LMFDB - Embedded newform 880.2.w.a.221.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(221,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.02683537787$
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			221.16
Character	$\chi$	$=$	880.221
Dual form			880.2.w.a.661.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.274668 + 1.38728i) q^{2} +(-1.78994 - 1.78994i) q^{3} +(-1.84912 - 0.762085i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.97480 - 1.99152i) q^{6} +3.39249i q^{7} +(1.56512 - 2.35593i) q^{8} +3.40779i q^{9} +(-0.786739 - 1.17518i) q^{10} +(0.707107 - 0.707107i) q^{11} +(1.94572 + 4.67390i) q^{12} +(-0.897789 - 0.897789i) q^{13} +(-4.70635 - 0.931808i) q^{14} +2.53136 q^{15} +(2.83845 + 2.81837i) q^{16} +4.06665 q^{17} +(-4.72757 - 0.936010i) q^{18} +(-0.119661 - 0.119661i) q^{19} +(1.84640 - 0.768646i) q^{20} +(6.07236 - 6.07236i) q^{21} +(0.786739 + 1.17518i) q^{22} +4.81496i q^{23} +(-7.01845 + 1.41550i) q^{24} -1.00000i q^{25} +(1.49208 - 0.998894i) q^{26} +(0.729914 - 0.729914i) q^{27} +(2.58537 - 6.27310i) q^{28} +(-5.24008 - 5.24008i) q^{29} +(-0.695284 + 3.51172i) q^{30} -8.63086 q^{31} +(-4.68951 + 3.16363i) q^{32} -2.53136 q^{33} +(-1.11698 + 5.64160i) q^{34} +(-2.39885 - 2.39885i) q^{35} +(2.59702 - 6.30139i) q^{36} +(2.70195 - 2.70195i) q^{37} +(0.198872 - 0.133137i) q^{38} +3.21398i q^{39} +(0.559185 + 2.77260i) q^{40} -6.30000i q^{41} +(6.75621 + 10.0920i) q^{42} +(3.98447 - 3.98447i) q^{43} +(-1.84640 + 0.768646i) q^{44} +(-2.40967 - 2.40967i) q^{45} +(-6.67972 - 1.32252i) q^{46} -12.5526 q^{47} +(-0.0359543 - 10.1254i) q^{48} -4.50899 q^{49} +(1.38728 + 0.274668i) q^{50} +(-7.27907 - 7.27907i) q^{51} +(0.975923 + 2.34431i) q^{52} +(-1.83419 + 1.83419i) q^{53} +(0.812115 + 1.21308i) q^{54} +1.00000i q^{55} +(7.99246 + 5.30966i) q^{56} +0.428374i q^{57} +(8.70876 - 5.83020i) q^{58} +(-0.676655 + 0.676655i) q^{59} +(-4.68078 - 1.92911i) q^{60} +(-6.64768 - 6.64768i) q^{61} +(2.37062 - 11.9735i) q^{62} -11.5609 q^{63} +(-3.10079 - 7.37463i) q^{64} +1.26967 q^{65} +(0.695284 - 3.51172i) q^{66} +(-8.17805 - 8.17805i) q^{67} +(-7.51971 - 3.09913i) q^{68} +(8.61850 - 8.61850i) q^{69} +(3.98678 - 2.66900i) q^{70} -11.8056i q^{71} +(8.02850 + 5.33360i) q^{72} +1.70333i q^{73} +(3.00624 + 4.49052i) q^{74} +(-1.78994 + 1.78994i) q^{75} +(0.130076 + 0.312460i) q^{76} +(2.39885 + 2.39885i) q^{77} +(-4.45870 - 0.882777i) q^{78} -10.6181 q^{79} +(-3.99997 + 0.0142035i) q^{80} +7.61035 q^{81} +(8.73990 + 1.73041i) q^{82} +(0.997339 + 0.997339i) q^{83} +(-15.8561 + 6.60084i) q^{84} +(-2.87556 + 2.87556i) q^{85} +(4.43318 + 6.62199i) q^{86} +18.7589i q^{87} +(-0.559185 - 2.77260i) q^{88} -6.83852i q^{89} +(4.00475 - 2.68104i) q^{90} +(3.04574 - 3.04574i) q^{91} +(3.66941 - 8.90342i) q^{92} +(15.4487 + 15.4487i) q^{93} +(3.44781 - 17.4141i) q^{94} +0.169227 q^{95} +(14.0567 + 2.73124i) q^{96} +10.3208 q^{97} +(1.23847 - 6.25525i) q^{98} +(2.40967 + 2.40967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) $ 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.274668	+	1.38728i	−0.194220	+	0.980958i
$2$	−0.274668	+	1.38728i	−0.194220	+	0.980958i
$3$	−1.78994	−	1.78994i	−1.03342	−	1.03342i	−0.999422	−	0.0340019i	$-0.989175\pi$
$3$	−1.78994	−	1.78994i	−1.03342	−	1.03342i	−0.0340019	−	0.999422i	$-0.510825\pi$
$4$	−1.84912	−	0.762085i	−0.924558	−	0.381043i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	2.97480	−	1.99152i	1.21446	−	0.813034i
$7$			3.39249i			1.28224i	0.767440	+	0.641120i	$0.221530\pi$
$7$			3.39249i			1.28224i	−0.767440	+	0.641120i	$0.778470\pi$
$8$	1.56512	−	2.35593i	0.553354	−	0.832946i
$9$			3.40779i			1.13593i
$10$	−0.786739	−	1.17518i	−0.248789	−	0.371624i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	1.94572	+	4.67390i	0.561681	+	1.34924i
$13$	−0.897789	−	0.897789i	−0.249002	−	0.249002i	0.571559	−	0.820561i	$-0.306339\pi$
$13$	−0.897789	−	0.897789i	−0.249002	−	0.249002i	−0.820561	+	0.571559i	$0.806339\pi$
$14$	−4.70635	−	0.931808i	−1.25782	−	0.249036i
$15$	2.53136			0.653595
$16$	2.83845	+	2.81837i	0.709613	+	0.704591i
$17$	4.06665			0.986308			0.493154	−	0.869942i	$-0.335844\pi$
$17$	4.06665			0.986308			0.493154	+	0.869942i	$0.335844\pi$
$18$	−4.72757	−	0.936010i	−1.11430	−	0.220620i
$19$	−0.119661	−	0.119661i	−0.0274522	−	0.0274522i	0.693247	−	0.720700i	$-0.256179\pi$
$19$	−0.119661	−	0.119661i	−0.0274522	−	0.0274522i	−0.720700	+	0.693247i	$0.756179\pi$
$20$	1.84640	−	0.768646i	0.412867	−	0.171875i
$21$	6.07236	−	6.07236i	1.32510	−	1.32510i
$22$	0.786739	+	1.17518i	0.167733	+	0.250549i
$23$			4.81496i			1.00399i	0.864871	+	0.501994i	$0.167400\pi$
$23$			4.81496i			1.00399i	−0.864871	+	0.501994i	$0.832600\pi$
$24$	−7.01845	+	1.41550i	−1.43264	+	0.288937i
$25$		−	1.00000i		−	0.200000i
$26$	1.49208	−	0.998894i	0.292621	−	0.195899i
$27$	0.729914	−	0.729914i	0.140472	−	0.140472i
$28$	2.58537	−	6.27310i	0.488588	−	1.18551i
$29$	−5.24008	−	5.24008i	−0.973058	−	0.973058i	0.0265880	−	0.999646i	$-0.491536\pi$
$29$	−5.24008	−	5.24008i	−0.973058	−	0.973058i	−0.999646	+	0.0265880i	$0.991536\pi$
$30$	−0.695284	+	3.51172i	−0.126941	+	0.641149i
$31$	−8.63086			−1.55015			−0.775075	−	0.631870i	$-0.782288\pi$
$31$	−8.63086			−1.55015			−0.775075	+	0.631870i	$0.782288\pi$
$32$	−4.68951	+	3.16363i	−0.828995	+	0.559255i
$33$	−2.53136			−0.440653
$34$	−1.11698	+	5.64160i	−0.191560	+	0.967527i
$35$	−2.39885	−	2.39885i	−0.405480	−	0.405480i
$36$	2.59702	−	6.30139i	0.432837	−	1.05023i
$37$	2.70195	−	2.70195i	0.444199	−	0.444199i	−0.449222	−	0.893420i	$-0.648299\pi$
$37$	2.70195	−	2.70195i	0.444199	−	0.444199i	0.893420	+	0.449222i	$0.148299\pi$
$38$	0.198872	−	0.133137i	0.0322612	−	0.0215977i
$39$			3.21398i			0.514649i
$40$	0.559185	+	2.77260i	0.0884149	+	0.438387i
$41$		−	6.30000i		−	0.983895i	−0.870625	−	0.491948i	$-0.836285\pi$
$41$		−	6.30000i		−	0.983895i	0.870625	−	0.491948i	$-0.163715\pi$
$42$	6.75621	+	10.0920i	1.04251	+	1.55723i
$43$	3.98447	−	3.98447i	0.607625	−	0.607625i	−0.334700	−	0.942325i	$-0.608635\pi$
$43$	3.98447	−	3.98447i	0.607625	−	0.607625i	0.942325	+	0.334700i	$0.108635\pi$
$44$	−1.84640	+	0.768646i	−0.278355	+	0.115878i
$45$	−2.40967	−	2.40967i	−0.359212	−	0.359212i
$46$	−6.67972	−	1.32252i	−0.984871	−	0.194994i
$47$	−12.5526			−1.83099			−0.915496	−	0.402327i	$-0.868201\pi$
$47$	−12.5526			−1.83099			−0.915496	+	0.402327i	$0.868201\pi$
$48$	−0.0359543	−	10.1254i	−0.00518955	−	1.46147i
$49$	−4.50899			−0.644141
$50$	1.38728	+	0.274668i	0.196192	+	0.0388439i
$51$	−7.27907	−	7.27907i	−1.01927	−	1.01927i
$52$	0.975923	+	2.34431i	0.135336	+	0.325097i
$53$	−1.83419	+	1.83419i	−0.251945	+	0.251945i	−0.821768	−	0.569822i	$-0.807012\pi$
$53$	−1.83419	+	1.83419i	−0.251945	+	0.251945i	0.569822	+	0.821768i	$0.307012\pi$
$54$	0.812115	+	1.21308i	0.110515	+	0.165080i
$55$			1.00000i			0.134840i
$56$	7.99246	+	5.30966i	1.06804	+	0.709533i
$57$			0.428374i			0.0567395i
$58$	8.70876	−	5.83020i	1.14352	−	0.765543i
$59$	−0.676655	+	0.676655i	−0.0880929	+	0.0880929i	−0.749780	−	0.661687i	$-0.769841\pi$
$59$	−0.676655	+	0.676655i	−0.0880929	+	0.0880929i	0.661687	+	0.749780i	$0.269841\pi$
$60$	−4.68078	−	1.92911i	−0.604286	−	0.249047i
$61$	−6.64768	−	6.64768i	−0.851148	−	0.851148i	0.139127	−	0.990275i	$-0.455570\pi$
$61$	−6.64768	−	6.64768i	−0.851148	−	0.851148i	−0.990275	+	0.139127i	$0.955570\pi$
$62$	2.37062	−	11.9735i	0.301069	−	1.52063i
$63$	−11.5609			−1.45653
$64$	−3.10079	−	7.37463i	−0.387599	−	0.921828i
$65$	1.26967			0.157483
$66$	0.695284	−	3.51172i	0.0855835	−	0.432262i
$67$	−8.17805	−	8.17805i	−0.999107	−	0.999107i	0.000892222	−	1.00000i	$-0.499716\pi$
$67$	−8.17805	−	8.17805i	−0.999107	−	0.999107i	−1.00000		0.000892222i	$0.999716\pi$
$68$	−7.51971	−	3.09913i	−0.911898	−	0.375825i
$69$	8.61850	−	8.61850i	1.03755	−	1.03755i
$70$	3.98678	−	2.66900i	0.476511	−	0.319007i
$71$		−	11.8056i		−	1.40106i	−0.713622	−	0.700531i	$-0.752947\pi$
$71$		−	11.8056i		−	1.40106i	0.713622	−	0.700531i	$-0.247053\pi$
$72$	8.02850	+	5.33360i	0.946168	+	0.628571i
$73$			1.70333i			0.199360i	0.995020	+	0.0996800i	$0.0317819\pi$
$73$			1.70333i			0.199360i	−0.995020	+	0.0996800i	$0.968218\pi$
$74$	3.00624	+	4.49052i	0.349468	+	0.522012i
$75$	−1.78994	+	1.78994i	−0.206685	+	0.206685i
$76$	0.130076	+	0.312460i	0.0149207	+	0.0358416i
$77$	2.39885	+	2.39885i	0.273375	+	0.273375i
$78$	−4.45870	−	0.882777i	−0.504849	−	0.0999549i
$79$	−10.6181			−1.19463			−0.597314	−	0.802007i	$-0.703766\pi$
$79$	−10.6181			−1.19463			−0.597314	+	0.802007i	$0.703766\pi$
$80$	−3.99997	+	0.0142035i	−0.447211	+	0.00158800i
$81$	7.61035			0.845594
$82$	8.73990	+	1.73041i	0.965160	+	0.191092i
$83$	0.997339	+	0.997339i	0.109472	+	0.109472i	0.759721	−	0.650249i	$-0.225335\pi$
$83$	0.997339	+	0.997339i	0.109472	+	0.109472i	−0.650249	+	0.759721i	$0.725335\pi$
$84$	−15.8561	+	6.60084i	−1.73005	+	0.720210i
$85$	−2.87556	+	2.87556i	−0.311898	+	0.311898i
$86$	4.43318	+	6.62199i	0.478042	+	0.714068i
$87$			18.7589i			2.01116i
$88$	−0.559185	−	2.77260i	−0.0596093	−	0.295560i
$89$		−	6.83852i		−	0.724881i	−0.932007	−	0.362441i	$-0.881944\pi$
$89$		−	6.83852i		−	0.724881i	0.932007	−	0.362441i	$-0.118056\pi$
$90$	4.00475	−	2.68104i	0.422138	−	0.282606i
$91$	3.04574	−	3.04574i	0.319280	−	0.319280i
$92$	3.66941	−	8.90342i	0.382563	−	0.928246i
$93$	15.4487	+	15.4487i	1.60196	+	1.60196i
$94$	3.44781	−	17.4141i	0.355614	−	1.79613i
$95$	0.169227			0.0173623
$96$	14.0567	+	2.73124i	1.43465	+	0.278756i
$97$	10.3208			1.04792			0.523959	−	0.851744i	$-0.324455\pi$
$97$	10.3208			1.04792			0.523959	+	0.851744i	$0.324455\pi$
$98$	1.23847	−	6.25525i	0.125105	−	0.631875i
$99$	2.40967	+	2.40967i	0.242181	+	0.242181i
$100$	−0.762085	+	1.84912i	−0.0762085	+	0.184912i
$101$	−10.1814	+	10.1814i	−1.01309	+	1.01309i	−0.0131743	+	0.999913i	$0.504194\pi$
$101$	−10.1814	+	10.1814i	−1.01309	+	1.01309i	−0.999913	+	0.0131743i	$0.995806\pi$
$102$	12.0975	−	8.09881i	1.19783	−	0.801902i
$103$			14.9589i			1.47394i	0.675924	+	0.736971i	$0.263745\pi$
$103$			14.9589i			1.47394i	−0.675924	+	0.736971i	$0.736255\pi$
$104$	−3.52027	+	0.709977i	−0.345191	+	0.0696190i
$105$			8.58762i			0.838065i
$106$	−2.04075	−	3.04834i	−0.198215	−	0.296081i
$107$	7.82713	−	7.82713i	0.756677	−	0.756677i	−0.219039	−	0.975716i	$-0.570292\pi$
$107$	7.82713	−	7.82713i	0.756677	−	0.756677i	0.975716	+	0.219039i	$0.0702921\pi$
$108$	−1.90595	+	0.793439i	−0.183400	+	0.0763487i
$109$	−6.81250	−	6.81250i	−0.652519	−	0.652519i	0.301080	−	0.953599i	$-0.402653\pi$
$109$	−6.81250	−	6.81250i	−0.652519	−	0.652519i	−0.953599	+	0.301080i	$0.902653\pi$
$110$	−1.38728	−	0.274668i	−0.132272	−	0.0261886i
$111$	−9.67269			−0.918091
$112$	−9.56128	+	9.62942i	−0.903456	+	0.909895i
$113$	7.12346			0.670119			0.335059	−	0.942197i	$-0.391244\pi$
$113$	7.12346			0.670119			0.335059	+	0.942197i	$0.391244\pi$
$114$	−0.594276	−	0.117661i	−0.0556591	−	0.0110199i
$115$	−3.40469	−	3.40469i	−0.317489	−	0.317489i
$116$	5.69612	+	13.6829i	0.528872	+	1.27043i
$117$	3.05947	−	3.05947i	0.282848	−	0.282848i
$118$	−0.752857	−	1.12457i	−0.0693061	−	0.103525i
$119$			13.7961i			1.26468i
$120$	3.96189	−	5.96370i	0.361669	−	0.544409i
$121$		−	1.00000i		−	0.0909091i
$122$	11.0481	−	7.39631i	1.00025	−	0.669631i
$123$	−11.2766	+	11.2766i	−1.01678	+	1.01678i
$124$	15.9595	+	6.57745i	1.43320	+	0.590673i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	3.17540	−	16.0382i	0.282887	−	1.42880i
$127$	−6.78831			−0.602365			−0.301183	−	0.953566i	$-0.597381\pi$
$127$	−6.78831			−0.602365			−0.301183	+	0.953566i	$0.597381\pi$
$128$	11.0824	−	2.27611i	0.979554	−	0.201181i
$129$	−14.2639			−1.25587
$130$	−0.348736	+	1.76139i	−0.0305862	+	0.154484i
$131$	9.65484	+	9.65484i	0.843548	+	0.843548i	0.989318	−	0.145771i	$-0.0465662\pi$
$131$	9.65484	+	9.65484i	0.843548	+	0.843548i	−0.145771	+	0.989318i	$0.546566\pi$
$132$	4.68078	+	1.92911i	0.407409	+	0.167908i
$133$	0.405950	−	0.405950i	0.0352003	−	0.0352003i
$134$	13.5915	−	9.09903i	1.17413	−	0.786036i
$135$			1.03225i			0.0888424i
$136$	6.36480	−	9.58074i	0.545777	−	0.821541i
$137$			13.3507i			1.14063i	0.821426	+	0.570315i	$0.193179\pi$
$137$			13.3507i			1.14063i	−0.821426	+	0.570315i	$0.806821\pi$
$138$	9.58909	+	14.3235i	0.816277	+	1.21930i
$139$	−10.8083	+	10.8083i	−0.916752	+	0.916752i	−0.996792	−	0.0800400i	$-0.974495\pi$
$139$	−10.8083	+	10.8083i	−0.916752	+	0.916752i	0.0800400	+	0.996792i	$0.474495\pi$
$140$	2.60762	+	6.26388i	0.220385	+	0.529395i
$141$	22.4685	+	22.4685i	1.89219	+	1.89219i
$142$	16.3777	+	3.24261i	1.37438	+	0.272114i
$143$	−1.26967			−0.106175
$144$	−9.60439	+	9.67284i	−0.800366	+	0.806070i
$145$	7.41059			0.615416
$146$	−2.36301	−	0.467851i	−0.195564	−	0.0387196i
$147$	8.07083	+	8.07083i	0.665671	+	0.665671i
$148$	−7.05535	+	2.93711i	−0.579946	+	0.241429i
$149$	3.91034	−	3.91034i	0.320348	−	0.320348i	−0.528553	−	0.848900i	$-0.677265\pi$
$149$	3.91034	−	3.91034i	0.320348	−	0.320348i	0.848900	+	0.528553i	$0.177265\pi$
$150$	−1.99152	−	2.97480i	−0.162607	−	0.242891i
$151$		−	5.79057i		−	0.471230i	−0.971847	−	0.235615i	$-0.924290\pi$
$151$		−	5.79057i		−	0.471230i	0.971847	−	0.235615i	$-0.0757104\pi$
$152$	−0.469198	+	0.0946290i	−0.0380570	+	0.00767543i
$153$			13.8583i			1.12038i
$154$	−3.98678	+	2.66900i	−0.321264	+	0.215074i
$155$	6.10294	−	6.10294i	0.490200	−	0.490200i
$156$	2.44933	−	5.94302i	0.196103	−	0.475822i
$157$	−14.7237	−	14.7237i	−1.17508	−	1.17508i	−0.980983	−	0.194094i	$-0.937823\pi$
$157$	−14.7237	−	14.7237i	−1.17508	−	1.17508i	−0.194094	−	0.980983i	$-0.562177\pi$
$158$	2.91645	−	14.7303i	0.232020	−	1.17188i
$159$	6.56619			0.520733
$160$	1.07896	−	5.55300i	0.0852993	−	0.439003i
$161$	−16.3347			−1.28736
$162$	−2.09032	+	10.5577i	−0.164231	+	0.829493i
$163$	−4.04354	−	4.04354i	−0.316715	−	0.316715i	0.530789	−	0.847504i	$-0.321896\pi$
$163$	−4.04354	−	4.04354i	−0.316715	−	0.316715i	−0.847504	+	0.530789i	$0.821896\pi$
$164$	−4.80114	+	11.6494i	−0.374906	+	0.909668i
$165$	1.78994	−	1.78994i	0.139347	−	0.139347i
$166$	−1.65753	+	1.10966i	−0.128649	+	0.0861259i
$167$			5.84262i			0.452115i	0.974114	+	0.226058i	$0.0725838\pi$
$167$			5.84262i			0.452115i	−0.974114	+	0.226058i	$0.927416\pi$
$168$	−4.80206	−	23.8100i	−0.370487	−	1.83698i
$169$		−	11.3880i		−	0.875996i
$170$	−3.19939	−	4.77904i	−0.245382	−	0.366535i
$171$	0.407781	−	0.407781i	0.0311838	−	0.0311838i
$172$	−10.4042	+	4.33123i	−0.793316	+	0.330253i
$173$	3.41163	+	3.41163i	0.259381	+	0.259381i	0.824802	−	0.565421i	$-0.191286\pi$
$173$	3.41163	+	3.41163i	0.259381	+	0.259381i	−0.565421	+	0.824802i	$0.691286\pi$
$174$	−26.0239	−	5.15246i	−1.97287	−	0.390607i
$175$	3.39249			0.256448
$176$	3.99997	−	0.0142035i	0.301509	−	0.00107063i
$177$	2.42235			0.182075
$178$	9.48697	+	1.87832i	0.711078	+	0.140786i
$179$	4.46172	+	4.46172i	0.333485	+	0.333485i	0.853908	−	0.520424i	$-0.174226\pi$
$179$	4.46172	+	4.46172i	0.333485	+	0.333485i	−0.520424	+	0.853908i	$0.674226\pi$
$180$	2.61938	+	6.29213i	0.195237	+	0.468988i
$181$	14.3369	−	14.3369i	1.06565	−	1.06565i	0.0679649	−	0.997688i	$-0.478349\pi$
$181$	14.3369	−	14.3369i	1.06565	−	1.06565i	0.997688	−	0.0679649i	$-0.0216506\pi$
$182$	3.38874	+	5.06187i	0.251190	+	0.375211i
$183$			23.7979i			1.75919i
$184$	11.3437	+	7.53600i	0.836269	+	0.555561i
$185$			3.82114i			0.280936i
$186$	−25.6751	+	17.1885i	−1.88259	+	1.26032i
$187$	2.87556	−	2.87556i	0.210282	−	0.210282i
$188$	23.2113	+	9.56618i	1.69286	+	0.697686i
$189$	2.47623	+	2.47623i	0.180119	+	0.180119i
$190$	−0.0464812	+	0.234766i	−0.00337210	+	0.0170317i
$191$	1.46624			0.106094			0.0530468	−	0.998592i	$-0.483107\pi$
$191$	1.46624			0.106094			0.0530468	+	0.998592i	$0.483107\pi$
$192$	−7.64992	+	18.7504i	−0.552085	+	1.35319i
$193$	−11.9357			−0.859150			−0.429575	−	0.903031i	$-0.641337\pi$
$193$	−11.9357			−0.859150			−0.429575	+	0.903031i	$0.641337\pi$
$194$	−2.83479	+	14.3179i	−0.203526	+	1.02796i
$195$	−2.27263	−	2.27263i	−0.162746	−	0.162746i
$196$	8.33764	+	3.43623i	0.595545	+	0.245445i
$197$	4.02516	−	4.02516i	0.286781	−	0.286781i	−0.549025	−	0.835806i	$-0.685001\pi$
$197$	4.02516	−	4.02516i	0.286781	−	0.286781i	0.835806	+	0.549025i	$0.185001\pi$
$198$	−4.00475	+	2.68104i	−0.284606	+	0.190533i
$199$		−	26.1295i		−	1.85227i	−0.377193	−	0.926135i	$-0.623111\pi$
$199$		−	26.1295i		−	1.85227i	0.377193	−	0.926135i	$-0.376889\pi$
$200$	−2.35593	−	1.56512i	−0.166589	−	0.110671i
$201$			29.2765i			2.06500i
$202$	−11.3280	−	16.9210i	−0.797035	−	1.19056i
$203$	17.7769	−	17.7769i	1.24770	−	1.24770i
$204$	7.91257	+	19.0071i	0.553991	+	1.33076i
$205$	4.45478	+	4.45478i	0.311135	+	0.311135i
$206$	−20.7522	−	4.10872i	−1.44588	−	0.286268i
$207$	−16.4084			−1.14046
$208$	−0.0180337	−	5.07863i	−0.00125041	−	0.352140i
$209$	−0.169227			−0.0117057
$210$	−11.9135	−	2.35874i	−0.822107	−	0.162769i
$211$	−16.2504	−	16.2504i	−1.11873	−	1.11873i	−0.991928	−	0.126799i	$-0.959530\pi$
$211$	−16.2504	−	16.2504i	−1.11873	−	1.11873i	−0.126799	−	0.991928i	$-0.540470\pi$
$212$	4.78944	−	1.99382i	0.328940	−	0.136936i
$213$	−21.1313	+	21.1313i	−1.44789	+	1.44789i
$214$	8.70859	+	13.0083i	0.595307	+	0.889230i
$215$			5.63488i			0.384296i
$216$	−0.577221	−	2.86203i	−0.0392749	−	0.194737i
$217$		−	29.2801i		−	1.98766i
$218$	11.3221	−	7.57970i	0.766826	−	0.513362i
$219$	3.04887	−	3.04887i	0.206023	−	0.206023i
$220$	0.762085	−	1.84912i	0.0513798	−	0.124667i
$221$	−3.65099	−	3.65099i	−0.245592	−	0.245592i
$222$	2.65678	−	13.4188i	0.178311	−	0.900609i
$223$	−21.9127			−1.46738			−0.733690	−	0.679484i	$-0.762204\pi$
$223$	−21.9127			−1.46738			−0.733690	+	0.679484i	$0.762204\pi$
$224$	−10.7326	−	15.9091i	−0.717100	−	1.06297i
$225$	3.40779			0.227186
$226$	−1.95659	+	9.88226i	−0.130150	+	0.657358i
$227$	12.8009	+	12.8009i	0.849626	+	0.849626i	0.990086	−	0.140460i	$-0.0448583\pi$
$227$	12.8009	+	12.8009i	0.849626	+	0.849626i	−0.140460	+	0.990086i	$0.544858\pi$
$228$	0.326457	−	0.792113i	0.0216202	−	0.0524589i
$229$	1.10535	−	1.10535i	0.0730437	−	0.0730437i	−0.669641	−	0.742685i	$-0.733552\pi$
$229$	1.10535	−	1.10535i	0.0730437	−	0.0730437i	0.742685	+	0.669641i	$0.233552\pi$
$230$	5.65844	−	3.78812i	0.373106	−	0.249781i
$231$		−	8.58762i		−	0.565024i
$232$	−20.5466	+	4.14389i	−1.34895	+	0.272060i
$233$		−	4.86768i		−	0.318892i	−0.987207	−	0.159446i	$-0.949029\pi$
$233$		−	4.86768i		−	0.318892i	0.987207	−	0.159446i	$-0.0509708\pi$
$234$	3.40402	+	5.08470i	0.222528	+	0.332397i
$235$	8.87606	−	8.87606i	0.579010	−	0.579010i
$236$	1.76688	−	0.735544i	0.115014	−	0.0478798i
$237$	19.0058	+	19.0058i	1.23456	+	1.23456i
$238$	−19.1391	−	3.78934i	−1.24060	−	0.245626i
$239$	4.88568			0.316029			0.158014	−	0.987437i	$-0.449491\pi$
$239$	4.88568			0.316029			0.158014	+	0.987437i	$0.449491\pi$
$240$	7.18515	+	7.13430i	0.463799	+	0.460517i
$241$	−12.3515			−0.795632			−0.397816	−	0.917465i	$-0.630232\pi$
$241$	−12.3515			−0.795632			−0.397816	+	0.917465i	$0.630232\pi$
$242$	1.38728	+	0.274668i	0.0891780	+	0.0176563i
$243$	−15.8118	−	15.8118i	−1.01433	−	1.01433i
$244$	7.22622	+	17.3584i	0.462612	+	1.11126i
$245$	3.18834	−	3.18834i	0.203695	−	0.203695i
$246$	−12.5466	−	18.7412i	−0.799941	−	1.19490i
$247$			0.214861i			0.0136713i
$248$	−13.5083	+	20.3337i	−0.857781	+	1.29119i
$249$		−	3.57036i		−	0.226262i
$250$	−1.17518	+	0.786739i	−0.0743248	+	0.0497577i
$251$	0.400460	−	0.400460i	0.0252768	−	0.0252768i	−0.694355	−	0.719632i	$-0.744310\pi$
$251$	0.400460	−	0.400460i	0.0252768	−	0.0252768i	0.719632	+	0.694355i	$0.244310\pi$
$252$	21.3774	+	8.81038i	1.34665	+	0.555001i
$253$	3.40469	+	3.40469i	0.214051	+	0.214051i
$254$	1.86453	−	9.41732i	0.116991	−	0.590895i
$255$	10.2942			0.644645
$256$	0.113628	+	15.9996i	0.00710172	+	0.999975i
$257$	1.60941			0.100392			0.0501960	−	0.998739i	$-0.484015\pi$
$257$	1.60941			0.100392			0.0501960	+	0.998739i	$0.484015\pi$
$258$	3.91784	−	19.7881i	0.243914	−	1.23195i
$259$	9.16635	+	9.16635i	0.569570	+	0.569570i
$260$	−2.34776	−	0.967593i	−0.145602	−	0.0600076i
$261$	17.8571	−	17.8571i	1.10533	−	1.10533i
$262$	−16.0459	+	10.7421i	−0.991318	+	0.663651i
$263$		−	21.0069i		−	1.29534i	−0.761922	−	0.647669i	$-0.775744\pi$
$263$		−	21.0069i		−	1.29534i	0.761922	−	0.647669i	$-0.224256\pi$
$264$	−3.96189	+	5.96370i	−0.243837	+	0.367041i
$265$		−	2.59394i		−	0.159344i
$266$	0.451667	+	0.674670i	0.0276935	+	0.0413666i
$267$	−12.2406	+	12.2406i	−0.749110	+	0.749110i
$268$	8.88978	+	21.3545i	0.543030	+	1.30443i
$269$	11.8083	+	11.8083i	0.719965	+	0.719965i	0.968598	−	0.248633i	$-0.0799813\pi$
$269$	11.8083	+	11.8083i	0.719965	+	0.719965i	−0.248633	+	0.968598i	$0.579981\pi$
$270$	−1.43203	−	0.283527i	−0.0871506	−	0.0172549i
$271$	−20.6840			−1.25646			−0.628232	−	0.778026i	$-0.716221\pi$
$271$	−20.6840			−1.25646			−0.628232	+	0.778026i	$0.716221\pi$
$272$	11.5430	+	11.4613i	0.699897	+	0.694944i
$273$	−10.9034			−0.659904
$274$	−18.5213	−	3.66702i	−1.11891	−	0.221533i
$275$	−0.707107	−	0.707107i	−0.0426401	−	0.0426401i
$276$	−22.5046	+	9.36857i	−1.35462	+	0.563922i
$277$	−7.70390	+	7.70390i	−0.462883	+	0.462883i	−0.899599	−	0.436717i	$-0.856141\pi$
$277$	−7.70390	+	7.70390i	−0.462883	+	0.462883i	0.436717	+	0.899599i	$0.356141\pi$
$278$	−12.0255	−	17.9629i	−0.721244	−	1.07735i
$279$		−	29.4121i		−	1.76086i
$280$	−9.40602	+	1.89703i	−0.562117	+	0.113369i
$281$			24.7971i			1.47927i	0.673009	+	0.739634i	$0.265001\pi$
$281$			24.7971i			1.47927i	−0.673009	+	0.739634i	$0.734999\pi$
$282$	−37.3416	+	24.9988i	−2.22366	+	1.48866i
$283$	6.05837	−	6.05837i	0.360133	−	0.360133i	−0.503729	−	0.863862i	$-0.668039\pi$
$283$	6.05837	−	6.05837i	0.360133	−	0.360133i	0.863862	+	0.503729i	$0.168039\pi$
$284$	−8.99684	+	21.8298i	−0.533864	+	1.29536i
$285$	−0.302906	−	0.302906i	−0.0179426	−	0.0179426i
$286$	0.348736	−	1.76139i	0.0206212	−	0.104153i
$287$	21.3727			1.26159
$288$	−10.7810	−	15.9808i	−0.635274	−	0.941680i
$289$	−0.462349			−0.0271970
$290$	−2.03545	+	10.2806i	−0.119526	+	0.603697i
$291$	−18.4736	−	18.4736i	−1.08294	−	1.08294i
$292$	1.29808	−	3.14966i	0.0759646	−	0.184320i
$293$	−6.47489	+	6.47489i	−0.378267	+	0.378267i	−0.870477	−	0.492209i	$-0.836189\pi$
$293$	−6.47489	+	6.47489i	−0.378267	+	0.378267i	0.492209	+	0.870477i	$0.336189\pi$
$294$	−13.4133	+	8.97973i	−0.782281	+	0.523709i
$295$		−	0.956934i		−	0.0557149i
$296$	−2.13672	−	10.5945i	−0.124195	−	0.615793i
$297$		−	1.03225i		−	0.0598975i
$298$	4.35071	+	6.49880i	0.252030	+	0.376465i
$299$	4.32282	−	4.32282i	0.249995	−	0.249995i
$300$	4.67390	−	1.94572i	0.269848	−	0.112336i
$301$	13.5173	+	13.5173i	0.779122	+	0.779122i
$302$	8.03316	+	1.59048i	0.462257	+	0.0915220i
$303$	36.4483			2.09390
$304$	−0.00240362	−	0.676903i	−0.000137857	−	0.0388230i
$305$	9.40124			0.538313
$306$	−19.2254	−	3.80643i	−1.09904	−	0.217599i
$307$	2.48712	+	2.48712i	0.141947	+	0.141947i	0.774510	−	0.632562i	$-0.217997\pi$
$307$	2.48712	+	2.48712i	0.141947	+	0.141947i	−0.632562	+	0.774510i	$0.717997\pi$
$308$	−2.60762	−	6.26388i	−0.148583	−	0.356918i
$309$	26.7755	−	26.7755i	1.52321	−	1.52321i
$310$	6.79023	+	10.1428i	0.385659	+	0.576072i
$311$			24.3497i			1.38075i	0.723453	+	0.690374i	$0.242554\pi$
$311$			24.3497i			1.38075i	−0.723453	+	0.690374i	$0.757446\pi$
$312$	7.57191	+	5.03027i	0.428675	+	0.284783i
$313$			25.9119i			1.46463i	0.680968	+	0.732313i	$0.261559\pi$
$313$			25.9119i			1.46463i	−0.680968	+	0.732313i	$0.738441\pi$
$314$	24.4700	−	16.3818i	1.38092	−	0.924478i
$315$	8.17478	−	8.17478i	0.460597	−	0.460597i
$316$	19.6341	+	8.09189i	1.10450	+	0.455204i
$317$	−1.19826	−	1.19826i	−0.0673009	−	0.0673009i	0.672655	−	0.739956i	$-0.265154\pi$
$317$	−1.19826	−	1.19826i	−0.0673009	−	0.0673009i	−0.739956	+	0.672655i	$0.765154\pi$
$318$	−1.80352	+	9.10917i	−0.101136	+	0.510817i
$319$	−7.41059			−0.414914
$320$	7.40724	+	3.02206i	0.414077	+	0.168938i
$321$	−28.0202			−1.56394
$322$	4.48662	−	22.6609i	0.250030	−	1.26284i
$323$	−0.486621	−	0.486621i	−0.0270763	−	0.0270763i
$324$	−14.0724	−	5.79973i	−0.781801	−	0.322207i
$325$	−0.897789	+	0.897789i	−0.0498004	+	0.0498004i
$326$	6.72017	−	4.49891i	0.372196	−	0.249172i
$327$			24.3880i			1.34866i
$328$	−14.8424	−	9.86027i	−0.819532	−	0.544442i
$329$		−	42.5847i		−	2.34777i
$330$	1.99152	+	2.97480i	0.109630	+	0.163757i
$331$	5.16893	−	5.16893i	0.284110	−	0.284110i	−0.550636	−	0.834746i	$-0.685615\pi$
$331$	5.16893	−	5.16893i	0.284110	−	0.284110i	0.834746	+	0.550636i	$0.185615\pi$
$332$	−1.08414	−	2.60425i	−0.0594997	−	0.142927i
$333$	9.20769	+	9.20769i	0.504578	+	0.504578i
$334$	−8.10537	−	1.60478i	−0.443506	−	0.0878097i
$335$	11.5655			0.631891
$336$	34.3502	−	0.121975i	1.87396	−	0.00665426i
$337$	2.42702			0.132208			0.0661040	−	0.997813i	$-0.478943\pi$
$337$	2.42702			0.132208			0.0661040	+	0.997813i	$0.478943\pi$
$338$	15.7983	+	3.12791i	0.859316	+	0.170136i
$339$	−12.7506	−	12.7506i	−0.692516	−	0.692516i
$340$	7.50865	−	3.12582i	0.407214	−	0.169521i
$341$	−6.10294	+	6.10294i	−0.330493	+	0.330493i
$342$	0.453703	+	0.677712i	0.0245335	+	0.0366465i
$343$			8.45074i			0.456297i
$344$	−3.15094	−	15.6233i	−0.169887	−	0.842351i
$345$			12.1884i			0.656202i
$346$	−5.66996	+	3.79583i	−0.304819	+	0.204065i
$347$	−4.40503	+	4.40503i	−0.236474	+	0.236474i	−0.815389	−	0.578914i	$-0.803477\pi$
$347$	−4.40503	+	4.40503i	−0.236474	+	0.236474i	0.578914	+	0.815389i	$0.303477\pi$
$348$	14.2959	−	34.6873i	0.766339	−	1.85944i
$349$	2.03183	+	2.03183i	0.108761	+	0.108761i	0.759393	−	0.650632i	$-0.225496\pi$
$349$	2.03183	+	2.03183i	0.108761	+	0.108761i	−0.650632	+	0.759393i	$0.725496\pi$
$350$	−0.931808	+	4.70635i	−0.0498072	+	0.251565i
$351$	−1.31062			−0.0699556
$352$	−1.07896	+	5.55300i	−0.0575088	+	0.295976i
$353$	−28.3441			−1.50860			−0.754302	−	0.656527i	$-0.772025\pi$
$353$	−28.3441			−1.50860			−0.754302	+	0.656527i	$0.772025\pi$
$354$	−0.665341	+	3.36048i	−0.0353625	+	0.178608i
$355$	8.34779	+	8.34779i	0.443055	+	0.443055i
$356$	−5.21153	+	12.6452i	−0.276211	+	0.670194i
$357$	24.6942	−	24.6942i	1.30695	−	1.30695i
$358$	−7.41517	+	4.96418i	−0.391904	+	0.262365i
$359$		−	12.8004i		−	0.675577i	−0.941222	−	0.337789i	$-0.890321\pi$
$359$		−	12.8004i		−	0.675577i	0.941222	−	0.337789i	$-0.109679\pi$
$360$	−9.44843	+	1.90558i	−0.497976	+	0.100433i
$361$		−	18.9714i		−	0.998493i
$362$	15.9515	+	23.8272i	0.838390	+	1.25233i
$363$	−1.78994	+	1.78994i	−0.0939476	+	0.0939476i
$364$	−7.95304	+	3.31081i	−0.416852	+	0.173534i
$365$	−1.20444	−	1.20444i	−0.0630432	−	0.0630432i
$366$	−33.0145	−	6.53653i	−1.72569	−	0.341670i
$367$	33.7794			1.76327			0.881636	−	0.471931i	$-0.156443\pi$
$367$	33.7794			1.76327			0.881636	+	0.471931i	$0.156443\pi$
$368$	−13.5703	+	13.6670i	−0.707402	+	0.712444i
$369$	21.4691			1.11764
$370$	−5.30101	−	1.04955i	−0.275586	−	0.0545633i
$371$	−6.22247	−	6.22247i	−0.323055	−	0.323055i
$372$	−16.7933	−	40.3398i	−0.870690	−	2.09152i
$373$	−6.80264	+	6.80264i	−0.352227	+	0.352227i	−0.860938	−	0.508710i	$-0.830122\pi$
$373$	−6.80264	+	6.80264i	−0.352227	+	0.352227i	0.508710	+	0.860938i	$0.330122\pi$
$374$	3.19939	+	4.77904i	0.165437	+	0.247118i
$375$		−	2.53136i		−	0.130719i
$376$	−19.6464	+	29.5731i	−1.01319	+	1.52512i
$377$			9.40897i			0.484587i
$378$	−4.11537	+	2.75509i	−0.211672	+	0.141707i
$379$	−6.41132	+	6.41132i	−0.329327	+	0.329327i	−0.852331	−	0.523003i	$-0.824811\pi$
$379$	−6.41132	+	6.41132i	−0.329327	+	0.329327i	0.523003	+	0.852331i	$0.324811\pi$
$380$	−0.312920	−	0.128965i	−0.0160524	−	0.00661577i
$381$	12.1507	+	12.1507i	0.622499	+	0.622499i
$382$	−0.402730	+	2.03410i	−0.0206055	+	0.104073i
$383$	26.9141			1.37525			0.687623	−	0.726068i	$-0.258654\pi$
$383$	26.9141			1.37525			0.687623	+	0.726068i	$0.258654\pi$
$384$	−23.9109	−	15.7627i	−1.22020	−	0.804389i
$385$	−3.39249			−0.172897
$386$	3.27835	−	16.5582i	0.166864	−	0.842790i
$387$	13.5782	+	13.5782i	0.690219	+	0.690219i
$388$	−19.0843	−	7.86532i	−0.968860	−	0.399301i
$389$	−18.1864	+	18.1864i	−0.922086	+	0.922086i	−0.997177	−	0.0750908i	$-0.976075\pi$
$389$	−18.1864	+	18.1864i	−0.922086	+	0.922086i	0.0750908	+	0.997177i	$0.476075\pi$
$390$	3.77700	−	2.52856i	0.191256	−	0.128039i
$391$			19.5808i			0.990242i
$392$	−7.05711	+	10.6228i	−0.356438	+	0.536535i
$393$		−	34.5632i		−	1.74348i
$394$	4.47846	+	6.68963i	0.225622	+	0.337019i
$395$	7.50812	−	7.50812i	0.377775	−	0.377775i
$396$	−2.61938	−	6.29213i	−0.131629	−	0.316191i
$397$	−21.7821	−	21.7821i	−1.09321	−	1.09321i	−0.995183	−	0.0980311i	$-0.968746\pi$
$397$	−21.7821	−	21.7821i	−1.09321	−	1.09321i	−0.0980311	−	0.995183i	$-0.531254\pi$
$398$	36.2490	+	7.17693i	1.81700	+	0.359747i
$399$	−1.45325			−0.0727537
$400$	2.81837	−	2.83845i	0.140918	−	0.141923i
$401$	−2.79559			−0.139605			−0.0698026	−	0.997561i	$-0.522237\pi$
$401$	−2.79559			−0.139605			−0.0698026	+	0.997561i	$0.522237\pi$
$402$	−40.6148	−	8.04131i	−2.02568	−	0.401064i
$403$	7.74869	+	7.74869i	0.385990	+	0.385990i
$404$	26.5857	−	11.0675i	1.32269	−	0.550628i
$405$	−5.38133	+	5.38133i	−0.267400	+	0.267400i
$406$	19.7789	+	29.5444i	0.981610	+	1.46626i
$407$		−	3.82114i		−	0.189407i
$408$	−28.5416	+	5.75634i	−1.41302	+	0.284981i
$409$			11.8689i			0.586879i	0.955978	+	0.293440i	$0.0948000\pi$
$409$			11.8689i			0.586879i	−0.955978	+	0.293440i	$0.905200\pi$
$410$	−7.40362	+	4.95646i	−0.365639	+	0.244782i
$411$	23.8970	−	23.8970i	1.17875	−	1.17875i
$412$	11.3999	−	27.6607i	0.561635	−	1.36274i
$413$	−2.29554	−	2.29554i	−0.112956	−	0.112956i
$414$	4.50685	−	22.7631i	0.221500	−	1.11874i
$415$	−1.41045			−0.0692363
$416$	7.05045	+	1.36992i	0.345677	+	0.0671658i
$417$	38.6926			1.89479
$418$	0.0464812	−	0.234766i	0.00227347	−	0.0114828i
$419$	−20.8790	−	20.8790i	−1.02001	−	1.02001i	−0.999796	−	0.0202108i	$-0.993566\pi$
$419$	−20.8790	−	20.8790i	−1.02001	−	1.02001i	−0.0202108	−	0.999796i	$-0.506434\pi$
$420$	6.54449	−	15.8795i	0.319339	−	0.774840i
$421$	19.6768	−	19.6768i	0.958987	−	0.958987i	−0.0402046	−	0.999191i	$-0.512801\pi$
$421$	19.6768	−	19.6768i	0.958987	−	0.958987i	0.999191	+	0.0402046i	$0.0128010\pi$
$422$	27.0075	−	18.0805i	1.31470	−	0.880146i
$423$		−	42.7767i		−	2.07988i
$424$	1.45049	+	7.19195i	0.0704420	+	0.349272i
$425$		−	4.06665i		−	0.197262i
$426$	−23.5110	−	35.1192i	−1.13911	−	1.70153i
$427$	22.5522	−	22.5522i	1.09138	−	1.09138i
$428$	−20.4382	+	8.50833i	−0.987918	+	0.411265i
$429$	2.27263	+	2.27263i	0.109723	+	0.109723i
$430$	−7.81719	−	1.54772i	−0.376978	−	0.0746378i
$431$	35.9349			1.73092			0.865461	−	0.500977i	$-0.167026\pi$
$431$	35.9349			1.73092			0.865461	+	0.500977i	$0.167026\pi$
$432$	4.12899	−	0.0146617i	0.198656	−	0.000705410i
$433$	−20.4228			−0.981458			−0.490729	−	0.871312i	$-0.663269\pi$
$433$	−20.4228			−0.981458			−0.490729	+	0.871312i	$0.663269\pi$
$434$	40.6199	+	8.04231i	1.94982	+	0.386043i
$435$	−13.2645	−	13.2645i	−0.635986	−	0.635986i
$436$	7.40539	+	17.7888i	0.354654	+	0.851929i
$437$	0.576165	−	0.576165i	0.0275617	−	0.0275617i
$438$	3.39222	+	5.06707i	0.162086	+	0.242114i
$439$		−	18.6377i		−	0.889529i	−0.895648	−	0.444764i	$-0.853287\pi$
$439$		−	18.6377i		−	0.889529i	0.895648	−	0.444764i	$-0.146713\pi$
$440$	2.35593	+	1.56512i	0.112314	+	0.0746142i
$441$		−	15.3657i		−	0.731698i
$442$	6.06778	−	4.06216i	0.288615	−	0.193217i
$443$	−12.8535	+	12.8535i	−0.610687	+	0.610687i	−0.943125	−	0.332438i	$-0.892129\pi$
$443$	−12.8535	+	12.8535i	−0.610687	+	0.610687i	0.332438	+	0.943125i	$0.392129\pi$
$444$	17.8859	+	7.37141i	0.848828	+	0.349832i
$445$	4.83556	+	4.83556i	0.229228	+	0.229228i
$446$	6.01871	−	30.3991i	0.284994	−	1.43944i
$447$	−13.9986			−0.662110
$448$	25.0183	−	10.5194i	1.18201	−	0.496995i
$449$	9.42682			0.444879			0.222440	−	0.974946i	$-0.428598\pi$
$449$	9.42682			0.444879			0.222440	+	0.974946i	$0.428598\pi$
$450$	−0.936010	+	4.72757i	−0.0441239	+	0.222860i
$451$	−4.45478	−	4.45478i	−0.209767	−	0.209767i
$452$	−13.1721	−	5.42868i	−0.619563	−	0.255344i
$453$	−10.3648	+	10.3648i	−0.486980	+	0.486980i
$454$	−21.2745	+	14.2425i	−0.998461	+	0.668433i
$455$			4.30733i			0.201931i
$456$	1.00922	+	0.670457i	0.0472610	+	0.0313970i
$457$		−	28.0958i		−	1.31427i	−0.753774	−	0.657134i	$-0.771769\pi$
$457$		−	28.0958i		−	1.31427i	0.753774	−	0.657134i	$-0.228231\pi$
$458$	1.22983	+	1.83704i	0.0574663	+	0.0858393i
$459$	2.96831	−	2.96831i	0.138549	−	0.138549i
$460$	3.70100	+	8.89033i	0.172560	+	0.414514i
$461$	0.612455	+	0.612455i	0.0285249	+	0.0285249i	0.721225	−	0.692700i	$-0.243579\pi$
$461$	0.612455	+	0.612455i	0.0285249	+	0.0285249i	−0.692700	+	0.721225i	$0.743579\pi$
$462$	11.9135	+	2.35874i	0.554264	+	0.109739i
$463$	22.4099			1.04148			0.520739	−	0.853716i	$-0.325657\pi$
$463$	22.4099			1.04148			0.520739	+	0.853716i	$0.325657\pi$
$464$	−0.105257	−	29.6422i	−0.00488642	−	1.37610i
$465$	−21.8478			−1.01317
$466$	6.75285	+	1.33699i	0.312820	+	0.0619351i
$467$	−20.9739	−	20.9739i	−0.970556	−	0.970556i	0.0290232	−	0.999579i	$-0.490760\pi$
$467$	−20.9739	−	20.9739i	−0.970556	−	0.970556i	−0.999579	+	0.0290232i	$0.990760\pi$
$468$	−7.98890	+	3.32574i	−0.369287	+	0.153732i
$469$	27.7439	−	27.7439i	1.28110	−	1.28110i
$470$	9.87565	+	14.7516i	0.455530	+	0.680440i
$471$			52.7090i			2.42870i
$472$	0.535103	+	2.65320i	0.0246301	+	0.122123i
$473$		−	5.63488i		−	0.259092i
$474$	−31.5867	+	21.1461i	−1.45082	+	0.971274i
$475$	−0.119661	+	0.119661i	−0.00549044	+	0.00549044i
$476$	10.5138	−	25.5105i	0.481898	−	1.16927i
$477$	−6.25053	−	6.25053i	−0.286192	−	0.286192i
$478$	−1.34194	+	6.77783i	−0.0613789	+	0.310011i
$479$	39.3433			1.79764			0.898821	−	0.438316i	$-0.144425\pi$
$479$	39.3433			1.79764			0.898821	+	0.438316i	$0.144425\pi$
$480$	−11.8708	+	8.00828i	−0.541827	+	0.365526i
$481$	−4.85157			−0.221213
$482$	3.39257	−	17.1351i	0.154527	−	0.780482i
$483$	29.2382	+	29.2382i	1.33038	+	1.33038i
$484$	−0.762085	+	1.84912i	−0.0346402	+	0.0840507i
$485$	−7.29790	+	7.29790i	−0.331381	+	0.331381i
$486$	26.2785	−	17.5925i	1.19202	−	0.798012i
$487$			18.7183i			0.848207i	0.905614	+	0.424104i	$0.139411\pi$
$487$			18.7183i			0.848207i	−0.905614	+	0.424104i	$0.860589\pi$
$488$	−26.0659	+	5.25703i	−1.17995	+	0.237974i
$489$			14.4754i			0.654601i
$490$	3.54739	+	5.29886i	0.160255	+	0.239378i
$491$	−22.6062	+	22.6062i	−1.02021	+	1.02021i	−0.0204134	+	0.999792i	$0.506498\pi$
$491$	−22.6062	+	22.6062i	−1.02021	+	1.02021i	−0.999792	+	0.0204134i	$0.993502\pi$
$492$	29.4456	−	12.2580i	1.32751	−	0.552636i
$493$	−21.3096	−	21.3096i	−0.959735	−	0.959735i
$494$	−0.298074	−	0.0590155i	−0.0134110	−	0.00265523i
$495$	−3.40779			−0.153169
$496$	−24.4983	−	24.3249i	−1.10001	−	1.09222i
$497$	40.0502			1.79650
$498$	4.95310	+	0.980663i	0.221954	+	0.0439445i
$499$	4.87372	+	4.87372i	0.218178	+	0.218178i	0.807730	−	0.589552i	$-0.200696\pi$
$499$	4.87372	+	4.87372i	0.218178	+	0.218178i	−0.589552	+	0.807730i	$0.700696\pi$
$500$	−0.768646	−	1.84640i	−0.0343749	−	0.0825734i
$501$	10.4579	−	10.4579i	0.467227	−	0.467227i
$502$	0.445559	+	0.665546i	0.0198863	+	0.0297048i
$503$			2.66169i			0.118679i	0.998238	+	0.0593395i	$0.0188994\pi$
$503$			2.66169i			0.118679i	−0.998238	+	0.0593395i	$0.981101\pi$
$504$	−18.0942	+	27.2366i	−0.805979	+	1.21321i
$505$		−	14.3987i		−	0.640733i
$506$	−5.65844	+	3.78812i	−0.251548	+	0.168402i
$507$	−20.3838	+	20.3838i	−0.905275	+	0.905275i
$508$	12.5524	+	5.17327i	0.556921	+	0.229527i
$509$	17.1949	+	17.1949i	0.762153	+	0.762153i	0.976711	−	0.214558i	$-0.0688312\pi$
$509$	17.1949	+	17.1949i	0.762153	+	0.762153i	−0.214558	+	0.976711i	$0.568831\pi$
$510$	−2.82748	+	14.2809i	−0.125203	+	0.632370i
$511$	−5.77854			−0.255627
$512$	−22.2272	−	4.23694i	−0.982313	−	0.187248i
$513$	−0.174685			−0.00771254
$514$	−0.442052	+	2.23270i	−0.0194981	+	0.0984803i
$515$	−10.5775	−	10.5775i	−0.466101	−	0.466101i
$516$	26.3756	+	10.8703i	1.16112	+	0.478539i
$517$	−8.87606	+	8.87606i	−0.390369	+	0.390369i
$518$	−15.2340	+	10.1986i	−0.669345	+	0.448102i
$519$		−	12.2132i		−	0.536101i
$520$	1.98718	−	2.99124i	0.0871436	−	0.131175i
$521$			42.6938i			1.87045i	0.354053	+	0.935225i	$0.384803\pi$
$521$			42.6938i			1.87045i	−0.354053	+	0.935225i	$0.615197\pi$
$522$	19.8681	+	29.6776i	0.869602	+	1.29895i
$523$	−28.7561	+	28.7561i	−1.25742	+	1.25742i	−0.305093	+	0.952323i	$0.598688\pi$
$523$	−28.7561	+	28.7561i	−1.25742	+	1.25742i	−0.952323	+	0.305093i	$0.901312\pi$
$524$	−10.4951	−	25.2107i	−0.458481	−	1.10134i
$525$	−6.07236	−	6.07236i	−0.265020	−	0.265020i
$526$	29.1425	+	5.76991i	1.27067	+	0.251580i
$527$	−35.0987			−1.52892
$528$	−7.18515	−	7.13430i	−0.312693	−	0.310481i
$529$	−0.183860			−0.00799390
$530$	3.59853	+	0.712471i	0.156310	+	0.0309478i
$531$	−2.30589	−	2.30589i	−0.100067	−	0.100067i
$532$	−1.06002	+	0.441280i	−0.0459576	+	0.0191319i
$533$	−5.65607	+	5.65607i	−0.244992	+	0.244992i
$534$	−13.6190	−	20.3432i	−0.589353	−	0.880337i
$535$			11.0692i			0.478565i
$536$	−32.0665	+	6.46725i	−1.38506	+	0.279343i
$537$		−	15.9725i		−	0.689262i
$538$	−19.6248	+	13.1381i	−0.846087	+	0.566424i
$539$	−3.18834	+	3.18834i	−0.137331	+	0.137331i
$540$	0.786666	−	1.90876i	0.0338527	−	0.0821399i
$541$	24.3289	+	24.3289i	1.04598	+	1.04598i	0.998891	+	0.0470923i	$0.0149955\pi$
$541$	24.3289	+	24.3289i	1.04598	+	1.04598i	0.0470923	+	0.998891i	$0.485004\pi$
$542$	5.68123	−	28.6946i	0.244030	−	1.23254i
$543$	−51.3244			−2.20254
$544$	−19.0706	+	12.8654i	−0.817645	+	0.551598i
$545$	9.63433			0.412689
$546$	2.99481	−	15.1261i	0.128166	−	0.647338i
$547$	29.7085	+	29.7085i	1.27024	+	1.27024i	0.945959	+	0.324285i	$0.105124\pi$
$547$	29.7085	+	29.7085i	1.27024	+	1.27024i	0.324285	+	0.945959i	$0.394876\pi$
$548$	10.1744	−	24.6870i	0.434629	−	1.05458i
$549$	22.6539	−	22.6539i	0.966844	−	0.966844i
$550$	1.17518	−	0.786739i	0.0501097	−	0.0335466i
$551$			1.25407i			0.0534252i
$552$	−6.81557	−	33.7936i	−0.290090	−	1.43835i
$553$		−	36.0218i		−	1.53180i
$554$	−8.57149	−	12.8035i	−0.364168	−	0.543969i
$555$	6.83962	−	6.83962i	0.290326	−	0.290326i
$556$	28.2227	−	11.7490i	1.19691	−	0.498268i
$557$	−25.1749	−	25.1749i	−1.06669	−	1.06669i	−0.997611	−	0.0690818i	$-0.977993\pi$
$557$	−25.1749	−	25.1749i	−1.06669	−	1.06669i	−0.0690818	−	0.997611i	$-0.522007\pi$
$558$	40.8030	+	8.07857i	1.72733	+	0.341993i
$559$	−7.15442			−0.302600
$560$	−0.0481854	−	13.5699i	−0.00203620	−	0.573432i
$561$	−10.2942			−0.434620
$562$	−34.4006	−	6.81096i	−1.45110	−	0.287303i
$563$	−31.1401	−	31.1401i	−1.31240	−	1.31240i	−0.919642	−	0.392757i	$-0.871521\pi$
$563$	−31.1401	−	31.1401i	−1.31240	−	1.31240i	−0.392757	−	0.919642i	$-0.628479\pi$
$564$	−24.4239	−	58.6698i	−1.02843	−	2.47044i
$565$	−5.03705	+	5.03705i	−0.211910	+	0.211910i
$566$	6.74064	+	10.0687i	0.283330	+	0.423220i
$567$			25.8180i			1.08426i
$568$	−27.8130	−	18.4771i	−1.16701	−	0.775283i
$569$		−	35.1248i		−	1.47251i	−0.676705	−	0.736255i	$-0.736593\pi$
$569$		−	35.1248i		−	1.47251i	0.676705	−	0.736255i	$-0.263407\pi$
$570$	0.503416	−	0.337018i	0.0210858	−	0.0141161i
$571$	−26.6573	+	26.6573i	−1.11557	+	1.11557i	−0.123192	+	0.992383i	$0.539313\pi$
$571$	−26.6573	+	26.6573i	−1.11557	+	1.11557i	−0.992383	+	0.123192i	$0.960687\pi$
$572$	2.34776	+	0.967593i	0.0981646	+	0.0404571i
$573$	−2.62449	−	2.62449i	−0.109640	−	0.109640i
$574$	−5.87040	+	29.6500i	−0.245026	+	1.23757i
$575$	4.81496			0.200798
$576$	25.1311	−	10.5668i	1.04713	−	0.440285i
$577$	−7.74826			−0.322564			−0.161282	−	0.986908i	$-0.551563\pi$
$577$	−7.74826			−0.322564			−0.161282	+	0.986908i	$0.551563\pi$
$578$	0.126993	−	0.641410i	0.00528219	−	0.0266791i
$579$	21.3642	+	21.3642i	0.887866	+	0.887866i
$580$	−13.7030	−	5.64750i	−0.568988	−	0.234500i
$581$	−3.38346	+	3.38346i	−0.140370	+	0.140370i
$582$	30.7023	−	20.5541i	1.27265	−	0.851993i
$583$			2.59394i			0.107430i
$584$	4.01293	+	2.66592i	0.166056	+	0.110317i
$585$			4.32675i			0.178889i
$586$	−7.20407	−	10.7610i	−0.297597	−	0.444531i
$587$	8.04642	−	8.04642i	0.332111	−	0.332111i	−0.521276	−	0.853388i	$-0.674544\pi$
$587$	8.04642	−	8.04642i	0.332111	−	0.332111i	0.853388	+	0.521276i	$0.174544\pi$
$588$	−8.77323	−	21.0745i	−0.361802	−	0.869100i
$589$	1.03278	+	1.03278i	0.0425550	+	0.0425550i
$590$	1.32754	+	0.262839i	0.0546539	+	0.0108209i
$591$	−14.4096			−0.592732
$592$	15.2845	−	0.0542737i	0.628188	−	0.00223064i
$593$	−4.32327			−0.177535			−0.0887677	−	0.996052i	$-0.528293\pi$
$593$	−4.32327			−0.177535			−0.0887677	+	0.996052i	$0.528293\pi$
$594$	1.43203	+	0.283527i	0.0587569	+	0.0116333i
$595$	−9.75530	−	9.75530i	−0.399928	−	0.399928i
$596$	−10.2107	+	4.25066i	−0.418246	+	0.174114i
$597$	−46.7703	+	46.7703i	−1.91418	+	1.91418i
$598$	4.80964	+	7.18432i	0.196681	+	0.293789i
$599$			0.0166255i			0.000679299i	1.00000		0.000339650i	$0.000108114\pi$
$599$			0.0166255i			0.000679299i	−1.00000		0.000339650i	$0.999892\pi$
$600$	1.41550	+	7.01845i	0.0577875	+	0.286527i
$601$		−	13.8076i		−	0.563225i	−0.959528	−	0.281613i	$-0.909131\pi$
$601$		−	13.8076i		−	0.563225i	0.959528	−	0.281613i	$-0.0908693\pi$
$602$	−22.4650	+	15.0395i	−0.915607	+	0.612965i
$603$	27.8690	−	27.8690i	1.13491	−	1.13491i
$604$	−4.41291	+	10.7074i	−0.179559	+	0.435679i
$605$	0.707107	+	0.707107i	0.0287480	+	0.0287480i
$606$	−10.0112	+	50.5641i	−0.406676	+	2.05403i
$607$	−18.7916			−0.762727			−0.381364	−	0.924425i	$-0.624545\pi$
$607$	−18.7916			−0.762727			−0.381364	+	0.924425i	$0.624545\pi$
$608$	0.939717	+	0.182589i	0.0381105	+	0.00740496i
$609$	−63.6393			−2.57880
$610$	−2.58222	+	13.0422i	−0.104551	+	0.528063i
$611$	11.2696	+	11.2696i	0.455920	+	0.455920i
$612$	10.5612	−	25.6256i	0.426911	−	1.03585i
$613$	7.02769	−	7.02769i	0.283846	−	0.283846i	−0.550795	−	0.834641i	$-0.685675\pi$
$613$	7.02769	−	7.02769i	0.283846	−	0.283846i	0.834641	+	0.550795i	$0.185675\pi$
$614$	−4.13347	+	2.76721i	−0.166813	+	0.111676i
$615$		−	15.9476i		−	0.643069i
$616$	9.40602	−	1.89703i	0.378979	−	0.0764334i
$617$			10.3767i			0.417749i	0.977942	+	0.208874i	$0.0669800\pi$
$617$			10.3767i			0.417749i	−0.977942	+	0.208874i	$0.933020\pi$
$618$	29.7909	+	44.4996i	1.19837	+	1.79004i
$619$	12.8695	−	12.8695i	0.517267	−	0.517267i	−0.399476	−	0.916744i	$-0.630808\pi$
$619$	12.8695	−	12.8695i	0.517267	−	0.517267i	0.916744	+	0.399476i	$0.130808\pi$
$620$	−15.9360	+	6.63408i	−0.640005	+	0.266431i
$621$	3.51451	+	3.51451i	0.141032	+	0.141032i
$622$	−33.7800	−	6.68809i	−1.35446	−	0.268168i
$623$	23.1996			0.929472
$624$	−9.05817	+	9.12273i	−0.362617	+	0.365202i
$625$	−1.00000			−0.0400000
$626$	−35.9472	−	7.11717i	−1.43674	−	0.284459i
$627$	0.302906	+	0.302906i	0.0120969	+	0.0120969i
$628$	16.0051	+	38.4464i	0.638672	+	1.53418i
$629$	10.9879	−	10.9879i	0.438117	−	0.438117i
$630$	9.09539	+	13.5861i	0.362369	+	0.541283i
$631$			42.7775i			1.70294i	0.524400	+	0.851472i	$0.324290\pi$
$631$			42.7775i			1.70294i	−0.524400	+	0.851472i	$0.675710\pi$
$632$	−16.6186	+	25.0155i	−0.661052	+	0.995061i
$633$			58.1747i			2.31224i
$634$	1.99145	−	1.33320i	0.0790905	−	0.0529482i
$635$	4.80006	−	4.80006i	0.190485	−	0.190485i
$636$	−12.1416	−	5.00399i	−0.481447	−	0.198421i
$637$	4.04812	+	4.04812i	0.160392	+	0.160392i
$638$	2.03545	−	10.2806i	0.0805843	−	0.407013i
$639$	40.2308			1.59151
$640$	−6.22698	+	9.44588i	−0.246143	+	0.373381i
$641$	−2.90615			−0.114786			−0.0573930	−	0.998352i	$-0.518279\pi$
$641$	−2.90615			−0.114786			−0.0573930	+	0.998352i	$0.518279\pi$
$642$	7.69626	−	38.8720i	0.303747	−	1.53416i
$643$	15.8587	+	15.8587i	0.625407	+	0.625407i	0.946909	−	0.321502i	$-0.104188\pi$
$643$	15.8587	+	15.8587i	0.625407	+	0.625407i	−0.321502	+	0.946909i	$0.604188\pi$
$644$	30.2048	+	12.4484i	1.19023	+	0.490537i
$645$	10.0861	−	10.0861i	0.397141	−	0.397141i
$646$	0.808741	−	0.541423i	0.0318195	−	0.0213020i
$647$			12.1664i			0.478310i	0.970981	+	0.239155i	$0.0768704\pi$
$647$			12.1664i			0.478310i	−0.970981	+	0.239155i	$0.923130\pi$
$648$	11.9111	−	17.9294i	0.467913	−	0.704335i
$649$			0.956934i			0.0375629i
$650$	−0.998894	−	1.49208i	−0.0391799	−	0.0585243i
$651$	−52.4097	+	52.4097i	−2.05410	+	2.05410i
$652$	4.39545	+	10.5585i	0.172139	+	0.413503i
$653$	−5.10466	−	5.10466i	−0.199761	−	0.199761i	0.600137	−	0.799898i	$-0.295113\pi$
$653$	−5.10466	−	5.10466i	−0.199761	−	0.199761i	−0.799898	+	0.600137i	$0.795113\pi$
$654$	−33.8330	−	6.69859i	−1.32298	−	0.261936i
$655$	−13.6540			−0.533506
$656$	17.7557	−	17.8823i	0.693244	−	0.698185i
$657$	−5.80459			−0.226459
$658$	59.0771	+	11.6967i	2.30307	+	0.455983i
$659$	−6.77788	−	6.77788i	−0.264029	−	0.264029i	0.562660	−	0.826689i	$-0.309778\pi$
$659$	−6.77788	−	6.77788i	−0.264029	−	0.264029i	−0.826689	+	0.562660i	$0.809778\pi$
$660$	−4.67390	+	1.94572i	−0.181931	+	0.0757371i
$661$	10.7837	−	10.7837i	0.419437	−	0.419437i	−0.465573	−	0.885010i	$-0.654152\pi$
$661$	10.7837	−	10.7837i	0.419437	−	0.419437i	0.885010	+	0.465573i	$0.154152\pi$
$662$	5.75104	+	8.59052i	0.223520	+	0.333880i
$663$			13.0701i			0.507602i
$664$	3.91061	−	0.788702i	0.151761	−	0.0306076i
$665$			0.574100i			0.0222626i
$666$	−15.3027	+	10.2446i	−0.592969	+	0.396971i
$667$	25.2308	−	25.2308i	0.976940	−	0.976940i
$668$	4.45257	−	10.8037i	0.172275	−	0.418007i
$669$	39.2224	+	39.2224i	1.51643	+	1.51643i
$670$	−3.17667	+	16.0446i	−0.122726	+	0.619859i
$671$	−9.40124			−0.362931
$672$	−9.26570	+	47.6871i	−0.357432	+	1.83957i
$673$	−12.4404			−0.479541			−0.239770	−	0.970830i	$-0.577072\pi$
$673$	−12.4404			−0.479541			−0.239770	+	0.970830i	$0.577072\pi$
$674$	−0.666624	+	3.36696i	−0.0256774	+	0.129691i
$675$	−0.729914	−	0.729914i	−0.0280944	−	0.0280944i
$676$	−8.67859	+	21.0576i	−0.333792	+	0.809909i
$677$	−11.9239	+	11.9239i	−0.458273	+	0.458273i	−0.898088	−	0.439815i	$-0.855044\pi$
$677$	−11.9239	+	11.9239i	−0.458273	+	0.458273i	0.439815	+	0.898088i	$0.355044\pi$
$678$	21.1909	−	14.1865i	0.813830	−	0.544829i
$679$			35.0132i			1.34368i
$680$	2.27401	+	11.2752i	0.0872043	+	0.432384i
$681$		−	45.8258i		−	1.75605i
$682$	−6.79023	−	10.1428i	−0.260011	−	0.388388i
$683$	−2.81159	+	2.81159i	−0.107582	+	0.107582i	−0.758849	−	0.651267i	$-0.774238\pi$
$683$	−2.81159	+	2.81159i	−0.107582	+	0.107582i	0.651267	+	0.758849i	$0.274238\pi$
$684$	−1.06480	+	0.443270i	−0.0407135	+	0.0169488i
$685$	−9.44039	−	9.44039i	−0.360699	−	0.360699i
$686$	−11.7236	−	2.32115i	−0.447608	−	0.0886218i
$687$	−3.95703			−0.150970
$688$	22.5394	−	0.0800353i	0.859306	−	0.00305132i
$689$	3.29343			0.125470
$690$	−16.9088	−	3.34776i	−0.643706	−	0.127447i
$691$	13.9359	+	13.9359i	0.530145	+	0.530145i	0.920615	−	0.390471i	$-0.127688\pi$
$691$	13.9359	+	13.9359i	0.530145	+	0.530145i	−0.390471	+	0.920615i	$0.627688\pi$
$692$	−3.70854	−	8.90844i	−0.140977	−	0.338648i
$693$	−8.17478	+	8.17478i	−0.310534	+	0.310534i
$694$	−4.90111	−	7.32095i	−0.186044	−	0.277900i
$695$		−	15.2853i		−	0.579805i
$696$	44.1946	+	29.3599i	1.67519	+	1.11289i
$697$		−	25.6199i		−	0.970424i
$698$	−3.37680	+	2.26064i	−0.127814	+	0.0855667i
$699$	−8.71286	+	8.71286i	−0.329551	+	0.329551i
$700$	−6.27310	−	2.58537i	−0.237101	−	0.0977176i
$701$	24.8207	+	24.8207i	0.937463	+	0.937463i	0.998156	−	0.0606933i	$-0.0193312\pi$
$701$	24.8207	+	24.8207i	0.937463	+	0.937463i	−0.0606933	+	0.998156i	$0.519331\pi$
$702$	0.359985	−	1.81820i	0.0135868	−	0.0686235i
$703$	−0.646639			−0.0243885
$704$	−7.40724	−	3.02206i	−0.279171	−	0.113898i
$705$	−31.7753			−1.19673
$706$	7.78522	−	39.3213i	0.293000	−	1.47988i
$707$	−34.5403	−	34.5403i	−1.29902	−	1.29902i
$708$	−4.47919	−	1.84603i	−0.168338	−	0.0693782i
$709$	−27.8979	+	27.8979i	−1.04773	+	1.04773i	−0.0489238	+	0.998803i	$0.515579\pi$
$709$	−27.8979	+	27.8979i	−1.04773	+	1.04773i	−0.998803	+	0.0489238i	$0.984421\pi$
$710$	−13.8736	+	9.28789i	−0.520668	+	0.348568i
$711$		−	36.1842i		−	1.35701i
$712$	−16.1111	−	10.7031i	−0.603787	−	0.401116i
$713$		−	41.5573i		−	1.55633i
$714$	27.4751	+	41.0405i	1.02823	+	1.53590i
$715$	0.897789	−	0.897789i	0.0335754	−	0.0335754i
$716$	−4.85003	−	11.6504i	−0.181254	−	0.435398i
$717$	−8.74509	−	8.74509i	−0.326591	−	0.326591i
$718$	17.7577	+	3.51585i	0.662713	+	0.131210i
$719$	−33.7316			−1.25798			−0.628988	−	0.777415i	$-0.716530\pi$
$719$	−33.7316			−1.25798			−0.628988	+	0.777415i	$0.716530\pi$
$720$	−0.0484026	−	13.6311i	−0.00180386	−	0.508000i
$721$	−50.7478			−1.88995
$722$	26.3187	+	5.21083i	0.979480	+	0.193927i
$723$	22.1085	+	22.1085i	0.822225	+	0.822225i
$724$	−37.4365	+	15.5846i	−1.39132	+	0.579198i
$725$	−5.24008	+	5.24008i	−0.194612	+	0.194612i
$726$	−1.99152	−	2.97480i	−0.0739122	−	0.110405i
$727$		−	12.9260i		−	0.479397i	−0.970847	−	0.239699i	$-0.922951\pi$
$727$		−	12.9260i		−	0.479397i	0.970847	−	0.239699i	$-0.0770486\pi$
$728$	−2.40859	−	11.9425i	−0.0892683	−	0.442618i
$729$			33.7735i			1.25087i
$730$	2.00172	−	1.34008i	0.0740869	−	0.0495985i
$731$	16.2034	−	16.2034i	0.599306	−	0.599306i
$732$	18.1360	−	44.0051i	0.670327	−	1.62647i
$733$	0.986409	+	0.986409i	0.0364338	+	0.0364338i	0.725089	−	0.688655i	$-0.241799\pi$
$733$	0.986409	+	0.986409i	0.0364338	+	0.0364338i	−0.688655	+	0.725089i	$0.741799\pi$
$734$	−9.27812	+	46.8617i	−0.342462	+	1.72970i
$735$	−11.4139			−0.421007
$736$	−15.2327	−	22.5798i	−0.561486	−	0.832302i
$737$	−11.5655			−0.426021
$738$	−5.89687	+	29.7837i	−0.217067	+	1.09635i
$739$	8.10009	+	8.10009i	0.297967	+	0.297967i	0.840217	−	0.542250i	$-0.182428\pi$
$739$	8.10009	+	8.10009i	0.297967	+	0.297967i	−0.542250	+	0.840217i	$0.682428\pi$
$740$	2.91203	−	7.06573i	0.107049	−	0.259741i
$741$	0.384589	−	0.384589i	0.0141282	−	0.0141282i
$742$	10.3414	−	6.92322i	0.379647	−	0.254160i
$743$		−	30.5686i		−	1.12145i	−0.828001	−	0.560727i	$-0.810522\pi$
$743$		−	30.5686i		−	1.12145i	0.828001	−	0.560727i	$-0.189478\pi$
$744$	60.5753	−	12.2170i	2.22080	−	0.447896i
$745$			5.53006i			0.202606i
$746$	−7.56872	−	11.3057i	−0.277111	−	0.413930i
$747$	−3.39872	+	3.39872i	−0.124353	+	0.124353i
$748$	−7.50865	+	3.12582i	−0.274544	+	0.114291i
$749$	26.5535	+	26.5535i	0.970242	+	0.970242i
$750$	3.51172	+	0.695284i	0.128230	+	0.0253882i
$751$	46.1402			1.68368			0.841841	−	0.539726i	$-0.181472\pi$
$751$	46.1402			1.68368			0.841841	+	0.539726i	$0.181472\pi$
$752$	−35.6301	−	35.3780i	−1.29930	−	1.29010i
$753$	−1.43360			−0.0522434
$754$	−13.0529	−	2.58434i	−0.475359	−	0.0941162i
$755$	4.09455	+	4.09455i	0.149016	+	0.149016i
$756$	−2.69173	−	6.46593i	−0.0978974	−	0.235163i
$757$	−2.55058	+	2.55058i	−0.0927024	+	0.0927024i	−0.751937	−	0.659235i	$-0.770880\pi$
$757$	−2.55058	+	2.55058i	−0.0927024	+	0.0927024i	0.659235	+	0.751937i	$0.270880\pi$
$758$	−7.13333	−	10.6553i	−0.259094	−	0.387018i
$759$		−	12.1884i		−	0.442411i
$760$	0.264860	−	0.398686i	0.00960750	−	0.0144619i
$761$			37.4200i			1.35647i	0.734844	+	0.678236i	$0.237255\pi$
$761$			37.4200i			1.35647i	−0.734844	+	0.678236i	$0.762745\pi$
$762$	−20.1939	+	13.5191i	−0.731547	+	0.489744i
$763$	23.1113	−	23.1113i	0.836687	−	0.836687i
$764$	−2.71125	−	1.11740i	−0.0980896	−	0.0404262i
$765$	−9.79928	−	9.79928i	−0.354294	−	0.354294i
$766$	−7.39244	+	37.3375i	−0.267100	+	1.34906i
$767$	1.21499			0.0438706
$768$	28.4350	−	28.8417i	1.02606	−	1.04074i
$769$	27.3235			0.985309			0.492655	−	0.870225i	$-0.336027\pi$
$769$	27.3235			0.985309			0.492655	+	0.870225i	$0.336027\pi$
$770$	0.931808	−	4.70635i	0.0335800	−	0.169605i
$771$	−2.88074	−	2.88074i	−0.103747	−	0.103747i
$772$	22.0705	+	9.09601i	0.794333	+	0.327373i
$773$	21.8968	−	21.8968i	0.787573	−	0.787573i	−0.193523	−	0.981096i	$-0.561991\pi$
$773$	21.8968	−	21.8968i	0.787573	−	0.787573i	0.981096	+	0.193523i	$0.0619913\pi$
$774$	−22.5663	+	15.1073i	−0.811130	+	0.543022i
$775$			8.63086i			0.310030i
$776$	16.1533	−	24.3150i	0.579869	−	0.872859i
$777$		−	32.8145i		−	1.17721i
$778$	−20.2345	−	30.2249i	−0.725440	−	1.08361i
$779$	−0.753867	+	0.753867i	−0.0270101	+	0.0270101i
$780$	2.47041	+	5.93428i	0.0884550	+	0.212481i
$781$	−8.34779	−	8.34779i	−0.298707	−	0.298707i
$782$	−27.1641	−	5.37821i	−0.971386	−	0.192324i
$783$	−7.64962			−0.273375
$784$	−12.7985	−	12.7080i	−0.457091	−	0.453856i
$785$	20.8224			0.743184
$786$	47.9490	+	9.49341i	1.71028	+	0.338619i
$787$	−22.7236	−	22.7236i	−0.810008	−	0.810008i	0.174627	−	0.984635i	$-0.444128\pi$
$787$	−22.7236	−	22.7236i	−0.810008	−	0.810008i	−0.984635	+	0.174627i	$0.944128\pi$
$788$	−10.5105	+	4.37547i	−0.374421	+	0.155870i
$789$	−37.6011	+	37.6011i	−1.33863	+	1.33863i
$790$	8.35366	+	12.4781i	0.297210	+	0.443952i
$791$			24.1663i			0.859253i
$792$	9.44843	−	1.90558i	0.335735	−	0.0677119i
$793$			11.9364i			0.423875i
$794$	36.2009	−	24.2352i	1.28472	−	0.860074i
$795$	−4.64300	+	4.64300i	−0.164670	+	0.164670i
$796$	−19.9129	+	48.3164i	−0.705793	+	1.71253i
$797$	−11.9710	−	11.9710i	−0.424036	−	0.424036i	0.462555	−	0.886591i	$-0.346933\pi$
$797$	−11.9710	−	11.9710i	−0.424036	−	0.424036i	−0.886591	+	0.462555i	$0.846933\pi$
$798$	0.399162	−	2.01608i	0.0141302	−	0.0713683i
$799$	−51.0472			−1.80592
$800$	3.16363	+	4.68951i	0.111851	+	0.165799i
$801$	23.3042			0.823414
$802$	0.767860	−	3.87828i	0.0271141	−	0.136947i
$803$	1.20444	+	1.20444i	0.0425037	+	0.0425037i
$804$	22.3112	−	54.1355i	0.786854	−	1.90921i
$805$	11.5504	−	11.5504i	0.407098	−	0.407098i
$806$	−12.8780	+	8.62132i	−0.453607	+	0.303673i
$807$		−	42.2724i		−	1.48806i
$808$	8.05152	+	39.9218i	0.283251	+	1.40444i
$809$		−	6.91094i		−	0.242976i	−0.992593	−	0.121488i	$-0.961233\pi$
$809$		−	6.91094i		−	0.242976i	0.992593	−	0.121488i	$-0.0387665\pi$
$810$	−5.98736	−	8.94351i	−0.210374	−	0.314243i
$811$	1.35658	−	1.35658i	0.0476358	−	0.0476358i	−0.682888	−	0.730523i	$-0.739276\pi$
$811$	1.35658	−	1.35658i	0.0476358	−	0.0476358i	0.730523	+	0.682888i	$0.239276\pi$
$812$	−46.4191	+	19.3240i	−1.62899	+	0.678141i
$813$	37.0232	+	37.0232i	1.29846	+	1.29846i
$814$	5.30101	+	1.04955i	0.185800	+	0.0367865i
$815$	5.71843			0.200308
$816$	−0.146213	−	41.1764i	−0.00511850	−	1.44146i
$817$	−0.953573			−0.0333613
$818$	−16.4655	−	3.26001i	−0.575704	−	0.113983i
$819$	10.3792	+	10.3792i	0.362680	+	0.362680i
$820$	−4.84247	−	11.6323i	−0.169107	−	0.406218i
$821$	0.671319	−	0.671319i	0.0234292	−	0.0234292i	−0.695295	−	0.718724i	$-0.744726\pi$
$821$	0.671319	−	0.671319i	0.0234292	−	0.0234292i	0.718724	+	0.695295i	$0.244726\pi$
$822$	26.5882	+	39.7157i	0.927371	+	1.38525i
$823$		−	30.7120i		−	1.07055i	−0.844677	−	0.535277i	$-0.820207\pi$
$823$		−	30.7120i		−	1.07055i	0.844677	−	0.535277i	$-0.179793\pi$
$824$	35.2420	+	23.4125i	1.22771	+	0.815611i
$825$			2.53136i			0.0881307i
$826$	3.81508	−	2.55406i	0.132744	−	0.0888671i
$827$	17.6149	−	17.6149i	0.612529	−	0.612529i	−0.331075	−	0.943604i	$-0.607411\pi$
$827$	17.6149	−	17.6149i	0.612529	−	0.612529i	0.943604	+	0.331075i	$0.107411\pi$
$828$	30.3410	+	12.5046i	1.05442	+	0.434564i
$829$	2.21182	+	2.21182i	0.0768197	+	0.0768197i	0.744473	−	0.667653i	$-0.232701\pi$
$829$	2.21182	+	2.21182i	0.0768197	+	0.0768197i	−0.667653	+	0.744473i	$0.732701\pi$
$830$	0.387405	−	1.95669i	0.0134470	−	0.0679179i
$831$	27.5791			0.956708
$832$	−3.83700	+	9.40471i	−0.133024	+	0.326050i
$833$	−18.3365			−0.635321
$834$	−10.6276	+	53.6777i	−0.368004	+	1.85871i
$835$	−4.13135	−	4.13135i	−0.142971	−	0.142971i
$836$	0.312920	+	0.128965i	0.0108226	+	0.00446035i
$837$	−6.29979	+	6.29979i	−0.217753	+	0.217753i
$838$	34.6999	−	23.2303i	1.19869	−	0.802478i
$839$			12.2721i			0.423679i	0.977304	+	0.211840i	$0.0679454\pi$
$839$			12.2721i			0.423679i	−0.977304	+	0.211840i	$0.932055\pi$
$840$	20.2318	+	13.4407i	0.698063	+	0.463747i
$841$			25.9169i			0.893685i
$842$	21.8927	+	32.7018i	0.754472	+	1.12698i
$843$	44.3853	−	44.3853i	1.52871	−	1.52871i
$844$	17.6647	+	42.4332i	0.608045	+	1.46061i
$845$	8.05250	+	8.05250i	0.277014	+	0.277014i
$846$	59.3435	+	11.7494i	2.04027	+	0.403953i
$847$	3.39249			0.116567
$848$	−10.3757	+	0.0368431i	−0.356302	+	0.00126520i
$849$	−21.6883			−0.744339
$850$	5.64160	+	1.11698i	0.193505	+	0.0383121i
$851$	13.0098	+	13.0098i	0.445971	+	0.445971i
$852$	55.1780	−	22.9703i	1.89037	−	0.786950i
$853$	−34.6580	+	34.6580i	−1.18667	+	1.18667i	−0.208685	+	0.977983i	$0.566918\pi$
$853$	−34.6580	+	34.6580i	−1.18667	+	1.18667i	−0.977983	+	0.208685i	$0.933082\pi$
$854$	25.0919	+	37.4806i	0.858628	+	1.28256i
$855$			0.576689i			0.0197223i
$856$	−6.18975	−	30.6906i	−0.211561	−	1.04898i
$857$		−	2.71107i		−	0.0926085i	−0.998927	−	0.0463042i	$-0.985256\pi$
$857$		−	2.71107i		−	0.0926085i	0.998927	−	0.0463042i	$-0.0147444\pi$
$858$	−3.77700	+	2.52856i	−0.128945	+	0.0863237i
$859$	−28.9609	+	28.9609i	−0.988132	+	0.988132i	−0.999930	−	0.0117983i	$-0.996244\pi$
$859$	−28.9609	+	28.9609i	−0.988132	+	0.988132i	0.0117983	+	0.999930i	$0.496244\pi$
$860$	4.29426	−	10.4196i	0.146433	−	0.355304i
$861$	−38.2559	−	38.2559i	−1.30376	−	1.30376i
$862$	−9.87015	+	49.8519i	−0.336179	+	1.69796i
$863$	26.7211			0.909595			0.454798	−	0.890595i	$-0.349712\pi$
$863$	26.7211			0.909595			0.454798	+	0.890595i	$0.349712\pi$
$864$	−1.11376	+	5.73212i	−0.0378910	+	0.195011i
$865$	−4.82477			−0.164047
$866$	5.60949	−	28.3322i	0.190618	−	0.962769i
$867$	0.827578	+	0.827578i	0.0281060	+	0.0281060i
$868$	−22.3139	+	54.1423i	−0.757385	+	1.83771i
$869$	−7.50812	+	7.50812i	−0.254696	+	0.254696i
$870$	22.0450	−	14.7583i	0.747396	−	0.500354i
$871$			14.6843i			0.497559i
$872$	−26.7122	+	5.38737i	−0.904588	+	0.182439i
$873$			35.1711i			1.19036i
$874$	0.641051	+	0.957559i	0.0216839	+	0.0323899i
$875$	−2.39885	+	2.39885i	−0.0810960	+	0.0810960i
$876$	−7.96120	+	3.31421i	−0.268984	+	0.111977i
$877$	19.3363	+	19.3363i	0.652941	+	0.652941i	0.953700	−	0.300759i	$-0.0972399\pi$
$877$	19.3363	+	19.3363i	0.652941	+	0.652941i	−0.300759	+	0.953700i	$0.597240\pi$
$878$	25.8558	+	5.11918i	0.872591	+	0.172764i
$879$	23.1794			0.781821
$880$	−2.81837	+	2.83845i	−0.0950071	+	0.0956842i
$881$	40.4976			1.36440			0.682200	−	0.731165i	$-0.261023\pi$
$881$	40.4976			1.36440			0.682200	+	0.731165i	$0.261023\pi$
$882$	21.3165	+	4.22046i	0.717765	+	0.142110i
$883$	−8.11653	−	8.11653i	−0.273143	−	0.273143i	0.557221	−	0.830364i	$-0.311868\pi$
$883$	−8.11653	−	8.11653i	−0.273143	−	0.273143i	−0.830364	+	0.557221i	$0.811868\pi$
$884$	3.96874	+	9.53348i	0.133483	+	0.320645i
$885$	−1.71286	+	1.71286i	−0.0575770	+	0.0575770i
$886$	−14.3010	−	21.3618i	−0.480451	−	0.717665i
$887$			47.2169i			1.58539i	0.609619	+	0.792695i	$0.291322\pi$
$887$			47.2169i			1.58539i	−0.609619	+	0.792695i	$0.708678\pi$
$888$	−15.1389	+	22.7882i	−0.508029	+	0.764720i
$889$		−	23.0293i		−	0.772377i
$890$	−8.03647	+	5.38012i	−0.269383	+	0.180342i
$891$	5.38133	−	5.38133i	0.180281	−	0.180281i
$892$	40.5190	+	16.6993i	1.35668	+	0.559134i
$893$	1.50207	+	1.50207i	0.0502648	+	0.0502648i
$894$	3.84496	−	19.4200i	0.128595	−	0.649502i
$895$	−6.30983			−0.210914
$896$	7.72166	+	37.5969i	0.257963	+	1.25602i
$897$	−15.4752			−0.516702
$898$	−2.58925	+	13.0777i	−0.0864043	+	0.436408i
$899$	45.2264	+	45.2264i	1.50839	+	1.50839i
$900$	−6.30139	−	2.59702i	−0.210046	−	0.0865674i
$901$	−7.45901	+	7.45901i	−0.248496	+	0.248496i
$902$	7.40362	−	4.95646i	0.246514	−	0.165032i
$903$		−	48.3902i		−	1.61033i
$904$	11.1491	−	16.7824i	0.370813	−	0.558173i
$905$			20.2754i			0.673978i
$906$	−11.5320	−	17.2258i	−0.383126	−	0.572288i
$907$	30.0192	−	30.0192i	0.996770	−	0.996770i	−0.00322502	−	0.999995i	$-0.501027\pi$
$907$	30.0192	−	30.0192i	0.996770	−	0.996770i	0.999995	+	0.00322502i	$0.00102656\pi$
$908$	−13.9150	−	33.4257i	−0.461784	−	1.10927i
$909$	−34.6961	−	34.6961i	−1.15080	−	1.15080i
$910$	−5.97549	−	1.18308i	−0.198085	−	0.0392189i
$911$	29.9785			0.993233			0.496616	−	0.867970i	$-0.334576\pi$
$911$	29.9785			0.993233			0.496616	+	0.867970i	$0.334576\pi$
$912$	−1.20731	+	1.21592i	−0.0399782	+	0.0402631i
$913$	1.41045			0.0466791
$914$	38.9769	+	7.71702i	1.28924	+	0.255256i
$915$	−16.8277	−	16.8277i	−0.556306	−	0.556306i
$916$	−2.88629	+	1.20155i	−0.0953659	+	0.0397003i
$917$	−32.7540	+	32.7540i	−1.08163	+	1.08163i
$918$	3.30259	+	4.93319i	0.109002	+	0.162819i
$919$		−	39.9665i		−	1.31837i	−0.751979	−	0.659187i	$-0.770900\pi$
$919$		−	39.9665i		−	1.31837i	0.751979	−	0.659187i	$-0.229100\pi$
$920$	−13.3500	+	2.69245i	−0.440135	+	0.0887675i
$921$		−	8.90360i		−	0.293384i
$922$	−1.01787	+	0.681428i	−0.0335218	+	0.0224416i
$923$	−10.5989	+	10.5989i	−0.348867	+	0.348867i
$924$	−6.54449	+	15.8795i	−0.215298	+	0.522397i
$925$	−2.70195	−	2.70195i	−0.0888397	−	0.0888397i
$926$	−6.15529	+	31.0889i	−0.202275	+	1.02165i
$927$	−50.9767			−1.67429
$928$	41.1510	+	7.99574i	1.35085	+	0.262473i
$929$	−30.7673			−1.00944			−0.504721	−	0.863283i	$-0.668405\pi$
$929$	−30.7673			−1.00944			−0.504721	+	0.863283i	$0.668405\pi$
$930$	6.00090	−	30.3092i	0.196777	−	0.993876i
$931$	0.539552	+	0.539552i	0.0176831	+	0.0176831i
$932$	−3.70958	+	9.00089i	−0.121511	+	0.294834i
$933$	43.5846	−	43.5846i	1.42690	−	1.42690i
$934$	34.8576	−	23.3359i	1.14058	−	0.763573i
$935$			4.06665i			0.132994i
$936$	−2.41945	−	11.9963i	−0.0790822	−	0.392113i
$937$			6.12012i			0.199936i	0.994991	+	0.0999679i	$0.0318740\pi$
$937$			6.12012i			0.199936i	−0.994991	+	0.0999679i	$0.968126\pi$
$938$	30.8684	+	46.1091i	1.00789	+	1.50552i
$939$	46.3808	−	46.3808i	1.51358	−	1.51358i
$940$	−23.1772	+	9.64854i	−0.755956	+	0.314701i
$941$	−32.5837	−	32.5837i	−1.06220	−	1.06220i	−0.997933	−	0.0642653i	$-0.979530\pi$
$941$	−32.5837	−	32.5837i	−1.06220	−	1.06220i	−0.0642653	−	0.997933i	$-0.520470\pi$
$942$	−73.1224	−	14.4775i	−2.38246	−	0.471702i
$943$	30.3343			0.987820
$944$	−3.82771	+	0.0135918i	−0.124581	+	0.000442377i
$945$	−3.50191			−0.113917
$946$	7.81719	+	1.54772i	0.254159	+	0.0503208i
$947$	14.9133	+	14.9133i	0.484618	+	0.484618i	0.906603	−	0.421985i	$-0.138666\pi$
$947$	14.9133	+	14.9133i	0.484618	+	0.484618i	−0.421985	+	0.906603i	$0.638666\pi$
$948$	−20.6598	−	49.6279i	−0.671000	−	1.61184i
$949$	1.52923	−	1.52923i	0.0496410	−	0.0496410i
$950$	−0.133137	−	0.198872i	−0.00431954	−	0.00645224i
$951$			4.28963i			0.139101i
$952$	32.5025	+	21.5925i	1.05341	+	0.699818i
$953$			29.6699i			0.961102i	0.876967	+	0.480551i	$0.159563\pi$
$953$			29.6699i			0.961102i	−0.876967	+	0.480551i	$0.840437\pi$
$954$	10.3881	−	6.95444i	0.336326	−	0.225158i
$955$	−1.03679	+	1.03679i	−0.0335497	+	0.0335497i
$956$	−9.03419	−	3.72331i	−0.292187	−	0.120420i
$957$	13.2645	+	13.2645i	0.428781	+	0.428781i
$958$	−10.8063	+	54.5804i	−0.349137	+	1.76341i
$959$	−45.2922			−1.46256
$960$	−7.84922	−	18.6678i	−0.253332	−	0.602502i
$961$	43.4918			1.40296
$962$	1.33257	−	6.73051i	0.0429638	−	0.217000i
$963$	26.6732	+	26.6732i	0.859532	+	0.859532i
$964$	22.8394	+	9.41292i	0.735608	+	0.303170i
$965$	8.43981	−	8.43981i	0.271687	−	0.271687i
$966$	−48.5925	+	32.5309i	−1.56344	+	1.04666i
$967$		−	19.6781i		−	0.632805i	−0.948625	−	0.316402i	$-0.897525\pi$
$967$		−	19.6781i		−	0.632805i	0.948625	−	0.316402i	$-0.102475\pi$
$968$	−2.35593	−	1.56512i	−0.0757224	−	0.0503049i
$969$			1.74205i			0.0559626i
$970$	−8.11977	−	12.1288i	−0.260710	−	0.389431i
$971$	−32.7945	+	32.7945i	−1.05243	+	1.05243i	−0.0538776	+	0.998548i	$0.517158\pi$
$971$	−32.7945	+	32.7945i	−1.05243	+	1.05243i	−0.998548	+	0.0538776i	$0.982842\pi$
$972$	17.1879	+	41.2879i	0.551303	+	1.32431i
$973$	−36.6672	−	36.6672i	−1.17550	−	1.17550i
$974$	−25.9676	−	5.14132i	−0.832056	−	0.164738i
$975$	3.21398			0.102930
$976$	−0.133531	−	37.6047i	−0.00427422	−	1.20370i
$977$	47.0076			1.50391			0.751954	−	0.659216i	$-0.229112\pi$
$977$	47.0076			1.50391			0.751954	+	0.659216i	$0.229112\pi$
$978$	−20.0815	−	3.97593i	−0.642136	−	0.127136i
$979$	−4.83556	−	4.83556i	−0.154545	−	0.154545i
$980$	−8.32538	+	3.46582i	−0.265945	+	0.110711i
$981$	23.2156	−	23.2156i	0.741216	−	0.741216i
$982$	−25.1521	−	37.5705i	−0.802635	−	1.19892i
$983$		−	38.9353i		−	1.24184i	−0.783872	−	0.620922i	$-0.786758\pi$
$983$		−	38.9353i		−	1.24184i	0.783872	−	0.620922i	$-0.213242\pi$
$984$	8.91764	+	44.2163i	0.284284	+	1.40956i
$985$			5.69244i			0.181376i
$986$	35.4155	−	23.7094i	1.12786	−	0.755061i
$987$	−76.2242	+	76.2242i	−2.42624	+	2.42624i
$988$	0.163743	−	0.397303i	0.00520935	−	0.0126399i
$989$	19.1850	+	19.1850i	0.610049	+	0.610049i
$990$	0.936010	−	4.72757i	0.0297483	−	0.150252i
$991$	35.8625			1.13921			0.569606	−	0.821918i	$-0.307096\pi$
$991$	35.8625			1.13921			0.569606	+	0.821918i	$0.307096\pi$
$992$	40.4745	−	27.3048i	1.28507	−	0.866929i
$993$	−18.5042			−0.587212
$994$	−11.0005	+	55.5611i	−0.348915	+	1.76229i
$995$	18.4763	+	18.4763i	0.585739	+	0.585739i
$996$	−2.72092	+	6.60200i	−0.0862155	+	0.209192i
$997$	−23.1538	+	23.1538i	−0.733288	+	0.733288i	−0.971270	−	0.237982i	$-0.923514\pi$
$997$	−23.1538	+	23.1538i	−0.733288	+	0.733288i	0.237982	+	0.971270i	$0.423514\pi$
$998$	−8.09990	+	5.42258i	−0.256398	+	0.171649i
$999$		−	3.94439i		−	0.124795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.w.a.221.16	✓	72
16.5	even	4	inner	880.2.w.a.661.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.w.a.221.16	✓	72	1.1	even	1	trivial
880.2.w.a.661.16	yes	72	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.274668 + 1.38728i) q^{2} +(-1.78994 - 1.78994i) q^{3} +(-1.84912 - 0.762085i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(2.97480 - 1.99152i) q^{6} +3.39249i q^{7} +(1.56512 - 2.35593i) q^{8} +3.40779i q^{9} +(-0.786739 - 1.17518i) q^{10} +(0.707107 - 0.707107i) q^{11} +(1.94572 + 4.67390i) q^{12} +(-0.897789 - 0.897789i) q^{13} +(-4.70635 - 0.931808i) q^{14} +2.53136 q^{15} +(2.83845 + 2.81837i) q^{16} +4.06665 q^{17} +(-4.72757 - 0.936010i) q^{18} +(-0.119661 - 0.119661i) q^{19} +(1.84640 - 0.768646i) q^{20} +(6.07236 - 6.07236i) q^{21} +(0.786739 + 1.17518i) q^{22} +4.81496i q^{23} +(-7.01845 + 1.41550i) q^{24} -1.00000i q^{25} +(1.49208 - 0.998894i) q^{26} +(0.729914 - 0.729914i) q^{27} +(2.58537 - 6.27310i) q^{28} +(-5.24008 - 5.24008i) q^{29} +(-0.695284 + 3.51172i) q^{30} -8.63086 q^{31} +(-4.68951 + 3.16363i) q^{32} -2.53136 q^{33} +(-1.11698 + 5.64160i) q^{34} +(-2.39885 - 2.39885i) q^{35} +(2.59702 - 6.30139i) q^{36} +(2.70195 - 2.70195i) q^{37} +(0.198872 - 0.133137i) q^{38} +3.21398i q^{39} +(0.559185 + 2.77260i) q^{40} -6.30000i q^{41} +(6.75621 + 10.0920i) q^{42} +(3.98447 - 3.98447i) q^{43} +(-1.84640 + 0.768646i) q^{44} +(-2.40967 - 2.40967i) q^{45} +(-6.67972 - 1.32252i) q^{46} -12.5526 q^{47} +(-0.0359543 - 10.1254i) q^{48} -4.50899 q^{49} +(1.38728 + 0.274668i) q^{50} +(-7.27907 - 7.27907i) q^{51} +(0.975923 + 2.34431i) q^{52} +(-1.83419 + 1.83419i) q^{53} +(0.812115 + 1.21308i) q^{54} +1.00000i q^{55} +(7.99246 + 5.30966i) q^{56} +0.428374i q^{57} +(8.70876 - 5.83020i) q^{58} +(-0.676655 + 0.676655i) q^{59} +(-4.68078 - 1.92911i) q^{60} +(-6.64768 - 6.64768i) q^{61} +(2.37062 - 11.9735i) q^{62} -11.5609 q^{63} +(-3.10079 - 7.37463i) q^{64} +1.26967 q^{65} +(0.695284 - 3.51172i) q^{66} +(-8.17805 - 8.17805i) q^{67} +(-7.51971 - 3.09913i) q^{68} +(8.61850 - 8.61850i) q^{69} +(3.98678 - 2.66900i) q^{70} -11.8056i q^{71} +(8.02850 + 5.33360i) q^{72} +1.70333i q^{73} +(3.00624 + 4.49052i) q^{74} +(-1.78994 + 1.78994i) q^{75} +(0.130076 + 0.312460i) q^{76} +(2.39885 + 2.39885i) q^{77} +(-4.45870 - 0.882777i) q^{78} -10.6181 q^{79} +(-3.99997 + 0.0142035i) q^{80} +7.61035 q^{81} +(8.73990 + 1.73041i) q^{82} +(0.997339 + 0.997339i) q^{83} +(-15.8561 + 6.60084i) q^{84} +(-2.87556 + 2.87556i) q^{85} +(4.43318 + 6.62199i) q^{86} +18.7589i q^{87} +(-0.559185 - 2.77260i) q^{88} -6.83852i q^{89} +(4.00475 - 2.68104i) q^{90} +(3.04574 - 3.04574i) q^{91} +(3.66941 - 8.90342i) q^{92} +(15.4487 + 15.4487i) q^{93} +(3.44781 - 17.4141i) q^{94} +0.169227 q^{95} +(14.0567 + 2.73124i) q^{96} +10.3208 q^{97} +(1.23847 - 6.25525i) q^{98} +(2.40967 + 2.40967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 56 q^{17} + 20 q^{18} + 8 q^{19} - 8 q^{20} + 4 q^{22} - 24 q^{24} - 24 q^{27} + 20 q^{28} - 20 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34}+ \cdots - 60 q^{98}+O(q^{100}) \) 72 * q + 12 * q^6 - 4 * q^10 + 12 * q^12 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 56 * q^17 + 20 * q^18 + 8 * q^19 - 8 * q^20 + 4 * q^22 - 24 * q^24 - 24 * q^27 + 20 * q^28 - 20 * q^30 + 20 * q^32 - 8 * q^33 + 4 * q^34 - 60 * q^36 + 12 * q^38 - 40 * q^42 + 8 * q^44 - 20 * q^46 + 40 * q^47 + 20 * q^48 - 24 * q^49 + 32 * q^51 - 84 * q^52 + 72 * q^54 + 8 * q^56 - 8 * q^58 + 32 * q^60 - 16 * q^61 - 96 * q^62 + 36 * q^64 - 40 * q^65 + 20 * q^66 - 76 * q^68 - 16 * q^69 + 24 * q^70 + 20 * q^72 + 56 * q^74 + 56 * q^76 - 132 * q^78 - 16 * q^79 + 56 * q^81 + 36 * q^82 - 40 * q^83 - 152 * q^84 + 16 * q^85 + 56 * q^86 - 36 * q^90 + 88 * q^91 + 80 * q^92 + 48 * q^93 - 76 * q^94 - 32 * q^96 - 64 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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