LMFDB - Embedded newform 414.2.p.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(5,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("414.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.p (of order $66$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	414.5
Dual form			414.2.p.a.83.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971812 + 0.235759i) q^{2} +(1.41656 + 0.996675i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.36798 - 1.86220i) q^{5} +(-1.61160 - 0.634614i) q^{6} +(-1.80599 - 1.28604i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.01328 + 2.82370i) q^{9} +O(q^{10})$	\(q+(-0.971812 + 0.235759i) q^{2} +(1.41656 + 0.996675i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.36798 - 1.86220i) q^{5} +(-1.61160 - 0.634614i) q^{6} +(-1.80599 - 1.28604i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.01328 + 2.82370i) q^{9} +(2.74026 + 1.25144i) q^{10} +(-2.82603 - 2.69461i) q^{11} +(1.71579 + 0.236775i) q^{12} +(-1.99573 - 2.80262i) q^{13} +(2.05828 + 0.824012i) q^{14} +(-1.49837 - 4.99802i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-5.27347 + 3.38906i) q^{17} +(-1.65043 - 2.50521i) q^{18} +(-0.0498236 + 0.0775271i) q^{19} +(-2.95805 - 0.570118i) q^{20} +(-1.27653 - 3.62175i) q^{21} +(3.38165 + 1.95240i) q^{22} +(-3.47055 - 3.30988i) q^{23} +(-1.72325 + 0.174412i) q^{24} +(0.960746 + 3.96025i) q^{25} +(2.60022 + 2.25310i) q^{26} +(-1.37894 + 5.00984i) q^{27} +(-2.19453 - 0.315526i) q^{28} +(1.81003 - 3.51097i) q^{29} +(2.63447 + 4.50388i) q^{30} +(3.12950 - 0.603162i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(-1.31758 - 6.63371i) q^{33} +(4.32582 - 4.53679i) q^{34} +(1.88169 + 6.40845i) q^{35} +(2.19453 + 2.04549i) q^{36} +(6.85751 - 0.985961i) q^{37} +(0.0301415 - 0.0870881i) q^{38} +(-0.0337766 - 5.95917i) q^{39} +(3.00908 - 0.143340i) q^{40} +(-0.152303 + 0.193668i) q^{41} +(2.09441 + 3.21870i) q^{42} +(-1.39519 + 7.23892i) q^{43} +(-3.74662 - 1.10011i) q^{44} +(2.85887 - 8.57339i) q^{45} +(4.15305 + 2.39837i) q^{46} +(3.34747 - 1.93266i) q^{47} +(1.63355 - 0.575766i) q^{48} +(-0.681765 - 1.96983i) q^{49} +(-1.86733 - 3.62211i) q^{50} +(-10.8480 - 0.455143i) q^{51} +(-3.05811 - 1.57657i) q^{52} +(-3.61340 - 7.91225i) q^{53} +(0.158957 - 5.19372i) q^{54} +(1.67407 + 11.6434i) q^{55} +(2.20706 - 0.210749i) q^{56} +(-0.147847 + 0.0601637i) q^{57} +(-0.931266 + 3.83873i) q^{58} +(4.51257 - 3.21339i) q^{59} +(-3.62204 - 3.75583i) q^{60} +(-3.36337 - 1.16407i) q^{61} +(-2.89909 + 1.32397i) q^{62} +(1.80142 - 6.40270i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.493174 + 10.3530i) q^{65} +(2.84440 + 6.13609i) q^{66} +(-7.45167 - 7.81509i) q^{67} +(-3.13429 + 5.42876i) q^{68} +(-1.61736 - 8.14765i) q^{69} +(-3.33950 - 5.78418i) q^{70} +(-3.89396 + 13.2616i) q^{71} +(-2.61491 - 1.47045i) q^{72} +(-2.47508 - 1.59064i) q^{73} +(-6.43176 + 2.57489i) q^{74} +(-2.58613 + 6.56748i) q^{75} +(-0.00876005 + 0.0917393i) q^{76} +(1.63841 + 8.50086i) q^{77} +(1.43775 + 5.78323i) q^{78} +(0.503745 + 5.27546i) q^{79} +(-2.89047 + 0.848718i) q^{80} +(-6.94654 + 5.72238i) q^{81} +(0.102350 - 0.224116i) q^{82} +(5.74887 - 4.52096i) q^{83} +(-2.79421 - 2.63420i) q^{84} +(18.7986 + 1.79505i) q^{85} +(-0.350781 - 7.36379i) q^{86} +(6.06331 - 3.16948i) q^{87} +(3.90037 + 0.185797i) q^{88} +(6.67567 - 7.70414i) q^{89} +(-0.757030 + 9.00572i) q^{90} +7.62811i q^{91} +(-4.60142 - 1.35164i) q^{92} +(5.03428 + 2.26468i) q^{93} +(-2.79747 + 2.66738i) q^{94} +(0.262352 - 0.0908010i) q^{95} +(-1.45176 + 0.944661i) q^{96} +(0.665204 + 1.66160i) q^{97} +(1.12695 + 1.75357i) q^{98} +(4.74522 - 10.7102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	$ 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) $ 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$2$	−0.971812	+	0.235759i	−0.687175	+	0.166707i
$3$	1.41656	+	0.996675i	0.817851	+	0.575431i
$3$	1.41656	+	0.996675i	0.817851	+	0.575431i
$4$	0.888835	−	0.458227i	0.444418	−	0.229113i
$5$	−2.36798	−	1.86220i	−1.05899	−	0.832801i	−0.0726256	−	0.997359i	$-0.523138\pi$
$5$	−2.36798	−	1.86220i	−1.05899	−	0.832801i	−0.986367	+	0.164558i	$0.947380\pi$
$6$	−1.61160	−	0.634614i	−0.657934	−	0.259080i
$7$	−1.80599	−	1.28604i	−0.682602	−	0.486079i	0.185385	−	0.982666i	$-0.440647\pi$
$7$	−1.80599	−	1.28604i	−0.682602	−	0.486079i	−0.867987	+	0.496587i	$0.834586\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	1.01328	+	2.82370i	0.337759	+	0.941233i
$10$	2.74026	+	1.25144i	0.866547	+	0.395739i
$11$	−2.82603	−	2.69461i	−0.852080	−	0.812457i	0.131802	−	0.991276i	$-0.457924\pi$
$11$	−2.82603	−	2.69461i	−0.852080	−	0.812457i	−0.983882	+	0.178819i	$0.942772\pi$
$12$	1.71579	+	0.236775i	0.495306	+	0.0683512i
$13$	−1.99573	−	2.80262i	−0.553517	−	0.777306i	0.439121	−	0.898428i	$-0.355290\pi$
$13$	−1.99573	−	2.80262i	−0.553517	−	0.777306i	−0.992638	+	0.121122i	$0.961351\pi$
$14$	2.05828	+	0.824012i	0.550099	+	0.220226i
$15$	−1.49837	−	4.99802i	−0.386879	−	1.29048i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	−5.27347	+	3.38906i	−1.27901	+	0.821967i	−0.990765	−	0.135591i	$-0.956707\pi$
$17$	−5.27347	+	3.38906i	−1.27901	+	0.821967i	−0.288240	+	0.957558i	$0.593070\pi$
$18$	−1.65043	−	2.50521i	−0.389009	−	0.590484i
$19$	−0.0498236	+	0.0775271i	−0.0114303	+	0.0177859i	−0.846922	−	0.531718i	$-0.821547\pi$
$19$	−0.0498236	+	0.0775271i	−0.0114303	+	0.0177859i	0.835491	+	0.549504i	$0.185183\pi$
$20$	−2.95805	−	0.570118i	−0.661441	−	0.127482i
$21$	−1.27653	−	3.62175i	−0.278562	−	0.790330i
$22$	3.38165	+	1.95240i	0.720970	+	0.416252i
$23$	−3.47055	−	3.30988i	−0.723659	−	0.690158i
$23$	−3.47055	−	3.30988i	−0.723659	−	0.690158i
$24$	−1.72325	+	0.174412i	−0.351756	+	0.0356017i
$25$	0.960746	+	3.96025i	0.192149	+	0.792050i
$26$	2.60022	+	2.25310i	0.509945	+	0.441870i
$27$	−1.37894	+	5.00984i	−0.265378	+	0.964145i
$28$	−2.19453	−	0.315526i	−0.414727	−	0.0596288i
$29$	1.81003	−	3.51097i	0.336114	−	0.651970i	−0.658842	−	0.752281i	$-0.728953\pi$
$29$	1.81003	−	3.51097i	0.336114	−	0.651970i	0.994956	+	0.100311i	$0.0319837\pi$
$30$	2.63447	+	4.50388i	0.480986	+	0.822293i
$31$	3.12950	−	0.603162i	0.562075	−	0.108331i	0.0997034	−	0.995017i	$-0.468211\pi$
$31$	3.12950	−	0.603162i	0.562075	−	0.108331i	0.462372	+	0.886686i	$0.346998\pi$
$32$	−0.371662	+	0.928368i	−0.0657013	+	0.164114i
$33$	−1.31758	−	6.63371i	−0.229362	−	1.15478i
$34$	4.32582	−	4.53679i	0.741872	−	0.778053i
$35$	1.88169	+	6.40845i	0.318064	+	1.08323i
$36$	2.19453	+	2.04549i	0.365755	+	0.340915i
$37$	6.85751	−	0.985961i	1.12737	−	0.162091i	0.446700	−	0.894684i	$-0.352599\pi$
$37$	6.85751	−	0.985961i	1.12737	−	0.162091i	0.680667	+	0.732593i	$0.261690\pi$
$38$	0.0301415	−	0.0870881i	0.00488959	−	0.0141276i
$39$	−0.0337766	−	5.95917i	−0.00540858	−	0.954231i
$40$	3.00908	−	0.143340i	0.475778	−	0.0226641i
$41$	−0.152303	+	0.193668i	−0.0237857	+	0.0302459i	−0.797800	−	0.602922i	$-0.794003\pi$
$41$	−0.152303	+	0.193668i	−0.0237857	+	0.0302459i	0.774015	+	0.633168i	$0.218246\pi$
$42$	2.09441	+	3.21870i	0.323174	+	0.496656i
$43$	−1.39519	+	7.23892i	−0.212764	+	1.10392i	0.705727	+	0.708484i	$0.250620\pi$
$43$	−1.39519	+	7.23892i	−0.212764	+	1.10392i	−0.918491	+	0.395441i	$0.870592\pi$
$44$	−3.74662	−	1.10011i	−0.564824	−	0.165847i
$45$	2.85887	−	8.57339i	0.426175	−	1.27804i
$46$	4.15305	+	2.39837i	0.612334	+	0.353620i
$47$	3.34747	−	1.93266i	0.488278	−	0.281908i	−0.235582	−	0.971855i	$-0.575699\pi$
$47$	3.34747	−	1.93266i	0.488278	−	0.281908i	0.723860	+	0.689947i	$0.242366\pi$
$48$	1.63355	−	0.575766i	0.235783	−	0.0831047i
$49$	−0.681765	−	1.96983i	−0.0973951	−	0.281405i
$50$	−1.86733	−	3.62211i	−0.264080	−	0.512244i
$51$	−10.8480	−	0.455143i	−1.51902	−	0.0637328i
$52$	−3.05811	−	1.57657i	−0.424084	−	0.218630i
$53$	−3.61340	−	7.91225i	−0.496339	−	1.08683i	−0.977642	−	0.210277i	$-0.932563\pi$
$53$	−3.61340	−	7.91225i	−0.496339	−	1.08683i	0.481303	−	0.876554i	$-0.340164\pi$
$54$	0.158957	−	5.19372i	0.0216313	−	0.706776i
$55$	1.67407	+	11.6434i	0.225732	+	1.57000i
$56$	2.20706	−	0.210749i	0.294931	−	0.0281625i
$57$	−0.147847	+	0.0601637i	−0.0195829	+	0.00796888i
$58$	−0.931266	+	3.83873i	−0.122281	+	0.504050i
$59$	4.51257	−	3.21339i	0.587487	−	0.418347i	−0.247286	−	0.968943i	$-0.579539\pi$
$59$	4.51257	−	3.21339i	0.587487	−	0.418347i	0.834772	+	0.550595i	$0.185599\pi$
$60$	−3.62204	−	3.75583i	−0.467603	−	0.484875i
$61$	−3.36337	−	1.16407i	−0.430635	−	0.149044i	0.103147	−	0.994666i	$-0.467109\pi$
$61$	−3.36337	−	1.16407i	−0.430635	−	0.149044i	−0.533783	+	0.845622i	$0.679230\pi$
$62$	−2.89909	+	1.32397i	−0.368184	+	0.168144i
$63$	1.80142	−	6.40270i	0.226958	−	0.806665i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−0.493174	+	10.3530i	−0.0611707	+	1.28413i
$66$	2.84440	+	6.13609i	0.350121	+	0.755300i
$67$	−7.45167	−	7.81509i	−0.910366	−	0.954765i	0.0887811	−	0.996051i	$-0.471703\pi$
$67$	−7.45167	−	7.81509i	−0.910366	−	0.954765i	−0.999147	+	0.0412865i	$0.986854\pi$
$68$	−3.13429	+	5.42876i	−0.380089	+	0.658334i
$69$	−1.61736	−	8.14765i	−0.194707	−	0.980861i
$70$	−3.33950	−	5.78418i	−0.399146	−	0.691342i
$71$	−3.89396	+	13.2616i	−0.462128	+	1.57386i	0.317904	+	0.948123i	$0.397021\pi$
$71$	−3.89396	+	13.2616i	−0.462128	+	1.57386i	−0.780032	+	0.625740i	$0.784797\pi$
$72$	−2.61491	−	1.47045i	−0.308170	−	0.173295i
$73$	−2.47508	−	1.59064i	−0.289687	−	0.186170i	0.387724	−	0.921776i	$-0.373261\pi$
$73$	−2.47508	−	1.59064i	−0.289687	−	0.186170i	−0.677410	+	0.735605i	$0.736898\pi$
$74$	−6.43176	+	2.57489i	−0.747677	+	0.299325i
$75$	−2.58613	+	6.56748i	−0.298620	+	0.758347i
$76$	−0.00876005	+	0.0917393i	−0.00100485	+	0.0105232i
$77$	1.63841	+	8.50086i	0.186714	+	0.968762i
$78$	1.43775	+	5.78323i	0.162793	+	0.654821i
$79$	0.503745	+	5.27546i	0.0566758	+	0.593536i	0.978545	+	0.206034i	$0.0660558\pi$
$79$	0.503745	+	5.27546i	0.0566758	+	0.593536i	−0.921869	+	0.387502i	$0.873338\pi$
$80$	−2.89047	+	0.848718i	−0.323164	+	0.0948895i
$81$	−6.94654	+	5.72238i	−0.771838	+	0.635820i
$82$	0.102350	−	0.224116i	0.0113027	−	0.0247495i
$83$	5.74887	−	4.52096i	0.631020	−	0.496240i	−0.250667	−	0.968073i	$-0.580650\pi$
$83$	5.74887	−	4.52096i	0.631020	−	0.496240i	0.881688	+	0.471833i	$0.156408\pi$
$84$	−2.79421	−	2.63420i	−0.304873	−	0.287414i
$85$	18.7986	+	1.79505i	2.03899	+	0.194700i
$86$	−0.350781	−	7.36379i	−0.0378257	−	0.794058i
$87$	6.06331	−	3.16948i	0.650055	−	0.339804i
$88$	3.90037	+	0.185797i	0.415781	+	0.0198061i
$89$	6.67567	−	7.70414i	0.707620	−	0.816637i	−0.282141	−	0.959373i	$-0.591045\pi$
$89$	6.67567	−	7.70414i	0.707620	−	0.816637i	0.989761	+	0.142736i	$0.0455900\pi$
$90$	−0.757030	+	9.00572i	−0.0797980	+	0.949286i
$91$			7.62811i			0.799643i
$92$	−4.60142	−	1.35164i	−0.479731	−	0.140918i
$93$	5.03428	+	2.26468i	0.522031	+	0.234837i
$94$	−2.79747	+	2.66738i	−0.288537	+	0.275119i
$95$	0.262352	−	0.0908010i	0.0269168	−	0.00931599i
$96$	−1.45176	+	0.944661i	−0.148170	+	0.0964141i
$97$	0.665204	+	1.66160i	0.0675412	+	0.168710i	0.958298	−	0.285770i	$-0.0922494\pi$
$97$	0.665204	+	1.66160i	0.0675412	+	0.168710i	−0.890757	+	0.454480i	$0.849825\pi$
$98$	1.12695	+	1.75357i	0.113839	+	0.177138i
$99$	4.74522	−	10.7102i	0.476913	−	1.07642i
$100$	2.66864	+	3.07977i	0.266864	+	0.307977i
$101$	10.4548	+	13.2944i	1.04030	+	1.32284i	0.944884	+	0.327406i	$0.106174\pi$
$101$	10.4548	+	13.2944i	1.04030	+	1.32284i	0.0954122	+	0.995438i	$0.469583\pi$
$102$	10.6495	−	2.11519i	1.05446	−	0.209435i
$103$	10.0906	+	2.44795i	0.994257	+	0.241204i	0.699705	−	0.714432i	$-0.253315\pi$
$103$	10.0906	+	2.44795i	0.994257	+	0.241204i	0.294551	+	0.955636i	$0.404830\pi$
$104$	3.34360	+	0.811148i	0.327867	+	0.0795396i
$105$	−3.72162	+	10.9534i	−0.363193	+	1.06894i
$106$	5.37693	+	6.83732i	0.522254	+	0.664100i
$107$	5.12054	+	5.90942i	0.495021	+	0.571285i	0.947200	−	0.320642i	$-0.103899\pi$
$107$	5.12054	+	5.90942i	0.495021	+	0.571285i	−0.452179	+	0.891927i	$0.649353\pi$
$108$	1.06999	+	5.08479i	0.102960	+	0.489284i
$109$	−7.05317	−	10.9749i	−0.675571	−	1.05121i	−0.994632	−	0.103475i	$-0.967004\pi$
$109$	−7.05317	−	10.9749i	−0.675571	−	1.05121i	0.319061	−	0.947734i	$-0.396632\pi$
$110$	−4.37192	−	10.9205i	−0.416847	−	1.04123i
$111$	10.6967	+	5.43804i	1.01529	+	0.516156i
$112$	−2.09516	+	0.725142i	−0.197974	+	0.0685195i
$113$	−12.5049	+	11.9234i	−1.17637	+	1.12166i	−0.186091	+	0.982533i	$0.559582\pi$
$113$	−12.5049	+	11.9234i	−1.17637	+	1.12166i	−0.990274	+	0.139129i	$0.955570\pi$
$114$	0.129496	−	0.0933241i	0.0121284	−	0.00874061i
$115$	2.05453	+	14.3006i	0.191586	+	1.33354i
$116$		−	3.95008i		−	0.366755i
$117$	5.89151	−	8.47518i	0.544670	−	0.783530i
$118$	−3.62778	+	4.18669i	−0.333965	+	0.385416i
$119$	13.8823	+	0.661297i	1.27259	+	0.0606210i
$120$	4.40541	+	2.79603i	0.402157	+	0.255241i
$121$	0.202099	+	4.24258i	0.0183726	+	0.385689i
$122$	3.54300	+	0.338316i	0.320768	+	0.0306297i
$123$	−0.408770	+	0.122547i	−0.0368576	+	0.0110497i
$124$	2.50523	−	1.97013i	0.224976	−	0.176923i
$125$	−1.15743	+	2.53441i	−0.103523	+	0.226685i
$126$	−0.241150	+	6.64692i	−0.0214833	+	0.592155i
$127$	−19.7896	+	5.81077i	−1.75605	+	0.515622i	−0.991631	−	0.129101i	$-0.958791\pi$
$127$	−19.7896	+	5.81077i	−1.75605	+	0.515622i	−0.764416	+	0.644723i	$0.776973\pi$
$128$	0.0950560	+	0.995472i	0.00840185	+	0.0879881i
$129$	−9.19121	+	8.86381i	−0.809241	+	0.780415i
$130$	−1.96154	−	10.1774i	−0.172038	−	0.892620i
$131$	1.59135	−	16.6654i	0.139037	−	1.45606i	−0.609403	−	0.792861i	$-0.708591\pi$
$131$	1.59135	−	16.6654i	0.139037	−	1.45606i	0.748440	−	0.663202i	$-0.230803\pi$
$132$	−4.21086	−	5.29253i	−0.366508	−	0.460655i
$133$	0.189684	−	0.0759382i	0.0164477	−	0.00658468i
$134$	9.08409	+	5.83799i	0.784746	+	0.504326i
$135$	12.5946	−	9.29534i	1.08397	−	0.800016i
$136$	1.76607	−	6.01467i	0.151439	−	0.515753i
$137$	−7.87172	−	13.6342i	−0.672527	−	1.16485i	−0.977185	−	0.212389i	$-0.931876\pi$
$137$	−7.87172	−	13.6342i	−0.672527	−	1.16485i	0.304659	−	0.952462i	$-0.401458\pi$
$138$	3.49265	+	7.53667i	0.297314	+	0.641564i
$139$	−3.02555	+	5.24041i	−0.256624	+	0.444486i	−0.965335	−	0.261013i	$-0.915944\pi$
$139$	−3.02555	+	5.24041i	−0.256624	+	0.444486i	0.708711	+	0.705499i	$0.249277\pi$
$140$	4.60903	+	4.83382i	0.389534	+	0.408532i
$141$	6.66812	+	0.598609i	0.561557	+	0.0504120i
$142$	0.657652	−	13.8058i	0.0551889	−	1.15856i
$143$	−1.91197	+	13.2980i	−0.159887	+	1.11204i
$144$	2.88787	+	0.812514i	0.240656	+	0.0677095i
$145$	−10.8242	+	4.94327i	−0.898904	+	0.410516i
$146$	2.78032	+	0.962279i	0.230101	+	0.0796388i
$147$	0.997522	−	3.46988i	0.0822742	−	0.286191i
$148$	5.64340	−	4.01865i	0.463885	−	0.330331i
$149$	−4.12510	+	17.0039i	−0.337941	+	1.39301i	0.508743	+	0.860918i	$0.330110\pi$
$149$	−4.12510	+	17.0039i	−0.337941	+	1.39301i	−0.846685	+	0.532095i	$0.821405\pi$
$150$	0.964888	−	6.99205i	0.0787828	−	0.570899i
$151$	4.56426	−	0.435834i	0.371434	−	0.0354677i	0.0923299	−	0.995728i	$-0.470569\pi$
$151$	4.56426	−	0.435834i	0.371434	−	0.0354677i	0.279104	+	0.960261i	$0.409962\pi$
$152$	−0.0131153	−	0.0912186i	−0.00106379	−	0.00739881i
$153$	−14.9132	−	11.4566i	−1.20566	−	0.926214i
$154$	−3.59637	−	7.87496i	−0.289804	−	0.634582i
$155$	−8.53381	−	4.39949i	−0.685452	−	0.353375i
$156$	−2.76067	−	5.28124i	−0.221031	−	0.422838i
$157$	−10.2875	−	19.9549i	−0.821030	−	1.59258i	−0.805424	−	0.592699i	$-0.798062\pi$
$157$	−10.2875	−	19.9549i	−0.821030	−	1.59258i	−0.0156062	−	0.999878i	$-0.504968\pi$
$158$	−1.73328	−	5.00799i	−0.137893	−	0.398414i
$159$	2.76734	−	14.8096i	0.219465	−	1.17447i
$160$	2.60890	−	1.50625i	0.206251	−	0.119079i
$161$	2.01114	+	10.4409i	0.158500	+	0.822858i
$162$	5.40162	−	7.19878i	0.424392	−	0.565590i
$163$	13.6662	+	4.01275i	1.07042	+	0.314303i	0.769039	−	0.639201i	$-0.220735\pi$
$163$	13.6662	+	4.01275i	1.07042	+	0.314303i	0.301379	+	0.953505i	$0.402553\pi$
$164$	−0.0466279	+	0.241928i	−0.00364103	+	0.0188914i
$165$	−9.23329	+	18.1621i	−0.718811	+	1.41392i
$166$	−4.52096	+	5.74887i	−0.350895	+	0.446199i
$167$	−9.82244	+	0.467900i	−0.760083	+	0.0362072i	−0.424045	−	0.905641i	$-0.639390\pi$
$167$	−9.82244	+	0.467900i	−0.760083	+	0.0362072i	−0.336038	+	0.941848i	$0.609087\pi$
$168$	3.33648	+	1.90118i	0.257415	+	0.146679i
$169$	0.380180	−	1.09846i	0.0292446	−	0.0844968i
$170$	−18.6919	+	2.68749i	−1.43360	+	0.206121i
$171$	−0.269398	−	0.0621304i	−0.0206014	−	0.00475123i
$172$	2.07697	+	7.07352i	0.158368	+	0.539351i
$173$	0.684171	−	0.717538i	0.0520166	−	0.0545534i	−0.697212	−	0.716865i	$-0.745576\pi$
$173$	0.684171	−	0.717538i	0.0520166	−	0.0545534i	0.749228	+	0.662312i	$0.230425\pi$
$174$	−5.14516	+	4.50962i	−0.390054	+	0.341873i
$175$	3.35795	−	8.38775i	0.253837	−	0.634054i
$176$	−3.83423	+	0.738987i	−0.289016	+	0.0557032i
$177$	9.59502	−	0.0543846i	0.721206	−	0.00408780i
$178$	−4.67118	+	9.06082i	−0.350120	+	0.679137i
$179$	21.9626	+	3.15774i	1.64156	+	0.236021i	0.900323	−	0.435222i	$-0.143330\pi$
$179$	21.9626	+	3.15774i	1.64156	+	0.236021i	0.741238	+	0.671242i	$0.234239\pi$
$180$	−1.38749	−	8.93034i	−0.103417	−	0.665628i
$181$	−15.4157	−	13.3578i	−1.14584	−	0.992874i	−0.999994	−	0.00356650i	$-0.998865\pi$
$181$	−15.4157	−	13.3578i	−1.14584	−	0.992874i	−0.145844	−	0.989308i	$-0.546590\pi$
$182$	−1.79840	−	7.41309i	−0.133306	−	0.549494i
$183$	−3.60421	−	5.00116i	−0.266431	−	0.369697i
$184$	4.79037	+	0.228715i	0.353151	+	0.0168611i
$185$	−18.0745	−	10.4353i	−1.32886	−	0.767220i
$186$	−5.42629	−	1.01397i	−0.397875	−	0.0743478i
$187$	24.0352	+	4.63240i	1.75763	+	0.338755i
$188$	2.08975	−	3.25172i	0.152411	−	0.237156i
$189$	8.93323	−	7.27437i	0.649797	−	0.529133i
$190$	−0.233550	+	0.150093i	−0.0169435	+	0.0108889i
$191$	13.2093	−	18.5499i	0.955794	−	1.34223i	0.0162240	−	0.999868i	$-0.494836\pi$
$191$	13.2093	−	18.5499i	0.955794	−	1.34223i	0.939570	−	0.342357i	$-0.111225\pi$
$192$	1.18813	−	1.26030i	0.0857457	−	0.0909542i
$193$	−15.2690	−	6.11278i	−1.09909	−	0.440008i	−0.249991	−	0.968248i	$-0.580428\pi$
$193$	−15.2690	−	6.11278i	−1.09909	−	0.440008i	−0.849095	+	0.528241i	$0.822852\pi$
$194$	−1.03819	−	1.45793i	−0.0745377	−	0.104674i
$195$	−11.0172	+	14.1741i	−0.788957	+	1.01503i
$196$	−1.50861	−	1.43845i	−0.107758	−	0.102747i
$197$	−6.67685	−	3.04922i	−0.475706	−	0.217248i	0.163109	−	0.986608i	$-0.447848\pi$
$197$	−6.67685	−	3.04922i	−0.475706	−	0.217248i	−0.638815	+	0.769360i	$0.720575\pi$
$198$	−2.08643	+	11.5271i	−0.148276	+	0.819193i
$199$	10.2789	−	8.90676i	0.728655	−	0.631383i	−0.209416	−	0.977827i	$-0.567156\pi$
$199$	10.2789	−	8.90676i	0.728655	−	0.631383i	0.938071	+	0.346444i	$0.112611\pi$
$200$	−3.31950	−	2.36380i	−0.234724	−	0.167146i
$201$	−2.76663	−	18.4974i	−0.195143	−	1.30471i
$202$	−13.2944	−	10.4548i	−0.935392	−	0.735600i
$203$	−7.78416	+	4.01301i	−0.546341	+	0.281658i
$204$	−9.85062	+	4.56628i	−0.689681	+	0.319704i
$205$	0.721299	−	0.174985i	0.0503777	−	0.0122215i
$206$	−10.3833			−0.723438
$207$	5.82947	−	13.1536i	0.405176	−	0.914239i
$208$	−3.44058			−0.238562
$209$	0.349709	−	0.0848384i	0.0241899	−	0.00586840i
$210$	1.03435	−	11.5220i	0.0713771	−	0.795095i
$211$	−18.6059	+	9.59201i	−1.28088	+	0.660341i	−0.958182	−	0.286160i	$-0.907621\pi$
$211$	−18.6059	+	9.59201i	−1.28088	+	0.660341i	−0.322701	+	0.946501i	$0.604591\pi$
$212$	−6.83732	−	5.37693i	−0.469589	−	0.369289i
$213$	−18.7335	+	14.9048i	−1.28360	+	1.02126i
$214$	−6.36940	−	4.53563i	−0.435403	−	0.310049i
$215$	16.7841	−	14.5435i	1.14467	−	0.991858i
$216$	−2.23861	−	4.68920i	−0.152318	−	0.319060i
$217$	−6.42756	−	2.93537i	−0.436331	−	0.199266i
$218$	9.44179	+	9.00273i	0.639479	+	0.609742i
$219$	−1.92075	−	4.72009i	−0.129792	−	0.318954i
$220$	6.82330	+	9.58199i	0.460027	+	0.646017i
$221$	20.0227	+	8.01587i	1.34687	+	0.539206i
$222$	−11.6773	−	2.76289i	−0.783728	−	0.185433i
$223$	−4.37762	+	6.14751i	−0.293147	+	0.411668i	−0.934715	−	0.355399i	$-0.884345\pi$
$223$	−4.37762	+	6.14751i	−0.293147	+	0.411668i	0.641567	+	0.767067i	$0.278284\pi$
$224$	1.86514	−	1.19865i	0.124620	−	0.0800884i
$225$	−10.2090	+	6.72569i	−0.680603	+	0.448379i
$226$	9.34138	−	14.5355i	0.621380	−	0.966886i
$227$	28.1696	+	5.42924i	1.86968	+	0.360352i	0.992743	−	0.120252i	$-0.0383703\pi$
$227$	28.1696	+	5.42924i	1.86968	+	0.360352i	0.876938	+	0.480604i	$0.159582\pi$
$228$	−0.103843	+	0.121223i	−0.00687720	+	0.00802821i
$229$	−4.70741	−	2.71783i	−0.311075	−	0.179599i	0.336333	−	0.941743i	$-0.390813\pi$
$229$	−4.70741	−	2.71783i	−0.311075	−	0.179599i	−0.647407	+	0.762144i	$0.724147\pi$
$230$	−5.36810	−	13.4131i	−0.353962	−	0.884434i
$231$	−6.15169	+	13.6749i	−0.404752	+	0.899744i
$232$	0.931266	+	3.83873i	0.0611406	+	0.252025i
$233$	−7.26805	−	6.29780i	−0.476145	−	0.412582i	0.383447	−	0.923563i	$-0.374737\pi$
$233$	−7.26805	−	6.29780i	−0.476145	−	0.412582i	−0.859592	+	0.510981i	$0.829282\pi$
$234$	−3.72734	+	9.62525i	−0.243664	+	0.629222i
$235$	−11.5257	−	1.65715i	−0.751857	−	0.108101i
$236$	2.53847	−	4.92395i	0.165241	−	0.320522i
$237$	−4.54433	+	7.97507i	−0.295186	+	0.518036i
$238$	−13.6469	+	2.63023i	−0.884598	+	0.170492i
$239$	7.19338	−	17.9682i	0.465301	−	1.16227i	−0.491332	−	0.870972i	$-0.663490\pi$
$239$	7.19338	−	17.9682i	0.465301	−	1.16227i	0.956634	−	0.291294i	$-0.0940858\pi$
$240$	−4.94041	−	1.67860i	−0.318902	−	0.108353i
$241$	0.0488606	−	0.0512435i	0.00314739	−	0.00330089i	−0.722158	−	0.691728i	$-0.756850\pi$
$241$	0.0488606	−	0.0512435i	0.00314739	−	0.00330089i	0.725306	+	0.688427i	$0.241698\pi$
$242$	−1.19663	−	4.07534i	−0.0769222	−	0.261973i
$243$	−15.5435	+	1.18264i	−0.997118	+	0.0758666i
$244$	−3.52289	+	0.506515i	−0.225530	+	0.0324263i
$245$	−2.05381	+	5.93411i	−0.131213	+	0.379116i
$246$	0.368356	−	0.215463i	0.0234855	−	0.0137374i
$247$	0.316713	−	0.0150869i	0.0201520	−	0.000959958i
$248$	−1.97013	+	2.50523i	−0.125104	+	0.159082i
$249$	12.6495	−	0.674452i	0.801632	−	0.0427416i
$250$	0.527290	−	2.73584i	0.0333488	−	0.173030i
$251$	2.86529	+	0.841326i	0.180856	+	0.0531040i	0.370906	−	0.928670i	$-0.379047\pi$
$251$	2.86529	+	0.841326i	0.180856	+	0.0531040i	−0.190051	+	0.981774i	$0.560865\pi$
$252$	−1.33272	−	6.51641i	−0.0839534	−	0.410495i
$253$	0.889022	+	18.7056i	0.0558923	+	1.17601i
$254$	17.8619	−	10.3126i	1.12075	−	0.647067i
$255$	24.8402	+	21.2789i	1.55555	+	1.33253i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	−5.92945	−	11.5015i	−0.369869	−	0.717445i	0.628298	−	0.777973i	$-0.283752\pi$
$257$	−5.92945	−	11.5015i	−0.369869	−	0.717445i	−0.998167	+	0.0605276i	$0.980722\pi$
$258$	6.84241	−	10.7809i	0.425990	−	0.671187i
$259$	−13.6526	−	7.03841i	−0.848332	−	0.437346i
$260$	4.30567	+	9.42810i	0.267026	+	0.584706i
$261$	11.7480	+	1.55339i	0.727181	+	0.0961526i
$262$	2.38252	+	16.5708i	0.147193	+	1.02375i
$263$	9.86079	−	0.941591i	0.608042	−	0.0580610i	0.213507	−	0.976942i	$-0.431511\pi$
$263$	9.86079	−	0.941591i	0.608042	−	0.0580610i	0.394536	+	0.918881i	$0.370905\pi$
$264$	5.33992	+	4.15059i	0.328649	+	0.255451i
$265$	−6.17773	+	25.4649i	−0.379495	+	1.56430i
$266$	−0.166434	+	0.118517i	−0.0102047	+	0.00726677i
$267$	17.1350	−	4.25989i	1.04865	−	0.260701i
$268$	−10.2044	−	3.53177i	−0.623332	−	0.215737i
$269$	14.5860	−	6.66122i	0.889326	−	0.406142i	0.0822659	−	0.996610i	$-0.473784\pi$
$269$	14.5860	−	6.66122i	0.889326	−	0.406142i	0.807061	+	0.590469i	$0.201057\pi$
$270$	−10.0482	+	12.0026i	−0.611511	+	0.730456i
$271$	2.66423	−	18.5301i	0.161840	−	1.12562i	−0.733321	−	0.679882i	$-0.762031\pi$
$271$	2.66423	−	18.5301i	0.161840	−	1.12562i	0.895162	−	0.445742i	$-0.147060\pi$
$272$	−0.298271	+	6.26149i	−0.0180854	+	0.379659i
$273$	−7.60275	+	10.8057i	−0.460139	+	0.653989i
$274$	10.8642	+	11.3941i	0.656332	+	0.688341i
$275$	7.95625	−	13.7806i	0.479780	−	0.831003i
$276$	−5.17103	−	6.50080i	−0.311260	−	0.391302i
$277$	6.61921	+	11.4648i	0.397710	+	0.688853i	0.993443	−	0.114329i	$-0.0364718\pi$
$277$	6.61921	+	11.4648i	0.397710	+	0.688853i	−0.595733	+	0.803182i	$0.703139\pi$
$278$	1.70479	−	5.80599i	0.102247	−	0.348220i
$279$	4.87420	+	8.22560i	0.291811	+	0.492454i
$280$	−5.61873	−	3.61094i	−0.335783	−	0.215795i
$281$	13.2459	−	5.30285i	0.790182	−	0.316341i	0.0587653	−	0.998272i	$-0.481284\pi$
$281$	13.2459	−	5.30285i	0.790182	−	0.316341i	0.731417	+	0.681931i	$0.238859\pi$
$282$	−6.62129	+	0.990334i	−0.394292	+	0.0589735i
$283$	0.443630	−	4.64590i	0.0263711	−	0.276170i	−0.972663	−	0.232222i	$-0.925400\pi$
$283$	0.443630	−	4.64590i	0.0263711	−	0.276170i	0.999034	−	0.0439480i	$-0.0139936\pi$
$284$	2.61573	+	13.5717i	0.155215	+	0.805332i
$285$	0.462137	+	0.132855i	0.0273746	+	0.00786966i
$286$	−1.27705	−	13.3739i	−0.0755138	−	0.790817i
$287$	0.524124	−	0.153897i	0.0309380	−	0.00908423i
$288$	−2.99803	−	0.108768i	−0.176660	−	0.00640923i
$289$	9.26177	−	20.2804i	0.544810	−	1.19297i
$290$	9.35370	−	7.35583i	0.549268	−	0.431949i
$291$	−0.713774	+	3.01675i	−0.0418422	+	0.176845i
$292$	−2.92882	−	0.279668i	−0.171396	−	0.0163663i
$293$	−1.00179	−	21.0302i	−0.0585253	−	1.22860i	−0.816900	−	0.576779i	$-0.804309\pi$
$293$	−1.00179	−	21.0302i	−0.0585253	−	1.22860i	0.758375	−	0.651819i	$-0.225994\pi$
$294$	−0.151348	+	3.60725i	−0.00882677	+	0.210379i
$295$	−16.6696	−	0.794073i	−0.970545	−	0.0462327i
$296$	−4.53689	+	5.23585i	−0.263702	+	0.304328i
$297$	17.3965	−	10.4422i	1.00945	−	0.605921i
$298$		−	17.4971i		−	1.01358i
$299$	−2.35003	+	16.3323i	−0.135906	+	0.944518i
$300$	0.710750	+	7.02244i	0.0410351	+	0.405441i
$301$	11.8293	−	11.2792i	0.681827	−	0.650121i
$302$	−4.33285	+	1.49961i	−0.249327	+	0.0862931i
$303$	1.55969	+	29.2524i	0.0896017	+	1.68051i
$304$	0.0342512	+	0.0855553i	0.00196444	+	0.00490693i
$305$	5.79665	+	9.01977i	0.331915	+	0.516471i
$306$	17.1938	+	7.61779i	0.982903	+	0.435480i
$307$	−10.3206	−	11.9106i	−0.589027	−	0.679774i	0.380493	−	0.924784i	$-0.375754\pi$
$307$	−10.3206	−	11.9106i	−0.589027	−	0.679774i	−0.969521	+	0.245010i	$0.921209\pi$
$308$	5.35159	+	6.80510i	0.304935	+	0.387757i
$309$	11.8541	+	13.5247i	0.674357	+	0.769395i
$310$	9.33048	+	2.26355i	0.529935	+	0.128561i
$311$	−21.8152	−	5.29232i	−1.23703	−	0.300100i	−0.436670	−	0.899622i	$-0.643842\pi$
$311$	−21.8152	−	5.29232i	−1.23703	−	0.300100i	−0.800358	+	0.599522i	$0.795357\pi$
$312$	3.92795	+	4.48152i	0.222377	+	0.253716i
$313$	−4.31024	−	5.48091i	−0.243629	−	0.309800i	0.648825	−	0.760938i	$-0.275261\pi$
$313$	−4.31024	−	5.48091i	−0.243629	−	0.309800i	−0.892454	+	0.451138i	$0.851018\pi$
$314$	14.7020	+	16.9671i	0.829685	+	0.957507i
$315$	−16.1888	+	11.8069i	−0.912138	+	0.665241i
$316$	2.86510	+	4.45819i	0.161175	+	0.250793i
$317$	−11.4814	−	28.6792i	−0.644861	−	1.61079i	−0.784177	−	0.620537i	$-0.786914\pi$
$317$	−11.4814	−	28.6792i	−0.644861	−	1.61079i	0.139316	−	0.990248i	$-0.455510\pi$
$318$	0.802148	+	15.0445i	0.0449822	+	0.843655i
$319$	−14.5759	+	5.04477i	−0.816094	+	0.282453i
$320$	−2.18024	+	2.07886i	−0.121879	+	0.116212i
$321$	1.36378	+	13.4745i	0.0761185	+	0.752076i
$322$	−4.41599	−	9.67244i	−0.246093	−	0.539024i
$323$		−	0.577692i		−	0.0321436i
$324$	−3.55218	+	8.26934i	−0.197344	+	0.459408i
$325$	9.18167	−	10.5962i	0.509307	−	0.587772i
$326$	−14.2270	−	0.677715i	−0.787960	−	0.0375352i
$327$	0.947226	−	22.5764i	0.0523817	−	1.24848i
$328$	−0.0117233	−	0.246102i	−0.000647310	−	0.0135887i
$329$	−8.53100	−	0.814611i	−0.470329	−	0.0449110i
$330$	4.69114	−	19.8270i	0.258239	−	1.09144i
$331$	−11.7846	+	9.26751i	−0.647740	+	0.509389i	−0.887121	−	0.461537i	$-0.847298\pi$
$331$	−11.7846	+	9.26751i	−0.647740	+	0.509389i	0.239381	+	0.970926i	$0.423056\pi$
$332$	3.03817	−	6.65267i	0.166741	−	0.365113i
$333$	9.73262	+	18.3645i	0.533344	+	1.00637i
$334$	9.43525	−	2.77044i	0.516274	−	0.151592i
$335$	3.09215	+	32.3825i	0.168942	+	1.76924i
$336$	−3.69065	−	1.06099i	−0.201341	−	0.0578816i
$337$	5.36145	+	27.8178i	0.292057	+	1.51533i	0.770628	+	0.637286i	$0.219943\pi$
$337$	5.36145	+	27.8178i	0.292057	+	1.51533i	−0.478571	+	0.878049i	$0.658845\pi$
$338$	−0.110492	+	1.15712i	−0.00600997	+	0.0629393i
$339$	−29.5978	+	4.42688i	−1.60753	+	0.240435i
$340$	17.5314	−	7.01851i	0.950773	−	0.380632i
$341$	−10.4694	−	6.72825i	−0.566948	−	0.364355i
$342$	0.276452	−	0.00313396i	0.0149488	−	0.000169465i
$343$	−5.67442	+	19.3253i	−0.306390	+	1.04347i
$344$	−3.68607	−	6.38446i	−0.198740	−	0.344227i
$345$	−11.3427	+	22.3053i	−0.610669	+	1.20088i
$346$	−0.495719	+	0.858611i	−0.0266500	+	0.0461592i
$347$	15.6900	+	16.4552i	0.842282	+	0.883360i	0.994473	−	0.104991i	$-0.0334813\pi$
$347$	15.6900	+	16.4552i	0.842282	+	0.883360i	−0.152191	+	0.988351i	$0.548633\pi$
$348$	3.93694	−	5.59552i	0.211042	−	0.299951i
$349$	1.59898	−	33.5666i	0.0855912	−	1.79678i	−0.393818	−	0.919189i	$-0.628846\pi$
$349$	1.59898	−	33.5666i	0.0855912	−	1.79678i	0.479409	−	0.877592i	$-0.340851\pi$
$350$	−1.28581	+	8.94298i	−0.0687292	+	0.478022i
$351$	16.7927	−	6.13367i	0.896326	−	0.327391i
$352$	3.55192	−	1.62211i	0.189318	−	0.0864587i
$353$	−29.5783	−	10.2372i	−1.57430	−	0.544869i	−0.606170	−	0.795335i	$-0.707295\pi$
$353$	−29.5783	−	10.2372i	−1.57430	−	0.544869i	−0.968125	+	0.250466i	$0.919416\pi$
$354$	−9.31173	+	2.31496i	−0.494913	+	0.123039i
$355$	33.9166	−	24.1519i	1.80011	−	1.28185i
$356$	2.40333	−	9.90668i	0.127376	−	0.525053i
$357$	19.0060	+	14.7729i	1.00591	+	0.781867i
$358$	−22.0880	+	2.10915i	−1.16739	+	0.111472i
$359$	−3.15139	−	21.9184i	−0.166324	−	1.15681i	−0.886403	−	0.462915i	$-0.846803\pi$
$359$	−3.15139	−	21.9184i	−0.166324	−	1.15681i	0.720079	−	0.693892i	$-0.244106\pi$
$360$	3.45378	+	8.35149i	0.182030	+	0.440162i
$361$	7.88936	+	17.2753i	0.415229	+	0.909225i
$362$	18.1303	+	9.34684i	0.952909	+	0.491259i
$363$	−3.94219	+	6.21129i	−0.206911	+	0.326008i
$364$	3.49540	+	6.78013i	0.183209	+	0.355376i
$365$	2.89886	+	8.37571i	0.151733	+	0.438405i
$366$	4.68168	+	4.01047i	0.244715	+	0.209630i
$367$	0.210758	−	0.121681i	0.0110015	−	0.00635170i	−0.494489	−	0.869184i	$-0.664645\pi$
$367$	0.210758	−	0.121681i	0.0110015	−	0.00635170i	0.505491	+	0.862832i	$0.331312\pi$
$368$	−4.70926	+	0.907106i	−0.245487	+	0.0472862i
$369$	−0.701186	−	0.233817i	−0.0365023	−	0.0121720i
$370$	20.0252	+	5.87994i	1.04106	+	0.305683i
$371$	−3.64971	+	18.9365i	−0.189483	+	0.983133i
$372$	5.51239	−	0.293911i	0.285804	−	0.0152386i
$373$	5.14322	−	6.54014i	0.266306	−	0.338636i	−0.634448	−	0.772966i	$-0.718772\pi$
$373$	5.14322	−	6.54014i	0.266306	−	0.338636i	0.900754	+	0.434330i	$0.143015\pi$
$374$	−24.4498	+	1.16469i	−1.26427	+	0.0602246i
$375$	−4.16555	+	2.43656i	−0.215108	+	0.125824i
$376$	−1.26422	+	3.65273i	−0.0651973	+	0.188375i
$377$	−13.4522	+	1.93414i	−0.692825	+	0.0996132i
$378$	−6.96642	+	9.17541i	−0.358314	+	0.471932i
$379$	0.671802	+	2.28795i	0.0345081	+	0.117524i	0.974946	−	0.222442i	$-0.0714027\pi$
$379$	0.671802	+	2.28795i	0.0345081	+	0.117524i	−0.940438	+	0.339966i	$0.889585\pi$
$380$	0.191581	−	0.200924i	0.00982788	−	0.0103072i
$381$	−33.8246	−	11.4926i	−1.73289	−	0.588782i
$382$	−8.46368	+	21.1412i	−0.433039	+	1.08168i
$383$	−11.8460	+	2.28313i	−0.605303	+	0.116663i	−0.482689	−	0.875792i	$-0.660340\pi$
$383$	−11.8460	+	2.28313i	−0.605303	+	0.116663i	−0.122614	+	0.992454i	$0.539128\pi$
$384$	−0.857510	+	1.50488i	−0.0437596	+	0.0767958i
$385$	11.9506	−	23.1809i	0.609058	−	1.18141i
$386$	16.2797	+	2.34067i	0.828616	+	0.119137i
$387$	−21.8542	+	3.39545i	−1.11091	+	0.172600i
$388$	1.35265	+	1.17207i	0.0686702	+	0.0595031i
$389$	4.80329	+	19.7994i	0.243536	+	1.00387i	0.953921	+	0.300057i	$0.0970058\pi$
$389$	4.80329	+	19.7994i	0.243536	+	1.00387i	−0.710385	+	0.703813i	$0.751479\pi$
$390$	7.36496	−	16.3719i	0.372939	−	0.829026i
$391$	29.5192	+	5.69268i	1.49285	+	0.287891i
$392$	1.80521	+	1.04224i	0.0911769	+	0.0526410i
$393$	18.8642	−	22.0215i	0.951575	−	1.11084i
$394$	7.20752	+	1.38914i	0.363110	+	0.0699836i
$395$	8.63110	−	13.4303i	0.434278	−	0.675750i
$396$	−0.689996	−	11.6940i	−0.0346736	−	0.587647i
$397$	20.3276	−	13.0637i	1.02021	−	0.655650i	0.0801951	−	0.996779i	$-0.474446\pi$
$397$	20.3276	−	13.0637i	1.02021	−	0.655650i	0.940016	+	0.341129i	$0.110809\pi$
$398$	−7.88935	+	11.0790i	−0.395457	+	0.555342i
$399$	0.344385	+	0.0814828i	0.0172408	+	0.00407924i
$400$	3.78321	+	1.51457i	0.189161	+	0.0757285i
$401$	13.7648	+	19.3300i	0.687382	+	0.965294i	0.999882	+	0.0153755i	$0.00489438\pi$
$401$	13.7648	+	19.3300i	0.687382	+	0.965294i	−0.312499	+	0.949918i	$0.601166\pi$
$402$	7.04957	+	17.3238i	0.351601	+	0.864030i
$403$	−7.93609	−	7.56705i	−0.395325	−	0.376941i
$404$	15.3845	+	7.02586i	0.765407	+	0.349550i
$405$	27.1055	−	0.614634i	1.34688	−	0.0305414i
$406$	6.61863	−	5.73508i	0.328477	−	0.284627i
$407$	−22.0363	−	15.6920i	−1.09230	−	0.777823i
$408$	8.49641	−	6.75994i	0.420635	−	0.334667i
$409$	8.63366	+	6.78959i	0.426907	+	0.335723i	0.808385	−	0.588655i	$-0.200342\pi$
$409$	8.63366	+	6.78959i	0.426907	+	0.335723i	−0.381478	+	0.924378i	$0.624585\pi$
$410$	−0.659712	+	0.340105i	−0.0325809	+	0.0167966i
$411$	2.43813	−	27.1592i	0.120264	−	1.33967i
$412$	10.0906	−	2.44795i	0.497128	−	0.120602i
$413$	−12.2822			−0.604369
$414$	−2.56407	+	14.1572i	−0.126017	+	0.695787i
$415$	−22.0321			−1.08152
$416$	3.34360	−	0.811148i	0.163933	−	0.0397698i
$417$	−9.50886	+	4.40786i	−0.465651	+	0.215854i
$418$	−0.319850	+	0.164894i	−0.0156444	+	0.00806522i
$419$	18.1061	+	14.2388i	0.884541	+	0.695611i	0.953301	−	0.302022i	$-0.0976617\pi$
$419$	18.1061	+	14.2388i	0.884541	+	0.695611i	−0.0687594	+	0.997633i	$0.521904\pi$
$420$	1.71122	+	11.4411i	0.0834992	+	0.558268i
$421$	2.23078	+	1.58853i	0.108721	+	0.0774201i	0.633125	−	0.774050i	$-0.281772\pi$
$421$	2.23078	+	1.58853i	0.108721	+	0.0774201i	−0.524403	+	0.851470i	$0.675712\pi$
$422$	15.8200	−	13.7081i	0.770107	−	0.667301i
$423$	8.84917	+	7.49392i	0.430261	+	0.364367i
$424$	7.91225	+	3.61340i	0.384253	+	0.175482i
$425$	−18.4880	−	17.6282i	−0.896798	−	0.855096i
$426$	14.6915	−	18.9013i	0.711806	−	0.915770i
$427$	4.57718	+	6.42775i	0.221505	+	0.311061i
$428$	7.25917	+	2.90613i	0.350885	+	0.140473i
$429$	−15.9622	+	16.9318i	−0.770663	+	0.817475i
$430$	−12.8822	+	18.0905i	−0.621236	+	0.872403i
$431$	−26.9692	+	17.3321i	−1.29906	+	0.834856i	−0.993109	−	0.117190i	$-0.962611\pi$
$431$	−26.9692	+	17.3321i	−1.29906	+	0.834856i	−0.305952	+	0.952047i	$0.598975\pi$
$432$	3.28103	+	4.02925i	0.157859	+	0.193857i
$433$	−5.63094	+	8.76191i	−0.270606	+	0.421071i	−0.949786	−	0.312901i	$-0.898699\pi$
$433$	−5.63094	+	8.76191i	−0.270606	+	0.421071i	0.679180	+	0.733972i	$0.262336\pi$
$434$	6.93842	+	1.33727i	0.333055	+	0.0641910i
$435$	−20.2600	−	3.78583i	−0.971393	−	0.181516i
$436$	−11.2981	−	6.52297i	−0.541082	−	0.312394i
$437$	0.429521	−	0.104151i	0.0205468	−	0.00498223i
$438$	2.97941	+	4.13420i	0.142362	+	0.197540i
$439$	−4.86966	−	20.0730i	−0.232416	−	0.958033i	−0.961762	−	0.273888i	$-0.911690\pi$
$439$	−4.86966	−	20.0730i	−0.232416	−	0.958033i	0.729345	−	0.684146i	$-0.239825\pi$
$440$	−8.89000	−	7.70323i	−0.423814	−	0.367237i
$441$	4.87139	−	3.92109i	0.231971	−	0.186718i
$442$	−21.3481	−	3.06939i	−1.01542	−	0.145996i
$443$	−13.0432	+	25.3002i	−0.619700	+	1.20205i	0.344977	+	0.938611i	$0.387887\pi$
$443$	−13.0432	+	25.3002i	−0.619700	+	1.20205i	−0.964676	+	0.263438i	$0.915143\pi$
$444$	11.9995	−	0.0680132i	0.569471	−	0.00322776i
$445$	−30.1545	+	5.81181i	−1.42946	+	0.275506i
$446$	2.80489	−	7.00629i	0.132816	−	0.331757i
$447$	−22.7908	+	19.9756i	−1.07797	+	0.944815i
$448$	−1.52997	+	1.60459i	−0.0722844	+	0.0758097i
$449$	−10.2624	−	34.9504i	−0.484311	−	1.64941i	−0.732549	−	0.680714i	$-0.761670\pi$
$449$	−10.2624	−	34.9504i	−0.484311	−	1.64941i	0.248238	−	0.968699i	$-0.420149\pi$
$450$	8.33563	−	8.94298i	0.392945	−	0.421576i
$451$	0.952273	−	0.136916i	0.0448408	−	0.00644713i
$452$	−5.65120	+	16.3281i	−0.265810	+	0.768007i
$453$	6.89993	+	3.93170i	0.324187	+	0.184727i
$454$	−28.6555	+	1.36503i	−1.34487	+	0.0640641i
$455$	14.2051	−	18.0632i	0.665944	−	0.846817i
$456$	0.0723368	−	0.142288i	0.00338748	−	0.00666325i
$457$	−0.129454	+	0.671670i	−0.00605559	+	0.0314194i	−0.984831	−	0.173517i	$-0.944487\pi$
$457$	−0.129454	+	0.671670i	−0.00605559	+	0.0314194i	0.978775	+	0.204937i	$0.0656989\pi$
$458$	5.21547	+	1.53140i	0.243703	+	0.0715576i
$459$	−9.70682	−	31.0926i	−0.453075	−	1.45128i
$460$	8.37904	+	11.7694i	0.390675	+	0.548752i
$461$	−1.30666	+	0.754399i	−0.0608571	+	0.0351359i	−0.530120	−	0.847923i	$-0.677853\pi$
$461$	−1.30666	+	0.754399i	−0.0608571	+	0.0351359i	0.469263	+	0.883059i	$0.344520\pi$
$462$	2.75430	−	14.7398i	0.128142	−	0.685756i
$463$	4.03834	+	11.6680i	0.187678	+	0.542259i	0.999110	−	0.0421879i	$-0.0134328\pi$
$463$	4.03834	+	11.6680i	0.187678	+	0.542259i	−0.811432	+	0.584447i	$0.801312\pi$
$464$	−1.81003	−	3.51097i	−0.0840285	−	0.162993i
$465$	−7.70379	−	14.7376i	−0.357255	−	0.683438i
$466$	8.54793	+	4.40677i	0.395975	+	0.204139i
$467$	5.29788	+	11.6007i	0.245157	+	0.536818i	0.991708	−	0.128509i	$-0.0410192\pi$
$467$	5.29788	+	11.6007i	0.245157	+	0.536818i	−0.746552	+	0.665327i	$0.768292\pi$
$468$	1.35303	−	10.2327i	0.0625439	−	0.473006i
$469$	3.40714	+	23.6972i	0.157327	+	1.09423i
$470$	11.5915	−	1.10686i	0.534678	−	0.0510555i
$471$	5.31576	−	38.5206i	0.244937	−	1.77494i
$472$	−1.30605	+	5.38362i	−0.0601159	+	0.247801i
$473$	23.4489	−	16.6979i	1.07818	−	0.767771i
$474$	2.53604	−	8.82163i	0.116484	−	0.405191i
$475$	−0.354895	−	0.122830i	−0.0162837	−	0.00563584i
$476$	12.6421	−	5.77347i	0.579451	−	0.264627i
$477$	18.6804	−	18.2205i	0.855318	−	0.834258i
$478$	−2.75445	+	19.1576i	−0.125986	+	0.876249i
$479$	−0.350340	+	7.35455i	−0.0160075	+	0.336038i	0.976631	+	0.214923i	$0.0689500\pi$
$479$	−0.350340	+	7.35455i	−0.0160075	+	0.336038i	−0.992638	+	0.121115i	$0.961353\pi$
$480$	5.19689	+	0.466535i	0.237205	+	0.0212943i
$481$	−16.4490	−	17.2513i	−0.750011	−	0.786589i
$482$	−0.0354022	+	0.0613184i	−0.00161253	+	0.00279298i
$483$	−7.55728	+	16.7946i	−0.343868	+	0.764181i
$484$	2.12370	+	3.67835i	0.0965316	+	0.167198i
$485$	1.51904	−	5.17338i	0.0689761	−	0.234911i
$486$	14.8266	−	4.81383i	0.672547	−	0.218360i
$487$	−2.17170	−	1.39566i	−0.0984090	−	0.0632436i	0.490511	−	0.871435i	$-0.336810\pi$
$487$	−2.17170	−	1.39566i	−0.0984090	−	0.0632436i	−0.588920	+	0.808192i	$0.700447\pi$
$488$	3.30417	−	1.32279i	0.149573	−	0.0598799i
$489$	15.3595	+	19.3050i	0.694582	+	0.873004i
$490$	0.596902	−	6.25104i	0.0269653	−	0.282393i
$491$	−0.0426344	−	0.221209i	−0.00192407	−	0.00998300i	0.980954	−	0.194240i	$-0.0622242\pi$
$491$	−0.0426344	−	0.221209i	−0.00192407	−	0.00998300i	−0.982878	+	0.184257i	$0.941012\pi$
$492$	−0.307175	+	0.296233i	−0.0138485	+	0.0133552i
$493$	2.35372	+	24.6493i	0.106006	+	1.11015i
$494$	−0.304229	+	0.0893297i	−0.0136879	+	0.00401913i
$495$	−31.1812	+	16.5251i	−1.40149	+	0.742748i
$496$	1.32397	−	2.89909i	0.0594479	−	0.130173i
$497$	24.0875	−	18.9426i	1.08047	−	0.849691i
$498$	−12.1340	+	3.63768i	−0.543736	+	0.163008i
$499$	18.3636	+	1.75351i	0.822068	+	0.0784980i	0.497609	−	0.867402i	$-0.334212\pi$
$499$	18.3636	+	1.75351i	0.822068	+	0.0784980i	0.324459	+	0.945900i	$0.394818\pi$
$500$	0.132572	+	2.78304i	0.00592882	+	0.124461i
$501$	−14.3804	−	9.12697i	−0.642469	−	0.407763i
$502$	−2.98287	−	0.142092i	−0.133132	−	0.00634187i
$503$	−9.47282	+	10.9322i	−0.422372	+	0.487443i	−0.926558	−	0.376152i	$-0.877247\pi$
$503$	−9.47282	+	10.9322i	−0.422372	+	0.487443i	0.504186	+	0.863595i	$0.331793\pi$
$504$	2.83145	+	6.01852i	0.126123	+	0.268086i
$505$		−	50.9499i		−	2.26724i
$506$	−5.27398	−	17.9687i	−0.234457	−	0.798807i
$507$	1.63335	−	1.17711i	0.0725398	−	0.0522775i
$508$	−14.9271	+	14.2330i	−0.662283	+	0.631485i
$509$	−7.35303	+	2.54491i	−0.325917	+	0.112801i	−0.485127	−	0.874444i	$-0.661227\pi$
$509$	−7.35303	+	2.54491i	−0.325917	+	0.112801i	0.159210	+	0.987245i	$0.449105\pi$
$510$	−29.1567	−	14.8227i	−1.29108	−	0.656362i
$511$	2.42436	+	6.05575i	0.107247	+	0.267891i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	−0.319695	−	0.356514i	−0.0141149	−	0.0157405i
$514$	8.47389	+	9.77939i	0.373767	+	0.431351i
$515$	−19.3358	−	24.5874i	−0.852036	−	1.08345i
$516$	−4.10785	+	12.0901i	−0.180838	+	0.532238i
$517$	−14.6678	−	3.55838i	−0.645090	−	0.156497i
$518$	14.9271	+	3.62128i	0.655861	+	0.159110i
$519$	1.68432	−	0.334538i	0.0739335	−	0.0146846i
$520$	−6.40705	−	8.14723i	−0.280968	−	0.357280i
$521$	4.88607	+	5.63883i	0.214063	+	0.247042i	0.852618	−	0.522534i	$-0.175013\pi$
$521$	4.88607	+	5.63883i	0.214063	+	0.247042i	−0.638556	+	0.769576i	$0.720468\pi$
$522$	−11.7830	+	1.26009i	−0.515730	+	0.0551524i
$523$	12.3941	+	19.2856i	0.541955	+	0.843299i	0.998933	−	0.0461793i	$-0.0147046\pi$
$523$	12.3941	+	19.2856i	0.541955	+	0.843299i	−0.456978	+	0.889478i	$0.651068\pi$
$524$	−6.22208	−	15.5420i	−0.271813	−	0.678956i
$525$	13.1166	−	8.53496i	0.572455	−	0.372496i
$526$	−9.36084	+	3.23982i	−0.408152	+	0.141263i
$527$	−14.4592	+	13.7868i	−0.629853	+	0.600563i
$528$	−6.16794	−	2.77466i	−0.268425	−	0.120752i
$529$	1.08939	+	22.9742i	0.0473650	+	0.998878i
$530$		−	26.2036i		−	1.13821i
$531$	13.6461	+	9.48608i	0.592191	+	0.411661i
$532$	0.133801	−	0.154415i	0.00580102	−	0.00669474i
$533$	0.846734	+	0.0403349i	0.0366761	+	0.00174710i
$534$	−15.6477	+	8.17954i	−0.677142	+	0.353963i
$535$	−1.12082	−	23.5288i	−0.0484571	−	1.01724i
$536$	10.7494	+	1.02644i	0.464303	+	0.0443355i
$537$	27.9641	+	26.3627i	1.20674	+	1.13763i
$538$	−12.6044	+	9.91224i	−0.543416	+	0.427347i
$539$	−3.38125	+	7.40390i	−0.145641	+	0.318909i
$540$	6.93519	−	14.0332i	0.298443	−	0.603894i
$541$	12.8307	−	3.76744i	0.551637	−	0.161975i	0.00597711	−	0.999982i	$-0.498097\pi$
$541$	12.8307	−	3.76744i	0.551637	−	0.161975i	0.545659	+	0.838007i	$0.316279\pi$
$542$	1.77951	+	18.6359i	0.0764366	+	0.800480i
$543$	−8.52386	−	34.2865i	−0.365794	−	1.47137i
$544$	−1.18634	−	6.15531i	−0.0508638	−	0.263907i
$545$	−3.73578	+	39.1229i	−0.160023	+	1.67584i
$546$	4.84091	−	12.2935i	0.207172	−	0.526113i
$547$	14.1026	−	5.64583i	0.602984	−	0.241398i	−0.0500257	−	0.998748i	$-0.515930\pi$
$547$	14.1026	−	5.64583i	0.602984	−	0.241398i	0.653010	+	0.757350i	$0.273506\pi$
$548$	−13.2442	−	8.51155i	−0.565765	−	0.363595i
$549$	−0.121035	−	10.6767i	−0.00516563	−	0.455669i
$550$	−4.48307	+	15.2679i	−0.191159	+	0.651027i
$551$	0.182013	+	0.315256i	0.00775401	+	0.0134303i
$552$	6.55789	+	5.09844i	0.279122	+	0.217004i
$553$	5.87471	−	10.1753i	0.249818	−	0.432697i
$554$	−9.13555	−	9.58109i	−0.388132	−	0.407061i
$555$	−15.2030	−	32.7967i	−0.645330	−	1.39214i
$556$	−0.287923	+	6.04425i	−0.0122107	+	0.256333i
$557$	−5.57432	+	38.7703i	−0.236192	+	1.64275i	0.434254	+	0.900790i	$0.357012\pi$
$557$	−5.57432	+	38.7703i	−0.236192	+	1.64275i	−0.670446	+	0.741959i	$0.733897\pi$
$558$	−6.67607	−	6.84460i	−0.282620	−	0.289755i
$559$	23.0723	−	10.5368i	0.975856	−	0.445658i
$560$	6.31166	+	2.18449i	0.266716	+	0.0923113i
$561$	29.4303	+	30.5173i	1.24255	+	1.28844i
$562$	−11.6223	+	8.27620i	−0.490257	+	0.349110i
$563$	1.39108	−	5.73411i	0.0586270	−	0.241664i	−0.934957	−	0.354761i	$-0.884562\pi$
$563$	1.39108	−	5.73411i	0.0586270	−	0.241664i	0.993584	+	0.113098i	$0.0360772\pi$
$564$	6.20116	−	2.52344i	0.261116	−	0.106256i
$565$	51.8153	−	4.94776i	2.17988	−	0.208154i
$566$	0.664188	+	4.61953i	0.0279179	+	0.194173i
$567$	19.9046	−	1.40104i	0.835916	−	0.0588381i
$568$	−5.74165	−	12.5725i	−0.240914	−	0.527528i
$569$	−25.6123	−	13.2040i	−1.07372	−	0.553542i	−0.171663	−	0.985156i	$-0.554914\pi$
$569$	−25.6123	−	13.2040i	−1.07372	−	0.553542i	−0.902059	+	0.431614i	$0.857944\pi$
$570$	−0.480432	−	0.0201572i	−0.0201231	−	0.000844294i
$571$	0.184226	+	0.357349i	0.00770962	+	0.0149546i	0.892659	−	0.450733i	$-0.148837\pi$
$571$	0.184226	+	0.357349i	0.00770962	+	0.0149546i	−0.884949	+	0.465688i	$0.845807\pi$
$572$	4.39408	+	12.6959i	0.183726	+	0.530840i
$573$	37.2000	−	13.1116i	1.55405	−	0.547746i
$574$	−0.473067	+	0.273125i	−0.0197454	+	0.0114000i
$575$	9.77363	−	16.9242i	0.407589	−	0.705787i
$576$	2.93916	−	0.601110i	0.122465	−	0.0250462i
$577$	21.7211	+	6.37790i	0.904263	+	0.265516i	0.700624	−	0.713531i	$-0.252905\pi$
$577$	21.7211	+	6.37790i	0.904263	+	0.265516i	0.203639	+	0.979046i	$0.434723\pi$
$578$	−4.21940	+	21.8923i	−0.175504	+	0.910600i
$579$	−15.5370	−	23.8773i	−0.645694	−	0.992308i
$580$	−7.35583	+	9.35370i	−0.305434	+	0.388391i
$581$	−16.1966	+	0.771538i	−0.671947	+	0.0320088i
$582$	−0.0175707	−	3.09999i	−0.000728330	−	0.128499i
$583$	−11.1089	+	32.0970i	−0.460083	+	1.32932i
$584$	2.91219	−	0.418710i	0.120507	−	0.0173263i
$585$	−29.7335	+	9.09788i	−1.22933	+	0.376151i
$586$	5.93161	+	20.2012i	0.245033	+	0.834504i
$587$	−4.48621	+	4.70500i	−0.185166	+	0.194196i	−0.809774	−	0.586742i	$-0.800410\pi$
$587$	−4.48621	+	4.70500i	−0.185166	+	0.194196i	0.624608	+	0.780938i	$0.285259\pi$
$588$	−0.703359	−	3.54124i	−0.0290060	−	0.146038i
$589$	−0.109162	+	0.272673i	−0.00449793	+	0.0112353i
$590$	16.3870	−	3.15833i	0.674641	−	0.130026i
$591$	−6.41907	−	10.9740i	−0.264045	−	0.451412i
$592$	3.17461	−	6.15788i	0.130475	−	0.253087i
$593$	−2.95540	−	0.424922i	−0.121364	−	0.0174494i	0.0813654	−	0.996684i	$-0.474072\pi$
$593$	−2.95540	−	0.424922i	−0.121364	−	0.0174494i	−0.202729	+	0.979235i	$0.564981\pi$
$594$	−14.4443	+	14.2493i	−0.592656	+	0.584655i
$595$	−31.6416	−	27.4176i	−1.29718	−	1.12401i
$596$	4.12510	+	17.0039i	0.168971	+	0.696507i
$597$	23.4379	−	2.37217i	0.959248	−	0.0970867i
$598$	−1.56668	−	16.4259i	−0.0640665	−	0.671705i
$599$	7.40646	+	4.27612i	0.302620	+	0.174718i	0.643619	−	0.765346i	$-0.277432\pi$
$599$	7.40646	+	4.27612i	0.302620	+	0.174718i	−0.340999	+	0.940064i	$0.610765\pi$
$600$	−2.34632	−	6.65692i	−0.0957880	−	0.271768i
$601$	−24.4331	−	4.70910i	−0.996648	−	0.192088i	−0.335255	−	0.942128i	$-0.608822\pi$
$601$	−24.4331	−	4.70910i	−0.996648	−	0.192088i	−0.661393	+	0.750039i	$0.730034\pi$
$602$	−8.83665	+	13.7501i	−0.360155	+	0.560412i
$603$	14.5168	−	28.9601i	0.591171	−	1.17935i
$604$	3.85716	−	2.47885i	0.156946	−	0.100863i
$605$	7.42197	−	10.4227i	0.301746	−	0.423743i
$606$	−8.41224	−	28.0601i	−0.341724	−	1.13986i
$607$	5.12989	+	2.05370i	0.208216	+	0.0833571i	0.473426	−	0.880834i	$-0.343017\pi$
$607$	5.12989	+	2.05370i	0.208216	+	0.0833571i	−0.265210	+	0.964191i	$0.585441\pi$
$608$	−0.0534561	−	0.0750686i	−0.00216793	−	0.00304443i
$609$	−15.0264	−	2.07361i	−0.608900	−	0.0840269i
$610$	−7.75975	−	7.39890i	−0.314183	−	0.299573i
$611$	−12.0972	−	5.52459i	−0.489399	−	0.223501i
$612$	−18.5051	−	3.34946i	−0.748024	−	0.135394i
$613$	−21.6925	+	18.7967i	−0.876154	+	0.759192i	−0.971696	−	0.236234i	$-0.924087\pi$
$613$	−21.6925	+	18.7967i	−0.876154	+	0.759192i	0.0955425	+	0.995425i	$0.469541\pi$
$614$	12.8377	+	9.14169i	0.518087	+	0.368928i
$615$	1.19617	+	0.471024i	0.0482341	+	0.0189935i
$616$	−6.80510	−	5.35159i	−0.274185	−	0.215622i
$617$	−9.95563	+	5.13248i	−0.400798	+	0.206626i	−0.646827	−	0.762637i	$-0.723905\pi$
$617$	−9.95563	+	5.13248i	−0.400798	+	0.206626i	0.246029	+	0.969263i	$0.420874\pi$
$618$	−14.7085	−	10.3488i	−0.591664	−	0.416289i
$619$	23.4177	−	5.68108i	0.941238	−	0.228342i	0.264349	−	0.964427i	$-0.414843\pi$
$619$	23.4177	−	5.68108i	0.941238	−	0.228342i	0.676889	+	0.736085i	$0.263328\pi$
$620$	−9.60112			−0.385590
$621$	21.3677	−	12.8228i	0.857455	−	0.514560i
$622$	22.4480			0.900083
$623$	−21.9641	+	5.32843i	−0.879972	+	0.213479i
$624$	−4.87379	−	3.42914i	−0.195108	−	0.137276i
$625$	25.5709	−	13.1827i	1.02284	−	0.527309i
$626$	5.48091	+	4.31024i	0.219061	+	0.172272i
$627$	0.579939	+	0.228367i	0.0231605	+	0.00912011i
$628$	−18.2878	−	13.0227i	−0.729761	−	0.519660i
$629$	−32.8214	+	28.4399i	−1.30868	+	1.13397i
$630$	12.9489	−	15.2907i	0.515898	−	0.609196i
$631$	3.70552	+	1.69226i	0.147515	+	0.0673677i	0.487804	−	0.872953i	$-0.337798\pi$
$631$	3.70552	+	1.69226i	0.147515	+	0.0673677i	−0.340290	+	0.940321i	$0.610525\pi$
$632$	−3.83540	−	3.65704i	−0.152564	−	0.145469i
$633$	−35.9165	−	4.95639i	−1.42755	−	0.196999i
$634$	17.9192	+	25.1639i	0.711661	+	0.999388i
$635$	57.6823	+	23.0925i	2.28905	+	0.916398i
$636$	−4.32642	−	14.4313i	−0.171554	−	0.572239i
$637$	−4.16006	+	5.84199i	−0.164828	+	0.231468i
$638$	12.9757	−	8.33897i	0.513712	−	0.330143i
$639$	−41.3924	+	2.44232i	−1.63746	+	0.0966168i
$640$	1.62868	−	2.53427i	0.0643791	−	0.100176i
$641$	5.86208	+	1.12982i	0.231538	+	0.0446253i	0.303700	−	0.952768i	$-0.401778\pi$
$641$	5.86208	+	1.12982i	0.231538	+	0.0446253i	−0.0721622	+	0.997393i	$0.522990\pi$
$642$	−4.50208	−	12.7732i	−0.177683	−	0.504118i
$643$	26.6449	+	15.3835i	1.05077	+	0.606665i	0.922866	−	0.385121i	$-0.125840\pi$
$643$	26.6449	+	15.3835i	1.05077	+	0.606665i	0.127908	+	0.991786i	$0.459174\pi$
$644$	6.57187	+	8.35868i	0.258968	+	0.329378i
$645$	38.2708	−	3.87343i	1.50691	−	0.152516i
$646$	0.136196	+	0.561408i	0.00535856	+	0.0220883i
$647$	−9.34948	−	8.10137i	−0.367566	−	0.318498i	0.451420	−	0.892312i	$-0.350918\pi$
$647$	−9.34948	−	8.10137i	−0.367566	−	0.318498i	−0.818986	+	0.573814i	$0.805463\pi$
$648$	1.50248	−	8.87370i	0.0590231	−	0.348592i
$649$	−21.4115	−	3.07851i	−0.840475	−	0.120842i
$650$	−6.42470	+	12.4622i	−0.251997	+	0.488807i
$651$	−6.17941	−	10.5643i	−0.242190	−	0.414048i
$652$	13.9857	−	2.69553i	0.547724	−	0.105565i
$653$	7.99339	−	19.9665i	0.312806	−	0.781350i	−0.685761	−	0.727827i	$-0.740530\pi$
$653$	7.99339	−	19.9665i	0.312806	−	0.781350i	0.998567	−	0.0535237i	$-0.0170453\pi$
$654$	4.40205	+	22.1633i	0.172134	+	0.866653i
$655$	−34.8026	+	36.4999i	−1.35985	+	1.42617i
$656$	0.0694135	+	0.236401i	0.00271014	+	0.00922990i
$657$	1.98354	−	8.60065i	0.0773853	−	0.335543i
$658$	8.48257	−	1.21961i	0.330685	−	0.0475453i
$659$	0.0169781	−	0.0490551i	0.000661374	−	0.00191092i	−0.944670	−	0.328023i	$-0.893618\pi$
$659$	0.0169781	−	0.0490551i	0.000661374	−	0.00191092i	0.945331	+	0.326112i	$0.105739\pi$
$660$	0.115480	+	20.3741i	0.00449506	+	0.793059i
$661$	6.50510	−	0.309876i	0.253019	−	0.0120528i	0.0793108	−	0.996850i	$-0.474728\pi$
$661$	6.50510	−	0.309876i	0.253019	−	0.0120528i	0.173708	+	0.984797i	$0.444425\pi$
$662$	9.26751	−	11.7846i	0.360192	−	0.458022i
$663$	20.3741	+	31.3110i	0.791263	+	1.21602i
$664$	−1.38411	+	7.18142i	−0.0537137	+	0.278693i
$665$	−0.590581	−	0.173410i	−0.0229018	−	0.00672456i
$666$	−13.7879	−	15.5523i	−0.534269	−	0.602638i
$667$	−17.9027	+	6.19400i	−0.693194	+	0.239833i
$668$	−8.51613	+	4.91679i	−0.329499	+	0.190236i
$669$	−12.3282	+	4.34524i	−0.476637	+	0.167997i
$670$	−10.6394	−	30.7407i	−0.411038	−	1.18762i
$671$	6.36825	+	12.3527i	0.245844	+	0.476870i
$672$	3.83675	+	0.160977i	0.148006	+	0.00620981i
$673$	−18.3359	−	9.45281i	−0.706796	−	0.364379i	0.0670522	−	0.997749i	$-0.478641\pi$
$673$	−18.3359	−	9.45281i	−0.706796	−	0.364379i	−0.773849	+	0.633371i	$0.781671\pi$
$674$	−11.7686	−	25.7697i	−0.453310	−	0.992611i
$675$	−21.1650	−	0.647769i	−0.814643	−	0.0249326i
$676$	−0.165425	−	1.15056i	−0.00636250	−	0.0442522i
$677$	−7.83115	+	0.747784i	−0.300975	+	0.0287397i	−0.244451	−	0.969662i	$-0.578608\pi$
$677$	−7.83115	+	0.747784i	−0.300975	+	0.0287397i	−0.0565241	+	0.998401i	$0.518002\pi$
$678$	27.7198	−	11.2800i	1.06457	−	0.433207i
$679$	0.935533	−	3.85632i	0.0359025	−	0.147992i
$680$	−15.3825	+	10.9538i	−0.589893	+	0.420061i
$681$	34.4927	+	35.7668i	1.32176	+	1.37059i
$682$	11.7605	+	4.07035i	0.450332	+	0.155862i
$683$	−10.8187	+	4.94073i	−0.413966	+	0.189052i	−0.611501	−	0.791244i	$-0.709434\pi$
$683$	−10.8187	+	4.94073i	−0.413966	+	0.189052i	0.197535	+	0.980296i	$0.436707\pi$
$684$	−0.267921	+	0.0682217i	−0.0102442	+	0.00260852i
$685$	−6.74957	+	46.9443i	−0.257888	+	1.79365i
$686$	0.958356	−	20.1184i	0.0365902	−	0.768123i
$687$	−3.95954	−	8.54172i	−0.151066	−	0.325887i
$688$	5.08736	+	5.33547i	0.193954	+	0.203413i
$689$	−14.9636	+	25.9177i	−0.570068	+	0.987387i
$690$	5.76427	−	24.3507i	0.219442	−	0.927015i
$691$	−2.84110	−	4.92094i	−0.108081	−	0.187201i	0.806912	−	0.590672i	$-0.201137\pi$
$691$	−2.84110	−	4.92094i	−0.108081	−	0.187201i	−0.914993	+	0.403470i	$0.867804\pi$
$692$	0.279321	−	0.951279i	0.0106182	−	0.0361622i
$693$	−22.3437	+	13.2401i	−0.848766	+	0.502949i
$694$	−19.1272	−	12.2923i	−0.726057	−	0.466609i
$695$	16.9231	−	6.77500i	0.641931	−	0.256991i
$696$	−2.50677	+	6.36596i	−0.0950190	+	0.241301i
$697$	0.146810	−	1.53747i	0.00556084	−	0.0582357i
$698$	6.35973	+	32.9974i	0.240719	+	1.24897i
$699$	−4.01876	−	16.1651i	−0.152003	−	0.611419i
$700$	−0.858826	−	8.99403i	−0.0324606	−	0.339942i
$701$	1.01539	−	0.298146i	0.0383508	−	0.0112608i	−0.262501	−	0.964932i	$-0.584547\pi$
$701$	1.01539	−	0.298146i	0.0383508	−	0.0112608i	0.300852	+	0.953671i	$0.402729\pi$
$702$	−14.8732	+	9.91979i	−0.561354	+	0.374398i
$703$	−0.265227	+	0.580767i	−0.0100032	+	0.0219040i
$704$	−3.06937	+	2.41378i	−0.115681	+	0.0909728i
$705$	−14.6752	−	13.8349i	−0.552702	−	0.521051i
$706$	31.1581	+	2.97523i	1.17265	+	0.111974i
$707$	−1.78420	−	37.4550i	−0.0671019	−	1.40864i
$708$	8.50348	−	4.44503i	0.319580	−	0.167055i
$709$	−2.62222	−	0.124912i	−0.0984795	−	0.00469116i	−0.00171567	−	0.999999i	$-0.500546\pi$
$709$	−2.62222	−	0.124912i	−0.0984795	−	0.00469116i	−0.0967638	+	0.995307i	$0.530849\pi$
$710$	−27.2665	+	31.4672i	−1.02329	+	1.18094i
$711$	−14.3859	+	6.76793i	−0.539512	+	0.253817i
$712$			10.1940i			0.382038i
$713$	−12.8575	−	8.26498i	−0.481517	−	0.309526i
$714$	−21.9531	−	9.87567i	−0.821576	−	0.369588i
$715$	29.2911	−	27.9290i	1.09542	−	1.04448i
$716$	20.9681	−	7.25713i	0.783614	−	0.271212i
$717$	28.0983	−	18.2835i	1.04935	−	0.682812i
$718$	8.23000	+	20.5576i	0.307141	+	0.767201i
$719$	−3.11764	−	4.85115i	−0.116268	−	0.180917i	0.778242	−	0.627965i	$-0.216112\pi$
$719$	−3.11764	−	4.85115i	−0.116268	−	0.180917i	−0.894510	+	0.447048i	$0.852475\pi$
$720$	−5.32537	−	7.30182i	−0.198465	−	0.272123i
$721$	−15.0754	−	17.3979i	−0.561437	−	0.647933i
$722$	−11.7398	−	14.9283i	−0.436909	−	0.555575i
$723$	0.120287	−	0.0238913i	0.00447353	−	0.000888528i
$724$	−19.8229	−	4.80898i	−0.736711	−	0.178724i
$725$	15.6433	+	3.79502i	0.580977	+	0.140944i
$726$	2.36670	−	6.96561i	0.0878364	−	0.258518i
$727$	−24.2861	−	30.8823i	−0.900723	−	1.14536i	−0.988800	−	0.149249i	$-0.952314\pi$
$727$	−24.2861	−	30.8823i	−0.900723	−	1.14536i	0.0880765	−	0.996114i	$-0.471928\pi$
$728$	−4.99535	−	5.76494i	−0.185140	−	0.213663i
$729$	−23.1970	−	13.8166i	−0.859149	−	0.511725i
$730$	−4.79179	−	7.45618i	−0.177352	−	0.275965i
$731$	−17.1756	−	42.9026i	−0.635263	−	1.58681i
$732$	−5.49521	−	2.79367i	−0.203109	−	0.103257i
$733$	−23.7526	+	8.22084i	−0.877321	+	0.303644i	−0.728356	−	0.685199i	$-0.759715\pi$
$733$	−23.7526	+	8.22084i	−0.877321	+	0.303644i	−0.148965	+	0.988842i	$0.547594\pi$
$734$	−0.176130	+	0.167939i	−0.00650106	+	0.00619875i
$735$	−8.82373	+	6.35903i	−0.325468	+	0.234556i
$736$	4.36266	−	1.99179i	0.160810	−	0.0734182i
$737$			42.1650i			1.55317i
$738$	0.736545	+	0.0619148i	0.0271126	+	0.00227911i
$739$	3.08470	−	3.55994i	0.113473	−	0.130954i	−0.696172	−	0.717875i	$-0.745115\pi$
$739$	3.08470	−	3.55994i	0.113473	−	0.130954i	0.809644	+	0.586921i	$0.199660\pi$
$740$	−20.8470	−	0.993065i	−0.766351	−	0.0365058i
$741$	0.463680	+	0.294289i	0.0170337	+	0.0108110i
$742$	−0.917616	−	19.2631i	−0.0336868	−	0.707172i
$743$	−16.6934	−	1.59403i	−0.612422	−	0.0584792i	−0.215764	−	0.976446i	$-0.569224\pi$
$743$	−16.6934	−	1.59403i	−0.612422	−	0.0584792i	−0.396658	+	0.917966i	$0.629830\pi$
$744$	−5.28771	+	1.58522i	−0.193857	+	0.0581170i
$745$	41.4328	−	32.5831i	1.51798	−	1.19375i
$746$	−3.45635	+	7.56834i	−0.126546	+	0.277097i
$747$	18.5910	+	11.6521i	0.680210	+	0.426327i
$748$	23.4860	−	6.89612i	0.858734	−	0.252147i
$749$	−1.64790	−	17.2576i	−0.0602130	−	0.630579i
$750$	3.47368	−	3.34994i	0.126841	−	0.122323i
$751$	4.53892	+	23.5501i	0.165627	+	0.859357i	0.965741	+	0.259508i	$0.0835605\pi$
$751$	4.53892	+	23.5501i	0.165627	+	0.859357i	−0.800113	+	0.599849i	$0.795227\pi$
$752$	0.367422	−	3.84782i	0.0133985	−	0.140316i
$753$	3.22033	+	4.04755i	0.117355	+	0.147501i
$754$	12.6170	−	5.05110i	0.459486	−	0.183950i
$755$	−11.6197	−	7.46752i	−0.422884	−	0.271771i
$756$	4.60687	−	10.5592i	0.167550	−	0.384033i
$757$	10.8541	−	36.9655i	0.394497	−	1.34353i	−0.487847	−	0.872929i	$-0.662217\pi$
$757$	10.8541	−	36.9655i	0.394497	−	1.34353i	0.882344	−	0.470605i	$-0.155964\pi$
$758$	−1.19227	−	2.06507i	−0.0433051	−	0.0750067i
$759$	−17.3841	+	27.3837i	−0.631001	+	0.993964i
$760$	−0.138811	+	0.240427i	−0.00503519	+	0.00872121i
$761$	−31.8878	−	33.4430i	−1.15593	−	1.21231i	−0.973401	−	0.229106i	$-0.926420\pi$
$761$	−31.8878	−	33.4430i	−1.15593	−	1.21231i	−0.182531	−	0.983200i	$-0.558429\pi$
$762$	35.5807	+	3.19414i	1.28895	+	0.115712i
$763$	−1.37627	+	28.8914i	−0.0498241	+	1.04594i
$764$	3.24086	−	22.5407i	0.117250	−	0.815494i
$765$	13.9795	+	54.9004i	0.505430	+	1.98493i
$766$	10.9738	−	5.01157i	0.396500	−	0.181076i
$767$	−18.0118	−	6.23394i	−0.650368	−	0.225094i
$768$	0.478548	−	1.66463i	0.0172681	−	0.0600671i
$769$	21.1873	−	15.0874i	0.764032	−	0.544065i	−0.130297	−	0.991475i	$-0.541593\pi$
$769$	21.1873	−	15.0874i	0.764032	−	0.544065i	0.894329	+	0.447410i	$0.147654\pi$
$770$	−6.14861	+	25.3449i	−0.221581	+	0.913368i
$771$	3.06387	−	22.2023i	0.110343	−	0.799597i
$772$	−16.3727	+	1.56340i	−0.589265	+	0.0562680i
$773$	−4.77273	−	33.1951i	−0.171663	−	1.19394i	−0.875370	−	0.483453i	$-0.839382\pi$
$773$	−4.77273	−	33.1951i	−0.171663	−	1.19394i	0.703707	−	0.710490i	$-0.251527\pi$
$774$	20.4377	−	8.45206i	0.734617	−	0.303803i
$775$	5.39533	+	11.8141i	0.193806	+	0.424376i
$776$	−1.59084	−	0.820137i	−0.0571080	−	0.0294412i
$777$	−12.3247	−	23.5775i	−0.442147	−	0.845840i
$778$	−9.33578	−	18.1089i	−0.334704	−	0.649235i
$779$	−0.00742629	−	0.0214568i	−0.000266074	−	0.000768771i
$780$	−3.29752	+	17.6468i	−0.118070	+	0.631857i
$781$	46.7394	−	26.9850i	1.67247	−	0.965598i
$782$	−30.0292	+	1.42720i	−1.07384	+	0.0510365i
$783$	15.0935	+	13.9094i	0.539397	+	0.497081i
$784$	−2.00004	−	0.587265i	−0.0714300	−	0.0209737i
$785$	−12.7995	+	66.4102i	−0.456835	+	2.37028i
$786$	−13.1407	+	25.8481i	−0.468714	+	0.921972i
$787$	−24.8985	+	31.6610i	−0.887535	+	1.12859i	0.103451	+	0.994635i	$0.467011\pi$
$787$	−24.8985	+	31.6610i	−0.887535	+	1.12859i	−0.990987	+	0.133959i	$0.957231\pi$
$788$	−7.33185	+	0.349259i	−0.261186	+	0.0124418i
$789$	14.9068	+	8.49418i	0.530698	+	0.302401i
$790$	−5.22150	+	15.0865i	−0.185773	+	0.536755i
$791$	37.9179	−	5.45177i	1.34820	−	0.193843i
$792$	3.42752	+	11.2017i	0.121792	+	0.398036i
$793$	3.44994	+	11.7494i	0.122511	+	0.417234i
$794$	−16.6747	+	17.4879i	−0.591762	+	0.620622i
$795$	−34.1314	+	29.9154i	−1.21052	+	1.06099i
$796$	5.05498	−	12.6267i	0.179169	−	0.447542i
$797$	32.9712	−	6.35468i	1.16790	−	0.225094i	0.431802	−	0.901969i	$-0.357878\pi$
$797$	32.9712	−	6.35468i	1.16790	−	0.225094i	0.736099	+	0.676874i	$0.236666\pi$
$798$	−0.353887	+	0.00200584i	−0.0125275	+	7.10058e-5i
$799$	−11.1029	+	21.5366i	−0.392792	+	0.761910i
$800$	−4.03364	−	0.579950i	−0.142611	−	0.0205043i
$801$	28.5185	+	11.0437i	1.00765	+	0.390208i
$802$	−17.9340	−	15.5399i	−0.633273	−	0.548734i
$803$	2.70850	+	11.1646i	0.0955809	+	0.393990i
$804$	−10.9351	−	15.1734i	−0.385651	−	0.535125i
$805$	14.6807	−	28.4690i	0.517427	−	1.00340i
$806$	9.49638	+	5.48274i	0.334496	+	0.193121i
$807$	27.3011	+	5.10153i	0.961043	+	0.179582i
$808$	−16.6072	−	3.20078i	−0.584241	−	0.112603i
$809$	21.7964	−	33.9159i	0.766322	−	1.19242i	−0.210338	−	0.977629i	$-0.567456\pi$
$809$	21.7964	−	33.9159i	0.766322	−	1.19242i	0.976660	−	0.214792i	$-0.0689072\pi$
$810$	−26.1965	+	6.98767i	−0.920452	+	0.245522i
$811$	−40.3391	+	25.9244i	−1.41650	+	0.910327i	−0.416498	+	0.909137i	$0.636743\pi$
$811$	−40.3391	+	25.9244i	−1.41650	+	0.910327i	−0.999999	+	0.00119072i	$0.999621\pi$
$812$	−5.07997	+	7.13382i	−0.178272	+	0.250348i
$813$	22.2425	−	23.5936i	0.780080	−	0.827464i
$814$	25.1147	+	10.0544i	0.880269	+	0.352406i
$815$	−24.8887	−	34.9513i	−0.871813	−	1.22429i
$816$	−6.66319	+	8.57249i	−0.233258	+	0.300097i
$817$	−0.491699	−	0.468834i	−0.0172024	−	0.0164024i
$818$	−9.99100	−	4.56274i	−0.349327	−	0.159532i
$819$	−21.5395	+	7.72939i	−0.752650	+	0.270087i
$820$	0.560933	−	0.486051i	0.0195886	−	0.0169737i
$821$	−15.1796	−	10.8093i	−0.529770	−	0.377248i	0.283647	−	0.958929i	$-0.408456\pi$
$821$	−15.1796	−	10.8093i	−0.529770	−	0.377248i	−0.813417	+	0.581681i	$0.802395\pi$
$822$	4.03362	+	26.9685i	0.140689	+	0.940633i
$823$	15.3643	+	12.0826i	0.535567	+	0.421174i	0.848966	−	0.528447i	$-0.177225\pi$
$823$	15.3643	+	12.0826i	0.535567	+	0.421174i	−0.313399	+	0.949621i	$0.601468\pi$
$824$	−9.22904	+	4.75790i	−0.321509	+	0.165749i
$825$	25.0053	−	11.5913i	0.870573	−	0.403556i
$826$	11.9360	−	2.89565i	0.415307	−	0.100752i
$827$	50.6285			1.76052			0.880262	−	0.474487i	$-0.157367\pi$
$827$	50.6285			1.76052			0.880262	+	0.474487i	$0.157367\pi$
$828$	−0.845888	−	14.3626i	−0.0293966	−	0.499135i
$829$	44.2589			1.53717			0.768587	−	0.639745i	$-0.220960\pi$
$829$	44.2589			1.53717			0.768587	+	0.639745i	$0.220960\pi$
$830$	21.4111	−	5.19427i	0.743190	−	0.180296i
$831$	−2.05019	+	22.8378i	−0.0711202	+	0.792233i
$832$	−3.05811	+	1.57657i	−0.106021	+	0.0546576i
$833$	10.2711	+	8.07731i	0.355874	+	0.279862i
$834$	8.20163	−	6.52541i	0.283999	−	0.225956i
$835$	24.1307	+	17.1834i	0.835076	+	0.594655i
$836$	0.271958	−	0.235653i	0.00940587	−	0.00815024i
$837$	−1.29366	+	16.5100i	−0.0447153	+	0.570671i
$838$	−20.9527	−	9.56876i	−0.723797	−	0.330547i
$839$	23.7005	+	22.5984i	0.818232	+	0.780183i	0.978359	−	0.206914i	$-0.0663420\pi$
$839$	23.7005	+	22.5984i	0.818232	+	0.780183i	−0.160127	+	0.987096i	$0.551190\pi$
$840$	−4.36033	−	10.7152i	−0.150446	−	0.369708i
$841$	7.77096	+	10.9128i	0.267964	+	0.376303i
$842$	−2.54240	−	1.01783i	−0.0876170	−	0.0350766i
$843$	24.0488	+	5.69003i	0.828283	+	0.195975i
$844$	−12.1423	+	17.0514i	−0.417954	+	0.586935i
$845$	−2.94581	+	1.89316i	−0.101339	+	0.0651265i
$846$	−10.3665	−	5.19640i	−0.356407	−	0.178656i
$847$	5.09115	−	7.92199i	0.174934	−	0.272203i
$848$	−8.54111	−	1.64616i	−0.293303	−	0.0565295i
$849$	5.25888	−	6.13904i	0.180484	−	0.210691i
$850$	22.1228	+	12.7726i	0.758807	+	0.438098i
$851$	−27.0627	−	19.2757i	−0.927698	−	0.660763i
$852$	−9.82124	+	21.8321i	−0.336470	+	0.747957i
$853$	−4.93264	−	20.3326i	−0.168890	−	0.696175i	−0.991778	−	0.127971i	$-0.959154\pi$
$853$	−4.93264	−	20.3326i	−0.168890	−	0.696175i	0.822888	−	0.568204i	$-0.192362\pi$
$854$	−5.96355	−	5.16745i	−0.204069	−	0.176826i
$855$	0.522230	+	0.648797i	0.0178599	+	0.0221884i
$856$	−7.73969	−	1.11280i	−0.264537	−	0.0380347i
$857$	−21.0270	+	40.7867i	−0.718269	+	1.39325i	0.192902	+	0.981218i	$0.438210\pi$
$857$	−21.0270	+	40.7867i	−0.718269	+	1.39325i	−0.911171	+	0.412029i	$0.864820\pi$
$858$	11.5204	−	20.2178i	0.393301	−	0.690223i
$859$	24.3552	−	4.69408i	0.830989	−	0.160160i	0.244021	−	0.969770i	$-0.421534\pi$
$859$	24.3552	−	4.69408i	0.830989	−	0.160160i	0.586968	+	0.809610i	$0.300321\pi$
$860$	8.25408	−	20.6177i	0.281462	−	0.703058i
$861$	0.895837	+	0.304377i	0.0305300	+	0.0103732i
$862$	22.1228	−	23.2017i	0.753506	−	0.790254i
$863$	11.6433	+	39.6534i	0.396343	+	1.34982i	0.880171	+	0.474656i	$0.157428\pi$
$863$	11.6433	+	39.6534i	0.396343	+	1.34982i	−0.483829	+	0.875163i	$0.660754\pi$
$864$	−4.13848	−	3.14214i	−0.140794	−	0.106898i
$865$	−2.95630	+	0.425052i	−0.100517	+	0.0144522i
$866$	3.40651	−	9.84247i	0.115758	−	0.334461i
$867$	33.3328	−	19.4975i	1.13204	−	0.662168i
$868$	−7.05811	+	0.336219i	−0.239568	+	0.0114120i
$869$	12.7917	−	16.2660i	0.433930	−	0.551787i
$870$	20.5814	−	1.09737i	0.697776	−	0.0372042i
$871$	−7.03114	+	36.4810i	−0.238241	+	1.23611i
$872$	12.5175	+	3.67547i	0.423896	+	0.124467i
$873$	−4.01782	+	3.56200i	−0.135983	+	0.120555i
$874$	−0.392859	+	0.202479i	−0.0132886	+	0.00684894i
$875$	5.34967	−	3.08863i	0.180852	−	0.104415i
$876$	−3.87010	−	3.31524i	−0.130759	−	0.112012i
$877$	−1.11170	−	3.21205i	−0.0375394	−	0.108463i	0.924674	−	0.380760i	$-0.124338\pi$
$877$	−1.11170	−	3.21205i	−0.0375394	−	0.108463i	−0.962213	+	0.272297i	$0.912217\pi$
$878$	9.46479	+	18.3591i	0.319421	+	0.619591i
$879$	19.5412	−	30.7890i	0.659108	−	1.03849i
$880$	10.4555	+	5.39019i	0.352455	+	0.181703i
$881$	13.7488	+	30.1056i	0.463208	+	1.01428i	0.986745	+	0.162281i	$0.0518852\pi$
$881$	13.7488	+	30.1056i	0.463208	+	1.01428i	−0.523536	+	0.852003i	$0.675388\pi$
$882$	−3.80964	+	4.95903i	−0.128277	+	0.166979i
$883$	7.47583	+	51.9956i	0.251582	+	1.74979i	0.588722	+	0.808336i	$0.299631\pi$
$883$	7.47583	+	51.9956i	0.251582	+	1.74979i	−0.337140	+	0.941455i	$0.609460\pi$
$884$	21.4699	−	2.05013i	0.722112	−	0.0689534i
$885$	−22.8221	−	17.7391i	−0.767157	−	0.596293i
$886$	6.71075	−	27.6621i	0.225452	−	0.929326i
$887$	−3.63315	+	2.58715i	−0.121989	+	0.0868680i	−0.639423	−	0.768855i	$-0.720827\pi$
$887$	−3.63315	+	2.58715i	−0.121989	+	0.0868680i	0.517434	+	0.855723i	$0.326887\pi$
$888$	−11.6452	+	2.89509i	−0.390788	+	0.0971527i
$889$	43.2129	+	14.9561i	1.44931	+	0.501612i
$890$	27.9343	−	12.7572i	0.936360	−	0.427622i
$891$	35.0507	+	2.54663i	1.17424	+	0.0853152i
$892$	−1.07403	+	7.47007i	−0.0359613	+	0.250116i
$893$	−0.0169494	+	0.355812i	−0.000567190	+	0.0119068i
$894$	17.4389	−	24.7857i	0.583245	−	0.828957i
$895$	−46.1266	−	48.3762i	−1.54184	−	1.61704i
$896$	1.10855	−	1.92006i	0.0370340	−	0.0641448i
$897$	−19.6069	+	20.7934i	−0.654656	+	0.694271i
$898$	18.2130	+	31.5458i	0.607775	+	1.05270i
$899$	3.54681	−	12.0793i	0.118293	−	0.402868i
$900$	−5.99227	+	10.6561i	−0.199742	+	0.355203i
$901$	45.8702	+	29.4790i	1.52816	+	0.982088i
$902$	−0.893151	+	0.357564i	−0.0297387	+	0.0119056i
$903$	27.9985	−	4.18769i	0.931732	−	0.139358i
$904$	1.64241	−	17.2001i	0.0546258	−	0.572067i
$905$	11.6292	+	60.3380i	0.386567	+	2.00570i
$906$	−7.63236	−	2.19415i	−0.253568	−	0.0728958i
$907$	−3.49032	−	36.5523i	−0.115894	−	1.21370i	−0.847060	−	0.531498i	$-0.821629\pi$
$907$	−3.49032	−	36.5523i	−0.115894	−	1.21370i	0.731166	−	0.682200i	$-0.238977\pi$
$908$	27.5260	−	8.08235i	0.913481	−	0.268222i
$909$	−26.9458	+	42.9923i	−0.893734	+	1.42596i
$910$	−9.54609	+	20.9030i	−0.316450	+	0.692928i
$911$	−37.7331	+	29.6736i	−1.25015	+	0.983131i	−0.250265	+	0.968177i	$0.580518\pi$
$911$	−37.7331	+	29.6736i	−1.25015	+	0.983131i	−0.999888	+	0.0149541i	$0.995240\pi$
$912$	−0.0367520	+	0.155331i	−0.00121698	+	0.00514353i
$913$	−28.4287	−	2.71461i	−0.940853	−	0.0898406i
$914$	−0.0325475	−	0.683257i	−0.00107658	−	0.0226001i
$915$	−0.778479	+	18.5544i	−0.0257357	+	0.613390i
$916$	−5.42950	−	0.258639i	−0.179396	−	0.00854566i
$917$	−24.3064	+	28.0511i	−0.802668	+	0.926328i
$918$	16.7636	+	27.9277i	0.553280	+	0.921750i
$919$		−	11.3946i		−	0.375873i	−0.982181	−	0.187936i	$-0.939820\pi$
$919$		−	11.3946i		−	0.375873i	0.982181	−	0.187936i	$-0.0601799\pi$
$920$	−10.9176	−	9.46223i	−0.359943	−	0.311960i
$921$	−2.74873	−	27.1583i	−0.0905737	−	0.894898i
$922$	1.09197	−	1.04119i	0.0359621	−	0.0342898i
$923$	44.9385	−	15.5534i	1.47917	−	0.511945i
$924$	0.798368	+	14.9736i	0.0262644	+	0.492596i
$925$	10.4930	+	26.2102i	0.345007	+	0.861786i
$926$	−6.67535	−	10.3870i	−0.219365	−	0.341339i
$927$	3.31230	+	30.9733i	0.108790	+	1.01730i
$928$	2.58675	+	2.98527i	0.0849142	+	0.0979963i
$929$	23.2904	+	29.6162i	0.764134	+	0.971675i	1.00000		0.000110142i	$-3.50593e-5\pi$
$929$	23.2904	+	29.6162i	0.764134	+	0.971675i	−0.235866	+	0.971786i	$0.575793\pi$
$930$	10.9611	+	12.5059i	0.359430	+	0.410085i
$931$	0.186683	+	0.0452889i	0.00611830	+	0.00148428i
$932$	−9.34591	−	2.26729i	−0.306136	−	0.0742677i
$933$	−25.6278	−	29.2396i	−0.839018	−	0.957261i
$934$	−7.88352	−	10.0247i	−0.257957	−	0.328019i
$935$	−48.2884	−	55.7278i	−1.57920	−	1.82249i
$936$	1.09756	+	10.2632i	0.0358747	+	0.335464i
$937$	−0.327598	−	0.509753i	−0.0107022	−	0.0166529i	0.835861	−	0.548941i	$-0.184969\pi$
$937$	−0.327598	−	0.509753i	−0.0107022	−	0.0166529i	−0.846563	+	0.532288i	$0.821332\pi$
$938$	−8.89792	−	22.2259i	−0.290527	−	0.725702i
$939$	−0.643015	−	12.0599i	−0.0209840	−	0.393561i
$940$	−11.0038	+	3.80847i	−0.358906	+	0.124218i
$941$	8.14009	−	7.76156i	0.265359	−	0.253020i	−0.545704	−	0.837978i	$-0.683738\pi$
$941$	8.14009	−	7.76156i	0.265359	−	0.253020i	0.811063	+	0.584958i	$0.198889\pi$
$942$	3.91566	+	38.6880i	0.127579	+	1.26052i
$943$	1.16959	−	0.168032i	0.0380872	−	0.00547189i
$944$		−	5.53978i		−	0.180304i
$945$	−34.7001	+	0.590091i	−1.12879	+	0.0191957i
$946$	−18.8513	+	21.7555i	−0.612907	+	0.707333i
$947$	7.72711	+	0.368087i	0.251097	+	0.0119612i	0.172753	−	0.984965i	$-0.444734\pi$
$947$	7.72711	+	0.368087i	0.251097	+	0.0119612i	0.0783440	+	0.996926i	$0.475037\pi$
$948$	−0.384778	+	9.17086i	−0.0124970	+	0.297856i
$949$	0.481656	+	10.1112i	0.0156352	+	0.328224i
$950$	0.373849	+	0.0356982i	0.0121293	+	0.00115820i
$951$	12.3197	−	52.0691i	0.399495	−	1.68845i
$952$	−10.9246	+	8.59122i	−0.354069	+	0.278443i
$953$	7.19766	−	15.7607i	0.233155	−	0.510539i	−0.756502	−	0.653991i	$-0.773093\pi$
$953$	7.19766	−	15.7607i	0.233155	−	0.510539i	0.989657	+	0.143453i	$0.0458205\pi$
$954$	−13.8582	+	22.1109i	−0.448676	+	0.715868i
$955$	−65.8231	+	19.3274i	−2.12999	+	0.625420i
$956$	−1.83977	−	19.2670i	−0.0595025	−	0.623138i
$957$	−25.6756	−	7.38123i	−0.829975	−	0.238601i
$958$	−1.39344	−	7.22983i	−0.0450199	−	0.233585i
$959$	−3.31791	+	34.7467i	−0.107141	+	1.12203i
$960$	−5.16039	+	0.771830i	−0.166551	+	0.0249107i
$961$	−19.3494	+	7.74634i	−0.624175	+	0.249882i
$962$	20.0525	+	12.8870i	0.646519	+	0.415492i
$963$	−11.4979	+	20.4467i	−0.370514	+	0.658887i
$964$	0.0199479	−	0.0679363i	0.000642479	−	0.00218808i
$965$	24.7734	+	42.9089i	0.797485	+	1.38129i
$966$	3.38478	−	18.1029i	0.108903	−	0.582451i
$967$	4.46693	−	7.73695i	0.143647	−	0.248804i	−0.785220	−	0.619216i	$-0.787450\pi$
$967$	4.46693	−	7.73695i	0.143647	−	0.248804i	0.928867	+	0.370413i	$0.120784\pi$
$968$	−2.93104	−	3.07398i	−0.0942071	−	0.0988015i
$969$	0.575771	−	0.818335i	0.0184964	−	0.0262887i
$970$	−0.256551	+	5.38568i	−0.00823737	+	0.172924i
$971$	4.12285	−	28.6750i	0.132308	−	0.920225i	−0.810226	−	0.586117i	$-0.800656\pi$
$971$	4.12285	−	28.6750i	0.132308	−	0.920225i	0.942535	−	0.334108i	$-0.108435\pi$
$972$	−13.2737	+	8.17363i	−0.425755	+	0.262169i
$973$	12.2035	−	5.57316i	0.391227	−	0.178667i
$974$	2.43952	+	0.844326i	0.0781673	+	0.0270540i
$975$	23.5673	−	5.85901i	0.754759	−	0.187639i
$976$	−2.89917	+	2.06449i	−0.0928002	+	0.0660827i
$977$	2.63535	−	10.8631i	0.0843125	−	0.347541i	−0.913993	−	0.405730i	$-0.867017\pi$
$977$	2.63535	−	10.8631i	0.0843125	−	0.347541i	0.998306	+	0.0581890i	$0.0185326\pi$
$978$	−19.4779	−	15.1397i	−0.622835	−	0.484115i
$979$	−39.6253	+	3.78376i	−1.26643	+	0.120930i
$980$	0.893662	+	6.21556i	0.0285470	+	0.198549i
$981$	23.8431	−	31.0367i	0.761252	−	0.990925i
$982$	0.0935845	+	0.204922i	0.00298640	+	0.00653931i
$983$	−26.9474	−	13.8923i	−0.859488	−	0.443097i	−0.0286359	−	0.999590i	$-0.509116\pi$
$983$	−26.9474	−	13.8923i	−0.859488	−	0.443097i	−0.830852	+	0.556493i	$0.812147\pi$
$984$	0.228677	−	0.360302i	0.00728995	−	0.0114860i
$985$	10.1324	+	19.6541i	0.322845	+	0.626232i
$986$	−8.09866	−	23.3996i	−0.257914	−	0.745194i
$987$	−11.2728	−	9.65658i	−0.358816	−	0.307372i
$988$	0.274593	−	0.158536i	0.00873596	−	0.00504371i
$989$	28.8020	−	20.5051i	0.915851	−	0.652024i
$990$	26.4063	−	23.4105i	0.839248	−	0.744036i
$991$	12.5600	+	3.68795i	0.398982	+	0.117152i	0.475067	−	0.879950i	$-0.342424\pi$
$991$	12.5600	+	3.68795i	0.398982	+	0.117152i	−0.0760852	+	0.997101i	$0.524242\pi$
$992$	−0.603162	+	3.12950i	−0.0191504	+	0.0993618i
$993$	−25.9303	+	1.38256i	−0.822873	+	0.0438741i
$994$	−18.9426	+	24.0875i	−0.600823	+	0.764008i
$995$	−40.9265	+	1.94957i	−1.29746	+	0.0618055i
$996$	10.9343	−	6.39583i	0.346467	−	0.202660i
$997$	−2.73469	+	7.90136i	−0.0866084	+	0.250239i	−0.979985	−	0.199069i	$-0.936208\pi$
$997$	−2.73469	+	7.90136i	−0.0866084	+	0.250239i	0.893377	+	0.449308i	$0.148329\pi$
$998$	−18.2594	+	2.62530i	−0.577990	+	0.0831025i
$999$	−4.51660	+	35.7146i	−0.142899	+	1.12996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.p.a.5.10	✓	480
9.2	odd	6	inner	414.2.p.a.281.3	yes	480
23.14	odd	22	inner	414.2.p.a.221.3	yes	480
207.83	even	66	inner	414.2.p.a.83.10	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.p.a.5.10	✓	480	1.1	even	1	trivial
414.2.p.a.83.10	yes	480	207.83	even	66	inner
414.2.p.a.221.3	yes	480	23.14	odd	22	inner
414.2.p.a.281.3	yes	480	9.2	odd	6	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.p (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.971812 + 0.235759i) q^{2} +(1.41656 + 0.996675i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.36798 - 1.86220i) q^{5} +(-1.61160 - 0.634614i) q^{6} +(-1.80599 - 1.28604i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.01328 + 2.82370i) q^{9} +O(q^{10})\)	\(q+(-0.971812 + 0.235759i) q^{2} +(1.41656 + 0.996675i) q^{3} +(0.888835 - 0.458227i) q^{4} +(-2.36798 - 1.86220i) q^{5} +(-1.61160 - 0.634614i) q^{6} +(-1.80599 - 1.28604i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.01328 + 2.82370i) q^{9} +(2.74026 + 1.25144i) q^{10} +(-2.82603 - 2.69461i) q^{11} +(1.71579 + 0.236775i) q^{12} +(-1.99573 - 2.80262i) q^{13} +(2.05828 + 0.824012i) q^{14} +(-1.49837 - 4.99802i) q^{15} +(0.580057 - 0.814576i) q^{16} +(-5.27347 + 3.38906i) q^{17} +(-1.65043 - 2.50521i) q^{18} +(-0.0498236 + 0.0775271i) q^{19} +(-2.95805 - 0.570118i) q^{20} +(-1.27653 - 3.62175i) q^{21} +(3.38165 + 1.95240i) q^{22} +(-3.47055 - 3.30988i) q^{23} +(-1.72325 + 0.174412i) q^{24} +(0.960746 + 3.96025i) q^{25} +(2.60022 + 2.25310i) q^{26} +(-1.37894 + 5.00984i) q^{27} +(-2.19453 - 0.315526i) q^{28} +(1.81003 - 3.51097i) q^{29} +(2.63447 + 4.50388i) q^{30} +(3.12950 - 0.603162i) q^{31} +(-0.371662 + 0.928368i) q^{32} +(-1.31758 - 6.63371i) q^{33} +(4.32582 - 4.53679i) q^{34} +(1.88169 + 6.40845i) q^{35} +(2.19453 + 2.04549i) q^{36} +(6.85751 - 0.985961i) q^{37} +(0.0301415 - 0.0870881i) q^{38} +(-0.0337766 - 5.95917i) q^{39} +(3.00908 - 0.143340i) q^{40} +(-0.152303 + 0.193668i) q^{41} +(2.09441 + 3.21870i) q^{42} +(-1.39519 + 7.23892i) q^{43} +(-3.74662 - 1.10011i) q^{44} +(2.85887 - 8.57339i) q^{45} +(4.15305 + 2.39837i) q^{46} +(3.34747 - 1.93266i) q^{47} +(1.63355 - 0.575766i) q^{48} +(-0.681765 - 1.96983i) q^{49} +(-1.86733 - 3.62211i) q^{50} +(-10.8480 - 0.455143i) q^{51} +(-3.05811 - 1.57657i) q^{52} +(-3.61340 - 7.91225i) q^{53} +(0.158957 - 5.19372i) q^{54} +(1.67407 + 11.6434i) q^{55} +(2.20706 - 0.210749i) q^{56} +(-0.147847 + 0.0601637i) q^{57} +(-0.931266 + 3.83873i) q^{58} +(4.51257 - 3.21339i) q^{59} +(-3.62204 - 3.75583i) q^{60} +(-3.36337 - 1.16407i) q^{61} +(-2.89909 + 1.32397i) q^{62} +(1.80142 - 6.40270i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.493174 + 10.3530i) q^{65} +(2.84440 + 6.13609i) q^{66} +(-7.45167 - 7.81509i) q^{67} +(-3.13429 + 5.42876i) q^{68} +(-1.61736 - 8.14765i) q^{69} +(-3.33950 - 5.78418i) q^{70} +(-3.89396 + 13.2616i) q^{71} +(-2.61491 - 1.47045i) q^{72} +(-2.47508 - 1.59064i) q^{73} +(-6.43176 + 2.57489i) q^{74} +(-2.58613 + 6.56748i) q^{75} +(-0.00876005 + 0.0917393i) q^{76} +(1.63841 + 8.50086i) q^{77} +(1.43775 + 5.78323i) q^{78} +(0.503745 + 5.27546i) q^{79} +(-2.89047 + 0.848718i) q^{80} +(-6.94654 + 5.72238i) q^{81} +(0.102350 - 0.224116i) q^{82} +(5.74887 - 4.52096i) q^{83} +(-2.79421 - 2.63420i) q^{84} +(18.7986 + 1.79505i) q^{85} +(-0.350781 - 7.36379i) q^{86} +(6.06331 - 3.16948i) q^{87} +(3.90037 + 0.185797i) q^{88} +(6.67567 - 7.70414i) q^{89} +(-0.757030 + 9.00572i) q^{90} +7.62811i q^{91} +(-4.60142 - 1.35164i) q^{92} +(5.03428 + 2.26468i) q^{93} +(-2.79747 + 2.66738i) q^{94} +(0.262352 - 0.0908010i) q^{95} +(-1.45176 + 0.944661i) q^{96} +(0.665204 + 1.66160i) q^{97} +(1.12695 + 1.75357i) q^{98} +(4.74522 - 10.7102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6}+O(q^{10}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6	\( 480 q - 4 q^{3} - 24 q^{4} + 8 q^{6} + 4 q^{12} - 44 q^{15} + 24 q^{16} + 28 q^{18} + 66 q^{21} + 6 q^{23} + 4 q^{24} + 12 q^{25} + 86 q^{27} - 48 q^{29} + 44 q^{30} - 12 q^{31} - 44 q^{33} + 24 q^{39} - 60 q^{41} + 12 q^{46} + 48 q^{47} + 8 q^{48} - 78 q^{49} + 24 q^{50} - 30 q^{54} - 24 q^{55} - 66 q^{56} - 66 q^{57} - 72 q^{59} - 22 q^{60} - 110 q^{63} + 48 q^{64} - 462 q^{65} - 88 q^{66} - 70 q^{69} + 12 q^{70} - 52 q^{72} - 264 q^{74} - 76 q^{75} - 12 q^{77} - 58 q^{78} - 96 q^{81} - 198 q^{83} - 22 q^{84} + 178 q^{87} + 6 q^{92} - 20 q^{93} - 12 q^{94} + 12 q^{95} - 4 q^{96} - 66 q^{97} - 132 q^{99}+O(q^{100}) \) 480 * q - 4 * q^3 - 24 * q^4 + 8 * q^6 + 4 * q^12 - 44 * q^15 + 24 * q^16 + 28 * q^18 + 66 * q^21 + 6 * q^23 + 4 * q^24 + 12 * q^25 + 86 * q^27 - 48 * q^29 + 44 * q^30 - 12 * q^31 - 44 * q^33 + 24 * q^39 - 60 * q^41 + 12 * q^46 + 48 * q^47 + 8 * q^48 - 78 * q^49 + 24 * q^50 - 30 * q^54 - 24 * q^55 - 66 * q^56 - 66 * q^57 - 72 * q^59 - 22 * q^60 - 110 * q^63 + 48 * q^64 - 462 * q^65 - 88 * q^66 - 70 * q^69 + 12 * q^70 - 52 * q^72 - 264 * q^74 - 76 * q^75 - 12 * q^77 - 58 * q^78 - 96 * q^81 - 198 * q^83 - 22 * q^84 + 178 * q^87 + 6 * q^92 - 20 * q^93 - 12 * q^94 + 12 * q^95 - 4 * q^96 - 66 * q^97 - 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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