LMFDB - Embedded newform 380.2.f.a.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(151,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("380.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.f (of order $2$, degree $1$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - 9x^{14} + 20x^{12} - 24x^{10} + 80x^{8} - 144x^{6} + 64x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + x^16 - 9x^14 + 20x^12 - 24x^10 + 80x^8 - 144x^6 + 64x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.3
Root			$1.31446 - 0.521712i$ of defining polynomial
Character	$\chi$	$=$	380.151
Dual form			380.2.f.a.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31446 - 0.521712i) q^{2} -2.15859 q^{3} +(1.45563 + 1.37154i) q^{4} -1.00000 q^{5} +(2.83739 + 1.12616i) q^{6} -1.66163i q^{7} +(-1.19783 - 2.56227i) q^{8} +1.65950 q^{9} +O(q^{10})$	\(q+(-1.31446 - 0.521712i) q^{2} -2.15859 q^{3} +(1.45563 + 1.37154i) q^{4} -1.00000 q^{5} +(2.83739 + 1.12616i) q^{6} -1.66163i q^{7} +(-1.19783 - 2.56227i) q^{8} +1.65950 q^{9} +(1.31446 + 0.521712i) q^{10} -1.77595i q^{11} +(-3.14211 - 2.96060i) q^{12} +0.769776i q^{13} +(-0.866891 + 2.18415i) q^{14} +2.15859 q^{15} +(0.237741 + 3.99293i) q^{16} -3.23899 q^{17} +(-2.18136 - 0.865781i) q^{18} +(1.23206 + 4.18115i) q^{19} +(-1.45563 - 1.37154i) q^{20} +3.58677i q^{21} +(-0.926532 + 2.33442i) q^{22} +3.06150i q^{23} +(2.58562 + 5.53087i) q^{24} +1.00000 q^{25} +(0.401601 - 1.01184i) q^{26} +2.89358 q^{27} +(2.27900 - 2.41872i) q^{28} +6.45515i q^{29} +(-2.83739 - 1.12616i) q^{30} +4.09806 q^{31} +(1.77065 - 5.37260i) q^{32} +3.83354i q^{33} +(4.25754 + 1.68982i) q^{34} +1.66163i q^{35} +(2.41563 + 2.27608i) q^{36} +5.34522i q^{37} +(0.561862 - 6.13875i) q^{38} -1.66163i q^{39} +(1.19783 + 2.56227i) q^{40} +3.83354i q^{41} +(1.87126 - 4.71469i) q^{42} +11.5381i q^{43} +(2.43579 - 2.58513i) q^{44} -1.65950 q^{45} +(1.59722 - 4.02424i) q^{46} -6.81499i q^{47} +(-0.513185 - 8.61909i) q^{48} +4.23899 q^{49} +(-1.31446 - 0.521712i) q^{50} +6.99164 q^{51} +(-1.05578 + 1.12051i) q^{52} +5.59198i q^{53} +(-3.80351 - 1.50962i) q^{54} +1.77595i q^{55} +(-4.25754 + 1.99035i) q^{56} +(-2.65950 - 9.02539i) q^{57} +(3.36773 - 8.48507i) q^{58} -5.35770 q^{59} +(3.14211 + 2.96060i) q^{60} -4.94753 q^{61} +(-5.38675 - 2.13800i) q^{62} -2.75748i q^{63} +(-5.13041 + 6.13831i) q^{64} -0.769776i q^{65} +(2.00000 - 5.03905i) q^{66} -6.72318 q^{67} +(-4.71478 - 4.44241i) q^{68} -6.60852i q^{69} +(0.866891 - 2.18415i) q^{70} +1.83362 q^{71} +(-1.98780 - 4.25208i) q^{72} +11.9331 q^{73} +(2.78866 - 7.02610i) q^{74} -2.15859 q^{75} +(-3.94121 + 7.77605i) q^{76} -2.95096 q^{77} +(-0.866891 + 2.18415i) q^{78} -9.41868 q^{79} +(-0.237741 - 3.99293i) q^{80} -11.2246 q^{81} +(2.00000 - 5.03905i) q^{82} +7.48061i q^{83} +(-4.91941 + 5.22103i) q^{84} +3.23899 q^{85} +(6.01957 - 15.1665i) q^{86} -13.9340i q^{87} +(-4.55045 + 2.12728i) q^{88} -16.0161i q^{89} +(2.18136 + 0.865781i) q^{90} +1.27908 q^{91} +(-4.19898 + 4.45643i) q^{92} -8.84602 q^{93} +(-3.55546 + 8.95807i) q^{94} +(-1.23206 - 4.18115i) q^{95} +(-3.82211 + 11.5972i) q^{96} -0.676382i q^{97} +(-5.57200 - 2.21153i) q^{98} -2.94719i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9	$ 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9} - 2 q^{16} + 20 q^{17} - 2 q^{20} + 26 q^{24} + 20 q^{25} - 14 q^{26} - 14 q^{28} + 6 q^{30} - 4 q^{36} + 10 q^{38} - 42 q^{42} + 8 q^{44} - 16 q^{45} - 30 q^{54} - 36 q^{57} + 62 q^{58} - 24 q^{61} - 40 q^{62} + 50 q^{64} + 40 q^{66} + 6 q^{68} - 36 q^{73} - 36 q^{74} - 28 q^{76} - 32 q^{77} + 2 q^{80} + 60 q^{81} + 40 q^{82} - 20 q^{85} + 26 q^{92} - 122 q^{96}+O(q^{100}) $ 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9 - 2 * q^16 + 20 * q^17 - 2 * q^20 + 26 * q^24 + 20 * q^25 - 14 * q^26 - 14 * q^28 + 6 * q^30 - 4 * q^36 + 10 * q^38 - 42 * q^42 + 8 * q^44 - 16 * q^45 - 30 * q^54 - 36 * q^57 + 62 * q^58 - 24 * q^61 - 40 * q^62 + 50 * q^64 + 40 * q^66 + 6 * q^68 - 36 * q^73 - 36 * q^74 - 28 * q^76 - 32 * q^77 + 2 * q^80 + 60 * q^81 + 40 * q^82 - 20 * q^85 + 26 * q^92 - 122 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.31446	−	0.521712i	−0.929467	−	0.368906i
$2$	−1.31446	−	0.521712i	−0.929467	−	0.368906i
$3$	−2.15859			−1.24626			−0.623131	−	0.782118i	$-0.714140\pi$
$3$	−2.15859			−1.24626			−0.623131	+	0.782118i	$0.714140\pi$
$4$	1.45563	+	1.37154i	0.727817	+	0.685771i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	2.83739	+	1.12616i	1.15836	+	0.459753i
$7$		−	1.66163i		−	0.628037i	−0.949417	−	0.314018i	$-0.898325\pi$
$7$		−	1.66163i		−	0.628037i	0.949417	−	0.314018i	$-0.101675\pi$
$8$	−1.19783	−	2.56227i	−0.423497	−	0.905898i
$9$	1.65950			0.553167
$10$	1.31446	+	0.521712i	0.415670	+	0.164980i
$11$		−	1.77595i		−	0.535468i	−0.963493	−	0.267734i	$-0.913725\pi$
$11$		−	1.77595i		−	0.535468i	0.963493	−	0.267734i	$-0.0862748\pi$
$12$	−3.14211	−	2.96060i	−0.907050	−	0.854650i
$13$			0.769776i			0.213497i	0.994286	+	0.106749i	$0.0340440\pi$
$13$			0.769776i			0.213497i	−0.994286	+	0.106749i	$0.965956\pi$
$14$	−0.866891	+	2.18415i	−0.231686	+	0.583739i
$15$	2.15859			0.557345
$16$	0.237741	+	3.99293i	0.0594353	+	0.998232i
$17$	−3.23899			−0.785570			−0.392785	−	0.919630i	$-0.628488\pi$
$17$	−3.23899			−0.785570			−0.392785	+	0.919630i	$0.628488\pi$
$18$	−2.18136	−	0.865781i	−0.514150	−	0.204067i
$19$	1.23206	+	4.18115i	0.282653	+	0.959222i
$19$	1.23206	+	4.18115i	0.282653	+	0.959222i
$20$	−1.45563	−	1.37154i	−0.325490	−	0.306686i
$21$			3.58677i			0.782698i
$22$	−0.926532	+	2.33442i	−0.197537	+	0.497700i
$23$			3.06150i			0.638367i	0.947693	+	0.319184i	$0.103409\pi$
$23$			3.06150i			0.638367i	−0.947693	+	0.319184i	$0.896591\pi$
$24$	2.58562	+	5.53087i	0.527788	+	1.12899i
$25$	1.00000			0.200000
$26$	0.401601	−	1.01184i	0.0787605	−	0.198439i
$27$	2.89358			0.556870
$28$	2.27900	−	2.41872i	0.430690	−	0.457096i
$29$			6.45515i			1.19869i	0.800490	+	0.599346i	$0.204573\pi$
$29$			6.45515i			1.19869i	−0.800490	+	0.599346i	$0.795427\pi$
$30$	−2.83739	−	1.12616i	−0.518034	−	0.205608i
$31$	4.09806			0.736033			0.368016	−	0.929819i	$-0.380037\pi$
$31$	4.09806			0.736033			0.368016	+	0.929819i	$0.380037\pi$
$32$	1.77065	−	5.37260i	0.313011	−	0.949750i
$33$			3.83354i			0.667333i
$34$	4.25754	+	1.68982i	0.730161	+	0.289801i
$35$			1.66163i			0.280867i
$36$	2.41563	+	2.27608i	0.402604	+	0.379346i
$37$			5.34522i			0.878749i	0.898304	+	0.439374i	$0.144800\pi$
$37$			5.34522i			0.878749i	−0.898304	+	0.439374i	$0.855200\pi$
$38$	0.561862	−	6.13875i	0.0911460	−	0.995838i
$39$		−	1.66163i		−	0.266074i
$40$	1.19783	+	2.56227i	0.189393	+	0.405130i
$41$			3.83354i			0.598698i	0.954144	+	0.299349i	$0.0967694\pi$
$41$			3.83354i			0.598698i	−0.954144	+	0.299349i	$0.903231\pi$
$42$	1.87126	−	4.71469i	0.288742	−	0.727492i
$43$			11.5381i			1.75955i	0.475393	+	0.879774i	$0.342306\pi$
$43$			11.5381i			1.75955i	−0.475393	+	0.879774i	$0.657694\pi$
$44$	2.43579	−	2.58513i	0.367209	−	0.389723i
$45$	−1.65950			−0.247384
$46$	1.59722	−	4.02424i	0.235497	−	0.593341i
$47$		−	6.81499i		−	0.994069i	−0.867731	−	0.497034i	$-0.834422\pi$
$47$		−	6.81499i		−	0.994069i	0.867731	−	0.497034i	$-0.165578\pi$
$48$	−0.513185	−	8.61909i	−0.0740719	−	1.24406i
$49$	4.23899			0.605570
$50$	−1.31446	−	0.521712i	−0.185893	−	0.0737812i
$51$	6.99164			0.979026
$52$	−1.05578	+	1.12051i	−0.146410	+	0.155387i
$53$			5.59198i			0.768118i	0.923309	+	0.384059i	$0.125474\pi$
$53$			5.59198i			0.768118i	−0.923309	+	0.384059i	$0.874526\pi$
$54$	−3.80351	−	1.50962i	−0.517593	−	0.205433i
$55$			1.77595i			0.239469i
$56$	−4.25754	+	1.99035i	−0.568937	+	0.265972i
$57$	−2.65950	−	9.02539i	−0.352260	−	1.19544i
$58$	3.36773	−	8.48507i	0.442204	−	1.11414i
$59$	−5.35770			−0.697513			−0.348756	−	0.937213i	$-0.613396\pi$
$59$	−5.35770			−0.697513			−0.348756	+	0.937213i	$0.613396\pi$
$60$	3.14211	+	2.96060i	0.405645	+	0.382211i
$61$	−4.94753			−0.633466			−0.316733	−	0.948515i	$-0.602586\pi$
$61$	−4.94753			−0.633466			−0.316733	+	0.948515i	$0.602586\pi$
$62$	−5.38675	−	2.13800i	−0.684118	−	0.271527i
$63$		−	2.75748i		−	0.347409i
$64$	−5.13041	+	6.13831i	−0.641301	+	0.767289i
$65$		−	0.769776i		−	0.0954790i
$66$	2.00000	−	5.03905i	0.246183	−	0.620264i
$67$	−6.72318			−0.821368			−0.410684	−	0.911778i	$-0.634710\pi$
$67$	−6.72318			−0.821368			−0.410684	+	0.911778i	$0.634710\pi$
$68$	−4.71478	−	4.44241i	−0.571751	−	0.538721i
$69$		−	6.60852i		−	0.795572i
$70$	0.866891	−	2.18415i	0.103613	−	0.261056i
$71$	1.83362			0.217611			0.108805	−	0.994063i	$-0.465297\pi$
$71$	1.83362			0.217611			0.108805	+	0.994063i	$0.465297\pi$
$72$	−1.98780	−	4.25208i	−0.234264	−	0.501113i
$73$	11.9331			1.39666			0.698332	−	0.715774i	$-0.253926\pi$
$73$	11.9331			1.39666			0.698332	+	0.715774i	$0.253926\pi$
$74$	2.78866	−	7.02610i	0.324175	−	0.816768i
$75$	−2.15859			−0.249252
$76$	−3.94121	+	7.77605i	−0.452087	+	0.891974i
$77$	−2.95096			−0.336294
$78$	−0.866891	+	2.18415i	−0.0981561	+	0.247307i
$79$	−9.41868			−1.05968			−0.529842	−	0.848096i	$-0.677749\pi$
$79$	−9.41868			−1.05968			−0.529842	+	0.848096i	$0.677749\pi$
$80$	−0.237741	−	3.99293i	−0.0265803	−	0.446423i
$81$	−11.2246			−1.24717
$82$	2.00000	−	5.03905i	0.220863	−	0.556470i
$83$			7.48061i			0.821103i	0.911837	+	0.410552i	$0.134664\pi$
$83$			7.48061i			0.821103i	−0.911837	+	0.410552i	$0.865336\pi$
$84$	−4.91941	+	5.22103i	−0.536752	+	0.569661i
$85$	3.23899			0.351318
$86$	6.01957	−	15.1665i	0.649107	−	1.63544i
$87$		−	13.9340i		−	1.49388i
$88$	−4.55045	+	2.12728i	−0.485079	+	0.226769i
$89$		−	16.0161i		−	1.69770i	−0.528633	−	0.848850i	$-0.677295\pi$
$89$		−	16.0161i		−	1.69770i	0.528633	−	0.848850i	$-0.322705\pi$
$90$	2.18136	+	0.865781i	0.229935	+	0.0912613i
$91$	1.27908			0.134084
$92$	−4.19898	+	4.45643i	−0.437774	+	0.464615i
$93$	−8.84602			−0.917289
$94$	−3.55546	+	8.95807i	−0.366718	+	0.923954i
$95$	−1.23206	−	4.18115i	−0.126406	−	0.428977i
$96$	−3.82211	+	11.5972i	−0.390093	+	1.18364i
$97$		−	0.676382i		−	0.0686762i	−0.999410	−	0.0343381i	$-0.989068\pi$
$97$		−	0.676382i		−	0.0686762i	0.999410	−	0.0343381i	$-0.0109323\pi$
$98$	−5.57200	−	2.21153i	−0.562857	−	0.223398i
$99$		−	2.94719i		−	0.296203i
$100$	1.45563	+	1.37154i	0.145563	+	0.137154i
$101$	−2.57949			−0.256669			−0.128334	−	0.991731i	$-0.540963\pi$
$101$	−2.57949			−0.256669			−0.128334	+	0.991731i	$0.540963\pi$
$102$	−9.19026	−	3.64762i	−0.909972	−	0.361168i
$103$	7.51628			0.740601			0.370301	−	0.928912i	$-0.379255\pi$
$103$	7.51628			0.740601			0.370301	+	0.928912i	$0.379255\pi$
$104$	1.97237	−	0.922061i	0.193407	−	0.0904155i
$105$		−	3.58677i		−	0.350033i
$106$	2.91740	−	7.35046i	0.283363	−	0.713940i
$107$	1.32842			0.128423			0.0642116	−	0.997936i	$-0.479547\pi$
$107$	1.32842			0.128423			0.0642116	+	0.997936i	$0.479547\pi$
$108$	4.21200	+	3.96867i	0.405300	+	0.381886i
$109$		−	2.43483i		−	0.233214i	−0.993178	−	0.116607i	$-0.962798\pi$
$109$		−	2.43483i		−	0.233214i	0.993178	−	0.116607i	$-0.0372018\pi$
$110$	0.926532	−	2.33442i	0.0883413	−	0.222578i
$111$		−	11.5381i		−	1.09515i
$112$	6.63477	−	0.395037i	0.626927	−	0.0373275i
$113$			17.9154i			1.68534i	0.538434	+	0.842668i	$0.319016\pi$
$113$			17.9154i			1.68534i	−0.538434	+	0.842668i	$0.680984\pi$
$114$	−1.21283	+	13.2510i	−0.113592	+	1.24107i
$115$		−	3.06150i		−	0.285487i
$116$	−8.85352	+	9.39634i	−0.822028	+	0.872428i
$117$			1.27744i			0.118100i
$118$	7.04250	+	2.79517i	0.648315	+	0.257316i
$119$			5.38200i			0.493367i
$120$	−2.58562	−	5.53087i	−0.236034	−	0.504897i
$121$	7.84602			0.713274
$122$	6.50335	+	2.58118i	0.588785	+	0.233689i
$123$		−	8.27502i		−	0.746134i
$124$	5.96527	+	5.62066i	0.535697	+	0.504750i
$125$	−1.00000			−0.0894427
$126$	−1.43861	+	3.62460i	−0.128161	+	0.322905i
$127$	15.9315			1.41369			0.706847	−	0.707367i	$-0.250117\pi$
$127$	15.9315			1.41369			0.706847	+	0.707367i	$0.250117\pi$
$128$	9.94617	−	5.39200i	0.879126	−	0.476590i
$129$		−	24.9061i		−	2.19286i
$130$	−0.401601	+	1.01184i	−0.0352227	+	0.0887445i
$131$		−	4.53342i		−	0.396087i	−0.980193	−	0.198043i	$-0.936541\pi$
$131$		−	4.53342i		−	0.396087i	0.980193	−	0.198043i	$-0.0634587\pi$
$132$	−5.25786	+	5.58023i	−0.457638	+	0.485696i
$133$	6.94753	−	2.04722i	0.602427	−	0.177517i
$134$	8.83739	+	3.50756i	0.763434	+	0.303007i
$135$	−2.89358			−0.249040
$136$	3.87976	+	8.29915i	0.332686	+	0.711646i
$137$	−19.4601			−1.66259			−0.831295	−	0.555832i	$-0.812400\pi$
$137$	−19.4601			−1.66259			−0.831295	+	0.555832i	$0.812400\pi$
$138$	−3.44774	+	8.68667i	−0.293491	+	0.739458i
$139$			7.75685i			0.657927i	0.944343	+	0.328964i	$0.106699\pi$
$139$			7.75685i			0.657927i	−0.944343	+	0.328964i	$0.893301\pi$
$140$	−2.27900	+	2.41872i	−0.192610	+	0.204419i
$141$			14.7108i			1.23887i
$142$	−2.41023	−	0.956621i	−0.202262	−	0.0802779i
$143$	1.36708			0.114321
$144$	0.394532	+	6.62627i	0.0328776	+	0.552189i
$145$		−	6.45515i		−	0.536071i
$146$	−15.6856	−	6.22563i	−1.29815	−	0.515237i
$147$	−9.15023			−0.754698
$148$	−7.33120	+	7.78068i	−0.602621	+	0.639568i
$149$	21.7516			1.78196			0.890979	−	0.454044i	$-0.150019\pi$
$149$	21.7516			1.78196			0.890979	+	0.454044i	$0.150019\pi$
$150$	2.83739	+	1.12616i	0.231672	+	0.0919506i
$151$	−13.9550			−1.13564			−0.567820	−	0.823153i	$-0.692213\pi$
$151$	−13.9550			−1.13564			−0.567820	+	0.823153i	$0.692213\pi$
$152$	9.23743	−	8.16516i	0.749254	−	0.662282i
$153$	−5.37511			−0.434552
$154$	3.87894	+	1.53955i	0.312574	+	0.124061i
$155$	−4.09806			−0.329164
$156$	2.27900	−	2.41872i	0.182466	−	0.193653i
$157$	−10.6941			−0.853483			−0.426741	−	0.904374i	$-0.640339\pi$
$157$	−10.6941			−0.853483			−0.426741	+	0.904374i	$0.640339\pi$
$158$	12.3805	+	4.91384i	0.984942	+	0.390924i
$159$		−	12.0708i		−	0.957275i
$160$	−1.77065	+	5.37260i	−0.139983	+	0.424741i
$161$	5.08708			0.400918
$162$	14.7543	+	5.85598i	1.15921	+	0.460089i
$163$			8.21487i			0.643438i	0.946835	+	0.321719i	$0.104261\pi$
$163$			8.21487i			0.643438i	−0.946835	+	0.321719i	$0.895739\pi$
$164$	−5.25786	+	5.58023i	−0.410570	+	0.435742i
$165$		−	3.83354i		−	0.298440i
$166$	3.90272	−	9.83299i	0.302910	−	0.763188i
$167$	−2.34064			−0.181124			−0.0905620	−	0.995891i	$-0.528866\pi$
$167$	−2.34064			−0.181124			−0.0905620	+	0.995891i	$0.528866\pi$
$168$	9.19026	−	4.29634i	0.709044	−	0.331470i
$169$	12.4074			0.954419
$170$	−4.25754	−	1.68982i	−0.326538	−	0.129603i
$171$	2.04460	+	6.93863i	0.156354	+	0.530610i
$172$	−15.8250	+	16.7953i	−1.20665	+	1.28063i
$173$			4.12231i			0.313413i	0.987645	+	0.156707i	$0.0500877\pi$
$173$			4.12231i			0.313413i	−0.987645	+	0.156707i	$0.949912\pi$
$174$	−7.26954	+	18.3158i	−0.551102	+	1.38851i
$175$		−	1.66163i		−	0.125607i
$176$	7.09123	−	0.422215i	0.534521	−	0.0318257i
$177$	11.5651			0.869283
$178$	−8.35577	+	21.0526i	−0.626292	+	1.57796i
$179$	−1.16740			−0.0872559			−0.0436280	−	0.999048i	$-0.513892\pi$
$179$	−1.16740			−0.0872559			−0.0436280	+	0.999048i	$0.513892\pi$
$180$	−2.41563	−	2.27608i	−0.180050	−	0.169649i
$181$		−	22.5328i		−	1.67485i	−0.546551	−	0.837426i	$-0.684060\pi$
$181$		−	22.5328i		−	1.67485i	0.546551	−	0.837426i	$-0.315940\pi$
$182$	−1.68131	−	0.667312i	−0.124627	−	0.0494645i
$183$	10.6797			0.789464
$184$	7.84438	−	3.66716i	0.578295	−	0.270346i
$185$		−	5.34522i		−	0.392988i
$186$	11.6278	+	4.61507i	0.852590	+	0.338393i
$187$			5.75227i			0.420648i
$188$	9.34705	−	9.92014i	0.681704	−	0.723500i
$189$		−	4.80806i		−	0.349735i
$190$	−0.561862	+	6.13875i	−0.0407617	+	0.445352i
$191$			20.5329i			1.48571i	0.669452	+	0.742855i	$0.266529\pi$
$191$			20.5329i			1.48571i	−0.669452	+	0.742855i	$0.733471\pi$
$192$	11.0744	−	13.2501i	0.799229	−	0.956243i
$193$			8.03672i			0.578495i	0.957254	+	0.289248i	$0.0934051\pi$
$193$			8.03672i			0.578495i	−0.957254	+	0.289248i	$0.906595\pi$
$194$	−0.352876	+	0.889081i	−0.0253351	+	0.0638323i
$195$			1.66163i			0.118992i
$196$	6.17042	+	5.81395i	0.440744	+	0.415282i
$197$	9.52701			0.678772			0.339386	−	0.940647i	$-0.389781\pi$
$197$	9.52701			0.678772			0.339386	+	0.940647i	$0.389781\pi$
$198$	−1.53758	+	3.87397i	−0.109271	+	0.275311i
$199$			6.98947i			0.495470i	0.968828	+	0.247735i	$0.0796863\pi$
$199$			6.98947i			0.495470i	−0.968828	+	0.247735i	$0.920314\pi$
$200$	−1.19783	−	2.56227i	−0.0846993	−	0.181180i
$201$	14.5126			1.02364
$202$	3.39064	+	1.34575i	0.238565	+	0.0946865i
$203$	10.7261			0.752822
$204$	10.1773	+	9.58933i	0.712551	+	0.671388i
$205$		−	3.83354i		−	0.267746i
$206$	−9.87989	−	3.92133i	−0.688364	−	0.273212i
$207$			5.08057i			0.353124i
$208$	−3.07366	+	0.183007i	−0.213120	+	0.0126893i
$209$	7.42550	−	2.18807i	0.513633	−	0.151352i
$210$	−1.87126	+	4.71469i	−0.129129	+	0.325344i
$211$	−17.9456			−1.23543			−0.617713	−	0.786404i	$-0.711941\pi$
$211$	−17.9456			−1.23543			−0.617713	+	0.786404i	$0.711941\pi$
$212$	−7.66964	+	8.13988i	−0.526753	+	0.559049i
$213$	−3.95803			−0.271200
$214$	−1.74616	−	0.693052i	−0.119365	−	0.0473761i
$215$		−	11.5381i		−	0.786894i
$216$	−3.46602	−	7.41413i	−0.235833	−	0.504468i
$217$		−	6.80945i		−	0.462256i
$218$	−1.27028	+	3.20050i	−0.0860341	+	0.216765i
$219$	−25.7586			−1.74061
$220$	−2.43579	+	2.58513i	−0.164221	+	0.174289i
$221$		−	2.49330i		−	0.167717i
$222$	−6.01957	+	15.1665i	−0.404007	+	1.01791i
$223$	−25.1311			−1.68290			−0.841451	−	0.540334i	$-0.818298\pi$
$223$	−25.1311			−1.68290			−0.841451	+	0.540334i	$0.818298\pi$
$224$	−8.92726	−	2.94217i	−0.596478	−	0.196582i
$225$	1.65950			0.110633
$226$	9.34665	−	23.5491i	0.621730	−	1.56646i
$227$	14.7465			0.978759			0.489379	−	0.872071i	$-0.337223\pi$
$227$	14.7465			0.978759			0.489379	+	0.872071i	$0.337223\pi$
$228$	8.50744	−	16.7853i	0.563419	−	1.11163i
$229$	−18.9606			−1.25295			−0.626477	−	0.779440i	$-0.715504\pi$
$229$	−18.9606			−1.25295			−0.626477	+	0.779440i	$0.715504\pi$
$230$	−1.59722	+	4.02424i	−0.105318	+	0.265350i
$231$	6.36992			0.419110
$232$	16.5398	−	7.73217i	1.08589	−	0.507642i
$233$	−18.6430			−1.22134			−0.610672	−	0.791884i	$-0.709100\pi$
$233$	−18.6430			−1.22134			−0.610672	+	0.791884i	$0.709100\pi$
$234$	0.666458	−	1.67916i	0.0435677	−	0.109770i
$235$			6.81499i			0.444561i
$236$	−7.79885	−	7.34831i	−0.507662	−	0.478334i
$237$	20.3311			1.32064
$238$	2.80785	−	7.07445i	0.182006	−	0.458568i
$239$			7.49509i			0.484817i	0.970174	+	0.242409i	$0.0779375\pi$
$239$			7.49509i			0.484817i	−0.970174	+	0.242409i	$0.922063\pi$
$240$	0.513185	+	8.61909i	0.0331259	+	0.556360i
$241$		−	4.87794i		−	0.314216i	−0.987581	−	0.157108i	$-0.949783\pi$
$241$		−	4.87794i		−	0.314216i	0.987581	−	0.157108i	$-0.0502171\pi$
$242$	−10.3133	−	4.09336i	−0.662965	−	0.263131i
$243$	15.5484			0.997433
$244$	−7.20179	−	6.78574i	−0.461047	−	0.434413i
$245$	−4.23899			−0.270819
$246$	−4.31718	+	10.8772i	−0.275253	+	0.693507i
$247$	−3.21855	+	0.948407i	−0.204792	+	0.0603457i
$248$	−4.90877	−	10.5003i	−0.311707	−	0.666770i
$249$		−	16.1475i		−	1.02331i
$250$	1.31446	+	0.521712i	0.0831340	+	0.0329959i
$251$			17.3716i			1.09648i	0.836319	+	0.548242i	$0.184703\pi$
$251$			17.3716i			1.09648i	−0.836319	+	0.548242i	$0.815297\pi$
$252$	3.78200	−	4.01388i	0.238243	−	0.252850i
$253$	5.43706			0.341825
$254$	−20.9414	−	8.31166i	−1.31398	−	0.521520i
$255$	−6.99164			−0.437834
$256$	−15.8870	+	1.89857i	−0.992935	+	0.118660i
$257$			24.5463i			1.53116i	0.643342	+	0.765579i	$0.277547\pi$
$257$			24.5463i			1.53116i	−0.643342	+	0.765579i	$0.722453\pi$
$258$	−12.9938	+	32.7381i	−0.808957	+	2.03819i
$259$	8.88177			0.551886
$260$	1.05578	−	1.12051i	0.0654767	−	0.0694912i
$261$			10.7123i			0.663077i
$262$	−2.36514	+	5.95902i	−0.146119	+	0.368150i
$263$		−	28.7200i		−	1.77095i	−0.464686	−	0.885476i	$-0.653833\pi$
$263$		−	28.7200i		−	1.77095i	0.464686	−	0.885476i	$-0.346167\pi$
$264$	9.82254	−	4.59192i	0.604535	−	0.282613i
$265$		−	5.59198i		−	0.343513i
$266$	−10.2003	−	0.933606i	−0.625423	−	0.0572430i
$267$			34.5721i			2.11578i
$268$	−9.78650	−	9.22113i	−0.597805	−	0.563270i
$269$			20.1815i			1.23049i	0.788337	+	0.615243i	$0.210942\pi$
$269$			20.1815i			1.23049i	−0.788337	+	0.615243i	$0.789058\pi$
$270$	3.80351	+	1.50962i	0.231474	+	0.0918723i
$271$			0.948407i			0.0576116i	0.999585	+	0.0288058i	$0.00917045\pi$
$271$			0.948407i			0.0576116i	−0.999585	+	0.0288058i	$0.990830\pi$
$272$	−0.770040	−	12.9330i	−0.0466906	−	0.784181i
$273$	−2.76101			−0.167104
$274$	25.5796	+	10.1526i	1.54532	+	0.613339i
$275$		−	1.77595i		−	0.107094i
$276$	9.06387	−	9.61959i	0.545581	−	0.579031i
$277$	17.3321			1.04139			0.520693	−	0.853744i	$-0.325674\pi$
$277$	17.3321			1.04139			0.520693	+	0.853744i	$0.325674\pi$
$278$	4.04684	−	10.1961i	0.242713	−	0.611522i
$279$	6.80073			0.407149
$280$	4.25754	−	1.99035i	0.254436	−	0.118946i
$281$			13.5353i			0.807449i	0.914881	+	0.403724i	$0.132284\pi$
$281$			13.5353i			0.807449i	−0.914881	+	0.403724i	$0.867716\pi$
$282$	7.67477	−	19.3368i	0.457026	−	1.15149i
$283$		−	7.04363i		−	0.418700i	−0.977841	−	0.209350i	$-0.932865\pi$
$283$		−	7.04363i		−	0.418700i	0.977841	−	0.209350i	$-0.0671348\pi$
$284$	2.66908	+	2.51489i	0.158381	+	0.149231i
$285$	2.65950	+	9.02539i	0.157535	+	0.534618i
$286$	−1.79698	−	0.713222i	−0.106258	−	0.0421737i
$287$	6.36992			0.376004
$288$	2.93840	−	8.91583i	0.173147	−	0.525370i
$289$	−6.50896			−0.382880
$290$	−3.36773	+	8.48507i	−0.197760	+	0.498260i
$291$			1.46003i			0.0855885i
$292$	17.3702	+	16.3668i	1.01652	+	0.957792i
$293$		−	9.35302i		−	0.546409i	−0.961956	−	0.273205i	$-0.911916\pi$
$293$		−	9.35302i		−	0.546409i	0.961956	−	0.273205i	$-0.0880836\pi$
$294$	12.0277	+	4.77378i	0.701467	+	0.278413i
$295$	5.35770			0.311937
$296$	13.6959	−	6.40266i	0.796056	−	0.372147i
$297$		−	5.13885i		−	0.298186i
$298$	−28.5917	−	11.3480i	−1.65627	−	0.657375i
$299$	−2.35667			−0.136290
$300$	−3.14211	−	2.96060i	−0.181410	−	0.170930i
$301$	19.1721			1.10506
$302$	18.3433	+	7.28047i	1.05554	+	0.418944i
$303$	5.56805			0.319876
$304$	−16.4021	+	5.91354i	−0.940727	+	0.339165i
$305$	4.94753			0.283294
$306$	7.06539	+	2.80425i	0.403901	+	0.160309i
$307$	−5.63492			−0.321602			−0.160801	−	0.986987i	$-0.551408\pi$
$307$	−5.63492			−0.321602			−0.160801	+	0.986987i	$0.551408\pi$
$308$	−4.29552	−	4.04737i	−0.244760	−	0.230621i
$309$	−16.2246			−0.922983
$310$	5.38675	+	2.13800i	0.305947	+	0.121430i
$311$		−	13.8045i		−	0.782779i	−0.920225	−	0.391390i	$-0.871994\pi$
$311$		−	13.8045i		−	0.782779i	0.920225	−	0.391390i	$-0.128006\pi$
$312$	−4.25754	+	1.99035i	−0.241035	+	0.112681i
$313$	−17.3620			−0.981360			−0.490680	−	0.871340i	$-0.663252\pi$
$313$	−17.3620			−0.981360			−0.490680	+	0.871340i	$0.663252\pi$
$314$	14.0570	+	5.57924i	0.793284	+	0.314855i
$315$			2.75748i			0.155366i
$316$	−13.7102	−	12.9181i	−0.771257	−	0.726702i
$317$		−	8.07275i		−	0.453411i	−0.973963	−	0.226705i	$-0.927205\pi$
$317$		−	8.07275i		−	0.453411i	0.973963	−	0.226705i	$-0.0727955\pi$
$318$	−6.29747	+	15.8666i	−0.353144	+	0.889756i
$319$	11.4640			0.641861
$320$	5.13041	−	6.13831i	0.286799	−	0.343142i
$321$	−2.86751			−0.160049
$322$	−6.68679	−	2.65399i	−0.372640	−	0.147901i
$323$	−3.99062	−	13.5427i	−0.222044	−	0.753536i
$324$	−16.3389	−	15.3950i	−0.907714	−	0.855276i
$325$			0.769776i			0.0426995i
$326$	4.28579	−	10.7981i	0.237368	−	0.598054i
$327$			5.25579i			0.290646i
$328$	9.82254	−	4.59192i	0.542359	−	0.253547i
$329$	−11.3240			−0.624312
$330$	−2.00000	+	5.03905i	−0.110096	+	0.277390i
$331$	−35.8536			−1.97069			−0.985347	−	0.170560i	$-0.945442\pi$
$331$	−35.8536			−1.97069			−0.985347	+	0.170560i	$0.945442\pi$
$332$	−10.2600	+	10.8890i	−0.563089	+	0.597613i
$333$			8.87040i			0.486095i
$334$	3.07669	+	1.22114i	0.168349	+	0.0668177i
$335$	6.72318			0.367327
$336$	−14.3217	+	0.852723i	−0.781314	+	0.0465199i
$337$			33.9314i			1.84836i	0.381953	+	0.924182i	$0.375252\pi$
$337$			33.9314i			1.84836i	−0.381953	+	0.924182i	$0.624748\pi$
$338$	−16.3091	−	6.47311i	−0.887101	−	0.352091i
$339$		−	38.6719i		−	2.10037i
$340$	4.71478	+	4.44241i	0.255695	+	0.240924i
$341$		−	7.27793i		−	0.394122i
$342$	0.932410	−	10.1873i	0.0504190	−	0.550865i
$343$		−	18.6750i		−	1.00836i
$344$	29.5637	−	13.8207i	1.59397	−	0.745163i
$345$			6.60852i			0.355791i
$346$	2.15066	−	5.41863i	0.115620	−	0.291307i
$347$			18.7299i			1.00548i	0.864439	+	0.502738i	$0.167674\pi$
$347$			18.7299i			1.00548i	−0.864439	+	0.502738i	$0.832326\pi$
$348$	19.1111	−	20.2828i	1.02446	−	1.08727i
$349$	4.20801			0.225250			0.112625	−	0.993638i	$-0.464074\pi$
$349$	4.20801			0.225250			0.112625	+	0.993638i	$0.464074\pi$
$350$	−0.866891	+	2.18415i	−0.0463373	+	0.116748i
$351$			2.22741i			0.118890i
$352$	−9.54144	−	3.14459i	−0.508560	−	0.167607i
$353$	−21.5221			−1.14550			−0.572752	−	0.819729i	$-0.694124\pi$
$353$	−21.5221			−1.14550			−0.572752	+	0.819729i	$0.694124\pi$
$354$	−15.2019	−	6.03362i	−0.807970	−	0.320684i
$355$	−1.83362			−0.0973185
$356$	21.9667	−	23.3135i	1.16423	−	1.23562i
$357$		−	11.6175i		−	0.614864i
$358$	1.53451	+	0.609049i	0.0811015	+	0.0321892i
$359$		−	17.2360i		−	0.909683i	−0.890572	−	0.454842i	$-0.849696\pi$
$359$		−	17.2360i		−	0.909683i	0.890572	−	0.454842i	$-0.150304\pi$
$360$	1.98780	+	4.25208i	0.104766	+	0.224104i
$361$	−15.9641	+	10.3028i	−0.840214	+	0.542254i
$362$	−11.7556	+	29.6186i	−0.617862	+	1.55672i
$363$	−16.9363			−0.888926
$364$	1.86188	+	1.75432i	0.0975888	+	0.0919512i
$365$	−11.9331			−0.624607
$366$	−14.0380	−	5.57171i	−0.733780	−	0.291238i
$367$		−	38.0242i		−	1.98485i	−0.122871	−	0.992423i	$-0.539210\pi$
$367$		−	38.0242i		−	1.98485i	0.122871	−	0.992423i	$-0.460790\pi$
$368$	−12.2244	+	0.727845i	−0.637239	+	0.0379415i
$369$			6.36176i			0.331180i
$370$	−2.78866	+	7.02610i	−0.144976	+	0.365270i
$371$	9.29180			0.482406
$372$	−12.8766	−	12.1327i	−0.667619	−	0.629051i
$373$		−	28.9684i		−	1.49993i	−0.661480	−	0.749963i	$-0.730071\pi$
$373$		−	28.9684i		−	1.49993i	0.661480	−	0.749963i	$-0.269929\pi$
$374$	3.00103	−	7.56115i	0.155179	−	0.390978i
$375$	2.15859			0.111469
$376$	−17.4618	+	8.16320i	−0.900525	+	0.420985i
$377$	−4.96902			−0.255918
$378$	−2.50842	+	6.32003i	−0.129019	+	0.325067i
$379$	36.2461			1.86183			0.930917	−	0.365230i	$-0.119010\pi$
$379$	36.2461			1.86183			0.930917	+	0.365230i	$0.119010\pi$
$380$	3.94121	−	7.77605i	0.202180	−	0.398903i
$381$	−34.3896			−1.76183
$382$	10.7123	−	26.9898i	0.548087	−	1.38092i
$383$	28.6181			1.46232			0.731158	−	0.682208i	$-0.238980\pi$
$383$	28.6181			1.46232			0.731158	+	0.682208i	$0.238980\pi$
$384$	−21.4697	+	11.6391i	−1.09562	+	0.593956i
$385$	2.95096			0.150395
$386$	4.19285	−	10.5640i	0.213410	−	0.537692i
$387$			19.1475i			0.973324i
$388$	0.927687	−	0.984565i	0.0470962	−	0.0499837i
$389$	−14.6860			−0.744609			−0.372305	−	0.928111i	$-0.621432\pi$
$389$	−14.6860			−0.744609			−0.372305	+	0.928111i	$0.621432\pi$
$390$	0.866891	−	2.18415i	0.0438967	−	0.110599i
$391$		−	9.91617i		−	0.501482i
$392$	−5.07759	−	10.8614i	−0.256457	−	0.548584i
$393$			9.78579i			0.493628i
$394$	−12.5229	−	4.97035i	−0.630896	−	0.250403i
$395$	9.41868			0.473905
$396$	4.04219	−	4.29002i	0.203128	−	0.215582i
$397$	−10.9560			−0.549864			−0.274932	−	0.961464i	$-0.588655\pi$
$397$	−10.9560			−0.549864			−0.274932	+	0.961464i	$0.588655\pi$
$398$	3.64649	−	9.18741i	0.182782	−	0.460523i
$399$	−14.9968	+	4.41911i	−0.750781	+	0.221232i
$400$	0.237741	+	3.99293i	0.0118871	+	0.199646i
$401$			34.9245i			1.74404i	0.489466	+	0.872022i	$0.337192\pi$
$401$			34.9245i			1.74404i	−0.489466	+	0.872022i	$0.662808\pi$
$402$	−19.0763	−	7.57138i	−0.951438	−	0.377626i
$403$			3.15459i			0.157141i
$404$	−3.75479	−	3.53788i	−0.186808	−	0.176016i
$405$	11.2246			0.557753
$406$	−14.0990	−	5.59591i	−0.699723	−	0.277721i
$407$	9.49282			0.470542
$408$	−8.37479	−	17.9144i	−0.414614	−	0.886897i
$409$		−	2.26893i		−	0.112192i	−0.998425	−	0.0560958i	$-0.982135\pi$
$409$		−	2.26893i		−	0.112192i	0.998425	−	0.0560958i	$-0.0178652\pi$
$410$	−2.00000	+	5.03905i	−0.0987730	+	0.248861i
$411$	42.0064			2.07202
$412$	10.9410	+	10.3089i	0.539022	+	0.507883i
$413$			8.90250i			0.438064i
$414$	2.65059	−	6.67823i	0.130269	−	0.328217i
$415$		−	7.48061i		−	0.367209i
$416$	4.13570	+	1.36301i	0.202769	+	0.0668270i
$417$		−	16.7438i		−	0.819949i
$418$	−10.9021	−	0.997836i	−0.533239	−	0.0488058i
$419$			4.00991i			0.195897i	0.995191	+	0.0979484i	$0.0312280\pi$
$419$			4.00991i			0.195897i	−0.995191	+	0.0979484i	$0.968772\pi$
$420$	4.91941	−	5.22103i	0.240043	−	0.254760i
$421$		−	27.1083i		−	1.32118i	−0.750749	−	0.660588i	$-0.770307\pi$
$421$		−	27.1083i		−	1.32118i	0.750749	−	0.660588i	$-0.229693\pi$
$422$	23.5888	+	9.36242i	1.14829	+	0.455756i
$423$		−	11.3095i		−	0.549886i
$424$	14.3281	−	6.69824i	0.695836	−	0.325295i
$425$	−3.23899			−0.157114
$426$	5.20269	+	2.06495i	0.252071	+	0.100047i
$427$			8.22095i			0.397840i
$428$	1.93369	+	1.82198i	0.0934686	+	0.0880690i
$429$	−2.95096			−0.142474
$430$	−6.01957	+	15.1665i	−0.290290	+	0.731391i
$431$	27.6130			1.33007			0.665037	−	0.746811i	$-0.268416\pi$
$431$	27.6130			1.33007			0.665037	+	0.746811i	$0.268416\pi$
$432$	0.687924	+	11.5539i	0.0330977	+	0.555886i
$433$			26.0792i			1.25329i	0.779306	+	0.626643i	$0.215572\pi$
$433$			26.0792i			1.25329i	−0.779306	+	0.626643i	$0.784428\pi$
$434$	−3.55257	+	8.95078i	−0.170529	+	0.429651i
$435$			13.9340i			0.668085i
$436$	3.33947	−	3.54422i	0.159932	−	0.169737i
$437$	−12.8006	+	3.77194i	−0.612336	+	0.180436i
$438$	33.8588	+	13.4386i	1.61784	+	0.642120i
$439$	5.65595			0.269944			0.134972	−	0.990849i	$-0.456906\pi$
$439$	5.65595			0.269944			0.134972	+	0.990849i	$0.456906\pi$
$440$	4.55045	−	2.12728i	0.216934	−	0.101414i
$441$	7.03461			0.334981
$442$	−1.30078	+	3.27735i	−0.0618719	+	0.155888i
$443$		−	3.53141i		−	0.167782i	−0.996475	−	0.0838911i	$-0.973265\pi$
$443$		−	3.53141i		−	0.167782i	0.996475	−	0.0838911i	$-0.0267348\pi$
$444$	15.8250	−	16.7953i	0.751023	−	0.797069i
$445$			16.0161i			0.759235i
$446$	33.0339	+	13.1112i	1.56420	+	0.620832i
$447$	−46.9527			−2.22079
$448$	10.1996	+	8.52484i	0.481886	+	0.402761i
$449$			21.1466i			0.997971i	0.866610	+	0.498986i	$0.166294\pi$
$449$			21.1466i			0.997971i	−0.866610	+	0.498986i	$0.833706\pi$
$450$	−2.18136	−	0.865781i	−0.102830	−	0.0408133i
$451$	6.80815			0.320583
$452$	−24.5717	+	26.0782i	−1.15576	+	1.22662i
$453$	30.1230			1.41530
$454$	−19.3837	−	7.69341i	−0.909724	−	0.361070i
$455$	−1.27908			−0.0599643
$456$	−19.9398	+	17.6252i	−0.933767	+	0.825377i
$457$	30.9871			1.44952			0.724758	−	0.689003i	$-0.241951\pi$
$457$	30.9871			1.44952			0.724758	+	0.689003i	$0.241951\pi$
$458$	24.9231	+	9.89198i	1.16458	+	0.462222i
$459$	−9.37228			−0.437461
$460$	4.19898	−	4.45643i	0.195778	−	0.207782i
$461$	−1.84809			−0.0860743			−0.0430371	−	0.999073i	$-0.513703\pi$
$461$	−1.84809			−0.0860743			−0.0430371	+	0.999073i	$0.513703\pi$
$462$	−8.37303	−	3.32326i	−0.389548	−	0.154612i
$463$			22.5105i			1.04615i	0.852287	+	0.523075i	$0.175215\pi$
$463$			22.5105i			1.04615i	−0.852287	+	0.523075i	$0.824785\pi$
$464$	−25.7750	+	1.53465i	−1.19657	+	0.0712445i
$465$	8.84602			0.410224
$466$	24.5056	+	9.72627i	1.13520	+	0.450561i
$467$		−	21.9652i		−	1.01643i	−0.861231	−	0.508213i	$-0.830306\pi$
$467$		−	21.9652i		−	1.01643i	0.861231	−	0.508213i	$-0.169694\pi$
$468$	−1.75207	+	1.85949i	−0.0809894	+	0.0859550i
$469$			11.1714i			0.515849i
$470$	3.55546	−	8.95807i	0.164001	−	0.413205i
$471$	23.0842			1.06366
$472$	6.41761	+	13.7278i	0.295394	+	0.631875i
$473$	20.4911			0.942181
$474$	−26.7245	−	10.6069i	−1.22749	−	0.487193i
$475$	1.23206	+	4.18115i	0.0565306	+	0.191844i
$476$	−7.38164	+	7.83422i	−0.338337	+	0.359081i
$477$			9.27990i			0.424898i
$478$	3.91028	−	9.85203i	0.178852	−	0.450622i
$479$			18.2719i			0.834865i	0.908708	+	0.417433i	$0.137070\pi$
$479$			18.2719i			0.834865i	−0.908708	+	0.417433i	$0.862930\pi$
$480$	3.82211	−	11.5972i	0.174455	−	0.529338i
$481$	−4.11462			−0.187611
$482$	−2.54488	+	6.41188i	−0.115916	+	0.292053i
$483$	−10.9809			−0.499649
$484$	11.4209	+	10.7611i	0.519133	+	0.489143i
$485$			0.676382i			0.0307129i
$486$	−20.4379	−	8.11180i	−0.927081	−	0.367959i
$487$	8.12733			0.368285			0.184142	−	0.982900i	$-0.441049\pi$
$487$	8.12733			0.368285			0.184142	+	0.982900i	$0.441049\pi$
$488$	5.92629	+	12.6769i	0.268271	+	0.573855i
$489$		−	17.7325i		−	0.801892i
$490$	5.57200	+	2.21153i	0.251717	+	0.0999067i
$491$			28.5523i			1.28855i	0.764796	+	0.644273i	$0.222840\pi$
$491$			28.5523i			1.28855i	−0.764796	+	0.644273i	$0.777160\pi$
$492$	11.3495	−	12.0454i	0.511677	−	0.543049i
$493$		−	20.9082i		−	0.941656i
$494$	4.72547	+	0.432508i	0.212609	+	0.0194594i
$495$			2.94719i			0.132466i
$496$	0.974276	+	16.3632i	0.0437463	+	0.734732i
$497$		−	3.04680i		−	0.136668i
$498$	−8.42436	+	21.2254i	−0.377505	+	0.951132i
$499$			11.8878i			0.532172i	0.963949	+	0.266086i	$0.0857305\pi$
$499$			11.8878i			0.532172i	−0.963949	+	0.266086i	$0.914269\pi$
$500$	−1.45563	−	1.37154i	−0.0650979	−	0.0613373i
$501$	5.05247			0.225728
$502$	9.06296	−	22.8343i	0.404500	−	1.01915i
$503$			13.7172i			0.611619i	0.952093	+	0.305809i	$0.0989270\pi$
$503$			13.7172i			0.611619i	−0.952093	+	0.305809i	$0.901073\pi$
$504$	−7.06539	+	3.30299i	−0.314717	+	0.147127i
$505$	2.57949			0.114786
$506$	−7.14683	−	2.83658i	−0.317715	−	0.126101i
$507$	−26.7826			−1.18946
$508$	23.1905	+	21.8508i	1.02891	+	0.969471i
$509$			9.78264i			0.433608i	0.976215	+	0.216804i	$0.0695632\pi$
$509$			9.78264i			0.433608i	−0.976215	+	0.216804i	$0.930437\pi$
$510$	9.19026	+	3.64762i	0.406952	+	0.161519i
$511$		−	19.8284i		−	0.877156i
$512$	21.8733	+	5.79281i	0.966675	+	0.256009i
$513$	3.56506	+	12.0985i	0.157401	+	0.534163i
$514$	12.8061	−	32.2653i	0.564853	−	1.42316i
$515$	−7.51628			−0.331207
$516$	34.1597	−	36.2541i	1.50380	−	1.59600i
$517$	−12.1031			−0.532292
$518$	−11.6748	−	4.63372i	−0.512960	−	0.203594i
$519$		−	8.89837i		−	0.390595i
$520$	−1.97237	+	0.922061i	−0.0864942	+	0.0404350i
$521$			34.7472i			1.52230i	0.648575	+	0.761150i	$0.275365\pi$
$521$			34.7472i			1.52230i	−0.648575	+	0.761150i	$0.724635\pi$
$522$	5.58875	−	14.0810i	0.244613	−	0.616308i
$523$	−15.1384			−0.661957			−0.330978	−	0.943638i	$-0.607379\pi$
$523$	−15.1384			−0.661957			−0.330978	+	0.943638i	$0.607379\pi$
$524$	6.21778	−	6.59900i	0.271625	−	0.288279i
$525$			3.58677i			0.156540i
$526$	−14.9836	+	37.7514i	−0.653314	+	1.64604i
$527$	−13.2736			−0.578205
$528$	−15.3070	+	0.911389i	−0.666153	+	0.0396631i
$529$	13.6272			0.592487
$530$	−2.91740	+	7.35046i	−0.126724	+	0.319284i
$531$	−8.89110			−0.385841
$532$	12.9209	+	6.54882i	0.560192	+	0.283928i
$533$	−2.95096			−0.127820
$534$	18.0367	−	45.4438i	0.780523	−	1.96655i
$535$	−1.32842			−0.0574326
$536$	8.05323	+	17.2266i	0.347847	+	0.744075i
$537$	2.51995			0.108744
$538$	10.5289	−	26.5278i	0.453934	−	1.14370i
$539$		−	7.52821i		−	0.324263i
$540$	−4.21200	−	3.96867i	−0.181256	−	0.170785i
$541$	−0.101510			−0.00436427			−0.00218214	−	0.999998i	$-0.500695\pi$
$541$	−0.101510			−0.00436427			−0.00218214	+	0.999998i	$0.500695\pi$
$542$	0.494795	−	1.24665i	0.0212533	−	0.0535481i
$543$			48.6391i			2.08730i
$544$	−5.73513	+	17.4018i	−0.245892	+	0.746095i
$545$			2.43483i			0.104297i
$546$	3.62925	+	1.44045i	0.155318	+	0.0616456i
$547$	4.87194			0.208309			0.104155	−	0.994561i	$-0.466786\pi$
$547$	4.87194			0.208309			0.104155	+	0.994561i	$0.466786\pi$
$548$	−28.3268	−	26.6904i	−1.21006	−	1.14016i
$549$	−8.21043			−0.350412
$550$	−0.926532	+	2.33442i	−0.0395074	+	0.0995399i
$551$	−26.9900	+	7.95311i	−1.14981	+	0.338814i
$552$	−16.9328	+	7.91588i	−0.720707	+	0.336922i
$553$			15.6504i			0.665521i
$554$	−22.7824	−	9.04236i	−0.967934	−	0.384173i
$555$			11.5381i			0.489766i
$556$	−10.6388	+	11.2911i	−0.451188	+	0.478851i
$557$	19.9620			0.845817			0.422908	−	0.906172i	$-0.361009\pi$
$557$	19.9620			0.845817			0.422908	+	0.906172i	$0.361009\pi$
$558$	−8.93932	−	3.54802i	−0.378432	−	0.150200i
$559$	−8.88177			−0.375659
$560$	−6.63477	+	0.395037i	−0.280370	+	0.0166934i
$561$		−	12.4168i		−	0.524237i
$562$	7.06152	−	17.7917i	0.297872	−	0.750497i
$563$	16.6366			0.701150			0.350575	−	0.936535i	$-0.385986\pi$
$563$	16.6366			0.701150			0.350575	+	0.936535i	$0.385986\pi$
$564$	−20.1764	+	21.4135i	−0.849581	+	0.901670i
$565$		−	17.9154i		−	0.753705i
$566$	−3.67474	+	9.25860i	−0.154461	+	0.389168i
$567$			18.6511i			0.783271i
$568$	−2.19636	−	4.69822i	−0.0921574	−	0.197133i
$569$		−	20.8399i		−	0.873654i	−0.899546	−	0.436827i	$-0.856102\pi$
$569$		−	20.8399i		−	0.873654i	0.899546	−	0.436827i	$-0.143898\pi$
$570$	1.21283	−	13.2510i	0.0507998	−	0.555025i
$571$		−	14.0220i		−	0.586801i	−0.955990	−	0.293400i	$-0.905213\pi$
$571$		−	14.0220i		−	0.586801i	0.955990	−	0.293400i	$-0.0947869\pi$
$572$	1.98997	+	1.87501i	0.0832048	+	0.0783981i
$573$		−	44.3221i		−	1.85158i
$574$	−8.37303	−	3.32326i	−0.349483	−	0.138710i
$575$			3.06150i			0.127673i
$576$	−8.51392	+	10.1865i	−0.354747	+	0.424439i
$577$	−28.0430			−1.16745			−0.583723	−	0.811953i	$-0.698405\pi$
$577$	−28.0430			−1.16745			−0.583723	+	0.811953i	$0.698405\pi$
$578$	8.55579	+	3.39580i	0.355874	+	0.141247i
$579$		−	17.3480i		−	0.720956i
$580$	8.85352	−	9.39634i	0.367622	−	0.390162i
$581$	12.4300			0.515683
$582$	0.761715	−	1.91916i	0.0315741	−	0.0795517i
$583$	9.93106			0.411302
$584$	−14.2938	−	30.5758i	−0.591482	−	1.26523i
$585$		−	1.27744i		−	0.0528158i
$586$	−4.87958	+	12.2942i	−0.201573	+	0.507869i
$587$			29.7491i			1.22788i	0.789353	+	0.613939i	$0.210416\pi$
$587$			29.7491i			1.22788i	−0.789353	+	0.613939i	$0.789584\pi$
$588$	−13.3194	−	12.5499i	−0.549282	−	0.517550i
$589$	5.04904	+	17.1346i	0.208042	+	0.706019i
$590$	−7.04250	−	2.79517i	−0.289935	−	0.115075i
$591$	−20.5649			−0.845927
$592$	−21.3431	+	1.27078i	−0.877195	+	0.0522286i
$593$	−11.3271			−0.465149			−0.232575	−	0.972579i	$-0.574715\pi$
$593$	−11.3271			−0.465149			−0.232575	+	0.972579i	$0.574715\pi$
$594$	−2.68100	+	6.75484i	−0.110003	+	0.277154i
$595$		−	5.38200i		−	0.220640i
$596$	31.6623	+	29.8332i	1.29694	+	1.22202i
$597$		−	15.0874i		−	0.617485i
$598$	3.09776	+	1.22950i	0.126677	+	0.0502781i
$599$	−18.8758			−0.771244			−0.385622	−	0.922657i	$-0.626013\pi$
$599$	−18.8758			−0.771244			−0.385622	+	0.922657i	$0.626013\pi$
$600$	2.58562	+	5.53087i	0.105558	+	0.225797i
$601$		−	37.4036i		−	1.52573i	−0.646560	−	0.762863i	$-0.723793\pi$
$601$		−	37.4036i		−	1.52573i	0.646560	−	0.762863i	$-0.276207\pi$
$602$	−25.2010	−	10.0023i	−1.02712	−	0.407663i
$603$	−11.1571			−0.454354
$604$	−20.3133	−	19.1399i	−0.826538	−	0.778789i
$605$	−7.84602			−0.318986
$606$	−7.31900	−	2.90492i	−0.297314	−	0.118004i
$607$	29.0143			1.17765			0.588826	−	0.808260i	$-0.299590\pi$
$607$	29.0143			1.17765			0.588826	+	0.808260i	$0.299590\pi$
$608$	24.6452	+	0.784040i	0.999494	+	0.0317970i
$609$	−23.1532			−0.938213
$610$	−6.50335	−	2.58118i	−0.263313	−	0.104509i
$611$	5.24602			0.212231
$612$	−7.82419	−	7.37219i	−0.316274	−	0.298003i
$613$	13.4421			0.542919			0.271460	−	0.962450i	$-0.412494\pi$
$613$	13.4421			0.542919			0.271460	+	0.962450i	$0.412494\pi$
$614$	7.40690	+	2.93980i	0.298918	+	0.118641i
$615$			8.27502i			0.333681i
$616$	3.53475	+	7.56115i	0.142419	+	0.304648i
$617$	46.9822			1.89143			0.945716	−	0.324995i	$-0.105363\pi$
$617$	46.9822			1.89143			0.945716	+	0.324995i	$0.105363\pi$
$618$	21.3266	+	8.46454i	0.857882	+	0.340494i
$619$			13.2142i			0.531125i	0.964094	+	0.265563i	$0.0855577\pi$
$619$			13.2142i			0.531125i	−0.964094	+	0.265563i	$0.914442\pi$
$620$	−5.96527	−	5.62066i	−0.239571	−	0.225731i
$621$			8.85871i			0.355488i
$622$	−7.20195	+	18.1455i	−0.288772	+	0.727567i
$623$	−26.6128			−1.06622
$624$	6.63477	−	0.395037i	0.265603	−	0.0158142i
$625$	1.00000			0.0400000
$626$	22.8218	+	9.05798i	0.912142	+	0.362030i
$627$	−16.0286	+	4.72313i	−0.640121	+	0.188624i
$628$	−15.5667	−	14.6674i	−0.621179	−	0.585294i
$629$		−	17.3131i		−	0.690319i
$630$	1.43861	−	3.62460i	0.0573155	−	0.144408i
$631$		−	28.5124i		−	1.13506i	−0.823352	−	0.567530i	$-0.807899\pi$
$631$		−	28.5124i		−	1.13506i	0.823352	−	0.567530i	$-0.192101\pi$
$632$	11.2820	+	24.1332i	0.448773	+	0.959966i
$633$	38.7371			1.53966
$634$	−4.21165	+	10.6113i	−0.167266	+	0.421430i
$635$	−15.9315			−0.632223
$636$	16.5556	−	17.5706i	0.656472	−	0.696721i
$637$			3.26307i			0.129288i
$638$	−15.0690	−	5.98090i	−0.596588	−	0.236786i
$639$	3.04290			0.120375
$640$	−9.94617	+	5.39200i	−0.393157	+	0.213138i
$641$		−	6.69678i		−	0.264507i	−0.991216	−	0.132253i	$-0.957779\pi$
$641$		−	6.69678i		−	0.264507i	0.991216	−	0.132253i	$-0.0422213\pi$
$642$	3.76924	+	1.49601i	0.148760	+	0.0590430i
$643$		−	6.10252i		−	0.240660i	−0.992734	−	0.120330i	$-0.961605\pi$
$643$		−	6.10252i		−	0.240660i	0.992734	−	0.120330i	$-0.0383953\pi$
$644$	7.40493	+	6.97715i	0.291795	+	0.274938i
$645$			24.9061i			0.980675i
$646$	−1.81986	+	19.8834i	−0.0716016	+	0.782300i
$647$		−	46.2880i		−	1.81977i	−0.414860	−	0.909885i	$-0.636169\pi$
$647$		−	46.2880i		−	1.81977i	0.414860	−	0.909885i	$-0.363831\pi$
$648$	13.4451	+	28.7603i	0.528174	+	1.12981i
$649$			9.51498i			0.373496i
$650$	0.401601	−	1.01184i	0.0157521	−	0.0396878i
$651$			14.6988i			0.576091i
$652$	−11.2670	+	11.9578i	−0.441251	+	0.468305i
$653$	−17.4421			−0.682560			−0.341280	−	0.939962i	$-0.610860\pi$
$653$	−17.4421			−0.682560			−0.341280	+	0.939962i	$0.610860\pi$
$654$	2.74201	−	6.90855i	0.107221	−	0.270146i
$655$			4.53342i			0.177135i
$656$	−15.3070	+	0.911389i	−0.597639	+	0.0355838i
$657$	19.8030			0.772588
$658$	14.8850	+	5.90786i	0.580277	+	0.230312i
$659$	3.47777			0.135475			0.0677373	−	0.997703i	$-0.478422\pi$
$659$	3.47777			0.135475			0.0677373	+	0.997703i	$0.478422\pi$
$660$	5.25786	−	5.58023i	0.204662	−	0.217210i
$661$		−	32.9565i		−	1.28186i	−0.767600	−	0.640930i	$-0.778549\pi$
$661$		−	32.9565i		−	1.28186i	0.767600	−	0.640930i	$-0.221451\pi$
$662$	47.1283	+	18.7053i	1.83170	+	0.727001i
$663$			5.38200i			0.209019i
$664$	19.1673	−	8.96049i	0.743836	−	0.347735i
$665$	−6.94753	+	2.04722i	−0.269413	+	0.0793878i
$666$	4.62779	−	11.6598i	0.179323	−	0.451809i
$667$	−19.7625			−0.765206
$668$	−3.40711	−	3.21029i	−0.131825	−	0.124210i
$669$	54.2476			2.09734
$670$	−8.83739	−	3.50756i	−0.341418	−	0.135509i
$671$			8.78654i			0.339201i
$672$	19.2703	+	6.35094i	0.743367	+	0.244993i
$673$		−	30.4788i		−	1.17487i	−0.809271	−	0.587435i	$-0.800138\pi$
$673$		−	30.4788i		−	1.17487i	0.809271	−	0.587435i	$-0.199862\pi$
$674$	17.7024	−	44.6017i	0.681872	−	1.71799i
$675$	2.89358			0.111374
$676$	18.0607	+	17.0173i	0.694642	+	0.654513i
$677$			21.1145i			0.811497i	0.913985	+	0.405749i	$0.132989\pi$
$677$			21.1145i			0.811497i	−0.913985	+	0.405749i	$0.867011\pi$
$678$	−20.1756	+	50.8328i	−0.774838	+	1.95222i
$679$	−1.12390			−0.0431312
$680$	−3.87976	−	8.29915i	−0.148782	−	0.318258i
$681$	−31.8316			−1.21979
$682$	−3.79698	+	9.56658i	−0.145394	+	0.366323i
$683$	12.4356			0.475837			0.237918	−	0.971285i	$-0.423535\pi$
$683$	12.4356			0.475837			0.237918	+	0.971285i	$0.423535\pi$
$684$	−6.54044	+	12.9044i	−0.250080	+	0.493411i
$685$	19.4601			0.743533
$686$	−9.74298	+	24.5477i	−0.371989	+	0.937234i
$687$	40.9282			1.56151
$688$	−46.0709	+	2.74309i	−1.75644	+	0.104579i
$689$	−4.30457			−0.163991
$690$	3.44774	−	8.68667i	0.131253	−	0.330696i
$691$		−	2.47203i		−	0.0940404i	−0.998894	−	0.0470202i	$-0.985027\pi$
$691$		−	2.47203i		−	0.0940404i	0.998894	−	0.0470202i	$-0.0149725\pi$
$692$	−5.65392	+	6.00058i	−0.214930	+	0.228108i
$693$	−4.89713			−0.186027
$694$	9.77163	−	24.6198i	0.370926	−	0.934556i
$695$		−	7.75685i		−	0.294234i
$696$	−35.7026	+	16.6906i	−1.35330	+	0.632655i
$697$		−	12.4168i		−	0.470319i
$698$	−5.53128	−	2.19537i	−0.209362	−	0.0830959i
$699$	40.2425			1.52211
$700$	2.27900	−	2.41872i	0.0861379	−	0.0914192i
$701$	20.4326			0.771727			0.385864	−	0.922556i	$-0.373903\pi$
$701$	20.4326			0.771727			0.385864	+	0.922556i	$0.373903\pi$
$702$	1.16207	−	2.92785i	0.0438594	−	0.110505i
$703$	−22.3492	+	6.58561i	−0.842915	+	0.248381i
$704$	10.9013	+	9.11133i	0.410859	+	0.343396i
$705$		−	14.7108i		−	0.554039i
$706$	28.2900	+	11.2283i	1.06471	+	0.422583i
$707$			4.28615i			0.161197i
$708$	16.8345	+	15.8620i	0.632679	+	0.596129i
$709$	−29.1721			−1.09558			−0.547790	−	0.836616i	$-0.684531\pi$
$709$	−29.1721			−1.09558			−0.547790	+	0.836616i	$0.684531\pi$
$710$	2.41023	+	0.956621i	0.0904543	+	0.0359013i
$711$	−15.6303			−0.586183
$712$	−41.0374	+	19.1845i	−1.53794	+	0.718971i
$713$			12.5462i			0.469859i
$714$	−6.06099	+	15.2708i	−0.226827	+	0.571496i
$715$	−1.36708			−0.0511259
$716$	−1.69931	−	1.60115i	−0.0635063	−	0.0598376i
$717$		−	16.1788i		−	0.604209i
$718$	−8.99224	+	22.6562i	−0.335587	+	0.845520i
$719$			17.2158i			0.642039i	0.947073	+	0.321020i	$0.104026\pi$
$719$			17.2158i			0.642039i	−0.947073	+	0.321020i	$0.895974\pi$
$720$	−0.394532	−	6.62627i	−0.0147033	−	0.246947i
$721$		−	12.4893i		−	0.465125i
$722$	26.3593	−	5.21406i	0.980992	−	0.194047i
$723$			10.5295i			0.391595i
$724$	30.9047	−	32.7995i	1.14857	−	1.21899i
$725$			6.45515i			0.239738i
$726$	22.2622	+	8.83587i	0.826227	+	0.327930i
$727$		−	31.6614i		−	1.17426i	−0.809494	−	0.587128i	$-0.800259\pi$
$727$		−	31.6614i		−	1.17426i	0.809494	−	0.587128i	$-0.199741\pi$
$728$	−1.53212	−	3.27735i	−0.0567842	−	0.121467i
$729$	0.110993			0.00411086
$730$	15.6856	+	6.22563i	0.580551	+	0.230421i
$731$		−	37.3718i		−	1.38225i
$732$	15.5457	+	14.6476i	0.574585	+	0.541392i
$733$	−25.0202			−0.924141			−0.462071	−	0.886843i	$-0.652893\pi$
$733$	−25.0202			−0.924141			−0.462071	+	0.886843i	$0.652893\pi$
$734$	−19.8376	+	49.9814i	−0.732221	+	1.84485i
$735$	9.15023			0.337511
$736$	16.4482	+	5.42086i	0.606289	+	0.199816i
$737$			11.9400i			0.439816i
$738$	3.31900	−	8.36231i	0.122174	−	0.307821i
$739$		−	46.5491i		−	1.71233i	−0.516699	−	0.856167i	$-0.672839\pi$
$739$		−	46.5491i		−	1.71233i	0.516699	−	0.856167i	$-0.327161\pi$
$740$	7.33120	−	7.78068i	0.269500	−	0.286024i
$741$	6.94753	−	2.04722i	0.255224	−	0.0752065i
$742$	−12.2137	−	4.84764i	−0.448381	−	0.177962i
$743$	−6.64028			−0.243608			−0.121804	−	0.992554i	$-0.538868\pi$
$743$	−6.64028			−0.243608			−0.121804	+	0.992554i	$0.538868\pi$
$744$	10.5960	+	22.6658i	0.388469	+	0.830970i
$745$	−21.7516			−0.796916
$746$	−15.1131	+	38.0779i	−0.553332	+	1.39413i
$747$			12.4141i			0.454207i
$748$	−7.88948	+	8.37320i	−0.288468	+	0.306154i
$749$		−	2.20734i		−	0.0806545i
$750$	−2.83739	−	1.12616i	−0.103607	−	0.0411216i
$751$	35.0039			1.27731			0.638656	−	0.769492i	$-0.279491\pi$
$751$	35.0039			1.27731			0.638656	+	0.769492i	$0.279491\pi$
$752$	27.2118	−	1.62020i	0.992312	−	0.0590827i
$753$		−	37.4981i		−	1.36651i
$754$	6.53160	+	2.59240i	0.237867	+	0.0944095i
$755$	13.9550			0.507874
$756$	6.59446	−	6.99878i	0.239838	−	0.254543i
$757$	−38.3062			−1.39226			−0.696131	−	0.717915i	$-0.745097\pi$
$757$	−38.3062			−1.39226			−0.696131	+	0.717915i	$0.745097\pi$
$758$	−47.6441	−	18.9100i	−1.73051	−	0.686842i
$759$	−11.7364			−0.426004
$760$	−9.23743	+	8.16516i	−0.335077	+	0.296182i
$761$	13.7624			0.498886			0.249443	−	0.968390i	$-0.419753\pi$
$761$	13.7624			0.498886			0.249443	+	0.968390i	$0.419753\pi$
$762$	45.2039	+	17.9414i	1.63756	+	0.649950i
$763$	−4.04578			−0.146467
$764$	−28.1618	+	29.8884i	−1.01886	+	1.08133i
$765$	5.37511			0.194337
$766$	−37.6175	−	14.9304i	−1.35917	−	0.539457i
$767$		−	4.12423i		−	0.148917i
$768$	34.2934	−	4.09822i	1.23746	−	0.147882i
$769$	−15.8867			−0.572888			−0.286444	−	0.958097i	$-0.592473\pi$
$769$	−15.8867			−0.572888			−0.286444	+	0.958097i	$0.592473\pi$
$770$	−3.87894	−	1.53955i	−0.139787	−	0.0554816i
$771$		−	52.9854i		−	1.90822i
$772$	−11.0227	+	11.6985i	−0.396716	+	0.421039i
$773$		−	48.1094i		−	1.73037i	−0.501449	−	0.865187i	$-0.667199\pi$
$773$		−	48.1094i		−	1.73037i	0.501449	−	0.865187i	$-0.332801\pi$
$774$	9.98949	−	25.1688i	0.359065	−	0.904672i
$775$	4.09806			0.147207
$776$	−1.73307	+	0.810191i	−0.0622136	+	0.0290842i
$777$	−19.1721			−0.687795
$778$	19.3042	+	7.66185i	0.692089	+	0.274691i
$779$	−16.0286	+	4.72313i	−0.574284	+	0.169224i
$780$	−2.27900	+	2.41872i	−0.0816011	+	0.0866042i
$781$		−	3.25641i		−	0.116524i
$782$	−5.17338	+	13.0345i	−0.185000	+	0.466111i
$783$			18.6785i			0.667516i
$784$	1.00778	+	16.9260i	0.0359922	+	0.604499i
$785$	10.6941			0.381689
$786$	5.10536	−	12.8631i	0.182102	−	0.458811i
$787$	42.6101			1.51889			0.759444	−	0.650573i	$-0.225471\pi$
$787$	42.6101			1.51889			0.759444	+	0.650573i	$0.225471\pi$
$788$	13.8678	+	13.0667i	0.494021	+	0.465482i
$789$			61.9946i			2.20707i
$790$	−12.3805	−	4.91384i	−0.440479	−	0.174826i
$791$	29.7687			1.05845
$792$	−7.55147	+	3.53023i	−0.268330	+	0.125441i
$793$		−	3.80849i		−	0.135243i
$794$	14.4012	+	5.71585i	0.511080	+	0.202848i
$795$			12.0708i			0.428107i
$796$	−9.58635	+	10.1741i	−0.339779	+	0.360612i
$797$		−	44.6109i		−	1.58020i	−0.612979	−	0.790099i	$-0.710029\pi$
$797$		−	44.6109i		−	1.58020i	0.612979	−	0.790099i	$-0.289971\pi$
$798$	22.0183	+	2.01527i	0.779440	+	0.0713398i
$799$			22.0737i			0.780911i
$800$	1.77065	−	5.37260i	0.0626021	−	0.189950i
$801$		−	26.5787i		−	0.939112i
$802$	18.2205	−	45.9070i	0.643388	−	1.62103i
$803$		−	21.1925i		−	0.747868i
$804$	21.1250	+	19.9046i	0.745022	+	0.701982i
$805$	−5.08708			−0.179296
$806$	1.64578	−	4.14659i	0.0579703	−	0.146057i
$807$		−	43.5635i		−	1.53351i
$808$	3.08979	+	6.60933i	0.108698	+	0.232515i
$809$	−31.0971			−1.09331			−0.546657	−	0.837357i	$-0.684100\pi$
$809$	−31.0971			−1.09331			−0.546657	+	0.837357i	$0.684100\pi$
$810$	−14.7543	−	5.85598i	−0.518413	−	0.205758i
$811$	−8.88630			−0.312040			−0.156020	−	0.987754i	$-0.549866\pi$
$811$	−8.88630			−0.312040			−0.156020	+	0.987754i	$0.549866\pi$
$812$	15.6132	+	14.7113i	0.547917	+	0.516264i
$813$		−	2.04722i		−	0.0717992i
$814$	−12.4780	−	4.95251i	−0.437353	−	0.173586i
$815$		−	8.21487i		−	0.287754i
$816$	1.66220	+	27.9171i	0.0581886	+	0.977295i
$817$	−48.2427	+	14.2156i	−1.68780	+	0.497341i
$818$	−1.18373	+	2.98243i	−0.0413881	+	0.104278i
$819$	2.12264			0.0741710
$820$	5.25786	−	5.58023i	0.183612	−	0.194870i
$821$	38.8722			1.35665			0.678325	−	0.734762i	$-0.262706\pi$
$821$	38.8722			1.35665			0.678325	+	0.734762i	$0.262706\pi$
$822$	−55.2159	−	21.9152i	−1.92587	−	0.764380i
$823$		−	7.15869i		−	0.249536i	−0.992186	−	0.124768i	$-0.960181\pi$
$823$		−	7.15869i		−	0.249536i	0.992186	−	0.124768i	$-0.0398187\pi$
$824$	−9.00323	−	19.2587i	−0.313642	−	0.670909i
$825$			3.83354i			0.133467i
$826$	4.64454	−	11.7020i	0.161604	−	0.407166i
$827$	−44.3377			−1.54177			−0.770886	−	0.636973i	$-0.780186\pi$
$827$	−44.3377			−1.54177			−0.770886	+	0.636973i	$0.780186\pi$
$828$	−6.96821	+	7.39545i	−0.242162	+	0.257010i
$829$			54.3640i			1.88814i	0.329744	+	0.944071i	$0.393038\pi$
$829$			54.3640i			1.88814i	−0.329744	+	0.944071i	$0.606962\pi$
$830$	−3.90272	+	9.83299i	−0.135465	+	0.341308i
$831$	−37.4129			−1.29784
$832$	−4.72513	−	3.94927i	−0.163814	−	0.136916i
$833$	−13.7300			−0.475717
$834$	−8.73545	+	22.0092i	−0.302484	+	0.762116i
$835$	2.34064			0.0810011
$836$	13.8098	+	6.99937i	0.477623	+	0.242078i
$837$	11.8581			0.409875
$838$	2.09202	−	5.27088i	0.0722675	−	0.182080i
$839$	27.8039			0.959896			0.479948	−	0.877297i	$-0.340656\pi$
$839$	27.8039			0.959896			0.479948	+	0.877297i	$0.340656\pi$
$840$	−9.19026	+	4.29634i	−0.317094	+	0.148238i
$841$	−12.6690			−0.436862
$842$	−14.1427	+	35.6328i	−0.487389	+	1.22799i
$843$		−	29.2171i		−	1.00629i
$844$	−26.1222	−	24.6132i	−0.899164	−	0.847220i
$845$	−12.4074			−0.426829
$846$	−5.90029	+	14.8659i	−0.202856	+	0.511101i
$847$		−	13.0372i		−	0.447962i
$848$	−22.3284	+	1.32944i	−0.766760	+	0.0456533i
$849$			15.2043i			0.521810i
$850$	4.25754	+	1.68982i	0.146032	+	0.0579603i
$851$	−16.3644			−0.560964
$852$	−5.76144	−	5.42861i	−0.197384	−	0.185981i
$853$	28.4880			0.975409			0.487704	−	0.873009i	$-0.337834\pi$
$853$	28.4880			0.975409			0.487704	+	0.873009i	$0.337834\pi$
$854$	4.28897	−	10.8062i	0.146765	−	0.369779i
$855$	−2.04460	−	6.93863i	−0.0699238	−	0.237296i
$856$	−1.59122	−	3.40376i	−0.0543868	−	0.116338i
$857$		−	40.9485i		−	1.39877i	−0.714744	−	0.699386i	$-0.753457\pi$
$857$		−	40.9485i		−	1.39877i	0.714744	−	0.699386i	$-0.246543\pi$
$858$	3.87894	+	1.53955i	0.132425	+	0.0525594i
$859$		−	35.8112i		−	1.22186i	−0.791683	−	0.610932i	$-0.790795\pi$
$859$		−	35.8112i		−	1.22186i	0.791683	−	0.610932i	$-0.209205\pi$
$860$	15.8250	−	16.7953i	0.539629	−	0.572715i
$861$	−13.7500			−0.468599
$862$	−36.2964	−	14.4060i	−1.23626	−	0.490672i
$863$	−11.3664			−0.386918			−0.193459	−	0.981108i	$-0.561971\pi$
$863$	−11.3664			−0.386918			−0.193459	+	0.981108i	$0.561971\pi$
$864$	5.12354	−	15.5461i	0.174306	−	0.528888i
$865$		−	4.12231i		−	0.140163i
$866$	13.6058	−	34.2802i	0.462345	−	1.16489i
$867$	14.0502			0.477168
$868$	9.33945	−	9.91207i	0.317002	−	0.336438i
$869$			16.7271i			0.567427i
$870$	7.26954	−	18.3158i	0.246460	−	0.620963i
$871$		−	5.17535i		−	0.175360i
$872$	−6.23868	+	2.91651i	−0.211268	+	0.0987655i
$873$		−	1.12246i		−	0.0379894i
$874$	18.7938	+	1.72014i	0.635710	+	0.0581846i
$875$			1.66163i			0.0561733i
$876$	−37.4951	−	35.3291i	−1.26684	−	1.19366i
$877$			0.163580i			0.00552371i	0.999996	+	0.00276186i	$0.000879127\pi$
$877$			0.163580i			0.00552371i	−0.999996	+	0.00276186i	$0.999121\pi$
$878$	−7.43455	−	2.95078i	−0.250904	−	0.0995839i
$879$			20.1893i			0.680969i
$880$	−7.09123	+	0.422215i	−0.239045	+	0.0142329i
$881$	−9.30245			−0.313408			−0.156704	−	0.987646i	$-0.550087\pi$
$881$	−9.30245			−0.313408			−0.156704	+	0.987646i	$0.550087\pi$
$882$	−9.24674	−	3.67004i	−0.311354	−	0.123577i
$883$			31.0359i			1.04444i	0.852810	+	0.522221i	$0.174896\pi$
$883$			31.0359i			1.04444i	−0.852810	+	0.522221i	$0.825104\pi$
$884$	3.41966	−	3.62933i	0.115016	−	0.122067i
$885$	−11.5651			−0.388755
$886$	−1.84238	+	4.64191i	−0.0618959	+	0.155948i
$887$	42.0820			1.41297			0.706487	−	0.707726i	$-0.250279\pi$
$887$	42.0820			1.41297			0.706487	+	0.707726i	$0.250279\pi$
$888$	−29.5637	+	13.8207i	−0.992094	+	0.463793i
$889$		−	26.4723i		−	0.887852i
$890$	8.35577	−	21.0526i	0.280086	−	0.705683i
$891$			19.9342i			0.667821i
$892$	−36.5817	−	34.4684i	−1.22484	−	1.15409i
$893$	28.4945	−	8.39645i	0.953533	−	0.280977i
$894$	61.7176	+	24.4958i	2.06415	+	0.819261i
$895$	1.16740			0.0390220
$896$	−8.95951	−	16.5268i	−0.299316	−	0.552123i
$897$	5.08708			0.169853
$898$	11.0324	−	27.7965i	0.368157	−	0.927581i
$899$			26.4536i			0.882276i
$900$	2.41563	+	2.27608i	0.0805209	+	0.0758692i
$901$		−	18.1124i		−	0.603410i
$902$	−8.94908	−	3.55189i	−0.297972	−	0.118265i
$903$	−41.3846			−1.37719
$904$	45.9039	−	21.4596i	1.52674	−	0.713734i
$905$			22.5328i			0.749016i
$906$	−39.5957	−	15.7155i	−1.31548	−	0.522114i
$907$	−3.59980			−0.119530			−0.0597648	−	0.998212i	$-0.519035\pi$
$907$	−3.59980			−0.119530			−0.0597648	+	0.998212i	$0.519035\pi$
$908$	21.4655	+	20.2254i	0.712357	+	0.671205i
$909$	−4.28066			−0.141981
$910$	1.68131	+	0.667312i	0.0557348	+	0.0221212i
$911$	−39.5505			−1.31037			−0.655184	−	0.755469i	$-0.727409\pi$
$911$	−39.5505			−1.31037			−0.655184	+	0.755469i	$0.727409\pi$
$912$	35.4054	−	12.7649i	1.17239	−	0.422688i
$913$	13.2852			0.439674
$914$	−40.7315	−	16.1663i	−1.34728	−	0.534735i
$915$	−10.6797			−0.353059
$916$	−27.5997	−	26.0053i	−0.911921	−	0.859240i
$917$	−7.53287			−0.248757
$918$	12.3195	+	4.88963i	0.406605	+	0.161382i
$919$			39.0368i			1.28771i	0.765149	+	0.643853i	$0.222665\pi$
$919$			39.0368i			1.28771i	−0.765149	+	0.643853i	$0.777335\pi$
$920$	−7.84438	+	3.66716i	−0.258622	+	0.120903i
$921$	12.1635			0.400800
$922$	2.42925	+	0.964172i	0.0800032	+	0.0317533i
$923$			1.41148i			0.0464593i
$924$	9.27227	+	8.73661i	0.305035	+	0.287413i
$925$			5.34522i			0.175750i
$926$	11.7440	−	29.5892i	0.385931	−	0.972362i
$927$	12.4733			0.409676
$928$	34.6809	+	11.4298i	1.13846	+	0.375203i
$929$	55.1653			1.80991			0.904957	−	0.425504i	$-0.139903\pi$
$929$	55.1653			1.80991			0.904957	+	0.425504i	$0.139903\pi$
$930$	−11.6278	−	4.61507i	−0.381290	−	0.151334i
$931$	5.22267	+	17.7239i	0.171166	+	0.580876i
$932$	−27.1374	−	25.5697i	−0.888914	−	0.837562i
$933$			29.7981i			0.975547i
$934$	−11.4595	+	28.8724i	−0.374966	+	0.944735i
$935$		−	5.75227i		−	0.188119i
$936$	3.27315	−	1.53016i	0.106986	−	0.0500149i
$937$	3.90000			0.127407			0.0637037	−	0.997969i	$-0.479709\pi$
$937$	3.90000			0.127407			0.0637037	+	0.997969i	$0.479709\pi$
$938$	5.82827	−	14.6845i	0.190300	−	0.479465i
$939$	37.4775			1.22303
$940$	−9.34705	+	9.92014i	−0.304867	+	0.323559i
$941$			12.3135i			0.401408i	0.979652	+	0.200704i	$0.0643229\pi$
$941$			12.3135i			0.401408i	−0.979652	+	0.200704i	$0.935677\pi$
$942$	−30.3433	−	12.0433i	−0.988639	−	0.392391i
$943$	−11.7364			−0.382189
$944$	−1.27374	−	21.3929i	−0.0414568	−	0.696280i
$945$			4.80806i			0.156406i
$946$	−26.9348	−	10.6904i	−0.875726	−	0.347576i
$947$			8.23515i			0.267607i	0.991008	+	0.133803i	$0.0427190\pi$
$947$			8.23515i			0.267607i	−0.991008	+	0.133803i	$0.957281\pi$
$948$	29.5946	+	27.8849i	0.961187	+	0.905660i
$949$			9.18581i			0.298184i
$950$	0.561862	−	6.13875i	0.0182292	−	0.199168i
$951$			17.4257i			0.565069i
$952$	13.7901	−	6.44672i	0.446940	−	0.208939i
$953$		−	51.7464i		−	1.67623i	−0.545494	−	0.838114i	$-0.683658\pi$
$953$		−	51.7464i		−	1.67623i	0.545494	−	0.838114i	$-0.316342\pi$
$954$	4.84143	−	12.1981i	0.156747	−	0.394928i
$955$		−	20.5329i		−	0.664430i
$956$	−10.2798	+	10.9101i	−0.332474	+	0.352858i
$957$	−24.7461			−0.799926
$958$	9.53267	−	24.0178i	0.307987	−	0.775980i
$959$			32.3355i			1.04417i
$960$	−11.0744	+	13.2501i	−0.357426	+	0.427645i
$961$	−14.2059			−0.458256
$962$	5.40852	+	2.14665i	0.174378	+	0.0692106i
$963$	2.20451			0.0710395
$964$	6.69031	−	7.10050i	0.215480	−	0.228692i
$965$		−	8.03672i		−	0.258711i
$966$	14.4340	+	5.72887i	0.464407	+	0.184323i
$967$			5.86800i			0.188702i	0.995539	+	0.0943510i	$0.0300776\pi$
$967$			5.86800i			0.188702i	−0.995539	+	0.0943510i	$0.969922\pi$
$968$	−9.39819	−	20.1036i	−0.302069	−	0.646153i
$969$	8.61409	+	29.2331i	0.276725	+	0.939103i
$970$	0.352876	−	0.889081i	0.0113302	−	0.0285467i
$971$	−31.2042			−1.00139			−0.500696	−	0.865623i	$-0.666922\pi$
$971$	−31.2042			−1.00139			−0.500696	+	0.865623i	$0.666922\pi$
$972$	22.6328	+	21.3254i	0.725949	+	0.684011i
$973$	12.8890			0.413203
$974$	−10.6831	−	4.24012i	−0.342308	−	0.135862i
$975$		−	1.66163i		−	0.0532147i
$976$	−1.17623	−	19.7551i	−0.0376502	−	0.632346i
$977$		−	23.7345i		−	0.759335i	−0.925123	−	0.379667i	$-0.876038\pi$
$977$		−	23.7345i		−	0.759335i	0.925123	−	0.379667i	$-0.123962\pi$
$978$	−9.25126	+	23.3088i	−0.295823	+	0.745332i
$979$	−28.4437			−0.909064
$980$	−6.17042	−	5.81395i	−0.197107	−	0.185720i
$981$		−	4.04060i		−	0.129006i
$982$	14.8961	−	37.5310i	0.475352	−	1.19766i
$983$	−8.16622			−0.260462			−0.130231	−	0.991484i	$-0.541572\pi$
$983$	−8.16622			−0.260462			−0.130231	+	0.991484i	$0.541572\pi$
$984$	−21.2028	+	9.91207i	−0.675921	+	0.315985i
$985$	−9.52701			−0.303556
$986$	−10.9080	+	27.4830i	−0.347382	+	0.875238i
$987$	24.4438			0.778056
$988$	−5.98581	−	3.03385i	−0.190434	−	0.0965195i
$989$	−35.3240			−1.12324
$990$	1.53758	−	3.87397i	0.0488675	−	0.123123i
$991$	−40.4095			−1.28365			−0.641825	−	0.766851i	$-0.721822\pi$
$991$	−40.4095			−1.28365			−0.641825	+	0.766851i	$0.721822\pi$
$992$	7.25624	−	22.0172i	0.230386	−	0.699047i
$993$	77.3932			2.45600
$994$	−1.58955	+	4.00491i	−0.0504174	+	0.127028i
$995$		−	6.98947i		−	0.221581i
$996$	22.1471	−	23.5049i	0.701756	−	0.744782i
$997$	−11.3678			−0.360023			−0.180012	−	0.983664i	$-0.557614\pi$
$997$	−11.3678			−0.360023			−0.180012	+	0.983664i	$0.557614\pi$
$998$	6.20202	−	15.6261i	0.196321	−	0.494636i
$999$			15.4668i			0.489349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.f.a.151.3	✓	20
4.3	odd	2	inner	380.2.f.a.151.17	yes	20
19.18	odd	2	inner	380.2.f.a.151.18	yes	20
76.75	even	2	inner	380.2.f.a.151.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.f.a.151.3	✓	20	1.1	even	1	trivial
380.2.f.a.151.4	yes	20	76.75	even	2	inner
380.2.f.a.151.17	yes	20	4.3	odd	2	inner
380.2.f.a.151.18	yes	20	19.18	odd	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31446 - 0.521712i) q^{2} -2.15859 q^{3} +(1.45563 + 1.37154i) q^{4} -1.00000 q^{5} +(2.83739 + 1.12616i) q^{6} -1.66163i q^{7} +(-1.19783 - 2.56227i) q^{8} +1.65950 q^{9} +O(q^{10})\)	\(q+(-1.31446 - 0.521712i) q^{2} -2.15859 q^{3} +(1.45563 + 1.37154i) q^{4} -1.00000 q^{5} +(2.83739 + 1.12616i) q^{6} -1.66163i q^{7} +(-1.19783 - 2.56227i) q^{8} +1.65950 q^{9} +(1.31446 + 0.521712i) q^{10} -1.77595i q^{11} +(-3.14211 - 2.96060i) q^{12} +0.769776i q^{13} +(-0.866891 + 2.18415i) q^{14} +2.15859 q^{15} +(0.237741 + 3.99293i) q^{16} -3.23899 q^{17} +(-2.18136 - 0.865781i) q^{18} +(1.23206 + 4.18115i) q^{19} +(-1.45563 - 1.37154i) q^{20} +3.58677i q^{21} +(-0.926532 + 2.33442i) q^{22} +3.06150i q^{23} +(2.58562 + 5.53087i) q^{24} +1.00000 q^{25} +(0.401601 - 1.01184i) q^{26} +2.89358 q^{27} +(2.27900 - 2.41872i) q^{28} +6.45515i q^{29} +(-2.83739 - 1.12616i) q^{30} +4.09806 q^{31} +(1.77065 - 5.37260i) q^{32} +3.83354i q^{33} +(4.25754 + 1.68982i) q^{34} +1.66163i q^{35} +(2.41563 + 2.27608i) q^{36} +5.34522i q^{37} +(0.561862 - 6.13875i) q^{38} -1.66163i q^{39} +(1.19783 + 2.56227i) q^{40} +3.83354i q^{41} +(1.87126 - 4.71469i) q^{42} +11.5381i q^{43} +(2.43579 - 2.58513i) q^{44} -1.65950 q^{45} +(1.59722 - 4.02424i) q^{46} -6.81499i q^{47} +(-0.513185 - 8.61909i) q^{48} +4.23899 q^{49} +(-1.31446 - 0.521712i) q^{50} +6.99164 q^{51} +(-1.05578 + 1.12051i) q^{52} +5.59198i q^{53} +(-3.80351 - 1.50962i) q^{54} +1.77595i q^{55} +(-4.25754 + 1.99035i) q^{56} +(-2.65950 - 9.02539i) q^{57} +(3.36773 - 8.48507i) q^{58} -5.35770 q^{59} +(3.14211 + 2.96060i) q^{60} -4.94753 q^{61} +(-5.38675 - 2.13800i) q^{62} -2.75748i q^{63} +(-5.13041 + 6.13831i) q^{64} -0.769776i q^{65} +(2.00000 - 5.03905i) q^{66} -6.72318 q^{67} +(-4.71478 - 4.44241i) q^{68} -6.60852i q^{69} +(0.866891 - 2.18415i) q^{70} +1.83362 q^{71} +(-1.98780 - 4.25208i) q^{72} +11.9331 q^{73} +(2.78866 - 7.02610i) q^{74} -2.15859 q^{75} +(-3.94121 + 7.77605i) q^{76} -2.95096 q^{77} +(-0.866891 + 2.18415i) q^{78} -9.41868 q^{79} +(-0.237741 - 3.99293i) q^{80} -11.2246 q^{81} +(2.00000 - 5.03905i) q^{82} +7.48061i q^{83} +(-4.91941 + 5.22103i) q^{84} +3.23899 q^{85} +(6.01957 - 15.1665i) q^{86} -13.9340i q^{87} +(-4.55045 + 2.12728i) q^{88} -16.0161i q^{89} +(2.18136 + 0.865781i) q^{90} +1.27908 q^{91} +(-4.19898 + 4.45643i) q^{92} -8.84602 q^{93} +(-3.55546 + 8.95807i) q^{94} +(-1.23206 - 4.18115i) q^{95} +(-3.82211 + 11.5972i) q^{96} -0.676382i q^{97} +(-5.57200 - 2.21153i) q^{98} -2.94719i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9	\( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9} - 2 q^{16} + 20 q^{17} - 2 q^{20} + 26 q^{24} + 20 q^{25} - 14 q^{26} - 14 q^{28} + 6 q^{30} - 4 q^{36} + 10 q^{38} - 42 q^{42} + 8 q^{44} - 16 q^{45} - 30 q^{54} - 36 q^{57} + 62 q^{58} - 24 q^{61} - 40 q^{62} + 50 q^{64} + 40 q^{66} + 6 q^{68} - 36 q^{73} - 36 q^{74} - 28 q^{76} - 32 q^{77} + 2 q^{80} + 60 q^{81} + 40 q^{82} - 20 q^{85} + 26 q^{92} - 122 q^{96}+O(q^{100}) \) 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9 - 2 * q^16 + 20 * q^17 - 2 * q^20 + 26 * q^24 + 20 * q^25 - 14 * q^26 - 14 * q^28 + 6 * q^30 - 4 * q^36 + 10 * q^38 - 42 * q^42 + 8 * q^44 - 16 * q^45 - 30 * q^54 - 36 * q^57 + 62 * q^58 - 24 * q^61 - 40 * q^62 + 50 * q^64 + 40 * q^66 + 6 * q^68 - 36 * q^73 - 36 * q^74 - 28 * q^76 - 32 * q^77 + 2 * q^80 + 60 * q^81 + 40 * q^82 - 20 * q^85 + 26 * q^92 - 122 * q^96

Introduction

L-functions

Modular forms

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Representations

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Database

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