LMFDB - Embedded newform 27.11.b.b.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,11,Mod(26,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("27.26");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	27.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.1546458222$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.2
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.11.b.b.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+51.9615i q^{2} -1676.00 q^{4} -831.384i q^{5} -16093.0 q^{7} -33878.9i q^{8} +43200.0 q^{10} -293479. i q^{11} +608639. q^{13} -836217. i q^{14} +44176.0 q^{16} -17459.1i q^{17} -2.10455e6 q^{19} +1.39340e6i q^{20} +1.52496e7 q^{22} +4.58342e6i q^{23} +9.07442e6 q^{25} +3.16258e7i q^{26} +2.69719e7 q^{28} -3.14679e7i q^{29} -2.60141e7 q^{31} -3.23966e7i q^{32} +907200. q^{34} +1.33795e7i q^{35} +5.19466e7 q^{37} -1.09356e8i q^{38} -2.81664e7 q^{40} -1.79637e8i q^{41} -7.19650e7 q^{43} +4.91870e8i q^{44} -2.38162e8 q^{46} -1.49783e8i q^{47} -2.34906e7 q^{49} +4.71521e8i q^{50} -1.02008e9 q^{52} -1.05218e8i q^{53} -2.43994e8 q^{55} +5.45213e8i q^{56} +1.63512e9 q^{58} -6.06334e8i q^{59} -3.56794e8 q^{61} -1.35173e9i q^{62} +1.72861e9 q^{64} -5.06013e8i q^{65} -5.91549e8 q^{67} +2.92614e7i q^{68} -6.95218e8 q^{70} -3.09009e9i q^{71} +4.13274e8 q^{73} +2.69922e9i q^{74} +3.52722e9 q^{76} +4.72295e9i q^{77} -1.08052e9 q^{79} -3.67272e7i q^{80} +9.33422e9 q^{82} +5.70129e9i q^{83} -1.45152e7 q^{85} -3.73941e9i q^{86} -9.94274e9 q^{88} +2.84786e9i q^{89} -9.79483e9 q^{91} -7.68182e9i q^{92} +7.78296e9 q^{94} +1.74969e9i q^{95} -1.36942e10 q^{97} -1.22061e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3352 q^{4} - 32186 q^{7} + 86400 q^{10} + 1217278 q^{13} + 88352 q^{16} - 4209098 q^{19} + 30499200 q^{22} + 18148850 q^{25} + 53943736 q^{28} - 52028252 q^{31} + 1814400 q^{34} + 103893214 q^{37}+ \cdots - 27388355186 q^{97}+O(q^{100}) $ 2 * q - 3352 * q^4 - 32186 * q^7 + 86400 * q^10 + 1217278 * q^13 + 88352 * q^16 - 4209098 * q^19 + 30499200 * q^22 + 18148850 * q^25 + 53943736 * q^28 - 52028252 * q^31 + 1814400 * q^34 + 103893214 * q^37 - 56332800 * q^40 - 143929964 * q^43 - 476323200 * q^46 - 46981200 * q^49 - 2040157928 * q^52 - 487987200 * q^55 + 3270240000 * q^58 - 713588402 * q^61 + 3457221248 * q^64 - 1183097978 * q^67 - 1390435200 * q^70 + 826548286 * q^73 + 7054448248 * q^76 - 2161039898 * q^79 + 18668448000 * q^82 - 29030400 * q^85 - 19885478400 * q^88 - 19589654854 * q^91 + 15565910400 * q^94 - 27388355186 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	51.9615i	1.62380i	0.583798	+	0.811899i	$0.301566\pi$
$2$	51.9615i	1.62380i	−0.583798	+	0.811899i	$0.698434\pi$
$3$	0	0
$3$	0	0
$4$	−1676.00	−1.63672
$5$	− 831.384i	− 0.266043i	−0.991113	−	0.133022i	$-0.957532\pi$
$5$	− 831.384i	− 0.266043i	0.991113	−	0.133022i	$-0.0424679\pi$
$6$	0	0
$7$	−16093.0	−0.957518	−0.478759	−	0.877946i	$-0.658913\pi$
$7$	−16093.0	−0.957518	−0.478759	+	0.877946i	$0.658913\pi$
$8$	− 33878.9i	− 1.03390i
$9$	0	0
$10$	43200.0	0.432000
$11$	− 293479.i	− 1.82227i	−0.412106	−	0.911136i	$-0.635207\pi$
$11$	− 293479.i	− 1.82227i	0.412106	−	0.911136i	$-0.364793\pi$
$12$	0	0
$13$	608639.	1.63924	0.819621	−	0.572906i	$-0.194184\pi$
$13$	608639.	1.63924	0.819621	+	0.572906i	$0.194184\pi$
$14$	− 836217.i	− 1.55481i
$15$	0	0
$16$	44176.0	0.0421295
$17$	− 17459.1i	− 0.0122964i	−0.999981	−	0.00614818i	$-0.998043\pi$
$17$	− 17459.1i	− 0.0122964i	0.999981	−	0.00614818i	$-0.00195704\pi$
$18$	0	0
$19$	−2.10455e6	−0.849945	−0.424973	−	0.905206i	$-0.639716\pi$
$19$	−2.10455e6	−0.849945	−0.424973	+	0.905206i	$0.639716\pi$
$20$	1.39340e6i	0.435438i
$21$	0	0
$22$	1.52496e7	2.95900
$23$	4.58342e6i	0.712116i	0.934464	+	0.356058i	$0.115879\pi$
$23$	4.58342e6i	0.712116i	−0.934464	+	0.356058i	$0.884121\pi$
$24$	0	0
$25$	9.07442e6	0.929221
$26$	3.16258e7i	2.66180i
$27$	0	0
$28$	2.69719e7	1.56719
$29$	− 3.14679e7i	− 1.53419i	−0.641536	−	0.767093i	$-0.721703\pi$
$29$	− 3.14679e7i	− 1.53419i	0.641536	−	0.767093i	$-0.278297\pi$
$30$	0	0
$31$	−2.60141e7	−0.908659	−0.454329	−	0.890834i	$-0.650121\pi$
$31$	−2.60141e7	−0.908659	−0.454329	+	0.890834i	$0.650121\pi$
$32$	− 3.23966e7i	− 0.965493i
$33$	0	0
$34$	907200.	0.0199668
$35$	1.33795e7i	0.254741i
$36$	0	0
$37$	5.19466e7	0.749115	0.374558	−	0.927204i	$-0.377795\pi$
$37$	5.19466e7	0.749115	0.374558	+	0.927204i	$0.377795\pi$
$38$	− 1.09356e8i	− 1.38014i
$39$	0	0
$40$	−2.81664e7	−0.275062
$41$	− 1.79637e8i	− 1.55052i	−0.631643	−	0.775259i	$-0.717619\pi$
$41$	− 1.79637e8i	− 1.55052i	0.631643	−	0.775259i	$-0.282381\pi$
$42$	0	0
$43$	−7.19650e7	−0.489530	−0.244765	−	0.969582i	$-0.578711\pi$
$43$	−7.19650e7	−0.489530	−0.244765	+	0.969582i	$0.578711\pi$
$44$	4.91870e8i	2.98255i
$45$	0	0
$46$	−2.38162e8	−1.15633
$47$	− 1.49783e8i	− 0.653090i	−0.945182	−	0.326545i	$-0.894115\pi$
$47$	− 1.49783e8i	− 0.653090i	0.945182	−	0.326545i	$-0.105885\pi$
$48$	0	0
$49$	−2.34906e7	−0.0831599
$50$	4.71521e8i	1.50887i
$51$	0	0
$52$	−1.02008e9	−2.68298
$53$	− 1.05218e8i	− 0.251601i	−0.992056	−	0.125800i	$-0.959850\pi$
$53$	− 1.05218e8i	− 0.251601i	0.992056	−	0.125800i	$-0.0401499\pi$
$54$	0	0
$55$	−2.43994e8	−0.484803
$56$	5.45213e8i	0.989980i
$57$	0	0
$58$	1.63512e9	2.49121
$59$	− 6.06334e8i	− 0.848110i	−0.905636	−	0.424055i	$-0.860606\pi$
$59$	− 6.06334e8i	− 0.848110i	0.905636	−	0.424055i	$-0.139394\pi$
$60$	0	0
$61$	−3.56794e8	−0.422443	−0.211222	−	0.977438i	$-0.567744\pi$
$61$	−3.56794e8	−0.422443	−0.211222	+	0.977438i	$0.567744\pi$
$62$	− 1.35173e9i	− 1.47548i
$63$	0	0
$64$	1.72861e9	1.60989
$65$	− 5.06013e8i	− 0.436109i
$66$	0	0
$67$	−5.91549e8	−0.438144	−0.219072	−	0.975709i	$-0.570303\pi$
$67$	−5.91549e8	−0.438144	−0.219072	+	0.975709i	$0.570303\pi$
$68$	2.92614e7i	0.0201257i
$69$	0	0
$70$	−6.95218e8	−0.413648
$71$	− 3.09009e9i	− 1.71269i	−0.516404	−	0.856345i	$-0.672730\pi$
$71$	− 3.09009e9i	− 1.71269i	0.516404	−	0.856345i	$-0.327270\pi$
$72$	0	0
$73$	4.13274e8	0.199354	0.0996768	−	0.995020i	$-0.468219\pi$
$73$	4.13274e8	0.199354	0.0996768	+	0.995020i	$0.468219\pi$
$74$	2.69922e9i	1.21641i
$75$	0	0
$76$	3.52722e9	1.39112
$77$	4.72295e9i	1.74486i
$78$	0	0
$79$	−1.08052e9	−0.351154	−0.175577	−	0.984466i	$-0.556179\pi$
$79$	−1.08052e9	−0.351154	−0.175577	+	0.984466i	$0.556179\pi$
$80$	− 3.67272e7i	− 0.0112083i
$81$	0	0
$82$	9.33422e9	2.51773
$83$	5.70129e9i	1.44738i	0.690125	+	0.723691i	$0.257556\pi$
$83$	5.70129e9i	1.44738i	−0.690125	+	0.723691i	$0.742444\pi$
$84$	0	0
$85$	−1.45152e7	−0.00327136
$86$	− 3.73941e9i	− 0.794897i
$87$	0	0
$88$	−9.94274e9	−1.88405
$89$	2.84786e9i	0.509998i	0.966941	+	0.254999i	$0.0820751\pi$
$89$	2.84786e9i	0.509998i	−0.966941	+	0.254999i	$0.917925\pi$
$90$	0	0
$91$	−9.79483e9	−1.56960
$92$	− 7.68182e9i	− 1.16553i
$93$	0	0
$94$	7.78296e9	1.06049
$95$	1.74969e9i	0.226122i
$96$	0	0
$97$	−1.36942e10	−1.59469	−0.797347	−	0.603521i	$-0.793764\pi$
$97$	−1.36942e10	−1.59469	−0.797347	+	0.603521i	$0.793764\pi$
$98$	− 1.22061e9i	− 0.135035i
$99$	0	0
$100$	−1.52087e10	−1.52087
$101$	− 1.23670e10i	− 1.17667i	−0.808616	−	0.588337i	$-0.799783\pi$
$101$	− 1.23670e10i	− 1.17667i	0.808616	−	0.588337i	$-0.200217\pi$
$102$	0	0
$103$	2.71632e9	0.234312	0.117156	−	0.993114i	$-0.462622\pi$
$103$	2.71632e9	0.234312	0.117156	+	0.993114i	$0.462622\pi$
$104$	− 2.06200e10i	− 1.69482i
$105$	0	0
$106$	5.46731e9	0.408549
$107$	1.23713e10i	0.882056i	0.897493	+	0.441028i	$0.145386\pi$
$107$	1.23713e10i	0.882056i	−0.897493	+	0.441028i	$0.854614\pi$
$108$	0	0
$109$	5.78399e9	0.375920	0.187960	−	0.982177i	$-0.439813\pi$
$109$	5.78399e9	0.375920	0.187960	+	0.982177i	$0.439813\pi$
$110$	− 1.26783e10i	− 0.787221i
$111$	0	0
$112$	−7.10924e8	−0.0403398
$113$	2.13143e10i	1.15685i	0.815735	+	0.578426i	$0.196333\pi$
$113$	2.13143e10i	1.15685i	−0.815735	+	0.578426i	$0.803667\pi$
$114$	0	0
$115$	3.81059e9	0.189453
$116$	5.27402e10i	2.51103i
$117$	0	0
$118$	3.15061e10	1.37716
$119$	2.80969e8i	0.0117740i
$120$	0	0
$121$	−6.01923e10	−2.32067
$122$	− 1.85396e10i	− 0.685963i
$123$	0	0
$124$	4.35997e10	1.48722
$125$	− 1.56633e10i	− 0.513256i
$126$	0	0
$127$	1.59955e9	0.0484148	0.0242074	−	0.999707i	$-0.492294\pi$
$127$	1.59955e9	0.0484148	0.0242074	+	0.999707i	$0.492294\pi$
$128$	5.66472e10i	1.64865i
$129$	0	0
$130$	2.62932e10	0.708152
$131$	1.75475e10i	0.454840i	0.973797	+	0.227420i	$0.0730290\pi$
$131$	1.75475e10i	0.454840i	−0.973797	+	0.227420i	$0.926971\pi$
$132$	0	0
$133$	3.38685e10	0.813838
$134$	− 3.07378e10i	− 0.711457i
$135$	0	0
$136$	−5.91494e8	−0.0127132
$137$	− 5.41009e10i	− 1.12099i	−0.828158	−	0.560495i	$-0.810611\pi$
$137$	− 5.41009e10i	− 1.12099i	0.828158	−	0.560495i	$-0.189389\pi$
$138$	0	0
$139$	2.58062e10	0.497336	0.248668	−	0.968589i	$-0.420007\pi$
$139$	2.58062e10	0.497336	0.248668	+	0.968589i	$0.420007\pi$
$140$	− 2.24240e10i	− 0.416939i
$141$	0	0
$142$	1.60566e11	2.78106
$143$	− 1.78623e11i	− 2.98714i
$144$	0	0
$145$	−2.61619e10	−0.408159
$146$	2.14744e10i	0.323710i
$147$	0	0
$148$	−8.70625e10	−1.22609
$149$	8.88933e10i	1.21042i	0.796064	+	0.605212i	$0.206912\pi$
$149$	8.88933e10i	1.21042i	−0.796064	+	0.605212i	$0.793088\pi$
$150$	0	0
$151$	−1.51414e11	−1.92878	−0.964389	−	0.264487i	$-0.914797\pi$
$151$	−1.51414e11	−1.92878	−0.964389	+	0.264487i	$0.914797\pi$
$152$	7.12998e10i	0.878761i
$153$	0	0
$154$	−2.45412e11	−2.83330
$155$	2.16277e10i	0.241742i
$156$	0	0
$157$	1.15944e11	1.21549	0.607745	−	0.794132i	$-0.292074\pi$
$157$	1.15944e11	1.21549	0.607745	+	0.794132i	$0.292074\pi$
$158$	− 5.61455e10i	− 0.570203i
$159$	0	0
$160$	−2.69340e10	−0.256863
$161$	− 7.37610e10i	− 0.681864i
$162$	0	0
$163$	9.85876e10	0.856809	0.428405	−	0.903587i	$-0.359076\pi$
$163$	9.85876e10	0.856809	0.428405	+	0.903587i	$0.359076\pi$
$164$	3.01072e11i	2.53776i
$165$	0	0
$166$	−2.96248e11	−2.35025
$167$	1.03461e11i	0.796518i	0.917273	+	0.398259i	$0.130386\pi$
$167$	1.03461e11i	0.796518i	−0.917273	+	0.398259i	$0.869614\pi$
$168$	0	0
$169$	2.32583e11	1.68711
$170$	− 7.54232e8i	− 0.00531203i
$171$	0	0
$172$	1.20613e11	0.801222
$173$	− 5.90424e10i	− 0.381008i	−0.981686	−	0.190504i	$-0.938988\pi$
$173$	− 5.90424e10i	− 0.381008i	0.981686	−	0.190504i	$-0.0610122\pi$
$174$	0	0
$175$	−1.46035e11	−0.889746
$176$	− 1.29647e10i	− 0.0767714i
$177$	0	0
$178$	−1.47979e11	−0.828133
$179$	2.18650e11i	1.18983i	0.803790	+	0.594913i	$0.202813\pi$
$179$	2.18650e11i	1.18983i	−0.803790	+	0.594913i	$0.797187\pi$
$180$	0	0
$181$	−8.39160e9	−0.0431968	−0.0215984	−	0.999767i	$-0.506876\pi$
$181$	−8.39160e9	−0.0431968	−0.0215984	+	0.999767i	$0.506876\pi$
$182$	− 5.08954e11i	− 2.54872i
$183$	0	0
$184$	1.55281e11	0.736258
$185$	− 4.31876e10i	− 0.199297i
$186$	0	0
$187$	−5.12387e9	−0.0224073
$188$	2.51036e11i	1.06893i
$189$	0	0
$190$	−9.09165e10	−0.367176
$191$	− 1.44581e11i	− 0.568780i	−0.958709	−	0.284390i	$-0.908209\pi$
$191$	− 1.44581e11i	− 0.568780i	0.958709	−	0.284390i	$-0.0917911\pi$
$192$	0	0
$193$	3.99338e10	0.149126	0.0745631	−	0.997216i	$-0.476244\pi$
$193$	3.99338e10	0.149126	0.0745631	+	0.997216i	$0.476244\pi$
$194$	− 7.11570e11i	− 2.58946i
$195$	0	0
$196$	3.93702e10	0.136109
$197$	2.03053e9i	0.00684351i	0.999994	+	0.00342175i	$0.00108918\pi$
$197$	2.03053e9i	0.00684351i	−0.999994	+	0.00342175i	$0.998911\pi$
$198$	0	0
$199$	4.87714e11	1.56279	0.781394	−	0.624038i	$-0.214509\pi$
$199$	4.87714e11	1.56279	0.781394	+	0.624038i	$0.214509\pi$
$200$	− 3.07432e11i	− 0.960724i
$201$	0	0
$202$	6.42606e11	1.91068
$203$	5.06413e11i	1.46901i
$204$	0	0
$205$	−1.49348e11	−0.412505
$206$	1.41144e11i	0.380475i
$207$	0	0
$208$	2.68872e10	0.0690605
$209$	6.17640e11i	1.54883i
$210$	0	0
$211$	5.65646e11	1.35248	0.676242	−	0.736679i	$-0.263607\pi$
$211$	5.65646e11	1.35248	0.676242	+	0.736679i	$0.263607\pi$
$212$	1.76346e11i	0.411800i
$213$	0	0
$214$	−6.42831e11	−1.43228
$215$	5.98306e10i	0.130236i
$216$	0	0
$217$	4.18645e11	0.870057
$218$	3.00545e11i	0.610418i
$219$	0	0
$220$	4.08933e11	0.793486
$221$	− 1.06263e10i	− 0.0201567i
$222$	0	0
$223$	−5.10500e11	−0.925703	−0.462852	−	0.886436i	$-0.653174\pi$
$223$	−5.10500e11	−0.925703	−0.462852	+	0.886436i	$0.653174\pi$
$224$	5.21358e11i	0.924476i
$225$	0	0
$226$	−1.10752e12	−1.87849
$227$	− 7.40075e11i	− 1.22785i	−0.789363	−	0.613927i	$-0.789589\pi$
$227$	− 7.40075e11i	− 1.22785i	0.789363	−	0.613927i	$-0.210411\pi$
$228$	0	0
$229$	−4.13154e11	−0.656047	−0.328023	−	0.944670i	$-0.606382\pi$
$229$	−4.13154e11	−0.656047	−0.328023	+	0.944670i	$0.606382\pi$
$230$	1.98004e11i	0.307634i
$231$	0	0
$232$	−1.06610e12	−1.58620
$233$	− 6.00400e10i	− 0.0874301i	−0.999044	−	0.0437150i	$-0.986081\pi$
$233$	− 6.00400e10i	− 0.0874301i	0.999044	−	0.0437150i	$-0.0139194\pi$
$234$	0	0
$235$	−1.24527e11	−0.173750
$236$	1.01622e12i	1.38812i
$237$	0	0
$238$	−1.45996e10	−0.0191186
$239$	− 3.72788e11i	− 0.478049i	−0.971014	−	0.239024i	$-0.923172\pi$
$239$	− 3.72788e11i	− 0.478049i	0.971014	−	0.239024i	$-0.0768276\pi$
$240$	0	0
$241$	5.07345e11	0.624049	0.312024	−	0.950074i	$-0.398993\pi$
$241$	5.07345e11	0.624049	0.312024	+	0.950074i	$0.398993\pi$
$242$	− 3.12768e12i	− 3.76831i
$243$	0	0
$244$	5.97987e11	0.691421
$245$	1.95297e10i	0.0221241i
$246$	0	0
$247$	−1.28091e12	−1.39327
$248$	8.81330e11i	0.939464i
$249$	0	0
$250$	8.13890e11	0.833424
$251$	− 1.29052e12i	− 1.29538i	−0.761905	−	0.647689i	$-0.775736\pi$
$251$	− 1.29052e12i	− 1.29538i	0.761905	−	0.647689i	$-0.224264\pi$
$252$	0	0
$253$	1.34514e12	1.29767
$254$	8.31149e10i	0.0786159i
$255$	0	0
$256$	−1.17338e12	−1.06718
$257$	− 1.10308e12i	− 0.983876i	−0.870630	−	0.491938i	$-0.836289\pi$
$257$	− 1.10308e12i	− 0.983876i	0.870630	−	0.491938i	$-0.163711\pi$
$258$	0	0
$259$	−8.35977e11	−0.717291
$260$	8.48078e11i	0.713787i
$261$	0	0
$262$	−9.11794e11	−0.738568
$263$	1.32992e12i	1.05693i	0.848955	+	0.528466i	$0.177232\pi$
$263$	1.32992e12i	1.05693i	−0.848955	+	0.528466i	$0.822768\pi$
$264$	0	0
$265$	−8.74769e10	−0.0669366
$266$	1.75986e12i	1.32151i
$267$	0	0
$268$	9.91436e11	0.717118
$269$	1.38777e12i	0.985275i	0.870235	+	0.492638i	$0.163967\pi$
$269$	1.38777e12i	0.985275i	−0.870235	+	0.492638i	$0.836033\pi$
$270$	0	0
$271$	−1.14179e12	−0.781159	−0.390579	−	0.920569i	$-0.627725\pi$
$271$	−1.14179e12	−0.781159	−0.390579	+	0.920569i	$0.627725\pi$
$272$	− 7.71272e8i	0 0.000518040i
$273$	0	0
$274$	2.81116e12	1.82026
$275$	− 2.66315e12i	− 1.69329i
$276$	0	0
$277$	−2.29508e12	−1.40734	−0.703670	−	0.710527i	$-0.748457\pi$
$277$	−2.29508e12	−1.40734	−0.703670	+	0.710527i	$0.748457\pi$
$278$	1.34093e12i	0.807574i
$279$	0	0
$280$	4.53282e11	0.263377
$281$	− 1.85770e12i	− 1.06034i	−0.847893	−	0.530168i	$-0.822129\pi$
$281$	− 1.85770e12i	− 1.06034i	0.847893	−	0.530168i	$-0.177871\pi$
$282$	0	0
$283$	3.74722e11	0.206432	0.103216	−	0.994659i	$-0.467087\pi$
$283$	3.74722e11	0.206432	0.103216	+	0.994659i	$0.467087\pi$
$284$	5.17898e12i	2.80319i
$285$	0	0
$286$	9.28150e12	4.85052
$287$	2.89090e12i	1.48465i
$288$	0	0
$289$	2.01569e12	0.999849
$290$	− 1.35941e12i	− 0.662768i
$291$	0	0
$292$	−6.92647e11	−0.326286
$293$	− 1.36489e12i	− 0.632062i	−0.948749	−	0.316031i	$-0.897650\pi$
$293$	− 1.36489e12i	− 0.632062i	0.948749	−	0.316031i	$-0.102350\pi$
$294$	0	0
$295$	−5.04097e11	−0.225634
$296$	− 1.75989e12i	− 0.774512i
$297$	0	0
$298$	−4.61903e12	−1.96548
$299$	2.78965e12i	1.16733i
$300$	0	0
$301$	1.15813e12	0.468733
$302$	− 7.86772e12i	− 3.13195i
$303$	0	0
$304$	−9.29706e10	−0.0358078
$305$	2.96633e11i	0.112388i
$306$	0	0
$307$	−1.96662e12	−0.721153	−0.360577	−	0.932730i	$-0.617420\pi$
$307$	−1.96662e12	−0.721153	−0.360577	+	0.932730i	$0.617420\pi$
$308$	− 7.91567e12i	− 2.85584i
$309$	0	0
$310$	−1.12381e12	−0.392541
$311$	5.77004e11i	0.198325i	0.995071	+	0.0991624i	$0.0316163\pi$
$311$	5.77004e11i	0.198325i	−0.995071	+	0.0991624i	$0.968384\pi$
$312$	0	0
$313$	−1.55124e12	−0.516366	−0.258183	−	0.966096i	$-0.583124\pi$
$313$	−1.55124e12	−0.516366	−0.258183	+	0.966096i	$0.583124\pi$
$314$	6.02465e12i	1.97371i
$315$	0	0
$316$	1.81095e12	0.574740
$317$	− 1.30028e12i	− 0.406201i	−0.979158	−	0.203100i	$-0.934898\pi$
$317$	− 1.30028e12i	− 0.406201i	0.979158	−	0.203100i	$-0.0651017\pi$
$318$	0	0
$319$	−9.23516e12	−2.79570
$320$	− 1.43714e12i	− 0.428301i
$321$	0	0
$322$	3.83273e12	1.10721
$323$	3.67435e10i	0.0104512i
$324$	0	0
$325$	5.52305e12	1.52322
$326$	5.12276e12i	1.39128i
$327$	0	0
$328$	−6.08591e12	−1.60309
$329$	2.41046e12i	0.625346i
$330$	0	0
$331$	−3.14492e12	−0.791533	−0.395767	−	0.918351i	$-0.629521\pi$
$331$	−3.14492e12	−0.791533	−0.395767	+	0.918351i	$0.629521\pi$
$332$	− 9.55537e12i	− 2.36896i
$333$	0	0
$334$	−5.37601e12	−1.29338
$335$	4.91805e11i	0.116565i
$336$	0	0
$337$	3.16283e12	0.727657	0.363828	−	0.931466i	$-0.381469\pi$
$337$	3.16283e12	0.727657	0.363828	+	0.931466i	$0.381469\pi$
$338$	1.20854e13i	2.73953i
$339$	0	0
$340$	2.43275e10	0.00535430
$341$	7.63459e12i	1.65582i
$342$	0	0
$343$	4.92391e12	1.03714
$344$	2.43810e12i	0.506126i
$345$	0	0
$346$	3.06794e12	0.618679
$347$	− 1.57357e12i	− 0.312781i	−0.987695	−	0.156390i	$-0.950014\pi$
$347$	− 1.57357e12i	− 0.312781i	0.987695	−	0.156390i	$-0.0499858\pi$
$348$	0	0
$349$	3.57543e12	0.690559	0.345279	−	0.938500i	$-0.387784\pi$
$349$	3.57543e12	0.690559	0.345279	+	0.938500i	$0.387784\pi$
$350$	− 7.58819e12i	− 1.44477i
$351$	0	0
$352$	−9.50770e12	−1.75939
$353$	8.03200e12i	1.46538i	0.680562	+	0.732690i	$0.261736\pi$
$353$	8.03200e12i	1.46538i	−0.680562	+	0.732690i	$0.738264\pi$
$354$	0	0
$355$	−2.56905e12	−0.455649
$356$	− 4.77301e12i	− 0.834723i
$357$	0	0
$358$	−1.13614e13	−1.93204
$359$	− 3.65454e12i	− 0.612859i	−0.951893	−	0.306430i	$-0.900866\pi$
$359$	− 3.65454e12i	− 0.612859i	0.951893	−	0.306430i	$-0.0991344\pi$
$360$	0	0
$361$	−1.70194e12	−0.277593
$362$	− 4.36040e11i	− 0.0701429i
$363$	0	0
$364$	1.64161e13	2.56900
$365$	− 3.43590e11i	− 0.0530366i
$366$	0	0
$367$	−1.70763e12	−0.256487	−0.128243	−	0.991743i	$-0.540934\pi$
$367$	−1.70763e12	−0.256487	−0.128243	+	0.991743i	$0.540934\pi$
$368$	2.02477e11i	0.0300011i
$369$	0	0
$370$	2.24409e12	0.323618
$371$	1.69328e12i	0.240912i
$372$	0	0
$373$	8.49123e12	1.17605	0.588026	−	0.808842i	$-0.299905\pi$
$373$	8.49123e12	1.17605	0.588026	+	0.808842i	$0.299905\pi$
$374$	− 2.66244e11i	− 0.0363849i
$375$	0	0
$376$	−5.07449e12	−0.675232
$377$	− 1.91526e13i	− 2.51490i
$378$	0	0
$379$	3.92340e12	0.501726	0.250863	−	0.968023i	$-0.419286\pi$
$379$	3.92340e12	0.501726	0.250863	+	0.968023i	$0.419286\pi$
$380$	− 2.93248e12i	− 0.370098i
$381$	0	0
$382$	7.51265e12	0.923584
$383$	− 3.50870e12i	− 0.425748i	−0.977080	−	0.212874i	$-0.931718\pi$
$383$	− 3.50870e12i	− 0.425748i	0.977080	−	0.212874i	$-0.0682823\pi$
$384$	0	0
$385$	3.92659e12	0.464207
$386$	2.07502e12i	0.242151i
$387$	0	0
$388$	2.29514e13	2.61007
$389$	− 1.28204e13i	− 1.43931i	−0.694334	−	0.719653i	$-0.744301\pi$
$389$	− 1.28204e13i	− 1.43931i	0.694334	−	0.719653i	$-0.255699\pi$
$390$	0	0
$391$	8.00223e10	0.00875643
$392$	7.95836e11i	0.0859792i
$393$	0	0
$394$	−1.05510e11	−0.0111125
$395$	8.98327e11i	0.0934220i
$396$	0	0
$397$	9.98220e12	1.01222	0.506108	−	0.862470i	$-0.331084\pi$
$397$	9.98220e12	1.01222	0.506108	+	0.862470i	$0.331084\pi$
$398$	2.53424e13i	2.53765i
$399$	0	0
$400$	4.00872e11	0.0391476
$401$	6.13719e12i	0.591900i	0.955204	+	0.295950i	$0.0956361\pi$
$401$	6.13719e12i	0.591900i	−0.955204	+	0.295950i	$0.904364\pi$
$402$	0	0
$403$	−1.58332e13	−1.48951
$404$	2.07270e13i	1.92588i
$405$	0	0
$406$	−2.63140e13	−2.38537
$407$	− 1.52452e13i	− 1.36509i
$408$	0	0
$409$	2.93317e12	0.256283	0.128142	−	0.991756i	$-0.459099\pi$
$409$	2.93317e12	0.256283	0.128142	+	0.991756i	$0.459099\pi$
$410$	− 7.76033e12i	− 0.669824i
$411$	0	0
$412$	−4.55255e12	−0.383503
$413$	9.75774e12i	0.812080i
$414$	0	0
$415$	4.73997e12	0.385066
$416$	− 1.97178e13i	− 1.58268i
$417$	0	0
$418$	−3.20935e13	−2.51499
$419$	2.51641e13i	1.94855i	0.225371	+	0.974273i	$0.427640\pi$
$419$	2.51641e13i	1.94855i	−0.225371	+	0.974273i	$0.572360\pi$
$420$	0	0
$421$	6.35524e12	0.480531	0.240266	−	0.970707i	$-0.422765\pi$
$421$	6.35524e12	0.480531	0.240266	+	0.970707i	$0.422765\pi$
$422$	2.93918e13i	2.19616i
$423$	0	0
$424$	−3.56468e12	−0.260131
$425$	− 1.58431e11i	− 0.0114260i
$426$	0	0
$427$	5.74189e12	0.404497
$428$	− 2.07343e13i	− 1.44368i
$429$	0	0
$430$	−3.10889e12	−0.211477
$431$	− 6.51142e12i	− 0.437814i	−0.975746	−	0.218907i	$-0.929751\pi$
$431$	− 6.51142e12i	− 0.437814i	0.975746	−	0.218907i	$-0.0702491\pi$
$432$	0	0
$433$	1.82238e13	1.19729	0.598646	−	0.801014i	$-0.295706\pi$
$433$	1.82238e13	1.19729	0.598646	+	0.801014i	$0.295706\pi$
$434$	2.17534e13i	1.41280i
$435$	0	0
$436$	−9.69397e12	−0.615275
$437$	− 9.64604e12i	− 0.605260i
$438$	0	0
$439$	7.24114e12	0.444103	0.222052	−	0.975035i	$-0.428725\pi$
$439$	7.24114e12	0.444103	0.222052	+	0.975035i	$0.428725\pi$
$440$	8.26624e12i	0.501239i
$441$	0	0
$442$	5.52157e11	0.0327304
$443$	− 1.61604e13i	− 0.947185i	−0.880744	−	0.473592i	$-0.842957\pi$
$443$	− 1.61604e13i	− 0.947185i	0.880744	−	0.473592i	$-0.157043\pi$
$444$	0	0
$445$	2.36766e12	0.135681
$446$	− 2.65264e13i	− 1.50315i
$447$	0	0
$448$	−2.78185e13	−1.54150
$449$	− 1.89232e13i	− 1.03696i	−0.855088	−	0.518482i	$-0.826497\pi$
$449$	− 1.89232e13i	− 1.03696i	0.855088	−	0.518482i	$-0.173503\pi$
$450$	0	0
$451$	−5.27197e13	−2.82547
$452$	− 3.57227e13i	− 1.89344i
$453$	0	0
$454$	3.84554e13	1.99379
$455$	8.14327e12i	0.417582i
$456$	0	0
$457$	2.27666e13	1.14214	0.571068	−	0.820903i	$-0.306529\pi$
$457$	2.27666e13	1.14214	0.571068	+	0.820903i	$0.306529\pi$
$458$	− 2.14681e13i	− 1.06529i
$459$	0	0
$460$	−6.38654e12	−0.310082
$461$	2.54886e13i	1.22417i	0.790793	+	0.612084i	$0.209669\pi$
$461$	2.54886e13i	1.22417i	−0.790793	+	0.612084i	$0.790331\pi$
$462$	0	0
$463$	−2.89243e13	−1.35943	−0.679716	−	0.733475i	$-0.737897\pi$
$463$	−2.89243e13	−1.35943	−0.679716	+	0.733475i	$0.737897\pi$
$464$	− 1.39013e12i	− 0.0646345i
$465$	0	0
$466$	3.11977e12	0.141969
$467$	1.23497e13i	0.555996i	0.960582	+	0.277998i	$0.0896708\pi$
$467$	1.23497e13i	0.555996i	−0.960582	+	0.277998i	$0.910329\pi$
$468$	0	0
$469$	9.51980e12	0.419530
$470$	− 6.47063e12i	− 0.282135i
$471$	0	0
$472$	−2.05420e13	−0.876863
$473$	2.11202e13i	0.892056i
$474$	0	0
$475$	−1.90976e13	−0.789787
$476$	− 4.70904e11i	− 0.0192707i
$477$	0	0
$478$	1.93706e13	0.776254
$479$	8.53563e12i	0.338499i	0.985573	+	0.169250i	$0.0541344\pi$
$479$	8.53563e12i	0.338499i	−0.985573	+	0.169250i	$0.945866\pi$
$480$	0	0
$481$	3.16167e13	1.22798
$482$	2.63624e13i	1.01333i
$483$	0	0
$484$	1.00882e14	3.79829
$485$	1.13851e13i	0.424257i
$486$	0	0
$487$	−2.84369e12	−0.103810	−0.0519048	−	0.998652i	$-0.516529\pi$
$487$	−2.84369e12	−0.103810	−0.0519048	+	0.998652i	$0.516529\pi$
$488$	1.20878e13i	0.436765i
$489$	0	0
$490$	−1.01479e12	−0.0359251
$491$	− 3.03433e12i	− 0.106330i	−0.998586	−	0.0531650i	$-0.983069\pi$
$491$	− 3.03433e12i	− 0.106330i	0.998586	−	0.0531650i	$-0.0169309\pi$
$492$	0	0
$493$	−5.49400e11	−0.0188649
$494$	− 6.65581e13i	− 2.26238i
$495$	0	0
$496$	−1.14920e12	−0.0382814
$497$	4.97288e13i	1.63993i
$498$	0	0
$499$	−1.92796e13	−0.623155	−0.311578	−	0.950221i	$-0.600857\pi$
$499$	−1.92796e13	−0.623155	−0.311578	+	0.950221i	$0.600857\pi$
$500$	2.62517e13i	0.840055i
$501$	0	0
$502$	6.70574e13	2.10343
$503$	− 7.96962e12i	− 0.247513i	−0.992313	−	0.123756i	$-0.960506\pi$
$503$	− 7.96962e12i	− 0.247513i	0.992313	−	0.123756i	$-0.0394942\pi$
$504$	0	0
$505$	−1.02817e13	−0.313046
$506$	6.98954e13i	2.10715i
$507$	0	0
$508$	−2.68084e12	−0.0792414
$509$	1.37925e13i	0.403695i	0.979417	+	0.201847i	$0.0646945\pi$
$509$	1.37925e13i	0.403695i	−0.979417	+	0.201847i	$0.935306\pi$
$510$	0	0
$511$	−6.65082e12	−0.190885
$512$	− 2.96370e12i	− 0.0842335i
$513$	0	0
$514$	5.73176e13	1.59761
$515$	− 2.25830e12i	− 0.0623370i
$516$	0	0
$517$	−4.39581e13	−1.19011
$518$	− 4.34386e13i	− 1.16474i
$519$	0	0
$520$	−1.71432e13	−0.450894
$521$	− 4.32531e13i	− 1.12675i	−0.826201	−	0.563376i	$-0.809502\pi$
$521$	− 4.32531e13i	− 1.12675i	0.826201	−	0.563376i	$-0.190498\pi$
$522$	0	0
$523$	4.88631e12	0.124874	0.0624371	−	0.998049i	$-0.480113\pi$
$523$	4.88631e12	0.124874	0.0624371	+	0.998049i	$0.480113\pi$
$524$	− 2.94096e13i	− 0.744445i
$525$	0	0
$526$	−6.91047e13	−1.71624
$527$	4.54183e11i	0.0111732i
$528$	0	0
$529$	2.04188e13	0.492891
$530$	− 4.54543e12i	− 0.108692i
$531$	0	0
$532$	−5.67636e13	−1.33202
$533$	− 1.09334e14i	− 2.54168i
$534$	0	0
$535$	1.02853e13	0.234665
$536$	2.00410e13i	0.452998i
$537$	0	0
$538$	−7.21109e13	−1.59989
$539$	6.89399e12i	0.151540i
$540$	0	0
$541$	−6.70080e13	−1.44591	−0.722953	−	0.690897i	$-0.757216\pi$
$541$	−6.70080e13	−1.44591	−0.722953	+	0.690897i	$0.757216\pi$
$542$	− 5.93291e13i	− 1.26844i
$543$	0	0
$544$	−5.65614e11	−0.0118720
$545$	− 4.80872e12i	− 0.100011i
$546$	0	0
$547$	−1.75593e11	−0.00358567	−0.00179284	−	0.999998i	$-0.500571\pi$
$547$	−1.75593e11	−0.00358567	−0.00179284	+	0.999998i	$0.500571\pi$
$548$	9.06730e13i	1.83474i
$549$	0	0
$550$	1.38381e14	2.74957
$551$	6.62257e13i	1.30397i
$552$	0	0
$553$	1.73888e13	0.336236
$554$	− 1.19256e14i	− 2.28523i
$555$	0	0
$556$	−4.32512e13	−0.814000
$557$	5.28769e13i	0.986256i	0.869957	+	0.493128i	$0.164147\pi$
$557$	5.28769e13i	0.986256i	−0.869957	+	0.493128i	$0.835853\pi$
$558$	0	0
$559$	−4.38007e13	−0.802457
$560$	5.91051e11i	0.0107321i
$561$	0	0
$562$	9.65288e13	1.72177
$563$	− 9.20469e13i	− 1.62730i	−0.581356	−	0.813650i	$-0.697478\pi$
$563$	− 9.20469e13i	− 1.62730i	0.581356	−	0.813650i	$-0.302522\pi$
$564$	0	0
$565$	1.77203e13	0.307773
$566$	1.94711e13i	0.335204i
$567$	0	0
$568$	−1.04689e14	−1.77075
$569$	− 6.27692e13i	− 1.05241i	−0.850357	−	0.526206i	$-0.823614\pi$
$569$	− 6.27692e13i	− 1.05241i	0.850357	−	0.526206i	$-0.176386\pi$
$570$	0	0
$571$	5.95299e13	0.980741	0.490371	−	0.871514i	$-0.336861\pi$
$571$	5.95299e13	0.980741	0.490371	+	0.871514i	$0.336861\pi$
$572$	2.99371e14i	4.88911i
$573$	0	0
$574$	−1.50216e14	−2.41077
$575$	4.15919e13i	0.661713i
$576$	0	0
$577$	−1.13204e14	−1.77003	−0.885016	−	0.465561i	$-0.845853\pi$
$577$	−1.13204e14	−1.77003	−0.885016	+	0.465561i	$0.845853\pi$
$578$	1.04738e14i	1.62355i
$579$	0	0
$580$	4.38474e13	0.668042
$581$	− 9.17509e13i	− 1.38589i
$582$	0	0
$583$	−3.08793e13	−0.458485
$584$	− 1.40013e13i	− 0.206112i
$585$	0	0
$586$	7.09218e13	1.02634
$587$	2.71880e13i	0.390110i	0.980792	+	0.195055i	$0.0624885\pi$
$587$	2.71880e13i	0.390110i	−0.980792	+	0.195055i	$0.937511\pi$
$588$	0	0
$589$	5.47480e13	0.772310
$590$	− 2.61936e13i	− 0.366384i
$591$	0	0
$592$	2.29479e12	0.0315599
$593$	9.56909e13i	1.30496i	0.757806	+	0.652480i	$0.226271\pi$
$593$	9.56909e13i	1.30496i	−0.757806	+	0.652480i	$0.773729\pi$
$594$	0	0
$595$	2.33593e11	0.00313239
$596$	− 1.48985e14i	− 1.98112i
$597$	0	0
$598$	−1.44954e14	−1.89551
$599$	− 6.04515e13i	− 0.783922i	−0.919982	−	0.391961i	$-0.871797\pi$
$599$	− 6.04515e13i	− 0.783922i	0.919982	−	0.391961i	$-0.128203\pi$
$600$	0	0
$601$	4.25151e13	0.542214	0.271107	−	0.962549i	$-0.412610\pi$
$601$	4.25151e13	0.542214	0.271107	+	0.962549i	$0.412610\pi$
$602$	6.01783e13i	0.761128i
$603$	0	0
$604$	2.53771e14	3.15687
$605$	5.00430e13i	0.617399i
$606$	0	0
$607$	−3.83936e13	−0.465924	−0.232962	−	0.972486i	$-0.574842\pi$
$607$	−3.83936e13	−0.465924	−0.232962	+	0.972486i	$0.574842\pi$
$608$	6.81801e13i	0.820616i
$609$	0	0
$610$	−1.54135e13	−0.182496
$611$	− 9.11638e13i	− 1.07057i
$612$	0	0
$613$	1.50166e14	1.73488	0.867439	−	0.497543i	$-0.165764\pi$
$613$	1.50166e14	1.73488	0.867439	+	0.497543i	$0.165764\pi$
$614$	− 1.02188e14i	− 1.17101i
$615$	0	0
$616$	1.60009e14	1.80401
$617$	− 4.36949e13i	− 0.488658i	−0.969692	−	0.244329i	$-0.921432\pi$
$617$	− 4.36949e13i	− 0.488658i	0.969692	−	0.244329i	$-0.0785677\pi$
$618$	0	0
$619$	1.31355e14	1.44541	0.722706	−	0.691155i	$-0.242898\pi$
$619$	1.31355e14	1.44541	0.722706	+	0.691155i	$0.242898\pi$
$620$	− 3.62481e13i	− 0.395664i
$621$	0	0
$622$	−2.99820e13	−0.322039
$623$	− 4.58306e13i	− 0.488332i
$624$	0	0
$625$	7.55952e13	0.792673
$626$	− 8.06049e13i	− 0.838474i
$627$	0	0
$628$	−1.94323e14	−1.98942
$629$	− 9.06940e11i	− 0.00921139i
$630$	0	0
$631$	3.88509e13	0.388377	0.194189	−	0.980964i	$-0.437793\pi$
$631$	3.88509e13	0.388377	0.194189	+	0.980964i	$0.437793\pi$
$632$	3.66068e13i	0.363059i
$633$	0	0
$634$	6.75645e13	0.659587
$635$	− 1.32984e12i	− 0.0128804i
$636$	0	0
$637$	−1.42973e13	−0.136319
$638$	− 4.79873e14i	− 4.53965i
$639$	0	0
$640$	4.70956e13	0.438612
$641$	1.40133e14i	1.29494i	0.762090	+	0.647471i	$0.224173\pi$
$641$	1.40133e14i	1.29494i	−0.762090	+	0.647471i	$0.775827\pi$
$642$	0	0
$643$	−1.41701e14	−1.28920	−0.644598	−	0.764522i	$-0.722975\pi$
$643$	−1.41701e14	−1.28920	−0.644598	+	0.764522i	$0.722975\pi$
$644$	1.23623e14i	1.11602i
$645$	0	0
$646$	−1.90925e12	−0.0169707
$647$	1.07999e14i	0.952570i	0.879291	+	0.476285i	$0.158017\pi$
$647$	1.07999e14i	0.952570i	−0.879291	+	0.476285i	$0.841983\pi$
$648$	0	0
$649$	−1.77946e14	−1.54549
$650$	2.86986e14i	2.47340i
$651$	0	0
$652$	−1.65233e14	−1.40236
$653$	1.71739e14i	1.44645i	0.690613	+	0.723224i	$0.257341\pi$
$653$	1.71739e14i	1.44645i	−0.690613	+	0.723224i	$0.742659\pi$
$654$	0	0
$655$	1.45887e13	0.121007
$656$	− 7.93565e12i	− 0.0653226i
$657$	0	0
$658$	−1.25251e14	−1.01543
$659$	1.09924e13i	0.0884434i	0.999022	+	0.0442217i	$0.0140808\pi$
$659$	1.09924e13i	0.0884434i	−0.999022	+	0.0442217i	$0.985919\pi$
$660$	0	0
$661$	8.24850e13	0.653684	0.326842	−	0.945079i	$-0.394016\pi$
$661$	8.24850e13	0.653684	0.326842	+	0.945079i	$0.394016\pi$
$662$	− 1.63415e14i	− 1.28529i
$663$	0	0
$664$	1.93154e14	1.49645
$665$	− 2.81577e13i	− 0.216516i
$666$	0	0
$667$	1.44231e14	1.09252
$668$	− 1.73401e14i	− 1.30368i
$669$	0	0
$670$	−2.55549e13	−0.189278
$671$	1.04711e14i	0.769807i
$672$	0	0
$673$	−5.31597e13	−0.385041	−0.192520	−	0.981293i	$-0.561666\pi$
$673$	−5.31597e13	−0.385041	−0.192520	+	0.981293i	$0.561666\pi$
$674$	1.64346e14i	1.18157i
$675$	0	0
$676$	−3.89809e14	−2.76133
$677$	1.08669e14i	0.764122i	0.924137	+	0.382061i	$0.124786\pi$
$677$	1.08669e14i	0.764122i	−0.924137	+	0.382061i	$0.875214\pi$
$678$	0	0
$679$	2.20380e14	1.52695
$680$	4.91759e11i	0.00338227i
$681$	0	0
$682$	−3.96705e14	−2.68872
$683$	9.47666e12i	0.0637605i	0.999492	+	0.0318803i	$0.0101495\pi$
$683$	9.47666e12i	0.0637605i	−0.999492	+	0.0318803i	$0.989850\pi$
$684$	0	0
$685$	−4.49786e13	−0.298231
$686$	2.55854e14i	1.68411i
$687$	0	0
$688$	−3.17913e12	−0.0206236
$689$	− 6.40400e13i	− 0.412435i
$690$	0	0
$691$	2.82614e14	1.79392	0.896961	−	0.442109i	$-0.145770\pi$
$691$	2.82614e14	1.79392	0.896961	+	0.442109i	$0.145770\pi$
$692$	9.89551e13i	0.623603i
$693$	0	0
$694$	8.17653e13	0.507892
$695$	− 2.14549e13i	− 0.132313i
$696$	0	0
$697$	−3.13630e12	−0.0190657
$698$	1.85785e14i	1.12133i
$699$	0	0
$700$	2.44754e14	1.45626
$701$	− 1.40290e14i	− 0.828778i	−0.910100	−	0.414389i	$-0.863995\pi$
$701$	− 1.40290e14i	− 0.828778i	0.910100	−	0.414389i	$-0.136005\pi$
$702$	0	0
$703$	−1.09324e14	−0.636707
$704$	− 5.07310e14i	− 2.93366i
$705$	0	0
$706$	−4.17355e14	−2.37948
$707$	1.99021e14i	1.12669i
$708$	0	0
$709$	−2.77750e14	−1.55032	−0.775162	−	0.631762i	$-0.782332\pi$
$709$	−2.77750e14	−1.55032	−0.775162	+	0.631762i	$0.782332\pi$
$710$	− 1.33492e14i	− 0.739882i
$711$	0	0
$712$	9.64823e13	0.527288
$713$	− 1.19234e14i	− 0.647070i
$714$	0	0
$715$	−1.48504e14	−0.794709
$716$	− 3.66457e14i	− 1.94741i
$717$	0	0
$718$	1.89896e14	0.995159
$719$	− 9.14397e13i	− 0.475872i	−0.971281	−	0.237936i	$-0.923529\pi$
$719$	− 9.14397e13i	− 0.475872i	0.971281	−	0.237936i	$-0.0764709\pi$
$720$	0	0
$721$	−4.37137e13	−0.224358
$722$	− 8.84354e13i	− 0.450755i
$723$	0	0
$724$	1.40643e13	0.0707011
$725$	− 2.85553e14i	− 1.42560i
$726$	0	0
$727$	2.33069e14	1.14766	0.573829	−	0.818975i	$-0.305457\pi$
$727$	2.33069e14	1.14766	0.573829	+	0.818975i	$0.305457\pi$
$728$	3.31838e14i	1.62282i
$729$	0	0
$730$	1.78534e13	0.0861207
$731$	1.25644e12i	0.00601943i
$732$	0	0
$733$	−2.37866e14	−1.12412	−0.562059	−	0.827097i	$-0.689991\pi$
$733$	−2.37866e14	−1.12412	−0.562059	+	0.827097i	$0.689991\pi$
$734$	− 8.87313e13i	− 0.416482i
$735$	0	0
$736$	1.48487e14	0.687543
$737$	1.73607e14i	0.798417i
$738$	0	0
$739$	2.85116e14	1.29360	0.646799	−	0.762660i	$-0.276107\pi$
$739$	2.85116e14	1.29360	0.646799	+	0.762660i	$0.276107\pi$
$740$	7.23824e13i	0.326193i
$741$	0	0
$742$	−8.79853e13	−0.391193
$743$	− 1.78676e14i	− 0.789083i	−0.918878	−	0.394541i	$-0.870903\pi$
$743$	− 1.78676e14i	− 0.789083i	0.918878	−	0.394541i	$-0.129097\pi$
$744$	0	0
$745$	7.39045e13	0.322025
$746$	4.41217e14i	1.90967i
$747$	0	0
$748$	8.58760e12	0.0366745
$749$	− 1.99091e14i	− 0.844585i
$750$	0	0
$751$	3.98917e13	0.166987	0.0834935	−	0.996508i	$-0.473392\pi$
$751$	3.98917e13	0.166987	0.0834935	+	0.996508i	$0.473392\pi$
$752$	− 6.61682e12i	− 0.0275144i
$753$	0	0
$754$	9.95198e14	4.08369
$755$	1.25884e14i	0.513138i
$756$	0	0
$757$	3.34577e13	0.134591	0.0672956	−	0.997733i	$-0.478563\pi$
$757$	3.34577e13	0.134591	0.0672956	+	0.997733i	$0.478563\pi$
$758$	2.03866e14i	0.814701i
$759$	0	0
$760$	5.92776e13	0.233788
$761$	1.40098e14i	0.548920i	0.961599	+	0.274460i	$0.0884990\pi$
$761$	1.40098e14i	0.548920i	−0.961599	+	0.274460i	$0.911501\pi$
$762$	0	0
$763$	−9.30818e13	−0.359950
$764$	2.42318e14i	0.930933i
$765$	0	0
$766$	1.82317e14	0.691328
$767$	− 3.69039e14i	− 1.39026i
$768$	0	0
$769$	1.53854e14	0.572106	0.286053	−	0.958214i	$-0.407657\pi$
$769$	1.53854e14	0.572106	0.286053	+	0.958214i	$0.407657\pi$
$770$	2.04032e14i	0.753778i
$771$	0	0
$772$	−6.69290e13	−0.244078
$773$	− 2.43492e14i	− 0.882243i	−0.897447	−	0.441121i	$-0.854581\pi$
$773$	− 2.43492e14i	− 0.882243i	0.897447	−	0.441121i	$-0.145419\pi$
$774$	0	0
$775$	−2.36063e14	−0.844345
$776$	4.63944e14i	1.64876i
$777$	0	0
$778$	6.66167e14	2.33714
$779$	3.78055e14i	1.31786i
$780$	0	0
$781$	−9.06874e14	−3.12099
$782$	4.15808e12i	0.0142187i
$783$	0	0
$784$	−1.03772e12	−0.00350348
$785$	− 9.63944e13i	− 0.323373i
$786$	0	0
$787$	3.47268e13	0.115025	0.0575123	−	0.998345i	$-0.481683\pi$
$787$	3.47268e13	0.115025	0.0575123	+	0.998345i	$0.481683\pi$
$788$	− 3.40317e12i	− 0.0112009i
$789$	0	0
$790$	−4.66785e13	−0.151698
$791$	− 3.43010e14i	− 1.10771i
$792$	0	0
$793$	−2.17159e14	−0.692487
$794$	5.18690e14i	1.64364i
$795$	0	0
$796$	−8.17409e14	−2.55785
$797$	4.86090e14i	1.51156i	0.654826	+	0.755780i	$0.272742\pi$
$797$	4.86090e14i	1.51156i	−0.654826	+	0.755780i	$0.727258\pi$
$798$	0	0
$799$	−2.61507e12	−0.00803064
$800$	− 2.93980e14i	− 0.897156i
$801$	0	0
$802$	−3.18898e14	−0.961125
$803$	− 1.21287e14i	− 0.363276i
$804$	0	0
$805$	−6.13238e13	−0.181405
$806$	− 8.22718e14i	− 2.41866i
$807$	0	0
$808$	−4.18979e14	−1.21657
$809$	− 1.50911e14i	− 0.435489i	−0.976006	−	0.217744i	$-0.930130\pi$
$809$	− 1.50911e14i	− 0.435489i	0.976006	−	0.217744i	$-0.0698699\pi$
$810$	0	0
$811$	5.05292e14	1.44025	0.720125	−	0.693844i	$-0.244084\pi$
$811$	5.05292e14	1.44025	0.720125	+	0.693844i	$0.244084\pi$
$812$	− 8.48748e14i	− 2.40436i
$813$	0	0
$814$	7.92165e14	2.21663
$815$	− 8.19642e13i	− 0.227948i
$816$	0	0
$817$	1.51454e14	0.416073
$818$	1.52412e14i	0.416152i
$819$	0	0
$820$	2.50307e14	0.675154
$821$	5.32014e14i	1.42629i	0.701017	+	0.713145i	$0.252730\pi$
$821$	5.32014e14i	1.42629i	−0.701017	+	0.713145i	$0.747270\pi$
$822$	0	0
$823$	−1.35362e14	−0.358506	−0.179253	−	0.983803i	$-0.557368\pi$
$823$	−1.35362e14	−0.358506	−0.179253	+	0.983803i	$0.557368\pi$
$824$	− 9.20259e13i	− 0.242256i
$825$	0	0
$826$	−5.07027e14	−1.31865
$827$	− 4.80302e14i	− 1.24162i	−0.783963	−	0.620808i	$-0.786805\pi$
$827$	− 4.80302e14i	− 1.24162i	0.783963	−	0.620808i	$-0.213195\pi$
$828$	0	0
$829$	−3.67003e14	−0.937340	−0.468670	−	0.883373i	$-0.655267\pi$
$829$	−3.67003e14	−0.937340	−0.468670	+	0.883373i	$0.655267\pi$
$830$	2.46296e14i	0.625269i
$831$	0	0
$832$	1.05210e15	2.63901
$833$	4.10124e11i	0.00102256i
$834$	0	0
$835$	8.60162e13	0.211908
$836$	− 1.03517e15i	− 2.53500i
$837$	0	0
$838$	−1.30756e15	−3.16404
$839$	5.69381e14i	1.36960i	0.728731	+	0.684800i	$0.240110\pi$
$839$	5.69381e14i	1.36960i	−0.728731	+	0.684800i	$0.759890\pi$
$840$	0	0
$841$	−5.69521e14	−1.35372
$842$	3.30228e14i	0.780285i
$843$	0	0
$844$	−9.48022e14	−2.21364
$845$	− 1.93366e14i	− 0.448845i
$846$	0	0
$847$	9.68675e14	2.22209
$848$	− 4.64813e12i	− 0.0105998i
$849$	0	0
$850$	8.23232e12	0.0185536
$851$	2.38093e14i	0.533457i
$852$	0	0
$853$	1.83927e13	0.0407286	0.0203643	−	0.999793i	$-0.493517\pi$
$853$	1.83927e13	0.0407286	0.0203643	+	0.999793i	$0.493517\pi$
$854$	2.98357e14i	0.656821i
$855$	0	0
$856$	4.19126e14	0.911960
$857$	− 7.22916e14i	− 1.56381i	−0.623398	−	0.781905i	$-0.714248\pi$
$857$	− 7.22916e14i	− 1.56381i	0.623398	−	0.781905i	$-0.285752\pi$
$858$	0	0
$859$	−5.83296e14	−1.24716	−0.623582	−	0.781758i	$-0.714323\pi$
$859$	−5.83296e14	−1.24716	−0.623582	+	0.781758i	$0.714323\pi$
$860$	− 1.00276e14i	− 0.213160i
$861$	0	0
$862$	3.38343e14	0.710921
$863$	3.20743e14i	0.670044i	0.942210	+	0.335022i	$0.108744\pi$
$863$	3.20743e14i	0.670044i	−0.942210	+	0.335022i	$0.891256\pi$
$864$	0	0
$865$	−4.90870e13	−0.101364
$866$	9.46937e14i	1.94416i
$867$	0	0
$868$	−7.01650e14	−1.42404
$869$	3.17110e14i	0.639898i
$870$	0	0
$871$	−3.60040e14	−0.718224
$872$	− 1.95955e14i	− 0.388664i
$873$	0	0
$874$	5.01223e14	0.982819
$875$	2.52070e14i	0.491451i
$876$	0	0
$877$	−8.65432e13	−0.166815	−0.0834075	−	0.996516i	$-0.526580\pi$
$877$	−8.65432e13	−0.166815	−0.0834075	+	0.996516i	$0.526580\pi$
$878$	3.76261e14i	0.721134i
$879$	0	0
$880$	−1.07787e13	−0.0204245
$881$	8.97308e14i	1.69068i	0.534227	+	0.845341i	$0.320603\pi$
$881$	8.97308e14i	1.69068i	−0.534227	+	0.845341i	$0.679397\pi$
$882$	0	0
$883$	2.43623e14	0.453853	0.226927	−	0.973912i	$-0.427132\pi$
$883$	2.43623e14	0.453853	0.226927	+	0.973912i	$0.427132\pi$
$884$	1.78096e13i	0.0329909i
$885$	0	0
$886$	8.39721e14	1.53804
$887$	− 3.92471e13i	− 0.0714808i	−0.999361	−	0.0357404i	$-0.988621\pi$
$887$	− 3.92471e13i	− 0.0714808i	0.999361	−	0.0357404i	$-0.0113789\pi$
$888$	0	0
$889$	−2.57415e13	−0.0463580
$890$	1.23027e14i	0.220319i
$891$	0	0
$892$	8.55599e14	1.51512
$893$	3.15226e14i	0.555091i
$894$	0	0
$895$	1.81782e14	0.316545
$896$	− 9.11623e14i	− 1.57861i
$897$	0	0
$898$	9.83281e14	1.68382
$899$	8.18610e14i	1.39405i
$900$	0	0
$901$	−1.83701e12	−0.00309377
$902$	− 2.73940e15i	− 4.58799i
$903$	0	0
$904$	7.22104e14	1.19607
$905$	6.97664e12i	0.0114922i
$906$	0	0
$907$	−1.09694e15	−1.78709	−0.893544	−	0.448975i	$-0.851789\pi$
$907$	−1.09694e15	−1.78709	−0.893544	+	0.448975i	$0.851789\pi$
$908$	1.24037e15i	2.00965i
$909$	0	0
$910$	−4.23137e14	−0.678069
$911$	8.26823e14i	1.31771i	0.752269	+	0.658856i	$0.228959\pi$
$911$	8.26823e14i	1.31771i	−0.752269	+	0.658856i	$0.771041\pi$
$912$	0	0
$913$	1.67321e15	2.63752
$914$	1.18299e15i	1.85460i
$915$	0	0
$916$	6.92447e14	1.07376
$917$	− 2.82392e14i	− 0.435517i
$918$	0	0
$919$	8.42155e14	1.28474	0.642368	−	0.766396i	$-0.277952\pi$
$919$	8.42155e14	1.28474	0.642368	+	0.766396i	$0.277952\pi$
$920$	− 1.29099e14i	− 0.195876i
$921$	0	0
$922$	−1.32443e15	−1.98780
$923$	− 1.88075e15i	− 2.80751i
$924$	0	0
$925$	4.71386e14	0.696094
$926$	− 1.50295e15i	− 2.20744i
$927$	0	0
$928$	−1.01945e15	−1.48124
$929$	− 8.33534e14i	− 1.20460i	−0.798268	−	0.602302i	$-0.794250\pi$
$929$	− 8.33534e14i	− 1.20460i	0.798268	−	0.602302i	$-0.205750\pi$
$930$	0	0
$931$	4.94371e13	0.0706813
$932$	1.00627e14i	0.143098i
$933$	0	0
$934$	−6.41708e14	−0.902824
$935$	4.25990e12i	0.00596131i
$936$	0	0
$937$	−2.78438e14	−0.385506	−0.192753	−	0.981247i	$-0.561742\pi$
$937$	−2.78438e14	−0.385506	−0.192753	+	0.981247i	$0.561742\pi$
$938$	4.94663e14i	0.681233i
$939$	0	0
$940$	2.08708e14	0.284380
$941$	− 7.38535e14i	− 1.00097i	−0.865744	−	0.500487i	$-0.833154\pi$
$941$	− 7.38535e14i	− 1.00097i	0.865744	−	0.500487i	$-0.166846\pi$
$942$	0	0
$943$	8.23353e14	1.10415
$944$	− 2.67854e13i	− 0.0357305i
$945$	0	0
$946$	−1.09744e15	−1.44852
$947$	− 7.85947e14i	− 1.03191i	−0.856615	−	0.515957i	$-0.827437\pi$
$947$	− 7.85947e14i	− 1.03191i	0.856615	−	0.515957i	$-0.172563\pi$
$948$	0	0
$949$	2.51535e14	0.326789
$950$	− 9.92339e14i	− 1.28245i
$951$	0	0
$952$	9.51892e12	0.0121731
$953$	5.37814e14i	0.684175i	0.939668	+	0.342088i	$0.111134\pi$
$953$	5.37814e14i	0.684175i	−0.939668	+	0.342088i	$0.888866\pi$
$954$	0	0
$955$	−1.20202e14	−0.151320
$956$	6.24792e14i	0.782431i
$957$	0	0
$958$	−4.43524e14	−0.549654
$959$	8.70645e14i	1.07337i
$960$	0	0
$961$	−1.42894e14	−0.174339
$962$	1.64285e15i	1.99399i
$963$	0	0
$964$	−8.50311e14	−1.02139
$965$	− 3.32003e13i	− 0.0396740i
$966$	0	0
$967$	−1.07681e15	−1.27353	−0.636763	−	0.771059i	$-0.719727\pi$
$967$	−1.07681e15	−1.27353	−0.636763	+	0.771059i	$0.719727\pi$
$968$	2.03925e15i	2.39935i
$969$	0	0
$970$	−5.91588e14	−0.688908
$971$	− 1.33870e14i	− 0.155091i	−0.996989	−	0.0775454i	$-0.975292\pi$
$971$	− 1.33870e14i	− 0.155091i	0.996989	−	0.0775454i	$-0.0247083\pi$
$972$	0	0
$973$	−4.15299e14	−0.476208
$974$	− 1.47762e14i	− 0.168566i
$975$	0	0
$976$	−1.57617e13	−0.0177973
$977$	− 6.28694e14i	− 0.706263i	−0.935574	−	0.353132i	$-0.885117\pi$
$977$	− 6.28694e14i	− 0.706263i	0.935574	−	0.353132i	$-0.114883\pi$
$978$	0	0
$979$	8.35785e14	0.929354
$980$	− 3.27318e13i	− 0.0362109i
$981$	0	0
$982$	1.57668e14	0.172658
$983$	− 9.03733e14i	− 0.984629i	−0.870417	−	0.492314i	$-0.836151\pi$
$983$	− 9.03733e14i	− 0.984629i	0.870417	−	0.492314i	$-0.163849\pi$
$984$	0	0
$985$	1.68815e12	0.00182067
$986$	− 2.85477e13i	− 0.0306328i
$987$	0	0
$988$	2.14681e15	2.28038
$989$	− 3.29846e14i	− 0.348602i
$990$	0	0
$991$	1.70337e15	1.78213	0.891067	−	0.453871i	$-0.149957\pi$
$991$	1.70337e15	1.78213	0.891067	+	0.453871i	$0.149957\pi$
$992$	8.42768e14i	0.877303i
$993$	0	0
$994$	−2.58398e15	−2.66292
$995$	− 4.05478e14i	− 0.415769i
$996$	0	0
$997$	−5.98425e14	−0.607482	−0.303741	−	0.952755i	$-0.598236\pi$
$997$	−5.98425e14	−0.607482	−0.303741	+	0.952755i	$0.598236\pi$
$998$	− 1.00180e15i	− 1.01188i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.b.b.26.2	yes	2
3.2	odd	2	inner	27.11.b.b.26.1	✓	2
9.2	odd	6		81.11.d.a.53.1		2
9.4	even	3		81.11.d.a.26.1		2
9.5	odd	6		81.11.d.c.26.1		2
9.7	even	3		81.11.d.c.53.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.b.b.26.1	✓	2	3.2	odd	2	inner
27.11.b.b.26.2	yes	2	1.1	even	1	trivial
81.11.d.a.26.1		2	9.4	even	3
81.11.d.a.53.1		2	9.2	odd	6
81.11.d.c.26.1		2	9.5	odd	6
81.11.d.c.53.1		2	9.7	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+51.9615i q^{2} -1676.00 q^{4} -831.384i q^{5} -16093.0 q^{7} -33878.9i q^{8} +43200.0 q^{10} -293479. i q^{11} +608639. q^{13} -836217. i q^{14} +44176.0 q^{16} -17459.1i q^{17} -2.10455e6 q^{19} +1.39340e6i q^{20} +1.52496e7 q^{22} +4.58342e6i q^{23} +9.07442e6 q^{25} +3.16258e7i q^{26} +2.69719e7 q^{28} -3.14679e7i q^{29} -2.60141e7 q^{31} -3.23966e7i q^{32} +907200. q^{34} +1.33795e7i q^{35} +5.19466e7 q^{37} -1.09356e8i q^{38} -2.81664e7 q^{40} -1.79637e8i q^{41} -7.19650e7 q^{43} +4.91870e8i q^{44} -2.38162e8 q^{46} -1.49783e8i q^{47} -2.34906e7 q^{49} +4.71521e8i q^{50} -1.02008e9 q^{52} -1.05218e8i q^{53} -2.43994e8 q^{55} +5.45213e8i q^{56} +1.63512e9 q^{58} -6.06334e8i q^{59} -3.56794e8 q^{61} -1.35173e9i q^{62} +1.72861e9 q^{64} -5.06013e8i q^{65} -5.91549e8 q^{67} +2.92614e7i q^{68} -6.95218e8 q^{70} -3.09009e9i q^{71} +4.13274e8 q^{73} +2.69922e9i q^{74} +3.52722e9 q^{76} +4.72295e9i q^{77} -1.08052e9 q^{79} -3.67272e7i q^{80} +9.33422e9 q^{82} +5.70129e9i q^{83} -1.45152e7 q^{85} -3.73941e9i q^{86} -9.94274e9 q^{88} +2.84786e9i q^{89} -9.79483e9 q^{91} -7.68182e9i q^{92} +7.78296e9 q^{94} +1.74969e9i q^{95} -1.36942e10 q^{97} -1.22061e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3352 q^{4} - 32186 q^{7} + 86400 q^{10} + 1217278 q^{13} + 88352 q^{16} - 4209098 q^{19} + 30499200 q^{22} + 18148850 q^{25} + 53943736 q^{28} - 52028252 q^{31} + 1814400 q^{34} + 103893214 q^{37}+ \cdots - 27388355186 q^{97}+O(q^{100}) \) 2 * q - 3352 * q^4 - 32186 * q^7 + 86400 * q^10 + 1217278 * q^13 + 88352 * q^16 - 4209098 * q^19 + 30499200 * q^22 + 18148850 * q^25 + 53943736 * q^28 - 52028252 * q^31 + 1814400 * q^34 + 103893214 * q^37 - 56332800 * q^40 - 143929964 * q^43 - 476323200 * q^46 - 46981200 * q^49 - 2040157928 * q^52 - 487987200 * q^55 + 3270240000 * q^58 - 713588402 * q^61 + 3457221248 * q^64 - 1183097978 * q^67 - 1390435200 * q^70 + 826548286 * q^73 + 7054448248 * q^76 - 2161039898 * q^79 + 18668448000 * q^82 - 29030400 * q^85 - 19885478400 * q^88 - 19589654854 * q^91 + 15565910400 * q^94 - 27388355186 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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