LMFDB - Embedded newform 930.2.bk.a.47.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (of order $20$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.5
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(-1.52046 + 0.829577i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.03771 - 0.920729i) q^{5} +(-0.581511 - 1.63152i) q^{6} +(-3.90942 + 1.99195i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.62360 - 2.52268i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.52046 + 0.829577i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.03771 - 0.920729i) q^{5} +(-0.581511 - 1.63152i) q^{6} +(-3.90942 + 1.99195i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.62360 - 2.52268i) q^{9} +(0.590625 + 2.15666i) q^{10} +(1.21824 + 0.395831i) q^{11} +(1.70240 - 0.319126i) q^{12} +(-0.842501 + 0.133439i) q^{13} +(-1.35586 - 4.17290i) q^{14} +(-2.33444 + 3.09037i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-3.16622 - 1.61327i) q^{17} +(2.23763 + 1.99825i) q^{18} +(-2.83404 - 3.90073i) q^{19} +(-2.22250 + 0.245979i) q^{20} +(4.29165 - 6.27185i) q^{21} +(-0.581532 + 1.14132i) q^{22} +(0.158885 - 0.311829i) q^{23} +(0.0488835 + 1.73136i) q^{24} +(3.30452 - 3.75236i) q^{25} -0.853003i q^{26} +(-0.375871 + 5.18254i) q^{27} +(4.33363 - 0.686379i) q^{28} +(0.738629 - 0.536645i) q^{29} +(-2.68713 - 2.78914i) q^{30} +(5.36705 - 1.48147i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.18066 + 0.408780i) q^{33} +(2.08871 - 2.87487i) q^{34} +(-6.13222 + 7.65853i) q^{35} +(-2.32369 + 1.89749i) q^{36} +(-3.05251 - 3.05251i) q^{37} +(4.29605 - 2.18894i) q^{38} +(1.17029 - 0.901809i) q^{39} +(0.104725 - 2.23361i) q^{40} +(-4.12043 - 5.67128i) q^{41} +(5.52327 + 5.21994i) q^{42} +(1.28649 - 8.12255i) q^{43} +(-1.03630 - 0.752915i) q^{44} +(0.985729 - 6.63539i) q^{45} +(0.283135 + 0.205709i) q^{46} +(0.969612 - 0.153571i) q^{47} +(-1.71769 - 0.222563i) q^{48} +(7.20121 - 9.91162i) q^{49} +(3.18922 + 3.85083i) q^{50} +(6.15245 - 0.173709i) q^{51} +(0.842501 + 0.133439i) q^{52} +(3.71831 - 7.29760i) q^{53} +(-5.05994 - 1.18197i) q^{54} +(2.84687 - 0.315083i) q^{55} +4.38765i q^{56} +(7.54501 + 3.57985i) q^{57} +(0.414491 + 0.813485i) q^{58} +(1.35197 + 0.982265i) q^{59} +(3.17516 - 2.21773i) q^{60} +10.3835 q^{61} +(0.623641 + 5.53273i) q^{62} +(-1.32230 + 13.0964i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.59391 + 1.04763i) q^{65} +(-0.0626166 - 2.21776i) q^{66} +(2.17028 + 2.17028i) q^{67} +(2.51273 + 2.51273i) q^{68} +(0.0171079 + 0.605931i) q^{69} +(-6.60495 - 7.25478i) q^{70} +(-7.50876 + 2.43975i) q^{71} +(-1.51062 - 2.59191i) q^{72} +(-0.230858 - 0.453085i) q^{73} +(3.49245 - 2.53741i) q^{74} +(-1.91152 + 8.44666i) q^{75} +(1.48995 + 4.58558i) q^{76} +(-5.55109 + 0.879207i) q^{77} +(0.707632 + 1.29696i) q^{78} +(0.512989 - 0.166680i) q^{79} +(2.18973 + 0.452850i) q^{80} +(-3.72782 - 8.19166i) q^{81} +(6.24604 - 3.18252i) q^{82} +(8.71514 + 1.38034i) q^{83} +(-6.01971 + 4.63869i) q^{84} +(-7.93722 - 0.372143i) q^{85} +(7.82130 + 2.54129i) q^{86} +(-0.677868 + 1.42870i) q^{87} +(0.905758 - 0.905758i) q^{88} +(-2.44397 + 7.52177i) q^{89} +(6.39949 + 2.01160i) q^{90} +(3.02789 - 2.19989i) q^{91} +(-0.247469 + 0.247469i) q^{92} +(-6.93140 + 6.70490i) q^{93} +0.981698i q^{94} +(-9.36647 - 5.33916i) q^{95} +(0.488529 - 1.66173i) q^{96} +(6.58295 - 3.35418i) q^{97} +(8.66307 + 8.66307i) q^{98} +(2.97650 - 2.43056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	−1.52046	+	0.829577i	−0.877839	+	0.478956i
$3$	−1.52046	+	0.829577i	−0.877839	+	0.478956i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	2.03771	−	0.920729i	0.911291	−	0.411763i
$5$	2.03771	−	0.920729i	0.911291	−	0.411763i
$6$	−0.581511	−	1.63152i	−0.237401	−	0.666064i
$7$	−3.90942	+	1.99195i	−1.47762	+	0.752886i	−0.992579	−	0.121604i	$-0.961196\pi$
$7$	−3.90942	+	1.99195i	−1.47762	+	0.752886i	−0.485044	+	0.874490i	$0.661196\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	1.62360	−	2.52268i	0.541201	−	0.840893i
$10$	0.590625	+	2.15666i	0.186772	+	0.681994i
$11$	1.21824	+	0.395831i	0.367314	+	0.119347i	0.486857	−	0.873481i	$-0.338143\pi$
$11$	1.21824	+	0.395831i	0.367314	+	0.119347i	−0.119544	+	0.992829i	$0.538143\pi$
$12$	1.70240	−	0.319126i	0.491440	−	0.0921238i
$13$	−0.842501	+	0.133439i	−0.233668	+	0.0370094i	−0.272170	−	0.962249i	$-0.587741\pi$
$13$	−0.842501	+	0.133439i	−0.233668	+	0.0370094i	0.0385022	+	0.999259i	$0.487741\pi$
$14$	−1.35586	−	4.17290i	−0.362368	−	1.11525i
$15$	−2.33444	+	3.09037i	−0.602750	+	0.797930i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−3.16622	−	1.61327i	−0.767922	−	0.391276i	0.0257138	−	0.999669i	$-0.491814\pi$
$17$	−3.16622	−	1.61327i	−0.767922	−	0.391276i	−0.793635	+	0.608394i	$0.791814\pi$
$18$	2.23763	+	1.99825i	0.527415	+	0.470992i
$19$	−2.83404	−	3.90073i	−0.650174	−	0.894888i	0.348932	−	0.937148i	$-0.386544\pi$
$19$	−2.83404	−	3.90073i	−0.650174	−	0.894888i	−0.999107	+	0.0422596i	$0.986544\pi$
$20$	−2.22250	+	0.245979i	−0.496966	+	0.0550025i
$21$	4.29165	−	6.27185i	0.936514	−	1.36863i
$22$	−0.581532	+	1.14132i	−0.123983	+	0.243331i
$23$	0.158885	−	0.311829i	0.0331297	−	0.0650208i	−0.873848	−	0.486199i	$-0.838383\pi$
$23$	0.158885	−	0.311829i	0.0331297	−	0.0650208i	0.906978	+	0.421178i	$0.138383\pi$
$24$	0.0488835	+	1.73136i	0.00997830	+	0.353413i
$25$	3.30452	−	3.75236i	0.660903	−	0.750471i
$26$		−	0.853003i		−	0.167288i
$27$	−0.375871	+	5.18254i	−0.0723364	+	0.997380i
$28$	4.33363	−	0.686379i	0.818978	−	0.129713i
$29$	0.738629	−	0.536645i	0.137160	−	0.0996525i	−0.517090	−	0.855931i	$-0.672985\pi$
$29$	0.738629	−	0.536645i	0.137160	−	0.0996525i	0.654250	+	0.756279i	$0.272985\pi$
$30$	−2.68713	−	2.78914i	−0.490601	−	0.509225i
$31$	5.36705	−	1.48147i	0.963951	−	0.266080i
$31$	5.36705	−	1.48147i	0.963951	−	0.266080i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.18066	+	0.408780i	−0.379604	+	0.0711594i
$34$	2.08871	−	2.87487i	0.358212	−	0.493036i
$35$	−6.13222	+	7.65853i	−1.03653	+	1.29453i
$36$	−2.32369	+	1.89749i	−0.387282	+	0.316248i
$37$	−3.05251	−	3.05251i	−0.501830	−	0.501830i	0.410176	−	0.912006i	$-0.365467\pi$
$37$	−3.05251	−	3.05251i	−0.501830	−	0.501830i	−0.912006	+	0.410176i	$0.865467\pi$
$38$	4.29605	−	2.18894i	0.696911	−	0.355094i
$39$	1.17029	−	0.901809i	0.187397	−	0.144405i
$40$	0.104725	−	2.23361i	0.0165585	−	0.353165i
$41$	−4.12043	−	5.67128i	−0.643503	−	0.885706i	0.355293	−	0.934755i	$-0.384381\pi$
$41$	−4.12043	−	5.67128i	−0.643503	−	0.885706i	−0.998796	+	0.0490489i	$0.984381\pi$
$42$	5.52327	+	5.21994i	0.852259	+	0.805455i
$43$	1.28649	−	8.12255i	0.196187	−	1.23868i	−0.671288	−	0.741197i	$-0.734258\pi$
$43$	1.28649	−	8.12255i	0.196187	−	1.23868i	0.867475	−	0.497481i	$-0.165742\pi$
$44$	−1.03630	−	0.752915i	−0.156228	−	0.113506i
$45$	0.985729	−	6.63539i	0.146944	−	0.989145i
$46$	0.283135	+	0.205709i	0.0417459	+	0.0303302i
$47$	0.969612	−	0.153571i	0.141432	−	0.0224007i	−0.0853168	−	0.996354i	$-0.527190\pi$
$47$	0.969612	−	0.153571i	0.141432	−	0.0224007i	0.226749	+	0.973953i	$0.427190\pi$
$48$	−1.71769	−	0.222563i	−0.247927	−	0.0321242i
$49$	7.20121	−	9.91162i	1.02874	−	1.41595i
$50$	3.18922	+	3.85083i	0.451024	+	0.544590i
$51$	6.15245	−	0.173709i	0.861515	−	0.0243242i
$52$	0.842501	+	0.133439i	0.116834	+	0.0185047i
$53$	3.71831	−	7.29760i	0.510749	−	1.00240i	−0.481300	−	0.876556i	$-0.659835\pi$
$53$	3.71831	−	7.29760i	0.510749	−	1.00240i	0.992050	−	0.125846i	$-0.0401646\pi$
$54$	−5.05994	−	1.18197i	−0.688570	−	0.160846i
$55$	2.84687	−	0.315083i	0.383873	−	0.0424857i
$56$			4.38765i			0.586324i
$57$	7.54501	+	3.57985i	0.999361	+	0.474162i
$58$	0.414491	+	0.813485i	0.0544254	+	0.106816i
$59$	1.35197	+	0.982265i	0.176012	+	0.127880i	0.672303	−	0.740276i	$-0.265305\pi$
$59$	1.35197	+	0.982265i	0.176012	+	0.127880i	−0.496291	+	0.868156i	$0.665305\pi$
$60$	3.17516	−	2.21773i	0.409912	−	0.286308i
$61$	10.3835			1.32947			0.664734	−	0.747080i	$-0.268545\pi$
$61$	10.3835			1.32947			0.664734	+	0.747080i	$0.268545\pi$
$62$	0.623641	+	5.53273i	0.0792025	+	0.702657i
$63$	−1.32230	+	13.0964i	−0.166595	+	1.64999i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−1.59391	+	1.04763i	−0.197700	+	0.129942i
$66$	−0.0626166	−	2.21776i	−0.00770757	−	0.272987i
$67$	2.17028	+	2.17028i	0.265142	+	0.265142i	0.827139	−	0.561997i	$-0.189967\pi$
$67$	2.17028	+	2.17028i	0.265142	+	0.265142i	−0.561997	+	0.827139i	$0.689967\pi$
$68$	2.51273	+	2.51273i	0.304713	+	0.304713i
$69$	0.0171079	+	0.605931i	0.00205955	+	0.0729455i
$70$	−6.60495	−	7.25478i	−0.789443	−	0.867112i
$71$	−7.50876	+	2.43975i	−0.891126	+	0.289544i	−0.718570	−	0.695455i	$-0.755203\pi$
$71$	−7.50876	+	2.43975i	−0.891126	+	0.289544i	−0.172557	+	0.985000i	$0.555203\pi$
$72$	−1.51062	−	2.59191i	−0.178029	−	0.305460i
$73$	−0.230858	−	0.453085i	−0.0270199	−	0.0530296i	0.877102	−	0.480304i	$-0.159474\pi$
$73$	−0.230858	−	0.453085i	−0.0270199	−	0.0530296i	−0.904122	+	0.427275i	$0.859474\pi$
$74$	3.49245	−	2.53741i	0.405989	−	0.294968i
$75$	−1.91152	+	8.44666i	−0.220723	+	0.975336i
$76$	1.48995	+	4.58558i	0.170908	+	0.526002i
$77$	−5.55109	+	0.879207i	−0.632606	+	0.100195i
$78$	0.707632	+	1.29696i	0.0801235	+	0.146852i
$79$	0.512989	−	0.166680i	0.0577158	−	0.0187530i	−0.280017	−	0.959995i	$-0.590340\pi$
$79$	0.512989	−	0.166680i	0.0577158	−	0.0187530i	0.337733	+	0.941242i	$0.390340\pi$
$80$	2.18973	+	0.452850i	0.244820	+	0.0506301i
$81$	−3.72782	−	8.19166i	−0.414202	−	0.910185i
$82$	6.24604	−	3.18252i	0.689760	−	0.351450i
$83$	8.71514	+	1.38034i	0.956611	+	0.151512i	0.615173	−	0.788392i	$-0.289086\pi$
$83$	8.71514	+	1.38034i	0.956611	+	0.151512i	0.341438	+	0.939904i	$0.389086\pi$
$84$	−6.01971	+	4.63869i	−0.656804	+	0.506122i
$85$	−7.93722	−	0.372143i	−0.860913	−	0.0403646i
$86$	7.82130	+	2.54129i	0.843393	+	0.274035i
$87$	−0.677868	+	1.42870i	−0.0726750	+	0.153172i
$88$	0.905758	−	0.905758i	0.0965541	−	0.0965541i
$89$	−2.44397	+	7.52177i	−0.259060	+	0.797306i	0.733942	+	0.679212i	$0.237678\pi$
$89$	−2.44397	+	7.52177i	−0.259060	+	0.797306i	−0.993002	+	0.118094i	$0.962322\pi$
$90$	6.39949	+	2.01160i	0.674566	+	0.212041i
$91$	3.02789	−	2.19989i	0.317409	−	0.230611i
$92$	−0.247469	+	0.247469i	−0.0258004	+	0.0258004i
$93$	−6.93140	+	6.70490i	−0.718753	+	0.695266i
$94$			0.981698i			0.101254i
$95$	−9.36647	−	5.33916i	−0.960980	−	0.547786i
$96$	0.488529	−	1.66173i	0.0498603	−	0.169599i
$97$	6.58295	−	3.35418i	0.668397	−	0.340565i	−0.0866473	−	0.996239i	$-0.527615\pi$
$97$	6.58295	−	3.35418i	0.668397	−	0.340565i	0.755044	+	0.655674i	$0.227615\pi$
$98$	8.66307	+	8.66307i	0.875103	+	0.875103i
$99$	2.97650	−	2.43056i	0.299149	−	0.244280i
$100$	−4.30232	+	2.54755i	−0.430232	+	0.254755i
$101$	6.05189	−	1.96638i	0.602185	−	0.195662i	0.00797045	−	0.999968i	$-0.497463\pi$
$101$	6.05189	−	1.96638i	0.602185	−	0.195662i	0.594215	+	0.804306i	$0.297463\pi$
$102$	−0.790885	+	6.10388i	−0.0783092	+	0.604374i
$103$	−2.56488	+	16.1940i	−0.252725	+	1.59564i	0.455882	+	0.890040i	$0.349324\pi$
$103$	−2.56488	+	16.1940i	−0.252725	+	1.59564i	−0.708607	+	0.705603i	$0.750676\pi$
$104$	−0.263593	+	0.811254i	−0.0258474	+	0.0795500i
$105$	2.97046	−	16.7316i	0.289887	−	1.63284i
$106$	6.62608	+	4.81413i	0.643582	+	0.467589i
$107$	−14.1491	−	7.20932i	−1.36784	−	0.696951i	−0.392937	−	0.919566i	$-0.628541\pi$
$107$	−14.1491	−	7.20932i	−1.36784	−	0.696951i	−0.974907	+	0.222615i	$0.928541\pi$
$108$	1.95897	−	4.81274i	0.188502	−	0.463106i
$109$	10.1246	−	13.9353i	0.969757	−	1.33476i	0.0275872	−	0.999619i	$-0.491218\pi$
$109$	10.1246	−	13.9353i	0.969757	−	1.33476i	0.942170	−	0.335136i	$-0.108782\pi$
$110$	−0.134146	+	2.86111i	−0.0127903	+	0.272797i
$111$	7.17352	+	2.10893i	0.680880	+	0.200171i
$112$	−4.33363	−	0.686379i	−0.409489	−	0.0648567i
$113$	4.75364	−	2.42210i	0.447185	−	0.227852i	−0.215871	−	0.976422i	$-0.569259\pi$
$113$	4.75364	−	2.42210i	0.447185	−	0.227852i	0.663056	+	0.748570i	$0.269259\pi$
$114$	−4.71607	+	6.89211i	−0.441701	+	0.645505i
$115$	0.0366509	−	0.781706i	0.00341772	−	0.0728945i
$116$	−0.868310	+	0.282131i	−0.0806206	+	0.0261952i
$117$	−1.03126	+	2.34201i	−0.0953405	+	0.216519i
$118$	−1.18167	+	1.18167i	−0.108781	+	0.108781i
$119$	15.5916			1.42928
$120$	1.69372	+	3.48300i	0.154615	+	0.317953i
$121$	−7.57176	−	5.50120i	−0.688341	−	0.500109i
$122$	−1.62433	+	10.2556i	−0.147060	+	0.928502i
$123$	10.9697	+	5.20476i	0.989106	+	0.469297i
$124$	−5.56217	−	0.249546i	−0.499498	−	0.0224099i
$125$	3.27874	−	10.6888i	0.293259	−	0.956033i
$126$	−12.7283	−	3.35474i	−1.13392	−	0.298864i
$127$	−2.50582	−	15.8211i	−0.222356	−	1.40390i	−0.806013	−	0.591898i	$-0.798379\pi$
$127$	−2.50582	−	15.8211i	−0.222356	−	1.40390i	0.583657	−	0.812000i	$-0.301621\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	4.78223	+	13.4173i	0.421052	+	1.18132i
$130$	−0.785385	−	1.73817i	−0.0688828	−	0.152448i
$131$	−15.6632	−	5.08927i	−1.36850	−	0.444651i	−0.469626	−	0.882865i	$-0.655611\pi$
$131$	−15.6632	−	5.08927i	−1.36850	−	0.444651i	−0.898871	+	0.438214i	$0.855611\pi$
$132$	2.20025	+	0.285089i	0.191507	+	0.0248138i
$133$	18.8495	+	9.60431i	1.63446	+	0.832800i
$134$	−2.48307	+	1.80406i	−0.214505	+	0.155847i
$135$	4.00580	+	10.9066i	0.344764	+	0.938689i
$136$	−2.87487	+	2.08871i	−0.246518	+	0.179106i
$137$	−22.0055	+	3.48533i	−1.88006	+	0.297772i	−0.988036	−	0.154223i	$-0.950713\pi$
$137$	−22.0055	+	3.48533i	−1.88006	+	0.297772i	−0.892021	+	0.451994i	$0.850713\pi$
$138$	−0.601147	−	0.0778911i	−0.0511730	−	0.00663053i
$139$	−1.67948	+	2.31161i	−0.142452	+	0.196068i	−0.874281	−	0.485420i	$-0.838667\pi$
$139$	−1.67948	+	2.31161i	−0.142452	+	0.196068i	0.731829	+	0.681488i	$0.238667\pi$
$140$	8.19870	−	5.38874i	0.692917	−	0.455431i
$141$	−1.34686	+	1.03787i	−0.113426	+	0.0874042i
$142$	−1.23508	−	7.79798i	−0.103645	−	0.654392i
$143$	−1.07919	−	0.170927i	−0.0902464	−	0.0142936i
$144$	2.79632	−	1.08656i	0.233026	−	0.0905466i
$145$	1.01101	−	1.77360i	0.0839594	−	0.147290i
$146$	0.483621	−	0.157138i	0.0400248	−	0.0130048i
$147$	−2.72671	+	21.0442i	−0.224896	+	1.73570i
$148$	1.95983	+	3.84639i	0.161097	+	0.316171i
$149$	−12.7460			−1.04419			−0.522097	−	0.852886i	$-0.674850\pi$
$149$	−12.7460			−1.04419			−0.522097	+	0.852886i	$0.674850\pi$
$150$	−8.04364	−	3.20934i	−0.656761	−	0.262041i
$151$	5.81907	−	17.9093i	0.473549	−	1.45743i	−0.374355	−	0.927285i	$-0.622136\pi$
$151$	5.81907	−	17.9093i	0.473549	−	1.45743i	0.847904	−	0.530149i	$-0.177864\pi$
$152$	−4.76220	+	0.754259i	−0.386266	+	0.0611785i
$153$	−9.21045	+	5.36805i	−0.744621	+	0.433981i
$154$		−	5.62029i		−	0.452896i
$155$	9.57245	−	7.96041i	0.768878	−	0.639395i
$156$	−1.39169	+	0.496031i	−0.111424	+	0.0397142i
$157$	−3.36439	−	0.532868i	−0.268508	−	0.0425275i	0.0207286	−	0.999785i	$-0.493401\pi$
$157$	−3.36439	−	0.532868i	−0.268508	−	0.0425275i	−0.289237	+	0.957258i	$0.593401\pi$
$158$	0.0843790	+	0.532748i	0.00671283	+	0.0423832i
$159$	0.400370	+	14.1803i	0.0317514	+	1.12457i
$160$	−0.789824	+	2.09193i	−0.0624411	+	0.165382i
$161$			1.53556i			0.121019i
$162$	8.67397	−	2.40046i	0.681492	−	0.188598i
$163$	−10.4972	−	5.34858i	−0.822203	−	0.418933i	−0.00832247	−	0.999965i	$-0.502649\pi$
$163$	−10.4972	−	5.34858i	−0.822203	−	0.418933i	−0.813881	+	0.581032i	$0.802649\pi$
$164$	2.16624	+	6.66700i	0.169155	+	0.520605i
$165$	−4.06718	+	2.84077i	−0.316629	+	0.221154i
$166$	−2.72670	+	8.39191i	−0.211633	+	0.651338i
$167$	1.62625	−	10.2678i	0.125843	−	0.794543i	−0.841348	−	0.540494i	$-0.818237\pi$
$167$	1.62625	−	10.2678i	0.125843	−	0.794543i	0.967191	−	0.254049i	$-0.0817625\pi$
$168$	−3.63989	−	6.67125i	−0.280824	−	0.514698i
$169$	−11.6717	+	3.79238i	−0.897826	+	0.291721i
$170$	1.60922	−	7.78129i	0.123421	−	0.596797i
$171$	−14.4417	+	0.816146i	−1.10438	+	0.0624123i
$172$	−3.73353	+	7.32746i	−0.284679	+	0.558714i
$173$	−3.99475	−	25.2219i	−0.303715	−	1.91758i	−0.389023	−	0.921228i	$-0.627187\pi$
$173$	−3.99475	−	25.2219i	−0.303715	−	1.91758i	0.0853074	−	0.996355i	$-0.472813\pi$
$174$	−1.30507	−	0.893020i	−0.0989368	−	0.0676996i
$175$	−5.44424	+	21.2520i	−0.411546	+	1.60650i
$176$	0.752915	+	1.03630i	0.0567531	+	0.0781139i
$177$	−2.87048	−	0.371931i	−0.215759	−	0.0279561i
$178$	−7.04684	−	3.59055i	−0.528183	−	0.269123i
$179$	−7.38448	+	22.7271i	−0.551942	+	1.69870i	0.151944	+	0.988389i	$0.451447\pi$
$179$	−7.38448	+	22.7271i	−0.551942	+	1.69870i	−0.703886	+	0.710313i	$0.748553\pi$
$180$	−2.98793	+	6.00602i	−0.222707	+	0.447662i
$181$	−5.44987			−0.405085			−0.202543	−	0.979273i	$-0.564920\pi$
$181$	−5.44987			−0.405085			−0.202543	+	0.979273i	$0.564920\pi$
$182$	1.69914	+	3.33475i	0.125949	+	0.247188i
$183$	−15.7877	+	8.61389i	−1.16706	+	0.636757i
$184$	−0.205709	−	0.283135i	−0.0151651	−	0.0208730i
$185$	−9.03067	−	3.40960i	−0.663948	−	0.250678i
$186$	−5.53804	−	7.89494i	−0.406069	−	0.578885i
$187$	−3.21864	−	3.21864i	−0.235370	−	0.235370i
$188$	−0.969612	−	0.153571i	−0.0707162	−	0.0112003i
$189$	−8.85392	−	21.0094i	−0.644028	−	1.52821i
$190$	6.73867	−	8.41593i	0.488874	−	0.610556i
$191$			0.144824i			0.0104791i	0.999986	+	0.00523955i	$0.00166781\pi$
$191$			0.144824i			0.0104791i	−0.999986	+	0.00523955i	$0.998332\pi$
$192$	1.56485	+	0.742466i	0.112933	+	0.0535829i
$193$	6.61777	+	12.9881i	0.476357	+	0.934904i	0.996718	+	0.0809568i	$0.0257976\pi$
$193$	6.61777	+	12.9881i	0.476357	+	0.934904i	−0.520360	+	0.853947i	$0.674202\pi$
$194$	2.28308	+	7.02661i	0.163916	+	0.504481i
$195$	1.55439	−	2.91515i	0.111312	−	0.208758i
$196$	−9.91162	+	7.20121i	−0.707973	+	0.514372i
$197$	4.20275	+	8.24837i	0.299434	+	0.587672i	0.990879	−	0.134757i	$-0.0430255\pi$
$197$	4.20275	+	8.24837i	0.299434	+	0.587672i	−0.691445	+	0.722429i	$0.743025\pi$
$198$	1.93501	+	3.32007i	0.137515	+	0.235947i
$199$	−14.1962	+	19.5394i	−1.00634	+	1.38511i	−0.0849924	+	0.996382i	$0.527087\pi$
$199$	−14.1962	+	19.5394i	−1.00634	+	1.38511i	−0.921351	+	0.388731i	$0.872913\pi$
$200$	−1.84315	−	4.64788i	−0.130331	−	0.328655i
$201$	−5.10025	−	1.49941i	−0.359744	−	0.105761i
$202$	0.995444	+	6.28499i	0.0700392	+	0.442210i
$203$	−1.81864	+	3.56928i	−0.127644	+	0.250515i
$204$	−5.90501	−	1.73600i	−0.413433	−	0.121545i
$205$	−13.6180	−	7.76263i	−0.951119	−	0.542166i
$206$	−15.5934	−	5.06660i	−1.08644	−	0.353007i
$207$	−0.528678	−	0.907102i	−0.0367457	−	0.0630479i
$208$	−0.760032	−	0.387255i	−0.0526987	−	0.0268513i
$209$	−1.90852	−	5.87383i	−0.132015	−	0.406301i
$210$	16.0610	+	5.55129i	1.10831	+	0.383075i
$211$	−5.90437			−0.406474			−0.203237	−	0.979130i	$-0.565146\pi$
$211$	−5.90437			−0.406474			−0.203237	+	0.979130i	$0.565146\pi$
$212$	−5.79140	+	5.79140i	−0.397755	+	0.397755i
$213$	9.39283	−	9.93863i	0.643586	−	0.680984i
$214$	9.33396	−	12.8471i	0.638056	−	0.878209i
$215$	−4.85719	−	17.7359i	−0.331257	−	1.20958i
$216$	4.44704	+	2.68773i	0.302582	+	0.182877i
$217$	−18.0310	+	16.4826i	−1.22403	+	1.11891i
$218$	12.1799	+	12.1799i	0.824924	+	0.824924i
$219$	0.726880	+	0.497383i	0.0491180	+	0.0336101i
$220$	−2.80490	−	0.580071i	−0.189107	−	0.0391084i
$221$	2.88282	+	0.936685i	0.193919	+	0.0630082i
$222$	−3.20515	+	6.75529i	−0.215116	+	0.453386i
$223$	8.29987	−	8.29987i	0.555800	−	0.555800i	−0.372309	−	0.928109i	$-0.621434\pi$
$223$	8.29987	−	8.29987i	0.555800	−	0.555800i	0.928109	+	0.372309i	$0.121434\pi$
$224$	1.35586	−	4.17290i	0.0905920	−	0.278814i
$225$	−4.10076	−	14.4286i	−0.273384	−	0.961905i
$226$	1.64865	+	5.07402i	0.109666	+	0.337519i
$227$	−2.18839	+	13.8169i	−0.145248	+	0.917063i	0.802177	+	0.597086i	$0.203675\pi$
$227$	−2.18839	+	13.8169i	−0.145248	+	0.917063i	−0.947426	+	0.319976i	$0.896325\pi$
$228$	−6.06950	−	5.73617i	−0.401962	−	0.379887i
$229$	10.5042	+	14.4578i	0.694139	+	0.955400i	0.999994	+	0.00332223i	$0.00105750\pi$
$229$	10.5042	+	14.4578i	0.694139	+	0.955400i	−0.305856	+	0.952078i	$0.598942\pi$
$230$	0.766348	+	0.158485i	0.0505315	+	0.0104502i
$231$	7.71085	−	5.94186i	0.507337	−	0.390946i
$232$	−0.142824	−	0.901755i	−0.00937685	−	0.0592031i
$233$	4.43232	+	27.9845i	0.290371	+	1.83333i	0.512955	+	0.858415i	$0.328551\pi$
$233$	4.43232	+	27.9845i	0.290371	+	1.83333i	−0.222585	+	0.974913i	$0.571449\pi$
$234$	−2.15185	−	1.38494i	−0.140671	−	0.0905364i
$235$	1.83439	−	1.20568i	0.119662	−	0.0786501i
$236$	−0.982265	−	1.35197i	−0.0639400	−	0.0880059i
$237$	−0.641706	+	0.678995i	−0.0416833	+	0.0441055i
$238$	−2.43907	+	15.3997i	−0.158101	+	0.998214i
$239$	−5.35775	−	16.4894i	−0.346564	−	1.06661i	−0.960741	−	0.277446i	$-0.910512\pi$
$239$	−5.35775	−	16.4894i	−0.346564	−	1.06661i	0.614178	−	0.789168i	$-0.289488\pi$
$240$	−3.70508	+	1.12801i	−0.239162	+	0.0728128i
$241$	−1.63971	+	5.04651i	−0.105623	+	0.325074i	−0.989876	−	0.141934i	$-0.954668\pi$
$241$	−1.63971	+	5.04651i	−0.105623	+	0.325074i	0.884253	+	0.467008i	$0.154668\pi$
$242$	6.61796	−	6.61796i	0.425418	−	0.425418i
$243$	12.4636	+	9.36260i	0.799541	+	0.600611i
$244$	−9.87527	−	3.20867i	−0.632199	−	0.205414i
$245$	5.54806	−	26.8274i	0.354453	−	1.71394i
$246$	−6.85672	+	10.0205i	−0.437168	+	0.638881i
$247$	2.90820	+	2.90820i	0.185044	+	0.185044i
$248$	1.11659	−	5.45465i	0.0709035	−	0.346371i
$249$	−14.3961	+	5.13112i	−0.912318	+	0.325172i
$250$	10.0443	+	4.91046i	0.635255	+	0.310565i
$251$	13.7083	−	18.8679i	0.865262	−	1.19093i	−0.115027	−	0.993362i	$-0.536695\pi$
$251$	13.7083	−	18.8679i	0.865262	−	1.19093i	0.980289	−	0.197569i	$-0.0633046\pi$
$252$	5.30458	−	12.0468i	0.334157	−	0.758874i
$253$	0.316991	−	0.316991i	0.0199291	−	0.0199291i
$254$	16.0183			1.00508
$255$	12.3770	−	6.01871i	0.775075	−	0.376906i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.97287	+	1.51475i	0.185443	+	0.0944877i	0.544247	−	0.838925i	$-0.316815\pi$
$257$	2.97287	+	1.51475i	0.185443	+	0.0944877i	−0.358804	+	0.933413i	$0.616815\pi$
$258$	−14.0002	+	2.62443i	−0.871613	+	0.163390i
$259$	18.0140	+	5.85311i	1.11934	+	0.363694i
$260$	1.83963	−	0.503805i	0.114089	−	0.0312447i
$261$	−0.154543	−	2.73462i	−0.00956595	−	0.169269i
$262$	7.47687	−	14.6742i	0.461923	−	0.906574i
$263$	−2.61989	−	16.5413i	−0.161549	−	1.01998i	−0.926610	−	0.376023i	$-0.877291\pi$
$263$	−2.61989	−	16.5413i	−0.161549	−	1.01998i	0.765061	−	0.643958i	$-0.222709\pi$
$264$	−0.625774	+	2.12857i	−0.0385137	+	0.131004i
$265$	0.857726	−	18.2939i	0.0526897	−	1.12379i
$266$	−12.4348	+	17.1150i	−0.762426	+	1.04939i
$267$	−2.52392	−	13.4640i	−0.154462	−	0.823985i
$268$	−1.39341	−	2.73472i	−0.0851159	−	0.167049i
$269$	−21.5093	+	15.6274i	−1.31144	+	0.952820i	−0.311447	+	0.950264i	$0.600814\pi$
$269$	−21.5093	+	15.6274i	−1.31144	+	0.952820i	−0.999997	+	0.00255618i	$0.999186\pi$
$270$	−11.3990	+	2.25032i	−0.693718	+	0.136950i
$271$	−3.58092	−	11.0209i	−0.217525	−	0.669474i	−0.998965	−	0.0454927i	$-0.985514\pi$
$271$	−3.58092	−	11.0209i	−0.217525	−	0.669474i	0.781439	−	0.623981i	$-0.214486\pi$
$272$	−1.61327	−	3.16622i	−0.0978189	−	0.191980i
$273$	−2.77881	+	5.85671i	−0.168181	+	0.354464i
$274$		−	22.2798i		−	1.34597i
$275$	5.51100	−	3.26325i	0.332326	−	0.196781i
$276$	0.170972	−	0.581561i	0.0102913	−	0.0350059i
$277$	12.0617	+	1.91038i	0.724717	+	0.114784i	0.507885	−	0.861425i	$-0.330428\pi$
$277$	12.0617	+	1.91038i	0.724717	+	0.114784i	0.216832	+	0.976209i	$0.430428\pi$
$278$	−2.02042	−	2.02042i	−0.121177	−	0.121177i
$279$	4.97669	−	15.9447i	0.297947	−	0.954583i
$280$	4.03983	+	8.94075i	0.241426	+	0.534312i
$281$	6.77588	+	9.32620i	0.404215	+	0.556354i	0.961796	−	0.273769i	$-0.0882702\pi$
$281$	6.77588	+	9.32620i	0.404215	+	0.556354i	−0.557581	+	0.830123i	$0.688270\pi$
$282$	−0.814394	−	1.49263i	−0.0484965	−	0.0888850i
$283$	−5.58529	−	10.9617i	−0.332011	−	0.651608i	0.663298	−	0.748355i	$-0.269156\pi$
$283$	−5.58529	−	10.9617i	−0.332011	−	0.651608i	−0.995309	+	0.0967471i	$0.969156\pi$
$284$	7.89518			0.468493
$285$	18.6706	+	0.347778i	1.10595	+	0.0206006i
$286$	0.337645	−	1.03916i	0.0199654	−	0.0614471i
$287$	27.4054	+	13.9638i	1.61769	+	0.824254i
$288$	0.635742	+	2.93187i	0.0374614	+	0.172762i
$289$	−2.57003	−	3.53734i	−0.151178	−	0.208079i
$290$	1.59361	+	1.27601i	0.0935801	+	0.0749299i
$291$	−7.22657	+	10.5610i	−0.423629	+	0.619094i
$292$	0.0795484	+	0.502249i	0.00465522	+	0.0293919i
$293$	−6.97156	+	13.6825i	−0.407283	+	0.799338i	−0.999981	−	0.00608658i	$-0.998063\pi$
$293$	−6.97156	+	13.6825i	−0.407283	+	0.799338i	0.592699	+	0.805424i	$0.298063\pi$
$294$	−20.3586	−	5.98518i	−1.18733	−	0.349063i
$295$	3.65932	+	0.756770i	0.213054	+	0.0440609i
$296$	−4.10562	+	1.33400i	−0.238634	+	0.0775370i
$297$	−2.50931	+	6.16480i	−0.145605	+	0.357718i
$298$	1.99391	−	12.5891i	0.115504	−	0.729266i
$299$	−0.0922504	+	0.283918i	−0.00533498	+	0.0164194i
$300$	4.42813	−	7.44256i	0.255658	−	0.429696i
$301$	11.1503	+	34.3171i	0.642693	+	1.97800i
$302$	16.7785	+	8.54905i	0.965492	+	0.491943i
$303$	−7.57040	+	8.01031i	−0.434908	+	0.460180i
$304$		−	4.82157i		−	0.276536i
$305$	21.1585	−	9.56037i	1.21153	−	0.547425i
$306$	−3.86113	−	9.93681i	−0.220726	−	0.568049i
$307$	−5.02589	−	31.7322i	−0.286843	−	1.81105i	−0.537820	−	0.843060i	$-0.680752\pi$
$307$	−5.02589	−	31.7322i	−0.286843	−	1.81105i	0.250977	−	0.967993i	$-0.419248\pi$
$308$	5.55109	+	0.879207i	0.316303	+	0.0500975i
$309$	−9.53438	−	26.7501i	−0.542392	−	1.52176i
$310$	6.36494	+	10.6999i	0.361504	+	0.607713i
$311$		−	10.3826i		−	0.588746i	−0.955691	−	0.294373i	$-0.904889\pi$
$311$		−	10.3826i		−	0.588746i	0.955691	−	0.294373i	$-0.0951107\pi$
$312$	−0.272216	−	1.45215i	−0.0154112	−	0.0822119i
$313$	17.8110	−	2.82098i	1.00674	−	0.159451i	0.368774	−	0.929519i	$-0.379778\pi$
$313$	17.8110	−	2.82098i	1.00674	−	0.159451i	0.637962	+	0.770068i	$0.279778\pi$
$314$	1.05261	−	3.23961i	0.0594025	−	0.182822i
$315$	9.36372	+	27.9040i	0.527586	+	1.57221i
$316$	−0.539389			−0.0303430
$317$	13.4066	+	26.3119i	0.752988	+	1.47782i	0.874393	+	0.485219i	$0.161260\pi$
$317$	13.4066	+	26.3119i	0.752988	+	1.47782i	−0.121405	+	0.992603i	$0.538740\pi$
$318$	−14.0684	−	1.82285i	−0.788916	−	0.102221i
$319$	1.11225	−	0.361392i	0.0622740	−	0.0202340i
$320$	−1.94262	−	1.10735i	−0.108596	−	0.0619028i
$321$	27.4938	−	0.776264i	1.53455	−	0.0433269i
$322$	−1.51666	−	0.240215i	−0.0845199	−	0.0133866i
$323$	2.68028	+	16.9227i	0.149135	+	0.941601i
$324$	1.01400	+	8.94270i	0.0563334	+	0.496816i
$325$	−2.28335	+	3.60232i	−0.126657	+	0.199821i
$326$	6.92486	−	9.53125i	0.383532	−	0.527887i
$327$	−3.83363	+	29.5871i	−0.212000	+	1.63617i
$328$	−6.92379	+	1.09662i	−0.382302	+	0.0605507i
$329$	−3.48471	+	2.53179i	−0.192119	+	0.139582i
$330$	−2.16955	−	4.46150i	−0.119430	−	0.245597i
$331$	11.6226	−	8.44431i	0.638836	−	0.464141i	−0.220614	−	0.975361i	$-0.570806\pi$
$331$	11.6226	−	8.44431i	0.638836	−	0.464141i	0.859450	+	0.511220i	$0.170806\pi$
$332$	−7.86204	−	4.00591i	−0.431485	−	0.219853i
$333$	−12.6566	+	2.74444i	−0.693576	+	0.150394i
$334$	9.88694	+	3.21246i	0.540989	+	0.175778i
$335$	6.42065	+	2.42416i	0.350797	+	0.132446i
$336$	7.15852	−	2.55146i	0.390529	−	0.139194i
$337$	13.2210	−	6.73641i	0.720191	−	0.366956i	−0.0551673	−	0.998477i	$-0.517569\pi$
$337$	13.2210	−	6.73641i	0.720191	−	0.366956i	0.775358	+	0.631521i	$0.217569\pi$
$338$	−1.91982	−	12.1213i	−0.104425	−	0.659311i
$339$	−5.21841	+	7.62622i	−0.283425	+	0.414200i
$340$	7.43375	+	2.80667i	0.403152	+	0.152213i
$341$	7.12478	+	0.319653i	0.385828	+	0.0173102i
$342$	1.45307	−	14.3915i	0.0785732	−	0.778205i
$343$	−3.60448	+	22.7578i	−0.194623	+	1.22880i
$344$	−6.65320	−	4.83383i	−0.358716	−	0.260623i
$345$	0.592759	+	1.21896i	0.0319131	+	0.0656265i
$346$	25.5363			1.37284
$347$	7.85826	−	7.85826i	0.421854	−	0.421854i	−0.463988	−	0.885842i	$-0.653582\pi$
$347$	7.85826	−	7.85826i	0.421854	−	0.421854i	0.885842	+	0.463988i	$0.153582\pi$
$348$	1.08618	−	1.14930i	0.0582255	−	0.0616089i
$349$	−21.5876	+	7.01424i	−1.15556	+	0.375464i	−0.823234	−	0.567702i	$-0.807833\pi$
$349$	−21.5876	+	7.01424i	−1.15556	+	0.375464i	−0.332324	+	0.943165i	$0.607833\pi$
$350$	−20.1387	−	8.70175i	−1.07646	−	0.465128i
$351$	−0.374882	−	4.41645i	−0.0200097	−	0.235733i
$352$	−1.14132	+	0.581532i	−0.0608326	+	0.0309958i
$353$	4.74954	+	0.752252i	0.252792	+	0.0400384i	0.281544	−	0.959548i	$-0.409153\pi$
$353$	4.74954	+	0.752252i	0.252792	+	0.0400384i	−0.0287521	+	0.999587i	$0.509153\pi$
$354$	0.816395	−	2.77696i	0.0433909	−	0.147594i
$355$	−13.0543	+	11.8850i	−0.692852	+	0.630792i
$356$	4.64871	−	6.39840i	0.246381	−	0.339115i
$357$	−23.7065	+	12.9345i	−1.25468	+	0.684565i
$358$	−21.2921	−	10.8489i	−1.12532	−	0.573380i
$359$	−0.876945	−	0.637138i	−0.0462834	−	0.0336268i	0.564403	−	0.825499i	$-0.309106\pi$
$359$	−0.876945	−	0.637138i	−0.0462834	−	0.0336268i	−0.610686	+	0.791873i	$0.709106\pi$
$360$	−5.46466	−	3.89069i	−0.288013	−	0.205058i
$361$	−1.31255	+	4.03960i	−0.0690814	+	0.212611i
$362$	0.852547	−	5.38277i	0.0448089	−	0.282912i
$363$	16.0762	+	2.08301i	0.843783	+	0.109330i
$364$	−3.55950	+	1.15655i	−0.186568	+	0.0606197i
$365$	−0.887591	−	0.710697i	−0.0464586	−	0.0371996i
$366$	−6.03810	−	16.9408i	−0.315617	−	0.885510i
$367$	−1.05839	−	1.05839i	−0.0552476	−	0.0552476i	0.678943	−	0.734191i	$-0.262438\pi$
$367$	−1.05839	−	1.05839i	−0.0552476	−	0.0552476i	−0.734191	+	0.678943i	$0.762438\pi$
$368$	0.311829	−	0.158885i	0.0162552	−	0.00828244i
$369$	−20.9968	+	1.18660i	−1.09305	+	0.0617718i
$370$	4.78033	−	8.38611i	0.248517	−	0.435973i
$371$			35.9361i			1.86571i
$372$	8.66408	−	4.23482i	0.449212	−	0.219565i
$373$	−13.1802	+	13.1802i	−0.682445	+	0.682445i	−0.960551	−	0.278105i	$-0.910294\pi$
$373$	−13.1802	+	13.1802i	−0.682445	+	0.682445i	0.278105	+	0.960551i	$0.410294\pi$
$374$	3.68252	−	2.67551i	0.190419	−	0.138347i
$375$	3.88197	+	18.9718i	0.200464	+	0.979701i
$376$	0.303361	−	0.933650i	0.0156447	−	0.0481493i
$377$	−0.550686	+	0.550686i	−0.0283618	+	0.0283618i
$378$	22.1358	−	5.45831i	1.13854	−	0.280745i
$379$	−1.34372	−	0.436600i	−0.0690221	−	0.0224266i	0.274302	−	0.961643i	$-0.411553\pi$
$379$	−1.34372	−	0.436600i	−0.0690221	−	0.0224266i	−0.343325	+	0.939217i	$0.611553\pi$
$380$	7.25815	+	7.97224i	0.372335	+	0.408967i
$381$	16.9349	+	21.9767i	0.867599	+	1.12590i
$382$	−0.143041	−	0.0226555i	−0.00731862	−	0.00115915i
$383$	−11.2446	+	5.72939i	−0.574571	+	0.292758i	−0.717030	−	0.697042i	$-0.754499\pi$
$383$	−11.2446	+	5.72939i	−0.574571	+	0.292758i	0.142459	+	0.989801i	$0.454499\pi$
$384$	−0.978121	+	1.42943i	−0.0499145	+	0.0729455i
$385$	−10.5020	+	6.90262i	−0.535232	+	0.351790i
$386$	−13.8634	+	4.50450i	−0.705630	+	0.229273i
$387$	−18.4019	−	16.4332i	−0.935419	−	0.835347i
$388$	−7.29725	+	1.15577i	−0.370462	+	0.0586754i
$389$	−7.48373	−	23.0326i	−0.379440	−	1.16780i	−0.940434	−	0.339977i	$-0.889581\pi$
$389$	−7.48373	−	23.0326i	−0.379440	−	1.16780i	0.560994	−	0.827820i	$-0.310419\pi$
$390$	2.63610	+	1.99129i	0.133484	+	0.100833i
$391$	−1.00613	+	0.730995i	−0.0508821	+	0.0369680i
$392$	−5.56204	−	10.9161i	−0.280925	−	0.551347i
$393$	28.0372	−	5.25576i	1.41429	−	0.265118i
$394$	−8.80427	+	2.86068i	−0.443553	+	0.144119i
$395$	0.891855	−	0.811970i	0.0448741	−	0.0408547i
$396$	−3.58190	+	1.39181i	−0.179997	+	0.0699412i
$397$	12.7312	+	12.7312i	0.638959	+	0.638959i	0.950299	−	0.311340i	$-0.100778\pi$
$397$	12.7312	+	12.7312i	0.638959	+	0.638959i	−0.311340	+	0.950299i	$0.600778\pi$
$398$	−17.0781	−	17.0781i	−0.856047	−	0.856047i
$399$	−36.6275	+	1.03415i	−1.83367	+	0.0517721i
$400$	4.87899	−	1.09337i	0.243949	−	0.0546687i
$401$	−5.16756	−	7.11254i	−0.258056	−	0.355183i	0.660256	−	0.751040i	$-0.270448\pi$
$401$	−5.16756	−	7.11254i	−0.258056	−	0.355183i	−0.918312	+	0.395857i	$0.870448\pi$
$402$	2.27881	−	4.80289i	0.113657	−	0.239547i
$403$	−4.32406	+	1.96432i	−0.215397	+	0.0978496i
$404$	−6.36333			−0.316588
$405$	−15.1385	−	13.2599i	−0.752239	−	0.658891i
$406$	−3.24084	−	2.35461i	−0.160840	−	0.116857i
$407$	−2.51042	−	4.92698i	−0.124437	−	0.244221i
$408$	2.63838	−	5.56073i	0.130619	−	0.275297i
$409$			10.0001i			0.494471i	0.968955	+	0.247235i	$0.0795221\pi$
$409$			10.0001i			0.494471i	−0.968955	+	0.247235i	$0.920478\pi$
$410$	9.79738	−	12.2360i	0.483858	−	0.604291i
$411$	30.5672	−	23.5546i	1.50777	−	1.16186i
$412$	7.44357	−	14.6088i	0.366718	−	0.719725i
$413$	−7.24205	−	1.14703i	−0.356358	−	0.0564415i
$414$	0.978637	−	0.380267i	0.0480974	−	0.0186891i
$415$	19.0298	−	5.21155i	0.934138	−	0.255825i
$416$	0.501383	−	0.690094i	0.0245823	−	0.0338347i
$417$	0.635931	−	4.90798i	0.0311417	−	0.240345i
$418$	6.10007	−	0.966157i	0.298364	−	0.0472563i
$419$	28.0284	+	20.3638i	1.36928	+	0.994837i	0.997793	+	0.0663963i	$0.0211501\pi$
$419$	28.0284	+	20.3638i	1.36928	+	0.994837i	0.371482	+	0.928440i	$0.378850\pi$
$420$	−7.99543	+	14.9948i	−0.390137	+	0.731672i
$421$	−11.4384	−	8.31046i	−0.557472	−	0.405027i	0.273061	−	0.961997i	$-0.411964\pi$
$421$	−11.4384	−	8.31046i	−0.557472	−	0.405027i	−0.830533	+	0.556970i	$0.811964\pi$
$422$	0.923648	−	5.83168i	0.0449625	−	0.283882i
$423$	1.18685	−	2.69536i	0.0577068	−	0.131053i
$424$	−4.81413	−	6.62608i	−0.233795	−	0.321791i
$425$	−16.5164	+	6.54971i	−0.801163	+	0.317708i
$426$	8.34691	+	10.8319i	0.404409	+	0.524809i
$427$	−40.5934	+	20.6834i	−1.96445	+	1.00094i
$428$	11.2288	+	11.2288i	0.542763	+	0.542763i
$429$	1.78266	−	0.635383i	0.0860678	−	0.0306766i
$430$	18.2774	−	2.02288i	0.881414	−	0.0975520i
$431$	2.66077	−	3.66224i	0.128165	−	0.176404i	−0.740112	−	0.672483i	$-0.765228\pi$
$431$	2.66077	−	3.66224i	0.128165	−	0.176404i	0.868277	+	0.496080i	$0.165228\pi$
$432$	−3.35031	+	3.97183i	−0.161192	+	0.191095i
$433$	25.9113	−	25.9113i	1.24522	−	1.24522i	0.287412	−	0.957807i	$-0.407205\pi$
$433$	25.9113	−	25.9113i	1.24522	−	1.24522i	0.957807	−	0.287412i	$-0.0927948\pi$
$434$	−13.4590	−	20.3875i	−0.646052	−	0.978631i
$435$	−0.0658540	+	3.53540i	−0.00315746	+	0.169510i
$436$	−13.9353	+	10.1246i	−0.667378	+	0.484878i
$437$	−1.66665	+	0.263971i	−0.0797265	+	0.0126274i
$438$	−0.604969	+	0.640123i	−0.0289065	+	0.0305863i
$439$			18.0474i			0.861354i	0.902506	+	0.430677i	$0.141725\pi$
$439$			18.0474i			0.861354i	−0.902506	+	0.430677i	$0.858275\pi$
$440$	1.01171	−	2.67963i	0.0482315	−	0.127746i
$441$	−13.3119	−	34.2589i	−0.633901	−	1.63138i
$442$	−1.37613	+	2.70080i	−0.0654556	+	0.128464i
$443$	−10.6616	+	20.9247i	−0.506550	+	0.994161i	0.486187	+	0.873855i	$0.338387\pi$
$443$	−10.6616	+	20.9247i	−0.506550	+	0.994161i	−0.992737	+	0.120306i	$0.961613\pi$
$444$	−6.17073	−	4.22245i	−0.292850	−	0.200389i
$445$	1.94541	+	17.5774i	0.0922213	+	0.833249i
$446$	6.89930	+	9.49607i	0.326691	+	0.449652i
$447$	19.3798	−	10.5738i	0.916633	−	0.500123i
$448$	3.90942	+	1.99195i	0.184703	+	0.0941108i
$449$	16.7719	+	12.1855i	0.791516	+	0.575070i	0.908413	−	0.418074i	$-0.137295\pi$
$449$	16.7719	+	12.1855i	0.791516	+	0.575070i	−0.116897	+	0.993144i	$0.537295\pi$
$450$	14.8924	−	1.79315i	0.702036	−	0.0845299i
$451$	−2.77481	−	8.53999i	−0.130661	−	0.402132i
$452$	−5.26945	+	0.834599i	−0.247854	+	0.0392562i
$453$	6.00944	+	32.0577i	0.282348	+	1.50620i
$454$	−13.3045	−	4.32289i	−0.624411	−	0.202883i
$455$	4.14445	−	7.27060i	0.194295	−	0.340851i
$456$	6.61503	−	5.09744i	0.309777	−	0.238709i
$457$	7.46640	−	14.6536i	0.349264	−	0.685469i	−0.647819	−	0.761794i	$-0.724319\pi$
$457$	7.46640	−	14.6536i	0.349264	−	0.685469i	0.997083	+	0.0763255i	$0.0243188\pi$
$458$	−15.9231	+	8.11320i	−0.744035	+	0.379105i
$459$	9.55093	−	15.8027i	0.445799	−	0.737606i
$460$	−0.276418	+	0.732121i	−0.0128880	+	0.0341353i
$461$	13.2728	+	4.31261i	0.618178	+	0.200858i	0.601331	−	0.799000i	$-0.294637\pi$
$461$	13.2728	+	4.31261i	0.618178	+	0.200858i	0.0168466	+	0.999858i	$0.494637\pi$
$462$	4.66246	+	8.54543i	0.216917	+	0.397569i
$463$	5.76061	−	36.3711i	0.267718	−	1.69031i	−0.377261	−	0.926107i	$-0.623134\pi$
$463$	5.76061	−	36.3711i	0.267718	−	1.69031i	0.644979	−	0.764200i	$-0.276866\pi$
$464$	0.912995			0.0423847
$465$	−7.95077	+	20.0446i	−0.368708	+	0.929545i
$466$	−28.3334			−1.31252
$467$	−5.55937	+	35.1005i	−0.257257	+	1.62426i	0.433490	+	0.901159i	$0.357282\pi$
$467$	−5.55937	+	35.1005i	−0.257257	+	1.62426i	−0.690747	+	0.723097i	$0.742718\pi$
$468$	1.70451	−	1.90871i	0.0787911	−	0.0882301i
$469$	−12.8076	−	4.16145i	−0.591402	−	0.192158i
$470$	0.903878	+	2.00041i	0.0416928	+	0.0922723i
$471$	5.55749	−	1.98082i	0.256075	−	0.0912713i
$472$	1.48899	−	0.758677i	0.0685362	−	0.0349209i
$473$	4.78241	−	9.38600i	0.219895	−	0.431569i
$474$	−0.570251	−	0.740024i	−0.0261925	−	0.0339904i
$475$	−24.0021	−	2.25567i	−1.10129	−	0.103497i
$476$	−14.8285	−	4.81808i	−0.679665	−	0.220837i
$477$	−12.3724	−	21.2285i	−0.566494	−	0.971987i
$478$	17.1246	−	2.71227i	0.783260	−	0.124056i
$479$	0.566626	+	1.74390i	0.0258898	+	0.0796807i	0.963167	−	0.268905i	$-0.0866619\pi$
$479$	0.566626	+	1.74390i	0.0258898	+	0.0796807i	−0.937277	+	0.348586i	$0.886662\pi$
$480$	−0.534521	−	3.83592i	−0.0243975	−	0.175085i
$481$	2.97907	+	2.16442i	0.135834	+	0.0986891i
$482$	−4.72787	−	2.40897i	−0.215349	−	0.109726i
$483$	−1.27387	−	2.33476i	−0.0579629	−	0.106235i
$484$	5.50120	+	7.57176i	0.250055	+	0.344171i
$485$	10.3258	−	12.8960i	0.468872	−	0.585575i
$486$	−11.1971	+	10.8455i	−0.507909	+	0.491964i
$487$	6.89077	−	13.5239i	0.312250	−	0.612826i	−0.680537	−	0.732714i	$-0.738253\pi$
$487$	6.89077	−	13.5239i	0.312250	−	0.612826i	0.992787	+	0.119888i	$0.0382534\pi$
$488$	4.71400	−	9.25174i	0.213393	−	0.418807i
$489$	20.3976	−	0.575910i	0.922413	−	0.0260435i
$490$	25.6292	+	9.67648i	1.15781	+	0.437139i
$491$			26.3678i			1.18996i	0.803739	+	0.594982i	$0.202841\pi$
$491$			26.3678i			1.18996i	−0.803739	+	0.594982i	$0.797159\pi$
$492$	−8.82447	−	8.33985i	−0.397838	−	0.375989i
$493$	−3.20442	+	0.507530i	−0.144320	+	0.0228580i
$494$	−3.32733	+	2.41745i	−0.149704	+	0.108766i
$495$	3.82735	−	7.69332i	0.172026	−	0.345789i
$496$	5.21282	+	1.95614i	0.234063	+	0.0878332i
$497$	24.4951	−	24.4951i	1.09875	−	1.09875i
$498$	−2.81590	−	15.0216i	−0.126183	−	0.673133i
$499$	11.7604	−	16.1868i	0.526469	−	0.724622i	−0.460118	−	0.887858i	$-0.652193\pi$
$499$	11.7604	−	16.1868i	0.526469	−	0.724622i	0.986587	+	0.163236i	$0.0521931\pi$
$500$	−6.42128	+	9.15244i	−0.287168	+	0.409310i
$501$	6.04524	+	16.9608i	0.270081	+	0.757754i
$502$	16.4911	+	16.4911i	0.736036	+	0.736036i
$503$	7.71069	−	3.92880i	0.343803	−	0.175176i	−0.273560	−	0.961855i	$-0.588201\pi$
$503$	7.71069	−	3.92880i	0.343803	−	0.175176i	0.617363	+	0.786679i	$0.288201\pi$
$504$	11.0686	+	7.12380i	0.493036	+	0.317319i
$505$	10.5215	−	9.57905i	0.468200	−	0.426262i
$506$	0.263500	+	0.362677i	0.0117140	+	0.0161230i
$507$	14.6003	−	15.4488i	0.648424	−	0.686103i
$508$	−2.50582	+	15.8211i	−0.111178	+	0.701949i
$509$	26.6876	+	19.3897i	1.18291	+	0.859433i	0.992497	−	0.122271i	$-0.0390179\pi$
$509$	26.6876	+	19.3897i	1.18291	+	0.859433i	0.190411	+	0.981704i	$0.439018\pi$
$510$	4.00842	+	13.1661i	0.177496	+	0.583005i
$511$	1.80505	+	1.31144i	0.0798505	+	0.0580148i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	21.2809	−	13.2214i	0.939575	−	0.583738i
$514$	−1.96116	+	2.69931i	−0.0865032	+	0.119061i
$515$	9.68382	+	35.3602i	0.426720	+	1.55816i
$516$	−0.402008	−	14.2384i	−0.0176974	−	0.626809i
$517$	1.24201	+	0.196715i	0.0546235	+	0.00865152i
$518$	−8.59906	+	16.8766i	−0.377821	+	0.741515i
$519$	26.9973	+	35.0349i	1.18505	+	1.53786i
$520$	0.209821	+	1.89580i	0.00920124	+	0.0831362i
$521$			13.4279i			0.588289i	0.955761	+	0.294144i	$0.0950346\pi$
$521$			13.4279i			0.588289i	−0.955761	+	0.294144i	$0.904965\pi$
$522$	2.72513	+	0.275149i	0.119276	+	0.0120430i
$523$	13.9426	+	27.3639i	0.609667	+	1.19654i	0.965111	+	0.261841i	$0.0843296\pi$
$523$	13.9426	+	27.3639i	0.609667	+	1.19654i	−0.355444	+	0.934698i	$0.615670\pi$
$524$	13.3239	+	9.68036i	0.582056	+	0.422889i
$525$	−9.35239	−	36.8292i	−0.408172	−	1.60736i
$526$	16.7475			0.730226
$527$	−19.3833	−	3.96784i	−0.844349	−	0.172842i
$528$	−2.00447	−	0.951051i	−0.0872332	−	0.0413892i
$529$	13.4471	+	18.5083i	0.584655	+	0.804709i
$530$	17.9345	+	3.70897i	0.779026	+	0.161107i
$531$	4.67301	−	1.81578i	0.202791	−	0.0787982i
$532$	−14.9591	−	14.9591i	−0.648558	−	0.648558i
$533$	4.22824	+	4.22824i	0.183145	+	0.183145i
$534$	13.6931	−	0.386613i	0.592558	−	0.0167304i
$535$	−35.4695	−	1.66302i	−1.53348	−	0.0718986i
$536$	2.91902	−	0.948448i	0.126083	−	0.0409667i
$537$	−7.62605	−	40.6816i	−0.329089	−	1.75554i
$538$	−12.0702	−	23.6891i	−0.520384	−	1.02131i
$539$	12.6961	−	9.22429i	0.546862	−	0.397318i
$540$	−0.439422	−	11.6106i	−0.0189097	−	0.499642i
$541$	−3.23334	−	9.95121i	−0.139012	−	0.427836i	0.857180	−	0.515017i	$-0.172214\pi$
$541$	−3.23334	−	9.95121i	−0.139012	−	0.427836i	−0.996193	+	0.0871807i	$0.972214\pi$
$542$	11.4454	−	1.81278i	0.491623	−	0.0778654i
$543$	8.28631	−	4.52108i	0.355600	−	0.194018i
$544$	3.37961	−	1.09810i	0.144900	−	0.0470807i
$545$	7.80031	−	37.7180i	0.334128	−	1.61566i
$546$	−5.34991	−	3.66079i	−0.228955	−	0.156667i
$547$	−9.42150	+	4.80049i	−0.402834	+	0.205254i	−0.643656	−	0.765315i	$-0.722583\pi$
$547$	−9.42150	+	4.80049i	−0.402834	+	0.205254i	0.240822	+	0.970569i	$0.422583\pi$
$548$	22.0055	+	3.48533i	0.940028	+	0.148886i
$549$	16.8587	−	26.1942i	0.719510	−	1.11794i
$550$	2.36096	+	5.95363i	0.100672	+	0.253864i
$551$	−4.18661	−	1.36031i	−0.178356	−	0.0579513i
$552$	0.547655	+	0.259843i	0.0233097	+	0.0110597i
$553$	−1.67347	+	1.67347i	−0.0711633	+	0.0711633i
$554$	−3.77373	+	11.6143i	−0.160330	+	0.493446i
$555$	16.5593	−	2.30748i	0.702903	−	0.0979470i
$556$	2.31161	−	1.67948i	0.0980342	−	0.0712260i
$557$	−21.6201	+	21.6201i	−0.916074	+	0.916074i	−0.996741	−	0.0806671i	$-0.974295\pi$
$557$	−21.6201	+	21.6201i	−0.916074	+	0.916074i	0.0806671	+	0.996741i	$0.474295\pi$
$558$	14.9698	+	7.40971i	0.633724	+	0.313678i
$559$			7.01493i			0.296700i
$560$	−9.46264	+	2.59146i	−0.399869	+	0.109509i
$561$	7.56393	+	2.22371i	0.319349	+	0.0938850i
$562$	−10.2714	+	5.23352i	−0.433271	+	0.220763i
$563$	−24.0699	−	24.0699i	−1.01443	−	1.01443i	−0.999894	−	0.0145309i	$-0.995374\pi$
$563$	−24.0699	−	24.0699i	−1.01443	−	1.01443i	−0.0145309	−	0.999894i	$-0.504626\pi$
$564$	1.60166	−	0.570868i	0.0674419	−	0.0240379i
$565$	7.45644	−	9.31235i	0.313695	−	0.391774i
$566$	11.7005	−	3.80173i	0.491810	−	0.159799i
$567$	30.8910	+	24.5990i	1.29730	+	1.03306i
$568$	−1.23508	+	7.79798i	−0.0518227	+	0.327196i
$569$	8.99333	−	27.6786i	0.377020	−	1.16035i	−0.565086	−	0.825032i	$-0.691157\pi$
$569$	8.99333	−	27.6786i	0.377020	−	1.16035i	0.942106	−	0.335316i	$-0.108843\pi$
$570$	−3.26422	+	18.3863i	−0.136723	+	0.770119i
$571$	33.4281	+	24.2869i	1.39892	+	1.01638i	0.994819	+	0.101664i	$0.0324166\pi$
$571$	33.4281	+	24.2869i	1.39892	+	1.01638i	0.404104	+	0.914713i	$0.367583\pi$
$572$	0.973551	+	0.496049i	0.0407062	+	0.0207409i
$573$	−0.120143	−	0.220199i	−0.00501903	−	0.00919896i
$574$	−18.0790	+	24.8836i	−0.754602	+	1.03862i
$575$	−0.645056	−	1.62664i	−0.0269007	−	0.0678354i
$576$	−2.99522	+	0.169270i	−0.124801	+	0.00705292i
$577$	25.5884	+	4.05281i	1.06526	+	0.168721i	0.664369	−	0.747405i	$-0.268700\pi$
$577$	25.5884	+	4.05281i	1.06526	+	0.168721i	0.400892	+	0.916126i	$0.368700\pi$
$578$	3.89584	−	1.98503i	0.162045	−	0.0825663i
$579$	−20.8367	−	14.2579i	−0.865943	−	0.592540i
$580$	−1.50960	+	1.37438i	−0.0626826	+	0.0570680i
$581$	−36.8207	+	11.9638i	−1.52758	+	0.496341i
$582$	−9.30045	−	8.78969i	−0.385516	−	0.364345i
$583$	7.41841	−	7.41841i	0.307239	−	0.307239i
$584$	−0.508509			−0.0210423
$585$	0.0549417	+	5.72186i	0.00227156	+	0.236570i
$586$	−12.4234	−	9.02614i	−0.513206	−	0.372866i
$587$	2.74297	−	17.3184i	0.113214	−	0.714807i	−0.864149	−	0.503237i	$-0.832142\pi$
$587$	2.74297	−	17.3184i	0.113214	−	0.714807i	0.977363	−	0.211570i	$-0.0678577\pi$
$588$	9.09627	−	19.1716i	0.375124	−	0.790624i
$589$	−20.9893	−	16.7368i	−0.864848	−	0.689630i
$590$	−1.31990	+	3.49589i	−0.0543393	+	0.143923i
$591$	−13.2328	−	9.05482i	−0.544324	−	0.372465i
$592$	−0.675313	−	4.26376i	−0.0277552	−	0.175239i
$593$	19.3000	−	9.83385i	0.792557	−	0.403828i	−0.0103395	−	0.999947i	$-0.503291\pi$
$593$	19.3000	−	9.83385i	0.792557	−	0.403828i	0.802896	+	0.596119i	$0.203291\pi$
$594$	−5.69636	−	3.44280i	−0.233725	−	0.141260i
$595$	31.7712	−	14.3557i	1.30249	−	0.588526i
$596$	12.1222	+	3.93873i	0.496543	+	0.161337i
$597$	5.37535	−	41.4858i	0.219998	−	1.69790i
$598$	−0.265991	−	0.135529i	−0.0108772	−	0.00554220i
$599$	1.48430	−	1.07841i	0.0606469	−	0.0440626i	−0.557049	−	0.830480i	$-0.688066\pi$
$599$	1.48430	−	1.07841i	0.0606469	−	0.0440626i	0.617696	+	0.786417i	$0.288066\pi$
$600$	6.65822	+	5.53788i	0.271821	+	0.226083i
$601$	−4.52491	+	3.28754i	−0.184575	+	0.134101i	−0.676236	−	0.736685i	$-0.736390\pi$
$601$	−4.52491	+	3.28754i	−0.184575	+	0.134101i	0.491661	+	0.870787i	$0.336390\pi$
$602$	−35.6389	+	5.64465i	−1.45253	+	0.230059i
$603$	8.99861	−	1.95125i	0.366452	−	0.0794609i
$604$	−11.0685	+	15.2345i	−0.450372	+	0.619884i
$605$	−20.4942	−	4.23831i	−0.833206	−	0.172312i
$606$	−6.72741	−	8.73028i	−0.273283	−	0.354643i
$607$	−2.75594	−	17.4003i	−0.111860	−	0.706258i	−0.978334	−	0.207035i	$-0.933619\pi$
$607$	−2.75594	−	17.4003i	−0.111860	−	0.706258i	0.866473	−	0.499223i	$-0.166381\pi$
$608$	4.76220	+	0.754259i	0.193133	+	0.0305892i
$609$	−0.195822	−	6.93566i	−0.00793512	−	0.281047i
$610$	6.13275	+	22.3936i	0.248308	+	0.906689i
$611$	−0.796407	+	0.258768i	−0.0322192	+	0.0104686i
$612$	10.4185	−	2.25913i	0.421142	−	0.0913199i
$613$	−18.9139	−	37.1206i	−0.763926	−	1.49929i	−0.863550	−	0.504263i	$-0.831764\pi$
$613$	−18.9139	−	37.1206i	−0.763926	−	1.49929i	0.0996246	−	0.995025i	$-0.468236\pi$
$614$	32.1278			1.29657
$615$	27.1453	+	0.505636i	1.09460	+	0.0203892i
$616$	−1.73676	+	5.34521i	−0.0699763	+	0.215365i
$617$	−46.7525	+	7.40487i	−1.88218	+	0.298109i	−0.988574	−	0.150736i	$-0.951836\pi$
$617$	−46.7525	+	7.40487i	−1.88218	+	0.298109i	−0.893610	+	0.448844i	$0.851836\pi$
$618$	27.9123	−	5.23235i	1.12280	−	0.210476i
$619$			26.7669i			1.07585i	0.842992	+	0.537926i	$0.180792\pi$
$619$			26.7669i			1.07585i	−0.842992	+	0.537926i	$0.819208\pi$
$620$	−11.5638	+	4.61275i	−0.464415	+	0.185252i
$621$	1.55634	+	0.940634i	0.0624540	+	0.0377463i
$622$	10.2548	+	1.62420i	0.411181	+	0.0651246i
$623$	−5.42847	−	34.2740i	−0.217487	−	1.37316i
$624$	1.47686	−	0.0416978i	0.0591216	−	0.00166925i
$625$	−3.16035	−	24.7994i	−0.126414	−	0.991978i
$626$			18.0330i			0.720744i
$627$	7.77463	+	7.34767i	0.310489	+	0.293437i
$628$	3.03506	+	1.54644i	0.121112	+	0.0617098i
$629$	4.74040	+	14.5895i	0.189012	+	0.581720i
$630$	−29.0253	+	4.88329i	−1.15640	+	0.194555i
$631$	4.53757	−	13.9652i	0.180638	−	0.555947i	−0.819208	−	0.573497i	$-0.805587\pi$
$631$	4.53757	−	13.9652i	0.180638	−	0.555947i	0.999846	+	0.0175500i	$0.00558661\pi$
$632$	0.0843790	−	0.532748i	0.00335642	−	0.0211916i
$633$	8.97737	−	4.89813i	0.356818	−	0.194683i
$634$	−28.0852	+	9.12543i	−1.11541	+	0.362417i
$635$	−19.6731	−	29.9317i	−0.780704	−	1.18780i
$636$	4.00119	−	13.6100i	0.158658	−	0.539672i
$637$	−4.74443	+	9.31148i	−0.187981	+	0.368934i
$638$	0.182948	+	1.15509i	0.00724299	+	0.0457304i
$639$	−6.03657	+	22.9034i	−0.238803	+	0.906044i
$640$	1.39761	−	1.74548i	0.0552454	−	0.0689960i
$641$	−1.72264	−	2.37100i	−0.0680400	−	0.0936490i	0.773641	−	0.633624i	$-0.218434\pi$
$641$	−1.72264	−	2.37100i	−0.0680400	−	0.0936490i	−0.841681	+	0.539975i	$0.818434\pi$
$642$	−3.53427	+	27.2767i	−0.139487	+	1.07653i
$643$	−5.32235	−	2.71187i	−0.209893	−	0.106946i	0.345884	−	0.938277i	$-0.387579\pi$
$643$	−5.32235	−	2.71187i	−0.209893	−	0.106946i	−0.555777	+	0.831332i	$0.687579\pi$
$644$	0.474514	−	1.46040i	0.0186985	−	0.0575480i
$645$	22.0985	+	22.9373i	0.870126	+	0.903157i
$646$	−17.1336			−0.674112
$647$	−13.2753	−	26.0542i	−0.521905	−	1.02430i	−0.990059	−	0.140650i	$-0.955081\pi$
$647$	−13.2753	−	26.0542i	−0.521905	−	1.02430i	0.468154	−	0.883647i	$-0.344919\pi$
$648$	−8.99122	−	0.397428i	−0.353209	−	0.0156124i
$649$	1.25822	+	1.73179i	0.0493894	+	0.0679786i
$650$	−3.20077	−	2.81876i	−0.125545	−	0.110561i
$651$	13.7419	−	40.0193i	0.538589	−	1.56848i
$652$	8.33062	+	8.33062i	0.326252	+	0.326252i
$653$	−38.6227	−	6.11724i	−1.51142	−	0.239386i	−0.654988	−	0.755639i	$-0.727326\pi$
$653$	−38.6227	−	6.11724i	−1.51142	−	0.239386i	−0.856436	+	0.516253i	$0.827326\pi$
$654$	−28.6231	−	8.41488i	−1.11925	−	0.329048i
$655$	−36.6028	+	4.05108i	−1.43019	+	0.158289i
$656$		−	7.01009i		−	0.273698i
$657$	−1.51781	−	0.153249i	−0.0592154	−	0.00597882i
$658$	−1.95549	−	3.83787i	−0.0762331	−	0.149616i
$659$	−2.66056	−	8.18836i	−0.103641	−	0.318973i	0.885768	−	0.464128i	$-0.153632\pi$
$659$	−2.66056	−	8.18836i	−0.103641	−	0.318973i	−0.989409	+	0.145154i	$0.953632\pi$
$660$	4.74596	−	1.44491i	0.184736	−	0.0562430i
$661$	−17.1223	+	12.4401i	−0.665981	+	0.483864i	−0.868678	−	0.495378i	$-0.835030\pi$
$661$	−17.1223	+	12.4401i	−0.665981	+	0.483864i	0.202696	+	0.979242i	$0.435030\pi$
$662$	6.52217	+	12.8005i	0.253491	+	0.497505i
$663$	−5.16027	+	0.967328i	−0.200408	+	0.0375679i
$664$	5.18648	−	7.13858i	0.201275	−	0.277031i
$665$	47.2528	+	2.21549i	1.83239	+	0.0859130i
$666$	−0.730722	−	12.9301i	−0.0283149	−	0.501031i
$667$	−0.0499846	−	0.315590i	−0.00193541	−	0.0122197i
$668$	−4.71957	+	9.26268i	−0.182606	+	0.358384i
$669$	−5.73425	+	19.5050i	−0.221699	+	0.754107i
$670$	−3.39873	+	5.96238i	−0.131304	+	0.230347i
$671$	12.6496	+	4.11010i	0.488332	+	0.158669i
$672$	1.40021	+	7.46952i	0.0540144	+	0.288143i
$673$	8.11236	+	4.13345i	0.312708	+	0.159333i	0.603300	−	0.797514i	$-0.293852\pi$
$673$	8.11236	+	4.13345i	0.312708	+	0.159333i	−0.290592	+	0.956847i	$0.593852\pi$
$674$	4.58526	+	14.1120i	0.176618	+	0.543573i
$675$	18.2047	+	18.5362i	0.700698	+	0.713458i
$676$	12.2724			0.472015
$677$	−14.2500	+	14.2500i	−0.547670	+	0.547670i	−0.925766	−	0.378096i	$-0.876579\pi$
$677$	−14.2500	+	14.2500i	−0.547670	+	0.547670i	0.378096	+	0.925766i	$0.376579\pi$
$678$	−6.71599	−	6.34716i	−0.257926	−	0.243761i
$679$	−19.0542	+	26.2258i	−0.731231	+	1.00645i
$680$	−3.93501	+	6.90317i	−0.150901	+	0.264724i
$681$	−8.13486	−	22.8236i	−0.311728	−	0.874601i
$682$	−1.43028	+	6.98706i	−0.0547682	+	0.267548i
$683$	−0.498234	−	0.498234i	−0.0190644	−	0.0190644i	0.697510	−	0.716575i	$-0.254291\pi$
$683$	−0.498234	−	0.498234i	−0.0190644	−	0.0190644i	−0.716575	+	0.697510i	$0.754291\pi$
$684$	13.9870	+	3.68651i	0.534807	+	0.140957i
$685$	−41.6318	+	27.3632i	−1.59067	+	1.04549i
$686$	−21.9137	−	7.12020i	−0.836669	−	0.271850i
$687$	−27.9651	−	13.2685i	−1.06694	−	0.506225i
$688$	5.81511	−	5.81511i	0.221699	−	0.221699i
$689$	−2.15890	+	6.64440i	−0.0822474	+	0.253132i
$690$	−1.29668	+	0.394774i	−0.0493637	+	0.0150288i
$691$	3.85197	+	11.8552i	0.146536	+	0.450992i	0.997205	−	0.0747097i	$-0.0238030\pi$
$691$	3.85197	+	11.8552i	0.146536	+	0.450992i	−0.850669	+	0.525701i	$0.823803\pi$
$692$	−3.99475	+	25.2219i	−0.151858	+	0.958791i
$693$	−6.79482	+	15.4311i	−0.258114	+	0.586180i
$694$	6.53221	+	8.99082i	0.247959	+	0.341287i
$695$	−1.29393	+	6.25674i	−0.0490816	+	0.237332i
$696$	0.965233	+	1.25260i	0.0365871	+	0.0474797i
$697$	3.89688	+	24.6039i	0.147605	+	0.931940i
$698$	−3.55084	−	22.4191i	−0.134401	−	0.848575i
$699$	−29.9545	−	38.8725i	−1.13298	−	1.47029i
$700$	11.7450	−	18.5295i	0.443919	−	0.700348i
$701$	−7.49714	−	10.3189i	−0.283163	−	0.389740i	0.643615	−	0.765349i	$-0.277434\pi$
$701$	−7.49714	−	10.3189i	−0.283163	−	0.389740i	−0.926778	+	0.375609i	$0.877434\pi$
$702$	4.42072	+	0.320619i	0.166849	+	0.0121010i
$703$	−3.25606	+	20.5580i	−0.122805	+	0.775359i
$704$	−0.395831	−	1.21824i	−0.0149184	−	0.0459142i
$705$	−1.78891	+	3.35496i	−0.0673742	+	0.126355i
$706$	−1.48598	+	4.57338i	−0.0559257	+	0.172122i
$707$	−19.7425	+	19.7425i	−0.742491	+	0.742491i
$708$	2.61506	+	1.24076i	0.0982800	+	0.0466305i
$709$	45.8980	+	14.9132i	1.72374	+	0.560076i	0.992521	−	0.122071i	$-0.0389537\pi$
$709$	45.8980	+	14.9132i	1.72374	+	0.560076i	0.731215	+	0.682147i	$0.238954\pi$
$710$	−9.69656	−	14.7528i	−0.363905	−	0.553664i
$711$	0.412411	−	1.56473i	0.0154666	−	0.0586820i
$712$	5.59241	+	5.59241i	0.209584	+	0.209584i
$713$	0.390777	−	1.90898i	0.0146347	−	0.0714920i
$714$	−9.06671	−	25.4380i	−0.339313	−	0.951994i
$715$	−2.35645	+	0.645342i	−0.0881263	+	0.0241344i
$716$	14.0461	−	19.3328i	0.524928	−	0.722501i
$717$	21.8255	+	20.6269i	0.815089	+	0.770326i
$718$	0.766478	−	0.766478i	0.0286047	−	0.0286047i
$719$	−41.9784			−1.56553			−0.782764	−	0.622318i	$-0.786191\pi$
$719$	−41.9784			−1.56553			−0.782764	+	0.622318i	$0.786191\pi$
$720$	4.69765	−	4.78874i	0.175071	−	0.178466i
$721$	−22.2305	−	68.4183i	−0.827906	−	2.54803i
$722$	−3.78454	−	1.92832i	−0.140846	−	0.0717646i
$723$	−1.69335	−	9.03329i	−0.0629765	−	0.335952i
$724$	5.18313	+	1.68410i	0.192630	+	0.0625891i
$725$	0.427127	−	4.54495i	0.0158631	−	0.168795i
$726$	−4.57224	+	15.5525i	−0.169692	+	0.577206i
$727$	12.3399	−	24.2183i	0.457660	−	0.898208i	−0.540714	−	0.841206i	$-0.681846\pi$
$727$	12.3399	−	24.2183i	0.457660	−	0.898208i	0.998374	−	0.0570019i	$-0.0181541\pi$
$728$	−0.585484	−	3.69660i	−0.0216995	−	0.137005i
$729$	−26.7174	−	3.89593i	−0.989535	−	0.144294i
$730$	0.840797	−	0.765485i	0.0311193	−	0.0283319i
$731$	−17.1772	+	23.6424i	−0.635321	+	0.874444i
$732$	17.6768	−	3.31364i	0.653354	−	0.122476i
$733$	−7.12587	−	13.9853i	−0.263200	−	0.516559i	0.721151	−	0.692778i	$-0.243613\pi$
$733$	−7.12587	−	13.9853i	−0.263200	−	0.516559i	−0.984351	+	0.176219i	$0.943613\pi$
$734$	1.21093	−	0.879792i	0.0446962	−	0.0324737i
$735$	13.8198	+	45.3925i	0.509749	+	1.67433i
$736$	0.108148	+	0.332845i	0.00398638	+	0.0122688i
$737$	1.78486	+	3.50299i	0.0657463	+	0.129034i
$738$	2.11263	−	20.9239i	0.0777670	−	0.770219i
$739$			30.7634i			1.13165i	0.824526	+	0.565824i	$0.191442\pi$
$739$			30.7634i			1.13165i	−0.824526	+	0.565824i	$0.808558\pi$
$740$	7.53505	+	6.03335i	0.276994	+	0.221790i
$741$	−6.83437	−	2.00923i	−0.251067	−	0.0738108i
$742$	−35.4936	−	5.62164i	−1.30301	−	0.206377i
$743$	−0.861577	−	0.861577i	−0.0316082	−	0.0316082i	0.691126	−	0.722734i	$-0.257115\pi$
$743$	−0.861577	−	0.861577i	−0.0316082	−	0.0316082i	−0.722734	+	0.691126i	$0.757115\pi$
$744$	2.82732	+	9.21988i	0.103655	+	0.338017i
$745$	−25.9726	+	11.7356i	−0.951564	+	0.429960i
$746$	−10.9561	−	15.0798i	−0.401131	−	0.552110i
$747$	17.6321	−	19.7444i	0.645125	−	0.722409i
$748$	2.06649	+	4.05572i	0.0755585	+	0.148292i
$749$	69.6753			2.54588
$750$	−19.3455	+	0.866324i	−0.706399	+	0.0316337i
$751$	−6.39127	+	19.6703i	−0.233221	+	0.717780i	0.764132	+	0.645060i	$0.223168\pi$
$751$	−6.39127	+	19.6703i	−0.233221	+	0.717780i	−0.997352	+	0.0727194i	$0.976832\pi$
$752$	0.874699	+	0.445682i	0.0318970	+	0.0162523i
$753$	−5.19061	+	40.0600i	−0.189156	+	1.45987i
$754$	−0.457760	−	0.630053i	−0.0166706	−	0.0229452i
$755$	−4.63200	−	41.8516i	−0.168576	−	1.52314i
$756$	1.92830	+	22.7172i	0.0701317	+	0.826216i
$757$	−1.19201	−	7.52605i	−0.0433243	−	0.273539i	0.956511	−	0.291697i	$-0.0942198\pi$
$757$	−1.19201	−	7.52605i	−0.0433243	−	0.273539i	−0.999835	+	0.0181579i	$0.994220\pi$
$758$	0.641429	−	1.25887i	0.0232977	−	0.0457244i
$759$	−0.219004	+	0.744942i	−0.00794935	+	0.0270397i
$760$	−9.00952	+	5.92166i	−0.326810	+	0.214801i
$761$	24.1058	−	7.83246i	0.873835	−	0.283926i	0.162440	−	0.986718i	$-0.448064\pi$
$761$	24.1058	−	7.83246i	0.873835	−	0.283926i	0.711395	+	0.702792i	$0.248064\pi$
$762$	−24.3553	+	13.2885i	−0.882299	+	0.481390i
$763$	−11.8228	+	74.6464i	−0.428015	+	2.70238i
$764$	0.0447531	−	0.137736i	0.00161911	−	0.00498311i
$765$	−13.8257	+	19.4189i	−0.499870	+	0.702090i
$766$	−3.89982	−	12.0024i	−0.140906	−	0.433664i
$767$	−1.27011	−	0.647154i	−0.0458610	−	0.0233674i
$768$	−1.25882	−	1.18969i	−0.0454239	−	0.0429293i
$769$		−	39.2089i		−	1.41391i	−0.707259	−	0.706954i	$-0.750069\pi$
$769$		−	39.2089i		−	1.41391i	0.707259	−	0.706954i	$-0.249931\pi$
$770$	−5.17476	−	11.4525i	−0.186486	−	0.412720i
$771$	−5.77674	+	0.163101i	−0.208044	+	0.00587395i
$772$	−2.28033	−	14.3974i	−0.0820707	−	0.518174i
$773$	14.4803	+	2.29346i	0.520821	+	0.0824900i	0.411310	−	0.911496i	$-0.365071\pi$
$773$	14.4803	+	2.29346i	0.520821	+	0.0824900i	0.109511	+	0.993986i	$0.465071\pi$
$774$	19.1096	−	15.6046i	0.686879	−	0.560895i
$775$	12.1765	−	25.0346i	0.437393	−	0.899271i
$776$		−	7.38821i		−	0.265221i
$777$	−32.2452	+	6.04458i	−1.15679	+	0.216848i
$778$	23.9197	−	3.78851i	0.857563	−	0.135825i
$779$	−10.4447	+	32.1454i	−0.374219	+	1.15173i
$780$	−2.37915	+	2.29213i	−0.0851871	+	0.0820716i
$781$	−10.1132			−0.361879
$782$	−0.564602	−	1.10809i	−0.0201901	−	0.0396254i
$783$	2.50356	+	4.02968i	0.0894698	+	0.144009i
$784$	11.6518	−	3.78590i	0.416136	−	0.135211i
$785$	−7.34628	+	2.01187i	−0.262200	+	0.0718066i
$786$	0.805073	+	28.5142i	0.0287160	+	1.01707i
$787$	39.4504	+	6.24833i	1.40625	+	0.222729i	0.812989	−	0.582278i	$-0.197839\pi$
$787$	39.4504	+	6.24833i	1.40625	+	0.222729i	0.593265	+	0.805007i	$0.297839\pi$
$788$	−1.44817	−	9.14339i	−0.0515889	−	0.325720i
$789$	17.7057	+	22.9770i	0.630340	+	0.818004i
$790$	0.662457	+	1.00790i	0.0235691	+	0.0358593i
$791$	−13.7593	+	18.9380i	−0.489224	+	0.673359i
$792$	−0.814344	−	3.75553i	−0.0289365	−	0.133447i
$793$	−8.74809	+	1.38556i	−0.310654	+	0.0492027i
$794$	−14.5660	+	10.5828i	−0.516929	+	0.375571i
$795$	13.8721	+	28.5268i	0.491992	+	1.01174i
$796$	19.5394	−	14.1962i	0.692557	−	0.503172i
$797$	13.2669	+	6.75983i	0.469938	+	0.239445i	0.672889	−	0.739743i	$-0.265053\pi$
$797$	13.2669	+	6.75983i	0.469938	+	0.239445i	−0.202951	+	0.979189i	$0.565053\pi$
$798$	4.70839	−	36.3383i	0.166675	−	1.28636i
$799$	−3.31776	−	1.07800i	−0.117374	−	0.0381371i
$800$	0.316671	+	4.98996i	0.0111960	+	0.176422i
$801$	15.0070	+	18.3777i	0.530245	+	0.649345i
$802$	7.83335	−	3.99129i	0.276605	−	0.140937i
$803$	−0.101896	−	0.643348i	−0.00359584	−	0.0227033i
$804$	4.38728	+	3.00209i	0.154727	+	0.105876i
$805$	1.41384	+	3.12903i	0.0498311	+	0.110284i
$806$	−1.26370	−	4.57811i	−0.0445120	−	0.161257i
$807$	19.7399	−	41.6045i	0.694877	−	1.46455i
$808$	0.995444	−	6.28499i	0.0350196	−	0.221105i
$809$	−7.96959	−	5.79024i	−0.280196	−	0.203574i	0.438807	−	0.898581i	$-0.355401\pi$
$809$	−7.96959	−	5.79024i	−0.280196	−	0.203574i	−0.719003	+	0.695007i	$0.755401\pi$
$810$	15.4649	−	12.8778i	0.543380	−	0.452481i
$811$	37.6875			1.32339			0.661693	−	0.749775i	$-0.269838\pi$
$811$	37.6875			1.32339			0.661693	+	0.749775i	$0.269838\pi$
$812$	2.83260	−	2.83260i	0.0994047	−	0.0994047i
$813$	14.5874	+	13.7862i	0.511601	+	0.483505i
$814$	5.25903	−	1.70876i	0.184329	−	0.0598921i
$815$	−26.3148	−	1.23379i	−0.921768	−	0.0432179i
$816$	5.07954	+	3.47579i	0.177819	+	0.121677i
$817$	−35.3298	+	18.0015i	−1.23603	+	0.629791i
$818$	−9.87694	−	1.56435i	−0.345339	−	0.0546963i
$819$	−0.633523	−	11.2101i	−0.0221371	−	0.391714i
$820$	10.5527	+	11.5909i	0.368515	+	0.404771i
$821$	4.99541	−	6.87559i	0.174341	−	0.239960i	−0.712900	−	0.701265i	$-0.752619\pi$
$821$	4.99541	−	6.87559i	0.174341	−	0.239960i	0.887241	+	0.461306i	$0.152619\pi$
$822$	18.4828	+	33.8756i	0.644662	+	1.18155i
$823$	16.2326	+	8.27092i	0.565833	+	0.288306i	0.713413	−	0.700744i	$-0.247148\pi$
$823$	16.2326	+	8.27092i	0.565833	+	0.288306i	−0.147580	+	0.989050i	$0.547148\pi$
$824$	13.2645	+	9.63725i	0.462092	+	0.335730i
$825$	−5.67214	+	9.53344i	−0.197479	+	0.331912i
$826$	2.26581	−	6.97345i	0.0788377	−	0.242637i
$827$	3.58626	−	22.6427i	0.124706	−	0.787365i	−0.843485	−	0.537153i	$-0.819500\pi$
$827$	3.58626	−	22.6427i	0.124706	−	0.787365i	0.968191	−	0.250212i	$-0.0805003\pi$
$828$	0.222493	+	1.02608i	0.00773216	+	0.0356586i
$829$	47.4811	−	15.4276i	1.64909	−	0.535821i	0.670546	−	0.741868i	$-0.266060\pi$
$829$	47.4811	−	15.4276i	1.64909	−	0.535821i	0.978542	+	0.206047i	$0.0660600\pi$
$830$	2.17046	+	19.6108i	0.0753378	+	0.680701i
$831$	−19.9241	+	7.10144i	−0.691161	+	0.246346i
$832$	0.603164	+	0.603164i	0.0209110	+	0.0209110i
$833$	−38.7908	+	19.7649i	−1.34402	+	0.684813i
$834$	4.74807	+	1.39588i	0.164412	+	0.0483353i
$835$	−6.13999	−	22.4200i	−0.212483	−	0.775878i
$836$			6.17611i			0.213605i
$837$	5.66047	+	28.3718i	0.195654	+	0.980673i
$838$	−24.4977	+	24.4977i	−0.846259	+	0.846259i
$839$	26.6962	−	19.3959i	0.921656	−	0.669622i	−0.0222797	−	0.999752i	$-0.507092\pi$
$839$	26.6962	−	19.3959i	0.921656	−	0.669622i	0.943936	+	0.330129i	$0.107092\pi$
$840$	−13.5594	−	10.2427i	−0.467845	−	0.353407i
$841$	−8.70391	+	26.7879i	−0.300135	+	0.923720i
$842$	9.99750	−	9.99750i	0.344536	−	0.344536i
$843$	−18.0393	−	8.55901i	−0.621305	−	0.294788i
$844$	5.61539	+	1.82455i	0.193290	+	0.0628037i
$845$	−20.2918	+	18.4743i	−0.698061	+	0.635534i
$846$	2.47651	+	1.59389i	0.0851441	+	0.0547990i
$847$	40.5593	+	6.42396i	1.39363	+	0.220730i
$848$	7.29760	−	3.71831i	0.250600	−	0.127687i
$849$	17.5858	+	12.0335i	0.603544	+	0.412988i
$850$	−3.88534	−	17.3377i	−0.133266	−	0.594677i
$851$	−1.43686	+	0.466864i	−0.0492549	+	0.0160039i
$852$	−12.0043	+	6.54966i	−0.411261	+	0.224388i
$853$	−31.1094	+	4.92725i	−1.06517	+	0.168706i	−0.664327	−	0.747442i	$-0.731282\pi$
$853$	−31.1094	+	4.92725i	−1.06517	+	0.168706i	−0.400840	+	0.916148i	$0.631282\pi$
$854$	−14.0785	−	43.3292i	−0.481757	−	1.48269i
$855$	−28.6764	+	14.9599i	−0.980713	+	0.511618i
$856$	−12.8471	+	9.33396i	−0.439105	+	0.319028i
$857$	−16.4407	−	32.2667i	−0.561604	−	1.10221i	−0.980928	−	0.194372i	$-0.937733\pi$
$857$	−16.4407	−	32.2667i	−0.561604	−	1.10221i	0.419324	−	0.907837i	$-0.362267\pi$
$858$	0.348691	+	1.86011i	0.0119041	+	0.0635031i
$859$	8.83191	−	2.86966i	0.301341	−	0.0979116i	−0.154444	−	0.988002i	$-0.549359\pi$
$859$	8.83191	−	2.86966i	0.301341	−	0.0979116i	0.455785	+	0.890090i	$0.349359\pi$
$860$	−0.861237	+	18.3688i	−0.0293679	+	0.626371i
$861$	−53.2529	+	1.50355i	−1.81485	+	0.0512408i
$862$	3.20091	+	3.20091i	0.109023	+	0.109023i
$863$	−18.2063	−	18.2063i	−0.619750	−	0.619750i	0.325717	−	0.945467i	$-0.394394\pi$
$863$	−18.2063	−	18.2063i	−0.619750	−	0.619750i	−0.945467	+	0.325717i	$0.894394\pi$
$864$	−3.39883	−	3.93039i	−0.115630	−	0.133715i
$865$	−31.3626	−	47.7167i	−1.06636	−	1.62242i
$866$	21.5389	+	29.6457i	0.731921	+	1.00740i
$867$	6.84213	+	3.24636i	0.232371	+	0.110252i
$868$	22.2419	−	10.1040i	0.754941	−	0.342951i
$869$	0.690922			0.0234379
$870$	−3.48157	−	0.618102i	−0.118036	−	0.0209556i
$871$	−2.11807	−	1.53887i	−0.0717680	−	0.0521425i
$872$	−7.81995	−	15.3475i	−0.264817	−	0.519733i
$873$	2.22658	−	22.0525i	0.0753585	−	0.746365i
$874$		−	1.68742i		−	0.0570779i
$875$	8.47353	+	48.3180i	0.286458	+	1.63345i
$876$	−0.537604	−	0.697658i	−0.0181640	−	0.0235717i
$877$	−8.93766	+	17.5411i	−0.301803	+	0.592322i	−0.991248	−	0.132016i	$-0.957855\pi$
$877$	−8.93766	+	17.5411i	−0.301803	+	0.592322i	0.689444	+	0.724339i	$0.257855\pi$
$878$	−17.8252	−	2.82323i	−0.601570	−	0.0952794i
$879$	−0.750664	−	26.5871i	−0.0253193	−	0.896760i
$880$	2.48837	+	1.41844i	0.0838830	+	0.0478157i
$881$	7.58675	−	10.4423i	0.255604	−	0.351809i	−0.661860	−	0.749627i	$-0.730233\pi$
$881$	7.58675	−	10.4423i	0.255604	−	0.351809i	0.917464	+	0.397819i	$0.130233\pi$
$882$	35.9196	−	7.78875i	1.20947	−	0.262261i
$883$	−36.6570	+	5.80590i	−1.23361	+	0.195384i	−0.738983	−	0.673724i	$-0.764694\pi$
$883$	−36.6570	+	5.80590i	−1.23361	+	0.195384i	−0.494623	+	0.869108i	$0.664694\pi$
$884$	−2.45227	−	1.78168i	−0.0824789	−	0.0599244i
$885$	−6.19166	+	1.88505i	−0.208130	+	0.0633653i
$886$	−18.9992	−	13.8037i	−0.638290	−	0.463745i
$887$	8.41166	−	53.1091i	0.282436	−	1.78323i	−0.283695	−	0.958915i	$-0.591560\pi$
$887$	8.41166	−	53.1091i	0.282436	−	1.78323i	0.566130	−	0.824316i	$-0.308440\pi$
$888$	5.13578	−	5.43422i	0.172346	−	0.182360i
$889$	41.3112	+	56.8600i	1.38553	+	1.90702i
$890$	−17.6653	−	0.828254i	−0.592143	−	0.0277631i
$891$	−1.29887	−	11.4550i	−0.0435138	−	0.383757i
$892$	−10.4584	+	5.32884i	−0.350175	+	0.178423i
$893$	−3.34696	−	3.34696i	−0.112002	−	0.112002i
$894$	7.41194	+	20.7953i	0.247892	+	0.695499i
$895$	5.87807	+	53.1103i	0.196482	+	1.77528i
$896$	−2.57899	+	3.54968i	−0.0861581	+	0.118586i
$897$	−0.0952683	−	0.508215i	−0.00318092	−	0.0169688i
$898$	−14.6592	+	14.6592i	−0.489184	+	0.489184i
$899$	3.16923	−	3.97446i	0.105700	−	0.132556i
$900$	−0.558617	+	14.9896i	−0.0186206	+	0.499653i
$901$	−23.5460	+	17.1072i	−0.784431	+	0.569922i
$902$	8.86892	−	1.40470i	0.295303	−	0.0467714i
$903$	−45.4223	−	42.9278i	−1.51156	−	1.42855i
$904$		−	5.33514i		−	0.177444i
$905$	−11.1052	+	5.01785i	−0.369151	+	0.166799i
$906$	−32.6031	+	0.920521i	−1.08317	+	0.0305823i
$907$	12.5121	−	24.5564i	0.415458	−	0.815383i	−0.584534	−	0.811369i	$-0.698723\pi$
$907$	12.5121	−	24.5564i	0.415458	−	0.815383i	0.999992	−	0.00401327i	$-0.00127747\pi$
$908$	6.35095	−	12.4644i	0.210764	−	0.413647i
$909$	4.86533	−	18.4596i	0.161373	−	0.612266i
$910$	6.53275	+	5.23080i	0.216559	+	0.173399i
$911$	−21.4516	−	29.5256i	−0.710723	−	0.978226i	−0.999781	−	0.0209149i	$-0.993342\pi$
$911$	−21.4516	−	29.5256i	−0.710723	−	0.978226i	0.289058	−	0.957312i	$-0.406658\pi$
$912$	3.99986	+	7.33100i	0.132449	+	0.242754i
$913$	10.0708	+	5.13131i	0.333294	+	0.169822i
$914$	13.3052	+	9.66682i	0.440098	+	0.319750i
$915$	−24.2396	+	32.0888i	−0.801337	+	1.06082i
$916$	−5.52240	−	16.9962i	−0.182465	−	0.561570i
$917$	71.3715	−	11.3041i	2.35689	−	0.373295i
$918$	14.1140	+	11.9054i	0.465833	+	0.392938i
$919$	−34.0597	−	11.0667i	−1.12353	−	0.365056i	−0.312414	−	0.949946i	$-0.601138\pi$
$919$	−34.0597	−	11.0667i	−1.12353	−	0.365056i	−0.811113	+	0.584890i	$0.801138\pi$
$920$	−0.679866	−	0.387543i	−0.0224145	−	0.0127769i
$921$	33.9660	+	44.0782i	1.11922	+	1.45243i
$922$	−6.33584	+	12.4348i	−0.208660	+	0.409518i
$923$	6.00059	−	3.05745i	0.197512	−	0.100637i
$924$	−9.16959	+	3.26826i	−0.301657	+	0.107518i
$925$	−21.5412	+	1.36704i	−0.708270	+	0.0449479i
$926$	35.0221	+	11.3794i	1.15090	+	0.373950i
$927$	36.6879	+	32.7630i	1.20499	+	1.07608i
$928$	−0.142824	+	0.901755i	−0.00468842	+	0.0296015i
$929$	−45.9545			−1.50772			−0.753860	−	0.657035i	$-0.771810\pi$
$929$	−45.9545			−1.50772			−0.753860	+	0.657035i	$0.771810\pi$
$930$	−18.5540	−	10.9885i	−0.608410	−	0.360329i
$931$	−59.0711			−1.93598
$932$	4.43232	−	27.9845i	0.145185	−	0.916664i
$933$	8.61320	+	15.7864i	0.281984	+	0.516824i
$934$	−33.7986	−	10.9818i	−1.10593	−	0.359337i
$935$	−9.52215	−	3.59516i	−0.311408	−	0.117574i
$936$	1.61856	+	1.98212i	0.0529044	+	0.0647875i
$937$	−38.3901	+	19.5607i	−1.25415	+	0.639021i	−0.949597	−	0.313475i	$-0.898507\pi$
$937$	−38.3901	+	19.5607i	−1.25415	+	0.639021i	−0.304553	+	0.952496i	$0.598507\pi$
$938$	6.11378	−	11.9990i	0.199622	−	0.391780i
$939$	−24.7407	+	19.0648i	−0.807382	+	0.622156i
$940$	−2.11718	+	0.579816i	−0.0690549	+	0.0189115i
$941$	13.1895	+	4.28554i	0.429967	+	0.139705i	0.516002	−	0.856587i	$-0.327420\pi$
$941$	13.1895	+	4.28554i	0.429967	+	0.139705i	−0.0860351	+	0.996292i	$0.527420\pi$
$942$	1.08705	+	5.79893i	0.0354180	+	0.188939i
$943$	−2.42314	+	0.383788i	−0.0789084	+	0.0124979i
$944$	0.516407	+	1.58934i	0.0168076	+	0.0517285i
$945$	−37.3857	−	34.6591i	−1.21616	−	1.12746i
$946$	8.52231	+	6.19182i	0.277084	+	0.201314i
$947$	33.7346	+	17.1886i	1.09623	+	0.558556i	0.906040	−	0.423192i	$-0.139090\pi$
$947$	33.7346	+	17.1886i	1.09623	+	0.558556i	0.190188	+	0.981748i	$0.439090\pi$
$948$	0.820120	−	0.447465i	0.0266363	−	0.0145330i
$949$	0.254958	+	0.350919i	0.00827628	+	0.0113913i
$950$	5.98265	−	23.3537i	0.194103	−	0.757694i
$951$	−42.2119	−	28.8844i	−1.36881	−	0.936641i
$952$	7.07846	−	13.8923i	0.229414	−	0.450251i
$953$	8.30255	−	16.2947i	0.268946	−	0.527836i	−0.716550	−	0.697536i	$-0.754280\pi$
$953$	8.30255	−	16.2947i	0.268946	−	0.527836i	0.985496	+	0.169700i	$0.0542798\pi$
$954$	22.9026	−	8.89923i	0.741500	−	0.288123i
$955$	0.133344	+	0.295109i	0.00431490	+	0.00954951i
$956$			17.3380i			0.560752i
$957$	−1.39133	+	1.47218i	−0.0449753	+	0.0475887i
$958$	−1.81107	+	0.286845i	−0.0585129	+	0.00926753i
$959$	79.0862	−	57.4595i	2.55383	−	1.85546i
$960$	3.87231	+	0.0721297i	0.124978	+	0.00232798i
$961$	26.6105	−	15.9023i	0.858403	−	0.512977i
$962$	−2.60380	+	2.60380i	−0.0839500	+	0.0839500i
$963$	−41.1593	+	23.9885i	−1.32634	+	0.773019i
$964$	3.11892	−	4.29282i	0.100454	−	0.138262i
$965$	25.4436	+	20.3728i	0.819058	+	0.655823i
$966$	2.50529	−	0.892945i	0.0806064	−	0.0287300i
$967$	12.1690	+	12.1690i	0.391329	+	0.391329i	0.875161	−	0.483832i	$-0.160755\pi$
$967$	12.1690	+	12.1690i	0.391329	+	0.391329i	−0.483832	+	0.875161i	$0.660755\pi$
$968$	−8.33911	+	4.24899i	−0.268029	+	0.136568i
$969$	−18.1139	−	23.5067i	−0.581903	−	0.755145i
$970$	11.1219	+	12.2161i	0.357102	+	0.392235i
$971$	−21.0377	−	28.9558i	−0.675131	−	0.929237i	0.324732	−	0.945806i	$-0.394726\pi$
$971$	−21.0377	−	28.9558i	−0.675131	−	0.929237i	−0.999863	+	0.0165686i	$0.994726\pi$
$972$	−8.96040	−	12.7558i	−0.287405	−	0.409143i
$973$	1.96120	−	12.3825i	0.0628731	−	0.396965i
$974$	12.2794	+	8.92153i	0.393459	+	0.285864i
$975$	0.483343	−	7.37140i	0.0154794	−	0.236074i
$976$	8.40041	+	6.10325i	0.268891	+	0.195360i
$977$	17.5397	−	2.77802i	0.561146	−	0.0888768i	0.130583	−	0.991437i	$-0.458315\pi$
$977$	17.5397	−	2.77802i	0.561146	−	0.0888768i	0.430563	+	0.902561i	$0.358315\pi$
$978$	−2.62207	+	20.2366i	−0.0838446	+	0.647095i
$979$	−5.95470	+	8.19594i	−0.190313	+	0.261943i
$980$	−13.5666	+	23.7999i	−0.433370	+	0.760260i
$981$	−18.7159	−	48.1664i	−0.597553	−	1.53783i
$982$	−26.0432	−	4.12484i	−0.831072	−	0.131629i
$983$	−27.6883	+	54.3414i	−0.883120	+	1.73322i	−0.234487	+	0.972119i	$0.575341\pi$
$983$	−27.6883	+	54.3414i	−0.883120	+	1.73322i	−0.648633	+	0.761101i	$0.724659\pi$
$984$	9.61762	−	7.41118i	0.306599	−	0.236260i
$985$	16.1585	+	12.9382i	0.514853	+	0.412245i
$986$		−	3.24436i		−	0.103321i
$987$	3.19806	−	6.74033i	0.101795	−	0.214547i
$988$	−1.86718	−	3.66454i	−0.0594028	−	0.116585i
$989$	−2.32844	−	1.69171i	−0.0740402	−	0.0537933i
$990$	6.99987	+	4.98373i	0.222471	+	0.158393i
$991$	34.6617			1.10106			0.550532	−	0.834814i	$-0.314425\pi$
$991$	34.6617			1.10106			0.550532	+	0.834814i	$0.314425\pi$
$992$	−2.74752	+	4.84264i	−0.0872338	+	0.153754i
$993$	−10.6665	+	22.4811i	−0.338491	+	0.713416i
$994$	20.3616	+	28.0254i	0.645831	+	0.888911i
$995$	−10.9373	+	52.8865i	−0.346734	+	1.67662i
$996$	15.2771	−	0.431337i	0.484075	−	0.0136674i
$997$	−3.52748	−	3.52748i	−0.111717	−	0.111717i	0.649039	−	0.760755i	$-0.275171\pi$
$997$	−3.52748	−	3.52748i	−0.111717	−	0.111717i	−0.760755	+	0.649039i	$0.775171\pi$
$998$	14.1478	+	14.1478i	0.447841	+	0.447841i
$999$	16.9671	−	14.6724i	0.536816	−	0.464215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.5	✓	512
3.2	odd	2	inner	930.2.bk.a.47.35	yes	512
5.3	odd	4	inner	930.2.bk.a.233.44	yes	512
15.8	even	4	inner	930.2.bk.a.233.19	yes	512
31.2	even	5	inner	930.2.bk.a.467.19	yes	512
93.2	odd	10	inner	930.2.bk.a.467.44	yes	512
155.33	odd	20	inner	930.2.bk.a.653.35	yes	512
465.188	even	20	inner	930.2.bk.a.653.5	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.5	✓	512	1.1	even	1	trivial
930.2.bk.a.47.35	yes	512	3.2	odd	2	inner
930.2.bk.a.233.19	yes	512	15.8	even	4	inner
930.2.bk.a.233.44	yes	512	5.3	odd	4	inner
930.2.bk.a.467.19	yes	512	31.2	even	5	inner
930.2.bk.a.467.44	yes	512	93.2	odd	10	inner
930.2.bk.a.653.5	yes	512	465.188	even	20	inner
930.2.bk.a.653.35	yes	512	155.33	odd	20	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.52046 + 0.829577i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.03771 - 0.920729i) q^{5} +(-0.581511 - 1.63152i) q^{6} +(-3.90942 + 1.99195i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.62360 - 2.52268i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-1.52046 + 0.829577i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.03771 - 0.920729i) q^{5} +(-0.581511 - 1.63152i) q^{6} +(-3.90942 + 1.99195i) q^{7} +(0.453990 - 0.891007i) q^{8} +(1.62360 - 2.52268i) q^{9} +(0.590625 + 2.15666i) q^{10} +(1.21824 + 0.395831i) q^{11} +(1.70240 - 0.319126i) q^{12} +(-0.842501 + 0.133439i) q^{13} +(-1.35586 - 4.17290i) q^{14} +(-2.33444 + 3.09037i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-3.16622 - 1.61327i) q^{17} +(2.23763 + 1.99825i) q^{18} +(-2.83404 - 3.90073i) q^{19} +(-2.22250 + 0.245979i) q^{20} +(4.29165 - 6.27185i) q^{21} +(-0.581532 + 1.14132i) q^{22} +(0.158885 - 0.311829i) q^{23} +(0.0488835 + 1.73136i) q^{24} +(3.30452 - 3.75236i) q^{25} -0.853003i q^{26} +(-0.375871 + 5.18254i) q^{27} +(4.33363 - 0.686379i) q^{28} +(0.738629 - 0.536645i) q^{29} +(-2.68713 - 2.78914i) q^{30} +(5.36705 - 1.48147i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.18066 + 0.408780i) q^{33} +(2.08871 - 2.87487i) q^{34} +(-6.13222 + 7.65853i) q^{35} +(-2.32369 + 1.89749i) q^{36} +(-3.05251 - 3.05251i) q^{37} +(4.29605 - 2.18894i) q^{38} +(1.17029 - 0.901809i) q^{39} +(0.104725 - 2.23361i) q^{40} +(-4.12043 - 5.67128i) q^{41} +(5.52327 + 5.21994i) q^{42} +(1.28649 - 8.12255i) q^{43} +(-1.03630 - 0.752915i) q^{44} +(0.985729 - 6.63539i) q^{45} +(0.283135 + 0.205709i) q^{46} +(0.969612 - 0.153571i) q^{47} +(-1.71769 - 0.222563i) q^{48} +(7.20121 - 9.91162i) q^{49} +(3.18922 + 3.85083i) q^{50} +(6.15245 - 0.173709i) q^{51} +(0.842501 + 0.133439i) q^{52} +(3.71831 - 7.29760i) q^{53} +(-5.05994 - 1.18197i) q^{54} +(2.84687 - 0.315083i) q^{55} +4.38765i q^{56} +(7.54501 + 3.57985i) q^{57} +(0.414491 + 0.813485i) q^{58} +(1.35197 + 0.982265i) q^{59} +(3.17516 - 2.21773i) q^{60} +10.3835 q^{61} +(0.623641 + 5.53273i) q^{62} +(-1.32230 + 13.0964i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.59391 + 1.04763i) q^{65} +(-0.0626166 - 2.21776i) q^{66} +(2.17028 + 2.17028i) q^{67} +(2.51273 + 2.51273i) q^{68} +(0.0171079 + 0.605931i) q^{69} +(-6.60495 - 7.25478i) q^{70} +(-7.50876 + 2.43975i) q^{71} +(-1.51062 - 2.59191i) q^{72} +(-0.230858 - 0.453085i) q^{73} +(3.49245 - 2.53741i) q^{74} +(-1.91152 + 8.44666i) q^{75} +(1.48995 + 4.58558i) q^{76} +(-5.55109 + 0.879207i) q^{77} +(0.707632 + 1.29696i) q^{78} +(0.512989 - 0.166680i) q^{79} +(2.18973 + 0.452850i) q^{80} +(-3.72782 - 8.19166i) q^{81} +(6.24604 - 3.18252i) q^{82} +(8.71514 + 1.38034i) q^{83} +(-6.01971 + 4.63869i) q^{84} +(-7.93722 - 0.372143i) q^{85} +(7.82130 + 2.54129i) q^{86} +(-0.677868 + 1.42870i) q^{87} +(0.905758 - 0.905758i) q^{88} +(-2.44397 + 7.52177i) q^{89} +(6.39949 + 2.01160i) q^{90} +(3.02789 - 2.19989i) q^{91} +(-0.247469 + 0.247469i) q^{92} +(-6.93140 + 6.70490i) q^{93} +0.981698i q^{94} +(-9.36647 - 5.33916i) q^{95} +(0.488529 - 1.66173i) q^{96} +(6.58295 - 3.35418i) q^{97} +(8.66307 + 8.66307i) q^{98} +(2.97650 - 2.43056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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