LMFDB - Embedded newform 637.2.u.h.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.h.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	$-0.273560\pi$
$3$	2.26165			1.30576			0.652882	+	0.757460i	$0.273560\pi$
$4$	1.22476	+	2.12135i	0.612380	+	1.06067i
$5$	3.11923	−	1.80089i	1.39496	−	0.805382i	0.401104	−	0.916033i	$-0.368627\pi$
$5$	3.11923	−	1.80089i	1.39496	−	0.805382i	0.993859	+	0.110650i	$0.0352933\pi$
$6$	−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	$-0.961233\pi$
$17$	−2.48008	−	4.29563i	−0.601508	−	1.04184i	0.391085	−	0.920355i	$-0.372100\pi$
$18$	−3.86375	−	2.23073i	−0.910694	−	0.525789i
$19$		−	2.37878i		−	0.545729i	−0.962053	−	0.272864i	$-0.912029\pi$
$19$		−	2.37878i		−	0.545729i	0.962053	−	0.272864i	$-0.0879710\pi$
$20$	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	0.983297	−	0.182006i	$-0.0582591\pi$
$31$	7.33455	+	4.23460i	1.31732	+	0.760557i	0.334027	+	0.942564i	$0.391592\pi$
$32$	−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	$-0.274071\pi$
$41$	10.4652	−	6.04207i	1.63438	−	0.943612i	0.982719	−	0.185106i	$-0.0592628\pi$
$42$		0			0
$43$	−1.82125	+	3.15450i	−0.277738	+	0.481056i	−0.970822	−	0.239800i	$-0.922918\pi$
$43$	−1.82125	+	3.15450i	−0.277738	+	0.481056i	0.693084	+	0.720856i	$0.256251\pi$
$44$	−1.88033	+	1.08561i	−0.283470	+	0.163662i
$45$	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	−0.299664	−	0.954045i	$-0.596874\pi$
$47$	2.58274	−	1.49115i	0.376731	−	0.217506i	0.676395	+	0.736539i	$0.263541\pi$
$48$	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	−0.852532	−	0.522675i	$-0.824934\pi$
$59$	−6.34577	+	3.66373i	−0.826148	+	0.476977i	0.0263837	+	0.999652i	$0.491601\pi$
$60$	17.2804	+	9.97684i	2.23089	+	1.28800i
$61$	−1.53926			−0.197082			−0.0985412	−	0.995133i	$-0.531418\pi$
$61$	−1.53926			−0.197082			−0.0985412	+	0.995133i	$0.531418\pi$
$62$	−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	0.816438	−	0.577433i	$-0.195946\pi$
$73$	6.19086	+	3.57430i	0.724586	+	0.418340i	−0.0918526	+	0.995773i	$0.529279\pi$
$74$	−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	$0.0842697\pi$
$83$			4.76766i			0.523319i	−0.965160	+	0.261659i	$0.915730\pi$
$84$		0			0
$85$	−15.4719	−	8.93270i	−1.67816	−	0.968888i
$86$	6.65406	−	3.84172i	0.717525	−	0.414263i
$87$	−1.44969	−	2.51093i	−0.155423	−	0.269200i
$88$	0.840480			0.0895955
$89$	−3.13400	−	1.80942i	−0.332204	−	0.191798i	0.324615	−	0.945846i	$-0.394765\pi$
$89$	−3.13400	−	1.80942i	−0.332204	−	0.191798i	−0.656819	+	0.754048i	$0.728098\pi$
$90$	−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	0.479492	−	0.877546i	$-0.340821\pi$
$97$	−0.401229	−	0.231650i	−0.0407386	−	0.0235205i	−0.520231	+	0.854026i	$0.674154\pi$
$98$		0			0
$99$			1.87475i			0.188419i
$100$	19.5296			1.95296
$101$	−5.82303			−0.579413			−0.289707	−	0.957115i	$-0.593558\pi$
$101$	−5.82303			−0.579413			−0.289707	+	0.957115i	$0.593558\pi$
$102$			23.6634i			2.34303i
$103$	4.11944	+	7.13508i	0.405901	+	0.703040i	0.994426	−	0.105438i	$-0.0336246\pi$
$103$	4.11944	+	7.13508i	0.405901	+	0.703040i	−0.588525	+	0.808479i	$0.700291\pi$
$104$	−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	0.987683	−	0.156470i	$-0.0500114\pi$
$131$	4.10133	+	7.10371i	0.358335	+	0.620654i	−0.629348	+	0.777123i	$0.716678\pi$
$132$	−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	$0.416805\pi$
$139$	−8.34028	+	14.4458i	−0.707413	+	1.22528i	−0.965813	+	0.259238i	$0.916529\pi$
$140$		0			0
$141$	5.84125	−	3.37245i	0.491922	−	0.284011i
$142$	6.80160	+	11.7807i	0.570778	+	0.988616i
$143$	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	$0.340020\pi$
$157$	−6.49155	+	11.2437i	−0.518082	+	0.897344i	−0.999779	+	0.0210065i	$0.993313\pi$
$158$			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	−0.884992	−	0.465607i	$-0.845836\pi$
$167$	−11.9441	+	6.89591i	−0.924260	+	0.533622i	−0.0392682	+	0.999229i	$0.512503\pi$
$168$		0			0
$169$	−10.2459	+	8.00140i	−0.788143	+	0.615493i
$170$	18.8425	+	32.6362i	1.44516	+	2.50309i
$171$		−	5.03124i		−	0.384748i
$172$	−8.92237			−0.680324
$173$	3.68432			0.280113			0.140057	−	0.990143i	$-0.455272\pi$
$173$	3.68432			0.280113			0.140057	+	0.990143i	$0.455272\pi$
$174$			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	$-0.525051\pi$
$181$	−2.11543			−0.157239			−0.0786193	+	0.996905i	$0.525051\pi$
$182$		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	0.804790	−	0.593560i	$-0.202278\pi$
$199$	−1.57492	−	2.72785i	−0.111643	−	0.193372i	−0.916433	+	0.400188i	$0.868945\pi$
$200$	−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	−0.367561	−	0.930000i	$-0.619807\pi$
$223$	3.79396	−	2.19044i	0.254062	−	0.146683i	0.621623	+	0.783317i	$0.286474\pi$
$224$		0			0
$225$	8.43147	−	14.6037i	0.562098	−	0.973582i
$226$	−8.96971	+	5.17866i	−0.596656	+	0.344480i
$227$	−11.7488	+	6.78316i	−0.779793	+	0.450214i	−0.836357	−	0.548185i	$-0.815319\pi$
$227$	−11.7488	+	6.78316i	−0.779793	+	0.450214i	0.0565636	+	0.998399i	$0.481986\pi$
$228$	11.4127	−	6.58915i	0.755827	−	0.436377i
$229$	14.3050	−	8.25900i	0.945302	−	0.545770i	0.0536833	−	0.998558i	$-0.482904\pi$
$229$	14.3050	−	8.25900i	0.945302	−	0.545770i	0.891618	+	0.452788i	$0.149571\pi$
$230$	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	$-0.267143\pi$
$241$	25.5602	−	14.7572i	1.64648	−	0.950593i	0.978458	−	0.206448i	$-0.0661904\pi$
$242$	−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	−0.994859	−	0.101267i	$-0.967710\pi$
$251$	−6.49134	+	11.2433i	−0.409730	+	0.709673i	0.585130	+	0.810940i	$0.301044\pi$
$252$		0			0
$253$	−2.96191	−	1.71006i	−0.186214	−	0.107511i
$254$			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	−0.928628	−	0.371011i	$-0.879011\pi$
$257$	−2.29261	+	3.97091i	−0.143009	+	0.247698i	0.785620	+	0.618710i	$0.212344\pi$
$258$	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	0.624984	−	0.780637i	$-0.285105\pi$
$269$	−5.96282	−	10.3279i	−0.363559	−	0.629703i	−0.988544	+	0.150934i	$0.951772\pi$
$270$	15.2060			0.925409
$271$	11.2828	+	6.51416i	0.685384	+	0.395707i	0.801881	−	0.597484i	$-0.203833\pi$
$271$	11.2828	+	6.51416i	0.685384	+	0.395707i	−0.116496	+	0.993191i	$0.537166\pi$
$272$	−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	$-0.282522\pi$
$283$	21.2402			1.26260			0.631299	+	0.775539i	$0.282522\pi$
$284$		−	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	0.489336	−	0.872095i	$-0.337239\pi$
$293$	−0.363782	−	0.210030i	−0.0212524	−	0.0122701i	−0.510589	+	0.859825i	$0.670572\pi$
$294$		0			0
$295$	−13.1959	+	22.8561i	−0.768298	+	1.33073i
$296$	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	$-0.868380\pi$
$307$		−	14.0807i		−	0.803628i	0.915721	−	0.401814i	$-0.131620\pi$
$308$		0			0
$309$	9.31673	+	16.1370i	0.530010	+	0.918004i
$310$	−55.7246	−	32.1726i	−3.16495	−	1.82728i
$311$	5.19240	−	8.99349i	0.294434	−	0.509974i	−0.680419	−	0.732823i	$-0.738202\pi$
$311$	5.19240	−	8.99349i	0.294434	−	0.509974i	0.974853	+	0.222849i	$0.0715356\pi$
$312$	−7.31119	+	2.51657i	−0.413915	+	0.142473i
$313$	−3.42379	−	5.93018i	−0.193524	−	0.335194i	0.752892	−	0.658145i	$-0.228658\pi$
$313$	−3.42379	−	5.93018i	−0.193524	−	0.335194i	−0.946416	+	0.322951i	$0.895325\pi$
$314$	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	0.0925892	−	0.995704i	$-0.470486\pi$
$349$	18.7038	−	10.7986i	1.00119	−	0.578037i	0.908600	+	0.417668i	$0.137152\pi$
$350$		0			0
$351$	2.34866	+	6.82338i	0.125362	+	0.364205i
$352$	−3.55055	−	6.14974i	−0.189245	−	0.327782i
$353$			21.6176i			1.15059i	0.817946	+	0.575295i	$0.195113\pi$
$353$			21.6176i			1.15059i	−0.817946	+	0.575295i	$0.804887\pi$
$354$	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	$-0.596276\pi$
$367$	−11.4128			−0.595741			−0.297871	+	0.954606i	$0.596276\pi$
$368$	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	$-0.865057\pi$
$383$		−	16.1006i		−	0.822705i	0.911476	−	0.411352i	$-0.134943\pi$
$384$	−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	$-0.893391\pi$
$397$		−	13.0984i		−	0.657390i	0.944436	−	0.328695i	$-0.106609\pi$
$398$			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	−0.917020	−	0.398840i	$-0.869413\pi$
$409$	−20.8330	+	12.0279i	−1.03013	+	0.594743i	−0.113105	+	0.993583i	$0.536079\pi$
$410$	−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	$-0.764415\pi$
$419$	−19.5119	−	33.7956i	−0.953218	−	1.65102i	−0.214825	−	0.976653i	$-0.568918\pi$
$420$		0			0
$421$		−	22.0284i		−	1.07360i	−0.843710	−	0.536799i	$-0.819633\pi$
$421$		−	22.0284i		−	1.07360i	0.843710	−	0.536799i	$-0.180367\pi$
$422$		−	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	−0.681155	−	0.732139i	$-0.738522\pi$
$433$	6.10678	−	10.5773i	0.293473	−	0.508310i	0.974629	+	0.223828i	$0.0718555\pi$
$434$		0			0
$435$	−9.04381	−	5.22145i	−0.433618	−	0.250349i
$436$		−	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	−0.990473	−	0.137706i	$-0.956027\pi$
$439$	−7.87765	+	13.6445i	−0.375980	+	0.651216i	0.614493	+	0.788922i	$0.289361\pi$
$440$	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	0.529397	−	0.848374i	$-0.322418\pi$
$461$	1.27498	+	0.736110i	0.0593817	+	0.0342840i	−0.470015	+	0.882658i	$0.655752\pi$
$462$		0			0
$463$		−	14.0366i		−	0.652335i	−0.945312	−	0.326168i	$-0.894243\pi$
$463$		−	14.0366i		−	0.652335i	0.945312	−	0.326168i	$-0.105757\pi$
$464$	−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	$0.0919841\pi$
$467$	15.6903	+	27.1764i	0.726060	+	1.25757i	−0.232476	+	0.972602i	$0.574683\pi$
$468$	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	$0.390230\pi$
$479$			41.1951i			1.88225i	−0.338059	+	0.941125i	$0.609770\pi$
$480$	−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	$0.361191\pi$
$503$	−12.8686	+	22.2891i	−0.573782	+	0.993820i	−0.996173	+	0.0874060i	$0.972142\pi$
$504$		0			0
$505$	−18.1634	+	10.4866i	−0.808260	+	0.466649i
$506$	3.60719	+	6.24783i	0.160359	+	0.277750i
$507$	−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	0.628995	−	0.777409i	$-0.283467\pi$
$509$	6.09682	+	3.52000i	0.270237	+	0.156021i	−0.358759	+	0.933430i	$0.616800\pi$
$510$	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	−0.987561	−	0.157234i	$-0.949742\pi$
$521$	−8.16266	+	14.1381i	−0.357613	+	0.619403i	0.629949	+	0.776637i	$0.283076\pi$
$522$			5.71948i			0.250335i
$523$	3.54473	−	6.13965i	0.155000	−	0.268468i	−0.778059	−	0.628191i	$-0.783796\pi$
$523$	3.54473	−	6.13965i	0.155000	−	0.268468i	0.933059	+	0.359723i	$0.117129\pi$
$524$	−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	$-0.990690\pi$
$563$	−12.4596	−	21.5807i	−0.525111	−	0.909519i	0.474461	−	0.880276i	$-0.342643\pi$
$564$	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	−0.323645	−	0.946179i	$-0.604908\pi$
$577$	−31.3443	−	18.0967i	−1.30488	−	0.753374i	−0.981237	+	0.192804i	$0.938242\pi$
$578$	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	0.323166	−	0.946342i	$-0.395253\pi$
$587$	31.6008	−	18.2447i	1.30431	−	0.753041i	0.981139	+	0.193301i	$0.0619195\pi$
$588$		0			0
$589$	10.0732	−	17.4472i	0.415058	−	0.718901i
$590$	48.2123	−	27.8354i	1.98487	−	1.14596i
$591$	−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	−0.970001	−	0.243102i	$-0.921835\pi$
$593$	−30.3048	+	17.4965i	−1.24447	+	0.718495i	−0.274468	+	0.961596i	$0.588502\pi$
$594$	−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	0.585334	−	0.810792i	$-0.300963\pi$
$601$	−10.0390	−	17.3881i	−0.409500	−	0.709275i	−0.994834	+	0.101518i	$0.967630\pi$
$602$		0			0
$603$			17.8225i			0.725788i
$604$			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	$-0.436822\pi$
$607$	9.71601			0.394361			0.197180	+	0.980367i	$0.436822\pi$
$608$	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	0.998602	−	0.0528581i	$-0.0168331\pi$
$619$	36.1285	+	20.8588i	1.45213	+	0.838386i	0.453525	+	0.891244i	$0.350166\pi$
$620$	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	0.769941	−	0.638115i	$-0.220286\pi$
$643$	15.2725	+	8.81757i	0.602288	+	0.347731i	−0.167653	+	0.985846i	$0.553619\pi$
$644$		0			0
$645$			29.6716i			1.16832i
$646$	24.8889			0.979241
$647$	−16.6726			−0.655469			−0.327735	−	0.944770i	$-0.606285\pi$
$647$	−16.6726			−0.655469			−0.327735	+	0.944770i	$0.606285\pi$
$648$			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	$-0.837207\pi$
$661$		−	25.1661i		−	0.978848i	0.872046	−	0.489424i	$-0.162793\pi$
$662$	−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	0.972094	−	0.234592i	$-0.0753753\pi$
$677$	7.36044	+	12.7487i	0.282885	+	0.489971i	−0.689209	+	0.724562i	$0.742042\pi$
$678$	−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	0.321916	−	0.946768i	$-0.395673\pi$
$691$	−8.86002	−	5.11534i	−0.337051	−	0.194597i	−0.658967	+	0.752172i	$0.729006\pi$
$692$	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	$-0.248559\pi$
$719$	38.0922			1.42060			0.710300	+	0.703899i	$0.248559\pi$
$720$		−	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	$-0.407778\pi$
$727$	15.4059			0.571374			0.285687	+	0.958323i	$0.407778\pi$
$728$		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	−0.674335	−	0.738426i	$-0.735570\pi$
$733$	−10.0717	+	5.81490i	−0.372007	+	0.214778i	0.302328	+	0.953204i	$0.402236\pi$
$734$	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	$-0.864017\pi$
$761$		−	22.8595i		−	0.828655i	0.910128	−	0.414328i	$-0.135983\pi$
$762$			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	$0.717462\pi$
$769$	−44.8839	+	25.9137i	−1.61855	+	0.934473i	−0.987294	+	0.158902i	$0.949205\pi$
$770$		0			0
$771$	−5.18507	+	8.98080i	−0.186736	+	0.323436i
$772$	−29.8884	+	17.2561i	−1.07571	+	0.621060i
$773$	4.93605	−	2.84983i	0.177538	−	0.102501i	−0.408598	−	0.912715i	$-0.633982\pi$
$773$	4.93605	−	2.84983i	0.177538	−	0.102501i	0.586135	+	0.810213i	$0.300649\pi$
$774$	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	−0.217490	−	0.976062i	$-0.569787\pi$
$787$	14.5614	−	8.40705i	0.519059	−	0.299679i	0.736550	+	0.676384i	$0.236454\pi$
$788$	−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	$-0.565227\pi$
$797$	21.0651	−	36.4858i	0.746163	−	1.29239i	0.949650	−	0.313314i	$-0.101439\pi$
$798$		0			0
$799$	−12.8108	−	7.39632i	−0.453214	−	0.261663i
$800$			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	$0.137178\pi$
$811$			23.7929i			0.835480i	−0.908567	+	0.417740i	$0.862822\pi$
$812$		0			0
$813$	25.5178	+	14.7327i	0.894950	+	0.516699i
$814$	15.6064	−	9.01034i	0.547003	−	0.315812i
$815$	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	$-0.634253\pi$
$829$	−23.5738			−0.818751			−0.409376	+	0.912366i	$0.634253\pi$
$830$		−	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	0.649865	−	0.760050i	$-0.274825\pi$
$839$	9.16975	+	5.29416i	0.316575	+	0.182775i	−0.333290	+	0.942824i	$0.608159\pi$
$840$		0			0
$841$	13.6783	−	23.6915i	0.471665	−	0.816947i
$842$	−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	$-0.880648\pi$
$853$		−	21.3925i		−	0.732464i	0.930524	−	0.366232i	$-0.119352\pi$
$854$		0			0
$855$	−9.06070	−	15.6936i	−0.309870	−	0.536710i
$856$	−3.14724	−	1.81706i	−0.107570	−	0.0621058i
$857$	3.61065	−	6.25382i	0.123337	−	0.213626i	−0.797744	−	0.602996i	$-0.793974\pi$
$857$	3.61065	−	6.25382i	0.123337	−	0.213626i	0.921082	+	0.389369i	$0.127307\pi$
$858$	−14.9662	−	2.91081i	−0.510939	−	0.0993734i
$859$	−28.5536	−	49.4563i	−0.974238	−	1.68743i	−0.682429	−	0.730952i	$-0.739076\pi$
$859$	−28.5536	−	49.4563i	−0.974238	−	1.68743i	−0.291809	−	0.956477i	$-0.594257\pi$
$860$	−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	0.999928	−	0.0120134i	$-0.00382406\pi$
$881$	14.5309	+	25.1683i	0.489560	+	0.847943i	−0.510368	+	0.859956i	$0.670491\pi$
$882$		0			0
$883$	4.83594			0.162742			0.0813711	−	0.996684i	$-0.474070\pi$
$883$	4.83594			0.162742			0.0813711	+	0.996684i	$0.474070\pi$
$884$	−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	−0.576355	−	0.817199i	$-0.695526\pi$
$887$	12.4949	−	21.6418i	0.419538	−	0.726660i	0.995893	+	0.0905387i	$0.0288589\pi$
$888$	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	$0.279568\pi$
$929$			46.9169i			1.53929i	−0.638469	+	0.769647i	$0.720432\pi$
$930$	−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	$-0.653497\pi$
$937$	−28.3912			−0.927501			−0.463750	+	0.885966i	$0.653497\pi$
$938$		0			0
$939$	−7.74342	−	13.4120i	−0.252697	−	0.437684i
$940$	26.3117			0.858192
$941$	−15.4774	−	8.93589i	−0.504549	−	0.291302i	0.226041	−	0.974118i	$-0.427422\pi$
$941$	−15.4774	−	8.93589i	−0.504549	−	0.291302i	−0.730590	+	0.682816i	$0.760755\pi$
$942$	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	$-0.223964\pi$
$971$	47.5213			1.52503			0.762516	+	0.646969i	$0.223964\pi$
$972$	−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	−0.255439	−	0.966825i	$-0.582220\pi$
$983$	−38.2647	−	22.0921i	−1.22045	−	0.704629i	−0.965015	+	0.262196i	$0.915553\pi$
$984$	−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	$0.126462\pi$
$997$	25.1384	+	43.5410i	0.796141	+	1.37896i	−0.125971	+	0.992034i	$0.540205\pi$
$998$	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.h.361.1		12
7.2	even	3		637.2.k.h.569.6		12
7.3	odd	6		637.2.q.h.491.6		12
7.4	even	3		91.2.q.a.36.6	✓	12
7.5	odd	6		637.2.k.g.569.6		12
7.6	odd	2		637.2.u.i.361.1		12
13.4	even	6		637.2.k.h.459.1		12
21.11	odd	6		819.2.ct.a.127.1		12
28.11	odd	6		1456.2.cc.c.673.5		12
91.4	even	6		91.2.q.a.43.6	yes	12
91.11	odd	12		1183.2.a.m.1.2		6
91.17	odd	6		637.2.q.h.589.6		12
91.24	even	12		8281.2.a.by.1.2		6
91.30	even	6	inner	637.2.u.h.30.1		12
91.67	odd	12		1183.2.a.p.1.5		6
91.69	odd	6		637.2.k.g.459.1		12
91.80	even	12		8281.2.a.ch.1.5		6
91.81	even	3		1183.2.c.i.337.11		12
91.82	odd	6		637.2.u.i.30.1		12
91.88	even	6		1183.2.c.i.337.2		12
273.95	odd	6		819.2.ct.a.316.1		12
364.95	odd	6		1456.2.cc.c.225.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.6	✓	12	7.4	even	3
91.2.q.a.43.6	yes	12	91.4	even	6
637.2.k.g.459.1		12	91.69	odd	6
637.2.k.g.569.6		12	7.5	odd	6
637.2.k.h.459.1		12	13.4	even	6
637.2.k.h.569.6		12	7.2	even	3
637.2.q.h.491.6		12	7.3	odd	6
637.2.q.h.589.6		12	91.17	odd	6
637.2.u.h.30.1		12	91.30	even	6	inner
637.2.u.h.361.1		12	1.1	even	1	trivial
637.2.u.i.30.1		12	91.82	odd	6
637.2.u.i.361.1		12	7.6	odd	2
819.2.ct.a.127.1		12	21.11	odd	6
819.2.ct.a.316.1		12	273.95	odd	6
1183.2.a.m.1.2		6	91.11	odd	12
1183.2.a.p.1.5		6	91.67	odd	12
1183.2.c.i.337.2		12	91.88	even	6
1183.2.c.i.337.11		12	91.81	even	3
1456.2.cc.c.225.5		12	364.95	odd	6
1456.2.cc.c.673.5		12	28.11	odd	6
8281.2.a.by.1.2		6	91.24	even	12
8281.2.a.ch.1.5		6	91.80	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.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

Modular forms

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Database

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