LMFDB - Embedded newform 780.2.bv.a.589.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [780,2,Mod(49,780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(780, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("780.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.bv (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			589.9
Character	$\chi$	$=$	780.589
Dual form			780.2.bv.a.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-1.27982 - 1.83359i) q^{5} +(0.828751 + 1.43544i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{3} +(-1.27982 - 1.83359i) q^{5} +(0.828751 + 1.43544i) q^{7} +(0.500000 + 0.866025i) q^{9} +(5.23601 + 3.02301i) q^{11} +(-2.06206 - 2.95768i) q^{13} +(-0.191563 - 2.22785i) q^{15} +(-0.993129 + 0.573383i) q^{17} +(1.97958 - 1.14291i) q^{19} +1.65750i q^{21} +(6.70988 + 3.87395i) q^{23} +(-1.72411 + 4.69334i) q^{25} +1.00000i q^{27} +(3.60753 - 6.24842i) q^{29} -4.26033i q^{31} +(3.02301 + 5.23601i) q^{33} +(1.57135 - 3.35670i) q^{35} +(-1.58417 + 2.74387i) q^{37} +(-0.306957 - 3.59246i) q^{39} +(9.30618 + 5.37292i) q^{41} +(-2.13661 + 1.23357i) q^{43} +(0.948025 - 2.02515i) q^{45} +10.5431 q^{47} +(2.12634 - 3.68294i) q^{49} -1.14677 q^{51} -4.38252i q^{53} +(-1.15819 - 13.4696i) q^{55} +2.28582 q^{57} +(-5.77915 + 3.33660i) q^{59} +(0.365010 + 0.632216i) q^{61} +(-0.828751 + 1.43544i) q^{63} +(-2.78411 + 7.56629i) q^{65} +(-1.80561 + 3.12741i) q^{67} +(3.87395 + 6.70988i) q^{69} +(-10.6742 + 6.16273i) q^{71} -12.4953 q^{73} +(-3.83979 + 3.20250i) q^{75} +10.0213i q^{77} +1.33438 q^{79} +(-0.500000 + 0.866025i) q^{81} -6.54486 q^{83} +(2.32238 + 1.08716i) q^{85} +(6.24842 - 3.60753i) q^{87} +(-5.19861 - 3.00142i) q^{89} +(2.53664 - 5.41115i) q^{91} +(2.13017 - 3.68956i) q^{93} +(-4.62914 - 2.16701i) q^{95} +(2.98648 + 5.17274i) q^{97} +6.04602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^9	$ 24 q + 12 q^{9} + 12 q^{11} - 6 q^{15} + 24 q^{19} + 16 q^{25} + 4 q^{29} - 2 q^{35} + 8 q^{39} + 72 q^{41} - 6 q^{45} - 8 q^{49} + 8 q^{51} + 4 q^{55} + 36 q^{59} + 44 q^{61} + 10 q^{65} + 8 q^{69} + 12 q^{71} + 8 q^{75} + 8 q^{79} - 12 q^{81} + 12 q^{85} + 4 q^{91} - 24 q^{95}+O(q^{100}) $ 24 * q + 12 * q^9 + 12 * q^11 - 6 * q^15 + 24 * q^19 + 16 * q^25 + 4 * q^29 - 2 * q^35 + 8 * q^39 + 72 * q^41 - 6 * q^45 - 8 * q^49 + 8 * q^51 + 4 * q^55 + 36 * q^59 + 44 * q^61 + 10 * q^65 + 8 * q^69 + 12 * q^71 + 8 * q^75 + 8 * q^79 - 12 * q^81 + 12 * q^85 + 4 * q^91 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	−1.27982	−	1.83359i	−0.572354	−	0.820007i
$5$	−1.27982	−	1.83359i	−0.572354	−	0.820007i
$6$		0			0
$7$	0.828751	+	1.43544i	0.313238	+	0.542545i	0.979061	−	0.203565i	$-0.0652528\pi$
$7$	0.828751	+	1.43544i	0.313238	+	0.542545i	−0.665823	+	0.746110i	$0.731919\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	5.23601	+	3.02301i	1.57872	+	0.911472i	0.995039	+	0.0994860i	$0.0317199\pi$
$11$	5.23601	+	3.02301i	1.57872	+	0.911472i	0.583677	+	0.811986i	$0.301613\pi$
$12$		0			0
$13$	−2.06206	−	2.95768i	−0.571913	−	0.820314i
$13$	−2.06206	−	2.95768i	−0.571913	−	0.820314i
$14$		0			0
$15$	−0.191563	−	2.22785i	−0.0494614	−	0.575228i
$16$		0			0
$17$	−0.993129	+	0.573383i	−0.240869	+	0.139066i	−0.615576	−	0.788077i	$-0.711077\pi$
$17$	−0.993129	+	0.573383i	−0.240869	+	0.139066i	0.374707	+	0.927143i	$0.377743\pi$
$18$		0			0
$19$	1.97958	−	1.14291i	0.454146	−	0.262201i	−0.255433	−	0.966827i	$-0.582218\pi$
$19$	1.97958	−	1.14291i	0.454146	−	0.262201i	0.709580	+	0.704625i	$0.248885\pi$
$20$		0			0
$21$			1.65750i			0.361697i
$22$		0			0
$23$	6.70988	+	3.87395i	1.39911	+	0.807775i	0.994299	−	0.106627i	$-0.0340050\pi$
$23$	6.70988	+	3.87395i	1.39911	+	0.807775i	0.404808	+	0.914402i	$0.367338\pi$
$24$		0			0
$25$	−1.72411	+	4.69334i	−0.344822	+	0.938668i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	3.60753	−	6.24842i	0.669901	−	1.16030i	−0.308031	−	0.951376i	$-0.599670\pi$
$29$	3.60753	−	6.24842i	0.669901	−	1.16030i	0.977931	−	0.208926i	$-0.0669967\pi$
$30$		0			0
$31$		−	4.26033i		−	0.765178i	−0.923919	−	0.382589i	$-0.875033\pi$
$31$		−	4.26033i		−	0.765178i	0.923919	−	0.382589i	$-0.124967\pi$
$32$		0			0
$33$	3.02301	+	5.23601i	0.526239	+	0.911472i
$34$		0			0
$35$	1.57135	−	3.35670i	0.265607	−	0.567385i
$36$		0			0
$37$	−1.58417	+	2.74387i	−0.260436	+	0.451089i	−0.966358	−	0.257201i	$-0.917200\pi$
$37$	−1.58417	+	2.74387i	−0.260436	+	0.451089i	0.705922	+	0.708290i	$0.250533\pi$
$38$		0			0
$39$	−0.306957	−	3.59246i	−0.0491524	−	0.575254i
$40$		0			0
$41$	9.30618	+	5.37292i	1.45338	+	0.839110i	0.998671	−	0.0515301i	$-0.0164098\pi$
$41$	9.30618	+	5.37292i	1.45338	+	0.839110i	0.454709	+	0.890640i	$0.349743\pi$
$42$		0			0
$43$	−2.13661	+	1.23357i	−0.325830	+	0.188118i	−0.653988	−	0.756505i	$-0.726905\pi$
$43$	−2.13661	+	1.23357i	−0.325830	+	0.188118i	0.328158	+	0.944623i	$0.393572\pi$
$44$		0			0
$45$	0.948025	−	2.02515i	0.141323	−	0.301892i
$46$		0			0
$47$	10.5431			1.53787			0.768935	−	0.639326i	$-0.220787\pi$
$47$	10.5431			1.53787			0.768935	+	0.639326i	$0.220787\pi$
$48$		0			0
$49$	2.12634	−	3.68294i	0.303763	−	0.526134i
$50$		0			0
$51$	−1.14677			−0.160579
$52$		0			0
$53$		−	4.38252i		−	0.601985i	−0.953627	−	0.300992i	$-0.902682\pi$
$53$		−	4.38252i		−	0.601985i	0.953627	−	0.300992i	$-0.0973179\pi$
$54$		0			0
$55$	−1.15819	−	13.4696i	−0.156171	−	1.81624i
$56$		0			0
$57$	2.28582			0.302764
$58$		0			0
$59$	−5.77915	+	3.33660i	−0.752382	+	0.434388i	−0.826554	−	0.562858i	$-0.809702\pi$
$59$	−5.77915	+	3.33660i	−0.752382	+	0.434388i	0.0741721	+	0.997245i	$0.476369\pi$
$60$		0			0
$61$	0.365010	+	0.632216i	0.0467347	+	0.0809469i	0.888446	−	0.458980i	$-0.151785\pi$
$61$	0.365010	+	0.632216i	0.0467347	+	0.0809469i	−0.841712	+	0.539927i	$0.818452\pi$
$62$		0			0
$63$	−0.828751	+	1.43544i	−0.104413	+	0.180848i
$64$		0			0
$65$	−2.78411	+	7.56629i	−0.345326	+	0.938483i
$66$		0			0
$67$	−1.80561	+	3.12741i	−0.220591	+	0.382075i	−0.954988	−	0.296646i	$-0.904132\pi$
$67$	−1.80561	+	3.12741i	−0.220591	+	0.382075i	0.734397	+	0.678720i	$0.237465\pi$
$68$		0			0
$69$	3.87395	+	6.70988i	0.466369	+	0.807775i
$70$		0			0
$71$	−10.6742	+	6.16273i	−1.26679	+	0.731382i	−0.974379	−	0.224911i	$-0.927791\pi$
$71$	−10.6742	+	6.16273i	−1.26679	+	0.731382i	−0.292411	+	0.956293i	$0.594458\pi$
$72$		0			0
$73$	−12.4953			−1.46247			−0.731235	−	0.682126i	$-0.761056\pi$
$73$	−12.4953			−1.46247			−0.731235	+	0.682126i	$0.761056\pi$
$74$		0			0
$75$	−3.83979	+	3.20250i	−0.443381	+	0.369792i
$76$		0			0
$77$			10.0213i			1.14203i
$78$		0			0
$79$	1.33438			0.150129			0.0750646	−	0.997179i	$-0.476084\pi$
$79$	1.33438			0.150129			0.0750646	+	0.997179i	$0.476084\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−6.54486			−0.718392			−0.359196	−	0.933262i	$-0.616949\pi$
$83$	−6.54486			−0.718392			−0.359196	+	0.933262i	$0.616949\pi$
$84$		0			0
$85$	2.32238	+	1.08716i	0.251897	+	0.117919i
$86$		0			0
$87$	6.24842	−	3.60753i	0.669901	−	0.386767i
$88$		0			0
$89$	−5.19861	−	3.00142i	−0.551051	−	0.318150i	0.198495	−	0.980102i	$-0.436395\pi$
$89$	−5.19861	−	3.00142i	−0.551051	−	0.318150i	−0.749546	+	0.661952i	$0.769728\pi$
$90$		0			0
$91$	2.53664	−	5.41115i	0.265912	−	0.567242i
$92$		0			0
$93$	2.13017	−	3.68956i	0.220888	−	0.382589i
$94$		0			0
$95$	−4.62914	−	2.16701i	−0.474939	−	0.222331i
$96$		0			0
$97$	2.98648	+	5.17274i	0.303231	+	0.525212i	0.976866	−	0.213853i	$-0.0686012\pi$
$97$	2.98648	+	5.17274i	0.303231	+	0.525212i	−0.673635	+	0.739064i	$0.735268\pi$
$98$		0			0
$99$			6.04602i			0.607648i
$100$		0			0
$101$	−0.102016	+	0.176697i	−0.0101510	+	0.0175820i	−0.871056	−	0.491183i	$-0.836565\pi$
$101$	−0.102016	+	0.176697i	−0.0101510	+	0.0175820i	0.860905	+	0.508765i	$0.169898\pi$
$102$		0			0
$103$		−	3.25947i		−	0.321165i	−0.987022	−	0.160582i	$-0.948663\pi$
$103$		−	3.25947i		−	0.321165i	0.987022	−	0.160582i	$-0.0513373\pi$
$104$		0			0
$105$	3.03918	−	2.12131i	0.296594	−	0.207018i
$106$		0			0
$107$	3.03801	+	1.75400i	0.293695	+	0.169565i	0.639607	−	0.768702i	$-0.279097\pi$
$107$	3.03801	+	1.75400i	0.293695	+	0.169565i	−0.345912	+	0.938267i	$0.612430\pi$
$108$		0			0
$109$		−	11.5163i		−	1.10307i	−0.834153	−	0.551533i	$-0.814043\pi$
$109$		−	11.5163i		−	1.10307i	0.834153	−	0.551533i	$-0.185957\pi$
$110$		0			0
$111$	−2.74387	+	1.58417i	−0.260436	+	0.150363i
$112$		0			0
$113$	0.167049	−	0.0964457i	0.0157146	−	0.00907284i	−0.492122	−	0.870526i	$-0.663779\pi$
$113$	0.167049	−	0.0964457i	0.0157146	−	0.00907284i	0.507837	+	0.861453i	$0.330445\pi$
$114$		0			0
$115$	−1.48421	−	17.2612i	−0.138403	−	1.60961i
$116$		0			0
$117$	1.53040	−	3.26464i	0.141485	−	0.301816i
$118$		0			0
$119$	−1.64611	−	0.950384i	−0.150899	−	0.0871215i
$120$		0			0
$121$	12.7772	+	22.1307i	1.16156	+	2.01189i
$122$		0			0
$123$	5.37292	+	9.30618i	0.484460	+	0.839110i
$124$		0			0
$125$	10.8122	−	2.84533i	0.967074	−	0.254494i
$126$		0			0
$127$	−16.6860	−	9.63368i	−1.48064	−	0.854851i	−0.480885	−	0.876783i	$-0.659685\pi$
$127$	−16.6860	−	9.63368i	−1.48064	−	0.854851i	−0.999759	+	0.0219328i	$0.993018\pi$
$128$		0			0
$129$	−2.46715			−0.217220
$130$		0			0
$131$	−3.62693			−0.316886			−0.158443	−	0.987368i	$-0.550647\pi$
$131$	−3.62693			−0.316886			−0.158443	+	0.987368i	$0.550647\pi$
$132$		0			0
$133$	3.28115	+	1.89437i	0.284512	+	0.164263i
$134$		0			0
$135$	1.83359	−	1.27982i	0.157810	−	0.110150i
$136$		0			0
$137$	−4.49658	−	7.78830i	−0.384169	−	0.665400i	0.607485	−	0.794331i	$-0.292179\pi$
$137$	−4.49658	−	7.78830i	−0.384169	−	0.665400i	−0.991653	+	0.128932i	$0.958845\pi$
$138$		0			0
$139$	−5.32861	−	9.22941i	−0.451966	−	0.782829i	0.546542	−	0.837432i	$-0.315944\pi$
$139$	−5.32861	−	9.22941i	−0.451966	−	0.782829i	−0.998508	+	0.0546031i	$0.982611\pi$
$140$		0			0
$141$	9.13060	+	5.27156i	0.768935	+	0.443945i
$142$		0			0
$143$	−1.85587	−	21.7201i	−0.155195	−	1.81633i
$144$		0			0
$145$	−16.0740	+	1.38214i	−1.33488	+	0.114780i
$146$		0			0
$147$	3.68294	−	2.12634i	0.303763	−	0.175378i
$148$		0			0
$149$	−18.7162	+	10.8058i	−1.53329	+	0.885245i	−0.534083	+	0.845432i	$0.679343\pi$
$149$	−18.7162	+	10.8058i	−1.53329	+	0.885245i	−0.999207	+	0.0398134i	$0.987324\pi$
$150$		0			0
$151$			17.2597i			1.40458i	0.711892	+	0.702289i	$0.247838\pi$
$151$			17.2597i			1.40458i	−0.711892	+	0.702289i	$0.752162\pi$
$152$		0			0
$153$	−0.993129	−	0.573383i	−0.0802897	−	0.0463553i
$154$		0			0
$155$	−7.81170	+	5.45247i	−0.627451	+	0.437953i
$156$		0			0
$157$		−	21.4448i		−	1.71148i	−0.517405	−	0.855741i	$-0.673102\pi$
$157$		−	21.4448i		−	1.71148i	0.517405	−	0.855741i	$-0.326898\pi$
$158$		0			0
$159$	2.19126	−	3.79537i	0.173778	−	0.300992i
$160$		0			0
$161$			12.8422i			1.01210i
$162$		0			0
$163$	−7.09876	−	12.2954i	−0.556018	−	0.963051i	−0.997824	−	0.0659406i	$-0.978995\pi$
$163$	−7.09876	−	12.2954i	−0.556018	−	0.963051i	0.441806	−	0.897111i	$-0.354338\pi$
$164$		0			0
$165$	5.73178	−	12.2441i	0.446219	−	0.953204i
$166$		0			0
$167$	3.18682	−	5.51973i	0.246603	−	0.427129i	−0.715978	−	0.698123i	$-0.754019\pi$
$167$	3.18682	−	5.51973i	0.246603	−	0.427129i	0.962581	+	0.270994i	$0.0873522\pi$
$168$		0			0
$169$	−4.49579	+	12.1979i	−0.345830	+	0.938297i
$170$		0			0
$171$	1.97958	+	1.14291i	0.151382	+	0.0874005i
$172$		0			0
$173$	14.9809	−	8.64924i	1.13898	−	0.657589i	0.192801	−	0.981238i	$-0.438243\pi$
$173$	14.9809	−	8.64924i	1.13898	−	0.657589i	0.946177	+	0.323648i	$0.104910\pi$
$174$		0			0
$175$	−8.16586	+	1.41475i	−0.617281	+	0.106945i
$176$		0			0
$177$	−6.67319			−0.501588
$178$		0			0
$179$	5.19861	−	9.00425i	0.388562	−	0.673010i	−0.603694	−	0.797216i	$-0.706305\pi$
$179$	5.19861	−	9.00425i	0.388562	−	0.673010i	0.992256	+	0.124206i	$0.0396385\pi$
$180$		0			0
$181$	−10.0711			−0.748582			−0.374291	−	0.927311i	$-0.622114\pi$
$181$	−10.0711			−0.748582			−0.374291	+	0.927311i	$0.622114\pi$
$182$		0			0
$183$			0.730020i			0.0539646i
$184$		0			0
$185$	7.05859	−	0.606938i	0.518958	−	0.0446229i
$186$		0			0
$187$	−6.93337			−0.507018
$188$		0			0
$189$	−1.43544	+	0.828751i	−0.104413	+	0.0602828i
$190$		0			0
$191$	10.3999	+	18.0132i	0.752513	+	1.30339i	0.946601	+	0.322407i	$0.104492\pi$
$191$	10.3999	+	18.0132i	0.752513	+	1.30339i	−0.194088	+	0.980984i	$0.562175\pi$
$192$		0			0
$193$	−13.7522	+	23.8195i	−0.989904	+	1.71456i	−0.372205	+	0.928151i	$0.621398\pi$
$193$	−13.7522	+	23.8195i	−0.989904	+	1.71456i	−0.617700	+	0.786414i	$0.711935\pi$
$194$		0			0
$195$	−6.19425	+	5.16054i	−0.443580	+	0.369554i
$196$		0			0
$197$	−10.7068	+	18.5448i	−0.762831	+	1.32126i	0.178555	+	0.983930i	$0.442858\pi$
$197$	−10.7068	+	18.5448i	−0.762831	+	1.32126i	−0.941386	+	0.337332i	$0.890475\pi$
$198$		0			0
$199$	−12.6961	−	21.9903i	−0.900005	−	1.55885i	−0.827486	−	0.561487i	$-0.810230\pi$
$199$	−12.6961	−	21.9903i	−0.900005	−	1.55885i	−0.0725188	−	0.997367i	$-0.523104\pi$
$200$		0			0
$201$	−3.12741	+	1.80561i	−0.220591	+	0.127358i
$202$		0			0
$203$	11.9590			0.839355
$204$		0			0
$205$	−2.05851	−	23.9401i	−0.143772	−	1.67205i
$206$		0			0
$207$			7.74791i			0.538517i
$208$		0			0
$209$	13.8201			0.955957
$210$		0			0
$211$	−0.926303	+	1.60440i	−0.0637693	+	0.110452i	−0.896147	−	0.443756i	$-0.853646\pi$
$211$	−0.926303	+	1.60440i	−0.0637693	+	0.110452i	0.832378	+	0.554208i	$0.186979\pi$
$212$		0			0
$213$	−12.3255			−0.844527
$214$		0			0
$215$	4.99635	+	2.33892i	0.340748	+	0.159513i
$216$		0			0
$217$	6.11544	−	3.53075i	0.415143	−	0.239683i
$218$		0			0
$219$	−10.8213	−	6.24767i	−0.731235	−	0.422179i
$220$		0			0
$221$	3.74378	+	1.75501i	0.251834	+	0.118055i
$222$		0			0
$223$	−5.24904	+	9.09160i	−0.351502	+	0.608819i	−0.986513	−	0.163684i	$-0.947662\pi$
$223$	−5.24904	+	9.09160i	−0.351502	+	0.608819i	0.635011	+	0.772503i	$0.280995\pi$
$224$		0			0
$225$	−4.92661	+	0.853546i	−0.328440	+	0.0569031i
$226$		0			0
$227$	−4.88536	−	8.46169i	−0.324252	−	0.561622i	0.657108	−	0.753796i	$-0.271779\pi$
$227$	−4.88536	−	8.46169i	−0.324252	−	0.561622i	−0.981361	+	0.192174i	$0.938446\pi$
$228$		0			0
$229$			16.9351i			1.11910i	0.828796	+	0.559550i	$0.189026\pi$
$229$			16.9351i			1.11910i	−0.828796	+	0.559550i	$0.810974\pi$
$230$		0			0
$231$	−5.01065	+	8.67869i	−0.329676	+	0.571016i
$232$		0			0
$233$		−	19.7938i		−	1.29674i	−0.761327	−	0.648368i	$-0.775452\pi$
$233$		−	19.7938i		−	1.29674i	0.761327	−	0.648368i	$-0.224548\pi$
$234$		0			0
$235$	−13.4933	−	19.3318i	−0.880206	−	1.26106i
$236$		0			0
$237$	1.15560	+	0.667188i	0.0750646	+	0.0433385i
$238$		0			0
$239$			1.00847i			0.0652328i	0.999468	+	0.0326164i	$0.0103840\pi$
$239$			1.00847i			0.0652328i	−0.999468	+	0.0326164i	$0.989616\pi$
$240$		0			0
$241$	7.67505	−	4.43119i	0.494393	−	0.285438i	−0.232002	−	0.972715i	$-0.574528\pi$
$241$	7.67505	−	4.43119i	0.494393	−	0.285438i	0.726395	+	0.687277i	$0.241194\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−9.47434	+	0.814658i	−0.605293	+	0.0520466i
$246$		0			0
$247$	−7.46238	−	3.49821i	−0.474820	−	0.222586i
$248$		0			0
$249$	−5.66801	−	3.27243i	−0.359196	−	0.207382i
$250$		0			0
$251$	1.40347	+	2.43088i	0.0885863	+	0.153436i	0.906914	−	0.421316i	$-0.138432\pi$
$251$	1.40347	+	2.43088i	0.0885863	+	0.153436i	−0.818327	+	0.574752i	$0.805098\pi$
$252$		0			0
$253$	23.4220	+	40.5681i	1.47253	+	2.55049i
$254$		0			0
$255$	1.46766	+	2.10270i	0.0919082	+	0.131676i
$256$		0			0
$257$	0.342236	+	0.197590i	0.0213481	+	0.0123253i	0.510636	−	0.859797i	$-0.329410\pi$
$257$	0.342236	+	0.197590i	0.0213481	+	0.0123253i	−0.489288	+	0.872122i	$0.662743\pi$
$258$		0			0
$259$	−5.25154			−0.326315
$260$		0			0
$261$	7.21505			0.446601
$262$		0			0
$263$	−21.2529	−	12.2704i	−1.31051	−	0.756623i	−0.328330	−	0.944563i	$-0.606486\pi$
$263$	−21.2529	−	12.2704i	−1.31051	−	0.756623i	−0.982181	+	0.187940i	$0.939819\pi$
$264$		0			0
$265$	−8.03574	+	5.60884i	−0.493632	+	0.344548i
$266$		0			0
$267$	−3.00142	−	5.19861i	−0.183684	−	0.318150i
$268$		0			0
$269$	6.07730	+	10.5262i	0.370540	+	0.641793i	0.989649	−	0.143512i	$-0.0458395\pi$
$269$	6.07730	+	10.5262i	0.370540	+	0.641793i	−0.619109	+	0.785305i	$0.712506\pi$
$270$		0			0
$271$	−3.19227	−	1.84306i	−0.193917	−	0.111958i	0.399898	−	0.916560i	$-0.369046\pi$
$271$	−3.19227	−	1.84306i	−0.193917	−	0.111958i	−0.593815	+	0.804602i	$0.702379\pi$
$272$		0			0
$273$	4.90237	−	3.41787i	0.296705	−	0.206859i
$274$		0			0
$275$	−23.2155	+	19.3624i	−1.39995	+	1.16759i
$276$		0			0
$277$	−0.697843	+	0.402900i	−0.0419293	+	0.0242079i	−0.520818	−	0.853668i	$-0.674373\pi$
$277$	−0.697843	+	0.402900i	−0.0419293	+	0.0242079i	0.478889	+	0.877876i	$0.341040\pi$
$278$		0			0
$279$	3.68956	−	2.13017i	0.220888	−	0.127530i
$280$		0			0
$281$			0.360243i			0.0214903i	0.999942	+	0.0107452i	$0.00342036\pi$
$281$			0.360243i			0.0214903i	−0.999942	+	0.0107452i	$0.996580\pi$
$282$		0			0
$283$	17.6039	+	10.1636i	1.04644	+	0.604163i	0.921651	−	0.388021i	$-0.126841\pi$
$283$	17.6039	+	10.1636i	1.04644	+	0.604163i	0.124790	+	0.992183i	$0.460174\pi$
$284$		0			0
$285$	−2.92544	−	4.19126i	−0.173288	−	0.248269i
$286$		0			0
$287$			17.8113i			1.05137i
$288$		0			0
$289$	−7.84246	+	13.5835i	−0.461321	+	0.799032i
$290$		0			0
$291$			5.97296i			0.350141i
$292$		0			0
$293$	−8.48753	−	14.7008i	−0.495847	−	0.858832i	0.504142	−	0.863621i	$-0.331809\pi$
$293$	−8.48753	−	14.7008i	−0.495847	−	0.858832i	−0.999989	+	0.00478898i	$0.998476\pi$
$294$		0			0
$295$	13.5142	+	6.32635i	0.786830	+	0.368335i
$296$		0			0
$297$	−3.02301	+	5.23601i	−0.175413	+	0.303824i
$298$		0			0
$299$	−2.37827	−	27.8340i	−0.137539	−	1.60968i
$300$		0			0
$301$	−3.54144	−	2.04465i	−0.204125	−	0.117852i
$302$		0			0
$303$	−0.176697	+	0.102016i	−0.0101510	+	0.00586067i
$304$		0			0
$305$	0.692077	−	1.47840i	0.0396282	−	0.0846531i
$306$		0			0
$307$	17.1770			0.980346			0.490173	−	0.871625i	$-0.336934\pi$
$307$	17.1770			0.980346			0.490173	+	0.871625i	$0.336934\pi$
$308$		0			0
$309$	1.62973	−	2.82278i	0.0927123	−	0.160582i
$310$		0			0
$311$	−18.4174			−1.04435			−0.522176	−	0.852837i	$-0.674880\pi$
$311$	−18.4174			−1.04435			−0.522176	+	0.852837i	$0.674880\pi$
$312$		0			0
$313$		−	8.10571i		−	0.458162i	−0.973407	−	0.229081i	$-0.926428\pi$
$313$		−	8.10571i		−	0.458162i	0.973407	−	0.229081i	$-0.0735721\pi$
$314$		0			0
$315$	3.69266	−	0.317516i	0.208058	−	0.0178900i
$316$		0			0
$317$	−4.06294			−0.228197			−0.114099	−	0.993469i	$-0.536398\pi$
$317$	−4.06294			−0.228197			−0.114099	+	0.993469i	$0.536398\pi$
$318$		0			0
$319$	37.7781	−	21.8112i	2.11517	−	1.22119i
$320$		0			0
$321$	1.75400	+	3.03801i	0.0978985	+	0.169565i
$322$		0			0
$323$	−1.31065	+	2.27011i	−0.0729265	+	0.126312i
$324$		0			0
$325$	17.4366	−	4.57859i	0.967211	−	0.253974i
$326$		0			0
$327$	5.75817	−	9.97344i	0.318428	−	0.551533i
$328$		0			0
$329$	8.73761	+	15.1340i	0.481720	+	0.834364i
$330$		0			0
$331$	17.3971	−	10.0442i	0.956233	−	0.552081i	0.0612213	−	0.998124i	$-0.480500\pi$
$331$	17.3971	−	10.0442i	0.956233	−	0.552081i	0.895012	+	0.446043i	$0.147167\pi$
$332$		0			0
$333$	−3.16834			−0.173624
$334$		0			0
$335$	8.04526	−	0.691778i	0.439560	−	0.0377959i
$336$		0			0
$337$			3.81854i			0.208009i	0.994577	+	0.104005i	$0.0331657\pi$
$337$			3.81854i			0.208009i	−0.994577	+	0.104005i	$0.966834\pi$
$338$		0			0
$339$	0.192891			0.0104764
$340$		0			0
$341$	12.8790	−	22.3071i	0.697438	−	1.20800i
$342$		0			0
$343$	18.6513			1.00708
$344$		0			0
$345$	7.34521	−	15.6907i	0.395453	−	0.844759i
$346$		0			0
$347$	28.1142	−	16.2317i	1.50925	−	0.871365i	0.509307	−	0.860585i	$-0.329902\pi$
$347$	28.1142	−	16.2317i	1.50925	−	0.871365i	0.999942	−	0.0107803i	$-0.00343155\pi$
$348$		0			0
$349$	−12.6256	−	7.28941i	−0.675834	−	0.390193i	0.122449	−	0.992475i	$-0.460925\pi$
$349$	−12.6256	−	7.28941i	−0.675834	−	0.390193i	−0.798284	+	0.602282i	$0.794258\pi$
$350$		0			0
$351$	2.95768	−	2.06206i	0.157870	−	0.110065i
$352$		0			0
$353$	10.3335	−	17.8982i	0.549999	−	0.952626i	−0.448275	−	0.893896i	$-0.647962\pi$
$353$	10.3335	−	17.8982i	0.549999	−	0.952626i	0.998274	−	0.0587300i	$-0.0187051\pi$
$354$		0			0
$355$	24.9610	+	11.6849i	1.32479	+	0.620167i
$356$		0			0
$357$	−0.950384	−	1.64611i	−0.0502996	−	0.0871215i
$358$		0			0
$359$		−	5.82021i		−	0.307179i	−0.988135	−	0.153589i	$-0.950917\pi$
$359$		−	5.82021i		−	0.307179i	0.988135	−	0.153589i	$-0.0490833\pi$
$360$		0			0
$361$	−6.88751	+	11.9295i	−0.362501	+	0.627870i
$362$		0			0
$363$			25.5544i			1.34126i
$364$		0			0
$365$	15.9918	+	22.9114i	0.837050	+	1.19924i
$366$		0			0
$367$	−12.3165	−	7.11095i	−0.642918	−	0.371189i	0.142820	−	0.989749i	$-0.454383\pi$
$367$	−12.3165	−	7.11095i	−0.642918	−	0.371189i	−0.785738	+	0.618560i	$0.787716\pi$
$368$		0			0
$369$			10.7458i			0.559407i
$370$		0			0
$371$	6.29083	−	3.63201i	0.326604	−	0.188565i
$372$		0			0
$373$	28.2085	−	16.2862i	1.46058	−	0.843266i	0.461542	−	0.887119i	$-0.347296\pi$
$373$	28.2085	−	16.2862i	1.46058	−	0.843266i	0.999038	+	0.0438524i	$0.0139631\pi$
$374$		0			0
$375$	10.7863	+	2.94199i	0.557003	+	0.151923i
$376$		0			0
$377$	−25.9198	+	2.21471i	−1.33494	+	0.114063i
$378$		0			0
$379$	25.5125	+	14.7296i	1.31049	+	0.756611i	0.982177	−	0.187959i	$-0.0601872\pi$
$379$	25.5125	+	14.7296i	1.31049	+	0.756611i	0.328311	+	0.944570i	$0.393520\pi$
$380$		0			0
$381$	−9.63368	−	16.6860i	−0.493548	−	0.854851i
$382$		0			0
$383$	15.7867	+	27.3433i	0.806660	+	1.39718i	0.915164	+	0.403081i	$0.132061\pi$
$383$	15.7867	+	27.3433i	0.806660	+	1.39718i	−0.108504	+	0.994096i	$0.534606\pi$
$384$		0			0
$385$	18.3749	−	12.8255i	0.936474	−	0.653646i
$386$		0			0
$387$	−2.13661	−	1.23357i	−0.108610	−	0.0627061i
$388$		0			0
$389$	22.6754			1.14969			0.574843	−	0.818263i	$-0.305063\pi$
$389$	22.6754			1.14969			0.574843	+	0.818263i	$0.305063\pi$
$390$		0			0
$391$	−8.88504			−0.449336
$392$		0			0
$393$	−3.14101	−	1.81346i	−0.158443	−	0.0914772i
$394$		0			0
$395$	−1.70777	−	2.44670i	−0.0859270	−	0.123107i
$396$		0			0
$397$	6.11707	+	10.5951i	0.307007	+	0.531752i	0.977706	−	0.209978i	$-0.0673392\pi$
$397$	6.11707	+	10.5951i	0.307007	+	0.531752i	−0.670699	+	0.741730i	$0.734006\pi$
$398$		0			0
$399$	1.89437	+	3.28115i	0.0948374	+	0.164263i
$400$		0			0
$401$	−15.1495	−	8.74659i	−0.756532	−	0.436784i	0.0715175	−	0.997439i	$-0.477216\pi$
$401$	−15.1495	−	8.74659i	−0.756532	−	0.436784i	−0.828049	+	0.560656i	$0.810549\pi$
$402$		0			0
$403$	−12.6007	+	8.78507i	−0.627686	+	0.437616i
$404$		0			0
$405$	2.22785	−	0.191563i	0.110703	−	0.00951884i
$406$		0			0
$407$	−16.5895	+	9.57794i	−0.822310	+	0.474761i
$408$		0			0
$409$	−31.6025	+	18.2457i	−1.56264	+	0.902192i	−0.565654	+	0.824643i	$0.691376\pi$
$409$	−31.6025	+	18.2457i	−1.56264	+	0.902192i	−0.996989	+	0.0775493i	$0.975290\pi$
$410$		0			0
$411$		−	8.99316i		−	0.443600i
$412$		0			0
$413$	−9.57896	−	5.53041i	−0.471350	−	0.272134i
$414$		0			0
$415$	8.37626	+	12.0006i	0.411174	+	0.589086i
$416$		0			0
$417$		−	10.6572i		−	0.521886i
$418$		0			0
$419$	−0.105105	+	0.182048i	−0.00513472	+	0.00889360i	−0.868581	−	0.495547i	$-0.834968\pi$
$419$	−0.105105	+	0.182048i	−0.00513472	+	0.00889360i	0.863447	+	0.504440i	$0.168301\pi$
$420$		0			0
$421$		−	8.61066i		−	0.419658i	−0.977738	−	0.209829i	$-0.932709\pi$
$421$		−	8.61066i		−	0.419658i	0.977738	−	0.209829i	$-0.0672907\pi$
$422$		0			0
$423$	5.27156	+	9.13060i	0.256312	+	0.443945i
$424$		0			0
$425$	−0.978818	−	5.64967i	−0.0474797	−	0.274049i
$426$		0			0
$427$	−0.605005	+	1.04790i	−0.0292782	+	0.0507114i
$428$		0			0
$429$	9.25282	−	19.7381i	0.446730	−	0.952964i
$430$		0			0
$431$	15.3283	+	8.84980i	0.738338	+	0.426280i	0.821465	−	0.570259i	$-0.193157\pi$
$431$	15.3283	+	8.84980i	0.738338	+	0.426280i	−0.0831267	+	0.996539i	$0.526491\pi$
$432$		0			0
$433$	−8.06065	+	4.65382i	−0.387370	+	0.223648i	−0.681020	−	0.732265i	$-0.738463\pi$
$433$	−8.06065	+	4.65382i	−0.387370	+	0.223648i	0.293650	+	0.955913i	$0.405130\pi$
$434$		0			0
$435$	−14.6116	−	6.84005i	−0.700572	−	0.327955i
$436$		0			0
$437$	17.7103			0.847199
$438$		0			0
$439$	6.22475	−	10.7816i	0.297091	−	0.514577i	−0.678378	−	0.734713i	$-0.737317\pi$
$439$	6.22475	−	10.7816i	0.297091	−	0.514577i	0.975469	+	0.220136i	$0.0706502\pi$
$440$		0			0
$441$	4.25269			0.202509
$442$		0			0
$443$		−	3.86088i		−	0.183436i	−0.995785	−	0.0917180i	$-0.970764\pi$
$443$		−	3.86088i		−	0.183436i	0.995785	−	0.0917180i	$-0.0292358\pi$
$444$		0			0
$445$	1.14992	+	13.3734i	0.0545115	+	0.633960i
$446$		0			0
$447$	−21.6116			−1.02219
$448$		0			0
$449$	−9.65851	+	5.57634i	−0.455813	+	0.263164i	−0.710282	−	0.703917i	$-0.751433\pi$
$449$	−9.65851	+	5.57634i	−0.455813	+	0.263164i	0.254469	+	0.967081i	$0.418099\pi$
$450$		0			0
$451$	32.4848	+	56.2654i	1.52965	+	2.64943i
$452$		0			0
$453$	−8.62987	+	14.9474i	−0.405467	+	0.702289i
$454$		0			0
$455$	−13.1683	+	2.27415i	−0.617338	+	0.106614i
$456$		0			0
$457$	0.647022	−	1.12068i	0.0302664	−	0.0524230i	−0.850495	−	0.525982i	$-0.823698\pi$
$457$	0.647022	−	1.12068i	0.0302664	−	0.0524230i	0.880762	+	0.473559i	$0.157031\pi$
$458$		0			0
$459$	−0.573383	−	0.993129i	−0.0267632	−	0.0463553i
$460$		0			0
$461$	13.9344	−	8.04505i	0.648991	−	0.374695i	−0.139078	−	0.990281i	$-0.544414\pi$
$461$	13.9344	−	8.04505i	0.648991	−	0.374695i	0.788070	+	0.615586i	$0.211081\pi$
$462$		0			0
$463$	−18.9707			−0.881645			−0.440823	−	0.897594i	$-0.645313\pi$
$463$	−18.9707			−0.881645			−0.440823	+	0.897594i	$0.645313\pi$
$464$		0			0
$465$	−9.49137	+	0.816122i	−0.440152	+	0.0378467i
$466$		0			0
$467$			33.7236i			1.56054i	0.625441	+	0.780272i	$0.284919\pi$
$467$			33.7236i			1.56054i	−0.625441	+	0.780272i	$0.715081\pi$
$468$		0			0
$469$	−5.98562			−0.276390
$470$		0			0
$471$	10.7224	−	18.5717i	0.494062	−	0.855741i
$472$		0			0
$473$	−14.9164			−0.685858
$474$		0			0
$475$	1.95105	+	11.2613i	0.0895204	+	0.516705i
$476$		0			0
$477$	3.79537	−	2.19126i	0.173778	−	0.100331i
$478$		0			0
$479$	2.68929	+	1.55266i	0.122877	+	0.0709429i	0.560179	−	0.828372i	$-0.310733\pi$
$479$	2.68929	+	1.55266i	0.122877	+	0.0709429i	−0.437302	+	0.899315i	$0.644066\pi$
$480$		0			0
$481$	11.3822	−	0.972544i	0.518982	−	0.0443442i
$482$		0			0
$483$	−6.42108	+	11.1216i	−0.292169	+	0.506052i
$484$		0			0
$485$	5.66252	−	12.0962i	0.257122	−	0.549259i
$486$		0			0
$487$	1.58427	+	2.74404i	0.0717902	+	0.124344i	0.899686	−	0.436538i	$-0.143795\pi$
$487$	1.58427	+	2.74404i	0.0717902	+	0.124344i	−0.827896	+	0.560882i	$0.810462\pi$
$488$		0			0
$489$		−	14.1975i		−	0.642034i
$490$		0			0
$491$	−13.0168	+	22.5458i	−0.587440	+	1.01748i	0.407126	+	0.913372i	$0.366531\pi$
$491$	−13.0168	+	22.5458i	−0.587440	+	1.01748i	−0.994566	+	0.104105i	$0.966802\pi$
$492$		0			0
$493$			8.27398i			0.372641i
$494$		0			0
$495$	11.0859	−	7.73783i	0.498275	−	0.347790i
$496$		0			0
$497$	−17.6924	−	10.2147i	−0.793615	−	0.458194i
$498$		0			0
$499$		−	19.4095i		−	0.868888i	−0.900699	−	0.434444i	$-0.856945\pi$
$499$		−	19.4095i		−	0.868888i	0.900699	−	0.434444i	$-0.143055\pi$
$500$		0			0
$501$	5.51973	−	3.18682i	0.246603	−	0.142376i
$502$		0			0
$503$	33.0342	−	19.0723i	1.47292	−	0.850391i	0.473385	−	0.880856i	$-0.343032\pi$
$503$	33.0342	−	19.0723i	1.47292	−	0.850391i	0.999536	+	0.0304646i	$0.00969867\pi$
$504$		0			0
$505$	0.454552	−	0.0390850i	0.0202273	−	0.00173926i
$506$		0			0
$507$	−9.99240	+	8.31576i	−0.443778	+	0.369316i
$508$		0			0
$509$	−35.6333	−	20.5729i	−1.57942	−	0.911878i	−0.994940	−	0.100470i	$-0.967966\pi$
$509$	−35.6333	−	20.5729i	−1.57942	−	0.911878i	−0.584479	−	0.811409i	$-0.698701\pi$
$510$		0			0
$511$	−10.3555	−	17.9363i	−0.458102	−	0.793455i
$512$		0			0
$513$	1.14291	+	1.97958i	0.0504607	+	0.0874005i
$514$		0			0
$515$	−5.97653	+	4.17154i	−0.263357	+	0.183820i
$516$		0			0
$517$	55.2038	+	31.8719i	2.42786	+	1.40173i
$518$		0			0
$519$	17.2985			0.759319
$520$		0			0
$521$	30.4270			1.33303			0.666516	−	0.745490i	$-0.267785\pi$
$521$	30.4270			1.33303			0.666516	+	0.745490i	$0.267785\pi$
$522$		0			0
$523$	−11.4487	−	6.60990i	−0.500616	−	0.289031i	0.228352	−	0.973579i	$-0.426666\pi$
$523$	−11.4487	−	6.60990i	−0.500616	−	0.289031i	−0.728968	+	0.684548i	$0.760000\pi$
$524$		0			0
$525$	−7.77922	−	2.85772i	−0.339513	−	0.124721i
$526$		0			0
$527$	2.44280	+	4.23106i	0.106410	+	0.184308i
$528$		0			0
$529$	18.5150	+	32.0690i	0.805001	+	1.39430i
$530$		0			0
$531$	−5.77915	−	3.33660i	−0.250794	−	0.144796i
$532$		0			0
$533$	−3.29851	−	38.6040i	−0.142874	−	1.67213i
$534$		0			0
$535$	−0.672001	−	7.81527i	−0.0290532	−	0.337884i
$536$		0			0
$537$	9.00425	−	5.19861i	0.388562	−	0.224337i
$538$		0			0
$539$	22.2671	−	12.8559i	0.959112	−	0.553744i
$540$		0			0
$541$		−	13.9179i		−	0.598378i	−0.954194	−	0.299189i	$-0.903284\pi$
$541$		−	13.9179i		−	0.598378i	0.954194	−	0.299189i	$-0.0967161\pi$
$542$		0			0
$543$	−8.72186	−	5.03557i	−0.374291	−	0.216097i
$544$		0			0
$545$	−21.1163	+	14.7389i	−0.904521	+	0.631344i
$546$		0			0
$547$		−	20.7737i		−	0.888219i	−0.895973	−	0.444109i	$-0.853520\pi$
$547$		−	20.7737i		−	0.888219i	0.895973	−	0.444109i	$-0.146480\pi$
$548$		0			0
$549$	−0.365010	+	0.632216i	−0.0155782	+	0.0269823i
$550$		0			0
$551$		−	16.4923i		−	0.702596i
$552$		0			0
$553$	1.10587	+	1.91542i	0.0470262	+	0.0814518i
$554$		0			0
$555$	6.41638	+	3.00367i	0.272360	+	0.127499i
$556$		0			0
$557$	−7.90255	+	13.6876i	−0.334842	+	0.579963i	−0.983454	−	0.181156i	$-0.942016\pi$
$557$	−7.90255	+	13.6876i	−0.334842	+	0.579963i	0.648613	+	0.761119i	$0.275350\pi$
$558$		0			0
$559$	8.05435	+	3.77572i	0.340663	+	0.159696i
$560$		0			0
$561$	−6.00448	−	3.46669i	−0.253509	−	0.146364i
$562$		0			0
$563$	−34.8721	+	20.1334i	−1.46968	+	0.848521i	−0.999422	−	0.0340062i	$-0.989173\pi$
$563$	−34.8721	+	20.1334i	−1.46968	+	0.848521i	−0.470261	+	0.882528i	$0.655840\pi$
$564$		0			0
$565$	−0.390635	−	0.182866i	−0.0164341	−	0.00769322i
$566$		0			0
$567$	−1.65750			−0.0696085
$568$		0			0
$569$	−7.65461	+	13.2582i	−0.320898	+	0.555812i	−0.980674	−	0.195651i	$-0.937318\pi$
$569$	−7.65461	+	13.2582i	−0.320898	+	0.555812i	0.659775	+	0.751463i	$0.270651\pi$
$570$		0			0
$571$	−3.13351			−0.131133			−0.0655666	−	0.997848i	$-0.520885\pi$
$571$	−3.13351			−0.131133			−0.0655666	+	0.997848i	$0.520885\pi$
$572$		0			0
$573$			20.7999i			0.868927i
$574$		0			0
$575$	−29.7504	+	24.8126i	−1.24068	+	1.03476i
$576$		0			0
$577$	29.1801			1.21478			0.607391	−	0.794403i	$-0.292216\pi$
$577$	29.1801			1.21478			0.607391	+	0.794403i	$0.292216\pi$
$578$		0			0
$579$	−23.8195	+	13.7522i	−0.989904	+	0.571522i
$580$		0			0
$581$	−5.42406	−	9.39474i	−0.225028	−	0.389760i
$582$		0			0
$583$	13.2484	−	22.9469i	0.548692	−	0.950363i
$584$		0			0
$585$	−7.94465	+	1.37204i	−0.328471	+	0.0567267i
$586$		0			0
$587$	2.27078	−	3.93311i	0.0937252	−	0.162337i	−0.815351	−	0.578967i	$-0.803456\pi$
$587$	2.27078	−	3.93311i	0.0937252	−	0.162337i	0.909076	+	0.416631i	$0.136789\pi$
$588$		0			0
$589$	−4.86917	−	8.43366i	−0.200631	−	0.347503i
$590$		0			0
$591$	−18.5448	+	10.7068i	−0.762831	+	0.440421i
$592$		0			0
$593$	3.21321			0.131951			0.0659754	−	0.997821i	$-0.478984\pi$
$593$	3.21321			0.131951			0.0659754	+	0.997821i	$0.478984\pi$
$594$		0			0
$595$	0.364117	+	4.23462i	0.0149273	+	0.173602i
$596$		0			0
$597$		−	25.3923i		−	1.03924i
$598$		0			0
$599$	4.32402			0.176675			0.0883373	−	0.996091i	$-0.471845\pi$
$599$	4.32402			0.176675			0.0883373	+	0.996091i	$0.471845\pi$
$600$		0			0
$601$	1.14660	−	1.98597i	0.0467709	−	0.0810096i	−0.841692	−	0.539958i	$-0.818440\pi$
$601$	1.14660	−	1.98597i	0.0467709	−	0.0810096i	0.888463	+	0.458948i	$0.151774\pi$
$602$		0			0
$603$	−3.61123			−0.147061
$604$		0			0
$605$	24.2262	−	51.7515i	0.984935	−	2.10400i
$606$		0			0
$607$	4.80097	−	2.77184i	0.194865	−	0.112506i	−0.399393	−	0.916780i	$-0.630779\pi$
$607$	4.80097	−	2.77184i	0.194865	−	0.112506i	0.594258	+	0.804274i	$0.297446\pi$
$608$		0			0
$609$	10.3568	+	5.97948i	0.419677	+	0.242301i
$610$		0			0
$611$	−21.7406	−	31.1832i	−0.879529	−	1.26154i
$612$		0			0
$613$	−3.66946	+	6.35569i	−0.148208	+	0.256704i	−0.930565	−	0.366126i	$-0.880684\pi$
$613$	−3.66946	+	6.35569i	−0.148208	+	0.256704i	0.782357	+	0.622830i	$0.214017\pi$
$614$		0			0
$615$	10.1873	−	21.7620i	0.410793	−	0.877528i
$616$		0			0
$617$	16.9539	+	29.3650i	0.682537	+	1.18219i	0.974204	+	0.225669i	$0.0724567\pi$
$617$	16.9539	+	29.3650i	0.682537	+	1.18219i	−0.291667	+	0.956520i	$0.594210\pi$
$618$		0			0
$619$			44.9279i			1.80580i	0.429847	+	0.902902i	$0.358568\pi$
$619$			44.9279i			1.80580i	−0.429847	+	0.902902i	$0.641432\pi$
$620$		0			0
$621$	−3.87395	+	6.70988i	−0.155456	+	0.269258i
$622$		0			0
$623$		−	9.94971i		−	0.398627i
$624$		0			0
$625$	−19.0549	−	16.1837i	−0.762195	−	0.647347i
$626$		0			0
$627$	11.9686	+	6.91006i	0.477979	+	0.275961i
$628$		0			0
$629$		−	3.63335i		−	0.144871i
$630$		0			0
$631$	−34.6730	+	20.0185i	−1.38031	+	0.796923i	−0.992196	−	0.124688i	$-0.960207\pi$
$631$	−34.6730	+	20.0185i	−1.38031	+	0.796923i	−0.388115	+	0.921611i	$0.626874\pi$
$632$		0			0
$633$	−1.60440	+	0.926303i	−0.0637693	+	0.0368172i
$634$		0			0
$635$	3.69091	+	42.9247i	0.146469	+	1.70342i
$636$		0			0
$637$	−15.2776	+	1.30539i	−0.605321	+	0.0517215i
$638$		0			0
$639$	−10.6742	−	6.16273i	−0.422263	−	0.243794i
$640$		0			0
$641$	−13.7186	−	23.7614i	−0.541854	−	0.938519i	−0.998798	−	0.0490230i	$-0.984389\pi$
$641$	−13.7186	−	23.7614i	−0.541854	−	0.938519i	0.456944	−	0.889496i	$-0.348944\pi$
$642$		0			0
$643$	6.73564	+	11.6665i	0.265628	+	0.460081i	0.967728	−	0.251998i	$-0.0810875\pi$
$643$	6.73564	+	11.6665i	0.265628	+	0.460081i	−0.702100	+	0.712078i	$0.747754\pi$
$644$		0			0
$645$	3.15751	+	4.52374i	0.124327	+	0.178122i
$646$		0			0
$647$	−29.3793	−	16.9621i	−1.15502	−	0.666851i	−0.204914	−	0.978780i	$-0.565691\pi$
$647$	−29.3793	−	16.9621i	−1.15502	−	0.666851i	−0.950105	+	0.311929i	$0.899025\pi$
$648$		0			0
$649$	−40.3463			−1.58373
$650$		0			0
$651$	7.06151			0.276762
$652$		0			0
$653$	−2.73259	−	1.57766i	−0.106934	−	0.0617386i	0.445579	−	0.895243i	$-0.352998\pi$
$653$	−2.73259	−	1.57766i	−0.106934	−	0.0617386i	−0.552513	+	0.833504i	$0.686331\pi$
$654$		0			0
$655$	4.64182	+	6.65030i	0.181371	+	0.259849i
$656$		0			0
$657$	−6.24767	−	10.8213i	−0.243745	−	0.422179i
$658$		0			0
$659$	5.37780	+	9.31463i	0.209489	+	0.362846i	0.951554	−	0.307482i	$-0.0994865\pi$
$659$	5.37780	+	9.31463i	0.209489	+	0.362846i	−0.742064	+	0.670329i	$0.766153\pi$
$660$		0			0
$661$	−33.5544	−	19.3727i	−1.30512	−	0.753509i	−0.323839	−	0.946112i	$-0.604974\pi$
$661$	−33.5544	−	19.3727i	−1.30512	−	0.753509i	−0.981277	+	0.192603i	$0.938307\pi$
$662$		0			0
$663$	2.36470	+	3.39177i	0.0918375	+	0.131726i
$664$		0			0
$665$	−0.725784	−	8.44076i	−0.0281447	−	0.327318i
$666$		0			0
$667$	48.4122	−	27.9508i	1.87453	−	1.08226i
$668$		0			0
$669$	−9.09160	+	5.24904i	−0.351502	+	0.202940i
$670$		0			0
$671$			4.41372i			0.170390i
$672$		0			0
$673$	−17.1608	−	9.90782i	−0.661502	−	0.381918i	0.131347	−	0.991336i	$-0.458070\pi$
$673$	−17.1608	−	9.90782i	−0.661502	−	0.381918i	−0.792849	+	0.609418i	$0.791403\pi$
$674$		0			0
$675$	−4.69334	−	1.72411i	−0.180647	−	0.0663611i
$676$		0			0
$677$		−	19.5883i		−	0.752841i	−0.926449	−	0.376421i	$-0.877155\pi$
$677$		−	19.5883i		−	0.752841i	0.926449	−	0.376421i	$-0.122845\pi$
$678$		0			0
$679$	−4.95010	+	8.57382i	−0.189967	+	0.329033i
$680$		0			0
$681$		−	9.77071i		−	0.374415i
$682$		0			0
$683$	−13.0282	−	22.5656i	−0.498511	−	0.863447i	0.501487	−	0.865165i	$-0.332786\pi$
$683$	−13.0282	−	22.5656i	−0.498511	−	0.863447i	−0.999999	+	0.00171806i	$0.999453\pi$
$684$		0			0
$685$	−8.52574	+	18.2125i	−0.325752	+	0.695865i
$686$		0			0
$687$	−8.46753	+	14.6662i	−0.323057	+	0.559550i
$688$		0			0
$689$	−12.9621	+	9.03702i	−0.493817	+	0.344283i
$690$		0			0
$691$	−6.99020	−	4.03579i	−0.265920	−	0.153529i	0.361112	−	0.932522i	$-0.382397\pi$
$691$	−6.99020	−	4.03579i	−0.265920	−	0.153529i	−0.627032	+	0.778994i	$0.715730\pi$
$692$		0			0
$693$	−8.67869	+	5.01065i	−0.329676	+	0.190339i
$694$		0			0
$695$	−10.1033	+	21.5825i	−0.383240	+	0.818671i
$696$		0			0
$697$	−12.3230			−0.466766
$698$		0			0
$699$	9.89691	−	17.1419i	0.374335	−	0.648368i
$700$		0			0
$701$	−15.9799			−0.603551			−0.301775	−	0.953379i	$-0.597579\pi$
$701$	−15.9799			−0.603551			−0.301775	+	0.953379i	$0.597579\pi$
$702$		0			0
$703$			7.24226i			0.273147i
$704$		0			0
$705$	−2.01967	−	23.4884i	−0.0760652	−	0.884626i
$706$		0			0
$707$	−0.338183			−0.0127187
$708$		0			0
$709$	21.5086	−	12.4180i	0.807772	−	0.466367i	−0.0384099	−	0.999262i	$-0.512229\pi$
$709$	21.5086	−	12.4180i	0.807772	−	0.466367i	0.846181	+	0.532895i	$0.178896\pi$
$710$		0			0
$711$	0.667188	+	1.15560i	0.0250215	+	0.0433385i
$712$		0			0
$713$	16.5043	−	28.5863i	0.618092	−	1.07057i
$714$		0			0
$715$	−37.4506	+	31.2008i	−1.40057	+	1.16684i
$716$		0			0
$717$	−0.504237	+	0.873364i	−0.0188311	+	0.0326164i
$718$		0			0
$719$	10.8491	+	18.7912i	0.404603	+	0.700794i	0.994275	−	0.106849i	$-0.0340763\pi$
$719$	10.8491	+	18.7912i	0.404603	+	0.700794i	−0.589672	+	0.807643i	$0.700743\pi$
$720$		0			0
$721$	4.67877	−	2.70129i	0.174246	−	0.100601i
$722$		0			0
$723$	8.86238			0.329596
$724$		0			0
$725$	23.1062	+	27.7043i	0.858142	+	1.02891i
$726$		0			0
$727$			34.2453i			1.27009i	0.772476	+	0.635044i	$0.219018\pi$
$727$			34.2453i			1.27009i	−0.772476	+	0.635044i	$0.780982\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	1.41462	−	2.45019i	0.0523216	−	0.0906237i
$732$		0			0
$733$	16.9049			0.624397			0.312199	−	0.950017i	$-0.398935\pi$
$733$	16.9049			0.624397			0.312199	+	0.950017i	$0.398935\pi$
$734$		0			0
$735$	−8.61235	−	4.03166i	−0.317671	−	0.148710i
$736$		0			0
$737$	−18.9084	+	10.9168i	−0.696501	+	0.402125i
$738$		0			0
$739$	17.0843	+	9.86363i	0.628456	+	0.362839i	0.780154	−	0.625588i	$-0.215141\pi$
$739$	17.0843	+	9.86363i	0.628456	+	0.362839i	−0.151698	+	0.988427i	$0.548474\pi$
$740$		0			0
$741$	−4.71350	−	6.76073i	−0.173155	−	0.248362i
$742$		0			0
$743$	12.7040	−	22.0040i	0.466064	−	0.807247i	−0.533185	−	0.845999i	$-0.679005\pi$
$743$	12.7040	−	22.0040i	0.466064	−	0.807247i	0.999249	+	0.0387519i	$0.0123382\pi$
$744$		0			0
$745$	43.7668	+	20.4883i	1.60349	+	0.750635i
$746$		0			0
$747$	−3.27243	−	5.66801i	−0.119732	−	0.207382i
$748$		0			0
$749$			5.81450i			0.212457i
$750$		0			0
$751$	22.0169	−	38.1343i	0.803407	−	1.39154i	−0.113954	−	0.993486i	$-0.536352\pi$
$751$	22.0169	−	38.1343i	0.803407	−	1.39154i	0.917361	−	0.398056i	$-0.130315\pi$
$752$		0			0
$753$			2.80694i			0.102291i
$754$		0			0
$755$	31.6473	−	22.0894i	1.15176	−	0.803915i
$756$		0			0
$757$	−17.6946	−	10.2160i	−0.643121	−	0.371306i	0.142695	−	0.989767i	$-0.454423\pi$
$757$	−17.6946	−	10.2160i	−0.643121	−	0.371306i	−0.785816	+	0.618461i	$0.787757\pi$
$758$		0			0
$759$			46.8440i			1.70033i
$760$		0			0
$761$	−11.4379	+	6.60370i	−0.414625	+	0.239384i	−0.692775	−	0.721154i	$-0.743612\pi$
$761$	−11.4379	+	6.60370i	−0.414625	+	0.239384i	0.278150	+	0.960538i	$0.410279\pi$
$762$		0			0
$763$	16.5310	−	9.54418i	0.598462	−	0.345522i
$764$		0			0
$765$	0.219678	+	2.55482i	0.00794247	+	0.0923697i
$766$		0			0
$767$	21.7856	+	10.2126i	0.786632	+	0.368757i
$768$		0			0
$769$	−8.23441	−	4.75414i	−0.296940	−	0.171439i	0.344127	−	0.938923i	$-0.388175\pi$
$769$	−8.23441	−	4.75414i	−0.296940	−	0.171439i	−0.641068	+	0.767484i	$0.721508\pi$
$770$		0			0
$771$	0.197590	+	0.342236i	0.00711604	+	0.0123253i
$772$		0			0
$773$	3.11490	+	5.39516i	0.112035	+	0.194050i	0.916591	−	0.399827i	$-0.130930\pi$
$773$	3.11490	+	5.39516i	0.112035	+	0.194050i	−0.804556	+	0.593877i	$0.797596\pi$
$774$		0			0
$775$	19.9952	+	7.34528i	0.718248	+	0.263850i
$776$		0			0
$777$	−4.54796	−	2.62577i	−0.163157	−	0.0941989i
$778$		0			0
$779$	24.5631			0.880063
$780$		0			0
$781$	−74.5200			−2.66654
$782$		0			0
$783$	6.24842	+	3.60753i	0.223300	+	0.128922i
$784$		0			0
$785$	−39.3210	+	27.4455i	−1.40343	+	0.979573i
$786$		0			0
$787$	−22.7635	−	39.4276i	−0.811433	−	1.40544i	−0.911861	−	0.410499i	$-0.865355\pi$
$787$	−22.7635	−	39.4276i	−0.811433	−	1.40544i	0.100428	−	0.994944i	$-0.467979\pi$
$788$		0			0
$789$	−12.2704	−	21.2529i	−0.436837	−	0.756623i
$790$		0			0
$791$	0.276884	+	0.159859i	0.00984485	+	0.00568393i
$792$		0			0
$793$	1.11722	−	2.38325i	0.0396737	−	0.0846318i
$794$		0			0
$795$	−9.76358	+	0.839528i	−0.346278	+	0.0297750i
$796$		0			0
$797$	20.0123	−	11.5541i	0.708871	−	0.409267i	−0.101772	−	0.994808i	$-0.532451\pi$
$797$	20.0123	−	11.5541i	0.708871	−	0.409267i	0.810643	+	0.585541i	$0.199118\pi$
$798$		0			0
$799$	−10.4707	+	6.04524i	−0.370426	+	0.213865i
$800$		0			0
$801$		−	6.00284i		−	0.212100i
$802$		0			0
$803$	−65.4257	−	37.7736i	−2.30882	−	1.33300i
$804$		0			0
$805$	23.5473	−	16.4357i	0.829933	−	0.579282i
$806$		0			0
$807$			12.1546i			0.427862i
$808$		0			0
$809$	−4.03014	+	6.98041i	−0.141692	+	0.245418i	−0.928134	−	0.372246i	$-0.878588\pi$
$809$	−4.03014	+	6.98041i	−0.141692	+	0.245418i	0.786442	+	0.617664i	$0.211921\pi$
$810$		0			0
$811$		−	48.6471i		−	1.70823i	−0.520084	−	0.854115i	$-0.674099\pi$
$811$		−	48.6471i		−	1.70823i	0.520084	−	0.854115i	$-0.325901\pi$
$812$		0			0
$813$	−1.84306	−	3.19227i	−0.0646389	−	0.111958i
$814$		0			0
$815$	−13.4596	+	28.7522i	−0.471470	+	1.00714i
$816$		0			0
$817$	−2.81973	+	4.88391i	−0.0986497	+	0.170866i
$818$		0			0
$819$	5.95451	−	0.508781i	0.208067	−	0.0177783i
$820$		0			0
$821$	−41.7461	−	24.1021i	−1.45695	−	0.841169i	−0.458088	−	0.888907i	$-0.651465\pi$
$821$	−41.7461	−	24.1021i	−1.45695	−	0.841169i	−0.998860	+	0.0477380i	$0.984799\pi$
$822$		0			0
$823$	−42.0960	+	24.3042i	−1.46738	+	0.847190i	−0.999333	−	0.0365160i	$-0.988374\pi$
$823$	−42.0960	+	24.3042i	−1.46738	+	0.847190i	−0.468043	+	0.883706i	$0.655041\pi$
$824$		0			0
$825$	−29.7864	+	5.16056i	−1.03703	+	0.179668i
$826$		0			0
$827$	20.1081			0.699229			0.349614	−	0.936894i	$-0.386313\pi$
$827$	20.1081			0.699229			0.349614	+	0.936894i	$0.386313\pi$
$828$		0			0
$829$	−10.5726	+	18.3123i	−0.367203	+	0.636014i	−0.989127	−	0.147063i	$-0.953018\pi$
$829$	−10.5726	+	18.3123i	−0.367203	+	0.636014i	0.621924	+	0.783077i	$0.286351\pi$
$830$		0			0
$831$	−0.805800			−0.0279529
$832$		0			0
$833$			4.87684i			0.168972i
$834$		0			0
$835$	−14.1995	+	1.22095i	−0.491393	+	0.0422528i
$836$		0			0
$837$	4.26033			0.147259
$838$		0			0
$839$	−12.3127	+	7.10874i	−0.425082	+	0.245421i	−0.697249	−	0.716829i	$-0.745593\pi$
$839$	−12.3127	+	7.10874i	−0.425082	+	0.245421i	0.272167	+	0.962250i	$0.412260\pi$
$840$		0			0
$841$	−11.5285	−	19.9679i	−0.397534	−	0.688549i
$842$		0			0
$843$	−0.180122	+	0.311980i	−0.00620372	+	0.0107452i
$844$		0			0
$845$	28.1197	−	7.36765i	0.967347	−	0.253455i
$846$		0			0
$847$	−21.1782	+	36.6817i	−0.727692	+	1.26040i
$848$		0			0
$849$	10.1636	+	17.6039i	0.348813	+	0.604163i
$850$		0			0
$851$	−21.2592	+	12.2740i	−0.728757	+	0.420748i
$852$		0			0
$853$	26.1008			0.893676			0.446838	−	0.894615i	$-0.352550\pi$
$853$	26.1008			0.893676			0.446838	+	0.894615i	$0.352550\pi$
$854$		0			0
$855$	−0.437878	−	5.09246i	−0.0149751	−	0.174158i
$856$		0			0
$857$		−	27.1782i		−	0.928390i	−0.885733	−	0.464195i	$-0.846344\pi$
$857$		−	27.1782i		−	0.928390i	0.885733	−	0.464195i	$-0.153656\pi$
$858$		0			0
$859$	33.8502			1.15495			0.577477	−	0.816407i	$-0.304037\pi$
$859$	33.8502			1.15495			0.577477	+	0.816407i	$0.304037\pi$
$860$		0			0
$861$	−8.90563	+	15.4250i	−0.303503	+	0.525683i
$862$		0			0
$863$	49.9350			1.69981			0.849904	−	0.526938i	$-0.176660\pi$
$863$	49.9350			1.69981			0.849904	+	0.526938i	$0.176660\pi$
$864$		0			0
$865$	−35.0321	−	16.3994i	−1.19113	−	0.557596i
$866$		0			0
$867$	−13.5835	+	7.84246i	−0.461321	+	0.266344i
$868$		0			0
$869$	6.98681	+	4.03384i	0.237011	+	0.136839i
$870$		0			0
$871$	12.9732	−	1.10849i	0.439580	−	0.0375598i
$872$		0			0
$873$	−2.98648	+	5.17274i	−0.101077	+	0.175071i
$874$		0			0
$875$	13.0449	+	13.1622i	0.440999	+	0.444964i
$876$		0			0
$877$	6.88339	+	11.9224i	0.232436	+	0.402590i	0.958524	−	0.285011i	$-0.0919972\pi$
$877$	6.88339	+	11.9224i	0.232436	+	0.402590i	−0.726089	+	0.687601i	$0.758664\pi$
$878$		0			0
$879$		−	16.9751i		−	0.572555i
$880$		0			0
$881$	−6.98061	+	12.0908i	−0.235183	+	0.407348i	−0.959326	−	0.282302i	$-0.908902\pi$
$881$	−6.98061	+	12.0908i	−0.235183	+	0.407348i	0.724143	+	0.689650i	$0.242235\pi$
$882$		0			0
$883$			5.95089i			0.200263i	0.994974	+	0.100132i	$0.0319264\pi$
$883$			5.95089i			0.200263i	−0.994974	+	0.100132i	$0.968074\pi$
$884$		0			0
$885$	8.54050	+	12.2359i	0.287086	+	0.411305i
$886$		0			0
$887$	17.0832	+	9.86299i	0.573598	+	0.331167i	0.758585	−	0.651574i	$-0.225891\pi$
$887$	17.0832	+	9.86299i	0.573598	+	0.331167i	−0.184987	+	0.982741i	$0.559224\pi$
$888$		0			0
$889$		−	31.9357i		−	1.07109i
$890$		0			0
$891$	−5.23601	+	3.02301i	−0.175413	+	0.101275i
$892$		0			0
$893$	20.8709	−	12.0498i	0.698418	−	0.403232i
$894$		0			0
$895$	−23.1634	+	1.99172i	−0.774267	+	0.0665759i
$896$		0			0
$897$	11.8574	−	25.2941i	0.395906	−	0.844546i
$898$		0			0
$899$	−26.6203	−	15.3693i	−0.887838	−	0.512593i
$900$		0			0
$901$	2.51286	+	4.35240i	0.0837155	+	0.145000i
$902$		0			0
$903$	−2.04465	−	3.54144i	−0.0680417	−	0.117852i
$904$		0			0
$905$	12.8893	+	18.4664i	0.428454	+	0.613842i
$906$		0			0
$907$	−13.9862	−	8.07493i	−0.464404	−	0.268124i	0.249490	−	0.968377i	$-0.419737\pi$
$907$	−13.9862	−	8.07493i	−0.464404	−	0.268124i	−0.713894	+	0.700254i	$0.753070\pi$
$908$		0			0
$909$	−0.204032			−0.00676732
$910$		0			0
$911$	35.1748			1.16539			0.582696	−	0.812690i	$-0.301998\pi$
$911$	35.1748			1.16539			0.582696	+	0.812690i	$0.301998\pi$
$912$		0			0
$913$	−34.2689	−	19.7852i	−1.13414	−	0.654794i
$914$		0			0
$915$	1.33856	−	0.934296i	0.0442514	−	0.0308869i
$916$		0			0
$917$	−3.00582	−	5.20623i	−0.0992610	−	0.171925i
$918$		0			0
$919$	7.24395	+	12.5469i	0.238956	+	0.413884i	0.960415	−	0.278573i	$-0.0898615\pi$
$919$	7.24395	+	12.5469i	0.238956	+	0.413884i	−0.721459	+	0.692457i	$0.756528\pi$
$920$		0			0
$921$	14.8758	+	8.58852i	0.490173	+	0.283001i
$922$		0			0
$923$	40.2382	+	18.8629i	1.32446	+	0.620879i
$924$		0			0
$925$	−10.1466	−	12.1658i	−0.333619	−	0.400009i
$926$		0			0
$927$	2.82278	−	1.62973i	0.0927123	−	0.0535275i
$928$		0			0
$929$	−32.4260	+	18.7212i	−1.06386	+	0.614222i	−0.926499	−	0.376298i	$-0.877197\pi$
$929$	−32.4260	+	18.7212i	−1.06386	+	0.614222i	−0.137365	+	0.990520i	$0.543863\pi$
$930$		0			0
$931$		−	9.72088i		−	0.318589i
$932$		0			0
$933$	−15.9499	−	9.20868i	−0.522176	−	0.301479i
$934$		0			0
$935$	8.87348	+	12.7130i	0.290194	+	0.415759i
$936$		0			0
$937$		−	56.2285i		−	1.83690i	−0.395533	−	0.918452i	$-0.629440\pi$
$937$		−	56.2285i		−	1.83690i	0.395533	−	0.918452i	$-0.370560\pi$
$938$		0			0
$939$	4.05286	−	7.01975i	0.132260	−	0.229081i
$940$		0			0
$941$		−	37.7863i		−	1.23180i	−0.787826	−	0.615898i	$-0.788793\pi$
$941$		−	37.7863i		−	1.23180i	0.787826	−	0.615898i	$-0.211207\pi$
$942$		0			0
$943$	41.6289	+	72.1034i	1.35562	+	2.34801i
$944$		0			0
$945$	3.35670	+	1.57135i	0.109193	+	0.0511161i
$946$		0			0
$947$	−5.01348	+	8.68360i	−0.162916	+	0.282179i	−0.935913	−	0.352230i	$-0.885423\pi$
$947$	−5.01348	+	8.68360i	−0.162916	+	0.282179i	0.772997	+	0.634409i	$0.218757\pi$
$948$		0			0
$949$	25.7662	+	36.9573i	0.836406	+	1.19968i
$950$		0			0
$951$	−3.51861	−	2.03147i	−0.114099	−	0.0658749i
$952$		0			0
$953$	0.501424	−	0.289497i	0.0162427	−	0.00937773i	−0.491857	−	0.870676i	$-0.663682\pi$
$953$	0.501424	−	0.289497i	0.0162427	−	0.00937773i	0.508099	+	0.861298i	$0.330348\pi$
$954$		0			0
$955$	19.7188	−	42.1230i	0.638086	−	1.36307i
$956$		0			0
$957$	43.6224			1.41011
$958$		0			0
$959$	7.45309	−	12.9091i	0.240673	−	0.416857i
$960$		0			0
$961$	12.8496			0.414502
$962$		0			0
$963$			3.50799i			0.113043i
$964$		0			0
$965$	61.2756	−	5.26882i	1.97253	−	0.169609i
$966$		0			0
$967$	−17.0784			−0.549205			−0.274602	−	0.961558i	$-0.588546\pi$
$967$	−17.0784			−0.549205			−0.274602	+	0.961558i	$0.588546\pi$
$968$		0			0
$969$	−2.27011	+	1.31065i	−0.0729265	+	0.0421042i
$970$		0			0
$971$	−21.5819	−	37.3810i	−0.692597	−	1.19961i	−0.970984	−	0.239144i	$-0.923133\pi$
$971$	−21.5819	−	37.3810i	−0.692597	−	1.19961i	0.278387	−	0.960469i	$-0.410200\pi$
$972$		0			0
$973$	8.83217	−	15.2978i	0.283146	−	0.490424i
$974$		0			0
$975$	17.3899	+	4.75315i	0.556922	+	0.152223i
$976$		0			0
$977$	−21.3061	+	36.9032i	−0.681641	+	1.18064i	0.292838	+	0.956162i	$0.405400\pi$
$977$	−21.3061	+	36.9032i	−0.681641	+	1.18064i	−0.974480	+	0.224476i	$0.927933\pi$
$978$		0			0
$979$	−18.1466	−	31.4309i	−0.579969	−	1.00454i
$980$		0			0
$981$	9.97344	−	5.75817i	0.318428	−	0.183844i
$982$		0			0
$983$	−45.6346			−1.45552			−0.727758	−	0.685834i	$-0.759438\pi$
$983$	−45.6346			−1.45552			−0.727758	+	0.685834i	$0.759438\pi$
$984$		0			0
$985$	47.7064	−	4.10207i	1.52005	−	0.130703i
$986$		0			0
$987$			17.4752i			0.556243i
$988$		0			0
$989$	−19.1152			−0.607829
$990$		0			0
$991$	3.76168	−	6.51542i	0.119494	−	0.206969i	−0.800073	−	0.599902i	$-0.795206\pi$
$991$	3.76168	−	6.51542i	0.119494	−	0.206969i	0.919567	+	0.392933i	$0.128540\pi$
$992$		0			0
$993$	20.0885			0.637489
$994$		0			0
$995$	−24.0725	+	51.4232i	−0.763149	+	1.63023i
$996$		0			0
$997$	−30.2852	+	17.4852i	−0.959141	+	0.553760i	−0.895909	−	0.444239i	$-0.853474\pi$
$997$	−30.2852	+	17.4852i	−0.959141	+	0.553760i	−0.0632324	+	0.997999i	$0.520141\pi$
$998$		0			0
$999$	−2.74387	−	1.58417i	−0.0868121	−	0.0501210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.bv.a.589.9	yes	24
3.2	odd	2		2340.2.cr.b.1369.8		24
5.2	odd	4		3900.2.cd.o.901.2		12
5.3	odd	4		3900.2.cd.n.901.5		12
5.4	even	2	inner	780.2.bv.a.589.4	yes	24
13.10	even	6	inner	780.2.bv.a.49.4	✓	24
15.14	odd	2		2340.2.cr.b.1369.5		24
39.23	odd	6		2340.2.cr.b.829.5		24
65.23	odd	12		3900.2.cd.n.2701.5		12
65.49	even	6	inner	780.2.bv.a.49.9	yes	24
65.62	odd	12		3900.2.cd.o.2701.2		12
195.179	odd	6		2340.2.cr.b.829.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.bv.a.49.4	✓	24	13.10	even	6	inner
780.2.bv.a.49.9	yes	24	65.49	even	6	inner
780.2.bv.a.589.4	yes	24	5.4	even	2	inner
780.2.bv.a.589.9	yes	24	1.1	even	1	trivial
2340.2.cr.b.829.5		24	39.23	odd	6
2340.2.cr.b.829.8		24	195.179	odd	6
2340.2.cr.b.1369.5		24	15.14	odd	2
2340.2.cr.b.1369.8		24	3.2	odd	2
3900.2.cd.n.901.5		12	5.3	odd	4
3900.2.cd.n.2701.5		12	65.23	odd	12
3900.2.cd.o.901.2		12	5.2	odd	4
3900.2.cd.o.2701.2		12	65.62	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.bv (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.27982 - 1.83359i) q^{5} +(0.828751 + 1.43544i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-1.27982 - 1.83359i) q^{5} +(0.828751 + 1.43544i) q^{7} +(0.500000 + 0.866025i) q^{9} +(5.23601 + 3.02301i) q^{11} +(-2.06206 - 2.95768i) q^{13} +(-0.191563 - 2.22785i) q^{15} +(-0.993129 + 0.573383i) q^{17} +(1.97958 - 1.14291i) q^{19} +1.65750i q^{21} +(6.70988 + 3.87395i) q^{23} +(-1.72411 + 4.69334i) q^{25} +1.00000i q^{27} +(3.60753 - 6.24842i) q^{29} -4.26033i q^{31} +(3.02301 + 5.23601i) q^{33} +(1.57135 - 3.35670i) q^{35} +(-1.58417 + 2.74387i) q^{37} +(-0.306957 - 3.59246i) q^{39} +(9.30618 + 5.37292i) q^{41} +(-2.13661 + 1.23357i) q^{43} +(0.948025 - 2.02515i) q^{45} +10.5431 q^{47} +(2.12634 - 3.68294i) q^{49} -1.14677 q^{51} -4.38252i q^{53} +(-1.15819 - 13.4696i) q^{55} +2.28582 q^{57} +(-5.77915 + 3.33660i) q^{59} +(0.365010 + 0.632216i) q^{61} +(-0.828751 + 1.43544i) q^{63} +(-2.78411 + 7.56629i) q^{65} +(-1.80561 + 3.12741i) q^{67} +(3.87395 + 6.70988i) q^{69} +(-10.6742 + 6.16273i) q^{71} -12.4953 q^{73} +(-3.83979 + 3.20250i) q^{75} +10.0213i q^{77} +1.33438 q^{79} +(-0.500000 + 0.866025i) q^{81} -6.54486 q^{83} +(2.32238 + 1.08716i) q^{85} +(6.24842 - 3.60753i) q^{87} +(-5.19861 - 3.00142i) q^{89} +(2.53664 - 5.41115i) q^{91} +(2.13017 - 3.68956i) q^{93} +(-4.62914 - 2.16701i) q^{95} +(2.98648 + 5.17274i) q^{97} +6.04602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^9	\( 24 q + 12 q^{9} + 12 q^{11} - 6 q^{15} + 24 q^{19} + 16 q^{25} + 4 q^{29} - 2 q^{35} + 8 q^{39} + 72 q^{41} - 6 q^{45} - 8 q^{49} + 8 q^{51} + 4 q^{55} + 36 q^{59} + 44 q^{61} + 10 q^{65} + 8 q^{69} + 12 q^{71} + 8 q^{75} + 8 q^{79} - 12 q^{81} + 12 q^{85} + 4 q^{91} - 24 q^{95}+O(q^{100}) \) 24 * q + 12 * q^9 + 12 * q^11 - 6 * q^15 + 24 * q^19 + 16 * q^25 + 4 * q^29 - 2 * q^35 + 8 * q^39 + 72 * q^41 - 6 * q^45 - 8 * q^49 + 8 * q^51 + 4 * q^55 + 36 * q^59 + 44 * q^61 + 10 * q^65 + 8 * q^69 + 12 * q^71 + 8 * q^75 + 8 * q^79 - 12 * q^81 + 12 * q^85 + 4 * q^91 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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