LMFDB - Embedded newform 637.2.f.e.393.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, 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:	$4$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.e.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 2.09077i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-1.91421 + 3.31552i) q^{4} -3.82843 q^{5} +(1.70711 - 2.95680i) q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.20711 + 2.09077i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-1.91421 + 3.31552i) q^{4} -3.82843 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} +5.41421 q^{12} +(3.50000 - 0.866025i) q^{13} +(2.70711 + 4.68885i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(-0.0857864 + 0.148586i) q^{17} +2.41421 q^{18} +(3.00000 - 5.19615i) q^{19} +(7.32843 - 12.6932i) q^{20} +(4.12132 - 7.13834i) q^{22} +(-0.707107 - 1.22474i) q^{23} +(3.12132 + 5.40629i) q^{24} +9.65685 q^{25} +(6.03553 + 6.27231i) q^{26} -5.65685 q^{27} +(-4.91421 - 8.51167i) q^{29} +(-6.53553 + 11.3199i) q^{30} -5.41421 q^{31} +(-0.792893 + 1.37333i) q^{32} +(-2.41421 + 4.18154i) q^{33} -0.414214 q^{34} +(1.91421 + 3.31552i) q^{36} +(-3.74264 - 6.48244i) q^{37} +14.4853 q^{38} +(-3.53553 - 3.67423i) q^{39} +16.8995 q^{40} +(2.91421 + 5.04757i) q^{41} +(-0.292893 + 0.507306i) q^{43} +13.0711 q^{44} +(-1.91421 + 3.31552i) q^{45} +(1.70711 - 2.95680i) q^{46} -7.65685 q^{47} +(-2.12132 + 3.67423i) q^{48} +(11.6569 + 20.1903i) q^{50} +0.242641 q^{51} +(-3.82843 + 13.2621i) q^{52} -3.00000 q^{53} +(-6.82843 - 11.8272i) q^{54} +(6.53553 + 11.3199i) q^{55} -8.48528 q^{57} +(11.8640 - 20.5490i) q^{58} +(-0.878680 + 1.52192i) q^{59} -20.7279 q^{60} +(4.91421 - 8.51167i) q^{61} +(-6.53553 - 11.3199i) q^{62} -9.82843 q^{64} +(-13.3995 + 3.31552i) q^{65} -11.6569 q^{66} +(2.12132 + 3.67423i) q^{67} +(-0.328427 - 0.568852i) q^{68} +(-1.00000 + 1.73205i) q^{69} +(0.171573 - 0.297173i) q^{71} +(-2.20711 + 3.82282i) q^{72} -0.656854 q^{73} +(9.03553 - 15.6500i) q^{74} +(-6.82843 - 11.8272i) q^{75} +(11.4853 + 19.8931i) q^{76} +(3.41421 - 11.8272i) q^{78} +10.2426 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} -1.41421 q^{86} +(-6.94975 + 12.0373i) q^{87} +(7.53553 + 13.0519i) q^{88} +(-3.65685 - 6.33386i) q^{89} -9.24264 q^{90} +5.41421 q^{92} +(3.82843 + 6.63103i) q^{93} +(-9.24264 - 16.0087i) q^{94} +(-11.4853 + 19.8931i) q^{95} +2.24264 q^{96} +(-2.58579 + 4.47871i) q^{97} -3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9} - 10 q^{10} - 4 q^{11} + 16 q^{12} + 14 q^{13} + 8 q^{15} - 6 q^{16} - 6 q^{17} + 4 q^{18} + 12 q^{19} + 18 q^{20} + 8 q^{22} + 4 q^{24} + 16 q^{25} + 10 q^{26} - 14 q^{29} - 12 q^{30} - 16 q^{31} - 6 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{36} + 2 q^{37} + 24 q^{38} + 28 q^{40} + 6 q^{41} - 4 q^{43} + 24 q^{44} - 2 q^{45} + 4 q^{46} - 8 q^{47} + 24 q^{50} - 16 q^{51} - 4 q^{52} - 12 q^{53} - 16 q^{54} + 12 q^{55} + 22 q^{58} - 12 q^{59} - 32 q^{60} + 14 q^{61} - 12 q^{62} - 28 q^{64} - 14 q^{65} - 24 q^{66} + 10 q^{68} - 4 q^{69} + 12 q^{71} - 6 q^{72} + 20 q^{73} + 22 q^{74} - 16 q^{75} + 12 q^{76} + 8 q^{78} + 24 q^{79} + 6 q^{80} + 10 q^{81} - 14 q^{82} + 24 q^{83} - 10 q^{85} - 8 q^{87} + 16 q^{88} + 8 q^{89} - 20 q^{90} + 16 q^{92} + 4 q^{93} - 20 q^{94} - 12 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9 - 10 * q^10 - 4 * q^11 + 16 * q^12 + 14 * q^13 + 8 * q^15 - 6 * q^16 - 6 * q^17 + 4 * q^18 + 12 * q^19 + 18 * q^20 + 8 * q^22 + 4 * q^24 + 16 * q^25 + 10 * q^26 - 14 * q^29 - 12 * q^30 - 16 * q^31 - 6 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^36 + 2 * q^37 + 24 * q^38 + 28 * q^40 + 6 * q^41 - 4 * q^43 + 24 * q^44 - 2 * q^45 + 4 * q^46 - 8 * q^47 + 24 * q^50 - 16 * q^51 - 4 * q^52 - 12 * q^53 - 16 * q^54 + 12 * q^55 + 22 * q^58 - 12 * q^59 - 32 * q^60 + 14 * q^61 - 12 * q^62 - 28 * q^64 - 14 * q^65 - 24 * q^66 + 10 * q^68 - 4 * q^69 + 12 * q^71 - 6 * q^72 + 20 * q^73 + 22 * q^74 - 16 * q^75 + 12 * q^76 + 8 * q^78 + 24 * q^79 + 6 * q^80 + 10 * q^81 - 14 * q^82 + 24 * q^83 - 10 * q^85 - 8 * q^87 + 16 * q^88 + 8 * q^89 - 20 * q^90 + 16 * q^92 + 4 * q^93 - 20 * q^94 - 12 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	0.877981	+	0.478696i	$0.158890\pi$
$2$	1.20711	+	2.09077i	0.853553	+	1.47840i	−0.0244272	+	0.999702i	$0.507776\pi$
$3$	−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	$0.967194\pi$
$4$	−1.91421	+	3.31552i	−0.957107	+	1.65776i
$5$	−3.82843			−1.71212			−0.856062	−	0.516873i	$-0.827096\pi$
$5$	−3.82843			−1.71212			−0.856062	+	0.516873i	$0.827096\pi$
$6$	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	$-0.338768\pi$
$12$	5.41421			1.56295
$13$	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
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	−0.0857864	+	0.148586i	−0.0208063	+	0.0360375i	−0.876241	−	0.481873i	$-0.839957\pi$
$17$	−0.0857864	+	0.148586i	−0.0208063	+	0.0360375i	0.855435	+	0.517911i	$0.173290\pi$
$18$	2.41421			0.569036
$19$	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
$23$	−0.707107	−	1.22474i	−0.147442	−	0.255377i	0.782839	−	0.622224i	$-0.213771\pi$
$23$	−0.707107	−	1.22474i	−0.147442	−	0.255377i	−0.930281	+	0.366847i	$0.880437\pi$
$24$	3.12132	+	5.40629i	0.637137	+	1.10355i
$25$	9.65685			1.93137
$26$	6.03553	+	6.27231i	1.18367	+	1.23010i
$27$	−5.65685			−1.08866
$28$		0			0
$29$	−4.91421	−	8.51167i	−0.912547	−	1.58058i	−0.810454	−	0.585802i	$-0.800780\pi$
$29$	−4.91421	−	8.51167i	−0.912547	−	1.58058i	−0.102092	−	0.994775i	$-0.532554\pi$
$30$	−6.53553	+	11.3199i	−1.19322	+	2.06672i
$31$	−5.41421			−0.972421			−0.486211	−	0.873842i	$-0.661621\pi$
$31$	−5.41421			−0.972421			−0.486211	+	0.873842i	$0.661621\pi$
$32$	−0.792893	+	1.37333i	−0.140165	+	0.242773i
$33$	−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
$37$	−3.74264	−	6.48244i	−0.615286	−	1.06571i	−0.990334	−	0.138702i	$-0.955707\pi$
$37$	−3.74264	−	6.48244i	−0.615286	−	1.06571i	0.375048	−	0.927005i	$-0.377626\pi$
$38$	14.4853			2.34982
$39$	−3.53553	−	3.67423i	−0.566139	−	0.588348i
$40$	16.8995			2.67204
$41$	2.91421	+	5.04757i	0.455124	+	0.788297i	0.998695	−	0.0510654i	$-0.0162617\pi$
$41$	2.91421	+	5.04757i	0.455124	+	0.788297i	−0.543572	+	0.839363i	$0.682928\pi$
$42$		0			0
$43$	−0.292893	+	0.507306i	−0.0446658	+	0.0773634i	−0.887494	−	0.460819i	$-0.847556\pi$
$43$	−0.292893	+	0.507306i	−0.0446658	+	0.0773634i	0.842828	+	0.538183i	$0.180889\pi$
$44$	13.0711			1.97054
$45$	−1.91421	+	3.31552i	−0.285354	+	0.494248i
$46$	1.70711	−	2.95680i	0.251699	−	0.435956i
$47$	−7.65685			−1.11687			−0.558433	−	0.829549i	$-0.688597\pi$
$47$	−7.65685			−1.11687			−0.558433	+	0.829549i	$0.688597\pi$
$48$	−2.12132	+	3.67423i	−0.306186	+	0.530330i
$49$		0			0
$50$	11.6569	+	20.1903i	1.64853	+	2.85533i
$51$	0.242641			0.0339765
$52$	−3.82843	+	13.2621i	−0.530907	+	1.83912i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	−6.82843	−	11.8272i	−0.929231	−	1.60948i
$55$	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
$59$	−0.878680	+	1.52192i	−0.114394	+	0.198137i	−0.917537	−	0.397649i	$-0.869826\pi$
$59$	−0.878680	+	1.52192i	−0.114394	+	0.198137i	0.803143	+	0.595786i	$0.203159\pi$
$60$	−20.7279			−2.67596
$61$	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
$65$	−13.3995	+	3.31552i	−1.66200	+	0.411239i
$66$	−11.6569			−1.43486
$67$	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	$0.749887\pi$
$68$	−0.328427	−	0.568852i	−0.0398276	−	0.0689835i
$69$	−1.00000	+	1.73205i	−0.120386	+	0.208514i
$70$		0			0
$71$	0.171573	−	0.297173i	0.0203620	−	0.0352679i	−0.855665	−	0.517530i	$-0.826851\pi$
$71$	0.171573	−	0.297173i	0.0203620	−	0.0352679i	0.876027	+	0.482262i	$0.160185\pi$
$72$	−2.20711	+	3.82282i	−0.260110	+	0.450524i
$73$	−0.656854			−0.0768790			−0.0384395	−	0.999261i	$-0.512239\pi$
$73$	−0.656854			−0.0768790			−0.0384395	+	0.999261i	$0.512239\pi$
$74$	9.03553	−	15.6500i	1.05036	−	1.81928i
$75$	−6.82843	−	11.8272i	−0.788479	−	1.36569i
$76$	11.4853	+	19.8931i	1.31745	+	2.28189i
$77$		0			0
$78$	3.41421	−	11.8272i	0.386584	−	1.33916i
$79$	10.2426			1.15239			0.576194	−	0.817313i	$-0.304537\pi$
$79$	10.2426			1.15239			0.576194	+	0.817313i	$0.304537\pi$
$80$	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
$86$	−1.41421			−0.152499
$87$	−6.94975	+	12.0373i	−0.745091	+	1.29054i
$88$	7.53553	+	13.0519i	0.803291	+	1.39134i
$89$	−3.65685	−	6.33386i	−0.387626	−	0.671388i	0.604504	−	0.796602i	$-0.293371\pi$
$89$	−3.65685	−	6.33386i	−0.387626	−	0.671388i	−0.992130	+	0.125215i	$0.960038\pi$
$90$	−9.24264			−0.974260
$91$		0			0
$92$	5.41421			0.564471
$93$	3.82843	+	6.63103i	0.396989	+	0.687606i
$94$	−9.24264	−	16.0087i	−0.953306	−	1.65117i
$95$	−11.4853	+	19.8931i	−1.17837	+	2.04099i
$96$	2.24264			0.228889
$97$	−2.58579	+	4.47871i	−0.262547	+	0.454744i	−0.966918	−	0.255087i	$-0.917896\pi$
$97$	−2.58579	+	4.47871i	−0.262547	+	0.454744i	0.704371	+	0.709832i	$0.251229\pi$
$98$		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
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	−15.4497	+	3.82282i	−1.51497	+	0.374858i
$105$		0			0
$106$	−3.62132	−	6.27231i	−0.351734	−	0.609221i
$107$	2.65685	+	4.60181i	0.256848	+	0.444873i	0.965396	−	0.260789i	$-0.0839828\pi$
$107$	2.65685	+	4.60181i	0.256848	+	0.444873i	−0.708548	+	0.705663i	$0.750649\pi$
$108$	10.8284	−	18.7554i	1.04197	−	1.80474i
$109$	−2.34315			−0.224433			−0.112216	−	0.993684i	$-0.535795\pi$
$109$	−2.34315			−0.224433			−0.112216	+	0.993684i	$0.535795\pi$
$110$	−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	−0.806468	−	0.591278i	$-0.798624\pi$
$113$	1.15685	−	2.00373i	0.108828	−	0.188495i	0.915296	+	0.402783i	$0.131957\pi$
$114$	−10.2426	−	17.7408i	−0.959311	−	1.66158i
$115$	2.70711	+	4.68885i	0.252439	+	0.437237i
$116$	37.6274			3.49362
$117$	1.00000	−	3.46410i	0.0924500	−	0.320256i
$118$	−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
$122$	23.7279			2.14823
$123$	4.12132	−	7.13834i	0.371607	−	0.643642i
$124$	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	0.995241	−	0.0974468i	$-0.0310676\pi$
$127$	4.65685	+	8.06591i	0.413229	+	0.715734i	−0.582012	+	0.813180i	$0.697734\pi$
$128$	−10.2782	−	17.8023i	−0.908471	−	1.57352i
$129$	0.828427			0.0729389
$130$	−23.1066	−	24.0131i	−2.02658	−	2.10609i
$131$	1.31371			0.114779			0.0573896	−	0.998352i	$-0.481722\pi$
$131$	1.31371			0.114779			0.0573896	+	0.998352i	$0.481722\pi$
$132$	−9.24264	−	16.0087i	−0.804469	−	1.39338i
$133$		0			0
$134$	−5.12132	+	8.87039i	−0.442415	+	0.766285i
$135$	21.6569			1.86393
$136$	0.378680	−	0.655892i	0.0324715	−	0.0562423i
$137$	2.91421	−	5.04757i	0.248978	−	0.431243i	−0.714264	−	0.699876i	$-0.753239\pi$
$137$	2.91421	−	5.04757i	0.248978	−	0.431243i	0.963243	+	0.268633i	$0.0865720\pi$
$138$	−4.82843			−0.411023
$139$	3.94975	−	6.84116i	0.335013	−	0.580260i	−0.648474	−	0.761237i	$-0.724593\pi$
$139$	3.94975	−	6.84116i	0.335013	−	0.580260i	0.983487	+	0.180977i	$0.0579259\pi$
$140$		0			0
$141$	5.41421	+	9.37769i	0.455959	+	0.789744i
$142$	0.828427			0.0695201
$143$	−8.53553	−	8.87039i	−0.713777	−	0.741779i
$144$	−3.00000			−0.250000
$145$	18.8137	+	32.5863i	1.56239	+	2.70614i
$146$	−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	$0.205881\pi$
$150$	16.4853	−	28.5533i	1.34602	−	2.33137i
$151$	−18.9706			−1.54380			−0.771901	−	0.635742i	$-0.780694\pi$
$151$	−18.9706			−1.54380			−0.771901	+	0.635742i	$0.780694\pi$
$152$	−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
$156$	18.9497	−	4.68885i	1.51719	−	0.375408i
$157$	11.4853			0.916625			0.458313	−	0.888791i	$-0.348454\pi$
$157$	11.4853			0.916625			0.458313	+	0.888791i	$0.348454\pi$
$158$	12.3640	+	21.4150i	0.983624	+	1.70369i
$159$	2.12132	+	3.67423i	0.168232	+	0.291386i
$160$	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	$0.960372\pi$
$164$	−22.3137			−1.74241
$165$	9.24264	−	16.0087i	0.719539	−	1.24628i
$166$	15.7782	+	27.3286i	1.22462	+	2.12111i
$167$	−9.36396	−	16.2189i	−0.724605	−	1.25505i	−0.959136	−	0.282944i	$-0.908689\pi$
$167$	−9.36396	−	16.2189i	−0.724605	−	1.25505i	0.234531	−	0.972109i	$-0.424644\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	1.58579			0.121624
$171$	−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
$177$	2.48528			0.186805
$178$	8.82843	−	15.2913i	0.661719	−	1.14613i
$179$	−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	$0.901138\pi$
$180$	−7.32843	−	12.6932i	−0.546229	−	0.946096i
$181$	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
$184$	3.12132	+	5.40629i	0.230107	+	0.398557i
$185$	14.3284	+	24.8176i	1.05345	+	1.82462i
$186$	−9.24264	+	16.0087i	−0.677703	+	1.17382i
$187$	0.585786			0.0428369
$188$	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	$0.558080\pi$
$194$	−12.4853			−0.896391
$195$	13.5355	+	14.0665i	0.969300	+	1.00733i
$196$		0			0
$197$	−4.58579	−	7.94282i	−0.326724	−	0.565902i	0.655136	−	0.755511i	$-0.272611\pi$
$197$	−4.58579	−	7.94282i	−0.326724	−	0.565902i	−0.981860	+	0.189609i	$0.939278\pi$
$198$	−4.12132	−	7.13834i	−0.292889	−	0.507299i
$199$	9.48528	−	16.4290i	0.672394	−	1.16462i	−0.304830	−	0.952407i	$-0.598600\pi$
$199$	9.48528	−	16.4290i	0.672394	−	1.16462i	0.977223	−	0.212213i	$-0.0680671\pi$
$200$	−42.6274			−3.01421
$201$	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
$205$	−11.1569	−	19.3242i	−0.779229	−	1.34966i
$206$	−16.8995	−	29.2708i	−1.17744	−	2.03939i
$207$	−1.41421			−0.0982946
$208$	−7.50000	−	7.79423i	−0.520031	−	0.540433i
$209$	−20.4853			−1.41700
$210$		0			0
$211$	0.363961	+	0.630399i	0.0250561	+	0.0433985i	0.878282	−	0.478144i	$-0.158690\pi$
$211$	0.363961	+	0.630399i	0.0250561	+	0.0433985i	−0.853225	+	0.521542i	$0.825357\pi$
$212$	5.74264	−	9.94655i	0.394406	−	0.683132i
$213$	−0.485281			−0.0332509
$214$	−6.41421	+	11.1097i	−0.438467	+	0.759446i
$215$	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
$219$	0.464466	+	0.804479i	0.0313857	+	0.0543616i
$220$	−50.0416			−3.37381
$221$	−0.171573	+	0.594346i	−0.0115412	+	0.0399800i
$222$	−25.5563			−1.71523
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$		0			0
$225$	4.82843	−	8.36308i	0.321895	−	0.557539i
$226$	5.58579			0.371561
$227$	−6.94975	+	12.0373i	−0.461271	+	0.798945i	−0.999025	−	0.0441573i	$-0.985940\pi$
$227$	−6.94975	+	12.0373i	−0.461271	+	0.798945i	0.537754	+	0.843102i	$0.319273\pi$
$228$	16.2426	−	28.1331i	1.07570	−	1.86316i
$229$	−4.48528			−0.296396			−0.148198	−	0.988958i	$-0.547347\pi$
$229$	−4.48528			−0.296396			−0.148198	+	0.988958i	$0.547347\pi$
$230$	−6.53553	+	11.3199i	−0.430940	+	0.746411i
$231$		0			0
$232$	21.6924	+	37.5723i	1.42418	+	2.46674i
$233$	−2.82843			−0.185296			−0.0926482	−	0.995699i	$-0.529533\pi$
$233$	−2.82843			−0.185296			−0.0926482	+	0.995699i	$0.529533\pi$
$234$	8.44975	−	2.09077i	0.552377	−	0.136678i
$235$	29.3137			1.91222
$236$	−3.36396	−	5.82655i	−0.218975	−	0.379276i
$237$	−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
$241$	−0.742641	+	1.28629i	−0.0478377	+	0.0828573i	−0.888953	−	0.457999i	$-0.848566\pi$
$241$	−0.742641	+	1.28629i	−0.0478377	+	0.0828573i	0.841115	+	0.540856i	$0.181900\pi$
$242$	−1.58579			−0.101938
$243$	−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
$247$	6.00000	−	20.7846i	0.381771	−	1.32249i
$248$	23.8995			1.51762
$249$	−9.24264	−	16.0087i	−0.585729	−	1.01451i
$250$	−21.5208	−	37.2751i	−1.36110	−	2.35749i
$251$	−5.48528	+	9.50079i	−0.346228	+	0.599684i	−0.985576	−	0.169233i	$-0.945871\pi$
$251$	−5.48528	+	9.50079i	−0.346228	+	0.599684i	0.639348	+	0.768917i	$0.279204\pi$
$252$		0			0
$253$	−2.41421	+	4.18154i	−0.151780	+	0.262891i
$254$	−11.2426	+	19.4728i	−0.705426	+	1.22183i
$255$	−0.928932			−0.0581720
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$	1.00000	+	1.73205i	0.0622573	+	0.107833i
$259$		0			0
$260$	14.6569	−	50.7728i	0.908980	−	3.14880i
$261$	−9.82843			−0.608364
$262$	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
$268$	−16.2426			−0.992177
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	26.1421	+	45.2795i	1.59096	+	2.75562i
$271$	−3.46447	−	6.00063i	−0.210451	−	0.364512i	0.741405	−	0.671058i	$-0.234160\pi$
$271$	−3.46447	−	6.00063i	−0.210451	−	0.364512i	−0.951856	+	0.306546i	$0.900827\pi$
$272$	0.514719			0.0312094
$273$		0			0
$274$	14.0711			0.850064
$275$	−16.4853	−	28.5533i	−0.994100	−	1.72183i
$276$	−3.82843	−	6.63103i	−0.230444	−	0.399141i
$277$	15.9853	−	27.6873i	0.960462	−	1.66357i	0.239122	−	0.970990i	$-0.423141\pi$
$277$	15.9853	−	27.6873i	0.960462	−	1.66357i	0.721341	−	0.692580i	$-0.243526\pi$
$278$	19.0711			1.14381
$279$	−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
$285$	32.4853			1.92426
$286$	8.24264	−	28.5533i	0.487398	−	1.68839i
$287$		0			0
$288$	0.792893	+	1.37333i	0.0467217	+	0.0809243i
$289$	8.48528	+	14.6969i	0.499134	+	0.864526i
$290$	−45.4203	+	78.6703i	−2.66717	+	4.61968i
$291$	7.31371			0.428737
$292$	1.25736	−	2.17781i	0.0735814	−	0.127447i
$293$	−11.2279	+	19.4473i	−0.655942	+	1.13613i	0.325714	+	0.945468i	$0.394395\pi$
$293$	−11.2279	+	19.4473i	−0.655942	+	1.13613i	−0.981657	+	0.190657i	$0.938938\pi$
$294$		0			0
$295$	3.36396	−	5.82655i	0.195857	−	0.339235i
$296$	16.5208	+	28.6149i	0.960253	+	1.66321i
$297$	9.65685	+	16.7262i	0.560348	+	0.970550i
$298$	−7.24264			−0.419555
$299$	−3.53553	−	3.67423i	−0.204465	−	0.212486i
$300$	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
$304$	−18.0000			−1.03237
$305$	−18.8137	+	32.5863i	−1.07727	+	1.86589i
$306$	−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
$310$	25.0208	+	43.3373i	1.42109	+	2.46139i
$311$	27.0711			1.53506			0.767530	−	0.641013i	$-0.221486\pi$
$311$	27.0711			1.53506			0.767530	+	0.641013i	$0.221486\pi$
$312$	15.6066	+	16.2189i	0.883550	+	0.918212i
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	13.8640	+	24.0131i	0.782389	+	1.35514i
$315$		0			0
$316$	−19.6066	+	33.9596i	−1.10296	+	1.91038i
$317$	21.3431			1.19875			0.599375	−	0.800468i	$-0.295416\pi$
$317$	21.3431			1.19875			0.599375	+	0.800468i	$0.295416\pi$
$318$	−5.12132	+	8.87039i	−0.287189	+	0.497427i
$319$	−16.7782	+	29.0607i	−0.939397	+	1.62708i
$320$	37.6274			2.10344
$321$	3.75736	−	6.50794i	0.209715	−	0.363238i
$322$		0			0
$323$	0.514719	+	0.891519i	0.0286397	+	0.0496054i
$324$	−19.1421			−1.06345
$325$	33.7990	−	8.36308i	1.87483	−	0.463900i
$326$	−37.2132			−2.06105
$327$	1.65685	+	2.86976i	0.0916242	+	0.158698i
$328$	−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	$0.874965\pi$
$332$	−25.0208	+	43.3373i	−1.37320	+	2.37844i
$333$	−7.48528			−0.410191
$334$	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	$0.380284\pi$
$338$	26.5563	+	16.7262i	1.44447	+	0.909783i
$339$	−3.27208			−0.177715
$340$	1.25736	+	2.17781i	0.0681899	+	0.118108i
$341$	9.24264	+	16.0087i	0.500517	+	0.866921i
$342$	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
$346$	43.7990			2.35465
$347$	12.9497	−	22.4296i	0.695179	−	1.20409i	−0.274941	−	0.961461i	$-0.588658\pi$
$347$	12.9497	−	22.4296i	0.695179	−	1.20409i	0.970120	−	0.242624i	$-0.0780082\pi$
$348$	−26.6066	−	46.0840i	−1.42626	−	2.47036i
$349$	−6.65685	−	11.5300i	−0.356333	−	0.617187i	0.631012	−	0.775773i	$-0.282640\pi$
$349$	−6.65685	−	11.5300i	−0.356333	−	0.617187i	−0.987345	+	0.158586i	$0.949307\pi$
$350$		0			0
$351$	−19.7990	+	4.89898i	−1.05679	+	0.261488i
$352$	5.41421			0.288579
$353$	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
$359$	16.9706			0.895672			0.447836	−	0.894116i	$-0.352195\pi$
$359$	16.9706			0.895672			0.447836	+	0.894116i	$0.352195\pi$
$360$	8.44975	−	14.6354i	0.445341	−	0.771353i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	23.1066	+	40.0218i	1.21446	+	2.10350i
$363$	0.928932			0.0487563
$364$		0			0
$365$	2.51472			0.131626
$366$	−16.7782	−	29.0607i	−0.877009	−	1.51902i
$367$	−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	$0.860550\pi$
$368$	−2.12132	+	3.67423i	−0.110581	+	0.191533i
$369$	5.82843			0.303416
$370$	−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
$376$	33.7990			1.74305
$377$	−24.5711	−	25.5350i	−1.26547	−	1.31512i
$378$		0			0
$379$	−4.12132	−	7.13834i	−0.211698	−	0.366672i	0.740548	−	0.672003i	$-0.234566\pi$
$379$	−4.12132	−	7.13834i	−0.211698	−	0.366672i	−0.952246	+	0.305332i	$0.901233\pi$
$380$	−43.9706	−	76.1592i	−2.25564	−	3.90689i
$381$	6.58579	−	11.4069i	0.337400	−	0.584394i
$382$	−18.7279			−0.958204
$383$	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
$387$	0.292893	+	0.507306i	0.0148886	+	0.0257878i
$388$	−9.89949	−	17.1464i	−0.502571	−	0.870478i
$389$	−1.14214			−0.0579086			−0.0289543	−	0.999581i	$-0.509218\pi$
$389$	−1.14214			−0.0579086			−0.0289543	+	0.999581i	$0.509218\pi$
$390$	−13.0711	+	45.2795i	−0.661879	+	2.29282i
$391$	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
$395$	−39.2132			−1.97303
$396$	6.53553	−	11.3199i	0.328423	−	0.568845i
$397$	−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
$401$	15.3995	+	26.6727i	0.769014	+	1.33197i	0.938098	+	0.346370i	$0.112586\pi$
$401$	15.3995	+	26.6727i	0.769014	+	1.33197i	−0.169084	+	0.985602i	$0.554081\pi$
$402$	14.4853			0.722460
$403$	−18.9497	+	4.68885i	−0.943954	+	0.233568i
$404$	−12.7990			−0.636774
$405$	−9.57107	−	16.5776i	−0.475590	−	0.823746i
$406$		0			0
$407$	−12.7782	+	22.1324i	−0.633391	+	1.09706i
$408$	−1.07107			−0.0530258
$409$	5.98528	−	10.3668i	0.295953	−	0.512606i	−0.679253	−	0.733904i	$-0.737696\pi$
$409$	5.98528	−	10.3668i	0.295953	−	0.512606i	0.975206	+	0.221298i	$0.0710294\pi$
$410$	26.9350	−	46.6528i	1.33023	−	2.30402i
$411$	−8.24264			−0.406579
$412$	26.7990	−	46.4172i	1.32029	−	2.28681i
$413$		0			0
$414$	−1.70711	−	2.95680i	−0.0838997	−	0.145319i
$415$	−50.0416			−2.45645
$416$	−1.58579	+	5.49333i	−0.0777496	+	0.269332i
$417$	−11.1716			−0.547074
$418$	−24.7279	−	42.8300i	−1.20948	−	2.09488i
$419$	9.77817	+	16.9363i	0.477695	+	0.827392i	0.999673	−	0.0255668i	$-0.00813904\pi$
$419$	9.77817	+	16.9363i	0.477695	+	0.827392i	−0.521978	+	0.852959i	$0.674806\pi$
$420$		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
$423$	−3.82843	+	6.63103i	−0.186144	+	0.322412i
$424$	13.2426			0.643119
$425$	−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
$429$	−4.82843	+	16.7262i	−0.233119	+	0.807547i
$430$	5.41421			0.261097
$431$	−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	$0.926659\pi$
$432$	8.48528	+	14.6969i	0.408248	+	0.707107i
$433$	0.257359	−	0.445759i	0.0123679	−	0.0214218i	−0.859775	−	0.510673i	$-0.829396\pi$
$433$	0.257359	−	0.445759i	0.0123679	−	0.0214218i	0.872143	+	0.489251i	$0.162730\pi$
$434$		0			0
$435$	26.6066	−	46.0840i	1.27569	−	2.20956i
$436$	4.48528	−	7.76874i	0.214806	−	0.372055i
$437$	−8.48528			−0.405906
$438$	−1.12132	+	1.94218i	−0.0535788	+	0.0928011i
$439$	−13.3640	−	23.1471i	−0.637827	−	1.10475i	−0.985909	−	0.167285i	$-0.946500\pi$
$439$	−13.3640	−	23.1471i	−0.637827	−	1.10475i	0.348082	−	0.937464i	$-0.386833\pi$
$440$	−28.8492	−	49.9684i	−1.37533	−	2.38215i
$441$		0			0
$442$	−1.44975	+	0.358719i	−0.0689575	+	0.0170625i
$443$	14.3431			0.681463			0.340732	−	0.940161i	$-0.389325\pi$
$443$	14.3431			0.681463			0.340732	+	0.940161i	$0.389325\pi$
$444$	−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	−0.988951	−	0.148244i	$-0.952638\pi$
$449$	−7.75736	+	13.4361i	−0.366092	+	0.634091i	0.622858	+	0.782335i	$0.285971\pi$
$450$	23.3137			1.09902
$451$	9.94975	−	17.2335i	0.468515	−	0.811492i
$452$	4.42893	+	7.67114i	0.208319	+	0.360820i
$453$	13.4142	+	23.2341i	0.630255	+	1.09163i
$454$	−33.5563			−1.57488
$455$		0			0
$456$	37.4558			1.75403
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	0.994910	+	0.100771i	$0.0321310\pi$
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	−0.410184	+	0.912003i	$0.634536\pi$
$458$	−5.41421	−	9.37769i	−0.252990	−	0.438191i
$459$	0.485281	−	0.840532i	0.0226510	−	0.0392327i
$460$	−20.7279			−0.966444
$461$	6.32843	−	10.9612i	0.294744	−	0.510512i	−0.680181	−	0.733044i	$-0.738099\pi$
$461$	6.32843	−	10.9612i	0.294744	−	0.510512i	0.974925	+	0.222532i	$0.0714322\pi$
$462$		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
$467$	−8.58579			−0.397303			−0.198651	−	0.980070i	$-0.563656\pi$
$467$	−8.58579			−0.397303			−0.198651	+	0.980070i	$0.563656\pi$
$468$	9.57107	+	9.94655i	0.442423	+	0.459779i
$469$		0			0
$470$	35.3848	+	61.2882i	1.63218	+	2.82702i
$471$	−8.12132	−	14.0665i	−0.374211	−	0.648152i
$472$	3.87868	−	6.71807i	0.178531	−	0.309224i
$473$	2.00000			0.0919601
$474$	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
$478$	−14.9497	−	25.8937i	−0.683786	−	1.18435i
$479$	−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	$-0.507074\pi$
$480$	−8.58579			−0.391886
$481$	−18.7132	−	19.4473i	−0.853249	−	0.886722i
$482$	−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
$486$	−23.8995			−1.08410
$487$	−10.4853	+	18.1610i	−0.475133	+	0.822955i	−0.999594	−	0.0284792i	$-0.990934\pi$
$487$	−10.4853	+	18.1610i	−0.475133	+	0.822955i	0.524461	+	0.851435i	$0.324267\pi$
$488$	−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	−0.921662	−	0.387993i	$-0.873169\pi$
$491$	−17.6569	−	30.5826i	−0.796843	−	1.38017i	0.124820	−	0.992179i	$-0.460165\pi$
$492$	15.7782	+	27.3286i	0.711335	+	1.23207i
$493$	1.68629			0.0759467
$494$	50.6985	−	12.5446i	2.28103	−	0.564409i
$495$	13.0711			0.587501
$496$	8.12132	+	14.0665i	0.364658	+	0.631606i
$497$		0			0
$498$	22.3137	−	38.6485i	0.999901	−	1.73188i
$499$	−28.0416			−1.25532			−0.627658	−	0.778489i	$-0.715986\pi$
$499$	−28.0416			−1.25532			−0.627658	+	0.778489i	$0.715986\pi$
$500$	34.1274	−	59.1104i	1.52622	−	2.64350i
$501$	−13.2426	+	22.9369i	−0.591638	+	1.02475i
$502$	−26.4853			−1.18210
$503$	−16.7782	+	29.0607i	−0.748102	+	1.29575i	0.200630	+	0.979667i	$0.435701\pi$
$503$	−16.7782	+	29.0607i	−0.748102	+	1.29575i	−0.948731	+	0.316083i	$0.897632\pi$
$504$		0			0
$505$	−6.39949	−	11.0843i	−0.284774	−	0.493243i
$506$	−11.6569			−0.518210
$507$	−15.5563	−	9.79796i	−0.690882	−	0.435143i
$508$	−35.6569			−1.58202
$509$	−3.32843	−	5.76500i	−0.147530	−	0.255529i	0.782784	−	0.622293i	$-0.213799\pi$
$509$	−3.32843	−	5.76500i	−0.147530	−	0.255529i	−0.930314	+	0.366764i	$0.880466\pi$
$510$	−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
$514$	−18.1066	+	31.3616i	−0.798648	+	1.38330i
$515$	53.5980			2.36181
$516$	−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
$520$	59.1482	−	14.6354i	2.59382	−	0.641804i
$521$	13.3431			0.584574			0.292287	−	0.956331i	$-0.405584\pi$
$521$	13.3431			0.584574			0.292287	+	0.956331i	$0.405584\pi$
$522$	−11.8640	−	20.5490i	−0.519271	−	0.899405i
$523$	8.48528	+	14.6969i	0.371035	+	0.642652i	0.989725	−	0.142983i	$-0.0456695\pi$
$523$	8.48528	+	14.6969i	0.371035	+	0.642652i	−0.618690	+	0.785635i	$0.712336\pi$
$524$	−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
$528$	14.4853			0.630391
$529$	10.5000	−	18.1865i	0.456522	−	0.790719i
$530$	13.8640	+	24.0131i	0.602212	+	1.04306i
$531$	0.878680	+	1.52192i	0.0381314	+	0.0660456i
$532$		0			0
$533$	14.5711	+	15.1427i	0.631143	+	0.655903i
$534$	−24.9706			−1.08058
$535$	−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
$541$	5.48528			0.235831			0.117915	−	0.993024i	$-0.462379\pi$
$541$	5.48528			0.235831			0.117915	+	0.993024i	$0.462379\pi$
$542$	8.36396	−	14.4868i	0.359263	−	0.622262i
$543$	−13.5355	−	23.4442i	−0.580865	−	1.00609i
$544$	−0.136039	−	0.235626i	−0.00583262	−	0.0101024i
$545$	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	$0.395579\pi$
$548$	11.1569	+	19.3242i	0.476597	+	0.825491i
$549$	−4.91421	−	8.51167i	−0.209734	−	0.363269i
$550$	39.7990	−	68.9339i	1.69703	−	2.93935i
$551$	−58.9706			−2.51223
$552$	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	$0.763216\pi$
$558$	−13.0711			−0.553342
$559$	−0.585786	+	2.02922i	−0.0247761	+	0.0858270i
$560$		0			0
$561$	−0.414214	−	0.717439i	−0.0174881	−	0.0302903i
$562$	−0.621320	−	1.07616i	−0.0262088	−	0.0453950i
$563$	9.94975	−	17.2335i	0.419332	−	0.726304i	−0.576541	−	0.817069i	$-0.695598\pi$
$563$	9.94975	−	17.2335i	0.419332	−	0.726304i	0.995872	+	0.0907645i	$0.0289310\pi$
$564$	−41.4558			−1.74561
$565$	−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
$569$	−6.58579	−	11.4069i	−0.276091	−	0.478203i	0.694319	−	0.719667i	$-0.255706\pi$
$569$	−6.58579	−	11.4069i	−0.276091	−	0.478203i	−0.970410	+	0.241464i	$0.922372\pi$
$570$	39.2132	+	67.9193i	1.64246	+	2.84482i
$571$	−4.97056			−0.208012			−0.104006	−	0.994577i	$-0.533166\pi$
$571$	−4.97056			−0.208012			−0.104006	+	0.994577i	$0.533166\pi$
$572$	45.7487	−	11.3199i	1.91285	−	0.473308i
$573$	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
$577$	36.3137			1.51176			0.755880	−	0.654710i	$-0.227209\pi$
$577$	36.3137			1.51176			0.755880	+	0.654710i	$0.227209\pi$
$578$	−20.4853	+	35.4815i	−0.852075	+	1.47584i
$579$	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
$583$	5.12132	+	8.87039i	0.212103	+	0.367374i
$584$	2.89949			0.119982
$585$	−3.82843	+	13.2621i	−0.158286	+	0.548319i
$586$	−54.2132			−2.23953
$587$	−9.17157	−	15.8856i	−0.378551	−	0.655670i	0.612300	−	0.790625i	$-0.290244\pi$
$587$	−9.17157	−	15.8856i	−0.378551	−	0.655670i	−0.990852	+	0.134955i	$0.956911\pi$
$588$		0			0
$589$	−16.2426	+	28.1331i	−0.669266	+	1.15920i
$590$	16.2426			0.668699
$591$	−6.48528	+	11.2328i	−0.266769	+	0.462057i
$592$	−11.2279	+	19.4473i	−0.461465	+	0.799280i
$593$	31.2843			1.28469			0.642346	−	0.766415i	$-0.277961\pi$
$593$	31.2843			1.28469			0.642346	+	0.766415i	$0.277961\pi$
$594$	−23.3137	+	40.3805i	−0.956573	+	1.65683i
$595$		0			0
$596$	−5.74264	−	9.94655i	−0.235228	−	0.407426i
$597$	−26.8284			−1.09801
$598$	3.41421	−	11.8272i	0.139618	−	0.483649i
$599$	39.6569			1.62034			0.810168	−	0.586198i	$-0.199376\pi$
$599$	39.6569			1.62034			0.810168	+	0.586198i	$0.199376\pi$
$600$	30.1421	+	52.2077i	1.23055	+	2.13137i
$601$	−18.4706	−	31.9920i	−0.753430	−	1.30498i	−0.946151	−	0.323725i	$-0.895065\pi$
$601$	−18.4706	−	31.9920i	−0.753430	−	1.30498i	0.192721	−	0.981254i	$-0.438269\pi$
$602$		0			0
$603$	4.24264			0.172774
$604$	36.3137	−	62.8972i	1.47758	−	2.55925i
$605$	1.25736	−	2.17781i	0.0511189	−	0.0885406i
$606$	11.4142			0.463671
$607$	−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
$611$	−26.7990	+	6.63103i	−1.08417	+	0.268263i
$612$	−0.656854			−0.0265518
$613$	−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	$-0.333631\pi$
$614$	8.77817	+	15.2042i	0.354258	+	0.613593i
$615$	−15.7782	+	27.3286i	−0.636237	+	1.10200i
$616$		0			0
$617$	1.42893	−	2.47498i	0.0575266	−	0.0996391i	−0.835828	−	0.548992i	$-0.815012\pi$
$617$	1.42893	−	2.47498i	0.0575266	−	0.0996391i	0.893355	+	0.449352i	$0.148345\pi$
$618$	−23.8995	+	41.3951i	−0.961379	+	1.66516i
$619$	−10.4437			−0.419766			−0.209883	−	0.977727i	$-0.567308\pi$
$619$	−10.4437			−0.419766			−0.209883	+	0.977727i	$0.567308\pi$
$620$	−39.6777	+	68.7237i	−1.59349	+	2.76001i
$621$	4.00000	+	6.92820i	0.160514	+	0.278019i
$622$	32.6777	+	56.5994i	1.31026	+	2.26943i
$623$		0			0
$624$	−4.24264	+	14.6969i	−0.169842	+	0.588348i
$625$	19.9706			0.798823
$626$	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	−0.342240	−	0.939613i	$-0.611186\pi$
$631$	16.1421	−	27.9590i	0.642608	−	1.11303i	0.984848	−	0.173418i	$-0.0554810\pi$
$632$	−45.2132			−1.79848
$633$	0.514719	−	0.891519i	0.0204582	−	0.0354347i
$634$	25.7635	+	44.6236i	1.02320	+	1.77223i
$635$	−17.8284	−	30.8797i	−0.707500	−	1.22543i
$636$	−16.2426			−0.644063
$637$		0			0
$638$	−81.0122			−3.20730
$639$	−0.171573	−	0.297173i	−0.00678732	−	0.0117560i
$640$	39.3492	+	68.1549i	1.55542	+	2.69406i
$641$	−12.3995	+	21.4766i	−0.489751	+	0.848273i	−0.999930	−	0.0117948i	$-0.996246\pi$
$641$	−12.3995	+	21.4766i	−0.489751	+	0.848273i	0.510180	+	0.860068i	$0.329579\pi$
$642$	18.1421			0.716013
$643$	24.4853	−	42.4098i	0.965605	−	1.67248i	0.257625	−	0.966245i	$-0.417060\pi$
$643$	24.4853	−	42.4098i	0.965605	−	1.67248i	0.707980	−	0.706232i	$-0.249607\pi$
$644$		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
$649$	6.00000			0.235521
$650$	58.2843	+	60.5708i	2.28610	+	2.37578i
$651$		0			0
$652$	−29.5061	−	51.1061i	−1.15555	−	2.00147i
$653$	1.07107	+	1.85514i	0.0419141	+	0.0725974i	0.886221	−	0.463262i	$-0.153321\pi$
$653$	1.07107	+	1.85514i	0.0419141	+	0.0725974i	−0.844307	+	0.535859i	$0.819988\pi$
$654$	−4.00000	+	6.92820i	−0.156412	+	0.270914i
$655$	−5.02944			−0.196516
$656$	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	−0.928419	−	0.371535i	$-0.878832\pi$
$659$	−3.65685	+	6.33386i	−0.142451	+	0.246732i	0.785968	+	0.618267i	$0.212165\pi$
$660$	35.3848	+	61.2882i	1.37735	+	2.38564i
$661$	−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	$0.863450\pi$
$662$	−69.6985			−2.70891
$663$	0.849242	−	0.210133i	0.0329818	−	0.00816089i
$664$	−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
$668$	71.6985			2.77410
$669$	1.41421	−	2.44949i	0.0546767	−	0.0947027i
$670$	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	−0.991759	−	0.128120i	$-0.959106\pi$
$673$	−15.7426	−	27.2671i	−0.606834	−	1.05107i	0.384925	−	0.922948i	$-0.374227\pi$
$674$	16.2782	+	28.1946i	0.627012	+	1.08602i
$675$	−54.6274			−2.10261
$676$	−1.91421	+	49.7327i	−0.0736236	+	1.91280i
$677$	6.34315			0.243787			0.121893	−	0.992543i	$-0.461103\pi$
$677$	6.34315			0.243787			0.121893	+	0.992543i	$0.461103\pi$
$678$	−3.94975	−	6.84116i	−0.151689	−	0.262733i
$679$		0			0
$680$	−1.44975	+	2.51104i	−0.0555953	+	0.0962938i
$681$	19.6569			0.753252
$682$	−22.3137	+	38.6485i	−0.854436	+	1.47993i
$683$	8.65685	−	14.9941i	0.331245	−	0.573734i	−0.651511	−	0.758639i	$-0.725865\pi$
$683$	8.65685	−	14.9941i	0.331245	−	0.573734i	0.982756	+	0.184905i	$0.0591979\pi$
$684$	22.9706			0.878301
$685$	−11.1569	+	19.3242i	−0.426281	+	0.738341i
$686$		0			0
$687$	3.17157	+	5.49333i	0.121003	+	0.209583i
$688$	1.75736			0.0669987
$689$	−10.5000	+	2.59808i	−0.400018	+	0.0989788i
$690$	18.4853			0.703723
$691$	−18.9706	−	32.8580i	−0.721674	−	1.24998i	−0.960328	−	0.278872i	$-0.910040\pi$
$691$	−18.9706	−	32.8580i	−0.721674	−	1.24998i	0.238654	−	0.971105i	$-0.423294\pi$
$692$	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
$696$	30.6777	−	53.1353i	1.16283	−	2.01409i
$697$	−1.00000			−0.0378777
$698$	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	$0.207028\pi$
$702$	−34.1421	−	35.4815i	−1.28861	−	1.33916i
$703$	−44.9117			−1.69388
$704$	16.7782	+	29.0607i	0.632351	+	1.09526i
$705$	−20.7279	−	35.9018i	−0.780659	−	1.35214i
$706$	−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	$-0.00694871\pi$
$710$	−3.17157			−0.119027
$711$	5.12132	−	8.87039i	0.192065	−	0.332666i
$712$	16.1421	+	27.9590i	0.604952	+	1.04781i
$713$	3.82843	+	6.63103i	0.143376	+	0.248334i
$714$		0			0
$715$	32.6777	+	33.9596i	1.22208	+	1.27002i
$716$	21.6569			0.809355
$717$	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
$723$	2.10051			0.0781186
$724$	−36.6421	+	63.4660i	−1.36179	+	2.35870i
$725$	−47.4558	−	82.1959i	−1.76247	−	3.05268i
$726$	1.12132	+	1.94218i	0.0416161	+	0.0720812i
$727$	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
$730$	3.03553	+	5.25770i	0.112350	+	0.194596i
$731$	−0.0502525	−	0.0870399i	−0.00185866	−	0.00321929i
$732$	26.6066	−	46.0840i	0.983408	−	1.70331i
$733$	21.0000			0.775653			0.387826	−	0.921732i	$-0.373226\pi$
$733$	21.0000			0.775653			0.387826	+	0.921732i	$0.373226\pi$
$734$	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	$-0.399246\pi$
$740$	−109.711			−4.03304
$741$	−29.6985	+	7.34847i	−1.09100	+	0.269953i
$742$		0			0
$743$	23.7990	+	41.2211i	0.873100	+	1.51225i	0.858773	+	0.512357i	$0.171227\pi$
$743$	23.7990	+	41.2211i	0.873100	+	1.51225i	0.0143275	+	0.999897i	$0.495439\pi$
$744$	−16.8995	−	29.2708i	−0.619566	−	1.07312i
$745$	5.74264	−	9.94655i	0.210394	−	0.364413i
$746$	59.0416			2.16167
$747$	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
$751$	−6.77817	−	11.7401i	−0.247339	−	0.428404i	0.715448	−	0.698666i	$-0.246223\pi$
$751$	−6.77817	−	11.7401i	−0.247339	−	0.428404i	−0.962787	+	0.270263i	$0.912889\pi$
$752$	11.4853	+	19.8931i	0.418825	+	0.725426i
$753$	15.5147			0.565388
$754$	23.7279	−	82.1959i	0.864120	−	2.99340i
$755$	72.6274			2.64318
$756$		0			0
$757$	10.7279	+	18.5813i	0.389913	+	0.675349i	0.992437	−	0.122751i	$-0.0391718\pi$
$757$	10.7279	+	18.5813i	0.389913	+	0.675349i	−0.602525	+	0.798100i	$0.705838\pi$
$758$	9.94975	−	17.2335i	0.361391	−	0.625948i
$759$	6.82843			0.247856
$760$	50.6985	−	87.8124i	1.83903	−	3.18529i
$761$	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
$765$	−0.328427	−	0.568852i	−0.0118743	−	0.0205669i
$766$	33.8995			1.22484
$767$	−1.75736	+	6.08767i	−0.0634546	+	0.219813i
$768$	−42.3848			−1.52943
$769$	0.727922	+	1.26080i	0.0262495	+	0.0454655i	0.878852	−	0.477095i	$-0.158310\pi$
$769$	0.727922	+	1.26080i	0.0262495	+	0.0454655i	−0.852602	+	0.522560i	$0.824977\pi$
$770$		0			0
$771$	10.6066	−	18.3712i	0.381987	−	0.661622i
$772$	−80.9411			−2.91313
$773$	8.82843	−	15.2913i	0.317536	−	0.549989i	−0.662437	−	0.749118i	$-0.730478\pi$
$773$	8.82843	−	15.2913i	0.317536	−	0.549989i	0.979973	+	0.199128i	$0.0638111\pi$
$774$	−0.707107	+	1.22474i	−0.0254164	+	0.0440225i
$775$	−52.2843			−1.87811
$776$	11.4142	−	19.7700i	0.409746	−	0.709702i
$777$		0			0
$778$	−1.37868	−	2.38794i	−0.0494281	−	0.0856119i
$779$	34.9706			1.25295
$780$	−72.5477	+	17.9509i	−2.59763	+	0.642746i
$781$	−1.17157			−0.0419222
$782$	0.292893	+	0.507306i	0.0104738	+	0.0181412i
$783$	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
$787$	2.94975	−	5.10911i	0.105147	−	0.182120i	−0.808651	−	0.588288i	$-0.799802\pi$
$787$	2.94975	−	5.10911i	0.105147	−	0.182120i	0.913798	+	0.406168i	$0.133135\pi$
$788$	35.1127			1.25084
$789$	−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
$793$	9.82843	−	34.0467i	0.349018	−	1.20903i
$794$	−93.2548			−3.30949
$795$	−8.12132	−	14.0665i	−0.288034	−	0.498889i
$796$	36.3137	+	62.8972i	1.28711	+	2.22933i
$797$	5.07107	−	8.78335i	0.179626	−	0.311122i	−0.762126	−	0.647429i	$-0.775844\pi$
$797$	5.07107	−	8.78335i	0.179626	−	0.311122i	0.941753	+	0.336306i	$0.109178\pi$
$798$		0			0
$799$	0.656854	−	1.13770i	0.0232378	−	0.0402491i
$800$	−7.65685	+	13.2621i	−0.270711	+	0.468885i
$801$	−7.31371			−0.258417
$802$	−37.1777	+	64.3936i	−1.31279	+	2.27382i
$803$	1.12132	+	1.94218i	0.0395705	+	0.0685382i
$804$	11.4853	+	19.8931i	0.405055	+	0.701575i
$805$		0			0
$806$	−32.6777	−	33.9596i	−1.15102	−	1.19618i
$807$	25.4558			0.896088
$808$	−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
$814$	−61.6985			−2.16253
$815$	29.5061	−	51.1061i	1.03355	−	1.79017i
$816$	−0.363961	−	0.630399i	−0.0127412	−	0.0220684i
$817$	1.75736	+	3.04384i	0.0614822	+	0.106490i
$818$	28.8995			1.01045
$819$		0			0
$820$	85.4264			2.98322
$821$	−13.9706	−	24.1977i	−0.487576	−	0.844506i	0.512322	−	0.858793i	$-0.328785\pi$
$821$	−13.9706	−	24.1977i	−0.487576	−	0.844506i	−0.999898	+	0.0142871i	$0.995452\pi$
$822$	−9.94975	−	17.2335i	−0.347037	−	0.601086i
$823$	1.65685	−	2.86976i	0.0577543	−	0.100033i	−0.835703	−	0.549182i	$-0.814939\pi$
$823$	1.65685	−	2.86976i	0.0577543	−	0.100033i	0.893457	+	0.449149i	$0.148273\pi$
$824$	61.7990			2.15287
$825$	−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
$831$	−45.2132			−1.56843
$832$	−34.3995	+	8.51167i	−1.19259	+	0.295089i
$833$		0			0
$834$	−13.4853	−	23.3572i	−0.466957	−	0.808793i
$835$	35.8492	+	62.0927i	1.24061	+	2.14881i
$836$	39.2132	−	67.9193i	1.35622	−	2.34904i
$837$	30.6274			1.05864
$838$	−23.6066	+	40.8878i	−0.815477	+	1.41245i
$839$	18.7990	−	32.5608i	0.649013	−	1.12412i	−0.334346	−	0.942450i	$-0.608515\pi$
$839$	18.7990	−	32.5608i	0.649013	−	1.12412i	0.983359	−	0.181673i	$-0.0581514\pi$
$840$		0			0
$841$	−33.7990	+	58.5416i	−1.16548	+	2.01867i
$842$	5.44975	+	9.43924i	0.187811	+	0.325298i
$843$	0.363961	+	0.630399i	0.0125355	+	0.0217121i
$844$	−2.78680			−0.0959255
$845$	−44.0269	+	23.2086i	−1.51457	+	0.798400i
$846$	−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
$850$	−4.00000			−0.137199
$851$	−5.29289	+	9.16756i	−0.181438	+	0.314260i
$852$	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
$856$	−11.7279	−	20.3134i	−0.400852	−	0.694296i
$857$	−40.7990			−1.39367			−0.696833	−	0.717233i	$-0.745408\pi$
$857$	−40.7990			−1.39367			−0.696833	+	0.717233i	$0.745408\pi$
$858$	−40.7990	+	10.0951i	−1.39285	+	0.344642i
$859$	27.0711			0.923653			0.461826	−	0.886970i	$-0.347194\pi$
$859$	27.0711			0.923653			0.461826	+	0.886970i	$0.347194\pi$
$860$	4.29289	+	7.43551i	0.146386	+	0.253549i
$861$		0			0
$862$	14.4853	−	25.0892i	0.493371	−	0.854543i
$863$	56.1838			1.91252			0.956259	−	0.292522i	$-0.0944944\pi$
$863$	56.1838			1.91252			0.956259	+	0.292522i	$0.0944944\pi$
$864$	4.48528	−	7.76874i	0.152592	−	0.264298i
$865$	−34.7279	+	60.1505i	−1.18078	+	2.04518i
$866$	1.24264			0.0422266
$867$	12.0000	−	20.7846i	0.407541	−	0.705882i
$868$		0			0
$869$	−17.4853	−	30.2854i	−0.593148	−	1.02736i
$870$	128.468			4.35547
$871$	10.6066	+	11.0227i	0.359391	+	0.373490i
$872$	10.3431			0.350263
$873$	2.58579	+	4.47871i	0.0875156	+	0.151581i
$874$	−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	$0.259333\pi$
$878$	32.2635	−	55.8819i	1.08884	−	1.88592i
$879$	31.7574			1.07115
$880$	19.6066	−	33.9596i	0.660938	−	1.14478i
$881$	−23.2279	−	40.2319i	−0.782569	−	1.35545i	−0.930441	−	0.366442i	$-0.880576\pi$
$881$	−23.2279	−	40.2319i	−0.782569	−	1.35545i	0.147872	−	0.989006i	$-0.452758\pi$
$882$		0			0
$883$	7.95837			0.267820			0.133910	−	0.990993i	$-0.457247\pi$
$883$	7.95837			0.267820			0.133910	+	0.990993i	$0.457247\pi$
$884$	−1.64214	−	1.70656i	−0.0552310	−	0.0573977i
$885$	−9.51472			−0.319834
$886$	17.3137	+	29.9882i	0.581665	+	1.00747i
$887$	5.31371	+	9.20361i	0.178417	+	0.309027i	0.941338	−	0.337464i	$-0.109569\pi$
$887$	5.31371	+	9.20361i	0.178417	+	0.309027i	−0.762922	+	0.646491i	$0.776236\pi$
$888$	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
$892$	−7.65685			−0.256370
$893$	−22.9706	+	39.7862i	−0.768681	+	1.33139i
$894$	5.12132	+	8.87039i	0.171283	+	0.296670i
$895$	10.8284	+	18.7554i	0.361954	+	0.626923i
$896$		0			0
$897$	−2.00000	+	6.92820i	−0.0667781	+	0.231326i
$898$	−37.4558			−1.24992
$899$	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
$905$	−73.2843			−2.43605
$906$	−32.3848	+	56.0921i	−1.07591	+	1.86353i
$907$	−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	$0.933972\pi$
$908$	−26.6066	−	46.0840i	−0.882971	−	1.52935i
$909$	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	$0.598278\pi$
$912$	12.7279	+	22.0454i	0.421464	+	0.729996i
$913$	−22.3137	−	38.6485i	−0.738476	−	1.27908i
$914$	−30.1777	+	52.2693i	−0.998189	+	1.72891i
$915$	53.2132			1.75917
$916$	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
$922$	30.5563			1.00632
$923$	0.343146	−	1.18869i	0.0112948	−	0.0391263i
$924$		0			0
$925$	−36.1421	−	62.6000i	−1.18835	−	2.05828i
$926$	−22.6066	−	39.1558i	−0.742899	−	1.28674i
$927$	−7.00000	+	12.1244i	−0.229910	+	0.398216i
$928$	15.5858			0.511629
$929$	−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
$933$	−19.1421	−	33.1552i	−0.626685	−	1.08545i
$934$	−10.3640	−	17.9509i	−0.339119	−	0.587372i
$935$	−2.24264			−0.0733422
$936$	−4.41421	+	15.2913i	−0.144283	+	0.499811i
$937$	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
$941$	−19.0294			−0.620342			−0.310171	−	0.950681i	$-0.600386\pi$
$941$	−19.0294			−0.620342			−0.310171	+	0.950681i	$0.600386\pi$
$942$	19.6066	−	33.9596i	0.638818	−	1.10646i
$943$	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
$947$	−9.29289	−	16.0958i	−0.301978	−	0.523042i	0.674606	−	0.738178i	$-0.264314\pi$
$947$	−9.29289	−	16.0958i	−0.301978	−	0.523042i	−0.976584	+	0.215136i	$0.930980\pi$
$948$	55.4558			1.80112
$949$	−2.29899	+	0.568852i	−0.0746284	+	0.0184657i
$950$	139.882			4.53838
$951$	−15.0919	−	26.1399i	−0.489388	−	0.847645i
$952$		0			0
$953$	19.3137	−	33.4523i	0.625632	−	1.08363i	−0.362786	−	0.931873i	$-0.618174\pi$
$953$	19.3137	−	33.4523i	0.625632	−	1.08363i	0.988418	−	0.151755i	$-0.0484923\pi$
$954$	−7.24264			−0.234489
$955$	14.8492	−	25.7196i	0.480510	−	0.832268i
$956$	23.7071	−	41.0619i	0.766743	−	1.32804i
$957$	47.4558			1.53403
$958$	46.3345	−	80.2537i	1.49700	−	2.59288i
$959$		0			0
$960$	−26.6066	−	46.0840i	−0.858724	−	1.48735i
$961$	−1.68629			−0.0543965
$962$	18.0711	−	62.6000i	0.582635	−	2.01831i
$963$	5.31371			0.171232
$964$	−2.84315	−	4.92447i	−0.0915716	−	0.158607i
$965$	−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
$969$	0.727922	−	1.26080i	0.0233842	−	0.0405027i
$970$	47.7990			1.53473
$971$	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
$975$	−34.1421	−	35.4815i	−1.09342	−	1.13632i
$976$	−29.4853			−0.943801
$977$	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	$0.549875\pi$
$978$	26.3137	+	45.5767i	0.841420	+	1.45738i
$979$	−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
$983$	42.0000			1.33959			0.669796	−	0.742545i	$-0.266382\pi$
$983$	42.0000			1.33959			0.669796	+	0.742545i	$0.266382\pi$
$984$	−18.1924	+	31.5101i	−0.579952	+	1.00451i
$985$	17.5563	+	30.4085i	0.559392	+	0.968895i
$986$	2.03553	+	3.52565i	0.0648246	+	0.112280i
$987$		0			0
$988$	57.4264	+	59.6793i	1.82698	+	1.89865i
$989$	0.828427			0.0263425
$990$	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
$996$	70.7696			2.24242
$997$	−9.98528	+	17.2950i	−0.316237	+	0.547739i	−0.979700	−	0.200471i	$-0.935753\pi$
$997$	−9.98528	+	17.2950i	−0.316237	+	0.547739i	0.663463	+	0.748209i	$0.269086\pi$
$998$	−33.8492	−	58.6286i	−1.07148	−	1.85586i
$999$	21.1716	+	36.6702i	0.669839	+	1.16020i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.e.295.2	✓	4	13.9	even	3	inner
637.2.f.e.393.2	yes	4	1.1	even	1	trivial
637.2.f.f.295.2	yes	4	91.48	odd	6
637.2.f.f.393.2	yes	4	7.6	odd	2
637.2.g.f.263.2		4	7.5	odd	6
637.2.g.f.373.2		4	91.87	odd	6
637.2.g.g.263.2		4	7.2	even	3
637.2.g.g.373.2		4	91.74	even	3
637.2.h.b.165.1		4	91.61	odd	6
637.2.h.b.471.1		4	7.3	odd	6
637.2.h.c.165.1		4	91.9	even	3
637.2.h.c.471.1		4	7.4	even	3
8281.2.a.o.1.1		2	13.3	even	3
8281.2.a.p.1.1		2	91.55	odd	6
8281.2.a.x.1.2		2	91.62	odd	6
8281.2.a.y.1.2		2	13.10	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 + 2.09077i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-1.91421 + 3.31552i) q^{4} -3.82843 q^{5} +(1.70711 - 2.95680i) q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.20711 + 2.09077i) q^{2} +(-0.707107 - 1.22474i) q^{3} +(-1.91421 + 3.31552i) q^{4} -3.82843 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} +5.41421 q^{12} +(3.50000 - 0.866025i) q^{13} +(2.70711 + 4.68885i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(-0.0857864 + 0.148586i) q^{17} +2.41421 q^{18} +(3.00000 - 5.19615i) q^{19} +(7.32843 - 12.6932i) q^{20} +(4.12132 - 7.13834i) q^{22} +(-0.707107 - 1.22474i) q^{23} +(3.12132 + 5.40629i) q^{24} +9.65685 q^{25} +(6.03553 + 6.27231i) q^{26} -5.65685 q^{27} +(-4.91421 - 8.51167i) q^{29} +(-6.53553 + 11.3199i) q^{30} -5.41421 q^{31} +(-0.792893 + 1.37333i) q^{32} +(-2.41421 + 4.18154i) q^{33} -0.414214 q^{34} +(1.91421 + 3.31552i) q^{36} +(-3.74264 - 6.48244i) q^{37} +14.4853 q^{38} +(-3.53553 - 3.67423i) q^{39} +16.8995 q^{40} +(2.91421 + 5.04757i) q^{41} +(-0.292893 + 0.507306i) q^{43} +13.0711 q^{44} +(-1.91421 + 3.31552i) q^{45} +(1.70711 - 2.95680i) q^{46} -7.65685 q^{47} +(-2.12132 + 3.67423i) q^{48} +(11.6569 + 20.1903i) q^{50} +0.242641 q^{51} +(-3.82843 + 13.2621i) q^{52} -3.00000 q^{53} +(-6.82843 - 11.8272i) q^{54} +(6.53553 + 11.3199i) q^{55} -8.48528 q^{57} +(11.8640 - 20.5490i) q^{58} +(-0.878680 + 1.52192i) q^{59} -20.7279 q^{60} +(4.91421 - 8.51167i) q^{61} +(-6.53553 - 11.3199i) q^{62} -9.82843 q^{64} +(-13.3995 + 3.31552i) q^{65} -11.6569 q^{66} +(2.12132 + 3.67423i) q^{67} +(-0.328427 - 0.568852i) q^{68} +(-1.00000 + 1.73205i) q^{69} +(0.171573 - 0.297173i) q^{71} +(-2.20711 + 3.82282i) q^{72} -0.656854 q^{73} +(9.03553 - 15.6500i) q^{74} +(-6.82843 - 11.8272i) q^{75} +(11.4853 + 19.8931i) q^{76} +(3.41421 - 11.8272i) q^{78} +10.2426 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} -1.41421 q^{86} +(-6.94975 + 12.0373i) q^{87} +(7.53553 + 13.0519i) q^{88} +(-3.65685 - 6.33386i) q^{89} -9.24264 q^{90} +5.41421 q^{92} +(3.82843 + 6.63103i) q^{93} +(-9.24264 - 16.0087i) q^{94} +(-11.4853 + 19.8931i) q^{95} +2.24264 q^{96} +(-2.58579 + 4.47871i) q^{97} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9} - 10 q^{10} - 4 q^{11} + 16 q^{12} + 14 q^{13} + 8 q^{15} - 6 q^{16} - 6 q^{17} + 4 q^{18} + 12 q^{19} + 18 q^{20} + 8 q^{22} + 4 q^{24} + 16 q^{25} + 10 q^{26} - 14 q^{29} - 12 q^{30} - 16 q^{31} - 6 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{36} + 2 q^{37} + 24 q^{38} + 28 q^{40} + 6 q^{41} - 4 q^{43} + 24 q^{44} - 2 q^{45} + 4 q^{46} - 8 q^{47} + 24 q^{50} - 16 q^{51} - 4 q^{52} - 12 q^{53} - 16 q^{54} + 12 q^{55} + 22 q^{58} - 12 q^{59} - 32 q^{60} + 14 q^{61} - 12 q^{62} - 28 q^{64} - 14 q^{65} - 24 q^{66} + 10 q^{68} - 4 q^{69} + 12 q^{71} - 6 q^{72} + 20 q^{73} + 22 q^{74} - 16 q^{75} + 12 q^{76} + 8 q^{78} + 24 q^{79} + 6 q^{80} + 10 q^{81} - 14 q^{82} + 24 q^{83} - 10 q^{85} - 8 q^{87} + 16 q^{88} + 8 q^{89} - 20 q^{90} + 16 q^{92} + 4 q^{93} - 20 q^{94} - 12 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 4 * q^6 - 12 * q^8 + 2 * q^9 - 10 * q^10 - 4 * q^11 + 16 * q^12 + 14 * q^13 + 8 * q^15 - 6 * q^16 - 6 * q^17 + 4 * q^18 + 12 * q^19 + 18 * q^20 + 8 * q^22 + 4 * q^24 + 16 * q^25 + 10 * q^26 - 14 * q^29 - 12 * q^30 - 16 * q^31 - 6 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^36 + 2 * q^37 + 24 * q^38 + 28 * q^40 + 6 * q^41 - 4 * q^43 + 24 * q^44 - 2 * q^45 + 4 * q^46 - 8 * q^47 + 24 * q^50 - 16 * q^51 - 4 * q^52 - 12 * q^53 - 16 * q^54 + 12 * q^55 + 22 * q^58 - 12 * q^59 - 32 * q^60 + 14 * q^61 - 12 * q^62 - 28 * q^64 - 14 * q^65 - 24 * q^66 + 10 * q^68 - 4 * q^69 + 12 * q^71 - 6 * q^72 + 20 * q^73 + 22 * q^74 - 16 * q^75 + 12 * q^76 + 8 * q^78 + 24 * q^79 + 6 * q^80 + 10 * q^81 - 14 * q^82 + 24 * q^83 - 10 * q^85 - 8 * q^87 + 16 * q^88 + 8 * q^89 - 20 * q^90 + 16 * q^92 + 4 * q^93 - 20 * q^94 - 12 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

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