LMFDB - Embedded newform 680.2.cf.a.37.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(37,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 8, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cf (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.18
Character	$\chi$	$=$	680.37
Dual form			680.2.cf.a.533.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20201 - 0.745099i) q^{2} +(1.73274 + 2.59324i) q^{3} +(0.889656 + 1.79123i) q^{4} +(1.99136 + 1.01710i) q^{5} +(-0.150560 - 4.40816i) q^{6} +(-1.15970 + 0.230678i) q^{7} +(0.265270 - 2.81596i) q^{8} +(-2.57442 + 6.21519i) q^{9} +(-1.63580 - 2.70632i) q^{10} +(-1.49211 + 0.296799i) q^{11} +(-3.10354 + 5.41084i) q^{12} -0.744874i q^{13} +(1.56584 + 0.586811i) q^{14} +(0.812949 + 6.92643i) q^{15} +(-2.41703 + 3.18716i) q^{16} +(-1.04538 + 3.98838i) q^{17} +(7.72541 - 5.55253i) q^{18} +(1.13650 - 0.470755i) q^{19} +(-0.0502305 + 4.47185i) q^{20} +(-2.60766 - 2.60766i) q^{21} +(2.01468 + 0.755014i) q^{22} +(1.66381 - 2.49007i) q^{23} +(7.76209 - 4.19143i) q^{24} +(2.93103 + 4.05081i) q^{25} +(-0.555005 + 0.895346i) q^{26} +(-11.4015 + 2.26790i) q^{27} +(-1.44493 - 1.87206i) q^{28} +(2.16207 - 1.44465i) q^{29} +(4.18371 - 8.93137i) q^{30} +(-0.668499 + 3.36077i) q^{31} +(5.28004 - 2.03007i) q^{32} +(-3.35512 - 3.35512i) q^{33} +(4.22829 - 4.01516i) q^{34} +(-2.54399 - 0.720160i) q^{35} +(-13.4232 + 0.918002i) q^{36} +(0.145162 - 0.0969941i) q^{37} +(-1.71685 - 0.280955i) q^{38} +(1.93163 - 1.29068i) q^{39} +(3.39235 - 5.33779i) q^{40} +(0.874238 - 1.30839i) q^{41} +(1.19147 + 5.07740i) q^{42} +(-1.95719 - 4.72508i) q^{43} +(-1.85910 - 2.40867i) q^{44} +(-11.4480 + 9.75826i) q^{45} +(-3.85526 + 1.75338i) q^{46} -11.0930i q^{47} +(-12.4531 - 0.745384i) q^{48} +(-5.17547 + 2.14375i) q^{49} +(-0.504875 - 7.05302i) q^{50} +(-12.1542 + 4.19993i) q^{51} +(1.33424 - 0.662681i) q^{52} +(9.47043 + 3.92278i) q^{53} +(15.3945 + 5.76920i) q^{54} +(-3.27320 - 0.926585i) q^{55} +(0.341947 + 3.32685i) q^{56} +(3.19005 + 2.13152i) q^{57} +(-3.67524 + 0.125527i) q^{58} +(-3.63428 + 8.77392i) q^{59} +(-11.6836 + 7.61832i) q^{60} +(-3.71889 + 5.56571i) q^{61} +(3.30765 - 3.54158i) q^{62} +(1.55183 - 7.80160i) q^{63} +(-7.85926 - 1.49398i) q^{64} +(0.757608 - 1.48331i) q^{65} +(1.53299 + 6.53277i) q^{66} +(-9.35836 - 9.35836i) q^{67} +(-8.07414 + 1.67577i) q^{68} +9.34029 q^{69} +(2.52132 + 2.76117i) q^{70} +(7.56079 + 1.50393i) q^{71} +(16.8188 + 8.89816i) q^{72} +(13.4251 + 2.67042i) q^{73} +(-0.246756 + 0.00842790i) q^{74} +(-5.42598 + 14.6199i) q^{75} +(1.85433 + 1.61693i) q^{76} +(1.66193 - 0.688393i) q^{77} +(-3.28352 + 0.112148i) q^{78} +(15.2623 - 3.03587i) q^{79} +(-8.05482 + 3.88844i) q^{80} +(-11.3663 - 11.3663i) q^{81} +(-2.02572 + 0.921303i) q^{82} +(5.43237 - 13.1149i) q^{83} +(2.35100 - 6.99084i) q^{84} +(-6.13829 + 6.87905i) q^{85} +(-1.16809 + 7.13789i) q^{86} +(7.49265 + 3.10356i) q^{87} +(0.439962 + 4.28045i) q^{88} +(6.79377 + 6.79377i) q^{89} +(21.0315 - 3.19960i) q^{90} +(0.171826 + 0.863827i) q^{91} +(5.94051 + 0.764968i) q^{92} +(-9.87361 + 4.08978i) q^{93} +(-8.26539 + 13.3339i) q^{94} +(2.74199 + 0.218490i) q^{95} +(14.4134 + 10.1748i) q^{96} +(-14.3175 - 2.84793i) q^{97} +(7.81828 + 1.27943i) q^{98} +(1.99665 - 10.0378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) $ 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.20201	−	0.745099i	−0.849949	−	0.526864i
$2$	−1.20201	−	0.745099i	−0.849949	−	0.526864i
$3$	1.73274	+	2.59324i	1.00040	+	1.49721i	0.862051	+	0.506822i	$0.169180\pi$
$3$	1.73274	+	2.59324i	1.00040	+	1.49721i	0.138350	+	0.990383i	$0.455820\pi$
$4$	0.889656	+	1.79123i	0.444828	+	0.895616i
$5$	1.99136	+	1.01710i	0.890563	+	0.454859i
$5$	1.99136	+	1.01710i	0.890563	+	0.454859i
$6$	−0.150560	−	4.40816i	−0.0614657	−	1.79962i
$7$	−1.15970	+	0.230678i	−0.438324	+	0.0871880i	−0.409319	−	0.912391i	$-0.634234\pi$
$7$	−1.15970	+	0.230678i	−0.438324	+	0.0871880i	−0.0290047	+	0.999579i	$0.509234\pi$
$8$	0.265270	−	2.81596i	0.0937871	−	0.995592i
$9$	−2.57442	+	6.21519i	−0.858139	+	2.07173i
$10$	−1.63580	−	2.70632i	−0.517285	−	0.855813i
$11$	−1.49211	+	0.296799i	−0.449888	+	0.0894883i	−0.414834	−	0.909897i	$-0.636160\pi$
$11$	−1.49211	+	0.296799i	−0.449888	+	0.0894883i	−0.0350540	+	0.999385i	$0.511160\pi$
$12$	−3.10354	+	5.41084i	−0.895915	+	1.56197i
$13$		−	0.744874i		−	0.206591i	−0.994651	−	0.103295i	$-0.967061\pi$
$13$		−	0.744874i		−	0.206591i	0.994651	−	0.103295i	$-0.0329387\pi$
$14$	1.56584	+	0.586811i	0.418489	+	0.156832i
$15$	0.812949	+	6.92643i	0.209903	+	1.78840i
$16$	−2.41703	+	3.18716i	−0.604256	+	0.796790i
$17$	−1.04538	+	3.98838i	−0.253542	+	0.967324i
$17$	−1.04538	+	3.98838i	−0.253542	+	0.967324i
$18$	7.72541	−	5.55253i	1.82090	−	1.30874i
$19$	1.13650	−	0.470755i	0.260732	−	0.107999i	−0.248489	−	0.968635i	$-0.579934\pi$
$19$	1.13650	−	0.470755i	0.260732	−	0.107999i	0.509220	+	0.860636i	$0.329934\pi$
$20$	−0.0502305	+	4.47185i	−0.0112319	+	0.999937i
$21$	−2.60766	−	2.60766i	−0.569038	−	0.569038i
$22$	2.01468	+	0.755014i	0.429530	+	0.160969i
$23$	1.66381	−	2.49007i	0.346928	−	0.519215i	−0.616438	−	0.787403i	$-0.711425\pi$
$23$	1.66381	−	2.49007i	0.346928	−	0.519215i	0.963367	+	0.268188i	$0.0864249\pi$
$24$	7.76209	−	4.19143i	1.58443	−	0.855573i
$25$	2.93103	+	4.05081i	0.586206	+	0.810162i
$26$	−0.555005	+	0.895346i	−0.108845	+	0.175592i
$27$	−11.4015	+	2.26790i	−2.19422	+	0.436457i
$28$	−1.44493	−	1.87206i	−0.273066	−	0.353786i
$29$	2.16207	−	1.44465i	0.401487	−	0.268265i	−0.338392	−	0.941005i	$-0.609883\pi$
$29$	2.16207	−	1.44465i	0.401487	−	0.268265i	0.739879	+	0.672740i	$0.234883\pi$
$30$	4.18371	−	8.93137i	0.763837	−	1.63064i
$31$	−0.668499	+	3.36077i	−0.120066	+	0.603612i	0.873162	+	0.487430i	$0.162066\pi$
$31$	−0.668499	+	3.36077i	−0.120066	+	0.603612i	−0.993228	+	0.116182i	$0.962934\pi$
$32$	5.28004	−	2.03007i	0.933388	−	0.358870i
$33$	−3.35512	−	3.35512i	−0.584051	−	0.584051i
$34$	4.22829	−	4.01516i	0.725146	−	0.688595i
$35$	−2.54399	−	0.720160i	−0.430013	−	0.121729i
$36$	−13.4232	+	0.918002i	−2.23720	+	0.153000i
$37$	0.145162	−	0.0969941i	0.0238645	−	0.0159457i	−0.543581	−	0.839357i	$-0.682932\pi$
$37$	0.145162	−	0.0969941i	0.0238645	−	0.0159457i	0.567445	+	0.823411i	$0.307932\pi$
$38$	−1.71685	−	0.280955i	−0.278509	−	0.0455769i
$39$	1.93163	−	1.29068i	0.309309	−	0.206674i
$40$	3.39235	−	5.33779i	0.536378	−	0.843978i
$41$	0.874238	−	1.30839i	0.136533	−	0.204336i	−0.756902	−	0.653528i	$-0.773288\pi$
$41$	0.874238	−	1.30839i	0.136533	−	0.204336i	0.893435	+	0.449192i	$0.148288\pi$
$42$	1.19147	+	5.07740i	0.183848	+	0.783459i
$43$	−1.95719	−	4.72508i	−0.298469	−	0.720568i	−0.999969	−	0.00789812i	$-0.997486\pi$
$43$	−1.95719	−	4.72508i	−0.298469	−	0.720568i	0.701500	−	0.712670i	$-0.252514\pi$
$44$	−1.85910	−	2.40867i	−0.280270	−	0.363120i
$45$	−11.4480	+	9.75826i	−1.70657	+	1.45468i
$46$	−3.85526	+	1.75338i	−0.568428	+	0.258522i
$47$		−	11.0930i		−	1.61808i	−0.587752	−	0.809041i	$-0.699987\pi$
$47$		−	11.0930i		−	1.61808i	0.587752	−	0.809041i	$-0.300013\pi$
$48$	−12.4531	−	0.745384i	−1.79746	−	0.107587i
$49$	−5.17547	+	2.14375i	−0.739353	+	0.306250i
$50$	−0.504875	−	7.05302i	−0.0714001	−	0.997448i
$51$	−12.1542	+	4.19993i	−1.70193	+	0.588108i
$52$	1.33424	−	0.662681i	0.185026	−	0.0918973i
$53$	9.47043	+	3.92278i	1.30086	+	0.538835i	0.922205	−	0.386701i	$-0.126386\pi$
$53$	9.47043	+	3.92278i	1.30086	+	0.538835i	0.378658	+	0.925537i	$0.376386\pi$
$54$	15.3945	+	5.76920i	2.09493	+	0.785088i
$55$	−3.27320	−	0.926585i	−0.441358	−	0.124941i
$56$	0.341947	+	3.32685i	0.0456946	+	0.444569i
$57$	3.19005	+	2.13152i	0.422532	+	0.282327i
$58$	−3.67524	+	0.125527i	−0.482583	+	0.0164825i
$59$	−3.63428	+	8.77392i	−0.473142	+	1.14227i	0.489624	+	0.871934i	$0.337134\pi$
$59$	−3.63428	+	8.77392i	−0.473142	+	1.14227i	−0.962767	+	0.270333i	$0.912866\pi$
$60$	−11.6836	+	7.61832i	−1.50835	+	0.983521i
$61$	−3.71889	+	5.56571i	−0.476155	+	0.712616i	−0.989334	−	0.145665i	$-0.953468\pi$
$61$	−3.71889	+	5.56571i	−0.476155	+	0.712616i	0.513179	+	0.858282i	$0.328468\pi$
$62$	3.30765	−	3.54158i	0.420072	−	0.449782i
$63$	1.55183	−	7.80160i	0.195513	−	0.982909i
$64$	−7.85926	−	1.49398i	−0.982408	−	0.186748i
$65$	0.757608	−	1.48331i	0.0939697	−	0.183982i
$66$	1.53299	+	6.53277i	0.188698	+	0.804129i
$67$	−9.35836	−	9.35836i	−1.14331	−	1.14331i	−0.987842	−	0.155464i	$-0.950313\pi$
$67$	−9.35836	−	9.35836i	−1.14331	−	1.14331i	−0.155464	−	0.987842i	$-0.549687\pi$
$68$	−8.07414	+	1.67577i	−0.979134	+	0.203217i
$69$	9.34029			1.12444
$70$	2.52132	+	2.76117i	0.301355	+	0.330022i
$71$	7.56079	+	1.50393i	0.897301	+	0.178484i	0.622133	−	0.782912i	$-0.286266\pi$
$71$	7.56079	+	1.50393i	0.897301	+	0.178484i	0.275168	+	0.961396i	$0.411266\pi$
$72$	16.8188	+	8.89816i	1.98212	+	1.04866i
$73$	13.4251	+	2.67042i	1.57129	+	0.312549i	0.902429	−	0.430839i	$-0.141782\pi$
$73$	13.4251	+	2.67042i	1.57129	+	0.312549i	0.668861	+	0.743388i	$0.266782\pi$
$74$	−0.246756	+	0.00842790i	−0.0286848	+	0.000979723i
$75$	−5.42598	+	14.6199i	−0.626538	+	1.68816i
$76$	1.85433	+	1.61693i	0.212706	+	0.185475i
$77$	1.66193	−	0.688393i	0.189394	−	0.0784497i
$78$	−3.28352	+	0.112148i	−0.371786	+	0.0126982i
$79$	15.2623	−	3.03587i	1.71715	−	0.341562i	0.764265	−	0.644902i	$-0.223102\pi$
$79$	15.2623	−	3.03587i	1.71715	−	0.341562i	0.952882	+	0.303340i	$0.0981019\pi$
$80$	−8.05482	+	3.88844i	−0.900556	+	0.434740i
$81$	−11.3663	−	11.3663i	−1.26293	−	1.26293i
$82$	−2.02572	+	0.921303i	−0.223704	+	0.101741i
$83$	5.43237	−	13.1149i	0.596280	−	1.43955i	−0.281066	−	0.959688i	$-0.590688\pi$
$83$	5.43237	−	13.1149i	0.596280	−	1.43955i	0.877346	−	0.479859i	$-0.159312\pi$
$84$	2.35100	−	6.99084i	0.256516	−	0.762763i
$85$	−6.13829	+	6.87905i	−0.665791	+	0.746138i
$86$	−1.16809	+	7.13789i	−0.125958	+	0.769699i
$87$	7.49265	+	3.10356i	0.803296	+	0.332736i
$88$	0.439962	+	4.28045i	0.0469001	+	0.456298i
$89$	6.79377	+	6.79377i	0.720138	+	0.720138i	0.968633	−	0.248495i	$-0.0799360\pi$
$89$	6.79377	+	6.79377i	0.720138	+	0.720138i	−0.248495	+	0.968633i	$0.579936\pi$
$90$	21.0315	−	3.19960i	2.21692	−	0.337268i
$91$	0.171826	+	0.863827i	0.0180122	+	0.0905537i
$92$	5.94051	+	0.764968i	0.619341	+	0.0797534i
$93$	−9.87361	+	4.08978i	−1.02385	+	0.424091i
$94$	−8.26539	+	13.3339i	−0.852510	+	1.37529i
$95$	2.74199	+	0.218490i	0.281322	+	0.0224166i
$96$	14.4134	+	10.1748i	1.47106	+	1.03846i
$97$	−14.3175	−	2.84793i	−1.45373	−	0.289164i	−0.595881	−	0.803073i	$-0.703197\pi$
$97$	−14.3175	−	2.84793i	−1.45373	−	0.289164i	−0.857845	+	0.513909i	$0.828197\pi$
$98$	7.81828	+	1.27943i	0.789765	+	0.129242i
$99$	1.99665	−	10.0378i	0.200671	−	1.00884i
$100$	−4.64833	+	8.85398i	−0.464833	+	0.885398i
$101$	14.7785			1.47051			0.735257	−	0.677789i	$-0.237062\pi$
$101$	14.7785			1.47051			0.735257	+	0.677789i	$0.237062\pi$
$102$	17.7388	+	4.00771i	1.75640	+	0.396823i
$103$	−5.61802	+	5.61802i	−0.553560	+	0.553560i	−0.927466	−	0.373906i	$-0.878018\pi$
$103$	−5.61802	+	5.61802i	−0.553560	+	0.553560i	0.373906	+	0.927466i	$0.378018\pi$
$104$	−2.09753	−	0.197593i	−0.205680	−	0.0193756i
$105$	−2.54055	−	7.84503i	−0.247932	−	0.765597i
$106$	−8.46069	−	11.7716i	−0.821775	−	1.14336i
$107$	−9.50844	−	1.89135i	−0.919216	−	0.182843i	−0.287264	−	0.957851i	$-0.592746\pi$
$107$	−9.50844	−	1.89135i	−0.919216	−	0.182843i	−0.631951	+	0.775008i	$0.717746\pi$
$108$	−14.2057	−	18.4051i	−1.36695	−	1.77103i
$109$	4.89821	−	7.33069i	0.469164	−	0.702153i	−0.519134	−	0.854693i	$-0.673745\pi$
$109$	4.89821	−	7.33069i	0.469164	−	0.702153i	0.988297	+	0.152540i	$0.0487453\pi$
$110$	3.24402	+	3.55262i	0.309305	+	0.338729i
$111$	0.503057	+	0.208373i	0.0477481	+	0.0197779i
$112$	2.06781	−	4.25369i	0.195389	−	0.401936i
$113$	9.52881	+	6.36694i	0.896395	+	0.598952i	0.916142	−	0.400853i	$-0.131286\pi$
$113$	9.52881	+	6.36694i	0.896395	+	0.598952i	−0.0197477	+	0.999805i	$0.506286\pi$
$114$	−2.24628	−	4.93901i	−0.210383	−	0.462581i
$115$	5.84589	−	3.26637i	0.545132	−	0.304590i
$116$	4.51121	+	2.58753i	0.418855	+	0.240247i
$117$	4.62954	+	1.91762i	0.428001	+	0.177284i
$118$	10.9059	−	7.83844i	1.00397	−	0.721587i
$119$	0.292291	−	4.86646i	0.0267942	−	0.446107i
$120$	19.7202	−	0.451856i	1.80020	−	0.0412486i
$121$	−8.02437	+	3.32380i	−0.729489	+	0.302164i
$122$	8.61715	−	3.91910i	0.780160	−	0.354819i
$123$	4.90779			0.442521
$124$	−6.61466	+	1.79249i	−0.594014	+	0.160971i
$125$	1.71668	+	11.0478i	0.153544	+	0.988142i
$126$	−7.67828	+	8.22133i	−0.684036	+	0.732414i
$127$	−11.0280	+	4.56793i	−0.978573	+	0.405338i	−0.813897	−	0.581010i	$-0.802658\pi$
$127$	−11.0280	+	4.56793i	−0.978573	+	0.405338i	−0.164676	+	0.986348i	$0.552658\pi$
$128$	8.33375	+	7.65171i	0.736606	+	0.676322i
$129$	8.86193	−	13.2628i	0.780249	−	1.16773i
$130$	−2.01587	+	1.21846i	−0.176803	+	0.106866i
$131$	10.1406	+	15.1765i	0.885991	+	1.32598i	0.944779	+	0.327708i	$0.106276\pi$
$131$	10.1406	+	15.1765i	0.885991	+	1.32598i	−0.0587882	+	0.998270i	$0.518724\pi$
$132$	3.02489	−	8.99469i	0.263283	−	0.782887i
$133$	−1.20941	+	0.808099i	−0.104869	+	0.0700711i
$134$	4.27594	+	18.2217i	0.369385	+	1.57412i
$135$	−25.0111	−	7.08021i	−2.15262	−	0.609367i
$136$	10.9538	+	4.00174i	0.939282	+	0.343147i
$137$	11.1571	+	11.1571i	0.953215	+	0.953215i	0.998953	−	0.0457384i	$-0.0145641\pi$
$137$	11.1571	+	11.1571i	0.953215	+	0.953215i	−0.0457384	+	0.998953i	$0.514564\pi$
$138$	−11.2271	−	6.95944i	−0.955716	−	0.592427i
$139$	−6.54669	−	1.30222i	−0.555283	−	0.110453i	−0.0905312	−	0.995894i	$-0.528856\pi$
$139$	−6.54669	−	1.30222i	−0.555283	−	0.110453i	−0.464752	+	0.885441i	$0.653856\pi$
$140$	−0.973306	−	5.19758i	−0.0822593	−	0.439276i
$141$	28.7668	−	19.2214i	2.42260	−	1.61873i
$142$	−7.96756	−	7.44128i	−0.668623	−	0.624458i
$143$	0.221078	+	1.11143i	0.0184875	+	0.0929427i
$144$	−13.5864	−	23.2274i	−1.13220	−	1.93561i
$145$	5.77482	−	0.677785i	0.479573	−	0.0562870i
$146$	−14.1474	−	13.2129i	−1.17085	−	1.09351i
$147$	−14.5270	−	9.70665i	−1.19817	−	0.800591i
$148$	0.302883	+	0.173727i	0.0248968	+	0.0142803i
$149$	−14.4621	−	14.4621i	−1.18478	−	1.18478i	−0.978490	−	0.206293i	$-0.933860\pi$
$149$	−14.4621	−	14.4621i	−1.18478	−	1.18478i	−0.206293	−	0.978490i	$-0.566140\pi$
$150$	17.4153	−	13.5303i	1.42196	−	1.10475i
$151$	−1.71352	−	4.13681i	−0.139444	−	0.336648i	0.838694	−	0.544603i	$-0.183320\pi$
$151$	−1.71352	−	4.13681i	−0.139444	−	0.336648i	−0.978139	+	0.207954i	$0.933320\pi$
$152$	−1.02415	−	3.32523i	−0.0830693	−	0.269711i
$153$	−22.0973	−	16.7650i	−1.78646	−	1.35537i
$154$	−2.51058	−	0.410845i	−0.202308	−	0.0331069i
$155$	−4.74945	+	6.01258i	−0.381485	+	0.482942i
$156$	4.03039	+	2.31175i	0.322689	+	0.185088i
$157$		−	18.6232i		−	1.48629i	−0.669129	−	0.743146i	$-0.733333\pi$
$157$		−	18.6232i		−	1.48629i	0.669129	−	0.743146i	$-0.266667\pi$
$158$	−20.6075	−	7.72281i	−1.63945	−	0.614394i
$159$	6.23714	+	31.3562i	0.494638	+	2.48671i
$160$	12.5792	+	1.32770i	0.994476	+	0.104964i
$161$	−1.35511	+	3.27153i	−0.106798	+	0.257832i
$162$	5.19341	+	22.1315i	0.408033	+	1.73881i
$163$	−0.0455855	−	0.229174i	−0.00357053	−	0.0179503i	0.978959	−	0.204057i	$-0.0654129\pi$
$163$	−0.0455855	−	0.229174i	−0.00357053	−	0.0179503i	−0.982529	+	0.186107i	$0.940413\pi$
$164$	3.12140	+	0.401947i	0.243740	+	0.0313868i
$165$	−3.26877	−	10.0937i	−0.254473	−	0.785795i
$166$	−16.3017	+	11.7166i	−1.26525	+	0.909383i
$167$	−0.278676	+	0.186205i	−0.0215646	+	0.0144090i	−0.566306	−	0.824195i	$-0.691628\pi$
$167$	−0.278676	+	0.186205i	−0.0215646	+	0.0144090i	0.544741	+	0.838604i	$0.316628\pi$
$168$	−8.03480	+	6.65133i	−0.619898	+	0.513161i
$169$	12.4452			0.957320
$170$	12.5039	−	3.69505i	0.959002	−	0.283398i
$171$			8.27551i			0.632844i
$172$	6.72249	−	7.70948i	0.512585	−	0.587842i
$173$	−12.5539	−	18.7882i	−0.954455	−	1.42844i	−0.902938	−	0.429771i	$-0.858594\pi$
$173$	−12.5539	−	18.7882i	−0.954455	−	1.42844i	−0.0515172	−	0.998672i	$-0.516406\pi$
$174$	−6.69378	−	9.31327i	−0.507454	−	0.706037i
$175$	−4.33354	−	4.02158i	−0.327585	−	0.304003i
$176$	2.66052	−	5.47296i	0.200544	−	0.412540i
$177$	−29.0501	+	5.77843i	−2.18354	+	0.434333i
$178$	−3.10415	−	13.2282i	−0.232666	−	0.991496i
$179$	−1.59987	−	0.662689i	−0.119580	−	0.0495317i	0.322091	−	0.946709i	$-0.395614\pi$
$179$	−1.59987	−	0.662689i	−0.119580	−	0.0495317i	−0.441671	+	0.897177i	$0.645614\pi$
$180$	−27.6641	−	11.8246i	−2.06196	−	0.881355i
$181$	−5.02962	+	1.00045i	−0.373849	+	0.0743632i	−0.378439	−	0.925626i	$-0.623539\pi$
$181$	−5.02962	+	1.00045i	−0.373849	+	0.0743632i	0.00458997	+	0.999989i	$0.498539\pi$
$182$	0.437100	−	1.16636i	0.0324000	−	0.0864561i
$183$	−20.8771			−1.54328
$184$	−6.57057	−	5.34576i	−0.484389	−	0.394095i
$185$	0.387722	−	0.0455066i	0.0285059	−	0.00334571i
$186$	14.9155	+	2.44086i	1.09366	+	0.178972i
$187$	0.376073	−	6.26137i	0.0275011	−	0.457877i
$188$	19.8702	−	9.86897i	1.44918	−	0.719768i
$189$	12.6991	−	5.26014i	0.923724	−	0.382619i
$190$	−3.13310	−	2.30568i	−0.227299	−	0.167272i
$191$	−0.851881	+	0.851881i	−0.0616399	+	0.0616399i	−0.737255	−	0.675615i	$-0.763878\pi$
$191$	−0.851881	+	0.851881i	−0.0616399	+	0.0616399i	0.675615	+	0.737255i	$0.263878\pi$
$192$	−9.74386	−	22.9696i	−0.703202	−	1.65769i
$193$	7.06212	−	10.5692i	0.508343	−	0.760789i	−0.485181	−	0.874414i	$-0.661246\pi$
$193$	7.06212	−	10.5692i	0.508343	−	0.760789i	0.993524	+	0.113625i	$0.0362463\pi$
$194$	15.0878	+	14.0912i	1.08324	+	1.01169i
$195$	5.15932	−	0.605544i	0.369467	−	0.0433639i
$196$	−8.44435	−	7.36328i	−0.603168	−	0.525948i
$197$	21.4450	−	4.26567i	1.52789	−	0.303916i	0.641597	−	0.767042i	$-0.278272\pi$
$197$	21.4450	−	4.26567i	1.52789	−	0.303916i	0.886293	+	0.463126i	$0.153272\pi$
$198$	−9.87917	+	10.5779i	−0.702082	+	0.751737i
$199$	3.79875	+	5.68523i	0.269286	+	0.403015i	0.941325	−	0.337500i	$-0.109581\pi$
$199$	3.79875	+	5.68523i	0.269286	+	0.403015i	−0.672039	+	0.740516i	$0.734581\pi$
$200$	12.1844	−	7.17911i	0.861570	−	0.507640i
$201$	8.05278	−	40.4841i	0.568000	−	2.85553i
$202$	−17.7639	−	11.0114i	−1.24986	−	0.774761i
$203$	−2.17410	+	2.17410i	−0.152592	+	0.152592i
$204$	−18.3361	−	18.0345i	−1.28378	−	1.26267i
$205$	3.07168	−	1.71629i	0.214535	−	0.119871i
$206$	10.9389	−	2.56694i	0.762149	−	0.178847i
$207$	11.1929	+	16.7514i	0.777961	+	1.16430i
$208$	2.37403	+	1.80038i	0.164609	+	0.124834i
$209$	−1.55607	+	1.03973i	−0.107635	+	0.0719197i
$210$	−2.79156	+	11.3228i	−0.192636	+	0.781345i
$211$	−0.634083	−	0.423680i	−0.0436520	−	0.0291674i	0.533553	−	0.845767i	$-0.320857\pi$
$211$	−0.634083	−	0.423680i	−0.0436520	−	0.0291674i	−0.577205	+	0.816599i	$0.695857\pi$
$212$	1.39881	+	20.4537i	0.0960707	+	1.40476i
$213$	9.20086	+	22.2128i	0.630433	+	1.52200i
$214$	10.0200	+	9.35814i	0.684953	+	0.639710i
$215$	0.908385	−	11.4000i	0.0619514	−	0.777472i
$216$	3.36183	+	32.7077i	0.228744	+	2.22548i
$217$		−	4.05168i		−	0.275046i
$218$	−11.3498	+	5.16191i	−0.768705	+	0.349609i
$219$	16.3373	+	39.4416i	1.10397	+	2.66522i
$220$	−1.25229	−	6.68740i	−0.0844295	−	0.450865i
$221$	2.97084	+	0.778676i	0.199840	+	0.0523794i
$222$	−0.449421	−	0.625294i	−0.0301632	−	0.0419670i
$223$	1.86472	−	4.50184i	0.124871	−	0.301466i	−0.849065	−	0.528289i	$-0.822834\pi$
$223$	1.86472	−	4.50184i	0.124871	−	0.301466i	0.973936	+	0.226823i	$0.0728339\pi$
$224$	−5.65495	+	3.57226i	−0.377837	+	0.238681i
$225$	−32.7223	+	7.78845i	−2.18148	+	0.519230i
$226$	−6.70972	−	14.7530i	−0.446324	−	0.981357i
$227$	11.0255	−	16.5008i	0.731788	−	1.09520i	−0.259788	−	0.965666i	$-0.583653\pi$
$227$	11.0255	−	16.5008i	0.731788	−	1.09520i	0.991575	−	0.129532i	$-0.0413474\pi$
$228$	−0.980007	+	7.61044i	−0.0649026	+	0.504014i
$229$	−2.68089	+	6.47224i	−0.177158	+	0.427698i	−0.987368	−	0.158442i	$-0.949353\pi$
$229$	−2.68089	+	6.47224i	−0.177158	+	0.427698i	0.810210	+	0.586140i	$0.199353\pi$
$230$	−9.46058	−	0.429555i	−0.623812	−	0.0283240i
$231$	4.66486	+	3.11696i	0.306926	+	0.205081i
$232$	−3.49455	−	6.47154i	−0.229428	−	0.424877i
$233$	0.418911	−	2.10601i	0.0274438	−	0.137969i	−0.964634	−	0.263592i	$-0.915093\pi$
$233$	0.418911	−	2.10601i	0.0274438	−	0.137969i	0.992078	+	0.125623i	$0.0400928\pi$
$234$	−4.13593	−	5.75445i	−0.270374	−	0.376180i
$235$	11.2827	−	22.0902i	0.736000	−	1.44101i
$236$	−18.9494	+	1.29593i	−1.23350	+	0.0843581i
$237$	34.3185	+	34.3185i	2.22922	+	2.22922i
$238$	−3.97733	+	5.63174i	−0.257812	+	0.365052i
$239$			21.0487i			1.36152i	0.732504	+	0.680762i	$0.238351\pi$
$239$			21.0487i			1.36152i	−0.732504	+	0.680762i	$0.761649\pi$
$240$	−24.0406	−	14.1504i	−1.55181	−	0.913403i
$241$	20.0010	+	3.97844i	1.28837	+	0.256274i	0.791297	−	0.611432i	$-0.209406\pi$
$241$	20.0010	+	3.97844i	1.28837	+	0.256274i	0.497078	+	0.867706i	$0.334406\pi$
$242$	12.1219	+	1.98371i	0.779228	+	0.127517i
$243$	2.97695	−	14.9661i	0.190971	−	0.960077i
$244$	−13.2780	−	1.70983i	−0.850038	−	0.109461i
$245$	−12.4866	−	0.994973i	−0.797742	−	0.0635665i
$246$	−5.89922	−	3.65679i	−0.376120	−	0.233148i
$247$	−0.350653	−	0.846552i	−0.0223115	−	0.0538648i
$248$	9.28647	+	2.77398i	0.589691	+	0.176148i
$249$	43.4229	−	8.63736i	2.75182	−	0.547370i
$250$	6.16821	−	14.5586i	0.390112	−	0.920767i
$251$	8.57650	−	8.57650i	0.541344	−	0.541344i	−0.382579	−	0.923923i	$-0.624964\pi$
$251$	8.57650	−	8.57650i	0.541344	−	0.541344i	0.923923	+	0.382579i	$0.124964\pi$
$252$	15.3551	−	4.16104i	0.967278	−	0.262121i
$253$	−1.74354	+	4.20927i	−0.109615	+	0.264635i
$254$	16.6593	+	2.72622i	1.04530	+	0.171058i
$255$	−28.4751	−	3.99840i	−1.78318	−	0.250390i
$256$	−4.31597	−	15.4069i	−0.269748	−	0.962931i
$257$	10.5516	+	4.37061i	0.658190	+	0.272631i	0.686677	−	0.726963i	$-0.259069\pi$
$257$	10.5516	+	4.37061i	0.658190	+	0.272631i	−0.0284864	+	0.999594i	$0.509069\pi$
$258$	−20.5342	+	9.33902i	−1.27841	+	0.581422i
$259$	−0.145969	+	0.145969i	−0.00907010	+	0.00907010i
$260$	3.33097	+	0.0374154i	0.206578	+	0.00232040i
$261$	3.41271	+	17.1569i	0.211241	+	1.06198i
$262$	−0.881127	−	25.7981i	−0.0544362	−	1.59381i
$263$	7.87922	+	19.0221i	0.485853	+	1.17295i	0.956788	+	0.290786i	$0.0939167\pi$
$263$	7.87922	+	19.0221i	0.485853	+	1.17295i	−0.470935	+	0.882168i	$0.656083\pi$
$264$	−10.3379	+	8.55786i	−0.636253	+	0.526700i
$265$	14.8692	+	17.4440i	0.913407	+	1.07158i
$266$	2.05583	−	0.0702164i	0.126051	−	0.00430524i
$267$	−5.84598	+	29.3897i	−0.357768	+	1.79862i
$268$	8.43728	−	25.0887i	0.515389	−	1.53254i
$269$	2.36512	−	11.8903i	0.144204	−	0.724963i	−0.839241	−	0.543759i	$-0.817001\pi$
$269$	2.36512	−	11.8903i	0.144204	−	0.724963i	0.983446	−	0.181204i	$-0.0579995\pi$
$270$	24.7882	+	27.1462i	1.50856	+	1.65207i
$271$		−	3.67656i		−	0.223335i	−0.993746	−	0.111667i	$-0.964381\pi$
$271$		−	3.67656i		−	0.223335i	0.993746	−	0.111667i	$-0.0356192\pi$
$272$	−10.1849	−	12.9718i	−0.617550	−	0.786531i
$273$	−1.94238	+	1.94238i	−0.117558	+	0.117558i
$274$	−5.09780	−	21.7241i	−0.307969	−	1.31240i
$275$	−5.57570	−	5.17432i	−0.336227	−	0.312023i
$276$	8.30965	+	16.7306i	0.500182	+	1.00707i
$277$	−3.06764	−	0.610192i	−0.184317	−	0.0366629i	0.102069	−	0.994777i	$-0.467454\pi$
$277$	−3.06764	−	0.610192i	−0.184317	−	0.0366629i	−0.286385	+	0.958114i	$0.592454\pi$
$278$	6.89891	+	6.44321i	0.413769	+	0.386438i
$279$	−19.1669	−	12.8069i	−1.14749	−	0.766728i
$280$	−2.70279	+	6.97275i	−0.161522	+	0.416701i
$281$	20.5740	+	8.52203i	1.22734	+	0.508382i	0.899737	−	0.436433i	$-0.143758\pi$
$281$	20.5740	+	8.52203i	1.22734	+	0.508382i	0.327606	+	0.944815i	$0.393758\pi$
$282$	−48.8998	+	1.67016i	−2.91194	+	0.0994566i
$283$	1.66258	−	2.48822i	0.0988300	−	0.147910i	−0.778759	−	0.627323i	$-0.784151\pi$
$283$	1.66258	−	2.48822i	0.0988300	−	0.147910i	0.877589	+	0.479414i	$0.159151\pi$
$284$	4.03260	+	14.8811i	0.239291	+	0.883032i
$285$	4.18457	+	7.48922i	0.247873	+	0.443623i
$286$	0.562390	−	1.50068i	0.0332548	−	0.0887370i
$287$	−0.712034	+	1.71900i	−0.0420300	+	0.101469i
$288$	−0.975716	+	38.0427i	−0.0574946	+	2.24169i
$289$	−14.8144	−	8.33874i	−0.871433	−	0.490514i
$290$	−7.44641	−	3.48811i	−0.437268	−	0.204829i
$291$	−17.4233	−	42.0635i	−1.02137	−	2.46581i
$292$	7.16038	+	26.4232i	0.419030	+	1.54630i
$293$	2.51896			0.147159			0.0735796	−	0.997289i	$-0.476558\pi$
$293$	2.51896			0.147159			0.0735796	+	0.997289i	$0.476558\pi$
$294$	10.2292	+	22.4916i	0.596580	+	1.31173i
$295$	−16.1611	+	13.7756i	−0.940934	+	0.802048i
$296$	−0.234625	−	0.434500i	−0.0136373	−	0.0252548i
$297$	16.3392	−	6.76790i	0.948094	−	0.392713i
$298$	6.60790	+	28.1593i	0.382786	+	1.63123i
$299$	−1.85479	−	1.23933i	−0.107265	−	0.0716722i
$300$	−31.0148	+	3.28747i	−1.79064	+	0.189802i
$301$	3.35972	+	5.02817i	0.193651	+	0.289819i
$302$	−1.02266	+	6.24922i	−0.0588475	+	0.359602i
$303$	25.6073	+	38.3241i	1.47110	+	2.20166i
$304$	−1.24659	+	4.76005i	−0.0714966	+	0.273007i
$305$	−13.0665	+	7.30087i	−0.748186	+	0.418046i
$306$	14.0696	+	36.6164i	0.804307	+	2.09322i
$307$	−7.54449	+	7.54449i	−0.430587	+	0.430587i	−0.888828	−	0.458241i	$-0.848480\pi$
$307$	−7.54449	+	7.54449i	−0.430587	+	0.430587i	0.458241	+	0.888828i	$0.348480\pi$
$308$	2.71162	+	2.36447i	0.154509	+	0.134728i
$309$	−24.3035	−	4.83426i	−1.38258	−	0.275011i
$310$	10.1889	−	3.68837i	0.578688	−	0.209485i
$311$	−13.6191	−	20.3825i	−0.772270	−	1.15578i	−0.983950	−	0.178445i	$-0.942893\pi$
$311$	−13.6191	−	20.3825i	−0.772270	−	1.15578i	0.211680	−	0.977339i	$-0.432107\pi$
$312$	−3.12209	−	5.78178i	−0.176753	−	0.327329i
$313$	−2.11966	−	10.6562i	−0.119810	−	0.602326i	−0.993308	−	0.115498i	$-0.963154\pi$
$313$	−2.11966	−	10.6562i	−0.119810	−	0.602326i	0.873498	−	0.486829i	$-0.161846\pi$
$314$	−13.8761	+	22.3853i	−0.783075	+	1.26327i
$315$	11.0252	−	13.9574i	0.621202	−	0.786412i
$316$	19.0162	+	24.6375i	1.06974	+	1.38597i
$317$	−11.3269	−	7.56836i	−0.636179	−	0.425082i	0.195218	−	0.980760i	$-0.437459\pi$
$317$	−11.3269	−	7.56836i	−0.636179	−	0.425082i	−0.831397	+	0.555678i	$0.812459\pi$
$318$	15.8664	−	42.3378i	0.889743	−	2.37419i
$319$	−2.79728	+	2.79728i	−0.156618	+	0.156618i
$320$	−14.1311	−	10.9687i	−0.789953	−	0.613168i
$321$	−11.5710	−	27.9349i	−0.645830	−	1.55917i
$322$	4.06647	−	2.92272i	0.226615	−	0.162877i
$323$	0.689474	+	5.02493i	0.0383634	+	0.279594i
$324$	10.2476	−	30.4719i	0.569313	−	1.69288i
$325$	3.01734	−	2.18325i	0.167372	−	0.121105i
$326$	−0.115963	+	0.309435i	−0.00642259	+	0.0171380i
$327$	27.4976			1.52062
$328$	−3.45246	−	2.80890i	−0.190630	−	0.155095i
$329$	2.55891	+	12.8645i	0.141077	+	0.709244i
$330$	−3.59172	+	14.5683i	−0.197718	+	0.801959i
$331$	3.48703	+	1.44437i	0.191664	+	0.0793900i	0.476451	−	0.879201i	$-0.341923\pi$
$331$	3.48703	+	1.44437i	0.191664	+	0.0793900i	−0.284787	+	0.958591i	$0.591923\pi$
$332$	28.3248	−	1.93711i	1.55452	−	0.106313i
$333$	0.229130	+	1.15191i	0.0125562	+	0.0631245i
$334$	0.473712	−	0.0161795i	0.0259204	−	0.000885303i
$335$	−9.11751	−	28.1542i	−0.498143	−	1.53823i
$336$	14.6138	−	2.00825i	0.797249	−	0.109559i
$337$	−7.05865	+	4.71644i	−0.384509	+	0.256921i	−0.732769	−	0.680477i	$-0.761773\pi$
$337$	−7.05865	+	4.71644i	−0.384509	+	0.256921i	0.348260	+	0.937398i	$0.386773\pi$
$338$	−14.9592	−	9.27288i	−0.813674	−	0.504378i
$339$			35.7427i			1.94128i
$340$	−17.7829	−	4.87512i	−0.964416	−	0.264391i
$341$		−	5.21305i		−	0.282302i
$342$	6.16607	−	9.94725i	0.333423	−	0.537885i
$343$	12.3895	−	8.27837i	0.668968	−	0.446990i
$344$	−13.8248	+	4.25795i	−0.745384	+	0.229573i
$345$	18.5999	+	9.49998i	1.00138	+	0.511462i
$346$	1.09082	+	31.9375i	0.0586427	+	1.71697i
$347$	−2.62807	−	13.2122i	−0.141082	−	0.709269i	−0.984967	−	0.172744i	$-0.944737\pi$
$347$	−2.62807	−	13.2122i	−0.141082	−	0.709269i	0.843885	−	0.536525i	$-0.180263\pi$
$348$	1.10669	+	16.1822i	0.0593246	+	0.867455i
$349$	−8.94668	−	3.70583i	−0.478905	−	0.198369i	0.130154	−	0.991494i	$-0.458453\pi$
$349$	−8.94668	−	3.70583i	−0.478905	−	0.198369i	−0.609059	+	0.793125i	$0.708453\pi$
$350$	2.21248	+	8.06290i	0.118262	+	0.430980i
$351$	1.68930	+	8.49267i	0.0901680	+	0.453305i
$352$	−7.27587	+	4.59620i	−0.387805	+	0.244978i
$353$	−12.5295			−0.666876			−0.333438	−	0.942772i	$-0.608209\pi$
$353$	−12.5295			−0.666876			−0.333438	+	0.942772i	$0.608209\pi$
$354$	39.2240	+	14.6995i	2.08473	+	0.781268i
$355$	13.5266	+	10.6849i	0.717918	+	0.567097i
$356$	−6.12510	+	18.2133i	−0.324630	+	0.965305i
$357$	13.1263	−	7.67435i	0.694719	−	0.406170i
$358$	1.42929	+	1.98862i	0.0755405	+	0.105102i
$359$	−11.8407	−	28.5859i	−0.624927	−	1.50871i	−0.845853	−	0.533416i	$-0.820908\pi$
$359$	−11.8407	−	28.5859i	−0.624927	−	1.50871i	0.220927	−	0.975290i	$-0.429092\pi$
$360$	24.4420	+	34.8258i	1.28821	+	1.83548i
$361$	−12.3650	+	12.3650i	−0.650789	+	0.650789i
$362$	6.79109	+	2.54501i	0.356932	+	0.133763i
$363$	−22.5236	−	15.0498i	−1.18218	−	0.789909i
$364$	−1.39445	+	1.07629i	−0.0730890	+	0.0564129i
$365$	24.0181	+	18.9724i	1.25717	+	0.993060i
$366$	25.0945	+	15.5555i	1.31171	+	0.813099i
$367$	−4.36342	−	21.9364i	−0.227769	−	1.14507i	−0.910216	−	0.414135i	$-0.864084\pi$
$367$	−4.36342	−	21.9364i	−0.227769	−	1.14507i	0.682447	−	0.730935i	$-0.260916\pi$
$368$	3.91477	+	11.3214i	0.204072	+	0.590168i
$369$	5.88124	+	8.80190i	0.306165	+	0.458209i
$370$	−0.499953	−	0.234192i	−0.0259913	−	0.0121751i
$371$	−11.8877	−	2.36461i	−0.617180	−	0.122765i
$372$	−16.1099	−	14.0474i	−0.835258	−	0.728326i
$373$	−19.7385	+	19.7385i	−1.02202	+	1.02202i	−0.0222684	+	0.999752i	$0.507089\pi$
$373$	−19.7385	+	19.7385i	−1.02202	+	1.02202i	−0.999752	+	0.0222684i	$0.992911\pi$
$374$	−5.11738	+	7.24602i	−0.264613	+	0.374683i
$375$	−25.6749	+	23.5947i	−1.32585	+	1.21842i
$376$	−31.2375	−	2.94265i	−1.61095	−	0.151755i
$377$	−1.07608	−	1.61047i	−0.0554211	−	0.0829436i
$378$	−19.1838	−	3.13934i	−0.986707	−	0.161470i
$379$	−0.192350	−	0.287872i	−0.00988036	−	0.0147870i	0.826497	−	0.562942i	$-0.190330\pi$
$379$	−0.192350	−	0.287872i	−0.00988036	−	0.0147870i	−0.836377	+	0.548155i	$0.815330\pi$
$380$	2.04806	+	5.10592i	0.105063	+	0.261928i
$381$	−30.9543	−	20.6830i	−1.58584	−	1.05962i
$382$	1.65870	−	0.389234i	0.0848667	−	0.0199149i
$383$	31.0734	−	12.8710i	1.58778	−	0.657678i	0.598155	−	0.801380i	$-0.295901\pi$
$383$	31.0734	−	12.8710i	1.58778	−	0.657678i	0.989621	+	0.143702i	$0.0459007\pi$
$384$	−5.40242	+	34.8698i	−0.275691	+	1.77944i
$385$	4.00966	+	0.319502i	0.204351	+	0.0162833i
$386$	−16.3639	+	7.44232i	−0.832898	+	0.378804i
$387$	34.4059			1.74895
$388$	−7.63636	−	28.1797i	−0.387678	−	1.43061i
$389$	1.86917	+	4.51257i	0.0947705	+	0.228796i	0.964155	−	0.265340i	$-0.0854843\pi$
$389$	1.86917	+	4.51257i	0.0947705	+	0.228796i	−0.869384	+	0.494137i	$0.835484\pi$
$390$	−6.65274	−	3.11633i	−0.336875	−	0.157802i
$391$	8.19203	+	9.23898i	0.414289	+	0.467235i
$392$	4.66382	+	15.1426i	0.235559	+	0.764817i
$393$	−21.7852	+	52.5941i	−1.09892	+	2.65302i
$394$	−28.9554	−	10.8512i	−1.45875	−	0.546677i
$395$	33.4806	+	9.47776i	1.68459	+	0.476878i
$396$	19.7564	−	5.35375i	0.992798	−	0.269036i
$397$	0.0741316	−	0.110946i	0.00372056	−	0.00556821i	−0.829605	−	0.558351i	$-0.811434\pi$
$397$	0.0741316	−	0.110946i	0.00372056	−	0.00556821i	0.833325	+	0.552783i	$0.186434\pi$
$398$	−0.330076	−	9.66415i	−0.0165452	−	0.484420i
$399$	−4.19118	−	1.73605i	−0.209822	−	0.0869110i
$400$	−19.9950	−	0.449247i	−0.999748	−	0.0224624i
$401$	8.71041	+	5.82011i	0.434977	+	0.290642i	0.753716	−	0.657200i	$-0.228259\pi$
$401$	8.71041	+	5.82011i	0.434977	+	0.290642i	−0.318739	+	0.947843i	$0.603259\pi$
$402$	−39.8442	+	42.6621i	−1.98725	+	2.12779i
$403$	2.50335	+	0.497947i	0.124701	+	0.0248045i
$404$	13.1478	+	26.4717i	0.654125	+	1.31702i
$405$	−11.0738	−	34.1951i	−0.550262	−	1.69917i
$406$	4.23321	−	0.993371i	0.210091	−	0.0493002i
$407$	−0.187810	+	0.187810i	−0.00930939	+	0.00930939i
$408$	8.60270	+	35.3398i	0.425897	+	1.74958i
$409$			16.2629i			0.804148i	0.915607	+	0.402074i	$0.131711\pi$
$409$			16.2629i			0.804148i	−0.915607	+	0.402074i	$0.868289\pi$
$410$	−4.97100	−	0.225707i	−0.245500	−	0.0111469i
$411$	−9.60058	+	48.2654i	−0.473562	+	2.38076i
$412$	−15.0613	−	5.06508i	−0.742016	−	0.249538i
$413$	2.19071	−	11.0134i	0.107798	−	0.541935i
$414$	−0.972561	−	28.4752i	−0.0477988	−	1.39948i
$415$	24.1569	−	20.5912i	1.18582	−	1.01078i
$416$	−1.51215	−	3.93296i	−0.0741392	−	0.192829i
$417$	−7.96679	−	19.2335i	−0.390135	−	0.941870i
$418$	2.64511	−	0.0903431i	0.129377	−	0.00441882i
$419$	−0.750436	−	3.77270i	−0.0366612	−	0.184308i	0.958116	−	0.286381i	$-0.0924524\pi$
$419$	−0.750436	−	3.77270i	−0.0366612	−	0.184308i	−0.994777	+	0.102073i	$0.967452\pi$
$420$	11.7921	−	11.5301i	0.575393	−	0.562611i
$421$	−3.64645	+	3.64645i	−0.177717	+	0.177717i	−0.790360	−	0.612643i	$-0.790106\pi$
$421$	−3.64645	+	3.64645i	−0.177717	+	0.177717i	0.612643	+	0.790360i	$0.290106\pi$
$422$	0.446490	+	0.981722i	0.0217348	+	0.0477895i
$423$	68.9453	+	28.5581i	3.35223	+	1.38854i
$424$	13.5586	−	25.6278i	0.658464	−	1.24459i
$425$	−19.2202	+	7.45544i	−0.932317	+	0.361642i
$426$	5.49124	−	33.5556i	0.266051	−	1.62577i
$427$	3.02889	−	7.31240i	0.146578	−	0.353872i
$428$	−5.07140	−	18.7145i	−0.245135	−	0.904598i
$429$	−2.49914	+	2.49914i	−0.120659	+	0.120659i
$430$	−9.58600	+	13.0261i	−0.462278	+	0.628172i
$431$	−33.0830	+	6.58061i	−1.59355	+	0.316977i	−0.910537	−	0.413429i	$-0.864331\pi$
$431$	−33.0830	+	6.58061i	−1.59355	+	0.316977i	−0.683014	+	0.730405i	$0.739331\pi$
$432$	20.3295	−	41.8199i	0.978105	−	2.01206i
$433$	−1.71921	−	4.15055i	−0.0826201	−	0.199463i	0.877171	−	0.480178i	$-0.159428\pi$
$433$	−1.71921	−	4.15055i	−0.0826201	−	0.199463i	−0.959791	+	0.280716i	$0.909428\pi$
$434$	−3.01890	+	4.87016i	−0.144912	+	0.233775i
$435$	11.7639	+	13.8010i	0.564038	+	0.661709i
$436$	17.4887	+	2.25204i	0.837557	+	0.107853i
$437$	0.718714	−	3.61322i	0.0343808	−	0.172844i
$438$	9.75036	−	59.5821i	0.465890	−	2.84694i
$439$	−19.2574	−	3.83053i	−0.919105	−	0.182821i	−0.287203	−	0.957870i	$-0.592725\pi$
$439$	−19.2574	−	3.83053i	−0.919105	−	0.182821i	−0.631902	+	0.775048i	$0.717725\pi$
$440$	−3.47751	+	8.97141i	−0.165784	+	0.427695i
$441$		−	37.6855i		−	1.79455i
$442$	−2.99079	−	3.14955i	−0.142257	−	0.149809i
$443$	27.8935	+	27.8935i	1.32526	+	1.32526i	0.909454	+	0.415805i	$0.136500\pi$
$443$	27.8935	+	27.8935i	1.32526	+	1.32526i	0.415805	+	0.909454i	$0.363500\pi$
$444$	0.0743031	+	1.08647i	0.00352627	+	0.0515617i
$445$	6.61892	+	20.4388i	0.313767	+	0.968890i
$446$	−5.59573	+	4.02185i	−0.264966	+	0.190440i
$447$	12.4445	−	62.5628i	0.588606	−	2.95912i
$448$	9.45898	−	0.0803955i	0.446895	−	0.00379833i
$449$	−20.2034	−	13.4995i	−0.953456	−	0.637079i	−0.0215458	−	0.999768i	$-0.506859\pi$
$449$	−20.2034	−	13.4995i	−0.953456	−	0.637079i	−0.931910	+	0.362689i	$0.881859\pi$
$450$	45.1357	+	15.0195i	2.12772	+	0.708027i
$451$	−0.916130	+	2.21173i	−0.0431389	+	0.104146i
$452$	−2.92732	+	22.7327i	−0.137690	+	1.06926i
$453$	7.75862	−	11.6116i	0.364532	−	0.545560i
$454$	−25.5475	+	11.6191i	−1.19900	+	0.545310i
$455$	−0.536428	+	1.89495i	−0.0251481	+	0.0888368i
$456$	6.84851	−	8.41762i	0.320711	−	0.394191i
$457$	−5.93595	+	14.3306i	−0.277672	+	0.670359i	−0.999770	−	0.0214312i	$-0.993178\pi$
$457$	−5.93595	+	14.3306i	−0.277672	+	0.670359i	0.722098	+	0.691790i	$0.243178\pi$
$458$	8.04492	−	5.78217i	0.375914	−	0.270183i
$459$	2.87364	−	47.8443i	0.134130	−	2.23318i
$460$	11.0516	+	7.56540i	0.515286	+	0.352738i
$461$	−11.4994	−	27.7619i	−0.535578	−	1.29300i	−0.927782	−	0.373122i	$-0.878287\pi$
$461$	−11.4994	−	27.7619i	−0.535578	−	1.29300i	0.392204	−	0.919878i	$-0.371713\pi$
$462$	−3.28477	−	7.22241i	−0.152821	−	0.336017i
$463$		−	4.00369i		−	0.186067i	−0.995663	−	0.0930336i	$-0.970344\pi$
$463$		−	4.00369i		−	0.186067i	0.995663	−	0.0930336i	$-0.0296564\pi$
$464$	−0.621453	+	10.3826i	−0.0288502	+	0.482002i
$465$	−23.8216	−	1.89818i	−1.10470	−	0.0880260i
$466$	−2.07272	+	2.21931i	−0.0960169	+	0.102808i
$467$	1.94531	+	4.69639i	0.0900181	+	0.217323i	0.962476	−	0.271366i	$-0.0874753\pi$
$467$	1.94531	+	4.69639i	0.0900181	+	0.217323i	−0.872458	+	0.488689i	$0.837475\pi$
$468$	0.683796	+	9.99859i	0.0316085	+	0.462185i
$469$	13.0116	+	8.69408i	0.600821	+	0.401456i
$470$	−30.0213	+	18.1459i	−1.38478	+	0.837009i
$471$	48.2943	−	32.2693i	2.22529	−	1.48689i
$472$	23.7429	+	12.5614i	1.09286	+	0.578187i
$473$	4.32274	+	6.46944i	0.198760	+	0.297465i
$474$	−15.6805	−	66.8218i	−0.720229	−	3.06923i
$475$	5.23807	+	3.22396i	0.240339	+	0.147925i
$476$	8.97699	−	3.80591i	0.411460	−	0.174444i
$477$	−48.7617	+	48.7617i	−2.23264	+	2.23264i
$478$	15.6833	−	25.3007i	0.717339	−	1.15723i
$479$	1.58775	−	7.98218i	0.0725463	−	0.364715i	−0.927410	−	0.374046i	$-0.877970\pi$
$479$	1.58775	−	7.98218i	0.0725463	−	0.364715i	0.999956	+	0.00933105i	$0.00297021\pi$
$480$	18.3536	+	34.9215i	0.837722	+	1.59394i
$481$	−0.0722484	−	0.108127i	−0.00329424	−	0.00493018i
$482$	−21.0770	−	19.6848i	−0.960032	−	0.896618i
$483$	−10.8319	+	2.15460i	−0.492869	+	0.0980377i
$484$	−13.0926	−	11.4165i	−0.595120	−	0.518931i
$485$	−25.6147	−	20.2336i	−1.16311	−	0.918759i
$486$	−14.7296	+	15.7713i	−0.668146	+	0.715401i
$487$	−6.34485	+	9.49573i	−0.287512	+	0.430293i	−0.946909	−	0.321503i	$-0.895812\pi$
$487$	−6.34485	+	9.49573i	−0.287512	+	0.430293i	0.659396	+	0.751796i	$0.270812\pi$
$488$	14.6863	+	11.9487i	0.664818	+	0.540890i
$489$	0.515313	−	0.515313i	0.0233033	−	0.0233033i
$490$	14.2677	+	10.4997i	0.644549	+	0.474330i
$491$	−12.0401	+	4.98717i	−0.543362	+	0.225068i	−0.637444	−	0.770497i	$-0.720008\pi$
$491$	−12.0401	+	4.98717i	−0.543362	+	0.225068i	0.0940823	+	0.995564i	$0.470008\pi$
$492$	4.36625	+	8.79100i	0.196846	+	0.396329i
$493$	3.50164	+	10.1334i	0.157706	+	0.456385i
$494$	−0.209276	+	1.27883i	−0.00941577	+	0.0575375i
$495$	14.1855	−	17.9582i	0.637590	−	0.807159i
$496$	−9.09554	−	10.2537i	−0.408402	−	0.460404i
$497$	−9.11514			−0.408870
$498$	−58.6305	−	21.9722i	−2.62729	−	0.984597i
$499$	−4.29706	+	0.854738i	−0.192363	+	0.0382633i	−0.290331	−	0.956926i	$-0.593766\pi$
$499$	−4.29706	+	0.854738i	−0.192363	+	0.0382633i	0.0979686	+	0.995190i	$0.468766\pi$
$500$	−18.2619	+	12.9037i	−0.816695	+	0.577070i
$501$	−0.965748	−	0.400026i	−0.0431464	−	0.0178718i
$502$	−16.6994	+	3.91870i	−0.745330	+	0.174900i
$503$	−33.8411	+	6.73142i	−1.50890	+	0.300139i	−0.879108	−	0.476623i	$-0.841861\pi$
$503$	−33.8411	+	6.73142i	−1.50890	+	0.300139i	−0.629794	+	0.776762i	$0.716861\pi$
$504$	−21.5573	−	6.43943i	−0.960240	−	0.286835i
$505$	29.4293	+	15.0311i	1.30959	+	0.668876i
$506$	5.23207	−	3.76048i	0.232594	−	0.167174i
$507$	21.5643	+	32.2732i	0.957704	+	1.43331i
$508$	−17.9933	−	15.6897i	−0.798324	−	0.696120i
$509$		−	21.9043i		−	0.970893i	−0.874267	−	0.485446i	$-0.838657\pi$
$509$		−	21.9043i		−	0.970893i	0.874267	−	0.485446i	$-0.161343\pi$
$510$	31.2482	+	26.0229i	1.38369	+	1.15231i
$511$	−16.1850			−0.715984
$512$	−6.29182	+	21.7351i	−0.278062	+	0.960563i
$513$	−11.8902	+	7.94478i	−0.524965	+	0.350771i
$514$	−9.42658	−	13.1155i	−0.415789	−	0.578500i
$515$	−16.9016	+	5.47344i	−0.744772	+	0.241188i
$516$	31.6408	+	4.07444i	1.39291	+	0.179367i
$517$	3.29240	+	16.5520i	0.144799	+	0.727956i
$518$	0.284218	−	0.0666950i	0.0124878	−	0.00293041i
$519$	26.9696	−	65.1104i	1.18384	−	2.85803i
$520$	−3.97598	−	2.52687i	−0.174358	−	0.110811i
$521$	−4.96360	−	24.9537i	−0.217459	−	1.09324i	−0.923067	−	0.384639i	$-0.874326\pi$
$521$	−4.96360	−	24.9537i	−0.217459	−	1.09324i	0.705608	−	0.708603i	$-0.250674\pi$
$522$	8.68144	−	23.1655i	0.379976	−	1.01393i
$523$			1.24046i			0.0542417i	0.999632	+	0.0271209i	$0.00863390\pi$
$523$			1.24046i			0.0542417i	−0.999632	+	0.0271209i	$0.991366\pi$
$524$	−18.1630	+	31.6661i	−0.793455	+	1.38334i
$525$	2.92000	−	18.2063i	0.127439	−	0.794586i
$526$	4.70246	−	28.7356i	0.205037	−	1.25293i
$527$	−12.7052	−	6.17951i	−0.553447	−	0.269184i
$528$	18.8027	−	2.58389i	0.818282	−	0.112449i
$529$	5.36954	+	12.9632i	0.233458	+	0.563618i
$530$	−4.87541	−	32.0469i	−0.211774	−	1.39203i
$531$	−45.1755	−	45.1755i	−1.96045	−	1.96045i
$532$	−2.52345	−	1.44740i	−0.109405	−	0.0627526i
$533$	−0.974585	−	0.651197i	−0.0422140	−	0.0282065i
$534$	28.9252	−	30.9709i	1.25171	−	1.34024i
$535$	−17.0110	−	13.4374i	−0.735452	−	0.580947i
$536$	−28.8353	+	23.8703i	−1.24549	+	1.03104i
$537$	−1.05366	−	5.29712i	−0.0454689	−	0.228587i
$538$	−11.7023	+	12.5300i	−0.504524	+	0.540206i
$539$	7.08611	−	4.73479i	0.305220	−	0.203942i
$540$	−9.56900	−	51.0997i	−0.411784	−	2.19898i
$541$	−16.8414	−	3.34996i	−0.724067	−	0.144026i	−0.180721	−	0.983534i	$-0.557843\pi$
$541$	−16.8414	−	3.34996i	−0.724067	−	0.144026i	−0.543347	+	0.839509i	$0.682843\pi$
$542$	−2.73940	+	4.41926i	−0.117667	+	0.189823i
$543$	−11.3095	−	11.3095i	−0.485336	−	0.485336i
$544$	2.57707	+	23.1810i	0.110491	+	0.993877i
$545$	17.2101	−	9.61610i	0.737201	−	0.411908i
$546$	3.78202	−	0.887494i	0.161855	−	0.0379812i
$547$	5.17347	−	3.45680i	0.221202	−	0.147802i	−0.440032	−	0.897982i	$-0.645033\pi$
$547$	5.17347	−	3.45680i	0.221202	−	0.147802i	0.661234	+	0.750180i	$0.270033\pi$
$548$	−10.0590	+	29.9109i	−0.429698	+	1.27773i
$549$	−25.0180	−	37.4421i	−1.06774	−	1.59799i
$550$	2.84666	+	10.3740i	0.121382	+	0.442350i
$551$	1.77713	−	2.65966i	0.0757082	−	0.113305i
$552$	2.47770	−	26.3019i	0.105458	−	1.11948i
$553$	−16.9994	+	7.04137i	−0.722887	+	0.299429i
$554$	3.23268	+	3.01915i	0.137343	+	0.128271i
$555$	0.789833	+	0.926604i	0.0335265	+	0.0393321i
$556$	−3.49173	−	12.8852i	−0.148082	−	0.546453i
$557$	19.0198			0.805894			0.402947	−	0.915223i	$-0.367986\pi$
$557$	19.0198			0.805894			0.402947	+	0.915223i	$0.367986\pi$
$558$	13.4964	+	29.6752i	0.571346	+	1.25625i
$559$	−3.51959	+	1.45786i	−0.148863	+	0.0616609i
$560$	8.44416	−	6.36747i	0.356831	−	0.269075i
$561$	16.8888	−	9.87411i	0.713048	−	0.416885i
$562$	−18.3804	−	25.5732i	−0.775331	−	1.07874i
$563$	−39.0855	−	16.1897i	−1.64726	−	0.682316i	−0.650255	−	0.759716i	$-0.725338\pi$
$563$	−39.0855	−	16.1897i	−1.64726	−	0.682316i	−0.997000	+	0.0774002i	$0.975338\pi$
$564$	60.0225	+	34.4276i	2.52740	+	1.44967i
$565$	12.4995	+	22.3706i	0.525857	+	0.941138i
$566$	−3.85241	+	1.75208i	−0.161929	+	0.0736456i
$567$	15.8035	+	10.5595i	0.663683	+	0.443459i
$568$	6.24067	−	20.8919i	0.261853	−	0.876606i
$569$	−8.85110	−	3.66624i	−0.371057	−	0.153697i	0.189359	−	0.981908i	$-0.439359\pi$
$569$	−8.85110	−	3.66624i	−0.371057	−	0.153697i	−0.560417	+	0.828211i	$0.689359\pi$
$570$	0.550307	−	12.1200i	0.0230498	−	0.507652i
$571$	18.9908	−	28.4218i	0.794742	−	1.18941i	−0.183719	−	0.982979i	$-0.558814\pi$
$571$	18.9908	−	28.4218i	0.794742	−	1.18941i	0.978460	−	0.206436i	$-0.0661865\pi$
$572$	−1.79415	+	1.38479i	−0.0750173	+	0.0579012i
$573$	−3.68522	−	0.733036i	−0.153952	−	0.0306230i
$574$	2.13670	−	1.53572i	0.0891840	−	0.0640998i
$575$	14.9635	−	0.558689i	0.624020	−	0.0232989i
$576$	29.5184	−	45.0007i	1.22993	−	1.87503i
$577$	−14.8956	+	14.8956i	−0.620112	+	0.620112i	−0.945560	−	0.325448i	$-0.894485\pi$
$577$	−14.8956	+	14.8956i	−0.620112	+	0.620112i	0.325448	+	0.945560i	$0.394485\pi$
$578$	11.5938	+	21.0614i	0.482240	+	0.876039i
$579$	39.6453			1.64760
$580$	6.35167	+	9.74105i	0.263739	+	0.404475i
$581$	−3.27458	+	16.4624i	−0.135852	+	0.682976i
$582$	−10.3985	+	63.5428i	−0.431032	+	2.63393i
$583$	−15.2952	−	3.04240i	−0.633462	−	0.126003i
$584$	11.0811	−	37.0962i	0.458538	−	1.53505i
$585$	7.26867	+	8.52735i	0.300523	+	0.352562i
$586$	−3.02782	−	1.87688i	−0.125078	−	0.0775330i
$587$	9.24072	−	3.82763i	0.381405	−	0.157983i	−0.183739	−	0.982975i	$-0.558820\pi$
$587$	9.24072	−	3.82763i	0.381405	−	0.157983i	0.565145	+	0.824992i	$0.308820\pi$
$588$	4.46281	−	34.6569i	0.184043	−	1.42922i
$589$	0.822349	+	4.13423i	0.0338843	+	0.170348i
$590$	29.6900	−	4.51684i	1.22232	−	0.185955i
$591$	48.2205	+	48.2205i	1.98353	+	1.98353i
$592$	−0.0417245	+	0.697092i	−0.00171487	+	0.0286503i
$593$	−26.2979	−	10.8929i	−1.07993	−	0.447320i	−0.229442	−	0.973322i	$-0.573690\pi$
$593$	−26.2979	−	10.8929i	−1.07993	−	0.447320i	−0.850483	+	0.526002i	$0.823690\pi$
$594$	−24.6826	−	4.03920i	−1.01274	−	0.165730i
$595$	5.53171	−	9.39358i	0.226778	−	0.385099i
$596$	13.0387	−	38.7713i	0.534086	−	1.58814i
$597$	−8.16088	+	19.7021i	−0.334003	+	0.806354i
$598$	1.30605	+	2.87168i	0.0534083	+	0.117432i
$599$	2.70400	+	2.70400i	0.110483	+	0.110483i	0.760187	−	0.649704i	$-0.225107\pi$
$599$	2.70400	+	2.70400i	0.110483	+	0.110483i	−0.649704	+	0.760187i	$0.725107\pi$
$600$	39.7296	+	19.1575i	1.62196	+	0.782104i
$601$	−0.332288	+	0.0660962i	−0.0135543	+	0.00269612i	−0.201863	−	0.979414i	$-0.564700\pi$
$601$	−0.332288	+	0.0660962i	−0.0135543	+	0.00269612i	0.188309	+	0.982110i	$0.439700\pi$
$602$	−0.291929	−	8.54724i	−0.0118981	−	0.348359i
$603$	82.2563	−	34.0717i	3.34974	−	1.38751i
$604$	5.88554	−	6.74965i	0.239479	−	0.274639i
$605$	−19.3600	−	1.54267i	−0.787098	−	0.0627183i
$606$	−2.22504	−	65.1459i	−0.0903861	−	2.64637i
$607$	0.914745	+	0.181954i	0.0371283	+	0.00738529i	0.213620	−	0.976917i	$-0.431475\pi$
$607$	0.914745	+	0.181954i	0.0371283	+	0.00738529i	−0.176491	+	0.984302i	$0.556475\pi$
$608$	5.04511	−	4.79279i	0.204606	−	0.194373i
$609$	−9.40512	−	1.87079i	−0.381115	−	0.0758084i
$610$	21.1459	+	0.960126i	0.856174	+	0.0388744i
$611$	−8.26290			−0.334281
$612$	10.3710	−	54.4965i	0.419222	−	2.20289i
$613$	−8.98729	−	8.98729i	−0.362993	−	0.362993i	0.501921	−	0.864914i	$-0.332627\pi$
$613$	−8.98729	−	8.98729i	−0.362993	−	0.362993i	−0.864914	+	0.501921i	$0.832627\pi$
$614$	14.6899	−	3.44716i	0.592838	−	0.139116i
$615$	9.77318	+	4.99170i	0.394093	+	0.201285i
$616$	−1.49763	−	4.86253i	−0.0603412	−	0.195917i
$617$	−5.51827	+	27.7422i	−0.222157	+	1.11686i	0.695207	+	0.718810i	$0.255313\pi$
$617$	−5.51827	+	27.7422i	−0.222157	+	1.11686i	−0.917364	+	0.398049i	$0.869687\pi$
$618$	25.6110	+	23.9193i	1.03023	+	0.962175i
$619$	0.855594	−	1.28049i	0.0343892	−	0.0514671i	−0.813877	−	0.581038i	$-0.802647\pi$
$619$	0.855594	−	1.28049i	0.0343892	−	0.0514671i	0.848266	+	0.529571i	$0.177647\pi$
$620$	−14.9953	−	3.15824i	−0.602226	−	0.126838i
$621$	−13.3227	+	32.1638i	−0.534621	+	1.29069i
$622$	1.18338	+	34.6475i	0.0474491	+	1.38924i
$623$	−9.44588	−	6.31153i	−0.378441	−	0.252866i
$624$	−0.555217	+	9.27602i	−0.0222265	+	0.371338i
$625$	−7.81811	+	23.7461i	−0.312725	+	0.949844i
$626$	−5.39210	+	14.3883i	−0.215512	+	0.575071i
$627$	−5.39254	−	2.23366i	−0.215357	−	0.0892039i
$628$	33.3585	−	16.5682i	1.33115	−	0.661144i
$629$	0.235100	+	0.680357i	0.00937406	+	0.0271276i
$630$	−23.6521	+	8.56207i	−0.942322	+	0.341121i
$631$	5.48017	−	2.26996i	0.218162	−	0.0903656i	−0.270926	−	0.962600i	$-0.587330\pi$
$631$	5.48017	−	2.26996i	0.218162	−	0.0903656i	0.489088	+	0.872235i	$0.337330\pi$
$632$	−4.50024	−	43.7835i	−0.179010	−	1.74161i
$633$		−	2.37846i		−	0.0945351i
$634$	7.97581	+	17.5369i	0.316760	+	0.696478i
$635$	−26.6066	−	2.12010i	−1.05585	−	0.0841335i
$636$	−50.6174	+	39.0684i	−2.00711	+	1.54916i
$637$	1.59682	+	3.85508i	0.0632685	+	0.152744i
$638$	5.44661	−	1.27811i	0.215633	−	0.0506008i
$639$	−28.8119	+	43.1200i	−1.13978	+	1.70580i
$640$	8.81298	+	23.7135i	0.348364	+	0.937360i
$641$	−38.8800	+	25.9788i	−1.53567	+	1.02610i	−0.554673	+	0.832068i	$0.687157\pi$
$641$	−38.8800	+	25.9788i	−1.53567	+	1.02610i	−0.980995	+	0.194032i	$0.937843\pi$
$642$	−6.90577	+	42.1995i	−0.272549	+	1.66548i
$643$	−40.4768	+	27.0458i	−1.59625	+	1.06658i	−0.642369	+	0.766395i	$0.722048\pi$
$643$	−40.4768	+	27.0458i	−1.59625	+	1.06658i	−0.953881	+	0.300185i	$0.902952\pi$
$644$	−7.06565	+	0.483214i	−0.278425	+	0.0190413i
$645$	31.1368	−	17.3976i	1.22601	−	0.685030i
$646$	2.91531	−	6.55374i	0.114701	−	0.257853i
$647$	3.70557	+	3.70557i	0.145681	+	0.145681i	0.776186	−	0.630505i	$-0.217152\pi$
$647$	3.70557	+	3.70557i	0.145681	+	0.145681i	−0.630505	+	0.776186i	$0.717152\pi$
$648$	−35.0223	+	28.9920i	−1.37581	+	1.13891i
$649$	2.81865	−	14.1703i	0.110642	−	0.556233i
$650$	−5.25361	+	0.376068i	−0.206064	+	0.0147506i
$651$	10.5070	−	7.02053i	0.411800	−	0.275156i
$652$	0.369948	−	0.285540i	0.0144883	−	0.0111826i
$653$	27.3095	−	5.43220i	1.06870	−	0.212578i	0.370758	−	0.928729i	$-0.379098\pi$
$653$	27.3095	−	5.43220i	1.06870	−	0.212578i	0.697945	+	0.716151i	$0.254098\pi$
$654$	−33.0524	−	20.4884i	−1.29245	−	0.801160i
$655$	4.75766	+	40.5359i	0.185897	+	1.58387i
$656$	2.05699	+	5.94875i	0.0803120	+	0.232260i
$657$	−51.1590	+	76.5649i	−1.99590	+	2.98708i
$658$	6.50950	−	17.3699i	0.253767	−	0.677151i
$659$	−14.3020	−	14.3020i	−0.557126	−	0.557126i	0.371362	−	0.928488i	$-0.378891\pi$
$659$	−14.3020	−	14.3020i	−0.557126	−	0.557126i	−0.928488	+	0.371362i	$0.878891\pi$
$660$	15.1721	−	14.8351i	0.590574	−	0.577454i
$661$	−36.7515	+	15.2230i	−1.42947	+	0.592105i	−0.957220	−	0.289360i	$-0.906558\pi$
$661$	−36.7515	+	15.2230i	−1.42947	+	0.592105i	−0.472248	+	0.881465i	$0.656558\pi$
$662$	−3.11524	−	4.33433i	−0.121077	−	0.168459i
$663$	3.12842	+	9.05334i	0.121498	+	0.351602i
$664$	−35.4900	−	18.7763i	−1.37728	−	0.728663i
$665$	−3.23028	+	0.379135i	−0.125265	+	0.0147022i
$666$	0.582873	−	1.55534i	0.0225859	−	0.0602680i
$667$		−	7.78734i		−	0.301527i
$668$	−0.581462	−	0.333514i	−0.0224974	−	0.0129041i
$669$	14.9054	−	2.96487i	0.576277	−	0.114629i
$670$	−10.0183	+	40.6351i	−0.387042	+	1.56987i
$671$	3.89709	−	9.40841i	0.150446	−	0.363208i
$672$	−19.0623	−	8.47480i	−0.735344	−	0.326922i
$673$	39.3320	−	7.82362i	1.51614	−	0.301578i	0.634283	−	0.773101i	$-0.281295\pi$
$673$	39.3320	−	7.82362i	1.51614	−	0.301578i	0.881854	+	0.471522i	$0.156295\pi$
$674$	11.9988	−	0.409815i	0.462176	−	0.0157855i
$675$	−42.6049	−	39.5380i	−1.63986	−	1.52182i
$676$	11.0719	+	22.2922i	0.425843	+	0.857391i
$677$	−5.75703	−	8.61600i	−0.221261	−	0.331140i	0.704188	−	0.710014i	$-0.251311\pi$
$677$	−5.75703	−	8.61600i	−0.221261	−	0.331140i	−0.925448	+	0.378874i	$0.876311\pi$
$678$	26.6319	−	42.9631i	1.02279	−	1.64999i
$679$	17.2609			0.662414
$680$	17.7428	+	19.1100i	0.680407	+	0.732835i
$681$	61.8949			2.37182
$682$	−3.88424	+	6.26614i	−0.148735	+	0.239943i
$683$	3.06360	+	4.58501i	0.117226	+	0.175440i	0.885442	−	0.464750i	$-0.153856\pi$
$683$	3.06360	+	4.58501i	0.117226	+	0.175440i	−0.768217	+	0.640190i	$0.778856\pi$
$684$	−14.8234	+	7.36235i	−0.566785	+	0.281507i
$685$	10.8700	+	33.5656i	0.415320	+	1.28248i
$686$	−21.0605	+	0.719314i	−0.804092	+	0.0274635i
$687$	−21.4293	+	4.26256i	−0.817581	+	0.162627i
$688$	19.7902	+	5.18275i	0.754493	+	0.197591i
$689$	2.92198	−	7.05427i	0.111318	−	0.268746i
$690$	−15.2788	−	25.2778i	−0.581655	−	0.962310i
$691$	38.7500	−	7.70785i	1.47412	−	0.293220i	0.608351	−	0.793668i	$-0.291831\pi$
$691$	38.7500	−	7.70785i	1.47412	−	0.293220i	0.865767	+	0.500448i	$0.166831\pi$
$692$	22.4854	−	39.2020i	0.854768	−	1.49024i
$693$			12.1014i			0.459695i
$694$	−6.68543	+	17.8394i	−0.253776	+	0.677174i
$695$	−11.7123	−	9.25180i	−0.444274	−	0.350941i
$696$	10.7271	−	20.2757i	0.406608	−	0.768549i
$697$	4.30445	+	4.85456i	0.163042	+	0.183879i
$698$	7.99278	+	11.1206i	0.302531	+	0.420921i
$699$	6.18724	−	2.56284i	0.234023	−	0.0969355i
$700$	3.34823	−	11.3402i	0.126551	−	0.428619i
$701$	−13.2312	−	13.2312i	−0.499734	−	0.499734i	0.411621	−	0.911355i	$-0.364963\pi$
$701$	−13.2312	−	13.2312i	−0.499734	−	0.499734i	−0.911355	+	0.411621i	$0.864963\pi$
$702$	4.29732	−	11.4670i	0.162192	−	0.432793i
$703$	0.119317	−	0.178570i	0.00450011	−	0.00673489i
$704$	12.1703	−	0.103440i	0.458685	−	0.00389854i
$705$	76.8351	−	9.01806i	2.89378	−	0.339640i
$706$	15.0605	+	9.33569i	0.566811	+	0.351353i
$707$	−17.1385	+	3.40907i	−0.644561	+	0.128211i
$708$	−36.1951	−	46.8947i	−1.36030	−	1.76241i
$709$	24.4519	−	16.3382i	0.918309	−	0.613594i	−0.00402336	−	0.999992i	$-0.501281\pi$
$709$	24.4519	−	16.3382i	0.918309	−	0.613594i	0.922332	+	0.386397i	$0.126281\pi$
$710$	−8.29779	−	22.9220i	−0.311411	−	0.860249i
$711$	−20.4231	+	102.674i	−0.765927	+	3.85058i
$712$	20.9332	−	17.3288i	0.784504	−	0.649424i
$713$	7.25630	+	7.25630i	0.271750	+	0.271750i
$714$	−21.4961	−	0.555774i	−0.804472	−	0.0207993i
$715$	−0.690189	+	2.43812i	−0.0258116	+	0.0911806i
$716$	−0.236306	−	3.45531i	−0.00883116	−	0.129131i
$717$	−54.5841	+	36.4720i	−2.03848	+	1.36207i
$718$	−7.06672	+	43.1830i	−0.263728	+	1.61158i
$719$	−32.3453	+	21.6124i	−1.20628	+	0.806008i	−0.985559	−	0.169330i	$-0.945840\pi$
$719$	−32.3453	+	21.6124i	−1.20628	+	0.806008i	−0.220716	+	0.975338i	$0.570840\pi$
$720$	−3.43092	−	60.0727i	−0.127863	−	2.23878i
$721$	5.21924	−	7.81115i	0.194375	−	0.290902i
$722$	24.0760	−	5.64971i	0.896016	−	0.210260i
$723$	24.3395	+	58.7608i	0.905196	+	2.18534i
$724$	−6.26668	−	8.11916i	−0.232899	−	0.301746i
$725$	12.1891	+	4.52383i	0.452692	+	0.168011i
$726$	15.8600	+	34.8723i	0.588620	+	1.29423i
$727$		−	25.5554i		−	0.947796i	−0.880580	−	0.473898i	$-0.842847\pi$
$727$		−	25.5554i		−	0.947796i	0.880580	−	0.473898i	$-0.157153\pi$
$728$	2.47808	−	0.254707i	0.0918439	−	0.00944008i
$729$	−0.583554	+	0.241716i	−0.0216131	+	0.00895244i
$730$	−14.7337	−	40.7009i	−0.545320	−	1.50641i
$731$	20.8914	−	2.86653i	0.772697	−	0.106022i
$732$	−18.5734	−	37.3957i	−0.686493	−	1.38219i
$733$	0.990253	+	0.410176i	0.0365758	+	0.0151502i	0.400896	−	0.916123i	$-0.368699\pi$
$733$	0.990253	+	0.410176i	0.0365758	+	0.0151502i	−0.364321	+	0.931274i	$0.618699\pi$
$734$	−11.0999	+	29.6189i	−0.409705	+	1.09325i
$735$	−19.0560	−	34.1048i	−0.702889	−	1.25798i
$736$	3.72996	−	16.5253i	0.137488	−	0.609131i
$737$	16.7412	+	11.1861i	0.616672	+	0.412047i
$738$	−0.511026	−	14.9621i	−0.0188111	−	0.550762i
$739$	0.302315	−	0.729852i	0.0111208	−	0.0268480i	−0.918222	−	0.396067i	$-0.870375\pi$
$739$	0.302315	−	0.729852i	0.0111208	−	0.0268480i	0.929342	+	0.369219i	$0.120375\pi$
$740$	0.426452	+	0.654015i	0.0156767	+	0.0240421i
$741$	1.58772	−	2.37618i	0.0583262	−	0.0872913i
$742$	12.5273	+	11.6998i	0.459891	+	0.429514i
$743$	−6.88723	+	34.6244i	−0.252668	+	1.27025i	0.621033	+	0.783784i	$0.286713\pi$
$743$	−6.88723	+	34.6244i	−0.252668	+	1.27025i	−0.873701	+	0.486463i	$0.838287\pi$
$744$	8.89750	+	28.8886i	0.326198	+	1.05911i
$745$	−14.0899	−	43.5087i	−0.516215	−	1.59403i
$746$	38.4330	−	9.01874i	1.40713	−	0.330199i
$747$	67.5265	+	67.5265i	2.47066	+	2.47066i
$748$	11.5501	−	4.89683i	0.422315	−	0.179046i
$749$	11.4632			0.418856
$750$	48.4419	−	9.23073i	1.76885	−	0.337059i
$751$	−33.4846	−	6.66050i	−1.22187	−	0.243045i	−0.458316	−	0.888789i	$-0.651547\pi$
$751$	−33.4846	−	6.66050i	−1.22187	−	0.243045i	−0.763554	+	0.645744i	$0.776547\pi$
$752$	35.3552	+	26.8121i	1.28927	+	0.977737i
$753$	37.1018	+	7.38001i	1.35206	+	0.268942i
$754$	0.0935017	+	2.73759i	0.00340513	+	0.0996972i
$755$	0.795291	−	9.98069i	0.0289436	−	0.363234i
$756$	20.7200	+	18.0673i	0.753578	+	0.657102i
$757$	39.5796	−	16.3944i	1.43855	−	0.595866i	0.479101	−	0.877760i	$-0.340963\pi$
$757$	39.5796	−	16.3944i	1.43855	−	0.595866i	0.959446	+	0.281894i	$0.0909627\pi$
$758$	0.0167134	+	0.489345i	0.000607059	+	0.0177738i
$759$	−13.9367	+	2.77219i	−0.505872	+	0.100624i
$760$	1.34263	−	7.66338i	0.0487022	−	0.277980i
$761$	−2.24507	−	2.24507i	−0.0813837	−	0.0813837i	0.665243	−	0.746627i	$-0.268328\pi$
$761$	−2.24507	−	2.24507i	−0.0813837	−	0.0813837i	−0.746627	+	0.665243i	$0.768328\pi$
$762$	21.7965	+	47.9253i	0.789605	+	1.73615i
$763$	−3.98941	+	9.63129i	−0.144426	+	0.348676i
$764$	−2.28380	−	0.768036i	−0.0826248	−	0.0277866i
$765$	−26.9521	−	55.8602i	−0.974456	−	2.01963i
$766$	−46.9407	−	7.68165i	−1.69604	−	0.277549i
$767$	6.53546	+	2.70708i	0.235982	+	0.0977469i
$768$	32.4752	−	37.8886i	1.17185	−	1.36719i
$769$	11.5714	+	11.5714i	0.417275	+	0.417275i	0.884263	−	0.466988i	$-0.154661\pi$
$769$	11.5714	+	11.5714i	0.417275	+	0.417275i	−0.466988	+	0.884263i	$0.654661\pi$
$770$	−4.58159	−	3.37164i	−0.165109	−	0.121505i
$771$	6.94919	+	34.9359i	0.250269	+	1.25819i
$772$	25.2148	+	3.24694i	0.907500	+	0.116860i
$773$	1.89439	−	0.784684i	0.0681366	−	0.0282231i	−0.348355	−	0.937363i	$-0.613260\pi$
$773$	1.89439	−	0.784684i	0.0681366	−	0.0282231i	0.416491	+	0.909140i	$0.363260\pi$
$774$	−41.3562	−	25.6358i	−1.48652	−	0.921460i
$775$	−15.5732	+	7.14256i	−0.559407	+	0.256568i
$776$	−11.8177	+	39.5621i	−0.424230	+	1.42020i
$777$	−0.631461	−	0.125605i	−0.0226535	−	0.00450607i
$778$	1.11555	−	6.81686i	0.0399945	−	0.244396i
$779$	0.377643	−	1.89854i	0.0135305	−	0.0680223i
$780$	5.67469	+	8.70281i	0.203186	+	0.311611i
$781$	−11.7279			−0.419657
$782$	−2.96295	−	17.2092i	−0.105955	−	0.615400i
$783$	−21.3745	+	21.3745i	−0.763864	+	0.763864i
$784$	5.67678	−	21.6766i	0.202742	−	0.774163i
$785$	18.9416	−	37.0855i	0.676054	−	1.32364i
$786$	65.3738	−	46.9865i	2.33181	−	1.67595i
$787$	37.4022	+	7.43975i	1.33324	+	0.265199i	0.809722	−	0.586814i	$-0.199618\pi$
$787$	37.4022	+	7.43975i	1.33324	+	0.265199i	0.523522	+	0.852012i	$0.324618\pi$
$788$	26.7194	+	34.6179i	0.951840	+	1.23321i
$789$	−35.6761	+	53.3931i	−1.27010	+	1.90085i
$790$	−33.1821	−	36.3387i	−1.18057	−	1.29287i
$791$	−12.5192	−	5.18564i	−0.445133	−	0.184380i
$792$	−27.7365	−	8.28522i	−0.985573	−	0.294403i
$793$	4.14575	+	2.77010i	0.147220	+	0.0983692i
$794$	−0.171772	+	0.0781226i	−0.00609598	+	0.00277247i
$795$	−19.4719	+	68.7853i	−0.690597	+	2.43956i
$796$	−6.80399	+	11.8623i	−0.241161	+	0.420450i
$797$	−31.1280	−	12.8936i	−1.10261	−	0.456716i	−0.244223	−	0.969719i	$-0.578533\pi$
$797$	−31.1280	−	12.8936i	−1.10261	−	0.456716i	−0.858387	+	0.513003i	$0.828533\pi$
$798$	3.74432	+	5.20959i	0.132547	+	0.184417i
$799$	44.2432	+	11.5964i	1.56521	+	0.410251i
$800$	23.6994	+	15.4382i	0.837900	+	0.545823i
$801$	−59.7146	+	24.7346i	−2.10991	+	0.873954i
$802$	−6.13344	−	13.4859i	−0.216579	−	0.476205i
$803$	−20.8243			−0.734874
$804$	79.6806	−	21.5925i	2.81012	−	0.761508i
$805$	−6.02597	+	5.13651i	−0.212388	+	0.181038i
$806$	−2.63803	−	2.46378i	−0.0929207	−	0.0867830i
$807$	34.9325	−	14.4695i	1.22968	−	0.509350i
$808$	3.92029	−	41.6156i	0.137915	−	1.46403i
$809$	−0.643553	+	0.963146i	−0.0226261	+	0.0338624i	−0.842610	−	0.538524i	$-0.818982\pi$
$809$	−0.643553	+	0.963146i	−0.0226261	+	0.0338624i	0.819984	+	0.572386i	$0.193982\pi$
$810$	−12.1679	+	49.3540i	−0.427537	+	1.73412i
$811$	−1.42093	−	2.12658i	−0.0498958	−	0.0746743i	0.805683	−	0.592347i	$-0.201799\pi$
$811$	−1.42093	−	2.12658i	−0.0498958	−	0.0746743i	−0.855579	+	0.517673i	$0.826799\pi$
$812$	−5.82852	−	1.96012i	−0.204541	−	0.0687867i
$813$	9.53418	−	6.37054i	0.334378	−	0.223424i
$814$	0.365686	−	0.0858124i	0.0128173	−	0.00300772i
$815$	0.142315	−	0.502732i	0.00498506	−	0.0176099i
$816$	15.9911	−	48.8887i	0.559802	−	1.71145i
$817$	−4.44871	−	4.44871i	−0.155641	−	0.155641i
$818$	12.1175	−	19.5482i	0.423677	−	0.683485i
$819$	−5.81121	−	1.15592i	−0.203060	−	0.0403911i
$820$	5.80701	+	3.97518i	0.202790	+	0.138819i
$821$	−5.95537	+	3.97925i	−0.207844	+	0.138877i	−0.655136	−	0.755511i	$-0.727389\pi$
$821$	−5.95537	+	3.97925i	−0.207844	+	0.138877i	0.447292	+	0.894388i	$0.352389\pi$
$822$	47.5025	−	50.8621i	1.65684	−	1.77402i
$823$	−2.45606	−	12.3474i	−0.0856127	−	0.430404i	−0.999691	−	0.0248659i	$-0.992084\pi$
$823$	−2.45606	−	12.3474i	−0.0856127	−	0.430404i	0.914078	−	0.405538i	$-0.132916\pi$
$824$	14.3298	+	17.3104i	0.499203	+	0.603037i
$825$	3.75699	−	23.4249i	0.130801	−	0.815550i
$826$	−10.8393	+	11.6060i	−0.377149	+	0.403823i
$827$	−45.7428	−	30.5644i	−1.59063	−	1.06283i	−0.957359	−	0.288901i	$-0.906710\pi$
$827$	−45.7428	−	30.5644i	−1.59063	−	1.06283i	−0.633275	−	0.773927i	$-0.718290\pi$
$828$	−20.0478	+	34.9521i	−0.696708	+	1.21467i
$829$	−6.89249	−	6.89249i	−0.239386	−	0.239386i	0.577210	−	0.816596i	$-0.304141\pi$
$829$	−6.89249	−	6.89249i	−0.239386	−	0.239386i	−0.816596	+	0.577210i	$0.804141\pi$
$830$	−44.3794	+	6.75159i	−1.54043	+	0.234351i
$831$	−3.73307	−	9.01242i	−0.129499	−	0.312637i
$832$	−1.11283	+	5.85416i	−0.0385803	+	0.202956i
$833$	−3.13977	−	22.8828i	−0.108786	−	0.792842i
$834$	−4.75472	+	29.0549i	−0.164642	+	1.00609i
$835$	−0.744332	+	0.0873616i	−0.0257587	+	0.00302327i
$836$	−3.24677	−	1.86228i	−0.112292	−	0.0644082i
$837$		−	39.8339i		−	1.37686i
$838$	−1.90900	+	5.09397i	−0.0659453	+	0.175968i
$839$	5.44461	+	27.3719i	0.187969	+	0.944982i	0.953456	+	0.301532i	$0.0974979\pi$
$839$	5.44461	+	27.3719i	0.187969	+	0.944982i	−0.765487	+	0.643451i	$0.777502\pi$
$840$	−22.7652	+	5.07303i	−0.785475	+	0.175036i
$841$	−8.51027	+	20.5456i	−0.293458	+	0.708469i
$842$	7.10004	−	1.66611i	0.244684	−	0.0574178i
$843$	13.5499	+	68.1198i	0.466682	+	2.34617i
$844$	0.194795	−	1.51272i	0.00670512	−	0.0520699i
$845$	24.7828	+	12.6579i	0.852554	+	0.435446i
$846$	−61.5943	−	85.6981i	−2.11766	−	2.94636i
$847$	8.53911	−	5.70565i	0.293407	−	0.196048i
$848$	−35.3928	+	20.7023i	−1.21539	+	0.710920i
$849$	9.33337			0.320321
$850$	28.6579	+	5.35945i	0.982959	+	0.183827i
$851$		−	0.522843i		−	0.0179228i
$852$	−31.6028	+	36.2427i	−1.08269	+	1.24165i
$853$	−13.2475	−	19.8263i	−0.453586	−	0.678839i	0.532243	−	0.846591i	$-0.321349\pi$
$853$	−13.2475	−	19.8263i	−0.453586	−	0.678839i	−0.985829	+	0.167752i	$0.946349\pi$
$854$	−9.08922	+	6.53275i	−0.311027	+	0.223546i
$855$	−8.41699	+	16.4795i	−0.287855	+	0.563588i
$856$	−7.84826	+	26.2737i	−0.268248	+	0.898016i
$857$	8.42852	−	1.67654i	0.287913	−	0.0572694i	−0.0490210	−	0.998798i	$-0.515610\pi$
$857$	8.42852	−	1.67654i	0.287913	−	0.0572694i	0.336934	+	0.941528i	$0.390610\pi$
$858$	4.86609	−	1.14188i	0.166126	−	0.0389833i
$859$	−42.0908	−	17.4346i	−1.43612	−	0.594861i	−0.477267	−	0.878759i	$-0.658372\pi$
$859$	−42.0908	−	17.4346i	−1.43612	−	0.594861i	−0.958855	+	0.283898i	$0.908372\pi$
$860$	21.2282	−	8.51493i	0.723875	−	0.290357i
$861$	−5.69155	+	1.13212i	−0.193967	+	0.0385825i
$862$	44.6693	+	16.7401i	1.52144	+	0.570171i
$863$	−42.1002			−1.43311			−0.716554	−	0.697532i	$-0.754282\pi$
$863$	−42.1002			−1.43311			−0.716554	+	0.697532i	$0.754282\pi$
$864$	−55.5963	+	35.1204i	−1.89142	+	1.19482i
$865$	−5.88989	−	50.1827i	−0.200262	−	1.70626i
$866$	−1.02606	+	6.26998i	−0.0348668	+	0.213063i
$867$	−4.04519	−	52.8661i	−0.137382	−	1.79543i
$868$	7.25750	−	3.60460i	0.246336	−	0.122348i
$869$	−21.8720	+	9.05970i	−0.741958	+	0.307329i
$870$	−3.85724	−	25.3543i	−0.130773	−	0.859591i
$871$	−6.97080	+	6.97080i	−0.236196	+	0.236196i
$872$	−19.3436	−	15.7378i	−0.655057	−	0.532949i
$873$	54.5598	−	81.6545i	1.84657	−	2.76359i
$874$	−3.55611	+	3.80761i	−0.120287	+	0.128794i
$875$	−4.53930	−	12.4160i	−0.153456	−	0.419739i
$876$	−56.1146	+	64.3533i	−1.89594	+	2.17430i
$877$	−40.3335	+	8.02283i	−1.36197	+	0.270912i	−0.821382	−	0.570379i	$-0.806796\pi$
$877$	−40.3335	+	8.02283i	−1.36197	+	0.270912i	−0.540583	+	0.841290i	$0.681796\pi$
$878$	20.2934	+	18.9530i	0.684871	+	0.639633i
$879$	4.36472	+	6.53226i	0.147218	+	0.220328i
$880$	10.8646	−	8.19263i	0.366245	−	0.276174i
$881$	9.24502	−	46.4779i	0.311473	−	1.56588i	−0.434980	−	0.900440i	$-0.643244\pi$
$881$	9.24502	−	46.4779i	0.311473	−	1.56588i	0.746452	−	0.665439i	$-0.231756\pi$
$882$	−28.0794	+	45.2983i	−0.945483	+	1.52527i
$883$	5.74264	−	5.74264i	0.193255	−	0.193255i	−0.603846	−	0.797101i	$-0.706366\pi$
$883$	5.74264	−	5.74264i	0.193255	−	0.193255i	0.797101	+	0.603846i	$0.206366\pi$
$884$	1.24824	+	6.01422i	0.0419827	+	0.202280i
$885$	−63.7265	−	18.0398i	−2.14214	−	0.606402i
$886$	−12.7448	−	54.3116i	−0.428171	−	1.82463i
$887$	10.2573	+	15.3511i	0.344406	+	0.515441i	0.962723	−	0.270488i	$-0.0871852\pi$
$887$	10.2573	+	15.3511i	0.344406	+	0.515441i	−0.618317	+	0.785929i	$0.712185\pi$
$888$	0.720217	−	1.36131i	0.0241689	−	0.0456827i
$889$	11.7354	−	7.84131i	0.393591	−	0.262989i
$890$	7.27288	−	29.4993i	0.243787	−	0.988820i
$891$	20.3333	+	13.5863i	0.681193	+	0.455158i
$892$	9.72281	−	0.664935i	0.325544	−	0.0222637i
$893$	−5.22210	−	12.6073i	−0.174751	−	0.421886i
$894$	−61.5739	+	65.9288i	−2.05934	+	2.20499i
$895$	−2.51190	−	2.94688i	−0.0839637	−	0.0985032i
$896$	−11.4297	−	6.95124i	−0.381839	−	0.232225i
$897$		−	6.95734i		−	0.232299i
$898$	14.2262	+	31.2800i	0.474735	+	1.04383i
$899$	3.40980	+	8.23199i	0.113723	+	0.274552i
$900$	−43.0625	−	51.6841i	−1.43542	−	1.72280i
$901$	−25.5457	+	33.6709i	−0.851052	+	1.12174i
$902$	2.74916	−	1.97592i	0.0915369	−	0.0657909i
$903$	−7.21771	+	17.4251i	−0.240190	+	0.579870i
$904$	20.4568	−	25.1438i	0.680382	−	0.836270i
$905$	−11.0333	−	3.12334i	−0.366761	−	0.103823i
$906$	−17.9777	+	8.17631i	−0.597270	+	0.271640i
$907$	−10.4506	+	15.6404i	−0.347007	+	0.519332i	−0.963386	−	0.268117i	$-0.913599\pi$
$907$	−10.4506	+	15.6404i	−0.347007	+	0.519332i	0.616380	+	0.787449i	$0.288599\pi$
$908$	39.3657	+	5.06917i	1.30640	+	0.168226i
$909$	−38.0460	+	91.8511i	−1.26190	+	3.04651i
$910$	2.05672	−	1.87806i	0.0681796	−	0.0622572i
$911$	14.6913	+	9.81640i	0.486744	+	0.325232i	0.774610	−	0.632439i	$-0.217946\pi$
$911$	14.6913	+	9.81640i	0.486744	+	0.325232i	−0.287867	+	0.957670i	$0.592946\pi$
$912$	−14.5039	+	5.01525i	−0.480273	+	0.166072i
$913$	−4.21320	+	21.1812i	−0.139437	+	0.700995i
$914$	17.8128	−	12.8027i	0.589195	−	0.423476i
$915$	−41.5738	−	21.2340i	−1.37439	−	0.701974i
$916$	−13.9784	+	0.955969i	−0.461858	+	0.0315861i
$917$	−15.2609	−	15.2609i	−0.503960	−	0.503960i
$918$	−39.1028	+	55.3681i	−1.29059	+	1.82742i
$919$		−	23.9841i		−	0.791161i	−0.918431	−	0.395581i	$-0.870543\pi$
$919$		−	23.9841i		−	0.791161i	0.918431	−	0.395581i	$-0.129457\pi$
$920$	−7.64722	−	17.3282i	−0.252122	−	0.571295i
$921$	−32.6373	−	6.49197i	−1.07544	−	0.213918i
$922$	−6.86302	+	41.9382i	−0.226021	+	1.38116i
$923$	1.12024	−	5.63183i	0.0368732	−	0.185374i
$924$	−1.43308	+	11.1289i	−0.0471449	+	0.366113i
$925$	0.818379	+	0.303731i	0.0269081	+	0.00998661i
$926$	−2.98314	+	4.81247i	−0.0980322	+	0.158148i
$927$	−20.4540	−	49.3802i	−0.671796	−	1.62186i
$928$	8.48308	−	12.0170i	0.278471	−	0.394477i
$929$	18.0382	−	3.58802i	0.591814	−	0.117719i	0.109908	−	0.993942i	$-0.464944\pi$
$929$	18.0382	−	3.58802i	0.591814	−	0.117719i	0.481907	+	0.876223i	$0.339944\pi$
$930$	27.2195	+	20.0311i	0.892562	+	0.656845i
$931$	−4.87276	+	4.87276i	−0.159698	+	0.159698i
$932$	4.14504	−	1.12326i	0.135775	−	0.0367934i
$933$	29.2581	−	70.6353i	0.957867	−	2.31249i
$934$	1.16099	−	7.09455i	0.0379889	−	0.232141i
$935$	7.11731	−	12.0861i	0.232761	−	0.395259i
$936$	6.62801	−	12.5279i	0.216643	−	0.409487i
$937$	−38.1864	−	15.8173i	−1.24749	−	0.516729i	−0.341445	−	0.939902i	$-0.610916\pi$
$937$	−38.1864	−	15.8173i	−1.24749	−	0.516729i	−0.906049	+	0.423173i	$0.860916\pi$
$938$	−9.16214	−	20.1453i	−0.299155	−	0.657768i
$939$	23.9613	−	23.9613i	0.781948	−	0.781948i
$940$	49.6064	+	0.557208i	1.61798	+	0.0181741i
$941$	−2.23067	−	11.2143i	−0.0727177	−	0.365577i	0.927243	−	0.374461i	$-0.122172\pi$
$941$	−2.23067	−	11.2143i	−0.0727177	−	0.365577i	−0.999961	+	0.00888401i	$0.997172\pi$
$942$	−82.0941	+	2.80390i	−2.67477	+	0.0913560i
$943$	−1.80341	−	4.35382i	−0.0587272	−	0.141780i
$944$	−19.1797	−	32.7898i	−0.624247	−	1.06722i
$945$	30.6386	+	2.44137i	0.996672	+	0.0794179i
$946$	−0.375606	−	10.9972i	−0.0122120	−	0.357550i
$947$	3.55277	−	17.8610i	0.115450	−	0.580404i	−0.879144	−	0.476557i	$-0.841885\pi$
$947$	3.55277	−	17.8610i	0.115450	−	0.580404i	0.994593	−	0.103847i	$-0.0331153\pi$
$948$	−30.9407	+	92.0040i	−1.00491	+	2.98815i
$949$	1.98913	−	10.0000i	0.0645698	−	0.324614i
$950$	−3.89404	−	7.77811i	−0.126339	−	0.252355i
$951$		−	42.4872i		−	1.37774i
$952$	−13.6262	−	2.11400i	−0.441628	−	0.0685153i
$953$	−20.8013	+	20.8013i	−0.673820	+	0.673820i	−0.958594	−	0.284775i	$-0.908081\pi$
$953$	−20.8013	+	20.8013i	−0.673820	+	0.673820i	0.284775	+	0.958594i	$0.408081\pi$
$954$	94.9443	−	22.2798i	3.07393	−	0.721334i
$955$	−2.56285	+	0.829957i	−0.0829317	+	0.0268568i
$956$	−37.7030	+	18.7261i	−1.21940	+	0.605644i
$957$	−12.1010	−	2.40704i	−0.391169	−	0.0778084i
$958$	−7.85601	+	8.41162i	−0.253816	+	0.271767i
$959$	−15.5125	−	10.3651i	−0.500926	−	0.334708i
$960$	3.95877	−	55.6512i	0.127769	−	1.79614i
$961$	17.7924	+	7.36984i	0.573947	+	0.237737i
$962$	0.00627772	+	0.183802i	0.000202402	+	0.00592603i
$963$	36.2338	−	54.2277i	1.16762	−	1.74746i
$964$	10.6677	+	39.3658i	0.343582	+	1.26789i
$965$	24.8131	−	13.8643i	0.798763	−	0.446306i
$966$	14.6254	+	5.48099i	0.470566	+	0.176348i
$967$	−7.50855	+	18.1272i	−0.241459	+	0.582933i	−0.997428	−	0.0716742i	$-0.977166\pi$
$967$	−7.50855	+	18.1272i	−0.241459	+	0.582933i	0.755969	+	0.654607i	$0.227166\pi$
$968$	7.23107	+	23.4780i	0.232416	+	0.754612i
$969$	−11.8361	+	10.4949i	−0.380232	+	0.337144i
$970$	15.7132	+	43.4065i	0.504519	+	1.39370i
$971$	16.5744	+	40.0142i	0.531898	+	1.28412i	0.930264	+	0.366890i	$0.119577\pi$
$971$	16.5744	+	40.0142i	0.531898	+	1.28412i	−0.398366	+	0.917227i	$0.630423\pi$
$972$	29.4562	−	7.98229i	0.944810	−	0.256032i
$973$	7.89256			0.253024
$974$	14.7018	−	6.68643i	0.471077	−	0.214247i
$975$	10.8900	+	4.04167i	0.348758	+	0.129437i
$976$	−8.75016	−	25.3052i	−0.280086	−	0.809998i
$977$	31.4469	−	13.0257i	1.00608	−	0.416730i	0.182054	−	0.983289i	$-0.441726\pi$
$977$	31.4469	−	13.0257i	1.00608	−	0.416730i	0.824021	+	0.566559i	$0.191726\pi$
$978$	−1.00337	+	0.235452i	−0.0320843	+	0.00752894i
$979$	−12.1534	−	8.12066i	−0.388425	−	0.259538i
$980$	−9.32658	−	23.2516i	−0.297927	−	0.742747i
$981$	32.9516	+	49.3156i	1.05206	+	1.57453i
$982$	18.1882	+	2.97643i	0.580410	+	0.0949817i
$983$	14.1905	+	21.2376i	0.452608	+	0.677375i	0.985667	−	0.168703i	$-0.0539577\pi$
$983$	14.1905	+	21.2376i	0.452608	+	0.677375i	−0.533059	+	0.846078i	$0.678958\pi$
$984$	1.30189	−	13.8202i	0.0415028	−	0.440570i
$985$	47.0432	+	13.3171i	1.49892	+	0.424318i
$986$	3.34137	−	14.7895i	0.106411	−	0.470993i
$987$	−28.9268	+	28.9268i	−0.920751	+	0.920751i
$988$	1.20441	−	1.38124i	0.0383174	−	0.0439431i
$989$	−15.0222	−	2.98809i	−0.477677	−	0.0950159i
$990$	−30.4317	+	11.0163i	−0.967183	+	0.350121i
$991$	−7.92479	−	11.8603i	−0.251739	−	0.376754i	0.683980	−	0.729501i	$-0.260248\pi$
$991$	−7.92479	−	11.8603i	−0.251739	−	0.376754i	−0.935719	+	0.352747i	$0.885248\pi$
$992$	3.29292	+	19.1021i	0.104550	+	0.606492i
$993$	2.29653	+	11.5454i	0.0728781	+	0.366383i
$994$	10.9565	+	6.79168i	0.347519	+	0.215419i
$995$	1.78225	+	15.1850i	0.0565012	+	0.481398i
$996$	54.1030	+	70.0963i	1.71432	+	2.22109i
$997$	−0.627373	−	0.419197i	−0.0198691	−	0.0132761i	0.545596	−	0.838048i	$-0.316303\pi$
$997$	−0.627373	−	0.419197i	−0.0198691	−	0.0132761i	−0.565465	+	0.824772i	$0.691303\pi$
$998$	5.80197	+	2.17433i	0.183658	+	0.0688272i
$999$	−1.43509	+	1.43509i	−0.0454042	+	0.0454042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cf.a.37.18	yes	832
5.3	odd	4		680.2.ct.a.173.36	yes	832
8.5	even	2	inner	680.2.cf.a.37.7	✓	832
17.6	odd	16		680.2.ct.a.397.46	yes	832
40.13	odd	4		680.2.ct.a.173.46	yes	832
85.23	even	16	inner	680.2.cf.a.533.7	yes	832
136.125	odd	16		680.2.ct.a.397.36	yes	832
680.533	even	16	inner	680.2.cf.a.533.18	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cf.a.37.7	✓	832	8.5	even	2	inner
680.2.cf.a.37.18	yes	832	1.1	even	1	trivial
680.2.cf.a.533.7	yes	832	85.23	even	16	inner
680.2.cf.a.533.18	yes	832	680.533	even	16	inner
680.2.ct.a.173.36	yes	832	5.3	odd	4
680.2.ct.a.173.46	yes	832	40.13	odd	4
680.2.ct.a.397.36	yes	832	136.125	odd	16
680.2.ct.a.397.46	yes	832	17.6	odd	16

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20201 - 0.745099i) q^{2} +(1.73274 + 2.59324i) q^{3} +(0.889656 + 1.79123i) q^{4} +(1.99136 + 1.01710i) q^{5} +(-0.150560 - 4.40816i) q^{6} +(-1.15970 + 0.230678i) q^{7} +(0.265270 - 2.81596i) q^{8} +(-2.57442 + 6.21519i) q^{9} +(-1.63580 - 2.70632i) q^{10} +(-1.49211 + 0.296799i) q^{11} +(-3.10354 + 5.41084i) q^{12} -0.744874i q^{13} +(1.56584 + 0.586811i) q^{14} +(0.812949 + 6.92643i) q^{15} +(-2.41703 + 3.18716i) q^{16} +(-1.04538 + 3.98838i) q^{17} +(7.72541 - 5.55253i) q^{18} +(1.13650 - 0.470755i) q^{19} +(-0.0502305 + 4.47185i) q^{20} +(-2.60766 - 2.60766i) q^{21} +(2.01468 + 0.755014i) q^{22} +(1.66381 - 2.49007i) q^{23} +(7.76209 - 4.19143i) q^{24} +(2.93103 + 4.05081i) q^{25} +(-0.555005 + 0.895346i) q^{26} +(-11.4015 + 2.26790i) q^{27} +(-1.44493 - 1.87206i) q^{28} +(2.16207 - 1.44465i) q^{29} +(4.18371 - 8.93137i) q^{30} +(-0.668499 + 3.36077i) q^{31} +(5.28004 - 2.03007i) q^{32} +(-3.35512 - 3.35512i) q^{33} +(4.22829 - 4.01516i) q^{34} +(-2.54399 - 0.720160i) q^{35} +(-13.4232 + 0.918002i) q^{36} +(0.145162 - 0.0969941i) q^{37} +(-1.71685 - 0.280955i) q^{38} +(1.93163 - 1.29068i) q^{39} +(3.39235 - 5.33779i) q^{40} +(0.874238 - 1.30839i) q^{41} +(1.19147 + 5.07740i) q^{42} +(-1.95719 - 4.72508i) q^{43} +(-1.85910 - 2.40867i) q^{44} +(-11.4480 + 9.75826i) q^{45} +(-3.85526 + 1.75338i) q^{46} -11.0930i q^{47} +(-12.4531 - 0.745384i) q^{48} +(-5.17547 + 2.14375i) q^{49} +(-0.504875 - 7.05302i) q^{50} +(-12.1542 + 4.19993i) q^{51} +(1.33424 - 0.662681i) q^{52} +(9.47043 + 3.92278i) q^{53} +(15.3945 + 5.76920i) q^{54} +(-3.27320 - 0.926585i) q^{55} +(0.341947 + 3.32685i) q^{56} +(3.19005 + 2.13152i) q^{57} +(-3.67524 + 0.125527i) q^{58} +(-3.63428 + 8.77392i) q^{59} +(-11.6836 + 7.61832i) q^{60} +(-3.71889 + 5.56571i) q^{61} +(3.30765 - 3.54158i) q^{62} +(1.55183 - 7.80160i) q^{63} +(-7.85926 - 1.49398i) q^{64} +(0.757608 - 1.48331i) q^{65} +(1.53299 + 6.53277i) q^{66} +(-9.35836 - 9.35836i) q^{67} +(-8.07414 + 1.67577i) q^{68} +9.34029 q^{69} +(2.52132 + 2.76117i) q^{70} +(7.56079 + 1.50393i) q^{71} +(16.8188 + 8.89816i) q^{72} +(13.4251 + 2.67042i) q^{73} +(-0.246756 + 0.00842790i) q^{74} +(-5.42598 + 14.6199i) q^{75} +(1.85433 + 1.61693i) q^{76} +(1.66193 - 0.688393i) q^{77} +(-3.28352 + 0.112148i) q^{78} +(15.2623 - 3.03587i) q^{79} +(-8.05482 + 3.88844i) q^{80} +(-11.3663 - 11.3663i) q^{81} +(-2.02572 + 0.921303i) q^{82} +(5.43237 - 13.1149i) q^{83} +(2.35100 - 6.99084i) q^{84} +(-6.13829 + 6.87905i) q^{85} +(-1.16809 + 7.13789i) q^{86} +(7.49265 + 3.10356i) q^{87} +(0.439962 + 4.28045i) q^{88} +(6.79377 + 6.79377i) q^{89} +(21.0315 - 3.19960i) q^{90} +(0.171826 + 0.863827i) q^{91} +(5.94051 + 0.764968i) q^{92} +(-9.87361 + 4.08978i) q^{93} +(-8.26539 + 13.3339i) q^{94} +(2.74199 + 0.218490i) q^{95} +(14.4134 + 10.1748i) q^{96} +(-14.3175 - 2.84793i) q^{97} +(7.81828 + 1.27943i) q^{98} +(1.99665 - 10.0378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) \) 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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