LMFDB - Embedded newform 27.11.b.d.26.3

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			26.3
Root			$6.88342 + 6.88342i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.11.b.d.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.26247i q^{2} +955.732 q^{4} -2842.36i q^{5} +2964.51 q^{7} -16357.5i q^{8} +O(q^{10})$	\(q-8.26247i q^{2} +955.732 q^{4} -2842.36i q^{5} +2964.51 q^{7} -16357.5i q^{8} -23484.9 q^{10} +57081.6i q^{11} +176309. q^{13} -24494.2i q^{14} +843516. q^{16} -2.37717e6i q^{17} -2.78240e6 q^{19} -2.71653e6i q^{20} +471635. q^{22} -6.45845e6i q^{23} +1.68663e6 q^{25} -1.45675e6i q^{26} +2.83328e6 q^{28} -3.39679e7i q^{29} -1.12079e7 q^{31} -2.37196e7i q^{32} -1.96413e7 q^{34} -8.42620e6i q^{35} +9.01790e7 q^{37} +2.29895e7i q^{38} -4.64938e7 q^{40} +1.73964e8i q^{41} +4.56447e7 q^{43} +5.45546e7i q^{44} -5.33627e7 q^{46} +1.90047e8i q^{47} -2.73687e8 q^{49} -1.39357e7i q^{50} +1.68504e8 q^{52} +3.24490e8i q^{53} +1.62246e8 q^{55} -4.84919e7i q^{56} -2.80659e8 q^{58} +4.01935e8i q^{59} +6.57960e8 q^{61} +9.26047e7i q^{62} +6.67778e8 q^{64} -5.01133e8i q^{65} -2.39364e9 q^{67} -2.27194e9i q^{68} -6.96213e7 q^{70} -2.19717e9i q^{71} +3.96217e9 q^{73} -7.45102e8i q^{74} -2.65923e9 q^{76} +1.69219e8i q^{77} +7.14012e8 q^{79} -2.39757e9i q^{80} +1.43737e9 q^{82} +3.95187e9i q^{83} -6.75678e9 q^{85} -3.77138e8i q^{86} +9.33710e8 q^{88} +5.68460e9i q^{89} +5.22670e8 q^{91} -6.17254e9i q^{92} +1.57026e9 q^{94} +7.90858e9i q^{95} +8.34375e9 q^{97} +2.26133e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 8.26247i	− 0.258202i	−0.991631	−	0.129101i	$-0.958791\pi$
$2$	− 8.26247i	− 0.258202i	0.991631	−	0.129101i	$-0.0412092\pi$
$3$	0	0
$3$	0	0
$4$	955.732	0.933332
$5$	− 2842.36i	− 0.909554i	−0.890605	−	0.454777i	$-0.849719\pi$
$5$	− 2842.36i	− 0.909554i	0.890605	−	0.454777i	$-0.150281\pi$
$6$	0	0
$7$	2964.51	0.176386	0.0881928	−	0.996103i	$-0.471891\pi$
$7$	2964.51	0.176386	0.0881928	+	0.996103i	$0.471891\pi$
$8$	− 16357.5i	− 0.499191i
$9$	0	0
$10$	−23484.9	−0.234849
$11$	57081.6i	0.354432i	0.984172	+	0.177216i	$0.0567091\pi$
$11$	57081.6i	0.354432i	−0.984172	+	0.177216i	$0.943291\pi$
$12$	0	0
$13$	176309.	0.474851	0.237426	−	0.971406i	$-0.423696\pi$
$13$	176309.	0.474851	0.237426	+	0.971406i	$0.423696\pi$
$14$	− 24494.2i	− 0.0455431i
$15$	0	0
$16$	843516.	0.804440
$17$	− 2.37717e6i	− 1.67423i	−0.547023	−	0.837117i	$-0.684239\pi$
$17$	− 2.37717e6i	− 1.67423i	0.547023	−	0.837117i	$-0.315761\pi$
$18$	0	0
$19$	−2.78240e6	−1.12370	−0.561852	−	0.827238i	$-0.689911\pi$
$19$	−2.78240e6	−1.12370	−0.561852	+	0.827238i	$0.689911\pi$
$20$	− 2.71653e6i	− 0.848916i
$21$	0	0
$22$	471635.	0.0915150
$23$	− 6.45845e6i	− 1.00343i	−0.865032	−	0.501717i	$-0.832702\pi$
$23$	− 6.45845e6i	− 1.00343i	0.865032	−	0.501717i	$-0.167298\pi$
$24$	0	0
$25$	1.68663e6	0.172711
$26$	− 1.45675e6i	− 0.122608i
$27$	0	0
$28$	2.83328e6	0.164626
$29$	− 3.39679e7i	− 1.65607i	−0.560677	−	0.828034i	$-0.689459\pi$
$29$	− 3.39679e7i	− 1.65607i	0.560677	−	0.828034i	$-0.310541\pi$
$30$	0	0
$31$	−1.12079e7	−0.391485	−0.195742	−	0.980655i	$-0.562712\pi$
$31$	−1.12079e7	−0.391485	−0.195742	+	0.980655i	$0.562712\pi$
$32$	− 2.37196e7i	− 0.706899i
$33$	0	0
$34$	−1.96413e7	−0.432291
$35$	− 8.42620e6i	− 0.160432i
$36$	0	0
$37$	9.01790e7	1.30046	0.650230	−	0.759738i	$-0.274673\pi$
$37$	9.01790e7	1.30046	0.650230	+	0.759738i	$0.274673\pi$
$38$	2.29895e7i	0.290143i
$39$	0	0
$40$	−4.64938e7	−0.454041
$41$	1.73964e8i	1.50155i	0.660560	+	0.750773i	$0.270319\pi$
$41$	1.73964e8i	1.50155i	−0.660560	+	0.750773i	$0.729681\pi$
$42$	0	0
$43$	4.56447e7	0.310490	0.155245	−	0.987876i	$-0.450383\pi$
$43$	4.56447e7	0.310490	0.155245	+	0.987876i	$0.450383\pi$
$44$	5.45546e7i	0.330802i
$45$	0	0
$46$	−5.33627e7	−0.259089
$47$	1.90047e8i	0.828653i	0.910128	+	0.414327i	$0.135983\pi$
$47$	1.90047e8i	0.828653i	−0.910128	+	0.414327i	$0.864017\pi$
$48$	0	0
$49$	−2.73687e8	−0.968888
$50$	− 1.39357e7i	− 0.0445943i
$51$	0	0
$52$	1.68504e8	0.443194
$53$	3.24490e8i	0.775929i	0.921674	+	0.387964i	$0.126822\pi$
$53$	3.24490e8i	0.775929i	−0.921674	+	0.387964i	$0.873178\pi$
$54$	0	0
$55$	1.62246e8	0.322375
$56$	− 4.84919e7i	− 0.0880500i
$57$	0	0
$58$	−2.80659e8	−0.427601
$59$	4.01935e8i	0.562206i	0.959678	+	0.281103i	$0.0907002\pi$
$59$	4.01935e8i	0.562206i	−0.959678	+	0.281103i	$0.909300\pi$
$60$	0	0
$61$	6.57960e8	0.779023	0.389512	−	0.921022i	$-0.372644\pi$
$61$	6.57960e8	0.779023	0.389512	+	0.921022i	$0.372644\pi$
$62$	9.26047e7i	0.101082i
$63$	0	0
$64$	6.67778e8	0.621917
$65$	− 5.01133e8i	− 0.431903i
$66$	0	0
$67$	−2.39364e9	−1.77291	−0.886453	−	0.462819i	$-0.846838\pi$
$67$	−2.39364e9	−1.77291	−0.886453	+	0.462819i	$0.846838\pi$
$68$	− 2.27194e9i	− 1.56262i
$69$	0	0
$70$	−6.96213e7	−0.0414240
$71$	− 2.19717e9i	− 1.21779i	−0.793252	−	0.608893i	$-0.791614\pi$
$71$	− 2.19717e9i	− 1.21779i	0.793252	−	0.608893i	$-0.208386\pi$
$72$	0	0
$73$	3.96217e9	1.91126	0.955628	−	0.294576i	$-0.0951783\pi$
$73$	3.96217e9	1.91126	0.955628	+	0.294576i	$0.0951783\pi$
$74$	− 7.45102e8i	− 0.335782i
$75$	0	0
$76$	−2.65923e9	−1.04879
$77$	1.69219e8i	0.0625166i
$78$	0	0
$79$	7.14012e8	0.232044	0.116022	−	0.993247i	$-0.462986\pi$
$79$	7.14012e8	0.232044	0.116022	+	0.993247i	$0.462986\pi$
$80$	− 2.39757e9i	− 0.731681i
$81$	0	0
$82$	1.43737e9	0.387703
$83$	3.95187e9i	1.00326i	0.865083	+	0.501629i	$0.167266\pi$
$83$	3.95187e9i	1.00326i	−0.865083	+	0.501629i	$0.832734\pi$
$84$	0	0
$85$	−6.75678e9	−1.52281
$86$	− 3.77138e8i	− 0.0801693i
$87$	0	0
$88$	9.33710e8	0.176929
$89$	5.68460e9i	1.01800i	0.860765	+	0.509002i	$0.169986\pi$
$89$	5.68460e9i	1.01800i	−0.860765	+	0.509002i	$0.830014\pi$
$90$	0	0
$91$	5.22670e8	0.0837569
$92$	− 6.17254e9i	− 0.936537i
$93$	0	0
$94$	1.57026e9	0.213960
$95$	7.90858e9i	1.02207i
$96$	0	0
$97$	8.34375e9	0.971634	0.485817	−	0.874061i	$-0.338522\pi$
$97$	8.34375e9	0.971634	0.485817	+	0.874061i	$0.338522\pi$
$98$	2.26133e9i	0.250169i
$99$	0	0
$100$	1.61196e9	0.161196
$101$	9.68545e9i	0.921537i	0.887520	+	0.460769i	$0.152426\pi$
$101$	9.68545e9i	0.921537i	−0.887520	+	0.460769i	$0.847574\pi$
$102$	0	0
$103$	−6.91291e9	−0.596314	−0.298157	−	0.954517i	$-0.596372\pi$
$103$	−6.91291e9	−0.596314	−0.298157	+	0.954517i	$0.596372\pi$
$104$	− 2.88397e9i	− 0.237041i
$105$	0	0
$106$	2.68109e9	0.200346
$107$	2.24789e10i	1.60272i	0.598184	+	0.801359i	$0.295889\pi$
$107$	2.24789e10i	1.60272i	−0.598184	+	0.801359i	$0.704111\pi$
$108$	0	0
$109$	−4.00271e9	−0.260149	−0.130074	−	0.991504i	$-0.541522\pi$
$109$	−4.00271e9	−0.260149	−0.130074	+	0.991504i	$0.541522\pi$
$110$	− 1.34055e9i	− 0.0832379i
$111$	0	0
$112$	2.50061e9	0.141892
$113$	1.04874e10i	0.569214i	0.958644	+	0.284607i	$0.0918632\pi$
$113$	1.04874e10i	0.569214i	−0.958644	+	0.284607i	$0.908137\pi$
$114$	0	0
$115$	−1.83572e10	−0.912678
$116$	− 3.24642e10i	− 1.54566i
$117$	0	0
$118$	3.32097e9	0.145163
$119$	− 7.04716e9i	− 0.295311i
$120$	0	0
$121$	2.26791e10	0.874378
$122$	− 5.43638e9i	− 0.201146i
$123$	0	0
$124$	−1.07117e10	−0.365385
$125$	− 3.25514e10i	− 1.06664i
$126$	0	0
$127$	5.86019e9	0.177375	0.0886877	−	0.996059i	$-0.471733\pi$
$127$	5.86019e9	0.177375	0.0886877	+	0.996059i	$0.471733\pi$
$128$	− 2.98063e10i	− 0.867479i
$129$	0	0
$130$	−4.14060e9	−0.111518
$131$	− 3.84919e10i	− 0.997729i	−0.866680	−	0.498865i	$-0.833750\pi$
$131$	− 3.84919e10i	− 0.997729i	0.866680	−	0.498865i	$-0.166250\pi$
$132$	0	0
$133$	−8.24846e9	−0.198205
$134$	1.97774e10i	0.457768i
$135$	0	0
$136$	−3.88846e10	−0.835762
$137$	2.57760e10i	0.534087i	0.963684	+	0.267044i	$0.0860468\pi$
$137$	2.57760e10i	0.534087i	−0.963684	+	0.267044i	$0.913953\pi$
$138$	0	0
$139$	8.50122e10	1.63835	0.819176	−	0.573542i	$-0.194431\pi$
$139$	8.50122e10	1.63835	0.819176	+	0.573542i	$0.194431\pi$
$140$	− 8.05319e9i	− 0.149736i
$141$	0	0
$142$	−1.81540e10	−0.314435
$143$	1.00640e10i	0.168302i
$144$	0	0
$145$	−9.65488e10	−1.50628
$146$	− 3.27373e10i	− 0.493491i
$147$	0	0
$148$	8.61869e10	1.21376
$149$	8.78047e9i	0.119560i	0.998212	+	0.0597801i	$0.0190399\pi$
$149$	8.78047e9i	0.119560i	−0.998212	+	0.0597801i	$0.980960\pi$
$150$	0	0
$151$	5.96135e10	0.759382	0.379691	−	0.925113i	$-0.376030\pi$
$151$	5.96135e10	0.759382	0.379691	+	0.925113i	$0.376030\pi$
$152$	4.55131e10i	0.560942i
$153$	0	0
$154$	1.39817e9	0.0161419
$155$	3.18568e10i	0.356077i
$156$	0	0
$157$	1.92443e10	0.201746	0.100873	−	0.994899i	$-0.467836\pi$
$157$	1.92443e10	0.201746	0.100873	+	0.994899i	$0.467836\pi$
$158$	− 5.89950e9i	− 0.0599142i
$159$	0	0
$160$	−6.74195e10	−0.642963
$161$	− 1.91461e10i	− 0.176991i
$162$	0	0
$163$	−1.03202e11	−0.896910	−0.448455	−	0.893805i	$-0.648026\pi$
$163$	−1.03202e11	−0.896910	−0.448455	+	0.893805i	$0.648026\pi$
$164$	1.66262e11i	1.40144i
$165$	0	0
$166$	3.26522e10	0.259043
$167$	1.83955e11i	1.41622i	0.706104	+	0.708108i	$0.250451\pi$
$167$	1.83955e11i	1.41622i	−0.706104	+	0.708108i	$0.749549\pi$
$168$	0	0
$169$	−1.06774e11	−0.774516
$170$	5.58277e10i	0.393192i
$171$	0	0
$172$	4.36241e10	0.289790
$173$	1.33623e10i	0.0862284i	0.999070	+	0.0431142i	$0.0137279\pi$
$173$	1.33623e10i	0.0862284i	−0.999070	+	0.0431142i	$0.986272\pi$
$174$	0	0
$175$	5.00003e9	0.0304637
$176$	4.81492e10i	0.285119i
$177$	0	0
$178$	4.69688e10	0.262851
$179$	− 1.32445e11i	− 0.720728i	−0.932812	−	0.360364i	$-0.882653\pi$
$179$	− 1.32445e11i	− 0.720728i	0.932812	−	0.360364i	$-0.117347\pi$
$180$	0	0
$181$	2.25585e11	1.16123	0.580613	−	0.814179i	$-0.302813\pi$
$181$	2.25585e11	1.16123	0.580613	+	0.814179i	$0.302813\pi$
$182$	− 4.31855e9i	− 0.0216262i
$183$	0	0
$184$	−1.05644e11	−0.500905
$185$	− 2.56321e11i	− 1.18284i
$186$	0	0
$187$	1.35693e11	0.593402
$188$	1.81634e11i	0.773408i
$189$	0	0
$190$	6.53444e10	0.263901
$191$	− 4.44175e11i	− 1.74738i	−0.486484	−	0.873689i	$-0.661721\pi$
$191$	− 4.44175e11i	− 1.74738i	0.486484	−	0.873689i	$-0.338279\pi$
$192$	0	0
$193$	−2.43994e11	−0.911156	−0.455578	−	0.890196i	$-0.650567\pi$
$193$	−2.43994e11	−0.911156	−0.455578	+	0.890196i	$0.650567\pi$
$194$	− 6.89400e10i	− 0.250878i
$195$	0	0
$196$	−2.61571e11	−0.904294
$197$	− 2.19368e11i	− 0.739336i	−0.929164	−	0.369668i	$-0.879471\pi$
$197$	− 2.19368e11i	− 0.739336i	0.929164	−	0.369668i	$-0.120529\pi$
$198$	0	0
$199$	−3.43482e9	−0.0110062	−0.00550312	−	0.999985i	$-0.501752\pi$
$199$	−3.43482e9	−0.0110062	−0.00550312	+	0.999985i	$0.501752\pi$
$200$	− 2.75890e10i	− 0.0862156i
$201$	0	0
$202$	8.00258e10	0.237943
$203$	− 1.00698e11i	− 0.292107i
$204$	0	0
$205$	4.94466e11	1.36574
$206$	5.71177e10i	0.153969i
$207$	0	0
$208$	1.48719e11	0.381989
$209$	− 1.58824e11i	− 0.398276i
$210$	0	0
$211$	−7.35797e11	−1.75932	−0.879662	−	0.475600i	$-0.842231\pi$
$211$	−7.35797e11	−1.75932	−0.879662	+	0.475600i	$0.842231\pi$
$212$	3.10125e11i	0.724199i
$213$	0	0
$214$	1.85732e11	0.413825
$215$	− 1.29739e11i	− 0.282408i
$216$	0	0
$217$	−3.32259e10	−0.0690522
$218$	3.30723e10i	0.0671710i
$219$	0	0
$220$	1.55064e11	0.300883
$221$	− 4.19117e11i	− 0.795013i
$222$	0	0
$223$	2.05109e11	0.371930	0.185965	−	0.982556i	$-0.440459\pi$
$223$	2.05109e11	0.371930	0.185965	+	0.982556i	$0.440459\pi$
$224$	− 7.03170e10i	− 0.124687i
$225$	0	0
$226$	8.66519e10	0.146972
$227$	5.33411e11i	0.884978i	0.896774	+	0.442489i	$0.145904\pi$
$227$	5.33411e11i	0.884978i	−0.896774	+	0.442489i	$0.854096\pi$
$228$	0	0
$229$	−7.68602e11	−1.22046	−0.610231	−	0.792224i	$-0.708923\pi$
$229$	−7.68602e11	−1.22046	−0.610231	+	0.792224i	$0.708923\pi$
$230$	1.51676e11i	0.235655i
$231$	0	0
$232$	−5.55629e11	−0.826694
$233$	1.57278e11i	0.229027i	0.993422	+	0.114514i	$0.0365310\pi$
$233$	1.57278e11i	0.229027i	−0.993422	+	0.114514i	$0.963469\pi$
$234$	0	0
$235$	5.40183e11	0.753705
$236$	3.84142e11i	0.524725i
$237$	0	0
$238$	−5.82270e10	−0.0762499
$239$	9.38193e11i	1.20310i	0.798834	+	0.601551i	$0.205450\pi$
$239$	9.38193e11i	1.20310i	−0.798834	+	0.601551i	$0.794550\pi$
$240$	0	0
$241$	6.28084e11	0.772560	0.386280	−	0.922382i	$-0.373760\pi$
$241$	6.28084e11	0.772560	0.386280	+	0.922382i	$0.373760\pi$
$242$	− 1.87386e11i	− 0.225766i
$243$	0	0
$244$	6.28833e11	0.727087
$245$	7.77916e11i	0.881256i
$246$	0	0
$247$	−4.90562e11	−0.533592
$248$	1.83333e11i	0.195425i
$249$	0	0
$250$	−2.68955e11	−0.275410
$251$	1.71502e12i	1.72147i	0.509053	+	0.860735i	$0.329996\pi$
$251$	1.71502e12i	1.72147i	−0.509053	+	0.860735i	$0.670004\pi$
$252$	0	0
$253$	3.68658e11	0.355649
$254$	− 4.84197e10i	− 0.0457987i
$255$	0	0
$256$	4.37531e11	0.397932
$257$	− 1.03998e12i	− 0.927600i	−0.885940	−	0.463800i	$-0.846486\pi$
$257$	− 1.03998e12i	− 0.927600i	0.885940	−	0.463800i	$-0.153514\pi$
$258$	0	0
$259$	2.67337e11	0.229382
$260$	− 4.78949e11i	− 0.403109i
$261$	0	0
$262$	−3.18038e11	−0.257616
$263$	− 6.63798e11i	− 0.527542i	−0.964585	−	0.263771i	$-0.915034\pi$
$263$	− 6.63798e11i	− 0.527542i	0.964585	−	0.263771i	$-0.0849664\pi$
$264$	0	0
$265$	9.22316e11	0.705749
$266$	6.81527e10i	0.0511770i
$267$	0	0
$268$	−2.28768e12	−1.65471
$269$	− 9.81199e11i	− 0.696620i	−0.937379	−	0.348310i	$-0.886756\pi$
$269$	− 9.81199e11i	− 0.696620i	0.937379	−	0.348310i	$-0.113244\pi$
$270$	0	0
$271$	−1.66962e12	−1.14227	−0.571137	−	0.820855i	$-0.693498\pi$
$271$	−1.66962e12	−1.14227	−0.571137	+	0.820855i	$0.693498\pi$
$272$	− 2.00518e12i	− 1.34682i
$273$	0	0
$274$	2.12973e11	0.137902
$275$	9.62754e10i	0.0612142i
$276$	0	0
$277$	1.54525e12	0.947543	0.473772	−	0.880648i	$-0.342892\pi$
$277$	1.54525e12	0.947543	0.473772	+	0.880648i	$0.342892\pi$
$278$	− 7.02411e11i	− 0.423026i
$279$	0	0
$280$	−1.37831e11	−0.0800863
$281$	5.20878e11i	0.297307i	0.988889	+	0.148653i	$0.0474939\pi$
$281$	5.20878e11i	0.297307i	−0.988889	+	0.148653i	$0.952506\pi$
$282$	0	0
$283$	1.09915e12	0.605516	0.302758	−	0.953068i	$-0.402093\pi$
$283$	1.09915e12	0.605516	0.302758	+	0.953068i	$0.402093\pi$
$284$	− 2.09990e12i	− 1.13660i
$285$	0	0
$286$	8.31535e10	0.0434560
$287$	5.15717e11i	0.264851i
$288$	0	0
$289$	−3.63496e12	−1.80306
$290$	7.97732e11i	0.388926i
$291$	0	0
$292$	3.78677e12	1.78384
$293$	6.80271e11i	0.315024i	0.987517	+	0.157512i	$0.0503474\pi$
$293$	6.80271e11i	0.315024i	−0.987517	+	0.157512i	$0.949653\pi$
$294$	0	0
$295$	1.14244e12	0.511357
$296$	− 1.47510e12i	− 0.649177i
$297$	0	0
$298$	7.25484e10	0.0308707
$299$	− 1.13868e12i	− 0.476482i
$300$	0	0
$301$	1.35314e11	0.0547660
$302$	− 4.92555e11i	− 0.196074i
$303$	0	0
$304$	−2.34700e12	−0.903951
$305$	− 1.87016e12i	− 0.708564i
$306$	0	0
$307$	−2.63985e11	−0.0968028	−0.0484014	−	0.998828i	$-0.515413\pi$
$307$	−2.63985e11	−0.0968028	−0.0484014	+	0.998828i	$0.515413\pi$
$308$	1.61728e11i	0.0583487i
$309$	0	0
$310$	2.63216e11	0.0919398
$311$	4.58632e12i	1.57638i	0.615430	+	0.788192i	$0.288983\pi$
$311$	4.58632e12i	1.57638i	−0.615430	+	0.788192i	$0.711017\pi$
$312$	0	0
$313$	−2.27641e12	−0.757755	−0.378877	−	0.925447i	$-0.623690\pi$
$313$	−2.27641e12	−0.757755	−0.378877	+	0.925447i	$0.623690\pi$
$314$	− 1.59006e11i	− 0.0520912i
$315$	0	0
$316$	6.82404e11	0.216574
$317$	− 1.60063e12i	− 0.500028i	−0.968242	−	0.250014i	$-0.919565\pi$
$317$	− 1.60063e12i	− 0.500028i	0.968242	−	0.250014i	$-0.0804353\pi$
$318$	0	0
$319$	1.93894e12	0.586963
$320$	− 1.89806e12i	− 0.565667i
$321$	0	0
$322$	−1.58194e11	−0.0456995
$323$	6.61425e12i	1.88134i
$324$	0	0
$325$	2.97368e11	0.0820120
$326$	8.52701e11i	0.231584i
$327$	0	0
$328$	2.84560e12	0.749558
$329$	5.63398e11i	0.146162i
$330$	0	0
$331$	2.78241e12	0.700294	0.350147	−	0.936695i	$-0.386132\pi$
$331$	2.78241e12	0.700294	0.350147	+	0.936695i	$0.386132\pi$
$332$	3.77693e12i	0.936372i
$333$	0	0
$334$	1.51992e12	0.365670
$335$	6.80359e12i	1.61255i
$336$	0	0
$337$	−4.52736e12	−1.04159	−0.520794	−	0.853683i	$-0.674364\pi$
$337$	−4.52736e12	−1.04159	−0.520794	+	0.853683i	$0.674364\pi$
$338$	8.82214e11i	0.199982i
$339$	0	0
$340$	−6.45767e12	−1.42128
$341$	− 6.39763e11i	− 0.138755i
$342$	0	0
$343$	−1.64875e12	−0.347283
$344$	− 7.46632e11i	− 0.154994i
$345$	0	0
$346$	1.10406e11	0.0222644
$347$	− 7.66402e11i	− 0.152338i	−0.997095	−	0.0761692i	$-0.975731\pi$
$347$	− 7.66402e11i	− 0.152338i	0.997095	−	0.0761692i	$-0.0242689\pi$
$348$	0	0
$349$	4.55840e12	0.880410	0.440205	−	0.897897i	$-0.354906\pi$
$349$	4.55840e12	0.880410	0.440205	+	0.897897i	$0.354906\pi$
$350$	− 4.13126e10i	− 0.00786579i
$351$	0	0
$352$	1.35395e12	0.250547
$353$	− 2.11871e12i	− 0.386544i	−0.981145	−	0.193272i	$-0.938090\pi$
$353$	− 2.11871e12i	− 0.386544i	0.981145	−	0.193272i	$-0.0619100\pi$
$354$	0	0
$355$	−6.24513e12	−1.10764
$356$	5.43295e12i	0.950136i
$357$	0	0
$358$	−1.09433e12	−0.186094
$359$	− 5.21959e12i	− 0.875314i	−0.899142	−	0.437657i	$-0.855808\pi$
$359$	− 5.21959e12i	− 0.875314i	0.899142	−	0.437657i	$-0.144192\pi$
$360$	0	0
$361$	1.61069e12	0.262709
$362$	− 1.86389e12i	− 0.299831i
$363$	0	0
$364$	4.99532e11	0.0781730
$365$	− 1.12619e13i	− 1.73839i
$366$	0	0
$367$	9.04907e12	1.35917	0.679585	−	0.733597i	$-0.262160\pi$
$367$	9.04907e12	1.35917	0.679585	+	0.733597i	$0.262160\pi$
$368$	− 5.44780e12i	− 0.807202i
$369$	0	0
$370$	−2.11785e12	−0.305412
$371$	9.61954e11i	0.136863i
$372$	0	0
$373$	5.54524e11	0.0768027	0.0384014	−	0.999262i	$-0.487773\pi$
$373$	5.54524e11	0.0768027	0.0384014	+	0.999262i	$0.487773\pi$
$374$	− 1.12116e12i	− 0.153218i
$375$	0	0
$376$	3.10870e12	0.413656
$377$	− 5.98884e12i	− 0.786387i
$378$	0	0
$379$	5.69814e11	0.0728681	0.0364340	−	0.999336i	$-0.488400\pi$
$379$	5.69814e11	0.0728681	0.0364340	+	0.999336i	$0.488400\pi$
$380$	7.55848e12i	0.953930i
$381$	0	0
$382$	−3.66998e12	−0.451177
$383$	2.73992e12i	0.332463i	0.986087	+	0.166232i	$0.0531599\pi$
$383$	2.73992e12i	0.332463i	−0.986087	+	0.166232i	$0.946840\pi$
$384$	0	0
$385$	4.80981e11	0.0568623
$386$	2.01599e12i	0.235262i
$387$	0	0
$388$	7.97439e12	0.906857
$389$	− 1.64988e13i	− 1.85228i	−0.377185	−	0.926138i	$-0.623108\pi$
$389$	− 1.64988e13i	− 1.85228i	0.377185	−	0.926138i	$-0.376892\pi$
$390$	0	0
$391$	−1.53528e13	−1.67998
$392$	4.47683e12i	0.483660i
$393$	0	0
$394$	−1.81252e12	−0.190898
$395$	− 2.02948e12i	− 0.211056i
$396$	0	0
$397$	8.37627e12	0.849373	0.424686	−	0.905341i	$-0.360384\pi$
$397$	8.37627e12	0.849373	0.424686	+	0.905341i	$0.360384\pi$
$398$	2.83801e10i	0.00284183i
$399$	0	0
$400$	1.42270e12	0.138935
$401$	− 1.39532e13i	− 1.34571i	−0.739772	−	0.672857i	$-0.765067\pi$
$401$	− 1.39532e13i	− 1.34571i	0.739772	−	0.672857i	$-0.234933\pi$
$402$	0	0
$403$	−1.97605e12	−0.185897
$404$	9.25669e12i	0.860100i
$405$	0	0
$406$	−8.32016e11	−0.0754226
$407$	5.14756e12i	0.460924i
$408$	0	0
$409$	−1.27027e13	−1.10988	−0.554942	−	0.831889i	$-0.687260\pi$
$409$	−1.27027e13	−1.10988	−0.554942	+	0.831889i	$0.687260\pi$
$410$	− 4.08551e12i	− 0.352637i
$411$	0	0
$412$	−6.60688e12	−0.556558
$413$	1.19154e12i	0.0991650i
$414$	0	0
$415$	1.12326e13	0.912517
$416$	− 4.18198e12i	− 0.335672i
$417$	0	0
$418$	−1.31228e12	−0.102836
$419$	5.02990e12i	0.389483i	0.980855	+	0.194742i	$0.0623868\pi$
$419$	5.02990e12i	0.389483i	−0.980855	+	0.194742i	$0.937613\pi$
$420$	0	0
$421$	1.29047e13	0.975745	0.487872	−	0.872915i	$-0.337773\pi$
$421$	1.29047e13	0.975745	0.487872	+	0.872915i	$0.337773\pi$
$422$	6.07950e12i	0.454261i
$423$	0	0
$424$	5.30783e12	0.387336
$425$	− 4.00941e12i	− 0.289158i
$426$	0	0
$427$	1.95053e12	0.137408
$428$	2.14838e13i	1.49587i
$429$	0	0
$430$	−1.07196e12	−0.0729183
$431$	1.47296e13i	0.990388i	0.868782	+	0.495194i	$0.164903\pi$
$431$	1.47296e13i	0.990388i	−0.868782	+	0.495194i	$0.835097\pi$
$432$	0	0
$433$	−8.34378e12	−0.548180	−0.274090	−	0.961704i	$-0.588377\pi$
$433$	−8.34378e12	−0.548180	−0.274090	+	0.961704i	$0.588377\pi$
$434$	2.74528e11i	0.0178294i
$435$	0	0
$436$	−3.82552e12	−0.242805
$437$	1.79700e13i	1.12756i
$438$	0	0
$439$	−1.33878e13	−0.821084	−0.410542	−	0.911842i	$-0.634660\pi$
$439$	−1.33878e13	−0.821084	−0.410542	+	0.911842i	$0.634660\pi$
$440$	− 2.65394e12i	− 0.160926i
$441$	0	0
$442$	−3.46294e12	−0.205274
$443$	2.99311e13i	1.75430i	0.480213	+	0.877152i	$0.340559\pi$
$443$	2.99311e13i	1.75430i	−0.480213	+	0.877152i	$0.659441\pi$
$444$	0	0
$445$	1.61577e13	0.925930
$446$	− 1.69471e12i	− 0.0960331i
$447$	0	0
$448$	1.97964e12	0.109697
$449$	− 1.91903e13i	− 1.05160i	−0.850609	−	0.525798i	$-0.823767\pi$
$449$	− 1.91903e13i	− 1.05160i	0.850609	−	0.525798i	$-0.176233\pi$
$450$	0	0
$451$	−9.93011e12	−0.532196
$452$	1.00231e13i	0.531266i
$453$	0	0
$454$	4.40729e12	0.228503
$455$	− 1.48562e12i	− 0.0761815i
$456$	0	0
$457$	1.06523e13	0.534394	0.267197	−	0.963642i	$-0.413903\pi$
$457$	1.06523e13	0.534394	0.267197	+	0.963642i	$0.413903\pi$
$458$	6.35055e12i	0.315126i
$459$	0	0
$460$	−1.75446e13	−0.851831
$461$	− 1.91295e13i	− 0.918755i	−0.888241	−	0.459378i	$-0.848072\pi$
$461$	− 1.91295e13i	− 0.918755i	0.888241	−	0.459378i	$-0.151928\pi$
$462$	0	0
$463$	2.64802e13	1.24456	0.622282	−	0.782794i	$-0.286206\pi$
$463$	2.64802e13	1.24456	0.622282	+	0.782794i	$0.286206\pi$
$464$	− 2.86524e13i	− 1.33221i
$465$	0	0
$466$	1.29950e12	0.0591354
$467$	1.80876e12i	0.0814324i	0.999171	+	0.0407162i	$0.0129640\pi$
$467$	1.80876e12i	0.0814324i	−0.999171	+	0.0407162i	$0.987036\pi$
$468$	0	0
$469$	−7.09599e12	−0.312715
$470$	− 4.46324e12i	− 0.194608i
$471$	0	0
$472$	6.57464e12	0.280648
$473$	2.60547e12i	0.110048i
$474$	0	0
$475$	−4.69288e12	−0.194076
$476$	− 6.73519e12i	− 0.275623i
$477$	0	0
$478$	7.75179e12	0.310644
$479$	− 9.26227e12i	− 0.367316i	−0.982990	−	0.183658i	$-0.941206\pi$
$479$	− 9.26227e12i	− 0.367316i	0.982990	−	0.183658i	$-0.0587939\pi$
$480$	0	0
$481$	1.58994e13	0.617525
$482$	− 5.18952e12i	− 0.199477i
$483$	0	0
$484$	2.16752e13	0.816085
$485$	− 2.37159e13i	− 0.883754i
$486$	0	0
$487$	−4.71874e13	−1.72259	−0.861293	−	0.508109i	$-0.830345\pi$
$487$	−4.71874e13	−1.72259	−0.861293	+	0.508109i	$0.830345\pi$
$488$	− 1.07626e13i	− 0.388881i
$489$	0	0
$490$	6.42751e12	0.227542
$491$	6.82609e12i	0.239202i	0.992822	+	0.119601i	$0.0381615\pi$
$491$	6.82609e12i	0.239202i	−0.992822	+	0.119601i	$0.961839\pi$
$492$	0	0
$493$	−8.07475e13	−2.77265
$494$	4.05326e12i	0.137775i
$495$	0	0
$496$	−9.45402e12	−0.314926
$497$	− 6.51352e12i	− 0.214800i
$498$	0	0
$499$	2.43870e13	0.788234	0.394117	−	0.919060i	$-0.371050\pi$
$499$	2.43870e13	0.788234	0.394117	+	0.919060i	$0.371050\pi$
$500$	− 3.11104e13i	− 0.995533i
$501$	0	0
$502$	1.41703e13	0.444487
$503$	3.33785e13i	1.03664i	0.855188	+	0.518319i	$0.173442\pi$
$503$	3.33785e13i	1.03664i	−0.855188	+	0.518319i	$0.826558\pi$
$504$	0	0
$505$	2.75295e13	0.838188
$506$	− 3.04603e12i	− 0.0918293i
$507$	0	0
$508$	5.60077e12	0.165550
$509$	− 2.03966e13i	− 0.596993i	−0.954411	−	0.298497i	$-0.903515\pi$
$509$	− 2.03966e13i	− 0.596993i	0.954411	−	0.298497i	$-0.0964852\pi$
$510$	0	0
$511$	1.17459e13	0.337118
$512$	− 3.41368e13i	− 0.970226i
$513$	0	0
$514$	−8.59284e12	−0.239508
$515$	1.96490e13i	0.542380i
$516$	0	0
$517$	−1.08482e13	−0.293701
$518$	− 2.20886e12i	− 0.0592270i
$519$	0	0
$520$	−8.19727e12	−0.215602
$521$	4.04464e12i	0.105364i	0.998611	+	0.0526819i	$0.0167769\pi$
$521$	4.04464e12i	0.105364i	−0.998611	+	0.0526819i	$0.983223\pi$
$522$	0	0
$523$	4.68609e13	1.19757	0.598787	−	0.800908i	$-0.295650\pi$
$523$	4.68609e13	1.19757	0.598787	+	0.800908i	$0.295650\pi$
$524$	− 3.67879e13i	− 0.931212i
$525$	0	0
$526$	−5.48461e12	−0.136213
$527$	2.66431e13i	0.655437i
$528$	0	0
$529$	−2.85001e11	−0.00687967
$530$	− 7.62061e12i	− 0.182226i
$531$	0	0
$532$	−7.88331e12	−0.184991
$533$	3.06713e13i	0.713012i
$534$	0	0
$535$	6.38932e13	1.45776
$536$	3.91540e13i	0.885017i
$537$	0	0
$538$	−8.10713e12	−0.179869
$539$	− 1.56225e13i	− 0.343405i
$540$	0	0
$541$	−4.24917e13	−0.916890	−0.458445	−	0.888723i	$-0.651593\pi$
$541$	−4.24917e13	−0.916890	−0.458445	+	0.888723i	$0.651593\pi$
$542$	1.37952e13i	0.294938i
$543$	0	0
$544$	−5.63856e13	−1.18351
$545$	1.13771e13i	0.236619i
$546$	0	0
$547$	−3.32499e13	−0.678976	−0.339488	−	0.940610i	$-0.610254\pi$
$547$	−3.32499e13	−0.678976	−0.339488	+	0.940610i	$0.610254\pi$
$548$	2.46349e13i	0.498480i
$549$	0	0
$550$	7.95473e11	0.0158056
$551$	9.45122e13i	1.86093i
$552$	0	0
$553$	2.11670e12	0.0409292
$554$	− 1.27676e13i	− 0.244658i
$555$	0	0
$556$	8.12488e13	1.52913
$557$	8.53820e13i	1.59254i	0.604941	+	0.796270i	$0.293197\pi$
$557$	8.53820e13i	1.59254i	−0.604941	+	0.796270i	$0.706803\pi$
$558$	0	0
$559$	8.04757e12	0.147437
$560$	− 7.10764e12i	− 0.129058i
$561$	0	0
$562$	4.30374e12	0.0767652
$563$	5.34036e13i	0.944124i	0.881565	+	0.472062i	$0.156490\pi$
$563$	5.34036e13i	0.944124i	−0.881565	+	0.472062i	$0.843510\pi$
$564$	0	0
$565$	2.98090e13	0.517732
$566$	− 9.08171e12i	− 0.156345i
$567$	0	0
$568$	−3.59401e13	−0.607907
$569$	− 6.85124e13i	− 1.14870i	−0.818609	−	0.574352i	$-0.805254\pi$
$569$	− 6.85124e13i	− 1.14870i	0.818609	−	0.574352i	$-0.194746\pi$
$570$	0	0
$571$	−5.61848e13	−0.925632	−0.462816	−	0.886454i	$-0.653161\pi$
$571$	−5.61848e13	−0.925632	−0.462816	+	0.886454i	$0.653161\pi$
$572$	9.61848e12i	0.157082i
$573$	0	0
$574$	4.26110e12	0.0683852
$575$	− 1.08930e13i	− 0.173304i
$576$	0	0
$577$	8.39282e13	1.31229	0.656143	−	0.754636i	$-0.272187\pi$
$577$	8.39282e13	1.31229	0.656143	+	0.754636i	$0.272187\pi$
$578$	3.00338e13i	0.465555i
$579$	0	0
$580$	−9.22748e13	−1.40586
$581$	1.17154e13i	0.176960i
$582$	0	0
$583$	−1.85224e13	−0.275014
$584$	− 6.48111e13i	− 0.954081i
$585$	0	0
$586$	5.62072e12	0.0813400
$587$	− 9.41546e13i	− 1.35099i	−0.737366	−	0.675494i	$-0.763931\pi$
$587$	− 9.41546e13i	− 1.35099i	0.737366	−	0.675494i	$-0.236069\pi$
$588$	0	0
$589$	3.11848e13	0.439913
$590$	− 9.43939e12i	− 0.132033i
$591$	0	0
$592$	7.60674e13	1.04614
$593$	4.51744e13i	0.616055i	0.951377	+	0.308027i	$0.0996688\pi$
$593$	4.51744e13i	0.616055i	−0.951377	+	0.308027i	$0.900331\pi$
$594$	0	0
$595$	−2.00305e13	−0.268601
$596$	8.39177e12i	0.111589i
$597$	0	0
$598$	−9.40833e12	−0.123029
$599$	− 1.44095e14i	− 1.86860i	−0.356489	−	0.934299i	$-0.616026\pi$
$599$	− 1.44095e14i	− 1.86860i	0.356489	−	0.934299i	$-0.383974\pi$
$600$	0	0
$601$	−7.28067e13	−0.928537	−0.464268	−	0.885695i	$-0.653683\pi$
$601$	−7.28067e13	−0.928537	−0.464268	+	0.885695i	$0.653683\pi$
$602$	− 1.11803e12i	− 0.0141407i
$603$	0	0
$604$	5.69745e13	0.708755
$605$	− 6.44622e13i	− 0.795295i
$606$	0	0
$607$	−1.46509e14	−1.77796	−0.888979	−	0.457949i	$-0.848584\pi$
$607$	−1.46509e14	−1.77796	−0.888979	+	0.457949i	$0.848584\pi$
$608$	6.59974e13i	0.794344i
$609$	0	0
$610$	−1.54521e13	−0.182953
$611$	3.35071e13i	0.393487i
$612$	0	0
$613$	8.70761e13	1.00600	0.502998	−	0.864287i	$-0.332230\pi$
$613$	8.70761e13	1.00600	0.502998	+	0.864287i	$0.332230\pi$
$614$	2.18117e12i	0.0249947i
$615$	0	0
$616$	2.76800e12	0.0312077
$617$	− 8.20522e13i	− 0.917623i	−0.888534	−	0.458811i	$-0.848275\pi$
$617$	− 8.20522e13i	− 0.917623i	0.888534	−	0.458811i	$-0.151725\pi$
$618$	0	0
$619$	5.35067e13	0.588782	0.294391	−	0.955685i	$-0.404883\pi$
$619$	5.35067e13	0.588782	0.294391	+	0.955685i	$0.404883\pi$
$620$	3.04465e13i	0.332338i
$621$	0	0
$622$	3.78943e13	0.407026
$623$	1.68521e13i	0.179561i
$624$	0	0
$625$	−7.60517e13	−0.797460
$626$	1.88088e13i	0.195654i
$627$	0	0
$628$	1.83924e13	0.188296
$629$	− 2.14371e14i	− 2.17727i
$630$	0	0
$631$	1.55764e14	1.55711	0.778556	−	0.627576i	$-0.215953\pi$
$631$	1.55764e14	1.55711	0.778556	+	0.627576i	$0.215953\pi$
$632$	− 1.16794e13i	− 0.115834i
$633$	0	0
$634$	−1.32252e13	−0.129108
$635$	− 1.66568e13i	− 0.161333i
$636$	0	0
$637$	−4.82535e13	−0.460078
$638$	− 1.60204e13i	− 0.151555i
$639$	0	0
$640$	−8.47203e13	−0.789019
$641$	1.35891e14i	1.25574i	0.778317	+	0.627872i	$0.216074\pi$
$641$	1.35891e14i	1.25574i	−0.778317	+	0.627872i	$0.783926\pi$
$642$	0	0
$643$	1.60532e14	1.46052	0.730258	−	0.683171i	$-0.239400\pi$
$643$	1.60532e14	1.46052	0.730258	+	0.683171i	$0.239400\pi$
$644$	− 1.82986e13i	− 0.165192i
$645$	0	0
$646$	5.46501e13	0.485767
$647$	− 1.21415e14i	− 1.07091i	−0.844565	−	0.535454i	$-0.820141\pi$
$647$	− 1.21415e14i	− 1.07091i	0.844565	−	0.535454i	$-0.179859\pi$
$648$	0	0
$649$	−2.29431e13	−0.199264
$650$	− 2.45699e12i	− 0.0211757i
$651$	0	0
$652$	−9.86331e13	−0.837114
$653$	6.47326e13i	0.545202i	0.962127	+	0.272601i	$0.0878839\pi$
$653$	6.47326e13i	0.545202i	−0.962127	+	0.272601i	$0.912116\pi$
$654$	0	0
$655$	−1.09408e14	−0.907489
$656$	1.46741e14i	1.20790i
$657$	0	0
$658$	4.65506e12	0.0377395
$659$	− 1.99057e14i	− 1.60158i	−0.598943	−	0.800792i	$-0.704412\pi$
$659$	− 1.99057e14i	− 1.60158i	0.598943	−	0.800792i	$-0.295588\pi$
$660$	0	0
$661$	−2.98244e13	−0.236355	−0.118177	−	0.992992i	$-0.537705\pi$
$661$	−2.98244e13	−0.236355	−0.118177	+	0.992992i	$0.537705\pi$
$662$	− 2.29895e13i	− 0.180817i
$663$	0	0
$664$	6.46426e13	0.500817
$665$	2.34451e13i	0.180278i
$666$	0	0
$667$	−2.19380e14	−1.66176
$668$	1.75812e14i	1.32180i
$669$	0	0
$670$	5.62145e13	0.416365
$671$	3.75574e13i	0.276110i
$672$	0	0
$673$	7.23511e13	0.524047	0.262023	−	0.965062i	$-0.415610\pi$
$673$	7.23511e13	0.524047	0.262023	+	0.965062i	$0.415610\pi$
$674$	3.74072e13i	0.268940i
$675$	0	0
$676$	−1.02047e14	−0.722880
$677$	2.34787e14i	1.65094i	0.564448	+	0.825469i	$0.309089\pi$
$677$	2.34787e14i	1.65094i	−0.564448	+	0.825469i	$0.690911\pi$
$678$	0	0
$679$	2.47351e13	0.171382
$680$	1.10524e14i	0.760171i
$681$	0	0
$682$	−5.28602e12	−0.0358267
$683$	1.85118e14i	1.24550i	0.782420	+	0.622751i	$0.213985\pi$
$683$	1.85118e14i	1.24550i	−0.782420	+	0.622751i	$0.786015\pi$
$684$	0	0
$685$	7.32645e13	0.485781
$686$	1.36227e13i	0.0896694i
$687$	0	0
$688$	3.85020e13	0.249771
$689$	5.72105e13i	0.368451i
$690$	0	0
$691$	5.51512e12	0.0350078	0.0175039	−	0.999847i	$-0.494428\pi$
$691$	5.51512e12	0.0350078	0.0175039	+	0.999847i	$0.494428\pi$
$692$	1.27708e13i	0.0804797i
$693$	0	0
$694$	−6.33237e12	−0.0393341
$695$	− 2.41635e14i	− 1.49017i
$696$	0	0
$697$	4.13542e14	2.51394
$698$	− 3.76636e13i	− 0.227324i
$699$	0	0
$700$	4.77869e12	0.0284327
$701$	1.69135e14i	0.999180i	0.866262	+	0.499590i	$0.166516\pi$
$701$	1.69135e14i	0.999180i	−0.866262	+	0.499590i	$0.833484\pi$
$702$	0	0
$703$	−2.50914e14	−1.46133
$704$	3.81178e13i	0.220427i
$705$	0	0
$706$	−1.75058e13	−0.0998065
$707$	2.87126e13i	0.162546i
$708$	0	0
$709$	−2.66430e14	−1.48714	−0.743570	−	0.668658i	$-0.766869\pi$
$709$	−2.66430e14	−1.48714	−0.743570	+	0.668658i	$0.766869\pi$
$710$	5.16002e13i	0.285996i
$711$	0	0
$712$	9.29857e13	0.508178
$713$	7.23854e13i	0.392829i
$714$	0	0
$715$	2.86055e13	0.153080
$716$	− 1.26582e14i	− 0.672678i
$717$	0	0
$718$	−4.31267e13	−0.226008
$719$	− 2.66062e14i	− 1.38464i	−0.721589	−	0.692322i	$-0.756588\pi$
$719$	− 2.66062e14i	− 1.38464i	0.721589	−	0.692322i	$-0.243412\pi$
$720$	0	0
$721$	−2.04934e13	−0.105181
$722$	− 1.33083e13i	− 0.0678322i
$723$	0	0
$724$	2.15599e14	1.08381
$725$	− 5.72912e13i	− 0.286021i
$726$	0	0
$727$	1.32805e14	0.653945	0.326973	−	0.945034i	$-0.393971\pi$
$727$	1.32805e14	0.653945	0.326973	+	0.945034i	$0.393971\pi$
$728$	− 8.54956e12i	− 0.0418107i
$729$	0	0
$730$	−9.30512e13	−0.448857
$731$	− 1.08505e14i	− 0.519834i
$732$	0	0
$733$	−2.40762e14	−1.13780	−0.568902	−	0.822405i	$-0.692632\pi$
$733$	−2.40762e14	−1.13780	−0.568902	+	0.822405i	$0.692632\pi$
$734$	− 7.47677e13i	− 0.350941i
$735$	0	0
$736$	−1.53192e14	−0.709326
$737$	− 1.36633e14i	− 0.628374i
$738$	0	0
$739$	8.67964e13	0.393804	0.196902	−	0.980423i	$-0.436912\pi$
$739$	8.67964e13	0.393804	0.196902	+	0.980423i	$0.436912\pi$
$740$	− 2.44974e14i	− 1.10398i
$741$	0	0
$742$	7.94812e12	0.0353382
$743$	1.44512e14i	0.638205i	0.947720	+	0.319102i	$0.103381\pi$
$743$	1.44512e14i	0.638205i	−0.947720	+	0.319102i	$0.896619\pi$
$744$	0	0
$745$	2.49572e13	0.108746
$746$	− 4.58174e12i	− 0.0198306i
$747$	0	0
$748$	1.29686e14	0.553841
$749$	6.66391e13i	0.282696i
$750$	0	0
$751$	3.64323e14	1.52506	0.762530	−	0.646952i	$-0.223957\pi$
$751$	3.64323e14	1.52506	0.762530	+	0.646952i	$0.223957\pi$
$752$	1.60308e14i	0.666601i
$753$	0	0
$754$	−4.94826e13	−0.203047
$755$	− 1.69443e14i	− 0.690699i
$756$	0	0
$757$	−1.48576e14	−0.597681	−0.298841	−	0.954303i	$-0.596600\pi$
$757$	−1.48576e14	−0.597681	−0.298841	+	0.954303i	$0.596600\pi$
$758$	− 4.70807e12i	− 0.0188147i
$759$	0	0
$760$	1.29364e14	0.510207
$761$	− 3.73879e13i	− 0.146490i	−0.997314	−	0.0732450i	$-0.976665\pi$
$761$	− 3.73879e13i	− 0.146490i	0.997314	−	0.0732450i	$-0.0233355\pi$
$762$	0	0
$763$	−1.18661e13	−0.0458865
$764$	− 4.24512e14i	− 1.63088i
$765$	0	0
$766$	2.26385e13	0.0858427
$767$	7.08647e13i	0.266964i
$768$	0	0
$769$	−1.92661e14	−0.716412	−0.358206	−	0.933642i	$-0.616612\pi$
$769$	−1.92661e14	−0.716412	−0.358206	+	0.933642i	$0.616612\pi$
$770$	− 3.97409e12i	− 0.0146820i
$771$	0	0
$772$	−2.33193e14	−0.850411
$773$	3.59730e14i	1.30340i	0.758475	+	0.651702i	$0.225945\pi$
$773$	3.59730e14i	1.30340i	−0.758475	+	0.651702i	$0.774055\pi$
$774$	0	0
$775$	−1.89035e13	−0.0676136
$776$	− 1.36483e14i	− 0.485030i
$777$	0	0
$778$	−1.36321e14	−0.478262
$779$	− 4.84036e14i	− 1.68729i
$780$	0	0
$781$	1.25418e14	0.431622
$782$	1.26852e14i	0.433776i
$783$	0	0
$784$	−2.30859e14	−0.779412
$785$	− 5.46992e13i	− 0.183499i
$786$	0	0
$787$	−2.93391e13	−0.0971793	−0.0485896	−	0.998819i	$-0.515473\pi$
$787$	−2.93391e13	−0.0971793	−0.0485896	+	0.998819i	$0.515473\pi$
$788$	− 2.09657e14i	− 0.690046i
$789$	0	0
$790$	−1.67685e13	−0.0544952
$791$	3.10900e13i	0.100401i
$792$	0	0
$793$	1.16004e14	0.369920
$794$	− 6.92087e13i	− 0.219310i
$795$	0	0
$796$	−3.28277e12	−0.0102725
$797$	2.41585e14i	0.751238i	0.926774	+	0.375619i	$0.122570\pi$
$797$	2.41585e14i	0.751238i	−0.926774	+	0.375619i	$0.877430\pi$
$798$	0	0
$799$	4.51776e14	1.38736
$800$	− 4.00061e13i	− 0.122089i
$801$	0	0
$802$	−1.15288e14	−0.347467
$803$	2.26167e14i	0.677410i
$804$	0	0
$805$	−5.44202e13	−0.160983
$806$	1.63270e13i	0.0479990i
$807$	0	0
$808$	1.58430e14	0.460023
$809$	3.39910e14i	0.980892i	0.871472	+	0.490446i	$0.163166\pi$
$809$	3.39910e14i	0.980892i	−0.871472	+	0.490446i	$0.836834\pi$
$810$	0	0
$811$	−2.85735e14	−0.814440	−0.407220	−	0.913330i	$-0.633502\pi$
$811$	−2.85735e14	−0.814440	−0.407220	+	0.913330i	$0.633502\pi$
$812$	− 9.62404e13i	− 0.272632i
$813$	0	0
$814$	4.25316e13	0.119012
$815$	2.93336e14i	0.815788i
$816$	0	0
$817$	−1.27002e14	−0.348899
$818$	1.04955e14i	0.286575i
$819$	0	0
$820$	4.72577e14	1.27469
$821$	5.03013e14i	1.34854i	0.738486	+	0.674269i	$0.235541\pi$
$821$	5.03013e14i	1.34854i	−0.738486	+	0.674269i	$0.764459\pi$
$822$	0	0
$823$	−3.22209e14	−0.853373	−0.426687	−	0.904400i	$-0.640319\pi$
$823$	−3.22209e14	−0.853373	−0.426687	+	0.904400i	$0.640319\pi$
$824$	1.13078e14i	0.297674i
$825$	0	0
$826$	9.84507e12	0.0256046
$827$	2.02983e14i	0.524726i	0.964969	+	0.262363i	$0.0845019\pi$
$827$	2.02983e14i	0.524726i	−0.964969	+	0.262363i	$0.915498\pi$
$828$	0	0
$829$	5.00471e14	1.27822	0.639111	−	0.769115i	$-0.279302\pi$
$829$	5.00471e14	1.27822	0.639111	+	0.769115i	$0.279302\pi$
$830$	− 9.28093e13i	− 0.235614i
$831$	0	0
$832$	1.17735e14	0.295318
$833$	6.50601e14i	1.62215i
$834$	0	0
$835$	5.22867e14	1.28813
$836$	− 1.51793e14i	− 0.371724i
$837$	0	0
$838$	4.15594e13	0.100565
$839$	8.96468e13i	0.215638i	0.994171	+	0.107819i	$0.0343867\pi$
$839$	8.96468e13i	0.215638i	−0.994171	+	0.107819i	$0.965613\pi$
$840$	0	0
$841$	−7.33109e14	−1.74256
$842$	− 1.06624e14i	− 0.251939i
$843$	0	0
$844$	−7.03224e14	−1.64203
$845$	3.03489e14i	0.704465i
$846$	0	0
$847$	6.72325e13	0.154228
$848$	2.73712e14i	0.624188i
$849$	0	0
$850$	−3.31276e13	−0.0746614
$851$	− 5.82416e14i	− 1.30493i
$852$	0	0
$853$	4.00884e14	0.887715	0.443858	−	0.896097i	$-0.353610\pi$
$853$	4.00884e14	0.887715	0.443858	+	0.896097i	$0.353610\pi$
$854$	− 1.61162e13i	− 0.0354792i
$855$	0	0
$856$	3.67699e14	0.800061
$857$	1.84324e14i	0.398728i	0.979926	+	0.199364i	$0.0638876\pi$
$857$	1.84324e14i	0.398728i	−0.979926	+	0.199364i	$0.936112\pi$
$858$	0	0
$859$	−7.27542e14	−1.55558	−0.777790	−	0.628525i	$-0.783659\pi$
$859$	−7.27542e14	−1.55558	−0.777790	+	0.628525i	$0.783659\pi$
$860$	− 1.23995e14i	− 0.263580i
$861$	0	0
$862$	1.21703e14	0.255720
$863$	− 8.25583e14i	− 1.72467i	−0.506336	−	0.862337i	$-0.669000\pi$
$863$	− 8.25583e14i	− 1.72467i	0.506336	−	0.862337i	$-0.331000\pi$
$864$	0	0
$865$	3.79804e13	0.0784294
$866$	6.89402e13i	0.141541i
$867$	0	0
$868$	−3.17550e13	−0.0644486
$869$	4.07569e13i	0.0822437i
$870$	0	0
$871$	−4.22021e14	−0.841867
$872$	6.54742e13i	0.129864i
$873$	0	0
$874$	1.48476e14	0.291139
$875$	− 9.64990e13i	− 0.188141i
$876$	0	0
$877$	−9.68621e13	−0.186705	−0.0933525	−	0.995633i	$-0.529758\pi$
$877$	−9.68621e13	−0.186705	−0.0933525	+	0.995633i	$0.529758\pi$
$878$	1.10617e14i	0.212006i
$879$	0	0
$880$	1.36857e14	0.259331
$881$	− 4.38566e14i	− 0.826333i	−0.910655	−	0.413167i	$-0.864423\pi$
$881$	− 4.38566e14i	− 0.826333i	0.910655	−	0.413167i	$-0.135577\pi$
$882$	0	0
$883$	2.23986e12	0.00417270	0.00208635	−	0.999998i	$-0.499336\pi$
$883$	2.23986e12	0.00417270	0.00208635	+	0.999998i	$0.499336\pi$
$884$	− 4.00564e14i	− 0.742011i
$885$	0	0
$886$	2.47305e14	0.452965
$887$	1.62994e14i	0.296861i	0.988923	+	0.148431i	$0.0474222\pi$
$887$	1.62994e14i	0.296861i	−0.988923	+	0.148431i	$0.952578\pi$
$888$	0	0
$889$	1.73726e13	0.0312865
$890$	− 1.33502e14i	− 0.239077i
$891$	0	0
$892$	1.96029e14	0.347134
$893$	− 5.28788e14i	− 0.931160i
$894$	0	0
$895$	−3.76457e14	−0.655541
$896$	− 8.83613e13i	− 0.153011i
$897$	0	0
$898$	−1.58559e14	−0.271525
$899$	3.80708e14i	0.648325i
$900$	0	0
$901$	7.71369e14	1.29909
$902$	8.20472e13i	0.137414i
$903$	0	0
$904$	1.71548e14	0.284146
$905$	− 6.41193e14i	− 1.05620i
$906$	0	0
$907$	6.97244e14	1.13592	0.567961	−	0.823056i	$-0.307732\pi$
$907$	6.97244e14	1.13592	0.567961	+	0.823056i	$0.307732\pi$
$908$	5.09798e14i	0.825978i
$909$	0	0
$910$	−1.22749e13	−0.0196702
$911$	− 4.25889e14i	− 0.678742i	−0.940653	−	0.339371i	$-0.889786\pi$
$911$	− 4.25889e14i	− 0.678742i	0.940653	−	0.339371i	$-0.110214\pi$
$912$	0	0
$913$	−2.25579e14	−0.355586
$914$	− 8.80141e13i	− 0.137982i
$915$	0	0
$916$	−7.34577e14	−1.13910
$917$	− 1.14110e14i	− 0.175985i
$918$	0	0
$919$	−1.00377e15	−1.53129	−0.765644	−	0.643264i	$-0.777580\pi$
$919$	−1.00377e15	−1.53129	−0.765644	+	0.643264i	$0.777580\pi$
$920$	3.00278e14i	0.455600i
$921$	0	0
$922$	−1.58057e14	−0.237225
$923$	− 3.87380e14i	− 0.578268i
$924$	0	0
$925$	1.52099e14	0.224604
$926$	− 2.18792e14i	− 0.321349i
$927$	0	0
$928$	−8.05704e14	−1.17067
$929$	− 8.98001e14i	− 1.29777i	−0.760886	−	0.648886i	$-0.775235\pi$
$929$	− 8.98001e14i	− 1.29777i	0.760886	−	0.648886i	$-0.224765\pi$
$930$	0	0
$931$	7.61507e14	1.08874
$932$	1.50315e14i	0.213758i
$933$	0	0
$934$	1.49448e13	0.0210260
$935$	− 3.85687e14i	− 0.539731i
$936$	0	0
$937$	2.71705e13	0.0376183	0.0188092	−	0.999823i	$-0.494013\pi$
$937$	2.71705e13	0.0376183	0.0188092	+	0.999823i	$0.494013\pi$
$938$	5.86304e13i	0.0807437i
$939$	0	0
$940$	5.16270e14	0.703457
$941$	7.42878e14i	1.00686i	0.864036	+	0.503431i	$0.167929\pi$
$941$	7.42878e14i	1.00686i	−0.864036	+	0.503431i	$0.832071\pi$
$942$	0	0
$943$	1.12353e15	1.50670
$944$	3.39038e14i	0.452261i
$945$	0	0
$946$	2.15276e13	0.0284145
$947$	− 9.02668e14i	− 1.18516i	−0.805510	−	0.592582i	$-0.798109\pi$
$947$	− 9.02668e14i	− 1.18516i	0.805510	−	0.592582i	$-0.201891\pi$
$948$	0	0
$949$	6.98566e14	0.907563
$950$	3.87748e13i	0.0501108i
$951$	0	0
$952$	−1.15274e14	−0.147416
$953$	− 2.78363e14i	− 0.354117i	−0.984200	−	0.177059i	$-0.943342\pi$
$953$	− 2.78363e14i	− 0.354117i	0.984200	−	0.177059i	$-0.0566583\pi$
$954$	0	0
$955$	−1.26250e15	−1.58934
$956$	8.96660e14i	1.12289i
$957$	0	0
$958$	−7.65292e13	−0.0948418
$959$	7.64132e13i	0.0942052i
$960$	0	0
$961$	−6.94012e14	−0.846740
$962$	− 1.31368e14i	− 0.159446i
$963$	0	0
$964$	6.00279e14	0.721055
$965$	6.93518e14i	0.828746i
$966$	0	0
$967$	7.58054e14	0.896536	0.448268	−	0.893899i	$-0.352041\pi$
$967$	7.58054e14	0.896536	0.448268	+	0.893899i	$0.352041\pi$
$968$	− 3.70973e14i	− 0.436481i
$969$	0	0
$970$	−1.95952e14	−0.228187
$971$	1.15979e15i	1.34364i	0.740714	+	0.671820i	$0.234487\pi$
$971$	1.15979e15i	1.34364i	−0.740714	+	0.671820i	$0.765513\pi$
$972$	0	0
$973$	2.52020e14	0.288982
$974$	3.89884e14i	0.444775i
$975$	0	0
$976$	5.55000e14	0.626677
$977$	1.97645e14i	0.222031i	0.993819	+	0.111015i	$0.0354103\pi$
$977$	1.97645e14i	0.222031i	−0.993819	+	0.111015i	$0.964590\pi$
$978$	0	0
$979$	−3.24486e14	−0.360813
$980$	7.43479e14i	0.822504i
$981$	0	0
$982$	5.64003e13	0.0617624
$983$	1.19721e15i	1.30437i	0.758058	+	0.652187i	$0.226149\pi$
$983$	1.19721e15i	1.30437i	−0.758058	+	0.652187i	$0.773851\pi$
$984$	0	0
$985$	−6.23522e14	−0.672466
$986$	6.67174e14i	0.715904i
$987$	0	0
$988$	−4.68846e14	−0.498018
$989$	− 2.94794e14i	− 0.311556i
$990$	0	0
$991$	−1.03777e15	−1.08576	−0.542880	−	0.839810i	$-0.682666\pi$
$991$	−1.03777e15	−1.08576	−0.542880	+	0.839810i	$0.682666\pi$
$992$	2.65846e14i	0.276740i
$993$	0	0
$994$	−5.38178e13	−0.0554618
$995$	9.76299e12i	0.0100108i
$996$	0	0
$997$	−1.09960e15	−1.11624	−0.558120	−	0.829761i	$-0.688477\pi$
$997$	−1.09960e15	−1.11624	−0.558120	+	0.829761i	$0.688477\pi$
$998$	− 2.01497e14i	− 0.203524i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.b.d.26.3	✓	6
3.2	odd	2	inner	27.11.b.d.26.4	yes	6
9.2	odd	6		81.11.d.g.53.4		12
9.4	even	3		81.11.d.g.26.4		12
9.5	odd	6		81.11.d.g.26.3		12
9.7	even	3		81.11.d.g.53.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.b.d.26.3	✓	6	1.1	even	1	trivial
27.11.b.d.26.4	yes	6	3.2	odd	2	inner
81.11.d.g.26.3		12	9.5	odd	6
81.11.d.g.26.4		12	9.4	even	3
81.11.d.g.53.3		12	9.7	even	3
81.11.d.g.53.4		12	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-8.26247i q^{2} +955.732 q^{4} -2842.36i q^{5} +2964.51 q^{7} -16357.5i q^{8} +O(q^{10})\)	\(q-8.26247i q^{2} +955.732 q^{4} -2842.36i q^{5} +2964.51 q^{7} -16357.5i q^{8} -23484.9 q^{10} +57081.6i q^{11} +176309. q^{13} -24494.2i q^{14} +843516. q^{16} -2.37717e6i q^{17} -2.78240e6 q^{19} -2.71653e6i q^{20} +471635. q^{22} -6.45845e6i q^{23} +1.68663e6 q^{25} -1.45675e6i q^{26} +2.83328e6 q^{28} -3.39679e7i q^{29} -1.12079e7 q^{31} -2.37196e7i q^{32} -1.96413e7 q^{34} -8.42620e6i q^{35} +9.01790e7 q^{37} +2.29895e7i q^{38} -4.64938e7 q^{40} +1.73964e8i q^{41} +4.56447e7 q^{43} +5.45546e7i q^{44} -5.33627e7 q^{46} +1.90047e8i q^{47} -2.73687e8 q^{49} -1.39357e7i q^{50} +1.68504e8 q^{52} +3.24490e8i q^{53} +1.62246e8 q^{55} -4.84919e7i q^{56} -2.80659e8 q^{58} +4.01935e8i q^{59} +6.57960e8 q^{61} +9.26047e7i q^{62} +6.67778e8 q^{64} -5.01133e8i q^{65} -2.39364e9 q^{67} -2.27194e9i q^{68} -6.96213e7 q^{70} -2.19717e9i q^{71} +3.96217e9 q^{73} -7.45102e8i q^{74} -2.65923e9 q^{76} +1.69219e8i q^{77} +7.14012e8 q^{79} -2.39757e9i q^{80} +1.43737e9 q^{82} +3.95187e9i q^{83} -6.75678e9 q^{85} -3.77138e8i q^{86} +9.33710e8 q^{88} +5.68460e9i q^{89} +5.22670e8 q^{91} -6.17254e9i q^{92} +1.57026e9 q^{94} +7.90858e9i q^{95} +8.34375e9 q^{97} +2.26133e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2658 q^{4} + 4638 q^{7}+O(q^{10}) \) 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

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