LMFDB - Embedded newform 162.13.b.a.161.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,13,Mod(161,162)] 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("162.161"); S:= CuspForms(chi, 13); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 13, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	162.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-24576,0,0,-220224] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$148.066998399$
Analytic rank:	$0$
Dimension:	$12$
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} + 203183964 x^{10} + \cdots + 19\!\cdots\!25 $ x^12 + 203183964x^10 + 15056550020439699x^8 + 488595602731974703089400x^6 + 6106079593638498256459255861875x^4 + 8387612844956239317242795880585937500*x^2 + 1922344403867033655870285573676910400390625
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{44} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.2
Root			$-5931.78i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.13.b.a.161.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-45.2548i q^{2} -2048.00 q^{4} -17795.3i q^{5} -80615.8 q^{7} +92681.9i q^{8} -805325. q^{10} -1.40435e6i q^{11} -1.64921e6 q^{13} +3.64825e6i q^{14} +4.19430e6 q^{16} -3.31933e7i q^{17} +1.85197e6 q^{19} +3.64449e7i q^{20} -6.35536e7 q^{22} -2.70921e8i q^{23} -7.25336e7 q^{25} +7.46349e7i q^{26} +1.65101e8 q^{28} -3.28911e8i q^{29} -9.06123e7 q^{31} -1.89813e8i q^{32} -1.50216e9 q^{34} +1.43459e9i q^{35} -9.35391e8 q^{37} -8.38105e7i q^{38} +1.64931e9 q^{40} -7.81432e9i q^{41} -4.03816e9 q^{43} +2.87611e9i q^{44} -1.22605e10 q^{46} +1.90580e9i q^{47} -7.34238e9 q^{49} +3.28249e9i q^{50} +3.37759e9 q^{52} -6.77780e9i q^{53} -2.49909e10 q^{55} -7.47162e9i q^{56} -1.48848e10 q^{58} -2.30841e10i q^{59} +1.75791e9 q^{61} +4.10064e9i q^{62} -8.58993e9 q^{64} +2.93483e10i q^{65} +1.44376e11 q^{67} +6.79799e10i q^{68} +6.49219e10 q^{70} -1.98243e11i q^{71} +2.42510e11 q^{73} +4.23310e10i q^{74} -3.79283e9 q^{76} +1.13213e11i q^{77} -3.70647e11 q^{79} -7.46391e10i q^{80} -3.53636e11 q^{82} +1.02751e11i q^{83} -5.90687e11 q^{85} +1.82746e11i q^{86} +1.30158e11 q^{88} -4.76895e11i q^{89} +1.32953e11 q^{91} +5.54847e11i q^{92} +8.62468e10 q^{94} -3.29564e10i q^{95} -7.77042e10 q^{97} +3.32278e11i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24576 q^{4} - 220224 q^{7} + 379008 q^{10} - 2372808 q^{13} + 50331648 q^{16} + 142669680 q^{19} + 70253568 q^{22} - 727623852 q^{25} + 451018752 q^{28} + 577374720 q^{31} + 2238076800 q^{34} - 3028165356 q^{37}+ \cdots - 2570481096384 q^{97}+O(q^{100}) $ 12 * q - 24576 * q^4 - 220224 * q^7 + 379008 * q^10 - 2372808 * q^13 + 50331648 * q^16 + 142669680 * q^19 + 70253568 * q^22 - 727623852 * q^25 + 451018752 * q^28 + 577374720 * q^31 + 2238076800 * q^34 - 3028165356 * q^37 - 776208384 * q^40 + 33702957168 * q^43 - 24923220480 * q^46 + 72166762836 * q^49 + 4859510784 * q^52 - 158201222256 * q^55 - 21247000704 * q^58 + 213044029980 * q^61 - 103079215104 * q^64 + 70227468528 * q^67 - 251325402624 * q^70 + 49653231360 * q^73 - 292187504640 * q^76 - 696725200560 * q^79 + 735561633024 * q^82 - 271807264548 * q^85 - 143879307264 * q^88 + 729235216704 * q^91 + 1211537346048 * q^94 - 2570481096384 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$-1$

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 $

$2$	− 45.2548i	− 0.707107i
$2$	− 45.2548i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−2048.00	−0.500000
$5$	− 17795.3i	− 1.13890i	−0.822025	−	0.569451i	$-0.807156\pi$
$5$	− 17795.3i	− 1.13890i	0.822025	−	0.569451i	$-0.192844\pi$
$6$	0	0
$7$	−80615.8	−0.685223	−0.342611	−	0.939477i	$-0.611311\pi$
$7$	−80615.8	−0.685223	−0.342611	+	0.939477i	$0.611311\pi$
$8$	92681.9i	0.353553i
$9$	0	0
$10$	−805325.	−0.805325
$11$	− 1.40435e6i	− 0.792719i	−0.918095	−	0.396359i	$-0.870273\pi$
$11$	− 1.40435e6i	− 0.792719i	0.918095	−	0.396359i	$-0.129727\pi$
$12$	0	0
$13$	−1.64921e6	−0.341678	−0.170839	−	0.985299i	$-0.554648\pi$
$13$	−1.64921e6	−0.341678	−0.170839	+	0.985299i	$0.554648\pi$
$14$	3.64825e6i	0.484526i
$15$	0	0
$16$	4.19430e6	0.250000
$17$	− 3.31933e7i	− 1.37517i	−0.726103	−	0.687586i	$-0.758670\pi$
$17$	− 3.31933e7i	− 1.37517i	0.726103	−	0.687586i	$-0.241330\pi$
$18$	0	0
$19$	1.85197e6	0.0393651	0.0196826	−	0.999806i	$-0.493734\pi$
$19$	1.85197e6	0.0393651	0.0196826	+	0.999806i	$0.493734\pi$
$20$	3.64449e7i	0.569451i
$21$	0	0
$22$	−6.35536e7	−0.560537
$23$	− 2.70921e8i	− 1.83011i	−0.403333	−	0.915053i	$-0.632148\pi$
$23$	− 2.70921e8i	− 1.83011i	0.403333	−	0.915053i	$-0.367852\pi$
$24$	0	0
$25$	−7.25336e7	−0.297097
$26$	7.46349e7i	0.241603i
$27$	0	0
$28$	1.65101e8	0.342611
$29$	− 3.28911e8i	− 0.552956i	−0.961020	−	0.276478i	$-0.910833\pi$
$29$	− 3.28911e8i	− 0.552956i	0.961020	−	0.276478i	$-0.0891674\pi$
$30$	0	0
$31$	−9.06123e7	−0.102098	−0.0510489	−	0.998696i	$-0.516256\pi$
$31$	−9.06123e7	−0.102098	−0.0510489	+	0.998696i	$0.516256\pi$
$32$	− 1.89813e8i	− 0.176777i
$33$	0	0
$34$	−1.50216e9	−0.972394
$35$	1.43459e9i	0.780402i
$36$	0	0
$37$	−9.35391e8	−0.364572	−0.182286	−	0.983246i	$-0.558350\pi$
$37$	−9.35391e8	−0.364572	−0.182286	+	0.983246i	$0.558350\pi$
$38$	− 8.38105e7i	− 0.0278354i
$39$	0	0
$40$	1.64931e9	0.402663
$41$	− 7.81432e9i	− 1.64508i	−0.568705	−	0.822542i	$-0.692555\pi$
$41$	− 7.81432e9i	− 1.64508i	0.568705	−	0.822542i	$-0.307445\pi$
$42$	0	0
$43$	−4.03816e9	−0.638812	−0.319406	−	0.947618i	$-0.603483\pi$
$43$	−4.03816e9	−0.638812	−0.319406	+	0.947618i	$0.603483\pi$
$44$	2.87611e9i	0.396359i
$45$	0	0
$46$	−1.22605e10	−1.29408
$47$	1.90580e9i	0.176804i	0.996085	+	0.0884018i	$0.0281759\pi$
$47$	1.90580e9i	0.176804i	−0.996085	+	0.0884018i	$0.971824\pi$
$48$	0	0
$49$	−7.34238e9	−0.530470
$50$	3.28249e9i	0.210080i
$51$	0	0
$52$	3.37759e9	0.170839
$53$	− 6.77780e9i	− 0.305797i	−0.988242	−	0.152899i	$-0.951139\pi$
$53$	− 6.77780e9i	− 0.305797i	0.988242	−	0.152899i	$-0.0488608\pi$
$54$	0	0
$55$	−2.49909e10	−0.902829
$56$	− 7.47162e9i	− 0.242263i
$57$	0	0
$58$	−1.48848e10	−0.390999
$59$	− 2.30841e10i	− 0.547268i	−0.961834	−	0.273634i	$-0.911774\pi$
$59$	− 2.30841e10i	− 0.547268i	0.961834	−	0.273634i	$-0.0882257\pi$
$60$	0	0
$61$	1.75791e9	0.0341207	0.0170604	−	0.999854i	$-0.494569\pi$
$61$	1.75791e9	0.0341207	0.0170604	+	0.999854i	$0.494569\pi$
$62$	4.10064e9i	0.0721941i
$63$	0	0
$64$	−8.58993e9	−0.125000
$65$	2.93483e10i	0.389137i
$66$	0	0
$67$	1.44376e11	1.59605	0.798026	−	0.602624i	$-0.205878\pi$
$67$	1.44376e11	1.59605	0.798026	+	0.602624i	$0.205878\pi$
$68$	6.79799e10i	0.687586i
$69$	0	0
$70$	6.49219e10	0.551827
$71$	− 1.98243e11i	− 1.54756i	−0.633453	−	0.773782i	$-0.718363\pi$
$71$	− 1.98243e11i	− 1.54756i	0.633453	−	0.773782i	$-0.281637\pi$
$72$	0	0
$73$	2.42510e11	1.60248	0.801241	−	0.598342i	$-0.204174\pi$
$73$	2.42510e11	1.60248	0.801241	+	0.598342i	$0.204174\pi$
$74$	4.23310e10i	0.257791i
$75$	0	0
$76$	−3.79283e9	−0.0196826
$77$	1.13213e11i	0.543189i
$78$	0	0
$79$	−3.70647e11	−1.52475	−0.762374	−	0.647137i	$-0.775966\pi$
$79$	−3.70647e11	−1.52475	−0.762374	+	0.647137i	$0.775966\pi$
$80$	− 7.46391e10i	− 0.284725i
$81$	0	0
$82$	−3.53636e11	−1.16325
$83$	1.02751e11i	0.314281i	0.987576	+	0.157141i	$0.0502276\pi$
$83$	1.02751e11i	0.314281i	−0.987576	+	0.157141i	$0.949772\pi$
$84$	0	0
$85$	−5.90687e11	−1.56619
$86$	1.82746e11i	0.451708i
$87$	0	0
$88$	1.30158e11	0.280268
$89$	− 4.76895e11i	− 0.959584i	−0.877382	−	0.479792i	$-0.840712\pi$
$89$	− 4.76895e11i	− 0.959584i	0.877382	−	0.479792i	$-0.159288\pi$
$90$	0	0
$91$	1.32953e11	0.234125
$92$	5.54847e11i	0.915053i
$93$	0	0
$94$	8.62468e10	0.125019
$95$	− 3.29564e10i	− 0.0448330i
$96$	0	0
$97$	−7.77042e10	−0.0932855	−0.0466428	−	0.998912i	$-0.514852\pi$
$97$	−7.77042e10	−0.0932855	−0.0466428	+	0.998912i	$0.514852\pi$
$98$	3.32278e11i	0.375099i
$99$	0	0
$100$	1.48549e11	0.148549
$101$	5.68686e11i	0.535728i	0.963457	+	0.267864i	$0.0863178\pi$
$101$	5.68686e11i	0.535728i	−0.963457	+	0.267864i	$0.913682\pi$
$102$	0	0
$103$	−7.32832e11	−0.613735	−0.306868	−	0.951752i	$-0.599281\pi$
$103$	−7.32832e11	−0.613735	−0.306868	+	0.951752i	$0.599281\pi$
$104$	− 1.52852e11i	− 0.120801i
$105$	0	0
$106$	−3.06728e11	−0.216231
$107$	6.55645e11i	0.436884i	0.975850	+	0.218442i	$0.0700974\pi$
$107$	6.55645e11i	0.436884i	−0.975850	+	0.218442i	$0.929903\pi$
$108$	0	0
$109$	−2.52928e12	−1.50813	−0.754063	−	0.656802i	$-0.771909\pi$
$109$	−2.52928e12	−1.50813	−0.754063	+	0.656802i	$0.771909\pi$
$110$	1.13096e12i	0.638396i
$111$	0	0
$112$	−3.38127e11	−0.171306
$113$	− 6.90427e11i	− 0.331625i	−0.986157	−	0.165812i	$-0.946975\pi$
$113$	− 6.90427e11i	− 0.331625i	0.986157	−	0.165812i	$-0.0530246\pi$
$114$	0	0
$115$	−4.82114e12	−2.08431
$116$	6.73610e11i	0.276478i
$117$	0	0
$118$	−1.04467e12	−0.386977
$119$	2.67591e12i	0.942300i
$120$	0	0
$121$	1.16623e12	0.371597
$122$	− 7.95540e10i	− 0.0241270i
$123$	0	0
$124$	1.85574e11	0.0510489
$125$	− 3.05381e12i	− 0.800537i
$126$	0	0
$127$	1.75985e12	0.419425	0.209712	−	0.977763i	$-0.432747\pi$
$127$	1.75985e12	0.419425	0.209712	+	0.977763i	$0.432747\pi$
$128$	3.88736e11i	0.0883883i
$129$	0	0
$130$	1.32815e12	0.275162
$131$	3.38027e12i	0.668842i	0.942424	+	0.334421i	$0.108541\pi$
$131$	3.38027e12i	0.668842i	−0.942424	+	0.334421i	$0.891459\pi$
$132$	0	0
$133$	−1.49298e11	−0.0269739
$134$	− 6.53372e12i	− 1.12858i
$135$	0	0
$136$	3.07642e12	0.486197
$137$	3.63692e12i	0.550061i	0.961436	+	0.275030i	$0.0886880\pi$
$137$	3.63692e12i	0.550061i	−0.961436	+	0.275030i	$0.911312\pi$
$138$	0	0
$139$	6.09509e12	0.845067	0.422533	−	0.906347i	$-0.361141\pi$
$139$	6.09509e12	0.845067	0.422533	+	0.906347i	$0.361141\pi$
$140$	− 2.93803e12i	− 0.390201i
$141$	0	0
$142$	−8.97147e12	−1.09429
$143$	2.31607e12i	0.270854i
$144$	0	0
$145$	−5.85309e12	−0.629763
$146$	− 1.09748e13i	− 1.13313i
$147$	0	0
$148$	1.91568e12	0.182286
$149$	1.54100e13i	1.40826i	0.710070	+	0.704132i	$0.248663\pi$
$149$	1.54100e13i	1.40826i	−0.710070	+	0.704132i	$0.751337\pi$
$150$	0	0
$151$	4.15634e12	0.350631	0.175315	−	0.984512i	$-0.443906\pi$
$151$	4.15634e12	0.350631	0.175315	+	0.984512i	$0.443906\pi$
$152$	1.71644e11i	0.0139177i
$153$	0	0
$154$	5.12342e12	0.384093
$155$	1.61248e12i	0.116279i
$156$	0	0
$157$	2.84489e13	1.89962	0.949812	−	0.312821i	$-0.101274\pi$
$157$	2.84489e13	1.89962	0.949812	+	0.312821i	$0.101274\pi$
$158$	1.67736e13i	1.07816i
$159$	0	0
$160$	−3.37778e12	−0.201331
$161$	2.18405e13i	1.25403i
$162$	0	0
$163$	5.56080e12	0.296491	0.148246	−	0.988951i	$-0.452637\pi$
$163$	5.56080e12	0.296491	0.148246	+	0.988951i	$0.452637\pi$
$164$	1.60037e13i	0.822542i
$165$	0	0
$166$	4.64999e12	0.222230
$167$	− 7.55232e12i	− 0.348162i	−0.984731	−	0.174081i	$-0.944304\pi$
$167$	− 7.55232e12i	− 0.348162i	0.984731	−	0.174081i	$-0.0556955\pi$
$168$	0	0
$169$	−2.05782e13	−0.883256
$170$	2.67314e13i	1.10746i
$171$	0	0
$172$	8.27016e12	0.319406
$173$	3.71218e13i	1.38469i	0.721567	+	0.692345i	$0.243422\pi$
$173$	3.71218e13i	1.38469i	−0.721567	+	0.692345i	$0.756578\pi$
$174$	0	0
$175$	5.84735e12	0.203578
$176$	− 5.89027e12i	− 0.198180i
$177$	0	0
$178$	−2.15818e13	−0.678528
$179$	4.85116e13i	1.47478i	0.675466	+	0.737391i	$0.263942\pi$
$179$	4.85116e13i	1.47478i	−0.675466	+	0.737391i	$0.736058\pi$
$180$	0	0
$181$	2.56709e12	0.0730079	0.0365039	−	0.999334i	$-0.488378\pi$
$181$	2.56709e12	0.0730079	0.0365039	+	0.999334i	$0.488378\pi$
$182$	− 6.01675e12i	− 0.165552i
$183$	0	0
$184$	2.51095e13	0.647040
$185$	1.66456e13i	0.415211i
$186$	0	0
$187$	−4.66150e13	−1.09013
$188$	− 3.90309e12i	− 0.0884018i
$189$	0	0
$190$	−1.49144e12	−0.0317017
$191$	− 3.87654e13i	− 0.798444i	−0.916854	−	0.399222i	$-0.869280\pi$
$191$	− 3.87654e13i	− 0.798444i	0.916854	−	0.399222i	$-0.130720\pi$
$192$	0	0
$193$	1.80183e13	0.348635	0.174317	−	0.984690i	$-0.444228\pi$
$193$	1.80183e13	0.348635	0.174317	+	0.984690i	$0.444228\pi$
$194$	3.51649e12i	0.0659628i
$195$	0	0
$196$	1.50372e13	0.265235
$197$	9.84871e13i	1.68493i	0.538751	+	0.842465i	$0.318896\pi$
$197$	9.84871e13i	1.68493i	−0.538751	+	0.842465i	$0.681104\pi$
$198$	0	0
$199$	7.13662e13	1.14914	0.574571	−	0.818455i	$-0.305169\pi$
$199$	7.13662e13	1.14914	0.574571	+	0.818455i	$0.305169\pi$
$200$	− 6.72255e12i	− 0.105040i
$201$	0	0
$202$	2.57358e13	0.378817
$203$	2.65154e13i	0.378898i
$204$	0	0
$205$	−1.39058e14	−1.87359
$206$	3.31642e13i	0.433976i
$207$	0	0
$208$	−6.91730e12	−0.0854194
$209$	− 2.60081e12i	− 0.0312055i
$210$	0	0
$211$	1.63603e14	1.85394	0.926970	−	0.375135i	$-0.122404\pi$
$211$	1.63603e14	1.85394	0.926970	+	0.375135i	$0.122404\pi$
$212$	1.38809e13i	0.152899i
$213$	0	0
$214$	2.96711e13	0.308923
$215$	7.18605e13i	0.727544i
$216$	0	0
$217$	7.30478e12	0.0699598
$218$	1.14462e14i	1.06641i
$219$	0	0
$220$	5.11813e13	0.451414
$221$	5.47429e13i	0.469866i
$222$	0	0
$223$	−1.71428e14	−1.39397	−0.696983	−	0.717088i	$-0.745475\pi$
$223$	−1.71428e14	−1.39397	−0.696983	+	0.717088i	$0.745475\pi$
$224$	1.53019e13i	0.121131i
$225$	0	0
$226$	−3.12452e13	−0.234494
$227$	7.75540e13i	0.566825i	0.958998	+	0.283412i	$0.0914665\pi$
$227$	7.75540e13i	0.566825i	−0.958998	+	0.283412i	$0.908533\pi$
$228$	0	0
$229$	2.24081e14	1.55379	0.776895	−	0.629630i	$-0.216793\pi$
$229$	2.24081e14	1.55379	0.776895	+	0.629630i	$0.216793\pi$
$230$	2.18180e14i	1.47383i
$231$	0	0
$232$	3.04841e13	0.195500
$233$	− 2.62174e14i	− 1.63853i	−0.573415	−	0.819265i	$-0.694382\pi$
$233$	− 2.62174e14i	− 1.63853i	0.573415	−	0.819265i	$-0.305618\pi$
$234$	0	0
$235$	3.39144e13	0.201362
$236$	4.72762e13i	0.273634i
$237$	0	0
$238$	1.21098e14	0.666307
$239$	2.55735e14i	1.37216i	0.727528	+	0.686078i	$0.240669\pi$
$239$	2.55735e14i	1.37216i	−0.727528	+	0.686078i	$0.759331\pi$
$240$	0	0
$241$	−1.43532e14	−0.732566	−0.366283	−	0.930504i	$-0.619370\pi$
$241$	−1.43532e14	−0.732566	−0.366283	+	0.930504i	$0.619370\pi$
$242$	− 5.27776e13i	− 0.262759i
$243$	0	0
$244$	−3.60020e12	−0.0170604
$245$	1.30660e14i	0.604153i
$246$	0	0
$247$	−3.05429e12	−0.0134502
$248$	− 8.39812e12i	− 0.0360971i
$249$	0	0
$250$	−1.38200e14	−0.566065
$251$	3.86858e14i	1.54707i	0.633754	+	0.773534i	$0.281513\pi$
$251$	3.86858e14i	1.54707i	−0.633754	+	0.773534i	$0.718487\pi$
$252$	0	0
$253$	−3.80468e14	−1.45076
$254$	− 7.96418e13i	− 0.296578i
$255$	0	0
$256$	1.75922e13	0.0625000
$257$	− 4.70047e14i	− 1.63133i	−0.578523	−	0.815666i	$-0.696371\pi$
$257$	− 4.70047e14i	− 1.63133i	0.578523	−	0.815666i	$-0.303629\pi$
$258$	0	0
$259$	7.54073e13	0.249813
$260$	− 6.01053e13i	− 0.194569i
$261$	0	0
$262$	1.52974e14	0.472943
$263$	5.51566e14i	1.66672i	0.552730	+	0.833360i	$0.313586\pi$
$263$	5.51566e14i	1.66672i	−0.552730	+	0.833360i	$0.686414\pi$
$264$	0	0
$265$	−1.20613e14	−0.348273
$266$	6.75645e12i	0.0190734i
$267$	0	0
$268$	−2.95682e14	−0.798026
$269$	− 1.08162e14i	− 0.285471i	−0.989761	−	0.142735i	$-0.954410\pi$
$269$	− 1.08162e14i	− 0.285471i	0.989761	−	0.142735i	$-0.0455898\pi$
$270$	0	0
$271$	3.17271e14	0.800967	0.400483	−	0.916304i	$-0.368842\pi$
$271$	3.17271e14	0.800967	0.400483	+	0.916304i	$0.368842\pi$
$272$	− 1.39223e14i	− 0.343793i
$273$	0	0
$274$	1.64588e14	0.388952
$275$	1.01862e14i	0.235515i
$276$	0	0
$277$	−7.94443e14	−1.75867	−0.879334	−	0.476205i	$-0.842012\pi$
$277$	−7.94443e14	−1.75867	−0.879334	+	0.476205i	$0.842012\pi$
$278$	− 2.75832e14i	− 0.597552i
$279$	0	0
$280$	−1.32960e14	−0.275914
$281$	− 1.43480e13i	− 0.0291443i	−0.999894	−	0.0145721i	$-0.995361\pi$
$281$	− 1.43480e13i	− 0.0291443i	0.999894	−	0.0145721i	$-0.00463862\pi$
$282$	0	0
$283$	−6.61614e14	−1.28791	−0.643956	−	0.765062i	$-0.722708\pi$
$283$	−6.61614e14	−1.28791	−0.643956	+	0.765062i	$0.722708\pi$
$284$	4.06002e14i	0.773782i
$285$	0	0
$286$	1.04813e14	0.191523
$287$	6.29957e14i	1.12725i
$288$	0	0
$289$	−5.19175e14	−0.891101
$290$	2.64881e14i	0.445310i
$291$	0	0
$292$	−4.96661e14	−0.801241
$293$	− 1.05497e14i	− 0.166738i	−0.996519	−	0.0833689i	$-0.973432\pi$
$293$	− 1.05497e14i	− 0.166738i	0.996519	−	0.0833689i	$-0.0265680\pi$
$294$	0	0
$295$	−4.10789e14	−0.623285
$296$	− 8.66939e13i	− 0.128896i
$297$	0	0
$298$	6.97375e14	0.995792
$299$	4.46807e14i	0.625306i
$300$	0	0
$301$	3.25540e14	0.437729
$302$	− 1.88095e14i	− 0.247933i
$303$	0	0
$304$	7.76772e12	0.00984129
$305$	− 3.12826e13i	− 0.0388601i
$306$	0	0
$307$	−1.12600e15	−1.34496	−0.672479	−	0.740116i	$-0.734770\pi$
$307$	−1.12600e15	−1.34496	−0.672479	+	0.740116i	$0.734770\pi$
$308$	− 2.31860e14i	− 0.271595i
$309$	0	0
$310$	7.29723e13	0.0822220
$311$	− 3.76373e14i	− 0.415964i	−0.978133	−	0.207982i	$-0.933310\pi$
$311$	− 3.76373e14i	− 0.415964i	0.978133	−	0.207982i	$-0.0666896\pi$
$312$	0	0
$313$	1.48461e15	1.57887	0.789436	−	0.613833i	$-0.210373\pi$
$313$	1.48461e15	1.57887	0.789436	+	0.613833i	$0.210373\pi$
$314$	− 1.28745e15i	− 1.34324i
$315$	0	0
$316$	7.59085e14	0.762374
$317$	1.85089e14i	0.182400i	0.995833	+	0.0912000i	$0.0290703\pi$
$317$	1.85089e14i	0.182400i	−0.995833	+	0.0912000i	$0.970930\pi$
$318$	0	0
$319$	−4.61907e14	−0.438339
$320$	1.52861e14i	0.142363i
$321$	0	0
$322$	9.88390e14	0.886734
$323$	− 6.14730e13i	− 0.0541339i
$324$	0	0
$325$	1.19623e14	0.101512
$326$	− 2.51653e14i	− 0.209651i
$327$	0	0
$328$	7.24246e14	0.581625
$329$	− 1.53638e14i	− 0.121150i
$330$	0	0
$331$	2.02219e15	1.53763	0.768817	−	0.639469i	$-0.220846\pi$
$331$	2.02219e15	1.53763	0.768817	+	0.639469i	$0.220846\pi$
$332$	− 2.10435e14i	− 0.157141i
$333$	0	0
$334$	−3.41779e14	−0.246188
$335$	− 2.56922e15i	− 1.81775i
$336$	0	0
$337$	−1.12540e15	−0.768294	−0.384147	−	0.923272i	$-0.625504\pi$
$337$	−1.12540e15	−0.768294	−0.384147	+	0.923272i	$0.625504\pi$
$338$	9.31262e14i	0.624557i
$339$	0	0
$340$	1.20973e15	0.783093
$341$	1.27251e14i	0.0809349i
$342$	0	0
$343$	1.70774e15	1.04871
$344$	− 3.74265e14i	− 0.225854i
$345$	0	0
$346$	1.67994e15	0.979124
$347$	− 1.68772e15i	− 0.966768i	−0.875408	−	0.483384i	$-0.839407\pi$
$347$	− 1.68772e15i	− 0.966768i	0.875408	−	0.483384i	$-0.160593\pi$
$348$	0	0
$349$	−1.14720e15	−0.634873	−0.317436	−	0.948280i	$-0.602822\pi$
$349$	−1.14720e15	−0.634873	−0.317436	+	0.948280i	$0.602822\pi$
$350$	− 2.64621e14i	− 0.143951i
$351$	0	0
$352$	−2.66563e14	−0.140134
$353$	− 3.15759e15i	− 1.63195i	−0.578084	−	0.815977i	$-0.696199\pi$
$353$	− 3.15759e15i	− 1.63195i	0.578084	−	0.815977i	$-0.303801\pi$
$354$	0	0
$355$	−3.52781e15	−1.76252
$356$	9.76681e14i	0.479792i
$357$	0	0
$358$	2.19539e15	1.04283
$359$	− 4.20788e14i	− 0.196561i	−0.995159	−	0.0982803i	$-0.968666\pi$
$359$	− 4.20788e14i	− 0.196561i	0.995159	−	0.0982803i	$-0.0313342\pi$
$360$	0	0
$361$	−2.20989e15	−0.998450
$362$	− 1.16173e14i	− 0.0516244i
$363$	0	0
$364$	−2.72287e14	−0.117063
$365$	− 4.31555e15i	− 1.82507i
$366$	0	0
$367$	2.97926e14	0.121931	0.0609653	−	0.998140i	$-0.480582\pi$
$367$	2.97926e14	0.121931	0.0609653	+	0.998140i	$0.480582\pi$
$368$	− 1.13633e15i	− 0.457527i
$369$	0	0
$370$	7.53294e14	0.293599
$371$	5.46398e14i	0.209539i
$372$	0	0
$373$	2.87969e15	1.06928	0.534642	−	0.845079i	$-0.320447\pi$
$373$	2.87969e15	1.06928	0.534642	+	0.845079i	$0.320447\pi$
$374$	2.10956e15i	0.770835i
$375$	0	0
$376$	−1.76633e14	−0.0625095
$377$	5.42445e14i	0.188933i
$378$	0	0
$379$	2.12894e15	0.718338	0.359169	−	0.933273i	$-0.383060\pi$
$379$	2.12894e15	0.718338	0.359169	+	0.933273i	$0.383060\pi$
$380$	6.74947e13i	0.0224165i
$381$	0	0
$382$	−1.75432e15	−0.564585
$383$	− 5.40020e15i	− 1.71087i	−0.517909	−	0.855435i	$-0.673290\pi$
$383$	− 5.40020e15i	− 1.71087i	0.517909	−	0.855435i	$-0.326710\pi$
$384$	0	0
$385$	2.01466e15	0.618639
$386$	− 8.15417e14i	− 0.246522i
$387$	0	0
$388$	1.59138e14	0.0466428
$389$	− 3.88453e15i	− 1.12109i	−0.828123	−	0.560546i	$-0.810591\pi$
$389$	− 3.88453e15i	− 1.12109i	0.828123	−	0.560546i	$-0.189409\pi$
$390$	0	0
$391$	−8.99278e15	−2.51671
$392$	− 6.80506e14i	− 0.187549i
$393$	0	0
$394$	4.45702e15	1.19143
$395$	6.59579e15i	1.73654i
$396$	0	0
$397$	−4.67139e15	−1.19317	−0.596586	−	0.802549i	$-0.703476\pi$
$397$	−4.67139e15	−1.19317	−0.596586	+	0.802549i	$0.703476\pi$
$398$	− 3.22966e15i	− 0.812567i
$399$	0	0
$400$	−3.04228e14	−0.0742744
$401$	− 7.53973e15i	− 1.81338i	−0.421794	−	0.906692i	$-0.638599\pi$
$401$	− 7.53973e15i	− 1.81338i	0.421794	−	0.906692i	$-0.361401\pi$
$402$	0	0
$403$	1.49439e14	0.0348846
$404$	− 1.16467e15i	− 0.267864i
$405$	0	0
$406$	1.19995e15	0.267922
$407$	1.31362e15i	0.289003i
$408$	0	0
$409$	−3.23196e15	−0.690440	−0.345220	−	0.938522i	$-0.612196\pi$
$409$	−3.23196e15	−0.690440	−0.345220	+	0.938522i	$0.612196\pi$
$410$	6.29307e15i	1.32483i
$411$	0	0
$412$	1.50084e15	0.306868
$413$	1.86094e15i	0.375001i
$414$	0	0
$415$	1.82849e15	0.357936
$416$	3.13041e14i	0.0604007i
$417$	0	0
$418$	−1.17699e14	−0.0220656
$419$	4.57380e15i	0.845266i	0.906301	+	0.422633i	$0.138894\pi$
$419$	4.57380e15i	0.845266i	−0.906301	+	0.422633i	$0.861106\pi$
$420$	0	0
$421$	7.87535e15	1.41442	0.707208	−	0.707006i	$-0.249954\pi$
$421$	7.87535e15	1.41442	0.707208	+	0.707006i	$0.249954\pi$
$422$	− 7.40381e15i	− 1.31093i
$423$	0	0
$424$	6.28179e14	0.108116
$425$	2.40763e15i	0.408560i
$426$	0	0
$427$	−1.41715e14	−0.0233803
$428$	− 1.34276e15i	− 0.218442i
$429$	0	0
$430$	3.25203e15	0.514452
$431$	− 7.06847e15i	− 1.10271i	−0.834270	−	0.551356i	$-0.814111\pi$
$431$	− 7.06847e15i	− 1.10271i	0.834270	−	0.551356i	$-0.185889\pi$
$432$	0	0
$433$	7.14671e14	0.108437	0.0542187	−	0.998529i	$-0.482733\pi$
$433$	7.14671e14	0.108437	0.0542187	+	0.998529i	$0.482733\pi$
$434$	− 3.30577e14i	− 0.0494691i
$435$	0	0
$436$	5.17996e15	0.754063
$437$	− 5.01738e14i	− 0.0720424i
$438$	0	0
$439$	−9.02499e15	−1.26084	−0.630420	−	0.776255i	$-0.717117\pi$
$439$	−9.02499e15	−1.26084	−0.630420	+	0.776255i	$0.717117\pi$
$440$	− 2.31620e15i	− 0.319198i
$441$	0	0
$442$	2.47738e15	0.332245
$443$	1.02564e16i	1.35698i	0.734611	+	0.678489i	$0.237365\pi$
$443$	1.02564e16i	1.35698i	−0.734611	+	0.678489i	$0.762635\pi$
$444$	0	0
$445$	−8.48651e15	−1.09287
$446$	7.75794e15i	0.985682i
$447$	0	0
$448$	6.92484e14	0.0856529
$449$	3.27833e15i	0.400106i	0.979785	+	0.200053i	$0.0641114\pi$
$449$	3.27833e15i	0.400106i	−0.979785	+	0.200053i	$0.935889\pi$
$450$	0	0
$451$	−1.09740e16	−1.30409
$452$	1.41399e15i	0.165812i
$453$	0	0
$454$	3.50969e15	0.400806
$455$	− 2.36594e15i	− 0.266646i
$456$	0	0
$457$	−5.97086e15	−0.655450	−0.327725	−	0.944773i	$-0.606282\pi$
$457$	−5.97086e15	−0.655450	−0.327725	+	0.944773i	$0.606282\pi$
$458$	− 1.01408e16i	− 1.09870i
$459$	0	0
$460$	9.87369e15	1.04216
$461$	− 4.22194e15i	− 0.439852i	−0.975517	−	0.219926i	$-0.929418\pi$
$461$	− 4.22194e15i	− 0.439852i	0.975517	−	0.219926i	$-0.0705816\pi$
$462$	0	0
$463$	3.28094e15	0.333052	0.166526	−	0.986037i	$-0.446745\pi$
$463$	3.28094e15	0.333052	0.166526	+	0.986037i	$0.446745\pi$
$464$	− 1.37955e15i	− 0.138239i
$465$	0	0
$466$	−1.18647e16	−1.15862
$467$	− 2.44371e15i	− 0.235585i	−0.993038	−	0.117793i	$-0.962418\pi$
$467$	− 2.44371e15i	− 0.235585i	0.993038	−	0.117793i	$-0.0375818\pi$
$468$	0	0
$469$	−1.16390e16	−1.09365
$470$	− 1.53479e15i	− 0.142384i
$471$	0	0
$472$	2.13947e15	0.193489
$473$	5.67099e15i	0.506398i
$474$	0	0
$475$	−1.34330e14	−0.0116953
$476$	− 5.48026e15i	− 0.471150i
$477$	0	0
$478$	1.15733e16	0.970261
$479$	− 5.13006e15i	− 0.424726i	−0.977191	−	0.212363i	$-0.931884\pi$
$479$	− 5.13006e15i	− 0.424726i	0.977191	−	0.212363i	$-0.0681160\pi$
$480$	0	0
$481$	1.54266e15	0.124566
$482$	6.49552e15i	0.518002i
$483$	0	0
$484$	−2.38844e15	−0.185799
$485$	1.38277e15i	0.106243i
$486$	0	0
$487$	−1.13473e16	−0.850584	−0.425292	−	0.905056i	$-0.639829\pi$
$487$	−1.13473e16	−0.850584	−0.425292	+	0.905056i	$0.639829\pi$
$488$	1.62927e14i	0.0120635i
$489$	0	0
$490$	5.91301e15	0.427201
$491$	− 9.54302e15i	− 0.681078i	−0.940230	−	0.340539i	$-0.889390\pi$
$491$	− 9.54302e15i	− 0.681078i	0.940230	−	0.340539i	$-0.110610\pi$
$492$	0	0
$493$	−1.09177e16	−0.760411
$494$	1.38221e14i	0.00951072i
$495$	0	0
$496$	−3.80055e14	−0.0255245
$497$	1.59815e16i	1.06043i
$498$	0	0
$499$	6.94132e15	0.449613	0.224807	−	0.974403i	$-0.427825\pi$
$499$	6.94132e15	0.449613	0.224807	+	0.974403i	$0.427825\pi$
$500$	6.25420e15i	0.400269i
$501$	0	0
$502$	1.75072e16	1.09394
$503$	1.94512e16i	1.20099i	0.799630	+	0.600493i	$0.205029\pi$
$503$	1.94512e16i	1.20099i	−0.799630	+	0.600493i	$0.794971\pi$
$504$	0	0
$505$	1.01200e16	0.610141
$506$	1.72180e16i	1.02584i
$507$	0	0
$508$	−3.60418e15	−0.209712
$509$	− 1.99293e16i	− 1.14600i	−0.819554	−	0.573002i	$-0.805779\pi$
$509$	− 1.99293e16i	− 1.14600i	0.819554	−	0.573002i	$-0.194221\pi$
$510$	0	0
$511$	−1.95502e16	−1.09806
$512$	− 7.96131e14i	− 0.0441942i
$513$	0	0
$514$	−2.12719e16	−1.15353
$515$	1.30410e16i	0.698984i
$516$	0	0
$517$	2.67641e15	0.140155
$518$	− 3.41255e15i	− 0.176644i
$519$	0	0
$520$	−2.72006e15	−0.137581
$521$	3.88760e16i	1.94382i	0.235359	+	0.971908i	$0.424373\pi$
$521$	3.88760e16i	1.94382i	−0.235359	+	0.971908i	$0.575627\pi$
$522$	0	0
$523$	−1.24049e16	−0.606152	−0.303076	−	0.952966i	$-0.598014\pi$
$523$	−1.24049e16	−0.606152	−0.303076	+	0.952966i	$0.598014\pi$
$524$	− 6.92279e15i	− 0.334421i
$525$	0	0
$526$	2.49610e16	1.17855
$527$	3.00772e15i	0.140402i
$528$	0	0
$529$	−5.14838e16	−2.34929
$530$	5.45833e15i	0.246266i
$531$	0	0
$532$	3.05762e14	0.0134870
$533$	1.28875e16i	0.562088i
$534$	0	0
$535$	1.16674e16	0.497568
$536$	1.33811e16i	0.564289i
$537$	0	0
$538$	−4.89486e15	−0.201858
$539$	1.03113e16i	0.420513i
$540$	0	0
$541$	2.24880e16	0.896950	0.448475	−	0.893795i	$-0.351967\pi$
$541$	2.24880e16	0.896950	0.448475	+	0.893795i	$0.351967\pi$
$542$	− 1.43580e16i	− 0.566369i
$543$	0	0
$544$	−6.30051e15	−0.243099
$545$	4.50094e16i	1.71761i
$546$	0	0
$547$	9.53519e15	0.355963	0.177982	−	0.984034i	$-0.443043\pi$
$547$	9.53519e15	0.355963	0.177982	+	0.984034i	$0.443043\pi$
$548$	− 7.44842e15i	− 0.275030i
$549$	0	0
$550$	4.60977e15	0.166534
$551$	− 6.09133e14i	− 0.0217672i
$552$	0	0
$553$	2.98800e16	1.04479
$554$	3.59524e16i	1.24357i
$555$	0	0
$556$	−1.24827e16	−0.422533
$557$	4.79821e14i	0.0160675i	0.999968	+	0.00803375i	$0.00255725\pi$
$557$	4.79821e14i	0.0160675i	−0.999968	+	0.00803375i	$0.997443\pi$
$558$	0	0
$559$	6.65979e15	0.218268
$560$	6.01709e15i	0.195100i
$561$	0	0
$562$	−6.49316e14	−0.0206081
$563$	− 1.41754e16i	− 0.445128i	−0.974918	−	0.222564i	$-0.928557\pi$
$563$	− 1.41754e16i	− 0.445128i	0.974918	−	0.222564i	$-0.0714426\pi$
$564$	0	0
$565$	−1.22864e16	−0.377688
$566$	2.99412e16i	0.910691i
$567$	0	0
$568$	1.83736e16	0.547146
$569$	7.35563e15i	0.216744i	0.994110	+	0.108372i	$0.0345637\pi$
$569$	7.35563e15i	0.216744i	−0.994110	+	0.108372i	$0.965436\pi$
$570$	0	0
$571$	2.75751e16	0.795611	0.397805	−	0.917470i	$-0.369772\pi$
$571$	2.75751e16	0.795611	0.397805	+	0.917470i	$0.369772\pi$
$572$	− 4.74331e15i	− 0.135427i
$573$	0	0
$574$	2.85086e16	0.797085
$575$	1.96509e16i	0.543720i
$576$	0	0
$577$	6.55740e16	1.77696	0.888478	−	0.458919i	$-0.151763\pi$
$577$	6.55740e16	1.77696	0.888478	+	0.458919i	$0.151763\pi$
$578$	2.34952e16i	0.630103i
$579$	0	0
$580$	1.19871e16	0.314882
$581$	− 8.28337e15i	− 0.215353i
$582$	0	0
$583$	−9.51840e15	−0.242411
$584$	2.24763e16i	0.566563i
$585$	0	0
$586$	−4.77425e15	−0.117901
$587$	− 5.86479e16i	− 1.43359i	−0.697285	−	0.716794i	$-0.745609\pi$
$587$	− 5.86479e16i	− 1.43359i	0.697285	−	0.716794i	$-0.254391\pi$
$588$	0	0
$589$	−1.67811e14	−0.00401910
$590$	1.85902e16i	0.440729i
$591$	0	0
$592$	−3.92332e15	−0.0911429
$593$	− 2.78445e16i	− 0.640341i	−0.947360	−	0.320171i	$-0.896260\pi$
$593$	− 2.78445e16i	− 0.640341i	0.947360	−	0.320171i	$-0.103740\pi$
$594$	0	0
$595$	4.76187e16	1.07319
$596$	− 3.15596e16i	− 0.704132i
$597$	0	0
$598$	2.02202e16	0.442158
$599$	2.63087e16i	0.569559i	0.958593	+	0.284779i	$0.0919204\pi$
$599$	2.63087e16i	0.569559i	−0.958593	+	0.284779i	$0.908080\pi$
$600$	0	0
$601$	3.66822e16	0.778410	0.389205	−	0.921151i	$-0.372750\pi$
$601$	3.66822e16	0.778410	0.389205	+	0.921151i	$0.372750\pi$
$602$	− 1.47322e16i	− 0.309521i
$603$	0	0
$604$	−8.51219e15	−0.175315
$605$	− 2.07535e16i	− 0.423213i
$606$	0	0
$607$	6.78770e16	1.35703	0.678516	−	0.734585i	$-0.262623\pi$
$607$	6.78770e16	1.35703	0.678516	+	0.734585i	$0.262623\pi$
$608$	− 3.51527e14i	− 0.00695884i
$609$	0	0
$610$	−1.41569e15	−0.0274783
$611$	− 3.14308e15i	− 0.0604098i
$612$	0	0
$613$	−7.22056e16	−1.36084	−0.680421	−	0.732821i	$-0.738203\pi$
$613$	−7.22056e16	−1.36084	−0.680421	+	0.732821i	$0.738203\pi$
$614$	5.09570e16i	0.951029i
$615$	0	0
$616$	−1.04928e16	−0.192046
$617$	3.20417e16i	0.580770i	0.956910	+	0.290385i	$0.0937834\pi$
$617$	3.20417e16i	0.580770i	−0.956910	+	0.290385i	$0.906217\pi$
$618$	0	0
$619$	−2.78401e16	−0.494910	−0.247455	−	0.968899i	$-0.579594\pi$
$619$	−2.78401e16	−0.494910	−0.247455	+	0.968899i	$0.579594\pi$
$620$	− 3.30235e15i	− 0.0581397i
$621$	0	0
$622$	−1.70327e16	−0.294131
$623$	3.84453e16i	0.657529i
$624$	0	0
$625$	−7.20519e16	−1.20883
$626$	− 6.71859e16i	− 1.11643i
$627$	0	0
$628$	−5.82634e16	−0.949812
$629$	3.10488e16i	0.501349i
$630$	0	0
$631$	−4.57187e16	−0.724299	−0.362150	−	0.932120i	$-0.617957\pi$
$631$	−4.57187e16	−0.724299	−0.362150	+	0.932120i	$0.617957\pi$
$632$	− 3.43523e16i	− 0.539080i
$633$	0	0
$634$	8.37617e15	0.128976
$635$	− 3.13172e16i	− 0.477684i
$636$	0	0
$637$	1.21092e16	0.181250
$638$	2.09035e16i	0.309952i
$639$	0	0
$640$	6.91769e15	0.100666
$641$	6.63001e16i	0.955798i	0.878415	+	0.477899i	$0.158602\pi$
$641$	6.63001e16i	0.955798i	−0.878415	+	0.477899i	$0.841398\pi$
$642$	0	0
$643$	1.10947e16	0.156982	0.0784909	−	0.996915i	$-0.474990\pi$
$643$	1.10947e16	0.156982	0.0784909	+	0.996915i	$0.474990\pi$
$644$	− 4.47294e16i	− 0.627015i
$645$	0	0
$646$	−2.78195e15	−0.0382784
$647$	6.18571e15i	0.0843264i	0.999111	+	0.0421632i	$0.0134250\pi$
$647$	6.18571e15i	0.0843264i	−0.999111	+	0.0421632i	$0.986575\pi$
$648$	0	0
$649$	−3.24181e16	−0.433830
$650$	− 5.41353e15i	− 0.0717795i
$651$	0	0
$652$	−1.13885e16	−0.148246
$653$	4.70621e16i	0.607005i	0.952831	+	0.303503i	$0.0981561\pi$
$653$	4.70621e16i	0.607005i	−0.952831	+	0.303503i	$0.901844\pi$
$654$	0	0
$655$	6.01531e16	0.761746
$656$	− 3.27756e16i	− 0.411271i
$657$	0	0
$658$	−6.95286e15	−0.0856659
$659$	− 4.67138e16i	− 0.570338i	−0.958477	−	0.285169i	$-0.907950\pi$
$659$	− 4.67138e16i	− 0.570338i	0.958477	−	0.285169i	$-0.0920497\pi$
$660$	0	0
$661$	−1.04028e16	−0.124722	−0.0623608	−	0.998054i	$-0.519863\pi$
$661$	−1.04028e16	−0.124722	−0.0623608	+	0.998054i	$0.519863\pi$
$662$	− 9.15137e16i	− 1.08727i
$663$	0	0
$664$	−9.52318e15	−0.111115
$665$	2.65681e15i	0.0307206i
$666$	0	0
$667$	−8.91091e16	−1.01197
$668$	1.54672e16i	0.174081i
$669$	0	0
$670$	−1.16270e17	−1.28534
$671$	− 2.46872e15i	− 0.0270481i
$672$	0	0
$673$	1.02093e17	1.09877	0.549386	−	0.835569i	$-0.314862\pi$
$673$	1.02093e17	1.09877	0.549386	+	0.835569i	$0.314862\pi$
$674$	5.09298e16i	0.543266i
$675$	0	0
$676$	4.21441e16	0.441628
$677$	5.99226e14i	0.00622384i	0.999995	+	0.00311192i	$0.000990556\pi$
$677$	5.99226e14i	0.00622384i	−0.999995	+	0.00311192i	$0.999009\pi$
$678$	0	0
$679$	6.26419e15	0.0639214
$680$	− 5.47460e16i	− 0.553731i
$681$	0	0
$682$	5.75874e15	0.0572296
$683$	− 1.82224e17i	− 1.79507i	−0.440943	−	0.897535i	$-0.645356\pi$
$683$	− 1.82224e17i	− 1.79507i	0.440943	−	0.897535i	$-0.354644\pi$
$684$	0	0
$685$	6.47203e16	0.626465
$686$	− 7.72834e16i	− 0.741552i
$687$	0	0
$688$	−1.69373e16	−0.159703
$689$	1.11780e16i	0.104484i
$690$	0	0
$691$	−1.16512e16	−0.107029	−0.0535145	−	0.998567i	$-0.517042\pi$
$691$	−1.16512e16	−0.107029	−0.0535145	+	0.998567i	$0.517042\pi$
$692$	− 7.60255e16i	− 0.692345i
$693$	0	0
$694$	−7.63773e16	−0.683609
$695$	− 1.08464e17i	− 0.962448i
$696$	0	0
$697$	−2.59383e17	−2.26227
$698$	5.19163e16i	0.448923i
$699$	0	0
$700$	−1.19754e16	−0.101789
$701$	− 1.87010e17i	− 1.57600i	−0.615675	−	0.788000i	$-0.711117\pi$
$701$	− 1.87010e17i	− 1.57600i	0.615675	−	0.788000i	$-0.288883\pi$
$702$	0	0
$703$	−1.73232e15	−0.0143514
$704$	1.20633e16i	0.0990898i
$705$	0	0
$706$	−1.42896e17	−1.15397
$707$	− 4.58451e16i	− 0.367093i
$708$	0	0
$709$	4.71016e16	0.370816	0.185408	−	0.982662i	$-0.440639\pi$
$709$	4.71016e16	0.370816	0.185408	+	0.982662i	$0.440639\pi$
$710$	1.59650e17i	1.24629i
$711$	0	0
$712$	4.41995e16	0.339264
$713$	2.45488e16i	0.186850i
$714$	0	0
$715$	4.12153e16	0.308476
$716$	− 9.93518e16i	− 0.737391i
$717$	0	0
$718$	−1.90427e16	−0.138989
$719$	− 1.87593e17i	− 1.35783i	−0.734218	−	0.678913i	$-0.762451\pi$
$719$	− 1.87593e17i	− 1.35783i	0.734218	−	0.678913i	$-0.237549\pi$
$720$	0	0
$721$	5.90778e16	0.420545
$722$	1.00008e17i	0.706011i
$723$	0	0
$724$	−5.25740e15	−0.0365039
$725$	2.38571e16i	0.164282i
$726$	0	0
$727$	2.25256e17	1.52570	0.762851	−	0.646575i	$-0.223799\pi$
$727$	2.25256e17	1.52570	0.762851	+	0.646575i	$0.223799\pi$
$728$	1.23223e16i	0.0827758i
$729$	0	0
$730$	−1.95300e17	−1.29052
$731$	1.34040e17i	0.878477i
$732$	0	0
$733$	2.39069e16	0.154134	0.0770670	−	0.997026i	$-0.475444\pi$
$733$	2.39069e16	0.154134	0.0770670	+	0.997026i	$0.475444\pi$
$734$	− 1.34826e16i	− 0.0862179i
$735$	0	0
$736$	−5.14243e16	−0.323520
$737$	− 2.02755e17i	− 1.26522i
$738$	0	0
$739$	3.22151e17	1.97785	0.988924	−	0.148426i	$-0.0474206\pi$
$739$	3.22151e17	1.97785	0.988924	+	0.148426i	$0.0474206\pi$
$740$	− 3.40902e16i	− 0.207606i
$741$	0	0
$742$	2.47271e16	0.148167
$743$	1.53596e17i	0.912947i	0.889737	+	0.456474i	$0.150888\pi$
$743$	1.53596e17i	0.912947i	−0.889737	+	0.456474i	$0.849112\pi$
$744$	0	0
$745$	2.74225e17	1.60387
$746$	− 1.30320e17i	− 0.756098i
$747$	0	0
$748$	9.54676e16	0.545063
$749$	− 5.28553e16i	− 0.299363i
$750$	0	0
$751$	−2.00387e17	−1.11694	−0.558471	−	0.829524i	$-0.688612\pi$
$751$	−2.00387e17	−1.11694	−0.558471	+	0.829524i	$0.688612\pi$
$752$	7.99352e15i	0.0442009i
$753$	0	0
$754$	2.45483e16	0.133596
$755$	− 7.39635e16i	− 0.399334i
$756$	0	0
$757$	−6.33454e16	−0.336620	−0.168310	−	0.985734i	$-0.553831\pi$
$757$	−6.33454e16	−0.336620	−0.168310	+	0.985734i	$0.553831\pi$
$758$	− 9.63450e16i	− 0.507942i
$759$	0	0
$760$	3.05446e15	0.0158509
$761$	1.02927e17i	0.529936i	0.964257	+	0.264968i	$0.0853613\pi$
$761$	1.02927e17i	0.529936i	−0.964257	+	0.264968i	$0.914639\pi$
$762$	0	0
$763$	2.03900e17	1.03340
$764$	7.93916e16i	0.399222i
$765$	0	0
$766$	−2.44385e17	−1.20977
$767$	3.80705e16i	0.186989i
$768$	0	0
$769$	2.58440e17	1.24969	0.624845	−	0.780749i	$-0.285162\pi$
$769$	2.58440e17	1.24969	0.624845	+	0.780749i	$0.285162\pi$
$770$	− 9.11731e16i	− 0.437444i
$771$	0	0
$772$	−3.69016e16	−0.174317
$773$	1.50948e17i	0.707539i	0.935333	+	0.353769i	$0.115100\pi$
$773$	1.50948e17i	0.707539i	−0.935333	+	0.353769i	$0.884900\pi$
$774$	0	0
$775$	6.57243e15	0.0303330
$776$	− 7.20178e15i	− 0.0329814i
$777$	0	0
$778$	−1.75794e17	−0.792732
$779$	− 1.44719e16i	− 0.0647589i
$780$	0	0
$781$	−2.78403e17	−1.22678
$782$	4.06967e17i	1.77958i
$783$	0	0
$784$	−3.07962e16	−0.132617
$785$	− 5.06258e17i	− 2.16349i
$786$	0	0
$787$	−4.27699e17	−1.80007	−0.900036	−	0.435816i	$-0.856460\pi$
$787$	−4.27699e17	−1.80007	−0.900036	+	0.435816i	$0.856460\pi$
$788$	− 2.01702e17i	− 0.842465i
$789$	0	0
$790$	2.98491e17	1.22792
$791$	5.56593e16i	0.227237i
$792$	0	0
$793$	−2.89917e15	−0.0116583
$794$	2.11403e17i	0.843700i
$795$	0	0
$796$	−1.46158e17	−0.574571
$797$	− 3.66912e17i	− 1.43157i	−0.698321	−	0.715785i	$-0.746069\pi$
$797$	− 3.66912e17i	− 1.43157i	0.698321	−	0.715785i	$-0.253931\pi$
$798$	0	0
$799$	6.32600e16	0.243135
$800$	1.37678e16i	0.0525199i
$801$	0	0
$802$	−3.41209e17	−1.28226
$803$	− 3.40569e17i	− 1.27032i
$804$	0	0
$805$	3.88660e17	1.42822
$806$	− 6.76283e15i	− 0.0246671i
$807$	0	0
$808$	−5.27069e16	−0.189408
$809$	− 2.91530e17i	− 1.03990i	−0.854196	−	0.519951i	$-0.825950\pi$
$809$	− 2.91530e17i	− 1.03990i	0.854196	−	0.519951i	$-0.174050\pi$
$810$	0	0
$811$	1.56399e17	0.549677	0.274839	−	0.961490i	$-0.411376\pi$
$811$	1.56399e17	0.549677	0.274839	+	0.961490i	$0.411376\pi$
$812$	− 5.43036e16i	− 0.189449i
$813$	0	0
$814$	5.94475e16	0.204356
$815$	− 9.89564e16i	− 0.337674i
$816$	0	0
$817$	−7.47855e15	−0.0251469
$818$	1.46262e17i	0.488215i
$819$	0	0
$820$	2.84792e17	0.936794
$821$	− 6.36807e16i	− 0.207945i	−0.994580	−	0.103973i	$-0.966845\pi$
$821$	− 6.36807e16i	− 0.207945i	0.994580	−	0.103973i	$-0.0331554\pi$
$822$	0	0
$823$	2.22940e17	0.717445	0.358723	−	0.933444i	$-0.383212\pi$
$823$	2.22940e17	0.717445	0.358723	+	0.933444i	$0.383212\pi$
$824$	− 6.79202e16i	− 0.216988i
$825$	0	0
$826$	8.42165e16	0.265166
$827$	7.84634e16i	0.245264i	0.992452	+	0.122632i	$0.0391335\pi$
$827$	7.84634e16i	0.245264i	−0.992452	+	0.122632i	$0.960866\pi$
$828$	0	0
$829$	−1.98881e17	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$829$	−1.98881e17	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$830$	− 8.27482e16i	− 0.253099i
$831$	0	0
$832$	1.41666e16	0.0427097
$833$	2.43718e17i	0.729487i
$834$	0	0
$835$	−1.34396e17	−0.396523
$836$	5.32646e15i	0.0156027i
$837$	0	0
$838$	2.06987e17	0.597693
$839$	6.04451e17i	1.73296i	0.499210	+	0.866481i	$0.333624\pi$
$839$	6.04451e17i	1.73296i	−0.499210	+	0.866481i	$0.666376\pi$
$840$	0	0
$841$	2.45632e17	0.694239
$842$	− 3.56397e17i	− 1.00014i
$843$	0	0
$844$	−3.35058e17	−0.926970
$845$	3.66196e17i	1.00594i
$846$	0	0
$847$	−9.40166e16	−0.254627
$848$	− 2.84282e16i	− 0.0764493i
$849$	0	0
$850$	1.08957e17	0.288896
$851$	2.53418e17i	0.667205i
$852$	0	0
$853$	5.55915e16	0.144316	0.0721579	−	0.997393i	$-0.477011\pi$
$853$	5.55915e16	0.144316	0.0721579	+	0.997393i	$0.477011\pi$
$854$	6.41331e15i	0.0165324i
$855$	0	0
$856$	−6.07664e16	−0.154462
$857$	− 3.09469e17i	− 0.781146i	−0.920572	−	0.390573i	$-0.872277\pi$
$857$	− 3.09469e17i	− 0.781146i	0.920572	−	0.390573i	$-0.127723\pi$
$858$	0	0
$859$	5.71426e16	0.142233	0.0711166	−	0.997468i	$-0.477344\pi$
$859$	5.71426e16	0.142233	0.0711166	+	0.997468i	$0.477344\pi$
$860$	− 1.47170e17i	− 0.363772i
$861$	0	0
$862$	−3.19883e17	−0.779735
$863$	1.52129e17i	0.368253i	0.982903	+	0.184127i	$0.0589457\pi$
$863$	1.52129e17i	0.368253i	−0.982903	+	0.184127i	$0.941054\pi$
$864$	0	0
$865$	6.60595e17	1.57703
$866$	− 3.23423e16i	− 0.0766768i
$867$	0	0
$868$	−1.49602e16	−0.0349799
$869$	5.20518e17i	1.20870i
$870$	0	0
$871$	−2.38107e17	−0.545335
$872$	− 2.34418e17i	− 0.533203i
$873$	0	0
$874$	−2.27061e16	−0.0509417
$875$	2.46185e17i	0.548546i
$876$	0	0
$877$	−6.51219e16	−0.143130	−0.0715648	−	0.997436i	$-0.522799\pi$
$877$	−6.51219e16	−0.143130	−0.0715648	+	0.997436i	$0.522799\pi$
$878$	4.08424e17i	0.891548i
$879$	0	0
$880$	−1.04819e17	−0.225707
$881$	1.94819e17i	0.416655i	0.978059	+	0.208328i	$0.0668020\pi$
$881$	1.94819e17i	0.416655i	−0.978059	+	0.208328i	$0.933198\pi$
$882$	0	0
$883$	−1.71267e17	−0.361336	−0.180668	−	0.983544i	$-0.557826\pi$
$883$	−1.71267e17	−0.361336	−0.180668	+	0.983544i	$0.557826\pi$
$884$	− 1.12113e17i	− 0.234933i
$885$	0	0
$886$	4.64152e17	0.959528
$887$	5.18623e17i	1.06490i	0.846461	+	0.532451i	$0.178729\pi$
$887$	5.18623e17i	1.06490i	−0.846461	+	0.532451i	$0.821271\pi$
$888$	0	0
$889$	−1.41872e17	−0.287399
$890$	3.84056e17i	0.772777i
$891$	0	0
$892$	3.51084e17	0.696983
$893$	3.52949e15i	0.00695990i
$894$	0	0
$895$	8.63281e17	1.67963
$896$	− 3.13383e16i	− 0.0605657i
$897$	0	0
$898$	1.48360e17	0.282918
$899$	2.98034e16i	0.0564557i
$900$	0	0
$901$	−2.24978e17	−0.420524
$902$	4.96628e17i	0.922130i
$903$	0	0
$904$	6.39901e16	0.117247
$905$	− 4.56822e16i	− 0.0831488i
$906$	0	0
$907$	8.76589e17	1.57454	0.787268	−	0.616611i	$-0.211495\pi$
$907$	8.76589e17	1.57454	0.787268	+	0.616611i	$0.211495\pi$
$908$	− 1.58831e17i	− 0.283412i
$909$	0	0
$910$	−1.07070e17	−0.188547
$911$	3.91876e17i	0.685550i	0.939418	+	0.342775i	$0.111367\pi$
$911$	3.91876e17i	0.685550i	−0.939418	+	0.342775i	$0.888633\pi$
$912$	0	0
$913$	1.44299e17	0.249137
$914$	2.70210e17i	0.463473i
$915$	0	0
$916$	−4.58918e17	−0.776895
$917$	− 2.72503e17i	− 0.458306i
$918$	0	0
$919$	6.52207e17	1.08266	0.541330	−	0.840810i	$-0.317921\pi$
$919$	6.52207e17	1.08266	0.541330	+	0.840810i	$0.317921\pi$
$920$	− 4.46832e17i	− 0.736915i
$921$	0	0
$922$	−1.91063e17	−0.311022
$923$	3.26945e17i	0.528768i
$924$	0	0
$925$	6.78473e16	0.108313
$926$	− 1.48478e17i	− 0.235504i
$927$	0	0
$928$	−6.24315e16	−0.0977498
$929$	9.01784e17i	1.40284i	0.712748	+	0.701420i	$0.247450\pi$
$929$	9.01784e17i	1.40284i	−0.712748	+	0.701420i	$0.752550\pi$
$930$	0	0
$931$	−1.35979e16	−0.0208820
$932$	5.36933e17i	0.819265i
$933$	0	0
$934$	−1.10590e17	−0.166584
$935$	8.29531e17i	1.24155i
$936$	0	0
$937$	−8.39529e17	−1.24050	−0.620252	−	0.784403i	$-0.712970\pi$
$937$	−8.39529e17	−1.24050	−0.620252	+	0.784403i	$0.712970\pi$
$938$	5.26721e17i	0.773328i
$939$	0	0
$940$	−6.94567e16	−0.100681
$941$	− 1.01204e17i	− 0.145767i	−0.997340	−	0.0728836i	$-0.976780\pi$
$941$	− 1.01204e17i	− 0.145767i	0.997340	−	0.0728836i	$-0.0232202\pi$
$942$	0	0
$943$	−2.11707e18	−3.01068
$944$	− 9.68216e16i	− 0.136817i
$945$	0	0
$946$	2.56640e17	0.358078
$947$	7.19849e17i	0.998025i	0.866595	+	0.499013i	$0.166304\pi$
$947$	7.19849e17i	0.998025i	−0.866595	+	0.499013i	$0.833696\pi$
$948$	0	0
$949$	−3.99951e17	−0.547532
$950$	6.07907e15i	0.00826982i
$951$	0	0
$952$	−2.48008e17	−0.333153
$953$	− 5.63147e17i	− 0.751735i	−0.926673	−	0.375867i	$-0.877345\pi$
$953$	− 5.63147e17i	− 0.751735i	0.926673	−	0.375867i	$-0.122655\pi$
$954$	0	0
$955$	−6.89844e17	−0.909349
$956$	− 5.23746e17i	− 0.686078i
$957$	0	0
$958$	−2.32160e17	−0.300327
$959$	− 2.93194e17i	− 0.376914i
$960$	0	0
$961$	−7.79452e17	−0.989576
$962$	− 6.98128e16i	− 0.0880815i
$963$	0	0
$964$	2.93954e17	0.366283
$965$	− 3.20643e17i	− 0.397061i
$966$	0	0
$967$	−1.25331e17	−0.153284	−0.0766422	−	0.997059i	$-0.524420\pi$
$967$	−1.25331e17	−0.153284	−0.0766422	+	0.997059i	$0.524420\pi$
$968$	1.08088e17i	0.131379i
$969$	0	0
$970$	6.25772e16	0.0751252
$971$	2.07951e17i	0.248111i	0.992275	+	0.124055i	$0.0395900\pi$
$971$	2.07951e17i	0.248111i	−0.992275	+	0.124055i	$0.960410\pi$
$972$	0	0
$973$	−4.91360e17	−0.579059
$974$	5.13518e17i	0.601454i
$975$	0	0
$976$	7.37322e15	0.00853018
$977$	4.92582e17i	0.566384i	0.959063	+	0.283192i	$0.0913933\pi$
$977$	4.92582e17i	0.566384i	−0.959063	+	0.283192i	$0.908607\pi$
$978$	0	0
$979$	−6.69727e17	−0.760680
$980$	− 2.67592e17i	− 0.302076i
$981$	0	0
$982$	−4.31868e17	−0.481595
$983$	1.15111e18i	1.27584i	0.770101	+	0.637922i	$0.220206\pi$
$983$	1.15111e18i	1.27584i	−0.770101	+	0.637922i	$0.779794\pi$
$984$	0	0
$985$	1.75261e18	1.91897
$986$	4.94077e17i	0.537692i
$987$	0	0
$988$	6.25519e15	0.00672510
$989$	1.09402e18i	1.16909i
$990$	0	0
$991$	1.49153e18	1.57467	0.787334	−	0.616526i	$-0.211461\pi$
$991$	1.49153e18	1.57467	0.787334	+	0.616526i	$0.211461\pi$
$992$	1.71993e16i	0.0180485i
$993$	0	0
$994$	7.23242e17	0.749834
$995$	− 1.26999e18i	− 1.30876i
$996$	0	0
$997$	−1.69332e18	−1.72412	−0.862062	−	0.506802i	$-0.830827\pi$
$997$	−1.69332e18	−1.72412	−0.862062	+	0.506802i	$0.830827\pi$
$998$	− 3.14128e17i	− 0.317924i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.13.b.a.161.2	✓	12
3.2	odd	2	inner	162.13.b.a.161.11	yes	12
9.2	odd	6		162.13.d.h.53.10		24
9.4	even	3		162.13.d.h.107.10		24
9.5	odd	6		162.13.d.h.107.3		24
9.7	even	3		162.13.d.h.53.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.13.b.a.161.2	✓	12	1.1	even	1	trivial
162.13.b.a.161.11	yes	12	3.2	odd	2	inner
162.13.d.h.53.3		24	9.7	even	3
162.13.d.h.53.10		24	9.2	odd	6
162.13.d.h.107.3		24	9.5	odd	6
162.13.d.h.107.10		24	9.4	even	3

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-45.2548i q^{2} -2048.00 q^{4} -17795.3i q^{5} -80615.8 q^{7} +92681.9i q^{8} -805325. q^{10} -1.40435e6i q^{11} -1.64921e6 q^{13} +3.64825e6i q^{14} +4.19430e6 q^{16} -3.31933e7i q^{17} +1.85197e6 q^{19} +3.64449e7i q^{20} -6.35536e7 q^{22} -2.70921e8i q^{23} -7.25336e7 q^{25} +7.46349e7i q^{26} +1.65101e8 q^{28} -3.28911e8i q^{29} -9.06123e7 q^{31} -1.89813e8i q^{32} -1.50216e9 q^{34} +1.43459e9i q^{35} -9.35391e8 q^{37} -8.38105e7i q^{38} +1.64931e9 q^{40} -7.81432e9i q^{41} -4.03816e9 q^{43} +2.87611e9i q^{44} -1.22605e10 q^{46} +1.90580e9i q^{47} -7.34238e9 q^{49} +3.28249e9i q^{50} +3.37759e9 q^{52} -6.77780e9i q^{53} -2.49909e10 q^{55} -7.47162e9i q^{56} -1.48848e10 q^{58} -2.30841e10i q^{59} +1.75791e9 q^{61} +4.10064e9i q^{62} -8.58993e9 q^{64} +2.93483e10i q^{65} +1.44376e11 q^{67} +6.79799e10i q^{68} +6.49219e10 q^{70} -1.98243e11i q^{71} +2.42510e11 q^{73} +4.23310e10i q^{74} -3.79283e9 q^{76} +1.13213e11i q^{77} -3.70647e11 q^{79} -7.46391e10i q^{80} -3.53636e11 q^{82} +1.02751e11i q^{83} -5.90687e11 q^{85} +1.82746e11i q^{86} +1.30158e11 q^{88} -4.76895e11i q^{89} +1.32953e11 q^{91} +5.54847e11i q^{92} +8.62468e10 q^{94} -3.29564e10i q^{95} -7.77042e10 q^{97} +3.32278e11i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24576 q^{4} - 220224 q^{7} + 379008 q^{10} - 2372808 q^{13} + 50331648 q^{16} + 142669680 q^{19} + 70253568 q^{22} - 727623852 q^{25} + 451018752 q^{28} + 577374720 q^{31} + 2238076800 q^{34} - 3028165356 q^{37}+ \cdots - 2570481096384 q^{97}+O(q^{100}) \) 12 * q - 24576 * q^4 - 220224 * q^7 + 379008 * q^10 - 2372808 * q^13 + 50331648 * q^16 + 142669680 * q^19 + 70253568 * q^22 - 727623852 * q^25 + 451018752 * q^28 + 577374720 * q^31 + 2238076800 * q^34 - 3028165356 * q^37 - 776208384 * q^40 + 33702957168 * q^43 - 24923220480 * q^46 + 72166762836 * q^49 + 4859510784 * q^52 - 158201222256 * q^55 - 21247000704 * q^58 + 213044029980 * q^61 - 103079215104 * q^64 + 70227468528 * q^67 - 251325402624 * q^70 + 49653231360 * q^73 - 292187504640 * q^76 - 696725200560 * q^79 + 735561633024 * q^82 - 271807264548 * q^85 - 143879307264 * q^88 + 729235216704 * q^91 + 1211537346048 * q^94 - 2570481096384 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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