LMFDB - Embedded newform 27.11.b.d.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("27.26");

S:= CuspForms(chi, 11);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.1546458222$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 196x^{3} + 11881x^{2} - 21364x + 19208 $ x^6 - 196x^3 + 11881x^2 - 21364*x + 19208
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.5
Root			$-7.79647 - 7.79647i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.11.b.d.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+43.0534i q^{2} -829.595 q^{4} +2154.41i q^{5} -11290.6 q^{7} +8369.79i q^{8} +O(q^{10})$	\(q+43.0534i q^{2} -829.595 q^{4} +2154.41i q^{5} -11290.6 q^{7} +8369.79i q^{8} -92754.7 q^{10} -98029.6i q^{11} -593576. q^{13} -486097. i q^{14} -1.20985e6 q^{16} -177138. i q^{17} +2.84390e6 q^{19} -1.78729e6i q^{20} +4.22051e6 q^{22} -1.06127e7i q^{23} +5.12414e6 q^{25} -2.55554e7i q^{26} +9.36660e6 q^{28} +2.16259e7i q^{29} -2.33215e7 q^{31} -4.35176e7i q^{32} +7.62640e6 q^{34} -2.43245e7i q^{35} -1.23334e8 q^{37} +1.22440e8i q^{38} -1.80320e7 q^{40} -9.53097e7i q^{41} -3.63196e7 q^{43} +8.13249e7i q^{44} +4.56912e8 q^{46} +4.01285e8i q^{47} -1.54998e8 q^{49} +2.20611e8i q^{50} +4.92427e8 q^{52} +2.69881e8i q^{53} +2.11196e8 q^{55} -9.44997e7i q^{56} -9.31068e8 q^{58} +1.44671e8i q^{59} -7.44337e8 q^{61} -1.00407e9i q^{62} +6.34692e8 q^{64} -1.27881e9i q^{65} -2.00528e9 q^{67} +1.46953e8i q^{68} +1.04725e9 q^{70} +1.82469e9i q^{71} +4.08582e8 q^{73} -5.30997e9i q^{74} -2.35929e9 q^{76} +1.10681e9i q^{77} +4.48653e9 q^{79} -2.60652e9i q^{80} +4.10341e9 q^{82} -1.61512e9i q^{83} +3.81628e8 q^{85} -1.56368e9i q^{86} +8.20487e8 q^{88} +6.49519e9i q^{89} +6.70181e9 q^{91} +8.80424e9i q^{92} -1.72767e10 q^{94} +6.12694e9i q^{95} -4.67264e9 q^{97} -6.67320e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2658 q^{4} + 4638 q^{7}+O(q^{10}) $ 6 * q - 2658 * q^4 + 4638 * q^7	$ 6 q - 2658 q^{4} + 4638 q^{7} + 233658 q^{10} + 131844 q^{13} - 1575102 q^{16} + 7706784 q^{19} - 11594718 q^{22} - 10669728 q^{25} - 6580266 q^{28} + 11591994 q^{31} + 119452644 q^{34} + 7171320 q^{37} - 330020298 q^{40} + 203012076 q^{43} + 583979112 q^{46} - 1195686288 q^{49} - 84347628 q^{52} + 2719163250 q^{55} - 5503711428 q^{58} + 2326158264 q^{61} + 6019783710 q^{64} - 6569458044 q^{67} + 6917324130 q^{70} + 2618820678 q^{73} - 21072468192 q^{76} + 5638333908 q^{79} + 19302295032 q^{82} - 26239380732 q^{85} + 12553208334 q^{88} + 24736096788 q^{91} - 35311712076 q^{94} - 4672763646 q^{97}+O(q^{100}) $ 6 * q - 2658 * q^4 + 4638 * q^7 + 233658 * q^10 + 131844 * q^13 - 1575102 * q^16 + 7706784 * q^19 - 11594718 * q^22 - 10669728 * q^25 - 6580266 * q^28 + 11591994 * q^31 + 119452644 * q^34 + 7171320 * q^37 - 330020298 * q^40 + 203012076 * q^43 + 583979112 * q^46 - 1195686288 * q^49 - 84347628 * q^52 + 2719163250 * q^55 - 5503711428 * q^58 + 2326158264 * q^61 + 6019783710 * q^64 - 6569458044 * q^67 + 6917324130 * q^70 + 2618820678 * q^73 - 21072468192 * q^76 + 5638333908 * q^79 + 19302295032 * q^82 - 26239380732 * q^85 + 12553208334 * q^88 + 24736096788 * q^91 - 35311712076 * q^94 - 4672763646 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	43.0534i	1.34542i	0.739907	+	0.672709i	$0.234870\pi$
$2$	43.0534i	1.34542i	−0.739907	+	0.672709i	$0.765130\pi$
$3$	0	0
$3$	0	0
$4$	−829.595	−0.810151
$5$	2154.41i	0.689412i	0.938711	+	0.344706i	$0.112021\pi$
$5$	2154.41i	0.689412i	−0.938711	+	0.344706i	$0.887979\pi$
$6$	0	0
$7$	−11290.6	−0.671778	−0.335889	−	0.941902i	$-0.609037\pi$
$7$	−11290.6	−0.671778	−0.335889	+	0.941902i	$0.609037\pi$
$8$	8369.79i	0.255426i
$9$	0	0
$10$	−92754.7	−0.927547
$11$	− 98029.6i	− 0.608687i	−0.952562	−	0.304343i	$-0.901563\pi$
$11$	− 98029.6i	− 0.608687i	0.952562	−	0.304343i	$-0.0984370\pi$
$12$	0	0
$13$	−593576.	−1.59867	−0.799336	−	0.600885i	$-0.794815\pi$
$13$	−593576.	−1.59867	−0.799336	+	0.600885i	$0.794815\pi$
$14$	− 486097.i	− 0.903823i
$15$	0	0
$16$	−1.20985e6	−1.15381
$17$	− 177138.i	− 0.124758i	−0.998053	−	0.0623788i	$-0.980131\pi$
$17$	− 177138.i	− 0.124758i	0.998053	−	0.0623788i	$-0.0198687\pi$
$18$	0	0
$19$	2.84390e6	1.14854	0.574271	−	0.818665i	$-0.305286\pi$
$19$	2.84390e6	1.14854	0.574271	+	0.818665i	$0.305286\pi$
$20$	− 1.78729e6i	− 0.558528i
$21$	0	0
$22$	4.22051e6	0.818939
$23$	− 1.06127e7i	− 1.64887i	−0.565957	−	0.824435i	$-0.691493\pi$
$23$	− 1.06127e7i	− 1.64887i	0.565957	−	0.824435i	$-0.308507\pi$
$24$	0	0
$25$	5.12414e6	0.524712
$26$	− 2.55554e7i	− 2.15088i
$27$	0	0
$28$	9.36660e6	0.544242
$29$	2.16259e7i	1.05435i	0.849757	+	0.527174i	$0.176748\pi$
$29$	2.16259e7i	1.05435i	−0.849757	+	0.527174i	$0.823252\pi$
$30$	0	0
$31$	−2.33215e7	−0.814608	−0.407304	−	0.913293i	$-0.633531\pi$
$31$	−2.33215e7	−0.814608	−0.407304	+	0.913293i	$0.633531\pi$
$32$	− 4.35176e7i	− 1.29693i
$33$	0	0
$34$	7.62640e6	0.167851
$35$	− 2.43245e7i	− 0.463132i
$36$	0	0
$37$	−1.23334e8	−1.77859	−0.889295	−	0.457334i	$-0.848804\pi$
$37$	−1.23334e8	−1.77859	−0.889295	+	0.457334i	$0.848804\pi$
$38$	1.22440e8i	1.54527i
$39$	0	0
$40$	−1.80320e7	−0.176093
$41$	− 9.53097e7i	− 0.822655i	−0.911488	−	0.411328i	$-0.865065\pi$
$41$	− 9.53097e7i	− 0.822655i	0.911488	−	0.411328i	$-0.134935\pi$
$42$	0	0
$43$	−3.63196e7	−0.247058	−0.123529	−	0.992341i	$-0.539421\pi$
$43$	−3.63196e7	−0.247058	−0.123529	+	0.992341i	$0.539421\pi$
$44$	8.13249e7i	0.493128i
$45$	0	0
$46$	4.56912e8	2.21842
$47$	4.01285e8i	1.74970i	0.484394	+	0.874850i	$0.339040\pi$
$47$	4.01285e8i	1.74970i	−0.484394	+	0.874850i	$0.660960\pi$
$48$	0	0
$49$	−1.54998e8	−0.548714
$50$	2.20611e8i	0.705957i
$51$	0	0
$52$	4.92427e8	1.29517
$53$	2.69881e8i	0.645347i	0.946510	+	0.322674i	$0.104582\pi$
$53$	2.69881e8i	0.645347i	−0.946510	+	0.322674i	$0.895418\pi$
$54$	0	0
$55$	2.11196e8	0.419636
$56$	− 9.44997e7i	− 0.171589i
$57$	0	0
$58$	−9.31068e8	−1.41854
$59$	1.44671e8i	0.202358i	0.994868	+	0.101179i	$0.0322615\pi$
$59$	1.44671e8i	0.202358i	−0.994868	+	0.101179i	$0.967739\pi$
$60$	0	0
$61$	−7.44337e8	−0.881294	−0.440647	−	0.897681i	$-0.645251\pi$
$61$	−7.44337e8	−0.881294	−0.440647	+	0.897681i	$0.645251\pi$
$62$	− 1.00407e9i	− 1.09599i
$63$	0	0
$64$	6.34692e8	0.591103
$65$	− 1.27881e9i	− 1.10214i
$66$	0	0
$67$	−2.00528e9	−1.48525	−0.742627	−	0.669706i	$-0.766420\pi$
$67$	−2.00528e9	−1.48525	−0.742627	+	0.669706i	$0.766420\pi$
$68$	1.46953e8i	0.101073i
$69$	0	0
$70$	1.04725e9	0.623106
$71$	1.82469e9i	1.01134i	0.862727	+	0.505669i	$0.168754\pi$
$71$	1.82469e9i	1.01134i	−0.862727	+	0.505669i	$0.831246\pi$
$72$	0	0
$73$	4.08582e8	0.197090	0.0985451	−	0.995133i	$-0.468581\pi$
$73$	4.08582e8	0.197090	0.0985451	+	0.995133i	$0.468581\pi$
$74$	− 5.30997e9i	− 2.39295i
$75$	0	0
$76$	−2.35929e9	−0.930493
$77$	1.10681e9i	0.408902i
$78$	0	0
$79$	4.48653e9	1.45806	0.729030	−	0.684482i	$-0.239971\pi$
$79$	4.48653e9	1.45806	0.729030	+	0.684482i	$0.239971\pi$
$80$	− 2.60652e9i	− 0.795447i
$81$	0	0
$82$	4.10341e9	1.10682
$83$	− 1.61512e9i	− 0.410028i	−0.978759	−	0.205014i	$-0.934276\pi$
$83$	− 1.61512e9i	− 0.410028i	0.978759	−	0.205014i	$-0.0657240\pi$
$84$	0	0
$85$	3.81628e8	0.0860094
$86$	− 1.56368e9i	− 0.332397i
$87$	0	0
$88$	8.20487e8	0.155474
$89$	6.49519e9i	1.16317i	0.813487	+	0.581584i	$0.197567\pi$
$89$	6.49519e9i	1.16317i	−0.813487	+	0.581584i	$0.802433\pi$
$90$	0	0
$91$	6.70181e9	1.07395
$92$	8.80424e9i	1.33583i
$93$	0	0
$94$	−1.72767e10	−2.35408
$95$	6.12694e9i	0.791818i
$96$	0	0
$97$	−4.67264e9	−0.544131	−0.272066	−	0.962279i	$-0.587707\pi$
$97$	−4.67264e9	−0.544131	−0.272066	+	0.962279i	$0.587707\pi$
$98$	− 6.67320e9i	− 0.738251i
$99$	0	0
$100$	−4.25096e9	−0.425096
$101$	1.83762e10i	1.74843i	0.485541	+	0.874214i	$0.338623\pi$
$101$	1.83762e10i	1.74843i	−0.485541	+	0.874214i	$0.661377\pi$
$102$	0	0
$103$	−2.54345e8	−0.0219400	−0.0109700	−	0.999940i	$-0.503492\pi$
$103$	−2.54345e8	−0.0219400	−0.0109700	+	0.999940i	$0.503492\pi$
$104$	− 4.96810e9i	− 0.408342i
$105$	0	0
$106$	−1.16193e10	−0.868263
$107$	4.77413e9i	0.340389i	0.985411	+	0.170194i	$0.0544396\pi$
$107$	4.77413e9i	0.340389i	−0.985411	+	0.170194i	$0.945560\pi$
$108$	0	0
$109$	6.79657e9	0.441730	0.220865	−	0.975304i	$-0.429112\pi$
$109$	6.79657e9	0.441730	0.220865	+	0.975304i	$0.429112\pi$
$110$	9.09271e9i	0.564586i
$111$	0	0
$112$	1.36599e10	0.775101
$113$	− 1.07273e10i	− 0.582236i	−0.956687	−	0.291118i	$-0.905973\pi$
$113$	− 1.07273e10i	− 0.582236i	0.956687	−	0.291118i	$-0.0940273\pi$
$114$	0	0
$115$	2.28641e10	1.13675
$116$	− 1.79407e10i	− 0.854181i
$117$	0	0
$118$	−6.22856e9	−0.272256
$119$	1.99999e9i	0.0838095i
$120$	0	0
$121$	1.63276e10	0.629500
$122$	− 3.20462e10i	− 1.18571i
$123$	0	0
$124$	1.93474e10	0.659956
$125$	3.20787e10i	1.05115i
$126$	0	0
$127$	−4.58028e10	−1.38635	−0.693176	−	0.720769i	$-0.743789\pi$
$127$	−4.58028e10	−1.38635	−0.693176	+	0.720769i	$0.743789\pi$
$128$	− 1.72364e10i	− 0.501645i
$129$	0	0
$130$	5.50569e10	1.48284
$131$	1.21259e10i	0.314310i	0.987574	+	0.157155i	$0.0502323\pi$
$131$	1.21259e10i	0.314310i	−0.987574	+	0.157155i	$0.949768\pi$
$132$	0	0
$133$	−3.21093e10	−0.771565
$134$	− 8.63340e10i	− 1.99829i
$135$	0	0
$136$	1.48261e9	0.0318663
$137$	− 9.10658e10i	− 1.88692i	−0.331493	−	0.943458i	$-0.607552\pi$
$137$	− 9.10658e10i	− 1.88692i	0.331493	−	0.943458i	$-0.392448\pi$
$138$	0	0
$139$	−3.23260e10	−0.622986	−0.311493	−	0.950249i	$-0.600829\pi$
$139$	−3.23260e10	−0.622986	−0.311493	+	0.950249i	$0.600829\pi$
$140$	2.01795e10i	0.375207i
$141$	0	0
$142$	−7.85590e10	−1.36067
$143$	5.81880e10i	0.973090i
$144$	0	0
$145$	−4.65911e10	−0.726880
$146$	1.75908e10i	0.265169i
$147$	0	0
$148$	1.02318e11	1.44093
$149$	4.15651e10i	0.565975i	0.959124	+	0.282987i	$0.0913255\pi$
$149$	4.15651e10i	0.565975i	−0.959124	+	0.282987i	$0.908675\pi$
$150$	0	0
$151$	−7.72689e10	−0.984283	−0.492142	−	0.870515i	$-0.663786\pi$
$151$	−7.72689e10	−0.984283	−0.492142	+	0.870515i	$0.663786\pi$
$152$	2.38029e10i	0.293367i
$153$	0	0
$154$	−4.76519e10	−0.550145
$155$	− 5.02442e10i	− 0.561600i
$156$	0	0
$157$	5.86439e10	0.614787	0.307394	−	0.951582i	$-0.400543\pi$
$157$	5.86439e10	0.614787	0.307394	+	0.951582i	$0.400543\pi$
$158$	1.93160e11i	1.96170i
$159$	0	0
$160$	9.37549e10	0.894116
$161$	1.19823e11i	1.10767i
$162$	0	0
$163$	6.80790e10	0.591664	0.295832	−	0.955240i	$-0.404403\pi$
$163$	6.80790e10	0.591664	0.295832	+	0.955240i	$0.404403\pi$
$164$	7.90685e10i	0.666475i
$165$	0	0
$166$	6.95363e10	0.551659
$167$	− 1.53056e11i	− 1.17834i	−0.808011	−	0.589168i	$-0.799456\pi$
$167$	− 1.53056e11i	− 1.17834i	0.808011	−	0.589168i	$-0.200544\pi$
$168$	0	0
$169$	2.14473e11	1.55575
$170$	1.64304e10i	0.115719i
$171$	0	0
$172$	3.01306e10	0.200154
$173$	− 1.28612e11i	− 0.829949i	−0.909833	−	0.414975i	$-0.863790\pi$
$173$	− 1.28612e11i	− 0.829949i	0.909833	−	0.414975i	$-0.136210\pi$
$174$	0	0
$175$	−5.78544e10	−0.352490
$176$	1.18601e11i	0.702306i
$177$	0	0
$178$	−2.79640e11	−1.56495
$179$	9.05388e10i	0.492685i	0.969183	+	0.246343i	$0.0792288\pi$
$179$	9.05388e10i	0.492685i	−0.969183	+	0.246343i	$0.920771\pi$
$180$	0	0
$181$	−1.59039e11	−0.818674	−0.409337	−	0.912383i	$-0.634240\pi$
$181$	−1.59039e11	−0.818674	−0.409337	+	0.912383i	$0.634240\pi$
$182$	2.88536e11i	1.44492i
$183$	0	0
$184$	8.88260e10	0.421164
$185$	− 2.65713e11i	− 1.22618i
$186$	0	0
$187$	−1.73648e10	−0.0759384
$188$	− 3.32904e11i	− 1.41752i
$189$	0	0
$190$	−2.63785e11	−1.06533
$191$	2.17166e11i	0.854329i	0.904174	+	0.427165i	$0.140488\pi$
$191$	2.17166e11i	0.854329i	−0.904174	+	0.427165i	$0.859512\pi$
$192$	0	0
$193$	−1.82287e11	−0.680719	−0.340360	−	0.940295i	$-0.610549\pi$
$193$	−1.82287e11	−0.680719	−0.340360	+	0.940295i	$0.610549\pi$
$194$	− 2.01173e11i	− 0.732084i
$195$	0	0
$196$	1.28586e11	0.444542
$197$	− 3.94415e11i	− 1.32930i	−0.747155	−	0.664650i	$-0.768581\pi$
$197$	− 3.94415e11i	− 1.32930i	0.747155	−	0.664650i	$-0.231419\pi$
$198$	0	0
$199$	3.83913e11	1.23018	0.615088	−	0.788459i	$-0.289121\pi$
$199$	3.83913e11	1.23018	0.615088	+	0.788459i	$0.289121\pi$
$200$	4.28879e10i	0.134025i
$201$	0	0
$202$	−7.91156e11	−2.35237
$203$	− 2.44169e11i	− 0.708288i
$204$	0	0
$205$	2.05336e11	0.567148
$206$	− 1.09504e10i	− 0.0295185i
$207$	0	0
$208$	7.18139e11	1.84456
$209$	− 2.78787e11i	− 0.699102i
$210$	0	0
$211$	7.22100e10	0.172657	0.0863287	−	0.996267i	$-0.472486\pi$
$211$	7.22100e10	0.172657	0.0863287	+	0.996267i	$0.472486\pi$
$212$	− 2.23892e11i	− 0.522829i
$213$	0	0
$214$	−2.05542e11	−0.457965
$215$	− 7.82474e10i	− 0.170325i
$216$	0	0
$217$	2.63313e11	0.547236
$218$	2.92615e11i	0.594312i
$219$	0	0
$220$	−1.75207e11	−0.339969
$221$	1.05145e11i	0.199447i
$222$	0	0
$223$	7.95419e11	1.44235	0.721177	−	0.692751i	$-0.243602\pi$
$223$	7.95419e11	1.44235	0.721177	+	0.692751i	$0.243602\pi$
$224$	4.91339e11i	0.871247i
$225$	0	0
$226$	4.61848e11	0.783352
$227$	− 3.80375e11i	− 0.631078i	−0.948913	−	0.315539i	$-0.897815\pi$
$227$	− 3.80375e11i	− 0.631078i	0.948913	−	0.315539i	$-0.102185\pi$
$228$	0	0
$229$	−1.73387e11	−0.275321	−0.137660	−	0.990479i	$-0.543958\pi$
$229$	−1.73387e11	−0.275321	−0.137660	+	0.990479i	$0.543958\pi$
$230$	9.84377e11i	1.52940i
$231$	0	0
$232$	−1.81004e11	−0.269308
$233$	6.06062e11i	0.882546i	0.897373	+	0.441273i	$0.145473\pi$
$233$	6.06062e11i	0.882546i	−0.897373	+	0.441273i	$0.854527\pi$
$234$	0	0
$235$	−8.64533e11	−1.20626
$236$	− 1.20018e11i	− 0.163941i
$237$	0	0
$238$	−8.61064e10	−0.112759
$239$	6.87962e11i	0.882216i	0.897454	+	0.441108i	$0.145415\pi$
$239$	6.87962e11i	0.882216i	−0.897454	+	0.441108i	$0.854585\pi$
$240$	0	0
$241$	−5.89148e10	−0.0724668	−0.0362334	−	0.999343i	$-0.511536\pi$
$241$	−5.89148e10	−0.0724668	−0.0362334	+	0.999343i	$0.511536\pi$
$242$	7.02959e11i	0.846942i
$243$	0	0
$244$	6.17499e11	0.713981
$245$	− 3.33930e11i	− 0.378290i
$246$	0	0
$247$	−1.68807e12	−1.83614
$248$	− 1.95196e11i	− 0.208072i
$249$	0	0
$250$	−1.38110e12	−1.41424
$251$	− 4.41013e11i	− 0.442673i	−0.975197	−	0.221337i	$-0.928958\pi$
$251$	− 4.41013e11i	− 0.442673i	0.975197	−	0.221337i	$-0.0710419\pi$
$252$	0	0
$253$	−1.04036e12	−1.00365
$254$	− 1.97197e12i	− 1.86522i
$255$	0	0
$256$	1.39201e12	1.26603
$257$	1.79444e12i	1.60053i	0.599648	+	0.800264i	$0.295307\pi$
$257$	1.79444e12i	1.60053i	−0.599648	+	0.800264i	$0.704693\pi$
$258$	0	0
$259$	1.39252e12	1.19482
$260$	1.06089e12i	0.892903i
$261$	0	0
$262$	−5.22062e11	−0.422879
$263$	2.34668e12i	1.86498i	0.361193	+	0.932491i	$0.382370\pi$
$263$	2.34668e12i	1.86498i	−0.361193	+	0.932491i	$0.617630\pi$
$264$	0	0
$265$	−5.81436e11	−0.444910
$266$	− 1.38241e12i	− 1.03808i
$267$	0	0
$268$	1.66357e12	1.20328
$269$	− 2.01543e12i	− 1.43089i	−0.698668	−	0.715446i	$-0.746224\pi$
$269$	− 2.01543e12i	− 1.43089i	0.698668	−	0.715446i	$-0.253776\pi$
$270$	0	0
$271$	1.78954e11	0.122432	0.0612160	−	0.998125i	$-0.480502\pi$
$271$	1.78954e11	0.122432	0.0612160	+	0.998125i	$0.480502\pi$
$272$	2.14311e11i	0.143946i
$273$	0	0
$274$	3.92069e12	2.53869
$275$	− 5.02317e11i	− 0.319385i
$276$	0	0
$277$	−1.31184e12	−0.804417	−0.402209	−	0.915548i	$-0.631757\pi$
$277$	−1.31184e12	−0.804417	−0.402209	+	0.915548i	$0.631757\pi$
$278$	− 1.39174e12i	− 0.838176i
$279$	0	0
$280$	2.03591e11	0.118296
$281$	− 1.74088e12i	− 0.993661i	−0.867848	−	0.496830i	$-0.834497\pi$
$281$	− 1.74088e12i	− 0.993661i	0.867848	−	0.496830i	$-0.165503\pi$
$282$	0	0
$283$	5.96984e11	0.328875	0.164437	−	0.986388i	$-0.447419\pi$
$283$	5.96984e11	0.328875	0.164437	+	0.986388i	$0.447419\pi$
$284$	− 1.51375e12i	− 0.819338i
$285$	0	0
$286$	−2.50519e12	−1.30921
$287$	1.07610e12i	0.552641i
$288$	0	0
$289$	1.98462e12	0.984436
$290$	− 2.00590e12i	− 0.977958i
$291$	0	0
$292$	−3.38958e11	−0.159673
$293$	− 2.08839e12i	− 0.967104i	−0.875316	−	0.483552i	$-0.839346\pi$
$293$	− 2.08839e12i	− 0.967104i	0.875316	−	0.483552i	$-0.160654\pi$
$294$	0	0
$295$	−3.11680e11	−0.139508
$296$	− 1.03228e12i	− 0.454298i
$297$	0	0
$298$	−1.78952e12	−0.761473
$299$	6.29943e12i	2.63600i
$300$	0	0
$301$	4.10069e11	0.165968
$302$	− 3.32669e12i	− 1.32427i
$303$	0	0
$304$	−3.44071e12	−1.32519
$305$	− 1.60361e12i	− 0.607574i
$306$	0	0
$307$	−4.30412e12	−1.57831	−0.789156	−	0.614193i	$-0.789482\pi$
$307$	−4.30412e12	−1.57831	−0.789156	+	0.614193i	$0.789482\pi$
$308$	− 9.18204e11i	− 0.331273i
$309$	0	0
$310$	2.16318e12	0.755588
$311$	3.75853e12i	1.29186i	0.763396	+	0.645930i	$0.223530\pi$
$311$	3.75853e12i	1.29186i	−0.763396	+	0.645930i	$0.776470\pi$
$312$	0	0
$313$	5.72063e12	1.90424	0.952120	−	0.305724i	$-0.0988984\pi$
$313$	5.72063e12	1.90424	0.952120	+	0.305724i	$0.0988984\pi$
$314$	2.52482e12i	0.827146i
$315$	0	0
$316$	−3.72201e12	−1.18125
$317$	4.02703e12i	1.25802i	0.777396	+	0.629011i	$0.216540\pi$
$317$	4.02703e12i	1.25802i	−0.777396	+	0.629011i	$0.783460\pi$
$318$	0	0
$319$	2.11998e12	0.641768
$320$	1.36739e12i	0.407513i
$321$	0	0
$322$	−5.15880e12	−1.49029
$323$	− 5.03763e11i	− 0.143289i
$324$	0	0
$325$	−3.04156e12	−0.838841
$326$	2.93103e12i	0.796036i
$327$	0	0
$328$	7.97722e11	0.210127
$329$	− 4.53073e12i	− 1.17541i
$330$	0	0
$331$	3.46028e12	0.870907	0.435453	−	0.900211i	$-0.356588\pi$
$331$	3.46028e12	0.870907	0.435453	+	0.900211i	$0.356588\pi$
$332$	1.33989e12i	0.332185i
$333$	0	0
$334$	6.58960e12	1.58536
$335$	− 4.32019e12i	− 1.02395i
$336$	0	0
$337$	−2.30017e12	−0.529189	−0.264595	−	0.964360i	$-0.585238\pi$
$337$	−2.30017e12	−0.529189	−0.264595	+	0.964360i	$0.585238\pi$
$338$	9.23381e12i	2.09314i
$339$	0	0
$340$	−3.16597e11	−0.0696806
$341$	2.28620e12i	0.495841i
$342$	0	0
$343$	4.93933e12	1.04039
$344$	− 3.03988e11i	− 0.0631050i
$345$	0	0
$346$	5.53719e12	1.11663
$347$	6.54266e12i	1.30049i	0.759725	+	0.650245i	$0.225334\pi$
$347$	6.54266e12i	1.30049i	−0.759725	+	0.650245i	$0.774666\pi$
$348$	0	0
$349$	8.53868e12	1.64916	0.824582	−	0.565743i	$-0.191411\pi$
$349$	8.53868e12	1.64916	0.824582	+	0.565743i	$0.191411\pi$
$350$	− 2.49083e12i	− 0.474246i
$351$	0	0
$352$	−4.26602e12	−0.789422
$353$	− 4.62537e12i	− 0.843865i	−0.906627	−	0.421932i	$-0.861352\pi$
$353$	− 4.62537e12i	− 0.843865i	0.906627	−	0.421932i	$-0.138648\pi$
$354$	0	0
$355$	−3.93113e12	−0.697229
$356$	− 5.38838e12i	− 0.942342i
$357$	0	0
$358$	−3.89800e12	−0.662868
$359$	1.98597e12i	0.333044i	0.986038	+	0.166522i	$0.0532536\pi$
$359$	1.98597e12i	0.333044i	−0.986038	+	0.166522i	$0.946746\pi$
$360$	0	0
$361$	1.95672e12	0.319148
$362$	− 6.84717e12i	− 1.10146i
$363$	0	0
$364$	−5.55979e12	−0.870064
$365$	8.80254e11i	0.135876i
$366$	0	0
$367$	−7.37618e12	−1.10790	−0.553951	−	0.832549i	$-0.686880\pi$
$367$	−7.37618e12	−1.10790	−0.553951	+	0.832549i	$0.686880\pi$
$368$	1.28398e13i	1.90248i
$369$	0	0
$370$	1.14399e13	1.64973
$371$	− 3.04712e12i	− 0.433530i
$372$	0	0
$373$	−1.00255e13	−1.38854	−0.694272	−	0.719712i	$-0.744274\pi$
$373$	−1.00255e13	−1.38854	−0.694272	+	0.719712i	$0.744274\pi$
$374$	− 7.47613e11i	− 0.102169i
$375$	0	0
$376$	−3.35867e12	−0.446918
$377$	− 1.28366e13i	− 1.68556i
$378$	0	0
$379$	−5.04373e12	−0.644995	−0.322497	−	0.946570i	$-0.604522\pi$
$379$	−5.04373e12	−0.644995	−0.322497	+	0.946570i	$0.604522\pi$
$380$	− 5.08288e12i	− 0.641493i
$381$	0	0
$382$	−9.34974e12	−1.14943
$383$	− 4.77021e12i	− 0.578820i	−0.957205	−	0.289410i	$-0.906541\pi$
$383$	− 4.77021e12i	− 0.578820i	0.957205	−	0.289410i	$-0.0934590\pi$
$384$	0	0
$385$	−2.38452e12	−0.281902
$386$	− 7.84805e12i	− 0.915852i
$387$	0	0
$388$	3.87640e12	0.440829
$389$	− 1.77163e13i	− 1.98895i	−0.104956	−	0.994477i	$-0.533470\pi$
$389$	− 1.77163e13i	− 1.98895i	0.104956	−	0.994477i	$-0.466530\pi$
$390$	0	0
$391$	−1.87991e12	−0.205709
$392$	− 1.29730e12i	− 0.140156i
$393$	0	0
$394$	1.69809e13	1.78846
$395$	9.66584e12i	1.00520i
$396$	0	0
$397$	−2.14906e12	−0.217919	−0.108959	−	0.994046i	$-0.534752\pi$
$397$	−2.14906e12	−0.217919	−0.108959	+	0.994046i	$0.534752\pi$
$398$	1.65287e13i	1.65510i
$399$	0	0
$400$	−6.19945e12	−0.605415
$401$	− 5.72523e12i	− 0.552168i	−0.961133	−	0.276084i	$-0.910963\pi$
$401$	− 5.72523e12i	− 0.552168i	0.961133	−	0.276084i	$-0.0890368\pi$
$402$	0	0
$403$	1.38431e13	1.30229
$404$	− 1.52448e13i	− 1.41649i
$405$	0	0
$406$	1.05123e13	0.952943
$407$	1.20904e13i	1.08260i
$408$	0	0
$409$	−2.10854e12	−0.184232	−0.0921161	−	0.995748i	$-0.529363\pi$
$409$	−2.10854e12	−0.184232	−0.0921161	+	0.995748i	$0.529363\pi$
$410$	8.84043e12i	0.763052i
$411$	0	0
$412$	2.11003e11	0.0177747
$413$	− 1.63341e12i	− 0.135940i
$414$	0	0
$415$	3.47963e12	0.282678
$416$	2.58310e13i	2.07336i
$417$	0	0
$418$	1.20027e13	0.940585
$419$	− 1.86683e12i	− 0.144556i	−0.997385	−	0.0722778i	$-0.976973\pi$
$419$	− 1.86683e12i	− 0.144556i	0.997385	−	0.0722778i	$-0.0230268\pi$
$420$	0	0
$421$	−1.08492e13	−0.820330	−0.410165	−	0.912011i	$-0.634529\pi$
$421$	−1.08492e13	−0.820330	−0.410165	+	0.912011i	$0.634529\pi$
$422$	3.10889e12i	0.232296i
$423$	0	0
$424$	−2.25885e12	−0.164838
$425$	− 9.07680e11i	− 0.0654618i
$426$	0	0
$427$	8.40399e12	0.592034
$428$	− 3.96059e12i	− 0.275766i
$429$	0	0
$430$	3.36882e12	0.229158
$431$	1.31622e13i	0.884997i	0.896769	+	0.442498i	$0.145908\pi$
$431$	1.31622e13i	0.884997i	−0.896769	+	0.442498i	$0.854092\pi$
$432$	0	0
$433$	−1.07858e12	−0.0708617	−0.0354309	−	0.999372i	$-0.511280\pi$
$433$	−1.07858e12	−0.0708617	−0.0354309	+	0.999372i	$0.511280\pi$
$434$	1.13365e13i	0.736261i
$435$	0	0
$436$	−5.63840e12	−0.357869
$437$	− 3.01815e13i	− 1.89380i
$438$	0	0
$439$	−2.14302e12	−0.131433	−0.0657164	−	0.997838i	$-0.520933\pi$
$439$	−2.14302e12	−0.131433	−0.0657164	+	0.997838i	$0.520933\pi$
$440$	1.76767e12i	0.107186i
$441$	0	0
$442$	−4.52684e12	−0.268339
$443$	4.19845e12i	0.246076i	0.992402	+	0.123038i	$0.0392638\pi$
$443$	4.19845e12i	0.246076i	−0.992402	+	0.123038i	$0.960736\pi$
$444$	0	0
$445$	−1.39933e13	−0.801901
$446$	3.42455e13i	1.94057i
$447$	0	0
$448$	−7.16604e12	−0.397090
$449$	− 1.45365e12i	− 0.0796580i	−0.999207	−	0.0398290i	$-0.987319\pi$
$449$	− 1.45365e12i	− 0.0796580i	0.999207	−	0.0398290i	$-0.0126813\pi$
$450$	0	0
$451$	−9.34317e12	−0.500739
$452$	8.89934e12i	0.471700i
$453$	0	0
$454$	1.63765e13	0.849064
$455$	1.44385e13i	0.740395i
$456$	0	0
$457$	−3.61163e12	−0.181185	−0.0905925	−	0.995888i	$-0.528876\pi$
$457$	−3.61163e12	−0.181185	−0.0905925	+	0.995888i	$0.528876\pi$
$458$	− 7.46490e12i	− 0.370422i
$459$	0	0
$460$	−1.89679e13	−0.920940
$461$	− 5.36209e11i	− 0.0257531i	−0.999917	−	0.0128765i	$-0.995901\pi$
$461$	− 5.36209e11i	− 0.0257531i	0.999917	−	0.0128765i	$-0.00409884\pi$
$462$	0	0
$463$	−1.82376e13	−0.857164	−0.428582	−	0.903503i	$-0.640987\pi$
$463$	−1.82376e13	−0.857164	−0.428582	+	0.903503i	$0.640987\pi$
$464$	− 2.61641e13i	− 1.21651i
$465$	0	0
$466$	−2.60930e13	−1.18739
$467$	2.80701e13i	1.26375i	0.775072	+	0.631873i	$0.217714\pi$
$467$	2.80701e13i	1.26375i	−0.775072	+	0.631873i	$0.782286\pi$
$468$	0	0
$469$	2.26407e13	0.997760
$470$	− 3.72211e13i	− 1.62293i
$471$	0	0
$472$	−1.21086e12	−0.0516874
$473$	3.56040e12i	0.150381i
$474$	0	0
$475$	1.45725e13	0.602653
$476$	− 1.65918e12i	− 0.0678984i
$477$	0	0
$478$	−2.96191e13	−1.18695
$479$	− 2.33803e13i	− 0.927198i	−0.886045	−	0.463599i	$-0.846558\pi$
$479$	− 2.33803e13i	− 0.927198i	0.886045	−	0.463599i	$-0.153442\pi$
$480$	0	0
$481$	7.32083e13	2.84338
$482$	− 2.53648e12i	− 0.0974982i
$483$	0	0
$484$	−1.35453e13	−0.509991
$485$	− 1.00668e13i	− 0.375130i
$486$	0	0
$487$	1.41373e13	0.516085	0.258043	−	0.966134i	$-0.416922\pi$
$487$	1.41373e13	0.516085	0.258043	+	0.966134i	$0.416922\pi$
$488$	− 6.22995e12i	− 0.225105i
$489$	0	0
$490$	1.43768e13	0.508959
$491$	3.72597e13i	1.30567i	0.757502	+	0.652833i	$0.226420\pi$
$491$	3.72597e13i	1.30567i	−0.757502	+	0.652833i	$0.773580\pi$
$492$	0	0
$493$	3.83077e12	0.131538
$494$	− 7.26772e13i	− 2.47038i
$495$	0	0
$496$	2.82156e13	0.939900
$497$	− 2.06018e13i	− 0.679395i
$498$	0	0
$499$	2.00587e13	0.648334	0.324167	−	0.946000i	$-0.394916\pi$
$499$	2.00587e13	0.648334	0.324167	+	0.946000i	$0.394916\pi$
$500$	− 2.66123e13i	− 0.851594i
$501$	0	0
$502$	1.89871e13	0.595581
$503$	1.89228e13i	0.587686i	0.955854	+	0.293843i	$0.0949342\pi$
$503$	1.89228e13i	0.587686i	−0.955854	+	0.293843i	$0.905066\pi$
$504$	0	0
$505$	−3.95898e13	−1.20539
$506$	− 4.47909e13i	− 1.35032i
$507$	0	0
$508$	3.79978e13	1.12315
$509$	− 1.97920e13i	− 0.579296i	−0.957133	−	0.289648i	$-0.906462\pi$
$509$	− 1.97920e13i	− 0.579296i	0.957133	−	0.289648i	$-0.0935382\pi$
$510$	0	0
$511$	−4.61312e12	−0.132401
$512$	4.22807e13i	1.20169i
$513$	0	0
$514$	−7.72567e13	−2.15338
$515$	− 5.47963e11i	− 0.0151257i
$516$	0	0
$517$	3.93378e13	1.06502
$518$	5.99526e13i	1.60753i
$519$	0	0
$520$	1.07033e13	0.281516
$521$	1.97239e13i	0.513813i	0.966436	+	0.256906i	$0.0827032\pi$
$521$	1.97239e13i	0.513813i	−0.966436	+	0.256906i	$0.917297\pi$
$522$	0	0
$523$	−1.19865e13	−0.306327	−0.153163	−	0.988201i	$-0.548946\pi$
$523$	−1.19865e13	−0.306327	−0.153163	+	0.988201i	$0.548946\pi$
$524$	− 1.00596e13i	− 0.254639i
$525$	0	0
$526$	−1.01032e14	−2.50918
$527$	4.13113e12i	0.101629i
$528$	0	0
$529$	−7.12027e13	−1.71877
$530$	− 2.50328e13i	− 0.598590i
$531$	0	0
$532$	2.66377e13	0.625084
$533$	5.65735e13i	1.31516i
$534$	0	0
$535$	−1.02854e13	−0.234668
$536$	− 1.67838e13i	− 0.379372i
$537$	0	0
$538$	8.67712e13	1.92515
$539$	1.51944e13i	0.333995i
$540$	0	0
$541$	9.53588e12	0.205766	0.102883	−	0.994693i	$-0.467193\pi$
$541$	9.53588e12	0.205766	0.102883	+	0.994693i	$0.467193\pi$
$542$	7.70457e12i	0.164722i
$543$	0	0
$544$	−7.70863e12	−0.161802
$545$	1.46426e13i	0.304534i
$546$	0	0
$547$	−8.08890e13	−1.65178	−0.825891	−	0.563829i	$-0.809328\pi$
$547$	−8.08890e13	−1.65178	−0.825891	+	0.563829i	$0.809328\pi$
$548$	7.55477e13i	1.52869i
$549$	0	0
$550$	2.16265e13	0.429706
$551$	6.15019e13i	1.21096i
$552$	0	0
$553$	−5.06555e13	−0.979493
$554$	− 5.64791e13i	− 1.08228i
$555$	0	0
$556$	2.68175e13	0.504713
$557$	− 6.27193e13i	− 1.16984i	−0.811092	−	0.584919i	$-0.801126\pi$
$557$	− 6.27193e13i	− 1.16984i	0.811092	−	0.584919i	$-0.198874\pi$
$558$	0	0
$559$	2.15584e13	0.394965
$560$	2.94291e13i	0.534364i
$561$	0	0
$562$	7.49510e13	1.33689
$563$	4.02793e13i	0.712098i	0.934467	+	0.356049i	$0.115876\pi$
$563$	4.02793e13i	0.712098i	−0.934467	+	0.356049i	$0.884124\pi$
$564$	0	0
$565$	2.31111e13	0.401401
$566$	2.57022e13i	0.442474i
$567$	0	0
$568$	−1.52723e13	−0.258322
$569$	3.72669e12i	0.0624831i	0.999512	+	0.0312415i	$0.00994611\pi$
$569$	3.72669e12i	0.0624831i	−0.999512	+	0.0312415i	$0.990054\pi$
$570$	0	0
$571$	−2.93198e13	−0.483038	−0.241519	−	0.970396i	$-0.577646\pi$
$571$	−2.93198e13	−0.483038	−0.241519	+	0.970396i	$0.577646\pi$
$572$	− 4.82725e13i	− 0.788351i
$573$	0	0
$574$	−4.63298e13	−0.743534
$575$	− 5.43809e13i	− 0.865181i
$576$	0	0
$577$	1.03696e14	1.62138	0.810690	−	0.585475i	$-0.199092\pi$
$577$	1.03696e14	1.62138	0.810690	+	0.585475i	$0.199092\pi$
$578$	8.54445e13i	1.32448i
$579$	0	0
$580$	3.86517e13	0.588883
$581$	1.82356e13i	0.275448i
$582$	0	0
$583$	2.64564e13	0.392814
$584$	3.41975e12i	0.0503419i
$585$	0	0
$586$	8.99122e13	1.30116
$587$	5.87462e13i	0.842926i	0.906846	+	0.421463i	$0.138483\pi$
$587$	5.87462e13i	0.842926i	−0.906846	+	0.421463i	$0.861517\pi$
$588$	0	0
$589$	−6.63242e13	−0.935611
$590$	− 1.34189e13i	− 0.187697i
$591$	0	0
$592$	1.49217e14	2.05215
$593$	3.49890e12i	0.0477154i	0.999715	+	0.0238577i	$0.00759486\pi$
$593$	3.49890e12i	0.0477154i	−0.999715	+	0.0238577i	$0.992405\pi$
$594$	0	0
$595$	−4.30880e12	−0.0577792
$596$	− 3.44822e13i	− 0.458525i
$597$	0	0
$598$	−2.71212e14	−3.54653
$599$	− 3.31454e13i	− 0.429822i	−0.976634	−	0.214911i	$-0.931054\pi$
$599$	− 3.31454e13i	− 0.429822i	0.976634	−	0.214911i	$-0.0689462\pi$
$600$	0	0
$601$	−6.64972e13	−0.848069	−0.424034	−	0.905646i	$-0.639386\pi$
$601$	−6.64972e13	−0.848069	−0.424034	+	0.905646i	$0.639386\pi$
$602$	1.76549e13i	0.223297i
$603$	0	0
$604$	6.41019e13	0.797419
$605$	3.51764e13i	0.433985i
$606$	0	0
$607$	1.19026e14	1.44443	0.722215	−	0.691668i	$-0.243124\pi$
$607$	1.19026e14	1.44443	0.722215	+	0.691668i	$0.243124\pi$
$608$	− 1.23760e14i	− 1.48957i
$609$	0	0
$610$	6.90408e13	0.817442
$611$	− 2.38193e14i	− 2.79719i
$612$	0	0
$613$	−3.57543e13	−0.413073	−0.206536	−	0.978439i	$-0.566219\pi$
$613$	−3.57543e13	−0.413073	−0.206536	+	0.978439i	$0.566219\pi$
$614$	− 1.85307e14i	− 2.12349i
$615$	0	0
$616$	−9.26377e12	−0.104444
$617$	− 2.49498e13i	− 0.279024i	−0.990220	−	0.139512i	$-0.955447\pi$
$617$	− 2.49498e13i	− 0.279024i	0.990220	−	0.139512i	$-0.0445533\pi$
$618$	0	0
$619$	−6.28356e13	−0.691436	−0.345718	−	0.938338i	$-0.612365\pi$
$619$	−6.28356e13	−0.691436	−0.345718	+	0.938338i	$0.612365\pi$
$620$	4.16823e13i	0.454981i
$621$	0	0
$622$	−1.61817e14	−1.73809
$623$	− 7.33345e13i	− 0.781390i
$624$	0	0
$625$	−1.90703e13	−0.199966
$626$	2.46292e14i	2.56200i
$627$	0	0
$628$	−4.86507e13	−0.498071
$629$	2.18472e13i	0.221893i
$630$	0	0
$631$	−9.30499e13	−0.930184	−0.465092	−	0.885262i	$-0.653979\pi$
$631$	−9.30499e13	−0.930184	−0.465092	+	0.885262i	$0.653979\pi$
$632$	3.75513e13i	0.372426i
$633$	0	0
$634$	−1.73377e14	−1.69257
$635$	− 9.86780e13i	− 0.955767i
$636$	0	0
$637$	9.20032e13	0.877214
$638$	9.12722e13i	0.863446i
$639$	0	0
$640$	3.71343e13	0.345840
$641$	− 1.58468e14i	− 1.46437i	−0.681104	−	0.732187i	$-0.738500\pi$
$641$	− 1.58468e14i	− 1.46437i	0.681104	−	0.732187i	$-0.261500\pi$
$642$	0	0
$643$	1.09613e14	0.997254	0.498627	−	0.866817i	$-0.333838\pi$
$643$	1.09613e14	0.997254	0.498627	+	0.866817i	$0.333838\pi$
$644$	− 9.94049e13i	− 0.897384i
$645$	0	0
$646$	2.16887e13	0.192784
$647$	1.57049e14i	1.38520i	0.721321	+	0.692601i	$0.243535\pi$
$647$	1.57049e14i	1.38520i	−0.721321	+	0.692601i	$0.756465\pi$
$648$	0	0
$649$	1.41820e13	0.123173
$650$	− 1.30950e14i	− 1.12859i
$651$	0	0
$652$	−5.64780e13	−0.479338
$653$	1.61532e14i	1.36048i	0.732989	+	0.680241i	$0.238125\pi$
$653$	1.61532e14i	1.36048i	−0.732989	+	0.680241i	$0.761875\pi$
$654$	0	0
$655$	−2.61242e13	−0.216689
$656$	1.15311e14i	0.949184i
$657$	0	0
$658$	1.95064e14	1.58142
$659$	− 2.82471e13i	− 0.227272i	−0.993522	−	0.113636i	$-0.963750\pi$
$659$	− 2.82471e13i	− 0.227272i	0.993522	−	0.113636i	$-0.0362498\pi$
$660$	0	0
$661$	5.58475e13	0.442584	0.221292	−	0.975208i	$-0.428973\pi$
$661$	5.58475e13	0.442584	0.221292	+	0.975208i	$0.428973\pi$
$662$	1.48977e14i	1.17173i
$663$	0	0
$664$	1.35182e13	0.104732
$665$	− 6.91766e13i	− 0.531926i
$666$	0	0
$667$	2.29509e14	1.73848
$668$	1.26975e14i	0.954631i
$669$	0	0
$670$	1.85999e14	1.37764
$671$	7.29671e13i	0.536432i
$672$	0	0
$673$	−1.01749e14	−0.736979	−0.368489	−	0.929632i	$-0.620125\pi$
$673$	−1.01749e14	−0.736979	−0.368489	+	0.929632i	$0.620125\pi$
$674$	− 9.90303e13i	− 0.711981i
$675$	0	0
$676$	−1.77926e14	−1.26039
$677$	2.22340e12i	0.0156341i	0.999969	+	0.00781706i	$0.00248827\pi$
$677$	2.22340e12i	0.0156341i	−0.999969	+	0.00781706i	$0.997512\pi$
$678$	0	0
$679$	5.27568e13	0.365535
$680$	3.19415e12i	0.0219690i
$681$	0	0
$682$	−9.84287e13	−0.667114
$683$	2.84285e13i	0.191272i	0.995416	+	0.0956358i	$0.0304884\pi$
$683$	2.84285e13i	0.191272i	−0.995416	+	0.0956358i	$0.969512\pi$
$684$	0	0
$685$	1.96193e14	1.30086
$686$	2.12655e14i	1.39976i
$687$	0	0
$688$	4.39414e13	0.285057
$689$	− 1.60195e14i	− 1.03170i
$690$	0	0
$691$	1.29297e14	0.820728	0.410364	−	0.911922i	$-0.365402\pi$
$691$	1.29297e14	0.820728	0.410364	+	0.911922i	$0.365402\pi$
$692$	1.06696e14i	0.672385i
$693$	0	0
$694$	−2.81684e14	−1.74970
$695$	− 6.96435e13i	− 0.429494i
$696$	0	0
$697$	−1.68830e13	−0.102633
$698$	3.67619e14i	2.21882i
$699$	0	0
$700$	4.79957e13	0.285570
$701$	7.07411e13i	0.417909i	0.977925	+	0.208954i	$0.0670060\pi$
$701$	7.07411e13i	0.417909i	−0.977925	+	0.208954i	$0.932994\pi$
$702$	0	0
$703$	−3.50751e14	−2.04278
$704$	− 6.22186e13i	− 0.359797i
$705$	0	0
$706$	1.99138e14	1.13535
$707$	− 2.07477e14i	− 1.17456i
$708$	0	0
$709$	−1.59319e14	−0.889274	−0.444637	−	0.895711i	$-0.646667\pi$
$709$	−1.59319e14	−0.889274	−0.444637	+	0.895711i	$0.646667\pi$
$710$	− 1.69248e14i	− 0.938065i
$711$	0	0
$712$	−5.43634e13	−0.297103
$713$	2.47504e14i	1.34318i
$714$	0	0
$715$	−1.25361e14	−0.670860
$716$	− 7.51105e13i	− 0.399150i
$717$	0	0
$718$	−8.55029e13	−0.448083
$719$	− 1.21166e14i	− 0.630573i	−0.948997	−	0.315287i	$-0.897899\pi$
$719$	− 1.21166e14i	− 0.630573i	0.948997	−	0.315287i	$-0.102101\pi$
$720$	0	0
$721$	2.87169e12	0.0147388
$722$	8.42433e13i	0.429387i
$723$	0	0
$724$	1.31938e14	0.663250
$725$	1.10814e14i	0.553228i
$726$	0	0
$727$	1.52440e14	0.750631	0.375315	−	0.926897i	$-0.377534\pi$
$727$	1.52440e14	0.750631	0.375315	+	0.926897i	$0.377534\pi$
$728$	5.60927e13i	0.274315i
$729$	0	0
$730$	−3.78979e13	−0.182810
$731$	6.43359e12i	0.0308224i
$732$	0	0
$733$	7.24402e13	0.342342	0.171171	−	0.985241i	$-0.445245\pi$
$733$	7.24402e13	0.342342	0.171171	+	0.985241i	$0.445245\pi$
$734$	− 3.17570e14i	− 1.49059i
$735$	0	0
$736$	−4.61839e14	−2.13846
$737$	1.96577e14i	0.904054i
$738$	0	0
$739$	−1.39615e14	−0.633444	−0.316722	−	0.948518i	$-0.602582\pi$
$739$	−1.39615e14	−0.633444	−0.316722	+	0.948518i	$0.602582\pi$
$740$	2.20434e14i	0.993392i
$741$	0	0
$742$	1.31189e14	0.583280
$743$	− 3.36896e14i	− 1.48782i	−0.668278	−	0.743912i	$-0.732968\pi$
$743$	− 3.36896e14i	− 1.48782i	0.668278	−	0.743912i	$-0.267032\pi$
$744$	0	0
$745$	−8.95483e13	−0.390190
$746$	− 4.31630e14i	− 1.86817i
$747$	0	0
$748$	1.44057e13	0.0615216
$749$	− 5.39026e13i	− 0.228666i
$750$	0	0
$751$	1.82354e14	0.763336	0.381668	−	0.924299i	$-0.375350\pi$
$751$	1.82354e14	0.763336	0.381668	+	0.924299i	$0.375350\pi$
$752$	− 4.85496e14i	− 2.01881i
$753$	0	0
$754$	5.52659e14	2.26778
$755$	− 1.66469e14i	− 0.678577i
$756$	0	0
$757$	−2.19825e14	−0.884296	−0.442148	−	0.896942i	$-0.645783\pi$
$757$	−2.19825e14	−0.884296	−0.442148	+	0.896942i	$0.645783\pi$
$758$	− 2.17150e14i	− 0.867788i
$759$	0	0
$760$	−5.12812e13	−0.202251
$761$	4.62821e14i	1.81338i	0.421793	+	0.906692i	$0.361401\pi$
$761$	4.62821e14i	1.81338i	−0.421793	+	0.906692i	$0.638599\pi$
$762$	0	0
$763$	−7.67372e13	−0.296745
$764$	− 1.80160e14i	− 0.692136i
$765$	0	0
$766$	2.05374e14	0.778755
$767$	− 8.58730e13i	− 0.323504i
$768$	0	0
$769$	−2.73931e13	−0.101861	−0.0509306	−	0.998702i	$-0.516219\pi$
$769$	−2.73931e13	−0.101861	−0.0509306	+	0.998702i	$0.516219\pi$
$770$	− 1.02662e14i	− 0.379276i
$771$	0	0
$772$	1.51224e14	0.551486
$773$	4.25630e14i	1.54218i	0.636728	+	0.771089i	$0.280288\pi$
$773$	4.25630e14i	1.54218i	−0.636728	+	0.771089i	$0.719712\pi$
$774$	0	0
$775$	−1.19503e14	−0.427434
$776$	− 3.91090e13i	− 0.138985i
$777$	0	0
$778$	7.62746e14	2.67598
$779$	− 2.71051e14i	− 0.944853i
$780$	0	0
$781$	1.78873e14	0.615589
$782$	− 8.09366e13i	− 0.276765i
$783$	0	0
$784$	1.87525e14	0.633110
$785$	1.26343e14i	0.423841i
$786$	0	0
$787$	−3.88256e14	−1.28601	−0.643005	−	0.765862i	$-0.722313\pi$
$787$	−3.88256e14	−1.28601	−0.643005	+	0.765862i	$0.722313\pi$
$788$	3.27205e14i	1.07693i
$789$	0	0
$790$	−4.16147e14	−1.35242
$791$	1.21118e14i	0.391134i
$792$	0	0
$793$	4.41820e14	1.40890
$794$	− 9.25241e13i	− 0.293192i
$795$	0	0
$796$	−3.18492e14	−0.996628
$797$	1.74729e14i	0.543341i	0.962390	+	0.271670i	$0.0875760\pi$
$797$	1.74729e14i	0.543341i	−0.962390	+	0.271670i	$0.912424\pi$
$798$	0	0
$799$	7.10828e13	0.218288
$800$	− 2.22990e14i	− 0.680512i
$801$	0	0
$802$	2.46491e14	0.742897
$803$	− 4.00531e13i	− 0.119966i
$804$	0	0
$805$	−2.58149e14	−0.763644
$806$	5.95992e14i	1.75213i
$807$	0	0
$808$	−1.53805e14	−0.446594
$809$	2.67003e14i	0.770502i	0.922812	+	0.385251i	$0.125885\pi$
$809$	2.67003e14i	0.770502i	−0.922812	+	0.385251i	$0.874115\pi$
$810$	0	0
$811$	−1.82073e14	−0.518969	−0.259484	−	0.965747i	$-0.583553\pi$
$811$	−1.82073e14	−0.518969	−0.259484	+	0.965747i	$0.583553\pi$
$812$	2.02561e14i	0.573820i
$813$	0	0
$814$	−5.20534e14	−1.45656
$815$	1.46670e14i	0.407900i
$816$	0	0
$817$	−1.03289e14	−0.283756
$818$	− 9.07798e13i	− 0.247869i
$819$	0	0
$820$	−1.70346e14	−0.459476
$821$	− 3.97038e14i	− 1.06443i	−0.846610	−	0.532214i	$-0.821360\pi$
$821$	− 3.97038e14i	− 1.06443i	0.846610	−	0.532214i	$-0.178640\pi$
$822$	0	0
$823$	−4.04459e14	−1.07121	−0.535606	−	0.844468i	$-0.679917\pi$
$823$	−4.04459e14	−1.07121	−0.535606	+	0.844468i	$0.679917\pi$
$824$	− 2.12881e12i	− 0.00560404i
$825$	0	0
$826$	7.03240e13	0.182896
$827$	1.68903e14i	0.436626i	0.975879	+	0.218313i	$0.0700554\pi$
$827$	1.68903e14i	0.436626i	−0.975879	+	0.218313i	$0.929945\pi$
$828$	0	0
$829$	1.84530e14	0.471298	0.235649	−	0.971838i	$-0.424278\pi$
$829$	1.84530e14	0.471298	0.235649	+	0.971838i	$0.424278\pi$
$830$	1.49810e14i	0.380320i
$831$	0	0
$832$	−3.76738e14	−0.944980
$833$	2.74561e13i	0.0684563i
$834$	0	0
$835$	3.29746e14	0.812359
$836$	2.31280e14i	0.566379i
$837$	0	0
$838$	8.03734e13	0.194488
$839$	− 2.91186e14i	− 0.700424i	−0.936671	−	0.350212i	$-0.886110\pi$
$839$	− 2.91186e14i	− 0.700424i	0.936671	−	0.350212i	$-0.113890\pi$
$840$	0	0
$841$	−4.69716e13	−0.111649
$842$	− 4.67096e14i	− 1.10369i
$843$	0	0
$844$	−5.99051e13	−0.139879
$845$	4.62064e14i	1.07255i
$846$	0	0
$847$	−1.84348e14	−0.422884
$848$	− 3.26517e14i	− 0.744606i
$849$	0	0
$850$	3.90787e13	0.0880735
$851$	1.30891e15i	2.93266i
$852$	0	0
$853$	2.03703e14	0.451079	0.225539	−	0.974234i	$-0.427586\pi$
$853$	2.03703e14	0.451079	0.225539	+	0.974234i	$0.427586\pi$
$854$	3.61820e14i	0.796533i
$855$	0	0
$856$	−3.99585e13	−0.0869440
$857$	1.13565e14i	0.245664i	0.992427	+	0.122832i	$0.0391977\pi$
$857$	1.13565e14i	0.245664i	−0.992427	+	0.122832i	$0.960802\pi$
$858$	0	0
$859$	8.87817e14	1.89827	0.949134	−	0.314873i	$-0.101962\pi$
$859$	8.87817e14	1.89827	0.949134	+	0.314873i	$0.101962\pi$
$860$	6.49137e13i	0.137989i
$861$	0	0
$862$	−5.66677e14	−1.19069
$863$	5.12941e12i	0.0107155i	0.999986	+	0.00535776i	$0.00170544\pi$
$863$	5.12941e12i	0.0107155i	−0.999986	+	0.00535776i	$0.998295\pi$
$864$	0	0
$865$	2.77084e14	0.572177
$866$	− 4.64364e13i	− 0.0953387i
$867$	0	0
$868$	−2.18444e14	−0.443344
$869$	− 4.39813e14i	− 0.887502i
$870$	0	0
$871$	1.19028e15	2.37443
$872$	5.68859e13i	0.112829i
$873$	0	0
$874$	1.29941e15	2.54795
$875$	− 3.62187e14i	− 0.706142i
$876$	0	0
$877$	−6.31788e14	−1.21779	−0.608896	−	0.793250i	$-0.708388\pi$
$877$	−6.31788e14	−1.21779	−0.608896	+	0.793250i	$0.708388\pi$
$878$	− 9.22643e13i	− 0.176832i
$879$	0	0
$880$	−2.55516e14	−0.484178
$881$	− 6.55067e14i	− 1.23426i	−0.786861	−	0.617130i	$-0.788295\pi$
$881$	− 6.55067e14i	− 1.23426i	0.786861	−	0.617130i	$-0.211705\pi$
$882$	0	0
$883$	−1.61675e14	−0.301189	−0.150595	−	0.988596i	$-0.548119\pi$
$883$	−1.61675e14	−0.301189	−0.150595	+	0.988596i	$0.548119\pi$
$884$	− 8.72276e13i	− 0.161582i
$885$	0	0
$886$	−1.80757e14	−0.331076
$887$	− 1.06554e15i	− 1.94067i	−0.241763	−	0.970335i	$-0.577726\pi$
$887$	− 1.06554e15i	− 1.94067i	0.241763	−	0.970335i	$-0.422274\pi$
$888$	0	0
$889$	5.17140e14	0.931320
$890$	− 6.02460e14i	− 1.07889i
$891$	0	0
$892$	−6.59876e14	−1.16852
$893$	1.14121e15i	2.00960i
$894$	0	0
$895$	−1.95058e14	−0.339663
$896$	1.94609e14i	0.336994i
$897$	0	0
$898$	6.25847e13	0.107173
$899$	− 5.04349e14i	− 0.858880i
$900$	0	0
$901$	4.78063e13	0.0805121
$902$	− 4.02255e14i	− 0.673704i
$903$	0	0
$904$	8.97855e13	0.148718
$905$	− 3.42636e14i	− 0.564403i
$906$	0	0
$907$	2.19079e14	0.356914	0.178457	−	0.983948i	$-0.442889\pi$
$907$	2.19079e14	0.356914	0.178457	+	0.983948i	$0.442889\pi$
$908$	3.15558e14i	0.511269i
$909$	0	0
$910$	−6.21624e14	−0.996142
$911$	− 1.88131e14i	− 0.299826i	−0.988699	−	0.149913i	$-0.952101\pi$
$911$	− 1.88131e14i	− 0.299826i	0.988699	−	0.149913i	$-0.0478993\pi$
$912$	0	0
$913$	−1.58329e14	−0.249579
$914$	− 1.55493e14i	− 0.243770i
$915$	0	0
$916$	1.43841e14	0.223052
$917$	− 1.36909e14i	− 0.211147i
$918$	0	0
$919$	1.65244e14	0.252086	0.126043	−	0.992025i	$-0.459772\pi$
$919$	1.65244e14	0.252086	0.126043	+	0.992025i	$0.459772\pi$
$920$	1.91368e14i	0.290355i
$921$	0	0
$922$	2.30856e13	0.0346487
$923$	− 1.08309e15i	− 1.61680i
$924$	0	0
$925$	−6.31982e14	−0.933246
$926$	− 7.85193e14i	− 1.15324i
$927$	0	0
$928$	9.41107e14	1.36741
$929$	6.09125e14i	0.880295i	0.897926	+	0.440147i	$0.145074\pi$
$929$	6.09125e14i	0.880295i	−0.897926	+	0.440147i	$0.854926\pi$
$930$	0	0
$931$	−4.40800e14	−0.630221
$932$	− 5.02786e14i	− 0.714996i
$933$	0	0
$934$	−1.20851e15	−1.70027
$935$	− 3.74109e13i	− 0.0523528i
$936$	0	0
$937$	−5.40811e14	−0.748769	−0.374384	−	0.927274i	$-0.622146\pi$
$937$	−5.40811e14	−0.748769	−0.374384	+	0.927274i	$0.622146\pi$
$938$	9.74760e14i	1.34241i
$939$	0	0
$940$	7.17212e14	0.977256
$941$	3.77351e14i	0.511443i	0.966751	+	0.255721i	$0.0823130\pi$
$941$	3.77351e14i	0.511443i	−0.966751	+	0.255721i	$0.917687\pi$
$942$	0	0
$943$	−1.01149e15	−1.35645
$944$	− 1.75030e14i	− 0.233482i
$945$	0	0
$946$	−1.53287e14	−0.202325
$947$	7.08608e14i	0.930371i	0.885213	+	0.465186i	$0.154012\pi$
$947$	7.08608e14i	0.930371i	−0.885213	+	0.465186i	$0.845988\pi$
$948$	0	0
$949$	−2.42524e14	−0.315082
$950$	6.27398e14i	0.810821i
$951$	0	0
$952$	−1.67395e13	−0.0214071
$953$	− 1.08323e15i	− 1.37802i	−0.724751	−	0.689011i	$-0.758045\pi$
$953$	− 1.08323e15i	− 1.37802i	0.724751	−	0.689011i	$-0.241955\pi$
$954$	0	0
$955$	−4.67865e14	−0.588985
$956$	− 5.70730e14i	− 0.714729i
$957$	0	0
$958$	1.00660e15	1.24747
$959$	1.02818e15i	1.26759i
$960$	0	0
$961$	−2.75734e14	−0.336414
$962$	3.15187e15i	3.82554i
$963$	0	0
$964$	4.88754e13	0.0587091
$965$	− 3.92720e14i	− 0.469296i
$966$	0	0
$967$	2.41074e14	0.285114	0.142557	−	0.989787i	$-0.454468\pi$
$967$	2.41074e14	0.285114	0.142557	+	0.989787i	$0.454468\pi$
$968$	1.36659e14i	0.160791i
$969$	0	0
$970$	4.33410e14	0.504708
$971$	− 1.00356e15i	− 1.16264i	−0.813675	−	0.581321i	$-0.802536\pi$
$971$	− 1.00356e15i	− 1.16264i	0.813675	−	0.581321i	$-0.197464\pi$
$972$	0	0
$973$	3.64979e14	0.418508
$974$	6.08659e14i	0.694351i
$975$	0	0
$976$	9.00539e14	1.01684
$977$	− 1.20290e15i	− 1.35131i	−0.737217	−	0.675656i	$-0.763860\pi$
$977$	− 1.20290e15i	− 1.35131i	0.737217	−	0.675656i	$-0.236140\pi$
$978$	0	0
$979$	6.36721e14	0.708004
$980$	2.77027e14i	0.306472i
$981$	0	0
$982$	−1.60416e15	−1.75667
$983$	− 9.23620e14i	− 1.00630i	−0.864200	−	0.503148i	$-0.832175\pi$
$983$	− 9.23620e14i	− 1.00630i	0.864200	−	0.503148i	$-0.167825\pi$
$984$	0	0
$985$	8.49733e14	0.916434
$986$	1.64928e14i	0.176974i
$987$	0	0
$988$	1.40042e15	1.48755
$989$	3.85449e14i	0.407367i
$990$	0	0
$991$	−2.75617e13	−0.0288362	−0.0144181	−	0.999896i	$-0.504590\pi$
$991$	−2.75617e13	−0.0288362	−0.0144181	+	0.999896i	$0.504590\pi$
$992$	1.01490e15i	1.05649i
$993$	0	0
$994$	8.86976e14	0.914071
$995$	8.27106e14i	0.848097i
$996$	0	0
$997$	3.94947e14	0.400925	0.200463	−	0.979701i	$-0.435755\pi$
$997$	3.94947e14	0.400925	0.200463	+	0.979701i	$0.435755\pi$
$998$	8.63593e14i	0.872281i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.b.d.26.5	yes	6
3.2	odd	2	inner	27.11.b.d.26.2	✓	6
9.2	odd	6		81.11.d.g.53.2		12
9.4	even	3		81.11.d.g.26.2		12
9.5	odd	6		81.11.d.g.26.5		12
9.7	even	3		81.11.d.g.53.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.b.d.26.2	✓	6	3.2	odd	2	inner
27.11.b.d.26.5	yes	6	1.1	even	1	trivial
81.11.d.g.26.2		12	9.4	even	3
81.11.d.g.26.5		12	9.5	odd	6
81.11.d.g.53.2		12	9.2	odd	6
81.11.d.g.53.5		12	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+43.0534i q^{2} -829.595 q^{4} +2154.41i q^{5} -11290.6 q^{7} +8369.79i q^{8} +O(q^{10})\)	\(q+43.0534i q^{2} -829.595 q^{4} +2154.41i q^{5} -11290.6 q^{7} +8369.79i q^{8} -92754.7 q^{10} -98029.6i q^{11} -593576. q^{13} -486097. i q^{14} -1.20985e6 q^{16} -177138. i q^{17} +2.84390e6 q^{19} -1.78729e6i q^{20} +4.22051e6 q^{22} -1.06127e7i q^{23} +5.12414e6 q^{25} -2.55554e7i q^{26} +9.36660e6 q^{28} +2.16259e7i q^{29} -2.33215e7 q^{31} -4.35176e7i q^{32} +7.62640e6 q^{34} -2.43245e7i q^{35} -1.23334e8 q^{37} +1.22440e8i q^{38} -1.80320e7 q^{40} -9.53097e7i q^{41} -3.63196e7 q^{43} +8.13249e7i q^{44} +4.56912e8 q^{46} +4.01285e8i q^{47} -1.54998e8 q^{49} +2.20611e8i q^{50} +4.92427e8 q^{52} +2.69881e8i q^{53} +2.11196e8 q^{55} -9.44997e7i q^{56} -9.31068e8 q^{58} +1.44671e8i q^{59} -7.44337e8 q^{61} -1.00407e9i q^{62} +6.34692e8 q^{64} -1.27881e9i q^{65} -2.00528e9 q^{67} +1.46953e8i q^{68} +1.04725e9 q^{70} +1.82469e9i q^{71} +4.08582e8 q^{73} -5.30997e9i q^{74} -2.35929e9 q^{76} +1.10681e9i q^{77} +4.48653e9 q^{79} -2.60652e9i q^{80} +4.10341e9 q^{82} -1.61512e9i q^{83} +3.81628e8 q^{85} -1.56368e9i q^{86} +8.20487e8 q^{88} +6.49519e9i q^{89} +6.70181e9 q^{91} +8.80424e9i q^{92} -1.72767e10 q^{94} +6.12694e9i q^{95} -4.67264e9 q^{97} -6.67320e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2658 q^{4} + 4638 q^{7}+O(q^{10}) \) 6 * q - 2658 * q^4 + 4638 * q^7	\( 6 q - 2658 q^{4} + 4638 q^{7} + 233658 q^{10} + 131844 q^{13} - 1575102 q^{16} + 7706784 q^{19} - 11594718 q^{22} - 10669728 q^{25} - 6580266 q^{28} + 11591994 q^{31} + 119452644 q^{34} + 7171320 q^{37} - 330020298 q^{40} + 203012076 q^{43} + 583979112 q^{46} - 1195686288 q^{49} - 84347628 q^{52} + 2719163250 q^{55} - 5503711428 q^{58} + 2326158264 q^{61} + 6019783710 q^{64} - 6569458044 q^{67} + 6917324130 q^{70} + 2618820678 q^{73} - 21072468192 q^{76} + 5638333908 q^{79} + 19302295032 q^{82} - 26239380732 q^{85} + 12553208334 q^{88} + 24736096788 q^{91} - 35311712076 q^{94} - 4672763646 q^{97}+O(q^{100}) \) 6 * q - 2658 * q^4 + 4638 * q^7 + 233658 * q^10 + 131844 * q^13 - 1575102 * q^16 + 7706784 * q^19 - 11594718 * q^22 - 10669728 * q^25 - 6580266 * q^28 + 11591994 * q^31 + 119452644 * q^34 + 7171320 * q^37 - 330020298 * q^40 + 203012076 * q^43 + 583979112 * q^46 - 1195686288 * q^49 - 84347628 * q^52 + 2719163250 * q^55 - 5503711428 * q^58 + 2326158264 * q^61 + 6019783710 * q^64 - 6569458044 * q^67 + 6917324130 * q^70 + 2618820678 * q^73 - 21072468192 * q^76 + 5638333908 * q^79 + 19302295032 * q^82 - 26239380732 * q^85 + 12553208334 * q^88 + 24736096788 * q^91 - 35311712076 * q^94 - 4672763646 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more