LMFDB - Embedded newform 280.2.w.a.43.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.17
Character	$\chi$	$=$	280.43
Dual form			280.2.w.a.267.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.205776 - 1.39916i) q^{2} +(1.94776 + 1.94776i) q^{3} +(-1.91531 + 0.575828i) q^{4} +(2.03914 + 0.917560i) q^{5} +(2.32443 - 3.12603i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.19980 + 2.56134i) q^{8} +4.58750i q^{9} +O(q^{10})$	\(q+(-0.205776 - 1.39916i) q^{2} +(1.94776 + 1.94776i) q^{3} +(-1.91531 + 0.575828i) q^{4} +(2.03914 + 0.917560i) q^{5} +(2.32443 - 3.12603i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.19980 + 2.56134i) q^{8} +4.58750i q^{9} +(0.864211 - 3.04190i) q^{10} -4.96845 q^{11} +(-4.85213 - 2.60899i) q^{12} +(-2.73283 + 2.73283i) q^{13} +(0.843852 - 1.13486i) q^{14} +(2.18456 + 5.75893i) q^{15} +(3.33684 - 2.20578i) q^{16} +(2.50105 - 2.50105i) q^{17} +(6.41866 - 0.943998i) q^{18} -5.82728i q^{19} +(-4.43394 - 0.583221i) q^{20} +2.75454i q^{21} +(1.02239 + 6.95167i) q^{22} +(4.49556 - 4.49556i) q^{23} +(-2.65195 + 7.32579i) q^{24} +(3.31617 + 3.74206i) q^{25} +(4.38603 + 3.26132i) q^{26} +(-3.09207 + 3.09207i) q^{27} +(-1.76150 - 0.947158i) q^{28} +3.12482 q^{29} +(7.60814 - 4.24160i) q^{30} -4.40466i q^{31} +(-3.77289 - 4.21489i) q^{32} +(-9.67733 - 9.67733i) q^{33} +(-4.01403 - 2.98472i) q^{34} +(0.793075 + 2.09070i) q^{35} +(-2.64161 - 8.78650i) q^{36} +(0.991822 + 0.991822i) q^{37} +(-8.15331 + 1.19911i) q^{38} -10.6458 q^{39} +(0.0963777 + 6.32382i) q^{40} +3.18008 q^{41} +(3.85405 - 0.566819i) q^{42} +(-4.01697 - 4.01697i) q^{43} +(9.51613 - 2.86097i) q^{44} +(-4.20931 + 9.35455i) q^{45} +(-7.21510 - 5.36494i) q^{46} +(-2.65726 - 2.65726i) q^{47} +(10.7957 + 2.20303i) q^{48} +1.00000i q^{49} +(4.55337 - 5.40988i) q^{50} +9.74286 q^{51} +(3.66058 - 6.80786i) q^{52} +(2.78266 - 2.78266i) q^{53} +(4.96258 + 3.69003i) q^{54} +(-10.1314 - 4.55885i) q^{55} +(-0.962753 + 2.65953i) q^{56} +(11.3501 - 11.3501i) q^{57} +(-0.643014 - 4.37213i) q^{58} +12.3297i q^{59} +(-7.50026 - 9.77221i) q^{60} +0.895384i q^{61} +(-6.16284 + 0.906373i) q^{62} +(-3.24385 + 3.24385i) q^{63} +(-5.12095 + 6.14621i) q^{64} +(-8.08015 + 3.06508i) q^{65} +(-11.5488 + 15.5315i) q^{66} +(-3.69144 + 3.69144i) q^{67} +(-3.35011 + 6.23046i) q^{68} +17.5125 q^{69} +(2.76204 - 1.53986i) q^{70} +8.61057i q^{71} +(-11.7502 + 5.50410i) q^{72} +(-10.7357 - 10.7357i) q^{73} +(1.18363 - 1.59181i) q^{74} +(-0.829546 + 13.7477i) q^{75} +(3.35551 + 11.1611i) q^{76} +(-3.51322 - 3.51322i) q^{77} +(2.19064 + 14.8952i) q^{78} -12.8846 q^{79} +(8.82822 - 1.43614i) q^{80} +1.71732 q^{81} +(-0.654384 - 4.44945i) q^{82} +(-3.46917 - 3.46917i) q^{83} +(-1.58614 - 5.27581i) q^{84} +(7.39484 - 2.80512i) q^{85} +(-4.79379 + 6.44699i) q^{86} +(6.08639 + 6.08639i) q^{87} +(-5.96116 - 12.7259i) q^{88} +4.83422i q^{89} +(13.9547 + 3.96457i) q^{90} -3.86481 q^{91} +(-6.02173 + 11.1991i) q^{92} +(8.57920 - 8.57920i) q^{93} +(-3.17114 + 4.26475i) q^{94} +(5.34688 - 11.8826i) q^{95} +(0.860905 - 15.5582i) q^{96} +(-1.03935 + 1.03935i) q^{97} +(1.39916 - 0.205776i) q^{98} -22.7928i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.205776	−	1.39916i	−0.145506	−	0.989357i
$2$	−0.205776	−	1.39916i	−0.145506	−	0.989357i
$3$	1.94776	+	1.94776i	1.12454	+	1.12454i	0.991051	+	0.133487i	$0.0426173\pi$
$3$	1.94776	+	1.94776i	1.12454	+	1.12454i	0.133487	+	0.991051i	$0.457383\pi$
$4$	−1.91531	+	0.575828i	−0.957656	+	0.287914i
$5$	2.03914	+	0.917560i	0.911930	+	0.410345i
$5$	2.03914	+	0.917560i	0.911930	+	0.410345i
$6$	2.32443	−	3.12603i	0.948943	−	1.27620i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	1.19980	+	2.56134i	0.424194	+	0.905571i
$9$			4.58750i			1.52917i
$10$	0.864211	−	3.04190i	0.273287	−	0.961932i
$11$	−4.96845			−1.49804			−0.749022	−	0.662545i	$-0.769476\pi$
$11$	−4.96845			−1.49804			−0.749022	+	0.662545i	$0.769476\pi$
$12$	−4.85213	−	2.60899i	−1.40069	−	0.753150i
$13$	−2.73283	+	2.73283i	−0.757951	+	0.757951i	−0.975949	−	0.217998i	$-0.930047\pi$
$13$	−2.73283	+	2.73283i	−0.757951	+	0.757951i	0.217998	+	0.975949i	$0.430047\pi$
$14$	0.843852	−	1.13486i	0.225529	−	0.303305i
$15$	2.18456	+	5.75893i	0.564051	+	1.48695i
$16$	3.33684	−	2.20578i	0.834211	−	0.551446i
$17$	2.50105	−	2.50105i	0.606593	−	0.606593i	−0.335461	−	0.942054i	$-0.608892\pi$
$17$	2.50105	−	2.50105i	0.606593	−	0.606593i	0.942054	+	0.335461i	$0.108892\pi$
$18$	6.41866	−	0.943998i	1.51289	−	0.222503i
$19$		−	5.82728i		−	1.33687i	−0.743771	−	0.668435i	$-0.766965\pi$
$19$		−	5.82728i		−	1.33687i	0.743771	−	0.668435i	$-0.233035\pi$
$20$	−4.43394	−	0.583221i	−0.991460	−	0.130412i
$21$			2.75454i			0.601090i
$22$	1.02239	+	6.95167i	0.217974	+	1.48210i
$23$	4.49556	−	4.49556i	0.937389	−	0.937389i	−0.0607632	−	0.998152i	$-0.519353\pi$
$23$	4.49556	−	4.49556i	0.937389	−	0.937389i	0.998152	+	0.0607632i	$0.0193535\pi$
$24$	−2.65195	+	7.32579i	−0.541326	+	1.49537i
$25$	3.31617	+	3.74206i	0.663233	+	0.748413i
$26$	4.38603	+	3.26132i	0.860170	+	0.639598i
$27$	−3.09207	+	3.09207i	−0.595069	+	0.595069i
$28$	−1.76150	−	0.947158i	−0.332893	−	0.178996i
$29$	3.12482			0.580265			0.290132	−	0.956986i	$-0.406301\pi$
$29$	3.12482			0.580265			0.290132	+	0.956986i	$0.406301\pi$
$30$	7.60814	−	4.24160i	1.38905	−	0.774407i
$31$		−	4.40466i		−	0.791100i	−0.918444	−	0.395550i	$-0.870554\pi$
$31$		−	4.40466i		−	0.791100i	0.918444	−	0.395550i	$-0.129446\pi$
$32$	−3.77289	−	4.21489i	−0.666959	−	0.745094i
$33$	−9.67733	−	9.67733i	−1.68461	−	1.68461i
$34$	−4.01403	−	2.98472i	−0.688400	−	0.511875i
$35$	0.793075	+	2.09070i	0.134054	+	0.353393i
$36$	−2.64161	−	8.78650i	−0.440269	−	1.46442i
$37$	0.991822	+	0.991822i	0.163055	+	0.163055i	0.783918	−	0.620864i	$-0.213218\pi$
$37$	0.991822	+	0.991822i	0.163055	+	0.163055i	−0.620864	+	0.783918i	$0.713218\pi$
$38$	−8.15331	+	1.19911i	−1.32264	+	0.194522i
$39$	−10.6458			−1.70469
$40$	0.0963777	+	6.32382i	0.0152387	+	0.999884i
$41$	3.18008			0.496645			0.248322	−	0.968677i	$-0.420121\pi$
$41$	3.18008			0.496645			0.248322	+	0.968677i	$0.420121\pi$
$42$	3.85405	−	0.566819i	0.594693	−	0.0874621i
$43$	−4.01697	−	4.01697i	−0.612582	−	0.612582i	0.331036	−	0.943618i	$-0.392602\pi$
$43$	−4.01697	−	4.01697i	−0.612582	−	0.612582i	−0.943618	+	0.331036i	$0.892602\pi$
$44$	9.51613	−	2.86097i	1.43461	−	0.431308i
$45$	−4.20931	+	9.35455i	−0.627487	+	1.39449i
$46$	−7.21510	−	5.36494i	−1.06381	−	0.791017i
$47$	−2.65726	−	2.65726i	−0.387602	−	0.387602i	0.486229	−	0.873831i	$-0.338372\pi$
$47$	−2.65726	−	2.65726i	−0.387602	−	0.387602i	−0.873831	+	0.486229i	$0.838372\pi$
$48$	10.7957	+	2.20303i	1.55822	+	0.317980i
$49$			1.00000i			0.142857i
$50$	4.55337	−	5.40988i	0.643944	−	0.765073i
$51$	9.74286			1.36427
$52$	3.66058	−	6.80786i	0.507631	−	0.944081i
$53$	2.78266	−	2.78266i	0.382228	−	0.382228i	−0.489676	−	0.871904i	$-0.662885\pi$
$53$	2.78266	−	2.78266i	0.382228	−	0.382228i	0.871904	+	0.489676i	$0.162885\pi$
$54$	4.96258	+	3.69003i	0.675322	+	0.502150i
$55$	−10.1314	−	4.55885i	−1.36611	−	0.614716i
$56$	−0.962753	+	2.65953i	−0.128653	+	0.355395i
$57$	11.3501	−	11.3501i	1.50336	−	1.50336i
$58$	−0.643014	−	4.37213i	−0.0844318	−	0.574089i
$59$			12.3297i			1.60518i	0.596528	+	0.802592i	$0.296546\pi$
$59$			12.3297i			1.60518i	−0.596528	+	0.802592i	$0.703454\pi$
$60$	−7.50026	−	9.77221i	−0.968280	−	1.26159i
$61$			0.895384i			0.114642i	0.998356	+	0.0573211i	$0.0182559\pi$
$61$			0.895384i			0.114642i	−0.998356	+	0.0573211i	$0.981744\pi$
$62$	−6.16284	+	0.906373i	−0.782681	+	0.115110i
$63$	−3.24385	+	3.24385i	−0.408687	+	0.408687i
$64$	−5.12095	+	6.14621i	−0.640118	+	0.768276i
$65$	−8.08015	+	3.06508i	−1.00222	+	0.380176i
$66$	−11.5488	+	15.5315i	−1.42156	+	1.91180i
$67$	−3.69144	+	3.69144i	−0.450981	+	0.450981i	−0.895680	−	0.444699i	$-0.853311\pi$
$67$	−3.69144	+	3.69144i	−0.450981	+	0.450981i	0.444699	+	0.895680i	$0.353311\pi$
$68$	−3.35011	+	6.23046i	−0.406261	+	0.755554i
$69$	17.5125			2.10826
$70$	2.76204	−	1.53986i	0.330126	−	0.184048i
$71$			8.61057i			1.02189i	0.859614	+	0.510943i	$0.170704\pi$
$71$			8.61057i			1.02189i	−0.859614	+	0.510943i	$0.829296\pi$
$72$	−11.7502	+	5.50410i	−1.38477	+	0.648665i
$73$	−10.7357	−	10.7357i	−1.25652	−	1.25652i	−0.952741	−	0.303783i	$-0.901750\pi$
$73$	−10.7357	−	10.7357i	−1.25652	−	1.25652i	−0.303783	−	0.952741i	$-0.598250\pi$
$74$	1.18363	−	1.59181i	0.137594	−	0.185045i
$75$	−0.829546	+	13.7477i	−0.0957877	+	1.58745i
$76$	3.35551	+	11.1611i	0.384904	+	1.28026i
$77$	−3.51322	−	3.51322i	−0.400369	−	0.400369i
$78$	2.19064	+	14.8952i	0.248042	+	1.68655i
$79$	−12.8846			−1.44963			−0.724817	−	0.688941i	$-0.758076\pi$
$79$	−12.8846			−1.44963			−0.724817	+	0.688941i	$0.758076\pi$
$80$	8.82822	−	1.43614i	0.987025	−	0.160565i
$81$	1.71732			0.190813
$82$	−0.654384	−	4.44945i	−0.0722646	−	0.491359i
$83$	−3.46917	−	3.46917i	−0.380791	−	0.380791i	0.490596	−	0.871387i	$-0.336779\pi$
$83$	−3.46917	−	3.46917i	−0.380791	−	0.380791i	−0.871387	+	0.490596i	$0.836779\pi$
$84$	−1.58614	−	5.27581i	−0.173062	−	0.575638i
$85$	7.39484	−	2.80512i	0.802083	−	0.304258i
$86$	−4.79379	+	6.44699i	−0.516928	+	0.695196i
$87$	6.08639	+	6.08639i	0.652530	+	0.652530i
$88$	−5.96116	−	12.7259i	−0.635462	−	1.35659i
$89$			4.83422i			0.512426i	0.966620	+	0.256213i	$0.0824749\pi$
$89$			4.83422i			0.512426i	−0.966620	+	0.256213i	$0.917525\pi$
$90$	13.9547	+	3.96457i	1.47096	+	0.417902i
$91$	−3.86481			−0.405142
$92$	−6.02173	+	11.1991i	−0.627809	+	1.16758i
$93$	8.57920	−	8.57920i	0.889622	−	0.889622i
$94$	−3.17114	+	4.26475i	−0.327079	+	0.439875i
$95$	5.34688	−	11.8826i	0.548578	−	1.21913i
$96$	0.860905	−	15.5582i	0.0878657	−	1.58791i
$97$	−1.03935	+	1.03935i	−0.105530	+	0.105530i	−0.757901	−	0.652370i	$-0.773775\pi$
$97$	−1.03935	+	1.03935i	−0.105530	+	0.105530i	0.652370	+	0.757901i	$0.273775\pi$
$98$	1.39916	−	0.205776i	0.141337	−	0.0207865i
$99$		−	22.7928i		−	2.29076i
$100$	−8.50628	−	5.25768i	−0.850628	−	0.525768i
$101$			10.0883i			1.00383i	0.864918	+	0.501914i	$0.167371\pi$
$101$			10.0883i			1.00383i	−0.864918	+	0.501914i	$0.832629\pi$
$102$	−2.00485	−	13.6318i	−0.198509	−	1.34975i
$103$	7.98337	−	7.98337i	0.786625	−	0.786625i	−0.194315	−	0.980939i	$-0.562248\pi$
$103$	7.98337	−	7.98337i	0.786625	−	0.786625i	0.980939	+	0.194315i	$0.0622483\pi$
$104$	−10.2786	−	3.72085i	−1.00790	−	0.364860i
$105$	−2.52746	+	5.61689i	−0.246655	+	0.548152i
$106$	−4.46601	−	3.32080i	−0.433777	−	0.322544i
$107$	−11.5628	+	11.5628i	−1.11782	+	1.11782i	−0.125759	+	0.992061i	$0.540137\pi$
$107$	−11.5628	+	11.5628i	−1.11782	+	1.11782i	−0.992061	+	0.125759i	$0.959863\pi$
$108$	4.14178	−	7.70278i	0.398543	−	0.741200i
$109$	0.468615			0.0448851			0.0224426	−	0.999748i	$-0.492856\pi$
$109$	0.468615			0.0448851			0.0224426	+	0.999748i	$0.492856\pi$
$110$	−4.29379	+	15.1135i	−0.409396	+	1.44102i
$111$			3.86365i			0.366722i
$112$	3.91923	+	0.799781i	0.370332	+	0.0755722i
$113$	6.78744	+	6.78744i	0.638509	+	0.638509i	0.950188	−	0.311679i	$-0.100891\pi$
$113$	6.78744	+	6.78744i	0.638509	+	0.638509i	−0.311679	+	0.950188i	$0.600891\pi$
$114$	−18.2162	−	13.5451i	−1.70611	−	1.26861i
$115$	13.2920	−	5.04212i	1.23949	−	0.470180i
$116$	−5.98501	+	1.79936i	−0.555694	+	0.167067i
$117$	−12.5369	−	12.5369i	−1.15903	−	1.15903i
$118$	17.2512	−	2.53715i	1.58810	−	0.233563i
$119$	3.53702			0.324238
$120$	−12.1295	+	12.5050i	−1.10727	+	1.14154i
$121$	13.6855			1.24414
$122$	1.25279	−	0.184248i	0.113422	−	0.0166811i
$123$	6.19402	+	6.19402i	0.558496	+	0.558496i
$124$	2.53633	+	8.43630i	0.227769	+	0.757602i
$125$	3.32855	+	10.6734i	0.297714	+	0.954655i
$126$	5.20619	+	3.87117i	0.463804	+	0.344872i
$127$	−10.1884	−	10.1884i	−0.904078	−	0.904078i	0.0917079	−	0.995786i	$-0.470767\pi$
$127$	−10.1884	−	10.1884i	−0.904078	−	0.904078i	−0.995786	+	0.0917079i	$0.970767\pi$
$128$	9.65332	+	5.90029i	0.853241	+	0.521517i
$129$		−	15.6481i		−	1.37774i
$130$	5.95125	+	10.6747i	0.521959	+	0.936236i
$131$	0.0438076			0.00382749			0.00191375	−	0.999998i	$-0.499391\pi$
$131$	0.0438076			0.00382749			0.00191375	+	0.999998i	$0.499391\pi$
$132$	24.1076	+	12.9626i	2.09830	+	1.12825i
$133$	4.12051	−	4.12051i	0.357293	−	0.357293i
$134$	5.92454	+	4.40532i	0.511802	+	0.380561i
$135$	−9.14232	+	3.46799i	−0.786845	+	0.298477i
$136$	9.40680	+	3.40527i	0.806627	+	0.292000i
$137$	6.76298	−	6.76298i	0.577800	−	0.577800i	−0.356496	−	0.934297i	$-0.616029\pi$
$137$	6.76298	−	6.76298i	0.577800	−	0.577800i	0.934297	+	0.356496i	$0.116029\pi$
$138$	−3.60365	−	24.5028i	−0.306763	−	2.08582i
$139$		−	1.07689i		−	0.0913405i	−0.998957	−	0.0456703i	$-0.985458\pi$
$139$		−	1.07689i		−	0.0913405i	0.998957	−	0.0456703i	$-0.0145424\pi$
$140$	−2.72287	−	3.54767i	−0.230125	−	0.299833i
$141$		−	10.3514i		−	0.871746i
$142$	12.0476	−	1.77185i	1.01101	−	0.148690i
$143$	13.5779	−	13.5779i	1.13544	−	1.13544i
$144$	10.1190	+	15.3078i	0.843253	+	1.27565i
$145$	6.37194	+	2.86721i	0.529161	+	0.238109i
$146$	−12.8119	+	17.2302i	−1.06032	+	1.42598i
$147$	−1.94776	+	1.94776i	−0.160648	+	0.160648i
$148$	−2.47077	−	1.32853i	−0.203096	−	0.109204i
$149$	−14.5524			−1.19218			−0.596091	−	0.802917i	$-0.703280\pi$
$149$	−14.5524			−1.19218			−0.596091	+	0.802917i	$0.703280\pi$
$150$	19.4060	−	1.66828i	1.58449	−	0.136214i
$151$			1.57649i			0.128293i	0.997940	+	0.0641465i	$0.0204325\pi$
$151$			1.57649i			0.128293i	−0.997940	+	0.0641465i	$0.979568\pi$
$152$	14.9257	−	6.99159i	1.21063	−	0.567092i
$153$	11.4736	+	11.4736i	0.927583	+	0.927583i
$154$	−4.19264	+	5.63851i	−0.337852	+	0.454364i
$155$	4.04154	−	8.98171i	0.324624	−	0.721428i
$156$	20.3900	−	6.13014i	1.63250	−	0.490804i
$157$	−6.58137	−	6.58137i	−0.525251	−	0.525251i	0.393902	−	0.919152i	$-0.371125\pi$
$157$	−6.58137	−	6.58137i	−0.525251	−	0.525251i	−0.919152	+	0.393902i	$0.871125\pi$
$158$	2.65135	+	18.0277i	0.210930	+	1.43421i
$159$	10.8399			0.859660
$160$	−3.82603	−	12.0566i	−0.302474	−	0.953158i
$161$	6.35768			0.501055
$162$	−0.353384	−	2.40281i	−0.0277644	−	0.188783i
$163$	1.84570	+	1.84570i	0.144566	+	0.144566i	0.775686	−	0.631120i	$-0.217404\pi$
$163$	1.84570	+	1.84570i	0.144566	+	0.144566i	−0.631120	+	0.775686i	$0.717404\pi$
$164$	−6.09084	+	1.83118i	−0.475615	+	0.142991i
$165$	−10.8539	−	28.6129i	−0.844973	−	2.22751i
$166$	−4.14006	+	5.56781i	−0.321331	+	0.432146i
$167$	6.11009	+	6.11009i	0.472813	+	0.472813i	0.902824	−	0.430011i	$-0.141490\pi$
$167$	6.11009	+	6.11009i	0.472813	+	0.472813i	−0.430011	+	0.902824i	$0.641490\pi$
$168$	−7.05533	+	3.30491i	−0.544330	+	0.254979i
$169$		−	1.93672i		−	0.148979i
$170$	−5.44650	−	9.76936i	−0.417727	−	0.749276i
$171$	26.7327			2.04430
$172$	10.0068	+	5.38066i	0.763014	+	0.410272i
$173$	−9.08117	+	9.08117i	−0.690429	+	0.690429i	−0.962326	−	0.271898i	$-0.912349\pi$
$173$	−9.08117	+	9.08117i	−0.690429	+	0.690429i	0.271898	+	0.962326i	$0.412349\pi$
$174$	7.26342	−	9.76828i	0.550638	−	0.740532i
$175$	−0.301156	+	4.99092i	−0.0227652	+	0.377278i
$176$	−16.5789	+	10.9593i	−1.24968	+	0.826090i
$177$	−24.0152	+	24.0152i	−1.80509	+	1.80509i
$178$	6.76386	−	0.994766i	0.506972	−	0.0745609i
$179$		−	9.51295i		−	0.711031i	−0.934670	−	0.355515i	$-0.884305\pi$
$179$		−	9.51295i		−	0.711031i	0.934670	−	0.355515i	$-0.115695\pi$
$180$	2.67553	−	20.3407i	0.199422	−	1.51611i
$181$		−	6.48964i		−	0.482371i	−0.970479	−	0.241186i	$-0.922464\pi$
$181$		−	6.48964i		−	0.482371i	0.970479	−	0.241186i	$-0.0775363\pi$
$182$	0.795284	+	5.40749i	0.0589504	+	0.400830i
$183$	−1.74399	+	1.74399i	−0.128919	+	0.128919i
$184$	16.9085	+	6.12088i	1.24651	+	0.451237i
$185$	1.11241	+	2.93252i	0.0817857	+	0.215603i
$186$	−13.7691	−	10.2383i	−1.00960	−	0.750709i
$187$	−12.4263	+	12.4263i	−0.908703	+	0.908703i
$188$	6.61962	+	3.55936i	0.482785	+	0.259593i
$189$	−4.37285			−0.318078
$190$	−17.7260	−	5.03599i	−1.28598	−	0.365349i
$191$		−	11.9275i		−	0.863045i	−0.902102	−	0.431522i	$-0.857977\pi$
$191$		−	11.9275i		−	0.863045i	0.902102	−	0.431522i	$-0.142023\pi$
$192$	−21.9457	+	1.99697i	−1.58379	+	0.144119i
$193$	−6.20681	−	6.20681i	−0.446776	−	0.446776i	0.447505	−	0.894281i	$-0.352313\pi$
$193$	−6.20681	−	6.20681i	−0.446776	−	0.446776i	−0.894281	+	0.447505i	$0.852313\pi$
$194$	1.66810	+	1.24035i	0.119763	+	0.0890520i
$195$	−21.7082	−	9.76814i	−1.55456	−	0.699511i
$196$	−0.575828	−	1.91531i	−0.0411306	−	0.136808i
$197$	7.70090	+	7.70090i	0.548667	+	0.548667i	0.926055	−	0.377388i	$-0.123178\pi$
$197$	7.70090	+	7.70090i	0.548667	+	0.548667i	−0.377388	+	0.926055i	$0.623178\pi$
$198$	−31.8908	+	4.69021i	−2.26638	+	0.333319i
$199$	−3.04511			−0.215862			−0.107931	−	0.994158i	$-0.534423\pi$
$199$	−3.04511			−0.215862			−0.107931	+	0.994158i	$0.534423\pi$
$200$	−5.60596	+	12.9836i	−0.396401	+	0.918077i
$201$	−14.3800			−1.01429
$202$	14.1152	−	2.07594i	0.993144	−	0.146063i
$203$	2.20958	+	2.20958i	0.155082	+	0.155082i
$204$	−18.6606	+	5.61021i	−1.30650	+	0.392794i
$205$	6.48462	+	2.91791i	0.452905	+	0.203796i
$206$	−12.8128	−	9.52724i	−0.892711	−	0.663795i
$207$	20.6234	+	20.6234i	1.43343	+	1.43343i
$208$	−3.09100	+	15.1471i	−0.214322	+	1.05026i
$209$			28.9525i			2.00269i
$210$	8.37904	+	2.38050i	0.578208	+	0.164270i
$211$	27.8859			1.91974			0.959872	−	0.280438i	$-0.0904796\pi$
$211$	27.8859			1.91974			0.959872	+	0.280438i	$0.0904796\pi$
$212$	−3.72734	+	6.93201i	−0.255994	+	0.476092i
$213$	−16.7713	+	16.7713i	−1.14915	+	1.14915i
$214$	18.5576	+	13.7989i	1.26857	+	0.943274i
$215$	−4.50534	−	11.8770i	−0.307262	−	0.810002i
$216$	−11.6297	−	4.20997i	−0.791302	−	0.286452i
$217$	3.11456	−	3.11456i	0.211430	−	0.211430i
$218$	−0.0964297	−	0.655668i	−0.00653104	−	0.0444075i
$219$		−	41.8212i		−	2.82602i
$220$	22.0298	+	2.89771i	1.48525	+	0.195363i
$221$			13.6699i			0.919535i
$222$	5.40588	−	0.795048i	0.362819	−	0.0533601i
$223$	−18.3863	+	18.3863i	−1.23124	+	1.23124i	−0.267748	+	0.963489i	$0.586280\pi$
$223$	−18.3863	+	18.3863i	−1.23124	+	1.23124i	−0.963489	+	0.267748i	$0.913720\pi$
$224$	0.312540	−	5.64821i	0.0208825	−	0.377387i
$225$	−17.1667	+	15.2129i	−1.14445	+	1.01419i
$226$	8.10004	−	10.8934i	0.538807	−	0.724620i
$227$	−3.32486	+	3.32486i	−0.220679	+	0.220679i	−0.808784	−	0.588105i	$-0.799874\pi$
$227$	−3.32486	+	3.32486i	−0.220679	+	0.220679i	0.588105	+	0.808784i	$0.299874\pi$
$228$	−15.2033	+	28.2747i	−1.00686	+	1.87254i
$229$	−25.5653			−1.68940			−0.844700	−	0.535239i	$-0.820221\pi$
$229$	−25.5653			−1.68940			−0.844700	+	0.535239i	$0.820221\pi$
$230$	−9.78992	−	17.5601i	−0.645528	−	1.15788i
$231$		−	13.6858i		−	0.900460i
$232$	3.74917	+	8.00374i	0.246145	+	0.525471i
$233$	−6.72310	−	6.72310i	−0.440445	−	0.440445i	0.451716	−	0.892162i	$-0.350812\pi$
$233$	−6.72310	−	6.72310i	−0.440445	−	0.440445i	−0.892162	+	0.451716i	$0.850812\pi$
$234$	−14.9613	+	20.1209i	−0.978053	+	1.31534i
$235$	−2.98033	−	7.85673i	−0.194415	−	0.512517i
$236$	−7.09977	−	23.6151i	−0.462155	−	1.53721i
$237$	−25.0961	−	25.0961i	−1.63017	−	1.63017i
$238$	−0.727833	−	4.94886i	−0.0471784	−	0.320787i
$239$	17.8417			1.15408			0.577040	−	0.816716i	$-0.304208\pi$
$239$	17.8417			1.15408			0.577040	+	0.816716i	$0.304208\pi$
$240$	19.9925	+	14.3980i	1.29051	+	0.929385i
$241$	−19.5797			−1.26124			−0.630619	−	0.776093i	$-0.717199\pi$
$241$	−19.5797			−1.26124			−0.630619	+	0.776093i	$0.717199\pi$
$242$	−2.81615	−	19.1482i	−0.181029	−	1.23089i
$243$	12.6211	+	12.6211i	0.809646	+	0.809646i
$244$	−0.515587	−	1.71494i	−0.0330071	−	0.109788i
$245$	−0.917560	+	2.03914i	−0.0586208	+	0.130276i
$246$	7.39186	−	9.94102i	0.471287	−	0.633816i
$247$	15.9250	+	15.9250i	1.01328	+	1.01328i
$248$	11.2818	−	5.28472i	0.716398	−	0.335580i
$249$		−	13.5142i		−	0.856427i
$250$	14.2488	−	6.85351i	0.901176	−	0.433454i
$251$	−1.98920			−0.125557			−0.0627785	−	0.998027i	$-0.519996\pi$
$251$	−1.98920			−0.125557			−0.0627785	+	0.998027i	$0.519996\pi$
$252$	4.34509	−	8.08090i	0.273715	−	0.509049i
$253$	−22.3360	+	22.3360i	−1.40425	+	1.40425i
$254$	−12.1588	+	16.3518i	−0.762908	+	1.02600i
$255$	19.8670	+	8.93966i	1.24412	+	0.559823i
$256$	6.26905	−	14.7207i	0.391815	−	0.920044i
$257$	−0.798299	+	0.798299i	−0.0497965	+	0.0497965i	−0.731567	−	0.681770i	$-0.761210\pi$
$257$	−0.798299	+	0.798299i	−0.0497965	+	0.0497965i	0.681770	+	0.731567i	$0.261210\pi$
$258$	−21.8943	+	3.22001i	−1.36308	+	0.200469i
$259$			1.40265i			0.0871563i
$260$	13.7111	−	10.5234i	0.850324	−	0.652632i
$261$			14.3351i			0.887323i
$262$	−0.00901456	−	0.0612940i	−0.000556922	−	0.00378676i
$263$	18.0156	−	18.0156i	1.11089	−	1.11089i	0.117859	−	0.993030i	$-0.462397\pi$
$263$	18.0156	−	18.0156i	1.11089	−	1.11089i	0.993030	−	0.117859i	$-0.0376032\pi$
$264$	13.1761	−	36.3978i	0.810930	−	2.24013i
$265$	8.22750	−	3.12097i	0.505411	−	0.191720i
$266$	−6.61316	−	4.91736i	−0.405479	−	0.301503i
$267$	−9.41587	+	9.41587i	−0.576242	+	0.576242i
$268$	4.94463	−	9.19590i	0.302041	−	0.561729i
$269$	27.3056			1.66485			0.832427	−	0.554134i	$-0.186951\pi$
$269$	27.3056			1.66485			0.832427	+	0.554134i	$0.186951\pi$
$270$	6.73356	+	12.0780i	0.409791	+	0.735041i
$271$			22.1942i			1.34820i	0.738640	+	0.674100i	$0.235468\pi$
$271$			22.1942i			1.34820i	−0.738640	+	0.674100i	$0.764532\pi$
$272$	2.82884	−	13.8624i	0.171523	−	0.840530i
$273$	−7.52770	−	7.52770i	−0.455597	−	0.455597i
$274$	−10.8542	−	8.07085i	−0.655724	−	0.487578i
$275$	−16.4762	−	18.5923i	−0.993552	−	1.12116i
$276$	−33.5419	+	10.0842i	−2.01899	+	0.606997i
$277$	14.8136	+	14.8136i	0.890064	+	0.890064i	0.994529	−	0.104464i	$-0.0333128\pi$
$277$	14.8136	+	14.8136i	0.890064	+	0.890064i	−0.104464	+	0.994529i	$0.533313\pi$
$278$	−1.50674	+	0.221598i	−0.0903684	+	0.0132906i
$279$	20.2064			1.20973
$280$	−4.40347	+	4.53977i	−0.263158	+	0.271303i
$281$	20.8354			1.24294			0.621469	−	0.783439i	$-0.286536\pi$
$281$	20.8354			1.24294			0.621469	+	0.783439i	$0.286536\pi$
$282$	−14.4833	+	2.13007i	−0.862468	+	0.126844i
$283$	−8.07810	−	8.07810i	−0.480193	−	0.480193i	0.425000	−	0.905193i	$-0.360274\pi$
$283$	−8.07810	−	8.07810i	−0.480193	−	0.480193i	−0.905193	+	0.425000i	$0.860274\pi$
$284$	−4.95821	−	16.4919i	−0.294216	−	0.978616i
$285$	33.5589	−	12.7300i	1.98786	−	0.754062i
$286$	−21.7917	−	16.2037i	−1.28857	−	0.958146i
$287$	2.24866	+	2.24866i	0.132734	+	0.132734i
$288$	19.3358	−	17.3082i	1.13937	−	1.01989i
$289$			4.48952i			0.264090i
$290$	2.70050	−	9.50539i	0.158579	−	0.558176i
$291$	−4.04881			−0.237346
$292$	26.7443	+	14.3804i	1.56509	+	0.841547i
$293$	9.50152	−	9.50152i	0.555085	−	0.555085i	−0.372819	−	0.927904i	$-0.621609\pi$
$293$	9.50152	−	9.50152i	0.555085	−	0.555085i	0.927904	+	0.372819i	$0.121609\pi$
$294$	3.12603	+	2.32443i	0.182314	+	0.135563i
$295$	−11.3132	+	25.1419i	−0.658680	+	1.46382i
$296$	−1.35040	+	3.73039i	−0.0784907	+	0.216824i
$297$	15.3628	−	15.3628i	0.891440	−	0.891440i
$298$	2.99454	+	20.3612i	0.173469	+	1.17949i
$299$			24.5712i			1.42099i
$300$	−6.32748	−	26.8088i	−0.365317	−	1.54781i
$301$		−	5.68085i		−	0.327439i
$302$	2.20577	−	0.324404i	0.126928	−	0.0186674i
$303$	−19.6496	+	19.6496i	−1.12884	+	1.12884i
$304$	−12.8537	−	19.4447i	−0.737211	−	1.11523i
$305$	−0.821568	+	1.82581i	−0.0470429	+	0.104546i
$306$	13.6924	−	18.4144i	0.782742	−	1.05268i
$307$	11.5575	−	11.5575i	0.659621	−	0.659621i	−0.295669	−	0.955290i	$-0.595543\pi$
$307$	11.5575	−	11.5575i	0.659621	−	0.659621i	0.955290	+	0.295669i	$0.0955426\pi$
$308$	8.75194	+	4.70591i	0.498688	+	0.268144i
$309$	31.0993			1.76918
$310$	−13.3985	−	3.80655i	−0.760985	−	0.216198i
$311$			1.48399i			0.0841492i	0.999114	+	0.0420746i	$0.0133967\pi$
$311$			1.48399i			0.0841492i	−0.999114	+	0.0420746i	$0.986603\pi$
$312$	−12.7728	−	27.2675i	−0.723119	−	1.54372i
$313$	2.82706	+	2.82706i	0.159795	+	0.159795i	0.782476	−	0.622681i	$-0.213957\pi$
$313$	2.82706	+	2.82706i	0.159795	+	0.159795i	−0.622681	+	0.782476i	$0.713957\pi$
$314$	−7.85412	+	10.5627i	−0.443234	+	0.596088i
$315$	−9.59110	+	3.63823i	−0.540397	+	0.204991i
$316$	24.6781	−	7.41933i	1.38825	−	0.417370i
$317$	9.79459	+	9.79459i	0.550119	+	0.550119i	0.926475	−	0.376356i	$-0.122823\pi$
$317$	9.79459	+	9.79459i	0.550119	+	0.550119i	−0.376356	+	0.926475i	$0.622823\pi$
$318$	−2.23059	−	15.1668i	−0.125085	−	0.850511i
$319$	−15.5255			−0.869262
$320$	−16.0818	+	7.83420i	−0.899002	+	0.437945i
$321$	−45.0431			−2.51406
$322$	−1.30826	−	8.89543i	−0.0729064	−	0.495723i
$323$	−14.5743	−	14.5743i	−0.810936	−	0.810936i
$324$	−3.28921	+	0.988882i	−0.182734	+	0.0549379i
$325$	−19.2889	−	1.16391i	−1.06996	−	0.0645620i
$326$	2.20263	−	2.96223i	0.121992	−	0.164063i
$327$	0.912747	+	0.912747i	0.0504750	+	0.0504750i
$328$	3.81547	+	8.14527i	0.210674	+	0.449747i
$329$		−	3.75794i		−	0.207182i
$330$	−37.8007	+	21.0742i	−2.08086	+	1.16010i
$331$	−11.5472			−0.634691			−0.317345	−	0.948310i	$-0.602791\pi$
$331$	−11.5472			−0.634691			−0.317345	+	0.948310i	$0.602791\pi$
$332$	8.64219	+	4.64690i	0.474302	+	0.255032i
$333$	−4.54999	+	4.54999i	−0.249338	+	0.249338i
$334$	7.29170	−	9.80632i	0.398984	−	0.536578i
$335$	−10.9145	+	4.14024i	−0.596322	+	0.226205i
$336$	6.07592	+	9.19148i	0.331469	+	0.501436i
$337$	11.2187	−	11.2187i	0.611120	−	0.611120i	−0.332118	−	0.943238i	$-0.607763\pi$
$337$	11.2187	−	11.2187i	0.611120	−	0.611120i	0.943238	+	0.332118i	$0.107763\pi$
$338$	−2.70979	+	0.398531i	−0.147393	+	0.0216772i
$339$			26.4406i			1.43605i
$340$	−12.5482	+	9.63084i	−0.680520	+	0.522305i
$341$			21.8843i			1.18510i
$342$	−5.50094	−	37.4033i	−0.297457	−	2.02254i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	5.46926	−	15.1084i	0.294883	−	0.814590i
$345$	35.7104	+	16.0688i	1.92258	+	0.865114i
$346$	14.5747	+	10.8373i	0.783542	+	0.582619i
$347$	14.3007	−	14.3007i	0.767704	−	0.767704i	−0.209998	−	0.977702i	$-0.567346\pi$
$347$	14.3007	−	14.3007i	0.767704	−	0.767704i	0.977702	+	0.209998i	$0.0673458\pi$
$348$	−15.1621	−	8.15262i	−0.812771	−	0.437026i
$349$	−16.4479			−0.880435			−0.440217	−	0.897891i	$-0.645099\pi$
$349$	−16.4479			−0.880435			−0.440217	+	0.897891i	$0.645099\pi$
$350$	7.04508	−	0.605647i	0.376576	−	0.0323732i
$351$		−	16.9002i		−	0.902066i
$352$	18.7454	+	20.9415i	0.999134	+	1.11618i
$353$	−4.81028	−	4.81028i	−0.256025	−	0.256025i	0.567410	−	0.823435i	$-0.307945\pi$
$353$	−4.81028	−	4.81028i	−0.256025	−	0.256025i	−0.823435	+	0.567410i	$0.807945\pi$
$354$	38.5429	+	28.6594i	2.04853	+	1.52323i
$355$	−7.90072	+	17.5581i	−0.419327	+	0.931889i
$356$	−2.78368	−	9.25904i	−0.147535	−	0.490728i
$357$	6.88924	+	6.88924i	0.364617	+	0.364617i
$358$	−13.3102	+	1.95754i	−0.703464	+	0.103459i
$359$	−14.3081			−0.755153			−0.377576	−	0.925978i	$-0.623242\pi$
$359$	−14.3081			−0.755153			−0.377576	+	0.925978i	$0.623242\pi$
$360$	−29.0106	+	0.442133i	−1.52899	+	0.0233025i
$361$	−14.9572			−0.787219
$362$	−9.08007	+	1.33541i	−0.477238	+	0.0701878i
$363$	26.6560	+	26.6560i	1.39908	+	1.39908i
$364$	7.40231	−	2.22546i	0.387986	−	0.116646i
$365$	−12.0410	−	31.7424i	−0.630253	−	1.66147i
$366$	2.79899	+	2.08125i	0.146306	+	0.108789i
$367$	−9.01109	−	9.01109i	−0.470375	−	0.470375i	0.431661	−	0.902036i	$-0.357928\pi$
$367$	−9.01109	−	9.01109i	−0.470375	−	0.470375i	−0.902036	+	0.431661i	$0.857928\pi$
$368$	5.08475	−	24.9172i	0.265061	−	1.29890i
$369$			14.5886i			0.759453i
$370$	3.87416	−	2.15988i	0.201408	−	0.112287i
$371$	3.93528			0.204310
$372$	−11.4917	+	21.3720i	−0.595817	+	1.10809i
$373$	19.1338	−	19.1338i	0.990713	−	0.990713i	−0.00924424	−	0.999957i	$-0.502943\pi$
$373$	19.1338	−	19.1338i	0.990713	−	0.990713i	0.999957	+	0.00924424i	$0.00294258\pi$
$374$	19.9435	+	14.8294i	1.03125	+	0.766811i
$375$	−14.3059	+	27.2723i	−0.738754	+	1.40834i
$376$	3.61797	−	9.99436i	0.186583	−	0.515420i
$377$	−8.53961	+	8.53961i	−0.439812	+	0.439812i
$378$	0.899827	+	6.11832i	0.0462821	+	0.314693i
$379$			9.38553i			0.482102i	0.970512	+	0.241051i	$0.0774921\pi$
$379$			9.38553i			0.482102i	−0.970512	+	0.241051i	$0.922508\pi$
$380$	−3.39859	+	25.8378i	−0.174344	+	1.32545i
$381$		−	39.6892i		−	2.03334i
$382$	−16.6885	+	2.45440i	−0.853860	+	0.125578i
$383$	−23.3553	+	23.3553i	−1.19340	+	1.19340i	−0.217291	+	0.976107i	$0.569722\pi$
$383$	−23.3553	+	23.3553i	−1.19340	+	1.19340i	−0.976107	+	0.217291i	$0.930278\pi$
$384$	7.30998	+	30.2946i	0.373036	+	1.54597i
$385$	−3.94035	−	10.3875i	−0.200819	−	0.529398i
$386$	−7.40712	+	9.96155i	−0.377013	+	0.507029i
$387$	18.4279	−	18.4279i	0.936740	−	0.936740i
$388$	1.39220	−	2.58918i	0.0706781	−	0.131445i
$389$	−24.7781			−1.25630			−0.628150	−	0.778092i	$-0.716188\pi$
$389$	−24.7781			−1.25630			−0.628150	+	0.778092i	$0.716188\pi$
$390$	−9.20019	+	32.3833i	−0.465870	+	1.63979i
$391$		−	22.4872i		−	1.13723i
$392$	−2.56134	+	1.19980i	−0.129367	+	0.0605992i
$393$	0.0853266	+	0.0853266i	0.00430416	+	0.00430416i
$394$	9.19015	−	12.3595i	0.462993	−	0.622661i
$395$	−26.2735	−	11.8224i	−1.32196	−	0.594851i
$396$	13.1247	+	43.6553i	0.659543	+	2.19376i
$397$	1.32585	+	1.32585i	0.0665427	+	0.0665427i	0.739595	−	0.673052i	$-0.235017\pi$
$397$	1.32585	+	1.32585i	0.0665427	+	0.0665427i	−0.673052	+	0.739595i	$0.735017\pi$
$398$	0.626610	+	4.26060i	0.0314091	+	0.213565i
$399$	16.0515			0.803579
$400$	19.3197	+	5.17194i	0.965985	+	0.258597i
$401$	7.01726			0.350425			0.175213	−	0.984531i	$-0.443939\pi$
$401$	7.01726			0.350425			0.175213	+	0.984531i	$0.443939\pi$
$402$	2.95907	+	20.1200i	0.147585	+	1.00350i
$403$	12.0372	+	12.0372i	0.599615	+	0.599615i
$404$	−5.80915	−	19.3223i	−0.289016	−	0.961322i
$405$	3.50185	+	1.57575i	0.174009	+	0.0782994i
$406$	2.63689	−	3.54625i	0.130867	−	0.175997i
$407$	−4.92782	−	4.92782i	−0.244263	−	0.244263i
$408$	11.6895	+	24.9548i	0.578717	+	1.23545i
$409$		−	8.59601i		−	0.425046i	−0.977156	−	0.212523i	$-0.931832\pi$
$409$		−	8.59601i		−	0.425046i	0.977156	−	0.212523i	$-0.0681680\pi$
$410$	2.74826	−	9.67347i	0.135727	−	0.477739i
$411$	26.3453			1.29952
$412$	−10.6936	+	19.8877i	−0.526836	+	0.979796i
$413$	−8.71838	+	8.71838i	−0.429004	+	0.429004i
$414$	24.6117	−	33.0993i	1.20960	−	1.62674i
$415$	−3.89094	−	10.2573i	−0.190999	−	0.503511i
$416$	21.8292	+	1.20791i	1.07027	+	0.0592225i
$417$	2.09752	−	2.09752i	0.102716	−	0.102716i
$418$	40.5093	−	5.95774i	1.98138	−	0.291403i
$419$			2.83105i			0.138306i	0.997606	+	0.0691530i	$0.0220297\pi$
$419$			2.83105i			0.138306i	−0.997606	+	0.0691530i	$0.977970\pi$
$420$	1.60651	−	12.2135i	0.0783896	−	0.595957i
$421$			8.77852i			0.427839i	0.976851	+	0.213920i	$0.0686230\pi$
$421$			8.77852i			0.427839i	−0.976851	+	0.213920i	$0.931377\pi$
$422$	−5.73825	−	39.0169i	−0.279334	−	1.89931i
$423$	12.1902	−	12.1902i	0.592708	−	0.592708i
$424$	10.4660	+	3.78871i	0.508274	+	0.183996i
$425$	17.6530	+	1.06519i	0.856295	+	0.0516694i
$426$	26.9169	+	20.0146i	1.30413	+	0.969712i
$427$	−0.633132	+	0.633132i	−0.0306394	+	0.0306394i
$428$	15.4882	−	28.8046i	0.748651	−	1.39232i
$429$	52.8930			2.55370
$430$	−15.6907	+	8.74770i	−0.756673	+	0.421851i
$431$			10.2783i			0.495086i	0.968877	+	0.247543i	$0.0796232\pi$
$431$			10.2783i			0.495086i	−0.968877	+	0.247543i	$0.920377\pi$
$432$	−3.49732	+	17.1382i	−0.168265	+	0.824561i
$433$	−5.26399	−	5.26399i	−0.252971	−	0.252971i	0.569216	−	0.822188i	$-0.307247\pi$
$433$	−5.26399	−	5.26399i	−0.252971	−	0.252971i	−0.822188	+	0.569216i	$0.807247\pi$
$434$	−4.99869	−	3.71688i	−0.239945	−	0.178416i
$435$	6.82636	+	17.9956i	0.327299	+	0.862824i
$436$	−0.897543	+	0.269842i	−0.0429845	+	0.0129231i
$437$	−26.1969	−	26.1969i	−1.25317	−	1.25317i
$438$	−58.5147	+	8.60581i	−2.79594	+	0.411201i
$439$	13.1390			0.627092			0.313546	−	0.949573i	$-0.398483\pi$
$439$	13.1390			0.627092			0.313546	+	0.949573i	$0.398483\pi$
$440$	−0.478848	−	31.4196i	−0.0228282	−	1.49787i
$441$	−4.58750			−0.218453
$442$	19.1264	−	2.81293i	0.909749	−	0.133798i
$443$	−12.0683	−	12.0683i	−0.573383	−	0.573383i	0.359689	−	0.933072i	$-0.382883\pi$
$443$	−12.0683	−	12.0683i	−0.573383	−	0.573383i	−0.933072	+	0.359689i	$0.882883\pi$
$444$	−2.22480	−	7.40011i	−0.105584	−	0.351193i
$445$	−4.43569	+	9.85764i	−0.210272	+	0.467297i
$446$	29.5089	+	21.9420i	1.39729	+	1.03898i
$447$	−28.3446	−	28.3446i	−1.34065	−	1.34065i
$448$	−7.96708	+	0.724973i	−0.376409	+	0.0342517i
$449$		−	32.4383i		−	1.53086i	−0.643520	−	0.765429i	$-0.722527\pi$
$449$		−	32.4383i		−	1.53086i	0.643520	−	0.765429i	$-0.277473\pi$
$450$	24.8179	+	20.8886i	1.16993	+	0.984698i
$451$	−15.8001			−0.743996
$452$	−16.9085	−	9.09167i	−0.795308	−	0.427636i
$453$	−3.07062	+	3.07062i	−0.144270	+	0.144270i
$454$	5.33620	+	3.96785i	0.250440	+	0.186220i
$455$	−7.88087	−	3.54619i	−0.369461	−	0.166248i
$456$	42.6894	+	15.4536i	1.99912	+	0.723682i
$457$	2.77670	−	2.77670i	0.129888	−	0.129888i	−0.639174	−	0.769062i	$-0.720724\pi$
$457$	2.77670	−	2.77670i	0.129888	−	0.129888i	0.769062	+	0.639174i	$0.220724\pi$
$458$	5.26072	+	35.7700i	0.245817	+	1.67142i
$459$			15.4668i			0.721929i
$460$	−22.5550	+	17.3111i	−1.05163	+	0.807137i
$461$			11.4770i			0.534535i	0.963622	+	0.267267i	$0.0861207\pi$
$461$			11.4770i			0.534535i	−0.963622	+	0.267267i	$0.913879\pi$
$462$	−19.1487	+	2.81621i	−0.890877	+	0.131022i
$463$	16.7196	−	16.7196i	0.777027	−	0.777027i	−0.202297	−	0.979324i	$-0.564841\pi$
$463$	16.7196	−	16.7196i	0.777027	−	0.777027i	0.979324	+	0.202297i	$0.0648407\pi$
$464$	10.4270	−	6.89268i	0.484063	−	0.319985i
$465$	25.3661	−	9.62224i	1.17632	−	0.446221i
$466$	−8.02326	+	10.7902i	−0.371670	+	0.499845i
$467$	9.99558	−	9.99558i	0.462540	−	0.462540i	−0.436947	−	0.899487i	$-0.643940\pi$
$467$	9.99558	−	9.99558i	0.462540	−	0.462540i	0.899487	+	0.436947i	$0.143940\pi$
$468$	31.2311	+	16.7929i	1.44366	+	0.776254i
$469$	−5.22049			−0.241060
$470$	−10.3796	+	5.78669i	−0.478774	+	0.266920i
$471$		−	25.6378i		−	1.18133i
$472$	−31.5805	+	14.7932i	−1.45361	+	0.680910i
$473$	19.9581	+	19.9581i	0.917674	+	0.917674i
$474$	−29.9494	+	40.2777i	−1.37562	+	1.85002i
$475$	21.8060	−	19.3242i	1.00053	−	0.886656i
$476$	−6.77449	+	2.03671i	−0.310508	+	0.0933526i
$477$	12.7655	+	12.7655i	0.584491	+	0.584491i
$478$	−3.67138	−	24.9634i	−0.167925	−	1.14180i
$479$	3.47313			0.158691			0.0793457	−	0.996847i	$-0.474717\pi$
$479$	3.47313			0.158691			0.0793457	+	0.996847i	$0.474717\pi$
$480$	16.0311	−	30.9355i	0.731718	−	1.41200i
$481$	−5.42096			−0.247175
$482$	4.02903	+	27.3952i	0.183517	+	1.24782i
$483$	12.3832	+	12.3832i	0.563456	+	0.563456i
$484$	−26.2120	+	7.88050i	−1.19145	+	0.358204i
$485$	−3.07305	+	1.16572i	−0.139540	+	0.0529324i
$486$	15.0619	−	20.2561i	0.683221	−	0.918837i
$487$	11.9556	+	11.9556i	0.541760	+	0.541760i	0.924045	−	0.382285i	$-0.124863\pi$
$487$	11.9556	+	11.9556i	0.541760	+	0.541760i	−0.382285	+	0.924045i	$0.624863\pi$
$488$	−2.29338	+	1.07428i	−0.103817	+	0.0486305i
$489$			7.18993i			0.325140i
$490$	3.04190	+	0.864211i	0.137419	+	0.0390411i
$491$	−9.41030			−0.424681			−0.212340	−	0.977196i	$-0.568109\pi$
$491$	−9.41030			−0.424681			−0.212340	+	0.977196i	$0.568109\pi$
$492$	−15.4302	−	8.29679i	−0.695646	−	0.374048i
$493$	7.81533	−	7.81533i	0.351985	−	0.351985i
$494$	19.0046	−	25.5586i	0.855059	−	1.14994i
$495$	20.9138	−	46.4776i	0.940003	−	2.08901i
$496$	−9.71572	−	14.6977i	−0.436249	−	0.659944i
$497$	−6.08859	+	6.08859i	−0.273111	+	0.273111i
$498$	−18.9086	+	2.78090i	−0.847312	+	0.124615i
$499$			34.1095i			1.52695i	0.645838	+	0.763475i	$0.276508\pi$
$499$			34.1095i			1.52695i	−0.645838	+	0.763475i	$0.723492\pi$
$500$	−12.5212	−	18.5262i	−0.559967	−	0.828515i
$501$			23.8019i			1.06339i
$502$	0.409329	+	2.78321i	0.0182693	+	0.124221i
$503$	8.89616	−	8.89616i	0.396660	−	0.396660i	−0.480393	−	0.877053i	$-0.659506\pi$
$503$	8.89616	−	8.89616i	0.396660	−	0.396660i	0.877053	+	0.480393i	$0.159506\pi$
$504$	−12.2006	−	4.41663i	−0.543458	−	0.196733i
$505$	−9.25666	+	20.5715i	−0.411916	+	0.915421i
$506$	35.8479	+	26.6554i	1.59363	+	1.18498i
$507$	3.77226	−	3.77226i	0.167532	−	0.167532i
$508$	25.3808	+	13.6473i	1.12609	+	0.605499i
$509$	−22.3517			−0.990721			−0.495361	−	0.868687i	$-0.664964\pi$
$509$	−22.3517			−0.990721			−0.495361	+	0.868687i	$0.664964\pi$
$510$	8.41988	−	29.6368i	0.372839	−	1.31234i
$511$		−	15.1826i		−	0.671640i
$512$	−21.8867	−	5.74225i	−0.967264	−	0.253774i
$513$	18.0183	+	18.0183i	0.795529	+	0.795529i
$514$	1.28122	+	0.952679i	0.0565122	+	0.0420209i
$515$	23.6044	−	8.95396i	1.04013	−	0.394559i
$516$	9.01064	+	29.9711i	0.396671	+	1.31940i
$517$	13.2025	+	13.2025i	0.580645	+	0.580645i
$518$	1.96253	−	0.288631i	0.0862288	−	0.0126817i
$519$	−35.3758			−1.55283
$520$	−17.5453	−	17.0185i	−0.769413	−	0.746313i
$521$	17.4188			0.763132			0.381566	−	0.924342i	$-0.375385\pi$
$521$	17.4188			0.763132			0.381566	+	0.924342i	$0.375385\pi$
$522$	20.0572	−	2.94983i	0.877879	−	0.129110i
$523$	−24.9080	−	24.9080i	−1.08915	−	1.08915i	−0.995616	−	0.0935346i	$-0.970183\pi$
$523$	−24.9080	−	24.9080i	−1.08915	−	1.08915i	−0.0935346	−	0.995616i	$-0.529817\pi$
$524$	−0.0839053	+	0.0252257i	−0.00366542	+	0.00110199i
$525$	−10.3077	+	9.13452i	−0.449864	+	0.398663i
$526$	−28.9139	−	21.4996i	−1.26071	−	0.937426i
$527$	−11.0163	−	11.0163i	−0.479876	−	0.479876i
$528$	−53.6378	−	10.9456i	−2.33429	−	0.476348i
$529$		−	17.4201i		−	0.757396i
$530$	−6.05977	−	10.8694i	−0.263220	−	0.472136i
$531$	−56.5623			−2.45460
$532$	−5.51935	+	10.2648i	−0.239294	+	0.445034i
$533$	−8.69061	+	8.69061i	−0.376432	+	0.376432i
$534$	15.1119	+	11.2368i	0.653956	+	0.486263i
$535$	−34.1878	+	12.9686i	−1.47807	+	0.560681i
$536$	−13.8840	−	5.02604i	−0.599699	−	0.217092i
$537$	18.5289	−	18.5289i	0.799581	−	0.799581i
$538$	−5.61885	−	38.2050i	−0.242246	−	1.64714i
$539$		−	4.96845i		−	0.214006i
$540$	15.5134	−	11.9067i	0.667591	−	0.512383i
$541$		−	33.9788i		−	1.46086i	−0.682986	−	0.730431i	$-0.739319\pi$
$541$		−	33.9788i		−	1.46086i	0.682986	−	0.730431i	$-0.260681\pi$
$542$	31.0533	−	4.56703i	1.33385	−	0.196171i
$543$	12.6402	−	12.6402i	0.542445	−	0.542445i
$544$	−19.9778	−	1.10546i	−0.856542	−	0.0473962i
$545$	0.955570	+	0.429982i	0.0409321	+	0.0184184i
$546$	−8.98345	+	12.0815i	−0.384456	+	0.517040i
$547$	−6.09800	+	6.09800i	−0.260732	+	0.260732i	−0.825351	−	0.564620i	$-0.809023\pi$
$547$	−6.09800	+	6.09800i	−0.260732	+	0.260732i	0.564620	+	0.825351i	$0.309023\pi$
$548$	−9.05890	+	16.8475i	−0.386977	+	0.719691i
$549$	−4.10758			−0.175307
$550$	−22.6232	+	26.8787i	−0.964656	+	1.14611i
$551$		−	18.2092i		−	0.775738i
$552$	21.0116	+	44.8555i	0.894311	+	1.90918i
$553$	−9.11081	−	9.11081i	−0.387431	−	0.387431i
$554$	17.6784	−	23.7750i	0.751082	−	1.01010i
$555$	−3.54514	+	7.87852i	−0.150483	+	0.334425i
$556$	0.620103	+	2.06258i	0.0262982	+	0.0874728i
$557$	25.0294	+	25.0294i	1.06053	+	1.06053i	0.998046	+	0.0624840i	$0.0199023\pi$
$557$	25.0294	+	25.0294i	1.06053	+	1.06053i	0.0624840	+	0.998046i	$0.480098\pi$
$558$	−4.15799	−	28.2720i	−0.176022	−	1.19685i
$559$	21.9554			0.928614
$560$	7.25800	+	5.22699i	0.306706	+	0.220881i
$561$	−48.4069			−2.04374
$562$	−4.28743	−	29.1522i	−0.180854	−	1.22971i
$563$	−13.6166	−	13.6166i	−0.573870	−	0.573870i	0.359338	−	0.933208i	$-0.383003\pi$
$563$	−13.6166	−	13.6166i	−0.573870	−	0.573870i	−0.933208	+	0.359338i	$0.883003\pi$
$564$	5.96063	+	19.8262i	0.250988	+	0.834833i
$565$	7.61264	+	20.0684i	0.320266	+	0.844285i
$566$	−9.64030	+	12.9649i	−0.405212	+	0.544954i
$567$	1.21433	+	1.21433i	0.0509970	+	0.0509970i
$568$	−22.0546	+	10.3310i	−0.925391	+	0.433479i
$569$			27.0676i			1.13473i	0.823465	+	0.567367i	$0.192038\pi$
$569$			27.0676i			1.13473i	−0.823465	+	0.567367i	$0.807962\pi$
$570$	−24.7170	−	44.3348i	−1.03528	−	1.85698i
$571$	7.52462			0.314895			0.157448	−	0.987527i	$-0.449673\pi$
$571$	7.52462			0.314895			0.157448	+	0.987527i	$0.449673\pi$
$572$	−18.1874	+	33.8245i	−0.760454	+	1.41427i
$573$	23.2319	−	23.2319i	0.970526	−	0.970526i
$574$	2.68351	−	3.60895i	0.112008	−	0.150635i
$575$	31.7307	+	1.91465i	1.32326	+	0.0798465i
$576$	−28.1958	−	23.4924i	−1.17482	−	0.978848i
$577$	−21.6199	+	21.6199i	−0.900049	+	0.900049i	−0.995440	−	0.0953910i	$-0.969590\pi$
$577$	−21.6199	+	21.6199i	−0.900049	+	0.900049i	0.0953910	+	0.995440i	$0.469590\pi$
$578$	6.28158	−	0.923837i	0.261279	−	0.0384265i
$579$		−	24.1787i		−	1.00483i
$580$	−13.8553	−	1.82246i	−0.575309	−	0.0756737i
$581$		−	4.90615i		−	0.203541i
$582$	0.833149	+	5.66495i	0.0345351	+	0.234820i
$583$	−13.8255	+	13.8255i	−0.572595	+	0.572595i
$584$	14.6171	−	40.3787i	0.604862	−	1.67088i
$585$	−14.0611	−	37.0677i	−0.581354	−	1.53256i
$586$	−15.2494	−	11.3390i	−0.629945	−	0.468409i
$587$	22.1254	−	22.1254i	0.913215	−	0.913215i	−0.0833088	−	0.996524i	$-0.526549\pi$
$587$	22.1254	−	22.1254i	0.913215	−	0.913215i	0.996524	+	0.0833088i	$0.0265488\pi$
$588$	2.60899	−	4.85213i	0.107593	−	0.200099i
$589$	−25.6672			−1.05760
$590$	37.5055	+	10.6554i	1.54408	+	0.438677i
$591$			29.9990i			1.23399i
$592$	5.49730	+	1.12181i	0.225938	+	0.0461062i
$593$	−28.6255	−	28.6255i	−1.17551	−	1.17551i	−0.980877	−	0.194630i	$-0.937649\pi$
$593$	−28.6255	−	28.6255i	−1.17551	−	1.17551i	−0.194630	−	0.980877i	$-0.562351\pi$
$594$	−24.6563	−	18.3337i	−1.01166	−	0.752243i
$595$	7.21246	+	3.24542i	0.295682	+	0.133049i
$596$	27.8724	−	8.37970i	1.14170	−	0.343246i
$597$	−5.93113	−	5.93113i	−0.242745	−	0.242745i
$598$	34.3791	−	5.05617i	1.40587	−	0.206762i
$599$	20.4804			0.836805			0.418403	−	0.908262i	$-0.362590\pi$
$599$	20.4804			0.836805			0.418403	+	0.908262i	$0.362590\pi$
$600$	−36.2079	+	14.3698i	−1.47818	+	0.586644i
$601$	23.8646			0.973459			0.486729	−	0.873553i	$-0.338190\pi$
$601$	23.8646			0.973459			0.486729	+	0.873553i	$0.338190\pi$
$602$	−7.94843	+	1.16898i	−0.323954	+	0.0476442i
$603$	−16.9345	−	16.9345i	−0.689626	−	0.689626i
$604$	−0.907788	−	3.01947i	−0.0369374	−	0.122861i
$605$	27.9066	+	12.5573i	1.13456	+	0.510525i
$606$	31.5364	+	23.4496i	1.28108	+	0.952575i
$607$	21.2236	+	21.2236i	0.861440	+	0.861440i	0.991505	−	0.130066i	$-0.0415189\pi$
$607$	21.2236	+	21.2236i	0.861440	+	0.861440i	−0.130066	+	0.991505i	$0.541519\pi$
$608$	−24.5613	+	21.9857i	−0.996094	+	0.891637i
$609$			8.60746i			0.348792i
$610$	2.72366	+	0.773800i	0.110278	+	0.0313302i
$611$	14.5237			0.587566
$612$	−28.5823	−	15.3687i	−1.15537	−	0.621241i
$613$	19.6848	−	19.6848i	0.795062	−	0.795062i	−0.187250	−	0.982312i	$-0.559958\pi$
$613$	19.6848	−	19.6848i	0.795062	−	0.795062i	0.982312	+	0.187250i	$0.0599575\pi$
$614$	−18.5491	−	13.7926i	−0.748580	−	0.556622i
$615$	6.94707	+	18.3138i	0.280133	+	0.738485i
$616$	4.78339	−	13.2137i	0.192728	−	0.532397i
$617$	2.42500	−	2.42500i	0.0976268	−	0.0976268i	−0.656607	−	0.754233i	$-0.728009\pi$
$617$	2.42500	−	2.42500i	0.0976268	−	0.0976268i	0.754233	+	0.656607i	$0.228009\pi$
$618$	−6.39949	−	43.5130i	−0.257425	−	1.75035i
$619$			19.1625i			0.770207i	0.922873	+	0.385104i	$0.125834\pi$
$619$			19.1625i			0.770207i	−0.922873	+	0.385104i	$0.874166\pi$
$620$	−2.56889	+	19.5300i	−0.103169	+	0.784344i
$621$			27.8012i			1.11562i
$622$	2.07634	−	0.305369i	0.0832537	−	0.0122442i
$623$	−3.41831	+	3.41831i	−0.136952	+	0.136952i
$624$	−35.5233	+	23.4823i	−1.42207	+	0.940043i
$625$	−3.00609	+	24.8186i	−0.120244	+	0.992744i
$626$	3.37377	−	4.53726i	0.134843	−	0.181345i
$627$	−56.3925	+	56.3925i	−2.25210	+	2.25210i
$628$	16.3951	+	8.81564i	0.654237	+	0.351782i
$629$	4.96119			0.197816
$630$	7.06410	+	12.6708i	0.281441	+	0.504819i
$631$		−	1.62356i		−	0.0646329i	−0.999478	−	0.0323164i	$-0.989712\pi$
$631$		−	1.62356i		−	0.0646329i	0.999478	−	0.0323164i	$-0.0102884\pi$
$632$	−15.4590	−	33.0019i	−0.614927	−	1.31275i
$633$	54.3149	+	54.3149i	2.15882	+	2.15882i
$634$	11.6887	−	15.7197i	0.464219	−	0.624310i
$635$	−11.4271	−	30.1241i	−0.453472	−	1.19544i
$636$	−20.7618	+	6.24192i	−0.823259	+	0.247508i
$637$	−2.73283	−	2.73283i	−0.108279	−	0.108279i
$638$	3.19478	+	21.7227i	0.126483	+	0.860011i
$639$	−39.5010			−1.56264
$640$	14.2706	+	20.8890i	0.564094	+	0.825711i
$641$	−29.5662			−1.16779			−0.583897	−	0.811828i	$-0.698473\pi$
$641$	−29.5662			−1.16779			−0.583897	+	0.811828i	$0.698473\pi$
$642$	9.26879	+	63.0226i	0.365810	+	2.48730i
$643$	14.8816	+	14.8816i	0.586875	+	0.586875i	0.936784	−	0.349909i	$-0.113788\pi$
$643$	14.8816	+	14.8816i	0.586875	+	0.586875i	−0.349909	+	0.936784i	$0.613788\pi$
$644$	−12.1769	+	3.66093i	−0.479839	+	0.144261i
$645$	14.3581	−	31.9087i	0.565350	−	1.25640i
$646$	−17.3928	+	23.3909i	−0.684309	+	0.920301i
$647$	11.9683	+	11.9683i	0.470521	+	0.470521i	0.902083	−	0.431562i	$-0.142037\pi$
$647$	11.9683	+	11.9683i	0.470521	+	0.470521i	−0.431562	+	0.902083i	$0.642037\pi$
$648$	2.06045	+	4.39865i	0.0809420	+	0.172795i
$649$		−	61.2593i		−	2.40464i
$650$	2.34071	+	27.2279i	0.0918101	+	1.06797i
$651$	12.1328			0.475523
$652$	−4.59789	−	2.47228i	−0.180067	−	0.0968219i
$653$	−10.4874	+	10.4874i	−0.410405	+	0.410405i	−0.881880	−	0.471475i	$-0.843722\pi$
$653$	−10.4874	+	10.4874i	−0.410405	+	0.410405i	0.471475	+	0.881880i	$0.343722\pi$
$654$	1.08926	−	1.46490i	0.0425934	−	0.0572822i
$655$	0.0893298	+	0.0401962i	0.00349040	+	0.00157059i
$656$	10.6114	−	7.01456i	0.414306	−	0.273873i
$657$	49.2503	−	49.2503i	1.92144	−	1.92144i
$658$	−5.25797	+	0.773294i	−0.204977	+	0.0301461i
$659$			45.3348i			1.76599i	0.469380	+	0.882996i	$0.344478\pi$
$659$			45.3348i			1.76599i	−0.469380	+	0.882996i	$0.655522\pi$
$660$	37.2647	+	48.5527i	1.45053	+	1.88991i
$661$		−	11.7352i		−	0.456444i	−0.973609	−	0.228222i	$-0.926709\pi$
$661$		−	11.7352i		−	0.456444i	0.973609	−	0.228222i	$-0.0732913\pi$
$662$	2.37613	+	16.1564i	0.0923511	+	0.627936i
$663$	−26.6256	+	26.6256i	−1.03405	+	1.03405i
$664$	4.72341	−	13.0481i	0.183304	−	0.506363i
$665$	12.1831	−	4.62147i	0.472440	−	0.179213i
$666$	7.30245	+	5.42989i	0.282964	+	0.210404i
$667$	14.0478	−	14.0478i	0.543934	−	0.543934i
$668$	−15.2211	−	8.18437i	−0.588922	−	0.316663i
$669$	−71.6240			−2.76914
$670$	8.03880	+	14.4192i	0.310566	+	0.557061i
$671$		−	4.44867i		−	0.171739i
$672$	11.6101	−	10.3926i	0.447869	−	0.400903i
$673$	10.7808	+	10.7808i	0.415570	+	0.415570i	0.883674	−	0.468103i	$-0.155063\pi$
$673$	10.7808	+	10.7808i	0.415570	+	0.415570i	−0.468103	+	0.883674i	$0.655063\pi$
$674$	−18.0053	−	13.3882i	−0.693538	−	0.515695i
$675$	−21.8245	−	1.31691i	−0.840027	−	0.0506878i
$676$	1.11522	+	3.70943i	0.0428931	+	0.142670i
$677$	−34.4843	−	34.4843i	−1.32534	−	1.32534i	−0.909386	−	0.415953i	$-0.863448\pi$
$677$	−34.4843	−	34.4843i	−1.32534	−	1.32534i	−0.415953	−	0.909386i	$-0.636552\pi$
$678$	36.9946	−	5.44083i	1.42077	−	0.208954i
$679$	−1.46987			−0.0564084
$680$	16.0572	+	15.5751i	0.615766	+	0.597279i
$681$	−12.9520			−0.496323
$682$	30.6197	−	4.50327i	1.17249	−	0.172439i
$683$	29.0992	+	29.0992i	1.11345	+	1.11345i	0.992681	+	0.120769i	$0.0385361\pi$
$683$	29.0992	+	29.0992i	1.11345	+	1.11345i	0.120769	+	0.992681i	$0.461464\pi$
$684$	−51.2014	+	15.3934i	−1.95773	+	0.588582i
$685$	19.9961	−	7.58520i	0.764011	−	0.289816i
$686$	1.13486	+	0.843852i	0.0433293	+	0.0322184i
$687$	−49.7949	−	49.7949i	−1.89979	−	1.89979i
$688$	−22.2645	−	4.54343i	−0.848828	−	0.173217i
$689$			15.2091i			0.579421i
$690$	15.1345	−	53.2712i	0.576160	−	2.02800i
$691$	−43.5975			−1.65853			−0.829263	−	0.558859i	$-0.811239\pi$
$691$	−43.5975			−1.65853			−0.829263	+	0.558859i	$0.811239\pi$
$692$	12.1641	−	22.6225i	0.462409	−	0.859978i
$693$	16.1169	−	16.1169i	0.612232	−	0.612232i
$694$	−22.9518	−	17.0663i	−0.871238	−	0.647828i
$695$	0.988111	−	2.19593i	0.0374812	−	0.0832962i
$696$	−8.28686	+	22.8918i	−0.314113	+	0.867711i
$697$	7.95353	−	7.95353i	0.301261	−	0.301261i
$698$	3.38458	+	23.0133i	0.128108	+	0.871065i
$699$		−	26.1899i		−	0.990594i
$700$	−2.29711	−	9.73259i	−0.0868225	−	0.367857i
$701$			7.31961i			0.276458i	0.990400	+	0.138229i	$0.0441409\pi$
$701$			7.31961i			0.276458i	−0.990400	+	0.138229i	$0.955859\pi$
$702$	−23.6461	+	3.47766i	−0.892466	+	0.131256i
$703$	5.77962	−	5.77962i	0.217983	−	0.217983i
$704$	25.4432	−	30.5371i	0.958925	−	1.15091i
$705$	9.49804	−	21.1079i	0.357717	−	0.794971i
$706$	−5.74052	+	7.72020i	−0.216047	+	0.290553i
$707$	−7.13354	+	7.13354i	−0.268284	+	0.268284i
$708$	32.1679	−	59.8251i	1.20894	−	2.24837i
$709$	−19.4599			−0.730832			−0.365416	−	0.930844i	$-0.619073\pi$
$709$	−19.4599			−0.730832			−0.365416	+	0.930844i	$0.619073\pi$
$710$	26.1925	+	7.44135i	0.982986	+	0.279269i
$711$		−	59.1083i		−	2.21673i
$712$	−12.3821	+	5.80011i	−0.464038	+	0.217368i
$713$	−19.8014	−	19.8014i	−0.741569	−	0.741569i
$714$	8.22153	−	11.0568i	0.307683	−	0.413791i
$715$	40.1458	−	15.2287i	1.50137	−	0.569521i
$716$	5.47782	+	18.2203i	0.204716	+	0.680923i
$717$	34.7512	+	34.7512i	1.29781	+	1.29781i
$718$	2.94426	+	20.0194i	0.109879	+	0.747116i
$719$	−4.16036			−0.155155			−0.0775776	−	0.996986i	$-0.524719\pi$
$719$	−4.16036			−0.155155			−0.0775776	+	0.996986i	$0.524719\pi$
$720$	6.58829	+	40.4995i	0.245531	+	1.50933i
$721$	11.2902			0.420469
$722$	3.07783	+	20.9275i	0.114545	+	0.778841i
$723$	−38.1364	−	38.1364i	−1.41831	−	1.41831i
$724$	3.73692	+	12.4297i	0.138882	+	0.461946i
$725$	10.3624	+	11.6933i	0.384851	+	0.434278i
$726$	31.8109	−	42.7812i	1.18061	−	1.58776i
$727$	−1.53832	−	1.53832i	−0.0570531	−	0.0570531i	0.678005	−	0.735058i	$-0.262845\pi$
$727$	−1.53832	−	1.53832i	−0.0570531	−	0.0570531i	−0.735058	+	0.678005i	$0.762845\pi$
$728$	−4.63701	−	9.89909i	−0.171859	−	0.366885i
$729$			44.0138i			1.63014i
$730$	−41.9350	+	23.3791i	−1.55208	+	0.865299i
$731$	−20.0932			−0.743176
$732$	2.33604	−	4.34452i	0.0863427	−	0.160578i
$733$	23.9118	−	23.9118i	0.883201	−	0.883201i	−0.110658	−	0.993859i	$-0.535296\pi$
$733$	23.9118	−	23.9118i	0.883201	−	0.883201i	0.993859	+	0.110658i	$0.0352957\pi$
$734$	−10.7537	+	14.4622i	−0.396927	+	0.533811i
$735$	−5.75893	+	2.18456i	−0.212421	+	0.0805787i
$736$	−35.9095	−	1.98703i	−1.32364	−	0.0732429i
$737$	18.3407	−	18.3407i	0.675590	−	0.675590i
$738$	20.4119	−	3.00199i	0.751371	−	0.110505i
$739$			19.4344i			0.714906i	0.933931	+	0.357453i	$0.116355\pi$
$739$			19.4344i			0.714906i	−0.933931	+	0.357453i	$0.883645\pi$
$740$	−3.81923	−	4.97614i	−0.140398	−	0.182926i
$741$			62.0359i			2.27894i
$742$	−0.809787	−	5.50610i	−0.0297282	−	0.202135i
$743$	20.4921	−	20.4921i	0.751783	−	0.751783i	−0.223029	−	0.974812i	$-0.571594\pi$
$743$	20.4921	−	20.4921i	0.751783	−	0.751783i	0.974812	+	0.223029i	$0.0715944\pi$
$744$	32.2676	+	11.6809i	1.18299	+	0.428243i
$745$	−29.6744	−	13.3527i	−1.08719	−	0.489206i
$746$	−30.7087	−	22.8341i	−1.12432	−	0.836015i
$747$	15.9148	−	15.9148i	0.582293	−	0.582293i
$748$	16.6449	−	30.9557i	0.608597	−	1.13185i
$749$	−16.3523			−0.597500
$750$	41.1022	+	14.4043i	1.50084	+	0.525971i
$751$			50.5961i			1.84628i	0.384465	+	0.923140i	$0.374386\pi$
$751$			50.5961i			1.84628i	−0.384465	+	0.923140i	$0.625614\pi$
$752$	−14.7282	−	3.00553i	−0.537083	−	0.109600i
$753$	−3.87447	−	3.87447i	−0.141194	−	0.141194i
$754$	13.7055	+	10.1911i	0.499127	+	0.371136i
$755$	−1.44653	+	3.21468i	−0.0526444	+	0.116994i
$756$	8.37537	−	2.51801i	0.304609	−	0.0915791i
$757$	−17.3973	−	17.3973i	−0.632315	−	0.632315i	0.316333	−	0.948648i	$-0.397548\pi$
$757$	−17.3973	−	17.3973i	−0.632315	−	0.632315i	−0.948648	+	0.316333i	$0.897548\pi$
$758$	13.1319	−	1.93132i	0.476971	−	0.0701486i
$759$	−87.0100			−3.15826
$760$	36.8507	−	0.561620i	1.33671	−	0.0203721i
$761$	33.2640			1.20582			0.602910	−	0.797809i	$-0.294008\pi$
$761$	33.2640			1.20582			0.602910	+	0.797809i	$0.294008\pi$
$762$	−55.5316	+	8.16709i	−2.01170	+	0.295862i
$763$	0.331361	+	0.331361i	0.0119961	+	0.0119961i
$764$	6.86820	+	22.8449i	0.248483	+	0.826500i
$765$	12.8685	+	33.9239i	0.465261	+	1.22652i
$766$	37.4838	+	27.8719i	1.35434	+	1.00705i
$767$	−33.6949	−	33.6949i	−1.21665	−	1.21665i
$768$	40.8829	−	16.4618i	1.47523	−	0.594012i
$769$			45.8098i			1.65194i	0.563712	+	0.825971i	$0.309373\pi$
$769$			45.8098i			1.65194i	−0.563712	+	0.825971i	$0.690627\pi$
$770$	−13.7230	+	7.65070i	−0.494544	+	0.275712i
$771$	−3.10978			−0.111996
$772$	15.4620	+	8.31392i	0.556491	+	0.299225i
$773$	−22.8403	+	22.8403i	−0.821510	+	0.821510i	−0.986325	−	0.164814i	$-0.947298\pi$
$773$	−22.8403	+	22.8403i	−0.821510	+	0.821510i	0.164814	+	0.986325i	$0.447298\pi$
$774$	−29.5756	−	21.9916i	−1.06307	−	0.790470i
$775$	16.4825	−	14.6066i	0.592070	−	0.524684i
$776$	−3.90916	−	1.41512i	−0.140331	−	0.0507999i
$777$	−2.73202	+	2.73202i	−0.0980105	+	0.0980105i
$778$	5.09874	+	34.6686i	0.182799	+	1.24293i
$779$		−	18.5312i		−	0.663949i
$780$	47.2027	+	6.20884i	1.69013	+	0.222312i
$781$		−	42.7812i		−	1.53083i
$782$	−31.4633	+	4.62733i	−1.12512	+	0.165473i
$783$	−9.66217	+	9.66217i	−0.345298	+	0.345298i
$784$	2.20578	+	3.33684i	0.0787779	+	0.119173i
$785$	−7.38152	−	19.4591i	−0.263458	−	0.694526i
$786$	0.101828	−	0.136944i	0.00363207	−	0.00488463i
$787$	−23.4151	+	23.4151i	−0.834657	+	0.834657i	−0.988150	−	0.153492i	$-0.950948\pi$
$787$	−23.4151	+	23.4151i	−0.834657	+	0.834657i	0.153492	+	0.988150i	$0.450948\pi$
$788$	−19.1840	−	10.3152i	−0.683403	−	0.367465i
$789$	70.1800			2.49847
$790$	−11.1350	+	39.1937i	−0.396167	+	1.39445i
$791$			9.59889i			0.341297i
$792$	58.3801	−	27.3468i	2.07445	−	0.971728i
$793$	−2.44693	−	2.44693i	−0.0868931	−	0.0868931i
$794$	1.58226	−	2.12792i	0.0561522	−	0.0755169i
$795$	22.1041	+	9.94627i	0.783950	+	0.352758i
$796$	5.83233	−	1.75346i	0.206722	−	0.0621497i
$797$	13.9493	+	13.9493i	0.494111	+	0.494111i	0.909599	−	0.415488i	$-0.136389\pi$
$797$	13.9493	+	13.9493i	0.494111	+	0.494111i	−0.415488	+	0.909599i	$0.636389\pi$
$798$	−3.30301	−	22.4586i	−0.116925	−	0.795027i
$799$	−13.2919			−0.470233
$800$	3.26085	−	28.0957i	0.115289	−	0.993332i
$801$	−22.1770			−0.783585
$802$	−1.44398	−	9.81829i	−0.0509888	−	0.346696i
$803$	53.3400	+	53.3400i	1.88233	+	1.88233i
$804$	27.5423	−	8.28044i	0.971342	−	0.292029i
$805$	12.9642	+	5.83356i	0.456928	+	0.205606i
$806$	14.3650	−	19.3189i	0.505986	−	0.680481i
$807$	53.1847	+	53.1847i	1.87219	+	1.87219i
$808$	−25.8397	+	12.1040i	−0.909037	+	0.425818i
$809$			44.2402i			1.55540i	0.628635	+	0.777701i	$0.283614\pi$
$809$			44.2402i			1.55540i	−0.628635	+	0.777701i	$0.716386\pi$
$810$	1.48413	−	5.22391i	0.0521469	−	0.183550i
$811$	9.19726			0.322959			0.161480	−	0.986876i	$-0.448373\pi$
$811$	9.19726			0.322959			0.161480	+	0.986876i	$0.448373\pi$
$812$	−5.50438	−	2.95970i	−0.193166	−	0.103865i
$813$	−43.2288	+	43.2288i	−1.51610	+	1.51610i
$814$	−5.88079	+	7.90885i	−0.206122	+	0.277205i
$815$	2.07009	+	5.45716i	0.0725121	+	0.191156i
$816$	32.5104	−	21.4906i	1.13809	−	0.752322i
$817$	−23.4080	+	23.4080i	−0.818942	+	0.818942i
$818$	−12.0272	+	1.76885i	−0.420522	+	0.0618465i
$819$		−	17.7298i		−	0.619530i
$820$	−14.1003	−	1.85469i	−0.492403	−	0.0647686i
$821$		−	33.5623i		−	1.17133i	−0.810552	−	0.585666i	$-0.800833\pi$
$821$		−	33.5623i		−	1.17133i	0.810552	−	0.585666i	$-0.199167\pi$
$822$	−5.42122	−	36.8613i	−0.189087	−	1.28569i
$823$	−15.2780	+	15.2780i	−0.532556	+	0.532556i	−0.921332	−	0.388776i	$-0.872898\pi$
$823$	−15.2780	+	15.2780i	−0.532556	+	0.532556i	0.388776	+	0.921332i	$0.372898\pi$
$824$	30.0266	+	10.8697i	1.04603	+	0.378663i
$825$	4.12156	−	68.3048i	0.143494	−	2.37807i
$826$	13.9925	+	10.4044i	0.486860	+	0.362015i
$827$	0.689674	−	0.689674i	0.0239823	−	0.0239823i	−0.695014	−	0.718996i	$-0.744602\pi$
$827$	0.689674	−	0.689674i	0.0239823	−	0.0239823i	0.718996	+	0.695014i	$0.244602\pi$
$828$	−51.3758	−	27.6247i	−1.78543	−	0.960025i
$829$	57.4990			1.99702			0.998512	−	0.0545294i	$-0.0173659\pi$
$829$	57.4990			1.99702			0.998512	+	0.0545294i	$0.0173659\pi$
$830$	−13.5510	+	7.55477i	−0.470360	+	0.262230i
$831$			57.7066i			2.00182i
$832$	−2.80188	−	30.7912i	−0.0971377	−	1.06749i
$833$	2.50105	+	2.50105i	0.0866562	+	0.0866562i
$834$	−3.36639	−	2.50315i	−0.116568	−	0.0866769i
$835$	6.85294	+	18.0657i	0.237156	+	0.625189i
$836$	−16.6717	−	55.4532i	−0.576603	−	1.91789i
$837$	13.6195	+	13.6195i	0.470759	+	0.470759i
$838$	3.96110	−	0.582563i	0.136834	−	0.0201243i
$839$	−16.0870			−0.555384			−0.277692	−	0.960670i	$-0.589570\pi$
$839$	−16.0870			−0.555384			−0.277692	+	0.960670i	$0.589570\pi$
$840$	−17.4192	+	0.265477i	−0.601021	+	0.00915981i
$841$	−19.2355			−0.663293
$842$	12.2826	−	1.80641i	0.423286	−	0.0622530i
$843$	40.5823	+	40.5823i	1.39773	+	1.39773i
$844$	−53.4102	+	16.0575i	−1.83846	+	0.552722i
$845$	1.77706	−	3.94924i	0.0611327	−	0.135858i
$846$	−19.5645	−	14.5476i	−0.672643	−	0.500158i
$847$	9.67711	+	9.67711i	0.332509	+	0.332509i
$848$	3.14736	−	15.4233i	0.108081	−	0.529637i
$849$		−	31.4683i		−	1.07999i
$850$	−2.14218	−	24.9186i	−0.0734762	−	0.854700i
$851$	8.91759			0.305691
$852$	22.4649	−	41.7796i	0.769634	−	1.43135i
$853$	10.7040	−	10.7040i	0.366497	−	0.366497i	−0.499701	−	0.866198i	$-0.666557\pi$
$853$	10.7040	−	10.7040i	0.366497	−	0.366497i	0.866198	+	0.499701i	$0.166557\pi$
$854$	1.01614	+	0.755571i	0.0347715	+	0.0258551i
$855$	54.5116	+	24.5288i	1.86426	+	0.838868i
$856$	−43.4894	−	15.7432i	−1.48644	−	0.538092i
$857$	−13.5293	+	13.5293i	−0.462152	+	0.462152i	−0.899360	−	0.437208i	$-0.855967\pi$
$857$	−13.5293	+	13.5293i	−0.462152	+	0.462152i	0.437208	+	0.899360i	$0.355967\pi$
$858$	−10.8841	−	74.0059i	−0.371577	−	2.52652i
$859$		−	24.1069i		−	0.822518i	−0.911518	−	0.411259i	$-0.865089\pi$
$859$		−	24.1069i		−	0.822518i	0.911518	−	0.411259i	$-0.134911\pi$
$860$	15.4682	+	20.1538i	0.527462	+	0.687238i
$861$			8.75966i			0.298528i
$862$	14.3810	−	2.11502i	0.489817	−	0.0720379i
$863$	18.5324	−	18.5324i	0.630852	−	0.630852i	−0.317430	−	0.948282i	$-0.602820\pi$
$863$	18.5324	−	18.5324i	0.630852	−	0.630852i	0.948282	+	0.317430i	$0.102820\pi$
$864$	24.6988	+	1.36669i	0.840269	+	0.0464957i
$865$	−26.8503	+	10.1852i	−0.912937	+	0.346308i
$866$	−6.28198	+	8.44839i	−0.213470	+	0.287088i
$867$	−8.74450	+	8.74450i	−0.296979	+	0.296979i
$868$	−4.17191	+	7.75882i	−0.141604	+	0.263351i
$869$	64.0166			2.17162
$870$	23.7741	−	13.2543i	0.806017	−	0.449361i
$871$		−	20.1762i		−	0.683643i
$872$	0.562245	+	1.20028i	0.0190400	+	0.0406467i
$873$	−4.76804	−	4.76804i	−0.161374	−	0.161374i
$874$	−31.2630	+	42.0444i	−1.05749	+	1.42217i
$875$	−5.19357	+	9.90085i	−0.175575	+	0.334710i
$876$	24.0818	+	80.1007i	0.813650	+	2.70635i
$877$	0.359005	+	0.359005i	0.0121227	+	0.0121227i	0.713142	−	0.701019i	$-0.247271\pi$
$877$	0.359005	+	0.359005i	0.0121227	+	0.0121227i	−0.701019	+	0.713142i	$0.747271\pi$
$878$	−2.70370	−	18.3837i	−0.0912454	−	0.620418i
$879$	37.0133			1.24843
$880$	−43.8626	+	7.13538i	−1.47861	+	0.240534i
$881$	33.8357			1.13995			0.569977	−	0.821660i	$-0.306952\pi$
$881$	33.8357			1.13995			0.569977	+	0.821660i	$0.306952\pi$
$882$	0.943998	+	6.41866i	0.0317861	+	0.216128i
$883$	25.4680	+	25.4680i	0.857068	+	0.857068i	0.990992	−	0.133924i	$-0.0427577\pi$
$883$	25.4680	+	25.4680i	0.857068	+	0.857068i	−0.133924	+	0.990992i	$0.542758\pi$
$884$	−7.87150	−	26.1821i	−0.264747	−	0.880599i
$885$	−71.0056	+	26.9349i	−2.38683	+	0.905405i
$886$	−14.4022	+	19.3689i	−0.483850	+	0.650711i
$887$	−9.87786	−	9.87786i	−0.331666	−	0.331666i	0.521553	−	0.853219i	$-0.325353\pi$
$887$	−9.87786	−	9.87786i	−0.331666	−	0.331666i	−0.853219	+	0.521553i	$0.825353\pi$
$888$	−9.89614	+	4.63562i	−0.332093	+	0.155561i
$889$		−	14.4086i		−	0.483250i
$890$	14.7052	+	4.17778i	0.492919	+	0.140040i
$891$	−8.53242			−0.285847
$892$	24.6281	−	45.8028i	0.824611	−	1.53359i
$893$	−15.4846	+	15.4846i	−0.518173	+	0.518173i
$894$	−33.8260	+	45.4913i	−1.13131	+	1.52146i
$895$	8.72870	−	19.3982i	0.291768	−	0.648411i
$896$	2.65379	+	10.9981i	0.0886569	+	0.367420i
$897$	−47.8587	+	47.8587i	−1.59796	+	1.59796i
$898$	−45.3865	+	6.67503i	−1.51457	+	0.222749i
$899$		−	13.7638i		−	0.459048i
$900$	24.1196	−	39.0226i	0.803987	−	1.30075i
$901$		−	13.9192i		−	0.463714i
$902$	3.25127	+	22.1069i	0.108256	+	0.736078i
$903$	11.0649	−	11.0649i	0.368217	−	0.368217i
$904$	−9.24137	+	25.5286i	−0.307363	+	0.849067i
$905$	5.95464	−	13.2333i	0.197939	−	0.439889i
$906$	4.92815	+	3.66443i	0.163727	+	0.121743i
$907$	−9.49904	+	9.49904i	−0.315411	+	0.315411i	−0.847001	−	0.531591i	$-0.821594\pi$
$907$	−9.49904	+	9.49904i	−0.315411	+	0.315411i	0.531591	+	0.847001i	$0.321594\pi$
$908$	4.45360	−	8.28270i	0.147798	−	0.274871i
$909$	−46.2803			−1.53502
$910$	−3.34001	+	11.7563i	−0.110720	+	0.389719i
$911$			42.0078i			1.39178i	0.718148	+	0.695890i	$0.244990\pi$
$911$			42.0078i			1.39178i	−0.718148	+	0.695890i	$0.755010\pi$
$912$	12.8377	−	62.9094i	0.425098	−	2.08314i
$913$	17.2364	+	17.2364i	0.570441	+	0.570441i
$914$	−4.45643	−	3.31367i	−0.147405	−	0.109607i
$915$	−5.15645	+	1.95602i	−0.170467	+	0.0646640i
$916$	48.9655	−	14.7212i	1.61787	−	0.486403i
$917$	0.0309767	+	0.0309767i	0.00102294	+	0.00102294i
$918$	21.6406	−	3.18270i	0.714246	−	0.105045i
$919$	43.7978			1.44476			0.722378	−	0.691498i	$-0.243049\pi$
$919$	43.7978			1.44476			0.722378	+	0.691498i	$0.243049\pi$
$920$	28.8624	+	27.9958i	0.951565	+	0.922996i
$921$	45.0224			1.48354
$922$	16.0581	−	2.36168i	0.528846	−	0.0777778i
$923$	−23.5312	−	23.5312i	−0.774540	−	0.774540i
$924$	7.88068	+	26.2126i	0.259255	+	0.862331i
$925$	−0.422415	+	7.00051i	−0.0138889	+	0.230175i
$926$	−26.8340	−	19.9530i	−0.881819	−	0.655695i
$927$	36.6237	+	36.6237i	1.20288	+	1.20288i
$928$	−11.7896	−	13.1708i	−0.387013	−	0.432352i
$929$			6.69434i			0.219634i	0.993952	+	0.109817i	$0.0350265\pi$
$929$			6.69434i			0.219634i	−0.993952	+	0.109817i	$0.964973\pi$
$930$	−18.6828	−	33.5113i	−0.612634	−	1.09888i
$931$	5.82728			0.190981
$932$	16.7482	+	9.00549i	0.548605	+	0.294985i
$933$	−2.89045	+	2.89045i	−0.0946289	+	0.0946289i
$934$	−16.0423	−	11.9286i	−0.524920	−	0.390316i
$935$	−36.7409	+	13.9371i	−1.20156	+	0.455792i
$936$	17.0694	−	47.1530i	0.557932	−	1.54124i
$937$	−30.7721	+	30.7721i	−1.00528	+	1.00528i	−0.00529627	+	0.999986i	$0.501686\pi$
$937$	−30.7721	+	30.7721i	−1.00528	+	1.00528i	−0.999986	+	0.00529627i	$0.998314\pi$
$938$	1.07425	+	7.30431i	0.0350755	+	0.238494i
$939$			11.0128i			0.359390i
$940$	10.2324	+	13.3319i	0.333744	+	0.434840i
$941$		−	57.1321i		−	1.86245i	−0.364439	−	0.931227i	$-0.618739\pi$
$941$		−	57.1321i		−	1.86245i	0.364439	−	0.931227i	$-0.381261\pi$
$942$	−35.8715	+	5.27565i	−1.16876	+	0.171890i
$943$	14.2962	−	14.2962i	0.465549	−	0.465549i
$944$	27.1965	+	41.1421i	0.885172	+	1.33906i
$945$	−8.91684	−	4.01235i	−0.290065	−	0.130522i
$946$	23.8177	−	32.0315i	0.774381	−	1.04143i
$947$	10.4235	−	10.4235i	0.338719	−	0.338719i	−0.517166	−	0.855885i	$-0.673013\pi$
$947$	10.4235	−	10.4235i	0.338719	−	0.338719i	0.855885	+	0.517166i	$0.173013\pi$
$948$	62.5179	+	33.6158i	2.03049	+	1.09179i
$949$	58.6780			1.90477
$950$	−31.5249	−	26.5337i	−1.02280	−	0.860868i
$951$			38.1549i			1.23726i
$952$	4.24372	+	9.05951i	0.137540	+	0.293620i
$953$	−30.0029	−	30.0029i	−0.971888	−	0.971888i	0.0277275	−	0.999616i	$-0.491173\pi$
$953$	−30.0029	−	30.0029i	−0.971888	−	0.971888i	−0.999616	+	0.0277275i	$0.991173\pi$
$954$	15.2342	−	20.4878i	0.493224	−	0.663318i
$955$	10.9442	−	24.3218i	0.354146	−	0.787036i
$956$	−34.1723	+	10.2737i	−1.10521	+	0.332276i
$957$	−30.2399	−	30.2399i	−0.977518	−	0.977518i
$958$	−0.714687	−	4.85948i	−0.0230905	−	0.157003i
$959$	9.56429			0.308847
$960$	−46.5826	−	16.0644i	−1.50345	−	0.518476i
$961$	11.5990			0.374160
$962$	1.11550	+	7.58481i	0.0359653	+	0.244544i
$963$	−53.0445	−	53.0445i	−1.70933	−	1.70933i
$964$	37.5012	−	11.2745i	1.20783	−	0.363128i
$965$	−6.96142	−	18.3517i	−0.224096	−	0.590761i
$966$	14.7780	−	19.8743i	0.475473	−	0.639445i
$967$	9.86610	+	9.86610i	0.317272	+	0.317272i	0.847719	−	0.530446i	$-0.177976\pi$
$967$	9.86610	+	9.86610i	0.317272	+	0.317272i	−0.530446	+	0.847719i	$0.677976\pi$
$968$	16.4199	+	35.0532i	0.527755	+	1.12665i
$969$		−	56.7743i		−	1.82385i
$970$	2.26339	+	4.05983i	0.0726730	+	0.130353i
$971$	−2.71827			−0.0872336			−0.0436168	−	0.999048i	$-0.513888\pi$
$971$	−2.71827			−0.0872336			−0.0436168	+	0.999048i	$0.513888\pi$
$972$	−31.4410	−	16.9058i	−1.00847	−	0.542254i
$973$	0.761476	−	0.761476i	0.0244118	−	0.0244118i
$974$	14.2677	−	19.1880i	0.457165	−	0.614823i
$975$	−35.3031	−	39.8372i	−1.13061	−	1.27581i
$976$	1.97502	+	2.98775i	0.0632189	+	0.0956357i
$977$	−5.94180	+	5.94180i	−0.190095	+	0.190095i	−0.795737	−	0.605642i	$-0.792916\pi$
$977$	−5.94180	+	5.94180i	−0.190095	+	0.190095i	0.605642	+	0.795737i	$0.292916\pi$
$978$	10.0599	−	1.47951i	0.321679	−	0.0473097i
$979$		−	24.0186i		−	0.767637i
$980$	0.583221	−	4.43394i	0.0186303	−	0.141637i
$981$			2.14977i			0.0686369i
$982$	1.93641	+	13.1665i	0.0617935	+	0.420161i
$983$	31.0579	−	31.0579i	0.990594	−	0.990594i	−0.00936180	−	0.999956i	$-0.502980\pi$
$983$	31.0579	−	31.0579i	0.990594	−	0.990594i	0.999956	+	0.00936180i	$0.00298000\pi$
$984$	−8.43339	+	23.2966i	−0.268847	+	0.742668i
$985$	8.63716	+	22.7692i	0.275203	+	0.725488i
$986$	−12.5431	−	9.32671i	−0.399454	−	0.297023i
$987$	7.31955	−	7.31955i	0.232984	−	0.232984i
$988$	−39.6713	−	21.3312i	−1.26211	−	0.678637i
$989$	−36.1170			−1.14845
$990$	−69.3333	−	19.6978i	−2.20356	−	0.626036i
$991$			7.18404i			0.228209i	0.993469	+	0.114104i	$0.0363998\pi$
$991$			7.18404i			0.228209i	−0.993469	+	0.114104i	$0.963600\pi$
$992$	−18.5652	+	16.6183i	−0.589444	+	0.527632i
$993$	−22.4911	−	22.4911i	−0.713733	−	0.713733i
$994$	9.77182	+	7.26605i	0.309943	+	0.230465i
$995$	−6.20939	−	2.79407i	−0.196851	−	0.0885780i
$996$	7.78185	+	25.8839i	0.246577	+	0.820163i
$997$	9.91715	+	9.91715i	0.314079	+	0.314079i	0.846488	−	0.532408i	$-0.178713\pi$
$997$	9.91715	+	9.91715i	0.314079	+	0.314079i	−0.532408	+	0.846488i	$0.678713\pi$
$998$	47.7247	−	7.01891i	1.51070	−	0.222180i
$999$	−6.13357			−0.194057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.43.17	✓	72
4.3	odd	2		1120.2.bi.a.463.5		72
5.2	odd	4	inner	280.2.w.a.267.36	yes	72
8.3	odd	2	inner	280.2.w.a.43.36	yes	72
8.5	even	2		1120.2.bi.a.463.6		72
20.7	even	4		1120.2.bi.a.687.6		72
40.27	even	4	inner	280.2.w.a.267.17	yes	72
40.37	odd	4		1120.2.bi.a.687.5		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.17	✓	72	1.1	even	1	trivial
280.2.w.a.43.36	yes	72	8.3	odd	2	inner
280.2.w.a.267.17	yes	72	40.27	even	4	inner
280.2.w.a.267.36	yes	72	5.2	odd	4	inner
1120.2.bi.a.463.5		72	4.3	odd	2
1120.2.bi.a.463.6		72	8.5	even	2
1120.2.bi.a.687.5		72	40.37	odd	4
1120.2.bi.a.687.6		72	20.7	even	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.205776 - 1.39916i) q^{2} +(1.94776 + 1.94776i) q^{3} +(-1.91531 + 0.575828i) q^{4} +(2.03914 + 0.917560i) q^{5} +(2.32443 - 3.12603i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.19980 + 2.56134i) q^{8} +4.58750i q^{9} +O(q^{10})\)	\(q+(-0.205776 - 1.39916i) q^{2} +(1.94776 + 1.94776i) q^{3} +(-1.91531 + 0.575828i) q^{4} +(2.03914 + 0.917560i) q^{5} +(2.32443 - 3.12603i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.19980 + 2.56134i) q^{8} +4.58750i q^{9} +(0.864211 - 3.04190i) q^{10} -4.96845 q^{11} +(-4.85213 - 2.60899i) q^{12} +(-2.73283 + 2.73283i) q^{13} +(0.843852 - 1.13486i) q^{14} +(2.18456 + 5.75893i) q^{15} +(3.33684 - 2.20578i) q^{16} +(2.50105 - 2.50105i) q^{17} +(6.41866 - 0.943998i) q^{18} -5.82728i q^{19} +(-4.43394 - 0.583221i) q^{20} +2.75454i q^{21} +(1.02239 + 6.95167i) q^{22} +(4.49556 - 4.49556i) q^{23} +(-2.65195 + 7.32579i) q^{24} +(3.31617 + 3.74206i) q^{25} +(4.38603 + 3.26132i) q^{26} +(-3.09207 + 3.09207i) q^{27} +(-1.76150 - 0.947158i) q^{28} +3.12482 q^{29} +(7.60814 - 4.24160i) q^{30} -4.40466i q^{31} +(-3.77289 - 4.21489i) q^{32} +(-9.67733 - 9.67733i) q^{33} +(-4.01403 - 2.98472i) q^{34} +(0.793075 + 2.09070i) q^{35} +(-2.64161 - 8.78650i) q^{36} +(0.991822 + 0.991822i) q^{37} +(-8.15331 + 1.19911i) q^{38} -10.6458 q^{39} +(0.0963777 + 6.32382i) q^{40} +3.18008 q^{41} +(3.85405 - 0.566819i) q^{42} +(-4.01697 - 4.01697i) q^{43} +(9.51613 - 2.86097i) q^{44} +(-4.20931 + 9.35455i) q^{45} +(-7.21510 - 5.36494i) q^{46} +(-2.65726 - 2.65726i) q^{47} +(10.7957 + 2.20303i) q^{48} +1.00000i q^{49} +(4.55337 - 5.40988i) q^{50} +9.74286 q^{51} +(3.66058 - 6.80786i) q^{52} +(2.78266 - 2.78266i) q^{53} +(4.96258 + 3.69003i) q^{54} +(-10.1314 - 4.55885i) q^{55} +(-0.962753 + 2.65953i) q^{56} +(11.3501 - 11.3501i) q^{57} +(-0.643014 - 4.37213i) q^{58} +12.3297i q^{59} +(-7.50026 - 9.77221i) q^{60} +0.895384i q^{61} +(-6.16284 + 0.906373i) q^{62} +(-3.24385 + 3.24385i) q^{63} +(-5.12095 + 6.14621i) q^{64} +(-8.08015 + 3.06508i) q^{65} +(-11.5488 + 15.5315i) q^{66} +(-3.69144 + 3.69144i) q^{67} +(-3.35011 + 6.23046i) q^{68} +17.5125 q^{69} +(2.76204 - 1.53986i) q^{70} +8.61057i q^{71} +(-11.7502 + 5.50410i) q^{72} +(-10.7357 - 10.7357i) q^{73} +(1.18363 - 1.59181i) q^{74} +(-0.829546 + 13.7477i) q^{75} +(3.35551 + 11.1611i) q^{76} +(-3.51322 - 3.51322i) q^{77} +(2.19064 + 14.8952i) q^{78} -12.8846 q^{79} +(8.82822 - 1.43614i) q^{80} +1.71732 q^{81} +(-0.654384 - 4.44945i) q^{82} +(-3.46917 - 3.46917i) q^{83} +(-1.58614 - 5.27581i) q^{84} +(7.39484 - 2.80512i) q^{85} +(-4.79379 + 6.44699i) q^{86} +(6.08639 + 6.08639i) q^{87} +(-5.96116 - 12.7259i) q^{88} +4.83422i q^{89} +(13.9547 + 3.96457i) q^{90} -3.86481 q^{91} +(-6.02173 + 11.1991i) q^{92} +(8.57920 - 8.57920i) q^{93} +(-3.17114 + 4.26475i) q^{94} +(5.34688 - 11.8826i) q^{95} +(0.860905 - 15.5582i) q^{96} +(-1.03935 + 1.03935i) q^{97} +(1.39916 - 0.205776i) q^{98} -22.7928i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more