LMFDB - Embedded newform 637.2.h.c.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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([4, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.c.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421 q^{2} +(-0.707107 - 1.22474i) q^{3} +3.82843 q^{4} +(1.91421 + 3.31552i) q^{5} +(1.70711 + 2.95680i) q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-2.41421 q^{2} +(-0.707107 - 1.22474i) q^{3} +3.82843 q^{4} +(1.91421 + 3.31552i) q^{5} +(1.70711 + 2.95680i) q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.62132 - 8.00436i) q^{10} +(-1.70711 - 2.95680i) q^{11} +(-2.70711 - 4.68885i) q^{12} +(3.50000 + 0.866025i) q^{13} +(2.70711 - 4.68885i) q^{15} +3.00000 q^{16} +0.171573 q^{17} +(-1.20711 + 2.09077i) q^{18} +(3.00000 - 5.19615i) q^{19} +(7.32843 + 12.6932i) q^{20} +(4.12132 + 7.13834i) q^{22} +1.41421 q^{23} +(3.12132 + 5.40629i) q^{24} +(-4.82843 + 8.36308i) q^{25} +(-8.44975 - 2.09077i) q^{26} -5.65685 q^{27} +(-4.91421 + 8.51167i) q^{29} +(-6.53553 + 11.3199i) q^{30} +(2.70711 - 4.68885i) q^{31} +1.58579 q^{32} +(-2.41421 + 4.18154i) q^{33} -0.414214 q^{34} +(1.91421 - 3.31552i) q^{36} +7.48528 q^{37} +(-7.24264 + 12.5446i) q^{38} +(-1.41421 - 4.89898i) q^{39} +(-8.44975 - 14.6354i) q^{40} +(2.91421 - 5.04757i) q^{41} +(-0.292893 - 0.507306i) q^{43} +(-6.53553 - 11.3199i) q^{44} +3.82843 q^{45} -3.41421 q^{46} +(3.82843 + 6.63103i) q^{47} +(-2.12132 - 3.67423i) q^{48} +(11.6569 - 20.1903i) q^{50} +(-0.121320 - 0.210133i) q^{51} +(13.3995 + 3.31552i) q^{52} +(1.50000 - 2.59808i) q^{53} +13.6569 q^{54} +(6.53553 - 11.3199i) q^{55} -8.48528 q^{57} +(11.8640 - 20.5490i) q^{58} +1.75736 q^{59} +(10.3640 - 17.9509i) q^{60} +(4.91421 - 8.51167i) q^{61} +(-6.53553 + 11.3199i) q^{62} -9.82843 q^{64} +(3.82843 + 13.2621i) q^{65} +(5.82843 - 10.0951i) q^{66} +(2.12132 + 3.67423i) q^{67} +0.656854 q^{68} +(-1.00000 - 1.73205i) q^{69} +(0.171573 + 0.297173i) q^{71} +(-2.20711 + 3.82282i) q^{72} +(0.328427 - 0.568852i) q^{73} -18.0711 q^{74} +13.6569 q^{75} +(11.4853 - 19.8931i) q^{76} +(3.41421 + 11.8272i) q^{78} +(-5.12132 - 8.87039i) q^{79} +(5.74264 + 9.94655i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-7.03553 + 12.1859i) q^{82} +13.0711 q^{83} +(0.328427 + 0.568852i) q^{85} +(0.707107 + 1.22474i) q^{86} +13.8995 q^{87} +(7.53553 + 13.0519i) q^{88} +7.31371 q^{89} -9.24264 q^{90} +5.41421 q^{92} -7.65685 q^{93} +(-9.24264 - 16.0087i) q^{94} +22.9706 q^{95} +(-1.12132 - 1.94218i) q^{96} +(-2.58579 - 4.47871i) q^{97} -3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9	$ 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9} - 10 q^{10} - 4 q^{11} - 8 q^{12} + 14 q^{13} + 8 q^{15} + 12 q^{16} + 12 q^{17} - 2 q^{18} + 12 q^{19} + 18 q^{20} + 8 q^{22} + 4 q^{24} - 8 q^{25} - 14 q^{26} - 14 q^{29} - 12 q^{30} + 8 q^{31} + 12 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 12 q^{38} - 14 q^{40} + 6 q^{41} - 4 q^{43} - 12 q^{44} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 24 q^{50} + 8 q^{51} + 14 q^{52} + 6 q^{53} + 32 q^{54} + 12 q^{55} + 22 q^{58} + 24 q^{59} + 16 q^{60} + 14 q^{61} - 12 q^{62} - 28 q^{64} + 4 q^{65} + 12 q^{66} - 20 q^{68} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 10 q^{73} - 44 q^{74} + 32 q^{75} + 12 q^{76} + 8 q^{78} - 12 q^{79} + 6 q^{80} + 10 q^{81} - 14 q^{82} + 24 q^{83} - 10 q^{85} + 16 q^{87} + 16 q^{88} - 16 q^{89} - 20 q^{90} + 16 q^{92} - 8 q^{93} - 20 q^{94} + 24 q^{95} + 4 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9 - 10 * q^10 - 4 * q^11 - 8 * q^12 + 14 * q^13 + 8 * q^15 + 12 * q^16 + 12 * q^17 - 2 * q^18 + 12 * q^19 + 18 * q^20 + 8 * q^22 + 4 * q^24 - 8 * q^25 - 14 * q^26 - 14 * q^29 - 12 * q^30 + 8 * q^31 + 12 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 12 * q^38 - 14 * q^40 + 6 * q^41 - 4 * q^43 - 12 * q^44 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 24 * q^50 + 8 * q^51 + 14 * q^52 + 6 * q^53 + 32 * q^54 + 12 * q^55 + 22 * q^58 + 24 * q^59 + 16 * q^60 + 14 * q^61 - 12 * q^62 - 28 * q^64 + 4 * q^65 + 12 * q^66 - 20 * q^68 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 10 * q^73 - 44 * q^74 + 32 * q^75 + 12 * q^76 + 8 * q^78 - 12 * q^79 + 6 * q^80 + 10 * q^81 - 14 * q^82 + 24 * q^83 - 10 * q^85 + 16 * q^87 + 16 * q^88 - 16 * q^89 - 20 * q^90 + 16 * q^92 - 8 * q^93 - 20 * q^94 + 24 * q^95 + 4 * q^96 - 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.41421			−1.70711			−0.853553	−	0.521005i	$-0.825557\pi$
$2$	−2.41421			−1.70711			−0.853553	+	0.521005i	$0.825557\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	0.586445	−	0.809989i	$-0.300527\pi$
$3$	−0.707107	−	1.22474i	−0.408248	−	0.707107i	−0.994694	+	0.102882i	$0.967194\pi$
$4$	3.82843			1.91421
$5$	1.91421	+	3.31552i	0.856062	+	1.48274i	0.875656	+	0.482935i	$0.160429\pi$
$5$	1.91421	+	3.31552i	0.856062	+	1.48274i	−0.0195936	+	0.999808i	$0.506237\pi$
$6$	1.70711	+	2.95680i	0.696923	+	1.20711i
$7$		0			0
$7$		0			0
$8$	−4.41421			−1.56066
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−4.62132	−	8.00436i	−1.46139	−	2.53120i
$11$	−1.70711	−	2.95680i	−0.514712	−	0.891507i	−0.999854	−	0.0170722i	$-0.994565\pi$
$11$	−1.70711	−	2.95680i	−0.514712	−	0.891507i	0.485142	−	0.874435i	$-0.338768\pi$
$12$	−2.70711	−	4.68885i	−0.781474	−	1.35355i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$		0			0
$15$	2.70711	−	4.68885i	0.698972	−	1.21065i
$16$	3.00000			0.750000
$17$	0.171573			0.0416125			0.0208063	−	0.999784i	$-0.493377\pi$
$17$	0.171573			0.0416125			0.0208063	+	0.999784i	$0.493377\pi$
$18$	−1.20711	+	2.09077i	−0.284518	+	0.492799i
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	7.32843	+	12.6932i	1.63869	+	2.83829i
$21$		0			0
$22$	4.12132	+	7.13834i	0.878668	+	1.52190i
$23$	1.41421			0.294884			0.147442	−	0.989071i	$-0.452896\pi$
$23$	1.41421			0.294884			0.147442	+	0.989071i	$0.452896\pi$
$24$	3.12132	+	5.40629i	0.637137	+	1.10355i
$25$	−4.82843	+	8.36308i	−0.965685	+	1.67262i
$26$	−8.44975	−	2.09077i	−1.65713	−	0.410034i
$27$	−5.65685			−1.08866
$28$		0			0
$29$	−4.91421	+	8.51167i	−0.912547	+	1.58058i	−0.102092	+	0.994775i	$0.532554\pi$
$29$	−4.91421	+	8.51167i	−0.912547	+	1.58058i	−0.810454	+	0.585802i	$0.800780\pi$
$30$	−6.53553	+	11.3199i	−1.19322	+	2.06672i
$31$	2.70711	−	4.68885i	0.486211	−	0.842142i	−0.513664	−	0.857992i	$-0.671712\pi$
$31$	2.70711	−	4.68885i	0.486211	−	0.842142i	0.999874	+	0.0158500i	$0.00504541\pi$
$32$	1.58579			0.280330
$33$	−2.41421	+	4.18154i	−0.420261	+	0.727913i
$34$	−0.414214			−0.0710370
$35$		0			0
$36$	1.91421	−	3.31552i	0.319036	−	0.552586i
$37$	7.48528			1.23057			0.615286	−	0.788304i	$-0.289040\pi$
$37$	7.48528			1.23057			0.615286	+	0.788304i	$0.289040\pi$
$38$	−7.24264	+	12.5446i	−1.17491	+	2.03501i
$39$	−1.41421	−	4.89898i	−0.226455	−	0.784465i
$40$	−8.44975	−	14.6354i	−1.33602	−	2.31406i
$41$	2.91421	−	5.04757i	0.455124	−	0.788297i	−0.543572	−	0.839363i	$-0.682928\pi$
$41$	2.91421	−	5.04757i	0.455124	−	0.788297i	0.998695	+	0.0510654i	$0.0162617\pi$
$42$		0			0
$43$	−0.292893	−	0.507306i	−0.0446658	−	0.0773634i	0.842828	−	0.538183i	$-0.180889\pi$
$43$	−0.292893	−	0.507306i	−0.0446658	−	0.0773634i	−0.887494	+	0.460819i	$0.847556\pi$
$44$	−6.53553	−	11.3199i	−0.985269	−	1.70654i
$45$	3.82843			0.570708
$46$	−3.41421			−0.503398
$47$	3.82843	+	6.63103i	0.558433	+	0.967235i	0.997628	+	0.0688429i	$0.0219307\pi$
$47$	3.82843	+	6.63103i	0.558433	+	0.967235i	−0.439194	+	0.898392i	$0.644736\pi$
$48$	−2.12132	−	3.67423i	−0.306186	−	0.530330i
$49$		0			0
$50$	11.6569	−	20.1903i	1.64853	−	2.85533i
$51$	−0.121320	−	0.210133i	−0.0169882	−	0.0294245i
$52$	13.3995	+	3.31552i	1.85818	+	0.459779i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	13.6569			1.85846
$55$	6.53553	−	11.3199i	0.881251	−	1.52637i
$56$		0			0
$57$	−8.48528			−1.12390
$58$	11.8640	−	20.5490i	1.55781	−	2.69821i
$59$	1.75736			0.228789			0.114394	−	0.993435i	$-0.463507\pi$
$59$	1.75736			0.228789			0.114394	+	0.993435i	$0.463507\pi$
$60$	10.3640	−	17.9509i	1.33798	−	2.31745i
$61$	4.91421	−	8.51167i	0.629201	−	1.08981i	−0.358512	−	0.933525i	$-0.616716\pi$
$61$	4.91421	−	8.51167i	0.629201	−	1.08981i	0.987712	−	0.156282i	$-0.0499509\pi$
$62$	−6.53553	+	11.3199i	−0.830014	+	1.43763i
$63$		0			0
$64$	−9.82843			−1.22855
$65$	3.82843	+	13.2621i	0.474858	+	1.64496i
$66$	5.82843	−	10.0951i	0.717430	−	1.24262i
$67$	2.12132	+	3.67423i	0.259161	+	0.448879i	0.966017	−	0.258478i	$-0.0832208\pi$
$67$	2.12132	+	3.67423i	0.259161	+	0.448879i	−0.706857	+	0.707357i	$0.749887\pi$
$68$	0.656854			0.0796553
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$		0			0
$71$	0.171573	+	0.297173i	0.0203620	+	0.0352679i	0.876027	−	0.482262i	$-0.160185\pi$
$71$	0.171573	+	0.297173i	0.0203620	+	0.0352679i	−0.855665	+	0.517530i	$0.826851\pi$
$72$	−2.20711	+	3.82282i	−0.260110	+	0.450524i
$73$	0.328427	−	0.568852i	0.0384395	−	0.0665791i	−0.846166	−	0.532920i	$-0.821095\pi$
$73$	0.328427	−	0.568852i	0.0384395	−	0.0665791i	0.884605	+	0.466341i	$0.154428\pi$
$74$	−18.0711			−2.10072
$75$	13.6569			1.57696
$76$	11.4853	−	19.8931i	1.31745	−	2.28189i
$77$		0			0
$78$	3.41421	+	11.8272i	0.386584	+	1.33916i
$79$	−5.12132	−	8.87039i	−0.576194	−	0.997997i	−0.995911	−	0.0903416i	$-0.971204\pi$
$79$	−5.12132	−	8.87039i	−0.576194	−	0.997997i	0.419717	−	0.907655i	$-0.362129\pi$
$80$	5.74264	+	9.94655i	0.642047	+	1.11206i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	−7.03553	+	12.1859i	−0.776945	+	1.34571i
$83$	13.0711			1.43474			0.717368	−	0.696694i	$-0.245347\pi$
$83$	13.0711			1.43474			0.717368	+	0.696694i	$0.245347\pi$
$84$		0			0
$85$	0.328427	+	0.568852i	0.0356229	+	0.0617007i
$86$	0.707107	+	1.22474i	0.0762493	+	0.132068i
$87$	13.8995			1.49018
$88$	7.53553	+	13.0519i	0.803291	+	1.39134i
$89$	7.31371			0.775252			0.387626	−	0.921817i	$-0.373295\pi$
$89$	7.31371			0.775252			0.387626	+	0.921817i	$0.373295\pi$
$90$	−9.24264			−0.974260
$91$		0			0
$92$	5.41421			0.564471
$93$	−7.65685			−0.793979
$94$	−9.24264	−	16.0087i	−0.953306	−	1.65117i
$95$	22.9706			2.35673
$96$	−1.12132	−	1.94218i	−0.114444	−	0.198223i
$97$	−2.58579	−	4.47871i	−0.262547	−	0.454744i	0.704371	−	0.709832i	$-0.251229\pi$
$97$	−2.58579	−	4.47871i	−0.262547	−	0.454744i	−0.966918	+	0.255087i	$0.917896\pi$
$98$		0			0
$99$	−3.41421			−0.343141
$100$	−18.4853	+	32.0174i	−1.84853	+	3.20174i
$101$	1.67157	+	2.89525i	0.166328	+	0.288088i	0.937126	−	0.348991i	$-0.113476\pi$
$101$	1.67157	+	2.89525i	0.166328	+	0.288088i	−0.770798	+	0.637079i	$0.780142\pi$
$102$	0.292893	+	0.507306i	0.0290008	+	0.0502308i
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$	−15.4497	−	3.82282i	−1.51497	−	0.374858i
$105$		0			0
$106$	−3.62132	+	6.27231i	−0.351734	+	0.609221i
$107$	−5.31371			−0.513696			−0.256848	−	0.966452i	$-0.582684\pi$
$107$	−5.31371			−0.513696			−0.256848	+	0.966452i	$0.582684\pi$
$108$	−21.6569			−2.08393
$109$	1.17157	−	2.02922i	0.112216	−	0.194364i	−0.804447	−	0.594024i	$-0.797538\pi$
$109$	1.17157	−	2.02922i	0.112216	−	0.194364i	0.916664	+	0.399660i	$0.130872\pi$
$110$	−15.7782	+	27.3286i	−1.50439	+	2.60568i
$111$	−5.29289	−	9.16756i	−0.502379	−	0.870146i
$112$		0			0
$113$	1.15685	+	2.00373i	0.108828	+	0.188495i	0.915296	−	0.402783i	$-0.131957\pi$
$113$	1.15685	+	2.00373i	0.108828	+	0.188495i	−0.806468	+	0.591278i	$0.798624\pi$
$114$	20.4853			1.91862
$115$	2.70711	+	4.68885i	0.252439	+	0.437237i
$116$	−18.8137	+	32.5863i	−1.74681	+	3.02556i
$117$	2.50000	−	2.59808i	0.231125	−	0.240192i
$118$	−4.24264			−0.390567
$119$		0			0
$120$	−11.9497	+	20.6976i	−1.09086	+	1.88942i
$121$	−0.328427	+	0.568852i	−0.0298570	+	0.0517139i
$122$	−11.8640	+	20.5490i	−1.07411	+	1.86042i
$123$	−8.24264			−0.743214
$124$	10.3640	−	17.9509i	0.930711	−	1.61204i
$125$	−17.8284			−1.59462
$126$		0			0
$127$	4.65685	−	8.06591i	0.413229	−	0.715734i	−0.582012	−	0.813180i	$-0.697734\pi$
$127$	4.65685	−	8.06591i	0.413229	−	0.715734i	0.995241	+	0.0974468i	$0.0310676\pi$
$128$	20.5563			1.81694
$129$	−0.414214	+	0.717439i	−0.0364695	+	0.0631670i
$130$	−9.24264	−	32.0174i	−0.810633	−	2.80812i
$131$	−0.656854	−	1.13770i	−0.0573896	−	0.0994017i	0.835903	−	0.548877i	$-0.184944\pi$
$131$	−0.656854	−	1.13770i	−0.0573896	−	0.0994017i	−0.893293	+	0.449475i	$0.851611\pi$
$132$	−9.24264	+	16.0087i	−0.804469	+	1.39338i
$133$		0			0
$134$	−5.12132	−	8.87039i	−0.442415	−	0.766285i
$135$	−10.8284	−	18.7554i	−0.931963	−	1.61421i
$136$	−0.757359			−0.0649430
$137$	−5.82843			−0.497956			−0.248978	−	0.968509i	$-0.580095\pi$
$137$	−5.82843			−0.497956			−0.248978	+	0.968509i	$0.580095\pi$
$138$	2.41421	+	4.18154i	0.205512	+	0.355956i
$139$	3.94975	+	6.84116i	0.335013	+	0.580260i	0.983487	−	0.180977i	$-0.0579259\pi$
$139$	3.94975	+	6.84116i	0.335013	+	0.580260i	−0.648474	+	0.761237i	$0.724593\pi$
$140$		0			0
$141$	5.41421	−	9.37769i	0.455959	−	0.789744i
$142$	−0.414214	−	0.717439i	−0.0347600	−	0.0602061i
$143$	−3.41421	−	11.8272i	−0.285511	−	0.989039i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−37.6274			−3.12479
$146$	−0.792893	+	1.37333i	−0.0656203	+	0.113658i
$147$		0			0
$148$	28.6569			2.35558
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$	−32.9706			−2.69204
$151$	9.48528	−	16.4290i	0.771901	−	1.33697i	−0.164618	−	0.986357i	$-0.552639\pi$
$151$	9.48528	−	16.4290i	0.771901	−	1.33697i	0.936520	−	0.350615i	$-0.114027\pi$
$152$	−13.2426	+	22.9369i	−1.07412	+	1.86043i
$153$	0.0857864	−	0.148586i	0.00693542	−	0.0120125i
$154$		0			0
$155$	20.7279			1.66491
$156$	−5.41421	−	18.7554i	−0.433484	−	1.50163i
$157$	−5.74264	+	9.94655i	−0.458313	+	0.793821i	−0.998872	−	0.0474852i	$-0.984879\pi$
$157$	−5.74264	+	9.94655i	−0.458313	+	0.793821i	0.540559	+	0.841306i	$0.318213\pi$
$158$	12.3640	+	21.4150i	0.983624	+	1.70369i
$159$	−4.24264			−0.336463
$160$	3.03553	+	5.25770i	0.239980	+	0.415658i
$161$		0			0
$162$	−6.03553	−	10.4539i	−0.474196	−	0.821332i
$163$	−7.70711	+	13.3491i	−0.603667	+	1.04558i	0.388593	+	0.921409i	$0.372961\pi$
$163$	−7.70711	+	13.3491i	−0.603667	+	1.04558i	−0.992261	+	0.124173i	$0.960372\pi$
$164$	11.1569	−	19.3242i	0.871204	−	1.50897i
$165$	−18.4853			−1.43908
$166$	−31.5563			−2.44925
$167$	−9.36396	+	16.2189i	−0.724605	+	1.25505i	0.234531	+	0.972109i	$0.424644\pi$
$167$	−9.36396	+	16.2189i	−0.724605	+	1.25505i	−0.959136	+	0.282944i	$0.908689\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	−0.792893	−	1.37333i	−0.0608121	−	0.105330i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−1.12132	−	1.94218i	−0.0854999	−	0.148090i
$173$	9.07107	−	15.7116i	0.689661	−	1.19453i	−0.282287	−	0.959330i	$-0.591093\pi$
$173$	9.07107	−	15.7116i	0.689661	−	1.19453i	0.971948	−	0.235197i	$-0.0755736\pi$
$174$	−33.5563			−2.54390
$175$		0			0
$176$	−5.12132	−	8.87039i	−0.386034	−	0.668631i
$177$	−1.24264	−	2.15232i	−0.0934026	−	0.161778i
$178$	−17.6569			−1.32344
$179$	−2.82843	−	4.89898i	−0.211407	−	0.366167i	0.740748	−	0.671783i	$-0.234471\pi$
$179$	−2.82843	−	4.89898i	−0.211407	−	0.366167i	−0.952155	+	0.305616i	$0.901138\pi$
$180$	14.6569			1.09246
$181$	19.1421			1.42282			0.711412	−	0.702775i	$-0.248056\pi$
$181$	19.1421			1.42282			0.711412	+	0.702775i	$0.248056\pi$
$182$		0			0
$183$	−13.8995			−1.02748
$184$	−6.24264			−0.460214
$185$	14.3284	+	24.8176i	1.05345	+	1.82462i
$186$	18.4853			1.35541
$187$	−0.292893	−	0.507306i	−0.0214185	−	0.0370979i
$188$	14.6569	+	25.3864i	1.06896	+	1.85149i
$189$		0			0
$190$	−55.4558			−4.02319
$191$	−3.87868	+	6.71807i	−0.280651	+	0.486103i	−0.971545	−	0.236854i	$-0.923884\pi$
$191$	−3.87868	+	6.71807i	−0.280651	+	0.486103i	0.690894	+	0.722956i	$0.257217\pi$
$192$	6.94975	+	12.0373i	0.501555	+	0.868718i
$193$	10.5711	+	18.3096i	0.760922	+	1.31796i	0.942376	+	0.334556i	$0.108586\pi$
$193$	10.5711	+	18.3096i	0.760922	+	1.31796i	−0.181454	+	0.983399i	$0.558080\pi$
$194$	6.24264	+	10.8126i	0.448195	+	0.776297i
$195$	13.5355	−	14.0665i	0.969300	−	1.00733i
$196$		0			0
$197$	−4.58579	+	7.94282i	−0.326724	+	0.565902i	−0.981860	−	0.189609i	$-0.939278\pi$
$197$	−4.58579	+	7.94282i	−0.326724	+	0.565902i	0.655136	+	0.755511i	$0.272611\pi$
$198$	8.24264			0.585779
$199$	−18.9706			−1.34479			−0.672394	−	0.740194i	$-0.734734\pi$
$199$	−18.9706			−1.34479			−0.672394	+	0.740194i	$0.734734\pi$
$200$	21.3137	−	36.9164i	1.50711	−	2.61039i
$201$	3.00000	−	5.19615i	0.211604	−	0.366508i
$202$	−4.03553	−	6.98975i	−0.283939	−	0.491797i
$203$		0			0
$204$	−0.464466	−	0.804479i	−0.0325191	−	0.0563248i
$205$	22.3137			1.55846
$206$	−16.8995	−	29.2708i	−1.17744	−	2.03939i
$207$	0.707107	−	1.22474i	0.0491473	−	0.0851257i
$208$	10.5000	+	2.59808i	0.728044	+	0.180144i
$209$	−20.4853			−1.41700
$210$		0			0
$211$	0.363961	−	0.630399i	0.0250561	−	0.0433985i	−0.853225	−	0.521542i	$-0.825357\pi$
$211$	0.363961	−	0.630399i	0.0250561	−	0.0433985i	0.878282	+	0.478144i	$0.158690\pi$
$212$	5.74264	−	9.94655i	0.394406	−	0.683132i
$213$	0.242641	−	0.420266i	0.0166255	−	0.0287962i
$214$	12.8284			0.876933
$215$	1.12132	−	1.94218i	0.0764734	−	0.132456i
$216$	24.9706			1.69903
$217$		0			0
$218$	−2.82843	+	4.89898i	−0.191565	+	0.331801i
$219$	−0.928932			−0.0627714
$220$	25.0208	−	43.3373i	1.68690	−	2.92180i
$221$	0.600505	+	0.148586i	0.0403943	+	0.00999501i
$222$	12.7782	+	22.1324i	0.857615	+	1.48543i
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	−0.830599	−	0.556871i	$-0.812002\pi$
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	0.897564	+	0.440884i	$0.145335\pi$
$224$		0			0
$225$	4.82843	+	8.36308i	0.321895	+	0.557539i
$226$	−2.79289	−	4.83743i	−0.185780	−	0.321781i
$227$	13.8995			0.922542			0.461271	−	0.887259i	$-0.347394\pi$
$227$	13.8995			0.922542			0.461271	+	0.887259i	$0.347394\pi$
$228$	−32.4853			−2.15139
$229$	2.24264	+	3.88437i	0.148198	+	0.256686i	0.930561	−	0.366136i	$-0.119319\pi$
$229$	2.24264	+	3.88437i	0.148198	+	0.256686i	−0.782364	+	0.622822i	$0.785986\pi$
$230$	−6.53553	−	11.3199i	−0.430940	−	0.746411i
$231$		0			0
$232$	21.6924	−	37.5723i	1.42418	−	2.46674i
$233$	1.41421	+	2.44949i	0.0926482	+	0.160471i	0.908625	−	0.417614i	$-0.137133\pi$
$233$	1.41421	+	2.44949i	0.0926482	+	0.160471i	−0.815976	+	0.578085i	$0.803800\pi$
$234$	−6.03553	+	6.27231i	−0.394555	+	0.410034i
$235$	−14.6569	+	25.3864i	−0.956108	+	1.65603i
$236$	6.72792			0.437950
$237$	−7.24264	+	12.5446i	−0.470460	+	0.814861i
$238$		0			0
$239$	−12.3848			−0.801105			−0.400552	−	0.916274i	$-0.631182\pi$
$239$	−12.3848			−0.801105			−0.400552	+	0.916274i	$0.631182\pi$
$240$	8.12132	−	14.0665i	0.524229	−	0.907991i
$241$	1.48528			0.0956754			0.0478377	−	0.998855i	$-0.484767\pi$
$241$	1.48528			0.0956754			0.0478377	+	0.998855i	$0.484767\pi$
$242$	0.792893	−	1.37333i	0.0509691	−	0.0882811i
$243$	−4.94975	+	8.57321i	−0.317526	+	0.549972i
$244$	18.8137	−	32.5863i	1.20442	−	2.08612i
$245$		0			0
$246$	19.8995			1.26875
$247$	15.0000	−	15.5885i	0.954427	−	0.991870i
$248$	−11.9497	+	20.6976i	−0.758810	+	1.31430i
$249$	−9.24264	−	16.0087i	−0.585729	−	1.01451i
$250$	43.0416			2.72219
$251$	−5.48528	−	9.50079i	−0.346228	−	0.599684i	0.639348	−	0.768917i	$-0.279204\pi$
$251$	−5.48528	−	9.50079i	−0.346228	−	0.599684i	−0.985576	+	0.169233i	$0.945871\pi$
$252$		0			0
$253$	−2.41421	−	4.18154i	−0.151780	−	0.262891i
$254$	−11.2426	+	19.4728i	−0.705426	+	1.22183i
$255$	0.464466	−	0.804479i	0.0290860	−	0.0503784i
$256$	−29.9706			−1.87316
$257$	−15.0000			−0.935674			−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000			−0.935674			−0.467837	+	0.883815i	$0.654967\pi$
$258$	1.00000	−	1.73205i	0.0622573	−	0.107833i
$259$		0			0
$260$	14.6569	+	50.7728i	0.908980	+	3.14880i
$261$	4.91421	+	8.51167i	0.304182	+	0.526859i
$262$	1.58579	+	2.74666i	0.0979702	+	0.169689i
$263$	−9.36396	−	16.2189i	−0.577407	−	1.00010i	−0.995776	−	0.0918204i	$-0.970731\pi$
$263$	−9.36396	−	16.2189i	−0.577407	−	1.00010i	0.418369	−	0.908277i	$-0.362602\pi$
$264$	10.6569	−	18.4582i	0.655884	−	1.13602i
$265$	11.4853			0.705535
$266$		0			0
$267$	−5.17157	−	8.95743i	−0.316495	−	0.548186i
$268$	8.12132	+	14.0665i	0.496089	+	0.859251i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$	26.1421	+	45.2795i	1.59096	+	2.75562i
$271$	6.92893			0.420903			0.210451	−	0.977604i	$-0.432507\pi$
$271$	6.92893			0.420903			0.210451	+	0.977604i	$0.432507\pi$
$272$	0.514719			0.0312094
$273$		0			0
$274$	14.0711			0.850064
$275$	32.9706			1.98820
$276$	−3.82843	−	6.63103i	−0.230444	−	0.399141i
$277$	−31.9706			−1.92092			−0.960462	−	0.278409i	$-0.910193\pi$
$277$	−31.9706			−1.92092			−0.960462	+	0.278409i	$0.910193\pi$
$278$	−9.53553	−	16.5160i	−0.571903	−	0.990566i
$279$	−2.70711	−	4.68885i	−0.162070	−	0.280714i
$280$		0			0
$281$	−0.514719			−0.0307055			−0.0153528	−	0.999882i	$-0.504887\pi$
$281$	−0.514719			−0.0307055			−0.0153528	+	0.999882i	$0.504887\pi$
$282$	−13.0711	+	22.6398i	−0.778371	+	1.34818i
$283$	−0.0502525	−	0.0870399i	−0.00298720	−	0.00517399i	0.864528	−	0.502585i	$-0.167618\pi$
$283$	−0.0502525	−	0.0870399i	−0.00298720	−	0.00517399i	−0.867515	+	0.497411i	$0.834284\pi$
$284$	0.656854	+	1.13770i	0.0389771	+	0.0675104i
$285$	−16.2426	−	28.1331i	−0.962131	−	1.66646i
$286$	8.24264	+	28.5533i	0.487398	+	1.68839i
$287$		0			0
$288$	0.792893	−	1.37333i	0.0467217	−	0.0809243i
$289$	−16.9706			−0.998268
$290$	90.8406			5.33434
$291$	−3.65685	+	6.33386i	−0.214369	+	0.371297i
$292$	1.25736	−	2.17781i	0.0735814	−	0.127447i
$293$	−11.2279	−	19.4473i	−0.655942	−	1.13613i	−0.981657	−	0.190657i	$-0.938938\pi$
$293$	−11.2279	−	19.4473i	−0.655942	−	1.13613i	0.325714	−	0.945468i	$-0.394395\pi$
$294$		0			0
$295$	3.36396	+	5.82655i	0.195857	+	0.339235i
$296$	−33.0416			−1.92051
$297$	9.65685	+	16.7262i	0.560348	+	0.970550i
$298$	3.62132	−	6.27231i	0.209777	−	0.363345i
$299$	4.94975	+	1.22474i	0.286251	+	0.0708288i
$300$	52.2843			3.01863
$301$		0			0
$302$	−22.8995	+	39.6631i	−1.31772	+	2.28235i
$303$	2.36396	−	4.09450i	0.135806	−	0.235223i
$304$	9.00000	−	15.5885i	0.516185	−	0.894059i
$305$	37.6274			2.15454
$306$	−0.207107	+	0.358719i	−0.0118395	+	0.0205066i
$307$	7.27208			0.415039			0.207520	−	0.978231i	$-0.433461\pi$
$307$	7.27208			0.415039			0.207520	+	0.978231i	$0.433461\pi$
$308$		0			0
$309$	9.89949	−	17.1464i	0.563163	−	0.975426i
$310$	−50.0416			−2.84217
$311$	−13.5355	+	23.4442i	−0.767530	+	1.32940i	0.171369	+	0.985207i	$0.445181\pi$
$311$	−13.5355	+	23.4442i	−0.767530	+	1.32940i	−0.938899	+	0.344194i	$0.888152\pi$
$312$	6.24264	+	21.6251i	0.353420	+	1.22428i
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	13.8640	−	24.0131i	0.782389	−	1.35514i
$315$		0			0
$316$	−19.6066	−	33.9596i	−1.10296	−	1.91038i
$317$	−10.6716	−	18.4837i	−0.599375	−	1.03815i	−0.992913	−	0.118840i	$-0.962082\pi$
$317$	−10.6716	−	18.4837i	−0.599375	−	1.03815i	0.393538	−	0.919308i	$-0.371251\pi$
$318$	10.2426			0.574379
$319$	33.5563			1.87879
$320$	−18.8137	−	32.5863i	−1.05172	−	1.82163i
$321$	3.75736	+	6.50794i	0.209715	+	0.363238i
$322$		0			0
$323$	0.514719	−	0.891519i	0.0286397	−	0.0496054i
$324$	9.57107	+	16.5776i	0.531726	+	0.920976i
$325$	−24.1421	+	25.0892i	−1.33916	+	1.39170i
$326$	18.6066	−	32.2276i	1.03052	−	1.78492i
$327$	−3.31371			−0.183248
$328$	−12.8640	+	22.2810i	−0.710293	+	1.23026i
$329$		0			0
$330$	44.6274			2.45666
$331$	−14.4350	+	25.0022i	−0.793421	+	1.37425i	0.130416	+	0.991459i	$0.458369\pi$
$331$	−14.4350	+	25.0022i	−0.793421	+	1.37425i	−0.923837	+	0.382786i	$0.874965\pi$
$332$	50.0416			2.74639
$333$	3.74264	−	6.48244i	0.205095	−	0.355236i
$334$	22.6066	−	39.1558i	1.23698	−	2.14251i
$335$	−8.12132	+	14.0665i	−0.443715	+	0.768537i
$336$		0			0
$337$	13.4853			0.734590			0.367295	−	0.930104i	$-0.380284\pi$
$337$	13.4853			0.734590			0.367295	+	0.930104i	$0.380284\pi$
$338$	−27.7635	−	14.6354i	−1.51013	−	0.796060i
$339$	1.63604	−	2.83370i	0.0888574	−	0.153906i
$340$	1.25736	+	2.17781i	0.0681899	+	0.118108i
$341$	−18.4853			−1.00103
$342$	7.24264	+	12.5446i	0.391637	+	0.678335i
$343$		0			0
$344$	1.29289	+	2.23936i	0.0697081	+	0.120738i
$345$	3.82843	−	6.63103i	0.206116	−	0.357003i
$346$	−21.8995	+	37.9310i	−1.17732	+	2.03919i
$347$	−25.8995			−1.39036			−0.695179	−	0.718837i	$-0.744675\pi$
$347$	−25.8995			−1.39036			−0.695179	+	0.718837i	$0.744675\pi$
$348$	53.2132			2.85253
$349$	−6.65685	+	11.5300i	−0.356333	+	0.617187i	−0.987345	−	0.158586i	$-0.949307\pi$
$349$	−6.65685	+	11.5300i	−0.356333	+	0.617187i	0.631012	+	0.775773i	$0.282640\pi$
$350$		0			0
$351$	−19.7990	−	4.89898i	−1.05679	−	0.261488i
$352$	−2.70711	−	4.68885i	−0.144289	−	0.249916i
$353$	0.0857864	+	0.148586i	0.00456595	+	0.00790846i	0.868299	−	0.496041i	$-0.165213\pi$
$353$	0.0857864	+	0.148586i	0.00456595	+	0.00790846i	−0.863733	+	0.503949i	$0.831880\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$	−0.656854	+	1.13770i	−0.0348622	+	0.0603831i
$356$	28.0000			1.48400
$357$		0			0
$358$	6.82843	+	11.8272i	0.360894	+	0.625086i
$359$	−8.48528	−	14.6969i	−0.447836	−	0.775675i	0.550409	−	0.834895i	$-0.314472\pi$
$359$	−8.48528	−	14.6969i	−0.447836	−	0.775675i	−0.998245	+	0.0592205i	$0.981138\pi$
$360$	−16.8995			−0.890682
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−46.2132			−2.42891
$363$	0.928932			0.0487563
$364$		0			0
$365$	2.51472			0.131626
$366$	33.5563			1.75402
$367$	−1.63604	−	2.83370i	−0.0854005	−	0.147918i	0.820161	−	0.572132i	$-0.193884\pi$
$367$	−1.63604	−	2.83370i	−0.0854005	−	0.147918i	−0.905562	+	0.424214i	$0.860550\pi$
$368$	4.24264			0.221163
$369$	−2.91421	−	5.04757i	−0.151708	−	0.262766i
$370$	−34.5919	−	59.9149i	−1.79835	−	3.11483i
$371$		0			0
$372$	−29.3137			−1.51984
$373$	12.2279	−	21.1794i	0.633138	−	1.09663i	−0.353769	−	0.935333i	$-0.615100\pi$
$373$	12.2279	−	21.1794i	0.633138	−	1.09663i	0.986906	−	0.161294i	$-0.0515667\pi$
$374$	0.707107	+	1.22474i	0.0365636	+	0.0633300i
$375$	12.6066	+	21.8353i	0.651002	+	1.12757i
$376$	−16.8995	−	29.2708i	−0.871525	−	1.50953i
$377$	−24.5711	+	25.5350i	−1.26547	+	1.31512i
$378$		0			0
$379$	−4.12132	+	7.13834i	−0.211698	+	0.366672i	−0.952246	−	0.305332i	$-0.901233\pi$
$379$	−4.12132	+	7.13834i	−0.211698	+	0.366672i	0.740548	+	0.672003i	$0.234566\pi$
$380$	87.9411			4.51128
$381$	−13.1716			−0.674800
$382$	9.36396	−	16.2189i	0.479102	−	0.829829i
$383$	7.02082	−	12.1604i	0.358747	−	0.621368i	−0.629005	−	0.777401i	$-0.716537\pi$
$383$	7.02082	−	12.1604i	0.358747	−	0.621368i	0.987752	+	0.156034i	$0.0498708\pi$
$384$	−14.5355	−	25.1763i	−0.741763	−	1.28477i
$385$		0			0
$386$	−25.5208	−	44.2033i	−1.29898	−	2.24989i
$387$	−0.585786			−0.0297772
$388$	−9.89949	−	17.1464i	−0.502571	−	0.870478i
$389$	0.571068	−	0.989118i	0.0289543	−	0.0501503i	−0.851185	−	0.524866i	$-0.824116\pi$
$389$	0.571068	−	0.989118i	0.0289543	−	0.0501503i	0.880139	+	0.474715i	$0.157449\pi$
$390$	−32.6777	+	33.9596i	−1.65470	+	1.71961i
$391$	0.242641			0.0122709
$392$		0			0
$393$	−0.928932	+	1.60896i	−0.0468584	+	0.0811612i
$394$	11.0711	−	19.1757i	0.557752	−	0.966055i
$395$	19.6066	−	33.9596i	0.986515	−	1.70869i
$396$	−13.0711			−0.656846
$397$	−19.3137	+	33.4523i	−0.969327	+	1.67892i	−0.271817	+	0.962349i	$0.587625\pi$
$397$	−19.3137	+	33.4523i	−0.969327	+	1.67892i	−0.697510	+	0.716575i	$0.745709\pi$
$398$	45.7990			2.29570
$399$		0			0
$400$	−14.4853	+	25.0892i	−0.724264	+	1.25446i
$401$	−30.7990			−1.53803			−0.769014	−	0.639232i	$-0.779252\pi$
$401$	−30.7990			−1.53803			−0.769014	+	0.639232i	$0.779252\pi$
$402$	−7.24264	+	12.5446i	−0.361230	+	0.625669i
$403$	13.5355	−	14.0665i	0.674253	−	0.700704i
$404$	6.39949	+	11.0843i	0.318387	+	0.551462i
$405$	−9.57107	+	16.5776i	−0.475590	+	0.823746i
$406$		0			0
$407$	−12.7782	−	22.1324i	−0.633391	−	1.09706i
$408$	0.535534	+	0.927572i	0.0265129	+	0.0459217i
$409$	−11.9706			−0.591906			−0.295953	−	0.955202i	$-0.595637\pi$
$409$	−11.9706			−0.591906			−0.295953	+	0.955202i	$0.595637\pi$
$410$	−53.8701			−2.66045
$411$	4.12132	+	7.13834i	0.203290	+	0.352108i
$412$	26.7990	+	46.4172i	1.32029	+	2.28681i
$413$		0			0
$414$	−1.70711	+	2.95680i	−0.0838997	+	0.145319i
$415$	25.0208	+	43.3373i	1.22822	+	2.12735i
$416$	5.55025	+	1.37333i	0.272124	+	0.0673331i
$417$	5.58579	−	9.67487i	0.273537	−	0.473780i
$418$	49.4558			2.41896
$419$	9.77817	−	16.9363i	0.477695	−	0.827392i	−0.521978	−	0.852959i	$-0.674806\pi$
$419$	9.77817	−	16.9363i	0.477695	−	0.827392i	0.999673	+	0.0255668i	$0.00813904\pi$
$420$		0			0
$421$	4.51472			0.220034			0.110017	−	0.993930i	$-0.464909\pi$
$421$	4.51472			0.220034			0.110017	+	0.993930i	$0.464909\pi$
$422$	−0.878680	+	1.52192i	−0.0427735	+	0.0740858i
$423$	7.65685			0.372289
$424$	−6.62132	+	11.4685i	−0.321560	+	0.556958i
$425$	−0.828427	+	1.43488i	−0.0401846	+	0.0696018i
$426$	−0.585786	+	1.01461i	−0.0283814	+	0.0491581i
$427$		0			0
$428$	−20.3431			−0.983323
$429$	−12.0711	+	12.5446i	−0.582797	+	0.605660i
$430$	−2.70711	+	4.68885i	−0.130548	+	0.226116i
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	−16.9706			−0.816497
$433$	0.257359	+	0.445759i	0.0123679	+	0.0214218i	0.872143	−	0.489251i	$-0.162730\pi$
$433$	0.257359	+	0.445759i	0.0123679	+	0.0214218i	−0.859775	+	0.510673i	$0.829396\pi$
$434$		0			0
$435$	26.6066	+	46.0840i	1.27569	+	2.20956i
$436$	4.48528	−	7.76874i	0.214806	−	0.372055i
$437$	4.24264	−	7.34847i	0.202953	−	0.351525i
$438$	2.24264			0.107158
$439$	26.7279			1.27565			0.637827	−	0.770180i	$-0.279833\pi$
$439$	26.7279			1.27565			0.637827	+	0.770180i	$0.279833\pi$
$440$	−28.8492	+	49.9684i	−1.37533	+	2.38215i
$441$		0			0
$442$	−1.44975	−	0.358719i	−0.0689575	−	0.0170625i
$443$	−7.17157	−	12.4215i	−0.340732	−	0.590165i	0.643837	−	0.765163i	$-0.277341\pi$
$443$	−7.17157	−	12.4215i	−0.340732	−	0.590165i	−0.984569	+	0.174998i	$0.944008\pi$
$444$	−20.2635	−	35.0973i	−0.961661	−	1.66565i
$445$	14.0000	+	24.2487i	0.663664	+	1.14950i
$446$	−2.41421	+	4.18154i	−0.114316	+	0.198002i
$447$	4.24264			0.200670
$448$		0			0
$449$	−7.75736	−	13.4361i	−0.366092	−	0.634091i	0.622858	−	0.782335i	$-0.285971\pi$
$449$	−7.75736	−	13.4361i	−0.366092	−	0.634091i	−0.988951	+	0.148244i	$0.952638\pi$
$450$	−11.6569	−	20.1903i	−0.549509	−	0.951778i
$451$	−19.8995			−0.937031
$452$	4.42893	+	7.67114i	0.208319	+	0.360820i
$453$	−26.8284			−1.26051
$454$	−33.5563			−1.57488
$455$		0			0
$456$	37.4558			1.75403
$457$	−25.0000			−1.16945			−0.584725	−	0.811231i	$-0.698798\pi$
$457$	−25.0000			−1.16945			−0.584725	+	0.811231i	$0.698798\pi$
$458$	−5.41421	−	9.37769i	−0.252990	−	0.438191i
$459$	−0.970563			−0.0453020
$460$	10.3640	+	17.9509i	0.483222	+	0.836965i
$461$	6.32843	+	10.9612i	0.294744	+	0.510512i	0.974925	−	0.222532i	$-0.0714322\pi$
$461$	6.32843	+	10.9612i	0.294744	+	0.510512i	−0.680181	+	0.733044i	$0.738099\pi$
$462$		0			0
$463$	−18.7279			−0.870360			−0.435180	−	0.900343i	$-0.643315\pi$
$463$	−18.7279			−0.870360			−0.435180	+	0.900343i	$0.643315\pi$
$464$	−14.7426	+	25.5350i	−0.684410	+	1.18543i
$465$	−14.6569	−	25.3864i	−0.679695	−	1.17727i
$466$	−3.41421	−	5.91359i	−0.158160	−	0.273942i
$467$	4.29289	+	7.43551i	0.198651	+	0.344074i	0.948091	−	0.317998i	$-0.103011\pi$
$467$	4.29289	+	7.43551i	0.198651	+	0.344074i	−0.749440	+	0.662072i	$0.769677\pi$
$468$	9.57107	−	9.94655i	0.442423	−	0.459779i
$469$		0			0
$470$	35.3848	−	61.2882i	1.63218	−	2.82702i
$471$	16.2426			0.748421
$472$	−7.75736			−0.357061
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$	17.4853	−	30.2854i	0.803126	−	1.39105i
$475$	28.9706	+	50.1785i	1.32926	+	2.30235i
$476$		0			0
$477$	−1.50000	−	2.59808i	−0.0686803	−	0.118958i
$478$	29.8995			1.36757
$479$	−19.1924	−	33.2422i	−0.876923	−	1.51887i	−0.854700	−	0.519121i	$-0.826259\pi$
$479$	−19.1924	−	33.2422i	−0.876923	−	1.51887i	−0.0222221	−	0.999753i	$-0.507074\pi$
$480$	4.29289	−	7.43551i	0.195943	−	0.339383i
$481$	26.1985	+	6.48244i	1.19455	+	0.295574i
$482$	−3.58579			−0.163328
$483$		0			0
$484$	−1.25736	+	2.17781i	−0.0571527	+	0.0989914i
$485$	9.89949	−	17.1464i	0.449513	−	0.778579i
$486$	11.9497	−	20.6976i	0.542052	−	0.938861i
$487$	20.9706			0.950267			0.475133	−	0.879914i	$-0.342400\pi$
$487$	20.9706			0.950267			0.475133	+	0.879914i	$0.342400\pi$
$488$	−21.6924	+	37.5723i	−0.981968	+	1.70082i
$489$	21.7990			0.985784
$490$		0			0
$491$	−17.6569	+	30.5826i	−0.796843	+	1.38017i	0.124820	+	0.992179i	$0.460165\pi$
$491$	−17.6569	+	30.5826i	−0.796843	+	1.38017i	−0.921662	+	0.387993i	$0.873169\pi$
$492$	−31.5563			−1.42267
$493$	−0.843146	+	1.46037i	−0.0379734	+	0.0657718i
$494$	−36.2132	+	37.6339i	−1.62931	+	1.69323i
$495$	−6.53553	−	11.3199i	−0.293750	−	0.508791i
$496$	8.12132	−	14.0665i	0.364658	−	0.631606i
$497$		0			0
$498$	22.3137	+	38.6485i	0.999901	+	1.73188i
$499$	14.0208	+	24.2848i	0.627658	+	1.08714i	0.988020	+	0.154323i	$0.0493196\pi$
$499$	14.0208	+	24.2848i	0.627658	+	1.08714i	−0.360363	+	0.932812i	$0.617347\pi$
$500$	−68.2548			−3.05245
$501$	26.4853			1.18328
$502$	13.2426	+	22.9369i	0.591048	+	1.02373i
$503$	−16.7782	−	29.0607i	−0.748102	−	1.29575i	−0.948731	−	0.316083i	$-0.897632\pi$
$503$	−16.7782	−	29.0607i	−0.748102	−	1.29575i	0.200630	−	0.979667i	$-0.435701\pi$
$504$		0			0
$505$	−6.39949	+	11.0843i	−0.284774	+	0.493243i
$506$	5.82843	+	10.0951i	0.259105	+	0.448783i
$507$	−0.707107	−	18.3712i	−0.0314037	−	0.815892i
$508$	17.8284	−	30.8797i	0.791009	−	1.37007i
$509$	6.65685			0.295060			0.147530	−	0.989058i	$-0.452868\pi$
$509$	6.65685			0.295060			0.147530	+	0.989058i	$0.452868\pi$
$510$	−1.12132	+	1.94218i	−0.0496529	+	0.0860013i
$511$		0			0
$512$	31.2426			1.38074
$513$	−16.9706	+	29.3939i	−0.749269	+	1.29777i
$514$	36.2132			1.59730
$515$	−26.7990	+	46.4172i	−1.18090	+	2.04539i
$516$	−1.58579	+	2.74666i	−0.0698104	+	0.120915i
$517$	13.0711	−	22.6398i	0.574865	−	0.995695i
$518$		0			0
$519$	−25.6569			−1.12621
$520$	−16.8995	−	58.5416i	−0.741092	−	2.56722i
$521$	−6.67157	+	11.5555i	−0.292287	+	0.506256i	−0.974350	−	0.225037i	$-0.927750\pi$
$521$	−6.67157	+	11.5555i	−0.292287	+	0.506256i	0.682063	+	0.731293i	$0.261083\pi$
$522$	−11.8640	−	20.5490i	−0.519271	−	0.899405i
$523$	−16.9706			−0.742071			−0.371035	−	0.928619i	$-0.620997\pi$
$523$	−16.9706			−0.742071			−0.371035	+	0.928619i	$0.620997\pi$
$524$	−2.51472	−	4.35562i	−0.109856	−	0.190276i
$525$		0			0
$526$	22.6066	+	39.1558i	0.985695	+	1.70727i
$527$	0.464466	−	0.804479i	0.0202325	−	0.0350437i
$528$	−7.24264	+	12.5446i	−0.315195	+	0.545935i
$529$	−21.0000			−0.913043
$530$	−27.7279			−1.20442
$531$	0.878680	−	1.52192i	0.0381314	−	0.0660456i
$532$		0			0
$533$	14.5711	−	15.1427i	0.631143	−	0.655903i
$534$	12.4853	+	21.6251i	0.540291	+	0.935811i
$535$	−10.1716	−	17.6177i	−0.439755	−	0.761679i
$536$	−9.36396	−	16.2189i	−0.404462	−	0.700548i
$537$	−4.00000	+	6.92820i	−0.172613	+	0.298974i
$538$	−43.4558			−1.87351
$539$		0			0
$540$	−41.4558	−	71.8036i	−1.78398	−	3.08994i
$541$	−2.74264	−	4.75039i	−0.117915	−	0.204235i	0.801026	−	0.598630i	$-0.204288\pi$
$541$	−2.74264	−	4.75039i	−0.117915	−	0.204235i	−0.918941	+	0.394394i	$0.870954\pi$
$542$	−16.7279			−0.718526
$543$	−13.5355	−	23.4442i	−0.580865	−	1.00609i
$544$	0.272078			0.0116652
$545$	8.97056			0.384257
$546$		0			0
$547$	15.0711			0.644392			0.322196	−	0.946673i	$-0.395579\pi$
$547$	15.0711			0.644392			0.322196	+	0.946673i	$0.395579\pi$
$548$	−22.3137			−0.953194
$549$	−4.91421	−	8.51167i	−0.209734	−	0.363269i
$550$	−79.5980			−3.39407
$551$	29.4853	+	51.0700i	1.25612	+	2.17566i
$552$	4.41421	+	7.64564i	0.187881	+	0.325420i
$553$		0			0
$554$	77.1838			3.27922
$555$	20.2635	−	35.0973i	0.860136	−	1.48980i
$556$	15.1213	+	26.1909i	0.641287	+	1.11074i
$557$	5.15685	+	8.93193i	0.218503	+	0.378458i	0.954350	−	0.298689i	$-0.0965493\pi$
$557$	5.15685	+	8.93193i	0.218503	+	0.378458i	−0.735848	+	0.677147i	$0.763216\pi$
$558$	6.53553	+	11.3199i	0.276671	+	0.479209i
$559$	−0.585786	−	2.02922i	−0.0247761	−	0.0858270i
$560$		0			0
$561$	−0.414214	+	0.717439i	−0.0174881	+	0.0302903i
$562$	1.24264			0.0524176
$563$	−19.8995			−0.838664			−0.419332	−	0.907833i	$-0.637736\pi$
$563$	−19.8995			−0.838664			−0.419332	+	0.907833i	$0.637736\pi$
$564$	20.7279	−	35.9018i	0.872803	−	1.51174i
$565$	−4.42893	+	7.67114i	−0.186327	+	0.322727i
$566$	0.121320	+	0.210133i	0.00509947	+	0.00883255i
$567$		0			0
$568$	−0.757359	−	1.31178i	−0.0317781	−	0.0550413i
$569$	13.1716			0.552181			0.276091	−	0.961132i	$-0.410961\pi$
$569$	13.1716			0.552181			0.276091	+	0.961132i	$0.410961\pi$
$570$	39.2132	+	67.9193i	1.64246	+	2.84482i
$571$	2.48528	−	4.30463i	0.104006	−	0.180143i	−0.809326	−	0.587360i	$-0.800167\pi$
$571$	2.48528	−	4.30463i	0.104006	−	0.180143i	0.913332	+	0.407217i	$0.133501\pi$
$572$	−13.0711	−	45.2795i	−0.546529	−	1.89323i
$573$	10.9706			0.458302
$574$		0			0
$575$	−6.82843	+	11.8272i	−0.284765	+	0.493228i
$576$	−4.91421	+	8.51167i	−0.204759	+	0.354653i
$577$	−18.1569	+	31.4486i	−0.755880	+	1.30922i	0.189056	+	0.981966i	$0.439457\pi$
$577$	−18.1569	+	31.4486i	−0.755880	+	1.30922i	−0.944936	+	0.327256i	$0.893876\pi$
$578$	40.9706			1.70415
$579$	14.9497	−	25.8937i	0.621290	−	1.07611i
$580$	−144.054			−5.98151
$581$		0			0
$582$	8.82843	−	15.2913i	0.365950	−	0.633844i
$583$	−10.2426			−0.424207
$584$	−1.44975	+	2.51104i	−0.0599910	+	0.103907i
$585$	13.3995	+	3.31552i	0.554001	+	0.137080i
$586$	27.1066	+	46.9500i	1.11976	+	1.93949i
$587$	−9.17157	+	15.8856i	−0.378551	+	0.655670i	−0.990852	−	0.134955i	$-0.956911\pi$
$587$	−9.17157	+	15.8856i	−0.378551	+	0.655670i	0.612300	+	0.790625i	$0.290244\pi$
$588$		0			0
$589$	−16.2426	−	28.1331i	−0.669266	−	1.15920i
$590$	−8.12132	−	14.0665i	−0.334349	−	0.579110i
$591$	12.9706			0.533538
$592$	22.4558			0.922930
$593$	−15.6421	−	27.0930i	−0.642346	−	1.11258i	−0.984908	−	0.173080i	$-0.944628\pi$
$593$	−15.6421	−	27.0930i	−0.642346	−	1.11258i	0.342562	−	0.939495i	$-0.388705\pi$
$594$	−23.3137	−	40.3805i	−0.956573	−	1.65683i
$595$		0			0
$596$	−5.74264	+	9.94655i	−0.235228	+	0.407426i
$597$	13.4142	+	23.2341i	0.549007	+	0.950908i
$598$	−11.9497	−	2.95680i	−0.488662	−	0.120912i
$599$	−19.8284	+	34.3438i	−0.810168	+	1.40325i	0.102579	+	0.994725i	$0.467291\pi$
$599$	−19.8284	+	34.3438i	−0.810168	+	1.40325i	−0.912746	+	0.408527i	$0.866043\pi$
$600$	−60.2843			−2.46110
$601$	−18.4706	+	31.9920i	−0.753430	+	1.30498i	0.192721	+	0.981254i	$0.438269\pi$
$601$	−18.4706	+	31.9920i	−0.753430	+	1.30498i	−0.946151	+	0.323725i	$0.895065\pi$
$602$		0			0
$603$	4.24264			0.172774
$604$	36.3137	−	62.8972i	1.47758	−	2.55925i
$605$	−2.51472			−0.102238
$606$	−5.70711	+	9.88500i	−0.231835	+	0.401551i
$607$	−21.8284	+	37.8079i	−0.885989	+	1.53458i	−0.0414121	+	0.999142i	$0.513186\pi$
$607$	−21.8284	+	37.8079i	−0.885989	+	1.53458i	−0.844576	+	0.535435i	$0.820148\pi$
$608$	4.75736	−	8.23999i	0.192936	−	0.334176i
$609$		0			0
$610$	−90.8406			−3.67803
$611$	7.65685	+	26.5241i	0.309763	+	1.07305i
$612$	0.328427	−	0.568852i	0.0132759	−	0.0229945i
$613$	−12.3995	−	21.4766i	−0.500811	−	0.867430i	−1.00000		0.000936581i	$-0.999702\pi$
$613$	−12.3995	−	21.4766i	−0.500811	−	0.867430i	0.499189	−	0.866493i	$-0.333631\pi$
$614$	−17.5563			−0.708517
$615$	−15.7782	−	27.3286i	−0.636237	−	1.10200i
$616$		0			0
$617$	1.42893	+	2.47498i	0.0575266	+	0.0996391i	0.893355	−	0.449352i	$-0.148345\pi$
$617$	1.42893	+	2.47498i	0.0575266	+	0.0996391i	−0.835828	+	0.548992i	$0.815012\pi$
$618$	−23.8995	+	41.3951i	−0.961379	+	1.66516i
$619$	5.22183	−	9.04447i	0.209883	−	0.363528i	−0.741795	−	0.670627i	$-0.766025\pi$
$619$	5.22183	−	9.04447i	0.209883	−	0.363528i	0.951677	+	0.307099i	$0.0993584\pi$
$620$	79.3553			3.18699
$621$	−8.00000			−0.321029
$622$	32.6777	−	56.5994i	1.31026	−	2.26943i
$623$		0			0
$624$	−4.24264	−	14.6969i	−0.169842	−	0.588348i
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$	16.8995	+	29.2708i	0.675440	+	1.16990i
$627$	14.4853	+	25.0892i	0.578486	+	1.00197i
$628$	−21.9853	+	38.0796i	−0.877308	+	1.51954i
$629$	1.28427			0.0512072
$630$		0			0
$631$	16.1421	+	27.9590i	0.642608	+	1.11303i	0.984848	+	0.173418i	$0.0554810\pi$
$631$	16.1421	+	27.9590i	0.642608	+	1.11303i	−0.342240	+	0.939613i	$0.611186\pi$
$632$	22.6066	+	39.1558i	0.899242	+	1.55753i
$633$	−1.02944			−0.0409165
$634$	25.7635	+	44.6236i	1.02320	+	1.77223i
$635$	35.6569			1.41500
$636$	−16.2426			−0.644063
$637$		0			0
$638$	−81.0122			−3.20730
$639$	0.343146			0.0135746
$640$	39.3492	+	68.1549i	1.55542	+	2.69406i
$641$	24.7990			0.979501			0.489751	−	0.871863i	$-0.337088\pi$
$641$	24.7990			0.979501			0.489751	+	0.871863i	$0.337088\pi$
$642$	−9.07107	−	15.7116i	−0.358006	−	0.620085i
$643$	24.4853	+	42.4098i	0.965605	+	1.67248i	0.707980	+	0.706232i	$0.249607\pi$
$643$	24.4853	+	42.4098i	0.965605	+	1.67248i	0.257625	+	0.966245i	$0.417060\pi$
$644$		0			0
$645$	−3.17157			−0.124881
$646$	−1.24264	+	2.15232i	−0.0488910	+	0.0846818i
$647$	2.65685	+	4.60181i	0.104452	+	0.180916i	0.913514	−	0.406807i	$-0.133358\pi$
$647$	2.65685	+	4.60181i	0.104452	+	0.180916i	−0.809062	+	0.587723i	$0.800025\pi$
$648$	−11.0355	−	19.1141i	−0.433517	−	0.750873i
$649$	−3.00000	−	5.19615i	−0.117760	−	0.203967i
$650$	58.2843	−	60.5708i	2.28610	−	2.37578i
$651$		0			0
$652$	−29.5061	+	51.1061i	−1.15555	+	2.00147i
$653$	−2.14214			−0.0838282			−0.0419141	−	0.999121i	$-0.513346\pi$
$653$	−2.14214			−0.0838282			−0.0419141	+	0.999121i	$0.513346\pi$
$654$	8.00000			0.312825
$655$	2.51472	−	4.35562i	0.0982582	−	0.170188i
$656$	8.74264	−	15.1427i	0.341343	−	0.591223i
$657$	−0.328427	−	0.568852i	−0.0128132	−	0.0221930i
$658$		0			0
$659$	−3.65685	−	6.33386i	−0.142451	−	0.246732i	0.785968	−	0.618267i	$-0.212165\pi$
$659$	−3.65685	−	6.33386i	−0.142451	−	0.246732i	−0.928419	+	0.371535i	$0.878832\pi$
$660$	−70.7696			−2.75470
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	0.814915	−	0.579581i	$-0.196784\pi$
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	−0.909389	+	0.415946i	$0.863450\pi$
$662$	34.8492	−	60.3607i	1.35445	−	2.34598i
$663$	−0.242641	−	0.840532i	−0.00942338	−	0.0326436i
$664$	−57.6985			−2.23914
$665$		0			0
$666$	−9.03553	+	15.6500i	−0.350120	+	0.606425i
$667$	−6.94975	+	12.0373i	−0.269095	+	0.466087i
$668$	−35.8492	+	62.0927i	−1.38705	+	2.40244i
$669$	−2.82843			−0.109353
$670$	19.6066	−	33.9596i	0.757469	−	1.31197i
$671$	−33.5563			−1.29543
$672$		0			0
$673$	−15.7426	+	27.2671i	−0.606834	+	1.05107i	0.384925	+	0.922948i	$0.374227\pi$
$673$	−15.7426	+	27.2671i	−0.606834	+	1.05107i	−0.991759	+	0.128120i	$0.959106\pi$
$674$	−32.5563			−1.25402
$675$	27.3137	−	47.3087i	1.05131	−	1.82091i
$676$	44.0269	+	23.2086i	1.69334	+	0.892639i
$677$	−3.17157	−	5.49333i	−0.121893	−	0.211126i	0.798621	−	0.601834i	$-0.205563\pi$
$677$	−3.17157	−	5.49333i	−0.121893	−	0.211126i	−0.920514	+	0.390709i	$0.872230\pi$
$678$	−3.94975	+	6.84116i	−0.151689	+	0.262733i
$679$		0			0
$680$	−1.44975	−	2.51104i	−0.0555953	−	0.0962938i
$681$	−9.82843	−	17.0233i	−0.376626	−	0.652336i
$682$	44.6274			1.70887
$683$	−17.3137			−0.662491			−0.331245	−	0.943545i	$-0.607469\pi$
$683$	−17.3137			−0.662491			−0.331245	+	0.943545i	$0.607469\pi$
$684$	−11.4853	−	19.8931i	−0.439151	−	0.760631i
$685$	−11.1569	−	19.3242i	−0.426281	−	0.738341i
$686$		0			0
$687$	3.17157	−	5.49333i	0.121003	−	0.209583i
$688$	−0.878680	−	1.52192i	−0.0334993	−	0.0580226i
$689$	7.50000	−	7.79423i	0.285727	−	0.296936i
$690$	−9.24264	+	16.0087i	−0.351861	+	0.609442i
$691$	37.9411			1.44335			0.721674	−	0.692233i	$-0.243373\pi$
$691$	37.9411			1.44335			0.721674	+	0.692233i	$0.243373\pi$
$692$	34.7279	−	60.1505i	1.32016	−	2.28658i
$693$		0			0
$694$	62.5269			2.37349
$695$	−15.1213	+	26.1909i	−0.573584	+	0.993477i
$696$	−61.3553			−2.32567
$697$	0.500000	−	0.866025i	0.0189389	−	0.0328031i
$698$	16.0711	−	27.8359i	0.608299	−	1.05360i
$699$	2.00000	−	3.46410i	0.0756469	−	0.131024i
$700$		0			0
$701$	42.1421			1.59169			0.795843	−	0.605503i	$-0.207028\pi$
$701$	42.1421			1.59169			0.795843	+	0.605503i	$0.207028\pi$
$702$	47.7990	+	11.8272i	1.80406	+	0.446388i
$703$	22.4558	−	38.8947i	0.846938	−	1.46694i
$704$	16.7782	+	29.0607i	0.632351	+	1.09526i
$705$	41.4558			1.56132
$706$	−0.207107	−	0.358719i	−0.00779457	−	0.0135006i
$707$		0			0
$708$	−4.75736	−	8.23999i	−0.178793	−	0.309678i
$709$	13.8137	−	23.9260i	0.518785	−	0.898561i	−0.480977	−	0.876733i	$-0.659718\pi$
$709$	13.8137	−	23.9260i	0.518785	−	0.898561i	0.999762	−	0.0218283i	$-0.00694871\pi$
$710$	1.58579	−	2.74666i	0.0595135	−	0.103080i
$711$	−10.2426			−0.384129
$712$	−32.2843			−1.20990
$713$	3.82843	−	6.63103i	0.143376	−	0.248334i
$714$		0			0
$715$	32.6777	−	33.9596i	1.22208	−	1.27002i
$716$	−10.8284	−	18.7554i	−0.404677	−	0.700922i
$717$	8.75736	+	15.1682i	0.327050	+	0.566466i
$718$	20.4853	+	35.4815i	0.764504	+	1.32416i
$719$	−18.1924	+	31.5101i	−0.678462	+	1.17513i	0.296983	+	0.954883i	$0.404020\pi$
$719$	−18.1924	+	31.5101i	−0.678462	+	1.17513i	−0.975444	+	0.220247i	$0.929314\pi$
$720$	11.4853			0.428031
$721$		0			0
$722$	20.5208	+	35.5431i	0.763706	+	1.32278i
$723$	−1.05025	−	1.81909i	−0.0390593	−	0.0676527i
$724$	73.2843			2.72359
$725$	−47.4558	−	82.1959i	−1.76247	−	3.05268i
$726$	−2.24264			−0.0832322
$727$	8.97056			0.332700			0.166350	−	0.986067i	$-0.446802\pi$
$727$	8.97056			0.332700			0.166350	+	0.986067i	$0.446802\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−6.07107			−0.224700
$731$	−0.0502525	−	0.0870399i	−0.00185866	−	0.00321929i
$732$	−53.2132			−1.96682
$733$	−10.5000	−	18.1865i	−0.387826	−	0.671735i	0.604331	−	0.796734i	$-0.293441\pi$
$733$	−10.5000	−	18.1865i	−0.387826	−	0.671735i	−0.992157	+	0.124999i	$0.960107\pi$
$734$	3.94975	+	6.84116i	0.145788	+	0.252512i
$735$		0			0
$736$	2.24264			0.0826648
$737$	7.24264	−	12.5446i	0.266786	−	0.462087i
$738$	7.03553	+	12.1859i	0.258982	+	0.448569i
$739$	−18.1421	−	31.4231i	−0.667369	−	1.15592i	−0.978637	−	0.205595i	$-0.934087\pi$
$739$	−18.1421	−	31.4231i	−0.667369	−	1.15592i	0.311268	−	0.950322i	$-0.399246\pi$
$740$	54.8553	+	95.0122i	2.01652	+	3.49272i
$741$	−29.6985	−	7.34847i	−1.09100	−	0.269953i
$742$		0			0
$743$	23.7990	−	41.2211i	0.873100	−	1.51225i	0.0143275	−	0.999897i	$-0.495439\pi$
$743$	23.7990	−	41.2211i	0.873100	−	1.51225i	0.858773	−	0.512357i	$-0.171227\pi$
$744$	33.7990			1.23913
$745$	−11.4853			−0.420788
$746$	−29.5208	+	51.1316i	−1.08083	+	1.87206i
$747$	6.53553	−	11.3199i	0.239123	−	0.414173i
$748$	−1.12132	−	1.94218i	−0.0409995	−	0.0710133i
$749$		0			0
$750$	−30.4350	−	52.7150i	−1.11133	−	1.92488i
$751$	13.5563			0.494678			0.247339	−	0.968929i	$-0.420444\pi$
$751$	13.5563			0.494678			0.247339	+	0.968929i	$0.420444\pi$
$752$	11.4853	+	19.8931i	0.418825	+	0.725426i
$753$	−7.75736	+	13.4361i	−0.282694	+	0.489640i
$754$	59.3198	−	61.6469i	2.16030	−	2.24505i
$755$	72.6274			2.64318
$756$		0			0
$757$	10.7279	−	18.5813i	0.389913	−	0.675349i	−0.602525	−	0.798100i	$-0.705838\pi$
$757$	10.7279	−	18.5813i	0.389913	−	0.675349i	0.992437	+	0.122751i	$0.0391718\pi$
$758$	9.94975	−	17.2335i	0.361391	−	0.625948i
$759$	−3.41421	+	5.91359i	−0.123928	+	0.214650i
$760$	−101.397			−3.67805
$761$	23.0711	−	39.9603i	0.836326	−	1.44856i	−0.0566210	−	0.998396i	$-0.518033\pi$
$761$	23.0711	−	39.9603i	0.836326	−	1.44856i	0.892947	−	0.450163i	$-0.148634\pi$
$762$	31.7990			1.15196
$763$		0			0
$764$	−14.8492	+	25.7196i	−0.537227	+	0.930504i
$765$	0.656854			0.0237486
$766$	−16.9497	+	29.3578i	−0.612419	+	1.06074i
$767$	6.15076	+	1.52192i	0.222091	+	0.0549533i
$768$	21.1924	+	36.7063i	0.764714	+	1.32452i
$769$	0.727922	−	1.26080i	0.0262495	−	0.0454655i	−0.852602	−	0.522560i	$-0.824977\pi$
$769$	0.727922	−	1.26080i	0.0262495	−	0.0454655i	0.878852	+	0.477095i	$0.158310\pi$
$770$		0			0
$771$	10.6066	+	18.3712i	0.381987	+	0.661622i
$772$	40.4706	+	70.0971i	1.45657	+	2.52285i
$773$	−17.6569			−0.635073			−0.317536	−	0.948246i	$-0.602856\pi$
$773$	−17.6569			−0.635073			−0.317536	+	0.948246i	$0.602856\pi$
$774$	1.41421			0.0508329
$775$	26.1421	+	45.2795i	0.939053	+	1.62649i
$776$	11.4142	+	19.7700i	0.409746	+	0.709702i
$777$		0			0
$778$	−1.37868	+	2.38794i	−0.0494281	+	0.0856119i
$779$	−17.4853	−	30.2854i	−0.626475	−	1.08509i
$780$	51.8198	−	53.8527i	1.85545	−	1.92824i
$781$	0.585786	−	1.01461i	0.0209611	−	0.0363057i
$782$	−0.585786			−0.0209477
$783$	27.7990	−	48.1493i	0.993455	−	1.72071i
$784$		0			0
$785$	−43.9706			−1.56938
$786$	2.24264	−	3.88437i	0.0799923	−	0.138551i
$787$	−5.89949			−0.210294			−0.105147	−	0.994457i	$-0.533531\pi$
$787$	−5.89949			−0.210294			−0.105147	+	0.994457i	$0.533531\pi$
$788$	−17.5563	+	30.4085i	−0.625419	+	1.08326i
$789$	−13.2426	+	22.9369i	−0.471450	+	0.816576i
$790$	−47.3345	+	81.9858i	−1.68409	+	2.91692i
$791$		0			0
$792$	15.0711			0.535527
$793$	24.5711	−	25.5350i	0.872544	−	0.906775i
$794$	46.6274	−	80.7611i	1.65475	−	2.86610i
$795$	−8.12132	−	14.0665i	−0.288034	−	0.498889i
$796$	−72.6274			−2.57421
$797$	5.07107	+	8.78335i	0.179626	+	0.311122i	0.941753	−	0.336306i	$-0.109178\pi$
$797$	5.07107	+	8.78335i	0.179626	+	0.311122i	−0.762126	+	0.647429i	$0.775844\pi$
$798$		0			0
$799$	0.656854	+	1.13770i	0.0232378	+	0.0402491i
$800$	−7.65685	+	13.2621i	−0.270711	+	0.468885i
$801$	3.65685	−	6.33386i	0.129209	−	0.223796i
$802$	74.3553			2.62558
$803$	−2.24264			−0.0791411
$804$	11.4853	−	19.8931i	0.405055	−	0.701575i
$805$		0			0
$806$	−32.6777	+	33.9596i	−1.15102	+	1.19618i
$807$	−12.7279	−	22.0454i	−0.448044	−	0.776035i
$808$	−7.37868	−	12.7802i	−0.259581	−	0.449608i
$809$	−3.42893	−	5.93908i	−0.120555	−	0.208807i	0.799432	−	0.600757i	$-0.205134\pi$
$809$	−3.42893	−	5.93908i	−0.120555	−	0.208807i	−0.919987	+	0.391950i	$0.871801\pi$
$810$	23.1066	−	40.0218i	0.811883	−	1.40622i
$811$	−34.1838			−1.20035			−0.600177	−	0.799867i	$-0.704903\pi$
$811$	−34.1838			−1.20035			−0.600177	+	0.799867i	$0.704903\pi$
$812$		0			0
$813$	−4.89949	−	8.48617i	−0.171833	−	0.297623i
$814$	30.8492	+	53.4325i	1.08127	+	1.87281i
$815$	−59.0122			−2.06711
$816$	−0.363961	−	0.630399i	−0.0127412	−	0.0220684i
$817$	−3.51472			−0.122964
$818$	28.8995			1.01045
$819$		0			0
$820$	85.4264			2.98322
$821$	27.9411			0.975152			0.487576	−	0.873081i	$-0.337881\pi$
$821$	27.9411			0.975152			0.487576	+	0.873081i	$0.337881\pi$
$822$	−9.94975	−	17.2335i	−0.347037	−	0.601086i
$823$	−3.31371			−0.115509			−0.0577543	−	0.998331i	$-0.518394\pi$
$823$	−3.31371			−0.115509			−0.0577543	+	0.998331i	$0.518394\pi$
$824$	−30.8995	−	53.5195i	−1.07643	−	1.86444i
$825$	−23.3137	−	40.3805i	−0.811679	−	1.40587i
$826$		0			0
$827$	40.6690			1.41420			0.707101	−	0.707113i	$-0.250003\pi$
$827$	40.6690			1.41420			0.707101	+	0.707113i	$0.250003\pi$
$828$	2.70711	−	4.68885i	0.0940785	−	0.162949i
$829$	11.8431	+	20.5129i	0.411329	+	0.712444i	0.995035	−	0.0995216i	$-0.0317312\pi$
$829$	11.8431	+	20.5129i	0.411329	+	0.712444i	−0.583706	+	0.811965i	$0.698398\pi$
$830$	−60.4056	−	104.626i	−2.09671	−	3.63161i
$831$	22.6066	+	39.1558i	0.784214	+	1.35830i
$832$	−34.3995	−	8.51167i	−1.19259	−	0.295089i
$833$		0			0
$834$	−13.4853	+	23.3572i	−0.466957	+	0.808793i
$835$	−71.6985			−2.48123
$836$	−78.4264			−2.71243
$837$	−15.3137	+	26.5241i	−0.529319	+	0.916808i
$838$	−23.6066	+	40.8878i	−0.815477	+	1.41245i
$839$	18.7990	+	32.5608i	0.649013	+	1.12412i	0.983359	+	0.181673i	$0.0581514\pi$
$839$	18.7990	+	32.5608i	0.649013	+	1.12412i	−0.334346	+	0.942450i	$0.608515\pi$
$840$		0			0
$841$	−33.7990	−	58.5416i	−1.16548	−	2.01867i
$842$	−10.8995			−0.375621
$843$	0.363961	+	0.630399i	0.0125355	+	0.0217121i
$844$	1.39340	−	2.41344i	0.0479627	−	0.0830739i
$845$	1.91421	+	49.7327i	0.0658509	+	1.71086i
$846$	−18.4853			−0.635537
$847$		0			0
$848$	4.50000	−	7.79423i	0.154531	−	0.267655i
$849$	−0.0710678	+	0.123093i	−0.00243904	+	0.00422454i
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	10.5858			0.362876
$852$	0.928932	−	1.60896i	0.0318247	−	0.0551220i
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$		0			0
$855$	11.4853	−	19.8931i	0.392788	−	0.680329i
$856$	23.4558			0.801704
$857$	20.3995	−	35.3330i	0.696833	−	1.20695i	−0.272725	−	0.962092i	$-0.587925\pi$
$857$	20.3995	−	35.3330i	0.696833	−	1.20695i	0.969559	−	0.244859i	$-0.0787417\pi$
$858$	29.1421	−	30.2854i	0.994896	−	1.03393i
$859$	−13.5355	−	23.4442i	−0.461826	−	0.799907i	0.537226	−	0.843439i	$-0.319472\pi$
$859$	−13.5355	−	23.4442i	−0.461826	−	0.799907i	−0.999052	+	0.0435317i	$0.986139\pi$
$860$	4.29289	−	7.43551i	0.146386	−	0.253549i
$861$		0			0
$862$	14.4853	+	25.0892i	0.493371	+	0.854543i
$863$	−28.0919	−	48.6566i	−0.956259	−	1.65629i	−0.731461	−	0.681883i	$-0.761161\pi$
$863$	−28.0919	−	48.6566i	−0.956259	−	1.65629i	−0.224798	−	0.974405i	$-0.572172\pi$
$864$	−8.97056			−0.305185
$865$	69.4558			2.36157
$866$	−0.621320	−	1.07616i	−0.0211133	−	0.0365694i
$867$	12.0000	+	20.7846i	0.407541	+	0.705882i
$868$		0			0
$869$	−17.4853	+	30.2854i	−0.593148	+	1.02736i
$870$	−64.2340	−	111.257i	−2.17774	−	3.77195i
$871$	4.24264	+	14.6969i	0.143756	+	0.497987i
$872$	−5.17157	+	8.95743i	−0.175132	+	0.303337i
$873$	−5.17157			−0.175031
$874$	−10.2426	+	17.7408i	−0.346462	+	0.600091i
$875$		0			0
$876$	−3.55635			−0.120158
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	−0.973098	−	0.230391i	$-0.925999\pi$
$877$	−8.50000	+	14.7224i	−0.287025	+	0.497141i	0.686074	+	0.727532i	$0.259333\pi$
$878$	−64.5269			−2.17768
$879$	−15.8787	+	27.5027i	−0.535575	+	0.927642i
$880$	19.6066	−	33.9596i	0.660938	−	1.14478i
$881$	−23.2279	+	40.2319i	−0.782569	+	1.35545i	0.147872	+	0.989006i	$0.452758\pi$
$881$	−23.2279	+	40.2319i	−0.782569	+	1.35545i	−0.930441	+	0.366442i	$0.880576\pi$
$882$		0			0
$883$	7.95837			0.267820			0.133910	−	0.990993i	$-0.457247\pi$
$883$	7.95837			0.267820			0.133910	+	0.990993i	$0.457247\pi$
$884$	2.29899	+	0.568852i	0.0773234	+	0.0191326i
$885$	4.75736	−	8.23999i	0.159917	−	0.276984i
$886$	17.3137	+	29.9882i	0.581665	+	1.00747i
$887$	−10.6274			−0.356834			−0.178417	−	0.983955i	$-0.557098\pi$
$887$	−10.6274			−0.356834			−0.178417	+	0.983955i	$0.557098\pi$
$888$	23.3640	+	40.4676i	0.784043	+	1.35800i
$889$		0			0
$890$	−33.7990	−	58.5416i	−1.13294	−	1.96232i
$891$	8.53553	−	14.7840i	0.285951	−	0.495282i
$892$	3.82843	−	6.63103i	0.128185	−	0.222023i
$893$	45.9411			1.53736
$894$	−10.2426			−0.342565
$895$	10.8284	−	18.7554i	0.361954	−	0.626923i
$896$		0			0
$897$	−2.00000	−	6.92820i	−0.0667781	−	0.231326i
$898$	18.7279	+	32.4377i	0.624959	+	1.08246i
$899$	26.6066	+	46.0840i	0.887380	+	1.53699i
$900$	18.4853	+	32.0174i	0.616176	+	1.06725i
$901$	0.257359	−	0.445759i	0.00857388	−	0.0148504i
$902$	48.0416			1.59961
$903$		0			0
$904$	−5.10660	−	8.84489i	−0.169843	−	0.294177i
$905$	36.6421	+	63.4660i	1.21803	+	2.10968i
$906$	64.7696			2.15182
$907$	−9.36396	−	16.2189i	−0.310925	−	0.538538i	0.667638	−	0.744486i	$-0.267306\pi$
$907$	−9.36396	−	16.2189i	−0.310925	−	0.538538i	−0.978563	+	0.205948i	$0.933972\pi$
$908$	53.2132			1.76594
$909$	3.34315			0.110885
$910$		0			0
$911$	−18.3431			−0.607736			−0.303868	−	0.952714i	$-0.598278\pi$
$911$	−18.3431			−0.607736			−0.303868	+	0.952714i	$0.598278\pi$
$912$	−25.4558			−0.842927
$913$	−22.3137	−	38.6485i	−0.738476	−	1.27908i
$914$	60.3553			1.99638
$915$	−26.6066	−	46.0840i	−0.879587	−	1.52349i
$916$	8.58579	+	14.8710i	0.283682	+	0.491352i
$917$		0			0
$918$	2.34315			0.0773353
$919$	−12.6569	+	21.9223i	−0.417511	+	0.723150i	−0.995688	−	0.0927607i	$-0.970431\pi$
$919$	−12.6569	+	21.9223i	−0.417511	+	0.723150i	0.578177	+	0.815911i	$0.303764\pi$
$920$	−11.9497	−	20.6976i	−0.393972	−	0.682379i
$921$	−5.14214	−	8.90644i	−0.169439	−	0.293477i
$922$	−15.2782	−	26.4626i	−0.503160	−	0.871498i
$923$	0.343146	+	1.18869i	0.0112948	+	0.0391263i
$924$		0			0
$925$	−36.1421	+	62.6000i	−1.18835	+	2.05828i
$926$	45.2132			1.48580
$927$	14.0000			0.459820
$928$	−7.79289	+	13.4977i	−0.255814	+	0.443083i
$929$	−9.47056	+	16.4035i	−0.310719	+	0.538181i	−0.978518	−	0.206160i	$-0.933903\pi$
$929$	−9.47056	+	16.4035i	−0.310719	+	0.538181i	0.667799	+	0.744342i	$0.267237\pi$
$930$	35.3848	+	61.2882i	1.16031	+	2.00972i
$931$		0			0
$932$	5.41421	+	9.37769i	0.177348	+	0.307177i
$933$	38.2843			1.25337
$934$	−10.3640	−	17.9509i	−0.339119	−	0.587372i
$935$	1.12132	−	1.94218i	0.0366711	−	0.0635162i
$936$	−11.0355	+	11.4685i	−0.360708	+	0.374858i
$937$	8.85786			0.289374			0.144687	−	0.989477i	$-0.453783\pi$
$937$	8.85786			0.289374			0.144687	+	0.989477i	$0.453783\pi$
$938$		0			0
$939$	−9.89949	+	17.1464i	−0.323058	+	0.559553i
$940$	−56.1127	+	97.1900i	−1.83019	+	3.16999i
$941$	9.51472	−	16.4800i	0.310171	−	0.537232i	−0.668228	−	0.743956i	$-0.732947\pi$
$941$	9.51472	−	16.4800i	0.310171	−	0.537232i	0.978399	+	0.206724i	$0.0662804\pi$
$942$	−39.2132			−1.27764
$943$	4.12132	−	7.13834i	0.134209	−	0.232456i
$944$	5.27208			0.171592
$945$		0			0
$946$	2.41421	−	4.18154i	0.0784929	−	0.135954i
$947$	18.5858			0.603957			0.301978	−	0.953315i	$-0.402353\pi$
$947$	18.5858			0.603957			0.301978	+	0.953315i	$0.402353\pi$
$948$	−27.7279	+	48.0262i	−0.900561	+	1.55982i
$949$	1.64214	−	1.70656i	0.0533060	−	0.0553972i
$950$	−69.9411	−	121.142i	−2.26919	−	3.93035i
$951$	−15.0919	+	26.1399i	−0.489388	+	0.847645i
$952$		0			0
$953$	19.3137	+	33.4523i	0.625632	+	1.08363i	0.988418	+	0.151755i	$0.0484923\pi$
$953$	19.3137	+	33.4523i	0.625632	+	1.08363i	−0.362786	+	0.931873i	$0.618174\pi$
$954$	3.62132	+	6.27231i	0.117245	+	0.203074i
$955$	−29.6985			−0.961020
$956$	−47.4142			−1.53349
$957$	−23.7279	−	41.0980i	−0.767015	−	1.32851i
$958$	46.3345	+	80.2537i	1.49700	+	2.59288i
$959$		0			0
$960$	−26.6066	+	46.0840i	−0.858724	+	1.48735i
$961$	0.843146	+	1.46037i	0.0271983	+	0.0471088i
$962$	−63.2487	−	15.6500i	−2.03922	−	0.504576i
$963$	−2.65685	+	4.60181i	−0.0856159	+	0.148291i
$964$	5.68629			0.183143
$965$	−40.4706	+	70.0971i	−1.30279	+	2.25650i
$966$		0			0
$967$	−28.2426			−0.908222			−0.454111	−	0.890945i	$-0.650043\pi$
$967$	−28.2426			−0.908222			−0.454111	+	0.890945i	$0.650043\pi$
$968$	1.44975	−	2.51104i	0.0465966	−	0.0807078i
$969$	−1.45584			−0.0467685
$970$	−23.8995	+	41.3951i	−0.767367	+	1.32912i
$971$	20.1716	−	34.9382i	0.647337	−	1.12122i	−0.336420	−	0.941712i	$-0.609216\pi$
$971$	20.1716	−	34.9382i	0.647337	−	1.12122i	0.983757	−	0.179508i	$-0.0574505\pi$
$972$	−18.9497	+	32.8219i	−0.607813	+	1.05276i
$973$		0			0
$974$	−50.6274			−1.62221
$975$	47.7990	+	11.8272i	1.53079	+	0.378773i
$976$	14.7426	−	25.5350i	0.471900	−	0.817356i
$977$	24.2990	+	42.0871i	0.777394	+	1.34649i	0.933439	+	0.358735i	$0.116792\pi$
$977$	24.2990	+	42.0871i	0.777394	+	1.34649i	−0.156046	+	0.987750i	$0.549875\pi$
$978$	−52.6274			−1.68284
$979$	−12.4853	−	21.6251i	−0.399031	−	0.691143i
$980$		0			0
$981$	−1.17157	−	2.02922i	−0.0374054	−	0.0647881i
$982$	42.6274	−	73.8329i	1.36030	−	2.35610i
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	0.308165	+	0.951333i	$0.400285\pi$
$983$	−21.0000	+	36.3731i	−0.669796	+	1.16012i	−0.977961	+	0.208788i	$0.933048\pi$
$984$	36.3848			1.15990
$985$	−35.1127			−1.11878
$986$	2.03553	−	3.52565i	0.0648246	−	0.112280i
$987$		0			0
$988$	57.4264	−	59.6793i	1.82698	−	1.89865i
$989$	−0.414214	−	0.717439i	−0.0131712	−	0.0228132i
$990$	15.7782	+	27.3286i	0.501463	+	0.868560i
$991$	−14.1213	−	24.4588i	−0.448579	−	0.776961i	0.549715	−	0.835352i	$-0.314736\pi$
$991$	−14.1213	−	24.4588i	−0.448579	−	0.776961i	−0.998294	+	0.0583913i	$0.981403\pi$
$992$	4.29289	−	7.43551i	0.136299	−	0.236078i
$993$	40.8284			1.29565
$994$		0			0
$995$	−36.3137	−	62.8972i	−1.15122	−	1.99397i
$996$	−35.3848	−	61.2882i	−1.12121	−	1.94199i
$997$	19.9706			0.632474			0.316237	−	0.948680i	$-0.397581\pi$
$997$	19.9706			0.632474			0.316237	+	0.948680i	$0.397581\pi$
$998$	−33.8492	−	58.6286i	−1.07148	−	1.85586i
$999$	−42.3431			−1.33968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.c.165.1		4
7.2	even	3		637.2.g.g.373.2		4
7.3	odd	6		637.2.f.f.295.2	yes	4
7.4	even	3		637.2.f.e.295.2	✓	4
7.5	odd	6		637.2.g.f.373.2		4
7.6	odd	2		637.2.h.b.165.1		4
13.3	even	3		637.2.g.g.263.2		4
91.3	odd	6		637.2.f.f.393.2	yes	4
91.4	even	6		8281.2.a.y.1.2		2
91.16	even	3	inner	637.2.h.c.471.1		4
91.17	odd	6		8281.2.a.x.1.2		2
91.55	odd	6		637.2.g.f.263.2		4
91.68	odd	6		637.2.h.b.471.1		4
91.74	even	3		8281.2.a.o.1.1		2
91.81	even	3		637.2.f.e.393.2	yes	4
91.87	odd	6		8281.2.a.p.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.e.295.2	✓	4	7.4	even	3
637.2.f.e.393.2	yes	4	91.81	even	3
637.2.f.f.295.2	yes	4	7.3	odd	6
637.2.f.f.393.2	yes	4	91.3	odd	6
637.2.g.f.263.2		4	91.55	odd	6
637.2.g.f.373.2		4	7.5	odd	6
637.2.g.g.263.2		4	13.3	even	3
637.2.g.g.373.2		4	7.2	even	3
637.2.h.b.165.1		4	7.6	odd	2
637.2.h.b.471.1		4	91.68	odd	6
637.2.h.c.165.1		4	1.1	even	1	trivial
637.2.h.c.471.1		4	91.16	even	3	inner
8281.2.a.o.1.1		2	91.74	even	3
8281.2.a.p.1.1		2	91.87	odd	6
8281.2.a.x.1.2		2	91.17	odd	6
8281.2.a.y.1.2		2	91.4	even	6

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.41421 q^{2} +(-0.707107 - 1.22474i) q^{3} +3.82843 q^{4} +(1.91421 + 3.31552i) q^{5} +(1.70711 + 2.95680i) q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-2.41421 q^{2} +(-0.707107 - 1.22474i) q^{3} +3.82843 q^{4} +(1.91421 + 3.31552i) q^{5} +(1.70711 + 2.95680i) q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.62132 - 8.00436i) q^{10} +(-1.70711 - 2.95680i) q^{11} +(-2.70711 - 4.68885i) q^{12} +(3.50000 + 0.866025i) q^{13} +(2.70711 - 4.68885i) q^{15} +3.00000 q^{16} +0.171573 q^{17} +(-1.20711 + 2.09077i) q^{18} +(3.00000 - 5.19615i) q^{19} +(7.32843 + 12.6932i) q^{20} +(4.12132 + 7.13834i) q^{22} +1.41421 q^{23} +(3.12132 + 5.40629i) q^{24} +(-4.82843 + 8.36308i) q^{25} +(-8.44975 - 2.09077i) q^{26} -5.65685 q^{27} +(-4.91421 + 8.51167i) q^{29} +(-6.53553 + 11.3199i) q^{30} +(2.70711 - 4.68885i) q^{31} +1.58579 q^{32} +(-2.41421 + 4.18154i) q^{33} -0.414214 q^{34} +(1.91421 - 3.31552i) q^{36} +7.48528 q^{37} +(-7.24264 + 12.5446i) q^{38} +(-1.41421 - 4.89898i) q^{39} +(-8.44975 - 14.6354i) q^{40} +(2.91421 - 5.04757i) q^{41} +(-0.292893 - 0.507306i) q^{43} +(-6.53553 - 11.3199i) q^{44} +3.82843 q^{45} -3.41421 q^{46} +(3.82843 + 6.63103i) q^{47} +(-2.12132 - 3.67423i) q^{48} +(11.6569 - 20.1903i) q^{50} +(-0.121320 - 0.210133i) q^{51} +(13.3995 + 3.31552i) q^{52} +(1.50000 - 2.59808i) q^{53} +13.6569 q^{54} +(6.53553 - 11.3199i) q^{55} -8.48528 q^{57} +(11.8640 - 20.5490i) q^{58} +1.75736 q^{59} +(10.3640 - 17.9509i) q^{60} +(4.91421 - 8.51167i) q^{61} +(-6.53553 + 11.3199i) q^{62} -9.82843 q^{64} +(3.82843 + 13.2621i) q^{65} +(5.82843 - 10.0951i) q^{66} +(2.12132 + 3.67423i) q^{67} +0.656854 q^{68} +(-1.00000 - 1.73205i) q^{69} +(0.171573 + 0.297173i) q^{71} +(-2.20711 + 3.82282i) q^{72} +(0.328427 - 0.568852i) q^{73} -18.0711 q^{74} +13.6569 q^{75} +(11.4853 - 19.8931i) q^{76} +(3.41421 + 11.8272i) q^{78} +(-5.12132 - 8.87039i) q^{79} +(5.74264 + 9.94655i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-7.03553 + 12.1859i) q^{82} +13.0711 q^{83} +(0.328427 + 0.568852i) q^{85} +(0.707107 + 1.22474i) q^{86} +13.8995 q^{87} +(7.53553 + 13.0519i) q^{88} +7.31371 q^{89} -9.24264 q^{90} +5.41421 q^{92} -7.65685 q^{93} +(-9.24264 - 16.0087i) q^{94} +22.9706 q^{95} +(-1.12132 - 1.94218i) q^{96} +(-2.58579 - 4.47871i) q^{97} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9} - 10 q^{10} - 4 q^{11} - 8 q^{12} + 14 q^{13} + 8 q^{15} + 12 q^{16} + 12 q^{17} - 2 q^{18} + 12 q^{19} + 18 q^{20} + 8 q^{22} + 4 q^{24} - 8 q^{25} - 14 q^{26} - 14 q^{29} - 12 q^{30} + 8 q^{31} + 12 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 12 q^{38} - 14 q^{40} + 6 q^{41} - 4 q^{43} - 12 q^{44} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 24 q^{50} + 8 q^{51} + 14 q^{52} + 6 q^{53} + 32 q^{54} + 12 q^{55} + 22 q^{58} + 24 q^{59} + 16 q^{60} + 14 q^{61} - 12 q^{62} - 28 q^{64} + 4 q^{65} + 12 q^{66} - 20 q^{68} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 10 q^{73} - 44 q^{74} + 32 q^{75} + 12 q^{76} + 8 q^{78} - 12 q^{79} + 6 q^{80} + 10 q^{81} - 14 q^{82} + 24 q^{83} - 10 q^{85} + 16 q^{87} + 16 q^{88} - 16 q^{89} - 20 q^{90} + 16 q^{92} - 8 q^{93} - 20 q^{94} + 24 q^{95} + 4 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9 - 10 * q^10 - 4 * q^11 - 8 * q^12 + 14 * q^13 + 8 * q^15 + 12 * q^16 + 12 * q^17 - 2 * q^18 + 12 * q^19 + 18 * q^20 + 8 * q^22 + 4 * q^24 - 8 * q^25 - 14 * q^26 - 14 * q^29 - 12 * q^30 + 8 * q^31 + 12 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 12 * q^38 - 14 * q^40 + 6 * q^41 - 4 * q^43 - 12 * q^44 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 24 * q^50 + 8 * q^51 + 14 * q^52 + 6 * q^53 + 32 * q^54 + 12 * q^55 + 22 * q^58 + 24 * q^59 + 16 * q^60 + 14 * q^61 - 12 * q^62 - 28 * q^64 + 4 * q^65 + 12 * q^66 - 20 * q^68 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 10 * q^73 - 44 * q^74 + 32 * q^75 + 12 * q^76 + 8 * q^78 - 12 * q^79 + 6 * q^80 + 10 * q^81 - 14 * q^82 + 24 * q^83 - 10 * q^85 + 16 * q^87 + 16 * q^88 - 16 * q^89 - 20 * q^90 + 16 * q^92 - 8 * q^93 - 20 * q^94 + 24 * q^95 + 4 * q^96 - 16 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more