LMFDB - Embedded newform 637.2.u.i.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
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:	$\Z[a_1, a_2, a_3]$
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			361.1
Root			$-1.30089 - 0.554694i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.i.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82678 - 1.05469i) q^{2} -2.26165 q^{3} +(1.22476 + 2.12135i) q^{4} +(-3.11923 + 1.80089i) q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +2.11505 q^{9} +O(q^{10})$	\(q+(-1.82678 - 1.05469i) q^{2} -2.26165 q^{3} +(1.22476 + 2.12135i) q^{4} +(-3.11923 + 1.80089i) q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +2.11505 q^{9} +7.59755 q^{10} +0.886384i q^{11} +(-2.76998 - 4.79774i) 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} +(-3.86375 - 2.23073i) q^{18} +2.37878i q^{19} +(-7.64062 - 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +(-1.92926 + 3.34157i) q^{23} +2.14452i q^{24} +(3.98641 - 6.90466i) q^{25} +(1.45200 - 7.46562i) q^{26} +2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} -17.1830 q^{30} +(-7.33455 - 4.23460i) q^{31} +(-6.93800 + 4.00566i) q^{32} -2.00469i q^{33} -10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} +(8.34686 + 4.81906i) q^{37} +(2.50888 - 4.34551i) q^{38} +(-2.65402 - 7.71051i) 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} +(-6.59734 + 3.80898i) q^{45} +(7.04867 - 4.06955i) 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} +(-5.79494 + 6.66487i) q^{52} +(-2.46016 + 4.26112i) q^{53} +(-3.65619 - 2.11090i) q^{54} +(-1.59628 - 2.76484i) q^{55} -5.37995i q^{57} +2.70418i q^{58} +(6.34577 - 3.66373i) q^{59} +(17.2804 + 9.97684i) q^{60} +1.53926 q^{61} +(8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(-9.80005 - 8.52090i) q^{65} +(-2.11433 + 3.66213i) q^{66} +8.42649i q^{67} +(-6.07501 + 10.5222i) q^{68} +(4.36330 - 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} -2.00552i q^{72} +(-6.19086 - 3.57430i) 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} +(-0.378775 - 0.656058i) q^{79} +10.4412i q^{80} -10.8717 q^{81} +25.4901 q^{82} -4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} +(6.65406 - 3.84172i) q^{86} +(1.44969 + 2.51093i) q^{87} +0.840480 q^{88} +(3.13400 + 1.80942i) q^{89} +16.0692 q^{90} -9.45150 q^{92} +(16.5882 + 9.57719i) q^{93} +6.29081 q^{94} +(-4.28391 - 7.41995i) 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 + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	$ 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.82678	−	1.05469i	−1.29173	−	0.745781i	−0.312770	−	0.949829i	$-0.601257\pi$
$2$	−1.82678	−	1.05469i	−1.29173	−	0.745781i	−0.978961	+	0.204047i	$0.934590\pi$
$3$	−2.26165			−1.30576			−0.652882	−	0.757460i	$-0.726440\pi$
$3$	−2.26165			−1.30576			−0.652882	+	0.757460i	$0.726440\pi$
$4$	1.22476	+	2.12135i	0.612380	+	1.06067i
$5$	−3.11923	+	1.80089i	−1.39496	+	0.805382i	−0.993859	−	0.110650i	$-0.964707\pi$
$5$	−3.11923	+	1.80089i	−1.39496	+	0.805382i	−0.401104	+	0.916033i	$0.631373\pi$
$6$	4.13154	+	2.38535i	1.68670	+	0.973814i
$7$		0			0
$7$		0			0
$8$		−	0.948212i		−	0.335243i
$9$	2.11505			0.705018
$10$	7.59755			2.40256
$11$			0.886384i			0.267255i	0.991032	+	0.133627i	$0.0426626\pi$
$11$			0.886384i			0.267255i	−0.991032	+	0.133627i	$0.957337\pi$
$12$	−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
$16$	1.44945	−	2.51051i	0.362362	−	0.627629i
$17$	2.48008	+	4.29563i	0.601508	+	1.04184i	0.992593	+	0.121488i	$0.0387665\pi$
$17$	2.48008	+	4.29563i	0.601508	+	1.04184i	−0.391085	+	0.920355i	$0.627900\pi$
$18$	−3.86375	−	2.23073i	−0.910694	−	0.525789i
$19$			2.37878i			0.545729i	0.962053	+	0.272864i	$0.0879710\pi$
$19$			2.37878i			0.545729i	−0.962053	+	0.272864i	$0.912029\pi$
$20$	−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	−0.994000	−	0.109376i	$-0.965115\pi$
$23$	−1.92926	+	3.34157i	−0.402278	+	0.696765i	0.591723	+	0.806142i	$0.298448\pi$
$24$			2.14452i			0.437749i
$25$	3.98641	−	6.90466i	0.797282	−	1.38093i
$26$	1.45200	−	7.46562i	0.284761	−	1.46413i
$27$	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	$0.871311\pi$
$30$	−17.1830			−3.13717
$31$	−7.33455	−	4.23460i	−1.31732	−	0.760557i	−0.334027	−	0.942564i	$-0.608408\pi$
$31$	−7.33455	−	4.23460i	−1.31732	−	0.760557i	−0.983297	+	0.182006i	$0.941741\pi$
$32$	−6.93800	+	4.00566i	−1.22648	+	0.708107i
$33$		−	2.00469i		−	0.348972i
$34$		−	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	$-0.0422435\pi$
$37$	8.34686	+	4.81906i	1.37222	+	0.792249i	0.381009	+	0.924571i	$0.375577\pi$
$38$	2.50888	−	4.34551i	0.406994	−	0.704935i
$39$	−2.65402	−	7.71051i	−0.424983	−	1.23467i
$40$	1.70762	+	2.95769i	0.269999	+	0.467652i
$41$	−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	$0.256251\pi$
$44$	−1.88033	+	1.08561i	−0.283470	+	0.163662i
$45$	−6.59734	+	3.80898i	−0.983474	+	0.567809i
$46$	7.04867	−	4.06955i	1.03927	−	0.600022i
$47$	−2.58274	+	1.49115i	−0.376731	+	0.217506i	−0.676395	−	0.736539i	$-0.736459\pi$
$47$	−2.58274	+	1.49115i	−0.376731	+	0.217506i	0.299664	+	0.954045i	$0.403126\pi$
$48$	−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
$52$	−5.79494	+	6.66487i	−0.803614	+	0.924252i
$53$	−2.46016	+	4.26112i	−0.337929	+	0.585310i	−0.984043	−	0.177931i	$-0.943060\pi$
$53$	−2.46016	+	4.26112i	−0.337929	+	0.585310i	0.646114	+	0.763241i	$0.276393\pi$
$54$	−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
$58$			2.70418i			0.355076i
$59$	6.34577	−	3.66373i	0.826148	−	0.476977i	−0.0263837	−	0.999652i	$-0.508399\pi$
$59$	6.34577	−	3.66373i	0.826148	−	0.476977i	0.852532	+	0.522675i	$0.175066\pi$
$60$	17.2804	+	9.97684i	2.23089	+	1.28800i
$61$	1.53926			0.197082			0.0985412	−	0.995133i	$-0.468582\pi$
$61$	1.53926			0.197082			0.0985412	+	0.995133i	$0.468582\pi$
$62$	8.93242	+	15.4714i	1.13442	+	1.96487i
$63$		0			0
$64$	11.1012			1.38765
$65$	−9.80005	−	8.52090i	−1.21555	−	1.05689i
$66$	−2.11433	+	3.66213i	−0.260257	+	0.450778i
$67$			8.42649i			1.02946i	0.857352	+	0.514730i	$0.172108\pi$
$67$			8.42649i			1.02946i	−0.857352	+	0.514730i	$0.827892\pi$
$68$	−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	$0.791662\pi$
$72$		−	2.00552i		−	0.236353i
$73$	−6.19086	−	3.57430i	−0.724586	−	0.418340i	0.0918526	−	0.995773i	$-0.470721\pi$
$73$	−6.19086	−	3.57430i	−0.724586	−	0.418340i	−0.816438	+	0.577433i	$0.804054\pi$
$74$	−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
$79$	−0.378775	−	0.656058i	−0.0426156	−	0.0738123i	0.843931	−	0.536452i	$-0.180236\pi$
$79$	−0.378775	−	0.656058i	−0.0426156	−	0.0738123i	−0.886546	+	0.462640i	$0.846902\pi$
$80$			10.4412i			1.16736i
$81$	−10.8717			−1.20797
$82$	25.4901			2.81491
$83$		−	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
$86$	6.65406	−	3.84172i	0.717525	−	0.414263i
$87$	1.44969	+	2.51093i	0.155423	+	0.269200i
$88$	0.840480			0.0895955
$89$	3.13400	+	1.80942i	0.332204	+	0.191798i	0.656819	−	0.754048i	$-0.271902\pi$
$89$	3.13400	+	1.80942i	0.332204	+	0.191798i	−0.324615	+	0.945846i	$0.605235\pi$
$90$	16.0692			1.69385
$91$		0			0
$92$	−9.45150			−0.985387
$93$	16.5882	+	9.57719i	1.72011	+	0.993108i
$94$	6.29081			0.648848
$95$	−4.28391	−	7.41995i	−0.439520	−	0.761271i
$96$	15.6913	−	9.05939i	1.60149	−	0.924620i
$97$	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
$100$	19.5296			1.95296
$101$	5.82303			0.579413			0.289707	−	0.957115i	$-0.406442\pi$
$101$	5.82303			0.579413			0.289707	+	0.957115i	$0.406442\pi$
$102$			23.6634i			2.34303i
$103$	−4.11944	−	7.13508i	−0.405901	−	0.703040i	0.588525	−	0.808479i	$-0.299709\pi$
$103$	−4.11944	−	7.13508i	−0.405901	−	0.703040i	−0.994426	+	0.105438i	$0.966375\pi$
$104$	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	−0.758407	−	0.651781i	$-0.774022\pi$
$107$	1.91630	−	3.31913i	0.185256	−	0.320872i	0.943663	+	0.330909i	$0.107355\pi$
$108$	2.45128	+	4.24574i	0.235875	+	0.408547i
$109$	−9.02229	−	5.20902i	−0.864178	−	0.498934i	0.00123094	−	0.999999i	$-0.499608\pi$
$109$	−9.02229	−	5.20902i	−0.864178	−	0.498934i	−0.865409	+	0.501066i	$0.832942\pi$
$110$			6.73435i			0.642095i
$111$	−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
$115$		−	13.8975i		−	1.29595i
$116$	1.57011	−	2.71951i	0.145781	−	0.252500i
$117$	2.48199	+	7.21073i	0.229460	+	0.666632i
$118$	−15.4565			−1.42288
$119$		0			0
$120$	−3.86205	−	6.68926i	−0.352555	−	0.610643i
$121$	10.2143			0.928575
$122$	−2.81190	−	1.62345i	−0.254578	−	0.146980i
$123$	23.6685	−	13.6650i	2.13412	−	1.23213i
$124$		−	20.7455i		−	1.86300i
$125$			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
$129$	4.11902	−	7.13436i	0.362660	−	0.628145i
$130$	8.91563	+	25.9019i	0.781953	+	2.27175i
$131$	−4.10133	−	7.10371i	−0.358335	−	0.620654i	0.629348	−	0.777123i	$-0.283322\pi$
$131$	−4.10133	−	7.10371i	−0.358335	−	0.620654i	−0.987683	+	0.156470i	$0.949989\pi$
$132$	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
$136$	4.07316	−	2.35164i	0.349271	−	0.201652i
$137$	−6.45670	+	3.72778i	−0.551633	+	0.318485i	−0.749780	−	0.661687i	$-0.769841\pi$
$137$	−6.45670	+	3.72778i	−0.551633	+	0.318485i	0.198147	+	0.980172i	$0.436508\pi$
$138$	−15.9416	+	9.20389i	−1.35704	+	0.783487i
$139$	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
$142$	6.80160	+	11.7807i	0.570778	+	0.988616i
$143$	−3.02190	+	1.04016i	−0.252704	+	0.0869826i
$144$	3.06566	−	5.30987i	0.255471	−	0.442489i
$145$	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
$149$			2.52163i			0.206580i	0.994651	+	0.103290i	$0.0329370\pi$
$149$			2.52163i			0.206580i	−0.994651	+	0.103290i	$0.967063\pi$
$150$	32.9400	−	19.0179i	2.68954	−	1.55281i
$151$	13.7674	+	7.94862i	1.12038	+	0.646849i	0.941497	−	0.337022i	$-0.109420\pi$
$151$	13.7674	+	7.94862i	1.12038	+	0.646849i	0.178879	+	0.983871i	$0.442753\pi$
$152$	2.25558			0.182952
$153$	5.24550	+	9.08548i	0.424074	+	0.734517i
$154$		0			0
$155$	30.5042			2.45016
$156$	13.1061	−	15.0736i	1.04933	−	1.20685i
$157$	6.49155	−	11.2437i	0.518082	−	0.897344i	−0.481697	−	0.876338i	$-0.659980\pi$
$157$	6.49155	−	11.2437i	0.518082	−	0.897344i	0.999779	−	0.0210065i	$-0.00668708\pi$
$158$			1.59797i			0.127128i
$159$	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
$163$			2.31948i			0.181676i	0.995866	+	0.0908378i	$0.0289545\pi$
$163$			2.31948i			0.181676i	−0.995866	+	0.0908378i	$0.971046\pi$
$164$	−25.6346	−	14.8002i	−2.00173	−	1.15570i
$165$	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
$170$	18.8425	+	32.6362i	1.44516	+	2.50309i
$171$			5.03124i			0.384748i
$172$	−8.92237			−0.680324
$173$	−3.68432			−0.280113			−0.140057	−	0.990143i	$-0.544728\pi$
$173$	−3.68432			−0.280113			−0.140057	+	0.990143i	$0.544728\pi$
$174$		−	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
$178$	−3.81677	−	6.61083i	−0.286079	−	0.495503i
$179$	5.89277			0.440446			0.220223	−	0.975450i	$-0.429322\pi$
$179$	5.89277			0.440446			0.220223	+	0.975450i	$0.429322\pi$
$180$	−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
$185$	−34.7144			−2.55225
$186$	−20.2020	−	34.9909i	−1.48128	−	2.56566i
$187$	−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
$191$	−11.3667			−0.822462			−0.411231	−	0.911531i	$-0.634901\pi$
$191$	−11.3667			−0.822462			−0.411231	+	0.911531i	$0.634901\pi$
$192$	−25.1070			−1.81194
$193$			14.0894i			1.01417i	0.861895	+	0.507087i	$0.169278\pi$
$193$			14.0894i			1.01417i	−0.861895	+	0.507087i	$0.830722\pi$
$194$	−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	$0.638148\pi$
$198$	1.97729	−	3.42476i	0.140520	−	0.243387i
$199$	1.57492	+	2.72785i	0.111643	+	0.193372i	0.916433	−	0.400188i	$-0.131055\pi$
$199$	1.57492	+	2.72785i	0.111643	+	0.193372i	−0.804790	+	0.593560i	$0.797722\pi$
$200$	−6.54708	−	3.77996i	−0.462949	−	0.267283i
$201$		−	19.0578i		−	1.34423i
$202$	−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
$206$			17.3790i			1.21085i
$207$	−4.08048	+	7.06760i	−0.283613	+	0.491232i
$208$	10.2599	+	1.99546i	0.711393	+	0.138360i
$209$	−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	$0.662374\pi$
$212$	−12.0524			−0.827764
$213$	12.6311	+	7.29255i	0.865467	+	0.499678i
$214$	−7.00133	+	4.04222i	−0.478601	+	0.276321i
$215$		−	13.1195i		−	0.894741i
$216$		−	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
$220$	3.91012	−	6.77253i	0.263620	−	0.456604i
$221$	−11.7345	+	13.4961i	−0.789347	+	0.907843i
$222$	22.9903	+	39.8203i	1.54301	+	2.67257i
$223$	−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
$226$	−8.96971	+	5.17866i	−0.596656	+	0.344480i
$227$	11.7488	−	6.78316i	0.779793	−	0.450214i	−0.0565636	−	0.998399i	$-0.518014\pi$
$227$	11.7488	−	6.78316i	0.779793	−	0.450214i	0.836357	+	0.548185i	$0.184681\pi$
$228$	11.4127	−	6.58915i	0.755827	−	0.436377i
$229$	−14.3050	+	8.25900i	−0.945302	+	0.545770i	−0.891618	−	0.452788i	$-0.850429\pi$
$229$	−14.3050	+	8.25900i	−0.945302	+	0.545770i	−0.0536833	+	0.998558i	$0.517096\pi$
$230$	−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	−0.998872	−	0.0474874i	$-0.984879\pi$
$233$	−8.25131	−	14.2917i	−0.540561	−	0.936279i	0.458311	−	0.888792i	$-0.348455\pi$
$234$	3.07106	−	15.7902i	0.200761	−	1.03224i
$235$	5.37078	−	9.30246i	0.350351	−	0.606826i
$236$	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	$-0.442780\pi$
$240$		−	23.6143i		−	1.52429i
$241$	−25.5602	+	14.7572i	−1.64648	+	0.950593i	−0.668018	+	0.744145i	$0.732857\pi$
$241$	−25.5602	+	14.7572i	−1.64648	+	0.950593i	−0.978458	+	0.206448i	$0.933810\pi$
$242$	−18.6594	−	10.7730i	−1.19947	−	0.692514i
$243$	18.5837			1.19214
$244$	1.88523	+	3.26531i	0.120689	+	0.209040i
$245$		0			0
$246$	−57.6497			−3.67561
$247$	−8.10982	+	2.79146i	−0.516015	+	0.177617i
$248$	−4.01530	+	6.95471i	−0.254972	+	0.441624i
$249$			10.7828i			0.683331i
$250$	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
$254$			25.9669i			1.62931i
$255$	34.9920	+	20.2026i	2.19128	+	1.26514i
$256$	−3.30268	−	5.72042i	−0.206418	−	0.357526i
$257$	2.29261	−	3.97091i	0.143009	−	0.247698i	−0.785620	−	0.618710i	$-0.787656\pi$
$257$	2.29261	−	3.97091i	0.143009	−	0.247698i	0.928628	+	0.371011i	$0.120989\pi$
$258$	−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
$262$			17.3026i			1.06896i
$263$	−2.66499			−0.164330			−0.0821652	−	0.996619i	$-0.526184\pi$
$263$	−2.66499			−0.164330			−0.0821652	+	0.996619i	$0.526184\pi$
$264$	−1.90087			−0.116990
$265$		−	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
$269$	5.96282	+	10.3279i	0.363559	+	0.629703i	0.988544	−	0.150934i	$-0.0482280\pi$
$269$	5.96282	+	10.3279i	0.363559	+	0.629703i	−0.624984	+	0.780637i	$0.714895\pi$
$270$	15.2060			0.925409
$271$	−11.2828	−	6.51416i	−0.685384	−	0.395707i	0.116496	−	0.993191i	$-0.462834\pi$
$271$	−11.2828	−	6.51416i	−0.685384	−	0.395707i	−0.801881	+	0.597484i	$0.796167\pi$
$272$	14.3790			0.871853
$273$		0			0
$274$	15.7267			0.950082
$275$	6.12018	+	3.53349i	0.369061	+	0.213077i
$276$	21.3760			1.28668
$277$	10.6824	+	18.5025i	0.641846	+	1.11171i	0.985020	+	0.172438i	$0.0551646\pi$
$277$	10.6824	+	18.5025i	0.641846	+	1.11171i	−0.343174	+	0.939272i	$0.611502\pi$
$278$	−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	$0.827772\pi$
$282$	−14.2276			−0.847242
$283$	−21.2402			−1.26260			−0.631299	−	0.775539i	$-0.717478\pi$
$283$	−21.2402			−1.26260			−0.631299	+	0.775539i	$0.717478\pi$
$284$		−	15.7967i		−	0.937360i
$285$	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
$289$	−3.80160	+	6.58457i	−0.223624	+	0.387327i
$290$	−4.86993	−	8.43496i	−0.285972	−	0.495318i
$291$	−0.907439	−	0.523910i	−0.0531950	−	0.0307122i
$292$		−	17.5106i		−	1.02473i
$293$	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
$297$			1.77404i			0.102940i
$298$	2.65955	−	4.60648i	0.154064	−	0.266846i
$299$	−13.6562	−	2.65601i	−0.789757	−	0.153601i
$300$	−44.1690			−2.55010
$301$		0			0
$302$	−16.7667	−	29.0408i	−0.964817	−	1.67111i
$303$	−13.1696			−0.756577
$304$	5.97195	+	3.44791i	0.342515	+	0.197751i
$305$	−4.80132	+	2.77204i	−0.274923	+	0.158727i
$306$		−	22.1296i		−	1.26507i
$307$			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
$311$	−5.19240	+	8.99349i	−0.294434	+	0.509974i	−0.974853	−	0.222849i	$-0.928464\pi$
$311$	−5.19240	+	8.99349i	−0.294434	+	0.509974i	0.680419	+	0.732823i	$0.261798\pi$
$312$	−7.31119	+	2.51657i	−0.413915	+	0.142473i
$313$	3.42379	+	5.93018i	0.193524	+	0.335194i	0.946416	−	0.322951i	$-0.104675\pi$
$313$	3.42379	+	5.93018i	0.193524	+	0.335194i	−0.752892	+	0.658145i	$0.771342\pi$
$314$	−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	$-0.660398\pi$
$317$	0.607299	−	0.350624i	0.0341093	−	0.0196930i	0.516958	+	0.856011i	$0.327064\pi$
$318$	−20.3285	+	11.7367i	−1.13997	+	0.658160i
$319$	0.984082	−	0.568160i	0.0550980	−	0.0318109i
$320$	−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
$325$	28.2177	+	5.48810i	1.56523	+	0.304425i
$326$	2.44634	−	4.23719i	0.135490	−	0.234676i
$327$	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
$331$		−	4.19865i		−	0.230778i	−0.993320	−	0.115389i	$-0.963188\pi$
$331$		−	4.19865i		−	0.230778i	0.993320	−	0.115389i	$-0.0368115\pi$
$332$	10.1139	−	5.83924i	0.555070	−	0.320470i
$333$	17.6541	+	10.1926i	0.967436	+	0.558550i
$334$	−29.0923			−1.59186
$335$	−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	$0.687813\pi$
$338$	27.1560	−	3.81059i	1.47709	−	0.207269i
$339$	−5.55247	+	9.61716i	−0.301569	+	0.522333i
$340$		−	43.7617i		−	2.37331i
$341$	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
$345$			31.4313i			1.69220i
$346$	6.73045	+	3.88583i	0.361831	+	0.208903i
$347$	−3.98500	−	6.90222i	−0.213926	−	0.370531i	0.739014	−	0.673690i	$-0.235292\pi$
$347$	−3.98500	−	6.90222i	−0.213926	−	0.370531i	−0.952940	+	0.303160i	$0.901959\pi$
$348$	−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
$352$	−3.55055	−	6.14974i	−0.189245	−	0.327782i
$353$		−	21.6176i		−	1.15059i	−0.817946	−	0.575295i	$-0.804887\pi$
$353$		−	21.6176i		−	1.15059i	0.817946	−	0.575295i	$-0.195113\pi$
$354$	34.9571			1.85795
$355$	23.2275			1.23279
$356$			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	$-0.549071\pi$
$359$	11.8501	−	6.84168i	0.625426	−	0.361090i	0.778979	+	0.627051i	$0.215738\pi$
$360$	3.61172	+	6.25568i	0.190354	+	0.329703i
$361$	13.3414			0.702180
$362$	−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
$367$	11.4128			0.595741			0.297871	−	0.954606i	$-0.403724\pi$
$367$	11.4128			0.595741			0.297871	+	0.954606i	$0.403724\pi$
$368$	5.59271	+	9.68685i	0.291540	+	0.504962i
$369$	−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
$373$	−31.2808			−1.61966			−0.809830	−	0.586664i	$-0.800441\pi$
$373$	−31.2808			−1.61966			−0.809830	+	0.586664i	$0.800441\pi$
$374$	9.27416			0.479555
$375$		−	24.2164i		−	1.25053i
$376$	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	$0.0846803\pi$
$380$	10.4935	−	18.1753i	0.538307	−	0.932374i
$381$	13.9206	+	24.1112i	0.713175	+	1.23526i
$382$	20.7644	+	11.9883i	1.06240	+	0.613377i
$383$			16.1006i			0.822705i	0.911476	+	0.411352i	$0.134943\pi$
$383$			16.1006i			0.822705i	−0.911476	+	0.411352i	$0.865057\pi$
$384$	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
$388$			1.13486i			0.0576139i
$389$	10.5690	−	18.3060i	0.535870	−	0.928153i	−0.463251	−	0.886227i	$-0.653317\pi$
$389$	10.5690	−	18.3060i	0.535870	−	0.928153i	0.999121	−	0.0419264i	$-0.0133495\pi$
$390$	−20.1640	−	58.5810i	−1.02104	−	2.96636i
$391$	−19.1388			−0.967893
$392$		0			0
$393$	9.27576	+	16.0661i	0.467900	+	0.810427i
$394$	48.4255			2.43964
$395$	2.36298	+	1.36427i	0.118894	+	0.0686437i
$396$	−3.97699	+	2.29612i	−0.199851	+	0.115384i
$397$			13.0984i			0.657390i	0.944436	+	0.328695i	$0.106609\pi$
$397$			13.0984i			0.657390i	−0.944436	+	0.328695i	$0.893391\pi$
$398$		−	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	$-0.494700\pi$
$401$	−16.8396	−	9.72236i	−0.840930	−	0.485511i	−0.857580	+	0.514350i	$0.828033\pi$
$402$	−20.1001	+	34.8144i	−1.00250	+	1.73639i
$403$	5.82979	−	29.9745i	0.290402	−	1.49314i
$404$	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
$409$	20.8330	−	12.0279i	1.03013	−	0.594743i	0.113105	−	0.993583i	$-0.463921\pi$
$409$	20.8330	−	12.0279i	1.03013	−	0.594743i	0.917020	+	0.398840i	$0.130587\pi$
$410$	−79.5096	+	45.9049i	−3.92670	+	2.26708i
$411$	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
$416$	−21.7979	−	18.9527i	−1.06873	−	0.929234i
$417$	−18.8628	+	32.6713i	−0.923714	+	1.59992i
$418$	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	$-0.180367\pi$
$422$		−	31.3536i		−	1.52627i
$423$	−5.46263	+	3.15385i	−0.265602	+	0.153346i
$424$	4.04045	+	2.33275i	0.196221	+	0.113289i
$425$	39.5465			1.91828
$426$	−15.3828	−	26.6438i	−0.745301	−	1.29090i
$427$		0			0
$428$	9.38803			0.453787
$429$	6.83447	−	2.35248i	0.329971	−	0.113579i
$430$	−13.8370	+	23.9664i	−0.667281	+	1.15576i
$431$		−	35.8797i		−	1.72826i	−0.503267	−	0.864131i	$-0.667869\pi$
$431$		−	35.8797i		−	1.72826i	0.503267	−	0.864131i	$-0.332131\pi$
$432$	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
$436$		−	25.5192i		−	1.22215i
$437$	−7.94884	−	4.58927i	−0.380245	−	0.219534i
$438$	−17.0519	−	29.5347i	−0.814770	−	1.41122i
$439$	7.87765	−	13.6445i	0.375980	−	0.651216i	−0.614493	−	0.788922i	$-0.710639\pi$
$439$	7.87765	−	13.6445i	0.375980	−	0.651216i	0.990473	+	0.137706i	$0.0439728\pi$
$440$	−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	0.987629	−	0.156809i	$-0.0501207\pi$
$443$	7.53532	+	13.0516i	0.358014	+	0.620099i	−0.629615	+	0.776907i	$0.716787\pi$
$444$		−	53.3947i		−	2.53400i
$445$	−13.0342			−0.617883
$446$	9.24099			0.437574
$447$		−	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
$451$	−5.35559	−	9.27616i	−0.252185	−	0.436797i
$452$	12.0274			0.565722
$453$	−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	$-0.275269\pi$
$457$	6.71687	+	3.87799i	0.314202	+	0.181405i	−0.334603	+	0.942359i	$0.608602\pi$
$458$	34.8429			1.62810
$459$	4.96373	+	8.59743i	0.231687	+	0.401294i
$460$	29.4814	−	17.0211i	1.37458	−	0.793613i
$461$	−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	$-0.105757\pi$
$464$	−3.71630			−0.172525
$465$	−68.9898			−3.19933
$466$			34.8104i			1.61256i
$467$	−15.6903	−	27.1764i	−0.726060	−	1.25757i	−0.958536	−	0.284971i	$-0.908016\pi$
$467$	−15.6903	−	27.1764i	−0.726060	−	1.25757i	0.232476	−	0.972602i	$-0.425317\pi$
$468$	−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
$473$	−2.79610	−	1.61433i	−0.128565	−	0.0742268i
$474$		−	3.61404i		−	0.165999i
$475$	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
$479$		−	41.1951i		−	1.88225i	−0.338059	−	0.941125i	$-0.609770\pi$
$479$		−	41.1951i		−	1.88225i	0.338059	−	0.941125i	$-0.390230\pi$
$480$	−32.6299	+	56.5167i	−1.48935	+	2.57962i
$481$	−6.63441	+	34.1116i	−0.302503	+	1.55535i
$482$	62.2572			2.83574
$483$		0			0
$484$	12.5101	+	21.6681i	0.568641	+	0.984914i
$485$	−1.66870			−0.0757719
$486$	−33.9484	−	19.6001i	−1.53993	−	0.889078i
$487$	−24.5314	+	14.1632i	−1.11163	+	0.641798i	−0.939250	−	0.343234i	$-0.888478\pi$
$487$	−24.5314	+	14.1632i	−1.11163	+	0.641798i	−0.172376	+	0.985031i	$0.555144\pi$
$488$		−	1.45955i		−	0.0660706i
$489$		−	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
$493$	3.17940	−	5.50687i	0.143193	−	0.248017i
$494$	17.7590	+	3.45398i	0.799016	+	0.155402i
$495$	−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	$-0.667162\pi$
$499$	−0.0601788	+	0.0347442i	−0.00269397	+	0.00155537i	0.498652	+	0.866802i	$0.333828\pi$
$500$	−22.7142	+	13.1140i	−1.01581	+	0.586477i
$501$	−27.0133	+	15.5961i	−1.20686	+	0.696783i
$502$	−23.7165	+	13.6928i	−1.05852	+	0.611138i
$503$	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
$506$	3.60719	+	6.24783i	0.160359	+	0.277750i
$507$	23.1725	−	18.0964i	1.02913	−	0.803688i
$508$	15.0770	−	26.1141i	0.668933	−	1.15863i
$509$	−6.09682	−	3.52000i	−0.270237	−	0.156021i	0.358759	−	0.933430i	$-0.383200\pi$
$509$	−6.09682	−	3.52000i	−0.270237	−	0.156021i	−0.628995	+	0.777409i	$0.716533\pi$
$510$	−42.6152	−	73.8117i	−1.88703	−	3.26844i
$511$		0			0
$512$			28.7215i			1.26932i
$513$			4.76097i			0.210202i
$514$	−8.37619	+	4.83599i	−0.369458	+	0.213307i
$515$	25.6990	+	14.8373i	1.13243	+	0.653810i
$516$	20.1793			0.888342
$517$	−1.32173	−	2.28930i	−0.0581295	−	0.100683i
$518$		0			0
$519$	8.33263			0.365762
$520$	−8.07961	+	9.29252i	−0.354314	+	0.407504i
$521$	8.16266	−	14.1381i	0.357613	−	0.619403i	−0.629949	−	0.776637i	$-0.716924\pi$
$521$	8.16266	−	14.1381i	0.357613	−	0.619403i	0.987561	+	0.157234i	$0.0502575\pi$
$522$			5.71948i			0.250335i
$523$	−3.54473	+	6.13965i	−0.155000	+	0.268468i	−0.933059	−	0.359723i	$-0.882871\pi$
$523$	−3.54473	+	6.13965i	−0.155000	+	0.268468i	0.778059	+	0.628191i	$0.216204\pi$
$524$	10.0463	−	17.4007i	0.438874	−	0.760152i
$525$		0			0
$526$	4.86836	+	2.81075i	0.212271	+	0.122555i
$527$		−	42.0086i		−	1.82993i
$528$	−5.03280	−	2.90569i	−0.219025	−	0.126454i
$529$	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
$534$	8.63218	+	14.9514i	0.373551	+	0.647009i
$535$			13.8042i			0.596807i
$536$	7.99010			0.345120
$537$	−13.3274			−0.575118
$538$		−	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	$-0.851473\pi$
$541$	−22.0977	+	12.7581i	−0.950055	+	0.548515i	−0.0569571	+	0.998377i	$0.518140\pi$
$542$	13.7409	+	23.7999i	0.590222	+	1.02229i
$543$	−4.78436			−0.205316
$544$	−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
$549$	3.25562			0.138947
$550$	−7.45350	−	12.9098i	−0.317818	−	0.550478i
$551$	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
$555$	78.5118			3.33264
$556$	40.8594			1.73282
$557$		−	17.0071i		−	0.720612i	−0.932834	−	0.360306i	$-0.882672\pi$
$557$		−	17.0071i		−	0.720612i	0.932834	−	0.360306i	$-0.117328\pi$
$558$	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
$562$	18.2122	−	31.5445i	0.768235	−	1.33062i
$563$	12.4596	+	21.5807i	0.525111	+	0.909519i	0.999572	+	0.0292428i	$0.00930961\pi$
$563$	12.4596	+	21.5807i	0.525111	+	0.909519i	−0.474461	+	0.880276i	$0.657357\pi$
$564$	14.3083	+	8.26088i	0.602486	+	0.347846i
$565$			17.6851i			0.744019i
$566$	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	−0.797780	−	0.602948i	$-0.793993\pi$
$569$	2.94065	−	5.09335i	0.123278	−	0.213524i	0.921059	+	0.389424i	$0.127326\pi$
$570$		−	40.8745i		−	1.71204i
$571$	4.46311	−	7.73034i	0.186775	−	0.323504i	−0.757398	−	0.652954i	$-0.773530\pi$
$571$	4.46311	−	7.73034i	0.186775	−	0.323504i	0.944173	+	0.329449i	$0.106863\pi$
$572$	−5.90764	−	5.13655i	−0.247011	−	0.214770i
$573$	25.7074			1.07394
$574$		0			0
$575$	15.3816	+	26.6417i	0.641457	+	1.11104i
$576$	23.4796			0.978317
$577$	31.3443	+	18.0967i	1.30488	+	0.753374i	0.981237	−	0.192804i	$-0.0617583\pi$
$577$	31.3443	+	18.0967i	1.30488	+	0.753374i	0.323645	+	0.946179i	$0.395092\pi$
$578$	13.8894	−	8.01905i	0.577723	−	0.333549i
$579$		−	31.8652i		−	1.32427i
$580$			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
$584$	−3.38919	+	5.87025i	−0.140246	+	0.242913i
$585$	−20.7276	−	18.0222i	−0.856982	−	0.745124i
$586$	−0.443035	−	0.767358i	−0.0183016	−	0.0316993i
$587$	−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
$590$	48.2123	−	27.8354i	1.98487	−	1.14596i
$591$	44.9649	−	25.9605i	1.84961	−	1.06787i
$592$	24.1967	−	13.9699i	0.994476	−	0.574161i
$593$	30.3048	−	17.4965i	1.24447	−	0.718495i	0.274468	−	0.961596i	$-0.411498\pi$
$593$	30.3048	−	17.4965i	1.24447	−	0.718495i	0.970001	+	0.243102i	$0.0781649\pi$
$594$	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
$598$	22.1456	+	19.2550i	0.905601	+	0.787397i
$599$	16.2526	−	28.1503i	0.664062	−	1.15019i	−0.315476	−	0.948934i	$-0.602164\pi$
$599$	16.2526	−	28.1503i	0.664062	−	1.15019i	0.979539	−	0.201256i	$-0.0645025\pi$
$600$	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
$604$			38.9406i			1.58447i
$605$	−31.8608	+	18.3949i	−1.29533	+	0.747858i
$606$	24.0581	+	13.8900i	0.977294	+	0.564241i
$607$	−9.71601			−0.394361			−0.197180	−	0.980367i	$-0.563178\pi$
$607$	−9.71601			−0.394361			−0.197180	+	0.980367i	$0.563178\pi$
$608$	−9.52856	−	16.5039i	−0.386434	−	0.669323i
$609$		0			0
$610$	11.6946			0.473502
$611$	−8.11449	−	7.05535i	−0.328277	−	0.285429i
$612$	−12.8490	+	22.2551i	−0.519389	+	0.899607i
$613$		−	11.8816i		−	0.479893i	−0.970786	−	0.239947i	$-0.922870\pi$
$613$		−	11.8816i		−	0.479893i	0.970786	−	0.239947i	$-0.0771299\pi$
$614$	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	$0.798474\pi$
$618$		−	39.3052i		−	1.58109i
$619$	−36.1285	−	20.8588i	−1.45213	−	0.838386i	−0.453525	−	0.891244i	$-0.649834\pi$
$619$	−36.1285	−	20.8588i	−1.45213	−	0.838386i	−0.998602	+	0.0528581i	$0.983167\pi$
$620$	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
$625$	0.649140	+	1.12434i	0.0259656	+	0.0449737i
$626$		−	14.4442i		−	0.577307i
$627$	4.76871			0.190444
$628$	31.8023			1.26905
$629$			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
$633$	−16.8084	−	29.1130i	−0.668073	−	1.15714i
$634$	−1.47921			−0.0587468
$635$	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
$640$	26.6319			1.05272
$641$	−5.46012	−	9.45721i	−0.215662	−	0.373537i	0.737815	−	0.675003i	$-0.235858\pi$
$641$	−5.46012	−	9.45721i	−0.215662	−	0.373537i	−0.953477	+	0.301465i	$0.902524\pi$
$642$	15.8346	−	9.14208i	0.624940	−	0.360809i
$643$	−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
$646$	24.8889			0.979241
$647$	16.6726			0.655469			0.327735	−	0.944770i	$-0.393715\pi$
$647$	16.6726			0.655469			0.327735	+	0.944770i	$0.393715\pi$
$648$			10.3087i			0.404963i
$649$	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
$653$	3.38664	−	5.86584i	0.132530	−	0.229548i	−0.792121	−	0.610364i	$-0.791023\pi$
$653$	3.38664	−	5.86584i	0.132530	−	0.229548i	0.924651	+	0.380816i	$0.124357\pi$
$654$	−24.8506	−	43.0426i	−0.971737	−	1.68310i
$655$	25.5860	+	14.7721i	0.999727	+	0.577193i
$656$			35.0306i			1.36772i
$657$	−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
$661$			25.1661i			0.978848i	0.872046	+	0.489424i	$0.162793\pi$
$661$			25.1661i			0.978848i	−0.872046	+	0.489424i	$0.837207\pi$
$662$	−4.42829	+	7.67002i	−0.172110	+	0.298104i
$663$	26.5393	−	30.5233i	1.03070	−	1.18543i
$664$	−4.52075			−0.175439
$665$		0			0
$666$	−21.5001	−	37.2393i	−0.833112	−	1.44299i
$667$	4.94651			0.191529
$668$	29.2572	+	16.8917i	1.13200	+	0.653558i
$669$	8.58060	−	4.95401i	0.331745	−	0.191533i
$670$			64.0207i			2.47334i
$671$			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
$675$	7.97855	−	13.8193i	0.307094	−	0.531903i
$676$	−29.5225	−	11.9352i	−1.13548	−	0.459047i
$677$	−7.36044	−	12.7487i	−0.282885	−	0.489971i	0.689209	−	0.724562i	$-0.257958\pi$
$677$	−7.36044	−	12.7487i	−0.282885	−	0.489971i	−0.972094	+	0.234592i	$0.924625\pi$
$678$	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
$682$	−13.7136	+	7.91756i	−0.525122	+	0.303179i
$683$	−6.87930	+	3.97177i	−0.263229	+	0.151975i	−0.625807	−	0.779978i	$-0.715230\pi$
$683$	−6.87930	+	3.97177i	−0.263229	+	0.151975i	0.362578	+	0.931954i	$0.381897\pi$
$684$	−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
$689$	−17.4142	−	3.38691i	−0.663427	−	0.129031i
$690$	33.1504	−	57.4182i	1.26201	−	2.18587i
$691$	8.86002	+	5.11534i	0.337051	+	0.194597i	0.658967	−	0.752172i	$-0.270994\pi$
$691$	8.86002	+	5.11534i	0.337051	+	0.194597i	−0.321916	+	0.946768i	$0.604327\pi$
$692$	−4.51240	−	7.81571i	−0.171536	−	0.297109i
$693$		0			0
$694$			16.8118i			0.638168i
$695$			60.0797i			2.27895i
$696$	2.38089	−	1.37461i	0.0902475	−	0.0521044i
$697$	−51.9089	−	29.9696i	−1.96619	−	1.13518i
$698$	45.5570			1.72436
$699$	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	$0.601483\pi$
$702$	2.90609	−	14.9420i	0.109683	−	0.563948i
$703$	−11.4635	+	19.8553i	−0.432353	+	0.748857i
$704$			9.83992i			0.370856i
$705$	−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
$709$		−	47.8659i		−	1.79764i	−0.438318	−	0.898820i	$-0.644426\pi$
$709$		−	47.8659i		−	1.79764i	0.438318	−	0.898820i	$-0.355574\pi$
$710$	−42.4316	−	24.4979i	−1.59243	−	0.919389i
$711$	−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
$716$	7.21722	+	12.5006i	0.269720	+	0.467169i
$717$			68.8017i			2.56944i
$718$	−28.8635			−1.07718
$719$	−38.0922			−1.42060			−0.710300	−	0.703899i	$-0.751441\pi$
$719$	−38.0922			−1.42060			−0.710300	+	0.703899i	$0.751441\pi$
$720$			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
$724$	2.59089	+	4.48756i	0.0962898	+	0.166779i
$725$	−10.2209			−0.379596
$726$	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
$731$	−18.0674			−0.668246
$732$	−4.26372	−	7.38498i	−0.157592	−	0.272957i
$733$	10.0717	−	5.81490i	0.372007	−	0.214778i	−0.302328	−	0.953204i	$-0.597764\pi$
$733$	10.0717	−	5.81490i	0.372007	−	0.214778i	0.674335	+	0.738426i	$0.264430\pi$
$734$	−20.8487	−	12.0370i	−0.769538	−	0.444293i
$735$		0			0
$736$		−	30.9117i		−	1.13942i
$737$	−7.46911			−0.275128
$738$	53.9130			1.98456
$739$			2.68901i			0.0989168i	0.998776	+	0.0494584i	$0.0157495\pi$
$739$			2.68901i			0.0989168i	−0.998776	+	0.0494584i	$0.984250\pi$
$740$	−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	$0.347744\pi$
$744$	9.08120	−	15.7291i	0.332933	−	0.576657i
$745$	−4.54118	−	7.86556i	−0.166376	−	0.288172i
$746$	57.1433	+	32.9917i	2.09217	+	1.20791i
$747$		−	10.0839i		−	0.368949i
$748$	−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	0.279405	+	0.960173i	$0.409863\pi$
$751$	−18.9592	+	32.8383i	−0.691832	+	1.19829i	−0.971237	+	0.238115i	$0.923471\pi$
$752$			8.64534i			0.315263i
$753$	−14.6811	+	25.4285i	−0.535010	+	0.926664i
$754$	−9.21920	+	3.17332i	−0.335743	+	0.115565i
$755$	−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	$-0.383447\pi$
$758$	−57.8290			−2.10044
$759$	6.69881	+	3.86756i	0.243151	+	0.140384i
$760$	−7.03569	+	4.06206i	−0.255211	+	0.147346i
$761$			22.8595i			0.828655i	0.910128	+	0.414328i	$0.135983\pi$
$761$			22.8595i			0.828655i	−0.910128	+	0.414328i	$0.864017\pi$
$762$		−	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
$766$	16.9813	−	29.4124i	0.613558	−	1.06271i
$767$	19.9372	+	17.3349i	0.719891	+	0.625927i
$768$	7.46951	+	12.9376i	0.269533	+	0.466844i
$769$	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
$772$	−29.8884	+	17.2561i	−1.07571	+	0.621060i
$773$	−4.93605	+	2.84983i	−0.177538	+	0.102501i	−0.586135	−	0.810213i	$-0.699351\pi$
$773$	−4.93605	+	2.84983i	−0.177538	+	0.102501i	0.408598	+	0.912715i	$0.366018\pi$
$774$	14.0737	−	8.12545i	0.505868	−	0.292063i
$775$	−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
$780$	−13.7351	+	70.6208i	−0.491797	+	2.52863i
$781$	2.85809	−	4.95037i	0.102271	−	0.177138i
$782$	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
$786$		−	39.1324i		−	1.39580i
$787$	−14.5614	+	8.40705i	−0.519059	+	0.299679i	−0.736550	−	0.676384i	$-0.763546\pi$
$787$	−14.5614	+	8.40705i	−0.519059	+	0.299679i	0.217490	+	0.976062i	$0.430213\pi$
$788$	−48.7000	−	28.1170i	−1.73487	−	1.00163i
$789$	6.02727			0.214577
$790$	−2.87777	−	4.98444i	−0.102386	−	0.177338i
$791$		0			0
$792$	1.77766			0.0631664
$793$	1.80631	+	5.24772i	0.0641438	+	0.186352i
$794$	13.8148	−	23.9280i	0.490270	−	0.849172i
$795$			40.0807i			1.42152i
$796$	−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
$800$			63.8727i			2.25824i
$801$	6.62859	+	3.82702i	0.234210	+	0.135221i
$802$	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
$807$	−13.4858	−	23.3581i	−0.474723	−	0.822244i
$808$		−	5.52147i		−	0.194245i
$809$	−30.1686			−1.06067			−0.530336	−	0.847787i	$-0.677934\pi$
$809$	−30.1686			−1.06067			−0.530336	+	0.847787i	$0.677934\pi$
$810$	−82.5984			−2.90221
$811$		−	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
$814$	15.6064	−	9.01034i	0.547003	−	0.315812i
$815$	−4.17712	−	7.23499i	−0.146318	−	0.253431i
$816$	−32.5202			−1.13843
$817$	−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	$-0.117946\pi$
$821$	31.0771	+	17.9424i	1.08460	+	0.626193i	0.152465	+	0.988309i	$0.451279\pi$
$822$	−35.5682			−1.24058
$823$	−6.11728	−	10.5954i	−0.213235	−	0.369334i	0.739490	−	0.673167i	$-0.235067\pi$
$823$	−6.11728	−	10.5954i	−0.213235	−	0.369334i	−0.952725	+	0.303833i	$0.901733\pi$
$824$	−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	$-0.157726\pi$
$828$	−19.9904			−0.694715
$829$	23.5738			0.818751			0.409376	−	0.912366i	$-0.365747\pi$
$829$	23.5738			0.818751			0.409376	+	0.912366i	$0.365747\pi$
$830$		−	36.2226i		−	1.25730i
$831$	−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
$835$	−24.8376	+	43.0199i	−0.859539	+	1.48877i
$836$	−2.58242	−	4.47288i	−0.0893148	−	0.154698i
$837$	−14.6796	−	8.47530i	−0.507403	−	0.292949i
$838$		−	82.3163i		−	2.84357i
$839$	−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
$843$		−	39.0536i		−	1.34508i
$844$	−18.2046	+	31.5313i	−0.626629	+	1.08535i
$845$	17.5496	−	43.4099i	0.603723	−	1.49335i
$846$	13.3054			0.457449
$847$		0			0
$848$	7.13174	+	12.3525i	0.244905	+	0.424188i
$849$	48.0379			1.64866
$850$	−72.2428	−	41.7094i	−2.47791	−	1.43062i
$851$	−32.2065	+	18.5944i	−1.10402	+	0.637408i
$852$			35.7265i			1.22397i
$853$			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
$857$	−3.61065	+	6.25382i	−0.123337	+	0.213626i	−0.921082	−	0.389369i	$-0.872693\pi$
$857$	−3.61065	+	6.25382i	−0.123337	+	0.213626i	0.797744	+	0.602996i	$0.206026\pi$
$858$	−14.9662	−	2.91081i	−0.510939	−	0.0993734i
$859$	28.5536	+	49.4563i	0.974238	+	1.68743i	0.682429	+	0.730952i	$0.260924\pi$
$859$	28.5536	+	49.4563i	0.974238	+	1.68743i	0.291809	+	0.956477i	$0.405743\pi$
$860$	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	0.513503	−	0.858088i	$-0.328347\pi$
$863$	44.4584	−	25.6681i	1.51338	−	0.873751i	0.999877	−	0.0156631i	$-0.00498592\pi$
$864$	−13.8860	+	8.01707i	−0.472411	+	0.272746i
$865$	11.4922	−	6.63505i	0.390748	−	0.225598i
$866$	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
$871$	−28.7280	+	9.88838i	−0.973410	+	0.335055i
$872$	−4.93925	+	8.55504i	−0.167264	+	0.289710i
$873$	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
$877$			21.4277i			0.723563i	0.932263	+	0.361781i	$0.117831\pi$
$877$			21.4277i			0.723563i	−0.932263	+	0.361781i	$0.882169\pi$
$878$	−28.7815	+	16.6170i	−0.971330	+	0.560798i
$879$	−0.822748	−	0.475014i	−0.0277506	−	0.0160218i
$880$	−9.25489			−0.311982
$881$	−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	$0.474070\pi$
$884$	−43.0017	−	8.36347i	−1.44630	−	0.281294i
$885$	29.8446	−	51.6924i	1.00322	−	1.73762i
$886$		−	31.7899i		−	1.06800i
$887$	−12.4949	+	21.6418i	−0.419538	+	0.726660i	−0.995893	−	0.0905387i	$-0.971141\pi$
$887$	−12.4949	+	21.6418i	−0.419538	+	0.726660i	0.576355	+	0.817199i	$0.304474\pi$
$888$	−10.3346	+	17.9000i	−0.346806	+	0.600685i
$889$		0			0
$890$	23.8108	+	13.7471i	0.798138	+	0.460805i
$891$		−	9.63651i		−	0.322835i
$892$	−9.29338	−	5.36553i	−0.311165	−	0.179651i
$893$	−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
$898$	−32.4662	−	56.2331i	−1.08341	−	1.87652i
$899$			10.8573i			0.362111i
$900$	41.3061			1.37687
$901$	−24.4056			−0.813068
$902$			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
$906$	37.9204	+	65.6801i	1.25982	+	2.18208i
$907$	−15.0412			−0.499435			−0.249717	−	0.968319i	$-0.580338\pi$
$907$	−15.0412			−0.499435			−0.249717	+	0.968319i	$0.580338\pi$
$908$	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
$913$	4.22598			0.139860
$914$	−8.18018	−	14.1685i	−0.270576	−	0.468652i
$915$	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
$919$	−45.0803			−1.48706			−0.743531	−	0.668701i	$-0.766851\pi$
$919$	−45.0803			−1.48706			−0.743531	+	0.668701i	$0.766851\pi$
$920$	−13.1778			−0.434459
$921$		−	31.8456i		−	1.04935i
$922$	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
$926$	−14.8043	+	25.6418i	−0.486499	+	0.842642i
$927$	−8.71284	−	15.0911i	−0.286167	−	0.495656i
$928$	8.89433	+	5.13514i	0.291971	+	0.168569i
$929$		−	46.9169i		−	1.53929i	−0.638469	−	0.769647i	$-0.720432\pi$
$929$		−	46.9169i		−	1.53929i	0.638469	−	0.769647i	$-0.279568\pi$
$930$	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
$934$			66.1939i			2.16593i
$935$	7.91781	−	13.7140i	0.258940	−	0.448497i
$936$	6.83730	−	2.35345i	0.223484	−	0.0769249i
$937$	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
$940$	26.3117			0.858192
$941$	15.4774	+	8.93589i	0.504549	+	0.291302i	0.730590	−	0.682816i	$-0.239245\pi$
$941$	15.4774	+	8.93589i	0.504549	+	0.291302i	−0.226041	+	0.974118i	$0.572578\pi$
$942$	53.6402	−	30.9692i	1.74769	−	1.00903i
$943$		−	46.6268i		−	1.51838i
$944$		−	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	$-0.382780\pi$
$947$	−8.24659	−	4.76117i	−0.267978	−	0.154717i	−0.627969	+	0.778239i	$0.716113\pi$
$948$	−2.09840	+	3.63453i	−0.0681528	+	0.118044i
$949$	4.92074	−	25.3005i	0.159734	−	0.821290i
$950$	−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
$955$	35.4552	−	20.4701i	1.14730	−	0.662397i
$956$	64.5335	−	37.2584i	2.08716	−	1.20502i
$957$	−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
$962$	48.0969	−	55.3172i	1.55071	−	1.78350i
$963$	4.05308	−	7.02013i	0.130609	−	0.226221i
$964$	−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	$-0.0666712\pi$
$968$		−	9.68534i		−	0.311299i
$969$	23.1103	−	13.3427i	0.742409	−	0.428630i
$970$	3.04836	+	1.75997i	0.0978769	+	0.0565093i
$971$	−47.5213			−1.52503			−0.762516	−	0.646969i	$-0.776036\pi$
$971$	−47.5213			−1.52503			−0.762516	+	0.646969i	$0.776036\pi$
$972$	22.7605	+	39.4224i	0.730044	+	1.26447i
$973$		0			0
$974$	59.7515			1.91456
$975$	−63.8184	−	12.4121i	−2.04383	−	0.397507i
$976$	2.23108	−	3.86434i	0.0714151	−	0.123695i
$977$			36.4942i			1.16755i	0.811915	+	0.583776i	$0.198425\pi$
$977$			36.4942i			1.16755i	−0.811915	+	0.583776i	$0.801575\pi$
$978$	−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
$982$		−	73.3777i		−	2.34158i
$983$	38.2647	+	22.0921i	1.22045	+	0.704629i	0.965015	−	0.262196i	$-0.0844466\pi$
$983$	38.2647	+	22.0921i	1.22045	+	0.704629i	0.255439	+	0.966825i	$0.417780\pi$
$984$	−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
$989$	−7.02731	−	12.1717i	−0.223455	−	0.387036i
$990$			14.2435i			0.452689i
$991$	−50.7097			−1.61085			−0.805424	−	0.592699i	$-0.798062\pi$
$991$	−50.7097			−1.61085			−0.805424	+	0.592699i	$0.798062\pi$
$992$	67.8495			2.15422
$993$			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
$997$	−25.1384	−	43.5410i	−0.796141	−	1.37896i	−0.922112	−	0.386923i	$-0.873538\pi$
$997$	−25.1384	−	43.5410i	−0.796141	−	1.37896i	0.125971	−	0.992034i	$-0.459795\pi$
$998$	0.146578			0.00463985
$999$	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.u.i.361.1		12
7.2	even	3		637.2.k.g.569.6		12
7.3	odd	6		91.2.q.a.36.6	✓	12
7.4	even	3		637.2.q.h.491.6		12
7.5	odd	6		637.2.k.h.569.6		12
7.6	odd	2		637.2.u.h.361.1		12
13.4	even	6		637.2.k.g.459.1		12
21.17	even	6		819.2.ct.a.127.1		12
28.3	even	6		1456.2.cc.c.673.5		12
91.3	odd	6		1183.2.c.i.337.11		12
91.4	even	6		637.2.q.h.589.6		12
91.10	odd	6		1183.2.c.i.337.2		12
91.11	odd	12		8281.2.a.by.1.2		6
91.17	odd	6		91.2.q.a.43.6	yes	12
91.24	even	12		1183.2.a.m.1.2		6
91.30	even	6	inner	637.2.u.i.30.1		12
91.67	odd	12		8281.2.a.ch.1.5		6
91.69	odd	6		637.2.k.h.459.1		12
91.80	even	12		1183.2.a.p.1.5		6
91.82	odd	6		637.2.u.h.30.1		12
273.17	even	6		819.2.ct.a.316.1		12
364.199	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	7.3	odd	6
91.2.q.a.43.6	yes	12	91.17	odd	6
637.2.k.g.459.1		12	13.4	even	6
637.2.k.g.569.6		12	7.2	even	3
637.2.k.h.459.1		12	91.69	odd	6
637.2.k.h.569.6		12	7.5	odd	6
637.2.q.h.491.6		12	7.4	even	3
637.2.q.h.589.6		12	91.4	even	6
637.2.u.h.30.1		12	91.82	odd	6
637.2.u.h.361.1		12	7.6	odd	2
637.2.u.i.30.1		12	91.30	even	6	inner
637.2.u.i.361.1		12	1.1	even	1	trivial
819.2.ct.a.127.1		12	21.17	even	6
819.2.ct.a.316.1		12	273.17	even	6
1183.2.a.m.1.2		6	91.24	even	12
1183.2.a.p.1.5		6	91.80	even	12
1183.2.c.i.337.2		12	91.10	odd	6
1183.2.c.i.337.11		12	91.3	odd	6
1456.2.cc.c.225.5		12	364.199	even	6
1456.2.cc.c.673.5		12	28.3	even	6
8281.2.a.by.1.2		6	91.11	odd	12
8281.2.a.ch.1.5		6	91.67	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.82678 - 1.05469i) q^{2} -2.26165 q^{3} +(1.22476 + 2.12135i) q^{4} +(-3.11923 + 1.80089i) q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +2.11505 q^{9} +O(q^{10})\)	\(q+(-1.82678 - 1.05469i) q^{2} -2.26165 q^{3} +(1.22476 + 2.12135i) q^{4} +(-3.11923 + 1.80089i) q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +2.11505 q^{9} +7.59755 q^{10} +0.886384i q^{11} +(-2.76998 - 4.79774i) 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} +(-3.86375 - 2.23073i) q^{18} +2.37878i q^{19} +(-7.64062 - 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +(-1.92926 + 3.34157i) q^{23} +2.14452i q^{24} +(3.98641 - 6.90466i) q^{25} +(1.45200 - 7.46562i) q^{26} +2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} -17.1830 q^{30} +(-7.33455 - 4.23460i) q^{31} +(-6.93800 + 4.00566i) q^{32} -2.00469i q^{33} -10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} +(8.34686 + 4.81906i) q^{37} +(2.50888 - 4.34551i) q^{38} +(-2.65402 - 7.71051i) 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} +(-6.59734 + 3.80898i) q^{45} +(7.04867 - 4.06955i) 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} +(-5.79494 + 6.66487i) q^{52} +(-2.46016 + 4.26112i) q^{53} +(-3.65619 - 2.11090i) q^{54} +(-1.59628 - 2.76484i) q^{55} -5.37995i q^{57} +2.70418i q^{58} +(6.34577 - 3.66373i) q^{59} +(17.2804 + 9.97684i) q^{60} +1.53926 q^{61} +(8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(-9.80005 - 8.52090i) q^{65} +(-2.11433 + 3.66213i) q^{66} +8.42649i q^{67} +(-6.07501 + 10.5222i) q^{68} +(4.36330 - 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} -2.00552i q^{72} +(-6.19086 - 3.57430i) 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} +(-0.378775 - 0.656058i) q^{79} +10.4412i q^{80} -10.8717 q^{81} +25.4901 q^{82} -4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} +(6.65406 - 3.84172i) q^{86} +(1.44969 + 2.51093i) q^{87} +0.840480 q^{88} +(3.13400 + 1.80942i) q^{89} +16.0692 q^{90} -9.45150 q^{92} +(16.5882 + 9.57719i) q^{93} +6.29081 q^{94} +(-4.28391 - 7.41995i) q^{95} +(15.6913 - 9.05939i) q^{96} +(0.401229 + 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Introduction

L-functions

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Database

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