LMFDB - Embedded newform 637.2.q.d.589.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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			589.2
Root			$-3.12250 + 1.80278i$ of defining polynomial
Character	$\chi$	$=$	637.589
Dual form			637.2.q.d.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.60555i q^{5} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.60555i q^{5} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(3.12250 - 5.40833i) q^{10} +(3.00000 + 1.73205i) q^{11} +(-3.12250 - 1.80278i) q^{13} +(2.50000 - 4.33013i) q^{16} +(-3.12250 - 5.40833i) q^{17} -5.19615i q^{18} +(-6.24500 + 3.60555i) q^{19} +(-3.12250 + 1.80278i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-2.00000 + 3.46410i) q^{23} -8.00000 q^{25} +(3.12250 + 5.40833i) q^{26} +(-0.500000 + 0.866025i) q^{29} +(-4.50000 + 2.59808i) q^{32} +10.8167i q^{34} +(-1.50000 + 2.59808i) q^{36} +(-1.50000 - 0.866025i) q^{37} +12.4900 q^{38} -6.24500 q^{40} +(3.12250 + 1.80278i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.46410i q^{44} +(-9.36750 + 5.40833i) q^{45} +(6.00000 - 3.46410i) q^{46} -7.21110i q^{47} +(12.0000 + 6.92820i) q^{50} -3.60555i q^{52} +5.00000 q^{53} +(-6.24500 + 10.8167i) q^{55} +(1.50000 - 0.866025i) q^{58} +(-6.24500 + 3.60555i) q^{59} +(3.12250 + 5.40833i) q^{61} -1.00000 q^{64} +(6.50000 - 11.2583i) q^{65} +(12.0000 + 6.92820i) q^{67} +(3.12250 - 5.40833i) q^{68} +(-9.00000 + 5.19615i) q^{71} +(-4.50000 + 2.59808i) q^{72} +10.8167i q^{73} +(1.50000 + 2.59808i) q^{74} +(-6.24500 - 3.60555i) q^{76} -6.00000 q^{79} +(15.6125 + 9.01388i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.12250 - 5.40833i) q^{82} -7.21110i q^{83} +(19.5000 - 11.2583i) q^{85} +10.3923i q^{86} +(-3.00000 + 5.19615i) q^{88} +(6.24500 + 3.60555i) q^{89} +18.7350 q^{90} -4.00000 q^{92} +(-6.24500 + 10.8167i) q^{94} +(-13.0000 - 22.5167i) q^{95} +(-6.24500 + 3.60555i) q^{97} +10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} + 2 q^{4} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 + 2 * q^4 + 6 * q^9	$ 4 q - 6 q^{2} + 2 q^{4} + 6 q^{9} + 12 q^{11} + 10 q^{16} - 12 q^{22} - 8 q^{23} - 32 q^{25} - 2 q^{29} - 18 q^{32} - 6 q^{36} - 6 q^{37} - 12 q^{43} + 24 q^{46} + 48 q^{50} + 20 q^{53} + 6 q^{58} - 4 q^{64} + 26 q^{65} + 48 q^{67} - 36 q^{71} - 18 q^{72} + 6 q^{74} - 24 q^{79} - 18 q^{81} + 78 q^{85} - 12 q^{88} - 16 q^{92} - 52 q^{95}+O(q^{100}) $ 4 * q - 6 * q^2 + 2 * q^4 + 6 * q^9 + 12 * q^11 + 10 * q^16 - 12 * q^22 - 8 * q^23 - 32 * q^25 - 2 * q^29 - 18 * q^32 - 6 * q^36 - 6 * q^37 - 12 * q^43 + 24 * q^46 + 48 * q^50 + 20 * q^53 + 6 * q^58 - 4 * q^64 + 26 * q^65 + 48 * q^67 - 36 * q^71 - 18 * q^72 + 6 * q^74 - 24 * q^79 - 18 * q^81 + 78 * q^85 - 12 * q^88 - 16 * q^92 - 52 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.925615	+	0.378467i	$0.876451\pi$
$3$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			3.60555i			1.61245i	0.591608	+	0.806226i	$0.298493\pi$
$5$			3.60555i			1.61245i	−0.591608	+	0.806226i	$0.701507\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	3.12250	−	5.40833i	0.987421	−	1.71026i
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$		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	$-0.440157\pi$
$18$		−	5.19615i		−	1.22474i
$19$	−6.24500	+	3.60555i	−1.43270	+	0.827170i	−0.997326	−	0.0730792i	$-0.976717\pi$
$19$	−6.24500	+	3.60555i	−1.43270	+	0.827170i	−0.435375	+	0.900249i	$0.643384\pi$
$20$	−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
$25$	−8.00000			−1.60000
$26$	3.12250	+	5.40833i	0.612372	+	1.06066i
$27$		0			0
$28$		0			0
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	−0.908708	−	0.417432i	$-0.862930\pi$
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	0.815861	+	0.578249i	$0.196264\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−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	0.371607	−	0.928390i	$-0.378807\pi$
$37$	−1.50000	−	0.866025i	−0.246598	−	0.142374i	−0.618206	+	0.786016i	$0.712140\pi$
$38$	12.4900			2.02614
$39$		0			0
$40$	−6.24500			−0.987421
$41$	3.12250	+	1.80278i	0.487652	+	0.281546i	0.723600	−	0.690220i	$-0.242486\pi$
$41$	3.12250	+	1.80278i	0.487652	+	0.281546i	−0.235948	+	0.971766i	$0.575819\pi$
$42$		0			0
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$			3.46410i			0.522233i
$45$	−9.36750	+	5.40833i	−1.39642	+	0.806226i
$46$	6.00000	−	3.46410i	0.884652	−	0.510754i
$47$		−	7.21110i		−	1.05185i	−0.850532	−	0.525924i	$-0.823720\pi$
$47$		−	7.21110i		−	1.05185i	0.850532	−	0.525924i	$-0.176280\pi$
$48$		0			0
$49$		0			0
$50$	12.0000	+	6.92820i	1.69706	+	0.979796i
$51$		0			0
$52$		−	3.60555i		−	0.500000i
$53$	5.00000			0.686803			0.343401	−	0.939189i	$-0.388421\pi$
$53$	5.00000			0.686803			0.343401	+	0.939189i	$0.388421\pi$
$54$		0			0
$55$	−6.24500	+	10.8167i	−0.842075	+	1.45852i
$56$		0			0
$57$		0			0
$58$	1.50000	−	0.866025i	0.196960	−	0.113715i
$59$	−6.24500	+	3.60555i	−0.813029	+	0.469403i	−0.848007	−	0.529985i	$-0.822197\pi$
$59$	−6.24500	+	3.60555i	−0.813029	+	0.469403i	0.0349773	+	0.999388i	$0.488864\pi$
$60$		0			0
$61$	3.12250	+	5.40833i	0.399795	+	0.692465i	0.993700	−	0.112070i	$-0.0357480\pi$
$61$	3.12250	+	5.40833i	0.399795	+	0.692465i	−0.593905	+	0.804535i	$0.702415\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.50000	−	11.2583i	0.806226	−	1.39642i
$66$		0			0
$67$	12.0000	+	6.92820i	1.46603	+	0.846415i	0.999279	−	0.0379722i	$-0.0120898\pi$
$67$	12.0000	+	6.92820i	1.46603	+	0.846415i	0.466755	+	0.884387i	$0.345423\pi$
$68$	3.12250	−	5.40833i	0.378659	−	0.655856i
$69$		0			0
$70$		0			0
$71$	−9.00000	+	5.19615i	−1.06810	+	0.616670i	−0.927663	−	0.373419i	$-0.878185\pi$
$71$	−9.00000	+	5.19615i	−1.06810	+	0.616670i	−0.140441	+	0.990089i	$0.544852\pi$
$72$	−4.50000	+	2.59808i	−0.530330	+	0.306186i
$73$			10.8167i			1.26599i	0.774154	+	0.632997i	$0.218175\pi$
$73$			10.8167i			1.26599i	−0.774154	+	0.632997i	$0.781825\pi$
$74$	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
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$	15.6125	+	9.01388i	1.74553	+	1.00778i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.12250	−	5.40833i	−0.344822	−	0.597250i
$83$		−	7.21110i		−	0.791521i	−0.918354	−	0.395761i	$-0.870481\pi$
$83$		−	7.21110i		−	0.791521i	0.918354	−	0.395761i	$-0.129519\pi$
$84$		0			0
$85$	19.5000	−	11.2583i	2.11507	−	1.22114i
$86$			10.3923i			1.12063i
$87$		0			0
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	6.24500	+	3.60555i	0.661968	+	0.382188i	0.793027	−	0.609187i	$-0.208504\pi$
$89$	6.24500	+	3.60555i	0.661968	+	0.382188i	−0.131058	+	0.991375i	$0.541837\pi$
$90$	18.7350			1.97484
$91$		0			0
$92$	−4.00000			−0.417029
$93$		0			0
$94$	−6.24500	+	10.8167i	−0.644122	+	1.11565i
$95$	−13.0000	−	22.5167i	−1.33377	−	2.31016i
$96$		0			0
$97$	−6.24500	+	3.60555i	−0.634083	+	0.366088i	−0.782332	−	0.622862i	$-0.785970\pi$
$97$	−6.24500	+	3.60555i	−0.634083	+	0.366088i	0.148248	+	0.988950i	$0.452637\pi$
$98$		0			0
$99$			10.3923i			1.04447i
$100$	−4.00000	−	6.92820i	−0.400000	−	0.692820i
$101$	−3.12250	+	5.40833i	−0.310700	+	0.538149i	−0.978514	−	0.206180i	$-0.933897\pi$
$101$	−3.12250	+	5.40833i	−0.310700	+	0.538149i	0.667814	+	0.744328i	$0.267230\pi$
$102$		0			0
$103$	−12.4900			−1.23068			−0.615338	−	0.788263i	$-0.710980\pi$
$103$	−12.4900			−1.23068			−0.615338	+	0.788263i	$0.710980\pi$
$104$	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
$109$		−	6.92820i		−	0.663602i	−0.943349	−	0.331801i	$-0.892344\pi$
$109$		−	6.92820i		−	0.663602i	0.943349	−	0.331801i	$-0.107656\pi$
$110$	18.7350	−	10.8167i	1.78631	−	1.03133i
$111$		0			0
$112$		0			0
$113$	−2.50000	−	4.33013i	−0.235180	−	0.407344i	0.724145	−	0.689648i	$-0.242235\pi$
$113$	−2.50000	−	4.33013i	−0.235180	−	0.407344i	−0.959325	+	0.282304i	$0.908901\pi$
$114$		0			0
$115$	−12.4900	−	7.21110i	−1.16470	−	0.672439i
$116$	−1.00000			−0.0928477
$117$		−	10.8167i		−	1.00000i
$118$	12.4900			1.14980
$119$		0			0
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		−	10.8167i		−	0.979294i
$123$		0			0
$124$		0			0
$125$		−	10.8167i		−	0.967471i
$126$		0			0
$127$	−9.00000	+	15.5885i	−0.798621	+	1.38325i	0.121894	+	0.992543i	$0.461103\pi$
$127$	−9.00000	+	15.5885i	−0.798621	+	1.38325i	−0.920514	+	0.390709i	$0.872230\pi$
$128$	10.5000	+	6.06218i	0.928078	+	0.535826i
$129$		0			0
$130$	−19.5000	+	11.2583i	−1.71026	+	0.987421i
$131$	12.4900			1.09126			0.545628	−	0.838027i	$-0.316291\pi$
$131$	12.4900			1.09126			0.545628	+	0.838027i	$0.316291\pi$
$132$		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	−0.144142	−	0.989557i	$-0.546042\pi$
$137$	7.50000	−	4.33013i	0.640768	−	0.369948i	0.784910	+	0.619609i	$0.212709\pi$
$138$		0			0
$139$	−6.24500	−	10.8167i	−0.529694	−	0.917457i	−0.999400	−	0.0346338i	$-0.988974\pi$
$139$	−6.24500	−	10.8167i	−0.529694	−	0.917457i	0.469706	−	0.882823i	$-0.344360\pi$
$140$		0			0
$141$		0			0
$142$	18.0000			1.51053
$143$	−6.24500	−	10.8167i	−0.522233	−	0.904534i
$144$	15.0000			1.25000
$145$	−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
$149$	13.5000	−	7.79423i	1.10596	−	0.638528i	0.168182	−	0.985756i	$-0.446210\pi$
$149$	13.5000	−	7.79423i	1.10596	−	0.638528i	0.937781	+	0.347228i	$0.112877\pi$
$150$		0			0
$151$		−	3.46410i		−	0.281905i	−0.990016	−	0.140952i	$-0.954984\pi$
$151$		−	3.46410i		−	0.281905i	0.990016	−	0.140952i	$-0.0450164\pi$
$152$	−6.24500	−	10.8167i	−0.506536	−	0.877346i
$153$	9.36750	−	16.2250i	0.757317	−	1.31171i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.24500			0.498405			0.249203	−	0.968451i	$-0.419832\pi$
$157$	6.24500			0.498405			0.249203	+	0.968451i	$0.419832\pi$
$158$	9.00000	+	5.19615i	0.716002	+	0.413384i
$159$		0			0
$160$	−9.36750	−	16.2250i	−0.740566	−	1.28270i
$161$		0			0
$162$	13.5000	−	7.79423i	1.06066	−	0.612372i
$163$	−9.00000	+	5.19615i	−0.704934	+	0.406994i	−0.809183	−	0.587557i	$-0.800090\pi$
$163$	−9.00000	+	5.19615i	−0.704934	+	0.406994i	0.104248	+	0.994551i	$0.466756\pi$
$164$			3.60555i			0.281546i
$165$		0			0
$166$	−6.24500	+	10.8167i	−0.484706	+	0.839535i
$167$	6.24500	+	3.60555i	0.483252	+	0.279006i	0.721771	−	0.692132i	$-0.243328\pi$
$167$	6.24500	+	3.60555i	0.483252	+	0.279006i	−0.238518	+	0.971138i	$0.576662\pi$
$168$		0			0
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$	−39.0000			−2.99116
$171$	−18.7350	−	10.8167i	−1.43270	−	0.827170i
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	12.4900	+	21.6333i	0.949597	+	1.64475i	0.746275	+	0.665638i	$0.231840\pi$
$173$	12.4900	+	21.6333i	0.949597	+	1.64475i	0.203322	+	0.979112i	$0.434826\pi$
$174$		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
$179$	−8.00000	+	13.8564i	−0.597948	+	1.03568i	0.395175	+	0.918606i	$0.370684\pi$
$179$	−8.00000	+	13.8564i	−0.597948	+	1.03568i	−0.993124	+	0.117071i	$0.962650\pi$
$180$	−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
$185$	3.12250	−	5.40833i	0.229571	−	0.397628i
$186$		0			0
$187$		−	21.6333i		−	1.58198i
$188$	6.24500	−	3.60555i	0.455463	−	0.262962i
$189$		0			0
$190$			45.0333i			3.26706i
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	7.50000	+	4.33013i	0.539862	+	0.311689i	0.745023	−	0.667039i	$-0.232439\pi$
$193$	7.50000	+	4.33013i	0.539862	+	0.311689i	−0.205161	+	0.978728i	$0.565772\pi$
$194$	12.4900			0.896729
$195$		0			0
$196$		0			0
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$	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	$0.687355\pi$
$200$		−	13.8564i		−	0.979796i
$201$		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
$206$	18.7350	+	10.8167i	1.30533	+	0.753632i
$207$	−12.0000			−0.834058
$208$	−15.6125	+	9.01388i	−1.08253	+	0.625000i
$209$	−24.9800			−1.72790
$210$		0			0
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$	2.50000	+	4.33013i	0.171701	+	0.297394i
$213$		0			0
$214$	3.00000	−	1.73205i	0.205076	−	0.118401i
$215$	18.7350	−	10.8167i	1.27772	−	0.737690i
$216$		0			0
$217$		0			0
$218$	−6.00000	+	10.3923i	−0.406371	+	0.703856i
$219$		0			0
$220$	−12.4900			−0.842075
$221$			22.5167i			1.51463i
$222$		0			0
$223$	6.24500	+	3.60555i	0.418196	+	0.241446i	0.694305	−	0.719681i	$-0.255712\pi$
$223$	6.24500	+	3.60555i	0.418196	+	0.241446i	−0.276109	+	0.961126i	$0.589045\pi$
$224$		0			0
$225$	−12.0000	−	20.7846i	−0.800000	−	1.38564i
$226$			8.66025i			0.576072i
$227$	12.4900	−	7.21110i	0.828990	−	0.478618i	−0.0245166	−	0.999699i	$-0.507805\pi$
$227$	12.4900	−	7.21110i	0.828990	−	0.478618i	0.853507	+	0.521082i	$0.174471\pi$
$228$		0			0
$229$			21.6333i			1.42957i	0.699345	+	0.714785i	$0.253475\pi$
$229$			21.6333i			1.42957i	−0.699345	+	0.714785i	$0.746525\pi$
$230$	12.4900	+	21.6333i	0.823566	+	1.42646i
$231$		0			0
$232$	−1.50000	−	0.866025i	−0.0984798	−	0.0568574i
$233$	2.00000			0.131024			0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000			0.131024			0.0655122	+	0.997852i	$0.479132\pi$
$234$	−9.36750	+	16.2250i	−0.612372	+	1.06066i
$235$	26.0000			1.69605
$236$	−6.24500	−	3.60555i	−0.406515	−	0.234701i
$237$		0			0
$238$		0			0
$239$		−	17.3205i		−	1.12037i	−0.828367	−	0.560185i	$-0.810730\pi$
$239$		−	17.3205i		−	1.12037i	0.828367	−	0.560185i	$-0.189270\pi$
$240$		0			0
$241$	9.36750	−	5.40833i	0.603414	−	0.348381i	−0.166970	−	0.985962i	$-0.553398\pi$
$241$	9.36750	−	5.40833i	0.603414	−	0.348381i	0.770383	+	0.637581i	$0.220065\pi$
$242$		−	1.73205i		−	0.111340i
$243$		0			0
$244$	−3.12250	+	5.40833i	−0.199898	+	0.346233i
$245$		0			0
$246$		0			0
$247$	26.0000			1.65434
$248$		0			0
$249$		0			0
$250$	−9.36750	+	16.2250i	−0.592453	+	1.02616i
$251$	6.24500	+	10.8167i	0.394181	+	0.682741i	0.992996	−	0.118146i	$-0.0376950\pi$
$251$	6.24500	+	10.8167i	0.394181	+	0.682741i	−0.598815	+	0.800887i	$0.704362\pi$
$252$		0			0
$253$	−12.0000	+	6.92820i	−0.754434	+	0.435572i
$254$	27.0000	−	15.5885i	1.69413	−	0.978107i
$255$		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
$261$	−3.00000			−0.185695
$262$	−18.7350	−	10.8167i	−1.15745	−	0.668255i
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	−0.895209	−	0.445647i	$-0.852974\pi$
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	0.833546	+	0.552450i	$0.186307\pi$
$264$		0			0
$265$			18.0278i			1.10744i
$266$		0			0
$267$		0			0
$268$			13.8564i			0.846415i
$269$	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	0.298182	−	0.954509i	$-0.403620\pi$
$271$	−6.24500	−	3.60555i	−0.379357	−	0.219022i	−0.677538	+	0.735487i	$0.736953\pi$
$272$	−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	$-0.437120\pi$
$278$			21.6333i			1.29748i
$279$		0			0
$280$		0			0
$281$			22.5167i			1.34323i	0.740900	+	0.671616i	$0.234399\pi$
$281$			22.5167i			1.34323i	−0.740900	+	0.671616i	$0.765601\pi$
$282$		0			0
$283$	6.24500	−	10.8167i	0.371227	−	0.642983i	−0.618528	−	0.785763i	$-0.712271\pi$
$283$	6.24500	−	10.8167i	0.371227	−	0.642983i	0.989755	+	0.142779i	$0.0456040\pi$
$284$	−9.00000	−	5.19615i	−0.534052	−	0.308335i
$285$		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
$292$	−9.36750	+	5.40833i	−0.548191	+	0.316498i
$293$	−15.6125	+	9.01388i	−0.912092	+	0.526596i	−0.881104	−	0.472923i	$-0.843199\pi$
$293$	−15.6125	+	9.01388i	−0.912092	+	0.526596i	−0.0309881	+	0.999520i	$0.509865\pi$
$294$		0			0
$295$	−13.0000	−	22.5167i	−0.756889	−	1.31097i
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$		0			0
$298$	−27.0000			−1.56407
$299$	12.4900	−	7.21110i	0.722315	−	0.417029i
$300$		0			0
$301$		0			0
$302$	−3.00000	+	5.19615i	−0.172631	+	0.299005i
$303$		0			0
$304$			36.0555i			2.06793i
$305$	−19.5000	+	11.2583i	−1.11657	+	0.644650i
$306$	−28.1025	+	16.2250i	−1.60651	+	0.927520i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−24.9800			−1.41649			−0.708243	−	0.705969i	$-0.750512\pi$
$311$	−24.9800			−1.41649			−0.708243	+	0.705969i	$0.750512\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$	−9.36750	−	5.40833i	−0.528638	−	0.305210i
$315$		0			0
$316$	−3.00000	−	5.19615i	−0.168763	−	0.292306i
$317$			15.5885i			0.875535i	0.899088	+	0.437767i	$0.144231\pi$
$317$			15.5885i			0.875535i	−0.899088	+	0.437767i	$0.855769\pi$
$318$		0			0
$319$	−3.00000	+	1.73205i	−0.167968	+	0.0969762i
$320$		−	3.60555i		−	0.201556i
$321$		0			0
$322$		0			0
$323$	39.0000	+	22.5167i	2.17002	+	1.25286i
$324$	−9.00000			−0.500000
$325$	24.9800	+	14.4222i	1.38564	+	0.800000i
$326$	18.0000			0.996928
$327$		0			0
$328$	−3.12250	+	5.40833i	−0.172411	+	0.298625i
$329$		0			0
$330$		0			0
$331$	9.00000	−	5.19615i	0.494685	−	0.285606i	−0.231831	−	0.972756i	$-0.574472\pi$
$331$	9.00000	−	5.19615i	0.494685	−	0.285606i	0.726516	+	0.687150i	$0.241138\pi$
$332$	6.24500	−	3.60555i	0.342739	−	0.197880i
$333$		−	5.19615i		−	0.284747i
$334$	−6.24500	−	10.8167i	−0.341711	−	0.591861i
$335$	−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	$0.403145\pi$
$338$		−	22.5167i		−	1.22474i
$339$		0			0
$340$	19.5000	+	11.2583i	1.05754	+	0.610569i
$341$		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
$346$		−	43.2666i		−	2.32603i
$347$	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	0.909094	−	0.416592i	$-0.136776\pi$
$349$	18.7350	+	10.8167i	1.00286	+	0.579002i	0.0937676	+	0.995594i	$0.470109\pi$
$350$		0			0
$351$		0			0
$352$	−18.0000			−0.959403
$353$	21.8575	+	12.6194i	1.16336	+	0.671664i	0.952106	−	0.305767i	$-0.0989130\pi$
$353$	21.8575	+	12.6194i	1.16336	+	0.671664i	0.211251	+	0.977432i	$0.432246\pi$
$354$		0			0
$355$	−18.7350	−	32.4500i	−0.994350	−	1.72227i
$356$			7.21110i			0.382188i
$357$		0			0
$358$	24.0000	−	13.8564i	1.26844	−	0.732334i
$359$			27.7128i			1.46263i	0.682042	+	0.731313i	$0.261092\pi$
$359$			27.7128i			1.46263i	−0.682042	+	0.731313i	$0.738908\pi$
$360$	−9.36750	−	16.2250i	−0.493710	−	0.855132i
$361$	16.5000	−	28.5788i	0.868421	−	1.50415i
$362$	9.36750	+	5.40833i	0.492345	+	0.284255i
$363$		0			0
$364$		0			0
$365$	−39.0000			−2.04135
$366$		0			0
$367$	12.4900	−	21.6333i	0.651972	−	1.12925i	−0.330671	−	0.943746i	$-0.607275\pi$
$367$	12.4900	−	21.6333i	0.651972	−	1.12925i	0.982644	−	0.185503i	$-0.0593916\pi$
$368$	10.0000	+	17.3205i	0.521286	+	0.902894i
$369$			10.8167i			0.563093i
$370$	−9.36750	+	5.40833i	−0.486993	+	0.281166i
$371$		0			0
$372$		0			0
$373$	−7.50000	−	12.9904i	−0.388335	−	0.672616i	0.603890	−	0.797067i	$-0.293616\pi$
$373$	−7.50000	−	12.9904i	−0.388335	−	0.672616i	−0.992226	+	0.124451i	$0.960283\pi$
$374$	−18.7350	+	32.4500i	−0.968763	+	1.67795i
$375$		0			0
$376$	12.4900			0.644122
$377$	3.12250	−	1.80278i	0.160817	−	0.0928477i
$378$		0			0
$379$	18.0000	+	10.3923i	0.924598	+	0.533817i	0.885099	−	0.465403i	$-0.154091\pi$
$379$	18.0000	+	10.3923i	0.924598	+	0.533817i	0.0394989	+	0.999220i	$0.487424\pi$
$380$	13.0000	−	22.5167i	0.666886	−	1.15508i
$381$		0			0
$382$			6.92820i			0.354478i
$383$	−31.2250	+	18.0278i	−1.59552	+	0.921175i	−0.603187	+	0.797600i	$0.706103\pi$
$383$	−31.2250	+	18.0278i	−1.59552	+	0.921175i	−0.992335	+	0.123576i	$0.960564\pi$
$384$		0			0
$385$		0			0
$386$	−7.50000	−	12.9904i	−0.381740	−	0.661193i
$387$	9.00000	−	15.5885i	0.457496	−	0.792406i
$388$	−6.24500	−	3.60555i	−0.317042	−	0.183044i
$389$	17.0000			0.861934			0.430967	−	0.902368i	$-0.358172\pi$
$389$	17.0000			0.861934			0.430967	+	0.902368i	$0.358172\pi$
$390$		0			0
$391$	24.9800			1.26329
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	21.6333i		−	1.08849i
$396$	−9.00000	+	5.19615i	−0.452267	+	0.261116i
$397$	−6.24500	+	3.60555i	−0.313427	+	0.180957i	−0.648459	−	0.761249i	$-0.724586\pi$
$397$	−6.24500	+	3.60555i	−0.313427	+	0.180957i	0.335032	+	0.942207i	$0.391253\pi$
$398$		−	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	0.675437	−	0.737418i	$-0.263955\pi$
$401$	7.50000	+	4.33013i	0.374532	+	0.216236i	−0.300904	+	0.953654i	$0.597289\pi$
$402$		0			0
$403$		0			0
$404$	−6.24500			−0.310700
$405$	−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	−0.931108	−	0.364744i	$-0.881156\pi$
$409$	−21.8575	+	12.6194i	−1.08078	+	0.623991i	−0.149676	+	0.988735i	$0.547823\pi$
$410$	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
$415$	26.0000			1.27629
$416$	18.7350			0.918559
$417$		0			0
$418$	37.4700	+	21.6333i	1.83272	+	1.05812i
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$			22.5167i			1.09739i	0.836021	+	0.548697i	$0.184876\pi$
$421$			22.5167i			1.09739i	−0.836021	+	0.548697i	$0.815124\pi$
$422$	−30.0000	+	17.3205i	−1.46038	+	0.843149i
$423$	18.7350	−	10.8167i	0.910927	−	0.525924i
$424$			8.66025i			0.420579i
$425$	24.9800	+	43.2666i	1.21171	+	2.09874i
$426$		0			0
$427$		0			0
$428$	−2.00000			−0.0966736
$429$		0			0
$430$	−37.4700			−1.80696
$431$	−24.0000	−	13.8564i	−1.15604	−	0.667440i	−0.205688	−	0.978618i	$-0.565943\pi$
$431$	−24.0000	−	13.8564i	−1.15604	−	0.667440i	−0.950352	+	0.311178i	$0.899276\pi$
$432$		0			0
$433$	−9.36750	−	16.2250i	−0.450173	−	0.779723i	0.548223	−	0.836332i	$-0.315304\pi$
$433$	−9.36750	−	16.2250i	−0.450173	−	0.779723i	−0.998396	+	0.0566092i	$0.981971\pi$
$434$		0			0
$435$		0			0
$436$	6.00000	−	3.46410i	0.287348	−	0.165900i
$437$		−	28.8444i		−	1.37982i
$438$		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
$443$	16.0000			0.760183			0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000			0.760183			0.380091	+	0.924949i	$0.375893\pi$
$444$		0			0
$445$	−13.0000	+	22.5167i	−0.616259	+	1.06739i
$446$	−6.24500	−	10.8167i	−0.295709	−	0.512183i
$447$		0			0
$448$		0			0
$449$	6.00000	−	3.46410i	0.283158	−	0.163481i	−0.351694	−	0.936115i	$-0.614394\pi$
$449$	6.00000	−	3.46410i	0.283158	−	0.163481i	0.634852	+	0.772634i	$0.281061\pi$
$450$			41.5692i			1.95959i
$451$	6.24500	+	10.8167i	0.294065	+	0.509336i
$452$	2.50000	−	4.33013i	0.117590	−	0.203672i
$453$		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	$-0.951613\pi$
$457$	−34.5000	−	19.9186i	−1.61384	−	0.931752i	−0.625373	−	0.780326i	$-0.715053\pi$
$458$	18.7350	−	32.4500i	0.875429	−	1.51629i
$459$		0			0
$460$		−	14.4222i		−	0.672439i
$461$	34.3475	−	19.8305i	1.59972	−	0.923600i	0.608182	−	0.793797i	$-0.291899\pi$
$461$	34.3475	−	19.8305i	1.59972	−	0.923600i	0.991540	−	0.129802i	$-0.0414343\pi$
$462$		0			0
$463$		−	10.3923i		−	0.482971i	−0.970404	−	0.241486i	$-0.922365\pi$
$463$		−	10.3923i		−	0.482971i	0.970404	−	0.241486i	$-0.0776347\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$		0			0
$466$	−3.00000	−	1.73205i	−0.138972	−	0.0802357i
$467$	12.4900			0.577968			0.288984	−	0.957334i	$-0.406683\pi$
$467$	12.4900			0.577968			0.288984	+	0.957334i	$0.406683\pi$
$468$	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
$473$		−	20.7846i		−	0.955677i
$474$		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
$479$	12.4900	+	7.21110i	0.570682	+	0.329484i	0.757422	−	0.652926i	$-0.226459\pi$
$479$	12.4900	+	7.21110i	0.570682	+	0.329484i	−0.186739	+	0.982409i	$0.559792\pi$
$480$		0			0
$481$	3.12250	+	5.40833i	0.142374	+	0.246598i
$482$	−18.7350			−0.853356
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	−13.0000	−	22.5167i	−0.590300	−	1.02243i
$486$		0			0
$487$	−18.0000	+	10.3923i	−0.815658	+	0.470920i	−0.848917	−	0.528526i	$-0.822745\pi$
$487$	−18.0000	+	10.3923i	−0.815658	+	0.470920i	0.0332590	+	0.999447i	$0.489411\pi$
$488$	−9.36750	+	5.40833i	−0.424047	+	0.244823i
$489$		0			0
$490$		0			0
$491$	2.00000	−	3.46410i	0.0902587	−	0.156333i	−0.817361	−	0.576126i	$-0.804564\pi$
$491$	2.00000	−	3.46410i	0.0902587	−	0.156333i	0.907620	+	0.419793i	$0.137897\pi$
$492$		0			0
$493$	6.24500			0.281261
$494$	−39.0000	−	22.5167i	−1.75469	−	1.01307i
$495$	−37.4700			−1.68415
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	27.7128i		−	1.24060i	−0.784366	−	0.620298i	$-0.787012\pi$
$499$		−	27.7128i		−	1.24060i	0.784366	−	0.620298i	$-0.212988\pi$
$500$	9.36750	−	5.40833i	0.418927	−	0.241868i
$501$		0			0
$502$		−	21.6333i		−	0.965542i
$503$	−6.24500	−	10.8167i	−0.278451	−	0.482291i	0.692549	−	0.721371i	$-0.256488\pi$
$503$	−6.24500	−	10.8167i	−0.278451	−	0.482291i	−0.971000	+	0.239080i	$0.923154\pi$
$504$		0			0
$505$	−19.5000	−	11.2583i	−0.867739	−	0.500989i
$506$	24.0000			1.06693
$507$		0			0
$508$	−18.0000			−0.798621
$509$	−3.12250	−	1.80278i	−0.138402	−	0.0799066i	0.429200	−	0.903209i	$-0.358796\pi$
$509$	−3.12250	−	1.80278i	−0.138402	−	0.0799066i	−0.567602	+	0.823303i	$0.692129\pi$
$510$		0			0
$511$		0			0
$512$			8.66025i			0.382733i
$513$		0			0
$514$	−28.1025	+	16.2250i	−1.23955	+	0.715653i
$515$		−	45.0333i		−	1.98441i
$516$		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
$521$	6.24500			0.273598			0.136799	−	0.990599i	$-0.456319\pi$
$521$	6.24500			0.273598			0.136799	+	0.990599i	$0.456319\pi$
$522$	4.50000	+	2.59808i	0.196960	+	0.113715i
$523$	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
$535$	−6.24500	−	3.60555i	−0.269995	−	0.155882i
$536$	−12.0000	+	20.7846i	−0.518321	+	0.897758i
$537$		0			0
$538$		−	43.2666i		−	1.86536i
$539$		0			0
$540$		0			0
$541$		−	5.19615i		−	0.223400i	−0.993742	−	0.111700i	$-0.964370\pi$
$541$		−	5.19615i		−	0.223400i	0.993742	−	0.111700i	$-0.0356296\pi$
$542$	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
$549$	−9.36750	+	16.2250i	−0.399795	+	0.692465i
$550$	24.0000	+	41.5692i	1.02336	+	1.77252i
$551$		−	7.21110i		−	0.307203i
$552$		0			0
$553$		0			0
$554$			43.3013i			1.83969i
$555$		0			0
$556$	6.24500	−	10.8167i	0.264847	−	0.458728i
$557$	−1.50000	−	0.866025i	−0.0635570	−	0.0366947i	0.467885	−	0.883789i	$-0.345016\pi$
$557$	−1.50000	−	0.866025i	−0.0635570	−	0.0366947i	−0.531442	+	0.847095i	$0.678350\pi$
$558$		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
$565$	15.6125	−	9.01388i	0.656823	−	0.379217i
$566$	−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
$571$	24.0000			1.00437			0.502184	−	0.864761i	$-0.332530\pi$
$571$	24.0000			1.00437			0.502184	+	0.864761i	$0.332530\pi$
$572$	6.24500	−	10.8167i	0.261116	−	0.452267i
$573$		0			0
$574$		0			0
$575$	16.0000	−	27.7128i	0.667246	−	1.15570i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$			18.0278i			0.750505i	0.926923	+	0.375253i	$0.122444\pi$
$577$			18.0278i			0.750505i	−0.926923	+	0.375253i	$0.877556\pi$
$578$	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
$584$	−18.7350			−0.775260
$585$	39.0000			1.61245
$586$	31.2250			1.28989
$587$	24.9800	+	14.4222i	1.03103	+	0.595268i	0.917281	−	0.398241i	$-0.130379\pi$
$587$	24.9800	+	14.4222i	1.03103	+	0.595268i	0.113754	+	0.993509i	$0.463713\pi$
$588$		0			0
$589$		0			0
$590$			45.0333i			1.85399i
$591$		0			0
$592$	−7.50000	+	4.33013i	−0.308248	+	0.177967i
$593$			18.0278i			0.740311i	0.928970	+	0.370156i	$0.120696\pi$
$593$			18.0278i			0.740311i	−0.928970	+	0.370156i	$0.879304\pi$
$594$		0			0
$595$		0			0
$596$	13.5000	+	7.79423i	0.552982	+	0.319264i
$597$		0			0
$598$	−24.9800			−1.02151
$599$	−10.0000			−0.408589			−0.204294	−	0.978909i	$-0.565490\pi$
$599$	−10.0000			−0.408589			−0.204294	+	0.978909i	$0.565490\pi$
$600$		0			0
$601$	21.8575	−	37.8583i	0.891586	−	1.54427i	0.0536116	−	0.998562i	$-0.482927\pi$
$601$	21.8575	−	37.8583i	0.891586	−	1.54427i	0.837974	−	0.545710i	$-0.183740\pi$
$602$		0			0
$603$			41.5692i			1.69283i
$604$	3.00000	−	1.73205i	0.122068	−	0.0704761i
$605$	−3.12250	+	1.80278i	−0.126948	+	0.0732933i
$606$		0			0
$607$	−18.7350	−	32.4500i	−0.760430	−	1.31710i	−0.942629	−	0.333842i	$-0.891655\pi$
$607$	−18.7350	−	32.4500i	−0.760430	−	1.31710i	0.182199	−	0.983262i	$-0.441678\pi$
$608$	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
$612$	18.7350			0.757317
$613$	−1.50000	−	0.866025i	−0.0605844	−	0.0349784i	0.469402	−	0.882985i	$-0.344470\pi$
$613$	−1.50000	−	0.866025i	−0.0605844	−	0.0349784i	−0.529986	+	0.848006i	$0.677803\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.5000	−	11.2583i	0.785040	−	0.453243i	−0.0531732	−	0.998585i	$-0.516934\pi$
$617$	19.5000	−	11.2583i	0.785040	−	0.453243i	0.838214	+	0.545342i	$0.183600\pi$
$618$		0			0
$619$			36.0555i			1.44919i	0.689173	+	0.724597i	$0.257974\pi$
$619$			36.0555i			1.44919i	−0.689173	+	0.724597i	$0.742026\pi$
$620$		0			0
$621$		0			0
$622$	37.4700	+	21.6333i	1.50241	+	0.867417i
$623$		0			0
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		0			0
$628$	3.12250	+	5.40833i	0.124601	+	0.215816i
$629$			10.8167i			0.431288i
$630$		0			0
$631$	−12.0000	+	6.92820i	−0.477712	+	0.275807i	−0.719463	−	0.694531i	$-0.755612\pi$
$631$	−12.0000	+	6.92820i	−0.477712	+	0.275807i	0.241750	+	0.970339i	$0.422279\pi$
$632$		−	10.3923i		−	0.413384i
$633$		0			0
$634$	13.5000	−	23.3827i	0.536153	−	0.928645i
$635$	−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
$640$	−21.8575	+	37.8583i	−0.863993	+	1.49648i
$641$	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	$-0.666667\pi$
$643$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$644$		0			0
$645$		0			0
$646$	−39.0000	−	67.5500i	−1.53443	−	2.65772i
$647$	6.24500	−	10.8167i	0.245516	−	0.425247i	−0.716760	−	0.697320i	$-0.754376\pi$
$647$	6.24500	−	10.8167i	0.245516	−	0.425247i	0.962277	+	0.272073i	$0.0877092\pi$
$648$	−13.5000	−	7.79423i	−0.530330	−	0.306186i
$649$	−24.9800			−0.980550
$650$	−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
$655$			45.0333i			1.75960i
$656$	15.6125	−	9.01388i	0.609566	−	0.351933i
$657$	−28.1025	+	16.2250i	−1.09638	+	0.632997i
$658$		0			0
$659$	2.00000	+	3.46410i	0.0779089	+	0.134942i	0.902348	−	0.431009i	$-0.141842\pi$
$659$	2.00000	+	3.46410i	0.0779089	+	0.134942i	−0.824439	+	0.565951i	$0.808509\pi$
$660$		0			0
$661$	9.36750	+	5.40833i	0.364353	+	0.210360i	0.670989	−	0.741468i	$-0.265870\pi$
$661$	9.36750	+	5.40833i	0.364353	+	0.210360i	−0.306635	+	0.951827i	$0.599203\pi$
$662$	−18.0000			−0.699590
$663$		0			0
$664$	12.4900			0.484706
$665$		0			0
$666$	−4.50000	+	7.79423i	−0.174371	+	0.302020i
$667$	−2.00000	−	3.46410i	−0.0774403	−	0.134131i
$668$			7.21110i			0.279006i
$669$		0			0
$670$	74.9400	−	43.2666i	2.89518	−	1.67154i
$671$			21.6333i			0.835145i
$672$		0			0
$673$	−1.50000	+	2.59808i	−0.0578208	+	0.100148i	−0.893487	−	0.449089i	$-0.851749\pi$
$673$	−1.50000	+	2.59808i	−0.0578208	+	0.100148i	0.835666	+	0.549238i	$0.185082\pi$
$674$	−16.5000	−	9.52628i	−0.635556	−	0.366939i
$675$		0			0
$676$	−6.50000	+	11.2583i	−0.250000	+	0.433013i
$677$	24.9800			0.960059			0.480030	−	0.877252i	$-0.340626\pi$
$677$	24.9800			0.960059			0.480030	+	0.877252i	$0.340626\pi$
$678$		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	−0.999961	−	0.00883113i	$-0.997189\pi$
$683$	−39.0000	+	22.5167i	−1.49229	+	0.861576i	−0.492333	+	0.870407i	$0.663856\pi$
$684$		−	21.6333i		−	0.827170i
$685$	15.6125	+	27.0416i	0.596523	+	1.03321i
$686$		0			0
$687$		0			0
$688$	−30.0000			−1.14374
$689$	−15.6125	−	9.01388i	−0.594789	−	0.343401i
$690$		0			0
$691$	−24.9800	−	14.4222i	−0.950284	−	0.548647i	−0.0571146	−	0.998368i	$-0.518190\pi$
$691$	−24.9800	−	14.4222i	−0.950284	−	0.548647i	−0.893169	+	0.449721i	$0.851523\pi$
$692$	−12.4900	+	21.6333i	−0.474798	+	0.822375i
$693$		0			0
$694$		−	48.4974i		−	1.84094i
$695$	39.0000	−	22.5167i	1.47935	−	0.854106i
$696$		0			0
$697$		−	22.5167i		−	0.852879i
$698$	−18.7350	−	32.4500i	−0.709130	−	1.22825i
$699$		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
$703$	12.4900			0.471069
$704$	−3.00000	−	1.73205i	−0.113067	−	0.0652791i
$705$		0			0
$706$	−21.8575	−	37.8583i	−0.822618	−	1.42482i
$707$		0			0
$708$		0			0
$709$	28.5000	−	16.4545i	1.07034	−	0.617961i	0.142066	−	0.989857i	$-0.454626\pi$
$709$	28.5000	−	16.4545i	1.07034	−	0.617961i	0.928274	+	0.371896i	$0.121292\pi$
$710$			64.8999i			2.43565i
$711$	−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
$716$	−16.0000			−0.597948
$717$		0			0
$718$	24.0000	−	41.5692i	0.895672	−	1.55135i
$719$	18.7350	+	32.4500i	0.698697	+	1.21018i	0.968918	+	0.247381i	$0.0795699\pi$
$719$	18.7350	+	32.4500i	0.698697	+	1.21018i	−0.270221	+	0.962798i	$0.587097\pi$
$720$			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
$725$	4.00000	−	6.92820i	0.148556	−	0.257307i
$726$		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
$731$	−18.7350	+	32.4500i	−0.692939	+	1.20021i
$732$		0			0
$733$			10.8167i			0.399522i	0.979845	+	0.199761i	$0.0640166\pi$
$733$			10.8167i			0.399522i	−0.979845	+	0.199761i	$0.935983\pi$
$734$	−37.4700	+	21.6333i	−1.38304	+	0.798500i
$735$		0			0
$736$		−	20.7846i		−	0.766131i
$737$	24.0000	+	41.5692i	0.884051	+	1.53122i
$738$	9.36750	−	16.2250i	0.344822	−	0.597250i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$	6.24500			0.229571
$741$		0			0
$742$		0			0
$743$	−18.0000	−	10.3923i	−0.660356	−	0.381257i	0.132057	−	0.991242i	$-0.457842\pi$
$743$	−18.0000	−	10.3923i	−0.660356	−	0.381257i	−0.792413	+	0.609985i	$0.791175\pi$
$744$		0			0
$745$	28.1025	+	48.6749i	1.02960	+	1.78331i
$746$			25.9808i			0.951223i
$747$	18.7350	−	10.8167i	0.685478	−	0.395761i
$748$	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	$0.888762\pi$
$752$	−31.2250	−	18.0278i	−1.13866	−	0.657405i
$753$		0			0
$754$	−6.24500			−0.227429
$755$	12.4900			0.454557
$756$		0			0
$757$	7.00000	−	12.1244i	0.254419	−	0.440667i	−0.710318	−	0.703881i	$-0.751449\pi$
$757$	7.00000	−	12.1244i	0.254419	−	0.440667i	0.964738	+	0.263213i	$0.0847823\pi$
$758$	−18.0000	−	31.1769i	−0.653789	−	1.13240i
$759$		0			0
$760$	39.0000	−	22.5167i	1.41468	−	0.816765i
$761$	−31.2250	+	18.0278i	−1.13191	+	0.653506i	−0.944413	−	0.328761i	$-0.893369\pi$
$761$	−31.2250	+	18.0278i	−1.13191	+	0.653506i	−0.187492	+	0.982266i	$0.560036\pi$
$762$		0			0
$763$		0			0
$764$	2.00000	−	3.46410i	0.0723575	−	0.125327i
$765$	58.5000	+	33.7750i	2.11507	+	1.22114i
$766$	62.4500			2.25641
$767$	26.0000			0.938806
$768$		0			0
$769$	18.7350	+	10.8167i	0.675601	+	0.390059i	0.798196	−	0.602398i	$-0.205788\pi$
$769$	18.7350	+	10.8167i	0.675601	+	0.390059i	−0.122594	+	0.992457i	$0.539121\pi$
$770$		0			0
$771$		0			0
$772$			8.66025i			0.311689i
$773$	6.24500	−	3.60555i	0.224617	−	0.129683i	−0.383469	−	0.923554i	$-0.625271\pi$
$773$	6.24500	−	3.60555i	0.224617	−	0.129683i	0.608086	+	0.793871i	$0.291937\pi$
$774$	−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
$779$	−26.0000			−0.931547
$780$		0			0
$781$	−36.0000			−1.28818
$782$	−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	−0.705809	−	0.708402i	$-0.749417\pi$
$787$	−12.4900	+	7.21110i	−0.445220	+	0.257048i	0.260589	+	0.965450i	$0.416083\pi$
$788$		0			0
$789$		0			0
$790$	−18.7350	+	32.4500i	−0.666561	+	1.15452i
$791$		0			0
$792$	−18.0000			−0.639602
$793$		−	22.5167i		−	0.799590i
$794$	12.4900			0.443253
$795$		0			0
$796$	−6.24500	+	10.8167i	−0.221348	+	0.383386i
$797$	−12.4900	−	21.6333i	−0.442418	−	0.766291i	0.555450	−	0.831550i	$-0.312546\pi$
$797$	−12.4900	−	21.6333i	−0.442418	−	0.766291i	−0.997868	+	0.0652589i	$0.979213\pi$
$798$		0			0
$799$	−39.0000	+	22.5167i	−1.37972	+	0.796582i
$800$	36.0000	−	20.7846i	1.27279	−	0.734847i
$801$			21.6333i			0.764375i
$802$	−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
$808$	−9.36750	−	5.40833i	−0.329547	−	0.190264i
$809$	3.50000	−	6.06218i	0.123053	−	0.213135i	−0.797917	−	0.602767i	$-0.794065\pi$
$809$	3.50000	−	6.06218i	0.123053	−	0.213135i	0.920970	+	0.389633i	$0.127398\pi$
$810$	28.1025	+	48.6749i	0.987421	+	1.71026i
$811$		−	43.2666i		−	1.51930i	−0.650334	−	0.759648i	$-0.725371\pi$
$811$		−	43.2666i		−	1.51930i	0.650334	−	0.759648i	$-0.274629\pi$
$812$		0			0
$813$		0			0
$814$			10.3923i			0.364250i
$815$	−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	0.275762	−	0.961226i	$-0.411070\pi$
$821$	−12.0000	−	6.92820i	−0.418803	−	0.241796i	−0.694565	+	0.719430i	$0.744403\pi$
$822$		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	$0.923291\pi$
$824$		−	21.6333i		−	0.753632i
$825$		0			0
$826$		0			0
$827$			17.3205i			0.602293i	0.953578	+	0.301147i	$0.0973693\pi$
$827$			17.3205i			0.602293i	−0.953578	+	0.301147i	$0.902631\pi$
$828$	−6.00000	−	10.3923i	−0.208514	−	0.361158i
$829$	−9.36750	+	16.2250i	−0.325347	+	0.563517i	−0.981582	−	0.191039i	$-0.938814\pi$
$829$	−9.36750	+	16.2250i	−0.325347	+	0.563517i	0.656236	+	0.754556i	$0.272148\pi$
$830$	−39.0000	−	22.5167i	−1.35371	−	0.781565i
$831$		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	−0.509267	+	0.860609i	$0.670083\pi$
$839$	−43.7150	+	25.2389i	−1.50921	+	0.871342i	−0.999942	+	0.0107333i	$0.996583\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	19.5000	−	33.7750i	0.672014	−	1.16396i
$843$		0			0
$844$	20.0000			0.688428
$845$	−40.5925	+	23.4361i	−1.39642	+	0.806226i
$846$	−37.4700			−1.28824
$847$		0			0
$848$	12.5000	−	21.6506i	0.429252	−	0.743486i
$849$		0			0
$850$		−	86.5332i		−	2.96807i
$851$	6.00000	−	3.46410i	0.205677	−	0.118748i
$852$		0			0
$853$			25.2389i			0.864162i	0.901835	+	0.432081i	$0.142221\pi$
$853$			25.2389i			0.864162i	−0.901835	+	0.432081i	$0.857779\pi$
$854$		0			0
$855$	39.0000	−	67.5500i	1.33377	−	2.31016i
$856$	−3.00000	−	1.73205i	−0.102538	−	0.0592003i
$857$	31.2250			1.06663			0.533313	−	0.845918i	$-0.320947\pi$
$857$	31.2250			1.06663			0.533313	+	0.845918i	$0.320947\pi$
$858$		0			0
$859$	49.9600			1.70461			0.852306	−	0.523043i	$-0.175203\pi$
$859$	49.9600			1.70461			0.852306	+	0.523043i	$0.175203\pi$
$860$	18.7350	+	10.8167i	0.638858	+	0.368845i
$861$		0			0
$862$	24.0000	+	41.5692i	0.817443	+	1.41585i
$863$		−	38.1051i		−	1.29711i	−0.761166	−	0.648557i	$-0.775373\pi$
$863$		−	38.1051i		−	1.29711i	0.761166	−	0.648557i	$-0.224627\pi$
$864$		0			0
$865$	−78.0000	+	45.0333i	−2.65208	+	1.53118i
$866$			32.4500i			1.10269i
$867$		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
$872$	12.0000			0.406371
$873$	−18.7350	−	10.8167i	−0.634083	−	0.366088i
$874$	−24.9800	+	43.2666i	−0.844961	+	1.46352i
$875$		0			0
$876$		0			0
$877$	−40.5000	+	23.3827i	−1.36759	+	0.789577i	−0.990620	−	0.136649i	$-0.956367\pi$
$877$	−40.5000	+	23.3827i	−1.36759	+	0.789577i	−0.376968	+	0.926226i	$0.623033\pi$
$878$	18.7350	−	10.8167i	0.632275	−	0.365044i
$879$		0			0
$880$	31.2250	+	54.0833i	1.05259	+	1.82315i
$881$	21.8575	−	37.8583i	0.736398	−	1.27548i	−0.217710	−	0.976014i	$-0.569859\pi$
$881$	21.8575	−	37.8583i	0.736398	−	1.27548i	0.954107	−	0.299465i	$-0.0968080\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	−19.5000	+	11.2583i	−0.655856	+	0.378659i
$885$		0			0
$886$	−24.0000	−	13.8564i	−0.806296	−	0.465515i
$887$	−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
$891$	−27.0000	+	15.5885i	−0.904534	+	0.522233i
$892$			7.21110i			0.241446i
$893$	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
$898$	−12.0000			−0.400445
$899$		0			0
$900$	12.0000	−	20.7846i	0.400000	−	0.692820i
$901$	−15.6125	−	27.0416i	−0.520128	−	0.900887i
$902$		−	21.6333i		−	0.720310i
$903$		0			0
$904$	7.50000	−	4.33013i	0.249446	−	0.144018i
$905$		−	22.5167i		−	0.748479i
$906$		0			0
$907$	11.0000	−	19.0526i	0.365249	−	0.632630i	−0.623567	−	0.781770i	$-0.714317\pi$
$907$	11.0000	−	19.0526i	0.365249	−	0.632630i	0.988816	+	0.149140i	$0.0476505\pi$
$908$	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
$913$	12.4900	−	21.6333i	0.413359	−	0.715958i
$914$	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
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	0.882048	−	0.471160i	$-0.156165\pi$
$919$	1.00000	+	1.73205i	0.0329870	+	0.0571351i	−0.849061	+	0.528295i	$0.822831\pi$
$920$	12.4900	−	21.6333i	0.411783	−	0.713229i
$921$		0			0
$922$	−68.6950			−2.26235
$923$	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
$928$		−	5.19615i		−	0.170572i
$929$	21.8575	−	12.6194i	0.717121	−	0.414030i	−0.0965711	−	0.995326i	$-0.530788\pi$
$929$	21.8575	−	12.6194i	0.717121	−	0.414030i	0.813692	+	0.581296i	$0.197454\pi$
$930$		0			0
$931$		0			0
$932$	1.00000	+	1.73205i	0.0327561	+	0.0567352i
$933$		0			0
$934$	−18.7350	−	10.8167i	−0.613028	−	0.353932i
$935$	78.0000			2.55087
$936$	18.7350			0.612372
$937$	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
$940$	13.0000	+	22.5167i	0.424013	+	0.734412i
$941$		−	7.21110i		−	0.235075i	−0.993068	−	0.117538i	$-0.962500\pi$
$941$		−	7.21110i		−	0.235075i	0.993068	−	0.117538i	$-0.0375001\pi$
$942$		0			0
$943$	−12.4900	+	7.21110i	−0.406730	+	0.234826i
$944$			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	0.178165	−	0.984001i	$-0.442984\pi$
$947$	−18.0000	−	10.3923i	−0.584921	−	0.337705i	−0.763087	+	0.646296i	$0.776317\pi$
$948$		0			0
$949$	19.5000	−	33.7750i	0.632997	−	1.09638i
$950$	−99.9200			−3.24183
$951$		0			0
$952$		0			0
$953$	5.00000	+	8.66025i	0.161966	+	0.280533i	0.935574	−	0.353132i	$-0.114883\pi$
$953$	5.00000	+	8.66025i	0.161966	+	0.280533i	−0.773608	+	0.633665i	$0.781550\pi$
$954$		−	25.9808i		−	0.841158i
$955$	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
$961$	31.0000			1.00000
$962$		−	10.8167i		−	0.348743i
$963$	−6.00000			−0.193347
$964$	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	$0.284672\pi$
$967$			48.4974i			1.55957i	−0.626046	+	0.779786i	$0.715328\pi$
$968$	−1.50000	+	0.866025i	−0.0482118	+	0.0278351i
$969$		0			0
$970$			45.0333i			1.44593i
$971$	−6.24500	−	10.8167i	−0.200412	−	0.347123i	0.748250	−	0.663417i	$-0.230895\pi$
$971$	−6.24500	−	10.8167i	−0.200412	−	0.347123i	−0.948661	+	0.316294i	$0.897561\pi$
$972$		0			0
$973$		0			0
$974$	36.0000			1.15351
$975$		0			0
$976$	31.2250			0.999488
$977$	4.50000	+	2.59808i	0.143968	+	0.0831198i	0.570254	−	0.821469i	$-0.306845\pi$
$977$	4.50000	+	2.59808i	0.143968	+	0.0831198i	−0.426286	+	0.904588i	$0.640178\pi$
$978$		0			0
$979$	12.4900	+	21.6333i	0.399182	+	0.691404i
$980$		0			0
$981$	18.0000	−	10.3923i	0.574696	−	0.331801i
$982$	−6.00000	+	3.46410i	−0.191468	+	0.110544i
$983$		−	50.4777i		−	1.60999i	−0.593282	−	0.804995i	$-0.702168\pi$
$983$		−	50.4777i		−	1.60999i	0.593282	−	0.804995i	$-0.297832\pi$
$984$		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
$989$	24.0000			0.763156
$990$	56.2050	+	32.4500i	1.78631	+	1.03133i
$991$	6.00000	−	10.3923i	0.190596	−	0.330122i	−0.754852	−	0.655895i	$-0.772291\pi$
$991$	6.00000	−	10.3923i	0.190596	−	0.330122i	0.945448	+	0.325773i	$0.105625\pi$
$992$		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	$0.997965\pi$
$998$	−24.0000	+	41.5692i	−0.759707	+	1.31585i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.d.589.2	yes	4
7.2	even	3		637.2.k.e.459.2		4
7.3	odd	6		637.2.u.f.30.2		4
7.4	even	3		637.2.u.f.30.1		4
7.5	odd	6		637.2.k.e.459.1		4
7.6	odd	2	inner	637.2.q.d.589.1	yes	4
13.6	odd	12		8281.2.a.br.1.4		4
13.7	odd	12		8281.2.a.br.1.1		4
13.10	even	6	inner	637.2.q.d.491.1	✓	4
91.6	even	12		8281.2.a.br.1.3		4
91.10	odd	6		637.2.k.e.569.1		4
91.20	even	12		8281.2.a.br.1.2		4
91.23	even	6		637.2.u.f.361.1		4
91.62	odd	6	inner	637.2.q.d.491.2	yes	4
91.75	odd	6		637.2.u.f.361.2		4
91.88	even	6		637.2.k.e.569.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.e.459.1		4	7.5	odd	6
637.2.k.e.459.2		4	7.2	even	3
637.2.k.e.569.1		4	91.10	odd	6
637.2.k.e.569.2		4	91.88	even	6
637.2.q.d.491.1	✓	4	13.10	even	6	inner
637.2.q.d.491.2	yes	4	91.62	odd	6	inner
637.2.q.d.589.1	yes	4	7.6	odd	2	inner
637.2.q.d.589.2	yes	4	1.1	even	1	trivial
637.2.u.f.30.1		4	7.4	even	3
637.2.u.f.30.2		4	7.3	odd	6
637.2.u.f.361.1		4	91.23	even	6
637.2.u.f.361.2		4	91.75	odd	6
8281.2.a.br.1.1		4	13.7	odd	12
8281.2.a.br.1.2		4	91.20	even	12
8281.2.a.br.1.3		4	91.6	even	12
8281.2.a.br.1.4		4	13.6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.60555i q^{5} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.60555i q^{5} +1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(3.12250 - 5.40833i) q^{10} +(3.00000 + 1.73205i) q^{11} +(-3.12250 - 1.80278i) q^{13} +(2.50000 - 4.33013i) q^{16} +(-3.12250 - 5.40833i) q^{17} -5.19615i q^{18} +(-6.24500 + 3.60555i) q^{19} +(-3.12250 + 1.80278i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-2.00000 + 3.46410i) q^{23} -8.00000 q^{25} +(3.12250 + 5.40833i) q^{26} +(-0.500000 + 0.866025i) q^{29} +(-4.50000 + 2.59808i) q^{32} +10.8167i q^{34} +(-1.50000 + 2.59808i) q^{36} +(-1.50000 - 0.866025i) q^{37} +12.4900 q^{38} -6.24500 q^{40} +(3.12250 + 1.80278i) q^{41} +(-3.00000 - 5.19615i) q^{43} +3.46410i q^{44} +(-9.36750 + 5.40833i) q^{45} +(6.00000 - 3.46410i) q^{46} -7.21110i q^{47} +(12.0000 + 6.92820i) q^{50} -3.60555i q^{52} +5.00000 q^{53} +(-6.24500 + 10.8167i) q^{55} +(1.50000 - 0.866025i) q^{58} +(-6.24500 + 3.60555i) q^{59} +(3.12250 + 5.40833i) q^{61} -1.00000 q^{64} +(6.50000 - 11.2583i) q^{65} +(12.0000 + 6.92820i) q^{67} +(3.12250 - 5.40833i) q^{68} +(-9.00000 + 5.19615i) q^{71} +(-4.50000 + 2.59808i) q^{72} +10.8167i q^{73} +(1.50000 + 2.59808i) q^{74} +(-6.24500 - 3.60555i) q^{76} -6.00000 q^{79} +(15.6125 + 9.01388i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.12250 - 5.40833i) q^{82} -7.21110i q^{83} +(19.5000 - 11.2583i) q^{85} +10.3923i q^{86} +(-3.00000 + 5.19615i) q^{88} +(6.24500 + 3.60555i) q^{89} +18.7350 q^{90} -4.00000 q^{92} +(-6.24500 + 10.8167i) q^{94} +(-13.0000 - 22.5167i) q^{95} +(-6.24500 + 3.60555i) q^{97} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} + 2 q^{4} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 + 2 * q^4 + 6 * q^9	\( 4 q - 6 q^{2} + 2 q^{4} + 6 q^{9} + 12 q^{11} + 10 q^{16} - 12 q^{22} - 8 q^{23} - 32 q^{25} - 2 q^{29} - 18 q^{32} - 6 q^{36} - 6 q^{37} - 12 q^{43} + 24 q^{46} + 48 q^{50} + 20 q^{53} + 6 q^{58} - 4 q^{64} + 26 q^{65} + 48 q^{67} - 36 q^{71} - 18 q^{72} + 6 q^{74} - 24 q^{79} - 18 q^{81} + 78 q^{85} - 12 q^{88} - 16 q^{92} - 52 q^{95}+O(q^{100}) \) 4 * q - 6 * q^2 + 2 * q^4 + 6 * q^9 + 12 * q^11 + 10 * q^16 - 12 * q^22 - 8 * q^23 - 32 * q^25 - 2 * q^29 - 18 * q^32 - 6 * q^36 - 6 * q^37 - 12 * q^43 + 24 * q^46 + 48 * q^50 + 20 * q^53 + 6 * q^58 - 4 * q^64 + 26 * q^65 + 48 * q^67 - 36 * q^71 - 18 * q^72 + 6 * q^74 - 24 * q^79 - 18 * q^81 + 78 * q^85 - 12 * q^88 - 16 * q^92 - 52 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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