LMFDB - Embedded newform 27.11.b.d.26.6

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			26.6
Root			$0.913049 - 0.913049i$ of defining polynomial
Character	$\chi$	$=$	27.26
Dual form			27.11.b.d.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+49.7909i q^{2} -1455.14 q^{4} -4680.95i q^{5} +10645.1 q^{7} -21466.7i q^{8} +O(q^{10})$	\(q+49.7909i q^{2} -1455.14 q^{4} -4680.95i q^{5} +10645.1 q^{7} -21466.7i q^{8} +233069. q^{10} +210671. i q^{11} +483189. q^{13} +530027. i q^{14} -421214. q^{16} -1.44085e6i q^{17} +3.79189e6 q^{19} +6.81141e6i q^{20} -1.04895e7 q^{22} +2.24057e6i q^{23} -1.21456e7 q^{25} +2.40584e7i q^{26} -1.54900e7 q^{28} +3.09319e7i q^{29} +4.03254e7 q^{31} -4.29545e7i q^{32} +7.17413e7 q^{34} -4.98289e7i q^{35} +3.67411e7 q^{37} +1.88802e8i q^{38} -1.00484e8 q^{40} -8.25527e7i q^{41} +9.21810e7 q^{43} -3.06555e8i q^{44} -1.11560e8 q^{46} +3.91525e7i q^{47} -1.69158e8 q^{49} -6.04742e8i q^{50} -7.03105e8 q^{52} -1.93130e8i q^{53} +9.86139e8 q^{55} -2.28514e8i q^{56} -1.54013e9 q^{58} +7.23179e8i q^{59} +1.24946e9 q^{61} +2.00784e9i q^{62} +1.70742e9 q^{64} -2.26178e9i q^{65} +1.11419e9 q^{67} +2.09663e9i q^{68} +2.48103e9 q^{70} -6.26847e8i q^{71} -3.06134e9 q^{73} +1.82937e9i q^{74} -5.51772e9 q^{76} +2.24260e9i q^{77} -2.38138e9 q^{79} +1.97168e9i q^{80} +4.11037e9 q^{82} -2.39278e9i q^{83} -6.74454e9 q^{85} +4.58978e9i q^{86} +4.52241e9 q^{88} -1.61876e9i q^{89} +5.14357e9 q^{91} -3.26034e9i q^{92} -1.94944e9 q^{94} -1.77496e10i q^{95} -6.00749e9 q^{97} -8.42253e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	49.7909i	1.55597i	0.628285	+	0.777983i	$0.283757\pi$
$2$	49.7909i	1.55597i	−0.628285	+	0.777983i	$0.716243\pi$
$3$	0	0
$3$	0	0
$4$	−1455.14	−1.42103
$5$	− 4680.95i	− 1.49790i	−0.662625	−	0.748951i	$-0.730558\pi$
$5$	− 4680.95i	− 1.49790i	0.662625	−	0.748951i	$-0.269442\pi$
$6$	0	0
$7$	10645.1	0.633371	0.316685	−	0.948531i	$-0.397430\pi$
$7$	10645.1	0.633371	0.316685	+	0.948531i	$0.397430\pi$
$8$	− 21466.7i	− 0.655111i
$9$	0	0
$10$	233069.	2.33069
$11$	210671.i	1.30810i	0.756451	+	0.654050i	$0.226932\pi$
$11$	210671.i	1.30810i	−0.756451	+	0.654050i	$0.773068\pi$
$12$	0	0
$13$	483189.	1.30137	0.650684	−	0.759349i	$-0.274482\pi$
$13$	483189.	1.30137	0.650684	+	0.759349i	$0.274482\pi$
$14$	530027.i	0.985503i
$15$	0	0
$16$	−421214.	−0.401701
$17$	− 1.44085e6i	− 1.01479i	−0.861715	−	0.507393i	$-0.830609\pi$
$17$	− 1.44085e6i	− 1.01479i	0.861715	−	0.507393i	$-0.169391\pi$
$18$	0	0
$19$	3.79189e6	1.53140	0.765698	−	0.643200i	$-0.222393\pi$
$19$	3.79189e6	1.53140	0.765698	+	0.643200i	$0.222393\pi$
$20$	6.81141e6i	2.12857i
$21$	0	0
$22$	−1.04895e7	−2.03536
$23$	2.24057e6i	0.348113i	0.984736	+	0.174056i	$0.0556875\pi$
$23$	2.24057e6i	0.348113i	−0.984736	+	0.174056i	$0.944313\pi$
$24$	0	0
$25$	−1.21456e7	−1.24371
$26$	2.40584e7i	2.02488i
$27$	0	0
$28$	−1.54900e7	−0.900040
$29$	3.09319e7i	1.50805i	0.656843	+	0.754027i	$0.271891\pi$
$29$	3.09319e7i	1.50805i	−0.656843	+	0.754027i	$0.728109\pi$
$30$	0	0
$31$	4.03254e7	1.40854	0.704272	−	0.709930i	$-0.251274\pi$
$31$	4.03254e7	1.40854	0.704272	+	0.709930i	$0.251274\pi$
$32$	− 4.29545e7i	− 1.28014i
$33$	0	0
$34$	7.17413e7	1.57897
$35$	− 4.98289e7i	− 0.948727i
$36$	0	0
$37$	3.67411e7	0.529838	0.264919	−	0.964271i	$-0.414655\pi$
$37$	3.67411e7	0.529838	0.264919	+	0.964271i	$0.414655\pi$
$38$	1.88802e8i	2.38280i
$39$	0	0
$40$	−1.00484e8	−0.981293
$41$	− 8.25527e7i	− 0.712544i	−0.934382	−	0.356272i	$-0.884048\pi$
$41$	− 8.25527e7i	− 0.712544i	0.934382	−	0.356272i	$-0.115952\pi$
$42$	0	0
$43$	9.21810e7	0.627045	0.313523	−	0.949581i	$-0.398491\pi$
$43$	9.21810e7	0.627045	0.313523	+	0.949581i	$0.398491\pi$
$44$	− 3.06555e8i	− 1.85885i
$45$	0	0
$46$	−1.11560e8	−0.541651
$47$	3.91525e7i	0.170715i	0.996350	+	0.0853573i	$0.0272032\pi$
$47$	3.91525e7i	0.170715i	−0.996350	+	0.0853573i	$0.972797\pi$
$48$	0	0
$49$	−1.69158e8	−0.598842
$50$	− 6.04742e8i	− 1.93517i
$51$	0	0
$52$	−7.03105e8	−1.84928
$53$	− 1.93130e8i	− 0.461817i	−0.972975	−	0.230909i	$-0.925830\pi$
$53$	− 1.93130e8i	− 0.461817i	0.972975	−	0.230909i	$-0.0741698\pi$
$54$	0	0
$55$	9.86139e8	1.95941
$56$	− 2.28514e8i	− 0.414928i
$57$	0	0
$58$	−1.54013e9	−2.34648
$59$	7.23179e8i	1.01155i	0.862666	+	0.505773i	$0.168793\pi$
$59$	7.23179e8i	1.01155i	−0.862666	+	0.505773i	$0.831207\pi$
$60$	0	0
$61$	1.24946e9	1.47935	0.739677	−	0.672962i	$-0.234978\pi$
$61$	1.24946e9	1.47935	0.739677	+	0.672962i	$0.234978\pi$
$62$	2.00784e9i	2.19165i
$63$	0	0
$64$	1.70742e9	1.59016
$65$	− 2.26178e9i	− 1.94932i
$66$	0	0
$67$	1.11419e9	0.825251	0.412626	−	0.910901i	$-0.364612\pi$
$67$	1.11419e9	0.825251	0.412626	+	0.910901i	$0.364612\pi$
$68$	2.09663e9i	1.44204i
$69$	0	0
$70$	2.48103e9	1.47619
$71$	− 6.26847e8i	− 0.347432i	−0.984796	−	0.173716i	$-0.944423\pi$
$71$	− 6.26847e8i	− 0.347432i	0.984796	−	0.173716i	$-0.0555774\pi$
$72$	0	0
$73$	−3.06134e9	−1.47672	−0.738359	−	0.674408i	$-0.764399\pi$
$73$	−3.06134e9	−1.47672	−0.738359	+	0.674408i	$0.764399\pi$
$74$	1.82937e9i	0.824410i
$75$	0	0
$76$	−5.51772e9	−2.17616
$77$	2.24260e9i	0.828513i
$78$	0	0
$79$	−2.38138e9	−0.773914	−0.386957	−	0.922098i	$-0.626474\pi$
$79$	−2.38138e9	−0.773914	−0.386957	+	0.922098i	$0.626474\pi$
$80$	1.97168e9i	0.601708i
$81$	0	0
$82$	4.11037e9	1.10869
$83$	− 2.39278e9i	− 0.607451i	−0.952760	−	0.303726i	$-0.901769\pi$
$83$	− 2.39278e9i	− 0.607451i	0.952760	−	0.303726i	$-0.0982306\pi$
$84$	0	0
$85$	−6.74454e9	−1.52005
$86$	4.58978e9i	0.975662i
$87$	0	0
$88$	4.52241e9	0.856952
$89$	− 1.61876e9i	− 0.289889i	−0.989440	−	0.144944i	$-0.953700\pi$
$89$	− 1.61876e9i	− 0.289889i	0.989440	−	0.144944i	$-0.0463003\pi$
$90$	0	0
$91$	5.14357e9	0.824248
$92$	− 3.26034e9i	− 0.494679i
$93$	0	0
$94$	−1.94944e9	−0.265626
$95$	− 1.77496e10i	− 2.29388i
$96$	0	0
$97$	−6.00749e9	−0.699575	−0.349788	−	0.936829i	$-0.613746\pi$
$97$	−6.00749e9	−0.699575	−0.349788	+	0.936829i	$0.613746\pi$
$98$	− 8.42253e9i	− 0.931778i
$99$	0	0
$100$	1.76735e10	1.76735
$101$	− 3.80975e9i	− 0.362484i	−0.983439	−	0.181242i	$-0.941988\pi$
$101$	− 3.80975e9i	− 0.362484i	0.983439	−	0.181242i	$-0.0580118\pi$
$102$	0	0
$103$	4.09964e9	0.353638	0.176819	−	0.984243i	$-0.443419\pi$
$103$	4.09964e9	0.353638	0.176819	+	0.984243i	$0.443419\pi$
$104$	− 1.03725e10i	− 0.852540i
$105$	0	0
$106$	9.61611e9	0.718572
$107$	1.27166e10i	0.906675i	0.891339	+	0.453337i	$0.149767\pi$
$107$	1.27166e10i	0.906675i	−0.891339	+	0.453337i	$0.850233\pi$
$108$	0	0
$109$	−6.24355e9	−0.405788	−0.202894	−	0.979201i	$-0.565035\pi$
$109$	−6.24355e9	−0.405788	−0.202894	+	0.979201i	$0.565035\pi$
$110$	4.91008e10i	3.04877i
$111$	0	0
$112$	−4.48384e9	−0.254425
$113$	− 2.14512e10i	− 1.16428i	−0.813088	−	0.582141i	$-0.802215\pi$
$113$	− 2.14512e10i	− 1.16428i	0.813088	−	0.582141i	$-0.197785\pi$
$114$	0	0
$115$	1.04880e10	0.521439
$116$	− 4.50102e10i	− 2.14299i
$117$	0	0
$118$	−3.60078e10	−1.57393
$119$	− 1.53379e10i	− 0.642735i
$120$	0	0
$121$	−1.84448e10	−0.711128
$122$	6.22116e10i	2.30182i
$123$	0	0
$124$	−5.86790e10	−2.00159
$125$	1.11407e10i	0.365057i
$126$	0	0
$127$	−4.09118e10	−1.23831	−0.619155	−	0.785269i	$-0.712525\pi$
$127$	−4.09118e10	−1.23831	−0.619155	+	0.785269i	$0.712525\pi$
$128$	4.10287e10i	1.19409i
$129$	0	0
$130$	1.12616e11	3.03308
$131$	− 3.58644e10i	− 0.929624i	−0.885409	−	0.464812i	$-0.846122\pi$
$131$	− 3.58644e10i	− 0.929624i	0.885409	−	0.464812i	$-0.153878\pi$
$132$	0	0
$133$	4.03649e10	0.969942
$134$	5.54767e10i	1.28406i
$135$	0	0
$136$	−3.09303e10	−0.664797
$137$	− 1.57234e10i	− 0.325793i	−0.986643	−	0.162897i	$-0.947916\pi$
$137$	− 1.57234e10i	− 0.325793i	0.986643	−	0.162897i	$-0.0520837\pi$
$138$	0	0
$139$	3.92210e10	0.755865	0.377933	−	0.925833i	$-0.376635\pi$
$139$	3.92210e10	0.755865	0.377933	+	0.925833i	$0.376635\pi$
$140$	7.25079e10i	1.34817i
$141$	0	0
$142$	3.12113e10	0.540592
$143$	1.01794e11i	1.70232i
$144$	0	0
$145$	1.44791e11	2.25892
$146$	− 1.52427e11i	− 2.29772i
$147$	0	0
$148$	−5.34633e10	−0.752917
$149$	4.00162e10i	0.544885i	0.962172	+	0.272442i	$0.0878314\pi$
$149$	4.00162e10i	0.544885i	−0.962172	+	0.272442i	$0.912169\pi$
$150$	0	0
$151$	−7.69749e10	−0.980538	−0.490269	−	0.871571i	$-0.663101\pi$
$151$	−7.69749e10	−0.980538	−0.490269	+	0.871571i	$0.663101\pi$
$152$	− 8.13993e10i	− 1.00324i
$153$	0	0
$154$	−1.11661e11	−1.28914
$155$	− 1.88761e11i	− 2.10986i
$156$	0	0
$157$	1.04406e11	1.09453	0.547265	−	0.836960i	$-0.315669\pi$
$157$	1.04406e11	1.09453	0.547265	+	0.836960i	$0.315669\pi$
$158$	− 1.18571e11i	− 1.20418i
$159$	0	0
$160$	−2.01068e11	−1.91753
$161$	2.38510e10i	0.220484i
$162$	0	0
$163$	−5.17612e10	−0.449849	−0.224924	−	0.974376i	$-0.572213\pi$
$163$	−5.17612e10	−0.449849	−0.224924	+	0.974376i	$0.572213\pi$
$164$	1.20125e11i	1.01255i
$165$	0	0
$166$	1.19138e11	0.945174
$167$	1.42458e11i	1.09675i	0.836234	+	0.548373i	$0.184753\pi$
$167$	1.42458e11i	1.09675i	−0.836234	+	0.548373i	$0.815247\pi$
$168$	0	0
$169$	9.56127e10	0.693557
$170$	− 3.35817e11i	− 2.36515i
$171$	0	0
$172$	−1.34136e11	−0.891051
$173$	3.99044e10i	0.257508i	0.991677	+	0.128754i	$0.0410977\pi$
$173$	3.99044e10i	0.257508i	−0.991677	+	0.128754i	$0.958902\pi$
$174$	0	0
$175$	−1.29291e11	−0.787731
$176$	− 8.87375e10i	− 0.525465i
$177$	0	0
$178$	8.05994e10	0.451057
$179$	1.50313e11i	0.817960i	0.912543	+	0.408980i	$0.134115\pi$
$179$	1.50313e11i	0.817960i	−0.912543	+	0.408980i	$0.865885\pi$
$180$	0	0
$181$	−3.52606e11	−1.81508	−0.907542	−	0.419961i	$-0.862044\pi$
$181$	−3.52606e11	−1.81508	−0.907542	+	0.419961i	$0.862044\pi$
$182$	2.56103e11i	1.28250i
$183$	0	0
$184$	4.80976e10	0.228052
$185$	− 1.71983e11i	− 0.793646i
$186$	0	0
$187$	3.03545e11	1.32744
$188$	− 5.69723e10i	− 0.242591i
$189$	0	0
$190$	8.83771e11	3.56921
$191$	5.78973e10i	0.227768i	0.993494	+	0.113884i	$0.0363291\pi$
$191$	5.78973e10i	0.227768i	−0.993494	+	0.113884i	$0.963671\pi$
$192$	0	0
$193$	−2.62472e11	−0.980160	−0.490080	−	0.871678i	$-0.663032\pi$
$193$	−2.62472e11	−0.980160	−0.490080	+	0.871678i	$0.663032\pi$
$194$	− 2.99119e11i	− 1.08852i
$195$	0	0
$196$	2.46148e11	0.850973
$197$	4.07228e11i	1.37248i	0.727375	+	0.686240i	$0.240740\pi$
$197$	4.07228e11i	1.37248i	−0.727375	+	0.686240i	$0.759260\pi$
$198$	0	0
$199$	−3.32881e10	−0.106665	−0.0533327	−	0.998577i	$-0.516984\pi$
$199$	−3.32881e10	−0.106665	−0.0533327	+	0.998577i	$0.516984\pi$
$200$	2.60726e11i	0.814770i
$201$	0	0
$202$	1.89691e11	0.564013
$203$	3.29272e11i	0.955157i
$204$	0	0
$205$	−3.86424e11	−1.06732
$206$	2.04125e11i	0.550249i
$207$	0	0
$208$	−2.03526e11	−0.522760
$209$	7.98841e11i	2.00322i
$210$	0	0
$211$	−3.89019e11	−0.930162	−0.465081	−	0.885268i	$-0.653975\pi$
$211$	−3.89019e11	−0.930162	−0.465081	+	0.885268i	$0.653975\pi$
$212$	2.81030e11i	0.656257i
$213$	0	0
$214$	−6.33170e11	−1.41076
$215$	− 4.31494e11i	− 0.939253i
$216$	0	0
$217$	4.29266e11	0.892130
$218$	− 3.10872e11i	− 0.631392i
$219$	0	0
$220$	−1.43497e12	−2.78438
$221$	− 6.96202e11i	− 1.32061i
$222$	0	0
$223$	1.66643e11	0.302178	0.151089	−	0.988520i	$-0.451722\pi$
$223$	1.66643e11	0.302178	0.151089	+	0.988520i	$0.451722\pi$
$224$	− 4.57253e11i	− 0.810805i
$225$	0	0
$226$	1.06807e12	1.81159
$227$	− 1.02475e12i	− 1.70016i	−0.526653	−	0.850080i	$-0.676553\pi$
$227$	− 1.02475e12i	− 1.70016i	0.526653	−	0.850080i	$-0.323447\pi$
$228$	0	0
$229$	−7.11191e11	−1.12930	−0.564649	−	0.825331i	$-0.690989\pi$
$229$	−7.11191e11	−1.12930	−0.564649	+	0.825331i	$0.690989\pi$
$230$	5.22207e11i	0.811341i
$231$	0	0
$232$	6.64006e11	0.987943
$233$	4.08645e11i	0.595068i	0.954711	+	0.297534i	$0.0961641\pi$
$233$	4.08645e11i	0.595068i	−0.954711	+	0.297534i	$0.903836\pi$
$234$	0	0
$235$	1.83271e11	0.255714
$236$	− 1.05232e12i	− 1.43744i
$237$	0	0
$238$	7.63690e11	1.00007
$239$	7.45382e11i	0.955849i	0.878401	+	0.477924i	$0.158611\pi$
$239$	7.45382e11i	0.955849i	−0.878401	+	0.477924i	$0.841389\pi$
$240$	0	0
$241$	1.42937e12	1.75816	0.879082	−	0.476670i	$-0.158156\pi$
$241$	1.42937e12	1.75816	0.879082	+	0.476670i	$0.158156\pi$
$242$	− 9.18385e11i	− 1.10649i
$243$	0	0
$244$	−1.81813e12	−2.10221
$245$	7.91819e11i	0.897007i
$246$	0	0
$247$	1.83220e12	1.99291
$248$	− 8.65653e11i	− 0.922753i
$249$	0	0
$250$	−5.54704e11	−0.568017
$251$	9.86209e10i	0.0989921i	0.998774	+	0.0494960i	$0.0157615\pi$
$251$	9.86209e10i	0.0989921i	−0.998774	+	0.0494960i	$0.984238\pi$
$252$	0	0
$253$	−4.72023e11	−0.455366
$254$	− 2.03703e12i	− 1.92677i
$255$	0	0
$256$	−2.94457e11	−0.267807
$257$	3.54000e11i	0.315746i	0.987459	+	0.157873i	$0.0504636\pi$
$257$	3.54000e11i	0.315746i	−0.987459	+	0.157873i	$0.949536\pi$
$258$	0	0
$259$	3.91111e11	0.335584
$260$	3.29120e12i	2.77005i
$261$	0	0
$262$	1.78572e12	1.44646
$263$	− 1.89826e12i	− 1.50861i	−0.656525	−	0.754304i	$-0.727974\pi$
$263$	− 1.89826e12i	− 1.50861i	0.656525	−	0.754304i	$-0.272026\pi$
$264$	0	0
$265$	−9.04030e11	−0.691757
$266$	2.00981e12i	1.50920i
$267$	0	0
$268$	−1.62130e12	−1.17271
$269$	− 2.22590e12i	− 1.58031i	−0.612904	−	0.790157i	$-0.709999\pi$
$269$	− 2.22590e12i	− 1.58031i	0.612904	−	0.790157i	$-0.290001\pi$
$270$	0	0
$271$	−9.34900e11	−0.639615	−0.319807	−	0.947483i	$-0.603618\pi$
$271$	−9.34900e11	−0.639615	−0.319807	+	0.947483i	$0.603618\pi$
$272$	6.06906e11i	0.407640i
$273$	0	0
$274$	7.82880e11	0.506924
$275$	− 2.55873e12i	− 1.62690i
$276$	0	0
$277$	2.54409e11	0.156003	0.0780016	−	0.996953i	$-0.475146\pi$
$277$	2.54409e11	0.156003	0.0780016	+	0.996953i	$0.475146\pi$
$278$	1.95285e12i	1.17610i
$279$	0	0
$280$	−1.06966e12	−0.621522
$281$	3.15241e12i	1.79933i	0.436582	+	0.899664i	$0.356189\pi$
$281$	3.15241e12i	1.79933i	−0.436582	+	0.899664i	$0.643811\pi$
$282$	0	0
$283$	−1.93116e12	−1.06387	−0.531933	−	0.846787i	$-0.678534\pi$
$283$	−1.93116e12	−1.06387	−0.531933	+	0.846787i	$0.678534\pi$
$284$	9.12147e11i	0.493712i
$285$	0	0
$286$	−5.06841e12	−2.64875
$287$	− 8.78778e11i	− 0.451304i
$288$	0	0
$289$	−6.00548e10	−0.0297892
$290$	7.20926e12i	3.51480i
$291$	0	0
$292$	4.45467e12	2.09846
$293$	1.24085e12i	0.574621i	0.957838	+	0.287310i	$0.0927611\pi$
$293$	1.24085e12i	0.574621i	−0.957838	+	0.287310i	$0.907239\pi$
$294$	0	0
$295$	3.38516e12	1.51520
$296$	− 7.88709e11i	− 0.347103i
$297$	0	0
$298$	−1.99244e12	−0.847822
$299$	1.08262e12i	0.453022i
$300$	0	0
$301$	9.81272e11	0.397152
$302$	− 3.83265e12i	− 1.52568i
$303$	0	0
$304$	−1.59720e12	−0.615163
$305$	− 5.84864e12i	− 2.21593i
$306$	0	0
$307$	9.98328e11	0.366085	0.183042	−	0.983105i	$-0.441405\pi$
$307$	9.98328e11	0.366085	0.183042	+	0.983105i	$0.441405\pi$
$308$	− 3.26330e12i	− 1.17734i
$309$	0	0
$310$	9.39859e12	3.28287
$311$	3.19383e12i	1.09777i	0.835900	+	0.548883i	$0.184947\pi$
$311$	3.19383e12i	1.09777i	−0.835900	+	0.548883i	$0.815053\pi$
$312$	0	0
$313$	5.09737e12	1.69678	0.848388	−	0.529375i	$-0.177574\pi$
$313$	5.09737e12	1.69678	0.848388	+	0.529375i	$0.177574\pi$
$314$	5.19848e12i	1.70305i
$315$	0	0
$316$	3.46523e12	1.09976
$317$	1.08170e12i	0.337916i	0.985623	+	0.168958i	$0.0540403\pi$
$317$	1.08170e12i	0.337916i	−0.985623	+	0.168958i	$0.945960\pi$
$318$	0	0
$319$	−6.51646e12	−1.97269
$320$	− 7.99235e12i	− 2.38191i
$321$	0	0
$322$	−1.18756e12	−0.343066
$323$	− 5.46355e12i	− 1.55404i
$324$	0	0
$325$	−5.86863e12	−1.61853
$326$	− 2.57724e12i	− 0.699949i
$327$	0	0
$328$	−1.77213e12	−0.466796
$329$	4.16781e11i	0.108126i
$330$	0	0
$331$	−6.90462e12	−1.73780	−0.868900	−	0.494987i	$-0.835173\pi$
$331$	−6.90462e12	−1.73780	−0.868900	+	0.494987i	$0.835173\pi$
$332$	3.48181e12i	0.863207i
$333$	0	0
$334$	−7.09314e12	−1.70650
$335$	− 5.21547e12i	− 1.23615i
$336$	0	0
$337$	4.86544e12	1.11937	0.559683	−	0.828707i	$-0.310923\pi$
$337$	4.86544e12	1.11937	0.559683	+	0.828707i	$0.310923\pi$
$338$	4.76065e12i	1.07915i
$339$	0	0
$340$	9.81423e12	2.16004
$341$	8.49539e12i	1.84252i
$342$	0	0
$343$	−4.80766e12	−1.01266
$344$	− 1.97882e12i	− 0.410784i
$345$	0	0
$346$	−1.98688e12	−0.400673
$347$	− 6.01051e12i	− 1.19471i	−0.801976	−	0.597357i	$-0.796218\pi$
$347$	− 6.01051e12i	− 1.19471i	0.801976	−	0.597357i	$-0.203782\pi$
$348$	0	0
$349$	−6.59283e12	−1.27334	−0.636671	−	0.771136i	$-0.719689\pi$
$349$	−6.59283e12	−1.27334	−0.636671	+	0.771136i	$0.719689\pi$
$350$	− 6.43752e12i	− 1.22568i
$351$	0	0
$352$	9.04927e12	1.67456
$353$	2.76327e12i	0.504138i	0.967709	+	0.252069i	$0.0811110\pi$
$353$	2.76327e12i	0.504138i	−0.967709	+	0.252069i	$0.918889\pi$
$354$	0	0
$355$	−2.93423e12	−0.520419
$356$	2.35551e12i	0.411941i
$357$	0	0
$358$	−7.48423e12	−1.27272
$359$	− 2.99046e12i	− 0.501493i	−0.968053	−	0.250747i	$-0.919324\pi$
$359$	− 2.99046e12i	− 0.501493i	0.968053	−	0.250747i	$-0.0806761\pi$
$360$	0	0
$361$	8.24737e12	1.34518
$362$	− 1.75566e13i	− 2.82421i
$363$	0	0
$364$	−7.48460e12	−1.17128
$365$	1.43300e13i	2.21198i
$366$	0	0
$367$	1.23302e13	1.85200	0.926001	−	0.377521i	$-0.123223\pi$
$367$	1.23302e13	1.85200	0.926001	+	0.377521i	$0.123223\pi$
$368$	− 9.43759e11i	− 0.139837i
$369$	0	0
$370$	8.56319e12	1.23489
$371$	− 2.05588e12i	− 0.292501i
$372$	0	0
$373$	−8.67713e12	−1.20180	−0.600900	−	0.799324i	$-0.705191\pi$
$373$	−8.67713e12	−1.20180	−0.600900	+	0.799324i	$0.705191\pi$
$374$	1.51138e13i	2.06545i
$375$	0	0
$376$	8.40475e11	0.111837
$377$	1.49460e13i	1.96253i
$378$	0	0
$379$	7.31888e12	0.935941	0.467970	−	0.883744i	$-0.344985\pi$
$379$	7.31888e12	0.935941	0.467970	+	0.883744i	$0.344985\pi$
$380$	2.58281e13i	3.25968i
$381$	0	0
$382$	−2.88276e12	−0.354399
$383$	− 9.00609e12i	− 1.09280i	−0.837523	−	0.546402i	$-0.815997\pi$
$383$	− 9.00609e12i	− 1.09280i	0.837523	−	0.546402i	$-0.184003\pi$
$384$	0	0
$385$	1.04975e13	1.24103
$386$	− 1.30687e13i	− 1.52510i
$387$	0	0
$388$	8.74172e12	0.994119
$389$	− 3.26405e12i	− 0.366445i	−0.983071	−	0.183223i	$-0.941347\pi$
$389$	− 3.26405e12i	− 0.366445i	0.983071	−	0.183223i	$-0.0586529\pi$
$390$	0	0
$391$	3.22833e12	0.353260
$392$	3.63126e12i	0.392308i
$393$	0	0
$394$	−2.02763e13	−2.13553
$395$	1.11471e13i	1.15925i
$396$	0	0
$397$	−2.38755e12	−0.242103	−0.121051	−	0.992646i	$-0.538627\pi$
$397$	−2.38755e12	−0.242103	−0.121051	+	0.992646i	$0.538627\pi$
$398$	− 1.65745e12i	− 0.165968i
$399$	0	0
$400$	5.11590e12	0.499600
$401$	− 8.31014e12i	− 0.801469i	−0.916194	−	0.400734i	$-0.868755\pi$
$401$	− 8.31014e12i	− 0.801469i	0.916194	−	0.400734i	$-0.131245\pi$
$402$	0	0
$403$	1.94848e13	1.83303
$404$	5.54370e12i	0.515102i
$405$	0	0
$406$	−1.63948e13	−1.48619
$407$	7.74028e12i	0.693082i
$408$	0	0
$409$	−4.06819e12	−0.355455	−0.177727	−	0.984080i	$-0.556875\pi$
$409$	−4.06819e12	−0.355455	−0.177727	+	0.984080i	$0.556875\pi$
$410$	− 1.92404e13i	− 1.66072i
$411$	0	0
$412$	−5.96553e12	−0.502531
$413$	7.69828e12i	0.640684i
$414$	0	0
$415$	−1.12005e13	−0.909903
$416$	− 2.07551e13i	− 1.66594i
$417$	0	0
$418$	−3.97750e13	−3.11695
$419$	− 1.97032e12i	− 0.152569i	−0.997086	−	0.0762844i	$-0.975694\pi$
$419$	− 1.97032e12i	− 0.152569i	0.997086	−	0.0762844i	$-0.0243057\pi$
$420$	0	0
$421$	−6.16396e12	−0.466068	−0.233034	−	0.972469i	$-0.574865\pi$
$421$	−6.16396e12	−0.466068	−0.233034	+	0.972469i	$0.574865\pi$
$422$	− 1.93696e13i	− 1.44730i
$423$	0	0
$424$	−4.14586e12	−0.302542
$425$	1.75000e13i	1.26210i
$426$	0	0
$427$	1.33005e13	0.936979
$428$	− 1.85044e13i	− 1.28841i
$429$	0	0
$430$	2.14845e13	1.46145
$431$	− 1.93378e13i	− 1.30023i	−0.759834	−	0.650117i	$-0.774720\pi$
$431$	− 1.93378e13i	− 1.30023i	0.759834	−	0.650117i	$-0.225280\pi$
$432$	0	0
$433$	−5.95811e12	−0.391443	−0.195722	−	0.980660i	$-0.562705\pi$
$433$	−5.95811e12	−0.391443	−0.195722	+	0.980660i	$0.562705\pi$
$434$	2.13736e13i	1.38812i
$435$	0	0
$436$	9.08521e12	0.576637
$437$	8.49600e12i	0.533099i
$438$	0	0
$439$	−5.87212e12	−0.360141	−0.180070	−	0.983654i	$-0.557633\pi$
$439$	−5.87212e12	−0.360141	−0.180070	+	0.983654i	$0.557633\pi$
$440$	− 2.11691e13i	− 1.28363i
$441$	0	0
$442$	3.46646e13	2.05482
$443$	− 8.54709e12i	− 0.500956i	−0.968122	−	0.250478i	$-0.919412\pi$
$443$	− 8.54709e12i	− 0.500956i	0.968122	−	0.250478i	$-0.0805878\pi$
$444$	0	0
$445$	−7.57731e12	−0.434225
$446$	8.29730e12i	0.470178i
$447$	0	0
$448$	1.81756e13	1.00716
$449$	2.85492e13i	1.56445i	0.622995	+	0.782226i	$0.285916\pi$
$449$	2.85492e13i	1.56445i	−0.622995	+	0.782226i	$0.714084\pi$
$450$	0	0
$451$	1.73914e13	0.932080
$452$	3.12144e13i	1.65448i
$453$	0	0
$454$	5.10234e13	2.64539
$455$	− 2.40768e13i	− 1.23464i
$456$	0	0
$457$	−2.95007e13	−1.47997	−0.739983	−	0.672626i	$-0.765166\pi$
$457$	−2.95007e13	−1.47997	−0.739983	+	0.672626i	$0.765166\pi$
$458$	− 3.54109e13i	− 1.75715i
$459$	0	0
$460$	−1.52615e13	−0.740981
$461$	− 3.35492e13i	− 1.61130i	−0.592390	−	0.805651i	$-0.701816\pi$
$461$	− 3.35492e13i	− 1.61130i	0.592390	−	0.805651i	$-0.298184\pi$
$462$	0	0
$463$	4.67378e11	0.0219666	0.0109833	−	0.999940i	$-0.496504\pi$
$463$	4.67378e11	0.0219666	0.0109833	+	0.999940i	$0.496504\pi$
$464$	− 1.30289e13i	− 0.605786i
$465$	0	0
$466$	−2.03468e13	−0.925905
$467$	− 3.90493e12i	− 0.175804i	−0.996129	−	0.0879020i	$-0.971984\pi$
$467$	− 3.90493e12i	− 0.175804i	0.996129	−	0.0879020i	$-0.0280162\pi$
$468$	0	0
$469$	1.18606e13	0.522690
$470$	9.12523e12i	0.397882i
$471$	0	0
$472$	1.55243e13	0.662675
$473$	1.94199e13i	0.820239i
$474$	0	0
$475$	−4.60549e13	−1.90462
$476$	2.23188e13i	0.913347i
$477$	0	0
$478$	−3.71132e13	−1.48727
$479$	− 2.17678e13i	− 0.863249i	−0.902053	−	0.431625i	$-0.857941\pi$
$479$	− 2.17678e13i	− 0.863249i	0.902053	−	0.431625i	$-0.142059\pi$
$480$	0	0
$481$	1.77529e13	0.689514
$482$	7.11697e13i	2.73565i
$483$	0	0
$484$	2.68397e13	1.01054
$485$	2.81207e13i	1.04790i
$486$	0	0
$487$	−2.28334e13	−0.833537	−0.416769	−	0.909013i	$-0.636837\pi$
$487$	−2.28334e13	−0.833537	−0.416769	+	0.909013i	$0.636837\pi$
$488$	− 2.68217e13i	− 0.969141i
$489$	0	0
$490$	−3.94254e13	−1.39571
$491$	1.36801e13i	0.479381i	0.970849	+	0.239691i	$0.0770460\pi$
$491$	1.36801e13i	0.479381i	−0.970849	+	0.239691i	$0.922954\pi$
$492$	0	0
$493$	4.45683e13	1.53035
$494$	9.12268e13i	3.10090i
$495$	0	0
$496$	−1.69856e13	−0.565813
$497$	− 6.67282e12i	− 0.220053i
$498$	0	0
$499$	−1.47086e13	−0.475411	−0.237705	−	0.971337i	$-0.576395\pi$
$499$	−1.47086e13	−0.475411	−0.237705	+	0.971337i	$0.576395\pi$
$500$	− 1.62112e13i	− 0.518758i
$501$	0	0
$502$	−4.91043e12	−0.154028
$503$	− 1.65433e13i	− 0.513785i	−0.966440	−	0.256892i	$-0.917301\pi$
$503$	− 1.65433e13i	− 0.513785i	0.966440	−	0.256892i	$-0.0826986\pi$
$504$	0	0
$505$	−1.78332e13	−0.542966
$506$	− 2.35025e13i	− 0.708535i
$507$	0	0
$508$	5.95322e13	1.75968
$509$	2.98840e13i	0.874681i	0.899296	+	0.437341i	$0.144080\pi$
$509$	2.98840e13i	0.874681i	−0.899296	+	0.437341i	$0.855920\pi$
$510$	0	0
$511$	−3.25882e13	−0.935310
$512$	2.73521e13i	0.777393i
$513$	0	0
$514$	−1.76260e13	−0.491290
$515$	− 1.91902e13i	− 0.529716i
$516$	0	0
$517$	−8.24830e12	−0.223312
$518$	1.94738e13i	0.522157i
$519$	0	0
$520$	−4.85529e13	−1.27702
$521$	− 5.93982e13i	− 1.54734i	−0.633590	−	0.773669i	$-0.718420\pi$
$521$	− 5.93982e13i	− 1.54734i	0.633590	−	0.773669i	$-0.281580\pi$
$522$	0	0
$523$	−1.90756e13	−0.487494	−0.243747	−	0.969839i	$-0.578377\pi$
$523$	−1.90756e13	−0.487494	−0.243747	+	0.969839i	$0.578377\pi$
$524$	5.21876e13i	1.32103i
$525$	0	0
$526$	9.45160e13	2.34734
$527$	− 5.81029e13i	− 1.42937i
$528$	0	0
$529$	3.64063e13	0.878818
$530$	− 4.50125e13i	− 1.07635i
$531$	0	0
$532$	−5.87364e13	−1.37832
$533$	− 3.98885e13i	− 0.927282i
$534$	0	0
$535$	5.95256e13	1.35811
$536$	− 2.39180e13i	− 0.540631i
$537$	0	0
$538$	1.10829e14	2.45892
$539$	− 3.56367e13i	− 0.783345i
$540$	0	0
$541$	6.21987e13	1.34213	0.671066	−	0.741398i	$-0.265837\pi$
$541$	6.21987e13	1.34213	0.671066	+	0.741398i	$0.265837\pi$
$542$	− 4.65495e13i	− 0.995219i
$543$	0	0
$544$	−6.18910e13	−1.29907
$545$	2.92257e13i	0.607830i
$546$	0	0
$547$	−1.20637e13	−0.246345	−0.123172	−	0.992385i	$-0.539307\pi$
$547$	−1.20637e13	−0.246345	−0.123172	+	0.992385i	$0.539307\pi$
$548$	2.28796e13i	0.462963i
$549$	0	0
$550$	1.27402e14	2.53140
$551$	1.17290e14i	2.30943i
$552$	0	0
$553$	−2.53499e13	−0.490175
$554$	1.26673e13i	0.242736i
$555$	0	0
$556$	−5.70719e13	−1.07411
$557$	− 1.13360e13i	− 0.211439i	−0.994396	−	0.105720i	$-0.966285\pi$
$557$	− 1.13360e13i	− 0.211439i	0.994396	−	0.105720i	$-0.0337146\pi$
$558$	0	0
$559$	4.45408e13	0.816016
$560$	2.09886e13i	0.381104i
$561$	0	0
$562$	−1.56961e14	−2.79969
$563$	− 9.31119e13i	− 1.64613i	−0.567950	−	0.823063i	$-0.692263\pi$
$563$	− 9.31119e13i	− 1.64613i	0.567950	−	0.823063i	$-0.307737\pi$
$564$	0	0
$565$	−1.00412e14	−1.74398
$566$	− 9.61544e13i	− 1.65534i
$567$	0	0
$568$	−1.34563e13	−0.227606
$569$	7.77452e13i	1.30350i	0.758433	+	0.651752i	$0.225966\pi$
$569$	7.77452e13i	1.30350i	−0.758433	+	0.651752i	$0.774034\pi$
$570$	0	0
$571$	1.71466e13	0.282486	0.141243	−	0.989975i	$-0.454890\pi$
$571$	1.71466e13	0.282486	0.141243	+	0.989975i	$0.454890\pi$
$572$	− 1.48124e14i	− 2.41905i
$573$	0	0
$574$	4.37552e13	0.702215
$575$	− 2.72132e13i	− 0.432952i
$576$	0	0
$577$	1.62170e13	0.253567	0.126783	−	0.991930i	$-0.459535\pi$
$577$	1.62170e13	0.253567	0.126783	+	0.991930i	$0.459535\pi$
$578$	− 2.99018e12i	− 0.0463509i
$579$	0	0
$580$	−2.10690e14	−3.20999
$581$	− 2.54712e13i	− 0.384742i
$582$	0	0
$583$	4.06868e13	0.604103
$584$	6.57169e13i	0.967415i
$585$	0	0
$586$	−6.17831e13	−0.894091
$587$	− 3.73351e13i	− 0.535707i	−0.963460	−	0.267853i	$-0.913686\pi$
$587$	− 3.73351e13i	− 0.535707i	0.963460	−	0.267853i	$-0.0863143\pi$
$588$	0	0
$589$	1.52910e14	2.15704
$590$	1.68550e14i	2.35760i
$591$	0	0
$592$	−1.54758e13	−0.212836
$593$	2.48218e13i	0.338501i	0.985573	+	0.169250i	$0.0541347\pi$
$593$	2.48218e13i	0.338501i	−0.985573	+	0.169250i	$0.945865\pi$
$594$	0	0
$595$	−7.17960e13	−0.962755
$596$	− 5.82290e13i	− 0.774298i
$597$	0	0
$598$	−5.39046e13	−0.704888
$599$	6.53144e13i	0.846983i	0.905900	+	0.423491i	$0.139196\pi$
$599$	6.53144e13i	0.846983i	−0.905900	+	0.423491i	$0.860804\pi$
$600$	0	0
$601$	−1.35148e14	−1.72360	−0.861801	−	0.507247i	$-0.830663\pi$
$601$	−1.35148e14	−1.72360	−0.861801	+	0.507247i	$0.830663\pi$
$602$	4.88584e13i	0.617955i
$603$	0	0
$604$	1.12009e14	1.39338
$605$	8.63392e13i	1.06520i
$606$	0	0
$607$	1.99544e13	0.242156	0.121078	−	0.992643i	$-0.461365\pi$
$607$	1.99544e13	0.242156	0.121078	+	0.992643i	$0.461365\pi$
$608$	− 1.62879e14i	− 1.96041i
$609$	0	0
$610$	2.91209e14	3.44791
$611$	1.89181e13i	0.222162i
$612$	0	0
$613$	1.37187e14	1.58493	0.792466	−	0.609917i	$-0.208797\pi$
$613$	1.37187e14	1.58493	0.792466	+	0.609917i	$0.208797\pi$
$614$	4.97077e13i	0.569615i
$615$	0	0
$616$	4.81413e13	0.542768
$617$	− 5.55852e13i	− 0.621631i	−0.950470	−	0.310816i	$-0.899398\pi$
$617$	− 5.55852e13i	− 0.621631i	0.950470	−	0.310816i	$-0.100602\pi$
$618$	0	0
$619$	1.57747e14	1.73584	0.867918	−	0.496707i	$-0.165458\pi$
$619$	1.57747e14	1.73584	0.867918	+	0.496707i	$0.165458\pi$
$620$	2.74673e14i	2.99818i
$621$	0	0
$622$	−1.59024e14	−1.70809
$623$	− 1.72318e13i	− 0.183607i
$624$	0	0
$625$	−6.64608e13	−0.696892
$626$	2.53803e14i	2.64013i
$627$	0	0
$628$	−1.51925e14	−1.55536
$629$	− 5.29384e13i	− 0.537672i
$630$	0	0
$631$	6.07015e13	0.606810	0.303405	−	0.952862i	$-0.401877\pi$
$631$	6.07015e13	0.606810	0.303405	+	0.952862i	$0.401877\pi$
$632$	5.11203e13i	0.507000i
$633$	0	0
$634$	−5.38587e13	−0.525786
$635$	1.91506e14i	1.85487i
$636$	0	0
$637$	−8.17352e13	−0.779313
$638$	− 3.24461e14i	− 3.06944i
$639$	0	0
$640$	1.92053e14	1.78863
$641$	− 2.29070e13i	− 0.211679i	−0.994383	−	0.105839i	$-0.966247\pi$
$641$	− 2.29070e13i	− 0.211679i	0.994383	−	0.105839i	$-0.0337530\pi$
$642$	0	0
$643$	−9.95929e13	−0.906095	−0.453047	−	0.891486i	$-0.649663\pi$
$643$	−9.95929e13	−0.906095	−0.453047	+	0.891486i	$0.649663\pi$
$644$	− 3.47065e13i	− 0.313315i
$645$	0	0
$646$	2.72035e14	2.41803
$647$	4.05682e13i	0.357819i	0.983865	+	0.178910i	$0.0572570\pi$
$647$	4.05682e13i	0.357819i	−0.983865	+	0.178910i	$0.942743\pi$
$648$	0	0
$649$	−1.52353e14	−1.32320
$650$	− 2.92204e14i	− 2.51837i
$651$	0	0
$652$	7.53196e13	0.639249
$653$	6.86364e13i	0.578081i	0.957317	+	0.289041i	$0.0933363\pi$
$653$	6.86364e13i	0.578081i	−0.957317	+	0.289041i	$0.906664\pi$
$654$	0	0
$655$	−1.67879e14	−1.39249
$656$	3.47723e13i	0.286229i
$657$	0	0
$658$	−2.07519e13	−0.168240
$659$	5.77017e13i	0.464260i	0.972685	+	0.232130i	$0.0745695\pi$
$659$	5.77017e13i	0.464260i	−0.972685	+	0.232130i	$0.925430\pi$
$660$	0	0
$661$	−5.55344e13	−0.440103	−0.220052	−	0.975488i	$-0.570623\pi$
$661$	−5.55344e13	−0.440103	−0.220052	+	0.975488i	$0.570623\pi$
$662$	− 3.43788e14i	− 2.70396i
$663$	0	0
$664$	−5.13649e13	−0.397948
$665$	− 1.88946e14i	− 1.45288i
$666$	0	0
$667$	−6.93052e13	−0.524973
$668$	− 2.07297e14i	− 1.55851i
$669$	0	0
$670$	2.59683e14	1.92340
$671$	2.63224e14i	1.93514i
$672$	0	0
$673$	1.44199e13	0.104445	0.0522223	−	0.998635i	$-0.483370\pi$
$673$	1.44199e13	0.104445	0.0522223	+	0.998635i	$0.483370\pi$
$674$	2.42255e14i	1.74170i
$675$	0	0
$676$	−1.39130e14	−0.985566
$677$	2.11299e13i	0.148578i	0.997237	+	0.0742889i	$0.0236687\pi$
$677$	2.11299e13i	0.148578i	−0.997237	+	0.0742889i	$0.976331\pi$
$678$	0	0
$679$	−6.39501e13	−0.443090
$680$	1.44783e14i	0.995802i
$681$	0	0
$682$	−4.22993e14	−2.86689
$683$	2.09343e14i	1.40849i	0.709956	+	0.704246i	$0.248715\pi$
$683$	2.09343e14i	1.40849i	−0.709956	+	0.704246i	$0.751285\pi$
$684$	0	0
$685$	−7.36002e13	−0.488007
$686$	− 2.39378e14i	− 1.57566i
$687$	0	0
$688$	−3.88279e13	−0.251885
$689$	− 9.33181e13i	− 0.600994i
$690$	0	0
$691$	−7.20104e13	−0.457093	−0.228547	−	0.973533i	$-0.573397\pi$
$691$	−7.20104e13	−0.457093	−0.228547	+	0.973533i	$0.573397\pi$
$692$	− 5.80663e13i	− 0.365927i
$693$	0	0
$694$	2.99269e14	1.85893
$695$	− 1.83591e14i	− 1.13221i
$696$	0	0
$697$	−1.18946e14	−0.723079
$698$	− 3.28263e14i	− 1.98128i
$699$	0	0
$700$	1.88136e14	1.11939
$701$	− 7.58881e13i	− 0.448316i	−0.974553	−	0.224158i	$-0.928037\pi$
$701$	− 7.58881e13i	− 0.448316i	0.974553	−	0.224158i	$-0.0719631\pi$
$702$	0	0
$703$	1.39318e14	0.811393
$704$	3.59704e14i	2.08009i
$705$	0	0
$706$	−1.37586e14	−0.784422
$707$	− 4.05550e13i	− 0.229587i
$708$	0	0
$709$	−1.75445e13	−0.0979287	−0.0489643	−	0.998801i	$-0.515592\pi$
$709$	−1.75445e13	−0.0979287	−0.0489643	+	0.998801i	$0.515592\pi$
$710$	− 1.46098e14i	− 0.809754i
$711$	0	0
$712$	−3.47493e13	−0.189909
$713$	9.03520e13i	0.490332i
$714$	0	0
$715$	4.76491e14	2.54991
$716$	− 2.18726e14i	− 1.16235i
$717$	0	0
$718$	1.48898e14	0.780307
$719$	− 4.70850e13i	− 0.245041i	−0.992466	−	0.122520i	$-0.960902\pi$
$719$	− 4.70850e13i	− 0.245041i	0.992466	−	0.122520i	$-0.0390976\pi$
$720$	0	0
$721$	4.36409e13	0.223984
$722$	4.10644e14i	2.09305i
$723$	0	0
$724$	5.13090e14	2.57929
$725$	− 3.75688e14i	− 1.87559i
$726$	0	0
$727$	1.55850e14	0.767424	0.383712	−	0.923453i	$-0.374646\pi$
$727$	1.55850e14	0.767424	0.383712	+	0.923453i	$0.374646\pi$
$728$	− 1.10415e14i	− 0.539974i
$729$	0	0
$730$	−7.13503e14	−3.44177
$731$	− 1.32819e14i	− 0.636316i
$732$	0	0
$733$	3.84004e14	1.81475	0.907374	−	0.420324i	$-0.138084\pi$
$733$	3.84004e14	1.81475	0.907374	+	0.420324i	$0.138084\pi$
$734$	6.13935e14i	2.88165i
$735$	0	0
$736$	9.62426e13	0.445634
$737$	2.34728e14i	1.07951i
$738$	0	0
$739$	−4.57239e13	−0.207453	−0.103727	−	0.994606i	$-0.533077\pi$
$739$	−4.57239e13	−0.207453	−0.103727	+	0.994606i	$0.533077\pi$
$740$	2.50259e14i	1.12780i
$741$	0	0
$742$	1.02364e14	0.455122
$743$	2.06556e14i	0.912207i	0.889927	+	0.456103i	$0.150755\pi$
$743$	2.06556e14i	0.912207i	−0.889927	+	0.456103i	$0.849245\pi$
$744$	0	0
$745$	1.87314e14	0.816184
$746$	− 4.32042e14i	− 1.86996i
$747$	0	0
$748$	−4.41700e14	−1.88634
$749$	1.35369e14i	0.574261i
$750$	0	0
$751$	−2.64381e14	−1.10670	−0.553352	−	0.832948i	$-0.686651\pi$
$751$	−2.64381e14	−1.10670	−0.553352	+	0.832948i	$0.686651\pi$
$752$	− 1.64916e13i	− 0.0685762i
$753$	0	0
$754$	−7.44173e14	−3.05364
$755$	3.60315e14i	1.46875i
$756$	0	0
$757$	1.09893e14	0.442069	0.221034	−	0.975266i	$-0.429057\pi$
$757$	1.09893e14	0.442069	0.221034	+	0.975266i	$0.429057\pi$
$758$	3.64414e14i	1.45629i
$759$	0	0
$760$	−3.81026e14	−1.50275
$761$	− 2.01468e14i	− 0.789374i	−0.918816	−	0.394687i	$-0.870853\pi$
$761$	− 2.01468e14i	− 0.789374i	0.918816	−	0.394687i	$-0.129147\pi$
$762$	0	0
$763$	−6.64629e13	−0.257014
$764$	− 8.42485e13i	− 0.323665i
$765$	0	0
$766$	4.48421e14	1.70037
$767$	3.49432e14i	1.31639i
$768$	0	0
$769$	−2.53136e14	−0.941288	−0.470644	−	0.882323i	$-0.655978\pi$
$769$	−2.53136e14	−0.941288	−0.470644	+	0.882323i	$0.655978\pi$
$770$	5.22681e14i	1.93100i
$771$	0	0
$772$	3.81933e14	1.39284
$773$	− 1.36109e14i	− 0.493162i	−0.969122	−	0.246581i	$-0.920693\pi$
$773$	− 1.36109e14i	− 0.493162i	0.969122	−	0.246581i	$-0.0793072\pi$
$774$	0	0
$775$	−4.89777e14	−1.75182
$776$	1.28961e14i	0.458300i
$777$	0	0
$778$	1.62520e14	0.570176
$779$	− 3.13031e14i	− 1.09119i
$780$	0	0
$781$	1.32058e14	0.454476
$782$	1.60741e14i	0.549660i
$783$	0	0
$784$	7.12516e13	0.240555
$785$	− 4.88719e14i	− 1.63950i
$786$	0	0
$787$	−1.97744e14	−0.654984	−0.327492	−	0.944854i	$-0.606203\pi$
$787$	−1.97744e14	−0.654984	−0.327492	+	0.944854i	$0.606203\pi$
$788$	− 5.92572e14i	− 1.95034i
$789$	0	0
$790$	−5.55025e14	−1.80375
$791$	− 2.28349e14i	− 0.737423i
$792$	0	0
$793$	6.03723e14	1.92518
$794$	− 1.18878e14i	− 0.376704i
$795$	0	0
$796$	4.84387e13	0.151575
$797$	− 4.43059e14i	− 1.37775i	−0.724881	−	0.688874i	$-0.758105\pi$
$797$	− 4.43059e14i	− 1.37775i	0.724881	−	0.688874i	$-0.241895\pi$
$798$	0	0
$799$	5.64129e13	0.173239
$800$	5.21709e14i	1.59213i
$801$	0	0
$802$	4.13770e14	1.24706
$803$	− 6.44936e14i	− 1.93170i
$804$	0	0
$805$	1.11645e14	0.330264
$806$	9.70165e14i	2.85214i
$807$	0	0
$808$	−8.17826e13	−0.237467
$809$	3.65168e14i	1.05378i	0.849933	+	0.526891i	$0.176642\pi$
$809$	3.65168e14i	1.05378i	−0.849933	+	0.526891i	$0.823358\pi$
$810$	0	0
$811$	−1.47814e14	−0.421320	−0.210660	−	0.977559i	$-0.567561\pi$
$811$	−1.47814e14	−0.421320	−0.210660	+	0.977559i	$0.567561\pi$
$812$	− 4.79136e14i	− 1.35731i
$813$	0	0
$814$	−3.85396e14	−1.07841
$815$	2.42291e14i	0.673829i
$816$	0	0
$817$	3.49540e14	0.960255
$818$	− 2.02559e14i	− 0.553076i
$819$	0	0
$820$	5.62300e14	1.51670
$821$	− 6.23937e14i	− 1.67273i	−0.548175	−	0.836364i	$-0.684677\pi$
$821$	− 6.23937e14i	− 1.67273i	0.548175	−	0.836364i	$-0.315323\pi$
$822$	0	0
$823$	−1.00471e14	−0.266097	−0.133048	−	0.991110i	$-0.542477\pi$
$823$	−1.00471e14	−0.266097	−0.133048	+	0.991110i	$0.542477\pi$
$824$	− 8.80056e13i	− 0.231672i
$825$	0	0
$826$	−3.83305e14	−0.996882
$827$	6.85722e14i	1.77264i	0.463072	+	0.886320i	$0.346747\pi$
$827$	6.85722e14i	1.77264i	−0.463072	+	0.886320i	$0.653253\pi$
$828$	0	0
$829$	−5.78466e13	−0.147742	−0.0738712	−	0.997268i	$-0.523535\pi$
$829$	−5.78466e13	−0.147742	−0.0738712	+	0.997268i	$0.523535\pi$
$830$	− 5.57681e14i	− 1.41578i
$831$	0	0
$832$	8.25007e14	2.06938
$833$	2.43731e14i	0.607696i
$834$	0	0
$835$	6.66840e14	1.64282
$836$	− 1.16242e15i	− 2.84664i
$837$	0	0
$838$	9.81039e13	0.237392
$839$	6.24170e14i	1.50139i	0.660650	+	0.750694i	$0.270281\pi$
$839$	6.24170e14i	1.50139i	−0.660650	+	0.750694i	$0.729719\pi$
$840$	0	0
$841$	−5.36077e14	−1.27423
$842$	− 3.06909e14i	− 0.725187i
$843$	0	0
$844$	5.66076e14	1.32179
$845$	− 4.47558e14i	− 1.03888i
$846$	0	0
$847$	−1.96346e14	−0.450407
$848$	8.13489e13i	0.185512i
$849$	0	0
$850$	−8.71343e14	−1.96379
$851$	8.23210e13i	0.184443i
$852$	0	0
$853$	−7.49866e14	−1.66050	−0.830250	−	0.557392i	$-0.811802\pi$
$853$	−7.49866e14	−1.66050	−0.830250	+	0.557392i	$0.811802\pi$
$854$	6.62246e14i	1.45791i
$855$	0	0
$856$	2.72983e14	0.593973
$857$	− 1.59864e14i	− 0.345818i	−0.984938	−	0.172909i	$-0.944683\pi$
$857$	− 1.59864e14i	− 0.345818i	0.984938	−	0.172909i	$-0.0553166\pi$
$858$	0	0
$859$	−2.33225e13	−0.0498665	−0.0249332	−	0.999689i	$-0.507937\pi$
$859$	−2.33225e13	−0.0498665	−0.0249332	+	0.999689i	$0.507937\pi$
$860$	6.27883e14i	1.33471i
$861$	0	0
$862$	9.62849e14	2.02312
$863$	− 4.65961e14i	− 0.973409i	−0.873567	−	0.486704i	$-0.838199\pi$
$863$	− 4.65961e14i	− 0.973409i	0.873567	−	0.486704i	$-0.161801\pi$
$864$	0	0
$865$	1.86790e14	0.385721
$866$	− 2.96660e14i	− 0.609072i
$867$	0	0
$868$	−6.24641e14	−1.26775
$869$	− 5.01687e14i	− 1.01236i
$870$	0	0
$871$	5.38365e14	1.07395
$872$	1.34028e14i	0.265836i
$873$	0	0
$874$	−4.23024e14	−0.829483
$875$	1.18593e14i	0.231217i
$876$	0	0
$877$	−9.69036e14	−1.86785	−0.933925	−	0.357469i	$-0.883640\pi$
$877$	−9.69036e14	−1.86785	−0.933925	+	0.357469i	$0.883640\pi$
$878$	− 2.92378e14i	− 0.560367i
$879$	0	0
$880$	−4.15375e14	−0.787095
$881$	− 5.28473e14i	− 0.995733i	−0.867254	−	0.497867i	$-0.834117\pi$
$881$	− 5.28473e14i	− 0.995733i	0.867254	−	0.497867i	$-0.165883\pi$
$882$	0	0
$883$	−8.85733e14	−1.65006	−0.825029	−	0.565090i	$-0.808841\pi$
$883$	−8.85733e14	−1.65006	−0.825029	+	0.565090i	$0.808841\pi$
$884$	1.01307e15i	1.87663i
$885$	0	0
$886$	4.25568e14	0.779471
$887$	− 3.61619e14i	− 0.658617i	−0.944222	−	0.329309i	$-0.893184\pi$
$887$	− 3.61619e14i	− 0.658617i	0.944222	−	0.329309i	$-0.106816\pi$
$888$	0	0
$889$	−4.35508e14	−0.784310
$890$	− 3.77281e14i	− 0.675640i
$891$	0	0
$892$	−2.42488e14	−0.429404
$893$	1.48462e14i	0.261432i
$894$	0	0
$895$	7.03608e14	1.22522
$896$	4.36753e14i	0.756303i
$897$	0	0
$898$	−1.42149e15	−2.43423
$899$	1.24734e15i	2.12416i
$900$	0	0
$901$	−2.78271e14	−0.468645
$902$	8.65936e14i	1.45028i
$903$	0	0
$904$	−4.60485e14	−0.762735
$905$	1.65053e15i	2.71882i
$906$	0	0
$907$	4.80092e14	0.782146	0.391073	−	0.920360i	$-0.372104\pi$
$907$	4.80092e14	0.782146	0.391073	+	0.920360i	$0.372104\pi$
$908$	1.49116e15i	2.41598i
$909$	0	0
$910$	1.19881e15	1.92106
$911$	8.66322e14i	1.38066i	0.723493	+	0.690331i	$0.242535\pi$
$911$	8.66322e14i	1.38066i	−0.723493	+	0.690331i	$0.757465\pi$
$912$	0	0
$913$	5.04088e14	0.794607
$914$	− 1.46887e15i	− 2.30278i
$915$	0	0
$916$	1.03488e15	1.60477
$917$	− 3.81779e14i	− 0.588797i
$918$	0	0
$919$	2.86617e14	0.437244	0.218622	−	0.975810i	$-0.429844\pi$
$919$	2.86617e14	0.437244	0.218622	+	0.975810i	$0.429844\pi$
$920$	− 2.25142e14i	− 0.341600i
$921$	0	0
$922$	1.67044e15	2.50713
$923$	− 3.02885e14i	− 0.452136i
$924$	0	0
$925$	−4.46244e14	−0.658966
$926$	2.32712e13i	0.0341793i
$927$	0	0
$928$	1.32867e15	1.93053
$929$	− 9.67048e14i	− 1.39756i	−0.715338	−	0.698779i	$-0.753727\pi$
$929$	− 9.67048e14i	− 1.39756i	0.715338	−	0.698779i	$-0.246273\pi$
$930$	0	0
$931$	−6.41428e14	−0.917064
$932$	− 5.94634e14i	− 0.845610i
$933$	0	0
$934$	1.94430e14	0.273545
$935$	− 1.42088e15i	− 1.98838i
$936$	0	0
$937$	8.16051e14	1.12985	0.564923	−	0.825143i	$-0.308906\pi$
$937$	8.16051e14	1.12985	0.564923	+	0.825143i	$0.308906\pi$
$938$	5.90552e14i	0.813288i
$939$	0	0
$940$	−2.66684e14	−0.363378
$941$	1.06131e15i	1.43845i	0.694778	+	0.719224i	$0.255503\pi$
$941$	1.06131e15i	1.43845i	−0.694778	+	0.719224i	$0.744497\pi$
$942$	0	0
$943$	1.84965e14	0.248046
$944$	− 3.04613e14i	− 0.406339i
$945$	0	0
$946$	−9.66932e14	−1.27626
$947$	1.46853e15i	1.92812i	0.265687	+	0.964059i	$0.414401\pi$
$947$	1.46853e15i	1.92812i	−0.265687	+	0.964059i	$0.585599\pi$
$948$	0	0
$949$	−1.47921e15	−1.92175
$950$	− 2.29312e15i	− 2.96352i
$951$	0	0
$952$	−3.29255e14	−0.421063
$953$	2.90137e14i	0.369095i	0.982824	+	0.184548i	$0.0590820\pi$
$953$	2.90137e14i	0.369095i	−0.982824	+	0.184548i	$0.940918\pi$
$954$	0	0
$955$	2.71014e14	0.341174
$956$	− 1.08463e15i	− 1.35829i
$957$	0	0
$958$	1.08384e15	1.34319
$959$	− 1.67376e14i	− 0.206348i
$960$	0	0
$961$	8.06510e14	0.983995
$962$	8.83932e14i	1.07286i
$963$	0	0
$964$	−2.07993e15	−2.49841
$965$	1.22862e15i	1.46818i
$966$	0	0
$967$	7.47828e14	0.884443	0.442221	−	0.896906i	$-0.354191\pi$
$967$	7.47828e14	0.884443	0.442221	+	0.896906i	$0.354191\pi$
$968$	3.95949e14i	0.465868i
$969$	0	0
$970$	−1.40016e15	−1.63049
$971$	− 7.78041e14i	− 0.901377i	−0.892681	−	0.450688i	$-0.851179\pi$
$971$	− 7.78041e14i	− 0.901377i	0.892681	−	0.450688i	$-0.148821\pi$
$972$	0	0
$973$	4.17510e14	0.478743
$974$	− 1.13689e15i	− 1.29696i
$975$	0	0
$976$	−5.26288e14	−0.594257
$977$	− 6.07896e14i	− 0.682899i	−0.939900	−	0.341450i	$-0.889082\pi$
$977$	− 6.07896e14i	− 0.682899i	0.939900	−	0.341450i	$-0.110918\pi$
$978$	0	0
$979$	3.41025e14	0.379204
$980$	− 1.15221e15i	− 1.27467i
$981$	0	0
$982$	−6.81143e14	−0.745901
$983$	− 4.42411e14i	− 0.482013i	−0.970524	−	0.241006i	$-0.922523\pi$
$983$	− 4.42411e14i	− 0.482013i	0.970524	−	0.241006i	$-0.0774775\pi$
$984$	0	0
$985$	1.90621e15	2.05584
$986$	2.21910e15i	2.38118i
$987$	0	0
$988$	−2.66610e15	−2.83199
$989$	2.06538e14i	0.218282i
$990$	0	0
$991$	−1.74251e15	−1.82309	−0.911543	−	0.411205i	$-0.865108\pi$
$991$	−1.74251e15	−1.82309	−0.911543	+	0.411205i	$0.865108\pi$
$992$	− 1.73216e15i	− 1.80314i
$993$	0	0
$994$	3.32246e14	0.342395
$995$	1.55820e14i	0.159774i
$996$	0	0
$997$	4.01737e14	0.407818	0.203909	−	0.978990i	$-0.434635\pi$
$997$	4.01737e14	0.407818	0.203909	+	0.978990i	$0.434635\pi$
$998$	− 7.32356e14i	− 0.739723i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.b.d.26.6	yes	6
3.2	odd	2	inner	27.11.b.d.26.1	✓	6
9.2	odd	6		81.11.d.g.53.1		12
9.4	even	3		81.11.d.g.26.1		12
9.5	odd	6		81.11.d.g.26.6		12
9.7	even	3		81.11.d.g.53.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.b.d.26.1	✓	6	3.2	odd	2	inner
27.11.b.d.26.6	yes	6	1.1	even	1	trivial
81.11.d.g.26.1		12	9.4	even	3
81.11.d.g.26.6		12	9.5	odd	6
81.11.d.g.53.1		12	9.2	odd	6
81.11.d.g.53.6		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)

\(f(q)\)	\(=\)	\(q+49.7909i q^{2} -1455.14 q^{4} -4680.95i q^{5} +10645.1 q^{7} -21466.7i q^{8} +O(q^{10})\)	\(q+49.7909i q^{2} -1455.14 q^{4} -4680.95i q^{5} +10645.1 q^{7} -21466.7i q^{8} +233069. q^{10} +210671. i q^{11} +483189. q^{13} +530027. i q^{14} -421214. q^{16} -1.44085e6i q^{17} +3.79189e6 q^{19} +6.81141e6i q^{20} -1.04895e7 q^{22} +2.24057e6i q^{23} -1.21456e7 q^{25} +2.40584e7i q^{26} -1.54900e7 q^{28} +3.09319e7i q^{29} +4.03254e7 q^{31} -4.29545e7i q^{32} +7.17413e7 q^{34} -4.98289e7i q^{35} +3.67411e7 q^{37} +1.88802e8i q^{38} -1.00484e8 q^{40} -8.25527e7i q^{41} +9.21810e7 q^{43} -3.06555e8i q^{44} -1.11560e8 q^{46} +3.91525e7i q^{47} -1.69158e8 q^{49} -6.04742e8i q^{50} -7.03105e8 q^{52} -1.93130e8i q^{53} +9.86139e8 q^{55} -2.28514e8i q^{56} -1.54013e9 q^{58} +7.23179e8i q^{59} +1.24946e9 q^{61} +2.00784e9i q^{62} +1.70742e9 q^{64} -2.26178e9i q^{65} +1.11419e9 q^{67} +2.09663e9i q^{68} +2.48103e9 q^{70} -6.26847e8i q^{71} -3.06134e9 q^{73} +1.82937e9i q^{74} -5.51772e9 q^{76} +2.24260e9i q^{77} -2.38138e9 q^{79} +1.97168e9i q^{80} +4.11037e9 q^{82} -2.39278e9i q^{83} -6.74454e9 q^{85} +4.58978e9i q^{86} +4.52241e9 q^{88} -1.61876e9i q^{89} +5.14357e9 q^{91} -3.26034e9i q^{92} -1.94944e9 q^{94} -1.77496e10i q^{95} -6.00749e9 q^{97} -8.42253e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2658 q^{4} + 4638 q^{7}+O(q^{10}) \) 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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