LMFDB - Embedded newform 637.2.bc.b.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.5
Character	$\chi$	$=$	637.31
Dual form			637.2.bc.b.411.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.694471 + 0.186083i) q^{2} +(-1.44134 - 0.832160i) q^{3} +(-1.28439 - 0.741542i) q^{4} +(0.501414 - 1.87130i) q^{5} +(-0.846120 - 0.846120i) q^{6} +(-1.77076 - 1.77076i) q^{8} +(-0.115021 - 0.199221i) q^{9} +O(q^{10})$	\(q+(0.694471 + 0.186083i) q^{2} +(-1.44134 - 0.832160i) q^{3} +(-1.28439 - 0.741542i) q^{4} +(0.501414 - 1.87130i) q^{5} +(-0.846120 - 0.846120i) q^{6} +(-1.77076 - 1.77076i) q^{8} +(-0.115021 - 0.199221i) q^{9} +(0.696434 - 1.20626i) q^{10} +(-3.08143 + 0.825667i) q^{11} +(1.23416 + 2.13763i) q^{12} +(0.846120 + 3.50487i) q^{13} +(-2.27993 + 2.27993i) q^{15} +(0.582851 + 1.00953i) q^{16} +(-0.254148 + 0.440197i) q^{17} +(-0.0428067 - 0.159757i) q^{18} +(0.710286 - 2.65082i) q^{19} +(-2.03166 + 2.03166i) q^{20} -2.29361 q^{22} +(-2.49648 + 1.44134i) q^{23} +(1.07872 + 4.02582i) q^{24} +(1.07978 + 0.623409i) q^{25} +(-0.0645898 + 2.59148i) q^{26} +5.37582i q^{27} -2.40426 q^{29} +(-2.00760 + 1.15909i) q^{30} +(-3.08857 + 0.827581i) q^{31} +(1.51320 + 5.64735i) q^{32} +(5.12849 + 1.37417i) q^{33} +(-0.258412 + 0.258412i) q^{34} +0.341170i q^{36} +(-2.51910 + 9.40142i) q^{37} +(0.986546 - 1.70875i) q^{38} +(1.69706 - 5.75582i) q^{39} +(-4.20150 + 2.42574i) q^{40} +(-5.34023 - 5.34023i) q^{41} -12.5736i q^{43} +(4.57002 + 1.22453i) q^{44} +(-0.430476 + 0.115346i) q^{45} +(-2.00194 + 0.536419i) q^{46} +(-10.7811 - 2.88879i) q^{47} -1.94010i q^{48} +(0.633867 + 0.633867i) q^{50} +(0.732629 - 0.422984i) q^{51} +(1.51226 - 5.12904i) q^{52} +(-3.42477 + 5.93187i) q^{53} +(-1.00035 + 3.73335i) q^{54} +6.18029i q^{55} +(-3.22968 + 3.22968i) q^{57} +(-1.66969 - 0.447392i) q^{58} +(-1.00352 - 3.74520i) q^{59} +(4.61898 - 1.23765i) q^{60} +(5.51719 - 3.18535i) q^{61} -2.29892 q^{62} +1.87209i q^{64} +(6.98291 + 0.174042i) q^{65} +(3.30587 + 1.90865i) q^{66} +(-1.75850 - 6.56281i) q^{67} +(0.652849 - 0.376923i) q^{68} +4.79771 q^{69} +(-1.90492 + 1.90492i) q^{71} +(-0.149099 + 0.556446i) q^{72} +(-0.0676442 - 0.252451i) q^{73} +(-3.49889 + 6.06025i) q^{74} +(-1.03755 - 1.79709i) q^{75} +(-2.87798 + 2.87798i) q^{76} +(2.24962 - 3.68146i) q^{78} +(-2.78380 - 4.82168i) q^{79} +(2.18138 - 0.584499i) q^{80} +(4.12848 - 7.15074i) q^{81} +(-2.71491 - 4.70236i) q^{82} +(5.86182 + 5.86182i) q^{83} +(0.696309 + 0.696309i) q^{85} +(2.33974 - 8.73203i) q^{86} +(3.46536 + 2.00073i) q^{87} +(6.91853 + 3.99441i) q^{88} +(11.8358 + 3.17139i) q^{89} -0.320417 q^{90} +4.27526 q^{92} +(5.14037 + 1.37736i) q^{93} +(-6.94962 - 4.01237i) q^{94} +(-4.60434 - 2.65832i) q^{95} +(2.51845 - 9.39899i) q^{96} +(-7.04713 - 7.04713i) q^{97} +(0.518918 + 0.518918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9	$ 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9} - 10 q^{11} - 44 q^{15} + 12 q^{16} - 4 q^{18} - 12 q^{19} - 8 q^{22} + 12 q^{24} - 24 q^{26} + 16 q^{29} - 24 q^{31} + 4 q^{32} - 48 q^{33} - 8 q^{37} - 6 q^{39} + 132 q^{40} - 42 q^{44} + 24 q^{45} + 12 q^{46} - 30 q^{47} + 88 q^{50} - 36 q^{52} - 12 q^{53} - 78 q^{54} + 40 q^{57} + 26 q^{58} + 54 q^{59} + 16 q^{60} + 48 q^{61} - 8 q^{65} - 12 q^{66} + 16 q^{67} + 48 q^{68} - 36 q^{71} + 22 q^{72} - 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} - 138 q^{80} + 16 q^{81} - 84 q^{85} + 42 q^{86} + 24 q^{87} + 60 q^{89} + 48 q^{92} + 6 q^{93} + 72 q^{94} + 42 q^{96} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9 - 10 * q^11 - 44 * q^15 + 12 * q^16 - 4 * q^18 - 12 * q^19 - 8 * q^22 + 12 * q^24 - 24 * q^26 + 16 * q^29 - 24 * q^31 + 4 * q^32 - 48 * q^33 - 8 * q^37 - 6 * q^39 + 132 * q^40 - 42 * q^44 + 24 * q^45 + 12 * q^46 - 30 * q^47 + 88 * q^50 - 36 * q^52 - 12 * q^53 - 78 * q^54 + 40 * q^57 + 26 * q^58 + 54 * q^59 + 16 * q^60 + 48 * q^61 - 8 * q^65 - 12 * q^66 + 16 * q^67 + 48 * q^68 - 36 * q^71 + 22 * q^72 - 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 - 138 * q^80 + 16 * q^81 - 84 * q^85 + 42 * q^86 + 24 * q^87 + 60 * q^89 + 48 * q^92 + 6 * q^93 + 72 * q^94 + 42 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.694471	+	0.186083i	0.491065	+	0.131581i	0.495850	−	0.868408i	$-0.334856\pi$
$2$	0.694471	+	0.186083i	0.491065	+	0.131581i	−0.00478511	+	0.999989i	$0.501523\pi$
$3$	−1.44134	−	0.832160i	−0.832160	−	0.480448i	0.0224319	−	0.999748i	$-0.492859\pi$
$3$	−1.44134	−	0.832160i	−0.832160	−	0.480448i	−0.854592	+	0.519301i	$0.826192\pi$
$4$	−1.28439	−	0.741542i	−0.642194	−	0.370771i
$5$	0.501414	−	1.87130i	0.224239	−	0.836871i	−0.758469	−	0.651709i	$-0.774052\pi$
$5$	0.501414	−	1.87130i	0.224239	−	0.836871i	0.982708	−	0.185162i	$-0.0592810\pi$
$6$	−0.846120	−	0.846120i	−0.345427	−	0.345427i
$7$		0			0
$7$		0			0
$8$	−1.77076	−	1.77076i	−0.626057	−	0.626057i
$9$	−0.115021	−	0.199221i	−0.0383402	−	0.0664071i
$10$	0.696434	−	1.20626i	0.220232	−	0.381453i
$11$	−3.08143	+	0.825667i	−0.929087	+	0.248948i	−0.691465	−	0.722410i	$-0.743034\pi$
$11$	−3.08143	+	0.825667i	−0.929087	+	0.248948i	−0.237621	+	0.971358i	$0.576368\pi$
$12$	1.23416	+	2.13763i	0.356272	+	0.617081i
$13$	0.846120	+	3.50487i	0.234671	+	0.972075i
$13$	0.846120	+	3.50487i	0.234671	+	0.972075i
$14$		0			0
$15$	−2.27993	+	2.27993i	−0.588675	+	0.588675i
$16$	0.582851	+	1.00953i	0.145713	+	0.252382i
$17$	−0.254148	+	0.440197i	−0.0616400	+	0.106764i	−0.895199	−	0.445667i	$-0.852966\pi$
$17$	−0.254148	+	0.440197i	−0.0616400	+	0.106764i	0.833559	+	0.552431i	$0.186300\pi$
$18$	−0.0428067	−	0.159757i	−0.0100896	−	0.0376550i
$19$	0.710286	−	2.65082i	0.162951	−	0.608141i	−0.835342	−	0.549731i	$-0.814730\pi$
$19$	0.710286	−	2.65082i	0.162951	−	0.608141i	0.998293	−	0.0584100i	$-0.0186031\pi$
$20$	−2.03166	+	2.03166i	−0.454292	+	0.454292i
$21$		0			0
$22$	−2.29361			−0.488999
$23$	−2.49648	+	1.44134i	−0.520552	+	0.300541i	−0.737160	−	0.675718i	$-0.763834\pi$
$23$	−2.49648	+	1.44134i	−0.520552	+	0.300541i	0.216609	+	0.976259i	$0.430500\pi$
$24$	1.07872	+	4.02582i	0.220192	+	0.821768i
$25$	1.07978	+	0.623409i	0.215955	+	0.124682i
$26$	−0.0645898	+	2.59148i	−0.0126671	+	0.508230i
$27$			5.37582i			1.03458i
$28$		0			0
$29$	−2.40426			−0.446460			−0.223230	−	0.974766i	$-0.571660\pi$
$29$	−2.40426			−0.446460			−0.223230	+	0.974766i	$0.571660\pi$
$30$	−2.00760	+	1.15909i	−0.366536	+	0.211620i
$31$	−3.08857	+	0.827581i	−0.554724	+	0.148638i	−0.525281	−	0.850929i	$-0.676040\pi$
$31$	−3.08857	+	0.827581i	−0.554724	+	0.148638i	−0.0294427	+	0.999566i	$0.509373\pi$
$32$	1.51320	+	5.64735i	0.267499	+	0.998319i
$33$	5.12849	+	1.37417i	0.892755	+	0.239213i
$34$	−0.258412	+	0.258412i	−0.0443172	+	0.0443172i
$35$		0			0
$36$			0.341170i			0.0568617i
$37$	−2.51910	+	9.40142i	−0.414138	+	1.54558i	0.372418	+	0.928065i	$0.378529\pi$
$37$	−2.51910	+	9.40142i	−0.414138	+	1.54558i	−0.786556	+	0.617519i	$0.788138\pi$
$38$	0.986546	−	1.70875i	0.160039	−	0.277196i
$39$	1.69706	−	5.75582i	0.271747	−	0.921669i
$40$	−4.20150	+	2.42574i	−0.664316	+	0.383543i
$41$	−5.34023	−	5.34023i	−0.834004	−	0.834004i	0.154058	−	0.988062i	$-0.450766\pi$
$41$	−5.34023	−	5.34023i	−0.834004	−	0.834004i	−0.988062	+	0.154058i	$0.950766\pi$
$42$		0			0
$43$		−	12.5736i		−	1.91746i	−0.284313	−	0.958732i	$-0.591765\pi$
$43$		−	12.5736i		−	1.91746i	0.284313	−	0.958732i	$-0.408235\pi$
$44$	4.57002	+	1.22453i	0.688956	+	0.184605i
$45$	−0.430476	+	0.115346i	−0.0641716	+	0.0171947i
$46$	−2.00194	+	0.536419i	−0.295170	+	0.0790906i
$47$	−10.7811	−	2.88879i	−1.57259	−	0.421374i	−0.635967	−	0.771716i	$-0.719399\pi$
$47$	−10.7811	−	2.88879i	−1.57259	−	0.421374i	−0.936622	+	0.350342i	$0.886065\pi$
$48$		−	1.94010i		−	0.280029i
$49$		0			0
$50$	0.633867	+	0.633867i	0.0896423	+	0.0896423i
$51$	0.732629	−	0.422984i	0.102589	−	0.0592296i
$52$	1.51226	−	5.12904i	0.209712	−	0.711270i
$53$	−3.42477	+	5.93187i	−0.470428	+	0.814805i	−0.999428	−	0.0338167i	$-0.989234\pi$
$53$	−3.42477	+	5.93187i	−0.470428	+	0.814805i	0.529000	+	0.848622i	$0.322567\pi$
$54$	−1.00035	+	3.73335i	−0.136130	+	0.508045i
$55$			6.18029i			0.833350i
$56$		0			0
$57$	−3.22968	+	3.22968i	−0.427781	+	0.427781i
$58$	−1.66969	−	0.447392i	−0.219241	−	0.0587454i
$59$	−1.00352	−	3.74520i	−0.130647	−	0.487583i	0.869330	−	0.494231i	$-0.164550\pi$
$59$	−1.00352	−	3.74520i	−0.130647	−	0.487583i	−0.999978	+	0.00664837i	$0.997884\pi$
$60$	4.61898	−	1.23765i	0.596307	−	0.159780i
$61$	5.51719	−	3.18535i	0.706404	−	0.407843i	−0.103324	−	0.994648i	$-0.532948\pi$
$61$	5.51719	−	3.18535i	0.706404	−	0.407843i	0.809728	+	0.586805i	$0.199614\pi$
$62$	−2.29892			−0.291963
$63$		0			0
$64$			1.87209i			0.234012i
$65$	6.98291	+	0.174042i	0.866124	+	0.0215872i
$66$	3.30587	+	1.90865i	0.406925	+	0.234938i
$67$	−1.75850	−	6.56281i	−0.214835	−	0.801775i	−0.986225	−	0.165412i	$-0.947105\pi$
$67$	−1.75850	−	6.56281i	−0.214835	−	0.801775i	0.771390	−	0.636363i	$-0.219562\pi$
$68$	0.652849	−	0.376923i	0.0791696	−	0.0457086i
$69$	4.79771			0.577576
$70$		0			0
$71$	−1.90492	+	1.90492i	−0.226072	+	0.226072i	−0.811049	−	0.584978i	$-0.801103\pi$
$71$	−1.90492	+	1.90492i	−0.226072	+	0.226072i	0.584978	+	0.811049i	$0.301103\pi$
$72$	−0.149099	+	0.556446i	−0.0175715	+	0.0655778i
$73$	−0.0676442	−	0.252451i	−0.00791715	−	0.0295472i	0.961854	−	0.273562i	$-0.0882020\pi$
$73$	−0.0676442	−	0.252451i	−0.00791715	−	0.0295472i	−0.969771	+	0.244015i	$0.921535\pi$
$74$	−3.49889	+	6.06025i	−0.406738	+	0.704490i
$75$	−1.03755	−	1.79709i	−0.119806	−	0.207510i
$76$	−2.87798	+	2.87798i	−0.330127	+	0.330127i
$77$		0			0
$78$	2.24962	−	3.68146i	0.254719	−	0.416843i
$79$	−2.78380	−	4.82168i	−0.313202	−	0.542481i	0.665852	−	0.746084i	$-0.268068\pi$
$79$	−2.78380	−	4.82168i	−0.313202	−	0.542481i	−0.979054	+	0.203603i	$0.934735\pi$
$80$	2.18138	−	0.584499i	0.243886	−	0.0653490i
$81$	4.12848	−	7.15074i	0.458720	−	0.794526i
$82$	−2.71491	−	4.70236i	−0.299812	−	0.519289i
$83$	5.86182	+	5.86182i	0.643419	+	0.643419i	0.951394	−	0.307975i	$-0.0996515\pi$
$83$	5.86182	+	5.86182i	0.643419	+	0.643419i	−0.307975	+	0.951394i	$0.599651\pi$
$84$		0			0
$85$	0.696309	+	0.696309i	0.0755253	+	0.0755253i
$86$	2.33974	−	8.73203i	0.252301	−	0.941599i
$87$	3.46536	+	2.00073i	0.371526	+	0.214500i
$88$	6.91853	+	3.99441i	0.737517	+	0.425806i
$89$	11.8358	+	3.17139i	1.25459	+	0.336166i	0.824108	−	0.566433i	$-0.191677\pi$
$89$	11.8358	+	3.17139i	1.25459	+	0.336166i	0.430482	+	0.902599i	$0.358344\pi$
$90$	−0.320417			−0.0337749
$91$		0			0
$92$	4.27526			0.445727
$93$	5.14037	+	1.37736i	0.533032	+	0.142825i
$94$	−6.94962	−	4.01237i	−0.716799	−	0.413844i
$95$	−4.60434	−	2.65832i	−0.472396	−	0.272738i
$96$	2.51845	−	9.39899i	0.257038	−	0.959280i
$97$	−7.04713	−	7.04713i	−0.715528	−	0.715528i	0.252158	−	0.967686i	$-0.418860\pi$
$97$	−7.04713	−	7.04713i	−0.715528	−	0.715528i	−0.967686	+	0.252158i	$0.918860\pi$
$98$		0			0
$99$	0.518918	+	0.518918i	0.0521533	+	0.0521533i
$100$	−0.924567	−	1.60140i	−0.0924567	−	0.160140i
$101$	−2.35974	+	4.08719i	−0.234803	+	0.406691i	−0.959215	−	0.282676i	$-0.908778\pi$
$101$	−2.35974	+	4.08719i	−0.234803	+	0.406691i	0.724412	+	0.689367i	$0.242111\pi$
$102$	0.587500	−	0.157420i	0.0581711	−	0.0155869i
$103$	2.22971	+	3.86197i	0.219700	+	0.380531i	0.954716	−	0.297518i	$-0.0961589\pi$
$103$	2.22971	+	3.86197i	0.219700	+	0.380531i	−0.735016	+	0.678049i	$0.762826\pi$
$104$	4.70799	−	7.70454i	0.461657	−	0.755492i
$105$		0			0
$106$	−3.48222	+	3.48222i	−0.338223	+	0.338223i
$107$	−9.65530	−	16.7235i	−0.933413	−	1.61672i	−0.777440	−	0.628957i	$-0.783482\pi$
$107$	−9.65530	−	16.7235i	−0.933413	−	1.61672i	−0.155973	−	0.987761i	$-0.549851\pi$
$108$	3.98639	−	6.90464i	0.383591	−	0.664399i
$109$	−2.81694	−	10.5129i	−0.269813	−	1.00696i	−0.959238	−	0.282600i	$-0.908803\pi$
$109$	−2.81694	−	10.5129i	−0.269813	−	1.00696i	0.689424	−	0.724358i	$-0.257864\pi$
$110$	−1.15005	+	4.29203i	−0.109653	+	0.409229i
$111$	11.4544	−	11.4544i	1.08720	−	1.08720i
$112$		0			0
$113$	11.1771			1.05145			0.525726	−	0.850654i	$-0.323794\pi$
$113$	11.1771			1.05145			0.525726	+	0.850654i	$0.323794\pi$
$114$	−2.84390	+	1.64193i	−0.266356	+	0.153781i
$115$	1.44542	+	5.39437i	0.134786	+	0.503028i
$116$	3.08800	+	1.78286i	0.286714	+	0.165534i
$117$	0.600923	−	0.571697i	0.0555554	−	0.0528534i
$118$		−	2.78767i		−	0.256626i
$119$		0			0
$120$	8.07441			0.737089
$121$	−0.712785	+	0.411527i	−0.0647987	+	0.0374115i
$122$	4.42427	−	1.18548i	0.400555	−	0.107328i
$123$	3.25318	+	12.1410i	0.293329	+	1.09472i
$124$	4.58061	+	1.22737i	0.411351	+	0.110221i
$125$	8.55744	−	8.55744i	0.765400	−	0.765400i
$126$		0			0
$127$			14.7463i			1.30852i	0.756269	+	0.654261i	$0.227020\pi$
$127$			14.7463i			1.30852i	−0.756269	+	0.654261i	$0.772980\pi$
$128$	2.67804	−	9.99458i	0.236707	−	0.883404i
$129$	−10.4633	+	18.1229i	−0.921241	+	1.59564i
$130$	4.81704	+	1.42027i	0.422483	+	0.124566i
$131$	−17.5068	+	10.1075i	−1.52957	+	0.883100i	−0.530194	+	0.847877i	$0.677881\pi$
$131$	−17.5068	+	10.1075i	−1.52957	+	0.883100i	−0.999379	+	0.0352230i	$0.988786\pi$
$132$	−5.56796	−	5.56796i	−0.484629	−	0.484629i
$133$		0			0
$134$		−	4.88491i		−	0.421992i
$135$	10.0598	+	2.69551i	0.865808	+	0.231992i
$136$	1.22952	−	0.329448i	0.105430	−	0.0282500i
$137$	8.18452	−	2.19304i	0.699251	−	0.187364i	0.108356	−	0.994112i	$-0.465441\pi$
$137$	8.18452	−	2.19304i	0.699251	−	0.187364i	0.590895	+	0.806748i	$0.298775\pi$
$138$	3.33187	+	0.892772i	0.283628	+	0.0759978i
$139$		−	2.42919i		−	0.206041i	−0.994679	−	0.103021i	$-0.967149\pi$
$139$		−	2.42919i		−	0.206041i	0.994679	−	0.103021i	$-0.0328507\pi$
$140$		0			0
$141$	13.1354	+	13.1354i	1.10620	+	1.10620i
$142$	−1.67738	+	0.968436i	−0.140763	+	0.0812694i
$143$	−5.50111	−	10.1014i	−0.460026	−	0.844721i
$144$	0.134080	−	0.232233i	0.0111733	−	0.0193527i
$145$	−1.20553	+	4.49909i	−0.100114	+	0.373629i
$146$		−	0.187908i		−	0.0155513i
$147$		0			0
$148$	10.2071	−	10.2071i	0.839015	−	0.839015i
$149$	−5.73207	−	1.53590i	−0.469590	−	0.125826i	0.0162614	−	0.999868i	$-0.494824\pi$
$149$	−5.73207	−	1.53590i	−0.469590	−	0.125826i	−0.485851	+	0.874042i	$0.661490\pi$
$150$	−0.386141	−	1.44110i	−0.0315283	−	0.117665i
$151$	−6.24701	+	1.67388i	−0.508374	+	0.136219i	−0.503884	−	0.863771i	$-0.668096\pi$
$151$	−6.24701	+	1.67388i	−0.508374	+	0.136219i	−0.00449055	+	0.999990i	$0.501429\pi$
$152$	−5.95171	+	3.43622i	−0.482748	+	0.278715i
$153$	0.116929			0.00945315
$154$		0			0
$155$			6.19461i			0.497563i
$156$	−6.44786	+	6.13426i	−0.516242	+	0.491134i
$157$	−5.54969	−	3.20411i	−0.442913	−	0.255716i	0.261919	−	0.965090i	$-0.415645\pi$
$157$	−5.54969	−	3.20411i	−0.442913	−	0.255716i	−0.704833	+	0.709374i	$0.748978\pi$
$158$	−1.03603	−	3.86653i	−0.0824225	−	0.307605i
$159$	9.87253	−	5.69991i	0.782942	−	0.452032i
$160$	11.3266			0.895448
$161$		0			0
$162$	4.19774	−	4.19774i	0.329805	−	0.329805i
$163$	0.177113	−	0.660995i	0.0138726	−	0.0517731i	−0.958643	−	0.284613i	$-0.908135\pi$
$163$	0.177113	−	0.660995i	0.0138726	−	0.0517731i	0.972515	+	0.232840i	$0.0748017\pi$
$164$	2.89892	+	10.8189i	0.226368	+	0.844816i
$165$	5.14299	−	8.90791i	0.400381	−	0.693480i
$166$	2.98008	+	5.16165i	0.231299	+	0.400622i
$167$	−2.47505	+	2.47505i	−0.191525	+	0.191525i	−0.796355	−	0.604830i	$-0.793241\pi$
$167$	−2.47505	+	2.47505i	−0.191525	+	0.191525i	0.604830	+	0.796355i	$0.293241\pi$
$168$		0			0
$169$	−11.5682	+	5.93107i	−0.889859	+	0.456236i
$170$	0.353995	+	0.613137i	0.0271502	+	0.0470255i
$171$	−0.609798	+	0.163395i	−0.0466325	+	0.0124951i
$172$	−9.32388	+	16.1494i	−0.710939	+	1.23138i
$173$	−12.3860	−	21.4531i	−0.941687	−	1.63105i	−0.762252	−	0.647280i	$-0.775906\pi$
$173$	−12.3860	−	21.4531i	−0.941687	−	1.63105i	−0.179435	−	0.983770i	$-0.557427\pi$
$174$	2.03429	+	2.03429i	0.154219	+	0.154219i
$175$		0			0
$176$	−2.62955	−	2.62955i	−0.198210	−	0.198210i
$177$	−1.67018	+	6.23320i	−0.125539	+	0.468516i
$178$	7.62946	+	4.40487i	0.571852	+	0.330159i
$179$	−16.6184	−	9.59464i	−1.24212	−	0.717137i	−0.272593	−	0.962129i	$-0.587881\pi$
$179$	−16.6184	−	9.59464i	−1.24212	−	0.717137i	−0.969525	+	0.244992i	$0.921215\pi$
$180$	0.638432	+	0.171067i	0.0475859	+	0.0127506i
$181$	−11.0428			−0.820803			−0.410401	−	0.911905i	$-0.634611\pi$
$181$	−11.0428			−0.820803			−0.410401	+	0.911905i	$0.634611\pi$
$182$		0			0
$183$	−10.6029			−0.783788
$184$	6.97293	+	1.86839i	0.514051	+	0.137740i
$185$	16.3298	+	9.42800i	1.20059	+	0.693161i
$186$	3.31354	+	1.91307i	0.242960	+	0.140273i
$187$	0.419683	−	1.56628i	0.0306903	−	0.114538i
$188$	11.7050	+	11.7050i	0.853674	+	0.853674i
$189$		0			0
$190$	−2.70291	−	2.70291i	−0.196090	−	0.196090i
$191$	−5.68132	−	9.84033i	−0.411086	−	0.712022i	0.583923	−	0.811809i	$-0.301517\pi$
$191$	−5.68132	−	9.84033i	−0.411086	−	0.712022i	−0.995009	+	0.0997875i	$0.968184\pi$
$192$	1.55788	−	2.69833i	0.112430	−	0.194735i
$193$	12.0487	−	3.22844i	0.867286	−	0.232388i	0.202372	−	0.979309i	$-0.435135\pi$
$193$	12.0487	−	3.22844i	0.867286	−	0.232388i	0.664914	+	0.746920i	$0.268468\pi$
$194$	−3.58268	−	6.20538i	−0.257221	−	0.445520i
$195$	−9.91994	−	6.06175i	−0.710382	−	0.434091i
$196$		0			0
$197$	−13.9343	+	13.9343i	−0.992775	+	0.992775i	−0.999974	−	0.00719943i	$-0.997708\pi$
$197$	−13.9343	+	13.9343i	−0.992775	+	0.992775i	0.00719943	+	0.999974i	$0.497708\pi$
$198$	0.263812	+	0.456936i	0.0187483	+	0.0324730i
$199$	0.413742	−	0.716622i	0.0293294	−	0.0508000i	−0.850988	−	0.525185i	$-0.823996\pi$
$199$	0.413742	−	0.716622i	0.0293294	−	0.0508000i	0.880318	+	0.474385i	$0.157329\pi$
$200$	−0.808115	−	3.01593i	−0.0571424	−	0.213258i
$201$	−2.92670	+	10.9226i	−0.206434	+	0.770422i
$202$	−2.39933	+	2.39933i	−0.168816	+	0.168816i
$203$		0			0
$204$	−1.25464			−0.0878424
$205$	−12.6708	+	7.31551i	−0.884970	+	0.510938i
$206$	0.829821	+	3.09694i	0.0578164	+	0.215774i
$207$	0.574293	+	0.331568i	0.0399161	+	0.0230456i
$208$	−3.04510	+	2.89700i	−0.211139	+	0.200871i
$209$			8.75479i			0.605582i
$210$		0			0
$211$	18.8543			1.29798			0.648992	−	0.760795i	$-0.275191\pi$
$211$	18.8543			1.29798			0.648992	+	0.760795i	$0.275191\pi$
$212$	8.79746	−	5.07921i	0.604212	−	0.348842i
$213$	4.33083	−	1.16044i	0.296744	−	0.0795122i
$214$	−3.59337	−	13.4106i	−0.245638	−	0.916733i
$215$	−23.5291	−	6.30460i	−1.60467	−	0.429970i
$216$	9.51928	−	9.51928i	0.647705	−	0.647705i
$217$		0			0
$218$		−	7.82512i		−	0.529984i
$219$	−0.112581	+	0.420160i	−0.00760755	+	0.0283918i
$220$	4.58294	−	7.93788i	0.308982	−	0.535172i
$221$	−1.75787	−	0.518295i	−0.118247	−	0.0348643i
$222$	10.0862	−	5.82327i	0.676941	−	0.390832i
$223$	−9.83194	−	9.83194i	−0.658396	−	0.658396i	0.296605	−	0.955000i	$-0.404146\pi$
$223$	−9.83194	−	9.83194i	−0.658396	−	0.658396i	−0.955000	+	0.296605i	$0.904146\pi$
$224$		0			0
$225$		−	0.286819i		−	0.0191213i
$226$	7.76216	+	2.07987i	0.516332	+	0.138351i
$227$	−15.1225	+	4.05207i	−1.00372	+	0.268945i	−0.723002	−	0.690846i	$-0.757238\pi$
$227$	−15.1225	+	4.05207i	−1.00372	+	0.268945i	−0.280715	+	0.959791i	$0.590572\pi$
$228$	6.54309	−	1.75322i	0.433327	−	0.116110i
$229$	4.62362	+	1.23889i	0.305537	+	0.0818684i	0.408330	−	0.912834i	$-0.366111\pi$
$229$	4.62362	+	1.23889i	0.305537	+	0.0818684i	−0.102793	+	0.994703i	$0.532778\pi$
$230$			4.01520i			0.264755i
$231$		0			0
$232$	4.25736	+	4.25736i	0.279509	+	0.279509i
$233$	2.74537	−	1.58504i	0.179855	−	0.103839i	−0.407369	−	0.913263i	$-0.633554\pi$
$233$	2.74537	−	1.58504i	0.179855	−	0.103839i	0.587225	+	0.809424i	$0.300221\pi$
$234$	0.523707	−	0.285205i	0.0342358	−	0.0186444i
$235$	−10.8116	+	18.7263i	−0.705271	+	1.22157i
$236$	−1.48831	+	5.55444i	−0.0968805	+	0.361563i
$237$			9.26626i			0.601908i
$238$		0			0
$239$	7.52256	−	7.52256i	0.486594	−	0.486594i	−0.420636	−	0.907230i	$-0.638193\pi$
$239$	7.52256	−	7.52256i	0.486594	−	0.486594i	0.907230	+	0.420636i	$0.138193\pi$
$240$	−3.63051	−	0.972793i	−0.234349	−	0.0627935i
$241$	0.507552	+	1.89421i	0.0326943	+	0.122017i	0.980344	−	0.197294i	$-0.0632153\pi$
$241$	0.507552	+	1.89421i	0.0326943	+	0.122017i	−0.947650	+	0.319311i	$0.896549\pi$
$242$	−0.571587	+	0.153156i	−0.0367430	+	0.00984526i
$243$	2.06568	−	1.19262i	0.132514	−	0.0765068i
$244$	−9.44829			−0.604865
$245$		0			0
$246$			9.03695i			0.576175i
$247$	9.89177	+	0.246542i	0.629398	+	0.0156871i
$248$	6.93456	+	4.00367i	0.440345	+	0.254233i
$249$	−3.57092	−	13.3269i	−0.226298	−	0.844556i
$250$	7.53528	−	4.35050i	0.476573	−	0.275150i
$251$	−1.64155			−0.103614			−0.0518070	−	0.998657i	$-0.516498\pi$
$251$	−1.64155			−0.103614			−0.0518070	+	0.998657i	$0.516498\pi$
$252$		0			0
$253$	6.50266	−	6.50266i	0.408819	−	0.408819i
$254$	−2.74403	+	10.2409i	−0.172176	+	0.642570i
$255$	−0.424180	−	1.58306i	−0.0265632	−	0.0991350i
$256$	5.59174	−	9.68517i	0.349483	−	0.605323i
$257$	10.9118	+	18.8997i	0.680657	+	1.17893i	0.974781	+	0.223165i	$0.0716389\pi$
$257$	10.9118	+	18.8997i	0.680657	+	1.17893i	−0.294124	+	0.955767i	$0.595028\pi$
$258$	−10.6388	+	10.6388i	−0.662344	+	0.662344i
$259$		0			0
$260$	−8.83971	−	5.40166i	−0.548216	−	0.334997i
$261$	0.276539	+	0.478980i	0.0171173	+	0.0296481i
$262$	−14.0388	+	3.76168i	−0.867319	+	0.232397i
$263$	−8.33334	+	14.4338i	−0.513856	+	0.890024i	0.486015	+	0.873950i	$0.338450\pi$
$263$	−8.33334	+	14.4338i	−0.513856	+	0.890024i	−0.999871	+	0.0160740i	$0.994883\pi$
$264$	−6.64798	−	11.5146i	−0.409155	−	0.708677i
$265$	9.38309	+	9.38309i	0.576399	+	0.576399i
$266$		0			0
$267$	−14.4203	−	14.4203i	−0.882509	−	0.882509i
$268$	−2.60800	+	9.73319i	−0.159309	+	0.594549i
$269$	−14.6567	−	8.46207i	−0.893637	−	0.515942i	−0.0185068	−	0.999829i	$-0.505891\pi$
$269$	−14.6567	−	8.46207i	−0.893637	−	0.515942i	−0.875130	+	0.483887i	$0.839225\pi$
$270$	6.48463	+	3.74391i	0.394642	+	0.227847i
$271$	13.4215	+	3.59627i	0.815295	+	0.218458i	0.642289	−	0.766463i	$-0.277985\pi$
$271$	13.4215	+	3.59627i	0.815295	+	0.218458i	0.173007	+	0.984921i	$0.444652\pi$
$272$	−0.592522			−0.0359269
$273$		0			0
$274$	6.09200			0.368031
$275$	−3.84198	−	1.02946i	−0.231680	−	0.0620785i
$276$	−6.16212	−	3.55770i	−0.370916	−	0.214148i
$277$	17.0084	+	9.81980i	1.02194	+	0.590015i	0.914664	−	0.404215i	$-0.132455\pi$
$277$	17.0084	+	9.81980i	1.02194	+	0.590015i	0.107272	+	0.994230i	$0.465789\pi$
$278$	0.452030	−	1.68700i	0.0271110	−	0.101180i
$279$	0.520121	+	0.520121i	0.0311388	+	0.0311388i
$280$		0			0
$281$	−17.2002	−	17.2002i	−1.02608	−	1.02608i	−0.999651	−	0.0264298i	$-0.991586\pi$
$281$	−17.2002	−	17.2002i	−1.02608	−	1.02608i	−0.0264298	−	0.999651i	$-0.508414\pi$
$282$	6.67786	+	11.5664i	0.397661	+	0.688769i
$283$	5.89745	−	10.2147i	0.350567	−	0.607200i	−0.635782	−	0.771869i	$-0.719322\pi$
$283$	5.89745	−	10.2147i	0.350567	−	0.607200i	0.986349	+	0.164669i	$0.0526555\pi$
$284$	3.85922	−	1.03408i	0.229003	−	0.0613611i
$285$	4.42429	+	7.66310i	0.262072	+	0.453923i
$286$	−1.94067	−	8.03878i	−0.114754	−	0.475343i
$287$		0			0
$288$	0.951023	−	0.951023i	0.0560396	−	0.0560396i
$289$	8.37082	+	14.4987i	0.492401	+	0.852864i
$290$	−1.67441	+	2.90016i	−0.0983247	+	0.170303i
$291$	4.29300	+	16.0217i	0.251660	+	0.939207i
$292$	−0.100322	+	0.374406i	−0.00587090	+	0.0219105i
$293$	18.5497	−	18.5497i	1.08368	−	1.08368i	0.0875204	−	0.996163i	$-0.472106\pi$
$293$	18.5497	−	18.5497i	1.08368	−	1.08368i	0.996163	−	0.0875204i	$-0.0278943\pi$
$294$		0			0
$295$	−7.51157			−0.437340
$296$	21.1084	−	12.1869i	1.22690	−	0.708350i
$297$	−4.43864	−	16.5652i	−0.257556	−	0.961212i
$298$	−3.69495	−	2.13328i	−0.214043	−	0.123578i
$299$	−7.16403	−	7.53027i	−0.414307	−	0.435487i
$300$			3.07755i			0.177682i
$301$		0			0
$302$	−4.64985			−0.267569
$303$	6.80239	−	3.92736i	0.390787	−	0.225621i
$304$	3.09007	−	0.827982i	0.177228	−	0.0474880i
$305$	−3.19436	−	11.9215i	−0.182908	−	0.682624i
$306$	0.0812038	+	0.0217585i	0.00464211	+	0.00124385i
$307$	1.29211	−	1.29211i	0.0737445	−	0.0737445i	−0.669273	−	0.743017i	$-0.733394\pi$
$307$	1.29211	−	1.29211i	0.0737445	−	0.0737445i	0.743017	+	0.669273i	$0.233394\pi$
$308$		0			0
$309$		−	7.42189i		−	0.422217i
$310$	−1.15271	+	4.30198i	−0.0654696	+	0.244336i
$311$	−1.35809	+	2.35229i	−0.0770104	+	0.133386i	−0.901959	−	0.431822i	$-0.857871\pi$
$311$	−1.35809	+	2.35229i	−0.0770104	+	0.133386i	0.824948	+	0.565208i	$0.191204\pi$
$312$	−13.1972	+	7.18708i	−0.747147	+	0.406888i
$313$	22.0145	−	12.7101i	1.24433	−	0.718415i	0.274359	−	0.961627i	$-0.411534\pi$
$313$	22.0145	−	12.7101i	1.24433	−	0.718415i	0.969973	+	0.243212i	$0.0782011\pi$
$314$	−3.25787	−	3.25787i	−0.183852	−	0.183852i
$315$		0			0
$316$			8.25721i			0.464504i
$317$	−29.3670	−	7.86887i	−1.64942	−	0.441960i	−0.689967	−	0.723841i	$-0.742375\pi$
$317$	−29.3670	−	7.86887i	−1.64942	−	0.441960i	−0.959449	+	0.281882i	$0.909041\pi$
$318$	7.91684	−	2.12131i	0.443954	−	0.118957i
$319$	7.40856	−	1.98512i	0.414800	−	0.111145i
$320$	3.50325	+	0.938694i	0.195838	+	0.0524746i
$321$			32.1390i			1.79382i
$322$		0			0
$323$	0.986368	+	0.986368i	0.0548830	+	0.0548830i
$324$	−10.6051	+	6.12288i	−0.589174	+	0.340160i
$325$	−1.27134	+	4.31195i	−0.0705214	+	0.239184i
$326$	0.246000	−	0.426084i	0.0136247	−	0.0235986i
$327$	−4.68828	+	17.4969i	−0.259262	+	0.967581i
$328$			18.9125i			1.04427i
$329$		0			0
$330$	5.22926	−	5.22926i	0.287862	−	0.287862i
$331$	−1.82858	−	0.489966i	−0.100508	−	0.0269310i	0.208215	−	0.978083i	$-0.433235\pi$
$331$	−1.82858	−	0.489966i	−0.100508	−	0.0269310i	−0.308722	+	0.951152i	$0.599901\pi$
$332$	−3.18207	−	11.8756i	−0.174639	−	0.651761i
$333$	2.16271	−	0.579497i	0.118516	−	0.0317563i
$334$	−2.17942	+	1.25829i	−0.119252	+	0.0688504i
$335$	−13.1627			−0.719157
$336$		0			0
$337$		−	15.8664i		−	0.864300i	−0.901802	−	0.432150i	$-0.857755\pi$
$337$		−	15.8664i		−	0.864300i	0.901802	−	0.432150i	$-0.142245\pi$
$338$	−9.13742	+	1.96632i	−0.497010	+	0.106954i
$339$	−16.1100	−	9.30112i	−0.874976	−	0.505168i
$340$	−0.377988	−	1.41067i	−0.0204993	−	0.0765044i
$341$	8.83392	−	5.10027i	0.478384	−	0.276195i
$342$	−0.453892			−0.0245437
$343$		0			0
$344$	−22.2649	+	22.2649i	−1.20044	+	1.20044i
$345$	2.40564	−	8.97796i	0.129515	−	0.483357i
$346$	−4.60963	−	17.2034i	−0.247815	−	0.924860i
$347$	−8.10074	+	14.0309i	−0.434871	+	0.753218i	−0.997285	−	0.0736374i	$-0.976539\pi$
$347$	−8.10074	+	14.0309i	−0.434871	+	0.753218i	0.562414	+	0.826856i	$0.309873\pi$
$348$	−2.96725	−	5.13942i	−0.159061	−	0.275502i
$349$	−18.7058	+	18.7058i	−1.00130	+	1.00130i	−0.00129933	+	0.999999i	$0.500414\pi$
$349$	−18.7058	+	18.7058i	−1.00130	+	1.00130i	−0.999999	+	0.00129933i	$0.999586\pi$
$350$		0			0
$351$	−18.8415	+	4.54859i	−1.00569	+	0.242786i
$352$	−9.32566	−	16.1525i	−0.497059	−	0.860932i
$353$	22.1601	−	5.93777i	1.17946	−	0.316036i	0.384748	−	0.923022i	$-0.374288\pi$
$353$	22.1601	−	5.93777i	1.17946	−	0.316036i	0.794712	+	0.606986i	$0.207622\pi$
$354$	−2.31978	+	4.01799i	−0.123295	+	0.213554i
$355$	2.60952	+	4.51982i	0.138499	+	0.239887i
$356$	−12.8500	−	12.8500i	−0.681049	−	0.681049i
$357$		0			0
$358$	−9.75560	−	9.75560i	−0.515600	−	0.515600i
$359$	1.92833	−	7.19663i	0.101773	−	0.379824i	−0.896186	−	0.443679i	$-0.853673\pi$
$359$	1.92833	−	7.19663i	0.101773	−	0.379824i	0.997959	+	0.0638554i	$0.0203397\pi$
$360$	0.966518	+	0.558020i	0.0509400	+	0.0294102i
$361$	9.93212	+	5.73431i	0.522743	+	0.301806i
$362$	−7.66889	−	2.05487i	−0.403068	−	0.108002i
$363$	1.36982			0.0718971
$364$		0			0
$365$	−0.506330			−0.0265025
$366$	−7.36340	−	1.97302i	−0.384891	−	0.103131i
$367$	30.3981	+	17.5504i	1.58677	+	0.916122i	0.993835	+	0.110871i	$0.0353639\pi$
$367$	30.3981	+	17.5504i	1.58677	+	0.916122i	0.592934	+	0.805251i	$0.297969\pi$
$368$	−2.91015	−	1.68018i	−0.151702	−	0.0875853i
$369$	−0.449652	+	1.67812i	−0.0234080	+	0.0873597i
$370$	9.58617	+	9.58617i	0.498361	+	0.498361i
$371$		0			0
$372$	−5.58086	−	5.58086i	−0.289354	−	0.289354i
$373$	7.82695	+	13.5567i	0.405264	+	0.701938i	0.994352	−	0.106131i	$-0.0338462\pi$
$373$	7.82695	+	13.5567i	0.405264	+	0.701938i	−0.589088	+	0.808069i	$0.700513\pi$
$374$	0.582916	−	1.00964i	0.0301419	−	0.0522072i
$375$	−19.4554	+	5.21305i	−1.00467	+	0.269201i
$376$	13.9754	+	24.2061i	0.720727	+	1.24834i
$377$	−2.03429	−	8.42660i	−0.104771	−	0.433992i
$378$		0			0
$379$	−17.5478	+	17.5478i	−0.901371	+	0.901371i	−0.995555	−	0.0941840i	$-0.969976\pi$
$379$	−17.5478	+	17.5478i	−0.901371	+	0.901371i	0.0941840	+	0.995555i	$0.469976\pi$
$380$	3.94251	+	6.82862i	0.202246	+	0.350301i
$381$	12.2713	−	21.2545i	0.628676	−	1.08890i
$382$	−2.11439	−	7.89102i	−0.108182	−	0.403740i
$383$	−0.255080	+	0.951971i	−0.0130340	+	0.0486435i	−0.972137	−	0.234415i	$-0.924682\pi$
$383$	−0.255080	+	0.951971i	−0.0130340	+	0.0486435i	0.959103	+	0.283059i	$0.0913491\pi$
$384$	−12.1771	+	12.1771i	−0.621408	+	0.621408i
$385$		0			0
$386$	8.96824			0.456471
$387$	−2.50494	+	1.44623i	−0.127333	+	0.0735159i
$388$	3.82551	+	14.2770i	0.194211	+	0.724805i
$389$	−4.37916	−	2.52831i	−0.222032	−	0.128190i	0.384859	−	0.922976i	$-0.374250\pi$
$389$	−4.37916	−	2.52831i	−0.222032	−	0.128190i	−0.606891	+	0.794785i	$0.707584\pi$
$390$	−5.76112	−	6.05564i	−0.291726	−	0.306639i
$391$		−	1.46526i		−	0.0741013i
$392$		0			0
$393$	33.6443			1.69713
$394$	−12.2699	+	7.08401i	−0.618147	+	0.356887i
$395$	−10.4186	+	2.79167i	−0.524219	+	0.140464i
$396$	−0.281693	−	1.05129i	−0.0141556	−	0.0528294i
$397$	1.12448	+	0.301304i	0.0564361	+	0.0151220i	0.286927	−	0.957953i	$-0.407366\pi$
$397$	1.12448	+	0.301304i	0.0564361	+	0.0151220i	−0.230491	+	0.973075i	$0.574033\pi$
$398$	0.420683	−	0.420683i	0.0210869	−	0.0210869i
$399$		0			0
$400$			1.45342i			0.0726709i
$401$	0.396969	−	1.48151i	0.0198237	−	0.0739830i	−0.955305	−	0.295621i	$-0.904474\pi$
$401$	0.396969	−	1.48151i	0.0198237	−	0.0739830i	0.975129	+	0.221638i	$0.0711402\pi$
$402$	−4.06502	+	7.04083i	−0.202745	+	0.351165i
$403$	−5.51386	−	10.1248i	−0.274665	−	0.504352i
$404$	6.06164	−	3.49969i	0.301578	−	0.174116i
$405$	−11.3111	−	11.3111i	−0.562053	−	0.562053i
$406$		0			0
$407$		−	31.0498i		−	1.53908i
$408$	−2.04631	−	0.548307i	−0.101307	−	0.0271453i
$409$	−10.3123	+	2.76317i	−0.509910	+	0.136630i	−0.504595	−	0.863356i	$-0.668358\pi$
$409$	−10.3123	+	2.76317i	−0.509910	+	0.136630i	−0.00531434	+	0.999986i	$0.501692\pi$
$410$	−10.1608	+	2.72258i	−0.501807	+	0.134459i
$411$	−13.6217	−	3.64991i	−0.671907	−	0.180037i
$412$		−	6.61369i		−	0.325833i
$413$		0			0
$414$	0.337130	+	0.337130i	0.0165691	+	0.0165691i
$415$	13.9084	−	8.03004i	0.682738	−	0.394179i
$416$	−18.5128	+	10.0819i	−0.907667	+	0.494306i
$417$	−2.02147	+	3.50129i	−0.0989919	+	0.171459i
$418$	−1.62912	+	6.07995i	−0.0796828	+	0.297380i
$419$			11.8652i			0.579653i	0.957079	+	0.289826i	$0.0935976\pi$
$419$			11.8652i			0.579653i	−0.957079	+	0.289826i	$0.906402\pi$
$420$		0			0
$421$	3.15236	−	3.15236i	0.153636	−	0.153636i	−0.626103	−	0.779740i	$-0.715351\pi$
$421$	3.15236	−	3.15236i	0.153636	−	0.153636i	0.779740	+	0.626103i	$0.215351\pi$
$422$	13.0938	+	3.50847i	0.637395	+	0.170789i
$423$	0.664541	+	2.48010i	0.0323111	+	0.120587i
$424$	16.5683	−	4.43947i	0.804630	−	0.215600i
$425$	−0.548846	+	0.316876i	−0.0266229	+	0.0153708i
$426$	3.22357			0.156183
$427$		0			0
$428$			28.6392i			1.38433i
$429$	−0.476979	+	19.1374i	−0.0230288	+	0.923961i
$430$	−15.1671	−	8.75672i	−0.731422	−	0.422286i
$431$	0.316193	+	1.18005i	0.0152305	+	0.0568410i	0.973123	−	0.230286i	$-0.0739663\pi$
$431$	0.316193	+	1.18005i	0.0152305	+	0.0568410i	−0.957892	+	0.287127i	$0.907300\pi$
$432$	−5.42704	+	3.13330i	−0.261109	+	0.150751i
$433$	18.1346			0.871493			0.435747	−	0.900069i	$-0.356484\pi$
$433$	18.1346			0.871493			0.435747	+	0.900069i	$0.356484\pi$
$434$		0			0
$435$	5.48154	−	5.48154i	0.262820	−	0.262820i
$436$	−4.17775	+	15.5916i	−0.200078	+	0.746701i
$437$	2.04753	+	7.64149i	0.0979467	+	0.365542i
$438$	−0.156369	+	0.270839i	−0.00747161	+	0.0129412i
$439$	−15.6253	−	27.0638i	−0.745755	−	1.29169i	−0.949841	−	0.312732i	$-0.898756\pi$
$439$	−15.6253	−	27.0638i	−0.745755	−	1.29169i	0.204087	−	0.978953i	$-0.434578\pi$
$440$	10.9438	−	10.9438i	0.521725	−	0.521725i
$441$		0			0
$442$	−1.12435	−	0.687051i	−0.0534797	−	0.0326797i
$443$	12.3867	+	21.4544i	0.588510	+	1.01933i	0.994428	+	0.105420i	$0.0336186\pi$
$443$	12.3867	+	21.4544i	0.588510	+	1.01933i	−0.405918	+	0.913910i	$0.633048\pi$
$444$	−23.2058	+	6.21797i	−1.10130	+	0.295092i
$445$	11.8692	−	20.5581i	0.562656	−	0.974549i
$446$	−4.99844	−	8.65756i	−0.236683	−	0.409947i
$447$	6.98376	+	6.98376i	0.330321	+	0.330321i
$448$		0			0
$449$	7.07560	+	7.07560i	0.333918	+	0.333918i	0.854072	−	0.520154i	$-0.174126\pi$
$449$	7.07560	+	7.07560i	0.333918	+	0.333918i	−0.520154	+	0.854072i	$0.674126\pi$
$450$	0.0533721	−	0.199188i	0.00251599	−	0.00938979i
$451$	20.8648	+	12.0463i	0.982485	+	0.567238i
$452$	−14.3557	−	8.28828i	−0.675236	−	0.389848i
$453$	10.3970	+	2.78587i	0.488495	+	0.130892i
$454$	−11.2562			−0.528278
$455$		0			0
$456$	11.4379			0.535631
$457$	20.2407	+	5.42349i	0.946821	+	0.253700i	0.699013	−	0.715109i	$-0.253623\pi$
$457$	20.2407	+	5.42349i	0.946821	+	0.253700i	0.247808	+	0.968809i	$0.420290\pi$
$458$	2.98043	+	1.72075i	0.139266	+	0.0804055i
$459$	−2.36642	−	1.36625i	−0.110455	−	0.0637713i
$460$	2.14367	−	8.00030i	0.0999494	−	0.373016i
$461$	−8.07954	−	8.07954i	−0.376302	−	0.376302i	0.493464	−	0.869766i	$-0.335730\pi$
$461$	−8.07954	−	8.07954i	−0.376302	−	0.376302i	−0.869766	+	0.493464i	$0.835730\pi$
$462$		0			0
$463$	−0.417027	−	0.417027i	−0.0193809	−	0.0193809i	0.697350	−	0.716731i	$-0.254362\pi$
$463$	−0.417027	−	0.417027i	−0.0193809	−	0.0193809i	−0.716731	+	0.697350i	$0.754362\pi$
$464$	−1.40133	−	2.42717i	−0.0650549	−	0.112678i
$465$	5.15490	−	8.92856i	0.239053	−	0.414052i
$466$	2.20153	−	0.589898i	0.101984	−	0.0273265i
$467$	2.80499	+	4.85839i	0.129800	+	0.224819i	0.923599	−	0.383360i	$-0.125233\pi$
$467$	2.80499	+	4.85839i	0.129800	+	0.224819i	−0.793799	+	0.608180i	$0.791900\pi$
$468$	−1.19576	+	0.288671i	−0.0552738	+	0.0133438i
$469$		0			0
$470$	−10.9930	+	10.9930i	−0.507069	+	0.507069i
$471$	5.33267	+	9.23646i	0.245716	+	0.425593i
$472$	−4.85484	+	8.40883i	−0.223462	+	0.387048i
$473$	10.3816	+	38.7448i	0.477349	+	1.78149i
$474$	−1.72429	+	6.43515i	−0.0791994	+	0.295576i
$475$	2.41950	−	2.41950i	0.111014	−	0.111014i
$476$		0			0
$477$	1.57567			0.0721452
$478$	6.62402	−	3.82438i	0.302976	−	0.174923i
$479$	3.70453	+	13.8255i	0.169264	+	0.631703i	0.997458	+	0.0712606i	$0.0227022\pi$
$479$	3.70453	+	13.8255i	0.169264	+	0.631703i	−0.828193	+	0.560442i	$0.810631\pi$
$480$	−16.3256	−	9.42556i	−0.745156	−	0.430216i
$481$	−35.0822	−	0.874387i	−1.59961	−	0.0398686i
$482$			1.40992i			0.0642201i
$483$		0			0
$484$	1.22066			0.0554844
$485$	−16.7208	+	9.65378i	−0.759254	+	0.438356i
$486$	1.65648	−	0.443853i	0.0751396	−	0.0201336i
$487$	−4.08170	−	15.2331i	−0.184959	−	0.690278i	−0.994639	−	0.103406i	$-0.967026\pi$
$487$	−4.08170	−	15.2331i	−0.184959	−	0.690278i	0.809680	−	0.586872i	$-0.199641\pi$
$488$	−15.4101	−	4.12913i	−0.697583	−	0.186917i
$489$	−0.805334	+	0.805334i	−0.0364185	+	0.0364185i
$490$		0			0
$491$		−	25.0495i		−	1.13047i	−0.824930	−	0.565234i	$-0.808786\pi$
$491$		−	25.0495i		−	1.13047i	0.824930	−	0.565234i	$-0.191214\pi$
$492$	4.82473	−	18.0062i	0.217516	−	0.811780i
$493$	0.611038	−	1.05835i	0.0275198	−	0.0476656i
$494$	6.82367	+	2.01191i	0.307011	+	0.0905199i
$495$	1.23125	−	0.710860i	0.0553404	−	0.0319508i
$496$	−2.63564	−	2.63564i	−0.118344	−	0.118344i
$497$		0			0
$498$		−	9.91961i		−	0.444509i
$499$	−22.6437	−	6.06736i	−1.01367	−	0.271612i	−0.286508	−	0.958078i	$-0.592495\pi$
$499$	−22.6437	−	6.06736i	−1.01367	−	0.271612i	−0.727162	+	0.686466i	$0.759161\pi$
$500$	−17.3368	+	4.64537i	−0.775324	+	0.207747i
$501$	5.62704	−	1.50776i	0.251398	−	0.0673618i
$502$	−1.14001	−	0.305465i	−0.0508812	−	0.0136336i
$503$		−	0.879009i		−	0.0391931i	−0.999808	−	0.0195965i	$-0.993762\pi$
$503$		−	0.879009i		−	0.0391931i	0.999808	−	0.0195965i	$-0.00623817\pi$
$504$		0			0
$505$	6.46516	+	6.46516i	0.287696	+	0.287696i
$506$	5.72594	−	3.30587i	0.254549	−	0.146964i
$507$	21.6093	+	1.07785i	0.959702	+	0.0478689i
$508$	10.9350	−	18.9400i	0.485162	−	0.840325i
$509$	2.58398	−	9.64356i	0.114533	−	0.427443i	−0.884719	−	0.466126i	$-0.845649\pi$
$509$	2.58398	−	9.64356i	0.114533	−	0.427443i	0.999252	+	0.0386826i	$0.0123161\pi$
$510$		−	1.17832i		−	0.0521769i
$511$		0			0
$512$	−8.94753	+	8.94753i	−0.395429	+	0.395429i
$513$	14.2504	+	3.81837i	0.629169	+	0.168585i
$514$	4.06099	+	15.1558i	0.179122	+	0.668494i
$515$	8.34491	−	2.23601i	0.367721	−	0.0985305i
$516$	26.8778	−	15.5179i	1.18323	−	0.683138i
$517$	35.6065			1.56597
$518$		0			0
$519$			41.2284i			1.80973i
$520$	−12.0569	−	12.6732i	−0.528728	−	0.555758i
$521$	13.4841	+	7.78505i	0.590749	+	0.341069i	0.765394	−	0.643562i	$-0.222544\pi$
$521$	13.4841	+	7.78505i	0.590749	+	0.341069i	−0.174644	+	0.984632i	$0.555878\pi$
$522$	0.102918	+	0.384097i	0.00450462	+	0.0168115i
$523$	−11.1498	+	6.43737i	−0.487549	+	0.281486i	−0.723557	−	0.690265i	$-0.757494\pi$
$523$	−11.1498	+	6.43737i	−0.487549	+	0.281486i	0.236008	+	0.971751i	$0.424161\pi$
$524$	29.9806			1.30971
$525$		0			0
$526$	−8.47314	+	8.47314i	−0.369447	+	0.369447i
$527$	0.420656	−	1.56991i	0.0183241	−	0.0683864i
$528$	1.60188	+	5.97829i	0.0697128	+	0.260172i
$529$	−7.34506	+	12.7220i	−0.319351	+	0.553131i
$530$	4.77025	+	8.26232i	0.207206	+	0.358892i
$531$	−0.630697	+	0.630697i	−0.0273699	+	0.0273699i
$532$		0			0
$533$	14.1983	−	23.2353i	0.614997	−	1.00643i
$534$	−7.33112	−	12.6979i	−0.317248	−	0.549490i
$535$	−36.1359	+	9.68260i	−1.56229	+	0.418615i
$536$	−8.50727	+	14.7350i	−0.367458	+	0.636456i
$537$	15.9686	+	27.6583i	0.689094	+	1.19355i
$538$	−8.60403	−	8.60403i	−0.370946	−	0.370946i
$539$		0			0
$540$	−10.9218	−	10.9218i	−0.470000	−	0.470000i
$541$	−4.11014	+	15.3392i	−0.176709	+	0.659485i	0.819546	+	0.573014i	$0.194226\pi$
$541$	−4.11014	+	15.3392i	−0.176709	+	0.659485i	−0.996254	+	0.0864715i	$0.972441\pi$
$542$	8.65161	+	4.99501i	0.371618	+	0.214554i
$543$	15.9164	+	9.18935i	0.683039	+	0.394353i
$544$	−2.87053	−	0.769155i	−0.123073	−	0.0329772i
$545$	−21.0853			−0.903197
$546$		0			0
$547$	29.5180			1.26210			0.631048	−	0.775743i	$-0.282625\pi$
$547$	29.5180			1.26210			0.631048	+	0.775743i	$0.282625\pi$
$548$	−12.1383	−	3.25245i	−0.518524	−	0.138938i
$549$	−1.26918	−	0.732762i	−0.0541673	−	0.0312735i
$550$	−2.47658	−	1.42985i	−0.105602	−	0.0609692i
$551$	−1.70771	+	6.37327i	−0.0727510	+	0.271510i
$552$	−8.49558	−	8.49558i	−0.361596	−	0.361596i
$553$		0			0
$554$	9.98454	+	9.98454i	0.424203	+	0.424203i
$555$	−15.6912	−	27.1780i	−0.666055	−	1.15364i
$556$	−1.80134	+	3.12002i	−0.0763940	+	0.132318i
$557$	1.96111	−	0.525477i	0.0830947	−	0.0222652i	−0.217032	−	0.976164i	$-0.569638\pi$
$557$	1.96111	−	0.525477i	0.0830947	−	0.0222652i	0.300127	+	0.953899i	$0.402971\pi$
$558$	0.264423	+	0.457995i	0.0111939	+	0.0193885i
$559$	44.0689	−	10.6388i	1.86392	−	0.449974i
$560$		0			0
$561$	−1.90830	+	1.90830i	−0.0805686	+	0.0805686i
$562$	−8.74440	−	15.1457i	−0.368860	−	0.638885i
$563$	11.9044	−	20.6190i	0.501711	−	0.868988i	−0.498287	−	0.867012i	$-0.666038\pi$
$563$	11.9044	−	20.6190i	0.501711	−	0.868988i	0.999998	−	0.00197638i	$-0.000629102\pi$
$564$	−7.13048	−	26.6113i	−0.300247	−	1.12054i
$565$	5.60434	−	20.9157i	0.235777	−	0.879930i
$566$	5.99639	−	5.99639i	0.252047	−	0.252047i
$567$		0			0
$568$	6.74629			0.283068
$569$	19.7784	−	11.4191i	0.829154	−	0.478712i	−0.0244092	−	0.999702i	$-0.507770\pi$
$569$	19.7784	−	11.4191i	0.829154	−	0.478712i	0.853563	+	0.520990i	$0.174437\pi$
$570$	1.64657	+	6.14508i	0.0689672	+	0.257389i
$571$	14.3799	+	8.30223i	0.601779	+	0.347437i	0.769741	−	0.638356i	$-0.220385\pi$
$571$	14.3799	+	8.30223i	0.601779	+	0.347437i	−0.167962	+	0.985793i	$0.553719\pi$
$572$	−0.425038	+	17.0534i	−0.0177717	+	0.713039i
$573$			18.9111i			0.790021i
$574$		0			0
$575$	−3.59418			−0.149888
$576$	0.372961	−	0.215329i	0.0155401	−	0.00897206i
$577$	23.7838	−	6.37286i	0.990134	−	0.265306i	0.272827	−	0.962063i	$-0.412041\pi$
$577$	23.7838	−	6.37286i	0.990134	−	0.265306i	0.717307	+	0.696757i	$0.245375\pi$
$578$	3.11533	+	11.6266i	0.129581	+	0.483602i
$579$	−20.0529	−	5.37316i	−0.833371	−	0.223301i
$580$	4.88463	−	4.88463i	0.202823	−	0.202823i
$581$		0			0
$582$			11.9254i			0.494325i
$583$	5.65543	−	21.1064i	0.234224	−	0.874136i
$584$	−0.327249	+	0.566812i	−0.0135417	+	0.0234548i
$585$	−0.768506	−	1.41116i	−0.0317738	−	0.0583445i
$586$	16.3340	−	9.43043i	0.674751	−	0.389567i
$587$	−30.7522	−	30.7522i	−1.26928	−	1.26928i	−0.946461	−	0.322819i	$-0.895369\pi$
$587$	−30.7522	−	30.7522i	−1.26928	−	1.26928i	−0.322819	−	0.946461i	$-0.604631\pi$
$588$		0			0
$589$			8.77508i			0.361571i
$590$	−5.21657	−	1.39777i	−0.214763	−	0.0575455i
$591$	31.6796	−	8.48851i	1.30312	−	0.349171i
$592$	−10.9593	+	2.93653i	−0.450423	+	0.120690i
$593$	−9.51478	−	2.54948i	−0.390725	−	0.104694i	0.0581076	−	0.998310i	$-0.481493\pi$
$593$	−9.51478	−	2.54948i	−0.390725	−	0.104694i	−0.448833	+	0.893616i	$0.648160\pi$
$594$		−	12.3300i		−	0.505907i
$595$		0			0
$596$	6.22327	+	6.22327i	0.254915	+	0.254915i
$597$	−1.19269	+	0.688599i	−0.0488135	+	0.0281825i
$598$	−3.57396	−	6.56266i	−0.146150	−	0.268367i
$599$	20.3493	−	35.2461i	0.831452	−	1.44012i	−0.0654350	−	0.997857i	$-0.520844\pi$
$599$	20.3493	−	35.2461i	0.831452	−	1.44012i	0.896887	−	0.442260i	$-0.145823\pi$
$600$	−1.34496	+	5.01946i	−0.0549078	+	0.204919i
$601$		−	10.7311i		−	0.437731i	−0.975755	−	0.218865i	$-0.929764\pi$
$601$		−	10.7311i		−	0.437731i	0.975755	−	0.218865i	$-0.0702356\pi$
$602$		0			0
$603$	−1.10519	+	1.10519i	−0.0450068	+	0.0450068i
$604$	9.26484	+	2.48251i	0.376981	+	0.101012i
$605$	0.412690	+	1.54018i	0.0167782	+	0.0626173i
$606$	5.45488	−	1.46163i	0.221589	−	0.0593747i
$607$	10.0602	−	5.80826i	0.408331	−	0.235750i	−0.281742	−	0.959490i	$-0.590912\pi$
$607$	10.0602	−	5.80826i	0.408331	−	0.235750i	0.690072	+	0.723741i	$0.257579\pi$
$608$	16.0449			0.650708
$609$		0			0
$610$		−	8.87356i		−	0.359280i
$611$	1.00271	−	40.2307i	0.0405652	−	1.62756i
$612$	−0.150182	−	0.0867077i	−0.00607076	−	0.00350495i
$613$	5.19678	+	19.3947i	0.209896	+	0.783343i	0.987901	+	0.155085i	$0.0495651\pi$
$613$	5.19678	+	19.3947i	0.209896	+	0.783343i	−0.778005	+	0.628258i	$0.783768\pi$
$614$	1.13777	−	0.656892i	0.0459167	−	0.0265100i
$615$	24.3507			0.981915
$616$		0			0
$617$	−2.09240	+	2.09240i	−0.0842369	+	0.0842369i	−0.747970	−	0.663733i	$-0.768971\pi$
$617$	−2.09240	+	2.09240i	−0.0842369	+	0.0842369i	0.663733	+	0.747970i	$0.268971\pi$
$618$	1.38109	−	5.15429i	0.0555555	−	0.207336i
$619$	−9.21770	−	34.4009i	−0.370491	−	1.38269i	−0.859823	−	0.510593i	$-0.829426\pi$
$619$	−9.21770	−	34.4009i	−0.370491	−	1.38269i	0.489332	−	0.872098i	$-0.337241\pi$
$620$	4.59356	−	7.95628i	0.184482	−	0.319532i
$621$	−7.74840	−	13.4206i	−0.310933	−	0.538551i
$622$	−1.38088	+	1.38088i	−0.0553681	+	0.0553681i
$623$		0			0
$624$	6.79979	−	1.64156i	0.272210	−	0.0657149i
$625$	−8.60568	−	14.9055i	−0.344227	−	0.596219i
$626$	17.6535	−	4.73025i	0.705578	−	0.189059i
$627$	7.28539	−	12.6187i	0.290950	−	0.503941i
$628$	4.75197	+	8.23065i	0.189624	+	0.328439i
$629$	−3.49826	−	3.49826i	−0.139485	−	0.139485i
$630$		0			0
$631$	9.03483	+	9.03483i	0.359671	+	0.359671i	0.863692	−	0.504021i	$-0.168146\pi$
$631$	9.03483	+	9.03483i	0.359671	+	0.359671i	−0.504021	+	0.863692i	$0.668146\pi$
$632$	−3.60859	+	13.4675i	−0.143542	+	0.535707i
$633$	−27.1755	−	15.6898i	−1.08013	−	0.623613i
$634$	−18.9303	−	10.9294i	−0.751817	−	0.434062i
$635$	27.5948	+	7.39399i	1.09506	+	0.293422i
$636$	−16.9069			−0.670401
$637$		0			0
$638$	5.51443			0.218318
$639$	0.598604	+	0.160396i	0.0236804	+	0.00634515i
$640$	−17.3601	−	10.0228i	−0.686217	−	0.396187i
$641$	−15.8985	−	9.17899i	−0.627952	−	0.362548i	0.152007	−	0.988379i	$-0.451426\pi$
$641$	−15.8985	−	9.17899i	−0.627952	−	0.362548i	−0.779958	+	0.625831i	$0.784760\pi$
$642$	−5.98052	+	22.3196i	−0.236032	+	0.880884i
$643$	−29.9544	−	29.9544i	−1.18129	−	1.18129i	−0.979412	−	0.201874i	$-0.935297\pi$
$643$	−29.9544	−	29.9544i	−1.18129	−	1.18129i	−0.201874	−	0.979412i	$-0.564703\pi$
$644$		0			0
$645$	28.6670	+	28.6670i	1.12876	+	1.12876i
$646$	0.501458	+	0.868551i	0.0197296	+	0.0341727i
$647$	−9.86908	+	17.0937i	−0.387993	+	0.672024i	−0.992180	−	0.124819i	$-0.960165\pi$
$647$	−9.86908	+	17.0937i	−0.387993	+	0.672024i	0.604186	+	0.796843i	$0.293498\pi$
$648$	−19.9728	+	5.35168i	−0.784604	+	0.210234i
$649$	6.18457	+	10.7120i	0.242766	+	0.420482i
$650$	−1.68529	+	2.75795i	−0.0661025	+	0.108176i
$651$		0			0
$652$	−0.717637	+	0.717637i	−0.0281049	+	0.0281049i
$653$	0.0419432	+	0.0726478i	0.00164136	+	0.00284293i	0.866845	−	0.498578i	$-0.166144\pi$
$653$	0.0419432	+	0.0726478i	0.00164136	+	0.00284293i	−0.865204	+	0.501421i	$0.832811\pi$
$654$	−6.51175	+	11.2787i	−0.254630	+	0.441031i
$655$	10.1361	+	37.8285i	0.396051	+	1.47808i
$656$	2.27855	−	8.50367i	0.0889625	−	0.332013i
$657$	−0.0425133	+	0.0425133i	−0.00165860	+	0.00165860i
$658$		0			0
$659$	40.2054			1.56618			0.783089	−	0.621909i	$-0.213643\pi$
$659$	40.2054			1.56618			0.783089	+	0.621909i	$0.213643\pi$
$660$	−13.2112	+	7.62747i	−0.514244	+	0.296899i
$661$	−6.89030	−	25.7149i	−0.268001	−	1.00020i	−0.960388	−	0.278668i	$-0.910107\pi$
$661$	−6.89030	−	25.7149i	−0.268001	−	1.00020i	0.692386	−	0.721527i	$-0.256560\pi$
$662$	−1.17872	−	0.680535i	−0.0458123	−	0.0264497i
$663$	2.10239	+	2.20987i	0.0816502	+	0.0858243i
$664$		−	20.7597i		−	0.805634i
$665$		0			0
$666$	1.60978			0.0623776
$667$	6.00218	−	3.46536i	0.232405	−	0.134179i
$668$	5.01428	−	1.34357i	0.194008	−	0.0519844i
$669$	5.98946	+	22.3530i	0.231566	+	0.864215i
$670$	−9.14113	−	2.44936i	−0.353153	−	0.0946270i
$671$	−14.3708	+	14.3708i	−0.554779	+	0.554779i
$672$		0			0
$673$		−	2.18487i		−	0.0842204i	−0.999113	−	0.0421102i	$-0.986592\pi$
$673$		−	2.18487i		−	0.0842204i	0.999113	−	0.0421102i	$-0.0134081\pi$
$674$	2.95247	−	11.0188i	0.113725	−	0.424428i
$675$	−3.35133	+	5.80468i	−0.128993	+	0.223422i
$676$	19.2561	+	0.960475i	0.740621	+	0.0369413i
$677$	3.62597	−	2.09346i	0.139357	−	0.0804580i	−0.428700	−	0.903447i	$-0.641028\pi$
$677$	3.62597	−	2.09346i	0.139357	−	0.0804580i	0.568058	+	0.822989i	$0.307695\pi$
$678$	−9.45716	−	9.45716i	−0.363200	−	0.363200i
$679$		0			0
$680$		−	2.46599i		−	0.0945663i
$681$	25.1687	+	6.74393i	0.964467	+	0.258428i
$682$	7.08397	−	1.89814i	0.271259	−	0.0726837i
$683$	11.4923	−	3.07935i	0.439740	−	0.117828i	−0.0321547	−	0.999483i	$-0.510237\pi$
$683$	11.4923	−	3.07935i	0.439740	−	0.117828i	0.471895	+	0.881655i	$0.343570\pi$
$684$	0.904382	+	0.242328i	0.0345799	+	0.00926566i
$685$		−	16.4153i		−	0.627197i
$686$		0			0
$687$	−5.63326	−	5.63326i	−0.214922	−	0.214922i
$688$	12.6934	−	7.32856i	0.483933	−	0.279399i
$689$	−23.6882	−	6.98427i	−0.902447	−	0.266080i
$690$	3.34129	−	5.78728i	0.127201	−	0.220318i
$691$	−9.70177	+	36.2075i	−0.369073	+	1.37740i	0.492742	+	0.870175i	$0.335995\pi$
$691$	−9.70177	+	36.2075i	−0.369073	+	1.37740i	−0.861815	+	0.507223i	$0.830672\pi$
$692$			36.7388i			1.39660i
$693$		0			0
$694$	−8.23664	+	8.23664i	−0.312659	+	0.312659i
$695$	−4.54574	−	1.21803i	−0.172430	−	0.0462024i
$696$	−2.59351	−	9.67912i	−0.0983068	−	0.366886i
$697$	3.70797	−	0.993546i	0.140449	−	0.0376333i
$698$	−16.4715	+	9.50980i	−0.623454	+	0.359951i
$699$	−5.27603			−0.199558
$700$		0			0
$701$		−	31.0974i		−	1.17453i	−0.809394	−	0.587266i	$-0.800204\pi$
$701$		−	31.0974i		−	1.17453i	0.809394	−	0.587266i	$-0.199796\pi$
$702$	−13.9313	−	0.347223i	−0.525803	−	0.0131051i
$703$	23.1322	+	13.3554i	0.872449	+	0.503709i
$704$	−1.54573	−	5.76873i	−0.0582568	−	0.217417i
$705$	31.1665	−	17.9940i	1.17380	−	0.677692i
$706$	16.4944			0.620776
$707$		0			0
$708$	6.76734	−	6.76734i	0.254332	−	0.254332i
$709$	3.92057	−	14.6318i	0.147240	−	0.549508i	−0.852405	−	0.522882i	$-0.824857\pi$
$709$	3.92057	−	14.6318i	0.147240	−	0.549508i	0.999645	−	0.0266262i	$-0.00847640\pi$
$710$	0.971174	+	3.62447i	0.0364475	+	0.136024i
$711$	−0.640388	+	1.10918i	−0.0240164	+	0.0415977i
$712$	−15.3425	−	26.5741i	−0.574986	−	0.995905i
$713$	6.51773	−	6.51773i	0.244091	−	0.244091i
$714$		0			0
$715$	−21.6611	+	5.22926i	−0.810078	+	0.195563i
$716$	14.2297	+	24.6465i	0.531787	+	0.921082i
$717$	−17.1026	+	4.58262i	−0.638707	+	0.171141i
$718$	2.67834	−	4.63902i	0.0999548	−	0.173127i
$719$	10.7088	+	18.5482i	0.399371	+	0.691732i	0.993648	−	0.112529i	$-0.0358951\pi$
$719$	10.7088	+	18.5482i	0.399371	+	0.691732i	−0.594277	+	0.804260i	$0.702562\pi$
$720$	−0.367348	−	0.367348i	−0.0136903	−	0.0136903i
$721$		0			0
$722$	5.83051	+	5.83051i	0.216989	+	0.216989i
$723$	0.844729	−	3.15257i	0.0314158	−	0.117245i
$724$	14.1832	+	8.18868i	0.527115	+	0.304330i
$725$	−2.59606	−	1.49884i	−0.0964152	−	0.0556654i
$726$	0.951303	+	0.254901i	0.0353062	+	0.00946026i
$727$	39.0080			1.44673			0.723363	−	0.690468i	$-0.242595\pi$
$727$	39.0080			1.44673			0.723363	+	0.690468i	$0.242595\pi$
$728$		0			0
$729$	−28.7407			−1.06447
$730$	−0.351632	−	0.0942194i	−0.0130145	−	0.00348722i
$731$	5.53489	+	3.19557i	0.204715	+	0.118192i
$732$	13.6182	+	7.86249i	0.503344	+	0.290606i
$733$	−0.430322	+	1.60598i	−0.0158943	+	0.0593183i	−0.973418	−	0.229038i	$-0.926442\pi$
$733$	−0.430322	+	1.60598i	−0.0158943	+	0.0593183i	0.957523	+	0.288356i	$0.0931087\pi$
$734$	17.8448	+	17.8448i	0.658663	+	0.658663i
$735$		0			0
$736$	−11.9174	−	11.9174i	−0.439283	−	0.439283i
$737$	10.8374	+	18.7709i	0.399200	+	0.691435i
$738$	−0.624541	+	1.08174i	−0.0229897	+	0.0398193i
$739$	−34.9673	+	9.36946i	−1.28629	+	0.344661i	−0.836251	−	0.548346i	$-0.815258\pi$
$739$	−34.9673	+	9.36946i	−1.28629	+	0.344661i	−0.450042	+	0.893008i	$0.648591\pi$
$740$	−13.9825	−	24.2184i	−0.514007	−	0.890287i
$741$	−14.0523	−	8.58688i	−0.516223	−	0.315447i
$742$		0			0
$743$	−2.82866	+	2.82866i	−0.103773	+	0.103773i	−0.757087	−	0.653314i	$-0.773378\pi$
$743$	−2.82866	+	2.82866i	−0.103773	+	0.103773i	0.653314	+	0.757087i	$0.273378\pi$
$744$	−6.66339	−	11.5413i	−0.244292	−	0.423125i
$745$	−5.74828	+	9.95631i	−0.210601	+	0.364771i
$746$	2.91292	+	10.8712i	0.106650	+	0.398022i
$747$	0.493571	−	1.84203i	0.0180588	−	0.0673964i
$748$	−1.70050	+	1.70050i	−0.0621764	+	0.0621764i
$749$		0			0
$750$	−14.4812			−0.528780
$751$	11.5377	−	6.66132i	0.421018	−	0.243075i	−0.274495	−	0.961589i	$-0.588511\pi$
$751$	11.5377	−	6.66132i	0.421018	−	0.243075i	0.695513	+	0.718514i	$0.255177\pi$
$752$	−3.36747	−	12.5676i	−0.122799	−	0.458293i
$753$	2.36604	+	1.36604i	0.0862234	+	0.0497811i
$754$	0.155291	−	6.23058i	0.00565535	−	0.226904i
$755$			12.5293i			0.455989i
$756$		0			0
$757$	16.0291			0.582587			0.291294	−	0.956634i	$-0.405914\pi$
$757$	16.0291			0.582587			0.291294	+	0.956634i	$0.405914\pi$
$758$	−15.4518	+	8.92110i	−0.561235	+	0.324029i
$759$	−14.7838	+	3.96131i	−0.536618	+	0.143786i
$760$	3.44594	+	12.8604i	0.124997	+	0.466496i
$761$	6.69953	+	1.79513i	0.242858	+	0.0650735i	0.378195	−	0.925726i	$-0.376545\pi$
$761$	6.69953	+	1.79513i	0.242858	+	0.0650735i	−0.135337	+	0.990800i	$0.543212\pi$
$762$	12.4771	−	12.4771i	0.451999	−	0.451999i
$763$		0			0
$764$			16.8517i			0.609675i
$765$	0.0586298	−	0.218809i	0.00211976	−	0.00791107i
$766$	−0.354291	+	0.613650i	−0.0128011	+	0.0221721i
$767$	12.2773	−	6.68609i	0.443308	−	0.241421i
$768$	−16.1192	+	9.30643i	−0.581652	+	0.335817i
$769$	12.5271	+	12.5271i	0.451740	+	0.451740i	0.895932	−	0.444192i	$-0.146509\pi$
$769$	12.5271	+	12.5271i	0.451740	+	0.451740i	−0.444192	+	0.895932i	$0.646509\pi$
$770$		0			0
$771$		−	36.3213i		−	1.30808i
$772$	−17.8692	−	4.78805i	−0.643128	−	0.172326i
$773$	47.2874	−	12.6706i	1.70081	−	0.455730i	0.727665	−	0.685932i	$-0.240605\pi$
$773$	47.2874	−	12.6706i	1.70081	−	0.455730i	0.973143	+	0.230202i	$0.0739387\pi$
$774$	−2.00873	+	0.538236i	−0.0722022	+	0.0193465i
$775$	−3.85089	−	1.03184i	−0.138328	−	0.0370648i
$776$			24.9575i			0.895923i
$777$		0			0
$778$	−2.57073	−	2.57073i	−0.0921650	−	0.0921650i
$779$	−17.9491	+	10.3629i	−0.643093	+	0.371290i
$780$	8.24601	+	15.1417i	0.295255	+	0.542160i
$781$	4.29704	−	7.44269i	0.153760	−	0.266320i
$782$	0.272660	−	1.01758i	0.00975029	−	0.0363886i
$783$		−	12.9249i		−	0.461897i
$784$		0			0
$785$	−8.77855	+	8.77855i	−0.313320	+	0.313320i
$786$	23.3650	+	6.26064i	0.833402	+	0.223310i
$787$	3.75252	+	14.0046i	0.133763	+	0.499210i	1.00000		0.000423598i	$-0.000134835\pi$
$787$	3.75252	+	14.0046i	0.133763	+	0.499210i	−0.866237	+	0.499633i	$0.833468\pi$
$788$	28.2298	−	7.56416i	1.00565	−	0.269462i
$789$	24.0224	−	13.8693i	0.855220	−	0.493762i
$790$	−7.75493			−0.275908
$791$		0			0
$792$		−	1.83776i		−	0.0653019i
$793$	15.8324	+	16.6418i	0.562227	+	0.590969i
$794$	0.724851	+	0.418493i	0.0257240	+	0.0148518i
$795$	−5.71602	−	21.3325i	−0.202726	−	0.756585i
$796$	−1.06281	+	0.613614i	−0.0376703	+	0.0217490i
$797$	−25.6379			−0.908139			−0.454070	−	0.890966i	$-0.650028\pi$
$797$	−25.6379			−0.908139			−0.454070	+	0.890966i	$0.650028\pi$
$798$		0			0
$799$	4.01164	−	4.01164i	0.141922	−	0.141922i
$800$	−1.88669	+	7.04121i	−0.0667044	+	0.248944i
$801$	−0.729549	−	2.72272i	−0.0257774	−	0.0962024i
$802$	0.551367	−	0.954996i	0.0194694	−	0.0337221i
$803$	0.416882	+	0.722060i	0.0147114	+	0.0254810i
$804$	11.8586	−	11.8586i	0.418220	−	0.418220i
$805$		0			0
$806$	−1.94516	−	8.05742i	−0.0685155	−	0.283810i
$807$	14.0836	+	24.3935i	0.495766	+	0.858692i
$808$	11.4160	−	3.05890i	0.401612	−	0.107612i
$809$	19.7540	−	34.2150i	0.694515	−	1.20293i	−0.275829	−	0.961207i	$-0.588952\pi$
$809$	19.7540	−	34.2150i	0.694515	−	1.20293i	0.970344	−	0.241728i	$-0.0777142\pi$
$810$	−5.75043	−	9.96004i	−0.202049	−	0.349960i
$811$	17.7080	+	17.7080i	0.621813	+	0.621813i	0.945995	−	0.324182i	$-0.105089\pi$
$811$	17.7080	+	17.7080i	0.621813	+	0.621813i	−0.324182	+	0.945995i	$0.605089\pi$
$812$		0			0
$813$	−16.3523	−	16.3523i	−0.573498	−	0.573498i
$814$	5.77784	−	21.5632i	0.202513	−	0.755789i
$815$	−1.14811	−	0.662864i	−0.0402167	−	0.0232191i
$816$	0.854027	+	0.493073i	0.0298969	+	0.0172610i
$817$	−33.3305	−	8.93089i	−1.16609	−	0.312452i
$818$	−7.67576			−0.268377
$819$		0			0
$820$	21.6990			0.757763
$821$	−18.9387	−	5.07462i	−0.660966	−	0.177105i	−0.0872842	−	0.996183i	$-0.527819\pi$
$821$	−18.9387	−	5.07462i	−0.660966	−	0.177105i	−0.573682	+	0.819078i	$0.694486\pi$
$822$	−8.78066	−	5.06952i	−0.306261	−	0.176820i
$823$	17.8932	+	10.3306i	0.623717	+	0.360103i	0.778315	−	0.627874i	$-0.216075\pi$
$823$	17.8932	+	10.3306i	0.623717	+	0.360103i	−0.154598	+	0.987978i	$0.549408\pi$
$824$	2.89034	−	10.7869i	0.100690	−	0.375779i
$825$	4.68094	+	4.68094i	0.162969	+	0.162969i
$826$		0			0
$827$	−18.0688	−	18.0688i	−0.628315	−	0.628315i	0.319329	−	0.947644i	$-0.396543\pi$
$827$	−18.0688	−	18.0688i	−0.628315	−	0.628315i	−0.947644	+	0.319329i	$0.896543\pi$
$828$	−0.491743	−	0.851724i	−0.0170893	−	0.0295994i
$829$	−20.2612	+	35.0934i	−0.703700	+	1.21884i	0.263459	+	0.964671i	$0.415137\pi$
$829$	−20.2612	+	35.0934i	−0.703700	+	1.21884i	−0.967159	+	0.254173i	$0.918197\pi$
$830$	11.1533	−	2.98851i	0.387135	−	0.103733i
$831$	−16.3433	−	28.3074i	−0.566942	−	0.981973i
$832$	−6.56144	+	1.58402i	−0.227477	+	0.0549159i
$833$		0			0
$834$	−2.05538	+	2.05538i	−0.0711721	+	0.0711721i
$835$	3.39054	+	5.87259i	0.117335	+	0.203229i
$836$	6.49204	−	11.2446i	0.224532	−	0.388901i
$837$	−4.44892	−	16.6036i	−0.153777	−	0.573905i
$838$	−2.20791	+	8.24004i	−0.0762710	+	0.284647i
$839$	−2.12585	+	2.12585i	−0.0733926	+	0.0733926i	−0.742850	−	0.669458i	$-0.766527\pi$
$839$	−2.12585	+	2.12585i	−0.0733926	+	0.0733926i	0.669458	+	0.742850i	$0.266527\pi$
$840$		0			0
$841$	−23.2195			−0.800674
$842$	2.77582	−	1.60262i	0.0956611	−	0.0552299i
$843$	10.4781	+	39.1048i	0.360885	+	1.34684i
$844$	−24.2162	−	13.9813i	−0.833557	−	0.481255i
$845$	5.29839	+	24.6214i	0.182270	+	0.847003i
$846$			1.84602i			0.0634674i
$847$		0			0
$848$	−7.98452			−0.274189
$849$	−17.0005	+	9.81525i	−0.583456	+	0.336858i
$850$	−0.440123	+	0.117931i	−0.0150961	+	0.00404498i
$851$	−7.26178	−	27.1014i	−0.248931	−	0.929022i
$852$	−6.42298	−	1.72103i	−0.220048	−	0.0589616i
$853$	−38.1991	+	38.1991i	−1.30791	+	1.30791i	−0.384992	+	0.922920i	$0.625796\pi$
$853$	−38.1991	+	38.1991i	−1.30791	+	1.30791i	−0.922920	+	0.384992i	$0.874204\pi$
$854$		0			0
$855$			1.22304i			0.0418273i
$856$	−12.5160	+	46.7104i	−0.427789	+	1.59653i
$857$	10.7700	−	18.6543i	0.367898	−	0.637218i	−0.621339	−	0.783542i	$-0.713411\pi$
$857$	10.7700	−	18.6543i	0.367898	−	0.637218i	0.989237	+	0.146324i	$0.0467443\pi$
$858$	−3.89239	+	13.2016i	−0.132884	+	0.450695i
$859$	−0.937124	+	0.541049i	−0.0319743	+	0.0184603i	−0.515902	−	0.856648i	$-0.672543\pi$
$859$	−0.937124	+	0.541049i	−0.0319743	+	0.0184603i	0.483928	+	0.875108i	$0.339210\pi$
$860$	25.5453	+	25.5453i	0.871089	+	0.871089i
$861$		0			0
$862$			0.878348i			0.0299167i
$863$	3.13385	+	0.839713i	0.106678	+	0.0285842i	0.311763	−	0.950160i	$-0.399081\pi$
$863$	3.13385	+	0.839713i	0.106678	+	0.0285842i	−0.205085	+	0.978744i	$0.565747\pi$
$864$	−30.3591	+	8.13470i	−1.03284	+	0.276748i
$865$	−46.3557	+	12.4210i	−1.57614	+	0.422326i
$866$	12.5939	+	3.37454i	0.427960	+	0.114671i
$867$		−	27.8634i		−	0.946292i
$868$		0			0
$869$	12.5592	+	12.5592i	0.426041	+	0.426041i
$870$	4.82679	−	2.78675i	0.163644	−	0.0944797i
$871$	21.5139	−	11.7162i	0.728969	−	0.396989i
$872$	−13.6278	+	23.6040i	−0.461495	+	0.799332i
$873$	−0.593375	+	2.21450i	−0.0200827	+	0.0749496i
$874$			5.68781i			0.192393i
$875$		0			0
$876$	0.456164	−	0.456164i	0.0154124	−	0.0154124i
$877$	−20.5585	−	5.50863i	−0.694211	−	0.186013i	−0.105575	−	0.994411i	$-0.533668\pi$
$877$	−20.5585	−	5.50863i	−0.694211	−	0.186013i	−0.588636	+	0.808398i	$0.700335\pi$
$878$	−5.81520	−	21.7026i	−0.196254	−	0.732428i
$879$	−42.1727	+	11.3001i	−1.42245	+	0.381144i
$880$	−6.23917	+	3.60219i	−0.210322	+	0.121430i
$881$	−34.2796			−1.15491			−0.577455	−	0.816423i	$-0.695954\pi$
$881$	−34.2796			−1.15491			−0.577455	+	0.816423i	$0.695954\pi$
$882$		0			0
$883$			8.76503i			0.294967i	0.989065	+	0.147483i	$0.0471173\pi$
$883$			8.76503i			0.294967i	−0.989065	+	0.147483i	$0.952883\pi$
$884$	1.87345	+	1.96923i	0.0630110	+	0.0662323i
$885$	10.8267	+	6.25082i	0.363937	+	0.210119i
$886$	4.60991	+	17.2044i	0.154873	+	0.577994i
$887$	7.22277	−	4.17007i	0.242517	−	0.140017i	−0.373816	−	0.927503i	$-0.621951\pi$
$887$	7.22277	−	4.17007i	0.242517	−	0.140017i	0.616333	+	0.787486i	$0.288618\pi$
$888$	−40.5659			−1.36130
$889$		0			0
$890$	12.0684	−	12.0684i	0.404532	−	0.404532i
$891$	−6.81750	+	25.4433i	−0.228395	+	0.852381i
$892$	5.33723	+	19.9188i	0.178704	+	0.666932i
$893$	−15.3154	+	26.5270i	−0.512509	+	0.887692i
$894$	3.55046	+	6.14958i	0.118745	+	0.205673i
$895$	−26.2872	+	26.2872i	−0.878683	+	0.878683i
$896$		0			0
$897$	4.05944	+	16.8153i	0.135541	+	0.561447i
$898$	3.59715	+	6.23045i	0.120038	+	0.207913i
$899$	7.42573	−	1.98972i	0.247662	−	0.0663608i
$900$	−0.212688	+	0.368387i	−0.00708961	+	0.0122796i
$901$	−1.74080	−	3.01515i	−0.0579943	−	0.100449i
$902$	12.2484	+	12.2484i	0.407827	+	0.407827i
$903$		0			0
$904$	−19.7919	−	19.7919i	−0.658269	−	0.658269i
$905$	−5.53700	+	20.6644i	−0.184056	+	0.686906i
$906$	6.70202	+	3.86942i	0.222660	+	0.128553i
$907$	3.67167	+	2.11984i	0.121916	+	0.0703882i	0.559718	−	0.828683i	$-0.310910\pi$
$907$	3.67167	+	2.11984i	0.121916	+	0.0703882i	−0.437802	+	0.899071i	$0.644243\pi$
$908$	22.4280	+	6.00955i	0.744298	+	0.199434i
$909$	1.08567			0.0360096
$910$		0			0
$911$	−1.59871			−0.0529676			−0.0264838	−	0.999649i	$-0.508431\pi$
$911$	−1.59871			−0.0529676			−0.0264838	+	0.999649i	$0.508431\pi$
$912$	−5.14287	−	1.37803i	−0.170297	−	0.0456310i
$913$	−22.9027	−	13.2229i	−0.757970	−	0.437614i
$914$	13.0474	+	7.53291i	0.431569	+	0.249166i
$915$	−5.31643	+	19.8412i	−0.175756	+	0.655930i
$916$	−5.01982	−	5.01982i	−0.165860	−	0.165860i
$917$		0			0
$918$	−1.38917	−	1.38917i	−0.0458496	−	0.0458496i
$919$	6.09990	+	10.5653i	0.201217	+	0.348518i	0.948921	−	0.315514i	$-0.102177\pi$
$919$	6.09990	+	10.5653i	0.201217	+	0.348518i	−0.747704	+	0.664032i	$0.768844\pi$
$920$	6.99264	−	12.1116i	0.230541	−	0.399308i
$921$	−2.93761	+	0.787131i	−0.0967976	+	0.0259368i
$922$	−4.10754	−	7.11447i	−0.135275	−	0.234303i
$923$	−8.28826	−	5.06469i	−0.272811	−	0.166706i
$924$		0			0
$925$	−8.58099	+	8.58099i	−0.282141	+	0.282141i
$926$	−0.212012	−	0.367215i	−0.00696714	−	0.0120674i
$927$	0.512925	−	0.888411i	0.0168467	−	0.0291793i
$928$	−3.63813	−	13.5777i	−0.119427	−	0.445709i
$929$	0.158183	−	0.590349i	0.00518983	−	0.0193687i	−0.963282	−	0.268490i	$-0.913475\pi$
$929$	0.158183	−	0.590349i	0.00518983	−	0.0193687i	0.968472	+	0.249122i	$0.0801419\pi$
$930$	5.24138	−	5.24138i	0.171872	−	0.171872i
$931$		0			0
$932$	−4.70149			−0.154002
$933$	3.91496	−	2.26030i	0.128170	−	0.0739989i
$934$	1.04392	+	3.89597i	0.0341582	+	0.127480i
$935$	−2.72055	−	1.57071i	−0.0889714	−	0.0513677i
$936$	−2.07643	−	0.0517527i	−0.0678701	−	0.00169159i
$937$		−	5.03265i		−	0.164410i	−0.996615	−	0.0822048i	$-0.973804\pi$
$937$		−	5.03265i		−	0.164410i	0.996615	−	0.0822048i	$-0.0261961\pi$
$938$		0			0
$939$	−42.3072			−1.38064
$940$	27.7726	−	16.0345i	0.905842	−	0.522988i
$941$	−46.5400	+	12.4703i	−1.51716	+	0.406522i	−0.918805	−	0.394711i	$-0.870845\pi$
$941$	−46.5400	+	12.4703i	−1.51716	+	0.406522i	−0.598354	+	0.801232i	$0.704178\pi$
$942$	1.98464	+	7.40677i	0.0646630	+	0.241326i
$943$	21.0289	+	5.63467i	0.684794	+	0.183490i
$944$	3.19597	−	3.19597i	0.104020	−	0.104020i
$945$		0			0
$946$			28.8390i			0.937637i
$947$	3.00627	−	11.2196i	0.0976907	−	0.364586i	−0.899723	−	0.436461i	$-0.856232\pi$
$947$	3.00627	−	11.2196i	0.0976907	−	0.364586i	0.997414	+	0.0718749i	$0.0228982\pi$
$948$	6.87132	−	11.9015i	0.223170	−	0.386542i
$949$	0.827573	−	0.450688i	0.0268642	−	0.0146299i
$950$	2.13050	−	1.23004i	0.0691224	−	0.0399079i
$951$	35.7798	+	35.7798i	1.16024	+	1.16024i
$952$		0			0
$953$			12.7370i			0.412592i	0.978490	+	0.206296i	$0.0661409\pi$
$953$			12.7370i			0.412592i	−0.978490	+	0.206296i	$0.933859\pi$
$954$	1.09426	+	0.293206i	0.0354280	+	0.00949290i
$955$	−21.2629	+	5.69738i	−0.688052	+	0.184363i
$956$	−15.2402	+	4.08359i	−0.492903	+	0.132073i
$957$	−12.3302	−	3.30387i	−0.398579	−	0.106799i
$958$			10.2908i			0.332479i
$959$		0			0
$960$	−4.26825	−	4.26825i	−0.137757	−	0.137757i
$961$	−17.9924	+	10.3879i	−0.580400	+	0.335094i
$962$	−24.2009	−	7.13543i	−0.780267	−	0.230056i
$963$	−2.22112	+	3.84708i	−0.0715744	+	0.123971i
$964$	0.752742	−	2.80927i	0.0242442	−	0.0904805i
$965$		−	24.1656i		−	0.777917i
$966$		0			0
$967$	1.70551	−	1.70551i	0.0548455	−	0.0548455i	−0.679152	−	0.733998i	$-0.737652\pi$
$967$	1.70551	−	1.70551i	0.0548455	−	0.0548455i	0.733998	+	0.679152i	$0.237652\pi$
$968$	1.99088	+	0.533456i	0.0639895	+	0.0171459i
$969$	−0.600879	−	2.24251i	−0.0193030	−	0.0720398i
$970$	−13.4085	+	3.59281i	−0.430522	+	0.115358i
$971$	−21.9961	+	12.6994i	−0.705887	+	0.407544i	−0.809536	−	0.587070i	$-0.800281\pi$
$971$	−21.9961	+	12.6994i	−0.705887	+	0.407544i	0.103649	+	0.994614i	$0.466948\pi$
$972$	−3.53752			−0.113466
$973$		0			0
$974$		−	11.3385i		−	0.363309i
$975$	5.42067	−	5.15703i	0.173600	−	0.165157i
$976$	6.43141	+	3.71317i	0.205864	+	0.118856i
$977$	5.56490	+	20.7685i	0.178037	+	0.664443i	0.996014	+	0.0891927i	$0.0284287\pi$
$977$	5.56490	+	20.7685i	0.178037	+	0.664443i	−0.817977	+	0.575250i	$0.804905\pi$
$978$	−0.709140	+	0.409422i	−0.0226758	+	0.0130919i
$979$	−39.0897			−1.24931
$980$		0			0
$981$	−1.77040	+	1.77040i	−0.0565245	+	0.0565245i
$982$	4.66129	−	17.3962i	0.148748	−	0.555134i
$983$	−9.29397	−	34.6856i	−0.296431	−	1.10630i	−0.940074	−	0.340971i	$-0.889244\pi$
$983$	−9.29397	−	34.6856i	−0.296431	−	1.10630i	0.643642	−	0.765326i	$-0.277422\pi$
$984$	15.7382	−	27.2594i	0.501716	−	0.868998i
$985$	19.0884	+	33.0620i	0.608206	+	1.05344i
$986$	0.621289	−	0.621289i	0.0197859	−	0.0197859i
$987$		0			0
$988$	−12.5220	−	7.65181i	−0.398379	−	0.243437i
$989$	18.1229	+	31.3898i	0.576276	+	0.998139i
$990$	0.987343	−	0.264558i	0.0313798	−	0.00840820i
$991$	−21.3172	+	36.9225i	−0.677164	+	1.17288i	0.298668	+	0.954357i	$0.403458\pi$
$991$	−21.3172	+	36.9225i	−0.677164	+	1.17288i	−0.975831	+	0.218525i	$0.929876\pi$
$992$	−9.34727	−	16.1899i	−0.296776	−	0.514031i
$993$	2.22788	+	2.22788i	0.0706996	+	0.0706996i
$994$		0			0
$995$	−1.13356	−	1.13356i	−0.0359363	−	0.0359363i
$996$	−5.29598	+	19.7649i	−0.167810	+	0.626274i
$997$	−49.9716	−	28.8511i	−1.58262	−	0.913724i	−0.994476	−	0.104966i	$-0.966527\pi$
$997$	−49.9716	−	28.8511i	−1.58262	−	0.913724i	−0.588141	−	0.808759i	$-0.700140\pi$
$998$	−14.5964	−	8.42721i	−0.462039	−	0.266759i
$999$	−50.5404	−	13.5422i	−1.59903	−	0.428458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.b.31.5		32
7.2	even	3		91.2.bb.a.5.4	✓	32
7.3	odd	6		637.2.i.a.538.7		32
7.4	even	3		637.2.i.a.538.8		32
7.5	odd	6	inner	637.2.bc.b.460.4		32
7.6	odd	2		91.2.bb.a.31.5	yes	32
13.8	odd	4	inner	637.2.bc.b.619.4		32
21.2	odd	6		819.2.fn.e.460.5		32
21.20	even	2		819.2.fn.e.577.4		32
91.34	even	4		91.2.bb.a.73.4	yes	32
91.47	even	12	inner	637.2.bc.b.411.5		32
91.60	odd	12		637.2.i.a.489.8		32
91.73	even	12		637.2.i.a.489.7		32
91.86	odd	12		91.2.bb.a.47.5	yes	32
273.86	even	12		819.2.fn.e.775.4		32
273.125	odd	4		819.2.fn.e.73.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.4	✓	32	7.2	even	3
91.2.bb.a.31.5	yes	32	7.6	odd	2
91.2.bb.a.47.5	yes	32	91.86	odd	12
91.2.bb.a.73.4	yes	32	91.34	even	4
637.2.i.a.489.7		32	91.73	even	12
637.2.i.a.489.8		32	91.60	odd	12
637.2.i.a.538.7		32	7.3	odd	6
637.2.i.a.538.8		32	7.4	even	3
637.2.bc.b.31.5		32	1.1	even	1	trivial
637.2.bc.b.411.5		32	91.47	even	12	inner
637.2.bc.b.460.4		32	7.5	odd	6	inner
637.2.bc.b.619.4		32	13.8	odd	4	inner
819.2.fn.e.73.5		32	273.125	odd	4
819.2.fn.e.460.5		32	21.2	odd	6
819.2.fn.e.577.4		32	21.20	even	2
819.2.fn.e.775.4		32	273.86	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.694471 + 0.186083i) q^{2} +(-1.44134 - 0.832160i) q^{3} +(-1.28439 - 0.741542i) q^{4} +(0.501414 - 1.87130i) q^{5} +(-0.846120 - 0.846120i) q^{6} +(-1.77076 - 1.77076i) q^{8} +(-0.115021 - 0.199221i) q^{9} +O(q^{10})\)	\(q+(0.694471 + 0.186083i) q^{2} +(-1.44134 - 0.832160i) q^{3} +(-1.28439 - 0.741542i) q^{4} +(0.501414 - 1.87130i) q^{5} +(-0.846120 - 0.846120i) q^{6} +(-1.77076 - 1.77076i) q^{8} +(-0.115021 - 0.199221i) q^{9} +(0.696434 - 1.20626i) q^{10} +(-3.08143 + 0.825667i) q^{11} +(1.23416 + 2.13763i) q^{12} +(0.846120 + 3.50487i) q^{13} +(-2.27993 + 2.27993i) q^{15} +(0.582851 + 1.00953i) q^{16} +(-0.254148 + 0.440197i) q^{17} +(-0.0428067 - 0.159757i) q^{18} +(0.710286 - 2.65082i) q^{19} +(-2.03166 + 2.03166i) q^{20} -2.29361 q^{22} +(-2.49648 + 1.44134i) q^{23} +(1.07872 + 4.02582i) q^{24} +(1.07978 + 0.623409i) q^{25} +(-0.0645898 + 2.59148i) q^{26} +5.37582i q^{27} -2.40426 q^{29} +(-2.00760 + 1.15909i) q^{30} +(-3.08857 + 0.827581i) q^{31} +(1.51320 + 5.64735i) q^{32} +(5.12849 + 1.37417i) q^{33} +(-0.258412 + 0.258412i) q^{34} +0.341170i q^{36} +(-2.51910 + 9.40142i) q^{37} +(0.986546 - 1.70875i) q^{38} +(1.69706 - 5.75582i) q^{39} +(-4.20150 + 2.42574i) q^{40} +(-5.34023 - 5.34023i) q^{41} -12.5736i q^{43} +(4.57002 + 1.22453i) q^{44} +(-0.430476 + 0.115346i) q^{45} +(-2.00194 + 0.536419i) q^{46} +(-10.7811 - 2.88879i) q^{47} -1.94010i q^{48} +(0.633867 + 0.633867i) q^{50} +(0.732629 - 0.422984i) q^{51} +(1.51226 - 5.12904i) q^{52} +(-3.42477 + 5.93187i) q^{53} +(-1.00035 + 3.73335i) q^{54} +6.18029i q^{55} +(-3.22968 + 3.22968i) q^{57} +(-1.66969 - 0.447392i) q^{58} +(-1.00352 - 3.74520i) q^{59} +(4.61898 - 1.23765i) q^{60} +(5.51719 - 3.18535i) q^{61} -2.29892 q^{62} +1.87209i q^{64} +(6.98291 + 0.174042i) q^{65} +(3.30587 + 1.90865i) q^{66} +(-1.75850 - 6.56281i) q^{67} +(0.652849 - 0.376923i) q^{68} +4.79771 q^{69} +(-1.90492 + 1.90492i) q^{71} +(-0.149099 + 0.556446i) q^{72} +(-0.0676442 - 0.252451i) q^{73} +(-3.49889 + 6.06025i) q^{74} +(-1.03755 - 1.79709i) q^{75} +(-2.87798 + 2.87798i) q^{76} +(2.24962 - 3.68146i) q^{78} +(-2.78380 - 4.82168i) q^{79} +(2.18138 - 0.584499i) q^{80} +(4.12848 - 7.15074i) q^{81} +(-2.71491 - 4.70236i) q^{82} +(5.86182 + 5.86182i) q^{83} +(0.696309 + 0.696309i) q^{85} +(2.33974 - 8.73203i) q^{86} +(3.46536 + 2.00073i) q^{87} +(6.91853 + 3.99441i) q^{88} +(11.8358 + 3.17139i) q^{89} -0.320417 q^{90} +4.27526 q^{92} +(5.14037 + 1.37736i) q^{93} +(-6.94962 - 4.01237i) q^{94} +(-4.60434 - 2.65832i) q^{95} +(2.51845 - 9.39899i) q^{96} +(-7.04713 - 7.04713i) q^{97} +(0.518918 + 0.518918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9	\( 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9} - 10 q^{11} - 44 q^{15} + 12 q^{16} - 4 q^{18} - 12 q^{19} - 8 q^{22} + 12 q^{24} - 24 q^{26} + 16 q^{29} - 24 q^{31} + 4 q^{32} - 48 q^{33} - 8 q^{37} - 6 q^{39} + 132 q^{40} - 42 q^{44} + 24 q^{45} + 12 q^{46} - 30 q^{47} + 88 q^{50} - 36 q^{52} - 12 q^{53} - 78 q^{54} + 40 q^{57} + 26 q^{58} + 54 q^{59} + 16 q^{60} + 48 q^{61} - 8 q^{65} - 12 q^{66} + 16 q^{67} + 48 q^{68} - 36 q^{71} + 22 q^{72} - 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} - 138 q^{80} + 16 q^{81} - 84 q^{85} + 42 q^{86} + 24 q^{87} + 60 q^{89} + 48 q^{92} + 6 q^{93} + 72 q^{94} + 42 q^{96} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9 - 10 * q^11 - 44 * q^15 + 12 * q^16 - 4 * q^18 - 12 * q^19 - 8 * q^22 + 12 * q^24 - 24 * q^26 + 16 * q^29 - 24 * q^31 + 4 * q^32 - 48 * q^33 - 8 * q^37 - 6 * q^39 + 132 * q^40 - 42 * q^44 + 24 * q^45 + 12 * q^46 - 30 * q^47 + 88 * q^50 - 36 * q^52 - 12 * q^53 - 78 * q^54 + 40 * q^57 + 26 * q^58 + 54 * q^59 + 16 * q^60 + 48 * q^61 - 8 * q^65 - 12 * q^66 + 16 * q^67 + 48 * q^68 - 36 * q^71 + 22 * q^72 - 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 - 138 * q^80 + 16 * q^81 - 84 * q^85 + 42 * q^86 + 24 * q^87 + 60 * q^89 + 48 * q^92 + 6 * q^93 + 72 * q^94 + 42 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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