LMFDB - Embedded newform 637.2.e.g.79.2

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			79.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.g.508.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.792893 - 1.37333i) q^{5} +2.00000 q^{6} +2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.792893 - 1.37333i) q^{5} +2.00000 q^{6} +2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.12132 - 1.94218i) q^{10} +(-2.12132 - 3.67423i) q^{11} +1.00000 q^{13} +2.24264 q^{15} +(2.00000 - 3.46410i) q^{16} +(0.707107 + 1.22474i) q^{17} +(-0.707107 - 1.22474i) q^{18} +(-3.62132 + 6.27231i) q^{19} -6.00000 q^{22} +(2.91421 - 5.04757i) q^{23} +(2.00000 + 3.46410i) q^{24} +(1.24264 + 2.15232i) q^{25} +(0.707107 - 1.22474i) q^{26} +5.65685 q^{27} +0.171573 q^{29} +(1.58579 - 2.74666i) q^{30} +(1.62132 + 2.80821i) q^{31} +(3.00000 - 5.19615i) q^{33} +2.00000 q^{34} +(-1.12132 + 1.94218i) q^{37} +(5.12132 + 8.87039i) q^{38} +(0.707107 + 1.22474i) q^{39} +(2.24264 - 3.88437i) q^{40} -8.82843 q^{41} -5.00000 q^{43} +(-0.792893 - 1.37333i) q^{45} +(-4.12132 - 7.13834i) q^{46} +(0.792893 - 1.37333i) q^{47} +5.65685 q^{48} +3.51472 q^{50} +(-1.00000 + 1.73205i) q^{51} +(0.0857864 + 0.148586i) q^{53} +(4.00000 - 6.92820i) q^{54} -6.72792 q^{55} -10.2426 q^{57} +(0.121320 - 0.210133i) q^{58} +(0.171573 + 0.297173i) q^{59} +(3.00000 - 5.19615i) q^{61} +4.58579 q^{62} +8.00000 q^{64} +(0.792893 - 1.37333i) q^{65} +(-4.24264 - 7.34847i) q^{66} +(7.24264 + 12.5446i) q^{67} +8.24264 q^{69} -13.0711 q^{71} +(1.41421 - 2.44949i) q^{72} +(-4.62132 - 8.00436i) q^{73} +(1.58579 + 2.74666i) q^{74} +(-1.75736 + 3.04384i) q^{75} +2.00000 q^{78} +(-7.74264 + 13.4106i) q^{79} +(-3.17157 - 5.49333i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-6.24264 + 10.8126i) q^{82} -13.2426 q^{83} +2.24264 q^{85} +(-3.53553 + 6.12372i) q^{86} +(0.121320 + 0.210133i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(0.792893 - 1.37333i) q^{89} -2.24264 q^{90} +(-2.29289 + 3.97141i) q^{93} +(-1.12132 - 1.94218i) q^{94} +(5.74264 + 9.94655i) q^{95} -11.7279 q^{97} -4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.666667\pi$
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i	1.00000			$0$
$3$	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
$5$	0.792893	−	1.37333i	0.354593	−	0.614172i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$	0.792893	−	1.37333i	0.354593	−	0.614172i	0.987048	+	0.160424i	$0.0512862\pi$
$6$	2.00000			0.816497
$7$		0			0
$7$		0			0
$8$	2.82843			1.00000
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.12132	−	1.94218i	−0.354593	−	0.614172i
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	−0.985520	−	0.169559i	$-0.945766\pi$
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	0.345918	−	0.938265i	$-0.387568\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	2.24264			0.579047
$16$	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
$19$	−3.62132	+	6.27231i	−0.830788	+	1.43897i	0.0666264	+	0.997778i	$0.478776\pi$
$19$	−3.62132	+	6.27231i	−0.830788	+	1.43897i	−0.897414	+	0.441189i	$0.854557\pi$
$20$		0			0
$21$		0			0
$22$	−6.00000			−1.27920
$23$	2.91421	−	5.04757i	0.607656	−	1.05249i	−0.383970	−	0.923345i	$-0.625443\pi$
$23$	2.91421	−	5.04757i	0.607656	−	1.05249i	0.991626	−	0.129145i	$-0.0412232\pi$
$24$	2.00000	+	3.46410i	0.408248	+	0.707107i
$25$	1.24264	+	2.15232i	0.248528	+	0.430463i
$26$	0.707107	−	1.22474i	0.138675	−	0.240192i
$27$	5.65685			1.08866
$28$		0			0
$29$	0.171573			0.0318603			0.0159301	−	0.999873i	$-0.494929\pi$
$29$	0.171573			0.0318603			0.0159301	+	0.999873i	$0.494929\pi$
$30$	1.58579	−	2.74666i	0.289524	−	0.501470i
$31$	1.62132	+	2.80821i	0.291198	+	0.504369i	0.974093	−	0.226147i	$-0.0726129\pi$
$31$	1.62132	+	2.80821i	0.291198	+	0.504369i	−0.682895	+	0.730516i	$0.739280\pi$
$32$		0			0
$33$	3.00000	−	5.19615i	0.522233	−	0.904534i
$34$	2.00000			0.342997
$35$		0			0
$36$		0			0
$37$	−1.12132	+	1.94218i	−0.184344	+	0.319293i	−0.943355	−	0.331784i	$-0.892349\pi$
$37$	−1.12132	+	1.94218i	−0.184344	+	0.319293i	0.759011	+	0.651077i	$0.225683\pi$
$38$	5.12132	+	8.87039i	0.830788	+	1.43897i
$39$	0.707107	+	1.22474i	0.113228	+	0.196116i
$40$	2.24264	−	3.88437i	0.354593	−	0.614172i
$41$	−8.82843			−1.37877			−0.689384	−	0.724396i	$-0.742119\pi$
$41$	−8.82843			−1.37877			−0.689384	+	0.724396i	$0.742119\pi$
$42$		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
$45$	−0.792893	−	1.37333i	−0.118198	−	0.204724i
$46$	−4.12132	−	7.13834i	−0.607656	−	1.05249i
$47$	0.792893	−	1.37333i	0.115655	−	0.200321i	−0.802386	−	0.596805i	$-0.796437\pi$
$47$	0.792893	−	1.37333i	0.115655	−	0.200321i	0.918042	+	0.396484i	$0.129770\pi$
$48$	5.65685			0.816497
$49$		0			0
$50$	3.51472			0.497056
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$		0			0
$53$	0.0857864	+	0.148586i	0.0117837	+	0.0204099i	0.871857	−	0.489760i	$-0.162916\pi$
$53$	0.0857864	+	0.148586i	0.0117837	+	0.0204099i	−0.860073	+	0.510170i	$0.829582\pi$
$54$	4.00000	−	6.92820i	0.544331	−	0.942809i
$55$	−6.72792			−0.907193
$56$		0			0
$57$	−10.2426			−1.35667
$58$	0.121320	−	0.210133i	0.0159301	−	0.0275918i
$59$	0.171573	+	0.297173i	0.0223369	+	0.0386886i	0.876978	−	0.480531i	$-0.159556\pi$
$59$	0.171573	+	0.297173i	0.0223369	+	0.0386886i	−0.854641	+	0.519220i	$0.826223\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	4.58579			0.582395
$63$		0			0
$64$	8.00000			1.00000
$65$	0.792893	−	1.37333i	0.0983463	−	0.170341i
$66$	−4.24264	−	7.34847i	−0.522233	−	0.904534i
$67$	7.24264	+	12.5446i	0.884829	+	1.53257i	0.845909	+	0.533327i	$0.179059\pi$
$67$	7.24264	+	12.5446i	0.884829	+	1.53257i	0.0389203	+	0.999242i	$0.487608\pi$
$68$		0			0
$69$	8.24264			0.992297
$70$		0			0
$71$	−13.0711			−1.55125			−0.775625	−	0.631194i	$-0.782565\pi$
$71$	−13.0711			−1.55125			−0.775625	+	0.631194i	$0.782565\pi$
$72$	1.41421	−	2.44949i	0.166667	−	0.288675i
$73$	−4.62132	−	8.00436i	−0.540885	−	0.936840i	−0.998854	−	0.0478714i	$-0.984756\pi$
$73$	−4.62132	−	8.00436i	−0.540885	−	0.936840i	0.457969	−	0.888968i	$-0.348577\pi$
$74$	1.58579	+	2.74666i	0.184344	+	0.319293i
$75$	−1.75736	+	3.04384i	−0.202922	+	0.351472i
$76$		0			0
$77$		0			0
$78$	2.00000			0.226455
$79$	−7.74264	+	13.4106i	−0.871115	+	1.50882i	−0.0102708	+	0.999947i	$0.503269\pi$
$79$	−7.74264	+	13.4106i	−0.871115	+	1.50882i	−0.860844	+	0.508868i	$0.830064\pi$
$80$	−3.17157	−	5.49333i	−0.354593	−	0.614172i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	−6.24264	+	10.8126i	−0.689384	+	1.19405i
$83$	−13.2426			−1.45357			−0.726784	−	0.686866i	$-0.758986\pi$
$83$	−13.2426			−1.45357			−0.726784	+	0.686866i	$0.758986\pi$
$84$		0			0
$85$	2.24264			0.243249
$86$	−3.53553	+	6.12372i	−0.381246	+	0.660338i
$87$	0.121320	+	0.210133i	0.0130069	+	0.0225286i
$88$	−6.00000	−	10.3923i	−0.639602	−	1.10782i
$89$	0.792893	−	1.37333i	0.0840465	−	0.145573i	−0.820938	−	0.571017i	$-0.806549\pi$
$89$	0.792893	−	1.37333i	0.0840465	−	0.145573i	0.904985	+	0.425445i	$0.139882\pi$
$90$	−2.24264			−0.236395
$91$		0			0
$92$		0			0
$93$	−2.29289	+	3.97141i	−0.237762	+	0.411816i
$94$	−1.12132	−	1.94218i	−0.115655	−	0.200321i
$95$	5.74264	+	9.94655i	0.589183	+	1.02049i
$96$		0			0
$97$	−11.7279			−1.19079			−0.595395	−	0.803433i	$-0.703004\pi$
$97$	−11.7279			−1.19079			−0.595395	+	0.803433i	$0.703004\pi$
$98$		0			0
$99$	−4.24264			−0.426401
$100$		0			0
$101$	5.12132	+	8.87039i	0.509590	+	0.882636i	0.999938	+	0.0111097i	$0.00353640\pi$
$101$	5.12132	+	8.87039i	0.509590	+	0.882636i	−0.490348	+	0.871527i	$0.663130\pi$
$102$	1.41421	+	2.44949i	0.140028	+	0.242536i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	2.82843			0.277350
$105$		0			0
$106$	0.242641			0.0235673
$107$	10.0711	−	17.4436i	0.973607	−	1.68634i	0.289149	−	0.957284i	$-0.406628\pi$
$107$	10.0711	−	17.4436i	0.973607	−	1.68634i	0.684458	−	0.729052i	$-0.260039\pi$
$108$		0			0
$109$	−8.36396	−	14.4868i	−0.801122	−	1.38758i	−0.918878	−	0.394542i	$-0.870903\pi$
$109$	−8.36396	−	14.4868i	−0.801122	−	1.38758i	0.117756	−	0.993043i	$-0.462430\pi$
$110$	−4.75736	+	8.23999i	−0.453596	+	0.785652i
$111$	−3.17157			−0.301032
$112$		0			0
$113$	2.31371			0.217655			0.108828	−	0.994061i	$-0.465290\pi$
$113$	2.31371			0.217655			0.108828	+	0.994061i	$0.465290\pi$
$114$	−7.24264	+	12.5446i	−0.678335	+	1.17491i
$115$	−4.62132	−	8.00436i	−0.430940	−	0.746411i
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	0.485281			0.0446738
$119$		0			0
$120$	6.34315			0.579047
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	−4.24264	−	7.34847i	−0.384111	−	0.665299i
$123$	−6.24264	−	10.8126i	−0.562880	−	0.974937i
$124$		0			0
$125$	11.8701			1.06169
$126$		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
$130$	−1.12132	−	1.94218i	−0.0983463	−	0.170341i
$131$	−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
$134$	20.4853			1.76966
$135$	4.48528	−	7.76874i	0.386032	−	0.668626i
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	2.29289	+	3.97141i	0.195895	+	0.339300i	0.947194	−	0.320662i	$-0.103905\pi$
$137$	2.29289	+	3.97141i	0.195895	+	0.339300i	−0.751298	+	0.659963i	$0.770572\pi$
$138$	5.82843	−	10.0951i	0.496149	−	0.859355i
$139$	−6.24264			−0.529494			−0.264747	−	0.964318i	$-0.585288\pi$
$139$	−6.24264			−0.529494			−0.264747	+	0.964318i	$0.585288\pi$
$140$		0			0
$141$	2.24264			0.188864
$142$	−9.24264	+	16.0087i	−0.775625	+	1.34342i
$143$	−2.12132	−	3.67423i	−0.177394	−	0.307255i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	0.136039	−	0.235626i	0.0112974	−	0.0195677i
$146$	−13.0711			−1.08177
$147$		0			0
$148$		0			0
$149$	−8.12132	+	14.0665i	−0.665324	+	1.15238i	0.313873	+	0.949465i	$0.398373\pi$
$149$	−8.12132	+	14.0665i	−0.665324	+	1.15238i	−0.979197	+	0.202911i	$0.934960\pi$
$150$	2.48528	+	4.30463i	0.202922	+	0.351472i
$151$	4.87868	+	8.45012i	0.397021	+	0.687661i	0.993357	−	0.115074i	$-0.0367106\pi$
$151$	4.87868	+	8.45012i	0.397021	+	0.687661i	−0.596336	+	0.802735i	$0.703377\pi$
$152$	−10.2426	+	17.7408i	−0.830788	+	1.43897i
$153$	1.41421			0.114332
$154$		0			0
$155$	5.14214			0.413026
$156$		0			0
$157$	−1.87868	−	3.25397i	−0.149935	−	0.259695i	0.781268	−	0.624195i	$-0.214573\pi$
$157$	−1.87868	−	3.25397i	−0.149935	−	0.259695i	−0.931203	+	0.364500i	$0.881240\pi$
$158$	10.9497	+	18.9655i	0.871115	+	1.50882i
$159$	−0.121320	+	0.210133i	−0.00962133	+	0.0166646i
$160$		0			0
$161$		0			0
$162$	7.07107			0.555556
$163$	−4.24264	+	7.34847i	−0.332309	+	0.575577i	−0.982964	−	0.183797i	$-0.941161\pi$
$163$	−4.24264	+	7.34847i	−0.332309	+	0.575577i	0.650655	+	0.759374i	$0.274494\pi$
$164$		0			0
$165$	−4.75736	−	8.23999i	−0.370360	−	0.641482i
$166$	−9.36396	+	16.2189i	−0.726784	+	1.25883i
$167$	−15.3848			−1.19051			−0.595255	−	0.803537i	$-0.702949\pi$
$167$	−15.3848			−1.19051			−0.595255	+	0.803537i	$0.702949\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	1.58579	−	2.74666i	0.121624	−	0.210659i
$171$	3.62132	+	6.27231i	0.276929	+	0.479656i
$172$		0			0
$173$	12.3640	−	21.4150i	0.940015	−	1.62815i	0.174576	−	0.984644i	$-0.444144\pi$
$173$	12.3640	−	21.4150i	0.940015	−	1.62815i	0.765438	−	0.643509i	$-0.222522\pi$
$174$	0.343146			0.0260138
$175$		0			0
$176$	−16.9706			−1.27920
$177$	−0.242641	+	0.420266i	−0.0182380	+	0.0315891i
$178$	−1.12132	−	1.94218i	−0.0840465	−	0.145573i
$179$	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
$181$	18.7279			1.39204			0.696018	−	0.718025i	$-0.254953\pi$
$181$	18.7279			1.39204			0.696018	+	0.718025i	$0.254953\pi$
$182$		0			0
$183$	8.48528			0.627250
$184$	8.24264	−	14.2767i	0.607656	−	1.05249i
$185$	1.77817	+	3.07989i	0.130734	+	0.226438i
$186$	3.24264	+	5.61642i	0.237762	+	0.411816i
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$		0			0
$189$		0			0
$190$	16.2426			1.17837
$191$	−7.58579	+	13.1390i	−0.548888	+	0.950702i	0.449463	+	0.893299i	$0.351615\pi$
$191$	−7.58579	+	13.1390i	−0.548888	+	0.950702i	−0.998351	+	0.0574033i	$0.981718\pi$
$192$	5.65685	+	9.79796i	0.408248	+	0.707107i
$193$	7.24264	+	12.5446i	0.521337	+	0.902982i	0.999692	+	0.0248153i	$0.00789976\pi$
$193$	7.24264	+	12.5446i	0.521337	+	0.902982i	−0.478355	+	0.878166i	$0.658767\pi$
$194$	−8.29289	+	14.3637i	−0.595395	+	1.03125i
$195$	2.24264			0.160599
$196$		0			0
$197$	12.3431			0.879413			0.439706	−	0.898142i	$-0.355083\pi$
$197$	12.3431			0.879413			0.439706	+	0.898142i	$0.355083\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	−1.87868	−	3.25397i	−0.133176	−	0.230668i	0.791723	−	0.610880i	$-0.209184\pi$
$199$	−1.87868	−	3.25397i	−0.133176	−	0.230668i	−0.924899	+	0.380212i	$0.875851\pi$
$200$	3.51472	+	6.08767i	0.248528	+	0.430463i
$201$	−10.2426	+	17.7408i	−0.722460	+	1.25134i
$202$	14.4853			1.01918
$203$		0			0
$204$		0			0
$205$	−7.00000	+	12.1244i	−0.488901	+	0.846802i
$206$	5.65685	+	9.79796i	0.394132	+	0.682656i
$207$	−2.91421	−	5.04757i	−0.202552	−	0.350830i
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	30.7279			2.12549
$210$		0			0
$211$	−15.9706			−1.09946			−0.549729	−	0.835343i	$-0.685269\pi$
$211$	−15.9706			−1.09946			−0.549729	+	0.835343i	$0.685269\pi$
$212$		0			0
$213$	−9.24264	−	16.0087i	−0.633295	−	1.09690i
$214$	−14.2426	−	24.6690i	−0.973607	−	1.68634i
$215$	−3.96447	+	6.86666i	−0.270374	+	0.468302i
$216$	16.0000			1.08866
$217$		0			0
$218$	−23.6569			−1.60224
$219$	6.53553	−	11.3199i	0.441630	−	0.764926i
$220$		0			0
$221$	0.707107	+	1.22474i	0.0475651	+	0.0823853i
$222$	−2.24264	+	3.88437i	−0.150516	+	0.260702i
$223$	−0.757359			−0.0507165			−0.0253583	−	0.999678i	$-0.508073\pi$
$223$	−0.757359			−0.0507165			−0.0253583	+	0.999678i	$0.508073\pi$
$224$		0			0
$225$	2.48528			0.165685
$226$	1.63604	−	2.83370i	0.108828	−	0.188495i
$227$	13.4142	+	23.2341i	0.890333	+	1.54210i	0.839477	+	0.543395i	$0.182862\pi$
$227$	13.4142	+	23.2341i	0.890333	+	1.54210i	0.0508557	+	0.998706i	$0.483805\pi$
$228$		0			0
$229$	14.7279	−	25.5095i	0.973248	−	1.68572i	0.287651	−	0.957735i	$-0.407126\pi$
$229$	14.7279	−	25.5095i	0.973248	−	1.68572i	0.685598	−	0.727980i	$-0.259541\pi$
$230$	−13.0711			−0.861881
$231$		0			0
$232$	0.485281			0.0318603
$233$	7.32843	−	12.6932i	0.480101	−	0.831560i	−0.519638	−	0.854386i	$-0.673933\pi$
$233$	7.32843	−	12.6932i	0.480101	−	0.831560i	0.999739	+	0.0228267i	$0.00726659\pi$
$234$	−0.707107	−	1.22474i	−0.0462250	−	0.0800641i
$235$	−1.25736	−	2.17781i	−0.0820211	−	0.142065i
$236$		0			0
$237$	−21.8995			−1.42253
$238$		0			0
$239$	3.51472			0.227348			0.113674	−	0.993518i	$-0.463738\pi$
$239$	3.51472			0.227348			0.113674	+	0.993518i	$0.463738\pi$
$240$	4.48528	−	7.76874i	0.289524	−	0.501470i
$241$	−10.1066	−	17.5051i	−0.651023	−	1.12761i	−0.982875	−	0.184274i	$-0.941007\pi$
$241$	−10.1066	−	17.5051i	−0.651023	−	1.12761i	0.331851	−	0.943332i	$-0.392327\pi$
$242$	4.94975	+	8.57321i	0.318182	+	0.551107i
$243$	4.94975	−	8.57321i	0.317526	−	0.549972i
$244$		0			0
$245$		0			0
$246$	−17.6569			−1.12576
$247$	−3.62132	+	6.27231i	−0.230419	+	0.399098i
$248$	4.58579	+	7.94282i	0.291198	+	0.504369i
$249$	−9.36396	−	16.2189i	−0.593417	−	1.02783i
$250$	8.39340	−	14.5378i	0.530845	−	0.919451i
$251$	−16.5858			−1.04689			−0.523443	−	0.852061i	$-0.675353\pi$
$251$	−16.5858			−1.04689			−0.523443	+	0.852061i	$0.675353\pi$
$252$		0			0
$253$	−24.7279			−1.55463
$254$	1.41421	−	2.44949i	0.0887357	−	0.153695i
$255$	1.58579	+	2.74666i	0.0993058	+	0.172003i
$256$		0			0
$257$	−9.70711	+	16.8132i	−0.605513	+	1.04878i	0.386458	+	0.922307i	$0.373699\pi$
$257$	−9.70711	+	16.8132i	−0.605513	+	1.04878i	−0.991970	+	0.126472i	$0.959635\pi$
$258$	−10.0000			−0.622573
$259$		0			0
$260$		0			0
$261$	0.0857864	−	0.148586i	0.00531005	−	0.00919727i
$262$	2.00000	+	3.46410i	0.123560	+	0.214013i
$263$	−0.985281	−	1.70656i	−0.0607551	−	0.105231i	0.834048	−	0.551692i	$-0.186018\pi$
$263$	−0.985281	−	1.70656i	−0.0607551	−	0.105231i	−0.894803	+	0.446461i	$0.852684\pi$
$264$	8.48528	−	14.6969i	0.522233	−	0.904534i
$265$	0.272078			0.0167136
$266$		0			0
$267$	2.24264			0.137247
$268$		0			0
$269$	4.58579	+	7.94282i	0.279600	+	0.484282i	0.971285	−	0.237917i	$-0.0764647\pi$
$269$	4.58579	+	7.94282i	0.279600	+	0.484282i	−0.691685	+	0.722199i	$0.743131\pi$
$270$	−6.34315	−	10.9867i	−0.386032	−	0.668626i
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	5.65685			0.342997
$273$		0			0
$274$	6.48528			0.391790
$275$	5.27208	−	9.13151i	0.317918	−	0.550651i
$276$		0			0
$277$	3.74264	+	6.48244i	0.224873	+	0.389492i	0.956281	−	0.292448i	$-0.0944698\pi$
$277$	3.74264	+	6.48244i	0.224873	+	0.389492i	−0.731408	+	0.681940i	$0.761136\pi$
$278$	−4.41421	+	7.64564i	−0.264747	+	0.458555i
$279$	3.24264			0.194132
$280$		0			0
$281$	15.5563			0.928014			0.464007	−	0.885832i	$-0.346411\pi$
$281$	15.5563			0.928014			0.464007	+	0.885832i	$0.346411\pi$
$282$	1.58579	−	2.74666i	0.0944322	−	0.163561i
$283$	−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
$285$	−8.12132	+	14.0665i	−0.481065	+	0.833230i
$286$	−6.00000			−0.354787
$287$		0			0
$288$		0			0
$289$	7.50000	−	12.9904i	0.441176	−	0.764140i
$290$	−0.192388	−	0.333226i	−0.0112974	−	0.0195677i
$291$	−8.29289	−	14.3637i	−0.486138	−	0.842016i
$292$		0			0
$293$	−15.3848			−0.898788			−0.449394	−	0.893334i	$-0.648360\pi$
$293$	−15.3848			−0.898788			−0.449394	+	0.893334i	$0.648360\pi$
$294$		0			0
$295$	0.544156			0.0316820
$296$	−3.17157	+	5.49333i	−0.184344	+	0.319293i
$297$	−12.0000	−	20.7846i	−0.696311	−	1.20605i
$298$	11.4853	+	19.8931i	0.665324	+	1.15238i
$299$	2.91421	−	5.04757i	0.168533	−	0.291908i
$300$		0			0
$301$		0			0
$302$	13.7990			0.794043
$303$	−7.24264	+	12.5446i	−0.416079	+	0.720670i
$304$	14.4853	+	25.0892i	0.830788	+	1.43897i
$305$	−4.75736	−	8.23999i	−0.272406	−	0.471820i
$306$	1.00000	−	1.73205i	0.0571662	−	0.0990148i
$307$	−13.2426			−0.755797			−0.377899	−	0.925847i	$-0.623353\pi$
$307$	−13.2426			−0.755797			−0.377899	+	0.925847i	$0.623353\pi$
$308$		0			0
$309$	−11.3137			−0.643614
$310$	3.63604	−	6.29780i	0.206513	−	0.357691i
$311$	−3.70711	−	6.42090i	−0.210211	−	0.364096i	0.741570	−	0.670876i	$-0.234082\pi$
$311$	−3.70711	−	6.42090i	−0.210211	−	0.364096i	−0.951780	+	0.306780i	$0.900748\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	11.6066	−	20.1032i	0.656044	−	1.13630i	−0.325587	−	0.945512i	$-0.605562\pi$
$313$	11.6066	−	20.1032i	0.656044	−	1.13630i	0.981631	−	0.190789i	$-0.0611047\pi$
$314$	−5.31371			−0.299870
$315$		0			0
$316$		0			0
$317$	5.65685	−	9.79796i	0.317721	−	0.550308i	−0.662291	−	0.749246i	$-0.730416\pi$
$317$	5.65685	−	9.79796i	0.317721	−	0.550308i	0.980012	+	0.198938i	$0.0637493\pi$
$318$	0.171573	+	0.297173i	0.00962133	+	0.0166646i
$319$	−0.363961	−	0.630399i	−0.0203779	−	0.0352956i
$320$	6.34315	−	10.9867i	0.354593	−	0.614172i
$321$	28.4853			1.58989
$322$		0			0
$323$	−10.2426			−0.569916
$324$		0			0
$325$	1.24264	+	2.15232i	0.0689293	+	0.119389i
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	11.8284	−	20.4874i	0.654114	−	1.13296i
$328$	−24.9706			−1.37877
$329$		0			0
$330$	−13.4558			−0.740720
$331$	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
$333$	1.12132	+	1.94218i	0.0614480	+	0.106431i
$334$	−10.8787	+	18.8424i	−0.595255	+	1.03101i
$335$	22.9706			1.25502
$336$		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
$339$	1.63604	+	2.83370i	0.0888574	+	0.153906i
$340$		0			0
$341$	6.87868	−	11.9142i	0.372501	−	0.645191i
$342$	10.2426			0.553859
$343$		0			0
$344$	−14.1421			−0.762493
$345$	6.53553	−	11.3199i	0.351861	−	0.609442i
$346$	−17.4853	−	30.2854i	−0.940015	−	1.62815i
$347$	2.82843	+	4.89898i	0.151838	+	0.262991i	0.931903	−	0.362707i	$-0.118147\pi$
$347$	2.82843	+	4.89898i	0.151838	+	0.262991i	−0.780065	+	0.625698i	$0.784814\pi$
$348$		0			0
$349$	25.7279			1.37718			0.688592	−	0.725149i	$-0.258229\pi$
$349$	25.7279			1.37718			0.688592	+	0.725149i	$0.258229\pi$
$350$		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	$0.905837\pi$
$354$	0.343146	+	0.594346i	0.0182380	+	0.0315891i
$355$	−10.3640	+	17.9509i	−0.550062	+	0.952735i
$356$		0			0
$357$		0			0
$358$	12.7279			0.672692
$359$	13.9497	−	24.1617i	0.736240	−	1.27520i	−0.217938	−	0.975963i	$-0.569933\pi$
$359$	13.9497	−	24.1617i	0.736240	−	1.27520i	0.954177	−	0.299242i	$-0.0967337\pi$
$360$	−2.24264	−	3.88437i	−0.118198	−	0.204724i
$361$	−16.7279	−	28.9736i	−0.880417	−	1.52493i
$362$	13.2426	−	22.9369i	0.696018	−	1.20554i
$363$	−9.89949			−0.519589
$364$		0			0
$365$	−14.6569			−0.767175
$366$	6.00000	−	10.3923i	0.313625	−	0.543214i
$367$	5.12132	+	8.87039i	0.267331	+	0.463030i	0.968172	−	0.250287i	$-0.0805250\pi$
$367$	5.12132	+	8.87039i	0.267331	+	0.463030i	−0.700841	+	0.713318i	$0.747192\pi$
$368$	−11.6569	−	20.1903i	−0.607656	−	1.05249i
$369$	−4.41421	+	7.64564i	−0.229795	+	0.398016i
$370$	5.02944			0.261468
$371$		0			0
$372$		0			0
$373$	−4.24264	+	7.34847i	−0.219676	+	0.380489i	−0.954709	−	0.297542i	$-0.903833\pi$
$373$	−4.24264	+	7.34847i	−0.219676	+	0.380489i	0.735033	+	0.678031i	$0.237167\pi$
$374$	−4.24264	−	7.34847i	−0.219382	−	0.379980i
$375$	8.39340	+	14.5378i	0.433433	+	0.750728i
$376$	2.24264	−	3.88437i	0.115655	−	0.200321i
$377$	0.171573			0.00883645
$378$		0			0
$379$	23.7574			1.22033			0.610167	−	0.792273i	$-0.291102\pi$
$379$	23.7574			1.22033			0.610167	+	0.792273i	$0.291102\pi$
$380$		0			0
$381$	1.41421	+	2.44949i	0.0724524	+	0.125491i
$382$	10.7279	+	18.5813i	0.548888	+	0.950702i
$383$	−10.2426	+	17.7408i	−0.523374	+	0.906511i	0.476255	+	0.879307i	$0.341994\pi$
$383$	−10.2426	+	17.7408i	−0.523374	+	0.906511i	−0.999630	+	0.0272042i	$0.991340\pi$
$384$	16.0000			0.816497
$385$		0			0
$386$	20.4853			1.04267
$387$	−2.50000	+	4.33013i	−0.127082	+	0.220113i
$388$		0			0
$389$	−14.8284	−	25.6836i	−0.751831	−	1.30221i	−0.946934	−	0.321427i	$-0.895838\pi$
$389$	−14.8284	−	25.6836i	−0.751831	−	1.30221i	0.195103	−	0.980783i	$-0.437496\pi$
$390$	1.58579	−	2.74666i	0.0802994	−	0.139083i
$391$	8.24264			0.416848
$392$		0			0
$393$	−4.00000			−0.201773
$394$	8.72792	−	15.1172i	0.439706	−	0.761594i
$395$	12.2782	+	21.2664i	0.617782	+	1.07003i
$396$		0			0
$397$	−9.10660	+	15.7731i	−0.457047	+	0.791629i	−0.998803	−	0.0489067i	$-0.984426\pi$
$397$	−9.10660	+	15.7731i	−0.457047	+	0.791629i	0.541756	+	0.840536i	$0.317760\pi$
$398$	−5.31371			−0.266352
$399$		0			0
$400$	9.94113			0.497056
$401$	−3.17157	+	5.49333i	−0.158381	+	0.274324i	−0.934285	−	0.356527i	$-0.883961\pi$
$401$	−3.17157	+	5.49333i	−0.158381	+	0.274324i	0.775904	+	0.630851i	$0.217294\pi$
$402$	14.4853	+	25.0892i	0.722460	+	1.25134i
$403$	1.62132	+	2.80821i	0.0807637	+	0.139887i
$404$		0			0
$405$	7.92893			0.393992
$406$		0			0
$407$	9.51472			0.471627
$408$	−2.82843	+	4.89898i	−0.140028	+	0.242536i
$409$	1.62132	+	2.80821i	0.0801691	+	0.138857i	0.903322	−	0.428962i	$-0.141121\pi$
$409$	1.62132	+	2.80821i	0.0801691	+	0.138857i	−0.823153	+	0.567819i	$0.807787\pi$
$410$	9.89949	+	17.1464i	0.488901	+	0.846802i
$411$	−3.24264	+	5.61642i	−0.159948	+	0.277037i
$412$		0			0
$413$		0			0
$414$	−8.24264			−0.405104
$415$	−10.5000	+	18.1865i	−0.515425	+	0.892742i
$416$		0			0
$417$	−4.41421	−	7.64564i	−0.216165	−	0.374409i
$418$	21.7279	−	37.6339i	1.06275	−	1.84073i
$419$	20.8701			1.01957			0.509785	−	0.860302i	$-0.329725\pi$
$419$	20.8701			1.01957			0.509785	+	0.860302i	$0.329725\pi$
$420$		0			0
$421$	6.72792			0.327899			0.163949	−	0.986469i	$-0.447577\pi$
$421$	6.72792			0.327899			0.163949	+	0.986469i	$0.447577\pi$
$422$	−11.2929	+	19.5599i	−0.549729	+	0.952159i
$423$	−0.792893	−	1.37333i	−0.0385518	−	0.0667737i
$424$	0.242641	+	0.420266i	0.0117837	+	0.0204099i
$425$	−1.75736	+	3.04384i	−0.0852444	+	0.147648i
$426$	−26.1421			−1.26659
$427$		0			0
$428$		0			0
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$	5.60660	+	9.71092i	0.270374	+	0.468302i
$431$	6.17157	+	10.6895i	0.297274	+	0.514894i	0.975511	−	0.219949i	$-0.0705891\pi$
$431$	6.17157	+	10.6895i	0.297274	+	0.514894i	−0.678237	+	0.734843i	$0.737256\pi$
$432$	11.3137	−	19.5959i	0.544331	−	0.942809i
$433$	24.9706			1.20001			0.600004	−	0.799997i	$-0.295166\pi$
$433$	24.9706			1.20001			0.600004	+	0.799997i	$0.295166\pi$
$434$		0			0
$435$	0.384776			0.0184486
$436$		0			0
$437$	21.1066	+	36.5577i	1.00967	+	1.74879i
$438$	−9.24264	−	16.0087i	−0.441630	−	0.764926i
$439$	−17.2426	+	29.8651i	−0.822946	+	1.42538i	0.0805324	+	0.996752i	$0.474338\pi$
$439$	−17.2426	+	29.8651i	−0.822946	+	1.42538i	−0.903479	+	0.428633i	$0.858995\pi$
$440$	−19.0294			−0.907193
$441$		0			0
$442$	2.00000			0.0951303
$443$	1.84315	−	3.19242i	0.0875705	−	0.151677i	−0.818913	−	0.573917i	$-0.805423\pi$
$443$	1.84315	−	3.19242i	0.0875705	−	0.151677i	0.906484	+	0.422241i	$0.138756\pi$
$444$		0			0
$445$	−1.25736	−	2.17781i	−0.0596045	−	0.103238i
$446$	−0.535534	+	0.927572i	−0.0253583	+	0.0439218i
$447$	−22.9706			−1.08647
$448$		0			0
$449$	21.1716			0.999148			0.499574	−	0.866271i	$-0.333490\pi$
$449$	21.1716			0.999148			0.499574	+	0.866271i	$0.333490\pi$
$450$	1.75736	−	3.04384i	0.0828427	−	0.143488i
$451$	18.7279	+	32.4377i	0.881863	+	1.52743i
$452$		0			0
$453$	−6.89949	+	11.9503i	−0.324167	+	0.561473i
$454$	37.9411			1.78067
$455$		0			0
$456$	−28.9706			−1.35667
$457$	3.60660	−	6.24682i	0.168710	−	0.292214i	−0.769257	−	0.638940i	$-0.779373\pi$
$457$	3.60660	−	6.24682i	0.168710	−	0.292214i	0.937966	+	0.346726i	$0.112707\pi$
$458$	−20.8284	−	36.0759i	−0.973248	−	1.68572i
$459$	4.00000	+	6.92820i	0.186704	+	0.323381i
$460$		0			0
$461$	−8.82843			−0.411181			−0.205590	−	0.978638i	$-0.565911\pi$
$461$	−8.82843			−0.411181			−0.205590	+	0.978638i	$0.565911\pi$
$462$		0			0
$463$	−4.24264			−0.197172			−0.0985861	−	0.995129i	$-0.531432\pi$
$463$	−4.24264			−0.197172			−0.0985861	+	0.995129i	$0.531432\pi$
$464$	0.343146	−	0.594346i	0.0159301	−	0.0275918i
$465$	3.63604	+	6.29780i	0.168617	+	0.292054i
$466$	−10.3640	−	17.9509i	−0.480101	−	0.831560i
$467$	−1.94975	+	3.37706i	−0.0902236	+	0.156272i	−0.907605	−	0.419825i	$-0.862091\pi$
$467$	−1.94975	+	3.37706i	−0.0902236	+	0.156272i	0.817382	+	0.576097i	$0.195425\pi$
$468$		0			0
$469$		0			0
$470$	−3.55635			−0.164042
$471$	2.65685	−	4.60181i	0.122421	−	0.212040i
$472$	0.485281	+	0.840532i	0.0223369	+	0.0386886i
$473$	10.6066	+	18.3712i	0.487692	+	0.844707i
$474$	−15.4853	+	26.8213i	−0.711263	+	1.23194i
$475$	−18.0000			−0.825897
$476$		0			0
$477$	0.171573			0.00785578
$478$	2.48528	−	4.30463i	0.113674	−	0.196889i
$479$	−3.10660	−	5.38079i	−0.141944	−	0.245855i	0.786284	−	0.617865i	$-0.212002\pi$
$479$	−3.10660	−	5.38079i	−0.141944	−	0.245855i	−0.928229	+	0.372010i	$0.878669\pi$
$480$		0			0
$481$	−1.12132	+	1.94218i	−0.0511278	+	0.0885560i
$482$	−28.5858			−1.30205
$483$		0			0
$484$		0			0
$485$	−9.29899	+	16.1063i	−0.422245	+	0.731350i
$486$	−7.00000	−	12.1244i	−0.317526	−	0.549972i
$487$	5.72792	+	9.92105i	0.259557	+	0.449566i	0.966123	−	0.258081i	$-0.0830901\pi$
$487$	5.72792	+	9.92105i	0.259557	+	0.449566i	−0.706566	+	0.707647i	$0.749757\pi$
$488$	8.48528	−	14.6969i	0.384111	−	0.665299i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	16.6274			0.750385			0.375192	−	0.926947i	$-0.377577\pi$
$491$	16.6274			0.750385			0.375192	+	0.926947i	$0.377577\pi$
$492$		0			0
$493$	0.121320	+	0.210133i	0.00546399	+	0.00946391i
$494$	5.12132	+	8.87039i	0.230419	+	0.399098i
$495$	−3.36396	+	5.82655i	−0.151199	+	0.261884i
$496$	12.9706			0.582395
$497$		0			0
$498$	−26.4853			−1.18683
$499$	6.63604	−	11.4940i	0.297070	−	0.514540i	−0.678394	−	0.734698i	$-0.737324\pi$
$499$	6.63604	−	11.4940i	0.297070	−	0.514540i	0.975464	+	0.220158i	$0.0706572\pi$
$500$		0			0
$501$	−10.8787	−	18.8424i	−0.486024	−	0.841818i
$502$	−11.7279	+	20.3134i	−0.523443	+	0.906629i
$503$	28.6274			1.27643			0.638217	−	0.769857i	$-0.279672\pi$
$503$	28.6274			1.27643			0.638217	+	0.769857i	$0.279672\pi$
$504$		0			0
$505$	16.2426			0.722788
$506$	−17.4853	+	30.2854i	−0.777316	+	1.34635i
$507$	0.707107	+	1.22474i	0.0314037	+	0.0543928i
$508$		0			0
$509$	−2.55025	+	4.41717i	−0.113038	+	0.195787i	−0.916994	−	0.398902i	$-0.869392\pi$
$509$	−2.55025	+	4.41717i	−0.113038	+	0.195787i	0.803956	+	0.594689i	$0.202725\pi$
$510$	4.48528			0.198612
$511$		0			0
$512$	22.6274			1.00000
$513$	−20.4853	+	35.4815i	−0.904447	+	1.56655i
$514$	13.7279	+	23.7775i	0.605513	+	1.04878i
$515$	6.34315	+	10.9867i	0.279512	+	0.484130i
$516$		0			0
$517$	−6.72792			−0.295894
$518$		0			0
$519$	34.9706			1.53504
$520$	2.24264	−	3.88437i	0.0983463	−	0.170341i
$521$	−3.17157	−	5.49333i	−0.138949	−	0.240667i	0.788150	−	0.615483i	$-0.211039\pi$
$521$	−3.17157	−	5.49333i	−0.138949	−	0.240667i	−0.927099	+	0.374816i	$0.877706\pi$
$522$	−0.121320	−	0.210133i	−0.00531005	−	0.00919727i
$523$	15.4853	−	26.8213i	0.677124	−	1.17281i	−0.298719	−	0.954341i	$-0.596559\pi$
$523$	15.4853	−	26.8213i	0.677124	−	1.17281i	0.975843	−	0.218472i	$-0.0701073\pi$
$524$		0			0
$525$		0			0
$526$	−2.78680			−0.121510
$527$	−2.29289	+	3.97141i	−0.0998800	+	0.172997i
$528$	−12.0000	−	20.7846i	−0.522233	−	0.904534i
$529$	−5.48528	−	9.50079i	−0.238490	−	0.413078i
$530$	0.192388	−	0.333226i	0.00835681	−	0.0144744i
$531$	0.343146			0.0148913
$532$		0			0
$533$	−8.82843			−0.382402
$534$	1.58579	−	2.74666i	0.0686237	−	0.118860i
$535$	−15.9706	−	27.6618i	−0.690468	−	1.19593i
$536$	20.4853	+	35.4815i	0.884829	+	1.53257i
$537$	−6.36396	+	11.0227i	−0.274625	+	0.475665i
$538$	12.9706			0.559201
$539$		0			0
$540$		0			0
$541$	3.60660	−	6.24682i	0.155060	−	0.268572i	−0.778021	−	0.628238i	$-0.783776\pi$
$541$	3.60660	−	6.24682i	0.155060	−	0.268572i	0.933081	+	0.359667i	$0.117110\pi$
$542$	−14.1421	−	24.4949i	−0.607457	−	1.05215i
$543$	13.2426	+	22.9369i	0.568296	+	0.984318i
$544$		0			0
$545$	−26.5269			−1.13629
$546$		0			0
$547$	35.4853			1.51724			0.758621	−	0.651533i	$-0.225874\pi$
$547$	35.4853			1.51724			0.758621	+	0.651533i	$0.225874\pi$
$548$		0			0
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	−7.45584	−	12.9139i	−0.317918	−	0.550651i
$551$	−0.621320	+	1.07616i	−0.0264691	+	0.0458459i
$552$	23.3137			0.992297
$553$		0			0
$554$	10.5858			0.449747
$555$	−2.51472	+	4.35562i	−0.106744	+	0.184886i
$556$		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	$0.915155\pi$
$558$	2.29289	−	3.97141i	0.0970659	−	0.168123i
$559$	−5.00000			−0.211477
$560$		0			0
$561$	8.48528			0.358249
$562$	11.0000	−	19.0526i	0.464007	−	0.803684i
$563$	−3.17157	−	5.49333i	−0.133666	−	0.231516i	0.791421	−	0.611271i	$-0.209342\pi$
$563$	−3.17157	−	5.49333i	−0.133666	−	0.231516i	−0.925087	+	0.379755i	$0.876008\pi$
$564$		0			0
$565$	1.83452	−	3.17749i	0.0771790	−	0.133678i
$566$	−12.0000			−0.504398
$567$		0			0
$568$	−36.9706			−1.55125
$569$	−2.57107	+	4.45322i	−0.107785	+	0.186689i	−0.914873	−	0.403743i	$-0.867709\pi$
$569$	−2.57107	+	4.45322i	−0.107785	+	0.186689i	0.807088	+	0.590431i	$0.201042\pi$
$570$	11.4853	+	19.8931i	0.481065	+	0.833230i
$571$	−21.2279	−	36.7678i	−0.888361	−	1.53869i	−0.841812	−	0.539770i	$-0.818511\pi$
$571$	−21.2279	−	36.7678i	−0.888361	−	1.53869i	−0.0465485	−	0.998916i	$-0.514822\pi$
$572$		0			0
$573$	−21.4558			−0.896331
$574$		0			0
$575$	14.4853			0.604078
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−3.48528	−	6.03668i	−0.145094	−	0.251310i	0.784314	−	0.620364i	$-0.213015\pi$
$577$	−3.48528	−	6.03668i	−0.145094	−	0.251310i	−0.929408	+	0.369054i	$0.879682\pi$
$578$	−10.6066	−	18.3712i	−0.441176	−	0.764140i
$579$	−10.2426	+	17.7408i	−0.425670	+	0.737281i
$580$		0			0
$581$		0			0
$582$	−23.4558			−0.972276
$583$	0.363961	−	0.630399i	0.0150737	−	0.0261085i
$584$	−13.0711	−	22.6398i	−0.540885	−	0.936840i
$585$	−0.792893	−	1.37333i	−0.0327821	−	0.0567803i
$586$	−10.8787	+	18.8424i	−0.449394	+	0.778373i
$587$	6.55635			0.270609			0.135305	−	0.990804i	$-0.456799\pi$
$587$	6.55635			0.270609			0.135305	+	0.990804i	$0.456799\pi$
$588$		0			0
$589$	−23.4853			−0.967694
$590$	0.384776	−	0.666452i	0.0158410	−	0.0274374i
$591$	8.72792	+	15.1172i	0.359019	+	0.621839i
$592$	4.48528	+	7.76874i	0.184344	+	0.319293i
$593$	−0.278175	+	0.481813i	−0.0114233	+	0.0197857i	−0.871681	−	0.490075i	$-0.836970\pi$
$593$	−0.278175	+	0.481813i	−0.0114233	+	0.0197857i	0.860257	+	0.509860i	$0.170303\pi$
$594$	−33.9411			−1.39262
$595$		0			0
$596$		0			0
$597$	2.65685	−	4.60181i	0.108738	−	0.188339i
$598$	−4.12132	−	7.13834i	−0.168533	−	0.291908i
$599$	14.3995	+	24.9407i	0.588347	+	1.01905i	0.994449	+	0.105220i	$0.0335546\pi$
$599$	14.3995	+	24.9407i	0.588347	+	1.01905i	−0.406102	+	0.913828i	$0.633112\pi$
$600$	−4.97056	+	8.60927i	−0.202922	+	0.351472i
$601$	38.9706			1.58964			0.794821	−	0.606844i	$-0.207565\pi$
$601$	38.9706			1.58964			0.794821	+	0.606844i	$0.207565\pi$
$602$		0			0
$603$	14.4853			0.589886
$604$		0			0
$605$	5.55025	+	9.61332i	0.225650	+	0.390837i
$606$	10.2426	+	17.7408i	0.416079	+	0.720670i
$607$	−13.3640	+	23.1471i	−0.542426	+	0.939510i	0.456338	+	0.889807i	$0.349161\pi$
$607$	−13.3640	+	23.1471i	−0.542426	+	0.939510i	−0.998764	+	0.0497034i	$0.984172\pi$
$608$		0			0
$609$		0			0
$610$	−13.4558			−0.544811
$611$	0.792893	−	1.37333i	0.0320770	−	0.0555590i
$612$		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	$0.728603\pi$
$614$	−9.36396	+	16.2189i	−0.377899	+	0.654540i
$615$	−19.7990			−0.798372
$616$		0			0
$617$	12.3431			0.496916			0.248458	−	0.968643i	$-0.420076\pi$
$617$	12.3431			0.496916			0.248458	+	0.968643i	$0.420076\pi$
$618$	−8.00000	+	13.8564i	−0.321807	+	0.557386i
$619$	0.485281	+	0.840532i	0.0195051	+	0.0337838i	0.875613	−	0.483013i	$-0.160458\pi$
$619$	0.485281	+	0.840532i	0.0195051	+	0.0337838i	−0.856108	+	0.516797i	$0.827124\pi$
$620$		0			0
$621$	16.4853	−	28.5533i	0.661532	−	1.14581i
$622$	−10.4853			−0.420421
$623$		0			0
$624$	5.65685			0.226455
$625$	3.19848	−	5.53994i	0.127939	−	0.221598i
$626$	−16.4142	−	28.4303i	−0.656044	−	1.13630i
$627$	21.7279	+	37.6339i	0.867730	+	1.50295i
$628$		0			0
$629$	−3.17157			−0.126459
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−21.8995	+	37.9310i	−0.871115	+	1.50882i
$633$	−11.2929	−	19.5599i	−0.448852	−	0.777435i
$634$	−8.00000	−	13.8564i	−0.317721	−	0.550308i
$635$	1.58579	−	2.74666i	0.0629300	−	0.108998i
$636$		0			0
$637$		0			0
$638$	−1.02944			−0.0407558
$639$	−6.53553	+	11.3199i	−0.258542	+	0.447807i
$640$	−8.97056	−	15.5375i	−0.354593	−	0.614172i
$641$	−7.67157	−	13.2876i	−0.303009	−	0.524827i	0.673807	−	0.738907i	$-0.264658\pi$
$641$	−7.67157	−	13.2876i	−0.303009	−	0.524827i	−0.976816	+	0.214080i	$0.931325\pi$
$642$	20.1421	−	34.8872i	0.794947	−	1.37689i
$643$	12.4853			0.492371			0.246186	−	0.969223i	$-0.420823\pi$
$643$	12.4853			0.492371			0.246186	+	0.969223i	$0.420823\pi$
$644$		0			0
$645$	−11.2132			−0.441519
$646$	−7.24264	+	12.5446i	−0.284958	+	0.493562i
$647$	7.26346	+	12.5807i	0.285556	+	0.494597i	0.972744	−	0.231882i	$-0.0744884\pi$
$647$	7.26346	+	12.5807i	0.285556	+	0.494597i	−0.687188	+	0.726480i	$0.741155\pi$
$648$	7.07107	+	12.2474i	0.277778	+	0.481125i
$649$	0.727922	−	1.26080i	0.0285734	−	0.0494907i
$650$	3.51472			0.137859
$651$		0			0
$652$		0			0
$653$	−8.65685	+	14.9941i	−0.338769	+	0.586765i	−0.984201	−	0.177052i	$-0.943344\pi$
$653$	−8.65685	+	14.9941i	−0.338769	+	0.586765i	0.645433	+	0.763817i	$0.276677\pi$
$654$	−16.7279	−	28.9736i	−0.654114	−	1.13296i
$655$	2.24264	+	3.88437i	0.0876272	+	0.151775i
$656$	−17.6569	+	30.5826i	−0.689384	+	1.19405i
$657$	−9.24264			−0.360590
$658$		0			0
$659$	−15.3431			−0.597684			−0.298842	−	0.954303i	$-0.596600\pi$
$659$	−15.3431			−0.597684			−0.298842	+	0.954303i	$0.596600\pi$
$660$		0			0
$661$	−5.37868	−	9.31615i	−0.209206	−	0.362356i	0.742258	−	0.670114i	$-0.233755\pi$
$661$	−5.37868	−	9.31615i	−0.209206	−	0.362356i	−0.951465	+	0.307758i	$0.900421\pi$
$662$	−12.7279	−	22.0454i	−0.494685	−	0.856819i
$663$	−1.00000	+	1.73205i	−0.0388368	+	0.0672673i
$664$	−37.4558			−1.45357
$665$		0			0
$666$	3.17157			0.122896
$667$	0.500000	−	0.866025i	0.0193601	−	0.0335326i
$668$		0			0
$669$	−0.535534	−	0.927572i	−0.0207049	−	0.0358620i
$670$	16.2426	−	28.1331i	0.627508	−	1.08688i
$671$	−25.4558			−0.982712
$672$		0			0
$673$	−26.9411			−1.03850			−0.519252	−	0.854621i	$-0.673789\pi$
$673$	−26.9411			−1.03850			−0.519252	+	0.854621i	$0.673789\pi$
$674$	−23.3345	+	40.4166i	−0.898812	+	1.55679i
$675$	7.02944	+	12.1753i	0.270563	+	0.468629i
$676$		0			0
$677$	−20.6777	+	35.8148i	−0.794707	+	1.37647i	0.128317	+	0.991733i	$0.459042\pi$
$677$	−20.6777	+	35.8148i	−0.794707	+	1.37647i	−0.923025	+	0.384740i	$0.874291\pi$
$678$	4.62742			0.177715
$679$		0			0
$680$	6.34315			0.243249
$681$	−18.9706	+	32.8580i	−0.726954	+	1.25912i
$682$	−9.72792	−	16.8493i	−0.372501	−	0.645191i
$683$	10.5858	+	18.3351i	0.405054	+	0.701574i	0.994328	−	0.106359i	$-0.0339194\pi$
$683$	10.5858	+	18.3351i	0.405054	+	0.701574i	−0.589274	+	0.807933i	$0.700586\pi$
$684$		0			0
$685$	7.27208			0.277852
$686$		0			0
$687$	41.6569			1.58931
$688$	−10.0000	+	17.3205i	−0.381246	+	0.660338i
$689$	0.0857864	+	0.148586i	0.00326820	+	0.00566069i
$690$	−9.24264	−	16.0087i	−0.351861	−	0.609442i
$691$	14.3492	−	24.8536i	0.545871	−	0.945476i	−0.452681	−	0.891673i	$-0.649532\pi$
$691$	14.3492	−	24.8536i	0.545871	−	0.945476i	0.998552	−	0.0538034i	$-0.0171344\pi$
$692$		0			0
$693$		0			0
$694$	8.00000			0.303676
$695$	−4.94975	+	8.57321i	−0.187755	+	0.325201i
$696$	0.343146	+	0.594346i	0.0130069	+	0.0225286i
$697$	−6.24264	−	10.8126i	−0.236457	−	0.409555i
$698$	18.1924	−	31.5101i	0.688592	−	1.19268i
$699$	20.7279			0.784002
$700$		0			0
$701$	−10.7990			−0.407872			−0.203936	−	0.978984i	$-0.565373\pi$
$701$	−10.7990			−0.407872			−0.203936	+	0.978984i	$0.565373\pi$
$702$	4.00000	−	6.92820i	0.150970	−	0.261488i
$703$	−8.12132	−	14.0665i	−0.306301	−	0.530530i
$704$	−16.9706	−	29.3939i	−0.639602	−	1.10782i
$705$	1.77817	−	3.07989i	0.0669699	−	0.115995i
$706$	−12.0000			−0.451626
$707$		0			0
$708$		0			0
$709$	−0.363961	+	0.630399i	−0.0136688	+	0.0236751i	−0.872779	−	0.488116i	$-0.837684\pi$
$709$	−0.363961	+	0.630399i	−0.0136688	+	0.0236751i	0.859110	+	0.511791i	$0.171018\pi$
$710$	14.6569	+	25.3864i	0.550062	+	0.952735i
$711$	7.74264	+	13.4106i	0.290372	+	0.502939i
$712$	2.24264	−	3.88437i	0.0840465	−	0.145573i
$713$	18.8995			0.707792
$714$		0			0
$715$	−6.72792			−0.251610
$716$		0			0
$717$	2.48528	+	4.30463i	0.0928145	+	0.160759i
$718$	−19.7279	−	34.1698i	−0.736240	−	1.27520i
$719$	−0.878680	+	1.52192i	−0.0327692	+	0.0567580i	−0.881945	−	0.471352i	$-0.843766\pi$
$719$	−0.878680	+	1.52192i	−0.0327692	+	0.0567580i	0.849176	+	0.528110i	$0.177099\pi$
$720$	−6.34315			−0.236395
$721$		0			0
$722$	−47.3137			−1.76083
$723$	14.2929	−	24.7560i	0.531558	−	0.920686i
$724$		0			0
$725$	0.213203	+	0.369279i	0.00791818	+	0.0137147i
$726$	−7.00000	+	12.1244i	−0.259794	+	0.449977i
$727$	−42.0000			−1.55769			−0.778847	−	0.627214i	$-0.784195\pi$
$727$	−42.0000			−1.55769			−0.778847	+	0.627214i	$0.784195\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−10.3640	+	17.9509i	−0.383587	+	0.664393i
$731$	−3.53553	−	6.12372i	−0.130766	−	0.226494i
$732$		0			0
$733$	−8.34924	+	14.4613i	−0.308386	+	0.534141i	−0.978010	−	0.208560i	$-0.933122\pi$
$733$	−8.34924	+	14.4613i	−0.308386	+	0.534141i	0.669623	+	0.742701i	$0.266456\pi$
$734$	14.4853			0.534661
$735$		0			0
$736$		0			0
$737$	30.7279	−	53.2223i	1.13188	−	1.96047i
$738$	6.24264	+	10.8126i	0.229795	+	0.398016i
$739$	8.84924	+	15.3273i	0.325525	+	0.563825i	0.981618	−	0.190854i	$-0.0611258\pi$
$739$	8.84924	+	15.3273i	0.325525	+	0.563825i	−0.656094	+	0.754679i	$0.727792\pi$
$740$		0			0
$741$	−10.2426			−0.376273
$742$		0			0
$743$	−29.6569			−1.08800			−0.544002	−	0.839084i	$-0.683092\pi$
$743$	−29.6569			−1.08800			−0.544002	+	0.839084i	$0.683092\pi$
$744$	−6.48528	+	11.2328i	−0.237762	+	0.411816i
$745$	12.8787	+	22.3065i	0.471838	+	0.817248i
$746$	6.00000	+	10.3923i	0.219676	+	0.380489i
$747$	−6.62132	+	11.4685i	−0.242261	+	0.419609i
$748$		0			0
$749$		0			0
$750$	23.7401			0.866866
$751$	−7.74264	+	13.4106i	−0.282533	+	0.489361i	−0.972008	−	0.234948i	$-0.924508\pi$
$751$	−7.74264	+	13.4106i	−0.282533	+	0.489361i	0.689475	+	0.724310i	$0.257841\pi$
$752$	−3.17157	−	5.49333i	−0.115655	−	0.200321i
$753$	−11.7279	−	20.3134i	−0.427389	−	0.740260i
$754$	0.121320	−	0.210133i	0.00441823	−	0.00765259i
$755$	15.4731			0.563123
$756$		0			0
$757$	21.4853			0.780896			0.390448	−	0.920625i	$-0.372320\pi$
$757$	21.4853			0.780896			0.390448	+	0.920625i	$0.372320\pi$
$758$	16.7990	−	29.0967i	0.610167	−	1.05684i
$759$	−17.4853	−	30.2854i	−0.634676	−	1.09929i
$760$	16.2426	+	28.1331i	0.589183	+	1.02049i
$761$	17.3787	−	30.1008i	0.629977	−	1.09115i	−0.357579	−	0.933883i	$-0.616398\pi$
$761$	17.3787	−	30.1008i	0.629977	−	1.09115i	0.987556	−	0.157269i	$-0.0502689\pi$
$762$	4.00000			0.144905
$763$		0			0
$764$		0			0
$765$	1.12132	−	1.94218i	0.0405414	−	0.0702198i
$766$	14.4853	+	25.0892i	0.523374	+	0.906511i
$767$	0.171573	+	0.297173i	0.00619514	+	0.0107303i
$768$		0			0
$769$	−52.2132			−1.88286			−0.941428	−	0.337214i	$-0.890516\pi$
$769$	−52.2132			−1.88286			−0.941428	+	0.337214i	$0.890516\pi$
$770$		0			0
$771$	−27.4558			−0.988798
$772$		0			0
$773$	−16.4142	−	28.4303i	−0.590378	−	1.02257i	−0.994181	−	0.107719i	$-0.965645\pi$
$773$	−16.4142	−	28.4303i	−0.590378	−	1.02257i	0.403803	−	0.914846i	$-0.367688\pi$
$774$	3.53553	+	6.12372i	0.127082	+	0.220113i
$775$	−4.02944	+	6.97919i	−0.144742	+	0.250700i
$776$	−33.1716			−1.19079
$777$		0			0
$778$	−41.9411			−1.50366
$779$	31.9706	−	55.3746i	1.14546	−	1.98400i
$780$		0			0
$781$	27.7279	+	48.0262i	0.992183	+	1.71851i
$782$	5.82843	−	10.0951i	0.208424	−	0.361001i
$783$	0.970563			0.0346851
$784$		0			0
$785$	−5.95837			−0.212663
$786$	−2.82843	+	4.89898i	−0.100887	+	0.174741i
$787$	−12.3787	−	21.4405i	−0.441252	−	0.764271i	0.556530	−	0.830827i	$-0.312132\pi$
$787$	−12.3787	−	21.4405i	−0.441252	−	0.764271i	−0.997783	+	0.0665559i	$0.978799\pi$
$788$		0			0
$789$	1.39340	−	2.41344i	0.0496063	−	0.0859206i
$790$	34.7279			1.23556
$791$		0			0
$792$	−12.0000			−0.426401
$793$	3.00000	−	5.19615i	0.106533	−	0.184521i
$794$	12.8787	+	22.3065i	0.457047	+	0.791629i
$795$	0.192388	+	0.333226i	0.00682330	+	0.0118183i
$796$		0			0
$797$	24.3431			0.862278			0.431139	−	0.902285i	$-0.358112\pi$
$797$	24.3431			0.862278			0.431139	+	0.902285i	$0.358112\pi$
$798$		0			0
$799$	2.24264			0.0793389
$800$		0			0
$801$	−0.792893	−	1.37333i	−0.0280155	−	0.0485243i
$802$	4.48528	+	7.76874i	0.158381	+	0.274324i
$803$	−19.6066	+	33.9596i	−0.691902	+	1.19841i
$804$		0			0
$805$		0			0
$806$	4.58579			0.161527
$807$	−6.48528	+	11.2328i	−0.228293	+	0.395415i
$808$	14.4853	+	25.0892i	0.509590	+	0.882636i
$809$	−8.74264	−	15.1427i	−0.307375	−	0.532389i	0.670412	−	0.741989i	$-0.266117\pi$
$809$	−8.74264	−	15.1427i	−0.307375	−	0.532389i	−0.977787	+	0.209600i	$0.932784\pi$
$810$	5.60660	−	9.71092i	0.196996	−	0.341207i
$811$	21.9411			0.770457			0.385229	−	0.922821i	$-0.374123\pi$
$811$	21.9411			0.770457			0.385229	+	0.922821i	$0.374123\pi$
$812$		0			0
$813$	28.2843			0.991973
$814$	6.72792	−	11.6531i	0.235814	−	0.408441i
$815$	6.72792	+	11.6531i	0.235669	+	0.408190i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	18.1066	−	31.3616i	0.633470	−	1.09720i
$818$	4.58579			0.160338
$819$		0			0
$820$		0			0
$821$	10.0711	−	17.4436i	0.351483	−	0.608786i	−0.635027	−	0.772490i	$-0.719011\pi$
$821$	10.0711	−	17.4436i	0.351483	−	0.608786i	0.986509	+	0.163704i	$0.0523443\pi$
$822$	4.58579	+	7.94282i	0.159948	+	0.277037i
$823$	−5.24264	−	9.08052i	−0.182747	−	0.316527i	0.760068	−	0.649844i	$-0.225166\pi$
$823$	−5.24264	−	9.08052i	−0.182747	−	0.316527i	−0.942815	+	0.333316i	$0.891832\pi$
$824$	−11.3137	+	19.5959i	−0.394132	+	0.682656i
$825$	14.9117			0.519158
$826$		0			0
$827$	−49.4558			−1.71975			−0.859874	−	0.510506i	$-0.829458\pi$
$827$	−49.4558			−1.71975			−0.859874	+	0.510506i	$0.829458\pi$
$828$		0			0
$829$	25.3640	+	43.9317i	0.880927	+	1.52581i	0.850312	+	0.526279i	$0.176413\pi$
$829$	25.3640	+	43.9317i	0.880927	+	1.52581i	0.0306146	+	0.999531i	$0.490254\pi$
$830$	14.8492	+	25.7196i	0.515425	+	0.892742i
$831$	−5.29289	+	9.16756i	−0.183608	+	0.318019i
$832$	8.00000			0.277350
$833$		0			0
$834$	−12.4853			−0.432330
$835$	−12.1985	+	21.1284i	−0.422146	+	0.731178i
$836$		0			0
$837$	9.17157	+	15.8856i	0.317016	+	0.549088i
$838$	14.7574	−	25.5605i	0.509785	−	0.882973i
$839$	33.1716			1.14521			0.572605	−	0.819831i	$-0.305933\pi$
$839$	33.1716			1.14521			0.572605	+	0.819831i	$0.305933\pi$
$840$		0			0
$841$	−28.9706			−0.998985
$842$	4.75736	−	8.23999i	0.163949	−	0.283969i
$843$	11.0000	+	19.0526i	0.378860	+	0.656205i
$844$		0			0
$845$	0.792893	−	1.37333i	0.0272764	−	0.0472440i
$846$	−2.24264			−0.0771036
$847$		0			0
$848$	0.686292			0.0235673
$849$	6.00000	−	10.3923i	0.205919	−	0.356663i
$850$	2.48528	+	4.30463i	0.0852444	+	0.147648i
$851$	6.53553	+	11.3199i	0.224035	+	0.388040i
$852$		0			0
$853$	−39.7279			−1.36026			−0.680129	−	0.733092i	$-0.738076\pi$
$853$	−39.7279			−1.36026			−0.680129	+	0.733092i	$0.738076\pi$
$854$		0			0
$855$	11.4853			0.392788
$856$	28.4853	−	49.3380i	0.973607	−	1.68634i
$857$	−27.3848	−	47.4318i	−0.935446	−	1.62024i	−0.773836	−	0.633385i	$-0.781665\pi$
$857$	−27.3848	−	47.4318i	−0.935446	−	1.62024i	−0.161610	−	0.986855i	$-0.551669\pi$
$858$	−4.24264	−	7.34847i	−0.144841	−	0.250873i
$859$	15.4853	−	26.8213i	0.528351	−	0.915131i	−0.471103	−	0.882078i	$-0.656144\pi$
$859$	15.4853	−	26.8213i	0.528351	−	0.915131i	0.999454	−	0.0330523i	$-0.0105228\pi$
$860$		0			0
$861$		0			0
$862$	17.4558			0.594548
$863$	−14.1421	+	24.4949i	−0.481404	+	0.833816i	−0.999772	−	0.0213414i	$-0.993206\pi$
$863$	−14.1421	+	24.4949i	−0.481404	+	0.833816i	0.518368	+	0.855157i	$0.326540\pi$
$864$		0			0
$865$	−19.6066	−	33.9596i	−0.666644	−	1.15466i
$866$	17.6569	−	30.5826i	0.600004	−	1.03924i
$867$	21.2132			0.720438
$868$		0			0
$869$	65.6985			2.22867
$870$	0.272078	−	0.471253i	0.00922431	−	0.0159770i
$871$	7.24264	+	12.5446i	0.245408	+	0.425058i
$872$	−23.6569	−	40.9749i	−0.801122	−	1.38758i
$873$	−5.86396	+	10.1567i	−0.198465	+	0.343751i
$874$	59.6985			2.01933
$875$		0			0
$876$		0			0
$877$	5.12132	−	8.87039i	0.172935	−	0.299532i	−0.766510	−	0.642232i	$-0.778008\pi$
$877$	5.12132	−	8.87039i	0.172935	−	0.299532i	0.939445	+	0.342701i	$0.111342\pi$
$878$	24.3848	+	42.2357i	0.822946	+	1.42538i
$879$	−10.8787	−	18.8424i	−0.366929	−	0.635539i
$880$	−13.4558	+	23.3062i	−0.453596	+	0.785652i
$881$	−13.1127			−0.441778			−0.220889	−	0.975299i	$-0.570896\pi$
$881$	−13.1127			−0.441778			−0.220889	+	0.975299i	$0.570896\pi$
$882$		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
$885$	0.384776	+	0.666452i	0.0129341	+	0.0224025i
$886$	−2.60660	−	4.51477i	−0.0875705	−	0.151677i
$887$	9.55635	−	16.5521i	0.320871	−	0.555765i	−0.659797	−	0.751444i	$-0.729358\pi$
$887$	9.55635	−	16.5521i	0.320871	−	0.555765i	0.980668	+	0.195679i	$0.0626911\pi$
$888$	−8.97056			−0.301032
$889$		0			0
$890$	−3.55635			−0.119209
$891$	10.6066	−	18.3712i	0.355335	−	0.615457i
$892$		0			0
$893$	5.74264	+	9.94655i	0.192170	+	0.332848i
$894$	−16.2426	+	28.1331i	−0.543235	+	0.940911i
$895$	14.2721			0.477063
$896$		0			0
$897$	8.24264			0.275214
$898$	14.9706	−	25.9298i	0.499574	−	0.865288i
$899$	0.278175	+	0.481813i	0.00927764	+	0.0160693i
$900$		0			0
$901$	−0.121320	+	0.210133i	−0.00404177	+	0.00700055i
$902$	52.9706			1.76373
$903$		0			0
$904$	6.54416			0.217655
$905$	14.8492	−	25.7196i	0.493606	−	0.854950i
$906$	9.75736	+	16.9002i	0.324167	+	0.561473i
$907$	−0.985281	−	1.70656i	−0.0327157	−	0.0566653i	0.849204	−	0.528065i	$-0.177082\pi$
$907$	−0.985281	−	1.70656i	−0.0327157	−	0.0566653i	−0.881920	+	0.471400i	$0.843749\pi$
$908$		0			0
$909$	10.2426			0.339727
$910$		0			0
$911$	−43.9706			−1.45681			−0.728405	−	0.685147i	$-0.759738\pi$
$911$	−43.9706			−1.45681			−0.728405	+	0.685147i	$0.759738\pi$
$912$	−20.4853	+	35.4815i	−0.678335	+	1.17491i
$913$	28.0919	+	48.6566i	0.929706	+	1.61030i
$914$	−5.10051	−	8.83433i	−0.168710	−	0.292214i
$915$	6.72792	−	11.6531i	0.222418	−	0.385240i
$916$		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	$0.296214\pi$
$920$	−13.0711	−	22.6398i	−0.430940	−	0.746411i
$921$	−9.36396	−	16.2189i	−0.308553	−	0.534429i
$922$	−6.24264	+	10.8126i	−0.205590	+	0.356093i
$923$	−13.0711			−0.430239
$924$		0			0
$925$	−5.57359			−0.183259
$926$	−3.00000	+	5.19615i	−0.0985861	+	0.170756i
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$		0			0
$929$	18.4497	−	31.9559i	0.605317	−	1.04844i	−0.386685	−	0.922212i	$-0.626380\pi$
$929$	18.4497	−	31.9559i	0.605317	−	1.04844i	0.992001	−	0.126227i	$-0.0402868\pi$
$930$	10.2843			0.337235
$931$		0			0
$932$		0			0
$933$	5.24264	−	9.08052i	0.171636	−	0.297283i
$934$	2.75736	+	4.77589i	0.0902236	+	0.156272i
$935$	−4.75736	−	8.23999i	−0.155582	−	0.269476i
$936$	1.41421	−	2.44949i	0.0462250	−	0.0800641i
$937$	−45.2132			−1.47705			−0.738525	−	0.674226i	$-0.764478\pi$
$937$	−45.2132			−1.47705			−0.738525	+	0.674226i	$0.764478\pi$
$938$		0			0
$939$	32.8284			1.07132
$940$		0			0
$941$	20.0355	+	34.7026i	0.653140	+	1.13127i	0.982357	+	0.187017i	$0.0598819\pi$
$941$	20.0355	+	34.7026i	0.653140	+	1.13127i	−0.329217	+	0.944254i	$0.606785\pi$
$942$	−3.75736	−	6.50794i	−0.122421	−	0.212040i
$943$	−25.7279	+	44.5621i	−0.837816	+	1.45114i
$944$	1.37258			0.0446738
$945$		0			0
$946$	30.0000			0.975384
$947$	−7.58579	+	13.1390i	−0.246505	+	0.426959i	−0.962554	−	0.271091i	$-0.912615\pi$
$947$	−7.58579	+	13.1390i	−0.246505	+	0.426959i	0.716049	+	0.698050i	$0.245949\pi$
$948$		0			0
$949$	−4.62132	−	8.00436i	−0.150014	−	0.259833i
$950$	−12.7279	+	22.0454i	−0.412948	+	0.715247i
$951$	16.0000			0.518836
$952$		0			0
$953$	11.1421			0.360929			0.180465	−	0.983581i	$-0.442240\pi$
$953$	11.1421			0.360929			0.180465	+	0.983581i	$0.442240\pi$
$954$	0.121320	−	0.210133i	0.00392789	−	0.00680331i
$955$	12.0294	+	20.8356i	0.389263	+	0.674224i
$956$		0			0
$957$	0.514719	−	0.891519i	0.0166385	−	0.0288187i
$958$	−8.78680			−0.283889
$959$		0			0
$960$	17.9411			0.579047
$961$	10.2426	−	17.7408i	0.330408	−	0.572283i
$962$	1.58579	+	2.74666i	0.0511278	+	0.0885560i
$963$	−10.0711	−	17.4436i	−0.324536	−	0.562112i
$964$		0			0
$965$	22.9706			0.739449
$966$		0			0
$967$	17.6985			0.569145			0.284572	−	0.958655i	$-0.408148\pi$
$967$	17.6985			0.569145			0.284572	+	0.958655i	$0.408148\pi$
$968$	−9.89949	+	17.1464i	−0.318182	+	0.551107i
$969$	−7.24264	−	12.5446i	−0.232667	−	0.402991i
$970$	13.1508	+	22.7778i	0.422245	+	0.731350i
$971$	21.7279	−	37.6339i	0.697282	−	1.20773i	−0.272123	−	0.962262i	$-0.587726\pi$
$971$	21.7279	−	37.6339i	0.697282	−	1.20773i	0.969405	−	0.245466i	$-0.0789409\pi$
$972$		0			0
$973$		0			0
$974$	16.2010			0.519114
$975$	−1.75736	+	3.04384i	−0.0562805	+	0.0974808i
$976$	−12.0000	−	20.7846i	−0.384111	−	0.665299i
$977$	−12.0208	−	20.8207i	−0.384580	−	0.666112i	0.607131	−	0.794602i	$-0.292320\pi$
$977$	−12.0208	−	20.8207i	−0.384580	−	0.666112i	−0.991711	+	0.128490i	$0.958987\pi$
$978$	−8.48528	+	14.6969i	−0.271329	+	0.469956i
$979$	−6.72792			−0.215025
$980$		0			0
$981$	−16.7279			−0.534081
$982$	11.7574	−	20.3643i	0.375192	−	0.649852i
$983$	−7.52082	−	13.0264i	−0.239877	−	0.415479i	0.720802	−	0.693141i	$-0.243774\pi$
$983$	−7.52082	−	13.0264i	−0.239877	−	0.415479i	−0.960679	+	0.277662i	$0.910440\pi$
$984$	−17.6569	−	30.5826i	−0.562880	−	0.974937i
$985$	9.78680	−	16.9512i	0.311833	−	0.540111i
$986$	0.343146			0.0109280
$987$		0			0
$988$		0			0
$989$	−14.5711	+	25.2378i	−0.463333	+	0.802516i
$990$	4.75736	+	8.23999i	0.151199	+	0.261884i
$991$	−0.514719	−	0.891519i	−0.0163506	−	0.0283200i	0.857734	−	0.514093i	$-0.171871\pi$
$991$	−0.514719	−	0.891519i	−0.0163506	−	0.0283200i	−0.874085	+	0.485773i	$0.838538\pi$
$992$		0			0
$993$	25.4558			0.807817
$994$		0			0
$995$	−5.95837			−0.188893
$996$		0			0
$997$	−5.75736	−	9.97204i	−0.182337	−	0.315818i	0.760339	−	0.649527i	$-0.225033\pi$
$997$	−5.75736	−	9.97204i	−0.182337	−	0.315818i	−0.942676	+	0.333709i	$0.891700\pi$
$998$	−9.38478	−	16.2549i	−0.297070	−	0.514540i
$999$	−6.34315	+	10.9867i	−0.200688	+	0.347602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.g.79.2		4
7.2	even	3		637.2.a.g.1.1		2
7.3	odd	6		637.2.e.f.508.2		4
7.4	even	3	inner	637.2.e.g.508.2		4
7.5	odd	6		91.2.a.c.1.1	✓	2
7.6	odd	2		637.2.e.f.79.2		4
21.2	odd	6		5733.2.a.s.1.2		2
21.5	even	6		819.2.a.h.1.2		2
28.19	even	6		1456.2.a.q.1.1		2
35.19	odd	6		2275.2.a.j.1.2		2
56.5	odd	6		5824.2.a.bl.1.1		2
56.19	even	6		5824.2.a.bk.1.2		2
91.5	even	12		1183.2.c.d.337.4		4
91.12	odd	6		1183.2.a.d.1.2		2
91.47	even	12		1183.2.c.d.337.2		4
91.51	even	6		8281.2.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.c.1.1	✓	2	7.5	odd	6
637.2.a.g.1.1		2	7.2	even	3
637.2.e.f.79.2		4	7.6	odd	2
637.2.e.f.508.2		4	7.3	odd	6
637.2.e.g.79.2		4	1.1	even	1	trivial
637.2.e.g.508.2		4	7.4	even	3	inner
819.2.a.h.1.2		2	21.5	even	6
1183.2.a.d.1.2		2	91.12	odd	6
1183.2.c.d.337.2		4	91.47	even	12
1183.2.c.d.337.4		4	91.5	even	12
1456.2.a.q.1.1		2	28.19	even	6
2275.2.a.j.1.2		2	35.19	odd	6
5733.2.a.s.1.2		2	21.2	odd	6
5824.2.a.bk.1.2		2	56.19	even	6
5824.2.a.bl.1.1		2	56.5	odd	6
8281.2.a.v.1.2		2	91.51	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.792893 - 1.37333i) q^{5} +2.00000 q^{6} +2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.792893 - 1.37333i) q^{5} +2.00000 q^{6} +2.82843 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.12132 - 1.94218i) q^{10} +(-2.12132 - 3.67423i) q^{11} +1.00000 q^{13} +2.24264 q^{15} +(2.00000 - 3.46410i) q^{16} +(0.707107 + 1.22474i) q^{17} +(-0.707107 - 1.22474i) q^{18} +(-3.62132 + 6.27231i) q^{19} -6.00000 q^{22} +(2.91421 - 5.04757i) q^{23} +(2.00000 + 3.46410i) q^{24} +(1.24264 + 2.15232i) q^{25} +(0.707107 - 1.22474i) q^{26} +5.65685 q^{27} +0.171573 q^{29} +(1.58579 - 2.74666i) q^{30} +(1.62132 + 2.80821i) q^{31} +(3.00000 - 5.19615i) q^{33} +2.00000 q^{34} +(-1.12132 + 1.94218i) q^{37} +(5.12132 + 8.87039i) q^{38} +(0.707107 + 1.22474i) q^{39} +(2.24264 - 3.88437i) q^{40} -8.82843 q^{41} -5.00000 q^{43} +(-0.792893 - 1.37333i) q^{45} +(-4.12132 - 7.13834i) q^{46} +(0.792893 - 1.37333i) q^{47} +5.65685 q^{48} +3.51472 q^{50} +(-1.00000 + 1.73205i) q^{51} +(0.0857864 + 0.148586i) q^{53} +(4.00000 - 6.92820i) q^{54} -6.72792 q^{55} -10.2426 q^{57} +(0.121320 - 0.210133i) q^{58} +(0.171573 + 0.297173i) q^{59} +(3.00000 - 5.19615i) q^{61} +4.58579 q^{62} +8.00000 q^{64} +(0.792893 - 1.37333i) q^{65} +(-4.24264 - 7.34847i) q^{66} +(7.24264 + 12.5446i) q^{67} +8.24264 q^{69} -13.0711 q^{71} +(1.41421 - 2.44949i) q^{72} +(-4.62132 - 8.00436i) q^{73} +(1.58579 + 2.74666i) q^{74} +(-1.75736 + 3.04384i) q^{75} +2.00000 q^{78} +(-7.74264 + 13.4106i) q^{79} +(-3.17157 - 5.49333i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-6.24264 + 10.8126i) q^{82} -13.2426 q^{83} +2.24264 q^{85} +(-3.53553 + 6.12372i) q^{86} +(0.121320 + 0.210133i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(0.792893 - 1.37333i) q^{89} -2.24264 q^{90} +(-2.29289 + 3.97141i) q^{93} +(-1.12132 - 1.94218i) q^{94} +(5.74264 + 9.94655i) q^{95} -11.7279 q^{97} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) 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

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