LMFDB - Embedded newform 637.2.u.f.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(30,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.30"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,6,0,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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 $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-13})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 13x^{2} + 169 $ x^4 - 13*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-3.12250 + 1.80278i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.f.30.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-3.12250 + 1.80278i) q^{5} -1.73205i q^{8} -3.00000 q^{9} -6.24500 q^{10} +3.46410i q^{11} +(-3.12250 + 1.80278i) q^{13} +(2.50000 - 4.33013i) q^{16} +(-3.12250 - 5.40833i) q^{17} +(-4.50000 - 2.59808i) q^{18} +7.21110i q^{19} +(-3.12250 - 1.80278i) q^{20} +(-3.00000 + 5.19615i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(4.00000 - 6.92820i) q^{25} -6.24500 q^{26} +(-0.500000 - 0.866025i) q^{29} +(4.50000 - 2.59808i) q^{32} -10.8167i q^{34} +(-1.50000 - 2.59808i) q^{36} +(1.50000 + 0.866025i) q^{37} +(-6.24500 + 10.8167i) q^{38} +(3.12250 + 5.40833i) q^{40} +(3.12250 - 1.80278i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(-3.00000 + 1.73205i) q^{44} +(9.36750 - 5.40833i) q^{45} +(-6.00000 + 3.46410i) q^{46} +(6.24500 - 3.60555i) q^{47} +(12.0000 - 6.92820i) q^{50} +(-3.12250 - 1.80278i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-6.24500 - 10.8167i) q^{55} -1.73205i q^{58} +(6.24500 - 3.60555i) q^{59} -6.24500 q^{61} -1.00000 q^{64} +(6.50000 - 11.2583i) q^{65} +13.8564i q^{67} +(3.12250 - 5.40833i) q^{68} +(-9.00000 - 5.19615i) q^{71} +5.19615i q^{72} +(9.36750 + 5.40833i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-6.24500 + 3.60555i) q^{76} +(3.00000 + 5.19615i) q^{79} +18.0278i q^{80} +9.00000 q^{81} +6.24500 q^{82} +7.21110i q^{83} +(19.5000 + 11.2583i) q^{85} +(-9.00000 + 5.19615i) q^{86} +6.00000 q^{88} +(-6.24500 - 3.60555i) q^{89} +18.7350 q^{90} -4.00000 q^{92} +12.4900 q^{94} +(-13.0000 - 22.5167i) q^{95} +(-6.24500 - 3.60555i) q^{97} -10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 2 q^{4} - 12 q^{9} + 10 q^{16} - 18 q^{18} - 12 q^{22} - 8 q^{23} + 16 q^{25} - 2 q^{29} + 18 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{43} - 12 q^{44} - 24 q^{46} + 48 q^{50} - 10 q^{53} - 4 q^{64}+ \cdots - 52 q^{95}+O(q^{100}) $ 4 * q + 6 * q^2 + 2 * q^4 - 12 * q^9 + 10 * q^16 - 18 * q^18 - 12 * q^22 - 8 * q^23 + 16 * q^25 - 2 * q^29 + 18 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^43 - 12 * q^44 - 24 * q^46 + 48 * q^50 - 10 * q^53 - 4 * q^64 + 26 * q^65 - 36 * q^71 + 6 * q^74 + 12 * q^79 + 36 * q^81 + 78 * q^85 - 36 * q^86 + 24 * q^88 - 16 * q^92 - 52 * q^95

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$		0			0			−	1.00000i	$-0.5\pi$
$3$		0			0				1.00000i	$0.5\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−3.12250	+	1.80278i	−1.39642	+	0.806226i	−0.994016	−	0.109235i	$-0.965160\pi$
$5$	−3.12250	+	1.80278i	−1.39642	+	0.806226i	−0.402408	+	0.915460i	$0.631827\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	−3.00000			−1.00000
$10$	−6.24500			−1.97484
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$		0			0
$13$	−3.12250	+	1.80278i	−0.866025	+	0.500000i
$13$	−3.12250	+	1.80278i	−0.866025	+	0.500000i
$14$		0			0
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−3.12250	−	5.40833i	−0.757317	−	1.31171i	−0.944214	−	0.329332i	$-0.893176\pi$
$17$	−3.12250	−	5.40833i	−0.757317	−	1.31171i	0.186897	−	0.982380i	$-0.440157\pi$
$18$	−4.50000	−	2.59808i	−1.06066	−	0.612372i
$19$			7.21110i			1.65434i	0.561951	+	0.827170i	$0.310051\pi$
$19$			7.21110i			1.65434i	−0.561951	+	0.827170i	$0.689949\pi$
$20$	−3.12250	−	1.80278i	−0.698212	−	0.403113i
$21$		0			0
$22$	−3.00000	+	5.19615i	−0.639602	+	1.10782i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	4.00000	−	6.92820i	0.800000	−	1.38564i
$26$	−6.24500			−1.22474
$27$		0			0
$28$		0			0
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$		0			0
$34$		−	10.8167i		−	1.85504i
$35$		0			0
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	0.618206	−	0.786016i	$-0.287860\pi$
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	−0.371607	+	0.928390i	$0.621193\pi$
$38$	−6.24500	+	10.8167i	−1.01307	+	1.75469i
$39$		0			0
$40$	3.12250	+	5.40833i	0.493710	+	0.855132i
$41$	3.12250	−	1.80278i	0.487652	−	0.281546i	−0.235948	−	0.971766i	$-0.575819\pi$
$41$	3.12250	−	1.80278i	0.487652	−	0.281546i	0.723600	+	0.690220i	$0.242486\pi$
$42$		0			0
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	−3.00000	+	1.73205i	−0.452267	+	0.261116i
$45$	9.36750	−	5.40833i	1.39642	−	0.806226i
$46$	−6.00000	+	3.46410i	−0.884652	+	0.510754i
$47$	6.24500	−	3.60555i	0.910927	−	0.525924i	0.0301974	−	0.999544i	$-0.490386\pi$
$47$	6.24500	−	3.60555i	0.910927	−	0.525924i	0.880729	+	0.473620i	$0.157053\pi$
$48$		0			0
$49$		0			0
$50$	12.0000	−	6.92820i	1.69706	−	0.979796i
$51$		0			0
$52$	−3.12250	−	1.80278i	−0.433013	−	0.250000i
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	−0.985062	−	0.172200i	$-0.944912\pi$
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	0.641661	+	0.766989i	$0.278246\pi$
$54$		0			0
$55$	−6.24500	−	10.8167i	−0.842075	−	1.45852i
$56$		0			0
$57$		0			0
$58$		−	1.73205i		−	0.227429i
$59$	6.24500	−	3.60555i	0.813029	−	0.469403i	−0.0349773	−	0.999388i	$-0.511136\pi$
$59$	6.24500	−	3.60555i	0.813029	−	0.469403i	0.848007	+	0.529985i	$0.177803\pi$
$60$		0			0
$61$	−6.24500			−0.799590			−0.399795	−	0.916605i	$-0.630919\pi$
$61$	−6.24500			−0.799590			−0.399795	+	0.916605i	$0.630919\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.50000	−	11.2583i	0.806226	−	1.39642i
$66$		0			0
$67$			13.8564i			1.69283i	0.532524	+	0.846415i	$0.321244\pi$
$67$			13.8564i			1.69283i	−0.532524	+	0.846415i	$0.678756\pi$
$68$	3.12250	−	5.40833i	0.378659	−	0.655856i
$69$		0			0
$70$		0			0
$71$	−9.00000	−	5.19615i	−1.06810	−	0.616670i	−0.140441	−	0.990089i	$-0.544852\pi$
$71$	−9.00000	−	5.19615i	−1.06810	−	0.616670i	−0.927663	+	0.373419i	$0.878185\pi$
$72$			5.19615i			0.612372i
$73$	9.36750	+	5.40833i	1.09638	+	0.632997i	0.935269	−	0.353939i	$-0.115158\pi$
$73$	9.36750	+	5.40833i	1.09638	+	0.632997i	0.161114	+	0.986936i	$0.448491\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$		0			0
$76$	−6.24500	+	3.60555i	−0.716350	+	0.413585i
$77$		0			0
$78$		0			0
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$			18.0278i			2.01556i
$81$	9.00000			1.00000
$82$	6.24500			0.689645
$83$			7.21110i			0.791521i	0.918354	+	0.395761i	$0.129519\pi$
$83$			7.21110i			0.791521i	−0.918354	+	0.395761i	$0.870481\pi$
$84$		0			0
$85$	19.5000	+	11.2583i	2.11507	+	1.22114i
$86$	−9.00000	+	5.19615i	−0.970495	+	0.560316i
$87$		0			0
$88$	6.00000			0.639602
$89$	−6.24500	−	3.60555i	−0.661968	−	0.382188i	0.131058	−	0.991375i	$-0.458163\pi$
$89$	−6.24500	−	3.60555i	−0.661968	−	0.382188i	−0.793027	+	0.609187i	$0.791496\pi$
$90$	18.7350			1.97484
$91$		0			0
$92$	−4.00000			−0.417029
$93$		0			0
$94$	12.4900			1.28824
$95$	−13.0000	−	22.5167i	−1.33377	−	2.31016i
$96$		0			0
$97$	−6.24500	−	3.60555i	−0.634083	−	0.366088i	0.148248	−	0.988950i	$-0.452637\pi$
$97$	−6.24500	−	3.60555i	−0.634083	−	0.366088i	−0.782332	+	0.622862i	$0.785970\pi$
$98$		0			0
$99$		−	10.3923i		−	1.04447i
$100$	8.00000			0.800000
$101$	6.24500			0.621401			0.310700	−	0.950508i	$-0.399436\pi$
$101$	6.24500			0.621401			0.310700	+	0.950508i	$0.399436\pi$
$102$		0			0
$103$	6.24500	+	10.8167i	0.615338	+	1.06580i	0.990325	+	0.138767i	$0.0443138\pi$
$103$	6.24500	+	10.8167i	0.615338	+	1.06580i	−0.374987	+	0.927030i	$0.622353\pi$
$104$	3.12250	+	5.40833i	0.306186	+	0.530330i
$105$		0			0
$106$	−7.50000	+	4.33013i	−0.728464	+	0.420579i
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$		0			0
$109$	−6.00000	−	3.46410i	−0.574696	−	0.331801i	0.184327	−	0.982865i	$-0.440990\pi$
$109$	−6.00000	−	3.46410i	−0.574696	−	0.331801i	−0.759023	+	0.651064i	$0.774323\pi$
$110$		−	21.6333i		−	2.06265i
$111$		0			0
$112$		0			0
$113$	−2.50000	+	4.33013i	−0.235180	+	0.407344i	−0.959325	−	0.282304i	$-0.908901\pi$
$113$	−2.50000	+	4.33013i	−0.235180	+	0.407344i	0.724145	+	0.689648i	$0.242235\pi$
$114$		0			0
$115$		−	14.4222i		−	1.34488i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$	9.36750	−	5.40833i	0.866025	−	0.500000i
$118$	12.4900			1.14980
$119$		0			0
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−9.36750	−	5.40833i	−0.848093	−	0.489647i
$123$		0			0
$124$		0			0
$125$			10.8167i			0.967471i
$126$		0			0
$127$	−9.00000	−	15.5885i	−0.798621	−	1.38325i	−0.920514	−	0.390709i	$-0.872230\pi$
$127$	−9.00000	−	15.5885i	−0.798621	−	1.38325i	0.121894	−	0.992543i	$-0.461103\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$		0			0
$130$	19.5000	−	11.2583i	1.71026	−	0.987421i
$131$	−6.24500	−	10.8167i	−0.545628	−	0.945055i	−0.998567	−	0.0535140i	$-0.982958\pi$
$131$	−6.24500	−	10.8167i	−0.545628	−	0.945055i	0.452939	−	0.891541i	$-0.350375\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000	+	20.7846i	−1.03664	+	1.79552i
$135$		0			0
$136$	−9.36750	+	5.40833i	−0.803256	+	0.463760i
$137$	−7.50000	+	4.33013i	−0.640768	+	0.369948i	−0.784910	−	0.619609i	$-0.787291\pi$
$137$	−7.50000	+	4.33013i	−0.640768	+	0.369948i	0.144142	+	0.989557i	$0.453958\pi$
$138$		0			0
$139$	−6.24500	+	10.8167i	−0.529694	+	0.917457i	0.469706	+	0.882823i	$0.344360\pi$
$139$	−6.24500	+	10.8167i	−0.529694	+	0.917457i	−0.999400	+	0.0346338i	$0.988974\pi$
$140$		0			0
$141$		0			0
$142$	−9.00000	−	15.5885i	−0.755263	−	1.30815i
$143$	−6.24500	−	10.8167i	−0.522233	−	0.904534i
$144$	−7.50000	+	12.9904i	−0.625000	+	1.08253i
$145$	3.12250	+	1.80278i	0.259309	+	0.149712i
$146$	9.36750	+	16.2250i	0.775260	+	1.34279i
$147$		0			0
$148$			1.73205i			0.142374i
$149$		−	15.5885i		−	1.27706i	−0.769599	−	0.638528i	$-0.779544\pi$
$149$		−	15.5885i		−	1.27706i	0.769599	−	0.638528i	$-0.220456\pi$
$150$		0			0
$151$	−3.00000	−	1.73205i	−0.244137	−	0.140952i	0.372940	−	0.927855i	$-0.378350\pi$
$151$	−3.00000	−	1.73205i	−0.244137	−	0.140952i	−0.617076	+	0.786903i	$0.711683\pi$
$152$	12.4900			1.01307
$153$	9.36750	+	16.2250i	0.757317	+	1.31171i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.12250	+	5.40833i	−0.249203	+	0.431631i	−0.963305	−	0.268410i	$-0.913502\pi$
$157$	−3.12250	+	5.40833i	−0.249203	+	0.431631i	0.714102	+	0.700041i	$0.246835\pi$
$158$			10.3923i			0.826767i
$159$		0			0
$160$	−9.36750	+	16.2250i	−0.740566	+	1.28270i
$161$		0			0
$162$	13.5000	+	7.79423i	1.06066	+	0.612372i
$163$			10.3923i			0.813988i	0.913431	+	0.406994i	$0.133423\pi$
$163$			10.3923i			0.813988i	−0.913431	+	0.406994i	$0.866577\pi$
$164$	3.12250	+	1.80278i	0.243826	+	0.140773i
$165$		0			0
$166$	−6.24500	+	10.8167i	−0.484706	+	0.839535i
$167$	6.24500	−	3.60555i	0.483252	−	0.279006i	−0.238518	−	0.971138i	$-0.576662\pi$
$167$	6.24500	−	3.60555i	0.483252	−	0.279006i	0.721771	+	0.692132i	$0.243328\pi$
$168$		0			0
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$	19.5000	+	33.7750i	1.49558	+	2.59042i
$171$		−	21.6333i		−	1.65434i
$172$	−6.00000			−0.457496
$173$	−24.9800			−1.89919			−0.949597	−	0.313474i	$-0.898507\pi$
$173$	−24.9800			−1.89919			−0.949597	+	0.313474i	$0.898507\pi$
$174$		0			0
$175$		0			0
$176$	15.0000	+	8.66025i	1.13067	+	0.652791i
$177$		0			0
$178$	−6.24500	−	10.8167i	−0.468082	−	0.810742i
$179$	16.0000			1.19590			0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000			1.19590			0.597948	+	0.801535i	$0.295983\pi$
$180$	9.36750	+	5.40833i	0.698212	+	0.403113i
$181$	−6.24500			−0.464187			−0.232094	−	0.972693i	$-0.574558\pi$
$181$	−6.24500			−0.464187			−0.232094	+	0.972693i	$0.574558\pi$
$182$		0			0
$183$		0			0
$184$	6.00000	+	3.46410i	0.442326	+	0.255377i
$185$	−6.24500			−0.459141
$186$		0			0
$187$	18.7350	−	10.8167i	1.37004	−	0.790992i
$188$	6.24500	+	3.60555i	0.455463	+	0.262962i
$189$		0			0
$190$		−	45.0333i		−	3.26706i
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$		0			0
$193$			8.66025i			0.623379i	0.950184	+	0.311689i	$0.100895\pi$
$193$			8.66025i			0.623379i	−0.950184	+	0.311689i	$0.899105\pi$
$194$	−6.24500	−	10.8167i	−0.448365	−	0.776590i
$195$		0			0
$196$		0			0
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$	9.00000	−	15.5885i	0.639602	−	1.10782i
$199$	6.24500	+	10.8167i	0.442696	+	0.766772i	0.997889	−	0.0649497i	$-0.0206887\pi$
$199$	6.24500	+	10.8167i	0.442696	+	0.766772i	−0.555192	+	0.831722i	$0.687355\pi$
$200$	−12.0000	−	6.92820i	−0.848528	−	0.489898i
$201$		0			0
$202$	9.36750	+	5.40833i	0.659095	+	0.380529i
$203$		0			0
$204$		0			0
$205$	−6.50000	+	11.2583i	−0.453980	+	0.786316i
$206$			21.6333i			1.50726i
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$			18.0278i			1.25000i
$209$	−24.9800			−1.72790
$210$		0			0
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	0.972346	+	0.233544i	$0.0750324\pi$
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	−0.283918	+	0.958849i	$0.591634\pi$
$212$	−5.00000			−0.343401
$213$		0			0
$214$	−3.00000	+	1.73205i	−0.205076	+	0.118401i
$215$		−	21.6333i		−	1.47538i
$216$		0			0
$217$		0			0
$218$	−6.00000	−	10.3923i	−0.406371	−	0.703856i
$219$		0			0
$220$	6.24500	−	10.8167i	0.421038	−	0.729259i
$221$	19.5000	+	11.2583i	1.31171	+	0.757317i
$222$		0			0
$223$	6.24500	−	3.60555i	0.418196	−	0.241446i	−0.276109	−	0.961126i	$-0.589045\pi$
$223$	6.24500	−	3.60555i	0.418196	−	0.241446i	0.694305	+	0.719681i	$0.255712\pi$
$224$		0			0
$225$	−12.0000	+	20.7846i	−0.800000	+	1.38564i
$226$	−7.50000	+	4.33013i	−0.498893	+	0.288036i
$227$	−12.4900	+	7.21110i	−0.828990	+	0.478618i	−0.853507	−	0.521082i	$-0.825529\pi$
$227$	−12.4900	+	7.21110i	−0.828990	+	0.478618i	0.0245166	+	0.999699i	$0.492195\pi$
$228$		0			0
$229$	−18.7350	+	10.8167i	−1.23804	+	0.714785i	−0.968694	−	0.248258i	$-0.920142\pi$
$229$	−18.7350	+	10.8167i	−1.23804	+	0.714785i	−0.269349	+	0.963043i	$0.586809\pi$
$230$	12.4900	−	21.6333i	0.823566	−	1.42646i
$231$		0			0
$232$	−1.50000	+	0.866025i	−0.0984798	+	0.0568574i
$233$	−1.00000	−	1.73205i	−0.0655122	−	0.113470i	0.831409	−	0.555661i	$-0.187535\pi$
$233$	−1.00000	−	1.73205i	−0.0655122	−	0.113470i	−0.896921	+	0.442191i	$0.854201\pi$
$234$	18.7350			1.22474
$235$	−13.0000	+	22.5167i	−0.848026	+	1.46882i
$236$	6.24500	+	3.60555i	0.406515	+	0.234701i
$237$		0			0
$238$		0			0
$239$			17.3205i			1.12037i	0.828367	+	0.560185i	$0.189270\pi$
$239$			17.3205i			1.12037i	−0.828367	+	0.560185i	$0.810730\pi$
$240$		0			0
$241$	−9.36750	+	5.40833i	−0.603414	+	0.348381i	−0.770383	−	0.637581i	$-0.779935\pi$
$241$	−9.36750	+	5.40833i	−0.603414	+	0.348381i	0.166970	+	0.985962i	$0.446602\pi$
$242$	−1.50000	−	0.866025i	−0.0964237	−	0.0556702i
$243$		0			0
$244$	−3.12250	−	5.40833i	−0.199898	−	0.346233i
$245$		0			0
$246$		0			0
$247$	−13.0000	−	22.5167i	−0.827170	−	1.43270i
$248$		0			0
$249$		0			0
$250$	−9.36750	+	16.2250i	−0.592453	+	1.02616i
$251$	6.24500	−	10.8167i	0.394181	−	0.682741i	−0.598815	−	0.800887i	$-0.704362\pi$
$251$	6.24500	−	10.8167i	0.394181	−	0.682741i	0.992996	+	0.118146i	$0.0376950\pi$
$252$		0			0
$253$	−12.0000	−	6.92820i	−0.754434	−	0.435572i
$254$		−	31.1769i		−	1.95621i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	9.36750	−	16.2250i	0.584328	−	1.01209i	−0.410630	−	0.911802i	$-0.634691\pi$
$257$	9.36750	−	16.2250i	0.584328	−	1.01209i	0.994959	−	0.100285i	$-0.0319753\pi$
$258$		0			0
$259$		0			0
$260$	13.0000			0.806226
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$		−	21.6333i		−	1.33651i
$263$	2.00000			0.123325			0.0616626	−	0.998097i	$-0.480360\pi$
$263$	2.00000			0.123325			0.0616626	+	0.998097i	$0.480360\pi$
$264$		0			0
$265$		−	18.0278i		−	1.10744i
$266$		0			0
$267$		0			0
$268$	−12.0000	+	6.92820i	−0.733017	+	0.423207i
$269$	12.4900	+	21.6333i	0.761528	+	1.31901i	0.942063	+	0.335437i	$0.108884\pi$
$269$	12.4900	+	21.6333i	0.761528	+	1.31901i	−0.180534	+	0.983569i	$0.557783\pi$
$270$		0			0
$271$	6.24500	+	3.60555i	0.379357	+	0.219022i	0.677538	−	0.735487i	$-0.263047\pi$
$271$	6.24500	+	3.60555i	0.379357	+	0.219022i	−0.298182	+	0.954509i	$0.596380\pi$
$272$	−31.2250			−1.89329
$273$		0			0
$274$	−15.0000			−0.906183
$275$	24.0000	+	13.8564i	1.44725	+	0.835573i
$276$		0			0
$277$	−12.5000	−	21.6506i	−0.751052	−	1.30086i	−0.947313	−	0.320309i	$-0.896213\pi$
$277$	−12.5000	−	21.6506i	−0.751052	−	1.30086i	0.196261	−	0.980552i	$-0.437120\pi$
$278$	−18.7350	+	10.8167i	−1.12365	+	0.648740i
$279$		0			0
$280$		0			0
$281$		−	22.5167i		−	1.34323i	−0.740900	−	0.671616i	$-0.765601\pi$
$281$		−	22.5167i		−	1.34323i	0.740900	−	0.671616i	$-0.234399\pi$
$282$		0			0
$283$	−12.4900			−0.742453			−0.371227	−	0.928542i	$-0.621063\pi$
$283$	−12.4900			−0.742453			−0.371227	+	0.928542i	$0.621063\pi$
$284$		−	10.3923i		−	0.616670i
$285$		0			0
$286$		−	21.6333i		−	1.27920i
$287$		0			0
$288$	−13.5000	+	7.79423i	−0.795495	+	0.459279i
$289$	−11.0000	+	19.0526i	−0.647059	+	1.12074i
$290$	3.12250	+	5.40833i	0.183359	+	0.317588i
$291$		0			0
$292$			10.8167i			0.632997i
$293$	−15.6125	−	9.01388i	−0.912092	−	0.526596i	−0.0309881	−	0.999520i	$-0.509865\pi$
$293$	−15.6125	−	9.01388i	−0.912092	−	0.526596i	−0.881104	+	0.472923i	$0.843199\pi$
$294$		0			0
$295$	−13.0000	+	22.5167i	−0.756889	+	1.31097i
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$		0			0
$298$	13.5000	−	23.3827i	0.782034	−	1.35452i
$299$		−	14.4222i		−	0.834058i
$300$		0			0
$301$		0			0
$302$	−3.00000	−	5.19615i	−0.172631	−	0.299005i
$303$		0			0
$304$	31.2250	+	18.0278i	1.79088	+	1.03396i
$305$	19.5000	−	11.2583i	1.11657	−	0.644650i
$306$			32.4500i			1.85504i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.4900	−	21.6333i	0.708243	−	1.22671i	−0.257266	−	0.966341i	$-0.582822\pi$
$311$	12.4900	−	21.6333i	0.708243	−	1.22671i	0.965508	−	0.260372i	$-0.0838451\pi$
$312$		0			0
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	−9.36750	+	5.40833i	−0.528638	+	0.305210i
$315$		0			0
$316$	−3.00000	+	5.19615i	−0.168763	+	0.292306i
$317$	−13.5000	+	7.79423i	−0.758236	+	0.437767i	−0.828662	−	0.559749i	$-0.810897\pi$
$317$	−13.5000	+	7.79423i	−0.758236	+	0.437767i	0.0704263	+	0.997517i	$0.477564\pi$
$318$		0			0
$319$	3.00000	−	1.73205i	0.167968	−	0.0969762i
$320$	3.12250	−	1.80278i	0.174553	−	0.100778i
$321$		0			0
$322$		0			0
$323$	39.0000	−	22.5167i	2.17002	−	1.25286i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$			28.8444i			1.60000i
$326$	−9.00000	+	15.5885i	−0.498464	+	0.863365i
$327$		0			0
$328$	−3.12250	−	5.40833i	−0.172411	−	0.298625i
$329$		0			0
$330$		0			0
$331$		−	10.3923i		−	0.571213i	−0.958347	−	0.285606i	$-0.907805\pi$
$331$		−	10.3923i		−	0.571213i	0.958347	−	0.285606i	$-0.0921950\pi$
$332$	−6.24500	+	3.60555i	−0.342739	+	0.197880i
$333$	−4.50000	−	2.59808i	−0.246598	−	0.142374i
$334$	12.4900			0.683422
$335$	−24.9800	−	43.2666i	−1.36480	−	2.36391i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	19.5000	−	11.2583i	1.06066	−	0.612372i
$339$		0			0
$340$			22.5167i			1.22114i
$341$		0			0
$342$	18.7350	−	32.4500i	1.01307	−	1.75469i
$343$		0			0
$344$	9.00000	+	5.19615i	0.485247	+	0.280158i
$345$		0			0
$346$	−37.4700	−	21.6333i	−2.01440	−	1.16301i
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$		0			0
$349$	18.7350	−	10.8167i	1.00286	−	0.579002i	0.0937676	−	0.995594i	$-0.470109\pi$
$349$	18.7350	−	10.8167i	1.00286	−	0.579002i	0.909094	+	0.416592i	$0.136776\pi$
$350$		0			0
$351$		0			0
$352$	9.00000	+	15.5885i	0.479702	+	0.830868i
$353$			25.2389i			1.34333i	0.740855	+	0.671664i	$0.234420\pi$
$353$			25.2389i			1.34333i	−0.740855	+	0.671664i	$0.765580\pi$
$354$		0			0
$355$	37.4700			1.98870
$356$		−	7.21110i		−	0.382188i
$357$		0			0
$358$	24.0000	+	13.8564i	1.26844	+	0.732334i
$359$	−24.0000	+	13.8564i	−1.26667	+	0.731313i	−0.974357	−	0.225009i	$-0.927759\pi$
$359$	−24.0000	+	13.8564i	−1.26667	+	0.731313i	−0.292315	+	0.956322i	$0.594426\pi$
$360$	−9.36750	−	16.2250i	−0.493710	−	0.855132i
$361$	−33.0000			−1.73684
$362$	−9.36750	−	5.40833i	−0.492345	−	0.284255i
$363$		0			0
$364$		0			0
$365$	−39.0000			−2.04135
$366$		0			0
$367$	−24.9800			−1.30394			−0.651972	−	0.758243i	$-0.726058\pi$
$367$	−24.9800			−1.30394			−0.651972	+	0.758243i	$0.726058\pi$
$368$	10.0000	+	17.3205i	0.521286	+	0.902894i
$369$	−9.36750	+	5.40833i	−0.487652	+	0.281546i
$370$	−9.36750	−	5.40833i	−0.486993	−	0.281166i
$371$		0			0
$372$		0			0
$373$	15.0000			0.776671			0.388335	−	0.921518i	$-0.373050\pi$
$373$	15.0000			0.776671			0.388335	+	0.921518i	$0.373050\pi$
$374$	37.4700			1.93753
$375$		0			0
$376$	−6.24500	−	10.8167i	−0.322061	−	0.557826i
$377$	3.12250	+	1.80278i	0.160817	+	0.0928477i
$378$		0			0
$379$	18.0000	−	10.3923i	0.924598	−	0.533817i	0.0394989	−	0.999220i	$-0.487424\pi$
$379$	18.0000	−	10.3923i	0.924598	−	0.533817i	0.885099	+	0.465403i	$0.154091\pi$
$380$	13.0000	−	22.5167i	0.666886	−	1.15508i
$381$		0			0
$382$	6.00000	+	3.46410i	0.306987	+	0.177239i
$383$			36.0555i			1.84235i	0.389148	+	0.921175i	$0.372770\pi$
$383$			36.0555i			1.84235i	−0.389148	+	0.921175i	$0.627230\pi$
$384$		0			0
$385$		0			0
$386$	−7.50000	+	12.9904i	−0.381740	+	0.661193i
$387$	9.00000	−	15.5885i	0.457496	−	0.792406i
$388$		−	7.21110i		−	0.366088i
$389$	−8.50000	+	14.7224i	−0.430967	+	0.746457i	−0.996957	−	0.0779554i	$-0.975161\pi$
$389$	−8.50000	+	14.7224i	−0.430967	+	0.746457i	0.565990	+	0.824412i	$0.308494\pi$
$390$		0			0
$391$	24.9800			1.26329
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−18.7350	−	10.8167i	−0.942660	−	0.544245i
$396$	9.00000	−	5.19615i	0.452267	−	0.261116i
$397$			7.21110i			0.361915i	0.983491	+	0.180957i	$0.0579196\pi$
$397$			7.21110i			0.361915i	−0.983491	+	0.180957i	$0.942080\pi$
$398$			21.6333i			1.08438i
$399$		0			0
$400$	−20.0000	−	34.6410i	−1.00000	−	1.73205i
$401$	−7.50000	−	4.33013i	−0.374532	−	0.216236i	0.300904	−	0.953654i	$-0.402711\pi$
$401$	−7.50000	−	4.33013i	−0.374532	−	0.216236i	−0.675437	+	0.737418i	$0.736045\pi$
$402$		0			0
$403$		0			0
$404$	3.12250	+	5.40833i	0.155350	+	0.269074i
$405$	−28.1025	+	16.2250i	−1.39642	+	0.806226i
$406$		0			0
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	21.8575	−	12.6194i	1.08078	−	0.623991i	0.149676	−	0.988735i	$-0.452177\pi$
$409$	21.8575	−	12.6194i	1.08078	−	0.623991i	0.931108	+	0.364744i	$0.118844\pi$
$410$	−19.5000	+	11.2583i	−0.963036	+	0.556009i
$411$		0			0
$412$	−6.24500	+	10.8167i	−0.307669	+	0.532898i
$413$		0			0
$414$	18.0000	−	10.3923i	0.884652	−	0.510754i
$415$	−13.0000	−	22.5167i	−0.638145	−	1.10530i
$416$	−9.36750	+	16.2250i	−0.459279	+	0.795495i
$417$		0			0
$418$	−37.4700	−	21.6333i	−1.83272	−	1.05812i
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$		−	22.5167i		−	1.09739i	−0.836021	−	0.548697i	$-0.815124\pi$
$421$		−	22.5167i		−	1.09739i	0.836021	−	0.548697i	$-0.184876\pi$
$422$			34.6410i			1.68630i
$423$	−18.7350	+	10.8167i	−0.910927	+	0.525924i
$424$	7.50000	+	4.33013i	0.364232	+	0.210290i
$425$	−49.9600			−2.42342
$426$		0			0
$427$		0			0
$428$	−2.00000			−0.0966736
$429$		0			0
$430$	18.7350	−	32.4500i	0.903482	−	1.56488i
$431$		−	27.7128i		−	1.33488i	−0.744664	−	0.667440i	$-0.767390\pi$
$431$		−	27.7128i		−	1.33488i	0.744664	−	0.667440i	$-0.232610\pi$
$432$		0			0
$433$	−9.36750	+	16.2250i	−0.450173	+	0.779723i	−0.998396	−	0.0566092i	$-0.981971\pi$
$433$	−9.36750	+	16.2250i	−0.450173	+	0.779723i	0.548223	+	0.836332i	$0.315304\pi$
$434$		0			0
$435$		0			0
$436$		−	6.92820i		−	0.331801i
$437$	−24.9800	−	14.4222i	−1.19496	−	0.689908i
$438$		0			0
$439$	−6.24500	+	10.8167i	−0.298057	+	0.516251i	−0.975691	−	0.219149i	$-0.929672\pi$
$439$	−6.24500	+	10.8167i	−0.298057	+	0.516251i	0.677634	+	0.735399i	$0.263005\pi$
$440$	−18.7350	+	10.8167i	−0.893156	+	0.515664i
$441$		0			0
$442$	19.5000	+	33.7750i	0.927520	+	1.60651i
$443$	−8.00000	−	13.8564i	−0.380091	−	0.658338i	0.610984	−	0.791643i	$-0.290774\pi$
$443$	−8.00000	−	13.8564i	−0.380091	−	0.658338i	−0.991075	+	0.133306i	$0.957441\pi$
$444$		0			0
$445$	26.0000			1.23252
$446$	12.4900			0.591418
$447$		0			0
$448$		0			0
$449$	6.00000	+	3.46410i	0.283158	+	0.163481i	0.634852	−	0.772634i	$-0.281061\pi$
$449$	6.00000	+	3.46410i	0.283158	+	0.163481i	−0.351694	+	0.936115i	$0.614394\pi$
$450$	−36.0000	+	20.7846i	−1.69706	+	0.979796i
$451$	6.24500	+	10.8167i	0.294065	+	0.509336i
$452$	−5.00000			−0.235180
$453$		0			0
$454$	−24.9800			−1.17237
$455$		0			0
$456$		0			0
$457$	34.5000	+	19.9186i	1.61384	+	0.931752i	0.988469	+	0.151426i	$0.0483867\pi$
$457$	34.5000	+	19.9186i	1.61384	+	0.931752i	0.625373	+	0.780326i	$0.284947\pi$
$458$	−37.4700			−1.75086
$459$		0			0
$460$	12.4900	−	7.21110i	0.582349	−	0.336219i
$461$	34.3475	+	19.8305i	1.59972	+	0.923600i	0.991540	+	0.129802i	$0.0414343\pi$
$461$	34.3475	+	19.8305i	1.59972	+	0.923600i	0.608182	+	0.793797i	$0.291899\pi$
$462$		0			0
$463$			10.3923i			0.482971i	0.970404	+	0.241486i	$0.0776347\pi$
$463$			10.3923i			0.482971i	−0.970404	+	0.241486i	$0.922365\pi$
$464$	−5.00000			−0.232119
$465$		0			0
$466$		−	3.46410i		−	0.160471i
$467$	−6.24500	−	10.8167i	−0.288984	−	0.500535i	0.684583	−	0.728934i	$-0.259984\pi$
$467$	−6.24500	−	10.8167i	−0.288984	−	0.500535i	−0.973568	+	0.228399i	$0.926651\pi$
$468$	9.36750	+	5.40833i	0.433013	+	0.250000i
$469$		0			0
$470$	−39.0000	+	22.5167i	−1.79894	+	1.03862i
$471$		0			0
$472$	−6.24500	−	10.8167i	−0.287449	−	0.497877i
$473$	−18.0000	−	10.3923i	−0.827641	−	0.477839i
$474$		0			0
$475$	49.9600	+	28.8444i	2.29232	+	1.32347i
$476$		0			0
$477$	7.50000	−	12.9904i	0.343401	−	0.594789i
$478$	−15.0000	+	25.9808i	−0.686084	+	1.18833i
$479$			14.4222i			0.658967i	0.944161	+	0.329484i	$0.106875\pi$
$479$			14.4222i			0.658967i	−0.944161	+	0.329484i	$0.893125\pi$
$480$		0			0
$481$	−6.24500			−0.284747
$482$	−18.7350			−0.853356
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	26.0000			1.18060
$486$		0			0
$487$	18.0000	−	10.3923i	0.815658	−	0.470920i	−0.0332590	−	0.999447i	$-0.510589\pi$
$487$	18.0000	−	10.3923i	0.815658	−	0.470920i	0.848917	+	0.528526i	$0.177255\pi$
$488$			10.8167i			0.489647i
$489$		0			0
$490$		0			0
$491$	2.00000	+	3.46410i	0.0902587	+	0.156333i	0.907620	−	0.419793i	$-0.137897\pi$
$491$	2.00000	+	3.46410i	0.0902587	+	0.156333i	−0.817361	+	0.576126i	$0.804564\pi$
$492$		0			0
$493$	−3.12250	+	5.40833i	−0.140630	+	0.243579i
$494$		−	45.0333i		−	2.02614i
$495$	18.7350	+	32.4500i	0.842075	+	1.45852i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	24.0000	−	13.8564i	1.07439	−	0.620298i	0.145011	−	0.989430i	$-0.453678\pi$
$499$	24.0000	−	13.8564i	1.07439	−	0.620298i	0.929377	+	0.369132i	$0.120345\pi$
$500$	−9.36750	+	5.40833i	−0.418927	+	0.241868i
$501$		0			0
$502$	18.7350	−	10.8167i	0.836184	−	0.482771i
$503$	−6.24500	+	10.8167i	−0.278451	+	0.482291i	−0.971000	−	0.239080i	$-0.923154\pi$
$503$	−6.24500	+	10.8167i	−0.278451	+	0.482291i	0.692549	+	0.721371i	$0.256488\pi$
$504$		0			0
$505$	−19.5000	+	11.2583i	−0.867739	+	0.500989i
$506$	−12.0000	−	20.7846i	−0.533465	−	0.923989i
$507$		0			0
$508$	9.00000	−	15.5885i	0.399310	−	0.691626i
$509$	3.12250	+	1.80278i	0.138402	+	0.0799066i	0.567602	−	0.823303i	$-0.307871\pi$
$509$	3.12250	+	1.80278i	0.138402	+	0.0799066i	−0.429200	+	0.903209i	$0.641204\pi$
$510$		0			0
$511$		0			0
$512$		−	8.66025i		−	0.382733i
$513$		0			0
$514$	28.1025	−	16.2250i	1.23955	−	0.715653i
$515$	−39.0000	−	22.5167i	−1.71855	−	0.992203i
$516$		0			0
$517$	12.4900	+	21.6333i	0.549309	+	0.951432i
$518$		0			0
$519$		0			0
$520$	−19.5000	−	11.2583i	−0.855132	−	0.493710i
$521$	−3.12250	+	5.40833i	−0.136799	+	0.236943i	−0.926283	−	0.376828i	$-0.877015\pi$
$521$	−3.12250	+	5.40833i	−0.136799	+	0.236943i	0.789484	+	0.613771i	$0.210348\pi$
$522$			5.19615i			0.227429i
$523$	12.4900	−	21.6333i	0.546149	−	0.945958i	−0.452384	−	0.891823i	$-0.649426\pi$
$523$	12.4900	−	21.6333i	0.546149	−	0.945958i	0.998534	−	0.0541354i	$-0.0172402\pi$
$524$	6.24500	−	10.8167i	0.272814	−	0.472528i
$525$		0			0
$526$	3.00000	+	1.73205i	0.130806	+	0.0755210i
$527$		0			0
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	15.6125	−	27.0416i	0.678163	−	1.17461i
$531$	−18.7350	+	10.8167i	−0.813029	+	0.469403i
$532$		0			0
$533$	−6.50000	+	11.2583i	−0.281546	+	0.487652i
$534$		0			0
$535$		−	7.21110i		−	0.311763i
$536$	24.0000			1.03664
$537$		0			0
$538$			43.2666i			1.86536i
$539$		0			0
$540$		0			0
$541$	4.50000	−	2.59808i	0.193470	−	0.111700i	−0.400136	−	0.916456i	$-0.631037\pi$
$541$	4.50000	−	2.59808i	0.193470	−	0.111700i	0.593606	+	0.804756i	$0.297704\pi$
$542$	6.24500	+	10.8167i	0.268246	+	0.464615i
$543$		0			0
$544$	−28.1025	−	16.2250i	−1.20488	−	0.695640i
$545$	24.9800			1.07003
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$	−7.50000	−	4.33013i	−0.320384	−	0.184974i
$549$	18.7350			0.799590
$550$	24.0000	+	41.5692i	1.02336	+	1.77252i
$551$	6.24500	−	3.60555i	0.266046	−	0.153602i
$552$		0			0
$553$		0			0
$554$		−	43.3013i		−	1.83969i
$555$		0			0
$556$	−12.4900			−0.529694
$557$		−	1.73205i		−	0.0733893i	−0.999327	−	0.0366947i	$-0.988317\pi$
$557$		−	1.73205i		−	0.0733893i	0.999327	−	0.0366947i	$-0.0116829\pi$
$558$		0			0
$559$		−	21.6333i		−	0.914991i
$560$		0			0
$561$		0			0
$562$	19.5000	−	33.7750i	0.822558	−	1.42471i
$563$	−6.24500	−	10.8167i	−0.263195	−	0.455868i	0.703894	−	0.710305i	$-0.251443\pi$
$563$	−6.24500	−	10.8167i	−0.263195	−	0.455868i	−0.967089	+	0.254437i	$0.918110\pi$
$564$		0			0
$565$		−	18.0278i		−	0.758433i
$566$	−18.7350	−	10.8167i	−0.787491	−	0.454658i
$567$		0			0
$568$	−9.00000	+	15.5885i	−0.377632	+	0.654077i
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	−12.0000	+	20.7846i	−0.502184	+	0.869809i	0.497812	+	0.867285i	$0.334137\pi$
$571$	−12.0000	+	20.7846i	−0.502184	+	0.869809i	−0.999997	+	0.00252413i	$0.999197\pi$
$572$	6.24500	−	10.8167i	0.261116	−	0.452267i
$573$		0			0
$574$		0			0
$575$	16.0000	+	27.7128i	0.667246	+	1.15570i
$576$	3.00000			0.125000
$577$	15.6125	+	9.01388i	0.649957	+	0.375253i	0.788440	−	0.615112i	$-0.210889\pi$
$577$	15.6125	+	9.01388i	0.649957	+	0.375253i	−0.138483	+	0.990365i	$0.544223\pi$
$578$	−33.0000	+	19.0526i	−1.37262	+	0.792482i
$579$		0			0
$580$			3.60555i			0.149712i
$581$		0			0
$582$		0			0
$583$	−15.0000	−	8.66025i	−0.621237	−	0.358671i
$584$	9.36750	−	16.2250i	0.387630	−	0.671394i
$585$	−19.5000	+	33.7750i	−0.806226	+	1.39642i
$586$	−15.6125	−	27.0416i	−0.644946	−	1.11708i
$587$	24.9800	−	14.4222i	1.03103	−	0.595268i	0.113754	−	0.993509i	$-0.463713\pi$
$587$	24.9800	−	14.4222i	1.03103	−	0.595268i	0.917281	+	0.398241i	$0.130379\pi$
$588$		0			0
$589$		0			0
$590$	−39.0000	+	22.5167i	−1.60560	+	0.926996i
$591$		0			0
$592$	7.50000	−	4.33013i	0.308248	−	0.177967i
$593$	−15.6125	+	9.01388i	−0.641128	+	0.370156i	−0.785049	−	0.619434i	$-0.787362\pi$
$593$	−15.6125	+	9.01388i	−0.641128	+	0.370156i	0.143921	+	0.989589i	$0.454029\pi$
$594$		0			0
$595$		0			0
$596$	13.5000	−	7.79423i	0.552982	−	0.319264i
$597$		0			0
$598$	12.4900	−	21.6333i	0.510754	−	0.884652i
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	−0.745613	−	0.666379i	$-0.767843\pi$
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	0.949908	+	0.312531i	$0.101177\pi$
$600$		0			0
$601$	21.8575	+	37.8583i	0.891586	+	1.54427i	0.837974	+	0.545710i	$0.183740\pi$
$601$	21.8575	+	37.8583i	0.891586	+	1.54427i	0.0536116	+	0.998562i	$0.482927\pi$
$602$		0			0
$603$		−	41.5692i		−	1.69283i
$604$		−	3.46410i		−	0.140952i
$605$	3.12250	−	1.80278i	0.126948	−	0.0732933i
$606$		0			0
$607$	37.4700			1.52086			0.760430	−	0.649420i	$-0.224988\pi$
$607$	37.4700			1.52086			0.760430	+	0.649420i	$0.224988\pi$
$608$	18.7350	+	32.4500i	0.759804	+	1.31602i
$609$		0			0
$610$	39.0000			1.57906
$611$	−13.0000	+	22.5167i	−0.525924	+	0.910927i
$612$	−9.36750	+	16.2250i	−0.378659	+	0.655856i
$613$		−	1.73205i		−	0.0699569i	−0.999388	−	0.0349784i	$-0.988864\pi$
$613$		−	1.73205i		−	0.0699569i	0.999388	−	0.0349784i	$-0.0111363\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.5000	+	11.2583i	0.785040	+	0.453243i	0.838214	−	0.545342i	$-0.183600\pi$
$617$	19.5000	+	11.2583i	0.785040	+	0.453243i	−0.0531732	+	0.998585i	$0.516934\pi$
$618$		0			0
$619$	31.2250	+	18.0278i	1.25504	+	0.724597i	0.972106	−	0.234543i	$-0.0753594\pi$
$619$	31.2250	+	18.0278i	1.25504	+	0.724597i	0.282933	+	0.959140i	$0.408693\pi$
$620$		0			0
$621$		0			0
$622$	37.4700	−	21.6333i	1.50241	−	0.867417i
$623$		0			0
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$	−6.24500			−0.249203
$629$		−	10.8167i		−	0.431288i
$630$		0			0
$631$	−12.0000	−	6.92820i	−0.477712	−	0.275807i	0.241750	−	0.970339i	$-0.422279\pi$
$631$	−12.0000	−	6.92820i	−0.477712	−	0.275807i	−0.719463	+	0.694531i	$0.755612\pi$
$632$	9.00000	−	5.19615i	0.358001	−	0.206692i
$633$		0			0
$634$	−27.0000			−1.07231
$635$	56.2050	+	32.4500i	2.23043	+	1.28774i
$636$		0			0
$637$		0			0
$638$	6.00000			0.237542
$639$	27.0000	+	15.5885i	1.06810	+	0.616670i
$640$	43.7150			1.72799
$641$	14.5000	+	25.1147i	0.572716	+	0.991972i	0.996286	+	0.0861092i	$0.0274434\pi$
$641$	14.5000	+	25.1147i	0.572716	+	0.991972i	−0.423570	+	0.905863i	$0.639223\pi$
$642$		0			0
$643$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$643$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$644$		0			0
$645$		0			0
$646$	78.0000			3.06887
$647$	−12.4900			−0.491032			−0.245516	−	0.969392i	$-0.578957\pi$
$647$	−12.4900			−0.491032			−0.245516	+	0.969392i	$0.578957\pi$
$648$		−	15.5885i		−	0.612372i
$649$	12.4900	+	21.6333i	0.490275	+	0.849182i
$650$	−24.9800	+	43.2666i	−0.979796	+	1.69706i
$651$		0			0
$652$	−9.00000	+	5.19615i	−0.352467	+	0.203497i
$653$	−19.0000	+	32.9090i	−0.743527	+	1.28783i	0.207352	+	0.978266i	$0.433515\pi$
$653$	−19.0000	+	32.9090i	−0.743527	+	1.28783i	−0.950880	+	0.309561i	$0.899818\pi$
$654$		0			0
$655$	39.0000	+	22.5167i	1.52386	+	0.879799i
$656$		−	18.0278i		−	0.703866i
$657$	−28.1025	−	16.2250i	−1.09638	−	0.632997i
$658$		0			0
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	−0.824439	−	0.565951i	$-0.808509\pi$
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	0.902348	+	0.431009i	$0.141842\pi$
$660$		0			0
$661$			10.8167i			0.420719i	0.977624	+	0.210360i	$0.0674635\pi$
$661$			10.8167i			0.420719i	−0.977624	+	0.210360i	$0.932537\pi$
$662$	9.00000	−	15.5885i	0.349795	−	0.605863i
$663$		0			0
$664$	12.4900			0.484706
$665$		0			0
$666$	−4.50000	−	7.79423i	−0.174371	−	0.302020i
$667$	4.00000			0.154881
$668$	6.24500	+	3.60555i	0.241626	+	0.139503i
$669$		0			0
$670$		−	86.5332i		−	3.34307i
$671$		−	21.6333i		−	0.835145i
$672$		0			0
$673$	−1.50000	−	2.59808i	−0.0578208	−	0.100148i	0.835666	−	0.549238i	$-0.185082\pi$
$673$	−1.50000	−	2.59808i	−0.0578208	−	0.100148i	−0.893487	+	0.449089i	$0.851749\pi$
$674$	16.5000	+	9.52628i	0.635556	+	0.366939i
$675$		0			0
$676$	13.0000			0.500000
$677$	−12.4900	−	21.6333i	−0.480030	−	0.831436i	0.519708	−	0.854344i	$-0.326041\pi$
$677$	−12.4900	−	21.6333i	−0.480030	−	0.831436i	−0.999738	+	0.0229084i	$0.992707\pi$
$678$		0			0
$679$		0			0
$680$	19.5000	−	33.7750i	0.747791	−	1.29521i
$681$		0			0
$682$		0			0
$683$	39.0000	−	22.5167i	1.49229	−	0.861576i	0.492333	−	0.870407i	$-0.336144\pi$
$683$	39.0000	−	22.5167i	1.49229	−	0.861576i	0.999961	+	0.00883113i	$0.00281107\pi$
$684$	18.7350	−	10.8167i	0.716350	−	0.413585i
$685$	15.6125	−	27.0416i	0.596523	−	1.03321i
$686$		0			0
$687$		0			0
$688$	15.0000	+	25.9808i	0.571870	+	0.990507i
$689$		−	18.0278i		−	0.686803i
$690$		0			0
$691$	24.9800	+	14.4222i	0.950284	+	0.548647i	0.893169	−	0.449721i	$-0.148477\pi$
$691$	24.9800	+	14.4222i	0.950284	+	0.548647i	0.0571146	+	0.998368i	$0.481810\pi$
$692$	−12.4900	−	21.6333i	−0.474798	−	0.822375i
$693$		0			0
$694$			48.4974i			1.84094i
$695$		−	45.0333i		−	1.70821i
$696$		0			0
$697$	−19.5000	−	11.2583i	−0.738615	−	0.426440i
$698$	37.4700			1.41826
$699$		0			0
$700$		0			0
$701$	14.0000			0.528773			0.264386	−	0.964417i	$-0.414831\pi$
$701$	14.0000			0.528773			0.264386	+	0.964417i	$0.414831\pi$
$702$		0			0
$703$	−6.24500	+	10.8167i	−0.235535	+	0.407958i
$704$		−	3.46410i		−	0.130558i
$705$		0			0
$706$	−21.8575	+	37.8583i	−0.822618	+	1.42482i
$707$		0			0
$708$		0			0
$709$		−	32.9090i		−	1.23592i	−0.786209	−	0.617961i	$-0.787959\pi$
$709$		−	32.9090i		−	1.23592i	0.786209	−	0.617961i	$-0.212041\pi$
$710$	56.2050	+	32.4500i	2.10934	+	1.21783i
$711$	−9.00000	−	15.5885i	−0.337526	−	0.584613i
$712$	−6.24500	+	10.8167i	−0.234041	+	0.405371i
$713$		0			0
$714$		0			0
$715$	39.0000	+	22.5167i	1.45852	+	0.842075i
$716$	8.00000	+	13.8564i	0.298974	+	0.517838i
$717$		0			0
$718$	−48.0000			−1.79134
$719$	−37.4700			−1.39739			−0.698697	−	0.715417i	$-0.746237\pi$
$719$	−37.4700			−1.39739			−0.698697	+	0.715417i	$0.746237\pi$
$720$		−	54.0833i		−	2.01556i
$721$		0			0
$722$	−49.5000	−	28.5788i	−1.84220	−	1.06359i
$723$		0			0
$724$	−3.12250	−	5.40833i	−0.116047	−	0.200999i
$725$	−8.00000			−0.297113
$726$		0			0
$727$	24.9800			0.926457			0.463228	−	0.886239i	$-0.346691\pi$
$727$	24.9800			0.926457			0.463228	+	0.886239i	$0.346691\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−58.5000	−	33.7750i	−2.16518	−	1.25007i
$731$	37.4700			1.38588
$732$		0			0
$733$	−9.36750	+	5.40833i	−0.345996	+	0.199761i	−0.662921	−	0.748690i	$-0.730683\pi$
$733$	−9.36750	+	5.40833i	−0.345996	+	0.199761i	0.316924	+	0.948451i	$0.397350\pi$
$734$	−37.4700	−	21.6333i	−1.38304	−	0.798500i
$735$		0			0
$736$			20.7846i			0.766131i
$737$	−48.0000			−1.76810
$738$	−18.7350			−0.689645
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$	−3.12250	−	5.40833i	−0.114785	−	0.198814i
$741$		0			0
$742$		0			0
$743$	−18.0000	+	10.3923i	−0.660356	+	0.381257i	−0.792413	−	0.609985i	$-0.791175\pi$
$743$	−18.0000	+	10.3923i	−0.660356	+	0.381257i	0.132057	+	0.991242i	$0.457842\pi$
$744$		0			0
$745$	28.1025	+	48.6749i	1.02960	+	1.78331i
$746$	22.5000	+	12.9904i	0.823784	+	0.475612i
$747$		−	21.6333i		−	0.791521i
$748$	18.7350	+	10.8167i	0.685019	+	0.395496i
$749$		0			0
$750$		0			0
$751$	−21.0000	+	36.3731i	−0.766301	+	1.32727i	0.173255	+	0.984877i	$0.444571\pi$
$751$	−21.0000	+	36.3731i	−0.766301	+	1.32727i	−0.939556	+	0.342395i	$0.888762\pi$
$752$		−	36.0555i		−	1.31481i
$753$		0			0
$754$	3.12250	+	5.40833i	0.113715	+	0.196960i
$755$	12.4900			0.454557
$756$		0			0
$757$	7.00000	+	12.1244i	0.254419	+	0.440667i	0.964738	−	0.263213i	$-0.0847823\pi$
$757$	7.00000	+	12.1244i	0.254419	+	0.440667i	−0.710318	+	0.703881i	$0.751449\pi$
$758$	36.0000			1.30758
$759$		0			0
$760$	−39.0000	+	22.5167i	−1.41468	+	0.816765i
$761$			36.0555i			1.30701i	0.756922	+	0.653506i	$0.226702\pi$
$761$			36.0555i			1.30701i	−0.756922	+	0.653506i	$0.773298\pi$
$762$		0			0
$763$		0			0
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$	−58.5000	−	33.7750i	−2.11507	−	1.22114i
$766$	−31.2250	+	54.0833i	−1.12820	+	1.95411i
$767$	−13.0000	+	22.5167i	−0.469403	+	0.813029i
$768$		0			0
$769$	18.7350	−	10.8167i	0.675601	−	0.390059i	−0.122594	−	0.992457i	$-0.539121\pi$
$769$	18.7350	−	10.8167i	0.675601	−	0.390059i	0.798196	+	0.602398i	$0.205788\pi$
$770$		0			0
$771$		0			0
$772$	−7.50000	+	4.33013i	−0.269931	+	0.155845i
$773$	−6.24500	+	3.60555i	−0.224617	+	0.129683i	−0.608086	−	0.793871i	$-0.708063\pi$
$773$	−6.24500	+	3.60555i	−0.224617	+	0.129683i	0.383469	+	0.923554i	$0.374729\pi$
$774$	27.0000	−	15.5885i	0.970495	−	0.560316i
$775$		0			0
$776$	−6.24500	+	10.8167i	−0.224182	+	0.388295i
$777$		0			0
$778$	−25.5000	+	14.7224i	−0.914219	+	0.527825i
$779$	13.0000	+	22.5167i	0.465773	+	0.806743i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$	37.4700	+	21.6333i	1.33992	+	0.773606i
$783$		0			0
$784$		0			0
$785$		−	22.5167i		−	0.803654i
$786$		0			0
$787$	12.4900	−	7.21110i	0.445220	−	0.257048i	−0.260589	−	0.965450i	$-0.583917\pi$
$787$	12.4900	−	7.21110i	0.445220	−	0.257048i	0.705809	+	0.708402i	$0.250583\pi$
$788$		0			0
$789$		0			0
$790$	−18.7350	−	32.4500i	−0.666561	−	1.15452i
$791$		0			0
$792$	−18.0000			−0.639602
$793$	19.5000	−	11.2583i	0.692465	−	0.399795i
$794$	−6.24500	+	10.8167i	−0.221627	+	0.383869i
$795$		0			0
$796$	−6.24500	+	10.8167i	−0.221348	+	0.383386i
$797$	−12.4900	+	21.6333i	−0.442418	+	0.766291i	−0.997868	−	0.0652589i	$-0.979213\pi$
$797$	−12.4900	+	21.6333i	−0.442418	+	0.766291i	0.555450	+	0.831550i	$0.312546\pi$
$798$		0			0
$799$	−39.0000	−	22.5167i	−1.37972	−	0.796582i
$800$		−	41.5692i		−	1.46969i
$801$	18.7350	+	10.8167i	0.661968	+	0.382188i
$802$	−7.50000	−	12.9904i	−0.264834	−	0.458706i
$803$	−18.7350	+	32.4500i	−0.661144	+	1.14513i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		−	10.8167i		−	0.380529i
$809$	−7.00000			−0.246107			−0.123053	−	0.992400i	$-0.539269\pi$
$809$	−7.00000			−0.246107			−0.123053	+	0.992400i	$0.539269\pi$
$810$	−56.2050			−1.97484
$811$			43.2666i			1.51930i	0.650334	+	0.759648i	$0.274629\pi$
$811$			43.2666i			1.51930i	−0.650334	+	0.759648i	$0.725371\pi$
$812$		0			0
$813$		0			0
$814$	−9.00000	+	5.19615i	−0.315450	+	0.182125i
$815$	−18.7350	−	32.4500i	−0.656258	−	1.13667i
$816$		0			0
$817$	−37.4700	−	21.6333i	−1.31091	−	0.756854i
$818$	43.7150			1.52846
$819$		0			0
$820$	−13.0000			−0.453980
$821$	12.0000	+	6.92820i	0.418803	+	0.241796i	0.694565	−	0.719430i	$-0.255597\pi$
$821$	12.0000	+	6.92820i	0.418803	+	0.241796i	−0.275762	+	0.961226i	$0.588930\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$	18.7350	−	10.8167i	0.652664	−	0.376816i
$825$		0			0
$826$		0			0
$827$		−	17.3205i		−	0.602293i	−0.953578	−	0.301147i	$-0.902631\pi$
$827$		−	17.3205i		−	0.602293i	0.953578	−	0.301147i	$-0.0973693\pi$
$828$	12.0000			0.417029
$829$	18.7350			0.650693			0.325347	−	0.945595i	$-0.394519\pi$
$829$	18.7350			0.650693			0.325347	+	0.945595i	$0.394519\pi$
$830$		−	45.0333i		−	1.56313i
$831$		0			0
$832$	3.12250	−	1.80278i	0.108253	−	0.0625000i
$833$		0			0
$834$		0			0
$835$	−13.0000	+	22.5167i	−0.449884	+	0.779221i
$836$	−12.4900	−	21.6333i	−0.431976	−	0.748204i
$837$		0			0
$838$		0			0
$839$	−43.7150	−	25.2389i	−1.50921	−	0.871342i	−0.999942	−	0.0107333i	$-0.996583\pi$
$839$	−43.7150	−	25.2389i	−1.50921	−	0.871342i	−0.509267	−	0.860609i	$-0.670083\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	19.5000	−	33.7750i	0.672014	−	1.16396i
$843$		0			0
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$			46.8722i			1.61245i
$846$	−37.4700			−1.28824
$847$		0			0
$848$	12.5000	+	21.6506i	0.429252	+	0.743486i
$849$		0			0
$850$	−74.9400	−	43.2666i	−2.57042	−	1.48403i
$851$	−6.00000	+	3.46410i	−0.205677	+	0.118748i
$852$		0			0
$853$		−	25.2389i		−	0.864162i	−0.901835	−	0.432081i	$-0.857779\pi$
$853$		−	25.2389i		−	0.864162i	0.901835	−	0.432081i	$-0.142221\pi$
$854$		0			0
$855$	39.0000	+	67.5500i	1.33377	+	2.31016i
$856$	3.00000	+	1.73205i	0.102538	+	0.0592003i
$857$	−15.6125	+	27.0416i	−0.533313	+	0.923725i	0.465930	+	0.884821i	$0.345720\pi$
$857$	−15.6125	+	27.0416i	−0.533313	+	0.923725i	−0.999243	+	0.0389032i	$0.987614\pi$
$858$		0			0
$859$	−24.9800	−	43.2666i	−0.852306	−	1.47624i	−0.879122	−	0.476597i	$-0.841870\pi$
$859$	−24.9800	−	43.2666i	−0.852306	−	1.47624i	0.0268153	−	0.999640i	$-0.491463\pi$
$860$	18.7350	−	10.8167i	0.638858	−	0.368845i
$861$		0			0
$862$	24.0000	−	41.5692i	0.817443	−	1.41585i
$863$	33.0000	−	19.0526i	1.12333	−	0.648557i	0.181083	−	0.983468i	$-0.442040\pi$
$863$	33.0000	−	19.0526i	1.12333	−	0.648557i	0.942250	+	0.334911i	$0.108706\pi$
$864$		0			0
$865$	78.0000	−	45.0333i	2.65208	−	1.53118i
$866$	−28.1025	+	16.2250i	−0.954962	+	0.551347i
$867$		0			0
$868$		0			0
$869$	−18.0000	+	10.3923i	−0.610608	+	0.352535i
$870$		0			0
$871$	−24.9800	−	43.2666i	−0.846415	−	1.46603i
$872$	−6.00000	+	10.3923i	−0.203186	+	0.351928i
$873$	18.7350	+	10.8167i	0.634083	+	0.366088i
$874$	−24.9800	−	43.2666i	−0.844961	−	1.46352i
$875$		0			0
$876$		0			0
$877$			46.7654i			1.57915i	0.613651	+	0.789577i	$0.289700\pi$
$877$			46.7654i			1.57915i	−0.613651	+	0.789577i	$0.710300\pi$
$878$	−18.7350	+	10.8167i	−0.632275	+	0.365044i
$879$		0			0
$880$	−62.4500			−2.10519
$881$	21.8575	+	37.8583i	0.736398	+	1.27548i	0.954107	+	0.299465i	$0.0968080\pi$
$881$	21.8575	+	37.8583i	0.736398	+	1.27548i	−0.217710	+	0.976014i	$0.569859\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$			22.5167i			0.757317i
$885$		0			0
$886$		−	27.7128i		−	0.931030i
$887$	−12.4900	+	21.6333i	−0.419373	+	0.726375i	−0.995877	−	0.0907193i	$-0.971083\pi$
$887$	−12.4900	+	21.6333i	−0.419373	+	0.726375i	0.576503	+	0.817095i	$0.304417\pi$
$888$		0			0
$889$		0			0
$890$	39.0000	+	22.5167i	1.30728	+	0.754760i
$891$			31.1769i			1.04447i
$892$	6.24500	+	3.60555i	0.209098	+	0.120723i
$893$	26.0000	+	45.0333i	0.870057	+	1.50698i
$894$		0			0
$895$	−49.9600	+	28.8444i	−1.66998	+	0.964162i
$896$		0			0
$897$		0			0
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$		0			0
$900$	−24.0000			−0.800000
$901$	31.2250			1.04026
$902$			21.6333i			0.720310i
$903$		0			0
$904$	7.50000	+	4.33013i	0.249446	+	0.144018i
$905$	19.5000	−	11.2583i	0.648202	−	0.374240i
$906$		0			0
$907$	−22.0000			−0.730498			−0.365249	−	0.930910i	$-0.619016\pi$
$907$	−22.0000			−0.730498			−0.365249	+	0.930910i	$0.619016\pi$
$908$	−12.4900	−	7.21110i	−0.414495	−	0.239309i
$909$	−18.7350			−0.621401
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$		0			0
$913$	−24.9800			−0.826717
$914$	34.5000	+	59.7558i	1.14116	+	1.97654i
$915$		0			0
$916$	−18.7350	−	10.8167i	−0.619022	−	0.357392i
$917$		0			0
$918$		0			0
$919$	−2.00000			−0.0659739			−0.0329870	−	0.999456i	$-0.510502\pi$
$919$	−2.00000			−0.0659739			−0.0329870	+	0.999456i	$0.510502\pi$
$920$	−24.9800			−0.823566
$921$		0			0
$922$	34.3475	+	59.4916i	1.13117	+	1.95925i
$923$	37.4700			1.23334
$924$		0			0
$925$	12.0000	−	6.92820i	0.394558	−	0.227798i
$926$	−9.00000	+	15.5885i	−0.295758	+	0.512268i
$927$	−18.7350	−	32.4500i	−0.615338	−	1.06580i
$928$	−4.50000	−	2.59808i	−0.147720	−	0.0852860i
$929$		−	25.2389i		−	0.828060i	−0.910263	−	0.414030i	$-0.864121\pi$
$929$		−	25.2389i		−	0.828060i	0.910263	−	0.414030i	$-0.135879\pi$
$930$		0			0
$931$		0			0
$932$	1.00000	−	1.73205i	0.0327561	−	0.0567352i
$933$		0			0
$934$		−	21.6333i		−	0.707863i
$935$	−39.0000	+	67.5500i	−1.27544	+	2.20912i
$936$	−9.36750	−	16.2250i	−0.306186	−	0.530330i
$937$	6.24500			0.204015			0.102008	−	0.994784i	$-0.467473\pi$
$937$	6.24500			0.204015			0.102008	+	0.994784i	$0.467473\pi$
$938$		0			0
$939$		0			0
$940$	−26.0000			−0.848026
$941$	−6.24500	−	3.60555i	−0.203581	−	0.117538i	0.394744	−	0.918791i	$-0.370833\pi$
$941$	−6.24500	−	3.60555i	−0.203581	−	0.117538i	−0.598325	+	0.801254i	$0.704167\pi$
$942$		0			0
$943$			14.4222i			0.469652i
$944$		−	36.0555i		−	1.17351i
$945$		0			0
$946$	−18.0000	−	31.1769i	−0.585230	−	1.01365i
$947$	18.0000	+	10.3923i	0.584921	+	0.337705i	0.763087	−	0.646296i	$-0.223683\pi$
$947$	18.0000	+	10.3923i	0.584921	+	0.337705i	−0.178165	+	0.984001i	$0.557016\pi$
$948$		0			0
$949$	−39.0000			−1.26599
$950$	49.9600	+	86.5332i	1.62092	+	2.80751i
$951$		0			0
$952$		0			0
$953$	5.00000	−	8.66025i	0.161966	−	0.280533i	−0.773608	−	0.633665i	$-0.781550\pi$
$953$	5.00000	−	8.66025i	0.161966	−	0.280533i	0.935574	+	0.353132i	$0.114883\pi$
$954$	22.5000	−	12.9904i	0.728464	−	0.420579i
$955$	−12.4900	+	7.21110i	−0.404167	+	0.233346i
$956$	−15.0000	+	8.66025i	−0.485135	+	0.280093i
$957$		0			0
$958$	−12.4900	+	21.6333i	−0.403533	+	0.698940i
$959$		0			0
$960$		0			0
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$	−9.36750	−	5.40833i	−0.302020	−	0.174371i
$963$	3.00000	−	5.19615i	0.0966736	−	0.167444i
$964$	−9.36750	−	5.40833i	−0.301707	−	0.174190i
$965$	−15.6125	−	27.0416i	−0.502584	−	0.870501i
$966$		0			0
$967$		−	48.4974i		−	1.55957i	−0.626046	−	0.779786i	$-0.715328\pi$
$967$		−	48.4974i		−	1.55957i	0.626046	−	0.779786i	$-0.284672\pi$
$968$			1.73205i			0.0556702i
$969$		0			0
$970$	39.0000	+	22.5167i	1.25221	+	0.722966i
$971$	12.4900			0.400823			0.200412	−	0.979712i	$-0.435772\pi$
$971$	12.4900			0.400823			0.200412	+	0.979712i	$0.435772\pi$
$972$		0			0
$973$		0			0
$974$	36.0000			1.15351
$975$		0			0
$976$	−15.6125	+	27.0416i	−0.499744	+	0.865582i
$977$			5.19615i			0.166240i	0.996540	+	0.0831198i	$0.0264884\pi$
$977$			5.19615i			0.166240i	−0.996540	+	0.0831198i	$0.973512\pi$
$978$		0			0
$979$	12.4900	−	21.6333i	0.399182	−	0.691404i
$980$		0			0
$981$	18.0000	+	10.3923i	0.574696	+	0.331801i
$982$			6.92820i			0.221088i
$983$	−43.7150	−	25.2389i	−1.39429	−	0.804995i	−0.400505	−	0.916295i	$-0.631165\pi$
$983$	−43.7150	−	25.2389i	−1.39429	−	0.804995i	−0.993787	+	0.111300i	$0.964499\pi$
$984$		0			0
$985$		0			0
$986$	−9.36750	+	5.40833i	−0.298322	+	0.172236i
$987$		0			0
$988$	13.0000	−	22.5167i	0.413585	−	0.716350i
$989$	−12.0000	−	20.7846i	−0.381578	−	0.660912i
$990$			64.8999i			2.06265i
$991$	−12.0000			−0.381193			−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000			−0.381193			−0.190596	+	0.981669i	$0.561042\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−39.0000	−	22.5167i	−1.23638	−	0.713826i
$996$		0			0
$997$	−15.6125	−	27.0416i	−0.494453	−	0.856417i	0.505527	−	0.862811i	$-0.331298\pi$
$997$	−15.6125	−	27.0416i	−0.494453	−	0.856417i	−0.999980	+	0.00639370i	$0.997965\pi$
$998$	48.0000			1.51941
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.f.361.1		4
7.2	even	3		637.2.k.e.569.2		4
7.3	odd	6		637.2.q.d.491.2	yes	4
7.4	even	3		637.2.q.d.491.1	✓	4
7.5	odd	6		637.2.k.e.569.1		4
7.6	odd	2	inner	637.2.u.f.361.2		4
13.4	even	6		637.2.k.e.459.2		4
91.4	even	6		637.2.q.d.589.2	yes	4
91.11	odd	12		8281.2.a.br.1.4		4
91.17	odd	6		637.2.q.d.589.1	yes	4
91.24	even	12		8281.2.a.br.1.3		4
91.30	even	6	inner	637.2.u.f.30.1		4
91.67	odd	12		8281.2.a.br.1.1		4
91.69	odd	6		637.2.k.e.459.1		4
91.80	even	12		8281.2.a.br.1.2		4
91.82	odd	6	inner	637.2.u.f.30.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.e.459.1		4	91.69	odd	6
637.2.k.e.459.2		4	13.4	even	6
637.2.k.e.569.1		4	7.5	odd	6
637.2.k.e.569.2		4	7.2	even	3
637.2.q.d.491.1	✓	4	7.4	even	3
637.2.q.d.491.2	yes	4	7.3	odd	6
637.2.q.d.589.1	yes	4	91.17	odd	6
637.2.q.d.589.2	yes	4	91.4	even	6
637.2.u.f.30.1		4	91.30	even	6	inner
637.2.u.f.30.2		4	91.82	odd	6	inner
637.2.u.f.361.1		4	1.1	even	1	trivial
637.2.u.f.361.2		4	7.6	odd	2	inner
8281.2.a.br.1.1		4	91.67	odd	12
8281.2.a.br.1.2		4	91.80	even	12
8281.2.a.br.1.3		4	91.24	even	12
8281.2.a.br.1.4		4	91.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-3.12250 + 1.80278i) q^{5} -1.73205i q^{8} -3.00000 q^{9} -6.24500 q^{10} +3.46410i q^{11} +(-3.12250 + 1.80278i) q^{13} +(2.50000 - 4.33013i) q^{16} +(-3.12250 - 5.40833i) q^{17} +(-4.50000 - 2.59808i) q^{18} +7.21110i q^{19} +(-3.12250 - 1.80278i) q^{20} +(-3.00000 + 5.19615i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(4.00000 - 6.92820i) q^{25} -6.24500 q^{26} +(-0.500000 - 0.866025i) q^{29} +(4.50000 - 2.59808i) q^{32} -10.8167i q^{34} +(-1.50000 - 2.59808i) q^{36} +(1.50000 + 0.866025i) q^{37} +(-6.24500 + 10.8167i) q^{38} +(3.12250 + 5.40833i) q^{40} +(3.12250 - 1.80278i) q^{41} +(-3.00000 + 5.19615i) q^{43} +(-3.00000 + 1.73205i) q^{44} +(9.36750 - 5.40833i) q^{45} +(-6.00000 + 3.46410i) q^{46} +(6.24500 - 3.60555i) q^{47} +(12.0000 - 6.92820i) q^{50} +(-3.12250 - 1.80278i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-6.24500 - 10.8167i) q^{55} -1.73205i q^{58} +(6.24500 - 3.60555i) q^{59} -6.24500 q^{61} -1.00000 q^{64} +(6.50000 - 11.2583i) q^{65} +13.8564i q^{67} +(3.12250 - 5.40833i) q^{68} +(-9.00000 - 5.19615i) q^{71} +5.19615i q^{72} +(9.36750 + 5.40833i) q^{73} +(1.50000 + 2.59808i) q^{74} +(-6.24500 + 3.60555i) q^{76} +(3.00000 + 5.19615i) q^{79} +18.0278i q^{80} +9.00000 q^{81} +6.24500 q^{82} +7.21110i q^{83} +(19.5000 + 11.2583i) q^{85} +(-9.00000 + 5.19615i) q^{86} +6.00000 q^{88} +(-6.24500 - 3.60555i) q^{89} +18.7350 q^{90} -4.00000 q^{92} +12.4900 q^{94} +(-13.0000 - 22.5167i) q^{95} +(-6.24500 - 3.60555i) q^{97} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 2 q^{4} - 12 q^{9} + 10 q^{16} - 18 q^{18} - 12 q^{22} - 8 q^{23} + 16 q^{25} - 2 q^{29} + 18 q^{32} - 6 q^{36} + 6 q^{37} - 12 q^{43} - 12 q^{44} - 24 q^{46} + 48 q^{50} - 10 q^{53} - 4 q^{64}+ \cdots - 52 q^{95}+O(q^{100}) \) 4 * q + 6 * q^2 + 2 * q^4 - 12 * q^9 + 10 * q^16 - 18 * q^18 - 12 * q^22 - 8 * q^23 + 16 * q^25 - 2 * q^29 + 18 * q^32 - 6 * q^36 + 6 * q^37 - 12 * q^43 - 12 * q^44 - 24 * q^46 + 48 * q^50 - 10 * q^53 - 4 * q^64 + 26 * q^65 - 36 * q^71 + 6 * q^74 + 12 * q^79 + 36 * q^81 + 78 * q^85 - 36 * q^86 + 24 * q^88 - 16 * q^92 - 52 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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