LMFDB - Embedded newform 520.2.cz.a.219.1

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			219.1
Root			$2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	520.219
Dual form			520.2.cz.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(1.21271 + 4.52590i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(1.21271 + 4.52590i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-5.40089 - 1.44716i) q^{11} +(3.31079 + 1.42783i) q^{13} +6.62638 q^{14} +(2.00000 + 3.46410i) q^{16} +(3.00000 + 3.00000i) q^{18} +(-7.17922 + 1.92366i) q^{19} +(1.15747 + 4.31975i) q^{20} +(-3.95373 + 6.84805i) q^{22} +(2.45754 - 1.41886i) q^{23} +5.00000i q^{25} +(3.16228 - 4.00000i) q^{26} +(2.42542 - 9.05180i) q^{28} +(5.46410 - 1.46410i) q^{32} +(5.23861 - 9.07354i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-1.72309 - 0.461700i) q^{37} +10.5111i q^{38} +6.32456 q^{40} +(2.68097 - 10.0055i) q^{41} +(7.90745 + 7.90745i) q^{44} +(6.47963 - 1.73621i) q^{45} +(-1.03868 - 3.87640i) q^{46} +(-9.21584 + 9.21584i) q^{47} +(-12.9509 + 7.47723i) q^{49} +(6.83013 + 1.83013i) q^{50} +(-4.30663 - 5.78385i) q^{52} -1.99168 q^{53} +(6.25139 + 10.8277i) q^{55} +(-11.4772 - 6.62638i) q^{56} +(3.71965 + 13.8819i) q^{59} +(-13.5777 - 3.63813i) q^{63} -8.00000i q^{64} +(-2.97723 - 7.49240i) q^{65} +(-10.4772 - 10.4772i) q^{70} +(-2.19615 - 8.19615i) q^{72} +(-1.26139 + 2.18479i) q^{74} +(14.3584 + 3.84733i) q^{76} -26.1989i q^{77} +(2.31495 - 8.63950i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-12.6865 - 7.32456i) q^{82} +(13.6961 - 7.90745i) q^{88} +(-9.89990 - 2.65267i) q^{89} -9.48683i q^{90} +(-2.44716 + 16.7158i) q^{91} -5.67544 q^{92} +(9.21584 + 15.9623i) q^{94} +(14.3929 + 8.30975i) q^{95} +(5.47371 + 20.4282i) q^{98} +(11.8612 - 11.8612i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$-1$	$-1$

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$		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
$7$	1.21271	+	4.52590i	0.458362	+	1.71063i	0.678012	+	0.735051i	$0.262842\pi$
$7$	1.21271	+	4.52590i	0.458362	+	1.71063i	−0.219650	+	0.975579i	$0.570491\pi$
$8$	−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
$11$	−5.40089	−	1.44716i	−1.62843	−	0.436336i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	−5.40089	−	1.44716i	−1.62843	−	0.436336i	−0.953463	+	0.301511i	$0.902509\pi$
$12$		0			0
$13$	3.31079	+	1.42783i	0.918247	+	0.396007i
$13$	3.31079	+	1.42783i	0.918247	+	0.396007i
$14$	6.62638			1.77097
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	3.00000	+	3.00000i	0.707107	+	0.707107i
$19$	−7.17922	+	1.92366i	−1.64702	+	0.441319i	−0.958778	−	0.284157i	$-0.908286\pi$
$19$	−7.17922	+	1.92366i	−1.64702	+	0.441319i	−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.15747	+	4.31975i	0.258819	+	0.965926i
$21$		0			0
$22$	−3.95373	+	6.84805i	−0.842937	+	1.46001i
$23$	2.45754	−	1.41886i	0.512432	−	0.295853i	−0.221401	−	0.975183i	$-0.571063\pi$
$23$	2.45754	−	1.41886i	0.512432	−	0.295853i	0.733833	+	0.679330i	$0.237729\pi$
$24$		0			0
$25$			5.00000i			1.00000i
$26$	3.16228	−	4.00000i	0.620174	−	0.784465i
$27$		0			0
$28$	2.42542	−	9.05180i	0.458362	−	1.71063i
$29$		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	$-0.750000\pi$
$31$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$		0			0
$34$		0			0
$35$	5.23861	−	9.07354i	0.885487	−	1.53371i
$36$	5.19615	−	3.00000i	0.866025	−	0.500000i
$37$	−1.72309	−	0.461700i	−0.283274	−	0.0759030i	0.114385	−	0.993437i	$-0.463510\pi$
$37$	−1.72309	−	0.461700i	−0.283274	−	0.0759030i	−0.397658	+	0.917534i	$0.630177\pi$
$38$			10.5111i			1.70513i
$39$		0			0
$40$	6.32456			1.00000
$41$	2.68097	−	10.0055i	0.418698	−	1.56260i	−0.358614	−	0.933486i	$-0.616751\pi$
$41$	2.68097	−	10.0055i	0.418698	−	1.56260i	0.777312	−	0.629115i	$-0.216583\pi$
$42$		0			0
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$	7.90745	+	7.90745i	1.19209	+	1.19209i
$45$	6.47963	−	1.73621i	0.965926	−	0.258819i
$46$	−1.03868	−	3.87640i	−0.153145	−	0.571544i
$47$	−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
$50$	6.83013	+	1.83013i	0.965926	+	0.258819i
$51$		0			0
$52$	−4.30663	−	5.78385i	−0.597222	−	0.802076i
$53$	−1.99168			−0.273578			−0.136789	−	0.990600i	$-0.543678\pi$
$53$	−1.99168			−0.273578			−0.136789	+	0.990600i	$0.543678\pi$
$54$		0			0
$55$	6.25139	+	10.8277i	0.842937	+	1.46001i
$56$	−11.4772	−	6.62638i	−1.53371	−	0.885487i
$57$		0			0
$58$		0			0
$59$	3.71965	+	13.8819i	0.484257	+	1.80727i	0.583382	+	0.812198i	$0.301729\pi$
$59$	3.71965	+	13.8819i	0.484257	+	1.80727i	−0.0991242	+	0.995075i	$0.531604\pi$
$60$		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
$63$	−13.5777	−	3.63813i	−1.71063	−	0.458362i
$64$		−	8.00000i		−	1.00000i
$65$	−2.97723	−	7.49240i	−0.369279	−	0.929318i
$66$		0			0
$67$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$67$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$68$		0			0
$69$		0			0
$70$	−10.4772	−	10.4772i	−1.25227	−	1.25227i
$71$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$71$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$72$	−2.19615	−	8.19615i	−0.258819	−	0.965926i
$73$		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
$76$	14.3584	+	3.84733i	1.64702	+	0.441319i
$77$		−	26.1989i		−	2.98564i
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	2.31495	−	8.63950i	0.258819	−	0.965926i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−12.6865	−	7.32456i	−1.40099	−	0.808862i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	13.6961	−	7.90745i	1.46001	−	0.842937i
$89$	−9.89990	−	2.65267i	−1.04939	−	0.281182i	−0.307389	−	0.951584i	$-0.599455\pi$
$89$	−9.89990	−	2.65267i	−1.04939	−	0.281182i	−0.741999	+	0.670402i	$0.766122\pi$
$90$		−	9.48683i		−	1.00000i
$91$	−2.44716	+	16.7158i	−0.256533	+	1.75230i
$92$	−5.67544			−0.591706
$93$		0			0
$94$	9.21584	+	15.9623i	0.950541	+	1.64639i
$95$	14.3929	+	8.30975i	1.47668	+	0.852563i
$96$		0			0
$97$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$97$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$98$	5.47371	+	20.4282i	0.552928	+	2.06356i
$99$	11.8612	−	11.8612i	1.19209	−	1.19209i
$100$	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
$103$			0.804604i			0.0792800i	0.999214	+	0.0396400i	$0.0126211\pi$
$103$			0.804604i			0.0792800i	−0.999214	+	0.0396400i	$0.987379\pi$
$104$	−9.47723	+	3.76593i	−0.929318	+	0.369279i
$105$		0			0
$106$	−0.729005	+	2.72069i	−0.0708073	+	0.264256i
$107$		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	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$	17.0791	−	4.57634i	1.62843	−	0.436336i
$111$		0			0
$112$	−13.2528	+	13.2528i	−1.25227	+	1.25227i
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$	−6.12913	−	1.64229i	−0.571544	−	0.153145i
$116$		0			0
$117$	−8.67578	+	6.45994i	−0.802076	+	0.597222i
$118$	20.3246			1.87103
$119$		0			0
$120$		0			0
$121$	17.5491	+	10.1320i	1.59537	+	0.921086i
$122$		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
$127$	7.37803	−	4.25971i	0.654695	−	0.377988i	−0.135558	−	0.990769i	$-0.543283\pi$
$127$	7.37803	−	4.25971i	0.654695	−	0.377988i	0.790253	+	0.612781i	$0.209949\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$		0			0
$130$	−11.3246	+	1.32456i	−0.993229	+	0.116171i
$131$	−15.8903			−1.38834			−0.694170	−	0.719811i	$-0.744228\pi$
$131$	−15.8903			−1.38834			−0.694170	+	0.719811i	$0.744228\pi$
$132$		0			0
$133$	−17.4126	−	30.1596i	−1.50987	−	2.61517i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$137$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$138$		0			0
$139$	1.31876	−	2.28416i	0.111856	−	0.193740i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$	1.31876	−	2.28416i	0.111856	−	0.193740i	0.916519	+	0.399992i	$0.130987\pi$
$140$	−18.1471	+	10.4772i	−1.53371	+	0.885487i
$141$		0			0
$142$		0			0
$143$	−15.8149	−	12.5028i	−1.32251	−	1.04553i
$144$	−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		0.965926	−	0.258819i	$-0.0833333\pi$
$149$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$150$		0			0
$151$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$151$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$152$	10.5111	−	18.2058i	0.852563	−	1.47668i
$153$		0			0
$154$	−35.7883	−	9.58946i	−2.88391	−	0.772741i
$155$		0			0
$156$		0			0
$157$	24.5270			1.95746			0.978732	−	0.205142i	$-0.0657655\pi$
$157$	24.5270			1.95746			0.978732	+	0.205142i	$0.0657655\pi$
$158$		0			0
$159$		0			0
$160$	−10.9545	−	6.32456i	−0.866025	−	0.500000i
$161$	9.40191	+	9.40191i	0.740974	+	0.740974i
$162$	−12.2942	+	3.29423i	−0.965926	+	0.258819i
$163$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$163$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$164$	−14.6491	+	14.6491i	−1.14390	+	1.14390i
$165$		0			0
$166$		0			0
$167$	16.0352	+	4.29663i	1.24084	+	0.332483i	0.818793	−	0.574089i	$-0.194644\pi$
$167$	16.0352	+	4.29663i	1.24084	+	0.332483i	0.422051	+	0.906572i	$0.361310\pi$
$168$		0			0
$169$	8.92263	+	9.45445i	0.686356	+	0.727265i
$170$		0			0
$171$	5.77099	−	21.5376i	0.441319	−	1.64702i
$172$		0			0
$173$	6.15125	+	3.55142i	0.467671	+	0.270010i	0.715264	−	0.698854i	$-0.246306\pi$
$173$	6.15125	+	3.55142i	0.467671	+	0.270010i	−0.247593	+	0.968864i	$0.579640\pi$
$174$		0			0
$175$	−22.6295	+	6.06356i	−1.71063	+	0.458362i
$176$	−5.78866	−	21.6036i	−0.436336	−	1.62843i
$177$		0			0
$178$	−7.24723	+	12.5526i	−0.543203	+	0.940855i
$179$	−5.47723	+	3.16228i	−0.409387	+	0.236360i	−0.690526	−	0.723307i	$-0.742621\pi$
$179$	−5.47723	+	3.16228i	−0.409387	+	0.236360i	0.281139	+	0.959667i	$0.409288\pi$
$180$	−12.9593	−	3.47242i	−0.965926	−	0.258819i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	21.9385	+	9.46131i	1.62619	+	0.701319i
$183$		0			0
$184$	−2.07736	+	7.75280i	−0.153145	+	0.571544i
$185$	1.99443	+	3.45445i	0.146633	+	0.253976i
$186$		0			0
$187$		0			0
$188$	25.1781	−	6.74646i	1.83630	−	0.492036i
$189$		0			0
$190$	16.6195	−	16.6195i	1.20571	−	1.20571i
$191$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$193$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$194$		0			0
$195$		0			0
$196$	29.9089			2.13635
$197$	−7.20816	+	26.9012i	−0.513560	+	1.91663i	−0.135775	+	0.990740i	$0.543352\pi$
$197$	−7.20816	+	26.9012i	−0.513560	+	1.91663i	−0.377785	+	0.925893i	$0.623314\pi$
$198$	−11.8612	−	20.5442i	−0.842937	−	1.46001i
$199$		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
$206$	1.09911	+	0.294506i	0.0765786	+	0.0205192i
$207$			8.51317i			0.591706i
$208$	1.67544	+	14.3246i	0.116171	+	0.993229i
$209$	41.5580			2.87463
$210$		0			0
$211$	2.71584	+	4.70397i	0.186966	+	0.323835i	0.944237	−	0.329266i	$-0.106801\pi$
$211$	2.71584	+	4.70397i	0.186966	+	0.323835i	−0.757271	+	0.653101i	$0.773468\pi$
$212$	3.44969	+	1.99168i	0.236926	+	0.136789i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		−	25.0056i		−	1.68587i
$221$		0			0
$222$		0			0
$223$	−2.44983	+	9.14290i	−0.164053	+	0.612254i	0.834106	+	0.551604i	$0.185984\pi$
$223$	−2.44983	+	9.14290i	−0.164053	+	0.612254i	−0.998159	+	0.0606498i	$0.980683\pi$
$224$	13.2528	+	22.9545i	0.885487	+	1.53371i
$225$	−12.9904	−	7.50000i	−0.866025	−	0.500000i
$226$		0			0
$227$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$227$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$228$		0			0
$229$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$229$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$230$	−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	$0.5\pi$
$234$	5.64889	+	14.2158i	0.369279	+	0.929318i
$235$	29.1430			1.90108
$236$	7.43930	−	27.7639i	0.484257	−	1.80727i
$237$		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
$241$	−7.53033	−	28.1036i	−0.485071	−	1.81031i	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−7.53033	−	28.1036i	−0.485071	−	1.81031i	0.0946700	−	0.995509i	$-0.469820\pi$
$242$	20.2639	−	20.2639i	1.30261	−	1.30261i
$243$		0			0
$244$		0			0
$245$	32.2998	+	8.65469i	2.06356	+	0.552928i
$246$		0			0
$247$	−26.5155	−	3.88182i	−1.68714	−	0.246994i
$248$		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	$-0.0201049\pi$
$251$	22.8511	+	13.1931i	1.44235	+	0.832739i	0.444340	+	0.895858i	$0.353438\pi$
$252$	19.8791	+	19.8791i	1.25227	+	1.25227i
$253$	−15.3262	+	4.10665i	−0.963552	+	0.258183i
$254$	−3.11832	−	11.6377i	−0.195661	−	0.730217i
$255$		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
$259$		−	8.35843i		−	0.519368i
$260$	−2.33570	+	15.9545i	−0.144854	+	0.989453i
$261$		0			0
$262$	−5.81625	+	21.7065i	−0.359329	+	1.34103i
$263$	16.2172	+	28.0890i	0.999996	+	1.73204i	0.502503	+	0.864575i	$0.332412\pi$
$263$	16.2172	+	28.0890i	0.999996	+	1.73204i	0.497492	+	0.867468i	$0.334254\pi$
$264$		0			0
$265$	3.14912	+	3.14912i	0.193449	+	0.193449i
$266$	−47.5722	+	12.7469i	−2.91684	+	0.781565i
$267$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$271$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.23582	−	27.0045i	0.436336	−	1.62843i
$276$		0			0
$277$	16.4809	+	9.51526i	0.990242	+	0.571717i	0.905347	−	0.424673i	$-0.139611\pi$
$277$	16.4809	+	9.51526i	0.990242	+	0.571717i	0.0848955	+	0.996390i	$0.472944\pi$
$278$	−2.63752	−	2.63752i	−0.158188	−	0.158188i
$279$		0			0
$280$	7.66986	+	28.6243i	0.458362	+	1.71063i
$281$	−1.64911	+	1.64911i	−0.0983777	+	0.0983777i	−0.754583	−	0.656205i	$-0.772161\pi$
$281$	−1.64911	+	1.64911i	−0.0983777	+	0.0983777i	0.656205	+	0.754583i	$0.272161\pi$
$282$		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
$286$	−22.8678	+	17.0272i	−1.35220	+	1.00684i
$287$	48.5353			2.86495
$288$	−4.39230	+	16.3923i	−0.258819	+	0.965926i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.02896	−	26.2324i	−0.410636	−	1.53251i	−0.793419	−	0.608676i	$-0.791701\pi$
$293$	−7.02896	−	26.2324i	−0.410636	−	1.53251i	0.382782	−	0.923838i	$-0.374966\pi$
$294$		0			0
$295$	16.0680	−	27.8305i	0.935513	−	1.62036i
$296$	4.36957	−	2.52277i	0.253976	−	0.146633i
$297$		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
$304$	−21.0222	−	21.0222i	−1.20571	−	1.20571i
$305$		0			0
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	−26.1989	+	45.3778i	−1.49282	+	2.58564i
$309$		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			$\pi$
$314$	8.97749	−	33.5045i	0.506629	−	1.89077i
$315$	15.7158	+	27.2206i	0.885487	+	1.53371i
$316$		0			0
$317$	−0.675667	−	0.675667i	−0.0379492	−	0.0379492i	0.687878	−	0.725827i	$-0.258543\pi$
$317$	−0.675667	−	0.675667i	−0.0379492	−	0.0379492i	−0.725827	+	0.687878i	$0.758543\pi$
$318$		0			0
$319$		0			0
$320$	−12.6491	+	12.6491i	−0.707107	+	0.707107i
$321$		0			0
$322$	16.2846	−	9.40191i	0.907505	−	0.523948i
$323$		0			0
$324$			18.0000i			1.00000i
$325$	−7.13913	+	16.5539i	−0.396007	+	0.918247i
$326$		0			0
$327$		0			0
$328$	14.6491	+	25.3730i	0.808862	+	1.40099i
$329$	−52.8861	−	30.5338i	−2.91571	−	1.68338i
$330$		0			0
$331$	−33.8930	+	9.08160i	−1.86293	+	0.499170i	−0.999981	−	0.00612670i	$-0.998050\pi$
$331$	−33.8930	+	9.08160i	−1.86293	+	0.499170i	−0.862946	+	0.505296i	$0.831383\pi$
$332$		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	$0.5\pi$
$338$	16.1809	−	8.72797i	0.880127	−	0.474739i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−27.3086	−	15.7667i	−1.47668	−	0.852563i
$343$	−26.3546	−	26.3546i	−1.42301	−	1.42301i
$344$		0			0
$345$		0			0
$346$	7.10285	−	7.10285i	0.381851	−	0.381851i
$347$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$349$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$350$			33.1319i			1.77097i
$351$		0			0
$352$	−31.6298			−1.68587
$353$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$353$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$354$		0			0
$355$		0			0
$356$	14.4945	+	14.4945i	0.768205	+	0.768205i
$357$		0			0
$358$	2.31495	+	8.63950i	0.122349	+	0.456612i
$359$		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
$361$	31.3862	−	18.1208i	1.65190	−	0.953727i
$362$		0			0
$363$		0			0
$364$	20.9545	−	26.5055i	1.09831	−	1.38927i
$365$		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
$370$	5.44888	−	1.46002i	0.283274	−	0.0759030i
$371$	−2.41533	−	9.01415i	−0.125398	−	0.467991i
$372$		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
$376$		−	36.8634i		−	1.90108i
$377$		0			0
$378$		0			0
$379$	−7.22901	+	26.9790i	−0.371329	+	1.38582i	0.487306	+	0.873231i	$0.337980\pi$
$379$	−7.22901	+	26.9790i	−0.371329	+	1.38582i	−0.858635	+	0.512588i	$0.828687\pi$
$380$	−16.6195	−	28.7858i	−0.852563	−	1.47668i
$381$		0			0
$382$		0			0
$383$	12.9593	−	3.47242i	0.662187	−	0.177432i	0.0879542	−	0.996125i	$-0.471967\pi$
$383$	12.9593	−	3.47242i	0.662187	−	0.177432i	0.574233	+	0.818692i	$0.305300\pi$
$384$		0			0
$385$	−41.4241	+	41.4241i	−2.11117	+	2.11117i
$386$		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
$392$	10.9474	−	40.8563i	0.552928	−	2.06356i
$393$		0			0
$394$	34.1094	+	19.6931i	1.71841	+	0.992122i
$395$		0			0
$396$	−32.4053	+	8.68299i	−1.62843	+	0.436336i
$397$	9.45438	+	35.2842i	0.474502	+	1.77086i	0.623285	+	0.781995i	$0.285798\pi$
$397$	9.45438	+	35.2842i	0.474502	+	1.77086i	−0.148783	+	0.988870i	$0.547536\pi$
$398$		0			0
$399$		0			0
$400$	−17.3205	+	10.0000i	−0.866025	+	0.500000i
$401$	38.6168	+	10.3473i	1.92843	+	0.516721i	0.979614	+	0.200888i	$0.0643827\pi$
$401$	38.6168	+	10.3473i	1.92843	+	0.516721i	0.948815	+	0.315833i	$0.102284\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−5.20863	+	19.4389i	−0.258819	+	0.965926i
$406$		0			0
$407$	8.63805	+	4.98718i	0.428172	+	0.247205i
$408$		0			0
$409$	−38.9053	+	10.4247i	−1.92375	+	0.515466i	−0.938187	+	0.346128i	$0.887496\pi$
$409$	−38.9053	+	10.4247i	−1.92375	+	0.515466i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	8.47798	+	31.6403i	0.418698	+	1.56260i
$411$		0			0
$412$	0.804604	−	1.39362i	0.0396400	−	0.0686585i
$413$	−58.3174	+	33.6696i	−2.86961	+	1.65677i
$414$	11.6292	+	3.11604i	0.571544	+	0.153145i
$415$		0			0
$416$	20.1810	+	2.95445i	0.989453	+	0.144854i
$417$		0			0
$418$	15.2113	−	56.7693i	0.744008	−	2.77668i
$419$	−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	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$	7.41981	−	1.98813i	0.361191	−	0.0967807i
$423$	−10.1197	−	37.7672i	−0.492036	−	1.83630i
$424$	3.98336	−	3.98336i	0.193449	−	0.193449i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$431$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$432$		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
$437$	−14.9138	+	14.9138i	−0.713423	+	0.713423i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−34.1582	−	9.15267i	−1.62843	−	0.436336i
$441$		−	44.8634i		−	2.13635i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	11.4589	+	19.8474i	0.543203	+	0.940855i
$446$	11.5927	+	6.69306i	0.548932	+	0.316926i
$447$		0			0
$448$	36.2072	−	9.70169i	1.71063	−	0.458362i
$449$	−4.04699	−	15.1036i	−0.190989	−	0.712781i	−0.993269	−	0.115833i	$-0.963046\pi$
$449$	−4.04699	−	15.1036i	−0.190989	−	0.712781i	0.802280	−	0.596948i	$-0.203620\pi$
$450$	−15.0000	+	15.0000i	−0.707107	+	0.707107i
$451$	−28.9593	+	50.1590i	−1.36364	+	2.36189i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	30.2994	−	22.5608i	1.42046	−	1.05766i
$456$		0			0
$457$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$457$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$458$		0			0
$459$		0			0
$460$	8.97367	+	8.97367i	0.418399	+	0.418399i
$461$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$461$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$462$		0			0
$463$	15.8114	−	15.8114i	0.734818	−	0.734818i	−0.236752	−	0.971570i	$-0.576083\pi$
$463$	15.8114	−	15.8114i	0.734818	−	0.734818i	0.971570	+	0.236752i	$0.0760830\pi$
$464$		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
$470$	10.6671	−	39.8101i	0.492036	−	1.83630i
$471$		0			0
$472$	−35.2032	−	20.3246i	−1.62036	−	0.935513i
$473$		0			0
$474$		0			0
$475$	−9.61832	−	35.8961i	−0.441319	−	1.64702i
$476$		0			0
$477$	2.98752	−	5.17454i	0.136789	−	0.236926i
$478$		0			0
$479$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$479$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$480$		0			0
$481$	−5.04555	−	3.98886i	−0.230057	−	0.181876i
$482$	−41.1465			−1.87417
$483$		0			0
$484$	−20.2639	−	35.0981i	−0.921086	−	1.59537i
$485$		0			0
$486$		0			0
$487$	−41.2134	+	11.0431i	−1.86756	+	0.500410i	−0.867561	+	0.497330i	$0.834314\pi$
$487$	−41.2134	+	11.0431i	−1.86756	+	0.500410i	−0.999995	+	0.00308010i	$0.999020\pi$
$488$		0			0
$489$		0			0
$490$	23.6451	−	40.9545i	1.06818	−	1.85013i
$491$	−20.6703	+	11.9340i	−0.932837	+	0.538574i	−0.887708	−	0.460407i	$-0.847703\pi$
$491$	−20.6703	+	11.9340i	−0.932837	+	0.538574i	−0.0451294	+	0.998981i	$0.514370\pi$
$492$		0			0
$493$		0			0
$494$	−15.0080	+	34.8000i	−0.675242	+	1.56573i
$495$	−37.5083			−1.68587
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.1359	−	19.1359i	−0.856642	−	0.856642i	0.134298	−	0.990941i	$-0.457122\pi$
$499$	−19.1359	−	19.1359i	−0.856642	−	0.856642i	−0.990941	+	0.134298i	$0.957122\pi$
$500$	−21.5988	+	5.78737i	−0.965926	+	0.258819i
$501$		0			0
$502$	26.3861	−	26.3861i	1.17767	−	1.17767i
$503$	−14.7708	+	25.5838i	−0.658598	+	1.14073i	0.322381	+	0.946610i	$0.395517\pi$
$503$	−14.7708	+	25.5838i	−0.658598	+	1.14073i	−0.980979	+	0.194115i	$0.937817\pi$
$504$	34.4317	−	19.8791i	1.53371	−	0.885487i
$505$		0			0
$506$			22.4392i			0.997542i
$507$		0			0
$508$	−17.0388			−0.755976
$509$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$509$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$		0			0
$515$	1.27219	−	1.27219i	0.0560594	−	0.0560594i
$516$		0			0
$517$	63.1106	−	36.4369i	2.77560	−	1.60249i
$518$	−11.4178	−	3.05940i	−0.501671	−	0.134422i
$519$		0			0
$520$	20.9393	+	9.03036i	0.918247	+	0.396007i
$521$	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	$-0.666667\pi$
$523$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$524$	27.5228	+	15.8903i	1.20234	+	0.694170i
$525$		0			0
$526$	44.3062	−	11.8718i	1.93184	−	0.517636i
$527$		0			0
$528$		0			0
$529$	−7.47367	+	12.9448i	−0.324942	+	0.562816i
$530$	5.45444	−	3.14912i	0.236926	−	0.136789i
$531$	−41.6458	−	11.1590i	−1.80727	−	0.484257i
$532$			69.6505i			3.01973i
$533$	23.1623	−	29.2982i	1.00327	−	1.26905i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	80.7674	−	21.6415i	3.47890	−	0.932167i
$540$		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
$550$	−34.2403	−	19.7686i	−1.46001	−	0.842937i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	19.0305	−	19.0305i	0.808529	−	0.808529i
$555$		0			0
$556$	−4.56832	+	2.63752i	−0.193740	+	0.111856i
$557$	−44.3360	−	11.8798i	−1.87858	−	0.503363i	−0.999651	−	0.0264067i	$-0.991594\pi$
$557$	−44.3360	−	11.8798i	−1.87858	−	0.503363i	−0.878927	−	0.476957i	$-0.841740\pi$
$558$		0			0
$559$		0			0
$560$	41.9089			1.77097
$561$		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
$567$	29.8187	−	29.8187i	1.25227	−	1.25227i
$568$		0			0
$569$	−29.4054	+	16.9772i	−1.23274	+	0.711722i	−0.967600	−	0.252488i	$-0.918751\pi$
$569$	−29.4054	+	16.9772i	−1.23274	+	0.711722i	−0.265139	+	0.964210i	$0.585418\pi$
$570$		0			0
$571$			47.3406i			1.98114i	0.137002	+	0.990571i	$0.456253\pi$
$571$			47.3406i			1.98114i	−0.137002	+	0.990571i	$0.543747\pi$
$572$	14.8894	+	37.4704i	0.622559	+	1.56671i
$573$		0			0
$574$	17.7651	−	66.3004i	0.741503	−	2.76733i
$575$	7.09431	+	12.2877i	0.295853	+	0.512432i
$576$	20.7846	+	12.0000i	0.866025	+	0.500000i
$577$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$577$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$578$	23.2224	−	6.22243i	0.965926	−	0.258819i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	10.7568	+	2.88229i	0.445503	+	0.119372i
$584$		0			0
$585$	23.9317	+	3.50355i	0.989453	+	0.144854i
$586$	−38.4069			−1.58658
$587$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$587$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$588$		0			0
$589$		0			0
$590$	−32.1359	−	32.1359i	−1.32302	−	1.32302i
$591$		0			0
$592$	−1.84680	−	6.89235i	−0.0759030	−	0.283274i
$593$		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
$598$	2.09598	−	14.3170i	0.0857109	−	0.585465i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	24.5111	+	42.4545i	0.999828	+	1.73175i	0.515968	+	0.856608i	$0.327432\pi$
$601$	24.5111	+	42.4545i	0.999828	+	1.73175i	0.483860	+	0.875145i	$0.339234\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11.7275	−	43.7675i	−0.476789	−	1.77940i
$606$		0			0
$607$	24.1247	−	41.7851i	0.979190	−	1.69601i	0.313838	−	0.949477i	$-0.398385\pi$
$607$	24.1247	−	41.7851i	0.979190	−	1.69601i	0.665352	−	0.746530i	$-0.268281\pi$
$608$	−36.4115	+	21.0222i	−1.47668	+	0.852563i
$609$		0			0
$610$		0			0
$611$	−43.6703	+	17.3531i	−1.76671	+	0.702030i
$612$		0			0
$613$	−5.09816	+	19.0266i	−0.205913	+	0.768476i	0.783257	+	0.621698i	$0.213557\pi$
$613$	−5.09816	+	19.0266i	−0.205913	+	0.768476i	−0.989169	+	0.146778i	$0.953110\pi$
$614$		0			0
$615$		0			0
$616$	52.3978	+	52.3978i	2.11117	+	2.11117i
$617$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$617$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$618$		0			0
$619$	21.3778	−	21.3778i	0.859248	−	0.859248i	−0.132002	−	0.991250i	$-0.542140\pi$
$619$	21.3778	−	21.3778i	0.859248	−	0.859248i	0.991250	+	0.132002i	$0.0421404\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	48.0229i		−	1.92400i
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$		0			0
$628$	−42.4819	−	24.5270i	−1.69521	−	0.978732i
$629$		0			0
$630$	42.9365	−	11.5048i	1.71063	−	0.458362i
$631$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$631$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$632$		0			0
$633$		0			0
$634$	−1.17029	+	0.675667i	−0.0464781	+	0.0268342i
$635$	−18.4009	−	4.93050i	−0.730217	−	0.195661i
$636$		0			0
$637$	−53.5540	+	6.26384i	−2.12189	+	0.248182i
$638$		0			0
$639$		0			0
$640$	12.6491	+	21.9089i	0.500000	+	0.866025i
$641$	−38.8134	−	22.4089i	−1.53304	−	0.885098i	−0.999220	−	0.0394976i	$-0.987424\pi$
$641$	−38.8134	−	22.4089i	−1.53304	−	0.885098i	−0.533816	−	0.845601i	$-0.679242\pi$
$642$		0			0
$643$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$643$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$644$	−6.88268	−	25.6865i	−0.271215	−	1.01219i
$645$		0			0
$646$		0			0
$647$	−26.6954	+	15.4126i	−1.04950	+	0.605932i	−0.922511	−	0.385972i	$-0.873866\pi$
$647$	−26.6954	+	15.4126i	−1.04950	+	0.605932i	−0.126994	+	0.991903i	$0.540533\pi$
$648$	24.5885	+	6.58846i	0.965926	+	0.258819i
$649$		−	80.3577i		−	3.15432i
$650$	20.0000	+	15.8114i	0.784465	+	0.620174i
$651$		0			0
$652$		0			0
$653$	24.0097	+	41.5861i	0.939573	+	1.62739i	0.766269	+	0.642520i	$0.222111\pi$
$653$	24.0097	+	41.5861i	0.939573	+	1.62739i	0.173304	+	0.984868i	$0.444556\pi$
$654$		0			0
$655$	25.1247	+	25.1247i	0.981705	+	0.981705i
$656$	40.0221	−	10.7239i	1.56260	−	0.418698i
$657$		0			0
$658$	−61.0676	+	61.0676i	−2.38066	+	2.38066i
$659$	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		−0.965926	−	0.258819i	$-0.916667\pi$
$661$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$662$			49.6228i			1.92864i
$663$		0			0
$664$		0			0
$665$	−20.1547	+	75.2183i	−0.781565	+	2.91684i
$666$	−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	$-0.166667\pi$
$673$		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		−0.258819	−	0.965926i	$-0.583333\pi$
$683$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$684$	−31.5333	+	31.5333i	−1.20571	+	1.20571i
$685$		0			0
$686$	−45.6475	+	26.3546i	−1.74283	+	1.00622i
$687$		0			0
$688$		0			0
$689$	−6.59403	−	2.84377i	−0.251212	−	0.108339i
$690$		0			0
$691$	10.7192	−	40.0045i	0.407776	−	1.52184i	−0.391102	−	0.920348i	$-0.627906\pi$
$691$	10.7192	−	40.0045i	0.407776	−	1.52184i	0.798878	−	0.601494i	$-0.205427\pi$
$692$	−7.10285	−	12.3025i	−0.270010	−	0.467671i
$693$	68.0667	+	39.2983i	2.58564	+	1.49282i
$694$		0			0
$695$	−5.69672	+	1.52643i	−0.216089	+	0.0579009i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	45.2590	+	12.1271i	1.71063	+	0.458362i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	13.2586			0.500056
$704$	−11.5773	+	43.2071i	−0.436336	+	1.62843i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$709$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$710$		0			0
$711$		0			0
$712$	25.1051	−	14.4945i	0.940855	−	0.543203i
$713$		0			0
$714$		0			0
$715$	5.23693	+	44.7742i	0.195850	+	1.67446i
$716$	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
$721$	−3.64156	+	0.975753i	−0.135619	+	0.0363389i
$722$	−13.2654	−	49.5070i	−0.493685	−	1.84246i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	18.2287i		−	0.676066i	−0.941134	−	0.338033i	$-0.890239\pi$
$727$		−	18.2287i		−	0.676066i	0.941134	−	0.338033i	$-0.109761\pi$
$728$	−28.5373	−	38.3260i	−1.05766	−	1.42046i
$729$	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	$0.279439\pi$
$734$	−51.6513	+	13.8399i	−1.90648	+	0.510841i
$735$		0			0
$736$	11.3509	−	11.3509i	0.418399	−	0.418399i
$737$		0			0
$738$	38.0595	−	21.9737i	1.40099	−	0.808862i
$739$	7.59911	+	2.03618i	0.279538	+	0.0749019i	0.395864	−	0.918309i	$-0.370445\pi$
$739$	7.59911	+	2.03618i	0.279538	+	0.0749019i	−0.116326	+	0.993211i	$0.537112\pi$
$740$		−	7.97771i		−	0.293267i
$741$		0			0
$742$	−13.1976			−0.484500
$743$	−10.4173	+	38.8778i	−0.382172	+	1.42629i	0.460404	+	0.887710i	$0.347705\pi$
$743$	−10.4173	+	38.8778i	−0.382172	+	1.42629i	−0.842576	+	0.538577i	$0.818962\pi$
$744$		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	$0.833333\pi$
$752$	−50.3563	−	13.4929i	−1.83630	−	0.492036i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	20.9755	+	36.3307i	0.762369	+	1.32046i	0.941626	+	0.336659i	$0.109297\pi$
$757$	20.9755	+	36.3307i	0.762369	+	1.32046i	−0.179258	+	0.983802i	$0.557370\pi$
$758$	34.2080	+	19.7500i	1.24249	+	0.717353i
$759$		0			0
$760$	−45.4053	+	12.1663i	−1.64702	+	0.441319i
$761$	8.88932	+	33.1754i	0.322238	+	1.20261i	0.917060	+	0.398750i	$0.130556\pi$
$761$	8.88932	+	33.1754i	0.322238	+	1.20261i	−0.594822	+	0.803857i	$0.702778\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		−	18.9737i		−	0.685546i
$767$	−7.50599	+	51.2711i	−0.271026	+	1.85129i
$768$		0			0
$769$	12.1976	−	45.5222i	0.439858	−	1.64157i	−0.289309	−	0.957236i	$-0.593425\pi$
$769$	12.1976	−	45.5222i	0.439858	−	1.64157i	0.729167	−	0.684336i	$-0.239908\pi$
$770$	41.4241	+	71.7486i	1.49282	+	2.58564i
$771$		0			0
$772$		0			0
$773$	−53.3878	+	14.3052i	−1.92023	+	0.514523i	−0.931763	+	0.363067i	$0.881730\pi$
$773$	−53.3878	+	14.3052i	−1.92023	+	0.514523i	−0.988464	+	0.151456i	$0.951604\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$			76.9891i			2.75842i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−51.8037	−	29.9089i	−1.85013	−	1.06818i
$785$	−38.7805	−	38.7805i	−1.38414	−	1.38414i
$786$		0			0
$787$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$787$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$788$	39.3861	−	39.3861i	1.40307	−	1.40307i
$789$		0			0
$790$		0			0
$791$		0			0
$792$			47.4447i			1.68587i
$793$		0			0
$794$	51.6597			1.83333
$795$		0			0
$796$		0			0
$797$	0.398804	+	0.230249i	0.0141264	+	0.00815585i	0.507047	−	0.861919i	$-0.330737\pi$
$797$	0.398804	+	0.230249i	0.0141264	+	0.00815585i	−0.492920	+	0.870075i	$0.664071\pi$
$798$		0			0
$799$		0			0
$800$	7.32051	+	27.3205i	0.258819	+	0.965926i
$801$	21.7417	−	21.7417i	0.768205	−	0.768205i
$802$	28.2694	−	48.9641i	0.998228	−	1.72898i
$803$		0			0
$804$		0			0
$805$		−	29.7315i		−	1.04790i
$806$		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
$811$	11.7833	+	11.7833i	0.413767	+	0.413767i	0.883049	−	0.469281i	$-0.155487\pi$
$811$	11.7833	+	11.7833i	0.413767	+	0.413767i	−0.469281	+	0.883049i	$0.655487\pi$
$812$		0			0
$813$		0			0
$814$	9.97436	−	9.97436i	0.349601	−	0.349601i
$815$		0			0
$816$		0			0
$817$		0			0
$818$			56.9614i			1.99161i
$819$	−39.7583	−	31.4317i	−1.38927	−	1.09831i
$820$	46.3246			1.61772
$821$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$821$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$822$		0			0
$823$	47.2392	+	27.2736i	1.64666	+	0.950698i	0.978388	+	0.206778i	$0.0662976\pi$
$823$	47.2392	+	27.2736i	1.64666	+	0.950698i	0.668269	+	0.743920i	$0.267036\pi$
$824$	−1.60921	−	1.60921i	−0.0560594	−	0.0560594i
$825$		0			0
$826$	24.6478	+	91.9869i	0.857607	+	3.20063i
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$	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
$832$	11.4226	−	26.4863i	0.396007	−	0.918247i
$833$		0			0
$834$		0			0
$835$	−18.5604	−	32.1475i	−0.642308	−	1.11251i
$836$	−71.9806	−	41.5580i	−2.48950	−	1.43731i
$837$		0			0
$838$	−43.1975	+	11.5747i	−1.49223	+	0.399843i
$839$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$839$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$840$		0			0
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$		0			0
$843$		0			0
$844$		−	10.8634i		−	0.373932i
$845$	0.840881	−	29.0567i	0.0289272	−	0.999582i
$846$	−55.2950			−1.90108
$847$	−24.5743	+	91.7124i	−0.844382	+	3.15128i
$848$	−3.98336	−	6.89938i	−0.136789	−	0.236926i
$849$		0			0
$850$		0			0
$851$	−4.88964	+	1.31018i	−0.167615	+	0.0449122i
$852$		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
$855$	−43.1788	+	24.9293i	−1.47668	+	0.852563i
$856$		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
$865$	−4.11068	−	15.3413i	−0.139767	−	0.521619i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	14.9138	+	25.8314i	0.504467	+	0.873762i
$875$	45.3677	+	26.1931i	1.53371	+	0.885487i
$876$		0			0
$877$	10.9282	−	2.92820i	0.369019	−	0.0988784i	−0.0695437	−	0.997579i	$-0.522154\pi$
$877$	10.9282	−	2.92820i	0.369019	−	0.0988784i	0.438563	+	0.898701i	$0.355488\pi$
$878$		0			0
$879$		0			0
$880$	−25.0056	+	43.3109i	−0.842937	+	1.46001i
$881$	15.6279	−	9.02277i	0.526517	−	0.303985i	−0.213080	−	0.977035i	$-0.568349\pi$
$881$	15.6279	−	9.02277i	0.526517	−	0.303985i	0.739597	+	0.673050i	$0.235016\pi$
$882$	−61.2845	−	16.4211i	−2.06356	−	0.552928i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−29.2653	−	50.6889i	−0.982632	−	1.70197i	−0.652022	−	0.758200i	$-0.726079\pi$
$887$	−29.2653	−	50.6889i	−0.982632	−	1.70197i	−0.330610	−	0.943767i	$-0.607254\pi$
$888$		0			0
$889$	28.2265	+	28.2265i	0.946685	+	0.946685i
$890$	31.3062	−	8.38848i	1.04939	−	0.281182i
$891$	13.0245	+	48.6080i	0.436336	+	1.62843i
$892$	13.3861	−	13.3861i	0.448201	−	0.448201i
$893$	48.4343	−	83.8907i	1.62079	−	2.80729i
$894$		0			0
$895$	13.6603	+	3.66025i	0.456612	+	0.122349i
$896$		−	53.0110i		−	1.77097i
$897$		0			0
$898$	−22.1131			−0.737925
$899$		0			0
$900$	15.0000	+	25.9808i	0.500000	+	0.866025i
$901$		0			0
$902$	57.9186	+	57.9186i	1.92848	+	1.92848i
$903$		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
$910$	−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
$917$	−19.2703	−	71.9178i	−0.636362	−	2.37494i
$918$		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
$925$	2.30850	−	8.61543i	0.0759030	−	0.283274i
$926$	−15.8114	−	27.3861i	−0.519594	−	0.899964i
$927$	−2.09042	−	1.20691i	−0.0686585	−	0.0396400i
$928$		0			0
$929$	57.7804	−	15.4822i	1.89571	−	0.507955i	0.898031	−	0.439932i	$-0.144997\pi$
$929$	57.7804	−	15.4822i	1.89571	−	0.507955i	0.997684	−	0.0680235i	$-0.0216693\pi$
$930$		0			0
$931$	78.5939	−	78.5939i	2.57581	−	2.57581i
$932$		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
$943$	−7.60786	−	28.3929i	−0.247746	−	0.924600i
$944$	−40.6491	+	40.6491i	−1.32302	+	1.32302i
$945$		0			0
$946$		0			0
$947$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$947$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$948$		0			0
$949$		0			0
$950$	−52.5555			−1.70513
$951$		0			0
$952$		0			0
$953$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$953$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$954$	−5.97504	−	5.97504i	−0.193449	−	0.193449i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$			31.0000i			1.00000i
$962$	−7.29568	+	5.43233i	−0.235222	+	0.175145i
$963$		0			0
$964$	−15.0607	+	56.2071i	−0.485071	+	1.81031i
$965$		0			0
$966$		0			0
$967$	21.8410	+	21.8410i	0.702359	+	0.702359i	0.964916	−	0.262557i	$-0.0845659\pi$
$967$	21.8410	+	21.8410i	0.702359	+	0.702359i	−0.262557	+	0.964916i	$0.584566\pi$
$968$	−55.3620	+	14.8342i	−1.77940	+	0.476789i
$969$		0			0
$970$		0			0
$971$	18.2386	−	31.5902i	0.585305	−	1.01378i	−0.409532	−	0.912296i	$-0.634308\pi$
$971$	18.2386	−	31.5902i	0.585305	−	1.01378i	0.994837	−	0.101482i	$-0.0323585\pi$
$972$		0			0
$973$	11.9372	+	3.19855i	0.382688	+	0.102541i
$974$			60.3406i			1.93344i
$975$		0			0
$976$		0			0
$977$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$977$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$978$		0			0
$979$	49.6294	+	28.6536i	1.58616	+	0.915772i
$980$	−47.2901	−	47.2901i	−1.51063	−	1.51063i
$981$		0			0
$982$	8.73629	+	32.6043i	0.278786	+	1.04044i
$983$	−15.2146	+	15.2146i	−0.485271	+	0.485271i	−0.906810	−	0.421539i	$-0.861490\pi$
$983$	−15.2146	+	15.2146i	−0.485271	+	0.485271i	0.421539	+	0.906810i	$0.361490\pi$
$984$		0			0
$985$	53.9317	−	31.1375i	1.71841	−	0.992122i
$986$		0			0
$987$		0			0
$988$	42.0444	+	33.2390i	1.33761	+	1.05747i
$989$		0			0
$990$	−13.7290	+	51.2373i	−0.436336	+	1.62843i
$991$		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
$997$	28.8830	−	50.0268i	0.914733	−	1.58436i	0.107442	−	0.994211i	$-0.465734\pi$
$997$	28.8830	−	50.0268i	0.914733	−	1.58436i	0.807291	−	0.590154i	$-0.200933\pi$
$998$	−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.219.1	yes	8
5.4	even	2		520.2.cz.b.219.2	yes	8
8.3	odd	2		520.2.cz.b.219.2	yes	8
13.6	odd	12	inner	520.2.cz.a.19.1	✓	8
40.19	odd	2	CM	520.2.cz.a.219.1	yes	8
65.19	odd	12		520.2.cz.b.19.2	yes	8
104.19	even	12		520.2.cz.b.19.2	yes	8
520.19	even	12	inner	520.2.cz.a.19.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.cz.a.19.1	✓	8	13.6	odd	12	inner
520.2.cz.a.19.1	✓	8	520.19	even	12	inner
520.2.cz.a.219.1	yes	8	1.1	even	1	trivial
520.2.cz.a.219.1	yes	8	40.19	odd	2	CM
520.2.cz.b.19.2	yes	8	65.19	odd	12
520.2.cz.b.19.2	yes	8	104.19	even	12
520.2.cz.b.219.2	yes	8	5.4	even	2
520.2.cz.b.219.2	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)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(1.21271 + 4.52590i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(1.21271 + 4.52590i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-5.40089 - 1.44716i) q^{11} +(3.31079 + 1.42783i) q^{13} +6.62638 q^{14} +(2.00000 + 3.46410i) q^{16} +(3.00000 + 3.00000i) q^{18} +(-7.17922 + 1.92366i) q^{19} +(1.15747 + 4.31975i) q^{20} +(-3.95373 + 6.84805i) q^{22} +(2.45754 - 1.41886i) q^{23} +5.00000i q^{25} +(3.16228 - 4.00000i) q^{26} +(2.42542 - 9.05180i) q^{28} +(5.46410 - 1.46410i) q^{32} +(5.23861 - 9.07354i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-1.72309 - 0.461700i) q^{37} +10.5111i q^{38} +6.32456 q^{40} +(2.68097 - 10.0055i) q^{41} +(7.90745 + 7.90745i) q^{44} +(6.47963 - 1.73621i) q^{45} +(-1.03868 - 3.87640i) q^{46} +(-9.21584 + 9.21584i) q^{47} +(-12.9509 + 7.47723i) q^{49} +(6.83013 + 1.83013i) q^{50} +(-4.30663 - 5.78385i) q^{52} -1.99168 q^{53} +(6.25139 + 10.8277i) q^{55} +(-11.4772 - 6.62638i) q^{56} +(3.71965 + 13.8819i) q^{59} +(-13.5777 - 3.63813i) q^{63} -8.00000i q^{64} +(-2.97723 - 7.49240i) q^{65} +(-10.4772 - 10.4772i) q^{70} +(-2.19615 - 8.19615i) q^{72} +(-1.26139 + 2.18479i) q^{74} +(14.3584 + 3.84733i) q^{76} -26.1989i q^{77} +(2.31495 - 8.63950i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-12.6865 - 7.32456i) q^{82} +(13.6961 - 7.90745i) q^{88} +(-9.89990 - 2.65267i) q^{89} -9.48683i q^{90} +(-2.44716 + 16.7158i) q^{91} -5.67544 q^{92} +(9.21584 + 15.9623i) q^{94} +(14.3929 + 8.30975i) q^{95} +(5.47371 + 20.4282i) q^{98} +(11.8612 - 11.8612i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 12 q^{7} - 16 q^{8} - 12 q^{9}+O(q^{10}) \) 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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