LMFDB - Embedded newform 27.15.b.c.26.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,15,Mod(26,27)] 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("27.26"); S:= CuspForms(chi, 15); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 15, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	27.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-22484] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$33.5688214010$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3196x^{2} + 2297460 $ x^4 + 3196*x^2 + 2297460
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{9}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.1
Root			$45.8705i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.15.b.c.26.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-197.702i q^{2} -22702.1 q^{4} +67180.2i q^{5} +453839. q^{7} +1.24910e6i q^{8} +1.32817e7 q^{10} +2.02634e6i q^{11} +6.90269e7 q^{13} -8.97249e7i q^{14} -1.25001e8 q^{16} -6.66755e8i q^{17} -1.19944e9 q^{19} -1.52513e9i q^{20} +4.00612e8 q^{22} -2.10269e9i q^{23} +1.59034e9 q^{25} -1.36468e10i q^{26} -1.03031e10 q^{28} -2.11520e10i q^{29} +3.86410e10 q^{31} +4.51783e10i q^{32} -1.31819e11 q^{34} +3.04890e10i q^{35} -1.72521e11 q^{37} +2.37132e11i q^{38} -8.39148e10 q^{40} +3.23308e10i q^{41} +5.94792e10 q^{43} -4.60023e10i q^{44} -4.15706e11 q^{46} +1.00148e11i q^{47} -4.72253e11 q^{49} -3.14414e11i q^{50} -1.56706e12 q^{52} -2.31329e12i q^{53} -1.36130e11 q^{55} +5.66891e11i q^{56} -4.18179e12 q^{58} +2.97124e11i q^{59} +1.74353e12 q^{61} -7.63941e12i q^{62} +6.88382e12 q^{64} +4.63724e12i q^{65} +3.39564e12 q^{67} +1.51367e13i q^{68} +6.02773e12 q^{70} -1.02339e13i q^{71} -5.19755e12 q^{73} +3.41078e13i q^{74} +2.72298e13 q^{76} +9.19634e11i q^{77} -1.50233e13 q^{79} -8.39761e12i q^{80} +6.39186e12 q^{82} -3.76556e13i q^{83} +4.47927e13 q^{85} -1.17592e13i q^{86} -2.53111e12 q^{88} -6.45740e13i q^{89} +3.13271e13 q^{91} +4.77355e13i q^{92} +1.97996e13 q^{94} -8.05787e13i q^{95} -1.57646e13 q^{97} +9.33654e13i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 22484 q^{4} + 448868 q^{7} + 13088520 q^{10} + 66488396 q^{13} - 148681016 q^{16} - 1385373196 q^{19} - 695847240 q^{22} - 3049909820 q^{25} - 25864209028 q^{28} - 6310989544 q^{31} - 241760528280 q^{34}+ \cdots - 243547238121892 q^{97}+O(q^{100}) $ 4 * q - 22484 * q^4 + 448868 * q^7 + 13088520 * q^10 + 66488396 * q^13 - 148681016 * q^16 - 1385373196 * q^19 - 695847240 * q^22 - 3049909820 * q^25 - 25864209028 * q^28 - 6310989544 * q^31 - 241760528280 * q^34 - 409258346932 * q^37 - 543023133840 * q^40 - 762882511048 * q^43 - 1669971531960 * q^46 - 2195699231040 * q^49 - 3954259388716 * q^52 - 2320711097760 * q^55 - 5557256089200 * q^58 + 685756320716 * q^61 + 10436251483696 * q^64 + 14034302053844 * q^67 + 15146651940840 * q^70 + 22197489967772 * q^73 + 66074632593116 * q^76 + 6868641127844 * q^79 + 55963348470000 * q^82 + 119520166805280 * q^85 - 46746836935920 * q^88 + 79071690629932 * q^91 + 47408619912120 * q^94 - 243547238121892 * 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 $

$2$	− 197.702i	− 1.54455i	−0.635290	−	0.772274i	$-0.719119\pi$
$2$	− 197.702i	− 1.54455i	0.635290	−	0.772274i	$-0.280881\pi$
$3$	0	0
$3$	0	0
$4$	−22702.1	−1.38563
$5$	67180.2i	0.859906i	0.902851	+	0.429953i	$0.141470\pi$
$5$	67180.2i	0.859906i	−0.902851	+	0.429953i	$0.858530\pi$
$6$	0	0
$7$	453839.	0.551081	0.275541	−	0.961289i	$-0.411143\pi$
$7$	453839.	0.551081	0.275541	+	0.961289i	$0.411143\pi$
$8$	1.24910e6i	0.595618i
$9$	0	0
$10$	1.32817e7	1.32817
$11$	2.02634e6i	0.103983i	0.998648	+	0.0519917i	$0.0165569\pi$
$11$	2.02634e6i	0.103983i	−0.998648	+	0.0519917i	$0.983443\pi$
$12$	0	0
$13$	6.90269e7	1.10006	0.550028	−	0.835146i	$-0.314617\pi$
$13$	6.90269e7	1.10006	0.550028	+	0.835146i	$0.314617\pi$
$14$	− 8.97249e7i	− 0.851171i
$15$	0	0
$16$	−1.25001e8	−0.465666
$17$	− 6.66755e8i	− 1.62489i	−0.583038	−	0.812445i	$-0.698136\pi$
$17$	− 6.66755e8i	− 1.62489i	0.583038	−	0.812445i	$-0.301864\pi$
$18$	0	0
$19$	−1.19944e9	−1.34185	−0.670925	−	0.741525i	$-0.734103\pi$
$19$	−1.19944e9	−1.34185	−0.670925	+	0.741525i	$0.734103\pi$
$20$	− 1.52513e9i	− 1.19151i
$21$	0	0
$22$	4.00612e8	0.160607
$23$	− 2.10269e9i	− 0.617562i	−0.951133	−	0.308781i	$-0.900079\pi$
$23$	− 2.10269e9i	− 0.617562i	0.951133	−	0.308781i	$-0.0999210\pi$
$24$	0	0
$25$	1.59034e9	0.260562
$26$	− 1.36468e10i	− 1.69909i
$27$	0	0
$28$	−1.03031e10	−0.763593
$29$	− 2.11520e10i	− 1.22621i	−0.790001	−	0.613106i	$-0.789920\pi$
$29$	− 2.11520e10i	− 1.22621i	0.790001	−	0.613106i	$-0.210080\pi$
$30$	0	0
$31$	3.86410e10	1.40448	0.702242	−	0.711939i	$-0.252183\pi$
$31$	3.86410e10	1.40448	0.702242	+	0.711939i	$0.252183\pi$
$32$	4.51783e10i	1.31486i
$33$	0	0
$34$	−1.31819e11	−2.50972
$35$	3.04890e10i	0.473878i
$36$	0	0
$37$	−1.72521e11	−1.81732	−0.908659	−	0.417539i	$-0.862893\pi$
$37$	−1.72521e11	−1.81732	−0.908659	+	0.417539i	$0.862893\pi$
$38$	2.37132e11i	2.07255i
$39$	0	0
$40$	−8.39148e10	−0.512176
$41$	3.23308e10i	0.166008i	0.996549	+	0.0830040i	$0.0264514\pi$
$41$	3.23308e10i	0.166008i	−0.996549	+	0.0830040i	$0.973549\pi$
$42$	0	0
$43$	5.94792e10	0.218820	0.109410	−	0.993997i	$-0.465104\pi$
$43$	5.94792e10	0.218820	0.109410	+	0.993997i	$0.465104\pi$
$44$	− 4.60023e10i	− 0.144082i
$45$	0	0
$46$	−4.15706e11	−0.953853
$47$	1.00148e11i	0.197678i	0.995103	+	0.0988392i	$0.0315129\pi$
$47$	1.00148e11i	0.197678i	−0.995103	+	0.0988392i	$0.968487\pi$
$48$	0	0
$49$	−4.72253e11	−0.696310
$50$	− 3.14414e11i	− 0.402450i
$51$	0	0
$52$	−1.56706e12	−1.52427
$53$	− 2.31329e12i	− 1.96924i	−0.174708	−	0.984620i	$-0.555898\pi$
$53$	− 2.31329e12i	− 1.96924i	0.174708	−	0.984620i	$-0.444102\pi$
$54$	0	0
$55$	−1.36130e11	−0.0894160
$56$	5.66891e11i	0.328234i
$57$	0	0
$58$	−4.18179e12	−1.89394
$59$	2.97124e11i	0.119391i	0.998217	+	0.0596957i	$0.0190130\pi$
$59$	2.97124e11i	0.119391i	−0.998217	+	0.0596957i	$0.980987\pi$
$60$	0	0
$61$	1.74353e12	0.554779	0.277390	−	0.960757i	$-0.410531\pi$
$61$	1.74353e12	0.554779	0.277390	+	0.960757i	$0.410531\pi$
$62$	− 7.63941e12i	− 2.16929i
$63$	0	0
$64$	6.88382e12	1.56520
$65$	4.63724e12i	0.945945i
$66$	0	0
$67$	3.39564e12	0.560271	0.280136	−	0.959960i	$-0.409621\pi$
$67$	3.39564e12	0.560271	0.280136	+	0.959960i	$0.409621\pi$
$68$	1.51367e13i	2.25149i
$69$	0	0
$70$	6.02773e12	0.731927
$71$	− 1.02339e13i	− 1.12521i	−0.826727	−	0.562603i	$-0.809800\pi$
$71$	− 1.02339e13i	− 1.12521i	0.826727	−	0.562603i	$-0.190200\pi$
$72$	0	0
$73$	−5.19755e12	−0.470477	−0.235239	−	0.971938i	$-0.575587\pi$
$73$	−5.19755e12	−0.470477	−0.235239	+	0.971938i	$0.575587\pi$
$74$	3.41078e13i	2.80693i
$75$	0	0
$76$	2.72298e13	1.85930
$77$	9.19634e11i	0.0573033i
$78$	0	0
$79$	−1.50233e13	−0.782306	−0.391153	−	0.920326i	$-0.627924\pi$
$79$	−1.50233e13	−0.782306	−0.391153	+	0.920326i	$0.627924\pi$
$80$	− 8.39761e12i	− 0.400429i
$81$	0	0
$82$	6.39186e12	0.256407
$83$	− 3.76556e13i	− 1.38766i	−0.720138	−	0.693831i	$-0.755922\pi$
$83$	− 3.76556e13i	− 1.38766i	0.720138	−	0.693831i	$-0.244078\pi$
$84$	0	0
$85$	4.47927e13	1.39725
$86$	− 1.17592e13i	− 0.337977i
$87$	0	0
$88$	−2.53111e12	−0.0619344
$89$	− 6.45740e13i	− 1.45991i	−0.683493	−	0.729957i	$-0.739540\pi$
$89$	− 6.45740e13i	− 1.45991i	0.683493	−	0.729957i	$-0.260460\pi$
$90$	0	0
$91$	3.13271e13	0.606220
$92$	4.77355e13i	0.855710i
$93$	0	0
$94$	1.97996e13	0.305324
$95$	− 8.05787e13i	− 1.15386i
$96$	0	0
$97$	−1.57646e13	−0.195110	−0.0975550	−	0.995230i	$-0.531102\pi$
$97$	−1.57646e13	−0.195110	−0.0975550	+	0.995230i	$0.531102\pi$
$98$	9.33654e13i	1.07548i
$99$	0	0
$100$	−3.61041e13	−0.361041
$101$	− 1.30468e14i	− 1.21690i	−0.793594	−	0.608448i	$-0.791793\pi$
$101$	− 1.30468e14i	− 1.21690i	0.793594	−	0.608448i	$-0.208207\pi$
$102$	0	0
$103$	−1.66672e14	−1.35520	−0.677598	−	0.735432i	$-0.736979\pi$
$103$	−1.66672e14	−1.35520	−0.677598	+	0.735432i	$0.736979\pi$
$104$	8.62216e13i	0.655214i
$105$	0	0
$106$	−4.57342e14	−3.04159
$107$	1.56335e14i	0.973577i	0.873520	+	0.486788i	$0.161832\pi$
$107$	1.56335e14i	0.973577i	−0.873520	+	0.486788i	$0.838168\pi$
$108$	0	0
$109$	1.01214e14	0.553676	0.276838	−	0.960917i	$-0.410714\pi$
$109$	1.01214e14	0.553676	0.276838	+	0.960917i	$0.410714\pi$
$110$	2.69132e13i	0.138107i
$111$	0	0
$112$	−5.67305e13	−0.256620
$113$	2.05587e14i	0.873867i	0.899494	+	0.436934i	$0.143936\pi$
$113$	2.05587e14i	0.873867i	−0.899494	+	0.436934i	$0.856064\pi$
$114$	0	0
$115$	1.41259e14	0.531045
$116$	4.80195e14i	1.69907i
$117$	0	0
$118$	5.87420e13	0.184406
$119$	− 3.02600e14i	− 0.895446i
$120$	0	0
$121$	3.75644e14	0.989187
$122$	− 3.44699e14i	− 0.856883i
$123$	0	0
$124$	−8.77232e14	−1.94609
$125$	5.16875e14i	1.08396i
$126$	0	0
$127$	−2.27500e14	−0.426930	−0.213465	−	0.976951i	$-0.568475\pi$
$127$	−2.27500e14	−0.426930	−0.213465	+	0.976951i	$0.568475\pi$
$128$	− 6.20744e14i	− 1.10266i
$129$	0	0
$130$	9.16792e14	1.46106
$131$	− 1.01807e15i	− 1.53772i	−0.639418	−	0.768859i	$-0.720825\pi$
$131$	− 1.01807e15i	− 1.53772i	0.639418	−	0.768859i	$-0.279175\pi$
$132$	0	0
$133$	−5.44354e14	−0.739468
$134$	− 6.71325e14i	− 0.865365i
$135$	0	0
$136$	8.32845e14	0.967814
$137$	4.00051e12i	0.00441643i	0.999998	+	0.00220822i	$0.000702898\pi$
$137$	4.00051e12i	0.00441643i	−0.999998	+	0.00220822i	$0.999297\pi$
$138$	0	0
$139$	1.27619e15	1.27296	0.636478	−	0.771295i	$-0.280391\pi$
$139$	1.27619e15	1.27296	0.636478	+	0.771295i	$0.280391\pi$
$140$	− 6.92164e14i	− 0.656618i
$141$	0	0
$142$	−2.02326e15	−1.73793
$143$	1.39872e14i	0.114388i
$144$	0	0
$145$	1.42100e15	1.05443
$146$	1.02757e15i	0.726674i
$147$	0	0
$148$	3.91660e15	2.51812
$149$	2.92608e15i	1.79466i	0.441359	+	0.897330i	$0.354496\pi$
$149$	2.92608e15i	1.79466i	−0.441359	+	0.897330i	$0.645504\pi$
$150$	0	0
$151$	1.58406e15	0.884981	0.442491	−	0.896773i	$-0.354095\pi$
$151$	1.58406e15	0.884981	0.442491	+	0.896773i	$0.354095\pi$
$152$	− 1.49822e15i	− 0.799230i
$153$	0	0
$154$	1.81813e14	0.0885077
$155$	2.59591e15i	1.20772i
$156$	0	0
$157$	−3.38611e14	−0.144013	−0.0720067	−	0.997404i	$-0.522940\pi$
$157$	−3.38611e14	−0.144013	−0.0720067	+	0.997404i	$0.522940\pi$
$158$	2.97014e15i	1.20831i
$159$	0	0
$160$	−3.03508e15	−1.13066
$161$	− 9.54283e14i	− 0.340327i
$162$	0	0
$163$	1.88393e15	0.616242	0.308121	−	0.951347i	$-0.400300\pi$
$163$	1.88393e15	0.616242	0.308121	+	0.951347i	$0.400300\pi$
$164$	− 7.33976e14i	− 0.230025i
$165$	0	0
$166$	−7.44460e15	−2.14331
$167$	4.12106e14i	0.113761i	0.998381	+	0.0568806i	$0.0181154\pi$
$167$	4.12106e14i	0.113761i	−0.998381	+	0.0568806i	$0.981885\pi$
$168$	0	0
$169$	8.27339e14	0.210124
$170$	− 8.85561e15i	− 2.15812i
$171$	0	0
$172$	−1.35030e15	−0.303202
$173$	7.55829e15i	1.62968i	0.579689	+	0.814838i	$0.303174\pi$
$173$	7.55829e15i	1.62968i	−0.579689	+	0.814838i	$0.696826\pi$
$174$	0	0
$175$	7.21759e14	0.143591
$176$	− 2.53296e14i	− 0.0484216i
$177$	0	0
$178$	−1.27664e16	−2.25491
$179$	− 7.30949e14i	− 0.124141i	−0.998072	−	0.0620706i	$-0.980230\pi$
$179$	− 7.30949e14i	− 0.124141i	0.998072	−	0.0620706i	$-0.0197704\pi$
$180$	0	0
$181$	5.53496e15	0.869689	0.434845	−	0.900505i	$-0.356803\pi$
$181$	5.53496e15	0.869689	0.434845	+	0.900505i	$0.356803\pi$
$182$	− 6.19343e15i	− 0.936336i
$183$	0	0
$184$	2.62647e15	0.367831
$185$	− 1.15900e16i	− 1.56272i
$186$	0	0
$187$	1.35108e15	0.168962
$188$	− 2.27358e15i	− 0.273908i
$189$	0	0
$190$	−1.59306e16	−1.78220
$191$	− 4.32337e15i	− 0.466218i	−0.972451	−	0.233109i	$-0.925110\pi$
$191$	− 4.32337e15i	− 0.466218i	0.972451	−	0.233109i	$-0.0748899\pi$
$192$	0	0
$193$	7.73145e15	0.775103	0.387552	−	0.921848i	$-0.373321\pi$
$193$	7.73145e15	0.775103	0.387552	+	0.921848i	$0.373321\pi$
$194$	3.11668e15i	0.301357i
$195$	0	0
$196$	1.07211e16	0.964825
$197$	1.17795e16i	1.02297i	0.859293	+	0.511484i	$0.170904\pi$
$197$	1.17795e16i	1.02297i	−0.859293	+	0.511484i	$0.829096\pi$
$198$	0	0
$199$	−7.56801e15	−0.612365	−0.306182	−	0.951973i	$-0.599052\pi$
$199$	−7.56801e15	−0.612365	−0.306182	+	0.951973i	$0.599052\pi$
$200$	1.98650e15i	0.155195i
$201$	0	0
$202$	−2.57937e16	−1.87955
$203$	− 9.59961e15i	− 0.675742i
$204$	0	0
$205$	−2.17199e15	−0.142751
$206$	3.29514e16i	2.09317i
$207$	0	0
$208$	−8.62845e15	−0.512259
$209$	− 2.43048e15i	− 0.139530i
$210$	0	0
$211$	3.16523e16	1.69992	0.849960	−	0.526848i	$-0.176626\pi$
$211$	3.16523e16	1.69992	0.849960	+	0.526848i	$0.176626\pi$
$212$	5.25165e16i	2.72863i
$213$	0	0
$214$	3.09078e16	1.50373
$215$	3.99583e15i	0.188164i
$216$	0	0
$217$	1.75368e16	0.773984
$218$	− 2.00102e16i	− 0.855178i
$219$	0	0
$220$	3.09044e15	0.123897
$221$	− 4.60241e16i	− 1.78747i
$222$	0	0
$223$	4.45689e16	1.62517	0.812583	−	0.582845i	$-0.198060\pi$
$223$	4.45689e16	1.62517	0.812583	+	0.582845i	$0.198060\pi$
$224$	2.05037e16i	0.724595i
$225$	0	0
$226$	4.06449e16	1.34973
$227$	− 1.97590e16i	− 0.636185i	−0.948060	−	0.318093i	$-0.896958\pi$
$227$	− 1.97590e16i	− 0.636185i	0.948060	−	0.318093i	$-0.103042\pi$
$228$	0	0
$229$	−4.39101e16	−1.32958	−0.664792	−	0.747028i	$-0.731480\pi$
$229$	−4.39101e16	−1.32958	−0.664792	+	0.747028i	$0.731480\pi$
$230$	− 2.79272e16i	− 0.820224i
$231$	0	0
$232$	2.64210e16	0.730354
$233$	− 1.78519e14i	− 0.00478843i	−0.999997	−	0.00239422i	$-0.999238\pi$
$233$	− 1.78519e14i	− 0.00478843i	0.999997	−	0.00239422i	$-0.000762103\pi$
$234$	0	0
$235$	−6.72799e15	−0.169985
$236$	− 6.74533e15i	− 0.165432i
$237$	0	0
$238$	−5.98246e16	−1.38306
$239$	− 2.62125e16i	− 0.588469i	−0.955733	−	0.294235i	$-0.904935\pi$
$239$	− 2.62125e16i	− 0.588469i	0.955733	−	0.294235i	$-0.0950647\pi$
$240$	0	0
$241$	2.94818e16	0.624359	0.312180	−	0.950023i	$-0.398941\pi$
$241$	2.94818e16	0.624359	0.312180	+	0.950023i	$0.398941\pi$
$242$	− 7.42655e16i	− 1.52785i
$243$	0	0
$244$	−3.95818e16	−0.768717
$245$	− 3.17260e16i	− 0.598761i
$246$	0	0
$247$	−8.27938e16	−1.47611
$248$	4.82665e16i	0.836536i
$249$	0	0
$250$	1.02187e17	1.67423
$251$	9.25186e16i	1.47405i	0.675864	+	0.737026i	$0.263770\pi$
$251$	9.25186e16i	1.47405i	−0.675864	+	0.737026i	$0.736230\pi$
$252$	0	0
$253$	4.26077e15	0.0642162
$254$	4.49773e16i	0.659413i
$255$	0	0
$256$	−9.93790e15	−0.137916
$257$	− 3.15238e16i	− 0.425702i	−0.977085	−	0.212851i	$-0.931725\pi$
$257$	− 3.15238e16i	− 0.425702i	0.977085	−	0.212851i	$-0.0682750\pi$
$258$	0	0
$259$	−7.82969e16	−1.00149
$260$	− 1.05275e17i	− 1.31073i
$261$	0	0
$262$	−2.01274e17	−2.37508
$263$	1.43237e17i	1.64575i	0.568221	+	0.822876i	$0.307632\pi$
$263$	1.43237e17i	1.64575i	−0.568221	+	0.822876i	$0.692368\pi$
$264$	0	0
$265$	1.55407e17	1.69336
$266$	1.07620e17i	1.14214i
$267$	0	0
$268$	−7.70882e16	−0.776326
$269$	9.50059e14i	0.00932147i	0.999989	+	0.00466074i	$0.00148356\pi$
$269$	9.50059e14i	0.00932147i	−0.999989	+	0.00466074i	$0.998516\pi$
$270$	0	0
$271$	8.74638e16	0.814786	0.407393	−	0.913253i	$-0.366438\pi$
$271$	8.74638e16	0.814786	0.407393	+	0.913253i	$0.366438\pi$
$272$	8.33453e16i	0.756656i
$273$	0	0
$274$	7.90910e14	0.00682139
$275$	3.22258e15i	0.0270941i
$276$	0	0
$277$	−9.43259e16	−0.753829	−0.376914	−	0.926248i	$-0.623015\pi$
$277$	−9.43259e16	−0.753829	−0.376914	+	0.926248i	$0.623015\pi$
$278$	− 2.52306e17i	− 1.96614i
$279$	0	0
$280$	−3.80838e16	−0.282250
$281$	1.74796e17i	1.26354i	0.775157	+	0.631769i	$0.217671\pi$
$281$	1.74796e17i	1.26354i	−0.775157	+	0.631769i	$0.782329\pi$
$282$	0	0
$283$	−1.92970e17	−1.32735	−0.663673	−	0.748023i	$-0.731003\pi$
$283$	−1.92970e17	−1.32735	−0.663673	+	0.748023i	$0.731003\pi$
$284$	2.32331e17i	1.55911i
$285$	0	0
$286$	2.76530e16	0.176677
$287$	1.46730e16i	0.0914838i
$288$	0	0
$289$	−2.76185e17	−1.64027
$290$	− 2.80934e17i	− 1.62861i
$291$	0	0
$292$	1.17995e17	0.651906
$293$	− 3.46578e16i	− 0.186951i	−0.995622	−	0.0934755i	$-0.970202\pi$
$293$	− 3.46578e16i	− 0.186951i	0.995622	−	0.0934755i	$-0.0297977\pi$
$294$	0	0
$295$	−1.99608e16	−0.102665
$296$	− 2.15497e17i	− 1.08243i
$297$	0	0
$298$	5.78492e17	2.77194
$299$	− 1.45142e17i	− 0.679353i
$300$	0	0
$301$	2.69940e16	0.120587
$302$	− 3.13173e17i	− 1.36690i
$303$	0	0
$304$	1.49932e17	0.624854
$305$	1.17131e17i	0.477058i
$306$	0	0
$307$	1.21136e17	0.471308	0.235654	−	0.971837i	$-0.424277\pi$
$307$	1.21136e17	0.471308	0.235654	+	0.971837i	$0.424277\pi$
$308$	− 2.08776e16i	− 0.0794010i
$309$	0	0
$310$	5.13217e17	1.86539
$311$	− 4.18108e17i	− 1.48582i	−0.669393	−	0.742908i	$-0.733446\pi$
$311$	− 4.18108e17i	− 1.48582i	0.669393	−	0.742908i	$-0.266554\pi$
$312$	0	0
$313$	−2.69808e17	−0.916737	−0.458369	−	0.888762i	$-0.651566\pi$
$313$	−2.69808e17	−0.916737	−0.458369	+	0.888762i	$0.651566\pi$
$314$	6.69440e16i	0.222436i
$315$	0	0
$316$	3.41061e17	1.08398
$317$	1.04365e17i	0.324443i	0.986754	+	0.162221i	$0.0518659\pi$
$317$	1.04365e17i	0.324443i	−0.986754	+	0.162221i	$0.948134\pi$
$318$	0	0
$319$	4.28612e16	0.127506
$320$	4.62456e17i	1.34592i
$321$	0	0
$322$	−1.88664e17	−0.525651
$323$	7.99734e17i	2.18036i
$324$	0	0
$325$	1.09776e17	0.286632
$326$	− 3.72457e17i	− 0.951815i
$327$	0	0
$328$	−4.03844e16	−0.0988773
$329$	4.54513e16i	0.108937i
$330$	0	0
$331$	2.08577e17	0.479149	0.239574	−	0.970878i	$-0.422992\pi$
$331$	2.08577e17	0.479149	0.239574	+	0.970878i	$0.422992\pi$
$332$	8.54862e17i	1.92278i
$333$	0	0
$334$	8.14743e16	0.175710
$335$	2.28120e17i	0.481781i
$336$	0	0
$337$	−5.96843e17	−1.20907	−0.604535	−	0.796579i	$-0.706641\pi$
$337$	−5.96843e17	−1.20907	−0.604535	+	0.796579i	$0.706641\pi$
$338$	− 1.63567e17i	− 0.324547i
$339$	0	0
$340$	−1.01689e18	−1.93607
$341$	7.82999e16i	0.146043i
$342$	0	0
$343$	−5.22131e17	−0.934804
$344$	7.42956e16i	0.130333i
$345$	0	0
$346$	1.49429e18	2.51711
$347$	− 9.73563e17i	− 1.60716i	−0.595200	−	0.803578i	$-0.702927\pi$
$347$	− 9.73563e17i	− 1.60716i	0.595200	−	0.803578i	$-0.297073\pi$
$348$	0	0
$349$	−5.44958e17	−0.864142	−0.432071	−	0.901840i	$-0.642217\pi$
$349$	−5.44958e17	−0.864142	−0.432071	+	0.901840i	$0.642217\pi$
$350$	− 1.42693e17i	− 0.221782i
$351$	0	0
$352$	−9.15467e16	−0.136724
$353$	− 3.14243e17i	− 0.460090i	−0.973180	−	0.230045i	$-0.926113\pi$
$353$	− 3.14243e17i	− 0.460090i	0.973180	−	0.230045i	$-0.0738873\pi$
$354$	0	0
$355$	6.87514e17	0.967571
$356$	1.46597e18i	2.02290i
$357$	0	0
$358$	−1.44510e17	−0.191742
$359$	− 6.48311e17i	− 0.843572i	−0.906695	−	0.421786i	$-0.861403\pi$
$359$	− 6.48311e17i	− 0.843572i	0.906695	−	0.421786i	$-0.138597\pi$
$360$	0	0
$361$	6.39654e17	0.800562
$362$	− 1.09427e18i	− 1.34328i
$363$	0	0
$364$	−7.11191e17	−0.839995
$365$	− 3.49172e17i	− 0.404566i
$366$	0	0
$367$	−1.10367e18	−1.23077	−0.615387	−	0.788225i	$-0.711000\pi$
$367$	−1.10367e18	−1.23077	−0.615387	+	0.788225i	$0.711000\pi$
$368$	2.62839e17i	0.287578i
$369$	0	0
$370$	−2.29137e18	−2.41370
$371$	− 1.04986e18i	− 1.08521i
$372$	0	0
$373$	−5.04833e16	−0.0502557	−0.0251279	−	0.999684i	$-0.507999\pi$
$373$	−5.04833e16	−0.0502557	−0.0251279	+	0.999684i	$0.507999\pi$
$374$	− 2.67110e17i	− 0.260969i
$375$	0	0
$376$	−1.25096e17	−0.117741
$377$	− 1.46006e18i	− 1.34890i
$378$	0	0
$379$	2.97698e17	0.265034	0.132517	−	0.991181i	$-0.457694\pi$
$379$	2.97698e17	0.265034	0.132517	+	0.991181i	$0.457694\pi$
$380$	1.82931e18i	1.59883i
$381$	0	0
$382$	−8.54739e17	−0.720095
$383$	2.20912e17i	0.182738i	0.995817	+	0.0913689i	$0.0291242\pi$
$383$	2.20912e17i	0.182738i	−0.995817	+	0.0913689i	$0.970876\pi$
$384$	0	0
$385$	−6.17811e16	−0.0492755
$386$	− 1.52852e18i	− 1.19718i
$387$	0	0
$388$	3.57888e17	0.270350
$389$	2.07624e18i	1.54039i	0.637810	+	0.770194i	$0.279841\pi$
$389$	2.07624e18i	1.54039i	−0.637810	+	0.770194i	$0.720159\pi$
$390$	0	0
$391$	−1.40198e18	−1.00347
$392$	− 5.89892e17i	− 0.414735i
$393$	0	0
$394$	2.32882e18	1.58002
$395$	− 1.00927e18i	− 0.672710i
$396$	0	0
$397$	2.18678e18	1.40693	0.703465	−	0.710730i	$-0.251635\pi$
$397$	2.18678e18	1.40693	0.703465	+	0.710730i	$0.251635\pi$
$398$	1.49621e18i	0.945826i
$399$	0	0
$400$	−1.98795e17	−0.121335
$401$	8.31779e17i	0.498882i	0.968390	+	0.249441i	$0.0802468\pi$
$401$	8.31779e17i	0.498882i	−0.968390	+	0.249441i	$0.919753\pi$
$402$	0	0
$403$	2.66727e18	1.54501
$404$	2.96189e18i	1.68616i
$405$	0	0
$406$	−1.89786e18	−1.04372
$407$	− 3.49588e17i	− 0.188971i
$408$	0	0
$409$	−4.87049e17	−0.254395	−0.127198	−	0.991877i	$-0.540598\pi$
$409$	−4.87049e17	−0.254395	−0.127198	+	0.991877i	$0.540598\pi$
$410$	4.29406e17i	0.220486i
$411$	0	0
$412$	3.78381e18	1.87780
$413$	1.34846e17i	0.0657944i
$414$	0	0
$415$	2.52971e18	1.19326
$416$	3.11852e18i	1.44642i
$417$	0	0
$418$	−4.80511e17	−0.215511
$419$	4.36743e18i	1.92632i	0.268935	+	0.963158i	$0.413328\pi$
$419$	4.36743e18i	1.92632i	−0.268935	+	0.963158i	$0.586672\pi$
$420$	0	0
$421$	−1.27692e18	−0.544738	−0.272369	−	0.962193i	$-0.587807\pi$
$421$	−1.27692e18	−0.544738	−0.272369	+	0.962193i	$0.587807\pi$
$422$	− 6.25773e18i	− 2.62561i
$423$	0	0
$424$	2.88953e18	1.17292
$425$	− 1.06037e18i	− 0.423384i
$426$	0	0
$427$	7.91282e17	0.305728
$428$	− 3.54914e18i	− 1.34901i
$429$	0	0
$430$	7.89983e17	0.290629
$431$	3.20431e18i	1.15983i	0.814678	+	0.579914i	$0.196914\pi$
$431$	3.20431e18i	1.15983i	−0.814678	+	0.579914i	$0.803086\pi$
$432$	0	0
$433$	−1.26415e18	−0.442980	−0.221490	−	0.975163i	$-0.571092\pi$
$433$	−1.26415e18	−0.442980	−0.221490	+	0.975163i	$0.571092\pi$
$434$	− 3.46706e18i	− 1.19546i
$435$	0	0
$436$	−2.29777e18	−0.767188
$437$	2.52205e18i	0.828675i
$438$	0	0
$439$	6.29832e17	0.200435	0.100217	−	0.994966i	$-0.468046\pi$
$439$	6.29832e17	0.200435	0.100217	+	0.994966i	$0.468046\pi$
$440$	− 1.70040e17i	− 0.0532578i
$441$	0	0
$442$	−9.09905e18	−2.76083
$443$	− 2.55161e18i	− 0.762057i	−0.924563	−	0.381028i	$-0.875570\pi$
$443$	− 2.55161e18i	− 0.762057i	0.924563	−	0.381028i	$-0.124430\pi$
$444$	0	0
$445$	4.33809e18	1.25539
$446$	− 8.81136e18i	− 2.51015i
$447$	0	0
$448$	3.12415e18	0.862552
$449$	− 4.08069e18i	− 1.10920i	−0.832117	−	0.554600i	$-0.812871\pi$
$449$	− 4.08069e18i	− 1.10920i	0.832117	−	0.554600i	$-0.187129\pi$
$450$	0	0
$451$	−6.55132e16	−0.0172621
$452$	− 4.66725e18i	− 1.21085i
$453$	0	0
$454$	−3.90639e18	−0.982618
$455$	2.10456e18i	0.521293i
$456$	0	0
$457$	3.24038e18	0.778363	0.389182	−	0.921161i	$-0.372758\pi$
$457$	3.24038e18	0.778363	0.389182	+	0.921161i	$0.372758\pi$
$458$	8.68111e18i	2.05361i
$459$	0	0
$460$	−3.20688e18	−0.735830
$461$	4.07880e17i	0.0921778i	0.998937	+	0.0460889i	$0.0146758\pi$
$461$	4.07880e17i	0.0921778i	−0.998937	+	0.0460889i	$0.985324\pi$
$462$	0	0
$463$	2.20295e18	0.482989	0.241494	−	0.970402i	$-0.422362\pi$
$463$	2.20295e18	0.482989	0.241494	+	0.970402i	$0.422362\pi$
$464$	2.64403e18i	0.571005i
$465$	0	0
$466$	−3.52936e16	−0.00739596
$467$	3.98643e18i	0.822936i	0.911424	+	0.411468i	$0.134984\pi$
$467$	3.98643e18i	0.822936i	−0.911424	+	0.411468i	$0.865016\pi$
$468$	0	0
$469$	1.54107e18	0.308755
$470$	1.33014e18i	0.262550i
$471$	0	0
$472$	−3.71138e17	−0.0711117
$473$	1.20525e17i	0.0227536i
$474$	0	0
$475$	−1.90752e18	−0.349635
$476$	6.86965e18i	1.24075i
$477$	0	0
$478$	−5.18227e18	−0.908919
$479$	1.34856e18i	0.233089i	0.993185	+	0.116545i	$0.0371818\pi$
$479$	1.34856e18i	0.233089i	−0.993185	+	0.116545i	$0.962818\pi$
$480$	0	0
$481$	−1.19086e19	−1.99915
$482$	− 5.82861e18i	− 0.964353i
$483$	0	0
$484$	−8.52790e18	−1.37064
$485$	− 1.05907e18i	− 0.167776i
$486$	0	0
$487$	1.06624e19	1.64117	0.820586	−	0.571523i	$-0.193647\pi$
$487$	1.06624e19	1.64117	0.820586	+	0.571523i	$0.193647\pi$
$488$	2.17784e18i	0.330437i
$489$	0	0
$490$	−6.27230e18	−0.924814
$491$	4.01847e18i	0.584104i	0.956402	+	0.292052i	$0.0943380\pi$
$491$	4.01847e18i	0.584104i	−0.956402	+	0.292052i	$0.905662\pi$
$492$	0	0
$493$	−1.41032e19	−1.99246
$494$	1.63685e19i	2.27992i
$495$	0	0
$496$	−4.83017e18	−0.654020
$497$	− 4.64454e18i	− 0.620080i
$498$	0	0
$499$	3.09132e18	0.401273	0.200637	−	0.979666i	$-0.435699\pi$
$499$	3.09132e18	0.401273	0.200637	+	0.979666i	$0.435699\pi$
$500$	− 1.17341e19i	− 1.50197i
$501$	0	0
$502$	1.82911e19	2.27674
$503$	− 3.42227e18i	− 0.420087i	−0.977692	−	0.210043i	$-0.932640\pi$
$503$	− 3.42227e18i	− 0.420087i	0.977692	−	0.210043i	$-0.0673605\pi$
$504$	0	0
$505$	8.76484e18	1.04642
$506$	− 8.42364e17i	− 0.0991850i
$507$	0	0
$508$	5.16474e18	0.591565
$509$	1.21195e19i	1.36918i	0.728929	+	0.684589i	$0.240018\pi$
$509$	1.21195e19i	1.36918i	−0.728929	+	0.684589i	$0.759982\pi$
$510$	0	0
$511$	−2.35885e18	−0.259271
$512$	− 8.20553e18i	− 0.889645i
$513$	0	0
$514$	−6.23231e18	−0.657518
$515$	− 1.11971e19i	− 1.16534i
$516$	0	0
$517$	−2.02935e17	−0.0205553
$518$	1.54795e19i	1.54685i
$519$	0	0
$520$	−5.79238e18	−0.563422
$521$	− 1.50118e19i	− 1.44068i	−0.693620	−	0.720341i	$-0.743985\pi$
$521$	− 1.50118e19i	− 1.44068i	0.693620	−	0.720341i	$-0.256015\pi$
$522$	0	0
$523$	1.79043e19	1.67281	0.836405	−	0.548113i	$-0.184653\pi$
$523$	1.79043e19	1.67281	0.836405	+	0.548113i	$0.184653\pi$
$524$	2.31122e19i	2.13070i
$525$	0	0
$526$	2.83182e19	2.54194
$527$	− 2.57641e19i	− 2.28213i
$528$	0	0
$529$	7.17153e18	0.618617
$530$	− 3.07243e19i	− 2.61548i
$531$	0	0
$532$	1.23580e19	1.02463
$533$	2.23169e18i	0.182618i
$534$	0	0
$535$	−1.05026e19	−0.837184
$536$	4.24150e18i	0.333708i
$537$	0	0
$538$	1.87829e17	0.0143975
$539$	− 9.56947e17i	− 0.0724047i
$540$	0	0
$541$	−1.88493e19	−1.38968	−0.694841	−	0.719163i	$-0.744525\pi$
$541$	−1.88493e19	−1.38968	−0.694841	+	0.719163i	$0.744525\pi$
$542$	− 1.72918e19i	− 1.25848i
$543$	0	0
$544$	3.01229e19	2.13651
$545$	6.79958e18i	0.476109i
$546$	0	0
$547$	−2.26178e19	−1.54361	−0.771807	−	0.635857i	$-0.780647\pi$
$547$	−2.26178e19	−1.54361	−0.771807	+	0.635857i	$0.780647\pi$
$548$	− 9.08201e16i	− 0.00611953i
$549$	0	0
$550$	6.37110e17	0.0418481
$551$	2.53706e19i	1.64539i
$552$	0	0
$553$	−6.81818e18	−0.431114
$554$	1.86484e19i	1.16432i
$555$	0	0
$556$	−2.89723e19	−1.76384
$557$	− 2.27079e19i	− 1.36518i	−0.730801	−	0.682591i	$-0.760853\pi$
$557$	− 2.27079e19i	− 1.36518i	0.730801	−	0.682591i	$-0.239147\pi$
$558$	0	0
$559$	4.10567e18	0.240714
$560$	− 3.81116e18i	− 0.220669i
$561$	0	0
$562$	3.45576e19	1.95159
$563$	1.32823e19i	0.740822i	0.928868	+	0.370411i	$0.120783\pi$
$563$	1.32823e19i	0.740822i	−0.928868	+	0.370411i	$0.879217\pi$
$564$	0	0
$565$	−1.38113e19	−0.751444
$566$	3.81505e19i	2.05015i
$567$	0	0
$568$	1.27832e19	0.670193
$569$	1.38392e19i	0.716681i	0.933591	+	0.358340i	$0.116657\pi$
$569$	1.38392e19i	0.716681i	−0.933591	+	0.358340i	$0.883343\pi$
$570$	0	0
$571$	2.92184e19	1.47640	0.738200	−	0.674582i	$-0.235676\pi$
$571$	2.92184e19	1.47640	0.738200	+	0.674582i	$0.235676\pi$
$572$	− 3.17539e18i	− 0.158499i
$573$	0	0
$574$	2.90087e18	0.141301
$575$	− 3.34400e18i	− 0.160913i
$576$	0	0
$577$	−1.13599e19	−0.533513	−0.266756	−	0.963764i	$-0.585952\pi$
$577$	−1.13599e19	−0.533513	−0.266756	+	0.963764i	$0.585952\pi$
$578$	5.46023e19i	2.53347i
$579$	0	0
$580$	−3.22596e19	−1.46104
$581$	− 1.70896e19i	− 0.764714i
$582$	0	0
$583$	4.68752e18	0.204768
$584$	− 6.49227e18i	− 0.280225i
$585$	0	0
$586$	−6.85192e18	−0.288755
$587$	− 3.38911e19i	− 1.41130i	−0.708561	−	0.705650i	$-0.750655\pi$
$587$	− 3.38911e19i	− 1.41130i	0.708561	−	0.705650i	$-0.249345\pi$
$588$	0	0
$589$	−4.63476e19	−1.88461
$590$	3.94630e18i	0.158572i
$591$	0	0
$592$	2.15654e19	0.846263
$593$	3.77796e19i	1.46512i	0.680700	+	0.732562i	$0.261676\pi$
$593$	3.77796e19i	1.46512i	−0.680700	+	0.732562i	$0.738324\pi$
$594$	0	0
$595$	2.03287e19	0.770000
$596$	− 6.64282e19i	− 2.48673i
$597$	0	0
$598$	−2.86949e19	−1.04929
$599$	6.93841e18i	0.250768i	0.992108	+	0.125384i	$0.0400163\pi$
$599$	6.93841e18i	0.250768i	−0.992108	+	0.125384i	$0.959984\pi$
$600$	0	0
$601$	−3.16963e19	−1.11915	−0.559573	−	0.828781i	$-0.689035\pi$
$601$	−3.16963e19	−1.11915	−0.559573	+	0.828781i	$0.689035\pi$
$602$	− 5.33677e18i	− 0.186253i
$603$	0	0
$604$	−3.59616e19	−1.22625
$605$	2.52358e19i	0.850608i
$606$	0	0
$607$	−2.01374e19	−0.663258	−0.331629	−	0.943410i	$-0.607598\pi$
$607$	−2.01374e19	−0.663258	−0.331629	+	0.943410i	$0.607598\pi$
$608$	− 5.41887e19i	− 1.76435i
$609$	0	0
$610$	2.31570e19	0.736839
$611$	6.91294e18i	0.217457i
$612$	0	0
$613$	3.59550e19	1.10544	0.552721	−	0.833366i	$-0.313589\pi$
$613$	3.59550e19	1.10544	0.552721	+	0.833366i	$0.313589\pi$
$614$	− 2.39488e19i	− 0.727957i
$615$	0	0
$616$	−1.14872e18	−0.0341309
$617$	− 4.71457e19i	− 1.38499i	−0.721424	−	0.692494i	$-0.756512\pi$
$617$	− 4.71457e19i	− 1.38499i	0.721424	−	0.692494i	$-0.243488\pi$
$618$	0	0
$619$	−1.84230e19	−0.529084	−0.264542	−	0.964374i	$-0.585221\pi$
$619$	−1.84230e19	−0.529084	−0.264542	+	0.964374i	$0.585221\pi$
$620$	− 5.89326e19i	− 1.67345i
$621$	0	0
$622$	−8.26607e19	−2.29491
$623$	− 2.93062e19i	− 0.804532i
$624$	0	0
$625$	−2.50170e19	−0.671546
$626$	5.33416e19i	1.41594i
$627$	0	0
$628$	7.68717e18	0.199549
$629$	1.15030e20i	2.95294i
$630$	0	0
$631$	3.09862e19	0.777970	0.388985	−	0.921244i	$-0.372826\pi$
$631$	3.09862e19	0.777970	0.388985	+	0.921244i	$0.372826\pi$
$632$	− 1.87657e19i	− 0.465956i
$633$	0	0
$634$	2.06331e19	0.501117
$635$	− 1.52835e19i	− 0.367119i
$636$	0	0
$637$	−3.25982e19	−0.765980
$638$	− 8.47375e18i	− 0.196939i
$639$	0	0
$640$	4.17017e19	0.948187
$641$	− 3.11130e19i	− 0.699738i	−0.936799	−	0.349869i	$-0.886226\pi$
$641$	− 3.11130e19i	− 0.699738i	0.936799	−	0.349869i	$-0.113774\pi$
$642$	0	0
$643$	3.73080e19	0.820965	0.410483	−	0.911868i	$-0.365360\pi$
$643$	3.73080e19	0.820965	0.410483	+	0.911868i	$0.365360\pi$
$644$	2.16642e19i	0.471566i
$645$	0	0
$646$	1.58109e20	3.36767
$647$	3.71262e19i	0.782258i	0.920336	+	0.391129i	$0.127915\pi$
$647$	3.71262e19i	0.782258i	−0.920336	+	0.391129i	$0.872085\pi$
$648$	0	0
$649$	−6.02075e17	−0.0124147
$650$	− 2.17030e19i	− 0.442717i
$651$	0	0
$652$	−4.27691e19	−0.853881
$653$	6.17557e19i	1.21979i	0.792482	+	0.609895i	$0.208788\pi$
$653$	6.17557e19i	1.21979i	−0.792482	+	0.609895i	$0.791212\pi$
$654$	0	0
$655$	6.83938e19	1.32229
$656$	− 4.04139e18i	− 0.0773043i
$657$	0	0
$658$	8.98581e18	0.168258
$659$	9.21580e19i	1.70740i	0.520766	+	0.853699i	$0.325646\pi$
$659$	9.21580e19i	1.70740i	−0.520766	+	0.853699i	$0.674354\pi$
$660$	0	0
$661$	1.57623e19	0.285897	0.142949	−	0.989730i	$-0.454342\pi$
$661$	1.57623e19	0.285897	0.142949	+	0.989730i	$0.454342\pi$
$662$	− 4.12361e19i	− 0.740068i
$663$	0	0
$664$	4.70357e19	0.826516
$665$	− 3.65698e19i	− 0.635873i
$666$	0	0
$667$	−4.44761e19	−0.757262
$668$	− 9.35568e18i	− 0.157630i
$669$	0	0
$670$	4.50997e19	0.744133
$671$	3.53299e18i	0.0576879i
$672$	0	0
$673$	−8.29579e19	−1.32664	−0.663318	−	0.748337i	$-0.730852\pi$
$673$	−8.29579e19	−1.32664	−0.663318	+	0.748337i	$0.730852\pi$
$674$	1.17997e20i	1.86746i
$675$	0	0
$676$	−1.87823e19	−0.291154
$677$	− 1.51438e19i	− 0.232335i	−0.993230	−	0.116167i	$-0.962939\pi$
$677$	− 1.51438e19i	− 0.232335i	0.993230	−	0.116167i	$-0.0370609\pi$
$678$	0	0
$679$	−7.15457e18	−0.107521
$680$	5.59507e19i	0.832229i
$681$	0	0
$682$	1.54801e19	0.225570
$683$	2.00907e18i	0.0289767i	0.999895	+	0.0144884i	$0.00461195\pi$
$683$	2.00907e18i	0.0289767i	−0.999895	+	0.0144884i	$0.995388\pi$
$684$	0	0
$685$	−2.68755e17	−0.00379772
$686$	1.03226e20i	1.44385i
$687$	0	0
$688$	−7.43498e18	−0.101897
$689$	− 1.59679e20i	− 2.16628i
$690$	0	0
$691$	1.17613e20	1.56354	0.781768	−	0.623570i	$-0.214318\pi$
$691$	1.17613e20	1.56354	0.781768	+	0.623570i	$0.214318\pi$
$692$	− 1.71589e20i	− 2.25812i
$693$	0	0
$694$	−1.92475e20	−2.48233
$695$	8.57350e19i	1.09462i
$696$	0	0
$697$	2.15567e19	0.269745
$698$	1.07739e20i	1.33471i
$699$	0	0
$700$	−1.63854e19	−0.198963
$701$	− 5.26394e19i	− 0.632826i	−0.948622	−	0.316413i	$-0.897521\pi$
$701$	− 5.26394e19i	− 0.632826i	0.948622	−	0.316413i	$-0.102479\pi$
$702$	0	0
$703$	2.06929e20	2.43857
$704$	1.39490e19i	0.162755i
$705$	0	0
$706$	−6.21265e19	−0.710630
$707$	− 5.92113e19i	− 0.670608i
$708$	0	0
$709$	5.88960e19	0.653977	0.326988	−	0.945028i	$-0.393966\pi$
$709$	5.88960e19	0.653977	0.326988	+	0.945028i	$0.393966\pi$
$710$	− 1.35923e20i	− 1.49446i
$711$	0	0
$712$	8.06595e19	0.869552
$713$	− 8.12501e19i	− 0.867355i
$714$	0	0
$715$	−9.39664e18	−0.0983627
$716$	1.65941e19i	0.172013i
$717$	0	0
$718$	−1.28172e20	−1.30294
$719$	− 1.75393e20i	− 1.76567i	−0.469685	−	0.882834i	$-0.655633\pi$
$719$	− 1.75393e20i	− 1.76567i	0.469685	−	0.882834i	$-0.344367\pi$
$720$	0	0
$721$	−7.56423e19	−0.746823
$722$	− 1.26461e20i	− 1.23651i
$723$	0	0
$724$	−1.25655e20	−1.20506
$725$	− 3.36389e19i	− 0.319504i
$726$	0	0
$727$	7.10115e19	0.661589	0.330794	−	0.943703i	$-0.392683\pi$
$727$	7.10115e19	0.661589	0.330794	+	0.943703i	$0.392683\pi$
$728$	3.91307e19i	0.361076i
$729$	0	0
$730$	−6.90321e19	−0.624872
$731$	− 3.96581e19i	− 0.355558i
$732$	0	0
$733$	−1.70600e20	−1.50055	−0.750274	−	0.661127i	$-0.770078\pi$
$733$	−1.70600e20	−1.50055	−0.750274	+	0.661127i	$0.770078\pi$
$734$	2.18199e20i	1.90099i
$735$	0	0
$736$	9.49959e19	0.812008
$737$	6.88074e18i	0.0582589i
$738$	0	0
$739$	8.06727e19	0.670217	0.335108	−	0.942180i	$-0.391227\pi$
$739$	8.06727e19	0.670217	0.335108	+	0.942180i	$0.391227\pi$
$740$	2.63118e20i	2.16535i
$741$	0	0
$742$	−2.07560e20	−1.67616
$743$	− 1.59131e19i	− 0.127302i	−0.997972	−	0.0636509i	$-0.979726\pi$
$743$	− 1.59131e19i	− 0.127302i	0.997972	−	0.0636509i	$-0.0202744\pi$
$744$	0	0
$745$	−1.96575e20	−1.54324
$746$	9.98065e18i	0.0776224i
$747$	0	0
$748$	−3.06722e19	−0.234118
$749$	7.09510e19i	0.536520i
$750$	0	0
$751$	1.99887e20	1.48356	0.741780	−	0.670643i	$-0.233982\pi$
$751$	1.99887e20	1.48356	0.741780	+	0.670643i	$0.233982\pi$
$752$	− 1.25187e19i	− 0.0920521i
$753$	0	0
$754$	−2.88656e20	−2.08344
$755$	1.06418e20i	0.761001i
$756$	0	0
$757$	−1.30575e20	−0.916617	−0.458308	−	0.888793i	$-0.651544\pi$
$757$	−1.30575e20	−0.916617	−0.458308	+	0.888793i	$0.651544\pi$
$758$	− 5.88556e19i	− 0.409358i
$759$	0	0
$760$	1.00651e20	0.687263
$761$	1.33468e20i	0.902994i	0.892273	+	0.451497i	$0.149110\pi$
$761$	1.33468e20i	0.902994i	−0.892273	+	0.451497i	$0.850890\pi$
$762$	0	0
$763$	4.59349e19	0.305120
$764$	9.81496e19i	0.646004i
$765$	0	0
$766$	4.36748e19	0.282247
$767$	2.05095e19i	0.131337i
$768$	0	0
$769$	9.53309e18	0.0599445	0.0299723	−	0.999551i	$-0.490458\pi$
$769$	9.53309e18	0.0599445	0.0299723	+	0.999551i	$0.490458\pi$
$770$	1.22143e19i	0.0761083i
$771$	0	0
$772$	−1.75520e20	−1.07400
$773$	2.24597e18i	0.0136191i	0.999977	+	0.00680953i	$0.00216756\pi$
$773$	2.24597e18i	0.0136191i	−0.999977	+	0.00680953i	$0.997832\pi$
$774$	0	0
$775$	6.14524e19	0.365954
$776$	− 1.96915e19i	− 0.116211i
$777$	0	0
$778$	4.10477e20	2.37920
$779$	− 3.87789e19i	− 0.222758i
$780$	0	0
$781$	2.07374e19	0.117003
$782$	2.77174e20i	1.54991i
$783$	0	0
$784$	5.90323e19	0.324248
$785$	− 2.27479e19i	− 0.123838i
$786$	0	0
$787$	3.02969e20	1.62022	0.810112	−	0.586276i	$-0.199406\pi$
$787$	3.02969e20	1.62022	0.810112	+	0.586276i	$0.199406\pi$
$788$	− 2.67418e20i	− 1.41745i
$789$	0	0
$790$	−1.99535e20	−1.03903
$791$	9.33032e19i	0.481572i
$792$	0	0
$793$	1.20350e20	0.610289
$794$	− 4.32332e20i	− 2.17307i
$795$	0	0
$796$	1.71810e20	0.848508
$797$	− 3.30838e19i	− 0.161960i	−0.996716	−	0.0809798i	$-0.974195\pi$
$797$	− 3.30838e19i	− 0.161960i	0.996716	−	0.0809798i	$-0.0258049\pi$
$798$	0	0
$799$	6.67745e19	0.321206
$800$	7.18489e19i	0.342602i
$801$	0	0
$802$	1.64444e20	0.770546
$803$	− 1.05320e19i	− 0.0489219i
$804$	0	0
$805$	6.41089e19	0.292649
$806$	− 5.27325e20i	− 2.38634i
$807$	0	0
$808$	1.62967e20	0.724805
$809$	1.41945e20i	0.625863i	0.949776	+	0.312931i	$0.101311\pi$
$809$	1.41945e20i	0.625863i	−0.949776	+	0.312931i	$0.898689\pi$
$810$	0	0
$811$	−2.86161e20	−1.24012	−0.620061	−	0.784553i	$-0.712892\pi$
$811$	−2.86161e20	−1.24012	−0.620061	+	0.784553i	$0.712892\pi$
$812$	2.17931e20i	0.936326i
$813$	0	0
$814$	−6.91142e19	−0.291875
$815$	1.26563e20i	0.529910i
$816$	0	0
$817$	−7.13419e19	−0.293623
$818$	9.62906e19i	0.392926i
$819$	0	0
$820$	4.93086e19	0.197800
$821$	− 2.09615e20i	− 0.833718i	−0.908971	−	0.416859i	$-0.863131\pi$
$821$	− 2.09615e20i	− 0.833718i	0.908971	−	0.416859i	$-0.136869\pi$
$822$	0	0
$823$	−1.94893e20	−0.762075	−0.381037	−	0.924560i	$-0.624433\pi$
$823$	−1.94893e20	−0.762075	−0.381037	+	0.924560i	$0.624433\pi$
$824$	− 2.08190e20i	− 0.807180i
$825$	0	0
$826$	2.66594e19	0.101623
$827$	− 2.18496e20i	− 0.825858i	−0.910763	−	0.412929i	$-0.864506\pi$
$827$	− 2.18496e20i	− 0.825858i	0.910763	−	0.412929i	$-0.135494\pi$
$828$	0	0
$829$	−1.33885e20	−0.497565	−0.248782	−	0.968559i	$-0.580030\pi$
$829$	−1.33885e20	−0.497565	−0.248782	+	0.968559i	$0.580030\pi$
$830$	− 5.00129e20i	− 1.84304i
$831$	0	0
$832$	4.75169e20	1.72181
$833$	3.14877e20i	1.13143i
$834$	0	0
$835$	−2.76854e19	−0.0978239
$836$	5.51770e19i	0.193337i
$837$	0	0
$838$	8.63450e20	2.97529
$839$	− 1.25271e20i	− 0.428073i	−0.976826	−	0.214037i	$-0.931339\pi$
$839$	− 1.25271e20i	− 0.428073i	0.976826	−	0.214037i	$-0.0686612\pi$
$840$	0	0
$841$	−1.49849e20	−0.503596
$842$	2.52449e20i	0.841374i
$843$	0	0
$844$	−7.18574e20	−2.35545
$845$	5.55808e19i	0.180687i
$846$	0	0
$847$	1.70482e20	0.545123
$848$	2.89164e20i	0.917009i
$849$	0	0
$850$	−2.09637e20	−0.653937
$851$	3.62759e20i	1.12231i
$852$	0	0
$853$	−9.53531e18	−0.0290196	−0.0145098	−	0.999895i	$-0.504619\pi$
$853$	−9.53531e18	−0.0290196	−0.0145098	+	0.999895i	$0.504619\pi$
$854$	− 1.56438e20i	− 0.472212i
$855$	0	0
$856$	−1.95278e20	−0.579880
$857$	2.60229e20i	0.766459i	0.923653	+	0.383230i	$0.125188\pi$
$857$	2.60229e20i	0.766459i	−0.923653	+	0.383230i	$0.874812\pi$
$858$	0	0
$859$	−1.41075e20	−0.408787	−0.204393	−	0.978889i	$-0.565522\pi$
$859$	−1.41075e20	−0.408787	−0.204393	+	0.978889i	$0.565522\pi$
$860$	− 9.07136e19i	− 0.260725i
$861$	0	0
$862$	6.33498e20	1.79141
$863$	− 2.15337e20i	− 0.604008i	−0.953307	−	0.302004i	$-0.902344\pi$
$863$	− 2.15337e20i	− 0.604008i	0.953307	−	0.302004i	$-0.0976556\pi$
$864$	0	0
$865$	−5.07767e20	−1.40137
$866$	2.49925e20i	0.684203i
$867$	0	0
$868$	−3.98122e20	−1.07245
$869$	− 3.04424e19i	− 0.0813469i
$870$	0	0
$871$	2.34391e20	0.616330
$872$	1.26427e20i	0.329779i
$873$	0	0
$874$	4.98615e20	1.27993
$875$	2.34578e20i	0.597352i
$876$	0	0
$877$	−7.00803e19	−0.175630	−0.0878150	−	0.996137i	$-0.527988\pi$
$877$	−7.00803e19	−0.175630	−0.0878150	+	0.996137i	$0.527988\pi$
$878$	− 1.24519e20i	− 0.309581i
$879$	0	0
$880$	1.70164e19	0.0416380
$881$	3.00963e20i	0.730604i	0.930889	+	0.365302i	$0.119034\pi$
$881$	3.00963e20i	0.730604i	−0.930889	+	0.365302i	$0.880966\pi$
$882$	0	0
$883$	3.38331e20	0.808382	0.404191	−	0.914675i	$-0.367553\pi$
$883$	3.38331e20	0.808382	0.404191	+	0.914675i	$0.367553\pi$
$884$	1.04484e21i	2.47677i
$885$	0	0
$886$	−5.04458e20	−1.17703
$887$	7.88391e20i	1.82506i	0.409013	+	0.912529i	$0.365873\pi$
$887$	7.88391e20i	1.82506i	−0.409013	+	0.912529i	$0.634127\pi$
$888$	0	0
$889$	−1.03249e20	−0.235273
$890$	− 8.57649e20i	− 1.93901i
$891$	0	0
$892$	−1.01181e21	−2.25187
$893$	− 1.20122e20i	− 0.265255i
$894$	0	0
$895$	4.91053e19	0.106750
$896$	− 2.81718e20i	− 0.607657i
$897$	0	0
$898$	−8.06762e20	−1.71321
$899$	− 8.17335e20i	− 1.72219i
$900$	0	0
$901$	−1.54240e21	−3.19980
$902$	1.29521e19i	0.0266621i
$903$	0	0
$904$	−2.56798e20	−0.520491
$905$	3.71839e20i	0.747851i
$906$	0	0
$907$	3.66869e20	0.726542	0.363271	−	0.931684i	$-0.381660\pi$
$907$	3.66869e20	0.726542	0.363271	+	0.931684i	$0.381660\pi$
$908$	4.48570e20i	0.881515i
$909$	0	0
$910$	4.16076e20	0.805161
$911$	− 8.57325e20i	− 1.64633i	−0.567802	−	0.823165i	$-0.692206\pi$
$911$	− 8.57325e20i	− 1.64633i	0.567802	−	0.823165i	$-0.307794\pi$
$912$	0	0
$913$	7.63033e19	0.144294
$914$	− 6.40630e20i	− 1.20222i
$915$	0	0
$916$	9.96851e20	1.84231
$917$	− 4.62038e20i	− 0.847408i
$918$	0	0
$919$	−7.87018e20	−1.42160	−0.710798	−	0.703396i	$-0.751666\pi$
$919$	−7.87018e20	−1.42160	−0.710798	+	0.703396i	$0.751666\pi$
$920$	1.76447e20i	0.316300i
$921$	0	0
$922$	8.06388e19	0.142373
$923$	− 7.06413e20i	− 1.23779i
$924$	0	0
$925$	−2.74368e20	−0.473523
$926$	− 4.35527e20i	− 0.745999i
$927$	0	0
$928$	9.55611e20	1.61230
$929$	− 3.90816e20i	− 0.654429i	−0.944950	−	0.327215i	$-0.893890\pi$
$929$	− 3.90816e20i	− 0.654429i	0.944950	−	0.327215i	$-0.106110\pi$
$930$	0	0
$931$	5.66440e20	0.934343
$932$	4.05276e18i	0.00663498i
$933$	0	0
$934$	7.88126e20	1.27106
$935$	9.07654e19i	0.145291i
$936$	0	0
$937$	4.72084e20	0.744462	0.372231	−	0.928140i	$-0.378593\pi$
$937$	4.72084e20	0.744462	0.372231	+	0.928140i	$0.378593\pi$
$938$	− 3.04674e20i	− 0.476886i
$939$	0	0
$940$	1.52739e20	0.235535
$941$	− 6.37124e19i	− 0.0975207i	−0.998811	−	0.0487603i	$-0.984473\pi$
$941$	− 6.37124e19i	− 0.0975207i	0.998811	−	0.0487603i	$-0.0155271\pi$
$942$	0	0
$943$	6.79816e19	0.102520
$944$	− 3.71409e19i	− 0.0555966i
$945$	0	0
$946$	2.38281e19	0.0351440
$947$	9.92846e20i	1.45356i	0.686872	+	0.726778i	$0.258983\pi$
$947$	9.92846e20i	1.45356i	−0.686872	+	0.726778i	$0.741017\pi$
$948$	0	0
$949$	−3.58771e20	−0.517552
$950$	3.77121e20i	0.540027i
$951$	0	0
$952$	3.77978e20	0.533344
$953$	− 9.21582e20i	− 1.29087i	−0.763813	−	0.645437i	$-0.776675\pi$
$953$	− 9.21582e20i	− 1.29087i	0.763813	−	0.645437i	$-0.223325\pi$
$954$	0	0
$955$	2.90445e20	0.400903
$956$	5.95080e20i	0.815399i
$957$	0	0
$958$	2.66613e20	0.360017
$959$	1.81559e18i	0.00243381i
$960$	0	0
$961$	7.36183e20	0.972573
$962$	2.35436e21i	3.08779i
$963$	0	0
$964$	−6.69299e20	−0.865129
$965$	5.19400e20i	0.666516i
$966$	0	0
$967$	−3.60043e20	−0.455375	−0.227687	−	0.973734i	$-0.573116\pi$
$967$	−3.60043e20	−0.455375	−0.227687	+	0.973734i	$0.573116\pi$
$968$	4.69217e20i	0.589178i
$969$	0	0
$970$	−2.09379e20	−0.259138
$971$	4.41176e20i	0.542097i	0.962566	+	0.271048i	$0.0873704\pi$
$971$	4.41176e20i	0.542097i	−0.962566	+	0.271048i	$0.912630\pi$
$972$	0	0
$973$	5.79187e20	0.701502
$974$	− 2.10799e21i	− 2.53487i
$975$	0	0
$976$	−2.17943e20	−0.258342
$977$	− 7.02053e20i	− 0.826244i	−0.910676	−	0.413122i	$-0.864438\pi$
$977$	− 7.02053e20i	− 0.826244i	0.910676	−	0.413122i	$-0.135562\pi$
$978$	0	0
$979$	1.30849e20	0.151807
$980$	7.20248e20i	0.829659i
$981$	0	0
$982$	7.94460e20	0.902176
$983$	− 1.28519e21i	− 1.44908i	−0.689232	−	0.724541i	$-0.742052\pi$
$983$	− 1.28519e21i	− 1.44908i	0.689232	−	0.724541i	$-0.257948\pi$
$984$	0	0
$985$	−7.91346e20	−0.879656
$986$	2.78823e21i	3.07745i
$987$	0	0
$988$	1.87959e21	2.04534
$989$	− 1.25066e20i	− 0.135135i
$990$	0	0
$991$	−5.70962e20	−0.608263	−0.304132	−	0.952630i	$-0.598366\pi$
$991$	−5.70962e20	−0.608263	−0.304132	+	0.952630i	$0.598366\pi$
$992$	1.74573e21i	1.84670i
$993$	0	0
$994$	−9.18234e20	−0.957743
$995$	− 5.08420e20i	− 0.526576i
$996$	0	0
$997$	9.32597e20	0.952419	0.476209	−	0.879332i	$-0.342010\pi$
$997$	9.32597e20	0.952419	0.476209	+	0.879332i	$0.342010\pi$
$998$	− 6.11161e20i	− 0.619786i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.15.b.c.26.1	✓	4
3.2	odd	2	inner	27.15.b.c.26.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.15.b.c.26.1	✓	4	1.1	even	1	trivial
27.15.b.c.26.4	yes	4	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	27.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-197.702i q^{2} -22702.1 q^{4} +67180.2i q^{5} +453839. q^{7} +1.24910e6i q^{8} +1.32817e7 q^{10} +2.02634e6i q^{11} +6.90269e7 q^{13} -8.97249e7i q^{14} -1.25001e8 q^{16} -6.66755e8i q^{17} -1.19944e9 q^{19} -1.52513e9i q^{20} +4.00612e8 q^{22} -2.10269e9i q^{23} +1.59034e9 q^{25} -1.36468e10i q^{26} -1.03031e10 q^{28} -2.11520e10i q^{29} +3.86410e10 q^{31} +4.51783e10i q^{32} -1.31819e11 q^{34} +3.04890e10i q^{35} -1.72521e11 q^{37} +2.37132e11i q^{38} -8.39148e10 q^{40} +3.23308e10i q^{41} +5.94792e10 q^{43} -4.60023e10i q^{44} -4.15706e11 q^{46} +1.00148e11i q^{47} -4.72253e11 q^{49} -3.14414e11i q^{50} -1.56706e12 q^{52} -2.31329e12i q^{53} -1.36130e11 q^{55} +5.66891e11i q^{56} -4.18179e12 q^{58} +2.97124e11i q^{59} +1.74353e12 q^{61} -7.63941e12i q^{62} +6.88382e12 q^{64} +4.63724e12i q^{65} +3.39564e12 q^{67} +1.51367e13i q^{68} +6.02773e12 q^{70} -1.02339e13i q^{71} -5.19755e12 q^{73} +3.41078e13i q^{74} +2.72298e13 q^{76} +9.19634e11i q^{77} -1.50233e13 q^{79} -8.39761e12i q^{80} +6.39186e12 q^{82} -3.76556e13i q^{83} +4.47927e13 q^{85} -1.17592e13i q^{86} -2.53111e12 q^{88} -6.45740e13i q^{89} +3.13271e13 q^{91} +4.77355e13i q^{92} +1.97996e13 q^{94} -8.05787e13i q^{95} -1.57646e13 q^{97} +9.33654e13i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 22484 q^{4} + 448868 q^{7} + 13088520 q^{10} + 66488396 q^{13} - 148681016 q^{16} - 1385373196 q^{19} - 695847240 q^{22} - 3049909820 q^{25} - 25864209028 q^{28} - 6310989544 q^{31} - 241760528280 q^{34}+ \cdots - 243547238121892 q^{97}+O(q^{100}) \) 4 * q - 22484 * q^4 + 448868 * q^7 + 13088520 * q^10 + 66488396 * q^13 - 148681016 * q^16 - 1385373196 * q^19 - 695847240 * q^22 - 3049909820 * q^25 - 25864209028 * q^28 - 6310989544 * q^31 - 241760528280 * q^34 - 409258346932 * q^37 - 543023133840 * q^40 - 762882511048 * q^43 - 1669971531960 * q^46 - 2195699231040 * q^49 - 3954259388716 * q^52 - 2320711097760 * q^55 - 5557256089200 * q^58 + 685756320716 * q^61 + 10436251483696 * q^64 + 14034302053844 * q^67 + 15146651940840 * q^70 + 22197489967772 * q^73 + 66074632593116 * q^76 + 6868641127844 * q^79 + 55963348470000 * q^82 + 119520166805280 * q^85 - 46746836935920 * q^88 + 79071690629932 * q^91 + 47408619912120 * q^94 - 243547238121892 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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