LMFDB - Embedded newform 637.2.f.h.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.100088711424.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 $ x^8 - 13x^6 + 130x^4 - 507*x^2 + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.2
Root			$2.49541 - 1.44073i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.h.393.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15139 + 1.99426i) q^{2} +(1.08365 - 1.87694i) q^{3} +(-1.65139 - 2.86029i) q^{4} -2.16731 q^{5} +(2.49541 + 4.32218i) q^{6} +3.00000 q^{8} +(-0.848612 - 1.46984i) q^{9} +(2.49541 - 4.32218i) q^{10} +(-2.45416 + 4.25074i) q^{11} -7.15813 q^{12} +(1.41176 - 3.31767i) q^{13} +(-2.34861 + 4.06792i) q^{15} +(-0.151388 + 0.262211i) q^{16} +(3.57907 + 6.19912i) q^{17} +3.90833 q^{18} +(1.08365 + 1.87694i) q^{19} +(3.57907 + 6.19912i) q^{20} +(-5.65139 - 9.78849i) q^{22} +(0.302776 - 0.524423i) q^{23} +(3.25096 - 5.63083i) q^{24} -0.302776 q^{25} +(4.99082 + 6.63534i) q^{26} +2.82352 q^{27} +(1.15139 - 1.99426i) q^{29} +(-5.40833 - 9.36750i) q^{30} +7.15813 q^{31} +(2.65139 + 4.59234i) q^{32} +(5.31893 + 9.21265i) q^{33} -16.4836 q^{34} +(-2.80278 + 4.85455i) q^{36} +(-4.30278 + 7.45263i) q^{37} -4.99082 q^{38} +(-4.69722 - 6.24500i) q^{39} -6.50192 q^{40} +(-4.99082 + 8.64436i) q^{41} +(6.25694 + 10.8373i) q^{43} +16.2111 q^{44} +(1.83920 + 3.18559i) q^{45} +(0.697224 + 1.20763i) q^{46} +1.51110 q^{47} +(0.328104 + 0.568293i) q^{48} +(0.348612 - 0.603814i) q^{50} +15.5139 q^{51} +(-11.8209 + 1.44073i) q^{52} +2.39445 q^{53} +(-3.25096 + 5.63083i) q^{54} +(5.31893 - 9.21265i) q^{55} +4.69722 q^{57} +(2.65139 + 4.59234i) q^{58} +(-1.41176 - 2.44524i) q^{59} +15.5139 q^{60} +(2.16731 + 3.75389i) q^{61} +(-8.24179 + 14.2752i) q^{62} -12.8167 q^{64} +(-3.05971 + 7.19041i) q^{65} -24.4966 q^{66} +(-0.500000 + 0.866025i) q^{67} +(11.8209 - 20.4743i) q^{68} +(-0.656208 - 1.13659i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(-2.54584 - 4.40952i) q^{72} +4.33462 q^{73} +(-9.90833 - 17.1617i) q^{74} +(-0.328104 + 0.568293i) q^{75} +(3.57907 - 6.19912i) q^{76} +(17.8625 - 2.17708i) q^{78} -6.60555 q^{79} +(0.328104 - 0.568293i) q^{80} +(5.60555 - 9.70910i) q^{81} +(-11.4927 - 19.9060i) q^{82} -2.82352 q^{83} +(-7.75694 - 13.4354i) q^{85} -28.8167 q^{86} +(-2.49541 - 4.32218i) q^{87} +(-7.36249 + 12.7522i) q^{88} +(3.25096 - 5.63083i) q^{89} -8.47055 q^{90} -2.00000 q^{92} +(7.75694 - 13.4354i) q^{93} +(-1.73986 + 3.01353i) q^{94} +(-2.34861 - 4.06792i) q^{95} +11.4927 q^{96} +(-6.83003 - 11.8300i) q^{97} +8.33053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} + 6 q^{16} - 12 q^{18} - 38 q^{22} - 12 q^{23} + 12 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} - 52 q^{39} + 14 q^{43} + 72 q^{44}+ \cdots - 92 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 14 * q^9 + 2 * q^11 - 26 * q^15 + 6 * q^16 - 12 * q^18 - 38 * q^22 - 12 * q^23 + 12 * q^25 + 2 * q^29 + 14 * q^32 - 8 * q^36 - 20 * q^37 - 52 * q^39 + 14 * q^43 + 72 * q^44 + 20 * q^46 + 10 * q^50 + 52 * q^51 + 48 * q^53 + 52 * q^57 + 14 * q^58 + 52 * q^60 - 16 * q^64 + 26 * q^65 - 4 * q^67 - 16 * q^71 - 42 * q^72 - 36 * q^74 + 78 * q^78 - 24 * q^79 + 16 * q^81 - 26 * q^85 - 144 * q^86 + 6 * q^88 - 16 * q^92 + 26 * q^93 - 26 * q^95 - 92 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.15139	+	1.99426i	−0.814154	+	1.41016i	0.0957796	+	0.995403i	$0.469466\pi$
$2$	−1.15139	+	1.99426i	−0.814154	+	1.41016i	−0.909934	+	0.414754i	$0.863868\pi$
$3$	1.08365	−	1.87694i	0.625648	−	1.08365i	−0.362767	−	0.931880i	$-0.618168\pi$
$3$	1.08365	−	1.87694i	0.625648	−	1.08365i	0.988415	−	0.151774i	$-0.0484987\pi$
$4$	−1.65139	−	2.86029i	−0.825694	−	1.43014i
$5$	−2.16731			−0.969250			−0.484625	−	0.874722i	$-0.661044\pi$
$5$	−2.16731			−0.969250			−0.484625	+	0.874722i	$0.661044\pi$
$6$	2.49541	+	4.32218i	1.01875	+	1.76452i
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$	−0.848612	−	1.46984i	−0.282871	−	0.489946i
$10$	2.49541	−	4.32218i	0.789119	−	1.36679i
$11$	−2.45416	+	4.25074i	−0.739958	+	1.28165i	0.212555	+	0.977149i	$0.431821\pi$
$11$	−2.45416	+	4.25074i	−0.739958	+	1.28165i	−0.952514	+	0.304496i	$0.901512\pi$
$12$	−7.15813			−2.06637
$13$	1.41176	−	3.31767i	0.391551	−	0.920156i
$13$	1.41176	−	3.31767i	0.391551	−	0.920156i
$14$		0			0
$15$	−2.34861	+	4.06792i	−0.606409	+	1.05033i
$16$	−0.151388	+	0.262211i	−0.0378470	+	0.0655528i
$17$	3.57907	+	6.19912i	0.868051	+	1.50351i	0.863985	+	0.503517i	$0.167961\pi$
$17$	3.57907	+	6.19912i	0.868051	+	1.50351i	0.00406561	+	0.999992i	$0.498706\pi$
$18$	3.90833			0.921201
$19$	1.08365	+	1.87694i	0.248607	+	0.430600i	0.963140	−	0.269002i	$-0.0866938\pi$
$19$	1.08365	+	1.87694i	0.248607	+	0.430600i	−0.714532	+	0.699602i	$0.753360\pi$
$20$	3.57907	+	6.19912i	0.800304	+	1.38617i
$21$		0			0
$22$	−5.65139	−	9.78849i	−1.20488	−	2.08691i
$23$	0.302776	−	0.524423i	0.0631331	−	0.109350i	−0.832731	−	0.553677i	$-0.813224\pi$
$23$	0.302776	−	0.524423i	0.0631331	−	0.109350i	0.895864	+	0.444328i	$0.146557\pi$
$24$	3.25096	−	5.63083i	0.663600	−	1.14939i
$25$	−0.302776			−0.0605551
$26$	4.99082	+	6.63534i	0.978781	+	1.30130i
$27$	2.82352			0.543386
$28$		0			0
$29$	1.15139	−	1.99426i	0.213807	−	0.370325i	−0.739096	−	0.673601i	$-0.764747\pi$
$29$	1.15139	−	1.99426i	0.213807	−	0.370325i	0.952903	+	0.303275i	$0.0980802\pi$
$30$	−5.40833	−	9.36750i	−0.987421	−	1.71026i
$31$	7.15813			1.28564			0.642819	−	0.766018i	$-0.277765\pi$
$31$	7.15813			1.28564			0.642819	+	0.766018i	$0.277765\pi$
$32$	2.65139	+	4.59234i	0.468704	+	0.811818i
$33$	5.31893	+	9.21265i	0.925907	+	1.60372i
$34$	−16.4836			−2.82691
$35$		0			0
$36$	−2.80278	+	4.85455i	−0.467129	+	0.809092i
$37$	−4.30278	+	7.45263i	−0.707372	+	1.22520i	0.258457	+	0.966023i	$0.416786\pi$
$37$	−4.30278	+	7.45263i	−0.707372	+	1.22520i	−0.965829	+	0.259181i	$0.916547\pi$
$38$	−4.99082			−0.809619
$39$	−4.69722	−	6.24500i	−0.752158	−	1.00000i
$40$	−6.50192			−1.02804
$41$	−4.99082	+	8.64436i	−0.779436	+	1.35002i	0.152832	+	0.988252i	$0.451161\pi$
$41$	−4.99082	+	8.64436i	−0.779436	+	1.35002i	−0.932267	+	0.361770i	$0.882173\pi$
$42$		0			0
$43$	6.25694	+	10.8373i	0.954174	+	1.65268i	0.736247	+	0.676713i	$0.236596\pi$
$43$	6.25694	+	10.8373i	0.954174	+	1.65268i	0.217928	+	0.975965i	$0.430070\pi$
$44$	16.2111			2.44392
$45$	1.83920	+	3.18559i	0.274172	+	0.474880i
$46$	0.697224	+	1.20763i	0.102800	+	0.178055i
$47$	1.51110			0.220417			0.110208	−	0.993909i	$-0.464848\pi$
$47$	1.51110			0.220417			0.110208	+	0.993909i	$0.464848\pi$
$48$	0.328104	+	0.568293i	0.0473577	+	0.0820260i
$49$		0			0
$50$	0.348612	−	0.603814i	0.0493012	−	0.0853922i
$51$	15.5139			2.17238
$52$	−11.8209	+	1.44073i	−1.63926	+	0.199793i
$53$	2.39445			0.328903			0.164451	−	0.986385i	$-0.447415\pi$
$53$	2.39445			0.328903			0.164451	+	0.986385i	$0.447415\pi$
$54$	−3.25096	+	5.63083i	−0.442400	+	0.766259i
$55$	5.31893	−	9.21265i	0.717204	−	1.24223i
$56$		0			0
$57$	4.69722			0.622163
$58$	2.65139	+	4.59234i	0.348144	+	0.603004i
$59$	−1.41176	−	2.44524i	−0.183795	−	0.318343i	0.759375	−	0.650654i	$-0.225505\pi$
$59$	−1.41176	−	2.44524i	−0.183795	−	0.318343i	−0.943170	+	0.332311i	$0.892172\pi$
$60$	15.5139			2.00283
$61$	2.16731	+	3.75389i	0.277495	+	0.480636i	0.970762	−	0.240045i	$-0.0771623\pi$
$61$	2.16731	+	3.75389i	0.277495	+	0.480636i	−0.693266	+	0.720682i	$0.743829\pi$
$62$	−8.24179	+	14.2752i	−1.04671	+	1.81295i
$63$		0			0
$64$	−12.8167			−1.60208
$65$	−3.05971	+	7.19041i	−0.379511	+	0.891861i
$66$	−24.4966			−3.01532
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i	−0.894951	−	0.446165i	$-0.852789\pi$
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i	0.833866	+	0.551967i	$0.186123\pi$
$68$	11.8209	−	20.4743i	1.43349	−	2.48288i
$69$	−0.656208	−	1.13659i	−0.0789982	−	0.136829i
$70$		0			0
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	0.722599	−	0.691268i	$-0.242948\pi$
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	−0.959955	+	0.280155i	$0.909614\pi$
$72$	−2.54584	−	4.40952i	−0.300030	−	0.519667i
$73$	4.33462			0.507328			0.253664	−	0.967292i	$-0.418364\pi$
$73$	4.33462			0.507328			0.253664	+	0.967292i	$0.418364\pi$
$74$	−9.90833	−	17.1617i	−1.15182	−	1.99501i
$75$	−0.328104	+	0.568293i	−0.0378862	+	0.0656208i
$76$	3.57907	−	6.19912i	0.410547	−	0.711088i
$77$		0			0
$78$	17.8625	−	2.17708i	2.02253	−	0.246506i
$79$	−6.60555			−0.743183			−0.371591	−	0.928396i	$-0.621188\pi$
$79$	−6.60555			−0.743183			−0.371591	+	0.928396i	$0.621188\pi$
$80$	0.328104	−	0.568293i	0.0366831	−	0.0635371i
$81$	5.60555	−	9.70910i	0.622839	−	1.07879i
$82$	−11.4927	−	19.9060i	−1.26916	−	2.19825i
$83$	−2.82352			−0.309921			−0.154961	−	0.987921i	$-0.549525\pi$
$83$	−2.82352			−0.309921			−0.154961	+	0.987921i	$0.549525\pi$
$84$		0			0
$85$	−7.75694	−	13.4354i	−0.841358	−	1.45728i
$86$	−28.8167			−3.10738
$87$	−2.49541	−	4.32218i	−0.267536	−	0.463386i
$88$	−7.36249	+	12.7522i	−0.784844	+	1.35939i
$89$	3.25096	−	5.63083i	0.344601	−	0.596867i	−0.640680	−	0.767808i	$-0.721347\pi$
$89$	3.25096	−	5.63083i	0.344601	−	0.596867i	0.985281	+	0.170941i	$0.0546808\pi$
$90$	−8.47055			−0.892874
$91$		0			0
$92$	−2.00000			−0.208514
$93$	7.75694	−	13.4354i	0.804357	−	1.39319i
$94$	−1.73986	+	3.01353i	−0.179453	+	0.310822i
$95$	−2.34861	−	4.06792i	−0.240963	−	0.417359i
$96$	11.4927			1.17297
$97$	−6.83003	−	11.8300i	−0.693484	−	1.20115i	−0.970689	−	0.240339i	$-0.922741\pi$
$97$	−6.83003	−	11.8300i	−0.693484	−	1.20115i	0.277205	−	0.960811i	$-0.410592\pi$
$98$		0			0
$99$	8.33053			0.837250
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.25096	+	5.63083i	−0.323483	+	0.560289i	−0.981204	−	0.192973i	$-0.938187\pi$
$101$	−3.25096	+	5.63083i	−0.323483	+	0.560289i	0.657721	+	0.753261i	$0.271520\pi$
$102$	−17.8625	+	30.9387i	−1.76865	+	3.06339i
$103$	−11.4927			−1.13241			−0.566207	−	0.824263i	$-0.691590\pi$
$103$	−11.4927			−1.13241			−0.566207	+	0.824263i	$0.691590\pi$
$104$	4.23527	−	9.95301i	0.415303	−	0.975973i
$105$		0			0
$106$	−2.75694	+	4.77516i	−0.267778	+	0.463804i
$107$	−2.84861	+	4.93394i	−0.275386	+	0.476982i	−0.970232	−	0.242176i	$-0.922139\pi$
$107$	−2.84861	+	4.93394i	−0.275386	+	0.476982i	0.694847	+	0.719158i	$0.255472\pi$
$108$	−4.66272	−	8.07607i	−0.448670	−	0.777120i
$109$	8.21110			0.786481			0.393240	−	0.919436i	$-0.371354\pi$
$109$	8.21110			0.786481			0.393240	+	0.919436i	$0.371354\pi$
$110$	12.2483	+	21.2147i	1.16783	+	2.02274i
$111$	9.32544	+	16.1521i	0.885132	+	1.53309i
$112$		0			0
$113$	−3.40833	−	5.90340i	−0.320628	−	0.555345i	0.659989	−	0.751275i	$-0.270561\pi$
$113$	−3.40833	−	5.90340i	−0.320628	−	0.555345i	−0.980618	+	0.195930i	$0.937227\pi$
$114$	−5.40833	+	9.36750i	−0.506536	+	0.877346i
$115$	−0.656208	+	1.13659i	−0.0611917	+	0.105987i
$116$	−7.60555			−0.706158
$117$	−6.07448	+	0.740358i	−0.561586	+	0.0684461i
$118$	6.50192			0.598551
$119$		0			0
$120$	−7.04584	+	12.2037i	−0.643194	+	1.11404i
$121$	−6.54584	−	11.3377i	−0.595076	−	1.03070i
$122$	−9.98165			−0.903696
$123$	10.8167	+	18.7350i	0.975305	+	1.68928i
$124$	−11.8209	−	20.4743i	−1.06154	−	1.83865i
$125$	11.4927			1.02794
$126$		0			0
$127$	−3.95416	+	6.84881i	−0.350875	+	0.607734i	−0.986403	−	0.164344i	$-0.947449\pi$
$127$	−3.95416	+	6.84881i	−0.350875	+	0.607734i	0.635528	+	0.772078i	$0.280783\pi$
$128$	9.45416	−	16.3751i	0.835638	−	1.44737i
$129$	27.1214			2.38791
$130$	−10.8167	−	14.3808i	−0.948683	−	1.26128i
$131$	10.6379			0.929434			0.464717	−	0.885459i	$-0.346156\pi$
$131$	10.6379			0.929434			0.464717	+	0.885459i	$0.346156\pi$
$132$	17.5672	−	30.4273i	1.52903	−	2.64836i
$133$		0			0
$134$	−1.15139	−	1.99426i	−0.0994648	−	0.172278i
$135$	−6.11943			−0.526677
$136$	10.7372	+	18.5974i	0.920707	+	1.59471i
$137$	−3.15139	−	5.45836i	−0.269241	−	0.466339i	0.699425	−	0.714706i	$-0.253440\pi$
$137$	−3.15139	−	5.45836i	−0.269241	−	0.466339i	−0.968666	+	0.248367i	$0.920106\pi$
$138$	3.02220			0.257267
$139$	−5.31893	−	9.21265i	−0.451146	−	0.781407i	0.547312	−	0.836929i	$-0.315651\pi$
$139$	−5.31893	−	9.21265i	−0.451146	−	0.781407i	−0.998457	+	0.0555216i	$0.982318\pi$
$140$		0			0
$141$	1.63751	−	2.83625i	0.137903	−	0.238855i
$142$	9.21110			0.772979
$143$	10.6379	+	14.1431i	0.889582	+	1.18271i
$144$	0.513878			0.0428232
$145$	−2.49541	+	4.32218i	−0.207233	+	0.358938i
$146$	−4.99082	+	8.64436i	−0.413044	+	0.715412i
$147$		0			0
$148$	28.4222			2.33629
$149$	8.75694	+	15.1675i	0.717396	+	1.24257i	0.962028	+	0.272951i	$0.0879997\pi$
$149$	8.75694	+	15.1675i	0.717396	+	1.24257i	−0.244632	+	0.969616i	$0.578667\pi$
$150$	−0.755550	−	1.30865i	−0.0616904	−	0.106851i
$151$	8.21110			0.668210			0.334105	−	0.942536i	$-0.391566\pi$
$151$	8.21110			0.668210			0.334105	+	0.942536i	$0.391566\pi$
$152$	3.25096	+	5.63083i	0.263688	+	0.456721i
$153$	6.07448	−	10.5213i	0.491092	−	0.850597i
$154$		0			0
$155$	−15.5139			−1.24610
$156$	−10.1056	+	23.7483i	−0.809092	+	1.90139i
$157$	0.656208			0.0523711			0.0261856	−	0.999657i	$-0.491664\pi$
$157$	0.656208			0.0523711			0.0261856	+	0.999657i	$0.491664\pi$
$158$	7.60555	−	13.1732i	0.605065	−	1.04800i
$159$	2.59475	−	4.49425i	0.205777	−	0.356417i
$160$	−5.74637	−	9.95301i	−0.454291	−	0.786855i
$161$		0			0
$162$	12.9083	+	22.3579i	1.01417	+	1.75660i
$163$	1.39445	+	2.41526i	0.109222	+	0.189177i	0.915455	−	0.402420i	$-0.131831\pi$
$163$	1.39445	+	2.41526i	0.109222	+	0.189177i	−0.806234	+	0.591597i	$0.798498\pi$
$164$	32.9671			2.57430
$165$	−11.5278	−	19.9667i	−0.897435	−	1.55440i
$166$	3.25096	−	5.63083i	0.252324	−	0.437037i
$167$	5.74637	−	9.95301i	0.444668	−	0.770187i	−0.553361	−	0.832941i	$-0.686655\pi$
$167$	5.74637	−	9.95301i	0.444668	−	0.770187i	0.998029	+	0.0627542i	$0.0199884\pi$
$168$		0			0
$169$	−9.01388	−	9.36750i	−0.693375	−	0.720577i
$170$	35.7250			2.73998
$171$	1.83920	−	3.18559i	0.140647	−	0.243609i
$172$	20.6653	−	35.7933i	1.57571	−	2.72921i
$173$	5.09017	+	8.81643i	0.386998	+	0.670300i	0.992044	−	0.125890i	$-0.0401786\pi$
$173$	5.09017	+	8.81643i	0.386998	+	0.670300i	−0.605046	+	0.796190i	$0.706845\pi$
$174$	11.4927			0.871263
$175$		0			0
$176$	−0.743061	−	1.28702i	−0.0560103	−	0.0970127i
$177$	−6.11943			−0.459964
$178$	7.48624	+	12.9665i	0.561117	+	0.971883i
$179$	−10.8028	+	18.7110i	−0.807437	+	1.39852i	0.107196	+	0.994238i	$0.465813\pi$
$179$	−10.8028	+	18.7110i	−0.807437	+	1.39852i	−0.914633	+	0.404285i	$0.867521\pi$
$180$	6.07448	−	10.5213i	0.452765	−	0.784212i
$181$	24.2979			1.80605			0.903025	−	0.429588i	$-0.141341\pi$
$181$	24.2979			1.80605			0.903025	+	0.429588i	$0.141341\pi$
$182$		0			0
$183$	9.39445			0.694458
$184$	0.908327	−	1.57327i	0.0669627	−	0.115983i
$185$	9.32544	−	16.1521i	0.685620	−	1.18753i
$186$	17.8625	+	30.9387i	1.30974	+	2.26854i
$187$	−35.1345			−2.56929
$188$	−2.49541	−	4.32218i	−0.181997	−	0.315227i
$189$		0			0
$190$	10.8167			0.784723
$191$	−7.84861	−	13.5942i	−0.567906	−	0.983641i	−0.996773	−	0.0802739i	$-0.974421\pi$
$191$	−7.84861	−	13.5942i	−0.567906	−	0.983641i	0.428867	−	0.903368i	$-0.358913\pi$
$192$	−13.8888	+	24.0561i	−1.00234	+	1.73610i
$193$	−9.90833	+	17.1617i	−0.713217	+	1.23533i	0.250426	+	0.968136i	$0.419429\pi$
$193$	−9.90833	+	17.1617i	−0.713217	+	1.23533i	−0.963643	+	0.267192i	$0.913904\pi$
$194$	31.4560			2.25841
$195$	10.1803	+	13.5348i	0.729029	+	0.969250i
$196$		0			0
$197$	0.545837	−	0.945417i	0.0388892	−	0.0673581i	−0.845926	−	0.533301i	$-0.820951\pi$
$197$	0.545837	−	0.945417i	0.0388892	−	0.0673581i	0.884815	+	0.465943i	$0.154285\pi$
$198$	−9.59167	+	16.6133i	−0.681651	+	1.18065i
$199$	−3.57907	−	6.19912i	−0.253713	−	0.439444i	0.710832	−	0.703362i	$-0.248319\pi$
$199$	−3.57907	−	6.19912i	−0.253713	−	0.439444i	−0.964545	+	0.263918i	$0.914985\pi$
$200$	−0.908327			−0.0642284
$201$	1.08365	+	1.87694i	0.0764351	+	0.132389i
$202$	−7.48624	−	12.9665i	−0.526730	−	0.912323i
$203$		0			0
$204$	−25.6194	−	44.3742i	−1.79372	−	3.10681i
$205$	10.8167	−	18.7350i	0.755468	−	1.30851i
$206$	13.2326	−	22.9196i	0.921960	−	1.59688i
$207$	−1.02776			−0.0714340
$208$	0.656208	+	0.872434i	0.0454998	+	0.0604924i
$209$	−10.6379			−0.735836
$210$		0			0
$211$	−7.50000	+	12.9904i	−0.516321	+	0.894295i	0.483499	+	0.875345i	$0.339366\pi$
$211$	−7.50000	+	12.9904i	−0.516321	+	0.894295i	−0.999820	+	0.0189499i	$0.993968\pi$
$212$	−3.95416	−	6.84881i	−0.271573	−	0.470378i
$213$	−8.66923			−0.594006
$214$	−6.55971	−	11.3618i	−0.448413	−	0.776674i
$215$	−13.5607	−	23.4878i	−0.924833	−	1.60186i
$216$	8.47055			0.576348
$217$		0			0
$218$	−9.45416	+	16.3751i	−0.640317	+	1.10906i
$219$	4.69722	−	8.13583i	0.317409	−	0.549769i
$220$	−35.1345			−2.36876
$221$	25.6194	−	3.12250i	1.72335	−	0.210042i
$222$	−42.9488			−2.88253
$223$	−8.99734	+	15.5838i	−0.602506	+	1.04357i	0.389934	+	0.920843i	$0.372498\pi$
$223$	−8.99734	+	15.5838i	−0.602506	+	1.04357i	−0.992440	+	0.122729i	$0.960836\pi$
$224$		0			0
$225$	0.256939	+	0.445032i	0.0171293	+	0.0296688i
$226$	15.6972			1.04416
$227$	−9.22610	−	15.9801i	−0.612358	−	1.06063i	−0.990842	−	0.135027i	$-0.956888\pi$
$227$	−9.22610	−	15.9801i	−0.612358	−	1.06063i	0.378484	−	0.925608i	$-0.376445\pi$
$228$	−7.75694	−	13.4354i	−0.513716	−	0.889782i
$229$	15.6287			1.03277			0.516386	−	0.856356i	$-0.327277\pi$
$229$	15.6287			1.03277			0.516386	+	0.856356i	$0.327277\pi$
$230$	−1.51110	−	2.61730i	−0.0996390	−	0.172580i
$231$		0			0
$232$	3.45416	−	5.98279i	0.226777	−	0.392789i
$233$	−13.0917			−0.857664			−0.428832	−	0.903384i	$-0.641075\pi$
$233$	−13.0917			−0.857664			−0.428832	+	0.903384i	$0.641075\pi$
$234$	5.51761	−	12.9665i	0.360698	−	0.847649i
$235$	−3.27502			−0.213639
$236$	−4.66272	+	8.07607i	−0.303517	+	0.525707i
$237$	−7.15813	+	12.3982i	−0.464971	+	0.805353i
$238$		0			0
$239$	4.39445			0.284253			0.142127	−	0.989848i	$-0.454606\pi$
$239$	4.39445			0.284253			0.142127	+	0.989848i	$0.454606\pi$
$240$	−0.711103	−	1.23167i	−0.0459015	−	0.0795037i
$241$	−4.66272	−	8.07607i	−0.300352	−	0.520225i	0.675863	−	0.737027i	$-0.263771\pi$
$241$	−4.66272	−	8.07607i	−0.300352	−	0.520225i	−0.976216	+	0.216802i	$0.930438\pi$
$242$	30.1472			1.93793
$243$	−7.91368	−	13.7069i	−0.507663	−	0.879298i
$244$	7.15813	−	12.3982i	0.458252	−	0.793717i
$245$		0			0
$246$	−49.8167			−3.17619
$247$	7.75694	−	0.945417i	0.493562	−	0.0601554i
$248$	21.4744			1.36363
$249$	−3.05971	+	5.29958i	−0.193902	+	0.335847i
$250$	−13.2326	+	22.9196i	−0.836904	+	1.44956i
$251$	14.9725	+	25.9331i	0.945054	+	1.63688i	0.755643	+	0.654984i	$0.227325\pi$
$251$	14.9725	+	25.9331i	0.945054	+	1.63688i	0.189411	+	0.981898i	$0.439342\pi$
$252$		0			0
$253$	1.48612	+	2.57404i	0.0934317	+	0.161828i
$254$	−9.10555	−	15.7713i	−0.571333	−	0.989578i
$255$	−33.6234			−2.10558
$256$	8.95416	+	15.5091i	0.559635	+	0.969317i
$257$	3.15162	−	5.45877i	0.196593	−	0.340508i	−0.750829	−	0.660497i	$-0.770346\pi$
$257$	3.15162	−	5.45877i	0.196593	−	0.340508i	0.947421	+	0.319988i	$0.103679\pi$
$258$	−31.2273	+	54.0872i	−1.94413	+	3.36732i
$259$		0			0
$260$	25.6194	−	3.12250i	1.58885	−	0.193649i
$261$	−3.90833			−0.241919
$262$	−12.2483	+	21.2147i	−0.756702	+	1.31065i
$263$	−7.71110	+	13.3560i	−0.475487	+	0.823568i	−0.999606	−	0.0280776i	$-0.991061\pi$
$263$	−7.71110	+	13.3560i	−0.475487	+	0.823568i	0.524119	+	0.851645i	$0.324395\pi$
$264$	15.9568	+	27.6380i	0.982072	+	1.70100i
$265$	−5.18951			−0.318789
$266$		0			0
$267$	−7.04584	−	12.2037i	−0.431198	−	0.746857i
$268$	3.30278			0.201749
$269$	−0.328104	−	0.568293i	−0.0200049	−	0.0346494i	0.855850	−	0.517225i	$-0.173035\pi$
$269$	−0.328104	−	0.568293i	−0.0200049	−	0.0346494i	−0.875855	+	0.482575i	$0.839702\pi$
$270$	7.04584	−	12.2037i	0.428796	−	0.742696i
$271$	7.25747	−	12.5703i	0.440860	−	0.763592i	−0.556893	−	0.830584i	$-0.688007\pi$
$271$	7.25747	−	12.5703i	0.440860	−	0.763592i	0.997754	+	0.0669918i	$0.0213401\pi$
$272$	−2.16731			−0.131412
$273$		0			0
$274$	14.5139			0.876815
$275$	0.743061	−	1.28702i	0.0448083	−	0.0776102i
$276$	−2.16731	+	3.75389i	−0.130457	+	0.225957i
$277$	0.105551	+	0.182820i	0.00634196	+	0.0109846i	0.869179	−	0.494498i	$-0.164648\pi$
$277$	0.105551	+	0.182820i	0.00634196	+	0.0109846i	−0.862837	+	0.505482i	$0.831315\pi$
$278$	24.4966			1.46921
$279$	−6.07448	−	10.5213i	−0.363670	−	0.629894i
$280$		0			0
$281$	23.8167			1.42078			0.710391	−	0.703807i	$-0.248518\pi$
$281$	23.8167			1.42078			0.710391	+	0.703807i	$0.248518\pi$
$282$	3.77082	+	6.53125i	0.224549	+	0.388930i
$283$	9.32544	−	16.1521i	0.554340	−	0.960145i	−0.443615	−	0.896218i	$-0.646304\pi$
$283$	9.32544	−	16.1521i	0.554340	−	0.960145i	0.997955	−	0.0639272i	$-0.0203626\pi$
$284$	−6.60555	+	11.4412i	−0.391967	+	0.678907i
$285$	−10.1803			−0.603031
$286$	−40.4534	+	4.93046i	−2.39206	+	0.291544i
$287$		0			0
$288$	4.50000	−	7.79423i	0.265165	−	0.459279i
$289$	−17.1194	+	29.6517i	−1.00703	+	1.74422i
$290$	−5.74637	−	9.95301i	−0.337439	−	0.584461i
$291$	−29.6056			−1.73551
$292$	−7.15813	−	12.3982i	−0.418898	−	0.725553i
$293$	−14.3163	−	24.7965i	−0.836365	−	1.44863i	−0.892914	−	0.450227i	$-0.851343\pi$
$293$	−14.3163	−	24.7965i	−0.836365	−	1.44863i	0.0565490	−	0.998400i	$-0.481990\pi$
$294$		0			0
$295$	3.05971	+	5.29958i	0.178143	+	0.308554i
$296$	−12.9083	+	22.3579i	−0.750281	+	1.29953i
$297$	−6.92937	+	12.0020i	−0.402083	+	0.696428i
$298$	−40.3305			−2.33628
$299$	−1.31242	−	1.74487i	−0.0758990	−	0.100908i
$300$	2.16731			0.125130
$301$		0			0
$302$	−9.45416	+	16.3751i	−0.544026	+	0.942281i
$303$	7.04584	+	12.2037i	0.404773	+	0.701087i
$304$	−0.656208			−0.0376361
$305$	−4.69722	−	8.13583i	−0.268962	−	0.465856i
$306$	13.9882	+	24.2282i	0.799650	+	1.38503i
$307$	−3.67841			−0.209938			−0.104969	−	0.994476i	$-0.533474\pi$
$307$	−3.67841			−0.209938			−0.104969	+	0.994476i	$0.533474\pi$
$308$		0			0
$309$	−12.4542	+	21.5712i	−0.708493	+	1.22715i
$310$	17.8625	−	30.9387i	1.01452	−	1.75720i
$311$	−10.6379			−0.603218			−0.301609	−	0.953432i	$-0.597524\pi$
$311$	−10.6379			−0.603218			−0.301609	+	0.953432i	$0.597524\pi$
$312$	−14.0917	−	18.7350i	−0.797784	−	1.06066i
$313$	5.64703			0.319189			0.159595	−	0.987183i	$-0.448981\pi$
$313$	5.64703			0.319189			0.159595	+	0.987183i	$0.448981\pi$
$314$	−0.755550	+	1.30865i	−0.0426382	+	0.0738514i
$315$		0			0
$316$	10.9083	+	18.8938i	0.613641	+	1.06286i
$317$	−6.21110			−0.348850			−0.174425	−	0.984670i	$-0.555807\pi$
$317$	−6.21110			−0.348850			−0.174425	+	0.984670i	$0.555807\pi$
$318$	5.97514	+	10.3492i	0.335069	+	0.580357i
$319$	5.65139	+	9.78849i	0.316417	+	0.548050i
$320$	27.7776			1.55282
$321$	6.17382	+	10.6934i	0.344589	+	0.596846i
$322$		0			0
$323$	−7.75694	+	13.4354i	−0.431608	+	0.747566i
$324$	−37.0278			−2.05710
$325$	−0.427446	+	1.00451i	−0.0237104	+	0.0557202i
$326$	−6.42221			−0.355693
$327$	8.89799	−	15.4118i	0.492060	−	0.852273i
$328$	−14.9725	+	25.9331i	−0.826717	+	1.43192i
$329$		0			0
$330$	53.0917			2.92260
$331$	−2.15139	−	3.72631i	−0.118251	−	0.204817i	0.800824	−	0.598900i	$-0.204395\pi$
$331$	−2.15139	−	3.72631i	−0.118251	−	0.204817i	−0.919075	+	0.394084i	$0.871062\pi$
$332$	4.66272	+	8.07607i	0.255900	+	0.443232i
$333$	14.6056			0.800379
$334$	13.2326	+	22.9196i	0.724056	+	1.25410i
$335$	1.08365	−	1.87694i	0.0592063	−	0.102548i
$336$		0			0
$337$	18.1194			0.987028			0.493514	−	0.869738i	$-0.335712\pi$
$337$	18.1194			0.987028			0.493514	+	0.869738i	$0.335712\pi$
$338$	29.0597	−	7.19041i	1.58064	−	0.391107i
$339$	−14.7738			−0.802402
$340$	−25.6194	+	44.3742i	−1.38941	+	2.40653i
$341$	−17.5672	+	30.4273i	−0.951319	+	1.64773i
$342$	4.23527	+	7.33571i	0.229017	+	0.396670i
$343$		0			0
$344$	18.7708	+	32.5120i	1.01205	+	1.75293i
$345$	1.42221	+	2.46333i	0.0765689	+	0.132621i
$346$	−23.4430			−1.26030
$347$	−7.60555	−	13.1732i	−0.408287	−	0.707174i	0.586411	−	0.810014i	$-0.300541\pi$
$347$	−7.60555	−	13.1732i	−0.408287	−	0.707174i	−0.994698	+	0.102839i	$0.967207\pi$
$348$	−8.24179	+	14.2752i	−0.441806	+	0.765231i
$349$	5.09017	−	8.81643i	0.272470	−	0.471932i	−0.697023	−	0.717048i	$-0.745493\pi$
$349$	5.09017	−	8.81643i	0.272470	−	0.471932i	0.969494	+	0.245116i	$0.0788260\pi$
$350$		0			0
$351$	3.98612	−	9.36750i	0.212763	−	0.500000i
$352$	−26.0278			−1.38728
$353$	−13.2326	+	22.9196i	−0.704301	+	1.21988i	0.262642	+	0.964893i	$0.415406\pi$
$353$	−13.2326	+	22.9196i	−0.704301	+	1.21988i	−0.966943	+	0.254992i	$0.917927\pi$
$354$	7.04584	−	12.2037i	0.374482	−	0.648622i
$355$	4.33462	+	7.50778i	0.230058	+	0.398471i
$356$	−21.4744			−1.13814
$357$		0			0
$358$	−24.8764	−	43.0871i	−1.31476	−	2.27723i
$359$	−12.0917			−0.638174			−0.319087	−	0.947725i	$-0.603376\pi$
$359$	−12.0917			−0.638174			−0.319087	+	0.947725i	$0.603376\pi$
$360$	5.51761	+	9.55678i	0.290804	+	0.503687i
$361$	7.15139	−	12.3866i	0.376389	−	0.651925i
$362$	−27.9763	+	48.4564i	−1.47040	+	2.54681i
$363$	−28.3737			−1.48923
$364$		0			0
$365$	−9.39445			−0.491728
$366$	−10.8167	+	18.7350i	−0.565396	+	0.979294i
$367$	12.8052	−	22.1792i	0.668424	−	1.15774i	−0.309921	−	0.950762i	$-0.600302\pi$
$367$	12.8052	−	22.1792i	0.668424	−	1.15774i	0.978345	−	0.206982i	$-0.0663642\pi$
$368$	0.0916731	+	0.158782i	0.00477879	+	0.00827711i
$369$	16.9411			0.881918
$370$	21.4744	+	37.1947i	1.11640	+	1.93366i
$371$		0			0
$372$	−51.2389			−2.65661
$373$	6.34861	+	10.9961i	0.328719	+	0.569357i	0.982258	−	0.187535i	$-0.0600499\pi$
$373$	6.34861	+	10.9961i	0.328719	+	0.569357i	−0.653539	+	0.756893i	$0.726717\pi$
$374$	40.4534	−	70.0673i	2.09179	−	3.62309i
$375$	12.4542	−	21.5712i	0.643130	−	1.11393i
$376$	4.53330			0.233787
$377$	−4.99082	−	6.63534i	−0.257041	−	0.341737i
$378$		0			0
$379$	6.05971	−	10.4957i	0.311267	−	0.539130i	−0.667370	−	0.744726i	$-0.732580\pi$
$379$	6.05971	−	10.4957i	0.311267	−	0.539130i	0.978637	+	0.205596i	$0.0659134\pi$
$380$	−7.75694	+	13.4354i	−0.397923	+	0.689222i
$381$	8.56989	+	14.8435i	0.439049	+	0.760455i
$382$	36.1472			1.84945
$383$	−11.1646	−	19.3377i	−0.570487	−	0.988112i	−0.996516	−	0.0834025i	$-0.973421\pi$
$383$	−11.1646	−	19.3377i	−0.570487	−	0.988112i	0.426029	−	0.904709i	$-0.359912\pi$
$384$	−20.4901	−	35.4899i	−1.04563	−	1.81108i
$385$		0			0
$386$	−22.8167	−	39.5196i	−1.16134	−	2.01149i
$387$	10.6194	−	18.3934i	0.539816	−	0.934989i
$388$	−22.5581	+	39.0717i	−1.14521	+	1.98356i
$389$	29.0278			1.47177			0.735883	−	0.677109i	$-0.236767\pi$
$389$	29.0278			1.47177			0.735883	+	0.677109i	$0.236767\pi$
$390$	−38.7135	+	4.71841i	−1.96034	+	0.238926i
$391$	4.33462			0.219211
$392$		0			0
$393$	11.5278	−	19.9667i	0.581498	−	1.00718i
$394$	1.25694	+	2.17708i	0.0633237	+	0.109680i
$395$	14.3163			0.720329
$396$	−13.7569	−	23.8277i	−0.691312	−	1.19739i
$397$	2.16731	+	3.75389i	0.108774	+	0.188402i	0.915274	−	0.402832i	$-0.131974\pi$
$397$	2.16731	+	3.75389i	0.108774	+	0.188402i	−0.806500	+	0.591234i	$0.798641\pi$
$398$	16.4836			0.826247
$399$		0			0
$400$	0.0458365	−	0.0793912i	0.00229183	−	0.00396956i
$401$	5.05971	−	8.76368i	0.252670	−	0.437637i	−0.711590	−	0.702595i	$-0.752025\pi$
$401$	5.05971	−	8.76368i	0.252670	−	0.437637i	0.964260	+	0.264958i	$0.0853579\pi$
$402$	−4.99082			−0.248920
$403$	10.1056	−	23.7483i	0.503393	−	1.18299i
$404$	21.4744			1.06839
$405$	−12.1490	+	21.0426i	−0.603687	+	1.04562i
$406$		0			0
$407$	−21.1194	−	36.5799i	−1.04685	−	1.81320i
$408$	46.5416			2.30415
$409$	1.73986	+	3.01353i	0.0860306	+	0.149009i	0.905830	−	0.423642i	$-0.139248\pi$
$409$	1.73986	+	3.01353i	0.0860306	+	0.149009i	−0.819799	+	0.572651i	$0.805915\pi$
$410$	24.9083	+	43.1425i	1.23013	+	2.13066i
$411$	−13.6601			−0.673801
$412$	18.9790	+	32.8726i	0.935027	+	1.61952i
$413$		0			0
$414$	1.18335	−	2.04962i	0.0581583	−	0.100733i
$415$	6.11943			0.300391
$416$	18.9790	−	2.31316i	0.930521	−	0.113412i
$417$	−23.0555			−1.12903
$418$	12.2483	−	21.2147i	0.599084	−	1.03764i
$419$	−8.56989	+	14.8435i	−0.418667	+	0.725152i	−0.995806	−	0.0914942i	$-0.970836\pi$
$419$	−8.56989	+	14.8435i	−0.418667	+	0.725152i	0.577139	+	0.816646i	$0.304169\pi$
$420$		0			0
$421$	5.02776			0.245038			0.122519	−	0.992466i	$-0.460903\pi$
$421$	5.02776			0.245038			0.122519	+	0.992466i	$0.460903\pi$
$422$	−17.2708	−	29.9139i	−0.840730	−	1.45619i
$423$	−1.28234	−	2.22107i	−0.0623494	−	0.107992i
$424$	7.18335			0.348854
$425$	−1.08365	−	1.87694i	−0.0525649	−	0.0910452i
$426$	9.98165	−	17.2887i	0.483612	−	0.837641i
$427$		0			0
$428$	18.8167			0.909537
$429$	38.0736	−	4.64041i	1.83821	−	0.224041i
$430$	62.4546			3.01183
$431$	10.4680	−	18.1312i	0.504228	−	0.873348i	−0.495760	−	0.868459i	$-0.665111\pi$
$431$	10.4680	−	18.1312i	0.504228	−	0.873348i	0.999988	−	0.00488877i	$-0.00155615\pi$
$432$	−0.427446	+	0.740358i	−0.0205655	+	0.0356205i
$433$	8.56989	+	14.8435i	0.411843	+	0.713332i	0.995091	−	0.0989613i	$-0.0315520\pi$
$433$	8.56989	+	14.8435i	0.411843	+	0.713332i	−0.583249	+	0.812294i	$0.698219\pi$
$434$		0			0
$435$	5.40833	+	9.36750i	0.259309	+	0.449137i
$436$	−13.5597	−	23.4861i	−0.649393	−	1.12478i
$437$	1.31242			0.0627814
$438$	10.8167	+	18.7350i	0.516840	+	0.895193i
$439$	−1.83920	+	3.18559i	−0.0877804	+	0.152040i	−0.906573	−	0.422050i	$-0.861311\pi$
$439$	−1.83920	+	3.18559i	−0.0877804	+	0.152040i	0.818792	+	0.574090i	$0.194644\pi$
$440$	15.9568	−	27.6380i	0.760710	−	1.31759i
$441$		0			0
$442$	−23.2708	+	54.6871i	−1.10688	+	2.60120i
$443$	−20.2389			−0.961577			−0.480789	−	0.876837i	$-0.659650\pi$
$443$	−20.2389			−0.961577			−0.480789	+	0.876837i	$0.659650\pi$
$444$	30.7998	−	53.3469i	1.46170	−	2.53173i
$445$	−7.04584	+	12.2037i	−0.334005	+	0.578513i
$446$	−20.7188	−	35.8861i	−0.981066	−	1.69926i
$447$	37.9580			1.79535
$448$		0			0
$449$	10.2111	+	17.6861i	0.481892	+	0.834661i	0.999784	−	0.0207849i	$-0.00661652\pi$
$449$	10.2111	+	17.6861i	0.481892	+	0.834661i	−0.517892	+	0.855446i	$0.673283\pi$
$450$	−1.18335			−0.0557835
$451$	−24.4966	−	42.4294i	−1.15350	−	1.99792i
$452$	−11.2569	+	19.4976i	−0.529482	+	0.917090i
$453$	8.89799	−	15.4118i	0.418064	−	0.724109i
$454$	42.4913			1.99421
$455$		0			0
$456$	14.0917			0.659903
$457$	−10.3028	+	17.8449i	−0.481944	+	0.834751i	−0.999785	−	0.0207258i	$-0.993402\pi$
$457$	−10.3028	+	17.8449i	−0.481944	+	0.834751i	0.517842	+	0.855476i	$0.326736\pi$
$458$	−17.9947	+	31.1677i	−0.840836	+	1.45637i
$459$	10.1056	+	17.5033i	0.471687	+	0.816985i
$460$	4.33462			0.202103
$461$	−12.5764	−	21.7830i	−0.585741	−	1.01453i	−0.994783	−	0.102018i	$-0.967470\pi$
$461$	−12.5764	−	21.7830i	−0.585741	−	1.01453i	0.409041	−	0.912516i	$-0.365863\pi$
$462$		0			0
$463$	−13.7889			−0.640824			−0.320412	−	0.947278i	$-0.603821\pi$
$463$	−13.7889			−0.640824			−0.320412	+	0.947278i	$0.603821\pi$
$464$	0.348612	+	0.603814i	0.0161839	+	0.0280314i
$465$	−16.8117	+	29.1187i	−0.779623	+	1.35035i
$466$	15.0736	−	26.1082i	0.698271	−	1.20944i
$467$	−12.8052			−0.592552			−0.296276	−	0.955102i	$-0.595745\pi$
$467$	−12.8052			−0.592552			−0.296276	+	0.955102i	$0.595745\pi$
$468$	12.1490	+	16.1521i	0.561586	+	0.746633i
$469$		0			0
$470$	3.77082	−	6.53125i	0.173935	−	0.301264i
$471$	0.711103	−	1.23167i	0.0327659	−	0.0567522i
$472$	−4.23527	−	7.33571i	−0.194944	−	0.337653i
$473$	−61.4222			−2.82420
$474$	−16.4836	−	28.5504i	−0.757116	−	1.31136i
$475$	−0.328104	−	0.568293i	−0.0150544	−	0.0260751i
$476$		0			0
$477$	−2.03196	−	3.51946i	−0.0930370	−	0.161145i
$478$	−5.05971	+	8.76368i	−0.231426	+	0.400842i
$479$	−8.24179	+	14.2752i	−0.376577	+	0.652250i	−0.990562	−	0.137068i	$-0.956232\pi$
$479$	−8.24179	+	14.2752i	−0.376577	+	0.652250i	0.613985	+	0.789318i	$0.289566\pi$
$480$	−24.9083			−1.13690
$481$	18.6509	+	24.7965i	0.850407	+	1.13062i
$482$	21.4744			0.978132
$483$		0			0
$484$	−21.6194	+	37.4460i	−0.982701	+	1.70209i
$485$	14.8028	+	25.6392i	0.672159	+	1.16421i
$486$	36.4469			1.65326
$487$	15.6514	+	27.1090i	0.709232	+	1.22843i	0.965142	+	0.261725i	$0.0842915\pi$
$487$	15.6514	+	27.1090i	0.709232	+	1.22843i	−0.255910	+	0.966701i	$0.582375\pi$
$488$	6.50192	+	11.2617i	0.294328	+	0.509792i
$489$	6.04440			0.273337
$490$		0			0
$491$	−9.86249	+	17.0823i	−0.445088	+	0.770915i	−0.998058	−	0.0622859i	$-0.980161\pi$
$491$	−9.86249	+	17.0823i	−0.445088	+	0.770915i	0.552970	+	0.833201i	$0.313494\pi$
$492$	35.7250	−	61.8775i	1.61061	−	2.78965i
$493$	16.4836			0.742383
$494$	−7.04584	+	16.5579i	−0.317007	+	0.744976i
$495$	−18.0548			−0.811504
$496$	−1.08365	+	1.87694i	−0.0486575	+	0.0842773i
$497$		0			0
$498$	−7.04584	−	12.2037i	−0.315731	−	0.546863i
$499$	−8.33053			−0.372926			−0.186463	−	0.982462i	$-0.559702\pi$
$499$	−8.33053			−0.372926			−0.186463	+	0.982462i	$0.559702\pi$
$500$	−18.9790	−	32.8726i	−0.848766	−	1.47011i
$501$	−12.4542	−	21.5712i	−0.556411	−	0.963732i
$502$	−68.9565			−3.07768
$503$	−9.75289	−	16.8925i	−0.434860	−	0.753199i	0.562424	−	0.826849i	$-0.309869\pi$
$503$	−9.75289	−	16.8925i	−0.434860	−	0.753199i	−0.997284	+	0.0736495i	$0.976535\pi$
$504$		0			0
$505$	7.04584	−	12.2037i	0.313536	−	0.543060i
$506$	−6.84441			−0.304271
$507$	−27.3502	+	6.76742i	−1.21466	+	0.300552i
$508$	26.1194			1.15886
$509$	10.7372	−	18.5974i	0.475918	−	0.824314i	−0.523701	−	0.851902i	$-0.675449\pi$
$509$	10.7372	−	18.5974i	0.475918	−	0.824314i	0.999619	+	0.0275878i	$0.00878258\pi$
$510$	38.7135	−	67.0538i	1.71426	−	2.96919i
$511$		0			0
$512$	−3.42221			−0.151242
$513$	3.05971	+	5.29958i	0.135090	+	0.233982i
$514$	7.25747	+	12.5703i	0.320113	+	0.554453i
$515$	24.9083			1.09759
$516$	−44.7880	−	77.5751i	−1.97168	−	3.41505i
$517$	−3.70849	+	6.42329i	−0.163099	+	0.282496i
$518$		0			0
$519$	22.0639			0.968498
$520$	−9.17914	+	21.5712i	−0.402532	+	0.945962i
$521$	21.6731			0.949515			0.474757	−	0.880117i	$-0.342536\pi$
$521$	21.6731			0.949515			0.474757	+	0.880117i	$0.342536\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	12.1490	−	21.0426i	0.531237	−	0.920129i	−0.468099	−	0.883676i	$-0.655061\pi$
$523$	12.1490	−	21.0426i	0.531237	−	0.920129i	0.999335	−	0.0364529i	$-0.0116059\pi$
$524$	−17.5672	−	30.4273i	−0.767428	−	1.32922i
$525$		0			0
$526$	−17.7569	−	30.7559i	−0.774239	−	1.34102i
$527$	25.6194	+	44.3742i	1.11600	+	1.93297i
$528$	−3.22088			−0.140171
$529$	11.3167	+	19.6010i	0.492028	+	0.852218i
$530$	5.97514	−	10.3492i	0.259543	−	0.449542i
$531$	−2.39607	+	4.15012i	−0.103981	+	0.180100i
$532$		0			0
$533$	21.6333	+	28.7617i	0.937043	+	1.24581i
$534$	32.4500			1.40425
$535$	6.17382	−	10.6934i	0.266918	−	0.462315i
$536$	−1.50000	+	2.59808i	−0.0647901	+	0.112220i
$537$	23.4129	+	40.5524i	1.01034	+	1.74997i
$538$	1.51110			0.0651481
$539$		0			0
$540$	10.1056	+	17.5033i	0.434874	+	0.753223i
$541$	27.9361			1.20107			0.600533	−	0.799600i	$-0.294955\pi$
$541$	27.9361			1.20107			0.600533	+	0.799600i	$0.294955\pi$
$542$	16.7123	+	28.9466i	0.717856	+	1.24336i
$543$	26.3305	−	45.6058i	1.12995	−	1.95713i
$544$	−18.9790	+	32.8726i	−0.813717	+	1.40940i
$545$	−17.7960			−0.762296
$546$		0			0
$547$	29.0000			1.23995			0.619975	−	0.784621i	$-0.287143\pi$
$547$	29.0000			1.23995			0.619975	+	0.784621i	$0.287143\pi$
$548$	−10.4083	+	18.0278i	−0.444622	+	0.770107i
$549$	3.67841	−	6.37119i	0.156991	−	0.271916i
$550$	1.71110	+	2.96372i	0.0729617	+	0.126373i
$551$	4.99082			0.212616
$552$	−1.96862	−	3.40976i	−0.0837902	−	0.145129i
$553$		0			0
$554$	−0.486122			−0.0206533
$555$	−20.2111	−	35.0067i	−0.857914	−	1.48595i
$556$	−17.5672	+	30.4273i	−0.745016	+	1.29041i
$557$	−3.04584	+	5.27554i	−0.129056	+	0.223532i	−0.923311	−	0.384053i	$-0.874528\pi$
$557$	−3.04584	+	5.27554i	−0.129056	+	0.223532i	0.794255	+	0.607585i	$0.207861\pi$
$558$	27.9763			1.18433
$559$	44.7880	−	5.45877i	1.89433	−	0.230881i
$560$		0			0
$561$	−38.0736	+	65.9454i	−1.60747	+	2.78422i
$562$	−27.4222	+	47.4967i	−1.15674	+	2.00353i
$563$	0.656208	+	1.13659i	0.0276559	+	0.0479014i	0.879522	−	0.475858i	$-0.157862\pi$
$563$	0.656208	+	1.13659i	0.0276559	+	0.0479014i	−0.851866	+	0.523759i	$0.824529\pi$
$564$	−10.8167			−0.455463
$565$	7.38689	+	12.7945i	0.310769	+	0.538268i
$566$	21.4744	+	37.1947i	0.902636	+	1.56341i
$567$		0			0
$568$	−6.00000	−	10.3923i	−0.251754	−	0.436051i
$569$	17.3028	−	29.9693i	0.725370	−	1.25638i	−0.233451	−	0.972368i	$-0.575002\pi$
$569$	17.3028	−	29.9693i	0.725370	−	1.25638i	0.958822	−	0.284009i	$-0.0916647\pi$
$570$	11.7215	−	20.3023i	0.490960	−	0.850368i
$571$	−10.7250			−0.448826			−0.224413	−	0.974494i	$-0.572047\pi$
$571$	−10.7250			−0.448826			−0.224413	+	0.974494i	$0.572047\pi$
$572$	22.8862	−	53.7831i	0.956918	−	2.24878i
$573$	−34.0207			−1.42124
$574$		0			0
$575$	−0.0916731	+	0.158782i	−0.00382303	+	0.00662169i
$576$	10.8764	+	18.8384i	0.453182	+	0.784934i
$577$	−33.1658			−1.38071			−0.690356	−	0.723470i	$-0.742546\pi$
$577$	−33.1658			−1.38071			−0.690356	+	0.723470i	$0.742546\pi$
$578$	−39.4222	−	68.2813i	−1.63975	−	2.84013i
$579$	21.4744	+	37.1947i	0.892445	+	1.54576i
$580$	16.4836			0.684443
$581$		0			0
$582$	34.0875	−	59.0412i	1.41297	−	2.44734i
$583$	−5.87637	+	10.1782i	−0.243374	+	0.421537i
$584$	13.0038			0.538103
$585$	13.1653	−	1.60458i	0.544317	−	0.0663414i
$586$	65.9343			2.72372
$587$	0.984312	−	1.70488i	0.0406269	−	0.0703679i	−0.844997	−	0.534771i	$-0.820398\pi$
$587$	0.984312	−	1.70488i	0.0406269	−	0.0703679i	0.885624	+	0.464403i	$0.153731\pi$
$588$		0			0
$589$	7.75694	+	13.4354i	0.319619	+	0.553597i
$590$	−14.0917			−0.580145
$591$	−1.18300	−	2.04901i	−0.0486620	−	0.0842850i
$592$	−1.30278	−	2.25647i	−0.0535437	−	0.0927405i
$593$	−6.30324			−0.258843			−0.129422	−	0.991590i	$-0.541312\pi$
$593$	−6.30324			−0.258843			−0.129422	+	0.991590i	$0.541312\pi$
$594$	−15.9568	−	27.6380i	−0.654715	−	1.13400i
$595$		0			0
$596$	28.9222	−	50.0947i	1.18470	−	2.05196i
$597$	−15.5139			−0.634941
$598$	4.99082	−	0.608282i	0.204090	−	0.0248745i
$599$	−10.5139			−0.429585			−0.214793	−	0.976660i	$-0.568908\pi$
$599$	−10.5139			−0.429585			−0.214793	+	0.976660i	$0.568908\pi$
$600$	−0.984312	+	1.70488i	−0.0401844	+	0.0696014i
$601$	4.56338	−	7.90400i	0.186144	−	0.322411i	−0.757817	−	0.652467i	$-0.773734\pi$
$601$	4.56338	−	7.90400i	0.186144	−	0.322411i	0.943961	+	0.330056i	$0.107068\pi$
$602$		0			0
$603$	1.69722			0.0691163
$604$	−13.5597	−	23.4861i	−0.551737	−	0.955636i
$605$	14.1868	+	24.5723i	0.576777	+	0.999008i
$606$	−32.4500			−1.31819
$607$	19.4064	+	33.6129i	0.787683	+	1.36431i	0.927383	+	0.374113i	$0.122053\pi$
$607$	19.4064	+	33.6129i	0.787683	+	1.36431i	−0.139701	+	0.990194i	$0.544614\pi$
$608$	−5.74637	+	9.95301i	−0.233046	+	0.403648i
$609$		0			0
$610$	21.6333			0.875907
$611$	2.13331	−	5.01333i	0.0863044	−	0.202818i
$612$	−40.1253			−1.62197
$613$	−15.9542	+	27.6334i	−0.644383	+	1.11610i	0.340061	+	0.940403i	$0.389552\pi$
$613$	−15.9542	+	27.6334i	−0.644383	+	1.11610i	−0.984444	+	0.175700i	$0.943781\pi$
$614$	4.23527	−	7.33571i	0.170922	−	0.296045i
$615$	−23.4430	−	40.6045i	−0.945314	−	1.63733i
$616$		0			0
$617$	−7.92221	−	13.7217i	−0.318936	−	0.552413i	0.661330	−	0.750095i	$-0.269992\pi$
$617$	−7.92221	−	13.7217i	−0.318936	−	0.552413i	−0.980266	+	0.197681i	$0.936659\pi$
$618$	−28.6791	−	49.6737i	−1.15364	−	1.99817i
$619$	29.9449			1.20359			0.601794	−	0.798651i	$-0.294453\pi$
$619$	29.9449			1.20359			0.601794	+	0.798651i	$0.294453\pi$
$620$	25.6194	+	44.3742i	1.02890	+	1.78211i
$621$	0.854892	−	1.48072i	0.0343056	−	0.0594191i
$622$	12.2483	−	21.2147i	0.491112	−	0.850631i
$623$		0			0
$624$	2.34861	−	0.286249i	0.0940197	−	0.0114591i
$625$	−23.3944			−0.935778
$626$	−6.50192	+	11.2617i	−0.259869	+	0.450107i
$627$	−11.5278	+	19.9667i	−0.460374	+	0.797392i
$628$	−1.08365	−	1.87694i	−0.0432425	−	0.0748982i
$629$	−61.5997			−2.45614
$630$		0			0
$631$	−11.4542	−	19.8392i	−0.455983	−	0.789786i	0.542761	−	0.839887i	$-0.317379\pi$
$631$	−11.4542	−	19.8392i	−0.455983	−	0.789786i	−0.998744	+	0.0501013i	$0.984046\pi$
$632$	−19.8167			−0.788264
$633$	16.2548	+	28.1542i	0.646071	+	1.11903i
$634$	7.15139	−	12.3866i	0.284018	−	0.491933i
$635$	8.56989	−	14.8435i	0.340086	−	0.589046i
$636$	−17.1398			−0.679637
$637$		0			0
$638$	−26.0278			−1.03045
$639$	−3.39445	+	5.87936i	−0.134282	+	0.232584i
$640$	−20.4901	+	35.4899i	−0.809942	+	1.40286i
$641$	7.25694	+	12.5694i	0.286632	+	0.496461i	0.973004	−	0.230790i	$-0.0741310\pi$
$641$	7.25694	+	12.5694i	0.286632	+	0.496461i	−0.686372	+	0.727251i	$0.740798\pi$
$642$	−28.4338			−1.12219
$643$	8.56989	+	14.8435i	0.337963	+	0.585370i	0.984050	−	0.177895i	$-0.0569286\pi$
$643$	8.56989	+	14.8435i	0.337963	+	0.585370i	−0.646086	+	0.763265i	$0.723595\pi$
$644$		0			0
$645$	−58.7805			−2.31448
$646$	−17.8625	−	30.9387i	−0.702790	−	1.21727i
$647$	−16.4836	+	28.5504i	−0.648036	+	1.12243i	0.335555	+	0.942021i	$0.391076\pi$
$647$	−16.4836	+	28.5504i	−0.648036	+	1.12243i	−0.983591	+	0.180411i	$0.942257\pi$
$648$	16.8167	−	29.1273i	0.660621	−	1.14423i
$649$	13.8587			0.544003
$650$	−1.51110	−	2.00902i	−0.0592702	−	0.0788002i
$651$		0			0
$652$	4.60555	−	7.97705i	0.180367	−	0.312405i
$653$	23.3764	−	40.4891i	0.914788	−	1.58446i	0.107577	−	0.994197i	$-0.465691\pi$
$653$	23.3764	−	40.4891i	0.914788	−	1.58446i	0.807211	−	0.590262i	$-0.200976\pi$
$654$	20.4901	+	35.4899i	0.801226	+	1.38776i
$655$	−23.0555			−0.900853
$656$	−1.51110	−	2.61730i	−0.0589985	−	0.102188i
$657$	−3.67841	−	6.37119i	−0.143508	−	0.248564i
$658$		0			0
$659$	9.81665	+	17.0029i	0.382403	+	0.662341i	0.991405	−	0.130828i	$-0.0417634\pi$
$659$	9.81665	+	17.0029i	0.382403	+	0.662341i	−0.609003	+	0.793168i	$0.708430\pi$
$660$	−38.0736	+	65.9454i	−1.48201	+	2.56692i
$661$	−11.4927	+	19.9060i	−0.447016	+	0.774255i	−0.998190	−	0.0601356i	$-0.980847\pi$
$661$	−11.4927	+	19.9060i	−0.447016	+	0.774255i	0.551174	+	0.834390i	$0.314180\pi$
$662$	9.90833			0.385098
$663$	21.9018	−	51.4699i	0.850597	−	1.99893i
$664$	−8.47055			−0.328721
$665$		0			0
$666$	−16.8167	+	29.1273i	−0.651632	+	1.12866i
$667$	−0.697224	−	1.20763i	−0.0269966	−	0.0467595i
$668$	−37.9580			−1.46864
$669$	19.5000	+	33.7750i	0.753914	+	1.30582i
$670$	2.49541	+	4.32218i	0.0964062	+	0.166980i
$671$	−21.2757			−0.821340
$672$		0			0
$673$	1.10555	−	1.91487i	0.0426159	−	0.0738129i	−0.843931	−	0.536452i	$-0.819764\pi$
$673$	1.10555	−	1.91487i	0.0426159	−	0.0738129i	0.886547	+	0.462639i	$0.153098\pi$
$674$	−20.8625	+	36.1349i	−0.803593	+	1.39186i
$675$	−0.854892			−0.0329048
$676$	−11.9083	+	41.2517i	−0.458013	+	1.58660i
$677$	26.4652			1.01714			0.508571	−	0.861020i	$-0.330174\pi$
$677$	26.4652			1.01714			0.508571	+	0.861020i	$0.330174\pi$
$678$	17.0104	−	29.4628i	0.653279	−	1.13151i
$679$		0			0
$680$	−23.2708	−	40.3062i	−0.892395	−	1.54567i
$681$	−39.9916			−1.53248
$682$	−40.4534	−	70.0673i	−1.54904	−	2.68302i
$683$	1.80278	+	3.12250i	0.0689813	+	0.119479i	0.898453	−	0.439069i	$-0.144692\pi$
$683$	1.80278	+	3.12250i	0.0689813	+	0.119479i	−0.829472	+	0.558549i	$0.811358\pi$
$684$	−12.1490			−0.464527
$685$	6.83003	+	11.8300i	0.260962	+	0.451999i
$686$		0			0
$687$	16.9361	−	29.3342i	0.646152	−	1.11917i
$688$	−3.78890			−0.144450
$689$	3.38038	−	7.94399i	0.128782	−	0.302642i
$690$	−6.55004			−0.249356
$691$	−18.8796	+	32.7005i	−0.718215	+	1.24399i	0.243491	+	0.969903i	$0.421707\pi$
$691$	−18.8796	+	32.7005i	−0.718215	+	1.24399i	−0.961706	+	0.274082i	$0.911626\pi$
$692$	16.8117	−	29.1187i	0.639084	−	1.10693i
$693$		0			0
$694$	35.0278			1.32964
$695$	11.5278	+	19.9667i	0.437273	+	0.757379i
$696$	−7.48624	−	12.9665i	−0.283765	−	0.491495i
$697$	−71.4500			−2.70636
$698$	11.7215	+	20.3023i	0.443666	+	0.768452i
$699$	−14.1868	+	24.5723i	−0.536596	+	0.929411i
$700$		0			0
$701$	9.02776			0.340974			0.170487	−	0.985360i	$-0.445466\pi$
$701$	9.02776			0.340974			0.170487	+	0.985360i	$0.445466\pi$
$702$	14.0917	+	18.7350i	0.531856	+	0.707107i
$703$	−18.6509			−0.703431
$704$	31.4542	−	54.4802i	1.18547	−	2.05330i
$705$	−3.54899	+	6.14703i	−0.133663	+	0.231510i
$706$	−30.4717	−	52.7786i	−1.14682	−	1.98635i
$707$		0			0
$708$	10.1056	+	17.5033i	0.379790	+	0.657815i
$709$	−16.3625	−	28.3407i	−0.614506	−	1.06436i	−0.990471	−	0.137722i	$-0.956022\pi$
$709$	−16.3625	−	28.3407i	−0.614506	−	1.06436i	0.375965	−	0.926634i	$-0.377311\pi$
$710$	−19.9633			−0.749209
$711$	5.60555	+	9.70910i	0.210225	+	0.364120i
$712$	9.75289	−	16.8925i	0.365505	−	0.633073i
$713$	2.16731	−	3.75389i	0.0811663	−	0.140584i
$714$		0			0
$715$	−23.0555	−	30.6525i	−0.862227	−	1.14634i
$716$	71.3583			2.66678
$717$	4.76206	−	8.24813i	0.177842	−	0.308032i
$718$	13.9222	−	24.1140i	0.519572	−	0.899925i
$719$	−11.3934	−	19.7340i	−0.424902	−	0.735952i	0.571509	−	0.820596i	$-0.306358\pi$
$719$	−11.3934	−	19.7340i	−0.424902	−	0.735952i	−0.996411	+	0.0846433i	$0.973025\pi$
$720$	−1.11373			−0.0415064
$721$		0			0
$722$	16.4680	+	28.5235i	0.612877	+	1.06153i
$723$	−20.2111			−0.751659
$724$	−40.1253	−	69.4990i	−1.49124	−	2.58291i
$725$	−0.348612	+	0.603814i	−0.0129471	+	0.0224251i
$726$	32.6691	−	56.5846i	1.21246	−	2.10005i
$727$	−37.1031			−1.37608			−0.688038	−	0.725674i	$-0.741528\pi$
$727$	−37.1031			−1.37608			−0.688038	+	0.725674i	$0.741528\pi$
$728$		0			0
$729$	−0.669468			−0.0247951
$730$	10.8167	−	18.7350i	0.400342	−	0.693413i
$731$	−44.7880	+	77.5751i	−1.65654	+	2.86922i
$732$	−15.5139	−	26.8708i	−0.573409	−	0.993174i
$733$	6.70061			0.247493			0.123746	−	0.992314i	$-0.460509\pi$
$733$	6.70061			0.247493			0.123746	+	0.992314i	$0.460509\pi$
$734$	29.4874	+	51.0737i	1.08840	+	1.88517i
$735$		0			0
$736$	3.21110			0.118363
$737$	−2.45416	−	4.25074i	−0.0904003	−	0.156578i
$738$	−19.5058	+	33.7850i	−0.718017	+	1.24364i
$739$	16.6056	−	28.7617i	0.610845	−	1.05801i	−0.380253	−	0.924882i	$-0.624163\pi$
$739$	16.6056	−	28.7617i	0.610845	−	1.05801i	0.991098	−	0.133132i	$-0.0425035\pi$
$740$	−61.5997			−2.26445
$741$	6.63134	−	15.5838i	0.243609	−	0.572487i
$742$		0			0
$743$	20.6514	−	35.7693i	0.757626	−	1.31225i	−0.186432	−	0.982468i	$-0.559692\pi$
$743$	20.6514	−	35.7693i	0.757626	−	1.31225i	0.944058	−	0.329779i	$-0.106974\pi$
$744$	23.2708	−	40.3062i	0.853150	−	1.47770i
$745$	−18.9790	−	32.8726i	−0.695336	−	1.20436i
$746$	−29.2389			−1.07051
$747$	2.39607	+	4.15012i	0.0876676	+	0.151845i
$748$	58.0206	+	100.495i	2.12144	+	3.67445i
$749$		0			0
$750$	28.6791	+	49.6737i	1.04721	+	1.81383i
$751$	5.80278	−	10.0507i	0.211746	−	0.366755i	−0.740515	−	0.672040i	$-0.765418\pi$
$751$	5.80278	−	10.0507i	0.211746	−	0.366755i	0.952261	+	0.305285i	$0.0987516\pi$
$752$	−0.228762	+	0.396228i	−0.00834210	+	0.0144489i
$753$	64.8999			2.36508
$754$	18.9790	−	2.31316i	0.691174	−	0.0842403i
$755$	−17.7960			−0.647662
$756$		0			0
$757$	−3.11943	+	5.40301i	−0.113378	+	0.196376i	−0.917130	−	0.398588i	$-0.869500\pi$
$757$	−3.11943	+	5.40301i	−0.113378	+	0.196376i	0.803752	+	0.594964i	$0.202834\pi$
$758$	13.9542	+	24.1693i	0.506838	+	0.877869i
$759$	6.44177			0.233821
$760$	−7.04584	−	12.2037i	−0.255579	−	0.442676i
$761$	−21.1463	−	36.6265i	−0.766553	−	1.32771i	−0.939422	−	0.342763i	$-0.888637\pi$
$761$	−21.1463	−	36.6265i	−0.766553	−	1.32771i	0.172869	−	0.984945i	$-0.444696\pi$
$762$	−39.4691			−1.42981
$763$		0			0
$764$	−25.9222	+	44.8986i	−0.937832	+	1.62437i
$765$	−13.1653	+	22.8029i	−0.475991	+	0.824441i
$766$	51.4193			1.85786
$767$	−10.1056	+	1.23167i	−0.364890	+	0.0444729i
$768$	38.8129			1.40054
$769$	23.5424	−	40.7766i	0.848959	−	1.47044i	−0.0331785	−	0.999449i	$-0.510563\pi$
$769$	23.5424	−	40.7766i	0.848959	−	1.47044i	0.882138	−	0.470991i	$-0.156104\pi$
$770$		0			0
$771$	−6.83053	−	11.8308i	−0.245996	−	0.426077i
$772$	65.4500			2.35560
$773$	14.2169	+	24.6244i	0.511347	+	0.885679i	0.999914	+	0.0131525i	$0.00418670\pi$
$773$	14.2169	+	24.6244i	0.511347	+	0.885679i	−0.488566	+	0.872527i	$0.662480\pi$
$774$	24.4542	+	42.3559i	0.878987	+	1.52245i
$775$	−2.16731			−0.0778520
$776$	−20.4901	−	35.4899i	−0.735551	−	1.27401i
$777$		0			0
$778$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15139 + 1.99426i) q^{2} +(1.08365 - 1.87694i) q^{3} +(-1.65139 - 2.86029i) q^{4} -2.16731 q^{5} +(2.49541 + 4.32218i) q^{6} +3.00000 q^{8} +(-0.848612 - 1.46984i) q^{9} +(2.49541 - 4.32218i) q^{10} +(-2.45416 + 4.25074i) q^{11} -7.15813 q^{12} +(1.41176 - 3.31767i) q^{13} +(-2.34861 + 4.06792i) q^{15} +(-0.151388 + 0.262211i) q^{16} +(3.57907 + 6.19912i) q^{17} +3.90833 q^{18} +(1.08365 + 1.87694i) q^{19} +(3.57907 + 6.19912i) q^{20} +(-5.65139 - 9.78849i) q^{22} +(0.302776 - 0.524423i) q^{23} +(3.25096 - 5.63083i) q^{24} -0.302776 q^{25} +(4.99082 + 6.63534i) q^{26} +2.82352 q^{27} +(1.15139 - 1.99426i) q^{29} +(-5.40833 - 9.36750i) q^{30} +7.15813 q^{31} +(2.65139 + 4.59234i) q^{32} +(5.31893 + 9.21265i) q^{33} -16.4836 q^{34} +(-2.80278 + 4.85455i) q^{36} +(-4.30278 + 7.45263i) q^{37} -4.99082 q^{38} +(-4.69722 - 6.24500i) q^{39} -6.50192 q^{40} +(-4.99082 + 8.64436i) q^{41} +(6.25694 + 10.8373i) q^{43} +16.2111 q^{44} +(1.83920 + 3.18559i) q^{45} +(0.697224 + 1.20763i) q^{46} +1.51110 q^{47} +(0.328104 + 0.568293i) q^{48} +(0.348612 - 0.603814i) q^{50} +15.5139 q^{51} +(-11.8209 + 1.44073i) q^{52} +2.39445 q^{53} +(-3.25096 + 5.63083i) q^{54} +(5.31893 - 9.21265i) q^{55} +4.69722 q^{57} +(2.65139 + 4.59234i) q^{58} +(-1.41176 - 2.44524i) q^{59} +15.5139 q^{60} +(2.16731 + 3.75389i) q^{61} +(-8.24179 + 14.2752i) q^{62} -12.8167 q^{64} +(-3.05971 + 7.19041i) q^{65} -24.4966 q^{66} +(-0.500000 + 0.866025i) q^{67} +(11.8209 - 20.4743i) q^{68} +(-0.656208 - 1.13659i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(-2.54584 - 4.40952i) q^{72} +4.33462 q^{73} +(-9.90833 - 17.1617i) q^{74} +(-0.328104 + 0.568293i) q^{75} +(3.57907 - 6.19912i) q^{76} +(17.8625 - 2.17708i) q^{78} -6.60555 q^{79} +(0.328104 - 0.568293i) q^{80} +(5.60555 - 9.70910i) q^{81} +(-11.4927 - 19.9060i) q^{82} -2.82352 q^{83} +(-7.75694 - 13.4354i) q^{85} -28.8167 q^{86} +(-2.49541 - 4.32218i) q^{87} +(-7.36249 + 12.7522i) q^{88} +(3.25096 - 5.63083i) q^{89} -8.47055 q^{90} -2.00000 q^{92} +(7.75694 - 13.4354i) q^{93} +(-1.73986 + 3.01353i) q^{94} +(-2.34861 - 4.06792i) q^{95} +11.4927 q^{96} +(-6.83003 - 11.8300i) q^{97} +8.33053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} + 6 q^{16} - 12 q^{18} - 38 q^{22} - 12 q^{23} + 12 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} - 52 q^{39} + 14 q^{43} + 72 q^{44}+ \cdots - 92 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 14 * q^9 + 2 * q^11 - 26 * q^15 + 6 * q^16 - 12 * q^18 - 38 * q^22 - 12 * q^23 + 12 * q^25 + 2 * q^29 + 14 * q^32 - 8 * q^36 - 20 * q^37 - 52 * q^39 + 14 * q^43 + 72 * q^44 + 20 * q^46 + 10 * q^50 + 52 * q^51 + 48 * q^53 + 52 * q^57 + 14 * q^58 + 52 * q^60 - 16 * q^64 + 26 * q^65 - 4 * q^67 - 16 * q^71 - 42 * q^72 - 36 * q^74 + 78 * q^78 - 24 * q^79 + 16 * q^81 - 26 * q^85 - 144 * q^86 + 6 * q^88 - 16 * q^92 + 26 * q^93 - 26 * q^95 - 92 * q^99

Introduction

L-functions

Modular forms

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