LMFDB - Embedded newform 468.2.j.a.133.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(133,468)] 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("468.133"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.11
Character	$\chi$	$=$	468.133
Dual form			468.2.j.a.373.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12041 + 1.32087i) q^{3} +(-1.31191 - 2.27229i) q^{5} +(-1.79663 - 3.11185i) q^{7} +(-0.489378 + 2.95982i) q^{9} +4.75537 q^{11} +(3.16282 - 1.73106i) q^{13} +(1.53152 - 4.27875i) q^{15} +(0.733833 - 1.27104i) q^{17} +(2.78567 - 4.82492i) q^{19} +(2.09739 - 5.85965i) q^{21} +(-1.70649 + 2.95573i) q^{23} +(-0.942208 + 1.63195i) q^{25} +(-4.45782 + 2.66979i) q^{27} +3.83704 q^{29} +(-4.73573 - 8.20253i) q^{31} +(5.32794 + 6.28121i) q^{33} +(-4.71403 + 8.16494i) q^{35} +(2.14495 + 3.71516i) q^{37} +(5.83014 + 2.23818i) q^{39} +(-3.67488 + 6.36507i) q^{41} +(1.28146 + 2.21955i) q^{43} +(7.36759 - 2.77100i) q^{45} +(-3.88207 + 6.72393i) q^{47} +(-2.95576 + 5.11952i) q^{49} +(2.50106 - 0.454782i) q^{51} +1.77064 q^{53} +(-6.23861 - 10.8056i) q^{55} +(9.49415 - 1.72637i) q^{57} -8.79316 q^{59} +(-3.18608 - 5.51845i) q^{61} +(10.0897 - 3.79482i) q^{63} +(-8.08280 - 4.91587i) q^{65} +(-2.12325 + 3.67758i) q^{67} +(-5.81609 + 1.05757i) q^{69} +(4.76526 - 8.25367i) q^{71} +11.1926 q^{73} +(-3.21125 + 0.583919i) q^{75} +(-8.54363 - 14.7980i) q^{77} +(-5.06674 + 8.77586i) q^{79} +(-8.52102 - 2.89694i) q^{81} +(-4.51894 + 7.82703i) q^{83} -3.85089 q^{85} +(4.29905 + 5.06822i) q^{87} +(6.36777 + 11.0293i) q^{89} +(-11.0692 - 6.73218i) q^{91} +(5.52850 - 15.4454i) q^{93} -14.6182 q^{95} +(-6.04292 - 10.4666i) q^{97} +(-2.32717 + 14.0750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{7} - 2 q^{9} + 8 q^{11} + q^{13} - 10 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} - 4 q^{23} - 14 q^{25} + 26 q^{29} + 2 q^{31} + 8 q^{33} + 3 q^{35} - q^{37} - 12 q^{39} + 4 q^{41} + 2 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) $ 28 * q + 2 * q^7 - 2 * q^9 + 8 * q^11 + q^13 - 10 * q^15 - 8 * q^17 - q^19 + 14 * q^21 - 4 * q^23 - 14 * q^25 + 26 * q^29 + 2 * q^31 + 8 * q^33 + 3 * q^35 - q^37 - 12 * q^39 + 4 * q^41 + 2 * q^43 + q^45 + 11 * q^47 - 12 * q^49 + 5 * q^51 + 52 * q^53 - q^57 + 16 * q^59 - 7 * q^61 - 24 * q^63 - 31 * q^65 - 7 * q^67 + 24 * q^69 - 12 * q^71 + 14 * q^73 + 16 * q^75 - 28 * q^77 + 5 * q^79 - 50 * q^81 + 9 * q^83 - 36 * q^85 - 21 * q^87 - 11 * q^89 - q^91 - 33 * q^93 - 56 * q^95 - 25 * q^97 - 29 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.12041	+	1.32087i	0.646867	+	0.762603i
$3$	1.12041	+	1.32087i	0.646867	+	0.762603i
$4$		0			0
$5$	−1.31191	−	2.27229i	−0.586703	−	1.01620i	−0.994661	−	0.103199i	$-0.967092\pi$
$5$	−1.31191	−	2.27229i	−0.586703	−	1.01620i	0.407957	−	0.913001i	$-0.366241\pi$
$6$		0			0
$7$	−1.79663	−	3.11185i	−0.679062	−	1.17617i	−0.975264	−	0.221045i	$-0.929053\pi$
$7$	−1.79663	−	3.11185i	−0.679062	−	1.17617i	0.296201	−	0.955126i	$-0.404280\pi$
$8$		0			0
$9$	−0.489378	+	2.95982i	−0.163126	+	0.986605i
$10$		0			0
$11$	4.75537			1.43380			0.716898	−	0.697178i	$-0.245561\pi$
$11$	4.75537			1.43380			0.716898	+	0.697178i	$0.245561\pi$
$12$		0			0
$13$	3.16282	−	1.73106i	0.877209	−	0.480108i
$13$	3.16282	−	1.73106i	0.877209	−	0.480108i
$14$		0			0
$15$	1.53152	−	4.27875i	0.395438	−	1.10477i
$16$		0			0
$17$	0.733833	−	1.27104i	0.177981	−	0.308272i	−0.763208	−	0.646153i	$-0.776377\pi$
$17$	0.733833	−	1.27104i	0.177981	−	0.308272i	0.941189	+	0.337881i	$0.109710\pi$
$18$		0			0
$19$	2.78567	−	4.82492i	0.639076	−	1.10691i	−0.346560	−	0.938028i	$-0.612650\pi$
$19$	2.78567	−	4.82492i	0.639076	−	1.10691i	0.985636	−	0.168884i	$-0.0540164\pi$
$20$		0			0
$21$	2.09739	−	5.85965i	0.457688	−	1.27868i
$22$		0			0
$23$	−1.70649	+	2.95573i	−0.355828	+	0.616312i	−0.987259	−	0.159120i	$-0.949134\pi$
$23$	−1.70649	+	2.95573i	−0.355828	+	0.616312i	0.631431	+	0.775432i	$0.282468\pi$
$24$		0			0
$25$	−0.942208	+	1.63195i	−0.188442	+	0.326390i
$26$		0			0
$27$	−4.45782	+	2.66979i	−0.857909	+	0.513802i
$28$		0			0
$29$	3.83704			0.712521			0.356260	−	0.934387i	$-0.384052\pi$
$29$	3.83704			0.712521			0.356260	+	0.934387i	$0.384052\pi$
$30$		0			0
$31$	−4.73573	−	8.20253i	−0.850563	−	1.47322i	−0.880701	−	0.473672i	$-0.842928\pi$
$31$	−4.73573	−	8.20253i	−0.850563	−	1.47322i	0.0301382	−	0.999546i	$-0.490405\pi$
$32$		0			0
$33$	5.32794	+	6.28121i	0.927476	+	1.09342i
$34$		0			0
$35$	−4.71403	+	8.16494i	−0.796816	+	1.38013i
$36$		0			0
$37$	2.14495	+	3.71516i	0.352628	+	0.610769i	0.986709	−	0.162497i	$-0.0519548\pi$
$37$	2.14495	+	3.71516i	0.352628	+	0.610769i	−0.634081	+	0.773266i	$0.718621\pi$
$38$		0			0
$39$	5.83014	+	2.23818i	0.933570	+	0.358396i
$40$		0			0
$41$	−3.67488	+	6.36507i	−0.573919	+	0.994057i	0.422239	+	0.906485i	$0.361244\pi$
$41$	−3.67488	+	6.36507i	−0.573919	+	0.994057i	−0.996158	+	0.0875727i	$0.972089\pi$
$42$		0			0
$43$	1.28146	+	2.21955i	0.195421	+	0.338479i	0.947038	−	0.321120i	$-0.104059\pi$
$43$	1.28146	+	2.21955i	0.195421	+	0.338479i	−0.751618	+	0.659599i	$0.770726\pi$
$44$		0			0
$45$	7.36759	−	2.77100i	1.09829	−	0.413076i
$46$		0			0
$47$	−3.88207	+	6.72393i	−0.566257	+	0.980787i	0.430674	+	0.902508i	$0.358276\pi$
$47$	−3.88207	+	6.72393i	−0.566257	+	0.980787i	−0.996931	+	0.0782791i	$0.975057\pi$
$48$		0			0
$49$	−2.95576	+	5.11952i	−0.422251	+	0.731361i
$50$		0			0
$51$	2.50106	−	0.454782i	0.350219	−	0.0636822i
$52$		0			0
$53$	1.77064			0.243216			0.121608	−	0.992578i	$-0.461195\pi$
$53$	1.77064			0.243216			0.121608	+	0.992578i	$0.461195\pi$
$54$		0			0
$55$	−6.23861	−	10.8056i	−0.841213	−	1.45702i
$56$		0			0
$57$	9.49415	−	1.72637i	1.25753	−	0.228664i
$58$		0			0
$59$	−8.79316			−1.14477			−0.572386	−	0.819984i	$-0.693982\pi$
$59$	−8.79316			−1.14477			−0.572386	+	0.819984i	$0.693982\pi$
$60$		0			0
$61$	−3.18608	−	5.51845i	−0.407936	−	0.706566i	0.586722	−	0.809788i	$-0.300418\pi$
$61$	−3.18608	−	5.51845i	−0.407936	−	0.706566i	−0.994658	+	0.103222i	$0.967085\pi$
$62$		0			0
$63$	10.0897	−	3.79482i	1.27119	−	0.478103i
$64$		0			0
$65$	−8.08280	−	4.91587i	−1.00255	−	0.609739i
$66$		0			0
$67$	−2.12325	+	3.67758i	−0.259396	+	0.449287i	−0.966080	−	0.258242i	$-0.916857\pi$
$67$	−2.12325	+	3.67758i	−0.259396	+	0.449287i	0.706684	+	0.707529i	$0.250190\pi$
$68$		0			0
$69$	−5.81609	+	1.05757i	−0.700175	+	0.127317i
$70$		0			0
$71$	4.76526	−	8.25367i	0.565532	−	0.979531i	−0.431468	−	0.902128i	$-0.642004\pi$
$71$	4.76526	−	8.25367i	0.565532	−	0.979531i	0.997000	−	0.0774024i	$-0.0246626\pi$
$72$		0			0
$73$	11.1926			1.31000			0.654999	−	0.755630i	$-0.272669\pi$
$73$	11.1926			1.31000			0.654999	+	0.755630i	$0.272669\pi$
$74$		0			0
$75$	−3.21125	+	0.583919i	−0.370803	+	0.0674251i
$76$		0			0
$77$	−8.54363	−	14.7980i	−0.973638	−	1.68639i
$78$		0			0
$79$	−5.06674	+	8.77586i	−0.570053	+	0.987361i	0.426507	+	0.904484i	$0.359744\pi$
$79$	−5.06674	+	8.77586i	−0.570053	+	0.987361i	−0.996560	+	0.0828765i	$0.973589\pi$
$80$		0			0
$81$	−8.52102	−	2.89694i	−0.946780	−	0.321882i
$82$		0			0
$83$	−4.51894	+	7.82703i	−0.496018	+	0.859129i	−0.999989	−	0.00459172i	$-0.998538\pi$
$83$	−4.51894	+	7.82703i	−0.496018	+	0.859129i	0.503971	+	0.863720i	$0.331872\pi$
$84$		0			0
$85$	−3.85089			−0.417687
$86$		0			0
$87$	4.29905	+	5.06822i	0.460906	+	0.543370i
$88$		0			0
$89$	6.36777	+	11.0293i	0.674983	+	1.16910i	0.976474	+	0.215635i	$0.0691822\pi$
$89$	6.36777	+	11.0293i	0.674983	+	1.16910i	−0.301491	+	0.953469i	$0.597484\pi$
$90$		0			0
$91$	−11.0692	−	6.73218i	−1.16037	−	0.705724i
$92$		0			0
$93$	5.52850	−	15.4454i	0.573279	−	1.60162i
$94$		0			0
$95$	−14.6182			−1.49979
$96$		0			0
$97$	−6.04292	−	10.4666i	−0.613565	−	1.06273i	−0.990634	−	0.136541i	$-0.956401\pi$
$97$	−6.04292	−	10.4666i	−0.613565	−	1.06273i	0.377069	−	0.926185i	$-0.376932\pi$
$98$		0			0
$99$	−2.32717	+	14.0750i	−0.233890	+	1.41459i
$100$		0			0
$101$	−4.35115			−0.432956			−0.216478	−	0.976288i	$-0.569457\pi$
$101$	−4.35115			−0.432956			−0.216478	+	0.976288i	$0.569457\pi$
$102$		0			0
$103$	4.23722	+	7.33908i	0.417505	+	0.723141i	0.995688	−	0.0927669i	$-0.0295711\pi$
$103$	4.23722	+	7.33908i	0.417505	+	0.723141i	−0.578182	+	0.815908i	$0.696238\pi$
$104$		0			0
$105$	−16.0664	+	2.92145i	−1.56792	+	0.285104i
$106$		0			0
$107$	8.89600	+	15.4083i	0.860009	+	1.48958i	0.871919	+	0.489649i	$0.162875\pi$
$107$	8.89600	+	15.4083i	0.860009	+	1.48958i	−0.0119108	+	0.999929i	$0.503791\pi$
$108$		0			0
$109$	18.5220			1.77409			0.887043	−	0.461686i	$-0.152755\pi$
$109$	18.5220			1.77409			0.887043	+	0.461686i	$0.152755\pi$
$110$		0			0
$111$	−2.50402	+	6.99569i	−0.237671	+	0.664002i
$112$		0			0
$113$	13.0488			1.22753			0.613764	−	0.789490i	$-0.289655\pi$
$113$	13.0488			1.22753			0.613764	+	0.789490i	$0.289655\pi$
$114$		0			0
$115$	8.95504			0.835062
$116$		0			0
$117$	3.57579	+	10.2085i	0.330582	+	0.943777i
$118$		0			0
$119$	−5.27371			−0.483440
$120$		0			0
$121$	11.6135			1.05577
$122$		0			0
$123$	−12.5248	+	2.27745i	−1.12932	+	0.205351i
$124$		0			0
$125$	−8.17472			−0.731169
$126$		0			0
$127$	−3.10087	−	5.37087i	−0.275158	−	0.476588i	0.695017	−	0.718993i	$-0.255397\pi$
$127$	−3.10087	−	5.37087i	−0.275158	−	0.476588i	−0.970175	+	0.242406i	$0.922063\pi$
$128$		0			0
$129$	−1.49598	+	4.17944i	−0.131713	+	0.367979i
$130$		0			0
$131$	−2.10548	−	3.64680i	−0.183957	−	0.318623i	0.759268	−	0.650779i	$-0.225557\pi$
$131$	−2.10548	−	3.64680i	−0.183957	−	0.318623i	−0.943225	+	0.332156i	$0.892224\pi$
$132$		0			0
$133$	−20.0193			−1.73589
$134$		0			0
$135$	11.9148	+	6.62695i	1.02546	+	0.570357i
$136$		0			0
$137$	0.582932	+	1.00967i	0.0498032	+	0.0862617i	0.889852	−	0.456249i	$-0.150807\pi$
$137$	0.582932	+	1.00967i	0.0498032	+	0.0862617i	−0.840049	+	0.542510i	$0.817474\pi$
$138$		0			0
$139$	−7.48846			−0.635163			−0.317582	−	0.948231i	$-0.602871\pi$
$139$	−7.48846			−0.635163			−0.317582	+	0.948231i	$0.602871\pi$
$140$		0			0
$141$	−13.2309	+	2.40585i	−1.11424	+	0.202609i
$142$		0			0
$143$	15.0404	−	8.23180i	1.25774	−	0.688378i
$144$		0			0
$145$	−5.03385	−	8.71888i	−0.418038	−	0.724063i
$146$		0			0
$147$	−10.0739	+	1.83179i	−0.830878	+	0.151083i
$148$		0			0
$149$	4.14377			0.339470			0.169735	−	0.985490i	$-0.445709\pi$
$149$	4.14377			0.339470			0.169735	+	0.985490i	$0.445709\pi$
$150$		0			0
$151$	−0.375131	+	0.649747i	−0.0305278	+	0.0528756i	−0.880886	−	0.473329i	$-0.843052\pi$
$151$	−0.375131	+	0.649747i	−0.0305278	+	0.0528756i	0.850358	+	0.526205i	$0.176385\pi$
$152$		0			0
$153$	3.40291	+	2.79403i	0.275109	+	0.225884i
$154$		0			0
$155$	−12.4257	+	21.5219i	−0.998056	+	1.72868i
$156$		0			0
$157$	0.905461	+	1.56830i	0.0722637	+	0.125164i	0.899893	−	0.436111i	$-0.143644\pi$
$157$	0.905461	+	1.56830i	0.0722637	+	0.125164i	−0.827629	+	0.561275i	$0.810311\pi$
$158$		0			0
$159$	1.98384	+	2.33878i	0.157328	+	0.185477i
$160$		0			0
$161$	12.2637			0.966517
$162$		0			0
$163$	−11.8289	+	20.4883i	−0.926513	+	1.60477i	−0.137402	+	0.990515i	$0.543875\pi$
$163$	−11.8289	+	20.4883i	−0.926513	+	1.60477i	−0.789110	+	0.614252i	$0.789458\pi$
$164$		0			0
$165$	7.28296	−	20.3470i	0.566978	−	1.58401i
$166$		0			0
$167$	−1.43127	+	2.47903i	−0.110755	+	0.191833i	−0.916075	−	0.401007i	$-0.868660\pi$
$167$	−1.43127	+	2.47903i	−0.110755	+	0.191833i	0.805320	+	0.592840i	$0.201993\pi$
$168$		0			0
$169$	7.00689	−	10.9500i	0.538992	−	0.842311i
$170$		0			0
$171$	12.9176	+	10.6063i	0.987835	+	0.811082i
$172$		0			0
$173$	11.0272	+	19.0997i	0.838384	+	1.45212i	0.891246	+	0.453521i	$0.149832\pi$
$173$	11.0272	+	19.0997i	0.838384	+	1.45212i	−0.0528621	+	0.998602i	$0.516834\pi$
$174$		0			0
$175$	6.77120			0.511854
$176$		0			0
$177$	−9.85191	−	11.6146i	−0.740515	−	0.873006i
$178$		0			0
$179$	−12.9994	−	22.5157i	−0.971624	−	1.68290i	−0.690655	−	0.723184i	$-0.742678\pi$
$179$	−12.9994	−	22.5157i	−0.971624	−	1.68290i	−0.280968	−	0.959717i	$-0.590656\pi$
$180$		0			0
$181$	−15.0145			−1.11602			−0.558009	−	0.829835i	$-0.688435\pi$
$181$	−15.0145			−1.11602			−0.558009	+	0.829835i	$0.688435\pi$
$182$		0			0
$183$	3.71944	−	10.3913i	0.274949	−	0.768147i
$184$		0			0
$185$	5.62796	−	9.74791i	0.413776	−	0.716681i
$186$		0			0
$187$	3.48965	−	6.04424i	0.255188	−	0.441999i
$188$		0			0
$189$	16.3171	+	9.07547i	1.18689	+	0.660143i
$190$		0			0
$191$	12.2527	+	21.2223i	0.886574	+	1.53559i	0.843899	+	0.536502i	$0.180255\pi$
$191$	12.2527	+	21.2223i	0.886574	+	1.53559i	0.0426749	+	0.999089i	$0.486412\pi$
$192$		0			0
$193$	−6.06911	+	10.5120i	−0.436864	+	0.756671i	−0.997446	−	0.0714280i	$-0.977244\pi$
$193$	−6.06911	+	10.5120i	−0.436864	+	0.756671i	0.560581	+	0.828099i	$0.310578\pi$
$194$		0			0
$195$	−2.56281	−	16.1841i	−0.183527	−	1.15897i
$196$		0			0
$197$	−0.295155	−	0.511223i	−0.0210289	−	0.0364231i	0.855319	−	0.518101i	$-0.173361\pi$
$197$	−0.295155	−	0.511223i	−0.0210289	−	0.0364231i	−0.876348	+	0.481678i	$0.840028\pi$
$198$		0			0
$199$	2.11664	−	3.66613i	0.150045	−	0.259885i	−0.781199	−	0.624282i	$-0.785392\pi$
$199$	2.11664	−	3.66613i	0.150045	−	0.259885i	0.931244	+	0.364397i	$0.118725\pi$
$200$		0			0
$201$	−7.23649	+	1.31585i	−0.510423	+	0.0928130i
$202$		0			0
$203$	−6.89374	−	11.9403i	−0.483846	−	0.838046i
$204$		0			0
$205$	19.2844			1.34688
$206$		0			0
$207$	−7.91329	−	6.49737i	−0.550012	−	0.451598i
$208$		0			0
$209$	13.2469	−	22.9443i	0.916305	−	1.58709i
$210$		0			0
$211$	11.9634	−	20.7213i	0.823598	−	1.42651i	−0.0793884	−	0.996844i	$-0.525297\pi$
$211$	11.9634	−	20.7213i	0.823598	−	1.42651i	0.902986	−	0.429669i	$-0.141370\pi$
$212$		0			0
$213$	16.2410	−	2.95320i	1.11282	−	0.202350i
$214$		0			0
$215$	3.36231	−	5.82370i	0.229308	−	0.397173i
$216$		0			0
$217$	−17.0167	+	29.4738i	−1.15517	+	2.00081i
$218$		0			0
$219$	12.5403	+	14.7840i	0.847394	+	0.999008i
$220$		0			0
$221$	0.120750	−	5.29037i	0.00812251	−	0.355869i
$222$		0			0
$223$	−1.09289			−0.0731856			−0.0365928	−	0.999330i	$-0.511650\pi$
$223$	−1.09289			−0.0731856			−0.0365928	+	0.999330i	$0.511650\pi$
$224$		0			0
$225$	−4.36918	−	3.58740i	−0.291279	−	0.239160i
$226$		0			0
$227$	−12.7383	−	22.0635i	−0.845473	−	1.46440i	−0.885210	−	0.465193i	$-0.845985\pi$
$227$	−12.7383	−	22.0635i	−0.845473	−	1.46440i	0.0397362	−	0.999210i	$-0.487348\pi$
$228$		0			0
$229$	6.27227	+	10.8639i	0.414483	+	0.717906i	0.995374	−	0.0960758i	$-0.0306291\pi$
$229$	6.27227	+	10.8639i	0.414483	+	0.717906i	−0.580891	+	0.813981i	$0.697296\pi$
$230$		0			0
$231$	9.97385	−	27.8648i	0.656231	−	1.83337i
$232$		0			0
$233$	11.3418			0.743024			0.371512	−	0.928428i	$-0.378839\pi$
$233$	11.3418			0.743024			0.371512	+	0.928428i	$0.378839\pi$
$234$		0			0
$235$	20.3717			1.32890
$236$		0			0
$237$	−17.2685	+	3.14004i	−1.12171	+	0.203967i
$238$		0			0
$239$	0.387292	+	0.670809i	0.0250518	+	0.0433910i	0.878280	−	0.478148i	$-0.158692\pi$
$239$	0.387292	+	0.670809i	0.0250518	+	0.0433910i	−0.853228	+	0.521539i	$0.825358\pi$
$240$		0			0
$241$	4.38293	+	7.59146i	0.282329	+	0.489009i	0.971958	−	0.235154i	$-0.0755595\pi$
$241$	4.38293	+	7.59146i	0.282329	+	0.489009i	−0.689629	+	0.724163i	$0.742226\pi$
$242$		0			0
$243$	−5.72054	−	14.5009i	−0.366973	−	0.930232i
$244$		0			0
$245$	15.5107			0.990945
$246$		0			0
$247$	0.458373	−	20.0825i	0.0291655	−	1.27782i
$248$		0			0
$249$	−15.4015	+	2.80054i	−0.976032	+	0.177477i
$250$		0			0
$251$	9.59084	−	16.6118i	0.605368	−	1.04853i	−0.386625	−	0.922237i	$-0.626359\pi$
$251$	9.59084	−	16.6118i	0.605368	−	1.04853i	0.991993	−	0.126292i	$-0.0403075\pi$
$252$		0			0
$253$	−8.11499	+	14.0556i	−0.510185	+	0.883666i
$254$		0			0
$255$	−4.31456	−	5.08651i	−0.270188	−	0.318530i
$256$		0			0
$257$	6.51412	−	11.2828i	0.406340	−	0.703801i	−0.588137	−	0.808762i	$-0.700138\pi$
$257$	6.51412	−	11.2828i	0.406340	−	0.703801i	0.994476	+	0.104961i	$0.0334716\pi$
$258$		0			0
$259$	7.70737	−	13.3496i	0.478913	−	0.829501i
$260$		0			0
$261$	−1.87776	+	11.3569i	−0.116231	+	0.702977i
$262$		0			0
$263$	−17.8655			−1.10163			−0.550817	−	0.834626i	$-0.685684\pi$
$263$	−17.8655			−1.10163			−0.550817	+	0.834626i	$0.685684\pi$
$264$		0			0
$265$	−2.32292	−	4.02341i	−0.142696	−	0.247156i
$266$		0			0
$267$	−7.43375	+	20.7683i	−0.454938	+	1.27100i
$268$		0			0
$269$	−0.348659	+	0.603895i	−0.0212581	+	0.0368201i	−0.876459	−	0.481477i	$-0.840101\pi$
$269$	−0.348659	+	0.603895i	−0.0212581	+	0.0368201i	0.855201	+	0.518297i	$0.173434\pi$
$270$		0			0
$271$	2.09858	+	3.63485i	0.127480	+	0.220801i	0.922700	−	0.385520i	$-0.125978\pi$
$271$	2.09858	+	3.63485i	0.127480	+	0.220801i	−0.795220	+	0.606321i	$0.792645\pi$
$272$		0			0
$273$	−3.50971	−	22.1637i	−0.212417	−	1.34141i
$274$		0			0
$275$	−4.48055	+	7.76053i	−0.270187	+	0.467978i
$276$		0			0
$277$	12.8475	+	22.2526i	0.771934	+	1.33703i	0.936502	+	0.350663i	$0.114044\pi$
$277$	12.8475	+	22.2526i	0.771934	+	1.33703i	−0.164568	+	0.986366i	$0.552623\pi$
$278$		0			0
$279$	26.5955	−	10.0028i	1.59223	−	0.598850i
$280$		0			0
$281$	6.73980	−	11.6737i	0.402063	−	0.696393i	−0.591912	−	0.806003i	$-0.701627\pi$
$281$	6.73980	−	11.6737i	0.402063	−	0.696393i	0.993975	+	0.109609i	$0.0349600\pi$
$282$		0			0
$283$	−8.27750	+	14.3371i	−0.492046	+	0.852249i	−0.999958	−	0.00915992i	$-0.997084\pi$
$283$	−8.27750	+	14.3371i	−0.492046	+	0.852249i	0.507912	+	0.861409i	$0.330418\pi$
$284$		0			0
$285$	−16.3783	−	19.3086i	−0.970166	−	1.14375i
$286$		0			0
$287$	26.4096			1.55891
$288$		0			0
$289$	7.42298	+	12.8570i	0.436646	+	0.756293i
$290$		0			0
$291$	7.05451	−	19.7088i	0.413543	−	1.15535i
$292$		0			0
$293$	−12.6711			−0.740252			−0.370126	−	0.928981i	$-0.620686\pi$
$293$	−12.6711			−0.740252			−0.370126	+	0.928981i	$0.620686\pi$
$294$		0			0
$295$	11.5358	+	19.9806i	0.671641	+	1.16332i
$296$		0			0
$297$	−21.1986	+	12.6959i	−1.23007	+	0.736688i
$298$		0			0
$299$	−0.280798	+	12.3025i	−0.0162389	+	0.711471i
$300$		0			0
$301$	4.60462	−	7.97543i	0.265406	−	0.459696i
$302$		0			0
$303$	−4.87506	−	5.74729i	−0.280065	−	0.330173i
$304$		0			0
$305$	−8.35970	+	14.4794i	−0.478675	+	0.829089i
$306$		0			0
$307$	9.08603			0.518567			0.259284	−	0.965801i	$-0.416514\pi$
$307$	9.08603			0.518567			0.259284	+	0.965801i	$0.416514\pi$
$308$		0			0
$309$	−4.94654	+	13.8196i	−0.281399	+	0.786167i
$310$		0			0
$311$	2.40367	+	4.16327i	0.136299	+	0.236077i	0.926093	−	0.377295i	$-0.123146\pi$
$311$	2.40367	+	4.16327i	0.136299	+	0.236077i	−0.789794	+	0.613373i	$0.789812\pi$
$312$		0			0
$313$	6.54378	−	11.3342i	0.369877	−	0.640645i	−0.619669	−	0.784863i	$-0.712733\pi$
$313$	6.54378	−	11.3342i	0.369877	−	0.640645i	0.989546	+	0.144218i	$0.0460666\pi$
$314$		0			0
$315$	−21.8598	−	17.9484i	−1.23166	−	1.01128i
$316$		0			0
$317$	−2.99255	+	5.18325i	−0.168078	+	0.291120i	−0.937744	−	0.347327i	$-0.887090\pi$
$317$	−2.99255	+	5.18325i	−0.168078	+	0.291120i	0.769666	+	0.638447i	$0.220423\pi$
$318$		0			0
$319$	18.2465			1.02161
$320$		0			0
$321$	−10.3852	+	29.0140i	−0.579645	+	1.61940i
$322$		0			0
$323$	−4.08843	−	7.08137i	−0.227486	−	0.394018i
$324$		0			0
$325$	−0.155037	+	6.79259i	−0.00859992	+	0.376785i
$326$		0			0
$327$	20.7522	+	24.4651i	1.14760	+	1.35292i
$328$		0			0
$329$	27.8985			1.53810
$330$		0			0
$331$	12.6517	+	21.9134i	0.695401	+	1.20447i	0.970045	+	0.242924i	$0.0781066\pi$
$331$	12.6517	+	21.9134i	0.695401	+	1.20447i	−0.274644	+	0.961546i	$0.588560\pi$
$332$		0			0
$333$	−12.0459	+	4.53054i	−0.660111	+	0.248272i
$334$		0			0
$335$	11.1420			0.608754
$336$		0			0
$337$	8.81119	+	15.2614i	0.479976	+	0.831343i	0.999736	−	0.0229694i	$-0.00731203\pi$
$337$	8.81119	+	15.2614i	0.479976	+	0.831343i	−0.519760	+	0.854312i	$0.673979\pi$
$338$		0			0
$339$	14.6200	+	17.2357i	0.794047	+	0.936116i
$340$		0			0
$341$	−22.5202	−	39.0060i	−1.21953	−	2.11230i
$342$		0			0
$343$	−3.91120			−0.211185
$344$		0			0
$345$	10.0333	+	11.8284i	0.540174	+	0.636820i
$346$		0			0
$347$	2.56873			0.137896			0.0689482	−	0.997620i	$-0.478036\pi$
$347$	2.56873			0.137896			0.0689482	+	0.997620i	$0.478036\pi$
$348$		0			0
$349$	9.13603			0.489041			0.244520	−	0.969644i	$-0.421370\pi$
$349$	9.13603			0.489041			0.244520	+	0.969644i	$0.421370\pi$
$350$		0			0
$351$	−9.47775	+	16.1608i	−0.505885	+	0.862601i
$352$		0			0
$353$	−6.37931			−0.339536			−0.169768	−	0.985484i	$-0.554302\pi$
$353$	−6.37931			−0.339536			−0.169768	+	0.985484i	$0.554302\pi$
$354$		0			0
$355$	−25.0063			−1.32720
$356$		0			0
$357$	−5.90870	−	6.96586i	−0.312721	−	0.368673i
$358$		0			0
$359$	−25.3664			−1.33879			−0.669394	−	0.742907i	$-0.733446\pi$
$359$	−25.3664			−1.33879			−0.669394	+	0.742907i	$0.733446\pi$
$360$		0			0
$361$	−6.01989	−	10.4268i	−0.316836	−	0.548776i
$362$		0			0
$363$	13.0119	+	15.3399i	0.682945	+	0.805136i
$364$		0			0
$365$	−14.6837	−	25.4329i	−0.768580	−	1.33122i
$366$		0			0
$367$	−9.63166			−0.502768			−0.251384	−	0.967887i	$-0.580886\pi$
$367$	−9.63166			−0.502768			−0.251384	+	0.967887i	$0.580886\pi$
$368$		0			0
$369$	−17.0410	−	13.9919i	−0.887121	−	0.728388i
$370$		0			0
$371$	−3.18118	−	5.50997i	−0.165159	−	0.286063i
$372$		0			0
$373$	−33.7946			−1.74982			−0.874909	−	0.484287i	$-0.839079\pi$
$373$	−33.7946			−1.74982			−0.874909	+	0.484287i	$0.839079\pi$
$374$		0			0
$375$	−9.15901	−	10.7977i	−0.472969	−	0.557592i
$376$		0			0
$377$	12.1359	−	6.64213i	0.625030	−	0.342087i
$378$		0			0
$379$	−12.7091	−	22.0129i	−0.652825	−	1.13073i	−0.982434	−	0.186608i	$-0.940250\pi$
$379$	−12.7091	−	22.0129i	−0.652825	−	1.13073i	0.329610	−	0.944117i	$-0.393083\pi$
$380$		0			0
$381$	3.61996	−	10.1134i	0.185456	−	0.518125i
$382$		0			0
$383$	29.2357			1.49388			0.746938	−	0.664894i	$-0.231523\pi$
$383$	29.2357			1.49388			0.746938	+	0.664894i	$0.231523\pi$
$384$		0			0
$385$	−22.4169	+	38.8273i	−1.14247	+	1.97882i
$386$		0			0
$387$	−7.19658	+	2.70668i	−0.365823	+	0.137588i
$388$		0			0
$389$	−14.2989	+	24.7664i	−0.724981	+	1.25570i	0.234000	+	0.972236i	$0.424818\pi$
$389$	−14.2989	+	24.7664i	−0.724981	+	1.25570i	−0.958982	+	0.283468i	$0.908515\pi$
$390$		0			0
$391$	2.50456	+	4.33802i	0.126661	+	0.219383i
$392$		0			0
$393$	2.45794	−	6.86697i	0.123987	−	0.346393i
$394$		0			0
$395$	26.5884			1.33781
$396$		0			0
$397$	13.8398	−	23.9712i	0.694597	−	1.20308i	−0.275719	−	0.961238i	$-0.588916\pi$
$397$	13.8398	−	23.9712i	0.694597	−	1.20308i	0.970316	−	0.241840i	$-0.0777508\pi$
$398$		0			0
$399$	−22.4297	−	26.4428i	−1.12289	−	1.32379i
$400$		0			0
$401$	10.1284	−	17.5430i	0.505790	−	0.876053i	−0.494188	−	0.869355i	$-0.664535\pi$
$401$	10.1284	−	17.5430i	0.505790	−	0.876053i	0.999978	−	0.00669810i	$-0.00213209\pi$
$402$		0			0
$403$	−29.1773	−	17.7453i	−1.45343	−	0.883958i
$404$		0			0
$405$	4.59611	+	23.1628i	0.228383	+	1.15097i
$406$		0			0
$407$	10.2000	+	17.6670i	0.505597	+	0.875719i
$408$		0			0
$409$	−15.6147			−0.772097			−0.386049	−	0.922478i	$-0.626160\pi$
$409$	−15.6147			−0.772097			−0.386049	+	0.922478i	$0.626160\pi$
$410$		0			0
$411$	−0.680515	+	1.90121i	−0.0335673	+	0.0937799i
$412$		0			0
$413$	15.7980	+	27.3630i	0.777371	+	1.34645i
$414$		0			0
$415$	23.7137			1.16406
$416$		0			0
$417$	−8.39012	−	9.89126i	−0.410866	−	0.484377i
$418$		0			0
$419$	−13.2803	+	23.0021i	−0.648785	+	1.12373i	0.334629	+	0.942350i	$0.391389\pi$
$419$	−13.2803	+	23.0021i	−0.648785	+	1.12373i	−0.983413	+	0.181378i	$0.941944\pi$
$420$		0			0
$421$	−3.31325	+	5.73872i	−0.161478	+	0.279688i	−0.935399	−	0.353594i	$-0.884959\pi$
$421$	−3.31325	+	5.73872i	−0.161478	+	0.279688i	0.773921	+	0.633282i	$0.218293\pi$
$422$		0			0
$423$	−18.0018	−	14.7807i	−0.875278	−	0.718664i
$424$		0			0
$425$	1.38285	+	2.39516i	0.0670779	+	0.116182i
$426$		0			0
$427$	−11.4484	+	19.8292i	−0.554028	+	0.959604i
$428$		0			0
$429$	27.7245	+	10.6434i	1.33855	+	0.513867i
$430$		0			0
$431$	−19.3047	−	33.4367i	−0.929874	−	1.61059i	−0.783529	−	0.621355i	$-0.786583\pi$
$431$	−19.3047	−	33.4367i	−0.929874	−	1.61059i	−0.146344	−	0.989234i	$-0.546751\pi$
$432$		0			0
$433$	−0.943893	+	1.63487i	−0.0453606	+	0.0785668i	−0.887814	−	0.460202i	$-0.847777\pi$
$433$	−0.943893	+	1.63487i	−0.0453606	+	0.0785668i	0.842454	+	0.538769i	$0.181110\pi$
$434$		0			0
$435$	5.87652	−	16.4177i	0.281758	−	0.787170i
$436$		0			0
$437$	9.50743	+	16.4674i	0.454802	+	0.787740i
$438$		0			0
$439$	−3.02192			−0.144229			−0.0721143	−	0.997396i	$-0.522975\pi$
$439$	−3.02192			−0.144229			−0.0721143	+	0.997396i	$0.522975\pi$
$440$		0			0
$441$	−13.7064	−	11.2539i	−0.652684	−	0.535899i
$442$		0			0
$443$	−0.0108117	+	0.0187264i	−0.000513680	+	0.000889719i	−0.866282	−	0.499555i	$-0.833497\pi$
$443$	−0.0108117	+	0.0187264i	−0.000513680	+	0.000889719i	0.865768	+	0.500445i	$0.166830\pi$
$444$		0			0
$445$	16.7079	−	28.9389i	0.792029	−	1.37183i
$446$		0			0
$447$	4.64270	+	5.47336i	0.219592	+	0.258881i
$448$		0			0
$449$	7.43393	−	12.8759i	0.350829	−	0.607653i	−0.635566	−	0.772047i	$-0.719233\pi$
$449$	7.43393	−	12.8759i	0.350829	−	0.607653i	0.986395	+	0.164393i	$0.0525665\pi$
$450$		0			0
$451$	−17.4754	+	30.2683i	−0.822884	+	1.42528i
$452$		0			0
$453$	−1.27853	+	0.232482i	−0.0600705	+	0.0109230i
$454$		0			0
$455$	−0.775678	+	33.9845i	−0.0363643	+	1.59322i
$456$		0			0
$457$	3.34792			0.156609			0.0783045	−	0.996929i	$-0.475049\pi$
$457$	3.34792			0.156609			0.0783045	+	0.996929i	$0.475049\pi$
$458$		0			0
$459$	0.122106	+	7.62524i	0.00569942	+	0.355916i
$460$		0			0
$461$	−7.03880	−	12.1916i	−0.327830	−	0.567818i	0.654251	−	0.756277i	$-0.272984\pi$
$461$	−7.03880	−	12.1916i	−0.327830	−	0.567818i	−0.982081	+	0.188460i	$0.939651\pi$
$462$		0			0
$463$	−15.2927	−	26.4878i	−0.710713	−	1.23099i	−0.964590	−	0.263755i	$-0.915039\pi$
$463$	−15.2927	−	26.4878i	−0.710713	−	1.23099i	0.253877	−	0.967237i	$-0.418294\pi$
$464$		0			0
$465$	−42.3495	+	7.70063i	−1.96391	+	0.357108i
$466$		0			0
$467$	22.0857			1.02200			0.511002	−	0.859579i	$-0.329274\pi$
$467$	22.0857			1.02200			0.511002	+	0.859579i	$0.329274\pi$
$468$		0			0
$469$	15.2588			0.704585
$470$		0			0
$471$	−1.05704	+	2.95313i	−0.0487057	+	0.136073i
$472$		0			0
$473$	6.09381	+	10.5548i	0.280194	+	0.485309i
$474$		0			0
$475$	5.24936	+	9.09215i	0.240857	+	0.417177i
$476$		0			0
$477$	−0.866512	+	5.24077i	−0.0396748	+	0.239958i
$478$		0			0
$479$	23.4564			1.07175			0.535876	−	0.844297i	$-0.319982\pi$
$479$	23.4564			1.07175			0.535876	+	0.844297i	$0.319982\pi$
$480$		0			0
$481$	13.2153	+	8.03738i	0.602564	+	0.366473i
$482$		0			0
$483$	13.7404	+	16.1988i	0.625208	+	0.737069i
$484$		0			0
$485$	−15.8555	+	27.4626i	−0.719962	+	1.24701i
$486$		0			0
$487$	−4.07543	+	7.05885i	−0.184675	+	0.319867i	−0.943467	−	0.331466i	$-0.892457\pi$
$487$	−4.07543	+	7.05885i	−0.184675	+	0.319867i	0.758792	+	0.651333i	$0.225790\pi$
$488$		0			0
$489$	−40.3155	+	7.33079i	−1.82313	+	0.331510i
$490$		0			0
$491$	5.59764	−	9.69540i	0.252618	−	0.437547i	−0.711628	−	0.702557i	$-0.752042\pi$
$491$	5.59764	−	9.69540i	0.252618	−	0.437547i	0.964246	+	0.265009i	$0.0853751\pi$
$492$		0			0
$493$	2.81575	−	4.87702i	0.126815	−	0.219650i
$494$		0			0
$495$	35.0356	−	13.1771i	1.57473	−	0.592267i
$496$		0			0
$497$	−34.2456			−1.53613
$498$		0			0
$499$	−0.839515	−	1.45408i	−0.0375818	−	0.0650936i	0.846623	−	0.532194i	$-0.178632\pi$
$499$	−0.839515	−	1.45408i	−0.0375818	−	0.0650936i	−0.884205	+	0.467100i	$0.845299\pi$
$500$		0			0
$501$	−4.87806	+	0.887005i	−0.217936	+	0.0396285i
$502$		0			0
$503$	−7.55237	+	13.0811i	−0.336743	+	0.583257i	−0.983818	−	0.179170i	$-0.942659\pi$
$503$	−7.55237	+	13.0811i	−0.336743	+	0.583257i	0.647075	+	0.762427i	$0.275992\pi$
$504$		0			0
$505$	5.70831	+	9.88708i	0.254016	+	0.439969i
$506$		0			0
$507$	22.3141	−	3.01333i	0.991005	−	0.133827i
$508$		0			0
$509$	−15.9569	+	27.6382i	−0.707279	+	1.22504i	0.258584	+	0.965989i	$0.416744\pi$
$509$	−15.9569	+	27.6382i	−0.707279	+	1.22504i	−0.965863	+	0.259054i	$0.916589\pi$
$510$		0			0
$511$	−20.1090	−	34.8298i	−0.889570	−	1.54078i
$512$		0			0
$513$	0.463521	+	28.9458i	0.0204649	+	1.27799i
$514$		0			0
$515$	11.1177	−	19.2564i	0.489904	−	0.848538i
$516$		0			0
$517$	−18.4606	+	31.9748i	−0.811898	+	1.40625i
$518$		0			0
$519$	−12.8732	+	35.9649i	−0.565070	+	1.57868i
$520$		0			0
$521$	−15.5056			−0.679315			−0.339657	−	0.940549i	$-0.610311\pi$
$521$	−15.5056			−0.679315			−0.339657	+	0.940549i	$0.610311\pi$
$522$		0			0
$523$	−20.4667	−	35.4494i	−0.894948	−	1.55009i	−0.833869	−	0.551962i	$-0.813879\pi$
$523$	−20.4667	−	35.4494i	−0.894948	−	1.55009i	−0.0610783	−	0.998133i	$-0.519454\pi$
$524$		0			0
$525$	7.58650	+	8.94385i	0.331102	+	0.390342i
$526$		0			0
$527$	−13.9010			−0.605535
$528$		0			0
$529$	5.67578	+	9.83074i	0.246773	+	0.427423i
$530$		0			0
$531$	4.30318	−	26.0261i	0.186742	−	1.12944i
$532$		0			0
$533$	−0.604689	+	26.4930i	−0.0261920	+	1.14754i
$534$		0			0
$535$	23.3415	−	40.4286i	1.00914	−	1.74788i
$536$		0			0
$537$	15.1756	−	42.3972i	0.654874	−	1.82958i
$538$		0			0
$539$	−14.0557	+	24.3452i	−0.605423	+	1.04862i
$540$		0			0
$541$	12.7245			0.547069			0.273534	−	0.961862i	$-0.411807\pi$
$541$	12.7245			0.547069			0.273534	+	0.961862i	$0.411807\pi$
$542$		0			0
$543$	−16.8223	−	19.8322i	−0.721916	−	0.851079i
$544$		0			0
$545$	−24.2992	−	42.0874i	−1.04086	−	1.80283i
$546$		0			0
$547$	−2.72430	+	4.71863i	−0.116483	+	0.201754i	−0.918371	−	0.395719i	$-0.870495\pi$
$547$	−2.72430	+	4.71863i	−0.116483	+	0.201754i	0.801889	+	0.597473i	$0.203829\pi$
$548$		0			0
$549$	17.8928	−	6.72960i	0.763646	−	0.287213i
$550$		0			0
$551$	10.6887	−	18.5134i	0.455355	−	0.788698i
$552$		0			0
$553$	36.4122			1.54841
$554$		0			0
$555$	19.1813	−	3.48784i	0.814201	−	0.148051i
$556$		0			0
$557$	−6.49410	−	11.2481i	−0.275164	−	0.476598i	0.695013	−	0.718997i	$-0.255399\pi$
$557$	−6.49410	−	11.2481i	−0.275164	−	0.476598i	−0.970176	+	0.242400i	$0.922065\pi$
$558$		0			0
$559$	7.89520	+	4.80177i	0.333931	+	0.203093i
$560$		0			0
$561$	11.8935	−	2.16265i	0.502142	−	0.0913073i
$562$		0			0
$563$	−20.4388			−0.861392			−0.430696	−	0.902497i	$-0.641732\pi$
$563$	−20.4388			−0.861392			−0.430696	+	0.902497i	$0.641732\pi$
$564$		0			0
$565$	−17.1188	−	29.6507i	−0.720195	−	1.24741i
$566$		0			0
$567$	6.29427	+	31.7209i	0.264335	+	1.33215i
$568$		0			0
$569$	−11.8791			−0.497999			−0.249000	−	0.968504i	$-0.580102\pi$
$569$	−11.8791			−0.497999			−0.249000	+	0.968504i	$0.580102\pi$
$570$		0			0
$571$	8.04840	+	13.9402i	0.336815	+	0.583381i	0.983832	−	0.179095i	$-0.0573169\pi$
$571$	8.04840	+	13.9402i	0.336815	+	0.583381i	−0.647017	+	0.762476i	$0.723984\pi$
$572$		0			0
$573$	−14.3038	+	39.9618i	−0.597551	+	1.66943i
$574$		0			0
$575$	−3.21574	−	5.56982i	−0.134106	−	0.232278i
$576$		0			0
$577$	8.72062			0.363044			0.181522	−	0.983387i	$-0.441898\pi$
$577$	8.72062			0.363044			0.181522	+	0.983387i	$0.441898\pi$
$578$		0			0
$579$	−20.6848	+	3.76124i	−0.859633	+	0.156312i
$580$		0			0
$581$	32.4755			1.34731
$582$		0			0
$583$	8.42004			0.348722
$584$		0			0
$585$	18.5056	−	21.5179i	0.765113	−	0.889655i
$586$		0			0
$587$	−21.2141			−0.875599			−0.437800	−	0.899073i	$-0.644242\pi$
$587$	−21.2141			−0.875599			−0.437800	+	0.899073i	$0.644242\pi$
$588$		0			0
$589$	−52.7687			−2.17430
$590$		0			0
$591$	0.344564	−	0.962637i	0.0141735	−	0.0395976i
$592$		0			0
$593$	2.20452			0.0905286			0.0452643	−	0.998975i	$-0.485587\pi$
$593$	2.20452			0.0905286			0.0452643	+	0.998975i	$0.485587\pi$
$594$		0			0
$595$	6.91862	+	11.9834i	0.283636	+	0.491272i
$596$		0			0
$597$	7.21396	−	1.31175i	0.295248	−	0.0536865i
$598$		0			0
$599$	−13.5519	−	23.4726i	−0.553715	−	0.959063i	−0.998002	−	0.0631787i	$-0.979876\pi$
$599$	−13.5519	−	23.4726i	−0.553715	−	0.959063i	0.444287	−	0.895885i	$-0.353457\pi$
$600$		0			0
$601$	14.6300			0.596770			0.298385	−	0.954446i	$-0.403552\pi$
$601$	14.6300			0.596770			0.298385	+	0.954446i	$0.403552\pi$
$602$		0			0
$603$	−9.84588	−	8.08415i	−0.400955	−	0.329212i
$604$		0			0
$605$	−15.2359	−	26.3893i	−0.619426	−	1.07288i
$606$		0			0
$607$	36.6831			1.48892			0.744461	−	0.667666i	$-0.232707\pi$
$607$	36.6831			1.48892			0.744461	+	0.667666i	$0.232707\pi$
$608$		0			0
$609$	8.04777	−	22.4837i	0.326112	−	0.911086i
$610$		0			0
$611$	−0.638781	+	27.9867i	−0.0258423	+	1.13222i
$612$		0			0
$613$	−4.48301	−	7.76481i	−0.181067	−	0.313618i	0.761177	−	0.648544i	$-0.224622\pi$
$613$	−4.48301	−	7.76481i	−0.181067	−	0.313618i	−0.942244	+	0.334927i	$0.891288\pi$
$614$		0			0
$615$	21.6064	+	25.4721i	0.871253	+	1.02714i
$616$		0			0
$617$	8.44166			0.339848			0.169924	−	0.985457i	$-0.445648\pi$
$617$	8.44166			0.339848			0.169924	+	0.985457i	$0.445648\pi$
$618$		0			0
$619$	−0.643084	+	1.11385i	−0.0258477	+	0.0447695i	−0.878660	−	0.477448i	$-0.841562\pi$
$619$	−0.643084	+	1.11385i	−0.0258477	+	0.0447695i	0.852812	+	0.522218i	$0.174895\pi$
$620$		0			0
$621$	−0.283951	−	17.7321i	−0.0113946	−	0.711565i
$622$		0			0
$623$	22.8811	−	39.6312i	0.916710	−	1.58779i
$624$		0			0
$625$	15.4355	+	26.7351i	0.617421	+	1.06940i
$626$		0			0
$627$	45.1482	−	8.20954i	1.80304	−	0.327858i
$628$		0			0
$629$	6.29615			0.251044
$630$		0			0
$631$	8.83740	−	15.3068i	0.351811	−	0.609355i	−0.634756	−	0.772713i	$-0.718899\pi$
$631$	8.83740	−	15.3068i	0.351811	−	0.609355i	0.986567	+	0.163358i	$0.0522326\pi$
$632$		0			0
$633$	40.7740	−	7.41416i	1.62062	−	0.294686i
$634$		0			0
$635$	−8.13612	+	14.0922i	−0.322872	+	0.559231i
$636$		0			0
$637$	−0.486360	+	21.3087i	−0.0192703	+	0.844283i
$638$		0			0
$639$	22.0973	+	18.1435i	0.874157	+	0.717744i
$640$		0			0
$641$	−10.6122	−	18.3808i	−0.419156	−	0.725999i	0.576699	−	0.816957i	$-0.304341\pi$
$641$	−10.6122	−	18.3808i	−0.419156	−	0.725999i	−0.995855	+	0.0909577i	$0.971007\pi$
$642$		0			0
$643$	19.8257			0.781850			0.390925	−	0.920423i	$-0.372155\pi$
$643$	19.8257			0.781850			0.390925	+	0.920423i	$0.372155\pi$
$644$		0			0
$645$	11.4595	−	2.08374i	0.451217	−	0.0820473i
$646$		0			0
$647$	0.739188	+	1.28031i	0.0290605	+	0.0503342i	0.880190	−	0.474622i	$-0.157415\pi$
$647$	0.739188	+	1.28031i	0.0290605	+	0.0503342i	−0.851129	+	0.524956i	$0.824082\pi$
$648$		0			0
$649$	−41.8147			−1.64137
$650$		0			0
$651$	−57.9967	+	10.5459i	−2.27307	+	0.413324i
$652$		0			0
$653$	5.57053	−	9.64844i	0.217992	−	0.377572i	−0.736202	−	0.676762i	$-0.763383\pi$
$653$	5.57053	−	9.64844i	0.217992	−	0.377572i	0.954194	+	0.299189i	$0.0967161\pi$
$654$		0			0
$655$	−5.52440	+	9.56855i	−0.215856	+	0.373874i
$656$		0			0
$657$	−5.47742	+	33.1281i	−0.213695	+	1.29245i
$658$		0			0
$659$	−2.23871	−	3.87757i	−0.0872079	−	0.151049i	0.819122	−	0.573619i	$-0.194461\pi$
$659$	−2.23871	−	3.87757i	−0.0872079	−	0.151049i	−0.906330	+	0.422571i	$0.861128\pi$
$660$		0			0
$661$	6.25885	−	10.8406i	0.243441	−	0.421652i	−0.718251	−	0.695784i	$-0.755057\pi$
$661$	6.25885	−	10.8406i	0.243441	−	0.421652i	0.961692	+	0.274132i	$0.0883904\pi$
$662$		0			0
$663$	7.12316	−	5.76787i	0.276641	−	0.224005i
$664$		0			0
$665$	26.2634	+	45.4896i	1.01845	+	1.76401i
$666$		0			0
$667$	−6.54787	+	11.3413i	−0.253535	+	0.439135i
$668$		0			0
$669$	−1.22449	−	1.44357i	−0.0473414	−	0.0558116i
$670$		0			0
$671$	−15.1510	−	26.2423i	−0.584897	−	1.01307i
$672$		0			0
$673$	−17.6922			−0.681982			−0.340991	−	0.940066i	$-0.610763\pi$
$673$	−17.6922			−0.681982			−0.340991	+	0.940066i	$0.610763\pi$
$674$		0			0
$675$	−0.156779	−	9.79046i	−0.00603441	−	0.376835i
$676$		0			0
$677$	−19.1654	+	33.1955i	−0.736587	+	1.27581i	0.217437	+	0.976074i	$0.430230\pi$
$677$	−19.1654	+	33.1955i	−0.736587	+	1.27581i	−0.954024	+	0.299731i	$0.903103\pi$
$678$		0			0
$679$	−21.7138	+	37.6094i	−0.833298	+	1.44331i
$680$		0			0
$681$	14.8708	−	41.5457i	0.569849	−	1.59203i
$682$		0			0
$683$	−23.3906	+	40.5137i	−0.895017	+	1.55021i	−0.0612334	+	0.998123i	$0.519503\pi$
$683$	−23.3906	+	40.5137i	−0.895017	+	1.55021i	−0.833784	+	0.552091i	$0.813830\pi$
$684$		0			0
$685$	1.52951	−	2.64918i	0.0584394	−	0.101220i
$686$		0			0
$687$	−7.32225	+	20.4568i	−0.279361	+	0.780475i
$688$		0			0
$689$	5.60022	−	3.06507i	0.213351	−	0.116770i
$690$		0			0
$691$	28.5592			1.08644			0.543222	−	0.839589i	$-0.317204\pi$
$691$	28.5592			1.08644			0.543222	+	0.839589i	$0.317204\pi$
$692$		0			0
$693$	47.9804	−	18.0458i	1.82263	−	0.685502i
$694$		0			0
$695$	9.82418	+	17.0160i	0.372652	+	0.645453i
$696$		0			0
$697$	5.39349	+	9.34180i	0.204293	+	0.353846i
$698$		0			0
$699$	12.7074	+	14.9810i	0.480638	+	0.566632i
$700$		0			0
$701$	−7.23324			−0.273196			−0.136598	−	0.990627i	$-0.543617\pi$
$701$	−7.23324			−0.273196			−0.136598	+	0.990627i	$0.543617\pi$
$702$		0			0
$703$	23.9005			0.901424
$704$		0			0
$705$	22.8245	+	26.9082i	0.859622	+	1.01342i
$706$		0			0
$707$	7.81740	+	13.5401i	0.294004	+	0.509229i
$708$		0			0
$709$	−18.4241	−	31.9114i	−0.691931	−	1.19846i	−0.971205	−	0.238247i	$-0.923427\pi$
$709$	−18.4241	−	31.9114i	−0.691931	−	1.19846i	0.279274	−	0.960211i	$-0.409906\pi$
$710$		0			0
$711$	−23.4954	−	19.2913i	−0.881145	−	0.723482i
$712$		0			0
$713$	32.3259			1.21062
$714$		0			0
$715$	−38.4367	−	23.3768i	−1.43745	−	0.874242i
$716$		0			0
$717$	−0.452125	+	1.26314i	−0.0168849	+	0.0471728i
$718$		0			0
$719$	6.09570	−	10.5581i	0.227331	−	0.393749i	−0.729685	−	0.683783i	$-0.760333\pi$
$719$	6.09570	−	10.5581i	0.227331	−	0.393749i	0.957016	+	0.290034i	$0.0936666\pi$
$720$		0			0
$721$	15.2254	−	26.3712i	0.567024	−	0.982115i
$722$		0			0
$723$	−5.11664	+	14.2948i	−0.190290	+	0.531629i
$724$		0			0
$725$	−3.61529	+	6.26187i	−0.134269	+	0.232560i
$726$		0			0
$727$	11.3403	−	19.6420i	0.420589	−	0.728482i	−0.575408	−	0.817866i	$-0.695157\pi$
$727$	11.3403	−	19.6420i	0.420589	−	0.728482i	0.995997	+	0.0893849i	$0.0284901\pi$
$728$		0			0
$729$	12.7444	−	23.8029i	0.472015	−	0.881591i
$730$		0			0
$731$	3.76151			0.139124
$732$		0			0
$733$	−9.20420	−	15.9421i	−0.339965	−	0.588836i	0.644461	−	0.764637i	$-0.277082\pi$
$733$	−9.20420	−	15.9421i	−0.339965	−	0.588836i	−0.984426	+	0.175801i	$0.943749\pi$
$734$		0			0
$735$	17.3783	+	20.4876i	0.641010	+	0.755697i
$736$		0			0
$737$	−10.0968	+	17.4882i	−0.371921	+	0.644187i
$738$		0			0
$739$	−7.08381	−	12.2695i	−0.260582	−	0.451341i	0.705815	−	0.708396i	$-0.250581\pi$
$739$	−7.08381	−	12.2695i	−0.260582	−	0.451341i	−0.966397	+	0.257055i	$0.917248\pi$
$740$		0			0
$741$	27.0399	−	21.8951i	0.993335	−	0.804337i
$742$		0			0
$743$	−13.7724	+	23.8544i	−0.505259	+	0.875134i	0.494723	+	0.869051i	$0.335270\pi$
$743$	−13.7724	+	23.8544i	−0.505259	+	0.875134i	−0.999981	+	0.00608305i	$0.998064\pi$
$744$		0			0
$745$	−5.43624	−	9.41585i	−0.199168	−	0.344970i
$746$		0			0
$747$	−20.9551	−	17.2056i	−0.766707	−	0.629520i
$748$		0			0
$749$	31.9656	−	55.3661i	1.16800	−	2.02303i
$750$		0			0
$751$	20.6350	−	35.7409i	0.752982	−	1.30420i	−0.193389	−	0.981122i	$-0.561948\pi$
$751$	20.6350	−	35.7409i	0.752982	−	1.30420i	0.946371	−	0.323081i	$-0.104719\pi$
$752$		0			0
$753$	32.6876	−	5.94377i	1.19120	−	0.216603i
$754$		0			0
$755$	1.96855			0.0716430
$756$		0			0
$757$	6.86589	+	11.8921i	0.249545	+	0.432225i	0.963400	−	0.268069i	$-0.0863856\pi$
$757$	6.86589	+	11.8921i	0.249545	+	0.432225i	−0.713854	+	0.700294i	$0.753052\pi$
$758$		0			0
$759$	−27.6576	+	5.02914i	−1.00391	+	0.182546i
$760$		0			0
$761$	−29.1925			−1.05823			−0.529113	−	0.848551i	$-0.677475\pi$
$761$	−29.1925			−1.05823			−0.529113	+	0.848551i	$0.677475\pi$
$762$		0			0
$763$	−33.2772	−	57.6378i	−1.20472	−	2.08663i
$764$		0			0
$765$	1.88454	−	11.3979i	0.0681357	−	0.412093i
$766$		0			0
$767$	−27.8112	+	15.2214i	−1.00420	+	0.549614i
$768$		0			0
$769$	18.0093	−	31.1931i	0.649433	−	1.12485i	−0.333825	−	0.942635i	$-0.608340\pi$
$769$	18.0093	−	31.1931i	0.649433	−	1.12485i	0.983258	−	0.182216i	$-0.0583271\pi$
$770$		0			0
$771$	22.2015	−	4.03703i	0.799568	−	0.145390i
$772$		0			0
$773$	−26.1726	+	45.3322i	−0.941361	+	1.63049i	−0.178483	+	0.983943i	$0.557119\pi$
$773$	−26.1726	+	45.3322i	−0.941361	+	1.63049i	−0.762878	+	0.646543i	$0.776214\pi$
$774$		0			0
$775$	17.8482			0.641126
$776$		0			0
$777$	26.2684	−	4.77652i	0.942372	−	0.171357i
$778$		0			0
$779$	20.4740	+	35.4620i	0.733556	+	1.27056i
$780$		0			0
$781$	22.6606	−	39.2492i	0.810859	−	1.40445i
$782$		0			0
$783$	−17.1049	+	10.2441i	−0.611278	+	0.366095i
$784$		0			0
$785$	2.37576	−	4.11494i	0.0847947	−	0.146869i
$786$		0			0
$787$	13.4115			0.478069			0.239035	−	0.971011i	$-0.423169\pi$
$787$	13.4115			0.478069			0.239035	+	0.971011i	$0.423169\pi$
$788$		0			0
$789$	−20.0166	−	23.5979i	−0.712611	−	0.840109i
$790$		0			0
$791$	−23.4439	−	40.6060i	−0.833568	−	1.44378i
$792$		0			0
$793$	−19.6298	−	11.9386i	−0.697073	−	0.423952i
$794$		0			0
$795$	2.71178	−	7.57612i	0.0961768	−	0.268697i
$796$		0			0
$797$	21.2067			0.751181			0.375591	−	0.926786i	$-0.377440\pi$
$797$	21.2067			0.751181			0.375591	+	0.926786i	$0.377440\pi$
$798$		0			0
$799$	5.69758	+	9.86849i	0.201566	+	0.349122i
$800$		0			0
$801$	−35.7610	+	13.4499i	−1.26355	+	0.475230i
$802$		0			0
$803$	53.2250			1.87827
$804$		0			0
$805$	−16.0889	−	27.8668i	−0.567059	−	0.982175i
$806$		0			0
$807$	−1.18830	+	0.216076i	−0.0418303	+	0.00760623i
$808$		0			0
$809$	−2.68990	−	4.65903i	−0.0945717	−	0.163803i	0.814858	−	0.579660i	$-0.196815\pi$
$809$	−2.68990	−	4.65903i	−0.0945717	−	0.163803i	−0.909430	+	0.415858i	$0.863481\pi$
$810$		0			0
$811$	−25.9549			−0.911399			−0.455700	−	0.890134i	$-0.650611\pi$
$811$	−25.9549			−0.911399			−0.455700	+	0.890134i	$0.650611\pi$
$812$		0			0
$813$	−2.44989	+	6.84445i	−0.0859213	+	0.240045i
$814$		0			0
$815$	62.0738			2.17435
$816$		0			0
$817$	14.2789			0.499555
$818$		0			0
$819$	25.3430	−	29.4683i	0.885557	−	1.02970i
$820$		0			0
$821$	−29.4353			−1.02730			−0.513649	−	0.858001i	$-0.671707\pi$
$821$	−29.4353			−1.02730			−0.513649	+	0.858001i	$0.671707\pi$
$822$		0			0
$823$	3.84352			0.133977			0.0669883	−	0.997754i	$-0.478661\pi$
$823$	3.84352			0.133977			0.0669883	+	0.997754i	$0.478661\pi$
$824$		0			0
$825$	−15.2707	+	2.77675i	−0.531656	+	0.0966740i
$826$		0			0
$827$	7.89362			0.274488			0.137244	−	0.990537i	$-0.456176\pi$
$827$	7.89362			0.274488			0.137244	+	0.990537i	$0.456176\pi$
$828$		0			0
$829$	−13.9381	−	24.1415i	−0.484091	−	0.838470i	0.515742	−	0.856744i	$-0.327516\pi$
$829$	−13.9381	−	24.1415i	−0.484091	−	0.838470i	−0.999833	+	0.0182738i	$0.994183\pi$
$830$		0			0
$831$	−14.9982	+	41.9018i	−0.520283	+	1.45356i
$832$		0			0
$833$	4.33807	+	7.51375i	0.150305	+	0.260336i
$834$		0			0
$835$	7.51076			0.259921
$836$		0			0
$837$	43.0101	+	23.9220i	1.48665	+	0.826866i
$838$		0			0
$839$	−0.509063	−	0.881723i	−0.0175748	−	0.0304405i	0.857104	−	0.515143i	$-0.172261\pi$
$839$	−0.509063	−	0.881723i	−0.0175748	−	0.0304405i	−0.874679	+	0.484703i	$0.838928\pi$
$840$		0			0
$841$	−14.2771			−0.492314
$842$		0			0
$843$	22.9707	−	4.17689i	0.791153	−	0.143860i
$844$		0			0
$845$	−34.0741	−	1.55626i	−1.17218	−	0.0535369i
$846$		0			0
$847$	−20.8652	−	36.1396i	−0.716936	−	1.24177i
$848$		0			0
$849$	−28.2115	+	5.12985i	−0.968216	+	0.176056i
$850$		0			0
$851$	−14.6414			−0.501899
$852$		0			0
$853$	5.26184	−	9.11377i	0.180162	−	0.312049i	−0.761774	−	0.647843i	$-0.775671\pi$
$853$	5.26184	−	9.11377i	0.180162	−	0.312049i	0.941936	+	0.335794i	$0.109005\pi$
$854$		0			0
$855$	7.15381	−	43.2671i	0.244655	−	1.47970i
$856$		0			0
$857$	27.4772	−	47.5919i	0.938602	−	1.62571i	0.170522	−	0.985354i	$-0.445455\pi$
$857$	27.4772	−	47.5919i	0.938602	−	1.62571i	0.768081	−	0.640353i	$-0.221212\pi$
$858$		0			0
$859$	24.2942	+	42.0789i	0.828909	+	1.43571i	0.898895	+	0.438164i	$0.144371\pi$
$859$	24.2942	+	42.0789i	0.828909	+	1.43571i	−0.0699862	+	0.997548i	$0.522296\pi$
$860$		0			0
$861$	29.5895	+	34.8835i	1.00841	+	1.18883i
$862$		0			0
$863$	−36.1609			−1.23093			−0.615466	−	0.788163i	$-0.711032\pi$
$863$	−36.1609			−1.23093			−0.615466	+	0.788163i	$0.711032\pi$
$864$		0			0
$865$	28.9334	−	50.1141i	0.983765	−	1.70393i
$866$		0			0
$867$	−8.66560	+	24.2098i	−0.294299	+	0.822208i
$868$		0			0
$869$	−24.0942	+	41.7324i	−0.817340	+	1.41568i
$870$		0			0
$871$	−0.349374	+	15.3070i	−0.0118381	+	0.518657i
$872$		0			0
$873$	33.9366	−	12.7638i	1.14858	−	0.431989i
$874$		0			0
$875$	14.6870	+	25.4385i	0.496510	+	0.859980i
$876$		0			0
$877$	−30.1766			−1.01899			−0.509495	−	0.860474i	$-0.670168\pi$
$877$	−30.1766			−1.01899			−0.509495	+	0.860474i	$0.670168\pi$
$878$		0			0
$879$	−14.1968	−	16.7368i	−0.478845	−	0.564518i
$880$		0			0
$881$	2.07896	+	3.60087i	0.0700420	+	0.121316i	0.898919	−	0.438114i	$-0.144353\pi$
$881$	2.07896	+	3.60087i	0.0700420	+	0.121316i	−0.828877	+	0.559430i	$0.811020\pi$
$882$		0			0
$883$	−26.0189			−0.875605			−0.437802	−	0.899071i	$-0.644243\pi$
$883$	−26.0189			−0.875605			−0.437802	+	0.899071i	$0.644243\pi$
$884$		0			0
$885$	−13.4669	+	37.6237i	−0.452686	+	1.26471i
$886$		0			0
$887$	−17.5818	+	30.4526i	−0.590339	+	1.02250i	0.403847	+	0.914826i	$0.367673\pi$
$887$	−17.5818	+	30.4526i	−0.590339	+	1.02250i	−0.994187	+	0.107671i	$0.965661\pi$
$888$		0			0
$889$	−11.1422	+	19.2989i	−0.373699	+	0.647265i
$890$		0			0
$891$	−40.5206	−	13.7760i	−1.35749	−	0.461513i
$892$		0			0
$893$	21.6283	+	37.4613i	0.723763	+	1.25359i
$894$		0			0
$895$	−34.1081	+	59.0770i	−1.14011	+	1.97473i
$896$		0			0
$897$	−16.5645	+	13.4129i	−0.553074	+	0.447843i
$898$		0			0
$899$	−18.1712	−	31.4734i	−0.606044	−	1.04970i
$900$		0			0
$901$	1.29935	−	2.25055i	0.0432877	−	0.0749766i
$902$		0			0
$903$	15.6935	−	2.85364i	0.522248	−	0.0949632i
$904$		0			0
$905$	19.6977	+	34.1173i	0.654772	+	1.13410i
$906$		0			0
$907$	−23.9356			−0.794767			−0.397384	−	0.917653i	$-0.630082\pi$
$907$	−23.9356			−0.794767			−0.397384	+	0.917653i	$0.630082\pi$
$908$		0			0
$909$	2.12936	−	12.8786i	0.0706263	−	0.427156i
$910$		0			0
$911$	5.01570	−	8.68744i	0.166177	−	0.287828i	−0.770895	−	0.636962i	$-0.780191\pi$
$911$	5.01570	−	8.68744i	0.166177	−	0.287828i	0.937073	+	0.349134i	$0.113524\pi$
$912$		0			0
$913$	−21.4892	+	37.2204i	−0.711189	+	1.23182i
$914$		0			0
$915$	−28.4916	+	5.18079i	−0.941904	+	0.171272i
$916$		0			0
$917$	−7.56555	+	13.1039i	−0.249836	+	0.432729i
$918$		0			0
$919$	−26.8145	+	46.4441i	−0.884530	+	1.53205i	−0.0382782	+	0.999267i	$0.512187\pi$
$919$	−26.8145	+	46.4441i	−0.884530	+	1.53205i	−0.846252	+	0.532783i	$0.821146\pi$
$920$		0			0
$921$	10.1800	+	12.0014i	0.335444	+	0.395461i
$922$		0			0
$923$	0.784108	−	34.3538i	0.0258092	−	1.13077i
$924$		0			0
$925$	−8.08396			−0.265799
$926$		0			0
$927$	−23.7959	+	8.94980i	−0.781560	+	0.293950i
$928$		0			0
$929$	−18.4795	−	32.0074i	−0.606292	−	1.05013i	−0.991846	−	0.127443i	$-0.959323\pi$
$929$	−18.4795	−	32.0074i	−0.606292	−	1.05013i	0.385554	−	0.922685i	$-0.374010\pi$
$930$		0			0
$931$	16.4675	+	28.5226i	0.539701	+	0.934790i
$932$		0			0
$933$	−2.80604	+	7.83948i	−0.0918657	+	0.256653i
$934$		0			0
$935$	−18.3124			−0.598879
$936$		0			0
$937$	15.2960			0.499697			0.249849	−	0.968285i	$-0.419619\pi$
$937$	15.2960			0.499697			0.249849	+	0.968285i	$0.419619\pi$
$938$		0			0
$939$	22.3026	−	4.05541i	0.727819	−	0.132343i
$940$		0			0
$941$	8.92739	+	15.4627i	0.291025	+	0.504069i	0.974052	−	0.226323i	$-0.0726705\pi$
$941$	8.92739	+	15.4627i	0.291025	+	0.504069i	−0.683028	+	0.730392i	$0.739337\pi$
$942$		0			0
$943$	−12.5423	−	21.7239i	−0.408433	−	0.707427i
$944$		0			0
$945$	−0.784390	−	48.9833i	−0.0255162	−	1.59343i
$946$		0			0
$947$	17.1814			0.558320			0.279160	−	0.960245i	$-0.409944\pi$
$947$	17.1814			0.558320			0.279160	+	0.960245i	$0.409944\pi$
$948$		0			0
$949$	35.4003	−	19.3751i	1.14914	−	0.628941i
$950$		0			0
$951$	−10.1993	+	1.85459i	−0.330734	+	0.0601391i
$952$		0			0
$953$	4.11751	−	7.13174i	0.133379	−	0.231020i	−0.791598	−	0.611042i	$-0.790750\pi$
$953$	4.11751	−	7.13174i	0.133379	−	0.231020i	0.924977	+	0.380023i	$0.124084\pi$
$954$		0			0
$955$	32.1488	−	55.6834i	1.04031	−	1.80187i
$956$		0			0
$957$	20.4435	+	24.1012i	0.660846	+	0.779083i
$958$		0			0
$959$	2.09462	−	3.62800i	0.0676390	−	0.117154i
$960$		0			0
$961$	−29.3544	+	50.8432i	−0.946915	+	1.64010i
$962$		0			0
$963$	−49.9593	+	18.7900i	−1.60992	+	0.605500i
$964$		0			0
$965$	31.8485			1.02524
$966$		0			0
$967$	11.5109	+	19.9375i	0.370166	+	0.641146i	0.989591	−	0.143910i	$-0.0459675\pi$
$967$	11.5109	+	19.9375i	0.370166	+	0.641146i	−0.619425	+	0.785056i	$0.712634\pi$
$968$		0			0
$969$	4.77284	−	13.3343i	0.153326	−	0.428359i
$970$		0			0
$971$	8.70378	−	15.0754i	0.279318	−	0.483792i	−0.691898	−	0.721996i	$-0.743225\pi$
$971$	8.70378	−	15.0754i	0.279318	−	0.483792i	0.971215	+	0.238203i	$0.0765584\pi$
$972$		0			0
$973$	13.4540	+	23.3030i	0.431315	+	0.747060i
$974$		0			0
$975$	−9.14581	+	7.40568i	−0.292900	+	0.237172i
$976$		0			0
$977$	−24.3975	+	42.2577i	−0.780546	+	1.35194i	0.151079	+	0.988522i	$0.451725\pi$
$977$	−24.3975	+	42.2577i	−0.780546	+	1.35194i	−0.931624	+	0.363423i	$0.881608\pi$
$978$		0			0
$979$	30.2811	+	52.4484i	0.967788	+	1.67626i
$980$		0			0
$981$	−9.06426	+	54.8217i	−0.289400	+	1.75032i
$982$		0			0
$983$	14.7251	−	25.5046i	0.469657	−	0.813470i	−0.529741	−	0.848160i	$-0.677711\pi$
$983$	14.7251	−	25.5046i	0.469657	−	0.813470i	0.999398	+	0.0346892i	$0.0110441\pi$
$984$		0			0
$985$	−0.774432	+	1.34136i	−0.0246755	+	0.0427391i
$986$		0			0
$987$	31.2577	+	36.8503i	0.994944	+	1.17296i
$988$		0			0
$989$	−8.74719			−0.278145
$990$		0			0
$991$	26.0112	+	45.0527i	0.826273	+	1.43115i	0.900943	+	0.433938i	$0.142876\pi$
$991$	26.0112	+	45.0527i	0.826273	+	1.43115i	−0.0746703	+	0.997208i	$0.523790\pi$
$992$		0			0
$993$	−14.7696	+	41.2632i	−0.468700	+	1.30945i
$994$		0			0
$995$	−11.1073			−0.352127
$996$		0			0
$997$	−30.8874	−	53.4986i	−0.978215	−	1.69432i	−0.668889	−	0.743362i	$-0.733230\pi$
$997$	−30.8874	−	53.4986i	−0.978215	−	1.69432i	−0.309326	−	0.950956i	$-0.600103\pi$
$998$		0			0
$999$	−19.4805	−	10.8350i	−0.616337	−	0.342803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.j.a.133.11	✓	28
3.2	odd	2		1404.2.j.a.289.12		28
9.4	even	3		468.2.k.a.445.9	yes	28
9.5	odd	6		1404.2.k.a.1225.12		28
13.9	even	3		468.2.k.a.61.9	yes	28
39.35	odd	6		1404.2.k.a.1153.12		28
117.22	even	3	inner	468.2.j.a.373.11	yes	28
117.113	odd	6		1404.2.j.a.685.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.11	✓	28	1.1	even	1	trivial
468.2.j.a.373.11	yes	28	117.22	even	3	inner
468.2.k.a.61.9	yes	28	13.9	even	3
468.2.k.a.445.9	yes	28	9.4	even	3
1404.2.j.a.289.12		28	3.2	odd	2
1404.2.j.a.685.12		28	117.113	odd	6
1404.2.k.a.1153.12		28	39.35	odd	6
1404.2.k.a.1225.12		28	9.5	odd	6

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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12041 + 1.32087i) q^{3} +(-1.31191 - 2.27229i) q^{5} +(-1.79663 - 3.11185i) q^{7} +(-0.489378 + 2.95982i) q^{9} +4.75537 q^{11} +(3.16282 - 1.73106i) q^{13} +(1.53152 - 4.27875i) q^{15} +(0.733833 - 1.27104i) q^{17} +(2.78567 - 4.82492i) q^{19} +(2.09739 - 5.85965i) q^{21} +(-1.70649 + 2.95573i) q^{23} +(-0.942208 + 1.63195i) q^{25} +(-4.45782 + 2.66979i) q^{27} +3.83704 q^{29} +(-4.73573 - 8.20253i) q^{31} +(5.32794 + 6.28121i) q^{33} +(-4.71403 + 8.16494i) q^{35} +(2.14495 + 3.71516i) q^{37} +(5.83014 + 2.23818i) q^{39} +(-3.67488 + 6.36507i) q^{41} +(1.28146 + 2.21955i) q^{43} +(7.36759 - 2.77100i) q^{45} +(-3.88207 + 6.72393i) q^{47} +(-2.95576 + 5.11952i) q^{49} +(2.50106 - 0.454782i) q^{51} +1.77064 q^{53} +(-6.23861 - 10.8056i) q^{55} +(9.49415 - 1.72637i) q^{57} -8.79316 q^{59} +(-3.18608 - 5.51845i) q^{61} +(10.0897 - 3.79482i) q^{63} +(-8.08280 - 4.91587i) q^{65} +(-2.12325 + 3.67758i) q^{67} +(-5.81609 + 1.05757i) q^{69} +(4.76526 - 8.25367i) q^{71} +11.1926 q^{73} +(-3.21125 + 0.583919i) q^{75} +(-8.54363 - 14.7980i) q^{77} +(-5.06674 + 8.77586i) q^{79} +(-8.52102 - 2.89694i) q^{81} +(-4.51894 + 7.82703i) q^{83} -3.85089 q^{85} +(4.29905 + 5.06822i) q^{87} +(6.36777 + 11.0293i) q^{89} +(-11.0692 - 6.73218i) q^{91} +(5.52850 - 15.4454i) q^{93} -14.6182 q^{95} +(-6.04292 - 10.4666i) q^{97} +(-2.32717 + 14.0750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{7} - 2 q^{9} + 8 q^{11} + q^{13} - 10 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} - 4 q^{23} - 14 q^{25} + 26 q^{29} + 2 q^{31} + 8 q^{33} + 3 q^{35} - q^{37} - 12 q^{39} + 4 q^{41} + 2 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) \) 28 * q + 2 * q^7 - 2 * q^9 + 8 * q^11 + q^13 - 10 * q^15 - 8 * q^17 - q^19 + 14 * q^21 - 4 * q^23 - 14 * q^25 + 26 * q^29 + 2 * q^31 + 8 * q^33 + 3 * q^35 - q^37 - 12 * q^39 + 4 * q^41 + 2 * q^43 + q^45 + 11 * q^47 - 12 * q^49 + 5 * q^51 + 52 * q^53 - q^57 + 16 * q^59 - 7 * q^61 - 24 * q^63 - 31 * q^65 - 7 * q^67 + 24 * q^69 - 12 * q^71 + 14 * q^73 + 16 * q^75 - 28 * q^77 + 5 * q^79 - 50 * q^81 + 9 * q^83 - 36 * q^85 - 21 * q^87 - 11 * q^89 - q^91 - 33 * q^93 - 56 * q^95 - 25 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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