LMFDB - Embedded newform 728.2.ds.a.405.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(293,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 6, 11]))

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

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

chi := DirichletCharacter("728.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.ds (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:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 8x^{12} + 40x^{10} - 161x^{8} + 360x^{6} + 648x^{4} - 2916x^{2} + 6561 $ x^16 - 4x^14 + 8x^12 + 40x^10 - 161x^8 + 360x^6 + 648x^4 - 2916*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			405.3
Root			$-1.61083 - 0.636563i$ of defining polynomial
Character	$\chi$	$=$	728.405
Dual form			728.2.ds.a.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.35670 + 2.34987i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.16031 + 1.16031i) q^{5} +(-0.993171 - 3.70657i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-2.18125 + 3.77804i) q^{9} +(2.00972 - 1.16031i) q^{10} +5.42679i q^{12} +(-1.89079 - 3.07000i) q^{13} +3.74166 q^{14} +(-4.30077 - 1.15239i) q^{15} +(2.00000 + 3.46410i) q^{16} +(4.36251 - 4.36251i) q^{18} +(-1.09222 - 4.07621i) q^{19} +(-3.17003 + 0.849407i) q^{20} +(-5.07630 - 5.07630i) q^{21} +(-8.21056 + 4.74037i) q^{23} +(1.98634 - 7.41313i) q^{24} +2.30735i q^{25} +(1.45917 + 4.88578i) q^{26} -3.69702 q^{27} +(-5.11120 - 1.36954i) q^{28} +(5.45316 + 3.14838i) q^{30} +(-1.46410 - 5.46410i) q^{32} +(2.17075 - 3.75984i) q^{35} +(-7.55609 + 4.36251i) q^{36} +5.96798i q^{38} +(4.64887 - 8.60817i) q^{39} +4.64125 q^{40} +(5.07630 + 8.79240i) q^{42} +(-1.85277 - 6.91465i) q^{45} +(12.9509 - 3.47019i) q^{46} +(-5.42679 + 9.39947i) q^{48} +(6.06218 - 3.50000i) q^{49} +(0.844549 - 3.15190i) q^{50} +(-0.204942 - 7.20819i) q^{52} +(5.05023 + 1.35320i) q^{54} +(6.48074 + 3.74166i) q^{56} +(8.09674 - 8.09674i) q^{57} +(-6.88963 + 1.84607i) q^{59} +(-6.29677 - 6.29677i) q^{60} +(6.35798 - 11.0123i) q^{61} +(2.98732 - 11.1488i) q^{63} +8.00000i q^{64} +(5.75607 + 1.36825i) q^{65} +(-22.2785 - 12.8625i) q^{69} +(-4.34149 + 4.34149i) q^{70} +(2.82612 + 10.5472i) q^{71} +(11.9186 - 3.19358i) q^{72} +(-5.42197 + 3.13038i) q^{75} +(2.18443 - 8.15241i) q^{76} +(-9.50129 + 10.0574i) q^{78} -8.25834 q^{79} +(-6.34006 - 1.69881i) q^{80} +(1.52802 + 2.64661i) q^{81} +(-12.2473 + 12.2473i) q^{83} +(-3.71611 - 13.8687i) q^{84} +10.1237i q^{90} +(6.93435 + 6.55094i) q^{91} -18.9615 q^{92} +(5.99698 + 3.46236i) q^{95} +(10.8536 - 10.8536i) q^{96} +(-9.56218 + 2.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 32 q^{8} - 32 q^{9} + 40 q^{15} + 32 q^{16} + 64 q^{18} - 96 q^{30} + 32 q^{32} - 48 q^{36} + 8 q^{39} + 24 q^{46} + 136 q^{50} - 72 q^{57} - 32 q^{60} - 112 q^{63} - 16 q^{65} + 16 q^{71}+ \cdots - 56 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 32 * q^8 - 32 * q^9 + 40 * q^15 + 32 * q^16 + 64 * q^18 - 96 * q^30 + 32 * q^32 - 48 * q^36 + 8 * q^39 + 24 * q^46 + 136 * q^50 - 72 * q^57 - 32 * q^60 - 112 * q^63 - 16 * q^65 + 16 * q^71 + 112 * q^72 - 144 * q^78 - 192 * q^79 - 96 * q^81 - 96 * q^92 + 312 * q^95 - 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$	1.35670	+	2.34987i	0.783289	+	1.35670i	0.930016	+	0.367520i	$0.119793\pi$
$3$	1.35670	+	2.34987i	0.783289	+	1.35670i	−0.146726	+	0.989177i	$0.546874\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	−1.16031	+	1.16031i	−0.518907	+	0.518907i	−0.917241	−	0.398333i	$-0.869589\pi$
$5$	−1.16031	+	1.16031i	−0.518907	+	0.518907i	0.398333	+	0.917241i	$0.369589\pi$
$6$	−0.993171	−	3.70657i	−0.405460	−	1.51320i
$7$	−2.55560	+	0.684771i	−0.965926	+	0.258819i
$7$	−2.55560	+	0.684771i	−0.965926	+	0.258819i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−2.18125	+	3.77804i	−0.727085	+	1.25935i
$10$	2.00972	−	1.16031i	0.635529	−	0.366923i
$11$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$11$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$12$			5.42679i			1.56658i
$13$	−1.89079	−	3.07000i	−0.524411	−	0.851465i
$13$	−1.89079	−	3.07000i	−0.524411	−	0.851465i
$14$	3.74166			1.00000
$15$	−4.30077	−	1.15239i	−1.11045	−	0.297545i
$16$	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	$0.166667\pi$
$18$	4.36251	−	4.36251i	1.02825	−	1.02825i
$19$	−1.09222	−	4.07621i	−0.250572	−	0.935146i	−0.970501	−	0.241098i	$-0.922492\pi$
$19$	−1.09222	−	4.07621i	−0.250572	−	0.935146i	0.719929	−	0.694048i	$-0.244174\pi$
$20$	−3.17003	+	0.849407i	−0.708841	+	0.189933i
$21$	−5.07630	−	5.07630i	−1.10774	−	1.10774i
$22$		0			0
$23$	−8.21056	+	4.74037i	−1.71202	+	0.988436i	−0.780189	+	0.625543i	$0.784877\pi$
$23$	−8.21056	+	4.74037i	−1.71202	+	0.988436i	−0.931831	+	0.362892i	$0.881789\pi$
$24$	1.98634	−	7.41313i	0.405460	−	1.51320i
$25$			2.30735i			0.461470i
$26$	1.45917	+	4.88578i	0.286166	+	0.958180i
$27$	−3.69702			−0.711493
$28$	−5.11120	−	1.36954i	−0.965926	−	0.258819i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	5.45316	+	3.14838i	0.995607	+	0.574814i
$31$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$31$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$		0			0
$34$		0			0
$35$	2.17075	−	3.75984i	0.366923	−	0.635529i
$36$	−7.55609	+	4.36251i	−1.25935	+	0.727085i
$37$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$37$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$38$			5.96798i			0.968134i
$39$	4.64887	−	8.60817i	0.744415	−	1.37841i
$40$	4.64125			0.733846
$41$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$41$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$42$	5.07630	+	8.79240i	0.783289	+	1.35670i
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$		0			0
$45$	−1.85277	−	6.91465i	−0.276195	−	1.03077i
$46$	12.9509	−	3.47019i	1.90951	−	0.511652i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	−5.42679	+	9.39947i	−0.783289	+	1.35670i
$49$	6.06218	−	3.50000i	0.866025	−	0.500000i
$50$	0.844549	−	3.15190i	0.119437	−	0.445746i
$51$		0			0
$52$	−0.204942	−	7.20819i	−0.0284203	−	0.999596i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	5.05023	+	1.35320i	0.687249	+	0.184148i
$55$		0			0
$56$	6.48074	+	3.74166i	0.866025	+	0.500000i
$57$	8.09674	−	8.09674i	1.07244	−	1.07244i
$58$		0			0
$59$	−6.88963	+	1.84607i	−0.896954	+	0.240338i	−0.677707	−	0.735332i	$-0.737026\pi$
$59$	−6.88963	+	1.84607i	−0.896954	+	0.240338i	−0.219246	+	0.975670i	$0.570360\pi$
$60$	−6.29677	−	6.29677i	−0.812909	−	0.812909i
$61$	6.35798	−	11.0123i	0.814056	−	1.40999i	−0.0959480	−	0.995386i	$-0.530588\pi$
$61$	6.35798	−	11.0123i	0.814056	−	1.40999i	0.910004	−	0.414600i	$-0.136078\pi$
$62$		0			0
$63$	2.98732	−	11.1488i	0.376367	−	1.40462i
$64$			8.00000i			1.00000i
$65$	5.75607	+	1.36825i	0.713952	+	0.169711i
$66$		0			0
$67$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$67$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$68$		0			0
$69$	−22.2785	−	12.8625i	−2.68202	−	1.54846i
$70$	−4.34149	+	4.34149i	−0.518907	+	0.518907i
$71$	2.82612	+	10.5472i	0.335399	+	1.25173i	0.903436	+	0.428723i	$0.141036\pi$
$71$	2.82612	+	10.5472i	0.335399	+	1.25173i	−0.568037	+	0.823003i	$0.692297\pi$
$72$	11.9186	−	3.19358i	1.40462	−	0.376367i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	−5.42197	+	3.13038i	−0.626075	+	0.361465i
$76$	2.18443	−	8.15241i	0.250572	−	0.935146i
$77$		0			0
$78$	−9.50129	+	10.0574i	−1.07581	+	1.13877i
$79$	−8.25834			−0.929136			−0.464568	−	0.885537i	$-0.653790\pi$
$79$	−8.25834			−0.929136			−0.464568	+	0.885537i	$0.653790\pi$
$80$	−6.34006	−	1.69881i	−0.708841	−	0.189933i
$81$	1.52802	+	2.64661i	0.169780	+	0.294068i
$82$		0			0
$83$	−12.2473	+	12.2473i	−1.34431	+	1.34431i	−0.452598	+	0.891715i	$0.649503\pi$
$83$	−12.2473	+	12.2473i	−1.34431	+	1.34431i	−0.891715	+	0.452598i	$0.850497\pi$
$84$	−3.71611	−	13.8687i	−0.405460	−	1.51320i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$89$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$90$			10.1237i			1.06714i
$91$	6.93435	+	6.55094i	0.726917	+	0.686725i
$92$	−18.9615			−1.97687
$93$		0			0
$94$		0			0
$95$	5.99698	+	3.46236i	0.615278	+	0.355231i
$96$	10.8536	−	10.8536i	1.10774	−	1.10774i
$97$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$97$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$98$	−9.56218	+	2.56218i	−0.965926	+	0.258819i
$99$		0			0
$100$	−2.30735	+	3.99645i	−0.230735	+	0.399645i
$101$	−17.3650	+	10.0257i	−1.72788	+	0.997594i	−0.829277	+	0.558838i	$0.811247\pi$
$101$	−17.3650	+	10.0257i	−1.72788	+	0.997594i	−0.898607	+	0.438755i	$0.855419\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−2.35843	+	9.92158i	−0.231263	+	0.972891i
$105$	11.7802			1.14963
$106$		0			0
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	−6.40343	−	3.69702i	−0.616171	−	0.355746i
$109$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$109$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$110$		0			0
$111$		0			0
$112$	−7.48331	−	7.48331i	−0.707107	−	0.707107i
$113$	−0.612486	+	1.06086i	−0.0576178	+	0.0997970i	−0.893396	−	0.449271i	$-0.851684\pi$
$113$	−0.612486	+	1.06086i	−0.0576178	+	0.0997970i	0.835778	+	0.549068i	$0.185017\pi$
$114$	−14.0240	+	8.09674i	−1.31347	+	0.758329i
$115$	4.02651	−	15.0271i	0.375474	−	1.40129i
$116$		0			0
$117$	15.7229	−	0.447030i	1.45358	−	0.0413279i
$118$	10.0871			0.928595
$119$		0			0
$120$	6.29677	+	10.9063i	0.574814	+	0.995607i
$121$	−9.52628	−	5.50000i	−0.866025	−	0.500000i
$122$	−12.7160	+	12.7160i	−1.15125	+	1.15125i
$123$		0			0
$124$		0			0
$125$	−8.47881	−	8.47881i	−0.758368	−	0.758368i
$126$	−8.16151	+	14.1361i	−0.727085	+	1.25935i
$127$	−11.2211	+	6.47851i	−0.995713	+	0.574875i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−11.2211	+	6.47851i	−0.995713	+	0.574875i	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		0			0
$130$	−7.36212	−	3.97594i	−0.645700	−	0.348713i
$131$	22.8686			1.99803			0.999017	−	0.0443221i	$-0.0141128\pi$
$131$	22.8686			1.99803			0.999017	+	0.0443221i	$0.0141128\pi$
$132$		0			0
$133$	5.58253	+	9.66923i	0.484067	+	0.838429i
$134$		0			0
$135$	4.28970	−	4.28970i	0.369199	−	0.369199i
$136$		0			0
$137$	−20.5359	+	5.50257i	−1.75450	+	0.470117i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−20.5359	+	5.50257i	−1.75450	+	0.470117i	−0.768922	+	0.639343i	$0.779207\pi$
$138$	25.7250	+	25.7250i	2.18986	+	2.18986i
$139$	−2.66420	+	4.61453i	−0.225974	+	0.391399i	−0.956611	−	0.291367i	$-0.905890\pi$
$139$	−2.66420	+	4.61453i	−0.225974	+	0.391399i	0.730637	+	0.682766i	$0.239223\pi$
$140$	7.51968	−	4.34149i	0.635529	−	0.366923i
$141$		0			0
$142$		−	15.4422i		−	1.29588i
$143$		0			0
$144$	−17.4500			−1.45417
$145$		0			0
$146$		0			0
$147$	16.4491	+	9.49688i	1.35670	+	0.783289i
$148$		0			0
$149$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$149$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$150$	8.55235	−	2.29160i	0.698296	−	0.187108i
$151$	17.1637	+	17.1637i	1.39676	+	1.39676i	0.809118	+	0.587646i	$0.199945\pi$
$151$	17.1637	+	17.1637i	1.39676	+	1.39676i	0.587646	+	0.809118i	$0.300055\pi$
$152$	−5.96798	+	10.3368i	−0.484067	+	0.838429i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	16.6603	−	10.2609i	1.33389	−	0.821531i
$157$	23.2323			1.85414			0.927071	−	0.374885i	$-0.122318\pi$
$157$	23.2323			1.85414			0.927071	+	0.374885i	$0.122318\pi$
$158$	11.2811	+	3.02276i	0.897477	+	0.240478i
$159$		0			0
$160$	8.03888	+	4.64125i	0.635529	+	0.366923i
$161$	17.7368	−	17.7368i	1.39786	−	1.39786i
$162$	−1.11859	−	4.17463i	−0.0878846	−	0.327990i
$163$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$163$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$164$		0			0
$165$		0			0
$166$	21.2129	−	12.2473i	1.64644	−	0.950573i
$167$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$167$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$168$			20.3052i			1.56658i
$169$	−5.84983	+	11.6095i	−0.449987	+	0.893035i
$170$		0			0
$171$	17.7825	+	4.76480i	1.35986	+	0.364374i
$172$		0			0
$173$	−6.57246	−	3.79461i	−0.499695	−	0.288499i	0.228893	−	0.973452i	$-0.426490\pi$
$173$	−6.57246	−	3.79461i	−0.499695	−	0.288499i	−0.728588	+	0.684953i	$0.759823\pi$
$174$		0			0
$175$	−1.58001	−	5.89667i	−0.119437	−	0.445746i
$176$		0			0
$177$	−13.6852	−	13.6852i	−1.02864	−	1.02864i
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	3.70555	−	13.8293i	0.276195	−	1.03077i
$181$		−	23.1116i		−	1.71787i	−0.512084	−	0.858936i	$-0.671126\pi$
$181$		−	23.1116i		−	1.71787i	0.512084	−	0.858936i	$-0.328874\pi$
$182$	−7.07469	−	11.4869i	−0.524411	−	0.851465i
$183$	34.5034			2.55057
$184$	25.9019	+	6.94038i	1.90951	+	0.511652i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	9.44811	−	2.53161i	0.687249	−	0.184148i
$190$	−6.92472	−	6.92472i	−0.502372	−	0.502372i
$191$	−13.6125	+	23.5775i	−0.984965	+	1.70601i	−0.342873	+	0.939382i	$0.611400\pi$
$191$	−13.6125	+	23.5775i	−0.984965	+	1.70601i	−0.642092	+	0.766627i	$0.721933\pi$
$192$	−18.7989	+	10.8536i	−1.35670	+	0.783289i
$193$	−5.32578	+	19.8761i	−0.383358	+	1.43071i	0.457381	+	0.889271i	$0.348787\pi$
$193$	−5.32578	+	19.8761i	−0.383358	+	1.43071i	−0.840739	+	0.541440i	$0.817879\pi$
$194$		0			0
$195$	4.59402	+	15.3823i	0.328985	+	1.10155i
$196$	14.0000			1.00000
$197$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$197$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	4.61470	−	4.61470i	0.326309	−	0.326309i
$201$		0			0
$202$	27.3907	−	7.33932i	1.92720	−	0.516393i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	41.3598i		−	2.87471i
$208$	6.85322	−	12.6899i	0.475185	−	0.879886i
$209$		0			0
$210$	−16.0920	−	4.31184i	−1.11045	−	0.297545i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	−20.9504	+	20.9504i	−1.43550	+	1.43550i
$214$		0			0
$215$		0			0
$216$	7.39405	+	7.39405i	0.503101	+	0.503101i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$223$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$224$	7.48331	+	12.9615i	0.500000	+	0.866025i
$225$	−8.71727	−	5.03292i	−0.581152	−	0.335528i
$226$	1.22497	−	1.22497i	0.0814839	−	0.0814839i
$227$	0.919796	+	3.43273i	0.0610490	+	0.227838i	0.989709	−	0.143094i	$-0.0457050\pi$
$227$	0.919796	+	3.43273i	0.0610490	+	0.227838i	−0.928660	+	0.370932i	$0.879038\pi$
$228$	22.1207	−	5.92723i	1.46498	−	0.392540i
$229$	16.6904	+	16.6904i	1.10293	+	1.10293i	0.994055	+	0.108880i	$0.0347264\pi$
$229$	16.6904	+	16.6904i	1.10293	+	1.10293i	0.108880	+	0.994055i	$0.465274\pi$
$230$	−11.0006	+	19.0536i	−0.725359	+	1.25636i
$231$		0			0
$232$		0			0
$233$			9.77048i			0.640085i	0.947403	+	0.320043i	$0.103697\pi$
$233$			9.77048i			0.640085i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	−21.6415	−	5.14433i	−1.41475	−	0.336295i
$235$		0			0
$236$	−13.7793	−	3.69214i	−0.896954	−	0.240338i
$237$	−11.2041	−	19.4060i	−0.727783	−	1.26056i
$238$		0			0
$239$	19.1208	−	19.1208i	1.23682	−	1.23682i	0.275533	−	0.961292i	$-0.411146\pi$
$239$	19.1208	−	19.1208i	1.23682	−	1.23682i	0.961292	−	0.275533i	$-0.0888542\pi$
$240$	−4.60955	−	17.2031i	−0.297545	−	1.11045i
$241$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$241$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$242$	11.0000	+	11.0000i	0.707107	+	0.707107i
$243$	−9.69166	+	16.7864i	−0.621720	+	1.07685i
$244$	22.0247	−	12.7160i	1.40999	−	0.814056i
$245$	−2.97293	+	11.0951i	−0.189933	+	0.708841i
$246$		0			0
$247$	−10.4488	+	11.0604i	−0.664842	+	0.703754i
$248$		0			0
$249$	−45.3953	−	12.1636i	−2.87681	−	0.770839i
$250$	8.47881	+	14.6857i	0.536247	+	0.928807i
$251$	22.3722	+	12.9166i	1.41212	+	0.815287i	0.995588	−	0.0938349i	$-0.0299126\pi$
$251$	22.3722	+	12.9166i	1.41212	+	0.815287i	0.416530	+	0.909122i	$0.363246\pi$
$252$	16.3230	−	16.3230i	1.02825	−	1.02825i
$253$		0			0
$254$	17.6996	−	4.74260i	1.11057	−	0.297577i
$255$		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
$259$		0			0
$260$	8.60155	+	8.12595i	0.533445	+	0.503950i
$261$		0			0
$262$	−31.2390	−	8.37047i	−1.92995	−	0.517129i
$263$	15.7146	+	27.2184i	0.969002	+	1.67836i	0.698456	+	0.715653i	$0.253871\pi$
$263$	15.7146	+	27.2184i	0.969002	+	1.67836i	0.270546	+	0.962707i	$0.412796\pi$
$264$		0			0
$265$		0			0
$266$	−4.08670	−	15.2518i	−0.250572	−	0.935146i
$267$		0			0
$268$		0			0
$269$	16.3975	−	28.4013i	0.999774	−	1.73166i	0.481467	−	0.876464i	$-0.340104\pi$
$269$	16.3975	−	28.4013i	0.999774	−	1.73166i	0.518307	−	0.855194i	$-0.326562\pi$
$270$	−7.42998	+	4.28970i	−0.452174	+	0.261063i
$271$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$271$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$272$		0			0
$273$	−5.98603	+	25.1824i	−0.362291	+	1.52411i
$274$	30.0666			1.81639
$275$		0			0
$276$	−25.7250	−	44.5570i	−1.54846	−	2.68202i
$277$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$277$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$278$	5.32840	−	5.32840i	0.319576	−	0.319576i
$279$		0			0
$280$	−11.8612	+	3.17819i	−0.708841	+	0.189933i
$281$	−22.4833	−	22.4833i	−1.34124	−	1.34124i	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−22.4833	−	22.4833i	−1.34124	−	1.34124i	−0.446417	−	0.894825i	$-0.647300\pi$
$282$		0			0
$283$	−28.7509	+	16.5994i	−1.70907	+	0.986729i	−0.773345	+	0.633985i	$0.781418\pi$
$283$	−28.7509	+	16.5994i	−1.70907	+	0.986729i	−0.935720	+	0.352744i	$0.885249\pi$
$284$	−5.65225	+	21.0945i	−0.335399	+	1.25173i
$285$			18.7895i			1.11299i
$286$		0			0
$287$		0			0
$288$	23.8372	+	6.38716i	1.40462	+	0.376367i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.47832	−	0.396114i	0.0863642	−	0.0231412i	−0.215378	−	0.976531i	$-0.569098\pi$
$293$	1.47832	−	0.396114i	0.0863642	−	0.0231412i	0.301742	+	0.953390i	$0.402432\pi$
$294$	−18.9938	−	18.9938i	−1.10774	−	1.10774i
$295$	5.85210	−	10.1361i	0.340723	−	0.590149i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	30.0774	+	16.2434i	1.73942	+	0.939380i
$300$	−12.5215			−0.722930
$301$		0			0
$302$	−17.1637	−	29.7284i	−0.987661	−	1.71068i
$303$	−47.1181	−	27.2037i	−2.70687	−	1.56281i
$304$	11.9360	−	11.9360i	0.684574	−	0.684574i
$305$	5.40052	+	20.1550i	0.309233	+	1.15407i
$306$		0			0
$307$	−23.8137	−	23.8137i	−1.35912	−	1.35912i	−0.875007	−	0.484110i	$-0.839143\pi$
$307$	−23.8137	−	23.8137i	−1.35912	−	1.35912i	−0.484110	−	0.875007i	$-0.660857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−26.5141	+	7.91860i	−1.50106	+	0.448302i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−31.7360	−	8.50363i	−1.79096	−	0.479887i
$315$	9.46990	+	16.4023i	0.533568	+	0.924167i
$316$	−14.3039	−	8.25834i	−0.804655	−	0.464568i
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$		0			0
$319$		0			0
$320$	−9.28250	−	9.28250i	−0.518907	−	0.518907i
$321$		0			0
$322$	−30.7211	+	17.7368i	−1.71202	+	0.988436i
$323$		0			0
$324$			6.11208i			0.339560i
$325$	7.08357	−	4.36272i	0.392926	−	0.242000i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$331$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$332$	−33.4602	+	8.96563i	−1.83637	+	0.492053i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	7.43221	−	27.7374i	0.405460	−	1.51320i
$337$		−	36.7083i		−	1.99963i	−0.0192914	−	0.999814i	$-0.506141\pi$
$337$		−	36.7083i		−	1.99963i	0.0192914	−	0.999814i	$-0.493859\pi$
$338$	12.2404	−	13.7176i	0.665788	−	0.746141i
$339$	−3.32383			−0.180526
$340$		0			0
$341$		0			0
$342$	−22.5473	−	13.0177i	−1.21922	−	0.703916i
$343$	−13.0958	+	13.0958i	−0.707107	+	0.707107i
$344$		0			0
$345$	40.7745	−	10.9255i	2.19523	−	0.588209i
$346$	7.58923	+	7.58923i	0.407999	+	0.407999i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$	−7.12731	+	26.5995i	−0.381516	+	1.42384i	0.462070	+	0.886843i	$0.347107\pi$
$349$	−7.12731	+	26.5995i	−0.381516	+	1.42384i	−0.843586	+	0.536994i	$0.819560\pi$
$350$			8.63332i			0.461470i
$351$	6.99030	+	11.3499i	0.373114	+	0.605811i
$352$		0			0
$353$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$353$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$354$	13.6852	+	23.7034i	0.727358	+	1.25982i
$355$	−15.5173	−	8.95890i	−0.823571	−	0.475489i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.9458	+	10.9458i	0.577696	+	0.577696i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	10.9458	+	10.9458i	0.577696	+	0.577696i	−0.356572	+	0.934268i	$0.616054\pi$
$360$	−10.1237	+	17.5348i	−0.533568	+	0.924167i
$361$	1.03196	−	0.595801i	0.0543135	−	0.0313579i
$362$	−8.45943	+	31.5710i	−0.444618	+	1.65934i
$363$		−	29.8473i		−	1.56658i
$364$	5.45971	+	18.2809i	0.286166	+	0.958180i
$365$		0			0
$366$	−47.1325	−	12.6291i	−2.46366	−	0.660135i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$	−32.8422	−	18.9615i	−1.71202	−	0.988436i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	8.42091	−	31.4273i	0.434854	−	1.62290i
$376$		0			0
$377$		0			0
$378$	−13.8330			−0.711493
$379$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$379$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$380$	6.92472	+	11.9940i	0.355231	+	0.615278i
$381$	−30.4473	−	17.5788i	−1.55986	−	0.900587i
$382$	27.2250	−	27.2250i	1.39295	−	1.39295i
$383$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$383$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$384$	29.6525	−	7.94537i	1.51320	−	0.405460i
$385$		0			0
$386$	14.5503	−	25.2019i	0.740591	−	1.28274i
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	−0.645235	−	22.6942i	−0.0326727	−	1.14916i
$391$		0			0
$392$	−19.1244	−	5.12436i	−0.965926	−	0.258819i
$393$	31.0257	+	53.7381i	1.56504	+	2.71073i
$394$		0			0
$395$	9.58226	−	9.58226i	0.482136	−	0.482136i
$396$		0			0
$397$	21.3772	−	5.72800i	1.07289	−	0.287480i	0.321211	−	0.947008i	$-0.395910\pi$
$397$	21.3772	−	5.72800i	1.07289	−	0.287480i	0.751680	+	0.659528i	$0.229244\pi$
$398$		0			0
$399$	−15.1476	+	26.2364i	−0.758329	+	1.31347i
$400$	−7.99290	+	4.61470i	−0.399645	+	0.230735i
$401$	4.10862	−	15.3336i	0.205175	−	0.765723i	−0.784221	−	0.620481i	$-0.786937\pi$
$401$	4.10862	−	15.3336i	0.205175	−	0.765723i	0.989396	−	0.145242i	$-0.0463961\pi$
$402$		0			0
$403$		0			0
$404$	−40.1028			−1.99519
$405$	−4.84387	−	1.29791i	−0.240694	−	0.0644938i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$409$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$410$		0			0
$411$	−40.7913	−	40.7913i	−2.01209	−	2.01209i
$412$		0			0
$413$	16.3430	−	9.43564i	0.804187	−	0.464297i
$414$	−15.1387	+	56.4986i	−0.744029	+	2.77675i
$415$		−	28.4213i		−	1.39515i
$416$	−14.0065	+	14.8263i	−0.686725	+	0.726917i
$417$	−14.4580			−0.708014
$418$		0			0
$419$	−13.3866	−	23.1864i	−0.653981	−	1.13273i	−0.982148	−	0.188108i	$-0.939764\pi$
$419$	−13.3866	−	23.1864i	−0.653981	−	1.13273i	0.328168	−	0.944619i	$-0.393569\pi$
$420$	20.4039	+	11.7802i	0.995607	+	0.574814i
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	36.2872	−	20.9504i	1.75812	−	1.01505i
$427$	−8.70752	+	32.4969i	−0.421386	+	1.57264i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−30.4101	−	8.14837i	−1.46480	−	0.392493i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	−30.4101	−	8.14837i	−1.46480	−	0.392493i	−0.901146	+	0.433515i	$0.857273\pi$
$432$	−7.39405	−	12.8069i	−0.355746	−	0.616171i
$433$		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
$437$	28.2904	+	28.2904i	1.35332	+	1.35332i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$			30.5376i			1.45417i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−5.47817	−	20.4448i	−0.258819	−	0.965926i
$449$	20.4281	−	5.47370i	0.964062	−	0.258320i	0.257743	−	0.966213i	$-0.417021\pi$
$449$	20.4281	−	5.47370i	0.964062	−	0.258320i	0.706319	+	0.707894i	$0.250354\pi$
$450$	10.0658	+	10.0658i	0.474508	+	0.474508i
$451$		0			0
$452$	−2.12171	+	1.22497i	−0.0997970	+	0.0576178i
$453$	−17.0465	+	63.6185i	−0.800915	+	2.98906i
$454$		−	5.02586i		−	0.235875i
$455$	−15.6471	+	0.444876i	−0.733549	+	0.0208561i
$456$	−32.3870			−1.51666
$457$	32.9348	+	8.82485i	1.54062	+	0.412809i	0.926467	−	0.376375i	$-0.122830\pi$
$457$	32.9348	+	8.82485i	1.54062	+	0.412809i	0.614157	+	0.789184i	$0.289496\pi$
$458$	−16.6904	−	28.9087i	−0.779893	−	1.35081i
$459$		0			0
$460$	22.0012	−	22.0012i	1.02581	−	1.02581i
$461$	9.70069	+	36.2035i	0.451806	+	1.68616i	0.697312	+	0.716768i	$0.254379\pi$
$461$	9.70069	+	36.2035i	0.451806	+	1.68616i	−0.245505	+	0.969395i	$0.578954\pi$
$462$		0			0
$463$	−4.20185	−	4.20185i	−0.195277	−	0.195277i	0.602695	−	0.797972i	$-0.294094\pi$
$463$	−4.20185	−	4.20185i	−0.195277	−	0.195277i	−0.797972	+	0.602695i	$0.794094\pi$
$464$		0			0
$465$		0			0
$466$	3.57624	−	13.3467i	0.165666	−	0.618275i
$467$		−	39.7569i		−	1.83973i	−0.392236	−	0.919865i	$-0.628298\pi$
$467$		−	39.7569i		−	1.83973i	0.392236	−	0.919865i	$-0.371702\pi$
$468$	27.6799	+	14.9486i	1.27950	+	0.691000i
$469$		0			0
$470$		0			0
$471$	31.5193	+	54.5929i	1.45233	+	2.51551i
$472$	17.4714	+	10.0871i	0.804187	+	0.464297i
$473$		0			0
$474$	8.20195	+	30.6101i	0.376728	+	1.40597i
$475$	9.40524	−	2.52013i	0.431542	−	0.115631i
$476$		0			0
$477$		0			0
$478$	−33.1183	+	19.1208i	−1.51479	+	0.874567i
$479$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$479$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$480$			25.1871i			1.14963i
$481$		0			0
$482$		0			0
$483$	65.7428	+	17.6157i	2.99140	+	0.801543i
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	19.3833	−	19.3833i	0.879245	−	0.879245i
$487$	7.99614	+	29.8420i	0.362340	+	1.35227i	0.870992	+	0.491298i	$0.163477\pi$
$487$	7.99614	+	29.8420i	0.362340	+	1.35227i	−0.508652	+	0.860972i	$0.669856\pi$
$488$	−34.7406	+	9.30873i	−1.57264	+	0.421386i
$489$		0			0
$490$	8.12218	−	14.0680i	0.366923	−	0.635529i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		0			0
$494$	18.3217	−	11.2842i	0.824333	−	0.507700i
$495$		0			0
$496$		0			0
$497$	−14.4449	−	25.0193i	−0.647941	−	1.12227i
$498$	57.5590	+	33.2317i	2.57928	+	1.48915i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	−6.20692	−	23.1645i	−0.277582	−	1.03595i
$501$		0			0
$502$	−25.8331	−	25.8331i	−1.15299	−	1.15299i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$	−28.2723	+	16.3230i	−1.25935	+	0.727085i
$505$	8.51590	−	31.7818i	0.378953	−	1.41427i
$506$		0			0
$507$	−35.2171	+	2.00419i	−1.56405	+	0.0890093i
$508$	−25.9140			−1.14975
$509$	−13.9376	−	3.73457i	−0.617773	−	0.165532i	−0.0636579	−	0.997972i	$-0.520277\pi$
$509$	−13.9376	−	3.73457i	−0.617773	−	0.165532i	−0.554115	+	0.832440i	$0.686943\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	4.03795	+	15.0698i	0.178280	+	0.665350i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	20.5926i		−	0.903913i
$520$	−8.77563	−	14.2486i	−0.384837	−	0.624844i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−21.5869	−	37.3896i	−0.943928	−	1.63493i	−0.757884	−	0.652390i	$-0.773767\pi$
$523$	−21.5869	−	37.3896i	−0.943928	−	1.63493i	−0.186044	−	0.982541i	$-0.559567\pi$
$524$	39.6095	+	22.8686i	1.73035	+	0.999017i
$525$	11.7128	−	11.7128i	0.511188	−	0.511188i
$526$	−11.5039	−	42.9330i	−0.501592	−	1.87197i
$527$		0			0
$528$		0			0
$529$	33.4422	−	57.9236i	1.45401	−	2.51842i
$530$		0			0
$531$	8.05350	−	30.0561i	0.349492	−	1.30432i
$532$			22.3301i			0.968134i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−32.7950	+	32.7950i	−1.41389	+	1.41389i
$539$		0			0
$540$	11.7197	−	3.14028i	0.504335	−	0.135136i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$	54.3092	−	31.3554i	2.33063	−	1.34559i
$544$		0			0
$545$		0			0
$546$	17.3945	−	32.2088i	0.744415	−	1.37841i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−41.0718	−	11.0051i	−1.75450	−	0.470117i
$549$	27.7367	+	48.0414i	1.18378	+	2.05036i
$550$		0			0
$551$		0			0
$552$	18.8320	+	70.2820i	0.801543	+	2.99140i
$553$	21.1050	−	5.65507i	0.897477	−	0.240478i
$554$		0			0
$555$		0			0
$556$	−9.22906	+	5.32840i	−0.391399	+	0.225974i
$557$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$557$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$558$		0			0
$559$		0			0
$560$	17.3660			0.733846
$561$		0			0
$562$	22.4833	+	38.9422i	0.948401	+	1.64268i
$563$	34.5173	+	19.9286i	1.45473	+	0.839889i	0.998744	−	0.0500986i	$-0.0159536\pi$
$563$	34.5173	+	19.9286i	1.45473	+	0.839889i	0.455985	+	0.889987i	$0.349287\pi$
$564$		0			0
$565$	−0.520250	−	1.94160i	−0.0218871	−	0.0816837i
$566$	45.3503	−	12.1516i	1.90621	−	0.510769i
$567$	−5.71733	−	5.71733i	−0.240105	−	0.240105i
$568$	15.4422	−	26.7467i	0.647941	−	1.12227i
$569$	40.4718	−	23.3664i	1.69667	−	0.979571i	0.747785	−	0.663941i	$-0.231117\pi$
$569$	40.4718	−	23.3664i	1.69667	−	0.979571i	0.948882	−	0.315631i	$-0.102216\pi$
$570$	6.87743	−	25.6669i	0.288064	−	1.07507i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	−73.8721			−3.08605
$574$		0			0
$575$	−10.9377	−	18.9447i	−0.456134	−	0.790047i
$576$	−30.2243	−	17.4500i	−1.25935	−	0.727085i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	−6.22243	−	23.2224i	−0.258819	−	0.965926i
$579$	−53.9316	+	14.4509i	−2.24132	+	0.600560i
$580$		0			0
$581$	22.9125	−	39.6857i	0.950573	−	1.64644i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−17.7248	+	18.7622i	−0.732829	+	0.775720i
$586$	−2.16441			−0.0894108
$587$	2.84437	+	0.762147i	0.117400	+	0.0314572i	0.317041	−	0.948412i	$-0.397311\pi$
$587$	2.84437	+	0.762147i	0.117400	+	0.0314572i	−0.199641	+	0.979869i	$0.563978\pi$
$588$	18.9938	+	32.8982i	0.783289	+	1.35670i
$589$		0			0
$590$	−11.7042	+	11.7042i	−0.481855	+	0.481855i
$591$		0			0
$592$		0			0
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−35.1410	−	33.1980i	−1.43702	−	1.35757i
$599$	−23.2541			−0.950136			−0.475068	−	0.879949i	$-0.657577\pi$
$599$	−23.2541			−0.950136			−0.475068	+	0.879949i	$0.657577\pi$
$600$	17.1047	+	4.58319i	0.698296	+	0.187108i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	12.5647	+	46.8922i	0.511251	+	1.90802i
$605$	17.4352	−	4.67174i	0.708841	−	0.189933i
$606$	54.4073	+	54.4073i	2.21015	+	2.21015i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−20.6737	+	11.9360i	−0.838429	+	0.484067i
$609$		0			0
$610$		−	29.5090i		−	1.19478i
$611$		0			0
$612$		0			0
$613$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$613$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$614$	23.8137	+	41.2465i	0.961041	+	1.66457i
$615$		0			0
$616$		0			0
$617$	2.99306	+	11.1703i	0.120496	+	0.449698i	0.999639	−	0.0268600i	$-0.00855084\pi$
$617$	2.99306	+	11.1703i	0.120496	+	0.449698i	−0.879143	+	0.476558i	$0.841884\pi$
$618$		0			0
$619$	22.3522	+	22.3522i	0.898411	+	0.898411i	0.995296	−	0.0968845i	$-0.0308877\pi$
$619$	22.3522	+	22.3522i	0.898411	+	0.898411i	−0.0968845	+	0.995296i	$0.530888\pi$
$620$		0			0
$621$	30.3547	−	17.5253i	1.21809	−	0.703265i
$622$		0			0
$623$		0			0
$624$	39.1173	−	1.11217i	1.56595	−	0.0445226i
$625$	8.13937			0.325575
$626$		0			0
$627$		0			0
$628$	40.2396	+	23.2323i	1.60573	+	0.927071i
$629$		0			0
$630$	−6.93245	−	25.8722i	−0.276195	−	1.03077i
$631$	−46.2815	+	12.4011i	−1.84244	+	0.493680i	−0.999048	−	0.0436231i	$-0.986110\pi$
$631$	−46.2815	+	12.4011i	−1.84244	+	0.493680i	−0.843389	+	0.537303i	$0.819443\pi$
$632$	16.5167	+	16.5167i	0.656998	+	0.656998i
$633$		0			0
$634$		0			0
$635$	5.50290	−	20.5371i	0.218376	−	0.814989i
$636$		0			0
$637$	−22.2073	−	11.9931i	−0.879886	−	0.475185i
$638$		0			0
$639$	−46.0124	−	12.3290i	−1.82022	−	0.487727i
$640$	9.28250	+	16.0778i	0.366923	+	0.635529i
$641$	−2.50172	−	1.44437i	−0.0988119	−	0.0570491i	0.449780	−	0.893140i	$-0.351502\pi$
$641$	−2.50172	−	1.44437i	−0.0988119	−	0.0570491i	−0.548592	+	0.836090i	$0.684836\pi$
$642$		0			0
$643$	11.8946	+	44.3912i	0.469077	+	1.75062i	0.643006	+	0.765861i	$0.277687\pi$
$643$	11.8946	+	44.3912i	0.469077	+	1.75062i	−0.173929	+	0.984758i	$0.555646\pi$
$644$	48.4580	−	12.9843i	1.90951	−	0.511652i
$645$		0			0
$646$		0			0
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	2.23718	−	8.34926i	0.0878846	−	0.327990i
$649$		0			0
$650$	−11.2732	+	3.36681i	−0.442172	+	0.132057i
$651$		0			0
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		0			0
$655$	−26.5347	+	26.5347i	−1.03679	+	1.03679i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$	−0.231024	+	0.862193i	−0.00898579	+	0.0335354i	−0.970273	−	0.242012i	$-0.922193\pi$
$661$	−0.231024	+	0.862193i	−0.00898579	+	0.0335354i	0.961287	+	0.275548i	$0.0888592\pi$
$662$		0			0
$663$		0			0
$664$	48.9891			1.90115
$665$	−17.6968	−	4.74185i	−0.686253	−	0.183881i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−20.3052	+	35.1696i	−0.783289	+	1.35670i
$673$	−38.8844	+	22.4499i	−1.49889	+	0.865382i	−0.999999	−	0.00128586i	$-0.999591\pi$
$673$	−38.8844	+	22.4499i	−1.49889	+	0.865382i	−0.498886	+	0.866668i	$0.666257\pi$
$674$	−13.4362	+	50.1445i	−0.517542	+	1.93149i
$675$		−	8.53034i		−	0.328333i
$676$	−21.7417	+	14.2583i	−0.836218	+	0.548398i
$677$	51.9688			1.99732			0.998662	−	0.0517163i	$-0.0164691\pi$
$677$	51.9688			1.99732			0.998662	+	0.0517163i	$0.0164691\pi$
$678$	4.54044	+	1.21661i	0.174375	+	0.0467235i
$679$		0			0
$680$		0			0
$681$	−6.81857	+	6.81857i	−0.261288	+	0.261288i
$682$		0			0
$683$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$683$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$684$	26.0354	+	26.0354i	0.995487	+	0.995487i
$685$	17.4433	−	30.2127i	0.666476	−	1.15437i
$686$	22.6826	−	13.0958i	0.866025	−	0.500000i
$687$	−16.5765	+	61.8642i	−0.632431	+	2.36027i
$688$		0			0
$689$		0			0
$690$	−59.6980			−2.27267
$691$	−49.5539	−	13.2779i	−1.88512	−	0.505116i	−0.999143	−	0.0413827i	$-0.986824\pi$
$691$	−49.5539	−	13.2779i	−1.88512	−	0.505116i	−0.885975	−	0.463733i	$-0.846510\pi$
$692$	−7.58923	−	13.1449i	−0.288499	−	0.499695i
$693$		0			0
$694$		0			0
$695$	−2.26299	−	8.44560i	−0.0858401	−	0.320360i
$696$		0			0
$697$		0			0
$698$	19.4722	−	33.7268i	0.737032	−	1.27658i
$699$	−22.9593	+	13.2556i	−0.868402	+	0.501372i
$700$	3.16001	−	11.7933i	0.119437	−	0.445746i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−5.39458	−	18.0628i	−0.203605	−	0.681738i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	37.5127	−	37.5127i	1.41081	−	1.41081i
$708$	−10.0182	−	37.3886i	−0.376508	−	1.40515i
$709$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$709$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$710$	17.9178	+	17.9178i	0.672443	+	0.672443i
$711$	18.0135	−	31.2004i	0.675561	−	1.17011i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	70.8726	+	18.9903i	2.64679	+	0.709205i
$718$	−10.9458	−	18.9587i	−0.408493	−	0.707531i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	20.2475	−	20.2475i	0.754579	−	0.754579i
$721$		0			0
$722$	−1.62776	+	0.436156i	−0.0605789	+	0.0162321i
$723$		0			0
$724$	23.1116	−	40.0304i	0.858936	−	1.48772i
$725$		0			0
$726$	−10.9249	+	40.7722i	−0.405460	+	1.51320i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−0.766821	−	26.9706i	−0.0284203	−	0.999596i
$729$	−43.4265			−1.60839
$730$		0			0
$731$		0			0
$732$	59.7617	+	34.5034i	2.20885	+	1.27528i
$733$	−0.0504373	+	0.0504373i	−0.00186294	+	0.00186294i	−0.708038	−	0.706175i	$-0.750419\pi$
$733$	−0.0504373	+	0.0504373i	−0.00186294	+	0.00186294i	0.706175	+	0.708038i	$0.250419\pi$
$734$		0			0
$735$	−30.1054	+	8.06672i	−1.11045	+	0.297545i
$736$	37.9230	+	37.9230i	1.39786	+	1.39786i
$737$		0			0
$738$		0			0
$739$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$739$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$740$		0			0
$741$	−40.1663	−	9.54778i	−1.47554	−	0.350746i
$742$		0			0
$743$	−41.9939	−	11.2522i	−1.54061	−	0.412804i	−0.614145	−	0.789193i	$-0.710499\pi$
$743$	−41.9939	−	11.2522i	−1.54061	−	0.412804i	−0.926462	+	0.376389i	$0.877166\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−19.5563	−	72.9852i	−0.715528	−	2.67039i
$748$		0			0
$749$		0			0
$750$	−23.0064	+	39.8482i	−0.840073	+	1.45505i
$751$	27.7789	−	16.0381i	1.01367	−	0.585240i	0.101403	−	0.994845i	$-0.467667\pi$
$751$	27.7789	−	16.0381i	1.01367	−	0.585240i	0.912263	+	0.409605i	$0.134333\pi$
$752$		0			0
$753$			70.0955i			2.55442i
$754$		0			0
$755$	−39.8306			−1.44958
$756$	18.8962	+	5.06323i	0.687249	+	0.184148i
$757$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$757$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$758$		0			0
$759$		0			0
$760$	−5.06925	−	18.9187i	−0.183881	−	0.686253i
$761$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$761$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$762$	35.1575	+	35.1575i	1.27362	+	1.27362i
$763$		0			0
$764$	−47.1550	+	27.2250i	−1.70601	+	0.984965i
$765$		0			0
$766$		0			0
$767$	18.6943	+	17.6606i	0.675012	+	0.637689i
$768$	−43.4143			−1.56658
$769$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$769$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$770$		0			0
$771$		0			0
$772$	−29.1006	+	29.1006i	−1.04735	+	1.04735i
$773$	1.32632	+	4.94989i	0.0477044	+	0.178035i	0.985667	−	0.168700i	$-0.0539569\pi$
$773$	1.32632	+	4.94989i	0.0477044	+	0.178035i	−0.937963	+	0.346735i	$0.887290\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−7.42523	+	31.2370i	−0.265866	+	1.11846i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	24.2487	+	14.0000i	0.866025	+	0.500000i
$785$	−26.9568	+	26.9568i	−0.962128	+	0.962128i
$786$	−22.7124	−	84.7638i	−0.810124	−	3.02342i
$787$	−52.0421	+	13.9446i	−1.85510	+	0.497072i	−0.999779	−	0.0210268i	$-0.993306\pi$
$787$	−52.0421	+	13.9446i	−1.85510	+	0.497072i	−0.855321	+	0.518099i	$0.826640\pi$
$788$		0			0
$789$	−42.6398	+	73.8543i	−1.51802	+	2.62928i
$790$	−16.5970	+	9.58226i	−0.590493	+	0.340921i
$791$	0.838825	−	3.13054i	0.0298252	−	0.111309i
$792$		0			0
$793$	−45.8295	+	1.30301i	−1.62745	+	0.0462714i
$794$	−31.2984			−1.11074
$795$		0			0
$796$		0			0
$797$	−34.1548	−	19.7193i	−1.20983	−	0.698493i	−0.247104	−	0.968989i	$-0.579479\pi$
$797$	−34.1548	−	19.7193i	−1.20983	−	0.698493i	−0.962721	+	0.270496i	$0.912812\pi$
$798$	30.2952	−	30.2952i	1.07244	−	1.07244i
$799$		0			0
$800$	12.6076	−	3.37820i	0.445746	−	0.119437i
$801$		0			0
$802$	−11.2250	+	19.4422i	−0.396368	+	0.686529i
$803$		0			0
$804$		0			0
$805$			41.1605i			1.45072i
$806$		0			0
$807$	88.9858			3.13245
$808$	54.7814	+	14.6786i	1.92720	+	0.516393i
$809$	−27.8375	−	48.2159i	−0.978713	−	1.69518i	−0.667094	−	0.744973i	$-0.732462\pi$
$809$	−27.8375	−	48.2159i	−0.978713	−	1.69518i	−0.311619	−	0.950207i	$-0.600871\pi$
$810$	6.14179	+	3.54596i	0.215800	+	0.124592i
$811$	40.0697	−	40.0697i	1.40704	−	1.40704i	0.632384	−	0.774655i	$-0.282076\pi$
$811$	40.0697	−	40.0697i	1.40704	−	1.40704i	0.774655	−	0.632384i	$-0.217924\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−39.8753	+	11.9090i	−1.39336	+	0.416135i
$820$		0			0
$821$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$821$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$822$	40.7913	+	70.6526i	1.42276	+	2.46429i
$823$	36.6582	+	21.1646i	1.27782	+	0.737752i	0.976448	−	0.215754i	$-0.0692209\pi$
$823$	36.6582	+	21.1646i	1.27782	+	0.737752i	0.301376	+	0.953506i	$0.402554\pi$
$824$		0			0
$825$		0			0
$826$	−25.7786	+	6.90737i	−0.896954	+	0.240338i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	41.3598	−	71.6373i	1.43735	−	2.48957i
$829$	−38.8545	+	22.4327i	−1.34947	+	0.779119i	−0.988175	−	0.153331i	$-0.951000\pi$
$829$	−38.8545	+	22.4327i	−1.34947	+	0.779119i	−0.361299	+	0.932450i	$0.617667\pi$
$830$	−10.4029	+	38.8242i	−0.361091	+	1.34761i
$831$		0			0
$832$	24.5600	−	15.1263i	0.851465	−	0.524411i
$833$		0			0
$834$	19.7501	+	5.29201i	0.683889	+	0.183247i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	9.79971	+	36.5730i	0.338525	+	1.26339i
$839$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$839$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$840$	−23.5604	−	23.5604i	−0.812909	−	0.812909i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$		0			0
$843$	22.3298	−	83.3359i	0.769079	−	2.87024i
$844$		0			0
$845$	−6.68297	−	20.2582i	−0.229901	−	0.696904i
$846$		0			0
$847$	28.1116	+	7.53248i	0.965926	+	0.258819i
$848$		0			0
$849$	−78.0126	−	45.0406i	−2.67739	−	1.54579i
$850$		0			0
$851$		0			0
$852$	−57.2376	+	15.3368i	−1.96093	+	0.525429i
$853$	10.7892	+	10.7892i	0.369415	+	0.369415i	0.867264	−	0.497849i	$-0.165877\pi$
$853$	10.7892	+	10.7892i	0.369415	+	0.369415i	−0.497849	+	0.867264i	$0.665877\pi$
$854$	23.7894	−	41.2044i	0.814056	−	1.40999i
$855$	−26.1619	+	15.1046i	−0.894718	+	0.516566i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−41.1363			−1.40355			−0.701776	−	0.712398i	$-0.747609\pi$
$859$	−41.1363			−1.40355			−0.701776	+	0.712398i	$0.747609\pi$
$860$		0			0
$861$		0			0
$862$	38.5585	+	22.2618i	1.31331	+	0.758239i
$863$	40.2535	−	40.2535i	1.37025	−	1.37025i	0.510174	−	0.860071i	$-0.329581\pi$
$863$	40.2535	−	40.2535i	1.37025	−	1.37025i	0.860071	−	0.510174i	$-0.170419\pi$
$864$	5.41282	+	20.2009i	0.184148	+	0.687249i
$865$	12.0290	−	3.22317i	0.409000	−	0.109591i
$866$		0			0
$867$	−23.0639	+	39.9478i	−0.783289	+	1.35670i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−28.2904	−	49.0005i	−0.956938	−	1.65747i
$875$	27.4745	+	15.8624i	0.928807	+	0.536247i
$876$		0			0
$877$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$877$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$878$		0			0
$879$	2.93644	+	2.93644i	0.0990438	+	0.0990438i
$880$		0			0
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$	11.1775	−	41.7151i	0.376367	−	1.40462i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	31.7581			1.06754
$886$		0			0
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	24.2404	−	24.2404i	0.812996	−	0.812996i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$			29.9333i			1.00000i
$897$	2.63606	+	92.7153i	0.0880155	+	3.09567i
$898$	−29.9088			−0.998071
$899$		0			0
$900$	−10.0658	−	17.4345i	−0.335528	−	0.581152i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	3.34669	−	0.896742i	0.111309	−	0.0298252i
$905$	26.8167	+	26.8167i	0.891416	+	0.891416i
$906$	46.5720	−	80.6650i	1.54725	−	2.67991i
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$	−1.83959	+	6.86545i	−0.0610490	+	0.227838i
$909$		−	87.4744i		−	2.90134i
$910$	21.5372	+	5.11954i	0.713952	+	0.169711i
$911$	0.210840			0.00698543			0.00349271	−	0.999994i	$-0.498888\pi$
$911$	0.210840			0.00698543			0.00349271	+	0.999994i	$0.498888\pi$
$912$	44.2414	+	11.8545i	1.46498	+	0.392540i
$913$		0			0
$914$	−41.7596	−	24.1099i	−1.38129	−	0.797486i
$915$	−40.0347	+	40.0347i	−1.32351	+	1.32351i
$916$	12.2182	+	45.5991i	0.403702	+	1.50664i
$917$	−58.4429	+	15.6597i	−1.92995	+	0.517129i
$918$		0			0
$919$	25.9154	−	44.8869i	0.854872	−	1.48068i	−0.0218926	−	0.999760i	$-0.506969\pi$
$919$	25.9154	−	44.8869i	0.854872	−	1.48068i	0.876764	−	0.480921i	$-0.159697\pi$
$920$	−38.1073	+	22.0012i	−1.25636	+	0.725359i
$921$	23.6510	−	88.2669i	0.779328	−	2.90849i
$922$		−	53.0056i		−	1.74564i
$923$	27.0364	−	28.6188i	0.889915	−	0.941999i
$924$		0			0
$925$		0			0
$926$	4.20185	+	7.27782i	0.138081	+	0.239164i
$927$		0			0
$928$		0			0
$929$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$929$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$930$		0			0
$931$	−20.8879	−	20.8879i	−0.684574	−	0.684574i
$932$	−9.77048	+	16.9230i	−0.320043	+	0.554330i
$933$		0			0
$934$	−14.5520	+	54.3089i	−0.476157	+	1.77704i
$935$		0			0
$936$	−32.3399	−	30.5517i	−1.05706	−	0.998615i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.98091	+	7.98091i	−0.260170	+	0.260170i	−0.825123	−	0.564953i	$-0.808894\pi$
$941$	−7.98091	+	7.98091i	−0.260170	+	0.260170i	0.564953	+	0.825123i	$0.308894\pi$
$942$	−23.0737	−	86.1122i	−0.751782	−	2.80569i
$943$		0			0
$944$	−20.1742	−	20.1742i	−0.656616	−	0.656616i
$945$	−8.02530	+	13.9002i	−0.261063	+	0.452174i
$946$		0			0
$947$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$947$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$948$		−	44.8163i		−	1.45557i
$949$		0			0
$950$	−13.7702			−0.446765
$951$		0			0
$952$		0			0
$953$	0.932742	+	0.538519i	0.0302145	+	0.0174443i	0.515031	−	0.857171i	$-0.327780\pi$
$953$	0.932742	+	0.538519i	0.0302145	+	0.0174443i	−0.484817	+	0.874616i	$0.661114\pi$
$954$		0			0
$955$	−11.5625	−	43.1520i	−0.374155	−	1.39637i
$956$	52.2391	−	13.9974i	1.68953	−	0.452709i
$957$		0			0
$958$		0			0
$959$	48.7135	−	28.1248i	1.57304	−	0.908196i
$960$	9.21911	−	34.4062i	0.297545	−	1.11045i
$961$		−	31.0000i		−	1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−16.8829	−	29.2420i	−0.543479	−	0.941334i
$966$	−83.3585	−	48.1270i	−2.68202	−	1.54846i
$967$	40.2250	−	40.2250i	1.29355	−	1.29355i	0.360971	−	0.932577i	$-0.382445\pi$
$967$	40.2250	−	40.2250i	1.29355	−	1.29355i	0.932577	−	0.360971i	$-0.117555\pi$
$968$	8.05256	+	30.0526i	0.258819	+	0.965926i
$969$		0			0
$970$		0			0
$971$	19.0235	−	32.9497i	0.610493	−	1.05741i	−0.380664	−	0.924713i	$-0.624305\pi$
$971$	19.0235	−	32.9497i	0.610493	−	1.05741i	0.991157	−	0.132692i	$-0.0423621\pi$
$972$	−33.5729	+	19.3833i	−1.07685	+	0.621720i
$973$	3.64873	−	13.6173i	0.116973	−	0.436549i
$974$		−	43.6917i		−	1.39997i
$975$	19.8621	+	10.7266i	0.636095	+	0.343526i
$976$	50.8638			1.62811
$977$	60.3562	+	16.1724i	1.93097	+	0.517401i	0.973317	+	0.229465i	$0.0736978\pi$
$977$	60.3562	+	16.1724i	1.93097	+	0.517401i	0.957650	+	0.287936i	$0.0929689\pi$
$978$		0			0
$979$		0			0
$980$	−16.2444	+	16.2444i	−0.518907	+	0.518907i
$981$		0			0
$982$		0			0
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−29.1582	+	8.70829i	−0.927647	+	0.277048i
$989$		0			0
$990$		0			0
$991$	11.3007	+	19.5735i	0.358980	+	0.621771i	0.987791	−	0.155787i	$-0.0497914\pi$
$991$	11.3007	+	19.5735i	0.358980	+	0.621771i	−0.628811	+	0.777558i	$0.716458\pi$
$992$		0			0
$993$		0			0
$994$	10.5744	+	39.4641i	0.335399	+	1.25173i
$995$		0			0
$996$	−66.4634	−	66.4634i	−2.10597	−	2.10597i
$997$	6.15232	−	10.6561i	0.194846	−	0.337483i	−0.752004	−	0.659158i	$-0.770913\pi$
$997$	6.15232	−	10.6561i	0.194846	−	0.337483i	0.946850	+	0.321675i	$0.104246\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.ds.a.405.3	yes	16
7.6	odd	2	inner	728.2.ds.a.405.2	yes	16
8.5	even	2	inner	728.2.ds.a.405.2	yes	16
13.7	odd	12	inner	728.2.ds.a.293.3	yes	16
56.13	odd	2	CM	728.2.ds.a.405.3	yes	16
91.20	even	12	inner	728.2.ds.a.293.2	✓	16
104.85	odd	12	inner	728.2.ds.a.293.2	✓	16
728.293	even	12	inner	728.2.ds.a.293.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.ds.a.293.2	✓	16	91.20	even	12	inner
728.2.ds.a.293.2	✓	16	104.85	odd	12	inner
728.2.ds.a.293.3	yes	16	13.7	odd	12	inner
728.2.ds.a.293.3	yes	16	728.293	even	12	inner
728.2.ds.a.405.2	yes	16	7.6	odd	2	inner
728.2.ds.a.405.2	yes	16	8.5	even	2	inner
728.2.ds.a.405.3	yes	16	1.1	even	1	trivial
728.2.ds.a.405.3	yes	16	56.13	odd	2	CM

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.ds (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.35670 + 2.34987i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.16031 + 1.16031i) q^{5} +(-0.993171 - 3.70657i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-2.18125 + 3.77804i) q^{9} +(2.00972 - 1.16031i) q^{10} +5.42679i q^{12} +(-1.89079 - 3.07000i) q^{13} +3.74166 q^{14} +(-4.30077 - 1.15239i) q^{15} +(2.00000 + 3.46410i) q^{16} +(4.36251 - 4.36251i) q^{18} +(-1.09222 - 4.07621i) q^{19} +(-3.17003 + 0.849407i) q^{20} +(-5.07630 - 5.07630i) q^{21} +(-8.21056 + 4.74037i) q^{23} +(1.98634 - 7.41313i) q^{24} +2.30735i q^{25} +(1.45917 + 4.88578i) q^{26} -3.69702 q^{27} +(-5.11120 - 1.36954i) q^{28} +(5.45316 + 3.14838i) q^{30} +(-1.46410 - 5.46410i) q^{32} +(2.17075 - 3.75984i) q^{35} +(-7.55609 + 4.36251i) q^{36} +5.96798i q^{38} +(4.64887 - 8.60817i) q^{39} +4.64125 q^{40} +(5.07630 + 8.79240i) q^{42} +(-1.85277 - 6.91465i) q^{45} +(12.9509 - 3.47019i) q^{46} +(-5.42679 + 9.39947i) q^{48} +(6.06218 - 3.50000i) q^{49} +(0.844549 - 3.15190i) q^{50} +(-0.204942 - 7.20819i) q^{52} +(5.05023 + 1.35320i) q^{54} +(6.48074 + 3.74166i) q^{56} +(8.09674 - 8.09674i) q^{57} +(-6.88963 + 1.84607i) q^{59} +(-6.29677 - 6.29677i) q^{60} +(6.35798 - 11.0123i) q^{61} +(2.98732 - 11.1488i) q^{63} +8.00000i q^{64} +(5.75607 + 1.36825i) q^{65} +(-22.2785 - 12.8625i) q^{69} +(-4.34149 + 4.34149i) q^{70} +(2.82612 + 10.5472i) q^{71} +(11.9186 - 3.19358i) q^{72} +(-5.42197 + 3.13038i) q^{75} +(2.18443 - 8.15241i) q^{76} +(-9.50129 + 10.0574i) q^{78} -8.25834 q^{79} +(-6.34006 - 1.69881i) q^{80} +(1.52802 + 2.64661i) q^{81} +(-12.2473 + 12.2473i) q^{83} +(-3.71611 - 13.8687i) q^{84} +10.1237i q^{90} +(6.93435 + 6.55094i) q^{91} -18.9615 q^{92} +(5.99698 + 3.46236i) q^{95} +(10.8536 - 10.8536i) q^{96} +(-9.56218 + 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 32 q^{8} - 32 q^{9} + 40 q^{15} + 32 q^{16} + 64 q^{18} - 96 q^{30} + 32 q^{32} - 48 q^{36} + 8 q^{39} + 24 q^{46} + 136 q^{50} - 72 q^{57} - 32 q^{60} - 112 q^{63} - 16 q^{65} + 16 q^{71}+ \cdots - 56 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 32 * q^8 - 32 * q^9 + 40 * q^15 + 32 * q^16 + 64 * q^18 - 96 * q^30 + 32 * q^32 - 48 * q^36 + 8 * q^39 + 24 * q^46 + 136 * q^50 - 72 * q^57 - 32 * q^60 - 112 * q^63 - 16 * q^65 + 16 * q^71 + 112 * q^72 - 144 * q^78 - 192 * q^79 - 96 * q^81 - 96 * q^92 + 312 * q^95 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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