LMFDB - Embedded newform 380.2.bh.a.117.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			117.6
Character	$\chi$	$=$	380.117
Dual form			380.2.bh.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.224420 + 0.104649i) q^{3} +(-2.15088 - 0.611320i) q^{5} +(0.357605 - 1.33460i) q^{7} +(-1.88895 - 2.25116i) q^{9} +O(q^{10})$	\(q+(0.224420 + 0.104649i) q^{3} +(-2.15088 - 0.611320i) q^{5} +(0.357605 - 1.33460i) q^{7} +(-1.88895 - 2.25116i) q^{9} +(0.00188012 - 0.00325647i) q^{11} +(-1.47530 - 3.16379i) q^{13} +(-0.418728 - 0.362280i) q^{15} +(0.0221536 + 0.253216i) q^{17} +(0.384763 - 4.34188i) q^{19} +(0.219918 - 0.262088i) q^{21} +(-3.63066 - 2.54221i) q^{23} +(4.25258 + 2.62975i) q^{25} +(-0.380604 - 1.42043i) q^{27} +(1.17897 - 0.989275i) q^{29} +(0.377920 - 0.218192i) q^{31} +(0.000762724 - 0.000534065i) q^{33} +(-1.58503 + 2.65195i) q^{35} +(0.496355 - 0.496355i) q^{37} -0.864406i q^{39} +(2.34618 + 6.44608i) q^{41} +(-3.96540 - 5.66318i) q^{43} +(2.68673 + 5.99673i) q^{45} +(-2.70864 - 0.236975i) q^{47} +(4.40890 + 2.54548i) q^{49} +(-0.0215271 + 0.0591453i) q^{51} +(-3.00243 + 4.28792i) q^{53} +(-0.00603466 + 0.00585492i) q^{55} +(0.540722 - 0.934142i) q^{57} +(7.08129 + 5.94191i) q^{59} +(-0.899822 - 5.10314i) q^{61} +(-3.67990 + 1.71597i) q^{63} +(1.23910 + 7.70680i) q^{65} +(1.01014 - 11.5460i) q^{67} +(-0.548754 - 0.950469i) q^{69} +(-1.85753 - 0.327532i) q^{71} +(-4.92742 + 10.5669i) q^{73} +(0.679164 + 1.03520i) q^{75} +(-0.00367374 - 0.00367374i) q^{77} +(10.2851 - 3.74347i) q^{79} +(-1.46766 + 8.32351i) q^{81} +(-1.18134 - 0.316538i) q^{83} +(0.107147 - 0.558181i) q^{85} +(0.368112 - 0.0986353i) q^{87} +(4.35576 + 1.58537i) q^{89} +(-4.74996 + 0.837546i) q^{91} +(0.107647 - 0.00941786i) q^{93} +(-3.48186 + 9.10366i) q^{95} +(17.5189 - 1.53271i) q^{97} +(-0.0108823 + 0.00191884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.224420	+	0.104649i	0.129569	+	0.0604191i	0.486322	−	0.873780i	$-0.338338\pi$
$3$	0.224420	+	0.104649i	0.129569	+	0.0604191i	−0.356753	+	0.934199i	$0.616116\pi$
$4$		0			0
$5$	−2.15088	−	0.611320i	−0.961903	−	0.273391i
$5$	−2.15088	−	0.611320i	−0.961903	−	0.273391i
$6$		0			0
$7$	0.357605	−	1.33460i	0.135162	−	0.504431i	−0.864835	−	0.502056i	$-0.832577\pi$
$7$	0.357605	−	1.33460i	0.135162	−	0.504431i	0.999997	−	0.00237552i	$-0.000756153\pi$
$8$		0			0
$9$	−1.88895	−	2.25116i	−0.629650	−	0.750388i
$10$		0			0
$11$	0.00188012	−	0.00325647i	0.000566878	−	0.000981862i	−0.865742	−	0.500491i	$-0.833153\pi$
$11$	0.00188012	−	0.00325647i	0.000566878	−	0.000981862i	0.866309	+	0.499509i	$0.166486\pi$
$12$		0			0
$13$	−1.47530	−	3.16379i	−0.409174	−	0.877476i	−0.997621	−	0.0689404i	$-0.978038\pi$
$13$	−1.47530	−	3.16379i	−0.409174	−	0.877476i	0.588447	−	0.808536i	$-0.299740\pi$
$14$		0			0
$15$	−0.418728	−	0.362280i	−0.108115	−	0.0935403i
$16$		0			0
$17$	0.0221536	+	0.253216i	0.00537303	+	0.0614140i	0.998408	−	0.0564073i	$-0.0179645\pi$
$17$	0.0221536	+	0.253216i	0.00537303	+	0.0614140i	−0.993035	+	0.117821i	$0.962409\pi$
$18$		0			0
$19$	0.384763	−	4.34188i	0.0882708	−	0.996097i
$19$	0.384763	−	4.34188i	0.0882708	−	0.996097i
$20$		0			0
$21$	0.219918	−	0.262088i	0.0479901	−	0.0571924i
$22$		0			0
$23$	−3.63066	−	2.54221i	−0.757045	−	0.530088i	0.130144	−	0.991495i	$-0.458456\pi$
$23$	−3.63066	−	2.54221i	−0.757045	−	0.530088i	−0.887189	+	0.461407i	$0.847345\pi$
$24$		0			0
$25$	4.25258	+	2.62975i	0.850515	+	0.525950i
$26$		0			0
$27$	−0.380604	−	1.42043i	−0.0732472	−	0.273362i
$28$		0			0
$29$	1.17897	−	0.989275i	0.218930	−	0.183704i	−0.526726	−	0.850035i	$-0.676581\pi$
$29$	1.17897	−	0.989275i	0.218930	−	0.183704i	0.745656	+	0.666331i	$0.232136\pi$
$30$		0			0
$31$	0.377920	−	0.218192i	0.0678765	−	0.0391885i	−0.465678	−	0.884954i	$-0.654189\pi$
$31$	0.377920	−	0.218192i	0.0678765	−	0.0391885i	0.533554	+	0.845766i	$0.320856\pi$
$32$		0			0
$33$	0.000762724	0	0.000534065i	0.000132773	0	9.29688e-5i
$34$		0			0
$35$	−1.58503	+	2.65195i	−0.267919	+	0.448262i
$36$		0			0
$37$	0.496355	−	0.496355i	0.0816002	−	0.0816002i	−0.665129	−	0.746729i	$-0.731623\pi$
$37$	0.496355	−	0.496355i	0.0816002	−	0.0816002i	0.746729	+	0.665129i	$0.231623\pi$
$38$		0			0
$39$		−	0.864406i		−	0.138416i
$40$		0			0
$41$	2.34618	+	6.44608i	0.366412	+	1.00671i	0.976715	+	0.214541i	$0.0688255\pi$
$41$	2.34618	+	6.44608i	0.366412	+	1.00671i	−0.610303	+	0.792168i	$0.708952\pi$
$42$		0			0
$43$	−3.96540	−	5.66318i	−0.604718	−	0.863627i	0.393735	−	0.919224i	$-0.371183\pi$
$43$	−3.96540	−	5.66318i	−0.604718	−	0.863627i	−0.998453	+	0.0555970i	$0.982294\pi$
$44$		0			0
$45$	2.68673	+	5.99673i	0.400513	+	0.893940i
$46$		0			0
$47$	−2.70864	−	0.236975i	−0.395096	−	0.0345664i	−0.112123	−	0.993694i	$-0.535765\pi$
$47$	−2.70864	−	0.236975i	−0.395096	−	0.0345664i	−0.282973	+	0.959128i	$0.591321\pi$
$48$		0			0
$49$	4.40890	+	2.54548i	0.629843	+	0.363640i
$50$		0			0
$51$	−0.0215271	+	0.0591453i	−0.00301440	+	0.00828200i
$52$		0			0
$53$	−3.00243	+	4.28792i	−0.412416	+	0.588991i	−0.970592	−	0.240732i	$-0.922613\pi$
$53$	−3.00243	+	4.28792i	−0.412416	+	0.588991i	0.558176	+	0.829723i	$0.311502\pi$
$54$		0			0
$55$	−0.00603466	+	0.00585492i	−0.000813714	+	0.000789477i
$56$		0			0
$57$	0.540722	−	0.934142i	0.0716204	−	0.123730i
$58$		0			0
$59$	7.08129	+	5.94191i	0.921906	+	0.773571i	0.974346	−	0.225053i	$-0.0722556\pi$
$59$	7.08129	+	5.94191i	0.921906	+	0.773571i	−0.0524407	+	0.998624i	$0.516700\pi$
$60$		0			0
$61$	−0.899822	−	5.10314i	−0.115210	−	0.653391i	−0.986646	−	0.162880i	$-0.947922\pi$
$61$	−0.899822	−	5.10314i	−0.115210	−	0.653391i	0.871435	−	0.490510i	$-0.163190\pi$
$62$		0			0
$63$	−3.67990	+	1.71597i	−0.463624	+	0.216191i
$64$		0			0
$65$	1.23910	+	7.70680i	0.153692	+	0.955911i
$66$		0			0
$67$	1.01014	−	11.5460i	0.123409	−	1.41057i	−0.641843	−	0.766836i	$-0.721830\pi$
$67$	1.01014	−	11.5460i	0.123409	−	1.41057i	0.765251	−	0.643732i	$-0.222615\pi$
$68$		0			0
$69$	−0.548754	−	0.950469i	−0.0660622	−	0.114423i
$70$		0			0
$71$	−1.85753	−	0.327532i	−0.220448	−	0.0388709i	0.0623331	−	0.998055i	$-0.480146\pi$
$71$	−1.85753	−	0.327532i	−0.220448	−	0.0388709i	−0.282781	+	0.959184i	$0.591257\pi$
$72$		0			0
$73$	−4.92742	+	10.5669i	−0.576711	+	1.23676i	0.374215	+	0.927342i	$0.377912\pi$
$73$	−4.92742	+	10.5669i	−0.576711	+	1.23676i	−0.950926	+	0.309419i	$0.899866\pi$
$74$		0			0
$75$	0.679164	+	1.03520i	0.0784231	+	0.119534i
$76$		0			0
$77$	−0.00367374	−	0.00367374i	−0.000418662	−	0.000418662i
$78$		0			0
$79$	10.2851	−	3.74347i	1.15716	−	0.421173i	0.309081	−	0.951036i	$-0.399979\pi$
$79$	10.2851	−	3.74347i	1.15716	−	0.421173i	0.848084	+	0.529863i	$0.177757\pi$
$80$		0			0
$81$	−1.46766	+	8.32351i	−0.163073	+	0.924835i
$82$		0			0
$83$	−1.18134	−	0.316538i	−0.129669	−	0.0347446i	0.193401	−	0.981120i	$-0.438048\pi$
$83$	−1.18134	−	0.316538i	−0.129669	−	0.0347446i	−0.323070	+	0.946375i	$0.604715\pi$
$84$		0			0
$85$	0.107147	−	0.558181i	0.0116217	−	0.0605433i
$86$		0			0
$87$	0.368112	−	0.0986353i	0.0394657	−	0.0105748i
$88$		0			0
$89$	4.35576	+	1.58537i	0.461710	+	0.168049i	0.562393	−	0.826870i	$-0.309881\pi$
$89$	4.35576	+	1.58537i	0.461710	+	0.168049i	−0.100683	+	0.994919i	$0.532103\pi$
$90$		0			0
$91$	−4.74996	+	0.837546i	−0.497931	+	0.0877987i
$92$		0			0
$93$	0.107647	−	0.00941786i	0.0111624	−	0.000976587i
$94$		0			0
$95$	−3.48186	+	9.10366i	−0.357231	+	0.934016i
$96$		0			0
$97$	17.5189	−	1.53271i	1.77878	−	0.155623i	0.850126	−	0.526579i	$-0.176526\pi$
$97$	17.5189	−	1.53271i	1.77878	−	0.155623i	0.928650	+	0.370956i	$0.120970\pi$
$98$		0			0
$99$	−0.0108823	+	0.00191884i	−0.00109371	+	0.000192851i
$100$		0			0
$101$	6.45708	+	2.35019i	0.642504	+	0.233852i	0.642664	−	0.766148i	$-0.277829\pi$
$101$	6.45708	+	2.35019i	0.642504	+	0.233852i	−0.000160786		1.00000i	$0.500051\pi$
$102$		0			0
$103$	−9.21083	+	2.46803i	−0.907570	+	0.243183i	−0.682264	−	0.731106i	$-0.739005\pi$
$103$	−9.21083	+	2.46803i	−0.907570	+	0.243183i	−0.225305	+	0.974288i	$0.572338\pi$
$104$		0			0
$105$	−0.633238	+	0.429281i	−0.0617977	+	0.0418935i
$106$		0			0
$107$	−10.4537	−	2.80105i	−1.01059	−	0.270787i	−0.284716	−	0.958612i	$-0.591899\pi$
$107$	−10.4537	−	2.80105i	−1.01059	−	0.270787i	−0.725877	+	0.687825i	$0.758566\pi$
$108$		0			0
$109$	−0.343957	+	1.95068i	−0.0329451	+	0.186841i	−0.996839	−	0.0794446i	$-0.974685\pi$
$109$	−0.343957	+	1.95068i	−0.0329451	+	0.186841i	0.963894	+	0.266286i	$0.0857964\pi$
$110$		0			0
$111$	0.163335	−	0.0594491i	0.0155031	−	0.00564266i
$112$		0			0
$113$	2.00324	+	2.00324i	0.188449	+	0.188449i	0.795025	−	0.606577i	$-0.207458\pi$
$113$	2.00324	+	2.00324i	0.188449	+	0.188449i	−0.606577	+	0.795025i	$0.707458\pi$
$114$		0			0
$115$	6.25501	+	7.68749i	0.583283	+	0.716863i
$116$		0			0
$117$	−4.33543	+	9.29737i	−0.400811	+	0.859542i
$118$		0			0
$119$	0.345865	+	0.0609853i	0.0317054	+	0.00559051i
$120$		0			0
$121$	5.49999	+	9.52627i	0.499999	+	0.866024i
$122$		0			0
$123$	−0.148045	+	1.69216i	−0.0133487	+	0.152577i
$124$		0			0
$125$	−7.53917	−	8.25597i	−0.674323	−	0.738436i
$126$		0			0
$127$	7.42551	−	3.46257i	0.658907	−	0.307253i	−0.0642532	−	0.997934i	$-0.520467\pi$
$127$	7.42551	−	3.46257i	0.658907	−	0.307253i	0.723160	+	0.690680i	$0.242689\pi$
$128$		0			0
$129$	−0.297271	−	1.68591i	−0.0261733	−	0.148436i
$130$		0			0
$131$	10.3105	+	8.65153i	0.900832	+	0.755888i	0.970353	−	0.241693i	$-0.0777025\pi$
$131$	10.3105	+	8.65153i	0.900832	+	0.755888i	−0.0695207	+	0.997581i	$0.522147\pi$
$132$		0			0
$133$	−5.65708	−	2.06618i	−0.490531	−	0.179161i
$134$		0			0
$135$	−0.0497052	+	3.28785i	−0.00427794	+	0.282973i
$136$		0			0
$137$	8.16634	−	11.6627i	0.697698	−	0.996416i	−0.301381	−	0.953504i	$-0.597448\pi$
$137$	8.16634	−	11.6627i	0.697698	−	0.996416i	0.999079	−	0.0429118i	$-0.0136634\pi$
$138$		0			0
$139$	0.514380	−	1.41325i	0.0436291	−	0.119870i	−0.915965	−	0.401259i	$-0.868573\pi$
$139$	0.514380	−	1.41325i	0.0436291	−	0.119870i	0.959594	+	0.281389i	$0.0907950\pi$
$140$		0			0
$141$	−0.583075	−	0.336638i	−0.0491037	−	0.0283501i
$142$		0			0
$143$	−0.0130765	−	0.00114405i	−0.00109351	−	9.56699e-5i
$144$		0			0
$145$	−3.14059	+	1.40708i	−0.260812	+	0.116852i
$146$		0			0
$147$	0.723066	+	1.03264i	0.0596374	+	0.0851711i
$148$		0			0
$149$	−6.46057	−	17.7503i	−0.529271	−	1.45416i	−0.859932	−	0.510409i	$-0.829494\pi$
$149$	−6.46057	−	17.7503i	−0.529271	−	1.45416i	0.330661	−	0.943750i	$-0.392728\pi$
$150$		0			0
$151$		−	18.5169i		−	1.50689i	−0.657514	−	0.753443i	$-0.728392\pi$
$151$		−	18.5169i		−	1.50689i	0.657514	−	0.753443i	$-0.271608\pi$
$152$		0			0
$153$	0.528184	−	0.528184i	0.0427012	−	0.0427012i
$154$		0			0
$155$	−0.946247	+	0.238276i	−0.0760044	+	0.0191388i
$156$		0			0
$157$	−0.530302	+	0.371321i	−0.0423227	+	0.0296347i	−0.594546	−	0.804061i	$-0.702668\pi$
$157$	−0.530302	+	0.371321i	−0.0423227	+	0.0296347i	0.552224	+	0.833696i	$0.313779\pi$
$158$		0			0
$159$	−1.12253	+	0.648095i	−0.0890227	+	0.0513973i
$160$		0			0
$161$	−4.69118	+	3.93637i	−0.369717	+	0.310229i
$162$		0			0
$163$	−2.73676	−	10.2137i	−0.214360	−	0.800001i	−0.986391	−	0.164417i	$-0.947426\pi$
$163$	−2.73676	−	10.2137i	−0.214360	−	0.800001i	0.772031	−	0.635585i	$-0.219241\pi$
$164$		0			0
$165$	−0.00196701		0.000682442i	−0.000153132		5.31280e-5i
$166$		0			0
$167$	−18.2514	−	12.7798i	−1.41233	−	0.988928i	−0.996849	−	0.0793282i	$-0.974722\pi$
$167$	−18.2514	−	12.7798i	−1.41233	−	0.988928i	−0.415486	−	0.909599i	$-0.636389\pi$
$168$		0			0
$169$	0.523202	−	0.623528i	0.0402463	−	0.0479637i
$170$		0			0
$171$	−10.5011	+	7.33544i	−0.803038	+	0.560955i
$172$		0			0
$173$	−1.40159	−	16.0203i	−0.106561	−	1.21800i	−0.841648	−	0.540027i	$-0.818414\pi$
$173$	−1.40159	−	16.0203i	−0.106561	−	1.21800i	0.735087	−	0.677973i	$-0.237141\pi$
$174$		0			0
$175$	5.03041	−	4.73508i	0.380263	−	0.357938i
$176$		0			0
$177$	0.967372	+	2.07454i	0.0727121	+	0.155932i
$178$		0			0
$179$	0.342820	−	0.593781i	0.0256235	−	0.0443813i	−0.852929	−	0.522026i	$-0.825176\pi$
$179$	0.342820	−	0.593781i	0.0256235	−	0.0443813i	0.878553	+	0.477645i	$0.158510\pi$
$180$		0			0
$181$	−10.0584	−	11.9871i	−0.747632	−	0.890993i	0.249367	−	0.968409i	$-0.419778\pi$
$181$	−10.0584	−	11.9871i	−0.747632	−	0.890993i	−0.996999	+	0.0774157i	$0.975333\pi$
$182$		0			0
$183$	0.332100	−	1.23942i	0.0245496	−	0.0916202i
$184$		0			0
$185$	−1.37103	+	0.764168i	−0.100800	+	0.0561828i
$186$		0			0
$187$	0.000866243	0	0.000403936i	6.33459e−5	0	2.95387e-5i
$188$		0			0
$189$	−2.03181			−0.147793
$190$		0			0
$191$	20.1498			1.45799			0.728995	−	0.684519i	$-0.239988\pi$
$191$	20.1498			1.45799			0.728995	+	0.684519i	$0.239988\pi$
$192$		0			0
$193$	−6.64426	−	3.09827i	−0.478265	−	0.223018i	0.168510	−	0.985700i	$-0.446105\pi$
$193$	−6.64426	−	3.09827i	−0.478265	−	0.223018i	−0.646774	+	0.762682i	$0.723882\pi$
$194$		0			0
$195$	−0.528429	+	1.85923i	−0.0378416	+	0.133143i
$196$		0			0
$197$	−3.49846	+	13.0564i	−0.249255	+	0.930233i	0.721942	+	0.691954i	$0.243250\pi$
$197$	−3.49846	+	13.0564i	−0.249255	+	0.930233i	−0.971197	+	0.238279i	$0.923417\pi$
$198$		0			0
$199$	−6.02198	−	7.17671i	−0.426887	−	0.508744i	0.509135	−	0.860687i	$-0.329965\pi$
$199$	−6.02198	−	7.17671i	−0.426887	−	0.508744i	−0.936021	+	0.351943i	$0.885521\pi$
$200$		0			0
$201$	1.43497	−	2.48545i	0.101215	−	0.175310i
$202$		0			0
$203$	−0.898680	−	1.92722i	−0.0630750	−	0.135265i
$204$		0			0
$205$	−1.10574	−	15.2990i	−0.0772283	−	1.06853i
$206$		0			0
$207$	1.13519	+	12.9753i	0.0789014	+	0.901847i
$208$		0			0
$209$	−0.0134158	−	0.00941624i	−0.000927991	−	0.000651335i
$210$		0			0
$211$	15.0959	−	17.9905i	1.03924	−	1.23852i	0.0686873	−	0.997638i	$-0.478119\pi$
$211$	15.0959	−	17.9905i	1.03924	−	1.23852i	0.970554	−	0.240882i	$-0.0774366\pi$
$212$		0			0
$213$	−0.382591	−	0.267893i	−0.0262147	−	0.0183558i
$214$		0			0
$215$	5.06709	+	14.6050i	0.345573	+	0.996050i
$216$		0			0
$217$	−0.156053	−	0.582399i	−0.0105936	−	0.0395358i
$218$		0			0
$219$	−2.21163	+	1.85578i	−0.149448	+	0.125402i
$220$		0			0
$221$	0.768440	−	0.443659i	0.0516908	−	0.0298437i
$222$		0			0
$223$	14.5195	−	10.1667i	0.972299	−	0.680811i	0.0245072	−	0.999700i	$-0.492198\pi$
$223$	14.5195	−	10.1667i	0.972299	−	0.680811i	0.947792	+	0.318888i	$0.103309\pi$
$224$		0			0
$225$	−2.11290	−	14.5407i	−0.140860	−	0.969381i
$226$		0			0
$227$	−15.5569	+	15.5569i	−1.03255	+	1.03255i	−0.0330931	+	0.999452i	$0.510536\pi$
$227$	−15.5569	+	15.5569i	−1.03255	+	1.03255i	−0.999452	+	0.0330931i	$0.989464\pi$
$228$		0			0
$229$			6.48853i			0.428774i	0.976749	+	0.214387i	$0.0687754\pi$
$229$			6.48853i			0.428774i	−0.976749	+	0.214387i	$0.931225\pi$
$230$		0			0
$231$	−0.000440009	−	0.00120892i	−2.89505e−5	−	7.95408e-5i
$232$		0			0
$233$	6.22663	+	8.89254i	0.407920	+	0.582570i	0.969573	−	0.244803i	$-0.0787233\pi$
$233$	6.22663	+	8.89254i	0.407920	+	0.582570i	−0.561653	+	0.827373i	$0.689834\pi$
$234$		0			0
$235$	5.68109	+	2.16555i	0.370594	+	0.141265i
$236$		0			0
$237$	2.69994	+	0.236214i	0.175380	+	0.0153437i
$238$		0			0
$239$	5.86957	+	3.38880i	0.379671	+	0.219203i	0.677675	−	0.735361i	$-0.262988\pi$
$239$	5.86957	+	3.38880i	0.379671	+	0.219203i	−0.298004	+	0.954565i	$0.596321\pi$
$240$		0			0
$241$	−3.18172	+	8.74169i	−0.204952	+	0.563102i	−0.998998	−	0.0447562i	$-0.985749\pi$
$241$	−3.18172	+	8.74169i	−0.204952	+	0.563102i	0.794046	+	0.607858i	$0.207971\pi$
$242$		0			0
$243$	−3.73082	+	5.32816i	−0.239332	+	0.341802i
$244$		0			0
$245$	−7.92692	−	8.17027i	−0.506432	−	0.521980i
$246$		0			0
$247$	−14.3044	+	5.18826i	−0.910169	+	0.330121i
$248$		0			0
$249$	−0.231991	−	0.194663i	−0.0147018	−	0.0123363i
$250$		0			0
$251$	−2.77788	−	15.7541i	−0.175338	−	0.994391i	−0.937753	−	0.347303i	$-0.887098\pi$
$251$	−2.77788	−	15.7541i	−0.175338	−	0.994391i	0.762415	−	0.647088i	$-0.224014\pi$
$252$		0			0
$253$	−0.0151047	+	0.00704345i	−0.000949626	+	0.000442818i
$254$		0			0
$255$	0.0824590	−	0.114055i	0.00516378	−	0.00714237i
$256$		0			0
$257$	2.36820	−	27.0686i	0.147724	−	1.68850i	−0.454957	−	0.890513i	$-0.650345\pi$
$257$	2.36820	−	27.0686i	0.147724	−	1.68850i	0.602681	−	0.797982i	$-0.294099\pi$
$258$		0			0
$259$	−0.484936	−	0.839934i	−0.0301324	−	0.0521909i
$260$		0			0
$261$	−4.45404	−	0.785367i	−0.275698	−	0.0486130i
$262$		0			0
$263$	−1.51093	+	3.24020i	−0.0931679	+	0.199799i	−0.947369	−	0.320143i	$-0.896269\pi$
$263$	−1.51093	+	3.24020i	−0.0931679	+	0.199799i	0.854201	+	0.519943i	$0.174047\pi$
$264$		0			0
$265$	9.07917	−	7.38736i	0.557729	−	0.453802i
$266$		0			0
$267$	0.811615	+	0.811615i	0.0496700	+	0.0496700i
$268$		0			0
$269$	−25.5549	+	9.30123i	−1.55811	+	0.567106i	−0.970302	−	0.241895i	$-0.922231\pi$
$269$	−25.5549	+	9.30123i	−1.55811	+	0.567106i	−0.587808	+	0.809001i	$0.700009\pi$
$270$		0			0
$271$	−2.49625	+	14.1569i	−0.151636	+	0.859972i	0.810160	+	0.586208i	$0.199380\pi$
$271$	−2.49625	+	14.1569i	−0.151636	+	0.859972i	−0.961797	+	0.273764i	$0.911731\pi$
$272$		0			0
$273$	−1.15364	−	0.309116i	−0.0698213	−	0.0187086i
$274$		0			0
$275$	0.0165591	−	0.00890412i	0.000998549	−	0.000536939i
$276$		0			0
$277$	22.3088	−	5.97763i	1.34041	−	0.359161i	0.483822	−	0.875166i	$-0.339248\pi$
$277$	22.3088	−	5.97763i	1.34041	−	0.359161i	0.856586	+	0.516005i	$0.172581\pi$
$278$		0			0
$279$	−1.20506	−	0.438606i	−0.0721450	−	0.0262586i
$280$		0			0
$281$	−23.1355	+	4.07942i	−1.38015	+	0.243358i	−0.813962	−	0.580919i	$-0.802693\pi$
$281$	−23.1355	+	4.07942i	−1.38015	+	0.243358i	−0.566188	+	0.824276i	$0.691582\pi$
$282$		0			0
$283$	16.0654	−	1.40554i	0.954989	−	0.0835507i	0.401003	−	0.916077i	$-0.368662\pi$
$283$	16.0654	−	1.40554i	0.954989	−	0.0835507i	0.553986	+	0.832526i	$0.313106\pi$
$284$		0			0
$285$	−1.73409	+	1.67867i	−0.102719	+	0.0994361i
$286$		0			0
$287$	9.44195	−	0.826063i	0.557341	−	0.0487610i
$288$		0			0
$289$	16.6781	−	2.94080i	0.981065	−	0.172988i
$290$		0			0
$291$	4.09200	+	1.48937i	0.239877	+	0.0873082i
$292$		0			0
$293$	27.6925	−	7.42019i	1.61781	−	0.433492i	0.667456	−	0.744650i	$-0.267383\pi$
$293$	27.6925	−	7.42019i	1.61781	−	0.433492i	0.950358	+	0.311158i	$0.100717\pi$
$294$		0			0
$295$	−11.5986	−	17.1093i	−0.675297	−	0.996140i
$296$		0			0
$297$	−0.00534117	−	0.00143116i	−0.000309926	−	8.30445e-5i
$298$		0			0
$299$	−2.68672	+	15.2371i	−0.155377	+	0.881187i
$300$		0			0
$301$	−8.97613	+	3.26704i	−0.517375	+	0.188309i
$302$		0			0
$303$	1.20316	+	1.20316i	0.0691195	+	0.0691195i
$304$		0			0
$305$	−1.18424	+	11.5263i	−0.0678096	+	0.659996i
$306$		0			0
$307$	−7.66464	+	16.4369i	−0.437444	+	0.938102i	0.556768	+	0.830668i	$0.312041\pi$
$307$	−7.66464	+	16.4369i	−0.437444	+	0.938102i	−0.994212	+	0.107434i	$0.965736\pi$
$308$		0			0
$309$	−2.32537	−	0.410026i	−0.132286	−	0.0233256i
$310$		0			0
$311$	5.84389	+	10.1219i	0.331376	+	0.573961i	0.982782	−	0.184769i	$-0.0591536\pi$
$311$	5.84389	+	10.1219i	0.331376	+	0.573961i	−0.651406	+	0.758730i	$0.725820\pi$
$312$		0			0
$313$	−2.41091	+	27.5568i	−0.136273	+	1.55760i	0.553049	+	0.833149i	$0.313464\pi$
$313$	−2.41091	+	27.5568i	−0.136273	+	1.55760i	−0.689322	+	0.724455i	$0.742091\pi$
$314$		0			0
$315$	8.96403	−	1.44124i	0.505066	−	0.0812048i
$316$		0			0
$317$	4.92918	−	2.29852i	0.276851	−	0.129098i	−0.279234	−	0.960223i	$-0.590081\pi$
$317$	4.92918	−	2.29852i	0.276851	−	0.129098i	0.556085	+	0.831125i	$0.312303\pi$
$318$		0			0
$319$	−0.00100493	−	0.00569924i	−5.62653e−5	−	0.000319096i
$320$		0			0
$321$	−2.05289	−	1.72258i	−0.114581	−	0.0961448i
$322$		0			0
$323$	1.10796	+	0.00124021i	0.0616486	+	6.90072e-5i
$324$		0			0
$325$	2.04616	−	17.3339i	0.113500	−	0.961512i
$326$		0			0
$327$	−0.281327	+	0.401777i	−0.0155574	+	0.0222183i
$328$		0			0
$329$	−1.28489	+	3.53021i	−0.0708383	+	0.194627i
$330$		0			0
$331$	−4.04564	−	2.33575i	−0.222368	−	0.128384i	0.384678	−	0.923051i	$-0.374312\pi$
$331$	−4.04564	−	2.33575i	−0.222368	−	0.128384i	−0.607046	+	0.794666i	$0.707646\pi$
$332$		0			0
$333$	−2.05496	−	0.179786i	−0.112611	−	0.00985221i
$334$		0			0
$335$	−9.23100	+	24.2165i	−0.504343	+	1.32309i
$336$		0			0
$337$	0.540751	+	0.772272i	0.0294566	+	0.0420683i	0.833610	−	0.552353i	$-0.186270\pi$
$337$	0.540751	+	0.772272i	0.0294566	+	0.0420683i	−0.804154	+	0.594421i	$0.797381\pi$
$338$		0			0
$339$	0.239930	+	0.659203i	0.0130312	+	0.0358030i
$340$		0			0
$341$		−	0.00164091i		−	8.88605e-5i
$342$		0			0
$343$	11.8128	−	11.8128i	0.637832	−	0.637832i
$344$		0			0
$345$	0.599263	+	2.37981i	0.0322632	+	0.128125i
$346$		0			0
$347$	10.3613	−	7.25503i	0.556221	−	0.389470i	−0.261397	−	0.965231i	$-0.584183\pi$
$347$	10.3613	−	7.25503i	0.556221	−	0.389470i	0.817618	+	0.575761i	$0.195294\pi$
$348$		0			0
$349$	−16.7762	+	9.68572i	−0.898007	+	0.518465i	−0.876553	−	0.481305i	$-0.840163\pi$
$349$	−16.7762	+	9.68572i	−0.898007	+	0.518465i	−0.0214539	+	0.999770i	$0.506830\pi$
$350$		0			0
$351$	−3.93244	+	3.29971i	−0.209898	+	0.176125i
$352$		0			0
$353$	8.09827	+	30.2232i	0.431028	+	1.60862i	0.750397	+	0.660987i	$0.229862\pi$
$353$	8.09827	+	30.2232i	0.431028	+	1.60862i	−0.319370	+	0.947630i	$0.603471\pi$
$354$		0			0
$355$	3.79510	+	1.84003i	0.201423	+	0.0976585i
$356$		0			0
$357$	0.0712371	+	0.0498807i	0.00377027	+	0.00263997i
$358$		0			0
$359$	−18.4166	+	21.9481i	−0.971991	+	1.15837i	0.0153687	+	0.999882i	$0.495108\pi$
$359$	−18.4166	+	21.9481i	−0.971991	+	1.15837i	−0.987360	+	0.158492i	$0.949337\pi$
$360$		0			0
$361$	−18.7039	−	3.34120i	−0.984417	−	0.175852i
$362$		0			0
$363$	0.237397	+	2.71346i	0.0124601	+	0.142420i
$364$		0			0
$365$	17.0580	−	19.7159i	0.892859	−	1.03198i
$366$		0			0
$367$	13.3042	+	28.5310i	0.694476	+	1.48931i	0.863846	+	0.503756i	$0.168049\pi$
$367$	13.3042	+	28.5310i	0.694476	+	1.48931i	−0.169370	+	0.985553i	$0.554173\pi$
$368$		0			0
$369$	10.0794	−	17.4580i	0.524711	−	0.908825i
$370$		0			0
$371$	4.64897	+	5.54043i	0.241363	+	0.287645i
$372$		0			0
$373$	−2.94672	+	10.9973i	−0.152575	+	0.569419i	0.846725	+	0.532030i	$0.178571\pi$
$373$	−2.94672	+	10.9973i	−0.152575	+	0.569419i	−0.999301	+	0.0373890i	$0.988096\pi$
$374$		0			0
$375$	−0.827964	−	2.64177i	−0.0427559	−	0.136421i
$376$		0			0
$377$	−4.86919	−	2.27054i	−0.250776	−	0.116939i
$378$		0			0
$379$	22.9659			1.17968			0.589839	−	0.807521i	$-0.299191\pi$
$379$	22.9659			1.17968			0.589839	+	0.807521i	$0.299191\pi$
$380$		0			0
$381$	2.02879			0.103938
$382$		0			0
$383$	12.6771	+	5.91143i	0.647769	+	0.302060i	0.718595	−	0.695429i	$-0.244786\pi$
$383$	12.6771	+	5.91143i	0.647769	+	0.302060i	−0.0708256	+	0.997489i	$0.522563\pi$
$384$		0			0
$385$	0.00565595	+	0.0101476i	0.000288254	+	0.000517170i
$386$		0			0
$387$	−5.25830	+	19.6242i	−0.267294	+	0.997556i
$388$		0			0
$389$	−0.108752	−	0.129605i	−0.00551394	−	0.00657126i	0.763280	−	0.646067i	$-0.223587\pi$
$389$	−0.108752	−	0.129605i	−0.00551394	−	0.00657126i	−0.768794	+	0.639496i	$0.779143\pi$
$390$		0			0
$391$	0.563299	−	0.975662i	0.0284872	−	0.0493413i
$392$		0			0
$393$	1.40851	+	3.02056i	0.0710500	+	0.152367i
$394$		0			0
$395$	−24.4105	+	1.76427i	−1.22822	+	0.0887702i
$396$		0			0
$397$	1.12109	+	12.8142i	0.0562661	+	0.643124i	0.971002	+	0.239072i	$0.0768432\pi$
$397$	1.12109	+	12.8142i	0.0562661	+	0.643124i	−0.914736	+	0.404053i	$0.867601\pi$
$398$		0			0
$399$	−1.05334	−	1.05570i	−0.0527330	−	0.0528512i
$400$		0			0
$401$	5.46417	−	6.51194i	0.272867	−	0.325191i	−0.612156	−	0.790737i	$-0.709698\pi$
$401$	5.46417	−	6.51194i	0.272867	−	0.325191i	0.885024	+	0.465546i	$0.154142\pi$
$402$		0			0
$403$	−1.24786	−	0.873760i	−0.0621603	−	0.0435251i
$404$		0			0
$405$	8.24509	−	17.0057i	0.409702	−	0.845019i
$406$		0			0
$407$	−0.000683155	−	0.00254957i	−3.38627e−5	−	0.000126377i
$408$		0			0
$409$	−0.525221	+	0.440713i	−0.0259705	+	0.0217919i	−0.655681	−	0.755038i	$-0.727618\pi$
$409$	−0.525221	+	0.440713i	−0.0259705	+	0.0217919i	0.629710	+	0.776830i	$0.283174\pi$
$410$		0			0
$411$	3.05319	−	1.76276i	0.150603	−	0.0869505i
$412$		0			0
$413$	10.4624	−	7.32584i	0.514820	−	0.360481i
$414$		0			0
$415$	2.34741	+	1.40301i	0.115230	+	0.0688711i
$416$		0			0
$417$	0.263332	−	0.263332i	0.0128954	−	0.0128954i
$418$		0			0
$419$			22.9059i			1.11903i	0.828821	+	0.559514i	$0.189012\pi$
$419$			22.9059i			1.11903i	−0.828821	+	0.559514i	$0.810988\pi$
$420$		0			0
$421$	−2.94071	−	8.07954i	−0.143322	−	0.393773i	0.847174	−	0.531315i	$-0.178302\pi$
$421$	−2.94071	−	8.07954i	−0.143322	−	0.393773i	−0.990496	+	0.137542i	$0.956080\pi$
$422$		0			0
$423$	4.58301	+	6.54522i	0.222834	+	0.318240i
$424$		0			0
$425$	−0.571687	+	1.13508i	−0.0277309	+	0.0550595i
$426$		0			0
$427$	−7.13244	−	0.624007i	−0.345163	−	0.0301978i
$428$		0			0
$429$	−0.00281491	−	0.00162519i	−0.000135905	−	7.84649e-5i
$430$		0			0
$431$	10.5001	−	28.8487i	0.505771	−	1.38959i	−0.379791	−	0.925073i	$-0.624004\pi$
$431$	10.5001	−	28.8487i	0.505771	−	1.38959i	0.885562	−	0.464522i	$-0.153774\pi$
$432$		0			0
$433$	−9.38437	+	13.4023i	−0.450984	+	0.644072i	−0.978687	−	0.205357i	$-0.934164\pi$
$433$	−9.38437	+	13.4023i	−0.450984	+	0.644072i	0.527703	+	0.849429i	$0.323053\pi$
$434$		0			0
$435$	−0.852062	−	0.0128813i	−0.0408533	−	0.000617613i
$436$		0			0
$437$	−12.4349	+	14.7857i	−0.594844	+	0.707298i
$438$		0			0
$439$	8.34650	+	7.00355i	0.398357	+	0.334261i	0.819858	−	0.572567i	$-0.194052\pi$
$439$	8.34650	+	7.00355i	0.398357	+	0.334261i	−0.421501	+	0.906828i	$0.638497\pi$
$440$		0			0
$441$	−2.59790	−	14.7334i	−0.123710	−	0.701592i
$442$		0			0
$443$	19.2375	−	8.97058i	0.913999	−	0.426205i	0.0920428	−	0.995755i	$-0.470660\pi$
$443$	19.2375	−	8.97058i	0.913999	−	0.426205i	0.821957	+	0.569550i	$0.192883\pi$
$444$		0			0
$445$	−8.39956	−	6.07270i	−0.398177	−	0.287874i
$446$		0			0
$447$	0.407664	−	4.65962i	0.0192818	−	0.220392i
$448$		0			0
$449$	1.99367	+	3.45313i	0.0940869	+	0.162963i	0.909227	−	0.416300i	$-0.136674\pi$
$449$	1.99367	+	3.45313i	0.0940869	+	0.162963i	−0.815140	+	0.579264i	$0.803340\pi$
$450$		0			0
$451$	0.0254026	+	0.00447916i	0.00119616	+	0.000210915i
$452$		0			0
$453$	1.93778	−	4.15557i	0.0910446	−	0.195246i
$454$		0			0
$455$	10.7286	+	1.10228i	0.502965	+	0.0516758i
$456$		0			0
$457$	1.31243	+	1.31243i	0.0613930	+	0.0613930i	0.737137	−	0.675744i	$-0.236177\pi$
$457$	1.31243	+	1.31243i	0.0613930	+	0.0613930i	−0.675744	+	0.737137i	$0.736177\pi$
$458$		0			0
$459$	0.351245	−	0.127843i	0.0163947	−	0.00596719i
$460$		0			0
$461$	0.247028	−	1.40097i	0.0115052	−	0.0652494i	−0.978515	−	0.206178i	$-0.933898\pi$
$461$	0.247028	−	1.40097i	0.0115052	−	0.0652494i	0.990020	+	0.140928i	$0.0450087\pi$
$462$		0			0
$463$	−2.07021	−	0.554712i	−0.0962110	−	0.0257797i	0.210392	−	0.977617i	$-0.432526\pi$
$463$	−2.07021	−	0.554712i	−0.0962110	−	0.0257797i	−0.306603	+	0.951837i	$0.599193\pi$
$464$		0			0
$465$	−0.237292	−	0.0455498i	−0.0110042	−	0.00211232i
$466$		0			0
$467$	−5.12937	+	1.37441i	−0.237359	+	0.0636001i	−0.375537	−	0.926807i	$-0.622542\pi$
$467$	−5.12937	+	1.37441i	−0.237359	+	0.0636001i	0.138179	+	0.990407i	$0.455875\pi$
$468$		0			0
$469$	−15.0481	−	5.47704i	−0.694855	−	0.252906i
$470$		0			0
$471$	−0.157869	+	0.0278365i	−0.00727421	+	0.00128264i
$472$		0			0
$473$	−0.0258974	+	0.00226573i	−0.00119076	+	0.000104178i
$474$		0			0
$475$	13.0543	−	17.4524i	0.598973	−	0.800769i
$476$		0			0
$477$	15.3243	−	1.34070i	0.701649	−	0.0613864i
$478$		0			0
$479$	−6.73006	+	1.18669i	−0.307504	+	0.0542213i	−0.325271	−	0.945621i	$-0.605456\pi$
$479$	−6.73006	+	1.18669i	−0.307504	+	0.0542213i	0.0177666	+	0.999842i	$0.494344\pi$
$480$		0			0
$481$	−2.30263	−	0.838089i	−0.104991	−	0.0382136i
$482$		0			0
$483$	−1.46473	+	0.392474i	−0.0666477	+	0.0178582i
$484$		0			0
$485$	−38.6181	−	7.41299i	−1.75356	−	0.336607i
$486$		0			0
$487$	−37.1686	−	9.95929i	−1.68427	−	0.451298i	−0.715368	−	0.698748i	$-0.753741\pi$
$487$	−37.1686	−	9.95929i	−1.68427	−	0.451298i	−0.968901	+	0.247449i	$0.920408\pi$
$488$		0			0
$489$	0.454671	−	2.57857i	0.0205609	−	0.116607i
$490$		0			0
$491$	−22.0874	+	8.03917i	−0.996792	+	0.362803i	−0.788347	−	0.615231i	$-0.789063\pi$
$491$	−22.0874	+	8.03917i	−0.996792	+	0.362803i	−0.208446	+	0.978034i	$0.566840\pi$
$492$		0			0
$493$	0.276619	+	0.276619i	0.0124583	+	0.0124583i
$494$		0			0
$495$	0.0245795	+	0.00252536i	0.00110477	+	0.000113507i
$496$		0			0
$497$	−1.10139	+	2.36193i	−0.0494039	+	0.105947i
$498$		0			0
$499$	−32.5945	−	5.74730i	−1.45913	−	0.257284i	−0.612926	−	0.790140i	$-0.710008\pi$
$499$	−32.5945	−	5.74730i	−1.45913	−	0.257284i	−0.846206	+	0.532856i	$0.821119\pi$
$500$		0			0
$501$	−2.75860	−	4.77803i	−0.123245	−	0.213467i
$502$		0			0
$503$	1.74190	−	19.9100i	0.0776675	−	0.887744i	−0.853008	−	0.521898i	$-0.825224\pi$
$503$	1.74190	−	19.9100i	0.0776675	−	0.887744i	0.930675	−	0.365846i	$-0.119220\pi$
$504$		0			0
$505$	−12.4517	−	9.00231i	−0.554093	−	0.400598i
$506$		0			0
$507$	0.182669	−	0.0851798i	0.00811260	−	0.00378297i
$508$		0			0
$509$	−4.71059	−	26.7151i	−0.208793	−	1.18412i	−0.891358	−	0.453300i	$-0.850247\pi$
$509$	−4.71059	−	26.7151i	−0.208793	−	1.18412i	0.682565	−	0.730825i	$-0.260864\pi$
$510$		0			0
$511$	12.3405	+	10.3549i	0.545912	+	0.458074i
$512$		0			0
$513$	−6.31380	+	1.10601i	−0.278761	+	0.0488314i
$514$		0			0
$515$	21.3201	+	0.322315i	0.939478	+	0.0142029i
$516$		0			0
$517$	−0.00586428	+	0.00837505i	−0.000257911	+	0.000368334i
$518$		0			0
$519$	1.36196	−	3.74195i	0.0597834	−	0.164254i
$520$		0			0
$521$	27.7266	+	16.0080i	1.21472	+	0.701321i	0.963785	−	0.266682i	$-0.0859273\pi$
$521$	27.7266	+	16.0080i	1.21472	+	0.701321i	0.250939	+	0.968003i	$0.419261\pi$
$522$		0			0
$523$	26.9256	+	2.35568i	1.17737	+	0.103007i	0.658997	−	0.752146i	$-0.270981\pi$
$523$	26.9256	+	2.35568i	1.17737	+	0.103007i	0.518376	+	0.855153i	$0.326537\pi$
$524$		0			0
$525$	1.62445	−	0.536220i	0.0708967	−	0.0234026i
$526$		0			0
$527$	0.0636222	+	0.0908619i	0.00277143	+	0.00395801i
$528$		0			0
$529$	−1.14764	−	3.15310i	−0.0498972	−	0.137091i
$530$		0			0
$531$		−	27.1651i		−	1.17887i
$532$		0			0
$533$	16.9327	−	16.9327i	0.733437	−	0.733437i
$534$		0			0
$535$	20.7722	+	12.4152i	0.898061	+	0.536758i
$536$		0			0
$537$	0.139074	−	0.0973808i	0.00600150	−	0.00420229i
$538$		0			0
$539$	0.0165786	−	0.00957163i	0.000714089	−	0.000412279i
$540$		0			0
$541$	−17.0675	+	14.3213i	−0.733789	+	0.615722i	−0.931162	−	0.364607i	$-0.881203\pi$
$541$	−17.0675	+	14.3213i	−0.733789	+	0.615722i	0.197373	+	0.980328i	$0.436759\pi$
$542$		0			0
$543$	−1.00287	−	3.74274i	−0.0430371	−	0.160617i
$544$		0			0
$545$	1.93230	−	3.98541i	0.0827706	−	0.170716i
$546$		0			0
$547$	10.5350	+	7.37668i	0.450444	+	0.315404i	0.776693	−	0.629880i	$-0.216896\pi$
$547$	10.5350	+	7.37668i	0.450444	+	0.315404i	−0.326249	+	0.945284i	$0.605785\pi$
$548$		0			0
$549$	−9.78829	+	11.6652i	−0.417754	+	0.497860i
$550$		0			0
$551$	−3.84169	−	5.49959i	−0.163662	−	0.234291i
$552$		0			0
$553$	−1.31803	−	15.0652i	−0.0560484	−	0.640636i
$554$		0			0
$555$	−0.387657	+	0.0280180i	−0.0164551	+	0.00118930i
$556$		0			0
$557$	0.990166	+	2.12342i	0.0419547	+	0.0899721i	0.926168	−	0.377111i	$-0.123083\pi$
$557$	0.990166	+	2.12342i	0.0419547	+	0.0899721i	−0.884213	+	0.467083i	$0.845305\pi$
$558$		0			0
$559$	−12.0669	+	20.9006i	−0.510377	+	0.883999i
$560$		0			0
$561$	0.000152131	0	0.000181303i	6.42298e−6	0	7.65461e-6i
$562$		0			0
$563$	9.53675	−	35.5916i	0.401926	−	1.50001i	−0.407730	−	0.913103i	$-0.633679\pi$
$563$	9.53675	−	35.5916i	0.401926	−	1.50001i	0.809656	−	0.586905i	$-0.199654\pi$
$564$		0			0
$565$	−3.08410	−	5.53334i	−0.129749	−	0.232789i
$566$		0			0
$567$	10.5837	+	4.93527i	0.444474	+	0.207262i
$568$		0			0
$569$	3.63395			0.152343			0.0761715	−	0.997095i	$-0.475730\pi$
$569$	3.63395			0.152343			0.0761715	+	0.997095i	$0.475730\pi$
$570$		0			0
$571$	2.09587			0.0877092			0.0438546	−	0.999038i	$-0.486036\pi$
$571$	2.09587			0.0877092			0.0438546	+	0.999038i	$0.486036\pi$
$572$		0			0
$573$	4.52203	+	2.10866i	0.188910	+	0.0880904i
$574$		0			0
$575$	−8.75426	−	20.3587i	−0.365078	−	0.849016i
$576$		0			0
$577$	−10.5659	+	39.4324i	−0.439864	+	1.64159i	0.289288	+	0.957242i	$0.406582\pi$
$577$	−10.5659	+	39.4324i	−0.439864	+	1.64159i	−0.729152	+	0.684352i	$0.760085\pi$
$578$		0			0
$579$	−1.16688	−	1.39063i	−0.0484938	−	0.0577926i
$580$		0			0
$581$	−0.844904	+	1.46342i	−0.0350525	+	0.0607127i
$582$		0			0
$583$	0.00831853	+	0.0178391i	0.000344518	+	0.000738822i
$584$		0			0
$585$	15.0087	−	17.3472i	0.620532	−	0.717218i
$586$		0			0
$587$	−3.56346	−	40.7305i	−0.147080	−	1.68113i	−0.608195	−	0.793787i	$-0.708106\pi$
$587$	−3.56346	−	40.7305i	−0.147080	−	1.68113i	0.461116	−	0.887340i	$-0.347449\pi$
$588$		0			0
$589$	−0.801956	−	1.72484i	−0.0330440	−	0.0710707i
$590$		0			0
$591$	−2.15147	+	2.56402i	−0.0884996	+	0.105470i
$592$		0			0
$593$	−13.5858	−	9.51289i	−0.557902	−	0.390647i	0.260343	−	0.965516i	$-0.416164\pi$
$593$	−13.5858	−	9.51289i	−0.557902	−	0.390647i	−0.818246	+	0.574869i	$0.805053\pi$
$594$		0			0
$595$	−0.706633	−	0.342606i	−0.0289691	−	0.0140455i
$596$		0			0
$597$	−0.600419	−	2.24079i	−0.0245735	−	0.0917096i
$598$		0			0
$599$	5.17412	−	4.34161i	0.211409	−	0.177393i	−0.530934	−	0.847413i	$-0.678159\pi$
$599$	5.17412	−	4.34161i	0.211409	−	0.177393i	0.742343	+	0.670020i	$0.233714\pi$
$600$		0			0
$601$	10.6978	−	6.17636i	0.436371	−	0.251939i	−0.265686	−	0.964060i	$-0.585598\pi$
$601$	10.6978	−	6.17636i	0.436371	−	0.251939i	0.702057	+	0.712121i	$0.252265\pi$
$602$		0			0
$603$	−27.9000	+	19.5358i	−1.13618	+	0.795560i
$604$		0			0
$605$	−6.00623	−	23.8521i	−0.244188	−	0.969727i
$606$		0			0
$607$	−12.9734	+	12.9734i	−0.526575	+	0.526575i	−0.919549	−	0.392974i	$-0.871446\pi$
$607$	−12.9734	+	12.9734i	−0.526575	+	0.526575i	0.392974	+	0.919549i	$0.371446\pi$
$608$		0			0
$609$		−	0.526554i		−	0.0213371i
$610$		0			0
$611$	3.24631	+	8.91916i	0.131332	+	0.360831i
$612$		0			0
$613$	7.42093	+	10.5982i	0.299728	+	0.428057i	0.940561	−	0.339624i	$-0.110300\pi$
$613$	7.42093	+	10.5982i	0.299728	+	0.428057i	−0.640833	+	0.767680i	$0.721411\pi$
$614$		0			0
$615$	1.35288	−	3.54913i	0.0545532	−	0.143115i
$616$		0			0
$617$	18.2229	+	1.59429i	0.733625	+	0.0641839i	0.447845	−	0.894111i	$-0.352192\pi$
$617$	18.2229	+	1.59429i	0.733625	+	0.0641839i	0.285780	+	0.958295i	$0.407747\pi$
$618$		0			0
$619$	−33.0921	−	19.1058i	−1.33009	−	0.767925i	−0.344773	−	0.938686i	$-0.612044\pi$
$619$	−33.0921	−	19.1058i	−1.33009	−	0.767925i	−0.985313	+	0.170761i	$0.945377\pi$
$620$		0			0
$621$	−2.22920	+	6.12468i	−0.0894548	+	0.245775i
$622$		0			0
$623$	3.67347	−	5.24626i	0.147175	−	0.210187i
$624$		0			0
$625$	11.1688	+	22.3664i	0.446752	+	0.894658i
$626$		0			0
$627$	−0.00202538	−	0.00351715i	−8.08859e−5	−	0.000140461i
$628$		0			0
$629$	0.136681	+	0.114689i	0.00544983	+	0.00457295i
$630$		0			0
$631$	−4.96956	−	28.1838i	−0.197835	−	1.12198i	−0.908323	−	0.418269i	$-0.862637\pi$
$631$	−4.96956	−	28.1838i	−0.197835	−	1.12198i	0.710488	−	0.703709i	$-0.248474\pi$
$632$		0			0
$633$	5.27051	−	2.45768i	0.209484	−	0.0976840i
$634$		0			0
$635$	−18.0881	+	2.90822i	−0.717805	+	0.115409i
$636$		0			0
$637$	1.54891	−	17.7042i	0.0613702	−	0.701464i
$638$		0			0
$639$	2.77145	+	4.80029i	0.109637	+	0.189897i
$640$		0			0
$641$	22.8527	+	4.02955i	0.902628	+	0.159158i	0.605654	−	0.795728i	$-0.292911\pi$
$641$	22.8527	+	4.02955i	0.902628	+	0.159158i	0.296974	+	0.954886i	$0.404023\pi$
$642$		0			0
$643$	−11.8294	+	25.3681i	−0.466504	+	1.00042i	0.522514	+	0.852631i	$0.324994\pi$
$643$	−11.8294	+	25.3681i	−0.466504	+	1.00042i	−0.989019	+	0.147791i	$0.952784\pi$
$644$		0			0
$645$	−0.391234	+	3.80792i	−0.0154048	+	0.149937i
$646$		0			0
$647$	−23.6174	−	23.6174i	−0.928497	−	0.928497i	0.0691115	−	0.997609i	$-0.477984\pi$
$647$	−23.6174	−	23.6174i	−0.928497	−	0.928497i	−0.997609	+	0.0691115i	$0.977984\pi$
$648$		0			0
$649$	0.0326633	−	0.0118885i	0.00128215	−	0.000466664i
$650$		0			0
$651$	0.0259259	−	0.147033i	0.00101612	−	0.00576268i
$652$		0			0
$653$	18.8022	+	5.03802i	0.735785	+	0.197153i	0.607204	−	0.794546i	$-0.292291\pi$
$653$	18.8022	+	5.03802i	0.735785	+	0.197153i	0.128581	+	0.991699i	$0.458958\pi$
$654$		0			0
$655$	−16.8878	−	24.9114i	−0.659861	−	0.973370i
$656$		0			0
$657$	33.0954	−	8.86790i	1.29118	−	0.345970i
$658$		0			0
$659$	2.29597	+	0.835666i	0.0894384	+	0.0325529i	0.386352	−	0.922351i	$-0.373735\pi$
$659$	2.29597	+	0.835666i	0.0894384	+	0.0325529i	−0.296913	+	0.954904i	$0.595957\pi$
$660$		0			0
$661$	−18.5356	+	3.26833i	−0.720953	+	0.127123i	−0.522073	−	0.852901i	$-0.674841\pi$
$661$	−18.5356	+	3.26833i	−0.720953	+	0.127123i	−0.198879	+	0.980024i	$0.563730\pi$
$662$		0			0
$663$	0.218882	−	0.0191497i	0.00850067	−	0.000743712i
$664$		0			0
$665$	10.9046	+	7.90240i	0.422863	+	0.306442i
$666$		0			0
$667$	−6.79539	+	0.594520i	−0.263119	+	0.0230199i
$668$		0			0
$669$	4.32241	−	0.762158i	0.167114	−	0.0294667i
$670$		0			0
$671$	−0.0183100	−	0.00666430i	−0.000706850	−	0.000257272i
$672$		0			0
$673$	−4.32141	+	1.15792i	−0.166578	+	0.0446345i	−0.341144	−	0.940011i	$-0.610814\pi$
$673$	−4.32141	+	1.15792i	−0.166578	+	0.0446345i	0.174566	+	0.984645i	$0.444148\pi$
$674$		0			0
$675$	2.11684	−	7.04139i	0.0814772	−	0.271023i
$676$		0			0
$677$	−23.8513	−	6.39095i	−0.916682	−	0.245624i	−0.230515	−	0.973069i	$-0.574041\pi$
$677$	−23.8513	−	6.39095i	−0.916682	−	0.245624i	−0.686166	+	0.727445i	$0.740708\pi$
$678$		0			0
$679$	4.21930	−	23.9289i	0.161922	−	0.918305i
$680$		0			0
$681$	−5.11929	+	1.86327i	−0.196172	+	0.0714006i
$682$		0			0
$683$	−30.5345	−	30.5345i	−1.16837	−	1.16837i	−0.982591	−	0.185781i	$-0.940519\pi$
$683$	−30.5345	−	30.5345i	−1.16837	−	1.16837i	−0.185781	−	0.982591i	$-0.559481\pi$
$684$		0			0
$685$	−24.6945	+	20.0929i	−0.943528	+	0.767711i
$686$		0			0
$687$	−0.679018	+	1.45616i	−0.0259062	+	0.0555559i
$688$		0			0
$689$	17.9955	+	3.17310i	0.685576	+	0.120885i
$690$		0			0
$691$	9.33721	+	16.1725i	0.355204	+	0.615231i	0.987153	−	0.159779i	$-0.0510781\pi$
$691$	9.33721	+	16.1725i	0.355204	+	0.615231i	−0.631949	+	0.775010i	$0.717745\pi$
$692$		0			0
$693$	−0.00133068	+	0.0152097i	−5.05482e−5	+	0.000577769i
$694$		0			0
$695$	−1.97032	+	2.72528i	−0.0747384	+	0.103376i
$696$		0			0
$697$	−1.58028	+	0.736896i	−0.0598573	+	0.0279119i
$698$		0			0
$699$	0.466786	+	2.64728i	0.0176555	+	0.100129i
$700$		0			0
$701$	−4.25437	−	3.56984i	−0.160685	−	0.134831i	0.558900	−	0.829235i	$-0.311224\pi$
$701$	−4.25437	−	3.56984i	−0.160685	−	0.134831i	−0.719585	+	0.694404i	$0.755668\pi$
$702$		0			0
$703$	−1.96413	−	2.34609i	−0.0740787	−	0.0884846i
$704$		0			0
$705$	1.04833	+	1.08051i	0.0394824	+	0.0406945i
$706$		0			0
$707$	5.44564	−	7.77718i	0.204804	−	0.292491i
$708$		0			0
$709$	−11.7377	+	32.2491i	−0.440819	+	1.21114i	0.498135	+	0.867099i	$0.334018\pi$
$709$	−11.7377	+	32.2491i	−0.440819	+	1.21114i	−0.938954	+	0.344041i	$0.888204\pi$
$710$		0			0
$711$	−27.8552	−	16.0822i	−1.04465	−	0.603130i
$712$		0			0
$713$	−1.92679	−	0.168572i	−0.0721589	−	0.00631309i
$714$		0			0
$715$	0.0274266	+	0.0104546i	0.00102570	+	0.000390981i
$716$		0			0
$717$	0.962617	+	1.37476i	0.0359496	+	0.0513414i
$718$		0			0
$719$	7.96206	+	21.8756i	0.296935	+	0.815821i	0.995008	+	0.0997949i	$0.0318187\pi$
$719$	7.96206	+	21.8756i	0.296935	+	0.815821i	−0.698073	+	0.716026i	$0.745959\pi$
$720$		0			0
$721$			13.1753i			0.490676i
$722$		0			0
$723$	−1.62885	+	1.62885i	−0.0605776	+	0.0605776i
$724$		0			0
$725$	7.61521	−	1.10656i	0.282822	−	0.0410967i
$726$		0			0
$727$	2.78300	−	1.94868i	0.103216	−	0.0722724i	−0.520829	−	0.853661i	$-0.674377\pi$
$727$	2.78300	−	1.94868i	0.103216	−	0.0722724i	0.624045	+	0.781389i	$0.285488\pi$
$728$		0			0
$729$	20.5639	−	11.8726i	0.761625	−	0.439724i
$730$		0			0
$731$	1.34616	−	1.12956i	0.0497896	−	0.0417785i
$732$		0			0
$733$	2.26756	+	8.46264i	0.0837541	+	0.312575i	0.995075	−	0.0991214i	$-0.0316032\pi$
$733$	2.26756	+	8.46264i	0.0837541	+	0.312575i	−0.911321	+	0.411696i	$0.864937\pi$
$734$		0			0
$735$	−0.923952	−	2.66312i	−0.0340805	−	0.0982307i
$736$		0			0
$737$	−0.0357000	−	0.0249974i	−0.00131503	−	0.000920791i
$738$		0			0
$739$	30.1312	−	35.9090i	1.10839	−	1.32093i	0.166114	−	0.986107i	$-0.446878\pi$
$739$	30.1312	−	35.9090i	1.10839	−	1.32093i	0.942280	−	0.334826i	$-0.108678\pi$
$740$		0			0
$741$	−3.75315	−	0.332592i	−0.137875	−	0.0122181i
$742$		0			0
$743$	3.63498	+	41.5481i	0.133355	+	1.52425i	0.708214	+	0.705998i	$0.249501\pi$
$743$	3.63498	+	41.5481i	0.133355	+	1.52425i	−0.574859	+	0.818252i	$0.694943\pi$
$744$		0			0
$745$	3.04483	+	42.1282i	0.111554	+	1.54346i
$746$		0			0
$747$	1.51891	+	3.25731i	0.0555739	+	0.119179i
$748$		0			0
$749$	−7.47656	+	12.9498i	−0.273187	+	0.473174i
$750$		0			0
$751$	18.3100	+	21.8210i	0.668140	+	0.796259i	0.988530	−	0.151027i	$-0.0482582\pi$
$751$	18.3100	+	21.8210i	0.668140	+	0.796259i	−0.320389	+	0.947286i	$0.603814\pi$
$752$		0			0
$753$	1.02524	−	3.82625i	0.0373618	−	0.139436i
$754$		0			0
$755$	−11.3198	+	39.8277i	−0.411968	+	1.44948i
$756$		0			0
$757$	43.1368	+	20.1150i	1.56783	+	0.731092i	0.996006	−	0.0892829i	$-0.0284575\pi$
$757$	43.1368	+	20.1150i	1.56783	+	0.731092i	0.571826	+	0.820375i	$0.306235\pi$
$758$		0			0
$759$	−0.00412690			−0.000149797
$760$		0			0
$761$	48.8091			1.76933			0.884665	−	0.466227i	$-0.154387\pi$
$761$	48.8091			1.76933			0.884665	+	0.466227i	$0.154387\pi$
$762$		0			0
$763$	2.48037	+	1.15662i	0.0897956	+	0.0418724i
$764$		0			0
$765$	−1.45895	+	0.813172i	−0.0527485	+	0.0294003i
$766$		0			0
$767$	8.35192	−	31.1698i	0.301570	−	1.12548i
$768$		0			0
$769$	6.31154	+	7.52180i	0.227600	+	0.271243i	0.867744	−	0.497012i	$-0.165570\pi$
$769$	6.31154	+	7.52180i	0.227600	+	0.271243i	−0.640144	+	0.768255i	$0.721125\pi$
$770$		0			0
$771$	3.36418	−	5.82693i	0.121158	−	0.209852i
$772$		0			0
$773$	4.16337	+	8.92837i	0.149746	+	0.321131i	0.966844	−	0.255367i	$-0.0821964\pi$
$773$	4.16337	+	8.92837i	0.149746	+	0.321131i	−0.817098	+	0.576499i	$0.804419\pi$
$774$		0			0
$775$	2.18093	+	0.0659569i	0.0783412	+	0.00236924i
$776$		0			0
$777$	−0.0209313	−	0.239246i	−0.000750907	−	0.00858291i
$778$		0			0
$779$	28.8909	−	7.70663i	1.03512	−	0.276119i
$780$		0			0
$781$	−0.00455898	+	0.00543318i	−0.000163133	+	0.000194415i
$782$		0			0
$783$	−1.85392	−	1.29813i	−0.0662536	−	0.0463913i
$784$		0			0
$785$	1.36761	−	0.474484i	0.0488121	−	0.0169350i
$786$		0			0
$787$	7.96060	+	29.7093i	0.283765	+	1.05902i	0.949737	+	0.313048i	$0.101350\pi$
$787$	7.96060	+	29.7093i	0.283765	+	1.05902i	−0.665973	+	0.745976i	$0.731983\pi$
$788$		0			0
$789$	−0.678166	+	0.569049i	−0.0241434	+	0.0202587i
$790$		0			0

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.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.224420 + 0.104649i) q^{3} +(-2.15088 - 0.611320i) q^{5} +(0.357605 - 1.33460i) q^{7} +(-1.88895 - 2.25116i) q^{9} +O(q^{10})\)	\(q+(0.224420 + 0.104649i) q^{3} +(-2.15088 - 0.611320i) q^{5} +(0.357605 - 1.33460i) q^{7} +(-1.88895 - 2.25116i) q^{9} +(0.00188012 - 0.00325647i) q^{11} +(-1.47530 - 3.16379i) q^{13} +(-0.418728 - 0.362280i) q^{15} +(0.0221536 + 0.253216i) q^{17} +(0.384763 - 4.34188i) q^{19} +(0.219918 - 0.262088i) q^{21} +(-3.63066 - 2.54221i) q^{23} +(4.25258 + 2.62975i) q^{25} +(-0.380604 - 1.42043i) q^{27} +(1.17897 - 0.989275i) q^{29} +(0.377920 - 0.218192i) q^{31} +(0.000762724 - 0.000534065i) q^{33} +(-1.58503 + 2.65195i) q^{35} +(0.496355 - 0.496355i) q^{37} -0.864406i q^{39} +(2.34618 + 6.44608i) q^{41} +(-3.96540 - 5.66318i) q^{43} +(2.68673 + 5.99673i) q^{45} +(-2.70864 - 0.236975i) q^{47} +(4.40890 + 2.54548i) q^{49} +(-0.0215271 + 0.0591453i) q^{51} +(-3.00243 + 4.28792i) q^{53} +(-0.00603466 + 0.00585492i) q^{55} +(0.540722 - 0.934142i) q^{57} +(7.08129 + 5.94191i) q^{59} +(-0.899822 - 5.10314i) q^{61} +(-3.67990 + 1.71597i) q^{63} +(1.23910 + 7.70680i) q^{65} +(1.01014 - 11.5460i) q^{67} +(-0.548754 - 0.950469i) q^{69} +(-1.85753 - 0.327532i) q^{71} +(-4.92742 + 10.5669i) q^{73} +(0.679164 + 1.03520i) q^{75} +(-0.00367374 - 0.00367374i) q^{77} +(10.2851 - 3.74347i) q^{79} +(-1.46766 + 8.32351i) q^{81} +(-1.18134 - 0.316538i) q^{83} +(0.107147 - 0.558181i) q^{85} +(0.368112 - 0.0986353i) q^{87} +(4.35576 + 1.58537i) q^{89} +(-4.74996 + 0.837546i) q^{91} +(0.107647 - 0.00941786i) q^{93} +(-3.48186 + 9.10366i) q^{95} +(17.5189 - 1.53271i) q^{97} +(-0.0108823 + 0.00191884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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