LMFDB - Embedded newform 980.2.g.a.391.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, 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("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.21
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.486718 - 1.32782i) q^{2} -0.812042 q^{3} +(-1.52621 - 1.29255i) q^{4} -1.00000i q^{5} +(-0.395235 + 1.07825i) q^{6} +(-2.45910 + 1.39743i) q^{8} -2.34059 q^{9} +(-1.32782 - 0.486718i) q^{10} -4.86043i q^{11} +(1.23935 + 1.04960i) q^{12} +0.895933i q^{13} +0.812042i q^{15} +(0.658646 + 3.94540i) q^{16} +5.89164i q^{17} +(-1.13921 + 3.10788i) q^{18} -2.91636 q^{19} +(-1.29255 + 1.52621i) q^{20} +(-6.45377 - 2.36566i) q^{22} -1.56151i q^{23} +(1.99689 - 1.13477i) q^{24} -1.00000 q^{25} +(1.18964 + 0.436066i) q^{26} +4.33678 q^{27} -9.73084 q^{29} +(1.07825 + 0.395235i) q^{30} +4.41515 q^{31} +(5.55936 + 1.04573i) q^{32} +3.94687i q^{33} +(7.82304 + 2.86757i) q^{34} +(3.57223 + 3.02532i) q^{36} -1.82136 q^{37} +(-1.41945 + 3.87241i) q^{38} -0.727535i q^{39} +(1.39743 + 2.45910i) q^{40} +10.4920i q^{41} +3.04581i q^{43} +(-6.28233 + 7.41804i) q^{44} +2.34059i q^{45} +(-2.07340 - 0.760014i) q^{46} -5.21932 q^{47} +(-0.534848 - 3.20383i) q^{48} +(-0.486718 + 1.32782i) q^{50} -4.78426i q^{51} +(1.15804 - 1.36738i) q^{52} +0.179724 q^{53} +(2.11079 - 5.75846i) q^{54} -4.86043 q^{55} +2.36821 q^{57} +(-4.73617 + 12.9208i) q^{58} -11.3657 q^{59} +(1.04960 - 1.23935i) q^{60} +6.15579i q^{61} +(2.14893 - 5.86252i) q^{62} +(4.09438 - 6.87285i) q^{64} +0.895933 q^{65} +(5.24073 + 1.92101i) q^{66} -7.79905i q^{67} +(7.61522 - 8.99190i) q^{68} +1.26801i q^{69} +8.38078i q^{71} +(5.75575 - 3.27081i) q^{72} -8.78095i q^{73} +(-0.886490 + 2.41844i) q^{74} +0.812042 q^{75} +(4.45099 + 3.76954i) q^{76} +(-0.966036 - 0.354104i) q^{78} +3.63368i q^{79} +(3.94540 - 0.658646i) q^{80} +3.50012 q^{81} +(13.9315 + 5.10665i) q^{82} +2.03796 q^{83} +5.89164 q^{85} +(4.04428 + 1.48245i) q^{86} +7.90185 q^{87} +(6.79211 + 11.9523i) q^{88} -1.76452i q^{89} +(3.10788 + 1.13921i) q^{90} +(-2.01832 + 2.38320i) q^{92} -3.58528 q^{93} +(-2.54034 + 6.93032i) q^{94} +2.91636i q^{95} +(-4.51443 - 0.849178i) q^{96} -7.83641i q^{97} +11.3763i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60}+ \cdots + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.486718	−	1.32782i	0.344161	−	0.938911i
$2$	0.486718	−	1.32782i	0.344161	−	0.938911i
$3$	−0.812042			−0.468833			−0.234416	−	0.972136i	$-0.575318\pi$
$3$	−0.812042			−0.468833			−0.234416	+	0.972136i	$0.575318\pi$
$4$	−1.52621	−	1.29255i	−0.763106	−	0.646273i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.395235	+	1.07825i	−0.161354	+	0.440192i
$7$		0			0
$7$		0			0
$8$	−2.45910	+	1.39743i	−0.869424	+	0.494066i
$9$	−2.34059			−0.780196
$10$	−1.32782	−	0.486718i	−0.419894	−	0.153914i
$11$		−	4.86043i		−	1.46547i	−0.680512	−	0.732737i	$-0.738243\pi$
$11$		−	4.86043i		−	1.46547i	0.680512	−	0.732737i	$-0.261757\pi$
$12$	1.23935	+	1.04960i	0.357769	+	0.302994i
$13$			0.895933i			0.248487i	0.992252	+	0.124244i	$0.0396504\pi$
$13$			0.895933i			0.248487i	−0.992252	+	0.124244i	$0.960350\pi$
$14$		0			0
$15$			0.812042i			0.209668i
$16$	0.658646	+	3.94540i	0.164662	+	0.986350i
$17$			5.89164i			1.42893i	0.699670	+	0.714467i	$0.253331\pi$
$17$			5.89164i			1.42893i	−0.699670	+	0.714467i	$0.746669\pi$
$18$	−1.13921	+	3.10788i	−0.268513	+	0.732534i
$19$	−2.91636			−0.669060			−0.334530	−	0.942385i	$-0.608578\pi$
$19$	−2.91636			−0.669060			−0.334530	+	0.942385i	$0.608578\pi$
$20$	−1.29255	+	1.52621i	−0.289022	+	0.341271i
$21$		0			0
$22$	−6.45377	−	2.36566i	−1.37595	−	0.504359i
$23$		−	1.56151i		−	0.325597i	−0.986659	−	0.162799i	$-0.947948\pi$
$23$		−	1.56151i		−	0.325597i	0.986659	−	0.162799i	$-0.0520521\pi$
$24$	1.99689	−	1.13477i	0.407614	−	0.231634i
$25$	−1.00000			−0.200000
$26$	1.18964	+	0.436066i	0.233307	+	0.0855197i
$27$	4.33678			0.834614
$28$		0			0
$29$	−9.73084			−1.80697			−0.903486	−	0.428618i	$-0.859001\pi$
$29$	−9.73084			−1.80697			−0.903486	+	0.428618i	$0.859001\pi$
$30$	1.07825	+	0.395235i	0.196860	+	0.0721597i
$31$	4.41515			0.792984			0.396492	−	0.918038i	$-0.370227\pi$
$31$	4.41515			0.792984			0.396492	+	0.918038i	$0.370227\pi$
$32$	5.55936	+	1.04573i	0.982765	+	0.184861i
$33$			3.94687i			0.687062i
$34$	7.82304	+	2.86757i	1.34164	+	0.491783i
$35$		0			0
$36$	3.57223	+	3.02532i	0.595372	+	0.504220i
$37$	−1.82136			−0.299431			−0.149715	−	0.988729i	$-0.547836\pi$
$37$	−1.82136			−0.299431			−0.149715	+	0.988729i	$0.547836\pi$
$38$	−1.41945	+	3.87241i	−0.230264	+	0.628187i
$39$		−	0.727535i		−	0.116499i
$40$	1.39743	+	2.45910i	0.220953	+	0.388818i
$41$			10.4920i			1.63858i	0.573381	+	0.819289i	$0.305632\pi$
$41$			10.4920i			1.63858i	−0.573381	+	0.819289i	$0.694368\pi$
$42$		0			0
$43$			3.04581i			0.464481i	0.972658	+	0.232240i	$0.0746056\pi$
$43$			3.04581i			0.464481i	−0.972658	+	0.232240i	$0.925394\pi$
$44$	−6.28233	+	7.41804i	−0.947097	+	1.11831i
$45$			2.34059i			0.348914i
$46$	−2.07340	−	0.760014i	−0.305707	−	0.112058i
$47$	−5.21932			−0.761316			−0.380658	−	0.924716i	$-0.624303\pi$
$47$	−5.21932			−0.761316			−0.380658	+	0.924716i	$0.624303\pi$
$48$	−0.534848	−	3.20383i	−0.0771987	−	0.462433i
$49$		0			0
$50$	−0.486718	+	1.32782i	−0.0688323	+	0.187782i
$51$		−	4.78426i		−	0.669930i
$52$	1.15804	−	1.36738i	0.160591	−	0.189622i
$53$	0.179724			0.0246870			0.0123435	−	0.999924i	$-0.496071\pi$
$53$	0.179724			0.0246870			0.0123435	+	0.999924i	$0.496071\pi$
$54$	2.11079	−	5.75846i	0.287242	−	0.783628i
$55$	−4.86043			−0.655380
$56$		0			0
$57$	2.36821			0.313677
$58$	−4.73617	+	12.9208i	−0.621890	+	1.69658i
$59$	−11.3657			−1.47969			−0.739846	−	0.672776i	$-0.765102\pi$
$59$	−11.3657			−1.47969			−0.739846	+	0.672776i	$0.765102\pi$
$60$	1.04960	−	1.23935i	0.135503	−	0.159999i
$61$			6.15579i			0.788168i	0.919075	+	0.394084i	$0.128938\pi$
$61$			6.15579i			0.788168i	−0.919075	+	0.394084i	$0.871062\pi$
$62$	2.14893	−	5.86252i	0.272914	−	0.744541i
$63$		0			0
$64$	4.09438	−	6.87285i	0.511798	−	0.859106i
$65$	0.895933			0.111127
$66$	5.24073	+	1.92101i	0.645090	+	0.236460i
$67$		−	7.79905i		−	0.952806i	−0.879227	−	0.476403i	$-0.841940\pi$
$67$		−	7.79905i		−	0.952806i	0.879227	−	0.476403i	$-0.158060\pi$
$68$	7.61522	−	8.99190i	0.923481	−	1.09043i
$69$			1.26801i			0.152651i
$70$		0			0
$71$			8.38078i			0.994616i	0.867574	+	0.497308i	$0.165678\pi$
$71$			8.38078i			0.994616i	−0.867574	+	0.497308i	$0.834322\pi$
$72$	5.75575	−	3.27081i	0.678321	−	0.385468i
$73$		−	8.78095i		−	1.02773i	−0.857870	−	0.513866i	$-0.828213\pi$
$73$		−	8.78095i		−	1.02773i	0.857870	−	0.513866i	$-0.171787\pi$
$74$	−0.886490	+	2.41844i	−0.103052	+	0.281138i
$75$	0.812042			0.0937665
$76$	4.45099	+	3.76954i	0.510564	+	0.432396i
$77$		0			0
$78$	−0.966036	−	0.354104i	−0.109382	−	0.0400944i
$79$			3.63368i			0.408821i	0.978885	+	0.204410i	$0.0655277\pi$
$79$			3.63368i			0.408821i	−0.978885	+	0.204410i	$0.934472\pi$
$80$	3.94540	−	0.658646i	0.441109	−	0.0736389i
$81$	3.50012			0.388902
$82$	13.9315	+	5.10665i	1.53848	+	0.563935i
$83$	2.03796			0.223695			0.111847	−	0.993725i	$-0.464323\pi$
$83$	2.03796			0.223695			0.111847	+	0.993725i	$0.464323\pi$
$84$		0			0
$85$	5.89164			0.639038
$86$	4.04428	+	1.48245i	0.436106	+	0.159856i
$87$	7.90185			0.847167
$88$	6.79211	+	11.9523i	0.724041	+	1.27412i
$89$		−	1.76452i		−	0.187039i	−0.995617	−	0.0935195i	$-0.970188\pi$
$89$		−	1.76452i		−	0.187039i	0.995617	−	0.0935195i	$-0.0298118\pi$
$90$	3.10788	+	1.13921i	0.327599	+	0.120083i
$91$		0			0
$92$	−2.01832	+	2.38320i	−0.210425	+	0.248465i
$93$	−3.58528			−0.371777
$94$	−2.54034	+	6.93032i	−0.262016	+	0.714808i
$95$			2.91636i			0.299213i
$96$	−4.51443	−	0.849178i	−0.460752	−	0.0866689i
$97$		−	7.83641i		−	0.795667i	−0.917458	−	0.397834i	$-0.869762\pi$
$97$		−	7.83641i		−	0.795667i	0.917458	−	0.397834i	$-0.130238\pi$
$98$		0			0
$99$			11.3763i			1.14336i
$100$	1.52621	+	1.29255i	0.152621	+	0.129255i
$101$		−	7.28536i		−	0.724920i	−0.931999	−	0.362460i	$-0.881937\pi$
$101$		−	7.28536i		−	0.724920i	0.931999	−	0.362460i	$-0.118063\pi$
$102$	−6.35264	−	2.32858i	−0.629005	−	0.230564i
$103$	−9.21049			−0.907537			−0.453768	−	0.891120i	$-0.649921\pi$
$103$	−9.21049			−0.907537			−0.453768	+	0.891120i	$0.649921\pi$
$104$	−1.25200	−	2.20319i	−0.122769	−	0.216041i
$105$		0			0
$106$	0.0874748	−	0.238641i	0.00849630	−	0.0231789i
$107$		−	14.9889i		−	1.44903i	−0.689258	−	0.724516i	$-0.742063\pi$
$107$		−	14.9889i		−	1.44903i	0.689258	−	0.724516i	$-0.257937\pi$
$108$	−6.61885	−	5.60549i	−0.636899	−	0.539389i
$109$	1.59122			0.152411			0.0762056	−	0.997092i	$-0.475719\pi$
$109$	1.59122			0.152411			0.0762056	+	0.997092i	$0.475719\pi$
$110$	−2.36566	+	6.45377i	−0.225556	+	0.615343i
$111$	1.47902			0.140383
$112$		0			0
$113$	3.57866			0.336652			0.168326	−	0.985731i	$-0.446164\pi$
$113$	3.57866			0.336652			0.168326	+	0.985731i	$0.446164\pi$
$114$	1.15265	−	3.14456i	0.107955	−	0.294515i
$115$	−1.56151			−0.145612
$116$	14.8513	+	12.5776i	1.37891	+	1.16780i
$117$		−	2.09701i		−	0.193869i
$118$	−5.53190	+	15.0917i	−0.509253	+	1.38930i
$119$		0			0
$120$	−1.13477	−	1.99689i	−0.103590	−	0.182291i
$121$	−12.6238			−1.14761
$122$	8.17377	+	2.99613i	0.740019	+	0.271257i
$123$		−	8.51996i		−	0.768219i
$124$	−6.73845	−	5.70678i	−0.605131	−	0.512484i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	7.67404i		−	0.680961i	−0.940252	−	0.340481i	$-0.889410\pi$
$127$		−	7.67404i		−	0.680961i	0.940252	−	0.340481i	$-0.110590\pi$
$128$	−7.13310	−	8.78174i	−0.630483	−	0.776203i
$129$		−	2.47332i		−	0.217764i
$130$	0.436066	−	1.18964i	0.0382456	−	0.104338i
$131$	−19.9081			−1.73938			−0.869689	−	0.493600i	$-0.835681\pi$
$131$	−19.9081			−1.73938			−0.869689	+	0.493600i	$0.835681\pi$
$132$	5.10151	−	6.02376i	0.444030	−	0.524301i
$133$		0			0
$134$	−10.3557	−	3.79593i	−0.894599	−	0.327919i
$135$		−	4.33678i		−	0.373251i
$136$	−8.23316	−	14.4882i	−0.705987	−	1.24235i
$137$	−8.83618			−0.754926			−0.377463	−	0.926025i	$-0.623203\pi$
$137$	−8.83618			−0.754926			−0.377463	+	0.926025i	$0.623203\pi$
$138$	1.68369	+	0.617163i	0.143325	+	0.0525364i
$139$	−7.91285			−0.671159			−0.335580	−	0.942012i	$-0.608932\pi$
$139$	−7.91285			−0.671159			−0.335580	+	0.942012i	$0.608932\pi$
$140$		0			0
$141$	4.23831			0.356930
$142$	11.1282	+	4.07907i	0.933855	+	0.342308i
$143$	4.35462			0.364152
$144$	−1.54162	−	9.23456i	−0.128468	−	0.769546i
$145$			9.73084i			0.808102i
$146$	−11.6595	−	4.27384i	−0.964949	−	0.353706i
$147$		0			0
$148$	2.77979	+	2.35420i	0.228497	+	0.193514i
$149$	−1.72300			−0.141154			−0.0705770	−	0.997506i	$-0.522484\pi$
$149$	−1.72300			−0.141154			−0.0705770	+	0.997506i	$0.522484\pi$
$150$	0.395235	−	1.07825i	0.0322708	−	0.0880384i
$151$		−	0.814130i		−	0.0662529i	−0.999451	−	0.0331265i	$-0.989454\pi$
$151$		−	0.814130i		−	0.0662529i	0.999451	−	0.0331265i	$-0.0105464\pi$
$152$	7.17164	−	4.07541i	0.581697	−	0.330560i
$153$		−	13.7899i		−	1.11485i
$154$		0			0
$155$		−	4.41515i		−	0.354633i
$156$	−0.940373	+	1.11037i	−0.0752901	+	0.0889010i
$157$			13.3553i			1.06587i	0.846157	+	0.532934i	$0.178911\pi$
$157$			13.3553i			1.06587i	−0.846157	+	0.532934i	$0.821089\pi$
$158$	4.82487	+	1.76858i	0.383846	+	0.140700i
$159$	−0.145943			−0.0115741
$160$	1.04573	−	5.55936i	0.0826724	−	0.439506i
$161$		0			0
$162$	1.70357	−	4.64753i	0.133845	−	0.365144i
$163$		−	8.97711i		−	0.703142i	−0.936161	−	0.351571i	$-0.885648\pi$
$163$		−	8.97711i		−	0.703142i	0.936161	−	0.351571i	$-0.114352\pi$
$164$	13.5614	−	16.0130i	1.05897	−	1.25041i
$165$	3.94687			0.307263
$166$	0.991910	−	2.70604i	0.0769871	−	0.210029i
$167$	−17.0324			−1.31801			−0.659003	−	0.752140i	$-0.729022\pi$
$167$	−17.0324			−1.31801			−0.659003	+	0.752140i	$0.729022\pi$
$168$		0			0
$169$	12.1973			0.938254
$170$	2.86757	−	7.82304i	0.219932	−	0.600000i
$171$	6.82601			0.521998
$172$	3.93685	−	4.64854i	0.300182	−	0.354448i
$173$		−	16.4660i		−	1.25188i	−0.779869	−	0.625942i	$-0.784715\pi$
$173$		−	16.4660i		−	1.25188i	0.779869	−	0.625942i	$-0.215285\pi$
$174$	3.84597	−	10.4922i	0.291562	−	0.795414i
$175$		0			0
$176$	19.1763	−	3.20130i	1.44547	−	0.241307i
$177$	9.22945			0.693728
$178$	−2.34297	−	0.858824i	−0.175613	−	0.0643716i
$179$			10.6983i			0.799629i	0.916596	+	0.399815i	$0.130926\pi$
$179$			10.6983i			0.799629i	−0.916596	+	0.399815i	$0.869074\pi$
$180$	3.02532	−	3.57223i	0.225494	−	0.266259i
$181$		−	10.8661i		−	0.807672i	−0.914831	−	0.403836i	$-0.867677\pi$
$181$		−	10.8661i		−	0.807672i	0.914831	−	0.403836i	$-0.132323\pi$
$182$		0			0
$183$		−	4.99875i		−	0.369519i
$184$	2.18210	+	3.83992i	0.160867	+	0.283082i
$185$			1.82136i			0.133909i
$186$	−1.74502	+	4.76061i	−0.127951	+	0.349065i
$187$	28.6359			2.09406
$188$	7.96579	+	6.74622i	0.580965	+	0.492018i
$189$		0			0
$190$	3.87241	+	1.41945i	0.280934	+	0.102977i
$191$			0.507180i			0.0366983i	0.999832	+	0.0183491i	$0.00584104\pi$
$191$			0.507180i			0.0366983i	−0.999832	+	0.0183491i	$0.994159\pi$
$192$	−3.32481	+	5.58104i	−0.239947	+	0.402777i
$193$	−20.8195			−1.49862			−0.749311	−	0.662218i	$-0.769615\pi$
$193$	−20.8195			−1.49862			−0.749311	+	0.662218i	$0.769615\pi$
$194$	−10.4053	−	3.81412i	−0.747060	−	0.273838i
$195$	−0.727535			−0.0520999
$196$		0			0
$197$	−8.86095			−0.631317			−0.315658	−	0.948873i	$-0.602225\pi$
$197$	−8.86095			−0.631317			−0.315658	+	0.948873i	$0.602225\pi$
$198$	15.1056	+	5.53702i	1.07351	+	0.393499i
$199$	−23.2162			−1.64576			−0.822878	−	0.568218i	$-0.807633\pi$
$199$	−23.2162			−1.64576			−0.822878	+	0.568218i	$0.807633\pi$
$200$	2.45910	−	1.39743i	0.173885	−	0.0988132i
$201$			6.33315i			0.446706i
$202$	−9.67365	−	3.54591i	−0.680635	−	0.249490i
$203$		0			0
$204$	−6.18388	+	7.30179i	−0.432958	+	0.511228i
$205$	10.4920			0.732794
$206$	−4.48291	+	12.2299i	−0.312339	+	0.852096i
$207$			3.65485i			0.254030i
$208$	−3.53482	+	0.590103i	−0.245095	+	0.0409163i
$209$			14.1748i			0.980490i
$210$		0			0
$211$		−	6.21092i		−	0.427578i	−0.976880	−	0.213789i	$-0.931420\pi$
$211$		−	6.21092i		−	0.427578i	0.976880	−	0.213789i	$-0.0685804\pi$
$212$	−0.274297	−	0.232301i	−0.0188388	−	0.0159545i
$213$		−	6.80555i		−	0.466308i
$214$	−19.9026	−	7.29536i	−1.36051	−	0.498701i
$215$	3.04581			0.207722
$216$	−10.6646	+	6.06035i	−0.725634	+	0.412354i
$217$		0			0
$218$	0.774475	−	2.11285i	0.0524541	−	0.143101i
$219$			7.13050i			0.481835i
$220$	7.41804	+	6.28233i	0.500124	+	0.423555i
$221$	−5.27852			−0.355072
$222$	0.719867	−	1.96388i	0.0483143	−	0.131807i
$223$	12.8221			0.858632			0.429316	−	0.903154i	$-0.358755\pi$
$223$	12.8221			0.858632			0.429316	+	0.903154i	$0.358755\pi$
$224$		0			0
$225$	2.34059			0.156039
$226$	1.74180	−	4.75182i	0.115863	−	0.316086i
$227$	−3.60664			−0.239381			−0.119691	−	0.992811i	$-0.538190\pi$
$227$	−3.60664			−0.239381			−0.119691	+	0.992811i	$0.538190\pi$
$228$	−3.61439	−	3.06102i	−0.239369	−	0.202721i
$229$		−	17.7880i		−	1.17546i	−0.809055	−	0.587732i	$-0.800021\pi$
$229$		−	17.7880i		−	1.17546i	0.809055	−	0.587732i	$-0.199979\pi$
$230$	−0.760014	+	2.07340i	−0.0501139	+	0.136716i
$231$		0			0
$232$	23.9291	−	13.5982i	1.57103	−	0.892763i
$233$	0.274073			0.0179551			0.00897756	−	0.999960i	$-0.497142\pi$
$233$	0.274073			0.0179551			0.00897756	+	0.999960i	$0.497142\pi$
$234$	−2.78445	−	1.02065i	−0.182025	−	0.0667221i
$235$			5.21932i			0.340471i
$236$	17.3465	+	14.6907i	1.12916	+	0.956286i
$237$		−	2.95070i		−	0.191668i
$238$		0			0
$239$		−	23.0254i		−	1.48939i	−0.667406	−	0.744694i	$-0.732595\pi$
$239$		−	23.0254i		−	1.48939i	0.667406	−	0.744694i	$-0.267405\pi$
$240$	−3.20383	+	0.534848i	−0.206806	+	0.0345243i
$241$			3.75520i			0.241894i	0.992659	+	0.120947i	$0.0385930\pi$
$241$			3.75520i			0.241894i	−0.992659	+	0.120947i	$0.961407\pi$
$242$	−6.14420	+	16.7621i	−0.394964	+	1.07751i
$243$	−15.8526			−1.01694
$244$	7.95664	−	9.39503i	0.509372	−	0.601455i
$245$		0			0
$246$	−11.3130	−	4.14681i	−0.721289	−	0.264391i
$247$		−	2.61287i		−	0.166253i
$248$	−10.8573	+	6.16986i	−0.689440	+	0.391786i
$249$	−1.65491			−0.104875
$250$	1.32782	+	0.486718i	0.0839787	+	0.0307827i
$251$	−0.268218			−0.0169298			−0.00846489	−	0.999964i	$-0.502694\pi$
$251$	−0.268218			−0.0169298			−0.00846489	+	0.999964i	$0.502694\pi$
$252$		0			0
$253$	−7.58961			−0.477155
$254$	−10.1897	−	3.73509i	−0.639362	−	0.234360i
$255$	−4.78426			−0.299602
$256$	−15.1324	+	5.19725i	−0.945773	+	0.324828i
$257$			31.0853i			1.93905i	0.244997	+	0.969524i	$0.421213\pi$
$257$			31.0853i			1.93905i	−0.244997	+	0.969524i	$0.578787\pi$
$258$	−3.28413	−	1.20381i	−0.204461	−	0.0749459i
$259$		0			0
$260$	−1.36738	−	1.15804i	−0.0848016	−	0.0718183i
$261$	22.7759			1.40979
$262$	−9.68962	+	26.4344i	−0.598627	+	1.63312i
$263$		−	27.8461i		−	1.71706i	−0.512760	−	0.858532i	$-0.671377\pi$
$263$		−	27.8461i		−	1.71706i	0.512760	−	0.858532i	$-0.328623\pi$
$264$	−5.51547	−	9.70576i	−0.339454	−	0.597348i
$265$		−	0.179724i		−	0.0110404i
$266$		0			0
$267$			1.43287i			0.0876900i
$268$	−10.0806	+	11.9030i	−0.615773	+	0.727092i
$269$		−	1.44485i		−	0.0880939i	−0.999029	−	0.0440470i	$-0.985975\pi$
$269$		−	1.44485i		−	0.0880939i	0.999029	−	0.0440470i	$-0.0140251\pi$
$270$	−5.75846	−	2.11079i	−0.350449	−	0.128458i
$271$	13.9942			0.850085			0.425042	−	0.905173i	$-0.360259\pi$
$271$	13.9942			0.850085			0.425042	+	0.905173i	$0.360259\pi$
$272$	−23.2449	+	3.88051i	−1.40943	+	0.235290i
$273$		0			0
$274$	−4.30072	+	11.7329i	−0.259816	+	0.708808i
$275$			4.86043i			0.293095i
$276$	1.63896	−	1.93525i	0.0986540	−	0.116489i
$277$	18.5135			1.11237			0.556184	−	0.831059i	$-0.312265\pi$
$277$	18.5135			1.11237			0.556184	+	0.831059i	$0.312265\pi$
$278$	−3.85132	+	10.5068i	−0.230987	+	0.630159i
$279$	−10.3340			−0.618683
$280$		0			0
$281$	−9.00853			−0.537404			−0.268702	−	0.963223i	$-0.586595\pi$
$281$	−9.00853			−0.537404			−0.268702	+	0.963223i	$0.586595\pi$
$282$	2.06286	−	5.62771i	0.122841	−	0.335125i
$283$	27.2951			1.62252			0.811261	−	0.584684i	$-0.198781\pi$
$283$	27.2951			1.62252			0.811261	+	0.584684i	$0.198781\pi$
$284$	10.8326	−	12.7909i	0.642794	−	0.758997i
$285$		−	2.36821i		−	0.140281i
$286$	2.11947	−	5.78215i	0.125327	−	0.341906i
$287$		0			0
$288$	−13.0122	−	2.44763i	−0.766749	−	0.144228i
$289$	−17.7114			−1.04185
$290$	12.9208	+	4.73617i	0.758736	+	0.278118i
$291$			6.36350i			0.373035i
$292$	−11.3498	+	13.4016i	−0.664196	+	0.784269i
$293$		−	10.6330i		−	0.621188i	−0.950543	−	0.310594i	$-0.899472\pi$
$293$		−	10.6330i		−	0.621188i	0.950543	−	0.310594i	$-0.100528\pi$
$294$		0			0
$295$			11.3657i			0.661739i
$296$	4.47892	−	2.54523i	0.260332	−	0.147938i
$297$		−	21.0786i		−	1.22310i
$298$	−0.838617	+	2.28784i	−0.0485798	+	0.132531i
$299$	1.39901			0.0809068
$300$	−1.23935	−	1.04960i	−0.0715538	−	0.0605988i
$301$		0			0
$302$	−1.08102	−	0.396251i	−0.0622056	−	0.0228017i
$303$			5.91602i			0.339866i
$304$	−1.92085	−	11.5062i	−0.110168	−	0.659927i
$305$	6.15579			0.352479
$306$	−18.3105	−	6.71179i	−1.04674	−	0.383688i
$307$	17.9812			1.02624			0.513120	−	0.858317i	$-0.328490\pi$
$307$	17.9812			1.02624			0.513120	+	0.858317i	$0.328490\pi$
$308$		0			0
$309$	7.47930			0.425483
$310$	−5.86252	−	2.14893i	−0.332969	−	0.122051i
$311$	−28.3158			−1.60564			−0.802821	−	0.596220i	$-0.796669\pi$
$311$	−28.3158			−1.60564			−0.802821	+	0.596220i	$0.796669\pi$
$312$	1.01668	+	1.78908i	0.0575581	+	0.101287i
$313$			5.59496i			0.316246i	0.987419	+	0.158123i	$0.0505442\pi$
$313$			5.59496i			0.316246i	−0.987419	+	0.158123i	$0.949456\pi$
$314$	17.7334	+	6.50025i	1.00075	+	0.366830i
$315$		0			0
$316$	4.69670	−	5.54576i	0.264210	−	0.311974i
$317$	31.3472			1.76064			0.880318	−	0.474383i	$-0.157329\pi$
$317$	31.3472			1.76064			0.880318	+	0.474383i	$0.157329\pi$
$318$	−0.0710332	+	0.193786i	−0.00398334	+	0.0108670i
$319$			47.2960i			2.64807i
$320$	−6.87285	−	4.09438i	−0.384204	−	0.228883i
$321$			12.1716i			0.679353i
$322$		0			0
$323$		−	17.1822i		−	0.956042i
$324$	−5.34192	−	4.52406i	−0.296773	−	0.251337i
$325$		−	0.895933i		−	0.0496974i
$326$	−11.9200	−	4.36932i	−0.660187	−	0.241994i
$327$	−1.29214			−0.0714554
$328$	−14.6619	−	25.8010i	−0.809566	−	1.42462i
$329$		0			0
$330$	1.92101	−	5.24073i	0.105748	−	0.288493i
$331$			21.5135i			1.18249i	0.806493	+	0.591244i	$0.201363\pi$
$331$			21.5135i			1.18249i	−0.806493	+	0.591244i	$0.798637\pi$
$332$	−3.11035	−	2.63415i	−0.170703	−	0.144568i
$333$	4.26306			0.233615
$334$	−8.28997	+	22.6160i	−0.453607	+	1.23749i
$335$	−7.79905			−0.426108
$336$		0			0
$337$	−0.0584151			−0.00318207			−0.00159104	−	0.999999i	$-0.500506\pi$
$337$	−0.0584151			−0.00318207			−0.00159104	+	0.999999i	$0.500506\pi$
$338$	5.93664	−	16.1958i	0.322911	−	0.880937i
$339$	−2.90602			−0.157833
$340$	−8.99190	−	7.61522i	−0.487654	−	0.412993i
$341$		−	21.4595i		−	1.16210i
$342$	3.32234	−	9.06371i	0.179651	−	0.490109i
$343$		0			0
$344$	−4.25630	−	7.48995i	−0.229484	−	0.403831i
$345$	1.26801			0.0682674
$346$	−21.8638	−	8.01428i	−1.17541	−	0.430850i
$347$		−	8.81362i		−	0.473140i	−0.971614	−	0.236570i	$-0.923977\pi$
$347$		−	8.81362i		−	0.473140i	0.971614	−	0.236570i	$-0.0760233\pi$
$348$	−12.0599	−	10.2135i	−0.646478	−	0.547502i
$349$			1.78555i			0.0955784i	0.998857	+	0.0477892i	$0.0152176\pi$
$349$			1.78555i			0.0955784i	−0.998857	+	0.0477892i	$0.984782\pi$
$350$		0			0
$351$			3.88547i			0.207391i
$352$	5.08270	−	27.0208i	0.270909	−	1.44022i
$353$			27.4929i			1.46330i	0.681679	+	0.731651i	$0.261250\pi$
$353$			27.4929i			1.46330i	−0.681679	+	0.731651i	$0.738750\pi$
$354$	4.49214	−	12.2551i	0.238754	−	0.651349i
$355$	8.38078			0.444806
$356$	−2.28073	+	2.69304i	−0.120878	+	0.142731i
$357$		0			0
$358$	14.2054	+	5.20706i	0.750780	+	0.275201i
$359$			18.6043i			0.981895i	0.871189	+	0.490948i	$0.163349\pi$
$359$			18.6043i			0.981895i	−0.871189	+	0.490948i	$0.836651\pi$
$360$	−3.27081	−	5.75575i	−0.172387	−	0.303355i
$361$	−10.4948			−0.552359
$362$	−14.4283	−	5.28873i	−0.758332	−	0.277970i
$363$	10.2510			0.538039
$364$		0			0
$365$	−8.78095			−0.459616
$366$	−6.63745	−	2.43298i	−0.346945	−	0.127174i
$367$	21.9844			1.14758			0.573788	−	0.819004i	$-0.305474\pi$
$367$	21.9844			1.14758			0.573788	+	0.819004i	$0.305474\pi$
$368$	6.16078	−	1.02848i	0.321153	−	0.0536134i
$369$		−	24.5575i		−	1.27841i
$370$	2.41844	+	0.886490i	0.125729	+	0.0460864i
$371$		0			0
$372$	5.47190	+	4.63415i	0.283705	+	0.240269i
$373$	0.565616			0.0292865			0.0146433	−	0.999893i	$-0.495339\pi$
$373$	0.565616			0.0292865			0.0146433	+	0.999893i	$0.495339\pi$
$374$	13.9376	−	38.0233i	0.720696	−	1.96614i
$375$		−	0.812042i		−	0.0419337i
$376$	12.8348	−	7.29363i	0.661907	−	0.376140i
$377$		−	8.71818i		−	0.449009i
$378$		0			0
$379$			28.3294i			1.45518i	0.686010	+	0.727592i	$0.259361\pi$
$379$			28.3294i			1.45518i	−0.686010	+	0.727592i	$0.740639\pi$
$380$	3.76954	−	4.45099i	0.193373	−	0.228331i
$381$			6.23164i			0.319257i
$382$	0.673444	+	0.246854i	0.0344564	+	0.0126301i
$383$	3.08601			0.157688			0.0788438	−	0.996887i	$-0.474877\pi$
$383$	3.08601			0.157688			0.0788438	+	0.996887i	$0.474877\pi$
$384$	5.79237	+	7.13114i	0.295591	+	0.363909i
$385$		0			0
$386$	−10.1332	+	27.6446i	−0.515768	+	1.40707i
$387$		−	7.12898i		−	0.362386i
$388$	−10.1289	+	11.9600i	−0.514219	+	0.607179i
$389$	16.3537			0.829165			0.414583	−	0.910012i	$-0.363928\pi$
$389$	16.3537			0.829165			0.414583	+	0.910012i	$0.363928\pi$
$390$	−0.354104	+	0.966036i	−0.0179308	+	0.0489171i
$391$	9.19986			0.465257
$392$		0			0
$393$	16.1662			0.815477
$394$	−4.31278	+	11.7658i	−0.217275	+	0.592750i
$395$	3.63368			0.182830
$396$	14.7043	−	17.3626i	0.738921	−	0.872503i
$397$			7.82460i			0.392706i	0.980533	+	0.196353i	$0.0629098\pi$
$397$			7.82460i			0.392706i	−0.980533	+	0.196353i	$0.937090\pi$
$398$	−11.2998	+	30.8270i	−0.566406	+	1.54522i
$399$		0			0
$400$	−0.658646	−	3.94540i	−0.0329323	−	0.197270i
$401$	−19.7876			−0.988145			−0.494072	−	0.869421i	$-0.664492\pi$
$401$	−19.7876			−0.988145			−0.494072	+	0.869421i	$0.664492\pi$
$402$	8.40929	+	3.08246i	0.419417	+	0.153739i
$403$			3.95568i			0.197046i
$404$	−9.41667	+	11.1190i	−0.468497	+	0.553191i
$405$		−	3.50012i		−	0.173922i
$406$		0			0
$407$			8.85261i			0.438808i
$408$	6.68567	+	11.7650i	0.330990	+	0.582454i
$409$			25.3014i			1.25107i	0.780195	+	0.625536i	$0.215120\pi$
$409$			25.3014i			1.25107i	−0.780195	+	0.625536i	$0.784880\pi$
$410$	5.10665	−	13.9315i	0.252199	−	0.688028i
$411$	7.17535			0.353934
$412$	14.0572	+	11.9050i	0.692547	+	0.586517i
$413$		0			0
$414$	4.85299	+	1.77888i	0.238511	+	0.0874272i
$415$		−	2.03796i		−	0.100039i
$416$	−0.936906	+	4.98081i	−0.0459356	+	0.244204i
$417$	6.42557			0.314661
$418$	18.8216	+	6.89911i	0.920592	+	0.337447i
$419$	−16.6804			−0.814889			−0.407445	−	0.913230i	$-0.633580\pi$
$419$	−16.6804			−0.814889			−0.407445	+	0.913230i	$0.633580\pi$
$420$		0			0
$421$	3.13305			0.152695			0.0763477	−	0.997081i	$-0.475674\pi$
$421$	3.13305			0.152695			0.0763477	+	0.997081i	$0.475674\pi$
$422$	−8.24699	−	3.02296i	−0.401457	−	0.147156i
$423$	12.2163			0.593976
$424$	−0.441960	+	0.251151i	−0.0214635	+	0.0121970i
$425$		−	5.89164i		−	0.285787i
$426$	−9.03654	−	3.31238i	−0.437822	−	0.160485i
$427$		0			0
$428$	−19.3739	+	22.8762i	−0.936470	+	1.10576i
$429$	−3.53613			−0.170726
$430$	1.48245	−	4.04428i	0.0714899	−	0.195033i
$431$		−	27.1921i		−	1.30980i	−0.755717	−	0.654898i	$-0.772711\pi$
$431$		−	27.1921i		−	1.30980i	0.755717	−	0.654898i	$-0.227289\pi$
$432$	2.85640	+	17.1103i	0.137429	+	0.823221i
$433$			32.0204i			1.53880i	0.638766	+	0.769401i	$0.279445\pi$
$433$			32.0204i			1.53880i	−0.638766	+	0.769401i	$0.720555\pi$
$434$		0			0
$435$		−	7.90185i		−	0.378865i
$436$	−2.42854	−	2.05673i	−0.116306	−	0.0984994i
$437$			4.55393i			0.217844i
$438$	9.46802	+	3.47054i	0.452400	+	0.165829i
$439$	20.1003			0.959335			0.479668	−	0.877450i	$-0.340757\pi$
$439$	20.1003			0.959335			0.479668	+	0.877450i	$0.340757\pi$
$440$	11.9523	−	6.79211i	0.569803	−	0.323801i
$441$		0			0
$442$	−2.56915	+	7.00892i	−0.122202	+	0.333380i
$443$			14.8968i			0.707768i	0.935289	+	0.353884i	$0.115139\pi$
$443$			14.8968i			0.707768i	−0.935289	+	0.353884i	$0.884861\pi$
$444$	−2.25730	−	1.91171i	−0.107127	−	0.0907256i
$445$	−1.76452			−0.0836464
$446$	6.24074	−	17.0255i	0.295508	−	0.806178i
$447$	1.39915			0.0661776
$448$		0			0
$449$	−6.18602			−0.291936			−0.145968	−	0.989289i	$-0.546630\pi$
$449$	−6.18602			−0.291936			−0.145968	+	0.989289i	$0.546630\pi$
$450$	1.13921	−	3.10788i	0.0537027	−	0.146507i
$451$	50.9957			2.40129
$452$	−5.46180	−	4.62559i	−0.256901	−	0.217569i
$453$			0.661107i			0.0310615i
$454$	−1.75542	+	4.78898i	−0.0823858	+	0.224758i
$455$		0			0
$456$	−5.82367	+	3.30941i	−0.272718	+	0.154977i
$457$	−23.3503			−1.09228			−0.546140	−	0.837694i	$-0.683903\pi$
$457$	−23.3503			−1.09228			−0.546140	+	0.837694i	$0.683903\pi$
$458$	−23.6193	−	8.65774i	−1.10366	−	0.404549i
$459$			25.5508i			1.19261i
$460$	2.38320	+	2.01832i	0.111117	+	0.0941049i
$461$		−	17.4080i		−	0.810772i	−0.914146	−	0.405386i	$-0.867137\pi$
$461$		−	17.4080i		−	0.810772i	0.914146	−	0.405386i	$-0.132863\pi$
$462$		0			0
$463$			0.962509i			0.0447316i	0.999750	+	0.0223658i	$0.00711985\pi$
$463$			0.962509i			0.0447316i	−0.999750	+	0.0223658i	$0.992880\pi$
$464$	−6.40918	−	38.3921i	−0.297539	−	1.78231i
$465$			3.58528i			0.166264i
$466$	0.133396	−	0.363920i	0.00617946	−	0.0168583i
$467$	0.290981			0.0134650			0.00673249	−	0.999977i	$-0.497857\pi$
$467$	0.290981			0.0134650			0.00673249	+	0.999977i	$0.497857\pi$
$468$	−2.71048	+	3.20048i	−0.125292	+	0.147942i
$469$		0			0
$470$	6.93032	+	2.54034i	0.319672	+	0.117177i
$471$		−	10.8450i		−	0.499713i
$472$	27.9495	−	15.8828i	1.28648	−	0.731066i
$473$	14.8039			0.680685
$474$	−3.91800	−	1.43616i	−0.179960	−	0.0659649i
$475$	2.91636			0.133812
$476$		0			0
$477$	−0.420660			−0.0192607
$478$	−30.5736	−	11.2069i	−1.39840	−	0.512590i
$479$	−19.7896			−0.904211			−0.452106	−	0.891964i	$-0.649327\pi$
$479$	−19.7896			−0.904211			−0.452106	+	0.891964i	$0.649327\pi$
$480$	−0.849178	+	4.51443i	−0.0387595	+	0.206055i
$481$		−	1.63182i		−	0.0744047i
$482$	4.98623	+	1.82772i	0.227116	+	0.0832504i
$483$		0			0
$484$	19.2665	+	16.3168i	0.875751	+	0.741672i
$485$	−7.83641			−0.355833
$486$	−7.71573	+	21.0494i	−0.349993	+	0.954819i
$487$			22.6215i			1.02508i	0.858664	+	0.512540i	$0.171295\pi$
$487$			22.6215i			1.02508i	−0.858664	+	0.512540i	$0.828705\pi$
$488$	−8.60228	−	15.1377i	−0.389407	−	0.685252i
$489$			7.28979i			0.329656i
$490$		0			0
$491$		−	38.9565i		−	1.75808i	−0.476745	−	0.879042i	$-0.658184\pi$
$491$		−	38.9565i		−	1.75808i	0.476745	−	0.879042i	$-0.341816\pi$
$492$	−11.0124	+	13.0033i	−0.496479	+	0.586232i
$493$		−	57.3306i		−	2.58204i
$494$	−3.46942	−	1.27173i	−0.156097	−	0.0572178i
$495$	11.3763			0.511325
$496$	2.90802	+	17.4195i	0.130574	+	0.782160i
$497$		0			0
$498$	−0.805472	+	2.19742i	−0.0360941	+	0.0984686i
$499$			37.6583i			1.68582i	0.538056	+	0.842909i	$0.319159\pi$
$499$			37.6583i			1.68582i	−0.538056	+	0.842909i	$0.680841\pi$
$500$	1.29255	−	1.52621i	0.0578044	−	0.0682543i
$501$	13.8310			0.617925
$502$	−0.130546	+	0.356145i	−0.00582657	+	0.0158955i
$503$	42.9688			1.91589			0.957943	−	0.286959i	$-0.0926442\pi$
$503$	42.9688			1.91589			0.957943	+	0.286959i	$0.0926442\pi$
$504$		0			0
$505$	−7.28536			−0.324194
$506$	−3.69400	+	10.0776i	−0.164218	+	0.448005i
$507$	−9.90472			−0.439884
$508$	−9.91906	+	11.7122i	−0.440087	+	0.519646i
$509$		−	4.77741i		−	0.211755i	−0.994379	−	0.105877i	$-0.966235\pi$
$509$		−	4.77741i		−	0.211755i	0.994379	−	0.105877i	$-0.0337651\pi$
$510$	−2.32858	+	6.35264i	−0.103111	+	0.281299i
$511$		0			0
$512$	−0.464182	+	22.6227i	−0.0205141	+	0.999790i
$513$	−12.6476			−0.558407
$514$	41.2757	+	15.1298i	1.82059	+	0.667345i
$515$			9.21049i			0.405863i
$516$	−3.19688	+	3.77481i	−0.140735	+	0.166177i
$517$			25.3681i			1.11569i
$518$		0			0
$519$			13.3711i			0.586924i
$520$	−2.20319	+	1.25200i	−0.0966164	+	0.0549040i
$521$		−	18.2934i		−	0.801448i	−0.916199	−	0.400724i	$-0.868759\pi$
$521$		−	18.2934i		−	0.801448i	0.916199	−	0.400724i	$-0.131241\pi$
$522$	11.0854	−	30.2423i	0.485196	−	1.32367i
$523$	18.5125			0.809494			0.404747	−	0.914429i	$-0.367360\pi$
$523$	18.5125			0.809494			0.404747	+	0.914429i	$0.367360\pi$
$524$	30.3840	+	25.7321i	1.32733	+	1.12411i
$525$		0			0
$526$	−36.9746	−	13.5532i	−1.61217	−	0.590947i
$527$			26.0125i			1.13312i
$528$	−15.5720	+	2.59959i	−0.677684	+	0.113133i
$529$	20.5617			0.893986
$530$	−0.238641	−	0.0874748i	−0.0103659	−	0.00379966i
$531$	26.6025			1.15445
$532$		0			0
$533$	−9.40015			−0.407166
$534$	1.90259	+	0.697401i	0.0823331	+	0.0301795i
$535$	−14.9889			−0.648027
$536$	10.8986	+	19.1787i	0.470749	+	0.828392i
$537$		−	8.68748i		−	0.374892i
$538$	−1.91850	−	0.703233i	−0.0827123	−	0.0303185i
$539$		0			0
$540$	−5.60549	+	6.61885i	−0.241222	+	0.284830i
$541$	−3.99622			−0.171811			−0.0859055	−	0.996303i	$-0.527378\pi$
$541$	−3.99622			−0.171811			−0.0859055	+	0.996303i	$0.527378\pi$
$542$	6.81120	−	18.5817i	0.292566	−	0.798153i
$543$			8.82374i			0.378663i
$544$	−6.16108	+	32.7537i	−0.264154	+	1.40430i
$545$		−	1.59122i		−	0.0681604i
$546$		0			0
$547$		−	13.3961i		−	0.572774i	−0.958114	−	0.286387i	$-0.907546\pi$
$547$		−	13.3961i		−	0.572774i	0.958114	−	0.286387i	$-0.0924543\pi$
$548$	13.4859	+	11.4212i	0.576088	+	0.487888i
$549$		−	14.4082i		−	0.614925i
$550$	6.45377	+	2.36566i	0.275190	+	0.100872i
$551$	28.3787			1.20897
$552$	−1.77196	−	3.11817i	−0.0754195	−	0.132718i
$553$		0			0
$554$	9.01084	−	24.5826i	0.382834	−	1.04441i
$555$		−	1.47902i		−	0.0627811i
$556$	12.0767	+	10.2277i	0.512166	+	0.433752i
$557$	14.4120			0.610654			0.305327	−	0.952248i	$-0.401234\pi$
$557$	14.4120			0.610654			0.305327	+	0.952248i	$0.401234\pi$
$558$	−5.02976	+	13.7217i	−0.212927	+	0.580888i
$559$	−2.72884			−0.115418
$560$		0			0
$561$	−23.2535			−0.981766
$562$	−4.38461	+	11.9617i	−0.184954	+	0.504574i
$563$	−6.67914			−0.281492			−0.140746	−	0.990046i	$-0.544950\pi$
$563$	−6.67914			−0.281492			−0.140746	+	0.990046i	$0.544950\pi$
$564$	−6.46855	−	5.47821i	−0.272375	−	0.230674i
$565$		−	3.57866i		−	0.150555i
$566$	13.2850	−	36.2429i	0.558410	−	1.52340i
$567$		0			0
$568$	−11.7116	−	20.6092i	−0.491406	−	0.864743i
$569$	20.9023			0.876269			0.438134	−	0.898909i	$-0.355639\pi$
$569$	20.9023			0.876269			0.438134	+	0.898909i	$0.355639\pi$
$570$	−3.14456	−	1.15265i	−0.131711	−	0.0482792i
$571$			5.58864i			0.233877i	0.993139	+	0.116939i	$0.0373081\pi$
$571$			5.58864i			0.233877i	−0.993139	+	0.116939i	$0.962692\pi$
$572$	−6.64607	−	5.62855i	−0.277886	−	0.235341i
$573$		−	0.411852i		−	0.0172053i
$574$		0			0
$575$			1.56151i			0.0651195i
$576$	−9.58326	+	16.0865i	−0.399302	+	0.670271i
$577$		−	1.81916i		−	0.0757328i	−0.999283	−	0.0378664i	$-0.987944\pi$
$577$		−	1.81916i		−	0.0757328i	0.999283	−	0.0378664i	$-0.0120561\pi$
$578$	−8.62047	+	23.5176i	−0.358564	+	0.978204i
$579$	16.9063			0.702603
$580$	12.5776	−	14.8513i	0.522255	−	0.616668i
$581$		0			0
$582$	8.44958	+	3.09723i	0.350246	+	0.128384i
$583$		−	0.873535i		−	0.0361781i
$584$	12.2708	+	21.5933i	0.507768	+	0.893536i
$585$	−2.09701			−0.0867007
$586$	−14.1188	−	5.17528i	−0.583240	−	0.213789i
$587$	−26.1792			−1.08053			−0.540265	−	0.841495i	$-0.681676\pi$
$587$	−26.1792			−1.08053			−0.540265	+	0.841495i	$0.681676\pi$
$588$		0			0
$589$	−12.8762			−0.530554
$590$	15.0917	+	5.53190i	0.621313	+	0.227745i
$591$	7.19547			0.295982
$592$	−1.19964	−	7.18601i	−0.0493047	−	0.295343i
$593$			27.6315i			1.13469i	0.823480	+	0.567345i	$0.192030\pi$
$593$			27.6315i			1.13469i	−0.823480	+	0.567345i	$0.807970\pi$
$594$	−27.9886	−	10.2593i	−1.14839	−	0.420945i
$595$		0			0
$596$	2.62967	+	2.22706i	0.107716	+	0.0912241i
$597$	18.8526			0.771584
$598$	0.680922	−	1.85763i	0.0278450	−	0.0759642i
$599$		−	5.56954i		−	0.227565i	−0.993506	−	0.113783i	$-0.963703\pi$
$599$		−	5.56954i		−	0.227565i	0.993506	−	0.113783i	$-0.0362967\pi$
$600$	−1.99689	+	1.13477i	−0.0815229	+	0.0463268i
$601$		−	30.5902i		−	1.24780i	−0.781504	−	0.623901i	$-0.785547\pi$
$601$		−	30.5902i		−	1.24780i	0.781504	−	0.623901i	$-0.214453\pi$
$602$		0			0
$603$			18.2544i			0.743375i
$604$	−1.05230	+	1.24253i	−0.0428175	+	0.0505580i
$605$			12.6238i			0.513229i
$606$	7.85541	+	2.87943i	0.319104	+	0.116969i
$607$	−20.2219			−0.820782			−0.410391	−	0.911910i	$-0.634608\pi$
$607$	−20.2219			−0.820782			−0.410391	+	0.911910i	$0.634608\pi$
$608$	−16.2131	−	3.04974i	−0.657528	−	0.123683i
$609$		0			0
$610$	2.99613	−	8.17377i	0.121310	−	0.330946i
$611$		−	4.67616i		−	0.189177i
$612$	−17.8241	+	21.0463i	−0.720497	+	0.850747i
$613$	−22.5021			−0.908850			−0.454425	−	0.890785i	$-0.650155\pi$
$613$	−22.5021			−0.908850			−0.454425	+	0.890785i	$0.650155\pi$
$614$	8.75175	−	23.8758i	0.353192	−	0.963547i
$615$	−8.51996			−0.343558
$616$		0			0
$617$	22.5772			0.908922			0.454461	−	0.890767i	$-0.349832\pi$
$617$	22.5772			0.908922			0.454461	+	0.890767i	$0.349832\pi$
$618$	3.64031	−	9.93117i	0.146435	−	0.399490i
$619$	−12.3143			−0.494952			−0.247476	−	0.968894i	$-0.579601\pi$
$619$	−12.3143			−0.494952			−0.247476	+	0.968894i	$0.579601\pi$
$620$	−5.70678	+	6.73845i	−0.229190	+	0.270623i
$621$		−	6.77193i		−	0.271748i
$622$	−13.7818	+	37.5983i	−0.552600	+	1.50755i
$623$		0			0
$624$	2.87042	−	0.479188i	0.114909	−	0.0191829i
$625$	1.00000			0.0400000
$626$	7.42909	+	2.72316i	0.296926	+	0.108839i
$627$		−	11.5105i		−	0.459686i
$628$	17.2623	−	20.3830i	0.688842	−	0.813370i
$629$		−	10.7308i		−	0.427866i
$630$		0			0
$631$			22.9961i			0.915459i	0.889091	+	0.457730i	$0.151337\pi$
$631$			22.9961i			0.915459i	−0.889091	+	0.457730i	$0.848663\pi$
$632$	−5.07781	−	8.93559i	−0.201984	−	0.355439i
$633$			5.04353i			0.200462i
$634$	15.2573	−	41.6235i	0.605943	−	1.65308i
$635$	−7.67404			−0.304535
$636$	0.222740	+	0.188639i	0.00883223	+	0.00748000i
$637$		0			0
$638$	62.8006	+	23.0198i	2.48630	+	0.911363i
$639$		−	19.6160i		−	0.775995i
$640$	−8.78174	+	7.13310i	−0.347129	+	0.281961i
$641$	−35.4754			−1.40120			−0.700598	−	0.713557i	$-0.747083\pi$
$641$	−35.4754			−1.40120			−0.700598	+	0.713557i	$0.747083\pi$
$642$	16.1617	+	5.92414i	0.637852	+	0.233807i
$643$	−8.46366			−0.333774			−0.166887	−	0.985976i	$-0.553372\pi$
$643$	−8.46366			−0.333774			−0.166887	+	0.985976i	$0.553372\pi$
$644$		0			0
$645$	−2.47332			−0.0973869
$646$	−22.8148	−	8.36287i	−0.897638	−	0.329033i
$647$	4.95408			0.194765			0.0973826	−	0.995247i	$-0.468953\pi$
$647$	4.95408			0.194765			0.0973826	+	0.995247i	$0.468953\pi$
$648$	−8.60715	+	4.89117i	−0.338121	+	0.192143i
$649$			55.2423i			2.16845i
$650$	−1.18964	−	0.436066i	−0.0466615	−	0.0171039i
$651$		0			0
$652$	−11.6033	+	13.7010i	−0.454422	+	0.536572i
$653$	−1.89138			−0.0740153			−0.0370076	−	0.999315i	$-0.511783\pi$
$653$	−1.89138			−0.0740153			−0.0370076	+	0.999315i	$0.511783\pi$
$654$	−0.628906	+	1.71573i	−0.0245922	+	0.0670902i
$655$			19.9081i			0.777873i
$656$	−41.3952	+	6.91053i	−1.61621	+	0.269811i
$657$			20.5526i			0.801833i
$658$		0			0
$659$			4.20598i			0.163842i	0.996639	+	0.0819209i	$0.0261055\pi$
$659$			4.20598i			0.163842i	−0.996639	+	0.0819209i	$0.973895\pi$
$660$	−6.02376	−	5.10151i	−0.234475	−	0.198576i
$661$			11.3045i			0.439693i	0.975534	+	0.219847i	$0.0705557\pi$
$661$			11.3045i			0.439693i	−0.975534	+	0.219847i	$0.929444\pi$
$662$	28.5660	+	10.4710i	1.11025	+	0.406967i
$663$	4.28638			0.166469
$664$	−5.01155	+	2.84790i	−0.194486	+	0.110520i
$665$		0			0
$666$	2.07491	−	5.66058i	0.0804011	−	0.219343i
$667$			15.1948i			0.588345i
$668$	25.9951	+	22.0152i	1.00578	+	0.851793i
$669$	−10.4121			−0.402555
$670$	−3.79593	+	10.3557i	−0.146650	+	0.400077i
$671$	29.9197			1.15504
$672$		0			0
$673$	−36.8435			−1.42021			−0.710106	−	0.704095i	$-0.751353\pi$
$673$	−36.8435			−1.42021			−0.710106	+	0.704095i	$0.751353\pi$
$674$	−0.0284316	+	0.0775647i	−0.00109515	+	0.00298768i
$675$	−4.33678			−0.166923
$676$	−18.6157	−	15.7656i	−0.715987	−	0.606369i
$677$		−	27.7945i		−	1.06823i	−0.845412	−	0.534115i	$-0.820645\pi$
$677$		−	27.7945i		−	1.06823i	0.845412	−	0.534115i	$-0.179355\pi$
$678$	−1.41441	+	3.85867i	−0.0543202	+	0.148191i
$679$		0			0
$680$	−14.4882	+	8.23316i	−0.555595	+	0.315727i
$681$	2.92875			0.112230
$682$	−28.4944	−	10.4447i	−1.09111	−	0.399949i
$683$		−	47.2406i		−	1.80761i	−0.427942	−	0.903806i	$-0.640761\pi$
$683$		−	47.2406i		−	1.80761i	0.427942	−	0.903806i	$-0.359239\pi$
$684$	−10.4179	−	8.82293i	−0.398340	−	0.337353i
$685$			8.83618i			0.337613i
$686$		0			0
$687$			14.4446i			0.551096i
$688$	−12.0169	+	2.00611i	−0.458141	+	0.0764822i
$689$			0.161021i			0.00613440i
$690$	0.617163	−	1.68369i	0.0234950	−	0.0640970i
$691$	−34.4431			−1.31028			−0.655139	−	0.755508i	$-0.727390\pi$
$691$	−34.4431			−1.31028			−0.655139	+	0.755508i	$0.727390\pi$
$692$	−21.2830	+	25.1306i	−0.809060	+	0.955321i
$693$		0			0
$694$	−11.7029	−	4.28974i	−0.444236	−	0.162836i
$695$			7.91285i			0.300152i
$696$	−19.4315	+	11.0423i	−0.736548	+	0.418556i
$697$	−61.8152			−2.34142
$698$	2.37089	+	0.869059i	0.0897396	+	0.0328944i
$699$	−0.222559			−0.00841795
$700$		0			0
$701$	−28.7191			−1.08470			−0.542352	−	0.840151i	$-0.682466\pi$
$701$	−28.7191			−1.08470			−0.542352	+	0.840151i	$0.682466\pi$
$702$	5.15920	+	1.89112i	0.194721	+	0.0713759i
$703$	5.31176			0.200337
$704$	−33.4050	−	19.9004i	−1.25900	−	0.750026i
$705$		−	4.23831i		−	0.159624i
$706$	36.5057	+	13.3813i	1.37391	+	0.503612i
$707$		0			0
$708$	−14.0861	−	11.9295i	−0.529388	−	0.448338i
$709$	49.4621			1.85759			0.928794	−	0.370597i	$-0.120847\pi$
$709$	49.4621			1.85759			0.928794	+	0.370597i	$0.120847\pi$
$710$	4.07907	−	11.1282i	0.153085	−	0.417633i
$711$		−	8.50495i		−	0.318960i
$712$	2.46580	+	4.33915i	0.0924097	+	0.162616i
$713$		−	6.89430i		−	0.258193i
$714$		0			0
$715$		−	4.35462i		−	0.162854i
$716$	13.8281	−	16.3279i	0.516779	−	0.610202i
$717$			18.6976i			0.698274i
$718$	24.7031	+	9.05502i	0.921912	+	0.337930i
$719$	−4.77325			−0.178012			−0.0890061	−	0.996031i	$-0.528369\pi$
$719$	−4.77325			−0.178012			−0.0890061	+	0.996031i	$0.528369\pi$
$720$	−9.23456	+	1.54162i	−0.344152	+	0.0574528i
$721$		0			0
$722$	−5.10801	+	13.9352i	−0.190101	+	0.518616i
$723$		−	3.04938i		−	0.113408i
$724$	−14.0450	+	16.5840i	−0.521977	+	0.616340i
$725$	9.73084			0.361394
$726$	4.98935	−	13.6115i	0.185172	−	0.505170i
$727$	20.9881			0.778405			0.389202	−	0.921152i	$-0.372751\pi$
$727$	20.9881			0.778405			0.389202	+	0.921152i	$0.372751\pi$
$728$		0			0
$729$	2.37261			0.0878744
$730$	−4.27384	+	11.6595i	−0.158182	+	0.431538i
$731$	−17.9448			−0.663712
$732$	−6.46112	+	7.62916i	−0.238810	+	0.281982i
$733$		−	18.9976i		−	0.701693i	−0.936433	−	0.350846i	$-0.885894\pi$
$733$		−	18.9976i		−	0.701693i	0.936433	−	0.350846i	$-0.114106\pi$
$734$	10.7002	−	29.1913i	0.394951	−	1.07747i
$735$		0			0
$736$	1.63292	−	8.68099i	0.0601903	−	0.319986i
$737$	−37.9067			−1.39631
$738$	−32.6079	−	11.9526i	−1.20031	−	0.439980i
$739$		−	17.5775i		−	0.646598i	−0.946297	−	0.323299i	$-0.895208\pi$
$739$		−	17.5775i		−	0.646598i	0.946297	−	0.323299i	$-0.104792\pi$
$740$	2.35420	−	2.77979i	0.0865421	−	0.102187i
$741$			2.12176i			0.0779447i
$742$		0			0
$743$		−	0.624385i		−	0.0229065i	−0.999934	−	0.0114532i	$-0.996354\pi$
$743$		−	0.624385i		−	0.0229065i	0.999934	−	0.0114532i	$-0.00364575\pi$
$744$	8.81658	−	5.01018i	0.323232	−	0.183682i
$745$			1.72300i			0.0631260i
$746$	0.275295	−	0.751037i	0.0100793	−	0.0274974i
$747$	−4.77002			−0.174526
$748$	−43.7045	−	37.0132i	−1.59799	−	1.35334i
$749$		0			0
$750$	−1.07825	−	0.395235i	−0.0393720	−	0.0144319i
$751$		−	33.1412i		−	1.20934i	−0.796476	−	0.604670i	$-0.793305\pi$
$751$		−	33.1412i		−	1.20934i	0.796476	−	0.604670i	$-0.206695\pi$
$752$	−3.43769	−	20.5923i	−0.125360	−	0.750924i
$753$	0.217804			0.00793723
$754$	−11.5762	−	4.24329i	−0.421580	−	0.154532i
$755$	−0.814130			−0.0296292
$756$		0			0
$757$	43.9649			1.59793			0.798966	−	0.601376i	$-0.205380\pi$
$757$	43.9649			1.59793			0.798966	+	0.601376i	$0.205380\pi$
$758$	37.6164	+	13.7884i	1.36629	+	0.500818i
$759$	6.16308			0.223706
$760$	−4.07541	−	7.17164i	−0.147831	−	0.260143i
$761$			7.42765i			0.269252i	0.990896	+	0.134626i	$0.0429833\pi$
$761$			7.42765i			0.269252i	−0.990896	+	0.134626i	$0.957017\pi$
$762$	8.27450	+	3.03305i	0.299754	+	0.109876i
$763$		0			0
$764$	0.655554	−	0.774065i	0.0237171	−	0.0280047i
$765$	−13.7899			−0.498575
$766$	1.50201	−	4.09766i	0.0542700	−	0.148055i
$767$		−	10.1829i		−	0.367685i
$768$	12.2881	−	4.22038i	0.443409	−	0.152290i
$769$			17.2607i			0.622438i	0.950338	+	0.311219i	$0.100737\pi$
$769$			17.2607i			0.622438i	−0.950338	+	0.311219i	$0.899263\pi$
$770$		0			0
$771$		−	25.2426i		−	0.909089i
$772$	31.7750	+	26.9102i	1.14361	+	0.968519i
$773$			35.3653i			1.27200i	0.771689	+	0.636000i	$0.219412\pi$
$773$			35.3653i			1.27200i	−0.771689	+	0.636000i	$0.780588\pi$
$774$	−9.46600	−	3.46980i	−0.340248	−	0.124719i
$775$	−4.41515			−0.158597
$776$	10.9508	+	19.2706i	0.393112	+	0.691773i
$777$		0			0
$778$	7.95963	−	21.7148i	0.285367	−	0.778512i
$779$		−	30.5985i		−	1.09631i
$780$	1.11037	+	0.940373i	0.0397577	+	0.0336708i
$781$	40.7342			1.45758
$782$	4.47773	−	12.2158i	0.160123	−	0.436835i
$783$	−42.2005			−1.50812

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.486718 - 1.32782i) q^{2} -0.812042 q^{3} +(-1.52621 - 1.29255i) q^{4} -1.00000i q^{5} +(-0.395235 + 1.07825i) q^{6} +(-2.45910 + 1.39743i) q^{8} -2.34059 q^{9} +(-1.32782 - 0.486718i) q^{10} -4.86043i q^{11} +(1.23935 + 1.04960i) q^{12} +0.895933i q^{13} +0.812042i q^{15} +(0.658646 + 3.94540i) q^{16} +5.89164i q^{17} +(-1.13921 + 3.10788i) q^{18} -2.91636 q^{19} +(-1.29255 + 1.52621i) q^{20} +(-6.45377 - 2.36566i) q^{22} -1.56151i q^{23} +(1.99689 - 1.13477i) q^{24} -1.00000 q^{25} +(1.18964 + 0.436066i) q^{26} +4.33678 q^{27} -9.73084 q^{29} +(1.07825 + 0.395235i) q^{30} +4.41515 q^{31} +(5.55936 + 1.04573i) q^{32} +3.94687i q^{33} +(7.82304 + 2.86757i) q^{34} +(3.57223 + 3.02532i) q^{36} -1.82136 q^{37} +(-1.41945 + 3.87241i) q^{38} -0.727535i q^{39} +(1.39743 + 2.45910i) q^{40} +10.4920i q^{41} +3.04581i q^{43} +(-6.28233 + 7.41804i) q^{44} +2.34059i q^{45} +(-2.07340 - 0.760014i) q^{46} -5.21932 q^{47} +(-0.534848 - 3.20383i) q^{48} +(-0.486718 + 1.32782i) q^{50} -4.78426i q^{51} +(1.15804 - 1.36738i) q^{52} +0.179724 q^{53} +(2.11079 - 5.75846i) q^{54} -4.86043 q^{55} +2.36821 q^{57} +(-4.73617 + 12.9208i) q^{58} -11.3657 q^{59} +(1.04960 - 1.23935i) q^{60} +6.15579i q^{61} +(2.14893 - 5.86252i) q^{62} +(4.09438 - 6.87285i) q^{64} +0.895933 q^{65} +(5.24073 + 1.92101i) q^{66} -7.79905i q^{67} +(7.61522 - 8.99190i) q^{68} +1.26801i q^{69} +8.38078i q^{71} +(5.75575 - 3.27081i) q^{72} -8.78095i q^{73} +(-0.886490 + 2.41844i) q^{74} +0.812042 q^{75} +(4.45099 + 3.76954i) q^{76} +(-0.966036 - 0.354104i) q^{78} +3.63368i q^{79} +(3.94540 - 0.658646i) q^{80} +3.50012 q^{81} +(13.9315 + 5.10665i) q^{82} +2.03796 q^{83} +5.89164 q^{85} +(4.04428 + 1.48245i) q^{86} +7.90185 q^{87} +(6.79211 + 11.9523i) q^{88} -1.76452i q^{89} +(3.10788 + 1.13921i) q^{90} +(-2.01832 + 2.38320i) q^{92} -3.58528 q^{93} +(-2.54034 + 6.93032i) q^{94} +2.91636i q^{95} +(-4.51443 - 0.849178i) q^{96} -7.83641i q^{97} +11.3763i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60}+ \cdots + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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