LMFDB - Embedded newform 99.4.f.e.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(37,99)]

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([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	99.91
Dual form			99.4.f.e.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39917 - 1.01656i) q^{2} +(-1.54785 + 4.76378i) q^{4} +(3.78707 + 2.75147i) q^{5} +(-2.91496 + 8.97133i) q^{7} +(6.95243 + 21.3974i) q^{8} +O(q^{10})$	\(q+(1.39917 - 1.01656i) q^{2} +(-1.54785 + 4.76378i) q^{4} +(3.78707 + 2.75147i) q^{5} +(-2.91496 + 8.97133i) q^{7} +(6.95243 + 21.3974i) q^{8} +8.09578 q^{10} +(20.8997 + 29.9032i) q^{11} +(-4.36138 + 3.16873i) q^{13} +(5.04133 + 15.5156i) q^{14} +(-0.939252 - 0.682406i) q^{16} +(68.6535 + 49.8797i) q^{17} +(-15.7316 - 48.4167i) q^{19} +(-18.9692 + 13.7819i) q^{20} +(59.6405 + 20.5940i) q^{22} +52.9969 q^{23} +(-31.8558 - 98.0420i) q^{25} +(-2.88112 + 8.86717i) q^{26} +(-38.2256 - 27.7725i) q^{28} +(35.2655 - 108.536i) q^{29} +(-67.7468 + 49.2209i) q^{31} -181.996 q^{32} +146.763 q^{34} +(-35.7235 + 25.9547i) q^{35} +(-47.0244 + 144.726i) q^{37} +(-71.2294 - 51.7512i) q^{38} +(-32.5449 + 100.163i) q^{40} +(-56.9163 - 175.170i) q^{41} -46.4843 q^{43} +(-174.802 + 53.2758i) q^{44} +(74.1517 - 53.8744i) q^{46} +(-120.309 - 370.274i) q^{47} +(205.505 + 149.308i) q^{49} +(-144.237 - 104.794i) q^{50} +(-8.34438 - 25.6814i) q^{52} +(462.541 - 336.055i) q^{53} +(-3.12935 + 170.751i) q^{55} -212.229 q^{56} +(-60.9906 - 187.710i) q^{58} +(-24.4445 + 75.2324i) q^{59} +(-584.546 - 424.697i) q^{61} +(-44.7534 + 137.737i) q^{62} +(-247.130 + 179.550i) q^{64} -25.2355 q^{65} +608.961 q^{67} +(-343.881 + 249.844i) q^{68} +(-23.5989 + 72.6299i) q^{70} +(740.521 + 538.020i) q^{71} +(186.265 - 573.266i) q^{73} +(81.3272 + 250.299i) q^{74} +254.997 q^{76} +(-329.194 + 100.331i) q^{77} +(298.418 - 216.813i) q^{79} +(-1.67939 - 5.16865i) q^{80} +(-257.706 - 187.234i) q^{82} +(797.245 + 579.233i) q^{83} +(122.753 + 377.796i) q^{85} +(-65.0394 + 47.2539i) q^{86} +(-494.548 + 655.099i) q^{88} +1156.34 q^{89} +(-15.7144 - 48.3641i) q^{91} +(-82.0312 + 252.466i) q^{92} +(-544.737 - 395.775i) q^{94} +(73.6406 - 226.643i) q^{95} +(-478.658 + 347.765i) q^{97} +439.317 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} - 28 q^{7}+O(q^{10}) $ 24 * q - 4 * q^4 - 28 * q^7	$ 24 q - 4 q^{4} - 28 q^{7} + 208 q^{10} + 20 q^{13} - 224 q^{16} - 40 q^{19} - 586 q^{22} + 362 q^{25} - 150 q^{28} + 670 q^{31} - 2520 q^{34} - 516 q^{37} + 2002 q^{40} + 4008 q^{43} + 2174 q^{46} + 342 q^{49} - 1894 q^{52} - 3300 q^{55} + 22 q^{58} - 2952 q^{61} - 3992 q^{64} - 1936 q^{67} - 1024 q^{70} + 2194 q^{73} + 15336 q^{76} + 1524 q^{79} + 2898 q^{82} - 7428 q^{85} - 3936 q^{88} - 6460 q^{91} - 16982 q^{94} - 1224 q^{97}+O(q^{100}) $ 24 * q - 4 * q^4 - 28 * q^7 + 208 * q^10 + 20 * q^13 - 224 * q^16 - 40 * q^19 - 586 * q^22 + 362 * q^25 - 150 * q^28 + 670 * q^31 - 2520 * q^34 - 516 * q^37 + 2002 * q^40 + 4008 * q^43 + 2174 * q^46 + 342 * q^49 - 1894 * q^52 - 3300 * q^55 + 22 * q^58 - 2952 * q^61 - 3992 * q^64 - 1936 * q^67 - 1024 * q^70 + 2194 * q^73 + 15336 * q^76 + 1524 * q^79 + 2898 * q^82 - 7428 * q^85 - 3936 * q^88 - 6460 * q^91 - 16982 * q^94 - 1224 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.39917	−	1.01656i	0.494681	−	0.359407i	−0.312301	−	0.949983i	$-0.601100\pi$
$2$	1.39917	−	1.01656i	0.494681	−	0.359407i	0.806982	+	0.590577i	$0.201100\pi$
$3$		0			0
$3$		0			0
$4$	−1.54785	+	4.76378i	−0.193481	+	0.595473i
$5$	3.78707	+	2.75147i	0.338726	+	0.246099i	0.744124	−	0.668041i	$-0.232867\pi$
$5$	3.78707	+	2.75147i	0.338726	+	0.246099i	−0.405398	+	0.914140i	$0.632867\pi$
$6$		0			0
$7$	−2.91496	+	8.97133i	−0.157393	+	0.484406i	−0.998396	−	0.0566252i	$-0.981966\pi$
$7$	−2.91496	+	8.97133i	−0.157393	+	0.484406i	0.841002	+	0.541031i	$0.181966\pi$
$8$	6.95243	+	21.3974i	0.307257	+	0.945640i
$9$		0			0
$10$	8.09578			0.256011
$11$	20.8997	+	29.9032i	0.572862	+	0.819652i
$11$	20.8997	+	29.9032i	0.572862	+	0.819652i
$12$		0			0
$13$	−4.36138	+	3.16873i	−0.0930483	+	0.0676036i	−0.633337	−	0.773876i	$-0.718315\pi$
$13$	−4.36138	+	3.16873i	−0.0930483	+	0.0676036i	0.540288	+	0.841480i	$0.318315\pi$
$14$	5.04133	+	15.5156i	0.0962395	+	0.296195i
$15$		0			0
$16$	−0.939252	−	0.682406i	−0.0146758	−	0.0106626i
$17$	68.6535	+	49.8797i	0.979466	+	0.711623i	0.957589	−	0.288137i	$-0.0930359\pi$
$17$	68.6535	+	49.8797i	0.979466	+	0.711623i	0.0218765	+	0.999761i	$0.493036\pi$
$18$		0			0
$19$	−15.7316	−	48.4167i	−0.189951	−	0.584608i	0.810048	−	0.586364i	$-0.199441\pi$
$19$	−15.7316	−	48.4167i	−0.189951	−	0.584608i	−0.999998	+	0.00175558i	$0.999441\pi$
$20$	−18.9692	+	13.7819i	−0.212082	+	0.154087i
$21$		0			0
$22$	59.6405	+	20.5940i	0.577973	+	0.199576i
$23$	52.9969			0.480462			0.240231	−	0.970716i	$-0.422777\pi$
$23$	52.9969			0.480462			0.240231	+	0.970716i	$0.422777\pi$
$24$		0			0
$25$	−31.8558	−	98.0420i	−0.254846	−	0.784336i
$26$	−2.88112	+	8.86717i	−0.0217321	+	0.0668844i
$27$		0			0
$28$	−38.2256	−	27.7725i	−0.257998	−	0.187447i
$29$	35.2655	−	108.536i	0.225815	−	0.694988i	−0.772393	−	0.635145i	$-0.780940\pi$
$29$	35.2655	−	108.536i	0.225815	−	0.694988i	0.998208	−	0.0598424i	$-0.0190598\pi$
$30$		0			0
$31$	−67.7468	+	49.2209i	−0.392506	+	0.285172i	−0.766482	−	0.642266i	$-0.777994\pi$
$31$	−67.7468	+	49.2209i	−0.392506	+	0.285172i	0.373976	+	0.927439i	$0.377994\pi$
$32$	−181.996			−1.00540
$33$		0			0
$34$	146.763			0.740285
$35$	−35.7235	+	25.9547i	−0.172525	+	0.125347i
$36$		0			0
$37$	−47.0244	+	144.726i	−0.208939	+	0.643049i	0.790589	+	0.612347i	$0.209774\pi$
$37$	−47.0244	+	144.726i	−0.208939	+	0.643049i	−0.999529	+	0.0307025i	$0.990226\pi$
$38$	−71.2294	−	51.7512i	−0.304077	−	0.220925i
$39$		0			0
$40$	−32.5449	+	100.163i	−0.128645	+	0.395929i
$41$	−56.9163	−	175.170i	−0.216801	−	0.667244i	−0.999021	−	0.0442420i	$-0.985913\pi$
$41$	−56.9163	−	175.170i	−0.216801	−	0.667244i	0.782220	−	0.623002i	$-0.214087\pi$
$42$		0			0
$43$	−46.4843			−0.164856			−0.0824278	−	0.996597i	$-0.526267\pi$
$43$	−46.4843			−0.164856			−0.0824278	+	0.996597i	$0.526267\pi$
$44$	−174.802	+	53.2758i	−0.598918	+	0.182537i
$45$		0			0
$46$	74.1517	−	53.8744i	0.237675	−	0.172681i
$47$	−120.309	−	370.274i	−0.373381	−	1.14915i	−0.944564	−	0.328326i	$-0.893515\pi$
$47$	−120.309	−	370.274i	−0.373381	−	1.14915i	0.571183	−	0.820823i	$-0.306485\pi$
$48$		0			0
$49$	205.505	+	149.308i	0.599140	+	0.435301i
$50$	−144.237	−	104.794i	−0.407963	−	0.296403i
$51$		0			0
$52$	−8.34438	−	25.6814i	−0.0222530	−	0.0684878i
$53$	462.541	−	336.055i	1.19877	−	0.870958i	0.204607	−	0.978844i	$-0.434408\pi$
$53$	462.541	−	336.055i	1.19877	−	0.870958i	0.994163	+	0.107887i	$0.0344083\pi$
$54$		0			0
$55$	−3.12935	+	170.751i	−0.00767204	+	0.418618i
$56$	−212.229			−0.506434
$57$		0			0
$58$	−60.9906	−	187.710i	−0.138077	−	0.424957i
$59$	−24.4445	+	75.2324i	−0.0539390	+	0.166007i	−0.974397	−	0.224834i	$-0.927816\pi$
$59$	−24.4445	+	75.2324i	−0.0539390	+	0.166007i	0.920458	+	0.390841i	$0.127816\pi$
$60$		0			0
$61$	−584.546	−	424.697i	−1.22694	−	0.891425i	−0.230284	−	0.973123i	$-0.573966\pi$
$61$	−584.546	−	424.697i	−1.22694	−	0.891425i	−0.996657	+	0.0816982i	$0.973966\pi$
$62$	−44.7534	+	137.737i	−0.0916724	+	0.282139i
$63$		0			0
$64$	−247.130	+	179.550i	−0.482675	+	0.350684i
$65$	−25.2355			−0.0481551
$66$		0			0
$67$	608.961			1.11039			0.555197	−	0.831719i	$-0.312643\pi$
$67$	608.961			1.11039			0.555197	+	0.831719i	$0.312643\pi$
$68$	−343.881	+	249.844i	−0.613260	+	0.445560i
$69$		0			0
$70$	−23.5989	+	72.6299i	−0.0402944	+	0.124013i
$71$	740.521	+	538.020i	1.23780	+	0.899313i	0.997450	−	0.0713741i	$-0.0227384\pi$
$71$	740.521	+	538.020i	1.23780	+	0.899313i	0.240348	+	0.970687i	$0.422738\pi$
$72$		0			0
$73$	186.265	−	573.266i	0.298640	−	0.919119i	−0.683335	−	0.730105i	$-0.739471\pi$
$73$	186.265	−	573.266i	0.298640	−	0.919119i	0.981975	−	0.189013i	$-0.0605290\pi$
$74$	81.3272	+	250.299i	0.127758	+	0.393199i
$75$		0			0
$76$	254.997			0.384870
$77$	−329.194	+	100.331i	−0.487209	+	0.148490i
$78$		0			0
$79$	298.418	−	216.813i	0.424996	−	0.308777i	−0.354649	−	0.935000i	$-0.615400\pi$
$79$	298.418	−	216.813i	0.424996	−	0.308777i	0.779645	+	0.626222i	$0.215400\pi$
$80$	−1.67939	−	5.16865i	−0.00234703	−	0.00722340i
$81$		0			0
$82$	−257.706	−	187.234i	−0.347059	−	0.252153i
$83$	797.245	+	579.233i	1.05433	+	0.766012i	0.973030	−	0.230678i	$-0.0740943\pi$
$83$	797.245	+	579.233i	1.05433	+	0.766012i	0.0812954	+	0.996690i	$0.474094\pi$
$84$		0			0
$85$	122.753	+	377.796i	0.156641	+	0.482091i
$86$	−65.0394	+	47.2539i	−0.0815510	+	0.0592502i
$87$		0			0
$88$	−494.548	+	655.099i	−0.599080	+	0.793565i
$89$	1156.34			1.37721			0.688605	−	0.725137i	$-0.258224\pi$
$89$	1156.34			1.37721			0.688605	+	0.725137i	$0.258224\pi$
$90$		0			0
$91$	−15.7144	−	48.3641i	−0.0181024	−	0.0557135i
$92$	−82.0312	+	252.466i	−0.0929602	+	0.286102i
$93$		0			0
$94$	−544.737	−	395.775i	−0.597717	−	0.434266i
$95$	73.6406	−	226.643i	0.0795302	−	0.244769i
$96$		0			0
$97$	−478.658	+	347.765i	−0.501035	+	0.364023i	−0.809412	−	0.587241i	$-0.800214\pi$
$97$	−478.658	+	347.765i	−0.501035	+	0.364023i	0.308377	+	0.951264i	$0.400214\pi$
$98$	439.317			0.452833
$99$		0			0
$100$	516.359			0.516359
$101$	−662.096	+	481.041i	−0.652287	+	0.473915i	−0.864050	−	0.503407i	$-0.832080\pi$
$101$	−662.096	+	481.041i	−0.652287	+	0.473915i	0.211762	+	0.977321i	$0.432080\pi$
$102$		0			0
$103$	−463.889	+	1427.70i	−0.443770	+	1.36578i	0.440057	+	0.897970i	$0.354958\pi$
$103$	−463.889	+	1427.70i	−0.443770	+	1.36578i	−0.883827	+	0.467814i	$0.845042\pi$
$104$	−98.1246	−	71.2917i	−0.0925184	−	0.0672185i
$105$		0			0
$106$	305.553	−	940.397i	0.279981	−	0.861692i
$107$	204.593	+	629.673i	0.184848	+	0.568904i	0.999946	−	0.0104195i	$-0.00331668\pi$
$107$	204.593	+	629.673i	0.184848	+	0.568904i	−0.815097	+	0.579324i	$0.803317\pi$
$108$		0			0
$109$	1666.14			1.46411			0.732053	−	0.681247i	$-0.238562\pi$
$109$	1666.14			1.46411			0.732053	+	0.681247i	$0.238562\pi$
$110$	169.199	+	242.090i	0.146659	+	0.209840i
$111$		0			0
$112$	8.85998	−	6.43715i	0.00747490	−	0.00543083i
$113$	−440.511	−	1355.75i	−0.366723	−	1.12866i	−0.948895	−	0.315593i	$-0.897797\pi$
$113$	−440.511	−	1355.75i	−0.366723	−	1.12866i	0.582171	−	0.813066i	$-0.302203\pi$
$114$		0			0
$115$	200.703	+	145.819i	0.162745	+	0.118241i
$116$	462.457	+	335.995i	0.370156	+	0.268934i
$117$		0			0
$118$	42.2760	+	130.112i	0.0329815	+	0.101507i
$119$	−647.609	+	470.516i	−0.498876	+	0.362455i
$120$		0			0
$121$	−457.409	+	1249.94i	−0.343658	+	0.939095i
$122$	−1249.61			−0.927329
$123$		0			0
$124$	−129.616	−	398.918i	−0.0938700	−	0.288902i
$125$	329.936	−	1015.44i	0.236083	−	0.726589i
$126$		0			0
$127$	−1998.96	−	1452.33i	−1.39668	−	1.01475i	−0.995095	−	0.0989279i	$-0.968459\pi$
$127$	−1998.96	−	1452.33i	−1.39668	−	1.01475i	−0.401587	−	0.915821i	$-0.631541\pi$
$128$	286.666	−	882.268i	0.197953	−	0.609236i
$129$		0			0
$130$	−35.3087	+	25.6533i	−0.0238214	+	0.0173073i
$131$	−1695.42			−1.13076			−0.565380	−	0.824831i	$-0.691270\pi$
$131$	−1695.42			−1.13076			−0.565380	+	0.824831i	$0.691270\pi$
$132$		0			0
$133$	480.219			0.313085
$134$	852.040	−	619.043i	0.549291	−	0.399083i
$135$		0			0
$136$	−589.986	+	1815.79i	−0.371992	+	1.14487i
$137$	−1029.78	−	748.176i	−0.642187	−	0.466576i	0.218414	−	0.975856i	$-0.429912\pi$
$137$	−1029.78	−	748.176i	−0.642187	−	0.466576i	−0.860601	+	0.509280i	$0.829912\pi$
$138$		0			0
$139$	999.189	−	3075.19i	0.609713	−	1.87650i	0.149319	−	0.988789i	$-0.452292\pi$
$139$	999.189	−	3075.19i	0.609713	−	1.87650i	0.460394	−	0.887715i	$-0.347708\pi$
$140$	−68.3478	−	210.353i	−0.0412603	−	0.126986i
$141$		0			0
$142$	1583.04			0.935534
$143$	−185.906	−	64.1940i	−0.108715	−	0.0375397i
$144$		0			0
$145$	432.187	−	314.002i	0.247525	−	0.179838i
$146$	−322.140	−	991.445i	−0.182606	−	0.562004i
$147$		0			0
$148$	−616.657	−	448.028i	−0.342493	−	0.248836i
$149$	−1327.84	−	964.731i	−0.730072	−	0.530428i	0.159514	−	0.987196i	$-0.449007\pi$
$149$	−1327.84	−	964.731i	−0.730072	−	0.530428i	−0.889586	+	0.456767i	$0.849007\pi$
$150$		0			0
$151$	−20.2191	−	62.2281i	−0.0108967	−	0.0335367i	0.945460	−	0.325737i	$-0.105613\pi$
$151$	−20.2191	−	62.2281i	−0.0108967	−	0.0335367i	−0.956357	+	0.292201i	$0.905613\pi$
$152$	926.619	−	673.228i	0.494465	−	0.359250i
$153$		0			0
$154$	−358.606	+	475.024i	−0.187645	+	0.248562i
$155$	−391.992			−0.203133
$156$		0			0
$157$	−429.420	−	1321.62i	−0.218290	−	0.671826i	−0.998904	−	0.0468130i	$-0.985094\pi$
$157$	−429.420	−	1321.62i	−0.218290	−	0.671826i	0.780614	−	0.625013i	$-0.214906\pi$
$158$	197.134	−	606.718i	0.0992606	−	0.305493i
$159$		0			0
$160$	−689.233	−	500.757i	−0.340554	−	0.247427i
$161$	−154.484	+	475.453i	−0.0756214	+	0.232739i
$162$		0			0
$163$	−2018.89	+	1466.81i	−0.970134	+	0.704844i	−0.955482	−	0.295049i	$-0.904664\pi$
$163$	−2018.89	+	1466.81i	−0.970134	+	0.704844i	−0.0146519	+	0.999893i	$0.504664\pi$
$164$	922.571			0.439273
$165$		0			0
$166$	1704.30			0.796865
$167$	−893.670	+	649.289i	−0.414097	+	0.300859i	−0.775259	−	0.631644i	$-0.782380\pi$
$167$	−893.670	+	649.289i	−0.414097	+	0.300859i	0.361161	+	0.932503i	$0.382380\pi$
$168$		0			0
$169$	−669.930	+	2061.83i	−0.304929	+	0.938476i
$170$	555.804	+	403.815i	0.250754	+	0.182183i
$171$		0			0
$172$	71.9506	−	221.441i	0.0318964	−	0.0981671i
$173$	−850.878	−	2618.73i	−0.373937	−	1.15086i	−0.944193	−	0.329393i	$-0.893156\pi$
$173$	−850.878	−	2618.73i	−0.373937	−	1.15086i	0.570256	−	0.821467i	$-0.306844\pi$
$174$		0			0
$175$	972.426			0.420048
$176$	0.776128	−	42.3487i	0.000332402	−	0.0181373i
$177$		0			0
$178$	1617.91	−	1175.48i	0.681279	−	0.494978i
$179$	1317.84	+	4055.88i	0.550277	+	1.69358i	0.708100	+	0.706112i	$0.249553\pi$
$179$	1317.84	+	4055.88i	0.550277	+	1.69358i	−0.157823	+	0.987467i	$0.550447\pi$
$180$		0			0
$181$	983.685	+	714.689i	0.403960	+	0.293494i	0.771152	−	0.636651i	$-0.219681\pi$
$181$	983.685	+	714.689i	0.403960	+	0.293494i	−0.367192	+	0.930145i	$0.619681\pi$
$182$	−71.1519	−	51.6949i	−0.0289787	−	0.0210543i
$183$		0			0
$184$	368.458	+	1134.00i	0.147625	+	0.454344i
$185$	−576.294	+	418.702i	−0.229027	+	0.166398i
$186$		0			0
$187$	−56.7301	+	3095.43i	−0.0221846	+	1.21048i
$188$	1950.13			0.756529
$189$		0			0
$190$	−127.359	−	391.971i	−0.0486295	−	0.149666i
$191$	−1378.93	+	4243.91i	−0.522387	+	1.60774i	0.247040	+	0.969005i	$0.420542\pi$
$191$	−1378.93	+	4243.91i	−0.522387	+	1.60774i	−0.769427	+	0.638735i	$0.779458\pi$
$192$		0			0
$193$	−3934.29	−	2858.43i	−1.46734	−	1.06608i	−0.981374	−	0.192105i	$-0.938469\pi$
$193$	−3934.29	−	2858.43i	−1.46734	−	1.06608i	−0.485964	−	0.873979i	$-0.661531\pi$
$194$	−316.201	+	973.165i	−0.117020	+	0.360151i
$195$		0			0
$196$	−1029.36	+	747.876i	−0.375132	+	0.272549i
$197$	1082.10			0.391353			0.195677	−	0.980668i	$-0.437310\pi$
$197$	1082.10			0.391353			0.195677	+	0.980668i	$0.437310\pi$
$198$		0			0
$199$	3503.59			1.24805			0.624027	−	0.781403i	$-0.285496\pi$
$199$	3503.59			1.24805			0.624027	+	0.781403i	$0.285496\pi$
$200$	1876.37	−	1363.26i	0.663396	−	0.481986i
$201$		0			0
$202$	−437.379	+	1346.12i	−0.152346	+	0.468873i
$203$	870.915	+	632.757i	0.301115	+	0.218773i
$204$		0			0
$205$	266.430	−	819.986i	0.0907720	−	0.279367i
$206$	802.281	+	2469.17i	0.271348	+	0.835122i
$207$		0			0
$208$	6.25879			0.00208639
$209$	1119.03	−	1482.32i	0.370360	−	0.490594i
$210$		0			0
$211$	−1346.68	+	978.420i	−0.439380	+	0.319229i	−0.785389	−	0.619003i	$-0.787537\pi$
$211$	−1346.68	+	978.420i	−0.439380	+	0.319229i	0.346008	+	0.938231i	$0.387537\pi$
$212$	884.953	+	2723.61i	0.286693	+	0.882349i
$213$		0			0
$214$	926.358	+	673.038i	0.295909	+	0.214990i
$215$	−176.040	−	127.900i	−0.0558409	−	0.0405708i
$216$		0			0
$217$	−244.098	−	751.256i	−0.0763615	−	0.235017i
$218$	2331.22	−	1693.73i	0.724266	−	0.526210i
$219$		0			0
$220$	−808.575	−	279.203i	−0.247791	−	0.0855631i
$221$	−457.479			−0.139246
$222$		0			0
$223$	−299.904	−	923.008i	−0.0900584	−	0.277171i	0.895876	−	0.444304i	$-0.146549\pi$
$223$	−299.904	−	923.008i	−0.0900584	−	0.277171i	−0.985934	+	0.167133i	$0.946549\pi$
$224$	530.512	−	1632.75i	0.158243	−	0.487021i
$225$		0			0
$226$	−1994.55	−	1449.12i	−0.587059	−	0.426523i
$227$	−926.181	+	2850.49i	−0.270805	+	0.833452i	0.719494	+	0.694499i	$0.244374\pi$
$227$	−926.181	+	2850.49i	−0.270805	+	0.833452i	−0.990299	+	0.138954i	$0.955626\pi$
$228$		0			0
$229$	65.2714	−	47.4224i	0.0188352	−	0.0136846i	−0.578328	−	0.815804i	$-0.696295\pi$
$229$	65.2714	−	47.4224i	0.0188352	−	0.0136846i	0.597163	+	0.802120i	$0.296295\pi$
$230$	429.052			0.123004
$231$		0			0
$232$	2567.57			0.726592
$233$	1982.72	−	1440.53i	0.557477	−	0.405031i	−0.273058	−	0.961998i	$-0.588035\pi$
$233$	1982.72	−	1440.53i	0.557477	−	0.405031i	0.830535	+	0.556967i	$0.188035\pi$
$234$		0			0
$235$	563.177	−	1733.28i	0.156330	−	0.481135i
$236$	−320.555	−	232.897i	−0.0884166	−	0.0642384i
$237$		0			0
$238$	−427.810	+	1316.66i	−0.116516	+	0.358599i
$239$	−28.2604	−	86.9764i	−0.00764858	−	0.0235399i	0.947159	−	0.320763i	$-0.103939\pi$
$239$	−28.2604	−	86.9764i	−0.00764858	−	0.0235399i	−0.954808	+	0.297223i	$0.903939\pi$
$240$		0			0
$241$	189.338			0.0506073			0.0253036	−	0.999680i	$-0.491945\pi$
$241$	189.338			0.0506073			0.0253036	+	0.999680i	$0.491945\pi$
$242$	630.637	+	2213.85i	0.167516	+	0.588065i
$243$		0			0
$244$	2927.95	−	2127.28i	0.768209	−	0.558137i
$245$	367.446	+	1130.88i	0.0958174	+	0.294896i
$246$		0			0
$247$	222.031	+	161.315i	0.0571962	+	0.0415555i
$248$	−1524.21	−	1107.40i	−0.390271	−	0.283548i
$249$		0			0
$250$	−570.614	−	1756.17i	−0.144355	−	0.444280i
$251$	−4126.35	+	2997.97i	−1.03766	+	0.753905i	−0.969828	−	0.243792i	$-0.921609\pi$
$251$	−4126.35	+	2997.97i	−1.03766	+	0.753905i	−0.0678331	+	0.997697i	$0.521609\pi$
$252$		0			0
$253$	1107.62	+	1584.78i	0.275238	+	0.393811i
$254$	−4273.25			−1.05562
$255$		0			0
$256$	−1250.94	−	3850.00i	−0.305406	−	0.939941i
$257$	791.745	−	2436.74i	0.192170	−	0.591439i	−0.807828	−	0.589418i	$-0.799357\pi$
$257$	791.745	−	2436.74i	0.192170	−	0.591439i	0.999998	−	0.00202014i	$-0.000643032\pi$
$258$		0			0
$259$	−1161.31	−	843.742i	−0.278612	−	0.202423i
$260$	39.0607	−	120.216i	0.00931708	−	0.0286750i
$261$		0			0
$262$	−2372.18	+	1723.49i	−0.559365	+	0.406403i
$263$	2068.82			0.485052			0.242526	−	0.970145i	$-0.422024\pi$
$263$	2068.82			0.485052			0.242526	+	0.970145i	$0.422024\pi$
$264$		0			0
$265$	2676.32			0.620397
$266$	671.908	−	488.170i	0.154877	−	0.112525i
$267$		0			0
$268$	−942.579	+	2900.96i	−0.214840	+	0.661210i
$269$	−5574.83	−	4050.35i	−1.26358	−	0.918045i	−0.264653	−	0.964344i	$-0.585257\pi$
$269$	−5574.83	−	4050.35i	−1.26358	−	0.918045i	−0.998928	+	0.0462986i	$0.985257\pi$
$270$		0			0
$271$	65.7913	−	202.485i	0.0147474	−	0.0453878i	−0.943412	−	0.331623i	$-0.892404\pi$
$271$	65.7913	−	202.485i	0.0147474	−	0.0453878i	0.958159	+	0.286235i	$0.0924038\pi$
$272$	−30.4447	−	93.6992i	−0.00678670	−	0.0208873i
$273$		0			0
$274$	−2201.39			−0.485369
$275$	2266.00	−	3001.64i	0.496891	−	0.658202i
$276$		0			0
$277$	−999.154	+	725.928i	−0.216727	+	0.157461i	−0.690852	−	0.722996i	$-0.742764\pi$
$277$	−999.154	+	725.928i	−0.216727	+	0.157461i	0.474125	+	0.880457i	$0.342764\pi$
$278$	−1728.07	−	5318.44i	−0.372815	−	1.14741i
$279$		0			0
$280$	−803.727	−	583.942i	−0.171542	−	0.124633i
$281$	−1117.78	−	812.117i	−0.237300	−	0.172409i	0.462779	−	0.886473i	$-0.346852\pi$
$281$	−1117.78	−	812.117i	−0.237300	−	0.172409i	−0.700080	+	0.714065i	$0.746852\pi$
$282$		0			0
$283$	540.993	+	1665.00i	0.113635	+	0.349732i	0.991660	−	0.128883i	$-0.0411390\pi$
$283$	540.993	+	1665.00i	0.113635	+	0.349732i	−0.878025	+	0.478615i	$0.841139\pi$
$284$	−3709.22	+	2694.91i	−0.775007	+	0.563075i
$285$		0			0
$286$	−325.371	+	99.1660i	−0.0672714	+	0.0205028i
$287$	1737.42			0.357340
$288$		0			0
$289$	707.119	+	2176.29i	0.143928	+	0.442965i
$290$	285.502	−	878.684i	0.0578112	−	0.177925i
$291$		0			0
$292$	2442.60	+	1774.66i	0.489529	+	0.355664i
$293$	2551.21	−	7851.82i	0.508680	−	1.56556i	−0.285814	−	0.958285i	$-0.592264\pi$
$293$	2551.21	−	7851.82i	0.508680	−	1.56556i	0.794495	−	0.607271i	$-0.207736\pi$
$294$		0			0
$295$	−299.573	+	217.652i	−0.0591247	+	0.0429566i
$296$	−3423.70			−0.672291
$297$		0			0
$298$	−2838.57			−0.551792
$299$	−231.140	+	167.933i	−0.0447062	+	0.0324809i
$300$		0			0
$301$	135.500	−	417.026i	0.0259471	−	0.0798571i
$302$	−91.5483	−	66.5137i	−0.0174438	−	0.0126736i
$303$		0			0
$304$	−18.2640	+	56.2108i	−0.00344576	+	0.0106050i
$305$	−1045.18	−	3216.72i	−0.196218	−	0.603898i
$306$		0			0
$307$	3649.18			0.678403			0.339201	−	0.940714i	$-0.389843\pi$
$307$	3649.18			0.678403			0.339201	+	0.940714i	$0.389843\pi$
$308$	31.5867	−	1723.50i	0.00584358	−	0.318850i
$309$		0			0
$310$	−548.463	+	398.482i	−0.100486	+	0.0730073i
$311$	1416.80	+	4360.46i	0.258326	+	0.795045i	0.993156	+	0.116794i	$0.0372617\pi$
$311$	1416.80	+	4360.46i	0.258326	+	0.795045i	−0.734830	+	0.678251i	$0.762738\pi$
$312$		0			0
$313$	2506.95	+	1821.41i	0.452720	+	0.328920i	0.790669	−	0.612244i	$-0.209733\pi$
$313$	2506.95	+	1821.41i	0.452720	+	0.328920i	−0.337949	+	0.941165i	$0.609733\pi$
$314$	−1944.33	−	1412.64i	−0.349443	−	0.253885i
$315$		0			0
$316$	570.947	+	1757.19i	0.101640	+	0.312816i
$317$	−2004.46	+	1456.33i	−0.355148	+	0.258030i	−0.751025	−	0.660273i	$-0.770440\pi$
$317$	−2004.46	+	1456.33i	−0.355148	+	0.258030i	0.395878	+	0.918303i	$0.370440\pi$
$318$		0			0
$319$	3982.62	−	1213.81i	0.699009	−	0.213042i
$320$	−1429.92			−0.249798
$321$		0			0
$322$	267.175	+	822.281i	0.0462394	+	0.142310i
$323$	1334.99	−	4108.66i	0.229971	−	0.707777i
$324$		0			0
$325$	449.603	+	326.656i	0.0767369	+	0.0557527i
$326$	−1333.68	+	4104.63i	−0.226581	+	0.697346i
$327$		0			0
$328$	3352.48	−	2435.72i	0.564359	−	0.410031i
$329$	3672.55			0.615423
$330$		0			0
$331$	−7320.24			−1.21558			−0.607790	−	0.794098i	$-0.707944\pi$
$331$	−7320.24			−1.21558			−0.607790	+	0.794098i	$0.707944\pi$
$332$	−3993.35	+	2901.34i	−0.660132	+	0.479614i
$333$		0			0
$334$	−590.357	+	1816.93i	−0.0967153	+	0.297659i
$335$	2306.18	+	1675.54i	0.376120	+	0.273267i
$336$		0			0
$337$	110.688	−	340.662i	0.0178918	−	0.0550654i	−0.941712	−	0.336420i	$-0.890784\pi$
$337$	110.688	−	340.662i	0.0178918	−	0.0550654i	0.959604	+	0.281355i	$0.0907838\pi$
$338$	1158.62	+	3565.87i	0.186452	+	0.573840i
$339$		0			0
$340$	−1989.74			−0.317379
$341$	−2887.75	−	997.149i	−0.458594	−	0.158354i
$342$		0			0
$343$	−4556.13	+	3310.22i	−0.717224	+	0.521093i
$344$	−323.179	−	994.643i	−0.0506531	−	0.155894i
$345$		0			0
$346$	−3852.61	−	2799.09i	−0.598606	−	0.434913i
$347$	4305.99	+	3128.49i	0.666161	+	0.483994i	0.868738	−	0.495272i	$-0.164932\pi$
$347$	4305.99	+	3128.49i	0.666161	+	0.483994i	−0.202577	+	0.979266i	$0.564932\pi$
$348$		0			0
$349$	−2741.98	−	8438.95i	−0.420559	−	1.29435i	−0.907184	−	0.420735i	$-0.861772\pi$
$349$	−2741.98	−	8438.95i	−0.420559	−	1.29435i	0.486625	−	0.873611i	$-0.338228\pi$
$350$	1360.59	−	988.525i	0.207790	−	0.150968i
$351$		0			0
$352$	−3803.66	−	5442.28i	−0.575954	−	0.824075i
$353$	6975.14			1.05170			0.525849	−	0.850578i	$-0.323748\pi$
$353$	6975.14			1.05170			0.525849	+	0.850578i	$0.323748\pi$
$354$		0			0
$355$	1324.06	+	4075.04i	0.197955	+	0.609241i
$356$	−1789.83	+	5508.55i	−0.266464	+	0.820091i
$357$		0			0
$358$	5966.90	+	4335.21i	0.880896	+	0.640008i
$359$	−1504.86	+	4631.50i	−0.221236	+	0.680894i	0.777416	+	0.628987i	$0.216530\pi$
$359$	−1504.86	+	4631.50i	−0.221236	+	0.680894i	−0.998652	+	0.0519074i	$0.983470\pi$
$360$		0			0
$361$	3452.35	−	2508.28i	0.503331	−	0.365692i
$362$	2102.86			0.305315
$363$		0			0
$364$	254.719			0.0366784
$365$	2282.72	−	1658.50i	0.327351	−	0.237835i
$366$		0			0
$367$	2530.11	−	7786.88i	0.359866	−	1.10755i	−0.593268	−	0.805005i	$-0.702163\pi$
$367$	2530.11	−	7786.88i	0.359866	−	1.10755i	0.953134	−	0.302548i	$-0.0978373\pi$
$368$	−49.7775	−	36.1654i	−0.00705117	−	0.00512297i
$369$		0			0
$370$	−380.699	+	1171.67i	−0.0534908	+	0.164628i
$371$	1666.58	+	5129.19i	0.233219	+	0.717775i
$372$		0			0
$373$	−817.268			−0.113449			−0.0567246	−	0.998390i	$-0.518066\pi$
$373$	−817.268			−0.113449			−0.0567246	+	0.998390i	$0.518066\pi$
$374$	3067.30	+	4388.70i	0.424082	+	0.606776i
$375$		0			0
$376$	7086.45	−	5148.61i	0.971957	−	0.706168i
$377$	190.115	+	585.113i	0.0259719	+	0.0799334i
$378$		0			0
$379$	−78.6699	−	57.1570i	−0.0106623	−	0.00774660i	0.582441	−	0.812873i	$-0.302098\pi$
$379$	−78.6699	−	57.1570i	−0.0106623	−	0.00774660i	−0.593104	+	0.805126i	$0.702098\pi$
$380$	965.692	+	701.616i	0.130366	+	0.0947162i
$381$		0			0
$382$	2384.82	+	7339.71i	0.319418	+	0.983068i
$383$	9880.66	−	7178.72i	1.31822	−	0.957743i	0.318267	−	0.948001i	$-0.396899\pi$
$383$	9880.66	−	7178.72i	1.31822	−	0.957743i	0.999953	−	0.00974165i	$-0.00310091\pi$
$384$		0			0
$385$	−1522.74	−	525.806i	−0.201574	−	0.0696040i
$386$	−8410.49			−1.10902
$387$		0			0
$388$	−915.790	−	2818.51i	−0.119825	−	0.368784i
$389$	−1344.09	+	4136.69i	−0.175188	+	0.539174i	−0.999642	−	0.0267554i	$-0.991482\pi$
$389$	−1344.09	+	4136.69i	−0.175188	+	0.539174i	0.824454	+	0.565929i	$0.191482\pi$
$390$		0			0
$391$	3638.42	+	2643.47i	0.470596	+	0.341908i
$392$	−1766.05	+	5435.33i	−0.227548	+	0.700320i
$393$		0			0
$394$	1514.04	−	1100.02i	0.193595	−	0.140655i
$395$	1726.69			0.219947
$396$		0			0
$397$	−11423.8			−1.44420			−0.722098	−	0.691791i	$-0.756822\pi$
$397$	−11423.8			−1.44420			−0.722098	+	0.691791i	$0.756822\pi$
$398$	4902.11	−	3561.59i	0.617388	−	0.448559i
$399$		0			0
$400$	−36.9839	+	113.825i	−0.00462299	+	0.0142281i
$401$	12585.5	+	9143.87i	1.56730	+	1.13871i	0.929684	+	0.368359i	$0.120080\pi$
$401$	12585.5	+	9143.87i	1.56730	+	1.13871i	0.637618	+	0.770352i	$0.279920\pi$
$402$		0			0
$403$	139.502	−	429.342i	0.0172434	−	0.0530696i
$404$	−1266.75	−	3898.66i	−0.155998	−	0.480113i
$405$		0			0
$406$	1861.79			0.227584
$407$	−5310.57	+	1618.55i	−0.646770	+	0.197121i
$408$		0			0
$409$	−9197.12	+	6682.10i	−1.11190	+	0.807845i	−0.982962	−	0.183808i	$-0.941158\pi$
$409$	−9197.12	+	6682.10i	−1.11190	+	0.807845i	−0.128940	+	0.991652i	$0.541158\pi$
$410$	−460.782	−	1418.14i	−0.0555034	−	0.170822i
$411$		0			0
$412$	−6083.24	−	4419.73i	−0.727427	−	0.528506i
$413$	−603.680	−	438.599i	−0.0719253	−	0.0522568i
$414$		0			0
$415$	1425.48	+	4387.19i	0.168613	+	0.518937i
$416$	793.754	−	576.696i	0.0935505	−	0.0679684i
$417$		0			0
$418$	58.8587	−	3211.57i	0.00688725	−	0.375797i
$419$	3798.45			0.442880			0.221440	−	0.975174i	$-0.428924\pi$
$419$	3798.45			0.442880			0.221440	+	0.975174i	$0.428924\pi$
$420$		0			0
$421$	4277.70	+	13165.4i	0.495208	+	1.52409i	0.816633	+	0.577157i	$0.195838\pi$
$421$	4277.70	+	13165.4i	0.495208	+	1.52409i	−0.321425	+	0.946935i	$0.604162\pi$
$422$	−889.614	+	2737.95i	−0.102620	+	0.315833i
$423$		0			0
$424$	10406.5	+	7560.76i	1.19194	+	0.865997i
$425$	2703.29	−	8319.88i	0.308539	−	0.949585i
$426$		0			0
$427$	5514.03	−	4006.18i	0.624924	−	0.454034i
$428$	−3316.30			−0.374532
$429$		0			0
$430$	−376.327			−0.0422049
$431$	−10280.2	+	7469.03i	−1.14891	+	0.834735i	−0.988336	−	0.152289i	$-0.951336\pi$
$431$	−10280.2	+	7469.03i	−1.14891	+	0.834735i	−0.160578	+	0.987023i	$0.551336\pi$
$432$		0			0
$433$	5000.41	−	15389.7i	0.554975	−	1.70804i	−0.141034	−	0.990005i	$-0.545043\pi$
$433$	5000.41	−	15389.7i	0.554975	−	1.70804i	0.696009	−	0.718033i	$-0.254957\pi$
$434$	−1105.23	−	802.995i	−0.122241	−	0.0888134i
$435$		0			0
$436$	−2578.94	+	7937.15i	−0.283277	+	0.871836i
$437$	−833.724	−	2565.94i	−0.0912641	−	0.280882i
$438$		0			0
$439$	−14356.7			−1.56084			−0.780419	−	0.625256i	$-0.784994\pi$
$439$	−14356.7			−1.56084			−0.780419	+	0.625256i	$0.784994\pi$
$440$	−3675.37	+	1120.17i	−0.398219	+	0.121368i
$441$		0			0
$442$	−640.090	+	465.053i	−0.0688823	+	0.0500459i
$443$	−1131.96	−	3483.80i	−0.121401	−	0.373635i	0.871827	−	0.489814i	$-0.162935\pi$
$443$	−1131.96	−	3483.80i	−0.121401	−	0.373635i	−0.993228	+	0.116179i	$0.962935\pi$
$444$		0			0
$445$	4379.14	+	3181.63i	0.466497	+	0.338930i
$446$	−1357.91	−	986.576i	−0.144167	−	0.104744i
$447$		0			0
$448$	−890.430	−	2740.46i	−0.0939037	−	0.289006i
$449$	2659.66	−	1932.36i	0.279548	−	0.203104i	−0.439172	−	0.898403i	$-0.644728\pi$
$449$	2659.66	−	1932.36i	0.279548	−	0.203104i	0.718720	+	0.695299i	$0.244728\pi$
$450$		0			0
$451$	4048.63	−	5362.98i	0.422711	−	0.559940i
$452$	7140.35			0.743040
$453$		0			0
$454$	1601.80	+	4929.83i	0.165586	+	0.509622i
$455$	73.5605	−	226.396i	0.00757928	−	0.0233266i
$456$		0			0
$457$	6050.71	+	4396.10i	0.619344	+	0.449980i	0.852692	−	0.522413i	$-0.174968\pi$
$457$	6050.71	+	4396.10i	0.619344	+	0.449980i	−0.233348	+	0.972393i	$0.574968\pi$
$458$	43.1182	−	132.704i	0.00439908	−	0.0135390i
$459$		0			0
$460$	−1005.31	+	730.401i	−0.101897	+	0.0740328i
$461$	−16077.1			−1.62427			−0.812134	−	0.583471i	$-0.801694\pi$
$461$	−16077.1			−1.62427			−0.812134	+	0.583471i	$0.801694\pi$
$462$		0			0
$463$	−8332.21			−0.836352			−0.418176	−	0.908366i	$-0.637330\pi$
$463$	−8332.21			−0.836352			−0.418176	+	0.908366i	$0.637330\pi$
$464$	−107.189	+	77.8773i	−0.0107244	+	0.00779173i
$465$		0			0
$466$	1309.78	−	4031.08i	0.130202	−	0.400722i
$467$	−14316.8	−	10401.7i	−1.41863	−	1.03070i	−0.991995	−	0.126274i	$-0.959698\pi$
$467$	−14316.8	−	10401.7i	−1.41863	−	1.03070i	−0.426637	−	0.904423i	$-0.640302\pi$
$468$		0			0
$469$	−1775.10	+	5463.19i	−0.174769	+	0.537882i
$470$	−973.997	−	2997.66i	−0.0955897	−	0.294195i
$471$		0			0
$472$	−1779.73			−0.173556
$473$	−971.506	−	1390.03i	−0.0944395	−	0.135124i
$474$		0			0
$475$	−4245.73	+	3084.71i	−0.410121	+	0.297971i
$476$	−1239.03	−	3813.36i	−0.119309	−	0.367195i
$477$		0			0
$478$	−127.957	−	92.9665i	−0.0122440	−	0.00889579i
$479$	6413.14	+	4659.42i	0.611741	+	0.444456i	0.850027	−	0.526739i	$-0.176586\pi$
$479$	6413.14	+	4659.42i	0.611741	+	0.444456i	−0.238286	+	0.971195i	$0.576586\pi$
$480$		0			0
$481$	−253.506	−	780.212i	−0.0240310	−	0.0739597i
$482$	264.916	−	192.473i	0.0250345	−	0.0181886i
$483$		0			0
$484$	−5246.42	−	4113.70i	−0.492714	−	0.386336i
$485$	−2769.58			−0.259299
$486$		0			0
$487$	−848.093	−	2610.16i	−0.0789133	−	0.242870i	0.903815	−	0.427923i	$-0.140754\pi$
$487$	−848.093	−	2610.16i	−0.0789133	−	0.242870i	−0.982729	+	0.185053i	$0.940754\pi$
$488$	5023.40	−	15460.4i	0.465981	−	1.43414i
$489$		0			0
$490$	1663.72	+	1208.77i	0.153386	+	0.111442i
$491$	4252.16	−	13086.8i	0.390830	−	1.20285i	−0.541332	−	0.840809i	$-0.682080\pi$
$491$	4252.16	−	13086.8i	0.390830	−	1.20285i	0.932162	−	0.362042i	$-0.117920\pi$
$492$		0			0
$493$	7834.85	−	5692.35i	0.715748	−	0.520021i
$494$	474.644			0.0432292
$495$		0			0
$496$	97.2200			0.00880102
$497$	−6985.34	+	5075.15i	−0.630454	+	0.458051i
$498$		0			0
$499$	3285.52	−	10111.8i	0.294750	−	0.907147i	−0.688555	−	0.725184i	$-0.741755\pi$
$499$	3285.52	−	10111.8i	0.294750	−	0.907147i	0.983305	−	0.181963i	$-0.0582452\pi$
$500$	4326.64	+	3143.49i	0.386987	+	0.281162i
$501$		0			0
$502$	−2725.86	+	8389.33i	−0.242353	+	0.745885i
$503$	−3896.04	−	11990.8i	−0.345360	−	1.06291i	−0.961391	−	0.275186i	$-0.911261\pi$
$503$	−3896.04	−	11990.8i	−0.345360	−	1.06291i	0.616032	−	0.787721i	$-0.288739\pi$
$504$		0			0
$505$	−3830.98			−0.337577
$506$	3160.76	+	1091.42i	0.277694	+	0.0958885i
$507$		0			0
$508$	10012.6	−	7274.61i	0.874487	−	0.635352i
$509$	−3953.17	−	12166.6i	−0.344246	−	1.05948i	−0.961986	−	0.273099i	$-0.911951\pi$
$509$	−3953.17	−	12166.6i	−0.344246	−	1.05948i	0.617740	−	0.786383i	$-0.288049\pi$
$510$		0			0
$511$	4600.00	+	3342.09i	0.398223	+	0.289326i
$512$	339.995	+	247.021i	0.0293472	+	0.0213220i
$513$		0			0
$514$	−1369.30	−	4214.27i	−0.117504	−	0.361641i
$515$	−5685.06	+	4130.44i	−0.486435	+	0.353415i
$516$		0			0
$517$	8557.97	−	11336.2i	0.728006	−	0.964346i
$518$	−2482.58			−0.210576
$519$		0			0
$520$	−175.448	−	539.974i	−0.0147960	−	0.0455374i
$521$	−3241.09	+	9975.04i	−0.272542	+	0.838799i	0.717317	+	0.696747i	$0.245370\pi$
$521$	−3241.09	+	9975.04i	−0.272542	+	0.838799i	−0.989859	+	0.142052i	$0.954630\pi$
$522$		0			0
$523$	5438.69	+	3951.44i	0.454718	+	0.330372i	0.791456	−	0.611227i	$-0.209324\pi$
$523$	5438.69	+	3951.44i	0.454718	+	0.330372i	−0.336738	+	0.941598i	$0.609324\pi$
$524$	2624.25	−	8076.61i	0.218780	−	0.673337i
$525$		0			0
$526$	2894.63	−	2103.07i	0.239946	−	0.174331i
$527$	−7106.18			−0.587382
$528$		0			0
$529$	−9358.32			−0.769156
$530$	3744.63	−	2720.63i	0.306898	−	0.222975i
$531$		0			0
$532$	−743.306	+	2287.66i	−0.0605760	+	0.186434i
$533$	803.300	+	583.632i	0.0652810	+	0.0474294i
$534$		0			0
$535$	−957.717	+	2947.55i	−0.0773938	+	0.238194i
$536$	4233.76	+	13030.2i	0.341177	+	1.05003i
$537$		0			0
$538$	−11917.5			−0.955021
$539$	−169.814	+	9265.76i	−0.0135703	+	0.740454i
$540$		0			0
$541$	−10028.7	+	7286.29i	−0.796984	+	0.579042i	−0.910028	−	0.414547i	$-0.863940\pi$
$541$	−10028.7	+	7286.29i	−0.796984	+	0.579042i	0.113044	+	0.993590i	$0.463940\pi$
$542$	−113.784	−	350.191i	−0.00901742	−	0.0277528i
$543$		0			0
$544$	−12494.7	−	9077.92i	−0.984752	−	0.715464i
$545$	6309.81	+	4584.34i	0.495931	+	0.360315i
$546$		0			0
$547$	−1865.99	−	5742.92i	−0.145857	−	0.448902i	0.851263	−	0.524739i	$-0.175837\pi$
$547$	−1865.99	−	5742.92i	−0.145857	−	0.448902i	−0.997120	+	0.0758369i	$0.975837\pi$
$548$	5158.08	−	3747.57i	0.402085	−	0.292132i
$549$		0			0
$550$	119.187	−	6503.31i	0.00924024	−	0.504186i
$551$	−5809.74			−0.449190
$552$		0			0
$553$	1075.23	+	3309.21i	0.0826823	+	0.254470i
$554$	−660.039	+	2031.39i	−0.0506180	+	0.155786i
$555$		0			0
$556$	13102.9	+	9519.84i	0.999439	+	0.726135i
$557$	−4667.78	+	14365.9i	−0.355081	+	1.09283i	0.600882	+	0.799338i	$0.294816\pi$
$557$	−4667.78	+	14365.9i	−0.355081	+	1.09283i	−0.955963	+	0.293488i	$0.905184\pi$
$558$		0			0
$559$	202.736	−	147.296i	0.0153395	−	0.0111448i
$560$	51.2650			0.00386847
$561$		0			0
$562$	−2389.53			−0.179353
$563$	1735.56	−	1260.96i	0.129920	−	0.0943927i	−0.520927	−	0.853601i	$-0.674414\pi$
$563$	1735.56	−	1260.96i	0.129920	−	0.0943927i	0.650848	+	0.759208i	$0.274414\pi$
$564$		0			0
$565$	2062.06	−	6346.38i	0.153543	−	0.472556i
$566$	2449.51	+	1779.67i	0.181909	+	0.132165i
$567$		0			0
$568$	−6363.80	+	19585.8i	−0.470104	+	1.44683i
$569$	6431.23	+	19793.3i	0.473833	+	1.45831i	0.847525	+	0.530755i	$0.178092\pi$
$569$	6431.23	+	19793.3i	0.473833	+	1.45831i	−0.373692	+	0.927553i	$0.621908\pi$
$570$		0			0
$571$	−4825.78			−0.353683			−0.176841	−	0.984239i	$-0.556588\pi$
$571$	−4825.78			−0.353683			−0.176841	+	0.984239i	$0.556588\pi$
$572$	593.561	−	786.256i	0.0433882	−	0.0574738i
$573$		0			0
$574$	2430.94	−	1766.18i	0.176769	−	0.128431i
$575$	−1688.26	−	5195.93i	−0.122444	−	0.376844i
$576$		0			0
$577$	16941.5	+	12308.7i	1.22233	+	0.888073i	0.996291	−	0.0860455i	$-0.0274230\pi$
$577$	16941.5	+	12308.7i	1.22233	+	0.888073i	0.226037	+	0.974119i	$0.427423\pi$
$578$	3201.70	+	2326.17i	0.230403	+	0.167398i
$579$		0			0
$580$	826.879	+	2544.87i	0.0591970	+	0.182190i
$581$	−7520.42	+	5463.91i	−0.537005	+	0.390157i
$582$		0			0
$583$	19716.1	+	6808.02i	1.40061	+	0.483635i
$584$	13561.4			0.960915
$585$		0			0
$586$	−4412.24	−	13579.5i	−0.311037	−	0.957274i
$587$	1727.29	−	5316.06i	0.121453	−	0.373794i	−0.871785	−	0.489889i	$-0.837037\pi$
$587$	1727.29	−	5316.06i	0.121453	−	0.373794i	0.993238	+	0.116094i	$0.0370375\pi$
$588$		0			0
$589$	3448.88	+	2505.76i	0.241271	+	0.175294i
$590$	−197.897	+	609.065i	−0.0138090	+	0.0424997i
$591$		0			0
$592$	142.930	−	103.845i	0.00992293	−	0.00720943i
$593$	21114.0			1.46214			0.731069	−	0.682303i	$-0.239022\pi$
$593$	21114.0			1.46214			0.731069	+	0.682303i	$0.239022\pi$
$594$		0			0
$595$	−3747.15			−0.258182
$596$	6651.06	−	4832.28i	0.457111	−	0.332110i
$597$		0			0
$598$	−152.690	+	469.933i	−0.0104414	+	0.0321354i
$599$	6571.14	+	4774.21i	0.448229	+	0.325658i	0.788896	−	0.614526i	$-0.210653\pi$
$599$	6571.14	+	4774.21i	0.448229	+	0.325658i	−0.340667	+	0.940184i	$0.610653\pi$
$600$		0			0
$601$	489.767	−	1507.35i	0.0332413	−	0.102306i	−0.933059	−	0.359723i	$-0.882871\pi$
$601$	489.767	−	1507.35i	0.0332413	−	0.102306i	0.966301	+	0.257417i	$0.0828713\pi$
$602$	−234.343	−	721.234i	−0.0158656	−	0.0488294i
$603$		0			0
$604$	327.737			0.0220785
$605$	−5171.40	+	3475.05i	−0.347516	+	0.233522i
$606$		0			0
$607$	−13583.2	+	9868.80i	−0.908281	+	0.659905i	−0.940579	−	0.339574i	$-0.889717\pi$
$607$	−13583.2	+	9868.80i	−0.908281	+	0.659905i	0.0322987	+	0.999478i	$0.489717\pi$
$608$	2863.08	+	8811.67i	0.190976	+	0.587764i
$609$		0			0
$610$	−4732.35	−	3438.26i	−0.314111	−	0.228215i
$611$	1698.01	+	1233.68i	0.112429	+	0.0816845i
$612$		0			0
$613$	−1429.28	−	4398.87i	−0.0941731	−	0.289835i	0.892864	−	0.450326i	$-0.148692\pi$
$613$	−1429.28	−	4398.87i	−0.0941731	−	0.289835i	−0.987037	+	0.160491i	$0.948692\pi$
$614$	5105.82	−	3709.60i	0.335593	−	0.243823i
$615$		0			0
$616$	−4435.52	−	6346.34i	−0.290117	−	0.415100i
$617$	−581.103			−0.0379163			−0.0189581	−	0.999820i	$-0.506035\pi$
$617$	−581.103			−0.0379163			−0.0189581	+	0.999820i	$0.506035\pi$
$618$		0			0
$619$	5742.03	+	17672.2i	0.372846	+	1.14750i	0.944920	+	0.327301i	$0.106139\pi$
$619$	5742.03	+	17672.2i	0.372846	+	1.14750i	−0.572074	+	0.820202i	$0.693861\pi$
$620$	606.744	−	1867.37i	0.0393023	−	0.120960i
$621$		0			0
$622$	6414.99	+	4660.76i	0.413533	+	0.300450i
$623$	−3370.68	+	10373.9i	−0.216763	+	0.667129i
$624$		0			0
$625$	−6381.50	+	4636.43i	−0.408416	+	0.296732i
$626$	5359.22			0.342168
$627$		0			0
$628$	6960.59			0.442289
$629$	−10447.3	+	7590.39i	−0.662258	+	0.481159i
$630$		0			0
$631$	3758.79	−	11568.4i	0.237139	−	0.729840i	−0.759691	−	0.650284i	$-0.774650\pi$
$631$	3758.79	−	11568.4i	0.237139	−	0.729840i	0.996830	−	0.0795558i	$-0.0253502\pi$
$632$	6713.98	+	4877.99i	0.422575	+	0.307019i
$633$		0			0
$634$	−1324.15	+	4075.30i	−0.0829472	+	0.255285i
$635$	−3574.16	−	11000.1i	−0.223364	−	0.687444i
$636$		0			0
$637$	−1369.40			−0.0851769
$638$	4338.45	−	5746.89i	0.269218	−	0.356617i
$639$		0			0
$640$	3513.16	−	2552.46i	0.216984	−	0.157648i
$641$	5677.31	+	17473.0i	0.349829	+	1.07666i	0.958948	+	0.283583i	$0.0915232\pi$
$641$	5677.31	+	17473.0i	0.349829	+	1.07666i	−0.609119	+	0.793079i	$0.708477\pi$
$642$		0			0
$643$	−370.655	−	269.297i	−0.0227328	−	0.0165164i	0.576361	−	0.817195i	$-0.304472\pi$
$643$	−370.655	−	269.297i	−0.0227328	−	0.0165164i	−0.599094	+	0.800679i	$0.704472\pi$
$644$	−2025.84	−	1471.86i	−0.123958	−	0.0900610i
$645$		0			0
$646$	−2308.82	−	7105.80i	−0.140618	−	0.432777i
$647$	6335.74	−	4603.19i	0.384983	−	0.279706i	−0.378414	−	0.925637i	$-0.623530\pi$
$647$	6335.74	−	4603.19i	0.384983	−	0.279706i	0.763396	+	0.645930i	$0.223530\pi$
$648$		0			0
$649$	−2760.57	+	841.362i	−0.166968	+	0.0508880i
$650$	961.135			0.0579982
$651$		0			0
$652$	−3862.63	−	11888.0i	−0.232013	−	0.714062i
$653$	−4743.85	+	14600.1i	−0.284289	+	0.874953i	0.702321	+	0.711860i	$0.252147\pi$
$653$	−4743.85	+	14600.1i	−0.284289	+	0.874953i	−0.986611	+	0.163093i	$0.947853\pi$
$654$		0			0
$655$	−6420.68	−	4664.89i	−0.383018	−	0.278279i
$656$	−66.0786	+	203.369i	−0.00393283	+	0.0121040i
$657$		0			0
$658$	5138.51	−	3733.35i	0.304438	−	0.221187i
$659$	−5177.35			−0.306041			−0.153020	−	0.988223i	$-0.548900\pi$
$659$	−5177.35			−0.306041			−0.153020	+	0.988223i	$0.548900\pi$
$660$		0			0
$661$	−11234.4			−0.661073			−0.330536	−	0.943793i	$-0.607230\pi$
$661$	−11234.4			−0.661073			−0.330536	+	0.943793i	$0.607230\pi$
$662$	−10242.3	+	7441.43i	−0.601324	+	0.436887i
$663$		0			0
$664$	−6851.27	+	21086.0i	−0.400423	+	1.23238i
$665$	1818.63	+	1321.31i	0.106050	+	0.0770499i
$666$		0			0
$667$	1868.96	−	5752.08i	0.108496	−	0.333915i
$668$	−1709.81	−	5262.25i	−0.0990337	−	0.304794i
$669$		0			0
$670$	4930.02			0.284273
$671$	483.025	−	26355.9i	0.0277898	−	1.51633i
$672$		0			0
$673$	7158.27	−	5200.79i	0.410002	−	0.297884i	−0.363601	−	0.931555i	$-0.618453\pi$
$673$	7158.27	−	5200.79i	0.410002	−	0.297884i	0.773603	+	0.633671i	$0.218453\pi$
$674$	−191.431	−	589.165i	−0.0109401	−	0.0336703i
$675$		0			0
$676$	−8785.17	−	6382.80i	−0.499839	−	0.363154i
$677$	−22816.5	−	16577.2i	−1.29529	−	0.941082i	−0.295391	−	0.955377i	$-0.595450\pi$
$677$	−22816.5	−	16577.2i	−1.29529	−	0.941082i	−0.999898	+	0.0142945i	$0.995450\pi$
$678$		0			0
$679$	−1724.65	−	5307.92i	−0.0974756	−	0.299999i
$680$	−7230.41	+	5253.20i	−0.407755	+	0.296252i
$681$		0			0
$682$	−5054.11	+	1540.38i	−0.283771	+	0.0864871i
$683$	1139.02			0.0638117			0.0319058	−	0.999491i	$-0.489842\pi$
$683$	1139.02			0.0638117			0.0319058	+	0.999491i	$0.489842\pi$
$684$		0			0
$685$	−1841.25	−	5666.79i	−0.102702	−	0.316083i
$686$	−3009.77	+	9263.11i	−0.167512	+	0.515550i
$687$		0			0
$688$	43.6605	+	31.7212i	0.00241939	+	0.00175779i
$689$	−952.446	+	2931.33i	−0.0526637	+	0.162082i
$690$		0			0
$691$	15183.7	−	11031.6i	0.835909	−	0.607324i	−0.0853155	−	0.996354i	$-0.527190\pi$
$691$	15183.7	−	11031.6i	0.835909	−	0.607324i	0.921225	+	0.389030i	$0.127190\pi$
$692$	13792.1			0.757655
$693$		0			0
$694$	9205.09			0.503488
$695$	12245.3	−	8896.72i	0.668331	−	0.485571i
$696$		0			0
$697$	4829.94	−	14865.0i	0.262478	−	0.807823i
$698$	−12415.2	−	9020.15i	−0.673239	−	0.489137i
$699$		0			0
$700$	−1505.17	+	4632.43i	−0.0812714	+	0.250128i
$701$	−1169.64	−	3599.79i	−0.0630196	−	0.193955i	0.914589	−	0.404384i	$-0.132514\pi$
$701$	−1169.64	−	3599.79i	−0.0630196	−	0.193955i	−0.977609	+	0.210429i	$0.932514\pi$
$702$		0			0
$703$	7746.93			0.415620
$704$	−10534.1	−	3637.44i	−0.563945	−	0.194732i
$705$		0			0
$706$	9759.41	−	7090.63i	0.520255	−	0.377988i
$707$	−2385.59	−	7342.10i	−0.126902	−	0.390563i
$708$		0			0
$709$	−1462.15	−	1062.32i	−0.0774503	−	0.0562709i	0.548386	−	0.836225i	$-0.315242\pi$
$709$	−1462.15	−	1062.32i	−0.0774503	−	0.0562709i	−0.625837	+	0.779954i	$0.715242\pi$
$710$	5995.09	+	4355.69i	0.316890	+	0.230234i
$711$		0			0
$712$	8039.37	+	24742.6i	0.423157	+	1.30234i
$713$	−3590.37	+	2608.56i	−0.188584	+	0.137014i
$714$		0			0
$715$	−527.413	−	754.624i	−0.0275862	−	0.0394704i
$716$	−21361.1			−1.11495
$717$		0			0
$718$	2602.62	+	8010.03i	0.135277	+	0.416339i
$719$	10208.8	−	31419.5i	0.529520	−	1.62970i	−0.225680	−	0.974202i	$-0.572460\pi$
$719$	10208.8	−	31419.5i	0.529520	−	1.62970i	0.755200	−	0.655494i	$-0.227540\pi$
$720$		0			0
$721$	−11456.2	−	8323.40i	−0.591748	−	0.429930i
$722$	2280.62	−	7019.01i	0.117556	−	0.361801i
$723$		0			0
$724$	−4927.22	+	3579.83i	−0.252926	+	0.183762i
$725$	−11764.5			−0.602652
$726$		0			0
$727$	1906.51			0.0972606			0.0486303	−	0.998817i	$-0.484514\pi$
$727$	1906.51			0.0972606			0.0486303	+	0.998817i	$0.484514\pi$
$728$	925.611	−	672.496i	0.0471228	−	0.0342367i
$729$		0			0
$730$	1507.96	−	4641.03i	0.0764551	−	0.235305i
$731$	−3191.31	−	2318.62i	−0.161470	−	0.117315i
$732$		0			0
$733$	2986.92	−	9192.78i	0.150511	−	0.463224i	−0.847168	−	0.531325i	$-0.821694\pi$
$733$	2986.92	−	9192.78i	0.150511	−	0.463224i	0.997678	+	0.0681014i	$0.0216941\pi$
$734$	−4375.75	−	13467.2i	−0.220043	−	0.677224i
$735$		0			0
$736$	−9645.24			−0.483055
$737$	12727.1	+	18209.9i	0.636103	+	0.910137i
$738$		0			0
$739$	−20359.0	+	14791.7i	−1.01342	+	0.736293i	−0.964924	−	0.262531i	$-0.915443\pi$
$739$	−20359.0	+	14791.7i	−1.01342	+	0.736293i	−0.0484964	+	0.998823i	$0.515443\pi$
$740$	−1102.59	−	3393.43i	−0.0547731	−	0.168574i
$741$		0			0
$742$	7545.93	+	5482.44i	0.373342	+	0.271249i
$743$	−25301.6	−	18382.7i	−1.24930	−	0.907667i	−0.251115	−	0.967957i	$-0.580797\pi$
$743$	−25301.6	−	18382.7i	−1.24930	−	0.907667i	−0.998181	+	0.0602905i	$0.980797\pi$
$744$		0			0
$745$	−2374.19	−	7307.01i	−0.116757	−	0.359340i
$746$	−1143.50	+	830.799i	−0.0561212	+	0.0407744i
$747$		0			0
$748$	−14658.2	−	5061.50i	−0.716518	−	0.247416i
$749$	−6245.38			−0.304675
$750$		0			0
$751$	4771.36	+	14684.7i	0.231837	+	0.713520i	0.997525	+	0.0703084i	$0.0223983\pi$
$751$	4771.36	+	14684.7i	0.231837	+	0.713520i	−0.765689	+	0.643211i	$0.777602\pi$
$752$	−139.677	+	429.880i	−0.00677325	+	0.0208459i
$753$		0			0
$754$	860.804	+	625.410i	0.0415764	+	0.0302070i
$755$	94.6473	−	291.295i	0.00456234	−	0.0140414i
$756$		0			0
$757$	−23225.1	+	16874.0i	−1.11510	+	0.810167i	−0.983459	−	0.181130i	$-0.942024\pi$
$757$	−23225.1	+	16874.0i	−1.11510	+	0.810167i	−0.131641	+	0.991298i	$0.542024\pi$
$758$	−168.176			−0.00805861
$759$		0			0
$760$	5361.54			0.255899
$761$	31306.9	−	22745.8i	1.49129	−	1.08349i	0.517602	−	0.855622i	$-0.326825\pi$
$761$	31306.9	−	22745.8i	1.49129	−	1.08349i	0.973692	−	0.227867i	$-0.0731751\pi$
$762$		0			0
$763$	−4856.74	+	14947.5i	−0.230440	+	0.709222i
$764$	−18082.7	−	13137.8i	−0.856294	−	0.622134i
$765$		0			0
$766$	6527.15	−	20088.5i	0.307879	−	0.947554i
$767$	−131.779	−	405.575i	−0.00620374	−	0.0190932i
$768$		0			0
$769$	9520.91			0.446467			0.223233	−	0.974765i	$-0.428339\pi$
$769$	9520.91			0.446467			0.223233	+	0.974765i	$0.428339\pi$
$770$	−2665.08	+	812.257i	−0.124731	+	0.0380152i
$771$		0			0
$772$	19706.6	−	14317.7i	0.918726	−	0.667494i
$773$	6442.57	+	19828.2i	0.299771	+	0.922601i	0.981577	+	0.191067i	$0.0611949\pi$
$773$	6442.57	+	19828.2i	0.299771	+	0.922601i	−0.681806	+	0.731533i	$0.738805\pi$
$774$		0			0
$775$	6983.85	+	5074.06i	0.323700	+	0.235182i
$776$	−10769.1	−	7824.22i	−0.498181	−	0.361950i
$777$		0			0
$778$	2324.57	+	7154.28i	0.107120	+	0.329683i
$779$	−7585.79	+	5511.40i	−0.348895	+	0.253487i
$780$		0			0
$781$	−611.911	+	33388.4i	−0.0280357	+	1.52975i
$782$	7778.01			0.355679
$783$		0			0
$784$	−91.1322	−	280.476i	−0.00415143	−	0.0127768i
$785$	2010.15	−	6186.61i	0.0913954	−	0.281286i
$786$		0			0
$787$	−22007.2	−	15989.1i	−0.996786	−	0.724207i	−0.0353890	−	0.999374i	$-0.511267\pi$
$787$	−22007.2	−	15989.1i	−0.996786	−	0.724207i	−0.961397	+	0.275166i	$0.911267\pi$
$788$	−1674.93	+	5154.90i	−0.0757194	+	0.233040i
$789$		0			0
$790$	2415.93	−	1755.27i	0.108804	−	0.0790504i
$791$	13447.0			0.604449
$792$		0			0
$793$	3895.17			0.174428
$794$	−15983.9	+	11613.0i	−0.714417	+	0.519054i
$795$		0			0
$796$	−5423.02	+	16690.3i	−0.241474	+	0.743182i
$797$	−10894.2	−	7915.11i	−0.484182	−	0.351778i	0.318761	−	0.947835i	$-0.396733\pi$
$797$	−10894.2	−	7915.11i	−0.484182	−	0.351778i	−0.802942	+	0.596057i	$0.796733\pi$
$798$		0			0
$799$	10209.5	−	31421.6i	0.452047	−	1.39126i
$800$	5797.63	+	17843.3i	0.256222	+	0.788569i
$801$		0			0
$802$	26904.5			1.18458
$803$	21035.4	−	6411.12i	0.924437	−	0.281748i
$804$		0			0
$805$	−1893.24	+	1375.52i	−0.0828917	+	0.0602244i
$806$	−241.264	−	742.534i	−0.0105436	−	0.0324499i
$807$		0			0
$808$	−14896.2	−	10822.7i	−0.648572	−	0.471215i
$809$	26245.3	+	19068.3i	1.14059	+	0.828686i	0.987201	−	0.159481i	$-0.0509819\pi$
$809$	26245.3	+	19068.3i	1.14059	+	0.828686i	0.153387	+	0.988166i	$0.450982\pi$
$810$		0			0
$811$	8831.27	+	27179.8i	0.382377	+	1.17684i	0.938365	+	0.345645i	$0.112340\pi$
$811$	8831.27	+	27179.8i	0.382377	+	1.17684i	−0.555988	+	0.831190i	$0.687660\pi$
$812$	−4362.36	+	3169.44i	−0.188533	+	0.136977i
$813$		0			0
$814$	−5785.05	+	7663.12i	−0.249098	+	0.329966i
$815$	−11681.6			−0.502071
$816$		0			0
$817$	731.270	+	2250.62i	0.0313145	+	0.0963760i
$818$	−6075.60	+	18698.8i	−0.259692	+	0.799251i
$819$		0			0
$820$	3493.85	+	2538.43i	0.148793	+	0.108105i
$821$	−2345.53	+	7218.81i	−0.0997072	+	0.306867i	−0.988452	−	0.151535i	$-0.951578\pi$
$821$	−2345.53	+	7218.81i	−0.0997072	+	0.306867i	0.888745	+	0.458403i	$0.151578\pi$
$822$		0			0
$823$	−3277.29	+	2381.09i	−0.138808	+	0.100850i	−0.655022	−	0.755609i	$-0.727341\pi$
$823$	−3277.29	+	2381.09i	−0.138808	+	0.100850i	0.516214	+	0.856460i	$0.327341\pi$
$824$	−33774.3			−1.42789
$825$		0			0
$826$	−1290.51			−0.0543615
$827$	23949.1	−	17400.0i	1.00700	−	0.731630i	0.0434246	−	0.999057i	$-0.486173\pi$
$827$	23949.1	−	17400.0i	1.00700	−	0.731630i	0.963578	+	0.267426i	$0.0861732\pi$
$828$		0			0
$829$	65.8920	−	202.795i	0.00276058	−	0.00849621i	−0.949667	−	0.313262i	$-0.898578\pi$
$829$	65.8920	−	202.795i	0.00276058	−	0.00849621i	0.952427	+	0.304766i	$0.0985782\pi$
$830$	6454.32	+	4689.34i	0.269919	+	0.196108i
$831$		0			0
$832$	508.880	−	1566.17i	0.0212046	−	0.0652611i
$833$	6661.20	+	20501.1i	0.277067	+	0.852724i
$834$		0			0
$835$	−5170.89			−0.214307
$836$	5329.35	+	7625.24i	0.220478	+	0.315460i
$837$		0			0
$838$	5314.68	−	3861.34i	0.219084	−	0.159174i
$839$	3132.38	+	9640.46i	0.128893	+	0.396693i	0.994590	−	0.103875i	$-0.0331243\pi$
$839$	3132.38	+	9640.46i	0.128893	+	0.396693i	−0.865697	+	0.500569i	$0.833124\pi$
$840$		0			0
$841$	9194.69	+	6680.33i	0.377001	+	0.273908i
$842$	19368.6	+	14072.1i	0.792739	+	0.575959i
$843$		0			0
$844$	−2576.53	−	7929.74i	−0.105080	−	0.323404i
$845$	−8210.14	+	5965.01i	−0.334245	+	0.242843i
$846$		0			0
$847$	−9880.25	−	7747.08i	−0.400814	−	0.314277i
$848$	−663.768			−0.0268796
$849$		0			0
$850$	−4675.26	−	14389.0i	−0.188659	−	0.580633i
$851$	−2492.15	+	7670.04i	−0.100387	+	0.308961i
$852$		0			0
$853$	−23714.3	−	17229.4i	−0.951888	−	0.691587i	−0.000635352	−	1.00000i	$-0.500202\pi$
$853$	−23714.3	−	17229.4i	−0.951888	−	0.691587i	−0.951253	+	0.308413i	$0.900202\pi$
$854$	3642.56	−	11210.6i	0.145955	−	0.449204i
$855$		0			0
$856$	−12050.9	+	8755.52i	−0.481183	+	0.349600i
$857$	22219.3			0.885642			0.442821	−	0.896610i	$-0.353978\pi$
$857$	22219.3			0.885642			0.442821	+	0.896610i	$0.353978\pi$
$858$		0			0
$859$	25401.2			1.00894			0.504468	−	0.863430i	$-0.331689\pi$
$859$	25401.2			1.00894			0.504468	+	0.863430i	$0.331689\pi$
$860$	881.771	−	640.644i	0.0349630	−	0.0254021i
$861$		0			0
$862$	−6791.11	+	20900.9i	−0.268337	+	0.825855i
$863$	2925.53	+	2125.52i	0.115395	+	0.0838395i	0.643986	−	0.765037i	$-0.277279\pi$
$863$	2925.53	+	2125.52i	0.115395	+	0.0838395i	−0.528591	+	0.848877i	$0.677279\pi$
$864$		0			0
$865$	3983.03	−	12258.5i	0.156563	−	0.481852i
$866$	−8648.05	−	26616.0i	−0.339345	−	1.04440i
$867$		0			0
$868$	3956.65			0.154721
$869$	12720.3	+	4392.35i	0.496554	+	0.171462i
$870$		0			0
$871$	−2655.91	+	1929.63i	−0.103320	+	0.0750666i
$872$	11583.8	+	35651.1i	0.449857	+	1.38452i
$873$		0			0
$874$	−3774.94	−	2742.66i	−0.146098	−	0.106146i
$875$	8148.09	+	5919.93i	0.314806	+	0.228720i
$876$		0			0
$877$	−4644.26	−	14293.6i	−0.178820	−	0.550352i	0.820967	−	0.570976i	$-0.193435\pi$
$877$	−4644.26	−	14293.6i	−0.178820	−	0.550352i	−0.999787	+	0.0206233i	$0.993435\pi$
$878$	−20087.5	+	14594.4i	−0.772117	+	0.560976i
$879$		0			0
$880$	119.461	−	158.242i	0.00457615	−	0.00606176i
$881$	41424.1			1.58412			0.792062	−	0.610440i	$-0.209008\pi$
$881$	41424.1			1.58412			0.792062	+	0.610440i	$0.209008\pi$
$882$		0			0
$883$	−9718.72	−	29911.2i	−0.370398	−	1.13997i	−0.946532	−	0.322611i	$-0.895439\pi$
$883$	−9718.72	−	29911.2i	−0.370398	−	1.13997i	0.576134	−	0.817355i	$-0.304561\pi$
$884$	708.107	−	2179.33i	0.0269414	−	0.0829172i
$885$		0			0
$886$	−5125.28	−	3723.73i	−0.194342	−	0.141198i
$887$	3774.50	−	11616.7i	0.142881	−	0.439742i	−0.853851	−	0.520517i	$-0.825739\pi$
$887$	3774.50	−	11616.7i	0.142881	−	0.439742i	0.996732	+	0.0807744i	$0.0257393\pi$
$888$		0			0
$889$	18856.2	−	13699.8i	0.711379	−	0.516847i
$890$	9361.46			0.352581
$891$		0			0
$892$	4861.22			0.182473
$893$	−16034.8	+	11650.0i	−0.600878	+	0.436564i
$894$		0			0
$895$	−6168.89	+	18985.9i	−0.230395	+	0.709082i
$896$	7079.49	+	5143.55i	0.263961	+	0.191779i
$897$		0			0
$898$	1756.97	−	5407.39i	0.0652904	−	0.200943i
$899$	2953.12	+	9088.78i	0.109557	+	0.337183i
$900$		0			0
$901$	48517.4			1.79395
$902$	212.949	−	11619.4i	0.00786078	−	0.428917i
$903$		0			0
$904$	25946.9	−	18851.6i	0.954626	−	0.693577i
$905$	1758.84	+	5413.16i	0.0646032	+	0.198828i
$906$		0			0
$907$	−9356.29	−	6797.74i	−0.342525	−	0.248859i	0.403201	−	0.915111i	$-0.367897\pi$
$907$	−9356.29	−	6797.74i	−0.342525	−	0.248859i	−0.745727	+	0.666252i	$0.767897\pi$
$908$	−12145.5	−	8824.25i	−0.443903	−	0.322514i
$909$		0			0
$910$	−127.221	−	391.545i	−0.00463442	−	0.0142633i
$911$	22625.1	−	16438.1i	0.822836	−	0.597826i	−0.0946871	−	0.995507i	$-0.530185\pi$
$911$	22625.1	−	16438.1i	0.822836	−	0.597826i	0.917524	+	0.397681i	$0.130185\pi$
$912$		0			0
$913$	−658.784	+	35946.0i	−0.0238801	+	1.30300i
$914$	12934.9			0.468104
$915$		0			0
$916$	124.880	+	384.342i	0.00450454	+	0.0138635i
$917$	4942.08	−	15210.2i	0.177974	−	0.547747i
$918$		0			0
$919$	−36164.5	−	26275.1i	−1.29810	−	0.943128i	−0.298170	−	0.954513i	$-0.596376\pi$
$919$	−36164.5	−	26275.1i	−1.29810	−	0.943128i	−0.999935	+	0.0113846i	$0.996376\pi$
$920$	−1724.78	+	5308.33i	−0.0618090	+	0.190229i
$921$		0			0
$922$	−22494.6	+	16343.3i	−0.803494	+	0.583773i
$923$	−4934.53			−0.175972
$924$		0			0
$925$	15687.2			0.557614
$926$	−11658.2	+	8470.16i	−0.413727	+	0.300591i
$927$		0			0
$928$	−6418.19	+	19753.2i	−0.227034	+	0.698739i
$929$	−532.665	−	387.004i	−0.0188118	−	0.0136676i	0.578340	−	0.815796i	$-0.303701\pi$
$929$	−532.665	−	387.004i	−0.0188118	−	0.0136676i	−0.597151	+	0.802129i	$0.703701\pi$
$930$		0			0
$931$	3996.10	−	12298.7i	0.140673	−	0.432948i
$932$	3793.42	+	11674.9i	0.133324	+	0.410328i
$933$		0			0
$934$	−30605.6			−1.07221
$935$	−8731.82	+	11566.5i	−0.305413	+	0.404563i
$936$		0			0
$937$	−14039.2	+	10200.1i	−0.489479	+	0.355627i	−0.804984	−	0.593297i	$-0.797826\pi$
$937$	−14039.2	+	10200.1i	−0.489479	+	0.355627i	0.315505	+	0.948924i	$0.397826\pi$
$938$	3069.98	+	9448.42i	0.106864	+	0.328893i
$939$		0			0
$940$	7385.27	+	5365.71i	0.256256	+	0.186181i
$941$	−14197.6	−	10315.1i	−0.491847	−	0.357348i	0.314047	−	0.949407i	$-0.398315\pi$
$941$	−14197.6	−	10315.1i	−0.491847	−	0.357348i	−0.805894	+	0.592060i	$0.798315\pi$
$942$		0			0
$943$	−3016.39	−	9283.49i	−0.104165	−	0.320585i
$944$	74.2986	−	53.9811i	0.00256167	−	0.00186116i
$945$		0			0
$946$	−2772.35	−	957.300i	−0.0952820	−	0.0329012i
$947$	−27129.0			−0.930912			−0.465456	−	0.885071i	$-0.654110\pi$
$947$	−27129.0			−0.930912			−0.465456	+	0.885071i	$0.654110\pi$
$948$		0			0
$949$	1004.15	+	3090.45i	0.0343478	+	0.105712i
$950$	−2804.72	+	8632.05i	−0.0957866	+	0.294801i
$951$		0			0
$952$	−14570.3	−	10585.9i	−0.496035	−	0.360390i
$953$	−11526.6	+	35475.1i	−0.391797	+	1.20583i	0.539631	+	0.841901i	$0.318564\pi$
$953$	−11526.6	+	35475.1i	−0.391797	+	1.20583i	−0.931428	+	0.363925i	$0.881436\pi$
$954$		0			0
$955$	−16899.1	+	12277.9i	−0.572609	+	0.416025i
$956$	458.080			0.0154972
$957$		0			0
$958$	13709.6			0.462357
$959$	9713.89	−	7057.55i	0.327088	−	0.237644i
$960$		0			0
$961$	−7039.00	+	21663.8i	−0.236279	+	0.727193i
$962$	−1147.83	−	833.946i	−0.0384693	−	0.0279496i
$963$		0			0
$964$	−293.067	+	901.967i	−0.00979154	+	0.0301353i
$965$	−7034.56	−	21650.2i	−0.234664	−	0.722221i
$966$		0			0
$967$	48055.1			1.59809			0.799043	−	0.601274i	$-0.205340\pi$
$967$	48055.1			1.59809			0.799043	+	0.601274i	$0.205340\pi$
$968$	−29925.5	−	1097.26i	−0.993637	−	0.0364331i
$969$		0			0
$970$	−3875.11	+	2815.43i	−0.128270	+	0.0931939i
$971$	−11666.7	−	35906.3i	−0.385583	−	1.18670i	−0.936056	−	0.351850i	$-0.885553\pi$
$971$	−11666.7	−	35906.3i	−0.385583	−	1.18670i	0.550473	−	0.834853i	$-0.314447\pi$
$972$		0			0
$973$	24675.9	+	17928.1i	0.813025	+	0.590698i
$974$	−3840.00	−	2789.93i	−0.126326	−	0.0917813i
$975$		0			0
$976$	259.220	+	797.796i	0.00850145	+	0.0261648i
$977$	24275.8	−	17637.4i	0.794935	−	0.577554i	−0.114489	−	0.993425i	$-0.536523\pi$
$977$	24275.8	−	17637.4i	0.794935	−	0.577554i	0.909424	+	0.415870i	$0.136523\pi$
$978$		0			0
$979$	24167.1	+	34578.3i	0.788951	+	1.12883i
$980$	−5956.03			−0.194141
$981$		0			0
$982$	−7353.98	−	22633.2i	−0.238977	−	0.735494i
$983$	−11384.0	+	35036.3i	−0.369372	+	1.13681i	0.577825	+	0.816161i	$0.303902\pi$
$983$	−11384.0	+	35036.3i	−0.369372	+	1.13681i	−0.947198	+	0.320651i	$0.896098\pi$
$984$		0			0
$985$	4098.00	+	2977.37i	0.132562	+	0.0963117i
$986$	5175.68	−	15929.1i	0.167168	−	0.514489i
$987$		0			0
$988$	−1112.14	+	808.015i	−0.0358115	+	0.0260186i
$989$	−2463.53			−0.0792069
$990$		0			0
$991$	22406.6			0.718233			0.359117	−	0.933293i	$-0.383078\pi$
$991$	22406.6			0.718233			0.359117	+	0.933293i	$0.383078\pi$
$992$	12329.7	−	8958.03i	0.394624	−	0.286711i
$993$		0			0
$994$	−4614.50	+	14202.0i	−0.147247	+	0.453179i
$995$	13268.3	+	9640.01i	0.422748	+	0.307145i
$996$		0			0
$997$	5913.47	−	18199.8i	0.187845	−	0.578127i	−0.812141	−	0.583462i	$-0.801698\pi$
$997$	5913.47	−	18199.8i	0.187845	−	0.578127i	0.999986	+	0.00533409i	$0.00169790\pi$
$998$	−5682.21	−	17488.0i	−0.180228	−	0.554684i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.e.91.4	yes	24
3.2	odd	2	inner	99.4.f.e.91.3	yes	24
11.2	odd	10		1089.4.a.bl.1.8		12
11.4	even	5	inner	99.4.f.e.37.4	yes	24
11.9	even	5		1089.4.a.bm.1.5		12
33.2	even	10		1089.4.a.bl.1.5		12
33.20	odd	10		1089.4.a.bm.1.8		12
33.26	odd	10	inner	99.4.f.e.37.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.4.f.e.37.3	✓	24	33.26	odd	10	inner
99.4.f.e.37.4	yes	24	11.4	even	5	inner
99.4.f.e.91.3	yes	24	3.2	odd	2	inner
99.4.f.e.91.4	yes	24	1.1	even	1	trivial
1089.4.a.bl.1.5		12	33.2	even	10
1089.4.a.bl.1.8		12	11.2	odd	10
1089.4.a.bm.1.5		12	11.9	even	5
1089.4.a.bm.1.8		12	33.20	odd	10

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39917 - 1.01656i) q^{2} +(-1.54785 + 4.76378i) q^{4} +(3.78707 + 2.75147i) q^{5} +(-2.91496 + 8.97133i) q^{7} +(6.95243 + 21.3974i) q^{8} +O(q^{10})\)	\(q+(1.39917 - 1.01656i) q^{2} +(-1.54785 + 4.76378i) q^{4} +(3.78707 + 2.75147i) q^{5} +(-2.91496 + 8.97133i) q^{7} +(6.95243 + 21.3974i) q^{8} +8.09578 q^{10} +(20.8997 + 29.9032i) q^{11} +(-4.36138 + 3.16873i) q^{13} +(5.04133 + 15.5156i) q^{14} +(-0.939252 - 0.682406i) q^{16} +(68.6535 + 49.8797i) q^{17} +(-15.7316 - 48.4167i) q^{19} +(-18.9692 + 13.7819i) q^{20} +(59.6405 + 20.5940i) q^{22} +52.9969 q^{23} +(-31.8558 - 98.0420i) q^{25} +(-2.88112 + 8.86717i) q^{26} +(-38.2256 - 27.7725i) q^{28} +(35.2655 - 108.536i) q^{29} +(-67.7468 + 49.2209i) q^{31} -181.996 q^{32} +146.763 q^{34} +(-35.7235 + 25.9547i) q^{35} +(-47.0244 + 144.726i) q^{37} +(-71.2294 - 51.7512i) q^{38} +(-32.5449 + 100.163i) q^{40} +(-56.9163 - 175.170i) q^{41} -46.4843 q^{43} +(-174.802 + 53.2758i) q^{44} +(74.1517 - 53.8744i) q^{46} +(-120.309 - 370.274i) q^{47} +(205.505 + 149.308i) q^{49} +(-144.237 - 104.794i) q^{50} +(-8.34438 - 25.6814i) q^{52} +(462.541 - 336.055i) q^{53} +(-3.12935 + 170.751i) q^{55} -212.229 q^{56} +(-60.9906 - 187.710i) q^{58} +(-24.4445 + 75.2324i) q^{59} +(-584.546 - 424.697i) q^{61} +(-44.7534 + 137.737i) q^{62} +(-247.130 + 179.550i) q^{64} -25.2355 q^{65} +608.961 q^{67} +(-343.881 + 249.844i) q^{68} +(-23.5989 + 72.6299i) q^{70} +(740.521 + 538.020i) q^{71} +(186.265 - 573.266i) q^{73} +(81.3272 + 250.299i) q^{74} +254.997 q^{76} +(-329.194 + 100.331i) q^{77} +(298.418 - 216.813i) q^{79} +(-1.67939 - 5.16865i) q^{80} +(-257.706 - 187.234i) q^{82} +(797.245 + 579.233i) q^{83} +(122.753 + 377.796i) q^{85} +(-65.0394 + 47.2539i) q^{86} +(-494.548 + 655.099i) q^{88} +1156.34 q^{89} +(-15.7144 - 48.3641i) q^{91} +(-82.0312 + 252.466i) q^{92} +(-544.737 - 395.775i) q^{94} +(73.6406 - 226.643i) q^{95} +(-478.658 + 347.765i) q^{97} +439.317 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 28 q^{7}+O(q^{10}) \) 24 * q - 4 * q^4 - 28 * q^7	\( 24 q - 4 q^{4} - 28 q^{7} + 208 q^{10} + 20 q^{13} - 224 q^{16} - 40 q^{19} - 586 q^{22} + 362 q^{25} - 150 q^{28} + 670 q^{31} - 2520 q^{34} - 516 q^{37} + 2002 q^{40} + 4008 q^{43} + 2174 q^{46} + 342 q^{49} - 1894 q^{52} - 3300 q^{55} + 22 q^{58} - 2952 q^{61} - 3992 q^{64} - 1936 q^{67} - 1024 q^{70} + 2194 q^{73} + 15336 q^{76} + 1524 q^{79} + 2898 q^{82} - 7428 q^{85} - 3936 q^{88} - 6460 q^{91} - 16982 q^{94} - 1224 q^{97}+O(q^{100}) \) 24 * q - 4 * q^4 - 28 * q^7 + 208 * q^10 + 20 * q^13 - 224 * q^16 - 40 * q^19 - 586 * q^22 + 362 * q^25 - 150 * q^28 + 670 * q^31 - 2520 * q^34 - 516 * q^37 + 2002 * q^40 + 4008 * q^43 + 2174 * q^46 + 342 * q^49 - 1894 * q^52 - 3300 * q^55 + 22 * q^58 - 2952 * q^61 - 3992 * q^64 - 1936 * q^67 - 1024 * q^70 + 2194 * q^73 + 15336 * q^76 + 1524 * q^79 + 2898 * q^82 - 7428 * q^85 - 3936 * q^88 - 6460 * q^91 - 16982 * q^94 - 1224 * q^97

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