LMFDB - Embedded newform 637.2.k.h.569.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(459,637)] 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("637.459"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-8,6] 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.6
Root			$-1.30089 + 0.554694i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.h.459.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.10939i q^{2} +(-1.13082 + 1.95864i) q^{3} -2.44952 q^{4} +(-3.11923 - 1.80089i) q^{5} +(-4.13154 - 2.38535i) q^{6} -0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +(3.79878 - 6.57967i) q^{10} +(-0.767631 - 0.443192i) q^{11} +(2.76998 - 4.79774i) q^{12} +(-1.17349 - 3.40924i) q^{13} +(7.05461 - 4.07298i) q^{15} -2.89889 q^{16} +4.96016 q^{17} +(3.86375 - 2.23073i) q^{18} +(-2.06008 + 1.18939i) q^{19} +(7.64062 + 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +3.85851 q^{23} +(1.85721 + 1.07226i) q^{24} +(3.98641 + 6.90466i) q^{25} +(7.19141 - 2.47534i) q^{26} -2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} +(8.59150 + 14.8809i) q^{30} +(-7.33455 + 4.23460i) q^{31} -8.01131i q^{32} +(1.73611 - 1.00234i) q^{33} +10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} -9.63812i q^{37} +(-2.50888 - 4.34551i) q^{38} +(8.00450 + 1.55681i) q^{39} +(-1.70762 + 2.95769i) q^{40} +(10.4652 - 6.04207i) q^{41} +(-1.82125 + 3.15450i) q^{43} +(1.88033 + 1.08561i) q^{44} +7.61796i q^{45} +8.13910i q^{46} +(-2.58274 - 1.49115i) q^{47} +(3.27814 - 5.67790i) q^{48} +(-14.5646 + 8.40888i) q^{50} +(-5.60907 + 9.71520i) q^{51} +(2.87448 + 8.35100i) q^{52} +(-2.46016 - 4.26112i) q^{53} -4.22181i q^{54} +(1.59628 + 2.76484i) q^{55} -5.37995i q^{57} +(2.34189 - 1.35209i) q^{58} -7.32746i q^{59} +(-17.2804 + 9.97684i) q^{60} +(0.769632 + 1.33304i) q^{61} +(-8.93242 - 15.4714i) q^{62} +11.1012 q^{64} +(-2.47929 + 12.7475i) q^{65} +(2.11433 + 3.66213i) q^{66} +(-7.29756 - 4.21325i) q^{67} -12.1500 q^{68} +(-4.36330 + 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} +(-1.73683 + 1.00276i) q^{72} +(-6.19086 + 3.57430i) q^{73} +20.3305 q^{74} -18.0317 q^{75} +(5.04621 - 2.91343i) q^{76} +(-3.28391 + 16.8846i) q^{78} +(-0.378775 + 0.656058i) q^{79} +(9.04232 + 5.22059i) q^{80} +(5.43585 - 9.41518i) q^{81} +(12.7451 + 22.0751i) q^{82} +4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} +(-6.65406 - 3.84172i) q^{86} +2.89937 q^{87} +(-0.420240 + 0.727877i) q^{88} +3.61884i q^{89} -16.0692 q^{90} -9.45150 q^{92} -19.1544i q^{93} +(3.14541 - 5.44800i) q^{94} +8.56783 q^{95} +(15.6913 + 9.05939i) q^{96} +(-0.401229 - 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26}+ \cdots + 6 q^{97}+O(q^{100}) $ 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9 + 12 * q^10 - 6 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^15 + 16 * q^16 + 8 * q^17 + 12 * q^18 - 12 * q^20 + 6 * q^22 + 24 * q^23 - 12 * q^24 + 10 * q^25 + 18 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 - 18 * q^31 + 30 * q^33 - 10 * q^36 - 2 * q^38 + 14 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 - 24 * q^44 - 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 - 28 * q^52 + 22 * q^53 - 6 * q^55 + 12 * q^58 - 66 * q^60 + 14 * q^61 - 4 * q^62 - 52 * q^64 - 18 * q^65 + 26 * q^66 + 24 * q^67 + 16 * q^68 + 4 * q^69 - 24 * q^71 - 60 * q^72 - 30 * q^73 - 12 * q^74 - 92 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 + 72 * q^80 + 2 * q^81 + 14 * q^82 - 48 * q^85 + 60 * q^86 + 4 * q^87 - 14 * q^88 + 24 * q^90 + 24 * q^92 + 4 * q^94 + 44 * q^95 - 6 * q^96 + 6 * q^97

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			2.10939i			1.49156i	0.666191	+	0.745781i	$0.267924\pi$
$2$			2.10939i			1.49156i	−0.666191	+	0.745781i	$0.732076\pi$
$3$	−1.13082	+	1.95864i	−0.652882	+	1.13082i	0.329539	+	0.944142i	$0.393107\pi$
$3$	−1.13082	+	1.95864i	−0.652882	+	1.13082i	−0.982420	+	0.186682i	$0.940227\pi$
$4$	−2.44952			−1.22476
$5$	−3.11923	−	1.80089i	−1.39496	−	0.805382i	−0.401104	−	0.916033i	$-0.631373\pi$
$5$	−3.11923	−	1.80089i	−1.39496	−	0.805382i	−0.993859	+	0.110650i	$0.964707\pi$
$6$	−4.13154	−	2.38535i	−1.68670	−	0.973814i
$7$		0			0
$7$		0			0
$8$		−	0.948212i		−	0.335243i
$9$	−1.05753	−	1.83169i	−0.352509	−	0.610563i
$10$	3.79878	−	6.57967i	1.20128	−	2.08068i
$11$	−0.767631	−	0.443192i	−0.231450	−	0.133627i	0.379791	−	0.925072i	$-0.375996\pi$
$11$	−0.767631	−	0.443192i	−0.231450	−	0.133627i	−0.611241	+	0.791445i	$0.709329\pi$
$12$	2.76998	−	4.79774i	0.799623	−	1.38499i
$13$	−1.17349	−	3.40924i	−0.325467	−	0.945553i
$13$	−1.17349	−	3.40924i	−0.325467	−	0.945553i
$14$		0			0
$15$	7.05461	−	4.07298i	1.82149	−	1.05164i
$16$	−2.89889			−0.724723
$17$	4.96016			1.20302			0.601508	−	0.798867i	$-0.294567\pi$
$17$	4.96016			1.20302			0.601508	+	0.798867i	$0.294567\pi$
$18$	3.86375	−	2.23073i	0.910694	−	0.525789i
$19$	−2.06008	+	1.18939i	−0.472615	+	0.272864i	−0.717334	−	0.696730i	$-0.754638\pi$
$19$	−2.06008	+	1.18939i	−0.472615	+	0.272864i	0.244719	+	0.969594i	$0.421304\pi$
$20$	7.64062	+	4.41132i	1.70849	+	0.986400i
$21$		0			0
$22$	0.934864	−	1.61923i	0.199314	−	0.345222i
$23$	3.85851			0.804555			0.402278	−	0.915518i	$-0.368219\pi$
$23$	3.85851			0.804555			0.402278	+	0.915518i	$0.368219\pi$
$24$	1.85721	+	1.07226i	0.379101	+	0.218874i
$25$	3.98641	+	6.90466i	0.797282	+	1.38093i
$26$	7.19141	−	2.47534i	1.41035	−	0.485454i
$27$	−2.00144			−0.385177
$28$		0			0
$29$	−0.640986	−	1.11022i	−0.119028	−	0.206163i	0.800355	−	0.599527i	$-0.204645\pi$
$29$	−0.640986	−	1.11022i	−0.119028	−	0.206163i	−0.919383	+	0.393364i	$0.871311\pi$
$30$	8.59150	+	14.8809i	1.56859	+	2.71687i
$31$	−7.33455	+	4.23460i	−1.31732	+	0.760557i	−0.983297	−	0.182006i	$-0.941741\pi$
$31$	−7.33455	+	4.23460i	−1.31732	+	0.760557i	−0.334027	+	0.942564i	$0.608408\pi$
$32$		−	8.01131i		−	1.41621i
$33$	1.73611	−	1.00234i	0.302218	−	0.174486i
$34$			10.4629i			1.79437i
$35$		0			0
$36$	2.59043	+	4.48676i	0.431739	+	0.747793i
$37$		−	9.63812i		−	1.58450i	−0.610198	−	0.792249i	$-0.708910\pi$
$37$		−	9.63812i		−	1.58450i	0.610198	−	0.792249i	$-0.291090\pi$
$38$	−2.50888	−	4.34551i	−0.406994	−	0.704935i
$39$	8.00450	+	1.55681i	1.28175	+	0.249289i
$40$	−1.70762	+	2.95769i	−0.269999	+	0.467652i
$41$	10.4652	−	6.04207i	1.63438	−	0.943612i	0.651666	−	0.758506i	$-0.274071\pi$
$41$	10.4652	−	6.04207i	1.63438	−	0.943612i	0.982719	−	0.185106i	$-0.0592628\pi$
$42$		0			0
$43$	−1.82125	+	3.15450i	−0.277738	+	0.481056i	−0.970822	−	0.239800i	$-0.922918\pi$
$43$	−1.82125	+	3.15450i	−0.277738	+	0.481056i	0.693084	+	0.720856i	$0.256251\pi$
$44$	1.88033	+	1.08561i	0.283470	+	0.163662i
$45$			7.61796i			1.13562i
$46$			8.13910i			1.20004i
$47$	−2.58274	−	1.49115i	−0.376731	−	0.217506i	0.299664	−	0.954045i	$-0.403126\pi$
$47$	−2.58274	−	1.49115i	−0.376731	−	0.217506i	−0.676395	+	0.736539i	$0.736459\pi$
$48$	3.27814	−	5.67790i	0.473158	−	0.819535i
$49$		0			0
$50$	−14.5646	+	8.40888i	−2.05975	+	1.18920i
$51$	−5.60907	+	9.71520i	−0.785427	+	1.36040i
$52$	2.87448	+	8.35100i	0.398619	+	1.15808i
$53$	−2.46016	−	4.26112i	−0.337929	−	0.585310i	0.646114	−	0.763241i	$-0.276393\pi$
$53$	−2.46016	−	4.26112i	−0.337929	−	0.585310i	−0.984043	+	0.177931i	$0.943060\pi$
$54$		−	4.22181i		−	0.574516i
$55$	1.59628	+	2.76484i	0.215242	+	0.372811i
$56$		0			0
$57$		−	5.37995i		−	0.712592i
$58$	2.34189	−	1.35209i	0.307505	−	0.177538i
$59$		−	7.32746i		−	0.953954i	−0.878916	−	0.476977i	$-0.841732\pi$
$59$		−	7.32746i		−	0.953954i	0.878916	−	0.476977i	$-0.158268\pi$
$60$	−17.2804	+	9.97684i	−2.23089	+	1.28800i
$61$	0.769632	+	1.33304i	0.0985412	+	0.170678i	0.911081	−	0.412227i	$-0.135249\pi$
$61$	0.769632	+	1.33304i	0.0985412	+	0.170678i	−0.812540	+	0.582906i	$0.801916\pi$
$62$	−8.93242	−	15.4714i	−1.13442	−	1.96487i
$63$		0			0
$64$	11.1012			1.38765
$65$	−2.47929	+	12.7475i	−0.307518	+	1.58114i
$66$	2.11433	+	3.66213i	0.260257	+	0.450778i
$67$	−7.29756	−	4.21325i	−0.891539	−	0.514730i	−0.0170931	−	0.999854i	$-0.505441\pi$
$67$	−7.29756	−	4.21325i	−0.891539	−	0.514730i	−0.874445	+	0.485124i	$0.838775\pi$
$68$	−12.1500			−1.47341
$69$	−4.36330	+	7.55745i	−0.525279	+	0.909811i
$70$		0			0
$71$	−5.58490	−	3.22444i	−0.662805	−	0.382671i	0.130540	−	0.991443i	$-0.458329\pi$
$71$	−5.58490	−	3.22444i	−0.662805	−	0.382671i	−0.793345	+	0.608772i	$0.791662\pi$
$72$	−1.73683	+	1.00276i	−0.204687	+	0.118176i
$73$	−6.19086	+	3.57430i	−0.724586	+	0.418340i	−0.816438	−	0.577433i	$-0.804054\pi$
$73$	−6.19086	+	3.57430i	−0.724586	+	0.418340i	0.0918526	+	0.995773i	$0.470721\pi$
$74$	20.3305			2.36338
$75$	−18.0317			−2.08212
$76$	5.04621	−	2.91343i	0.578840	−	0.334193i
$77$		0			0
$78$	−3.28391	+	16.8846i	−0.371830	+	1.91180i
$79$	−0.378775	+	0.656058i	−0.0426156	+	0.0738123i	−0.886546	−	0.462640i	$-0.846902\pi$
$79$	−0.378775	+	0.656058i	−0.0426156	+	0.0738123i	0.843931	+	0.536452i	$0.180236\pi$
$80$	9.04232	+	5.22059i	1.01096	+	0.583679i
$81$	5.43585	−	9.41518i	0.603984	−	1.04613i
$82$	12.7451	+	22.0751i	1.40746	+	2.43779i
$83$			4.76766i			0.523319i	0.965160	+	0.261659i	$0.0842697\pi$
$83$			4.76766i			0.523319i	−0.965160	+	0.261659i	$0.915730\pi$
$84$		0			0
$85$	−15.4719	−	8.93270i	−1.67816	−	0.968888i
$86$	−6.65406	−	3.84172i	−0.717525	−	0.414263i
$87$	2.89937			0.310845
$88$	−0.420240	+	0.727877i	−0.0447977	+	0.0775919i
$89$			3.61884i			0.383596i	0.981434	+	0.191798i	$0.0614318\pi$
$89$			3.61884i			0.383596i	−0.981434	+	0.191798i	$0.938568\pi$
$90$	−16.0692			−1.69385
$91$		0			0
$92$	−9.45150			−0.985387
$93$		−	19.1544i		−	1.98622i
$94$	3.14541	−	5.44800i	0.324424	−	0.561919i
$95$	8.56783			0.879040
$96$	15.6913	+	9.05939i	1.60149	+	0.924620i
$97$	−0.401229	−	0.231650i	−0.0407386	−	0.0235205i	0.479492	−	0.877546i	$-0.340821\pi$
$97$	−0.401229	−	0.231650i	−0.0407386	−	0.0235205i	−0.520231	+	0.854026i	$0.674154\pi$
$98$		0			0
$99$			1.87475i			0.188419i
$100$	−9.76479	−	16.9131i	−0.976479	−	1.69131i
$101$	2.91152	−	5.04289i	0.289707	−	0.501787i	−0.684033	−	0.729451i	$-0.739776\pi$
$101$	2.91152	−	5.04289i	0.289707	−	0.501787i	0.973740	+	0.227664i	$0.0731089\pi$
$102$	−20.4931	−	11.8317i	−2.02912	−	1.17151i
$103$	4.11944	−	7.13508i	0.405901	−	0.703040i	−0.588525	−	0.808479i	$-0.700291\pi$
$103$	4.11944	−	7.13508i	0.405901	−	0.703040i	0.994426	+	0.105438i	$0.0336246\pi$
$104$	−3.23268	+	1.11271i	−0.316991	+	0.109111i
$105$		0			0
$106$	8.98837	−	5.18944i	0.873027	−	0.504043i
$107$	−3.83260			−0.370511			−0.185256	−	0.982690i	$-0.559311\pi$
$107$	−3.83260			−0.370511			−0.185256	+	0.982690i	$0.559311\pi$
$108$	4.90256			0.471749
$109$	9.02229	−	5.20902i	0.864178	−	0.498934i	−0.00123094	−	0.999999i	$-0.500392\pi$
$109$	9.02229	−	5.20902i	0.864178	−	0.498934i	0.865409	+	0.501066i	$0.167058\pi$
$110$	−5.83212	+	3.36718i	−0.556071	+	0.321048i
$111$	18.8777	+	10.8990i	1.79179	+	1.03449i
$112$		0			0
$113$	2.45505	−	4.25228i	0.230952	−	0.400021i	−0.727136	−	0.686493i	$-0.759149\pi$
$113$	2.45505	−	4.25228i	0.230952	−	0.400021i	0.958089	+	0.286472i	$0.0924826\pi$
$114$	11.3484			1.06288
$115$	−12.0356	−	6.94875i	−1.12233	−	0.647975i
$116$	1.57011	+	2.71951i	0.145781	+	0.252500i
$117$	−5.00368	+	5.75483i	−0.462590	+	0.532034i
$118$	15.4565			1.42288
$119$		0			0
$120$	−3.86205	−	6.68926i	−0.352555	−	0.610643i
$121$	−5.10716	−	8.84586i	−0.464287	−	0.804169i
$122$	−2.81190	+	1.62345i	−0.254578	+	0.146980i
$123$			27.3301i			2.46427i
$124$	17.9661	−	10.3727i	1.61341	−	0.931500i
$125$		−	10.7074i		−	0.957702i
$126$		0			0
$127$	−6.15508	−	10.6609i	−0.546175	−	0.946003i	−0.998532	−	0.0541658i	$-0.982750\pi$
$127$	−6.15508	−	10.6609i	−0.546175	−	0.946003i	0.452357	−	0.891837i	$-0.350583\pi$
$128$			7.39409i			0.653551i
$129$	−4.11902	−	7.13436i	−0.362660	−	0.628145i
$130$	−26.8895	−	5.22978i	−2.35837	−	0.458682i
$131$	4.10133	−	7.10371i	0.358335	−	0.620654i	−0.629348	−	0.777123i	$-0.716678\pi$
$131$	4.10133	−	7.10371i	0.358335	−	0.620654i	0.987683	+	0.156470i	$0.0500114\pi$
$132$	−4.25264	+	2.45526i	−0.370145	+	0.213703i
$133$		0			0
$134$	8.88737	−	15.3934i	0.767752	−	1.32979i
$135$	6.24295	+	3.60437i	0.537308	+	0.310215i
$136$		−	4.70328i		−	0.403303i
$137$		−	7.45555i		−	0.636971i	−0.947928	−	0.318485i	$-0.896826\pi$
$137$		−	7.45555i		−	0.636971i	0.947928	−	0.318485i	$-0.103174\pi$
$138$	−15.9416	−	9.20389i	−1.35704	−	0.783487i
$139$	−8.34028	+	14.4458i	−0.707413	+	1.22528i	0.258400	+	0.966038i	$0.416805\pi$
$139$	−8.34028	+	14.4458i	−0.707413	+	1.22528i	−0.965813	+	0.259238i	$0.916529\pi$
$140$		0			0
$141$	5.84125	−	3.37245i	0.491922	−	0.284011i
$142$	6.80160	−	11.7807i	0.570778	−	0.988616i
$143$	−0.610143	+	3.13712i	−0.0510228	+	0.262339i
$144$	3.06566	+	5.30987i	0.255471	+	0.442489i
$145$			4.61738i			0.383453i
$146$	−7.53958	−	13.0589i	−0.623980	−	1.08076i
$147$		0			0
$148$			23.6088i			1.94063i
$149$	2.18380	−	1.26082i	0.178904	−	0.103290i	−0.407874	−	0.913038i	$-0.633730\pi$
$149$	2.18380	−	1.26082i	0.178904	−	0.103290i	0.586777	+	0.809748i	$0.300396\pi$
$150$		−	38.0359i		−	3.10562i
$151$	−13.7674	+	7.94862i	−1.12038	+	0.646849i	−0.941497	−	0.337022i	$-0.890580\pi$
$151$	−13.7674	+	7.94862i	−1.12038	+	0.646849i	−0.178879	+	0.983871i	$0.557247\pi$
$152$	1.12779	+	1.95339i	0.0914760	+	0.158441i
$153$	−5.24550	−	9.08548i	−0.424074	−	0.734517i
$154$		0			0
$155$	30.5042			2.45016
$156$	−19.6072	−	3.81343i	−1.56983	−	0.305319i
$157$	−6.49155	−	11.2437i	−0.518082	−	0.897344i	−0.999779	−	0.0210065i	$-0.993313\pi$
$157$	−6.49155	−	11.2437i	−0.518082	−	0.897344i	0.481697	−	0.876338i	$-0.340020\pi$
$158$	−1.38388	−	0.798985i	−0.110096	−	0.0635638i
$159$	11.1280			0.882511
$160$	−14.4275	+	24.9892i	−1.14059	+	1.97557i
$161$		0			0
$162$	19.8603	+	11.4663i	1.56037	+	0.900880i
$163$	2.00873	−	1.15974i	0.157336	−	0.0908378i	−0.419265	−	0.907864i	$-0.637712\pi$
$163$	2.00873	−	1.15974i	0.157336	−	0.0908378i	0.576601	+	0.817026i	$0.304379\pi$
$164$	−25.6346	+	14.8002i	−2.00173	+	1.15570i
$165$	−7.22045			−0.562111
$166$	−10.0569			−0.780563
$167$	−11.9441	+	6.89591i	−0.924260	+	0.533622i	−0.884992	−	0.465607i	$-0.845836\pi$
$167$	−11.9441	+	6.89591i	−0.924260	+	0.533622i	−0.0392682	+	0.999229i	$0.512503\pi$
$168$		0			0
$169$	−10.2459	+	8.00140i	−0.788143	+	0.615493i
$170$	18.8425	−	32.6362i	1.44516	−	2.50309i
$171$	4.35718	+	2.51562i	0.333202	+	0.192374i
$172$	4.46118	−	7.72700i	0.340162	−	0.589178i
$173$	−1.84216	−	3.19071i	−0.140057	−	0.242585i	0.787461	−	0.616364i	$-0.211395\pi$
$173$	−1.84216	−	3.19071i	−0.140057	−	0.242585i	−0.927518	+	0.373779i	$0.878062\pi$
$174$			6.11590i			0.463645i
$175$		0			0
$176$	2.22528	+	1.28477i	0.167737	+	0.0968429i
$177$	14.3519	+	8.28607i	1.07875	+	0.622819i
$178$	−7.63353			−0.572157
$179$	−2.94638	+	5.10328i	−0.220223	+	0.381437i	−0.954876	−	0.297006i	$-0.904012\pi$
$179$	−2.94638	+	5.10328i	−0.220223	+	0.381437i	0.734653	+	0.678443i	$0.237345\pi$
$180$		−	18.6603i		−	1.39086i
$181$	−2.11543			−0.157239			−0.0786193	−	0.996905i	$-0.525051\pi$
$181$	−2.11543			−0.157239			−0.0786193	+	0.996905i	$0.525051\pi$
$182$		0			0
$183$	−3.48127			−0.257343
$184$		−	3.65869i		−	0.269722i
$185$	−17.3572	+	30.0635i	−1.27613	+	2.21032i
$186$	40.4040			2.96257
$187$	−3.80758	−	2.19830i	−0.278437	−	0.160756i
$188$	6.32647	+	3.65259i	0.461406	+	0.266393i
$189$		0			0
$190$			18.0729i			1.31114i
$191$	5.68333	+	9.84381i	0.411231	+	0.712273i	0.995025	−	0.0996290i	$-0.0317656\pi$
$191$	5.68333	+	9.84381i	0.411231	+	0.712273i	−0.583794	+	0.811902i	$0.698432\pi$
$192$	−12.5535	+	21.7433i	−0.905970	+	1.56919i
$193$	−12.2017	−	7.04468i	−0.878301	−	0.507087i	−0.00820314	−	0.999966i	$-0.502611\pi$
$193$	−12.2017	−	7.04468i	−0.878301	−	0.507087i	−0.870098	+	0.492879i	$0.835945\pi$
$194$	0.488639	−	0.846348i	0.0350823	−	0.0607643i
$195$	−22.1643	−	19.2713i	−1.58722	−	1.38004i
$196$		0			0
$197$	−19.8815	+	11.4786i	−1.41650	+	0.817814i	−0.995989	−	0.0894753i	$-0.971481\pi$
$197$	−19.8815	+	11.4786i	−1.41650	+	0.817814i	−0.420507	+	0.907289i	$0.638148\pi$
$198$	−3.95458			−0.281040
$199$	3.14985			0.223287			0.111643	−	0.993748i	$-0.464389\pi$
$199$	3.14985			0.223287			0.111643	+	0.993748i	$0.464389\pi$
$200$	6.54708	−	3.77996i	0.462949	−	0.267283i
$201$	16.5045	−	9.52888i	1.16414	−	0.672116i
$202$	10.6374	+	6.14152i	0.748446	+	0.432116i
$203$		0			0
$204$	13.7395	−	23.7976i	0.961959	−	1.66616i
$205$	−43.5244			−3.03987
$206$	15.0507	+	8.68950i	1.04863	+	0.605426i
$207$	−4.08048	−	7.06760i	−0.283613	−	0.491232i
$208$	3.40181	+	9.88303i	0.235873	+	0.685265i
$209$	2.10851			0.145849
$210$		0			0
$211$	7.43191	+	12.8725i	0.511634	+	0.886176i	0.999909	+	0.0134864i	$0.00429298\pi$
$211$	7.43191	+	12.8725i	0.511634	+	0.886176i	−0.488275	+	0.872690i	$0.662374\pi$
$212$	6.02621	+	10.4377i	0.413882	+	0.716865i
$213$	12.6311	−	7.29255i	0.865467	−	0.499678i
$214$		−	8.08444i		−	0.552641i
$215$	11.3618	−	6.55974i	0.774868	−	0.447370i
$216$			1.89779i			0.129128i
$217$		0			0
$218$	10.9878	+	19.0315i	0.744191	+	1.28898i
$219$		−	16.1676i		−	1.09251i
$220$	−3.91012	−	6.77253i	−0.263620	−	0.456604i
$221$	−5.82069	−	16.9104i	−0.391542	−	1.13752i
$222$	−22.9903	+	39.8203i	−1.54301	+	2.67257i
$223$	3.79396	−	2.19044i	0.254062	−	0.146683i	−0.367561	−	0.930000i	$-0.619807\pi$
$223$	3.79396	−	2.19044i	0.254062	−	0.146683i	0.621623	+	0.783317i	$0.286474\pi$
$224$		0			0
$225$	8.43147	−	14.6037i	0.562098	−	0.973582i
$226$	8.96971	+	5.17866i	0.596656	+	0.344480i
$227$		−	13.5663i		−	0.900428i	−0.892921	−	0.450214i	$-0.851348\pi$
$227$		−	13.5663i		−	0.900428i	0.892921	−	0.450214i	$-0.148652\pi$
$228$			13.1783i			0.872754i
$229$	−14.3050	−	8.25900i	−0.945302	−	0.545770i	−0.0536833	−	0.998558i	$-0.517096\pi$
$229$	−14.3050	−	8.25900i	−0.945302	−	0.545770i	−0.891618	+	0.452788i	$0.850429\pi$
$230$	14.6576	−	25.3877i	0.966495	−	1.67402i
$231$		0			0
$232$	−1.05272	+	0.607791i	−0.0691147	+	0.0399034i
$233$	−8.25131	+	14.2917i	−0.540561	+	0.936279i	0.458311	+	0.888792i	$0.348455\pi$
$233$	−8.25131	+	14.2917i	−0.540561	+	0.936279i	−0.998872	+	0.0474874i	$0.984879\pi$
$234$	−12.1392	−	10.5547i	−0.793562	−	0.689983i
$235$	5.37078	+	9.30246i	0.350351	+	0.606826i
$236$			17.9488i			1.16836i
$237$	−0.856657	−	1.48377i	−0.0556458	−	0.0963814i
$238$		0			0
$239$		−	30.4210i		−	1.96777i	−0.178796	−	0.983886i	$-0.557220\pi$
$239$		−	30.4210i		−	1.96777i	0.178796	−	0.983886i	$-0.442780\pi$
$240$	−20.4506	+	11.8071i	−1.32008	+	0.762147i
$241$			29.5143i			1.90119i	0.310440	+	0.950593i	$0.399524\pi$
$241$			29.5143i			1.90119i	−0.310440	+	0.950593i	$0.600476\pi$
$242$	18.6594	−	10.7730i	1.19947	−	0.692514i
$243$	9.29184	+	16.0939i	0.596072	+	1.03243i
$244$	−1.88523	−	3.26531i	−0.120689	−	0.209040i
$245$		0			0
$246$	−57.6497			−3.67561
$247$	6.47239	+	5.62758i	0.411828	+	0.358074i
$248$	4.01530	+	6.95471i	0.254972	+	0.441624i
$249$	−9.33816	−	5.39139i	−0.591782	−	0.341665i
$250$	22.5861			1.42847
$251$	−6.49134	+	11.2433i	−0.409730	+	0.709673i	−0.994859	−	0.101267i	$-0.967710\pi$
$251$	−6.49134	+	11.2433i	−0.409730	+	0.709673i	0.585130	+	0.810940i	$0.301044\pi$
$252$		0			0
$253$	−2.96191	−	1.71006i	−0.186214	−	0.107511i
$254$	22.4880	−	12.9835i	1.41102	−	0.814654i
$255$	34.9920	−	20.2026i	2.19128	−	1.26514i
$256$	6.60537			0.412836
$257$	4.58521			0.286018			0.143009	−	0.989721i	$-0.454322\pi$
$257$	4.58521			0.286018			0.143009	+	0.989721i	$0.454322\pi$
$258$	15.0491	−	8.68862i	0.936918	−	0.540930i
$259$		0			0
$260$	6.07307	−	31.2253i	0.376636	−	1.93651i
$261$	−1.35572	+	2.34818i	−0.0839170	+	0.145348i
$262$	14.9845	+	8.65129i	0.925744	+	0.534479i
$263$	1.33250	−	2.30795i	0.0821652	−	0.142314i	−0.822015	−	0.569466i	$-0.807150\pi$
$263$	1.33250	−	2.30795i	0.0821652	−	0.142314i	0.904180	+	0.427152i	$0.140483\pi$
$264$	−0.950435	−	1.64620i	−0.0584952	−	0.101317i
$265$			17.7219i			1.08865i
$266$		0			0
$267$	−7.08801	−	4.09227i	−0.433779	−	0.250443i
$268$	17.8755	+	10.3204i	1.09192	+	0.630421i
$269$	11.9256			0.727119			0.363559	−	0.931571i	$-0.381561\pi$
$269$	11.9256			0.727119			0.363559	+	0.931571i	$0.381561\pi$
$270$	−7.60301	+	13.1688i	−0.462705	+	0.801428i
$271$		−	13.0283i		−	0.791414i	−0.918377	−	0.395707i	$-0.870500\pi$
$271$		−	13.0283i		−	0.791414i	0.918377	−	0.395707i	$-0.129500\pi$
$272$	−14.3790			−0.871853
$273$		0			0
$274$	15.7267			0.950082
$275$		−	7.06698i		−	0.426155i
$276$	10.6880	−	18.5121i	0.643341	−	1.11430i
$277$	−21.3649			−1.28369			−0.641846	−	0.766833i	$-0.721831\pi$
$277$	−21.3649			−1.28369			−0.641846	+	0.766833i	$0.721831\pi$
$278$	−30.4718	−	17.5929i	−1.82758	−	1.05515i
$279$	15.5130	+	8.95641i	0.928737	+	0.536206i
$280$		0			0
$281$			17.2678i			1.03011i	0.857158	+	0.515054i	$0.172228\pi$
$281$			17.2678i			1.03011i	−0.857158	+	0.515054i	$0.827772\pi$
$282$	7.11380	+	12.3215i	0.423621	+	0.733733i
$283$	−10.6201	+	18.3946i	−0.631299	+	1.09344i	0.355987	+	0.934491i	$0.384145\pi$
$283$	−10.6201	+	18.3946i	−0.631299	+	1.09344i	−0.987286	+	0.158952i	$0.949189\pi$
$284$	13.6803	+	7.89833i	0.811777	+	0.468680i
$285$	−9.68870	+	16.7813i	−0.573909	+	0.994040i
$286$	−6.61741	−	1.28703i	−0.391295	−	0.0761037i
$287$		0			0
$288$	−14.6742	+	8.47218i	−0.864688	+	0.499228i
$289$	7.60320			0.447247
$290$	−9.73985			−0.571944
$291$	0.907439	−	0.523910i	0.0531950	−	0.0307122i
$292$	15.1646	−	8.75531i	0.887443	−	0.512366i
$293$	−0.363782	−	0.210030i	−0.0212524	−	0.0122701i	0.489336	−	0.872095i	$-0.337239\pi$
$293$	−0.363782	−	0.210030i	−0.0212524	−	0.0122701i	−0.510589	+	0.859825i	$0.670572\pi$
$294$		0			0
$295$	−13.1959	+	22.8561i	−0.768298	+	1.33073i
$296$	−9.13898			−0.531192
$297$	1.53637	+	0.887022i	0.0891490	+	0.0514702i
$298$	2.65955	+	4.60648i	0.154064	+	0.266846i
$299$	−4.52791	−	13.1546i	−0.261856	−	0.760750i
$300$	44.1690			2.55010
$301$		0			0
$302$	−16.7667	−	29.0408i	−0.964817	−	1.67111i
$303$	6.58482	+	11.4053i	0.378288	+	0.655215i
$304$	5.97195	−	3.44791i	0.342515	−	0.197751i
$305$		−	5.54409i		−	0.317453i
$306$	19.1648	−	11.0648i	1.09558	−	0.632533i
$307$		−	14.0807i		−	0.803628i	−0.915721	−	0.401814i	$-0.868380\pi$
$307$		−	14.0807i		−	0.803628i	0.915721	−	0.401814i	$-0.131620\pi$
$308$		0			0
$309$	9.31673	+	16.1370i	0.530010	+	0.918004i
$310$			64.3453i			3.65456i
$311$	5.19240	+	8.99349i	0.294434	+	0.509974i	0.974853	−	0.222849i	$-0.0715356\pi$
$311$	5.19240	+	8.99349i	0.294434	+	0.509974i	−0.680419	+	0.732823i	$0.738202\pi$
$312$	1.47618	−	7.58996i	0.0835724	−	0.429697i
$313$	−3.42379	+	5.93018i	−0.193524	+	0.335194i	−0.946416	−	0.322951i	$-0.895325\pi$
$313$	−3.42379	+	5.93018i	−0.193524	+	0.335194i	0.752892	+	0.658145i	$0.228658\pi$
$314$	23.7173	−	13.6932i	1.33845	−	0.772752i
$315$		0			0
$316$	0.927818	−	1.60703i	0.0521938	−	0.0904024i
$317$	−0.607299	−	0.350624i	−0.0341093	−	0.0196930i	0.482848	−	0.875704i	$-0.339602\pi$
$317$	−0.607299	−	0.350624i	−0.0341093	−	0.0196930i	−0.516958	+	0.856011i	$0.672936\pi$
$318$			23.4734i			1.31632i
$319$			1.13632i			0.0636217i
$320$	−34.6272	−	19.9920i	−1.93572	−	1.11759i
$321$	4.33400	−	7.50670i	0.241900	−	0.418983i
$322$		0			0
$323$	−10.2183	+	5.89956i	−0.568563	+	0.328260i
$324$	−13.3152	+	23.0627i	−0.739735	+	1.28126i
$325$	18.8617	−	21.6932i	1.04626	−	1.20332i
$326$	2.44634	+	4.23719i	0.135490	+	0.234676i
$327$			23.5619i			1.30298i
$328$	−5.72916	−	9.92319i	−0.316340	−	0.547917i
$329$		0			0
$330$		−	15.2307i		−	0.838424i
$331$	−3.63613	+	2.09932i	−0.199860	+	0.115389i	−0.596590	−	0.802546i	$-0.703478\pi$
$331$	−3.63613	+	2.09932i	−0.199860	+	0.115389i	0.396730	+	0.917935i	$0.370145\pi$
$332$		−	11.6785i		−	0.640940i
$333$	−17.6541	+	10.1926i	−0.967436	+	0.558550i
$334$	−14.5462	−	25.1947i	−0.795930	−	1.37859i
$335$	15.1752	+	26.2842i	0.829109	+	1.43606i
$336$		0			0
$337$	−20.4278			−1.11278			−0.556388	−	0.830923i	$-0.687813\pi$
$337$	−20.4278			−1.11278			−0.556388	+	0.830923i	$0.687813\pi$
$338$	−16.8781	−	21.6125i	−0.918046	−	1.17556i
$339$	5.55247	+	9.61716i	0.301569	+	0.522333i
$340$	37.8987	+	21.8808i	2.05535	+	1.18665i
$341$	7.50697			0.406525
$342$	−5.30642	+	9.19098i	−0.286938	+	0.496991i
$343$		0			0
$344$	2.99113	+	1.72693i	0.161271	+	0.0931098i
$345$	27.2203	−	15.7156i	1.46549	−	0.846102i
$346$	6.73045	−	3.88583i	0.361831	−	0.208903i
$347$	7.97000			0.427852			0.213926	−	0.976850i	$-0.431375\pi$
$347$	7.97000			0.427852			0.213926	+	0.976850i	$0.431375\pi$
$348$	−7.10207			−0.380711
$349$	18.7038	−	10.7986i	1.00119	−	0.578037i	0.0925892	−	0.995704i	$-0.470486\pi$
$349$	18.7038	−	10.7986i	1.00119	−	0.578037i	0.908600	+	0.417668i	$0.137152\pi$
$350$		0			0
$351$	2.34866	+	6.82338i	0.125362	+	0.364205i
$352$	−3.55055	+	6.14974i	−0.189245	+	0.327782i
$353$	−18.7214	−	10.8088i	−0.996439	−	0.575295i	−0.0892465	−	0.996010i	$-0.528446\pi$
$353$	−18.7214	−	10.8088i	−0.996439	−	0.575295i	−0.907193	+	0.420715i	$0.861779\pi$
$354$	−17.4785	+	30.2737i	−0.928974	+	1.60903i
$355$	11.6137	+	20.1156i	0.616393	+	1.06762i
$356$		−	8.86441i		−	0.469813i
$357$		0			0
$358$	−10.7648	−	6.21507i	−0.568938	−	0.328476i
$359$	−11.8501	−	6.84168i	−0.625426	−	0.361090i	0.153552	−	0.988141i	$-0.450929\pi$
$359$	−11.8501	−	6.84168i	−0.625426	−	0.361090i	−0.778979	+	0.627051i	$0.784262\pi$
$360$	7.22344			0.380708
$361$	−6.67071	+	11.5540i	−0.351090	+	0.608106i
$362$		−	4.46226i		−	0.234531i
$363$	23.1012			1.21250
$364$		0			0
$365$	25.7477			1.34769
$366$		−	7.34335i		−	0.383843i
$367$	5.70638	−	9.88374i	0.297871	−	0.515927i	−0.677778	−	0.735267i	$-0.737057\pi$
$367$	5.70638	−	9.88374i	0.297871	−	0.515927i	0.975649	+	0.219339i	$0.0703902\pi$
$368$	−11.1854			−0.583080
$369$	−22.1344	−	12.7793i	−1.15227	−	0.665263i
$370$	−63.4157	−	36.6131i	−3.29683	−	1.90342i
$371$		0			0
$372$			46.9190i			2.43264i
$373$	15.6404	+	27.0900i	0.809830	+	1.40267i	0.912981	+	0.408002i	$0.133774\pi$
$373$	15.6404	+	27.0900i	0.809830	+	1.40267i	−0.103151	+	0.994666i	$0.532892\pi$
$374$	4.63708	−	8.03166i	0.239778	−	0.415307i
$375$	20.9721	+	12.1082i	1.08299	+	0.625266i
$376$	−1.41392	+	2.44898i	−0.0729175	+	0.126297i
$377$	−3.03282	+	3.48811i	−0.156198	+	0.179647i
$378$		0			0
$379$	23.7421	−	13.7075i	1.21955	−	0.704108i	0.254729	−	0.967012i	$-0.418014\pi$
$379$	23.7421	−	13.7075i	1.21955	−	0.704108i	0.964822	+	0.262904i	$0.0846803\pi$
$380$	−20.9871			−1.07661
$381$	27.8412			1.42635
$382$	−20.7644	+	11.9883i	−1.06240	+	0.613377i
$383$	−13.9436	+	8.05032i	−0.712483	+	0.411352i	−0.811980	−	0.583686i	$-0.801610\pi$
$383$	−13.9436	+	8.05032i	−0.712483	+	0.411352i	0.0994967	+	0.995038i	$0.468277\pi$
$384$	−14.4824	−	8.36142i	−0.739052	−	0.426692i
$385$		0			0
$386$	14.8600	−	25.7382i	0.756353	−	1.31004i
$387$	7.70408			0.391620
$388$	0.982819	+	0.567431i	0.0498951	+	0.0288069i
$389$	10.5690	+	18.3060i	0.535870	+	0.928153i	0.999121	+	0.0419264i	$0.0133495\pi$
$389$	10.5690	+	18.3060i	0.535870	+	0.928153i	−0.463251	+	0.886227i	$0.653317\pi$
$390$	40.6506	−	46.7530i	2.05842	−	2.36743i
$391$	19.1388			0.967893
$392$		0			0
$393$	9.27576	+	16.0661i	0.467900	+	0.810427i
$394$	−24.2128	−	41.9377i	−1.21982	−	2.11279i
$395$	2.36298	−	1.36427i	0.118894	−	0.0686437i
$396$		−	4.59224i		−	0.230769i
$397$	−11.3436	+	6.54921i	−0.569317	+	0.328695i	−0.756876	−	0.653558i	$-0.773276\pi$
$397$	−11.3436	+	6.54921i	−0.569317	+	0.328695i	0.187560	+	0.982253i	$0.439942\pi$
$398$			6.64426i			0.333046i
$399$		0			0
$400$	−11.5562	−	20.0159i	−0.577808	−	1.00079i
$401$			19.4447i			0.971022i	0.874230	+	0.485511i	$0.161367\pi$
$401$			19.4447i			0.971022i	−0.874230	+	0.485511i	$0.838633\pi$
$402$	20.1001	+	34.8144i	1.00250	+	1.73639i
$403$	23.0438	+	20.0360i	1.14789	+	0.998064i
$404$	−7.13182	+	12.3527i	−0.354821	+	0.614568i
$405$	−33.9114	+	19.5788i	−1.68507	+	0.972876i
$406$		0			0
$407$	−4.27154	+	7.39853i	−0.211732	+	0.366731i
$408$	9.21206	+	5.31859i	0.456065	+	0.263309i
$409$		−	24.0559i		−	1.18949i	−0.803916	−	0.594743i	$-0.797254\pi$
$409$		−	24.0559i		−	1.18949i	0.803916	−	0.594743i	$-0.202746\pi$
$410$		−	91.8098i		−	4.53416i
$411$	14.6028	+	8.43092i	0.720302	+	0.415867i
$412$	−10.0907	+	17.4775i	−0.497131	+	0.861056i
$413$		0			0
$414$	14.9083	−	8.60732i	0.732703	−	0.423026i
$415$	8.58603	−	14.8714i	0.421472	−	0.730011i
$416$	−27.3125	+	9.40118i	−1.33911	+	0.460931i
$417$	−18.8628	−	32.6713i	−0.923714	−	1.59992i
$418$			4.44767i			0.217542i
$419$	−19.5119	−	33.7956i	−0.953218	−	1.65102i	−0.738394	−	0.674370i	$-0.764415\pi$
$419$	−19.5119	−	33.7956i	−0.953218	−	1.65102i	−0.214825	−	0.976653i	$-0.568918\pi$
$420$		0			0
$421$		−	22.0284i		−	1.07360i	−0.843710	−	0.536799i	$-0.819633\pi$
$421$		−	22.0284i		−	1.07360i	0.843710	−	0.536799i	$-0.180367\pi$
$422$	−27.1530	+	15.6768i	−1.32179	+	0.763134i
$423$			6.30771i			0.306691i
$424$	−4.04045	+	2.33275i	−0.196221	+	0.113289i
$425$	19.7732	+	34.2482i	0.959142	+	1.66128i
$426$	15.3828	+	26.6438i	0.745301	+	1.29090i
$427$		0			0
$428$	9.38803			0.453787
$429$	−5.45454	−	4.74259i	−0.263348	−	0.228974i
$430$	13.8370	+	23.9664i	0.667281	+	1.15576i
$431$	31.0727	+	17.9398i	1.49672	+	0.864131i	0.999993	−	0.00377645i	$-0.00120209\pi$
$431$	31.0727	+	17.9398i	1.49672	+	0.864131i	0.496726	+	0.867907i	$0.334535\pi$
$432$	5.80195			0.279147
$433$	6.10678	−	10.5773i	0.293473	−	0.508310i	−0.681155	−	0.732139i	$-0.738522\pi$
$433$	6.10678	−	10.5773i	0.293473	−	0.508310i	0.974629	+	0.223828i	$0.0718555\pi$
$434$		0			0
$435$	−9.04381	−	5.22145i	−0.433618	−	0.250349i
$436$	−22.1003	+	12.7596i	−1.05841	+	0.611074i
$437$	−7.94884	+	4.58927i	−0.380245	+	0.219534i
$438$	34.1037			1.62954
$439$	15.7553			0.751960			0.375980	−	0.926628i	$-0.377306\pi$
$439$	15.7553			0.751960			0.375980	+	0.926628i	$0.377306\pi$
$440$	2.62165	−	1.51361i	0.124982	−	0.0721586i
$441$		0			0
$442$	35.6706	−	12.2781i	1.69668	−	0.584009i
$443$	7.53532	−	13.0516i	0.358014	−	0.620099i	−0.629615	−	0.776907i	$-0.716787\pi$
$443$	7.53532	−	13.0516i	0.358014	−	0.620099i	0.987629	+	0.156809i	$0.0501207\pi$
$444$	−46.2412	−	26.6974i	−2.19451	−	1.26700i
$445$	6.51712	−	11.2880i	0.308941	−	0.535102i
$446$	4.62050	+	8.00293i	0.218787	+	0.378950i
$447$			5.70305i			0.269745i
$448$		0			0
$449$	26.6585	+	15.3913i	1.25809	+	0.726360i	0.972703	−	0.232052i	$-0.0745441\pi$
$449$	26.6585	+	15.3913i	1.25809	+	0.726360i	0.285388	+	0.958412i	$0.407877\pi$
$450$	30.8049	+	17.7852i	1.45216	+	0.838404i
$451$	−10.7112			−0.504370
$452$	−6.01371	+	10.4160i	−0.282861	+	0.489929i
$453$		−	35.9540i		−	1.68926i
$454$	28.6166			1.34304
$455$		0			0
$456$	−5.10133			−0.238892
$457$		−	7.75597i		−	0.362809i	−0.983409	−	0.181405i	$-0.941936\pi$
$457$		−	7.75597i		−	0.362809i	0.983409	−	0.181405i	$-0.0580643\pi$
$458$	17.4214	−	30.1748i	0.814050	−	1.40998i
$459$	−9.92745			−0.463374
$460$	29.4814	+	17.0211i	1.37458	+	0.793613i
$461$	1.27498	+	0.736110i	0.0593817	+	0.0342840i	0.529397	−	0.848374i	$-0.322418\pi$
$461$	1.27498	+	0.736110i	0.0593817	+	0.0342840i	−0.470015	+	0.882658i	$0.655752\pi$
$462$		0			0
$463$		−	14.0366i		−	0.652335i	−0.945312	−	0.326168i	$-0.894243\pi$
$463$		−	14.0366i		−	0.652335i	0.945312	−	0.326168i	$-0.105757\pi$
$464$	1.85815	+	3.21841i	0.0862625	+	0.149411i
$465$	−34.4949	+	59.7469i	−1.59966	+	2.77070i
$466$	−30.1467	−	17.4052i	−1.39652	−	0.806281i
$467$	15.6903	−	27.1764i	0.726060	−	1.25757i	−0.232476	−	0.972602i	$-0.574683\pi$
$467$	15.6903	−	27.1764i	0.726060	−	1.25757i	0.958536	−	0.284971i	$-0.0919841\pi$
$468$	12.2566	−	14.0966i	0.566562	−	0.651614i
$469$		0			0
$470$	−19.6225	+	11.3291i	−0.905119	+	0.522571i
$471$	29.3632			1.35298
$472$	−6.94798			−0.319807
$473$	2.79610	−	1.61433i	0.128565	−	0.0742268i
$474$	3.12985	−	1.80702i	0.143759	−	0.0829993i
$475$	−16.4246	−	9.48277i	−0.753614	−	0.435099i
$476$		0			0
$477$	−5.20337	+	9.01251i	−0.238246	+	0.412654i
$478$	64.1698			2.93506
$479$	−35.6760	−	20.5975i	−1.63008	−	0.941125i	−0.984068	−	0.177795i	$-0.943104\pi$
$479$	−35.6760	−	20.5975i	−1.63008	−	0.941125i	−0.646009	−	0.763330i	$-0.723563\pi$
$480$	−32.6299	−	56.5167i	−1.48935	−	2.57962i
$481$	−32.8587	+	11.3102i	−1.49823	+	0.515701i
$482$	−62.2572			−2.83574
$483$		0			0
$484$	12.5101	+	21.6681i	0.568641	+	0.984914i
$485$	0.834351	+	1.44514i	0.0378859	+	0.0656204i
$486$	−33.9484	+	19.6001i	−1.53993	+	0.889078i
$487$		−	28.3265i		−	1.28360i	−0.766874	−	0.641798i	$-0.778189\pi$
$487$		−	28.3265i		−	1.28360i	0.766874	−	0.641798i	$-0.221811\pi$
$488$	1.26400	−	0.729774i	0.0572188	−	0.0330353i
$489$			5.24584i			0.237225i
$490$		0			0
$491$	17.3931	+	30.1258i	0.784941	+	1.35956i	0.929034	+	0.369993i	$0.120640\pi$
$491$	17.3931	+	30.1258i	0.784941	+	1.35956i	−0.144094	+	0.989564i	$0.546027\pi$
$492$		−	66.9455i		−	3.01814i
$493$	−3.17940	−	5.50687i	−0.143193	−	0.248017i
$494$	−11.8707	+	13.6528i	−0.534090	+	0.614268i
$495$	3.37622	−	5.84778i	0.151750	−	0.262838i
$496$	21.2621	−	12.2757i	0.954695	−	0.551194i
$497$		0			0
$498$	11.3725	−	19.6978i	0.509615	−	0.882680i
$499$	0.0601788	+	0.0347442i	0.00269397	+	0.00155537i	0.501346	−	0.865247i	$-0.332838\pi$
$499$	0.0601788	+	0.0347442i	0.00269397	+	0.00155537i	−0.498652	+	0.866802i	$0.666172\pi$
$500$			26.2281i			1.17295i
$501$		−	31.1923i		−	1.39357i
$502$	−23.7165	−	13.6928i	−1.05852	−	0.611138i
$503$	−12.8686	+	22.2891i	−0.573782	+	0.993820i	0.422391	+	0.906414i	$0.361191\pi$
$503$	−12.8686	+	22.2891i	−0.573782	+	0.993820i	−0.996173	+	0.0874060i	$0.972142\pi$
$504$		0			0
$505$	−18.1634	+	10.4866i	−0.808260	+	0.466649i
$506$	3.60719	−	6.24783i	0.160359	−	0.277750i
$507$	−4.08565	−	29.1162i	−0.181450	−	1.29309i
$508$	15.0770	+	26.1141i	0.668933	+	1.15863i
$509$		−	7.04000i		−	0.312042i	−0.987754	−	0.156021i	$-0.950133\pi$
$509$		−	7.04000i		−	0.312042i	0.987754	−	0.156021i	$-0.0498668\pi$
$510$	42.6152	+	73.8117i	1.88703	+	3.26844i
$511$		0			0
$512$			28.7215i			1.26932i
$513$	4.12312	−	2.38049i	0.182040	−	0.105101i
$514$			9.67199i			0.426613i
$515$	−25.6990	+	14.8373i	−1.13243	+	0.653810i
$516$	10.0896	+	17.4758i	0.444171	+	0.769327i
$517$	1.32173	+	2.28930i	0.0581295	+	0.100683i
$518$		0			0
$519$	8.33263			0.365762
$520$	12.0874	+	2.35089i	0.530066	+	0.103093i
$521$	−8.16266	−	14.1381i	−0.357613	−	0.619403i	0.629949	−	0.776637i	$-0.283076\pi$
$521$	−8.16266	−	14.1381i	−0.357613	−	0.619403i	−0.987561	+	0.157234i	$0.949742\pi$
$522$	−4.95322	−	2.85974i	−0.216796	−	0.125167i
$523$	−7.08946			−0.310000			−0.155000	−	0.987914i	$-0.549538\pi$
$523$	−7.08946			−0.310000			−0.155000	+	0.987914i	$0.549538\pi$
$524$	−10.0463	+	17.4007i	−0.438874	+	0.760152i
$525$		0			0
$526$	4.86836	+	2.81075i	0.212271	+	0.122555i
$527$	−36.3805	+	21.0043i	−1.58476	+	0.914963i
$528$	−5.03280	+	2.90569i	−0.219025	+	0.126454i
$529$	−8.11189			−0.352691
$530$	−37.3824			−1.62379
$531$	−13.4216	+	7.74899i	−0.582449	+	0.336277i
$532$		0			0
$533$	−32.8796	−	28.5880i	−1.42417	−	1.23828i
$534$	8.63218	−	14.9514i	0.373551	−	0.647009i
$535$	11.9548	+	6.90209i	0.516850	+	0.298403i
$536$	−3.99505	+	6.91963i	−0.172560	+	0.298882i
$537$	−6.66368	−	11.5418i	−0.287559	−	0.498067i
$538$			25.1558i			1.08454i
$539$		0			0
$540$	−15.2922	−	8.82897i	−0.658073	−	0.379938i
$541$	22.0977	+	12.7581i	0.950055	+	0.548515i	0.893098	−	0.449862i	$-0.148527\pi$
$541$	22.0977	+	12.7581i	0.950055	+	0.548515i	0.0569571	+	0.998377i	$0.481860\pi$
$542$	27.4818			1.18044
$543$	2.39218	−	4.14338i	0.102658	−	0.177809i
$544$		−	39.7374i		−	1.70373i
$545$	−37.5235			−1.60733
$546$		0			0
$547$	−13.3073			−0.568978			−0.284489	−	0.958679i	$-0.591824\pi$
$547$	−13.3073			−0.568978			−0.284489	+	0.958679i	$0.591824\pi$
$548$			18.2625i			0.780136i
$549$	1.62781	−	2.81945i	0.0694733	−	0.120331i
$550$	14.9070			0.635637
$551$	2.64097	+	1.52476i	0.112509	+	0.0649571i
$552$	7.16607	+	4.13733i	0.305008	+	0.176096i
$553$		0			0
$554$		−	45.0669i		−	1.91471i
$555$	−39.2559	−	67.9932i	−1.66632	−	2.88615i
$556$	20.4297	−	35.3852i	0.866412	−	1.50067i
$557$	14.7285	+	8.50353i	0.624069	+	0.360306i	0.778451	−	0.627705i	$-0.216006\pi$
$557$	14.7285	+	8.50353i	0.624069	+	0.360306i	−0.154383	+	0.988011i	$0.549339\pi$
$558$	−18.8926	+	32.7229i	−0.799786	+	1.38527i
$559$	12.8916	+	2.50732i	0.545259	+	0.106048i
$560$		0			0
$561$	8.61140	−	4.97179i	0.363573	−	0.209909i
$562$	−36.4244			−1.53647
$563$	24.9193			1.05022			0.525111	−	0.851034i	$-0.324024\pi$
$563$	24.9193			1.05022			0.525111	+	0.851034i	$0.324024\pi$
$564$	−14.3083	+	8.26088i	−0.602486	+	0.347846i
$565$	−15.3158	+	8.84257i	−0.644340	+	0.372010i
$566$	−38.8013	−	22.4019i	−1.63094	−	0.941623i
$567$		0			0
$568$	−3.05745	+	5.29566i	−0.128288	+	0.222201i
$569$	−5.88129			−0.246557			−0.123278	−	0.992372i	$-0.539341\pi$
$569$	−5.88129			−0.246557			−0.123278	+	0.992372i	$0.539341\pi$
$570$	−35.3983	−	20.4372i	−1.48267	−	0.856022i
$571$	4.46311	+	7.73034i	0.186775	+	0.323504i	0.944173	−	0.329449i	$-0.106863\pi$
$571$	4.46311	+	7.73034i	0.186775	+	0.323504i	−0.757398	+	0.652954i	$0.773530\pi$
$572$	1.49456	−	7.68444i	0.0624906	−	0.321303i
$573$	−25.7074			−1.07394
$574$		0			0
$575$	15.3816	+	26.6417i	0.641457	+	1.11104i
$576$	−11.7398	−	20.3339i	−0.489158	−	0.847247i
$577$	31.3443	−	18.0967i	1.30488	−	0.753374i	0.323645	−	0.946179i	$-0.395092\pi$
$577$	31.3443	−	18.0967i	1.30488	−	0.753374i	0.981237	+	0.192804i	$0.0617583\pi$
$578$			16.0381i			0.667097i
$579$	27.5961	−	15.9326i	1.14685	−	0.662136i
$580$		−	11.3104i		−	0.469638i
$581$		0			0
$582$	1.10513	+	1.91414i	0.0458091	+	0.0793437i
$583$			4.36130i			0.180626i
$584$	3.38919	+	5.87025i	0.140246	+	0.242913i
$585$	25.9715	−	8.93958i	1.07379	−	0.369606i
$586$	0.443035	−	0.767358i	0.0183016	−	0.0316993i
$587$	31.6008	−	18.2447i	1.30431	−	0.753041i	0.323166	−	0.946342i	$-0.395253\pi$
$587$	31.6008	−	18.2447i	1.30431	−	0.753041i	0.981139	+	0.193301i	$0.0619195\pi$
$588$		0			0
$589$	10.0732	−	17.4472i	0.415058	−	0.718901i
$590$	−48.2123	−	27.8354i	−1.98487	−	1.14596i
$591$		−	51.9210i		−	2.13574i
$592$			27.9399i			1.14832i
$593$	30.3048	+	17.4965i	1.24447	+	0.718495i	0.970001	−	0.243102i	$-0.0781649\pi$
$593$	30.3048	+	17.4965i	1.24447	+	0.718495i	0.274468	+	0.961596i	$0.411498\pi$
$594$	−1.87107	+	3.24079i	−0.0767711	+	0.132971i
$595$		0			0
$596$	−5.34926	+	3.08839i	−0.219114	+	0.126506i
$597$	−3.56193	+	6.16944i	−0.145780	+	0.252498i
$598$	27.7482	−	9.55113i	1.13471	−	0.390575i
$599$	16.2526	+	28.1503i	0.664062	+	1.15019i	0.979539	+	0.201256i	$0.0645025\pi$
$599$	16.2526	+	28.1503i	0.664062	+	1.15019i	−0.315476	+	0.948934i	$0.602164\pi$
$600$			17.0979i			0.698018i
$601$	−10.0390	−	17.3881i	−0.409500	−	0.709275i	0.585334	−	0.810792i	$-0.300963\pi$
$601$	−10.0390	−	17.3881i	−0.409500	−	0.709275i	−0.994834	+	0.101518i	$0.967630\pi$
$602$		0			0
$603$			17.8225i			0.725788i
$604$	33.7235	−	19.4703i	1.37219	−	0.792235i
$605$			36.7897i			1.49572i
$606$	−24.0581	+	13.8900i	−0.977294	+	0.564241i
$607$	−4.85800	−	8.41431i	−0.197180	−	0.341526i	0.750433	−	0.660947i	$-0.229845\pi$
$607$	−4.85800	−	8.41431i	−0.197180	−	0.341526i	−0.947613	+	0.319420i	$0.896512\pi$
$608$	9.52856	+	16.5039i	0.386434	+	0.669323i
$609$		0			0
$610$	11.6946			0.473502
$611$	−2.05286	+	10.5550i	−0.0830500	+	0.427011i
$612$	12.8490	+	22.2551i	0.519389	+	0.899607i
$613$	10.2898	+	5.94080i	0.415600	+	0.239947i	0.693193	−	0.720752i	$-0.256203\pi$
$613$	10.2898	+	5.94080i	0.415600	+	0.239947i	−0.277593	+	0.960699i	$0.589537\pi$
$614$	29.7017			1.19866
$615$	49.2184	−	85.2488i	1.98468	−	3.43756i
$616$		0			0
$617$	−17.3105	−	9.99422i	−0.696895	−	0.402352i	0.109295	−	0.994009i	$-0.465141\pi$
$617$	−17.3105	−	9.99422i	−0.696895	−	0.402352i	−0.806190	+	0.591657i	$0.798474\pi$
$618$	−34.0393	+	19.6526i	−1.36926	+	0.790543i
$619$	−36.1285	+	20.8588i	−1.45213	+	0.838386i	−0.998602	−	0.0528581i	$-0.983167\pi$
$619$	−36.1285	+	20.8588i	−1.45213	+	0.838386i	−0.453525	+	0.891244i	$0.649834\pi$
$620$	−74.7207			−3.00086
$621$	−7.72257			−0.309896
$622$	−18.9708	+	10.9528i	−0.760659	+	0.439166i
$623$		0			0
$624$	−23.2042	−	4.51302i	−0.928911	−	0.180665i
$625$	0.649140	−	1.12434i	0.0259656	−	0.0449737i
$626$	−12.5091	−	7.22211i	−0.499963	−	0.288654i
$627$	−2.38435	+	4.12982i	−0.0952219	+	0.164929i
$628$	15.9012	+	27.5416i	0.634526	+	1.09903i
$629$		−	47.8066i		−	1.90618i
$630$		0			0
$631$	15.2780	+	8.82074i	0.608206	+	0.351148i	0.772263	−	0.635303i	$-0.219125\pi$
$631$	15.2780	+	8.82074i	0.608206	+	0.351148i	−0.164057	+	0.986451i	$0.552458\pi$
$632$	0.622082	+	0.359159i	0.0247451	+	0.0142866i
$633$	−33.6168			−1.33615
$634$	0.739603	−	1.28103i	0.0293734	−	0.0508762i
$635$			44.3385i			1.75952i
$636$	−27.2584			−1.08086
$637$		0			0
$638$	−2.39694			−0.0948958
$639$			13.6397i			0.539580i
$640$	13.3159	−	23.0639i	0.526359	−	0.911680i
$641$	10.9202			0.431324			0.215662	−	0.976468i	$-0.430809\pi$
$641$	10.9202			0.431324			0.215662	+	0.976468i	$0.430809\pi$
$642$	15.8346	+	9.14208i	0.624940	+	0.360809i
$643$	15.2725	+	8.81757i	0.602288	+	0.347731i	0.769941	−	0.638115i	$-0.220286\pi$
$643$	15.2725	+	8.81757i	0.602288	+	0.347731i	−0.167653	+	0.985846i	$0.553619\pi$
$644$		0			0
$645$			29.6716i			1.16832i
$646$	−12.4445	−	21.5544i	−0.489620	−	0.848048i
$647$	8.33632	−	14.4389i	0.327735	−	0.567653i	−0.654327	−	0.756211i	$-0.727048\pi$
$647$	8.33632	−	14.4389i	0.327735	−	0.567653i	0.982062	+	0.188558i	$0.0603815\pi$
$648$	−8.92758	−	5.15434i	−0.350708	−	0.202482i
$649$	−3.24747	+	5.62479i	−0.127474	+	0.220792i
$650$	45.7593	+	39.7866i	1.79483	+	1.56056i
$651$		0			0
$652$	−4.92042	+	2.84080i	−0.192698	+	0.111254i
$653$	−6.77329			−0.265059			−0.132530	−	0.991179i	$-0.542310\pi$
$653$	−6.77329			−0.265059			−0.132530	+	0.991179i	$0.542310\pi$
$654$	−49.7013			−1.94347
$655$	−25.5860	+	14.7721i	−0.999727	+	0.577193i
$656$	−30.3374	+	17.5153i	−1.18448	+	0.683858i
$657$	13.0940	+	7.55983i	0.510846	+	0.294937i
$658$		0			0
$659$	−16.7680	+	29.0431i	−0.653190	+	1.13136i	0.329154	+	0.944276i	$0.393236\pi$
$659$	−16.7680	+	29.0431i	−0.653190	+	1.13136i	−0.982344	+	0.187082i	$0.940097\pi$
$660$	17.6866			0.688451
$661$	21.7945	+	12.5830i	0.847707	+	0.489424i	0.859876	−	0.510502i	$-0.170540\pi$
$661$	21.7945	+	12.5830i	0.847707	+	0.489424i	−0.0121696	+	0.999926i	$0.503874\pi$
$662$	−4.42829	−	7.67002i	−0.172110	−	0.298104i
$663$	39.7036	+	7.72202i	1.54196	+	0.299898i
$664$	4.52075			0.175439
$665$		0			0
$666$	−21.5001	−	37.2393i	−0.833112	−	1.44299i
$667$	−2.47325	−	4.28380i	−0.0957647	−	0.165869i
$668$	29.2572	−	16.8917i	1.13200	−	0.653558i
$669$			9.90802i			0.383066i
$670$	−55.4436	+	32.0104i	−2.14197	+	1.23667i
$671$		−	1.36438i		−	0.0526713i
$672$		0			0
$673$	−0.927341	−	1.60620i	−0.0357464	−	0.0619145i	0.847599	−	0.530638i	$-0.178048\pi$
$673$	−0.927341	−	1.60620i	−0.0357464	−	0.0619145i	−0.883345	+	0.468723i	$0.844714\pi$
$674$		−	43.0902i		−	1.65977i
$675$	−7.97855	−	13.8193i	−0.307094	−	0.531903i
$676$	25.0974	−	19.5996i	0.965286	−	0.753831i
$677$	7.36044	−	12.7487i	0.282885	−	0.489971i	−0.689209	−	0.724562i	$-0.742042\pi$
$677$	7.36044	−	12.7487i	0.282885	−	0.489971i	0.972094	+	0.234592i	$0.0753753\pi$
$678$	−20.2863	+	11.7123i	−0.779092	+	0.449809i
$679$		0			0
$680$	−8.47009	+	14.6706i	−0.324813	+	0.562593i
$681$	26.5716	+	15.3411i	1.01823	+	0.587873i
$682$			15.8351i			0.606358i
$683$		−	7.94353i		−	0.303951i	−0.988384	−	0.151975i	$-0.951437\pi$
$683$		−	7.94353i		−	0.303951i	0.988384	−	0.151975i	$-0.0485634\pi$
$684$	−10.6730	−	6.16206i	−0.408092	−	0.235612i
$685$	−13.4266	+	23.2556i	−0.513005	+	0.888551i
$686$		0			0
$687$	32.3529	−	18.6790i	1.23434	−	0.712647i
$688$	5.27960	−	9.14454i	0.201283	−	0.348632i
$689$	−11.6402	+	13.3877i	−0.443458	+	0.510029i
$690$	33.1504	+	57.4182i	1.26201	+	2.18587i
$691$			10.2307i			0.389193i	0.980883	+	0.194597i	$0.0623397\pi$
$691$			10.2307i			0.389193i	−0.980883	+	0.194597i	$0.937660\pi$
$692$	4.51240	+	7.81571i	0.171536	+	0.297109i
$693$		0			0
$694$			16.8118i			0.638168i
$695$	52.0306	−	30.0399i	1.97363	−	1.13948i
$696$		−	2.74922i		−	0.104209i
$697$	51.9089	−	29.9696i	1.96619	−	1.13518i
$698$	22.7785	+	39.4535i	0.862178	+	1.49334i
$699$	−18.6616	−	32.3228i	−0.705845	−	1.22256i
$700$		0			0
$701$	−16.5978			−0.626891			−0.313445	−	0.949606i	$-0.601483\pi$
$701$	−16.5978			−0.626891			−0.313445	+	0.949606i	$0.601483\pi$
$702$	−14.3932	+	4.95424i	−0.543235	+	0.186986i
$703$	11.4635	+	19.8553i	0.432353	+	0.748857i
$704$	−8.52162	−	4.91996i	−0.321171	−	0.185428i
$705$	−24.2936			−0.914951
$706$	22.8000	−	39.4907i	0.858088	−	1.48625i
$707$		0			0
$708$	−35.1552	−	20.2969i	−1.32121	−	0.762804i
$709$	−41.4531	+	23.9329i	−1.55680	+	0.898820i	−0.559242	+	0.829004i	$0.688908\pi$
$709$	−41.4531	+	23.9329i	−1.55680	+	0.898820i	−0.997560	+	0.0698158i	$0.977759\pi$
$710$	−42.4316	+	24.4979i	−1.59243	+	0.919389i
$711$	1.60226			0.0600895
$712$	3.43142			0.128598
$713$	−28.3004	+	16.3393i	−1.05986	+	0.611910i
$714$		0			0
$715$	7.55279	−	8.68661i	0.282458	−	0.324861i
$716$	7.21722	−	12.5006i	0.269720	−	0.467169i
$717$	59.5840	+	34.4008i	2.22520	+	1.28472i
$718$	14.4318	−	24.9965i	0.538588	−	0.932862i
$719$	−19.0461	−	32.9888i	−0.710300	−	1.23028i	−0.964744	−	0.263188i	$-0.915226\pi$
$719$	−19.0461	−	32.9888i	−0.710300	−	1.23028i	0.254444	−	0.967087i	$-0.418107\pi$
$720$		−	22.0836i		−	0.823009i
$721$		0			0
$722$	−24.3719	−	14.0711i	−0.907028	−	0.523673i
$723$	−57.8081	−	33.3755i	−2.14991	−	1.24125i
$724$	5.18179			0.192580
$725$	5.11047	−	8.85159i	0.189798	−	0.328740i
$726$			48.7294i			1.80852i
$727$	15.4059			0.571374			0.285687	−	0.958323i	$-0.407778\pi$
$727$	15.4059			0.571374			0.285687	+	0.958323i	$0.407778\pi$
$728$		0			0
$729$	−9.41460			−0.348689
$730$			54.3118i			2.01017i
$731$	−9.03369	+	15.6468i	−0.334123	+	0.578718i
$732$	8.52744			0.315183
$733$	10.0717	+	5.81490i	0.372007	+	0.214778i	0.674335	−	0.738426i	$-0.264430\pi$
$733$	10.0717	+	5.81490i	0.372007	+	0.214778i	−0.302328	+	0.953204i	$0.597764\pi$
$734$	20.8487	+	12.0370i	0.769538	+	0.444293i
$735$		0			0
$736$		−	30.9117i		−	1.13942i
$737$	3.73456	+	6.46844i	0.137564	+	0.238268i
$738$	26.9565	−	46.6900i	0.992282	−	1.71868i
$739$	−2.32875	−	1.34451i	−0.0856645	−	0.0494584i	0.456556	−	0.889695i	$-0.349083\pi$
$739$	−2.32875	−	1.34451i	−0.0856645	−	0.0494584i	−0.542220	+	0.840236i	$0.682416\pi$
$740$	42.5168	−	73.6413i	1.56295	−	2.70711i
$741$	−18.3416	+	6.31331i	−0.673794	+	0.231925i
$742$		0			0
$743$	−2.13665	+	1.23360i	−0.0783862	+	0.0452563i	−0.538681	−	0.842510i	$-0.681077\pi$
$743$	−2.13665	+	1.23360i	−0.0783862	+	0.0452563i	0.460295	+	0.887766i	$0.347744\pi$
$744$	−18.1624			−0.665866
$745$	−9.08236			−0.332752
$746$	−57.1433	+	32.9917i	−2.09217	+	1.20791i
$747$	8.73288	−	5.04193i	0.319519	−	0.184475i
$748$	9.32673	+	5.38479i	0.341019	+	0.196887i
$749$		0			0
$750$	−25.5409	+	44.2382i	−0.932623	+	1.61535i
$751$	37.9185			1.38366			0.691832	−	0.722058i	$-0.256804\pi$
$751$	37.9185			1.38366			0.691832	+	0.722058i	$0.256804\pi$
$752$	7.48709	+	4.32267i	0.273026	+	0.157632i
$753$	−14.6811	−	25.4285i	−0.535010	−	0.926664i
$754$	−7.35777	−	6.39740i	−0.267954	−	0.232980i
$755$	57.2583			2.08384
$756$		0			0
$757$	−17.3225	−	30.0035i	−0.629598	−	1.09050i	−0.987632	−	0.156788i	$-0.949886\pi$
$757$	−17.3225	−	30.0035i	−0.629598	−	1.09050i	0.358034	−	0.933709i	$-0.383447\pi$
$758$	28.9145	+	50.0814i	1.05022	+	1.81904i
$759$	6.69881	−	3.86756i	0.243151	−	0.140384i
$760$		−	8.12411i		−	0.294692i
$761$	−19.7969	+	11.4297i	−0.717636	+	0.414328i	−0.813882	−	0.581030i	$-0.802650\pi$
$761$	−19.7969	+	11.4297i	−0.717636	+	0.414328i	0.0962458	+	0.995358i	$0.469317\pi$
$762$			58.7280i			2.12749i
$763$		0			0
$764$	−13.9214	−	24.1126i	−0.503659	−	0.872363i
$765$			37.7863i			1.36617i
$766$	−16.9813	−	29.4124i	−0.613558	−	1.06271i
$767$	−24.9811	+	8.59868i	−0.902015	+	0.310480i
$768$	−7.46951	+	12.9376i	−0.269533	+	0.466844i
$769$	−44.8839	+	25.9137i	−1.61855	+	0.934473i	−0.631260	+	0.775571i	$0.717462\pi$
$769$	−44.8839	+	25.9137i	−1.61855	+	0.934473i	−0.987294	+	0.158902i	$0.949205\pi$
$770$		0			0
$771$	−5.18507	+	8.98080i	−0.186736	+	0.323436i
$772$	29.8884	+	17.2561i	1.07571	+	0.621060i
$773$			5.69966i			0.205003i	0.994733	+	0.102501i	$0.0326846\pi$
$773$			5.69966i			0.205003i	−0.994733	+	0.102501i	$0.967315\pi$
$774$			16.2509i			0.584126i
$775$	−58.4770	−	33.7617i	−2.10056	−	1.21276i
$776$	−0.219653	+	0.380450i	−0.00788508	+	0.0136574i
$777$		0			0
$778$	−38.6146	+	22.2941i	−1.38440	+	0.799283i
$779$	−14.3727	+	24.8943i	−0.514956	+	0.891930i
$780$	54.2918	+	47.2054i	1.94396	+	1.69022i
$781$	2.85809	+	4.95037i	0.102271	+	0.177138i
$782$			40.3712i			1.44367i
$783$	1.28289	+	2.22204i	0.0458469	+	0.0794092i
$784$		0			0
$785$			46.7622i			1.66902i
$786$	−33.8896	+	19.5662i	−1.20880	+	0.697902i
$787$			16.8141i			0.599358i	0.954040	+	0.299679i	$0.0968796\pi$
$787$			16.8141i			0.599358i	−0.954040	+	0.299679i	$0.903120\pi$
$788$	48.7000	−	28.1170i	1.73487	−	1.00163i
$789$	3.01364	+	5.21977i	0.107288	+	0.185829i
$790$	2.87777	+	4.98444i	0.102386	+	0.177338i
$791$		0			0
$792$	1.77766			0.0631664
$793$	3.64151	−	4.18817i	0.129314	−	0.148726i
$794$	−13.8148	−	23.9280i	−0.490270	−	0.849172i
$795$	−34.7109	−	20.0404i	−1.23107	−	0.710759i
$796$	−7.71562			−0.273473
$797$	21.0651	−	36.4858i	0.746163	−	1.29239i	−0.203487	−	0.979078i	$-0.565227\pi$
$797$	21.0651	−	36.4858i	0.746163	−	1.29239i	0.949650	−	0.313314i	$-0.101439\pi$
$798$		0			0
$799$	−12.8108	−	7.39632i	−0.453214	−	0.261663i
$800$	55.3154	−	31.9364i	1.95570	−	1.12912i
$801$	6.62859	−	3.82702i	0.234210	−	0.135221i
$802$	−41.0164			−1.44834
$803$	6.33640			0.223607
$804$	−40.4281	+	23.3412i	−1.42579	+	0.823180i
$805$		0			0
$806$	−42.2637	+	48.6083i	−1.48868	+	1.71215i
$807$	−13.4858	+	23.3581i	−0.474723	+	0.822244i
$808$	−4.78173	−	2.76073i	−0.168221	−	0.0971223i
$809$	15.0843	−	26.1268i	0.530336	−	0.918569i	−0.469037	−	0.883178i	$-0.655399\pi$
$809$	15.0843	−	26.1268i	0.530336	−	0.918569i	0.999374	−	0.0353910i	$-0.0112677\pi$
$810$	−41.2992	−	71.5323i	−1.45111	−	2.51339i
$811$			23.7929i			0.835480i	0.908567	+	0.417740i	$0.137178\pi$
$811$			23.7929i			0.835480i	−0.908567	+	0.417740i	$0.862822\pi$
$812$		0			0
$813$	25.5178	+	14.7327i	0.894950	+	0.516699i
$814$	−15.6064	−	9.01034i	−0.547003	−	0.315812i
$815$	−8.35425			−0.292637
$816$	16.2601	−	28.1633i	0.569217	−	0.985913i
$817$		−	8.66468i		−	0.303139i
$818$	50.7432			1.77419
$819$		0			0
$820$	106.614			3.72312
$821$		−	35.8847i		−	1.25239i	−0.779668	−	0.626193i	$-0.784612\pi$
$821$		−	35.8847i		−	1.25239i	0.779668	−	0.626193i	$-0.215388\pi$
$822$	−17.7841	+	30.8029i	−0.620291	+	1.07438i
$823$	12.2346			0.426470			0.213235	−	0.977001i	$-0.431600\pi$
$823$	12.2346			0.426470			0.213235	+	0.977001i	$0.431600\pi$
$824$	−6.76557	−	3.90610i	−0.235690	−	0.136076i
$825$	13.8417	+	7.99151i	0.481906	+	0.278229i
$826$		0			0
$827$		−	27.3474i		−	0.950962i	−0.879726	−	0.475481i	$-0.842274\pi$
$827$		−	27.3474i		−	0.950962i	0.879726	−	0.475481i	$-0.157726\pi$
$828$	9.99521	+	17.3122i	0.347358	+	0.601641i
$829$	11.7869	−	20.4155i	0.409376	−	0.709060i	−0.585444	−	0.810713i	$-0.699080\pi$
$829$	11.7869	−	20.4155i	0.409376	−	0.709060i	0.994820	+	0.101653i	$0.0324132\pi$
$830$	31.3697	+	18.1113i	1.08886	+	0.628652i
$831$	24.1599	−	41.8463i	0.838099	−	1.45163i
$832$	−13.0271	−	37.8466i	−0.451634	−	1.31210i
$833$		0			0
$834$	68.9165	−	39.7889i	2.38638	−	1.37778i
$835$	49.6751			1.71908
$836$	−5.16483			−0.178630
$837$	14.6796	−	8.47530i	0.507403	−	0.292949i
$838$	71.2880	−	41.1582i	2.46260	−	1.42179i
$839$	9.16975	+	5.29416i	0.316575	+	0.182775i	0.649865	−	0.760050i	$-0.274825\pi$
$839$	9.16975	+	5.29416i	0.316575	+	0.182775i	−0.333290	+	0.942824i	$0.608159\pi$
$840$		0			0
$841$	13.6783	−	23.6915i	0.471665	−	0.816947i
$842$	46.4664			1.60134
$843$	−33.8214	−	19.5268i	−1.16487	−	0.672538i
$844$	−18.2046	−	31.5313i	−0.626629	−	1.08535i
$845$	46.3689	−	6.50658i	1.59514	−	0.223833i
$846$	−13.3054			−0.457449
$847$		0			0
$848$	7.13174	+	12.3525i	0.244905	+	0.424188i
$849$	−24.0189	−	41.6020i	−0.824328	−	1.42778i
$850$	−72.2428	+	41.7094i	−2.47791	+	1.43062i
$851$		−	37.1888i		−	1.27482i
$852$	−30.9401	+	17.8633i	−1.05999	+	0.611985i
$853$		−	21.3925i		−	0.732464i	−0.930524	−	0.366232i	$-0.880648\pi$
$853$		−	21.3925i		−	0.732464i	0.930524	−	0.366232i	$-0.119352\pi$
$854$		0			0
$855$	−9.06070	−	15.6936i	−0.309870	−	0.536710i
$856$			3.63412i			0.124212i
$857$	3.61065	+	6.25382i	0.123337	+	0.213626i	0.921082	−	0.389369i	$-0.127307\pi$
$857$	3.61065	+	6.25382i	0.123337	+	0.213626i	−0.797744	+	0.602996i	$0.793974\pi$
$858$	10.0040	−	11.5057i	0.341529	−	0.392800i
$859$	−28.5536	+	49.4563i	−0.974238	+	1.68743i	−0.291809	+	0.956477i	$0.594257\pi$
$859$	−28.5536	+	49.4563i	−0.974238	+	1.68743i	−0.682429	+	0.730952i	$0.739076\pi$
$860$	−27.8309	+	16.0682i	−0.949027	+	0.547921i
$861$		0			0
$862$	−37.8421	+	65.5444i	−1.28891	+	2.23245i
$863$	−44.4584	−	25.6681i	−1.51338	−	0.873751i	−0.999877	−	0.0156631i	$-0.995014\pi$
$863$	−44.4584	−	25.6681i	−1.51338	−	0.873751i	−0.513503	−	0.858088i	$-0.671653\pi$
$864$			16.0341i			0.545493i
$865$			13.2701i			0.451197i
$866$	22.3115	+	12.8816i	0.758177	+	0.437734i
$867$	−8.59788	+	14.8920i	−0.291999	+	0.505758i
$868$		0			0
$869$	0.581520	−	0.335741i	0.0197267	−	0.0113892i
$870$	11.0141	−	19.0769i	0.373412	−	0.646768i
$871$	−5.80039	+	29.8233i	−0.196539	+	1.01052i
$872$	−4.93925	−	8.55504i	−0.167264	−	0.289710i
$873$			0.979903i			0.0331647i
$874$	−9.68055	−	16.7672i	−0.327449	−	0.567159i
$875$		0			0
$876$			39.6029i			1.33806i
$877$	18.5570	−	10.7139i	0.626624	−	0.361781i	−0.152820	−	0.988254i	$-0.548835\pi$
$877$	18.5570	−	10.7139i	0.626624	−	0.361781i	0.779443	+	0.626473i	$0.215502\pi$
$878$			33.2341i			1.12160i
$879$	0.822748	−	0.475014i	0.0277506	−	0.0160218i
$880$	−4.62745	−	8.01497i	−0.155991	−	0.270185i
$881$	14.5309	+	25.1683i	0.489560	+	0.847943i	0.999928	−	0.0120134i	$-0.00382406\pi$
$881$	14.5309	+	25.1683i	0.489560	+	0.847943i	−0.510368	+	0.859956i	$0.670491\pi$
$882$		0			0
$883$	4.83594			0.162742			0.0813711	−	0.996684i	$-0.474070\pi$
$883$	4.83594			0.162742			0.0813711	+	0.996684i	$0.474070\pi$
$884$	14.2579	+	41.4223i	0.479545	+	1.39318i
$885$	−29.8446	−	51.6924i	−1.00322	−	1.73762i
$886$	27.5308	+	15.8949i	0.924916	+	0.534000i
$887$	−24.9898			−0.839075			−0.419538	−	0.907738i	$-0.637808\pi$
$887$	−24.9898			−0.839075			−0.419538	+	0.907738i	$0.637808\pi$
$888$	10.3346	−	17.9000i	0.346806	−	0.600685i
$889$		0			0
$890$	23.8108	+	13.7471i	0.798138	+	0.460805i
$891$	−8.34546	+	4.81826i	−0.279584	+	0.161418i
$892$	−9.29338	+	5.36553i	−0.311165	+	0.179651i
$893$	7.09420			0.237398
$894$	−12.0299			−0.402341
$895$	18.3809	−	10.6122i	0.614406	−	0.354727i
$896$		0			0
$897$	30.8855	+	6.00696i	1.03124	+	0.200567i
$898$	−32.4662	+	56.2331i	−1.08341	+	1.87652i
$899$	9.40269	+	5.42865i	0.313597	+	0.181055i
$900$	−20.6530	+	35.7721i	−0.688435	+	1.19240i
$901$	−12.2028	−	21.1359i	−0.406534	−	0.704138i
$902$		−	22.5940i		−	0.752300i
$903$		0			0
$904$	−4.03206	−	2.32791i	−0.134104	−	0.0774252i
$905$	6.59852	+	3.80966i	0.219342	+	0.126637i
$906$	75.8409			2.51964
$907$	7.52060	−	13.0261i	0.249717	−	0.432523i	−0.713730	−	0.700421i	$-0.752996\pi$
$907$	7.52060	−	13.0261i	0.249717	−	0.432523i	0.963447	+	0.267898i	$0.0863290\pi$
$908$			33.2310i			1.10281i
$909$	−12.3160			−0.408497
$910$		0			0
$911$	−9.22150			−0.305522			−0.152761	−	0.988263i	$-0.548816\pi$
$911$	−9.22150			−0.305522			−0.152761	+	0.988263i	$0.548816\pi$
$912$			15.5959i			0.516432i
$913$	2.11299	−	3.65981i	0.0699298	−	0.121122i
$914$	16.3604			0.541153
$915$	10.8589	+	6.26939i	0.358984	+	0.207260i
$916$	35.0404	+	20.2306i	1.15777	+	0.668437i
$917$		0			0
$918$		−	20.9409i		−	0.691151i
$919$	22.5402	+	39.0407i	0.743531	+	1.28783i	0.950878	+	0.309567i	$0.100184\pi$
$919$	22.5402	+	39.0407i	0.743531	+	1.28783i	−0.207346	+	0.978268i	$0.566483\pi$
$920$	−6.58889	+	11.4123i	−0.217229	+	0.376252i
$921$	27.5791	+	15.9228i	0.908762	+	0.524674i
$922$	−1.55274	+	2.68943i	−0.0511368	+	0.0885716i
$923$	−4.43910	+	22.8241i	−0.146115	+	0.751265i
$924$		0			0
$925$	66.5480	−	38.4215i	2.18808	−	1.26329i
$926$	29.6086			0.972999
$927$	−17.4257			−0.572334
$928$	−8.89433	+	5.13514i	−0.291971	+	0.168569i
$929$	40.6313	−	23.4585i	1.33307	−	0.769647i	0.347300	−	0.937754i	$-0.387099\pi$
$929$	40.6313	−	23.4585i	1.33307	−	0.769647i	0.985769	+	0.168107i	$0.0537654\pi$
$930$	−126.030	−	72.7632i	−4.13267	−	2.38600i
$931$		0			0
$932$	20.2117	−	35.0078i	0.662058	−	1.14672i
$933$	−23.4867			−0.768921
$934$	57.3256	+	33.0969i	1.87575	+	1.08296i
$935$	7.91781	+	13.7140i	0.258940	+	0.448497i
$936$	5.45680	+	4.74455i	0.178361	+	0.155080i
$937$	−28.3912			−0.927501			−0.463750	−	0.885966i	$-0.653497\pi$
$937$	−28.3912			−0.927501			−0.463750	+	0.885966i	$0.653497\pi$
$938$		0			0
$939$	−7.74342	−	13.4120i	−0.252697	−	0.437684i
$940$	−13.1558	−	22.7866i	−0.429096	−	0.743216i
$941$	15.4774	−	8.93589i	0.504549	−	0.291302i	−0.226041	−	0.974118i	$-0.572578\pi$
$941$	15.4774	−	8.93589i	0.504549	−	0.291302i	0.730590	+	0.682816i	$0.239245\pi$
$942$			61.9384i			2.01806i
$943$	40.3800	−	23.3134i	1.31495	−	0.759188i
$944$			21.2415i			0.691353i
$945$		0			0
$946$	3.40524	+	5.89805i	0.110714	+	0.191762i
$947$			9.52234i			0.309435i	0.987959	+	0.154717i	$0.0494467\pi$
$947$			9.52234i			0.309435i	−0.987959	+	0.154717i	$0.950553\pi$
$948$	2.09840	+	3.63453i	0.0681528	+	0.118044i
$949$	19.4505	+	16.9118i	0.631391	+	0.548979i
$950$	20.0028	−	34.6459i	0.648978	−	1.12406i
$951$	1.37350	−	0.792989i	0.0445387	−	0.0257144i
$952$		0			0
$953$	−6.70900	+	11.6203i	−0.217326	+	0.376419i	−0.953990	−	0.299840i	$-0.903067\pi$
$953$	−6.70900	+	11.6203i	−0.217326	+	0.376419i	0.736664	+	0.676259i	$0.236400\pi$
$954$	−19.0109	−	10.9759i	−0.615500	−	0.355359i
$955$		−	40.9402i		−	1.32479i
$956$			74.5169i			2.41005i
$957$	−2.22565	−	1.28498i	−0.0719450	−	0.0415375i
$958$	43.4482	−	75.2545i	1.40375	−	2.43136i
$959$		0			0
$960$	78.3145	−	45.2149i	2.52759	−	1.45931i
$961$	20.3637	−	35.2710i	0.656895	−	1.13778i
$962$	−23.8576	−	69.3117i	−0.769201	−	2.23470i
$963$	4.05308	+	7.02013i	0.130609	+	0.226221i
$964$		−	72.2960i		−	2.32850i
$965$	25.3734	+	43.9480i	0.816798	+	1.41474i
$966$		0			0
$967$		−	12.9316i		−	0.415851i	−0.978145	−	0.207926i	$-0.933329\pi$
$967$		−	12.9316i		−	0.415851i	0.978145	−	0.207926i	$-0.0666712\pi$
$968$	−8.38775	+	4.84267i	−0.269593	+	0.155649i
$969$		−	26.6854i		−	0.857260i
$970$	−3.04836	+	1.75997i	−0.0978769	+	0.0565093i
$971$	−23.7607	−	41.1547i	−0.762516	−	1.32072i	−0.941550	−	0.336874i	$-0.890630\pi$
$971$	−23.7607	−	41.1547i	−0.762516	−	1.32072i	0.179034	−	0.983843i	$-0.442703\pi$
$972$	−22.7605	−	39.4224i	−0.730044	−	1.26447i
$973$		0			0
$974$	59.7515			1.91456
$975$	21.1600	+	61.4744i	0.677662	+	1.96876i
$976$	−2.23108	−	3.86434i	−0.0714151	−	0.123695i
$977$	−31.6049	−	18.2471i	−1.01113	−	0.583776i	−0.0996074	−	0.995027i	$-0.531759\pi$
$977$	−31.6049	−	18.2471i	−1.01113	−	0.583776i	−0.911522	+	0.411251i	$0.865092\pi$
$978$	−11.0655			−0.353836
$979$	1.60384	−	2.77793i	0.0512589	−	0.0887831i
$980$		0			0
$981$	−19.0826	−	11.0174i	−0.609261	−	0.351757i
$982$	−63.5470	+	36.6889i	−2.02787	+	1.17079i
$983$	38.2647	−	22.0921i	1.22045	−	0.704629i	0.255439	−	0.966825i	$-0.417780\pi$
$983$	38.2647	−	22.0921i	1.22045	−	0.704629i	0.965015	+	0.262196i	$0.0844466\pi$
$984$	25.9147			0.826130
$985$	82.6865			2.63461
$986$	11.6161	−	6.70658i	0.369933	−	0.213581i
$987$		0			0
$988$	−15.8542	−	13.7849i	−0.504391	−	0.438555i
$989$	−7.02731	+	12.1717i	−0.223455	+	0.387036i
$990$	12.3352	+	7.12176i	0.392040	+	0.226344i
$991$	25.3549	−	43.9159i	0.805424	−	1.39504i	−0.110581	−	0.993867i	$-0.535271\pi$
$991$	25.3549	−	43.9159i	0.805424	−	1.39504i	0.916005	−	0.401168i	$-0.131396\pi$
$992$	33.9247	+	58.7594i	1.07711	+	1.86561i
$993$		−	9.49586i		−	0.301342i
$994$		0			0
$995$	−9.82511	−	5.67253i	−0.311477	−	0.179831i
$996$	22.8740	+	13.2063i	0.724790	+	0.418458i
$997$	−50.2768			−1.59228			−0.796141	−	0.605111i	$-0.793129\pi$
$997$	−50.2768			−1.59228			−0.796141	+	0.605111i	$0.793129\pi$
$998$	−0.0732891	+	0.126940i	−0.00231993	+	0.00401823i
$999$			19.2901i			0.610312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.h.569.6		12
7.2	even	3		91.2.q.a.36.6	✓	12
7.3	odd	6		637.2.u.i.361.1		12
7.4	even	3		637.2.u.h.361.1		12
7.5	odd	6		637.2.q.h.491.6		12
7.6	odd	2		637.2.k.g.569.6		12
13.4	even	6		637.2.u.h.30.1		12
21.2	odd	6		819.2.ct.a.127.1		12
28.23	odd	6		1456.2.cc.c.673.5		12
91.2	odd	12		1183.2.a.p.1.5		6
91.4	even	6	inner	637.2.k.h.459.1		12
91.16	even	3		1183.2.c.i.337.11		12
91.17	odd	6		637.2.k.g.459.1		12
91.23	even	6		1183.2.c.i.337.2		12
91.30	even	6		91.2.q.a.43.6	yes	12
91.37	odd	12		1183.2.a.m.1.2		6
91.54	even	12		8281.2.a.ch.1.5		6
91.69	odd	6		637.2.u.i.30.1		12
91.82	odd	6		637.2.q.h.589.6		12
91.89	even	12		8281.2.a.by.1.2		6
273.212	odd	6		819.2.ct.a.316.1		12
364.303	odd	6		1456.2.cc.c.225.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.6	✓	12	7.2	even	3
91.2.q.a.43.6	yes	12	91.30	even	6
637.2.k.g.459.1		12	91.17	odd	6
637.2.k.g.569.6		12	7.6	odd	2
637.2.k.h.459.1		12	91.4	even	6	inner
637.2.k.h.569.6		12	1.1	even	1	trivial
637.2.q.h.491.6		12	7.5	odd	6
637.2.q.h.589.6		12	91.82	odd	6
637.2.u.h.30.1		12	13.4	even	6
637.2.u.h.361.1		12	7.4	even	3
637.2.u.i.30.1		12	91.69	odd	6
637.2.u.i.361.1		12	7.3	odd	6
819.2.ct.a.127.1		12	21.2	odd	6
819.2.ct.a.316.1		12	273.212	odd	6
1183.2.a.m.1.2		6	91.37	odd	12
1183.2.a.p.1.5		6	91.2	odd	12
1183.2.c.i.337.2		12	91.23	even	6
1183.2.c.i.337.11		12	91.16	even	3
1456.2.cc.c.225.5		12	364.303	odd	6
1456.2.cc.c.673.5		12	28.23	odd	6
8281.2.a.by.1.2		6	91.89	even	12
8281.2.a.ch.1.5		6	91.54	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.10939i q^{2} +(-1.13082 + 1.95864i) q^{3} -2.44952 q^{4} +(-3.11923 - 1.80089i) q^{5} +(-4.13154 - 2.38535i) q^{6} -0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +(3.79878 - 6.57967i) q^{10} +(-0.767631 - 0.443192i) q^{11} +(2.76998 - 4.79774i) q^{12} +(-1.17349 - 3.40924i) q^{13} +(7.05461 - 4.07298i) q^{15} -2.89889 q^{16} +4.96016 q^{17} +(3.86375 - 2.23073i) q^{18} +(-2.06008 + 1.18939i) q^{19} +(7.64062 + 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +3.85851 q^{23} +(1.85721 + 1.07226i) q^{24} +(3.98641 + 6.90466i) q^{25} +(7.19141 - 2.47534i) q^{26} -2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} +(8.59150 + 14.8809i) q^{30} +(-7.33455 + 4.23460i) q^{31} -8.01131i q^{32} +(1.73611 - 1.00234i) q^{33} +10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} -9.63812i q^{37} +(-2.50888 - 4.34551i) q^{38} +(8.00450 + 1.55681i) q^{39} +(-1.70762 + 2.95769i) q^{40} +(10.4652 - 6.04207i) q^{41} +(-1.82125 + 3.15450i) q^{43} +(1.88033 + 1.08561i) q^{44} +7.61796i q^{45} +8.13910i q^{46} +(-2.58274 - 1.49115i) q^{47} +(3.27814 - 5.67790i) q^{48} +(-14.5646 + 8.40888i) q^{50} +(-5.60907 + 9.71520i) q^{51} +(2.87448 + 8.35100i) q^{52} +(-2.46016 - 4.26112i) q^{53} -4.22181i q^{54} +(1.59628 + 2.76484i) q^{55} -5.37995i q^{57} +(2.34189 - 1.35209i) q^{58} -7.32746i q^{59} +(-17.2804 + 9.97684i) q^{60} +(0.769632 + 1.33304i) q^{61} +(-8.93242 - 15.4714i) q^{62} +11.1012 q^{64} +(-2.47929 + 12.7475i) q^{65} +(2.11433 + 3.66213i) q^{66} +(-7.29756 - 4.21325i) q^{67} -12.1500 q^{68} +(-4.36330 + 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} +(-1.73683 + 1.00276i) q^{72} +(-6.19086 + 3.57430i) q^{73} +20.3305 q^{74} -18.0317 q^{75} +(5.04621 - 2.91343i) q^{76} +(-3.28391 + 16.8846i) q^{78} +(-0.378775 + 0.656058i) q^{79} +(9.04232 + 5.22059i) q^{80} +(5.43585 - 9.41518i) q^{81} +(12.7451 + 22.0751i) q^{82} +4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} +(-6.65406 - 3.84172i) q^{86} +2.89937 q^{87} +(-0.420240 + 0.727877i) q^{88} +3.61884i q^{89} -16.0692 q^{90} -9.45150 q^{92} -19.1544i q^{93} +(3.14541 - 5.44800i) q^{94} +8.56783 q^{95} +(15.6913 + 9.05939i) q^{96} +(-0.401229 - 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26}+ \cdots + 6 q^{97}+O(q^{100}) \) 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9 + 12 * q^10 - 6 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^15 + 16 * q^16 + 8 * q^17 + 12 * q^18 - 12 * q^20 + 6 * q^22 + 24 * q^23 - 12 * q^24 + 10 * q^25 + 18 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 - 18 * q^31 + 30 * q^33 - 10 * q^36 - 2 * q^38 + 14 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 - 24 * q^44 - 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 - 28 * q^52 + 22 * q^53 - 6 * q^55 + 12 * q^58 - 66 * q^60 + 14 * q^61 - 4 * q^62 - 52 * q^64 - 18 * q^65 + 26 * q^66 + 24 * q^67 + 16 * q^68 + 4 * q^69 - 24 * q^71 - 60 * q^72 - 30 * q^73 - 12 * q^74 - 92 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 + 72 * q^80 + 2 * q^81 + 14 * q^82 - 48 * q^85 + 60 * q^86 + 4 * q^87 - 14 * q^88 + 24 * q^90 + 24 * q^92 + 4 * q^94 + 44 * q^95 - 6 * q^96 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more