LMFDB - Embedded newform 520.2.cz.a.59.2

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			59.2
Root			$0.578737 - 2.15988i$ of defining polynomial
Character	$\chi$	$=$	520.59
Dual form			520.2.cz.a.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.58114 + 1.58114i) q^{5} +(4.52590 + 1.21271i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.58114 + 1.58114i) q^{5} +(4.52590 + 1.21271i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(0.923665 + 3.44716i) q^{11} +(1.42783 + 3.31079i) q^{13} -6.62638 q^{14} +(2.00000 - 3.46410i) q^{16} +(3.00000 + 3.00000i) q^{18} +(1.17922 - 4.40089i) q^{19} +(4.31975 + 1.15747i) q^{20} +(-2.52350 - 4.37083i) q^{22} +(-7.93477 - 4.58114i) q^{23} +5.00000i q^{25} +(-3.16228 - 4.00000i) q^{26} +(9.05180 - 2.42542i) q^{28} +(-1.46410 + 5.46410i) q^{32} +(5.23861 + 9.07354i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(0.461700 + 1.72309i) q^{37} +6.44335i q^{38} -6.32456 q^{40} +(7.27348 - 1.94892i) q^{41} +(5.04700 + 5.04700i) q^{44} +(1.73621 - 6.47963i) q^{45} +(12.5159 + 3.35363i) q^{46} +(-9.21584 + 9.21584i) q^{47} +(12.9509 + 7.47723i) q^{49} +(-1.83013 - 6.83013i) q^{50} +(5.78385 + 4.30663i) q^{52} +14.4234 q^{53} +(-3.99000 + 6.91089i) q^{55} +(-11.4772 + 6.62638i) q^{56} +(-5.24243 - 1.40470i) q^{59} +(-3.63813 - 13.5777i) q^{63} -8.00000i q^{64} +(-2.97723 + 7.49240i) q^{65} +(-10.4772 - 10.4772i) q^{70} +(8.19615 + 2.19615i) q^{72} +(-1.26139 - 2.18479i) q^{74} +(-2.35843 - 8.80178i) q^{76} +16.7217i q^{77} +(8.63950 - 2.31495i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-9.22240 + 5.32456i) q^{82} +(-8.74166 - 5.04700i) q^{88} +(-4.10010 - 15.3018i) q^{89} +9.48683i q^{90} +(2.44716 + 16.7158i) q^{91} -18.3246 q^{92} +(9.21584 - 15.9623i) q^{94} +(8.82292 - 5.09392i) q^{95} +(-20.4282 - 5.47371i) q^{98} +(7.57050 - 7.57050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$-1$	$-1$

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	$-0.333333\pi$
$3$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$4$	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
$7$	4.52590	+	1.21271i	1.71063	+	0.458362i	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	4.52590	+	1.21271i	1.71063	+	0.458362i	0.735051	+	0.678012i	$0.237158\pi$
$8$	−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
$11$	0.923665	+	3.44716i	0.278495	+	1.03936i	0.953463	+	0.301511i	$0.0974911\pi$
$11$	0.923665	+	3.44716i	0.278495	+	1.03936i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$	1.42783	+	3.31079i	0.396007	+	0.918247i
$13$	1.42783	+	3.31079i	0.396007	+	0.918247i
$14$	−6.62638			−1.77097
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	3.00000	+	3.00000i	0.707107	+	0.707107i
$19$	1.17922	−	4.40089i	0.270530	−	1.00963i	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	1.17922	−	4.40089i	0.270530	−	1.00963i	0.958778	−	0.284157i	$-0.0917138\pi$
$20$	4.31975	+	1.15747i	0.965926	+	0.258819i
$21$		0			0
$22$	−2.52350	−	4.37083i	−0.538012	−	0.931864i
$23$	−7.93477	−	4.58114i	−1.65451	−	0.955233i	−0.975183	−	0.221401i	$-0.928937\pi$
$23$	−7.93477	−	4.58114i	−1.65451	−	0.955233i	−0.679330	−	0.733833i	$-0.737729\pi$
$24$		0			0
$25$			5.00000i			1.00000i
$26$	−3.16228	−	4.00000i	−0.620174	−	0.784465i
$27$		0			0
$28$	9.05180	−	2.42542i	1.71063	−	0.458362i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$31$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$		0			0
$34$		0			0
$35$	5.23861	+	9.07354i	0.885487	+	1.53371i
$36$	−5.19615	−	3.00000i	−0.866025	−	0.500000i
$37$	0.461700	+	1.72309i	0.0759030	+	0.283274i	0.993437	−	0.114385i	$-0.0364896\pi$
$37$	0.461700	+	1.72309i	0.0759030	+	0.283274i	−0.917534	+	0.397658i	$0.869823\pi$
$38$			6.44335i			1.04525i
$39$		0			0
$40$	−6.32456			−1.00000
$41$	7.27348	−	1.94892i	1.13593	−	0.304371i	0.358614	−	0.933486i	$-0.383249\pi$
$41$	7.27348	−	1.94892i	1.13593	−	0.304371i	0.777312	+	0.629115i	$0.216583\pi$
$42$		0			0
$43$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$43$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$44$	5.04700	+	5.04700i	0.760864	+	0.760864i
$45$	1.73621	−	6.47963i	0.258819	−	0.965926i
$46$	12.5159	+	3.35363i	1.84537	+	0.494465i
$47$	−9.21584	+	9.21584i	−1.34427	+	1.34427i	−0.452508	+	0.891761i	$0.649470\pi$
$47$	−9.21584	+	9.21584i	−1.34427	+	1.34427i	−0.891761	+	0.452508i	$0.850530\pi$
$48$		0			0
$49$	12.9509	+	7.47723i	1.85013	+	1.06818i
$50$	−1.83013	−	6.83013i	−0.258819	−	0.965926i
$51$		0			0
$52$	5.78385	+	4.30663i	0.802076	+	0.597222i
$53$	14.4234			1.98120			0.990600	−	0.136789i	$-0.0436783\pi$
$53$	14.4234			1.98120			0.990600	+	0.136789i	$0.0436783\pi$
$54$		0			0
$55$	−3.99000	+	6.91089i	−0.538012	+	0.931864i
$56$	−11.4772	+	6.62638i	−1.53371	+	0.885487i
$57$		0			0
$58$		0			0
$59$	−5.24243	−	1.40470i	−0.682506	−	0.182877i	−0.0991242	−	0.995075i	$-0.531604\pi$
$59$	−5.24243	−	1.40470i	−0.682506	−	0.182877i	−0.583382	+	0.812198i	$0.698271\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$	−3.63813	−	13.5777i	−0.458362	−	1.71063i
$64$		−	8.00000i		−	1.00000i
$65$	−2.97723	+	7.49240i	−0.369279	+	0.929318i
$66$		0			0
$67$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$67$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$68$		0			0
$69$		0			0
$70$	−10.4772	−	10.4772i	−1.25227	−	1.25227i
$71$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$71$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$72$	8.19615	+	2.19615i	0.965926	+	0.258819i
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$	−1.26139	−	2.18479i	−0.146633	−	0.253976i
$75$		0			0
$76$	−2.35843	−	8.80178i	−0.270530	−	1.00963i
$77$			16.7217i			1.90561i
$78$		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
$82$	−9.22240	+	5.32456i	−1.01844	+	0.587999i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−8.74166	−	5.04700i	−0.931864	−	0.538012i
$89$	−4.10010	−	15.3018i	−0.434610	−	1.62199i	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−4.10010	−	15.3018i	−0.434610	−	1.62199i	0.307389	−	0.951584i	$-0.400545\pi$
$90$			9.48683i			1.00000i
$91$	2.44716	+	16.7158i	0.256533	+	1.75230i
$92$	−18.3246			−1.91047
$93$		0			0
$94$	9.21584	−	15.9623i	0.950541	−	1.64639i
$95$	8.82292	−	5.09392i	0.905213	−	0.522625i
$96$		0			0
$97$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$97$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$98$	−20.4282	−	5.47371i	−2.06356	−	0.552928i
$99$	7.57050	−	7.57050i	0.760864	−	0.760864i
$100$	5.00000	+	8.66025i	0.500000	+	0.866025i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$		−	20.2818i		−	1.99843i	−0.0396400	−	0.999214i	$-0.512621\pi$
$103$		−	20.2818i		−	1.99843i	0.0396400	−	0.999214i	$-0.487379\pi$
$104$	−9.47723	−	3.76593i	−0.929318	−	0.369279i
$105$		0			0
$106$	−19.7027	+	5.27931i	−1.91369	+	0.512772i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$		0			0
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$	2.92088	−	10.9009i	0.278495	−	1.03936i
$111$		0			0
$112$	13.2528	−	13.2528i	1.25227	−	1.25227i
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$		0			0
$115$	−5.30255	−	19.7894i	−0.494465	−	1.84537i
$116$		0			0
$117$	6.45994	−	8.67578i	0.597222	−	0.802076i
$118$	7.67544			0.706582
$119$		0			0
$120$		0			0
$121$	−1.50351	+	0.868049i	−0.136682	+	0.0789135i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.90569	+	7.90569i	−0.707107	+	0.707107i
$126$	9.93957	+	17.2158i	0.885487	+	1.53371i
$127$	−18.0711	−	10.4334i	−1.60355	−	0.925810i	−0.990769	−	0.135558i	$-0.956717\pi$
$127$	−18.0711	−	10.4334i	−1.60355	−	0.925810i	−0.612781	−	0.790253i	$-0.709949\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$		0			0
$130$	1.32456	−	11.3246i	0.116171	−	0.993229i
$131$	15.8903			1.38834			0.694170	−	0.719811i	$-0.255772\pi$
$131$	15.8903			1.38834			0.694170	+	0.719811i	$0.255772\pi$
$132$		0			0
$133$	10.6740	−	18.4879i	0.925555	−	1.60311i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$137$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$138$		0			0
$139$	−1.31876	−	2.28416i	−0.111856	−	0.193740i	0.804663	−	0.593732i	$-0.202346\pi$
$139$	−1.31876	−	2.28416i	−0.111856	−	0.193740i	−0.916519	+	0.399992i	$0.869013\pi$
$140$	18.1471	+	10.4772i	1.53371	+	0.885487i
$141$		0			0
$142$		0			0
$143$	−10.0940	+	7.98001i	−0.844102	+	0.667322i
$144$	−12.0000			−1.00000
$145$		0			0
$146$		0			0
$147$		0			0
$148$	2.52277	+	2.52277i	0.207371	+	0.207371i
$149$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$149$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$150$		0			0
$151$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$151$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$152$	6.44335	+	11.1602i	0.522625	+	0.905213i
$153$		0			0
$154$	−6.12055	−	22.8422i	−0.493208	−	1.84068i
$155$		0			0
$156$		0			0
$157$	−5.14083			−0.410283			−0.205142	−	0.978732i	$-0.565765\pi$
$157$	−5.14083			−0.410283			−0.205142	+	0.978732i	$0.565765\pi$
$158$		0			0
$159$		0			0
$160$	−10.9545	+	6.32456i	−0.866025	+	0.500000i
$161$	−30.3564	−	30.3564i	−2.39242	−	2.39242i
$162$	3.29423	−	12.2942i	0.258819	−	0.965926i
$163$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$163$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$164$	10.6491	−	10.6491i	0.831556	−	0.831556i
$165$		0			0
$166$		0			0
$167$	−4.29663	−	16.0352i	−0.332483	−	1.24084i	−0.906572	−	0.422051i	$-0.861310\pi$
$167$	−4.29663	−	16.0352i	−0.332483	−	1.24084i	0.574089	−	0.818793i	$-0.305356\pi$
$168$		0			0
$169$	−8.92263	+	9.45445i	−0.686356	+	0.727265i
$170$		0			0
$171$	−13.2027	+	3.53765i	−1.00963	+	0.270530i
$172$		0			0
$173$	−21.9354	+	12.6644i	−1.66772	+	0.962858i	−0.698854	+	0.715264i	$0.746306\pi$
$173$	−21.9354	+	12.6644i	−1.66772	+	0.962858i	−0.968864	+	0.247593i	$0.920360\pi$
$174$		0			0
$175$	−6.06356	+	22.6295i	−0.458362	+	1.71063i
$176$	13.7887	+	3.69466i	1.03936	+	0.278495i
$177$		0			0
$178$	11.2017	+	19.4019i	0.839601	+	1.45423i
$179$	−5.47723	−	3.16228i	−0.409387	−	0.236360i	0.281139	−	0.959667i	$-0.409288\pi$
$179$	−5.47723	−	3.16228i	−0.409387	−	0.236360i	−0.690526	+	0.723307i	$0.742621\pi$
$180$	−3.47242	−	12.9593i	−0.258819	−	0.965926i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−9.46131	−	21.9385i	−0.701319	−	1.62619i
$183$		0			0
$184$	25.0318	−	6.70725i	1.84537	−	0.494465i
$185$	−1.99443	+	3.45445i	−0.146633	+	0.253976i
$186$		0			0
$187$		0			0
$188$	−6.74646	+	25.1781i	−0.492036	+	1.83630i
$189$		0			0
$190$	−10.1878	+	10.1878i	−0.739103	+	0.739103i
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$		0			0
$193$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$193$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$194$		0			0
$195$		0			0
$196$	29.9089			2.13635
$197$	26.9012	−	7.20816i	1.91663	−	0.513560i	0.925893	−	0.377785i	$-0.123314\pi$
$197$	26.9012	−	7.20816i	1.91663	−	0.513560i	0.990740	−	0.135775i	$-0.0433525\pi$
$198$	−7.57050	+	13.1125i	−0.538012	+	0.931864i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−10.0000	−	10.0000i	−0.707107	−	0.707107i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	14.5819	+	8.41886i	1.01844	+	0.587999i
$206$	7.42366	+	27.7055i	0.517231	+	1.93033i
$207$			27.4868i			1.91047i
$208$	14.3246	+	1.67544i	0.993229	+	0.116171i
$209$	16.2598			1.12471
$210$		0			0
$211$	2.71584	−	4.70397i	0.186966	−	0.323835i	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	2.71584	−	4.70397i	0.186966	−	0.323835i	0.944237	+	0.329266i	$0.106801\pi$
$212$	24.9820	−	14.4234i	1.71577	−	0.990600i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$			15.9600i			1.07602i
$221$		0			0
$222$		0			0
$223$	9.14290	−	2.44983i	0.612254	−	0.164053i	0.0606498	−	0.998159i	$-0.480683\pi$
$223$	9.14290	−	2.44983i	0.612254	−	0.164053i	0.551604	+	0.834106i	$0.314016\pi$
$224$	−13.2528	+	22.9545i	−0.885487	+	1.53371i
$225$	12.9904	−	7.50000i	0.866025	−	0.500000i
$226$		0			0
$227$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$227$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$228$		0			0
$229$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$229$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$230$	14.4868	+	25.0919i	0.955233	+	1.65451i
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	−5.64889	+	14.2158i	−0.369279	+	0.929318i
$235$	−29.1430			−1.90108
$236$	−10.4849	+	2.80941i	−0.682506	+	0.182877i
$237$		0			0
$238$		0			0
$239$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$239$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$240$		0			0
$241$	−10.4697	−	2.80534i	−0.674411	−	0.180708i	−0.0946700	−	0.995509i	$-0.530180\pi$
$241$	−10.4697	−	2.80534i	−0.674411	−	0.180708i	−0.579741	+	0.814801i	$0.696846\pi$
$242$	1.73610	−	1.73610i	0.111601	−	0.111601i
$243$		0			0
$244$		0			0
$245$	8.65469	+	32.2998i	0.552928	+	2.06356i
$246$		0			0
$247$	16.2541	−	2.37957i	1.03423	−	0.151408i
$248$		0			0
$249$		0			0
$250$	7.90569	−	13.6931i	0.500000	−	0.866025i
$251$	−22.8511	+	13.1931i	−1.44235	+	0.832739i	−0.998006	−	0.0631194i	$-0.979895\pi$
$251$	−22.8511	+	13.1931i	−1.44235	+	0.832739i	−0.444340	+	0.895858i	$0.646562\pi$
$252$	−19.8791	−	19.8791i	−1.25227	−	1.25227i
$253$	8.46287	−	31.5839i	0.532056	−	1.98566i
$254$	28.5045	+	7.63774i	1.78853	+	0.479235i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$			8.35843i			0.519368i
$260$	2.33570	+	15.9545i	0.144854	+	0.989453i
$261$		0			0
$262$	−21.7065	+	5.81625i	−1.34103	+	0.359329i
$263$	−0.0469174	+	0.0812633i	−0.00289305	+	0.00501091i	−0.867468	−	0.497492i	$-0.834254\pi$
$263$	−0.0469174	+	0.0812633i	−0.00289305	+	0.00501091i	0.864575	+	0.502503i	$0.167588\pi$
$264$		0			0
$265$	22.8053	+	22.8053i	1.40092	+	1.40092i
$266$	−7.81393	+	29.1620i	−0.479103	+	1.78804i
$267$		0			0
$268$		0			0
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$		0			0
$271$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$271$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−17.2358	+	4.61832i	−1.03936	+	0.278495i
$276$		0			0
$277$	−23.6512	+	13.6550i	−1.42106	+	0.820451i	−0.996390	−	0.0848955i	$-0.972944\pi$
$277$	−23.6512	+	13.6550i	−1.42106	+	0.820451i	−0.424673	+	0.905347i	$0.639611\pi$
$278$	2.63752	+	2.63752i	0.158188	+	0.158188i
$279$		0			0
$280$	−28.6243	−	7.66986i	−1.71063	−	0.458362i
$281$	23.6491	−	23.6491i	1.41079	−	1.41079i	0.656205	−	0.754583i	$-0.272161\pi$
$281$	23.6491	−	23.6491i	1.41079	−	1.41079i	0.754583	−	0.656205i	$-0.227839\pi$
$282$		0			0
$283$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$283$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$284$		0			0
$285$		0			0
$286$	10.8678	−	14.5955i	0.642625	−	0.863053i
$287$	35.2825			2.08266
$288$	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
$293$	−26.2324	−	7.02896i	−1.53251	−	0.410636i	−0.608676	−	0.793419i	$-0.708299\pi$
$293$	−26.2324	−	7.02896i	−1.53251	−	0.410636i	−0.923838	+	0.382782i	$0.874966\pi$
$294$		0			0
$295$	−6.06797	−	10.5100i	−0.353291	−	0.611918i
$296$	−4.36957	−	2.52277i	−0.253976	−	0.146633i
$297$		0			0
$298$		0			0
$299$	3.83772	−	32.8114i	0.221941	−	1.89753i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−12.8867	−	12.8867i	−0.739103	−	0.739103i
$305$		0			0
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	16.7217	+	28.9628i	0.952805	+	1.65031i
$309$		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			$\pi$
$314$	7.02251	−	1.88168i	0.396303	−	0.106189i
$315$	15.7158	−	27.2206i	0.885487	−	1.53371i
$316$		0			0
$317$	0.675667	+	0.675667i	0.0379492	+	0.0379492i	0.725827	−	0.687878i	$-0.241457\pi$
$317$	0.675667	+	0.675667i	0.0379492	+	0.0379492i	−0.687878	+	0.725827i	$0.741457\pi$
$318$		0			0
$319$		0			0
$320$	12.6491	−	12.6491i	0.707107	−	0.707107i
$321$		0			0
$322$	52.5788	+	30.3564i	2.93010	+	1.69169i
$323$		0			0
$324$			18.0000i			1.00000i
$325$	−16.5539	+	7.13913i	−0.918247	+	0.396007i
$326$		0			0
$327$		0			0
$328$	−10.6491	+	18.4448i	−0.587999	+	1.01844i
$329$	−52.8861	+	30.5338i	−2.91571	+	1.68338i
$330$		0			0
$331$	−2.49314	+	9.30453i	−0.137035	+	0.511423i	0.862946	+	0.505296i	$0.168617\pi$
$331$	−2.49314	+	9.30453i	−0.137035	+	0.511423i	−0.999981	+	0.00612670i	$0.998050\pi$
$332$		0			0
$333$	3.78416	−	3.78416i	0.207371	−	0.207371i
$334$	11.7386	+	20.3319i	0.642308	+	1.11251i
$335$		0			0
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	8.72797	−	16.1809i	0.474739	−	0.880127i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	16.7403	−	9.66503i	0.905213	−	0.522625i
$343$	26.3546	+	26.3546i	1.42301	+	1.42301i
$344$		0			0
$345$		0			0
$346$	25.3288	−	25.3288i	1.36169	−	1.36169i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$349$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$350$		−	33.1319i		−	1.77097i
$351$		0			0
$352$	−20.1880			−1.07602
$353$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$353$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$354$		0			0
$355$		0			0
$356$	−22.4034	−	22.4034i	−1.18738	−	1.18738i
$357$		0			0
$358$	8.63950	+	2.31495i	0.456612	+	0.122349i
$359$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$359$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$360$	9.48683	+	16.4317i	0.500000	+	0.866025i
$361$	−1.52281	−	0.879192i	−0.0801477	−	0.0462733i
$362$		0			0
$363$		0			0
$364$	20.9545	+	26.5055i	1.09831	+	1.38927i
$365$		0			0
$366$		0			0
$367$	−3.09431	+	5.35949i	−0.161521	+	0.279763i	−0.935415	−	0.353553i	$-0.884973\pi$
$367$	−3.09431	+	5.35949i	−0.161521	+	0.279763i	0.773893	+	0.633316i	$0.218307\pi$
$368$	−31.7391	+	18.3246i	−1.65451	+	0.955233i
$369$	−15.9737	−	15.9737i	−0.831556	−	0.831556i
$370$	1.46002	−	5.44888i	0.0759030	−	0.283274i
$371$	65.2787	+	17.4914i	3.38910	+	0.908107i
$372$		0			0
$373$	−19.0680	−	33.0267i	−0.987302	−	1.71006i	−0.631222	−	0.775602i	$-0.717446\pi$
$373$	−19.0680	−	33.0267i	−0.987302	−	1.71006i	−0.356080	−	0.934456i	$-0.615887\pi$
$374$		0			0
$375$		0			0
$376$		−	36.8634i		−	1.90108i
$377$		0			0
$378$		0			0
$379$	−26.2027	+	7.02098i	−1.34594	+	0.360644i	−0.858635	−	0.512588i	$-0.828687\pi$
$379$	−26.2027	+	7.02098i	−1.34594	+	0.360644i	−0.487306	+	0.873231i	$0.662020\pi$
$380$	10.1878	−	17.6458i	0.522625	−	0.905213i
$381$		0			0
$382$		0			0
$383$	3.47242	−	12.9593i	0.177432	−	0.662187i	−0.818692	−	0.574233i	$-0.805300\pi$
$383$	3.47242	−	12.9593i	0.177432	−	0.662187i	0.996125	−	0.0879542i	$-0.0280329\pi$
$384$		0			0
$385$	−26.4393	+	26.4393i	−1.34747	+	1.34747i
$386$		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
$392$	−40.8563	+	10.9474i	−2.06356	+	0.552928i
$393$		0			0
$394$	−34.1094	+	19.6931i	−1.71841	+	0.992122i
$395$		0			0
$396$	5.54199	−	20.6830i	0.278495	−	1.03936i
$397$	35.2842	+	9.45438i	1.77086	+	0.474502i	0.988870	−	0.148783i	$-0.0475356\pi$
$397$	35.2842	+	9.45438i	1.77086	+	0.474502i	0.781995	+	0.623285i	$0.214202\pi$
$398$		0			0
$399$		0			0
$400$	17.3205	+	10.0000i	0.866025	+	0.500000i
$401$	−0.616760	−	2.30178i	−0.0307995	−	0.114945i	0.948815	−	0.315833i	$-0.102284\pi$
$401$	−0.616760	−	2.30178i	−0.0307995	−	0.114945i	−0.979614	+	0.200888i	$0.935617\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−19.4389	+	5.20863i	−0.965926	+	0.258819i
$406$		0			0
$407$	−5.51331	+	3.18311i	−0.273285	+	0.157781i
$408$		0			0
$409$	−0.958011	+	3.57534i	−0.0473706	+	0.176789i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−0.958011	+	3.57534i	−0.0473706	+	0.176789i	0.938187	+	0.346128i	$0.112504\pi$
$410$	−23.0008	−	6.16303i	−1.13593	−	0.304371i
$411$		0			0
$412$	−20.2818	−	35.1292i	−0.999214	−	1.73069i
$413$	−22.0232	−	12.7151i	−1.08369	−	0.625669i
$414$	−10.0609	−	37.5477i	−0.494465	−	1.84537i
$415$		0			0
$416$	−20.1810	+	2.95445i	−0.989453	+	0.144854i
$417$		0			0
$418$	−22.2113	+	5.95150i	−1.08639	+	0.291097i
$419$	15.8114	−	27.3861i	0.772437	−	1.33790i	−0.163787	−	0.986496i	$-0.552371\pi$
$419$	15.8114	−	27.3861i	0.772437	−	1.33790i	0.936224	−	0.351404i	$-0.114296\pi$
$420$		0			0
$421$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$	−1.98813	+	7.41981i	−0.0967807	+	0.361191i
$423$	37.7672	+	10.1197i	1.83630	+	0.492036i
$424$	−28.8467	+	28.8467i	−1.40092	+	1.40092i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$431$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$432$		0			0
$433$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$433$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−29.5179	+	29.5179i	−1.41203	+	1.41203i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	−5.84177	−	21.8018i	−0.278495	−	1.03936i
$441$		−	44.8634i		−	2.13635i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	17.7114	−	30.6771i	0.839601	−	1.45423i
$446$	−11.5927	+	6.69306i	−0.548932	+	0.316926i
$447$		0			0
$448$	9.70169	−	36.2072i	0.458362	−	1.71063i
$449$	38.0470	+	10.1947i	1.79555	+	0.481116i	0.993269	−	0.115833i	$-0.0369536\pi$
$449$	38.0470	+	10.1947i	1.79555	+	0.481116i	0.802280	+	0.596948i	$0.203620\pi$
$450$	−15.0000	+	15.0000i	−0.707107	+	0.707107i
$451$	13.4365	+	23.2727i	0.632701	+	1.09587i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−22.5608	+	30.2994i	−1.05766	+	1.42046i
$456$		0			0
$457$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$457$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$458$		0			0
$459$		0			0
$460$	−28.9737	−	28.9737i	−1.35090	−	1.35090i
$461$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$461$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$462$		0			0
$463$	−15.8114	+	15.8114i	−0.734818	+	0.734818i	−0.971570	−	0.236752i	$-0.923917\pi$
$463$	−15.8114	+	15.8114i	−0.734818	+	0.734818i	0.236752	+	0.971570i	$0.423917\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$	2.51317	−	21.4868i	0.116171	−	0.993229i
$469$		0			0
$470$	39.8101	−	10.6671i	1.83630	−	0.492036i
$471$		0			0
$472$	13.2943	−	7.67544i	0.611918	−	0.353291i
$473$		0			0
$474$		0			0
$475$	22.0045	+	5.89608i	1.00963	+	0.270530i
$476$		0			0
$477$	−21.6350	−	37.4730i	−0.990600	−	1.71577i
$478$		0			0
$479$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$479$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$480$		0			0
$481$	−5.04555	+	3.98886i	−0.230057	+	0.181876i
$482$	15.3287			0.698202
$483$		0			0
$484$	−1.73610	+	3.00701i	−0.0789135	+	0.136682i
$485$		0			0
$486$		0			0
$487$	11.0431	−	41.2134i	0.500410	−	1.86756i	0.00308010	−	0.999995i	$-0.499020\pi$
$487$	11.0431	−	41.2134i	0.500410	−	1.86756i	0.497330	−	0.867561i	$-0.334314\pi$
$488$		0			0
$489$		0			0
$490$	−23.6451	−	40.9545i	−1.06818	−	1.85013i
$491$	−20.6703	−	11.9340i	−0.932837	−	0.538574i	−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−20.6703	−	11.9340i	−0.932837	−	0.538574i	−0.887708	+	0.460407i	$0.847703\pi$
$492$		0			0
$493$		0			0
$494$	−21.3326	+	9.19998i	−0.959798	+	0.413927i
$495$	23.9400			1.07602
$496$		0			0
$497$		0			0
$498$		0			0
$499$	25.1359	+	25.1359i	1.12524	+	1.12524i	0.990941	+	0.134298i	$0.0428781\pi$
$499$	25.1359	+	25.1359i	1.12524	+	1.12524i	0.134298	+	0.990941i	$0.457122\pi$
$500$	−5.78737	+	21.5988i	−0.258819	+	0.965926i
$501$		0			0
$502$	26.3861	−	26.3861i	1.17767	−	1.17767i
$503$	−16.8767	−	29.2313i	−0.752495	−	1.30336i	−0.946610	−	0.322381i	$-0.895517\pi$
$503$	−16.8767	−	29.2313i	−0.752495	−	1.30336i	0.194115	−	0.980979i	$-0.437817\pi$
$504$	34.4317	+	19.8791i	1.53371	+	0.885487i
$505$		0			0
$506$			46.2420i			2.05571i
$507$		0			0
$508$	−41.7334			−1.85162
$509$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$509$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$		0			0
$515$	32.0684	−	32.0684i	1.41310	−	1.41310i
$516$		0			0
$517$	−40.2809	−	23.2562i	−1.77155	−	1.02280i
$518$	−3.05940	−	11.4178i	−0.134422	−	0.501671i
$519$		0			0
$520$	−9.03036	−	20.9393i	−0.396007	−	0.918247i
$521$	2.90890			0.127441			0.0637207	−	0.997968i	$-0.479703\pi$
$521$	2.90890			0.127441			0.0637207	+	0.997968i	$0.479703\pi$
$522$		0			0
$523$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$523$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$524$	27.5228	−	15.8903i	1.20234	−	0.694170i
$525$		0			0
$526$	0.0343459	−	0.128181i	0.00149755	−	0.00558894i
$527$		0			0
$528$		0			0
$529$	30.4737	+	52.7819i	1.32494	+	2.29487i
$530$	−39.5000	−	22.8053i	−1.71577	−	0.990600i
$531$	4.21411	+	15.7273i	0.182877	+	0.682506i
$532$		−	42.6961i		−	1.85111i
$533$	16.8377	+	21.2982i	0.729323	+	0.922528i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.8129	+	51.5504i	−0.594964	+	2.22044i
$540$		0			0
$541$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$541$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$542$		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
$550$	21.8541	−	12.6175i	0.931864	−	0.538012i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	27.3101	−	27.3101i	1.16029	−	1.16029i
$555$		0			0
$556$	−4.56832	−	2.63752i	−0.193740	−	0.111856i
$557$	−11.8798	−	44.3360i	−0.503363	−	1.87858i	−0.476957	−	0.878927i	$-0.658260\pi$
$557$	−11.8798	−	44.3360i	−0.503363	−	1.87858i	−0.0264067	−	0.999651i	$-0.508406\pi$
$558$		0			0
$559$		0			0
$560$	41.9089			1.77097
$561$		0			0
$562$	−23.6491	+	40.9615i	−0.997578	+	1.72785i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−29.8187	+	29.8187i	−1.25227	+	1.25227i
$568$		0			0
$569$	29.4054	+	16.9772i	1.23274	+	0.711722i	0.967600	−	0.252488i	$-0.0812488\pi$
$569$	29.4054	+	16.9772i	1.23274	+	0.711722i	0.265139	+	0.964210i	$0.414582\pi$
$570$		0			0
$571$			47.3406i			1.98114i	0.137002	+	0.990571i	$0.456253\pi$
$571$			47.3406i			1.98114i	−0.137002	+	0.990571i	$0.543747\pi$
$572$	−9.50331	+	23.9158i	−0.397353	+	0.999969i
$573$		0			0
$574$	−48.1968	+	12.9143i	−2.01170	+	0.539032i
$575$	22.9057	−	39.6738i	0.955233	−	1.65451i
$576$	−20.7846	+	12.0000i	−0.866025	+	0.500000i
$577$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$577$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$578$	−6.22243	+	23.2224i	−0.258819	+	0.965926i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	13.3223	+	49.7197i	0.551755	+	2.05918i
$584$		0			0
$585$	23.9317	−	3.50355i	0.989453	−	0.144854i
$586$	38.4069			1.58658
$587$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$587$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$588$		0			0
$589$		0			0
$590$	12.1359	+	12.1359i	0.499629	+	0.499629i
$591$		0			0
$592$	6.89235	+	1.84680i	0.283274	+	0.0759030i
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	6.76738	+	46.2259i	0.276739	+	1.89032i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	−24.5111	+	42.4545i	−0.999828	+	1.73175i	−0.483860	+	0.875145i	$0.660766\pi$
$601$	−24.5111	+	42.4545i	−0.999828	+	1.73175i	−0.515968	+	0.856608i	$0.672568\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.74976	−	1.00474i	−0.152449	−	0.0408487i
$606$		0			0
$607$	5.00008	+	8.66039i	0.202947	+	0.351515i	0.949477	−	0.313838i	$-0.101615\pi$
$607$	5.00008	+	8.66039i	0.202947	+	0.351515i	−0.746530	+	0.665352i	$0.768281\pi$
$608$	22.3204	+	12.8867i	0.905213	+	0.522625i
$609$		0			0
$610$		0			0
$611$	−43.6703	−	17.3531i	−1.76671	−	0.702030i
$612$		0			0
$613$	−19.0266	+	5.09816i	−0.768476	+	0.205913i	−0.621698	−	0.783257i	$-0.713557\pi$
$613$	−19.0266	+	5.09816i	−0.768476	+	0.205913i	−0.146778	+	0.989169i	$0.546890\pi$
$614$		0			0
$615$		0			0
$616$	−33.4433	−	33.4433i	−1.34747	−	1.34747i
$617$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$617$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$618$		0			0
$619$	−27.9462	+	27.9462i	−1.12325	+	1.12325i	−0.132002	+	0.991250i	$0.542140\pi$
$619$	−27.9462	+	27.9462i	−1.12325	+	1.12325i	−0.991250	+	0.132002i	$0.957860\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	74.2266i		−	2.97383i
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$		0			0
$628$	−8.90418	+	5.14083i	−0.355316	+	0.205142i
$629$		0			0
$630$	−11.5048	+	42.9365i	−0.458362	+	1.71063i
$631$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$631$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$632$		0			0
$633$		0			0
$634$	−1.17029	−	0.675667i	−0.0464781	−	0.0268342i
$635$	−12.0763	−	45.0695i	−0.479235	−	1.78853i
$636$		0			0
$637$	−6.26384	+	53.5540i	−0.248182	+	2.12189i
$638$		0			0
$639$		0			0
$640$	−12.6491	+	21.9089i	−0.500000	+	0.866025i
$641$	38.8134	−	22.4089i	1.53304	−	0.885098i	0.533816	−	0.845601i	$-0.320758\pi$
$641$	38.8134	−	22.4089i	1.53304	−	0.885098i	0.999220	−	0.0394976i	$-0.0125758\pi$
$642$		0			0
$643$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$643$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$644$	−82.9351	−	22.2224i	−3.26810	−	0.875685i
$645$		0			0
$646$		0			0
$647$	35.0479	+	20.2349i	1.37787	+	0.795516i	0.991903	−	0.126994i	$-0.0405330\pi$
$647$	35.0479	+	20.2349i	1.37787	+	0.795516i	0.385972	+	0.922511i	$0.373866\pi$
$648$	−6.58846	−	24.5885i	−0.258819	−	0.965926i
$649$		−	19.3690i		−	0.760299i
$650$	20.0000	−	15.8114i	0.784465	−	0.620174i
$651$		0			0
$652$		0			0
$653$	−8.74833	+	15.1526i	−0.342349	+	0.592965i	−0.984868	−	0.173304i	$-0.944556\pi$
$653$	−8.74833	+	15.1526i	−0.342349	+	0.592965i	0.642520	+	0.766269i	$0.277889\pi$
$654$		0			0
$655$	25.1247	+	25.1247i	0.981705	+	0.981705i
$656$	7.79569	−	29.0939i	0.304371	−	1.13593i
$657$		0			0
$658$	61.0676	−	61.0676i	2.38066	−	2.38066i
$659$	−22.1359	−	38.3406i	−0.862294	−	1.49354i	−0.869709	−	0.493564i	$-0.835694\pi$
$659$	−22.1359	−	38.3406i	−0.862294	−	1.49354i	0.00741531	−	0.999973i	$-0.497640\pi$
$660$		0			0
$661$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$661$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$662$		−	13.6228i		−	0.529464i
$663$		0			0
$664$		0			0
$665$	46.1091	−	12.3549i	1.78804	−	0.479103i
$666$	−3.78416	+	6.55436i	−0.146633	+	0.253976i
$667$		0			0
$668$	−23.4772	−	23.4772i	−0.908361	−	0.908361i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$673$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$674$		0			0
$675$		0			0
$676$	−6.00000	+	25.2982i	−0.230769	+	0.973009i
$677$	22.7851			0.875701			0.437850	−	0.899048i	$-0.355740\pi$
$677$	22.7851			0.875701			0.437850	+	0.899048i	$0.355740\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$683$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$684$	−19.3301	+	19.3301i	−0.739103	+	0.739103i
$685$		0			0
$686$	−45.6475	−	26.3546i	−1.74283	−	1.00622i
$687$		0			0
$688$		0			0
$689$	20.5940	+	47.7527i	0.784570	+	1.81923i
$690$		0			0
$691$	31.2808	−	8.38168i	1.18998	−	0.318854i	0.391102	−	0.920348i	$-0.372094\pi$
$691$	31.2808	−	8.38168i	1.18998	−	0.318854i	0.798878	+	0.601494i	$0.205427\pi$
$692$	−25.3288	+	43.8708i	−0.962858	+	1.66772i
$693$	43.4442	−	25.0825i	1.65031	−	0.952805i
$694$		0			0
$695$	1.52643	−	5.69672i	0.0579009	−	0.216089i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	12.1271	+	45.2590i	0.458362	+	1.71063i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	8.12756			0.306537
$704$	27.5773	−	7.38932i	1.03936	−	0.278495i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$709$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$710$		0			0
$711$		0			0
$712$	38.8038	+	22.4034i	1.45423	+	0.839601i
$713$		0			0
$714$		0			0
$715$	−28.5775	−	3.34251i	−1.06874	−	0.125003i
$716$	−12.6491			−0.472719
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−18.9737	−	18.9737i	−0.707107	−	0.707107i
$721$	24.5960	−	91.7936i	0.916003	−	3.41857i
$722$	2.40200	+	0.643614i	0.0893931	+	0.0239528i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$			50.7515i			1.88227i	0.338033	+	0.941134i	$0.390239\pi$
$727$			50.7515i			1.88227i	−0.338033	+	0.941134i	$0.609761\pi$
$728$	−38.3260	−	28.5373i	−1.42046	−	1.05766i
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	38.1247	+	38.1247i	1.40817	+	1.40817i	0.769390	+	0.638780i	$0.220561\pi$
$733$	38.1247	+	38.1247i	1.40817	+	1.40817i	0.638780	+	0.769390i	$0.279439\pi$
$734$	2.26519	−	8.45380i	0.0836097	−	0.312035i
$735$		0			0
$736$	36.6491	−	36.6491i	1.35090	−	1.35090i
$737$		0			0
$738$	27.6672	+	15.9737i	1.01844	+	0.587999i
$739$	13.9237	+	51.9638i	0.512190	+	1.91152i	0.395864	+	0.918309i	$0.370445\pi$
$739$	13.9237	+	51.9638i	0.512190	+	1.91152i	0.116326	+	0.993211i	$0.462888\pi$
$740$			7.97771i			0.293267i
$741$		0			0
$742$	−95.5746			−3.50866
$743$	−38.8778	+	10.4173i	−1.42629	+	0.382172i	−0.887710	−	0.460404i	$-0.847705\pi$
$743$	−38.8778	+	10.4173i	−1.42629	+	0.382172i	−0.538577	+	0.842576i	$0.681038\pi$
$744$		0			0
$745$		0			0
$746$	38.1359	+	38.1359i	1.39626	+	1.39626i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$751$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$752$	13.4929	+	50.3563i	0.492036	+	1.83630i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−17.8052	+	30.8396i	−0.647143	+	1.12088i	0.336659	+	0.941626i	$0.390703\pi$
$757$	−17.8052	+	30.8396i	−0.647143	+	1.12088i	−0.983802	+	0.179258i	$0.942630\pi$
$758$	33.2237	−	19.1817i	1.20674	−	0.696710i
$759$		0			0
$760$	−7.45801	+	27.8337i	−0.270530	+	1.00963i
$761$	−41.7071	−	11.1754i	−1.51188	−	0.405108i	−0.594822	−	0.803857i	$-0.702778\pi$
$761$	−41.7071	−	11.1754i	−1.51188	−	0.405108i	−0.917060	+	0.398750i	$0.869444\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$			18.9737i			0.685546i
$767$	−2.83459	−	19.3622i	−0.102351	−	0.699130i
$768$		0			0
$769$	−28.2432	+	7.56774i	−1.01848	+	0.272900i	−0.729167	−	0.684336i	$-0.760092\pi$
$769$	−28.2432	+	7.56774i	−1.01848	+	0.272900i	−0.289309	+	0.957236i	$0.593425\pi$
$770$	26.4393	−	45.7942i	0.952805	−	1.65031i
$771$		0			0
$772$		0			0
$773$	−14.3052	+	53.3878i	−0.514523	+	1.92023i	−0.151456	+	0.988464i	$0.548396\pi$
$773$	−14.3052	+	53.3878i	−0.514523	+	1.92023i	−0.363067	+	0.931763i	$0.618270\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	34.3080i		−	1.22921i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	51.8037	−	29.9089i	1.85013	−	1.06818i
$785$	−8.12837	−	8.12837i	−0.290114	−	0.290114i
$786$		0			0
$787$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$787$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$788$	39.3861	−	39.3861i	1.40307	−	1.40307i
$789$		0			0
$790$		0			0
$791$		0			0
$792$			30.2820i			1.07602i
$793$		0			0
$794$	−51.6597			−1.83333
$795$		0			0
$796$		0			0
$797$	48.8962	−	28.2302i	1.73199	−	0.999967i	0.861919	−	0.507047i	$-0.169263\pi$
$797$	48.8962	−	28.2302i	1.73199	−	0.999967i	0.870075	−	0.492920i	$-0.164071\pi$
$798$		0			0
$799$		0			0
$800$	−27.3205	−	7.32051i	−0.965926	−	0.258819i
$801$	−33.6050	+	33.6050i	−1.18738	+	1.18738i
$802$	1.68502	+	2.91854i	0.0595001	+	0.103057i
$803$		0			0
$804$		0			0
$805$		−	95.9952i		−	3.38339i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−25.2982	+	43.8178i	−0.889438	+	1.54055i	−0.0488972	+	0.998804i	$0.515571\pi$
$809$	−25.2982	+	43.8178i	−0.889438	+	1.54055i	−0.840541	+	0.541748i	$0.817763\pi$
$810$	24.6475	−	14.2302i	0.866025	−	0.500000i
$811$	38.5117	+	38.5117i	1.35233	+	1.35233i	0.883049	+	0.469281i	$0.155487\pi$
$811$	38.5117	+	38.5117i	1.35233	+	1.35233i	0.469281	+	0.883049i	$0.344513\pi$
$812$		0			0
$813$		0			0
$814$	6.36622	−	6.36622i	0.223136	−	0.223136i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		−	5.23467i		−	0.183026i
$819$	39.7583	−	31.4317i	1.38927	−	1.09831i
$820$	33.6754			1.17600
$821$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$821$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$822$		0			0
$823$	−15.4095	+	8.89670i	−0.537143	+	0.310119i	−0.743920	−	0.668269i	$-0.767036\pi$
$823$	−15.4095	+	8.89670i	−0.537143	+	0.310119i	0.206778	+	0.978388i	$0.433702\pi$
$824$	40.5637	+	40.5637i	1.41310	+	1.41310i
$825$		0			0
$826$	34.7383	+	9.30810i	1.20870	+	0.323870i
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$	27.4868	+	47.6086i	0.955233	+	1.65451i
$829$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$829$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$830$		0			0
$831$		0			0
$832$	26.4863	−	11.4226i	0.918247	−	0.396007i
$833$		0			0
$834$		0			0
$835$	18.5604	−	32.1475i	0.642308	−	1.11251i
$836$	28.1628	−	16.2598i	0.974030	−	0.562357i
$837$		0			0
$838$	−11.5747	+	43.1975i	−0.399843	+	1.49223i
$839$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$839$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$840$		0			0
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$		0			0
$844$		−	10.8634i		−	0.373932i
$845$	−29.0567	+	0.840881i	−0.999582	+	0.0289272i
$846$	−55.2950			−1.90108
$847$	−7.85741	+	2.10539i	−0.269984	+	0.0723419i
$848$	28.8467	−	49.9640i	0.990600	−	1.71577i
$849$		0			0
$850$		0			0
$851$	4.23022	−	15.7874i	0.145010	−	0.541185i
$852$		0			0
$853$	−4.00000	+	4.00000i	−0.136957	+	0.136957i	−0.772262	−	0.635304i	$-0.780875\pi$
$853$	−4.00000	+	4.00000i	−0.136957	+	0.136957i	0.635304	+	0.772262i	$0.280875\pi$
$854$		0			0
$855$	−26.4688	−	15.2817i	−0.905213	−	0.522625i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−42.2950			−1.44309			−0.721544	−	0.692369i	$-0.756567\pi$
$859$	−42.2950			−1.44309			−0.721544	+	0.692369i	$0.756567\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.00000	+	6.00000i	0.204242	+	0.204242i	0.801815	−	0.597573i	$-0.203868\pi$
$863$	6.00000	+	6.00000i	0.204242	+	0.204242i	−0.597573	+	0.801815i	$0.703868\pi$
$864$		0			0
$865$	−54.7071	−	14.6587i	−1.86010	−	0.498412i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	29.5179	−	51.1265i	0.998457	−	1.72938i
$875$	−45.3677	+	26.1931i	−1.53371	+	0.885487i
$876$		0			0
$877$	−2.92820	+	10.9282i	−0.0988784	+	0.369019i	−0.997579	−	0.0695437i	$-0.977846\pi$
$877$	−2.92820	+	10.9282i	−0.0988784	+	0.369019i	0.898701	+	0.438563i	$0.144512\pi$
$878$		0			0
$879$		0			0
$880$	15.9600	+	27.6436i	0.538012	+	0.931864i
$881$	−15.6279	−	9.02277i	−0.526517	−	0.303985i	0.213080	−	0.977035i	$-0.431651\pi$
$881$	−15.6279	−	9.02277i	−0.526517	−	0.303985i	−0.739597	+	0.673050i	$0.764984\pi$
$882$	16.4211	+	61.2845i	0.552928	+	2.06356i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.52666	−	9.57245i	0.185567	−	0.321411i	−0.758200	−	0.652022i	$-0.773921\pi$
$887$	5.52666	−	9.57245i	0.185567	−	0.321411i	0.943767	+	0.330610i	$0.107254\pi$
$888$		0			0
$889$	−69.1354	−	69.1354i	−2.31873	−	2.31873i
$890$	−12.9657	+	48.3885i	−0.434610	+	1.62199i
$891$	−31.0245	−	8.31298i	−1.03936	−	0.278495i
$892$	13.3861	−	13.3861i	0.448201	−	0.448201i
$893$	29.6904	+	51.4254i	0.993553	+	1.72088i
$894$		0			0
$895$	−3.66025	−	13.6603i	−0.122349	−	0.456612i
$896$			53.0110i			1.77097i
$897$		0			0
$898$	−55.7047			−1.85889
$899$		0			0
$900$	15.0000	−	25.9808i	0.500000	−	0.866025i
$901$		0			0
$902$	−26.8730	−	26.8730i	−0.894774	−	0.894774i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$		0			0
$909$		0			0
$910$	19.7282	−	49.6475i	0.653984	−	1.64580i
$911$		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
$917$	71.9178	+	19.2703i	2.37494	+	0.636362i
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$	50.1839	+	28.9737i	1.65451	+	0.955233i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−8.61543	+	2.30850i	−0.283274	+	0.0759030i
$926$	15.8114	−	27.3861i	0.519594	−	0.899964i
$927$	−52.6937	+	30.4227i	−1.73069	+	0.999214i
$928$		0			0
$929$	3.03736	−	11.3356i	0.0996525	−	0.371908i	−0.898031	−	0.439932i	$-0.855003\pi$
$929$	3.03736	−	11.3356i	0.0996525	−	0.371908i	0.997684	+	0.0680235i	$0.0216693\pi$
$930$		0			0
$931$	48.1784	−	48.1784i	1.57898	−	1.57898i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	4.43168	+	30.2714i	0.144854	+	0.989453i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$	−50.4772	+	29.1430i	−1.64639	+	0.950541i
$941$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$941$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$942$		0			0
$943$	−66.6416	−	17.8566i	−2.17015	−	0.581490i
$944$	−15.3509	+	15.3509i	−0.499629	+	0.499629i
$945$		0			0
$946$		0			0
$947$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$947$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$948$		0			0
$949$		0			0
$950$	−32.2168			−1.04525
$951$		0			0
$952$		0			0
$953$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$953$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$954$	43.2701	+	43.2701i	1.40092	+	1.40092i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$			31.0000i			1.00000i
$962$	5.43233	−	7.29568i	0.175145	−	0.235222i
$963$		0			0
$964$	−20.9393	+	5.61068i	−0.674411	+	0.180708i
$965$		0			0
$966$		0			0
$967$	−21.8410	−	21.8410i	−0.702359	−	0.702359i	0.262557	−	0.964916i	$-0.415434\pi$
$967$	−21.8410	−	21.8410i	−0.702359	−	0.702359i	−0.964916	+	0.262557i	$0.915434\pi$
$968$	1.27091	−	4.74311i	0.0408487	−	0.152449i
$969$		0			0
$970$		0			0
$971$	18.2386	+	31.5902i	0.585305	+	1.01378i	0.994837	+	0.101482i	$0.0323585\pi$
$971$	18.2386	+	31.5902i	0.585305	+	1.01378i	−0.409532	+	0.912296i	$0.634308\pi$
$972$		0			0
$973$	−3.19855	−	11.9372i	−0.102541	−	0.382688i
$974$			60.3406i			1.93344i
$975$		0			0
$976$		0			0
$977$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$977$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$978$		0			0
$979$	48.9606	−	28.2674i	1.56479	−	0.903431i
$980$	47.2901	+	47.2901i	1.51063	+	1.51063i
$981$		0			0
$982$	32.6043	+	8.73629i	1.04044	+	0.278786i
$983$	15.2146	−	15.2146i	0.485271	−	0.485271i	−0.421539	−	0.906810i	$-0.638510\pi$
$983$	15.2146	−	15.2146i	0.485271	−	0.485271i	0.906810	+	0.421539i	$0.138510\pi$
$984$		0			0
$985$	53.9317	+	31.1375i	1.71841	+	0.992122i
$986$		0			0
$987$		0			0
$988$	25.7734	−	20.3757i	0.819961	−	0.648236i
$989$		0			0
$990$	−32.7027	+	8.76265i	−1.03936	+	0.278495i
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−12.7582	−	22.0979i	−0.404058	−	0.699849i	0.590154	−	0.807291i	$-0.299067\pi$
$997$	−12.7582	−	22.0979i	−0.404058	−	0.699849i	−0.994211	+	0.107442i	$0.965734\pi$
$998$	−43.5367	−	25.1359i	−1.37813	−	0.795664i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.cz.a.59.2	✓	8	1.1	even	1	trivial
520.2.cz.a.59.2	✓	8	40.19	odd	2	CM
520.2.cz.a.379.2	yes	8	13.2	odd	12	inner
520.2.cz.a.379.2	yes	8	520.379	even	12	inner
520.2.cz.b.59.1	yes	8	5.4	even	2
520.2.cz.b.59.1	yes	8	8.3	odd	2
520.2.cz.b.379.1	yes	8	65.54	odd	12
520.2.cz.b.379.1	yes	8	104.67	even	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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.58114 + 1.58114i) q^{5} +(4.52590 + 1.21271i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.58114 + 1.58114i) q^{5} +(4.52590 + 1.21271i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(0.923665 + 3.44716i) q^{11} +(1.42783 + 3.31079i) q^{13} -6.62638 q^{14} +(2.00000 - 3.46410i) q^{16} +(3.00000 + 3.00000i) q^{18} +(1.17922 - 4.40089i) q^{19} +(4.31975 + 1.15747i) q^{20} +(-2.52350 - 4.37083i) q^{22} +(-7.93477 - 4.58114i) q^{23} +5.00000i q^{25} +(-3.16228 - 4.00000i) q^{26} +(9.05180 - 2.42542i) q^{28} +(-1.46410 + 5.46410i) q^{32} +(5.23861 + 9.07354i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(0.461700 + 1.72309i) q^{37} +6.44335i q^{38} -6.32456 q^{40} +(7.27348 - 1.94892i) q^{41} +(5.04700 + 5.04700i) q^{44} +(1.73621 - 6.47963i) q^{45} +(12.5159 + 3.35363i) q^{46} +(-9.21584 + 9.21584i) q^{47} +(12.9509 + 7.47723i) q^{49} +(-1.83013 - 6.83013i) q^{50} +(5.78385 + 4.30663i) q^{52} +14.4234 q^{53} +(-3.99000 + 6.91089i) q^{55} +(-11.4772 + 6.62638i) q^{56} +(-5.24243 - 1.40470i) q^{59} +(-3.63813 - 13.5777i) q^{63} -8.00000i q^{64} +(-2.97723 + 7.49240i) q^{65} +(-10.4772 - 10.4772i) q^{70} +(8.19615 + 2.19615i) q^{72} +(-1.26139 - 2.18479i) q^{74} +(-2.35843 - 8.80178i) q^{76} +16.7217i q^{77} +(8.63950 - 2.31495i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-9.22240 + 5.32456i) q^{82} +(-8.74166 - 5.04700i) q^{88} +(-4.10010 - 15.3018i) q^{89} +9.48683i q^{90} +(2.44716 + 16.7158i) q^{91} -18.3246 q^{92} +(9.21584 - 15.9623i) q^{94} +(8.82292 - 5.09392i) q^{95} +(-20.4282 - 5.47371i) q^{98} +(7.57050 - 7.57050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 12 q^{7} - 16 q^{8} - 12 q^{9}+O(q^{10}) \) 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

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