LMFDB - Embedded newform 828.2.e.f.91.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,2,Mod(91,828)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("828.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.15
Character	$\chi$	$=$	828.91
Dual form			828.2.e.f.91.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.279557 + 1.38631i) q^{2} +(-1.84370 + 0.775104i) q^{4} -1.27568i q^{5} -2.49131 q^{7} +(-1.58995 - 2.33924i) q^{8} +(1.76848 - 0.356624i) q^{10} +5.92184 q^{11} -2.46678 q^{13} +(-0.696464 - 3.45372i) q^{14} +(2.79843 - 2.85811i) q^{16} -6.74152i q^{17} +2.53999 q^{19} +(0.988782 + 2.35196i) q^{20} +(1.65549 + 8.20949i) q^{22} +(4.75259 + 0.642542i) q^{23} +3.37265 q^{25} +(-0.689606 - 3.41972i) q^{26} +(4.59322 - 1.93103i) q^{28} -5.45110 q^{29} +3.02410i q^{31} +(4.74454 + 3.08047i) q^{32} +(9.34581 - 1.88464i) q^{34} +3.17811i q^{35} -4.92988i q^{37} +(0.710072 + 3.52121i) q^{38} +(-2.98411 + 2.02826i) q^{40} +9.26643 q^{41} +10.1120 q^{43} +(-10.9181 + 4.59004i) q^{44} +(0.437861 + 6.76818i) q^{46} -9.93569i q^{47} -0.793365 q^{49} +(0.942849 + 4.67553i) q^{50} +(4.54799 - 1.91201i) q^{52} +2.08399i q^{53} -7.55435i q^{55} +(3.96106 + 5.82778i) q^{56} +(-1.52389 - 7.55690i) q^{58} -7.43825i q^{59} -2.14403i q^{61} +(-4.19233 + 0.845409i) q^{62} +(-2.94411 + 7.43856i) q^{64} +3.14681i q^{65} -3.96649 q^{67} +(5.22538 + 12.4293i) q^{68} +(-4.40583 + 0.888462i) q^{70} +12.1146i q^{71} -4.45034 q^{73} +(6.83433 - 1.37818i) q^{74} +(-4.68297 + 1.96876i) q^{76} -14.7532 q^{77} -3.65421 q^{79} +(-3.64602 - 3.56988i) q^{80} +(2.59050 + 12.8461i) q^{82} -3.03863 q^{83} -8.59999 q^{85} +(2.82688 + 14.0184i) q^{86} +(-9.41544 - 13.8526i) q^{88} -5.81313i q^{89} +6.14552 q^{91} +(-9.26037 + 2.49910i) q^{92} +(13.7739 - 2.77759i) q^{94} -3.24020i q^{95} +4.52256i q^{97} +(-0.221791 - 1.09985i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 4 q^{8} + 8 q^{16} - 24 q^{25} - 40 q^{26} + 32 q^{29} + 36 q^{32} - 16 q^{41} + 40 q^{49} + 12 q^{50} - 40 q^{52} + 24 q^{58} + 40 q^{62} + 48 q^{64} + 72 q^{70} - 16 q^{77} - 40 q^{82}+ \cdots + 52 q^{98}+O(q^{100}) $ 24 * q - 4 * q^2 - 4 * q^8 + 8 * q^16 - 24 * q^25 - 40 * q^26 + 32 * q^29 + 36 * q^32 - 16 * q^41 + 40 * q^49 + 12 * q^50 - 40 * q^52 + 24 * q^58 + 40 * q^62 + 48 * q^64 + 72 * q^70 - 16 * q^77 - 40 * q^82 - 64 * q^85 - 44 * q^92 + 72 * q^94 + 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.279557	+	1.38631i	0.197677	+	0.980267i
$2$	0.279557	+	1.38631i	0.197677	+	0.980267i
$3$		0			0
$3$		0			0
$4$	−1.84370	+	0.775104i	−0.921848	+	0.387552i
$5$		−	1.27568i		−	0.570499i	−0.958453	−	0.285250i	$-0.907923\pi$
$5$		−	1.27568i		−	0.570499i	0.958453	−	0.285250i	$-0.0920765\pi$
$6$		0			0
$7$	−2.49131			−0.941627			−0.470814	−	0.882233i	$-0.656040\pi$
$7$	−2.49131			−0.941627			−0.470814	+	0.882233i	$0.656040\pi$
$8$	−1.58995	−	2.33924i	−0.562133	−	0.827047i
$9$		0			0
$10$	1.76848	−	0.356624i	0.559242	−	0.112774i
$11$	5.92184			1.78550			0.892751	−	0.450550i	$-0.148772\pi$
$11$	5.92184			1.78550			0.892751	+	0.450550i	$0.148772\pi$
$12$		0			0
$13$	−2.46678			−0.684162			−0.342081	−	0.939670i	$-0.611132\pi$
$13$	−2.46678			−0.684162			−0.342081	+	0.939670i	$0.611132\pi$
$14$	−0.696464	−	3.45372i	−0.186138	−	0.923047i
$15$		0			0
$16$	2.79843	−	2.85811i	0.699607	−	0.714528i
$17$		−	6.74152i		−	1.63506i	−0.575887	−	0.817529i	$-0.695343\pi$
$17$		−	6.74152i		−	1.63506i	0.575887	−	0.817529i	$-0.304657\pi$
$18$		0			0
$19$	2.53999			0.582714			0.291357	−	0.956614i	$-0.405893\pi$
$19$	2.53999			0.582714			0.291357	+	0.956614i	$0.405893\pi$
$20$	0.988782	+	2.35196i	0.221098	+	0.525914i
$21$		0			0
$22$	1.65549	+	8.20949i	0.352952	+	1.75027i
$23$	4.75259	+	0.642542i	0.990984	+	0.133979i
$23$	4.75259	+	0.642542i	0.990984	+	0.133979i
$24$		0			0
$25$	3.37265			0.674530
$26$	−0.689606	−	3.41972i	−0.135243	−	0.670662i
$27$		0			0
$28$	4.59322	−	1.93103i	0.868037	−	0.364930i
$29$	−5.45110			−1.01224			−0.506122	−	0.862462i	$-0.668921\pi$
$29$	−5.45110			−1.01224			−0.506122	+	0.862462i	$0.668921\pi$
$30$		0			0
$31$			3.02410i			0.543144i	0.962418	+	0.271572i	$0.0875436\pi$
$31$			3.02410i			0.543144i	−0.962418	+	0.271572i	$0.912456\pi$
$32$	4.74454	+	3.08047i	0.838725	+	0.544556i
$33$		0			0
$34$	9.34581	−	1.88464i	1.60279	−	0.323213i
$35$			3.17811i			0.537198i
$36$		0			0
$37$		−	4.92988i		−	0.810468i	−0.914213	−	0.405234i	$-0.867190\pi$
$37$		−	4.92988i		−	0.810468i	0.914213	−	0.405234i	$-0.132810\pi$
$38$	0.710072	+	3.52121i	0.115189	+	0.571215i
$39$		0			0
$40$	−2.98411	+	2.02826i	−0.471830	+	0.320696i
$41$	9.26643			1.44717			0.723587	−	0.690233i	$-0.242492\pi$
$41$	9.26643			1.44717			0.723587	+	0.690233i	$0.242492\pi$
$42$		0			0
$43$	10.1120			1.54207			0.771033	−	0.636795i	$-0.219740\pi$
$43$	10.1120			1.54207			0.771033	+	0.636795i	$0.219740\pi$
$44$	−10.9181	+	4.59004i	−1.64596	+	0.691975i
$45$		0			0
$46$	0.437861	+	6.76818i	0.0645591	+	0.997914i
$47$		−	9.93569i		−	1.44927i	−0.689133	−	0.724635i	$-0.742008\pi$
$47$		−	9.93569i		−	1.44927i	0.689133	−	0.724635i	$-0.257992\pi$
$48$		0			0
$49$	−0.793365			−0.113338
$50$	0.942849	+	4.67553i	0.133339	+	0.661220i
$51$		0			0
$52$	4.54799	−	1.91201i	0.630693	−	0.265148i
$53$			2.08399i			0.286258i	0.989704	+	0.143129i	$0.0457164\pi$
$53$			2.08399i			0.286258i	−0.989704	+	0.143129i	$0.954284\pi$
$54$		0			0
$55$		−	7.55435i		−	1.01863i
$56$	3.96106	+	5.82778i	0.529319	+	0.778770i
$57$		0			0
$58$	−1.52389	−	7.55690i	−0.200097	−	0.992269i
$59$		−	7.43825i		−	0.968378i	−0.874963	−	0.484189i	$-0.839115\pi$
$59$		−	7.43825i		−	0.968378i	0.874963	−	0.484189i	$-0.160885\pi$
$60$		0			0
$61$		−	2.14403i		−	0.274515i	−0.990535	−	0.137257i	$-0.956171\pi$
$61$		−	2.14403i		−	0.274515i	0.990535	−	0.137257i	$-0.0438287\pi$
$62$	−4.19233	+	0.845409i	−0.532427	+	0.107367i
$63$		0			0
$64$	−2.94411	+	7.43856i	−0.368014	+	0.929820i
$65$			3.14681i			0.390314i
$66$		0			0
$67$	−3.96649			−0.484584			−0.242292	−	0.970203i	$-0.577899\pi$
$67$	−3.96649			−0.484584			−0.242292	+	0.970203i	$0.577899\pi$
$68$	5.22538	+	12.4293i	0.633670	+	1.50727i
$69$		0			0
$70$	−4.40583	+	0.888462i	−0.526598	+	0.106192i
$71$			12.1146i			1.43773i	0.695148	+	0.718867i	$0.255339\pi$
$71$			12.1146i			1.43773i	−0.695148	+	0.718867i	$0.744661\pi$
$72$		0			0
$73$	−4.45034			−0.520873			−0.260436	−	0.965491i	$-0.583866\pi$
$73$	−4.45034			−0.520873			−0.260436	+	0.965491i	$0.583866\pi$
$74$	6.83433	−	1.37818i	0.794475	−	0.160211i
$75$		0			0
$76$	−4.68297	+	1.96876i	−0.537173	+	0.225832i
$77$	−14.7532			−1.68128
$78$		0			0
$79$	−3.65421			−0.411131			−0.205565	−	0.978643i	$-0.565903\pi$
$79$	−3.65421			−0.411131			−0.205565	+	0.978643i	$0.565903\pi$
$80$	−3.64602	−	3.56988i	−0.407638	−	0.399125i
$81$		0			0
$82$	2.59050	+	12.8461i	0.286073	+	1.41862i
$83$	−3.03863			−0.333533			−0.166766	−	0.985996i	$-0.553333\pi$
$83$	−3.03863			−0.333533			−0.166766	+	0.985996i	$0.553333\pi$
$84$		0			0
$85$	−8.59999			−0.932800
$86$	2.82688	+	14.0184i	0.304831	+	1.51164i
$87$		0			0
$88$	−9.41544	−	13.8526i	−1.00369	−	1.47669i
$89$		−	5.81313i		−	0.616190i	−0.951356	−	0.308095i	$-0.900309\pi$
$89$		−	5.81313i		−	0.616190i	0.951356	−	0.308095i	$-0.0996915\pi$
$90$		0			0
$91$	6.14552			0.644226
$92$	−9.26037	+	2.49910i	−0.965460	+	0.260550i
$93$		0			0
$94$	13.7739	−	2.77759i	1.42067	−	0.286487i
$95$		−	3.24020i		−	0.332438i
$96$		0			0
$97$			4.52256i			0.459197i	0.973285	+	0.229598i	$0.0737412\pi$
$97$			4.52256i			0.459197i	−0.973285	+	0.229598i	$0.926259\pi$
$98$	−0.221791	−	1.09985i	−0.0224042	−	0.111101i
$99$		0			0
$100$	−6.21814	+	2.61416i	−0.621814	+	0.261416i
$101$	9.44751			0.940062			0.470031	−	0.882650i	$-0.344243\pi$
$101$	9.44751			0.940062			0.470031	+	0.882650i	$0.344243\pi$
$102$		0			0
$103$	1.68300			0.165831			0.0829154	−	0.996557i	$-0.473577\pi$
$103$	1.68300			0.165831			0.0829154	+	0.996557i	$0.473577\pi$
$104$	3.92206	+	5.77040i	0.384590	+	0.565834i
$105$		0			0
$106$	−2.88905	+	0.582594i	−0.280609	+	0.0565865i
$107$	−14.4223			−1.39425			−0.697126	−	0.716949i	$-0.745538\pi$
$107$	−14.4223			−1.39425			−0.697126	+	0.716949i	$0.745538\pi$
$108$		0			0
$109$		−	11.3390i		−	1.08608i	−0.839707	−	0.543040i	$-0.817273\pi$
$109$		−	11.3390i		−	1.08608i	0.839707	−	0.543040i	$-0.182727\pi$
$110$	10.4726	−	2.11187i	0.998528	−	0.201359i
$111$		0			0
$112$	−6.97175	+	7.12045i	−0.658769	+	0.672819i
$113$		−	17.9670i		−	1.69019i	−0.534612	−	0.845097i	$-0.679542\pi$
$113$		−	17.9670i		−	1.69019i	0.534612	−	0.845097i	$-0.320458\pi$
$114$		0			0
$115$	0.819675	−	6.06277i	0.0764351	−	0.565356i
$116$	10.0502	−	4.22517i	0.933135	−	0.392297i
$117$		0			0
$118$	10.3117	−	2.07942i	0.949269	−	0.191426i
$119$			16.7952i			1.53962i
$120$		0			0
$121$	24.0682			2.18802
$122$	2.97228	−	0.599378i	0.269098	−	0.0542652i
$123$		0			0
$124$	−2.34399	−	5.57552i	−0.210497	−	0.500696i
$125$		−	10.6808i		−	0.955319i
$126$		0			0
$127$			0.555947i			0.0493323i	0.999696	+	0.0246662i	$0.00785228\pi$
$127$			0.555947i			0.0493323i	−0.999696	+	0.0246662i	$0.992148\pi$
$128$	−11.1352	−	2.00194i	−0.984220	−	0.176948i
$129$		0			0
$130$	−4.36245	+	0.879714i	−0.382612	+	0.0771560i
$131$		−	0.593855i		−	0.0518854i	−0.999663	−	0.0259427i	$-0.991741\pi$
$131$		−	0.593855i		−	0.0518854i	0.999663	−	0.0259427i	$-0.00825874\pi$
$132$		0			0
$133$	−6.32791			−0.548699
$134$	−1.10886	−	5.49877i	−0.0957909	−	0.475021i
$135$		0			0
$136$	−15.7700	+	10.7187i	−1.35227	+	0.919119i
$137$		−	12.1761i		−	1.04027i	−0.854083	−	0.520136i	$-0.825881\pi$
$137$		−	12.1761i		−	1.04027i	0.854083	−	0.520136i	$-0.174119\pi$
$138$		0			0
$139$			12.5827i			1.06725i	0.845721	+	0.533626i	$0.179171\pi$
$139$			12.5827i			1.06725i	−0.845721	+	0.533626i	$0.820829\pi$
$140$	−2.46336	−	5.85946i	−0.208192	−	0.495215i
$141$		0			0
$142$	−16.7945	+	3.38671i	−1.40936	+	0.284206i
$143$	−14.6079			−1.22157
$144$		0			0
$145$			6.95383i			0.577485i
$146$	−1.24412	−	6.16954i	−0.102964	−	0.510595i
$147$		0			0
$148$	3.82117	+	9.08921i	0.314099	+	0.747128i
$149$			17.4838i			1.43233i	0.697932	+	0.716164i	$0.254104\pi$
$149$			17.4838i			1.43233i	−0.697932	+	0.716164i	$0.745896\pi$
$150$		0			0
$151$			22.2343i			1.80940i	0.426046	+	0.904701i	$0.359906\pi$
$151$			22.2343i			1.80940i	−0.426046	+	0.904701i	$0.640094\pi$
$152$	−4.03846	−	5.94165i	−0.327562	−	0.481932i
$153$		0			0
$154$	−4.12435	−	20.4524i	−0.332350	−	1.64810i
$155$	3.85777			0.309864
$156$		0			0
$157$			18.2974i			1.46029i	0.683290	+	0.730147i	$0.260548\pi$
$157$			18.2974i			1.46029i	−0.683290	+	0.730147i	$0.739452\pi$
$158$	−1.02156	−	5.06586i	−0.0812710	−	0.403018i
$159$		0			0
$160$	3.92969	−	6.05250i	0.310669	−	0.478492i
$161$	−11.8402	−	1.60077i	−0.933138	−	0.126158i
$162$		0			0
$163$			2.10553i			0.164918i	0.996594	+	0.0824591i	$0.0262774\pi$
$163$			2.10553i			0.164918i	−0.996594	+	0.0824591i	$0.973723\pi$
$164$	−17.0845	+	7.18245i	−1.33407	+	0.560855i
$165$		0			0
$166$	−0.849471	−	4.21247i	−0.0659317	−	0.326951i
$167$		−	4.43024i		−	0.342823i	−0.985200	−	0.171411i	$-0.945167\pi$
$167$		−	4.43024i		−	0.342823i	0.985200	−	0.171411i	$-0.0548327\pi$
$168$		0			0
$169$	−6.91499			−0.531922
$170$	−2.40419	−	11.9222i	−0.184393	−	0.914393i
$171$		0			0
$172$	−18.6435	+	7.83786i	−1.42155	+	0.597631i
$173$	5.29846			0.402835			0.201417	−	0.979505i	$-0.435445\pi$
$173$	5.29846			0.402835			0.201417	+	0.979505i	$0.435445\pi$
$174$		0			0
$175$	−8.40233			−0.635156
$176$	16.5718	−	16.9253i	1.24915	−	1.27579i
$177$		0			0
$178$	8.05878	−	1.62510i	0.604031	−	0.121806i
$179$		−	6.37775i		−	0.476696i	−0.971180	−	0.238348i	$-0.923394\pi$
$179$		−	6.37775i		−	0.476696i	0.971180	−	0.238348i	$-0.0766058\pi$
$180$		0			0
$181$		−	20.8442i		−	1.54934i	−0.632368	−	0.774668i	$-0.717917\pi$
$181$		−	20.8442i		−	1.54934i	0.632368	−	0.774668i	$-0.282083\pi$
$182$	1.71802	+	8.51958i	0.127348	+	0.631513i
$183$		0			0
$184$	−6.05333	−	12.1391i	−0.446257	−	0.894905i
$185$	−6.28893			−0.462372
$186$		0			0
$187$		−	39.9222i		−	2.91940i
$188$	7.70120	+	18.3184i	0.561668	+	1.33601i
$189$		0			0
$190$	4.49192	−	0.905822i	0.325878	−	0.0657152i
$191$	0.120078			0.00868856			0.00434428	−	0.999991i	$-0.498617\pi$
$191$	0.120078			0.00868856			0.00434428	+	0.999991i	$0.498617\pi$
$192$		0			0
$193$	−5.99420			−0.431472			−0.215736	−	0.976452i	$-0.569215\pi$
$193$	−5.99420			−0.431472			−0.215736	+	0.976452i	$0.569215\pi$
$194$	−6.26966	+	1.26431i	−0.450135	+	0.0907725i
$195$		0			0
$196$	1.46272	−	0.614940i	0.104480	−	0.0439243i
$197$	12.4182			0.884761			0.442380	−	0.896827i	$-0.354134\pi$
$197$	12.4182			0.884761			0.442380	+	0.896827i	$0.354134\pi$
$198$		0			0
$199$	−9.56523			−0.678061			−0.339030	−	0.940775i	$-0.610099\pi$
$199$	−9.56523			−0.678061			−0.339030	+	0.940775i	$0.610099\pi$
$200$	−5.36235	−	7.88945i	−0.379175	−	0.557868i
$201$		0			0
$202$	2.64112	+	13.0971i	0.185828	+	0.921512i
$203$	13.5804			0.953157
$204$		0			0
$205$		−	11.8210i		−	0.825612i
$206$	0.470494	+	2.33315i	0.0327809	+	0.162558i
$207$		0			0
$208$	−6.90311	+	7.05034i	−0.478644	+	0.488853i
$209$	15.0414			1.04044
$210$		0			0
$211$		−	2.54447i		−	0.175169i	−0.996157	−	0.0875843i	$-0.972085\pi$
$211$		−	2.54447i		−	0.175169i	0.996157	−	0.0875843i	$-0.0279147\pi$
$212$	−1.61531	−	3.84224i	−0.110940	−	0.263886i
$213$		0			0
$214$	−4.03184	−	19.9937i	−0.275611	−	1.36674i
$215$		−	12.8996i		−	0.879748i
$216$		0			0
$217$		−	7.53398i		−	0.511440i
$218$	15.7193	−	3.16990i	1.06465	−	0.214693i
$219$		0			0
$220$	5.85541	+	13.9279i	0.394772	+	0.939020i
$221$			16.6298i			1.11864i
$222$		0			0
$223$			8.25462i			0.552770i	0.961047	+	0.276385i	$0.0891365\pi$
$223$			8.25462i			0.552770i	−0.961047	+	0.276385i	$0.910864\pi$
$224$	−11.8201	−	7.67442i	−0.789766	−	0.512769i
$225$		0			0
$226$	24.9078	−	5.02281i	1.65684	−	0.334112i
$227$	10.9045			0.723755			0.361877	−	0.932226i	$-0.382136\pi$
$227$	10.9045			0.723755			0.361877	+	0.932226i	$0.382136\pi$
$228$		0			0
$229$		−	14.3196i		−	0.946264i	−0.880992	−	0.473132i	$-0.843123\pi$
$229$		−	14.3196i		−	0.946264i	0.880992	−	0.473132i	$-0.156877\pi$
$230$	8.63400	−	0.558569i	0.569309	−	0.0368309i
$231$		0			0
$232$	8.66698	+	12.7514i	0.569015	+	0.837173i
$233$	−10.5570			−0.691615			−0.345808	−	0.938305i	$-0.612395\pi$
$233$	−10.5570			−0.691615			−0.345808	+	0.938305i	$0.612395\pi$
$234$		0			0
$235$	−12.6747			−0.826808
$236$	5.76542	+	13.7139i	0.375297	+	0.892697i
$237$		0			0
$238$	−23.2833	+	4.69522i	−1.50923	+	0.304346i
$239$			4.84386i			0.313323i	0.987652	+	0.156662i	$0.0500732\pi$
$239$			4.84386i			0.313323i	−0.987652	+	0.156662i	$0.949927\pi$
$240$		0			0
$241$			22.0218i			1.41855i	0.704933	+	0.709274i	$0.250977\pi$
$241$			22.0218i			1.41855i	−0.704933	+	0.709274i	$0.749023\pi$
$242$	6.72844	+	33.3659i	0.432521	+	2.14484i
$243$		0			0
$244$	1.66185	+	3.95294i	0.106389	+	0.253061i
$245$			1.01208i			0.0646592i
$246$		0			0
$247$	−6.26560			−0.398671
$248$	7.07410	−	4.80817i	0.449206	−	0.305319i
$249$		0			0
$250$	14.8069	−	2.98589i	0.936468	−	0.188844i
$251$	−1.49664			−0.0944669			−0.0472334	−	0.998884i	$-0.515040\pi$
$251$	−1.49664			−0.0944669			−0.0472334	+	0.998884i	$0.515040\pi$
$252$		0			0
$253$	28.1441	+	3.80503i	1.76940	+	0.239220i
$254$	−0.770713	+	0.155419i	−0.0483588	+	0.00975185i
$255$		0			0
$256$	−0.337613	−	15.9964i	−0.0211008	−	0.999777i
$257$	−15.3146			−0.955301			−0.477650	−	0.878550i	$-0.658511\pi$
$257$	−15.3146			−0.955301			−0.477650	+	0.878550i	$0.658511\pi$
$258$		0			0
$259$			12.2819i			0.763159i
$260$	−2.43911	−	5.80176i	−0.151267	−	0.359810i
$261$		0			0
$262$	0.823266	−	0.166016i	0.0508615	−	0.0102565i
$263$	2.19677			0.135458			0.0677292	−	0.997704i	$-0.478425\pi$
$263$	2.19677			0.135458			0.0677292	+	0.997704i	$0.478425\pi$
$264$		0			0
$265$	2.65849			0.163310
$266$	−1.76901	−	8.77242i	−0.108465	−	0.537872i
$267$		0			0
$268$	7.31299	−	3.07444i	0.446712	−	0.187801i
$269$	8.15180			0.497024			0.248512	−	0.968629i	$-0.420058\pi$
$269$	8.15180			0.497024			0.248512	+	0.968629i	$0.420058\pi$
$270$		0			0
$271$		−	17.0762i		−	1.03731i	−0.854984	−	0.518654i	$-0.826433\pi$
$271$		−	17.0762i		−	1.03731i	0.854984	−	0.518654i	$-0.173567\pi$
$272$	−19.2680	−	18.8656i	−1.16829	−	1.14390i
$273$		0			0
$274$	16.8798	−	3.40391i	1.01975	−	0.205638i
$275$	19.9723			1.20438
$276$		0			0
$277$	13.9801			0.839982			0.419991	−	0.907528i	$-0.362033\pi$
$277$	13.9801			0.839982			0.419991	+	0.907528i	$0.362033\pi$
$278$	−17.4435	+	3.51759i	−1.04619	+	0.210971i
$279$		0			0
$280$	7.43436	−	5.05303i	0.444288	−	0.301976i
$281$			22.1413i			1.32084i	0.750896	+	0.660420i	$0.229622\pi$
$281$			22.1413i			1.32084i	−0.750896	+	0.660420i	$0.770378\pi$
$282$		0			0
$283$	14.2647			0.847946			0.423973	−	0.905675i	$-0.360635\pi$
$283$	14.2647			0.847946			0.423973	+	0.905675i	$0.360635\pi$
$284$	−9.39004	−	22.3356i	−0.557197	−	1.32537i
$285$		0			0
$286$	−4.08374	−	20.2510i	−0.241477	−	1.19747i
$287$	−23.0856			−1.36270
$288$		0			0
$289$	−28.4481			−1.67341
$290$	−9.64015	+	1.94399i	−0.566089	+	0.114155i
$291$		0			0
$292$	8.20507	−	3.44948i	0.480166	−	0.201865i
$293$		−	9.44315i		−	0.551675i	−0.961204	−	0.275837i	$-0.911045\pi$
$293$		−	9.44315i		−	0.551675i	0.961204	−	0.275837i	$-0.0889552\pi$
$294$		0			0
$295$	−9.48880			−0.552459
$296$	−11.5322	+	7.83827i	−0.670295	+	0.455590i
$297$		0			0
$298$	−24.2379	+	4.88772i	−1.40407	+	0.283138i
$299$	−11.7236	−	1.58501i	−0.677994	−	0.0916635i
$300$		0			0
$301$	−25.1922			−1.45205
$302$	−30.8236	+	6.21576i	−1.77370	+	0.357677i
$303$		0			0
$304$	7.10798	−	7.25958i	0.407670	−	0.416365i
$305$	−2.73508			−0.156610
$306$		0			0
$307$			16.9520i			0.967504i	0.875205	+	0.483752i	$0.160726\pi$
$307$			16.9520i			0.967504i	−0.875205	+	0.483752i	$0.839274\pi$
$308$	27.2003	−	11.4352i	1.54988	−	0.651583i
$309$		0			0
$310$	1.07847	+	5.34805i	0.0612528	+	0.303749i
$311$			19.6873i			1.11636i	0.829719	+	0.558182i	$0.188501\pi$
$311$			19.6873i			1.11636i	−0.829719	+	0.558182i	$0.811499\pi$
$312$		0			0
$313$		−	1.61663i		−	0.0913772i	−0.998956	−	0.0456886i	$-0.985452\pi$
$313$		−	1.61663i		−	0.0913772i	0.998956	−	0.0456886i	$-0.0145482\pi$
$314$	−25.3658	+	5.11518i	−1.43148	+	0.288666i
$315$		0			0
$316$	6.73725	−	2.83239i	0.379000	−	0.159335i
$317$	24.6211			1.38286			0.691430	−	0.722444i	$-0.256981\pi$
$317$	24.6211			1.38286			0.691430	+	0.722444i	$0.256981\pi$
$318$		0			0
$319$	−32.2806			−1.80736
$320$	9.48919	+	3.75573i	0.530462	+	0.209952i
$321$		0			0
$322$	−1.09085	−	16.8617i	−0.0607906	−	0.939663i
$323$		−	17.1234i		−	0.952771i
$324$		0			0
$325$	−8.31959			−0.461488
$326$	−2.91892	+	0.588617i	−0.161664	+	0.0326005i
$327$		0			0
$328$	−14.7332	−	21.6764i	−0.813503	−	1.19688i
$329$			24.7529i			1.36467i
$330$		0			0
$331$			24.9576i			1.37179i	0.727699	+	0.685896i	$0.240590\pi$
$331$			24.9576i			1.37179i	−0.727699	+	0.685896i	$0.759410\pi$
$332$	5.60231	−	2.35525i	0.307467	−	0.129261i
$333$		0			0
$334$	6.14168	−	1.23851i	0.336058	−	0.0677681i
$335$			5.05995i			0.276455i
$336$		0			0
$337$			16.3446i			0.890347i	0.895444	+	0.445173i	$0.146858\pi$
$337$			16.3446i			0.890347i	−0.895444	+	0.445173i	$0.853142\pi$
$338$	−1.93314	−	9.58630i	−0.105149	−	0.521426i
$339$		0			0
$340$	15.8558	−	6.66589i	0.859899	−	0.361508i
$341$			17.9082i			0.969786i
$342$		0			0
$343$	19.4157			1.04835
$344$	−16.0776	−	23.6544i	−0.866846	−	1.27536i
$345$		0			0
$346$	1.48122	+	7.34530i	0.0796311	+	0.394886i
$347$			18.8134i			1.00995i	0.863133	+	0.504977i	$0.168499\pi$
$347$			18.8134i			1.00995i	−0.863133	+	0.504977i	$0.831501\pi$
$348$		0			0
$349$	13.5829			0.727078			0.363539	−	0.931579i	$-0.381568\pi$
$349$	13.5829			0.727078			0.363539	+	0.931579i	$0.381568\pi$
$350$	−2.34893	−	11.6482i	−0.125556	−	0.622623i
$351$		0			0
$352$	28.0964	+	18.2421i	1.49754	+	0.972306i
$353$	−31.5063			−1.67691			−0.838456	−	0.544969i	$-0.816541\pi$
$353$	−31.5063			−1.67691			−0.838456	+	0.544969i	$0.816541\pi$
$354$		0			0
$355$	15.4542			0.820226
$356$	4.50578	+	10.7176i	0.238806	+	0.568033i
$357$		0			0
$358$	8.84152	−	1.78295i	0.467289	−	0.0942316i
$359$	18.4884			0.975779			0.487890	−	0.872905i	$-0.337767\pi$
$359$	18.4884			0.975779			0.487890	+	0.872905i	$0.337767\pi$
$360$		0			0
$361$	−12.5485			−0.660445
$362$	28.8965	−	5.82714i	1.51876	−	0.306268i
$363$		0			0
$364$	−11.3305	+	4.76342i	−0.593878	+	0.249671i
$365$			5.67719i			0.297158i
$366$		0			0
$367$	−3.17955			−0.165971			−0.0829855	−	0.996551i	$-0.526446\pi$
$367$	−3.17955			−0.165971			−0.0829855	+	0.996551i	$0.526446\pi$
$368$	15.1362	−	11.7853i	0.789031	−	0.614353i
$369$		0			0
$370$	−1.75812	−	8.71839i	−0.0914001	−	0.453248i
$371$		−	5.19187i		−	0.269548i
$372$		0			0
$373$			17.7910i			0.921186i	0.887612	+	0.460593i	$0.152363\pi$
$373$			17.7910i			0.921186i	−0.887612	+	0.460593i	$0.847637\pi$
$374$	55.3444	−	11.1605i	2.86179	−	0.577098i
$375$		0			0
$376$	−23.2420	+	15.7973i	−1.19861	+	0.814682i
$377$	13.4467			0.692539
$378$		0			0
$379$	−13.2435			−0.680273			−0.340136	−	0.940376i	$-0.610473\pi$
$379$	−13.2435			−0.680273			−0.340136	+	0.940376i	$0.610473\pi$
$380$	2.51150	+	5.97395i	0.128837	+	0.306457i
$381$		0			0
$382$	0.0335687	+	0.166465i	0.00171753	+	0.00851711i
$383$	9.71405			0.496365			0.248182	−	0.968713i	$-0.420167\pi$
$383$	9.71405			0.496365			0.248182	+	0.968713i	$0.420167\pi$
$384$		0			0
$385$			18.8202i			0.959168i
$386$	−1.67572	−	8.30980i	−0.0852920	−	0.422958i
$387$		0			0
$388$	−3.50546	−	8.33823i	−0.177963	−	0.423309i
$389$			27.6072i			1.39974i	0.714271	+	0.699870i	$0.246759\pi$
$389$			27.6072i			1.39974i	−0.714271	+	0.699870i	$0.753241\pi$
$390$		0			0
$391$	4.33171	−	32.0397i	0.219064	−	1.62032i
$392$	1.26141	+	1.85587i	0.0637109	+	0.0937357i
$393$		0			0
$394$	3.47160	+	17.2155i	0.174897	+	0.867302i
$395$			4.66159i			0.234550i
$396$		0			0
$397$	12.2838			0.616508			0.308254	−	0.951304i	$-0.400255\pi$
$397$	12.2838			0.616508			0.308254	+	0.951304i	$0.400255\pi$
$398$	−2.67403	−	13.2603i	−0.134037	−	0.664681i
$399$		0			0
$400$	9.43812	−	9.63942i	0.471906	−	0.481971i
$401$			17.1714i			0.857499i	0.903423	+	0.428750i	$0.141046\pi$
$401$			17.1714i			0.857499i	−0.903423	+	0.428750i	$0.858954\pi$
$402$		0			0
$403$		−	7.45979i		−	0.371599i
$404$	−17.4183	+	7.32280i	−0.866594	+	0.364323i
$405$		0			0
$406$	3.79650	+	18.8266i	0.188417	+	0.934348i
$407$		−	29.1940i		−	1.44709i
$408$		0			0
$409$	24.7976			1.22616			0.613082	−	0.790019i	$-0.289930\pi$
$409$	24.7976			1.22616			0.613082	+	0.790019i	$0.289930\pi$
$410$	16.3875	−	3.30463i	0.809320	−	0.163204i
$411$		0			0
$412$	−3.10294	+	1.30450i	−0.152871	+	0.0642681i
$413$			18.5310i			0.911851i
$414$		0			0
$415$			3.87631i			0.190280i
$416$	−11.7037	−	7.59885i	−0.573823	−	0.372564i
$417$		0			0
$418$	4.20494	+	20.8520i	0.205670	+	1.01991i
$419$	14.3462			0.700856			0.350428	−	0.936590i	$-0.386036\pi$
$419$	14.3462			0.700856			0.350428	+	0.936590i	$0.386036\pi$
$420$		0			0
$421$			34.0216i			1.65811i	0.559166	+	0.829056i	$0.311121\pi$
$421$			34.0216i			1.65811i	−0.559166	+	0.829056i	$0.688879\pi$
$422$	3.52742	−	0.711325i	0.171712	−	0.0346267i
$423$		0			0
$424$	4.87496	−	3.31344i	0.236749	−	0.160915i
$425$		−	22.7368i		−	1.10290i
$426$		0			0
$427$			5.34144i			0.258491i
$428$	26.5902	−	11.1787i	1.28529	−	0.540345i
$429$		0			0
$430$	17.8829	−	3.60619i	0.862388	−	0.173906i
$431$	−24.1892			−1.16515			−0.582575	−	0.812777i	$-0.697955\pi$
$431$	−24.1892			−1.16515			−0.582575	+	0.812777i	$0.697955\pi$
$432$		0			0
$433$		−	26.3588i		−	1.26672i	−0.773856	−	0.633362i	$-0.781675\pi$
$433$		−	26.3588i		−	1.26672i	0.773856	−	0.633362i	$-0.218325\pi$
$434$	10.4444	−	2.10618i	0.501347	−	0.101100i
$435$		0			0
$436$	8.78891	+	20.9057i	0.420912	+	1.00120i
$437$	12.0715	+	1.63205i	0.577460	+	0.0780715i
$438$		0			0
$439$			3.36175i			0.160448i	0.996777	+	0.0802238i	$0.0255635\pi$
$439$			3.36175i			0.160448i	−0.996777	+	0.0802238i	$0.974437\pi$
$440$	−17.6715	+	12.0110i	−0.842454	+	0.572604i
$441$		0			0
$442$	−23.0541	+	4.64899i	−1.09657	+	0.221130i
$443$			24.2964i			1.15436i	0.816618	+	0.577179i	$0.195846\pi$
$443$			24.2964i			1.15436i	−0.816618	+	0.577179i	$0.804154\pi$
$444$		0			0
$445$	−7.41566			−0.351536
$446$	−11.4434	+	2.30764i	−0.541862	+	0.109270i
$447$		0			0
$448$	7.33470	−	18.5318i	0.346532	−	0.875544i
$449$	2.97429			0.140365			0.0701826	−	0.997534i	$-0.477642\pi$
$449$	2.97429			0.140365			0.0701826	+	0.997534i	$0.477642\pi$
$450$		0			0
$451$	54.8744			2.58393
$452$	13.9263	+	33.1257i	0.655039	+	1.55810i
$453$		0			0
$454$	3.04842	+	15.1169i	0.143070	+	0.709473i
$455$		−	7.83969i		−	0.367530i
$456$		0			0
$457$			30.9823i			1.44929i	0.689123	+	0.724644i	$0.257996\pi$
$457$			30.9823i			1.44929i	−0.689123	+	0.724644i	$0.742004\pi$
$458$	19.8513	−	4.00314i	0.927592	−	0.187054i
$459$		0			0
$460$	3.18805	+	11.8132i	0.148643	+	0.550795i
$461$	−42.5845			−1.98336			−0.991679	−	0.128738i	$-0.958907\pi$
$461$	−42.5845			−1.98336			−0.991679	+	0.128738i	$0.958907\pi$
$462$		0			0
$463$		−	28.2192i		−	1.31146i	−0.754997	−	0.655728i	$-0.772362\pi$
$463$		−	28.2192i		−	1.31146i	0.754997	−	0.655728i	$-0.227638\pi$
$464$	−15.2545	+	15.5799i	−0.708173	+	0.723277i
$465$		0			0
$466$	−2.95130	−	14.6353i	−0.136716	−	0.677968i
$467$	16.9236			0.783130			0.391565	−	0.920150i	$-0.371934\pi$
$467$	16.9236			0.783130			0.391565	+	0.920150i	$0.371934\pi$
$468$		0			0
$469$	9.88176			0.456297
$470$	−3.54331	−	17.5711i	−0.163441	−	0.810492i
$471$		0			0
$472$	−17.3999	+	11.8265i	−0.800894	+	0.544357i
$473$	59.8817			2.75336
$474$		0			0
$475$	8.56650			0.393058
$476$	−13.0180	−	30.9653i	−0.596681	−	1.41929i
$477$		0			0
$478$	−6.71508	+	1.35414i	−0.307141	+	0.0619368i
$479$	−25.7641			−1.17719			−0.588595	−	0.808428i	$-0.700319\pi$
$479$	−25.7641			−1.17719			−0.588595	+	0.808428i	$0.700319\pi$
$480$		0			0
$481$			12.1609i			0.554491i
$482$	−30.5290	+	6.15635i	−1.39056	+	0.280414i
$483$		0			0
$484$	−44.3745	+	18.6554i	−2.01702	+	0.847972i
$485$	5.76932			0.261971
$486$		0			0
$487$			21.2924i			0.964850i	0.875937	+	0.482425i	$0.160244\pi$
$487$			21.2924i			0.964850i	−0.875937	+	0.482425i	$0.839756\pi$
$488$	−5.01540	+	3.40890i	−0.227037	+	0.154314i
$489$		0			0
$490$	−1.40305	+	0.282933i	−0.0633833	+	0.0127816i
$491$		−	7.54351i		−	0.340434i	−0.985407	−	0.170217i	$-0.945553\pi$
$491$		−	7.54351i		−	0.340434i	0.985407	−	0.170217i	$-0.0544468\pi$
$492$		0			0
$493$			36.7487i			1.65508i
$494$	−1.75159	−	8.68605i	−0.0788079	−	0.390804i
$495$		0			0
$496$	8.64322	+	8.46272i	0.388092	+	0.379987i
$497$		−	30.1811i		−	1.35381i
$498$		0			0
$499$		−	18.4954i		−	0.827970i	−0.910284	−	0.413985i	$-0.864137\pi$
$499$		−	18.4954i		−	0.827970i	0.910284	−	0.413985i	$-0.135863\pi$
$500$	8.27872	+	19.6921i	0.370236	+	0.880658i
$501$		0			0
$502$	−0.418395	−	2.07480i	−0.0186739	−	0.0926028i
$503$	−41.5195			−1.85126			−0.925632	−	0.378425i	$-0.876466\pi$
$503$	−41.5195			−1.85126			−0.925632	+	0.378425i	$0.876466\pi$
$504$		0			0
$505$		−	12.0520i		−	0.536305i
$506$	2.59294	+	40.0801i	0.115270	+	1.78178i
$507$		0			0
$508$	−0.430917	−	1.02500i	−0.0191188	−	0.0454769i
$509$	0.524721			0.0232579			0.0116289	−	0.999932i	$-0.496298\pi$
$509$	0.524721			0.0232579			0.0116289	+	0.999932i	$0.496298\pi$
$510$		0			0
$511$	11.0872			0.490468
$512$	22.0816	−	4.93995i	0.975878	−	0.218317i
$513$		0			0
$514$	−4.28131	−	21.2308i	−0.188841	−	0.936450i
$515$		−	2.14696i		−	0.0946064i
$516$		0			0
$517$		−	58.8376i		−	2.58767i
$518$	−17.0265	+	3.43349i	−0.748100	+	0.150859i
$519$		0			0
$520$	7.36116	−	5.00328i	0.322808	−	0.219408i
$521$			14.1174i			0.618493i	0.950982	+	0.309247i	$0.100077\pi$
$521$			14.1174i			0.618493i	−0.950982	+	0.309247i	$0.899923\pi$
$522$		0			0
$523$	26.2501			1.14784			0.573918	−	0.818913i	$-0.305423\pi$
$523$	26.2501			1.14784			0.573918	+	0.818913i	$0.305423\pi$
$524$	0.460300	+	1.09489i	0.0201083	+	0.0478304i
$525$		0			0
$526$	0.614122	+	3.04539i	0.0267770	+	0.132786i
$527$	20.3870			0.888072
$528$		0			0
$529$	22.1743	+	6.10748i	0.964099	+	0.265543i
$530$	0.743201	+	3.68549i	0.0322826	+	0.160087i
$531$		0			0
$532$	11.6667	−	4.90479i	0.505817	−	0.212650i
$533$	−22.8583			−0.990101
$534$		0			0
$535$			18.3981i			0.795420i
$536$	6.30652	+	9.27858i	0.272400	+	0.400773i
$537$		0			0
$538$	2.27889	+	11.3009i	0.0982501	+	0.487216i
$539$	−4.69818			−0.202365
$540$		0			0
$541$	22.3639			0.961498			0.480749	−	0.876858i	$-0.340365\pi$
$541$	22.3639			0.961498			0.480749	+	0.876858i	$0.340365\pi$
$542$	23.6729	−	4.77378i	1.01684	−	0.205052i
$543$		0			0
$544$	20.7671	−	31.9854i	0.890381	−	1.37136i
$545$	−14.4649			−0.619608
$546$		0			0
$547$		−	20.2548i		−	0.866033i	−0.901386	−	0.433017i	$-0.857449\pi$
$547$		−	20.2548i		−	0.866033i	0.901386	−	0.433017i	$-0.142551\pi$
$548$	9.43773	+	22.4490i	0.403160	+	0.958973i
$549$		0			0
$550$	5.58340	+	27.6878i	0.238077	+	1.18061i
$551$	−13.8457			−0.589848
$552$		0			0
$553$	9.10378			0.387132
$554$	3.90823	+	19.3807i	0.166045	+	0.823407i
$555$		0			0
$556$	−9.75291	−	23.1987i	−0.413616	−	0.983843i
$557$		−	28.8162i		−	1.22098i	−0.792023	−	0.610491i	$-0.790972\pi$
$557$		−	28.8162i		−	1.22098i	0.792023	−	0.610491i	$-0.209028\pi$
$558$		0			0
$559$	−24.9441			−1.05502
$560$	9.08338	+	8.89370i	0.383843	+	0.375827i
$561$		0			0
$562$	−30.6947	+	6.18977i	−1.29478	+	0.261100i
$563$	−20.5741			−0.867095			−0.433548	−	0.901131i	$-0.642738\pi$
$563$	−20.5741			−0.867095			−0.433548	+	0.901131i	$0.642738\pi$
$564$		0			0
$565$	−22.9201			−0.964255
$566$	3.98779	+	19.7752i	0.167619	+	0.831214i
$567$		0			0
$568$	28.3389	−	19.2616i	1.18907	−	0.808197i
$569$			33.7758i			1.41596i	0.706234	+	0.707979i	$0.250393\pi$
$569$			33.7758i			1.41596i	−0.706234	+	0.707979i	$0.749607\pi$
$570$		0			0
$571$	34.0122			1.42337			0.711684	−	0.702500i	$-0.247933\pi$
$571$	34.0122			1.42337			0.711684	+	0.702500i	$0.247933\pi$
$572$	26.9325	−	11.3226i	1.12610	−	0.473423i
$573$		0			0
$574$	−6.45374	−	32.0037i	−0.269374	−	1.33581i
$575$	16.0288	+	2.16707i	0.668449	+	0.0903730i
$576$		0			0
$577$	−32.4491			−1.35088			−0.675438	−	0.737417i	$-0.736045\pi$
$577$	−32.4491			−1.35088			−0.675438	+	0.737417i	$0.736045\pi$
$578$	−7.95286	−	39.4377i	−0.330795	−	1.64039i
$579$		0			0
$580$	−5.38995	−	12.8208i	−0.223805	−	0.532353i
$581$	7.57017			0.314064
$582$		0			0
$583$			12.3411i			0.511114i
$584$	7.07582	+	10.4104i	0.292800	+	0.430787i
$585$		0			0
$586$	13.0911	−	2.63990i	0.540789	−	0.109053i
$587$			4.92756i			0.203382i	0.994816	+	0.101691i	$0.0324254\pi$
$587$			4.92756i			0.203382i	−0.994816	+	0.101691i	$0.967575\pi$
$588$		0			0
$589$			7.68118i			0.316498i
$590$	−2.65266	−	13.1544i	−0.109208	−	0.541558i
$591$		0			0
$592$	−14.0902	−	13.7959i	−0.579102	−	0.567009i
$593$	19.1860			0.787875			0.393938	−	0.919137i	$-0.371113\pi$
$593$	19.1860			0.787875			0.393938	+	0.919137i	$0.371113\pi$
$594$		0			0
$595$	21.4253			0.878350
$596$	−13.5518	−	32.2348i	−0.555102	−	1.32039i
$597$		0			0
$598$	−1.08011	−	16.6956i	−0.0441689	−	0.682735i
$599$		−	35.3094i		−	1.44270i	−0.692568	−	0.721352i	$-0.743521\pi$
$599$		−	35.3094i		−	1.44270i	0.692568	−	0.721352i	$-0.256479\pi$
$600$		0			0
$601$	−35.4004			−1.44401			−0.722006	−	0.691887i	$-0.756780\pi$
$601$	−35.4004			−1.44401			−0.722006	+	0.691887i	$0.756780\pi$
$602$	−7.04265	−	34.9241i	−0.287037	−	1.42340i
$603$		0			0
$604$	−17.2339	−	40.9933i	−0.701238	−	1.66799i
$605$		−	30.7032i		−	1.24826i
$606$		0			0
$607$			41.3927i			1.68008i	0.542525	+	0.840039i	$0.317468\pi$
$607$			41.3927i			1.68008i	−0.542525	+	0.840039i	$0.682532\pi$
$608$	12.0511	+	7.82437i	0.488736	+	0.317320i
$609$		0			0
$610$	−0.764612	−	3.79167i	−0.0309583	−	0.153520i
$611$			24.5092i			0.991535i
$612$		0			0
$613$		−	21.8461i		−	0.882354i	−0.897420	−	0.441177i	$-0.854561\pi$
$613$		−	21.8461i		−	0.882354i	0.897420	−	0.441177i	$-0.145439\pi$
$614$	−23.5007	+	4.73906i	−0.948413	+	0.191253i
$615$		0			0
$616$	23.4568	+	34.5112i	0.945101	+	1.39050i
$617$		−	23.4324i		−	0.943354i	−0.881771	−	0.471677i	$-0.843649\pi$
$617$		−	23.4324i		−	0.943354i	0.881771	−	0.471677i	$-0.156351\pi$
$618$		0			0
$619$	−18.8898			−0.759247			−0.379624	−	0.925141i	$-0.623946\pi$
$619$	−18.8898			−0.759247			−0.379624	+	0.925141i	$0.623946\pi$
$620$	−7.11255	+	2.99017i	−0.285647	+	0.120088i
$621$		0			0
$622$	−27.2926	+	5.50372i	−1.09433	+	0.220679i
$623$			14.4823i			0.580221i
$624$		0			0
$625$	3.23804			0.129522
$626$	2.24114	−	0.451940i	0.0895741	−	0.0180631i
$627$		0			0
$628$	−14.1824	−	33.7349i	−0.565940	−	1.34617i
$629$	−33.2349			−1.32516
$630$		0			0
$631$	−17.4008			−0.692717			−0.346358	−	0.938102i	$-0.612582\pi$
$631$	−17.4008			−0.692717			−0.346358	+	0.938102i	$0.612582\pi$
$632$	5.81001	+	8.54808i	0.231110	+	0.340024i
$633$		0			0
$634$	6.88301	+	34.1324i	0.273359	+	1.35557i
$635$	0.709208			0.0281441
$636$		0			0
$637$	1.95706			0.0775414
$638$	−9.02426	−	44.7508i	−0.357274	−	1.77170i
$639$		0			0
$640$	−2.55383	+	14.2049i	−0.100949	+	0.561497i
$641$		−	7.29894i		−	0.288291i	−0.989557	−	0.144145i	$-0.953957\pi$
$641$		−	7.29894i		−	0.288291i	0.989557	−	0.144145i	$-0.0460433\pi$
$642$		0			0
$643$	−6.74160			−0.265863			−0.132931	−	0.991125i	$-0.542439\pi$
$643$	−6.74160			−0.265863			−0.132931	+	0.991125i	$0.542439\pi$
$644$	23.0705	−	6.22605i	0.909104	−	0.245341i
$645$		0			0
$646$	23.7383	−	4.78697i	0.933970	−	0.188341i
$647$			4.47981i			0.176120i	0.996115	+	0.0880598i	$0.0280667\pi$
$647$			4.47981i			0.176120i	−0.996115	+	0.0880598i	$0.971933\pi$
$648$		0			0
$649$		−	44.0482i		−	1.72904i
$650$	−2.32580	−	11.5335i	−0.0912255	−	0.452382i
$651$		0			0
$652$	−1.63201	−	3.88196i	−0.0639144	−	0.152029i
$653$	−0.978338			−0.0382853			−0.0191427	−	0.999817i	$-0.506094\pi$
$653$	−0.978338			−0.0382853			−0.0191427	+	0.999817i	$0.506094\pi$
$654$		0			0
$655$	−0.757567			−0.0296006
$656$	25.9314	−	26.4845i	1.01245	−	1.03405i
$657$		0			0
$658$	−34.3151	+	6.91985i	−1.33774	+	0.269764i
$659$	33.2279			1.29437			0.647187	−	0.762331i	$-0.275945\pi$
$659$	33.2279			1.29437			0.647187	+	0.762331i	$0.275945\pi$
$660$		0			0
$661$		−	10.6444i		−	0.414021i	−0.978339	−	0.207010i	$-0.933627\pi$
$661$		−	10.6444i		−	0.414021i	0.978339	−	0.207010i	$-0.0663734\pi$
$662$	−34.5989	+	6.97707i	−1.34472	+	0.271172i
$663$		0			0
$664$	4.83127	+	7.10809i	0.187490	+	0.275847i
$665$			8.07236i			0.313033i
$666$		0			0
$667$	−25.9069	−	3.50256i	−1.00312	−	0.135620i
$668$	3.43390	+	8.16802i	0.132862	+	0.316030i
$669$		0			0
$670$	−7.01465	+	1.41455i	−0.270999	+	0.0546487i
$671$		−	12.6966i		−	0.490147i
$672$		0			0
$673$	15.5105			0.597885			0.298943	−	0.954271i	$-0.403366\pi$
$673$	15.5105			0.597885			0.298943	+	0.954271i	$0.403366\pi$
$674$	−22.6586	+	4.56925i	−0.872778	+	0.176001i
$675$		0			0
$676$	12.7491	−	5.35984i	0.490352	−	0.206148i
$677$			10.7034i			0.411365i	0.978619	+	0.205683i	$0.0659415\pi$
$677$			10.7034i			0.411365i	−0.978619	+	0.205683i	$0.934059\pi$
$678$		0			0
$679$		−	11.2671i		−	0.432392i
$680$	13.6736	+	20.1175i	0.524357	+	0.771469i
$681$		0			0
$682$	−24.8263	+	5.00638i	−0.950649	+	0.191704i
$683$			36.5249i			1.39759i	0.715324	+	0.698793i	$0.246279\pi$
$683$			36.5249i			1.39759i	−0.715324	+	0.698793i	$0.753721\pi$
$684$		0			0
$685$	−15.5327			−0.593475
$686$	5.42780	+	26.9161i	0.207234	+	1.02766i
$687$		0			0
$688$	28.2977	−	28.9013i	1.07884	−	1.10185i
$689$		−	5.14075i		−	0.195847i
$690$		0			0
$691$		−	47.9613i		−	1.82453i	−0.409596	−	0.912267i	$-0.634330\pi$
$691$		−	47.9613i		−	1.82453i	0.409596	−	0.912267i	$-0.365670\pi$
$692$	−9.76876	+	4.10686i	−0.371352	+	0.156119i
$693$		0			0
$694$	−26.0811	+	5.25941i	−0.990025	+	0.199645i
$695$	16.0515			0.608866
$696$		0			0
$697$		−	62.4698i		−	2.36621i
$698$	3.79721	+	18.8301i	0.143726	+	0.712731i
$699$		0			0
$700$	15.4913	−	6.51268i	0.585517	−	0.246156i
$701$		−	35.8504i		−	1.35405i	−0.735960	−	0.677025i	$-0.763269\pi$
$701$		−	35.8504i		−	1.35405i	0.735960	−	0.677025i	$-0.236731\pi$
$702$		0			0
$703$		−	12.5219i		−	0.472271i
$704$	−17.4346	+	44.0500i	−0.657090	+	1.66020i
$705$		0			0
$706$	−8.80782	−	43.6774i	−0.331486	−	1.64382i
$707$	−23.5367			−0.885188
$708$		0			0
$709$			18.1038i			0.679902i	0.940443	+	0.339951i	$0.110410\pi$
$709$			18.1038i			0.679902i	−0.940443	+	0.339951i	$0.889590\pi$
$710$	4.32034	+	21.4243i	0.162140	+	0.804041i
$711$		0			0
$712$	−13.5983	+	9.24258i	−0.509618	+	0.346380i
$713$	−1.94311	+	14.3723i	−0.0727700	+	0.538247i
$714$		0			0
$715$			18.6349i			0.696907i
$716$	4.94342	+	11.7586i	0.184744	+	0.439441i
$717$		0			0
$718$	5.16856	+	25.6306i	0.192889	+	0.956525i
$719$			4.13110i			0.154064i	0.997029	+	0.0770319i	$0.0245443\pi$
$719$			4.13110i			0.154064i	−0.997029	+	0.0770319i	$0.975456\pi$
$720$		0			0
$721$	−4.19287			−0.156151
$722$	−3.50801	−	17.3960i	−0.130555	−	0.647412i
$723$		0			0
$724$	16.1564	+	38.4303i	0.600449	+	1.42825i
$725$	−18.3847			−0.682789
$726$		0			0
$727$	−47.9031			−1.77663			−0.888314	−	0.459237i	$-0.848123\pi$
$727$	−47.9031			−1.77663			−0.888314	+	0.459237i	$0.848123\pi$
$728$	−9.77108	−	14.3759i	−0.362140	−	0.532805i
$729$		0			0
$730$	−7.87033	+	1.58710i	−0.291294	+	0.0587412i
$731$		−	68.1703i		−	2.52137i
$732$		0			0
$733$		−	15.5853i		−	0.575657i	−0.957682	−	0.287829i	$-0.907067\pi$
$733$		−	15.5853i		−	0.575657i	0.957682	−	0.287829i	$-0.0929334\pi$
$734$	−0.888865	−	4.40783i	−0.0328086	−	0.162696i
$735$		0			0
$736$	20.5695	+	17.6888i	0.758204	+	0.652018i
$737$	−23.4889			−0.865225
$738$		0			0
$739$		−	1.51685i		−	0.0557982i	−0.999611	−	0.0278991i	$-0.991118\pi$
$739$		−	1.51685i		−	0.0557982i	0.999611	−	0.0278991i	$-0.00888172\pi$
$740$	11.5949	−	4.87458i	0.426236	−	0.179193i
$741$		0			0
$742$	7.19752	−	1.45142i	0.264229	−	0.0532834i
$743$	−13.3402			−0.489406			−0.244703	−	0.969598i	$-0.578690\pi$
$743$	−13.3402			−0.489406			−0.244703	+	0.969598i	$0.578690\pi$
$744$		0			0
$745$	22.3037			0.817143
$746$	−24.6639	+	4.97362i	−0.903008	+	0.182097i
$747$		0			0
$748$	30.9439	+	73.6044i	1.13142	+	2.69124i
$749$	35.9303			1.31287
$750$		0			0
$751$	−2.46508			−0.0899519			−0.0449760	−	0.998988i	$-0.514321\pi$
$751$	−2.46508			−0.0899519			−0.0449760	+	0.998988i	$0.514321\pi$
$752$	−28.3973	−	27.8043i	−1.03554	−	1.01392i
$753$		0			0
$754$	3.75911	+	18.6412i	0.136899	+	0.678873i
$755$	28.3638			1.03226
$756$		0			0
$757$		−	4.61509i		−	0.167738i	−0.996477	−	0.0838692i	$-0.973272\pi$
$757$		−	4.61509i		−	0.167738i	0.996477	−	0.0838692i	$-0.0267278\pi$
$758$	−3.70231	−	18.3596i	−0.134474	−	0.666849i
$759$		0			0
$760$	−7.57962	+	5.15176i	−0.274942	+	0.186874i
$761$	35.9097			1.30172			0.650862	−	0.759196i	$-0.274408\pi$
$761$	35.9097			1.30172			0.650862	+	0.759196i	$0.274408\pi$
$762$		0			0
$763$			28.2490i			1.02268i
$764$	−0.221388	+	0.0930732i	−0.00800953	+	0.00336727i
$765$		0			0
$766$	2.71563	+	13.4667i	0.0981198	+	0.486570i
$767$			18.3485i			0.662527i
$768$		0			0
$769$		−	22.0207i		−	0.794087i	−0.917800	−	0.397044i	$-0.870036\pi$
$769$		−	22.0207i		−	0.794087i	0.917800	−	0.397044i	$-0.129964\pi$
$770$	−26.0906	+	5.26133i	−0.940241	+	0.189605i
$771$		0			0
$772$	11.0515	−	4.64613i	0.397751	−	0.167218i
$773$		−	26.2098i		−	0.942700i	−0.881946	−	0.471350i	$-0.843767\pi$
$773$		−	26.2098i		−	0.942700i	0.881946	−	0.471350i	$-0.156233\pi$
$774$		0			0
$775$			10.1992i			0.366367i
$776$	10.5794	−	7.19065i	0.379777	−	0.258129i
$777$		0			0
$778$	−38.2720	+	7.71778i	−1.37212	+	0.276696i
$779$	23.5366			0.843288
$780$		0			0
$781$			71.7405i			2.56708i
$782$	45.6278	−	2.95185i	1.63165	−	0.105558i
$783$		0			0
$784$	−2.22017	+	2.26753i	−0.0792919	+	0.0809830i
$785$	23.3416			0.833097
$786$		0			0
$787$	30.7607			1.09650			0.548250	−	0.836315i	$-0.315294\pi$
$787$	30.7607			1.09650			0.548250	+	0.836315i	$0.315294\pi$
$788$	−22.8954	+	9.62541i	−0.815615	+	0.342891i
$789$		0			0
$790$	−6.46239	+	1.30318i	−0.229922	+	0.0463650i
$791$			44.7614i			1.59153i
$792$		0			0
$793$			5.28885i			0.187813i
$794$	3.43403	+	17.0292i	0.121869	+	0.604343i
$795$		0			0
$796$	17.6354	−	7.41405i	0.625069	−	0.262784i
$797$		−	54.7924i		−	1.94085i	−0.241408	−	0.970424i	$-0.577609\pi$
$797$		−	54.7924i		−	1.94085i	0.241408	−	0.970424i	$-0.422391\pi$
$798$		0			0
$799$	−66.9816			−2.36964
$800$	16.0017	+	10.3894i	0.565745	+	0.367320i
$801$		0			0
$802$	−23.8048	+	4.80039i	−0.840578	+	0.169508i
$803$	−26.3542			−0.930020
$804$		0			0
$805$	−2.04207	+	15.1042i	−0.0719734	+	0.532355i
$806$	10.3416	−	2.08544i	0.364266	−	0.0734564i
$807$		0			0
$808$	−15.0211	−	22.1000i	−0.528440	−	0.777476i
$809$	−42.9727			−1.51084			−0.755421	−	0.655240i	$-0.772567\pi$
$809$	−42.9727			−1.51084			−0.755421	+	0.655240i	$0.772567\pi$
$810$		0			0
$811$			1.35261i			0.0474966i	0.999718	+	0.0237483i	$0.00756003\pi$
$811$			1.35261i			0.0474966i	−0.999718	+	0.0237483i	$0.992440\pi$
$812$	−25.0381	+	10.5262i	−0.878665	+	0.369398i
$813$		0			0
$814$	40.4719	−	8.16139i	1.41854	−	0.286057i
$815$	2.68598			0.0940857
$816$		0			0
$817$	25.6844			0.898583
$818$	6.93235	+	34.3771i	0.242384	+	1.20197i
$819$		0			0
$820$	9.16248	+	21.7943i	0.319968	+	0.761088i
$821$	8.46867			0.295559			0.147779	−	0.989020i	$-0.452787\pi$
$821$	8.46867			0.295559			0.147779	+	0.989020i	$0.452787\pi$
$822$		0			0
$823$		−	28.1188i		−	0.980160i	−0.871677	−	0.490080i	$-0.836967\pi$
$823$		−	28.1188i		−	0.980160i	0.871677	−	0.490080i	$-0.163033\pi$
$824$	−2.67588	−	3.93694i	−0.0932189	−	0.137150i
$825$		0			0
$826$	−25.6897	+	5.18047i	−0.893858	+	0.180252i
$827$	9.58345			0.333249			0.166625	−	0.986020i	$-0.446713\pi$
$827$	9.58345			0.333249			0.166625	+	0.986020i	$0.446713\pi$
$828$		0			0
$829$	−16.3484			−0.567803			−0.283902	−	0.958853i	$-0.591629\pi$
$829$	−16.3484			−0.567803			−0.283902	+	0.958853i	$0.591629\pi$
$830$	−5.37375	+	1.08365i	−0.186526	+	0.0376140i
$831$		0			0
$832$	7.26248	−	18.3493i	0.251781	−	0.636148i
$833$			5.34848i			0.185314i
$834$		0			0
$835$	−5.65155			−0.195580
$836$	−27.7318	+	11.6587i	−0.959124	+	0.403223i
$837$		0			0
$838$	4.01057	+	19.8882i	0.138543	+	0.687026i
$839$	46.3381			1.59977			0.799884	−	0.600155i	$-0.204894\pi$
$839$	46.3381			1.59977			0.799884	+	0.600155i	$0.204894\pi$
$840$		0			0
$841$	0.714489			0.0246376
$842$	−47.1644	+	9.51098i	−1.62539	+	0.327770i
$843$		0			0
$844$	1.97223	+	4.69123i	0.0678869	+	0.161479i
$845$			8.82129i			0.303461i
$846$		0			0
$847$	−59.9614			−2.06030
$848$	5.95628	+	5.83189i	0.204539	+	0.200268i
$849$		0			0
$850$	31.5202	−	6.35623i	1.08113	−	0.218017i
$851$	3.16766	−	23.4297i	0.108586	−	0.803161i
$852$		0			0
$853$	−22.0557			−0.755173			−0.377587	−	0.925974i	$-0.623246\pi$
$853$	−22.0557			−0.755173			−0.377587	+	0.925974i	$0.623246\pi$
$854$	−7.40488	+	1.49324i	−0.253390	+	0.0510976i
$855$		0			0
$856$	22.9307	+	33.7371i	0.783754	+	1.15311i
$857$	−44.6464			−1.52509			−0.762546	−	0.646935i	$-0.776051\pi$
$857$	−44.6464			−1.52509			−0.762546	+	0.646935i	$0.776051\pi$
$858$		0			0
$859$			28.3561i			0.967496i	0.875207	+	0.483748i	$0.160725\pi$
$859$			28.3561i			0.967496i	−0.875207	+	0.483748i	$0.839275\pi$
$860$	9.99857	+	23.7830i	0.340948	+	0.810994i
$861$		0			0
$862$	−6.76225	−	33.5336i	−0.230323	−	1.14216i
$863$		−	48.0292i		−	1.63493i	−0.575975	−	0.817467i	$-0.695377\pi$
$863$		−	48.0292i		−	1.63493i	0.575975	−	0.817467i	$-0.304623\pi$
$864$		0			0
$865$		−	6.75912i		−	0.229817i
$866$	36.5414	−	7.36879i	1.24173	−	0.250402i
$867$		0			0
$868$	5.83962	+	13.8904i	0.198209	+	0.471469i
$869$	−21.6397			−0.734075
$870$		0			0
$871$	9.78445			0.331534
$872$	−26.5247	+	18.0285i	−0.898239	+	0.610521i
$873$		0			0
$874$	1.11216	+	17.1911i	0.0376195	+	0.581498i
$875$			26.6092i			0.899554i
$876$		0			0
$877$	−36.8661			−1.24488			−0.622440	−	0.782668i	$-0.713858\pi$
$877$	−36.8661			−1.24488			−0.622440	+	0.782668i	$0.713858\pi$
$878$	−4.66042	+	0.939801i	−0.157281	+	0.0317167i
$879$		0			0
$880$	−21.5912	−	21.1403i	−0.727839	−	0.712639i
$881$		−	39.9739i		−	1.34675i	−0.739299	−	0.673377i	$-0.764843\pi$
$881$		−	39.9739i		−	1.34675i	0.739299	−	0.673377i	$-0.235157\pi$
$882$		0			0
$883$			27.9445i			0.940406i	0.882558	+	0.470203i	$0.155819\pi$
$883$			27.9445i			0.940406i	−0.882558	+	0.470203i	$0.844181\pi$
$884$	−12.8899	−	30.6604i	−0.433533	−	1.03122i
$885$		0			0
$886$	−33.6823	+	6.79223i	−1.13158	+	0.228190i
$887$			20.8547i			0.700233i	0.936706	+	0.350117i	$0.113858\pi$
$887$			20.8547i			0.700233i	−0.936706	+	0.350117i	$0.886142\pi$
$888$		0			0
$889$		−	1.38504i		−	0.0464526i
$890$	−2.07310	−	10.2804i	−0.0694905	−	0.344599i
$891$		0			0
$892$	−6.39819	−	15.2190i	−0.214227	−	0.509570i
$893$		−	25.2366i		−	0.844509i
$894$		0			0
$895$	−8.13594			−0.271955
$896$	27.7412	+	4.98746i	0.926769	+	0.166619i
$897$		0			0
$898$	0.831483	+	4.12327i	0.0277469	+	0.137595i
$899$		−	16.4847i		−	0.549794i
$900$		0			0
$901$	14.0492			0.468048
$902$	15.3405	+	76.0727i	0.510783	+	2.53294i
$903$		0			0
$904$	−42.0292	+	28.5667i	−1.39787	+	0.950114i
$905$	−26.5904			−0.883896
$906$		0			0
$907$	−12.8699			−0.427337			−0.213669	−	0.976906i	$-0.568541\pi$
$907$	−12.8699			−0.427337			−0.213669	+	0.976906i	$0.568541\pi$
$908$	−20.1045	+	8.45210i	−0.667192	+	0.280493i
$909$		0			0
$910$	10.8682	−	2.19164i	0.360278	−	0.0726522i
$911$	−12.5529			−0.415896			−0.207948	−	0.978140i	$-0.566678\pi$
$911$	−12.5529			−0.415896			−0.207948	+	0.978140i	$0.566678\pi$
$912$		0			0
$913$	−17.9943			−0.595524
$914$	−42.9509	+	8.66131i	−1.42069	+	0.286491i
$915$		0			0
$916$	11.0992	+	26.4009i	0.366727	+	0.872311i
$917$			1.47948i			0.0488567i
$918$		0			0
$919$	25.9215			0.855070			0.427535	−	0.903999i	$-0.359382\pi$
$919$	25.9215			0.855070			0.427535	+	0.903999i	$0.359382\pi$
$920$	−15.4855	+	7.72208i	−0.510543	+	0.254590i
$921$		0			0
$922$	−11.9048	−	59.0352i	−0.392064	−	1.94422i
$923$		−	29.8840i		−	0.983643i
$924$		0			0
$925$		−	16.6268i		−	0.546685i
$926$	39.1204	−	7.88887i	1.28558	−	0.259244i
$927$		0			0
$928$	−25.8630	−	16.7920i	−0.848994	−	0.551223i
$929$	40.8765			1.34111			0.670557	−	0.741858i	$-0.266055\pi$
$929$	40.8765			1.34111			0.670557	+	0.741858i	$0.266055\pi$
$930$		0			0
$931$	−2.01514			−0.0660435
$932$	19.4640	−	8.18281i	0.637564	−	0.268037i
$933$		0			0
$934$	4.73111	+	23.4613i	0.154807	+	0.767676i
$935$	−50.9278			−1.66552
$936$		0			0
$937$			14.6250i			0.477778i	0.971047	+	0.238889i	$0.0767832\pi$
$937$			14.6250i			0.477778i	−0.971047	+	0.238889i	$0.923217\pi$
$938$	2.76252	+	13.6992i	0.0901993	+	0.447293i
$939$		0			0
$940$	23.3683	−	9.82423i	0.762191	−	0.320431i
$941$		−	6.12552i		−	0.199686i	−0.995003	−	0.0998431i	$-0.968166\pi$
$941$		−	6.12552i		−	0.199686i	0.995003	−	0.0998431i	$-0.0318341\pi$
$942$		0			0
$943$	44.0396	+	5.95407i	1.43413	+	0.193891i
$944$	−21.2594	−	20.8154i	−0.691933	−	0.677484i
$945$		0			0
$946$	16.7404	+	83.0145i	0.544276	+	2.69903i
$947$		−	6.15274i		−	0.199937i	−0.994991	−	0.0999686i	$-0.968126\pi$
$947$		−	6.15274i		−	0.199937i	0.994991	−	0.0999686i	$-0.0318742\pi$
$948$		0			0
$949$	10.9780			0.356361
$950$	2.39483	+	11.8758i	0.0776984	+	0.385302i
$951$		0			0
$952$	39.2881	−	26.7036i	1.27333	−	0.865468i
$953$			10.5440i			0.341552i	0.985310	+	0.170776i	$0.0546275\pi$
$953$			10.5440i			0.341552i	−0.985310	+	0.170776i	$0.945373\pi$
$954$		0			0
$955$		−	0.153181i		−	0.00495682i
$956$	−3.75450	−	8.93061i	−0.121429	−	0.288837i
$957$		0			0
$958$	−7.20253	−	35.7169i	−0.232703	−	1.15396i
$959$			30.3344i			0.979549i
$960$		0			0
$961$	21.8548			0.704994
$962$	−16.8588	+	3.39968i	−0.543550	+	0.109610i
$963$		0			0
$964$	−17.0692	−	40.6015i	−0.549761	−	1.30769i
$965$			7.64665i			0.246154i
$966$		0			0
$967$		−	13.7270i		−	0.441430i	−0.975338	−	0.220715i	$-0.929161\pi$
$967$		−	13.7270i		−	0.441430i	0.975338	−	0.220715i	$-0.0708391\pi$
$968$	−38.2673	−	56.3014i	−1.22996	−	1.80960i
$969$		0			0
$970$	1.61286	+	7.99805i	0.0517857	+	0.256802i
$971$	4.43428			0.142303			0.0711514	−	0.997466i	$-0.477333\pi$
$971$	4.43428			0.142303			0.0711514	+	0.997466i	$0.477333\pi$
$972$		0			0
$973$		−	31.3475i		−	1.00495i
$974$	−29.5178	+	5.95244i	−0.945811	+	0.190728i
$975$		0			0
$976$	−6.12787	−	5.99991i	−0.196148	−	0.192052i
$977$			7.21336i			0.230776i	0.993321	+	0.115388i	$0.0368111\pi$
$977$			7.21336i			0.230776i	−0.993321	+	0.115388i	$0.963189\pi$
$978$		0			0
$979$		−	34.4244i		−	1.10021i
$980$	−0.784464	−	1.86596i	−0.0250588	−	0.0596059i
$981$		0			0
$982$	10.4576	−	2.10884i	0.333716	−	0.0672959i
$983$	51.7339			1.65006			0.825028	−	0.565092i	$-0.191159\pi$
$983$	51.7339			1.65006			0.825028	+	0.565092i	$0.191159\pi$
$984$		0			0
$985$		−	15.8416i		−	0.504756i
$986$	−50.9450	+	10.2734i	−1.62242	+	0.327170i
$987$		0			0
$988$	11.5519	−	4.85649i	0.367514	−	0.154506i
$989$	48.0583	+	6.49739i	1.52816	+	0.206605i
$990$		0			0
$991$			5.11827i			0.162587i	0.996690	+	0.0812936i	$0.0259051\pi$
$991$			5.11827i			0.162587i	−0.996690	+	0.0812936i	$0.974095\pi$
$992$	−9.31566	+	14.3480i	−0.295772	+	0.455548i
$993$		0			0
$994$	41.8403	−	8.43735i	1.32709	−	0.267617i
$995$			12.2021i			0.386833i
$996$		0			0
$997$	30.9514			0.980242			0.490121	−	0.871654i	$-0.336953\pi$
$997$	30.9514			0.980242			0.490121	+	0.871654i	$0.336953\pi$
$998$	25.6404	−	5.17053i	0.811632	−	0.163670i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.e.f.91.15		24
3.2	odd	2		276.2.e.a.91.10	yes	24
4.3	odd	2	inner	828.2.e.f.91.13		24
12.11	even	2		276.2.e.a.91.12	yes	24
23.22	odd	2	inner	828.2.e.f.91.16		24
24.5	odd	2		4416.2.i.d.1471.9		24
24.11	even	2		4416.2.i.d.1471.12		24
69.68	even	2		276.2.e.a.91.9	✓	24
92.91	even	2	inner	828.2.e.f.91.14		24
276.275	odd	2		276.2.e.a.91.11	yes	24
552.275	odd	2		4416.2.i.d.1471.11		24
552.413	even	2		4416.2.i.d.1471.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.e.a.91.9	✓	24	69.68	even	2
276.2.e.a.91.10	yes	24	3.2	odd	2
276.2.e.a.91.11	yes	24	276.275	odd	2
276.2.e.a.91.12	yes	24	12.11	even	2
828.2.e.f.91.13		24	4.3	odd	2	inner
828.2.e.f.91.14		24	92.91	even	2	inner
828.2.e.f.91.15		24	1.1	even	1	trivial
828.2.e.f.91.16		24	23.22	odd	2	inner
4416.2.i.d.1471.9		24	24.5	odd	2
4416.2.i.d.1471.10		24	552.413	even	2
4416.2.i.d.1471.11		24	552.275	odd	2
4416.2.i.d.1471.12		24	24.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.279557 + 1.38631i) q^{2} +(-1.84370 + 0.775104i) q^{4} -1.27568i q^{5} -2.49131 q^{7} +(-1.58995 - 2.33924i) q^{8} +(1.76848 - 0.356624i) q^{10} +5.92184 q^{11} -2.46678 q^{13} +(-0.696464 - 3.45372i) q^{14} +(2.79843 - 2.85811i) q^{16} -6.74152i q^{17} +2.53999 q^{19} +(0.988782 + 2.35196i) q^{20} +(1.65549 + 8.20949i) q^{22} +(4.75259 + 0.642542i) q^{23} +3.37265 q^{25} +(-0.689606 - 3.41972i) q^{26} +(4.59322 - 1.93103i) q^{28} -5.45110 q^{29} +3.02410i q^{31} +(4.74454 + 3.08047i) q^{32} +(9.34581 - 1.88464i) q^{34} +3.17811i q^{35} -4.92988i q^{37} +(0.710072 + 3.52121i) q^{38} +(-2.98411 + 2.02826i) q^{40} +9.26643 q^{41} +10.1120 q^{43} +(-10.9181 + 4.59004i) q^{44} +(0.437861 + 6.76818i) q^{46} -9.93569i q^{47} -0.793365 q^{49} +(0.942849 + 4.67553i) q^{50} +(4.54799 - 1.91201i) q^{52} +2.08399i q^{53} -7.55435i q^{55} +(3.96106 + 5.82778i) q^{56} +(-1.52389 - 7.55690i) q^{58} -7.43825i q^{59} -2.14403i q^{61} +(-4.19233 + 0.845409i) q^{62} +(-2.94411 + 7.43856i) q^{64} +3.14681i q^{65} -3.96649 q^{67} +(5.22538 + 12.4293i) q^{68} +(-4.40583 + 0.888462i) q^{70} +12.1146i q^{71} -4.45034 q^{73} +(6.83433 - 1.37818i) q^{74} +(-4.68297 + 1.96876i) q^{76} -14.7532 q^{77} -3.65421 q^{79} +(-3.64602 - 3.56988i) q^{80} +(2.59050 + 12.8461i) q^{82} -3.03863 q^{83} -8.59999 q^{85} +(2.82688 + 14.0184i) q^{86} +(-9.41544 - 13.8526i) q^{88} -5.81313i q^{89} +6.14552 q^{91} +(-9.26037 + 2.49910i) q^{92} +(13.7739 - 2.77759i) q^{94} -3.24020i q^{95} +4.52256i q^{97} +(-0.221791 - 1.09985i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 4 q^{8} + 8 q^{16} - 24 q^{25} - 40 q^{26} + 32 q^{29} + 36 q^{32} - 16 q^{41} + 40 q^{49} + 12 q^{50} - 40 q^{52} + 24 q^{58} + 40 q^{62} + 48 q^{64} + 72 q^{70} - 16 q^{77} - 40 q^{82}+ \cdots + 52 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 - 4 * q^8 + 8 * q^16 - 24 * q^25 - 40 * q^26 + 32 * q^29 + 36 * q^32 - 16 * q^41 + 40 * q^49 + 12 * q^50 - 40 * q^52 + 24 * q^58 + 40 * q^62 + 48 * q^64 + 72 * q^70 - 16 * q^77 - 40 * q^82 - 64 * q^85 - 44 * q^92 + 72 * q^94 + 52 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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