+	9.21388i	0.0416422	+	0.686762i
$181$	−8.00275			−0.594840			−0.297420	−	0.954747i	$-0.596126\pi$
$181$	−8.00275			−0.594840			−0.297420	+	0.954747i	$0.596126\pi$
$182$	−8.06123	−	2.10542i	−0.597538	−	0.156064i
$183$	−11.7214	+	11.7214i	−0.866474	+	0.866474i
$184$	−4.73493	+	1.60305i	−0.349064	+	0.118179i
$185$	9.58613	−	6.96489i	0.704787	−	0.512069i
$186$	0.0998422	+	0.913913i	0.00732078	+	0.0670114i
$187$	−3.12635	+	3.12635i	−0.228622	+	0.228622i
$188$	8.77530	+	5.59709i	0.640004	+	0.408210i
$189$	−3.44141			−0.250326
$190$	11.7251	−	10.6448i	0.850629	−	0.772257i
$191$		−	17.4340i		−	1.26148i	−0.775995	−	0.630739i	$-0.782752\pi$
$191$		−	17.4340i		−	1.26148i	0.775995	−	0.630739i	$-0.217248\pi$
$192$	17.8450	+	2.37851i	1.28785	+	0.171654i
$193$	−14.2418	+	14.2418i	−1.02514	+	1.02514i	−0.0254690	+	0.999676i	$0.508108\pi$
$193$	−14.2418	+	14.2418i	−1.02514	+	1.02514i	−0.999676	+	0.0254690i	$0.991892\pi$
$194$	−4.05180	+	0.442646i	−0.290902	+	0.0317801i
$195$	−17.5141	+	4.73502i	−1.25421	+	0.339082i
$196$	8.45601	−	1.86990i	0.604001	−	0.133564i
$197$	−14.4839	−	14.4839i	−1.03193	−	1.03193i	−0.999473	−	0.0324598i	$-0.989666\pi$
$197$	−14.4839	−	14.4839i	−1.03193	−	1.03193i	−0.0324598	−	0.999473i	$-0.510334\pi$
$198$	−2.27944	−	1.83045i	−0.161993	−	0.130084i
$199$	17.4123			1.23432			0.617162	−	0.786836i	$-0.288282\pi$
$199$	17.4123			1.23432			0.617162	+	0.786836i	$0.288282\pi$
$200$	−10.1223	−	9.87617i	−0.715756	−	0.698351i
$201$		−	15.0569i		−	1.06203i
$202$	−3.43267	+	4.27467i	−0.241522	+	0.300765i
$203$	−9.60477	−	9.60477i	−0.674123	−	0.674123i
$204$	−19.4005	+	4.29010i	−1.35831	+	0.300367i
$205$	12.4696	+	1.97486i	0.870914	+	0.137930i
$206$	−0.00377455	−	0.0345507i	−0.000262986	−	0.00240726i
$207$	2.57954	+	2.57954i	0.179290	+	0.179290i
$208$	1.02276	+	14.3859i	0.0709153	+	0.997482i
$209$			5.01543i			0.346924i
$210$	−8.60904	+	7.81586i	−0.594080	+	0.539346i
$211$			12.6836i			0.873177i	0.899661	+	0.436589i	$0.143813\pi$
$211$			12.6836i			0.873177i	−0.899661	+	0.436589i	$0.856187\pi$
$212$	7.70355	−	12.0779i	0.529082	−	0.829512i
$213$	−6.60197	+	6.60197i	−0.452360	+	0.452360i
$214$	−12.1577	+	1.32820i	−0.831086	+	0.0907936i
$215$	−14.0566	−	19.3469i	−0.958654	−	1.31945i
$216$	1.91033	+	5.64253i	0.129981	+	0.383926i
$217$	−0.333768	+	0.333768i	−0.0226577	+	0.0226577i
$218$	4.20234	−	5.23313i	0.284618	−	0.354432i
$219$		−	20.6595i		−	1.39604i
$220$	4.47065	−	0.271080i	0.301411	−	0.0182762i
$221$	−6.50664	−	14.5268i	−0.437684	−	0.977178i
$222$	−10.5593	+	13.1494i	−0.708694	+	0.882530i
$223$	10.1526	+	10.1526i	0.679871	+	0.679871i	0.959971	−	0.280100i	$-0.0903675\pi$
$223$	10.1526	+	10.1526i	0.679871	+	0.679871i	−0.280100	+	0.959971i	$0.590367\pi$
$224$	4.78450	+	7.90847i	0.319678	+	0.528407i
$225$	−3.18896	+	9.81531i	−0.212597	+	0.654354i
$226$	13.3652	−	1.46011i	0.889041	−	0.0971249i
$227$	−10.7707	+	10.7707i	−0.714874	+	0.714874i	−0.967551	−	0.252677i	$-0.918689\pi$
$227$	−10.7707	+	10.7707i	−0.714874	+	0.714874i	0.252677	+	0.967551i	$0.418689\pi$
$228$	−12.1204	+	19.0028i	−0.802693	+	1.25849i
$229$	−8.19357			−0.541447			−0.270723	−	0.962657i	$-0.587263\pi$
$229$	−8.19357			−0.541447			−0.270723	+	0.962657i	$0.587263\pi$
$230$	−5.58248	−	0.269585i	−0.368098	−	0.0177759i
$231$		−	3.68253i		−	0.242292i
$232$	−10.4164	+	21.0796i	−0.683867	+	1.38394i
$233$	13.2877	+	13.2877i	0.870506	+	0.870506i	0.992527	−	0.122021i	$-0.0389376\pi$
$233$	13.2877	+	13.2877i	0.870506	+	0.870506i	−0.122021	+	0.992527i	$0.538938\pi$
$234$	9.08121	−	5.31994i	0.593657	−	0.347776i
$235$	6.84007	+	9.41435i	0.446197	+	0.614124i
$236$	25.5582	−	5.65177i	1.66370	−	0.367899i
$237$	−22.1325	+	22.1325i	−1.43766	+	1.43766i
$238$	−7.95420	−	6.38742i	−0.515594	−	0.414035i
$239$		−	17.2458i		−	1.11554i	−0.829996	−	0.557770i	$-0.811657\pi$
$239$		−	17.2458i		−	1.11554i	0.829996	−	0.557770i	$-0.188343\pi$
$240$	17.5938	+	9.77678i	1.13567	+	0.631089i
$241$		−	19.8540i		−	1.27891i	−0.768829	−	0.639454i	$-0.779160\pi$
$241$		−	19.8540i		−	1.27891i	0.768829	−	0.639454i	$-0.220840\pi$
$242$	8.85218	−	11.0235i	0.569040	−	0.708620i
$243$	12.9273	−	12.9273i	0.829285	−	0.829285i
$244$	3.18099	+	14.3850i	0.203642	+	0.920904i
$245$	9.56331	+	1.51458i	0.610978	+	0.0967628i
$246$	−17.8622	+	1.95139i	−1.13885	+	0.124416i
$247$	−16.8714	−	6.43313i	−1.07350	−	0.409330i
$248$	0.732521	+	0.361971i	0.0465151	+	0.0229852i
$249$	5.66681			0.359119
$250$	−6.49063	−	14.4178i	−0.410503	−	0.911859i
$251$			11.9518i			0.754393i	0.926133	+	0.377197i	$0.123112\pi$
$251$			11.9518i			0.754393i	−0.926133	+	0.377197i	$0.876888\pi$
$252$	3.62727	−	5.68695i	0.228496	−	0.358244i
$253$	1.25161	−	1.25161i	0.0786882	−	0.0786882i
$254$	5.30786	−	0.579867i	0.333045	−	0.0363841i
$255$	−21.9410	−	3.47488i	−1.37400	−	0.217605i
$256$	10.3108	−	12.2347i	0.644427	−	0.764666i
$257$	0.510300	−	0.510300i	0.0318316	−	0.0318316i	−0.691012	−	0.722843i	$-0.742835\pi$
$257$	0.510300	−	0.510300i	0.0318316	−	0.0318316i	0.722843	+	0.691012i	$0.242835\pi$
$258$	26.5383	+	21.3109i	1.65220	+	1.32676i
$259$	−8.65860			−0.538019
$260$	−4.82247	+	15.3865i	−0.299077	+	0.954229i
$261$	17.1586			1.06209
$262$	20.7045	+	16.6262i	1.27913	+	1.02717i
$263$	21.4699	−	21.4699i	1.32389	−	1.32389i	0.413291	−	0.910599i	$-0.364379\pi$
$263$	21.4699	−	21.4699i	1.32389	−	1.32389i	0.910599	−	0.413291i	$-0.135621\pi$
$264$	−6.03786	+	2.04417i	−0.371605	+	0.125810i
$265$	12.9574	−	9.41433i	0.795969	−	0.578318i
$266$	−11.5037	+	1.25674i	−0.705338	+	0.0770560i
$267$	19.8740	−	19.8740i	1.21627	−	1.21627i
$268$	−11.2823	−	7.19612i	−0.689176	−	0.439573i
$269$			0.456688i			0.0278448i	0.999903	+	0.0139224i	$0.00443178\pi$
$269$			0.456688i			0.0278448i	−0.999903	+	0.0139224i	$0.995568\pi$
$270$	−0.321260	+	6.65253i	−0.0195513	+	0.404860i
$271$	6.62292			0.402314			0.201157	−	0.979559i	$-0.435530\pi$
$271$	6.62292			0.402314			0.201157	+	0.979559i	$0.435530\pi$
$272$	−6.05743	+	16.5874i	−0.367286	+	1.00576i
$273$	12.3876	+	4.72346i	0.749733	+	0.285877i
$274$	1.73987	−	0.190075i	0.105109	−	0.0114828i
$275$	4.76246	+	1.54731i	0.287187	+	0.0933062i
$276$	7.76686	−	1.71751i	0.467510	−	0.103382i
$277$	16.5166	−	16.5166i	0.992386	−	0.992386i	−0.00758480	−	0.999971i	$-0.502414\pi$
$277$	16.5166	−	16.5166i	0.992386	−	0.992386i	0.999971	+	0.00758480i	$0.00241434\pi$
$278$	−7.68030	+	9.56421i	−0.460634	+	0.573623i
$279$		−	0.596267i		−	0.0356976i
$280$	1.74200	+	10.1862i	0.104105	+	0.608744i
$281$		−	8.40674i		−	0.501504i	−0.968051	−	0.250752i	$-0.919322\pi$
$281$		−	8.40674i		−	0.501504i	0.968051	−	0.250752i	$-0.0806779\pi$
$282$	−12.9138	−	10.3701i	−0.769003	−	0.617529i
$283$	−2.63565	+	2.63565i	−0.156673	+	0.156673i	−0.781091	−	0.624418i	$-0.785336\pi$
$283$	−2.63565	+	2.63565i	−0.156673	+	0.156673i	0.624418	+	0.781091i	$0.285336\pi$
$284$	1.79166	+	8.10218i	0.106315	+	0.480776i
$285$	−20.3866	+	14.8121i	−1.20760	+	0.877391i
$286$	−2.58128	−	4.40627i	−0.152634	−	0.260548i
$287$	−6.52342	−	6.52342i	−0.385065	−	0.385065i
$288$	−11.3378	−	2.79044i	−0.668087	−	0.164428i
$289$		−	2.48954i		−	0.146443i
$290$	−19.4634	+	17.6702i	−1.14293	+	1.03763i
$291$	6.48573			0.380200
$292$	−15.4804	−	9.87375i	−0.905921	−	0.577818i
$293$	−0.626995	+	0.626995i	−0.0366294	+	0.0366294i	−0.725184	−	0.688555i	$-0.758245\pi$
$293$	−0.626995	+	0.626995i	−0.0366294	+	0.0366294i	0.688555	+	0.725184i	$0.258245\pi$
$294$	−13.6991	+	1.49658i	−0.798946	+	0.0872824i
$295$	28.9050	+	4.57780i	1.68292	+	0.266530i
$296$	4.80639	+	14.1966i	0.279366	+	0.825163i
$297$	−1.49152	−	1.49152i	−0.0865469	−	0.0865469i
$298$	−4.46397	+	5.55894i	−0.258591	+	0.322021i
$299$	2.60489	+	5.81569i	0.150645	+	0.336330i
$300$	14.3050	+	17.3716i	0.825902	+	1.00295i
$301$			17.4749i			1.00724i
$302$	−11.1676	+	13.9069i	−0.642622	+	0.800251i
$303$	6.16858	−	6.16858i	0.354376	−	0.354376i
$304$	8.44627	+	18.1639i	0.484427	+	1.04177i
$305$	−2.57653	+	16.2687i	−0.147532	+	0.931541i
$306$	12.8104	−	1.39950i	0.732324	−	0.0800041i
$307$	18.5017	−	18.5017i	1.05595	−	1.05595i	0.0576092	−	0.998339i	$-0.481652\pi$
$307$	18.5017	−	18.5017i	1.05595	−	1.05595i	0.998339	−	0.0576092i	$-0.0183477\pi$
$308$	−2.75935	−	1.75998i	−0.157229	−	0.100284i
$309$			0.0553054i			0.00314622i
$310$	0.614044	+	0.676359i	0.0348754	+	0.0384146i
$311$			14.7101i			0.834135i	0.908875	+	0.417068i	$0.136942\pi$
$311$			14.7101i			0.834135i	−0.908875	+	0.417068i	$0.863058\pi$
$312$	0.868199	−	22.9327i	0.0491521	−	1.29831i
$313$	−24.4854	−	24.4854i	−1.38400	−	1.38400i	−0.837383	−	0.546616i	$-0.815916\pi$
$313$	−24.4854	−	24.4854i	−1.38400	−	1.38400i	−0.546616	−	0.837383i	$-0.684084\pi$
$314$	−1.84301	−	16.8702i	−0.104007	−	0.952039i
$315$	6.10109	−	4.43280i	0.343758	−	0.249760i
$316$	6.00638	+	27.1618i	0.337885	+	1.52797i
$317$	−16.1489	−	16.1489i	−0.907014	−	0.907014i	0.0890163	−	0.996030i	$-0.471628\pi$
$317$	−16.1489	−	16.1489i	−0.907014	−	0.907014i	−0.996030	+	0.0890163i	$0.971628\pi$
$318$	−14.2728	+	17.7738i	−0.800382	+	0.996708i
$319$		−	8.32550i		−	0.466139i
$320$	15.7344	−	8.51057i	0.879578	−	0.475756i
$321$	19.4610			1.08620
$322$	3.18440	+	2.55716i	0.177460	+	0.142505i
$323$	−15.6330	−	15.6330i	−0.869842	−	0.869842i
$324$	−4.72073	−	21.3479i	−0.262263	−	1.18600i
$325$	−11.3136	+	14.0357i	−0.627567	+	0.778562i
$326$	14.5750	−	1.59227i	0.807235	−	0.0881879i
$327$	−7.55170	+	7.55170i	−0.417610	+	0.417610i
$328$	−7.07464	+	14.3169i	−0.390631	+	0.790521i
$329$		−	8.50344i		−	0.468810i
$330$	−7.11863	−	0.343768i	−0.391868	−	0.0189238i
$331$	−28.3312			−1.55722			−0.778611	−	0.627507i	$-0.784075\pi$
$331$	−28.3312			−1.55722			−0.778611	+	0.627507i	$0.784075\pi$
$332$	2.70832	−	4.24619i	0.148638	−	0.233040i
$333$	7.73417	−	7.73417i	0.423830	−	0.423830i
$334$	−2.94677	−	26.9735i	−0.161240	−	1.47593i
$335$	−8.79421	−	12.1039i	−0.480479	−	0.661308i
$336$	−6.20159	−	13.3366i	−0.338324	−	0.727572i
$337$	3.62117	−	3.62117i	0.197258	−	0.197258i	−0.601566	−	0.798823i	$-0.705456\pi$
$337$	3.62117	−	3.62117i	0.197258	−	0.197258i	0.798823	+	0.601566i	$0.205456\pi$
$338$	18.1331	−	3.03136i	0.986313	−	0.164884i
$339$	−21.3938			−1.16195
$340$	−13.0899	+	14.7799i	−0.709902	+	0.801550i
$341$	−0.289313			−0.0156672
$342$	9.15296	−	11.3981i	0.494935	−	0.616338i
$343$	−13.0907	−	13.0907i	−0.706834	−	0.706834i
$344$	28.6518	−	9.70033i	1.54480	−	0.523007i
$345$	8.78392	+	1.39114i	0.472910	+	0.0748965i
$346$	−3.69312	+	0.403462i	−0.198544	+	0.0216903i
$347$	10.8781	+	10.8781i	0.583968	+	0.583968i	0.935991	−	0.352023i	$-0.114506\pi$
$347$	10.8781	+	10.8781i	0.583968	+	0.583968i	−0.352023	+	0.935991i	$0.614506\pi$
$348$	20.1196	−	31.5442i	1.07852	−	1.69095i
$349$	8.12287			0.434807			0.217404	−	0.976082i	$-0.430241\pi$
$349$	8.12287			0.434807			0.217404	+	0.976082i	$0.430241\pi$
$350$	−2.35565	+	11.3112i	−0.125915	+	0.604610i
$351$	6.93045	−	3.10420i	0.369920	−	0.165690i
$352$	−1.35394	+	5.50119i	−0.0721653	+	0.293214i
$353$	−18.6772	+	18.6772i	−0.994085	+	0.994085i	−0.999983	−	0.00589744i	$-0.998123\pi$
$353$	−18.6772	+	18.6772i	−0.994085	+	0.994085i	0.00589744	+	0.999983i	$0.498123\pi$
$354$	−41.4053	+	4.52340i	−2.20067	+	0.240416i
$355$	−1.45120	+	9.16314i	−0.0770217	+	0.486329i
$356$	−5.39346	−	24.3901i	−0.285853	−	1.29267i
$357$	11.4783	+	11.4783i	0.607499	+	0.607499i
$358$	21.9618	−	27.3489i	1.16072	−	1.44543i
$359$			23.8423i			1.25835i	0.777265	+	0.629174i	$0.216607\pi$
$359$			23.8423i			1.25835i	−0.777265	+	0.629174i	$0.783393\pi$
$360$	−10.6547	−	7.54269i	−0.561554	−	0.397535i
$361$	−6.07907			−0.319951
$362$	7.08632	−	8.82453i	0.372449	−	0.463807i
$363$	−15.9076	+	15.9076i	−0.834932	+	0.834932i
$364$	9.45971	−	7.02469i	0.495823	−	0.368194i
$365$	−12.0665	−	16.6077i	−0.631589	−	0.869288i
$366$	−2.54592	−	23.3042i	−0.133077	−	1.21813i
$367$	−8.50113	−	8.50113i	−0.443755	−	0.443755i	0.449517	−	0.893272i	$-0.351596\pi$
$367$	−8.50113	−	8.50113i	−0.443755	−	0.443755i	−0.893272	+	0.449517i	$0.851596\pi$
$368$	2.42505	−	6.64062i	0.126414	−	0.346166i
$369$	11.6539			0.606678
$370$	−0.808291	+	16.7378i	−0.0420211	+	0.870157i
$371$	−11.7037			−0.607626
$372$	−1.09617	−	0.699162i	−0.0568337	−	0.0362498i
$373$	17.2997	+	17.2997i	0.895745	+	0.895745i	0.995056	−	0.0993115i	$-0.0316640\pi$
$373$	17.2997	+	17.2997i	0.895745	+	0.895745i	−0.0993115	+	0.995056i	$0.531664\pi$
$374$	−0.679048	−	6.21572i	−0.0351127	−	0.321407i
$375$	7.77551	+	23.9280i	0.401526	+	1.23564i
$376$	−13.9422	+	4.72026i	−0.719015	+	0.243429i
$377$	28.0061	+	10.6789i	1.44239	+	0.549989i
$378$	3.04732	−	3.79480i	0.156737	−	0.195183i
$379$			3.24187i			0.166524i	0.996528	+	0.0832618i	$0.0265338\pi$
$379$			3.24187i			0.166524i	−0.996528	+	0.0832618i	$0.973466\pi$
$380$	1.35551	+	22.3550i	0.0695360	+	1.14678i
$381$	−8.49631			−0.435279
$382$	19.2242	+	15.4375i	0.983596	+	0.789853i
$383$	6.74298	+	6.74298i	0.344550	+	0.344550i	0.858075	−	0.513525i	$-0.171661\pi$
$383$	6.74298	+	6.74298i	0.344550	+	0.344550i	−0.513525	+	0.858075i	$0.671661\pi$
$384$	−18.4242	+	17.5713i	−0.940206	+	0.896681i
$385$	−2.15083	−	2.96030i	−0.109616	−	0.150871i
$386$	−3.09333	−	28.3151i	−0.157446	−	1.44120i
$387$	−15.6092	−	15.6092i	−0.793461	−	0.793461i
$388$	3.09970	−	4.85982i	0.157364	−	0.246720i
$389$			15.0240i			0.761747i	0.924627	+	0.380874i	$0.124377\pi$
$389$			15.0240i			0.761747i	−0.924627	+	0.380874i	$0.875623\pi$
$390$	10.2872	−	23.5054i	0.520914	−	1.19024i
$391$			7.80249i			0.394589i
$392$	−5.42575	+	10.9801i	−0.274042	+	0.554579i
$393$	−29.8777	−	29.8777i	−1.50713	−	1.50713i
$394$	28.7964	−	3.14592i	1.45074	−	0.158489i
$395$	−4.86502	+	30.7186i	−0.244786	+	1.54562i
$396$	4.03682	−	0.892675i	0.202858	−	0.0448586i
$397$	13.0440	+	13.0440i	0.654661	+	0.654661i	0.954112	−	0.299451i	$-0.0968035\pi$
$397$	13.0440	+	13.0440i	0.654661	+	0.654661i	−0.299451	+	0.954112i	$0.596804\pi$
$398$	−15.4183	+	19.2003i	−0.772850	+	0.962423i
$399$	18.4140			0.921855
$400$	19.8535	−	2.41654i	0.992674	−	0.120827i
$401$		−	10.9286i		−	0.545750i	−0.962049	−	0.272875i	$-0.912025\pi$
$401$		−	10.9286i		−	0.545750i	0.962049	−	0.272875i	$-0.0879746\pi$
$402$	16.6031	+	13.3327i	0.828086	+	0.664974i
$403$	0.371093	−	0.973219i	0.0184855	−	0.0484795i
$404$	−1.67404	−	7.57031i	−0.0832868	−	0.376637i
$405$	3.82368	−	24.1434i	0.190000	−	1.19969i
$406$	19.0959	−	2.08617i	0.947715	−	0.103535i
$407$	−3.75268	−	3.75268i	−0.186013	−	0.186013i
$408$	12.4482	−	25.1915i	0.616280	−	1.24717i
$409$	−28.8310			−1.42560			−0.712801	−	0.701366i	$-0.752574\pi$
$409$	−28.8310			−1.42560			−0.712801	+	0.701366i	$0.752574\pi$
$410$	−13.2193	+	12.0013i	−0.652854	+	0.592704i
$411$	−2.78501			−0.137375
$412$	0.0414409	+	0.0264320i	0.00204164	+	0.00130221i
$413$	−15.1216	−	15.1216i	−0.744083	−	0.744083i
$414$	−5.12857	+	0.560280i	−0.252055	+	0.0275362i
$415$	4.55541	−	3.30977i	0.223616	−	0.162470i
$416$	−16.7688	−	11.6107i	−0.822156	−	0.569262i
$417$	13.8017	−	13.8017i	0.675871	−	0.675871i
$418$	−5.53044	−	4.44108i	−0.270503	−	0.217221i
$419$	25.0475			1.22365			0.611825	−	0.790993i	$-0.290436\pi$
$419$	25.0475			1.22365			0.611825	+	0.790993i	$0.290436\pi$
$420$	−0.995266	−	16.4139i	−0.0485640	−	0.800916i
$421$			27.6601i			1.34807i	0.738698	+	0.674037i	$0.235441\pi$
$421$			27.6601i			1.34807i	−0.738698	+	0.674037i	$0.764559\pi$
$422$	−13.9861	−	11.2312i	−0.680831	−	0.546724i
$423$	7.59557	+	7.59557i	0.369309	+	0.369309i
$424$	6.49673	+	19.1894i	0.315509	+	0.931918i
$425$	−19.6674	+	10.0216i	−0.954009	+	0.486117i
$426$	−1.43396	−	13.1258i	−0.0694755	−	0.635949i
$427$	8.51089	−	8.51089i	0.411871	−	0.411871i
$428$	9.30091	−	14.5823i	0.449577	−	0.704861i
$429$	3.32168	+	7.41602i	0.160372	+	0.358049i
$430$	33.7805	+	1.63130i	1.62904	+	0.0786685i
$431$	−9.74272			−0.469290			−0.234645	−	0.972081i	$-0.575393\pi$
$431$	−9.74272			−0.469290			−0.234645	+	0.972081i	$0.575393\pi$
$432$	−7.91351	−	2.88988i	−0.380739	−	0.139040i
$433$	8.43954	+	8.43954i	0.405578	+	0.405578i	0.880193	−	0.474615i	$-0.157413\pi$
$433$	8.43954	+	8.43954i	0.405578	+	0.405578i	−0.474615	+	0.880193i	$0.657413\pi$
$434$	−0.0724949	−	0.663588i	−0.00347987	−	0.0318533i
$435$	33.8413	−	24.5877i	1.62257	−	1.17889i
$436$	2.04940	+	9.26771i	0.0981483	+	0.443843i
$437$	6.25854	+	6.25854i	0.299387	+	0.299387i
$438$	22.7810	+	18.2937i	1.08852	+	0.874107i
$439$	−19.7703			−0.943584			−0.471792	−	0.881710i	$-0.656393\pi$
$439$	−19.7703			−0.943584			−0.471792	+	0.881710i	$0.656393\pi$
$440$	−3.65977	+	5.16976i	−0.174473	+	0.246458i
$441$	8.93773			0.425606
$442$	21.7800	+	5.68846i	1.03597	+	0.270573i
$443$	−11.5972	+	11.5972i	−0.551000	+	0.551000i	−0.926729	−	0.375730i	$-0.877392\pi$
$443$	−11.5972	+	11.5972i	−0.551000	+	0.551000i	0.375730	+	0.926729i	$0.377392\pi$
$444$	−5.14956	−	23.2872i	−0.244387	−	1.10516i
$445$	4.36858	−	27.5840i	0.207090	−	1.30761i
$446$	−20.1852	+	2.20517i	−0.955797	+	0.104418i
$447$	8.02186	−	8.02186i	0.379421	−	0.379421i
$448$	−12.9572	−	1.72702i	−0.612168	−	0.0815942i
$449$	−23.1178			−1.09100			−0.545499	−	0.838111i	$-0.683660\pi$
$449$	−23.1178			−1.09100			−0.545499	+	0.838111i	$0.683660\pi$
$450$	−7.99943	−	12.2077i	−0.377097	−	0.575478i
$451$		−	5.65456i		−	0.266263i
$452$	−10.2247	+	16.0305i	−0.480927	+	0.754013i
$453$	20.0684	−	20.0684i	0.942896	−	0.942896i
$454$	−2.33940	−	21.4139i	−0.109794	−	1.00501i
$455$	12.7169	−	3.43808i	0.596178	−	0.161180i
$456$	−10.2216	−	30.1916i	−0.478672	−	1.41385i
$457$	−8.57872	−	8.57872i	−0.401296	−	0.401296i	0.477394	−	0.878689i	$-0.341582\pi$
$457$	−8.57872	−	8.57872i	−0.401296	−	0.401296i	−0.878689	+	0.477394i	$0.841582\pi$
$458$	7.25529	−	9.03494i	0.339017	−	0.422175i
$459$	9.29809			0.433998
$460$	5.24046	−	5.91700i	0.244338	−	0.275882i
$461$		−	15.6754i		−	0.730078i	−0.930992	−	0.365039i	$-0.881056\pi$
$461$		−	15.6754i		−	0.730078i	0.930992	−	0.365039i	$-0.118944\pi$
$462$	4.06067	+	3.26082i	0.188919	+	0.151707i
$463$	22.6186	+	22.6186i	1.05118	+	1.05118i	0.998618	+	0.0525571i	$0.0167372\pi$
$463$	22.6186	+	22.6186i	1.05118	+	1.05118i	0.0525571	+	0.998618i	$0.483263\pi$
$464$	−14.0206	−	30.1516i	−0.650892	−	1.39975i
$465$	−0.854429	−	1.17600i	−0.0396232	−	0.0545355i
$466$	−26.4182	+	2.88611i	−1.22380	+	0.133696i
$467$	5.52619	+	5.52619i	0.255722	+	0.255722i	0.823311	−	0.567590i	$-0.192124\pi$
$467$	5.52619	+	5.52619i	0.255722	+	0.255722i	−0.567590	+	0.823311i	$0.692124\pi$
$468$	−2.17504	+	14.7244i	−0.100541	+	0.680638i
$469$			10.9328i			0.504829i
$470$	−16.4378	−	0.793806i	−0.758221	−	0.0366155i
$471$			27.0042i			1.24429i
$472$	−16.3993	+	33.1873i	−0.754839	+	1.52757i
$473$	−7.57371	+	7.57371i	−0.348239	+	0.348239i
$474$	−4.80722	−	44.0032i	−0.220803	−	2.02114i
$475$	−7.73714	+	23.8141i	−0.355004	+	1.09267i
$476$	14.0866	−	3.11502i	0.645660	−	0.142777i
$477$	10.4542	−	10.4542i	0.478663	−	0.478663i
$478$	19.0167	+	15.2709i	0.869805	+	0.698475i
$479$			3.20609i			0.146490i	0.997314	+	0.0732451i	$0.0233355\pi$
$479$			3.20609i			0.146490i	−0.997314	+	0.0732451i	$0.976664\pi$
$480$	−26.3597	+	10.7432i	−1.20315	+	0.490358i
$481$	17.4370	−	7.81017i	0.795061	−	0.356113i
$482$	21.8927	+	17.5804i	0.997186	+	0.800766i
$483$	−4.59527	−	4.59527i	−0.209092	−	0.209092i
$484$	4.31704	+	19.5224i	0.196229	+	0.887380i
$485$	5.21373	−	3.78808i	0.236743	−	0.172008i
$486$	2.80782	+	25.7016i	0.127365	+	1.16585i
$487$	10.5303	−	10.5303i	0.477174	−	0.477174i	−0.427053	−	0.904227i	$-0.640448\pi$
$487$	10.5303	−	10.5303i	0.477174	−	0.477174i	0.904227	+	0.427053i	$0.140448\pi$
$488$	−18.6788	−	9.23005i	−0.845552	−	0.417825i
$489$	−23.3303			−1.05503
$490$	−10.1383	+	9.20420i	−0.458000	+	0.415803i
$491$		−	4.79494i		−	0.216393i	−0.994130	−	0.108196i	$-0.965492\pi$
$491$		−	4.79494i		−	0.216393i	0.994130	−	0.108196i	$-0.0345075\pi$
$492$	13.6649	−	21.4243i	0.616063	−	0.965884i
$493$	25.9504	+	25.9504i	1.16875	+	1.16875i
$494$	22.0331	−	12.9074i	0.991314	−	0.580730i
$495$	4.56544	+	0.723046i	0.205201	+	0.0324985i
$496$	−1.04778	+	0.487221i	−0.0470466	+	0.0218769i
$497$	4.79366	−	4.79366i	0.215025	−	0.215025i
$498$	−5.01787	+	6.24871i	−0.224856	+	0.280011i
$499$			30.1159i			1.34817i	0.738653	+	0.674086i	$0.235462\pi$
$499$			30.1159i			1.34817i	−0.738653	+	0.674086i	$0.764538\pi$
$500$	21.6456	+	5.60958i	0.968021	+	0.250868i
$501$			43.1767i			1.92899i
$502$	−13.1791	−	10.5832i	−0.588213	−	0.472350i
$503$	−17.3309	+	17.3309i	−0.772749	+	0.772749i	−0.978586	−	0.205838i	$-0.934008\pi$
$503$	−17.3309	+	17.3309i	−0.772749	+	0.772749i	0.205838	+	0.978586i	$0.434008\pi$
$504$	3.05903	+	9.03544i	0.136260	+	0.402471i
$505$	1.35594	−	8.56162i	0.0603384	−	0.380987i
$506$	0.271852	+	2.48842i	0.0120853	+	0.110624i
$507$	−29.2073	+	1.66150i	−1.29714	+	0.0737899i
$508$	−4.06062	+	6.36637i	−0.180161	+	0.282462i
$509$	23.5534			1.04399			0.521993	−	0.852950i	$-0.325189\pi$
$509$	23.5534			1.04399			0.521993	+	0.852950i	$0.325189\pi$
$510$	23.2601	−	21.1171i	1.02998	−	0.935080i
$511$			15.0008i			0.663596i
$512$	4.36090	+	22.2032i	0.192726	+	0.981253i
$513$	7.45819	−	7.45819i	0.329287	−	0.329287i
$514$	0.110838	+	1.01456i	0.00488885	+	0.0447505i
$515$	0.0323019	+	0.0444587i	0.00142339	+	0.00195909i
$516$	−46.9985	+	10.3929i	−2.06900	+	0.457523i
$517$	3.68543	−	3.68543i	0.162085	−	0.162085i
$518$	7.66706	−	9.54772i	0.336871	−	0.419503i
$519$	5.91160			0.259490
$520$	−12.6962	−	18.9422i	−0.556767	−	0.830669i
$521$	−16.0659			−0.703859			−0.351929	−	0.936027i	$-0.614474\pi$
$521$	−16.0659			−0.703859			−0.351929	+	0.936027i	$0.614474\pi$
$522$	−15.1937	+	18.9206i	−0.665011	+	0.828132i
$523$	0.229641	−	0.229641i	0.0100415	−	0.0100415i	−0.702068	−	0.712110i	$-0.747740\pi$
$523$	0.229641	−	0.229641i	0.0100415	−	0.0100415i	0.712110	+	0.702068i	$0.247740\pi$
$524$	−36.6670	+	8.10827i	−1.60180	+	0.354212i
$525$	5.68091	−	17.4853i	0.247935	−	0.763121i
$526$	4.66329	+	42.6858i	0.203329	+	1.86119i
$527$	0.901783	−	0.901783i	0.0392823	−	0.0392823i
$528$	3.09236	−	8.46795i	0.134578	−	0.368520i
$529$			19.8763i			0.864188i
$530$	−1.09256	+	22.6242i	−0.0474576	+	0.982734i
$531$	27.0142			1.17232
$532$	8.80057	−	13.7978i	0.381553	−	0.598211i
$533$	19.0213	+	7.25292i	0.823905	+	0.314159i
$534$	4.31667	+	39.5130i	0.186800	+	1.70989i
$535$	15.6442	−	11.3664i	0.676358	−	0.491414i
$536$	17.9254	−	6.06879i	0.774258	−	0.262132i
$537$	−39.4659	+	39.4659i	−1.70308	+	1.70308i
$538$	−0.503584	−	0.404391i	−0.0217110	−	0.0174345i
$539$		−	4.33665i		−	0.186793i
$540$	−7.05118	−	6.24496i	−0.303435	−	0.268740i
$541$		−	34.3843i		−	1.47830i	−0.673543	−	0.739148i	$-0.735228\pi$
$541$		−	34.3843i		−	1.47830i	0.673543	−	0.739148i	$-0.264772\pi$
$542$	−5.86449	+	7.30300i	−0.251901	+	0.313691i
$543$	−12.7343	+	12.7343i	−0.546480	+	0.546480i
$544$	−12.9269	−	21.3673i	−0.554235	−	0.916115i
$545$	−1.65996	+	10.4813i	−0.0711050	+	0.448970i
$546$	−16.1775	+	9.47711i	−0.692335	+	0.405583i
$547$	−9.62082	−	9.62082i	−0.411357	−	0.411357i	0.470854	−	0.882211i	$-0.343946\pi$
$547$	−9.62082	−	9.62082i	−0.411357	−	0.411357i	−0.882211	+	0.470854i	$0.843946\pi$
$548$	−1.33103	+	2.08684i	−0.0568589	+	0.0891452i
$549$			15.2045i			0.648911i
$550$	−5.92328	+	3.88138i	−0.252570	+	0.165503i
$551$	41.6307			1.77353
$552$	−4.98356	+	10.0852i	−0.212115	+	0.429256i
$553$	16.0703	−	16.0703i	0.683380	−	0.683380i
$554$	3.58743	+	32.8378i	0.152415	+	1.39515i
$555$	4.17103	−	26.3366i	0.177050	−	1.11793i
$556$	−3.74553	−	16.9379i	−0.158846	−	0.718328i
$557$	−30.3726	−	30.3726i	−1.28693	−	1.28693i	−0.936643	−	0.350287i	$-0.886084\pi$
$557$	−30.3726	−	30.3726i	−1.28693	−	1.28693i	−0.350287	−	0.936643i	$-0.613916\pi$
$558$	0.657496	+	0.527986i	0.0278340	+	0.0223514i
$559$	−15.7626	−	35.1917i	−0.666687	−	1.48845i
$560$	−12.7747	−	7.09888i	−0.539832	−	0.299982i
$561$			9.94954i			0.420070i
$562$	9.27000	+	7.44404i	0.391031	+	0.314008i
$563$	−11.3315	+	11.3315i	−0.477564	+	0.477564i	−0.904352	−	0.426788i	$-0.859645\pi$
$563$	−11.3315	+	11.3315i	−0.477564	+	0.477564i	0.426788	+	0.904352i	$0.359645\pi$
$564$	22.8699	−	5.05728i	0.962995	−	0.212950i
$565$	−17.1979	+	12.4953i	−0.723523	+	0.525682i
$566$	−0.572467	−	5.24013i	−0.0240626	−	0.220259i
$567$	−12.6305	+	12.6305i	−0.530432	+	0.530432i
$568$	−10.5206	−	5.19872i	−0.441436	−	0.218133i
$569$			10.8043i			0.452940i	0.974018	+	0.226470i	$0.0727185\pi$
$569$			10.8043i			0.452940i	−0.974018	+	0.226470i	$0.927281\pi$
$570$	1.71897	−	35.5959i	0.0719999	−	1.49095i
$571$			3.57025i			0.149410i	0.997206	+	0.0747052i	$0.0238016\pi$
$571$			3.57025i			0.149410i	−0.997206	+	0.0747052i	$0.976198\pi$
$572$	7.14441	+	1.05535i	0.298723	+	0.0441263i
$573$	−27.7416	−	27.7416i	−1.15892	−	1.15892i
$574$	12.9697	−	1.41690i	0.541344	−	0.0591401i
$575$	7.87370	−	4.01206i	0.328356	−	0.167314i
$576$	13.1164	−	10.0312i	0.546518	−	0.417965i
$577$	6.27627	+	6.27627i	0.261285	+	0.261285i	0.825576	−	0.564291i	$-0.190850\pi$
$577$	6.27627	+	6.27627i	0.261285	+	0.261285i	−0.564291	+	0.825576i	$0.690850\pi$
$578$	2.74518	+	2.20445i	0.114184	+	0.0916930i
$579$			45.3240i			1.88360i
$580$	−2.25011	−	37.1088i	−0.0934308	−	1.54086i
$581$	−4.11464			−0.170704
$582$	−5.74301	+	7.15172i	−0.238056	+	0.296448i
$583$	−5.07244	−	5.07244i	−0.210079	−	0.210079i
$584$	24.5953	−	8.32695i	1.01776	−	0.344572i
$585$	−8.28819	+	14.4302i	−0.342674	+	0.596616i
$586$	−0.136184	−	1.24657i	−0.00562572	−	0.0514955i
$587$	21.1579	−	21.1579i	0.873281	−	0.873281i	−0.119548	−	0.992828i	$-0.538144\pi$
$587$	21.1579	−	21.1579i	0.873281	−	0.873281i	0.992828	+	0.119548i	$0.0381444\pi$
$588$	10.4801	−	16.4310i	0.432191	−	0.677602i
$589$		−	1.44668i		−	0.0596094i
$590$	−30.6428	+	27.8196i	−1.26155	+	1.14532i
$591$	−46.0945			−1.89608
$592$	−19.9104	−	7.27096i	−0.818313	−	0.298835i
$593$	−3.26613	+	3.26613i	−0.134124	+	0.134124i	−0.770981	−	0.636858i	$-0.780234\pi$
$593$	−3.26613	+	3.26613i	−0.134124	+	0.134124i	0.636858	+	0.770981i	$0.280234\pi$
$594$	2.96540	−	0.323961i	0.121672	−	0.0132923i
$595$	15.9313	+	2.52309i	0.653118	+	0.103437i
$596$	−2.17699	−	9.84471i	−0.0891730	−	0.403255i
$597$	27.7071	−	27.7071i	1.13397	−	1.13397i
$598$	−8.71947	−	2.27733i	−0.356566	−	0.0931271i
$599$	6.95501			0.284174			0.142087	−	0.989854i	$-0.454619\pi$
$599$	6.95501			0.284174			0.142087	+	0.989854i	$0.454619\pi$
$600$	−31.8223	+	0.391676i	−1.29914	+	0.0159901i
$601$	−2.34998			−0.0958579			−0.0479289	−	0.998851i	$-0.515262\pi$
$601$	−2.34998			−0.0958579			−0.0479289	+	0.998851i	$0.515262\pi$
$602$	−19.2693	−	15.4738i	−0.785360	−	0.630664i
$603$	−9.76554	−	9.76554i	−0.397684	−	0.397684i
$604$	−5.44621	−	24.6287i	−0.221603	−	1.00213i
$605$	−3.49670	+	22.0788i	−0.142161	+	0.897630i
$606$	1.33983	+	12.2642i	0.0544267	+	0.498199i
$607$	−11.4273	−	11.4273i	−0.463820	−	0.463820i	0.436085	−	0.899905i	$-0.356365\pi$
$607$	−11.4273	−	11.4273i	−0.463820	−	0.463820i	−0.899905	+	0.436085i	$0.856365\pi$
$608$	−27.5081	−	6.77023i	−1.11560	−	0.274569i
$609$	−30.5669			−1.23863
$610$	−15.6578	−	17.2468i	−0.633964	−	0.698301i
$611$	7.67021	+	17.1246i	0.310303	+	0.692786i
$612$	−9.80024	+	15.3651i	−0.396151	+	0.621099i
$613$	−17.5720	+	17.5720i	−0.709725	+	0.709725i	−0.966477	−	0.256752i	$-0.917348\pi$
$613$	−17.5720	+	17.5720i	−0.709725	+	0.709725i	0.256752	+	0.966477i	$0.417348\pi$
$614$	4.01860	+	36.7846i	0.162177	+	1.48450i
$615$	22.9845	−	16.6996i	0.926826	−	0.673393i
$616$	4.38407	−	1.48426i	0.176639	−	0.0598027i
$617$	1.31051	+	1.31051i	0.0527592	+	0.0527592i	0.732994	−	0.680235i	$-0.238122\pi$
$617$	1.31051	+	1.31051i	0.0527592	+	0.0527592i	−0.680235	+	0.732994i	$0.738122\pi$
$618$	−0.0609845	−	0.0489721i	−0.00245316	−	0.00196995i
$619$		−	3.36316i		−	0.135177i	−0.997713	−	0.0675884i	$-0.978470\pi$
$619$		−	3.36316i		−	0.135177i	0.997713	−	0.0675884i	$-0.0215305\pi$
$620$	−1.28954	+	0.0781920i	−0.0517891	+	0.00314027i
$621$	−3.72242			−0.149376
$622$	−16.2207	−	13.0256i	−0.650389	−	0.522279i
$623$	−14.4304	+	14.4304i	−0.578144	+	0.578144i
$624$	24.5188	+	21.2639i	0.981538	+	0.851238i
$625$	20.2260	+	14.6938i	0.809042	+	0.587752i
$626$	48.6813	−	5.31827i	1.94569	−	0.212561i
$627$	7.98073	+	7.98073i	0.318720	+	0.318720i
$628$	20.2345	+	12.9060i	0.807443	+	0.515006i
$629$	23.3940			0.932781
$630$	−0.514437	+	10.6528i	−0.0204956	+	0.424416i
$631$	−21.0999			−0.839972			−0.419986	−	0.907531i	$-0.637965\pi$
$631$	−21.0999			−0.839972			−0.419986	+	0.907531i	$0.637965\pi$
$632$	−35.2695	−	17.4282i	−1.40295	−	0.693258i
$633$	20.1827	+	20.1827i	0.802189	+	0.802189i
$634$	32.1068	−	3.50757i	1.27512	−	0.139303i
$635$	−6.82999	+	4.96239i	−0.271040	+	0.196926i
$636$	−6.96059	−	31.4769i	−0.276005	−	1.24814i
$637$	14.5880	+	5.56249i	0.577999	+	0.220394i
$638$	9.18042	+	7.37211i	0.363456	+	0.291865i
$639$			8.56374i			0.338776i
$640$	−4.54805	+	24.8860i	−0.179777	+	0.983707i
$641$	11.0927			0.438134			0.219067	−	0.975710i	$-0.429699\pi$
$641$	11.0927			0.438134			0.219067	+	0.975710i	$0.429699\pi$
$642$	−17.2324	+	21.4593i	−0.680108	+	0.846932i
$643$	15.9665	+	15.9665i	0.629657	+	0.629657i	0.947982	−	0.318324i	$-0.103120\pi$
$643$	15.9665	+	15.9665i	0.629657	+	0.629657i	−0.318324	+	0.947982i	$0.603120\pi$
$644$	−5.63948	+	1.24708i	−0.222227	+	0.0491416i
$645$	−53.1529	−	8.41802i	−2.09289	−	0.331459i
$646$	31.0810	−	3.39550i	1.22287	−	0.133594i
$647$	−17.8371	−	17.8371i	−0.701250	−	0.701250i	0.263429	−	0.964679i	$-0.415147\pi$
$647$	−17.8371	−	17.8371i	−0.701250	−	0.701250i	−0.964679	+	0.263429i	$0.915147\pi$
$648$	27.7202	+	13.6978i	1.08895	+	0.538100i
$649$		−	13.1075i		−	0.514515i
$650$	−5.45896	−	24.9038i	−0.214118	−	0.976808i
$651$			1.06221i			0.0416312i
$652$	−11.1502	+	17.4816i	−0.436674	+	0.684632i
$653$	−30.6085	−	30.6085i	−1.19780	−	1.19780i	−0.974823	−	0.222980i	$-0.928422\pi$
$653$	−30.6085	−	30.6085i	−1.19780	−	1.19780i	−0.222980	−	0.974823i	$-0.571578\pi$
$654$	−1.64024	−	15.0141i	−0.0641384	−	0.587096i
$655$	−41.4684	−	6.56751i	−1.62031	−	0.256614i
$656$	−9.52261	−	20.4785i	−0.371795	−	0.799552i
$657$	−13.3993	−	13.3993i	−0.522755	−	0.522755i
$658$	9.37662	+	7.52966i	0.365539	+	0.293537i
$659$	18.0735			0.704042			0.352021	−	0.935992i	$-0.385495\pi$
$659$	18.0735			0.704042			0.352021	+	0.935992i	$0.385495\pi$
$660$	6.68250	−	7.54521i	0.260116	−	0.293697i
$661$			39.3650i			1.53112i	0.643364	+	0.765561i	$0.277538\pi$
$661$			39.3650i			1.53112i	−0.643364	+	0.765561i	$0.722462\pi$
$662$	25.0868	−	31.2404i	0.975027	−	1.21419i
$663$	−33.4692	−	12.7619i	−1.29984	−	0.495633i
$664$	2.28404	+	6.74636i	0.0886379	+	0.261810i
$665$	14.8026	−	10.7550i	0.574021	−	0.417060i
$666$	1.67987	+	15.3769i	0.0650938	+	0.595841i
$667$	−10.3891	−	10.3891i	−0.402266	−	0.402266i
$668$	32.3527	+	20.6353i	1.25176	+	0.798403i
$669$	32.3105			1.24920
$670$	21.1340	+	1.02059i	0.816476	+	0.0394288i
$671$	7.37732			0.284798
$672$	20.1975	+	4.97097i	0.779136	+	0.191759i
$673$	0.342425	+	0.342425i	0.0131995	+	0.0131995i	0.713676	−	0.700476i	$-0.247029\pi$
$673$	0.342425	+	0.342425i	0.0131995	+	0.0131995i	−0.700476	+	0.713676i	$0.747029\pi$
$674$	0.786524	+	7.19951i	0.0302958	+	0.277315i
$675$	−4.78109	−	9.38294i	−0.184024	−	0.361150i
$676$	−12.7140	+	22.6794i	−0.488999	+	0.872284i
$677$	−24.6839	+	24.6839i	−0.948681	+	0.948681i	−0.998746	−	0.0500652i	$-0.984057\pi$
$677$	−24.6839	+	24.6839i	−0.948681	+	0.948681i	0.0500652	+	0.998746i	$0.484057\pi$
$678$	18.9439	−	23.5906i	0.727534	−	0.905992i
$679$	−4.70926			−0.180725
$680$	−4.70659	−	27.5214i	−0.180489	−	1.05540i
$681$			34.2774i			1.31351i
$682$	0.256183	−	0.319022i	0.00980974	−	0.0122160i
$683$	23.5902	+	23.5902i	0.902655	+	0.902655i	0.995665	−	0.0930103i	$-0.0296490\pi$
$683$	23.5902	+	23.5902i	0.902655	+	0.902655i	−0.0930103	+	0.995665i	$0.529649\pi$
$684$	4.46372	+	20.1857i	0.170675	+	0.771819i
$685$	−2.23881	+	1.62662i	−0.0855404	+	0.0621501i
$686$	26.0266	−	2.84333i	0.993701	−	0.108559i
$687$	−13.0379	+	13.0379i	−0.497428	+	0.497428i
$688$	−14.6744	+	40.1835i	−0.559454	+	1.53198i
$689$	23.5694	−	10.5569i	0.897923	−	0.402185i
$690$	−9.31202	+	8.45407i	−0.354502	+	0.321841i
$691$	−26.4329			−1.00555			−0.502777	−	0.864416i	$-0.667688\pi$
$691$	−26.4329			−1.00555			−0.502777	+	0.864416i	$0.667688\pi$
$692$	2.82531	−	4.42962i	0.107402	−	0.168389i
$693$	−2.38839	−	2.38839i	−0.0907275	−	0.0907275i
$694$	−21.6276	+	2.36274i	−0.820971	+	0.0896885i
$695$	3.03379	−	19.1559i	0.115078	−	0.726625i
$696$	16.9677	+	50.1175i	0.643160	+	1.89970i
$697$	17.6251	+	17.6251i	0.667599	+	0.667599i
$698$	−7.19267	+	8.95697i	−0.272247	+	0.339026i
$699$	42.2878			1.59947
$700$	−10.3868	−	12.6134i	−0.392585	−	0.476744i
$701$	−16.5669			−0.625722			−0.312861	−	0.949799i	$-0.601287\pi$
$701$	−16.5669			−0.625722			−0.312861	+	0.949799i	$0.601287\pi$
$702$	−2.71386	+	10.3908i	−0.102428	+	0.392177i
$703$	18.7648	−	18.7648i	0.707729	−	0.707729i
$704$	−4.86719	−	6.36419i	−0.183439	−	0.239860i
$705$	25.8646	+	4.09628i	0.974118	+	0.154275i
$706$	−4.05671	−	37.1334i	−0.152676	−	1.39753i
$707$	−4.47898	+	4.47898i	−0.168449	+	0.168449i
$708$	31.6759	−	49.6625i	1.19045	−	1.86643i
$709$	39.7153			1.49154			0.745770	−	0.666203i	$-0.232082\pi$
$709$	39.7153			1.49154			0.745770	+	0.666203i	$0.232082\pi$
$710$	−8.81905	−	9.71404i	−0.330973	−	0.364561i
$711$			28.7092i			1.07668i
$712$	31.6705	+	15.6498i	1.18690	+	0.586501i
$713$	−0.361022	+	0.361022i	−0.0135204	+	0.0135204i
$714$	−22.8209	+	2.49311i	−0.854051	+	0.0933024i
$715$	7.00165	+	4.02149i	0.261847	+	0.150395i
$716$	10.7104	+	48.4340i	0.400265	+	1.81006i
$717$	−27.4422	−	27.4422i	−1.02485	−	1.02485i
$718$	−26.2906	−	21.1120i	−0.981155	−	0.787892i
$719$	−5.97682			−0.222898			−0.111449	−	0.993770i	$-0.535549\pi$
$719$	−5.97682			−0.222898			−0.111449	+	0.993770i	$0.535549\pi$
$720$	17.7518	−	5.06989i	0.661572	−	0.188943i
$721$		−	0.0401570i		−	0.00149553i
$722$	5.38292	−	6.70331i	0.200332	−	0.249471i
$723$	−31.5924	−	31.5924i	−1.17493	−	1.17493i
$724$	3.45586	+	15.6280i	0.128436	+	0.580809i
$725$	12.8435	−	39.5310i	0.476995	−	1.46814i
$726$	−3.45515	−	31.6270i	−0.128233	−	1.17379i
$727$	−18.1517	−	18.1517i	−0.673209	−	0.673209i	0.285246	−	0.958454i	$-0.407925\pi$
$727$	−18.1517	−	18.1517i	−0.673209	−	0.673209i	−0.958454	+	0.285246i	$0.907925\pi$
$728$	−0.630395	+	16.6513i	−0.0233640	+	0.617140i
$729$		−	8.34523i		−	0.309082i
$730$	28.9978	+	1.40034i	1.07326	+	0.0518290i
$731$		−	47.2142i		−	1.74628i
$732$	27.9516	+	17.8282i	1.03312	+	0.658949i
$733$	12.9042	−	12.9042i	0.476627	−	0.476627i	−0.427425	−	0.904051i	$-0.640579\pi$
$733$	12.9042	−	12.9042i	0.476627	−	0.476627i	0.904051	+	0.427425i	$0.140579\pi$
$734$	16.9017	−	1.84646i	0.623853	−	0.0681540i
$735$	17.6275	−	12.8074i	0.650202	−	0.472410i
$736$	5.17518	+	8.55424i	0.190760	+	0.315313i
$737$	−4.73832	+	4.73832i	−0.174538	+	0.174538i
$738$	−10.3193	+	12.8506i	−0.379860	+	0.473037i
$739$		−	47.6831i		−	1.75405i	−0.480445	−	0.877025i	$-0.659525\pi$
$739$		−	47.6831i		−	1.75405i	0.480445	−	0.877025i	$-0.340475\pi$
$740$	−17.7408	−	15.7124i	−0.652165	−	0.577598i
$741$	−37.0830	+	16.6097i	−1.36228	+	0.610173i
$742$	10.3635	−	12.9055i	0.380454	−	0.473776i
$743$	−4.23660	−	4.23660i	−0.155426	−	0.155426i	0.625111	−	0.780536i	$-0.285054\pi$
$743$	−4.23660	−	4.23660i	−0.155426	−	0.155426i	−0.780536	+	0.625111i	$0.785054\pi$
$744$	1.74160	−	0.589633i	0.0638500	−	0.0216170i
$745$	1.76331	−	11.1339i	0.0646027	−	0.407913i
$746$	−34.3948	+	3.75752i	−1.25928	+	0.137573i
$747$	3.67534	−	3.67534i	0.134474	−	0.134474i
$748$	7.45528	+	4.75515i	0.272592	+	0.173866i
$749$	−14.1305			−0.516318
$750$	−33.2702	−	12.6139i	−1.21486	−	0.460596i
$751$			33.1141i			1.20835i	0.796851	+	0.604176i	$0.206497\pi$
$751$			33.1141i			1.20835i	−0.796851	+	0.604176i	$0.793503\pi$
$752$	7.14066	−	19.5536i	0.260393	−	0.713047i
$753$	19.0182	+	19.0182i	0.693062	+	0.693062i
$754$	−36.5744	+	21.4260i	−1.33196	+	0.780288i
$755$	4.41130	−	27.8537i	0.160544	−	1.01370i
$756$	1.48612	+	6.72047i	0.0540495	+	0.244421i
$757$	4.76161	−	4.76161i	0.173064	−	0.173064i	−0.615260	−	0.788324i	$-0.710949\pi$
$757$	4.76161	−	4.76161i	0.173064	−	0.173064i	0.788324	+	0.615260i	$0.210949\pi$
$758$	−3.57476	−	2.87063i	−0.129841	−	0.104266i
$759$		−	3.98322i		−	0.144582i
$760$	−25.8508	−	18.3003i	−0.937706	−	0.663821i
$761$		−	14.4698i		−	0.524530i	−0.964996	−	0.262265i	$-0.915531\pi$
$761$		−	14.4698i		−	0.524530i	0.964996	−	0.262265i	$-0.0844694\pi$
$762$	7.52336	−	9.36877i	0.272542	−	0.339395i
$763$	5.48325	−	5.48325i	0.198507	−	0.198507i
$764$	−34.0455	+	7.52858i	−1.23172	+	0.272374i
$765$	−16.4841	+	11.9766i	−0.595983	+	0.433017i
$766$	−13.4062	+	1.46458i	−0.484385	+	0.0529176i
$767$	44.0922	+	16.8126i	1.59208	+	0.607067i
$768$	−3.06126	−	35.8752i	−0.110464	−	1.29454i
$769$	19.4815			0.702520			0.351260	−	0.936278i	$-0.385753\pi$
$769$	19.4815			0.702520			0.351260	+	0.936278i	$0.385753\pi$
$770$	5.16880	+	0.249609i	0.186271	+	0.00899527i
$771$		−	1.62402i		−	0.0584875i
$772$	33.9617	+	21.6616i	1.22231	+	0.779617i
$773$	10.9215	−	10.9215i	0.392819	−	0.392819i	−0.482872	−	0.875691i	$-0.660406\pi$
$773$	10.9215	−	10.9215i	0.392819	−	0.392819i	0.875691	+	0.482872i	$0.160406\pi$
$774$	31.0338	−	3.39034i	1.11549	−	0.121863i
$775$	−1.37371	−	0.446314i	−0.0493452	−	0.0160321i
$776$	2.61411	+	7.72129i	0.0938411	+	0.277178i
$777$	−13.7779	+	13.7779i	−0.494279	+	0.494279i
$778$	−16.5668	−	13.3035i	−0.593947	−	0.476954i
$779$	28.2750			1.01306
$780$	16.8098	+	32.1572i	0.601889	+	1.15141i
$781$	4.15519			0.148684
$782$	−8.60370	−	6.90899i	−0.307668	−	0.247065i
$783$	−12.3804	+	12.3804i	−0.442441	+	0.442441i
$784$	−7.30318	−	15.7056i	−0.260828	−	0.560915i
$785$	15.7722	+	21.7080i	0.562932	+	0.774793i
$786$	59.4019	−	6.48947i	2.11880	−	0.231472i
$787$	−20.3710	+	20.3710i	−0.726146	+	0.726146i	−0.969850	−	0.243704i	$-0.921638\pi$
$787$	−20.3710	+	20.3710i	−0.726146	+	0.726146i	0.243704	+	0.969850i	$0.421638\pi$
$788$	−22.0298	+	34.5391i	−0.784780	+	1.23040i
$789$		−	68.3274i		−	2.43252i
$790$	−29.5651	−	32.5655i	−1.05188	−	1.15863i
$791$	15.5339			0.552322
$792$	−2.59021	+	5.24180i	−0.0920390	+	0.186259i
$793$	−9.46265	+	24.8165i	−0.336029	+	0.881260i
$794$	−25.9337	+	2.83318i	−0.920354	+	0.100546i
$795$	5.63791	−	35.5988i	0.199956	−	1.26256i
$796$	−7.51921	−	34.0031i	−0.266511	−	1.20521i
$797$	33.0775	−	33.0775i	1.17167	−	1.17167i	0.189854	−	0.981812i	$-0.439199\pi$
$797$	33.0775	−	33.0775i	1.17167	−	1.17167i	0.981812	−	0.189854i	$-0.0608013\pi$
$798$	−16.3054	+	20.3049i	−0.577203	+	0.718786i
$799$			22.9748i			0.812790i
$800$	−14.9153	+	24.0320i	−0.527334	+	0.849658i
$801$		−	25.7796i		−	0.910876i
$802$	12.0509	+	9.67714i	0.425531	+	0.341712i
$803$	−6.50142	+	6.50142i	−0.229430	+	0.229430i
$804$	−29.4035	+	6.50209i	−1.03698	+	0.229311i
$805$	−6.37796	−	1.01010i	−0.224794	−	0.0356014i
$806$	0.744558	+	1.27097i	0.0262260	+	0.0447680i
$807$	0.726700	+	0.726700i	0.0255810	+	0.0255810i
$808$	9.83001	+	4.85745i	0.345819	+	0.170884i
$809$			32.4000i			1.13912i	0.821949	+	0.569561i	$0.192887\pi$
$809$			32.4000i			1.13912i	−0.821949	+	0.569561i	$0.807113\pi$
$810$	23.2368	+	25.5949i	0.816457	+	0.899314i
$811$	−13.9272			−0.489052			−0.244526	−	0.969643i	$-0.578632\pi$
$811$	−13.9272			−0.489052			−0.244526	+	0.969643i	$0.578632\pi$
$812$	−14.6088	+	22.9041i	−0.512667	+	0.803776i
$813$	10.5386	−	10.5386i	0.369606	−	0.369606i
$814$	7.46097	−	0.815087i	0.261507	−	0.0285688i
$815$	−18.7547	+	13.6264i	−0.656948	+	0.477311i
$816$	16.7556	+	36.0332i	0.586563	+	1.26141i
$817$	−37.8715	−	37.8715i	−1.32495	−	1.32495i
$818$	25.5294	−	31.7916i	0.892616	−	1.11157i
$819$	11.0978	−	4.97078i	0.387789	−	0.173693i
$820$	−1.52824	−	25.2037i	−0.0533686	−	0.880152i
$821$		−	11.6823i		−	0.407717i	−0.979000	−	0.203858i	$-0.934652\pi$
$821$		−	11.6823i		−	0.407717i	0.979000	−	0.203858i	$-0.0653482\pi$
$822$	2.46609	−	3.07099i	0.0860146	−	0.107113i
$823$	5.22036	−	5.22036i	0.181970	−	0.181970i	−0.610244	−	0.792214i	$-0.708928\pi$
$823$	5.22036	−	5.22036i	0.181970	−	0.181970i	0.792214	+	0.610244i	$0.208928\pi$
$824$	−0.0658414	+	0.0222912i	−0.00229369	+	0.000776550i
$825$	10.0403	−	5.11607i	0.349560	−	0.178119i
$826$	30.0642	−	3.28442i	1.04607	−	0.114280i
$827$	25.2929	−	25.2929i	0.879522	−	0.879522i	−0.113963	−	0.993485i	$-0.536355\pi$
$827$	25.2929	−	25.2929i	0.879522	−	0.879522i	0.993485	+	0.113963i	$0.0363546\pi$
$828$	3.92345	−	6.15132i	0.136349	−	0.213773i
$829$		−	15.7376i		−	0.546591i	−0.961930	−	0.273295i	$-0.911886\pi$
$829$		−	15.7376i		−	0.546591i	0.961930	−	0.273295i	$-0.0881137\pi$
$830$	−0.384107	+	7.95394i	−0.0133325	+	0.276085i
$831$		−	52.5637i		−	1.82341i
$832$	27.6515	−	8.20957i	0.958642	−	0.284616i
$833$	13.5173	+	13.5173i	0.468345	+	0.468345i
$834$	2.99775	+	27.4401i	0.103803	+	0.950173i
$835$	25.2179	+	34.7087i	0.872702	+	1.20114i
$836$	9.79424	−	2.16583i	0.338741	−	0.0749068i
$837$	0.430224	+	0.430224i	0.0148707	+	0.0148707i
$838$	−22.1792	+	27.6195i	−0.766167	+	0.954101i
$839$		−	15.0154i		−	0.518389i	−0.965825	−	0.259194i	$-0.916543\pi$
$839$		−	15.0154i		−	0.518389i	0.965825	−	0.259194i	$-0.0834570\pi$
$840$	18.9807	+	13.4368i	0.654895	+	0.463613i
$841$	−40.1062			−1.38297
$842$	−30.5005	−	24.4926i	−1.05112	−	0.844072i
$843$	−13.3771	−	13.3771i	−0.460732	−	0.460732i
$844$	24.7689	−	5.47722i	0.852580	−	0.188534i
$845$	−22.5087	+	18.3946i	−0.774321	+	0.632792i
$846$	−15.1013	+	1.64977i	−0.519193	+	0.0567202i
$847$	11.5504	−	11.5504i	0.396877	−	0.396877i
$848$	−26.9126	−	9.82805i	−0.924183	−	0.337496i
$849$			8.38790i			0.287872i
$850$	6.36455	−	30.5609i	0.218302	−	1.04823i
$851$	−9.36562			−0.321049
$852$	15.7434	+	10.0415i	0.539361	+	0.344017i
$853$	29.4224	−	29.4224i	1.00740	−	1.00740i	0.00743020	−	0.999972i	$-0.497635\pi$
$853$	29.4224	−	29.4224i	1.00740	−	1.00740i	0.999972	−	0.00743020i	$-0.00236513\pi$
$854$	1.84858	+	16.9211i	0.0632570	+	0.579028i
$855$	−3.61551	+	22.8290i	−0.123648	+	0.780734i
$856$	7.84385	+	23.1684i	0.268097	+	0.791879i
$857$	−9.77983	+	9.77983i	−0.334073	+	0.334073i	−0.854131	−	0.520058i	$-0.825910\pi$
$857$	−9.77983	+	9.77983i	−0.334073	+	0.334073i	0.520058	+	0.854131i	$0.325910\pi$
$858$	−11.1188	−	2.90400i	−0.379591	−	0.0991408i
$859$	−2.40710			−0.0821291			−0.0410646	−	0.999156i	$-0.513075\pi$
$859$	−2.40710			−0.0821291			−0.0410646	+	0.999156i	$0.513075\pi$
$860$	−31.7109	+	35.8048i	−1.08133	+	1.22093i
$861$	−20.7606			−0.707520
$862$	8.62703	−	10.7432i	0.293838	−	0.365914i
$863$	−27.0230	−	27.0230i	−0.919873	−	0.919873i	0.0771465	−	0.997020i	$-0.475419\pi$
$863$	−27.0230	−	27.0230i	−0.919873	−	0.919873i	−0.997020	+	0.0771465i	$0.975419\pi$
$864$	10.1939	−	6.16717i	0.346804	−	0.209811i
$865$	4.75220	−	3.45275i	0.161580	−	0.117397i
$866$	−16.7792	+	1.83308i	−0.570182	+	0.0622906i
$867$	−3.96145	−	3.96145i	−0.134538	−	0.134538i
$868$	0.795923	+	0.507658i	0.0270154	+	0.0172310i
$869$	13.9299			0.472540
$870$	−2.85346	+	59.0884i	−0.0967414	+	2.00329i
$871$	−9.86150	−	22.0169i	−0.334144	−	0.746013i
$872$	−12.0341	−	5.94658i	−0.407526	−	0.201377i
$873$	4.20648	−	4.20648i	0.142368	−	0.142368i
$874$	−12.4431	+	1.35936i	−0.420893	+	0.0459812i
$875$	−5.64577	−	17.3740i	−0.190862	−	0.587349i
$876$	−40.3444	+	8.92149i	−1.36311	+	0.301429i
$877$	11.3985	+	11.3985i	0.384900	+	0.384900i	0.872864	−	0.487964i	$-0.162260\pi$
$877$	11.3985	+	11.3985i	0.384900	+	0.384900i	−0.487964	+	0.872864i	$0.662260\pi$
$878$	17.5063	−	21.8004i	0.590808	−	0.735728i
$879$			1.99540i			0.0673030i
$880$	−2.45995	−	8.61332i	−0.0829248	−	0.290355i
$881$	20.6377			0.695303			0.347652	−	0.937624i	$-0.386979\pi$
$881$	20.6377			0.695303			0.347652	+	0.937624i	$0.386979\pi$
$882$	−7.91422	+	9.85551i	−0.266486	+	0.331852i
$883$	39.7368	−	39.7368i	1.33725	−	1.33725i	0.438540	−	0.898712i	$-0.355496\pi$
$883$	39.7368	−	39.7368i	1.33725	−	1.33725i	0.898712	−	0.438540i	$-0.144504\pi$
$884$	−25.5585	+	18.9795i	−0.859624	+	0.638349i
$885$	53.2791	−	38.7104i	1.79096	−	1.30124i
$886$	−2.51893	−	23.0572i	−0.0846251	−	0.774623i
$887$	−7.65630	−	7.65630i	−0.257073	−	0.257073i	0.566789	−	0.823863i	$-0.308185\pi$
$887$	−7.65630	−	7.65630i	−0.257073	−	0.257073i	−0.823863	+	0.566789i	$0.808185\pi$
$888$	30.2383	+	14.9421i	1.01473	+	0.501424i
$889$	6.16914			0.206906
$890$	26.5481	+	29.2423i	0.889896	+	0.980206i
$891$	−10.9483			−0.366780
$892$	15.4421	−	24.2106i	0.517039	−	0.810630i
$893$	18.4286	+	18.4286i	0.616688	+	0.616688i
$894$	1.74236	+	15.9488i	0.0582732	+	0.533409i
$895$	−8.67514	+	54.7764i	−0.289978	+	1.83097i
$896$	13.3777	−	12.7584i	0.446919	−	0.426229i
$897$	13.3991	+	5.10915i	0.447384	+	0.170590i
$898$	20.4705	−	25.4917i	0.683109	−	0.850670i
$899$			2.40146i			0.0800931i
$900$	20.5447	+	1.98890i	0.684822	+	0.0662966i
$901$	31.6214			1.05346
$902$	6.23520	+	5.00703i	0.207610	+	0.166716i
$903$	27.8067	+	27.8067i	0.925350	+	0.925350i
$904$	−8.62288	−	25.4694i	−0.286793	−	0.847099i
$905$	−2.79916	+	17.6744i	−0.0930474	+	0.587518i
$906$	4.35889	+	39.8994i	0.144814	+	1.32557i
$907$	20.0975	+	20.0975i	0.667327	+	0.667327i	0.957096	−	0.289770i	$-0.0935787\pi$
$907$	20.0975	+	20.0975i	0.667327	+	0.667327i	−0.289770	+	0.957096i	$0.593579\pi$
$908$	25.6843	+	16.3821i	0.852365	+	0.543658i
$909$		−	8.00157i		−	0.265395i
$910$	−7.46951	+	17.0671i	−0.247612	+	0.565770i
$911$			19.1370i			0.634036i	0.948420	+	0.317018i	$0.102682\pi$
$911$			19.1370i			0.634036i	−0.948420	+	0.317018i	$0.897318\pi$
$912$	42.3430	+	15.4630i	1.40212	+	0.512030i
$913$	−1.78330	−	1.78330i	−0.0590188	−	0.0590188i
$914$	17.0560	−	1.86331i	0.564161	−	0.0616328i
$915$	21.7874	+	29.9872i	0.720271	+	0.991346i
$916$	3.53826	+	16.0006i	0.116907	+	0.528675i
$917$	21.6941	+	21.6941i	0.716401	+	0.716401i
$918$	−8.23331	+	10.2529i	−0.271740	+	0.338395i
$919$	−19.5027			−0.643336			−0.321668	−	0.946853i	$-0.604243\pi$
$919$	−19.5027			−0.643336			−0.321668	+	0.946853i	$0.604243\pi$
$920$	1.88425	+	11.0180i	0.0621218	+	0.363253i
$921$		−	58.8812i		−	1.94020i
$922$	17.2851	+	13.8804i	0.569254	+	0.457125i
$923$	−5.32973	+	13.9776i	−0.175430	+	0.460079i
$924$	−7.19132	+	1.59024i	−0.236577	+	0.0523150i
$925$	−12.0293	−	23.6075i	−0.395519	−	0.776211i
$926$	−44.9696	+	4.91279i	−1.47779	+	0.161444i
$927$	0.0358697	+	0.0358697i	0.00117811	+	0.00117811i
$928$	45.6628	+	11.2384i	1.49896	+	0.368920i
$929$	−8.21752			−0.269608			−0.134804	−	0.990872i	$-0.543040\pi$
$929$	−8.21752			−0.269608			−0.134804	+	0.990872i	$0.543040\pi$
$930$	2.05334	+	0.0991585i	0.0673316	+	0.00325154i
$931$	21.6849			0.710695
$932$	20.2105	−	31.6866i	0.662016	−	1.03793i
$933$	23.4073	+	23.4073i	0.766321	+	0.766321i
$934$	−10.9870	+	1.20030i	−0.359506	+	0.0392749i
$935$	5.81116	+	7.99820i	0.190045	+	0.261569i
$936$	−14.3105	−	15.4367i	−0.467753	−	0.504563i
$937$	−23.9181	+	23.9181i	−0.781371	+	0.781371i	−0.980062	−	0.198691i	$-0.936331\pi$
$937$	−23.9181	+	23.9181i	−0.781371	+	0.781371i	0.198691	+	0.980062i	$0.436331\pi$
$938$	−12.0554	−	9.68081i	−0.393623	−	0.316090i
$939$	−77.9243			−2.54296
$940$	15.4308	−	17.4229i	0.503297	−	0.568272i
$941$			26.8793i			0.876240i	0.898917	+	0.438120i	$0.144355\pi$
$941$			26.8793i			0.876240i	−0.898917	+	0.438120i	$0.855645\pi$
$942$	−29.7771	−	23.9118i	−0.970191	−	0.779088i
$943$	−7.05609	−	7.05609i	−0.229778	−	0.229778i
$944$	−22.0738	−	47.4701i	−0.718441	−	1.54502i
$945$	−1.20372	+	7.60050i	−0.0391570	+	0.247244i
$946$	−1.64502	−	15.0578i	−0.0534842	−	0.489572i
$947$	−4.82725	+	4.82725i	−0.156865	+	0.156865i	−0.781176	−	0.624311i	$-0.785380\pi$
$947$	−4.82725	+	4.82725i	−0.156865	+	0.156865i	0.624311	+	0.781176i	$0.285380\pi$
$948$	52.7785	+	33.6633i	1.71417	+	1.09333i
$949$	−13.5309	−	30.2092i	−0.439232	−	0.980633i
$950$	−19.4084	−	29.6187i	−0.629692	−	0.960957i
$951$	−51.3935			−1.66655
$952$	−9.03862	+	18.2914i	−0.292943	+	0.592829i
$953$	0.799613	+	0.799613i	0.0259020	+	0.0259020i	0.719939	−	0.694037i	$-0.244170\pi$
$953$	0.799613	+	0.799613i	0.0259020	+	0.0259020i	−0.694037	+	0.719939i	$0.744170\pi$
$954$	2.27066	+	20.7847i	0.0735153	+	0.672928i
$955$	−38.5037	−	6.09797i	−1.24595	−	0.197326i
$956$	−33.6780	+	7.44732i	−1.08923	+	0.240864i
$957$	−13.2479	−	13.2479i	−0.428242	−	0.428242i
$958$	−3.53532	−	2.83895i	−0.114221	−	0.0917222i
$959$	2.02218			0.0652998
$960$	11.4948	−	38.5794i	0.370992	−	1.24515i
$961$	−30.9165			−0.997308
$962$	−6.82807	+	26.1434i	−0.220146	+	0.842896i
$963$	12.6219	−	12.6219i	0.406734	−	0.406734i
$964$	−38.7713	+	8.57362i	−1.24874	+	0.276138i
$965$	26.4721	+	36.4349i	0.852168	+	1.17288i
$966$	9.13618	−	0.998099i	0.293952	−	0.0321133i
$967$	13.2019	−	13.2019i	0.424546	−	0.424546i	−0.462220	−	0.886766i	$-0.652947\pi$
$967$	13.2019	−	13.2019i	0.424546	−	0.424546i	0.886766	+	0.462220i	$0.152947\pi$
$968$	−25.3497	−	12.5264i	−0.814770	−	0.402614i
$969$	−49.7515			−1.59825
$970$	−0.439615	+	9.10339i	−0.0141152	+	0.292292i
$971$			44.3991i			1.42484i	0.701756	+	0.712418i	$0.252400\pi$
$971$			44.3991i			1.42484i	−0.701756	+	0.712418i	$0.747600\pi$
$972$	−30.8271	−	19.6622i	−0.988780	−	0.630667i
$973$	−10.0213	+	10.0213i	−0.321269	+	0.321269i
$974$	2.28720	+	20.9361i	0.0732866	+	0.670835i
$975$	4.33150	+	40.3368i	0.138719	+	1.29181i
$976$	26.7177	−	12.4238i	0.855212	−	0.397677i
$977$	8.94867	+	8.94867i	0.286293	+	0.286293i	0.835613	−	0.549319i	$-0.185113\pi$
$977$	8.94867	+	8.94867i	0.286293	+	0.286293i	−0.549319	+	0.835613i	$0.685113\pi$
$978$	20.6586	−	25.7260i	0.660590	−	0.822626i
$979$	−12.5084			−0.399772
$980$	−1.17206	−	19.3295i	−0.0374400	−	0.617458i
$981$			9.79567i			0.312752i
$982$	5.28732	+	4.24585i	0.168725	+	0.135490i
$983$	−15.0935	−	15.0935i	−0.481408	−	0.481408i	0.424173	−	0.905581i	$-0.360565\pi$
$983$	−15.0935	−	15.0935i	−0.481408	−	0.481408i	−0.905581	+	0.424173i	$0.860565\pi$
$984$	11.5242	+	34.0391i	0.367379	+	1.08513i
$985$	−37.0543	+	26.9221i	−1.18065	+	0.857810i
$986$	−51.5938	+	5.63647i	−1.64308	+	0.179502i
$987$	−13.5310	−	13.5310i	−0.430696	−	0.430696i
$988$	−5.27714	+	35.7248i	−0.167888	+	1.13656i
$989$			18.9018i			0.601043i
$990$	−4.83992	+	4.39400i	−0.153823	+	0.139650i
$991$			3.15639i			0.100266i	0.998743	+	0.0501330i	$0.0159645\pi$
$991$			3.15639i			0.100266i	−0.998743	+	0.0501330i	$0.984035\pi$
$992$	0.390539	−	1.58680i	0.0123996	−	0.0503808i
$993$	−45.0816	+	45.0816i	−1.43062	+	1.43062i
$994$	1.04119	+	9.53062i	0.0330245	+	0.302293i
$995$	6.09038	−	38.4558i	0.193078	−	1.21913i
$996$	−2.44712	−	11.0663i	−0.0775399	−	0.350648i
$997$	4.47950	−	4.47950i	0.141867	−	0.141867i	−0.632606	−	0.774474i	$-0.718015\pi$
$997$	4.47950	−	4.47950i	0.141867	−	0.141867i	0.774474	+	0.632606i	$0.218015\pi$
$998$	−33.2083	−	26.6671i	−1.05119	−	0.844133i
$999$			11.1608i			0.353113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.p.d.103.9	yes	64
4.3	odd	2	inner	260.2.p.d.103.25	yes	64
5.2	odd	4	inner	260.2.p.d.207.8	yes	64
13.12	even	2	inner	260.2.p.d.103.24	yes	64
20.7	even	4	inner	260.2.p.d.207.24	yes	64
52.51	odd	2	inner	260.2.p.d.103.8	✓	64
65.12	odd	4	inner	260.2.p.d.207.25	yes	64
260.207	even	4	inner	260.2.p.d.207.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.p.d.103.8	✓	64	52.51	odd	2	inner
260.2.p.d.103.9	yes	64	1.1	even	1	trivial
260.2.p.d.103.24	yes	64	13.12	even	2	inner
260.2.p.d.103.25	yes	64	4.3	odd	2	inner
260.2.p.d.207.8	yes	64	5.2	odd	4	inner
260.2.p.d.207.9	yes	64	260.207	even	4	inner
260.2.p.d.207.24	yes	64	20.7	even	4	inner
260.2.p.d.207.25	yes	64	65.12	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.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.885485 + 1.10269i) q^{2} +(1.59124 - 1.59124i) q^{3} +(-0.431834 - 1.95282i) q^{4} +(0.349775 - 2.20854i) q^{5} +(0.345619 + 3.16365i) q^{6} +(-1.15539 + 1.15539i) q^{7} +(2.53573 + 1.25302i) q^{8} -2.06407i q^{9} +O(q^{10})\)	\(q+(-0.885485 + 1.10269i) q^{2} +(1.59124 - 1.59124i) q^{3} +(-0.431834 - 1.95282i) q^{4} +(0.349775 - 2.20854i) q^{5} +(0.345619 + 3.16365i) q^{6} +(-1.15539 + 1.15539i) q^{7} +(2.53573 + 1.25302i) q^{8} -2.06407i q^{9} +(2.12561 + 2.34132i) q^{10} -1.00150 q^{11} +(-3.79455 - 2.42026i) q^{12} +(1.28460 - 3.36895i) q^{13} +(-0.250952 - 2.29711i) q^{14} +(-2.95774 - 4.07089i) q^{15} +(-3.62704 + 1.68659i) q^{16} +(3.12166 - 3.12166i) q^{17} +(2.27602 + 1.82770i) q^{18} -5.00790i q^{19} +(-4.46394 + 0.270674i) q^{20} +3.67700i q^{21} +(0.886815 - 1.10434i) q^{22} +(-1.24973 + 1.24973i) q^{23} +(6.02880 - 2.04110i) q^{24} +(-4.75531 - 1.54499i) q^{25} +(2.57740 + 4.39966i) q^{26} +(1.48928 + 1.48928i) q^{27} +(2.75521 + 1.75734i) q^{28} +8.31301i q^{29} +(7.10795 + 0.343252i) q^{30} +0.288879 q^{31} +(1.35191 - 5.49294i) q^{32} +(-1.59363 + 1.59363i) q^{33} +(0.678029 + 6.20640i) q^{34} +(2.14760 + 2.95585i) q^{35} +(-4.03077 + 0.891335i) q^{36} +(3.74705 + 3.74705i) q^{37} +(5.52214 + 4.43442i) q^{38} +(-3.31670 - 7.40489i) q^{39} +(3.65428 - 5.16200i) q^{40} +5.64607i q^{41} +(-4.05458 - 3.25593i) q^{42} +(7.56234 - 7.56234i) q^{43} +(0.432483 + 1.95576i) q^{44} +(-4.55859 - 0.721961i) q^{45} +(-0.271444 - 2.48468i) q^{46} +(-3.67990 + 3.67990i) q^{47} +(-3.08772 + 8.45524i) q^{48} +4.33015i q^{49} +(5.91439 - 3.87556i) q^{50} -9.93461i q^{51} +(-7.13369 - 1.05376i) q^{52} +(5.06483 + 5.06483i) q^{53} +(-2.96095 + 0.323475i) q^{54} +(-0.350301 + 2.21186i) q^{55} +(-4.37749 + 1.48204i) q^{56} +(-7.96876 - 7.96876i) q^{57} +(-9.16664 - 7.36105i) q^{58} +13.0878i q^{59} +(-6.67248 + 7.53389i) q^{60} -7.36625 q^{61} +(-0.255798 + 0.318543i) q^{62} +(2.38481 + 2.38481i) q^{63} +(4.85989 + 6.35464i) q^{64} +(-6.99114 - 4.01546i) q^{65} +(-0.346138 - 3.16841i) q^{66} +(4.73121 - 4.73121i) q^{67} +(-7.44409 - 4.74802i) q^{68} +3.97725i q^{69} +(-5.16105 - 0.249234i) q^{70} -4.14895 q^{71} +(2.58632 - 5.23393i) q^{72} +(6.49166 - 6.49166i) q^{73} +(-7.44977 + 0.813864i) q^{74} +(-10.0253 + 5.10839i) q^{75} +(-9.77955 + 2.16258i) q^{76} +(1.15713 - 1.15713i) q^{77} +(11.1022 + 2.89964i) q^{78} -13.9090 q^{79} +(2.45626 + 8.60040i) q^{80} +10.9318 q^{81} +(-6.22585 - 4.99951i) q^{82} +(1.78063 + 1.78063i) q^{83} +(7.18053 - 1.58785i) q^{84} +(-5.80244 - 7.98620i) q^{85} +(1.64255 + 15.0352i) q^{86} +(13.2280 + 13.2280i) q^{87} +(-2.53954 - 1.25490i) q^{88} +12.4897 q^{89} +(4.83266 - 4.38741i) q^{90} +(2.40824 + 5.37666i) q^{91} +(2.98019 + 1.90083i) q^{92} +(0.459675 - 0.459675i) q^{93} +(-0.799279 - 7.31627i) q^{94} +(-11.0602 - 1.75164i) q^{95} +(-6.58935 - 10.8918i) q^{96} +(2.03795 + 2.03795i) q^{97} +(-4.77479 - 3.83428i) q^{98} +2.06717i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) \) 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Introduction

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