LMFDB - Embedded newform 380.2.f.a.151.12

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			151.12
Root			$-0.482046 + 1.32952i$ of defining polynomial
Character	$\chi$	$=$	380.151
Dual form			380.2.f.a.151.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.482046 + 1.32952i) q^{2} -0.428612 q^{3} +(-1.53526 + 1.28178i) q^{4} -1.00000 q^{5} +(-0.206611 - 0.569850i) q^{6} +1.38367i q^{7} +(-2.44423 - 1.42329i) q^{8} -2.81629 q^{9} +O(q^{10})$	\(q+(0.482046 + 1.32952i) q^{2} -0.428612 q^{3} +(-1.53526 + 1.28178i) q^{4} -1.00000 q^{5} +(-0.206611 - 0.569850i) q^{6} +1.38367i q^{7} +(-2.44423 - 1.42329i) q^{8} -2.81629 q^{9} +(-0.482046 - 1.32952i) q^{10} +3.50970i q^{11} +(0.658033 - 0.549387i) q^{12} -3.22827i q^{13} +(-1.83963 + 0.666994i) q^{14} +0.428612 q^{15} +(0.714069 - 3.93575i) q^{16} -4.08544 q^{17} +(-1.35758 - 3.74432i) q^{18} +(-4.23761 - 1.02110i) q^{19} +(1.53526 - 1.28178i) q^{20} -0.593060i q^{21} +(-4.66622 + 1.69183i) q^{22} +7.75831i q^{23} +(1.04763 + 0.610040i) q^{24} +1.00000 q^{25} +(4.29206 - 1.55617i) q^{26} +2.49293 q^{27} +(-1.77357 - 2.12431i) q^{28} -3.98410i q^{29} +(0.206611 + 0.569850i) q^{30} -0.741862 q^{31} +(5.57688 - 0.947838i) q^{32} -1.50430i q^{33} +(-1.96937 - 5.43169i) q^{34} -1.38367i q^{35} +(4.32375 - 3.60987i) q^{36} +8.37605i q^{37} +(-0.685141 - 6.12622i) q^{38} +1.38367i q^{39} +(2.44423 + 1.42329i) q^{40} -1.50430i q^{41} +(0.788487 - 0.285882i) q^{42} +3.59008i q^{43} +(-4.49867 - 5.38831i) q^{44} +2.81629 q^{45} +(-10.3148 + 3.73986i) q^{46} +2.78456i q^{47} +(-0.306059 + 1.68691i) q^{48} +5.08544 q^{49} +(0.482046 + 1.32952i) q^{50} +1.75107 q^{51} +(4.13793 + 4.95624i) q^{52} +7.46481i q^{53} +(1.20171 + 3.31441i) q^{54} -3.50970i q^{55} +(1.96937 - 3.38201i) q^{56} +(1.81629 + 0.437658i) q^{57} +(5.29696 - 1.92052i) q^{58} +5.98229 q^{59} +(-0.658033 + 0.549387i) q^{60} +0.587124 q^{61} +(-0.357611 - 0.986323i) q^{62} -3.89683i q^{63} +(3.94849 + 6.95769i) q^{64} +3.22827i q^{65} +(2.00000 - 0.725141i) q^{66} +12.0183 q^{67} +(6.27224 - 5.23665i) q^{68} -3.32530i q^{69} +(1.83963 - 0.666994i) q^{70} -0.374851 q^{71} +(6.88365 + 4.00840i) q^{72} -13.0529 q^{73} +(-11.1362 + 4.03764i) q^{74} -0.428612 q^{75} +(7.81468 - 3.86403i) q^{76} -4.85628 q^{77} +(-1.83963 + 0.666994i) q^{78} -15.9491 q^{79} +(-0.714069 + 3.93575i) q^{80} +7.38037 q^{81} +(2.00000 - 0.725141i) q^{82} +10.2715i q^{83} +(0.760173 + 0.910503i) q^{84} +4.08544 q^{85} +(-4.77309 + 1.73058i) q^{86} +1.70764i q^{87} +(4.99532 - 8.57849i) q^{88} +8.43864i q^{89} +(1.35758 + 3.74432i) q^{90} +4.46687 q^{91} +(-9.94446 - 11.9110i) q^{92} +0.317971 q^{93} +(-3.70213 + 1.34228i) q^{94} +(4.23761 + 1.02110i) q^{95} +(-2.39032 + 0.406255i) q^{96} -4.99238i q^{97} +(2.45142 + 6.76122i) q^{98} -9.88433i 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 $

$2$	0.482046	+	1.32952i	0.340858	+	0.940115i
$2$	0.482046	+	1.32952i	0.340858	+	0.940115i
$3$	−0.428612			−0.247459			−0.123730	−	0.992316i	$-0.539486\pi$
$3$	−0.428612			−0.247459			−0.123730	+	0.992316i	$0.539486\pi$
$4$	−1.53526	+	1.28178i	−0.767632	+	0.640891i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.206611	−	0.569850i	−0.0843485	−	0.232640i
$7$			1.38367i			0.522980i	0.965206	+	0.261490i	$0.0842138\pi$
$7$			1.38367i			0.522980i	−0.965206	+	0.261490i	$0.915786\pi$
$8$	−2.44423	−	1.42329i	−0.864165	−	0.503209i
$9$	−2.81629			−0.938764
$10$	−0.482046	−	1.32952i	−0.152436	−	0.420432i
$11$			3.50970i			1.05821i	0.848555	+	0.529107i	$0.177473\pi$
$11$			3.50970i			1.05821i	−0.848555	+	0.529107i	$0.822527\pi$
$12$	0.658033	−	0.549387i	0.189958	−	0.158594i
$13$		−	3.22827i		−	0.895360i	−0.894194	−	0.447680i	$-0.852250\pi$
$13$		−	3.22827i		−	0.895360i	0.894194	−	0.447680i	$-0.147750\pi$
$14$	−1.83963	+	0.666994i	−0.491661	+	0.178262i
$15$	0.428612			0.110667
$16$	0.714069	−	3.93575i	0.178517	−	0.983937i
$17$	−4.08544			−0.990866			−0.495433	−	0.868646i	$-0.664991\pi$
$17$	−4.08544			−0.990866			−0.495433	+	0.868646i	$0.664991\pi$
$18$	−1.35758	−	3.74432i	−0.319985	−	0.882546i
$19$	−4.23761	−	1.02110i	−0.972175	−	0.234257i
$19$	−4.23761	−	1.02110i	−0.972175	−	0.234257i
$20$	1.53526	−	1.28178i	0.343295	−	0.286615i
$21$		−	0.593060i		−	0.129416i
$22$	−4.66622	+	1.69183i	−0.994842	+	0.360700i
$23$			7.75831i			1.61772i	0.588002	+	0.808859i	$0.299915\pi$
$23$			7.75831i			1.61772i	−0.588002	+	0.808859i	$0.700085\pi$
$24$	1.04763	+	0.610040i	0.213846	+	0.124524i
$25$	1.00000			0.200000
$26$	4.29206	−	1.55617i	0.841741	−	0.305191i
$27$	2.49293			0.479765
$28$	−1.77357	−	2.12431i	−0.335173	−	0.401456i
$29$		−	3.98410i		−	0.739830i	−0.929066	−	0.369915i	$-0.879387\pi$
$29$		−	3.98410i		−	0.739830i	0.929066	−	0.369915i	$-0.120613\pi$
$30$	0.206611	+	0.569850i	0.0377218	+	0.104040i
$31$	−0.741862			−0.133242			−0.0666212	−	0.997778i	$-0.521222\pi$
$31$	−0.741862			−0.133242			−0.0666212	+	0.997778i	$0.521222\pi$
$32$	5.57688	−	0.947838i	0.985863	−	0.167556i
$33$		−	1.50430i		−	0.261865i
$34$	−1.96937	−	5.43169i	−0.337744	−	0.931528i
$35$		−	1.38367i		−	0.233884i
$36$	4.32375	−	3.60987i	0.720625	−	0.601645i
$37$			8.37605i			1.37701i	0.725230	+	0.688507i	$0.241734\pi$
$37$			8.37605i			1.37701i	−0.725230	+	0.688507i	$0.758266\pi$
$38$	−0.685141	−	6.12622i	−0.111145	−	0.993804i
$39$			1.38367i			0.221565i
$40$	2.44423	+	1.42329i	0.386466	+	0.225042i
$41$		−	1.50430i		−	0.234932i	−0.993077	−	0.117466i	$-0.962523\pi$
$41$		−	1.50430i		−	0.234932i	0.993077	−	0.117466i	$-0.0374771\pi$
$42$	0.788487	−	0.285882i	0.121666	−	0.0441125i
$43$			3.59008i			0.547482i	0.961804	+	0.273741i	$0.0882610\pi$
$43$			3.59008i			0.547482i	−0.961804	+	0.273741i	$0.911739\pi$
$44$	−4.49867	−	5.38831i	−0.678199	−	0.812318i
$45$	2.81629			0.419828
$46$	−10.3148	+	3.73986i	−1.52084	+	0.551412i
$47$			2.78456i			0.406169i	0.979161	+	0.203085i	$0.0650966\pi$
$47$			2.78456i			0.406169i	−0.979161	+	0.203085i	$0.934903\pi$
$48$	−0.306059	+	1.68691i	−0.0441758	+	0.243484i
$49$	5.08544			0.726492
$50$	0.482046	+	1.32952i	0.0681716	+	0.188023i
$51$	1.75107			0.245199
$52$	4.13793	+	4.95624i	0.573828	+	0.687307i
$53$			7.46481i			1.02537i	0.858577	+	0.512685i	$0.171349\pi$
$53$			7.46481i			1.02537i	−0.858577	+	0.512685i	$0.828651\pi$
$54$	1.20171	+	3.31441i	0.163532	+	0.451034i
$55$		−	3.50970i		−	0.473247i
$56$	1.96937	−	3.38201i	0.263168	−	0.451941i
$57$	1.81629	+	0.437658i	0.240574	+	0.0579692i
$58$	5.29696	−	1.92052i	0.695525	−	0.252177i
$59$	5.98229			0.778828			0.389414	−	0.921063i	$-0.372678\pi$
$59$	5.98229			0.778828			0.389414	+	0.921063i	$0.372678\pi$
$60$	−0.658033	+	0.549387i	−0.0849517	+	0.0709256i
$61$	0.587124			0.0751736			0.0375868	−	0.999293i	$-0.488033\pi$
$61$	0.587124			0.0751736			0.0375868	+	0.999293i	$0.488033\pi$
$62$	−0.357611	−	0.986323i	−0.0454167	−	0.125263i
$63$		−	3.89683i		−	0.490955i
$64$	3.94849	+	6.95769i	0.493561	+	0.869711i
$65$			3.22827i			0.400417i
$66$	2.00000	−	0.725141i	0.246183	−	0.0892587i
$67$	12.0183			1.46827			0.734137	−	0.679002i	$-0.237587\pi$
$67$	12.0183			1.46827			0.734137	+	0.679002i	$0.237587\pi$
$68$	6.27224	−	5.23665i	0.760620	−	0.635037i
$69$		−	3.32530i		−	0.400320i
$70$	1.83963	−	0.666994i	0.219878	−	0.0797211i
$71$	−0.374851			−0.0444866			−0.0222433	−	0.999753i	$-0.507081\pi$
$71$	−0.374851			−0.0444866			−0.0222433	+	0.999753i	$0.507081\pi$
$72$	6.88365	+	4.00840i	0.811246	+	0.472395i
$73$	−13.0529			−1.52773			−0.763866	−	0.645375i	$-0.776701\pi$
$73$	−13.0529			−1.52773			−0.763866	+	0.645375i	$0.776701\pi$
$74$	−11.1362	+	4.03764i	−1.29455	+	0.469366i
$75$	−0.428612			−0.0494919
$76$	7.81468	−	3.86403i	0.896406	−	0.443235i
$77$	−4.85628			−0.553424
$78$	−1.83963	+	0.666994i	−0.208297	+	0.0755222i
$79$	−15.9491			−1.79441			−0.897207	−	0.441611i	$-0.854407\pi$
$79$	−15.9491			−1.79441			−0.897207	+	0.441611i	$0.854407\pi$
$80$	−0.714069	+	3.93575i	−0.0798354	+	0.440030i
$81$	7.38037			0.820041
$82$	2.00000	−	0.725141i	0.220863	−	0.0800784i
$83$			10.2715i			1.12744i	0.825966	+	0.563720i	$0.190630\pi$
$83$			10.2715i			1.12744i	−0.825966	+	0.563720i	$0.809370\pi$
$84$	0.760173	+	0.910503i	0.0829417	+	0.0993440i
$85$	4.08544			0.443129
$86$	−4.77309	+	1.73058i	−0.514696	+	0.186613i
$87$			1.70764i			0.183078i
$88$	4.99532	−	8.57849i	0.532503	−	0.914470i
$89$			8.43864i			0.894494i	0.894411	+	0.447247i	$0.147595\pi$
$89$			8.43864i			0.894494i	−0.894411	+	0.447247i	$0.852405\pi$
$90$	1.35758	+	3.74432i	0.143102	+	0.394687i
$91$	4.46687			0.468255
$92$	−9.94446	−	11.9110i	−1.03678	−	1.24181i
$93$	0.317971			0.0329721
$94$	−3.70213	+	1.34228i	−0.381846	+	0.138446i
$95$	4.23761	+	1.02110i	0.434770	+	0.104763i
$96$	−2.39032	+	0.406255i	−0.243961	+	0.0414632i
$97$		−	4.99238i		−	0.506899i	−0.967349	−	0.253450i	$-0.918435\pi$
$97$		−	4.99238i		−	0.506899i	0.967349	−	0.253450i	$-0.0815652\pi$
$98$	2.45142	+	6.76122i	0.247631	+	0.682986i
$99$		−	9.88433i		−	0.993412i
$100$	−1.53526	+	1.28178i	−0.153526	+	0.128178i
$101$	−7.90174			−0.786252			−0.393126	−	0.919485i	$-0.628606\pi$
$101$	−7.90174			−0.786252			−0.393126	+	0.919485i	$0.628606\pi$
$102$	0.844097	+	2.32809i	0.0835780	+	0.230515i
$103$	−5.55368			−0.547220			−0.273610	−	0.961841i	$-0.588218\pi$
$103$	−5.55368			−0.547220			−0.273610	+	0.961841i	$0.588218\pi$
$104$	−4.59476	+	7.89062i	−0.450554	+	0.773738i
$105$			0.593060i			0.0578767i
$106$	−9.92464	+	3.59838i	−0.963966	+	0.349506i
$107$	16.6372			1.60838			0.804189	−	0.594373i	$-0.202600\pi$
$107$	16.6372			1.60838			0.804189	+	0.594373i	$0.202600\pi$
$108$	−3.82731	+	3.19540i	−0.368283	+	0.307477i
$109$		−	13.9615i		−	1.33727i	−0.743592	−	0.668634i	$-0.766879\pi$
$109$		−	13.9615i		−	1.33727i	0.743592	−	0.668634i	$-0.233121\pi$
$110$	4.66622	−	1.69183i	0.444907	−	0.161310i
$111$		−	3.59008i		−	0.340755i
$112$	5.44579	+	0.988040i	0.514579	+	0.0933610i
$113$			9.53973i			0.897422i	0.893677	+	0.448711i	$0.148117\pi$
$113$			9.53973i			0.897422i	−0.893677	+	0.448711i	$0.851883\pi$
$114$	0.293660	+	2.62577i	0.0275038	+	0.245926i
$115$		−	7.75831i		−	0.723466i
$116$	5.10675	+	6.11665i	0.474150	+	0.567917i
$117$			9.09174i			0.840532i
$118$	2.88374	+	7.95359i	0.265470	+	0.732187i
$119$		−	5.65293i		−	0.518203i
$120$	−1.04763	−	0.610040i	−0.0956347	−	0.0556888i
$121$	−1.31797			−0.119816
$122$	0.283021	+	0.780595i	0.0256235	+	0.0706718i
$123$			0.644761i			0.0581361i
$124$	1.13895	−	0.950905i	0.102281	−	0.0853938i
$125$	−1.00000			−0.0894427
$126$	5.18093	−	1.87845i	0.461554	−	0.167346i
$127$	−5.43831			−0.482572			−0.241286	−	0.970454i	$-0.577569\pi$
$127$	−5.43831			−0.482572			−0.241286	+	0.970454i	$0.577569\pi$
$128$	−7.34706	+	8.60353i	−0.649395	+	0.760452i
$129$		−	1.53875i		−	0.135479i
$130$	−4.29206	+	1.55617i	−0.376438	+	0.136485i
$131$		−	0.387134i		−	0.0338241i	−0.999857	−	0.0169120i	$-0.994616\pi$
$131$		−	0.387134i		−	0.0338241i	0.999857	−	0.0169120i	$-0.00538352\pi$
$132$	1.92818	+	2.30950i	0.167827	+	0.201016i
$133$	1.41288	−	5.86347i	0.122512	−	0.508428i
$134$	5.79339	+	15.9787i	0.500473	+	1.38035i
$135$	−2.49293			−0.214558
$136$	9.98575	+	5.81478i	0.856271	+	0.498613i
$137$	5.73833			0.490259			0.245129	−	0.969490i	$-0.421170\pi$
$137$	5.73833			0.490259			0.245129	+	0.969490i	$0.421170\pi$
$138$	4.42107	−	1.60295i	0.376346	−	0.136452i
$139$		−	22.1004i		−	1.87453i	−0.348614	−	0.937266i	$-0.613348\pi$
$139$		−	22.1004i		−	1.87453i	0.348614	−	0.937266i	$-0.386652\pi$
$140$	1.77357	+	2.12431i	0.149894	+	0.179537i
$141$		−	1.19349i		−	0.100510i
$142$	−0.180695	−	0.498373i	−0.0151636	−	0.0418225i
$143$	11.3302			0.947482
$144$	−2.01103	+	11.0842i	−0.167586	+	0.923684i
$145$			3.98410i			0.330862i
$146$	−6.29212	−	17.3542i	−0.520739	−	1.43624i
$147$	−2.17968			−0.179777
$148$	−10.7363	−	12.8594i	−0.882516	−	1.05704i
$149$	2.93424			0.240382			0.120191	−	0.992751i	$-0.461649\pi$
$149$	2.93424			0.240382			0.120191	+	0.992751i	$0.461649\pi$
$150$	−0.206611	−	0.569850i	−0.0168697	−	0.0465280i
$151$	−18.4054			−1.49781			−0.748905	−	0.662677i	$-0.769420\pi$
$151$	−18.4054			−1.49781			−0.748905	+	0.662677i	$0.769420\pi$
$152$	8.90435	+	8.52716i	0.722238	+	0.691644i
$153$	11.5058			0.930189
$154$	−2.34095	−	6.45653i	−0.188639	−	0.520282i
$155$	0.741862			0.0595878
$156$	−1.77357	−	2.12431i	−0.141999	−	0.170081i
$157$	15.1384			1.20817			0.604087	−	0.796918i	$-0.293538\pi$
$157$	15.1384			1.20817			0.604087	+	0.796918i	$0.293538\pi$
$158$	−7.68819	−	21.2047i	−0.611640	−	1.68695i
$159$		−	3.19951i		−	0.253738i
$160$	−5.57688	+	0.947838i	−0.440891	+	0.0749332i
$161$	−10.7350			−0.846034
$162$	3.55768	+	9.81238i	0.279518	+	0.770933i
$163$			6.35743i			0.497952i	0.968510	+	0.248976i	$0.0800940\pi$
$163$			6.35743i			0.497952i	−0.968510	+	0.248976i	$0.919906\pi$
$164$	1.92818	+	2.30950i	0.150566	+	0.180341i
$165$			1.50430i			0.117109i
$166$	−13.6561	+	4.95132i	−1.05992	+	0.384297i
$167$	−24.7009			−1.91142			−0.955708	−	0.294316i	$-0.904908\pi$
$167$	−24.7009			−1.91142			−0.955708	+	0.294316i	$0.904908\pi$
$168$	−0.844097	+	1.44957i	−0.0651235	+	0.111837i
$169$	2.57829			0.198330
$170$	1.96937	+	5.43169i	0.151044	+	0.416592i
$171$	11.9343	+	2.87573i	0.912642	+	0.219912i
$172$	−4.60170	−	5.51171i	−0.350876	−	0.420264i
$173$		−	4.60993i		−	0.350487i	−0.984525	−	0.175243i	$-0.943929\pi$
$173$		−	4.60993i		−	0.350487i	0.984525	−	0.175243i	$-0.0560712\pi$
$174$	−2.27034	+	0.823158i	−0.172114	+	0.0624035i
$175$			1.38367i			0.104596i
$176$	13.8133	+	2.50617i	1.04122	+	0.188909i
$177$	−2.56408			−0.192728
$178$	−11.2194	+	4.06781i	−0.840927	+	0.304895i
$179$	−19.4384			−1.45290			−0.726449	−	0.687220i	$-0.758831\pi$
$179$	−19.4384			−1.45290			−0.726449	+	0.687220i	$0.758831\pi$
$180$	−4.32375	+	3.60987i	−0.322273	+	0.269064i
$181$		−	18.9496i		−	1.40852i	−0.709944	−	0.704258i	$-0.751280\pi$
$181$		−	18.9496i		−	1.40852i	0.709944	−	0.704258i	$-0.248720\pi$
$182$	2.15324	+	5.93881i	0.159608	+	0.440214i
$183$	−0.251649			−0.0186024
$184$	11.0423	−	18.9631i	0.814051	−	1.39798i
$185$		−	8.37605i		−	0.615819i
$186$	0.153277	+	0.422750i	0.0112388	+	0.0309975i
$187$		−	14.3387i		−	1.04855i
$188$	−3.56919	−	4.27503i	−0.260310	−	0.311788i
$189$			3.44941i			0.250908i
$190$	0.685141	+	6.12622i	0.0497054	+	0.444443i
$191$			20.8775i			1.51064i	0.655355	+	0.755321i	$0.272519\pi$
$191$			20.8775i			1.51064i	−0.655355	+	0.755321i	$0.727481\pi$
$192$	−1.69237	−	2.98215i	−0.122136	−	0.215218i
$193$		−	12.6350i		−	0.909490i	−0.890622	−	0.454745i	$-0.849730\pi$
$193$		−	12.6350i		−	0.909490i	0.890622	−	0.454745i	$-0.150270\pi$
$194$	6.63749	−	2.40656i	0.476544	−	0.172781i
$195$		−	1.38367i		−	0.0990870i
$196$	−7.80750	+	6.51843i	−0.557679	+	0.465602i
$197$	9.31461			0.663639			0.331819	−	0.943343i	$-0.392338\pi$
$197$	9.31461			0.663639			0.331819	+	0.943343i	$0.392338\pi$
$198$	13.1414	−	4.76470i	0.933922	−	0.338612i
$199$		−	11.9128i		−	0.844473i	−0.906486	−	0.422237i	$-0.861245\pi$
$199$		−	11.9128i		−	0.844473i	0.906486	−	0.422237i	$-0.138755\pi$
$200$	−2.44423	−	1.42329i	−0.172833	−	0.100642i
$201$	−5.15121			−0.363338
$202$	−3.80900	−	10.5055i	−0.268000	−	0.739167i
$203$	5.51270			0.386916
$204$	−2.68836	+	2.24449i	−0.188223	+	0.157146i
$205$			1.50430i			0.105065i
$206$	−2.67713	−	7.38374i	−0.186524	−	0.514450i
$207$		−	21.8497i		−	1.51866i
$208$	−12.7056	−	2.30521i	−0.880978	−	0.159837i
$209$	3.58377	−	14.8727i	0.247894	−	1.02877i
$210$	−0.788487	+	0.285882i	−0.0544107	+	0.0197277i
$211$	−1.09288			−0.0752368			−0.0376184	−	0.999292i	$-0.511977\pi$
$211$	−1.09288			−0.0752368			−0.0376184	+	0.999292i	$0.511977\pi$
$212$	−9.56826	−	11.4605i	−0.657151	−	0.787107i
$213$	0.160666			0.0110086
$214$	8.01989	+	22.1195i	0.548228	+	1.51206i
$215$		−	3.59008i		−	0.244841i
$216$	−6.09329	−	3.54817i	−0.414596	−	0.241422i
$217$		−	1.02650i		−	0.0696830i
$218$	18.5621	−	6.73008i	1.25719	−	0.455818i
$219$	5.59465			0.378051
$220$	4.49867	+	5.38831i	0.303300	+	0.363280i
$221$			13.1889i			0.887182i
$222$	4.77309	−	1.73058i	0.320349	−	0.116149i
$223$	−8.91169			−0.596771			−0.298386	−	0.954445i	$-0.596448\pi$
$223$	−8.91169			−0.596771			−0.298386	+	0.954445i	$0.596448\pi$
$224$	1.31150	+	7.71659i	0.0876283	+	0.515586i
$225$	−2.81629			−0.187753
$226$	−12.6833	+	4.59859i	−0.843680	+	0.305893i
$227$	7.50378			0.498043			0.249022	−	0.968498i	$-0.419891\pi$
$227$	7.50378			0.498043			0.249022	+	0.968498i	$0.419891\pi$
$228$	−3.34947	+	1.65617i	−0.221824	+	0.109683i
$229$	21.3581			1.41138			0.705691	−	0.708519i	$-0.250637\pi$
$229$	21.3581			1.41138			0.705691	+	0.708519i	$0.250637\pi$
$230$	10.3148	−	3.73986i	0.680141	−	0.246599i
$231$	2.08146			0.136950
$232$	−5.67054	+	9.73805i	−0.372289	+	0.639334i
$233$	−2.22034			−0.145459			−0.0727295	−	0.997352i	$-0.523171\pi$
$233$	−2.22034			−0.145459			−0.0727295	+	0.997352i	$0.523171\pi$
$234$	−12.0877	+	4.38264i	−0.790196	+	0.286502i
$235$		−	2.78456i		−	0.181644i
$236$	−9.18439	+	7.66799i	−0.597853	+	0.499144i
$237$	6.83598			0.444044
$238$	7.51570	−	2.72497i	0.487170	−	0.176634i
$239$		−	11.5748i		−	0.748709i	−0.927286	−	0.374354i	$-0.877864\pi$
$239$		−	11.5748i		−	0.748709i	0.927286	−	0.374354i	$-0.122136\pi$
$240$	0.306059	−	1.68691i	0.0197560	−	0.108890i
$241$			21.9807i			1.41590i	0.706262	+	0.707950i	$0.250380\pi$
$241$			21.9807i			1.41590i	−0.706262	+	0.707950i	$0.749620\pi$
$242$	−0.635322	−	1.75227i	−0.0408401	−	0.112640i
$243$	−10.6421			−0.682692
$244$	−0.901391	+	0.752566i	−0.0577056	+	0.0481781i
$245$	−5.08544			−0.324897
$246$	−0.857224	+	0.310804i	−0.0546546	+	0.0198162i
$247$	−3.29640	+	13.6801i	−0.209745	+	0.870446i
$248$	1.81328	+	1.05589i	0.115143	+	0.0670488i
$249$		−	4.40247i		−	0.278995i
$250$	−0.482046	−	1.32952i	−0.0304873	−	0.0840864i
$251$		−	6.60101i		−	0.416652i	−0.978059	−	0.208326i	$-0.933199\pi$
$251$		−	6.60101i		−	0.416652i	0.978059	−	0.208326i	$-0.0668015\pi$
$252$	4.99489	+	5.98266i	0.314648	+	0.376872i
$253$	−27.2293			−1.71189
$254$	−2.62152	−	7.23036i	−0.164489	−	0.453673i
$255$	−1.75107			−0.109656
$256$	−14.9802	−	5.62079i	−0.936263	−	0.351300i
$257$		−	22.8961i		−	1.42822i	−0.700032	−	0.714111i	$-0.746831\pi$
$257$		−	22.8961i		−	1.42822i	0.700032	−	0.714111i	$-0.253169\pi$
$258$	2.04580	−	0.741748i	0.127366	−	0.0461792i
$259$	−11.5897			−0.720151
$260$	−4.13793	−	4.95624i	−0.256624	−	0.307373i
$261$			11.2204i			0.694525i
$262$	0.514704	−	0.186616i	0.0317985	−	0.0115292i
$263$			8.99843i			0.554867i	0.960745	+	0.277433i	$0.0894838\pi$
$263$			8.99843i			0.554867i	−0.960745	+	0.277433i	$0.910516\pi$
$264$	−2.14105	+	3.67685i	−0.131773	+	0.226294i
$265$		−	7.46481i		−	0.458560i
$266$	8.47670	−	0.948012i	0.519740	−	0.0581264i
$267$		−	3.61690i		−	0.221351i
$268$	−18.4513	+	15.4049i	−1.12709	+	0.941003i
$269$			30.8288i			1.87967i	0.341632	+	0.939834i	$0.389021\pi$
$269$			30.8288i			1.87967i	−0.341632	+	0.939834i	$0.610979\pi$
$270$	−1.20171	−	3.31441i	−0.0731336	−	0.201709i
$271$			13.6801i			0.831009i	0.909591	+	0.415505i	$0.136395\pi$
$271$			13.6801i			0.831009i	−0.909591	+	0.415505i	$0.863605\pi$
$272$	−2.91729	+	16.0793i	−0.176887	+	0.974949i
$273$	−1.91456			−0.115874
$274$	2.76614	+	7.62924i	0.167109	+	0.460899i
$275$			3.50970i			0.211643i
$276$	4.26232	+	5.10522i	0.256561	+	0.307298i
$277$	−26.4036			−1.58644			−0.793218	−	0.608938i	$-0.791596\pi$
$277$	−26.4036			−1.58644			−0.793218	+	0.608938i	$0.791596\pi$
$278$	29.3830	−	10.6534i	1.76228	−	0.638949i
$279$	2.08930			0.125083
$280$	−1.96937	+	3.38201i	−0.117692	+	0.202114i
$281$			3.05042i			0.181973i	0.995852	+	0.0909865i	$0.0290020\pi$
$281$			3.05042i			0.181973i	−0.995852	+	0.0909865i	$0.970998\pi$
$282$	1.58678	−	0.575319i	0.0944913	−	0.0342597i
$283$			7.03660i			0.418282i	0.977885	+	0.209141i	$0.0670668\pi$
$283$			7.03660i			0.418282i	−0.977885	+	0.209141i	$0.932933\pi$
$284$	0.575495	−	0.480477i	0.0341493	−	0.0285111i
$285$	−1.81629	−	0.437658i	−0.107588	−	0.0259246i
$286$	5.46169	+	15.0638i	0.322957	+	0.890742i
$287$	2.08146			0.122865
$288$	−15.7061	+	2.66939i	−0.925492	+	0.157295i
$289$	−0.309139			−0.0181847
$290$	−5.29696	+	1.92052i	−0.311048	+	0.112777i
$291$			2.13980i			0.125437i
$292$	20.0397	−	16.7310i	1.17274	−	0.979109i
$293$			7.86970i			0.459753i	0.973220	+	0.229876i	$0.0738322\pi$
$293$			7.86970i			0.459753i	−0.973220	+	0.229876i	$0.926168\pi$
$294$	−1.05071	−	2.89794i	−0.0612785	−	0.169011i
$295$	−5.98229			−0.348302
$296$	11.9216	−	20.4730i	0.692926	−	1.18997i
$297$			8.74944i			0.507694i
$298$	1.41444	+	3.90114i	0.0819362	+	0.225987i
$299$	25.0459			1.44844
$300$	0.658033	−	0.549387i	0.0379915	−	0.0317189i
$301$	−4.96750			−0.286322
$302$	−8.87225	−	24.4704i	−0.510540	−	1.40811i
$303$	3.38678			0.194565
$304$	−7.04476	+	15.9490i	−0.404044	+	0.914739i
$305$	−0.587124			−0.0336186
$306$	5.54632	+	15.2972i	0.317062	+	0.874485i
$307$	−0.0171385			−0.000978148			−0.000489074	−	1.00000i	$-0.500156\pi$
$307$	−0.0171385			−0.000978148			−0.000489074		1.00000i	$0.500156\pi$
$308$	7.45567	−	6.22469i	0.424826	−	0.354685i
$309$	2.38037			0.135415
$310$	0.357611	+	0.986323i	0.0203110	+	0.0560194i
$311$			14.6973i			0.833409i	0.909042	+	0.416704i	$0.136815\pi$
$311$			14.6973i			0.833409i	−0.909042	+	0.416704i	$0.863185\pi$
$312$	1.96937	−	3.38201i	0.111494	−	0.191469i
$313$	4.02577			0.227550			0.113775	−	0.993507i	$-0.463706\pi$
$313$	4.02577			0.227550			0.113775	+	0.993507i	$0.463706\pi$
$314$	7.29740	+	20.1268i	0.411816	+	1.13582i
$315$			3.89683i			0.219562i
$316$	24.4861	−	20.4433i	1.37745	−	1.15002i
$317$			4.02425i			0.226024i	0.993594	+	0.113012i	$0.0360499\pi$
$317$			4.02425i			0.226024i	−0.993594	+	0.113012i	$0.963950\pi$
$318$	4.25382	−	1.54231i	0.238542	−	0.0864884i
$319$	13.9830			0.782897
$320$	−3.94849	−	6.95769i	−0.220727	−	0.388947i
$321$	−7.13090			−0.398008
$322$	−5.17475	−	14.2724i	−0.288377	−	0.795369i
$323$	17.3125	+	4.17166i	0.963295	+	0.232118i
$324$	−11.3308	+	9.46003i	−0.629490	+	0.525557i
$325$		−	3.22827i		−	0.179072i
$326$	−8.45234	+	3.06457i	−0.468132	+	0.169731i
$327$			5.98406i			0.330920i
$328$	−2.14105	+	3.67685i	−0.118220	+	0.203020i
$329$	−3.85292			−0.212418
$330$	−2.00000	+	0.725141i	−0.110096	+	0.0399177i
$331$	28.1892			1.54942			0.774708	−	0.632319i	$-0.217897\pi$
$331$	28.1892			1.54942			0.774708	+	0.632319i	$0.217897\pi$
$332$	−13.1658	−	15.7694i	−0.722566	−	0.865459i
$333$		−	23.5894i		−	1.29269i
$334$	−11.9070	−	32.8405i	−0.651521	−	1.79695i
$335$	−12.0183			−0.656632
$336$	−2.33413	−	0.423486i	−0.127337	−	0.0231030i
$337$			1.10109i			0.0599804i	0.999550	+	0.0299902i	$0.00954760\pi$
$337$			1.10109i			0.0599804i	−0.999550	+	0.0299902i	$0.990452\pi$
$338$	1.24286	+	3.42790i	0.0676024	+	0.186453i
$339$		−	4.08884i		−	0.222076i
$340$	−6.27224	+	5.23665i	−0.340160	+	0.283997i
$341$		−	2.60371i		−	0.140999i
$342$	1.92956	+	17.2532i	0.104338	+	0.932948i
$343$			16.7223i			0.902920i
$344$	5.10972	−	8.77496i	0.275498	−	0.473114i
$345$			3.32530i			0.179028i
$346$	6.12901	−	2.22220i	0.329498	−	0.119466i
$347$			25.1158i			1.34829i	0.738601	+	0.674143i	$0.235487\pi$
$347$			25.1158i			1.34829i	−0.738601	+	0.674143i	$0.764513\pi$
$348$	−2.18882	−	2.62167i	−0.117333	−	0.140536i
$349$	12.9472			0.693047			0.346524	−	0.938041i	$-0.387362\pi$
$349$	12.9472			0.693047			0.346524	+	0.938041i	$0.387362\pi$
$350$	−1.83963	+	0.666994i	−0.0983322	+	0.0356524i
$351$		−	8.04785i		−	0.429563i
$352$	3.32663	+	19.5732i	0.177310	+	1.04325i
$353$	19.4618			1.03585			0.517924	−	0.855426i	$-0.326705\pi$
$353$	19.4618			1.03585			0.517924	+	0.855426i	$0.326705\pi$
$354$	−1.23600	−	3.40901i	−0.0656929	−	0.181187i
$355$	0.374851			0.0198950
$356$	−10.8165	−	12.9555i	−0.573273	−	0.686642i
$357$			2.42291i			0.128234i
$358$	−9.37022	−	25.8439i	−0.495232	−	1.36589i
$359$			7.71234i			0.407042i	0.979071	+	0.203521i	$0.0652385\pi$
$359$			7.71234i			0.407042i	−0.979071	+	0.203521i	$0.934762\pi$
$360$	−6.88365	−	4.00840i	−0.362800	−	0.211261i
$361$	16.9147	+	8.65408i	0.890247	+	0.455478i
$362$	25.1940	−	9.13460i	1.32417	−	0.480104i
$363$	0.564898			0.0296495
$364$	−6.85782	+	5.72555i	−0.359448	+	0.300101i
$365$	13.0529			0.683222
$366$	−0.121306	−	0.334573i	−0.00634078	−	0.0174884i
$367$			30.3565i			1.58460i	0.610134	+	0.792298i	$0.291116\pi$
$367$			30.3565i			1.58460i	−0.610134	+	0.792298i	$0.708884\pi$
$368$	30.5347	+	5.53997i	1.59173	+	0.288791i
$369$			4.23654i			0.220546i
$370$	11.1362	−	4.03764i	0.578941	−	0.209907i
$371$	−10.3289			−0.536248
$372$	−0.488169	+	0.407570i	−0.0253104	+	0.0211315i
$373$			18.6012i			0.963136i	0.876409	+	0.481568i	$0.159933\pi$
$373$			18.6012i			0.963136i	−0.876409	+	0.481568i	$0.840067\pi$
$374$	19.0636	−	6.91190i	0.985755	−	0.357406i
$375$	0.428612			0.0221334
$376$	3.96323	−	6.80608i	0.204388	−	0.350997i
$377$	−12.8618			−0.662414
$378$	−4.58607	+	1.66277i	−0.235882	+	0.0855238i
$379$	5.45224			0.280063			0.140032	−	0.990147i	$-0.455280\pi$
$379$	5.45224			0.280063			0.140032	+	0.990147i	$0.455280\pi$
$380$	−7.81468	+	3.86403i	−0.400885	+	0.198221i
$381$	2.33093			0.119417
$382$	−27.7571	+	10.0639i	−1.42018	+	0.514914i
$383$	25.9775			1.32739			0.663694	−	0.748004i	$-0.268988\pi$
$383$	25.9775			1.32739			0.663694	+	0.748004i	$0.268988\pi$
$384$	3.14904	−	3.68758i	0.160699	−	0.188181i
$385$	4.85628			0.247499
$386$	16.7986	−	6.09066i	0.855025	−	0.310007i
$387$		−	10.1107i		−	0.513956i
$388$	6.39914	+	7.66462i	0.324867	+	0.389112i
$389$	−25.1181			−1.27354			−0.636769	−	0.771055i	$-0.719729\pi$
$389$	−25.1181			−1.27354			−0.636769	+	0.771055i	$0.719729\pi$
$390$	1.83963	−	0.666994i	0.0931531	−	0.0337746i
$391$		−	31.6961i		−	1.60294i
$392$	−12.4300	−	7.23807i	−0.627809	−	0.365578i
$393$			0.165930i			0.00837008i
$394$	4.49007	+	12.3840i	0.226206	+	0.623897i
$395$	15.9491			0.802486
$396$	12.6696	+	15.1751i	0.636669	+	0.762575i
$397$	−14.3418			−0.719793			−0.359897	−	0.932992i	$-0.617188\pi$
$397$	−14.3418			−0.719793			−0.359897	+	0.932992i	$0.617188\pi$
$398$	15.8383	−	5.74250i	0.793902	−	0.287845i
$399$	−0.605576	+	2.51316i	−0.0303167	+	0.125815i
$400$	0.714069	−	3.93575i	0.0357035	−	0.196787i
$401$		−	13.3490i		−	0.666619i	−0.942817	−	0.333310i	$-0.891835\pi$
$401$		−	13.3490i		−	0.666619i	0.942817	−	0.333310i	$-0.108165\pi$
$402$	−2.48312	−	6.84865i	−0.123847	−	0.341580i
$403$			2.39493i			0.119300i
$404$	12.1312	−	10.1283i	0.603552	−	0.503902i
$405$	−7.38037			−0.366734
$406$	2.65738	+	7.32927i	0.131883	+	0.363745i
$407$	−29.3974			−1.45717
$408$	−4.28001	−	2.49228i	−0.211892	−	0.123386i
$409$		−	8.35193i		−	0.412976i	−0.978449	−	0.206488i	$-0.933797\pi$
$409$		−	8.35193i		−	0.412976i	0.978449	−	0.206488i	$-0.0662035\pi$
$410$	−2.00000	+	0.725141i	−0.0987730	+	0.0358122i
$411$	−2.45952			−0.121319
$412$	8.52636	−	7.11860i	0.420064	−	0.350708i
$413$			8.27754i			0.407311i
$414$	29.0496	−	10.5325i	1.42771	−	0.517646i
$415$		−	10.2715i		−	0.504206i
$416$	−3.05988	−	18.0037i	−0.150023	−	0.882702i
$417$			9.47251i			0.463871i
$418$	21.5012	−	2.40464i	1.05166	−	0.117615i
$419$			21.4384i			1.04734i	0.851922	+	0.523668i	$0.175437\pi$
$419$			21.4384i			1.04734i	−0.851922	+	0.523668i	$0.824563\pi$
$420$	−0.760173	−	0.910503i	−0.0370927	−	0.0444280i
$421$		−	30.5540i		−	1.48911i	−0.667562	−	0.744555i	$-0.732662\pi$
$421$		−	30.5540i		−	1.48911i	0.667562	−	0.744555i	$-0.267338\pi$
$422$	−0.526817	−	1.45301i	−0.0256451	−	0.0707312i
$423$		−	7.84212i		−	0.381297i
$424$	10.6246	−	18.2457i	0.515976	−	0.886089i
$425$	−4.08544			−0.198173
$426$	0.0774482	+	0.213609i	0.00375238	+	0.0103494i
$427$			0.812389i			0.0393143i
$428$	−25.5425	+	21.3253i	−1.23464	+	1.03080i
$429$	−4.85628			−0.234463
$430$	4.77309	−	1.73058i	0.230179	−	0.0834560i
$431$	−7.22252			−0.347897			−0.173948	−	0.984755i	$-0.555653\pi$
$431$	−7.22252			−0.347897			−0.173948	+	0.984755i	$0.555653\pi$
$432$	1.78013	−	9.81156i	0.0856464	−	0.472059i
$433$			36.3933i			1.74895i	0.485069	+	0.874476i	$0.338794\pi$
$433$			36.3933i			1.74895i	−0.485069	+	0.874476i	$0.661206\pi$
$434$	1.36475	−	0.494818i	0.0655101	−	0.0237520i
$435$		−	1.70764i		−	0.0818748i
$436$	17.8956	+	21.4346i	0.857043	+	1.02653i
$437$	7.92204	−	32.8767i	0.378963	−	1.57271i
$438$	2.69688	+	7.43822i	0.128862	+	0.355412i
$439$	27.0907			1.29297			0.646485	−	0.762927i	$-0.276238\pi$
$439$	27.0907			1.29297			0.646485	+	0.762927i	$0.276238\pi$
$440$	−4.99532	+	8.57849i	−0.238143	+	0.408964i
$441$	−14.3221			−0.682005
$442$	−17.5350	+	6.35766i	−0.834053	+	0.302403i
$443$		−	26.7052i		−	1.26880i	−0.773004	−	0.634401i	$-0.781247\pi$
$443$		−	26.7052i		−	1.26880i	0.773004	−	0.634401i	$-0.218753\pi$
$444$	4.60170	+	5.51171i	0.218387	+	0.261574i
$445$		−	8.43864i		−	0.400030i
$446$	−4.29584	−	11.8483i	−0.203414	−	0.561033i
$447$	−1.25765			−0.0594848
$448$	−9.62718	+	5.46342i	−0.454841	+	0.258122i
$449$			32.7156i			1.54394i	0.635656	+	0.771972i	$0.280730\pi$
$449$			32.7156i			1.54394i	−0.635656	+	0.771972i	$0.719270\pi$
$450$	−1.35758	−	3.74432i	−0.0639970	−	0.176509i
$451$	5.27963			0.248608
$452$	−12.2279	−	14.6460i	−0.575150	−	0.688890i
$453$	7.88878			0.370647
$454$	3.61716	+	9.97645i	0.169762	+	0.468218i
$455$	−4.46687			−0.209410
$456$	−3.81651	−	3.65485i	−0.178725	−	0.171154i
$457$	5.57628			0.260847			0.130424	−	0.991458i	$-0.458366\pi$
$457$	5.57628			0.260847			0.130424	+	0.991458i	$0.458366\pi$
$458$	10.2956	+	28.3961i	0.481081	+	1.32686i
$459$	−10.1847			−0.475383
$460$	9.94446	+	11.9110i	0.463663	+	0.555355i
$461$	14.8204			0.690256			0.345128	−	0.938556i	$-0.387836\pi$
$461$	14.8204			0.690256			0.345128	+	0.938556i	$0.387836\pi$
$462$	1.00336	+	2.76735i	0.0466805	+	0.128749i
$463$			13.8443i			0.643401i	0.946842	+	0.321700i	$0.104254\pi$
$463$			13.8443i			0.643401i	−0.946842	+	0.321700i	$0.895746\pi$
$464$	−15.6804	−	2.84493i	−0.727945	−	0.132072i
$465$	−0.317971			−0.0147456
$466$	−1.07030	−	2.95199i	−0.0495808	−	0.136748i
$467$			13.2161i			0.611566i	0.952101	+	0.305783i	$0.0989183\pi$
$467$			13.2161i			0.611566i	−0.952101	+	0.305783i	$0.901082\pi$
$468$	−11.6536	−	13.9582i	−0.538689	−	0.645219i
$469$			16.6295i			0.767877i
$470$	3.70213	−	1.34228i	0.170767	−	0.0619149i
$471$	−6.48850			−0.298974
$472$	−14.6221	−	8.51454i	−0.673035	−	0.391913i
$473$	−12.6001			−0.579352
$474$	3.29525	+	9.08859i	0.151356	+	0.417453i
$475$	−4.23761	−	1.02110i	−0.194435	−	0.0468515i
$476$	7.24582	+	8.67873i	0.332112	+	0.397789i
$477$		−	21.0231i		−	0.962581i
$478$	15.3889	−	5.57956i	0.703872	−	0.255203i
$479$		−	3.34207i		−	0.152703i	−0.997081	−	0.0763515i	$-0.975673\pi$
$479$		−	3.34207i		−	0.152703i	0.997081	−	0.0763515i	$-0.0243271\pi$
$480$	2.39032	−	0.406255i	0.109103	−	0.0185429i
$481$	27.0401			1.23292
$482$	−29.2238	+	10.5957i	−1.33111	+	0.482621i
$483$	4.60114			0.209359
$484$	2.02343	−	1.68935i	0.0919742	−	0.0767887i
$485$			4.99238i			0.226692i
$486$	−5.12999	−	14.1489i	−0.232701	−	0.641809i
$487$	−23.3613			−1.05860			−0.529302	−	0.848434i	$-0.677546\pi$
$487$	−23.3613			−1.05860			−0.529302	+	0.848434i	$0.677546\pi$
$488$	−1.43506	−	0.835649i	−0.0649623	−	0.0378280i
$489$		−	2.72487i		−	0.123223i
$490$	−2.45142	−	6.76122i	−0.110744	−	0.305441i
$491$			25.2134i			1.13786i	0.822385	+	0.568931i	$0.192643\pi$
$491$			25.2134i			1.13786i	−0.822385	+	0.568931i	$0.807357\pi$
$492$	−0.826443	−	0.989878i	−0.0372589	−	0.0446271i
$493$			16.2768i			0.733072i
$494$	−19.7771	+	2.21182i	−0.889813	+	0.0995144i
$495$			9.88433i			0.444268i
$496$	−0.529741	+	2.91978i	−0.0237861	+	0.131102i
$497$		−	0.518672i		−	0.0232656i
$498$	5.85319	−	2.12219i	0.262288	−	0.0950978i
$499$			22.2956i			0.998088i	0.866577	+	0.499044i	$0.166315\pi$
$499$			22.2956i			0.998088i	−0.866577	+	0.499044i	$0.833685\pi$
$500$	1.53526	−	1.28178i	0.0686591	−	0.0573230i
$501$	10.5871			0.472998
$502$	8.77619	−	3.18199i	0.391701	−	0.142019i
$503$		−	13.2999i		−	0.593012i	−0.955031	−	0.296506i	$-0.904179\pi$
$503$		−	13.2999i		−	0.593012i	0.955031	−	0.296506i	$-0.0958215\pi$
$504$	−5.54632	+	9.52474i	−0.247053	+	0.424265i
$505$	7.90174			0.351623
$506$	−13.1258	−	36.2020i	−0.583512	−	1.60937i
$507$	−1.10509			−0.0490787
$508$	8.34925	−	6.97073i	0.370438	−	0.309276i
$509$		−	1.96608i		−	0.0871449i	−0.999050	−	0.0435724i	$-0.986126\pi$
$509$		−	1.96608i		−	0.0871449i	0.999050	−	0.0435724i	$-0.0138739\pi$
$510$	−0.844097	−	2.32809i	−0.0373772	−	0.103090i
$511$		−	18.0610i		−	0.798973i
$512$	0.251828	−	22.6260i	0.0111293	−	0.999938i
$513$	−10.5641	−	2.54554i	−0.466416	−	0.112389i
$514$	30.4410	−	11.0370i	1.34269	−	0.486821i
$515$	5.55368			0.244724
$516$	1.97234	+	2.36239i	0.0868276	+	0.103998i
$517$	−9.77295			−0.429814
$518$	−5.58678	−	15.4088i	−0.245469	−	0.677024i
$519$			1.97587i			0.0867312i
$520$	4.59476	−	7.89062i	0.201494	−	0.346026i
$521$		−	27.5777i		−	1.20820i	−0.796908	−	0.604101i	$-0.793532\pi$
$521$		−	27.5777i		−	1.20820i	0.796908	−	0.604101i	$-0.206468\pi$
$522$	−14.9178	+	5.40875i	−0.652933	+	0.236734i
$523$	11.9030			0.520481			0.260240	−	0.965544i	$-0.416198\pi$
$523$	11.9030			0.520481			0.260240	+	0.965544i	$0.416198\pi$
$524$	0.496222	+	0.594353i	0.0216775	+	0.0259644i
$525$		−	0.593060i		−	0.0258832i
$526$	−11.9636	+	4.33765i	−0.521639	+	0.189131i
$527$	3.03084			0.132025
$528$	−5.92054	−	1.07417i	−0.257658	−	0.0467474i
$529$	−37.1913			−1.61701
$530$	9.92464	−	3.59838i	0.431099	−	0.156304i
$531$	−16.8479			−0.731135
$532$	5.34656	+	10.8130i	0.231803	+	0.468802i
$533$	−4.85628			−0.210349
$534$	4.80875	−	1.74351i	0.208095	−	0.0754492i
$535$	−16.6372			−0.719289
$536$	−29.3755	−	17.1056i	−1.26883	−	0.738849i
$537$	8.33156			0.359533
$538$	−40.9877	+	14.8609i	−1.76710	+	0.640700i
$539$			17.8484i			0.768784i
$540$	3.82731	−	3.19540i	0.164701	−	0.137508i
$541$	−3.73085			−0.160402			−0.0802008	−	0.996779i	$-0.525556\pi$
$541$	−3.73085			−0.160402			−0.0802008	+	0.996779i	$0.525556\pi$
$542$	−18.1881	+	6.59445i	−0.781244	+	0.283256i
$543$			8.12205i			0.348551i
$544$	−22.7840	+	3.87234i	−0.976858	+	0.166025i
$545$			13.9615i			0.598045i
$546$	−0.922903	−	2.54545i	−0.0394966	−	0.108935i
$547$	20.7371			0.886652			0.443326	−	0.896360i	$-0.353798\pi$
$547$	20.7371			0.886652			0.443326	+	0.896360i	$0.353798\pi$
$548$	−8.80985	+	7.35529i	−0.376338	+	0.314202i
$549$	−1.65351			−0.0705702
$550$	−4.66622	+	1.69183i	−0.198968	+	0.0721401i
$551$	−4.06818	+	16.8831i	−0.173310	+	0.719243i
$552$	−4.73288	+	8.12780i	−0.201445	+	0.345942i
$553$		−	22.0684i		−	0.938442i
$554$	−12.7277	−	35.1041i	−0.540749	−	1.49143i
$555$			3.59008i			0.152390i
$556$	28.3279	+	33.9300i	1.20137	+	1.43895i
$557$	−5.41225			−0.229324			−0.114662	−	0.993405i	$-0.536579\pi$
$557$	−5.41225			−0.229324			−0.114662	+	0.993405i	$0.536579\pi$
$558$	1.00714	+	2.77777i	0.0426356	+	0.117592i
$559$	11.5897			0.490193
$560$	−5.44579	−	0.988040i	−0.230127	−	0.0417523i
$561$			6.14573i			0.259473i
$562$	−4.05561	+	1.47044i	−0.171076	+	0.0620269i
$563$	−5.83702			−0.246001			−0.123001	−	0.992407i	$-0.539252\pi$
$563$	−5.83702			−0.246001			−0.123001	+	0.992407i	$0.539252\pi$
$564$	1.52980	+	1.83233i	0.0644162	+	0.0771550i
$565$		−	9.53973i		−	0.401339i
$566$	−9.35532	+	3.39196i	−0.393234	+	0.142575i
$567$			10.2120i			0.428865i
$568$	0.916220	+	0.533522i	0.0384438	+	0.0223861i
$569$		−	18.0968i		−	0.758656i	−0.925262	−	0.379328i	$-0.876155\pi$
$569$		−	18.0968i		−	0.758656i	0.925262	−	0.379328i	$-0.123845\pi$
$570$	−0.293660	−	2.62577i	−0.0123001	−	0.109982i
$571$		−	27.5235i		−	1.15182i	−0.817512	−	0.575912i	$-0.804647\pi$
$571$		−	27.5235i		−	1.15182i	0.817512	−	0.575912i	$-0.195353\pi$
$572$	−17.3949	+	14.5229i	−0.727317	+	0.607233i
$573$		−	8.94835i		−	0.373823i
$574$	1.00336	+	2.76735i	0.0418794	+	0.115507i
$575$			7.75831i			0.323544i
$576$	−11.1201	−	19.5949i	−0.463337	−	0.816454i
$577$	−15.6068			−0.649720			−0.324860	−	0.945762i	$-0.605317\pi$
$577$	−15.6068			−0.649720			−0.324860	+	0.945762i	$0.605317\pi$
$578$	−0.149019	−	0.411008i	−0.00619839	−	0.0170957i
$579$			5.41553i			0.225062i
$580$	−5.10675	−	6.11665i	−0.212046	−	0.253980i
$581$	−14.2124			−0.589628
$582$	−2.84491	+	1.03148i	−0.117925	+	0.0427562i
$583$	−26.1992			−1.08506
$584$	31.9043	+	18.5781i	1.32021	+	0.768769i
$585$		−	9.09174i		−	0.375897i
$586$	−10.4629	+	3.79355i	−0.432220	+	0.156710i
$587$		−	29.7117i		−	1.22633i	−0.789953	−	0.613167i	$-0.789895\pi$
$587$		−	29.7117i		−	1.22633i	0.789953	−	0.613167i	$-0.210105\pi$
$588$	3.34639	−	2.79388i	0.138003	−	0.115218i
$589$	3.14372	+	0.757518i	0.129535	+	0.0312130i
$590$	−2.88374	−	7.95359i	−0.118722	−	0.327444i
$591$	−3.99236			−0.164224
$592$	32.9660	+	5.98108i	1.35489	+	0.245821i
$593$	33.8891			1.39166			0.695828	−	0.718208i	$-0.255037\pi$
$593$	33.8891			1.39166			0.695828	+	0.718208i	$0.255037\pi$
$594$	−11.6326	+	4.21763i	−0.477291	+	0.173051i
$595$			5.65293i			0.231747i
$596$	−4.50483	+	3.76105i	−0.184525	+	0.154059i
$597$			5.10596i			0.208973i
$598$	12.0733	+	33.2991i	0.493712	+	1.36170i
$599$	1.73537			0.0709054			0.0354527	−	0.999371i	$-0.488713\pi$
$599$	1.73537			0.0709054			0.0354527	+	0.999371i	$0.488713\pi$
$600$	1.04763	+	0.610040i	0.0427691	+	0.0249048i
$601$			40.6804i			1.65939i	0.558217	+	0.829695i	$0.311486\pi$
$601$			40.6804i			1.65939i	−0.558217	+	0.829695i	$0.688514\pi$
$602$	−2.39456	−	6.60440i	−0.0975950	−	0.269175i
$603$	−33.8471			−1.37836
$604$	28.2571	−	23.5917i	1.14977	−	0.959933i
$605$	1.31797			0.0535831
$606$	1.63258	+	4.50280i	0.0663192	+	0.182914i
$607$	−24.9715			−1.01356			−0.506781	−	0.862075i	$-0.669165\pi$
$607$	−24.9715			−1.01356			−0.506781	+	0.862075i	$0.669165\pi$
$608$	−24.6005	−	1.67801i	−0.997682	−	0.0680521i
$609$	−2.36281			−0.0957460
$610$	−0.283021	−	0.780595i	−0.0114592	−	0.0316054i
$611$	8.98929			0.363668
$612$	−17.6644	+	14.7479i	−0.714043	+	0.596150i
$613$	−17.7438			−0.716665			−0.358333	−	0.933594i	$-0.616655\pi$
$613$	−17.7438			−0.716665			−0.358333	+	0.933594i	$0.616655\pi$
$614$	−0.00826156	−	0.0227861i	−0.000333410	−	0.000919572i
$615$		−	0.644761i		−	0.0259993i
$616$	11.8698	+	6.91190i	0.478250	+	0.278488i
$617$	−19.2002			−0.772969			−0.386485	−	0.922296i	$-0.626311\pi$
$617$	−19.2002			−0.772969			−0.386485	+	0.922296i	$0.626311\pi$
$618$	1.14745	+	3.16476i	0.0461572	+	0.127305i
$619$		−	19.6398i		−	0.789391i	−0.918812	−	0.394695i	$-0.870850\pi$
$619$		−	19.6398i		−	0.789391i	0.918812	−	0.394695i	$-0.129150\pi$
$620$	−1.13895	+	0.950905i	−0.0457415	+	0.0381893i
$621$			19.3409i			0.776125i
$622$	−19.5404	+	7.08478i	−0.783500	+	0.284074i
$623$	−11.6763			−0.467802
$624$	5.44579	+	0.988040i	0.218006	+	0.0395532i
$625$	1.00000			0.0400000
$626$	1.94061	+	5.35236i	0.0775623	+	0.213923i
$627$	−1.53605	+	6.37463i	−0.0613437	+	0.254578i
$628$	−23.2414	+	19.4041i	−0.927434	+	0.774308i
$629$		−	34.2199i		−	1.36444i
$630$	−5.18093	+	1.87845i	−0.206413	+	0.0748393i
$631$		−	6.40339i		−	0.254915i	−0.991844	−	0.127458i	$-0.959318\pi$
$631$		−	6.40339i		−	0.254915i	0.991844	−	0.127458i	$-0.0406816\pi$
$632$	38.9832	+	22.7002i	1.55067	+	0.902966i
$633$	0.468421			0.0186181
$634$	−5.35033	+	1.93987i	−0.212489	+	0.0770422i
$635$	5.43831			0.215813
$636$	4.10107	+	4.91209i	0.162618	+	0.194777i
$637$		−	16.4172i		−	0.650472i
$638$	6.74044	+	18.5907i	0.266857	+	0.736014i
$639$	1.05569			0.0417624
$640$	7.34706	−	8.60353i	0.290418	−	0.340084i
$641$		−	47.1403i		−	1.86193i	−0.365107	−	0.930966i	$-0.618968\pi$
$641$		−	47.1403i		−	1.86193i	0.365107	−	0.930966i	$-0.381032\pi$
$642$	−3.43742	−	9.48070i	−0.135664	−	0.374173i
$643$		−	49.2412i		−	1.94188i	−0.239317	−	0.970941i	$-0.576924\pi$
$643$		−	49.2412i		−	1.94188i	0.239317	−	0.970941i	$-0.423076\pi$
$644$	16.4810	−	13.7599i	0.649443	−	0.542216i
$645$			1.53875i			0.0605882i
$646$	2.79911	+	25.0283i	0.110129	+	0.984727i
$647$		−	15.4716i		−	0.608253i	−0.952632	−	0.304126i	$-0.901635\pi$
$647$		−	15.4716i		−	0.608253i	0.952632	−	0.304126i	$-0.0983646\pi$
$648$	−18.0393	−	10.5044i	−0.708651	−	0.412653i
$649$			20.9960i			0.824166i
$650$	4.29206	−	1.55617i	0.168348	−	0.0610381i
$651$			0.439968i			0.0172437i
$652$	−8.14883	−	9.76033i	−0.319133	−	0.382244i
$653$	13.7438			0.537837			0.268918	−	0.963163i	$-0.413334\pi$
$653$	13.7438			0.537837			0.268918	+	0.963163i	$0.413334\pi$
$654$	−7.95595	+	2.88459i	−0.311102	+	0.112797i
$655$			0.387134i			0.0151266i
$656$	−5.92054	−	1.07417i	−0.231158	−	0.0419394i
$657$	36.7609			1.43418
$658$	−1.85728	−	5.12254i	−0.0724044	−	0.199698i
$659$	−28.2124			−1.09900			−0.549499	−	0.835494i	$-0.685181\pi$
$659$	−28.2124			−1.09900			−0.549499	+	0.835494i	$0.685181\pi$
$660$	−1.92818	−	2.30950i	−0.0750544	−	0.0898970i
$661$			41.5757i			1.61711i	0.588424	+	0.808553i	$0.299749\pi$
$661$			41.5757i			1.61711i	−0.588424	+	0.808553i	$0.700251\pi$
$662$	13.5885	+	37.4781i	0.528131	+	1.45663i
$663$		−	5.65293i		−	0.219541i
$664$	14.6193	−	25.1058i	0.567338	−	0.974293i
$665$	−1.41288	+	5.86347i	−0.0547890	+	0.227376i
$666$	31.3627	−	11.3712i	1.21528	−	0.440624i
$667$	30.9099			1.19684
$668$	37.9225	−	31.6612i	1.46726	−	1.22501i
$669$	3.81966			0.147677
$670$	−5.79339	−	15.9787i	−0.223818	−	0.617309i
$671$			2.06063i			0.0795497i
$672$	−0.562125	−	3.30742i	−0.0216844	−	0.127587i
$673$		−	46.8968i		−	1.80774i	−0.427810	−	0.903868i	$-0.640715\pi$
$673$		−	46.8968i		−	1.80774i	0.427810	−	0.903868i	$-0.359285\pi$
$674$	−1.46393	+	0.530777i	−0.0563884	+	0.0204448i
$675$	2.49293			0.0959530
$676$	−3.95836	+	3.30481i	−0.152245	+	0.127108i
$677$			0.848653i			0.0326164i	0.999867	+	0.0163082i	$0.00519129\pi$
$677$			0.848653i			0.0326164i	−0.999867	+	0.0163082i	$0.994809\pi$
$678$	5.43621	−	1.97101i	0.208776	−	0.0756962i
$679$	6.90783			0.265098
$680$	−9.98575	−	5.81478i	−0.382936	−	0.222987i
$681$	−3.21621			−0.123245
$682$	3.46169	−	1.25511i	0.132555	−	0.0480606i
$683$	2.10644			0.0806006			0.0403003	−	0.999188i	$-0.487169\pi$
$683$	2.10644			0.0806006			0.0403003	+	0.999188i	$0.487169\pi$
$684$	−22.0084	+	10.8822i	−0.841513	+	0.416093i
$685$	−5.73833			−0.219250
$686$	−22.2327	+	8.06092i	−0.848849	+	0.307768i
$687$	−9.15434			−0.349260
$688$	14.1296	+	2.56356i	0.538687	+	0.0977350i
$689$	24.0984			0.918076
$690$	−4.42107	+	1.60295i	−0.168307	+	0.0610232i
$691$		−	39.7777i		−	1.51322i	−0.653868	−	0.756608i	$-0.726855\pi$
$691$		−	39.7777i		−	1.51322i	0.653868	−	0.756608i	$-0.273145\pi$
$692$	5.90893	+	7.07746i	0.224624	+	0.269045i
$693$	13.6767			0.519535
$694$	−33.3920	+	12.1070i	−1.26754	+	0.459574i
$695$			22.1004i			0.838316i
$696$	2.43046	−	4.17385i	0.0921264	−	0.158209i
$697$			6.14573i			0.232786i
$698$	6.24114	+	17.2136i	0.236231	+	0.651544i
$699$	0.951663			0.0359952
$700$	−1.77357	−	2.12431i	−0.0670346	−	0.0802912i
$701$	10.5668			0.399103			0.199552	−	0.979887i	$-0.436051\pi$
$701$	10.5668			0.399103			0.199552	+	0.979887i	$0.436051\pi$
$702$	10.6998	−	3.87943i	0.403838	−	0.146420i
$703$	8.55282	−	35.4944i	0.322576	−	1.33870i
$704$	−24.4194	+	13.8580i	−0.920340	+	0.522292i
$705$			1.19349i			0.0449496i
$706$	9.38149	+	25.8750i	0.353077	+	0.973817i
$707$		−	10.9334i		−	0.411194i
$708$	3.93654	−	3.28659i	0.147944	−	0.123518i
$709$	−5.03250			−0.189000			−0.0944998	−	0.995525i	$-0.530125\pi$
$709$	−5.03250			−0.189000			−0.0944998	+	0.995525i	$0.530125\pi$
$710$	0.180695	+	0.498373i	0.00678137	+	0.0187036i
$711$	44.9173			1.68453
$712$	12.0106	−	20.6259i	0.450118	−	0.772990i
$713$		−	5.75559i		−	0.215549i
$714$	−3.22132	+	1.16795i	−0.120555	+	0.0437096i
$715$	−11.3302			−0.423727
$716$	29.8431	−	24.9159i	1.11529	−	0.931149i
$717$			4.96108i			0.185275i
$718$	−10.2537	+	3.71770i	−0.382666	+	0.138743i
$719$			18.0998i			0.675009i	0.941324	+	0.337505i	$0.109583\pi$
$719$			18.0998i			0.675009i	−0.941324	+	0.337505i	$0.890417\pi$
$720$	2.01103	−	11.0842i	0.0749466	−	0.413084i
$721$		−	7.68448i		−	0.286185i
$722$	−3.35215	+	26.6601i	−0.124754	+	0.992188i
$723$		−	9.42119i		−	0.350378i
$724$	24.2893	+	29.0927i	0.902705	+	1.08122i
$725$		−	3.98410i		−	0.147966i
$726$	0.272307	+	0.751046i	0.0101063	+	0.0278739i
$727$		−	4.85183i		−	0.179945i	−0.995944	−	0.0899723i	$-0.971322\pi$
$727$		−	4.85183i		−	0.179945i	0.995944	−	0.0899723i	$-0.0286778\pi$
$728$	−10.9180	−	6.35766i	−0.404650	−	0.235630i
$729$	−17.5798			−0.651103
$730$	6.29212	+	17.3542i	0.232882	+	0.642307i
$731$		−	14.6671i		−	0.542481i
$732$	0.386347	−	0.322559i	0.0142798	−	0.0119221i
$733$	15.7879			0.583140			0.291570	−	0.956550i	$-0.405822\pi$
$733$	15.7879			0.583140			0.291570	+	0.956550i	$0.405822\pi$
$734$	−40.3597	+	14.6332i	−1.48970	+	0.540122i
$735$	2.17968			0.0803988
$736$	7.35362	+	43.2672i	0.271058	+	1.59485i
$737$			42.1807i			1.55375i
$738$	−5.63258	+	2.04221i	−0.207338	+	0.0751747i
$739$			32.0159i			1.17773i	0.808233	+	0.588863i	$0.200424\pi$
$739$			32.0159i			1.17773i	−0.808233	+	0.588863i	$0.799576\pi$
$740$	10.7363	+	12.8594i	0.394673	+	0.472723i
$741$	1.41288	−	5.86347i	0.0519033	−	0.215400i
$742$	−4.97899	−	13.7325i	−0.182784	−	0.504135i
$743$	−41.0981			−1.50774			−0.753872	−	0.657021i	$-0.771816\pi$
$743$	−41.0981			−1.50774			−0.753872	+	0.657021i	$0.771816\pi$
$744$	−0.777193	−	0.452565i	−0.0284933	−	0.0165919i
$745$	−2.93424			−0.107502
$746$	−24.7308	+	8.96665i	−0.905458	+	0.328292i
$747$		−	28.9274i		−	1.05840i
$748$	18.3791	+	22.0136i	0.672005	+	0.804899i
$749$			23.0205i			0.841149i
$750$	0.206611	+	0.569850i	0.00754436	+	0.0208080i
$751$	−4.84729			−0.176880			−0.0884401	−	0.996081i	$-0.528188\pi$
$751$	−4.84729			−0.176880			−0.0884401	+	0.996081i	$0.528188\pi$
$752$	10.9593	+	1.98837i	0.399645	+	0.0725083i
$753$			2.82927i			0.103104i
$754$	−6.19995	−	17.1000i	−0.225789	−	0.622745i
$755$	18.4054			0.669841
$756$	−4.42139	−	5.29575i	−0.160804	−	0.192605i
$757$	35.3472			1.28472			0.642359	−	0.766404i	$-0.277956\pi$
$757$	35.3472			1.28472			0.642359	+	0.766404i	$0.277956\pi$
$758$	2.62823	+	7.24889i	0.0954617	+	0.263291i
$759$	11.6708			0.423624
$760$	−8.90435	−	8.52716i	−0.322995	−	0.309313i
$761$	27.8604			1.00994			0.504969	−	0.863137i	$-0.331504\pi$
$761$	27.8604			1.00994			0.504969	+	0.863137i	$0.331504\pi$
$762$	1.12361	+	3.09902i	0.0407042	+	0.112266i
$763$	19.3182			0.699364
$764$	−26.7604	−	32.0525i	−0.968157	−	1.15962i
$765$	−11.5058			−0.415993
$766$	12.5223	+	34.5377i	0.452451	+	1.24790i
$767$		−	19.3124i		−	0.697331i
$768$	6.42070	+	2.40914i	0.231687	+	0.0869324i
$769$	43.3941			1.56483			0.782416	−	0.622757i	$-0.213987\pi$
$769$	43.3941			1.56483			0.782416	+	0.622757i	$0.213987\pi$
$770$	2.34095	+	6.45653i	0.0843619	+	0.232677i
$771$			9.81357i			0.353427i
$772$	16.1954	+	19.3981i	0.582884	+	0.698153i
$773$			38.5654i			1.38710i	0.720408	+	0.693550i	$0.243954\pi$
$773$			38.5654i			1.38710i	−0.720408	+	0.693550i	$0.756046\pi$
$774$	13.4424	−	4.87382i	0.483178	−	0.175186i
$775$	−0.741862			−0.0266485
$776$	−7.10561	+	12.2025i	−0.255077	+	0.438045i
$777$	4.96750			0.178208
$778$	−12.1081	−	33.3951i	−0.434095	−	1.19727i
$779$	−1.53605	+	6.37463i	−0.0550345	+	0.228395i
$780$	1.77357	+	2.12431i	0.0635040	+	0.0760623i
$781$		−	1.31561i		−	0.0470763i
$782$	42.1407	−	15.2790i	1.50695	−	0.546376i
$783$		−	9.93211i		−	0.354944i
$784$	3.63136	−	20.0150i	0.129691	−	0.714822i
$785$	−15.1384			−0.540312
$786$	−0.220608	+	0.0799860i	−0.00786884	+	0.00285301i
$787$	21.7097			0.773866			0.386933	−	0.922108i	$-0.373535\pi$
$787$	21.7097			0.773866			0.386933	+	0.922108i	$0.373535\pi$
$788$	−14.3004	+	11.9393i	−0.509430	+	0.425320i
$789$		−	3.85684i		−	0.137307i
$790$	7.68819	+	21.2047i	0.273534	+	0.754429i
$791$	−13.1999			−0.469334
$792$	−14.0683	+	24.1595i	−0.499894	+	0.858472i
$793$		−	1.89539i		−	0.0673074i
$794$	−6.91339	−	19.0677i	−0.245347	−	0.676688i
$795$			3.19951i			0.113475i
$796$	15.2696	+	18.2892i	0.541215	+	0.648245i
$797$		−	5.84272i		−	0.206960i	−0.994632	−	0.103480i	$-0.967002\pi$
$797$		−	5.84272i		−	0.206960i	0.994632	−	0.103480i	$-0.0329977\pi$
$798$	−3.63321	+	0.406330i	−0.128614	+	0.0143839i
$799$		−	11.3761i		−	0.402459i
$800$	5.57688	−	0.947838i	0.197173	−	0.0335111i
$801$		−	23.7657i		−	0.839718i
$802$	17.7479	−	6.43485i	0.626699	−	0.227222i
$803$		−	45.8119i		−	1.61667i
$804$	7.90846	−	6.60272i	0.278910	−	0.232860i
$805$	10.7350			0.378358
$806$	−3.18411	+	1.15447i	−0.112156	+	0.0406643i
$807$		−	13.2136i		−	0.465141i
$808$	19.3136	+	11.2465i	0.679451	+	0.395649i
$809$	−18.2360			−0.641145			−0.320572	−	0.947224i	$-0.603875\pi$
$809$	−18.2360			−0.641145			−0.320572	+	0.947224i	$0.603875\pi$
$810$	−3.55768	−	9.81238i	−0.125004	−	0.344772i
$811$	−12.1825			−0.427787			−0.213893	−	0.976857i	$-0.568614\pi$
$811$	−12.1825			−0.427787			−0.213893	+	0.976857i	$0.568614\pi$
$812$	−8.46345	+	7.06608i	−0.297009	+	0.247971i
$813$		−	5.86347i		−	0.205641i
$814$	−14.1709	−	39.0845i	−0.496689	−	1.36991i
$815$		−	6.35743i		−	0.222691i
$816$	1.25039	−	6.89177i	0.0437723	−	0.241260i
$817$	3.66584	−	15.2133i	0.128252	−	0.532248i
$818$	11.1041	−	4.02601i	0.388245	−	0.140766i
$819$	−12.5800			−0.439581
$820$	−1.92818	−	2.30950i	−0.0673351	−	0.0806511i
$821$	−39.8599			−1.39112			−0.695560	−	0.718468i	$-0.744844\pi$
$821$	−39.8599			−1.39112			−0.695560	+	0.718468i	$0.744844\pi$
$822$	−1.18560	−	3.26999i	−0.0413526	−	0.114054i
$823$		−	27.7993i		−	0.969023i	−0.874785	−	0.484511i	$-0.838997\pi$
$823$		−	27.7993i		−	0.969023i	0.874785	−	0.484511i	$-0.161003\pi$
$824$	13.5744	+	7.90450i	0.472888	+	0.275366i
$825$		−	1.50430i		−	0.0523730i
$826$	−11.0052	+	3.99015i	−0.382919	+	0.138835i
$827$	6.19617			0.215462			0.107731	−	0.994180i	$-0.465641\pi$
$827$	6.19617			0.215462			0.107731	+	0.994180i	$0.465641\pi$
$828$	28.0065	+	33.5450i	0.973293	+	1.16577i
$829$			4.37119i			0.151818i	0.997115	+	0.0759088i	$0.0241858\pi$
$829$			4.37119i			0.151818i	−0.997115	+	0.0759088i	$0.975814\pi$
$830$	13.6561	−	4.95132i	0.474012	−	0.171863i
$831$	11.3169			0.392578
$832$	22.4613	−	12.7468i	0.778705	−	0.441915i
$833$	−20.7763			−0.719856
$834$	−12.5939	+	4.56618i	−0.436092	+	0.158114i
$835$	24.7009			0.854811
$836$	13.5616	+	27.4272i	0.469037	+	0.948588i
$837$	−1.84941			−0.0639250
$838$	−28.5029	+	10.3343i	−0.984617	+	0.356993i
$839$	9.27983			0.320375			0.160188	−	0.987087i	$-0.448790\pi$
$839$	9.27983			0.320375			0.160188	+	0.987087i	$0.448790\pi$
$840$	0.844097	−	1.44957i	0.0291241	−	0.0500150i
$841$	13.1269			0.452652
$842$	40.6222	−	14.7284i	1.39993	−	0.507575i
$843$		−	1.30745i		−	0.0450309i
$844$	1.67786	−	1.40083i	0.0577542	−	0.0482186i
$845$	−2.57829			−0.0886960
$846$	10.4263	−	3.78026i	0.358463	−	0.129968i
$847$		−	1.82364i		−	0.0626611i
$848$	29.3796	+	5.33039i	1.00890	+	0.183046i
$849$		−	3.01597i		−	0.103508i
$850$	−1.96937	−	5.43169i	−0.0675489	−	0.186306i
$851$	−64.9840			−2.22762
$852$	−0.246664	+	0.205938i	−0.00845057	+	0.00705533i
$853$	33.1419			1.13476			0.567378	−	0.823457i	$-0.307958\pi$
$853$	33.1419			1.13476			0.567378	+	0.823457i	$0.307958\pi$
$854$	−1.08009	+	0.391609i	−0.0369599	+	0.0134006i
$855$	−11.9343	−	2.87573i	−0.408146	−	0.0983478i
$856$	−40.6651	−	23.6796i	−1.38990	−	0.809351i
$857$			9.52644i			0.325417i	0.986674	+	0.162709i	$0.0520230\pi$
$857$			9.52644i			0.325417i	−0.986674	+	0.162709i	$0.947977\pi$
$858$	−2.34095	−	6.45653i	−0.0799187	−	0.220422i
$859$			44.1549i			1.50654i	0.657709	+	0.753272i	$0.271526\pi$
$859$			44.1549i			1.50654i	−0.657709	+	0.753272i	$0.728474\pi$
$860$	4.60170	+	5.51171i	0.156917	+	0.187948i
$861$	−0.892139			−0.0304040
$862$	−3.48158	−	9.60251i	−0.118583	−	0.327063i
$863$	46.0395			1.56720			0.783602	−	0.621264i	$-0.213380\pi$
$863$	46.0395			1.56720			0.783602	+	0.621264i	$0.213380\pi$
$864$	13.9028	−	2.36290i	0.472983	−	0.0803874i
$865$			4.60993i			0.156742i
$866$	−48.3858	+	17.5432i	−1.64422	+	0.596144i
$867$	0.132501			0.00449997
$868$	1.31574	+	1.57594i	0.0446592	+	0.0534909i
$869$		−	55.9765i		−	1.89887i
$870$	2.27034	−	0.823158i	0.0769718	−	0.0279077i
$871$		−	38.7984i		−	1.31463i
$872$	−19.8713	+	34.1250i	−0.672926	+	1.15562i
$873$			14.0600i			0.475859i
$874$	47.5291	−	5.31553i	1.60770	−	0.179801i
$875$		−	1.38367i		−	0.0467767i
$876$	−8.58926	+	7.17112i	−0.290204	+	0.242290i
$877$			44.7080i			1.50968i	0.655907	+	0.754842i	$0.272286\pi$
$877$			44.7080i			1.50968i	−0.655907	+	0.754842i	$0.727714\pi$
$878$	13.0590	+	36.0177i	0.440719	+	1.21554i
$879$		−	3.37305i		−	0.113770i
$880$	−13.8133	−	2.50617i	−0.465646	−	0.0844829i
$881$	−27.6950			−0.933068			−0.466534	−	0.884503i	$-0.654497\pi$
$881$	−27.6950			−0.933068			−0.466534	+	0.884503i	$0.654497\pi$
$882$	−6.90391	−	19.0416i	−0.232467	−	0.641163i
$883$			57.0592i			1.92020i	0.279664	+	0.960098i	$0.409777\pi$
$883$			57.0592i			1.92020i	−0.279664	+	0.960098i	$0.590223\pi$
$884$	−16.9053	−	20.2485i	−0.568587	−	0.681029i
$885$	2.56408			0.0861907
$886$	35.5052	−	12.8731i	1.19282	−	0.432481i
$887$	−13.5991			−0.456615			−0.228307	−	0.973589i	$-0.573319\pi$
$887$	−13.5991			−0.456615			−0.228307	+	0.973589i	$0.573319\pi$
$888$	−5.10972	+	8.77496i	−0.171471	+	0.294468i
$889$		−	7.52486i		−	0.252376i
$890$	11.2194	−	4.06781i	0.376074	−	0.136353i
$891$			25.9029i			0.867779i
$892$	13.6818	−	11.4228i	0.458101	−	0.382465i
$893$	2.84332	−	11.7999i	0.0951481	−	0.394867i
$894$	−0.606245	−	1.67208i	−0.0202759	−	0.0559226i
$895$	19.4384			0.649756
$896$	−11.9045	−	10.1659i	−0.397701	−	0.339620i
$897$	−10.7350			−0.358430
$898$	−43.4961	+	15.7704i	−1.45148	+	0.526265i
$899$			2.95565i			0.0985766i
$900$	4.32375	−	3.60987i	0.144125	−	0.120329i
$901$		−	30.4971i		−	1.01600i
$902$	2.54502	+	7.01939i	0.0847400	+	0.233720i
$903$	2.12913			0.0708530
$904$	13.5778	−	23.3173i	0.451591	−	0.775520i
$905$			18.9496i			0.629908i
$906$	3.80275	+	10.4883i	0.126338	+	0.348451i
$907$	33.5876			1.11526			0.557630	−	0.830090i	$-0.311711\pi$
$907$	33.5876			1.11526			0.557630	+	0.830090i	$0.311711\pi$
$908$	−11.5203	+	9.61821i	−0.382314	+	0.319191i
$909$	22.2536			0.738105
$910$	−2.15324	−	5.93881i	−0.0713791	−	0.196870i
$911$	54.8024			1.81569			0.907843	−	0.419311i	$-0.137728\pi$
$911$	54.8024			1.81569			0.907843	+	0.419311i	$0.137728\pi$
$912$	3.01947	−	6.83595i	0.0999846	−	0.226361i
$913$	−36.0497			−1.19307
$914$	2.68802	+	7.41380i	0.0889119	+	0.245227i
$915$	0.251649			0.00831925
$916$	−32.7903	+	27.3764i	−1.08342	+	0.904542i
$917$	0.535668			0.0176893
$918$	−4.90951	−	13.5409i	−0.162038	−	0.446915i
$919$			37.9101i			1.25054i	0.780409	+	0.625269i	$0.215011\pi$
$919$			37.9101i			1.25054i	−0.780409	+	0.625269i	$0.784989\pi$
$920$	−11.0423	+	18.9631i	−0.364055	+	0.625194i
$921$	0.00734579			0.000242052
$922$	7.14412	+	19.7041i	0.235279	+	0.648920i
$923$			1.21012i			0.0398315i
$924$	−3.19559	+	2.66798i	−0.105127	+	0.0877700i
$925$			8.37605i			0.275403i
$926$	−18.4064	+	6.67360i	−0.604871	+	0.219308i
$927$	15.6408			0.513710
$928$	−3.77629	−	22.2189i	−0.123963	−	0.729370i
$929$	−23.1452			−0.759371			−0.379685	−	0.925116i	$-0.623968\pi$
$929$	−23.1452			−0.759371			−0.379685	+	0.925116i	$0.623968\pi$
$930$	−0.153277	−	0.422750i	−0.00502614	−	0.0138625i
$931$	−21.5501	−	5.19277i	−0.706277	−	0.170186i
$932$	3.40880	−	2.84599i	0.111659	−	0.0932234i
$933$		−	6.29945i		−	0.206235i
$934$	−17.5711	+	6.37075i	−0.574943	+	0.208457i
$935$			14.3387i			0.468925i
$936$	12.9402	−	22.2223i	0.422963	−	0.726358i
$937$	33.6022			1.09774			0.548868	−	0.835909i	$-0.315059\pi$
$937$	33.6022			1.09774			0.548868	+	0.835909i	$0.315059\pi$
$938$	−22.1093	+	8.01616i	−0.721893	+	0.261737i
$939$	−1.72550			−0.0563094
$940$	3.56919	+	4.27503i	0.116414	+	0.139436i
$941$			36.1363i			1.17801i	0.808130	+	0.589004i	$0.200480\pi$
$941$			36.1363i			1.17801i	−0.808130	+	0.589004i	$0.799520\pi$
$942$	−3.12775	−	8.62661i	−0.101908	−	0.281070i
$943$	11.6708			0.380054
$944$	4.27177	−	23.5448i	0.139034	−	0.766317i
$945$		−	3.44941i		−	0.112209i
$946$	−6.07382	−	16.7521i	−0.197477	−	0.544658i
$947$		−	19.4547i		−	0.632194i	−0.948727	−	0.316097i	$-0.897628\pi$
$947$		−	19.4547i		−	0.632194i	0.948727	−	0.316097i	$-0.102372\pi$
$948$	−10.4950	+	8.76223i	−0.340863	+	0.284584i
$949$			42.1384i			1.36787i
$950$	−0.685141	−	6.12622i	−0.0222289	−	0.198761i
$951$		−	1.72484i		−	0.0559318i
$952$	−8.04576	+	13.8170i	−0.260765	+	0.447813i
$953$			16.4052i			0.531415i	0.964054	+	0.265708i	$0.0856056\pi$
$953$			16.4052i			0.531415i	−0.964054	+	0.265708i	$0.914394\pi$
$954$	27.9507	−	10.1341i	0.904937	−	0.328103i
$955$		−	20.8775i		−	0.675580i
$956$	14.8363	+	17.7703i	0.479841	+	0.574733i
$957$	−5.99328			−0.193735
$958$	4.44336	−	1.61103i	0.143558	−	0.0520500i
$959$			7.93998i			0.256395i
$960$	1.69237	+	2.98215i	0.0546210	+	0.0962485i
$961$	−30.4496			−0.982246
$962$	13.0346	+	35.9505i	0.420252	+	1.15909i
$963$	−46.8552			−1.50989
$964$	−28.1745	−	33.7462i	−0.907438	−	1.08689i
$965$			12.6350i			0.406736i
$966$	2.21796	+	6.11732i	0.0713617	+	0.196822i
$967$			51.1258i			1.64410i	0.569418	+	0.822048i	$0.307169\pi$
$967$			51.1258i			1.64410i	−0.569418	+	0.822048i	$0.692831\pi$
$968$	3.22142	+	1.87586i	0.103540	+	0.0602923i
$969$	−7.42036	−	1.78803i	−0.238376	−	0.0574397i
$970$	−6.63749	+	2.40656i	−0.213117	+	0.0772699i
$971$	−12.1270			−0.389174			−0.194587	−	0.980885i	$-0.562337\pi$
$971$	−12.1270			−0.389174			−0.194587	+	0.980885i	$0.562337\pi$
$972$	16.3385	−	13.6409i	0.524056	−	0.437531i
$973$	30.5798			0.980343
$974$	−11.2612	−	31.0594i	−0.360833	−	0.995209i
$975$			1.38367i			0.0443130i
$976$	0.419248	−	2.31077i	0.0134198	−	0.0739660i
$977$			17.4735i			0.559026i	0.960142	+	0.279513i	$0.0901731\pi$
$977$			17.4735i			0.559026i	−0.960142	+	0.279513i	$0.909827\pi$
$978$	3.62278	−	1.31351i	0.115844	−	0.0420015i
$979$	−29.6171			−0.946565
$980$	7.80750	−	6.51843i	0.249401	−	0.208224i
$981$			39.3196i			1.25538i
$982$	−33.5217	+	12.1540i	−1.06972	+	0.387850i
$983$	3.94675			0.125882			0.0629409	−	0.998017i	$-0.479952\pi$
$983$	3.94675			0.125882			0.0629409	+	0.998017i	$0.479952\pi$
$984$	0.917682	−	1.57594i	0.0292546	−	0.0502392i
$985$	−9.31461			−0.296788
$986$	−21.6404	+	7.84618i	−0.689172	+	0.249873i
$987$	1.65141			0.0525649
$988$	−12.4741	−	25.2279i	−0.396855	−	0.802606i
$989$	−27.8529			−0.885671
$990$	−13.1414	+	4.76470i	−0.417663	+	0.151432i
$991$	32.8661			1.04403			0.522013	−	0.852937i	$-0.325181\pi$
$991$	32.8661			1.04403			0.522013	+	0.852937i	$0.325181\pi$
$992$	−4.13728	+	0.703165i	−0.131359	+	0.0223255i
$993$	−12.0822			−0.383417
$994$	0.689586	−	0.250023i	0.0218723	−	0.00793026i
$995$			11.9128i			0.377660i
$996$	5.64301	+	6.75896i	0.178806	+	0.214166i
$997$	−21.4149			−0.678216			−0.339108	−	0.940747i	$-0.610125\pi$
$997$	−21.4149			−0.678216			−0.339108	+	0.940747i	$0.610125\pi$
$998$	−29.6425	+	10.7475i	−0.938317	+	0.340206i
$999$			20.8809i			0.660644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.f.a.151.12	yes	20
4.3	odd	2	inner	380.2.f.a.151.10	yes	20
19.18	odd	2	inner	380.2.f.a.151.9	✓	20
76.75	even	2	inner	380.2.f.a.151.11	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.f.a.151.9	✓	20	19.18	odd	2	inner
380.2.f.a.151.10	yes	20	4.3	odd	2	inner
380.2.f.a.151.11	yes	20	76.75	even	2	inner
380.2.f.a.151.12	yes	20	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.482046 + 1.32952i) q^{2} -0.428612 q^{3} +(-1.53526 + 1.28178i) q^{4} -1.00000 q^{5} +(-0.206611 - 0.569850i) q^{6} +1.38367i q^{7} +(-2.44423 - 1.42329i) q^{8} -2.81629 q^{9} +O(q^{10})\)	\(q+(0.482046 + 1.32952i) q^{2} -0.428612 q^{3} +(-1.53526 + 1.28178i) q^{4} -1.00000 q^{5} +(-0.206611 - 0.569850i) q^{6} +1.38367i q^{7} +(-2.44423 - 1.42329i) q^{8} -2.81629 q^{9} +(-0.482046 - 1.32952i) q^{10} +3.50970i q^{11} +(0.658033 - 0.549387i) q^{12} -3.22827i q^{13} +(-1.83963 + 0.666994i) q^{14} +0.428612 q^{15} +(0.714069 - 3.93575i) q^{16} -4.08544 q^{17} +(-1.35758 - 3.74432i) q^{18} +(-4.23761 - 1.02110i) q^{19} +(1.53526 - 1.28178i) q^{20} -0.593060i q^{21} +(-4.66622 + 1.69183i) q^{22} +7.75831i q^{23} +(1.04763 + 0.610040i) q^{24} +1.00000 q^{25} +(4.29206 - 1.55617i) q^{26} +2.49293 q^{27} +(-1.77357 - 2.12431i) q^{28} -3.98410i q^{29} +(0.206611 + 0.569850i) q^{30} -0.741862 q^{31} +(5.57688 - 0.947838i) q^{32} -1.50430i q^{33} +(-1.96937 - 5.43169i) q^{34} -1.38367i q^{35} +(4.32375 - 3.60987i) q^{36} +8.37605i q^{37} +(-0.685141 - 6.12622i) q^{38} +1.38367i q^{39} +(2.44423 + 1.42329i) q^{40} -1.50430i q^{41} +(0.788487 - 0.285882i) q^{42} +3.59008i q^{43} +(-4.49867 - 5.38831i) q^{44} +2.81629 q^{45} +(-10.3148 + 3.73986i) q^{46} +2.78456i q^{47} +(-0.306059 + 1.68691i) q^{48} +5.08544 q^{49} +(0.482046 + 1.32952i) q^{50} +1.75107 q^{51} +(4.13793 + 4.95624i) q^{52} +7.46481i q^{53} +(1.20171 + 3.31441i) q^{54} -3.50970i q^{55} +(1.96937 - 3.38201i) q^{56} +(1.81629 + 0.437658i) q^{57} +(5.29696 - 1.92052i) q^{58} +5.98229 q^{59} +(-0.658033 + 0.549387i) q^{60} +0.587124 q^{61} +(-0.357611 - 0.986323i) q^{62} -3.89683i q^{63} +(3.94849 + 6.95769i) q^{64} +3.22827i q^{65} +(2.00000 - 0.725141i) q^{66} +12.0183 q^{67} +(6.27224 - 5.23665i) q^{68} -3.32530i q^{69} +(1.83963 - 0.666994i) q^{70} -0.374851 q^{71} +(6.88365 + 4.00840i) q^{72} -13.0529 q^{73} +(-11.1362 + 4.03764i) q^{74} -0.428612 q^{75} +(7.81468 - 3.86403i) q^{76} -4.85628 q^{77} +(-1.83963 + 0.666994i) q^{78} -15.9491 q^{79} +(-0.714069 + 3.93575i) q^{80} +7.38037 q^{81} +(2.00000 - 0.725141i) q^{82} +10.2715i q^{83} +(0.760173 + 0.910503i) q^{84} +4.08544 q^{85} +(-4.77309 + 1.73058i) q^{86} +1.70764i q^{87} +(4.99532 - 8.57849i) q^{88} +8.43864i q^{89} +(1.35758 + 3.74432i) q^{90} +4.46687 q^{91} +(-9.94446 - 11.9110i) q^{92} +0.317971 q^{93} +(-3.70213 + 1.34228i) q^{94} +(4.23761 + 1.02110i) q^{95} +(-2.39032 + 0.406255i) q^{96} -4.99238i q^{97} +(2.45142 + 6.76122i) q^{98} -9.88433i 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more