LMFDB - Embedded newform 637.2.q.j.491.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.7
Character	$\chi$	$=$	637.491
Dual form			637.2.q.j.589.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.250157 + 0.144428i) q^{2} +(-0.969921 - 1.67995i) q^{3} +(-0.958281 + 1.65979i) q^{4} +4.29339i q^{5} +(0.485264 + 0.280167i) q^{6} -1.13132i q^{8} +(-0.381493 + 0.660765i) q^{9} +O(q^{10})$	\(q+(-0.250157 + 0.144428i) q^{2} +(-0.969921 - 1.67995i) q^{3} +(-0.958281 + 1.65979i) q^{4} +4.29339i q^{5} +(0.485264 + 0.280167i) q^{6} -1.13132i q^{8} +(-0.381493 + 0.660765i) q^{9} +(-0.620085 - 1.07402i) q^{10} +(1.60793 - 0.928339i) q^{11} +3.71783 q^{12} +(2.29711 + 2.77908i) q^{13} +(7.21268 - 4.16424i) q^{15} +(-1.75317 - 3.03658i) q^{16} +(-2.59834 + 4.50045i) q^{17} -0.220393i q^{18} +(-5.70993 - 3.29663i) q^{19} +(-7.12613 - 4.11427i) q^{20} +(-0.268156 + 0.464460i) q^{22} +(-0.245284 - 0.424844i) q^{23} +(-1.90057 + 1.09729i) q^{24} -13.4332 q^{25} +(-0.976014 - 0.363437i) q^{26} -4.33945 q^{27} +(0.495440 + 0.858128i) q^{29} +(-1.20287 + 2.08343i) q^{30} +6.53629i q^{31} +(2.83664 + 1.63774i) q^{32} +(-3.11913 - 1.80083i) q^{33} -1.50109i q^{34} +(-0.731154 - 1.26640i) q^{36} +(-2.75725 + 1.59190i) q^{37} +1.90450 q^{38} +(2.44070 - 6.55452i) q^{39} +4.85720 q^{40} +(-0.129576 + 0.0748106i) q^{41} +(-0.126776 + 0.219583i) q^{43} +3.55844i q^{44} +(-2.83692 - 1.63790i) q^{45} +(0.122719 + 0.0708516i) q^{46} -9.64902i q^{47} +(-3.40087 + 5.89048i) q^{48} +(3.36040 - 1.94013i) q^{50} +10.0807 q^{51} +(-6.81397 + 1.14959i) q^{52} +0.777194 q^{53} +(1.08554 - 0.626739i) q^{54} +(3.98572 + 6.90346i) q^{55} +12.7899i q^{57} +(-0.247875 - 0.143111i) q^{58} +(-7.25519 - 4.18878i) q^{59} +15.9621i q^{60} +(-3.54492 + 6.13998i) q^{61} +(-0.944023 - 1.63510i) q^{62} +6.06653 q^{64} +(-11.9317 + 9.86239i) q^{65} +1.04036 q^{66} +(-0.319884 + 0.184685i) q^{67} +(-4.97987 - 8.62539i) q^{68} +(-0.475811 + 0.824129i) q^{69} +(-0.482043 - 0.278308i) q^{71} +(0.747538 + 0.431591i) q^{72} -4.83067i q^{73} +(0.459830 - 0.796449i) q^{74} +(13.0291 + 22.5671i) q^{75} +(10.9434 - 6.31819i) q^{76} +(0.336099 + 1.99216i) q^{78} -7.82988 q^{79} +(13.0372 - 7.52703i) q^{80} +(5.35340 + 9.27237i) q^{81} +(0.0216095 - 0.0374287i) q^{82} +6.38123i q^{83} +(-19.3222 - 11.1557i) q^{85} -0.0732401i q^{86} +(0.961075 - 1.66463i) q^{87} +(-1.05025 - 1.81909i) q^{88} +(-8.26717 + 4.77306i) q^{89} +0.946231 q^{90} +0.940203 q^{92} +(10.9806 - 6.33968i) q^{93} +(1.39359 + 2.41377i) q^{94} +(14.1537 - 24.5149i) q^{95} -6.35389i q^{96} +(-4.30357 - 2.48467i) q^{97} +1.41662i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 28 * q^9	$ 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.250157	+	0.144428i	−0.176887	+	0.102126i	−0.585829	−	0.810434i	$-0.699231\pi$
$2$	−0.250157	+	0.144428i	−0.176887	+	0.102126i	0.408942	+	0.912560i	$0.365898\pi$
$3$	−0.969921	−	1.67995i	−0.559984	−	0.969921i	−0.997497	−	0.0707087i	$-0.977474\pi$
$3$	−0.969921	−	1.67995i	−0.559984	−	0.969921i	0.437513	−	0.899212i	$-0.355859\pi$
$4$	−0.958281	+	1.65979i	−0.479141	+	0.829896i
$5$			4.29339i			1.92006i	0.279896	+	0.960030i	$0.409700\pi$
$5$			4.29339i			1.92006i	−0.279896	+	0.960030i	$0.590300\pi$
$6$	0.485264	+	0.280167i	0.198108	+	0.114378i
$7$		0			0
$7$		0			0
$8$		−	1.13132i		−	0.399983i
$9$	−0.381493	+	0.660765i	−0.127164	+	0.220255i
$10$	−0.620085	−	1.07402i	−0.196088	−	0.339635i
$11$	1.60793	−	0.928339i	0.484809	−	0.279905i	−0.237609	−	0.971361i	$-0.576364\pi$
$11$	1.60793	−	0.928339i	0.484809	−	0.279905i	0.722418	+	0.691456i	$0.243030\pi$
$12$	3.71783			1.07324
$13$	2.29711	+	2.77908i	0.637104	+	0.770778i
$13$	2.29711	+	2.77908i	0.637104	+	0.770778i
$14$		0			0
$15$	7.21268	−	4.16424i	1.86231	−	1.07520i
$16$	−1.75317	−	3.03658i	−0.438292	−	0.759144i
$17$	−2.59834	+	4.50045i	−0.630189	+	1.09152i	0.357324	+	0.933981i	$0.383689\pi$
$17$	−2.59834	+	4.50045i	−0.630189	+	1.09152i	−0.987513	+	0.157539i	$0.949644\pi$
$18$		−	0.220393i		−	0.0519471i
$19$	−5.70993	−	3.29663i	−1.30995	−	0.756298i	−0.327860	−	0.944726i	$-0.606327\pi$
$19$	−5.70993	−	3.29663i	−1.30995	−	0.756298i	−0.982087	+	0.188428i	$0.939661\pi$
$20$	−7.12613	−	4.11427i	−1.59345	−	0.919979i
$21$		0			0
$22$	−0.268156	+	0.464460i	−0.0571711	+	0.0990232i
$23$	−0.245284	−	0.424844i	−0.0511452	−	0.0885860i	0.839319	−	0.543639i	$-0.182954\pi$
$23$	−0.245284	−	0.424844i	−0.0511452	−	0.0885860i	−0.890465	+	0.455053i	$0.849620\pi$
$24$	−1.90057	+	1.09729i	−0.387952	+	0.223984i
$25$	−13.4332			−2.68663
$26$	−0.976014	−	0.363437i	−0.191412	−	0.0712759i
$27$	−4.33945			−0.835128
$28$		0			0
$29$	0.495440	+	0.858128i	0.0920009	+	0.159350i	0.908353	−	0.418204i	$-0.137340\pi$
$29$	0.495440	+	0.858128i	0.0920009	+	0.159350i	−0.816352	+	0.577555i	$0.804007\pi$
$30$	−1.20287	+	2.08343i	−0.219612	+	0.380380i
$31$			6.53629i			1.17395i	0.809604	+	0.586976i	$0.199682\pi$
$31$			6.53629i			1.17395i	−0.809604	+	0.586976i	$0.800318\pi$
$32$	2.83664	+	1.63774i	0.501452	+	0.289513i
$33$	−3.11913	−	1.80083i	−0.542971	−	0.313484i
$34$		−	1.50109i		−	0.257435i
$35$		0			0
$36$	−0.731154	−	1.26640i	−0.121859	−	0.211066i
$37$	−2.75725	+	1.59190i	−0.453289	+	0.261707i	−0.709218	−	0.704989i	$-0.750952\pi$
$37$	−2.75725	+	1.59190i	−0.453289	+	0.261707i	0.255929	+	0.966696i	$0.417619\pi$
$38$	1.90450			0.308951
$39$	2.44070	−	6.55452i	0.390825	−	1.04956i
$40$	4.85720			0.767991
$41$	−0.129576	+	0.0748106i	−0.0202363	+	0.0116834i	−0.510084	−	0.860125i	$-0.670386\pi$
$41$	−0.129576	+	0.0748106i	−0.0202363	+	0.0116834i	0.489848	+	0.871808i	$0.337052\pi$
$42$		0			0
$43$	−0.126776	+	0.219583i	−0.0193332	+	0.0334861i	−0.875530	−	0.483164i	$-0.839488\pi$
$43$	−0.126776	+	0.219583i	−0.0193332	+	0.0334861i	0.856197	+	0.516650i	$0.172821\pi$
$44$			3.55844i			0.536455i
$45$	−2.83692	−	1.63790i	−0.422903	−	0.244163i
$46$	0.122719	+	0.0708516i	0.0180939	+	0.0104465i
$47$		−	9.64902i		−	1.40745i	−0.710470	−	0.703727i	$-0.751518\pi$
$47$		−	9.64902i		−	1.40745i	0.710470	−	0.703727i	$-0.248482\pi$
$48$	−3.40087	+	5.89048i	−0.490873	+	0.850217i
$49$		0			0
$50$	3.36040	−	1.94013i	0.475232	−	0.274375i
$51$	10.0807			1.41158
$52$	−6.81397	+	1.14959i	−0.944928	+	0.159420i
$53$	0.777194			0.106756			0.0533779	−	0.998574i	$-0.483001\pi$
$53$	0.777194			0.106756			0.0533779	+	0.998574i	$0.483001\pi$
$54$	1.08554	−	0.626739i	0.147724	−	0.0852883i
$55$	3.98572	+	6.90346i	0.537434	+	0.930863i
$56$		0			0
$57$			12.7899i			1.69406i
$58$	−0.247875	−	0.143111i	−0.0325476	−	0.0187914i
$59$	−7.25519	−	4.18878i	−0.944545	−	0.545333i	−0.0531627	−	0.998586i	$-0.516930\pi$
$59$	−7.25519	−	4.18878i	−0.944545	−	0.545333i	−0.891382	+	0.453253i	$0.850264\pi$
$60$			15.9621i			2.06069i
$61$	−3.54492	+	6.13998i	−0.453881	+	0.786144i	−0.998623	−	0.0524592i	$-0.983294\pi$
$61$	−3.54492	+	6.13998i	−0.453881	+	0.786144i	0.544742	+	0.838603i	$0.316627\pi$
$62$	−0.944023	−	1.63510i	−0.119891	−	0.207657i
$63$		0			0
$64$	6.06653			0.758316
$65$	−11.9317	+	9.86239i	−1.47994	+	1.22328i
$66$	1.04036			0.128060
$67$	−0.319884	+	0.184685i	−0.0390800	+	0.0225628i	−0.519413	−	0.854524i	$-0.673849\pi$
$67$	−0.319884	+	0.184685i	−0.0390800	+	0.0225628i	0.480333	+	0.877086i	$0.340516\pi$
$68$	−4.97987	−	8.62539i	−0.603898	−	1.04598i
$69$	−0.475811	+	0.824129i	−0.0572810	+	0.0992135i
$70$		0			0
$71$	−0.482043	−	0.278308i	−0.0572080	−	0.0330291i	0.471123	−	0.882067i	$-0.343849\pi$
$71$	−0.482043	−	0.278308i	−0.0572080	−	0.0330291i	−0.528331	+	0.849038i	$0.677182\pi$
$72$	0.747538	+	0.431591i	0.0880982	+	0.0508635i
$73$		−	4.83067i		−	0.565387i	−0.959210	−	0.282694i	$-0.908772\pi$
$73$		−	4.83067i		−	0.565387i	0.959210	−	0.282694i	$-0.0912280\pi$
$74$	0.459830	−	0.796449i	0.0534541	−	0.0925853i
$75$	13.0291	+	22.5671i	1.50447	+	2.60582i
$76$	10.9434	−	6.31819i	1.25530	−	0.724746i
$77$		0			0
$78$	0.336099	+	1.99216i	0.0380558	+	0.225568i
$79$	−7.82988			−0.880931			−0.440465	−	0.897770i	$-0.645187\pi$
$79$	−7.82988			−0.880931			−0.440465	+	0.897770i	$0.645187\pi$
$80$	13.0372	−	7.52703i	1.45760	−	0.841547i
$81$	5.35340	+	9.27237i	0.594823	+	1.03026i
$82$	0.0216095	−	0.0374287i	0.00238637	−	0.00413331i
$83$			6.38123i			0.700431i	0.936669	+	0.350216i	$0.113892\pi$
$83$			6.38123i			0.700431i	−0.936669	+	0.350216i	$0.886108\pi$
$84$		0			0
$85$	−19.3222	−	11.1557i	−2.09578	−	1.21000i
$86$		−	0.0732401i		−	0.00789768i
$87$	0.961075	−	1.66463i	0.103038	−	0.178467i
$88$	−1.05025	−	1.81909i	−0.111957	−	0.193915i
$89$	−8.26717	+	4.77306i	−0.876319	+	0.505943i	−0.869443	−	0.494033i	$-0.835522\pi$
$89$	−8.26717	+	4.77306i	−0.876319	+	0.505943i	−0.00687590	+	0.999976i	$0.502189\pi$
$90$	0.946231			0.0997416
$91$		0			0
$92$	0.940203			0.0980229
$93$	10.9806	−	6.33968i	1.13864	−	0.657394i
$94$	1.39359	+	2.41377i	0.143738	+	0.248961i
$95$	14.1537	−	24.5149i	1.45214	−	2.51518i
$96$		−	6.35389i		−	0.648492i
$97$	−4.30357	−	2.48467i	−0.436961	−	0.252280i	0.265346	−	0.964153i	$-0.414514\pi$
$97$	−4.30357	−	2.48467i	−0.436961	−	0.252280i	−0.702308	+	0.711873i	$0.747847\pi$
$98$		0			0
$99$			1.41662i			0.142375i
$100$	12.8728	−	22.2963i	1.28728	−	2.22963i
$101$	7.92728	+	13.7304i	0.788794	+	1.36623i	0.926706	+	0.375786i	$0.122627\pi$
$101$	7.92728	+	13.7304i	0.788794	+	1.36623i	−0.137913	+	0.990444i	$0.544039\pi$
$102$	−2.52176	+	1.45594i	−0.249691	+	0.144159i
$103$	9.84334			0.969894			0.484947	−	0.874544i	$-0.338839\pi$
$103$	9.84334			0.969894			0.484947	+	0.874544i	$0.338839\pi$
$104$	3.14403	−	2.59877i	0.308298	−	0.254831i
$105$		0			0
$106$	−0.194420	+	0.112249i	−0.0188838	+	0.0109025i
$107$	−2.49709	−	4.32509i	−0.241403	−	0.418123i	0.719711	−	0.694274i	$-0.244274\pi$
$107$	−2.49709	−	4.32509i	−0.241403	−	0.418123i	−0.961114	+	0.276151i	$0.910941\pi$
$108$	4.15842	−	7.20259i	0.400144	−	0.693070i
$109$		−	3.24070i		−	0.310403i	−0.987883	−	0.155201i	$-0.950397\pi$
$109$		−	3.24070i		−	0.310403i	0.987883	−	0.155201i	$-0.0496026\pi$
$110$	−1.99411	−	1.15130i	−0.190131	−	0.109772i
$111$	5.34863	+	3.08803i	0.507670	+	0.293103i
$112$		0			0
$113$	2.43982	−	4.22589i	0.229519	−	0.397538i	−0.728147	−	0.685421i	$-0.759618\pi$
$113$	2.43982	−	4.22589i	0.229519	−	0.397538i	0.957666	+	0.287883i	$0.0929514\pi$
$114$	−1.84722	−	3.19947i	−0.173008	−	0.299658i
$115$	1.82402	−	1.05310i	0.170091	−	0.0982018i
$116$	−1.89908			−0.176326
$117$	−2.71265	+	0.457653i	−0.250784	+	0.0423100i
$118$	2.41991			0.222771
$119$		0			0
$120$	−4.71110	−	8.15987i	−0.430063	−	0.744891i
$121$	−3.77637	+	6.54087i	−0.343307	+	0.594625i
$122$		−	2.04794i		−	0.185412i
$123$	0.251356	+	0.145121i	0.0226640	+	0.0130851i
$124$	−10.8489	−	6.26360i	−0.974258	−	0.562488i
$125$		−	36.2069i		−	3.23844i
$126$		0			0
$127$	5.39150	+	9.33835i	0.478418	+	0.828645i	0.999694	−	0.0247436i	$-0.00787692\pi$
$127$	5.39150	+	9.33835i	0.478418	+	0.828645i	−0.521275	+	0.853388i	$0.674544\pi$
$128$	−7.19086	+	4.15165i	−0.635589	+	0.366957i
$129$	0.491851			0.0433051
$130$	1.56038	−	4.19041i	0.136854	−	0.367523i
$131$	12.3140			1.07588			0.537939	−	0.842984i	$-0.319203\pi$
$131$	12.3140			1.07588			0.537939	+	0.842984i	$0.319203\pi$
$132$	5.97801	−	3.45140i	0.520319	−	0.300406i
$133$		0			0
$134$	0.0533473	−	0.0924003i	0.00460851	−	0.00798217i
$135$		−	18.6310i		−	1.60350i
$136$	5.09146	+	2.93956i	0.436589	+	0.252065i
$137$	−9.84943	−	5.68657i	−0.841493	−	0.485836i	0.0162783	−	0.999867i	$-0.494818\pi$
$137$	−9.84943	−	5.68657i	−0.841493	−	0.485836i	−0.857771	+	0.514031i	$0.828152\pi$
$138$		−	0.274882i		−	0.0233995i
$139$	−6.00674	+	10.4040i	−0.509485	+	0.882454i	0.490454	+	0.871467i	$0.336831\pi$
$139$	−6.00674	+	10.4040i	−0.509485	+	0.882454i	−0.999940	+	0.0109874i	$0.996503\pi$
$140$		0			0
$141$	−16.2099	+	9.35878i	−1.36512	+	0.788152i
$142$	0.160782			0.0134925
$143$	6.27352	+	2.33606i	0.524618	+	0.195351i
$144$	2.67528			0.222940
$145$	−3.68427	+	2.12712i	−0.305962	+	0.176647i
$146$	0.697684	+	1.20842i	0.0577407	+	0.100010i
$147$		0			0
$148$		−	6.10195i		−	0.501577i
$149$	15.2776	+	8.82051i	1.25159	+	0.722605i	0.971425	−	0.237348i	$-0.0762780\pi$
$149$	15.2776	+	8.82051i	1.25159	+	0.722605i	0.280163	+	0.959952i	$0.409611\pi$
$150$	−6.51863	−	3.76354i	−0.532244	−	0.307291i
$151$			12.3904i			1.00831i	0.863612	+	0.504157i	$0.168197\pi$
$151$			12.3904i			1.00831i	−0.863612	+	0.504157i	$0.831803\pi$
$152$	−3.72955	+	6.45977i	−0.302506	+	0.523956i
$153$	−1.98249	−	3.43378i	−0.160275	−	0.277604i
$154$		0			0
$155$	−28.0628			−2.25406
$156$	8.54027	+	10.3321i	0.683769	+	0.827232i
$157$	19.8802			1.58661			0.793306	−	0.608823i	$-0.208358\pi$
$157$	19.8802			1.58661			0.793306	+	0.608823i	$0.208358\pi$
$158$	1.95870	−	1.13085i	0.155826	−	0.0899659i
$159$	−0.753817	−	1.30565i	−0.0597815	−	0.103545i
$160$	−7.03143	+	12.1788i	−0.555883	+	0.962818i
$161$		0			0
$162$	−2.67838	−	1.54636i	−0.210433	−	0.121494i
$163$	9.13359	+	5.27328i	0.715398	+	0.413035i	0.813056	−	0.582185i	$-0.197802\pi$
$163$	9.13359	+	5.27328i	0.715398	+	0.413035i	−0.0976588	+	0.995220i	$0.531135\pi$
$164$		−	0.286758i		−	0.0223921i
$165$	7.73166	−	13.3916i	0.601909	−	1.04254i
$166$	−0.921628	−	1.59631i	−0.0715322	−	0.123897i
$167$	6.44673	−	3.72202i	0.498863	−	0.288019i	−0.229381	−	0.973337i	$-0.573670\pi$
$167$	6.44673	−	3.72202i	0.498863	−	0.288019i	0.728244	+	0.685318i	$0.240337\pi$
$168$		0			0
$169$	−2.44655	+	12.7677i	−0.188196	+	0.982132i
$170$	6.44476			0.494290
$171$	4.35659	−	2.51528i	0.333157	−	0.192348i
$172$	−0.242974	−	0.420844i	−0.0185266	−	0.0320891i
$173$	8.61835	−	14.9274i	0.655241	−	1.13491i	−0.326592	−	0.945165i	$-0.605900\pi$
$173$	8.61835	−	14.9274i	0.655241	−	1.13491i	0.981833	−	0.189746i	$-0.0607663\pi$
$174$			0.555225i			0.0420915i
$175$		0			0
$176$	−5.63794	−	3.25507i	−0.424976	−	0.245360i
$177$			16.2512i			1.22151i
$178$	1.37873	−	2.38802i	0.103340	−	0.178990i
$179$	7.55237	+	13.0811i	0.564491	+	0.977727i	0.997097	+	0.0761439i	$0.0242608\pi$
$179$	7.55237	+	13.0811i	0.564491	+	0.977727i	−0.432606	+	0.901583i	$0.642406\pi$
$180$	5.43713	−	3.13913i	0.405260	−	0.233977i
$181$	−8.77797			−0.652461			−0.326231	−	0.945290i	$-0.605779\pi$
$181$	−8.77797			−0.652461			−0.326231	+	0.945290i	$0.605779\pi$
$182$		0			0
$183$	13.7532			1.01666
$184$	−0.480635	+	0.277495i	−0.0354329	+	0.0204572i
$185$	−6.83464	−	11.8379i	−0.502493	−	0.870343i
$186$	−1.83125	+	3.17183i	−0.134274	+	0.232570i
$187$			9.64855i			0.705572i
$188$	16.0154	+	9.24647i	1.16804	+	0.674368i
$189$		0			0
$190$			8.17676i			0.593204i
$191$	−4.53643	+	7.85732i	−0.328244	+	0.568536i	−0.982164	−	0.188029i	$-0.939790\pi$
$191$	−4.53643	+	7.85732i	−0.328244	+	0.568536i	0.653919	+	0.756564i	$0.273124\pi$
$192$	−5.88405	−	10.1915i	−0.424645	−	0.735507i
$193$	0.670760	−	0.387263i	0.0482823	−	0.0278758i	−0.475665	−	0.879627i	$-0.657792\pi$
$193$	0.670760	−	0.387263i	0.0482823	−	0.0278758i	0.523947	+	0.851751i	$0.324459\pi$
$194$	1.43542			0.103057
$195$	28.1411	+	10.4789i	2.01523	+	0.750407i
$196$		0			0
$197$	16.6055	−	9.58720i	1.18309	−	0.683060i	0.226366	−	0.974042i	$-0.427315\pi$
$197$	16.6055	−	9.58720i	1.18309	−	0.683060i	0.956728	+	0.290982i	$0.0939821\pi$
$198$	−0.204599	−	0.354376i	−0.0145402	−	0.0251844i
$199$	−2.75227	+	4.76708i	−0.195104	+	0.337929i	−0.946934	−	0.321427i	$-0.895838\pi$
$199$	−2.75227	+	4.76708i	−0.195104	+	0.337929i	0.751831	+	0.659356i	$0.229171\pi$
$200$			15.1972i			1.07461i
$201$	0.620523	+	0.358259i	0.0437683	+	0.0252697i
$202$	−3.96612	−	2.28984i	−0.279055	−	0.161113i
$203$		0			0
$204$	−9.66017	+	16.7319i	−0.676347	+	1.17147i
$205$	−0.321191	−	0.556319i	−0.0224329	−	0.0388550i
$206$	−2.46238	+	1.42165i	−0.171562	+	0.0990513i
$207$	0.374296			0.0260153
$208$	4.41166	−	11.8475i	0.305893	−	0.821479i
$209$	−12.2415			−0.846766
$210$		0			0
$211$	10.1935	+	17.6556i	0.701748	+	1.21546i	0.967852	+	0.251519i	$0.0809302\pi$
$211$	10.1935	+	17.6556i	0.701748	+	1.21546i	−0.266104	+	0.963944i	$0.585736\pi$
$212$	−0.744770	+	1.28998i	−0.0511510	+	0.0885962i
$213$			1.07975i			0.0739830i
$214$	1.24933	+	0.721301i	0.0854024	+	0.0493071i
$215$	−0.942754	−	0.544299i	−0.0642953	−	0.0371209i
$216$			4.90932i			0.334037i
$217$		0			0
$218$	0.468047	+	0.810682i	0.0317002	+	0.0549063i
$219$	−8.11530	+	4.68537i	−0.548381	+	0.316608i
$220$	−15.2777			−1.03003
$221$	−18.4758	+	3.11706i	−1.24282	+	0.209676i
$222$	−1.78399			−0.119734
$223$	−22.1378	+	12.7813i	−1.48246	+	0.855896i	−0.999802	−	0.0199148i	$-0.993661\pi$
$223$	−22.1378	+	12.7813i	−1.48246	+	0.855896i	−0.482654	+	0.875811i	$0.660327\pi$
$224$		0			0
$225$	5.12465	−	8.87616i	0.341644	−	0.591744i
$226$			1.40951i			0.0937594i
$227$	−9.28491	−	5.36064i	−0.616261	−	0.355798i	0.159151	−	0.987254i	$-0.449124\pi$
$227$	−9.28491	−	5.36064i	−0.616261	−	0.355798i	−0.775412	+	0.631456i	$0.782458\pi$
$228$	−21.2285	−	12.2563i	−1.40589	−	0.811693i
$229$			20.2856i			1.34051i	0.742131	+	0.670255i	$0.233815\pi$
$229$			20.2856i			1.34051i	−0.742131	+	0.670255i	$0.766185\pi$
$230$	−0.304193	+	0.526879i	−0.0200579	+	0.0347413i
$231$		0			0
$232$	0.970819	−	0.560503i	0.0637374	−	0.0367988i
$233$	7.66933			0.502434			0.251217	−	0.967931i	$-0.419169\pi$
$233$	7.66933			0.502434			0.251217	+	0.967931i	$0.419169\pi$
$234$	0.612489	−	0.506267i	0.0400396	−	0.0330957i
$235$	41.4270			2.70240
$236$	13.9050	−	8.02807i	0.905139	−	0.522583i
$237$	7.59437	+	13.1538i	0.493307	+	0.854433i
$238$		0			0
$239$			6.85013i			0.443098i	0.975149	+	0.221549i	$0.0711113\pi$
$239$			6.85013i			0.443098i	−0.975149	+	0.221549i	$0.928889\pi$
$240$	−25.2901	−	14.6012i	−1.63247	−	0.942506i
$241$	17.3539	+	10.0193i	1.11786	+	0.645398i	0.940854	−	0.338812i	$-0.110025\pi$
$241$	17.3539	+	10.0193i	1.11786	+	0.645398i	0.177007	+	0.984210i	$0.443358\pi$
$242$		−	2.18166i		−	0.140242i
$243$	3.87557	−	6.71269i	0.248618	−	0.430619i
$244$	−6.79406	−	11.7677i	−0.434945	−	0.753347i
$245$		0			0
$246$	−0.0838379			−0.00534531
$247$	−3.95476	−	23.4411i	−0.251635	−	1.49152i
$248$	7.39465			0.469561
$249$	10.7202	−	6.18929i	0.679363	−	0.392230i
$250$	5.22928	+	9.05738i	0.330729	+	0.572839i
$251$	11.3800	−	19.7107i	0.718297	−	1.24413i	−0.243377	−	0.969932i	$-0.578255\pi$
$251$	11.3800	−	19.7107i	0.718297	−	1.24413i	0.961674	−	0.274196i	$-0.0884116\pi$
$252$		0			0
$253$	−0.788798	−	0.455413i	−0.0495913	−	0.0286315i
$254$	−2.69744	−	1.55737i	−0.169252	−	0.0977179i
$255$			43.2804i			2.71033i
$256$	−4.86730	+	8.43042i	−0.304206	+	0.526901i
$257$	−11.0565	−	19.1504i	−0.689685	−	1.19457i	−0.971940	−	0.235230i	$-0.924416\pi$
$257$	−11.0565	−	19.1504i	−0.689685	−	1.19457i	0.282255	−	0.959340i	$-0.408918\pi$
$258$	−0.123040	+	0.0710371i	−0.00766013	+	0.00442258i
$259$		0			0
$260$	−4.93564	−	29.2550i	−0.306095	−	1.81432i
$261$	−0.756027			−0.0467969
$262$	−3.08042	+	1.77848i	−0.190309	+	0.109875i
$263$	−13.7007	−	23.7302i	−0.844819	−	1.46327i	−0.885778	−	0.464108i	$-0.846375\pi$
$263$	−13.7007	−	23.7302i	−0.844819	−	1.46327i	0.0409597	−	0.999161i	$-0.486958\pi$
$264$	−2.03732	+	3.52874i	−0.125388	+	0.217179i
$265$			3.33679i			0.204978i
$266$		0			0
$267$	16.0370	+	9.25897i	0.981449	+	0.566640i
$268$		−	0.707920i		−	0.0432431i
$269$	2.62595	−	4.54828i	0.160107	−	0.277313i	−0.774800	−	0.632207i	$-0.782149\pi$
$269$	2.62595	−	4.54828i	0.160107	−	0.277313i	0.934907	+	0.354893i	$0.115483\pi$
$270$	2.69083	+	4.66066i	0.163759	+	0.283638i
$271$	−5.07066	+	2.92755i	−0.308021	+	0.177836i	−0.646040	−	0.763303i	$-0.723576\pi$
$271$	−5.07066	+	2.92755i	−0.308021	+	0.177836i	0.338020	+	0.941139i	$0.390243\pi$
$272$	18.2213			1.10483
$273$		0			0
$274$	3.28520			0.198466
$275$	−21.5996	+	12.4705i	−1.30250	+	0.752001i
$276$	−0.911922	−	1.57950i	−0.0548913	−	0.0950745i
$277$	−11.5171	+	19.9482i	−0.691994	+	1.19857i	0.279189	+	0.960236i	$0.409934\pi$
$277$	−11.5171	+	19.9482i	−0.691994	+	1.19857i	−0.971183	+	0.238333i	$0.923399\pi$
$278$		−	3.47017i		−	0.208127i
$279$	−4.31895	−	2.49354i	−0.258569	−	0.149285i
$280$		0			0
$281$			8.52231i			0.508398i	0.967152	+	0.254199i	$0.0818119\pi$
$281$			8.52231i			0.508398i	−0.967152	+	0.254199i	$0.918188\pi$
$282$	2.70334	−	4.68232i	0.160982	−	0.278828i
$283$	−4.45195	−	7.71100i	−0.264641	−	0.458371i	0.702829	−	0.711359i	$-0.251920\pi$
$283$	−4.45195	−	7.71100i	−0.264641	−	0.458371i	−0.967469	+	0.252988i	$0.918587\pi$
$284$	0.923866	−	0.533394i	0.0548214	−	0.0316511i
$285$	−54.9119			−3.25270
$286$	−1.90676	+	0.321690i	−0.112749	+	0.0190219i
$287$		0			0
$288$	−2.16431	+	1.24957i	−0.127533	+	0.0736315i
$289$	−5.00271	−	8.66494i	−0.294277	−	0.509702i
$290$	0.614430	−	1.06422i	0.0360806	−	0.0624934i
$291$			9.63972i			0.565091i
$292$	8.01791	+	4.62914i	0.469213	+	0.270900i
$293$	−5.28278	−	3.05001i	−0.308623	−	0.178184i	0.337687	−	0.941258i	$-0.390355\pi$
$293$	−5.28278	−	3.05001i	−0.308623	−	0.178184i	−0.646310	+	0.763075i	$0.723689\pi$
$294$		0			0
$295$	17.9841	−	31.1493i	1.04707	−	1.81358i
$296$	1.80095	+	3.11934i	0.104678	+	0.181308i
$297$	−6.97754	+	4.02848i	−0.404878	+	0.233756i
$298$	−5.09572			−0.295187
$299$	0.617230	−	1.65758i	0.0356953	−	0.0958601i
$300$	−49.9422			−2.88341
$301$		0			0
$302$	−1.78951	−	3.09953i	−0.102975	−	0.178358i
$303$	15.3777	−	26.6349i	0.883424	−	1.53013i
$304$			23.1182i			1.32592i
$305$	−26.3613	−	15.2197i	−1.50944	−	0.871478i
$306$	0.991867	+	0.572655i	0.0567013	+	0.0327365i
$307$		−	18.5928i		−	1.06115i	−0.847639	−	0.530574i	$-0.821977\pi$
$307$		−	18.5928i		−	1.06115i	0.847639	−	0.530574i	$-0.178023\pi$
$308$		0			0
$309$	−9.54726	−	16.5363i	−0.543125	−	0.940720i
$310$	7.02010	−	4.05305i	0.398715	−	0.230198i
$311$	−16.9136			−0.959085			−0.479542	−	0.877519i	$-0.659197\pi$
$311$	−16.9136			−0.959085			−0.479542	+	0.877519i	$0.659197\pi$
$312$	−7.41528	−	2.76122i	−0.419808	−	0.156323i
$313$	17.0180			0.961913			0.480957	−	0.876744i	$-0.340289\pi$
$313$	17.0180			0.961913			0.480957	+	0.876744i	$0.340289\pi$
$314$	−4.97316	+	2.87126i	−0.280652	+	0.162034i
$315$		0			0
$316$	7.50323	−	12.9960i	0.422090	−	0.731081i
$317$			14.5924i			0.819593i	0.912177	+	0.409797i	$0.134400\pi$
$317$			14.5924i			0.819593i	−0.912177	+	0.409797i	$0.865600\pi$
$318$	0.377144	+	0.217744i	0.0211492	+	0.0122105i
$319$	1.59327	+	0.919873i	0.0892058	+	0.0515030i
$320$			26.0460i			1.45601i
$321$	−4.84397	+	8.39000i	−0.270364	+	0.468284i
$322$		0			0
$323$	29.6726	−	17.1315i	1.65103	−	0.953222i
$324$	−20.5203			−1.14001
$325$	−30.8575	−	37.3318i	−1.71167	−	2.07080i
$326$	−3.04644			−0.168726
$327$	−5.44422	+	3.14322i	−0.301066	+	0.173820i
$328$	0.0846349	+	0.146592i	0.00467318	+	0.00809418i
$329$		0			0
$330$			4.46667i			0.245882i
$331$	14.8202	+	8.55647i	0.814594	+	0.470306i	0.848549	−	0.529117i	$-0.177477\pi$
$331$	14.8202	+	8.55647i	0.814594	+	0.470306i	−0.0339549	+	0.999423i	$0.510810\pi$
$332$	−10.5915	−	6.11501i	−0.581285	−	0.335605i
$333$		−	2.42919i		−	0.133119i
$334$	−1.07513	+	1.86218i	−0.0588284	+	0.101894i
$335$	−0.792924	−	1.37338i	−0.0433220	−	0.0750360i
$336$		0			0
$337$	11.6543			0.634850			0.317425	−	0.948283i	$-0.397182\pi$
$337$	11.6543			0.634850			0.317425	+	0.948283i	$0.397182\pi$
$338$	−1.23199	−	3.54728i	−0.0670117	−	0.192946i
$339$	−9.46573			−0.514108
$340$	37.0322	−	21.3805i	2.00835	−	1.15952i
$341$	6.06789	+	10.5099i	0.328595	+	0.569142i
$342$	−0.726553	+	1.25843i	−0.0392875	+	0.0680479i
$343$		0			0
$344$	0.248419	+	0.143425i	0.0133939	+	0.00773294i
$345$	−3.53831	−	2.04284i	−0.190496	−	0.109983i
$346$			4.97892i			0.267669i
$347$	−3.04185	+	5.26863i	−0.163295	+	0.282835i	−0.936048	−	0.351871i	$-0.885546\pi$
$347$	−3.04185	+	5.26863i	−0.163295	+	0.282835i	0.772754	+	0.634706i	$0.218879\pi$
$348$	1.84196	+	3.19037i	0.0987395	+	0.171022i
$349$	2.57227	−	1.48510i	0.137691	−	0.0794958i	−0.429572	−	0.903032i	$-0.641336\pi$
$349$	2.57227	−	1.48510i	0.137691	−	0.0794958i	0.567263	+	0.823537i	$0.308002\pi$
$350$		0			0
$351$	−9.96822	−	12.0597i	−0.532064	−	0.643698i
$352$	6.08149			0.324145
$353$	−8.17045	+	4.71721i	−0.434869	+	0.251072i	−0.701419	−	0.712749i	$-0.747450\pi$
$353$	−8.17045	+	4.71721i	−0.434869	+	0.251072i	0.266549	+	0.963821i	$0.414116\pi$
$354$	−2.34712	−	4.06533i	−0.124748	−	0.216070i
$355$	1.19488	−	2.06960i	0.0634178	−	0.109843i
$356$		−	18.2957i		−	0.969671i
$357$		0			0
$358$	−3.77855	−	2.18155i	−0.199703	−	0.115298i
$359$			18.5908i			0.981184i	0.871389	+	0.490592i	$0.163219\pi$
$359$			18.5908i			0.981184i	−0.871389	+	0.490592i	$0.836781\pi$
$360$	−1.85299	+	3.20947i	−0.0976610	+	0.169154i
$361$	12.2355	+	21.1925i	0.643974	+	1.11540i
$362$	2.19587	−	1.26778i	0.115412	−	0.0666332i
$363$	14.6511			0.768985
$364$		0			0
$365$	20.7399			1.08558
$366$	−3.44045	+	1.98634i	−0.179835	+	0.103828i
$367$	11.8877	+	20.5900i	0.620531	+	1.07479i	0.989387	+	0.145305i	$0.0464164\pi$
$367$	11.8877	+	20.5900i	0.620531	+	1.07479i	−0.368856	+	0.929487i	$0.620250\pi$
$368$	−0.860047	+	1.48964i	−0.0448330	+	0.0776531i
$369$		−	0.114159i		−	0.00594286i
$370$	3.41946	+	1.97423i	0.177769	+	0.102635i
$371$		0			0
$372$			24.3008i			1.25994i
$373$	−9.62071	+	16.6636i	−0.498141	+	0.862806i	−0.999998	−	0.00214471i	$-0.999317\pi$
$373$	−9.62071	+	16.6636i	−0.498141	+	0.862806i	0.501856	+	0.864951i	$0.332651\pi$
$374$	−1.39352	−	2.41365i	−0.0720572	−	0.124807i
$375$	−60.8258	+	35.1178i	−3.14103	+	1.81347i
$376$	−10.9161			−0.562957
$377$	−1.24672	+	3.34808i	−0.0642094	+	0.172435i
$378$		0			0
$379$	−22.9392	+	13.2440i	−1.17831	+	0.680297i	−0.955623	−	0.294593i	$-0.904816\pi$
$379$	−22.9392	+	13.2440i	−1.17831	+	0.680297i	−0.222686	+	0.974890i	$0.571482\pi$
$380$	27.1264	+	46.9844i	1.39156	+	2.41025i
$381$	10.4587	−	18.1149i	0.535813	−	0.928056i
$382$		−	2.62075i		−	0.134089i
$383$	5.03457	+	2.90671i	0.257254	+	0.148526i	0.623081	−	0.782157i	$-0.285881\pi$
$383$	5.03457	+	2.90671i	0.257254	+	0.148526i	−0.365827	+	0.930683i	$0.619214\pi$
$384$	13.9491	+	8.05354i	0.711839	+	0.410980i
$385$		0			0
$386$	−0.111863	+	0.193753i	−0.00569369	+	0.00986176i
$387$	−0.0967284	−	0.167538i	−0.00491698	−	0.00851646i
$388$	8.24806	−	4.76202i	0.418732	−	0.241755i
$389$	25.6917			1.30262			0.651310	−	0.758812i	$-0.274220\pi$
$389$	25.6917			1.30262			0.651310	+	0.758812i	$0.274220\pi$
$390$	−8.55313	+	1.44300i	−0.433104	+	0.0730694i
$391$	2.54932			0.128925
$392$		0			0
$393$	−11.9436	−	20.6869i	−0.602474	−	1.04352i
$394$	−2.76932	+	4.79660i	−0.139516	+	0.241649i
$395$		−	33.6167i		−	1.69144i
$396$	−2.35129	−	1.35752i	−0.118157	−	0.0682178i
$397$	2.67963	+	1.54708i	0.134487	+	0.0776459i	0.565734	−	0.824588i	$-0.308593\pi$
$397$	2.67963	+	1.54708i	0.134487	+	0.0776459i	−0.431247	+	0.902234i	$0.641926\pi$
$398$		−	1.59002i		−	0.0797006i
$399$		0			0
$400$	23.5506	+	40.7908i	1.17753	+	2.03954i
$401$	15.0537	−	8.69128i	0.751748	−	0.434022i	−0.0745774	−	0.997215i	$-0.523761\pi$
$401$	15.0537	−	8.69128i	0.751748	−	0.434022i	0.826325	+	0.563194i	$0.190427\pi$
$402$	−0.206971			−0.0103228
$403$	−18.1648	+	15.0146i	−0.904856	+	0.747930i
$404$	−30.3862			−1.51177
$405$	−39.8099	+	22.9842i	−1.97817	+	1.14210i
$406$		0			0
$407$	−2.95565	+	5.11933i	−0.146506	+	0.253756i
$408$		−	11.4045i		−	0.564609i
$409$	−25.4166	−	14.6743i	−1.25677	−	0.725597i	−0.284325	−	0.958728i	$-0.591769\pi$
$409$	−25.4166	−	14.6743i	−1.25677	−	0.725597i	−0.972445	+	0.233131i	$0.925103\pi$
$410$	0.160696	+	0.0927778i	0.00793621	+	0.00458197i
$411$			22.0621i			1.08824i
$412$	−9.43269	+	16.3379i	−0.464715	+	0.804911i
$413$		0			0
$414$	−0.0936325	+	0.0540587i	−0.00460179	+	0.00265684i
$415$	−27.3971			−1.34487
$416$	1.96469	+	11.6453i	0.0963268	+	0.570958i
$417$	23.3043			1.14121
$418$	3.06230	−	1.76802i	0.149782	−	0.0864768i
$419$	3.82585	+	6.62657i	0.186905	+	0.323729i	0.944217	−	0.329324i	$-0.106821\pi$
$419$	3.82585	+	6.62657i	0.186905	+	0.323729i	−0.757312	+	0.653054i	$0.773488\pi$
$420$		0			0
$421$		−	26.7548i		−	1.30395i	−0.758240	−	0.651976i	$-0.773940\pi$
$421$		−	26.7548i		−	1.30395i	0.758240	−	0.651976i	$-0.226060\pi$
$422$	−5.09993	−	2.94445i	−0.248261	−	0.143333i
$423$	6.37573	+	3.68103i	0.309999	+	0.178978i
$424$		−	0.879257i		−	0.0427005i
$425$	34.9039	−	60.4553i	1.69309	−	2.93251i
$426$	−0.155946	−	0.270106i	−0.00755559	−	0.0130867i
$427$		0			0
$428$	9.57167			0.462664
$429$	−2.16034	−	12.8050i	−0.104302	−	0.618232i
$430$	0.314448			0.0151640
$431$	1.69368	−	0.977849i	0.0815819	−	0.0471013i	−0.458654	−	0.888615i	$-0.651668\pi$
$431$	1.69368	−	0.977849i	0.0815819	−	0.0471013i	0.540236	+	0.841514i	$0.318335\pi$
$432$	7.60779	+	13.1771i	0.366030	+	0.633983i
$433$	−18.3025	+	31.7009i	−0.879564	+	1.52345i	−0.0277446	+	0.999615i	$0.508833\pi$
$433$	−18.3025	+	31.7009i	−0.879564	+	1.52345i	−0.851820	+	0.523835i	$0.824501\pi$
$434$		0			0
$435$	7.14691	+	4.12627i	0.342668	+	0.197839i
$436$	5.37888	+	3.10550i	0.257602	+	0.148726i
$437$			3.23444i			0.154724i
$438$	1.35340	−	2.34415i	0.0646678	−	0.112008i
$439$	−9.46146	−	16.3877i	−0.451571	−	0.782144i	0.546913	−	0.837190i	$-0.315803\pi$
$439$	−9.46146	−	16.3877i	−0.451571	−	0.782144i	−0.998484	+	0.0550456i	$0.982470\pi$
$440$	7.81004	−	4.50913i	0.372329	−	0.214964i
$441$		0			0
$442$	4.17165	−	3.44817i	0.198425	−	0.164013i
$443$	−11.2897			−0.536388			−0.268194	−	0.963365i	$-0.586427\pi$
$443$	−11.2897			−0.536388			−0.268194	+	0.963365i	$0.586427\pi$
$444$	−10.2510	+	5.91841i	−0.486490	+	0.280875i
$445$	−20.4926	−	35.4942i	−0.971441	−	1.68259i
$446$	3.69194	−	6.39463i	0.174819	−	0.302795i
$447$		−	34.2208i		−	1.61859i
$448$		0			0
$449$	0.187397	+	0.108194i	0.00884382	+	0.00510598i	0.504415	−	0.863461i	$-0.331708\pi$
$449$	0.187397	+	0.108194i	0.00884382	+	0.00510598i	−0.495572	+	0.868567i	$0.665041\pi$
$450$			2.96057i			0.139563i
$451$	−0.138899	+	0.240580i	−0.00654050	+	0.0113285i
$452$	4.67607	+	8.09918i	0.219944	+	0.380954i
$453$	20.8152	−	12.0177i	0.977984	−	0.564639i
$454$	3.09691			0.145345
$455$		0			0
$456$	14.4695			0.677595
$457$	0.727995	−	0.420308i	0.0340542	−	0.0196612i	−0.482876	−	0.875689i	$-0.660408\pi$
$457$	0.727995	−	0.420308i	0.0340542	−	0.0196612i	0.516930	+	0.856027i	$0.327075\pi$
$458$	−2.92981	−	5.07458i	−0.136901	−	0.237119i
$459$	11.2754	−	19.5295i	0.526289	−	0.911559i
$460$			4.03665i			0.188210i
$461$	−12.9612	−	7.48313i	−0.603662	−	0.348524i	0.166819	−	0.985988i	$-0.446650\pi$
$461$	−12.9612	−	7.48313i	−0.603662	−	0.348524i	−0.770481	+	0.637463i	$0.779984\pi$
$462$		0			0
$463$			29.1641i			1.35537i	0.735353	+	0.677684i	$0.237016\pi$
$463$			29.1641i			1.35537i	−0.735353	+	0.677684i	$0.762984\pi$
$464$	1.73718	−	3.00888i	0.0806465	−	0.139684i
$465$	27.2187	+	47.1442i	1.26224	+	2.18626i
$466$	−1.91853	+	1.10767i	−0.0888743	+	0.0513116i
$467$	19.2076			0.888822			0.444411	−	0.895823i	$-0.353413\pi$
$467$	19.2076			0.888822			0.444411	+	0.895823i	$0.353413\pi$
$468$	1.83987	−	4.94099i	0.0850480	−	0.228397i
$469$		0			0
$470$	−10.3632	+	5.98321i	−0.478020	+	0.275985i
$471$	−19.2822	−	33.3978i	−0.888478	−	1.53889i
$472$	−4.73886	+	8.20795i	−0.218124	+	0.377802i
$473$			0.470765i			0.0216458i
$474$	−3.79956	−	2.19368i	−0.174520	−	0.100759i
$475$	76.7024	+	44.2842i	3.51935	+	2.03190i
$476$		0			0
$477$	−0.296494	+	0.513542i	−0.0135755	+	0.0235135i
$478$	−0.989351	−	1.71361i	−0.0452519	−	0.0783785i
$479$	−28.2358	+	16.3020i	−1.29013	+	0.744855i	−0.978677	−	0.205407i	$-0.934148\pi$
$479$	−28.2358	+	16.3020i	−1.29013	+	0.744855i	−0.311451	+	0.950262i	$0.600815\pi$
$480$	27.2797			1.24514
$481$	−10.7577	−	4.00584i	−0.490510	−	0.182651i
$482$	−5.78825			−0.263648
$483$		0			0
$484$	−7.23766	−	12.5360i	−0.328984	−	0.569818i
$485$	10.6676	−	18.4769i	0.484393	−	0.838993i
$486$			2.23897i			0.101562i
$487$	−1.62035	−	0.935507i	−0.0734249	−	0.0423919i	0.462838	−	0.886443i	$-0.346831\pi$
$487$	−1.62035	−	0.935507i	−0.0734249	−	0.0423919i	−0.536263	+	0.844051i	$0.680164\pi$
$488$	6.94630	+	4.01045i	0.314444	+	0.181544i
$489$		−	20.4586i		−	0.925172i
$490$		0			0
$491$	6.09623	+	10.5590i	0.275119	+	0.476520i	0.970165	−	0.242445i	$-0.0779494\pi$
$491$	6.09623	+	10.5590i	0.275119	+	0.476520i	−0.695046	+	0.718965i	$0.744616\pi$
$492$	−0.481740	+	0.278133i	−0.0217185	+	0.0125392i
$493$	−5.14928			−0.231912
$494$	4.37485	+	5.29276i	0.196834	+	0.238132i
$495$	−6.08209			−0.273369
$496$	19.8479	−	11.4592i	0.891198	−	0.514534i
$497$		0			0
$498$	−1.78781	+	3.09658i	−0.0801138	+	0.138761i
$499$			1.46694i			0.0656693i	0.999461	+	0.0328347i	$0.0104535\pi$
$499$			1.46694i			0.0656693i	−0.999461	+	0.0328347i	$0.989547\pi$
$500$	60.0958	+	34.6963i	2.68757	+	1.55167i
$501$	−12.5056	−	7.22013i	−0.558711	−	0.322572i
$502$			6.57434i			0.293427i
$503$	4.91578	−	8.51438i	0.219184	−	0.379637i	−0.735375	−	0.677660i	$-0.762994\pi$
$503$	4.91578	−	8.51438i	0.219184	−	0.379637i	0.954559	+	0.298023i	$0.0963273\pi$
$504$		0			0
$505$	−58.9501	+	34.0349i	−2.62325	+	1.51453i
$506$	0.263097			0.0116961
$507$	23.8221	−	8.27359i	1.05798	−	0.367443i
$508$	−20.6663			−0.916919
$509$	−8.58870	+	4.95869i	−0.380687	+	0.219790i	−0.678117	−	0.734954i	$-0.737204\pi$
$509$	−8.58870	+	4.95869i	−0.380687	+	0.219790i	0.297430	+	0.954744i	$0.403871\pi$
$510$	−6.25091	−	10.8269i	−0.276795	−	0.479423i
$511$		0			0
$512$		−	19.4185i		−	0.858184i
$513$	24.7780	+	14.3056i	1.09397	+	0.631606i
$514$	5.53171	+	3.19373i	0.243993	+	0.140870i
$515$			42.2613i			1.86225i
$516$	−0.471332	+	0.816371i	−0.0207492	+	0.0359387i
$517$	−8.95756	−	15.5149i	−0.393953	−	0.682346i
$518$		0			0
$519$	−33.4365			−1.46770
$520$	11.1575	+	13.4985i	0.489291	+	0.591950i
$521$	20.3284			0.890604			0.445302	−	0.895380i	$-0.353096\pi$
$521$	20.3284			0.890604			0.445302	+	0.895380i	$0.353096\pi$
$522$	0.189125	−	0.109191i	0.00827778	−	0.00477918i
$523$	−6.09390	−	10.5549i	−0.266467	−	0.461535i	0.701480	−	0.712690i	$-0.252523\pi$
$523$	−6.09390	−	10.5549i	−0.266467	−	0.461535i	−0.967947	+	0.251154i	$0.919190\pi$
$524$	−11.8003	+	20.4386i	−0.515497	+	0.892866i
$525$		0			0
$526$	6.85462	+	3.95752i	0.298876	+	0.172556i
$527$	−29.4162	−	16.9835i	−1.28139	−	0.739812i
$528$			12.6286i			0.549590i
$529$	11.3797	−	19.7102i	0.494768	−	0.856964i
$530$	−0.481926	−	0.834721i	−0.0209335	−	0.0362580i
$531$	5.53560	−	3.19598i	0.240225	−	0.138694i
$532$		0			0
$533$	−0.505554	−	0.188253i	−0.0218980	−	0.00815413i
$534$	−5.34902			−0.231475
$535$	18.5693	−	10.7210i	0.802821	−	0.463509i
$536$	0.208938	+	0.361891i	0.00902475	+	0.0156313i
$537$	14.6504	−	25.3753i	0.632212	−	1.09502i
$538$			1.51704i			0.0654043i
$539$		0			0
$540$	30.9235	+	17.8537i	1.33074	+	0.768301i
$541$		−	29.4232i		−	1.26500i	−0.774560	−	0.632500i	$-0.782029\pi$
$541$		−	29.4232i		−	1.26500i	0.774560	−	0.632500i	$-0.217971\pi$
$542$	0.845639	−	1.46469i	0.0363233	−	0.0629138i
$543$	8.51393	+	14.7466i	0.365368	+	0.632836i
$544$	−14.7411	+	8.51077i	−0.632019	+	0.364896i
$545$	13.9136			0.595992
$546$		0			0
$547$	−38.5683			−1.64906			−0.824530	−	0.565818i	$-0.808561\pi$
$547$	−38.5683			−1.64906			−0.824530	+	0.565818i	$0.808561\pi$
$548$	18.8770	−	10.8987i	0.806387	−	0.465568i
$549$	−2.70472	−	4.68472i	−0.115435	−	0.199939i
$550$	3.60219	−	6.23917i	0.153598	−	0.266039i
$551$		−	6.53313i		−	0.278321i
$552$	0.932356	+	0.538296i	0.0396837	+	0.0229114i
$553$		0			0
$554$		−	6.65355i		−	0.282682i
$555$	−13.2581	+	22.9637i	−0.562776	+	0.974757i
$556$	−11.5123	−	19.9399i	−0.488230	−	0.845639i
$557$	13.8297	−	7.98457i	0.585982	−	0.338317i	−0.177525	−	0.984116i	$-0.556809\pi$
$557$	13.8297	−	7.98457i	0.585982	−	0.338317i	0.763507	+	0.645799i	$0.223476\pi$
$558$	1.44055			0.0609834
$559$	−0.901457	+	0.152086i	−0.0381276	+	0.00643253i
$560$		0			0
$561$	16.2091	−	9.35833i	0.684349	−	0.395109i
$562$	−1.23086	−	2.13191i	−0.0519207	−	0.0899293i
$563$	22.9974	−	39.8327i	0.969226	−	1.67875i	0.271423	−	0.962460i	$-0.412506\pi$
$563$	22.9974	−	39.8327i	0.969226	−	1.67875i	0.697804	−	0.716289i	$-0.254161\pi$
$564$		−	35.8734i		−	1.51054i
$565$	18.1434	+	10.4751i	0.763298	+	0.440690i
$566$	2.22737	+	1.28597i	0.0936233	+	0.0540534i
$567$		0			0
$568$	−0.314856	+	0.545346i	−0.0132111	+	0.0228822i
$569$	14.3683	+	24.8867i	0.602352	+	1.04330i	0.992464	+	0.122537i	$0.0391029\pi$
$569$	14.3683	+	24.8867i	0.602352	+	1.04330i	−0.390112	+	0.920767i	$0.627564\pi$
$570$	13.7366	−	7.93081i	0.575361	−	0.332185i
$571$	−14.8407			−0.621064			−0.310532	−	0.950563i	$-0.600507\pi$
$571$	−14.8407			−0.621064			−0.310532	+	0.950563i	$0.600507\pi$
$572$	−9.88918	+	8.17413i	−0.413487	+	0.341778i
$573$	17.5999			0.735246
$574$		0			0
$575$	3.29494	+	5.70700i	0.137408	+	0.237998i
$576$	−2.31434	+	4.00855i	−0.0964307	+	0.167023i
$577$		−	10.6483i		−	0.443294i	−0.975127	−	0.221647i	$-0.928857\pi$
$577$		−	10.6483i		−	0.443294i	0.975127	−	0.221647i	$-0.0711433\pi$
$578$	2.50292	+	1.44506i	0.104108	+	0.0601066i
$579$	−1.30117	−	0.751229i	−0.0540747	−	0.0312200i
$580$		−	8.15350i		−	0.338556i
$581$		0			0
$582$	−1.39225	−	2.41144i	−0.0577104	−	0.0999574i
$583$	1.24967	−	0.721499i	0.0517562	−	0.0298814i
$584$	−5.46505			−0.226145
$585$	−1.96488	−	11.6464i	−0.0812378	−	0.481521i
$586$	1.76203			0.0727888
$587$	−25.4320	+	14.6832i	−1.04969	+	0.606040i	−0.922563	−	0.385846i	$-0.873909\pi$
$587$	−25.4320	+	14.6832i	−1.04969	+	0.606040i	−0.127129	+	0.991886i	$0.540576\pi$
$588$		0			0
$589$	21.5477	−	37.3217i	0.887858	−	1.53781i
$590$			10.3896i			0.427733i
$591$	−32.2121	−	18.5977i	−1.32503	−	0.765005i
$592$	9.66785	+	5.58174i	0.397346	+	0.229408i
$593$			20.9569i			0.860596i	0.902687	+	0.430298i	$0.141592\pi$
$593$			20.9569i			0.860596i	−0.902687	+	0.430298i	$0.858408\pi$
$594$	1.16365	−	2.01550i	0.0477452	−	0.0826971i
$595$		0			0
$596$	−29.2804	+	16.9051i	−1.19937	+	0.692458i
$597$	10.6779			0.437019
$598$	0.0849963	+	0.503799i	0.00347576	+	0.0206019i
$599$	14.7342			0.602025			0.301012	−	0.953620i	$-0.402675\pi$
$599$	14.7342			0.602025			0.301012	+	0.953620i	$0.402675\pi$
$600$	25.5306	−	14.7401i	1.04228	−	0.601763i
$601$	−15.5499	−	26.9331i	−0.634292	−	1.09863i	−0.986665	−	0.162766i	$-0.947958\pi$
$601$	−15.5499	−	26.9331i	−0.634292	−	1.09863i	0.352373	−	0.935860i	$-0.385375\pi$
$602$		0			0
$603$		−	0.281824i		−	0.0114767i
$604$	−20.5654	−	11.8734i	−0.836795	−	0.483124i
$605$	−28.0825	−	16.2134i	−1.14172	−	0.659170i
$606$			8.88386i			0.360882i
$607$	−5.25353	+	9.09937i	−0.213234	+	0.369332i	−0.952725	−	0.303834i	$-0.901733\pi$
$607$	−5.25353	+	9.09937i	−0.213234	+	0.369332i	0.739491	+	0.673167i	$0.235066\pi$
$608$	−10.7980	−	18.7027i	−0.437917	−	0.758494i
$609$		0			0
$610$	8.79261			0.356002
$611$	26.8154	−	22.1649i	1.08483	−	0.896695i
$612$	7.59914			0.307177
$613$	−30.6744	+	17.7099i	−1.23893	+	0.715296i	−0.968875	−	0.247550i	$-0.920375\pi$
$613$	−30.6744	+	17.7099i	−1.23893	+	0.715296i	−0.270053	+	0.962845i	$0.587041\pi$
$614$	2.68532	+	4.65111i	0.108371	+	0.187704i
$615$	−0.623059	+	1.07917i	−0.0251242	+	0.0435163i
$616$		0			0
$617$	−34.8047	−	20.0945i	−1.40118	−	0.808974i	−0.406670	−	0.913575i	$-0.633310\pi$
$617$	−34.8047	−	20.0945i	−1.40118	−	0.808974i	−0.994514	+	0.104601i	$0.966643\pi$
$618$	4.77662	+	2.75778i	0.192144	+	0.110934i
$619$			0.763184i			0.0306750i	0.999882	+	0.0153375i	$0.00488226\pi$
$619$			0.763184i			0.0306750i	−0.999882	+	0.0153375i	$0.995118\pi$
$620$	26.8921	−	46.5784i	1.08001	−	1.87063i
$621$	1.06440	+	1.84359i	0.0427128	+	0.0739807i
$622$	4.23106	−	2.44280i	0.169650	−	0.0979475i
$623$		0			0
$624$	−24.1823	+	4.07981i	−0.968065	+	0.163323i
$625$	88.2842			3.53137
$626$	−4.25716	+	2.45787i	−0.170150	+	0.0982363i
$627$	11.8733	+	20.5652i	0.474175	+	0.821296i
$628$	−19.0508	+	32.9970i	−0.760210	+	1.31672i
$629$		−	16.5452i		−	0.659699i
$630$		0			0
$631$	−10.4840	−	6.05291i	−0.417360	−	0.240963i	0.276587	−	0.960989i	$-0.410796\pi$
$631$	−10.4840	−	6.05291i	−0.417360	−	0.240963i	−0.693947	+	0.720026i	$0.744130\pi$
$632$			8.85812i			0.352357i
$633$	19.7737	−	34.2491i	0.785936	−	1.36128i
$634$	−2.10756	−	3.65040i	−0.0837018	−	0.144976i
$635$	−40.0932	+	23.1478i	−1.59105	+	0.918592i
$636$	2.88947			0.114575
$637$		0			0
$638$	−0.531421			−0.0210392
$639$	0.367792	−	0.212345i	0.0145496	−	0.00840023i
$640$	−17.8246	−	30.8732i	−0.704580	−	1.22037i
$641$	10.3081	−	17.8541i	0.407145	−	0.705196i	−0.587424	−	0.809280i	$-0.699858\pi$
$641$	10.3081	−	17.8541i	0.407145	−	0.705196i	0.994569	+	0.104084i	$0.0331910\pi$
$642$		−	2.79842i		−	0.110445i
$643$	17.1248	+	9.88699i	0.675335	+	0.389905i	0.798095	−	0.602531i	$-0.205841\pi$
$643$	17.1248	+	9.88699i	0.675335	+	0.389905i	−0.122760	+	0.992436i	$0.539175\pi$
$644$		0			0
$645$			2.11171i			0.0831484i
$646$	−4.94853	+	8.57111i	−0.194697	+	0.337226i
$647$	2.80226	+	4.85365i	0.110168	+	0.190817i	0.915838	−	0.401548i	$-0.131528\pi$
$647$	2.80226	+	4.85365i	0.110168	+	0.190817i	−0.805670	+	0.592365i	$0.798194\pi$
$648$	10.4900	−	6.05643i	0.412088	−	0.237919i
$649$	−15.5544			−0.610565
$650$	13.1110	+	4.88211i	0.514254	+	0.191492i
$651$		0			0
$652$	−17.5051	+	10.1066i	−0.685552	+	0.395804i
$653$	5.88259	+	10.1889i	0.230204	+	0.398724i	0.957868	−	0.287209i	$-0.0927275\pi$
$653$	5.88259	+	10.1889i	0.230204	+	0.398724i	−0.727664	+	0.685933i	$0.759394\pi$
$654$	0.907938	−	1.57259i	0.0355032	−	0.0614933i
$655$			52.8687i			2.06575i
$656$	0.454336	+	0.262311i	0.0177388	+	0.0102415i
$657$	3.19194	+	1.84287i	0.124529	+	0.0718970i
$658$		0			0
$659$	−6.26141	+	10.8451i	−0.243910	+	0.422464i	−0.961825	−	0.273667i	$-0.911763\pi$
$659$	−6.26141	+	10.8451i	−0.243910	+	0.422464i	0.717915	+	0.696131i	$0.245097\pi$
$660$	14.8182	+	25.6659i	0.576798	+	0.999043i
$661$	2.60972	−	1.50672i	0.101506	−	0.0586048i	−0.448387	−	0.893839i	$-0.648001\pi$
$661$	2.60972	−	1.50672i	0.101506	−	0.0586048i	0.549894	+	0.835235i	$0.314668\pi$
$662$	−4.94317			−0.192122
$663$	23.1566	+	28.0151i	0.899326	+	1.08802i
$664$	7.21923			0.280160
$665$		0			0
$666$	0.350843	+	0.607678i	0.0135949	+	0.0235471i
$667$	0.243047	−	0.420969i	0.00941081	−	0.0163000i
$668$			14.2670i			0.552006i
$669$	42.9438	+	24.7936i	1.66030	+	0.958576i
$670$	0.396710	+	0.229041i	0.0153262	+	0.00884861i
$671$			13.1635i			0.508173i
$672$		0			0
$673$	−13.5747	−	23.5120i	−0.523266	−	0.906323i	−0.999633	−	0.0270765i	$-0.991380\pi$
$673$	−13.5747	−	23.5120i	−0.523266	−	0.906323i	0.476368	−	0.879246i	$-0.341953\pi$
$674$	−2.91540	+	1.68321i	−0.112297	+	0.0648347i
$675$	58.2926			2.24368
$676$	−18.8473	−	16.2958i	−0.724895	−	0.626762i
$677$	23.2783			0.894658			0.447329	−	0.894369i	$-0.352375\pi$
$677$	23.2783			0.894658			0.447329	+	0.894369i	$0.352375\pi$
$678$	2.36791	−	1.36712i	0.0909392	−	0.0525038i
$679$		0			0
$680$	−12.6207	+	21.8596i	−0.483980	+	0.838278i
$681$			20.7976i			0.796966i
$682$	−3.03584	−	1.75275i	−0.116248	−	0.0671161i
$683$	8.87363	+	5.12319i	0.339540	+	0.196033i	0.660069	−	0.751205i	$-0.270527\pi$
$683$	8.87363	+	5.12319i	0.339540	+	0.196033i	−0.320529	+	0.947239i	$0.603861\pi$
$684$			9.64137i			0.368647i
$685$	24.4146	−	42.2874i	0.932835	−	1.61572i
$686$		0			0
$687$	34.0789	−	19.6754i	1.30019	−	0.750665i
$688$	0.889040			0.0338943
$689$	1.78530	+	2.15988i	0.0680146	+	0.0822850i
$690$	1.18017			0.0449285
$691$	38.5203	−	22.2397i	1.46538	−	0.846038i	0.466129	−	0.884717i	$-0.345648\pi$
$691$	38.5203	−	22.2397i	1.46538	−	0.846038i	0.999252	+	0.0386792i	$0.0123151\pi$
$692$	16.5176	+	28.6093i	0.627905	+	1.08756i
$693$		0			0
$694$		−	1.75731i		−	0.0667066i
$695$	−44.6683	−	25.7893i	−1.69437	−	0.978243i
$696$	−1.88323	−	1.08729i	−0.0713838	−	0.0412135i
$697$		−	0.777532i		−	0.0294511i
$698$	−0.428981	+	0.743017i	−0.0162372	+	0.0281236i
$699$	−7.43864	−	12.8841i	−0.281355	−	0.487322i
$700$		0			0
$701$	27.1138			1.02407			0.512037	−	0.858963i	$-0.328891\pi$
$701$	27.1138			1.02407			0.512037	+	0.858963i	$0.328891\pi$
$702$	4.23537	+	1.57712i	0.159854	+	0.0595245i
$703$	20.9916			0.791714
$704$	9.75456	−	5.63180i	0.367639	−	0.212256i
$705$	−40.1809	−	69.5953i	−1.51330	−	2.62111i
$706$	1.36260	−	2.36008i	0.0512820	−	0.0888229i
$707$		0			0
$708$	−26.9735	−	15.5732i	−1.01373	−	0.585276i
$709$	−9.67182	−	5.58403i	−0.363233	−	0.209713i	0.307265	−	0.951624i	$-0.400586\pi$
$709$	−9.67182	−	5.58403i	−0.363233	−	0.209713i	−0.670498	+	0.741911i	$0.733920\pi$
$710$			0.690298i			0.0259064i
$711$	2.98704	−	5.17371i	0.112023	−	0.194029i
$712$	5.39986	+	9.35284i	0.202368	+	0.350512i
$713$	2.77690	−	1.60324i	0.103996	−	0.0600420i
$714$		0			0
$715$	−10.0296	+	26.9347i	−0.375087	+	1.00730i
$716$	−28.9492			−1.08188
$717$	11.5079	−	6.64409i	0.429770	−	0.248128i
$718$	−2.68503	−	4.65061i	−0.100204	−	0.173559i
$719$	−25.0303	+	43.3537i	−0.933472	+	1.61682i	−0.156134	+	0.987736i	$0.549903\pi$
$719$	−25.0303	+	43.3537i	−0.933472	+	1.61682i	−0.777337	+	0.629084i	$0.783430\pi$
$720$			11.4860i			0.428059i
$721$		0			0
$722$	−6.12159	−	3.53430i	−0.227822	−	0.131533i
$723$		−	38.8716i		−	1.44565i
$724$	8.41176	−	14.5696i	0.312621	−	0.541475i
$725$	−6.65533	−	11.5274i	−0.247173	−	0.428116i
$726$	−3.66508	+	2.11603i	−0.136024	+	0.0785334i
$727$	26.0097			0.964646			0.482323	−	0.875994i	$-0.339793\pi$
$727$	26.0097			0.964646			0.482323	+	0.875994i	$0.339793\pi$
$728$		0			0
$729$	17.0844			0.632756
$730$	−5.18823	+	2.99543i	−0.192025	+	0.110866i
$731$	−0.658814	−	1.14110i	−0.0243671	−	0.0422051i
$732$	−13.1794	+	22.8274i	−0.487125	+	0.843725i
$733$		−	9.51378i		−	0.351399i	−0.984444	−	0.175700i	$-0.943781\pi$
$733$		−	9.51378i		−	0.351399i	0.984444	−	0.175700i	$-0.0562188\pi$
$734$	−5.94756	−	3.43382i	−0.219528	−	0.126745i
$735$		0			0
$736$		−	1.60684i		−	0.0592289i
$737$	−0.342900	+	0.593921i	−0.0126309	+	0.0218773i
$738$	0.0164877	+	0.0285576i	0.000606921	+	0.00105122i
$739$	28.7471	−	16.5971i	1.05748	−	0.610536i	0.132745	−	0.991150i	$-0.457621\pi$
$739$	28.7471	−	16.5971i	1.05748	−	0.610536i	0.924734	+	0.380615i	$0.124288\pi$
$740$	26.1980			0.963059
$741$	−35.5440	+	29.3798i	−1.30574	+	1.07929i
$742$		0			0
$743$	32.7404	−	18.9027i	1.20113	−	0.693473i	0.240323	−	0.970693i	$-0.422747\pi$
$743$	32.7404	−	18.9027i	1.20113	−	0.693473i	0.960806	+	0.277220i	$0.0894132\pi$
$744$	−7.17222	−	12.4227i	−0.262946	−	0.455437i
$745$	−37.8699	+	65.5926i	−1.38745	+	2.40313i
$746$		−	5.55800i		−	0.203493i
$747$	−4.21649	−	2.43439i	−0.154273	−	0.0890697i
$748$	−16.0146	−	9.24602i	−0.585551	−	0.338068i
$749$		0			0
$750$	10.1440	−	17.5699i	0.370406	−	0.641562i
$751$	−11.9681	−	20.7294i	−0.436723	−	0.756426i	0.560712	−	0.828011i	$-0.310528\pi$
$751$	−11.9681	−	20.7294i	−0.436723	−	0.756426i	−0.997434	+	0.0715853i	$0.977194\pi$
$752$	−29.3000	+	16.9163i	−1.06846	+	0.616876i
$753$	−44.1507			−1.60894
$754$	−0.171681	−	1.01761i	−0.00625226	−	0.0370590i
$755$	−53.1966			−1.93602
$756$		0			0
$757$	−3.90984	−	6.77205i	−0.142106	−	0.246134i	0.786184	−	0.617993i	$-0.212054\pi$
$757$	−3.90984	−	6.77205i	−0.142106	−	0.246134i	−0.928289	+	0.371859i	$0.878721\pi$
$758$	3.82560	−	6.62613i	0.138952	−	0.240672i
$759$			1.76686i			0.0641328i
$760$	−27.7343	−	16.0124i	−1.00603	−	0.580831i
$761$	−2.24476	−	1.29601i	−0.0813726	−	0.0469805i	0.458762	−	0.888559i	$-0.348293\pi$
$761$	−2.24476	−	1.29601i	−0.0813726	−	0.0469805i	−0.540134	+	0.841579i	$0.681627\pi$
$762$			6.04209i			0.218882i
$763$		0			0
$764$	−8.69434	−	15.0590i	−0.314550	−	0.544817i
$765$	14.7425	−	8.51161i	0.533017	−	0.307738i
$766$	−1.67924			−0.0606734
$767$	−5.02502	−	29.7848i	−0.181443	−	1.07547i
$768$	18.8836			0.681403
$769$	7.78758	−	4.49616i	0.280827	−	0.162136i	−0.352971	−	0.935634i	$-0.614828\pi$
$769$	7.78758	−	4.49616i	0.280827	−	0.162136i	0.633798	+	0.773499i	$0.281495\pi$
$770$		0			0
$771$	−21.4478	+	37.1488i	−0.772425	+	1.33788i
$772$			1.48443i			0.0534258i
$773$	10.9194	+	6.30431i	0.392743	+	0.226750i	0.683348	−	0.730093i	$-0.260523\pi$
$773$	10.9194	+	6.30431i	0.392743	+	0.226750i	−0.290605	+	0.956843i	$0.593857\pi$
$774$	0.0483945	+	0.0279406i	0.00173950	+	0.00100430i
$775$		−	87.8030i		−	3.15398i
$776$	−2.81096	+	4.86873i	−0.100908	+	0.174777i
$777$		0			0
$778$	−6.42694	+	3.71060i	−0.230417	+	0.133031i
$779$	0.986490			0.0353447
$780$	−44.3598	+	36.6667i	−1.58834	+	1.31288i
$781$	−1.03346			−0.0369800
$782$	−0.637729	+	0.368193i	−0.0228051	+	0.0131665i
$783$	−2.14994	−	3.72381i	−0.0768326	−	0.133078i
$784$		0			0
$785$			85.3534i			3.04639i
$786$	5.97553	+	3.44998i	0.213140	+	0.123057i
$787$	34.9448	+	20.1754i	1.24565	+	0.719175i	0.970238	−	0.242152i	$-0.0778532\pi$
$787$	34.9448	+	20.1754i	1.24565	+	0.719175i	0.275410	+	0.961327i	$0.411187\pi$
$788$			36.7489i			1.30913i
$789$	−26.5771	+	46.0329i	−0.946170	+	1.63881i
$790$	4.85519	+	8.40944i	0.172740	+	0.299195i
$791$		0			0
$792$	1.60265			0.0569477
$793$	−25.2066	+	4.25262i	−0.895112	+	0.151015i
$794$	−0.893769			−0.0317187
$795$	5.60565	−	3.23643i	0.198812	−	0.114784i
$796$	−5.27490	−	9.13640i	−0.186964	−	0.323831i
$797$	10.3087	−	17.8552i	0.365153	−	0.632464i	−0.623647	−	0.781706i	$-0.714350\pi$
$797$	10.3087	−	17.8552i	0.365153	−	0.632464i	0.988801	+	0.149242i	$0.0476832\pi$
$798$		0			0
$799$	43.4249	+	25.0714i	1.53626	+	0.886962i
$800$	−38.1051	−	22.0000i	−1.34722	−	0.777816i
$801$		−	7.28354i		−	0.257351i
$802$	−2.51053	+	4.34836i	−0.0886498	+	0.153546i
$803$	−4.48450	−	7.76738i	−0.158255	−	0.274105i
$804$	−1.18927	+	0.686626i	−0.0419424	+	0.0242154i
$805$		0			0
$806$	2.37553	−	6.37951i	0.0836745	−	0.224709i
$807$	−10.1878			−0.358629
$808$	15.5336	−	8.96831i	0.546469	−	0.315504i
$809$	22.2177	+	38.4822i	0.781133	+	1.35296i	0.931282	+	0.364298i	$0.118691\pi$
$809$	22.2177	+	38.4822i	0.781133	+	1.35296i	−0.150150	+	0.988663i	$0.547976\pi$
$810$	6.63913	−	11.4993i	0.233275	−	0.404045i
$811$			21.1557i			0.742878i	0.928457	+	0.371439i	$0.121135\pi$
$811$			21.1557i			0.742878i	−0.928457	+	0.371439i	$0.878865\pi$
$812$		0			0
$813$	9.83627	+	5.67898i	0.344973	+	0.199170i
$814$		−	1.70751i		−	0.0598482i
$815$	−22.6402	+	39.2140i	−0.793052	+	1.37361i
$816$	−17.6732	−	30.6109i	−0.618686	−	1.07159i
$817$	1.44777	−	0.835868i	0.0506509	−	0.0292433i
$818$	8.47751			0.296409
$819$		0			0
$820$	1.23116			0.0429941
$821$	−7.58383	+	4.37852i	−0.264677	+	0.152812i	−0.626466	−	0.779448i	$-0.715499\pi$
$821$	−7.58383	+	4.37852i	−0.264677	+	0.152812i	0.361789	+	0.932260i	$0.382166\pi$
$822$	−3.18638	−	5.51898i	−0.111138	−	0.192496i
$823$	1.82005	−	3.15243i	0.0634431	−	0.109887i	−0.832559	−	0.553936i	$-0.813125\pi$
$823$	1.82005	−	3.15243i	0.0634431	−	0.109887i	0.896002	+	0.444049i	$0.146459\pi$
$824$		−	11.1360i		−	0.387941i
$825$	41.8998	+	24.1909i	1.45876	+	0.842217i
$826$		0			0
$827$		−	33.9069i		−	1.17906i	−0.807747	−	0.589529i	$-0.799313\pi$
$827$		−	33.9069i		−	1.17906i	0.807747	−	0.589529i	$-0.200687\pi$
$828$	−0.358680	+	0.621253i	−0.0124650	+	0.0215900i
$829$	11.4687	+	19.8643i	0.398323	+	0.689916i	0.993519	−	0.113665i	$-0.0362590\pi$
$829$	11.4687	+	19.8643i	0.398323	+	0.689916i	−0.595196	+	0.803580i	$0.702926\pi$
$830$	6.85356	−	3.95691i	0.237891	−	0.137346i
$831$	44.6826			1.55002
$832$	13.9355	+	16.8594i	0.483127	+	0.584493i
$833$		0			0
$834$	−5.82971	+	3.36579i	−0.201866	+	0.116548i
$835$	15.9801	+	27.6783i	0.553013	+	0.957847i
$836$	11.7308	−	20.3184i	0.405720	−	0.702727i
$837$		−	28.3639i		−	0.980400i
$838$	−1.91412	−	1.10512i	−0.0661223	−	0.0381757i
$839$	−20.0581	−	11.5806i	−0.692483	−	0.399805i	0.112059	−	0.993702i	$-0.464256\pi$
$839$	−20.0581	−	11.5806i	−0.692483	−	0.399805i	−0.804542	+	0.593896i	$0.797589\pi$
$840$		0			0
$841$	14.0091	−	24.2644i	0.483072	−	0.836705i
$842$	3.86415	+	6.69290i	0.133167	+	0.230653i
$843$	14.3171	−	8.26596i	0.493106	−	0.284695i
$844$	−39.0729			−1.34494
$845$	−54.8167	−	10.5040i	−1.88575	−	0.361348i
$846$	−2.12657			−0.0731131
$847$		0			0
$848$	−1.36255	−	2.36001i	−0.0467902	−	0.0810430i
$849$	−8.63608	+	14.9581i	−0.296389	+	0.513361i
$850$			20.1644i			0.691633i
$851$	1.35262	+	0.780934i	0.0463671	+	0.0267701i
$852$	−1.79215	−	1.03470i	−0.0613982	−	0.0354483i
$853$		−	39.2271i		−	1.34311i	−0.740955	−	0.671555i	$-0.765627\pi$
$853$		−	39.2271i		−	1.34311i	0.740955	−	0.671555i	$-0.234373\pi$
$854$		0			0
$855$	10.7991	+	18.7045i	0.369320	+	0.639681i
$856$	−4.89308	+	2.82502i	−0.167242	+	0.0965571i
$857$	−15.9401			−0.544503			−0.272252	−	0.962226i	$-0.587768\pi$
$857$	−15.9401			−0.544503			−0.272252	+	0.962226i	$0.587768\pi$
$858$	2.38983	+	2.89124i	0.0815873	+	0.0987054i
$859$	10.3774			0.354071			0.177036	−	0.984204i	$-0.443349\pi$
$859$	10.3774			0.354071			0.177036	+	0.984204i	$0.443349\pi$
$860$	1.80685	−	1.04318i	0.0616130	−	0.0355723i
$861$		0			0
$862$	−0.282457	+	0.489231i	−0.00962054	+	0.0166633i
$863$			38.3357i			1.30496i	0.757805	+	0.652481i	$0.226272\pi$
$863$			38.3357i			1.30496i	−0.757805	+	0.652481i	$0.773728\pi$
$864$	−12.3095	−	7.10688i	−0.418777	−	0.241781i
$865$	64.0892	+	37.0019i	2.17910	+	1.25810i
$866$		−	10.5736i		−	0.359306i
$867$	−9.70446	+	16.8086i	−0.329581	+	0.570850i
$868$		0			0
$869$	−12.5899	+	7.26878i	−0.427083	+	0.246577i
$870$	−2.38379			−0.0808182
$871$	−1.24806	−	0.464739i	−0.0422890	−	0.0157471i
$872$	−3.66627			−0.124156
$873$	3.28356	−	1.89576i	0.111132	−	0.0641619i
$874$	−0.467143	−	0.809115i	−0.0158013	−	0.0273687i
$875$		0			0
$876$		−	17.9596i		−	0.606799i
$877$	3.89050	+	2.24618i	0.131373	+	0.0758482i	0.564246	−	0.825607i	$-0.309167\pi$
$877$	3.89050	+	2.24618i	0.131373	+	0.0758482i	−0.432873	+	0.901455i	$0.642500\pi$
$878$	4.73369	+	2.73300i	0.159754	+	0.0922343i
$879$			11.8331i			0.399120i
$880$	13.9753	−	24.2059i	0.471106	−	0.815979i
$881$	17.9256	+	31.0480i	0.603928	+	1.04603i	0.992220	+	0.124498i	$0.0397319\pi$
$881$	17.9256	+	31.0480i	0.603928	+	1.04603i	−0.388292	+	0.921536i	$0.626935\pi$
$882$		0			0
$883$	13.3947			0.450769			0.225384	−	0.974270i	$-0.427636\pi$
$883$	13.3947			0.450769			0.225384	+	0.974270i	$0.427636\pi$
$884$	12.5313	−	33.6530i	0.421474	−	1.13187i
$885$	−69.7725			−2.34538
$886$	2.82418	−	1.63054i	0.0948803	−	0.0547792i
$887$	13.4105	+	23.2277i	0.450280	+	0.779908i	0.998403	−	0.0564894i	$-0.0179907\pi$
$887$	13.4105	+	23.2277i	0.450280	+	0.779908i	−0.548123	+	0.836398i	$0.684657\pi$
$888$	3.49356	−	6.05103i	0.117236	−	0.203059i
$889$		0			0
$890$	10.2527	+	5.91940i	0.343671	+	0.198419i
$891$	17.2158	+	9.93955i	0.576751	+	0.332987i
$892$		−	48.9921i		−	1.64038i
$893$	−31.8092	+	55.0952i	−1.06445	+	1.84369i
$894$	4.94244	+	8.56056i	0.165300	+	0.286308i
$895$	−56.1622	+	32.4253i	−1.87730	+	1.08386i
$896$		0			0
$897$	−3.38331	+	0.570801i	−0.112966	+	0.0190585i
$898$	−0.0625048			−0.00208581
$899$	−5.60897	+	3.23834i	−0.187070	+	0.108005i
$900$	9.82172	+	17.0117i	0.327391	+	0.567057i
$901$	−2.01941	+	3.49772i	−0.0672764	+	0.116526i
$902$		−	0.0802437i		−	0.00267182i
$903$		0			0
$904$	−4.78084	−	2.76022i	−0.159009	−	0.0918036i
$905$		−	37.6872i		−	1.25276i
$906$	−3.47137	+	6.01260i	−0.115329	+	0.199755i
$907$	−28.6907	−	49.6937i	−0.952658	−	1.65005i	−0.739639	−	0.673003i	$-0.765004\pi$
$907$	−28.6907	−	49.6937i	−0.952658	−	1.65005i	−0.213018	−	0.977048i	$-0.568329\pi$
$908$	17.7951	−	10.2740i	0.590551	−	0.340955i
$909$	−12.0968			−0.401225
$910$		0			0
$911$	47.2148			1.56430			0.782148	−	0.623093i	$-0.214124\pi$
$911$	47.2148			1.56430			0.782148	+	0.623093i	$0.214124\pi$
$912$	38.8374	−	22.4228i	1.28604	−	0.742493i
$913$	5.92394	+	10.2606i	0.196054	+	0.339575i
$914$	−0.121409	+	0.210286i	−0.00401584	+	0.00695563i
$915$			59.0477i			1.95206i
$916$	−33.6699	−	19.4393i	−1.11248	−	0.642293i
$917$		0			0
$918$			6.51391i			0.214991i
$919$	−14.6416	+	25.3600i	−0.482981	+	0.836548i	−0.999809	−	0.0195416i	$-0.993779\pi$
$919$	−14.6416	+	25.3600i	−0.482981	+	0.836548i	0.516828	+	0.856089i	$0.327113\pi$
$920$	−1.19139	−	2.06355i	−0.0392791	−	0.0680333i
$921$	−31.2350	+	18.0335i	−1.02923	+	0.594225i
$922$	4.32310			0.142374
$923$	−0.333869	−	1.97894i	−0.0109894	−	0.0651376i
$924$		0			0
$925$	37.0386	−	21.3843i	1.21782	−	0.703110i
$926$	−4.21211	−	7.29558i	−0.138418	−	0.239748i
$927$	−3.75516	+	6.50413i	−0.123336	+	0.213624i
$928$			3.24560i			0.106542i
$929$	−21.5938	−	12.4672i	−0.708470	−	0.409036i	0.102024	−	0.994782i	$-0.467468\pi$
$929$	−21.5938	−	12.4672i	−0.708470	−	0.409036i	−0.810494	+	0.585746i	$0.800801\pi$
$930$	−13.6179	−	7.86228i	−0.446548	−	0.257814i
$931$		0			0
$932$	−7.34937	+	12.7295i	−0.240737	+	0.416968i
$933$	16.4049	+	28.4141i	0.537072	+	0.930236i
$934$	−4.80491	+	2.77412i	−0.157221	+	0.0907718i
$935$	−41.4249			−1.35474
$936$	0.517753	+	3.06888i	0.0169233	+	0.100309i
$937$	−26.4803			−0.865074			−0.432537	−	0.901616i	$-0.642382\pi$
$937$	−26.4803			−0.865074			−0.432537	+	0.901616i	$0.642382\pi$
$938$		0			0
$939$	−16.5061	−	28.5894i	−0.538656	−	0.932979i
$940$	−39.6987	+	68.7601i	−1.29483	+	2.24271i
$941$		−	25.6786i		−	0.837098i	−0.908194	−	0.418549i	$-0.862539\pi$
$941$		−	25.6786i		−	0.837098i	0.908194	−	0.418549i	$-0.137461\pi$
$942$	9.64715	+	5.56978i	0.314321	+	0.181473i
$943$	0.0635656	+	0.0366996i	0.00206998	+	0.00119510i
$944$			29.3746i			0.956061i
$945$		0			0
$946$	−0.0679916	−	0.117765i	−0.00221060	−	0.00382887i
$947$	−6.29251	+	3.63299i	−0.204479	+	0.118056i	−0.598743	−	0.800941i	$-0.704333\pi$
$947$	−6.29251	+	3.63299i	−0.204479	+	0.118056i	0.394264	+	0.918997i	$0.371000\pi$
$948$	−29.1102			−0.945454
$949$	13.4248	−	11.0966i	0.435788	−	0.360211i
$950$	−25.5835			−0.830038
$951$	24.5146	−	14.1535i	0.794940	−	0.458959i
$952$		0			0
$953$	−9.21278	+	15.9570i	−0.298431	+	0.516898i	−0.975777	−	0.218767i	$-0.929797\pi$
$953$	−9.21278	+	15.9570i	−0.298431	+	0.516898i	0.677346	+	0.735665i	$0.263130\pi$
$954$		−	0.171288i		−	0.00554565i
$955$	−33.7345	−	19.4766i	−1.09162	−	0.630249i
$956$	−11.3698	−	6.56435i	−0.367725	−	0.212306i
$957$		−	3.56881i		−	0.115363i
$958$	4.70892	−	8.15608i	0.152138	−	0.263511i
$959$		0			0
$960$	43.7560	−	25.2625i	1.41222	−	0.815344i
$961$	−11.7230			−0.378163
$962$	3.26967	−	0.551629i	0.105419	−	0.0177852i
$963$	3.81049			0.122791
$964$	−33.2598	+	19.2025i	−1.07123	+	0.618472i
$965$	1.66267	+	2.87983i	0.0535233	+	0.0927050i
$966$		0			0
$967$		−	44.2717i		−	1.42368i	−0.702341	−	0.711840i	$-0.747862\pi$
$967$		−	44.2717i		−	1.42368i	0.702341	−	0.711840i	$-0.252138\pi$
$968$	7.39983	+	4.27230i	0.237840	+	0.137317i
$969$	−57.5602	−	33.2324i	−1.84910	−	1.06758i
$970$			6.16282i			0.197876i
$971$	2.83417	−	4.90893i	0.0909529	−	0.157535i	−0.816959	−	0.576695i	$-0.804342\pi$
$971$	2.83417	−	4.90893i	0.0909529	−	0.157535i	0.907912	+	0.419160i	$0.137675\pi$
$972$	7.42778	+	12.8653i	0.238246	+	0.412654i
$973$		0			0
$974$	0.540454			0.0173172
$975$	−32.7863	+	88.0480i	−1.05000	+	2.81979i
$976$	24.8594			0.795729
$977$	−34.4288	+	19.8775i	−1.10148	+	0.635937i	−0.936608	−	0.350379i	$-0.886053\pi$
$977$	−34.4288	+	19.8775i	−1.10148	+	0.635937i	−0.164867	+	0.986316i	$0.552720\pi$
$978$	2.95480	+	5.11787i	0.0944841	+	0.163651i
$979$	−8.86202	+	15.3495i	−0.283232	+	0.490571i
$980$		0			0
$981$	2.14134	+	1.23630i	0.0683677	+	0.0394721i
$982$	−3.05003	−	1.76093i	−0.0973302	−	0.0561936i
$983$		−	4.39959i		−	0.140325i	−0.997536	−	0.0701626i	$-0.977648\pi$
$983$		−	4.39959i		−	0.140325i	0.997536	−	0.0701626i	$-0.0223518\pi$
$984$	0.164178	−	0.284365i	0.00523381	−	0.00906523i
$985$	41.1616	+	71.2939i	1.31152	+	2.27161i
$986$	1.28813	−	0.743700i	0.0410223	−	0.0236842i
$987$		0			0
$988$	42.6970	+	15.8990i	1.35837	+	0.505816i
$989$	0.124385			0.00395520
$990$	1.52147	−	0.878423i	0.0483556	−	0.0279181i
$991$	−11.4362	−	19.8081i	−0.363283	−	0.629224i	0.625216	−	0.780452i	$-0.285011\pi$
$991$	−11.4362	−	19.8081i	−0.363283	−	0.629224i	−0.988499	+	0.151227i	$0.951677\pi$
$992$	−10.7047	+	18.5411i	−0.339875	+	0.588680i
$993$		−	33.1964i		−	1.05346i
$994$		0			0
$995$	−20.4669	−	11.8166i	−0.648845	−	0.374611i
$996$			23.7243i			0.751734i
$997$	7.15884	−	12.3995i	0.226723	−	0.392695i	−0.730112	−	0.683327i	$-0.760532\pi$
$997$	7.15884	−	12.3995i	0.226723	−	0.392695i	0.956835	+	0.290632i	$0.0938655\pi$
$998$	−0.211867	−	0.366965i	−0.00670655	−	0.0116161i
$999$	11.9650	−	6.90798i	0.378555	−	0.218559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.j.491.7	✓	32
7.2	even	3		637.2.u.j.361.10		32
7.3	odd	6		637.2.k.j.569.8		32
7.4	even	3		637.2.k.j.569.7		32
7.5	odd	6		637.2.u.j.361.9		32
7.6	odd	2	inner	637.2.q.j.491.8	yes	32
13.2	odd	12		8281.2.a.cx.1.16		32
13.4	even	6	inner	637.2.q.j.589.7	yes	32
13.11	odd	12		8281.2.a.cx.1.18		32
91.4	even	6		637.2.u.j.30.10		32
91.17	odd	6		637.2.u.j.30.9		32
91.30	even	6		637.2.k.j.459.9		32
91.41	even	12		8281.2.a.cx.1.15		32
91.69	odd	6	inner	637.2.q.j.589.8	yes	32
91.76	even	12		8281.2.a.cx.1.17		32
91.82	odd	6		637.2.k.j.459.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.9		32	91.30	even	6
637.2.k.j.459.10		32	91.82	odd	6
637.2.k.j.569.7		32	7.4	even	3
637.2.k.j.569.8		32	7.3	odd	6
637.2.q.j.491.7	✓	32	1.1	even	1	trivial
637.2.q.j.491.8	yes	32	7.6	odd	2	inner
637.2.q.j.589.7	yes	32	13.4	even	6	inner
637.2.q.j.589.8	yes	32	91.69	odd	6	inner
637.2.u.j.30.9		32	91.17	odd	6
637.2.u.j.30.10		32	91.4	even	6
637.2.u.j.361.9		32	7.5	odd	6
637.2.u.j.361.10		32	7.2	even	3
8281.2.a.cx.1.15		32	91.41	even	12
8281.2.a.cx.1.16		32	13.2	odd	12
8281.2.a.cx.1.17		32	91.76	even	12
8281.2.a.cx.1.18		32	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.250157 + 0.144428i) q^{2} +(-0.969921 - 1.67995i) q^{3} +(-0.958281 + 1.65979i) q^{4} +4.29339i q^{5} +(0.485264 + 0.280167i) q^{6} -1.13132i q^{8} +(-0.381493 + 0.660765i) q^{9} +O(q^{10})\)	\(q+(-0.250157 + 0.144428i) q^{2} +(-0.969921 - 1.67995i) q^{3} +(-0.958281 + 1.65979i) q^{4} +4.29339i q^{5} +(0.485264 + 0.280167i) q^{6} -1.13132i q^{8} +(-0.381493 + 0.660765i) q^{9} +(-0.620085 - 1.07402i) q^{10} +(1.60793 - 0.928339i) q^{11} +3.71783 q^{12} +(2.29711 + 2.77908i) q^{13} +(7.21268 - 4.16424i) q^{15} +(-1.75317 - 3.03658i) q^{16} +(-2.59834 + 4.50045i) q^{17} -0.220393i q^{18} +(-5.70993 - 3.29663i) q^{19} +(-7.12613 - 4.11427i) q^{20} +(-0.268156 + 0.464460i) q^{22} +(-0.245284 - 0.424844i) q^{23} +(-1.90057 + 1.09729i) q^{24} -13.4332 q^{25} +(-0.976014 - 0.363437i) q^{26} -4.33945 q^{27} +(0.495440 + 0.858128i) q^{29} +(-1.20287 + 2.08343i) q^{30} +6.53629i q^{31} +(2.83664 + 1.63774i) q^{32} +(-3.11913 - 1.80083i) q^{33} -1.50109i q^{34} +(-0.731154 - 1.26640i) q^{36} +(-2.75725 + 1.59190i) q^{37} +1.90450 q^{38} +(2.44070 - 6.55452i) q^{39} +4.85720 q^{40} +(-0.129576 + 0.0748106i) q^{41} +(-0.126776 + 0.219583i) q^{43} +3.55844i q^{44} +(-2.83692 - 1.63790i) q^{45} +(0.122719 + 0.0708516i) q^{46} -9.64902i q^{47} +(-3.40087 + 5.89048i) q^{48} +(3.36040 - 1.94013i) q^{50} +10.0807 q^{51} +(-6.81397 + 1.14959i) q^{52} +0.777194 q^{53} +(1.08554 - 0.626739i) q^{54} +(3.98572 + 6.90346i) q^{55} +12.7899i q^{57} +(-0.247875 - 0.143111i) q^{58} +(-7.25519 - 4.18878i) q^{59} +15.9621i q^{60} +(-3.54492 + 6.13998i) q^{61} +(-0.944023 - 1.63510i) q^{62} +6.06653 q^{64} +(-11.9317 + 9.86239i) q^{65} +1.04036 q^{66} +(-0.319884 + 0.184685i) q^{67} +(-4.97987 - 8.62539i) q^{68} +(-0.475811 + 0.824129i) q^{69} +(-0.482043 - 0.278308i) q^{71} +(0.747538 + 0.431591i) q^{72} -4.83067i q^{73} +(0.459830 - 0.796449i) q^{74} +(13.0291 + 22.5671i) q^{75} +(10.9434 - 6.31819i) q^{76} +(0.336099 + 1.99216i) q^{78} -7.82988 q^{79} +(13.0372 - 7.52703i) q^{80} +(5.35340 + 9.27237i) q^{81} +(0.0216095 - 0.0374287i) q^{82} +6.38123i q^{83} +(-19.3222 - 11.1557i) q^{85} -0.0732401i q^{86} +(0.961075 - 1.66463i) q^{87} +(-1.05025 - 1.81909i) q^{88} +(-8.26717 + 4.77306i) q^{89} +0.946231 q^{90} +0.940203 q^{92} +(10.9806 - 6.33968i) q^{93} +(1.39359 + 2.41377i) q^{94} +(14.1537 - 24.5149i) q^{95} -6.35389i q^{96} +(-4.30357 - 2.48467i) q^{97} +1.41662i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 28 * q^9	\( 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more