LMFDB - Embedded newform 520.2.cz.a.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(19,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 6, 5]))

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

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

chi := DirichletCharacter("520.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.cz (of order $12$, degree $4$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.3317760000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			379.1
Root			$-0.578737 - 2.15988i$ of defining polynomial
Character	$\chi$	$=$	520.379
Dual form			520.2.cz.a.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-1.58114 + 1.58114i) q^{5} +(0.206150 - 0.0552376i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-1.58114 + 1.58114i) q^{5} +(0.206150 - 0.0552376i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(0.0763351 - 0.284887i) q^{11} +(-2.89193 - 2.15331i) q^{13} -0.301824 q^{14} +(2.00000 + 3.46410i) q^{16} +(3.00000 - 3.00000i) q^{18} +(-1.98306 - 7.40089i) q^{19} +(-4.31975 + 1.15747i) q^{20} +(-0.208551 + 0.361222i) q^{22} +(-2.45754 + 1.41886i) q^{23} -5.00000i q^{25} +(3.16228 + 4.00000i) q^{26} +(0.412299 + 0.110475i) q^{28} +(-1.46410 - 5.46410i) q^{32} +(-0.238613 + 0.413289i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(2.46650 - 9.20512i) q^{37} +10.8357i q^{38} +6.32456 q^{40} +(-10.0055 - 2.68097i) q^{41} +(0.417103 - 0.417103i) q^{44} +(-1.73621 - 6.47963i) q^{45} +(3.87640 - 1.03868i) q^{46} +(7.21584 + 7.21584i) q^{47} +(-6.02273 + 3.47723i) q^{49} +(-1.83013 + 6.83013i) q^{50} +(-2.85565 - 6.62158i) q^{52} -11.4952 q^{53} +(0.329749 + 0.571142i) q^{55} +(-0.522774 - 0.301824i) q^{56} +(-13.8819 + 3.71965i) q^{59} +(-0.165713 + 0.618449i) q^{63} +8.00000i q^{64} +(7.97723 - 1.16785i) q^{65} +(0.477226 - 0.477226i) q^{70} +(8.19615 - 2.19615i) q^{72} +(-6.73861 + 11.6716i) q^{74} +(3.96613 - 14.8018i) q^{76} -0.0629458i q^{77} +(-8.63950 - 2.31495i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(12.6865 + 7.32456i) q^{82} +(-0.722443 + 0.417103i) q^{88} +(2.22446 - 8.30178i) q^{89} +9.48683i q^{90} +(-0.715113 - 0.284162i) q^{91} -5.67544 q^{92} +(-7.21584 - 12.4982i) q^{94} +(14.8373 + 8.56634i) q^{95} +(9.49996 - 2.54551i) q^{98} +(0.625654 + 0.625654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 12 q^{7} - 16 q^{8} - 12 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 12 * q^7 - 16 * q^8 - 12 * q^9	$ 8 q - 4 q^{2} + 12 q^{7} - 16 q^{8} - 12 q^{9} + 4 q^{11} + 8 q^{13} + 16 q^{16} + 24 q^{18} - 24 q^{19} - 4 q^{22} + 24 q^{28} + 16 q^{32} + 20 q^{35} - 16 q^{37} - 4 q^{41} + 8 q^{44} + 24 q^{46} - 8 q^{47} + 20 q^{50} - 16 q^{52} - 16 q^{53} + 20 q^{55} - 48 q^{56} - 28 q^{59} - 36 q^{63} + 20 q^{65} - 40 q^{70} + 24 q^{72} - 32 q^{74} + 48 q^{76} - 36 q^{81} - 24 q^{88} - 56 q^{89} - 96 q^{92} + 8 q^{94} + 60 q^{95} - 16 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 12 * q^7 - 16 * q^8 - 12 * q^9 + 4 * q^11 + 8 * q^13 + 16 * q^16 + 24 * q^18 - 24 * q^19 - 4 * q^22 + 24 * q^28 + 16 * q^32 + 20 * q^35 - 16 * q^37 - 4 * q^41 + 8 * q^44 + 24 * q^46 - 8 * q^47 + 20 * q^50 - 16 * q^52 - 16 * q^53 + 20 * q^55 - 48 * q^56 - 28 * q^59 - 36 * q^63 + 20 * q^65 - 40 * q^70 + 24 * q^72 - 32 * q^74 + 48 * q^76 - 36 * q^81 - 24 * q^88 - 56 * q^89 - 96 * q^92 + 8 * q^94 + 60 * q^95 - 16 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$3$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	−1.58114	+	1.58114i	−0.707107	+	0.707107i
$5$	−1.58114	+	1.58114i	−0.707107	+	0.707107i
$6$		0			0
$7$	0.206150	−	0.0552376i	0.0779172	−	0.0208779i	−0.219650	−	0.975579i	$-0.570491\pi$
$7$	0.206150	−	0.0552376i	0.0779172	−	0.0208779i	0.297567	+	0.954701i	$0.403825\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	2.73861	−	1.58114i	0.866025	−	0.500000i
$11$	0.0763351	−	0.284887i	0.0230159	−	0.0858965i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$	0.0763351	−	0.284887i	0.0230159	−	0.0858965i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−2.89193	−	2.15331i	−0.802076	−	0.597222i
$13$	−2.89193	−	2.15331i	−0.802076	−	0.597222i
$14$	−0.301824			−0.0806658
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	3.00000	−	3.00000i	0.707107	−	0.707107i
$19$	−1.98306	−	7.40089i	−0.454946	−	1.69788i	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−1.98306	−	7.40089i	−0.454946	−	1.69788i	0.233301	−	0.972404i	$-0.425047\pi$
$20$	−4.31975	+	1.15747i	−0.965926	+	0.258819i
$21$		0			0
$22$	−0.208551	+	0.361222i	−0.0444633	+	0.0770127i
$23$	−2.45754	+	1.41886i	−0.512432	+	0.295853i	−0.733833	−	0.679330i	$-0.762271\pi$
$23$	−2.45754	+	1.41886i	−0.512432	+	0.295853i	0.221401	+	0.975183i	$0.428937\pi$
$24$		0			0
$25$		−	5.00000i		−	1.00000i
$26$	3.16228	+	4.00000i	0.620174	+	0.784465i
$27$		0			0
$28$	0.412299	+	0.110475i	0.0779172	+	0.0208779i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$		0			0
$31$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$31$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$		0			0
$34$		0			0
$35$	−0.238613	+	0.413289i	−0.0403329	+	0.0698587i
$36$	−5.19615	+	3.00000i	−0.866025	+	0.500000i
$37$	2.46650	−	9.20512i	0.405491	−	1.51331i	−0.397658	−	0.917534i	$-0.630177\pi$
$37$	2.46650	−	9.20512i	0.405491	−	1.51331i	0.803149	−	0.595778i	$-0.203156\pi$
$38$			10.8357i			1.75778i
$39$		0			0
$40$	6.32456			1.00000
$41$	−10.0055	−	2.68097i	−1.56260	−	0.418698i	−0.629115	−	0.777312i	$-0.716583\pi$
$41$	−10.0055	−	2.68097i	−1.56260	−	0.418698i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$	0.417103	−	0.417103i	0.0628806	−	0.0628806i
$45$	−1.73621	−	6.47963i	−0.258819	−	0.965926i
$46$	3.87640	−	1.03868i	0.571544	−	0.153145i
$47$	7.21584	+	7.21584i	1.05254	+	1.05254i	0.998541	+	0.0539971i	$0.0171962\pi$
$47$	7.21584	+	7.21584i	1.05254	+	1.05254i	0.0539971	+	0.998541i	$0.482804\pi$
$48$		0			0
$49$	−6.02273	+	3.47723i	−0.860390	+	0.496747i
$50$	−1.83013	+	6.83013i	−0.258819	+	0.965926i
$51$		0			0
$52$	−2.85565	−	6.62158i	−0.396007	−	0.918247i
$53$	−11.4952			−1.57898			−0.789490	−	0.613763i	$-0.789655\pi$
$53$	−11.4952			−1.57898			−0.789490	+	0.613763i	$0.789655\pi$
$54$		0			0
$55$	0.329749	+	0.571142i	0.0444633	+	0.0770127i
$56$	−0.522774	−	0.301824i	−0.0698587	−	0.0403329i
$57$		0			0
$58$		0			0
$59$	−13.8819	+	3.71965i	−1.80727	+	0.484257i	−0.995075	−	0.0991242i	$-0.968396\pi$
$59$	−13.8819	+	3.71965i	−1.80727	+	0.484257i	−0.812198	+	0.583382i	$0.801729\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	−0.165713	+	0.618449i	−0.0208779	+	0.0779172i
$64$			8.00000i			1.00000i
$65$	7.97723	−	1.16785i	0.989453	−	0.144854i
$66$		0			0
$67$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$67$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$68$		0			0
$69$		0			0
$70$	0.477226	−	0.477226i	0.0570394	−	0.0570394i
$71$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$71$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$72$	8.19615	−	2.19615i	0.965926	−	0.258819i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$	−6.73861	+	11.6716i	−0.783348	+	1.35680i
$75$		0			0
$76$	3.96613	−	14.8018i	0.454946	−	1.69788i
$77$		−	0.0629458i		−	0.00717334i
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	−8.63950	−	2.31495i	−0.965926	−	0.258819i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	12.6865	+	7.32456i	1.40099	+	0.808862i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.722443	+	0.417103i	−0.0770127	+	0.0444633i
$89$	2.22446	−	8.30178i	0.235792	−	0.879987i	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	2.22446	−	8.30178i	0.235792	−	0.879987i	0.977790	−	0.209585i	$-0.0672115\pi$
$90$			9.48683i			1.00000i
$91$	−0.715113	−	0.284162i	−0.0749643	−	0.0297882i
$92$	−5.67544			−0.591706
$93$		0			0
$94$	−7.21584	−	12.4982i	−0.744257	−	1.28909i
$95$	14.8373	+	8.56634i	1.52228	+	0.878888i
$96$		0			0
$97$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$97$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$98$	9.49996	−	2.54551i	0.959641	−	0.257135i
$99$	0.625654	+	0.625654i	0.0628806	+	0.0628806i
$100$	5.00000	−	8.66025i	0.500000	−	0.866025i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$			17.9669i			1.77033i	0.465278	+	0.885165i	$0.345954\pi$
$103$			17.9669i			1.77033i	−0.465278	+	0.885165i	$0.654046\pi$
$104$	1.47723	+	10.0905i	0.144854	+	0.989453i
$105$		0			0
$106$	15.7027	+	4.20752i	1.52518	+	0.408670i
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$		0			0
$109$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$109$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$110$	−0.241393	−	0.900890i	−0.0230159	−	0.0858965i
$111$		0			0
$112$	0.603648	+	0.603648i	0.0570394	+	0.0570394i
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$	1.64229	−	6.12913i	0.153145	−	0.571544i
$116$		0			0
$117$	9.93236	−	4.28348i	0.918247	−	0.396007i
$118$	20.3246			1.87103
$119$		0			0
$120$		0			0
$121$	9.45095	+	5.45651i	0.859177	+	0.496046i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.90569	+	7.90569i	0.707107	+	0.707107i
$126$	0.452736	−	0.784162i	0.0403329	−	0.0698587i
$127$	19.3390	−	11.1654i	1.71606	−	0.990769i	0.790253	−	0.612781i	$-0.209949\pi$
$127$	19.3390	−	11.1654i	1.71606	−	0.990769i	0.925810	−	0.377988i	$-0.123384\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		0			0
$130$	−11.3246	−	1.32456i	−0.993229	−	0.116171i
$131$	22.2148			1.94092			0.970460	−	0.241264i	$-0.0775618\pi$
$131$	22.2148			1.94092			0.970460	+	0.241264i	$0.0775618\pi$
$132$		0			0
$133$	−0.817615	−	1.41615i	−0.0708962	−	0.122796i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$137$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$138$		0			0
$139$	−10.8056	+	18.7158i	−0.916519	+	1.58746i	−0.111856	+	0.993724i	$0.535679\pi$
$139$	−10.8056	+	18.7158i	−0.916519	+	1.58746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$	−0.826579	+	0.477226i	−0.0698587	+	0.0403329i
$141$		0			0
$142$		0			0
$143$	−0.834206	+	0.659498i	−0.0697598	+	0.0551500i
$144$	−12.0000			−1.00000
$145$		0			0
$146$		0			0
$147$		0			0
$148$	13.4772	−	13.4772i	1.10782	−	1.10782i
$149$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$149$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$150$		0			0
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$	−10.8357	+	18.7679i	−0.878888	+	1.52228i
$153$		0			0
$154$	−0.0230398	+	0.0859856i	−0.00185660	+	0.00692892i
$155$		0			0
$156$		0			0
$157$	−16.7156			−1.33405			−0.667024	−	0.745036i	$-0.732432\pi$
$157$	−16.7156			−1.33405			−0.667024	+	0.745036i	$0.732432\pi$
$158$		0			0
$159$		0			0
$160$	10.9545	+	6.32456i	0.866025	+	0.500000i
$161$	−0.428246	+	0.428246i	−0.0337505	+	0.0337505i
$162$	3.29423	+	12.2942i	0.258819	+	0.965926i
$163$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$163$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$164$	−14.6491	−	14.6491i	−1.14390	−	1.14390i
$165$		0			0
$166$		0			0
$167$	−2.29183	+	8.55321i	−0.177347	+	0.661868i	0.818793	+	0.574089i	$0.194644\pi$
$167$	−2.29183	+	8.55321i	−0.177347	+	0.661868i	−0.996140	+	0.0877789i	$0.972023\pi$
$168$		0			0
$169$	3.72648	+	12.4545i	0.286652	+	0.958035i
$170$		0			0
$171$	22.2027	+	5.94919i	1.69788	+	0.454946i
$172$		0			0
$173$	−15.9210	−	9.19199i	−1.21045	−	0.698854i	−0.247593	−	0.968864i	$-0.579640\pi$
$173$	−15.9210	−	9.19199i	−1.21045	−	0.698854i	−0.962858	+	0.270010i	$0.912973\pi$
$174$		0			0
$175$	−0.276188	−	1.03075i	−0.0208779	−	0.0779172i
$176$	1.13955	−	0.305341i	0.0858965	−	0.0230159i
$177$		0			0
$178$	−6.07733	+	10.5262i	−0.455515	+	0.788975i
$179$	5.47723	−	3.16228i	0.409387	−	0.236360i	−0.281139	−	0.959667i	$-0.590712\pi$
$179$	5.47723	−	3.16228i	0.409387	−	0.236360i	0.690526	+	0.723307i	$0.257379\pi$
$180$	3.47242	−	12.9593i	0.258819	−	0.965926i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	0.872853	+	0.649922i	0.0647001	+	0.0481754i
$183$		0			0
$184$	7.75280	+	2.07736i	0.571544	+	0.153145i
$185$	10.6547	+	18.4545i	0.783348	+	1.35680i
$186$		0			0
$187$		0			0
$188$	5.28236	+	19.7140i	0.385256	+	1.43779i
$189$		0			0
$190$	−17.1327	−	17.1327i	−1.24293	−	1.24293i
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$		0			0
$193$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$193$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$194$		0			0
$195$		0			0
$196$	−13.9089			−0.993493
$197$	−10.5089	−	2.81586i	−0.748730	−	0.200621i	−0.135775	−	0.990740i	$-0.543352\pi$
$197$	−10.5089	−	2.81586i	−0.748730	−	0.200621i	−0.612955	+	0.790118i	$0.710019\pi$
$198$	−0.625654	−	1.08367i	−0.0444633	−	0.0770127i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−10.0000	+	10.0000i	−0.707107	+	0.707107i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	20.0591	−	11.5811i	1.40099	−	0.808862i
$206$	6.57634	−	24.5432i	0.458195	−	1.71001i
$207$		−	8.51317i		−	0.591706i
$208$	1.67544	−	14.3246i	0.116171	−	0.993229i
$209$	−2.25979			−0.156313
$210$		0			0
$211$	−13.7158	−	23.7565i	−0.944237	−	1.63547i	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−13.7158	−	23.7565i	−0.944237	−	1.63547i	−0.186966	−	0.982366i	$-0.559865\pi$
$212$	−19.9102	−	11.4952i	−1.36744	−	0.789490i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$			1.31900i			0.0889266i
$221$		0			0
$222$		0			0
$223$	−28.2673	−	7.57419i	−1.89292	−	0.507205i	−0.998159	−	0.0606498i	$-0.980683\pi$
$223$	−28.2673	−	7.57419i	−1.89292	−	0.507205i	−0.894756	−	0.446555i	$-0.852651\pi$
$224$	−0.603648	−	1.04555i	−0.0403329	−	0.0698587i
$225$	12.9904	+	7.50000i	0.866025	+	0.500000i
$226$		0			0
$227$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$227$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$228$		0			0
$229$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$229$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$230$	−4.48683	+	7.77142i	−0.295853	+	0.512432i
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	−15.1357	+	2.21584i	−0.989453	+	0.144854i
$235$	−22.8185			−1.48851
$236$	−27.7639	−	7.43930i	−1.80727	−	0.484257i
$237$		0			0
$238$		0			0
$239$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$239$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$240$		0			0
$241$	−23.1188	+	6.19466i	−1.48921	+	0.399033i	−0.909471	−	0.415768i	$-0.863513\pi$
$241$	−23.1188	+	6.19466i	−1.48921	+	0.399033i	−0.579741	+	0.814801i	$0.696846\pi$
$242$	−10.9130	−	10.9130i	−0.701515	−	0.701515i
$243$		0			0
$244$		0			0
$245$	4.02480	−	15.0208i	0.257135	−	0.959641i
$246$		0			0
$247$	−10.2016	+	25.6730i	−0.649110	+	1.63353i
$248$		0			0
$249$		0			0
$250$	−7.90569	−	13.6931i	−0.500000	−	0.866025i
$251$	24.5831	+	14.1931i	1.55167	+	0.895858i	0.998006	+	0.0631194i	$0.0201049\pi$
$251$	24.5831	+	14.1931i	1.55167	+	0.895858i	0.553666	+	0.832739i	$0.313228\pi$
$252$	−0.905472	+	0.905472i	−0.0570394	+	0.0570394i
$253$	0.216618	+	0.808429i	0.0136187	+	0.0508255i
$254$	−30.5045	+	8.17364i	−1.91402	+	0.512860i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$		−	2.03387i		−	0.126379i
$260$	14.9848	+	5.95445i	0.929318	+	0.369279i
$261$		0			0
$262$	−30.3460	−	8.13119i	−1.87478	−	0.502347i
$263$	−8.14924	−	14.1149i	−0.502503	−	0.870361i	−0.999996	−	0.00289305i	$-0.999079\pi$
$263$	−8.14924	−	14.1149i	−0.502503	−	0.870361i	0.497492	−	0.867468i	$-0.334254\pi$
$264$		0			0
$265$	18.1754	−	18.1754i	1.11651	−	1.11651i
$266$	0.598536	+	2.23377i	0.0366986	+	0.136961i
$267$		0			0
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$		0			0
$271$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$271$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.42443	−	0.381676i	−0.0858965	−	0.0230159i
$276$		0			0
$277$	28.7230	+	16.5832i	1.72580	+	0.996390i	0.905347	+	0.424673i	$0.139611\pi$
$277$	28.7230	+	16.5832i	1.72580	+	0.996390i	0.820451	+	0.571717i	$0.193722\pi$
$278$	21.6112	−	21.6112i	1.29615	−	1.29615i
$279$		0			0
$280$	1.30380	−	0.349353i	0.0779172	−	0.0208779i
$281$	−1.64911	−	1.64911i	−0.0983777	−	0.0983777i	0.656205	−	0.754583i	$-0.272161\pi$
$281$	−1.64911	−	1.64911i	−0.0983777	−	0.0983777i	−0.754583	+	0.656205i	$0.772161\pi$
$282$		0			0
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$		0			0
$286$	1.38094	−	0.595550i	0.0816566	−	0.0352156i
$287$	−2.21073			−0.130495
$288$	16.3923	+	4.39230i	0.965926	+	0.258819i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−30.5522	+	8.18643i	−1.78488	+	0.478256i	−0.991459	−	0.130420i	$-0.958367\pi$
$293$	−30.5522	+	8.18643i	−1.78488	+	0.478256i	−0.793419	+	0.608676i	$0.791701\pi$
$294$		0			0
$295$	16.0680	−	27.8305i	0.935513	−	1.62036i
$296$	−23.3432	+	13.4772i	−1.35680	+	0.783348i
$297$		0			0
$298$		0			0
$299$	10.1623	+	1.18861i	0.587700	+	0.0687392i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	21.6713	−	21.6713i	1.24293	−	1.24293i
$305$		0			0
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	0.0629458	−	0.109025i	0.00358667	−	0.00621230i
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	22.8339	+	6.11832i	1.28859	+	0.345277i
$315$	−0.715838	−	1.23987i	−0.0403329	−	0.0698587i
$316$		0			0
$317$	−21.4603	+	21.4603i	−1.20533	+	1.20533i	−0.232806	+	0.972523i	$0.574791\pi$
$317$	−21.4603	+	21.4603i	−1.20533	+	1.20533i	−0.972523	+	0.232806i	$0.925209\pi$
$318$		0			0
$319$		0			0
$320$	−12.6491	−	12.6491i	−0.707107	−	0.707107i
$321$		0			0
$322$	0.741744	−	0.428246i	0.0413358	−	0.0238652i
$323$		0			0
$324$		−	18.0000i		−	1.00000i
$325$	−10.7666	+	14.4596i	−0.597222	+	0.802076i
$326$		0			0
$327$		0			0
$328$	14.6491	+	25.3730i	0.808862	+	1.40099i
$329$	1.88613	+	1.08896i	0.103986	+	0.0600361i
$330$		0			0
$331$	9.08160	+	33.8930i	0.499170	+	1.86293i	0.505296	+	0.862946i	$0.331383\pi$
$331$	9.08160	+	33.8930i	0.499170	+	1.86293i	−0.00612670	+	0.999981i	$0.501950\pi$
$332$		0			0
$333$	20.2158	+	20.2158i	1.10782	+	1.10782i
$334$	6.26139	−	10.8450i	0.342608	−	0.593414i
$335$		0			0
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−0.531820	−	18.3771i	−0.0289272	−	0.999582i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−28.1519	−	16.2535i	−1.52228	−	0.878888i
$343$	−2.10589	+	2.10589i	−0.113708	+	0.113708i
$344$		0			0
$345$		0			0
$346$	18.3840	+	18.3840i	0.988329	+	0.988329i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$349$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$350$			1.50912i			0.0806658i
$351$		0			0
$352$	−1.66841			−0.0889266
$353$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$353$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$354$		0			0
$355$		0			0
$356$	12.1547	−	12.1547i	0.644195	−	0.644195i
$357$		0			0
$358$	−8.63950	+	2.31495i	−0.456612	+	0.122349i
$359$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$359$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$360$	−9.48683	+	16.4317i	−0.500000	+	0.866025i
$361$	−34.3862	+	19.8529i	−1.80980	+	1.04489i
$362$		0			0
$363$		0			0
$364$	−0.954451	−	1.20730i	−0.0500268	−	0.0632795i
$365$		0			0
$366$		0			0
$367$	−18.9057	−	32.7456i	−0.986869	−	1.70931i	−0.633316	−	0.773893i	$-0.718307\pi$
$367$	−18.9057	−	32.7456i	−0.986869	−	1.70931i	−0.353553	−	0.935415i	$-0.615027\pi$
$368$	−9.83016	−	5.67544i	−0.512432	−	0.295853i
$369$	21.9737	−	21.9737i	1.14390	−	1.14390i
$370$	−7.79977	−	29.1091i	−0.405491	−	1.51331i
$371$	−2.36972	+	0.634965i	−0.123030	+	0.0329657i
$372$		0			0
$373$	3.06797	−	5.31388i	0.158854	−	0.275142i	−0.775602	−	0.631222i	$-0.782554\pi$
$373$	3.06797	−	5.31388i	0.158854	−	0.275142i	0.934456	+	0.356080i	$0.115887\pi$
$374$		0			0
$375$		0			0
$376$		−	28.8634i		−	1.48851i
$377$		0			0
$378$		0			0
$379$	9.20267	+	2.46585i	0.472709	+	0.126662i	0.487306	−	0.873231i	$-0.337980\pi$
$379$	9.20267	+	2.46585i	0.472709	+	0.126662i	−0.0145964	+	0.999893i	$0.504646\pi$
$380$	17.1327	+	29.6747i	0.878888	+	1.52228i
$381$		0			0
$382$		0			0
$383$	−3.47242	−	12.9593i	−0.177432	−	0.662187i	−0.996125	−	0.0879542i	$-0.971967\pi$
$383$	−3.47242	−	12.9593i	−0.177432	−	0.662187i	0.818692	−	0.574233i	$-0.194700\pi$
$384$		0			0
$385$	0.0995261	+	0.0995261i	0.00507232	+	0.00507232i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$		0			0
$391$		0			0
$392$	18.9999	+	5.09101i	0.959641	+	0.257135i
$393$		0			0
$394$	13.3248	+	7.69306i	0.671293	+	0.387571i
$395$		0			0
$396$	0.458011	+	1.70932i	0.0230159	+	0.0858965i
$397$	30.9645	−	8.29691i	1.55406	−	0.416410i	0.623285	−	0.781995i	$-0.285798\pi$
$397$	30.9645	−	8.29691i	1.55406	−	0.416410i	0.930778	+	0.365585i	$0.119131\pi$
$398$		0			0
$399$		0			0
$400$	17.3205	−	10.0000i	0.866025	−	0.500000i
$401$	5.70779	−	21.3018i	0.285034	−	1.06376i	−0.663781	−	0.747927i	$-0.731049\pi$
$401$	5.70779	−	21.3018i	0.285034	−	1.06376i	0.948815	−	0.315833i	$-0.102284\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	19.4389	+	5.20863i	0.965926	+	0.258819i
$406$		0			0
$407$	−2.43413	−	1.40535i	−0.120656	−	0.0696605i
$408$		0			0
$409$	−6.04199	−	22.5490i	−0.298757	−	1.11498i	−0.938187	−	0.346128i	$-0.887496\pi$
$409$	−6.04199	−	22.5490i	−0.298757	−	1.11498i	0.639430	−	0.768849i	$-0.279170\pi$
$410$	−31.6403	+	8.47798i	−1.56260	+	0.418698i
$411$		0			0
$412$	−17.9669	+	31.1196i	−0.885165	+	1.53315i
$413$	−2.65629	+	1.53361i	−0.130707	+	0.0754640i
$414$	−3.11604	+	11.6292i	−0.153145	+	0.571544i
$415$		0			0
$416$	−7.53185	+	18.9545i	−0.369279	+	0.929318i
$417$		0			0
$418$	3.08693	+	0.827141i	0.150987	+	0.0404568i
$419$	−15.8114	−	27.3861i	−0.772437	−	1.33790i	−0.936224	−	0.351404i	$-0.885704\pi$
$419$	−15.8114	−	27.3861i	−0.772437	−	1.33790i	0.163787	−	0.986496i	$-0.447629\pi$
$420$		0			0
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$	10.0407	+	37.4724i	0.488773	+	1.82413i
$423$	−29.5711	+	7.92354i	−1.43779	+	0.385256i
$424$	22.9903	+	22.9903i	1.11651	+	1.11651i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$431$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$432$		0			0
$433$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$433$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.3743	+	15.3743i	0.735452	+	0.735452i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	0.482786	−	1.80178i	0.0230159	−	0.0858965i
$441$		−	20.8634i		−	0.993493i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	9.60910	+	16.6434i	0.455515	+	0.788975i
$446$	35.8414	+	20.6931i	1.69714	+	0.979845i
$447$		0			0
$448$	0.441901	+	1.64920i	0.0208779	+	0.0779172i
$449$	25.3979	−	6.80534i	1.19860	−	0.321164i	0.396320	−	0.918112i	$-0.370287\pi$
$449$	25.3979	−	6.80534i	1.19860	−	0.321164i	0.802280	+	0.596948i	$0.203620\pi$
$450$	−15.0000	−	15.0000i	−0.707107	−	0.707107i
$451$	−1.52755	+	2.64579i	−0.0719294	+	0.124585i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.57999	−	0.681395i	0.0740712	−	0.0319443i
$456$		0			0
$457$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$457$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$458$		0			0
$459$		0			0
$460$	8.97367	−	8.97367i	0.418399	−	0.418399i
$461$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$461$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$462$		0			0
$463$	15.8114	+	15.8114i	0.734818	+	0.734818i	0.971570	−	0.236752i	$-0.0760830\pi$
$463$	15.8114	+	15.8114i	0.734818	+	0.734818i	−0.236752	+	0.971570i	$0.576083\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$	21.4868	+	2.51317i	0.993229	+	0.116171i
$469$		0			0
$470$	31.1706	+	8.35214i	1.43779	+	0.385256i
$471$		0			0
$472$	35.2032	+	20.3246i	1.62036	+	0.935513i
$473$		0			0
$474$		0			0
$475$	−37.0045	+	9.91531i	−1.69788	+	0.454946i
$476$		0			0
$477$	17.2427	−	29.8653i	0.789490	−	1.36744i
$478$		0			0
$479$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$479$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$480$		0			0
$481$	−26.9545	+	21.3094i	−1.22902	+	0.971623i
$482$	33.8482			1.54175
$483$		0			0
$484$	10.9130	+	18.9019i	0.496046	+	0.859177i
$485$		0			0
$486$		0			0
$487$	−2.99053	−	11.1608i	−0.135514	−	0.505745i	−0.999995	−	0.00308010i	$-0.999020\pi$
$487$	−2.99053	−	11.1608i	−0.135514	−	0.505745i	0.864481	−	0.502665i	$-0.167647\pi$
$488$		0			0
$489$		0			0
$490$	−10.9960	+	19.0455i	−0.496747	+	0.860390i
$491$	17.6703	−	10.2019i	0.797449	−	0.460407i	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	17.6703	−	10.2019i	0.797449	−	0.460407i	0.842578	+	0.538574i	$0.181037\pi$
$492$		0			0
$493$		0			0
$494$	23.3326	−	31.3359i	1.04978	−	1.40987i
$495$	−1.97849			−0.0889266
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.1359	+	19.1359i	−0.856642	+	0.856642i	−0.990941	−	0.134298i	$-0.957122\pi$
$499$	−19.1359	+	19.1359i	−0.856642	+	0.856642i	0.134298	+	0.990941i	$0.457122\pi$
$500$	5.78737	+	21.5988i	0.258819	+	0.965926i
$501$		0			0
$502$	−28.3861	−	28.3861i	−1.26693	−	1.26693i
$503$	22.0011	−	38.1070i	0.980979	−	1.69911i	0.322381	−	0.946610i	$-0.395517\pi$
$503$	22.0011	−	38.1070i	0.980979	−	1.69911i	0.658598	−	0.752495i	$-0.271150\pi$
$504$	1.56832	−	0.905472i	0.0698587	−	0.0403329i
$505$		0			0
$506$		−	1.18362i		−	0.0526184i
$507$		0			0
$508$	44.6616			1.98154
$509$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$509$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$		0			0
$515$	−28.4081	−	28.4081i	−1.25181	−	1.25181i
$516$		0			0
$517$	2.60652	−	1.50487i	0.114635	−	0.0661843i
$518$	−0.744450	+	2.77832i	−0.0327092	+	0.122073i
$519$		0			0
$520$	−18.2901	−	13.6188i	−0.802076	−	0.597222i
$521$	−40.9089			−1.79225			−0.896126	−	0.443800i	$-0.853630\pi$
$521$	−40.9089			−1.79225			−0.896126	+	0.443800i	$0.853630\pi$
$522$		0			0
$523$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$523$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$524$	38.4772	+	22.2148i	1.68089	+	0.970460i
$525$		0			0
$526$	5.96565	+	22.2641i	0.260115	+	0.970762i
$527$		0			0
$528$		0			0
$529$	−7.47367	+	12.9448i	−0.324942	+	0.562816i
$530$	−31.4808	+	18.1754i	−1.36744	+	0.789490i
$531$	11.1590	−	41.6458i	0.484257	−	1.80727i
$532$		−	3.27046i		−	0.141792i
$533$	23.1623	+	29.2982i	1.00327	+	1.26905i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.530869	+	1.98123i	0.0228661	+	0.0853376i
$540$		0			0
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$		0			0
$550$	1.80611	+	1.04276i	0.0770127	+	0.0444633i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−33.1665	−	33.1665i	−1.40911	−	1.40911i
$555$		0			0
$556$	−37.4317	+	21.6112i	−1.58746	+	0.916519i
$557$	−8.40738	+	31.3768i	−0.356232	+	1.32948i	0.522695	+	0.852520i	$0.324927\pi$
$557$	−8.40738	+	31.3768i	−0.356232	+	1.32948i	−0.878927	+	0.476957i	$0.841740\pi$
$558$		0			0
$559$		0			0
$560$	−1.90890			−0.0806658
$561$		0			0
$562$	1.64911	+	2.85634i	0.0695635	+	0.120488i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.35821	−	1.35821i	−0.0570394	−	0.0570394i
$568$		0			0
$569$	10.4318	−	6.02277i	0.437322	−	0.252488i	−0.265139	−	0.964210i	$-0.585418\pi$
$569$	10.4318	−	6.02277i	0.437322	−	0.252488i	0.702461	+	0.711722i	$0.252085\pi$
$570$		0			0
$571$			29.3406i			1.22787i	0.789359	+	0.613933i	$0.210413\pi$
$571$			29.3406i			1.22787i	−0.789359	+	0.613933i	$0.789587\pi$
$572$	−2.10438	+	0.308078i	−0.0879887	+	0.0128814i
$573$		0			0
$574$	3.01991	+	0.809182i	0.126049	+	0.0337746i
$575$	7.09431	+	12.2877i	0.295853	+	0.512432i
$576$	−20.7846	−	12.0000i	−0.866025	−	0.500000i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	−6.22243	−	23.2224i	−0.258819	−	0.965926i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.877484	+	3.27481i	−0.0363417	+	0.135629i
$584$		0			0
$585$	−8.93168	+	22.4772i	−0.369279	+	0.929318i
$586$	44.7315			1.84784
$587$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$587$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$588$		0			0
$589$		0			0
$590$	−32.1359	+	32.1359i	−1.32302	+	1.32302i
$591$		0			0
$592$	36.8205	−	9.86601i	1.51331	−	0.405491i
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−13.4469	−	5.34333i	−0.549883	−	0.218505i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	−11.8620	−	20.5455i	−0.483860	−	0.838070i	0.515968	−	0.856608i	$-0.327432\pi$
$601$	−11.8620	−	20.5455i	−0.483860	−	0.838070i	−0.999828	+	0.0185374i	$0.994099\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−23.5708	+	6.31576i	−0.958287	+	0.256772i
$606$		0			0
$607$	−7.73213	+	13.3924i	−0.313838	+	0.543583i	−0.979190	−	0.202947i	$-0.934948\pi$
$607$	−7.73213	+	13.3924i	−0.313838	+	0.543583i	0.665352	+	0.746530i	$0.268281\pi$
$608$	−37.5358	+	21.6713i	−1.52228	+	0.878888i
$609$		0			0
$610$		0			0
$611$	−5.32971	−	36.4056i	−0.215617	−	1.47281i
$612$		0			0
$613$	28.4907	+	7.63406i	1.15073	+	0.308337i	0.783257	−	0.621698i	$-0.213557\pi$
$613$	28.4907	+	7.63406i	1.15073	+	0.308337i	0.367471	+	0.930035i	$0.380224\pi$
$614$		0			0
$615$		0			0
$616$	−0.125892	+	0.125892i	−0.00507232	+	0.00507232i
$617$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$617$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$618$		0			0
$619$	−34.8910	−	34.8910i	−1.40239	−	1.40239i	−0.792446	−	0.609941i	$-0.791193\pi$
$619$	−34.8910	−	34.8910i	−1.40239	−	1.40239i	−0.609941	−	0.792446i	$-0.708807\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	1.83428i		−	0.0734890i
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$		0			0
$628$	−28.9522	−	16.7156i	−1.15532	−	0.667024i
$629$		0			0
$630$	0.524030	+	1.95571i	0.0208779	+	0.0779172i
$631$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$631$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$632$		0			0
$633$		0			0
$634$	37.1703	−	21.4603i	1.47622	−	0.852296i
$635$	−12.9237	+	48.2318i	−0.512860	+	1.91402i
$636$		0			0
$637$	24.9049	+	2.91295i	0.986766	+	0.115415i
$638$		0			0
$639$		0			0
$640$	12.6491	+	21.9089i	0.500000	+	0.866025i
$641$	−37.0813	−	21.4089i	−1.46462	−	0.845601i	−0.465404	−	0.885098i	$-0.654091\pi$
$641$	−37.0813	−	21.4089i	−1.46462	−	0.845601i	−0.999220	+	0.0394976i	$0.987424\pi$
$642$		0			0
$643$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$643$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$644$	−1.16999	+	0.313498i	−0.0461041	+	0.0123536i
$645$		0			0
$646$		0			0
$647$	17.0047	−	9.81765i	0.668522	−	0.385972i	−0.126994	−	0.991903i	$-0.540533\pi$
$647$	17.0047	−	9.81765i	0.668522	−	0.385972i	0.795516	+	0.605932i	$0.207200\pi$
$648$	−6.58846	+	24.5885i	−0.258819	+	0.965926i
$649$			4.23872i			0.166384i
$650$	20.0000	−	15.8114i	0.784465	−	0.620174i
$651$		0			0
$652$		0			0
$653$	−4.42858	−	7.67053i	−0.173304	−	0.300171i	0.766269	−	0.642520i	$-0.222111\pi$
$653$	−4.42858	−	7.67053i	−0.173304	−	0.300171i	−0.939573	+	0.342349i	$0.888778\pi$
$654$		0			0
$655$	−35.1247	+	35.1247i	−1.37244	+	1.37244i
$656$	−10.7239	−	40.0221i	−0.418698	−	1.56260i
$657$		0			0
$658$	−2.17791	−	2.17791i	−0.0849039	−	0.0849039i
$659$	22.1359	−	38.3406i	0.862294	−	1.49354i	−0.00741531	−	0.999973i	$-0.502360\pi$
$659$	22.1359	−	38.3406i	0.862294	−	1.49354i	0.869709	−	0.493564i	$-0.164306\pi$
$660$		0			0
$661$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$661$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$662$		−	49.6228i		−	1.92864i
$663$		0			0
$664$		0			0
$665$	3.53189	+	0.946368i	0.136961	+	0.0366986i
$666$	−20.2158	−	35.0149i	−0.783348	−	1.35680i
$667$		0			0
$668$	−12.5228	+	12.5228i	−0.484521	+	0.484521i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$673$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$674$		0			0
$675$		0			0
$676$	−6.00000	+	25.2982i	−0.230769	+	0.973009i
$677$	−46.7851			−1.79810			−0.899048	−	0.437850i	$-0.855740\pi$
$677$	−46.7851			−1.79810			−0.899048	+	0.437850i	$0.855740\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$683$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$684$	32.5070	+	32.5070i	1.24293	+	1.24293i
$685$		0			0
$686$	3.64752	−	2.10589i	0.139263	−	0.0804034i
$687$		0			0
$688$		0			0
$689$	33.2431	+	24.7527i	1.26646	+	0.943002i
$690$		0			0
$691$	47.0922	+	12.6183i	1.79147	+	0.480024i	0.992595	−	0.121470i	$-0.0387608\pi$
$691$	47.0922	+	12.6183i	1.79147	+	0.480024i	0.798878	+	0.601494i	$0.205427\pi$
$692$	−18.3840	−	31.8420i	−0.698854	−	1.21045i
$693$	0.163538	+	0.0944187i	0.00621230	+	0.00358667i
$694$		0			0
$695$	−12.5072	−	46.6775i	−0.474425	−	1.77058i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.552376	−	2.06150i	0.0208779	−	0.0779172i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−73.0173			−2.75390
$704$	2.27909	+	0.610681i	0.0858965	+	0.0230159i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$709$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$710$		0			0
$711$		0			0
$712$	−21.0525	+	12.1547i	−0.788975	+	0.455515i
$713$		0			0
$714$		0			0
$715$	0.276238	−	2.36175i	0.0103307	−	0.0883245i
$716$	12.6491			0.472719
$717$		0			0
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	18.9737	−	18.9737i	0.707107	−	0.707107i
$721$	0.992448	+	3.70387i	0.0369607	+	0.137939i
$722$	54.2390	−	14.5333i	2.01857	−	0.540873i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	53.0664i		−	1.96813i	−0.177822	−	0.984063i	$-0.556905\pi$
$727$		−	53.0664i		−	1.96813i	0.177822	−	0.984063i	$-0.443095\pi$
$728$	0.861904	+	1.99855i	0.0319443	+	0.0740712i
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−22.1247	+	22.1247i	−0.817196	+	0.817196i	−0.985701	−	0.168505i	$-0.946106\pi$
$733$	−22.1247	+	22.1247i	−0.817196	+	0.817196i	0.168505	+	0.985701i	$0.446106\pi$
$734$	13.8399	+	51.6513i	0.510841	+	1.90648i
$735$		0			0
$736$	11.3509	+	11.3509i	0.418399	+	0.418399i
$737$		0			0
$738$	−38.0595	+	21.9737i	−1.40099	+	0.808862i
$739$	13.0763	−	48.8015i	0.481021	−	1.79519i	−0.116326	−	0.993211i	$-0.537112\pi$
$739$	13.0763	−	48.8015i	0.481021	−	1.79519i	0.597347	−	0.801983i	$-0.296222\pi$
$740$			42.6187i			1.56670i
$741$		0			0
$742$	3.46951			0.127370
$743$	38.8778	+	10.4173i	1.42629	+	0.382172i	0.887710	−	0.460404i	$-0.152295\pi$
$743$	38.8778	+	10.4173i	1.42629	+	0.382172i	0.538577	+	0.842576i	$0.318962\pi$
$744$		0			0
$745$		0			0
$746$	−6.13594	+	6.13594i	−0.224653	+	0.224653i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$751$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$752$	−10.5647	+	39.4281i	−0.385256	+	1.43779i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−25.9076	−	44.8732i	−0.941626	−	1.63094i	−0.762369	−	0.647143i	$-0.775964\pi$
$757$	−25.9076	−	44.8732i	−0.941626	−	1.63094i	−0.179258	−	0.983802i	$-0.557370\pi$
$758$	−11.6685	−	6.73682i	−0.423820	−	0.244692i
$759$		0			0
$760$	−12.5420	−	46.8073i	−0.454946	−	1.69788i
$761$	52.7071	−	14.1228i	1.91063	−	0.511952i	0.917060	−	0.398750i	$-0.130556\pi$
$761$	52.7071	−	14.1228i	1.91063	−	0.511952i	0.993572	−	0.113203i	$-0.0361109\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$			18.9737i			0.685546i
$767$	48.1551	+	19.1352i	1.73878	+	0.690932i
$768$		0			0
$769$	−45.5222	−	12.1976i	−1.64157	−	0.439858i	−0.684336	−	0.729167i	$-0.739908\pi$
$769$	−45.5222	−	12.1976i	−1.64157	−	0.439858i	−0.957236	+	0.289309i	$0.906575\pi$
$770$	−0.0995261	−	0.172384i	−0.00358667	−	0.00621230i
$771$		0			0
$772$		0			0
$773$	−8.51786	−	31.7891i	−0.306366	−	1.14337i	−0.931763	−	0.363067i	$-0.881730\pi$
$773$	−8.51786	−	31.7891i	−0.306366	−	1.14337i	0.625397	−	0.780307i	$-0.284937\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$			79.3664i			2.84359i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−24.0909	−	13.9089i	−0.860390	−	0.496747i
$785$	26.4296	−	26.4296i	0.943314	−	0.943314i
$786$		0			0
$787$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$787$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$788$	−15.3861	−	15.3861i	−0.548108	−	0.548108i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		−	2.50262i		−	0.0889266i
$793$		0			0
$794$	−45.3351			−1.60888
$795$		0			0
$796$		0			0
$797$	−0.398804	−	0.230249i	−0.0141264	−	0.00815585i	0.492920	−	0.870075i	$-0.335929\pi$
$797$	−0.398804	−	0.230249i	−0.0141264	−	0.00815585i	−0.507047	+	0.861919i	$0.669263\pi$
$798$		0			0
$799$		0			0
$800$	−27.3205	+	7.32051i	−0.965926	+	0.258819i
$801$	18.2320	+	18.2320i	0.644195	+	0.644195i
$802$	−15.5940	+	27.0096i	−0.550643	+	0.953741i
$803$		0			0
$804$		0			0
$805$		−	1.35423i		−	0.0477305i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	25.2982	+	43.8178i	0.889438	+	1.54055i	0.840541	+	0.541748i	$0.182237\pi$
$809$	25.2982	+	43.8178i	0.889438	+	1.54055i	0.0488972	+	0.998804i	$0.484429\pi$
$810$	−24.6475	−	14.2302i	−0.866025	−	0.500000i
$811$	−39.2438	+	39.2438i	−1.37804	+	1.37804i	−0.530102	+	0.847934i	$0.677846\pi$
$811$	−39.2438	+	39.2438i	−1.37804	+	1.37804i	−0.847934	+	0.530102i	$0.822154\pi$
$812$		0			0
$813$		0			0
$814$	2.81069	+	2.81069i	0.0985148	+	0.0985148i
$815$		0			0
$816$		0			0
$817$		0			0
$818$			33.0140i			1.15431i
$819$	1.81094	−	1.43168i	0.0632795	−	0.0500268i
$820$	46.3246			1.61772
$821$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$821$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$822$		0			0
$823$	36.9647	+	21.3416i	1.28851	+	0.743920i	0.978388	−	0.206778i	$-0.0662976\pi$
$823$	36.9647	+	21.3416i	1.28851	+	0.743920i	0.310119	+	0.950698i	$0.399631\pi$
$824$	35.9338	−	35.9338i	1.25181	−	1.25181i
$825$		0			0
$826$	4.18990	−	1.12268i	0.145785	−	0.0390630i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	8.51317	−	14.7452i	0.295853	−	0.512432i
$829$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$829$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$830$		0			0
$831$		0			0
$832$	17.2265	−	23.1354i	0.597222	−	0.802076i
$833$		0			0
$834$		0			0
$835$	−9.90012	−	17.1475i	−0.342608	−	0.593414i
$836$	−3.91407	−	2.25979i	−0.135371	−	0.0781565i
$837$		0			0
$838$	11.5747	+	43.1975i	0.399843	+	1.49223i
$839$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$839$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$840$		0			0
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$		0			0
$843$		0			0
$844$		−	54.8634i		−	1.88847i
$845$	−25.5843	−	13.8001i	−0.880127	−	0.474739i
$846$	43.2950			1.48851
$847$	2.24971	+	0.602809i	0.0773011	+	0.0207128i
$848$	−22.9903	−	39.8204i	−0.789490	−	1.36744i
$849$		0			0
$850$		0			0
$851$	6.99925	+	26.1216i	0.239931	+	0.895436i
$852$		0			0
$853$	−4.00000	−	4.00000i	−0.136957	−	0.136957i	0.635304	−	0.772262i	$-0.280875\pi$
$853$	−4.00000	−	4.00000i	−0.136957	−	0.136957i	−0.772262	+	0.635304i	$0.780875\pi$
$854$		0			0
$855$	−44.5120	+	25.6990i	−1.52228	+	0.878888i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	56.2950			1.92076			0.960381	−	0.278691i	$-0.0899005\pi$
$859$	56.2950			1.92076			0.960381	+	0.278691i	$0.0899005\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.00000	−	6.00000i	0.204242	−	0.204242i	−0.597573	−	0.801815i	$-0.703868\pi$
$863$	6.00000	−	6.00000i	0.204242	−	0.204242i	0.801815	+	0.597573i	$0.203868\pi$
$864$		0			0
$865$	39.7071	−	10.6395i	1.35008	−	0.361754i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−15.3743	−	26.6291i	−0.520043	−	0.900741i
$875$	2.06645	+	1.19306i	0.0698587	+	0.0403329i
$876$		0			0
$877$	−2.92820	−	10.9282i	−0.0988784	−	0.369019i	0.898701	−	0.438563i	$-0.144512\pi$
$877$	−2.92820	−	10.9282i	−0.0988784	−	0.369019i	−0.997579	+	0.0695437i	$0.977846\pi$
$878$		0			0
$879$		0			0
$880$	−1.31900	+	2.28457i	−0.0444633	+	0.0770127i
$881$	−34.6016	+	19.9772i	−1.16576	+	0.673050i	−0.952677	−	0.303985i	$-0.901683\pi$
$881$	−34.6016	+	19.9772i	−1.16576	+	0.673050i	−0.213080	+	0.977035i	$0.568349\pi$
$882$	−7.63652	+	28.4999i	−0.257135	+	0.959641i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.84641	+	17.0545i	0.330610	+	0.572633i	0.982632	−	0.185567i	$-0.0594122\pi$
$887$	9.84641	+	17.0545i	0.330610	+	0.572633i	−0.652022	+	0.758200i	$0.726079\pi$
$888$		0			0
$889$	3.36999	−	3.36999i	0.113026	−	0.113026i
$890$	−7.03435	−	26.2525i	−0.235792	−	0.879987i
$891$	−2.56398	+	0.687016i	−0.0858965	+	0.0230159i
$892$	−41.3861	−	41.3861i	−1.38571	−	1.38571i
$893$	39.0942	−	67.7131i	1.30824	−	2.26593i
$894$		0			0
$895$	−3.66025	+	13.6603i	−0.122349	+	0.456612i
$896$		−	2.41459i		−	0.0806658i
$897$		0			0
$898$	−37.1851			−1.24088
$899$		0			0
$900$	15.0000	+	25.9808i	0.500000	+	0.866025i
$901$		0			0
$902$	3.05509	−	3.05509i	0.101723	−	0.101723i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$		0			0
$909$		0			0
$910$	−2.40772	+	0.352485i	−0.0798151	+	0.0116848i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.57958	−	1.22709i	0.151231	−	0.0405222i
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$	−15.5428	+	8.97367i	−0.512432	+	0.295853i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−46.0256	−	12.3325i	−1.51331	−	0.405491i
$926$	−15.8114	−	27.3861i	−0.519594	−	0.899964i
$927$	−46.6793	−	26.9503i	−1.53315	−	0.885165i
$928$		0			0
$929$	−15.4822	−	57.7804i	−0.507955	−	1.89571i	−0.439932	−	0.898031i	$-0.644997\pi$
$929$	−15.4822	−	57.7804i	−0.507955	−	1.89571i	−0.0680235	−	0.997684i	$-0.521669\pi$
$930$		0			0
$931$	37.6780	+	37.6780i	1.23485	+	1.23485i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−28.4317	−	11.2978i	−0.929318	−	0.369279i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$	−39.5228	−	22.8185i	−1.28909	−	0.744257i
$941$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$941$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$942$		0			0
$943$	28.3929	−	7.60786i	0.924600	−	0.247746i
$944$	−40.6491	−	40.6491i	−1.32302	−	1.32302i
$945$		0			0
$946$		0			0
$947$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$947$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$948$		0			0
$949$		0			0
$950$	54.1783			1.75778
$951$		0			0
$952$		0			0
$953$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$953$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$954$	−34.4855	+	34.4855i	−1.11651	+	1.11651i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		−	31.0000i		−	1.00000i
$962$	44.6202	−	19.2431i	1.43861	−	0.620423i
$963$		0			0
$964$	−46.2376	−	12.3893i	−1.48921	−	0.399033i
$965$		0			0
$966$		0			0
$967$	−43.9769	+	43.9769i	−1.41420	+	1.41420i	−0.704363	+	0.709840i	$0.748767\pi$
$967$	−43.9769	+	43.9769i	−1.41420	+	1.41420i	−0.709840	+	0.704363i	$0.751233\pi$
$968$	−7.98888	−	29.8149i	−0.256772	−	0.958287i
$969$		0			0
$970$		0			0
$971$	12.7614	−	22.1034i	0.409532	−	0.709331i	−0.585305	−	0.810813i	$-0.699025\pi$
$971$	12.7614	−	22.1034i	0.409532	−	0.709331i	0.994837	+	0.101482i	$0.0323585\pi$
$972$		0			0
$973$	−1.19375	+	4.45514i	−0.0382699	+	0.142825i
$974$			16.3406i			0.523586i
$975$		0			0
$976$		0			0
$977$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$977$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$978$		0			0
$979$	−2.19526	−	1.26744i	−0.0701609	−	0.0405074i
$980$	21.9919	−	21.9919i	0.702506	−	0.702506i
$981$		0			0
$982$	−27.8722	+	7.46834i	−0.889439	+	0.238324i
$983$	43.6751	+	43.6751i	1.39302	+	1.39302i	0.818469	+	0.574551i	$0.194823\pi$
$983$	43.6751	+	43.6751i	1.39302	+	1.39302i	0.574551	+	0.818469i	$0.305177\pi$
$984$		0			0
$985$	21.0683	−	12.1638i	0.671293	−	0.387571i
$986$		0			0
$987$		0			0
$988$	−43.3426	+	34.2654i	−1.37891	+	1.09013i
$989$		0			0
$990$	2.70267	+	0.724179i	0.0858965	+	0.0230159i
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−25.4905	+	44.1508i	−0.807291	+	1.39827i	0.107442	+	0.994211i	$0.465734\pi$
$997$	−25.4905	+	44.1508i	−0.807291	+	1.39827i	−0.914733	+	0.404058i	$0.867599\pi$
$998$	33.1444	−	19.1359i	1.04917	−	0.605738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.cz.a.379.1	yes	8
5.4	even	2		520.2.cz.b.379.2	yes	8
8.3	odd	2		520.2.cz.b.379.2	yes	8
13.7	odd	12	inner	520.2.cz.a.59.1	✓	8
40.19	odd	2	CM	520.2.cz.a.379.1	yes	8
65.59	odd	12		520.2.cz.b.59.2	yes	8
104.59	even	12		520.2.cz.b.59.2	yes	8
520.59	even	12	inner	520.2.cz.a.59.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.cz.a.59.1	✓	8	13.7	odd	12	inner
520.2.cz.a.59.1	✓	8	520.59	even	12	inner
520.2.cz.a.379.1	yes	8	1.1	even	1	trivial
520.2.cz.a.379.1	yes	8	40.19	odd	2	CM
520.2.cz.b.59.2	yes	8	65.59	odd	12
520.2.cz.b.59.2	yes	8	104.59	even	12
520.2.cz.b.379.2	yes	8	5.4	even	2
520.2.cz.b.379.2	yes	8	8.3	odd	2

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-1.58114 + 1.58114i) q^{5} +(0.206150 - 0.0552376i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(-1.58114 + 1.58114i) q^{5} +(0.206150 - 0.0552376i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(0.0763351 - 0.284887i) q^{11} +(-2.89193 - 2.15331i) q^{13} -0.301824 q^{14} +(2.00000 + 3.46410i) q^{16} +(3.00000 - 3.00000i) q^{18} +(-1.98306 - 7.40089i) q^{19} +(-4.31975 + 1.15747i) q^{20} +(-0.208551 + 0.361222i) q^{22} +(-2.45754 + 1.41886i) q^{23} -5.00000i q^{25} +(3.16228 + 4.00000i) q^{26} +(0.412299 + 0.110475i) q^{28} +(-1.46410 - 5.46410i) q^{32} +(-0.238613 + 0.413289i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(2.46650 - 9.20512i) q^{37} +10.8357i q^{38} +6.32456 q^{40} +(-10.0055 - 2.68097i) q^{41} +(0.417103 - 0.417103i) q^{44} +(-1.73621 - 6.47963i) q^{45} +(3.87640 - 1.03868i) q^{46} +(7.21584 + 7.21584i) q^{47} +(-6.02273 + 3.47723i) q^{49} +(-1.83013 + 6.83013i) q^{50} +(-2.85565 - 6.62158i) q^{52} -11.4952 q^{53} +(0.329749 + 0.571142i) q^{55} +(-0.522774 - 0.301824i) q^{56} +(-13.8819 + 3.71965i) q^{59} +(-0.165713 + 0.618449i) q^{63} +8.00000i q^{64} +(7.97723 - 1.16785i) q^{65} +(0.477226 - 0.477226i) q^{70} +(8.19615 - 2.19615i) q^{72} +(-6.73861 + 11.6716i) q^{74} +(3.96613 - 14.8018i) q^{76} -0.0629458i q^{77} +(-8.63950 - 2.31495i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(12.6865 + 7.32456i) q^{82} +(-0.722443 + 0.417103i) q^{88} +(2.22446 - 8.30178i) q^{89} +9.48683i q^{90} +(-0.715113 - 0.284162i) q^{91} -5.67544 q^{92} +(-7.21584 - 12.4982i) q^{94} +(14.8373 + 8.56634i) q^{95} +(9.49996 - 2.54551i) q^{98} +(0.625654 + 0.625654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 12 q^{7} - 16 q^{8} - 12 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 12 * q^7 - 16 * q^8 - 12 * q^9	\( 8 q - 4 q^{2} + 12 q^{7} - 16 q^{8} - 12 q^{9} + 4 q^{11} + 8 q^{13} + 16 q^{16} + 24 q^{18} - 24 q^{19} - 4 q^{22} + 24 q^{28} + 16 q^{32} + 20 q^{35} - 16 q^{37} - 4 q^{41} + 8 q^{44} + 24 q^{46} - 8 q^{47} + 20 q^{50} - 16 q^{52} - 16 q^{53} + 20 q^{55} - 48 q^{56} - 28 q^{59} - 36 q^{63} + 20 q^{65} - 40 q^{70} + 24 q^{72} - 32 q^{74} + 48 q^{76} - 36 q^{81} - 24 q^{88} - 56 q^{89} - 96 q^{92} + 8 q^{94} + 60 q^{95} - 16 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 12 * q^7 - 16 * q^8 - 12 * q^9 + 4 * q^11 + 8 * q^13 + 16 * q^16 + 24 * q^18 - 24 * q^19 - 4 * q^22 + 24 * q^28 + 16 * q^32 + 20 * q^35 - 16 * q^37 - 4 * q^41 + 8 * q^44 + 24 * q^46 - 8 * q^47 + 20 * q^50 - 16 * q^52 - 16 * q^53 + 20 * q^55 - 48 * q^56 - 28 * q^59 - 36 * q^63 + 20 * q^65 - 40 * q^70 + 24 * q^72 - 32 * q^74 + 48 * q^76 - 36 * q^81 - 24 * q^88 - 56 * q^89 - 96 * q^92 + 8 * q^94 + 60 * q^95 - 16 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more