LMFDB - Embedded newform 99.2.j.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(8,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 $ x^16 + 2x^14 - 16x^12 - 72x^10 + 26x^8 + 360x^6 + 725x^4 + 1000*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.3
Root			$0.752864 - 0.902863i$ of defining polynomial
Character	$\chi$	$=$	99.8
Dual form			99.2.j.a.62.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.205228 - 0.149107i) q^{2} +(-0.598148 + 1.84091i) q^{4} +(1.71735 - 2.36373i) q^{5} +(2.58586 + 0.840196i) q^{7} +(0.308515 + 0.949513i) q^{8} -0.741170i q^{10} +(-2.71994 + 1.89788i) q^{11} +(-1.67869 - 2.31052i) q^{13} +(0.655969 - 0.213137i) q^{14} +(-2.92705 - 2.12663i) q^{16} +(-3.60998 - 2.62280i) q^{17} +(-1.81761 + 0.590579i) q^{19} +(3.32418 + 4.57534i) q^{20} +(-0.275220 + 0.795058i) q^{22} -0.816370i q^{23} +(-1.09283 - 3.36340i) q^{25} +(-0.689029 - 0.223879i) q^{26} +(-3.09345 + 4.25777i) q^{28} +(-2.95006 + 9.07936i) q^{29} +(4.84281 - 3.51851i) q^{31} -2.91456 q^{32} -1.13195 q^{34} +(6.42681 - 4.66935i) q^{35} +(1.83750 - 5.65524i) q^{37} +(-0.284966 + 0.392222i) q^{38} +(2.77422 + 0.901398i) q^{40} +(-2.60604 - 8.02058i) q^{41} +11.8763i q^{43} +(-1.86690 - 6.14238i) q^{44} +(-0.121726 - 0.167542i) q^{46} +(7.34041 - 2.38504i) q^{47} +(0.317615 + 0.230761i) q^{49} +(-0.725785 - 0.527314i) q^{50} +(5.25758 - 1.70829i) q^{52} +(6.14564 + 8.45874i) q^{53} +(-0.185009 + 9.68851i) q^{55} +2.71452i q^{56} +(0.748358 + 2.30321i) q^{58} +(-0.0887332 - 0.0288312i) q^{59} +(1.26024 - 1.73457i) q^{61} +(0.469246 - 1.44419i) q^{62} +(5.25595 - 3.81867i) q^{64} -8.34434 q^{65} -1.40778 q^{67} +(6.98766 - 5.07683i) q^{68} +(0.622728 - 1.91656i) q^{70} +(2.12141 - 2.91987i) q^{71} +(-1.67338 - 0.543714i) q^{73} +(-0.466129 - 1.43460i) q^{74} -3.69932i q^{76} +(-8.62796 + 2.62237i) q^{77} +(-4.19260 - 5.77063i) q^{79} +(-10.0535 + 3.26659i) q^{80} +(-1.73075 - 1.25747i) q^{82} +(6.33808 + 4.60488i) q^{83} +(-12.3992 + 4.02874i) q^{85} +(1.77084 + 2.43735i) q^{86} +(-2.64120 - 1.99709i) q^{88} +2.06830i q^{89} +(-2.39957 - 7.38512i) q^{91} +(1.50286 + 0.488310i) q^{92} +(1.15083 - 1.58398i) q^{94} +(-1.72551 + 5.31057i) q^{95} +(-1.35141 + 0.981858i) q^{97} +0.0995913 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70}+ \cdots + 60 q^{97}+O(q^{100}) $ 16 * q - 4 * q^4 - 20 * q^16 - 48 * q^22 - 32 * q^25 + 40 * q^28 + 16 * q^31 + 40 * q^34 - 12 * q^37 + 60 * q^40 - 40 * q^46 - 24 * q^49 - 40 * q^52 + 16 * q^55 + 12 * q^58 + 36 * q^64 + 96 * q^67 + 76 * q^70 - 20 * q^73 - 12 * q^82 - 100 * q^85 - 12 * q^88 - 72 * q^91 - 80 * q^94 + 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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 $

$2$	0.205228	−	0.149107i	0.145118	−	0.105434i	−0.512857	−	0.858474i	$-0.671413\pi$
$2$	0.205228	−	0.149107i	0.145118	−	0.105434i	0.657975	+	0.753039i	$0.271413\pi$
$3$		0			0
$3$		0			0
$4$	−0.598148	+	1.84091i	−0.299074	+	0.920456i
$5$	1.71735	−	2.36373i	0.768021	−	1.05709i	−0.228483	−	0.973548i	$-0.573376\pi$
$5$	1.71735	−	2.36373i	0.768021	−	1.05709i	0.996504	−	0.0835427i	$-0.0266235\pi$
$6$		0			0
$7$	2.58586	+	0.840196i	0.977363	+	0.317564i	0.753785	−	0.657122i	$-0.228226\pi$
$7$	2.58586	+	0.840196i	0.977363	+	0.317564i	0.223578	+	0.974686i	$0.428226\pi$
$8$	0.308515	+	0.949513i	0.109077	+	0.335704i
$9$		0			0
$10$		−	0.741170i		−	0.234379i
$11$	−2.71994	+	1.89788i	−0.820092	+	0.572232i
$11$	−2.71994	+	1.89788i	−0.820092	+	0.572232i
$12$		0			0
$13$	−1.67869	−	2.31052i	−0.465586	−	0.640824i	0.510070	−	0.860133i	$-0.329620\pi$
$13$	−1.67869	−	2.31052i	−0.465586	−	0.640824i	−0.975655	+	0.219309i	$0.929620\pi$
$14$	0.655969	−	0.213137i	0.175315	−	0.0569633i
$15$		0			0
$16$	−2.92705	−	2.12663i	−0.731763	−	0.531657i
$17$	−3.60998	−	2.62280i	−0.875549	−	0.636124i	0.0565211	−	0.998401i	$-0.481999\pi$
$17$	−3.60998	−	2.62280i	−0.875549	−	0.636124i	−0.932070	+	0.362278i	$0.881999\pi$
$18$		0			0
$19$	−1.81761	+	0.590579i	−0.416989	+	0.135488i	−0.509995	−	0.860178i	$-0.670353\pi$
$19$	−1.81761	+	0.590579i	−0.416989	+	0.135488i	0.0930053	+	0.995666i	$0.470353\pi$
$20$	3.32418	+	4.57534i	0.743310	+	1.02308i
$21$		0			0
$22$	−0.275220	+	0.795058i	−0.0586771	+	0.169507i
$23$		−	0.816370i		−	0.170225i	−0.996371	−	0.0851124i	$-0.972875\pi$
$23$		−	0.816370i		−	0.170225i	0.996371	−	0.0851124i	$-0.0271249\pi$
$24$		0			0
$25$	−1.09283	−	3.36340i	−0.218567	−	0.672680i
$26$	−0.689029	−	0.223879i	−0.135130	−	0.0439063i
$27$		0			0
$28$	−3.09345	+	4.25777i	−0.584608	+	0.804644i
$29$	−2.95006	+	9.07936i	−0.547813	+	1.68599i	0.166394	+	0.986059i	$0.446788\pi$
$29$	−2.95006	+	9.07936i	−0.547813	+	1.68599i	−0.714207	+	0.699935i	$0.753212\pi$
$30$		0			0
$31$	4.84281	−	3.51851i	0.869795	−	0.631943i	−0.0607369	−	0.998154i	$-0.519345\pi$
$31$	4.84281	−	3.51851i	0.869795	−	0.631943i	0.930532	+	0.366211i	$0.119345\pi$
$32$	−2.91456			−0.515226
$33$		0			0
$34$	−1.13195			−0.194127
$35$	6.42681	−	4.66935i	1.08633	−	0.789265i
$36$		0			0
$37$	1.83750	−	5.65524i	0.302083	−	0.929717i	−0.678666	−	0.734447i	$-0.737442\pi$
$37$	1.83750	−	5.65524i	0.302083	−	0.929717i	0.980750	−	0.195270i	$-0.0625583\pi$
$38$	−0.284966	+	0.392222i	−0.0462275	+	0.0636267i
$39$		0			0
$40$	2.77422	+	0.901398i	0.438642	+	0.142524i
$41$	−2.60604	−	8.02058i	−0.406996	−	1.25260i	−0.919217	−	0.393751i	$-0.871177\pi$
$41$	−2.60604	−	8.02058i	−0.406996	−	1.25260i	0.512221	−	0.858853i	$-0.328823\pi$
$42$		0			0
$43$			11.8763i			1.81112i	0.424214	+	0.905562i	$0.360550\pi$
$43$			11.8763i			1.81112i	−0.424214	+	0.905562i	$0.639450\pi$
$44$	−1.86690	−	6.14238i	−0.281446	−	0.925998i
$45$		0			0
$46$	−0.121726	−	0.167542i	−0.0179475	−	0.0247027i
$47$	7.34041	−	2.38504i	1.07071	−	0.347894i	0.279945	−	0.960016i	$-0.409684\pi$
$47$	7.34041	−	2.38504i	1.07071	−	0.347894i	0.790764	+	0.612122i	$0.209684\pi$
$48$		0			0
$49$	0.317615	+	0.230761i	0.0453735	+	0.0329658i
$50$	−0.725785	−	0.527314i	−0.102641	−	0.0745734i
$51$		0			0
$52$	5.25758	−	1.70829i	0.729094	−	0.236897i
$53$	6.14564	+	8.45874i	0.844168	+	1.16190i	0.985118	+	0.171881i	$0.0549845\pi$
$53$	6.14564	+	8.45874i	0.844168	+	1.16190i	−0.140950	+	0.990017i	$0.545016\pi$
$54$		0			0
$55$	−0.185009	+	9.68851i	−0.0249466	+	1.30640i
$56$			2.71452i			0.362743i
$57$		0			0
$58$	0.748358	+	2.30321i	0.0982642	+	0.302426i
$59$	−0.0887332	−	0.0288312i	−0.0115521	−	0.00375350i	0.303235	−	0.952916i	$-0.401933\pi$
$59$	−0.0887332	−	0.0288312i	−0.0115521	−	0.00375350i	−0.314787	+	0.949162i	$0.601933\pi$
$60$		0			0
$61$	1.26024	−	1.73457i	0.161357	−	0.222089i	−0.720681	−	0.693267i	$-0.756171\pi$
$61$	1.26024	−	1.73457i	0.161357	−	0.222089i	0.882038	+	0.471177i	$0.156171\pi$
$62$	0.469246	−	1.44419i	0.0595943	−	0.183412i
$63$		0			0
$64$	5.25595	−	3.81867i	0.656994	−	0.477334i
$65$	−8.34434			−1.03499
$66$		0			0
$67$	−1.40778			−0.171988			−0.0859941	−	0.996296i	$-0.527407\pi$
$67$	−1.40778			−0.171988			−0.0859941	+	0.996296i	$0.527407\pi$
$68$	6.98766	−	5.07683i	0.847378	−	0.615656i
$69$		0			0
$70$	0.622728	−	1.91656i	0.0744303	−	0.229073i
$71$	2.12141	−	2.91987i	0.251765	−	0.346525i	−0.664363	−	0.747410i	$-0.731297\pi$
$71$	2.12141	−	2.91987i	0.251765	−	0.346525i	0.916128	+	0.400885i	$0.131297\pi$
$72$		0			0
$73$	−1.67338	−	0.543714i	−0.195854	−	0.0636369i	0.209447	−	0.977820i	$-0.432833\pi$
$73$	−1.67338	−	0.543714i	−0.195854	−	0.0636369i	−0.405302	+	0.914183i	$0.632833\pi$
$74$	−0.466129	−	1.43460i	−0.0541863	−	0.166768i
$75$		0			0
$76$		−	3.69932i		−	0.424341i
$77$	−8.62796	+	2.62237i	−0.983247	+	0.298846i
$78$		0			0
$79$	−4.19260	−	5.77063i	−0.471705	−	0.649246i	0.505180	−	0.863014i	$-0.331426\pi$
$79$	−4.19260	−	5.77063i	−0.471705	−	0.649246i	−0.976884	+	0.213768i	$0.931426\pi$
$80$	−10.0535	+	3.26659i	−1.12402	+	0.365216i
$81$		0			0
$82$	−1.73075	−	1.25747i	−0.191130	−	0.138864i
$83$	6.33808	+	4.60488i	0.695695	+	0.505452i	0.878527	−	0.477692i	$-0.158527\pi$
$83$	6.33808	+	4.60488i	0.695695	+	0.505452i	−0.182833	+	0.983144i	$0.558527\pi$
$84$		0			0
$85$	−12.3992	+	4.02874i	−1.34488	+	0.436978i
$86$	1.77084	+	2.43735i	0.190955	+	0.262826i
$87$		0			0
$88$	−2.64120	−	1.99709i	−0.281553	−	0.212890i
$89$			2.06830i			0.219240i	0.993974	+	0.109620i	$0.0349633\pi$
$89$			2.06830i			0.219240i	−0.993974	+	0.109620i	$0.965037\pi$
$90$		0			0
$91$	−2.39957	−	7.38512i	−0.251543	−	0.774171i
$92$	1.50286	+	0.488310i	0.156684	+	0.0509099i
$93$		0			0
$94$	1.15083	−	1.58398i	0.118699	−	0.163375i
$95$	−1.72551	+	5.31057i	−0.177034	+	0.544853i
$96$		0			0
$97$	−1.35141	+	0.981858i	−0.137215	+	0.0996926i	−0.654275	−	0.756256i	$-0.727026\pi$
$97$	−1.35141	+	0.981858i	−0.137215	+	0.0996926i	0.517060	+	0.855949i	$0.327026\pi$
$98$	0.0995913			0.0100602
$99$		0			0
$100$	6.84540			0.684540
$101$	−7.31972	+	5.31809i	−0.728339	+	0.529170i	−0.889038	−	0.457834i	$-0.848625\pi$
$101$	−7.31972	+	5.31809i	−0.728339	+	0.529170i	0.160698	+	0.987004i	$0.448625\pi$
$102$		0			0
$103$	−5.12132	+	15.7618i	−0.504618	+	1.55306i	0.296793	+	0.954942i	$0.404083\pi$
$103$	−5.12132	+	15.7618i	−0.504618	+	1.55306i	−0.801411	+	0.598114i	$0.795917\pi$
$104$	1.67597	−	2.30677i	0.164342	−	0.226198i
$105$		0			0
$106$	2.52251	+	0.819613i	0.245008	+	0.0796079i
$107$	2.19803	+	6.76484i	0.212492	+	0.653982i	0.999322	+	0.0368130i	$0.0117206\pi$
$107$	2.19803	+	6.76484i	0.212492	+	0.653982i	−0.786830	+	0.617169i	$0.788279\pi$
$108$		0			0
$109$		−	8.62045i		−	0.825690i	−0.910801	−	0.412845i	$-0.864535\pi$
$109$		−	8.62045i		−	0.825690i	0.910801	−	0.412845i	$-0.135465\pi$
$110$	1.40665	+	2.01594i	0.134119	+	0.192212i
$111$		0			0
$112$	−5.78216	−	7.95845i	−0.546362	−	0.752003i
$113$	10.8495	−	3.52523i	1.02064	−	0.331626i	0.249556	−	0.968360i	$-0.419715\pi$
$113$	10.8495	−	3.52523i	1.02064	−	0.331626i	0.771083	+	0.636735i	$0.219715\pi$
$114$		0			0
$115$	−1.92967	−	1.40199i	−0.179943	−	0.130736i
$116$	−14.9497	−	10.8616i	−1.38805	−	1.00847i
$117$		0			0
$118$	−0.0225094	+	0.00731376i	−0.00207216	+	0.000673286i
$119$	−7.13123	−	9.81529i	−0.653719	−	0.899767i
$120$		0			0
$121$	3.79611	−	10.3242i	0.345101	−	0.938566i
$122$		−	0.543892i		−	0.0492417i
$123$		0			0
$124$	3.58054	+	11.0198i	0.321542	+	0.989606i
$125$	4.06670	+	1.32135i	0.363737	+	0.118185i
$126$		0			0
$127$	−1.69463	+	2.33246i	−0.150374	+	0.206973i	−0.877558	−	0.479470i	$-0.840829\pi$
$127$	−1.69463	+	2.33246i	−0.150374	+	0.206973i	0.727184	+	0.686443i	$0.240829\pi$
$128$	2.31057	−	7.11122i	0.204228	−	0.628549i
$129$		0			0
$130$	−1.71249	+	1.24420i	−0.150195	+	0.109123i
$131$	2.10155			0.183613			0.0918067	−	0.995777i	$-0.470736\pi$
$131$	2.10155			0.183613			0.0918067	+	0.995777i	$0.470736\pi$
$132$		0			0
$133$	−5.19630			−0.450576
$134$	−0.288916	+	0.209910i	−0.0249586	+	0.0181335i
$135$		0			0
$136$	1.37665	−	4.23690i	0.118047	−	0.363311i
$137$	2.98245	−	4.10498i	0.254808	−	0.350712i	−0.662380	−	0.749168i	$-0.730454\pi$
$137$	2.98245	−	4.10498i	0.254808	−	0.350712i	0.917188	+	0.398455i	$0.130454\pi$
$138$		0			0
$139$	16.6282	+	5.40283i	1.41039	+	0.458262i	0.912535	−	0.409000i	$-0.134122\pi$
$139$	16.6282	+	5.40283i	1.41039	+	0.458262i	0.497852	+	0.867262i	$0.334122\pi$
$140$	4.75168	+	14.6242i	0.401590	+	1.23597i
$141$		0			0
$142$		−	0.915555i		−	0.0768317i
$143$	8.95103	+	3.09852i	0.748523	+	0.259111i
$144$		0			0
$145$	16.3948	+	22.5656i	1.36152	+	1.87397i
$146$	−0.424495	+	0.137927i	−0.0351315	+	0.0114149i
$147$		0			0
$148$	9.31171	+	6.76535i	0.765418	+	0.556108i
$149$	4.57623	+	3.32483i	0.374900	+	0.272381i	0.759240	−	0.650811i	$-0.225571\pi$
$149$	4.57623	+	3.32483i	0.374900	+	0.272381i	−0.384340	+	0.923192i	$0.625571\pi$
$150$		0			0
$151$	8.72640	−	2.83538i	0.710145	−	0.230740i	0.0683995	−	0.997658i	$-0.478211\pi$
$151$	8.72640	−	2.83538i	0.710145	−	0.230740i	0.641745	+	0.766918i	$0.278211\pi$
$152$	−1.12152	−	1.54365i	−0.0909677	−	0.125206i
$153$		0			0
$154$	−1.37968	+	1.82467i	−0.111178	+	0.147036i
$155$		−	17.4896i		−	1.40480i
$156$		0			0
$157$	−0.943653	−	2.90426i	−0.0753117	−	0.231785i	0.906313	−	0.422607i	$-0.138885\pi$
$157$	−0.943653	−	2.90426i	−0.0753117	−	0.231785i	−0.981625	+	0.190821i	$0.938885\pi$
$158$	−1.72088	−	0.559147i	−0.136906	−	0.0444833i
$159$		0			0
$160$	−5.00531	+	6.88922i	−0.395705	+	0.544641i
$161$	0.685911	−	2.11102i	0.0540573	−	0.166371i
$162$		0			0
$163$	−6.39488	+	4.64615i	−0.500885	+	0.363914i	−0.809355	−	0.587320i	$-0.800183\pi$
$163$	−6.39488	+	4.64615i	−0.500885	+	0.363914i	0.308470	+	0.951234i	$0.400183\pi$
$164$	16.3240			1.27469
$165$		0			0
$166$	1.98737			0.154250
$167$	−13.3065	+	9.66777i	−1.02969	+	0.748115i	−0.968247	−	0.249996i	$-0.919571\pi$
$167$	−13.3065	+	9.66777i	−1.02969	+	0.748115i	−0.0614446	+	0.998110i	$0.519571\pi$
$168$		0			0
$169$	1.49672	−	4.60642i	0.115132	−	0.354340i
$170$	−1.94394	+	2.67561i	−0.149094	+	0.205210i
$171$		0			0
$172$	−21.8633	−	7.10381i	−1.66706	−	0.541660i
$173$	−4.79669	−	14.7627i	−0.364686	−	1.12239i	−0.950178	−	0.311709i	$-0.899099\pi$
$173$	−4.79669	−	14.7627i	−0.364686	−	1.12239i	0.585492	−	0.810678i	$-0.300901\pi$
$174$		0			0
$175$		−	9.61547i		−	0.726861i
$176$	11.9975	+	0.229100i	0.904344	+	0.0172691i
$177$		0			0
$178$	0.308398	+	0.424473i	0.0231154	+	0.0318156i
$179$	−4.93538	+	1.60360i	−0.368888	+	0.119859i	−0.487594	−	0.873071i	$-0.662125\pi$
$179$	−4.93538	+	1.60360i	−0.368888	+	0.119859i	0.118706	+	0.992929i	$0.462125\pi$
$180$		0			0
$181$	−4.29773	−	3.12248i	−0.319448	−	0.232092i	0.416492	−	0.909139i	$-0.363259\pi$
$181$	−4.29773	−	3.12248i	−0.319448	−	0.232092i	−0.735940	+	0.677047i	$0.763259\pi$
$182$	−1.59363	−	1.15784i	−0.118128	−	0.0858247i
$183$		0			0
$184$	0.775154	−	0.251863i	0.0571451	−	0.0185676i
$185$	−10.2118	−	14.0554i	−0.750788	−	1.03337i
$186$		0			0
$187$	14.7967	+	0.282553i	1.08204	+	0.0206624i
$188$			14.9396i			1.08959i
$189$		0			0
$190$	0.437719	+	1.34716i	0.0317555	+	0.0977334i
$191$	−10.3662	−	3.36817i	−0.750069	−	0.243712i	−0.0910582	−	0.995846i	$-0.529025\pi$
$191$	−10.3662	−	3.36817i	−0.750069	−	0.243712i	−0.659011	+	0.752133i	$0.729025\pi$
$192$		0			0
$193$	9.03216	−	12.4317i	0.650149	−	0.894853i	−0.348956	−	0.937139i	$-0.613464\pi$
$193$	9.03216	−	12.4317i	0.650149	−	0.894853i	0.999106	+	0.0422855i	$0.0134639\pi$
$194$	−0.130946	+	0.403009i	−0.00940134	+	0.0289344i
$195$		0			0
$196$	−0.614791	+	0.446672i	−0.0439136	+	0.0319051i
$197$	7.24149			0.515935			0.257967	−	0.966154i	$-0.416947\pi$
$197$	7.24149			0.515935			0.257967	+	0.966154i	$0.416947\pi$
$198$		0			0
$199$	−11.3726			−0.806181			−0.403090	−	0.915160i	$-0.632064\pi$
$199$	−11.3726			−0.806181			−0.403090	+	0.915160i	$0.632064\pi$
$200$	2.85643	−	2.07532i	0.201980	−	0.146747i
$201$		0			0
$202$	−0.709247	+	2.18284i	−0.0499024	+	0.153584i
$203$	−15.2569	+	20.9993i	−1.07082	+	1.47386i
$204$		0			0
$205$	−23.4339	−	7.61415i	−1.63670	−	0.531795i
$206$	1.29915	+	3.99838i	0.0905162	+	0.278580i
$207$		0			0
$208$			10.3330i			0.716463i
$209$	3.82295	−	5.05595i	0.264439	−	0.349727i
$210$		0			0
$211$	−2.17376	−	2.99193i	−0.149648	−	0.205973i	0.727611	−	0.685990i	$-0.240631\pi$
$211$	−2.17376	−	2.99193i	−0.149648	−	0.205973i	−0.877259	+	0.480017i	$0.840631\pi$
$212$	−19.2478	+	6.25399i	−1.32194	+	0.429526i
$213$		0			0
$214$	1.45978	+	1.06059i	0.0997885	+	0.0725006i
$215$	28.0724	+	20.3958i	1.91452	+	1.39098i
$216$		0			0
$217$	15.4791	−	5.02946i	1.05079	−	0.341422i
$218$	−1.28537	−	1.76916i	−0.0870560	−	0.119822i
$219$		0			0
$220$	−17.7250	−	6.13575i	−1.19502	−	0.413672i
$221$			12.7438i			0.857243i
$222$		0			0
$223$	−0.0875209	−	0.269362i	−0.00586083	−	0.0180378i	0.948083	−	0.318022i	$-0.103019\pi$
$223$	−0.0875209	−	0.269362i	−0.00586083	−	0.0180378i	−0.953944	+	0.299984i	$0.903019\pi$
$224$	−7.53664	−	2.44880i	−0.503563	−	0.163618i
$225$		0			0
$226$	1.70099	−	2.34121i	0.113148	−	0.155735i
$227$	5.64140	−	17.3625i	0.374433	−	1.15239i	−0.569427	−	0.822042i	$-0.692835\pi$
$227$	5.64140	−	17.3625i	0.374433	−	1.15239i	0.943860	−	0.330345i	$-0.107165\pi$
$228$		0			0
$229$	−21.3385	+	15.5033i	−1.41009	+	1.02449i	−0.416777	+	0.909009i	$0.636840\pi$
$229$	−21.3385	+	15.5033i	−1.41009	+	1.02449i	−0.993310	+	0.115479i	$0.963160\pi$
$230$	−0.605069			−0.0398971
$231$		0			0
$232$	−9.53111			−0.625748
$233$	−8.73916	+	6.34937i	−0.572521	+	0.415961i	−0.836020	−	0.548699i	$-0.815123\pi$
$233$	−8.73916	+	6.34937i	−0.572521	+	0.415961i	0.263499	+	0.964660i	$0.415123\pi$
$234$		0			0
$235$	6.96844	−	21.4467i	0.454571	−	1.39903i
$236$	0.106151	−	0.146105i	0.00690986	−	0.00951060i
$237$		0			0
$238$	−2.92705	−	0.951057i	−0.189733	−	0.0616478i
$239$	−2.29393	−	7.06000i	−0.148382	−	0.456673i	0.849048	−	0.528315i	$-0.177176\pi$
$239$	−2.29393	−	7.06000i	−0.148382	−	0.456673i	−0.997430	+	0.0716420i	$0.977176\pi$
$240$		0			0
$241$		−	2.66873i		−	0.171908i	−0.996299	−	0.0859539i	$-0.972606\pi$
$241$		−	2.66873i		−	0.171908i	0.996299	−	0.0859539i	$-0.0273938\pi$
$242$	−0.760344	−	2.68484i	−0.0488767	−	0.172588i
$243$		0			0
$244$	2.43938	+	3.35752i	0.156165	+	0.214943i
$245$	1.09091	−	0.354458i	0.0696957	−	0.0226455i
$246$		0			0
$247$	4.41576	+	3.20824i	0.280968	+	0.204135i
$248$	4.83495	+	3.51280i	0.307020	+	0.223063i
$249$		0			0
$250$	1.03162	−	0.335194i	0.0652455	−	0.0211996i
$251$	−14.2630	−	19.6313i	−0.900271	−	1.23912i	−0.970382	−	0.241577i	$-0.922335\pi$
$251$	−14.2630	−	19.6313i	−0.900271	−	1.23912i	0.0701107	−	0.997539i	$-0.477665\pi$
$252$		0			0
$253$	1.54937	+	2.22047i	0.0974081	+	0.139600i
$254$			0.731367i			0.0458901i
$255$		0			0
$256$	3.42906	+	10.5535i	0.214316	+	0.659597i
$257$	15.9360	+	5.17791i	0.994059	+	0.322989i	0.760489	−	0.649351i	$-0.224959\pi$
$257$	15.9360	+	5.17791i	0.994059	+	0.322989i	0.233570	+	0.972340i	$0.424959\pi$
$258$		0			0
$259$	9.50303	−	13.0798i	0.590490	−	0.812739i
$260$	4.99116	−	15.3612i	0.309538	−	0.952661i
$261$		0			0
$262$	0.431296	−	0.313355i	0.0266456	−	0.0193591i
$263$	−10.9146			−0.673021			−0.336511	−	0.941680i	$-0.609247\pi$
$263$	−10.9146			−0.673021			−0.336511	+	0.941680i	$0.609247\pi$
$264$		0			0
$265$	30.5484			1.87657
$266$	−1.06642	+	0.774802i	−0.0653866	+	0.0475062i
$267$		0			0
$268$	0.842064	−	2.59161i	0.0514373	−	0.158308i
$269$	−9.22041	+	12.6908i	−0.562178	+	0.773772i	−0.991601	−	0.129331i	$-0.958717\pi$
$269$	−9.22041	+	12.6908i	−0.562178	+	0.773772i	0.429423	+	0.903103i	$0.358717\pi$
$270$		0			0
$271$	−2.76289	−	0.897717i	−0.167834	−	0.0545324i	0.223895	−	0.974613i	$-0.428123\pi$
$271$	−2.76289	−	0.897717i	−0.167834	−	0.0545324i	−0.391728	+	0.920081i	$0.628123\pi$
$272$	4.98887	+	15.3542i	0.302495	+	0.930983i
$273$		0			0
$274$		−	1.28716i		−	0.0777601i
$275$	9.35577	+	7.07416i	0.564174	+	0.426588i
$276$		0			0
$277$	12.4111	+	17.0824i	0.745709	+	1.02638i	0.998270	+	0.0587992i	$0.0187272\pi$
$277$	12.4111	+	17.0824i	0.745709	+	1.02638i	−0.252561	+	0.967581i	$0.581273\pi$
$278$	4.21817	−	1.37057i	0.252989	−	0.0822011i
$279$		0			0
$280$	6.41638	+	4.66177i	0.383452	+	0.278594i
$281$	2.50015	+	1.81647i	0.149147	+	0.108361i	0.659856	−	0.751392i	$-0.270617\pi$
$281$	2.50015	+	1.81647i	0.149147	+	0.108361i	−0.510709	+	0.859753i	$0.670617\pi$
$282$		0			0
$283$	−21.3272	+	6.92961i	−1.26777	+	0.411923i	−0.864256	−	0.503052i	$-0.832211\pi$
$283$	−21.3272	+	6.92961i	−1.26777	+	0.411923i	−0.403512	+	0.914975i	$0.632211\pi$
$284$	4.10631	+	5.65185i	0.243664	+	0.335375i
$285$		0			0
$286$	2.29901	−	0.698757i	0.135943	−	0.0413183i
$287$		−	22.9297i		−	1.35350i
$288$		0			0
$289$	0.899570	+	2.76859i	0.0529159	+	0.162858i
$290$	6.72935	+	2.18650i	0.395161	+	0.128396i
$291$		0			0
$292$	2.00186	−	2.75532i	0.117150	−	0.161243i
$293$	6.40930	−	19.7258i	0.374435	−	1.15239i	−0.569423	−	0.822044i	$-0.692833\pi$
$293$	6.40930	−	19.7258i	0.374435	−	1.15239i	0.943859	−	0.330349i	$-0.107167\pi$
$294$		0			0
$295$	−0.220535	+	0.160228i	−0.0128400	+	0.00932883i
$296$	5.93663			0.345059
$297$		0			0
$298$	1.43492			0.0831229
$299$	−1.88624	+	1.37043i	−0.109084	+	0.0792543i
$300$		0			0
$301$	−9.97845	+	30.7105i	−0.575148	+	1.77012i
$302$	1.36813	−	1.88306i	0.0787268	−	0.108358i
$303$		0			0
$304$	6.57619	+	2.13673i	0.377170	+	0.122550i
$305$	−1.93578	−	5.95772i	−0.110843	−	0.341138i
$306$		0			0
$307$			15.0077i			0.856533i	0.903652	+	0.428267i	$0.140876\pi$
$307$			15.0077i			0.856533i	−0.903652	+	0.428267i	$0.859124\pi$
$308$	0.333256	−	17.4519i	0.0189890	−	0.994413i
$309$		0			0
$310$	−2.60781	−	3.58935i	−0.148114	−	0.203861i
$311$	−1.95824	+	0.636270i	−0.111042	+	0.0360796i	−0.364011	−	0.931395i	$-0.618593\pi$
$311$	−1.95824	+	0.636270i	−0.111042	+	0.0360796i	0.252969	+	0.967474i	$0.418593\pi$
$312$		0			0
$313$	20.1223	+	14.6197i	1.13738	+	0.826355i	0.986752	−	0.162236i	$-0.0518705\pi$
$313$	20.1223	+	14.6197i	1.13738	+	0.826355i	0.150628	+	0.988591i	$0.451870\pi$
$314$	−0.626709	−	0.455330i	−0.0353672	−	0.0256958i
$315$		0			0
$316$	13.1310	−	4.26652i	0.738677	−	0.240011i
$317$	0.254351	+	0.350085i	0.0142858	+	0.0196627i	0.816100	−	0.577910i	$-0.196132\pi$
$317$	0.254351	+	0.350085i	0.0142858	+	0.0196627i	−0.801814	+	0.597573i	$0.796132\pi$
$318$		0			0
$319$	−9.20754	−	30.2941i	−0.515523	−	1.69615i
$320$		−	18.9816i		−	1.06111i
$321$		0			0
$322$	−0.173999	−	0.535513i	−0.00969657	−	0.0298430i
$323$	8.11053	+	2.63527i	0.451282	+	0.146630i
$324$		0			0
$325$	−5.93668	+	8.17113i	−0.329308	+	0.453253i
$326$	−0.619634	+	1.90704i	−0.0343183	+	0.105621i
$327$		0			0
$328$	6.81164	−	4.94895i	0.376110	−	0.273260i
$329$	20.9852			1.15695
$330$		0			0
$331$	−17.3090			−0.951391			−0.475696	−	0.879610i	$-0.657804\pi$
$331$	−17.3090			−0.951391			−0.475696	+	0.879610i	$0.657804\pi$
$332$	−12.2683	+	8.91344i	−0.673310	+	0.489189i
$333$		0			0
$334$	−1.28934	+	3.96819i	−0.0705497	+	0.217130i
$335$	−2.41766	+	3.32762i	−0.132091	+	0.181807i
$336$		0			0
$337$	23.8381	+	7.74548i	1.29855	+	0.421923i	0.875076	−	0.483986i	$-0.160812\pi$
$337$	23.8381	+	7.74548i	1.29855	+	0.421923i	0.423471	+	0.905910i	$0.360812\pi$
$338$	−0.379680	−	1.16853i	−0.0206519	−	0.0635599i
$339$		0			0
$340$		−	25.2356i		−	1.36859i
$341$	−6.49444	+	18.7612i	−0.351694	+	1.01598i
$342$		0			0
$343$	−10.5596	−	14.5341i	−0.570166	−	0.784766i
$344$	−11.2767	+	3.66403i	−0.608001	+	0.197551i
$345$		0			0
$346$	−3.18563	−	2.31449i	−0.171260	−	0.124428i
$347$	−16.8866	−	12.2688i	−0.906519	−	0.658625i	0.0336127	−	0.999435i	$-0.489299\pi$
$347$	−16.8866	−	12.2688i	−0.906519	−	0.658625i	−0.940132	+	0.340810i	$0.889299\pi$
$348$		0			0
$349$	−17.1385	+	5.56865i	−0.917405	+	0.298083i	−0.729402	−	0.684085i	$-0.760202\pi$
$349$	−17.1385	+	5.56865i	−0.917405	+	0.298083i	−0.188003	+	0.982168i	$0.560202\pi$
$350$	−1.43373	−	1.97336i	−0.0766361	−	0.105481i
$351$		0			0
$352$	7.92742	−	5.53148i	0.422533	−	0.294829i
$353$			16.2953i			0.867313i	0.901078	+	0.433656i	$0.142777\pi$
$353$			16.2953i			0.867313i	−0.901078	+	0.433656i	$0.857223\pi$
$354$		0			0
$355$	−3.25858	−	10.0289i	−0.172947	−	0.532277i
$356$	−3.80756	−	1.23715i	−0.201800	−	0.0655689i
$357$		0			0
$358$	−0.773769	+	1.06500i	−0.0408949	+	0.0562871i
$359$	−7.65875	+	23.5712i	−0.404213	+	1.24404i	0.517337	+	0.855782i	$0.326923\pi$
$359$	−7.65875	+	23.5712i	−0.404213	+	1.24404i	−0.921550	+	0.388259i	$0.873077\pi$
$360$		0			0
$361$	−12.4164	+	9.02103i	−0.653494	+	0.474791i
$362$	−1.34760			−0.0708281
$363$		0			0
$364$	15.0306			0.787820
$365$	−4.15897	+	3.02167i	−0.217690	+	0.158161i
$366$		0			0
$367$	2.76683	−	8.51544i	0.144428	−	0.444502i	−0.852509	−	0.522712i	$-0.824920\pi$
$367$	2.76683	−	8.51544i	0.144428	−	0.444502i	0.996937	+	0.0782097i	$0.0249204\pi$
$368$	−1.73611	+	2.38956i	−0.0905012	+	0.124564i
$369$		0			0
$370$	−4.19150	−	1.36190i	−0.217906	−	0.0708018i
$371$	8.78474	+	27.0367i	0.456081	+	1.40367i
$372$		0			0
$373$		−	16.9007i		−	0.875088i	−0.899197	−	0.437544i	$-0.855848\pi$
$373$		−	16.9007i		−	0.875088i	0.899197	−	0.437544i	$-0.144152\pi$
$374$	3.07882	−	2.14830i	0.159202	−	0.111086i
$375$		0			0
$376$	4.52926	+	6.23399i	0.233579	+	0.321493i
$377$	25.9303	−	8.42527i	1.33548	−	0.433923i
$378$		0			0
$379$	−15.9625	−	11.5975i	−0.819940	−	0.595722i	0.0967550	−	0.995308i	$-0.469154\pi$
$379$	−15.9625	−	11.5975i	−0.819940	−	0.595722i	−0.916695	+	0.399587i	$0.869154\pi$
$380$	−8.74419	−	6.35302i	−0.448567	−	0.325903i
$381$		0			0
$382$	−2.62964	+	0.854422i	−0.134544	+	0.0437160i
$383$	2.93889	+	4.04503i	0.150170	+	0.206691i	0.877474	−	0.479624i	$-0.159227\pi$
$383$	2.93889	+	4.04503i	0.150170	+	0.206691i	−0.727304	+	0.686315i	$0.759227\pi$
$384$		0			0
$385$	−8.61865	+	24.8977i	−0.439247	+	1.26890i
$386$		−	3.89808i		−	0.198407i
$387$		0			0
$388$	−0.999169	−	3.07513i	−0.0507251	−	0.156116i
$389$	−9.37115	−	3.04487i	−0.475136	−	0.154381i	0.0616527	−	0.998098i	$-0.480363\pi$
$389$	−9.37115	−	3.04487i	−0.475136	−	0.154381i	−0.536789	+	0.843716i	$0.680363\pi$
$390$		0			0
$391$	−2.14118	+	2.94708i	−0.108284	+	0.149040i
$392$	−0.121121	+	0.372773i	−0.00611754	+	0.0188279i
$393$		0			0
$394$	1.48615	−	1.07975i	0.0748714	−	0.0543972i
$395$	−20.8403			−1.04859
$396$		0			0
$397$	−19.0245			−0.954812			−0.477406	−	0.878683i	$-0.658423\pi$
$397$	−19.0245			−0.954812			−0.477406	+	0.878683i	$0.658423\pi$
$398$	−2.33397	+	1.69573i	−0.116991	+	0.0849991i
$399$		0			0
$400$	−3.95391	+	12.1689i	−0.197696	+	0.608445i
$401$	18.0482	−	24.8413i	0.901286	−	1.24051i	−0.0687699	−	0.997633i	$-0.521907\pi$
$401$	18.0482	−	24.8413i	0.901286	−	1.24051i	0.970056	−	0.242881i	$-0.0780926\pi$
$402$		0			0
$403$	−16.2592	−	5.28293i	−0.809928	−	0.263162i
$404$	−5.41185	−	16.6560i	−0.269250	−	0.828665i
$405$		0			0
$406$			6.58454i			0.326785i
$407$	5.73509	+	18.8693i	0.284278	+	0.935315i
$408$		0			0
$409$	−6.97905	−	9.60583i	−0.345092	−	0.474978i	0.600828	−	0.799378i	$-0.294838\pi$
$409$	−6.97905	−	9.60583i	−0.345092	−	0.474978i	−0.945920	+	0.324400i	$0.894838\pi$
$410$	−5.94461	+	1.93152i	−0.293584	+	0.0953911i
$411$		0			0
$412$	−25.9528	−	18.8558i	−1.27860	−	0.928958i
$413$	−0.205228	−	0.149107i	−0.0100986	−	0.00733706i
$414$		0			0
$415$	21.7694	−	7.07330i	1.06862	−	0.347215i
$416$	4.89265	+	6.73416i	0.239882	+	0.330169i
$417$		0			0
$418$	0.0306992	−	1.60765i	0.00150155	−	0.0786326i
$419$			10.0629i			0.491606i	0.969320	+	0.245803i	$0.0790516\pi$
$419$			10.0629i			0.491606i	−0.969320	+	0.245803i	$0.920948\pi$
$420$		0			0
$421$	−1.93337	−	5.95029i	−0.0942265	−	0.289999i	0.892825	−	0.450404i	$-0.148720\pi$
$421$	−1.93337	−	5.95029i	−0.0942265	−	0.289999i	−0.987051	+	0.160405i	$0.948720\pi$
$422$	−0.892232	−	0.289904i	−0.0434332	−	0.0141123i
$423$		0			0
$424$	−6.13566	+	8.44502i	−0.297974	+	0.410126i
$425$	−4.87643	+	15.0081i	−0.236541	+	0.728000i
$426$		0			0
$427$	4.71618	−	3.42651i	0.228232	−	0.165820i
$428$	−13.7682			−0.665512
$429$		0			0
$430$	8.80238			0.424489
$431$	15.8885	−	11.5436i	0.765321	−	0.556038i	−0.135217	−	0.990816i	$-0.543173\pi$
$431$	15.8885	−	11.5436i	0.765321	−	0.556038i	0.900538	+	0.434778i	$0.143173\pi$
$432$		0			0
$433$	9.66882	−	29.7576i	0.464654	−	1.43006i	−0.394764	−	0.918783i	$-0.629174\pi$
$433$	9.66882	−	29.7576i	0.464654	−	1.43006i	0.859418	−	0.511274i	$-0.170826\pi$
$434$	2.42681	−	3.34022i	0.116491	−	0.160335i
$435$		0			0
$436$	15.8695	+	5.15631i	0.760011	+	0.246942i
$437$	0.482131	+	1.48385i	0.0230634	+	0.0709820i
$438$		0			0
$439$			20.1935i			0.963782i	0.876231	+	0.481891i	$0.160050\pi$
$439$			20.1935i			0.963782i	−0.876231	+	0.481891i	$0.839950\pi$
$440$	−9.25644	+	2.81339i	−0.441283	+	0.134123i
$441$		0			0
$442$	1.90019	+	2.61539i	0.0903828	+	0.124401i
$443$	−23.1752	+	7.53009i	−1.10109	+	0.357765i	−0.802521	−	0.596624i	$-0.796509\pi$
$443$	−23.1752	+	7.53009i	−1.10109	+	0.357765i	−0.298567	+	0.954389i	$0.596509\pi$
$444$		0			0
$445$	4.88890	+	3.55199i	0.231756	+	0.168381i
$446$	−0.0581253	−	0.0422305i	−0.00275231	−	0.00199967i
$447$		0			0
$448$	16.7996	−	5.45852i	0.793706	−	0.257891i
$449$	−1.94082	−	2.67131i	−0.0915930	−	0.126067i	0.760761	−	0.649032i	$-0.224826\pi$
$449$	−1.94082	−	2.67131i	−0.0915930	−	0.126067i	−0.852354	+	0.522965i	$0.824826\pi$
$450$		0			0
$451$	22.3104	+	16.8695i	1.05055	+	0.794354i
$452$			22.0817i			1.03863i
$453$		0			0
$454$	−1.43109	−	4.40443i	−0.0671642	−	0.206710i
$455$	−21.5773	−	7.01089i	−1.01156	−	0.328675i
$456$		0			0
$457$	−9.17968	+	12.6347i	−0.429407	+	0.591028i	−0.967817	−	0.251655i	$-0.919025\pi$
$457$	−9.17968	+	12.6347i	−0.429407	+	0.591028i	0.538410	+	0.842683i	$0.319025\pi$
$458$	−2.06760	+	6.36342i	−0.0966126	+	0.297343i
$459$		0			0
$460$	3.73517	−	2.71376i	0.174153	−	0.126530i
$461$	36.5685			1.70316			0.851582	−	0.524221i	$-0.175644\pi$
$461$	36.5685			1.70316			0.851582	+	0.524221i	$0.175644\pi$
$462$		0			0
$463$	4.45531			0.207056			0.103528	−	0.994627i	$-0.466987\pi$
$463$	4.45531			0.207056			0.103528	+	0.994627i	$0.466987\pi$
$464$	27.9434	−	20.3021i	1.29724	−	0.942499i
$465$		0			0
$466$	−0.846784	+	2.60613i	−0.0392265	+	0.120727i
$467$	24.4676	−	33.6768i	1.13223	−	1.55838i	0.348458	−	0.937325i	$-0.386706\pi$
$467$	24.4676	−	33.6768i	1.13223	−	1.55838i	0.783769	−	0.621052i	$-0.213294\pi$
$468$		0			0
$469$	−3.64033	−	1.18282i	−0.168095	−	0.0546173i
$470$	−1.76772	−	5.44049i	−0.0815390	−	0.250951i
$471$		0			0
$472$		−	0.0931482i		−	0.00428749i
$473$	−22.5398	−	32.3029i	−1.03638	−	1.48529i
$474$		0			0
$475$	3.97270	+	5.46796i	0.182280	+	0.250887i
$476$	22.3346	−	7.25696i	1.02371	−	0.332622i
$477$		0			0
$478$	−1.52347	−	1.10687i	−0.0696819	−	0.0506269i
$479$	−2.84896	−	2.06989i	−0.130172	−	0.0945756i	0.520794	−	0.853682i	$-0.325636\pi$
$479$	−2.84896	−	2.06989i	−0.130172	−	0.0945756i	−0.650966	+	0.759107i	$0.725636\pi$
$480$		0			0
$481$	−16.1512	+	5.24783i	−0.736430	+	0.239281i
$482$	−0.397925	−	0.547696i	−0.0181250	−	0.0249469i
$483$		0			0
$484$	16.7353	+	13.1637i	0.760697	+	0.598351i
$485$			4.88056i			0.221615i
$486$		0			0
$487$	9.85775	+	30.3390i	0.446697	+	1.37479i	0.880611	+	0.473839i	$0.157132\pi$
$487$	9.85775	+	30.3390i	0.446697	+	1.37479i	−0.433914	+	0.900954i	$0.642868\pi$
$488$	2.03580	+	0.661472i	0.0921564	+	0.0299434i
$489$		0			0
$490$	0.171033	−	0.235407i	0.00772648	−	0.0106346i
$491$	−7.54595	+	23.2241i	−0.340544	+	1.04809i	0.623382	+	0.781917i	$0.285758\pi$
$491$	−7.54595	+	23.2241i	−0.340544	+	1.04809i	−0.963926	+	0.266170i	$0.914242\pi$
$492$		0			0
$493$	34.4630	−	25.0389i	1.55214	−	1.12769i
$494$	1.38461			0.0622964
$495$		0			0
$496$	−21.6577			−0.972460
$497$	7.93893	−	5.76797i	0.356110	−	0.258729i
$498$		0			0
$499$	−7.19057	+	22.1303i	−0.321894	+	0.990689i	0.650929	+	0.759139i	$0.274380\pi$
$499$	−7.19057	+	22.1303i	−0.321894	+	0.990689i	−0.972823	+	0.231550i	$0.925620\pi$
$500$	−4.86498	+	6.69608i	−0.217569	+	0.299458i
$501$		0			0
$502$	−5.85431	−	1.90218i	−0.261291	−	0.0848985i
$503$	−11.2856	−	34.7334i	−0.503199	−	1.54869i	−0.803778	−	0.594930i	$-0.797180\pi$
$503$	−11.2856	−	34.7334i	−0.503199	−	1.54869i	0.300579	−	0.953757i	$-0.402820\pi$
$504$		0			0
$505$			26.4348i			1.17633i
$506$	0.649061	+	0.224681i	0.0288543	+	0.00998829i
$507$		0			0
$508$	−3.28022	−	4.51483i	−0.145536	−	0.200313i
$509$	23.6347	−	7.67938i	1.04759	−	0.340383i	0.265868	−	0.964009i	$-0.414341\pi$
$509$	23.6347	−	7.67938i	1.04759	−	0.340383i	0.781722	+	0.623627i	$0.214341\pi$
$510$		0			0
$511$	−3.87030	−	2.81193i	−0.171212	−	0.124393i
$512$	14.3757	+	10.4445i	0.635321	+	0.461588i
$513$		0			0
$514$	4.04257	−	1.31351i	0.178310	−	0.0579364i
$515$	28.4615	+	39.1739i	1.25416	+	1.72621i
$516$		0			0
$517$	−15.4389	+	20.4184i	−0.679003	+	0.897999i
$518$		−	4.10130i		−	0.180201i
$519$		0			0
$520$	−2.57436	−	7.92306i	−0.112893	−	0.347449i
$521$	−9.26334	−	3.00984i	−0.405834	−	0.131864i	0.0989844	−	0.995089i	$-0.468441\pi$
$521$	−9.26334	−	3.00984i	−0.405834	−	0.131864i	−0.504819	+	0.863225i	$0.668441\pi$
$522$		0			0
$523$	19.5526	−	26.9118i	0.854975	−	1.17677i	−0.127769	−	0.991804i	$-0.540782\pi$
$523$	19.5526	−	26.9118i	0.854975	−	1.17677i	0.982744	−	0.184968i	$-0.0592182\pi$
$524$	−1.25704	+	3.86877i	−0.0549140	+	0.169008i
$525$		0			0
$526$	−2.23997	+	1.62743i	−0.0976674	+	0.0709595i
$527$	−26.7108			−1.16354
$528$		0			0
$529$	22.3335			0.971023
$530$	6.26937	−	4.55496i	0.272324	−	0.197855i
$531$		0			0
$532$	3.10816	−	9.56592i	0.134756	−	0.414735i
$533$	−14.1570	+	19.4854i	−0.613207	+	0.844007i
$534$		0			0
$535$	19.7650	+	6.42205i	0.854517	+	0.277649i
$536$	−0.434323	−	1.33671i	−0.0187599	−	0.0577371i
$537$		0			0
$538$			3.97933i			0.171561i
$539$	−1.30185	−	0.0248597i	−0.0560746	−	0.00107078i
$540$		0			0
$541$	−6.85075	−	9.42925i	−0.294537	−	0.405395i	0.635944	−	0.771735i	$-0.280611\pi$
$541$	−6.85075	−	9.42925i	−0.294537	−	0.405395i	−0.930481	+	0.366340i	$0.880611\pi$
$542$	−0.700877	+	0.227729i	−0.0301052	+	0.00978178i
$543$		0			0
$544$	10.5215	+	7.64432i	0.451106	+	0.327748i
$545$	−20.3764	−	14.8043i	−0.872829	−	0.634147i
$546$		0			0
$547$	0.773004	−	0.251164i	0.0330513	−	0.0107390i	−0.292445	−	0.956282i	$-0.594469\pi$
$547$	0.773004	−	0.251164i	0.0330513	−	0.0107390i	0.325496	+	0.945543i	$0.394469\pi$
$548$	5.77297	+	7.94581i	0.246609	+	0.339428i
$549$		0			0
$550$	2.97487	+	0.0568072i	0.126849	+	0.00242227i
$551$		−	18.2450i		−	0.777264i
$552$		0			0
$553$	−5.99302	−	18.4446i	−0.254849	−	0.784345i
$554$	5.09419	+	1.65520i	0.216431	+	0.0703228i
$555$		0			0
$556$	−19.8923	+	27.3794i	−0.843620	+	1.16114i
$557$	−2.14843	+	6.61219i	−0.0910320	+	0.280168i	−0.986199	−	0.165563i	$-0.947056\pi$
$557$	−2.14843	+	6.61219i	−0.0910320	+	0.280168i	0.895167	+	0.445730i	$0.147056\pi$
$558$		0			0
$559$	27.4405	−	19.9367i	1.16061	−	0.843233i
$560$	−28.7416			−1.21455
$561$		0			0
$562$	0.783948			0.0330689
$563$	23.2654	−	16.9033i	0.980519	−	0.712388i	0.0226941	−	0.999742i	$-0.492776\pi$
$563$	23.2654	−	16.9033i	0.980519	−	0.712388i	0.957824	+	0.287354i	$0.0927756\pi$
$564$		0			0
$565$	10.2998	−	31.6994i	0.433314	−	1.33360i
$566$	−3.34367	+	4.60217i	−0.140545	+	0.193444i
$567$		0			0
$568$	3.42694	+	1.11348i	0.143791	+	0.0467207i
$569$	3.22890	+	9.93752i	0.135362	+	0.416602i	0.995646	−	0.0932129i	$-0.0297137\pi$
$569$	3.22890	+	9.93752i	0.135362	+	0.416602i	−0.860284	+	0.509815i	$0.829714\pi$
$570$		0			0
$571$		−	21.2530i		−	0.889409i	−0.895677	−	0.444704i	$-0.853309\pi$
$571$		−	21.2530i		−	0.889409i	0.895677	−	0.444704i	$-0.146691\pi$
$572$	−11.0581	+	14.6247i	−0.462364	+	0.611489i
$573$		0			0
$574$	−3.41897	−	4.70580i	−0.142705	−	0.196416i
$575$	−2.74578	+	0.892157i	−0.114507	+	0.0372055i
$576$		0			0
$577$	−12.6856	−	9.21665i	−0.528110	−	0.383694i	0.291541	−	0.956558i	$-0.405832\pi$
$577$	−12.6856	−	9.21665i	−0.528110	−	0.383694i	−0.819650	+	0.572864i	$0.805832\pi$
$578$	0.597432	+	0.434060i	0.0248499	+	0.0180545i
$579$		0			0
$580$	−51.3477	+	16.6839i	−2.13210	+	0.692761i
$581$	12.5204	+	17.2328i	0.519432	+	0.714937i
$582$		0			0
$583$	−32.7694	−	11.3436i	−1.35717	−	0.469803i
$584$		−	1.75664i		−	0.0726903i
$585$		0			0
$586$	−1.62588	−	5.00395i	−0.0671646	−	0.206711i
$587$	19.1691	+	6.22843i	0.791195	+	0.257075i	0.676613	−	0.736339i	$-0.263447\pi$
$587$	19.1691	+	6.22843i	0.791195	+	0.257075i	0.114582	+	0.993414i	$0.463447\pi$
$588$		0			0
$589$	−6.72441	+	9.25536i	−0.277075	+	0.381360i
$590$	−0.0213688	+	0.0657664i	−0.000879739	+	0.00270756i
$591$		0			0
$592$	−17.4051	+	12.6455i	−0.715343	+	0.519727i
$593$	−40.5694			−1.66599			−0.832993	−	0.553284i	$-0.813374\pi$
$593$	−40.5694			−1.66599			−0.832993	+	0.553284i	$0.813374\pi$
$594$		0			0
$595$	−35.4475			−1.45320
$596$	−8.85798	+	6.43570i	−0.362837	+	0.263617i
$597$		0			0
$598$	−0.182768	+	0.562502i	−0.00747394	+	0.0230024i
$599$	6.42889	−	8.84861i	0.262678	−	0.361545i	−0.657223	−	0.753696i	$-0.728269\pi$
$599$	6.42889	−	8.84861i	0.262678	−	0.361545i	0.919901	+	0.392151i	$0.128269\pi$
$600$		0			0
$601$	15.5556	+	5.05433i	0.634527	+	0.206170i	0.608580	−	0.793493i	$-0.291740\pi$
$601$	15.5556	+	5.05433i	0.634527	+	0.206170i	0.0259478	+	0.999663i	$0.491740\pi$
$602$	2.53129	+	7.79050i	0.103168	+	0.317517i
$603$		0			0
$604$			17.7605i			0.722665i
$605$	−17.8844	−	26.7032i	−0.727104	−	1.08564i
$606$		0			0
$607$	−14.0272	−	19.3068i	−0.569348	−	0.783641i	0.423129	−	0.906069i	$-0.360932\pi$
$607$	−14.0272	−	19.3068i	−0.569348	−	0.783641i	−0.992477	+	0.122429i	$0.960932\pi$
$608$	5.29755	−	1.72128i	0.214844	−	0.0698070i
$609$		0			0
$610$	−1.28561	−	0.934052i	−0.0520529	−	0.0378187i
$611$	−17.8330	−	12.9564i	−0.721445	−	0.524161i
$612$		0			0
$613$	0.0461533	−	0.0149961i	0.00186411	−	0.000605687i	−0.308085	−	0.951359i	$-0.599688\pi$
$613$	0.0461533	−	0.0149961i	0.00186411	−	0.000605687i	0.309949	+	0.950753i	$0.399688\pi$
$614$	2.23774	+	3.07999i	0.0903080	+	0.124298i
$615$		0			0
$616$	−5.15183	−	7.38332i	−0.207573	−	0.297482i
$617$			8.24561i			0.331956i	0.986129	+	0.165978i	$0.0530780\pi$
$617$			8.24561i			0.331956i	−0.986129	+	0.165978i	$0.946922\pi$
$618$		0			0
$619$	−0.537464	−	1.65414i	−0.0216025	−	0.0664857i	0.939674	−	0.342071i	$-0.111128\pi$
$619$	−0.537464	−	1.65414i	−0.0216025	−	0.0664857i	−0.961277	+	0.275585i	$0.911128\pi$
$620$	32.1968	+	10.4614i	1.29305	+	0.420139i
$621$		0			0
$622$	−0.307013	+	0.422567i	−0.0123101	+	0.0169434i
$623$	−1.73778	+	5.34834i	−0.0696227	+	0.214277i
$624$		0			0
$625$	24.4126	−	17.7368i	0.976506	−	0.709473i
$626$	6.30955			0.252180
$627$		0			0
$628$	5.91094			0.235872
$629$	−21.4659	+	15.5959i	−0.855903	+	0.621850i
$630$		0			0
$631$	−8.14182	+	25.0580i	−0.324121	+	0.997541i	0.647715	+	0.761883i	$0.275725\pi$
$631$	−8.14182	+	25.0580i	−0.324121	+	0.997541i	−0.971836	+	0.235659i	$0.924275\pi$
$632$	4.18580	−	5.76126i	0.166502	−	0.229171i
$633$		0			0
$634$	0.104400	+	0.0339216i	0.00414625	+	0.00134720i
$635$	2.60303	+	8.01130i	0.103298	+	0.317919i
$636$		0			0
$637$		−	1.12123i		−	0.0444249i
$638$	−6.40670	−	4.84429i	−0.253644	−	0.191787i
$639$		0			0
$640$	−12.8409	−	17.6740i	−0.507582	−	0.698626i
$641$	8.27017	−	2.68714i	0.326652	−	0.106136i	−0.141100	−	0.989995i	$-0.545064\pi$
$641$	8.27017	−	2.68714i	0.326652	−	0.106136i	0.467752	+	0.883860i	$0.345064\pi$
$642$		0			0
$643$	17.4877	+	12.7055i	0.689646	+	0.501057i	0.876544	−	0.481322i	$-0.159843\pi$
$643$	17.4877	+	12.7055i	0.689646	+	0.501057i	−0.186897	+	0.982379i	$0.559843\pi$
$644$	3.47592	+	2.52540i	0.136970	+	0.0995148i
$645$		0			0
$646$	2.05744	−	0.668503i	0.0809489	−	0.0263019i
$647$	17.2616	+	23.7586i	0.678625	+	0.934048i	0.999916	−	0.0129330i	$-0.00411681\pi$
$647$	17.2616	+	23.7586i	0.678625	+	0.934048i	−0.321291	+	0.946980i	$0.604117\pi$
$648$		0			0
$649$	0.296067	−	0.0899860i	0.0116216	−	0.00353226i
$650$			2.56214i			0.100495i
$651$		0			0
$652$	−4.72806	−	14.5515i	−0.185165	−	0.569880i
$653$	22.5339	+	7.32170i	0.881818	+	0.286520i	0.714712	−	0.699419i	$-0.246558\pi$
$653$	22.5339	+	7.32170i	0.881818	+	0.286520i	0.167106	+	0.985939i	$0.446558\pi$
$654$		0			0
$655$	3.60909	−	4.96749i	0.141019	−	0.194096i
$656$	−9.42876	+	29.0187i	−0.368131	+	1.13299i
$657$		0			0
$658$	4.30674	−	3.12903i	0.167894	−	0.121982i
$659$	−34.5941			−1.34759			−0.673797	−	0.738916i	$-0.735338\pi$
$659$	−34.5941			−1.34759			−0.673797	+	0.738916i	$0.735338\pi$
$660$		0			0
$661$	35.4913			1.38045			0.690225	−	0.723595i	$-0.257512\pi$
$661$	35.4913			1.38045			0.690225	+	0.723595i	$0.257512\pi$
$662$	−3.55229	+	2.58089i	−0.138064	+	0.100309i
$663$		0			0
$664$	−2.41700	+	7.43877i	−0.0937979	+	0.288680i
$665$	−8.92385	+	12.2826i	−0.346052	+	0.476300i
$666$		0			0
$667$	7.41211	+	2.40834i	0.286998	+	0.0932513i
$668$	−9.83822	−	30.2789i	−0.380652	−	1.17153i
$669$		0			0
$670$			1.04341i			0.0403104i
$671$	−0.135765	+	7.10971i	−0.00524115	+	0.274467i
$672$		0			0
$673$	−12.2854	−	16.9095i	−0.473569	−	0.651812i	0.503684	−	0.863888i	$-0.331978\pi$
$673$	−12.2854	−	16.9095i	−0.473569	−	0.651812i	−0.977253	+	0.212076i	$0.931978\pi$
$674$	6.04715	−	1.96484i	0.232928	−	0.0756827i
$675$		0			0
$676$	7.58475	+	5.51064i	0.291721	+	0.211948i
$677$	−19.6090	−	14.2468i	−0.753634	−	0.547547i	0.143317	−	0.989677i	$-0.454223\pi$
$677$	−19.6090	−	14.2468i	−0.753634	−	0.547547i	−0.896951	+	0.442130i	$0.854223\pi$
$678$		0			0
$679$	−4.31951	+	1.40350i	−0.165768	+	0.0538612i
$680$	−7.65068	−	10.5303i	−0.293390	−	0.403817i
$681$		0			0
$682$	1.46458	+	4.81868i	0.0560817	+	0.184517i
$683$		−	17.6311i		−	0.674636i	−0.941391	−	0.337318i	$-0.890480\pi$
$683$		−	17.6311i		−	0.674636i	0.941391	−	0.337318i	$-0.109520\pi$
$684$		0			0
$685$	−4.58116	−	14.0994i	−0.175037	−	0.538709i
$686$	−4.33425	−	1.40828i	−0.165482	−	0.0537685i
$687$		0			0
$688$	25.2565	−	34.7626i	0.962896	−	1.32531i
$689$	9.22748	−	28.3993i	0.351539	−	1.08193i
$690$		0			0
$691$	−23.5718	+	17.1259i	−0.896713	+	0.651500i	−0.937620	−	0.347663i	$-0.886976\pi$
$691$	−23.5718	+	17.1259i	−0.896713	+	0.651500i	0.0409063	+	0.999163i	$0.486976\pi$
$692$	30.0459			1.14218
$693$		0			0
$694$	−5.29496			−0.200994
$695$	41.3272	−	30.0260i	1.56763	−	1.13895i
$696$		0			0
$697$	−11.6286	+	35.7893i	−0.440466	+	1.35562i
$698$	−2.68698	+	3.69831i	−0.101704	+	0.139983i
$699$		0			0
$700$	17.7012	+	5.75148i	0.669044	+	0.217385i
$701$	4.54301	+	13.9820i	0.171587	+	0.528091i	0.999461	−	0.0328229i	$-0.0104497\pi$
$701$	4.54301	+	13.9820i	0.171587	+	0.528091i	−0.827874	+	0.560914i	$0.810450\pi$
$702$		0			0
$703$			11.3642i			0.428611i
$704$	−7.04848	+	20.3617i	−0.265649	+	0.767411i
$705$		0			0
$706$	2.42974	+	3.34425i	0.0914445	+	0.125863i
$707$	−23.3960	+	7.60182i	−0.879897	+	0.285896i
$708$		0			0
$709$	−8.72312	−	6.33772i	−0.327604	−	0.238018i	0.411810	−	0.911270i	$-0.364897\pi$
$709$	−8.72312	−	6.33772i	−0.327604	−	0.238018i	−0.739413	+	0.673252i	$0.764897\pi$
$710$	−2.16412	−	1.57233i	−0.0812180	−	0.0590083i
$711$		0			0
$712$	−1.96388	+	0.638103i	−0.0735995	+	0.0239139i
$713$	−2.87241	−	3.95353i	−0.107572	−	0.148061i
$714$		0			0
$715$	22.6961	−	15.8366i	0.848785	−	0.592254i
$716$		−	10.0448i		−	0.375391i
$717$		0			0
$718$	1.94284	+	5.97944i	0.0725060	+	0.223151i
$719$	−30.1960	−	9.81128i	−1.12612	−	0.365899i	−0.314020	−	0.949416i	$-0.601676\pi$
$719$	−30.1960	−	9.81128i	−1.12612	−	0.365899i	−0.812101	+	0.583517i	$0.801676\pi$
$720$		0			0
$721$	−26.4860	+	36.4549i	−0.986390	+	1.35765i
$722$	−1.20309	+	3.70273i	−0.0447744	+	0.137801i
$723$		0			0
$724$	8.31889	−	6.04403i	0.309169	−	0.224625i
$725$	33.7614			1.25387
$726$		0			0
$727$	23.6418			0.876828			0.438414	−	0.898773i	$-0.355540\pi$
$727$	23.6418			0.876828			0.438414	+	0.898773i	$0.355540\pi$
$728$	6.27196	−	4.55685i	0.232454	−	0.168888i
$729$		0			0
$730$	−0.402984	+	1.24026i	−0.0149151	+	0.0459040i
$731$	31.1493	−	42.8733i	1.15210	−	1.58573i
$732$		0			0
$733$	15.6206	+	5.07543i	0.576959	+	0.187465i	0.582938	−	0.812517i	$-0.301903\pi$
$733$	15.6206	+	5.07543i	0.576959	+	0.187465i	−0.00597872	+	0.999982i	$0.501903\pi$
$734$	−0.701877	−	2.16016i	−0.0259068	−	0.0797328i
$735$		0			0
$736$			2.37936i			0.0877043i
$737$	3.82908	−	2.67181i	0.141046	−	0.0984172i
$738$		0			0
$739$	20.4813	+	28.1901i	0.753417	+	1.03699i	0.997733	+	0.0672942i	$0.0214366\pi$
$739$	20.4813	+	28.1901i	0.753417	+	1.03699i	−0.244316	+	0.969696i	$0.578563\pi$
$740$	31.9829	−	10.3919i	1.17571	−	0.382013i
$741$		0			0
$742$	5.83422	+	4.23881i	0.214181	+	0.155611i
$743$	42.7101	+	31.0307i	1.56688	+	1.13841i	0.930068	+	0.367387i	$0.119748\pi$
$743$	42.7101	+	31.0307i	1.56688	+	1.13841i	0.636813	+	0.771019i	$0.280252\pi$
$744$		0			0
$745$	15.7180	−	5.10708i	0.575862	−	0.187109i
$746$	−2.52001	−	3.46850i	−0.0922643	−	0.126991i
$747$		0			0
$748$	−9.37077	+	27.0704i	−0.342629	+	0.989791i
$749$			19.3397i			0.706657i
$750$		0			0
$751$	15.8766	+	48.8631i	0.579345	+	1.78304i	0.620883	+	0.783903i	$0.286774\pi$
$751$	15.8766	+	48.8631i	0.579345	+	1.78304i	−0.0415382	+	0.999137i	$0.513226\pi$
$752$	−26.5578	−	8.62917i	−0.968465	−	0.314673i
$753$		0			0
$754$	4.06535	−	5.59548i	0.148051	−	0.203775i
$755$	8.28421	−	25.4962i	0.301493	−	0.927900i
$756$		0			0
$757$	5.71877	−	4.15493i	0.207852	−	0.151013i	−0.478989	−	0.877821i	$-0.658997\pi$
$757$	5.71877	−	4.15493i	0.207852	−	0.151013i	0.686841	+	0.726807i	$0.258997\pi$
$758$	−5.00521			−0.181797
$759$		0			0
$760$	−5.57481			−0.202219
$761$	−23.5688	+	17.1238i	−0.854370	+	0.620736i	−0.926347	−	0.376670i	$-0.877069\pi$
$761$	−23.5688	+	17.1238i	−0.854370	+	0.620736i	0.0719775	+	0.997406i	$0.477069\pi$
$762$		0			0
$763$	7.24287	−	22.2913i	0.262210	−	0.806998i
$764$	12.4010	−	17.0685i	0.448653	−	0.617517i
$765$		0			0
$766$	1.20628	+	0.391945i	0.0435847	+	0.0141615i
$767$	0.0823407	+	0.253419i	0.00297315	+	0.00915042i
$768$		0			0
$769$		−	44.2408i		−	1.59536i	−0.603079	−	0.797682i	$-0.706060\pi$
$769$		−	44.2408i		−	1.59536i	0.603079	−	0.797682i	$-0.293940\pi$
$770$	1.94362	+	6.39479i	0.0700432	+	0.230452i
$771$		0			0
$772$	17.4831	+	24.0634i	0.629230	+	0.866061i
$773$	−38.0786	+	12.3725i	−1.36959	+	0.445007i	−0.899234	−	0.437468i	$-0.855875\pi$
$773$	−38.0786	+	12.3725i	−1.36959	+	0.445007i	−0.470358	+	0.882476i	$0.655875\pi$
$774$		0			0
$775$	−17.1266	−	12.4432i	−0.615204	−	0.446972i
$776$	−1.34922	−	0.980265i	−0.0484341	−	0.0351895i
$777$		0			0
$778$	−2.37723	+	0.772409i	−0.0852279	+	0.0276922i
$779$	9.47357	+	13.0393i	0.339426	+	0.467180i
$780$		0			0
$781$	−0.228538	+	11.9680i	−0.00817775	+	0.428250i
$782$			0.924086i			0.0330453i
$783$		0			0
$784$	−0.438933	−	1.35090i	−0.0156762	−	0.0482463i
$785$	−8.48547	−	2.75709i	−0.302859	−	0.0984049i
$786$		0			0
$787$	−16.6720	+	22.9470i	−0.594292	+	0.817973i	−0.995171	−	0.0981579i	$-0.968705\pi$
$787$	−16.6720	+	22.9470i	−0.594292	+	0.817973i	0.400878	+	0.916131i	$0.368705\pi$
$788$	−4.33149	+	13.3309i	−0.154303	+	0.474895i
$789$		0			0
$790$	−4.27701	+	3.10743i	−0.152169	+	0.110558i
$791$	31.0173			1.10285
$792$		0			0
$793$	−6.12332			−0.217446
$794$	−3.90435	+	2.83668i	−0.138560	+	0.100670i
$795$		0			0
$796$	6.80249	−	20.9359i	0.241108	−	0.742054i
$797$	−8.78371	+	12.0897i	−0.311135	+	0.428241i	−0.935735	−	0.352704i	$-0.885262\pi$
$797$	−8.78371	+	12.0897i	−0.311135	+	0.428241i	0.624600	+	0.780945i	$0.285262\pi$
$798$		0			0
$799$	−32.7542	−	10.6425i	−1.15876	−	0.376504i
$800$	3.18513	+	9.80283i	0.112611	+	0.346582i
$801$		0			0
$802$		−	7.78923i		−	0.275047i
$803$	5.58339	−	1.69700i	0.197034	−	0.0598860i
$804$		0			0
$805$	−3.81192	−	5.24666i	−0.134352	−	0.184920i
$806$	−4.12456	+	1.34015i	−0.145281	+	0.0472048i
$807$		0			0
$808$	−7.30784	−	5.30946i	−0.257089	−	0.186786i
$809$	−24.0892	−	17.5019i	−0.846933	−	0.615333i	0.0773660	−	0.997003i	$-0.475349\pi$
$809$	−24.0892	−	17.5019i	−0.846933	−	0.615333i	−0.924299	+	0.381670i	$0.875349\pi$
$810$		0			0
$811$	41.9856	−	13.6420i	1.47432	−	0.479034i	0.541906	−	0.840439i	$-0.317703\pi$
$811$	41.9856	−	13.6420i	1.47432	−	0.479034i	0.932409	+	0.361405i	$0.117703\pi$
$812$	−29.5320	−	40.6473i	−1.03637	−	1.42644i
$813$		0			0
$814$	3.99053	+	3.01735i	0.139868	+	0.105758i
$815$			23.0948i			0.808975i
$816$		0			0
$817$	−7.01391	−	21.5866i	−0.245386	−	0.755220i
$818$	−2.86459	−	0.930761i	−0.100158	−	0.0325433i
$819$		0			0
$820$	28.0340	−	38.5854i	0.978988	−	1.34746i
$821$	1.23760	−	3.80893i	0.0431924	−	0.132933i	−0.927135	−	0.374728i	$-0.877736\pi$
$821$	1.23760	−	3.80893i	0.0431924	−	0.132933i	0.970327	+	0.241795i	$0.0777362\pi$
$822$		0			0
$823$	−34.1262	+	24.7941i	−1.18956	+	0.864268i	−0.993218	−	0.116266i	$-0.962907\pi$
$823$	−34.1262	+	24.7941i	−1.18956	+	0.864268i	−0.196345	+	0.980535i	$0.562907\pi$
$824$	−16.5460			−0.576409
$825$		0			0
$826$	−0.0643512			−0.00223906
$827$	21.5183	−	15.6340i	0.748266	−	0.543647i	−0.147023	−	0.989133i	$-0.546969\pi$
$827$	21.5183	−	15.6340i	0.748266	−	0.543647i	0.895289	+	0.445486i	$0.146969\pi$
$828$		0			0
$829$	3.77976	−	11.6329i	0.131276	−	0.404027i	−0.863716	−	0.503979i	$-0.831869\pi$
$829$	3.77976	−	11.6329i	0.131276	−	0.404027i	0.994992	+	0.0999518i	$0.0318689\pi$
$830$	3.41300	−	4.69759i	0.118467	−	0.163056i
$831$		0			0
$832$	−17.6463	−	5.73362i	−0.611774	−	0.198777i
$833$	−0.541343	−	1.66608i	−0.0187564	−	0.0577264i
$834$		0			0
$835$			48.0560i			1.66305i
$836$	7.02087	+	10.0619i	0.242822	+	0.347999i
$837$		0			0
$838$	1.50045	+	2.06519i	0.0518321	+	0.0713408i
$839$	9.17434	−	2.98092i	0.316733	−	0.102913i	−0.146336	−	0.989235i	$-0.546748\pi$
$839$	9.17434	−	2.98092i	0.316733	−	0.102913i	0.463069	+	0.886322i	$0.346748\pi$
$840$		0			0
$841$	−50.2704	−	36.5236i	−1.73346	−	1.25943i
$842$	−1.28401	−	0.932887i	−0.0442498	−	0.0321494i
$843$		0			0
$844$	6.80810	−	2.21209i	0.234345	−	0.0761432i
$845$	−8.31793	−	11.4486i	−0.286146	−	0.393846i
$846$		0			0
$847$	18.4906	−	23.5075i	0.635344	−	0.807727i
$848$		−	37.8287i		−	1.29904i
$849$		0			0
$850$	1.23703	+	3.80718i	0.0424298	+	0.130585i
$851$	−4.61677	−	1.50008i	−0.158261	−	0.0514221i
$852$		0			0
$853$	−6.89976	+	9.49670i	−0.236243	+	0.325161i	−0.910634	−	0.413214i	$-0.864406\pi$
$853$	−6.89976	+	9.49670i	−0.236243	+	0.325161i	0.674391	+	0.738374i	$0.264406\pi$
$854$	0.456976	−	1.40643i	0.0156374	−	0.0481270i
$855$		0			0
$856$	−5.74518	+	4.17412i	−0.196366	+	0.142668i
$857$	48.7738			1.66608			0.833041	−	0.553212i	$-0.186598\pi$
$857$	48.7738			1.66608			0.833041	+	0.553212i	$0.186598\pi$
$858$		0			0
$859$	−31.0880			−1.06071			−0.530355	−	0.847776i	$-0.677941\pi$
$859$	−31.0880			−1.06071			−0.530355	+	0.847776i	$0.677941\pi$
$860$	−54.3383	+	39.4791i	−1.85292	+	1.34623i
$861$		0			0
$862$	1.53952	−	4.73815i	0.0524362	−	0.161382i
$863$	−30.6459	+	42.1805i	−1.04320	+	1.43584i	−0.148641	+	0.988891i	$0.547490\pi$
$863$	−30.6459	+	42.1805i	−1.04320	+	1.43584i	−0.894559	+	0.446950i	$0.852510\pi$
$864$		0			0
$865$	−43.1325	−	14.0146i	−1.46655	−	0.476511i
$866$	−2.45274	−	7.54876i	−0.0833475	−	0.256517i
$867$		0			0
$868$			31.5040i			1.06931i
$869$	22.3556	+	7.73868i	0.758361	+	0.262517i
$870$		0			0
$871$	2.36324	+	3.25272i	0.0800753	+	0.110214i
$872$	8.18523	−	2.65954i	0.277187	−	0.0900635i
$873$		0			0
$874$	0.320198	+	0.232637i	0.0108309	+	0.00786907i
$875$	9.40572	+	6.83366i	0.317971	+	0.231020i
$876$		0			0
$877$	16.1564	−	5.24952i	0.545561	−	0.177264i	−0.0232530	−	0.999730i	$-0.507402\pi$
$877$	16.1564	−	5.24952i	0.545561	−	0.177264i	0.568814	+	0.822466i	$0.307402\pi$
$878$	3.01098	+	4.14426i	0.101616	+	0.139862i
$879$		0			0
$880$	21.1454	−	27.9653i	0.712810	−	0.942710i
$881$			50.3115i			1.69504i	0.530765	+	0.847519i	$0.321905\pi$
$881$			50.3115i			1.69504i	−0.530765	+	0.847519i	$0.678095\pi$
$882$		0			0
$883$	4.44037	+	13.6660i	0.149430	+	0.459899i	0.997554	−	0.0698990i	$-0.0222677\pi$
$883$	4.44037	+	13.6660i	0.149430	+	0.459899i	−0.848124	+	0.529798i	$0.822268\pi$
$884$	−23.4603	−	7.62270i	−0.789054	−	0.256379i
$885$		0			0
$886$	−3.63341	+	5.00096i	−0.122067	+	0.168011i
$887$	−12.7625	+	39.2790i	−0.428523	+	1.31886i	0.471057	+	0.882103i	$0.343873\pi$
$887$	−12.7625	+	39.2790i	−0.428523	+	1.31886i	−0.899580	+	0.436756i	$0.856127\pi$
$888$		0			0
$889$	−6.34181	+	4.60760i	−0.212698	+	0.154534i
$890$	1.53296			0.0513851
$891$		0			0
$892$	0.548221			0.0183558
$893$	−11.9335	+	8.67018i	−0.399339	+	0.290136i
$894$		0			0
$895$	−4.68529	+	14.4198i	−0.156612	+	0.482002i
$896$	11.9496	−	16.4473i	0.399209	−	0.549465i
$897$		0			0
$898$	−0.796620	−	0.258838i	−0.0265836	−	0.00863752i
$899$	17.6592	+	54.3495i	0.588968	+	1.81266i
$900$		0			0
$901$		−	46.6547i		−	1.55429i
$902$	7.09406	+	0.135466i	0.236206	+	0.00451053i
$903$		0			0
$904$	6.69450	+	9.21419i	0.222656	+	0.306460i
$905$	−14.7614	+	4.79627i	−0.490685	+	0.159433i
$906$		0			0
$907$	21.1288	+	15.3510i	0.701571	+	0.509721i	0.880444	−	0.474151i	$-0.157245\pi$
$907$	21.1288	+	15.3510i	0.701571	+	0.509721i	−0.178872	+	0.983872i	$0.557245\pi$
$908$	28.5883	+	20.7706i	0.948738	+	0.689298i
$909$		0			0
$910$	−5.47363	+	1.77849i	−0.181449	+	0.0589563i
$911$	−26.6929	−	36.7397i	−0.884377	−	1.21724i	−0.975189	−	0.221372i	$-0.928946\pi$
$911$	−26.6929	−	36.7397i	−0.884377	−	1.21724i	0.0908128	−	0.995868i	$-0.471054\pi$
$912$		0			0
$913$	−25.9787	−	0.496082i	−0.859769	−	0.0164179i
$914$			3.96175i			0.131043i
$915$		0			0
$916$	−15.7767	−	48.5555i	−0.521275	−	1.60432i
$917$	5.43431	+	1.76572i	0.179457	+	0.0583091i
$918$		0			0
$919$	−16.3737	+	22.5365i	−0.540119	+	0.743410i	−0.988630	−	0.150367i	$-0.951954\pi$
$919$	−16.3737	+	22.5365i	−0.540119	+	0.743410i	0.448511	+	0.893777i	$0.351954\pi$
$920$	0.735874	−	2.26479i	0.0242610	−	0.0746678i
$921$		0			0
$922$	7.50486	−	5.45260i	0.247160	−	0.179572i
$923$	−10.3076			−0.339280
$924$		0			0
$925$	−21.0289			−0.691427
$926$	0.914353	−	0.664317i	0.0300475	−	0.0218308i
$927$		0			0
$928$	8.59813	−	26.4623i	0.282248	−	0.868669i
$929$	−29.2450	+	40.2523i	−0.959497	+	1.32063i	−0.0123191	+	0.999924i	$0.503921\pi$
$929$	−29.2450	+	40.2523i	−0.959497	+	1.32063i	−0.947178	+	0.320710i	$0.896079\pi$
$930$		0			0
$931$	−0.713584	−	0.231857i	−0.0233868	−	0.00759882i
$932$	−6.46131	−	19.8859i	−0.211647	−	0.651384i
$933$		0			0
$934$		−	10.5597i		−	0.345524i
$935$	26.0789	−	34.4901i	0.852872	−	1.12795i
$936$		0			0
$937$	11.9943	+	16.5087i	0.391837	+	0.539317i	0.958672	−	0.284514i	$-0.0918323\pi$
$937$	11.9943	+	16.5087i	0.391837	+	0.539317i	−0.566835	+	0.823831i	$0.691832\pi$
$938$	−0.923462	+	0.300051i	−0.0301521	+	0.00979702i
$939$		0			0
$940$	35.3132	+	25.6566i	1.15179	+	0.836825i
$941$	−14.1929	−	10.3117i	−0.462675	−	0.336153i	0.331904	−	0.943313i	$-0.392309\pi$
$941$	−14.1929	−	10.3117i	−0.462675	−	0.336153i	−0.794580	+	0.607160i	$0.792309\pi$
$942$		0			0
$943$	−6.54776	+	2.12750i	−0.213224	+	0.0692808i
$944$	0.198413	+	0.273093i	0.00645781	+	0.00888841i
$945$		0			0
$946$	−9.44237	−	3.26860i	−0.306998	−	0.106271i
$947$		−	47.0672i		−	1.52948i	−0.644340	−	0.764739i	$-0.722868\pi$
$947$		−	47.0672i		−	1.52948i	0.644340	−	0.764739i	$-0.277132\pi$
$948$		0			0
$949$	1.55283	+	4.77911i	0.0504069	+	0.155136i
$950$	1.63062	+	0.529820i	0.0529042	+	0.0171896i
$951$		0			0
$952$	7.11966	−	9.79937i	0.230749	−	0.317599i
$953$	15.9545	−	49.1029i	0.516817	−	1.59060i	−0.263136	−	0.964759i	$-0.584757\pi$
$953$	15.9545	−	49.1029i	0.516817	−	1.59060i	0.779952	−	0.625839i	$-0.215243\pi$
$954$		0			0
$955$	−25.7637	+	18.7185i	−0.833695	+	0.605715i
$956$	14.3689			0.464725
$957$		0			0
$958$	−0.893318			−0.0288618
$959$	11.1612	−	8.10907i	0.360413	−	0.261855i
$960$		0			0
$961$	1.49341	−	4.59623i	0.0481744	−	0.148266i
$962$	−2.53218	+	3.48525i	−0.0816408	+	0.112369i
$963$		0			0
$964$	4.91289	+	1.59629i	0.158233	+	0.0514132i
$965$	−13.8738	−	42.6991i	−0.446613	−	1.37453i
$966$		0			0
$967$		−	33.6964i		−	1.08360i	−0.840506	−	0.541802i	$-0.817742\pi$
$967$		−	33.6964i		−	1.08360i	0.840506	−	0.541802i	$-0.182258\pi$
$968$	10.9741	+	0.419271i	0.352722	+	0.0134759i
$969$		0			0
$970$	0.727724	+	1.00163i	0.0233658	+	0.0321603i
$971$	−53.1467	+	17.2684i	−1.70556	+	0.554170i	−0.989584	−	0.143955i	$-0.954018\pi$
$971$	−53.1467	+	17.2684i	−1.70556	+	0.554170i	−0.715976	+	0.698125i	$0.754018\pi$
$972$		0			0
$973$	38.4588	+	27.9419i	1.23293	+	0.895777i
$974$	6.54684	+	4.75656i	0.209774	+	0.152410i
$975$		0			0
$976$	−7.37757	+	2.39712i	−0.236150	+	0.0767299i
$977$	−12.1432	−	16.7137i	−0.388496	−	0.534719i	0.569314	−	0.822120i	$-0.307209\pi$
$977$	−12.1432	−	16.7137i	−0.388496	−	0.534719i	−0.957810	+	0.287401i	$0.907209\pi$
$978$		0			0
$979$	−3.92539	−	5.62565i	−0.125456	−	0.179797i
$980$			2.22029i			0.0709245i
$981$		0			0
$982$	1.91422	+	5.89137i	0.0610853	+	0.188001i
$983$	47.6740	+	15.4902i	1.52056	+	0.494061i	0.945936	−	0.324354i	$-0.105147\pi$
$983$	47.6740	+	15.4902i	1.52056	+	0.494061i	0.574628	+	0.818415i	$0.305147\pi$
$984$		0			0
$985$	12.4362	−	17.1169i	0.396249	−	0.545390i
$986$	3.33931	−	10.2773i	0.106345	−	0.327297i
$987$		0			0
$988$	−8.54737	+	6.21003i	−0.271928	+	0.197567i
$989$	9.69548			0.308298
$990$		0			0
$991$	45.3068			1.43922			0.719609	−	0.694379i	$-0.244321\pi$
$991$	45.3068			1.43922			0.719609	+	0.694379i	$0.244321\pi$
$992$	−14.1147	+	10.2549i	−0.448141	+	0.325594i
$993$		0			0
$994$	0.769246	−	2.36750i	0.0243990	−	0.0750924i
$995$	−19.5307	+	26.8817i	−0.619164	+	0.852206i
$996$		0			0
$997$	9.77676	+	3.17666i	0.309633	+	0.100606i	0.459712	−	0.888068i	$-0.347953\pi$
$997$	9.77676	+	3.17666i	0.309633	+	0.100606i	−0.150079	+	0.988674i	$0.547953\pi$
$998$	1.82407	+	5.61392i	0.0577400	+	0.177705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.j.a.8.3	yes	16
3.2	odd	2	inner	99.2.j.a.8.2	✓	16
4.3	odd	2		1584.2.cd.c.305.3		16
9.2	odd	6		891.2.u.c.701.3		32
9.4	even	3		891.2.u.c.107.3		32
9.5	odd	6		891.2.u.c.107.2		32
9.7	even	3		891.2.u.c.701.2		32
11.2	odd	10		1089.2.d.g.1088.10		16
11.7	odd	10	inner	99.2.j.a.62.2	yes	16
11.9	even	5		1089.2.d.g.1088.8		16
12.11	even	2		1584.2.cd.c.305.2		16
33.2	even	10		1089.2.d.g.1088.7		16
33.20	odd	10		1089.2.d.g.1088.9		16
33.29	even	10	inner	99.2.j.a.62.3	yes	16
44.7	even	10		1584.2.cd.c.161.2		16
99.7	odd	30		891.2.u.c.458.2		32
99.29	even	30		891.2.u.c.458.3		32
99.40	odd	30		891.2.u.c.755.3		32
99.95	even	30		891.2.u.c.755.2		32
132.95	odd	10		1584.2.cd.c.161.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.2	✓	16	3.2	odd	2	inner
99.2.j.a.8.3	yes	16	1.1	even	1	trivial
99.2.j.a.62.2	yes	16	11.7	odd	10	inner
99.2.j.a.62.3	yes	16	33.29	even	10	inner
891.2.u.c.107.2		32	9.5	odd	6
891.2.u.c.107.3		32	9.4	even	3
891.2.u.c.458.2		32	99.7	odd	30
891.2.u.c.458.3		32	99.29	even	30
891.2.u.c.701.2		32	9.7	even	3
891.2.u.c.701.3		32	9.2	odd	6
891.2.u.c.755.2		32	99.95	even	30
891.2.u.c.755.3		32	99.40	odd	30
1089.2.d.g.1088.7		16	33.2	even	10
1089.2.d.g.1088.8		16	11.9	even	5
1089.2.d.g.1088.9		16	33.20	odd	10
1089.2.d.g.1088.10		16	11.2	odd	10
1584.2.cd.c.161.2		16	44.7	even	10
1584.2.cd.c.161.3		16	132.95	odd	10
1584.2.cd.c.305.2		16	12.11	even	2
1584.2.cd.c.305.3		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.205228 - 0.149107i) q^{2} +(-0.598148 + 1.84091i) q^{4} +(1.71735 - 2.36373i) q^{5} +(2.58586 + 0.840196i) q^{7} +(0.308515 + 0.949513i) q^{8} -0.741170i q^{10} +(-2.71994 + 1.89788i) q^{11} +(-1.67869 - 2.31052i) q^{13} +(0.655969 - 0.213137i) q^{14} +(-2.92705 - 2.12663i) q^{16} +(-3.60998 - 2.62280i) q^{17} +(-1.81761 + 0.590579i) q^{19} +(3.32418 + 4.57534i) q^{20} +(-0.275220 + 0.795058i) q^{22} -0.816370i q^{23} +(-1.09283 - 3.36340i) q^{25} +(-0.689029 - 0.223879i) q^{26} +(-3.09345 + 4.25777i) q^{28} +(-2.95006 + 9.07936i) q^{29} +(4.84281 - 3.51851i) q^{31} -2.91456 q^{32} -1.13195 q^{34} +(6.42681 - 4.66935i) q^{35} +(1.83750 - 5.65524i) q^{37} +(-0.284966 + 0.392222i) q^{38} +(2.77422 + 0.901398i) q^{40} +(-2.60604 - 8.02058i) q^{41} +11.8763i q^{43} +(-1.86690 - 6.14238i) q^{44} +(-0.121726 - 0.167542i) q^{46} +(7.34041 - 2.38504i) q^{47} +(0.317615 + 0.230761i) q^{49} +(-0.725785 - 0.527314i) q^{50} +(5.25758 - 1.70829i) q^{52} +(6.14564 + 8.45874i) q^{53} +(-0.185009 + 9.68851i) q^{55} +2.71452i q^{56} +(0.748358 + 2.30321i) q^{58} +(-0.0887332 - 0.0288312i) q^{59} +(1.26024 - 1.73457i) q^{61} +(0.469246 - 1.44419i) q^{62} +(5.25595 - 3.81867i) q^{64} -8.34434 q^{65} -1.40778 q^{67} +(6.98766 - 5.07683i) q^{68} +(0.622728 - 1.91656i) q^{70} +(2.12141 - 2.91987i) q^{71} +(-1.67338 - 0.543714i) q^{73} +(-0.466129 - 1.43460i) q^{74} -3.69932i q^{76} +(-8.62796 + 2.62237i) q^{77} +(-4.19260 - 5.77063i) q^{79} +(-10.0535 + 3.26659i) q^{80} +(-1.73075 - 1.25747i) q^{82} +(6.33808 + 4.60488i) q^{83} +(-12.3992 + 4.02874i) q^{85} +(1.77084 + 2.43735i) q^{86} +(-2.64120 - 1.99709i) q^{88} +2.06830i q^{89} +(-2.39957 - 7.38512i) q^{91} +(1.50286 + 0.488310i) q^{92} +(1.15083 - 1.58398i) q^{94} +(-1.72551 + 5.31057i) q^{95} +(-1.35141 + 0.981858i) q^{97} +0.0995913 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70}+ \cdots + 60 q^{97}+O(q^{100}) \) 16 * q - 4 * q^4 - 20 * q^16 - 48 * q^22 - 32 * q^25 + 40 * q^28 + 16 * q^31 + 40 * q^34 - 12 * q^37 + 60 * q^40 - 40 * q^46 - 24 * q^49 - 40 * q^52 + 16 * q^55 + 12 * q^58 + 36 * q^64 + 96 * q^67 + 76 * q^70 - 20 * q^73 - 12 * q^82 - 100 * q^85 - 12 * q^88 - 72 * q^91 - 80 * q^94 + 60 * q^97

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