LMFDB - Embedded newform 936.2.dg.f.829.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.16
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.f.901.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.132250 + 1.40802i) q^{2} +(-1.96502 + 0.372419i) q^{4} -2.34484 q^{5} +(3.69507 + 2.13335i) q^{7} +(-0.784245 - 2.71753i) q^{8} +(-0.310104 - 3.30158i) q^{10} +(1.33516 + 2.31256i) q^{11} +(2.96097 + 2.05735i) q^{13} +(-2.51512 + 5.48486i) q^{14} +(3.72261 - 1.46362i) q^{16} +(2.86144 - 4.95615i) q^{17} +(-3.67163 + 6.35946i) q^{19} +(4.60766 - 0.873264i) q^{20} +(-3.07955 + 2.18576i) q^{22} +(-1.42407 - 2.46656i) q^{23} +0.498285 q^{25} +(-2.50519 + 4.44117i) q^{26} +(-8.05539 - 2.81596i) q^{28} +(-4.01604 + 2.31866i) q^{29} +6.91551i q^{31} +(2.55312 + 5.04793i) q^{32} +(7.35677 + 3.37350i) q^{34} +(-8.66436 - 5.00237i) q^{35} +(-0.806558 - 1.39700i) q^{37} +(-9.43979 - 4.32869i) q^{38} +(1.83893 + 6.37217i) q^{40} +(-5.52067 + 3.18736i) q^{41} +(-3.98283 - 2.29949i) q^{43} +(-3.48486 - 4.04699i) q^{44} +(3.28462 - 2.33131i) q^{46} +4.83325i q^{47} +(5.60238 + 9.70360i) q^{49} +(0.0658980 + 0.701593i) q^{50} +(-6.58455 - 2.94001i) q^{52} +2.67224i q^{53} +(-3.13074 - 5.42260i) q^{55} +(2.89960 - 11.7145i) q^{56} +(-3.79583 - 5.34801i) q^{58} +(-3.87932 + 6.71918i) q^{59} +(1.83248 + 1.05798i) q^{61} +(-9.73715 + 0.914574i) q^{62} +(-6.76992 + 4.26242i) q^{64} +(-6.94300 - 4.82416i) q^{65} +(-4.32233 - 7.48649i) q^{67} +(-3.77701 + 10.8046i) q^{68} +(5.89756 - 12.8611i) q^{70} +(11.6191 + 6.70831i) q^{71} -10.5359i q^{73} +(1.86033 - 1.32040i) q^{74} +(4.84645 - 13.8638i) q^{76} +11.3935i q^{77} +1.92081 q^{79} +(-8.72893 + 3.43196i) q^{80} +(-5.21796 - 7.35166i) q^{82} +2.73834 q^{83} +(-6.70962 + 11.6214i) q^{85} +(2.71099 - 5.91199i) q^{86} +(5.23736 - 5.44195i) q^{88} +(-15.0637 + 8.69704i) q^{89} +(6.55193 + 13.9188i) q^{91} +(3.71692 + 4.31649i) q^{92} +(-6.80530 + 0.639196i) q^{94} +(8.60940 - 14.9119i) q^{95} +(4.06104 + 2.34464i) q^{97} +(-12.9219 + 9.17153i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) $ 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.132250	+	1.40802i	0.0935146	+	0.995618i
$2$	0.132250	+	1.40802i	0.0935146	+	0.995618i
$3$		0			0
$3$		0			0
$4$	−1.96502	+	0.372419i	−0.982510	+	0.186210i
$5$	−2.34484			−1.04865			−0.524323	−	0.851520i	$-0.675681\pi$
$5$	−2.34484			−1.04865			−0.524323	+	0.851520i	$0.675681\pi$
$6$		0			0
$7$	3.69507	+	2.13335i	1.39661	+	0.806331i	0.994035	−	0.109058i	$-0.0347834\pi$
$7$	3.69507	+	2.13335i	1.39661	+	0.806331i	0.402571	+	0.915389i	$0.368117\pi$
$8$	−0.784245	−	2.71753i	−0.277273	−	0.960791i
$9$		0			0
$10$	−0.310104	−	3.30158i	−0.0980636	−	1.04405i
$11$	1.33516	+	2.31256i	0.402566	+	0.697264i	0.994035	−	0.109063i	$-0.0347852\pi$
$11$	1.33516	+	2.31256i	0.402566	+	0.697264i	−0.591469	+	0.806328i	$0.701452\pi$
$12$		0			0
$13$	2.96097	+	2.05735i	0.821224	+	0.570606i
$13$	2.96097	+	2.05735i	0.821224	+	0.570606i
$14$	−2.51512	+	5.48486i	−0.672195	+	1.46589i
$15$		0			0
$16$	3.72261	−	1.46362i	0.930652	−	0.365906i
$17$	2.86144	−	4.95615i	0.694000	−	1.20204i	−0.276516	−	0.961009i	$-0.589180\pi$
$17$	2.86144	−	4.95615i	0.694000	−	1.20204i	0.970517	−	0.241035i	$-0.0774868\pi$
$18$		0			0
$19$	−3.67163	+	6.35946i	−0.842331	+	1.45896i	0.0455885	+	0.998960i	$0.485484\pi$
$19$	−3.67163	+	6.35946i	−0.842331	+	1.45896i	−0.887919	+	0.459999i	$0.847850\pi$
$20$	4.60766	−	0.873264i	1.03030	−	0.195268i
$21$		0			0
$22$	−3.07955	+	2.18576i	−0.656563	+	0.466006i
$23$	−1.42407	−	2.46656i	−0.296939	−	0.514313i	0.678495	−	0.734605i	$-0.262632\pi$
$23$	−1.42407	−	2.46656i	−0.296939	−	0.514313i	−0.975434	+	0.220292i	$0.929299\pi$
$24$		0			0
$25$	0.498285			0.0996569
$26$	−2.50519	+	4.44117i	−0.491309	+	0.870985i
$27$		0			0
$28$	−8.05539	−	2.81596i	−1.52233	−	0.532167i
$29$	−4.01604	+	2.31866i	−0.745760	+	0.430565i	−0.824160	−	0.566357i	$-0.808352\pi$
$29$	−4.01604	+	2.31866i	−0.745760	+	0.430565i	0.0783999	+	0.996922i	$0.475019\pi$
$30$		0			0
$31$			6.91551i			1.24206i	0.783786	+	0.621031i	$0.213286\pi$
$31$			6.91551i			1.24206i	−0.783786	+	0.621031i	$0.786714\pi$
$32$	2.55312	+	5.04793i	0.451332	+	0.892356i
$33$		0			0
$34$	7.35677	+	3.37350i	1.26168	+	0.578551i
$35$	−8.66436	−	5.00237i	−1.46454	−	0.845555i
$36$		0			0
$37$	−0.806558	−	1.39700i	−0.132597	−	0.229665i	0.792080	−	0.610418i	$-0.208998\pi$
$37$	−0.806558	−	1.39700i	−0.132597	−	0.229665i	−0.924677	+	0.380752i	$0.875665\pi$
$38$	−9.43979	−	4.32869i	−1.53134	−	0.702206i
$39$		0			0
$40$	1.83893	+	6.37217i	0.290761	+	1.00753i
$41$	−5.52067	+	3.18736i	−0.862184	+	0.497782i	−0.864743	−	0.502215i	$-0.832519\pi$
$41$	−5.52067	+	3.18736i	−0.862184	+	0.497782i	0.00255936	+	0.999997i	$0.499185\pi$
$42$		0			0
$43$	−3.98283	−	2.29949i	−0.607375	−	0.350668i	0.164562	−	0.986367i	$-0.447379\pi$
$43$	−3.98283	−	2.29949i	−0.607375	−	0.350668i	−0.771938	+	0.635698i	$0.780712\pi$
$44$	−3.48486	−	4.04699i	−0.525362	−	0.610107i
$45$		0			0
$46$	3.28462	−	2.33131i	0.484291	−	0.343734i
$47$			4.83325i			0.705003i	0.935811	+	0.352501i	$0.114669\pi$
$47$			4.83325i			0.705003i	−0.935811	+	0.352501i	$0.885331\pi$
$48$		0			0
$49$	5.60238	+	9.70360i	0.800339	+	1.38623i
$50$	0.0658980	+	0.701593i	0.00931938	+	0.0992202i
$51$		0			0
$52$	−6.58455	−	2.94001i	−0.913113	−	0.407706i
$53$			2.67224i			0.367060i	0.983014	+	0.183530i	$0.0587524\pi$
$53$			2.67224i			0.367060i	−0.983014	+	0.183530i	$0.941248\pi$
$54$		0			0
$55$	−3.13074	−	5.42260i	−0.422149	−	0.731183i
$56$	2.89960	−	11.7145i	0.387475	−	1.56542i
$57$		0			0
$58$	−3.79583	−	5.34801i	−0.498417	−	0.702228i
$59$	−3.87932	+	6.71918i	−0.505045	+	0.874763i	0.494938	+	0.868928i	$0.335191\pi$
$59$	−3.87932	+	6.71918i	−0.505045	+	0.874763i	−0.999983	+	0.00583488i	$0.998143\pi$
$60$		0			0
$61$	1.83248	+	1.05798i	0.234625	+	0.135461i	0.612704	−	0.790312i	$-0.290082\pi$
$61$	1.83248	+	1.05798i	0.234625	+	0.135461i	−0.378079	+	0.925773i	$0.623415\pi$
$62$	−9.73715	+	0.914574i	−1.23662	+	0.116151i
$63$		0			0
$64$	−6.76992	+	4.26242i	−0.846240	+	0.532802i
$65$	−6.94300	−	4.82416i	−0.861173	−	0.598363i
$66$		0			0
$67$	−4.32233	−	7.48649i	−0.528057	−	0.914621i	−0.999465	−	0.0327058i	$-0.989588\pi$
$67$	−4.32233	−	7.48649i	−0.528057	−	0.914621i	0.471408	−	0.881915i	$-0.343746\pi$
$68$	−3.77701	+	10.8046i	−0.458030	+	1.31025i
$69$		0			0
$70$	5.89756	−	12.8611i	0.704894	−	1.53720i
$71$	11.6191	+	6.70831i	1.37894	+	0.796130i	0.992032	−	0.125988i	$-0.0402102\pi$
$71$	11.6191	+	6.70831i	1.37894	+	0.796130i	0.386907	+	0.922119i	$0.373544\pi$
$72$		0			0
$73$		−	10.5359i		−	1.23314i	−0.787301	−	0.616569i	$-0.788522\pi$
$73$		−	10.5359i		−	1.23314i	0.787301	−	0.616569i	$-0.211478\pi$
$74$	1.86033	−	1.32040i	0.216259	−	0.153493i
$75$		0			0
$76$	4.84645	−	13.8638i	0.555926	−	1.59029i
$77$			11.3935i			1.29840i
$78$		0			0
$79$	1.92081			0.216109			0.108054	−	0.994145i	$-0.465538\pi$
$79$	1.92081			0.216109			0.108054	+	0.994145i	$0.465538\pi$
$80$	−8.72893	+	3.43196i	−0.975924	+	0.383705i
$81$		0			0
$82$	−5.21796	−	7.35166i	−0.576227	−	0.811855i
$83$	2.73834			0.300572			0.150286	−	0.988643i	$-0.451981\pi$
$83$	2.73834			0.300572			0.150286	+	0.988643i	$0.451981\pi$
$84$		0			0
$85$	−6.70962	+	11.6214i	−0.727760	+	1.26052i
$86$	2.71099	−	5.91199i	0.292333	−	0.637506i
$87$		0			0
$88$	5.23736	−	5.44195i	0.558305	−	0.580114i
$89$	−15.0637	+	8.69704i	−1.59675	+	0.921884i	−0.604643	+	0.796497i	$0.706684\pi$
$89$	−15.0637	+	8.69704i	−1.59675	+	0.921884i	−0.992108	+	0.125388i	$0.959983\pi$
$90$		0			0
$91$	6.55193	+	13.9188i	0.686829	+	1.45909i
$92$	3.71692	+	4.31649i	0.387516	+	0.450025i
$93$		0			0
$94$	−6.80530	+	0.639196i	−0.701913	+	0.0659280i
$95$	8.60940	−	14.9119i	0.883306	−	1.52993i
$96$		0			0
$97$	4.06104	+	2.34464i	0.412336	+	0.238062i	0.691793	−	0.722096i	$-0.256821\pi$
$97$	4.06104	+	2.34464i	0.412336	+	0.238062i	−0.279457	+	0.960158i	$0.590154\pi$
$98$	−12.9219	+	9.17153i	−1.30531	+	0.926465i
$99$		0			0
$100$	−0.979139	+	0.185571i	−0.0979139	+	0.0185571i
$101$	9.77593	−	5.64414i	0.972741	−	0.561612i	0.0726704	−	0.997356i	$-0.476848\pi$
$101$	9.77593	−	5.64414i	0.972741	−	0.561612i	0.900071	+	0.435744i	$0.143515\pi$
$102$		0			0
$103$	19.3944			1.91099			0.955495	−	0.295007i	$-0.0953219\pi$
$103$	19.3944			1.91099			0.955495	+	0.295007i	$0.0953219\pi$
$104$	3.26878	−	9.65997i	0.320530	−	0.947238i
$105$		0			0
$106$	−3.76255	+	0.353402i	−0.365451	+	0.0343255i
$107$	11.9910	−	6.92299i	1.15921	−	0.669271i	0.208096	−	0.978108i	$-0.433273\pi$
$107$	11.9910	−	6.92299i	1.15921	−	0.669271i	0.951115	+	0.308838i	$0.0999400\pi$
$108$		0			0
$109$	6.87021			0.658047			0.329023	−	0.944322i	$-0.393280\pi$
$109$	6.87021			0.658047			0.329023	+	0.944322i	$0.393280\pi$
$110$	7.22107	−	5.12527i	0.688502	−	0.488675i
$111$		0			0
$112$	16.8777	+	2.53344i	1.59480	+	0.239387i
$113$	−9.79113	+	16.9587i	−0.921072	+	1.59534i	−0.123313	+	0.992368i	$0.539352\pi$
$113$	−9.79113	+	16.9587i	−0.921072	+	1.59534i	−0.797759	+	0.602977i	$0.793981\pi$
$114$		0			0
$115$	3.33922	+	5.78369i	0.311384	+	0.539332i
$116$	7.02809	−	6.05187i	0.652541	−	0.561902i
$117$		0			0
$118$	−9.97376	−	4.57354i	−0.918159	−	0.421028i
$119$	21.1464	−	12.2089i	1.93849	−	1.11919i
$120$		0			0
$121$	1.93470	−	3.35100i	0.175882	−	0.304636i
$122$	−1.24731	+	2.72008i	−0.112927	+	0.246265i
$123$		0			0
$124$	−2.57547	−	13.5891i	−0.231284	−	1.22034i
$125$	10.5558			0.944141
$126$		0			0
$127$	−1.64966	−	2.85730i	−0.146384	−	0.253544i	0.783505	−	0.621386i	$-0.213430\pi$
$127$	−1.64966	−	2.85730i	−0.146384	−	0.253544i	−0.929888	+	0.367842i	$0.880097\pi$
$128$	−6.89687	−	8.96845i	−0.609603	−	0.792707i
$129$		0			0
$130$	5.87429	−	10.4138i	0.515209	−	0.913355i
$131$		−	11.9694i		−	1.04577i	−0.852403	−	0.522885i	$-0.824856\pi$
$131$		−	11.9694i		−	1.04577i	0.852403	−	0.522885i	$-0.175144\pi$
$132$		0			0
$133$	−27.1339	+	15.6658i	−2.35281	+	1.35839i
$134$	9.96948	−	7.07600i	0.861232	−	0.611273i
$135$		0			0
$136$	−15.7126	−	3.88919i	−1.34734	−	0.333496i
$137$	−7.47619	−	4.31638i	−0.638734	−	0.368773i	0.145393	−	0.989374i	$-0.453555\pi$
$137$	−7.47619	−	4.31638i	−0.638734	−	0.368773i	−0.784127	+	0.620601i	$0.786889\pi$
$138$		0			0
$139$	0.164241	+	0.0948244i	0.0139307	+	0.00804290i	0.506949	−	0.861976i	$-0.330773\pi$
$139$	0.164241	+	0.0948244i	0.0139307	+	0.00804290i	−0.493018	+	0.870019i	$0.664107\pi$
$140$	18.8886	+	6.60299i	1.59638	+	0.558054i
$141$		0			0
$142$	−7.90879	+	17.2471i	−0.663691	+	1.44735i
$143$	−0.804390	+	9.59431i	−0.0672665	+	0.802316i
$144$		0			0
$145$	9.41698	−	5.43690i	0.782038	−	0.451510i
$146$	14.8348	−	1.39337i	1.22773	−	0.115316i
$147$		0			0
$148$	2.10517	+	2.44475i	0.173044	+	0.200958i
$149$	−8.56775	+	14.8398i	−0.701897	+	1.21572i	0.265902	+	0.964000i	$0.414330\pi$
$149$	−8.56775	+	14.8398i	−0.701897	+	1.21572i	−0.967800	+	0.251722i	$0.919003\pi$
$150$		0			0
$151$		−	3.17400i		−	0.258297i	−0.991625	−	0.129148i	$-0.958776\pi$
$151$		−	3.17400i		−	0.258297i	0.991625	−	0.129148i	$-0.0412243\pi$
$152$	20.1615	+	4.99039i	1.63531	+	0.404774i
$153$		0			0
$154$	−16.0422	+	1.50678i	−1.29271	+	0.121420i
$155$		−	16.2158i		−	1.30248i
$156$		0			0
$157$		−	17.7702i		−	1.41822i	−0.705099	−	0.709109i	$-0.749097\pi$
$157$		−	17.7702i		−	1.41822i	0.705099	−	0.709109i	$-0.250903\pi$
$158$	0.254027	+	2.70454i	0.0202093	+	0.215161i
$159$		0			0
$160$	−5.98666	−	11.8366i	−0.473287	−	0.935765i
$161$		−	12.1522i		−	0.957724i
$162$		0			0
$163$	0.0275364	−	0.0476944i	0.00215681	−	0.00373571i	−0.864945	−	0.501867i	$-0.832647\pi$
$163$	0.0275364	−	0.0476944i	0.00215681	−	0.00373571i	0.867102	+	0.498131i	$0.165980\pi$
$164$	9.66119	−	8.31923i	0.754412	−	0.649623i
$165$		0			0
$166$	0.362145	+	3.85563i	0.0281079	+	0.299255i
$167$	11.6579	−	6.73072i	0.902119	−	0.520839i	0.0242321	−	0.999706i	$-0.492286\pi$
$167$	11.6579	−	6.73072i	0.902119	−	0.520839i	0.877887	+	0.478868i	$0.158953\pi$
$168$		0			0
$169$	4.53463	+	12.1835i	0.348818	+	0.937191i
$170$	−17.2505	−	7.91033i	−1.32305	−	0.606694i
$171$		0			0
$172$	8.68271	+	3.03526i	0.662050	+	0.231436i
$173$	−13.8424	−	7.99194i	−1.05242	−	0.607616i	−0.129095	−	0.991632i	$-0.541207\pi$
$173$	−13.8424	−	7.99194i	−1.05242	−	0.607616i	−0.923326	+	0.384016i	$0.874541\pi$
$174$		0			0
$175$	1.84120	+	1.06302i	0.139181	+	0.0803565i
$176$	8.35499	+	6.65460i	0.629781	+	0.501609i
$177$		0			0
$178$	−14.2377	−	20.0598i	−1.06716	−	1.50354i
$179$	0.703881	−	0.406386i	0.0526106	−	0.0303747i	−0.473464	−	0.880813i	$-0.656997\pi$
$179$	0.703881	−	0.406386i	0.0526106	−	0.0303747i	0.526075	+	0.850438i	$0.323663\pi$
$180$		0			0
$181$			4.40522i			0.327437i	0.986507	+	0.163719i	$0.0523489\pi$
$181$			4.40522i			0.327437i	−0.986507	+	0.163719i	$0.947651\pi$
$182$	−18.7315	+	11.0660i	−1.38847	+	0.820266i
$183$		0			0
$184$	−5.58613	+	5.80434i	−0.411815	+	0.427901i
$185$	1.89125	+	3.27574i	0.139048	+	0.240837i
$186$		0			0
$187$	15.2819			1.11752
$188$	−1.80000	−	9.49744i	−0.131278	−	0.692672i
$189$		0			0
$190$	22.1348	+	10.1501i	1.60583	+	0.736365i
$191$	−4.99011	+	8.64312i	−0.361072	+	0.625395i	−0.988138	−	0.153572i	$-0.950922\pi$
$191$	−4.99011	+	8.64312i	−0.361072	+	0.625395i	0.627066	+	0.778966i	$0.284256\pi$
$192$		0			0
$193$	−6.08787	+	3.51483i	−0.438215	+	0.253003i	−0.702840	−	0.711348i	$-0.748085\pi$
$193$	−6.08787	+	3.51483i	−0.438215	+	0.253003i	0.264625	+	0.964351i	$0.414752\pi$
$194$	−2.76422	+	6.02809i	−0.198460	+	0.432791i
$195$		0			0
$196$	−14.6226	−	16.9813i	−1.04447	−	1.21295i
$197$	11.4687	+	19.8644i	0.817111	+	1.41528i	0.907802	+	0.419399i	$0.137759\pi$
$197$	11.4687	+	19.8644i	0.817111	+	1.41528i	−0.0906911	+	0.995879i	$0.528908\pi$
$198$		0			0
$199$	−0.0585459	+	0.101404i	−0.00415021	+	0.00718837i	−0.868093	−	0.496402i	$-0.834654\pi$
$199$	−0.0585459	+	0.101404i	−0.00415021	+	0.00718837i	0.863943	+	0.503590i	$0.167988\pi$
$200$	−0.390777	−	1.35410i	−0.0276321	−	0.0957495i
$201$		0			0
$202$	9.23990	+	13.0182i	0.650117	+	0.915960i
$203$	−19.7861			−1.38871
$204$		0			0
$205$	12.9451	−	7.47385i	0.904125	−	0.521997i
$206$	2.56491	+	27.3077i	0.178705	+	1.90262i
$207$		0			0
$208$	14.0337	+	3.32497i	0.973062	+	0.230545i
$209$	−19.6089			−1.35637
$210$		0			0
$211$	−12.7439	+	7.35770i	−0.877327	+	0.506525i	−0.869776	−	0.493446i	$-0.835737\pi$
$211$	−12.7439	+	7.35770i	−0.877327	+	0.506525i	−0.00755106	+	0.999971i	$0.502404\pi$
$212$	−0.995192	−	5.25100i	−0.0683501	−	0.360640i
$213$		0			0
$214$	11.3335	+	15.9679i	0.774741	+	1.09154i
$215$	9.33910	+	5.39193i	0.636921	+	0.367727i
$216$		0			0
$217$	−14.7532	+	25.5533i	−1.00151	+	1.73467i
$218$	0.908583	+	9.67337i	0.0615370	+	0.655163i
$219$		0			0
$220$	8.17144	+	9.48956i	0.550918	+	0.639786i
$221$	18.6692	−	8.78803i	1.25582	−	0.591147i
$222$		0			0
$223$	−10.9380	+	6.31505i	−0.732462	+	0.422887i	−0.819322	−	0.573333i	$-0.805650\pi$
$223$	−10.9380	+	6.31505i	−0.732462	+	0.422887i	0.0868600	+	0.996221i	$0.472317\pi$
$224$	−1.33505	+	24.0992i	−0.0892018	+	1.61019i
$225$		0			0
$226$	−25.1731	−	11.5433i	−1.67449	−	0.767848i
$227$	9.00775	−	15.6019i	0.597865	−	1.03553i	−0.395270	−	0.918565i	$-0.629349\pi$
$227$	9.00775	−	15.6019i	0.597865	−	1.03553i	0.993136	−	0.116968i	$-0.0373176\pi$
$228$		0			0
$229$	5.09964			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$229$	5.09964			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$230$	−7.70193	+	5.46656i	−0.507850	+	0.360455i
$231$		0			0
$232$	9.45059	+	9.09530i	0.620462	+	0.597136i
$233$	15.3036			1.00257			0.501286	−	0.865282i	$-0.332861\pi$
$233$	15.3036			1.00257			0.501286	+	0.865282i	$0.332861\pi$
$234$		0			0
$235$		−	11.3332i		−	0.739298i
$236$	5.12059	−	14.6481i	0.333322	−	0.953508i
$237$		0			0
$238$	19.9869	+	28.1599i	1.29556	+	1.82534i
$239$		−	10.7527i		−	0.695533i	−0.937581	−	0.347766i	$-0.886940\pi$
$239$		−	10.7527i		−	0.695533i	0.937581	−	0.347766i	$-0.113060\pi$
$240$		0			0
$241$	−4.82911	−	2.78809i	−0.311070	−	0.179596i	0.336335	−	0.941742i	$-0.390813\pi$
$241$	−4.82911	−	2.78809i	−0.311070	−	0.179596i	−0.647405	+	0.762146i	$0.724146\pi$
$242$	4.97412	+	2.28092i	0.319749	+	0.146623i
$243$		0			0
$244$	−3.99488	−	1.39651i	−0.255746	−	0.0894023i
$245$	−13.1367	−	22.7534i	−0.839272	−	1.45366i
$246$		0			0
$247$	−23.9552	+	11.2763i	−1.52423	+	0.717494i
$248$	18.7931	−	5.42346i	1.19336	−	0.344390i
$249$		0			0
$250$	1.39600	+	14.8628i	0.0882909	+	0.940003i
$251$	17.4469	+	10.0730i	1.10124	+	0.635801i	0.936546	−	0.350544i	$-0.114003\pi$
$251$	17.4469	+	10.0730i	1.10124	+	0.635801i	0.164693	+	0.986345i	$0.447337\pi$
$252$		0			0
$253$	3.80272	−	6.58650i	0.239075	−	0.414090i
$254$	3.80496	−	2.70063i	0.238744	−	0.169452i
$255$		0			0
$256$	11.7156	−	10.8970i	0.732226	−	0.681062i
$257$	2.14179	+	3.70969i	0.133601	+	0.231404i	0.925062	−	0.379815i	$-0.124012\pi$
$257$	2.14179	+	3.70969i	0.133601	+	0.231404i	−0.791461	+	0.611220i	$0.790679\pi$
$258$		0			0
$259$		−	6.88268i		−	0.427669i
$260$	15.4397	+	6.89386i	0.957532	+	0.427539i
$261$		0			0
$262$	16.8531	−	1.58295i	1.04119	−	0.0977948i
$263$	10.7244	+	18.5751i	0.661293	+	1.14539i	0.980276	+	0.197632i	$0.0633251\pi$
$263$	10.7244	+	18.5751i	0.661293	+	1.14539i	−0.318984	+	0.947760i	$0.603342\pi$
$264$		0			0
$265$		−	6.26597i		−	0.384916i
$266$	−25.6461	−	36.1332i	−1.57246	−	2.21547i
$267$		0			0
$268$	11.2816	+	13.1014i	0.689132	+	0.800295i
$269$	−5.23857	−	3.02449i	−0.319401	−	0.184406i	0.331724	−	0.943376i	$-0.392370\pi$
$269$	−5.23857	−	3.02449i	−0.319401	−	0.184406i	−0.651126	+	0.758970i	$0.725703\pi$
$270$		0			0
$271$	9.09680	−	5.25204i	0.552591	−	0.319039i	−0.197575	−	0.980288i	$-0.563307\pi$
$271$	9.09680	−	5.25204i	0.552591	−	0.319039i	0.750166	+	0.661249i	$0.229973\pi$
$272$	3.39807	−	22.6379i	0.206038	−	1.37262i
$273$		0			0
$274$	5.08881	−	11.0974i	0.307426	−	0.670421i
$275$	0.665289	+	1.15231i	0.0401185	+	0.0694872i
$276$		0			0
$277$	−4.73869	−	2.73588i	−0.284720	−	0.164383i	0.350838	−	0.936436i	$-0.385897\pi$
$277$	−4.73869	−	2.73588i	−0.284720	−	0.164383i	−0.635558	+	0.772053i	$0.719230\pi$
$278$	−0.111794	+	0.243794i	−0.00670493	+	0.0146218i
$279$		0			0
$280$	−6.79910	+	27.4687i	−0.406324	+	1.64157i
$281$		−	13.2774i		−	0.792063i	−0.918237	−	0.396032i	$-0.870387\pi$
$281$		−	13.2774i		−	0.792063i	0.918237	−	0.396032i	$-0.129613\pi$
$282$		0			0
$283$	14.8438	−	8.57010i	0.882375	−	0.509439i	0.0109341	−	0.999940i	$-0.496520\pi$
$283$	14.8438	−	8.57010i	0.882375	−	0.509439i	0.871441	+	0.490501i	$0.163186\pi$
$284$	−25.3302	−	8.85478i	−1.50307	−	0.525435i
$285$		0			0
$286$	−13.6153	+	0.136249i	−0.805091	+	0.00805659i
$287$	−27.1990			−1.60551
$288$		0			0
$289$	−7.87564	−	13.6410i	−0.463273	−	0.802413i
$290$	8.90063	+	12.5402i	0.522663	+	0.736388i
$291$		0			0
$292$	3.92378	+	20.7033i	0.229622	+	1.21157i
$293$	12.4999	−	21.6505i	0.730254	−	1.26484i	−0.226521	−	0.974006i	$-0.572735\pi$
$293$	12.4999	−	21.6505i	0.730254	−	1.26484i	0.956775	−	0.290831i	$-0.0939316\pi$
$294$		0			0
$295$	9.09640	−	15.7554i	0.529613	−	0.917316i
$296$	−3.16385	+	3.28743i	−0.183895	+	0.191078i
$297$		0			0
$298$	−22.0277	−	10.1010i	−1.27603	−	0.585134i
$299$	0.857955	−	10.2332i	0.0496168	−	0.591802i
$300$		0			0
$301$	−9.81122	−	16.9935i	−0.565510	−	0.979491i
$302$	4.46905	−	0.419761i	0.257165	−	0.0241545i
$303$		0			0
$304$	−4.36021	+	29.0477i	−0.250075	+	1.66600i
$305$	−4.29688	−	2.48081i	−0.246039	−	0.142051i
$306$		0			0
$307$	−4.78769			−0.273248			−0.136624	−	0.990623i	$-0.543625\pi$
$307$	−4.78769			−0.273248			−0.136624	+	0.990623i	$0.543625\pi$
$308$	−4.24314	−	22.3884i	−0.241775	−	1.27570i
$309$		0			0
$310$	22.8321	−	2.14453i	1.29678	−	0.121801i
$311$	15.0703			0.854556			0.427278	−	0.904120i	$-0.359473\pi$
$311$	15.0703			0.854556			0.427278	+	0.904120i	$0.359473\pi$
$312$		0			0
$313$	28.3272			1.60115			0.800573	−	0.599236i	$-0.204529\pi$
$313$	28.3272			1.60115			0.800573	+	0.599236i	$0.204529\pi$
$314$	25.0208	−	2.35011i	1.41200	−	0.132624i
$315$		0			0
$316$	−3.77444	+	0.715348i	−0.212329	+	0.0402415i
$317$	14.9982			0.842384			0.421192	−	0.906972i	$-0.361612\pi$
$317$	14.9982			0.842384			0.421192	+	0.906972i	$0.361612\pi$
$318$		0			0
$319$	−10.7241	−	6.19157i	−0.600435	−	0.346661i
$320$	15.8744	−	9.99470i	0.887405	−	0.558721i
$321$		0			0
$322$	17.1104	−	1.60712i	0.953527	−	0.0895612i
$323$	21.0123	+	36.3944i	1.16916	+	2.02504i
$324$		0			0
$325$	1.47540	+	1.02515i	0.0818407	+	0.0568648i
$326$	0.0707961	+	0.0324641i	0.00392103	+	0.00179802i
$327$		0			0
$328$	12.9913	+	12.5029i	0.717324	+	0.690357i
$329$	−10.3110	+	17.8592i	−0.568465	+	0.984611i
$330$		0			0
$331$	12.4044	−	21.4851i	0.681808	−	1.18093i	−0.292620	−	0.956229i	$-0.594527\pi$
$331$	12.4044	−	21.4851i	0.681808	−	1.18093i	0.974429	−	0.224698i	$-0.0721395\pi$
$332$	−5.38090	+	1.01981i	−0.295315	+	0.0559694i
$333$		0			0
$334$	11.0187	+	15.5244i	0.602918	+	0.849460i
$335$	10.1352	+	17.5546i	0.553744	+	0.959113i
$336$		0			0
$337$	−31.0333			−1.69049			−0.845246	−	0.534378i	$-0.820546\pi$
$337$	−31.0333			−1.69049			−0.845246	+	0.534378i	$0.820546\pi$
$338$	−16.5548	+	7.99609i	−0.900464	+	0.434930i
$339$		0			0
$340$	8.85650	−	25.3351i	0.480311	−	1.37399i
$341$	−15.9926	+	9.23331i	−0.866046	+	0.500012i
$342$		0			0
$343$			17.9404i			0.968692i
$344$	−3.12540	+	12.6268i	−0.168511	+	0.680792i
$345$		0			0
$346$	9.42212	−	20.5473i	0.506536	−	1.10463i
$347$	−9.66192	−	5.57831i	−0.518679	−	0.299459i	0.217715	−	0.976012i	$-0.430140\pi$
$347$	−9.66192	−	5.57831i	−0.518679	−	0.299459i	−0.736394	+	0.676553i	$0.763473\pi$
$348$		0			0
$349$	17.4633	+	30.2474i	0.934791	+	1.61910i	0.775007	+	0.631953i	$0.217746\pi$
$349$	17.4633	+	30.2474i	0.934791	+	1.61910i	0.159784	+	0.987152i	$0.448920\pi$
$350$	−1.25325	+	2.73302i	−0.0669888	+	0.146086i
$351$		0			0
$352$	−8.26484	+	12.6440i	−0.440517	+	0.673929i
$353$	26.0211	−	15.0233i	1.38496	−	0.799610i	0.392222	−	0.919870i	$-0.371706\pi$
$353$	26.0211	−	15.0233i	1.38496	−	0.799610i	0.992742	+	0.120261i	$0.0383730\pi$
$354$		0			0
$355$	−27.2451	−	15.7299i	−1.44602	−	0.834858i
$356$	26.3616	−	22.6999i	1.39716	−	1.20309i
$357$		0			0
$358$	0.665286	+	0.937332i	0.0351615	+	0.0495395i
$359$			2.34283i			0.123650i	0.998087	+	0.0618249i	$0.0196920\pi$
$359$			2.34283i			0.123650i	−0.998087	+	0.0618249i	$0.980308\pi$
$360$		0			0
$361$	−17.4618	−	30.2447i	−0.919042	−	1.59183i
$362$	−6.20262	+	0.582588i	−0.326002	+	0.0306202i
$363$		0			0
$364$	−18.0583	−	24.9107i	−0.946513	−	1.30568i
$365$			24.7051i			1.29312i
$366$		0			0
$367$	4.58886	+	7.94814i	0.239537	+	0.414890i	0.960581	−	0.277999i	$-0.0896711\pi$
$367$	4.58886	+	7.94814i	0.239537	+	0.414890i	−0.721045	+	0.692889i	$0.756338\pi$
$368$	−8.91136	−	7.09774i	−0.464537	−	0.369995i
$369$		0			0
$370$	−4.36218	+	3.09613i	−0.226779	+	0.160960i
$371$	−5.70082	+	9.87411i	−0.295972	+	0.512638i
$372$		0			0
$373$	1.54067	+	0.889508i	0.0797731	+	0.0460570i	0.539356	−	0.842078i	$-0.318668\pi$
$373$	1.54067	+	0.889508i	0.0797731	+	0.0460570i	−0.459583	+	0.888135i	$0.652001\pi$
$374$	2.02102	+	21.5172i	0.104505	+	1.11263i
$375$		0			0
$376$	13.1345	−	3.79046i	0.677360	−	0.195478i
$377$	−16.6617	−	1.39692i	−0.858119	−	0.0719450i
$378$		0			0
$379$	5.63066	+	9.75258i	0.289227	+	0.500956i	0.973626	−	0.228152i	$-0.0732683\pi$
$379$	5.63066	+	9.75258i	0.289227	+	0.500956i	−0.684398	+	0.729108i	$0.739935\pi$
$380$	−11.3642	+	32.5085i	−0.582969	+	1.66765i
$381$		0			0
$382$	−12.8296	−	5.88311i	−0.656420	−	0.301006i
$383$	−29.2793	−	16.9044i	−1.49610	−	0.863776i	−0.496114	−	0.868258i	$-0.665240\pi$
$383$	−29.2793	−	16.9044i	−1.49610	−	0.863776i	−0.999990	+	0.00448179i	$0.998573\pi$
$384$		0			0
$385$		−	26.7159i		−	1.36157i
$386$	−5.75406	−	8.10699i	−0.292874	−	0.412635i
$387$		0			0
$388$	−8.85321	−	3.09486i	−0.449454	−	0.157118i
$389$			29.7349i			1.50762i	0.657092	+	0.753811i	$0.271786\pi$
$389$			29.7349i			1.50762i	−0.657092	+	0.753811i	$0.728214\pi$
$390$		0			0
$391$	−16.2995			−0.824303
$392$	21.9762	−	22.8346i	1.10996	−	1.15332i
$393$		0			0
$394$	−26.4526	+	18.7752i	−1.33266	+	0.945879i
$395$	−4.50401			−0.226621
$396$		0			0
$397$	9.49768	−	16.4505i	0.476675	−	0.825625i	−0.522968	−	0.852352i	$-0.675175\pi$
$397$	9.49768	−	16.4505i	0.476675	−	0.825625i	0.999643	+	0.0267274i	$0.00850862\pi$
$398$	−0.150522	−	0.0690228i	−0.00754497	−	0.00345980i
$399$		0			0
$400$	1.85492	−	0.729301i	0.0927459	−	0.0364650i
$401$	−10.5876	+	6.11273i	−0.528718	+	0.305255i	−0.740494	−	0.672063i	$-0.765408\pi$
$401$	−10.5876	+	6.11273i	−0.528718	+	0.305255i	0.211776	+	0.977318i	$0.432075\pi$
$402$		0			0
$403$	−14.2276	+	20.4766i	−0.708728	+	1.02001i
$404$	−17.1079	+	14.7316i	−0.851150	+	0.732924i
$405$		0			0
$406$	−2.61670	−	27.8591i	−0.129865	−	1.38263i
$407$	2.15377	−	3.73043i	0.106758	−	0.184911i
$408$		0			0
$409$	12.5862	+	7.26664i	0.622347	+	0.359312i	0.777782	−	0.628534i	$-0.216345\pi$
$409$	12.5862	+	7.26664i	0.622347	+	0.359312i	−0.155435	+	0.987846i	$0.549678\pi$
$410$	12.2353	+	17.2385i	0.604258	+	0.851348i
$411$		0			0
$412$	−38.1105	+	7.22286i	−1.87757	+	0.355845i
$413$	−28.6688	+	16.5519i	−1.41070	+	0.814466i
$414$		0			0
$415$	−6.42098			−0.315193
$416$	−2.82566	+	20.1994i	−0.138539	+	0.990357i
$417$		0			0
$418$	−2.59326	−	27.6096i	−0.126841	−	1.35043i
$419$	−9.78683	+	5.65043i	−0.478118	+	0.276042i	−0.719632	−	0.694356i	$-0.755689\pi$
$419$	−9.78683	+	5.65043i	−0.478118	+	0.276042i	0.241514	+	0.970397i	$0.422356\pi$
$420$		0			0
$421$	9.68826			0.472177			0.236088	−	0.971732i	$-0.424134\pi$
$421$	9.68826			0.472177			0.236088	+	0.971732i	$0.424134\pi$
$422$	−12.0451	−	16.9706i	−0.586348	−	0.826115i
$423$		0			0
$424$	7.26188	−	2.09569i	0.352668	−	0.101776i
$425$	1.42581	−	2.46958i	0.0691620	−	0.119792i
$426$		0			0
$427$	4.51411	+	7.81866i	0.218453	+	0.378372i
$428$	−20.9842	+	18.0695i	−1.01431	+	0.873421i
$429$		0			0
$430$	−6.35684	+	13.8627i	−0.306554	+	0.668518i
$431$	3.01093	−	1.73836i	0.145031	−	0.0837339i	−0.425728	−	0.904851i	$-0.639982\pi$
$431$	3.01093	−	1.73836i	0.145031	−	0.0837339i	0.570760	+	0.821117i	$0.306649\pi$
$432$		0			0
$433$	−6.49678	+	11.2528i	−0.312215	+	0.540773i	−0.978842	−	0.204619i	$-0.934404\pi$
$433$	−6.49678	+	11.2528i	−0.312215	+	0.540773i	0.666626	+	0.745392i	$0.267738\pi$
$434$	−37.9306	−	17.3934i	−1.82073	−	0.834908i
$435$		0			0
$436$	−13.5001	+	2.55860i	−0.646538	+	0.122535i
$437$	20.9146			1.00048
$438$		0			0
$439$	−13.8320	−	23.9578i	−0.660167	−	1.14344i	−0.980572	−	0.196162i	$-0.937152\pi$
$439$	−13.8320	−	23.9578i	−0.660167	−	1.14344i	0.320405	−	0.947281i	$-0.396181\pi$
$440$	−12.2808	+	12.7605i	−0.585464	+	0.608334i
$441$		0			0
$442$	14.8427	+	25.1243i	0.705994	+	1.19504i
$443$		−	27.0342i		−	1.28443i	−0.766523	−	0.642216i	$-0.778015\pi$
$443$		−	27.0342i		−	1.28443i	0.766523	−	0.642216i	$-0.221985\pi$
$444$		0			0
$445$	35.3220	−	20.3932i	1.67443	−	0.966730i
$446$	−10.3382	−	14.5657i	−0.489530	−	0.689706i
$447$		0			0
$448$	−34.1086	+	1.30733i	−1.61148	+	0.0617657i
$449$	−3.32814	−	1.92150i	−0.157064	−	0.0906812i	0.419408	−	0.907798i	$-0.362238\pi$
$449$	−3.32814	−	1.92150i	−0.157064	−	0.0906812i	−0.576472	+	0.817117i	$0.695571\pi$
$450$		0			0
$451$	−14.7419	−	8.51126i	−0.694171	−	0.400780i
$452$	12.9240	−	36.9707i	0.607894	−	1.73895i
$453$		0			0
$454$	23.1590	+	10.6197i	1.08690	+	0.498408i
$455$	−15.3633	−	32.6375i	−0.720240	−	1.53007i
$456$		0			0
$457$	−3.45666	+	1.99570i	−0.161696	+	0.0933550i	−0.578664	−	0.815566i	$-0.696426\pi$
$457$	−3.45666	+	1.99570i	−0.161696	+	0.0933550i	0.416969	+	0.908921i	$0.363092\pi$
$458$	0.674426	+	7.18038i	0.0315138	+	0.335517i
$459$		0			0
$460$	−8.71559	−	10.1215i	−0.406366	−	0.471917i
$461$	2.82779	−	4.89787i	0.131703	−	0.228117i	−0.792630	−	0.609703i	$-0.791289\pi$
$461$	2.82779	−	4.89787i	0.131703	−	0.228117i	0.924333	+	0.381586i	$0.124622\pi$
$462$		0			0
$463$		−	11.5821i		−	0.538268i	−0.963103	−	0.269134i	$-0.913263\pi$
$463$		−	11.5821i		−	0.538268i	0.963103	−	0.269134i	$-0.0867374\pi$
$464$	−11.5565	+	14.5094i	−0.536497	+	0.673584i
$465$		0			0
$466$	2.02389	+	21.5477i	0.0937551	+	0.998178i
$467$		−	18.5963i		−	0.860536i	−0.902701	−	0.430268i	$-0.858419\pi$
$467$		−	18.5963i		−	0.860536i	0.902701	−	0.430268i	$-0.141581\pi$
$468$		0			0
$469$		−	36.8842i		−	1.70315i
$470$	15.9574	−	1.49881i	0.736058	−	0.0691351i
$471$		0			0
$472$	21.3019	+	5.27268i	0.980500	+	0.242695i
$473$		−	12.2807i		−	0.564668i
$474$		0			0
$475$	−1.82952	+	3.16882i	−0.0839441	+	0.145395i
$476$	−37.0063	+	31.8661i	−1.69618	+	1.46058i
$477$		0			0
$478$	15.1399	−	1.42204i	0.692485	−	0.0650424i
$479$	17.3136	−	9.99603i	0.791080	−	0.456730i	−0.0492627	−	0.998786i	$-0.515687\pi$
$479$	17.3136	−	9.99603i	0.791080	−	0.456730i	0.840343	+	0.542056i	$0.182354\pi$
$480$		0			0
$481$	0.485925	−	5.79584i	0.0221563	−	0.264267i
$482$	3.28702	−	7.16819i	0.149720	−	0.326502i
$483$		0			0
$484$	−2.55375	+	7.30530i	−0.116079	+	0.332059i
$485$	−9.52249	−	5.49781i	−0.432394	−	0.249643i
$486$		0			0
$487$	4.25869	+	2.45876i	0.192980	+	0.111417i	0.593377	−	0.804925i	$-0.297794\pi$
$487$	4.25869	+	2.45876i	0.192980	+	0.111417i	−0.400397	+	0.916342i	$0.631128\pi$
$488$	1.43799	−	5.80954i	0.0650946	−	0.262986i
$489$		0			0
$490$	30.2998	−	21.5058i	1.36881	−	0.971533i
$491$	−6.28406	+	3.62810i	−0.283596	+	0.163734i	−0.635050	−	0.772471i	$-0.719021\pi$
$491$	−6.28406	+	3.62810i	−0.283596	+	0.163734i	0.351455	+	0.936205i	$0.385687\pi$
$492$		0			0
$493$			26.5388i			1.19525i
$494$	−19.0453	−	32.2380i	−0.856888	−	1.45046i
$495$		0			0
$496$	10.1217	+	25.7437i	0.454478	+	1.15593i
$497$	28.6224	+	49.5754i	1.28389	+	2.22376i
$498$		0			0
$499$	11.7940			0.527974			0.263987	−	0.964526i	$-0.414962\pi$
$499$	11.7940			0.527974			0.263987	+	0.964526i	$0.414962\pi$
$500$	−20.7424	+	3.93119i	−0.927628	+	0.175808i
$501$		0			0
$502$	−11.8756	+	25.8977i	−0.530033	+	1.15587i
$503$	−13.3082	+	23.0505i	−0.593383	+	1.02777i	0.400390	+	0.916345i	$0.368875\pi$
$503$	−13.3082	+	23.0505i	−0.593383	+	1.02777i	−0.993773	+	0.111424i	$0.964459\pi$
$504$		0			0
$505$	−22.9230	+	13.2346i	−1.02006	+	0.588932i
$506$	9.77681	+	4.48323i	0.434632	+	0.199304i
$507$		0			0
$508$	4.30573	+	5.00028i	0.191036	+	0.221852i
$509$	−8.86015	−	15.3462i	−0.392719	−	0.680210i	0.600088	−	0.799934i	$-0.295132\pi$
$509$	−8.86015	−	15.3462i	−0.392719	−	0.680210i	−0.992807	+	0.119724i	$0.961799\pi$
$510$		0			0
$511$	22.4768	−	38.9310i	0.994317	−	1.72221i
$512$	16.8925	+	15.0547i	0.746551	+	0.665328i
$513$		0			0
$514$	−4.94006	+	3.50628i	−0.217897	+	0.154656i
$515$	−45.4769			−2.00395
$516$		0			0
$517$	−11.1772	+	6.45316i	−0.491573	+	0.283810i
$518$	9.69093	−	0.910232i	0.425795	−	0.0399933i
$519$		0			0
$520$	−7.66477	+	22.6511i	−0.336123	+	0.993317i
$521$	−4.65649			−0.204004			−0.102002	−	0.994784i	$-0.532525\pi$
$521$	−4.65649			−0.204004			−0.102002	+	0.994784i	$0.532525\pi$
$522$		0			0
$523$	16.4234	−	9.48204i	0.718144	−	0.414621i	−0.0959250	−	0.995389i	$-0.530581\pi$
$523$	16.4234	−	9.48204i	0.718144	−	0.414621i	0.814069	+	0.580768i	$0.197248\pi$
$524$	4.45763	+	23.5201i	0.194733	+	1.02748i
$525$		0			0
$526$	−24.7358	+	17.5566i	−1.07853	+	0.765506i
$527$	34.2743	+	19.7883i	1.49301	+	0.861992i
$528$		0			0
$529$	7.44405	−	12.8935i	0.323655	−	0.560586i
$530$	8.82259	−	0.828672i	0.383229	−	0.0359952i
$531$		0			0
$532$	47.4845	−	40.8887i	2.05871	−	1.77275i
$533$	−22.9040	−	1.92028i	−0.992083	−	0.0831766i
$534$		0			0
$535$	−28.1169	+	16.2333i	−1.21560	+	0.701828i
$536$	−16.9550	+	17.6173i	−0.732344	+	0.760951i
$537$		0			0
$538$	3.56573	−	7.77598i	0.153730	−	0.335246i
$539$	−14.9601	+	25.9117i	−0.644378	+	1.11610i
$540$		0			0
$541$	−31.4401			−1.35172			−0.675859	−	0.737031i	$-0.736227\pi$
$541$	−31.4401			−1.35172			−0.675859	+	0.737031i	$0.736227\pi$
$542$	8.59800	+	12.1139i	0.369316	+	0.520335i
$543$		0			0
$544$	32.3239	+	1.79069i	1.38588	+	0.0767750i
$545$	−16.1096			−0.690058
$546$		0			0
$547$		−	32.9113i		−	1.40719i	−0.710603	−	0.703593i	$-0.751578\pi$
$547$		−	32.9113i		−	1.40719i	0.710603	−	0.703593i	$-0.248422\pi$
$548$	16.2984	+	5.69750i	0.696232	+	0.243385i
$549$		0			0
$550$	−1.53449	+	1.08913i	−0.0654310	+	0.0464407i
$551$		−	34.0531i		−	1.45071i
$552$		0			0
$553$	7.09755	+	4.09777i	0.301818	+	0.174255i
$554$	3.22548	−	7.03397i	0.137037	−	0.298845i
$555$		0			0
$556$	−0.358051	−	0.125165i	−0.0151847	−	0.00530820i
$557$	−15.3182	−	26.5319i	−0.649054	−	1.12419i	−0.983349	−	0.181726i	$-0.941832\pi$
$557$	−15.3182	−	26.5319i	−0.649054	−	1.12419i	0.334295	−	0.942468i	$-0.391502\pi$
$558$		0			0
$559$	−7.06217	−	15.0028i	−0.298698	−	0.634549i
$560$	−39.5756	−	5.94051i	−1.67237	−	0.251033i
$561$		0			0
$562$	18.6948	−	1.75593i	0.788593	−	0.0740695i
$563$	11.9974	+	6.92670i	0.505630	+	0.291925i	0.731035	−	0.682340i	$-0.239037\pi$
$563$	11.9974	+	6.92670i	0.505630	+	0.291925i	−0.225406	+	0.974265i	$0.572371\pi$
$564$		0			0
$565$	22.9587	−	39.7656i	0.965878	−	1.67295i
$566$	14.0299	+	19.7670i	0.589722	+	0.830868i
$567$		0			0
$568$	9.11777	−	36.8363i	0.382573	−	1.54562i
$569$	−1.42336	−	2.46532i	−0.0596702	−	0.103352i	0.834647	−	0.550785i	$-0.185672\pi$
$569$	−1.42336	−	2.46532i	−0.0596702	−	0.103352i	−0.894317	+	0.447433i	$0.852338\pi$
$570$		0			0
$571$		−	1.58567i		−	0.0663582i	−0.999449	−	0.0331791i	$-0.989437\pi$
$571$		−	1.58567i		−	0.0663582i	0.999449	−	0.0331791i	$-0.0105632\pi$
$572$	−1.99246	−	19.1526i	−0.0833090	−	0.800810i
$573$		0			0
$574$	−3.59706	−	38.2967i	−0.150138	−	1.59847i
$575$	−0.709592	−	1.22905i	−0.0295920	−	0.0512549i
$576$		0			0
$577$		−	12.1207i		−	0.504591i	−0.967650	−	0.252296i	$-0.918814\pi$
$577$		−	12.1207i		−	0.504591i	0.967650	−	0.252296i	$-0.0811855\pi$
$578$	18.1652	−	12.8931i	0.755574	−	0.536280i
$579$		0			0
$580$	−16.4798	+	14.1907i	−0.684284	+	0.589236i
$581$	10.1184	+	5.84184i	0.419781	+	0.242361i
$582$		0			0
$583$	−6.17972	+	3.56786i	−0.255938	+	0.147766i
$584$	−28.6317	+	8.26276i	−1.18479	+	0.341915i
$585$		0			0
$586$	32.1374	+	14.7368i	1.32758	+	0.608773i
$587$	6.10053	+	10.5664i	0.251796	+	0.436123i	0.964020	−	0.265829i	$-0.0856456\pi$
$587$	6.10053	+	10.5664i	0.251796	+	0.436123i	−0.712225	+	0.701952i	$0.752312\pi$
$588$		0			0
$589$	−43.9789	−	25.3912i	−1.81212	−	1.04623i
$590$	23.3869	+	10.7242i	0.962823	+	0.441509i
$591$		0			0
$592$	−5.04718	−	4.01998i	−0.207438	−	0.165220i
$593$		−	27.8522i		−	1.14375i	−0.820340	−	0.571876i	$-0.806216\pi$
$593$		−	27.8522i		−	1.14375i	0.820340	−	0.571876i	$-0.193784\pi$
$594$		0			0
$595$	−49.5851	+	28.6279i	−2.03279	+	1.17363i
$596$	11.3092	−	32.3513i	0.463242	−	1.32516i
$597$		0			0
$598$	14.5220	−	0.145322i	0.593848	−	0.00594267i
$599$	2.82455			0.115408			0.0577040	−	0.998334i	$-0.481622\pi$
$599$	2.82455			0.115408			0.0577040	+	0.998334i	$0.481622\pi$
$600$		0			0
$601$	−12.3364	−	21.3673i	−0.503212	−	0.871589i	−0.999993	−	0.00371312i	$-0.998818\pi$
$601$	−12.3364	−	21.3673i	−0.503212	−	0.871589i	0.496781	−	0.867876i	$-0.334515\pi$
$602$	22.6296	−	16.0618i	0.922316	−	0.654628i
$603$		0			0
$604$	1.18206	+	6.23698i	0.0480973	+	0.253779i
$605$	−4.53657	+	7.85756i	−0.184438	+	0.319455i
$606$		0			0
$607$	−11.8980	+	20.6079i	−0.482925	+	0.836451i	−0.999808	−	0.0196055i	$-0.993759\pi$
$607$	−11.8980	+	20.6079i	−0.482925	+	0.836451i	0.516883	+	0.856056i	$0.327092\pi$
$608$	−41.4762	−	2.29771i	−1.68208	−	0.0931843i
$609$		0			0
$610$	2.92476	−	6.37817i	0.118420	−	0.258245i
$611$	−9.94369	+	14.3111i	−0.402279	+	0.578965i
$612$		0			0
$613$	16.8079	+	29.1122i	0.678866	+	1.17583i	0.975323	+	0.220785i	$0.0708618\pi$
$613$	16.8079	+	29.1122i	0.678866	+	1.17583i	−0.296456	+	0.955046i	$0.595805\pi$
$614$	−0.633170	−	6.74115i	−0.0255527	−	0.272051i
$615$		0			0
$616$	30.9620	−	8.93526i	1.24750	−	0.360012i
$617$	4.78893	+	2.76489i	0.192795	+	0.111310i	0.593290	−	0.804988i	$-0.297829\pi$
$617$	4.78893	+	2.76489i	0.192795	+	0.111310i	−0.400495	+	0.916299i	$0.631162\pi$
$618$		0			0
$619$	45.0671			1.81140			0.905700	−	0.423920i	$-0.139346\pi$
$619$	45.0671			1.81140			0.905700	+	0.423920i	$0.139346\pi$
$620$	6.03907	+	31.8643i	0.242535	+	1.27970i
$621$		0			0
$622$	1.99304	+	21.2192i	0.0799134	+	0.850811i
$623$	−74.2154			−2.97338
$624$		0			0
$625$	−27.2431			−1.08973
$626$	3.74625	+	39.8851i	0.149730	+	1.59413i
$627$		0			0
$628$	6.61798	+	34.9189i	0.264086	+	1.39341i
$629$	−9.23166			−0.368090
$630$		0			0
$631$	19.1700	+	11.0678i	0.763146	+	0.440603i	0.830424	−	0.557132i	$-0.188098\pi$
$631$	19.1700	+	11.0678i	0.763146	+	0.440603i	−0.0672781	+	0.997734i	$0.521431\pi$
$632$	−1.50639	−	5.21987i	−0.0599210	−	0.207635i
$633$		0			0
$634$	1.98351	+	21.1177i	0.0787752	+	0.838693i
$635$	3.86820	+	6.69991i	0.153505	+	0.265878i
$636$		0			0
$637$	−3.37525	+	40.2581i	−0.133732	+	1.59508i
$638$	7.29957	−	15.9185i	0.288993	−	0.630221i
$639$		0			0
$640$	16.1721	+	21.0296i	0.639258	+	0.831268i
$641$	4.25471	−	7.36938i	0.168051	−	0.291073i	−0.769684	−	0.638426i	$-0.779586\pi$
$641$	4.25471	−	7.36938i	0.168051	−	0.291073i	0.937735	+	0.347353i	$0.112919\pi$
$642$		0			0
$643$	16.6171	−	28.7817i	0.655316	−	1.13504i	−0.326499	−	0.945198i	$-0.605869\pi$
$643$	16.6171	−	28.7817i	0.655316	−	1.13504i	0.981815	−	0.189842i	$-0.0607977\pi$
$644$	4.52570	+	23.8792i	0.178337	+	0.940974i
$645$		0			0
$646$	−48.4650	+	34.3988i	−1.90683	+	1.35340i
$647$	−0.419692	−	0.726928i	−0.0164998	−	0.0285785i	0.857658	−	0.514221i	$-0.171919\pi$
$647$	−0.419692	−	0.726928i	−0.0164998	−	0.0285785i	−0.874157	+	0.485643i	$0.838586\pi$
$648$		0			0
$649$	−20.7180			−0.813254
$650$	−1.24830	+	2.21297i	−0.0489624	+	0.0867997i
$651$		0			0
$652$	−0.0363472	+	0.103975i	−0.00142347	+	0.00407199i
$653$	17.5839	−	10.1521i	0.688112	−	0.397282i	−0.114792	−	0.993390i	$-0.536620\pi$
$653$	17.5839	−	10.1521i	0.688112	−	0.397282i	0.802904	+	0.596108i	$0.203287\pi$
$654$		0			0
$655$			28.0663i			1.09664i
$656$	−15.8862	+	19.9455i	−0.620252	+	0.778740i
$657$		0			0
$658$	−26.5097	−	12.1562i	−1.03346	−	0.473899i
$659$	14.9226	+	8.61559i	0.581304	+	0.335616i	0.761651	−	0.647987i	$-0.224389\pi$
$659$	14.9226	+	8.61559i	0.581304	+	0.335616i	−0.180348	+	0.983603i	$0.557722\pi$
$660$		0			0
$661$	−6.11325	−	10.5885i	−0.237778	−	0.411844i	0.722298	−	0.691582i	$-0.243086\pi$
$661$	−6.11325	−	10.5885i	−0.237778	−	0.411844i	−0.960076	+	0.279738i	$0.909752\pi$
$662$	31.8918	+	14.6242i	1.23951	+	0.568387i
$663$		0			0
$664$	−2.14753	−	7.44152i	−0.0833404	−	0.288787i
$665$	63.6247	−	36.7338i	2.46726	−	1.42447i
$666$		0			0
$667$	11.4382	+	6.60387i	0.442890	+	0.255703i
$668$	−20.4015	+	17.5676i	−0.789356	+	0.679713i
$669$		0			0
$670$	−23.3769	+	16.5921i	−0.903127	+	0.641008i
$671$			5.65031i			0.218128i
$672$		0			0
$673$	23.0768	+	39.9702i	0.889545	+	1.54074i	0.840414	+	0.541945i	$0.182312\pi$
$673$	23.0768	+	39.9702i	0.889545	+	1.54074i	0.0491314	+	0.998792i	$0.484355\pi$
$674$	−4.10414	−	43.6954i	−0.158086	−	1.68308i
$675$		0			0
$676$	−13.4480	−	22.2520i	−0.517231	−	0.855846i
$677$		−	37.1452i		−	1.42761i	−0.700346	−	0.713804i	$-0.746971\pi$
$677$		−	37.1452i		−	1.42761i	0.700346	−	0.713804i	$-0.253029\pi$
$678$		0			0
$679$	10.0039	+	17.3272i	0.383914	+	0.664959i
$680$	36.8435	+	9.11955i	1.41288	+	0.349719i
$681$		0			0
$682$	−15.1157	−	21.2967i	−0.578809	−	0.815492i
$683$	−12.9363	+	22.4064i	−0.494994	+	0.857355i	−0.999983	−	0.00577053i	$-0.998163\pi$
$683$	−12.9363	+	22.4064i	−0.494994	+	0.857355i	0.504989	+	0.863126i	$0.331497\pi$
$684$		0			0
$685$	17.5305	+	10.1212i	0.669805	+	0.386712i
$686$	−25.2604	+	2.37261i	−0.964447	+	0.0905868i
$687$		0			0
$688$	−18.1921	−	2.73073i	−0.693567	−	0.104108i
$689$	−5.49772	+	7.91240i	−0.209447	+	0.301438i
$690$		0			0
$691$	21.3019	+	36.8960i	0.810363	+	1.40359i	0.912610	+	0.408831i	$0.134064\pi$
$691$	21.3019	+	36.8960i	0.810363	+	1.40359i	−0.102247	+	0.994759i	$0.532603\pi$
$692$	30.1770	+	10.5491i	1.14716	+	0.401018i
$693$		0			0
$694$	6.57657	−	14.3419i	0.249643	−	0.544410i
$695$	−0.385119	−	0.222348i	−0.0146084	−	0.00843415i
$696$		0			0
$697$			36.4817i			1.38184i
$698$	−40.2793	+	28.5889i	−1.52459	+	1.08210i
$699$		0			0
$700$	−4.01388	−	1.40315i	−0.151710	−	0.0530341i
$701$			23.0213i			0.869502i	0.900551	+	0.434751i	$0.143164\pi$
$701$			23.0213i			0.869502i	−0.900551	+	0.434751i	$0.856836\pi$
$702$		0			0
$703$	11.8455			0.446763
$704$	−18.8960	−	9.96486i	−0.712171	−	0.375565i
$705$		0			0
$706$	24.5943	+	34.6513i	0.925620	+	1.30412i
$707$	48.1637			1.81138
$708$		0			0
$709$	7.09063	−	12.2813i	0.266294	−	0.461235i	−0.701608	−	0.712563i	$-0.747534\pi$
$709$	7.09063	−	12.2813i	0.266294	−	0.461235i	0.967902	+	0.251329i	$0.0808674\pi$
$710$	18.5449	−	40.4418i	0.695976	−	1.51775i
$711$		0			0
$712$	35.4481	+	34.1155i	1.32847	+	1.27853i
$713$	17.0575	−	9.84817i	0.638809	−	0.368817i
$714$		0			0
$715$	1.88617	−	22.4971i	0.0705387	−	0.841345i
$716$	−1.23180	+	1.06070i	−0.0460343	+	0.0396401i
$717$		0			0
$718$	−3.29874	+	0.309838i	−0.123108	+	0.0115631i
$719$	7.72475	−	13.3797i	0.288085	−	0.498977i	−0.685268	−	0.728291i	$-0.740315\pi$
$719$	7.72475	−	13.3797i	0.288085	−	0.498977i	0.973353	+	0.229314i	$0.0736483\pi$
$720$		0			0
$721$	71.6638	+	41.3751i	2.66890	+	1.54089i
$722$	40.2758	−	28.5864i	1.49891	−	1.06387i
$723$		0			0
$724$	−1.64059	−	8.65634i	−0.0609720	−	0.321710i
$725$	−2.00113	+	1.15535i	−0.0743201	+	0.0429088i
$726$		0			0
$727$	−4.72802			−0.175353			−0.0876763	−	0.996149i	$-0.527944\pi$
$727$	−4.72802			−0.175353			−0.0876763	+	0.996149i	$0.527944\pi$
$728$	32.6865	−	28.7208i	1.21144	−	1.06447i
$729$		0			0
$730$	−34.7852	+	3.26724i	−1.28746	+	0.120926i
$731$	−22.7932	+	13.1597i	−0.843038	+	0.486728i
$732$		0			0
$733$	−49.7495			−1.83754			−0.918770	−	0.394793i	$-0.870816\pi$
$733$	−49.7495			−1.83754			−0.918770	+	0.394793i	$0.870816\pi$
$734$	−10.5842	+	7.51233i	−0.390671	+	0.277285i
$735$		0			0
$736$	8.81520	−	13.4860i	0.324933	−	0.497101i
$737$	11.5420	−	19.9913i	0.425155	−	0.736390i
$738$		0			0
$739$	−18.1362	−	31.4129i	−0.667152	−	1.15554i	−0.978697	−	0.205310i	$-0.934180\pi$
$739$	−18.1362	−	31.4129i	−0.667152	−	1.15554i	0.311545	−	0.950231i	$-0.399154\pi$
$740$	−4.93630	−	5.73256i	−0.181462	−	0.210733i
$741$		0			0
$742$	−14.6568	−	6.72100i	−0.538069	−	0.246736i
$743$	−40.0642	+	23.1311i	−1.46981	+	0.848597i	−0.999426	−	0.0338625i	$-0.989219\pi$
$743$	−40.0642	+	23.1311i	−1.46981	+	0.848597i	−0.470387	+	0.882460i	$0.655886\pi$
$744$		0			0
$745$	20.0900	−	34.7969i	0.736041	−	1.27486i
$746$	−1.04869	+	2.28693i	−0.0383952	+	0.0837305i
$747$		0			0
$748$	−30.0292	+	5.69127i	−1.09798	+	0.208093i
$749$	59.0767			2.15861
$750$		0			0
$751$	−5.01579	−	8.68760i	−0.183029	−	0.317015i	0.759882	−	0.650061i	$-0.225257\pi$
$751$	−5.01579	−	8.68760i	−0.183029	−	0.317015i	−0.942911	+	0.333046i	$0.891923\pi$
$752$	7.07406	+	17.9923i	0.257964	+	0.656112i
$753$		0			0
$754$	−0.236613	−	23.6446i	−0.00861694	−	0.861086i
$755$			7.44254i			0.270862i
$756$		0			0
$757$	−12.5144	+	7.22517i	−0.454842	+	0.262603i	−0.709873	−	0.704330i	$-0.751248\pi$
$757$	−12.5144	+	7.22517i	−0.454842	+	0.262603i	0.255031	+	0.966933i	$0.417914\pi$
$758$	−12.9871	+	9.21783i	−0.471714	+	0.334807i
$759$		0			0
$760$	−47.2755	−	11.7017i	−1.71486	−	0.424465i
$761$	39.8657	+	23.0165i	1.44513	+	0.834347i	0.998186	−	0.0602132i	$-0.0191781\pi$
$761$	39.8657	+	23.0165i	1.44513	+	0.834347i	0.446947	+	0.894561i	$0.352511\pi$
$762$		0			0
$763$	25.3859	+	14.6566i	0.919032	+	0.530604i
$764$	6.58680	−	18.8423i	0.238302	−	0.681691i
$765$		0			0
$766$	19.9295	−	43.4614i	0.720083	−	1.57032i
$767$	−25.3102	+	11.9141i	−0.913900	+	0.430195i
$768$		0			0
$769$	−41.3732	+	23.8868i	−1.49196	+	0.861381i	−0.999958	−	0.00921592i	$-0.997066\pi$
$769$	−41.3732	+	23.8868i	−1.49196	+	0.861381i	−0.491998	+	0.870597i	$0.663733\pi$
$770$	37.6164	−	3.53316i	1.35560	−	0.127326i
$771$		0			0
$772$	10.6538	−	9.17396i	0.383439	−	0.330178i
$773$	14.9570	−	25.9063i	0.537966	−	0.931784i	−0.461048	−	0.887375i	$-0.652526\pi$
$773$	14.9570	−	25.9063i	0.537966	−	0.931784i	0.999013	−	0.0444085i	$-0.0141403\pi$
$774$		0			0
$775$			3.44589i			0.123780i
$776$	3.18678	−	12.8748i	0.114399	−	0.462177i
$777$		0			0
$778$	−41.8673	+	3.93243i	−1.50101	+	0.140985i
$779$		−	46.8113i		−	1.67719i
$780$		0			0
$781$			35.8267i			1.28198i
$782$	−2.15561	−	22.9500i	−0.0770844	−	0.820691i
$783$		0			0
$784$	35.0579	+	27.9229i	1.25207	+	0.997247i
$785$			41.6684i			1.48721i
$786$		0			0
$787$	−12.5521	+	21.7409i	−0.447435	+	0.774981i	−0.998218	−	0.0596677i	$-0.980996\pi$
$787$	−12.5521	+	21.7409i	−0.447435	+	0.774981i	0.550783	+	0.834649i	$0.314329\pi$
$788$	−29.9341	−	34.7627i	−1.06636	−	1.23837i
$789$		0			0
$790$	−0.595653	−	6.34171i	−0.0211924	−	0.225628i
$791$	−72.3579	+	41.7759i	−2.57275	+	1.48538i
$792$		0			0
$793$	3.24928	+	6.90271i	0.115385	+	0.245123i
$794$	24.4186	+	11.1973i	0.866583	+	0.397378i
$795$		0			0
$796$	0.0772789	−	0.221065i	0.00273908	−	0.00783545i
$797$	−3.08814	−	1.78294i	−0.109388	−	0.0631550i	0.444308	−	0.895874i	$-0.353450\pi$
$797$	−3.08814	−	1.78294i	−0.109388	−	0.0631550i	−0.553696	+	0.832719i	$0.686783\pi$
$798$		0			0
$799$	23.9544	+	13.8301i	0.847444	+	0.489272i
$800$	1.27218	+	2.51531i	0.0449783	+	0.0889295i
$801$		0			0
$802$	−10.0070	−	14.0991i	−0.353360	−	0.497855i
$803$	24.3650	−	14.0671i	0.859822	−	0.496419i
$804$		0			0
$805$			28.4949i			1.00431i
$806$	−30.7130	−	17.3247i	−1.08182	−	0.610237i
$807$		0			0
$808$	−23.0048	−	22.1400i	−0.809307	−	0.778882i
$809$	−1.68066	−	2.91098i	−0.0590887	−	0.102345i	0.834968	−	0.550299i	$-0.185486\pi$
$809$	−1.68066	−	2.91098i	−0.0590887	−	0.102345i	−0.894057	+	0.447954i	$0.852153\pi$
$810$		0			0
$811$	43.4005			1.52400			0.762000	−	0.647577i	$-0.224218\pi$
$811$	43.4005			1.52400			0.762000	+	0.647577i	$0.224218\pi$
$812$	38.8800	−	7.36872i	1.36442	−	0.258591i
$813$		0			0
$814$	5.53734	+	2.53919i	0.194084	+	0.0889986i
$815$	−0.0645684	+	0.111836i	−0.00226173	+	0.00391744i
$816$		0			0
$817$	29.2470	−	16.8857i	1.02322	−	0.590757i
$818$	−8.56703	+	18.6826i	−0.299539	+	0.653221i
$819$		0			0
$820$	−22.6540	+	19.5073i	−0.791111	+	0.681224i
$821$	2.76506	+	4.78922i	0.0965011	+	0.167145i	0.910234	−	0.414094i	$-0.135902\pi$
$821$	2.76506	+	4.78922i	0.0965011	+	0.167145i	−0.813733	+	0.581239i	$0.802568\pi$
$822$		0			0
$823$	24.7831	−	42.9256i	0.863884	−	1.49629i	−0.00426724	−	0.999991i	$-0.501358\pi$
$823$	24.7831	−	42.9256i	0.863884	−	1.49629i	0.868151	−	0.496300i	$-0.165308\pi$
$824$	−15.2100	−	52.7049i	−0.529865	−	1.83606i
$825$		0			0
$826$	−27.0968	−	38.1771i	−0.942818	−	1.32835i
$827$	49.4336			1.71898			0.859488	−	0.511156i	$-0.170783\pi$
$827$	49.4336			1.71898			0.859488	+	0.511156i	$0.170783\pi$
$828$		0			0
$829$	−43.7886	+	25.2814i	−1.52084	+	0.878059i	−0.521144	+	0.853469i	$0.674495\pi$
$829$	−43.7886	+	25.2814i	−1.52084	+	0.878059i	−0.999698	+	0.0245900i	$0.992172\pi$
$830$	−0.849172	−	9.04084i	−0.0294752	−	0.313812i
$831$		0			0
$832$	−28.8148	−	1.30721i	−0.998973	−	0.0453194i
$833$	64.1234			2.22174
$834$		0			0
$835$	−27.3361	+	15.7825i	−0.946003	+	0.546175i
$836$	38.5318	−	7.30272i	1.33265	−	0.252570i
$837$		0			0
$838$	−9.25020	−	13.0328i	−0.319543	−	0.450209i
$839$	−8.26161	−	4.76984i	−0.285222	−	0.164673i	0.350563	−	0.936539i	$-0.385990\pi$
$839$	−8.26161	−	4.76984i	−0.285222	−	0.164673i	−0.635785	+	0.771866i	$0.719324\pi$
$840$		0			0
$841$	−3.74761	+	6.49106i	−0.129228	+	0.223830i
$842$	1.28127	+	13.6412i	0.0441554	+	0.470108i
$843$		0			0
$844$	22.3019	−	19.2041i	0.767663	−	0.661033i
$845$	−10.6330	−	28.5683i	−0.365786	−	0.982780i
$846$		0			0
$847$	14.2977	−	8.25479i	0.491275	−	0.283638i
$848$	3.91115	+	9.94769i	0.134309	+	0.341605i
$849$		0			0
$850$	3.66577	+	1.68096i	0.125735	+	0.0576566i
$851$	−2.29719	+	3.97885i	−0.0787466	+	0.136393i
$852$		0			0
$853$	19.1280			0.654931			0.327466	−	0.944863i	$-0.393805\pi$
$853$	19.1280			0.654931			0.327466	+	0.944863i	$0.393805\pi$
$854$	−10.4118	+	7.38995i	−0.356285	+	0.252879i
$855$		0			0
$856$	−28.2173	−	27.1565i	−0.964447	−	0.928189i
$857$	21.6279			0.738796			0.369398	−	0.929271i	$-0.379564\pi$
$857$	21.6279			0.738796			0.369398	+	0.929271i	$0.379564\pi$
$858$		0			0
$859$			6.82379i			0.232825i	0.993201	+	0.116412i	$0.0371394\pi$
$859$			6.82379i			0.232825i	−0.993201	+	0.116412i	$0.962861\pi$
$860$	−20.3596	−	7.11719i	−0.694256	−	0.242694i
$861$		0			0
$862$	2.84584	+	4.00954i	0.0969296	+	0.136566i
$863$			33.7913i			1.15027i	0.818059	+	0.575134i	$0.195050\pi$
$863$			33.7913i			1.15027i	−0.818059	+	0.575134i	$0.804950\pi$
$864$		0			0
$865$	32.4583	+	18.7398i	1.10362	+	0.637173i
$866$	−16.7033	−	7.65940i	−0.567600	−	0.260277i
$867$		0			0
$868$	19.4738	−	55.7072i	0.660984	−	1.89082i
$869$	2.56459	+	4.44201i	0.0869979	+	0.150685i
$870$		0			0
$871$	2.60406	−	31.0598i	0.0882353	−	1.05242i
$872$	−5.38793	−	18.6700i	−0.182458	−	0.632246i
$873$		0			0
$874$	2.76595	+	29.4482i	0.0935598	+	0.996099i
$875$	39.0045	+	22.5193i	1.31859	+	0.761290i
$876$		0			0
$877$	10.6606	−	18.4647i	0.359983	−	0.623510i	−0.627974	−	0.778234i	$-0.716116\pi$
$877$	10.6606	−	18.4647i	0.359983	−	0.623510i	0.987958	+	0.154725i	$0.0494490\pi$
$878$	31.9037	−	22.6441i	1.07670	−	0.764202i
$879$		0			0
$880$	−19.5911	−	15.6040i	−0.660417	−	0.526010i
$881$	4.05760	+	7.02796i	0.136704	+	0.236778i	0.926247	−	0.376917i	$-0.123016\pi$
$881$	4.05760	+	7.02796i	0.136704	+	0.236778i	−0.789543	+	0.613695i	$0.789682\pi$
$882$		0			0
$883$			51.4630i			1.73187i	0.500157	+	0.865935i	$0.333276\pi$
$883$			51.4630i			1.73187i	−0.500157	+	0.865935i	$0.666724\pi$
$884$	−33.4124	+	24.2214i	−1.12378	+	0.814654i
$885$		0			0
$886$	38.0646	−	3.57526i	1.27880	−	0.120113i
$887$	20.3583	+	35.2616i	0.683564	+	1.18397i	0.973886	+	0.227038i	$0.0729043\pi$
$887$	20.3583	+	35.2616i	0.683564	+	1.18397i	−0.290322	+	0.956929i	$0.593762\pi$
$888$		0			0
$889$		−	14.0772i		−	0.472135i
$890$	33.3853	+	47.0370i	1.11908	+	1.57668i
$891$		0			0
$892$	19.1415	−	16.4827i	0.640906	−	0.551883i
$893$	−30.7369	−	17.7459i	−1.02857	−	0.593845i
$894$		0			0
$895$	−1.65049	+	0.952911i	−0.0551698	+	0.0318523i
$896$	−6.35159	−	47.8525i	−0.212192	−	1.59864i
$897$		0			0
$898$	2.26536	−	4.94019i	0.0755960	−	0.164856i
$899$	−16.0347	−	27.7730i	−0.534788	−	0.926281i
$900$		0			0
$901$	13.2440	+	7.64644i	0.441222	+	0.254740i
$902$	10.0344	−	21.8825i	0.334108	−	0.728608i
$903$		0			0
$904$	53.7645	+	13.3079i	1.78818	+	0.442613i
$905$		−	10.3295i		−	0.343366i
$906$		0			0
$907$	−21.6049	+	12.4736i	−0.717380	+	0.414180i	−0.813788	−	0.581162i	$-0.802598\pi$
$907$	−21.6049	+	12.4736i	−0.717380	+	0.414180i	0.0964076	+	0.995342i	$0.469265\pi$
$908$	−11.8900	+	34.0127i	−0.394583	+	1.12875i
$909$		0			0
$910$	43.9223	−	25.9480i	1.45601	−	0.860168i
$911$	5.75030			0.190516			0.0952580	−	0.995453i	$-0.469632\pi$
$911$	5.75030			0.190516			0.0952580	+	0.995453i	$0.469632\pi$
$912$		0			0
$913$	3.65612	+	6.33259i	0.121000	+	0.209578i
$914$	−3.26712	−	4.60310i	−0.108067	−	0.152257i
$915$		0			0
$916$	−10.0209	+	1.89920i	−0.331100	+	0.0627515i
$917$	25.5349	−	44.2278i	0.843237	−	1.46053i
$918$		0			0
$919$	−11.6516	+	20.1812i	−0.384351	+	0.665716i	−0.991679	−	0.128735i	$-0.958908\pi$
$919$	−11.6516	+	20.1812i	−0.384351	+	0.665716i	0.607328	+	0.794452i	$0.292242\pi$
$920$	13.0986	−	13.6103i	0.431848	−	0.448717i
$921$		0			0
$922$	7.27025	+	3.33383i	0.239433	+	0.109794i
$923$	20.6025	+	43.7677i	0.678141	+	1.44063i
$924$		0			0
$925$	−0.401895	−	0.696103i	−0.0132142	−	0.0228877i
$926$	16.3078	−	1.53173i	0.535909	−	0.0503359i
$927$		0			0
$928$	−21.9579	−	14.3529i	−0.720802	−	0.471156i
$929$	−3.29824	−	1.90424i	−0.108212	−	0.0624760i	0.444917	−	0.895572i	$-0.353233\pi$
$929$	−3.29824	−	1.90424i	−0.108212	−	0.0624760i	−0.553129	+	0.833096i	$0.686566\pi$
$930$		0			0
$931$	−82.2795			−2.69660
$932$	−30.0719	+	5.69935i	−0.985037	+	0.186688i
$933$		0			0
$934$	26.1840	−	2.45936i	0.856765	−	0.0804727i
$935$	−35.8336			−1.17189
$936$		0			0
$937$	55.3478			1.80813			0.904067	−	0.427391i	$-0.140567\pi$
$937$	55.3478			1.80813			0.904067	+	0.427391i	$0.140567\pi$
$938$	51.9335	−	4.87792i	1.69569	−	0.159270i
$939$		0			0
$940$	4.22071	+	22.2700i	0.137664	+	0.726367i
$941$	−45.3754			−1.47920			−0.739599	−	0.673048i	$-0.764985\pi$
$941$	−45.3754			−1.47920			−0.739599	+	0.673048i	$0.764985\pi$
$942$		0			0
$943$	15.7236	+	9.07804i	0.512032	+	0.295622i
$944$	−4.60685	+	30.6907i	−0.149940	+	0.998899i
$945$		0			0
$946$	17.2915	−	1.62412i	0.562194	−	0.0528047i
$947$	−16.5629	−	28.6878i	−0.538222	−	0.932229i	−0.999000	−	0.0447128i	$-0.985763\pi$
$947$	−16.5629	−	28.6878i	−0.538222	−	0.932229i	0.460778	−	0.887516i	$-0.347571\pi$
$948$		0			0
$949$	21.6761	−	31.1965i	0.703635	−	1.01268i
$950$	−4.70370	−	2.15692i	−0.152608	−	0.0699797i
$951$		0			0
$952$	−49.7620	−	47.8913i	−1.61280	−	1.55216i
$953$	27.5249	−	47.6746i	0.891620	−	1.54433i	0.0536867	−	0.998558i	$-0.482903\pi$
$953$	27.5249	−	47.6746i	0.891620	−	1.54433i	0.837933	−	0.545773i	$-0.183764\pi$
$954$		0			0
$955$	11.7010	−	20.2668i	0.378636	−	0.655817i
$956$	4.00450	+	21.1292i	0.129515	+	0.683368i
$957$		0			0
$958$	16.3643	+	23.0559i	0.528706	+	0.744902i
$959$	−18.4167	−	31.8987i	−0.594706	−	1.03006i
$960$		0			0
$961$	−16.8243			−0.542720
$962$	8.22490	−	0.0823070i	0.265181	−	0.00265368i
$963$		0			0
$964$	10.5276	+	3.68019i	0.339072	+	0.118531i
$965$	14.2751	−	8.24173i	0.459532	−	0.265311i
$966$		0			0
$967$			32.3383i			1.03993i	0.854188	+	0.519965i	$0.174055\pi$
$967$			32.3383i			1.03993i	−0.854188	+	0.519965i	$0.825945\pi$
$968$	−10.6237	−	2.62960i	−0.341459	−	0.0845184i
$969$		0			0
$970$	6.48167	−	14.1349i	0.208114	−	0.453845i
$971$	31.4063	+	18.1325i	1.00788	+	0.581898i	0.910569	−	0.413356i	$-0.135644\pi$
$971$	31.4063	+	18.1325i	1.00788	+	0.581898i	0.0973076	+	0.995254i	$0.468977\pi$
$972$		0			0
$973$	0.404588	+	0.700766i	0.0129705	+	0.0224655i
$974$	−2.89876	+	6.32148i	−0.0928822	+	0.202553i
$975$		0			0
$976$	8.37011	+	1.25640i	0.267921	+	0.0402163i
$977$	−17.6625	+	10.1975i	−0.565074	+	0.326246i	−0.755180	−	0.655518i	$-0.772450\pi$
$977$	−17.6625	+	10.1975i	−0.565074	+	0.326246i	0.190105	+	0.981764i	$0.439117\pi$
$978$		0			0
$979$	−40.2249	−	23.2239i	−1.28559	−	0.742238i
$980$	34.2877	+	39.8185i	1.09528	+	1.27196i
$981$		0			0
$982$	−5.93949	−	8.36824i	−0.189537	−	0.267041i
$983$		−	28.2445i		−	0.900860i	−0.892812	−	0.450430i	$-0.851271\pi$
$983$		−	28.2445i		−	0.900860i	0.892812	−	0.450430i	$-0.148729\pi$
$984$		0			0
$985$	−26.8923	−	46.5788i	−0.856860	−	1.48412i
$986$	−37.3671	+	3.50975i	−1.19001	+	0.111773i
$987$		0			0
$988$	42.8729	−	31.0795i	1.36397	−	0.988772i
$989$			13.0985i			0.416508i
$990$		0			0
$991$	−4.37500	−	7.57772i	−0.138977	−	0.240714i	0.788133	−	0.615505i	$-0.211048\pi$
$991$	−4.37500	−	7.57772i	−0.138977	−	0.240714i	−0.927109	+	0.374791i	$0.877715\pi$
$992$	−34.9090	+	17.6561i	−1.10836	+	0.560582i
$993$		0			0
$994$	−66.0177	+	46.8571i	−2.09395	+	1.48622i
$995$	0.137281	−	0.237777i	0.00435209	−	0.00753805i
$996$		0			0
$997$	−9.67774	−	5.58745i	−0.306497	−	0.176956i	0.338861	−	0.940837i	$-0.389958\pi$
$997$	−9.67774	−	5.58745i	−0.306497	−	0.176956i	−0.645358	+	0.763880i	$0.723292\pi$
$998$	1.55976	+	16.6062i	0.0493733	+	0.525660i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.f.829.16	yes	56
3.2	odd	2	inner	936.2.dg.f.829.13	yes	56
8.5	even	2	inner	936.2.dg.f.829.7	✓	56
13.4	even	6	inner	936.2.dg.f.901.7	yes	56
24.5	odd	2	inner	936.2.dg.f.829.22	yes	56
39.17	odd	6	inner	936.2.dg.f.901.22	yes	56
104.69	even	6	inner	936.2.dg.f.901.16	yes	56
312.173	odd	6	inner	936.2.dg.f.901.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.dg.f.829.7	✓	56	8.5	even	2	inner
936.2.dg.f.829.13	yes	56	3.2	odd	2	inner
936.2.dg.f.829.16	yes	56	1.1	even	1	trivial
936.2.dg.f.829.22	yes	56	24.5	odd	2	inner
936.2.dg.f.901.7	yes	56	13.4	even	6	inner
936.2.dg.f.901.13	yes	56	312.173	odd	6	inner
936.2.dg.f.901.16	yes	56	104.69	even	6	inner
936.2.dg.f.901.22	yes	56	39.17	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.132250 + 1.40802i) q^{2} +(-1.96502 + 0.372419i) q^{4} -2.34484 q^{5} +(3.69507 + 2.13335i) q^{7} +(-0.784245 - 2.71753i) q^{8} +(-0.310104 - 3.30158i) q^{10} +(1.33516 + 2.31256i) q^{11} +(2.96097 + 2.05735i) q^{13} +(-2.51512 + 5.48486i) q^{14} +(3.72261 - 1.46362i) q^{16} +(2.86144 - 4.95615i) q^{17} +(-3.67163 + 6.35946i) q^{19} +(4.60766 - 0.873264i) q^{20} +(-3.07955 + 2.18576i) q^{22} +(-1.42407 - 2.46656i) q^{23} +0.498285 q^{25} +(-2.50519 + 4.44117i) q^{26} +(-8.05539 - 2.81596i) q^{28} +(-4.01604 + 2.31866i) q^{29} +6.91551i q^{31} +(2.55312 + 5.04793i) q^{32} +(7.35677 + 3.37350i) q^{34} +(-8.66436 - 5.00237i) q^{35} +(-0.806558 - 1.39700i) q^{37} +(-9.43979 - 4.32869i) q^{38} +(1.83893 + 6.37217i) q^{40} +(-5.52067 + 3.18736i) q^{41} +(-3.98283 - 2.29949i) q^{43} +(-3.48486 - 4.04699i) q^{44} +(3.28462 - 2.33131i) q^{46} +4.83325i q^{47} +(5.60238 + 9.70360i) q^{49} +(0.0658980 + 0.701593i) q^{50} +(-6.58455 - 2.94001i) q^{52} +2.67224i q^{53} +(-3.13074 - 5.42260i) q^{55} +(2.89960 - 11.7145i) q^{56} +(-3.79583 - 5.34801i) q^{58} +(-3.87932 + 6.71918i) q^{59} +(1.83248 + 1.05798i) q^{61} +(-9.73715 + 0.914574i) q^{62} +(-6.76992 + 4.26242i) q^{64} +(-6.94300 - 4.82416i) q^{65} +(-4.32233 - 7.48649i) q^{67} +(-3.77701 + 10.8046i) q^{68} +(5.89756 - 12.8611i) q^{70} +(11.6191 + 6.70831i) q^{71} -10.5359i q^{73} +(1.86033 - 1.32040i) q^{74} +(4.84645 - 13.8638i) q^{76} +11.3935i q^{77} +1.92081 q^{79} +(-8.72893 + 3.43196i) q^{80} +(-5.21796 - 7.35166i) q^{82} +2.73834 q^{83} +(-6.70962 + 11.6214i) q^{85} +(2.71099 - 5.91199i) q^{86} +(5.23736 - 5.44195i) q^{88} +(-15.0637 + 8.69704i) q^{89} +(6.55193 + 13.9188i) q^{91} +(3.71692 + 4.31649i) q^{92} +(-6.80530 + 0.639196i) q^{94} +(8.60940 - 14.9119i) q^{95} +(4.06104 + 2.34464i) q^{97} +(-12.9219 + 9.17153i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{10} - 4 q^{16} + 64 q^{25} - 48 q^{28} - 48 q^{40} + 20 q^{49} - 12 q^{52} + 16 q^{55} + 12 q^{58} - 72 q^{64} - 84 q^{76} + 80 q^{79} - 12 q^{82} - 12 q^{88} - 24 q^{94} + 24 q^{97}+O(q^{100}) \) 56 * q - 4 * q^10 - 4 * q^16 + 64 * q^25 - 48 * q^28 - 48 * q^40 + 20 * q^49 - 12 * q^52 + 16 * q^55 + 12 * q^58 - 72 * q^64 - 84 * q^76 + 80 * q^79 - 12 * q^82 - 12 * q^88 - 24 * q^94 + 24 * q^97

Introduction

L-functions

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