LMFDB - Embedded newform 312.2.t.e.307.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(187,312)] 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("312.187"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-24,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.8
Character	$\chi$	$=$	312.307
Dual form			312.2.t.e.187.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.437240 - 1.34492i) q^{2} -1.00000 q^{3} +(-1.61764 - 1.17611i) q^{4} +(-1.98058 + 1.98058i) q^{5} +(-0.437240 + 1.34492i) q^{6} +(3.05943 + 3.05943i) q^{7} +(-2.28908 + 1.66136i) q^{8} +1.00000 q^{9} +(1.79774 + 3.52971i) q^{10} +(-1.08518 + 1.08518i) q^{11} +(1.61764 + 1.17611i) q^{12} +(3.57990 - 0.429300i) q^{13} +(5.45240 - 2.77699i) q^{14} +(1.98058 - 1.98058i) q^{15} +(1.23353 + 3.80505i) q^{16} +5.70052i q^{17} +(0.437240 - 1.34492i) q^{18} +(-4.39498 - 4.39498i) q^{19} +(5.53324 - 0.874489i) q^{20} +(-3.05943 - 3.05943i) q^{21} +(0.984999 + 1.93397i) q^{22} +2.95135 q^{23} +(2.28908 - 1.66136i) q^{24} -2.84537i q^{25} +(0.987901 - 5.00240i) q^{26} -1.00000 q^{27} +(-1.35084 - 8.54727i) q^{28} +6.96062i q^{29} +(-1.79774 - 3.52971i) q^{30} +(-3.05943 + 3.05943i) q^{31} +(5.65685 + 0.00471188i) q^{32} +(1.08518 - 1.08518i) q^{33} +(7.66677 + 2.49250i) q^{34} -12.1189 q^{35} +(-1.61764 - 1.17611i) q^{36} +(5.14026 + 5.14026i) q^{37} +(-7.83257 + 3.98925i) q^{38} +(-3.57990 + 0.429300i) q^{39} +(1.24323 - 7.82415i) q^{40} +(-2.77963 - 2.77963i) q^{41} +(-5.45240 + 2.77699i) q^{42} -3.00392i q^{43} +(3.03172 - 0.479142i) q^{44} +(-1.98058 + 1.98058i) q^{45} +(1.29045 - 3.96934i) q^{46} +(-6.40146 - 6.40146i) q^{47} +(-1.23353 - 3.80505i) q^{48} +11.7202i q^{49} +(-3.82681 - 1.24411i) q^{50} -5.70052i q^{51} +(-6.29590 - 3.51590i) q^{52} +4.28172i q^{53} +(-0.437240 + 1.34492i) q^{54} -4.29856i q^{55} +(-12.0861 - 1.92044i) q^{56} +(4.39498 + 4.39498i) q^{57} +(9.36150 + 3.04346i) q^{58} +(3.00033 - 3.00033i) q^{59} +(-5.53324 + 0.874489i) q^{60} -1.13106i q^{61} +(2.77699 + 5.45240i) q^{62} +(3.05943 + 3.05943i) q^{63} +(2.47974 - 7.60598i) q^{64} +(-6.24001 + 7.94053i) q^{65} +(-0.984999 - 1.93397i) q^{66} +(7.39889 + 7.39889i) q^{67} +(6.70444 - 9.22140i) q^{68} -2.95135 q^{69} +(-5.29885 + 16.2989i) q^{70} +(3.20281 - 3.20281i) q^{71} +(-2.28908 + 1.66136i) q^{72} +(7.87480 - 7.87480i) q^{73} +(9.16078 - 4.66573i) q^{74} +2.84537i q^{75} +(1.94053 + 12.2785i) q^{76} -6.64004 q^{77} +(-0.987901 + 5.00240i) q^{78} -4.46803i q^{79} +(-9.97930 - 5.09309i) q^{80} +1.00000 q^{81} +(-4.95376 + 2.52303i) q^{82} +(-9.78962 - 9.78962i) q^{83} +(1.35084 + 8.54727i) q^{84} +(-11.2903 - 11.2903i) q^{85} +(-4.04004 - 1.31343i) q^{86} -6.96062i q^{87} +(0.681180 - 4.28693i) q^{88} +(4.24001 - 4.24001i) q^{89} +(1.79774 + 3.52971i) q^{90} +(12.2659 + 9.63903i) q^{91} +(-4.77422 - 3.47111i) q^{92} +(3.05943 - 3.05943i) q^{93} +(-11.4085 + 5.81050i) q^{94} +17.4092 q^{95} +(-5.65685 - 0.00471188i) q^{96} +(-11.5753 - 11.5753i) q^{97} +(15.7627 + 5.12453i) q^{98} +(-1.08518 + 1.08518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} - 6 q^{8} + 24 q^{9} + 8 q^{11} + 36 q^{14} + 28 q^{16} + 20 q^{19} - 20 q^{20} + 20 q^{22} + 6 q^{24} + 12 q^{26} - 24 q^{27} - 16 q^{28} - 30 q^{32} - 8 q^{33} + 16 q^{34} + 16 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q - 24 * q^3 - 6 * q^8 + 24 * q^9 + 8 * q^11 + 36 * q^14 + 28 * q^16 + 20 * q^19 - 20 * q^20 + 20 * q^22 + 6 * q^24 + 12 * q^26 - 24 * q^27 - 16 * q^28 - 30 * q^32 - 8 * q^33 + 16 * q^34 + 16 * q^35 + 36 * q^40 - 12 * q^41 - 36 * q^42 - 32 * q^44 - 44 * q^46 - 28 * q^48 - 36 * q^50 + 4 * q^52 - 20 * q^57 + 32 * q^58 - 16 * q^59 + 20 * q^60 - 76 * q^65 - 20 * q^66 + 28 * q^67 + 32 * q^68 - 40 * q^70 - 6 * q^72 - 8 * q^73 - 32 * q^74 - 36 * q^76 - 12 * q^78 - 32 * q^80 + 24 * q^81 - 72 * q^83 + 16 * q^84 + 4 * q^86 + 28 * q^89 - 4 * q^91 + 32 * q^92 + 28 * q^94 + 30 * q^96 + 24 * q^97 + 68 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.437240	−	1.34492i	0.309175	−	0.951005i
$2$	0.437240	−	1.34492i	0.309175	−	0.951005i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.61764	−	1.17611i	−0.808821	−	0.588055i
$5$	−1.98058	+	1.98058i	−0.885741	+	0.885741i	−0.994111	−	0.108370i	$-0.965437\pi$
$5$	−1.98058	+	1.98058i	−0.885741	+	0.885741i	0.108370	+	0.994111i	$0.465437\pi$
$6$	−0.437240	+	1.34492i	−0.178503	+	0.549063i
$7$	3.05943	+	3.05943i	1.15635	+	1.15635i	0.985254	+	0.171100i	$0.0547323\pi$
$7$	3.05943	+	3.05943i	1.15635	+	1.15635i	0.171100	+	0.985254i	$0.445268\pi$
$8$	−2.28908	+	1.66136i	−0.809311	+	0.587381i
$9$	1.00000			0.333333
$10$	1.79774	+	3.52971i	0.568495	+	1.11619i
$11$	−1.08518	+	1.08518i	−0.327194	+	0.327194i	−0.851518	−	0.524325i	$-0.824318\pi$
$11$	−1.08518	+	1.08518i	−0.327194	+	0.327194i	0.524325	+	0.851518i	$0.324318\pi$
$12$	1.61764	+	1.17611i	0.466973	+	0.339514i
$13$	3.57990	−	0.429300i	0.992886	−	0.119066i
$13$	3.57990	−	0.429300i	0.992886	−	0.119066i
$14$	5.45240	−	2.77699i	1.45721	−	0.742182i
$15$	1.98058	−	1.98058i	0.511383	−	0.511383i
$16$	1.23353	+	3.80505i	0.308383	+	0.951262i
$17$			5.70052i			1.38258i	0.722578	+	0.691290i	$0.242957\pi$
$17$			5.70052i			1.38258i	−0.722578	+	0.691290i	$0.757043\pi$
$18$	0.437240	−	1.34492i	0.103058	−	0.317002i
$19$	−4.39498	−	4.39498i	−1.00828	−	1.00828i	−0.999965	−	0.00831097i	$-0.997355\pi$
$19$	−4.39498	−	4.39498i	−1.00828	−	1.00828i	−0.00831097	−	0.999965i	$-0.502645\pi$
$20$	5.53324	−	0.874489i	1.23727	−	0.195542i
$21$	−3.05943	−	3.05943i	−0.667621	−	0.667621i
$22$	0.984999	+	1.93397i	0.210003	+	0.412323i
$23$	2.95135			0.615398			0.307699	−	0.951484i	$-0.400441\pi$
$23$	2.95135			0.615398			0.307699	+	0.951484i	$0.400441\pi$
$24$	2.28908	−	1.66136i	0.467256	−	0.339124i
$25$		−	2.84537i		−	0.569074i
$26$	0.987901	−	5.00240i	0.193743	−	0.981052i
$27$	−1.00000			−0.192450
$28$	−1.35084	−	8.54727i	−0.255284	−	1.61528i
$29$			6.96062i			1.29255i	0.763103	+	0.646277i	$0.223675\pi$
$29$			6.96062i			1.29255i	−0.763103	+	0.646277i	$0.776325\pi$
$30$	−1.79774	−	3.52971i	−0.328221	−	0.644435i
$31$	−3.05943	+	3.05943i	−0.549489	+	0.549489i	−0.926293	−	0.376804i	$-0.877023\pi$
$31$	−3.05943	+	3.05943i	−0.549489	+	0.549489i	0.376804	+	0.926293i	$0.377023\pi$
$32$	5.65685	+	0.00471188i	1.00000	+	0.000832951i
$33$	1.08518	−	1.08518i	0.188905	−	0.188905i
$34$	7.66677	+	2.49250i	1.31484	+	0.427460i
$35$	−12.1189			−2.04846
$36$	−1.61764	−	1.17611i	−0.269607	−	0.196018i
$37$	5.14026	+	5.14026i	0.845053	+	0.845053i	0.989511	−	0.144458i	$-0.0461438\pi$
$37$	5.14026	+	5.14026i	0.845053	+	0.845053i	−0.144458	+	0.989511i	$0.546144\pi$
$38$	−7.83257	+	3.98925i	−1.27061	+	0.647142i
$39$	−3.57990	+	0.429300i	−0.573243	+	0.0687430i
$40$	1.24323	−	7.82415i	0.196572	−	1.23711i
$41$	−2.77963	−	2.77963i	−0.434106	−	0.434106i	0.455917	−	0.890022i	$-0.349311\pi$
$41$	−2.77963	−	2.77963i	−0.434106	−	0.434106i	−0.890022	+	0.455917i	$0.849311\pi$
$42$	−5.45240	+	2.77699i	−0.841323	+	0.428499i
$43$		−	3.00392i		−	0.458093i	−0.973415	−	0.229046i	$-0.926439\pi$
$43$		−	3.00392i		−	0.458093i	0.973415	−	0.229046i	$-0.0735608\pi$
$44$	3.03172	−	0.479142i	0.457049	−	0.0722333i
$45$	−1.98058	+	1.98058i	−0.295247	+	0.295247i
$46$	1.29045	−	3.96934i	0.190266	−	0.585247i
$47$	−6.40146	−	6.40146i	−0.933749	−	0.933749i	0.0641887	−	0.997938i	$-0.479554\pi$
$47$	−6.40146	−	6.40146i	−0.933749	−	0.933749i	−0.997938	+	0.0641887i	$0.979554\pi$
$48$	−1.23353	−	3.80505i	−0.178045	−	0.549211i
$49$			11.7202i			1.67431i
$50$	−3.82681	−	1.24411i	−0.541192	−	0.175944i
$51$		−	5.70052i		−	0.798233i
$52$	−6.29590	−	3.51590i	−0.873085	−	0.487568i
$53$			4.28172i			0.588140i	0.955784	+	0.294070i	$0.0950099\pi$
$53$			4.28172i			0.588140i	−0.955784	+	0.294070i	$0.904990\pi$
$54$	−0.437240	+	1.34492i	−0.0595008	+	0.183021i
$55$		−	4.29856i		−	0.579618i
$56$	−12.0861	−	1.92044i	−1.61507	−	0.256629i
$57$	4.39498	+	4.39498i	0.582129	+	0.582129i
$58$	9.36150	+	3.04346i	1.22923	+	0.399626i
$59$	3.00033	−	3.00033i	0.390610	−	0.390610i	−0.484295	−	0.874905i	$-0.660924\pi$
$59$	3.00033	−	3.00033i	0.390610	−	0.390610i	0.874905	+	0.484295i	$0.160924\pi$
$60$	−5.53324	+	0.874489i	−0.714338	+	0.112896i
$61$		−	1.13106i		−	0.144817i	−0.997375	−	0.0724084i	$-0.976932\pi$
$61$		−	1.13106i		−	0.144817i	0.997375	−	0.0724084i	$-0.0230685\pi$
$62$	2.77699	+	5.45240i	0.352678	+	0.692455i
$63$	3.05943	+	3.05943i	0.385451	+	0.385451i
$64$	2.47974	−	7.60598i	0.309967	−	0.950747i
$65$	−6.24001	+	7.94053i	−0.773978	+	0.984902i
$66$	−0.984999	−	1.93397i	−0.121245	−	0.238055i
$67$	7.39889	+	7.39889i	0.903918	+	0.903918i	0.995772	−	0.0918540i	$-0.0292793\pi$
$67$	7.39889	+	7.39889i	0.903918	+	0.903918i	−0.0918540	+	0.995772i	$0.529279\pi$
$68$	6.70444	−	9.22140i	0.813033	−	1.11826i
$69$	−2.95135			−0.355300
$70$	−5.29885	+	16.2989i	−0.633334	+	1.94810i
$71$	3.20281	−	3.20281i	0.380104	−	0.380104i	−0.491036	−	0.871139i	$-0.663382\pi$
$71$	3.20281	−	3.20281i	0.380104	−	0.380104i	0.871139	+	0.491036i	$0.163382\pi$
$72$	−2.28908	+	1.66136i	−0.269770	+	0.195794i
$73$	7.87480	−	7.87480i	0.921675	−	0.921675i	−0.0754728	−	0.997148i	$-0.524047\pi$
$73$	7.87480	−	7.87480i	0.921675	−	0.921675i	0.997148	+	0.0754728i	$0.0240466\pi$
$74$	9.16078	−	4.66573i	1.06492	−	0.542380i
$75$			2.84537i			0.328555i
$76$	1.94053	+	12.2785i	0.222594	+	1.40844i
$77$	−6.64004			−0.756703
$78$	−0.987901	+	5.00240i	−0.111858	+	0.566411i
$79$		−	4.46803i		−	0.502693i	−0.967897	−	0.251347i	$-0.919127\pi$
$79$		−	4.46803i		−	0.502693i	0.967897	−	0.251347i	$-0.0808734\pi$
$80$	−9.97930	−	5.09309i	−1.11572	−	0.569424i
$81$	1.00000			0.111111
$82$	−4.95376	+	2.52303i	−0.547051	+	0.278622i
$83$	−9.78962	−	9.78962i	−1.07455	−	1.07455i	−0.996987	−	0.0775625i	$-0.975286\pi$
$83$	−9.78962	−	9.78962i	−1.07455	−	1.07455i	−0.0775625	−	0.996987i	$-0.524714\pi$
$84$	1.35084	+	8.54727i	0.147388	+	0.932584i
$85$	−11.2903	−	11.2903i	−1.22461	−	1.22461i
$86$	−4.04004	−	1.31343i	−0.435649	−	0.141631i
$87$		−	6.96062i		−	0.746256i
$88$	0.681180	−	4.28693i	0.0726140	−	0.456989i
$89$	4.24001	−	4.24001i	0.449440	−	0.449440i	−0.445728	−	0.895168i	$-0.647055\pi$
$89$	4.24001	−	4.24001i	0.449440	−	0.449440i	0.895168	+	0.445728i	$0.147055\pi$
$90$	1.79774	+	3.52971i	0.189498	+	0.372064i
$91$	12.2659	+	9.63903i	1.28581	+	1.01045i
$92$	−4.77422	−	3.47111i	−0.497747	−	0.361888i
$93$	3.05943	−	3.05943i	0.317248	−	0.317248i
$94$	−11.4085	+	5.81050i	−1.17669	+	0.599308i
$95$	17.4092			1.78614
$96$	−5.65685	−	0.00471188i	−0.577350	−	0.000480904i
$97$	−11.5753	−	11.5753i	−1.17530	−	1.17530i	−0.980929	−	0.194366i	$-0.937735\pi$
$97$	−11.5753	−	11.5753i	−1.17530	−	1.17530i	−0.194366	−	0.980929i	$-0.562265\pi$
$98$	15.7627	+	5.12453i	1.59228	+	0.517655i
$99$	−1.08518	+	1.08518i	−0.109065	+	0.109065i
$100$	−3.34647	+	4.60279i	−0.334647	+	0.460279i
$101$	5.67835			0.565017			0.282509	−	0.959265i	$-0.408833\pi$
$101$	5.67835			0.565017			0.282509	+	0.959265i	$0.408833\pi$
$102$	−7.66677	−	2.49250i	−0.759123	−	0.246794i
$103$	1.20900			0.119126			0.0595630	−	0.998225i	$-0.481029\pi$
$103$	1.20900			0.119126			0.0595630	+	0.998225i	$0.481029\pi$
$104$	−7.48145	+	6.93022i	−0.733616	+	0.679564i
$105$	12.1189			1.18268
$106$	5.75859	+	1.87214i	0.559324	+	0.181838i
$107$	−11.6314			−1.12445			−0.562225	−	0.826984i	$-0.690055\pi$
$107$	−11.6314			−1.12445			−0.562225	+	0.826984i	$0.690055\pi$
$108$	1.61764	+	1.17611i	0.155658	+	0.113171i
$109$	−7.32910	+	7.32910i	−0.702001	+	0.702001i	−0.964840	−	0.262839i	$-0.915341\pi$
$109$	−7.32910	+	7.32910i	−0.702001	+	0.702001i	0.262839	+	0.964840i	$0.415341\pi$
$110$	−5.78124	−	1.87950i	−0.551219	−	0.179204i
$111$	−5.14026	−	5.14026i	−0.487892	−	0.487892i
$112$	−7.86736	+	15.4152i	−0.743396	+	1.45660i
$113$	15.2598			1.43552			0.717760	−	0.696291i	$-0.245168\pi$
$113$	15.2598			1.43552			0.717760	+	0.696291i	$0.245168\pi$
$114$	7.83257	−	3.98925i	0.733587	−	0.373627i
$115$	−5.84537	+	5.84537i	−0.545084	+	0.545084i
$116$	8.18645	−	11.2598i	0.760092	−	1.04544i
$117$	3.57990	−	0.429300i	0.330962	−	0.0396888i
$118$	−2.72336	−	5.34709i	−0.250705	−	0.492239i
$119$	−17.4403	+	17.4403i	−1.59875	+	1.59875i
$120$	−1.24323	+	7.82415i	−0.113491	+	0.714244i
$121$			8.64478i			0.785889i
$122$	−1.52118	−	0.494543i	−0.137722	−	0.0447738i
$123$	2.77963	+	2.77963i	0.250631	+	0.250631i
$124$	8.54727	−	1.35084i	0.767568	−	0.121309i
$125$	−4.26741	−	4.26741i	−0.381689	−	0.381689i
$126$	5.45240	−	2.77699i	0.485738	−	0.247394i
$127$	−5.22910			−0.464008			−0.232004	−	0.972715i	$-0.574528\pi$
$127$	−5.22910			−0.464008			−0.232004	+	0.972715i	$0.574528\pi$
$128$	−9.14522	−	6.66070i	−0.808331	−	0.588728i
$129$			3.00392i			0.264480i
$130$	7.95103	+	11.8643i	0.697352	+	1.04056i
$131$	17.2100			1.50364			0.751821	−	0.659367i	$-0.229176\pi$
$131$	17.2100			1.50364			0.751821	+	0.659367i	$0.229176\pi$
$132$	−3.03172	+	0.479142i	−0.263877	+	0.0417039i
$133$		−	26.8922i		−	2.33185i
$134$	13.1860	−	6.71586i	1.13910	−	0.580162i
$135$	1.98058	−	1.98058i	0.170461	−	0.170461i
$136$	−9.47064	−	13.0489i	−0.812101	−	1.11894i
$137$	2.23218	−	2.23218i	0.190708	−	0.190708i	−0.605294	−	0.796002i	$-0.706944\pi$
$137$	2.23218	−	2.23218i	0.190708	−	0.190708i	0.796002	+	0.605294i	$0.206944\pi$
$138$	−1.29045	+	3.96934i	−0.109850	+	0.337892i
$139$	16.1346			1.36852			0.684259	−	0.729239i	$-0.260126\pi$
$139$	16.1346			1.36852			0.684259	+	0.729239i	$0.260126\pi$
$140$	19.6040	+	14.2531i	1.65684	+	1.20461i
$141$	6.40146	+	6.40146i	0.539100	+	0.539100i
$142$	−2.90714	−	5.70793i	−0.243962	−	0.478999i
$143$	−3.41897	+	4.35070i	−0.285908	+	0.363824i
$144$	1.23353	+	3.80505i	0.102794	+	0.317087i
$145$	−13.7860	−	13.7860i	−1.14487	−	1.14487i
$146$	−7.14783	−	14.0342i	−0.591558	−	1.16148i
$147$		−	11.7202i		−	0.966663i
$148$	−2.26959	−	14.3606i	−0.186559	−	1.18043i
$149$	9.30975	−	9.30975i	0.762684	−	0.762684i	−0.214123	−	0.976807i	$-0.568689\pi$
$149$	9.30975	−	9.30975i	0.762684	−	0.762684i	0.976807	+	0.214123i	$0.0686893\pi$
$150$	3.82681	+	1.24411i	0.312457	+	0.101581i
$151$	6.21009	+	6.21009i	0.505370	+	0.505370i	0.913102	−	0.407732i	$-0.133680\pi$
$151$	6.21009	+	6.21009i	0.505370	+	0.505370i	−0.407732	+	0.913102i	$0.633680\pi$
$152$	17.3621	+	2.75878i	1.40825	+	0.223767i
$153$			5.70052i			0.460860i
$154$	−2.90329	+	8.93036i	−0.233954	+	0.719629i
$155$		−	12.1189i		−	0.973410i
$156$	6.29590	+	3.51590i	0.504076	+	0.281498i
$157$			13.0048i			1.03789i	0.854807	+	0.518947i	$0.173676\pi$
$157$			13.0048i			1.03789i	−0.854807	+	0.518947i	$0.826324\pi$
$158$	−6.00917	−	1.95360i	−0.478064	−	0.155420i
$159$		−	4.28172i		−	0.339563i
$160$	−11.2132	+	11.1945i	−0.886478	+	0.885003i
$161$	9.02943	+	9.02943i	0.711618	+	0.711618i
$162$	0.437240	−	1.34492i	0.0343528	−	0.105667i
$163$	4.16037	−	4.16037i	0.325865	−	0.325865i	−0.525146	−	0.851012i	$-0.675989\pi$
$163$	4.16037	−	4.16037i	0.325865	−	0.325865i	0.851012	+	0.525146i	$0.175989\pi$
$164$	1.22730	+	7.76560i	0.0958359	+	0.606392i
$165$			4.29856i			0.334642i
$166$	−17.4467	+	8.88588i	−1.35413	+	0.689678i
$167$	9.56896	+	9.56896i	0.740469	+	0.740469i	0.972668	−	0.232199i	$-0.0745922\pi$
$167$	9.56896	+	9.56896i	0.740469	+	0.740469i	−0.232199	+	0.972668i	$0.574592\pi$
$168$	12.0861	+	1.92044i	0.932461	+	0.148165i
$169$	12.6314	−	3.07370i	0.971646	−	0.236439i
$170$	−20.1212	+	10.2480i	−1.54323	+	0.785989i
$171$	−4.39498	−	4.39498i	−0.336092	−	0.336092i
$172$	−3.53293	+	4.85926i	−0.269384	+	0.370515i
$173$	10.9034			0.828968			0.414484	−	0.910057i	$-0.363962\pi$
$173$	10.9034			0.828968			0.414484	+	0.910057i	$0.363962\pi$
$174$	−9.36150	−	3.04346i	−0.709693	−	0.230724i
$175$	8.70520	−	8.70520i	0.658051	−	0.658051i
$176$	−5.46776	−	2.79055i	−0.412148	−	0.210346i
$177$	−3.00033	+	3.00033i	−0.225519	+	0.225519i
$178$	−3.84859	−	7.55640i	−0.288464	−	0.566376i
$179$			6.70998i			0.501527i	0.968048	+	0.250764i	$0.0806817\pi$
$179$			6.70998i			0.501527i	−0.968048	+	0.250764i	$0.919318\pi$
$180$	5.53324	−	0.874489i	0.412423	−	0.0651806i
$181$	15.8485			1.17801			0.589003	−	0.808131i	$-0.299521\pi$
$181$	15.8485			1.17801			0.589003	+	0.808131i	$0.299521\pi$
$182$	18.3269	−	12.2821i	1.35848	−	0.910408i
$183$			1.13106i			0.0836100i
$184$	−6.75586	+	4.90326i	−0.498048	+	0.361473i
$185$	−20.3614			−1.49700
$186$	−2.77699	−	5.45240i	−0.203619	−	0.399789i
$187$	−6.18608	−	6.18608i	−0.452371	−	0.452371i
$188$	2.82645	+	17.8841i	0.206140	+	1.30433i
$189$	−3.05943	−	3.05943i	−0.222540	−	0.222540i
$190$	7.61199	−	23.4140i	0.552232	−	1.69863i
$191$		−	17.4715i		−	1.26419i	−0.774890	−	0.632096i	$-0.782195\pi$
$191$		−	17.4715i		−	1.26419i	0.774890	−	0.632096i	$-0.217805\pi$
$192$	−2.47974	+	7.60598i	−0.178960	+	0.548914i
$193$	12.6490	−	12.6490i	0.910496	−	0.910496i	−0.0858148	−	0.996311i	$-0.527349\pi$
$193$	12.6490	−	12.6490i	0.910496	−	0.910496i	0.996311	+	0.0858148i	$0.0273493\pi$
$194$	−20.6291	+	10.5067i	−1.48108	+	0.754339i
$195$	6.24001	−	7.94053i	0.446856	−	0.568633i
$196$	13.7842	−	18.9590i	0.984586	−	1.35422i
$197$	−4.24269	+	4.24269i	−0.302279	+	0.302279i	−0.841905	−	0.539626i	$-0.818566\pi$
$197$	−4.24269	+	4.24269i	−0.302279	+	0.302279i	0.539626	+	0.841905i	$0.318566\pi$
$198$	0.984999	+	1.93397i	0.0700008	+	0.137441i
$199$	−8.86969			−0.628755			−0.314378	−	0.949298i	$-0.601796\pi$
$199$	−8.86969			−0.628755			−0.314378	+	0.949298i	$0.601796\pi$
$200$	4.72719	+	6.51327i	0.334263	+	0.460558i
$201$	−7.39889	−	7.39889i	−0.521878	−	0.521878i
$202$	2.48280	−	7.63695i	0.174689	−	0.537334i
$203$	−21.2955	+	21.2955i	−1.49465	+	1.49465i
$204$	−6.70444	+	9.22140i	−0.469405	+	0.645627i
$205$	11.0105			0.769010
$206$	0.528622	−	1.62601i	0.0368308	−	0.113289i
$207$	2.95135			0.205133
$208$	6.04943	+	13.0921i	0.419453	+	0.907777i
$209$	9.53866			0.659803
$210$	5.29885	−	16.2989i	0.365655	−	1.12473i
$211$	8.48028			0.583807			0.291903	−	0.956448i	$-0.405711\pi$
$211$	8.48028			0.583807			0.291903	+	0.956448i	$0.405711\pi$
$212$	5.03578	−	6.92630i	0.345859	−	0.475700i
$213$	−3.20281	+	3.20281i	−0.219453	+	0.219453i
$214$	−5.08572	+	15.6434i	−0.347652	+	1.06936i
$215$	5.94949	+	5.94949i	0.405752	+	0.405752i
$216$	2.28908	−	1.66136i	0.155752	−	0.113041i
$217$	−18.7202			−1.27081
$218$	6.65251	+	13.0617i	0.450565	+	0.884647i
$219$	−7.87480	+	7.87480i	−0.532129	+	0.532129i
$220$	−5.05558	+	6.95353i	−0.340847	+	0.468807i
$221$	2.44723	+	20.4073i	0.164619	+	1.37274i
$222$	−9.16078	+	4.66573i	−0.614832	+	0.313143i
$223$	−16.9807	+	16.9807i	−1.13711	+	1.13711i	−0.148143	+	0.988966i	$0.547330\pi$
$223$	−16.9807	+	16.9807i	−1.13711	+	1.13711i	−0.988966	+	0.148143i	$0.952670\pi$
$224$	17.2923	+	17.3211i	1.15539	+	1.15732i
$225$		−	2.84537i		−	0.189691i
$226$	6.67219	−	20.5233i	0.443827	−	1.36519i
$227$	8.63107	+	8.63107i	0.572864	+	0.572864i	0.932928	−	0.360064i	$-0.117245\pi$
$227$	8.63107	+	8.63107i	0.572864	+	0.572864i	−0.360064	+	0.932928i	$0.617245\pi$
$228$	−1.94053	−	12.2785i	−0.128514	−	0.813162i
$229$	−4.16041	−	4.16041i	−0.274928	−	0.274928i	0.556153	−	0.831080i	$-0.312277\pi$
$229$	−4.16041	−	4.16041i	−0.274928	−	0.274928i	−0.831080	+	0.556153i	$0.812277\pi$
$230$	5.30575	+	10.4174i	0.349851	+	0.686904i
$231$	6.64004			0.436883
$232$	−11.5641	−	15.9334i	−0.759221	−	1.04608i
$233$		−	2.78928i		−	0.182732i	−0.995817	−	0.0913660i	$-0.970877\pi$
$233$		−	2.78928i		−	0.182732i	0.995817	−	0.0913660i	$-0.0291233\pi$
$234$	0.987901	−	5.00240i	0.0645811	−	0.327017i
$235$	25.3572			1.65412
$236$	−8.38219	+	1.32475i	−0.545634	+	0.0862336i
$237$			4.46803i			0.290230i
$238$	15.8303	+	31.0815i	1.02613	+	2.01472i
$239$	−3.17166	+	3.17166i	−0.205158	+	0.205158i	−0.802206	−	0.597048i	$-0.796340\pi$
$239$	−3.17166	+	3.17166i	−0.205158	+	0.205158i	0.597048	+	0.802206i	$0.296340\pi$
$240$	9.97930	+	5.09309i	0.644161	+	0.328757i
$241$	−19.8233	+	19.8233i	−1.27693	+	1.27693i	−0.334554	+	0.942377i	$0.608586\pi$
$241$	−19.8233	+	19.8233i	−1.27693	+	1.27693i	−0.942377	+	0.334554i	$0.891414\pi$
$242$	11.6266	+	3.77984i	0.747384	+	0.242977i
$243$	−1.00000			−0.0641500
$244$	−1.33025	+	1.82964i	−0.0851602	+	0.117131i
$245$	−23.2127	−	23.2127i	−1.48300	−	1.48300i
$246$	4.95376	−	2.52303i	0.315840	−	0.160862i
$247$	−17.6203	−	13.8468i	−1.12116	−	0.881052i
$248$	1.92044	−	12.0861i	0.121948	−	0.767467i
$249$	9.78962	+	9.78962i	0.620392	+	0.620392i
$250$	−7.60523	+	3.87346i	−0.480997	+	0.244979i
$251$		−	5.23069i		−	0.330158i	−0.986280	−	0.165079i	$-0.947212\pi$
$251$		−	5.23069i		−	0.330158i	0.986280	−	0.165079i	$-0.0527879\pi$
$252$	−1.35084	−	8.54727i	−0.0850947	−	0.538428i
$253$	−3.20274	+	3.20274i	−0.201354	+	0.201354i
$254$	−2.28637	+	7.03275i	−0.143460	+	0.441274i
$255$	11.2903	+	11.2903i	0.707027	+	0.707027i
$256$	−12.9568	+	9.38730i	−0.809800	+	0.586707i
$257$		−	8.93669i		−	0.557455i	−0.960370	−	0.278728i	$-0.910087\pi$
$257$		−	8.93669i		−	0.557455i	0.960370	−	0.278728i	$-0.0899127\pi$
$258$	4.04004	+	1.31343i	0.251522	+	0.0817707i
$259$			31.4525i			1.95436i
$260$	19.4330	−	5.50600i	1.20519	−	0.341468i
$261$			6.96062i			0.430851i
$262$	7.52489	−	23.1461i	0.464889	−	1.42997i
$263$		−	6.37699i		−	0.393222i	−0.980482	−	0.196611i	$-0.937006\pi$
$263$		−	6.37699i		−	0.393222i	0.980482	−	0.196611i	$-0.0629936\pi$
$264$	−0.681180	+	4.28693i	−0.0419237	+	0.263842i
$265$	−8.48028	−	8.48028i	−0.520940	−	0.520940i
$266$	−36.1680	−	11.7583i	−2.21760	−	0.720950i
$267$	−4.24001	+	4.24001i	−0.259484	+	0.259484i
$268$	−3.26685	−	20.6707i	−0.199555	−	1.26266i
$269$			15.2813i			0.931717i	0.884859	+	0.465859i	$0.154255\pi$
$269$			15.2813i			0.931717i	−0.884859	+	0.465859i	$0.845745\pi$
$270$	−1.79774	−	3.52971i	−0.109407	−	0.214812i
$271$	−1.94520	−	1.94520i	−0.118163	−	0.118163i	0.645553	−	0.763716i	$-0.276627\pi$
$271$	−1.94520	−	1.94520i	−0.118163	−	0.118163i	−0.763716	+	0.645553i	$0.776627\pi$
$272$	−21.6908	+	7.03178i	−1.31520	+	0.426364i
$273$	−12.2659	−	9.63903i	−0.742363	−	0.583381i
$274$	−2.02611	−	3.97811i	−0.122402	−	0.240326i
$275$	3.08773	+	3.08773i	0.186197	+	0.186197i
$276$	4.77422	+	3.47111i	0.287374	+	0.208936i
$277$	−6.63729			−0.398796			−0.199398	−	0.979919i	$-0.563899\pi$
$277$	−6.63729			−0.398796			−0.199398	+	0.979919i	$0.563899\pi$
$278$	7.05469	−	21.6998i	0.423112	−	1.30147i
$279$	−3.05943	+	3.05943i	−0.183163	+	0.183163i
$280$	27.7410	−	20.1338i	1.65784	−	1.20323i
$281$	−13.3992	+	13.3992i	−0.799331	+	0.799331i	−0.982990	−	0.183659i	$-0.941206\pi$
$281$	−13.3992	+	13.3992i	−0.799331	+	0.799331i	0.183659	+	0.982990i	$0.441206\pi$
$282$	11.4085	−	5.81050i	0.679364	−	0.346011i
$283$		−	8.82007i		−	0.524299i	−0.965027	−	0.262149i	$-0.915569\pi$
$283$		−	8.82007i		−	0.524299i	0.965027	−	0.262149i	$-0.0844313\pi$
$284$	−8.94786	+	1.41415i	−0.530958	+	0.0839141i
$285$	−17.4092			−1.03123
$286$	4.35645	+	6.50055i	0.257602	+	0.384386i
$287$		−	17.0082i		−	1.00396i
$288$	5.65685	+	0.00471188i	0.333333	+	0.000277650i
$289$	−15.4959			−0.911526
$290$	−24.5690	+	12.5134i	−1.44274	+	0.734810i
$291$	11.5753	+	11.5753i	0.678557	+	0.678557i
$292$	−22.0002	+	3.47698i	−1.28747	+	0.203475i
$293$	−12.6596	−	12.6596i	−0.739582	−	0.739582i	0.232915	−	0.972497i	$-0.425174\pi$
$293$	−12.6596	−	12.6596i	−0.739582	−	0.739582i	−0.972497	+	0.232915i	$0.925174\pi$
$294$	−15.7627	−	5.12453i	−0.919301	−	0.298868i
$295$			11.8848i			0.691959i
$296$	−20.3063	−	3.22660i	−1.18028	−	0.187542i
$297$	1.08518	−	1.08518i	0.0629684	−	0.0629684i
$298$	−8.45031	−	16.5915i	−0.489513	−	0.961120i
$299$	10.5655	−	1.26701i	0.611021	−	0.0732732i
$300$	3.34647	−	4.60279i	0.193208	−	0.265742i
$301$	9.19026	−	9.19026i	0.529718	−	0.529718i
$302$	11.0674	−	5.63680i	0.636858	−	0.324362i
$303$	−5.67835			−0.326213
$304$	11.3017	−	22.1444i	0.648200	−	1.27007i
$305$	2.24014	+	2.24014i	0.128270	+	0.128270i
$306$	7.66677	+	2.49250i	0.438280	+	0.142487i
$307$	−11.6407	+	11.6407i	−0.664371	+	0.664371i	−0.956407	−	0.292036i	$-0.905667\pi$
$307$	−11.6407	+	11.6407i	−0.664371	+	0.664371i	0.292036	+	0.956407i	$0.405667\pi$
$308$	10.7412	+	7.80942i	0.612038	+	0.444983i
$309$	−1.20900			−0.0687774
$310$	−16.2989	−	5.29885i	−0.925718	−	0.300954i
$311$	14.2715			0.809263			0.404632	−	0.914480i	$-0.367400\pi$
$311$	14.2715			0.809263			0.404632	+	0.914480i	$0.367400\pi$
$312$	7.48145	−	6.93022i	0.423554	−	0.392346i
$313$	−20.4770			−1.15743			−0.578714	−	0.815531i	$-0.696445\pi$
$313$	−20.4770			−1.15743			−0.578714	+	0.815531i	$0.696445\pi$
$314$	17.4904	+	5.68620i	0.987042	+	0.320891i
$315$	−12.1189			−0.682820
$316$	−5.25490	+	7.22768i	−0.295611	+	0.406589i
$317$	18.4519	−	18.4519i	1.03636	−	1.03636i	0.0370478	−	0.999313i	$-0.488205\pi$
$317$	18.4519	−	18.4519i	1.03636	−	1.03636i	0.999313	−	0.0370478i	$-0.0117954\pi$
$318$	−5.75859	−	1.87214i	−0.322926	−	0.104984i
$319$	−7.55351	−	7.55351i	−0.422915	−	0.422915i
$320$	10.1529	+	19.9755i	0.567565	+	1.11667i
$321$	11.6314			0.649202
$322$	16.0919	−	8.19587i	0.896768	−	0.456738i
$323$	25.0537	−	25.0537i	1.39402	−	1.39402i
$324$	−1.61764	−	1.17611i	−0.0898690	−	0.0653394i
$325$	−1.22152	−	10.1861i	−0.0677575	−	0.565026i
$326$	−3.77630	−	7.41447i	−0.209150	−	0.410649i
$327$	7.32910	−	7.32910i	0.405300	−	0.405300i
$328$	10.9808	+	1.74481i	0.606312	+	0.0963410i
$329$		−	39.1696i		−	2.15949i
$330$	5.78124	+	1.87950i	0.318247	+	0.103463i
$331$	−9.99851	−	9.99851i	−0.549568	−	0.549568i	0.376748	−	0.926316i	$-0.377042\pi$
$331$	−9.99851	−	9.99851i	−0.549568	−	0.549568i	−0.926316	+	0.376748i	$0.877042\pi$
$332$	4.32244	+	27.3498i	0.237224	+	1.50101i
$333$	5.14026	+	5.14026i	0.281684	+	0.281684i
$334$	17.0535	−	8.68560i	0.933124	−	0.475255i
$335$	−29.3081			−1.60128
$336$	7.86736	−	15.4152i	0.429200	−	0.840966i
$337$		−	13.7956i		−	0.751492i	−0.926723	−	0.375746i	$-0.877387\pi$
$337$		−	13.7956i		−	0.751492i	0.926723	−	0.375746i	$-0.122613\pi$
$338$	1.38906	−	18.3322i	0.0755549	−	0.997142i
$339$	−15.2598			−0.828798
$340$	4.98505	+	31.5424i	0.270352	+	1.71062i
$341$		−	6.64004i		−	0.359579i
$342$	−7.83257	+	3.98925i	−0.423537	+	0.215714i
$343$	−14.4410	+	14.4410i	−0.779740	+	0.779740i
$344$	4.99060	+	6.87619i	0.269075	+	0.370739i
$345$	5.84537	−	5.84537i	0.314704	−	0.314704i
$346$	4.76739	−	14.6642i	0.256296	−	0.788353i
$347$	2.33288			0.125236			0.0626178	−	0.998038i	$-0.480055\pi$
$347$	2.33288			0.125236			0.0626178	+	0.998038i	$0.480055\pi$
$348$	−8.18645	+	11.2598i	−0.438840	+	0.603588i
$349$	14.8829	+	14.8829i	0.796661	+	0.796661i	0.982567	−	0.185906i	$-0.0595221\pi$
$349$	14.8829	+	14.8829i	0.796661	+	0.796661i	−0.185906	+	0.982567i	$0.559522\pi$
$350$	−7.90157	−	15.5141i	−0.422357	−	0.829263i
$351$	−3.57990	+	0.429300i	−0.191081	+	0.0229143i
$352$	−6.14381	+	6.13358i	−0.327466	+	0.326921i
$353$	−3.75999	−	3.75999i	−0.200124	−	0.200124i	0.599929	−	0.800053i	$-0.295195\pi$
$353$	−3.75999	−	3.75999i	−0.200124	−	0.200124i	−0.800053	+	0.599929i	$0.795195\pi$
$354$	2.72336	+	5.34709i	0.144745	+	0.284194i
$355$			12.6868i			0.673347i
$356$	−11.8455	+	1.87210i	−0.627812	+	0.0992213i
$357$	17.4403	−	17.4403i	0.923040	−	0.923040i
$358$	9.02441	+	2.93387i	0.476955	+	0.155060i
$359$	17.6464	+	17.6464i	0.931343	+	0.931343i	0.997790	−	0.0664468i	$-0.0211663\pi$
$359$	17.6464	+	17.6464i	0.931343	+	0.931343i	−0.0664468	+	0.997790i	$0.521166\pi$
$360$	1.24323	−	7.82415i	0.0655241	−	0.412369i
$361$			19.6316i			1.03324i
$362$	6.92958	−	21.3150i	0.364211	−	1.12029i
$363$		−	8.64478i		−	0.453733i
$364$	−8.50520	−	30.0185i	−0.445794	−	1.57340i
$365$			31.1933i			1.63273i
$366$	1.52118	+	0.494543i	0.0795136	+	0.0258502i
$367$			37.0651i			1.93478i	0.253290	+	0.967390i	$0.418487\pi$
$367$			37.0651i			1.93478i	−0.253290	+	0.967390i	$0.581513\pi$
$368$	3.64058	+	11.2300i	0.189779	+	0.585405i
$369$	−2.77963	−	2.77963i	−0.144702	−	0.144702i
$370$	−8.90280	+	27.3845i	−0.462834	+	1.42365i
$371$	−13.0996	+	13.0996i	−0.680098	+	0.680098i
$372$	−8.54727	+	1.35084i	−0.443156	+	0.0700376i
$373$		−	17.1978i		−	0.890470i	−0.895414	−	0.445235i	$-0.853120\pi$
$373$		−	17.1978i		−	0.890470i	0.895414	−	0.445235i	$-0.146880\pi$
$374$	−11.0246	+	5.61501i	−0.570069	+	0.290345i
$375$	4.26741	+	4.26741i	0.220368	+	0.220368i
$376$	25.2886	+	4.01828i	1.30416	+	0.207227i
$377$	2.98819	+	24.9183i	0.153900	+	1.28336i
$378$	−5.45240	+	2.77699i	−0.280441	+	0.142833i
$379$	−20.6610	−	20.6610i	−1.06129	−	1.06129i	−0.997995	−	0.0632908i	$-0.979840\pi$
$379$	−20.6610	−	20.6610i	−1.06129	−	1.06129i	−0.0632908	−	0.997995i	$-0.520160\pi$
$380$	−28.1618	−	20.4751i	−1.44467	−	1.05035i
$381$	5.22910			0.267895
$382$	−23.4978	−	7.63923i	−1.20225	−	0.390857i
$383$	14.2843	−	14.2843i	0.729894	−	0.729894i	−0.240705	−	0.970598i	$-0.577379\pi$
$383$	14.2843	−	14.2843i	0.729894	−	0.729894i	0.970598	+	0.240705i	$0.0773785\pi$
$384$	9.14522	+	6.66070i	0.466690	+	0.339902i
$385$	13.1511	−	13.1511i	0.670243	−	0.670243i
$386$	−11.4813	−	22.5426i	−0.584383	−	1.14739i
$387$		−	3.00392i		−	0.152698i
$388$	5.11088	+	32.3386i	0.259466	+	1.64174i
$389$	3.02809			0.153530			0.0767651	−	0.997049i	$-0.475541\pi$
$389$	3.02809			0.153530			0.0767651	+	0.997049i	$0.475541\pi$
$390$	−7.95103	−	11.8643i	−0.402616	−	0.600770i
$391$			16.8242i			0.850837i
$392$	−19.4715	−	26.8284i	−0.983457	−	1.35504i
$393$	−17.2100			−0.868128
$394$	3.85102	+	7.56117i	0.194012	+	0.380926i
$395$	8.84929	+	8.84929i	0.445256	+	0.445256i
$396$	3.03172	−	0.479142i	0.152350	−	0.0240778i
$397$	−5.46083	−	5.46083i	−0.274071	−	0.274071i	0.556666	−	0.830737i	$-0.312080\pi$
$397$	−5.46083	−	5.46083i	−0.274071	−	0.274071i	−0.830737	+	0.556666i	$0.812080\pi$
$398$	−3.87818	+	11.9291i	−0.194396	+	0.597950i
$399$			26.8922i			1.34629i
$400$	10.8268	−	3.50986i	0.541339	−	0.175493i
$401$	−14.1868	+	14.1868i	−0.708456	+	0.708456i	−0.966210	−	0.257754i	$-0.917017\pi$
$401$	−14.1868	+	14.1868i	−0.708456	+	0.708456i	0.257754	+	0.966210i	$0.417017\pi$
$402$	−13.1860	+	6.71586i	−0.657660	+	0.334956i
$403$	−9.63903	+	12.2659i	−0.480154	+	0.611006i
$404$	−9.18554	−	6.67836i	−0.456998	−	0.332261i
$405$	−1.98058	+	1.98058i	−0.0984157	+	0.0984157i
$406$	19.3296	+	37.9520i	0.959310	+	1.88353i
$407$	−11.1562			−0.552992
$408$	9.47064	+	13.0489i	0.468867	+	0.646018i
$409$	−9.80736	−	9.80736i	−0.484943	−	0.484943i	0.421763	−	0.906706i	$-0.361411\pi$
$409$	−9.80736	−	9.80736i	−0.484943	−	0.484943i	−0.906706	+	0.421763i	$0.861411\pi$
$410$	4.81425	−	14.8084i	0.237759	−	0.731332i
$411$	−2.23218	+	2.23218i	−0.110105	+	0.110105i
$412$	−1.95572	−	1.42191i	−0.0963516	−	0.0700526i
$413$	18.3586			0.903367
$414$	1.29045	−	3.96934i	0.0634220	−	0.195082i
$415$	38.7782			1.90355
$416$	20.2530	−	2.41162i	0.992985	−	0.118239i
$417$	−16.1346			−0.790114
$418$	4.17069	−	12.8288i	0.203995	−	0.627476i
$419$	17.4997			0.854915			0.427457	−	0.904036i	$-0.359409\pi$
$419$	17.4997			0.854915			0.427457	+	0.904036i	$0.359409\pi$
$420$	−19.6040	−	14.2531i	−0.956576	−	0.695480i
$421$	11.9652	−	11.9652i	0.583147	−	0.583147i	−0.352620	−	0.935767i	$-0.614709\pi$
$421$	11.9652	−	11.9652i	0.583147	−	0.583147i	0.935767	+	0.352620i	$0.114709\pi$
$422$	3.70792	−	11.4053i	0.180499	−	0.555203i
$423$	−6.40146	−	6.40146i	−0.311250	−	0.311250i
$424$	−7.11350	−	9.80119i	−0.345462	−	0.475988i
$425$	16.2201			0.786790
$426$	2.90714	+	5.70793i	0.140851	+	0.276550i
$427$	3.46038	−	3.46038i	0.167460	−	0.167460i
$428$	18.8154	+	13.6798i	0.909479	+	0.661238i
$429$	3.41897	−	4.35070i	0.165069	−	0.210054i
$430$	10.6030	−	5.40026i	0.511320	−	0.260423i
$431$	0.239905	−	0.239905i	0.0115558	−	0.0115558i	−0.701305	−	0.712861i	$-0.747399\pi$
$431$	0.239905	−	0.239905i	0.0115558	−	0.0115558i	0.712861	+	0.701305i	$0.247399\pi$
$432$	−1.23353	−	3.80505i	−0.0593484	−	0.183070i
$433$		−	20.0909i		−	0.965507i	−0.875756	−	0.482754i	$-0.839637\pi$
$433$		−	20.0909i		−	0.965507i	0.875756	−	0.482754i	$-0.160363\pi$
$434$	−8.18521	+	25.1772i	−0.392902	+	1.20854i
$435$	13.7860	+	13.7860i	0.660990	+	0.660990i
$436$	20.4757	−	3.23604i	0.980608	−	0.154978i
$437$	−12.9711	−	12.9711i	−0.620492	−	0.620492i
$438$	7.14783	+	14.0342i	0.341536	+	0.670579i
$439$	−2.49150			−0.118913			−0.0594565	−	0.998231i	$-0.518937\pi$
$439$	−2.49150			−0.118913			−0.0594565	+	0.998231i	$0.518937\pi$
$440$	7.14147	+	9.83973i	0.340456	+	0.469091i
$441$			11.7202i			0.558103i
$442$	28.5163	+	5.63155i	1.35638	+	0.267866i
$443$	13.5192			0.642318			0.321159	−	0.947025i	$-0.395928\pi$
$443$	13.5192			0.642318			0.321159	+	0.947025i	$0.395928\pi$
$444$	2.26959	+	14.3606i	0.107710	+	0.681524i
$445$			16.7953i			0.796175i
$446$	15.4131	+	30.2623i	0.729830	+	1.43296i
$447$	−9.30975	+	9.30975i	−0.440336	+	0.440336i
$448$	30.8565	−	15.6833i	1.45783	−	0.740968i
$449$	12.8287	−	12.8287i	0.605424	−	0.605424i	−0.336323	−	0.941747i	$-0.609183\pi$
$449$	12.8287	−	12.8287i	0.605424	−	0.605424i	0.941747	+	0.336323i	$0.109183\pi$
$450$	−3.82681	−	1.24411i	−0.180397	−	0.0586479i
$451$	6.03279			0.284073
$452$	−24.6849	−	17.9472i	−1.16108	−	0.844164i
$453$	−6.21009	−	6.21009i	−0.291776	−	0.291776i
$454$	15.3820	−	7.83429i	0.721912	−	0.367681i
$455$	−43.3843	+	5.20262i	−2.03389	+	0.243903i
$456$	−17.3621	−	2.75878i	−0.813054	−	0.129192i
$457$	21.9620	+	21.9620i	1.02734	+	1.02734i	0.999616	+	0.0277231i	$0.00882568\pi$
$457$	21.9620	+	21.9620i	1.02734	+	1.02734i	0.0277231	+	0.999616i	$0.491174\pi$
$458$	−7.41453	+	3.77634i	−0.346458	+	0.176457i
$459$		−	5.70052i		−	0.266078i
$460$	16.3305	−	2.58092i	0.761414	−	0.120336i
$461$	−20.6299	+	20.6299i	−0.960830	+	0.960830i	−0.999261	−	0.0384313i	$-0.987764\pi$
$461$	−20.6299	+	20.6299i	−0.960830	+	0.960830i	0.0384313	+	0.999261i	$0.487764\pi$
$462$	2.90329	−	8.93036i	0.135073	−	0.415478i
$463$	−0.0796856	−	0.0796856i	−0.00370330	−	0.00370330i	0.705253	−	0.708956i	$-0.250834\pi$
$463$	−0.0796856	−	0.0796856i	−0.00370330	−	0.00370330i	−0.708956	+	0.705253i	$0.750834\pi$
$464$	−26.4855	+	8.58615i	−1.22956	+	0.398602i
$465$			12.1189i			0.561998i
$466$	−3.75137	−	1.21959i	−0.173779	−	0.0564962i
$467$		−	21.9896i		−	1.01756i	−0.860898	−	0.508778i	$-0.830097\pi$
$467$		−	21.9896i		−	1.01756i	0.860898	−	0.508778i	$-0.169903\pi$
$468$	−6.29590	−	3.51590i	−0.291028	−	0.162523i
$469$			45.2727i			2.09050i
$470$	11.0872	−	34.1035i	0.511413	−	1.57308i
$471$		−	13.0048i		−	0.599228i
$472$	−1.88335	+	11.8526i	−0.0866880	+	0.545562i
$473$	3.25979	+	3.25979i	0.149885	+	0.149885i
$474$	6.00917	+	1.95360i	0.276010	+	0.0897320i
$475$	−12.5053	+	12.5053i	−0.573784	+	0.573784i
$476$	48.7239	−	7.70047i	2.23326	−	0.352951i
$477$			4.28172i			0.196047i
$478$	2.87887	+	5.65242i	0.131676	+	0.258536i
$479$	−4.31955	−	4.31955i	−0.197365	−	0.197365i	0.601504	−	0.798870i	$-0.294568\pi$
$479$	−4.31955	−	4.31955i	−0.197365	−	0.197365i	−0.798870	+	0.601504i	$0.794568\pi$
$480$	11.2132	−	11.1945i	0.511809	−	0.510957i
$481$	20.6083	+	16.1949i	0.939659	+	0.738424i
$482$	17.9933	+	35.3284i	0.819572	+	1.60916i
$483$	−9.02943	−	9.02943i	−0.410853	−	0.410853i
$484$	10.1672	−	13.9842i	0.462146	−	0.635643i
$485$	45.8516			2.08201
$486$	−0.437240	+	1.34492i	−0.0198336	+	0.0610070i
$487$	28.5902	−	28.5902i	1.29555	−	1.29555i	0.364243	−	0.931304i	$-0.381328\pi$
$487$	28.5902	−	28.5902i	1.29555	−	1.29555i	0.931304	−	0.364243i	$-0.118672\pi$
$488$	1.87909	+	2.58907i	0.0850626	+	0.117202i
$489$	−4.16037	+	4.16037i	−0.188139	+	0.188139i
$490$	−41.3688	+	21.0698i	−1.86885	+	0.951836i
$491$			12.4888i			0.563611i	0.959472	+	0.281805i	$0.0909333\pi$
$491$			12.4888i			0.563611i	−0.959472	+	0.281805i	$0.909067\pi$
$492$	−1.22730	−	7.76560i	−0.0553309	−	0.350100i
$493$	−39.6791			−1.78706
$494$	−26.3272	+	17.6436i	−1.18452	+	0.793825i
$495$		−	4.29856i		−	0.193206i
$496$	−15.4152	−	7.86736i	−0.692161	−	0.353255i
$497$	19.5975			0.879069
$498$	17.4467	−	8.88588i	0.781806	−	0.398186i
$499$	10.2871	+	10.2871i	0.460512	+	0.460512i	0.898823	−	0.438311i	$-0.144423\pi$
$499$	10.2871	+	10.2871i	0.460512	+	0.460512i	−0.438311	+	0.898823i	$0.644423\pi$
$500$	1.88420	+	11.9221i	0.0842640	+	0.533172i
$501$	−9.56896	−	9.56896i	−0.427510	−	0.427510i
$502$	−7.03488	−	2.28707i	−0.313982	−	0.102077i
$503$		−	20.3269i		−	0.906329i	−0.891427	−	0.453165i	$-0.850295\pi$
$503$		−	20.3269i		−	0.906329i	0.891427	−	0.453165i	$-0.149705\pi$
$504$	−12.0861	−	1.92044i	−0.538357	−	0.0855431i
$505$	−11.2464	+	11.2464i	−0.500459	+	0.500459i
$506$	2.90707	+	5.70781i	0.129235	+	0.253743i
$507$	−12.6314	+	3.07370i	−0.560980	+	0.136508i
$508$	8.45882	+	6.15000i	0.375299	+	0.272862i
$509$	−2.36729	+	2.36729i	−0.104928	+	0.104928i	−0.757622	−	0.652694i	$-0.773639\pi$
$509$	−2.36729	+	2.36729i	−0.104928	+	0.104928i	0.652694	+	0.757622i	$0.273639\pi$
$510$	20.1212	−	10.2480i	0.890982	−	0.453791i
$511$	48.1847			2.13157
$512$	6.95998	+	21.5304i	0.307591	+	0.951519i
$513$	4.39498	+	4.39498i	0.194043	+	0.194043i
$514$	−12.0192	−	3.90748i	−0.530143	−	0.172351i
$515$	−2.39451	+	2.39451i	−0.105515	+	0.105515i
$516$	3.53293	−	4.85926i	0.155529	−	0.213917i
$517$	13.8935			0.611033
$518$	42.3012	+	13.7523i	1.85861	+	0.604240i
$519$	−10.9034			−0.478605
$520$	1.09175	−	28.5434i	0.0478762	−	1.25171i
$521$	−25.2723			−1.10720			−0.553600	−	0.832782i	$-0.686746\pi$
$521$	−25.2723			−1.10720			−0.553600	+	0.832782i	$0.686746\pi$
$522$	9.36150	+	3.04346i	0.409742	+	0.133209i
$523$	−14.5946			−0.638178			−0.319089	−	0.947725i	$-0.603377\pi$
$523$	−14.5946			−0.638178			−0.319089	+	0.947725i	$0.603377\pi$
$524$	−27.8396	−	20.2408i	−1.21618	−	0.884224i
$525$	−8.70520	+	8.70520i	−0.379926	+	0.379926i
$526$	−8.57657	−	2.78828i	−0.373956	−	0.121575i
$527$	−17.4403	−	17.4403i	−0.759712	−	0.759712i
$528$	5.46776	+	2.79055i	0.237954	+	0.121443i
$529$	−14.2896			−0.621285
$530$	−15.1133	+	7.69742i	−0.656478	+	0.334355i
$531$	3.00033	−	3.00033i	0.130203	−	0.130203i
$532$	−31.6282	+	43.5019i	−1.37125	+	1.88605i
$533$	−11.1441	−	8.75752i	−0.482705	−	0.379330i
$534$	3.84859	+	7.55640i	0.166545	+	0.326997i
$535$	23.0369	−	23.0369i	0.995972	−	0.995972i
$536$	−29.2289	−	4.64437i	−1.26250	−	0.200606i
$537$		−	6.70998i		−	0.289557i
$538$	20.5522	+	6.68160i	0.886068	+	0.288064i
$539$	−12.7185	−	12.7185i	−0.547823	−	0.547823i
$540$	−5.53324	+	0.874489i	−0.238113	+	0.0376320i
$541$	0.0297801	+	0.0297801i	0.00128035	+	0.00128035i	0.707747	−	0.706466i	$-0.249712\pi$
$541$	0.0297801	+	0.0297801i	0.00128035	+	0.00128035i	−0.706466	+	0.707747i	$0.749712\pi$
$542$	−3.46667	+	1.76563i	−0.148906	+	0.0758403i
$543$	−15.8485			−0.680122
$544$	−0.0268602	+	32.2470i	−0.00115162	+	1.38258i
$545$		−	29.0317i		−	1.24358i
$546$	−18.3269	+	12.2821i	−0.784319	+	0.525624i
$547$	8.90794			0.380876			0.190438	−	0.981699i	$-0.439009\pi$
$547$	8.90794			0.380876			0.190438	+	0.981699i	$0.439009\pi$
$548$	−6.23615	+	0.985580i	−0.266395	+	0.0421019i
$549$		−	1.13106i		−	0.0482723i
$550$	5.50285	−	2.80269i	0.234642	−	0.119507i
$551$	30.5917	−	30.5917i	1.30325	−	1.30325i
$552$	6.75586	−	4.90326i	0.287548	−	0.208697i
$553$	13.6696	−	13.6696i	0.581291	−	0.581291i
$554$	−2.90209	+	8.92665i	−0.123298	+	0.379257i
$555$	20.3614			0.864291
$556$	−26.1000	−	18.9760i	−1.10689	−	0.804763i
$557$	−3.04221	−	3.04221i	−0.128902	−	0.128902i	0.639712	−	0.768615i	$-0.279054\pi$
$557$	−3.04221	−	3.04221i	−0.128902	−	0.128902i	−0.768615	+	0.639712i	$0.779054\pi$
$558$	2.77699	+	5.45240i	0.117559	+	0.230818i
$559$	−1.28958	−	10.7537i	−0.0545434	−	0.454834i
$560$	−14.9490	−	46.1128i	−0.631711	−	1.94862i
$561$	6.18608	+	6.18608i	0.261177	+	0.261177i
$562$	12.1623	+	23.8796i	0.513034	+	1.00730i
$563$		−	19.1221i		−	0.805900i	−0.915222	−	0.402950i	$-0.867985\pi$
$563$		−	19.1221i		−	0.805900i	0.915222	−	0.402950i	$-0.132015\pi$
$564$	−2.82645	−	17.8841i	−0.119015	−	0.753056i
$565$	−30.2232	+	30.2232i	−1.27150	+	1.27150i
$566$	−11.8623	−	3.85649i	−0.498611	−	0.162100i
$567$	3.05943	+	3.05943i	0.128484	+	0.128484i
$568$	−2.01044	+	12.6525i	−0.0843563	+	0.530887i
$569$		−	17.6181i		−	0.738590i	−0.929312	−	0.369295i	$-0.879599\pi$
$569$		−	17.6181i		−	0.738590i	0.929312	−	0.369295i	$-0.120401\pi$
$570$	−7.61199	+	23.4140i	−0.318831	+	0.980705i
$571$			3.59788i			0.150567i	0.997162	+	0.0752833i	$0.0239861\pi$
$571$			3.59788i			0.150567i	−0.997162	+	0.0752833i	$0.976014\pi$
$572$	10.6476	−	3.01680i	0.445197	−	0.126139i
$573$			17.4715i			0.729881i
$574$	−22.8747	−	7.43665i	−0.954770	−	0.310400i
$575$		−	8.39767i		−	0.350207i
$576$	2.47974	−	7.60598i	0.103322	−	0.316916i
$577$	26.9842	+	26.9842i	1.12337	+	1.12337i	0.991232	+	0.132135i	$0.0421832\pi$
$577$	26.9842	+	26.9842i	1.12337	+	1.12337i	0.132135	+	0.991232i	$0.457817\pi$
$578$	−6.77545	+	20.8409i	−0.281822	+	0.866866i
$579$	−12.6490	+	12.6490i	−0.525675	+	0.525675i
$580$	6.08698	+	38.5148i	0.252748	+	1.59924i
$581$		−	59.9012i		−	2.48512i
$582$	20.6291	−	10.5067i	0.855104	−	0.435518i
$583$	−4.64644	−	4.64644i	−0.192436	−	0.192436i
$584$	−4.94311	+	31.1089i	−0.204547	+	1.28730i
$585$	−6.24001	+	7.94053i	−0.257993	+	0.328301i
$586$	−22.5615	+	11.4909i	−0.932007	+	0.474686i
$587$	15.2640	+	15.2640i	0.630014	+	0.630014i	0.948071	−	0.318057i	$-0.103030\pi$
$587$	15.2640	+	15.2640i	0.630014	+	0.630014i	−0.318057	+	0.948071i	$0.603030\pi$
$588$	−13.7842	+	18.9590i	−0.568451	+	0.781857i
$589$	26.8922			1.10807
$590$	15.9841	+	5.19650i	0.658056	+	0.213937i
$591$	4.24269	−	4.24269i	0.174521	−	0.174521i
$592$	−13.2183	+	25.8996i	−0.543267	+	1.06447i
$593$	17.5925	−	17.5925i	0.722439	−	0.722439i	−0.246663	−	0.969101i	$-0.579334\pi$
$593$	17.5925	−	17.5925i	0.722439	−	0.722439i	0.969101	+	0.246663i	$0.0793339\pi$
$594$	−0.984999	−	1.93397i	−0.0404150	−	0.0793516i
$595$		−	69.0838i		−	2.83216i
$596$	−26.0091	+	4.11056i	−1.06537	+	0.168375i
$597$	8.86969			0.363012
$598$	2.91564	−	14.7638i	0.119229	−	0.603738i
$599$			12.8652i			0.525659i	0.964842	+	0.262829i	$0.0846556\pi$
$599$			12.8652i			0.525659i	−0.964842	+	0.262829i	$0.915344\pi$
$600$	−4.72719	−	6.51327i	−0.192987	−	0.265903i
$601$	25.5562			1.04246			0.521230	−	0.853416i	$-0.325473\pi$
$601$	25.5562			1.04246			0.521230	+	0.853416i	$0.325473\pi$
$602$	−8.34185	−	16.3785i	−0.339988	−	0.667540i
$603$	7.39889	+	7.39889i	0.301306	+	0.301306i
$604$	−2.74196	−	17.3495i	−0.111569	−	0.705940i
$605$	−17.1216	−	17.1216i	−0.696094	−	0.696094i
$606$	−2.48280	+	7.63695i	−0.100857	+	0.310230i
$607$			31.7217i			1.28754i	0.765218	+	0.643771i	$0.222631\pi$
$607$			31.7217i			1.28754i	−0.765218	+	0.643771i	$0.777369\pi$
$608$	−24.8410	−	24.8824i	−1.00744	−	1.00912i
$609$	21.2955	−	21.2955i	0.862936	−	0.862936i
$610$	3.99230	−	2.03334i	0.161644	−	0.0823276i
$611$	−25.6648	−	20.1685i	−1.03828	−	0.815929i
$612$	6.70444	−	9.22140i	0.271011	−	0.372753i
$613$	11.2028	−	11.2028i	0.452477	−	0.452477i	−0.443699	−	0.896176i	$-0.646334\pi$
$613$	11.2028	−	11.2028i	0.452477	−	0.452477i	0.896176	+	0.443699i	$0.146334\pi$
$614$	10.5661	+	20.7457i	0.426413	+	0.837227i
$615$	−11.0105			−0.443988
$616$	15.1996	−	11.0315i	0.612408	−	0.444473i
$617$	13.6394	+	13.6394i	0.549100	+	0.549100i	0.926181	−	0.377080i	$-0.123072\pi$
$617$	13.6394	+	13.6394i	0.549100	+	0.549100i	−0.377080	+	0.926181i	$0.623072\pi$
$618$	−0.528622	+	1.62601i	−0.0212643	+	0.0654077i
$619$	24.5702	−	24.5702i	0.987561	−	0.987561i	−0.0123622	−	0.999924i	$-0.503935\pi$
$619$	24.5702	−	24.5702i	0.987561	−	0.987561i	0.999924	+	0.0123622i	$0.00393510\pi$
$620$	−14.2531	+	19.6040i	−0.572418	+	0.787314i
$621$	−2.95135			−0.118433
$622$	6.24008	−	19.1941i	0.250204	−	0.769614i
$623$	25.9440			1.03942
$624$	−6.04943	−	13.0921i	−0.242171	−	0.524105i
$625$	31.1307			1.24523
$626$	−8.95336	+	27.5400i	−0.357848	+	1.10072i
$627$	−9.53866			−0.380938
$628$	15.2950	−	21.0371i	0.610338	−	0.839470i
$629$	−29.3022	+	29.3022i	−1.16835	+	1.16835i
$630$	−5.29885	+	16.2989i	−0.211111	+	0.649365i
$631$	−14.4587	−	14.4587i	−0.575593	−	0.575593i	0.358093	−	0.933686i	$-0.383427\pi$
$631$	−14.4587	−	14.4587i	−0.575593	−	0.575593i	−0.933686	+	0.358093i	$0.883427\pi$
$632$	7.42303	+	10.2277i	0.295272	+	0.406835i
$633$	−8.48028			−0.337061
$634$	−16.7485	−	32.8843i	−0.665167	−	1.30600i
$635$	10.3566	−	10.3566i	0.410991	−	0.410991i
$636$	−5.03578	+	6.92630i	−0.199682	+	0.274646i
$637$	5.03146	+	41.9570i	0.199354	+	1.66240i
$638$	−13.4616	+	6.85620i	−0.532950	+	0.271440i
$639$	3.20281	−	3.20281i	0.126701	−	0.126701i
$640$	31.3048	−	4.92079i	1.23743	−	0.194511i
$641$			29.9697i			1.18373i	0.806037	+	0.591866i	$0.201608\pi$
$641$			29.9697i			1.18373i	−0.806037	+	0.591866i	$0.798392\pi$
$642$	5.08572	−	15.6434i	0.200717	−	0.617394i
$643$	−19.9356	−	19.9356i	−0.786183	−	0.786183i	0.194683	−	0.980866i	$-0.437632\pi$
$643$	−19.9356	−	19.9356i	−0.786183	−	0.786183i	−0.980866	+	0.194683i	$0.937632\pi$
$644$	−3.98679	−	25.2260i	−0.157101	−	0.994043i
$645$	−5.94949	−	5.94949i	−0.234261	−	0.234261i
$646$	−22.7408	−	44.6497i	−0.894725	−	1.75672i
$647$	27.3423			1.07494			0.537469	−	0.843283i	$-0.319380\pi$
$647$	27.3423			1.07494			0.537469	+	0.843283i	$0.319380\pi$
$648$	−2.28908	+	1.66136i	−0.0899234	+	0.0652645i
$649$			6.51179i			0.255610i
$650$	−14.2337	−	2.81094i	−0.558291	−	0.110254i
$651$	18.7202			0.733701
$652$	−11.6230	+	1.83694i	−0.455194	+	0.0719401i
$653$			9.37861i			0.367013i	0.983018	+	0.183507i	$0.0587449\pi$
$653$			9.37861i			0.367013i	−0.983018	+	0.183507i	$0.941255\pi$
$654$	−6.65251	−	13.0617i	−0.260134	−	0.510751i
$655$	−34.0857	+	34.0857i	−1.33184	+	1.33184i
$656$	7.14787	−	14.0054i	0.279077	−	0.546819i
$657$	7.87480	−	7.87480i	0.307225	−	0.307225i
$658$	−52.6801	−	17.1265i	−2.05368	−	0.667661i
$659$	−16.9639			−0.660821			−0.330411	−	0.943837i	$-0.607187\pi$
$659$	−16.9639			−0.660821			−0.330411	+	0.943837i	$0.607187\pi$
$660$	5.05558	−	6.95353i	0.196788	−	0.270666i
$661$	−29.9758	−	29.9758i	−1.16592	−	1.16592i	−0.983156	−	0.182768i	$-0.941494\pi$
$661$	−29.9758	−	29.9758i	−1.16592	−	1.16592i	−0.182768	−	0.983156i	$-0.558506\pi$
$662$	−17.8190	+	9.07549i	−0.692555	+	0.352729i
$663$	−2.44723	−	20.4073i	−0.0950426	−	0.792554i
$664$	38.6733	+	6.14506i	1.50081	+	0.238475i
$665$	53.2621	+	53.2621i	2.06541	+	2.06541i
$666$	9.16078	−	4.66573i	0.354973	−	0.180793i
$667$			20.5432i			0.795436i
$668$	−4.22501	−	26.7333i	−0.163471	−	1.03434i
$669$	16.9807	−	16.9807i	0.656510	−	0.656510i
$670$	−12.8147	+	39.4172i	−0.495075	+	1.52282i
$671$	1.22740	+	1.22740i	0.0473831	+	0.0473831i
$672$	−17.2923	−	17.3211i	−0.667065	−	0.668177i
$673$		−	6.87865i		−	0.265152i	−0.991173	−	0.132576i	$-0.957675\pi$
$673$		−	6.87865i		−	0.265152i	0.991173	−	0.132576i	$-0.0423249\pi$
$674$	−18.5540	−	6.03197i	−0.714672	−	0.232343i
$675$			2.84537i			0.109518i
$676$	−24.0481	−	9.88376i	−0.924927	−	0.380145i
$677$		−	13.0371i		−	0.501057i	−0.968109	−	0.250528i	$-0.919396\pi$
$677$		−	13.0371i		−	0.501057i	0.968109	−	0.250528i	$-0.0806043\pi$
$678$	−6.67219	+	20.5233i	−0.256244	+	0.788191i
$679$		−	70.8276i		−	2.71812i
$680$	44.6017	+	7.08707i	1.71040	+	0.271777i
$681$	−8.63107	−	8.63107i	−0.330743	−	0.330743i
$682$	−8.93036	−	2.90329i	−0.341961	−	0.111173i
$683$	−20.9718	+	20.9718i	−0.802463	+	0.802463i	−0.983480	−	0.181017i	$-0.942061\pi$
$683$	−20.9718	+	20.9718i	−0.802463	+	0.802463i	0.181017	+	0.983480i	$0.442061\pi$
$684$	1.94053	+	12.2785i	0.0741978	+	0.469479i
$685$			8.84200i			0.337836i
$686$	13.1079	+	25.7362i	0.500460	+	0.982613i
$687$	4.16041	+	4.16041i	0.158730	+	0.158730i
$688$	11.4300	−	3.70543i	0.435767	−	0.141268i
$689$	1.83814	+	15.3282i	0.0700277	+	0.583956i
$690$	−5.30575	−	10.4174i	−0.201986	−	0.396584i
$691$	−33.4370	−	33.4370i	−1.27200	−	1.27200i	−0.945035	−	0.326969i	$-0.893973\pi$
$691$	−33.4370	−	33.4370i	−1.27200	−	1.27200i	−0.326969	−	0.945035i	$-0.606027\pi$
$692$	−17.6377	−	12.8236i	−0.670487	−	0.487478i
$693$	−6.64004			−0.252234
$694$	1.02003	−	3.13755i	0.0387198	−	0.119100i
$695$	−31.9558	+	31.9558i	−1.21215	+	1.21215i
$696$	11.5641	+	15.9334i	0.438337	+	0.603953i
$697$	15.8454	−	15.8454i	0.600185	−	0.600185i
$698$	26.5237	−	13.5089i	1.00394	−	0.511321i
$699$			2.78928i			0.105500i
$700$	−24.3202	+	3.84363i	−0.919215	+	0.145276i
$701$	15.0565			0.568675			0.284338	−	0.958724i	$-0.408226\pi$
$701$	15.0565			0.568675			0.284338	+	0.958724i	$0.408226\pi$
$702$	−0.987901	+	5.00240i	−0.0372859	+	0.188804i
$703$		−	45.1826i		−	1.70409i
$704$	5.56288	+	10.9448i	0.209659	+	0.412498i
$705$	−25.3572			−0.955006
$706$	−6.70092	+	3.41288i	−0.252192	+	0.128446i
$707$	17.3725	+	17.3725i	0.653360	+	0.653360i
$708$	8.38219	−	1.32475i	0.315022	−	0.0497870i
$709$	14.4736	+	14.4736i	0.543569	+	0.543569i	0.924573	−	0.381004i	$-0.124422\pi$
$709$	14.4736	+	14.4736i	0.543569	+	0.543569i	−0.381004	+	0.924573i	$0.624422\pi$
$710$	17.0628	+	5.54719i	0.640356	+	0.208182i
$711$		−	4.46803i		−	0.167564i
$712$	−2.66151	+	16.7499i	−0.0997442	+	0.627729i
$713$	−9.02943	+	9.02943i	−0.338155	+	0.338155i
$714$	−15.8303	−	31.0815i	−0.592434	−	1.16320i
$715$	−1.84537	−	15.3884i	−0.0690129	−	0.575494i
$716$	7.89167	−	10.8543i	0.294925	−	0.405646i
$717$	3.17166	−	3.17166i	0.118448	−	0.118448i
$718$	31.4488	−	16.0174i	1.17366	−	0.597764i
$719$	−30.9497			−1.15423			−0.577114	−	0.816663i	$-0.695821\pi$
$719$	−30.9497			−1.15423			−0.577114	+	0.816663i	$0.695821\pi$
$720$	−9.97930	−	5.09309i	−0.371906	−	0.189808i
$721$	3.69883	+	3.69883i	0.137752	+	0.137752i
$722$	26.4030	+	8.58373i	0.982619	+	0.319453i
$723$	19.8233	−	19.8233i	0.737236	−	0.737236i
$724$	−25.6371	−	18.6395i	−0.952797	−	0.692732i
$725$	19.8055			0.735559
$726$	−11.6266	−	3.77984i	−0.431502	−	0.140283i
$727$	−34.8766			−1.29350			−0.646750	−	0.762702i	$-0.723872\pi$
$727$	−34.8766			−1.29350			−0.646750	+	0.762702i	$0.723872\pi$
$728$	−44.0914	−	1.68644i	−1.63414	−	0.0625034i
$729$	1.00000			0.0370370
$730$	41.9526	+	13.6389i	1.55274	+	0.504800i
$731$	17.1239			0.633350
$732$	1.33025	−	1.82964i	0.0491673	−	0.0676256i
$733$	2.70878	−	2.70878i	0.100051	−	0.100051i	−0.655309	−	0.755361i	$-0.727462\pi$
$733$	2.70878	−	2.70878i	0.100051	−	0.100051i	0.755361	+	0.655309i	$0.227462\pi$
$734$	49.8497	+	16.2063i	1.83999	+	0.598187i
$735$	23.2127	+	23.2127i	0.856213	+	0.856213i
$736$	16.6953	+	0.0139064i	0.615398	+	0.000512596i
$737$	−16.0582			−0.591513
$738$	−4.95376	+	2.52303i	−0.182350	+	0.0928739i
$739$	−36.0138	+	36.0138i	−1.32479	+	1.32479i	−0.414938	+	0.909850i	$0.636197\pi$
$739$	−36.0138	+	36.0138i	−1.32479	+	1.32479i	−0.909850	+	0.414938i	$0.863803\pi$
$740$	32.9374	+	23.9472i	1.21080	+	0.880316i
$741$	17.6203	+	13.8468i	0.647299	+	0.508676i
$742$	11.8903	+	23.3457i	0.436507	+	0.857046i
$743$	−34.5489	+	34.5489i	−1.26747	+	1.26747i	−0.320086	+	0.947388i	$0.603712\pi$
$743$	−34.5489	+	34.5489i	−1.26747	+	1.26747i	−0.947388	+	0.320086i	$0.896288\pi$
$744$	−1.92044	+	12.0861i	−0.0704067	+	0.443097i
$745$			36.8773i			1.35108i
$746$	−23.1298	−	7.51958i	−0.846841	−	0.275311i
$747$	−9.78962	−	9.78962i	−0.358183	−	0.358183i
$748$	2.73136	+	17.2824i	0.0998683	+	0.631906i
$749$	−35.5854	−	35.5854i	−1.30026	−	1.30026i
$750$	7.60523	−	3.87346i	0.277704	−	0.141439i
$751$	−33.5927			−1.22582			−0.612908	−	0.790154i	$-0.710000\pi$
$751$	−33.5927			−1.22582			−0.612908	+	0.790154i	$0.710000\pi$
$752$	16.4615	−	32.2543i	0.600288	−	1.17619i
$753$			5.23069i			0.190617i
$754$	34.8198	+	6.87640i	1.26806	+	0.250424i
$755$	−24.5991			−0.895254
$756$	1.35084	+	8.54727i	0.0491294	+	0.310861i
$757$		−	43.6629i		−	1.58695i	−0.608600	−	0.793477i	$-0.708269\pi$
$757$		−	43.6629i		−	1.58695i	0.608600	−	0.793477i	$-0.291731\pi$
$758$	−36.8214	+	18.7537i	−1.33741	+	0.681165i
$759$	3.20274	−	3.20274i	0.116252	−	0.116252i
$760$	−39.8509	+	28.9230i	−1.44554	+	1.04915i
$761$	−8.82087	+	8.82087i	−0.319756	+	0.319756i	−0.848673	−	0.528917i	$-0.822598\pi$
$761$	−8.82087	+	8.82087i	−0.319756	+	0.319756i	0.528917	+	0.848673i	$0.322598\pi$
$762$	2.28637	−	7.03275i	0.0828266	−	0.254770i
$763$	−44.8457			−1.62352
$764$	−20.5484	+	28.2626i	−0.743414	+	1.02250i
$765$	−11.2903	−	11.2903i	−0.408202	−	0.408202i
$766$	−12.9656	−	25.4570i	−0.468467	−	0.919798i
$767$	9.45286	−	12.0289i	0.341323	−	0.434340i
$768$	12.9568	−	9.38730i	0.467538	−	0.338735i
$769$	34.6156	+	34.6156i	1.24827	+	1.24827i	0.956483	+	0.291787i	$0.0942499\pi$
$769$	34.6156	+	34.6156i	1.24827	+	1.24827i	0.291787	+	0.956483i	$0.405750\pi$
$770$	−11.9371	−	23.4375i	−0.430182	−	0.844627i
$771$			8.93669i			0.321847i
$772$	−35.3382	+	5.58496i	−1.27185	+	0.201007i
$773$	−29.1933	+	29.1933i	−1.05001	+	1.05001i	−0.0513298	+	0.998682i	$0.516346\pi$
$773$	−29.1933	+	29.1933i	−1.05001	+	1.05001i	−0.998682	+	0.0513298i	$0.983654\pi$
$774$	−4.04004	−	1.31343i	−0.145216	−	0.0472104i
$775$	8.70520	+	8.70520i	0.312700	+	0.312700i
$776$	45.7276	+	7.26597i	1.64153	+	0.260833i
$777$		−	31.4525i		−	1.12835i
$778$	1.32400	−	4.07255i	0.0474678	−	0.146008i
$779$			24.4328i			0.875397i
$780$	−19.4330	+	5.50600i	−0.695815	+	0.197147i
$781$			6.95124i			0.248735i
$782$	22.6273	+	7.35622i	0.809151	+	0.263058i
$783$		−	6.96062i		−	0.248752i
$784$	−44.5958	+	14.4572i	−1.59271	+	0.516329i
$785$	−25.7569	−	25.7569i	−0.919305	−	0.919305i
$786$	−7.52489	+	23.1461i	−0.268404	+	0.825594i
$787$	7.46253	−	7.46253i	0.266011	−	0.266011i	−0.561480	−	0.827490i	$-0.689768\pi$
$787$	7.46253	−	7.46253i	0.266011	−	0.266011i	0.827490	+	0.561480i	$0.189768\pi$
$788$	11.8530	−	1.87329i	0.422246	−	0.0667330i
$789$			6.37699i			0.227027i
$790$	15.7709	−	8.03236i	0.561103	−	0.285778i
$791$	46.6862	+	46.6862i	1.65997	+	1.65997i
$792$	0.681180	−	4.28693i	0.0242047	−	0.152330i
$793$	−0.485562	−	4.04907i	−0.0172428	−	0.143787i
$794$	−9.73209	+	4.95671i	−0.345379	+	0.175907i
$795$	8.48028	+	8.48028i	0.300765	+	0.300765i
$796$	14.3480	+	10.4317i	0.508551	+	0.369743i
$797$	22.8833			0.810568			0.405284	−	0.914191i	$-0.367173\pi$
$797$	22.8833			0.810568			0.405284	+	0.914191i	$0.367173\pi$
$798$	36.1680	+	11.7583i	1.28033	+	0.416241i
$799$	36.4917	−	36.4917i	1.29098	−	1.29098i
$800$	0.0134070	−	16.0958i	0.000474010	−	0.569074i
$801$	4.24001	−	4.24001i	0.149813	−	0.149813i
$802$	12.8772	+	25.2832i	0.454708	+	0.892782i
$803$			17.0911i			0.603132i
$804$	3.26685	+	20.6707i	0.115213	+	0.728998i
$805$	−35.7669			−1.26062
$806$	12.2821	+	18.3269i	0.432618	+	0.645537i
$807$		−	15.2813i		−	0.537927i
$808$	−12.9982	+	9.43381i	−0.457274	+	0.331880i
$809$	44.2093			1.55432			0.777158	−	0.629306i	$-0.216661\pi$
$809$	44.2093			1.55432			0.777158	+	0.629306i	$0.216661\pi$
$810$	1.79774	+	3.52971i	0.0631661	+	0.124021i
$811$	−2.94966	−	2.94966i	−0.103576	−	0.103576i	0.653420	−	0.756996i	$-0.273334\pi$
$811$	−2.94966	−	2.94966i	−0.103576	−	0.103576i	−0.756996	+	0.653420i	$0.773334\pi$
$812$	59.4943	−	9.40265i	2.08784	−	0.329968i
$813$	1.94520	+	1.94520i	0.0682213	+	0.0682213i
$814$	−4.87794	+	15.0042i	−0.170972	+	0.525898i
$815$			16.4799i			0.577265i
$816$	21.6908	−	7.03178i	0.759329	−	0.246162i
$817$	−13.2021	+	13.2021i	−0.461884	+	0.461884i
$818$	−17.4783	+	8.90199i	−0.611116	+	0.311251i
$819$	12.2659	+	9.63903i	0.428604	+	0.336815i
$820$	−17.8111	−	12.9496i	−0.621992	−	0.452220i
$821$	21.8863	−	21.8863i	0.763837	−	0.763837i	−0.213177	−	0.977014i	$-0.568381\pi$
$821$	21.8863	−	21.8863i	0.763837	−	0.763837i	0.977014	+	0.213177i	$0.0683811\pi$
$822$	2.02611	+	3.97811i	0.0706688	+	0.138752i
$823$	4.14879			0.144618			0.0723088	−	0.997382i	$-0.476963\pi$
$823$	4.14879			0.144618			0.0723088	+	0.997382i	$0.476963\pi$
$824$	−2.76748	+	2.00858i	−0.0964099	+	0.0699723i
$825$	−3.08773	−	3.08773i	−0.107501	−	0.107501i
$826$	8.02711	−	24.6909i	0.279299	−	0.859107i
$827$	−10.6504	+	10.6504i	−0.370350	+	0.370350i	−0.867605	−	0.497255i	$-0.834341\pi$
$827$	−10.6504	+	10.6504i	−0.370350	+	0.370350i	0.497255	+	0.867605i	$0.334341\pi$
$828$	−4.77422	−	3.47111i	−0.165916	−	0.120629i
$829$	−0.216258			−0.00751097			−0.00375548	−	0.999993i	$-0.501195\pi$
$829$	−0.216258			−0.00751097			−0.00375548	+	0.999993i	$0.501195\pi$
$830$	16.9554	−	52.1537i	0.588530	−	1.81028i
$831$	6.63729			0.230245
$832$	5.61198	−	28.2932i	0.194561	−	0.980891i
$833$	−66.8111			−2.31487
$834$	−7.05469	+	21.6998i	−0.244284	+	0.751402i
$835$	−37.9041			−1.31173
$836$	−15.4301	−	11.2185i	−0.533663	−	0.388000i
$837$	3.05943	−	3.05943i	0.105749	−	0.105749i
$838$	7.65156	−	23.5357i	0.264319	−	0.813028i
$839$	25.0859	+	25.0859i	0.866061	+	0.866061i	0.992034	−	0.125972i	$-0.0402050\pi$
$839$	25.0859	+	25.0859i	0.866061	+	0.866061i	−0.125972	+	0.992034i	$0.540205\pi$
$840$	−27.7410	+	20.1338i	−0.957155	+	0.694683i
$841$	−19.4502			−0.670695
$842$	−10.8606	−	21.3239i	−0.374281	−	0.734871i
$843$	13.3992	−	13.3992i	0.461494	−	0.461494i
$844$	−13.7181	−	9.97374i	−0.472195	−	0.343310i
$845$	−18.9298	+	31.1052i	−0.651204	+	1.07005i
$846$	−11.4085	+	5.81050i	−0.392231	+	0.199769i
$847$	−26.4480	+	26.4480i	−0.908766	+	0.908766i
$848$	−16.2922	+	5.28165i	−0.559475	+	0.181373i
$849$			8.82007i			0.302704i
$850$	7.09207	−	21.8148i	0.243256	−	0.748241i
$851$	15.1707	+	15.1707i	0.520044	+	0.520044i
$852$	8.94786	−	1.41415i	0.306549	−	0.0484478i
$853$	−11.0517	−	11.0517i	−0.378403	−	0.378403i	0.492123	−	0.870526i	$-0.336221\pi$
$853$	−11.0517	−	11.0517i	−0.378403	−	0.378403i	−0.870526	+	0.492123i	$0.836221\pi$
$854$	−3.14093	−	6.16696i	−0.107480	−	0.211029i
$855$	17.4092			0.595381
$856$	26.6252	−	19.3240i	0.910030	−	0.660481i
$857$		−	51.1359i		−	1.74677i	−0.487031	−	0.873385i	$-0.661920\pi$
$857$		−	51.1359i		−	1.74677i	0.487031	−	0.873385i	$-0.338080\pi$
$858$	−4.35645	−	6.50055i	−0.148727	−	0.221925i
$859$	7.91145			0.269935			0.134968	−	0.990850i	$-0.456907\pi$
$859$	7.91145			0.269935			0.134968	+	0.990850i	$0.456907\pi$
$860$	−2.62689	−	16.6214i	−0.0895763	−	0.566785i
$861$			17.0082i			0.579636i
$862$	−0.217758	−	0.427550i	−0.00741686	−	0.0145624i
$863$	12.9345	−	12.9345i	0.440294	−	0.440294i	−0.451817	−	0.892111i	$-0.649224\pi$
$863$	12.9345	−	12.9345i	0.440294	−	0.440294i	0.892111	+	0.451817i	$0.149224\pi$
$864$	−5.65685	−	0.00471188i	−0.192450	−	0.000160301i
$865$	−21.5950	+	21.5950i	−0.734251	+	0.734251i
$866$	−27.0208	−	8.78455i	−0.918202	−	0.298511i
$867$	15.4959			0.526270
$868$	30.2825	+	22.0170i	1.02786	+	0.747304i
$869$	4.84861	+	4.84861i	0.164478	+	0.164478i
$870$	24.5690	−	12.5134i	0.832966	−	0.424243i
$871$	29.6637	+	23.3110i	1.00511	+	0.789862i
$872$	4.60057	−	28.9532i	0.155795	−	0.980478i
$873$	−11.5753	−	11.5753i	−0.391765	−	0.391765i
$874$	−23.1166	+	11.7737i	−0.781932	+	0.398250i
$875$		−	26.1116i		−	0.882735i
$876$	22.0002	−	3.47698i	0.743319	−	0.117476i
$877$	−14.4085	+	14.4085i	−0.486539	+	0.486539i	−0.907212	−	0.420673i	$-0.861794\pi$
$877$	−14.4085	+	14.4085i	−0.486539	+	0.486539i	0.420673	+	0.907212i	$0.361794\pi$
$878$	−1.08939	+	3.35088i	−0.0367650	+	0.113087i
$879$	12.6596	+	12.6596i	0.426998	+	0.426998i
$880$	16.3562	−	5.30241i	0.551368	−	0.178744i
$881$		−	22.8221i		−	0.768895i	−0.923147	−	0.384448i	$-0.874392\pi$
$881$		−	22.8221i		−	0.768895i	0.923147	−	0.384448i	$-0.125608\pi$
$882$	15.7627	+	5.12453i	0.530759	+	0.172552i
$883$			16.8248i			0.566199i	0.959091	+	0.283099i	$0.0913626\pi$
$883$			16.8248i			0.566199i	−0.959091	+	0.283099i	$0.908637\pi$
$884$	20.0425	−	35.8899i	0.674102	−	1.20711i
$885$		−	11.8848i		−	0.399503i
$886$	5.91115	−	18.1823i	0.198589	−	0.610848i
$887$			13.8258i			0.464226i	0.972689	+	0.232113i	$0.0745640\pi$
$887$			13.8258i			0.464226i	−0.972689	+	0.232113i	$0.925436\pi$
$888$	20.3063	+	3.22660i	0.681434	+	0.108278i
$889$	−15.9981	−	15.9981i	−0.536557	−	0.536557i
$890$	22.5885	+	7.34359i	0.757167	+	0.246158i
$891$	−1.08518	+	1.08518i	−0.0363548	+	0.0363548i
$892$	47.4397	−	7.49751i	1.58840	−	0.251035i
$893$			56.2685i			1.88295i
$894$	8.45031	+	16.5915i	0.282621	+	0.554903i
$895$	−13.2896	−	13.2896i	−0.444223	−	0.444223i
$896$	−7.60121	−	48.3570i	−0.253939	−	1.61550i
$897$	−10.5655	+	1.26701i	−0.352773	+	0.0423043i
$898$	−11.6444	−	22.8629i	−0.388579	−	0.762943i
$899$	−21.2955	−	21.2955i	−0.710244	−	0.710244i
$900$	−3.34647	+	4.60279i	−0.111549	+	0.153426i
$901$	−24.4081			−0.813151
$902$	2.63778	−	8.11365i	0.0878284	−	0.270155i
$903$	−9.19026	+	9.19026i	−0.305833	+	0.305833i
$904$	−34.9308	+	25.3521i	−1.16178	+	0.843197i
$905$	−31.3891	+	31.3891i	−1.04341	+	1.04341i
$906$	−11.0674	+	5.63680i	−0.367690	+	0.187270i
$907$		−	0.155764i		−	0.00517206i	−0.999997	−	0.00258603i	$-0.999177\pi$
$907$		−	0.155764i		−	0.00517206i	0.999997	−	0.00258603i	$-0.000823160\pi$
$908$	−3.81090	−	24.1131i	−0.126469	−	0.800220i
$909$	5.67835			0.188339
$910$	−11.9722	+	60.6234i	−0.396876	+	2.00965i
$911$		−	3.37534i		−	0.111830i	−0.998436	−	0.0559150i	$-0.982192\pi$
$911$		−	3.37534i		−	0.111830i	0.998436	−	0.0559150i	$-0.0178076\pi$
$912$	−11.3017	+	22.1444i	−0.374238	+	0.733276i
$913$	21.2470			0.703172
$914$	39.1399	−	19.9346i	1.29463	−	0.659376i
$915$	−2.24014	−	2.24014i	−0.0740568	−	0.0740568i
$916$	1.83696	+	11.6232i	0.0606948	+	0.384040i
$917$	52.6526	+	52.6526i	1.73874	+	1.73874i
$918$	−7.66677	−	2.49250i	−0.253041	−	0.0822646i
$919$			25.7638i			0.849869i	0.905224	+	0.424935i	$0.139703\pi$
$919$			25.7638i			0.849869i	−0.905224	+	0.424935i	$0.860297\pi$
$920$	3.66921	−	23.0918i	0.120970	−	0.761314i
$921$	11.6407	−	11.6407i	0.383575	−	0.383575i
$922$	18.7254	+	36.7659i	0.616689	+	1.21082i
$923$	10.0908	−	12.8407i	0.332142	−	0.422657i
$924$	−10.7412	−	7.80942i	−0.353360	−	0.256911i
$925$	14.6259	−	14.6259i	0.480898	−	0.480898i
$926$	−0.142013	+	0.0723294i	−0.00466683	+	0.00237689i
$927$	1.20900			0.0397087
$928$	−0.0327976	+	39.3752i	−0.00107663	+	1.29255i
$929$	−28.3002	−	28.3002i	−0.928499	−	0.928499i	0.0691097	−	0.997609i	$-0.477984\pi$
$929$	−28.3002	−	28.3002i	−0.928499	−	0.928499i	−0.997609	+	0.0691097i	$0.977984\pi$
$930$	16.2989	+	5.29885i	0.534463	+	0.173756i
$931$	51.5098	−	51.5098i	1.68817	−	1.68817i
$932$	−3.28050	+	4.51206i	−0.107456	+	0.147798i
$933$	−14.2715			−0.467228
$934$	−29.5743	−	9.61473i	−0.967702	−	0.314604i
$935$	24.5040			0.801367
$936$	−7.48145	+	6.93022i	−0.244539	+	0.226521i
$937$	42.3237			1.38266			0.691328	−	0.722541i	$-0.257026\pi$
$937$	42.3237			1.38266			0.691328	+	0.722541i	$0.257026\pi$
$938$	60.8884	+	19.7950i	1.98808	+	0.646331i
$939$	20.4770			0.668241
$940$	−41.0188	−	29.8228i	−1.33789	−	0.972713i
$941$	21.0672	−	21.0672i	0.686769	−	0.686769i	−0.274747	−	0.961517i	$-0.588594\pi$
$941$	21.0672	−	21.0672i	0.686769	−	0.686769i	0.961517	+	0.274747i	$0.0885941\pi$
$942$	−17.4904	−	5.68620i	−0.569869	−	0.185267i
$943$	−8.20366	−	8.20366i	−0.267148	−	0.267148i
$944$	15.1174	+	7.71541i	0.492030	+	0.251115i
$945$	12.1189			0.394226
$946$	5.80947	−	2.95886i	0.188882	−	0.0962007i
$947$	−37.8829	+	37.8829i	−1.23103	+	1.23103i	−0.267459	+	0.963569i	$0.586184\pi$
$947$	−37.8829	+	37.8829i	−1.23103	+	1.23103i	−0.963569	+	0.267459i	$0.913816\pi$
$948$	5.25490	−	7.22768i	0.170671	−	0.234744i
$949$	24.8104	−	31.5716i	0.805378	−	1.02486i
$950$	11.3509	+	22.2866i	0.368271	+	0.723071i
$951$	−18.4519	+	18.4519i	−0.598343	+	0.598343i
$952$	10.9475	−	68.8969i	0.354811	−	2.23296i
$953$		−	35.9170i		−	1.16346i	−0.813380	−	0.581732i	$-0.802375\pi$
$953$		−	35.9170i		−	1.16346i	0.813380	−	0.581732i	$-0.197625\pi$
$954$	5.75859	+	1.87214i	0.186441	+	0.0606128i
$955$	34.6036	+	34.6036i	1.11975	+	1.11975i
$956$	8.86084	−	1.40039i	0.286580	−	0.0452919i
$957$	7.55351	+	7.55351i	0.244170	+	0.244170i
$958$	−7.69815	+	3.92079i	−0.248716	+	0.126675i
$959$	13.6584			0.441052
$960$	−10.1529	−	19.9755i	−0.327684	−	0.644708i
$961$			12.2798i			0.396124i
$962$	30.7917	−	20.6356i	0.992765	−	0.665318i
$963$	−11.6314			−0.374817
$964$	55.3814	−	8.75263i	1.78371	−	0.281903i
$965$			50.1047i			1.61293i
$966$	−16.0919	+	8.19587i	−0.517749	+	0.263698i
$967$	24.7361	−	24.7361i	0.795460	−	0.795460i	−0.186916	−	0.982376i	$-0.559849\pi$
$967$	24.7361	−	24.7361i	0.795460	−	0.795460i	0.982376	+	0.186916i	$0.0598492\pi$
$968$	−14.3621	−	19.7885i	−0.461616	−	0.636028i
$969$	−25.0537	+	25.0537i	−0.804839	+	0.804839i
$970$	20.0482	−	61.6669i	0.643708	−	1.98001i
$971$	−19.1899			−0.615834			−0.307917	−	0.951413i	$-0.599632\pi$
$971$	−19.1899			−0.615834			−0.307917	+	0.951413i	$0.599632\pi$
$972$	1.61764	+	1.17611i	0.0518859	+	0.0377237i
$973$	49.3625	+	49.3625i	1.58249	+	1.58249i
$974$	−25.9509	−	50.9525i	−0.831520	−	1.63262i
$975$	1.22152	+	10.1861i	0.0391198	+	0.326218i
$976$	4.30372	−	1.39519i	0.137759	−	0.0446591i
$977$	−22.9975	−	22.9975i	−0.735755	−	0.735755i	0.235999	−	0.971753i	$-0.424164\pi$
$977$	−22.9975	−	22.9975i	−0.735755	−	0.735755i	−0.971753	+	0.235999i	$0.924164\pi$
$978$	3.77630	+	7.41447i	0.120753	+	0.237088i
$979$			9.20234i			0.294108i
$980$	10.2492	+	64.8505i	0.327397	+	2.07157i
$981$	−7.32910	+	7.32910i	−0.234000	+	0.234000i
$982$	16.7965	+	5.46060i	0.535997	+	0.174255i
$983$	1.02696	+	1.02696i	0.0327549	+	0.0327549i	0.723295	−	0.690540i	$-0.242627\pi$
$983$	1.02696	+	1.02696i	0.0327549	+	0.0327549i	−0.690540	+	0.723295i	$0.742627\pi$
$984$	−10.9808	−	1.74481i	−0.350054	−	0.0556225i
$985$		−	16.8059i		−	0.535482i
$986$	−17.3493	+	53.3654i	−0.552515	+	1.69950i
$987$			39.1696i			1.24678i
$988$	12.2180	+	43.1227i	0.388707	+	1.37191i
$989$		−	8.86560i		−	0.281910i
$990$	−5.78124	−	1.87950i	−0.183740	−	0.0597345i
$991$			57.0449i			1.81209i	0.423181	+	0.906045i	$0.360913\pi$
$991$			57.0449i			1.81209i	−0.423181	+	0.906045i	$0.639087\pi$
$992$	−17.3211	+	17.2923i	−0.549946	+	0.549031i
$993$	9.99851	+	9.99851i	0.317293	+	0.317293i
$994$	8.56882	−	26.3572i	0.271786	−	0.835999i
$995$	17.5671	−	17.5671i	0.556914	−	0.556914i
$996$	−4.32244	−	27.3498i	−0.136962	−	0.866610i
$997$			12.0315i			0.381042i	0.981683	+	0.190521i	$0.0610177\pi$
$997$			12.0315i			0.381042i	−0.981683	+	0.190521i	$0.938982\pi$
$998$	18.3332	−	9.33740i	0.580328	−	0.295570i
$999$	−5.14026	−	5.14026i	−0.162631	−	0.162631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.t.e.307.8	yes	24
3.2	odd	2		936.2.w.j.307.5		24
4.3	odd	2		1248.2.bb.f.463.2		24
8.3	odd	2	inner	312.2.t.e.307.3	yes	24
8.5	even	2		1248.2.bb.f.463.11		24
13.5	odd	4	inner	312.2.t.e.187.3	✓	24
24.11	even	2		936.2.w.j.307.10		24
39.5	even	4		936.2.w.j.811.10		24
52.31	even	4		1248.2.bb.f.655.11		24
104.5	odd	4		1248.2.bb.f.655.2		24
104.83	even	4	inner	312.2.t.e.187.8	yes	24
312.83	odd	4		936.2.w.j.811.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.3	✓	24	13.5	odd	4	inner
312.2.t.e.187.8	yes	24	104.83	even	4	inner
312.2.t.e.307.3	yes	24	8.3	odd	2	inner
312.2.t.e.307.8	yes	24	1.1	even	1	trivial
936.2.w.j.307.5		24	3.2	odd	2
936.2.w.j.307.10		24	24.11	even	2
936.2.w.j.811.5		24	312.83	odd	4
936.2.w.j.811.10		24	39.5	even	4
1248.2.bb.f.463.2		24	4.3	odd	2
1248.2.bb.f.463.11		24	8.5	even	2
1248.2.bb.f.655.2		24	104.5	odd	4
1248.2.bb.f.655.11		24	52.31	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.437240 - 1.34492i) q^{2} -1.00000 q^{3} +(-1.61764 - 1.17611i) q^{4} +(-1.98058 + 1.98058i) q^{5} +(-0.437240 + 1.34492i) q^{6} +(3.05943 + 3.05943i) q^{7} +(-2.28908 + 1.66136i) q^{8} +1.00000 q^{9} +(1.79774 + 3.52971i) q^{10} +(-1.08518 + 1.08518i) q^{11} +(1.61764 + 1.17611i) q^{12} +(3.57990 - 0.429300i) q^{13} +(5.45240 - 2.77699i) q^{14} +(1.98058 - 1.98058i) q^{15} +(1.23353 + 3.80505i) q^{16} +5.70052i q^{17} +(0.437240 - 1.34492i) q^{18} +(-4.39498 - 4.39498i) q^{19} +(5.53324 - 0.874489i) q^{20} +(-3.05943 - 3.05943i) q^{21} +(0.984999 + 1.93397i) q^{22} +2.95135 q^{23} +(2.28908 - 1.66136i) q^{24} -2.84537i q^{25} +(0.987901 - 5.00240i) q^{26} -1.00000 q^{27} +(-1.35084 - 8.54727i) q^{28} +6.96062i q^{29} +(-1.79774 - 3.52971i) q^{30} +(-3.05943 + 3.05943i) q^{31} +(5.65685 + 0.00471188i) q^{32} +(1.08518 - 1.08518i) q^{33} +(7.66677 + 2.49250i) q^{34} -12.1189 q^{35} +(-1.61764 - 1.17611i) q^{36} +(5.14026 + 5.14026i) q^{37} +(-7.83257 + 3.98925i) q^{38} +(-3.57990 + 0.429300i) q^{39} +(1.24323 - 7.82415i) q^{40} +(-2.77963 - 2.77963i) q^{41} +(-5.45240 + 2.77699i) q^{42} -3.00392i q^{43} +(3.03172 - 0.479142i) q^{44} +(-1.98058 + 1.98058i) q^{45} +(1.29045 - 3.96934i) q^{46} +(-6.40146 - 6.40146i) q^{47} +(-1.23353 - 3.80505i) q^{48} +11.7202i q^{49} +(-3.82681 - 1.24411i) q^{50} -5.70052i q^{51} +(-6.29590 - 3.51590i) q^{52} +4.28172i q^{53} +(-0.437240 + 1.34492i) q^{54} -4.29856i q^{55} +(-12.0861 - 1.92044i) q^{56} +(4.39498 + 4.39498i) q^{57} +(9.36150 + 3.04346i) q^{58} +(3.00033 - 3.00033i) q^{59} +(-5.53324 + 0.874489i) q^{60} -1.13106i q^{61} +(2.77699 + 5.45240i) q^{62} +(3.05943 + 3.05943i) q^{63} +(2.47974 - 7.60598i) q^{64} +(-6.24001 + 7.94053i) q^{65} +(-0.984999 - 1.93397i) q^{66} +(7.39889 + 7.39889i) q^{67} +(6.70444 - 9.22140i) q^{68} -2.95135 q^{69} +(-5.29885 + 16.2989i) q^{70} +(3.20281 - 3.20281i) q^{71} +(-2.28908 + 1.66136i) q^{72} +(7.87480 - 7.87480i) q^{73} +(9.16078 - 4.66573i) q^{74} +2.84537i q^{75} +(1.94053 + 12.2785i) q^{76} -6.64004 q^{77} +(-0.987901 + 5.00240i) q^{78} -4.46803i q^{79} +(-9.97930 - 5.09309i) q^{80} +1.00000 q^{81} +(-4.95376 + 2.52303i) q^{82} +(-9.78962 - 9.78962i) q^{83} +(1.35084 + 8.54727i) q^{84} +(-11.2903 - 11.2903i) q^{85} +(-4.04004 - 1.31343i) q^{86} -6.96062i q^{87} +(0.681180 - 4.28693i) q^{88} +(4.24001 - 4.24001i) q^{89} +(1.79774 + 3.52971i) q^{90} +(12.2659 + 9.63903i) q^{91} +(-4.77422 - 3.47111i) q^{92} +(3.05943 - 3.05943i) q^{93} +(-11.4085 + 5.81050i) q^{94} +17.4092 q^{95} +(-5.65685 - 0.00471188i) q^{96} +(-11.5753 - 11.5753i) q^{97} +(15.7627 + 5.12453i) q^{98} +(-1.08518 + 1.08518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} - 6 q^{8} + 24 q^{9} + 8 q^{11} + 36 q^{14} + 28 q^{16} + 20 q^{19} - 20 q^{20} + 20 q^{22} + 6 q^{24} + 12 q^{26} - 24 q^{27} - 16 q^{28} - 30 q^{32} - 8 q^{33} + 16 q^{34} + 16 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q - 24 * q^3 - 6 * q^8 + 24 * q^9 + 8 * q^11 + 36 * q^14 + 28 * q^16 + 20 * q^19 - 20 * q^20 + 20 * q^22 + 6 * q^24 + 12 * q^26 - 24 * q^27 - 16 * q^28 - 30 * q^32 - 8 * q^33 + 16 * q^34 + 16 * q^35 + 36 * q^40 - 12 * q^41 - 36 * q^42 - 32 * q^44 - 44 * q^46 - 28 * q^48 - 36 * q^50 + 4 * q^52 - 20 * q^57 + 32 * q^58 - 16 * q^59 + 20 * q^60 - 76 * q^65 - 20 * q^66 + 28 * q^67 + 32 * q^68 - 40 * q^70 - 6 * q^72 - 8 * q^73 - 32 * q^74 - 36 * q^76 - 12 * q^78 - 32 * q^80 + 24 * q^81 - 72 * q^83 + 16 * q^84 + 4 * q^86 + 28 * q^89 - 4 * q^91 + 32 * q^92 + 28 * q^94 + 30 * q^96 + 24 * q^97 + 68 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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