LMFDB - Embedded newform 637.2.q.h.491.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, 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:	$12$
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			491.6
Root			$-1.30089 + 0.554694i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.h.589.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82678 - 1.05469i) q^{2} +(1.13082 + 1.95864i) q^{3} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +(-1.05753 + 1.83169i) q^{9} +O(q^{10})$	\(q+(1.82678 - 1.05469i) q^{2} +(1.13082 + 1.95864i) q^{3} +(1.22476 - 2.12135i) q^{4} -3.60178i 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} +5.53995 q^{12} +(1.17349 + 3.40924i) q^{13} +(7.05461 - 4.07298i) q^{15} +(1.44945 + 2.51051i) q^{16} +(2.48008 - 4.29563i) q^{17} +4.46147i q^{18} +(-2.06008 - 1.18939i) q^{19} +(-7.64062 - 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +(-1.92926 - 3.34157i) q^{23} +(1.85721 - 1.07226i) q^{24} -7.97282 q^{25} +(5.73942 + 4.99028i) q^{26} +2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} +(8.59150 - 14.8809i) q^{30} +8.46921i q^{31} +(6.93800 + 4.00566i) q^{32} +(1.73611 + 1.00234i) q^{33} -10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} +(-8.34686 + 4.81906i) q^{37} -5.01776 q^{38} +(-5.35049 + 6.15370i) q^{39} -3.41525 q^{40} +(-10.4652 + 6.04207i) q^{41} +(-1.82125 + 3.15450i) q^{43} -2.17122i q^{44} +(6.59734 + 3.80898i) q^{45} +(-7.04867 - 4.06955i) q^{46} -2.98229i q^{47} +(-3.27814 + 5.67790i) q^{48} +(-14.5646 + 8.40888i) q^{50} +11.2181 q^{51} +(8.66942 + 1.68613i) q^{52} +4.92032 q^{53} +(3.65619 - 2.11090i) q^{54} +(-1.59628 - 2.76484i) q^{55} -5.37995i q^{57} +(-2.34189 - 1.35209i) q^{58} +(-6.34577 - 3.66373i) q^{59} -19.9537i q^{60} +(-0.769632 + 1.33304i) q^{61} +(8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(12.2793 - 4.22664i) q^{65} +4.22867 q^{66} +(7.29756 - 4.21325i) q^{67} +(-6.07501 - 10.5222i) q^{68} +(4.36330 - 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} +(1.73683 + 1.00276i) q^{72} +7.14859i q^{73} +(-10.1653 + 17.6068i) q^{74} +(-9.01585 - 15.6159i) q^{75} +(-5.04621 + 2.91343i) q^{76} +(-3.28391 + 16.8846i) q^{78} +0.757551 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} +7.68344i q^{86} +(1.44969 - 2.51093i) q^{87} +(-0.420240 - 0.727877i) q^{88} +(-3.13400 + 1.80942i) q^{89} +16.0692 q^{90} -9.45150 q^{92} +(-16.5882 + 9.57719i) q^{93} +(-3.14541 - 5.44800i) q^{94} +(-4.28391 + 7.41995i) q^{95} +18.1188i q^{96} +(0.401229 + 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.82678	−	1.05469i	1.29173	−	0.745781i	0.312770	−	0.949829i	$-0.398743\pi$
$2$	1.82678	−	1.05469i	1.29173	−	0.745781i	0.978961	+	0.204047i	$0.0654097\pi$
$3$	1.13082	+	1.95864i	0.652882	+	1.13082i	0.982420	+	0.186682i	$0.0597734\pi$
$3$	1.13082	+	1.95864i	0.652882	+	1.13082i	−0.329539	+	0.944142i	$0.606893\pi$
$4$	1.22476	−	2.12135i	0.612380	−	1.06067i
$5$		−	3.60178i		−	1.61076i	−0.592756	−	0.805382i	$-0.701960\pi$
$5$		−	3.60178i		−	1.61076i	0.592756	−	0.805382i	$-0.298040\pi$
$6$	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	$-0.624004\pi$
$11$	0.767631	−	0.443192i	0.231450	−	0.133627i	0.611241	+	0.791445i	$0.290671\pi$
$12$	5.53995			1.59925
$13$	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
$16$	1.44945	+	2.51051i	0.362362	+	0.627629i
$17$	2.48008	−	4.29563i	0.601508	−	1.04184i	−0.391085	−	0.920355i	$-0.627900\pi$
$17$	2.48008	−	4.29563i	0.601508	−	1.04184i	0.992593	−	0.121488i	$-0.0387665\pi$
$18$			4.46147i			1.05158i
$19$	−2.06008	−	1.18939i	−0.472615	−	0.272864i	0.244719	−	0.969594i	$-0.421304\pi$
$19$	−2.06008	−	1.18939i	−0.472615	−	0.272864i	−0.717334	+	0.696730i	$0.754638\pi$
$20$	−7.64062	−	4.41132i	−1.70849	−	0.986400i
$21$		0			0
$22$	0.934864	−	1.61923i	0.199314	−	0.345222i
$23$	−1.92926	−	3.34157i	−0.402278	−	0.696765i	0.591723	−	0.806142i	$-0.298448\pi$
$23$	−1.92926	−	3.34157i	−0.402278	−	0.696765i	−0.994000	+	0.109376i	$0.965115\pi$
$24$	1.85721	−	1.07226i	0.379101	−	0.218874i
$25$	−7.97282			−1.59456
$26$	5.73942	+	4.99028i	1.12559	+	0.978674i
$27$	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
$31$			8.46921i			1.52111i	0.649271	+	0.760557i	$0.275074\pi$
$31$			8.46921i			1.52111i	−0.649271	+	0.760557i	$0.724926\pi$
$32$	6.93800	+	4.00566i	1.22648	+	0.708107i
$33$	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
$37$	−8.34686	+	4.81906i	−1.37222	+	0.792249i	−0.991207	−	0.132323i	$-0.957757\pi$
$37$	−8.34686	+	4.81906i	−1.37222	+	0.792249i	−0.381009	+	0.924571i	$0.624423\pi$
$38$	−5.01776			−0.813988
$39$	−5.35049	+	6.15370i	−0.856763	+	0.985380i
$40$	−3.41525			−0.539998
$41$	−10.4652	+	6.04207i	−1.63438	+	0.943612i	−0.651666	+	0.758506i	$0.725929\pi$
$41$	−10.4652	+	6.04207i	−1.63438	+	0.943612i	−0.982719	+	0.185106i	$0.940737\pi$
$42$		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	$0.256251\pi$
$44$		−	2.17122i		−	0.327323i
$45$	6.59734	+	3.80898i	0.983474	+	0.567809i
$46$	−7.04867	−	4.06955i	−1.03927	−	0.600022i
$47$		−	2.98229i		−	0.435012i	−0.976059	−	0.217506i	$-0.930208\pi$
$47$		−	2.98229i		−	0.435012i	0.976059	−	0.217506i	$-0.0697922\pi$
$48$	−3.27814	+	5.67790i	−0.473158	+	0.819535i
$49$		0			0
$50$	−14.5646	+	8.40888i	−2.05975	+	1.18920i
$51$	11.2181			1.57085
$52$	8.66942	+	1.68613i	1.20223	+	0.233824i
$53$	4.92032			0.675858			0.337929	−	0.941172i	$-0.390274\pi$
$53$	4.92032			0.675858			0.337929	+	0.941172i	$0.390274\pi$
$54$	3.65619	−	2.11090i	0.497545	−	0.287258i
$55$	−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
$59$	−6.34577	−	3.66373i	−0.826148	−	0.476977i	0.0263837	−	0.999652i	$-0.491601\pi$
$59$	−6.34577	−	3.66373i	−0.826148	−	0.476977i	−0.852532	+	0.522675i	$0.824934\pi$
$60$		−	19.9537i		−	2.57601i
$61$	−0.769632	+	1.33304i	−0.0985412	+	0.170678i	−0.911081	−	0.412227i	$-0.864751\pi$
$61$	−0.769632	+	1.33304i	−0.0985412	+	0.170678i	0.812540	+	0.582906i	$0.198084\pi$
$62$	8.93242	+	15.4714i	1.13442	+	1.96487i
$63$		0			0
$64$	11.1012			1.38765
$65$	12.2793	−	4.22664i	1.52306	−	0.524250i
$66$	4.22867			0.520513
$67$	7.29756	−	4.21325i	0.891539	−	0.514730i	0.0170931	−	0.999854i	$-0.494559\pi$
$67$	7.29756	−	4.21325i	0.891539	−	0.514730i	0.874445	+	0.485124i	$0.161225\pi$
$68$	−6.07501	−	10.5222i	−0.736703	−	1.27601i
$69$	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
$73$			7.14859i			0.836679i	0.908291	+	0.418340i	$0.137388\pi$
$73$			7.14859i			0.836679i	−0.908291	+	0.418340i	$0.862612\pi$
$74$	−10.1653	+	17.6068i	−1.18169	+	2.04675i
$75$	−9.01585	−	15.6159i	−1.04106	−	1.80317i
$76$	−5.04621	+	2.91343i	−0.578840	+	0.334193i
$77$		0			0
$78$	−3.28391	+	16.8846i	−0.371830	+	1.91180i
$79$	0.757551			0.0852311			0.0426156	−	0.999092i	$-0.486431\pi$
$79$	0.757551			0.0852311			0.0426156	+	0.999092i	$0.486431\pi$
$80$	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	$-0.915730\pi$
$83$		−	4.76766i		−	0.523319i	0.965160	−	0.261659i	$-0.0842697\pi$
$84$		0			0
$85$	−15.4719	−	8.93270i	−1.67816	−	0.968888i
$86$			7.68344i			0.828527i
$87$	1.44969	−	2.51093i	0.155423	−	0.269200i
$88$	−0.420240	−	0.727877i	−0.0447977	−	0.0775919i
$89$	−3.13400	+	1.80942i	−0.332204	+	0.191798i	−0.656819	−	0.754048i	$-0.728098\pi$
$89$	−3.13400	+	1.80942i	−0.332204	+	0.191798i	0.324615	+	0.945846i	$0.394765\pi$
$90$	16.0692			1.69385
$91$		0			0
$92$	−9.45150			−0.985387
$93$	−16.5882	+	9.57719i	−1.72011	+	0.993108i
$94$	−3.14541	−	5.44800i	−0.324424	−	0.561919i
$95$	−4.28391	+	7.41995i	−0.439520	+	0.761271i
$96$			18.1188i			1.84924i
$97$	0.401229	+	0.231650i	0.0407386	+	0.0235205i	0.520231	−	0.854026i	$-0.325846\pi$
$97$	0.401229	+	0.231650i	0.0407386	+	0.0235205i	−0.479492	+	0.877546i	$0.659179\pi$
$98$		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	$-0.260224\pi$
$101$	−2.91152	−	5.04289i	−0.289707	−	0.501787i	−0.973740	+	0.227664i	$0.926891\pi$
$102$	20.4931	−	11.8317i	2.02912	−	1.17151i
$103$	8.23888			0.811801			0.405901	−	0.913917i	$-0.366958\pi$
$103$	8.23888			0.811801			0.405901	+	0.913917i	$0.366958\pi$
$104$	3.23268	−	1.11271i	0.316991	−	0.109111i
$105$		0			0
$106$	8.98837	−	5.18944i	0.873027	−	0.504043i
$107$	1.91630	+	3.31913i	0.185256	+	0.320872i	0.943663	−	0.330909i	$-0.107355\pi$
$107$	1.91630	+	3.31913i	0.185256	+	0.320872i	−0.758407	+	0.651781i	$0.774022\pi$
$108$	2.45128	−	4.24574i	0.235875	−	0.408547i
$109$			10.4180i			0.997867i	0.866640	+	0.498934i	$0.166275\pi$
$109$			10.4180i			0.997867i	−0.866640	+	0.498934i	$0.833725\pi$
$110$	−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	$0.0924826\pi$
$114$	−5.67421	−	9.82801i	−0.531438	−	0.920478i
$115$	−12.0356	+	6.94875i	−1.12233	+	0.647975i
$116$	−3.14022			−0.291562
$117$	−7.48567	−	1.45590i	−0.692050	−	0.134598i
$118$	−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
$122$			3.24690i			0.293961i
$123$	−23.6685	−	13.6650i	−2.13412	−	1.23213i
$124$	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	$-0.350583\pi$
$128$	6.40347	−	3.69704i	0.565992	−	0.326776i
$129$	−8.23805			−0.725320
$130$	17.9739	−	20.6721i	1.57641	−	1.81306i
$131$	8.20265			0.716669			0.358335	−	0.933593i	$-0.383345\pi$
$131$	8.20265			0.716669			0.358335	+	0.933593i	$0.383345\pi$
$132$	4.25264	−	2.45526i	0.370145	−	0.213703i
$133$		0			0
$134$	8.88737	−	15.3934i	0.767752	−	1.32979i
$135$		−	7.20874i		−	0.620429i
$136$	−4.07316	−	2.35164i	−0.349271	−	0.201652i
$137$	6.45670	+	3.72778i	0.551633	+	0.318485i	0.749780	−	0.661687i	$-0.230159\pi$
$137$	6.45670	+	3.72778i	0.551633	+	0.318485i	−0.198147	+	0.980172i	$0.563492\pi$
$138$		−	18.4078i		−	1.56697i
$139$	8.34028	−	14.4458i	0.707413	−	1.22528i	−0.258400	−	0.966038i	$-0.583195\pi$
$139$	8.34028	−	14.4458i	0.707413	−	1.22528i	0.965813	−	0.259238i	$-0.0834714\pi$
$140$		0			0
$141$	5.84125	−	3.37245i	0.491922	−	0.284011i
$142$	−13.6032			−1.14156
$143$	2.41175	+	2.09696i	0.201681	+	0.175357i
$144$	−6.13131			−0.510943
$145$	−3.99877	+	2.30869i	−0.332080	+	0.191726i
$146$	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	$-0.366270\pi$
$149$	−2.18380	−	1.26082i	−0.178904	−	0.103290i	−0.586777	+	0.809748i	$0.699604\pi$
$150$	−32.9400	−	19.0179i	−2.68954	−	1.55281i
$151$		−	15.8972i		−	1.29370i	−0.762618	−	0.646849i	$-0.776086\pi$
$151$		−	15.8972i		−	1.29370i	0.762618	−	0.646849i	$-0.223914\pi$
$152$	−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
$156$	6.50106	+	18.8870i	0.520502	+	1.51217i
$157$	−12.9831			−1.03616			−0.518082	−	0.855331i	$-0.673354\pi$
$157$	−12.9831			−1.03616			−0.518082	+	0.855331i	$0.673354\pi$
$158$	1.38388	−	0.798985i	0.110096	−	0.0635638i
$159$	5.56402	+	9.63717i	0.441256	+	0.764277i
$160$	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	$-0.362288\pi$
$163$	−2.00873	−	1.15974i	−0.157336	−	0.0908378i	−0.576601	+	0.817026i	$0.695621\pi$
$164$			29.6003i			2.31140i
$165$	3.61023	−	6.25309i	0.281056	−	0.486803i
$166$	−5.02843	−	8.70949i	−0.390282	−	0.675987i
$167$	11.9441	−	6.89591i	0.924260	−	0.533622i	0.0392682	−	0.999229i	$-0.487497\pi$
$167$	11.9441	−	6.89591i	0.924260	−	0.533622i	0.884992	+	0.465607i	$0.154164\pi$
$168$		0			0
$169$	−10.2459	+	8.00140i	−0.788143	+	0.615493i
$170$	−37.6851			−2.89031
$171$	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	$-0.788605\pi$
$173$	1.84216	−	3.19071i	0.140057	−	0.242585i	0.927518	+	0.373779i	$0.121938\pi$
$174$		−	6.11590i		−	0.463645i
$175$		0			0
$176$	2.22528	+	1.28477i	0.167737	+	0.0968429i
$177$		−	16.5721i		−	1.24564i
$178$	−3.81677	+	6.61083i	−0.286079	+	0.495503i
$179$	−2.94638	−	5.10328i	−0.220223	−	0.381437i	0.734653	−	0.678443i	$-0.237345\pi$
$179$	−2.94638	−	5.10328i	−0.220223	−	0.381437i	−0.954876	+	0.297006i	$0.904012\pi$
$180$	16.1603	−	9.33017i	1.20452	−	0.695430i
$181$	2.11543			0.157239			0.0786193	−	0.996905i	$-0.474949\pi$
$181$	2.11543			0.157239			0.0786193	+	0.996905i	$0.474949\pi$
$182$		0			0
$183$	−3.48127			−0.257343
$184$	−3.16851	+	1.82934i	−0.233586	+	0.134861i
$185$	17.3572	+	30.0635i	1.27613	+	2.21032i
$186$	−20.2020	+	34.9909i	−1.48128	+	2.56566i
$187$		−	4.39661i		−	0.321512i
$188$	−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	−0.583794	−	0.811902i	$-0.698432\pi$
$191$	5.68333	−	9.84381i	0.411231	−	0.712273i	0.995025	+	0.0996290i	$0.0317656\pi$
$192$	12.5535	+	21.7433i	0.905970	+	1.56919i
$193$	12.2017	−	7.04468i	0.878301	−	0.507087i	0.00820314	−	0.999966i	$-0.497389\pi$
$193$	12.2017	−	7.04468i	0.878301	−	0.507087i	0.870098	+	0.492879i	$0.164055\pi$
$194$	0.977279			0.0701645
$195$	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	$0.638148\pi$
$198$	1.97729	+	3.42476i	0.140520	+	0.243387i
$199$	1.57492	−	2.72785i	0.111643	−	0.193372i	−0.804790	−	0.593560i	$-0.797722\pi$
$199$	1.57492	−	2.72785i	0.111643	−	0.193372i	0.916433	+	0.400188i	$0.131055\pi$
$200$			7.55992i			0.534567i
$201$	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
$205$	21.7622	+	37.6932i	1.51994	+	2.63261i
$206$	15.0507	−	8.68950i	1.04863	−	0.605426i
$207$	8.16096			0.567226
$208$	−6.85804	+	7.88757i	−0.475520	+	0.546905i
$209$	−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
$213$		−	14.5851i		−	0.999355i
$214$	7.00133	+	4.04222i	0.478601	+	0.276321i
$215$	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
$219$	−14.0016	+	8.08380i	−0.946137	+	0.546253i
$220$	−7.82024			−0.527241
$221$	17.5552	+	3.41433i	1.18089	+	0.229673i
$222$	−45.9805			−3.08601
$223$	−3.79396	+	2.19044i	−0.254062	+	0.146683i	−0.621623	−	0.783317i	$-0.713526\pi$
$223$	−3.79396	+	2.19044i	−0.254062	+	0.146683i	0.367561	+	0.930000i	$0.380193\pi$
$224$		0			0
$225$	8.43147	−	14.6037i	0.562098	−	0.973582i
$226$		−	10.3573i		−	0.688959i
$227$	−11.7488	−	6.78316i	−0.779793	−	0.450214i	0.0565636	−	0.998399i	$-0.481986\pi$
$227$	−11.7488	−	6.78316i	−0.779793	−	0.450214i	−0.836357	+	0.548185i	$0.815319\pi$
$228$	−11.4127	−	6.58915i	−0.755827	−	0.436377i
$229$		−	16.5180i		−	1.09154i	−0.837935	−	0.545770i	$-0.816237\pi$
$229$		−	16.5180i		−	1.09154i	0.837935	−	0.545770i	$-0.183763\pi$
$230$	−14.6576	+	25.3877i	−0.966495	+	1.67402i
$231$		0			0
$232$	−1.05272	+	0.607791i	−0.0691147	+	0.0399034i
$233$	16.5026			1.08112			0.540561	−	0.841305i	$-0.318212\pi$
$233$	16.5026			1.08112			0.540561	+	0.841305i	$0.318212\pi$
$234$	−15.2102	+	5.23548i	−0.994324	+	0.342254i
$235$	−10.7416			−0.700702
$236$	−15.5441	+	8.97438i	−1.01183	+	0.584182i
$237$	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
$241$	25.5602	+	14.7572i	1.64648	+	0.950593i	0.978458	+	0.206448i	$0.0661904\pi$
$241$	25.5602	+	14.7572i	1.64648	+	0.950593i	0.668018	+	0.744145i	$0.267143\pi$
$242$			21.5460i			1.38503i
$243$	−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
$247$	1.63743	−	8.41904i	0.104187	−	0.535691i
$248$	8.03060			0.509944
$249$	9.33816	−	5.39139i	0.591782	−	0.341665i
$250$	11.2931	+	19.5602i	0.714236	+	1.23709i
$251$	6.49134	−	11.2433i	0.409730	−	0.709673i	−0.585130	−	0.810940i	$-0.698956\pi$
$251$	6.49134	−	11.2433i	0.409730	−	0.709673i	0.994859	+	0.101267i	$0.0322897\pi$
$252$		0			0
$253$	−2.96191	−	1.71006i	−0.186214	−	0.107511i
$254$	−22.4880	−	12.9835i	−1.41102	−	0.814654i
$255$		−	40.4053i		−	2.53028i
$256$	−3.30268	+	5.72042i	−0.206418	+	0.357526i
$257$	2.29261	+	3.97091i	0.143009	+	0.247698i	0.928628	−	0.371011i	$-0.120989\pi$
$257$	2.29261	+	3.97091i	0.143009	+	0.247698i	−0.785620	+	0.618710i	$0.787656\pi$
$258$	−15.0491	+	8.68862i	−0.936918	+	0.540930i
$259$		0			0
$260$	6.07307	−	31.2253i	0.376636	−	1.93651i
$261$	2.71144			0.167834
$262$	14.9845	−	8.65129i	0.925744	−	0.534479i
$263$	1.33250	+	2.30795i	0.0821652	+	0.142314i	0.904180	−	0.427152i	$-0.140483\pi$
$263$	1.33250	+	2.30795i	0.0821652	+	0.142314i	−0.822015	+	0.569466i	$0.807150\pi$
$264$	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
$268$		−	20.6409i		−	1.26084i
$269$	5.96282	−	10.3279i	0.363559	−	0.629703i	−0.624984	−	0.780637i	$-0.714895\pi$
$269$	5.96282	−	10.3279i	0.363559	−	0.629703i	0.988544	+	0.150934i	$0.0482280\pi$
$270$	−7.60301	−	13.1688i	−0.462705	−	0.801428i
$271$	11.2828	−	6.51416i	0.685384	−	0.395707i	−0.116496	−	0.993191i	$-0.537166\pi$
$271$	11.2828	−	6.51416i	0.685384	−	0.395707i	0.801881	+	0.597484i	$0.203833\pi$
$272$	14.3790			0.871853
$273$		0			0
$274$	15.7267			0.950082
$275$	−6.12018	+	3.53349i	−0.369061	+	0.213077i
$276$	−10.6880	−	18.5121i	−0.643341	−	1.11430i
$277$	10.6824	−	18.5025i	0.641846	−	1.11171i	−0.343174	−	0.939272i	$-0.611502\pi$
$277$	10.6824	−	18.5025i	0.641846	−	1.11171i	0.985020	−	0.172438i	$-0.0551646\pi$
$278$		−	35.1858i		−	2.11030i
$279$	−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	0.987286	+	0.158952i	$0.0508114\pi$
$283$	10.6201	+	18.3946i	0.631299	+	1.09344i	−0.355987	+	0.934491i	$0.615855\pi$
$284$	−13.6803	+	7.89833i	−0.811777	+	0.468680i
$285$	−19.3774			−1.14782
$286$	6.61741	+	1.28703i	0.391295	+	0.0761037i
$287$		0			0
$288$	−14.6742	+	8.47218i	−0.864688	+	0.499228i
$289$	−3.80160	−	6.58457i	−0.223624	−	0.387327i
$290$	−4.86993	+	8.43496i	−0.285972	+	0.495318i
$291$			1.04782i			0.0614243i
$292$	15.1646	+	8.75531i	0.887443	+	0.512366i
$293$	0.363782	+	0.210030i	0.0212524	+	0.0122701i	0.510589	−	0.859825i	$-0.329428\pi$
$293$	0.363782	+	0.210030i	0.0212524	+	0.0122701i	−0.489336	+	0.872095i	$0.662761\pi$
$294$		0			0
$295$	−13.1959	+	22.8561i	−0.768298	+	1.33073i
$296$	4.56949	+	7.91459i	0.265596	+	0.460026i
$297$	1.53637	−	0.887022i	0.0891490	−	0.0514702i
$298$	−5.31910			−0.308127
$299$	9.12826	−	10.4986i	0.527901	−	0.607149i
$300$	−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
$304$		−	6.89581i		−	0.395502i
$305$	4.80132	+	2.77204i	0.274923	+	0.158727i
$306$	19.1648	+	11.0648i	1.09558	+	0.632533i
$307$			14.0807i			0.803628i	0.915721	+	0.401814i	$0.131620\pi$
$307$			14.0807i			0.803628i	−0.915721	+	0.401814i	$0.868380\pi$
$308$		0			0
$309$	9.31673	+	16.1370i	0.530010	+	0.918004i
$310$	55.7246	−	32.1726i	3.16495	−	1.82728i
$311$	10.3848			0.588867			0.294434	−	0.955672i	$-0.404869\pi$
$311$	10.3848			0.588867			0.294434	+	0.955672i	$0.404869\pi$
$312$	5.83501	+	5.07339i	0.330342	+	0.287224i
$313$	−6.84759			−0.387048			−0.193524	−	0.981096i	$-0.561992\pi$
$313$	−6.84759			−0.387048			−0.193524	+	0.981096i	$0.561992\pi$
$314$	−23.7173	+	13.6932i	−1.33845	+	0.772752i
$315$		0			0
$316$	0.927818	−	1.60703i	0.0521938	−	0.0904024i
$317$			0.701249i			0.0393861i	0.999806	+	0.0196930i	$0.00626889\pi$
$317$			0.701249i			0.0393861i	−0.999806	+	0.0196930i	$0.993731\pi$
$318$	20.3285	+	11.7367i	1.13997	+	0.658160i
$319$	−0.984082	−	0.568160i	−0.0550980	−	0.0318109i
$320$		−	39.9840i		−	2.23518i
$321$	−4.33400	+	7.50670i	−0.241900	+	0.418983i
$322$		0			0
$323$	−10.2183	+	5.89956i	−0.568563	+	0.328260i
$324$	26.6305			1.47947
$325$	−9.35600	−	27.1813i	−0.518977	−	1.50774i
$326$	−4.89268			−0.270980
$327$	−20.4052	+	11.7810i	−1.12841	+	0.651489i
$328$	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	$-0.296522\pi$
$331$	3.63613	+	2.09932i	0.199860	+	0.115389i	−0.396730	+	0.917935i	$0.629855\pi$
$332$	−10.1139	−	5.83924i	−0.555070	−	0.320470i
$333$		−	20.3851i		−	1.11710i
$334$	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	$0.687813\pi$
$338$	−10.2779	+	25.4231i	−0.559046	+	1.38283i
$339$	11.1049			0.603138
$340$	−37.8987	+	21.8808i	−2.05535	+	1.18665i
$341$	3.75349	+	6.50123i	0.203263	+	0.352061i
$342$	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
$346$		−	7.77165i		−	0.417807i
$347$	−3.98500	+	6.90222i	−0.213926	+	0.370531i	−0.952940	−	0.303160i	$-0.901959\pi$
$347$	−3.98500	+	6.90222i	−0.213926	+	0.370531i	0.739014	+	0.673690i	$0.235292\pi$
$348$	−3.55103	−	6.15057i	−0.190355	−	0.329705i
$349$	−18.7038	+	10.7986i	−1.00119	+	0.578037i	−0.908600	−	0.417668i	$-0.862848\pi$
$349$	−18.7038	+	10.7986i	−1.00119	+	0.578037i	−0.0925892	+	0.995704i	$0.529514\pi$
$350$		0			0
$351$	2.34866	+	6.82338i	0.125362	+	0.364205i
$352$	7.10110			0.378490
$353$	−18.7214	+	10.8088i	−0.996439	+	0.575295i	−0.907193	−	0.420715i	$-0.861779\pi$
$353$	−18.7214	+	10.8088i	−0.996439	+	0.575295i	−0.0892465	+	0.996010i	$0.528446\pi$
$354$	−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
$359$			13.6834i			0.722180i	0.932531	+	0.361090i	$0.117595\pi$
$359$			13.6834i			0.722180i	−0.932531	+	0.361090i	$0.882405\pi$
$360$	3.61172	−	6.25568i	0.190354	−	0.329703i
$361$	−6.67071	−	11.5540i	−0.351090	−	0.608106i
$362$	3.86443	−	2.23113i	0.203110	−	0.117266i
$363$	−23.1012			−1.21250
$364$		0			0
$365$	25.7477			1.34769
$366$	−6.35953	+	3.67168i	−0.332418	+	0.191922i
$367$	−5.70638	−	9.88374i	−0.297871	−	0.515927i	0.677778	−	0.735267i	$-0.262943\pi$
$367$	−5.70638	−	9.88374i	−0.297871	−	0.515927i	−0.975649	+	0.219339i	$0.929610\pi$
$368$	5.59271	−	9.68685i	0.291540	−	0.504962i
$369$		−	25.5586i		−	1.33053i
$370$	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	−0.103151	−	0.994666i	$-0.532892\pi$
$373$	15.6404	−	27.0900i	0.809830	−	1.40267i	0.912981	−	0.408002i	$-0.133774\pi$
$374$	−4.63708	−	8.03166i	−0.239778	−	0.415307i
$375$	−20.9721	+	12.1082i	−1.08299	+	0.625266i
$376$	−2.82784			−0.145835
$377$	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	$0.0846803\pi$
$380$	10.4935	+	18.1753i	0.538307	+	0.932374i
$381$	13.9206	−	24.1112i	0.713175	−	1.23526i
$382$		−	23.9767i		−	1.22675i
$383$	−13.9436	−	8.05032i	−0.712483	−	0.411352i	0.0994967	−	0.995038i	$-0.468277\pi$
$383$	−13.9436	−	8.05032i	−0.712483	−	0.411352i	−0.811980	+	0.583686i	$0.801610\pi$
$384$	14.4824	+	8.36142i	0.739052	+	0.426692i
$385$		0			0
$386$	14.8600	−	25.7382i	0.756353	−	1.31004i
$387$	−3.85204	−	6.67193i	−0.195810	−	0.339153i
$388$	0.982819	−	0.567431i	0.0498951	−	0.0288069i
$389$	−21.1380			−1.07174			−0.535870	−	0.844301i	$-0.680016\pi$
$389$	−21.1380			−1.07174			−0.535870	+	0.844301i	$0.680016\pi$
$390$	60.8146	+	11.8279i	3.07947	+	0.598930i
$391$	−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
$395$		−	2.72853i		−	0.137287i
$396$	3.97699	+	2.29612i	0.199851	+	0.115384i
$397$	−11.3436	−	6.54921i	−0.569317	−	0.328695i	0.187560	−	0.982253i	$-0.439942\pi$
$397$	−11.3436	−	6.54921i	−0.569317	−	0.328695i	−0.756876	+	0.653558i	$0.773276\pi$
$398$		−	6.64426i		−	0.333046i
$399$		0			0
$400$	−11.5562	−	20.0159i	−0.577808	−	1.00079i
$401$	16.8396	−	9.72236i	0.840930	−	0.485511i	−0.0166501	−	0.999861i	$-0.505300\pi$
$401$	16.8396	−	9.72236i	0.840930	−	0.485511i	0.857580	+	0.514350i	$0.171967\pi$
$402$	40.2002			2.00501
$403$	−28.8736	+	9.93851i	−1.43830	+	0.495072i
$404$	−14.2636			−0.709642
$405$	33.9114	−	19.5788i	1.68507	−	0.972876i
$406$		0			0
$407$	−4.27154	+	7.39853i	−0.211732	+	0.366731i
$408$		−	10.6372i		−	0.526618i
$409$	−20.8330	−	12.0279i	−1.03013	−	0.594743i	−0.113105	−	0.993583i	$-0.536079\pi$
$409$	−20.8330	−	12.0279i	−1.03013	−	0.594743i	−0.917020	+	0.398840i	$0.869413\pi$
$410$	79.5096	+	45.9049i	3.92670	+	2.26708i
$411$			16.8618i			0.831733i
$412$	10.0907	−	17.4775i	0.497131	−	0.861056i
$413$		0			0
$414$	14.9083	−	8.60732i	0.732703	−	0.423026i
$415$	−17.1721			−0.842944
$416$	−5.51460	+	28.3539i	−0.270375	+	1.39016i
$417$	37.7256			1.84743
$418$	−3.85179	+	2.22383i	−0.188397	+	0.108771i
$419$	19.5119	+	33.7956i	0.953218	+	1.65102i	0.738394	+	0.674370i	$0.235585\pi$
$419$	19.5119	+	33.7956i	0.953218	+	1.65102i	0.214825	+	0.976653i	$0.431082\pi$
$420$		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
$423$	5.46263	+	3.15385i	0.265602	+	0.153346i
$424$		−	4.66551i		−	0.226577i
$425$	−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
$429$	−1.37993	+	7.09506i	−0.0666237	+	0.342553i
$430$	27.6741			1.33456
$431$	−31.0727	+	17.9398i	−1.49672	+	0.864131i	−0.999993	−	0.00377645i	$-0.998798\pi$
$431$	−31.0727	+	17.9398i	−1.49672	+	0.864131i	−0.496726	+	0.867907i	$0.665465\pi$
$432$	2.90098	+	5.02464i	0.139573	+	0.241748i
$433$	−6.10678	+	10.5773i	−0.293473	+	0.508310i	−0.974629	−	0.223828i	$-0.928144\pi$
$433$	−6.10678	+	10.5773i	−0.293473	+	0.508310i	0.681155	+	0.732139i	$0.261478\pi$
$434$		0			0
$435$	−9.04381	−	5.22145i	−0.433618	−	0.250349i
$436$	22.1003	+	12.7596i	1.05841	+	0.611074i
$437$			9.17853i			0.439069i
$438$	−17.0519	+	29.5347i	−0.814770	+	1.41122i
$439$	7.87765	+	13.6445i	0.375980	+	0.651216i	0.990473	−	0.137706i	$-0.0439728\pi$
$439$	7.87765	+	13.6445i	0.375980	+	0.651216i	−0.614493	+	0.788922i	$0.710639\pi$
$440$	−2.62165	+	1.51361i	−0.124982	+	0.0721586i
$441$		0			0
$442$	35.6706	−	12.2781i	1.69668	−	0.584009i
$443$	−15.0706			−0.716028			−0.358014	−	0.933716i	$-0.616546\pi$
$443$	−15.0706			−0.716028			−0.358014	+	0.933716i	$0.616546\pi$
$444$	−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	$0.407877\pi$
$450$		−	35.5705i		−	1.67681i
$451$	−5.35559	+	9.27616i	−0.252185	+	0.436797i
$452$	−6.01371	−	10.4160i	−0.282861	−	0.489929i
$453$	31.1370	−	17.9770i	1.46295	−	0.844632i
$454$	−28.6166			−1.34304
$455$		0			0
$456$	−5.10133			−0.238892
$457$	−6.71687	+	3.87799i	−0.314202	+	0.181405i	−0.648805	−	0.760955i	$-0.724731\pi$
$457$	−6.71687	+	3.87799i	−0.314202	+	0.181405i	0.334603	+	0.942359i	$0.391398\pi$
$458$	−17.4214	−	30.1748i	−0.814050	−	1.40998i
$459$	4.96373	−	8.59743i	0.231687	−	0.401294i
$460$			34.0422i			1.58723i
$461$	−1.27498	−	0.736110i	−0.0593817	−	0.0342840i	0.470015	−	0.882658i	$-0.344248\pi$
$461$	−1.27498	−	0.736110i	−0.0593817	−	0.0342840i	−0.529397	+	0.848374i	$0.677582\pi$
$462$		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
$467$	31.3806			1.45212			0.726060	−	0.687631i	$-0.241349\pi$
$467$	31.3806			1.45212			0.726060	+	0.687631i	$0.241349\pi$
$468$	−12.2566	+	14.0966i	−0.566562	+	0.651614i
$469$		0			0
$470$	−19.6225	+	11.3291i	−0.905119	+	0.522571i
$471$	−14.6816	−	25.4293i	−0.676492	−	1.17172i
$472$	−3.47399	+	6.01713i	−0.159903	+	0.276961i
$473$			3.22865i			0.148454i
$474$	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
$478$	−32.0849	−	55.5726i	−1.46753	−	2.54183i
$479$	−35.6760	+	20.5975i	−1.63008	+	0.941125i	−0.646009	+	0.763330i	$0.723563\pi$
$479$	−35.6760	+	20.5975i	−1.63008	+	0.941125i	−0.984068	+	0.177795i	$0.943104\pi$
$480$	65.2598			2.97869
$481$	−26.2243	−	22.8014i	−1.19572	−	1.03965i
$482$	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
$486$			39.2002i			1.77816i
$487$	24.5314	+	14.1632i	1.11163	+	0.641798i	0.939250	−	0.343234i	$-0.111522\pi$
$487$	24.5314	+	14.1632i	1.11163	+	0.641798i	0.172376	+	0.985031i	$0.444856\pi$
$488$	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	$0.546027\pi$
$492$	−57.9765	+	33.4728i	−2.61378	+	1.50907i
$493$	−6.35879			−0.286386
$494$	−5.88828	−	17.1068i	−0.264926	−	0.769670i
$495$	6.75244			0.303499
$496$	−21.2621	+	12.2757i	−0.954695	+	0.551194i
$497$		0			0
$498$	11.3725	−	19.6978i	0.509615	−	0.882680i
$499$		−	0.0694885i		−	0.00311073i	−0.999999	−	0.00155537i	$-0.999505\pi$
$499$		−	0.0694885i		−	0.00311073i	0.999999	−	0.00155537i	$-0.000495089\pi$
$500$	22.7142	+	13.1140i	1.01581	+	0.586477i
$501$	27.0133	+	15.5961i	1.20686	+	0.696783i
$502$		−	27.3855i		−	1.22228i
$503$	12.8686	−	22.2891i	0.573782	−	0.993820i	−0.422391	−	0.906414i	$-0.638809\pi$
$503$	12.8686	−	22.2891i	0.573782	−	0.993820i	0.996173	−	0.0874060i	$-0.0278578\pi$
$504$		0			0
$505$	−18.1634	+	10.4866i	−0.808260	+	0.466649i
$506$	−7.21437			−0.320718
$507$	−27.2582	−	11.0198i	−1.21058	−	0.489407i
$508$	−30.1540			−1.33787
$509$	6.09682	−	3.52000i	0.270237	−	0.156021i	−0.358759	−	0.933430i	$-0.616800\pi$
$509$	6.09682	−	3.52000i	0.270237	−	0.156021i	0.628995	+	0.777409i	$0.283467\pi$
$510$	−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
$514$	8.37619	+	4.83599i	0.369458	+	0.213307i
$515$		−	29.6746i		−	1.30762i
$516$	−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
$520$	−4.00775	−	11.6434i	−0.175752	−	0.510597i
$521$	−16.3253			−0.715225			−0.357613	−	0.933870i	$-0.616409\pi$
$521$	−16.3253			−0.715225			−0.357613	+	0.933870i	$0.616409\pi$
$522$	4.95322	−	2.85974i	0.216796	−	0.125167i
$523$	−3.54473	−	6.13965i	−0.155000	−	0.268468i	0.778059	−	0.628191i	$-0.216204\pi$
$523$	−3.54473	−	6.13965i	−0.155000	−	0.268468i	−0.933059	+	0.359723i	$0.882871\pi$
$524$	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
$528$			5.81138i			0.252908i
$529$	4.05594	−	7.02510i	0.176345	−	0.305439i
$530$	−18.6912	−	32.3741i	−0.811894	−	1.40624i
$531$	13.4216	−	7.74899i	0.582449	−	0.336277i
$532$		0			0
$533$	−32.8796	−	28.5880i	−1.42417	−	1.23828i
$534$	−17.2644			−0.747102
$535$	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
$541$		−	25.5162i		−	1.09703i	−0.836141	−	0.548515i	$-0.815194\pi$
$541$		−	25.5162i		−	1.09703i	0.836141	−	0.548515i	$-0.184806\pi$
$542$	13.7409	−	23.7999i	0.590222	−	1.02229i
$543$	2.39218	+	4.14338i	0.102658	+	0.177809i
$544$	34.4136	−	19.8687i	1.47547	−	0.851864i
$545$	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	$0.591824\pi$
$548$	15.8158	−	9.13126i	0.675618	−	0.390068i
$549$	−1.62781	−	2.81945i	−0.0694733	−	0.120331i
$550$	−7.45350	+	12.9098i	−0.317818	+	0.550478i
$551$			3.04952i			0.129914i
$552$	−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	$-0.783994\pi$
$557$	−14.7285	+	8.50353i	−0.624069	+	0.360306i	0.154383	+	0.988011i	$0.450661\pi$
$558$	−37.7851			−1.59957
$559$	−12.8916	−	2.50732i	−0.545259	−	0.106048i
$560$		0			0
$561$	8.61140	−	4.97179i	0.363573	−	0.209909i
$562$	18.2122	+	31.5445i	0.768235	+	1.33062i
$563$	12.4596	−	21.5807i	0.525111	−	0.909519i	−0.474461	−	0.880276i	$-0.657357\pi$
$563$	12.4596	−	21.5807i	0.525111	−	0.909519i	0.999572	−	0.0292428i	$-0.00930961\pi$
$564$		−	16.5218i		−	0.695691i
$565$	−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
$569$	2.94065	+	5.09335i	0.123278	+	0.213524i	0.921059	−	0.389424i	$-0.127326\pi$
$569$	2.94065	+	5.09335i	0.123278	+	0.213524i	−0.797780	+	0.602948i	$0.793993\pi$
$570$	−35.3983	+	20.4372i	−1.48267	+	0.856022i
$571$	−8.92622			−0.373551			−0.186775	−	0.982403i	$-0.559804\pi$
$571$	−8.92622			−0.373551			−0.186775	+	0.982403i	$0.559804\pi$
$572$	7.40220	−	2.54789i	0.309501	−	0.106533i
$573$	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
$577$		−	36.1933i		−	1.50675i	−0.657592	−	0.753374i	$-0.728425\pi$
$577$		−	36.1933i		−	1.50675i	0.657592	−	0.753374i	$-0.271575\pi$
$578$	−13.8894	−	8.01905i	−0.577723	−	0.333549i
$579$	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
$583$	3.77699	−	2.18065i	0.156427	−	0.0903132i
$584$	6.77838			0.280491
$585$	−5.24383	+	26.9617i	−0.216806	+	1.11473i
$586$	0.886069			0.0366032
$587$	−31.6008	+	18.2447i	−1.30431	+	0.753041i	−0.981139	−	0.193301i	$-0.938080\pi$
$587$	−31.6008	+	18.2447i	−1.30431	+	0.753041i	−0.323166	+	0.946342i	$0.604747\pi$
$588$		0			0
$589$	10.0732	−	17.4472i	0.415058	−	0.718901i
$590$			55.6708i			2.29193i
$591$	−44.9649	−	25.9605i	−1.84961	−	1.06787i
$592$	−24.1967	−	13.9699i	−0.994476	−	0.574161i
$593$			34.9930i			1.43699i	0.695533	+	0.718495i	$0.255168\pi$
$593$			34.9930i			1.43699i	−0.695533	+	0.718495i	$0.744832\pi$
$594$	1.87107	−	3.24079i	0.0767711	−	0.132971i
$595$		0			0
$596$	−5.34926	+	3.08839i	−0.219114	+	0.126506i
$597$	7.12385			0.291560
$598$	5.60256	−	28.8062i	0.229106	−	1.17797i
$599$	−32.5052			−1.32812			−0.664062	−	0.747677i	$-0.731169\pi$
$599$	−32.5052			−1.32812			−0.664062	+	0.747677i	$0.731169\pi$
$600$	−14.8072	+	8.54894i	−0.604501	+	0.349009i
$601$	10.0390	+	17.3881i	0.409500	+	0.709275i	0.994834	−	0.101518i	$-0.0323699\pi$
$601$	10.0390	+	17.3881i	0.409500	+	0.709275i	−0.585334	+	0.810792i	$0.699037\pi$
$602$		0			0
$603$			17.8225i			0.725788i
$604$	−33.7235	−	19.4703i	−1.37219	−	0.792235i
$605$	31.8608	+	18.3949i	1.29533	+	0.747858i
$606$		−	27.7799i		−	1.12848i
$607$	4.85800	−	8.41431i	0.197180	−	0.341526i	−0.750433	−	0.660947i	$-0.770155\pi$
$607$	4.85800	−	8.41431i	0.197180	−	0.341526i	0.947613	+	0.319420i	$0.103488\pi$
$608$	−9.52856	−	16.5039i	−0.386434	−	0.669323i
$609$		0			0
$610$	11.6946			0.473502
$611$	10.1674	−	3.49968i	0.411327	−	0.141582i
$612$	25.6979			1.03878
$613$	−10.2898	+	5.94080i	−0.415600	+	0.239947i	−0.693193	−	0.720752i	$-0.743797\pi$
$613$	−10.2898	+	5.94080i	−0.415600	+	0.239947i	0.277593	+	0.960699i	$0.410463\pi$
$614$	14.8508	+	25.7224i	0.599331	+	1.03807i
$615$	−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
$619$			41.7176i			1.67677i	0.545078	+	0.838386i	$0.316500\pi$
$619$			41.7176i			1.67677i	−0.545078	+	0.838386i	$0.683500\pi$
$620$	37.3603	−	64.7100i	1.50043	−	2.59882i
$621$	−3.86129	−	6.68794i	−0.154948	−	0.268378i
$622$	18.9708	−	10.9528i	0.760659	−	0.439166i
$623$		0			0
$624$	−23.2042	−	4.51302i	−0.928911	−	0.180665i
$625$	−1.29828			−0.0519312
$626$	−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	$0.552458\pi$
$632$		−	0.718319i		−	0.0285732i
$633$	−16.8084	+	29.1130i	−0.668073	+	1.15714i
$634$	0.739603	+	1.28103i	0.0293734	+	0.0508762i
$635$	−38.3982	+	22.1692i	−1.52379	+	0.879759i
$636$	27.2584			1.08086
$637$		0			0
$638$	−2.39694			−0.0948958
$639$	11.8124	−	6.81987i	0.467290	−	0.269790i
$640$	−13.3159	−	23.0639i	−0.526359	−	0.911680i
$641$	−5.46012	+	9.45721i	−0.215662	+	0.373537i	−0.953477	−	0.301465i	$-0.902524\pi$
$641$	−5.46012	+	9.45721i	−0.215662	+	0.373537i	0.737815	+	0.675003i	$0.235858\pi$
$642$			18.2842i			0.721618i
$643$	−15.2725	−	8.81757i	−0.602288	−	0.347731i	0.167653	−	0.985846i	$-0.446381\pi$
$643$	−15.2725	−	8.81757i	−0.602288	−	0.347731i	−0.769941	+	0.638115i	$0.779714\pi$
$644$		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	$-0.272952\pi$
$647$	−8.33632	−	14.4389i	−0.327735	−	0.567653i	−0.982062	+	0.188558i	$0.939619\pi$
$648$	8.92758	−	5.15434i	0.350708	−	0.202482i
$649$	−6.49495			−0.254949
$650$	−45.7593	−	39.7866i	−1.79483	−	1.56056i
$651$		0			0
$652$	−4.92042	+	2.84080i	−0.192698	+	0.111254i
$653$	3.38664	+	5.86584i	0.132530	+	0.229548i	0.924651	−	0.380816i	$-0.124357\pi$
$653$	3.38664	+	5.86584i	0.132530	+	0.229548i	−0.792121	+	0.610364i	$0.791023\pi$
$654$	−24.8506	+	43.0426i	−0.971737	+	1.68310i
$655$		−	29.5441i		−	1.15439i
$656$	−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	$0.940097\pi$
$660$	−8.84332	−	15.3171i	−0.344226	−	0.596216i
$661$	21.7945	−	12.5830i	0.847707	−	0.489424i	−0.0121696	−	0.999926i	$-0.503874\pi$
$661$	21.7945	−	12.5830i	0.847707	−	0.489424i	0.859876	+	0.510502i	$0.170540\pi$
$662$	8.85657			0.344221
$663$	13.1643	+	38.2454i	0.511261	+	1.48533i
$664$	−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
$668$		−	33.7833i		−	1.30712i
$669$	−8.58060	−	4.95401i	−0.331745	−	0.191533i
$670$	−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	$0.844714\pi$
$674$	−37.3172	+	21.5451i	−1.43741	+	0.829887i
$675$	−15.9571			−0.614189
$676$	4.42503	+	31.5348i	0.170194	+	1.21288i
$677$	14.7209			0.565770			0.282885	−	0.959154i	$-0.408709\pi$
$677$	14.7209			0.565770			0.282885	+	0.959154i	$0.408709\pi$
$678$	20.2863	−	11.7123i	0.779092	−	0.449809i
$679$		0			0
$680$	−8.47009	+	14.6706i	−0.324813	+	0.562593i
$681$		−	30.6822i		−	1.17575i
$682$	13.7136	+	7.91756i	0.525122	+	0.303179i
$683$	6.87930	+	3.97177i	0.263229	+	0.151975i	0.625807	−	0.779978i	$-0.284770\pi$
$683$	6.87930	+	3.97177i	0.263229	+	0.151975i	−0.362578	+	0.931954i	$0.618103\pi$
$684$		−	12.3241i		−	0.471224i
$685$	13.4266	−	23.2556i	0.513005	−	0.888551i
$686$		0			0
$687$	32.3529	−	18.6790i	1.23434	−	0.712647i
$688$	−10.5592			−0.402566
$689$	5.77394	+	16.7746i	0.219969	+	0.639060i
$690$	−66.3008			−2.52403
$691$	−8.86002	+	5.11534i	−0.337051	+	0.194597i	−0.658967	−	0.752172i	$-0.729006\pi$
$691$	−8.86002	+	5.11534i	−0.337051	+	0.194597i	0.321916	+	0.946768i	$0.395673\pi$
$692$	−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
$696$	−2.38089	−	1.37461i	−0.0902475	−	0.0521044i
$697$			59.9392i			2.27036i
$698$	−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	$0.601483\pi$
$702$	11.4871	+	9.98773i	0.433552	+	0.376963i
$703$	22.9269			0.864706
$704$	8.52162	−	4.91996i	0.321171	−	0.185428i
$705$	−12.1468	−	21.0389i	−0.457475	−	0.792371i
$706$	−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	0.997560	+	0.0698158i	$0.0222412\pi$
$709$	41.4531	+	23.9329i	1.55680	+	0.898820i	0.559242	+	0.829004i	$0.311092\pi$
$710$			48.9957i			1.83878i
$711$	−0.801130	+	1.38760i	−0.0300447	+	0.0520390i
$712$	1.71571	+	2.97170i	0.0642990	+	0.111369i
$713$	28.3004	−	16.3393i	1.05986	−	0.611910i
$714$		0			0
$715$	7.55279	−	8.68661i	0.282458	−	0.324861i
$716$	−14.4344			−0.539441
$717$	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	−0.254444	−	0.967087i	$-0.581893\pi$
$719$	19.0461	−	32.9888i	0.710300	−	1.23028i	0.964744	−	0.263188i	$-0.0847741\pi$
$720$			22.0836i			0.823009i
$721$		0			0
$722$	−24.3719	−	14.0711i	−0.907028	−	0.523673i
$723$			66.7511i			2.48250i
$724$	2.59089	−	4.48756i	0.0962898	−	0.166779i
$725$	5.11047	+	8.85159i	0.189798	+	0.328740i
$726$	−42.2009	+	24.3647i	−1.56622	+	0.904259i
$727$	−15.4059			−0.571374			−0.285687	−	0.958323i	$-0.592222\pi$
$727$	−15.4059			−0.571374			−0.285687	+	0.958323i	$0.592222\pi$
$728$		0			0
$729$	−9.41460			−0.348689
$730$	47.0354	−	27.1559i	1.74086	−	1.00508i
$731$	9.03369	+	15.6468i	0.334123	+	0.578718i
$732$	−4.26372	+	7.38498i	−0.157592	+	0.272957i
$733$			11.6298i			0.429557i	0.976663	+	0.214778i	$0.0689029\pi$
$733$			11.6298i			0.429557i	−0.976663	+	0.214778i	$0.931097\pi$
$734$	−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	$-0.650917\pi$
$739$	2.32875	−	1.34451i	0.0856645	−	0.0494584i	0.542220	+	0.840236i	$0.317584\pi$
$740$	85.0336			3.12590
$741$	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	$0.347744\pi$
$744$	9.08120	+	15.7291i	0.332933	+	0.576657i
$745$	−4.54118	+	7.86556i	−0.166376	+	0.288172i
$746$		−	65.9835i		−	2.41583i
$747$	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
$751$	−18.9592	−	32.8383i	−0.691832	−	1.19829i	−0.971237	−	0.238115i	$-0.923471\pi$
$751$	−18.9592	−	32.8383i	−0.691832	−	1.19829i	0.279405	−	0.960173i	$-0.409863\pi$
$752$	7.48709	−	4.32267i	0.273026	−	0.157632i
$753$	29.3623			1.07002
$754$	1.86142	−	9.57072i	0.0677890	−	0.348545i
$755$	−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
$759$		−	7.73512i		−	0.280767i
$760$	7.03569	+	4.06206i	0.255211	+	0.147346i
$761$	−19.7969	−	11.4297i	−0.717636	−	0.414328i	0.0962458	−	0.995358i	$-0.469317\pi$
$761$	−19.7969	−	11.4297i	−0.717636	−	0.414328i	−0.813882	+	0.581030i	$0.802650\pi$
$762$		−	58.7280i		−	2.12749i
$763$		0			0
$764$	−13.9214	−	24.1126i	−0.503659	−	0.872363i
$765$	32.7239	−	18.8931i	1.18313	−	0.683083i
$766$	−33.9625			−1.22712
$767$	5.04386	−	25.9336i	0.182123	−	0.936408i
$768$	−14.9390			−0.539065
$769$	44.8839	−	25.9137i	1.61855	−	0.934473i	0.631260	−	0.775571i	$-0.282538\pi$
$769$	44.8839	−	25.9137i	1.61855	−	0.934473i	0.987294	−	0.158902i	$-0.0507953\pi$
$770$		0			0
$771$	−5.18507	+	8.98080i	−0.186736	+	0.323436i
$772$		−	34.5122i		−	1.24212i
$773$	4.93605	+	2.84983i	0.177538	+	0.102501i	0.586135	−	0.810213i	$-0.300649\pi$
$773$	4.93605	+	2.84983i	0.177538	+	0.102501i	−0.408598	+	0.912715i	$0.633982\pi$
$774$	−14.0737	−	8.12545i	−0.505868	−	0.292063i
$775$		−	67.5234i		−	2.42551i
$776$	0.219653	−	0.380450i	0.00788508	−	0.0136574i
$777$		0			0
$778$	−38.6146	+	22.2941i	−1.38440	+	0.799283i
$779$	28.7454			1.02991
$780$	68.0269	−	23.4154i	2.43576	−	0.838406i
$781$	−5.71619			−0.204541
$782$	−34.9625	+	20.1856i	−1.25026	+	0.721836i
$783$	−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
$787$	14.5614	+	8.40705i	0.519059	+	0.299679i	0.736550	−	0.676384i	$-0.236454\pi$
$787$	14.5614	+	8.40705i	0.519059	+	0.299679i	−0.217490	+	0.976062i	$0.569787\pi$
$788$			56.2340i			2.00325i
$789$	−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
$793$	−5.44781	−	1.05955i	−0.193457	−	0.0376258i
$794$	−27.6296			−0.980539
$795$	34.7109	−	20.0404i	1.23107	−	0.710759i
$796$	−3.85781	−	6.68192i	−0.136736	−	0.236834i
$797$	−21.0651	+	36.4858i	−0.746163	+	1.29239i	0.203487	+	0.979078i	$0.434773\pi$
$797$	−21.0651	+	36.4858i	−0.746163	+	1.29239i	−0.949650	+	0.313314i	$0.898561\pi$
$798$		0			0
$799$	−12.8108	−	7.39632i	−0.453214	−	0.261663i
$800$	−55.3154	−	31.9364i	−1.95570	−	1.12912i
$801$		−	7.65403i		−	0.270442i
$802$	20.5082	−	35.5213i	0.724171	−	1.25430i
$803$	3.16820	+	5.48748i	0.111803	+	0.193649i
$804$	40.4281	−	23.3412i	1.42579	−	0.823180i
$805$		0			0
$806$	−42.2637	+	48.6083i	−1.48868	+	1.71215i
$807$	26.9716			0.949445
$808$	−4.78173	+	2.76073i	−0.168221	+	0.0971223i
$809$	15.0843	+	26.1268i	0.530336	+	0.918569i	0.999374	+	0.0353910i	$0.0112677\pi$
$809$	15.0843	+	26.1268i	0.530336	+	0.918569i	−0.469037	+	0.883178i	$0.655399\pi$
$810$	41.2992	−	71.5323i	1.45111	−	2.51339i
$811$		−	23.7929i		−	0.835480i	−0.908567	−	0.417740i	$-0.862822\pi$
$811$		−	23.7929i		−	0.835480i	0.908567	−	0.417740i	$-0.137178\pi$
$812$		0			0
$813$	25.5178	+	14.7327i	0.894950	+	0.516699i
$814$			18.0207i			0.631624i
$815$	−4.17712	+	7.23499i	−0.146318	+	0.253431i
$816$	16.2601	+	28.1633i	0.569217	+	0.985913i
$817$	7.50384	−	4.33234i	0.262526	−	0.151569i
$818$	−50.7432			−1.77419
$819$		0			0
$820$	106.614			3.72312
$821$	−31.0771	+	17.9424i	−1.08460	+	0.626193i	−0.932133	−	0.362116i	$-0.882054\pi$
$821$	−31.0771	+	17.9424i	−1.08460	+	0.626193i	−0.152465	+	0.988309i	$0.548721\pi$
$822$	17.7841	+	30.8029i	0.620291	+	1.07438i
$823$	−6.11728	+	10.5954i	−0.213235	+	0.369334i	−0.952725	−	0.303833i	$-0.901733\pi$
$823$	−6.11728	+	10.5954i	−0.213235	+	0.369334i	0.739490	+	0.673167i	$0.235067\pi$
$824$		−	7.81220i		−	0.272151i
$825$	−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	$-0.300920\pi$
$829$	−11.7869	−	20.4155i	−0.409376	−	0.709060i	−0.994820	+	0.101653i	$0.967587\pi$
$830$	−31.3697	+	18.1113i	−1.08886	+	0.628652i
$831$	48.3199			1.67620
$832$	13.0271	+	37.8466i	0.451634	+	1.31210i
$833$		0			0
$834$	68.9165	−	39.7889i	2.38638	−	1.37778i
$835$	−24.8376	−	43.0199i	−0.859539	−	1.48877i
$836$	−2.58242	+	4.47288i	−0.0893148	+	0.154698i
$837$			16.9506i			0.585898i
$838$	71.2880	+	41.1582i	2.46260	+	1.42179i
$839$	−9.16975	−	5.29416i	−0.316575	−	0.182775i	0.333290	−	0.942824i	$-0.391841\pi$
$839$	−9.16975	−	5.29416i	−0.316575	−	0.182775i	−0.649865	+	0.760050i	$0.725175\pi$
$840$		0			0
$841$	13.6783	−	23.6915i	0.471665	−	0.816947i
$842$	−23.2332	−	40.2411i	−0.800669	−	1.38680i
$843$	−33.8214	+	19.5268i	−1.16487	+	0.672538i
$844$	36.4092			1.25326
$845$	28.8193	+	36.9033i	0.991414	+	1.26951i
$846$	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
$850$			83.4188i			2.86124i
$851$	32.2065	+	18.5944i	1.10402	+	0.637408i
$852$	−30.9401	−	17.8633i	−1.05999	−	0.611985i
$853$			21.3925i			0.732464i	0.930524	+	0.366232i	$0.119352\pi$
$853$			21.3925i			0.732464i	−0.930524	+	0.366232i	$0.880648\pi$
$854$		0			0
$855$	−9.06070	−	15.6936i	−0.309870	−	0.536710i
$856$	3.14724	−	1.81706i	0.107570	−	0.0621058i
$857$	7.22129			0.246675			0.123337	−	0.992365i	$-0.460640\pi$
$857$	7.22129			0.246675			0.123337	+	0.992365i	$0.460640\pi$
$858$	4.96229	+	14.4166i	0.169410	+	0.492173i
$859$	−57.1073			−1.94848			−0.974238	−	0.225524i	$-0.927590\pi$
$859$	−57.1073			−1.94848			−0.974238	+	0.225524i	$0.927590\pi$
$860$	27.8309	−	16.0682i	0.949027	−	0.547921i
$861$		0			0
$862$	−37.8421	+	65.5444i	−1.28891	+	2.23245i
$863$			51.3361i			1.74750i	0.486374	+	0.873751i	$0.338319\pi$
$863$			51.3361i			1.74750i	−0.486374	+	0.873751i	$0.661681\pi$
$864$	13.8860	+	8.01707i	0.472411	+	0.272746i
$865$	−11.4922	−	6.63505i	−0.390748	−	0.225598i
$866$			25.7631i			0.875467i
$867$	8.59788	−	14.8920i	0.291999	−	0.505758i
$868$		0			0
$869$	0.581520	−	0.335741i	0.0197267	−	0.0113892i
$870$	−22.0281			−0.746823
$871$	22.9276	+	19.9349i	0.776871	+	0.675470i
$872$	9.87851			0.334528
$873$	−0.848621	+	0.489952i	−0.0287215	+	0.0165824i
$874$	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	$-0.451165\pi$
$877$	−18.5570	−	10.7139i	−0.626624	−	0.361781i	−0.779443	+	0.626473i	$0.784498\pi$
$878$	28.7815	+	16.6170i	0.971330	+	0.560798i
$879$			0.950027i			0.0320436i
$880$	4.62745	−	8.01497i	0.155991	−	0.270185i
$881$	−14.5309	−	25.1683i	−0.489560	−	0.847943i	0.510368	−	0.859956i	$-0.329509\pi$
$881$	−14.5309	−	25.1683i	−0.489560	−	0.847943i	−0.999928	+	0.0120134i	$0.996176\pi$
$882$		0			0
$883$	4.83594			0.162742			0.0813711	−	0.996684i	$-0.474070\pi$
$883$	4.83594			0.162742			0.0813711	+	0.996684i	$0.474070\pi$
$884$	28.7438	−	33.0589i	0.966760	−	1.11189i
$885$	−59.6892			−2.00643
$886$	−27.5308	+	15.8949i	−0.924916	+	0.534000i
$887$	−12.4949	−	21.6418i	−0.419538	−	0.726660i	0.576355	−	0.817199i	$-0.304474\pi$
$887$	−12.4949	−	21.6418i	−0.419538	−	0.726660i	−0.995893	+	0.0905387i	$0.971141\pi$
$888$	−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
$892$			10.7311i			0.359303i
$893$	−3.54710	+	6.14376i	−0.118699	+	0.205593i
$894$	−6.01497	−	10.4182i	−0.201171	−	0.348438i
$895$	−18.3809	+	10.6122i	−0.614406	+	0.354727i
$896$		0			0
$897$	30.8855	+	6.00696i	1.03124	+	0.200567i
$898$	64.9324			2.16682
$899$	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
$905$		−	7.61931i		−	0.253274i
$906$	37.9204	−	65.6801i	1.25982	−	2.18208i
$907$	7.52060	+	13.0261i	0.249717	+	0.432523i	0.963447	−	0.267898i	$-0.0863290\pi$
$907$	7.52060	+	13.0261i	0.249717	+	0.432523i	−0.713730	+	0.700421i	$0.752996\pi$
$908$	−28.7789	+	16.6155i	−0.955060	+	0.551404i
$909$	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	$0.548816\pi$
$912$	13.5065	−	7.79795i	0.447243	−	0.258216i
$913$	−2.11299	−	3.65981i	−0.0699298	−	0.121122i
$914$	−8.18018	+	14.1685i	−0.270576	+	0.468652i
$915$			12.5388i			0.414519i
$916$	−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	−0.207346	−	0.978268i	$-0.566483\pi$
$919$	22.5402	−	39.0407i	0.743531	−	1.28783i	0.950878	−	0.309567i	$-0.100184\pi$
$920$	6.58889	+	11.4123i	0.217229	+	0.376252i
$921$	−27.5791	+	15.9228i	−0.908762	+	0.524674i
$922$	−3.10548			−0.102274
$923$	4.43910	−	22.8241i	0.146115	−	0.751265i
$924$		0			0
$925$	66.5480	−	38.4215i	2.18808	−	1.26329i
$926$	−14.8043	−	25.6418i	−0.486499	−	0.842642i
$927$	−8.71284	+	15.0911i	−0.286167	+	0.495656i
$928$		−	10.2703i		−	0.337139i
$929$	40.6313	+	23.4585i	1.33307	+	0.769647i	0.985769	−	0.168107i	$-0.0537654\pi$
$929$	40.6313	+	23.4585i	1.33307	+	0.769647i	0.347300	+	0.937754i	$0.387099\pi$
$930$	126.030	+	72.7632i	4.13267	+	2.38600i
$931$		0			0
$932$	20.2117	−	35.0078i	0.662058	−	1.14672i
$933$	11.7434	+	20.3401i	0.384461	+	0.665906i
$934$	57.3256	−	33.0969i	1.87575	−	1.08296i
$935$	−15.8356			−0.517880
$936$	−1.38050	+	7.09800i	−0.0451231	+	0.232005i
$937$	28.3912			0.927501			0.463750	−	0.885966i	$-0.346503\pi$
$937$	28.3912			0.927501			0.463750	+	0.885966i	$0.346503\pi$
$938$		0			0
$939$	−7.74342	−	13.4120i	−0.252697	−	0.437684i
$940$	−13.1558	+	22.7866i	−0.429096	+	0.743216i
$941$		−	17.8718i		−	0.582603i	−0.956631	−	0.291302i	$-0.905912\pi$
$941$		−	17.8718i		−	0.582603i	0.956631	−	0.291302i	$-0.0940883\pi$
$942$	−53.6402	−	30.9692i	−1.74769	−	1.00903i
$943$	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
$947$	8.24659	−	4.76117i	0.267978	−	0.154717i	−0.359990	−	0.932956i	$-0.617220\pi$
$947$	8.24659	−	4.76117i	0.267978	−	0.154717i	0.627969	+	0.778239i	$0.283887\pi$
$948$	4.19680			0.136306
$949$	−24.3713	+	8.38878i	−0.791125	+	0.272311i
$950$	40.0057			1.29796
$951$	−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	$0.236400\pi$
$954$			21.9519i			0.710718i
$955$	−35.4552	−	20.4701i	−1.14730	−	0.662397i
$956$	−64.5335	−	37.2584i	−2.08716	−	1.20502i
$957$		−	2.56996i		−	0.0830749i
$958$	−43.4482	+	75.2545i	−1.40375	+	2.43136i
$959$		0			0
$960$	78.3145	−	45.2149i	2.52759	−	1.45931i
$961$	−40.7275			−1.31379
$962$	−71.9545	−	13.9946i	−2.31991	−	0.451202i
$963$	−8.10615			−0.261217
$964$	62.6102	−	36.1480i	2.01654	−	1.16425i
$965$	−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
$969$	−23.1103	−	13.3427i	−0.742409	−	0.428630i
$970$		−	3.51994i		−	0.113019i
$971$	23.7607	−	41.1547i	0.762516	−	1.32072i	−0.179034	−	0.983843i	$-0.557297\pi$
$971$	23.7607	−	41.1547i	0.762516	−	1.32072i	0.941550	−	0.336874i	$-0.109370\pi$
$972$	22.7605	+	39.4224i	0.730044	+	1.26447i
$973$		0			0
$974$	59.7515			1.91456
$975$	42.6584	−	49.0623i	1.36616	−	1.57125i
$976$	−4.46216			−0.142830
$977$	31.6049	−	18.2471i	1.01113	−	0.583776i	0.0996074	−	0.995027i	$-0.468241\pi$
$977$	31.6049	−	18.2471i	1.01113	−	0.583776i	0.911522	+	0.411251i	$0.134908\pi$
$978$	−5.53276	−	9.58302i	−0.176918	−	0.306431i
$979$	−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
$983$		−	44.1843i		−	1.40926i	−0.709576	−	0.704629i	$-0.751113\pi$
$983$		−	44.1843i		−	1.40926i	0.709576	−	0.704629i	$-0.248887\pi$
$984$	−12.9573	+	22.4428i	−0.413065	+	0.715449i
$985$	41.3433	+	71.6087i	1.31731	+	2.28164i
$986$	−11.6161	+	6.70658i	−0.369933	+	0.213581i
$987$		0			0
$988$	−15.8542	−	13.7849i	−0.504391	−	0.438555i
$989$	14.0546			0.446911
$990$	12.3352	−	7.12176i	0.392040	−	0.226344i
$991$	25.3549	+	43.9159i	0.805424	+	1.39504i	0.916005	+	0.401168i	$0.131396\pi$
$991$	25.3549	+	43.9159i	0.805424	+	1.39504i	−0.110581	+	0.993867i	$0.535271\pi$
$992$	−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
$996$		−	26.4126i		−	0.836916i
$997$	−25.1384	+	43.5410i	−0.796141	+	1.37896i	0.125971	+	0.992034i	$0.459795\pi$
$997$	−25.1384	+	43.5410i	−0.796141	+	1.37896i	−0.922112	+	0.386923i	$0.873538\pi$
$998$	−0.0732891	−	0.126940i	−0.00231993	−	0.00401823i
$999$	−16.7057	+	9.64505i	−0.528546	+	0.305156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.h.491.6		12
7.2	even	3		637.2.u.i.361.1		12
7.3	odd	6		637.2.k.h.569.6		12
7.4	even	3		637.2.k.g.569.6		12
7.5	odd	6		637.2.u.h.361.1		12
7.6	odd	2		91.2.q.a.36.6	✓	12
13.2	odd	12		8281.2.a.ch.1.5		6
13.4	even	6	inner	637.2.q.h.589.6		12
13.11	odd	12		8281.2.a.by.1.2		6
21.20	even	2		819.2.ct.a.127.1		12
28.27	even	2		1456.2.cc.c.673.5		12
91.4	even	6		637.2.u.i.30.1		12
91.17	odd	6		637.2.u.h.30.1		12
91.30	even	6		637.2.k.g.459.1		12
91.41	even	12		1183.2.a.p.1.5		6
91.55	odd	6		1183.2.c.i.337.11		12
91.62	odd	6		1183.2.c.i.337.2		12
91.69	odd	6		91.2.q.a.43.6	yes	12
91.76	even	12		1183.2.a.m.1.2		6
91.82	odd	6		637.2.k.h.459.1		12
273.251	even	6		819.2.ct.a.316.1		12
364.251	even	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	7.6	odd	2
91.2.q.a.43.6	yes	12	91.69	odd	6
637.2.k.g.459.1		12	91.30	even	6
637.2.k.g.569.6		12	7.4	even	3
637.2.k.h.459.1		12	91.82	odd	6
637.2.k.h.569.6		12	7.3	odd	6
637.2.q.h.491.6		12	1.1	even	1	trivial
637.2.q.h.589.6		12	13.4	even	6	inner
637.2.u.h.30.1		12	91.17	odd	6
637.2.u.h.361.1		12	7.5	odd	6
637.2.u.i.30.1		12	91.4	even	6
637.2.u.i.361.1		12	7.2	even	3
819.2.ct.a.127.1		12	21.20	even	2
819.2.ct.a.316.1		12	273.251	even	6
1183.2.a.m.1.2		6	91.76	even	12
1183.2.a.p.1.5		6	91.41	even	12
1183.2.c.i.337.2		12	91.62	odd	6
1183.2.c.i.337.11		12	91.55	odd	6
1456.2.cc.c.225.5		12	364.251	even	6
1456.2.cc.c.673.5		12	28.27	even	2
8281.2.a.by.1.2		6	13.11	odd	12
8281.2.a.ch.1.5		6	13.2	odd	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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82678 - 1.05469i) q^{2} +(1.13082 + 1.95864i) q^{3} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +(-1.05753 + 1.83169i) q^{9} +O(q^{10})\)	\(q+(1.82678 - 1.05469i) q^{2} +(1.13082 + 1.95864i) q^{3} +(1.22476 - 2.12135i) q^{4} -3.60178i 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} +5.53995 q^{12} +(1.17349 + 3.40924i) q^{13} +(7.05461 - 4.07298i) q^{15} +(1.44945 + 2.51051i) q^{16} +(2.48008 - 4.29563i) q^{17} +4.46147i q^{18} +(-2.06008 - 1.18939i) q^{19} +(-7.64062 - 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +(-1.92926 - 3.34157i) q^{23} +(1.85721 - 1.07226i) q^{24} -7.97282 q^{25} +(5.73942 + 4.99028i) q^{26} +2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} +(8.59150 - 14.8809i) q^{30} +8.46921i q^{31} +(6.93800 + 4.00566i) q^{32} +(1.73611 + 1.00234i) q^{33} -10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} +(-8.34686 + 4.81906i) q^{37} -5.01776 q^{38} +(-5.35049 + 6.15370i) q^{39} -3.41525 q^{40} +(-10.4652 + 6.04207i) q^{41} +(-1.82125 + 3.15450i) q^{43} -2.17122i q^{44} +(6.59734 + 3.80898i) q^{45} +(-7.04867 - 4.06955i) q^{46} -2.98229i q^{47} +(-3.27814 + 5.67790i) q^{48} +(-14.5646 + 8.40888i) q^{50} +11.2181 q^{51} +(8.66942 + 1.68613i) q^{52} +4.92032 q^{53} +(3.65619 - 2.11090i) q^{54} +(-1.59628 - 2.76484i) q^{55} -5.37995i q^{57} +(-2.34189 - 1.35209i) q^{58} +(-6.34577 - 3.66373i) q^{59} -19.9537i q^{60} +(-0.769632 + 1.33304i) q^{61} +(8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(12.2793 - 4.22664i) q^{65} +4.22867 q^{66} +(7.29756 - 4.21325i) q^{67} +(-6.07501 - 10.5222i) q^{68} +(4.36330 - 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} +(1.73683 + 1.00276i) q^{72} +7.14859i q^{73} +(-10.1653 + 17.6068i) q^{74} +(-9.01585 - 15.6159i) q^{75} +(-5.04621 + 2.91343i) q^{76} +(-3.28391 + 16.8846i) q^{78} +0.757551 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} +7.68344i q^{86} +(1.44969 - 2.51093i) q^{87} +(-0.420240 - 0.727877i) q^{88} +(-3.13400 + 1.80942i) q^{89} +16.0692 q^{90} -9.45150 q^{92} +(-16.5882 + 9.57719i) q^{93} +(-3.14541 - 5.44800i) q^{94} +(-4.28391 + 7.41995i) q^{95} +18.1188i q^{96} +(0.401229 + 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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