LMFDB - Embedded newform 637.2.e.f.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (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:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.f.508.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-2.20711 + 3.82282i) q^{5} -2.00000 q^{6} -2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-2.20711 + 3.82282i) q^{5} -2.00000 q^{6} -2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.12132 - 5.40629i) q^{10} +(2.12132 + 3.67423i) q^{11} -1.00000 q^{13} -6.24264 q^{15} +(2.00000 - 3.46410i) q^{16} +(0.707107 + 1.22474i) q^{17} +(0.707107 + 1.22474i) q^{18} +(-0.621320 + 1.07616i) q^{19} -6.00000 q^{22} +(0.0857864 - 0.148586i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(-7.24264 - 12.5446i) q^{25} +(0.707107 - 1.22474i) q^{26} +5.65685 q^{27} +5.82843 q^{29} +(4.41421 - 7.64564i) q^{30} +(2.62132 + 4.54026i) q^{31} +(-3.00000 + 5.19615i) q^{33} -2.00000 q^{34} +(3.12132 - 5.40629i) q^{37} +(-0.878680 - 1.52192i) q^{38} +(-0.707107 - 1.22474i) q^{39} +(6.24264 - 10.8126i) q^{40} +3.17157 q^{41} -5.00000 q^{43} +(2.20711 + 3.82282i) q^{45} +(0.121320 + 0.210133i) q^{46} +(-2.20711 + 3.82282i) q^{47} +5.65685 q^{48} +20.4853 q^{50} +(-1.00000 + 1.73205i) q^{51} +(2.91421 + 5.04757i) q^{53} +(-4.00000 + 6.92820i) q^{54} -18.7279 q^{55} -1.75736 q^{57} +(-4.12132 + 7.13834i) q^{58} +(-5.82843 - 10.0951i) q^{59} +(-3.00000 + 5.19615i) q^{61} -7.41421 q^{62} +8.00000 q^{64} +(2.20711 - 3.82282i) q^{65} +(-4.24264 - 7.34847i) q^{66} +(-1.24264 - 2.15232i) q^{67} +0.242641 q^{69} +1.07107 q^{71} +(-1.41421 + 2.44949i) q^{72} +(0.378680 + 0.655892i) q^{73} +(4.41421 + 7.64564i) q^{74} +(10.2426 - 17.7408i) q^{75} +2.00000 q^{78} +(0.742641 - 1.28629i) q^{79} +(8.82843 + 15.2913i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-2.24264 + 3.88437i) q^{82} +4.75736 q^{83} -6.24264 q^{85} +(3.53553 - 6.12372i) q^{86} +(4.12132 + 7.13834i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(-2.20711 + 3.82282i) q^{89} -6.24264 q^{90} +(-3.70711 + 6.42090i) q^{93} +(-3.12132 - 5.40629i) q^{94} +(-2.74264 - 4.75039i) q^{95} -13.7279 q^{97} +4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{5} - 8 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q - 6 * q^5 - 8 * q^6 + 2 * q^9	$ 4 q - 6 q^{5} - 8 q^{6} + 2 q^{9} - 4 q^{10} - 4 q^{13} - 8 q^{15} + 8 q^{16} + 6 q^{19} - 24 q^{22} + 6 q^{23} - 8 q^{24} - 12 q^{25} + 12 q^{29} + 12 q^{30} + 2 q^{31} - 12 q^{33} - 8 q^{34} + 4 q^{37} - 12 q^{38} + 8 q^{40} + 24 q^{41} - 20 q^{43} + 6 q^{45} - 8 q^{46} - 6 q^{47} + 48 q^{50} - 4 q^{51} + 6 q^{53} - 16 q^{54} - 24 q^{55} - 24 q^{57} - 8 q^{58} - 12 q^{59} - 12 q^{61} - 24 q^{62} + 32 q^{64} + 6 q^{65} + 12 q^{67} - 16 q^{69} - 24 q^{71} + 10 q^{73} + 12 q^{74} + 24 q^{75} + 8 q^{78} - 14 q^{79} + 24 q^{80} + 10 q^{81} + 8 q^{82} + 36 q^{83} - 8 q^{85} + 8 q^{87} - 24 q^{88} - 6 q^{89} - 8 q^{90} - 12 q^{93} - 4 q^{94} + 6 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q - 6 * q^5 - 8 * q^6 + 2 * q^9 - 4 * q^10 - 4 * q^13 - 8 * q^15 + 8 * q^16 + 6 * q^19 - 24 * q^22 + 6 * q^23 - 8 * q^24 - 12 * q^25 + 12 * q^29 + 12 * q^30 + 2 * q^31 - 12 * q^33 - 8 * q^34 + 4 * q^37 - 12 * q^38 + 8 * q^40 + 24 * q^41 - 20 * q^43 + 6 * q^45 - 8 * q^46 - 6 * q^47 + 48 * q^50 - 4 * q^51 + 6 * q^53 - 16 * q^54 - 24 * q^55 - 24 * q^57 - 8 * q^58 - 12 * q^59 - 12 * q^61 - 24 * q^62 + 32 * q^64 + 6 * q^65 + 12 * q^67 - 16 * q^69 - 24 * q^71 + 10 * q^73 + 12 * q^74 + 24 * q^75 + 8 * q^78 - 14 * q^79 + 24 * q^80 + 10 * q^81 + 8 * q^82 + 36 * q^83 - 8 * q^85 + 8 * q^87 - 24 * q^88 - 6 * q^89 - 8 * q^90 - 12 * q^93 - 4 * q^94 + 6 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i	−1.00000			$\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	0.994694	−	0.102882i	$-0.0328064\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	−0.586445	+	0.809989i	$0.699473\pi$
$4$		0			0
$5$	−2.20711	+	3.82282i	−0.987048	+	1.70962i	−0.354593	+	0.935021i	$0.615380\pi$
$5$	−2.20711	+	3.82282i	−0.987048	+	1.70962i	−0.632456	+	0.774597i	$0.717953\pi$
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$	−2.82843			−1.00000
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−3.12132	−	5.40629i	−0.987048	−	1.70962i
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	0.985520	+	0.169559i	$0.0542342\pi$
$11$	2.12132	+	3.67423i	0.639602	+	1.10782i	−0.345918	+	0.938265i	$0.612432\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−6.24264			−1.61184
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	0.707107	+	1.22474i	0.171499	+	0.297044i	0.938944	−	0.344070i	$-0.111806\pi$
$17$	0.707107	+	1.22474i	0.171499	+	0.297044i	−0.767445	+	0.641114i	$0.778472\pi$
$18$	0.707107	+	1.22474i	0.166667	+	0.288675i
$19$	−0.621320	+	1.07616i	−0.142541	+	0.246888i	−0.928453	−	0.371451i	$-0.878861\pi$
$19$	−0.621320	+	1.07616i	−0.142541	+	0.246888i	0.785912	+	0.618338i	$0.212194\pi$
$20$		0			0
$21$		0			0
$22$	−6.00000			−1.27920
$23$	0.0857864	−	0.148586i	0.0178877	−	0.0309824i	−0.856943	−	0.515411i	$-0.827639\pi$
$23$	0.0857864	−	0.148586i	0.0178877	−	0.0309824i	0.874831	+	0.484429i	$0.160973\pi$
$24$	−2.00000	−	3.46410i	−0.408248	−	0.707107i
$25$	−7.24264	−	12.5446i	−1.44853	−	2.50892i
$26$	0.707107	−	1.22474i	0.138675	−	0.240192i
$27$	5.65685			1.08866
$28$		0			0
$29$	5.82843			1.08231			0.541156	−	0.840922i	$-0.317987\pi$
$29$	5.82843			1.08231			0.541156	+	0.840922i	$0.317987\pi$
$30$	4.41421	−	7.64564i	0.805921	−	1.39590i
$31$	2.62132	+	4.54026i	0.470803	+	0.815455i	0.999442	−	0.0333918i	$-0.0106309\pi$
$31$	2.62132	+	4.54026i	0.470803	+	0.815455i	−0.528639	+	0.848847i	$0.677298\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	−2.00000			−0.342997
$35$		0			0
$36$		0			0
$37$	3.12132	−	5.40629i	0.513142	−	0.888788i	−0.486742	−	0.873546i	$-0.661815\pi$
$37$	3.12132	−	5.40629i	0.513142	−	0.888788i	0.999884	−	0.0152420i	$-0.00485188\pi$
$38$	−0.878680	−	1.52192i	−0.142541	−	0.246888i
$39$	−0.707107	−	1.22474i	−0.113228	−	0.196116i
$40$	6.24264	−	10.8126i	0.987048	−	1.70962i
$41$	3.17157			0.495316			0.247658	−	0.968847i	$-0.420339\pi$
$41$	3.17157			0.495316			0.247658	+	0.968847i	$0.420339\pi$
$42$		0			0
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$		0			0
$45$	2.20711	+	3.82282i	0.329016	+	0.569873i
$46$	0.121320	+	0.210133i	0.0178877	+	0.0309824i
$47$	−2.20711	+	3.82282i	−0.321940	+	0.557616i	−0.980888	−	0.194572i	$-0.937668\pi$
$47$	−2.20711	+	3.82282i	−0.321940	+	0.557616i	0.658949	+	0.752188i	$0.271001\pi$
$48$	5.65685			0.816497
$49$		0			0
$50$	20.4853			2.89706
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$		0			0
$53$	2.91421	+	5.04757i	0.400298	+	0.693337i	0.993762	−	0.111524i	$-0.0355733\pi$
$53$	2.91421	+	5.04757i	0.400298	+	0.693337i	−0.593464	+	0.804861i	$0.702240\pi$
$54$	−4.00000	+	6.92820i	−0.544331	+	0.942809i
$55$	−18.7279			−2.52527
$56$		0			0
$57$	−1.75736			−0.232768
$58$	−4.12132	+	7.13834i	−0.541156	+	0.937309i
$59$	−5.82843	−	10.0951i	−0.758797	−	1.31427i	−0.943465	−	0.331473i	$-0.892454\pi$
$59$	−5.82843	−	10.0951i	−0.758797	−	1.31427i	0.184668	−	0.982801i	$-0.440879\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	−7.41421			−0.941606
$63$		0			0
$64$	8.00000			1.00000
$65$	2.20711	−	3.82282i	0.273758	−	0.474163i
$66$	−4.24264	−	7.34847i	−0.522233	−	0.904534i
$67$	−1.24264	−	2.15232i	−0.151813	−	0.262947i	0.780081	−	0.625678i	$-0.215178\pi$
$67$	−1.24264	−	2.15232i	−0.151813	−	0.262947i	−0.931894	+	0.362731i	$0.881844\pi$
$68$		0			0
$69$	0.242641			0.0292105
$70$		0			0
$71$	1.07107			0.127112			0.0635562	−	0.997978i	$-0.479756\pi$
$71$	1.07107			0.127112			0.0635562	+	0.997978i	$0.479756\pi$
$72$	−1.41421	+	2.44949i	−0.166667	+	0.288675i
$73$	0.378680	+	0.655892i	0.0443211	+	0.0767664i	0.887335	−	0.461125i	$-0.152554\pi$
$73$	0.378680	+	0.655892i	0.0443211	+	0.0767664i	−0.843014	+	0.537892i	$0.819221\pi$
$74$	4.41421	+	7.64564i	0.513142	+	0.888788i
$75$	10.2426	−	17.7408i	1.18272	−	2.04853i
$76$		0			0
$77$		0			0
$78$	2.00000			0.226455
$79$	0.742641	−	1.28629i	0.0835536	−	0.144719i	−0.821220	−	0.570611i	$-0.806706\pi$
$79$	0.742641	−	1.28629i	0.0835536	−	0.144719i	0.904774	+	0.425892i	$0.140040\pi$
$80$	8.82843	+	15.2913i	0.987048	+	1.70962i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	−2.24264	+	3.88437i	−0.247658	+	0.428957i
$83$	4.75736			0.522188			0.261094	−	0.965313i	$-0.415917\pi$
$83$	4.75736			0.522188			0.261094	+	0.965313i	$0.415917\pi$
$84$		0			0
$85$	−6.24264			−0.677109
$86$	3.53553	−	6.12372i	0.381246	−	0.660338i
$87$	4.12132	+	7.13834i	0.441852	+	0.765310i
$88$	−6.00000	−	10.3923i	−0.639602	−	1.10782i
$89$	−2.20711	+	3.82282i	−0.233953	+	0.405218i	−0.958968	−	0.283515i	$-0.908499\pi$
$89$	−2.20711	+	3.82282i	−0.233953	+	0.405218i	0.725015	+	0.688733i	$0.241833\pi$
$90$	−6.24264			−0.658032
$91$		0			0
$92$		0			0
$93$	−3.70711	+	6.42090i	−0.384409	+	0.665816i
$94$	−3.12132	−	5.40629i	−0.321940	−	0.557616i
$95$	−2.74264	−	4.75039i	−0.281389	−	0.487380i
$96$		0			0
$97$	−13.7279			−1.39386			−0.696930	−	0.717139i	$-0.745451\pi$
$97$	−13.7279			−1.39386			−0.696930	+	0.717139i	$0.745451\pi$
$98$		0			0
$99$	4.24264			0.426401
$100$		0			0
$101$	−0.878680	−	1.52192i	−0.0874319	−	0.151436i	0.818993	−	0.573803i	$-0.194533\pi$
$101$	−0.878680	−	1.52192i	−0.0874319	−	0.151436i	−0.906425	+	0.422367i	$0.861199\pi$
$102$	−1.41421	−	2.44949i	−0.140028	−	0.242536i
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	2.82843			0.277350
$105$		0			0
$106$	−8.24264			−0.800596
$107$	−4.07107	+	7.05130i	−0.393565	+	0.681675i	−0.992917	−	0.118811i	$-0.962092\pi$
$107$	−4.07107	+	7.05130i	−0.393565	+	0.681675i	0.599352	+	0.800486i	$0.295425\pi$
$108$		0			0
$109$	4.36396	+	7.55860i	0.417992	+	0.723983i	0.995737	−	0.0922340i	$-0.0294008\pi$
$109$	4.36396	+	7.55860i	0.417992	+	0.723983i	−0.577746	+	0.816217i	$0.696067\pi$
$110$	13.2426	−	22.9369i	1.26264	−	2.18695i
$111$	8.82843			0.837957
$112$		0			0
$113$	−20.3137			−1.91095			−0.955476	−	0.295067i	$-0.904658\pi$
$113$	−20.3137			−1.91095			−0.955476	+	0.295067i	$0.904658\pi$
$114$	1.24264	−	2.15232i	0.116384	−	0.201583i
$115$	0.378680	+	0.655892i	0.0353121	+	0.0611623i
$116$		0			0
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	16.4853			1.51759
$119$		0			0
$120$	17.6569			1.61184
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	−4.24264	−	7.34847i	−0.384111	−	0.665299i
$123$	2.24264	+	3.88437i	0.202212	+	0.350242i
$124$		0			0
$125$	41.8701			3.74497
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−5.65685	+	9.79796i	−0.500000	+	0.866025i
$129$	−3.53553	−	6.12372i	−0.311286	−	0.539164i
$130$	3.12132	+	5.40629i	0.273758	+	0.474163i
$131$	−1.41421	+	2.44949i	−0.123560	+	0.214013i	−0.921169	−	0.389162i	$-0.872765\pi$
$131$	−1.41421	+	2.44949i	−0.123560	+	0.214013i	0.797609	+	0.603175i	$0.206098\pi$
$132$		0			0
$133$		0			0
$134$	3.51472			0.303625
$135$	−12.4853	+	21.6251i	−1.07456	+	1.86120i
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	3.70711	+	6.42090i	0.316720	+	0.548574i	0.979802	−	0.199972i	$-0.0640853\pi$
$137$	3.70711	+	6.42090i	0.316720	+	0.548574i	−0.663082	+	0.748547i	$0.730752\pi$
$138$	−0.171573	+	0.297173i	−0.0146053	+	0.0252970i
$139$	−2.24264			−0.190218			−0.0951092	−	0.995467i	$-0.530320\pi$
$139$	−2.24264			−0.190218			−0.0951092	+	0.995467i	$0.530320\pi$
$140$		0			0
$141$	−6.24264			−0.525725
$142$	−0.757359	+	1.31178i	−0.0635562	+	0.110083i
$143$	−2.12132	−	3.67423i	−0.177394	−	0.307255i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	−12.8640	+	22.2810i	−1.06829	+	1.85034i
$146$	−1.07107			−0.0886422
$147$		0			0
$148$		0			0
$149$	−3.87868	+	6.71807i	−0.317754	+	0.550366i	−0.980019	−	0.198904i	$-0.936262\pi$
$149$	−3.87868	+	6.71807i	−0.317754	+	0.550366i	0.662265	+	0.749270i	$0.269595\pi$
$150$	14.4853	+	25.0892i	1.18272	+	2.04853i
$151$	9.12132	+	15.7986i	0.742283	+	1.28567i	0.951454	+	0.307792i	$0.0995901\pi$
$151$	9.12132	+	15.7986i	0.742283	+	1.28567i	−0.209171	+	0.977879i	$0.567077\pi$
$152$	1.75736	−	3.04384i	0.142541	−	0.246888i
$153$	1.41421			0.114332
$154$		0			0
$155$	−23.1421			−1.85882
$156$		0			0
$157$	6.12132	+	10.6024i	0.488535	+	0.846167i	0.999913	−	0.0131889i	$-0.00419829\pi$
$157$	6.12132	+	10.6024i	0.488535	+	0.846167i	−0.511378	+	0.859356i	$0.670865\pi$
$158$	1.05025	+	1.81909i	0.0835536	+	0.144719i
$159$	−4.12132	+	7.13834i	−0.326842	+	0.566107i
$160$		0			0
$161$		0			0
$162$	−7.07107			−0.555556
$163$	4.24264	−	7.34847i	0.332309	−	0.575577i	−0.650655	−	0.759374i	$-0.725506\pi$
$163$	4.24264	−	7.34847i	0.332309	−	0.575577i	0.982964	+	0.183797i	$0.0588389\pi$
$164$		0			0
$165$	−13.2426	−	22.9369i	−1.03094	−	1.78564i
$166$	−3.36396	+	5.82655i	−0.261094	+	0.452228i
$167$	−21.3848			−1.65480			−0.827402	−	0.561610i	$-0.810182\pi$
$167$	−21.3848			−1.65480			−0.827402	+	0.561610i	$0.810182\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	4.41421	−	7.64564i	0.338555	−	0.586394i
$171$	0.621320	+	1.07616i	0.0475136	+	0.0822959i
$172$		0			0
$173$	0.363961	−	0.630399i	0.0276714	−	0.0479283i	−0.851858	−	0.523773i	$-0.824524\pi$
$173$	0.363961	−	0.630399i	0.0276714	−	0.0479283i	0.879530	+	0.475844i	$0.157857\pi$
$174$	−11.6569			−0.883704
$175$		0			0
$176$	16.9706			1.27920
$177$	8.24264	−	14.2767i	0.619555	−	1.07310i
$178$	−3.12132	−	5.40629i	−0.233953	−	0.405218i
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$		0			0
$181$	6.72792			0.500083			0.250041	−	0.968235i	$-0.419556\pi$
$181$	6.72792			0.500083			0.250041	+	0.968235i	$0.419556\pi$
$182$		0			0
$183$	−8.48528			−0.627250
$184$	−0.242641	+	0.420266i	−0.0178877	+	0.0309824i
$185$	13.7782	+	23.8645i	1.01299	+	1.75455i
$186$	−5.24264	−	9.08052i	−0.384409	−	0.665816i
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$		0			0
$189$		0			0
$190$	7.75736			0.562778
$191$	−10.4142	+	18.0379i	−0.753546	+	1.30518i	0.192548	+	0.981288i	$0.438325\pi$
$191$	−10.4142	+	18.0379i	−0.753546	+	1.30518i	−0.946094	+	0.323892i	$0.895008\pi$
$192$	5.65685	+	9.79796i	0.408248	+	0.707107i
$193$	−1.24264	−	2.15232i	−0.0894472	−	0.154927i	0.817830	−	0.575459i	$-0.195177\pi$
$193$	−1.24264	−	2.15232i	−0.0894472	−	0.154927i	−0.907278	+	0.420532i	$0.861843\pi$
$194$	9.70711	−	16.8132i	0.696930	−	1.20712i
$195$	6.24264			0.447045
$196$		0			0
$197$	23.6569			1.68548			0.842741	−	0.538320i	$-0.180941\pi$
$197$	23.6569			1.68548			0.842741	+	0.538320i	$0.180941\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	6.12132	+	10.6024i	0.433929	+	0.751587i	0.997208	−	0.0746801i	$-0.0237936\pi$
$199$	6.12132	+	10.6024i	0.433929	+	0.751587i	−0.563279	+	0.826267i	$0.690460\pi$
$200$	20.4853	+	35.4815i	1.44853	+	2.50892i
$201$	1.75736	−	3.04384i	0.123955	−	0.214696i
$202$	2.48528			0.174864
$203$		0			0
$204$		0			0
$205$	−7.00000	+	12.1244i	−0.488901	+	0.846802i
$206$	5.65685	+	9.79796i	0.394132	+	0.682656i
$207$	−0.0857864	−	0.148586i	−0.00596257	−	0.0103275i
$208$	−2.00000	+	3.46410i	−0.138675	+	0.240192i
$209$	−5.27208			−0.364677
$210$		0			0
$211$	17.9706			1.23714			0.618572	−	0.785728i	$-0.287711\pi$
$211$	17.9706			1.23714			0.618572	+	0.785728i	$0.287711\pi$
$212$		0			0
$213$	0.757359	+	1.31178i	0.0518934	+	0.0898820i
$214$	−5.75736	−	9.97204i	−0.393565	−	0.681675i
$215$	11.0355	−	19.1141i	0.752617	−	1.30357i
$216$	−16.0000			−1.08866
$217$		0			0
$218$	−12.3431			−0.835983
$219$	−0.535534	+	0.927572i	−0.0361880	+	0.0626795i
$220$		0			0
$221$	−0.707107	−	1.22474i	−0.0475651	−	0.0823853i
$222$	−6.24264	+	10.8126i	−0.418979	+	0.725692i
$223$	9.24264			0.618933			0.309466	−	0.950910i	$-0.399850\pi$
$223$	9.24264			0.618933			0.309466	+	0.950910i	$0.399850\pi$
$224$		0			0
$225$	−14.4853			−0.965685
$226$	14.3640	−	24.8791i	0.955476	−	1.65493i
$227$	−10.5858	−	18.3351i	−0.702603	−	1.21694i	−0.967550	−	0.252681i	$-0.918688\pi$
$227$	−10.5858	−	18.3351i	−0.702603	−	1.21694i	0.264946	−	0.964263i	$-0.414646\pi$
$228$		0			0
$229$	10.7279	−	18.5813i	0.708921	−	1.22789i	−0.256337	−	0.966588i	$-0.582516\pi$
$229$	10.7279	−	18.5813i	0.708921	−	1.22789i	0.965258	−	0.261300i	$-0.0841511\pi$
$230$	−1.07107			−0.0706241
$231$		0			0
$232$	−16.4853			−1.08231
$233$	1.67157	−	2.89525i	0.109508	−	0.189674i	−0.806063	−	0.591830i	$-0.798406\pi$
$233$	1.67157	−	2.89525i	0.109508	−	0.189674i	0.915571	+	0.402156i	$0.131739\pi$
$234$	−0.707107	−	1.22474i	−0.0462250	−	0.0800641i
$235$	−9.74264	−	16.8747i	−0.635540	−	1.10079i
$236$		0			0
$237$	2.10051			0.136442
$238$		0			0
$239$	20.4853			1.32508			0.662541	−	0.749025i	$-0.269478\pi$
$239$	20.4853			1.32508			0.662541	+	0.749025i	$0.269478\pi$
$240$	−12.4853	+	21.6251i	−0.805921	+	1.39590i
$241$	−11.1066	−	19.2372i	−0.715439	−	1.23918i	−0.962790	−	0.270251i	$-0.912893\pi$
$241$	−11.1066	−	19.2372i	−0.715439	−	1.23918i	0.247351	−	0.968926i	$-0.420440\pi$
$242$	−4.94975	−	8.57321i	−0.318182	−	0.551107i
$243$	4.94975	−	8.57321i	0.317526	−	0.549972i
$244$		0			0
$245$		0			0
$246$	−6.34315			−0.404424
$247$	0.621320	−	1.07616i	0.0395337	−	0.0684743i
$248$	−7.41421	−	12.8418i	−0.470803	−	0.815455i
$249$	3.36396	+	5.82655i	0.213182	+	0.369243i
$250$	−29.6066	+	51.2801i	−1.87249	+	3.24324i
$251$	19.4142			1.22541			0.612707	−	0.790310i	$-0.290081\pi$
$251$	19.4142			1.22541			0.612707	+	0.790310i	$0.290081\pi$
$252$		0			0
$253$	0.727922			0.0457641
$254$	−1.41421	+	2.44949i	−0.0887357	+	0.153695i
$255$	−4.41421	−	7.64564i	−0.276429	−	0.478789i
$256$		0			0
$257$	8.29289	−	14.3637i	0.517296	−	0.895984i	−0.482502	−	0.875895i	$-0.660272\pi$
$257$	8.29289	−	14.3637i	0.517296	−	0.895984i	0.999798	−	0.0200887i	$-0.00639488\pi$
$258$	10.0000			0.622573
$259$		0			0
$260$		0			0
$261$	2.91421	−	5.04757i	0.180385	−	0.312436i
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$	15.9853	+	27.6873i	0.985695	+	1.70727i	0.638808	+	0.769366i	$0.279428\pi$
$263$	15.9853	+	27.6873i	0.985695	+	1.70727i	0.346887	+	0.937907i	$0.387239\pi$
$264$	8.48528	−	14.6969i	0.522233	−	0.904534i
$265$	−25.7279			−1.58045
$266$		0			0
$267$	−6.24264			−0.382043
$268$		0			0
$269$	−7.41421	−	12.8418i	−0.452053	−	0.782978i	0.546461	−	0.837485i	$-0.315975\pi$
$269$	−7.41421	−	12.8418i	−0.452053	−	0.782978i	−0.998513	+	0.0545066i	$0.982641\pi$
$270$	−17.6569	−	30.5826i	−1.07456	−	1.86120i
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$	5.65685			0.342997
$273$		0			0
$274$	−10.4853			−0.633439
$275$	30.7279	−	53.2223i	1.85296	−	3.20943i
$276$		0			0
$277$	−4.74264	−	8.21449i	−0.284958	−	0.493561i	0.687641	−	0.726051i	$-0.258646\pi$
$277$	−4.74264	−	8.21449i	−0.284958	−	0.493561i	−0.972599	+	0.232489i	$0.925313\pi$
$278$	1.58579	−	2.74666i	0.0951092	−	0.164734i
$279$	5.24264			0.313869
$280$		0			0
$281$	−15.5563			−0.928014			−0.464007	−	0.885832i	$-0.653589\pi$
$281$	−15.5563			−0.928014			−0.464007	+	0.885832i	$0.653589\pi$
$282$	4.41421	−	7.64564i	0.262863	−	0.455291i
$283$	−4.24264	−	7.34847i	−0.252199	−	0.436821i	0.711932	−	0.702248i	$-0.247820\pi$
$283$	−4.24264	−	7.34847i	−0.252199	−	0.436821i	−0.964131	+	0.265427i	$0.914487\pi$
$284$		0			0
$285$	3.87868	−	6.71807i	0.229753	−	0.397944i
$286$	6.00000			0.354787
$287$		0			0
$288$		0			0
$289$	7.50000	−	12.9904i	0.441176	−	0.764140i
$290$	−18.1924	−	31.5101i	−1.06829	−	1.85034i
$291$	−9.70711	−	16.8132i	−0.569041	−	0.985607i
$292$		0			0
$293$	−21.3848			−1.24931			−0.624656	−	0.780900i	$-0.714761\pi$
$293$	−21.3848			−1.24931			−0.624656	+	0.780900i	$0.714761\pi$
$294$		0			0
$295$	51.4558			2.99588
$296$	−8.82843	+	15.2913i	−0.513142	+	0.888788i
$297$	12.0000	+	20.7846i	0.696311	+	1.20605i
$298$	−5.48528	−	9.50079i	−0.317754	−	0.550366i
$299$	−0.0857864	+	0.148586i	−0.00496116	+	0.00859298i
$300$		0			0
$301$		0			0
$302$	−25.7990			−1.48457
$303$	1.24264	−	2.15232i	0.0713878	−	0.123647i
$304$	2.48528	+	4.30463i	0.142541	+	0.246888i
$305$	−13.2426	−	22.9369i	−0.758271	−	1.31336i
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	4.75736			0.271517			0.135758	−	0.990742i	$-0.456653\pi$
$307$	4.75736			0.271517			0.135758	+	0.990742i	$0.456653\pi$
$308$		0			0
$309$	11.3137			0.643614
$310$	16.3640	−	28.3432i	0.929411	−	1.60979i
$311$	2.29289	+	3.97141i	0.130018	+	0.225198i	0.923683	−	0.383157i	$-0.125163\pi$
$311$	2.29289	+	3.97141i	0.130018	+	0.225198i	−0.793665	+	0.608355i	$0.791830\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	9.60660	−	16.6391i	0.542997	−	0.940499i	−0.455733	−	0.890117i	$-0.650623\pi$
$313$	9.60660	−	16.6391i	0.542997	−	0.940499i	0.998730	−	0.0503822i	$-0.0160439\pi$
$314$	−17.3137			−0.977069
$315$		0			0
$316$		0			0
$317$	−5.65685	+	9.79796i	−0.317721	+	0.550308i	−0.980012	−	0.198938i	$-0.936251\pi$
$317$	−5.65685	+	9.79796i	−0.317721	+	0.550308i	0.662291	+	0.749246i	$0.269584\pi$
$318$	−5.82843	−	10.0951i	−0.326842	−	0.566107i
$319$	12.3640	+	21.4150i	0.692249	+	1.19901i
$320$	−17.6569	+	30.5826i	−0.987048	+	1.70962i
$321$	−11.5147			−0.642689
$322$		0			0
$323$	−1.75736			−0.0977821
$324$		0			0
$325$	7.24264	+	12.5446i	0.401749	+	0.695850i
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	−6.17157	+	10.6895i	−0.341289	+	0.591129i
$328$	−8.97056			−0.495316
$329$		0			0
$330$	37.4558			2.06188
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	−0.505296	−	0.862946i	$-0.668617\pi$
$331$	9.00000	−	15.5885i	0.494685	−	0.856819i	0.999981	+	0.00612670i	$0.00195020\pi$
$332$		0			0
$333$	−3.12132	−	5.40629i	−0.171047	−	0.296263i
$334$	15.1213	−	26.1909i	0.827402	−	1.43310i
$335$	10.9706			0.599386
$336$		0			0
$337$	−33.0000			−1.79762			−0.898812	−	0.438334i	$-0.855569\pi$
$337$	−33.0000			−1.79762			−0.898812	+	0.438334i	$0.855569\pi$
$338$	−0.707107	+	1.22474i	−0.0384615	+	0.0666173i
$339$	−14.3640	−	24.8791i	−0.780143	−	1.35125i
$340$		0			0
$341$	−11.1213	+	19.2627i	−0.602253	+	1.04313i
$342$	−1.75736			−0.0950271
$343$		0			0
$344$	14.1421			0.762493
$345$	−0.535534	+	0.927572i	−0.0288322	+	0.0499388i
$346$	0.514719	+	0.891519i	0.0276714	+	0.0479283i
$347$	−2.82843	−	4.89898i	−0.151838	−	0.262991i	0.780065	−	0.625698i	$-0.215186\pi$
$347$	−2.82843	−	4.89898i	−0.151838	−	0.262991i	−0.931903	+	0.362707i	$0.881853\pi$
$348$		0			0
$349$	−0.272078			−0.0145640			−0.00728200	−	0.999973i	$-0.502318\pi$
$349$	−0.272078			−0.0145640			−0.00728200	+	0.999973i	$0.502318\pi$
$350$		0			0
$351$	−5.65685			−0.301941
$352$		0			0
$353$	−4.24264	−	7.34847i	−0.225813	−	0.391120i	0.730750	−	0.682645i	$-0.239170\pi$
$353$	−4.24264	−	7.34847i	−0.225813	−	0.391120i	−0.956563	+	0.291526i	$0.905837\pi$
$354$	11.6569	+	20.1903i	0.619555	+	1.07310i
$355$	−2.36396	+	4.09450i	−0.125466	+	0.217314i
$356$		0			0
$357$		0			0
$358$	−12.7279			−0.672692
$359$	4.05025	−	7.01524i	0.213764	−	0.370250i	−0.739125	−	0.673568i	$-0.764761\pi$
$359$	4.05025	−	7.01524i	0.213764	−	0.370250i	0.952890	+	0.303317i	$0.0980943\pi$
$360$	−6.24264	−	10.8126i	−0.329016	−	0.569873i
$361$	8.72792	+	15.1172i	0.459364	+	0.795642i
$362$	−4.75736	+	8.23999i	−0.250041	+	0.433084i
$363$	−9.89949			−0.519589
$364$		0			0
$365$	−3.34315			−0.174988
$366$	6.00000	−	10.3923i	0.313625	−	0.543214i
$367$	−0.878680	−	1.52192i	−0.0458667	−	0.0794435i	0.842181	−	0.539196i	$-0.181272\pi$
$367$	−0.878680	−	1.52192i	−0.0458667	−	0.0794435i	−0.888047	+	0.459752i	$0.847938\pi$
$368$	−0.343146	−	0.594346i	−0.0178877	−	0.0309824i
$369$	1.58579	−	2.74666i	0.0825527	−	0.142986i
$370$	−38.9706			−2.02598
$371$		0			0
$372$		0			0
$373$	4.24264	−	7.34847i	0.219676	−	0.380489i	−0.735033	−	0.678031i	$-0.762833\pi$
$373$	4.24264	−	7.34847i	0.219676	−	0.380489i	0.954709	+	0.297542i	$0.0961668\pi$
$374$	−4.24264	−	7.34847i	−0.219382	−	0.379980i
$375$	29.6066	+	51.2801i	1.52888	+	2.64809i
$376$	6.24264	−	10.8126i	0.321940	−	0.557616i
$377$	−5.82843			−0.300179
$378$		0			0
$379$	32.2426			1.65619			0.828097	−	0.560585i	$-0.189424\pi$
$379$	32.2426			1.65619			0.828097	+	0.560585i	$0.189424\pi$
$380$		0			0
$381$	1.41421	+	2.44949i	0.0724524	+	0.125491i
$382$	−14.7279	−	25.5095i	−0.753546	−	1.30518i
$383$	1.75736	−	3.04384i	0.0897969	−	0.155533i	−0.817628	−	0.575746i	$-0.804712\pi$
$383$	1.75736	−	3.04384i	0.0897969	−	0.155533i	0.907425	+	0.420214i	$0.138045\pi$
$384$	−16.0000			−0.816497
$385$		0			0
$386$	3.51472			0.178894
$387$	−2.50000	+	4.33013i	−0.127082	+	0.220113i
$388$		0			0
$389$	−9.17157	−	15.8856i	−0.465017	−	0.805433i	0.534185	−	0.845368i	$-0.320619\pi$
$389$	−9.17157	−	15.8856i	−0.465017	−	0.805433i	−0.999202	+	0.0399341i	$0.987285\pi$
$390$	−4.41421	+	7.64564i	−0.223522	+	0.387152i
$391$	0.242641			0.0122709
$392$		0			0
$393$	−4.00000			−0.201773
$394$	−16.7279	+	28.9736i	−0.842741	+	1.45967i
$395$	3.27817	+	5.67796i	0.164943	+	0.285689i
$396$		0			0
$397$	−12.1066	+	20.9692i	−0.607613	+	1.05242i	0.384020	+	0.923325i	$0.374539\pi$
$397$	−12.1066	+	20.9692i	−0.607613	+	1.05242i	−0.991633	+	0.129092i	$0.958794\pi$
$398$	−17.3137			−0.867858
$399$		0			0
$400$	−57.9411			−2.89706
$401$	−8.82843	+	15.2913i	−0.440871	+	0.763610i	−0.997754	−	0.0669802i	$-0.978664\pi$
$401$	−8.82843	+	15.2913i	−0.440871	+	0.763610i	0.556884	+	0.830590i	$0.311997\pi$
$402$	2.48528	+	4.30463i	0.123955	+	0.214696i
$403$	−2.62132	−	4.54026i	−0.130577	−	0.226166i
$404$		0			0
$405$	−22.0711			−1.09672
$406$		0			0
$407$	26.4853			1.31283
$408$	2.82843	−	4.89898i	0.140028	−	0.242536i
$409$	2.62132	+	4.54026i	0.129616	+	0.224501i	0.923528	−	0.383531i	$-0.125292\pi$
$409$	2.62132	+	4.54026i	0.129616	+	0.224501i	−0.793912	+	0.608033i	$0.791959\pi$
$410$	−9.89949	−	17.1464i	−0.488901	−	0.846802i
$411$	−5.24264	+	9.08052i	−0.258600	+	0.447909i
$412$		0			0
$413$		0			0
$414$	0.242641			0.0119251
$415$	−10.5000	+	18.1865i	−0.515425	+	0.892742i
$416$		0			0
$417$	−1.58579	−	2.74666i	−0.0776563	−	0.134505i
$418$	3.72792	−	6.45695i	0.182339	−	0.315820i
$419$	32.8701			1.60581			0.802904	−	0.596109i	$-0.203287\pi$
$419$	32.8701			1.60581			0.802904	+	0.596109i	$0.203287\pi$
$420$		0			0
$421$	−18.7279			−0.912743			−0.456372	−	0.889789i	$-0.650851\pi$
$421$	−18.7279			−0.912743			−0.456372	+	0.889789i	$0.650851\pi$
$422$	−12.7071	+	22.0094i	−0.618572	+	1.07140i
$423$	2.20711	+	3.82282i	0.107313	+	0.185872i
$424$	−8.24264	−	14.2767i	−0.400298	−	0.693337i
$425$	10.2426	−	17.7408i	0.496841	−	0.860554i
$426$	−2.14214			−0.103787
$427$		0			0
$428$		0			0
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$	15.6066	+	27.0314i	0.752617	+	1.30357i
$431$	11.8284	+	20.4874i	0.569755	+	0.986845i	0.996590	+	0.0825154i	$0.0262953\pi$
$431$	11.8284	+	20.4874i	0.569755	+	0.986845i	−0.426835	+	0.904330i	$0.640371\pi$
$432$	11.3137	−	19.5959i	0.544331	−	0.942809i
$433$	8.97056			0.431098			0.215549	−	0.976493i	$-0.430846\pi$
$433$	8.97056			0.431098			0.215549	+	0.976493i	$0.430846\pi$
$434$		0			0
$435$	−36.3848			−1.74452
$436$		0			0
$437$	0.106602	+	0.184640i	0.00509945	+	0.00883251i
$438$	−0.757359	−	1.31178i	−0.0361880	−	0.0626795i
$439$	8.75736	−	15.1682i	0.417966	−	0.723938i	−0.577769	−	0.816200i	$-0.696076\pi$
$439$	8.75736	−	15.1682i	0.417966	−	0.723938i	0.995735	+	0.0922622i	$0.0294098\pi$
$440$	52.9706			2.52527
$441$		0			0
$442$	2.00000			0.0951303
$443$	13.1569	−	22.7883i	0.625101	−	1.08271i	−0.363420	−	0.931625i	$-0.618391\pi$
$443$	13.1569	−	22.7883i	0.625101	−	1.08271i	0.988521	−	0.151081i	$-0.0482756\pi$
$444$		0			0
$445$	−9.74264	−	16.8747i	−0.461845	−	0.799940i
$446$	−6.53553	+	11.3199i	−0.309466	+	0.536012i
$447$	−10.9706			−0.518890
$448$		0			0
$449$	26.8284			1.26611			0.633056	−	0.774106i	$-0.281800\pi$
$449$	26.8284			1.26611			0.633056	+	0.774106i	$0.281800\pi$
$450$	10.2426	−	17.7408i	0.482843	−	0.836308i
$451$	6.72792	+	11.6531i	0.316805	+	0.548723i
$452$		0			0
$453$	−12.8995	+	22.3426i	−0.606071	+	1.04975i
$454$	29.9411			1.40521
$455$		0			0
$456$	4.97056			0.232768
$457$	−17.6066	+	30.4955i	−0.823602	+	1.42652i	0.0793809	+	0.996844i	$0.474706\pi$
$457$	−17.6066	+	30.4955i	−0.823602	+	1.42652i	−0.902983	+	0.429676i	$0.858628\pi$
$458$	15.1716	+	26.2779i	0.708921	+	1.22789i
$459$	4.00000	+	6.92820i	0.186704	+	0.323381i
$460$		0			0
$461$	3.17157			0.147715			0.0738574	−	0.997269i	$-0.476469\pi$
$461$	3.17157			0.147715			0.0738574	+	0.997269i	$0.476469\pi$
$462$		0			0
$463$	4.24264			0.197172			0.0985861	−	0.995129i	$-0.468568\pi$
$463$	4.24264			0.197172			0.0985861	+	0.995129i	$0.468568\pi$
$464$	11.6569	−	20.1903i	0.541156	−	0.937309i
$465$	−16.3640	−	28.3432i	−0.758861	−	1.31438i
$466$	2.36396	+	4.09450i	0.109508	+	0.189674i
$467$	−7.94975	+	13.7694i	−0.367870	+	0.637170i	−0.989232	−	0.146353i	$-0.953246\pi$
$467$	−7.94975	+	13.7694i	−0.367870	+	0.637170i	0.621362	+	0.783524i	$0.286580\pi$
$468$		0			0
$469$		0			0
$470$	27.5563			1.27108
$471$	−8.65685	+	14.9941i	−0.398887	+	0.690892i
$472$	16.4853	+	28.5533i	0.758797	+	1.31427i
$473$	−10.6066	−	18.3712i	−0.487692	−	0.844707i
$474$	−1.48528	+	2.57258i	−0.0682212	+	0.118163i
$475$	18.0000			0.825897
$476$		0			0
$477$	5.82843			0.266865
$478$	−14.4853	+	25.0892i	−0.662541	+	1.14756i
$479$	−18.1066	−	31.3616i	−0.827312	−	1.43295i	−0.900140	−	0.435601i	$-0.856536\pi$
$479$	−18.1066	−	31.3616i	−0.827312	−	1.43295i	0.0728279	−	0.997345i	$-0.476798\pi$
$480$		0			0
$481$	−3.12132	+	5.40629i	−0.142320	+	0.246505i
$482$	31.4142			1.43088
$483$		0			0
$484$		0			0
$485$	30.2990	−	52.4794i	1.37581	−	2.38297i
$486$	7.00000	+	12.1244i	0.317526	+	0.549972i
$487$	−19.7279	−	34.1698i	−0.893957	−	1.54838i	−0.835090	−	0.550114i	$-0.814584\pi$
$487$	−19.7279	−	34.1698i	−0.893957	−	1.54838i	−0.0588679	−	0.998266i	$-0.518749\pi$
$488$	8.48528	−	14.6969i	0.384111	−	0.665299i
$489$	12.0000			0.542659
$490$		0			0
$491$	−28.6274			−1.29194			−0.645969	−	0.763364i	$-0.723546\pi$
$491$	−28.6274			−1.29194			−0.645969	+	0.763364i	$0.723546\pi$
$492$		0			0
$493$	4.12132	+	7.13834i	0.185615	+	0.321494i
$494$	0.878680	+	1.52192i	0.0395337	+	0.0684743i
$495$	−9.36396	+	16.2189i	−0.420879	+	0.728983i
$496$	20.9706			0.941606
$497$		0			0
$498$	−9.51472			−0.426365
$499$	19.3640	−	33.5394i	0.866850	−	1.50143i	0.00165145	−	0.999999i	$-0.499474\pi$
$499$	19.3640	−	33.5394i	0.866850	−	1.50143i	0.865198	−	0.501430i	$-0.167192\pi$
$500$		0			0
$501$	−15.1213	−	26.1909i	−0.675571	−	1.17012i
$502$	−13.7279	+	23.7775i	−0.612707	+	1.06124i
$503$	16.6274			0.741380			0.370690	−	0.928757i	$-0.379121\pi$
$503$	16.6274			0.741380			0.370690	+	0.928757i	$0.379121\pi$
$504$		0			0
$505$	7.75736			0.345198
$506$	−0.514719	+	0.891519i	−0.0228820	+	0.0396328i
$507$	0.707107	+	1.22474i	0.0314037	+	0.0543928i
$508$		0			0
$509$	12.4497	−	21.5636i	0.551825	−	0.955790i	−0.446318	−	0.894875i	$-0.647265\pi$
$509$	12.4497	−	21.5636i	0.551825	−	0.955790i	0.998143	−	0.0609149i	$-0.0194018\pi$
$510$	12.4853			0.552858
$511$		0			0
$512$	−22.6274			−1.00000
$513$	−3.51472	+	6.08767i	−0.155179	+	0.268777i
$514$	11.7279	+	20.3134i	0.517296	+	0.895984i
$515$	17.6569	+	30.5826i	0.778054	+	1.34763i
$516$		0			0
$517$	−18.7279			−0.823653
$518$		0			0
$519$	1.02944			0.0451873
$520$	−6.24264	+	10.8126i	−0.273758	+	0.474163i
$521$	8.82843	+	15.2913i	0.386780	+	0.669923i	0.992014	−	0.126124i	$-0.0402538\pi$
$521$	8.82843	+	15.2913i	0.386780	+	0.669923i	−0.605234	+	0.796048i	$0.706920\pi$
$522$	4.12132	+	7.13834i	0.180385	+	0.312436i
$523$	1.48528	−	2.57258i	0.0649468	−	0.112491i	−0.831724	−	0.555190i	$-0.812646\pi$
$523$	1.48528	−	2.57258i	0.0649468	−	0.112491i	0.896670	+	0.442699i	$0.145979\pi$
$524$		0			0
$525$		0			0
$526$	−45.2132			−1.97139
$527$	−3.70711	+	6.42090i	−0.161484	+	0.279699i
$528$	12.0000	+	20.7846i	0.522233	+	0.904534i
$529$	11.4853	+	19.8931i	0.499360	+	0.864917i
$530$	18.1924	−	31.5101i	0.790227	−	1.36871i
$531$	−11.6569			−0.505864
$532$		0			0
$533$	−3.17157			−0.137376
$534$	4.41421	−	7.64564i	0.191022	−	0.330859i
$535$	−17.9706	−	31.1259i	−0.776935	−	1.34569i
$536$	3.51472	+	6.08767i	0.151813	+	0.262947i
$537$	−6.36396	+	11.0227i	−0.274625	+	0.475665i
$538$	20.9706			0.904105
$539$		0			0
$540$		0			0
$541$	−17.6066	+	30.4955i	−0.756967	+	1.31111i	0.187424	+	0.982279i	$0.439986\pi$
$541$	−17.6066	+	30.4955i	−0.756967	+	1.31111i	−0.944391	+	0.328826i	$0.893347\pi$
$542$	−14.1421	−	24.4949i	−0.607457	−	1.05215i
$543$	4.75736	+	8.23999i	0.204158	+	0.353612i
$544$		0			0
$545$	−38.5269			−1.65031
$546$		0			0
$547$	18.5147			0.791632			0.395816	−	0.918330i	$-0.370462\pi$
$547$	18.5147			0.791632			0.395816	+	0.918330i	$0.370462\pi$
$548$		0			0
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$	43.4558	+	75.2677i	1.85296	+	3.20943i
$551$	−3.62132	+	6.27231i	−0.154273	+	0.267209i
$552$	−0.686292			−0.0292105
$553$		0			0
$554$	13.4142			0.569915
$555$	−19.4853	+	33.7495i	−0.827104	+	1.43259i
$556$		0			0
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	0.710457	−	0.703740i	$-0.248488\pi$
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	−0.964686	+	0.263404i	$0.915155\pi$
$558$	−3.70711	+	6.42090i	−0.156934	+	0.271818i
$559$	5.00000			0.211477
$560$		0			0
$561$	−8.48528			−0.358249
$562$	11.0000	−	19.0526i	0.464007	−	0.803684i
$563$	8.82843	+	15.2913i	0.372074	+	0.644451i	0.989884	−	0.141876i	$-0.0453135\pi$
$563$	8.82843	+	15.2913i	0.372074	+	0.644451i	−0.617811	+	0.786327i	$0.711980\pi$
$564$		0			0
$565$	44.8345	−	77.6557i	1.88620	−	3.26700i
$566$	12.0000			0.504398
$567$		0			0
$568$	−3.02944			−0.127112
$569$	11.5711	−	20.0417i	0.485084	−	0.840191i	−0.514769	−	0.857329i	$-0.672122\pi$
$569$	11.5711	−	20.0417i	0.485084	−	0.840191i	0.999853	+	0.0171383i	$0.00545554\pi$
$570$	5.48528	+	9.50079i	0.229753	+	0.397944i
$571$	4.22792	+	7.32298i	0.176933	+	0.306457i	0.940829	−	0.338883i	$-0.110049\pi$
$571$	4.22792	+	7.32298i	0.176933	+	0.306457i	−0.763896	+	0.645340i	$0.776716\pi$
$572$		0			0
$573$	−29.4558			−1.23054
$574$		0			0
$575$	−2.48528			−0.103643
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−13.4853	−	23.3572i	−0.561400	−	0.972373i	−0.997375	−	0.0724139i	$-0.976930\pi$
$577$	−13.4853	−	23.3572i	−0.561400	−	0.972373i	0.435975	−	0.899959i	$-0.356404\pi$
$578$	10.6066	+	18.3712i	0.441176	+	0.764140i
$579$	1.75736	−	3.04384i	0.0730334	−	0.126497i
$580$		0			0
$581$		0			0
$582$	27.4558			1.13808
$583$	−12.3640	+	21.4150i	−0.512063	+	0.886919i
$584$	−1.07107	−	1.85514i	−0.0443211	−	0.0767664i
$585$	−2.20711	−	3.82282i	−0.0912526	−	0.158054i
$586$	15.1213	−	26.1909i	0.624656	−	1.08194i
$587$	24.5563			1.01355			0.506775	−	0.862079i	$-0.330838\pi$
$587$	24.5563			1.01355			0.506775	+	0.862079i	$0.330838\pi$
$588$		0			0
$589$	−6.51472			−0.268434
$590$	−36.3848	+	63.0203i	−1.49794	+	2.59450i
$591$	16.7279	+	28.9736i	0.688095	+	1.19182i
$592$	−12.4853	−	21.6251i	−0.513142	−	0.888788i
$593$	−15.2782	+	26.4626i	−0.627399	+	1.08669i	0.360672	+	0.932693i	$0.382547\pi$
$593$	−15.2782	+	26.4626i	−0.627399	+	1.08669i	−0.988072	+	0.153995i	$0.950786\pi$
$594$	−33.9411			−1.39262
$595$		0			0
$596$		0			0
$597$	−8.65685	+	14.9941i	−0.354301	+	0.613668i
$598$	−0.121320	−	0.210133i	−0.00496116	−	0.00859298i
$599$	−5.39949	−	9.35220i	−0.220617	−	0.382121i	0.734378	−	0.678740i	$-0.237474\pi$
$599$	−5.39949	−	9.35220i	−0.220617	−	0.382121i	−0.954996	+	0.296620i	$0.904141\pi$
$600$	−28.9706	+	50.1785i	−1.18272	+	2.04853i
$601$	−5.02944			−0.205155			−0.102578	−	0.994725i	$-0.532709\pi$
$601$	−5.02944			−0.205155			−0.102578	+	0.994725i	$0.532709\pi$
$602$		0			0
$603$	−2.48528			−0.101208
$604$		0			0
$605$	−15.4497	−	26.7597i	−0.628122	−	1.08794i
$606$	1.75736	+	3.04384i	0.0713878	+	0.123647i
$607$	0.636039	−	1.10165i	0.0258160	−	0.0447147i	−0.852829	−	0.522191i	$-0.825115\pi$
$607$	0.636039	−	1.10165i	0.0258160	−	0.0447147i	0.878645	+	0.477476i	$0.158448\pi$
$608$		0			0
$609$		0			0
$610$	37.4558			1.51654
$611$	2.20711	−	3.82282i	0.0892900	−	0.154655i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−3.36396	+	5.82655i	−0.135758	+	0.235140i
$615$	−19.7990			−0.798372
$616$		0			0
$617$	23.6569			0.952389			0.476195	−	0.879340i	$-0.342016\pi$
$617$	23.6569			0.952389			0.476195	+	0.879340i	$0.342016\pi$
$618$	−8.00000	+	13.8564i	−0.321807	+	0.557386i
$619$	16.4853	+	28.5533i	0.662599	+	1.14766i	0.979930	+	0.199341i	$0.0638801\pi$
$619$	16.4853	+	28.5533i	0.662599	+	1.14766i	−0.317331	+	0.948315i	$0.602787\pi$
$620$		0			0
$621$	0.485281	−	0.840532i	0.0194737	−	0.0337294i
$622$	−6.48528			−0.260036
$623$		0			0
$624$	−5.65685			−0.226455
$625$	−56.1985	+	97.3386i	−2.24794	+	3.89355i
$626$	13.5858	+	23.5313i	0.542997	+	0.940499i
$627$	−3.72792	−	6.45695i	−0.148879	−	0.257866i
$628$		0			0
$629$	8.82843			0.352012
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−2.10051	+	3.63818i	−0.0835536	+	0.144719i
$633$	12.7071	+	22.0094i	0.505062	+	0.874793i
$634$	−8.00000	−	13.8564i	−0.317721	−	0.550308i
$635$	−4.41421	+	7.64564i	−0.175173	+	0.303408i
$636$		0			0
$637$		0			0
$638$	−34.9706			−1.38450
$639$	0.535534	−	0.927572i	0.0211854	−	0.0366942i
$640$	−24.9706	−	43.2503i	−0.987048	−	1.70962i
$641$	−13.3284	−	23.0855i	−0.526441	−	0.911823i	−0.999525	−	0.0308057i	$-0.990193\pi$
$641$	−13.3284	−	23.0855i	−0.526441	−	0.911823i	0.473084	−	0.881017i	$-0.343141\pi$
$642$	8.14214	−	14.1026i	0.321344	−	0.556585i
$643$	4.48528			0.176882			0.0884411	−	0.996081i	$-0.471811\pi$
$643$	4.48528			0.176882			0.0884411	+	0.996081i	$0.471811\pi$
$644$		0			0
$645$	31.2132			1.22902
$646$	1.24264	−	2.15232i	0.0488910	−	0.0846818i
$647$	25.2635	+	43.7576i	0.993209	+	1.72029i	0.597362	+	0.801972i	$0.296216\pi$
$647$	25.2635	+	43.7576i	0.993209	+	1.72029i	0.395847	+	0.918316i	$0.370451\pi$
$648$	−7.07107	−	12.2474i	−0.277778	−	0.481125i
$649$	24.7279	−	42.8300i	0.970656	−	1.68123i
$650$	−20.4853			−0.803499
$651$		0			0
$652$		0			0
$653$	2.65685	−	4.60181i	0.103971	−	0.180083i	−0.809346	−	0.587331i	$-0.800179\pi$
$653$	2.65685	−	4.60181i	0.103971	−	0.180083i	0.913317	+	0.407249i	$0.133512\pi$
$654$	−8.72792	−	15.1172i	−0.341289	−	0.591129i
$655$	−6.24264	−	10.8126i	−0.243920	−	0.422482i
$656$	6.34315	−	10.9867i	0.247658	−	0.428957i
$657$	0.757359			0.0295474
$658$		0			0
$659$	−26.6569			−1.03840			−0.519202	−	0.854652i	$-0.673771\pi$
$659$	−26.6569			−1.03840			−0.519202	+	0.854652i	$0.673771\pi$
$660$		0			0
$661$	9.62132	+	16.6646i	0.374226	+	0.648178i	0.990211	−	0.139580i	$-0.0445751\pi$
$661$	9.62132	+	16.6646i	0.374226	+	0.648178i	−0.615985	+	0.787758i	$0.711242\pi$
$662$	12.7279	+	22.0454i	0.494685	+	0.856819i
$663$	1.00000	−	1.73205i	0.0388368	−	0.0672673i
$664$	−13.4558			−0.522188
$665$		0			0
$666$	8.82843			0.342095
$667$	0.500000	−	0.866025i	0.0193601	−	0.0335326i
$668$		0			0
$669$	6.53553	+	11.3199i	0.252678	+	0.437652i
$670$	−7.75736	+	13.4361i	−0.299693	+	0.519083i
$671$	−25.4558			−0.982712
$672$		0			0
$673$	40.9411			1.57816			0.789082	−	0.614288i	$-0.210557\pi$
$673$	40.9411			1.57816			0.789082	+	0.614288i	$0.210557\pi$
$674$	23.3345	−	40.4166i	0.898812	−	1.55679i
$675$	−40.9706	−	70.9631i	−1.57696	−	2.73137i
$676$		0			0
$677$	−14.6777	+	25.4225i	−0.564109	+	0.977065i	0.433023	+	0.901383i	$0.357447\pi$
$677$	−14.6777	+	25.4225i	−0.564109	+	0.977065i	−0.997132	+	0.0756822i	$0.975887\pi$
$678$	40.6274			1.56029
$679$		0			0
$680$	17.6569			0.677109
$681$	14.9706	−	25.9298i	0.573673	−	0.993631i
$682$	−15.7279	−	27.2416i	−0.602253	−	1.04313i
$683$	13.4142	+	23.2341i	0.513281	+	0.889028i	0.999881	+	0.0154036i	$0.00490332\pi$
$683$	13.4142	+	23.2341i	0.513281	+	0.889028i	−0.486601	+	0.873624i	$0.661763\pi$
$684$		0			0
$685$	−32.7279			−1.25047
$686$		0			0
$687$	30.3431			1.15766
$688$	−10.0000	+	17.3205i	−0.381246	+	0.660338i
$689$	−2.91421	−	5.04757i	−0.111023	−	0.192297i
$690$	−0.757359	−	1.31178i	−0.0288322	−	0.0499388i
$691$	15.3492	−	26.5857i	0.583913	−	1.01137i	−0.411097	−	0.911591i	$-0.634854\pi$
$691$	15.3492	−	26.5857i	0.583913	−	1.01137i	0.995010	−	0.0997750i	$-0.0318123\pi$
$692$		0			0
$693$		0			0
$694$	8.00000			0.303676
$695$	4.94975	−	8.57321i	0.187755	−	0.325201i
$696$	−11.6569	−	20.1903i	−0.441852	−	0.765310i
$697$	2.24264	+	3.88437i	0.0849461	+	0.147131i
$698$	0.192388	−	0.333226i	0.00728200	−	0.0126128i
$699$	4.72792			0.178826
$700$		0			0
$701$	28.7990			1.08772			0.543861	−	0.839175i	$-0.316962\pi$
$701$	28.7990			1.08772			0.543861	+	0.839175i	$0.316962\pi$
$702$	4.00000	−	6.92820i	0.150970	−	0.261488i
$703$	3.87868	+	6.71807i	0.146287	+	0.253377i
$704$	16.9706	+	29.3939i	0.639602	+	1.10782i
$705$	13.7782	−	23.8645i	0.518916	−	0.898789i
$706$	12.0000			0.451626
$707$		0			0
$708$		0			0
$709$	12.3640	−	21.4150i	0.464338	−	0.804258i	−0.534833	−	0.844958i	$-0.679626\pi$
$709$	12.3640	−	21.4150i	0.464338	−	0.804258i	0.999171	+	0.0407002i	$0.0129589\pi$
$710$	−3.34315	−	5.79050i	−0.125466	−	0.217314i
$711$	−0.742641	−	1.28629i	−0.0278512	−	0.0482397i
$712$	6.24264	−	10.8126i	0.233953	−	0.405218i
$713$	0.899495			0.0336864
$714$		0			0
$715$	18.7279			0.700385
$716$		0			0
$717$	14.4853	+	25.0892i	0.540963	+	0.936975i
$718$	5.72792	+	9.92105i	0.213764	+	0.370250i
$719$	5.12132	−	8.87039i	0.190993	−	0.330810i	−0.754587	−	0.656201i	$-0.772163\pi$
$719$	5.12132	−	8.87039i	0.190993	−	0.330810i	0.945580	+	0.325391i	$0.105496\pi$
$720$	17.6569			0.658032
$721$		0			0
$722$	−24.6863			−0.918729
$723$	15.7071	−	27.2055i	0.584154	−	1.01178i
$724$		0			0
$725$	−42.2132	−	73.1154i	−1.56776	−	2.71544i
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	42.0000			1.55769			0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000			1.55769			0.778847	+	0.627214i	$0.215805\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	2.36396	−	4.09450i	0.0874941	−	0.151544i
$731$	−3.53553	−	6.12372i	−0.130766	−	0.226494i
$732$		0			0
$733$	−21.3492	+	36.9780i	−0.788552	+	1.36581i	0.138302	+	0.990390i	$0.455836\pi$
$733$	−21.3492	+	36.9780i	−0.788552	+	1.36581i	−0.926854	+	0.375422i	$0.877498\pi$
$734$	2.48528			0.0917334
$735$		0			0
$736$		0			0
$737$	5.27208	−	9.13151i	0.194199	−	0.336363i
$738$	2.24264	+	3.88437i	0.0825527	+	0.142986i
$739$	−20.8492	−	36.1119i	−0.766952	−	1.32840i	−0.939208	−	0.343347i	$-0.888439\pi$
$739$	−20.8492	−	36.1119i	−0.766952	−	1.32840i	0.172257	−	0.985052i	$-0.444894\pi$
$740$		0			0
$741$	1.75736			0.0645582
$742$		0			0
$743$	−18.3431			−0.672945			−0.336472	−	0.941693i	$-0.609234\pi$
$743$	−18.3431			−0.672945			−0.336472	+	0.941693i	$0.609234\pi$
$744$	10.4853	−	18.1610i	0.384409	−	0.665816i
$745$	−17.1213	−	29.6550i	−0.627277	−	1.08648i
$746$	6.00000	+	10.3923i	0.219676	+	0.380489i
$747$	2.37868	−	4.11999i	0.0870313	−	0.150743i
$748$		0			0
$749$		0			0
$750$	−83.7401			−3.05776
$751$	0.742641	−	1.28629i	0.0270993	−	0.0469374i	−0.852158	−	0.523285i	$-0.824706\pi$
$751$	0.742641	−	1.28629i	0.0270993	−	0.0469374i	0.879257	+	0.476348i	$0.158040\pi$
$752$	8.82843	+	15.2913i	0.321940	+	0.557616i
$753$	13.7279	+	23.7775i	0.500273	+	0.866499i
$754$	4.12132	−	7.13834i	0.150090	−	0.259963i
$755$	−80.5269			−2.93067
$756$		0			0
$757$	4.51472			0.164090			0.0820451	−	0.996629i	$-0.473855\pi$
$757$	4.51472			0.164090			0.0820451	+	0.996629i	$0.473855\pi$
$758$	−22.7990	+	39.4890i	−0.828097	+	1.43431i
$759$	0.514719	+	0.891519i	0.0186831	+	0.0323601i
$760$	7.75736	+	13.4361i	0.281389	+	0.487380i
$761$	−21.6213	+	37.4492i	−0.783772	+	1.35753i	0.145958	+	0.989291i	$0.453374\pi$
$761$	−21.6213	+	37.4492i	−0.783772	+	1.35753i	−0.929730	+	0.368243i	$0.879960\pi$
$762$	−4.00000			−0.144905
$763$		0			0
$764$		0			0
$765$	−3.12132	+	5.40629i	−0.112852	+	0.195465i
$766$	2.48528	+	4.30463i	0.0897969	+	0.155533i
$767$	5.82843	+	10.0951i	0.210452	+	0.364514i
$768$		0			0
$769$	9.78680			0.352921			0.176460	−	0.984308i	$-0.443535\pi$
$769$	9.78680			0.352921			0.176460	+	0.984308i	$0.443535\pi$
$770$		0			0
$771$	23.4558			0.844742
$772$		0			0
$773$	13.5858	+	23.5313i	0.488647	+	0.846361i	0.999915	−	0.0130603i	$-0.00415735\pi$
$773$	13.5858	+	23.5313i	0.488647	+	0.846361i	−0.511268	+	0.859421i	$0.670824\pi$
$774$	−3.53553	−	6.12372i	−0.127082	−	0.220113i
$775$	37.9706	−	65.7669i	1.36394	−	2.36242i
$776$	38.8284			1.39386
$777$		0			0
$778$	25.9411			0.930034
$779$	−1.97056	+	3.41311i	−0.0706027	+	0.122288i
$780$		0			0
$781$	2.27208	+	3.93535i	0.0813013	+	0.140818i
$782$	−0.171573	+	0.297173i	−0.00613543	+	0.0106269i
$783$	32.9706			1.17827
$784$		0			0
$785$	−54.0416			−1.92883
$786$	2.82843	−	4.89898i	0.100887	−	0.174741i
$787$	16.6213	+	28.7890i	0.592486	+	1.02622i	0.993896	+	0.110318i	$0.0351868\pi$
$787$	16.6213	+	28.7890i	0.592486	+	1.02622i	−0.401410	+	0.915898i	$0.631480\pi$
$788$		0			0
$789$	−22.6066	+	39.1558i	−0.804816	+	1.39398i
$790$	−9.27208			−0.329886
$791$		0			0
$792$	−12.0000			−0.426401
$793$	3.00000	−	5.19615i	0.106533	−	0.184521i
$794$	−17.1213	−	29.6550i	−0.607613	−	1.05242i
$795$	−18.1924	−	31.5101i	−0.645218	−	1.11755i
$796$		0			0
$797$	−35.6569			−1.26303			−0.631515	−	0.775363i	$-0.717567\pi$
$797$	−35.6569			−1.26303			−0.631515	+	0.775363i	$0.717567\pi$
$798$		0			0
$799$	−6.24264			−0.220849
$800$		0			0
$801$	2.20711	+	3.82282i	0.0779843	+	0.135073i
$802$	−12.4853	−	21.6251i	−0.440871	−	0.763610i
$803$	−1.60660	+	2.78272i	−0.0566957	+	0.0981999i
$804$		0			0
$805$		0			0
$806$	7.41421			0.261155
$807$	10.4853	−	18.1610i	0.369099	−	0.639299i
$808$	2.48528	+	4.30463i	0.0874319	+	0.151436i
$809$	−0.257359	−	0.445759i	−0.00904827	−	0.0156721i	0.861466	−	0.507816i	$-0.169547\pi$
$809$	−0.257359	−	0.445759i	−0.00904827	−	0.0156721i	−0.870514	+	0.492143i	$0.836214\pi$
$810$	15.6066	−	27.0314i	0.548360	−	0.949788i
$811$	45.9411			1.61321			0.806606	−	0.591090i	$-0.201302\pi$
$811$	45.9411			1.61321			0.806606	+	0.591090i	$0.201302\pi$
$812$		0			0
$813$	−28.2843			−0.991973
$814$	−18.7279	+	32.4377i	−0.656413	+	1.13694i
$815$	18.7279	+	32.4377i	0.656010	+	1.13624i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	3.10660	−	5.38079i	0.108686	−	0.188250i
$818$	−7.41421			−0.259232
$819$		0			0
$820$		0			0
$821$	−4.07107	+	7.05130i	−0.142081	+	0.246092i	−0.928280	−	0.371882i	$-0.878713\pi$
$821$	−4.07107	+	7.05130i	−0.142081	+	0.246092i	0.786199	+	0.617973i	$0.212046\pi$
$822$	−7.41421	−	12.8418i	−0.258600	−	0.447909i
$823$	3.24264	+	5.61642i	0.113031	+	0.195776i	0.916991	−	0.398908i	$-0.130611\pi$
$823$	3.24264	+	5.61642i	0.113031	+	0.195776i	−0.803960	+	0.594684i	$0.797277\pi$
$824$	−11.3137	+	19.5959i	−0.394132	+	0.682656i
$825$	86.9117			3.02588
$826$		0			0
$827$	1.45584			0.0506247			0.0253123	−	0.999680i	$-0.491942\pi$
$827$	1.45584			0.0506247			0.0253123	+	0.999680i	$0.491942\pi$
$828$		0			0
$829$	−12.6360	−	21.8863i	−0.438868	−	0.760141i	0.558735	−	0.829346i	$-0.311287\pi$
$829$	−12.6360	−	21.8863i	−0.438868	−	0.760141i	−0.997602	+	0.0692052i	$0.977954\pi$
$830$	−14.8492	−	25.7196i	−0.515425	−	0.892742i
$831$	6.70711	−	11.6170i	0.232667	−	0.402991i
$832$	−8.00000			−0.277350
$833$		0			0
$834$	4.48528			0.155313
$835$	47.1985	−	81.7502i	1.63337	−	2.82908i
$836$		0			0
$837$	14.8284	+	25.6836i	0.512545	+	0.887755i
$838$	−23.2426	+	40.2574i	−0.802904	+	1.39067i
$839$	−38.8284			−1.34051			−0.670253	−	0.742133i	$-0.733814\pi$
$839$	−38.8284			−1.34051			−0.670253	+	0.742133i	$0.733814\pi$
$840$		0			0
$841$	4.97056			0.171399
$842$	13.2426	−	22.9369i	0.456372	−	0.790459i
$843$	−11.0000	−	19.0526i	−0.378860	−	0.656205i
$844$		0			0
$845$	−2.20711	+	3.82282i	−0.0759268	+	0.131509i
$846$	−6.24264			−0.214626
$847$		0			0
$848$	23.3137			0.800596
$849$	6.00000	−	10.3923i	0.205919	−	0.356663i
$850$	14.4853	+	25.0892i	0.496841	+	0.860554i
$851$	−0.535534	−	0.927572i	−0.0183579	−	0.0317968i
$852$		0			0
$853$	14.2721			0.488667			0.244333	−	0.969691i	$-0.421431\pi$
$853$	14.2721			0.488667			0.244333	+	0.969691i	$0.421431\pi$
$854$		0			0
$855$	−5.48528			−0.187593
$856$	11.5147	−	19.9441i	0.393565	−	0.681675i
$857$	−9.38478	−	16.2549i	−0.320578	−	0.555257i	0.660030	−	0.751240i	$-0.270544\pi$
$857$	−9.38478	−	16.2549i	−0.320578	−	0.555257i	−0.980607	+	0.195983i	$0.937210\pi$
$858$	4.24264	+	7.34847i	0.144841	+	0.250873i
$859$	1.48528	−	2.57258i	0.0506771	−	0.0877754i	−0.839574	−	0.543245i	$-0.817195\pi$
$859$	1.48528	−	2.57258i	0.0506771	−	0.0877754i	0.890251	+	0.455470i	$0.150529\pi$
$860$		0			0
$861$		0			0
$862$	−33.4558			−1.13951
$863$	14.1421	−	24.4949i	0.481404	−	0.833816i	−0.518368	−	0.855157i	$-0.673460\pi$
$863$	14.1421	−	24.4949i	0.481404	−	0.833816i	0.999772	+	0.0213414i	$0.00679371\pi$
$864$		0			0
$865$	1.60660	+	2.78272i	0.0546261	+	0.0946152i
$866$	−6.34315	+	10.9867i	−0.215549	+	0.373342i
$867$	21.2132			0.720438
$868$		0			0
$869$	6.30152			0.213764
$870$	25.7279	−	44.5621i	0.872258	−	1.51080i
$871$	1.24264	+	2.15232i	0.0421053	+	0.0729285i
$872$	−12.3431	−	21.3790i	−0.417992	−	0.723983i
$873$	−6.86396	+	11.8887i	−0.232310	+	0.402373i
$874$	−0.301515			−0.0101989
$875$		0			0
$876$		0			0
$877$	0.878680	−	1.52192i	0.0296709	−	0.0513915i	−0.850809	−	0.525476i	$-0.823887\pi$
$877$	0.878680	−	1.52192i	0.0296709	−	0.0513915i	0.880480	+	0.474084i	$0.157221\pi$
$878$	12.3848	+	21.4511i	0.417966	+	0.723938i
$879$	−15.1213	−	26.1909i	−0.510029	−	0.883397i
$880$	−37.4558	+	64.8754i	−1.26264	+	2.18695i
$881$	−49.1127			−1.65465			−0.827324	−	0.561724i	$-0.810138\pi$
$881$	−49.1127			−1.65465			−0.827324	+	0.561724i	$0.810138\pi$
$882$		0			0
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$		0			0
$885$	36.3848	+	63.0203i	1.22306	+	2.11840i
$886$	18.6066	+	32.2276i	0.625101	+	1.08271i
$887$	21.5563	−	37.3367i	0.723791	−	1.25364i	−0.235678	−	0.971831i	$-0.575731\pi$
$887$	21.5563	−	37.3367i	0.723791	−	1.25364i	0.959470	−	0.281812i	$-0.0909355\pi$
$888$	−24.9706			−0.837957
$889$		0			0
$890$	27.5563			0.923691
$891$	−10.6066	+	18.3712i	−0.355335	+	0.615457i
$892$		0			0
$893$	−2.74264	−	4.75039i	−0.0917790	−	0.158966i
$894$	7.75736	−	13.4361i	0.259445	−	0.449372i
$895$	−39.7279			−1.32796
$896$		0			0
$897$	−0.242641			−0.00810154
$898$	−18.9706	+	32.8580i	−0.633056	+	1.09648i
$899$	15.2782	+	26.4626i	0.509556	+	0.882576i
$900$		0			0
$901$	−4.12132	+	7.13834i	−0.137301	+	0.237812i
$902$	−19.0294			−0.633611
$903$		0			0
$904$	57.4558			1.91095
$905$	−14.8492	+	25.7196i	−0.493606	+	0.854950i
$906$	−18.2426	−	31.5972i	−0.606071	−	1.04975i
$907$	15.9853	+	27.6873i	0.530783	+	0.919342i	0.999355	+	0.0359172i	$0.0114352\pi$
$907$	15.9853	+	27.6873i	0.530783	+	0.919342i	−0.468572	+	0.883425i	$0.655231\pi$
$908$		0			0
$909$	−1.75736			−0.0582879
$910$		0			0
$911$	−10.0294			−0.332290			−0.166145	−	0.986101i	$-0.553132\pi$
$911$	−10.0294			−0.332290			−0.166145	+	0.986101i	$0.553132\pi$
$912$	−3.51472	+	6.08767i	−0.116384	+	0.201583i
$913$	10.0919	+	17.4797i	0.333993	+	0.578492i
$914$	−24.8995	−	43.1272i	−0.823602	−	1.42652i
$915$	18.7279	−	32.4377i	0.619126	−	1.07236i
$916$		0			0
$917$		0			0
$918$	−11.3137			−0.373408
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	−0.993208	−	0.116348i	$-0.962881\pi$
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	0.597365	+	0.801970i	$0.296214\pi$
$920$	−1.07107	−	1.85514i	−0.0353121	−	0.0611623i
$921$	3.36396	+	5.82655i	0.110846	+	0.191991i
$922$	−2.24264	+	3.88437i	−0.0738574	+	0.127925i
$923$	−1.07107			−0.0352546
$924$		0			0
$925$	−90.4264			−2.97320
$926$	−3.00000	+	5.19615i	−0.0985861	+	0.170756i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$		0			0
$929$	−8.55025	+	14.8095i	−0.280525	+	0.485883i	−0.971514	−	0.236982i	$-0.923842\pi$
$929$	−8.55025	+	14.8095i	−0.280525	+	0.485883i	0.690989	+	0.722865i	$0.257175\pi$
$930$	46.2843			1.51772
$931$		0			0
$932$		0			0
$933$	−3.24264	+	5.61642i	−0.106159	+	0.183873i
$934$	−11.2426	−	19.4728i	−0.367870	−	0.637170i
$935$	−13.2426	−	22.9369i	−0.433081	−	0.750118i
$936$	1.41421	−	2.44949i	0.0462250	−	0.0800641i
$937$	2.78680			0.0910407			0.0455203	−	0.998963i	$-0.485505\pi$
$937$	2.78680			0.0910407			0.0455203	+	0.998963i	$0.485505\pi$
$938$		0			0
$939$	27.1716			0.886711
$940$		0			0
$941$	−12.9645	−	22.4551i	−0.422630	−	0.732016i	0.573566	−	0.819159i	$-0.305560\pi$
$941$	−12.9645	−	22.4551i	−0.422630	−	0.732016i	−0.996196	+	0.0871434i	$0.972226\pi$
$942$	−12.2426	−	21.2049i	−0.398887	−	0.690892i
$943$	0.272078	−	0.471253i	0.00886008	−	0.0153461i
$944$	−46.6274			−1.51759
$945$		0			0
$946$	30.0000			0.975384
$947$	−10.4142	+	18.0379i	−0.338416	+	0.586155i	−0.984135	−	0.177421i	$-0.943225\pi$
$947$	−10.4142	+	18.0379i	−0.338416	+	0.586155i	0.645719	+	0.763575i	$0.276558\pi$
$948$		0			0
$949$	−0.378680	−	0.655892i	−0.0122925	−	0.0212912i
$950$	−12.7279	+	22.0454i	−0.412948	+	0.715247i
$951$	−16.0000			−0.518836
$952$		0			0
$953$	−17.1421			−0.555288			−0.277644	−	0.960684i	$-0.589554\pi$
$953$	−17.1421			−0.555288			−0.277644	+	0.960684i	$0.589554\pi$
$954$	−4.12132	+	7.13834i	−0.133433	+	0.231112i
$955$	−45.9706	−	79.6234i	−1.48757	−	2.57655i
$956$		0			0
$957$	−17.4853	+	30.2854i	−0.565219	+	0.978988i
$958$	51.2132			1.65462
$959$		0			0
$960$	−49.9411			−1.61184
$961$	1.75736	−	3.04384i	0.0566890	−	0.0981882i
$962$	−4.41421	−	7.64564i	−0.142320	−	0.246505i
$963$	4.07107	+	7.05130i	0.131188	+	0.227225i
$964$		0			0
$965$	10.9706			0.353155
$966$		0			0
$967$	−41.6985			−1.34093			−0.670466	−	0.741940i	$-0.733906\pi$
$967$	−41.6985			−1.34093			−0.670466	+	0.741940i	$0.733906\pi$
$968$	9.89949	−	17.1464i	0.318182	−	0.551107i
$969$	−1.24264	−	2.15232i	−0.0399194	−	0.0691424i
$970$	42.8492	+	74.2171i	1.37581	+	2.38297i
$971$	3.72792	−	6.45695i	0.119635	−	0.207213i	−0.799988	−	0.600016i	$-0.795161\pi$
$971$	3.72792	−	6.45695i	0.119635	−	0.207213i	0.919623	+	0.392802i	$0.128494\pi$
$972$		0			0
$973$		0			0
$974$	55.7990			1.78791
$975$	−10.2426	+	17.7408i	−0.328027	+	0.568159i
$976$	12.0000	+	20.7846i	0.384111	+	0.665299i
$977$	12.0208	+	20.8207i	0.384580	+	0.666112i	0.991711	−	0.128490i	$-0.0410130\pi$
$977$	12.0208	+	20.8207i	0.384580	+	0.666112i	−0.607131	+	0.794602i	$0.707680\pi$
$978$	−8.48528	+	14.6969i	−0.271329	+	0.469956i
$979$	−18.7279			−0.598547
$980$		0			0
$981$	8.72792			0.278661
$982$	20.2426	−	35.0613i	0.645969	−	1.11885i
$983$	−16.5208	−	28.6149i	−0.526932	−	0.912673i	−0.999507	−	0.0313830i	$-0.990009\pi$
$983$	−16.5208	−	28.6149i	−0.526932	−	0.912673i	0.472575	−	0.881290i	$-0.343324\pi$
$984$	−6.34315	−	10.9867i	−0.202212	−	0.350242i
$985$	−52.2132	+	90.4359i	−1.66365	+	2.88153i
$986$	−11.6569			−0.371230
$987$		0			0
$988$		0			0
$989$	−0.428932	+	0.742932i	−0.0136393	+	0.0236239i
$990$	−13.2426	−	22.9369i	−0.420879	−	0.728983i
$991$	−17.4853	−	30.2854i	−0.555438	−	0.962047i	−0.997869	−	0.0652448i	$-0.979217\pi$
$991$	−17.4853	−	30.2854i	−0.555438	−	0.962047i	0.442431	−	0.896803i	$-0.354116\pi$
$992$		0			0
$993$	25.4558			0.807817
$994$		0			0
$995$	−54.0416			−1.71323
$996$		0			0
$997$	14.2426	+	24.6690i	0.451069	+	0.781274i	0.998453	−	0.0556074i	$-0.0177095\pi$
$997$	14.2426	+	24.6690i	0.451069	+	0.781274i	−0.547384	+	0.836882i	$0.684376\pi$
$998$	27.3848	+	47.4318i	0.866850	+	1.50143i
$999$	17.6569	−	30.5826i	0.558638	−	0.967590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.f.79.1		4
7.2	even	3		91.2.a.c.1.2	✓	2
7.3	odd	6		637.2.e.g.508.1		4
7.4	even	3	inner	637.2.e.f.508.1		4
7.5	odd	6		637.2.a.g.1.2		2
7.6	odd	2		637.2.e.g.79.1		4
21.2	odd	6		819.2.a.h.1.1		2
21.5	even	6		5733.2.a.s.1.1		2
28.23	odd	6		1456.2.a.q.1.2		2
35.9	even	6		2275.2.a.j.1.1		2
56.37	even	6		5824.2.a.bl.1.2		2
56.51	odd	6		5824.2.a.bk.1.1		2
91.12	odd	6		8281.2.a.v.1.1		2
91.44	odd	12		1183.2.c.d.337.1		4
91.51	even	6		1183.2.a.d.1.1		2
91.86	odd	12		1183.2.c.d.337.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.c.1.2	✓	2	7.2	even	3
637.2.a.g.1.2		2	7.5	odd	6
637.2.e.f.79.1		4	1.1	even	1	trivial
637.2.e.f.508.1		4	7.4	even	3	inner
637.2.e.g.79.1		4	7.6	odd	2
637.2.e.g.508.1		4	7.3	odd	6
819.2.a.h.1.1		2	21.2	odd	6
1183.2.a.d.1.1		2	91.51	even	6
1183.2.c.d.337.1		4	91.44	odd	12
1183.2.c.d.337.3		4	91.86	odd	12
1456.2.a.q.1.2		2	28.23	odd	6
2275.2.a.j.1.1		2	35.9	even	6
5733.2.a.s.1.1		2	21.5	even	6
5824.2.a.bk.1.1		2	56.51	odd	6
5824.2.a.bl.1.2		2	56.37	even	6
8281.2.a.v.1.1		2	91.12	odd	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-2.20711 + 3.82282i) q^{5} -2.00000 q^{6} -2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-2.20711 + 3.82282i) q^{5} -2.00000 q^{6} -2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.12132 - 5.40629i) q^{10} +(2.12132 + 3.67423i) q^{11} -1.00000 q^{13} -6.24264 q^{15} +(2.00000 - 3.46410i) q^{16} +(0.707107 + 1.22474i) q^{17} +(0.707107 + 1.22474i) q^{18} +(-0.621320 + 1.07616i) q^{19} -6.00000 q^{22} +(0.0857864 - 0.148586i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(-7.24264 - 12.5446i) q^{25} +(0.707107 - 1.22474i) q^{26} +5.65685 q^{27} +5.82843 q^{29} +(4.41421 - 7.64564i) q^{30} +(2.62132 + 4.54026i) q^{31} +(-3.00000 + 5.19615i) q^{33} -2.00000 q^{34} +(3.12132 - 5.40629i) q^{37} +(-0.878680 - 1.52192i) q^{38} +(-0.707107 - 1.22474i) q^{39} +(6.24264 - 10.8126i) q^{40} +3.17157 q^{41} -5.00000 q^{43} +(2.20711 + 3.82282i) q^{45} +(0.121320 + 0.210133i) q^{46} +(-2.20711 + 3.82282i) q^{47} +5.65685 q^{48} +20.4853 q^{50} +(-1.00000 + 1.73205i) q^{51} +(2.91421 + 5.04757i) q^{53} +(-4.00000 + 6.92820i) q^{54} -18.7279 q^{55} -1.75736 q^{57} +(-4.12132 + 7.13834i) q^{58} +(-5.82843 - 10.0951i) q^{59} +(-3.00000 + 5.19615i) q^{61} -7.41421 q^{62} +8.00000 q^{64} +(2.20711 - 3.82282i) q^{65} +(-4.24264 - 7.34847i) q^{66} +(-1.24264 - 2.15232i) q^{67} +0.242641 q^{69} +1.07107 q^{71} +(-1.41421 + 2.44949i) q^{72} +(0.378680 + 0.655892i) q^{73} +(4.41421 + 7.64564i) q^{74} +(10.2426 - 17.7408i) q^{75} +2.00000 q^{78} +(0.742641 - 1.28629i) q^{79} +(8.82843 + 15.2913i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-2.24264 + 3.88437i) q^{82} +4.75736 q^{83} -6.24264 q^{85} +(3.53553 - 6.12372i) q^{86} +(4.12132 + 7.13834i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(-2.20711 + 3.82282i) q^{89} -6.24264 q^{90} +(-3.70711 + 6.42090i) q^{93} +(-3.12132 - 5.40629i) q^{94} +(-2.74264 - 4.75039i) q^{95} -13.7279 q^{97} +4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{5} - 8 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q - 6 * q^5 - 8 * q^6 + 2 * q^9	\( 4 q - 6 q^{5} - 8 q^{6} + 2 q^{9} - 4 q^{10} - 4 q^{13} - 8 q^{15} + 8 q^{16} + 6 q^{19} - 24 q^{22} + 6 q^{23} - 8 q^{24} - 12 q^{25} + 12 q^{29} + 12 q^{30} + 2 q^{31} - 12 q^{33} - 8 q^{34} + 4 q^{37} - 12 q^{38} + 8 q^{40} + 24 q^{41} - 20 q^{43} + 6 q^{45} - 8 q^{46} - 6 q^{47} + 48 q^{50} - 4 q^{51} + 6 q^{53} - 16 q^{54} - 24 q^{55} - 24 q^{57} - 8 q^{58} - 12 q^{59} - 12 q^{61} - 24 q^{62} + 32 q^{64} + 6 q^{65} + 12 q^{67} - 16 q^{69} - 24 q^{71} + 10 q^{73} + 12 q^{74} + 24 q^{75} + 8 q^{78} - 14 q^{79} + 24 q^{80} + 10 q^{81} + 8 q^{82} + 36 q^{83} - 8 q^{85} + 8 q^{87} - 24 q^{88} - 6 q^{89} - 8 q^{90} - 12 q^{93} - 4 q^{94} + 6 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q - 6 * q^5 - 8 * q^6 + 2 * q^9 - 4 * q^10 - 4 * q^13 - 8 * q^15 + 8 * q^16 + 6 * q^19 - 24 * q^22 + 6 * q^23 - 8 * q^24 - 12 * q^25 + 12 * q^29 + 12 * q^30 + 2 * q^31 - 12 * q^33 - 8 * q^34 + 4 * q^37 - 12 * q^38 + 8 * q^40 + 24 * q^41 - 20 * q^43 + 6 * q^45 - 8 * q^46 - 6 * q^47 + 48 * q^50 - 4 * q^51 + 6 * q^53 - 16 * q^54 - 24 * q^55 - 24 * q^57 - 8 * q^58 - 12 * q^59 - 12 * q^61 - 24 * q^62 + 32 * q^64 + 6 * q^65 + 12 * q^67 - 16 * q^69 - 24 * q^71 + 10 * q^73 + 12 * q^74 + 24 * q^75 + 8 * q^78 - 14 * q^79 + 24 * q^80 + 10 * q^81 + 8 * q^82 + 36 * q^83 - 8 * q^85 + 8 * q^87 - 24 * q^88 - 6 * q^89 - 8 * q^90 - 12 * q^93 - 4 * q^94 + 6 * q^95 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more