LMFDB - Embedded newform 784.2.bb.a.111.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.3
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.a.671.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.683449 - 0.857018i) q^{3} +(-1.48324 + 1.18285i) q^{5} +(-2.57717 + 0.598513i) q^{7} +(0.400186 - 1.75333i) q^{9} +O(q^{10})$	\(q+(-0.683449 - 0.857018i) q^{3} +(-1.48324 + 1.18285i) q^{5} +(-2.57717 + 0.598513i) q^{7} +(0.400186 - 1.75333i) q^{9} +(-3.19446 + 0.729114i) q^{11} +(4.87901 - 1.11360i) q^{13} +(2.02744 + 0.462750i) q^{15} +(-0.421211 + 0.874654i) q^{17} +7.47964 q^{19} +(2.27430 + 1.79962i) q^{21} +(1.73866 + 3.61037i) q^{23} +(-0.311721 + 1.36574i) q^{25} +(-4.73898 + 2.28217i) q^{27} +(9.12423 + 4.39400i) q^{29} -0.116769 q^{31} +(2.80811 + 2.23939i) q^{33} +(3.11461 - 3.93613i) q^{35} +(8.70110 + 4.19023i) q^{37} +(-4.28893 - 3.42031i) q^{39} +(-5.62925 + 4.48918i) q^{41} +(-4.92223 - 3.92534i) q^{43} +(1.48035 + 3.07397i) q^{45} +(0.387704 + 1.69864i) q^{47} +(6.28356 - 3.08493i) q^{49} +(1.03747 - 0.236796i) q^{51} +(-3.77343 + 1.81719i) q^{53} +(3.87572 - 4.86000i) q^{55} +(-5.11195 - 6.41019i) q^{57} +(6.73482 - 8.44520i) q^{59} +(3.39006 - 7.03954i) q^{61} +(0.0180445 + 4.75813i) q^{63} +(-5.91954 + 7.42287i) q^{65} +14.4091i q^{67} +(1.90586 - 3.95757i) q^{69} +(3.98262 + 8.27000i) q^{71} +(1.76859 + 0.403670i) q^{73} +(1.38351 - 0.666263i) q^{75} +(7.79626 - 3.79097i) q^{77} -5.52012i q^{79} +(0.333751 + 0.160726i) q^{81} +(3.87416 - 16.9738i) q^{83} +(-0.409823 - 1.79555i) q^{85} +(-2.47021 - 10.8227i) q^{87} +(-8.43160 - 1.92446i) q^{89} +(-11.9075 + 5.79009i) q^{91} +(0.0798054 + 0.100073i) q^{93} +(-11.0941 + 8.84727i) q^{95} -7.90451i q^{97} +5.89271i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 14 q^{17} + 12 q^{25} + 28 q^{29} + 42 q^{37} + 28 q^{41} + 56 q^{49} - 38 q^{53} + 42 q^{57} + 84 q^{61} + 8 q^{65} + 56 q^{69} - 42 q^{73} - 42 q^{77} - 44 q^{81} - 12 q^{85} - 28 q^{89} + 98 q^{93}+O(q^{100}) $ 48 * q - 4 * q^9 + 14 * q^17 + 12 * q^25 + 28 * q^29 + 42 * q^37 + 28 * q^41 + 56 * q^49 - 38 * q^53 + 42 * q^57 + 84 * q^61 + 8 * q^65 + 56 * q^69 - 42 * q^73 - 42 * q^77 - 44 * q^81 - 12 * q^85 - 28 * q^89 + 98 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.683449	−	0.857018i	−0.394589	−	0.494799i	0.544361	−	0.838851i	$-0.316772\pi$
$3$	−0.683449	−	0.857018i	−0.394589	−	0.494799i	−0.938951	+	0.344051i	$0.888201\pi$
$4$		0			0
$5$	−1.48324	+	1.18285i	−0.663327	+	0.528985i	−0.896272	−	0.443505i	$-0.853735\pi$
$5$	−1.48324	+	1.18285i	−0.663327	+	0.528985i	0.232946	+	0.972490i	$0.425164\pi$
$6$		0			0
$7$	−2.57717	+	0.598513i	−0.974077	+	0.226217i
$7$	−2.57717	+	0.598513i	−0.974077	+	0.226217i
$8$		0			0
$9$	0.400186	−	1.75333i	0.133395	−	0.584443i
$10$		0			0
$11$	−3.19446	+	0.729114i	−0.963165	+	0.219836i	−0.675060	−	0.737763i	$-0.735882\pi$
$11$	−3.19446	+	0.729114i	−0.963165	+	0.219836i	−0.288105	+	0.957599i	$0.593025\pi$
$12$		0			0
$13$	4.87901	−	1.11360i	1.35319	−	0.308858i	0.516387	−	0.856355i	$-0.327277\pi$
$13$	4.87901	−	1.11360i	1.35319	−	0.308858i	0.836807	+	0.547497i	$0.184419\pi$
$14$		0			0
$15$	2.02744	+	0.462750i	0.523483	+	0.119482i
$16$		0			0
$17$	−0.421211	+	0.874654i	−0.102159	+	0.212135i	−0.945783	−	0.324799i	$-0.894703\pi$
$17$	−0.421211	+	0.874654i	−0.102159	+	0.212135i	0.843624	+	0.536934i	$0.180418\pi$
$18$		0			0
$19$	7.47964			1.71595			0.857974	−	0.513693i	$-0.171723\pi$
$19$	7.47964			1.71595			0.857974	+	0.513693i	$0.171723\pi$
$20$		0			0
$21$	2.27430	+	1.79962i	0.496292	+	0.392710i
$22$		0			0
$23$	1.73866	+	3.61037i	0.362536	+	0.752814i	0.999842	−	0.0177973i	$-0.00566534\pi$
$23$	1.73866	+	3.61037i	0.362536	+	0.752814i	−0.637306	+	0.770611i	$0.719951\pi$
$24$		0			0
$25$	−0.311721	+	1.36574i	−0.0623442	+	0.273148i
$26$		0			0
$27$	−4.73898	+	2.28217i	−0.912016	+	0.439204i
$28$		0			0
$29$	9.12423	+	4.39400i	1.69433	+	0.815945i	0.994858	+	0.101282i	$0.0322946\pi$
$29$	9.12423	+	4.39400i	1.69433	+	0.815945i	0.699469	+	0.714662i	$0.253420\pi$
$30$		0			0
$31$	−0.116769			−0.0209723			−0.0104861	−	0.999945i	$-0.503338\pi$
$31$	−0.116769			−0.0209723			−0.0104861	+	0.999945i	$0.503338\pi$
$32$		0			0
$33$	2.80811	+	2.23939i	0.488829	+	0.389828i
$34$		0			0
$35$	3.11461	−	3.93613i	0.526466	−	0.665328i
$36$		0			0
$37$	8.70110	+	4.19023i	1.43045	+	0.688870i	0.979082	−	0.203467i	$-0.0652209\pi$
$37$	8.70110	+	4.19023i	1.43045	+	0.688870i	0.451371	+	0.892337i	$0.350935\pi$
$38$		0			0
$39$	−4.28893	−	3.42031i	−0.686779	−	0.547688i
$40$		0			0
$41$	−5.62925	+	4.48918i	−0.879141	+	0.701092i	−0.955184	−	0.296013i	$-0.904343\pi$
$41$	−5.62925	+	4.48918i	−0.879141	+	0.701092i	0.0760428	+	0.997105i	$0.475771\pi$
$42$		0			0
$43$	−4.92223	−	3.92534i	−0.750632	−	0.598609i	0.171636	−	0.985161i	$-0.445095\pi$
$43$	−4.92223	−	3.92534i	−0.750632	−	0.598609i	−0.922268	+	0.386551i	$0.873666\pi$
$44$		0			0
$45$	1.48035	+	3.07397i	0.220677	+	0.458241i
$46$		0			0
$47$	0.387704	+	1.69864i	0.0565525	+	0.247773i	0.995301	−	0.0968308i	$-0.0308706\pi$
$47$	0.387704	+	1.69864i	0.0565525	+	0.247773i	−0.938748	+	0.344603i	$0.888013\pi$
$48$		0			0
$49$	6.28356	−	3.08493i	0.897652	−	0.440705i
$50$		0			0
$51$	1.03747	−	0.236796i	0.145275	−	0.0331580i
$52$		0			0
$53$	−3.77343	+	1.81719i	−0.518321	+	0.249610i	−0.674707	−	0.738086i	$-0.735730\pi$
$53$	−3.77343	+	1.81719i	−0.518321	+	0.249610i	0.156386	+	0.987696i	$0.450016\pi$
$54$		0			0
$55$	3.87572	−	4.86000i	0.522603	−	0.655323i
$56$		0			0
$57$	−5.11195	−	6.41019i	−0.677095	−	0.849050i
$58$		0			0
$59$	6.73482	−	8.44520i	0.876799	−	1.09947i	−0.117525	−	0.993070i	$-0.537496\pi$
$59$	6.73482	−	8.44520i	0.876799	−	1.09947i	0.994323	−	0.106401i	$-0.0339327\pi$
$60$		0			0
$61$	3.39006	−	7.03954i	0.434053	−	0.901320i	−0.563134	−	0.826366i	$-0.690404\pi$
$61$	3.39006	−	7.03954i	0.434053	−	0.901320i	0.997187	−	0.0749548i	$-0.0238812\pi$
$62$		0			0
$63$	0.0180445	+	4.75813i	0.00227340	+	0.599468i
$64$		0			0
$65$	−5.91954	+	7.42287i	−0.734229	+	0.920693i
$66$		0			0
$67$			14.4091i			1.76035i	0.474653	+	0.880173i	$0.342574\pi$
$67$			14.4091i			1.76035i	−0.474653	+	0.880173i	$0.657426\pi$
$68$		0			0
$69$	1.90586	−	3.95757i	0.229439	−	0.476435i
$70$		0			0
$71$	3.98262	+	8.27000i	0.472650	+	0.981468i	0.991921	+	0.126858i	$0.0404893\pi$
$71$	3.98262	+	8.27000i	0.472650	+	0.981468i	−0.519271	+	0.854610i	$0.673796\pi$
$72$		0			0
$73$	1.76859	+	0.403670i	0.206998	+	0.0472460i	0.324762	−	0.945796i	$-0.394716\pi$
$73$	1.76859	+	0.403670i	0.206998	+	0.0472460i	−0.117764	+	0.993042i	$0.537573\pi$
$74$		0			0
$75$	1.38351	−	0.666263i	0.159754	−	0.0769334i
$76$		0			0
$77$	7.79626	−	3.79097i	0.888466	−	0.432021i
$78$		0			0
$79$		−	5.52012i		−	0.621062i	−0.950563	−	0.310531i	$-0.899493\pi$
$79$		−	5.52012i		−	0.621062i	0.950563	−	0.310531i	$-0.100507\pi$
$80$		0			0
$81$	0.333751	+	0.160726i	0.0370835	+	0.0178585i
$82$		0			0
$83$	3.87416	−	16.9738i	0.425245	−	1.86312i	−0.0749221	−	0.997189i	$-0.523871\pi$
$83$	3.87416	−	16.9738i	0.425245	−	1.86312i	0.500167	−	0.865929i	$-0.333272\pi$
$84$		0			0
$85$	−0.409823	−	1.79555i	−0.0444516	−	0.194755i
$86$		0			0
$87$	−2.47021	−	10.8227i	−0.264834	−	1.16032i
$88$		0			0
$89$	−8.43160	−	1.92446i	−0.893748	−	0.203992i	−0.249106	−	0.968476i	$-0.580137\pi$
$89$	−8.43160	−	1.92446i	−0.893748	−	0.203992i	−0.644643	+	0.764484i	$0.722994\pi$
$90$		0			0
$91$	−11.9075	+	5.79009i	−1.24825	+	0.606966i
$92$		0			0
$93$	0.0798054	+	0.100073i	0.00827544	+	0.0103771i
$94$		0			0
$95$	−11.0941	+	8.84727i	−1.13823	+	0.907711i
$96$		0			0
$97$		−	7.90451i		−	0.802581i	−0.915951	−	0.401291i	$-0.868562\pi$
$97$		−	7.90451i		−	0.802581i	0.915951	−	0.401291i	$-0.131438\pi$
$98$		0			0
$99$			5.89271i			0.592240i
$100$		0			0
$101$	−2.81823	+	2.24747i	−0.280425	+	0.223631i	−0.753594	−	0.657340i	$-0.771681\pi$
$101$	−2.81823	+	2.24747i	−0.280425	+	0.223631i	0.473169	+	0.880972i	$0.343110\pi$
$102$		0			0
$103$	8.01700	+	10.0530i	0.789939	+	0.990552i	0.999917	+	0.0128461i	$0.00408917\pi$
$103$	8.01700	+	10.0530i	0.789939	+	0.990552i	−0.209979	+	0.977706i	$0.567339\pi$
$104$		0			0
$105$	−5.50201	+	0.0208656i	−0.536942	+	0.00203627i
$106$		0			0
$107$	14.2190	+	3.24540i	1.37460	+	0.313744i	0.845120	−	0.534576i	$-0.179529\pi$
$107$	14.2190	+	3.24540i	1.37460	+	0.313744i	0.529483	+	0.848321i	$0.322386\pi$
$108$		0			0
$109$	0.591879	+	2.59319i	0.0566917	+	0.248382i	0.995331	−	0.0965169i	$-0.0307702\pi$
$109$	0.591879	+	2.59319i	0.0566917	+	0.248382i	−0.938640	+	0.344899i	$0.887913\pi$
$110$		0			0
$111$	−2.35566	−	10.3208i	−0.223589	−	0.979608i
$112$		0			0
$113$	−2.65993	+	11.6539i	−0.250226	+	1.09631i	0.681120	+	0.732172i	$0.261493\pi$
$113$	−2.65993	+	11.6539i	−0.250226	+	1.09631i	−0.931345	+	0.364138i	$0.881364\pi$
$114$		0			0
$115$	−6.84937	−	3.29848i	−0.638707	−	0.307585i
$116$		0			0
$117$		−	9.00016i		−	0.832065i
$118$		0			0
$119$	0.562039	−	2.50623i	0.0515220	−	0.229746i
$120$		0			0
$121$	−0.237719	+	0.114480i	−0.0216108	+	0.0104072i
$122$		0			0
$123$	7.69461	+	1.75624i	0.693799	+	0.158355i
$124$		0			0
$125$	−5.26879	−	10.9408i	−0.471255	−	0.978571i
$126$		0			0
$127$	−6.34033	+	13.1658i	−0.562613	+	1.16828i	0.404642	+	0.914475i	$0.367396\pi$
$127$	−6.34033	+	13.1658i	−0.562613	+	1.16828i	−0.967256	+	0.253804i	$0.918318\pi$
$128$		0			0
$129$			6.90121i			0.607617i
$130$		0			0
$131$	−5.92404	+	7.42851i	−0.517586	+	0.649032i	−0.970094	−	0.242728i	$-0.921958\pi$
$131$	−5.92404	+	7.42851i	−0.517586	+	0.649032i	0.452508	+	0.891760i	$0.350529\pi$
$132$		0			0
$133$	−19.2763	+	4.47666i	−1.67147	+	0.388176i
$134$		0			0
$135$	4.32960	−	8.99050i	0.372632	−	0.773779i
$136$		0			0
$137$	4.83787	−	6.06649i	0.413327	−	0.518296i	−0.530970	−	0.847391i	$-0.678172\pi$
$137$	4.83787	−	6.06649i	0.413327	−	0.518296i	0.944297	+	0.329095i	$0.106744\pi$
$138$		0			0
$139$	3.90114	+	4.89188i	0.330891	+	0.414924i	0.919249	−	0.393677i	$-0.128797\pi$
$139$	3.90114	+	4.89188i	0.330891	+	0.414924i	−0.588358	+	0.808600i	$0.700226\pi$
$140$		0			0
$141$	1.19079	−	1.49320i	0.100283	−	0.125751i
$142$		0			0
$143$	−14.7738	+	7.11471i	−1.23545	+	0.594962i
$144$		0			0
$145$	−18.7309	+	4.27520i	−1.55552	+	0.355036i
$146$		0			0
$147$	−6.93834	−	3.27673i	−0.572264	−	0.270260i
$148$		0			0
$149$	0.218323	+	0.956536i	0.0178857	+	0.0783625i	0.983083	−	0.183160i	$-0.0586326\pi$
$149$	0.218323	+	0.956536i	0.0178857	+	0.0783625i	−0.965197	+	0.261522i	$0.915775\pi$
$150$		0			0
$151$	−7.90658	−	16.4182i	−0.643429	−	1.33609i	−0.926246	−	0.376920i	$-0.876983\pi$
$151$	−7.90658	−	16.4182i	−0.643429	−	1.33609i	0.282817	−	0.959174i	$-0.408731\pi$
$152$		0			0
$153$	1.36499	+	1.08855i	0.110353	+	0.0880037i
$154$		0			0
$155$	0.173196	−	0.138119i	0.0139115	−	0.0110940i
$156$		0			0
$157$	0.194297	+	0.154947i	0.0155066	+	0.0123661i	0.631212	−	0.775610i	$-0.282558\pi$
$157$	0.194297	+	0.154947i	0.0155066	+	0.0123661i	−0.615706	+	0.787976i	$0.711129\pi$
$158$		0			0
$159$	4.13631	+	1.99194i	0.328031	+	0.157971i
$160$		0			0
$161$	−6.64167	−	8.26391i	−0.523437	−	0.651287i
$162$		0			0
$163$	6.36932	+	5.07936i	0.498884	+	0.397846i	0.840347	−	0.542049i	$-0.182351\pi$
$163$	6.36932	+	5.07936i	0.498884	+	0.397846i	−0.341464	+	0.939895i	$0.610923\pi$
$164$		0			0
$165$	−6.81397			−0.530467
$166$		0			0
$167$	2.35440	+	1.13382i	0.182189	+	0.0877375i	0.522755	−	0.852483i	$-0.324904\pi$
$167$	2.35440	+	1.13382i	0.182189	+	0.0877375i	−0.340566	+	0.940221i	$0.610619\pi$
$168$		0			0
$169$	10.8521	−	5.22607i	0.834773	−	0.402006i
$170$		0			0
$171$	2.99325	−	13.1143i	0.228899	−	1.00287i
$172$		0			0
$173$	6.96965	+	14.4726i	0.529893	+	1.10033i	0.978432	+	0.206571i	$0.0662303\pi$
$173$	6.96965	+	14.4726i	0.529893	+	1.10033i	−0.448539	+	0.893763i	$0.648055\pi$
$174$		0			0
$175$	−0.0140556	−	3.70631i	−0.00106251	−	0.280170i
$176$		0			0
$177$	−11.8406			−0.889993
$178$		0			0
$179$	−6.31512	+	13.1135i	−0.472015	+	0.980148i	0.520017	+	0.854156i	$0.325926\pi$
$179$	−6.31512	+	13.1135i	−0.472015	+	0.980148i	−0.992031	+	0.125992i	$0.959789\pi$
$180$		0			0
$181$	15.2622	+	3.48349i	1.13443	+	0.258926i	0.748197	−	0.663477i	$-0.230920\pi$
$181$	15.2622	+	3.48349i	1.13443	+	0.258926i	0.386230	+	0.922402i	$0.373777\pi$
$182$		0			0
$183$	−8.34994	+	1.90582i	−0.617246	+	0.140882i
$184$		0			0
$185$	−17.8623	+	4.07694i	−1.31326	+	0.299743i
$186$		0			0
$187$	0.707818	−	3.10115i	0.0517608	−	0.226779i
$188$		0			0
$189$	10.8472	−	8.71787i	0.789019	−	0.634132i
$190$		0			0
$191$	1.85681	−	1.48076i	0.134354	−	0.107144i	−0.554007	−	0.832512i	$-0.686902\pi$
$191$	1.85681	−	1.48076i	0.134354	−	0.107144i	0.688361	+	0.725368i	$0.258331\pi$
$192$		0			0
$193$	−10.9648	−	13.7495i	−0.789267	−	0.989709i	−0.999926	−	0.0121494i	$-0.996133\pi$
$193$	−10.9648	−	13.7495i	−0.789267	−	0.989709i	0.210660	−	0.977559i	$-0.432439\pi$
$194$		0			0
$195$	10.4072			0.745277
$196$		0			0
$197$	−14.2122			−1.01258			−0.506289	−	0.862364i	$-0.668983\pi$
$197$	−14.2122			−1.01258			−0.506289	+	0.862364i	$0.668983\pi$
$198$		0			0
$199$	0.137329	+	0.172205i	0.00973499	+	0.0122073i	0.786675	−	0.617367i	$-0.211801\pi$
$199$	0.137329	+	0.172205i	0.00973499	+	0.0122073i	−0.776940	+	0.629574i	$0.783229\pi$
$200$		0			0
$201$	12.3488	−	9.84785i	0.871018	−	0.694614i
$202$		0			0
$203$	−26.1445	−	5.86309i	−1.83499	−	0.411508i
$204$		0			0
$205$	3.03954	−	13.3171i	0.212290	−	0.930105i
$206$		0			0
$207$	7.02595	−	1.60363i	0.488337	−	0.111460i
$208$		0			0
$209$	−23.8934	+	5.45351i	−1.65274	+	0.377227i
$210$		0			0
$211$	10.4138	+	2.37689i	0.716919	+	0.163632i	0.565393	−	0.824821i	$-0.308724\pi$
$211$	10.4138	+	2.37689i	0.716919	+	0.163632i	0.151525	+	0.988453i	$0.451582\pi$
$212$		0			0
$213$	4.36562	−	9.06530i	0.299127	−	0.621144i
$214$		0			0
$215$	11.9439			0.814570
$216$		0			0
$217$	0.300932	−	0.0698875i	0.0204286	−	0.00474428i
$218$		0			0
$219$	−0.862790	−	1.79160i	−0.0583020	−	0.121065i
$220$		0			0
$221$	−1.08108	+	4.73651i	−0.0727211	+	0.318612i
$222$		0			0
$223$	13.5743	−	6.53705i	0.909004	−	0.437753i	0.0798712	−	0.996805i	$-0.474549\pi$
$223$	13.5743	−	6.53705i	0.909004	−	0.437753i	0.829133	+	0.559052i	$0.188835\pi$
$224$		0			0
$225$	2.26984	+	1.09310i	0.151323	+	0.0728733i
$226$		0			0
$227$	−19.6980			−1.30740			−0.653702	−	0.756752i	$-0.726785\pi$
$227$	−19.6980			−1.30740			−0.653702	+	0.756752i	$0.726785\pi$
$228$		0			0
$229$	−8.10997	−	6.46748i	−0.535922	−	0.427383i	0.317766	−	0.948169i	$-0.397067\pi$
$229$	−8.10997	−	6.46748i	−0.535922	−	0.427383i	−0.853687	+	0.520786i	$0.825639\pi$
$230$		0			0
$231$	−8.57727	−	4.09060i	−0.564343	−	0.269141i
$232$		0			0
$233$	−5.71213	−	2.75082i	−0.374214	−	0.180212i	0.237317	−	0.971432i	$-0.423732\pi$
$233$	−5.71213	−	2.75082i	−0.374214	−	0.180212i	−0.611531	+	0.791220i	$0.709446\pi$
$234$		0			0
$235$	−2.58429	−	2.06091i	−0.168581	−	0.134439i
$236$		0			0
$237$	−4.73084	+	3.77272i	−0.307301	+	0.245064i
$238$		0			0
$239$	20.5078	+	16.3544i	1.32654	+	1.05788i	0.993364	+	0.115011i	$0.0366905\pi$
$239$	20.5078	+	16.3544i	1.32654	+	1.05788i	0.333172	+	0.942866i	$0.391881\pi$
$240$		0			0
$241$	−10.7389	−	22.2995i	−0.691751	−	1.43644i	−0.889850	−	0.456253i	$-0.849191\pi$
$241$	−10.7389	−	22.2995i	−0.691751	−	1.43644i	0.198099	−	0.980182i	$-0.436523\pi$
$242$		0			0
$243$	3.42093	+	14.9881i	0.219453	+	0.961487i
$244$		0			0
$245$	−5.67105	+	12.0082i	−0.362310	+	0.767176i
$246$		0			0
$247$	36.4933	−	8.32935i	2.32201	−	0.529984i
$248$		0			0
$249$	−17.1947	+	8.28051i	−1.08967	+	0.524756i
$250$		0			0
$251$	6.84131	−	8.57873i	0.431820	−	0.541485i	−0.517547	−	0.855655i	$-0.673155\pi$
$251$	6.84131	−	8.57873i	0.431820	−	0.541485i	0.949367	+	0.314170i	$0.101726\pi$
$252$		0			0
$253$	−8.18645	−	10.2655i	−0.514678	−	0.645385i
$254$		0			0
$255$	−1.25873	+	1.57839i	−0.0788246	+	0.0988429i
$256$		0			0
$257$	−4.06039	+	8.43149i	−0.253280	+	0.525942i	−0.988377	−	0.152020i	$-0.951422\pi$
$257$	−4.06039	+	8.43149i	−0.253280	+	0.525942i	0.735097	+	0.677962i	$0.237137\pi$
$258$		0			0
$259$	−24.9321	−	5.59120i	−1.54920	−	0.347420i
$260$		0			0
$261$	11.3555	−	14.2394i	0.702888	−	0.881394i
$262$		0			0
$263$			5.96881i			0.368053i	0.982921	+	0.184026i	$0.0589132\pi$
$263$			5.96881i			0.368053i	−0.982921	+	0.184026i	$0.941087\pi$
$264$		0			0
$265$	3.44746	−	7.15873i	0.211776	−	0.439757i
$266$		0			0
$267$	4.11327	+	8.54130i	0.251728	+	0.522719i
$268$		0			0
$269$	9.48566	+	2.16504i	0.578351	+	0.132005i	0.501683	−	0.865052i	$-0.332715\pi$
$269$	9.48566	+	2.16504i	0.578351	+	0.132005i	0.0766685	+	0.997057i	$0.475572\pi$
$270$		0			0
$271$	11.3318	−	5.45710i	0.688358	−	0.331496i	−0.0567985	−	0.998386i	$-0.518089\pi$
$271$	11.3318	−	5.45710i	0.688358	−	0.331496i	0.745156	+	0.666890i	$0.232375\pi$
$272$		0			0
$273$	13.1004	+	6.24772i	0.792871	+	0.378129i
$274$		0			0
$275$		−	4.59008i		−	0.276792i
$276$		0			0
$277$	12.5898	+	6.06292i	0.756447	+	0.364286i	0.772024	−	0.635593i	$-0.219244\pi$
$277$	12.5898	+	6.06292i	0.756447	+	0.364286i	−0.0155773	+	0.999879i	$0.504959\pi$
$278$		0			0
$279$	−0.0467292	+	0.204734i	−0.00279760	+	0.0122571i
$280$		0			0
$281$	1.33187	+	5.83529i	0.0794525	+	0.348104i	0.998992	−	0.0448939i	$-0.0142950\pi$
$281$	1.33187	+	5.83529i	0.0794525	+	0.348104i	−0.919539	+	0.392998i	$0.871438\pi$
$282$		0			0
$283$	−1.55220	−	6.80063i	−0.0922687	−	0.404255i	0.907610	−	0.419814i	$-0.137905\pi$
$283$	−1.55220	−	6.80063i	−0.0922687	−	0.404255i	−0.999879	+	0.0155583i	$0.995047\pi$
$284$		0			0
$285$	15.1645	+	3.46121i	0.898270	+	0.205024i
$286$		0			0
$287$	11.8207	−	14.9385i	0.697753	−	0.881794i
$288$		0			0
$289$	10.0117	+	12.5543i	0.588925	+	0.738489i
$290$		0			0
$291$	−6.77430	+	5.40233i	−0.397117	+	0.316690i
$292$		0			0
$293$			33.2019i			1.93968i	0.243749	+	0.969838i	$0.421623\pi$
$293$			33.2019i			1.93968i	−0.243749	+	0.969838i	$0.578377\pi$
$294$		0			0
$295$			20.4925i			1.19312i
$296$		0			0
$297$	13.4745	−	10.7455i	0.781869	−	0.623520i
$298$		0			0
$299$	12.5035	+	15.6789i	0.723094	+	0.906732i
$300$		0			0
$301$	15.0348	+	7.17025i	0.866589	+	0.413286i
$302$		0			0
$303$	3.85224	+	0.879248i	0.221305	+	0.0505115i
$304$		0			0
$305$	3.29841	+	14.4513i	0.188866	+	0.827477i
$306$		0			0
$307$	1.05700	+	4.63103i	0.0603263	+	0.264307i	0.996093	−	0.0883137i	$-0.0281478\pi$
$307$	1.05700	+	4.63103i	0.0603263	+	0.264307i	−0.935766	+	0.352621i	$0.885291\pi$
$308$		0			0
$309$	3.13639	−	13.7414i	0.178423	−	0.781723i
$310$		0			0
$311$	−9.29896	−	4.47814i	−0.527296	−	0.253932i	0.151243	−	0.988497i	$-0.451672\pi$
$311$	−9.29896	−	4.47814i	−0.527296	−	0.253932i	−0.678539	+	0.734564i	$0.737387\pi$
$312$		0			0
$313$			1.19947i			0.0677982i	0.999425	+	0.0338991i	$0.0107925\pi$
$313$			1.19947i			0.0677982i	−0.999425	+	0.0338991i	$0.989208\pi$
$314$		0			0
$315$	−5.65491	−	7.03613i	−0.318618	−	0.396441i
$316$		0			0
$317$	−8.40996	+	4.05003i	−0.472351	+	0.227472i	−0.654887	−	0.755727i	$-0.727284\pi$
$317$	−8.40996	+	4.05003i	−0.472351	+	0.227472i	0.182536	+	0.983199i	$0.441569\pi$
$318$		0			0
$319$	−32.3507	−	7.38383i	−1.81129	−	0.413415i
$320$		0			0
$321$	−6.93660	−	14.4040i	−0.387163	−	0.803953i
$322$		0			0
$323$	−3.15051	+	6.54210i	−0.175299	+	0.364012i
$324$		0			0
$325$			7.01059i			0.388878i
$326$		0			0
$327$	1.81789	−	2.27956i	0.100530	−	0.126060i
$328$		0			0
$329$	−2.01584	−	4.14564i	−0.111137	−	0.228556i
$330$		0			0
$331$	11.1163	−	23.0832i	0.611006	−	1.26877i	−0.334265	−	0.942479i	$-0.608488\pi$
$331$	11.1163	−	23.0832i	0.611006	−	1.26877i	0.945271	−	0.326287i	$-0.105798\pi$
$332$		0			0
$333$	10.8289	−	13.5790i	0.593420	−	0.744126i
$334$		0			0
$335$	−17.0437	−	21.3721i	−0.931197	−	1.16768i
$336$		0			0
$337$	−7.49796	+	9.40215i	−0.408440	+	0.512168i	−0.942923	−	0.333012i	$-0.891935\pi$
$337$	−7.49796	+	9.40215i	−0.408440	+	0.512168i	0.534483	+	0.845179i	$0.320506\pi$
$338$		0			0
$339$	11.8056	−	5.68526i	0.641190	−	0.308781i
$340$		0			0
$341$	0.373012	−	0.0851376i	0.0201997	−	0.00461046i
$342$		0			0
$343$	−14.3474	+	11.7112i	−0.774688	+	0.632344i
$344$		0			0
$345$	1.85434	+	8.12438i	0.0998341	+	0.437402i
$346$		0			0
$347$	9.50105	+	19.7291i	0.510043	+	1.05912i	0.983934	+	0.178532i	$0.0571348\pi$
$347$	9.50105	+	19.7291i	0.510043	+	1.05912i	−0.473891	+	0.880584i	$0.657151\pi$
$348$		0			0
$349$	5.37276	+	4.28464i	0.287597	+	0.229351i	0.756652	−	0.653818i	$-0.226834\pi$
$349$	5.37276	+	4.28464i	0.287597	+	0.229351i	−0.469054	+	0.883169i	$0.655405\pi$
$350$		0			0
$351$	−20.5801	+	16.4121i	−1.09848	+	0.876012i
$352$		0			0
$353$	1.79041	+	1.42781i	0.0952940	+	0.0759944i	0.669978	−	0.742381i	$-0.266304\pi$
$353$	1.79041	+	1.42781i	0.0952940	+	0.0759944i	−0.574684	+	0.818375i	$0.694875\pi$
$354$		0			0
$355$	−15.6893	−	7.55559i	−0.832704	−	0.401009i
$356$		0			0
$357$	−2.53201	+	1.23120i	−0.134008	+	0.0651621i
$358$		0			0
$359$	−21.9202	−	17.4808i	−1.15690	−	0.922600i	−0.158998	−	0.987279i	$-0.550826\pi$
$359$	−21.9202	−	17.4808i	−1.15690	−	0.922600i	−0.997906	+	0.0646787i	$0.979398\pi$
$360$		0			0
$361$	36.9451			1.94448
$362$		0			0
$363$	0.260580	+	0.125489i	0.0136769	+	0.00658645i
$364$		0			0
$365$	−3.10073	+	1.49323i	−0.162300	+	0.0781594i
$366$		0			0
$367$	3.59948	−	15.7703i	0.187891	−	0.823205i	−0.789835	−	0.613320i	$-0.789834\pi$
$367$	3.59948	−	15.7703i	0.187891	−	0.823205i	0.977726	−	0.209885i	$-0.0673091\pi$
$368$		0			0
$369$	5.61826	+	11.6664i	0.292475	+	0.607330i
$370$		0			0
$371$	8.63715	−	6.94164i	0.448418	−	0.360392i
$372$		0			0
$373$	−20.4902			−1.06094			−0.530471	−	0.847703i	$-0.677985\pi$
$373$	−20.4902			−1.06094			−0.530471	+	0.847703i	$0.677985\pi$
$374$		0			0
$375$	−5.77548	+	11.9929i	−0.298244	+	0.619311i
$376$		0			0
$377$	49.4104	+	11.2776i	2.54477	+	0.580826i
$378$		0			0
$379$	10.4102	−	2.37606i	0.534735	−	0.122050i	0.0533779	−	0.998574i	$-0.483001\pi$
$379$	10.4102	−	2.37606i	0.534735	−	0.122050i	0.481357	+	0.876525i	$0.340144\pi$
$380$		0			0
$381$	15.6166	−	3.56440i	0.800065	−	0.182610i
$382$		0			0
$383$	−0.285641	+	1.25147i	−0.0145956	+	0.0639473i	−0.981701	−	0.190428i	$-0.939013\pi$
$383$	−0.285641	+	1.25147i	−0.0145956	+	0.0639473i	0.967106	+	0.254375i	$0.0818697\pi$
$384$		0			0
$385$	−7.07961	+	14.8447i	−0.360810	+	0.756556i
$386$		0			0
$387$	−8.85222	+	7.05941i	−0.449984	+	0.358850i
$388$		0			0
$389$	−7.35586	−	9.22396i	−0.372957	−	0.467673i	0.559565	−	0.828786i	$-0.310968\pi$
$389$	−7.35586	−	9.22396i	−0.372957	−	0.467673i	−0.932522	+	0.361113i	$0.882397\pi$
$390$		0			0
$391$	−3.89017			−0.196734
$392$		0			0
$393$	10.4151			0.525375
$394$		0			0
$395$	6.52945	+	8.18767i	0.328532	+	0.411967i
$396$		0			0
$397$	2.88894	−	2.30385i	0.144992	−	0.115627i	−0.548308	−	0.836277i	$-0.684728\pi$
$397$	2.88894	−	2.30385i	0.144992	−	0.115627i	0.693299	+	0.720650i	$0.256156\pi$
$398$		0			0
$399$	17.0109	+	13.4605i	0.851612	+	0.673870i
$400$		0			0
$401$	5.56862	−	24.3977i	0.278084	−	1.21836i	−0.622129	−	0.782915i	$-0.713732\pi$
$401$	5.56862	−	24.3977i	0.278084	−	1.21836i	0.900213	−	0.435450i	$-0.143411\pi$
$402$		0			0
$403$	−0.569716	+	0.130034i	−0.0283796	+	0.00647745i
$404$		0			0
$405$	−0.685149	+	0.156381i	−0.0340453	+	0.00777062i
$406$		0			0
$407$	−30.8504	−	7.04141i	−1.52920	−	0.349030i
$408$		0			0
$409$	−1.91095	+	3.96814i	−0.0944906	+	0.196212i	−0.942857	−	0.333198i	$-0.891872\pi$
$409$	−1.91095	+	3.96814i	−0.0944906	+	0.196212i	0.848366	+	0.529410i	$0.177587\pi$
$410$		0			0
$411$	−8.50553			−0.419547
$412$		0			0
$413$	−12.3022	+	25.7955i	−0.605351	+	1.26932i
$414$		0			0
$415$	14.3311	+	29.7588i	0.703486	+	1.46080i
$416$		0			0
$417$	1.52620	−	6.68670i	0.0747381	−	0.327449i
$418$		0			0
$419$	29.6907	−	14.2983i	1.45049	−	0.698517i	0.467807	−	0.883831i	$-0.345044\pi$
$419$	29.6907	−	14.2983i	1.45049	−	0.698517i	0.982679	+	0.185313i	$0.0593300\pi$
$420$		0			0
$421$	4.00094	+	1.92675i	0.194994	+	0.0939042i	0.528833	−	0.848726i	$-0.322630\pi$
$421$	4.00094	+	1.92675i	0.194994	+	0.0939042i	−0.333839	+	0.942630i	$0.608344\pi$
$422$		0			0
$423$	3.13343			0.152353
$424$		0			0
$425$	−1.06325	−	0.847913i	−0.0515752	−	0.0411298i
$426$		0			0
$427$	−4.52350	+	20.1710i	−0.218907	+	0.976146i
$428$		0			0
$429$	16.1946	+	7.79891i	0.781882	+	0.376535i
$430$		0			0
$431$	18.9828	+	15.1383i	0.914370	+	0.729186i	0.962963	−	0.269633i	$-0.0869023\pi$
$431$	18.9828	+	15.1383i	0.914370	+	0.729186i	−0.0485931	+	0.998819i	$0.515474\pi$
$432$		0			0
$433$	−22.0615	+	17.5935i	−1.06021	+	0.845489i	−0.988392	−	0.151928i	$-0.951452\pi$
$433$	−22.0615	+	17.5935i	−1.06021	+	0.845489i	−0.0718186	+	0.997418i	$0.522880\pi$
$434$		0			0
$435$	16.4655	+	13.1308i	0.789461	+	0.629574i
$436$		0			0
$437$	13.0046	+	27.0043i	0.622093	+	1.29179i
$438$		0			0
$439$	3.25251	+	14.2502i	0.155234	+	0.680124i	0.991314	+	0.131516i	$0.0419846\pi$
$439$	3.25251	+	14.2502i	0.155234	+	0.680124i	−0.836080	+	0.548607i	$0.815158\pi$
$440$		0			0
$441$	−2.89431	−	12.2517i	−0.137824	−	0.583414i
$442$		0			0
$443$	−13.0221	+	2.97221i	−0.618699	+	0.141214i	−0.520371	−	0.853940i	$-0.674207\pi$
$443$	−13.0221	+	2.97221i	−0.618699	+	0.141214i	−0.0983278	+	0.995154i	$0.531349\pi$
$444$		0			0
$445$	14.7825	−	7.11886i	0.700756	−	0.337466i
$446$		0			0
$447$	0.670556	−	0.840850i	0.0317162	−	0.0397709i
$448$		0			0
$449$	0.984873	+	1.23499i	0.0464790	+	0.0582829i	0.804528	−	0.593915i	$-0.202419\pi$
$449$	0.984873	+	1.23499i	0.0464790	+	0.0582829i	−0.758049	+	0.652198i	$0.773847\pi$
$450$		0			0
$451$	14.7093	−	18.4448i	0.692632	−	0.868533i
$452$		0			0
$453$	−8.66693	+	17.9971i	−0.407208	+	0.845576i
$454$		0			0
$455$	10.8130	−	22.6729i	0.506919	−	1.06292i
$456$		0			0
$457$	6.17599	−	7.74444i	0.288901	−	0.362270i	−0.616109	−	0.787661i	$-0.711292\pi$
$457$	6.17599	−	7.74444i	0.288901	−	0.362270i	0.905010	+	0.425391i	$0.139863\pi$
$458$		0			0
$459$		−	5.10624i		−	0.238339i
$460$		0			0
$461$	7.26233	−	15.0804i	0.338240	−	0.702363i	−0.660588	−	0.750748i	$-0.729693\pi$
$461$	7.26233	−	15.0804i	0.338240	−	0.702363i	0.998829	+	0.0483849i	$0.0154074\pi$
$462$		0			0
$463$	−1.62730	−	3.37913i	−0.0756271	−	0.157041i	0.859727	−	0.510753i	$-0.170634\pi$
$463$	−1.62730	−	3.37913i	−0.0756271	−	0.157041i	−0.935354	+	0.353712i	$0.884919\pi$
$464$		0			0
$465$	−0.236742	−	0.0540347i	−0.0109786	−	0.00250580i
$466$		0			0
$467$	−7.48511	+	3.60464i	−0.346370	+	0.166803i	−0.598977	−	0.800766i	$-0.704426\pi$
$467$	−7.48511	+	3.60464i	−0.346370	+	0.166803i	0.252608	+	0.967569i	$0.418712\pi$
$468$		0			0
$469$	−8.62400	−	37.1345i	−0.398219	−	1.71471i
$470$		0			0
$471$		−	0.272414i		−	0.0125522i
$472$		0			0
$473$	18.5859	+	8.95047i	0.854578	+	0.411543i
$474$		0			0
$475$	−2.33156	+	10.2152i	−0.106979	+	0.468708i
$476$		0			0
$477$	1.67606	+	7.34328i	0.0767413	+	0.336226i
$478$		0			0
$479$	−0.243042	−	1.06484i	−0.0111049	−	0.0486537i	0.969072	−	0.246779i	$-0.0793720\pi$
$479$	−0.243042	−	1.06484i	−0.0111049	−	0.0486537i	−0.980177	+	0.198125i	$0.936515\pi$
$480$		0			0
$481$	47.1190	+	10.7546i	2.14844	+	0.490368i
$482$		0			0
$483$	−2.54307	+	11.3400i	−0.115714	+	0.515987i
$484$		0			0
$485$	9.34983	+	11.7243i	0.424554	+	0.532374i
$486$		0			0
$487$	−11.4378	+	9.12137i	−0.518298	+	0.413329i	−0.847391	−	0.530969i	$-0.821828\pi$
$487$	−11.4378	+	9.12137i	−0.518298	+	0.413329i	0.329094	+	0.944297i	$0.393257\pi$
$488$		0			0
$489$		−	8.93010i		−	0.403833i
$490$		0			0
$491$		−	17.0636i		−	0.770070i	−0.922902	−	0.385035i	$-0.874189\pi$
$491$		−	17.0636i		−	0.770070i	0.922902	−	0.385035i	$-0.125811\pi$
$492$		0			0
$493$	−7.68645	+	6.12974i	−0.346180	+	0.276070i
$494$		0			0
$495$	−6.97017	−	8.74032i	−0.313286	−	0.392848i
$496$		0			0
$497$	−15.2136	−	18.9295i	−0.682422	−	0.849104i
$498$		0			0
$499$	5.42952	+	1.23925i	0.243058	+	0.0554765i	0.342315	−	0.939585i	$-0.388789\pi$
$499$	5.42952	+	1.23925i	0.243058	+	0.0554765i	−0.0992561	+	0.995062i	$0.531646\pi$
$500$		0			0
$501$	−0.637408	−	2.79267i	−0.0284773	−	0.124767i
$502$		0			0
$503$	−2.14957	−	9.41790i	−0.0958448	−	0.419923i	0.904128	−	0.427261i	$-0.140521\pi$
$503$	−2.14957	−	9.41790i	−0.0958448	−	0.419923i	−0.999973	+	0.00733762i	$0.997664\pi$
$504$		0			0
$505$	1.52172	−	6.66708i	0.0677155	−	0.296681i
$506$		0			0
$507$	−11.8957	−	5.72865i	−0.528305	−	0.254418i
$508$		0			0
$509$		−	16.7274i		−	0.741428i	−0.928747	−	0.370714i	$-0.879113\pi$
$509$		−	16.7274i		−	0.741428i	0.928747	−	0.370714i	$-0.120887\pi$
$510$		0			0
$511$	−4.79956	+	0.0182016i	−0.212320	+	0.000805193i
$512$		0			0
$513$	−35.4458	+	17.0698i	−1.56497	+	0.753651i
$514$		0			0
$515$	−23.7823	−	5.42816i	−1.04797	−	0.239193i
$516$		0			0
$517$	−2.47701	−	5.14356i	−0.108939	−	0.226213i
$518$		0			0
$519$	7.63990	−	15.8644i	0.335355	−	0.696371i
$520$		0			0
$521$		−	16.6663i		−	0.730166i	−0.930975	−	0.365083i	$-0.881041\pi$
$521$		−	16.6663i		−	0.730166i	0.930975	−	0.365083i	$-0.118959\pi$
$522$		0			0
$523$	19.0641	−	23.9056i	0.833614	−	1.04532i	−0.164646	−	0.986353i	$-0.552648\pi$
$523$	19.0641	−	23.9056i	0.833614	−	1.04532i	0.998260	−	0.0589659i	$-0.0187803\pi$
$524$		0			0
$525$	−3.16676	+	2.54512i	−0.138209	+	0.111078i
$526$		0			0
$527$	0.0491843	−	0.102132i	0.00214250	−	0.00444895i
$528$		0			0
$529$	4.32845	−	5.42770i	0.188193	−	0.235987i
$530$		0			0
$531$	−12.1120	−	15.1880i	−0.525617	−	0.659103i
$532$		0			0
$533$	−22.4660	+	28.1715i	−0.973111	+	1.22024i
$534$		0			0
$535$	−24.9291	+	12.0052i	−1.07778	+	0.519030i
$536$		0			0
$537$	15.5546	−	3.55023i	0.671229	−	0.153204i
$538$		0			0
$539$	−17.8233	+	14.4361i	−0.767704	+	0.621807i
$540$		0			0
$541$	−7.30313	−	31.9971i	−0.313986	−	1.37566i	−0.847914	−	0.530133i	$-0.822142\pi$
$541$	−7.30313	−	31.9971i	−0.313986	−	1.37566i	0.533928	−	0.845530i	$-0.320715\pi$
$542$		0			0
$543$	−7.44549	−	15.4607i	−0.319517	−	0.663483i
$544$		0			0
$545$	−3.94525	−	3.14623i	−0.168996	−	0.134770i
$546$		0			0
$547$	5.25226	−	4.18854i	0.224570	−	0.179089i	−0.504741	−	0.863271i	$-0.668412\pi$
$547$	5.25226	−	4.18854i	0.224570	−	0.179089i	0.729311	+	0.684182i	$0.239841\pi$
$548$		0			0
$549$	−10.9860	−	8.76102i	−0.468870	−	0.373911i
$550$		0			0
$551$	68.2460	+	32.8655i	2.90738	+	1.40012i
$552$		0			0
$553$	3.30386	+	14.2263i	0.140494	+	0.604962i
$554$		0			0
$555$	15.7019	+	12.5219i	0.666511	+	0.531524i
$556$		0			0
$557$	−33.2712			−1.40974			−0.704872	−	0.709334i	$-0.748996\pi$
$557$	−33.2712			−1.40974			−0.704872	+	0.709334i	$0.748996\pi$
$558$		0			0
$559$	−28.3869	−	13.6704i	−1.20064	−	0.578196i
$560$		0			0
$561$	−3.14150	+	1.51287i	−0.132634	+	0.0638733i
$562$		0			0
$563$	7.70464	−	33.7562i	0.324712	−	1.42266i	−0.504350	−	0.863499i	$-0.668268\pi$
$563$	7.70464	−	33.7562i	0.324712	−	1.42266i	0.829062	−	0.559156i	$-0.188875\pi$
$564$		0			0
$565$	−9.83949	−	20.4319i	−0.413950	−	0.859577i
$566$		0			0
$567$	−0.956329	−	0.214464i	−0.0401621	−	0.00900662i
$568$		0			0
$569$	24.8098			1.04008			0.520041	−	0.854141i	$-0.325917\pi$
$569$	24.8098			1.04008			0.520041	+	0.854141i	$0.325917\pi$
$570$		0			0
$571$	5.70069	−	11.8376i	0.238566	−	0.495388i	−0.746969	−	0.664859i	$-0.768492\pi$
$571$	5.70069	−	11.8376i	0.238566	−	0.495388i	0.985535	+	0.169471i	$0.0542059\pi$
$572$		0			0
$573$	−2.53807	−	0.579297i	−0.106029	−	0.0242005i
$574$		0			0
$575$	−5.47280	+	1.24913i	−0.228232	+	0.0520924i
$576$		0			0
$577$	38.8052	−	8.85703i	1.61548	−	0.368723i	0.683136	−	0.730292i	$-0.260616\pi$
$577$	38.8052	−	8.85703i	1.61548	−	0.368723i	0.932346	+	0.361569i	$0.117759\pi$
$578$		0			0
$579$	−4.28964	+	18.7941i	−0.178271	+	0.781057i
$580$		0			0
$581$	0.174688	+	46.0631i	0.00724726	+	1.91102i
$582$		0			0
$583$	10.7291	−	8.55619i	0.444355	−	0.354361i
$584$		0			0
$585$	10.6458	+	13.3494i	0.440150	+	0.551931i
$586$		0			0
$587$	15.6864			0.647448			0.323724	−	0.946152i	$-0.395065\pi$
$587$	15.6864			0.647448			0.323724	+	0.946152i	$0.395065\pi$
$588$		0			0
$589$	−0.873388			−0.0359873
$590$		0			0
$591$	9.71332	+	12.1801i	0.399552	+	0.501023i
$592$		0			0
$593$	1.53749	−	1.22611i	0.0631372	−	0.0503502i	−0.591413	−	0.806369i	$-0.701430\pi$
$593$	1.53749	−	1.22611i	0.0631372	−	0.0503502i	0.654550	+	0.756019i	$0.272858\pi$
$594$		0			0
$595$	2.13084	+	4.38215i	0.0873561	+	0.179651i
$596$		0			0
$597$	0.0537255	−	0.235387i	0.00219884	−	0.00963374i
$598$		0			0
$599$	2.01937	−	0.460908i	0.0825092	−	0.0188322i	−0.181067	−	0.983471i	$-0.557955\pi$
$599$	2.01937	−	0.460908i	0.0825092	−	0.0188322i	0.263576	+	0.964639i	$0.415098\pi$
$600$		0			0
$601$	−13.5551	+	3.09386i	−0.552923	+	0.126201i	−0.489848	−	0.871808i	$-0.662948\pi$
$601$	−13.5551	+	3.09386i	−0.552923	+	0.126201i	−0.0630747	+	0.998009i	$0.520091\pi$
$602$		0			0
$603$	25.2638	+	5.76630i	1.02882	+	0.234822i
$604$		0			0
$605$	0.217184	−	0.450986i	0.00882977	−	0.0183352i
$606$		0			0
$607$	3.19621			0.129730			0.0648650	−	0.997894i	$-0.479338\pi$
$607$	3.19621			0.129730			0.0648650	+	0.997894i	$0.479338\pi$
$608$		0			0
$609$	12.8437	+	26.4134i	0.520452	+	1.07033i
$610$		0			0
$611$	3.78323	+	7.85595i	0.153053	+	0.317818i
$612$		0			0
$613$	−5.42970	+	23.7891i	−0.219303	+	0.960831i	0.738691	+	0.674044i	$0.235444\pi$
$613$	−5.42970	+	23.7891i	−0.219303	+	0.960831i	−0.957994	+	0.286787i	$0.907413\pi$
$614$		0			0
$615$	−13.4903	+	6.49661i	−0.543983	+	0.261968i
$616$		0			0
$617$	−16.8703	−	8.12429i	−0.679171	−	0.327072i	0.0622989	−	0.998058i	$-0.480157\pi$
$617$	−16.8703	−	8.12429i	−0.679171	−	0.327072i	−0.741470	+	0.670986i	$0.765871\pi$
$618$		0			0
$619$	−26.3760			−1.06014			−0.530071	−	0.847953i	$-0.677835\pi$
$619$	−26.3760			−1.06014			−0.530071	+	0.847953i	$0.677835\pi$
$620$		0			0
$621$	−16.4790	−	13.1415i	−0.661278	−	0.527351i
$622$		0			0
$623$	22.8815	−	0.0867746i	0.916726	−	0.00347655i
$624$		0			0
$625$	14.4455	+	6.95658i	0.577819	+	0.278263i
$626$		0			0
$627$	21.0037	+	16.7499i	0.838805	+	0.668925i
$628$		0			0
$629$	−7.33000	+	5.84548i	−0.292266	+	0.233075i
$630$		0			0
$631$	−27.8557	−	22.2142i	−1.10892	−	0.884333i	−0.114881	−	0.993379i	$-0.536649\pi$
$631$	−27.8557	−	22.2142i	−1.10892	−	0.884333i	−0.994037	+	0.109047i	$0.965220\pi$
$632$		0			0
$633$	−5.08029	−	10.5493i	−0.201923	−	0.419298i
$634$		0			0
$635$	−6.16891	−	27.0278i	−0.244806	−	1.07256i
$636$		0			0
$637$	27.2222	−	22.0488i	1.07858	−	0.873606i
$638$		0			0
$639$	16.0938	−	3.67331i	0.636661	−	0.145314i
$640$		0			0
$641$	−13.0578	+	6.28829i	−0.515751	+	0.248373i	−0.673607	−	0.739090i	$-0.735256\pi$
$641$	−13.0578	+	6.28829i	−0.515751	+	0.248373i	0.157856	+	0.987462i	$0.449542\pi$
$642$		0			0
$643$	−5.97018	+	7.48637i	−0.235441	+	0.295234i	−0.885490	−	0.464659i	$-0.846177\pi$
$643$	−5.97018	+	7.48637i	−0.235441	+	0.295234i	0.650049	+	0.759892i	$0.274748\pi$
$644$		0			0
$645$	−8.16307	−	10.2362i	−0.321421	−	0.403049i
$646$		0			0
$647$	−11.5541	+	14.4883i	−0.454237	+	0.569595i	−0.955233	−	0.295855i	$-0.904396\pi$
$647$	−11.5541	+	14.4883i	−0.454237	+	0.569595i	0.500996	+	0.865449i	$0.332967\pi$
$648$		0			0
$649$	−15.3566	+	31.8883i	−0.602798	+	1.25172i
$650$		0			0
$651$	−0.265567	−	0.210140i	−0.0104084	−	0.00823602i
$652$		0			0
$653$	−9.75049	+	12.2267i	−0.381566	+	0.478469i	−0.935113	−	0.354349i	$-0.884702\pi$
$653$	−9.75049	+	12.2267i	−0.381566	+	0.478469i	0.553547	+	0.832818i	$0.313274\pi$
$654$		0			0
$655$		−	18.0255i		−	0.704316i
$656$		0			0
$657$	1.41553	−	2.93938i	0.0552251	−	0.114676i
$658$		0			0
$659$	−14.9133	−	30.9678i	−0.580939	−	1.20633i	−0.959749	−	0.280859i	$-0.909381\pi$
$659$	−14.9133	−	30.9678i	−0.580939	−	1.20633i	0.378810	−	0.925475i	$-0.376333\pi$
$660$		0			0
$661$	−31.8001	−	7.25816i	−1.23688	−	0.282310i	−0.446420	−	0.894824i	$-0.647301\pi$
$661$	−31.8001	−	7.25816i	−1.23688	−	0.282310i	−0.790460	+	0.612514i	$0.790158\pi$
$662$		0			0
$663$	4.79813	−	2.31066i	0.186344	−	0.0897385i
$664$		0			0
$665$	23.2962	−	29.4409i	0.903388	−	1.14167i
$666$		0			0
$667$			40.5815i			1.57132i
$668$		0			0
$669$	−14.8797	−	7.16570i	−0.575283	−	0.277042i
$670$		0			0
$671$	−5.69678	+	24.9592i	−0.219922	+	0.963540i
$672$		0			0
$673$	−0.0497445	−	0.217945i	−0.00191751	−	0.00840117i	0.973960	−	0.226719i	$-0.0728000\pi$
$673$	−0.0497445	−	0.217945i	−0.00191751	−	0.00840117i	−0.975878	+	0.218318i	$0.929943\pi$
$674$		0			0
$675$	−1.63961	−	7.18361i	−0.0631087	−	0.276497i
$676$		0			0
$677$	−22.3759	−	5.10714i	−0.859974	−	0.196283i	−0.230278	−	0.973125i	$-0.573964\pi$
$677$	−22.3759	−	5.10714i	−0.859974	−	0.196283i	−0.629696	+	0.776841i	$0.716821\pi$
$678$		0			0
$679$	4.73095	+	20.3712i	0.181557	+	0.781776i
$680$		0			0
$681$	13.4626	+	16.8816i	0.515888	+	0.646903i
$682$		0			0
$683$	−1.20560	+	0.961434i	−0.0461310	+	0.0367883i	−0.646284	−	0.763097i	$-0.723678\pi$
$683$	−1.20560	+	0.961434i	−0.0461310	+	0.0367883i	0.600153	+	0.799885i	$0.295106\pi$
$684$		0			0
$685$			14.7205i			0.562443i
$686$		0			0
$687$			11.3706i			0.433815i
$688$		0			0
$689$	−16.3870	+	13.0682i	−0.624295	+	0.497858i
$690$		0			0
$691$	−26.7938	−	33.5984i	−1.01928	−	1.27814i	−0.960030	−	0.279899i	$-0.909699\pi$
$691$	−26.7938	−	33.5984i	−1.01928	−	1.27814i	−0.0592544	−	0.998243i	$-0.518872\pi$
$692$		0			0
$693$	−3.52686	−	15.1865i	−0.133974	−	0.576887i
$694$		0			0
$695$	−11.5727	−	2.64139i	−0.438977	−	0.100194i
$696$		0			0
$697$	−1.55537	−	6.81454i	−0.0589140	−	0.258119i
$698$		0			0
$699$	1.54645	+	6.77544i	0.0584921	+	0.256271i
$700$		0			0
$701$	9.22442	−	40.4148i	0.348401	−	1.52645i	−0.432408	−	0.901678i	$-0.642336\pi$
$701$	9.22442	−	40.4148i	0.348401	−	1.52645i	0.780810	−	0.624769i	$-0.214807\pi$
$702$		0			0
$703$	65.0811	+	31.3414i	2.45458	+	1.18206i
$704$		0			0
$705$			3.62331i			0.136462i
$706$		0			0
$707$	5.91792	−	7.47884i	0.222566	−	0.281271i
$708$		0			0
$709$	−40.1251	+	19.3232i	−1.50693	+	0.725700i	−0.991363	−	0.131149i	$-0.958133\pi$
$709$	−40.1251	+	19.3232i	−1.50693	+	0.725700i	−0.515568	+	0.856849i	$0.672419\pi$
$710$		0			0
$711$	−9.67857	−	2.20907i	−0.362975	−	0.0828467i
$712$		0			0
$713$	−0.203021	−	0.421578i	−0.00760321	−	0.0157882i
$714$		0			0
$715$	13.4976	−	28.0280i	0.504781	−	1.04819i
$716$		0			0
$717$		−	28.7529i		−	1.07380i
$718$		0			0
$719$	−23.1800	+	29.0668i	−0.864470	+	1.08401i	0.131228	+	0.991352i	$0.458108\pi$
$719$	−23.1800	+	29.0668i	−0.864470	+	1.08401i	−0.995698	+	0.0926584i	$0.970464\pi$
$720$		0			0
$721$	−26.6780	−	21.1100i	−0.993541	−	0.786177i
$722$		0			0
$723$	−11.7716	+	24.4439i	−0.437790	+	0.909080i
$724$		0			0
$725$	−8.84527	+	11.0916i	−0.328505	+	0.411933i
$726$		0			0
$727$	19.6789	+	24.6765i	0.729849	+	0.915201i	0.998850	−	0.0479385i	$-0.0152651\pi$
$727$	19.6789	+	24.6765i	0.729849	+	0.915201i	−0.269002	+	0.963140i	$0.586694\pi$
$728$		0			0
$729$	11.1999	−	14.0443i	0.414812	−	0.520157i
$730$		0			0
$731$	5.50661	−	2.65185i	0.203669	−	0.0980820i
$732$		0			0
$733$	−4.64726	+	1.06071i	−0.171651	+	0.0391781i	−0.307482	−	0.951554i	$-0.599486\pi$
$733$	−4.64726	+	1.06071i	−0.171651	+	0.0391781i	0.135832	+	0.990732i	$0.456629\pi$
$734$		0			0
$735$	14.1671	−	3.34680i	0.522562	−	0.123449i
$736$		0			0
$737$	−10.5058	−	46.0291i	−0.386987	−	1.69550i
$738$		0			0
$739$	7.42151	+	15.4109i	0.273005	+	0.566900i	0.991722	−	0.128402i	$-0.0409849\pi$
$739$	7.42151	+	15.4109i	0.273005	+	0.566900i	−0.718718	+	0.695302i	$0.755271\pi$
$740$		0			0
$741$	−32.0797	−	25.5827i	−1.17848	−	0.939804i
$742$		0			0
$743$	12.6352	−	10.0762i	0.463539	−	0.369660i	−0.363695	−	0.931518i	$-0.618485\pi$
$743$	12.6352	−	10.0762i	0.463539	−	0.369660i	0.827234	+	0.561858i	$0.189913\pi$
$744$		0			0
$745$	−1.45526	−	1.16053i	−0.0533167	−	0.0425186i
$746$		0			0
$747$	−28.2103	−	13.5854i	−1.03216	−	0.497062i
$748$		0			0
$749$	−38.5871	+	0.146336i	−1.40994	+	0.00534701i
$750$		0			0
$751$	−33.1457	−	26.4329i	−1.20951	−	0.964548i	−0.209593	−	0.977789i	$-0.567214\pi$
$751$	−33.1457	−	26.4329i	−1.20951	−	0.964548i	−0.999912	+	0.0132403i	$0.995785\pi$
$752$		0			0
$753$	−12.0278			−0.438318
$754$		0			0
$755$	31.1476	+	14.9999i	1.13358	+	0.545902i
$756$		0			0
$757$	16.0168	−	7.71329i	0.582141	−	0.280344i	−0.119547	−	0.992829i	$-0.538144\pi$
$757$	16.0168	−	7.71329i	0.582141	−	0.280344i	0.701688	+	0.712484i	$0.252430\pi$
$758$		0			0
$759$	−3.20268	+	14.0319i	−0.116250	+	0.509324i
$760$		0			0
$761$	−3.43954	−	7.14227i	−0.124683	−	0.258907i	0.829279	−	0.558835i	$-0.188752\pi$
$761$	−3.43954	−	7.14227i	−0.124683	−	0.258907i	−0.953962	+	0.299928i	$0.903037\pi$
$762$		0			0
$763$	−3.07743	−	6.32883i	−0.111410	−	0.229119i
$764$		0			0
$765$	−3.31220			−0.119753
$766$		0			0
$767$	23.4547	−	48.7041i	0.846899	−	1.75860i
$768$		0			0
$769$	36.6875	+	8.37367i	1.32298	+	0.301962i	0.824955	−	0.565198i	$-0.191200\pi$
$769$	36.6875	+	8.37367i	1.32298	+	0.301962i	0.498028	+	0.867161i	$0.334058\pi$
$770$		0			0
$771$	10.0010	−	2.28266i	0.360177	−	0.0822081i
$772$		0			0
$773$	−53.6365	+	12.2422i	−1.92917	+	0.440321i	−0.932259	+	0.361791i	$0.882166\pi$
$773$	−53.6365	+	12.2422i	−1.92917	+	0.440321i	−0.996912	+	0.0785302i	$0.974977\pi$
$774$		0			0
$775$	0.0363993	−	0.159476i	0.00130750	−	0.00572853i
$776$		0			0
$777$	12.2481	+	25.1885i	0.439396	+	0.903634i
$778$		0			0
$779$	−42.1048	+	33.5774i	−1.50856	+	1.20304i
$780$		0			0
$781$	−18.7521	−	23.5144i	−0.671002	−	0.841410i
$782$		0			0
$783$	−53.2674			−1.90362
$784$		0			0
$785$	−0.471468			−0.0168274
$786$		0			0
$787$	−7.25903	−	9.10254i	−0.258757	−	0.324471i	0.635435	−	0.772154i	$-0.280821\pi$
$787$	−7.25903	−	9.10254i	−0.258757	−	0.324471i	−0.894192	+	0.447683i	$0.852249\pi$
$788$		0			0
$789$	5.11538	−	4.07938i	0.182112	−	0.145230i
$790$		0			0
$791$	−0.119938	−	31.6261i	−0.00426449	−	1.12450i
$792$		0			0
$793$	8.70091	−	38.1212i	0.308978	−	1.35372i
$794$		0			0
$795$	−8.49132	+	1.93809i	−0.301156	+	0.0687369i
$796$		0			0
$797$	−10.8392	+	2.47398i	−0.383945	+	0.0876330i	−0.410137	−	0.912024i	$-0.634519\pi$
$797$	−10.8392	+	2.47398i	−0.383945	+	0.0876330i	0.0261918	+	0.999657i	$0.491662\pi$
$798$		0			0
$799$	−1.64903	−	0.376380i	−0.0583385	−	0.0133154i
$800$		0			0
$801$	−6.74842	+	14.0132i	−0.238444	+	0.495133i
$802$		0			0
$803$	−5.94401			−0.209760
$804$		0			0
$805$	19.6262	+	4.40130i	0.691731	+	0.155126i
$806$		0			0
$807$	−4.62749	−	9.60908i	−0.162895	−	0.338256i
$808$		0			0
$809$	9.24447	−	40.5027i	0.325018	−	1.42400i	−0.503481	−	0.864007i	$-0.667947\pi$
$809$	9.24447	−	40.5027i	0.325018	−	1.42400i	0.828499	−	0.559991i	$-0.189195\pi$
$810$		0			0
$811$	−23.3157	+	11.2282i	−0.818723	+	0.394276i	−0.795874	−	0.605463i	$-0.792988\pi$
$811$	−23.3157	+	11.2282i	−0.818723	+	0.394276i	−0.0228495	+	0.999739i	$0.507274\pi$
$812$		0			0
$813$	−12.4215	−	5.98190i	−0.435642	−	0.209794i
$814$		0			0
$815$	−15.4554			−0.541378
$816$		0			0
$817$	−36.8165	−	29.3602i	−1.28805	−	1.02718i
$818$		0			0
$819$	5.38671	+	23.1949i	0.188227	+	0.810495i
$820$		0			0
$821$	13.3831	+	6.44496i	0.467074	+	0.224931i	0.652591	−	0.757710i	$-0.273682\pi$
$821$	13.3831	+	6.44496i	0.467074	+	0.224931i	−0.185518	+	0.982641i	$0.559396\pi$
$822$		0			0
$823$	−13.5223	−	10.7836i	−0.471357	−	0.375894i	0.358809	−	0.933411i	$-0.383183\pi$
$823$	−13.5223	−	10.7836i	−0.471357	−	0.375894i	−0.830166	+	0.557517i	$0.811754\pi$
$824$		0			0
$825$	−3.93378	+	3.13708i	−0.136956	+	0.109219i
$826$		0			0
$827$	−26.0595	−	20.7818i	−0.906178	−	0.722653i	0.0550275	−	0.998485i	$-0.482475\pi$
$827$	−26.0595	−	20.7818i	−0.906178	−	0.722653i	−0.961206	+	0.275832i	$0.911047\pi$
$828$		0			0
$829$	4.22947	+	8.78258i	0.146895	+	0.305032i	0.961414	−	0.275106i	$-0.0887130\pi$
$829$	4.22947	+	8.78258i	0.146895	+	0.305032i	−0.814518	+	0.580138i	$0.802999\pi$
$830$		0			0
$831$	−3.40844	−	14.9334i	−0.118238	−	0.518033i
$832$		0			0
$833$	0.0515415	+	6.79535i	0.00178581	+	0.235445i
$834$		0			0
$835$	−4.83328	+	1.10316i	−0.167262	+	0.0381766i
$836$		0			0
$837$	0.553364	−	0.266486i	0.0191271	−	0.00921111i
$838$		0			0
$839$	−0.880313	+	1.10388i	−0.0303918	+	0.0381101i	−0.796795	−	0.604250i	$-0.793473\pi$
$839$	−0.880313	+	1.10388i	−0.0303918	+	0.0381101i	0.766403	+	0.642360i	$0.222044\pi$
$840$		0			0
$841$	45.8632	+	57.5106i	1.58149	+	1.98312i
$842$		0			0
$843$	4.09068	−	5.12956i	0.140891	−	0.176671i
$844$		0			0
$845$	−9.91459	+	20.5879i	−0.341072	+	0.708244i
$846$		0			0
$847$	0.544124	−	0.437311i	0.0186963	−	0.0150262i
$848$		0			0
$849$	−4.76741	+	5.97814i	−0.163617	+	0.205169i
$850$		0			0
$851$			38.6996i			1.32660i
$852$		0			0
$853$	13.5974	−	28.2353i	0.465566	−	0.966758i	−0.527539	−	0.849531i	$-0.676885\pi$
$853$	13.5974	−	28.2353i	0.465566	−	0.966758i	0.993105	−	0.117227i	$-0.0374005\pi$
$854$		0			0
$855$	11.0725	+	22.9922i	0.378670	+	0.786317i
$856$		0			0
$857$	14.9054	+	3.40205i	0.509158	+	0.116212i	0.469379	−	0.882997i	$-0.344478\pi$
$857$	14.9054	+	3.40205i	0.509158	+	0.116212i	0.0397783	+	0.999209i	$0.487335\pi$
$858$		0			0
$859$	−8.41659	+	4.05322i	−0.287170	+	0.138294i	−0.571924	−	0.820307i	$-0.693803\pi$
$859$	−8.41659	+	4.05322i	−0.287170	+	0.138294i	0.284753	+	0.958601i	$0.408088\pi$
$860$		0			0
$861$	−20.8814	+	0.0791898i	−0.711637	+	0.00269878i
$862$		0			0
$863$		−	54.2586i		−	1.84699i	−0.383616	−	0.923493i	$-0.625321\pi$
$863$		−	54.2586i		−	1.84699i	0.383616	−	0.923493i	$-0.374679\pi$
$864$		0			0
$865$	−27.4566	−	13.2224i	−0.933553	−	0.449575i
$866$		0			0
$867$	3.91676	−	17.1605i	0.133020	−	0.582800i
$868$		0			0
$869$	4.02479	+	17.6338i	0.136532	+	0.598184i
$870$		0			0
$871$	16.0460	+	70.3019i	0.543697	+	2.38209i
$872$		0			0
$873$	−13.8592	−	3.16327i	−0.469063	−	0.107061i
$874$		0			0
$875$	20.1267	+	25.0427i	0.680408	+	0.846598i
$876$		0			0
$877$	19.5753	+	24.5466i	0.661011	+	0.828881i	0.993453	−	0.114242i	$-0.0364441\pi$
$877$	19.5753	+	24.5466i	0.661011	+	0.828881i	−0.332442	+	0.943124i	$0.607873\pi$
$878$		0			0
$879$	28.4546	−	22.6918i	0.959751	−	0.765376i
$880$		0			0
$881$			9.85540i			0.332037i	0.986123	+	0.166018i	$0.0530911\pi$
$881$			9.85540i			0.332037i	−0.986123	+	0.166018i	$0.946909\pi$
$882$		0			0
$883$			9.11576i			0.306770i	0.988167	+	0.153385i	$0.0490174\pi$
$883$			9.11576i			0.306770i	−0.988167	+	0.153385i	$0.950983\pi$
$884$		0			0
$885$	17.5625	−	14.0056i	0.590356	−	0.470793i
$886$		0			0
$887$	6.32557	+	7.93202i	0.212392	+	0.266331i	0.876603	−	0.481214i	$-0.159804\pi$
$887$	6.32557	+	7.93202i	0.212392	+	0.266331i	−0.664211	+	0.747545i	$0.731232\pi$
$888$		0			0
$889$	8.46016	−	37.7253i	0.283745	−	1.26527i
$890$		0			0
$891$	−1.18334	−	0.270090i	−0.0396434	−	0.00904836i
$892$		0			0
$893$	2.89989	+	12.7052i	0.0970411	+	0.425165i
$894$		0			0
$895$	−6.14439	−	26.9203i	−0.205384	−	0.899847i
$896$		0			0
$897$	4.89157	−	21.4314i	0.163325	−	0.715573i
$898$		0			0
$899$	−1.06542	−	0.513081i	−0.0355339	−	0.0171122i
$900$		0			0
$901$		−	4.06587i		−	0.135454i
$902$		0			0
$903$	−4.13046	−	17.7856i	−0.137453	−	0.591866i
$904$		0			0
$905$	−26.7579	+	12.8859i	−0.889464	+	0.428343i
$906$		0			0
$907$	32.0451	+	7.31407i	1.06404	+	0.242860i	0.718487	−	0.695540i	$-0.244835\pi$
$907$	32.0451	+	7.31407i	1.06404	+	0.242860i	0.345551	+	0.938400i	$0.387692\pi$
$908$		0			0
$909$	2.81273	+	5.84069i	0.0932923	+	0.193724i
$910$		0			0
$911$	−23.2535	+	48.2863i	−0.770422	+	1.59980i	0.0294052	+	0.999568i	$0.490639\pi$
$911$	−23.2535	+	48.2863i	−0.770422	+	1.59980i	−0.799827	+	0.600230i	$0.795076\pi$
$912$		0			0
$913$			57.0468i			1.88797i
$914$		0			0
$915$	10.1307	−	12.7035i	0.334911	−	0.419965i
$916$		0			0
$917$	10.8212	−	22.6901i	0.357347	−	0.749294i
$918$		0			0
$919$	10.6042	−	22.0197i	0.349799	−	0.726364i	−0.649627	−	0.760253i	$-0.725075\pi$
$919$	10.6042	−	22.0197i	0.349799	−	0.726364i	0.999426	+	0.0338887i	$0.0107892\pi$
$920$		0			0
$921$	3.24647	−	4.07094i	0.106975	−	0.134142i
$922$		0			0
$923$	28.6407	+	35.9144i	0.942722	+	1.18214i
$924$		0			0
$925$	−8.43508	+	10.5773i	−0.277344	+	0.347778i
$926$		0			0
$927$	20.8345	−	10.0334i	0.684295	−	0.329539i
$928$		0			0
$929$	−17.4510	+	3.98307i	−0.572548	+	0.130680i	−0.498986	−	0.866610i	$-0.666294\pi$
$929$	−17.4510	+	3.98307i	−0.572548	+	0.130680i	−0.0735624	+	0.997291i	$0.523437\pi$
$930$		0			0
$931$	46.9988	−	23.0742i	1.54032	−	0.756226i
$932$		0			0
$933$	2.51752	+	11.0300i	0.0824198	+	0.361105i
$934$		0			0
$935$	2.61832	+	5.43701i	0.0856283	+	0.177809i
$936$		0			0
$937$	−30.4811	−	24.3079i	−0.995774	−	0.794104i	−0.0171697	−	0.999853i	$-0.505466\pi$
$937$	−30.4811	−	24.3079i	−0.995774	−	0.794104i	−0.978605	+	0.205749i	$0.934037\pi$
$938$		0			0
$939$	1.02797	−	0.819778i	0.0335465	−	0.0267524i
$940$		0			0
$941$	28.8207	+	22.9838i	0.939529	+	0.749249i	0.968158	−	0.250341i	$-0.0805427\pi$
$941$	28.8207	+	22.9838i	0.939529	+	0.749249i	−0.0286291	+	0.999590i	$0.509114\pi$
$942$		0			0
$943$	−25.9949	−	12.5185i	−0.846512	−	0.407659i
$944$		0			0
$945$	−5.77716	+	25.7613i	−0.187931	+	0.838016i
$946$		0			0
$947$	−45.6778	−	36.4268i	−1.48433	−	1.18371i	−0.938240	−	0.345986i	$-0.887544\pi$
$947$	−45.6778	−	36.4268i	−1.48433	−	1.18371i	−0.546090	−	0.837727i	$-0.683884\pi$
$948$		0			0
$949$	9.07851			0.294701
$950$		0			0
$951$	9.21872	+	4.43950i	0.298938	+	0.143961i
$952$		0			0
$953$	−4.00257	+	1.92753i	−0.129656	+	0.0624390i	−0.497587	−	0.867414i	$-0.665780\pi$
$953$	−4.00257	+	1.92753i	−0.129656	+	0.0624390i	0.367931	+	0.929853i	$0.380066\pi$
$954$		0			0
$955$	−1.00259	+	4.39264i	−0.0324431	+	0.142143i
$956$		0			0
$957$	15.7820	+	32.7716i	0.510158	+	1.05935i
$958$		0			0
$959$	−8.83711	+	18.5299i	−0.285365	+	0.598361i
$960$		0			0
$961$	−30.9864			−0.999560
$962$		0			0
$963$	11.3805	−	23.6318i	0.366731	−	0.761525i
$964$		0			0
$965$	32.5271	+	7.42409i	1.04708	+	0.238990i
$966$		0			0
$967$	4.56111	−	1.04104i	0.146675	−	0.0334777i	−0.148553	−	0.988904i	$-0.547461\pi$
$967$	4.56111	−	1.04104i	0.146675	−	0.0334777i	0.295228	+	0.955427i	$0.404604\pi$
$968$		0			0
$969$	7.75991	−	1.77115i	0.249284	−	0.0568975i
$970$		0			0
$971$	3.10897	−	13.6213i	0.0997717	−	0.437128i	−0.900227	−	0.435421i	$-0.856599\pi$
$971$	3.10897	−	13.6213i	0.0997717	−	0.437128i	0.999999	−	0.00170718i	$-0.000543411\pi$
$972$		0			0
$973$	−12.9817	−	10.2723i	−0.416176	−	0.329315i
$974$		0			0
$975$	6.00820	−	4.79138i	0.192417	−	0.153447i
$976$		0			0
$977$	14.3042	+	17.9369i	0.457631	+	0.573852i	0.956094	−	0.293060i	$-0.0946734\pi$
$977$	14.3042	+	17.9369i	0.457631	+	0.573852i	−0.498463	+	0.866911i	$0.666102\pi$
$978$		0			0
$979$	28.3375			0.905671
$980$		0			0
$981$	4.78357			0.152728
$982$		0			0
$983$	16.5592	+	20.7646i	0.528157	+	0.662288i	0.972319	−	0.233659i	$-0.0750698\pi$
$983$	16.5592	+	20.7646i	0.528157	+	0.662288i	−0.444162	+	0.895947i	$0.646498\pi$
$984$		0			0
$985$	21.0802	−	16.8109i	0.671670	−	0.535639i
$986$		0			0
$987$	−2.17516	+	4.56094i	−0.0692362	+	0.145176i
$988$		0			0
$989$	5.61385	−	24.5959i	0.178510	−	0.782104i
$990$		0			0
$991$	1.60811	−	0.367040i	0.0510832	−	0.0116594i	−0.196903	−	0.980423i	$-0.563088\pi$
$991$	1.60811	−	0.367040i	0.0510832	−	0.0116594i	0.247986	+	0.968764i	$0.420231\pi$
$992$		0			0
$993$	−27.3801	+	6.24933i	−0.868881	+	0.198316i
$994$		0			0
$995$	−0.407384	−	0.0929829i	−0.0129150	−	0.00294775i
$996$		0			0
$997$	−6.40161	+	13.2931i	−0.202741	+	0.420996i	−0.977404	−	0.211378i	$-0.932205\pi$
$997$	−6.40161	+	13.2931i	−0.202741	+	0.420996i	0.774664	+	0.632374i	$0.217919\pi$
$998$		0			0
$999$	−50.7971			−1.60715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.a.111.3	✓	48
4.3	odd	2	inner	784.2.bb.a.111.6	yes	48
49.34	odd	14	inner	784.2.bb.a.671.6	yes	48
196.83	even	14	inner	784.2.bb.a.671.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.a.111.3	✓	48	1.1	even	1	trivial
784.2.bb.a.111.6	yes	48	4.3	odd	2	inner
784.2.bb.a.671.3	yes	48	196.83	even	14	inner
784.2.bb.a.671.6	yes	48	49.34	odd	14	inner

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.683449 - 0.857018i) q^{3} +(-1.48324 + 1.18285i) q^{5} +(-2.57717 + 0.598513i) q^{7} +(0.400186 - 1.75333i) q^{9} +O(q^{10})\)	\(q+(-0.683449 - 0.857018i) q^{3} +(-1.48324 + 1.18285i) q^{5} +(-2.57717 + 0.598513i) q^{7} +(0.400186 - 1.75333i) q^{9} +(-3.19446 + 0.729114i) q^{11} +(4.87901 - 1.11360i) q^{13} +(2.02744 + 0.462750i) q^{15} +(-0.421211 + 0.874654i) q^{17} +7.47964 q^{19} +(2.27430 + 1.79962i) q^{21} +(1.73866 + 3.61037i) q^{23} +(-0.311721 + 1.36574i) q^{25} +(-4.73898 + 2.28217i) q^{27} +(9.12423 + 4.39400i) q^{29} -0.116769 q^{31} +(2.80811 + 2.23939i) q^{33} +(3.11461 - 3.93613i) q^{35} +(8.70110 + 4.19023i) q^{37} +(-4.28893 - 3.42031i) q^{39} +(-5.62925 + 4.48918i) q^{41} +(-4.92223 - 3.92534i) q^{43} +(1.48035 + 3.07397i) q^{45} +(0.387704 + 1.69864i) q^{47} +(6.28356 - 3.08493i) q^{49} +(1.03747 - 0.236796i) q^{51} +(-3.77343 + 1.81719i) q^{53} +(3.87572 - 4.86000i) q^{55} +(-5.11195 - 6.41019i) q^{57} +(6.73482 - 8.44520i) q^{59} +(3.39006 - 7.03954i) q^{61} +(0.0180445 + 4.75813i) q^{63} +(-5.91954 + 7.42287i) q^{65} +14.4091i q^{67} +(1.90586 - 3.95757i) q^{69} +(3.98262 + 8.27000i) q^{71} +(1.76859 + 0.403670i) q^{73} +(1.38351 - 0.666263i) q^{75} +(7.79626 - 3.79097i) q^{77} -5.52012i q^{79} +(0.333751 + 0.160726i) q^{81} +(3.87416 - 16.9738i) q^{83} +(-0.409823 - 1.79555i) q^{85} +(-2.47021 - 10.8227i) q^{87} +(-8.43160 - 1.92446i) q^{89} +(-11.9075 + 5.79009i) q^{91} +(0.0798054 + 0.100073i) q^{93} +(-11.0941 + 8.84727i) q^{95} -7.90451i q^{97} +5.89271i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 14 q^{17} + 12 q^{25} + 28 q^{29} + 42 q^{37} + 28 q^{41} + 56 q^{49} - 38 q^{53} + 42 q^{57} + 84 q^{61} + 8 q^{65} + 56 q^{69} - 42 q^{73} - 42 q^{77} - 44 q^{81} - 12 q^{85} - 28 q^{89} + 98 q^{93}+O(q^{100}) \) 48 * q - 4 * q^9 + 14 * q^17 + 12 * q^25 + 28 * q^29 + 42 * q^37 + 28 * q^41 + 56 * q^49 - 38 * q^53 + 42 * q^57 + 84 * q^61 + 8 * q^65 + 56 * q^69 - 42 * q^73 - 42 * q^77 - 44 * q^81 - 12 * q^85 - 28 * q^89 + 98 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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