LMFDB - Embedded newform 468.2.k.a.61.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(61,468)] 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("468.61"); 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, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.k (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			61.9
Character	$\chi$	$=$	468.61
Dual form			468.2.k.a.445.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.583701 - 1.63073i) q^{3} +(-1.31191 - 2.27229i) q^{5} +3.59326 q^{7} +(-2.31859 - 1.90372i) q^{9} +(-2.37768 - 4.11827i) q^{11} +(-3.08055 + 1.87356i) q^{13} +(-4.47127 + 0.813035i) q^{15} +(0.733833 + 1.27104i) q^{17} +(2.78567 + 4.82492i) q^{19} +(2.09739 - 5.85965i) q^{21} +3.41298 q^{23} +(-0.942208 + 1.63195i) q^{25} +(-4.45782 + 2.66979i) q^{27} +(-1.91852 - 3.32297i) q^{29} +(-4.73573 - 8.20253i) q^{31} +(-8.10366 + 1.47353i) q^{33} +(-4.71403 - 8.16494i) q^{35} +(2.14495 - 3.71516i) q^{37} +(1.25715 + 6.11715i) q^{39} +7.34975 q^{41} -2.56292 q^{43} +(-1.28404 + 7.76602i) q^{45} +(-3.88207 + 6.72393i) q^{47} +5.91152 q^{49} +(2.50106 - 0.454782i) q^{51} +1.77064 q^{53} +(-6.23861 + 10.8056i) q^{55} +(9.49415 - 1.72637i) q^{57} +(4.39658 - 7.61510i) q^{59} +6.37216 q^{61} +(-8.33128 - 6.84057i) q^{63} +(8.29867 + 4.54197i) q^{65} +4.24650 q^{67} +(1.99216 - 5.56567i) q^{69} +(4.76526 + 8.25367i) q^{71} +11.1926 q^{73} +(2.11131 + 2.48906i) q^{75} +(-8.54363 - 14.7980i) q^{77} +(-5.06674 + 8.77586i) q^{79} +(1.75169 + 8.82789i) q^{81} +(-4.51894 + 7.82703i) q^{83} +(1.92544 - 3.33497i) q^{85} +(-6.53873 + 1.18897i) q^{87} +(6.36777 - 11.0293i) q^{89} +(-11.0692 + 6.73218i) q^{91} +(-16.1404 + 2.93490i) q^{93} +(7.30908 - 12.6597i) q^{95} +12.0858 q^{97} +(-2.32717 + 14.0750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) $ 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Character values

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

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

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
$3$	0.583701	−	1.63073i	0.337000	−	0.941505i
$3$	0.583701	−	1.63073i	0.337000	−	0.941505i
$4$		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
$7$	3.59326			1.35812			0.679062	−	0.734081i	$-0.262387\pi$
$7$	3.59326			1.35812			0.679062	+	0.734081i	$0.262387\pi$
$8$		0			0
$9$	−2.31859	−	1.90372i	−0.772862	−	0.634574i
$10$		0			0
$11$	−2.37768	−	4.11827i	−0.716898	−	1.24170i	−0.962223	−	0.272264i	$-0.912228\pi$
$11$	−2.37768	−	4.11827i	−0.716898	−	1.24170i	0.245324	−	0.969441i	$-0.421106\pi$
$12$		0			0
$13$	−3.08055	+	1.87356i	−0.854391	+	0.519631i
$13$	−3.08055	+	1.87356i	−0.854391	+	0.519631i
$14$		0			0
$15$	−4.47127	+	0.813035i	−1.15448	+	0.209925i
$16$		0			0
$17$	0.733833	+	1.27104i	0.177981	+	0.308272i	0.941189	−	0.337881i	$-0.109710\pi$
$17$	0.733833	+	1.27104i	0.177981	+	0.308272i	−0.763208	+	0.646153i	$0.776377\pi$
$18$		0			0
$19$	2.78567	+	4.82492i	0.639076	+	1.10691i	0.985636	+	0.168884i	$0.0540164\pi$
$19$	2.78567	+	4.82492i	0.639076	+	1.10691i	−0.346560	+	0.938028i	$0.612650\pi$
$20$		0			0
$21$	2.09739	−	5.85965i	0.457688	−	1.27868i
$22$		0			0
$23$	3.41298			0.711656			0.355828	−	0.934551i	$-0.384199\pi$
$23$	3.41298			0.711656			0.355828	+	0.934551i	$0.384199\pi$
$24$		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
$29$	−1.91852	−	3.32297i	−0.356260	−	0.617061i	0.631073	−	0.775724i	$-0.282615\pi$
$29$	−1.91852	−	3.32297i	−0.356260	−	0.617061i	−0.987333	+	0.158663i	$0.949282\pi$
$30$		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
$33$	−8.10366	+	1.47353i	−1.41067	+	0.256509i
$34$		0			0
$35$	−4.71403	−	8.16494i	−0.796816	−	1.38013i
$36$		0			0
$37$	2.14495	−	3.71516i	0.352628	−	0.610769i	−0.634081	−	0.773266i	$-0.718621\pi$
$37$	2.14495	−	3.71516i	0.352628	−	0.610769i	0.986709	+	0.162497i	$0.0519548\pi$
$38$		0			0
$39$	1.25715	+	6.11715i	0.201306	+	0.979528i
$40$		0			0
$41$	7.34975			1.14784			0.573919	−	0.818912i	$-0.305422\pi$
$41$	7.34975			1.14784			0.573919	+	0.818912i	$0.305422\pi$
$42$		0			0
$43$	−2.56292			−0.390841			−0.195421	−	0.980720i	$-0.562607\pi$
$43$	−2.56292			−0.390841			−0.195421	+	0.980720i	$0.562607\pi$
$44$		0			0
$45$	−1.28404	+	7.76602i	−0.191413	+	1.15769i
$46$		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
$49$	5.91152			0.844503
$50$		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
$59$	4.39658	−	7.61510i	0.572386	−	0.991401i	−0.423935	−	0.905693i	$-0.639351\pi$
$59$	4.39658	−	7.61510i	0.572386	−	0.991401i	0.996320	−	0.0857084i	$-0.0273153\pi$
$60$		0			0
$61$	6.37216			0.815872			0.407936	−	0.913011i	$-0.366249\pi$
$61$	6.37216			0.815872			0.407936	+	0.913011i	$0.366249\pi$
$62$		0			0
$63$	−8.33128	−	6.84057i	−1.04964	−	0.861830i
$64$		0			0
$65$	8.29867	+	4.54197i	1.02932	+	0.563362i
$66$		0			0
$67$	4.24650			0.518792			0.259396	−	0.965771i	$-0.416476\pi$
$67$	4.24650			0.518792			0.259396	+	0.965771i	$0.416476\pi$
$68$		0			0
$69$	1.99216	−	5.56567i	0.239828	−	0.670027i
$70$		0			0
$71$	4.76526	+	8.25367i	0.565532	+	0.979531i	0.997000	+	0.0774024i	$0.0246626\pi$
$71$	4.76526	+	8.25367i	0.565532	+	0.979531i	−0.431468	+	0.902128i	$0.642004\pi$
$72$		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
$75$	2.11131	+	2.48906i	0.243793	+	0.287412i
$76$		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
$81$	1.75169	+	8.82789i	0.194632	+	0.980876i
$82$		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
$85$	1.92544	−	3.33497i	0.208844	−	0.361728i
$86$		0			0
$87$	−6.53873	+	1.18897i	−0.701025	+	0.127471i
$88$		0			0
$89$	6.36777	−	11.0293i	0.674983	−	1.16910i	−0.301491	−	0.953469i	$-0.597484\pi$
$89$	6.36777	−	11.0293i	0.674983	−	1.16910i	0.976474	−	0.215635i	$-0.0691822\pi$
$90$		0			0
$91$	−11.0692	+	6.73218i	−1.16037	+	0.705724i
$92$		0			0
$93$	−16.1404	+	2.93490i	−1.67368	+	0.304335i
$94$		0			0
$95$	7.30908	−	12.6597i	0.749896	−	1.29886i
$96$		0			0
$97$	12.0858			1.22713			0.613565	−	0.789644i	$-0.289735\pi$
$97$	12.0858			1.22713			0.613565	+	0.789644i	$0.289735\pi$
$98$		0			0
$99$	−2.32717	+	14.0750i	−0.233890	+	1.41459i
$100$		0			0
$101$	2.17557	+	3.76821i	0.216478	+	0.374950i	0.953729	−	0.300669i	$-0.0972098\pi$
$101$	2.17557	+	3.76821i	0.216478	+	0.374950i	−0.737251	+	0.675619i	$0.763876\pi$
$102$		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	−0.0119108	−	0.999929i	$-0.503791\pi$
$107$	8.89600	−	15.4083i	0.860009	−	1.48958i	0.871919	−	0.489649i	$-0.162875\pi$
$108$		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
$111$	−4.80644	−	5.66639i	−0.456207	−	0.537830i
$112$		0			0
$113$	−6.52440	+	11.3006i	−0.613764	+	1.06307i	0.376836	+	0.926280i	$0.377012\pi$
$113$	−6.52440	+	11.3006i	−0.613764	+	1.06307i	−0.990600	+	0.136790i	$0.956321\pi$
$114$		0			0
$115$	−4.47752	−	7.75529i	−0.417531	−	0.723185i
$116$		0			0
$117$	10.7093	+	1.52050i	0.990071	+	0.140571i
$118$		0			0
$119$	2.63685	+	4.56716i	0.241720	+	0.418671i
$120$		0			0
$121$	−5.80676	+	10.0576i	−0.527887	+	0.914327i
$122$		0			0
$123$	4.29006	−	11.9855i	0.386821	−	1.08070i
$124$		0			0
$125$	−8.17472			−0.731169
$126$		0			0
$127$	−3.10087	+	5.37087i	−0.275158	+	0.476588i	−0.970175	−	0.242406i	$-0.922063\pi$
$127$	−3.10087	+	5.37087i	−0.275158	+	0.476588i	0.695017	+	0.718993i	$0.255397\pi$
$128$		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
$133$	10.0096	+	17.3372i	0.867945	+	1.50332i
$134$		0			0
$135$	11.9148	+	6.62695i	1.02546	+	0.570357i
$136$		0			0
$137$	−1.16586			−0.0996064			−0.0498032	−	0.998759i	$-0.515859\pi$
$137$	−1.16586			−0.0996064			−0.0498032	+	0.998759i	$0.515859\pi$
$138$		0			0
$139$	3.74423	−	6.48520i	0.317582	−	0.550067i	−0.662401	−	0.749149i	$-0.730463\pi$
$139$	3.74423	−	6.48520i	0.317582	−	0.550067i	0.979983	+	0.199082i	$0.0637960\pi$
$140$		0			0
$141$	8.69898	+	10.2554i	0.732587	+	0.863659i
$142$		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
$147$	3.45056	−	9.64011i	0.284597	−	0.795103i
$148$		0			0
$149$	−2.07188	+	3.58861i	−0.169735	+	0.293990i	−0.938327	−	0.345750i	$-0.887625\pi$
$149$	−2.07188	+	3.58861i	−0.169735	+	0.293990i	0.768591	+	0.639740i	$0.220958\pi$
$150$		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
$153$	0.718243	−	4.34402i	0.0580665	−	0.351193i
$154$		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
$159$	1.03352	−	2.88744i	0.0819638	−	0.228989i
$160$		0			0
$161$	12.2637			0.966517
$162$		0			0
$163$	−11.8289	−	20.4883i	−0.926513	−	1.60477i	−0.789110	−	0.614252i	$-0.789458\pi$
$163$	−11.8289	−	20.4883i	−0.926513	−	1.60477i	−0.137402	−	0.990515i	$-0.543875\pi$
$164$		0			0
$165$	13.9796	+	16.4807i	1.08831	+	1.28302i
$166$		0			0
$167$	2.86253			0.221509			0.110755	−	0.993848i	$-0.464673\pi$
$167$	2.86253			0.221509			0.110755	+	0.993848i	$0.464673\pi$
$168$		0			0
$169$	5.97957	−	11.5432i	0.459967	−	0.887936i
$170$		0			0
$171$	2.72649	−	16.4901i	0.208500	−	1.26103i
$172$		0			0
$173$	−22.0544			−1.67677			−0.838384	−	0.545081i	$-0.816499\pi$
$173$	−22.0544			−1.67677			−0.838384	+	0.545081i	$0.816499\pi$
$174$		0			0
$175$	−3.38560	+	5.86403i	−0.255927	+	0.443279i
$176$		0			0
$177$	−9.85191	−	11.6146i	−0.740515	−	0.873006i
$178$		0			0
$179$	−12.9994	+	22.5157i	−0.971624	+	1.68290i	−0.280968	+	0.959717i	$0.590656\pi$
$179$	−12.9994	+	22.5157i	−0.971624	+	1.68290i	−0.690655	+	0.723184i	$0.742678\pi$
$180$		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
$185$	−11.2559			−0.827552
$186$		0			0
$187$	3.48965	−	6.04424i	0.255188	−	0.441999i
$188$		0			0
$189$	−16.0181	+	9.59326i	−1.16515	+	0.697807i
$190$		0			0
$191$	−24.5054			−1.77315			−0.886574	−	0.462587i	$-0.846921\pi$
$191$	−24.5054			−1.77315			−0.886574	+	0.462587i	$0.846921\pi$
$192$		0			0
$193$	12.1382			0.873729			0.436864	−	0.899527i	$-0.356089\pi$
$193$	12.1382			0.873729			0.436864	+	0.899527i	$0.356089\pi$
$194$		0			0
$195$	12.2507	−	10.8818i	0.877290	−	0.779260i
$196$		0			0
$197$	−0.295155	+	0.511223i	−0.0210289	+	0.0364231i	−0.876348	−	0.481678i	$-0.840028\pi$
$197$	−0.295155	+	0.511223i	−0.0210289	+	0.0364231i	0.855319	+	0.518101i	$0.173361\pi$
$198$		0			0
$199$	2.11664	+	3.66613i	0.150045	+	0.259885i	0.931244	−	0.364397i	$-0.118725\pi$
$199$	2.11664	+	3.66613i	0.150045	+	0.259885i	−0.781199	+	0.624282i	$0.785392\pi$
$200$		0			0
$201$	2.47868	−	6.92491i	0.174833	−	0.488445i
$202$		0			0
$203$	−6.89374	−	11.9403i	−0.483846	−	0.838046i
$204$		0			0
$205$	−9.64220	−	16.7008i	−0.673441	−	1.16643i
$206$		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
$211$	−23.9269			−1.64720			−0.823598	−	0.567174i	$-0.808037\pi$
$211$	−23.9269			−1.64720			−0.823598	+	0.567174i	$0.808037\pi$
$212$		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
$219$	6.53314	−	18.2522i	0.441469	−	1.23337i
$220$		0			0
$221$	−4.64197	−	2.54061i	−0.312253	−	0.170900i
$222$		0			0
$223$	0.546447	+	0.946475i	0.0365928	+	0.0633806i	0.883742	−	0.467975i	$-0.155016\pi$
$223$	0.546447	+	0.946475i	0.0365928	+	0.0633806i	−0.847149	+	0.531355i	$0.821683\pi$
$224$		0			0
$225$	5.29137	−	1.99012i	0.352758	−	0.132675i
$226$		0			0
$227$	25.4767			1.69095			0.845473	−	0.534018i	$-0.179318\pi$
$227$	25.4767			1.69095			0.845473	+	0.534018i	$0.179318\pi$
$228$		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
$231$	−29.1185	+	5.29478i	−1.91586	+	0.348371i
$232$		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
$237$	11.3536	+	13.3850i	0.737497	+	0.869448i
$238$		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
$241$	−8.76586			−0.564659			−0.282329	−	0.959318i	$-0.591107\pi$
$241$	−8.76586			−0.564659			−0.282329	+	0.959318i	$0.591107\pi$
$242$		0			0
$243$	15.4184	+	2.29631i	0.989091	+	0.147308i
$244$		0			0
$245$	−7.75537	−	13.4327i	−0.495472	−	0.858183i
$246$		0			0
$247$	−17.6211	−	9.64429i	−1.12121	−	0.613651i
$248$		0			0
$249$	10.1261	+	11.9378i	0.641716	+	0.756530i
$250$		0			0
$251$	9.59084	+	16.6118i	0.605368	+	1.04853i	0.991993	+	0.126292i	$0.0403075\pi$
$251$	9.59084	+	16.6118i	0.605368	+	1.04853i	−0.386625	+	0.922237i	$0.626359\pi$
$252$		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
$257$	−13.0282			−0.812679			−0.406340	−	0.913722i	$-0.633195\pi$
$257$	−13.0282			−0.812679			−0.406340	+	0.913722i	$0.633195\pi$
$258$		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
$263$	8.93275	+	15.4720i	0.550817	+	0.954043i	0.998216	+	0.0597084i	$0.0190171\pi$
$263$	8.93275	+	15.4720i	0.550817	+	0.954043i	−0.447399	+	0.894334i	$0.647650\pi$
$264$		0			0
$265$	−2.32292	−	4.02341i	−0.142696	−	0.247156i
$266$		0			0
$267$	−14.2690	−	16.8220i	−0.873248	−	1.02949i
$268$		0			0
$269$	−0.348659	−	0.603895i	−0.0212581	−	0.0368201i	0.855201	−	0.518297i	$-0.173434\pi$
$269$	−0.348659	−	0.603895i	−0.0212581	−	0.0368201i	−0.876459	+	0.481477i	$0.840101\pi$
$270$		0			0
$271$	2.09858	−	3.63485i	0.127480	−	0.220801i	−0.795220	−	0.606321i	$-0.792645\pi$
$271$	2.09858	−	3.63485i	0.127480	−	0.220801i	0.922700	+	0.385520i	$0.125978\pi$
$272$		0			0
$273$	4.51728	+	21.9805i	0.273398	+	1.33032i
$274$		0			0
$275$	8.96109			0.540374
$276$		0			0
$277$	−25.6951			−1.54387			−0.771934	−	0.635703i	$-0.780710\pi$
$277$	−25.6951			−1.54387			−0.771934	+	0.635703i	$0.780710\pi$
$278$		0			0
$279$	−4.63513	+	28.0338i	−0.277498	+	1.67834i
$280$		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
$283$	16.5550			0.984093			0.492046	−	0.870569i	$-0.336249\pi$
$283$	16.5550			0.984093			0.492046	+	0.870569i	$0.336249\pi$
$284$		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
$293$	6.33554	−	10.9735i	0.370126	−	0.641077i	−0.619458	−	0.785029i	$-0.712648\pi$
$293$	6.33554	−	10.9735i	0.370126	−	0.641077i	0.989585	+	0.143952i	$0.0459811\pi$
$294$		0			0
$295$	−23.0716			−1.34328
$296$		0			0
$297$	21.5942	+	12.0106i	1.25302	+	0.696925i
$298$		0			0
$299$	−10.5139	+	6.39442i	−0.608032	+	0.369799i
$300$		0			0
$301$	−9.20923			−0.530811
$302$		0			0
$303$	7.41483	−	1.34828i	0.425971	−	0.0774566i
$304$		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
$309$	14.4413	−	2.62595i	0.821540	−	0.149385i
$310$		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
$315$	−4.61388	+	27.9053i	−0.259963	+	1.57229i
$316$		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
$319$	−9.12327	+	15.8020i	−0.510805	+	0.884740i
$320$		0			0
$321$	−19.9343	−	23.5009i	−1.11262	−	1.31169i
$322$		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
$327$	10.8113	−	30.2045i	0.597867	−	1.67031i
$328$		0			0
$329$	−13.9493	+	24.1608i	−0.769048	+	1.33203i
$330$		0			0
$331$	−25.3034			−1.39080			−0.695401	−	0.718622i	$-0.744773\pi$
$331$	−25.3034			−1.39080			−0.695401	+	0.718622i	$0.744773\pi$
$332$		0			0
$333$	−12.0459	+	4.53054i	−0.660111	+	0.248272i
$334$		0			0
$335$	−5.57102	−	9.64929i	−0.304377	−	0.527197i
$336$		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
$345$	−15.2604	+	2.77487i	−0.821590	+	0.149394i
$346$		0			0
$347$	−1.28436	+	2.22458i	−0.0689482	+	0.119422i	−0.898439	−	0.439099i	$-0.855298\pi$
$347$	−1.28436	+	2.22458i	−0.0689482	+	0.119422i	0.829490	+	0.558521i	$0.188631\pi$
$348$		0			0
$349$	−4.56802	−	7.91204i	−0.244520	−	0.423522i	0.717476	−	0.696583i	$-0.245297\pi$
$349$	−4.56802	−	7.91204i	−0.244520	−	0.423522i	−0.961997	+	0.273061i	$0.911964\pi$
$350$		0			0
$351$	8.73054	−	16.5764i	0.466002	−	0.884784i
$352$		0			0
$353$	3.18965	+	5.52464i	0.169768	+	0.294047i	0.938338	−	0.345718i	$-0.112365\pi$
$353$	3.18965	+	5.52464i	0.169768	+	0.294047i	−0.768570	+	0.639766i	$0.779031\pi$
$354$		0			0
$355$	12.5032	−	21.6561i	0.663600	−	1.14939i
$356$		0			0
$357$	8.98696	−	1.63415i	0.475640	−	0.0864883i
$358$		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
$367$	4.81583	+	8.34126i	0.251384	+	0.435410i	0.963907	−	0.266239i	$-0.0857809\pi$
$367$	4.81583	+	8.34126i	0.251384	+	0.435410i	−0.712523	+	0.701649i	$0.752448\pi$
$368$		0			0
$369$	−17.0410	−	13.9919i	−0.887121	−	0.728388i
$370$		0			0
$371$	6.36237			0.330318
$372$		0			0
$373$	16.8973	−	29.2670i	0.874909	−	1.51539i	0.0180502	−	0.999837i	$-0.494254\pi$
$373$	16.8973	−	29.2670i	0.874909	−	1.51539i	0.856859	−	0.515550i	$-0.172413\pi$
$374$		0			0
$375$	−4.77159	+	13.3308i	−0.246404	+	0.688399i
$376$		0			0
$377$	12.1359	+	6.64213i	0.625030	+	0.342087i
$378$		0			0
$379$	−12.7091	+	22.0129i	−0.652825	+	1.13073i	0.329610	+	0.944117i	$0.393083\pi$
$379$	−12.7091	+	22.0129i	−0.652825	+	1.13073i	−0.982434	+	0.186608i	$0.940250\pi$
$380$		0			0
$381$	6.94848	+	8.19168i	0.355981	+	0.419672i
$382$		0			0
$383$	−14.6179	+	25.3189i	−0.746938	+	1.29373i	0.202346	+	0.979314i	$0.435144\pi$
$383$	−14.6179	+	25.3189i	−0.746938	+	1.29373i	−0.949284	+	0.314420i	$0.898190\pi$
$384$		0			0
$385$	−22.4169	+	38.8273i	−1.14247	+	1.97882i
$386$		0			0
$387$	5.94235	+	4.87908i	0.302066	+	0.248018i
$388$		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
$393$	−7.17594	+	1.30484i	−0.361978	+	0.0658205i
$394$		0			0
$395$	26.5884			1.33781
$396$		0			0
$397$	13.8398	+	23.9712i	0.694597	+	1.20308i	0.970316	+	0.241840i	$0.0777508\pi$
$397$	13.8398	+	23.9712i	0.694597	+	1.20308i	−0.275719	+	0.961238i	$0.588916\pi$
$398$		0			0
$399$	34.1150	−	6.20331i	1.70788	−	0.310554i
$400$		0			0
$401$	−20.2569			−1.01158			−0.505790	−	0.862657i	$-0.668799\pi$
$401$	−20.2569			−1.01158			−0.505790	+	0.862657i	$0.668799\pi$
$402$		0			0
$403$	29.9566	+	16.3956i	1.49224	+	0.816725i
$404$		0			0
$405$	17.7615	−	15.5617i	0.882575	−	0.773269i
$406$		0			0
$407$	−20.4001			−1.01119
$408$		0			0
$409$	7.80735	−	13.5227i	0.386049	−	0.668656i	−0.605865	−	0.795567i	$-0.707173\pi$
$409$	7.80735	−	13.5227i	0.386049	−	0.668656i	0.991914	+	0.126911i	$0.0405063\pi$
$410$		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
$419$	26.5606			1.29757			0.648785	−	0.760972i	$-0.275278\pi$
$419$	26.5606			1.29757			0.648785	+	0.760972i	$0.275278\pi$
$420$		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
$423$	21.8014	−	8.19965i	1.06002	−	0.398681i
$424$		0			0
$425$	−2.76569			−0.134156
$426$		0			0
$427$	22.8968			1.10806
$428$		0			0
$429$	22.2030	−	19.7220i	1.07197	−	0.952185i
$430$		0			0
$431$	−19.3047	+	33.4367i	−0.929874	+	1.61059i	−0.146344	+	0.989234i	$0.546751\pi$
$431$	−19.3047	+	33.4367i	−0.929874	+	1.61059i	−0.783529	+	0.621355i	$0.786583\pi$
$432$		0			0
$433$	−0.943893	−	1.63487i	−0.0453606	−	0.0785668i	0.842454	−	0.538769i	$-0.181110\pi$
$433$	−0.943893	−	1.63487i	−0.0453606	−	0.0785668i	−0.887814	+	0.460202i	$0.847777\pi$
$434$		0			0
$435$	11.2799	+	13.2981i	0.540830	+	0.637594i
$436$		0			0
$437$	9.50743	+	16.4674i	0.454802	+	0.787740i
$438$		0			0
$439$	1.51096	+	2.61706i	0.0721143	+	0.124906i	0.899828	−	0.436245i	$-0.143692\pi$
$439$	1.51096	+	2.61706i	0.0721143	+	0.124906i	−0.827713	+	0.561151i	$0.810359\pi$
$440$		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
$445$	−33.4157			−1.58406
$446$		0			0
$447$	4.64270	+	5.47336i	0.219592	+	0.258881i
$448$		0			0
$449$	7.43393	+	12.8759i	0.350829	+	0.607653i	0.986395	−	0.164393i	$-0.0525665\pi$
$449$	7.43393	+	12.8759i	0.350829	+	0.607653i	−0.635566	+	0.772047i	$0.719233\pi$
$450$		0			0
$451$	−17.4754	−	30.2683i	−0.822884	−	1.42528i
$452$		0			0
$453$	0.840600	+	0.990997i	0.0394948	+	0.0465611i
$454$		0			0
$455$	29.8193	+	16.3205i	1.39795	+	0.765116i
$456$		0			0
$457$	−1.67396	−	2.89938i	−0.0783045	−	0.135627i	0.824214	−	0.566278i	$-0.191617\pi$
$457$	−1.67396	−	2.89938i	−0.0783045	−	0.135627i	−0.902519	+	0.430651i	$0.858284\pi$
$458$		0			0
$459$	−6.66470	−	3.70687i	−0.311082	−	0.173022i
$460$		0			0
$461$	14.0776			0.655659			0.327830	−	0.944737i	$-0.393683\pi$
$461$	14.0776			0.655659			0.327830	+	0.944737i	$0.393683\pi$
$462$		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
$465$	27.8437	+	32.8254i	1.29122	+	1.52224i
$466$		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
$471$	3.08601	−	0.561145i	0.142196	−	0.0258562i
$472$		0			0
$473$	6.09381	+	10.5548i	0.280194	+	0.485309i
$474$		0			0
$475$	−10.4987			−0.481714
$476$		0			0
$477$	−4.10538	−	3.37080i	−0.187972	−	0.154339i
$478$		0			0
$479$	−11.7282	−	20.3139i	−0.535876	−	0.928164i	−0.999120	−	0.0419336i	$-0.986648\pi$
$479$	−11.7282	−	20.3139i	−0.535876	−	0.928164i	0.463245	−	0.886230i	$-0.346685\pi$
$480$		0			0
$481$	0.352945	+	15.4634i	0.0160929	+	0.705072i
$482$		0			0
$483$	7.15835	−	19.9989i	0.325716	−	0.909981i
$484$		0			0
$485$	−15.8555	−	27.4626i	−0.719962	−	1.24701i
$486$		0			0
$487$	−4.07543	−	7.05885i	−0.184675	−	0.319867i	0.758792	−	0.651333i	$-0.225790\pi$
$487$	−4.07543	−	7.05885i	−0.184675	−	0.319867i	−0.943467	+	0.331466i	$0.892457\pi$
$488$		0			0
$489$	−40.3155	+	7.33079i	−1.82313	+	0.331510i
$490$		0			0
$491$	−11.1953			−0.505236			−0.252618	−	0.967566i	$-0.581292\pi$
$491$	−11.1953			−0.505236			−0.252618	+	0.967566i	$0.581292\pi$
$492$		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
$497$	17.1228	+	29.6576i	0.768064	+	1.33033i
$498$		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
$501$	1.67086	−	4.66803i	0.0746486	−	0.208552i
$502$		0			0
$503$	−7.55237	−	13.0811i	−0.336743	−	0.583257i	0.647075	−	0.762427i	$-0.275992\pi$
$503$	−7.55237	−	13.0811i	−0.336743	−	0.583257i	−0.983818	+	0.179170i	$0.942659\pi$
$504$		0			0
$505$	5.70831	−	9.88708i	0.254016	−	0.439969i
$506$		0			0
$507$	−15.3336	−	16.4888i	−0.680987	−	0.732295i
$508$		0			0
$509$	31.9139			1.41456			0.707279	−	0.706935i	$-0.249922\pi$
$509$	31.9139			1.41456			0.707279	+	0.706935i	$0.249922\pi$
$510$		0			0
$511$	40.2180			1.77914
$512$		0			0
$513$	−25.2996	−	14.0715i	−1.11700	−	0.621271i
$514$		0			0
$515$	11.1177	−	19.2564i	0.489904	−	0.848538i
$516$		0			0
$517$	36.9213			1.62380
$518$		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	−0.0610783	+	0.998133i	$0.519454\pi$
$523$	−20.4667	+	35.4494i	−0.894948	+	1.55009i	−0.833869	+	0.551962i	$0.813879\pi$
$524$		0			0
$525$	7.58650	+	8.94385i	0.331102	+	0.390342i
$526$		0			0
$527$	6.95048	−	12.0386i	0.302768	−	0.524409i
$528$		0			0
$529$	−11.3516			−0.493546
$530$		0			0
$531$	−24.6909	+	9.28640i	−1.07149	+	0.402996i
$532$		0			0
$533$	−22.6413	+	13.7702i	−0.980702	+	0.596453i
$534$		0			0
$535$	−46.6829			−2.01828
$536$		0			0
$537$	29.1293	+	34.3410i	1.25702	+	1.48193i
$538$		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
$543$	−8.76398	+	24.4847i	−0.376098	+	1.05074i
$544$		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
$549$	−14.7744	−	12.1308i	−0.630557	−	0.517731i
$550$		0			0
$551$	10.6887	−	18.5134i	0.455355	−	0.788698i
$552$		0			0
$553$	−18.2061	+	31.5339i	−0.774203	+	1.34096i
$554$		0			0
$555$	−6.57009	+	18.3554i	−0.278885	+	0.779144i
$556$		0			0
$557$	−6.49410	+	11.2481i	−0.275164	+	0.476598i	−0.970176	−	0.242400i	$-0.922065\pi$
$557$	−6.49410	+	11.2481i	−0.275164	+	0.476598i	0.695013	+	0.718997i	$0.255399\pi$
$558$		0			0
$559$	7.89520	−	4.80177i	0.333931	−	0.203093i
$560$		0			0
$561$	−7.81964	−	9.21871i	−0.330146	−	0.389214i
$562$		0			0
$563$	10.2194	−	17.7005i	0.430696	−	0.745987i	−0.566237	−	0.824242i	$-0.691601\pi$
$563$	10.2194	−	17.7005i	0.430696	−	0.745987i	0.996933	+	0.0782548i	$0.0249348\pi$
$564$		0			0
$565$	34.2377			1.44039
$566$		0			0
$567$	6.29427	+	31.7209i	0.264335	+	1.33215i
$568$		0			0
$569$	5.93957	+	10.2876i	0.249000	+	0.431280i	0.963248	−	0.268612i	$-0.0865649\pi$
$569$	5.93957	+	10.2876i	0.249000	+	0.431280i	−0.714249	+	0.699892i	$0.753232\pi$
$570$		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
$579$	7.08509	−	19.7942i	0.294446	−	0.822620i
$580$		0			0
$581$	−16.2377	+	28.1246i	−0.673655	+	1.16680i
$582$		0			0
$583$	−4.21002	−	7.29197i	−0.174361	−	0.302002i
$584$		0			0
$585$	−10.5945	−	26.3293i	−0.438030	−	1.08858i
$586$		0			0
$587$	10.6070	+	18.3719i	0.437800	+	0.758291i	0.997520	−	0.0703906i	$-0.0224246\pi$
$587$	10.6070	+	18.3719i	0.437800	+	0.758291i	−0.559720	+	0.828682i	$0.689091\pi$
$588$		0			0
$589$	26.3844	−	45.6991i	1.08715	−	1.88300i
$590$		0			0
$591$	0.661386	+	0.779720i	0.0272058	+	0.0320734i
$592$		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
$601$	−7.31500	−	12.6699i	−0.298385	−	0.516818i	0.677382	−	0.735632i	$-0.263115\pi$
$601$	−7.31500	−	12.6699i	−0.298385	−	0.516818i	−0.975767	+	0.218814i	$0.929781\pi$
$602$		0			0
$603$	−9.84588	−	8.08415i	−0.400955	−	0.329212i
$604$		0			0
$605$	30.4717			1.23885
$606$		0			0
$607$	−18.3416	+	31.7685i	−0.744461	+	1.28944i	0.205985	+	0.978555i	$0.433960\pi$
$607$	−18.3416	+	31.7685i	−0.744461	+	1.28944i	−0.950446	+	0.310889i	$0.899373\pi$
$608$		0			0
$609$	−23.4954	+	4.27229i	−0.952080	+	0.173122i
$610$		0			0
$611$	−0.638781	−	27.9867i	−0.0258423	−	1.13222i
$612$		0			0
$613$	−4.48301	+	7.76481i	−0.181067	+	0.313618i	−0.942244	−	0.334927i	$-0.891288\pi$
$613$	−4.48301	+	7.76481i	−0.181067	+	0.313618i	0.761177	+	0.648544i	$0.224622\pi$
$614$		0			0
$615$	−32.8627	+	5.97561i	−1.32515	+	0.240960i
$616$		0			0
$617$	−4.22083	+	7.31069i	−0.169924	+	0.294317i	−0.938393	−	0.345570i	$-0.887686\pi$
$617$	−4.22083	+	7.31069i	−0.169924	+	0.294317i	0.768469	+	0.639887i	$0.221019\pi$
$618$		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
$621$	−15.2145	+	9.11196i	−0.610536	+	0.365650i
$622$		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
$627$	−29.6838	−	34.9947i	−1.18546	−	1.39755i
$628$		0			0
$629$	6.29615			0.251044
$630$		0			0
$631$	8.83740	+	15.3068i	0.351811	+	0.609355i	0.986567	−	0.163358i	$-0.0522326\pi$
$631$	8.83740	+	15.3068i	0.351811	+	0.609355i	−0.634756	+	0.772713i	$0.718899\pi$
$632$		0			0
$633$	−13.9662	+	39.0184i	−0.555105	+	1.55084i
$634$		0			0
$635$	16.2722			0.645744
$636$		0			0
$637$	−18.2107	+	11.0756i	−0.721535	+	0.438830i
$638$		0			0
$639$	4.66403	−	28.2086i	0.184506	−	1.11591i
$640$		0			0
$641$	21.2243			0.838311			0.419156	−	0.907914i	$-0.362326\pi$
$641$	21.2243			0.838311			0.419156	+	0.907914i	$0.362326\pi$
$642$		0			0
$643$	−9.91286	+	17.1696i	−0.390925	+	0.677102i	−0.992572	−	0.121660i	$-0.961178\pi$
$643$	−9.91286	+	17.1696i	−0.390925	+	0.677102i	0.601647	+	0.798762i	$0.294511\pi$
$644$		0			0
$645$	11.4595	−	2.08374i	0.451217	−	0.0820473i
$646$		0			0
$647$	0.739188	−	1.28031i	0.0290605	−	0.0503342i	−0.851129	−	0.524956i	$-0.824082\pi$
$647$	0.739188	−	1.28031i	0.0290605	−	0.0503342i	0.880190	+	0.474622i	$0.157415\pi$
$648$		0			0
$649$	−41.8147			−1.64137
$650$		0			0
$651$	−57.9967	+	10.5459i	−2.27307	+	0.413324i
$652$		0			0
$653$	−11.1411			−0.435983			−0.217992	−	0.975951i	$-0.569951\pi$
$653$	−11.1411			−0.435983			−0.217992	+	0.975951i	$0.569951\pi$
$654$		0			0
$655$	−5.52440	+	9.56855i	−0.215856	+	0.373874i
$656$		0			0
$657$	−25.9511	−	21.3076i	−1.01245	−	0.831290i
$658$		0			0
$659$	4.47743			0.174416			0.0872079	−	0.996190i	$-0.472206\pi$
$659$	4.47743			0.174416			0.0872079	+	0.996190i	$0.472206\pi$
$660$		0			0
$661$	−12.5177			−0.486882			−0.243441	−	0.969916i	$-0.578276\pi$
$661$	−12.5177			−0.486882			−0.243441	+	0.969916i	$0.578276\pi$
$662$		0			0
$663$	−6.85258	+	6.08686i	−0.266132	+	0.236394i
$664$		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
$669$	1.86241	−	0.338652i	0.0720049	−	0.0130931i
$670$		0			0
$671$	−15.1510	−	26.2423i	−0.584897	−	1.01307i
$672$		0			0
$673$	8.84608	+	15.3219i	0.340991	+	0.590614i	0.984617	−	0.174726i	$-0.0559040\pi$
$673$	8.84608	+	15.3219i	0.340991	+	0.590614i	−0.643626	+	0.765340i	$0.722571\pi$
$674$		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
$679$	43.4276			1.66660
$680$		0			0
$681$	14.8708	−	41.5457i	0.569849	−	1.59203i
$682$		0			0
$683$	−23.3906	−	40.5137i	−0.895017	−	1.55021i	−0.833784	−	0.552091i	$-0.813830\pi$
$683$	−23.3906	−	40.5137i	−0.895017	−	1.55021i	−0.0612334	−	0.998123i	$-0.519503\pi$
$684$		0			0
$685$	1.52951	+	2.64918i	0.0584394	+	0.101220i
$686$		0			0
$687$	21.3772	−	3.88714i	0.815592	−	0.148304i
$688$		0			0
$689$	−5.45454	+	3.31739i	−0.207801	+	0.126383i
$690$		0			0
$691$	−14.2796	−	24.7330i	−0.543222	−	0.940888i	−0.998716	−	0.0506495i	$-0.983871\pi$
$691$	−14.2796	−	24.7330i	−0.543222	−	0.940888i	0.455494	−	0.890239i	$-0.349462\pi$
$692$		0			0
$693$	−8.36213	+	50.5752i	−0.317651	+	1.92119i
$694$		0			0
$695$	−19.6484			−0.745305
$696$		0			0
$697$	5.39349	+	9.34180i	0.204293	+	0.353846i
$698$		0			0
$699$	6.62020	−	18.4954i	0.250399	−	0.699561i
$700$		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
$705$	11.8910	−	33.2208i	0.447839	−	1.25117i
$706$		0			0
$707$	7.81740	+	13.5401i	0.294004	+	0.509229i
$708$		0			0
$709$	36.8481			1.38386			0.691931	−	0.721964i	$-0.256760\pi$
$709$	36.8481			1.38386			0.691931	+	0.721964i	$0.256760\pi$
$710$		0			0
$711$	28.4545	−	10.7019i	1.06713	−	0.401353i
$712$		0			0
$713$	−16.1630	−	27.9951i	−0.605308	−	1.04842i
$714$		0			0
$715$	−1.02654	−	44.9755i	−0.0383905	−	1.68199i
$716$		0			0
$717$	1.31997	−	0.240018i	0.0492953	−	0.00896364i
$718$		0			0
$719$	6.09570	+	10.5581i	0.227331	+	0.393749i	0.957016	−	0.290034i	$-0.0936666\pi$
$719$	6.09570	+	10.5581i	0.227331	+	0.393749i	−0.729685	+	0.683783i	$0.760333\pi$
$720$		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
$725$	7.23058			0.268537
$726$		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
$731$	−1.88075	−	3.25756i	−0.0695622	−	0.120485i
$732$		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
$735$	−26.4320	+	4.80627i	−0.974958	+	0.177282i
$736$		0			0
$737$	−10.0968	−	17.4882i	−0.371921	−	0.644187i
$738$		0			0
$739$	−7.08381	+	12.2695i	−0.260582	+	0.451341i	−0.966397	−	0.257055i	$-0.917248\pi$
$739$	−7.08381	+	12.2695i	−0.260582	+	0.451341i	0.705815	+	0.708396i	$0.250581\pi$
$740$		0			0
$741$	−26.0127	+	23.1060i	−0.955602	+	0.848821i
$742$		0			0
$743$	27.5447			1.01052			0.505259	−	0.862968i	$-0.331397\pi$
$743$	27.5447			1.01052			0.505259	+	0.862968i	$0.331397\pi$
$744$		0			0
$745$	10.8725			0.398337
$746$		0			0
$747$	25.3781	−	9.54485i	0.928534	−	0.349228i
$748$		0			0
$749$	31.9656	−	55.3661i	1.16800	−	2.02303i
$750$		0			0
$751$	−41.2700			−1.50596			−0.752982	−	0.658041i	$-0.771385\pi$
$751$	−41.2700			−1.50596			−0.752982	+	0.658041i	$0.771385\pi$
$752$		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	−0.713854	−	0.700294i	$-0.753052\pi$
$757$	6.86589	−	11.8921i	0.249545	−	0.432225i	0.963400	+	0.268069i	$0.0863856\pi$
$758$		0			0
$759$	−27.6576	+	5.02914i	−1.00391	+	0.182546i
$760$		0			0
$761$	14.5962	−	25.2814i	0.529113	−	0.916451i	−0.470311	−	0.882501i	$-0.655858\pi$
$761$	14.5962	−	25.2814i	0.529113	−	0.916451i	0.999424	−	0.0339496i	$-0.0108086\pi$
$762$		0			0
$763$	66.5544			2.40943
$764$		0			0
$765$	−10.8132	+	4.06690i	−0.390950	+	0.147039i
$766$		0			0
$767$	0.723443	+	31.6959i	0.0261220	+	1.14447i
$768$		0			0
$769$	−36.0187			−1.29887			−0.649433	−	0.760419i	$-0.724994\pi$
$769$	−36.0187			−1.29887			−0.649433	+	0.760419i	$0.724994\pi$
$770$		0			0
$771$	−7.60460	+	21.2456i	−0.273873	+	0.765142i
$772$		0			0
$773$	−26.1726	−	45.3322i	−0.941361	−	1.63049i	−0.762878	−	0.646543i	$-0.776214\pi$
$773$	−26.1726	−	45.3322i	−0.941361	−	1.63049i	−0.178483	−	0.983943i	$-0.557119\pi$
$774$		0			0
$775$	17.8482			0.641126
$776$		0			0
$777$	−17.2708	−	20.3608i	−0.619586	−	0.730440i
$778$		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
$783$	17.4241	+	9.69118i	0.622686	+	0.346335i
$784$		0			0
$785$	2.37576	−	4.11494i	0.0847947	−	0.146869i
$786$		0			0
$787$	−6.70576	+	11.6147i	−0.239035	+	0.414020i	−0.960438	−	0.278495i	$-0.910164\pi$
$787$	−6.70576	+	11.6147i	−0.239035	+	0.414020i	0.721403	+	0.692516i	$0.243498\pi$
$788$		0			0
$789$	30.4447	−	5.53593i	1.08386	−	0.197084i
$790$		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
$795$	−7.91700	+	1.43959i	−0.280787	+	0.0510571i
$796$		0			0
$797$	−10.6034	+	18.3656i	−0.375591	+	0.650542i	−0.990415	−	0.138122i	$-0.955893\pi$
$797$	−10.6034	+	18.3656i	−0.375591	+	0.650542i	0.614825	+	0.788664i	$0.289227\pi$
$798$		0			0
$799$	−11.3952			−0.403132
$800$		0			0
$801$	−35.7610	+	13.4499i	−1.26355	+	0.475230i
$802$		0			0
$803$	−26.6125	−	46.0942i	−0.939135	−	1.62663i
$804$		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	−0.909430	−	0.415858i	$-0.863481\pi$
$809$	−2.68990	+	4.65903i	−0.0945717	+	0.163803i	0.814858	+	0.579660i	$0.196815\pi$
$810$		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
$813$	−4.70253	−	5.54389i	−0.164925	−	0.194433i
$814$		0			0
$815$	−31.0369	+	53.7575i	−1.08718	+	1.88304i
$816$		0			0
$817$	−7.13944	−	12.3659i	−0.249777	−	0.432627i
$818$		0			0
$819$	38.4811	+	5.46357i	1.34464	+	0.190912i
$820$		0			0
$821$	14.7176	+	25.4917i	0.513649	+	0.889666i	0.999875	+	0.0158326i	$0.00503989\pi$
$821$	14.7176	+	25.4917i	0.513649	+	0.889666i	−0.486226	+	0.873833i	$0.661627\pi$
$822$		0			0
$823$	−1.92176	+	3.32858i	−0.0669883	+	0.116027i	−0.897574	−	0.440863i	$-0.854672\pi$
$823$	−1.92176	+	3.32858i	−0.0669883	+	0.116027i	0.830586	+	0.556890i	$0.188006\pi$
$824$		0			0
$825$	5.23060	−	14.6132i	0.182106	−	0.508765i
$826$		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	−0.999833	−	0.0182738i	$-0.994183\pi$
$829$	−13.9381	+	24.1415i	−0.484091	+	0.838470i	0.515742	+	0.856744i	$0.327516\pi$
$830$		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
$835$	−3.75538	−	6.50451i	−0.129960	−	0.225098i
$836$		0			0
$837$	43.0101	+	23.9220i	1.48665	+	0.826866i
$838$		0			0
$839$	1.01813			0.0351496			0.0175748	−	0.999846i	$-0.494405\pi$
$839$	1.01813			0.0351496			0.0175748	+	0.999846i	$0.494405\pi$
$840$		0			0
$841$	7.13856	−	12.3643i	0.246157	−	0.426357i
$842$		0			0
$843$	−15.1026	−	17.8048i	−0.520162	−	0.613229i
$844$		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
$849$	9.66317	−	26.9968i	0.331639	−	0.926528i
$850$		0			0
$851$	7.32068	−	12.6798i	0.250950	−	0.434658i
$852$		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
$855$	−41.0473	+	15.4382i	−1.40379	+	0.527974i
$856$		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
$861$	15.4153	−	43.0670i	0.525352	−	1.46772i
$862$		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
$867$	−16.6335	−	19.6095i	−0.564904	−	0.665975i
$868$		0			0
$869$	48.1884			1.63468
$870$		0			0
$871$	−13.0815	+	7.95606i	−0.443251	+	0.269581i
$872$		0			0
$873$	−28.0221	−	23.0081i	−0.948403	−	0.778705i
$874$		0			0
$875$	−29.3739			−0.993019
$876$		0			0
$877$	15.0883	−	26.1337i	0.509495	−	0.882471i	−0.490445	−	0.871472i	$-0.663166\pi$
$877$	15.0883	−	26.1337i	0.509495	−	0.882471i	0.999940	−	0.0109987i	$-0.00350106\pi$
$878$		0			0
$879$	−14.1968	−	16.7368i	−0.478845	−	0.564518i
$880$		0			0
$881$	2.07896	−	3.60087i	0.0700420	−	0.121316i	−0.828877	−	0.559430i	$-0.811020\pi$
$881$	2.07896	−	3.60087i	0.0700420	−	0.121316i	0.898919	+	0.438114i	$0.144353\pi$
$882$		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
$887$	35.1636			1.18068			0.590339	−	0.807155i	$-0.298994\pi$
$887$	35.1636			1.18068			0.590339	+	0.807155i	$0.298994\pi$
$888$		0			0
$889$	−11.1422	+	19.2989i	−0.373699	+	0.647265i
$890$		0			0
$891$	32.1906	−	28.2038i	1.07843	−	0.944864i
$892$		0			0
$893$	−43.2566			−1.44753
$894$		0			0
$895$	68.2163			2.28022
$896$		0			0
$897$	4.29064	+	20.8777i	0.143260	+	0.697087i
$898$		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
$903$	−5.37544	+	15.0178i	−0.178883	+	0.499761i
$904$		0			0
$905$	19.6977	+	34.1173i	0.654772	+	1.13410i
$906$		0			0
$907$	11.9678	+	20.7288i	0.397384	+	0.688289i	0.993402	−	0.114682i	$-0.0365849\pi$
$907$	11.9678	+	20.7288i	0.397384	+	0.688289i	−0.596019	+	0.802971i	$0.703252\pi$
$908$		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
$913$	42.9784			1.42238
$914$		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	−0.846252	−	0.532783i	$-0.821146\pi$
$919$	−26.8145	−	46.4441i	−0.884530	−	1.53205i	−0.0382782	−	0.999267i	$-0.512187\pi$
$920$		0			0
$921$	5.30352	−	14.8169i	0.174757	−	0.488233i
$922$		0			0
$923$	−30.1433	−	16.4979i	−0.992180	−	0.543034i
$924$		0			0
$925$	4.04198	+	7.00092i	0.132900	+	0.230189i
$926$		0			0
$927$	4.14720	−	25.0828i	0.136212	−	0.823826i
$928$		0			0
$929$	36.9590			1.21258			0.606292	−	0.795242i	$-0.292656\pi$
$929$	36.9590			1.21258			0.606292	+	0.795242i	$0.292656\pi$
$930$		0			0
$931$	16.4675	+	28.5226i	0.539701	+	0.934790i
$932$		0			0
$933$	8.19221	−	1.48963i	0.268201	−	0.0487684i
$934$		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
$939$	−14.6634	−	17.2869i	−0.478522	−	0.564138i
$940$		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
$943$	25.0846			0.816866
$944$		0			0
$945$	42.8130	+	23.8124i	1.39271	+	0.774616i
$946$		0			0
$947$	−8.59070	−	14.8795i	−0.279160	−	0.483520i	0.692016	−	0.721882i	$-0.256723\pi$
$947$	−8.59070	−	14.8795i	−0.279160	−	0.483520i	−0.971176	+	0.238362i	$0.923389\pi$
$948$		0			0
$949$	−34.4794	+	20.9700i	−1.11925	+	0.680716i
$950$		0			0
$951$	6.70575	+	7.90553i	0.217449	+	0.256354i
$952$		0			0
$953$	4.11751	+	7.13174i	0.133379	+	0.231020i	0.924977	−	0.380023i	$-0.124084\pi$
$953$	4.11751	+	7.13174i	0.133379	+	0.231020i	−0.791598	+	0.611042i	$0.790750\pi$
$954$		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
$959$	−4.18925			−0.135278
$960$		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
$965$	−15.9242	−	27.5816i	−0.512620	−	0.887883i
$966$		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
$969$	9.16141	+	10.8005i	0.294307	+	0.346963i
$970$		0			0
$971$	8.70378	+	15.0754i	0.279318	+	0.483792i	0.971215	−	0.238203i	$-0.0765584\pi$
$971$	8.70378	+	15.0754i	0.279318	+	0.483792i	−0.691898	+	0.721996i	$0.743225\pi$
$972$		0			0
$973$	13.4540	−	23.3030i	0.431315	−	0.747060i
$974$		0			0
$975$	−11.1674	−	3.71202i	−0.357643	−	0.118880i
$976$		0			0
$977$	48.7950			1.56109			0.780546	−	0.625099i	$-0.214941\pi$
$977$	48.7950			1.56109			0.780546	+	0.625099i	$0.214941\pi$
$978$		0			0
$979$	−60.5622			−1.93558
$980$		0			0
$981$	−42.9449	−	35.2607i	−1.37112	−	1.12579i
$982$		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
$985$	1.54886			0.0493509
$986$		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	−0.0746703	−	0.997208i	$-0.523790\pi$
$991$	26.0112	−	45.0527i	0.826273	−	1.43115i	0.900943	−	0.433938i	$-0.142876\pi$
$992$		0			0
$993$	−14.7696	+	41.2632i	−0.468700	+	1.30945i
$994$		0			0
$995$	5.55367	−	9.61924i	0.176063	−	0.304951i
$996$		0			0
$997$	61.7749			1.95643			0.978215	−	0.207594i	$-0.0665634\pi$
$997$	61.7749			1.95643			0.978215	+	0.207594i	$0.0665634\pi$
$998$		0			0
$999$	0.356909	+	22.2881i	0.0112921	+	0.705165i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.11	✓	28	13.3	even	3
468.2.j.a.373.11	yes	28	9.4	even	3
468.2.k.a.61.9	yes	28	1.1	even	1	trivial
468.2.k.a.445.9	yes	28	117.94	even	3	inner
1404.2.j.a.289.12		28	39.29	odd	6
1404.2.j.a.685.12		28	9.5	odd	6
1404.2.k.a.1153.12		28	3.2	odd	2
1404.2.k.a.1225.12		28	117.68	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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.583701 - 1.63073i) q^{3} +(-1.31191 - 2.27229i) q^{5} +3.59326 q^{7} +(-2.31859 - 1.90372i) q^{9} +(-2.37768 - 4.11827i) q^{11} +(-3.08055 + 1.87356i) q^{13} +(-4.47127 + 0.813035i) q^{15} +(0.733833 + 1.27104i) q^{17} +(2.78567 + 4.82492i) q^{19} +(2.09739 - 5.85965i) q^{21} +3.41298 q^{23} +(-0.942208 + 1.63195i) q^{25} +(-4.45782 + 2.66979i) q^{27} +(-1.91852 - 3.32297i) q^{29} +(-4.73573 - 8.20253i) q^{31} +(-8.10366 + 1.47353i) q^{33} +(-4.71403 - 8.16494i) q^{35} +(2.14495 - 3.71516i) q^{37} +(1.25715 + 6.11715i) q^{39} +7.34975 q^{41} -2.56292 q^{43} +(-1.28404 + 7.76602i) q^{45} +(-3.88207 + 6.72393i) q^{47} +5.91152 q^{49} +(2.50106 - 0.454782i) q^{51} +1.77064 q^{53} +(-6.23861 + 10.8056i) q^{55} +(9.49415 - 1.72637i) q^{57} +(4.39658 - 7.61510i) q^{59} +6.37216 q^{61} +(-8.33128 - 6.84057i) q^{63} +(8.29867 + 4.54197i) q^{65} +4.24650 q^{67} +(1.99216 - 5.56567i) q^{69} +(4.76526 + 8.25367i) q^{71} +11.1926 q^{73} +(2.11131 + 2.48906i) q^{75} +(-8.54363 - 14.7980i) q^{77} +(-5.06674 + 8.77586i) q^{79} +(1.75169 + 8.82789i) q^{81} +(-4.51894 + 7.82703i) q^{83} +(1.92544 - 3.33497i) q^{85} +(-6.53873 + 1.18897i) q^{87} +(6.36777 - 11.0293i) q^{89} +(-11.0692 + 6.73218i) q^{91} +(-16.1404 + 2.93490i) q^{93} +(7.30908 - 12.6597i) q^{95} +12.0858 q^{97} +(-2.32717 + 14.0750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{7} - 2 q^{9} - 4 q^{11} + q^{13} - 4 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} + 8 q^{23} - 14 q^{25} - 13 q^{29} + 2 q^{31} - 25 q^{33} + 3 q^{35} - q^{37} - 3 q^{39} - 8 q^{41} - 4 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) \) 28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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