LMFDB - Embedded newform 3276.2.cf.b.1765.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3276,2,Mod(1765,3276)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3276.1765"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3276, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3276.cf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.1589917022$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 37 x^{10} - 130 x^{9} + 414 x^{8} - 942 x^{7} + 1855 x^{6} - 2748 x^{5} + 3355 x^{4} + \cdots + 229 $ x^12 - 6x^11 + 37x^10 - 130x^9 + 414x^8 - 942x^7 + 1855x^6 - 2748x^5 + 3355x^4 - 3002x^3 + 2040x^2 - 874*x + 229
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1092)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1765.5
Root			$0.500000 - 0.610858i$ of defining polynomial
Character	$\chi$	$=$	3276.1765
Dual form			3276.2.cf.b.2773.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.47688i q^{5} +(0.866025 + 0.500000i) q^{7} +(4.71635 - 2.72299i) q^{11} +(0.0198889 + 3.60550i) q^{13} +(3.43453 - 5.94878i) q^{17} +(-5.79187 - 3.34394i) q^{19} +(-3.76241 - 6.51668i) q^{23} -1.13495 q^{25} +(-2.28310 - 3.95444i) q^{29} -7.78715i q^{31} +(-1.23844 + 2.14504i) q^{35} +(8.54751 - 4.93491i) q^{37} +(10.5809 - 6.10890i) q^{41} +(-0.781824 + 1.35416i) q^{43} +0.470035i q^{47} +(0.500000 + 0.866025i) q^{49} -1.91885 q^{53} +(6.74453 + 11.6819i) q^{55} +(-1.88476 - 1.08816i) q^{59} +(-1.56200 + 2.70546i) q^{61} +(-8.93040 + 0.0492624i) q^{65} +(-7.75111 + 4.47511i) q^{67} +(-2.01120 - 1.16117i) q^{71} +3.69299i q^{73} +5.44598 q^{77} -15.4633 q^{79} +6.27682i q^{83} +(14.7344 + 8.50693i) q^{85} +(4.53203 - 2.61657i) q^{89} +(-1.78552 + 3.13240i) q^{91} +(8.28255 - 14.3458i) q^{95} +(4.04658 + 2.33629i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{11} - 10 q^{13} + 4 q^{17} - 6 q^{23} + 4 q^{25} + 2 q^{29} - 6 q^{35} - 12 q^{37} + 36 q^{41} - 2 q^{43} + 6 q^{49} - 24 q^{53} + 6 q^{55} - 4 q^{61} + 14 q^{65} + 6 q^{67} + 18 q^{71} - 8 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) $ 12 * q + 12 * q^11 - 10 * q^13 + 4 * q^17 - 6 * q^23 + 4 * q^25 + 2 * q^29 - 6 * q^35 - 12 * q^37 + 36 * q^41 - 2 * q^43 + 6 * q^49 - 24 * q^53 + 6 * q^55 - 4 * q^61 + 14 * q^65 + 6 * q^67 + 18 * q^71 - 8 * q^77 - 36 * q^79 + 54 * q^85 + 30 * q^89 - 4 * q^95 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3276\mathbb{Z}\right)^\times$.

$n$	$1639$	$2017$	$2341$	$2549$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$			2.47688i			1.10770i	0.832618	+	0.553848i	$0.186841\pi$
$5$			2.47688i			1.10770i	−0.832618	+	0.553848i	$0.813159\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.71635	−	2.72299i	1.42203	−	0.821012i	0.425562	−	0.904929i	$-0.360077\pi$
$11$	4.71635	−	2.72299i	1.42203	−	0.821012i	0.996473	+	0.0839174i	$0.0267432\pi$
$12$		0			0
$13$	0.0198889	+	3.60550i	0.00551618	+	0.999985i
$13$	0.0198889	+	3.60550i	0.00551618	+	0.999985i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.43453	−	5.94878i	0.832996	−	1.44279i	−0.0626554	−	0.998035i	$-0.519957\pi$
$17$	3.43453	−	5.94878i	0.832996	−	1.44279i	0.895652	−	0.444756i	$-0.146710\pi$
$18$		0			0
$19$	−5.79187	−	3.34394i	−1.32875	−	0.767152i	−0.343641	−	0.939101i	$-0.611660\pi$
$19$	−5.79187	−	3.34394i	−1.32875	−	0.767152i	−0.985106	+	0.171949i	$0.944994\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.76241	−	6.51668i	−0.784516	−	1.35882i	−0.929288	−	0.369357i	$-0.879578\pi$
$23$	−3.76241	−	6.51668i	−0.784516	−	1.35882i	0.144771	−	0.989465i	$-0.453755\pi$
$24$		0			0
$25$	−1.13495			−0.226991
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.28310	−	3.95444i	−0.423960	−	0.734321i	0.572362	−	0.820001i	$-0.306027\pi$
$29$	−2.28310	−	3.95444i	−0.423960	−	0.734321i	−0.996323	+	0.0856801i	$0.972694\pi$
$30$		0			0
$31$		−	7.78715i		−	1.39861i	−0.714821	−	0.699307i	$-0.753492\pi$
$31$		−	7.78715i		−	1.39861i	0.714821	−	0.699307i	$-0.246508\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.23844	+	2.14504i	−0.209335	+	0.362579i
$36$		0			0
$37$	8.54751	−	4.93491i	1.40520	−	0.811294i	0.410282	−	0.911959i	$-0.365430\pi$
$37$	8.54751	−	4.93491i	1.40520	−	0.811294i	0.994920	+	0.100665i	$0.0320970\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	10.5809	−	6.10890i	1.65246	−	0.954050i	0.676409	−	0.736527i	$-0.263535\pi$
$41$	10.5809	−	6.10890i	1.65246	−	0.954050i	0.976055	−	0.217524i	$-0.0697980\pi$
$42$		0			0
$43$	−0.781824	+	1.35416i	−0.119227	+	0.206507i	−0.919462	−	0.393180i	$-0.871375\pi$
$43$	−0.781824	+	1.35416i	−0.119227	+	0.206507i	0.800235	+	0.599687i	$0.204708\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			0.470035i			0.0685616i	0.999412	+	0.0342808i	$0.0109141\pi$
$47$			0.470035i			0.0685616i	−0.999412	+	0.0342808i	$0.989086\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.91885			−0.263574			−0.131787	−	0.991278i	$-0.542071\pi$
$53$	−1.91885			−0.263574			−0.131787	+	0.991278i	$0.542071\pi$
$54$		0			0
$55$	6.74453	+	11.6819i	0.909432	+	1.57518i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.88476	−	1.08816i	−0.245374	−	0.141667i	0.372270	−	0.928124i	$-0.378580\pi$
$59$	−1.88476	−	1.08816i	−0.245374	−	0.141667i	−0.617644	+	0.786458i	$0.711913\pi$
$60$		0			0
$61$	−1.56200	+	2.70546i	−0.199994	+	0.346399i	−0.948526	−	0.316699i	$-0.897425\pi$
$61$	−1.56200	+	2.70546i	−0.199994	+	0.346399i	0.748532	+	0.663098i	$0.230759\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.93040	+	0.0492624i	−1.10768	+	0.00611025i
$66$		0			0
$67$	−7.75111	+	4.47511i	−0.946949	+	0.546721i	−0.892132	−	0.451775i	$-0.850791\pi$
$67$	−7.75111	+	4.47511i	−0.946949	+	0.546721i	−0.0548174	+	0.998496i	$0.517458\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.01120	−	1.16117i	−0.238686	−	0.137805i	0.375887	−	0.926666i	$-0.377338\pi$
$71$	−2.01120	−	1.16117i	−0.238686	−	0.137805i	−0.614573	+	0.788860i	$0.710671\pi$
$72$		0			0
$73$			3.69299i			0.432232i	0.976368	+	0.216116i	$0.0693389\pi$
$73$			3.69299i			0.432232i	−0.976368	+	0.216116i	$0.930661\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.44598			0.620627
$78$		0			0
$79$	−15.4633			−1.73975			−0.869876	−	0.493270i	$-0.835802\pi$
$79$	−15.4633			−1.73975			−0.869876	+	0.493270i	$0.835802\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			6.27682i			0.688971i	0.938792	+	0.344485i	$0.111947\pi$
$83$			6.27682i			0.688971i	−0.938792	+	0.344485i	$0.888053\pi$
$84$		0			0
$85$	14.7344	+	8.50693i	1.59817	+	0.922707i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.53203	−	2.61657i	0.480394	−	0.277355i	−0.240187	−	0.970727i	$-0.577209\pi$
$89$	4.53203	−	2.61657i	0.480394	−	0.277355i	0.720581	+	0.693371i	$0.243875\pi$
$90$		0			0
$91$	−1.78552	+	3.13240i	−0.187174	+	0.328364i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.28255	−	14.3458i	0.849771	−	1.47185i
$96$		0			0
$97$	4.04658	+	2.33629i	0.410868	+	0.237215i	0.691163	−	0.722699i	$-0.257099\pi$
$97$	4.04658	+	2.33629i	0.410868	+	0.237215i	−0.280295	+	0.959914i	$0.590432\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.00804	+	1.74598i	0.100304	+	0.173731i	0.911810	−	0.410613i	$-0.134685\pi$
$101$	1.00804	+	1.74598i	0.100304	+	0.173731i	−0.811506	+	0.584344i	$0.801352\pi$
$102$		0			0
$103$	−0.222790			−0.0219521			−0.0109761	−	0.999940i	$-0.503494\pi$
$103$	−0.222790			−0.0219521			−0.0109761	+	0.999940i	$0.503494\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.43406	+	2.48386i	0.138636	+	0.240124i	0.926980	−	0.375110i	$-0.122395\pi$
$107$	1.43406	+	2.48386i	0.138636	+	0.240124i	−0.788345	+	0.615234i	$0.789062\pi$
$108$		0			0
$109$			0.961436i			0.0920888i	0.998939	+	0.0460444i	$0.0146616\pi$
$109$			0.961436i			0.0920888i	−0.998939	+	0.0460444i	$0.985338\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.73164	−	11.6595i	0.633259	−	1.09684i	−0.353622	−	0.935388i	$-0.615050\pi$
$113$	6.73164	−	11.6595i	0.633259	−	1.09684i	0.986881	−	0.161448i	$-0.0516165\pi$
$114$		0			0
$115$	16.1411	−	9.31905i	1.50516	−	0.869006i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.94878	−	3.43453i	0.545324	−	0.314843i
$120$		0			0
$121$	9.32933	−	16.1589i	0.848121	−	1.46899i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			9.57327i			0.856259i
$126$		0			0
$127$	6.72739	+	11.6522i	0.596959	+	1.03396i	0.993267	+	0.115846i	$0.0369580\pi$
$127$	6.72739	+	11.6522i	0.596959	+	1.03396i	−0.396308	+	0.918118i	$0.629709\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.4240			1.52234			0.761170	−	0.648552i	$-0.224625\pi$
$131$	17.4240			1.52234			0.761170	+	0.648552i	$0.224625\pi$
$132$		0			0
$133$	−3.34394	−	5.79187i	−0.289956	−	0.502219i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.16836	−	4.13865i	−0.612434	−	0.353589i	0.161483	−	0.986875i	$-0.448372\pi$
$137$	−7.16836	−	4.13865i	−0.612434	−	0.353589i	−0.773918	+	0.633286i	$0.781706\pi$
$138$		0			0
$139$	−1.04017	+	1.80163i	−0.0882263	+	0.152812i	−0.906761	−	0.421644i	$-0.861453\pi$
$139$	−1.04017	+	1.80163i	−0.0882263	+	0.152812i	0.818535	+	0.574456i	$0.194787\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.91153	+	16.9506i	0.828844	+	1.41748i
$144$		0			0
$145$	9.79468	−	5.65496i	0.813404	−	0.469619i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.16915	−	5.29381i	−0.751166	−	0.433686i	0.0749493	−	0.997187i	$-0.476121\pi$
$149$	−9.16915	−	5.29381i	−0.751166	−	0.433686i	−0.826115	+	0.563502i	$0.809454\pi$
$150$		0			0
$151$			3.53003i			0.287270i	0.989631	+	0.143635i	$0.0458791\pi$
$151$			3.53003i			0.287270i	−0.989631	+	0.143635i	$0.954121\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	19.2879			1.54924
$156$		0			0
$157$	9.62352			0.768040			0.384020	−	0.923325i	$-0.374539\pi$
$157$	9.62352			0.768040			0.384020	+	0.923325i	$0.374539\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	7.52482i		−	0.593039i
$162$		0			0
$163$	−17.0628	−	9.85120i	−1.33646	−	0.771605i	−0.350179	−	0.936683i	$-0.613879\pi$
$163$	−17.0628	−	9.85120i	−1.33646	−	0.771605i	−0.986281	+	0.165077i	$0.947213\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.5575	−	7.25009i	0.971731	−	0.561029i	0.0719673	−	0.997407i	$-0.477072\pi$
$167$	12.5575	−	7.25009i	0.971731	−	0.561029i	0.899763	+	0.436378i	$0.143739\pi$
$168$		0			0
$169$	−12.9992	+	0.143418i	−0.999939	+	0.0110322i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.11160	+	14.0497i	−0.616714	+	1.06818i	0.373368	+	0.927683i	$0.378203\pi$
$173$	−8.11160	+	14.0497i	−0.616714	+	1.06818i	−0.990081	+	0.140496i	$0.955130\pi$
$174$		0			0
$175$	−0.982898	−	0.567476i	−0.0743001	−	0.0428972i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.29636	−	3.97742i	−0.171638	−	0.297286i	0.767354	−	0.641223i	$-0.221573\pi$
$179$	−2.29636	−	3.97742i	−0.171638	−	0.297286i	−0.938993	+	0.343937i	$0.888239\pi$
$180$		0			0
$181$	9.14445			0.679702			0.339851	−	0.940479i	$-0.389623\pi$
$181$	9.14445			0.679702			0.339851	+	0.940479i	$0.389623\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.2232	+	21.1712i	0.898667	+	1.55654i
$186$		0			0
$187$		−	37.4088i		−	2.73560i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.462606	+	0.801258i	−0.0334730	+	0.0579770i	−0.882277	−	0.470731i	$-0.843990\pi$
$191$	−0.462606	+	0.801258i	−0.0334730	+	0.0579770i	0.848804	+	0.528708i	$0.177323\pi$
$192$		0			0
$193$	11.2841	−	6.51490i	0.812250	−	0.468953i	−0.0354863	−	0.999370i	$-0.511298\pi$
$193$	11.2841	−	6.51490i	0.812250	−	0.468953i	0.847737	+	0.530417i	$0.177965\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.02212	−	2.32217i	0.286564	−	0.165448i	−0.349827	−	0.936814i	$-0.613760\pi$
$197$	4.02212	−	2.32217i	0.286564	−	0.165448i	0.636391	+	0.771366i	$0.280426\pi$
$198$		0			0
$199$	1.17377	−	2.03303i	0.0832065	−	0.144118i	−0.821419	−	0.570325i	$-0.806817\pi$
$199$	1.17377	−	2.03303i	0.0832065	−	0.144118i	0.904626	+	0.426207i	$0.140151\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	4.56619i		−	0.320484i
$204$		0			0
$205$	15.1310	+	26.2077i	1.05680	+	1.83043i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−36.4220			−2.51936
$210$		0			0
$211$	−0.701975	−	1.21586i	−0.0483259	−	0.0837030i	0.840851	−	0.541267i	$-0.182055\pi$
$211$	−0.701975	−	1.21586i	−0.0483259	−	0.0837030i	−0.889177	+	0.457564i	$0.848722\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.35409	−	1.93649i	−0.228747	−	0.132067i
$216$		0			0
$217$	3.89358	−	6.74387i	0.264313	−	0.457804i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	21.5166	+	12.2649i	1.44736	+	0.825025i
$222$		0			0
$223$	−21.2092	+	12.2451i	−1.42027	+	0.819996i	−0.996322	−	0.0856890i	$-0.972691\pi$
$223$	−21.2092	+	12.2451i	−1.42027	+	0.819996i	−0.423952	+	0.905685i	$0.639358\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.91834	−	5.14901i	−0.591931	−	0.341752i	0.173930	−	0.984758i	$-0.444353\pi$
$227$	−8.91834	−	5.14901i	−0.591931	−	0.341752i	−0.765861	+	0.643006i	$0.777687\pi$
$228$		0			0
$229$			17.9669i			1.18729i	0.804728	+	0.593643i	$0.202311\pi$
$229$			17.9669i			1.18729i	−0.804728	+	0.593643i	$0.797689\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	21.6058			1.41545			0.707723	−	0.706490i	$-0.249723\pi$
$233$	21.6058			1.41545			0.707723	+	0.706490i	$0.249723\pi$
$234$		0			0
$235$	−1.16422			−0.0759454
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	10.4485i		−	0.675859i	−0.941171	−	0.337929i	$-0.890274\pi$
$239$		−	10.4485i		−	0.675859i	0.941171	−	0.337929i	$-0.109726\pi$
$240$		0			0
$241$	18.1574	+	10.4832i	1.16962	+	0.675281i	0.953591	−	0.301105i	$-0.0973555\pi$
$241$	18.1574	+	10.4832i	1.16962	+	0.675281i	0.216031	+	0.976387i	$0.430689\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.14504	+	1.23844i	−0.137042	+	0.0791211i
$246$		0			0
$247$	11.9414	−	20.9491i	0.759811	−	1.33296i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.38623	+	9.32922i	−0.339976	+	0.588855i	−0.984428	−	0.175790i	$-0.943752\pi$
$251$	−5.38623	+	9.32922i	−0.339976	+	0.588855i	0.644452	+	0.764645i	$0.277086\pi$
$252$		0			0
$253$	−35.4897	−	20.4900i	−2.23122	−	1.28819i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.42369	+	4.19795i	0.151185	+	0.261861i	0.931664	−	0.363322i	$-0.118358\pi$
$257$	2.42369	+	4.19795i	0.151185	+	0.261861i	−0.780478	+	0.625183i	$0.785024\pi$
$258$		0			0
$259$	9.86982			0.613280
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.59477	+	7.95837i	0.283326	+	0.490734i	0.972202	−	0.234145i	$-0.0752290\pi$
$263$	4.59477	+	7.95837i	0.283326	+	0.490734i	−0.688876	+	0.724879i	$0.741896\pi$
$264$		0			0
$265$		−	4.75276i		−	0.291960i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.7323	+	22.0530i	−0.776302	+	1.34459i	0.157758	+	0.987478i	$0.449573\pi$
$269$	−12.7323	+	22.0530i	−0.776302	+	1.34459i	−0.934060	+	0.357117i	$0.883760\pi$
$270$		0			0
$271$	20.3211	−	11.7324i	1.23442	−	0.712690i	0.266469	−	0.963844i	$-0.414143\pi$
$271$	20.3211	−	11.7324i	1.23442	−	0.712690i	0.967947	+	0.251153i	$0.0808098\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.35284	+	3.09046i	−0.322788	+	0.186362i
$276$		0			0
$277$	−14.5556	+	25.2111i	−0.874563	+	1.51479i	−0.0173360	+	0.999850i	$0.505519\pi$
$277$	−14.5556	+	25.2111i	−0.874563	+	1.51479i	−0.857227	+	0.514938i	$0.827815\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	24.0881i		−	1.43697i	−0.695540	−	0.718487i	$-0.744835\pi$
$281$		−	24.0881i		−	1.43697i	0.695540	−	0.718487i	$-0.255165\pi$
$282$		0			0
$283$	−10.9024	−	18.8835i	−0.648082	−	1.12251i	−0.983581	−	0.180470i	$-0.942238\pi$
$283$	−10.9024	−	18.8835i	−0.648082	−	1.12251i	0.335499	−	0.942041i	$-0.391095\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.2178			0.721194
$288$		0			0
$289$	−15.0920	−	26.1401i	−0.887765	−	1.53765i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	27.3743	+	15.8045i	1.59922	+	0.923311i	0.991637	+	0.129057i	$0.0411949\pi$
$293$	27.3743	+	15.8045i	1.59922	+	0.923311i	0.607585	+	0.794255i	$0.292138\pi$
$294$		0			0
$295$	2.69526	−	4.66832i	0.156924	−	0.271800i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	23.4210	−	13.6950i	1.35447	−	0.792000i
$300$		0			0
$301$	−1.35416	+	0.781824i	−0.0780524	+	0.0450636i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.70112	−	3.86889i	−0.383705	−	0.221532i
$306$		0			0
$307$		−	6.58096i		−	0.375595i	−0.982208	−	0.187798i	$-0.939865\pi$
$307$		−	6.58096i		−	0.375595i	0.982208	−	0.187798i	$-0.0601349\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.82186			−0.330127			−0.165064	−	0.986283i	$-0.552783\pi$
$311$	−5.82186			−0.330127			−0.165064	+	0.986283i	$0.552783\pi$
$312$		0			0
$313$	17.7789			1.00492			0.502461	−	0.864600i	$-0.332428\pi$
$313$	17.7789			1.00492			0.502461	+	0.864600i	$0.332428\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			22.1182i			1.24228i	0.783698	+	0.621142i	$0.213331\pi$
$317$			22.1182i			1.24228i	−0.783698	+	0.621142i	$0.786669\pi$
$318$		0			0
$319$	−21.5358	−	12.4337i	−1.20577	−	0.696153i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−39.7847	+	22.9697i	−2.21368	+	1.27807i
$324$		0			0
$325$	−0.0225729	−	4.09207i	−0.00125212	−	0.226987i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.235017	+	0.407062i	−0.0129569	+	0.0224421i
$330$		0			0
$331$	−7.55702	−	4.36305i	−0.415371	−	0.239815i	0.277724	−	0.960661i	$-0.410420\pi$
$331$	−7.55702	−	4.36305i	−0.415371	−	0.239815i	−0.693095	+	0.720846i	$0.743753\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.0843	−	19.1986i	−0.605601	−	1.04893i
$336$		0			0
$337$	−19.6305			−1.06934			−0.534670	−	0.845061i	$-0.679564\pi$
$337$	−19.6305			−1.06934			−0.534670	+	0.845061i	$0.679564\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−21.2043	−	36.7270i	−1.14828	−	1.98888i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.44485	−	7.69871i	0.238612	−	0.413288i	−0.721704	−	0.692202i	$-0.756641\pi$
$347$	4.44485	−	7.69871i	0.238612	−	0.413288i	0.960316	+	0.278913i	$0.0899742\pi$
$348$		0			0
$349$	−10.9700	+	6.33353i	−0.587210	+	0.339026i	−0.763994	−	0.645224i	$-0.776764\pi$
$349$	−10.9700	+	6.33353i	−0.587210	+	0.339026i	0.176783	+	0.984250i	$0.443431\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.50611	−	2.02425i	0.186611	−	0.107740i	−0.403784	−	0.914854i	$-0.632305\pi$
$353$	3.50611	−	2.02425i	0.186611	−	0.107740i	0.590395	+	0.807114i	$0.298972\pi$
$354$		0			0
$355$	2.87608	−	4.98151i	0.152646	−	0.264391i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			15.1406i			0.799090i	0.916714	+	0.399545i	$0.130832\pi$
$359$			15.1406i			0.799090i	−0.916714	+	0.399545i	$0.869168\pi$
$360$		0			0
$361$	12.8638	+	22.2808i	0.677045	+	1.17268i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.14711			−0.478782
$366$		0			0
$367$	15.0219	+	26.0188i	0.784139	+	1.35817i	0.929512	+	0.368792i	$0.120229\pi$
$367$	15.0219	+	26.0188i	0.784139	+	1.35817i	−0.145373	+	0.989377i	$0.546438\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.66177	−	0.959423i	−0.0862748	−	0.0498108i
$372$		0			0
$373$	12.7449	−	22.0749i	0.659908	−	1.14299i	−0.320731	−	0.947170i	$-0.603928\pi$
$373$	12.7449	−	22.0749i	0.659908	−	1.14299i	0.980639	−	0.195824i	$-0.0627383\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.2123	−	8.31034i	0.731971	−	0.428004i
$378$		0			0
$379$	24.7386	−	14.2828i	1.27074	−	0.733660i	0.295609	−	0.955309i	$-0.404477\pi$
$379$	24.7386	−	14.2828i	1.27074	−	0.733660i	0.975126	+	0.221649i	$0.0711440\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.6200	+	6.70881i	0.593754	+	0.342804i	0.766581	−	0.642148i	$-0.221957\pi$
$383$	11.6200	+	6.70881i	0.593754	+	0.342804i	−0.172826	+	0.984952i	$0.555290\pi$
$384$		0			0
$385$			13.4891i			0.687466i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.7559			0.798856			0.399428	−	0.916764i	$-0.369209\pi$
$389$	15.7559			0.798856			0.399428	+	0.916764i	$0.369209\pi$
$390$		0			0
$391$	−51.6884			−2.61400
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	38.3007i		−	1.92712i
$396$		0			0
$397$	−25.8457	−	14.9220i	−1.29716	−	0.748915i	−0.317247	−	0.948343i	$-0.602758\pi$
$397$	−25.8457	−	14.9220i	−1.29716	−	0.748915i	−0.979913	+	0.199428i	$0.936092\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−25.9054	+	14.9565i	−1.29365	+	0.746892i	−0.979300	−	0.202414i	$-0.935121\pi$
$401$	−25.9054	+	14.9565i	−1.29365	+	0.746892i	−0.314354	+	0.949306i	$0.601788\pi$
$402$		0			0
$403$	28.0766	−	0.154878i	1.39859	−	0.00771500i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	26.8754	−	46.5496i	1.33216	−	2.30738i
$408$		0			0
$409$	8.74842	+	5.05090i	0.432582	+	0.249751i	0.700446	−	0.713706i	$-0.252985\pi$
$409$	8.74842	+	5.05090i	0.432582	+	0.249751i	−0.267864	+	0.963457i	$0.586318\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.08816	−	1.88476i	−0.0535451	−	0.0927428i
$414$		0			0
$415$	−15.5470			−0.763170
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.8960	−	22.3364i	−0.630008	−	1.09121i	−0.987549	−	0.157309i	$-0.949718\pi$
$419$	−12.8960	−	22.3364i	−0.630008	−	1.09121i	0.357541	−	0.933897i	$-0.383615\pi$
$420$		0			0
$421$			5.04452i			0.245855i	0.992416	+	0.122927i	$0.0392282\pi$
$421$			5.04452i			0.245855i	−0.992416	+	0.122927i	$0.960772\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.89803	+	6.75159i	−0.189082	+	0.327500i
$426$		0			0
$427$	−2.70546	+	1.56200i	−0.130927	+	0.0755905i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.44919	+	2.56874i	−0.214310	+	0.123732i	−0.603313	−	0.797505i	$-0.706153\pi$
$431$	−4.44919	+	2.56874i	−0.214310	+	0.123732i	0.389003	+	0.921237i	$0.372820\pi$
$432$		0			0
$433$	−11.8619	+	20.5455i	−0.570049	+	0.987353i	0.426512	+	0.904482i	$0.359742\pi$
$433$	−11.8619	+	20.5455i	−0.570049	+	0.987353i	−0.996560	+	0.0828710i	$0.973591\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			50.3250i			2.40737i
$438$		0			0
$439$	12.6408	+	21.8944i	0.603311	+	1.04496i	0.992316	+	0.123729i	$0.0394854\pi$
$439$	12.6408	+	21.8944i	0.603311	+	1.04496i	−0.389005	+	0.921235i	$0.627181\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−29.0623			−1.38079			−0.690395	−	0.723432i	$-0.742563\pi$
$443$	−29.0623			−1.38079			−0.690395	+	0.723432i	$0.742563\pi$
$444$		0			0
$445$	6.48093	+	11.2253i	0.307226	+	0.532130i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−13.2312	−	7.63904i	−0.624419	−	0.360508i	0.154169	−	0.988045i	$-0.450730\pi$
$449$	−13.2312	−	7.63904i	−0.624419	−	0.360508i	−0.778587	+	0.627536i	$0.784063\pi$
$450$		0			0
$451$	33.2689	−	57.6235i	1.56657	−	2.71338i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.75858	−	4.42254i	−0.363728	−	0.207332i
$456$		0			0
$457$	1.03285	−	0.596315i	0.0483146	−	0.0278944i	−0.475648	−	0.879636i	$-0.657786\pi$
$457$	1.03285	−	0.596315i	0.0483146	−	0.0278944i	0.523963	+	0.851741i	$0.324453\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.2910	−	5.94150i	−0.479299	−	0.276723i	0.240825	−	0.970568i	$-0.422582\pi$
$461$	−10.2910	−	5.94150i	−0.479299	−	0.276723i	−0.720124	+	0.693845i	$0.755915\pi$
$462$		0			0
$463$		−	14.5531i		−	0.676338i	−0.941085	−	0.338169i	$-0.890192\pi$
$463$		−	14.5531i		−	0.676338i	0.941085	−	0.338169i	$-0.109808\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	23.8134			1.10195			0.550977	−	0.834520i	$-0.314255\pi$
$467$	23.8134			1.10195			0.550977	+	0.834520i	$0.314255\pi$
$468$		0			0
$469$	−8.95022			−0.413283
$470$		0			0
$471$		0			0
$472$		0			0
$473$			8.51559i			0.391547i
$474$		0			0
$475$	6.57350	+	3.79521i	0.301613	+	0.174136i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.1919	+	8.19368i	−0.648443	+	0.374379i	−0.787859	−	0.615855i	$-0.788811\pi$
$479$	−14.1919	+	8.19368i	−0.648443	+	0.374379i	0.139416	+	0.990234i	$0.455477\pi$
$480$		0			0
$481$	17.9628	+	30.7199i	0.819033	+	1.40071i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.78673	+	10.0229i	−0.262762	+	0.455117i
$486$		0			0
$487$	31.4746	+	18.1719i	1.42625	+	0.823446i	0.996823	−	0.0796545i	$-0.0253817\pi$
$487$	31.4746	+	18.1719i	1.42625	+	0.823446i	0.429428	+	0.903101i	$0.358715\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.8222	+	22.2086i	0.578656	+	1.00226i	0.995634	+	0.0933451i	$0.0297560\pi$
$491$	12.8222	+	22.2086i	0.578656	+	1.00226i	−0.416978	+	0.908917i	$0.636911\pi$
$492$		0			0
$493$	−31.3655			−1.41263
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.16117	−	2.01120i	−0.0520855	−	0.0902147i
$498$		0			0
$499$			35.3041i			1.58043i	0.612830	+	0.790215i	$0.290031\pi$
$499$			35.3041i			1.58043i	−0.612830	+	0.790215i	$0.709969\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.49443	+	16.4448i	−0.423336	+	0.733239i	−0.996263	−	0.0863668i	$-0.972474\pi$
$503$	−9.49443	+	16.4448i	−0.423336	+	0.733239i	0.572928	+	0.819606i	$0.305808\pi$
$504$		0			0
$505$	−4.32458	+	2.49680i	−0.192441	+	0.111106i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.24530	−	1.29633i	0.0995212	−	0.0574586i	−0.449413	−	0.893324i	$-0.648367\pi$
$509$	2.24530	−	1.29633i	0.0995212	−	0.0574586i	0.548935	+	0.835865i	$0.315034\pi$
$510$		0			0
$511$	−1.84650	+	3.19822i	−0.0816841	+	0.141481i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	0.551825i		−	0.0243163i
$516$		0			0
$517$	1.27990	+	2.21685i	0.0562899	+	0.0974970i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.45529			−0.414244			−0.207122	−	0.978315i	$-0.566410\pi$
$521$	−9.45529			−0.414244			−0.207122	+	0.978315i	$0.566410\pi$
$522$		0			0
$523$	1.22463	+	2.12113i	0.0535494	+	0.0927503i	0.891558	−	0.452907i	$-0.149613\pi$
$523$	1.22463	+	2.12113i	0.0535494	+	0.0927503i	−0.838008	+	0.545658i	$0.816280\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−46.3241	−	26.7452i	−2.01791	−	1.16504i
$528$		0			0
$529$	−16.8114	+	29.1182i	−0.730931	+	1.26601i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	22.2361	+	38.0280i	0.963151	+	1.64718i
$534$		0			0
$535$	−6.15224	+	3.55200i	−0.265984	+	0.153566i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.71635	+	2.72299i	0.203148	+	0.117287i
$540$		0			0
$541$			27.4190i			1.17883i	0.807829	+	0.589417i	$0.200642\pi$
$541$			27.4190i			1.17883i	−0.807829	+	0.589417i	$0.799358\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.38136			−0.102006
$546$		0			0
$547$	−1.78529			−0.0763334			−0.0381667	−	0.999271i	$-0.512152\pi$
$547$	−1.78529			−0.0763334			−0.0381667	+	0.999271i	$0.512152\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			30.5381i			1.30097i
$552$		0			0
$553$	−13.3916	−	7.73163i	−0.569468	−	0.328782i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.9009	−	12.6445i	0.927972	−	0.535765i	0.0418021	−	0.999126i	$-0.486690\pi$
$557$	21.9009	−	12.6445i	0.927972	−	0.535765i	0.886169	+	0.463361i	$0.153357\pi$
$558$		0			0
$559$	−4.89796	−	2.79193i	−0.207162	−	0.118086i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.54261	−	9.60009i	0.233593	−	0.404596i	−0.725270	−	0.688465i	$-0.758285\pi$
$563$	5.54261	−	9.60009i	0.233593	−	0.404596i	0.958863	+	0.283869i	$0.0916182\pi$
$564$		0			0
$565$	28.8793	+	16.6735i	1.21496	+	0.701458i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.85755	−	17.0738i	−0.413250	−	0.715770i	0.581993	−	0.813194i	$-0.302273\pi$
$569$	−9.85755	−	17.0738i	−0.413250	−	0.715770i	−0.995243	+	0.0974240i	$0.968940\pi$
$570$		0			0
$571$	−4.76181			−0.199276			−0.0996378	−	0.995024i	$-0.531768\pi$
$571$	−4.76181			−0.199276			−0.0996378	+	0.995024i	$0.531768\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.27016	+	7.39613i	0.178078	+	0.308440i
$576$		0			0
$577$		−	33.0438i		−	1.37563i	−0.725885	−	0.687816i	$-0.758570\pi$
$577$		−	33.0438i		−	1.37563i	0.725885	−	0.687816i	$-0.241430\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.13841	+	5.43589i	−0.130203	+	0.225519i
$582$		0			0
$583$	−9.04996	+	5.22500i	−0.374811	+	0.216397i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.0331	+	9.25671i	−0.661756	+	0.382065i	−0.792946	−	0.609292i	$-0.791454\pi$
$587$	−16.0331	+	9.25671i	−0.661756	+	0.382065i	0.131190	+	0.991357i	$0.458120\pi$
$588$		0			0
$589$	−26.0398	+	45.1022i	−1.07295	+	1.85840i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1.25752i			0.0516401i	0.999667	+	0.0258201i	$0.00821969\pi$
$593$			1.25752i			0.0516401i	−0.999667	+	0.0258201i	$0.991780\pi$
$594$		0			0
$595$	8.50693	+	14.7344i	0.348750	+	0.604053i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	44.3582			1.81243			0.906213	−	0.422821i	$-0.138960\pi$
$599$	44.3582			1.81243			0.906213	+	0.422821i	$0.138960\pi$
$600$		0			0
$601$	−4.34601	−	7.52751i	−0.177277	−	0.307054i	0.763670	−	0.645607i	$-0.223396\pi$
$601$	−4.34601	−	7.52751i	−0.177277	−	0.307054i	−0.940947	+	0.338554i	$0.890062\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	40.0237	+	23.1077i	1.62719	+	0.939461i
$606$		0			0
$607$	−7.35085	+	12.7321i	−0.298362	+	0.516778i	−0.975761	−	0.218837i	$-0.929774\pi$
$607$	−7.35085	+	12.7321i	−0.298362	+	0.516778i	0.677399	+	0.735615i	$0.263107\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.69471	+	0.00934846i	−0.0685606	+	0.000378198i
$612$		0			0
$613$	27.4352	−	15.8397i	1.10810	−	0.639761i	0.169762	−	0.985485i	$-0.445700\pi$
$613$	27.4352	−	15.8397i	1.10810	−	0.639761i	0.938336	+	0.345724i	$0.112367\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.3842	−	10.0368i	−0.699863	−	0.404066i	0.107434	−	0.994212i	$-0.465737\pi$
$617$	−17.3842	−	10.0368i	−0.699863	−	0.404066i	−0.807296	+	0.590146i	$0.799070\pi$
$618$		0			0
$619$		−	1.42652i		−	0.0573368i	−0.999589	−	0.0286684i	$-0.990873\pi$
$619$		−	1.42652i		−	0.0573368i	0.999589	−	0.0286684i	$-0.00912668\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5.23313			0.209661
$624$		0			0
$625$	−29.3866			−1.17547
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	67.7964i		−	2.70322i
$630$		0			0
$631$	−22.9922	−	13.2746i	−0.915305	−	0.528452i	−0.0331708	−	0.999450i	$-0.510561\pi$
$631$	−22.9922	−	13.2746i	−0.915305	−	0.528452i	−0.882134	+	0.470998i	$0.843894\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−28.8611	+	16.6630i	−1.14532	+	0.661250i
$636$		0			0
$637$	−3.11251	+	1.81997i	−0.123322	+	0.0721099i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.87679	+	4.98275i	−0.113627	+	0.196807i	−0.917230	−	0.398358i	$-0.869580\pi$
$641$	−2.87679	+	4.98275i	−0.113627	+	0.196807i	0.803603	+	0.595165i	$0.202913\pi$
$642$		0			0
$643$	41.6405	+	24.0412i	1.64214	+	0.948091i	0.980070	+	0.198651i	$0.0636560\pi$
$643$	41.6405	+	24.0412i	1.64214	+	0.948091i	0.662072	+	0.749440i	$0.269677\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.51493	−	2.62394i	−0.0595580	−	0.103158i	0.834709	−	0.550691i	$-0.185636\pi$
$647$	−1.51493	−	2.62394i	−0.0595580	−	0.103158i	−0.894267	+	0.447534i	$0.852302\pi$
$648$		0			0
$649$	−11.8522			−0.465241
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.4298	−	19.7969i	−0.447281	−	0.774714i	0.550927	−	0.834554i	$-0.314274\pi$
$653$	−11.4298	−	19.7969i	−0.447281	−	0.774714i	−0.998208	+	0.0598398i	$0.980941\pi$
$654$		0			0
$655$			43.1572i			1.68629i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.2417	−	22.9352i	0.515822	−	0.893429i	−0.484010	−	0.875063i	$-0.660820\pi$
$659$	13.2417	−	22.9352i	0.515822	−	0.893429i	0.999831	−	0.0183666i	$-0.00584659\pi$
$660$		0			0
$661$	11.0472	−	6.37812i	0.429687	−	0.248080i	−0.269526	−	0.962993i	$-0.586867\pi$
$661$	11.0472	−	6.37812i	0.429687	−	0.248080i	0.699213	+	0.714913i	$0.253534\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	14.3458	−	8.28255i	0.556306	−	0.321183i
$666$		0			0
$667$	−17.1799	+	29.7564i	−0.665207	+	1.15217i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			17.0132i			0.656789i
$672$		0			0
$673$	12.1461	+	21.0377i	0.468199	+	0.810944i	0.999339	−	0.0363398i	$-0.0115699\pi$
$673$	12.1461	+	21.0377i	0.468199	+	0.810944i	−0.531141	+	0.847284i	$0.678237\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−37.3653			−1.43607			−0.718033	−	0.696009i	$-0.754957\pi$
$677$	−37.3653			−1.43607			−0.718033	+	0.696009i	$0.754957\pi$
$678$		0			0
$679$	2.33629	+	4.04658i	0.0896587	+	0.155293i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−26.6651	−	15.3951i	−1.02031	−	0.589077i	−0.106117	−	0.994354i	$-0.533842\pi$
$683$	−26.6651	−	15.3951i	−1.02031	−	0.589077i	−0.914194	+	0.405277i	$0.867175\pi$
$684$		0			0
$685$	10.2510	−	17.7552i	0.391669	−	0.678391i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0381637	−	6.91839i	−0.00145392	−	0.263570i
$690$		0			0
$691$	−32.8616	+	18.9726i	−1.25011	+	0.721753i	−0.971132	−	0.238543i	$-0.923330\pi$
$691$	−32.8616	+	18.9726i	−1.25011	+	0.721753i	−0.278981	+	0.960296i	$0.589997\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.46243	−	2.57639i	−0.169270	−	0.0977279i
$696$		0			0
$697$		−	83.9249i		−	3.17888i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−25.4219			−0.960172			−0.480086	−	0.877221i	$-0.659395\pi$
$701$	−25.4219			−0.960172			−0.480086	+	0.877221i	$0.659395\pi$
$702$		0			0
$703$	−66.0081			−2.48954
$704$		0			0
$705$		0			0
$706$		0			0
$707$			2.01608i			0.0758225i
$708$		0			0
$709$	−5.13695	−	2.96582i	−0.192922	−	0.111384i	0.400428	−	0.916328i	$-0.368862\pi$
$709$	−5.13695	−	2.96582i	−0.192922	−	0.111384i	−0.593350	+	0.804945i	$0.702195\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−50.7464	+	29.2985i	−1.90047	+	1.09724i
$714$		0			0
$715$	−41.9848	+	24.5497i	−1.57014	+	0.918107i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.0528	−	38.1966i	0.822432	−	1.42449i	−0.0814338	−	0.996679i	$-0.525950\pi$
$719$	22.0528	−	38.1966i	0.822432	−	1.42449i	0.903866	−	0.427816i	$-0.140717\pi$
$720$		0			0
$721$	−0.192942	−	0.111395i	−0.00718552	−	0.00414856i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.59121	+	4.48810i	0.0962350	+	0.166684i
$726$		0			0
$727$	28.8610			1.07039			0.535197	−	0.844727i	$-0.320237\pi$
$727$	28.8610			1.07039			0.535197	+	0.844727i	$0.320237\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.37040	+	9.30180i	0.198631	+	0.344039i
$732$		0			0
$733$		−	35.9193i		−	1.32671i	−0.748305	−	0.663355i	$-0.769132\pi$
$733$		−	35.9193i		−	1.32671i	0.748305	−	0.663355i	$-0.230868\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−24.3713	+	42.2124i	−0.897730	+	1.55491i
$738$		0			0
$739$	−11.3878	+	6.57476i	−0.418908	+	0.241857i	−0.694610	−	0.719387i	$-0.744423\pi$
$739$	−11.3878	+	6.57476i	−0.418908	+	0.241857i	0.275702	+	0.961243i	$0.411090\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.0394	+	5.79624i	−0.368309	+	0.212643i	−0.672719	−	0.739898i	$-0.734874\pi$
$743$	−10.0394	+	5.79624i	−0.368309	+	0.212643i	0.304410	+	0.952541i	$0.401541\pi$
$744$		0			0
$745$	13.1121	−	22.7109i	0.480392	−	0.832063i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			2.86812i			0.104799i
$750$		0			0
$751$	−5.26997	−	9.12785i	−0.192304	−	0.333080i	0.753710	−	0.657208i	$-0.228263\pi$
$751$	−5.26997	−	9.12785i	−0.192304	−	0.333080i	−0.946013	+	0.324128i	$0.894929\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.74348			−0.318208
$756$		0			0
$757$	20.1930	+	34.9753i	0.733926	+	1.27120i	0.955193	+	0.295984i	$0.0956475\pi$
$757$	20.1930	+	34.9753i	0.733926	+	1.27120i	−0.221267	+	0.975213i	$0.571019\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.6681	+	14.8195i	0.930469	+	0.537207i	0.886960	−	0.461846i	$-0.152813\pi$
$761$	25.6681	+	14.8195i	0.930469	+	0.537207i	0.0435092	+	0.999053i	$0.486146\pi$
$762$		0			0
$763$	−0.480718	+	0.832628i	−0.0174032	+	0.0301431i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.88589	−	6.81712i	0.140311	−	0.246152i
$768$		0			0
$769$	−35.9082	+	20.7316i	−1.29488	+	0.747601i	−0.979515	−	0.201369i	$-0.935461\pi$
$769$	−35.9082	+	20.7316i	−1.29488	+	0.747601i	−0.315367	+	0.948970i	$0.602128\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	32.6117	+	18.8284i	1.17296	+	0.677209i	0.954375	−	0.298609i	$-0.0965228\pi$
$773$	32.6117	+	18.8284i	1.17296	+	0.677209i	0.218584	+	0.975818i	$0.429856\pi$
$774$		0			0
$775$			8.83805i			0.317472i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−81.7112			−2.92761
$780$		0			0
$781$	−12.6474			−0.452559
$782$		0			0
$783$		0			0
$784$		0			0
$785$			23.8363i			0.850755i
$786$		0			0
$787$	36.4498	+	21.0443i	1.29929	+	0.750148i	0.980282	−	0.197602i	$-0.0633155\pi$
$787$	36.4498	+	21.0443i	1.29929	+	0.750148i	0.319012	+	0.947751i	$0.396649\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	11.6595	−	6.73164i	0.414565	−	0.239349i
$792$		0			0
$793$	−9.78561	−	5.57798i	−0.347497	−	0.198080i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.77791	−	16.9358i	0.346351	−	0.599898i	−0.639247	−	0.769002i	$-0.720754\pi$
$797$	9.77791	−	16.9358i	0.346351	−	0.599898i	0.985598	+	0.169103i	$0.0540871\pi$
$798$		0			0
$799$	2.79613	+	1.61435i	0.0989201	+	0.0571116i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.0560	+	17.4175i	0.354868	+	0.614649i
$804$		0			0
$805$	18.6381			0.656906
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.8643	+	25.7457i	0.522601	+	0.905171i	0.999654	+	0.0262970i	$0.00837156\pi$
$809$	14.8643	+	25.7457i	0.522601	+	0.905171i	−0.477053	+	0.878874i	$0.658295\pi$
$810$		0			0
$811$		−	24.5115i		−	0.860717i	−0.902658	−	0.430358i	$-0.858387\pi$
$811$		−	24.5115i		−	0.860717i	0.902658	−	0.430358i	$-0.141613\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	24.4003	−	42.2625i	0.854704	−	1.48039i
$816$		0			0
$817$	9.05644	−	5.22874i	0.316845	−	0.182930i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.1551	+	9.90448i	−0.598716	+	0.345669i	−0.768536	−	0.639806i	$-0.779015\pi$
$821$	−17.1551	+	9.90448i	−0.598716	+	0.345669i	0.169820	+	0.985475i	$0.445681\pi$
$822$		0			0
$823$	14.0679	−	24.3663i	0.490376	−	0.849356i	−0.509563	−	0.860434i	$-0.670193\pi$
$823$	14.0679	−	24.3663i	0.490376	−	0.849356i	0.999939	+	0.0110775i	$0.00352614\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			2.88561i			0.100343i	0.998741	+	0.0501713i	$0.0159767\pi$
$827$			2.88561i			0.100343i	−0.998741	+	0.0501713i	$0.984023\pi$
$828$		0			0
$829$	0.952423	+	1.64965i	0.0330790	+	0.0572945i	0.882091	−	0.471079i	$-0.156135\pi$
$829$	0.952423	+	1.64965i	0.0330790	+	0.0572945i	−0.849012	+	0.528374i	$0.822802\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.86906			0.237999
$834$		0			0
$835$	17.9576	+	31.1035i	0.621450	+	1.07638i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−40.6215	−	23.4528i	−1.40241	−	0.809681i	−0.407769	−	0.913085i	$-0.633693\pi$
$839$	−40.6215	−	23.4528i	−1.40241	−	0.809681i	−0.994639	+	0.103404i	$0.967026\pi$
$840$		0			0
$841$	4.07495	−	7.05802i	0.140515	−	0.243380i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.355231	−	32.1975i	−0.0122203	−	1.10763i
$846$		0			0
$847$	16.1589	−	9.32933i	0.555226	−	0.320560i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−64.3184	−	37.1343i	−2.20481	−	1.27295i
$852$		0			0
$853$		−	30.8198i		−	1.05525i	−0.849478	−	0.527625i	$-0.823083\pi$
$853$		−	30.8198i		−	1.05525i	0.849478	−	0.527625i	$-0.176917\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.88680			0.0986113			0.0493056	−	0.998784i	$-0.484299\pi$
$857$	2.88680			0.0986113			0.0493056	+	0.998784i	$0.484299\pi$
$858$		0			0
$859$	40.9476			1.39711			0.698557	−	0.715554i	$-0.253826\pi$
$859$	40.9476			1.39711			0.698557	+	0.715554i	$0.253826\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			3.44875i			0.117397i	0.998276	+	0.0586983i	$0.0186950\pi$
$863$			3.44875i			0.117397i	−0.998276	+	0.0586983i	$0.981305\pi$
$864$		0			0
$865$	−34.7995	−	20.0915i	−1.18322	−	0.683131i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−72.9302	+	42.1063i	−2.47399	+	1.42836i
$870$		0			0
$871$	−16.2891	−	27.8576i	−0.551937	−	0.943919i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.78664	+	8.29070i	−0.161818	+	0.280277i
$876$		0			0
$877$	20.9753	+	12.1101i	0.708286	+	0.408929i	0.810426	−	0.585841i	$-0.199236\pi$
$877$	20.9753	+	12.1101i	0.708286	+	0.408929i	−0.102140	+	0.994770i	$0.532569\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	7.78313	+	13.4808i	0.262220	+	0.454179i	0.966832	−	0.255414i	$-0.0822119\pi$
$881$	7.78313	+	13.4808i	0.262220	+	0.454179i	−0.704611	+	0.709594i	$0.748879\pi$
$882$		0			0
$883$	54.7132			1.84125			0.920624	−	0.390451i	$-0.127681\pi$
$883$	54.7132			1.84125			0.920624	+	0.390451i	$0.127681\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.6681	+	25.4059i	0.492507	+	0.853047i	0.999963	−	0.00863106i	$-0.00274739\pi$
$887$	14.6681	+	25.4059i	0.492507	+	0.853047i	−0.507456	+	0.861678i	$0.669414\pi$
$888$		0			0
$889$			13.4548i			0.451259i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.57177	−	2.72238i	0.0525972	−	0.0911010i
$894$		0			0
$895$	9.85160	−	5.68783i	0.329303	−	0.190123i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.7938	+	17.7788i	−1.02703	+	0.592957i
$900$		0			0
$901$	−6.59034	+	11.4148i	−0.219556	+	0.380282i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			22.6497i			0.752903i
$906$		0			0
$907$	17.2556	+	29.8875i	0.572961	+	0.992398i	0.996260	+	0.0864080i	$0.0275389\pi$
$907$	17.2556	+	29.8875i	0.572961	+	0.992398i	−0.423298	+	0.905990i	$0.639128\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14.4041			−0.477229			−0.238614	−	0.971114i	$-0.576693\pi$
$911$	−14.4041			−0.477229			−0.238614	+	0.971114i	$0.576693\pi$
$912$		0			0
$913$	17.0917	+	29.6037i	0.565653	+	0.979740i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.0896	+	8.71199i	0.498303	+	0.287695i
$918$		0			0
$919$	12.7295	−	22.0482i	0.419908	−	0.727301i	−0.576022	−	0.817434i	$-0.695396\pi$
$919$	12.7295	−	22.0482i	0.419908	−	0.727301i	0.995930	+	0.0901327i	$0.0287291\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.14659	−	7.27447i	0.136487	−	0.239442i
$924$		0			0
$925$	−9.70102	+	5.60089i	−0.318968	+	0.184156i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	36.0971	+	20.8407i	1.18431	+	0.683760i	0.957007	−	0.290065i	$-0.0936768\pi$
$929$	36.0971	+	20.8407i	1.18431	+	0.683760i	0.227300	+	0.973825i	$0.427010\pi$
$930$		0			0
$931$		−	6.68788i		−	0.219186i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	92.6571			3.03021
$936$		0			0
$937$	12.2637			0.400636			0.200318	−	0.979731i	$-0.435802\pi$
$937$	12.2637			0.400636			0.200318	+	0.979731i	$0.435802\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	1.42137i		−	0.0463353i	−0.999732	−	0.0231676i	$-0.992625\pi$
$941$		−	1.42137i		−	0.0463353i	0.999732	−	0.0231676i	$-0.00737514\pi$
$942$		0			0
$943$	−79.6195	−	45.9684i	−2.59277	−	1.49694i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.0361202	−	0.0208540i	0.00117375	−	0.000677665i	−0.499413	−	0.866364i	$-0.666451\pi$
$947$	0.0361202	−	0.0208540i	0.00117375	−	0.000677665i	0.500587	+	0.865686i	$0.333118\pi$
$948$		0			0
$949$	−13.3151	+	0.0734494i	−0.432225	+	0.00238427i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.135787	−	0.235190i	0.00439857	−	0.00761855i	−0.863818	−	0.503804i	$-0.831933\pi$
$953$	0.135787	−	0.235190i	0.00439857	−	0.00761855i	0.868216	+	0.496186i	$0.165267\pi$
$954$		0			0
$955$	−1.98462	−	1.14582i	−0.0642209	−	0.0370779i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.13865	−	7.16836i	−0.133644	−	0.231478i
$960$		0			0
$961$	−29.6398			−0.956122
$962$		0			0
$963$		0			0
$964$		0			0
$965$	16.1367	+	27.9495i	0.519457	+	0.899727i
$966$		0			0
$967$		−	40.0864i		−	1.28909i	−0.764565	−	0.644546i	$-0.777046\pi$
$967$		−	40.0864i		−	1.28909i	0.764565	−	0.644546i	$-0.222954\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.0757	+	31.3080i	−0.580077	+	1.00472i	0.415393	+	0.909642i	$0.363644\pi$
$971$	−18.0757	+	31.3080i	−0.580077	+	1.00472i	−0.995470	+	0.0950802i	$0.969689\pi$
$972$		0			0
$973$	−1.80163	+	1.04017i	−0.0577577	+	0.0333464i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−35.0014	+	20.2081i	−1.11980	+	0.646514i	−0.941349	−	0.337436i	$-0.890440\pi$
$977$	−35.0014	+	20.2081i	−1.11980	+	0.646514i	−0.178446	+	0.983950i	$0.557107\pi$
$978$		0			0
$979$	14.2498	−	24.6813i	0.455424	−	0.788818i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	25.9746i		−	0.828461i	−0.910172	−	0.414230i	$-0.864051\pi$
$983$		−	25.9746i		−	0.828461i	0.910172	−	0.414230i	$-0.135949\pi$
$984$		0			0
$985$	5.75175	+	9.96232i	0.183266	+	0.317426i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	11.7662			0.374142
$990$		0			0
$991$	−12.0491	−	20.8696i	−0.382751	−	0.662944i	0.608704	−	0.793398i	$-0.291690\pi$
$991$	−12.0491	−	20.8696i	−0.382751	−	0.662944i	−0.991454	+	0.130454i	$0.958357\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5.03559	+	2.90730i	0.159639	+	0.0921675i
$996$		0			0
$997$	−5.82563	+	10.0903i	−0.184499	+	0.319562i	−0.943408	−	0.331635i	$-0.892400\pi$
$997$	−5.82563	+	10.0903i	−0.184499	+	0.319562i	0.758908	+	0.651198i	$0.225733\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3276.2.cf.b.1765.5		12
3.2	odd	2		1092.2.bg.a.673.2	yes	12
13.4	even	6	inner	3276.2.cf.b.2773.2		12
39.17	odd	6		1092.2.bg.a.589.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1092.2.bg.a.589.5	✓	12	39.17	odd	6
1092.2.bg.a.673.2	yes	12	3.2	odd	2
3276.2.cf.b.1765.5		12	1.1	even	1	trivial
3276.2.cf.b.2773.2		12	13.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3276.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.47688i q^{5} +(0.866025 + 0.500000i) q^{7} +(4.71635 - 2.72299i) q^{11} +(0.0198889 + 3.60550i) q^{13} +(3.43453 - 5.94878i) q^{17} +(-5.79187 - 3.34394i) q^{19} +(-3.76241 - 6.51668i) q^{23} -1.13495 q^{25} +(-2.28310 - 3.95444i) q^{29} -7.78715i q^{31} +(-1.23844 + 2.14504i) q^{35} +(8.54751 - 4.93491i) q^{37} +(10.5809 - 6.10890i) q^{41} +(-0.781824 + 1.35416i) q^{43} +0.470035i q^{47} +(0.500000 + 0.866025i) q^{49} -1.91885 q^{53} +(6.74453 + 11.6819i) q^{55} +(-1.88476 - 1.08816i) q^{59} +(-1.56200 + 2.70546i) q^{61} +(-8.93040 + 0.0492624i) q^{65} +(-7.75111 + 4.47511i) q^{67} +(-2.01120 - 1.16117i) q^{71} +3.69299i q^{73} +5.44598 q^{77} -15.4633 q^{79} +6.27682i q^{83} +(14.7344 + 8.50693i) q^{85} +(4.53203 - 2.61657i) q^{89} +(-1.78552 + 3.13240i) q^{91} +(8.28255 - 14.3458i) q^{95} +(4.04658 + 2.33629i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{11} - 10 q^{13} + 4 q^{17} - 6 q^{23} + 4 q^{25} + 2 q^{29} - 6 q^{35} - 12 q^{37} + 36 q^{41} - 2 q^{43} + 6 q^{49} - 24 q^{53} + 6 q^{55} - 4 q^{61} + 14 q^{65} + 6 q^{67} + 18 q^{71} - 8 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) \) 12 * q + 12 * q^11 - 10 * q^13 + 4 * q^17 - 6 * q^23 + 4 * q^25 + 2 * q^29 - 6 * q^35 - 12 * q^37 + 36 * q^41 - 2 * q^43 + 6 * q^49 - 24 * q^53 + 6 * q^55 - 4 * q^61 + 14 * q^65 + 6 * q^67 + 18 * q^71 - 8 * q^77 - 36 * q^79 + 54 * q^85 + 30 * q^89 - 4 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more