LMFDB - Embedded newform 930.2.j.g.497.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] 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("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.20
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(1.73148 - 0.0444250i) q^{3} -1.00000i q^{4} +(0.142194 + 2.23154i) q^{5} +(1.19293 - 1.25576i) q^{6} +(2.34383 + 2.34383i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99605 - 0.153842i) q^{9} +(1.67849 + 1.47739i) q^{10} -5.32287i q^{11} +(-0.0444250 - 1.73148i) q^{12} +(-2.57481 + 2.57481i) q^{13} +3.31467 q^{14} +(0.345343 + 3.85756i) q^{15} -1.00000 q^{16} +(2.33223 - 2.33223i) q^{17} +(2.00975 - 2.22731i) q^{18} +5.87131i q^{19} +(2.23154 - 0.142194i) q^{20} +(4.16242 + 3.95417i) q^{21} +(-3.76384 - 3.76384i) q^{22} +(-2.05643 - 2.05643i) q^{23} +(-1.25576 - 1.19293i) q^{24} +(-4.95956 + 0.634625i) q^{25} +3.64134i q^{26} +(5.18077 - 0.399474i) q^{27} +(2.34383 - 2.34383i) q^{28} +4.07771 q^{29} +(2.97190 + 2.48351i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.236468 - 9.21645i) q^{33} -3.29827i q^{34} +(-4.89707 + 5.56363i) q^{35} +(-0.153842 - 2.99605i) q^{36} +(0.718205 + 0.718205i) q^{37} +(4.15164 + 4.15164i) q^{38} +(-4.34385 + 4.57263i) q^{39} +(1.47739 - 1.67849i) q^{40} +9.62849i q^{41} +(5.73929 - 0.147254i) q^{42} +(1.71966 - 1.71966i) q^{43} -5.32287 q^{44} +(0.769326 + 6.66394i) q^{45} -2.90823 q^{46} +(6.49628 - 6.49628i) q^{47} +(-1.73148 + 0.0444250i) q^{48} +3.98705i q^{49} +(-3.05819 + 3.95569i) q^{50} +(3.93461 - 4.14183i) q^{51} +(2.57481 + 2.57481i) q^{52} +(-5.55295 - 5.55295i) q^{53} +(3.38089 - 3.94583i) q^{54} +(11.8782 - 0.756881i) q^{55} -3.31467i q^{56} +(0.260833 + 10.1661i) q^{57} +(2.88338 - 2.88338i) q^{58} -6.86460 q^{59} +(3.85756 - 0.345343i) q^{60} -0.913500 q^{61} +(0.707107 - 0.707107i) q^{62} +(7.38281 + 6.66165i) q^{63} +1.00000i q^{64} +(-6.11193 - 5.37968i) q^{65} +(-6.68422 - 6.34980i) q^{66} +(-9.72000 - 9.72000i) q^{67} +(-2.33223 - 2.33223i) q^{68} +(-3.65203 - 3.46932i) q^{69} +(0.471327 + 7.39683i) q^{70} -8.59895i q^{71} +(-2.22731 - 2.00975i) q^{72} +(-5.80419 + 5.80419i) q^{73} +1.01570 q^{74} +(-8.55919 + 1.31917i) q^{75} +5.87131 q^{76} +(12.4759 - 12.4759i) q^{77} +(0.161766 + 6.30490i) q^{78} -10.0091i q^{79} +(-0.142194 - 2.23154i) q^{80} +(8.95267 - 0.921838i) q^{81} +(6.80837 + 6.80837i) q^{82} +(-4.35290 - 4.35290i) q^{83} +(3.95417 - 4.16242i) q^{84} +(5.53610 + 4.87285i) q^{85} -2.43196i q^{86} +(7.06048 - 0.181152i) q^{87} +(-3.76384 + 3.76384i) q^{88} -3.15398 q^{89} +(5.25612 + 4.16812i) q^{90} -12.0698 q^{91} +(-2.05643 + 2.05643i) q^{92} +(1.73148 - 0.0444250i) q^{93} -9.18712i q^{94} +(-13.1021 + 0.834866i) q^{95} +(-1.19293 + 1.25576i) q^{96} +(-7.10018 - 7.10018i) q^{97} +(2.81927 + 2.81927i) q^{98} +(-0.818881 - 15.9476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.73148	−	0.0444250i	0.999671	−	0.0256488i
$3$	1.73148	−	0.0444250i	0.999671	−	0.0256488i
$4$		−	1.00000i		−	0.500000i
$5$	0.142194	+	2.23154i	0.0635912	+	0.997976i
$5$	0.142194	+	2.23154i	0.0635912	+	0.997976i
$6$	1.19293	−	1.25576i	0.487011	−	0.512660i
$7$	2.34383	+	2.34383i	0.885883	+	0.885883i	0.994125	−	0.108241i	$-0.0345219\pi$
$7$	2.34383	+	2.34383i	0.885883	+	0.885883i	−0.108241	+	0.994125i	$0.534522\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.99605	−	0.153842i	0.998684	−	0.0512807i
$10$	1.67849	+	1.47739i	0.530784	+	0.467192i
$11$		−	5.32287i		−	1.60491i	−0.596716	−	0.802453i	$-0.703528\pi$
$11$		−	5.32287i		−	1.60491i	0.596716	−	0.802453i	$-0.296472\pi$
$12$	−0.0444250	−	1.73148i	−0.0128244	−	0.499836i
$13$	−2.57481	+	2.57481i	−0.714125	+	0.714125i	−0.967395	−	0.253271i	$-0.918494\pi$
$13$	−2.57481	+	2.57481i	−0.714125	+	0.714125i	0.253271	+	0.967395i	$0.418494\pi$
$14$	3.31467			0.885883
$15$	0.345343	+	3.85756i	0.0891671	+	0.996017i
$16$	−1.00000			−0.250000
$17$	2.33223	−	2.33223i	0.565649	−	0.565649i	−0.365257	−	0.930907i	$-0.619019\pi$
$17$	2.33223	−	2.33223i	0.565649	−	0.565649i	0.930907	+	0.365257i	$0.119019\pi$
$18$	2.00975	−	2.22731i	0.473702	−	0.524982i
$19$			5.87131i			1.34697i	0.739201	+	0.673485i	$0.235204\pi$
$19$			5.87131i			1.34697i	−0.739201	+	0.673485i	$0.764796\pi$
$20$	2.23154	−	0.142194i	0.498988	−	0.0317956i
$21$	4.16242	+	3.95417i	0.908314	+	0.862870i
$22$	−3.76384	−	3.76384i	−0.802453	−	0.802453i
$23$	−2.05643	−	2.05643i	−0.428796	−	0.428796i	0.459422	−	0.888218i	$-0.348057\pi$
$23$	−2.05643	−	2.05643i	−0.428796	−	0.428796i	−0.888218	+	0.459422i	$0.848057\pi$
$24$	−1.25576	−	1.19293i	−0.256330	−	0.243506i
$25$	−4.95956	+	0.634625i	−0.991912	+	0.126925i
$26$			3.64134i			0.714125i
$27$	5.18077	−	0.399474i	0.997040	−	0.0768789i
$28$	2.34383	−	2.34383i	0.442942	−	0.442942i
$29$	4.07771			0.757212			0.378606	−	0.925558i	$-0.376403\pi$
$29$	4.07771			0.757212			0.378606	+	0.925558i	$0.376403\pi$
$30$	2.97190	+	2.48351i	0.542592	+	0.453425i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.236468	−	9.21645i	−0.0411639	−	1.60438i
$34$		−	3.29827i		−	0.565649i
$35$	−4.89707	+	5.56363i	−0.827756	+	0.940425i
$36$	−0.153842	−	2.99605i	−0.0256403	−	0.499342i
$37$	0.718205	+	0.718205i	0.118072	+	0.118072i	0.763674	−	0.645602i	$-0.223393\pi$
$37$	0.718205	+	0.718205i	0.118072	+	0.118072i	−0.645602	+	0.763674i	$0.723393\pi$
$38$	4.15164	+	4.15164i	0.673485	+	0.673485i
$39$	−4.34385	+	4.57263i	−0.695573	+	0.732206i
$40$	1.47739	−	1.67849i	0.233596	−	0.265392i
$41$			9.62849i			1.50372i	0.659325	+	0.751858i	$0.270842\pi$
$41$			9.62849i			1.50372i	−0.659325	+	0.751858i	$0.729158\pi$
$42$	5.73929	−	0.147254i	0.885592	−	0.0227218i
$43$	1.71966	−	1.71966i	0.262245	−	0.262245i	−0.563720	−	0.825966i	$-0.690630\pi$
$43$	1.71966	−	1.71966i	0.262245	−	0.262245i	0.825966	+	0.563720i	$0.190630\pi$
$44$	−5.32287			−0.802453
$45$	0.769326	+	6.66394i	0.114684	+	0.993402i
$46$	−2.90823			−0.428796
$47$	6.49628	−	6.49628i	0.947579	−	0.947579i	−0.0511135	−	0.998693i	$-0.516277\pi$
$47$	6.49628	−	6.49628i	0.947579	−	0.947579i	0.998693	+	0.0511135i	$0.0162770\pi$
$48$	−1.73148	+	0.0444250i	−0.249918	+	0.00641220i
$49$			3.98705i			0.569578i
$50$	−3.05819	+	3.95569i	−0.432494	+	0.559419i
$51$	3.93461	−	4.14183i	0.550955	−	0.579972i
$52$	2.57481	+	2.57481i	0.357062	+	0.357062i
$53$	−5.55295	−	5.55295i	−0.762756	−	0.762756i	0.214064	−	0.976820i	$-0.431330\pi$
$53$	−5.55295	−	5.55295i	−0.762756	−	0.762756i	−0.976820	+	0.214064i	$0.931330\pi$
$54$	3.38089	−	3.94583i	0.460081	−	0.536960i
$55$	11.8782	−	0.756881i	1.60166	−	0.102058i
$56$		−	3.31467i		−	0.442942i
$57$	0.260833	+	10.1661i	0.0345482	+	1.34653i
$58$	2.88338	−	2.88338i	0.378606	−	0.378606i
$59$	−6.86460			−0.893694			−0.446847	−	0.894610i	$-0.647453\pi$
$59$	−6.86460			−0.893694			−0.446847	+	0.894610i	$0.647453\pi$
$60$	3.85756	−	0.345343i	0.498008	−	0.0445836i
$61$	−0.913500			−0.116962			−0.0584808	−	0.998289i	$-0.518626\pi$
$61$	−0.913500			−0.116962			−0.0584808	+	0.998289i	$0.518626\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	7.38281	+	6.66165i	0.930146	+	0.839289i
$64$			1.00000i			0.125000i
$65$	−6.11193	−	5.37968i	−0.758091	−	0.667267i
$66$	−6.68422	−	6.34980i	−0.822771	−	0.781607i
$67$	−9.72000	−	9.72000i	−1.18749	−	1.18749i	−0.977760	−	0.209727i	$-0.932743\pi$
$67$	−9.72000	−	9.72000i	−1.18749	−	1.18749i	−0.209727	−	0.977760i	$-0.567257\pi$
$68$	−2.33223	−	2.33223i	−0.282825	−	0.282825i
$69$	−3.65203	−	3.46932i	−0.439653	−	0.417657i
$70$	0.471327	+	7.39683i	0.0563344	+	0.884090i
$71$		−	8.59895i		−	1.02051i	−0.860024	−	0.510254i	$-0.829551\pi$
$71$		−	8.59895i		−	1.02051i	0.860024	−	0.510254i	$-0.170449\pi$
$72$	−2.22731	−	2.00975i	−0.262491	−	0.236851i
$73$	−5.80419	+	5.80419i	−0.679329	+	0.679329i	−0.959848	−	0.280519i	$-0.909493\pi$
$73$	−5.80419	+	5.80419i	−0.679329	+	0.679329i	0.280519	+	0.959848i	$0.409493\pi$
$74$	1.01570			0.118072
$75$	−8.55919	+	1.31917i	−0.988331	+	0.152325i
$76$	5.87131			0.673485
$77$	12.4759	−	12.4759i	1.42176	−	1.42176i
$78$	0.161766	+	6.30490i	0.0183164	+	0.713890i
$79$		−	10.0091i		−	1.12611i	−0.826419	−	0.563056i	$-0.809626\pi$
$79$		−	10.0091i		−	1.12611i	0.826419	−	0.563056i	$-0.190374\pi$
$80$	−0.142194	−	2.23154i	−0.0158978	−	0.249494i
$81$	8.95267	−	0.921838i	0.994741	−	0.102426i
$82$	6.80837	+	6.80837i	0.751858	+	0.751858i
$83$	−4.35290	−	4.35290i	−0.477793	−	0.477793i	0.426632	−	0.904425i	$-0.359700\pi$
$83$	−4.35290	−	4.35290i	−0.477793	−	0.477793i	−0.904425	+	0.426632i	$0.859700\pi$
$84$	3.95417	−	4.16242i	0.431435	−	0.454157i
$85$	5.53610	+	4.87285i	0.600475	+	0.528534i
$86$		−	2.43196i		−	0.262245i
$87$	7.06048	−	0.181152i	0.756963	−	0.0194216i
$88$	−3.76384	+	3.76384i	−0.401226	+	0.401226i
$89$	−3.15398			−0.334322			−0.167161	−	0.985930i	$-0.553460\pi$
$89$	−3.15398			−0.334322			−0.167161	+	0.985930i	$0.553460\pi$
$90$	5.25612	+	4.16812i	0.554043	+	0.439359i
$91$	−12.0698			−1.26526
$92$	−2.05643	+	2.05643i	−0.214398	+	0.214398i
$93$	1.73148	−	0.0444250i	0.179546	−	0.00460666i
$94$		−	9.18712i		−	0.947579i
$95$	−13.1021	+	0.834866i	−1.34424	+	0.0856554i
$96$	−1.19293	+	1.25576i	−0.121753	+	0.128165i
$97$	−7.10018	−	7.10018i	−0.720914	−	0.720914i	0.247878	−	0.968791i	$-0.420267\pi$
$97$	−7.10018	−	7.10018i	−0.720914	−	0.720914i	−0.968791	+	0.247878i	$0.920267\pi$
$98$	2.81927	+	2.81927i	0.284789	+	0.284789i
$99$	−0.818881	−	15.9476i	−0.0823007	−	1.60279i
$100$	0.634625	+	4.95956i	0.0634625	+	0.495956i
$101$			12.6296i			1.25669i	0.777933	+	0.628347i	$0.216268\pi$
$101$			12.6296i			1.25669i	−0.777933	+	0.628347i	$0.783732\pi$
$102$	−0.146526	−	5.71090i	−0.0145082	−	0.565463i
$103$	−8.68173	+	8.68173i	−0.855436	+	0.855436i	−0.990796	−	0.135360i	$-0.956781\pi$
$103$	−8.68173	+	8.68173i	−0.855436	+	0.855436i	0.135360	+	0.990796i	$0.456781\pi$
$104$	3.64134			0.357062
$105$	−8.23202	+	9.85087i	−0.803363	+	0.961346i
$106$	−7.85306			−0.762756
$107$	−7.38945	+	7.38945i	−0.714365	+	0.714365i	−0.967445	−	0.253080i	$-0.918556\pi$
$107$	−7.38945	+	7.38945i	−0.714365	+	0.714365i	0.253080	+	0.967445i	$0.418556\pi$
$108$	−0.399474	−	5.18077i	−0.0384394	−	0.498520i
$109$		−	7.31869i		−	0.701004i	−0.936562	−	0.350502i	$-0.886011\pi$
$109$		−	7.31869i		−	0.701004i	0.936562	−	0.350502i	$-0.113989\pi$
$110$	7.86397	−	8.93436i	0.749800	−	0.851857i
$111$	1.27546	+	1.21165i	0.121062	+	0.115005i
$112$	−2.34383	−	2.34383i	−0.221471	−	0.221471i
$113$	−10.6053	−	10.6053i	−0.997665	−	0.997665i	0.00233179	−	0.999997i	$-0.499258\pi$
$113$	−10.6053	−	10.6053i	−0.997665	−	0.997665i	−0.999997	+	0.00233179i	$0.999258\pi$
$114$	7.37293	+	7.00405i	0.690538	+	0.655990i
$115$	4.29660	−	4.88143i	0.400660	−	0.455196i
$116$		−	4.07771i		−	0.378606i
$117$	−7.31816	+	8.11039i	−0.676564	+	0.749806i
$118$	−4.85400	+	4.85400i	−0.446847	+	0.446847i
$119$	10.9327			1.00220
$120$	2.48351	−	2.97190i	0.226712	−	0.271296i
$121$	−17.3329			−1.57572
$122$	−0.645942	+	0.645942i	−0.0584808	+	0.0584808i
$123$	0.427745	+	16.6715i	0.0385685	+	1.50322i
$124$		−	1.00000i		−	0.0898027i
$125$	−2.12141	−	10.9772i	−0.189745	−	0.981833i
$126$	9.93093	−	0.509936i	0.884718	−	0.0454287i
$127$	11.9179	+	11.9179i	1.05754	+	1.05754i	0.998240	+	0.0593044i	$0.0188883\pi$
$127$	11.9179	+	11.9179i	1.05754	+	1.05754i	0.0593044	+	0.998240i	$0.481112\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	2.90116	−	3.05395i	0.255433	−	0.268885i
$130$	−8.12579	+	0.517777i	−0.712679	+	0.0454120i
$131$			9.02710i			0.788701i	0.918960	+	0.394351i	$0.129030\pi$
$131$			9.02710i			0.788701i	−0.918960	+	0.394351i	$0.870970\pi$
$132$	−9.21645	+	0.236468i	−0.802189	+	0.0205819i
$133$	−13.7613	+	13.7613i	−1.19326	+	1.19326i
$134$	−13.7462			−1.18749
$135$	1.62812	+	11.5043i	0.140126	+	0.990134i
$136$	−3.29827			−0.282825
$137$	4.99130	−	4.99130i	0.426435	−	0.426435i	−0.460977	−	0.887412i	$-0.652501\pi$
$137$	4.99130	−	4.99130i	0.426435	−	0.426435i	0.887412	+	0.460977i	$0.152501\pi$
$138$	−5.03555	+	0.129198i	−0.428655	+	0.0109981i
$139$		−	5.06021i		−	0.429202i	−0.976702	−	0.214601i	$-0.931155\pi$
$139$		−	5.06021i		−	0.429202i	0.976702	−	0.214601i	$-0.0688451\pi$
$140$	5.56363	+	4.89707i	0.470212	+	0.413878i
$141$	10.9596	−	11.5368i	0.922963	−	0.971572i
$142$	−6.08038	−	6.08038i	−0.510254	−	0.510254i
$143$	13.7054	+	13.7054i	1.14610	+	1.14610i
$144$	−2.99605	+	0.153842i	−0.249671	+	0.0128202i
$145$	0.579827	+	9.09959i	0.0481520	+	0.755680i
$146$			8.20836i			0.679329i
$147$	0.177125	+	6.90350i	0.0146090	+	0.569391i
$148$	0.718205	−	0.718205i	0.0590361	−	0.0590361i
$149$	7.97693			0.653496			0.326748	−	0.945112i	$-0.394047\pi$
$149$	7.97693			0.653496			0.326748	+	0.945112i	$0.394047\pi$
$150$	−5.11947	+	6.98506i	−0.418003	+	0.570328i
$151$	3.74299			0.304601			0.152300	−	0.988334i	$-0.451332\pi$
$151$	3.74299			0.304601			0.152300	+	0.988334i	$0.451332\pi$
$152$	4.15164	−	4.15164i	0.336743	−	0.336743i
$153$	6.62870	−	7.34629i	0.535898	−	0.593912i
$154$		−	17.6436i		−	1.42176i
$155$	0.142194	+	2.23154i	0.0114213	+	0.179242i
$156$	4.57263	+	4.34385i	0.366103	+	0.347787i
$157$	13.3446	+	13.3446i	1.06501	+	1.06501i	0.997734	+	0.0672799i	$0.0214320\pi$
$157$	13.3446	+	13.3446i	1.06501	+	1.06501i	0.0672799	+	0.997734i	$0.478568\pi$
$158$	−7.07750	−	7.07750i	−0.563056	−	0.563056i
$159$	−9.86151	−	9.36814i	−0.782069	−	0.742941i
$160$	−1.67849	−	1.47739i	−0.132696	−	0.116798i
$161$		−	9.63984i		−	0.759726i
$162$	5.67865	−	6.98233i	0.446157	−	0.548584i
$163$	−3.35423	+	3.35423i	−0.262723	+	0.262723i	−0.826160	−	0.563436i	$-0.809479\pi$
$163$	−3.35423	+	3.35423i	−0.262723	+	0.262723i	0.563436	+	0.826160i	$0.309479\pi$
$164$	9.62849			0.751858
$165$	20.5333	−	1.83821i	1.59851	−	0.143105i
$166$	−6.15593			−0.477793
$167$	16.7823	−	16.7823i	1.29865	−	1.29865i	0.369370	−	0.929282i	$-0.379573\pi$
$167$	16.7823	−	16.7823i	1.29865	−	1.29865i	0.929282	−	0.369370i	$-0.120427\pi$
$168$	−0.147254	−	5.73929i	−0.0113609	−	0.442796i
$169$		−	0.259324i		−	0.0199480i
$170$	7.36024	−	0.468995i	0.564505	−	0.0359703i
$171$	0.903254	+	17.5908i	0.0690736	+	1.34520i
$172$	−1.71966	−	1.71966i	−0.131123	−	0.131123i
$173$	−5.10781	−	5.10781i	−0.388339	−	0.388339i	0.485756	−	0.874095i	$-0.338545\pi$
$173$	−5.10781	−	5.10781i	−0.388339	−	0.388339i	−0.874095	+	0.485756i	$0.838545\pi$
$174$	4.86442	−	5.12061i	0.368771	−	0.388192i
$175$	−13.1118	−	10.1369i	−0.991159	−	0.766278i
$176$			5.32287i			0.401226i
$177$	−11.8859	+	0.304960i	−0.893400	+	0.0229222i
$178$	−2.23020	+	2.23020i	−0.167161	+	0.167161i
$179$	−17.1413			−1.28120			−0.640602	−	0.767873i	$-0.721315\pi$
$179$	−17.1413			−1.28120			−0.640602	+	0.767873i	$0.721315\pi$
$180$	6.66394	−	0.769326i	0.496701	−	0.0573422i
$181$	9.34856			0.694873			0.347436	−	0.937704i	$-0.387052\pi$
$181$	9.34856			0.694873			0.347436	+	0.937704i	$0.387052\pi$
$182$	−8.53466	+	8.53466i	−0.632631	+	0.632631i
$183$	−1.58171	+	0.0405822i	−0.116923	+	0.00299992i
$184$			2.90823i			0.214398i
$185$	−1.50058	+	1.70483i	−0.110325	+	0.125342i
$186$	1.19293	−	1.25576i	0.0874698	−	0.0920764i
$187$	−12.4142	−	12.4142i	−0.907814	−	0.907814i
$188$	−6.49628	−	6.49628i	−0.473790	−	0.473790i
$189$	13.0791	+	11.2065i	0.951367	+	0.815156i
$190$	−8.67423	+	9.85490i	−0.629294	+	0.714950i
$191$			19.7911i			1.43203i	0.698083	+	0.716017i	$0.254037\pi$
$191$			19.7911i			1.43203i	−0.698083	+	0.716017i	$0.745963\pi$
$192$	0.0444250	+	1.73148i	0.00320610	+	0.124959i
$193$	−0.289823	+	0.289823i	−0.0208619	+	0.0208619i	−0.717461	−	0.696599i	$-0.754696\pi$
$193$	−0.289823	+	0.289823i	−0.0208619	+	0.0208619i	0.696599	+	0.717461i	$0.254696\pi$
$194$	−10.0412			−0.720914
$195$	−10.8217	−	9.04329i	−0.774957	−	0.647604i
$196$	3.98705			0.284789
$197$	−12.1490	+	12.1490i	−0.865584	+	0.865584i	−0.991980	−	0.126396i	$-0.959659\pi$
$197$	−12.1490	+	12.1490i	−0.865584	+	0.865584i	0.126396	+	0.991980i	$0.459659\pi$
$198$	−11.8557	−	10.6976i	−0.842547	−	0.760247i
$199$		−	16.3567i		−	1.15950i	−0.814796	−	0.579748i	$-0.803151\pi$
$199$		−	16.3567i		−	1.15950i	0.814796	−	0.579748i	$-0.196849\pi$
$200$	3.95569	+	3.05819i	0.279709	+	0.216247i
$201$	−17.2618	−	16.3982i	−1.21755	−	1.15664i
$202$	8.93049	+	8.93049i	0.628347	+	0.628347i
$203$	9.55746	+	9.55746i	0.670802	+	0.670802i
$204$	−4.14183	−	3.93461i	−0.289986	−	0.275478i
$205$	−21.4864	+	1.36911i	−1.50067	+	0.0956231i
$206$			12.2778i			0.855436i
$207$	−6.47755	−	5.84481i	−0.450221	−	0.406243i
$208$	2.57481	−	2.57481i	0.178531	−	0.178531i
$209$	31.2522			2.16176
$210$	1.14470	+	12.7865i	0.0789917	+	0.882355i
$211$	19.7796			1.36168			0.680841	−	0.732431i	$-0.261614\pi$
$211$	19.7796			1.36168			0.680841	+	0.732431i	$0.261614\pi$
$212$	−5.55295	+	5.55295i	−0.381378	+	0.381378i
$213$	−0.382008	−	14.8889i	−0.0261748	−	1.02017i
$214$			10.4503i			0.714365i
$215$	4.08201	+	3.59296i	0.278391	+	0.245038i
$216$	−3.94583	−	3.38089i	−0.268480	−	0.230040i
$217$	2.34383	+	2.34383i	0.159109	+	0.159109i
$218$	−5.17510	−	5.17510i	−0.350502	−	0.350502i
$219$	−9.79199	+	10.3077i	−0.661681	+	0.696529i
$220$	−0.756881	−	11.8782i	−0.0510289	−	0.800829i
$221$			12.0101i			0.807888i
$222$	1.75866	−	0.0451223i	0.118033	−	0.00302841i
$223$	4.74368	−	4.74368i	0.317660	−	0.317660i	−0.530208	−	0.847868i	$-0.677886\pi$
$223$	4.74368	−	4.74368i	0.317660	−	0.317660i	0.847868	+	0.530208i	$0.177886\pi$
$224$	−3.31467			−0.221471
$225$	−14.7615	+	2.66436i	−0.984098	+	0.177624i
$226$	−14.9982			−0.997665
$227$	1.30263	−	1.30263i	0.0864587	−	0.0864587i	−0.662555	−	0.749013i	$-0.730528\pi$
$227$	1.30263	−	1.30263i	0.0864587	−	0.0864587i	0.749013	+	0.662555i	$0.230528\pi$
$228$	10.1661	−	0.260833i	0.673264	−	0.0172741i
$229$			17.4858i			1.15550i	0.816215	+	0.577748i	$0.196068\pi$
$229$			17.4858i			1.15550i	−0.816215	+	0.577748i	$0.803932\pi$
$230$	−0.413534	−	6.48985i	−0.0272676	−	0.427928i
$231$	21.0475	−	22.1560i	1.38482	−	1.45776i
$232$	−2.88338	−	2.88338i	−0.189303	−	0.189303i
$233$	−10.5213	−	10.5213i	−0.689271	−	0.689271i	0.272800	−	0.962071i	$-0.412050\pi$
$233$	−10.5213	−	10.5213i	−0.689271	−	0.689271i	−0.962071	+	0.272800i	$0.912050\pi$
$234$	0.560191	+	10.9096i	0.0366208	+	0.713185i
$235$	15.4204	+	13.5730i	1.00592	+	0.885404i
$236$			6.86460i			0.446847i
$237$	−0.444654	−	17.3306i	−0.0288834	−	1.12574i
$238$	7.73058	−	7.73058i	0.501099	−	0.501099i
$239$	6.58020			0.425638			0.212819	−	0.977092i	$-0.431736\pi$
$239$	6.58020			0.425638			0.212819	+	0.977092i	$0.431736\pi$
$240$	−0.345343	−	3.85756i	−0.0222918	−	0.249004i
$241$	6.44072			0.414883			0.207442	−	0.978247i	$-0.433486\pi$
$241$	6.44072			0.414883			0.207442	+	0.978247i	$0.433486\pi$
$242$	−12.2562	+	12.2562i	−0.787861	+	0.787861i
$243$	15.4604	−	1.99387i	0.991786	−	0.127907i
$244$			0.913500i			0.0584808i
$245$	−8.89727	+	0.566935i	−0.568426	+	0.0362202i
$246$	12.0910	+	11.4861i	0.770895	+	0.732327i
$247$	−15.1175	−	15.1175i	−0.961905	−	0.961905i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	−7.73034	−	7.34358i	−0.489890	−	0.465381i
$250$	−9.26214	−	6.26201i	−0.585789	−	0.396044i
$251$			5.87064i			0.370551i	0.982687	+	0.185276i	$0.0593178\pi$
$251$			5.87064i			0.370551i	−0.982687	+	0.185276i	$0.940682\pi$
$252$	6.66165	−	7.38281i	0.419645	−	0.465073i
$253$	−10.9461	+	10.9461i	−0.688177	+	0.688177i
$254$	16.8545			1.05754
$255$	9.80214	+	8.19130i	0.613834	+	0.512959i
$256$	1.00000			0.0625000
$257$	−2.94491	+	2.94491i	−0.183698	+	0.183698i	−0.792965	−	0.609267i	$-0.791464\pi$
$257$	−2.94491	+	2.94491i	−0.183698	+	0.183698i	0.609267	+	0.792965i	$0.291464\pi$
$258$	−0.108040	−	4.21090i	−0.00672627	−	0.262159i
$259$			3.36670i			0.209196i
$260$	−5.37968	+	6.11193i	−0.333634	+	0.379046i
$261$	12.2170	−	0.627324i	0.756216	−	0.0388304i
$262$	6.38312	+	6.38312i	0.394351	+	0.394351i
$263$	1.15541	+	1.15541i	0.0712457	+	0.0712457i	0.741832	−	0.670586i	$-0.233957\pi$
$263$	1.15541	+	1.15541i	0.0712457	+	0.0712457i	−0.670586	+	0.741832i	$0.733957\pi$
$264$	−6.34980	+	6.68422i	−0.390803	+	0.411385i
$265$	11.6020	−	13.1812i	0.712708	−	0.809717i
$266$			19.4615i			1.19326i
$267$	−5.46106	+	0.140116i	−0.334212	+	0.00857495i
$268$	−9.72000	+	9.72000i	−0.593743	+	0.593743i
$269$	−19.2490			−1.17363			−0.586817	−	0.809720i	$-0.699619\pi$
$269$	−19.2490			−1.17363			−0.586817	+	0.809720i	$0.699619\pi$
$270$	9.28603	+	6.98352i	0.565130	+	0.425004i
$271$	−10.0388			−0.609816			−0.304908	−	0.952382i	$-0.598626\pi$
$271$	−10.0388			−0.609816			−0.304908	+	0.952382i	$0.598626\pi$
$272$	−2.33223	+	2.33223i	−0.141412	+	0.141412i
$273$	−20.8987	+	0.536202i	−1.26485	+	0.0324524i
$274$		−	7.05876i		−	0.426435i
$275$	3.37802	+	26.3991i	0.203703	+	1.59193i
$276$	−3.46932	+	3.65203i	−0.208828	+	0.219826i
$277$	−12.1820	−	12.1820i	−0.731945	−	0.731945i	0.239060	−	0.971005i	$-0.423161\pi$
$277$	−12.1820	−	12.1820i	−0.731945	−	0.731945i	−0.971005	+	0.239060i	$0.923161\pi$
$278$	−3.57811	−	3.57811i	−0.214601	−	0.214601i
$279$	2.99605	−	0.153842i	0.179369	−	0.00921028i
$280$	7.39683	−	0.471327i	0.442045	−	0.0281672i
$281$		−	26.5997i		−	1.58681i	−0.608697	−	0.793403i	$-0.708308\pi$
$281$		−	26.5997i		−	1.58681i	0.608697	−	0.793403i	$-0.291692\pi$
$282$	−0.408138	−	15.9073i	−0.0243043	−	0.947268i
$283$	−12.7232	+	12.7232i	−0.756315	+	0.756315i	−0.975650	−	0.219335i	$-0.929611\pi$
$283$	−12.7232	+	12.7232i	−0.756315	+	0.756315i	0.219335	+	0.975650i	$0.429611\pi$
$284$	−8.59895			−0.510254
$285$	−22.6489	+	2.02761i	−1.34161	+	0.120105i
$286$	19.3824			1.14610
$287$	−22.5675	+	22.5675i	−1.33212	+	1.33212i
$288$	−2.00975	+	2.22731i	−0.118425	+	0.131246i
$289$			6.12138i			0.360081i
$290$	6.84438	+	6.02438i	0.401916	+	0.353764i
$291$	−12.6092	−	11.9784i	−0.739167	−	0.702186i
$292$	5.80419	+	5.80419i	0.339664	+	0.339664i
$293$	9.75762	+	9.75762i	0.570046	+	0.570046i	0.932141	−	0.362095i	$-0.117938\pi$
$293$	9.75762	+	9.75762i	0.570046	+	0.570046i	−0.362095	+	0.932141i	$0.617938\pi$
$294$	5.00676	+	4.75627i	0.292000	+	0.277391i
$295$	−0.976106	−	15.3186i	−0.0568311	−	0.891885i
$296$		−	1.01570i		−	0.0590361i
$297$	−2.12635	−	27.5766i	−0.123383	−	1.60016i
$298$	5.64054	−	5.64054i	0.326748	−	0.326748i
$299$	10.5899			0.612427
$300$	1.31917	+	8.55919i	0.0761623	+	0.494165i
$301$	8.06116			0.464637
$302$	2.64670	−	2.64670i	0.152300	−	0.152300i
$303$	0.561071	+	21.8680i	0.0322327	+	1.25628i
$304$		−	5.87131i		−	0.336743i
$305$	−0.129894	−	2.03851i	−0.00743773	−	0.116725i
$306$	−0.507413	−	9.88180i	−0.0290069	−	0.564905i
$307$	0.0921439	+	0.0921439i	0.00525893	+	0.00525893i	0.709731	−	0.704472i	$-0.248816\pi$
$307$	0.0921439	+	0.0921439i	0.00525893	+	0.00525893i	−0.704472	+	0.709731i	$0.748816\pi$
$308$	−12.4759	−	12.4759i	−0.710879	−	0.710879i
$309$	−14.6466	+	15.4179i	−0.833214	+	0.877096i
$310$	1.67849	+	1.47739i	0.0953315	+	0.0839102i
$311$			8.45397i			0.479381i	0.970849	+	0.239690i	$0.0770459\pi$
$311$			8.45397i			0.479381i	−0.970849	+	0.239690i	$0.922954\pi$
$312$	6.30490	−	0.161766i	0.356945	−	0.00915821i
$313$	−23.0864	+	23.0864i	−1.30492	+	1.30492i	−0.379885	+	0.925034i	$0.624036\pi$
$313$	−23.0864	+	23.0864i	−1.30492	+	1.30492i	−0.925034	+	0.379885i	$0.875964\pi$
$314$	18.8721			1.06501
$315$	−13.8160	+	17.4223i	−0.778441	+	0.981635i
$316$	−10.0091			−0.563056
$317$	9.01722	−	9.01722i	0.506458	−	0.506458i	−0.406980	−	0.913437i	$-0.633418\pi$
$317$	9.01722	−	9.01722i	0.506458	−	0.506458i	0.913437	+	0.406980i	$0.133418\pi$
$318$	−13.5974	+	0.348872i	−0.762505	+	0.0195638i
$319$		−	21.7051i		−	1.21525i
$320$	−2.23154	+	0.142194i	−0.124747	+	0.00794890i
$321$	−12.4664	+	13.1230i	−0.695807	+	0.732452i
$322$	−6.81640	−	6.81640i	−0.379863	−	0.379863i
$323$	13.6933	+	13.6933i	0.761913	+	0.761913i
$324$	−0.921838	−	8.95267i	−0.0512132	−	0.497370i
$325$	11.1359	−	14.4040i	0.617709	−	0.798989i
$326$			4.74360i			0.262723i
$327$	−0.325133	−	12.6722i	−0.0179799	−	0.700773i
$328$	6.80837	−	6.80837i	0.375929	−	0.375929i
$329$	30.4523			1.67889
$330$	13.2194	−	15.8190i	0.727704	−	0.870809i
$331$	23.1909			1.27469			0.637344	−	0.770580i	$-0.280033\pi$
$331$	23.1909			1.27469			0.637344	+	0.770580i	$0.280033\pi$
$332$	−4.35290	+	4.35290i	−0.238896	+	0.238896i
$333$	2.26227	+	2.04129i	0.123972	+	0.111862i
$334$		−	23.7337i		−	1.29865i
$335$	20.3085	−	23.0727i	1.10957	−	1.26060i
$336$	−4.16242	−	3.95417i	−0.227078	−	0.215718i
$337$	−12.6434	−	12.6434i	−0.688728	−	0.688728i	0.273223	−	0.961951i	$-0.411910\pi$
$337$	−12.6434	−	12.6434i	−0.688728	−	0.688728i	−0.961951	+	0.273223i	$0.911910\pi$
$338$	−0.183370	−	0.183370i	−0.00997402	−	0.00997402i
$339$	−18.8341	−	17.8918i	−1.02293	−	0.971748i
$340$	4.87285	−	5.53610i	0.264267	−	0.300237i
$341$		−	5.32287i		−	0.288250i
$342$	13.0772	+	11.7998i	0.707136	+	0.638062i
$343$	7.06184	−	7.06184i	0.381303	−	0.381303i
$344$	−2.43196			−0.131123
$345$	7.22263	−	8.64298i	0.388853	−	0.465322i
$346$	−7.22353			−0.388339
$347$	−22.9418	+	22.9418i	−1.23158	+	1.23158i	−0.268225	+	0.963356i	$0.586437\pi$
$347$	−22.9418	+	22.9418i	−1.23158	+	1.23158i	−0.963356	+	0.268225i	$0.913563\pi$
$348$	−0.181152	−	7.06048i	−0.00971079	−	0.378482i
$349$		−	35.3989i		−	1.89486i	−0.319965	−	0.947429i	$-0.603671\pi$
$349$		−	35.3989i		−	1.89486i	0.319965	−	0.947429i	$-0.396329\pi$
$350$	−16.4393	+	2.10357i	−0.878719	+	0.112441i
$351$	−12.3110	+	14.3681i	−0.657110	+	0.766912i
$352$	3.76384	+	3.76384i	0.200613	+	0.200613i
$353$	−15.6878	−	15.6878i	−0.834976	−	0.834976i	0.153217	−	0.988193i	$-0.451037\pi$
$353$	−15.6878	−	15.6878i	−0.834976	−	0.834976i	−0.988193	+	0.153217i	$0.951037\pi$
$354$	−8.18897	+	8.62025i	−0.435239	+	0.458161i
$355$	19.1889	−	1.22272i	1.01844	−	0.0648953i
$356$			3.15398i			0.167161i
$357$	18.9298	−	0.485685i	1.00187	−	0.0257052i
$358$	−12.1208	+	12.1208i	−0.640602	+	0.640602i
$359$	31.0215			1.63725			0.818626	−	0.574327i	$-0.194736\pi$
$359$	31.0215			1.63725			0.818626	+	0.574327i	$0.194736\pi$
$360$	4.16812	−	5.25612i	0.219679	−	0.277022i
$361$	−15.4723			−0.814330
$362$	6.61043	−	6.61043i	0.347436	−	0.347436i
$363$	−30.0116	+	0.770016i	−1.57520	+	0.0404153i
$364$			12.0698i			0.632631i
$365$	−13.7776	−	12.1270i	−0.721153	−	0.634755i
$366$	−1.08974	+	1.14713i	−0.0569616	+	0.0599615i
$367$	18.5964	+	18.5964i	0.970723	+	0.970723i	0.999583	−	0.0288601i	$-0.00918772\pi$
$367$	18.5964	+	18.5964i	0.970723	+	0.970723i	−0.0288601	+	0.999583i	$0.509188\pi$
$368$	2.05643	+	2.05643i	0.107199	+	0.107199i
$369$	1.48127	+	28.8475i	0.0771116	+	1.50174i
$370$	0.144426	+	2.26657i	0.00750835	+	0.117833i
$371$		−	26.0303i		−	1.35143i
$372$	−0.0444250	−	1.73148i	−0.00230333	−	0.0897731i
$373$	7.03959	−	7.03959i	0.364496	−	0.364496i	−0.500969	−	0.865465i	$-0.667023\pi$
$373$	7.03959	−	7.03959i	0.364496	−	0.364496i	0.865465	+	0.500969i	$0.167023\pi$
$374$	−17.5563			−0.907814
$375$	−4.16085	−	18.9126i	−0.214865	−	0.976644i
$376$	−9.18712			−0.473790
$377$	−10.4994	+	10.4994i	−0.540744	+	0.540744i
$378$	17.1726	−	1.32413i	0.883261	−	0.0681057i
$379$			31.2352i			1.60444i	0.597027	+	0.802221i	$0.296349\pi$
$379$			31.2352i			1.60444i	−0.597027	+	0.802221i	$0.703651\pi$
$380$	0.834866	+	13.1021i	0.0428277	+	0.672122i
$381$	21.1651	+	20.1062i	1.08432	+	1.03007i
$382$	13.9944	+	13.9944i	0.716017	+	0.716017i
$383$	15.8078	+	15.8078i	0.807742	+	0.807742i	0.984292	−	0.176550i	$-0.0564937\pi$
$383$	15.8078	+	15.8078i	0.807742	+	0.807742i	−0.176550	+	0.984292i	$0.556494\pi$
$384$	1.25576	+	1.19293i	0.0640825	+	0.0608764i
$385$	29.6145	+	26.0665i	1.50929	+	1.32847i
$386$			0.409872i			0.0208619i
$387$	4.88763	−	5.41674i	0.248452	−	0.275348i
$388$	−7.10018	+	7.10018i	−0.360457	+	0.360457i
$389$	−12.8441			−0.651220			−0.325610	−	0.945504i	$-0.605570\pi$
$389$	−12.8441			−0.651220			−0.325610	+	0.945504i	$0.605570\pi$
$390$	−14.0467	+	1.25751i	−0.711280	+	0.0636764i
$391$	−9.59216			−0.485096
$392$	2.81927	−	2.81927i	0.142395	−	0.142395i
$393$	0.401029	+	15.6302i	0.0202292	+	0.788442i
$394$			17.1814i			0.865584i
$395$	22.3357	−	1.42324i	1.12383	−	0.0716108i
$396$	−15.9476	+	0.818881i	−0.801397	+	0.0411503i
$397$	−19.6869	−	19.6869i	−0.988058	−	0.988058i	0.0118711	−	0.999930i	$-0.496221\pi$
$397$	−19.6869	−	19.6869i	−0.988058	−	0.988058i	−0.999930	+	0.0118711i	$0.996221\pi$
$398$	−11.5659	−	11.5659i	−0.579748	−	0.579748i
$399$	−23.2161	+	24.4388i	−1.16226	+	1.22347i
$400$	4.95956	−	0.634625i	0.247978	−	0.0317312i
$401$		−	38.0122i		−	1.89824i	−0.314916	−	0.949119i	$-0.601976\pi$
$401$		−	38.0122i		−	1.89824i	0.314916	−	0.949119i	$-0.398024\pi$
$402$	−23.8012	+	0.610673i	−1.18710	+	0.0304576i
$403$	−2.57481	+	2.57481i	−0.128261	+	0.128261i
$404$	12.6296			0.628347
$405$	3.33014	+	19.8472i	0.165476	+	0.986214i
$406$	13.5163			0.670802
$407$	3.82291	−	3.82291i	0.189495	−	0.189495i
$408$	−5.71090	+	0.146526i	−0.282732	+	0.00725411i
$409$			17.6761i			0.874026i	0.899455	+	0.437013i	$0.143964\pi$
$409$			17.6761i			0.874026i	−0.899455	+	0.437013i	$0.856036\pi$
$410$	−14.2251	+	16.1613i	−0.702525	+	0.798148i
$411$	8.42060	−	8.86408i	0.415358	−	0.437233i
$412$	8.68173	+	8.68173i	0.427718	+	0.427718i
$413$	−16.0894	−	16.0894i	−0.791709	−	0.791709i
$414$	−8.71323	+	0.447409i	−0.428232	+	0.0219889i
$415$	9.09472	−	10.3326i	0.446442	−	0.507209i
$416$		−	3.64134i		−	0.178531i
$417$	−0.224800	−	8.76167i	−0.0110085	−	0.429061i
$418$	22.0986	−	22.0986i	1.08088	−	1.08088i
$419$	24.1973			1.18212			0.591058	−	0.806629i	$-0.298710\pi$
$419$	24.1973			1.18212			0.591058	+	0.806629i	$0.298710\pi$
$420$	9.85087	+	8.23202i	0.480673	+	0.401681i
$421$	20.5246			1.00031			0.500154	−	0.865936i	$-0.333277\pi$
$421$	20.5246			1.00031			0.500154	+	0.865936i	$0.333277\pi$
$422$	13.9863	−	13.9863i	0.680841	−	0.680841i
$423$	18.4638	−	20.4626i	0.897740	−	0.994925i
$424$			7.85306i			0.381378i
$425$	−10.0868	+	13.0469i	−0.489280	+	0.632870i
$426$	−10.7982	−	10.2579i	−0.523174	−	0.496999i
$427$	−2.14109	−	2.14109i	−0.103614	−	0.103614i
$428$	7.38945	+	7.38945i	0.357182	+	0.357182i
$429$	24.3395	+	23.1218i	1.17512	+	1.11633i
$430$	5.42703	−	0.345811i	0.261714	−	0.0166765i
$431$		−	23.9070i		−	1.15156i	−0.817605	−	0.575780i	$-0.804698\pi$
$431$		−	23.9070i		−	1.15156i	0.817605	−	0.575780i	$-0.195302\pi$
$432$	−5.18077	+	0.399474i	−0.249260	+	0.0192197i
$433$	−8.97114	+	8.97114i	−0.431125	+	0.431125i	−0.889011	−	0.457886i	$-0.848607\pi$
$433$	−8.97114	+	8.97114i	−0.431125	+	0.431125i	0.457886	+	0.889011i	$0.348607\pi$
$434$	3.31467			0.159109
$435$	1.40821	+	15.7300i	0.0675185	+	0.754196i
$436$	−7.31869			−0.350502
$437$	12.0740	−	12.0740i	0.577575	−	0.577575i
$438$	0.364656	+	14.2126i	0.0174240	+	0.679105i
$439$			28.6135i			1.36565i	0.730583	+	0.682824i	$0.239248\pi$
$439$			28.6135i			1.36565i	−0.730583	+	0.682824i	$0.760752\pi$
$440$	−8.93436	−	7.86397i	−0.425929	−	0.374900i
$441$	0.613376	+	11.9454i	0.0292084	+	0.568829i
$442$	8.49244	+	8.49244i	0.403944	+	0.403944i
$443$	−21.3536	−	21.3536i	−1.01454	−	1.01454i	−0.999893	−	0.0146498i	$-0.995337\pi$
$443$	−21.3536	−	21.3536i	−1.01454	−	1.01454i	−0.0146498	−	0.999893i	$-0.504663\pi$
$444$	1.21165	−	1.27546i	0.0575025	−	0.0605309i
$445$	−0.448478	−	7.03825i	−0.0212599	−	0.333645i
$446$		−	6.70857i		−	0.317660i
$447$	13.8119	−	0.354375i	0.653281	−	0.0167614i
$448$	−2.34383	+	2.34383i	−0.110735	+	0.110735i
$449$	38.9162			1.83657			0.918285	−	0.395921i	$-0.129575\pi$
$449$	38.9162			1.83657			0.918285	+	0.395921i	$0.129575\pi$
$450$	−8.55395	+	12.3219i	−0.403237	+	0.580861i
$451$	51.2512			2.41332
$452$	−10.6053	+	10.6053i	−0.498833	+	0.498833i
$453$	6.48092	−	0.166282i	0.304500	−	0.00781263i
$454$		−	1.84220i		−	0.0864587i
$455$	−1.71626	−	26.9343i	−0.0804595	−	1.26270i
$456$	7.00405	−	7.37293i	0.327995	−	0.345269i
$457$	2.63616	+	2.63616i	0.123314	+	0.123314i	0.766071	−	0.642756i	$-0.222209\pi$
$457$	2.63616	+	2.63616i	0.123314	+	0.123314i	−0.642756	+	0.766071i	$0.722209\pi$
$458$	12.3644	+	12.3644i	0.577748	+	0.577748i
$459$	11.1511	−	13.0144i	0.520489	−	0.607462i
$460$	−4.88143	−	4.29660i	−0.227598	−	0.200330i
$461$			27.1612i			1.26502i	0.774552	+	0.632511i	$0.217976\pi$
$461$			27.1612i			1.26502i	−0.774552	+	0.632511i	$0.782024\pi$
$462$	−0.783815	−	30.5495i	−0.0364664	−	1.42129i
$463$	−13.7006	+	13.7006i	−0.636723	+	0.636723i	−0.949746	−	0.313023i	$-0.898658\pi$
$463$	−13.7006	+	13.7006i	−0.636723	+	0.636723i	0.313023	+	0.949746i	$0.398658\pi$
$464$	−4.07771			−0.189303
$465$	0.345343	+	3.85756i	0.0160149	+	0.178890i
$466$	−14.8793			−0.689271
$467$	17.5028	−	17.5028i	0.809934	−	0.809934i	−0.174690	−	0.984624i	$-0.555892\pi$
$467$	17.5028	−	17.5028i	0.809934	−	0.809934i	0.984624	+	0.174690i	$0.0558922\pi$
$468$	8.11039	+	7.31816i	0.374903	+	0.338282i
$469$		−	45.5640i		−	2.10395i
$470$	20.5015	−	1.30636i	0.945662	−	0.0602577i
$471$	23.6987	+	22.5131i	1.09198	+	1.03735i
$472$	4.85400	+	4.85400i	0.223424	+	0.223424i
$473$	−9.15351	−	9.15351i	−0.420879	−	0.420879i
$474$	−12.5690	−	11.9401i	−0.577312	−	0.548429i
$475$	−3.72608	−	29.1191i	−0.170964	−	1.33608i
$476$		−	10.9327i		−	0.501099i
$477$	−17.4912	−	15.7827i	−0.800867	−	0.722638i
$478$	4.65290	−	4.65290i	0.212819	−	0.212819i
$479$	8.40205			0.383899			0.191950	−	0.981405i	$-0.438519\pi$
$479$	8.40205			0.383899			0.191950	+	0.981405i	$0.438519\pi$
$480$	−2.97190	−	2.48351i	−0.135648	−	0.113356i
$481$	−3.69849			−0.168637
$482$	4.55428	−	4.55428i	0.207442	−	0.207442i
$483$	−0.428250	−	16.6912i	−0.0194861	−	0.759476i
$484$			17.3329i			0.787861i
$485$	14.8347	−	16.8539i	0.673611	−	0.765298i
$486$	9.52229	−	12.3420i	0.431940	−	0.559846i
$487$	21.7600	+	21.7600i	0.986041	+	0.986041i	0.999904	−	0.0138629i	$-0.00441284\pi$
$487$	21.7600	+	21.7600i	0.986041	+	0.986041i	−0.0138629	+	0.999904i	$0.504413\pi$
$488$	0.645942	+	0.645942i	0.0292404	+	0.0292404i
$489$	−5.65877	+	5.95679i	−0.255898	+	0.269376i
$490$	−5.89043	+	6.69220i	−0.266103	+	0.302323i
$491$		−	19.7006i		−	0.889074i	−0.895760	−	0.444537i	$-0.853368\pi$
$491$		−	19.7006i		−	0.889074i	0.895760	−	0.444537i	$-0.146632\pi$
$492$	16.6715	−	0.427745i	0.751611	−	0.0192843i
$493$	9.51018	−	9.51018i	0.428317	−	0.428317i
$494$	−21.3794			−0.961905
$495$	35.4713	−	4.09502i	1.59432	−	0.184058i
$496$	−1.00000			−0.0449013
$497$	20.1545	−	20.1545i	0.904051	−	0.904051i
$498$	−10.6589	+	0.273477i	−0.477636	+	0.0122548i
$499$			13.1915i			0.590534i	0.955415	+	0.295267i	$0.0954086\pi$
$499$			13.1915i			0.590534i	−0.955415	+	0.295267i	$0.904591\pi$
$500$	−10.9772	+	2.12141i	−0.490917	+	0.0948725i
$501$	28.3127	−	29.8038i	1.26492	−	1.33153i
$502$	4.15117	+	4.15117i	0.185276	+	0.185276i
$503$	10.7177	+	10.7177i	0.477879	+	0.477879i	0.904453	−	0.426574i	$-0.140280\pi$
$503$	10.7177	+	10.7177i	0.477879	+	0.477879i	−0.426574	+	0.904453i	$0.640280\pi$
$504$	−0.509936	−	9.93093i	−0.0227144	−	0.442359i
$505$	−28.1835	+	1.79586i	−1.25415	+	0.0799147i
$506$			15.4802i			0.688177i
$507$	−0.0115205	−	0.449015i	−0.000511643	−	0.0199415i
$508$	11.9179	−	11.9179i	0.528772	−	0.528772i
$509$	−5.08723			−0.225487			−0.112744	−	0.993624i	$-0.535964\pi$
$509$	−5.08723			−0.225487			−0.112744	+	0.993624i	$0.535964\pi$
$510$	12.7233	−	1.13904i	0.563396	−	0.0504373i
$511$	−27.2080			−1.20361
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	2.34544	+	30.4179i	0.103554	+	1.34298i
$514$			4.16473i			0.183698i
$515$	−20.6081	−	18.1392i	−0.908103	−	0.799307i
$516$	−3.05395	−	2.90116i	−0.134443	−	0.127716i
$517$	−34.5788	−	34.5788i	−1.52078	−	1.52078i
$518$	2.38061	+	2.38061i	0.104598	+	0.104598i
$519$	−9.07098	−	8.61715i	−0.398172	−	0.378251i
$520$	0.517777	+	8.12579i	0.0227060	+	0.356340i
$521$			39.9892i			1.75196i	0.482348	+	0.875980i	$0.339784\pi$
$521$			39.9892i			1.75196i	−0.482348	+	0.875980i	$0.660216\pi$
$522$	8.19517	−	9.08234i	0.358693	−	0.397523i
$523$	30.0563	−	30.0563i	1.31427	−	1.31427i	0.396034	−	0.918236i	$-0.370386\pi$
$523$	30.0563	−	30.0563i	1.31427	−	1.31427i	0.918236	−	0.396034i	$-0.129614\pi$
$524$	9.02710			0.394351
$525$	−23.1532	−	16.9694i	−1.01049	−	0.740604i
$526$	1.63400			0.0712457
$527$	2.33223	−	2.33223i	0.101594	−	0.101594i
$528$	0.236468	+	9.21645i	0.0102910	+	0.401094i
$529$		−	14.5422i		−	0.632268i
$530$	−1.11666	−	17.5244i	−0.0485046	−	0.761212i
$531$	−20.5667	+	1.05606i	−0.892518	+	0.0458293i
$532$	13.7613	+	13.7613i	0.596629	+	0.596629i
$533$	−24.7916	−	24.7916i	−1.07384	−	1.07384i
$534$	−3.76248	+	3.96063i	−0.162818	+	0.171393i
$535$	−17.5406	−	15.4391i	−0.758346	−	0.667492i
$536$			13.7462i			0.593743i
$537$	−29.6799	+	0.761504i	−1.28078	+	0.0328613i
$538$	−13.6111	+	13.6111i	−0.586817	+	0.586817i
$539$	21.2225			0.914119
$540$	11.5043	−	1.62812i	0.495067	−	0.0700631i
$541$	−15.1376			−0.650816			−0.325408	−	0.945574i	$-0.605502\pi$
$541$	−15.1376			−0.650816			−0.325408	+	0.945574i	$0.605502\pi$
$542$	−7.09853	+	7.09853i	−0.304908	+	0.304908i
$543$	16.1869	−	0.415310i	0.694644	−	0.0178226i
$544$			3.29827i			0.141412i
$545$	16.3320	−	1.04068i	0.699585	−	0.0445776i
$546$	−14.3984	+	15.1568i	−0.616197	+	0.648649i
$547$	29.5556	+	29.5556i	1.26371	+	1.26371i	0.949282	+	0.314426i	$0.101812\pi$
$547$	29.5556	+	29.5556i	1.26371	+	1.26371i	0.314426	+	0.949282i	$0.398188\pi$
$548$	−4.99130	−	4.99130i	−0.213218	−	0.213218i
$549$	−2.73689	+	0.140535i	−0.116808	+	0.00599787i
$550$	21.0556	+	16.2784i	0.897814	+	0.694111i
$551$			23.9415i			1.01994i
$552$	0.129198	+	5.03555i	0.00549905	+	0.214327i
$553$	23.4596	−	23.4596i	0.997604	−	0.997604i
$554$	−17.2279			−0.731945
$555$	−2.52249	+	3.01854i	−0.107074	+	0.128130i
$556$	−5.06021			−0.214601
$557$	−9.13927	+	9.13927i	−0.387243	+	0.387243i	−0.873703	−	0.486460i	$-0.838288\pi$
$557$	−9.13927	+	9.13927i	−0.387243	+	0.387243i	0.486460	+	0.873703i	$0.338288\pi$
$558$	2.00975	−	2.22731i	0.0850794	−	0.0942896i
$559$			8.85559i			0.374552i
$560$	4.89707	−	5.56363i	0.206939	−	0.235106i
$561$	−22.0464	−	20.9434i	−0.930799	−	0.884231i
$562$	−18.8088	−	18.8088i	−0.793403	−	0.793403i
$563$	2.02094	+	2.02094i	0.0851725	+	0.0851725i	0.748409	−	0.663237i	$-0.230818\pi$
$563$	2.02094	+	2.02094i	0.0851725	+	0.0851725i	−0.663237	+	0.748409i	$0.730818\pi$
$564$	−11.5368	−	10.9596i	−0.485786	−	0.461482i
$565$	22.1582	−	25.1743i	0.932204	−	1.05909i
$566$			17.9933i			0.756315i
$567$	23.1441	+	18.8229i	0.971962	+	0.790486i
$568$	−6.08038	+	6.08038i	−0.255127	+	0.255127i
$569$	26.1347			1.09562			0.547812	−	0.836601i	$-0.315461\pi$
$569$	26.1347			1.09562			0.547812	+	0.836601i	$0.315461\pi$
$570$	−14.5815	+	17.4489i	−0.610750	+	0.730855i
$571$	12.5432			0.524917			0.262458	−	0.964943i	$-0.415467\pi$
$571$	12.5432			0.524917			0.262458	+	0.964943i	$0.415467\pi$
$572$	13.7054	−	13.7054i	0.573051	−	0.573051i
$573$	0.879220	+	34.2679i	0.0367299	+	1.43156i
$574$			31.9153i			1.33212i
$575$	11.5041	+	8.89394i	0.479753	+	0.370903i
$576$	0.153842	+	2.99605i	0.00641009	+	0.124836i
$577$	16.3900	+	16.3900i	0.682326	+	0.682326i	0.960524	−	0.278198i	$-0.0897372\pi$
$577$	16.3900	+	16.3900i	0.682326	+	0.682326i	−0.278198	+	0.960524i	$0.589737\pi$
$578$	4.32847	+	4.32847i	0.180041	+	0.180041i
$579$	−0.488948	+	0.514699i	−0.0203200	+	0.0213902i
$580$	9.09959	−	0.579827i	0.377840	−	0.0240760i
$581$		−	20.4049i		−	0.846537i
$582$	−17.3861	+	0.446079i	−0.720676	+	0.0184906i
$583$	−29.5576	+	29.5576i	−1.22415	+	1.22415i
$584$	8.20836			0.339664
$585$	−19.1393	−	15.1775i	−0.791312	−	0.627514i
$586$	13.7994			0.570046
$587$	−28.8017	+	28.8017i	−1.18877	+	1.18877i	−0.211368	+	0.977407i	$0.567792\pi$
$587$	−28.8017	+	28.8017i	−1.18877	+	1.18877i	−0.977407	+	0.211368i	$0.932208\pi$
$588$	6.90350	−	0.177125i	0.284696	−	0.00730450i
$589$			5.87131i			0.241923i
$590$	−11.5221	−	10.1417i	−0.474358	−	0.417527i
$591$	−20.4961	+	21.5756i	−0.843098	+	0.887500i
$592$	−0.718205	−	0.718205i	−0.0295180	−	0.0295180i
$593$	−10.9951	−	10.9951i	−0.451516	−	0.451516i	0.444341	−	0.895858i	$-0.353438\pi$
$593$	−10.9951	−	10.9951i	−0.451516	−	0.451516i	−0.895858	+	0.444341i	$0.853438\pi$
$594$	−21.0031	−	17.9960i	−0.861769	−	0.738386i
$595$	1.55457	+	24.3968i	0.0637310	+	1.00017i
$596$		−	7.97693i		−	0.326748i
$597$	−0.726646	−	28.3213i	−0.0297397	−	1.15911i
$598$	7.48816	−	7.48816i	0.306214	−	0.306214i
$599$	4.97456			0.203255			0.101627	−	0.994823i	$-0.467595\pi$
$599$	4.97456			0.203255			0.101627	+	0.994823i	$0.467595\pi$
$600$	6.98506	+	5.11947i	0.285164	+	0.209002i
$601$	13.7463			0.560723			0.280362	−	0.959894i	$-0.409546\pi$
$601$	13.7463			0.560723			0.280362	+	0.959894i	$0.409546\pi$
$602$	5.70010	−	5.70010i	0.232319	−	0.232319i
$603$	−30.6170	−	27.6263i	−1.24682	−	1.12503i
$604$		−	3.74299i		−	0.152300i
$605$	−2.46464	−	38.6792i	−0.100202	−	1.57253i
$606$	15.8597	+	15.0662i	0.644257	+	0.612024i
$607$	−9.89383	−	9.89383i	−0.401578	−	0.401578i	0.477211	−	0.878789i	$-0.341648\pi$
$607$	−9.89383	−	9.89383i	−0.401578	−	0.401578i	−0.878789	+	0.477211i	$0.841648\pi$
$608$	−4.15164	−	4.15164i	−0.168371	−	0.168371i
$609$	16.9731	+	16.1240i	0.687786	+	0.653376i
$610$	−1.53330	−	1.34960i	−0.0620813	−	0.0546436i
$611$			33.4534i			1.35338i
$612$	−7.34629	−	6.62870i	−0.296956	−	0.267949i
$613$	−3.39739	+	3.39739i	−0.137219	+	0.137219i	−0.772380	−	0.635161i	$-0.780934\pi$
$613$	−3.39739	+	3.39739i	−0.137219	+	0.137219i	0.635161	+	0.772380i	$0.280934\pi$
$614$	0.130311			0.00525893
$615$	−37.1424	+	3.32513i	−1.49773	+	0.134082i
$616$	−17.6436			−0.710879
$617$	6.92230	−	6.92230i	0.278681	−	0.278681i	−0.553901	−	0.832583i	$-0.686861\pi$
$617$	6.92230	−	6.92230i	0.278681	−	0.278681i	0.832583	+	0.553901i	$0.186861\pi$
$618$	0.545442	+	21.2588i	0.0219409	+	0.855155i
$619$			13.4874i			0.542103i	0.962565	+	0.271051i	$0.0873713\pi$
$619$			13.4874i			0.542103i	−0.962565	+	0.271051i	$0.912629\pi$
$620$	2.23154	−	0.142194i	0.0896209	−	0.00571066i
$621$	−11.4754	−	9.83242i	−0.460492	−	0.394561i
$622$	5.97786	+	5.97786i	0.239690	+	0.239690i
$623$	−7.39239	−	7.39239i	−0.296170	−	0.296170i
$624$	4.34385	−	4.57263i	0.173893	−	0.183052i
$625$	24.1945	−	6.29492i	0.967780	−	0.251797i
$626$			32.6491i			1.30492i
$627$	54.1126	−	1.38838i	2.16105	−	0.0554465i
$628$	13.3446	−	13.3446i	0.532507	−	0.532507i
$629$	3.35004			0.133575
$630$	2.55006	+	22.0888i	0.101597	+	0.880038i
$631$	38.3139			1.52525			0.762627	−	0.646839i	$-0.223909\pi$
$631$	38.3139			1.52525			0.762627	+	0.646839i	$0.223909\pi$
$632$	−7.07750	+	7.07750i	−0.281528	+	0.281528i
$633$	34.2480	−	0.878707i	1.36123	−	0.0349255i
$634$		−	12.7523i		−	0.506458i
$635$	−24.9007	+	28.2900i	−0.988153	+	1.12265i
$636$	−9.36814	+	9.86151i	−0.371471	+	0.391035i
$637$	−10.2659	−	10.2659i	−0.406750	−	0.406750i
$638$	−15.3479	−	15.3479i	−0.607627	−	0.607627i
$639$	−1.32288	−	25.7629i	−0.0523324	−	1.01917i
$640$	−1.47739	+	1.67849i	−0.0583991	+	0.0663480i
$641$		−	17.1624i		−	0.677873i	−0.940809	−	0.338936i	$-0.889933\pi$
$641$		−	17.1624i		−	0.677873i	0.940809	−	0.338936i	$-0.110067\pi$
$642$	0.464253	+	18.0944i	0.0183226	+	0.714130i
$643$	8.57949	−	8.57949i	0.338342	−	0.338342i	−0.517401	−	0.855743i	$-0.673100\pi$
$643$	8.57949	−	8.57949i	0.338342	−	0.338342i	0.855743	+	0.517401i	$0.173100\pi$
$644$	−9.63984			−0.379863
$645$	7.22754	+	6.03980i	0.284584	+	0.237817i
$646$	19.3652			0.761913
$647$	−24.5435	+	24.5435i	−0.964905	+	0.964905i	−0.999405	−	0.0344995i	$-0.989016\pi$
$647$	−24.5435	+	24.5435i	−0.964905	+	0.964905i	0.0344995	+	0.999405i	$0.489016\pi$
$648$	−6.98233	−	5.67865i	−0.274292	−	0.223079i
$649$			36.5393i			1.43429i
$650$	−2.31088	−	18.0594i	−0.0906402	−	0.708349i
$651$	4.16242	+	3.95417i	0.163138	+	0.154976i
$652$	3.35423	+	3.35423i	0.131362	+	0.131362i
$653$	−9.73348	−	9.73348i	−0.380901	−	0.380901i	0.490526	−	0.871427i	$-0.336805\pi$
$653$	−9.73348	−	9.73348i	−0.380901	−	0.380901i	−0.871427	+	0.490526i	$0.836805\pi$
$654$	−9.19049	−	8.73068i	−0.359377	−	0.341397i
$655$	−20.1444	+	1.28360i	−0.787105	+	0.0501544i
$656$		−	9.62849i		−	0.375929i
$657$	−16.4967	+	18.2826i	−0.643599	+	0.713271i
$658$	21.5330	−	21.5330i	0.839445	−	0.839445i
$659$	4.25839			0.165883			0.0829417	−	0.996554i	$-0.473568\pi$
$659$	4.25839			0.165883			0.0829417	+	0.996554i	$0.473568\pi$
$660$	−1.83821	−	20.5333i	−0.0715524	−	0.799256i
$661$	0.330451			0.0128530			0.00642652	−	0.999979i	$-0.497954\pi$
$661$	0.330451			0.0128530			0.00642652	+	0.999979i	$0.497954\pi$
$662$	16.3984	−	16.3984i	0.637344	−	0.637344i
$663$	0.533550	+	20.7953i	0.0207214	+	0.807623i
$664$			6.15593i			0.238896i
$665$	−32.6658	−	28.7522i	−1.26672	−	1.11496i
$666$	3.04308	−	0.156257i	0.117917	−	0.00605482i
$667$	−8.38554	−	8.38554i	−0.324690	−	0.324690i
$668$	−16.7823	−	16.7823i	−0.649326	−	0.649326i
$669$	8.00285	−	8.42432i	0.309408	−	0.325703i
$670$	−1.95462	−	30.6751i	−0.0755137	−	1.18508i
$671$			4.86244i			0.187712i
$672$	−5.73929	+	0.147254i	−0.221398	+	0.00568046i
$673$	30.2191	−	30.2191i	1.16486	−	1.16486i	0.181464	−	0.983398i	$-0.441916\pi$
$673$	30.2191	−	30.2191i	1.16486	−	1.16486i	0.983398	−	0.181464i	$-0.0580837\pi$
$674$	−17.8804			−0.688728
$675$	−25.4409	+	5.26906i	−0.979219	+	0.202806i
$676$	−0.259324			−0.00997402
$677$	−17.5604	+	17.5604i	−0.674901	+	0.674901i	−0.958842	−	0.283941i	$-0.908358\pi$
$677$	−17.5604	+	17.5604i	−0.674901	+	0.674901i	0.283941	+	0.958842i	$0.408358\pi$
$678$	−25.9691	+	0.666295i	−0.997337	+	0.0255889i
$679$		−	33.2832i		−	1.27729i
$680$	−0.468995	−	7.36024i	−0.0179852	−	0.282252i
$681$	2.19761	−	2.31335i	0.0842127	−	0.0886478i
$682$	−3.76384	−	3.76384i	−0.144125	−	0.144125i
$683$	28.7718	+	28.7718i	1.10092	+	1.10092i	0.994300	+	0.106622i	$0.0340033\pi$
$683$	28.7718	+	28.7718i	1.10092	+	1.10092i	0.106622	+	0.994300i	$0.465997\pi$
$684$	17.5908	−	0.903254i	0.672599	−	0.0345368i
$685$	11.8480	+	10.4286i	0.452690	+	0.398455i
$686$		−	9.98694i		−	0.381303i
$687$	0.776808	+	30.2764i	0.0296371	+	1.15512i
$688$	−1.71966	+	1.71966i	−0.0655613	+	0.0655613i
$689$	28.5956			1.08941
$690$	−1.00434	−	11.2187i	−0.0382345	−	0.427088i
$691$	29.8168			1.13429			0.567143	−	0.823620i	$-0.308049\pi$
$691$	29.8168			1.13429			0.567143	+	0.823620i	$0.308049\pi$
$692$	−5.10781	+	5.10781i	−0.194170	+	0.194170i
$693$	35.4591	−	39.2977i	1.34698	−	1.49280i
$694$			32.4446i			1.23158i
$695$	11.2921	−	0.719533i	0.428333	−	0.0272934i
$696$	−5.12061	−	4.86442i	−0.194096	−	0.184385i
$697$	22.4559	+	22.4559i	0.850577	+	0.850577i
$698$	−25.0308	−	25.0308i	−0.947429	−	0.947429i
$699$	−18.6848	−	17.7500i	−0.706723	−	0.671365i
$700$	−10.1369	+	13.1118i	−0.383139	+	0.495580i
$701$			17.0513i			0.644020i	0.946736	+	0.322010i	$0.104359\pi$
$701$			17.0513i			0.644020i	−0.946736	+	0.322010i	$0.895641\pi$
$702$	1.45462	+	18.8649i	0.0549011	+	0.712011i
$703$	−4.21680	+	4.21680i	−0.159040	+	0.159040i
$704$	5.32287			0.200613
$705$	27.3032	+	22.8163i	1.02830	+	0.859312i
$706$	−22.1859			−0.834976
$707$	−29.6017	+	29.6017i	−1.11328	+	1.11328i
$708$	0.304960	+	11.8859i	0.0114611	+	0.446700i
$709$			24.4984i			0.920059i	0.887904	+	0.460029i	$0.152161\pi$
$709$			24.4984i			0.920059i	−0.887904	+	0.460029i	$0.847839\pi$
$710$	12.7040	−	14.4332i	0.476774	−	0.541669i
$711$	−1.53982	−	29.9878i	−0.0577478	−	1.12463i
$712$	2.23020	+	2.23020i	0.0835804	+	0.0835804i
$713$	−2.05643	−	2.05643i	−0.0770140	−	0.0770140i
$714$	13.0419	−	13.7288i	0.488082	−	0.513787i
$715$	−28.6353	+	32.5330i	−1.07090	+	1.21666i
$716$			17.1413i			0.640602i
$717$	11.3935	−	0.292325i	0.425498	−	0.0109171i
$718$	21.9355	−	21.9355i	0.818626	−	0.818626i
$719$	11.2341			0.418963			0.209481	−	0.977813i	$-0.432822\pi$
$719$	11.2341			0.418963			0.209481	+	0.977813i	$0.432822\pi$
$720$	−0.769326	−	6.66394i	−0.0286711	−	0.248350i
$721$	−40.6969			−1.51563
$722$	−10.9405	+	10.9405i	−0.407165	+	0.407165i
$723$	11.1520	−	0.286129i	0.414747	−	0.0106412i
$724$		−	9.34856i		−	0.347436i
$725$	−20.2237	+	2.58782i	−0.751088	+	0.0961091i
$726$	−20.6770	+	21.7659i	−0.767394	+	0.807809i
$727$	27.4216	+	27.4216i	1.01701	+	1.01701i	0.999853	+	0.0171593i	$0.00546226\pi$
$727$	27.4216	+	27.4216i	1.01701	+	1.01701i	0.0171593	+	0.999853i	$0.494538\pi$
$728$	8.53466	+	8.53466i	0.316316	+	0.316316i
$729$	26.6808	−	4.13917i	0.988179	−	0.153303i
$730$	−18.3173	+	1.16718i	−0.677954	+	0.0431993i
$731$		−	8.02128i		−	0.296678i
$732$	0.0405822	+	1.58171i	0.00149996	+	0.0584616i
$733$	8.57269	−	8.57269i	0.316639	−	0.316639i	−0.530836	−	0.847475i	$-0.678122\pi$
$733$	8.57269	−	8.57269i	0.316639	−	0.316639i	0.847475	+	0.530836i	$0.178122\pi$
$734$	26.2993			0.970723
$735$	−15.3803	+	1.37690i	−0.567310	+	0.0507877i
$736$	2.90823			0.107199
$737$	−51.7383	+	51.7383i	−1.90580	+	1.90580i
$738$	21.4456	+	19.3508i	0.789425	+	0.712313i
$739$		−	8.21308i		−	0.302123i	−0.988524	−	0.151062i	$-0.951731\pi$
$739$		−	8.21308i		−	0.302123i	0.988524	−	0.151062i	$-0.0482692\pi$
$740$	1.70483	+	1.50058i	0.0626708	+	0.0551624i
$741$	−26.8473	−	25.5041i	−0.986260	−	0.936917i
$742$	−18.4062	−	18.4062i	−0.675713	−	0.675713i
$743$	−2.02106	−	2.02106i	−0.0741456	−	0.0741456i	0.669061	−	0.743207i	$-0.266696\pi$
$743$	−2.02106	−	2.02106i	−0.0741456	−	0.0741456i	−0.743207	+	0.669061i	$0.766696\pi$
$744$	−1.25576	−	1.19293i	−0.0460382	−	0.0437349i
$745$	1.13427	+	17.8009i	0.0415566	+	0.652173i
$746$		−	9.95549i		−	0.364496i
$747$	−13.7112	−	12.3719i	−0.501666	−	0.452663i
$748$	−12.4142	+	12.4142i	−0.453907	+	0.453907i
$749$	−34.6392			−1.26569
$750$	−16.3154	−	10.4311i	−0.595755	−	0.380889i
$751$	9.64510			0.351955			0.175977	−	0.984394i	$-0.443691\pi$
$751$	9.64510			0.351955			0.175977	+	0.984394i	$0.443691\pi$
$752$	−6.49628	+	6.49628i	−0.236895	+	0.236895i
$753$	0.260803	+	10.1649i	0.00950419	+	0.370430i
$754$			14.8483i			0.540744i
$755$	0.532232	+	8.35265i	0.0193699	+	0.303984i
$756$	11.2065	−	13.0791i	0.407578	−	0.475684i
$757$	29.8289	+	29.8289i	1.08415	+	1.08415i	0.996118	+	0.0880304i	$0.0280573\pi$
$757$	29.8289	+	29.8289i	1.08415	+	1.08415i	0.0880304	+	0.996118i	$0.471943\pi$
$758$	22.0866	+	22.0866i	0.802221	+	0.802221i
$759$	−18.4667	+	19.4393i	−0.670299	+	0.705601i
$760$	9.85490	+	8.67423i	0.357475	+	0.314647i
$761$		−	1.75145i		−	0.0634902i	−0.999496	−	0.0317451i	$-0.989894\pi$
$761$		−	1.75145i		−	0.0634902i	0.999496	−	0.0317451i	$-0.0101065\pi$
$762$	29.1832	−	0.748760i	1.05720	−	0.0271247i
$763$	17.1538	−	17.1538i	0.621008	−	0.621008i
$764$	19.7911			0.716017
$765$	17.3361	+	13.7476i	0.626788	+	0.497046i
$766$	22.3556			0.807742
$767$	17.6751	−	17.6751i	0.638209	−	0.638209i
$768$	1.73148	−	0.0444250i	0.0624794	−	0.00160305i
$769$		−	20.9102i		−	0.754042i	−0.926205	−	0.377021i	$-0.876948\pi$
$769$		−	20.9102i		−	0.754042i	0.926205	−	0.377021i	$-0.123052\pi$
$770$	39.3724	−	2.50881i	1.41888	−	0.0904113i
$771$	−4.96822	+	5.22988i	−0.178926	+	0.188349i
$772$	0.289823	+	0.289823i	0.0104310	+	0.0104310i
$773$	35.1192	+	35.1192i	1.26315	+	1.26315i	0.949557	+	0.313593i	$0.101533\pi$
$773$	35.1192	+	35.1192i	1.26315	+	1.26315i	0.313593	+	0.949557i	$0.398467\pi$
$774$	−0.374138	−	7.28629i	−0.0134481	−	0.261900i
$775$	−4.95956	+	0.634625i	−0.178153	+	0.0227964i
$776$			10.0412i			0.360457i
$777$	0.149565	+	5.82937i	0.00536563	+	0.209128i
$778$	−9.08213	+	9.08213i	−0.325610	+	0.325610i
$779$	−56.5318			−2.02546
$780$	−9.04329	+	10.8217i	−0.323802	+	0.387478i
$781$	−45.7711			−1.63782
$782$	−6.78268	+	6.78268i	−0.242548	+	0.242548i
$783$	21.1257	−	1.62894i	0.754971	−	0.0582136i
$784$		−	3.98705i		−	0.142395i
$785$	−27.8815	+	31.6765i	−0.995133	+	1.13058i
$786$	11.3358	+	10.7687i	0.404336	+	0.384106i
$787$	−11.5196	−	11.5196i	−0.410629	−	0.410629i	0.471329	−	0.881957i	$-0.343774\pi$
$787$	−11.5196	−	11.5196i	−0.410629	−	0.410629i	−0.881957	+	0.471329i	$0.843774\pi$
$788$	12.1490	+	12.1490i	0.432792	+	0.432792i
$789$	2.05190	+	1.94924i	0.0730496	+	0.0693949i
$790$	14.7874	−	16.8001i	0.526111	−	0.597722i
$791$		−	49.7141i		−	1.76763i
$792$	−10.6976	+	11.8557i	−0.380123	+	0.421274i
$793$	2.35209	−	2.35209i	0.0835252	−	0.0835252i
$794$	−27.8415			−0.988058
$795$	19.5031	−	23.3385i	0.691705	−	0.827731i
$796$	−16.3567			−0.579748
$797$	0.995608	−	0.995608i	0.0352662	−	0.0352662i	−0.689254	−	0.724520i	$-0.742061\pi$
$797$	0.995608	−	0.995608i	0.0352662	−	0.0352662i	0.724520	+	0.689254i	$0.242061\pi$
$798$	0.864575	+	33.6971i	0.0306056	+	1.19287i
$799$		−	30.3017i		−	1.07200i
$800$	3.05819	−	3.95569i	0.108123	−	0.139855i
$801$	−9.44951	+	0.485216i	−0.333882	+	0.0171442i
$802$	−26.8787	−	26.8787i	−0.949119	−	0.949119i
$803$	30.8949	+	30.8949i	1.09026	+	1.09026i
$804$	−16.3982	+	17.2618i	−0.578319	+	0.608777i
$805$	21.5117	−	1.37073i	0.758188	−	0.0483119i
$806$			3.64134i			0.128261i
$807$	−33.3293	+	0.855138i	−1.17325	+	0.0301023i
$808$	8.93049	−	8.93049i	0.314174	−	0.314174i
$809$	−38.0612			−1.33816			−0.669080	−	0.743190i	$-0.733312\pi$
$809$	−38.0612			−1.33816			−0.669080	+	0.743190i	$0.733312\pi$
$810$	16.3888	+	11.6793i	0.575845	+	0.410369i
$811$	−49.7487			−1.74691			−0.873457	−	0.486901i	$-0.838127\pi$
$811$	−49.7487			−1.74691			−0.873457	+	0.486901i	$0.838127\pi$
$812$	9.55746	−	9.55746i	0.335401	−	0.335401i
$813$	−17.3821	+	0.445976i	−0.609616	+	0.0156410i
$814$		−	5.40641i		−	0.189495i
$815$	−7.96205	−	7.00815i	−0.278899	−	0.245485i
$816$	−3.93461	+	4.14183i	−0.137739	+	0.144993i
$817$	10.0966	+	10.0966i	0.353237	+	0.353237i
$818$	12.4989	+	12.4989i	0.437013	+	0.437013i
$819$	−36.1619	+	1.85685i	−1.26360	+	0.0648835i
$820$	1.36911	+	21.4864i	0.0478116	+	0.750337i
$821$			28.4532i			0.993025i	0.868030	+	0.496512i	$0.165386\pi$
$821$			28.4532i			0.993025i	−0.868030	+	0.496512i	$0.834614\pi$
$822$	−0.313585	−	12.2221i	−0.0109375	−	0.426295i
$823$	5.51218	−	5.51218i	0.192142	−	0.192142i	−0.604479	−	0.796621i	$-0.706619\pi$
$823$	5.51218	−	5.51218i	0.192142	−	0.192142i	0.796621	+	0.604479i	$0.206619\pi$
$824$	12.2778			0.427718
$825$	7.02176	+	45.5595i	0.244466	+	1.58618i
$826$	−22.7539			−0.791709
$827$	−10.3809	+	10.3809i	−0.360978	+	0.360978i	−0.864173	−	0.503195i	$-0.832158\pi$
$827$	−10.3809	+	10.3809i	−0.360978	+	0.360978i	0.503195	+	0.864173i	$0.332158\pi$
$828$	−5.84481	+	6.47755i	−0.203121	+	0.225110i
$829$		−	22.4738i		−	0.780549i	−0.920699	−	0.390274i	$-0.872380\pi$
$829$		−	22.4738i		−	0.780549i	0.920699	−	0.390274i	$-0.127620\pi$
$830$	−0.875337	−	13.7372i	−0.0303834	−	0.476826i
$831$	−21.6341	−	20.5517i	−0.750478	−	0.712931i
$832$	−2.57481	−	2.57481i	−0.0892656	−	0.0892656i
$833$	9.29872	+	9.29872i	0.322182	+	0.322182i
$834$	−6.35439	−	6.03648i	−0.220035	−	0.209026i
$835$	39.8367	+	35.0640i	1.37861	+	1.21344i
$836$		−	31.2522i		−	1.08088i
$837$	5.18077	−	0.399474i	0.179074	−	0.0138078i
$838$	17.1101	−	17.1101i	0.591058	−	0.591058i
$839$	−5.01157			−0.173019			−0.0865093	−	0.996251i	$-0.527571\pi$
$839$	−5.01157			−0.173019			−0.0865093	+	0.996251i	$0.527571\pi$
$840$	12.7865	−	1.14470i	0.441177	−	0.0394958i
$841$	−12.3722			−0.426629
$842$	14.5131	−	14.5131i	0.500154	−	0.500154i
$843$	−1.18169	−	46.0569i	−0.0406996	−	1.58628i
$844$		−	19.7796i		−	0.680841i
$845$	0.578693	−	0.0368744i	0.0199077	−	0.00126852i
$846$	−1.41337	−	27.5251i	−0.0485925	−	0.946333i
$847$	−40.6254	−	40.6254i	−1.39591	−	1.39591i
$848$	5.55295	+	5.55295i	0.190689	+	0.190689i
$849$	−21.4647	+	22.5952i	−0.736668	+	0.775465i
$850$	2.09317	+	16.3580i	0.0717950	+	0.561075i
$851$		−	2.95388i		−	0.101258i
$852$	−14.8889	+	0.382008i	−0.510086	+	0.0130874i
$853$	−15.5225	+	15.5225i	−0.531480	+	0.531480i	−0.921013	−	0.389532i	$-0.872637\pi$
$853$	−15.5225	+	15.5225i	−0.531480	+	0.531480i	0.389532	+	0.921013i	$0.372637\pi$
$854$	−3.02795			−0.103614
$855$	−39.1261	+	4.51695i	−1.33808	+	0.154477i
$856$	10.4503			0.357182
$857$	−6.05485	+	6.05485i	−0.206830	+	0.206830i	−0.802919	−	0.596089i	$-0.796721\pi$
$857$	−6.05485	+	6.05485i	−0.206830	+	0.206830i	0.596089	+	0.802919i	$0.296721\pi$
$858$	33.5602	−	0.861061i	1.14573	−	0.0293961i
$859$		−	36.8937i		−	1.25880i	−0.777082	−	0.629399i	$-0.783301\pi$
$859$		−	36.8937i		−	1.25880i	0.777082	−	0.629399i	$-0.216699\pi$
$860$	3.59296	−	4.08201i	0.122519	−	0.139195i
$861$	−38.0726	+	40.0778i	−1.29751	+	1.36585i
$862$	−16.9048	−	16.9048i	−0.575780	−	0.575780i
$863$	−11.9650	−	11.9650i	−0.407292	−	0.407292i	0.473501	−	0.880793i	$-0.342990\pi$
$863$	−11.9650	−	11.9650i	−0.407292	−	0.407292i	−0.880793	+	0.473501i	$0.842990\pi$
$864$	−3.38089	+	3.94583i	−0.115020	+	0.134240i
$865$	10.6720	−	12.1246i	0.362858	−	0.412248i
$866$			12.6871i			0.431125i
$867$	0.271942	+	10.5991i	0.00923565	+	0.359963i
$868$	2.34383	−	2.34383i	0.0795547	−	0.0795547i
$869$	−53.2771			−1.80730
$870$	12.1186	+	10.1270i	0.410857	+	0.343339i
$871$	50.0544			1.69603
$872$	−5.17510	+	5.17510i	−0.175251	+	0.175251i
$873$	−22.3648	−	20.1802i	−0.756934	−	0.682996i
$874$		−	17.0751i		−	0.577575i
$875$	20.7565	−	30.7010i	0.701698	−	1.03788i
$876$	10.3077	+	9.79199i	0.348265	+	0.330841i
$877$	−2.74612	−	2.74612i	−0.0927299	−	0.0927299i	0.659220	−	0.751950i	$-0.270887\pi$
$877$	−2.74612	−	2.74612i	−0.0927299	−	0.0927299i	−0.751950	+	0.659220i	$0.770887\pi$
$878$	20.2328	+	20.2328i	0.682824	+	0.682824i
$879$	17.3286	+	16.4616i	0.584480	+	0.555238i
$880$	−11.8782	+	0.756881i	−0.400414	+	0.0255145i
$881$		−	24.1429i		−	0.813393i	−0.913563	−	0.406697i	$-0.866681\pi$
$881$		−	24.1429i		−	0.813393i	0.913563	−	0.406697i	$-0.133319\pi$
$882$	8.88040	+	8.01296i	0.299019	+	0.269810i
$883$	−10.9140	+	10.9140i	−0.367287	+	0.367287i	−0.866487	−	0.499200i	$-0.833627\pi$
$883$	−10.9140	+	10.9140i	−0.367287	+	0.367287i	0.499200	+	0.866487i	$0.333627\pi$
$884$	12.0101			0.403944
$885$	−2.37064	−	26.4806i	−0.0796881	−	0.890134i
$886$	−30.1986			−1.01454
$887$	−19.5350	+	19.5350i	−0.655920	+	0.655920i	−0.954412	−	0.298492i	$-0.903516\pi$
$887$	−19.5350	+	19.5350i	−0.655920	+	0.655920i	0.298492	+	0.954412i	$0.403516\pi$
$888$	−0.0451223	−	1.75866i	−0.00151420	−	0.0590167i
$889$			55.8671i			1.87372i
$890$	−5.29392	−	4.65967i	−0.177452	−	0.156193i
$891$	−4.90682	−	47.6539i	−0.164385	−	1.59646i
$892$	−4.74368	−	4.74368i	−0.158830	−	0.158830i
$893$	38.1416	+	38.1416i	1.27636	+	1.27636i
$894$	9.51591	−	10.0171i	0.318260	−	0.335021i
$895$	−2.43740	−	38.2516i	−0.0814733	−	1.27861i
$896$			3.31467i			0.110735i
$897$	18.3361	−	0.470454i	0.612226	−	0.0157080i
$898$	27.5179	−	27.5179i	0.918285	−	0.918285i
$899$	4.07771			0.135999
$900$	2.66436	+	14.7615i	0.0888119	+	0.492049i
$901$	−25.9015			−0.862905
$902$	36.2401	−	36.2401i	1.20666	−	1.20666i
$903$	13.9577	−	0.358117i	0.464484	−	0.0119174i
$904$			14.9982i			0.498833i
$905$	1.32931	+	20.8617i	0.0441878	+	0.693467i
$906$	4.46512	−	4.70028i	0.148344	−	0.156156i
$907$	6.70921	+	6.70921i	0.222776	+	0.222776i	0.809666	−	0.586891i	$-0.199648\pi$
$907$	6.70921	+	6.70921i	0.222776	+	0.222776i	−0.586891	+	0.809666i	$0.699648\pi$
$908$	−1.30263	−	1.30263i	−0.0432293	−	0.0432293i
$909$	1.94297	+	37.8390i	0.0644442	+	1.25504i
$910$	−20.2590	−	17.8319i	−0.671580	−	0.591121i
$911$			4.06585i			0.134708i	0.997729	+	0.0673539i	$0.0214557\pi$
$911$			4.06585i			0.134708i	−0.997729	+	0.0673539i	$0.978544\pi$
$912$	−0.260833	−	10.1661i	−0.00863704	−	0.336632i
$913$	−23.1699	+	23.1699i	−0.766812	+	0.766812i
$914$	3.72809			0.123314
$915$	−0.315471	−	3.52388i	−0.0104291	−	0.116496i
$916$	17.4858			0.577748
$917$	−21.1580	+	21.1580i	−0.698697	+	0.698697i
$918$	−1.31758	−	17.0876i	−0.0434865	−	0.563975i
$919$			21.3756i			0.705116i	0.935790	+	0.352558i	$0.114688\pi$
$919$			21.3756i			0.705116i	−0.935790	+	0.352558i	$0.885312\pi$
$920$	−6.48985	+	0.413534i	−0.213964	+	0.0136338i
$921$	0.163639	+	0.155452i	0.00539208	+	0.00512231i
$922$	19.2058	+	19.2058i	0.632511	+	0.632511i
$923$	22.1407	+	22.1407i	0.728770	+	0.728770i
$924$	−22.1560	−	21.0475i	−0.728879	−	0.692412i
$925$	−4.01777	−	3.10619i	−0.132104	−	0.102131i
$926$			19.3756i			0.636723i
$927$	−24.6753	+	27.3465i	−0.810443	+	0.898178i
$928$	−2.88338	+	2.88338i	−0.0946516	+	0.0946516i
$929$	−10.1375			−0.332601			−0.166300	−	0.986075i	$-0.553182\pi$
$929$	−10.1375			−0.332601			−0.166300	+	0.986075i	$0.553182\pi$
$930$	2.97190	+	2.48351i	0.0974524	+	0.0814375i
$931$	−23.4092			−0.767205
$932$	−10.5213	+	10.5213i	−0.344636	+	0.344636i
$933$	0.375568	+	14.6379i	0.0122955	+	0.479223i
$934$		−	24.7527i		−	0.809934i
$935$	25.9375	−	29.4680i	0.848248	−	0.963705i
$936$	10.9096	−	0.560191i	0.356593	−	0.0183104i
$937$	8.17703	+	8.17703i	0.267132	+	0.267132i	0.827944	−	0.560811i	$-0.189511\pi$
$937$	8.17703	+	8.17703i	0.267132	+	0.267132i	−0.560811	+	0.827944i	$0.689511\pi$
$938$	−32.2186	−	32.2186i	−1.05197	−	1.05197i
$939$	−38.9480	+	40.9992i	−1.27102	+	1.33796i
$940$	13.5730	−	15.4204i	0.442702	−	0.502960i
$941$		−	32.3646i		−	1.05506i	−0.849538	−	0.527528i	$-0.823119\pi$
$941$		−	32.3646i		−	1.05506i	0.849538	−	0.527528i	$-0.176881\pi$
$942$	32.6767	−	0.838393i	1.06466	−	0.0273163i
$943$	19.8003	−	19.8003i	0.644788	−	0.644788i
$944$	6.86460			0.223424
$945$	−23.1481	+	30.7801i	−0.753007	+	1.00128i
$946$	−12.9450			−0.420879
$947$	19.1741	−	19.1741i	0.623076	−	0.623076i	−0.323241	−	0.946317i	$-0.604772\pi$
$947$	19.1741	−	19.1741i	0.623076	−	0.623076i	0.946317	+	0.323241i	$0.104772\pi$
$948$	−17.3306	+	0.444654i	−0.562871	+	0.0144417i
$949$		−	29.8894i		−	0.970251i
$950$	−23.2251	−	17.9556i	−0.753520	−	0.582556i
$951$	15.2126	−	16.0137i	0.493301	−	0.519281i
$952$	−7.73058	−	7.73058i	−0.250550	−	0.250550i
$953$	−20.7857	−	20.7857i	−0.673316	−	0.673316i	0.285163	−	0.958479i	$-0.407952\pi$
$953$	−20.7857	−	20.7857i	−0.673316	−	0.673316i	−0.958479	+	0.285163i	$0.907952\pi$
$954$	−23.5282	+	1.20813i	−0.761753	+	0.0391147i
$955$	−44.1647	+	2.81418i	−1.42914	+	0.0910647i
$956$		−	6.58020i		−	0.212819i
$957$	−0.964251	−	37.5820i	−0.0311698	−	1.21485i
$958$	5.94114	−	5.94114i	0.191950	−	0.191950i
$959$	23.3975			0.755544
$960$	−3.85756	+	0.345343i	−0.124502	+	0.0111459i
$961$	1.00000			0.0322581
$962$	−2.61523	+	2.61523i	−0.0843183	+	0.0843183i
$963$	−21.0024	+	23.2760i	−0.676792	+	0.750058i
$964$		−	6.44072i		−	0.207442i
$965$	−0.687964	−	0.605542i	−0.0221464	−	0.0194931i
$966$	−12.1053	−	11.4996i	−0.389481	−	0.369995i
$967$	−26.6176	−	26.6176i	−0.855964	−	0.855964i	0.134896	−	0.990860i	$-0.456930\pi$
$967$	−26.6176	−	26.6176i	−0.855964	−	0.855964i	−0.990860	+	0.134896i	$0.956930\pi$
$968$	12.2562	+	12.2562i	0.393930	+	0.393930i
$969$	24.3179	+	23.1013i	0.781205	+	0.742120i
$970$	−1.42780	−	22.4073i	−0.0458437	−	0.719454i
$971$		−	27.0245i		−	0.867259i	−0.901091	−	0.433629i	$-0.857233\pi$
$971$		−	27.0245i		−	0.867259i	0.901091	−	0.433629i	$-0.142767\pi$
$972$	−1.99387	−	15.4604i	−0.0639533	−	0.495893i
$973$	11.8603	−	11.8603i	0.380223	−	0.380223i
$974$	30.7733			0.986041
$975$	18.6417	−	25.4349i	0.597013	−	0.814570i
$976$	0.913500			0.0292404
$977$	−24.0131	+	24.0131i	−0.768246	+	0.768246i	−0.977798	−	0.209552i	$-0.932800\pi$
$977$	−24.0131	+	24.0131i	−0.768246	+	0.768246i	0.209552	+	0.977798i	$0.432800\pi$
$978$	0.210734	+	8.21344i	0.00673854	+	0.262637i
$979$			16.7882i			0.536555i
$980$	0.566935	+	8.89727i	0.0181101	+	0.284213i
$981$	−1.12592	−	21.9272i	−0.0359480	−	0.700081i
$982$	−13.9304	−	13.9304i	−0.444537	−	0.444537i
$983$	−20.9700	−	20.9700i	−0.668839	−	0.668839i	0.288609	−	0.957447i	$-0.406807\pi$
$983$	−20.9700	−	20.9700i	−0.668839	−	0.668839i	−0.957447	+	0.288609i	$0.906807\pi$
$984$	11.4861	−	12.0910i	0.366163	−	0.385448i
$985$	−28.8386	−	25.3836i	−0.918876	−	0.808789i
$986$		−	13.4494i		−	0.428317i
$987$	52.7276	−	1.35284i	1.67834	−	0.0430615i
$988$	−15.1175	+	15.1175i	−0.480952	+	0.480952i
$989$	−7.07272			−0.224899
$990$	22.1864	−	27.9776i	0.705129	−	0.889187i
$991$	43.3152			1.37595			0.687976	−	0.725733i	$-0.258499\pi$
$991$	43.3152			1.37595			0.687976	+	0.725733i	$0.258499\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	40.1546	−	1.03026i	1.27427	−	0.0326942i
$994$		−	28.5027i		−	0.904051i
$995$	36.5007	−	2.32583i	1.15715	−	0.0737337i
$996$	−7.34358	+	7.73034i	−0.232690	+	0.244945i
$997$	−31.0340	−	31.0340i	−0.982858	−	0.982858i	0.0169979	−	0.999856i	$-0.494589\pi$
$997$	−31.0340	−	31.0340i	−0.982858	−	0.982858i	−0.999856	+	0.0169979i	$0.994589\pi$
$998$	9.32782	+	9.32782i	0.295267	+	0.295267i
$999$	4.00776	+	3.43395i	0.126800	+	0.108645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.20	yes	40
3.2	odd	2	inner	930.2.j.g.497.6	✓	40
5.3	odd	4	inner	930.2.j.g.683.6	yes	40
15.8	even	4	inner	930.2.j.g.683.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.6	✓	40	3.2	odd	2	inner
930.2.j.g.497.20	yes	40	1.1	even	1	trivial
930.2.j.g.683.6	yes	40	5.3	odd	4	inner
930.2.j.g.683.20	yes	40	15.8	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.73148 - 0.0444250i) q^{3} -1.00000i q^{4} +(0.142194 + 2.23154i) q^{5} +(1.19293 - 1.25576i) q^{6} +(2.34383 + 2.34383i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.99605 - 0.153842i) q^{9} +(1.67849 + 1.47739i) q^{10} -5.32287i q^{11} +(-0.0444250 - 1.73148i) q^{12} +(-2.57481 + 2.57481i) q^{13} +3.31467 q^{14} +(0.345343 + 3.85756i) q^{15} -1.00000 q^{16} +(2.33223 - 2.33223i) q^{17} +(2.00975 - 2.22731i) q^{18} +5.87131i q^{19} +(2.23154 - 0.142194i) q^{20} +(4.16242 + 3.95417i) q^{21} +(-3.76384 - 3.76384i) q^{22} +(-2.05643 - 2.05643i) q^{23} +(-1.25576 - 1.19293i) q^{24} +(-4.95956 + 0.634625i) q^{25} +3.64134i q^{26} +(5.18077 - 0.399474i) q^{27} +(2.34383 - 2.34383i) q^{28} +4.07771 q^{29} +(2.97190 + 2.48351i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.236468 - 9.21645i) q^{33} -3.29827i q^{34} +(-4.89707 + 5.56363i) q^{35} +(-0.153842 - 2.99605i) q^{36} +(0.718205 + 0.718205i) q^{37} +(4.15164 + 4.15164i) q^{38} +(-4.34385 + 4.57263i) q^{39} +(1.47739 - 1.67849i) q^{40} +9.62849i q^{41} +(5.73929 - 0.147254i) q^{42} +(1.71966 - 1.71966i) q^{43} -5.32287 q^{44} +(0.769326 + 6.66394i) q^{45} -2.90823 q^{46} +(6.49628 - 6.49628i) q^{47} +(-1.73148 + 0.0444250i) q^{48} +3.98705i q^{49} +(-3.05819 + 3.95569i) q^{50} +(3.93461 - 4.14183i) q^{51} +(2.57481 + 2.57481i) q^{52} +(-5.55295 - 5.55295i) q^{53} +(3.38089 - 3.94583i) q^{54} +(11.8782 - 0.756881i) q^{55} -3.31467i q^{56} +(0.260833 + 10.1661i) q^{57} +(2.88338 - 2.88338i) q^{58} -6.86460 q^{59} +(3.85756 - 0.345343i) q^{60} -0.913500 q^{61} +(0.707107 - 0.707107i) q^{62} +(7.38281 + 6.66165i) q^{63} +1.00000i q^{64} +(-6.11193 - 5.37968i) q^{65} +(-6.68422 - 6.34980i) q^{66} +(-9.72000 - 9.72000i) q^{67} +(-2.33223 - 2.33223i) q^{68} +(-3.65203 - 3.46932i) q^{69} +(0.471327 + 7.39683i) q^{70} -8.59895i q^{71} +(-2.22731 - 2.00975i) q^{72} +(-5.80419 + 5.80419i) q^{73} +1.01570 q^{74} +(-8.55919 + 1.31917i) q^{75} +5.87131 q^{76} +(12.4759 - 12.4759i) q^{77} +(0.161766 + 6.30490i) q^{78} -10.0091i q^{79} +(-0.142194 - 2.23154i) q^{80} +(8.95267 - 0.921838i) q^{81} +(6.80837 + 6.80837i) q^{82} +(-4.35290 - 4.35290i) q^{83} +(3.95417 - 4.16242i) q^{84} +(5.53610 + 4.87285i) q^{85} -2.43196i q^{86} +(7.06048 - 0.181152i) q^{87} +(-3.76384 + 3.76384i) q^{88} -3.15398 q^{89} +(5.25612 + 4.16812i) q^{90} -12.0698 q^{91} +(-2.05643 + 2.05643i) q^{92} +(1.73148 - 0.0444250i) q^{93} -9.18712i q^{94} +(-13.1021 + 0.834866i) q^{95} +(-1.19293 + 1.25576i) q^{96} +(-7.10018 - 7.10018i) q^{97} +(2.81927 + 2.81927i) q^{98} +(-0.818881 - 15.9476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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