LMFDB - Embedded newform 162.11.b.a.161.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,11,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, 11); 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, 11, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	162.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$102.927874933$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11512x^{6} + 49652044x^{4} + 95092179048x^{2} + 68231796144516 $ x^8 + 11512x^6 + 49652044x^4 + 95092179048*x^2 + 68231796144516
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.7
Root			$-54.1327i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.11.b.a.161.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+22.6274i q^{2} -512.000 q^{4} +2601.86i q^{5} +19795.7 q^{7} -11585.2i q^{8} -58873.3 q^{10} +130660. i q^{11} -613747. q^{13} +447927. i q^{14} +262144. q^{16} -772189. i q^{17} +1.92534e6 q^{19} -1.33215e6i q^{20} -2.95651e6 q^{22} -7.74063e6i q^{23} +2.99596e6 q^{25} -1.38875e7i q^{26} -1.01354e7 q^{28} +2.44027e7i q^{29} -2.82557e7 q^{31} +5.93164e6i q^{32} +1.74726e7 q^{34} +5.15057e7i q^{35} -1.12383e8 q^{37} +4.35656e7i q^{38} +3.01431e7 q^{40} +1.28028e8i q^{41} -1.64197e8 q^{43} -6.68981e7i q^{44} +1.75150e8 q^{46} -1.19321e8i q^{47} +1.09396e8 q^{49} +6.77909e7i q^{50} +3.14239e8 q^{52} +1.34883e8i q^{53} -3.39960e8 q^{55} -2.29338e8i q^{56} -5.52169e8 q^{58} +2.75491e8i q^{59} +3.91932e8 q^{61} -6.39354e8i q^{62} -1.34218e8 q^{64} -1.59688e9i q^{65} +1.53946e8 q^{67} +3.95361e8i q^{68} -1.16544e9 q^{70} -1.45431e9i q^{71} -3.59722e7 q^{73} -2.54293e9i q^{74} -9.85776e8 q^{76} +2.58652e9i q^{77} -5.62198e9 q^{79} +6.82061e8i q^{80} -2.89695e9 q^{82} +4.04913e9i q^{83} +2.00913e9 q^{85} -3.71536e9i q^{86} +1.51373e9 q^{88} -6.43282e9i q^{89} -1.21496e10 q^{91} +3.96320e9i q^{92} +2.69993e9 q^{94} +5.00947e9i q^{95} +1.05653e10 q^{97} +2.47536e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4096 q^{4} + 45112 q^{7} - 174720 q^{10} - 721448 q^{13} + 2097152 q^{16} - 731192 q^{19} - 13824 q^{22} + 27586040 q^{25} - 23097344 q^{28} + 72502528 q^{31} + 70417536 q^{34} - 166952240 q^{37}+ \cdots + 2247775936 q^{97}+O(q^{100}) $ 8 * q - 4096 * q^4 + 45112 * q^7 - 174720 * q^10 - 721448 * q^13 + 2097152 * q^16 - 731192 * q^19 - 13824 * q^22 + 27586040 * q^25 - 23097344 * q^28 + 72502528 * q^31 + 70417536 * q^34 - 166952240 * q^37 + 89456640 * q^40 - 12510440 * q^43 - 269948160 * q^46 + 188021592 * q^49 + 369381376 * q^52 - 181251000 * q^55 - 154795392 * q^58 - 1782273248 * q^61 - 1073741824 * q^64 + 108743656 * q^67 + 62250240 * q^70 + 5102234368 * q^73 + 374370304 * q^76 - 9246201752 * q^79 - 478119936 * q^82 + 20649676320 * q^85 + 7077888 * q^88 - 18226522120 * q^91 + 20130964224 * q^94 + 2247775936 * 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 $

$2$	22.6274i	0.707107i
$2$	22.6274i	0.707107i
$3$	0	0
$3$	0	0
$4$	−512.000	−0.500000
$5$	2601.86i	0.832594i	0.909229	+	0.416297i	$0.136672\pi$
$5$	2601.86i	0.832594i	−0.909229	+	0.416297i	$0.863328\pi$
$6$	0	0
$7$	19795.7	1.17783	0.588914	−	0.808196i	$-0.299556\pi$
$7$	19795.7	1.17783	0.588914	+	0.808196i	$0.299556\pi$
$8$	− 11585.2i	− 0.353553i
$9$	0	0
$10$	−58873.3	−0.588733
$11$	130660.i	0.811298i	0.914029	+	0.405649i	$0.132954\pi$
$11$	130660.i	0.811298i	−0.914029	+	0.405649i	$0.867046\pi$
$12$	0	0
$13$	−613747.	−1.65300	−0.826500	−	0.562937i	$-0.809671\pi$
$13$	−613747.	−1.65300	−0.826500	+	0.562937i	$0.809671\pi$
$14$	447927.i	0.832850i
$15$	0	0
$16$	262144.	0.250000
$17$	− 772189.i	− 0.543850i	−0.962318	−	0.271925i	$-0.912340\pi$
$17$	− 772189.i	− 0.543850i	0.962318	−	0.271925i	$-0.0876603\pi$
$18$	0	0
$19$	1.92534e6	0.777571	0.388786	−	0.921328i	$-0.372895\pi$
$19$	1.92534e6	0.777571	0.388786	+	0.921328i	$0.372895\pi$
$20$	− 1.33215e6i	− 0.416297i
$21$	0	0
$22$	−2.95651e6	−0.573674
$23$	− 7.74063e6i	− 1.20264i	−0.799007	−	0.601322i	$-0.794641\pi$
$23$	− 7.74063e6i	− 1.20264i	0.799007	−	0.601322i	$-0.205359\pi$
$24$	0	0
$25$	2.99596e6	0.306787
$26$	− 1.38875e7i	− 1.16885i
$27$	0	0
$28$	−1.01354e7	−0.588914
$29$	2.44027e7i	1.18973i	0.803827	+	0.594864i	$0.202794\pi$
$29$	2.44027e7i	1.18973i	−0.803827	+	0.594864i	$0.797206\pi$
$30$	0	0
$31$	−2.82557e7	−0.986957	−0.493478	−	0.869758i	$-0.664275\pi$
$31$	−2.82557e7	−0.986957	−0.493478	+	0.869758i	$0.664275\pi$
$32$	5.93164e6i	0.176777i
$33$	0	0
$34$	1.74726e7	0.384560
$35$	5.15057e7i	0.980653i
$36$	0	0
$37$	−1.12383e8	−1.62066	−0.810330	−	0.585974i	$-0.800712\pi$
$37$	−1.12383e8	−1.62066	−0.810330	+	0.585974i	$0.800712\pi$
$38$	4.35656e7i	0.549826i
$39$	0	0
$40$	3.01431e7	0.294367
$41$	1.28028e8i	1.10506i	0.833492	+	0.552531i	$0.186338\pi$
$41$	1.28028e8i	1.10506i	−0.833492	+	0.552531i	$0.813662\pi$
$42$	0	0
$43$	−1.64197e8	−1.11693	−0.558463	−	0.829530i	$-0.688609\pi$
$43$	−1.64197e8	−1.11693	−0.558463	+	0.829530i	$0.688609\pi$
$44$	− 6.68981e7i	− 0.405649i
$45$	0	0
$46$	1.75150e8	0.850397
$47$	− 1.19321e8i	− 0.520270i	−0.965572	−	0.260135i	$-0.916233\pi$
$47$	− 1.19321e8i	− 0.520270i	0.965572	−	0.260135i	$-0.0837671\pi$
$48$	0	0
$49$	1.09396e8	0.387278
$50$	6.77909e7i	0.216931i
$51$	0	0
$52$	3.14239e8	0.826500
$53$	1.34883e8i	0.322535i	0.986911	+	0.161268i	$0.0515582\pi$
$53$	1.34883e8i	0.322535i	−0.986911	+	0.161268i	$0.948442\pi$
$54$	0	0
$55$	−3.39960e8	−0.675482
$56$	− 2.29338e8i	− 0.416425i
$57$	0	0
$58$	−5.52169e8	−0.841264
$59$	2.75491e8i	0.385343i	0.981263	+	0.192672i	$0.0617152\pi$
$59$	2.75491e8i	0.385343i	−0.981263	+	0.192672i	$0.938285\pi$
$60$	0	0
$61$	3.91932e8	0.464047	0.232023	−	0.972710i	$-0.425465\pi$
$61$	3.91932e8	0.464047	0.232023	+	0.972710i	$0.425465\pi$
$62$	− 6.39354e8i	− 0.697884i
$63$	0	0
$64$	−1.34218e8	−0.125000
$65$	− 1.59688e9i	− 1.37628i
$66$	0	0
$67$	1.53946e8	0.114023	0.0570116	−	0.998374i	$-0.481843\pi$
$67$	1.53946e8	0.114023	0.0570116	+	0.998374i	$0.481843\pi$
$68$	3.95361e8i	0.271925i
$69$	0	0
$70$	−1.16544e9	−0.693426
$71$	− 1.45431e9i	− 0.806059i	−0.915187	−	0.403029i	$-0.867957\pi$
$71$	− 1.45431e9i	− 0.806059i	0.915187	−	0.403029i	$-0.132043\pi$
$72$	0	0
$73$	−3.59722e7	−0.0173521	−0.00867607	−	0.999962i	$-0.502762\pi$
$73$	−3.59722e7	−0.0173521	−0.00867607	+	0.999962i	$0.502762\pi$
$74$	− 2.54293e9i	− 1.14598i
$75$	0	0
$76$	−9.85776e8	−0.388786
$77$	2.58652e9i	0.955569i
$78$	0	0
$79$	−5.62198e9	−1.82706	−0.913532	−	0.406768i	$-0.866656\pi$
$79$	−5.62198e9	−1.82706	−0.913532	+	0.406768i	$0.866656\pi$
$80$	6.82061e8i	0.208149i
$81$	0	0
$82$	−2.89695e9	−0.781397
$83$	4.04913e9i	1.02795i	0.857805	+	0.513975i	$0.171828\pi$
$83$	4.04913e9i	1.02795i	−0.857805	+	0.513975i	$0.828172\pi$
$84$	0	0
$85$	2.00913e9	0.452806
$86$	− 3.71536e9i	− 0.789786i
$87$	0	0
$88$	1.51373e9	0.286837
$89$	− 6.43282e9i	− 1.15200i	−0.817451	−	0.575999i	$-0.804613\pi$
$89$	− 6.43282e9i	− 1.15200i	0.817451	−	0.575999i	$-0.195387\pi$
$90$	0	0
$91$	−1.21496e10	−1.94695
$92$	3.96320e9i	0.601322i
$93$	0	0
$94$	2.69993e9	0.367886
$95$	5.00947e9i	0.647402i
$96$	0	0
$97$	1.05653e10	1.23034	0.615169	−	0.788396i	$-0.289088\pi$
$97$	1.05653e10	1.23034	0.615169	+	0.788396i	$0.289088\pi$
$98$	2.47536e9i	0.273847i
$99$	0	0
$100$	−1.53393e9	−0.153393
$101$	− 1.74061e10i	− 1.65613i	−0.560629	−	0.828067i	$-0.689441\pi$
$101$	− 1.74061e10i	− 1.65613i	0.560629	−	0.828067i	$-0.310559\pi$
$102$	0	0
$103$	−4.82075e9	−0.415842	−0.207921	−	0.978146i	$-0.566670\pi$
$103$	−4.82075e9	−0.415842	−0.207921	+	0.978146i	$0.566670\pi$
$104$	7.11041e9i	0.584424i
$105$	0	0
$106$	−3.05205e9	−0.228067
$107$	− 1.21829e10i	− 0.868621i	−0.900763	−	0.434311i	$-0.856992\pi$
$107$	− 1.21829e10i	− 0.868621i	0.900763	−	0.434311i	$-0.143008\pi$
$108$	0	0
$109$	−5.43243e9	−0.353071	−0.176535	−	0.984294i	$-0.556489\pi$
$109$	−5.43243e9	−0.353071	−0.176535	+	0.984294i	$0.556489\pi$
$110$	− 7.69241e9i	− 0.477638i
$111$	0	0
$112$	5.18934e9	0.294457
$113$	− 3.39900e10i	− 1.84484i	−0.386185	−	0.922421i	$-0.626207\pi$
$113$	− 3.39900e10i	− 1.84484i	0.386185	−	0.922421i	$-0.373793\pi$
$114$	0	0
$115$	2.01400e10	1.00131
$116$	− 1.24942e10i	− 0.594864i
$117$	0	0
$118$	−6.23365e9	−0.272479
$119$	− 1.52861e10i	− 0.640562i
$120$	0	0
$121$	8.86530e9	0.341796
$122$	8.86841e9i	0.328131i
$123$	0	0
$124$	1.44669e10	0.493478
$125$	3.32038e10i	1.08802i
$126$	0	0
$127$	−4.29609e10	−1.30033	−0.650166	−	0.759792i	$-0.725301\pi$
$127$	−4.29609e10	−1.30033	−0.650166	+	0.759792i	$0.725301\pi$
$128$	− 3.03700e9i	− 0.0883883i
$129$	0	0
$130$	3.61333e10	0.973176
$131$	− 4.29311e10i	− 1.11280i	−0.830916	−	0.556398i	$-0.812183\pi$
$131$	− 4.29311e10i	− 1.11280i	0.830916	−	0.556398i	$-0.187817\pi$
$132$	0	0
$133$	3.81136e10	0.915845
$134$	3.48339e9i	0.0806266i
$135$	0	0
$136$	−8.94600e9	−0.192280
$137$	1.64960e10i	0.341802i	0.985288	+	0.170901i	$0.0546678\pi$
$137$	1.64960e10i	0.341802i	−0.985288	+	0.170901i	$0.945332\pi$
$138$	0	0
$139$	9.14748e10	1.76290	0.881449	−	0.472279i	$-0.156568\pi$
$139$	9.14748e10	1.76290	0.881449	+	0.472279i	$0.156568\pi$
$140$	− 2.63709e10i	− 0.490326i
$141$	0	0
$142$	3.29074e10	0.569970
$143$	− 8.01924e10i	− 1.34108i
$144$	0	0
$145$	−6.34923e10	−0.990560
$146$	− 8.13958e8i	− 0.0122698i
$147$	0	0
$148$	5.75401e10	0.810330
$149$	− 1.01047e11i	− 1.37592i	−0.725748	−	0.687961i	$-0.758506\pi$
$149$	− 1.01047e11i	− 1.37592i	0.725748	−	0.687961i	$-0.241494\pi$
$150$	0	0
$151$	−8.61479e10	−1.09739	−0.548694	−	0.836024i	$-0.684875\pi$
$151$	−8.61479e10	−1.09739	−0.548694	+	0.836024i	$0.684875\pi$
$152$	− 2.23056e10i	− 0.274913i
$153$	0	0
$154$	−5.85262e10	−0.675689
$155$	− 7.35174e10i	− 0.821735i
$156$	0	0
$157$	5.55888e10	0.582759	0.291380	−	0.956607i	$-0.405886\pi$
$157$	5.55888e10	0.582759	0.291380	+	0.956607i	$0.405886\pi$
$158$	− 1.27211e11i	− 1.29193i
$159$	0	0
$160$	−1.54333e10	−0.147183
$161$	− 1.53231e11i	− 1.41651i
$162$	0	0
$163$	−1.33750e11	−1.16240	−0.581201	−	0.813760i	$-0.697417\pi$
$163$	−1.33750e11	−1.16240	−0.581201	+	0.813760i	$0.697417\pi$
$164$	− 6.55505e10i	− 0.552531i
$165$	0	0
$166$	−9.16215e10	−0.726870
$167$	− 2.62414e10i	− 0.202025i	−0.994885	−	0.101012i	$-0.967792\pi$
$167$	− 2.62414e10i	− 0.202025i	0.994885	−	0.101012i	$-0.0322081\pi$
$168$	0	0
$169$	2.38827e11	1.73241
$170$	4.54613e10i	0.320183i
$171$	0	0
$172$	8.40691e10	0.558463
$173$	2.52825e11i	1.63151i	0.578396	+	0.815756i	$0.303679\pi$
$173$	2.52825e11i	1.63151i	−0.578396	+	0.815756i	$0.696321\pi$
$174$	0	0
$175$	5.93073e10	0.361342
$176$	3.42518e10i	0.202824i
$177$	0	0
$178$	1.45558e11	0.814585
$179$	− 3.20195e10i	− 0.174241i	−0.996198	−	0.0871204i	$-0.972234\pi$
$179$	− 3.20195e10i	− 0.174241i	0.996198	−	0.0871204i	$-0.0277665\pi$
$180$	0	0
$181$	−2.59451e11	−1.33555	−0.667777	−	0.744361i	$-0.732754\pi$
$181$	−2.59451e11	−1.33555	−0.667777	+	0.744361i	$0.732754\pi$
$182$	− 2.74914e11i	− 1.37670i
$183$	0	0
$184$	−8.96770e10	−0.425199
$185$	− 2.92404e11i	− 1.34935i
$186$	0	0
$187$	1.00895e11	0.441224
$188$	6.10925e10i	0.260135i
$189$	0	0
$190$	−1.13351e11	−0.457782
$191$	− 4.66570e11i	− 1.83548i	−0.397178	−	0.917741i	$-0.630011\pi$
$191$	− 4.66570e11i	− 1.83548i	0.397178	−	0.917741i	$-0.369989\pi$
$192$	0	0
$193$	3.36033e11	1.25486	0.627430	−	0.778673i	$-0.284107\pi$
$193$	3.36033e11	1.25486	0.627430	+	0.778673i	$0.284107\pi$
$194$	2.39066e11i	0.869980i
$195$	0	0
$196$	−5.60109e10	−0.193639
$197$	3.06058e9i	0.0103151i	0.999987	+	0.00515755i	$0.00164171\pi$
$197$	3.06058e9i	0.0103151i	−0.999987	+	0.00515755i	$0.998358\pi$
$198$	0	0
$199$	−1.68434e11	−0.539713	−0.269857	−	0.962900i	$-0.586976\pi$
$199$	−1.68434e11	−0.539713	−0.269857	+	0.962900i	$0.586976\pi$
$200$	− 3.47089e10i	− 0.108465i
$201$	0	0
$202$	3.93856e11	1.17106
$203$	4.83069e11i	1.40129i
$204$	0	0
$205$	−3.33111e11	−0.920068
$206$	− 1.09081e11i	− 0.294045i
$207$	0	0
$208$	−1.60890e11	−0.413250
$209$	2.51566e11i	0.630842i
$210$	0	0
$211$	−4.58392e11	−1.09604	−0.548018	−	0.836467i	$-0.684617\pi$
$211$	−4.58392e11	−1.09604	−0.548018	+	0.836467i	$0.684617\pi$
$212$	− 6.90600e10i	− 0.161268i
$213$	0	0
$214$	2.75667e11	0.614208
$215$	− 4.27218e11i	− 0.929946i
$216$	0	0
$217$	−5.59343e11	−1.16247
$218$	− 1.22922e11i	− 0.249659i
$219$	0	0
$220$	1.74059e11	0.337741
$221$	4.73929e11i	0.898984i
$222$	0	0
$223$	−6.03295e11	−1.09397	−0.546985	−	0.837142i	$-0.684225\pi$
$223$	−6.03295e11	−1.09397	−0.546985	+	0.837142i	$0.684225\pi$
$224$	1.17421e11i	0.208212i
$225$	0	0
$226$	7.69107e11	1.30450
$227$	2.39393e11i	0.397176i	0.980083	+	0.198588i	$0.0636355\pi$
$227$	2.39393e11i	0.397176i	−0.980083	+	0.198588i	$0.936364\pi$
$228$	0	0
$229$	−1.02322e12	−1.62477	−0.812383	−	0.583124i	$-0.801830\pi$
$229$	−1.02322e12	−1.62477	−0.812383	+	0.583124i	$0.801830\pi$
$230$	4.55716e11i	0.708036i
$231$	0	0
$232$	2.82711e11	0.420632
$233$	4.04354e11i	0.588819i	0.955679	+	0.294409i	$0.0951229\pi$
$233$	4.04354e11i	0.588819i	−0.955679	+	0.294409i	$0.904877\pi$
$234$	0	0
$235$	3.10457e11	0.433174
$236$	− 1.41051e11i	− 0.192672i
$237$	0	0
$238$	3.45884e11	0.452945
$239$	− 1.28961e12i	− 1.65374i	−0.562393	−	0.826870i	$-0.690119\pi$
$239$	− 1.28961e12i	− 1.65374i	0.562393	−	0.826870i	$-0.309881\pi$
$240$	0	0
$241$	1.72054e11	0.211631	0.105815	−	0.994386i	$-0.466255\pi$
$241$	1.72054e11	0.211631	0.105815	+	0.994386i	$0.466255\pi$
$242$	2.00599e11i	0.241686i
$243$	0	0
$244$	−2.00669e11	−0.232023
$245$	2.84634e11i	0.322445i
$246$	0	0
$247$	−1.18167e12	−1.28533
$248$	3.27349e11i	0.348942i
$249$	0	0
$250$	−7.51317e11	−0.769349
$251$	− 1.67024e12i	− 1.67652i	−0.545270	−	0.838260i	$-0.683573\pi$
$251$	− 1.67024e12i	− 1.67652i	0.545270	−	0.838260i	$-0.316427\pi$
$252$	0	0
$253$	1.01139e12	0.975702
$254$	− 9.72094e11i	− 0.919474i
$255$	0	0
$256$	6.87195e10	0.0625000
$257$	− 1.75788e11i	− 0.156792i	−0.996922	−	0.0783959i	$-0.975020\pi$
$257$	− 1.75788e11i	− 0.156792i	0.996922	−	0.0783959i	$-0.0249798\pi$
$258$	0	0
$259$	−2.22470e12	−1.90886
$260$	8.17604e11i	0.688139i
$261$	0	0
$262$	9.71420e11	0.786866
$263$	2.09595e12i	1.66572i	0.553481	+	0.832862i	$0.313299\pi$
$263$	2.09595e12i	1.66572i	−0.553481	+	0.832862i	$0.686701\pi$
$264$	0	0
$265$	−3.50946e11	−0.268541
$266$	8.62413e11i	0.647600i
$267$	0	0
$268$	−7.88201e10	−0.0570116
$269$	5.70798e11i	0.405248i	0.979257	+	0.202624i	$0.0649470\pi$
$269$	5.70798e11i	0.405248i	−0.979257	+	0.202624i	$0.935053\pi$
$270$	0	0
$271$	8.88438e11	0.607828	0.303914	−	0.952699i	$-0.401706\pi$
$271$	8.88438e11	0.607828	0.303914	+	0.952699i	$0.401706\pi$
$272$	− 2.02425e11i	− 0.135963i
$273$	0	0
$274$	−3.73261e11	−0.241691
$275$	3.91453e11i	0.248895i
$276$	0	0
$277$	1.77844e12	1.09054	0.545270	−	0.838261i	$-0.316427\pi$
$277$	1.77844e12	1.09054	0.545270	+	0.838261i	$0.316427\pi$
$278$	2.06984e12i	1.24656i
$279$	0	0
$280$	5.96706e11	0.346713
$281$	1.82407e12i	1.04114i	0.853819	+	0.520570i	$0.174281\pi$
$281$	1.82407e12i	1.04114i	−0.853819	+	0.520570i	$0.825719\pi$
$282$	0	0
$283$	2.18587e12	1.20418	0.602091	−	0.798428i	$-0.294335\pi$
$283$	2.18587e12	1.20418	0.602091	+	0.798428i	$0.294335\pi$
$284$	7.44609e11i	0.403029i
$285$	0	0
$286$	1.81455e12	0.948283
$287$	2.53442e12i	1.30157i
$288$	0	0
$289$	1.41972e12	0.704227
$290$	− 1.43667e12i	− 0.700432i
$291$	0	0
$292$	1.84178e10	0.00867607
$293$	3.26664e12i	1.51274i	0.654146	+	0.756369i	$0.273028\pi$
$293$	3.26664e12i	1.51274i	−0.654146	+	0.756369i	$0.726972\pi$
$294$	0	0
$295$	−7.16789e11	−0.320834
$296$	1.30198e12i	0.572989i
$297$	0	0
$298$	2.28644e12	0.972924
$299$	4.75079e12i	1.98797i
$300$	0	0
$301$	−3.25041e12	−1.31555
$302$	− 1.94930e12i	− 0.775970i
$303$	0	0
$304$	5.04717e11	0.194393
$305$	1.01975e12i	0.386363i
$306$	0	0
$307$	3.63463e12	1.33281	0.666406	−	0.745589i	$-0.267832\pi$
$307$	3.63463e12	1.33281	0.666406	+	0.745589i	$0.267832\pi$
$308$	− 1.32430e12i	− 0.477784i
$309$	0	0
$310$	1.66351e12	0.581054
$311$	− 2.77172e12i	− 0.952680i	−0.879261	−	0.476340i	$-0.841963\pi$
$311$	− 2.77172e12i	− 0.952680i	0.879261	−	0.476340i	$-0.158037\pi$
$312$	0	0
$313$	−4.60648e12	−1.53337	−0.766686	−	0.642022i	$-0.778096\pi$
$313$	−4.60648e12	−1.53337	−0.766686	+	0.642022i	$0.778096\pi$
$314$	1.25783e12i	0.412073i
$315$	0	0
$316$	2.87845e12	0.913532
$317$	3.54869e12i	1.10859i	0.832319	+	0.554296i	$0.187013\pi$
$317$	3.54869e12i	1.10859i	−0.832319	+	0.554296i	$0.812987\pi$
$318$	0	0
$319$	−3.18846e12	−0.965223
$320$	− 3.49215e11i	− 0.104074i
$321$	0	0
$322$	3.46723e12	1.00162
$323$	− 1.48673e12i	− 0.422882i
$324$	0	0
$325$	−1.83876e12	−0.507118
$326$	− 3.02642e12i	− 0.821942i
$327$	0	0
$328$	1.48324e12	0.390698
$329$	− 2.36206e12i	− 0.612788i
$330$	0	0
$331$	1.04493e11	0.0262994	0.0131497	−	0.999914i	$-0.495814\pi$
$331$	1.04493e11	0.0262994	0.0131497	+	0.999914i	$0.495814\pi$
$332$	− 2.07316e12i	− 0.513975i
$333$	0	0
$334$	5.93774e11	0.142853
$335$	4.00544e11i	0.0949351i
$336$	0	0
$337$	−5.21436e12	−1.19964	−0.599821	−	0.800134i	$-0.704762\pi$
$337$	−5.21436e12	−1.19964	−0.599821	+	0.800134i	$0.704762\pi$
$338$	5.40405e12i	1.22500i
$339$	0	0
$340$	−1.02867e12	−0.226403
$341$	− 3.69190e12i	− 0.800716i
$342$	0	0
$343$	−3.42623e12	−0.721681
$344$	1.90227e12i	0.394893i
$345$	0	0
$346$	−5.72079e12	−1.15365
$347$	− 3.01740e12i	− 0.599771i	−0.953975	−	0.299886i	$-0.903051\pi$
$347$	− 3.01740e12i	− 0.599771i	0.953975	−	0.299886i	$-0.0969485\pi$
$348$	0	0
$349$	−2.71540e12	−0.524453	−0.262227	−	0.965006i	$-0.584457\pi$
$349$	−2.71540e12	−0.524453	−0.262227	+	0.965006i	$0.584457\pi$
$350$	1.34197e12i	0.255507i
$351$	0	0
$352$	−7.75030e11	−0.143419
$353$	3.39294e12i	0.619017i	0.950897	+	0.309508i	$0.100164\pi$
$353$	3.39294e12i	0.619017i	−0.950897	+	0.309508i	$0.899836\pi$
$354$	0	0
$355$	3.78392e12	0.671120
$356$	3.29361e12i	0.575999i
$357$	0	0
$358$	7.24519e11	0.123207
$359$	8.22311e12i	1.37900i	0.724287	+	0.689499i	$0.242169\pi$
$359$	8.22311e12i	1.37900i	−0.724287	+	0.689499i	$0.757831\pi$
$360$	0	0
$361$	−2.42412e12	−0.395383
$362$	− 5.87070e12i	− 0.944380i
$363$	0	0
$364$	6.22059e12	0.973474
$365$	− 9.35946e10i	− 0.0144473i
$366$	0	0
$367$	−4.04651e12	−0.607786	−0.303893	−	0.952706i	$-0.598286\pi$
$367$	−4.04651e12	−0.607786	−0.303893	+	0.952706i	$0.598286\pi$
$368$	− 2.02916e12i	− 0.300661i
$369$	0	0
$370$	6.61635e12	0.954136
$371$	2.67011e12i	0.379891i
$372$	0	0
$373$	4.07806e12	0.564819	0.282410	−	0.959294i	$-0.408866\pi$
$373$	4.07806e12	0.564819	0.282410	+	0.959294i	$0.408866\pi$
$374$	2.28298e12i	0.311993i
$375$	0	0
$376$	−1.38237e12	−0.183943
$377$	− 1.49771e13i	− 1.96662i
$378$	0	0
$379$	9.60625e11	0.122845	0.0614225	−	0.998112i	$-0.480436\pi$
$379$	9.60625e11	0.122845	0.0614225	+	0.998112i	$0.480436\pi$
$380$	− 2.56485e12i	− 0.323701i
$381$	0	0
$382$	1.05573e13	1.29788
$383$	3.43778e12i	0.417142i	0.978007	+	0.208571i	$0.0668813\pi$
$383$	3.43778e12i	0.417142i	−0.978007	+	0.208571i	$0.933119\pi$
$384$	0	0
$385$	−6.72975e12	−0.795601
$386$	7.60355e12i	0.887320i
$387$	0	0
$388$	−5.40945e12	−0.615169
$389$	− 1.01383e13i	− 1.13820i	−0.822268	−	0.569100i	$-0.807292\pi$
$389$	− 1.01383e13i	− 1.13820i	0.822268	−	0.569100i	$-0.192708\pi$
$390$	0	0
$391$	−5.97723e12	−0.654058
$392$	− 1.26738e12i	− 0.136923i
$393$	0	0
$394$	−6.92531e10	−0.00729387
$395$	− 1.46276e13i	− 1.52120i
$396$	0	0
$397$	−1.80155e13	−1.82682	−0.913408	−	0.407045i	$-0.866559\pi$
$397$	−1.80155e13	−1.82682	−0.913408	+	0.407045i	$0.866559\pi$
$398$	− 3.81122e12i	− 0.381635i
$399$	0	0
$400$	7.85374e11	0.0766967
$401$	8.08306e11i	0.0779568i	0.999240	+	0.0389784i	$0.0124103\pi$
$401$	8.08306e11i	0.0779568i	−0.999240	+	0.0389784i	$0.987590\pi$
$402$	0	0
$403$	1.73419e13	1.63144
$404$	8.91194e12i	0.828067i
$405$	0	0
$406$	−1.09306e13	−0.990864
$407$	− 1.46840e13i	− 1.31484i
$408$	0	0
$409$	−7.36515e12	−0.643524	−0.321762	−	0.946821i	$-0.604275\pi$
$409$	−7.36515e12	−0.643524	−0.321762	+	0.946821i	$0.604275\pi$
$410$	− 7.53745e12i	− 0.650587i
$411$	0	0
$412$	2.46822e12	0.207921
$413$	5.45355e12i	0.453868i
$414$	0	0
$415$	−1.05353e13	−0.855865
$416$	− 3.64053e12i	− 0.292212i
$417$	0	0
$418$	−5.69229e12	−0.446073
$419$	8.81979e12i	0.682949i	0.939891	+	0.341474i	$0.110926\pi$
$419$	8.81979e12i	0.682949i	−0.939891	+	0.341474i	$0.889074\pi$
$420$	0	0
$421$	1.21472e13	0.918474	0.459237	−	0.888314i	$-0.348123\pi$
$421$	1.21472e13	0.918474	0.459237	+	0.888314i	$0.348123\pi$
$422$	− 1.03722e13i	− 0.775014i
$423$	0	0
$424$	1.56265e12	0.114033
$425$	− 2.31345e12i	− 0.166846i
$426$	0	0
$427$	7.75859e12	0.546567
$428$	6.23763e12i	0.434311i
$429$	0	0
$430$	9.66685e12	0.657571
$431$	− 1.51152e13i	− 1.01632i	−0.861264	−	0.508158i	$-0.830327\pi$
$431$	− 1.51152e13i	− 1.01632i	0.861264	−	0.508158i	$-0.169673\pi$
$432$	0	0
$433$	−4.80955e11	−0.0315984	−0.0157992	−	0.999875i	$-0.505029\pi$
$433$	−4.80955e11	−0.0315984	−0.0157992	+	0.999875i	$0.505029\pi$
$434$	− 1.26565e13i	− 0.821987i
$435$	0	0
$436$	2.78140e12	0.176535
$437$	− 1.49034e13i	− 0.935141i
$438$	0	0
$439$	5.88103e12	0.360687	0.180344	−	0.983604i	$-0.442279\pi$
$439$	5.88103e12	0.360687	0.180344	+	0.983604i	$0.442279\pi$
$440$	3.93851e12i	0.238819i
$441$	0	0
$442$	−1.07238e13	−0.635678
$443$	1.25806e13i	0.737363i	0.929556	+	0.368682i	$0.120191\pi$
$443$	1.25806e13i	0.737363i	−0.929556	+	0.368682i	$0.879809\pi$
$444$	0	0
$445$	1.67373e13	0.959147
$446$	− 1.36510e13i	− 0.773554i
$447$	0	0
$448$	−2.65694e12	−0.147228
$449$	3.73718e12i	0.204792i	0.994744	+	0.102396i	$0.0326508\pi$
$449$	3.73718e12i	0.204792i	−0.994744	+	0.102396i	$0.967349\pi$
$450$	0	0
$451$	−1.67282e13	−0.896534
$452$	1.74029e13i	0.922421i
$453$	0	0
$454$	−5.41685e12	−0.280846
$455$	− 3.16115e13i	− 1.62102i
$456$	0	0
$457$	−1.35581e13	−0.680171	−0.340086	−	0.940394i	$-0.610456\pi$
$457$	−1.35581e13	−0.680171	−0.340086	+	0.940394i	$0.610456\pi$
$458$	− 2.31528e13i	− 1.14888i
$459$	0	0
$460$	−1.03117e13	−0.500657
$461$	9.69207e12i	0.465492i	0.972538	+	0.232746i	$0.0747710\pi$
$461$	9.69207e12i	0.465492i	−0.972538	+	0.232746i	$0.925229\pi$
$462$	0	0
$463$	7.11112e12	0.334220	0.167110	−	0.985938i	$-0.446556\pi$
$463$	7.11112e12	0.334220	0.167110	+	0.985938i	$0.446556\pi$
$464$	6.39701e12i	0.297432i
$465$	0	0
$466$	−9.14948e12	−0.416358
$467$	− 9.68713e12i	− 0.436125i	−0.975935	−	0.218062i	$-0.930026\pi$
$467$	− 9.68713e12i	− 0.436125i	0.975935	−	0.218062i	$-0.0699736\pi$
$468$	0	0
$469$	3.04747e12	0.134300
$470$	7.02484e12i	0.306300i
$471$	0	0
$472$	3.19163e12	0.136239
$473$	− 2.14541e13i	− 0.906159i
$474$	0	0
$475$	5.76826e12	0.238548
$476$	7.82646e12i	0.320281i
$477$	0	0
$478$	2.91804e13	1.16937
$479$	− 8.20294e12i	− 0.325306i	−0.986683	−	0.162653i	$-0.947995\pi$
$479$	− 8.20294e12i	− 0.325306i	0.986683	−	0.162653i	$-0.0520051\pi$
$480$	0	0
$481$	6.89747e13	2.67895
$482$	3.89313e12i	0.149646i
$483$	0	0
$484$	−4.53904e12	−0.170898
$485$	2.74895e13i	1.02437i
$486$	0	0
$487$	−5.34165e13	−1.94998	−0.974991	−	0.222245i	$-0.928662\pi$
$487$	−5.34165e13	−1.94998	−0.974991	+	0.222245i	$0.928662\pi$
$488$	− 4.54063e12i	− 0.164065i
$489$	0	0
$490$	−6.44053e12	−0.228003
$491$	2.94811e13i	1.03308i	0.856262	+	0.516542i	$0.172781\pi$
$491$	2.94811e13i	1.03308i	−0.856262	+	0.516542i	$0.827219\pi$
$492$	0	0
$493$	1.88435e13	0.647033
$494$	− 2.67382e13i	− 0.908862i
$495$	0	0
$496$	−7.40707e12	−0.246739
$497$	− 2.87892e13i	− 0.949398i
$498$	0	0
$499$	−4.62777e13	−1.49578	−0.747892	−	0.663821i	$-0.768934\pi$
$499$	−4.62777e13	−1.49578	−0.747892	+	0.663821i	$0.768934\pi$
$500$	− 1.70004e13i	− 0.544012i
$501$	0	0
$502$	3.77931e13	1.18548
$503$	4.25769e13i	1.32231i	0.750249	+	0.661156i	$0.229934\pi$
$503$	4.25769e13i	1.32231i	−0.750249	+	0.661156i	$0.770066\pi$
$504$	0	0
$505$	4.52883e13	1.37889
$506$	2.28852e13i	0.689925i
$507$	0	0
$508$	2.19960e13	0.650166
$509$	− 1.24275e13i	− 0.363744i	−0.983322	−	0.181872i	$-0.941784\pi$
$509$	− 1.24275e13i	− 0.363744i	0.983322	−	0.181872i	$-0.0582156\pi$
$510$	0	0
$511$	−7.12097e11	−0.0204378
$512$	1.55494e12i	0.0441942i
$513$	0	0
$514$	3.97763e12	0.110869
$515$	− 1.25429e13i	− 0.346228i
$516$	0	0
$517$	1.55906e13	0.422094
$518$	− 5.03393e13i	− 1.34977i
$519$	0	0
$520$	−1.85003e13	−0.486588
$521$	− 2.20659e13i	− 0.574820i	−0.957808	−	0.287410i	$-0.907206\pi$
$521$	− 2.20659e13i	− 0.574820i	0.957808	−	0.287410i	$-0.0927943\pi$
$522$	0	0
$523$	4.20766e13	1.07531	0.537653	−	0.843166i	$-0.319311\pi$
$523$	4.20766e13	1.07531	0.537653	+	0.843166i	$0.319311\pi$
$524$	2.19807e13i	0.556398i
$525$	0	0
$526$	−4.74260e13	−1.17784
$527$	2.18188e13i	0.536757i
$528$	0	0
$529$	−1.84908e13	−0.446351
$530$	− 7.94100e12i	− 0.189887i
$531$	0	0
$532$	−1.95142e13	−0.457922
$533$	− 7.85770e13i	− 1.82667i
$534$	0	0
$535$	3.16981e13	0.723209
$536$	− 1.78350e12i	− 0.0403133i
$537$	0	0
$538$	−1.29157e13	−0.286554
$539$	1.42938e13i	0.314198i
$540$	0	0
$541$	8.16143e13	1.76108	0.880541	−	0.473969i	$-0.157179\pi$
$541$	8.16143e13	1.76108	0.880541	+	0.473969i	$0.157179\pi$
$542$	2.01031e13i	0.429799i
$543$	0	0
$544$	4.58035e12	0.0961400
$545$	− 1.41344e13i	− 0.293965i
$546$	0	0
$547$	1.62573e13	0.331980	0.165990	−	0.986127i	$-0.446918\pi$
$547$	1.62573e13	0.331980	0.165990	+	0.986127i	$0.446918\pi$
$548$	− 8.44593e12i	− 0.170901i
$549$	0	0
$550$	−8.85758e12	−0.175996
$551$	4.69835e13i	0.925098i
$552$	0	0
$553$	−1.11291e14	−2.15197
$554$	4.02416e13i	0.771128i
$555$	0	0
$556$	−4.68351e13	−0.881449
$557$	6.26553e13i	1.16864i	0.811522	+	0.584321i	$0.198639\pi$
$557$	6.26553e13i	1.16864i	−0.811522	+	0.584321i	$0.801361\pi$
$558$	0	0
$559$	1.00776e14	1.84628
$560$	1.35019e13i	0.245163i
$561$	0	0
$562$	−4.12740e13	−0.736198
$563$	8.22227e13i	1.45362i	0.686841	+	0.726808i	$0.258997\pi$
$563$	8.22227e13i	1.45362i	−0.686841	+	0.726808i	$0.741003\pi$
$564$	0	0
$565$	8.84372e13	1.53601
$566$	4.94606e13i	0.851485i
$567$	0	0
$568$	−1.68486e13	−0.284985
$569$	9.46922e13i	1.58764i	0.608151	+	0.793822i	$0.291912\pi$
$569$	9.46922e13i	1.58764i	−0.608151	+	0.793822i	$0.708088\pi$
$570$	0	0
$571$	5.10607e13	0.841214	0.420607	−	0.907243i	$-0.361817\pi$
$571$	5.10607e13	0.841214	0.420607	+	0.907243i	$0.361817\pi$
$572$	4.10585e13i	0.670538i
$573$	0	0
$574$	−5.73473e13	−0.920351
$575$	− 2.31906e13i	− 0.368955i
$576$	0	0
$577$	−1.09872e14	−1.71794	−0.858972	−	0.512023i	$-0.828896\pi$
$577$	−1.09872e14	−1.71794	−0.858972	+	0.512023i	$0.828896\pi$
$578$	3.21245e13i	0.497964i
$579$	0	0
$580$	3.25080e13	0.495280
$581$	8.01556e13i	1.21075i
$582$	0	0
$583$	−1.76238e13	−0.261672
$584$	4.16747e11i	0.00613490i
$585$	0	0
$586$	−7.39157e13	−1.06967
$587$	− 7.74556e13i	− 1.11138i	−0.831390	−	0.555689i	$-0.812454\pi$
$587$	− 7.74556e13i	− 1.11138i	0.831390	−	0.555689i	$-0.187546\pi$
$588$	0	0
$589$	−5.44020e13	−0.767429
$590$	− 1.62191e13i	− 0.226864i
$591$	0	0
$592$	−2.94605e13	−0.405165
$593$	− 1.66356e13i	− 0.226864i	−0.993546	−	0.113432i	$-0.963816\pi$
$593$	− 1.66356e13i	− 0.226864i	0.993546	−	0.113432i	$-0.0361843\pi$
$594$	0	0
$595$	3.97722e13	0.533328
$596$	5.17363e13i	0.687961i
$597$	0	0
$598$	−1.07498e14	−1.40571
$599$	1.16818e14i	1.51487i	0.652912	+	0.757434i	$0.273547\pi$
$599$	1.16818e14i	1.51487i	−0.652912	+	0.757434i	$0.726453\pi$
$600$	0	0
$601$	−1.18710e14	−1.51396	−0.756978	−	0.653441i	$-0.773325\pi$
$601$	−1.18710e14	−1.51396	−0.756978	+	0.653441i	$0.773325\pi$
$602$	− 7.35484e13i	− 0.930231i
$603$	0	0
$604$	4.41077e13	0.548694
$605$	2.30663e13i	0.284577i
$606$	0	0
$607$	3.06737e12	0.0372240	0.0186120	−	0.999827i	$-0.494075\pi$
$607$	3.06737e12	0.0372240	0.0186120	+	0.999827i	$0.494075\pi$
$608$	1.14204e13i	0.137456i
$609$	0	0
$610$	−2.30743e13	−0.273200
$611$	7.32332e13i	0.860006i
$612$	0	0
$613$	1.06163e14	1.22651	0.613253	−	0.789887i	$-0.289861\pi$
$613$	1.06163e14	1.22651	0.613253	+	0.789887i	$0.289861\pi$
$614$	8.22424e13i	0.942440i
$615$	0	0
$616$	2.99654e13	0.337845
$617$	1.57758e12i	0.0176427i	0.999961	+	0.00882136i	$0.00280796\pi$
$617$	1.57758e12i	0.0176427i	−0.999961	+	0.00882136i	$0.997192\pi$
$618$	0	0
$619$	−3.52563e13	−0.387957	−0.193978	−	0.981006i	$-0.562139\pi$
$619$	−3.52563e13	−0.387957	−0.193978	+	0.981006i	$0.562139\pi$
$620$	3.76409e13i	0.410867i
$621$	0	0
$622$	6.27168e13	0.673647
$623$	− 1.27343e14i	− 1.35685i
$624$	0	0
$625$	−5.71342e13	−0.599095
$626$	− 1.04233e14i	− 1.08426i
$627$	0	0
$628$	−2.84615e13	−0.291380
$629$	8.67809e13i	0.881396i
$630$	0	0
$631$	1.04706e14	1.04670	0.523352	−	0.852117i	$-0.324681\pi$
$631$	1.04706e14	1.04670	0.523352	+	0.852117i	$0.324681\pi$
$632$	6.51319e13i	0.645964i
$633$	0	0
$634$	−8.02977e13	−0.783893
$635$	− 1.11778e14i	− 1.08265i
$636$	0	0
$637$	−6.71417e13	−0.640170
$638$	− 7.21466e13i	− 0.682516i
$639$	0	0
$640$	7.90184e12	0.0735916
$641$	− 6.85708e13i	− 0.633649i	−0.948484	−	0.316825i	$-0.897383\pi$
$641$	− 6.85708e13i	− 0.633649i	0.948484	−	0.316825i	$-0.102617\pi$
$642$	0	0
$643$	−1.02080e14	−0.928725	−0.464362	−	0.885645i	$-0.653716\pi$
$643$	−1.02080e14	−0.928725	−0.464362	+	0.885645i	$0.653716\pi$
$644$	7.84545e13i	0.708253i
$645$	0	0
$646$	3.36409e13	0.299023
$647$	− 5.93094e13i	− 0.523121i	−0.965187	−	0.261561i	$-0.915763\pi$
$647$	− 5.93094e13i	− 0.523121i	0.965187	−	0.261561i	$-0.0842371\pi$
$648$	0	0
$649$	−3.59958e13	−0.312628
$650$	− 4.16065e13i	− 0.358587i
$651$	0	0
$652$	6.84801e13	0.581201
$653$	1.80812e14i	1.52286i	0.648244	+	0.761432i	$0.275503\pi$
$653$	1.80812e14i	1.52286i	−0.648244	+	0.761432i	$0.724497\pi$
$654$	0	0
$655$	1.11701e14	0.926508
$656$	3.35618e13i	0.276266i
$657$	0	0
$658$	5.34472e13	0.433307
$659$	3.93674e13i	0.316745i	0.987379	+	0.158373i	$0.0506247\pi$
$659$	3.93674e13i	0.316745i	−0.987379	+	0.158373i	$0.949375\pi$
$660$	0	0
$661$	8.05192e12	0.0638105	0.0319052	−	0.999491i	$-0.489843\pi$
$661$	8.05192e12	0.0638105	0.0319052	+	0.999491i	$0.489843\pi$
$662$	2.36440e12i	0.0185965i
$663$	0	0
$664$	4.69102e13	0.363435
$665$	9.91662e13i	0.762527i
$666$	0	0
$667$	1.88892e14	1.43082
$668$	1.34356e13i	0.101012i
$669$	0	0
$670$	−9.06329e12	−0.0671292
$671$	5.12100e13i	0.376480i
$672$	0	0
$673$	8.72601e13	0.632034	0.316017	−	0.948753i	$-0.397654\pi$
$673$	8.72601e13	0.632034	0.316017	+	0.948753i	$0.397654\pi$
$674$	− 1.17988e14i	− 0.848275i
$675$	0	0
$676$	−1.22280e14	−0.866205
$677$	− 2.00620e14i	− 1.41069i	−0.708866	−	0.705343i	$-0.750793\pi$
$677$	− 2.00620e14i	− 1.41069i	0.708866	−	0.705343i	$-0.249207\pi$
$678$	0	0
$679$	2.09148e14	1.44912
$680$	− 2.32762e13i	− 0.160091i
$681$	0	0
$682$	8.35383e13	0.566192
$683$	1.58661e14i	1.06750i	0.845644	+	0.533748i	$0.179217\pi$
$683$	1.58661e14i	1.06750i	−0.845644	+	0.533748i	$0.820783\pi$
$684$	0	0
$685$	−4.29201e13	−0.284583
$686$	− 7.75266e13i	− 0.510306i
$687$	0	0
$688$	−4.30434e13	−0.279231
$689$	− 8.27840e13i	− 0.533151i
$690$	0	0
$691$	−1.51620e14	−0.962423	−0.481211	−	0.876605i	$-0.659803\pi$
$691$	−1.51620e14	−0.962423	−0.481211	+	0.876605i	$0.659803\pi$
$692$	− 1.29447e14i	− 0.815756i
$693$	0	0
$694$	6.82760e13	0.424102
$695$	2.38004e14i	1.46778i
$696$	0	0
$697$	9.88621e13	0.600988
$698$	− 6.14425e13i	− 0.370845i
$699$	0	0
$700$	−3.03653e13	−0.180671
$701$	8.58518e13i	0.507177i	0.967312	+	0.253588i	$0.0816109\pi$
$701$	8.58518e13i	0.507177i	−0.967312	+	0.253588i	$0.918389\pi$
$702$	0	0
$703$	−2.16376e14	−1.26018
$704$	− 1.75369e13i	− 0.101412i
$705$	0	0
$706$	−7.67734e13	−0.437711
$707$	− 3.44568e14i	− 1.95064i
$708$	0	0
$709$	−6.97936e13	−0.389569	−0.194785	−	0.980846i	$-0.562401\pi$
$709$	−6.97936e13	−0.389569	−0.194785	+	0.980846i	$0.562401\pi$
$710$	8.56203e13i	0.474553i
$711$	0	0
$712$	−7.45258e13	−0.407293
$713$	2.18717e14i	1.18696i
$714$	0	0
$715$	2.08649e14	1.11657
$716$	1.63940e13i	0.0871204i
$717$	0	0
$718$	−1.86068e14	−0.975099
$719$	− 3.31589e14i	− 1.72566i	−0.505492	−	0.862831i	$-0.668689\pi$
$719$	− 3.31589e14i	− 1.72566i	0.505492	−	0.862831i	$-0.331311\pi$
$720$	0	0
$721$	−9.54303e13	−0.489790
$722$	− 5.48515e13i	− 0.279578i
$723$	0	0
$724$	1.32839e14	0.667777
$725$	7.31095e13i	0.364992i
$726$	0	0
$727$	3.40767e14	1.67798	0.838988	−	0.544151i	$-0.183148\pi$
$727$	3.40767e14	1.67798	0.838988	+	0.544151i	$0.183148\pi$
$728$	1.40756e14i	0.688350i
$729$	0	0
$730$	2.11780e12	0.0102158
$731$	1.26792e14i	0.607440i
$732$	0	0
$733$	1.41028e14	0.666480	0.333240	−	0.942842i	$-0.391858\pi$
$733$	1.41028e14	0.666480	0.333240	+	0.942842i	$0.391858\pi$
$734$	− 9.15621e13i	− 0.429769i
$735$	0	0
$736$	4.59146e13	0.212599
$737$	2.01146e13i	0.0925068i
$738$	0	0
$739$	9.02083e11	0.00409283	0.00204642	−	0.999998i	$-0.499349\pi$
$739$	9.02083e11	0.00409283	0.00204642	+	0.999998i	$0.499349\pi$
$740$	1.49711e14i	0.674676i
$741$	0	0
$742$	−6.04176e13	−0.268623
$743$	− 2.18791e14i	− 0.966241i	−0.875554	−	0.483120i	$-0.839503\pi$
$743$	− 2.18791e14i	− 0.966241i	0.875554	−	0.483120i	$-0.160497\pi$
$744$	0	0
$745$	2.62911e14	1.14559
$746$	9.22760e13i	0.399388i
$747$	0	0
$748$	−5.16580e13	−0.220612
$749$	− 2.41169e14i	− 1.02309i
$750$	0	0
$751$	−1.26489e13	−0.0529485	−0.0264742	−	0.999649i	$-0.508428\pi$
$751$	−1.26489e13	−0.0529485	−0.0264742	+	0.999649i	$0.508428\pi$
$752$	− 3.12794e13i	− 0.130068i
$753$	0	0
$754$	3.38893e14	1.39061
$755$	− 2.24144e14i	− 0.913678i
$756$	0	0
$757$	−3.88219e14	−1.56170	−0.780850	−	0.624718i	$-0.785214\pi$
$757$	−3.88219e14	−1.56170	−0.780850	+	0.624718i	$0.785214\pi$
$758$	2.17365e13i	0.0868646i
$759$	0	0
$760$	5.80359e13	0.228891
$761$	− 1.32230e14i	− 0.518093i	−0.965865	−	0.259046i	$-0.916592\pi$
$761$	− 1.32230e14i	− 0.518093i	0.965865	−	0.259046i	$-0.0834083\pi$
$762$	0	0
$763$	−1.07539e14	−0.415856
$764$	2.38884e14i	0.917741i
$765$	0	0
$766$	−7.77881e13	−0.294964
$767$	− 1.69082e14i	− 0.636972i
$768$	0	0
$769$	−3.91186e14	−1.45463	−0.727314	−	0.686305i	$-0.759231\pi$
$769$	−3.91186e14	−1.45463	−0.727314	+	0.686305i	$0.759231\pi$
$770$	− 1.52277e14i	− 0.562575i
$771$	0	0
$772$	−1.72049e14	−0.627430
$773$	− 5.71983e13i	− 0.207246i	−0.994617	−	0.103623i	$-0.966957\pi$
$773$	− 5.71983e13i	− 0.207246i	0.994617	−	0.103623i	$-0.0330435\pi$
$774$	0	0
$775$	−8.46532e13	−0.302785
$776$	− 1.22402e14i	− 0.434990i
$777$	0	0
$778$	2.29404e14	0.804829
$779$	2.46498e14i	0.859265i
$780$	0	0
$781$	1.90021e14	0.653954
$782$	− 1.35249e14i	− 0.462489i
$783$	0	0
$784$	2.86776e13	0.0968194
$785$	1.44634e14i	0.485202i
$786$	0	0
$787$	−3.09644e14	−1.02563	−0.512813	−	0.858500i	$-0.671397\pi$
$787$	−3.09644e14	−1.02563	−0.512813	+	0.858500i	$0.671397\pi$
$788$	− 1.56702e12i	− 0.00515755i
$789$	0	0
$790$	3.30984e14	1.07565
$791$	− 6.72858e14i	− 2.17291i
$792$	0	0
$793$	−2.40547e14	−0.767069
$794$	− 4.07645e14i	− 1.29175i
$795$	0	0
$796$	8.62380e13	0.269857
$797$	− 4.04996e14i	− 1.25939i	−0.776844	−	0.629693i	$-0.783181\pi$
$797$	− 4.04996e14i	− 1.25939i	0.776844	−	0.629693i	$-0.216819\pi$
$798$	0	0
$799$	−9.21387e13	−0.282949
$800$	1.77710e13i	0.0542327i
$801$	0	0
$802$	−1.82899e13	−0.0551238
$803$	− 4.70014e12i	− 0.0140777i
$804$	0	0
$805$	3.98686e14	1.17938
$806$	3.92402e14i	1.15360i
$807$	0	0
$808$	−2.01654e14	−0.585532
$809$	− 2.19164e14i	− 0.632450i	−0.948684	−	0.316225i	$-0.897584\pi$
$809$	− 2.19164e14i	− 0.632450i	0.948684	−	0.316225i	$-0.102416\pi$
$810$	0	0
$811$	−2.58801e14	−0.737669	−0.368835	−	0.929495i	$-0.620243\pi$
$811$	−2.58801e14	−0.737669	−0.368835	+	0.929495i	$0.620243\pi$
$812$	− 2.47331e14i	− 0.700647i
$813$	0	0
$814$	3.32261e14	0.929730
$815$	− 3.47999e14i	− 0.967809i
$816$	0	0
$817$	−3.16137e14	−0.868489
$818$	− 1.66654e14i	− 0.455040i
$819$	0	0
$820$	1.70553e14	0.460034
$821$	− 4.98874e14i	− 1.33744i	−0.743513	−	0.668721i	$-0.766842\pi$
$821$	− 4.98874e14i	− 1.33744i	0.743513	−	0.668721i	$-0.233158\pi$
$822$	0	0
$823$	5.37456e14	1.42345	0.711727	−	0.702456i	$-0.247913\pi$
$823$	5.37456e14	1.42345	0.711727	+	0.702456i	$0.247913\pi$
$824$	5.58495e13i	0.147022i
$825$	0	0
$826$	−1.23400e14	−0.320933
$827$	2.54187e14i	0.657092i	0.944488	+	0.328546i	$0.106559\pi$
$827$	2.54187e14i	0.657092i	−0.944488	+	0.328546i	$0.893441\pi$
$828$	0	0
$829$	−6.22901e13	−0.159091	−0.0795456	−	0.996831i	$-0.525347\pi$
$829$	−6.22901e13	−0.159091	−0.0795456	+	0.996831i	$0.525347\pi$
$830$	− 2.38386e14i	− 0.605188i
$831$	0	0
$832$	8.23758e13	0.206625
$833$	− 8.44747e13i	− 0.210621i
$834$	0	0
$835$	6.82763e13	0.168204
$836$	− 1.28802e14i	− 0.315421i
$837$	0	0
$838$	−1.99569e14	−0.482918
$839$	− 1.42382e14i	− 0.342488i	−0.985229	−	0.171244i	$-0.945221\pi$
$839$	− 1.42382e14i	− 0.342488i	0.985229	−	0.171244i	$-0.0547786\pi$
$840$	0	0
$841$	−1.74783e14	−0.415451
$842$	2.74861e14i	0.649459i
$843$	0	0
$844$	2.34697e14	0.548018
$845$	6.21395e14i	1.44239i
$846$	0	0
$847$	1.75495e14	0.402577
$848$	3.53587e13i	0.0806338i
$849$	0	0
$850$	5.23474e13	0.117978
$851$	8.69914e14i	1.94907i
$852$	0	0
$853$	−2.58849e14	−0.573194	−0.286597	−	0.958051i	$-0.592524\pi$
$853$	−2.58849e14	−0.573194	−0.286597	+	0.958051i	$0.592524\pi$
$854$	1.75557e14i	0.386481i
$855$	0	0
$856$	−1.41141e14	−0.307104
$857$	5.61997e14i	1.21571i	0.794048	+	0.607855i	$0.207970\pi$
$857$	5.61997e14i	1.21571i	−0.794048	+	0.607855i	$0.792030\pi$
$858$	0	0
$859$	−2.99284e14	−0.639909	−0.319955	−	0.947433i	$-0.603668\pi$
$859$	−2.99284e14	−0.639909	−0.319955	+	0.947433i	$0.603668\pi$
$860$	2.18736e14i	0.464973i
$861$	0	0
$862$	3.42019e14	0.718643
$863$	− 3.86656e14i	− 0.807738i	−0.914817	−	0.403869i	$-0.867665\pi$
$863$	− 3.86656e14i	− 0.807738i	0.914817	−	0.403869i	$-0.132335\pi$
$864$	0	0
$865$	−6.57816e14	−1.35839
$866$	− 1.08828e13i	− 0.0223434i
$867$	0	0
$868$	2.86384e14	0.581233
$869$	− 7.34569e14i	− 1.48229i
$870$	0	0
$871$	−9.44837e13	−0.188480
$872$	6.29360e13i	0.124829i
$873$	0	0
$874$	3.37225e14	0.661245
$875$	6.57295e14i	1.28150i
$876$	0	0
$877$	−8.54621e14	−1.64731	−0.823656	−	0.567090i	$-0.808069\pi$
$877$	−8.54621e14	−1.64731	−0.823656	+	0.567090i	$0.808069\pi$
$878$	1.33072e14i	0.255044i
$879$	0	0
$880$	−8.91184e13	−0.168871
$881$	2.74022e13i	0.0516305i	0.999667	+	0.0258152i	$0.00821816\pi$
$881$	2.74022e13i	0.0516305i	−0.999667	+	0.0258152i	$0.991782\pi$
$882$	0	0
$883$	−1.96454e14	−0.365979	−0.182990	−	0.983115i	$-0.558577\pi$
$883$	−1.96454e14	−0.365979	−0.182990	+	0.983115i	$0.558577\pi$
$884$	− 2.42652e14i	− 0.449492i
$885$	0	0
$886$	−2.84666e14	−0.521394
$887$	7.53937e14i	1.37315i	0.727060	+	0.686573i	$0.240886\pi$
$887$	7.53937e14i	1.37315i	−0.727060	+	0.686573i	$0.759114\pi$
$888$	0	0
$889$	−8.50443e14	−1.53157
$890$	3.78722e14i	0.678219i
$891$	0	0
$892$	3.08887e14	0.546985
$893$	− 2.29735e14i	− 0.404547i
$894$	0	0
$895$	8.33102e13	0.145072
$896$	− 6.01197e13i	− 0.104106i
$897$	0	0
$898$	−8.45627e13	−0.144810
$899$	− 6.89516e14i	− 1.17421i
$900$	0	0
$901$	1.04155e14	0.175411
$902$	− 3.78516e14i	− 0.633946i
$903$	0	0
$904$	−3.93783e14	−0.652250
$905$	− 6.75053e14i	− 1.11198i
$906$	0	0
$907$	−1.62058e14	−0.264018	−0.132009	−	0.991249i	$-0.542143\pi$
$907$	−1.62058e14	−0.264018	−0.132009	+	0.991249i	$0.542143\pi$
$908$	− 1.22569e14i	− 0.198588i
$909$	0	0
$910$	7.15286e14	1.14623
$911$	1.60882e14i	0.256399i	0.991748	+	0.128199i	$0.0409198\pi$
$911$	1.60882e14i	0.256399i	−0.991748	+	0.128199i	$0.959080\pi$
$912$	0	0
$913$	−5.29061e14	−0.833973
$914$	− 3.06785e14i	− 0.480954i
$915$	0	0
$916$	5.23888e14	0.812383
$917$	− 8.49853e14i	− 1.31068i
$918$	0	0
$919$	−6.90875e14	−1.05395	−0.526977	−	0.849879i	$-0.676675\pi$
$919$	−6.90875e14	−1.05395	−0.526977	+	0.849879i	$0.676675\pi$
$920$	− 2.33327e14i	− 0.354018i
$921$	0	0
$922$	−2.19307e14	−0.329152
$923$	8.92582e14i	1.33242i
$924$	0	0
$925$	−3.36695e14	−0.497196
$926$	1.60906e14i	0.236329i
$927$	0	0
$928$	−1.44748e14	−0.210316
$929$	1.20193e15i	1.73700i	0.495689	+	0.868500i	$0.334916\pi$
$929$	1.20193e15i	1.73700i	−0.495689	+	0.868500i	$0.665084\pi$
$930$	0	0
$931$	2.10626e14	0.301136
$932$	− 2.07029e14i	− 0.294409i
$933$	0	0
$934$	2.19195e14	0.308387
$935$	2.62513e14i	0.367361i
$936$	0	0
$937$	8.71595e14	1.20675	0.603374	−	0.797458i	$-0.293823\pi$
$937$	8.71595e14	1.20675	0.603374	+	0.797458i	$0.293823\pi$
$938$	6.89563e13i	0.0949642i
$939$	0	0
$940$	−1.58954e14	−0.216587
$941$	− 2.13649e14i	− 0.289569i	−0.989463	−	0.144785i	$-0.953751\pi$
$941$	− 2.13649e14i	− 0.289569i	0.989463	−	0.144785i	$-0.0462489\pi$
$942$	0	0
$943$	9.91019e14	1.32900
$944$	7.22183e13i	0.0963358i
$945$	0	0
$946$	4.85451e14	0.640751
$947$	3.71704e14i	0.488031i	0.969771	+	0.244015i	$0.0784647\pi$
$947$	3.71704e14i	0.488031i	−0.969771	+	0.244015i	$0.921535\pi$
$948$	0	0
$949$	2.20778e13	0.0286831
$950$	1.30521e14i	0.168679i
$951$	0	0
$952$	−1.77093e14	−0.226473
$953$	1.25331e15i	1.59439i	0.603723	+	0.797194i	$0.293683\pi$
$953$	1.25331e15i	1.59439i	−0.603723	+	0.797194i	$0.706317\pi$
$954$	0	0
$955$	1.21395e15	1.52821
$956$	6.60278e14i	0.826870i
$957$	0	0
$958$	1.85611e14	0.230026
$959$	3.26550e14i	0.402584i
$960$	0	0
$961$	−2.12414e13	−0.0259159
$962$	1.56072e15i	1.89430i
$963$	0	0
$964$	−8.80915e13	−0.105815
$965$	8.74309e14i	1.04479i
$966$	0	0
$967$	−4.79849e14	−0.567509	−0.283754	−	0.958897i	$-0.591580\pi$
$967$	−4.79849e14	−0.567509	−0.283754	+	0.958897i	$0.591580\pi$
$968$	− 1.02707e14i	− 0.120843i
$969$	0	0
$970$	−6.22016e14	−0.724340
$971$	3.60884e14i	0.418091i	0.977906	+	0.209046i	$0.0670357\pi$
$971$	3.60884e14i	0.418091i	−0.977906	+	0.209046i	$0.932964\pi$
$972$	0	0
$973$	1.81081e15	2.07639
$974$	− 1.20868e15i	− 1.37885i
$975$	0	0
$976$	1.02743e14	0.116012
$977$	1.37806e14i	0.154809i	0.997000	+	0.0774045i	$0.0246633\pi$
$977$	1.37806e14i	0.154809i	−0.997000	+	0.0774045i	$0.975337\pi$
$978$	0	0
$979$	8.40515e14	0.934613
$980$	− 1.45732e14i	− 0.161223i
$981$	0	0
$982$	−6.67081e14	−0.730501
$983$	1.25441e15i	1.36670i	0.730091	+	0.683349i	$0.239477\pi$
$983$	1.25441e15i	1.36670i	−0.730091	+	0.683349i	$0.760523\pi$
$984$	0	0
$985$	−7.96320e12	−0.00858829
$986$	4.26379e14i	0.457522i
$987$	0	0
$988$	6.05017e14	0.642663
$989$	1.27099e15i	1.34326i
$990$	0	0
$991$	3.10912e14	0.325288	0.162644	−	0.986685i	$-0.447998\pi$
$991$	3.10912e14	0.325288	0.162644	+	0.986685i	$0.447998\pi$
$992$	− 1.67603e14i	− 0.174471i
$993$	0	0
$994$	6.51426e14	0.671326
$995$	− 4.38240e14i	− 0.449362i
$996$	0	0
$997$	−1.44711e15	−1.46902	−0.734508	−	0.678600i	$-0.762587\pi$
$997$	−1.44711e15	−1.46902	−0.734508	+	0.678600i	$0.762587\pi$
$998$	− 1.04714e15i	− 1.05768i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.11.b.a.161.7	yes	8
3.2	odd	2	inner	162.11.b.a.161.2	✓	8
9.2	odd	6		162.11.d.e.53.3		16
9.4	even	3		162.11.d.e.107.3		16
9.5	odd	6		162.11.d.e.107.6		16
9.7	even	3		162.11.d.e.53.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.11.b.a.161.2	✓	8	3.2	odd	2	inner
162.11.b.a.161.7	yes	8	1.1	even	1	trivial
162.11.d.e.53.3		16	9.2	odd	6
162.11.d.e.53.6		16	9.7	even	3
162.11.d.e.107.3		16	9.4	even	3
162.11.d.e.107.6		16	9.5	odd	6

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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+22.6274i q^{2} -512.000 q^{4} +2601.86i q^{5} +19795.7 q^{7} -11585.2i q^{8} -58873.3 q^{10} +130660. i q^{11} -613747. q^{13} +447927. i q^{14} +262144. q^{16} -772189. i q^{17} +1.92534e6 q^{19} -1.33215e6i q^{20} -2.95651e6 q^{22} -7.74063e6i q^{23} +2.99596e6 q^{25} -1.38875e7i q^{26} -1.01354e7 q^{28} +2.44027e7i q^{29} -2.82557e7 q^{31} +5.93164e6i q^{32} +1.74726e7 q^{34} +5.15057e7i q^{35} -1.12383e8 q^{37} +4.35656e7i q^{38} +3.01431e7 q^{40} +1.28028e8i q^{41} -1.64197e8 q^{43} -6.68981e7i q^{44} +1.75150e8 q^{46} -1.19321e8i q^{47} +1.09396e8 q^{49} +6.77909e7i q^{50} +3.14239e8 q^{52} +1.34883e8i q^{53} -3.39960e8 q^{55} -2.29338e8i q^{56} -5.52169e8 q^{58} +2.75491e8i q^{59} +3.91932e8 q^{61} -6.39354e8i q^{62} -1.34218e8 q^{64} -1.59688e9i q^{65} +1.53946e8 q^{67} +3.95361e8i q^{68} -1.16544e9 q^{70} -1.45431e9i q^{71} -3.59722e7 q^{73} -2.54293e9i q^{74} -9.85776e8 q^{76} +2.58652e9i q^{77} -5.62198e9 q^{79} +6.82061e8i q^{80} -2.89695e9 q^{82} +4.04913e9i q^{83} +2.00913e9 q^{85} -3.71536e9i q^{86} +1.51373e9 q^{88} -6.43282e9i q^{89} -1.21496e10 q^{91} +3.96320e9i q^{92} +2.69993e9 q^{94} +5.00947e9i q^{95} +1.05653e10 q^{97} +2.47536e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4096 q^{4} + 45112 q^{7} - 174720 q^{10} - 721448 q^{13} + 2097152 q^{16} - 731192 q^{19} - 13824 q^{22} + 27586040 q^{25} - 23097344 q^{28} + 72502528 q^{31} + 70417536 q^{34} - 166952240 q^{37}+ \cdots + 2247775936 q^{97}+O(q^{100}) \) 8 * q - 4096 * q^4 + 45112 * q^7 - 174720 * q^10 - 721448 * q^13 + 2097152 * q^16 - 731192 * q^19 - 13824 * q^22 + 27586040 * q^25 - 23097344 * q^28 + 72502528 * q^31 + 70417536 * q^34 - 166952240 * q^37 + 89456640 * q^40 - 12510440 * q^43 - 269948160 * q^46 + 188021592 * q^49 + 369381376 * q^52 - 181251000 * q^55 - 154795392 * q^58 - 1782273248 * q^61 - 1073741824 * q^64 + 108743656 * q^67 + 62250240 * q^70 + 5102234368 * q^73 + 374370304 * q^76 - 9246201752 * q^79 - 478119936 * q^82 + 20649676320 * q^85 + 7077888 * q^88 - 18226522120 * q^91 + 20130964224 * q^94 + 2247775936 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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