LMFDB - Embedded newform 126.9.b.b.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(71,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("126.71");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.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:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} - 5134 x^{6} + 15416 x^{5} + 8006273 x^{4} - 16038244 x^{3} - 3602633684 x^{2} + \cdots + 501832517832 $ x^8 - 4x^7 - 5134x^6 + 15416x^5 + 8006273x^4 - 16038244x^3 - 3602633684x^2 + 3610655376*x + 501832517832
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.4
Root			$48.0766 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	126.71
Dual form			126.9.b.b.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3137i q^{2} -128.000 q^{4} +1211.10i q^{5} -907.493 q^{7} +1448.15i q^{8} +O(q^{10})$	\(q-11.3137i q^{2} -128.000 q^{4} +1211.10i q^{5} -907.493 q^{7} +1448.15i q^{8} +13702.0 q^{10} +10710.6i q^{11} +13600.2 q^{13} +10267.1i q^{14} +16384.0 q^{16} +47861.7i q^{17} +244074. q^{19} -155021. i q^{20} +121177. q^{22} +434984. i q^{23} -1.07613e6 q^{25} -153869. i q^{26} +116159. q^{28} -1.19354e6i q^{29} -302120. q^{31} -185364. i q^{32} +541494. q^{34} -1.09906e6i q^{35} -2.71909e6 q^{37} -2.76139e6i q^{38} -1.75386e6 q^{40} +1.71384e6i q^{41} -5.26089e6 q^{43} -1.37096e6i q^{44} +4.92128e6 q^{46} +3.08259e6i q^{47} +823543. q^{49} +1.21751e7i q^{50} -1.74083e6 q^{52} +2.09484e6i q^{53} -1.29716e7 q^{55} -1.31419e6i q^{56} -1.35033e7 q^{58} -3.20325e6i q^{59} +1.98256e7 q^{61} +3.41810e6i q^{62} -2.09715e6 q^{64} +1.64712e7i q^{65} +9.17847e6 q^{67} -6.12630e6i q^{68} -1.24345e7 q^{70} -1.91539e7i q^{71} -2.89130e7 q^{73} +3.07630e7i q^{74} -3.12415e7 q^{76} -9.71982e6i q^{77} -5.38663e7 q^{79} +1.98426e7i q^{80} +1.93898e7 q^{82} -8.19595e6i q^{83} -5.79653e7 q^{85} +5.95202e7i q^{86} -1.55107e7 q^{88} +9.29268e7i q^{89} -1.23421e7 q^{91} -5.56779e7i q^{92} +3.48755e7 q^{94} +2.95598e8i q^{95} -1.92146e7 q^{97} -9.31733e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1024 q^{4}+O(q^{10}) $ 8 * q - 1024 * q^4	$ 8 q - 1024 q^{4} + 4480 q^{10} + 156632 q^{13} + 131072 q^{16} + 321160 q^{19} + 65216 q^{22} - 2280096 q^{25} - 2427880 q^{31} + 4914560 q^{34} + 2032696 q^{37} - 573440 q^{40} - 14076032 q^{43} + 13935680 q^{46} + 6588344 q^{49} - 20048896 q^{52} + 21354536 q^{55} - 4103168 q^{58} + 46591832 q^{61} - 16777216 q^{64} - 26848632 q^{67} - 39798976 q^{70} + 94257072 q^{73} - 41108480 q^{76} - 244539784 q^{79} + 10967040 q^{82} + 163925624 q^{85} - 8347648 q^{88} - 57547168 q^{91} - 28288512 q^{94} + 109673088 q^{97}+O(q^{100}) $ 8 * q - 1024 * q^4 + 4480 * q^10 + 156632 * q^13 + 131072 * q^16 + 321160 * q^19 + 65216 * q^22 - 2280096 * q^25 - 2427880 * q^31 + 4914560 * q^34 + 2032696 * q^37 - 573440 * q^40 - 14076032 * q^43 + 13935680 * q^46 + 6588344 * q^49 - 20048896 * q^52 + 21354536 * q^55 - 4103168 * q^58 + 46591832 * q^61 - 16777216 * q^64 - 26848632 * q^67 - 39798976 * q^70 + 94257072 * q^73 - 41108480 * q^76 - 244539784 * q^79 + 10967040 * q^82 + 163925624 * q^85 - 8347648 * q^88 - 57547168 * q^91 - 28288512 * q^94 + 109673088 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 11.3137i	− 0.707107i
$2$	− 11.3137i	− 0.707107i
$3$	0	0
$3$	0	0
$4$	−128.000	−0.500000
$5$	1211.10i	1.93776i	0.247536	+	0.968879i	$0.420379\pi$
$5$	1211.10i	1.93776i	−0.247536	+	0.968879i	$0.579621\pi$
$6$	0	0
$7$	−907.493	−0.377964
$7$	−907.493	−0.377964
$8$	1448.15i	0.353553i
$9$	0	0
$10$	13702.0	1.37020
$11$	10710.6i	0.731551i	0.930703	+	0.365775i	$0.119196\pi$
$11$	10710.6i	0.731551i	−0.930703	+	0.365775i	$0.880804\pi$
$12$	0	0
$13$	13600.2	0.476182	0.238091	−	0.971243i	$-0.423478\pi$
$13$	13600.2	0.476182	0.238091	+	0.971243i	$0.423478\pi$
$14$	10267.1i	0.267261i
$15$	0	0
$16$	16384.0	0.250000
$17$	47861.7i	0.573050i	0.958073	+	0.286525i	$0.0925002\pi$
$17$	47861.7i	0.573050i	−0.958073	+	0.286525i	$0.907500\pi$
$18$	0	0
$19$	244074.	1.87287	0.936435	−	0.350841i	$-0.114104\pi$
$19$	244074.	1.87287	0.936435	+	0.350841i	$0.114104\pi$
$20$	− 155021.i	− 0.968879i
$21$	0	0
$22$	121177.	0.517285
$23$	434984.i	1.55440i	0.629256	+	0.777198i	$0.283360\pi$
$23$	434984.i	1.55440i	−0.629256	+	0.777198i	$0.716640\pi$
$24$	0	0
$25$	−1.07613e6	−2.75490
$26$	− 153869.i	− 0.336712i
$27$	0	0
$28$	116159.	0.188982
$29$	− 1.19354e6i	− 1.68750i	−0.536737	−	0.843749i	$-0.680343\pi$
$29$	− 1.19354e6i	− 1.68750i	0.536737	−	0.843749i	$-0.319657\pi$
$30$	0	0
$31$	−302120.	−0.327139	−0.163570	−	0.986532i	$-0.552301\pi$
$31$	−302120.	−0.327139	−0.163570	+	0.986532i	$0.552301\pi$
$32$	− 185364.i	− 0.176777i
$33$	0	0
$34$	541494.	0.405208
$35$	− 1.09906e6i	− 0.732404i
$36$	0	0
$37$	−2.71909e6	−1.45083	−0.725417	−	0.688310i	$-0.758353\pi$
$37$	−2.71909e6	−1.45083	−0.725417	+	0.688310i	$0.758353\pi$
$38$	− 2.76139e6i	− 1.32432i
$39$	0	0
$40$	−1.75386e6	−0.685101
$41$	1.71384e6i	0.606504i	0.952910	+	0.303252i	$0.0980724\pi$
$41$	1.71384e6i	0.606504i	−0.952910	+	0.303252i	$0.901928\pi$
$42$	0	0
$43$	−5.26089e6	−1.53881	−0.769406	−	0.638761i	$-0.779447\pi$
$43$	−5.26089e6	−1.53881	−0.769406	+	0.638761i	$0.779447\pi$
$44$	− 1.37096e6i	− 0.365775i
$45$	0	0
$46$	4.92128e6	1.09912
$47$	3.08259e6i	0.631720i	0.948806	+	0.315860i	$0.102293\pi$
$47$	3.08259e6i	0.631720i	−0.948806	+	0.315860i	$0.897707\pi$
$48$	0	0
$49$	823543.	0.142857
$50$	1.21751e7i	1.94801i
$51$	0	0
$52$	−1.74083e6	−0.238091
$53$	2.09484e6i	0.265490i	0.991150	+	0.132745i	$0.0423791\pi$
$53$	2.09484e6i	0.265490i	−0.991150	+	0.132745i	$0.957621\pi$
$54$	0	0
$55$	−1.29716e7	−1.41757
$56$	− 1.31419e6i	− 0.133631i
$57$	0	0
$58$	−1.35033e7	−1.19324
$59$	− 3.20325e6i	− 0.264352i	−0.991226	−	0.132176i	$-0.957804\pi$
$59$	− 3.20325e6i	− 0.264352i	0.991226	−	0.132176i	$-0.0421965\pi$
$60$	0	0
$61$	1.98256e7	1.43188	0.715940	−	0.698162i	$-0.245998\pi$
$61$	1.98256e7	1.43188	0.715940	+	0.698162i	$0.245998\pi$
$62$	3.41810e6i	0.231322i
$63$	0	0
$64$	−2.09715e6	−0.125000
$65$	1.64712e7i	0.922726i
$66$	0	0
$67$	9.17847e6	0.455482	0.227741	−	0.973722i	$-0.426866\pi$
$67$	9.17847e6	0.455482	0.227741	+	0.973722i	$0.426866\pi$
$68$	− 6.12630e6i	− 0.286525i
$69$	0	0
$70$	−1.24345e7	−0.517888
$71$	− 1.91539e7i	− 0.753742i	−0.926266	−	0.376871i	$-0.877000\pi$
$71$	− 1.91539e7i	− 0.753742i	0.926266	−	0.376871i	$-0.123000\pi$
$72$	0	0
$73$	−2.89130e7	−1.01813	−0.509064	−	0.860729i	$-0.670008\pi$
$73$	−2.89130e7	−1.01813	−0.509064	+	0.860729i	$0.670008\pi$
$74$	3.07630e7i	1.02589i
$75$	0	0
$76$	−3.12415e7	−0.936435
$77$	− 9.71982e6i	− 0.276500i
$78$	0	0
$79$	−5.38663e7	−1.38296	−0.691478	−	0.722397i	$-0.743040\pi$
$79$	−5.38663e7	−1.38296	−0.691478	+	0.722397i	$0.743040\pi$
$80$	1.98426e7i	0.484439i
$81$	0	0
$82$	1.93898e7	0.428863
$83$	− 8.19595e6i	− 0.172698i	−0.996265	−	0.0863489i	$-0.972480\pi$
$83$	− 8.19595e6i	− 0.172698i	0.996265	−	0.0863489i	$-0.0275200\pi$
$84$	0	0
$85$	−5.79653e7	−1.11043
$86$	5.95202e7i	1.08810i
$87$	0	0
$88$	−1.55107e7	−0.258642
$89$	9.29268e7i	1.48109i	0.672007	+	0.740544i	$0.265432\pi$
$89$	9.29268e7i	1.48109i	−0.672007	+	0.740544i	$0.734568\pi$
$90$	0	0
$91$	−1.23421e7	−0.179980
$92$	− 5.56779e7i	− 0.777198i
$93$	0	0
$94$	3.48755e7	0.446693
$95$	2.95598e8i	3.62917i
$96$	0	0
$97$	−1.92146e7	−0.217042	−0.108521	−	0.994094i	$-0.534612\pi$
$97$	−1.92146e7	−0.217042	−0.108521	+	0.994094i	$0.534612\pi$
$98$	− 9.31733e6i	− 0.101015i
$99$	0	0
$100$	1.37745e8	1.37745
$101$	− 1.02928e8i	− 0.989120i	−0.869143	−	0.494560i	$-0.835329\pi$
$101$	− 1.02928e8i	− 0.989120i	0.869143	−	0.494560i	$-0.164671\pi$
$102$	0	0
$103$	−1.37969e8	−1.22584	−0.612918	−	0.790147i	$-0.710004\pi$
$103$	−1.37969e8	−1.22584	−0.612918	+	0.790147i	$0.710004\pi$
$104$	1.96953e7i	0.168356i
$105$	0	0
$106$	2.37004e7	0.187730
$107$	2.31521e7i	0.176626i	0.996093	+	0.0883131i	$0.0281476\pi$
$107$	2.31521e7i	0.176626i	−0.996093	+	0.0883131i	$0.971852\pi$
$108$	0	0
$109$	1.58159e8	1.12044	0.560221	−	0.828343i	$-0.310716\pi$
$109$	1.58159e8	1.12044	0.560221	+	0.828343i	$0.310716\pi$
$110$	1.46757e8i	1.00237i
$111$	0	0
$112$	−1.48684e7	−0.0944911
$113$	− 3.92216e7i	− 0.240553i	−0.992740	−	0.120277i	$-0.961622\pi$
$113$	− 3.92216e7i	− 0.240553i	0.992740	−	0.120277i	$-0.0383782\pi$
$114$	0	0
$115$	−5.26808e8	−3.01204
$116$	1.52773e8i	0.843749i
$117$	0	0
$118$	−3.62407e7	−0.186925
$119$	− 4.34342e7i	− 0.216593i
$120$	0	0
$121$	9.96411e7	0.464833
$122$	− 2.24301e8i	− 1.01249i
$123$	0	0
$124$	3.86713e7	0.163570
$125$	− 8.30220e8i	− 3.40058i
$126$	0	0
$127$	−1.99919e7	−0.0768492	−0.0384246	−	0.999262i	$-0.512234\pi$
$127$	−1.99919e7	−0.0768492	−0.0384246	+	0.999262i	$0.512234\pi$
$128$	2.37266e7i	0.0883883i
$129$	0	0
$130$	1.86351e8	0.652466
$131$	− 5.10331e8i	− 1.73287i	−0.499286	−	0.866437i	$-0.666404\pi$
$131$	− 5.10331e8i	− 1.73287i	0.499286	−	0.866437i	$-0.333596\pi$
$132$	0	0
$133$	−2.21496e8	−0.707878
$134$	− 1.03842e8i	− 0.322074i
$135$	0	0
$136$	−6.93112e7	−0.202604
$137$	1.92870e8i	0.547496i	0.961801	+	0.273748i	$0.0882635\pi$
$137$	1.92870e8i	0.547496i	−0.961801	+	0.273748i	$0.911736\pi$
$138$	0	0
$139$	−3.39798e8	−0.910252	−0.455126	−	0.890427i	$-0.650406\pi$
$139$	−3.39798e8	−0.910252	−0.455126	+	0.890427i	$0.650406\pi$
$140$	1.40680e8i	0.366202i
$141$	0	0
$142$	−2.16701e8	−0.532976
$143$	1.45667e8i	0.348352i
$144$	0	0
$145$	1.44549e9	3.26996
$146$	3.27113e8i	0.719925i
$147$	0	0
$148$	3.48044e8	0.725417
$149$	− 4.44471e8i	− 0.901775i	−0.892581	−	0.450887i	$-0.851108\pi$
$149$	− 4.44471e8i	− 0.901775i	0.892581	−	0.450887i	$-0.148892\pi$
$150$	0	0
$151$	9.99963e6	0.0192343	0.00961714	−	0.999954i	$-0.496939\pi$
$151$	9.99963e6	0.0192343	0.00961714	+	0.999954i	$0.496939\pi$
$152$	3.53457e8i	0.662160i
$153$	0	0
$154$	−1.09967e8	−0.195515
$155$	− 3.65897e8i	− 0.633916i
$156$	0	0
$157$	8.96126e7	0.147493	0.0737464	−	0.997277i	$-0.476504\pi$
$157$	8.96126e7	0.147493	0.0737464	+	0.997277i	$0.476504\pi$
$158$	6.09427e8i	0.977898i
$159$	0	0
$160$	2.24494e8	0.342550
$161$	− 3.94745e8i	− 0.587507i
$162$	0	0
$163$	4.27168e8	0.605130	0.302565	−	0.953129i	$-0.402157\pi$
$163$	4.27168e8	0.605130	0.302565	+	0.953129i	$0.402157\pi$
$164$	− 2.19371e8i	− 0.303252i
$165$	0	0
$166$	−9.27266e7	−0.122116
$167$	2.59562e8i	0.333715i	0.985981	+	0.166857i	$0.0533619\pi$
$167$	2.59562e8i	0.333715i	−0.985981	+	0.166857i	$0.946638\pi$
$168$	0	0
$169$	−6.30764e8	−0.773250
$170$	6.55802e8i	0.785194i
$171$	0	0
$172$	6.73394e8	0.769406
$173$	9.99513e7i	0.111585i	0.998442	+	0.0557923i	$0.0177685\pi$
$173$	9.99513e7i	0.111585i	−0.998442	+	0.0557923i	$0.982232\pi$
$174$	0	0
$175$	9.76584e8	1.04126
$176$	1.75483e8i	0.182888i
$177$	0	0
$178$	1.05135e9	1.04729
$179$	− 7.39339e8i	− 0.720164i	−0.932921	−	0.360082i	$-0.882749\pi$
$179$	− 7.39339e8i	− 0.720164i	0.932921	−	0.360082i	$-0.117251\pi$
$180$	0	0
$181$	1.29398e9	1.20563	0.602815	−	0.797881i	$-0.294046\pi$
$181$	1.29398e9	1.20563	0.602815	+	0.797881i	$0.294046\pi$
$182$	1.39635e8i	0.127265i
$183$	0	0
$184$	−6.29924e8	−0.549562
$185$	− 3.29309e9i	− 2.81136i
$186$	0	0
$187$	−5.12630e8	−0.419215
$188$	− 3.94572e8i	− 0.315860i
$189$	0	0
$190$	3.34431e9	2.56621
$191$	− 3.11282e8i	− 0.233895i	−0.993138	−	0.116948i	$-0.962689\pi$
$191$	− 3.11282e8i	− 0.233895i	0.993138	−	0.116948i	$-0.0373109\pi$
$192$	0	0
$193$	−1.14336e9	−0.824054	−0.412027	−	0.911172i	$-0.635179\pi$
$193$	−1.14336e9	−0.824054	−0.412027	+	0.911172i	$0.635179\pi$
$194$	2.17389e8i	0.153472i
$195$	0	0
$196$	−1.05414e8	−0.0714286
$197$	2.21979e9i	1.47383i	0.675985	+	0.736916i	$0.263719\pi$
$197$	2.21979e9i	1.47383i	−0.675985	+	0.736916i	$0.736281\pi$
$198$	0	0
$199$	−1.05847e9	−0.674939	−0.337470	−	0.941336i	$-0.609571\pi$
$199$	−1.05847e9	−0.674939	−0.337470	+	0.941336i	$0.609571\pi$
$200$	− 1.55841e9i	− 0.974006i
$201$	0	0
$202$	−1.16450e9	−0.699414
$203$	1.08313e9i	0.637815i
$204$	0	0
$205$	−2.07562e9	−1.17526
$206$	1.56094e9i	0.866796i
$207$	0	0
$208$	2.22826e8	0.119046
$209$	2.61419e9i	1.37010i
$210$	0	0
$211$	−4.72317e8	−0.238289	−0.119144	−	0.992877i	$-0.538015\pi$
$211$	−4.72317e8	−0.238289	−0.119144	+	0.992877i	$0.538015\pi$
$212$	− 2.68140e8i	− 0.132745i
$213$	0	0
$214$	2.61936e8	0.124894
$215$	− 6.37146e9i	− 2.98184i
$216$	0	0
$217$	2.74171e8	0.123647
$218$	− 1.78937e9i	− 0.792272i
$219$	0	0
$220$	1.66037e9	0.708784
$221$	6.50931e8i	0.272876i
$222$	0	0
$223$	3.36540e9	1.36087	0.680435	−	0.732808i	$-0.261791\pi$
$223$	3.36540e9	1.36087	0.680435	+	0.732808i	$0.261791\pi$
$224$	1.68216e8i	0.0668153i
$225$	0	0
$226$	−4.43742e8	−0.170097
$227$	4.66054e9i	1.75523i	0.479370	+	0.877613i	$0.340865\pi$
$227$	4.66054e9i	1.75523i	−0.479370	+	0.877613i	$0.659135\pi$
$228$	0	0
$229$	5.88783e8	0.214098	0.107049	−	0.994254i	$-0.465860\pi$
$229$	5.88783e8	0.214098	0.107049	+	0.994254i	$0.465860\pi$
$230$	5.96016e9i	2.12984i
$231$	0	0
$232$	1.72842e9	0.596621
$233$	− 3.84476e9i	− 1.30451i	−0.758001	−	0.652253i	$-0.773824\pi$
$233$	− 3.84476e9i	− 1.30451i	0.758001	−	0.652253i	$-0.226176\pi$
$234$	0	0
$235$	−3.73332e9	−1.22412
$236$	4.10017e8i	0.132176i
$237$	0	0
$238$	−4.91402e8	−0.153154
$239$	5.24098e9i	1.60628i	0.595790	+	0.803140i	$0.296839\pi$
$239$	5.24098e9i	1.60628i	−0.595790	+	0.803140i	$0.703161\pi$
$240$	0	0
$241$	−3.70650e9	−1.09874	−0.549371	−	0.835578i	$-0.685133\pi$
$241$	−3.70650e9	−1.09874	−0.549371	+	0.835578i	$0.685133\pi$
$242$	− 1.12731e9i	− 0.328687i
$243$	0	0
$244$	−2.53767e9	−0.715940
$245$	9.97392e8i	0.276823i
$246$	0	0
$247$	3.31947e9	0.891828
$248$	− 4.37516e8i	− 0.115661i
$249$	0	0
$250$	−9.39286e9	−2.40457
$251$	− 3.34179e8i	− 0.0841947i	−0.999114	−	0.0420973i	$-0.986596\pi$
$251$	− 3.34179e8i	− 0.0841947i	0.999114	−	0.0420973i	$-0.0134040\pi$
$252$	0	0
$253$	−4.65895e9	−1.13712
$254$	2.26183e8i	0.0543406i
$255$	0	0
$256$	2.68435e8	0.0625000
$257$	1.88328e8i	0.0431700i	0.999767	+	0.0215850i	$0.00687126\pi$
$257$	1.88328e8i	0.0431700i	−0.999767	+	0.0215850i	$0.993129\pi$
$258$	0	0
$259$	2.46756e9	0.548363
$260$	− 2.10832e9i	− 0.461363i
$261$	0	0
$262$	−5.77374e9	−1.22533
$263$	− 5.33830e9i	− 1.11578i	−0.829914	−	0.557892i	$-0.811610\pi$
$263$	− 5.33830e9i	− 1.11578i	0.829914	−	0.557892i	$-0.188390\pi$
$264$	0	0
$265$	−2.53706e9	−0.514455
$266$	2.50594e9i	0.500546i
$267$	0	0
$268$	−1.17484e9	−0.227741
$269$	1.89274e9i	0.361479i	0.983531	+	0.180739i	$0.0578491\pi$
$269$	1.89274e9i	0.361479i	−0.983531	+	0.180739i	$0.942151\pi$
$270$	0	0
$271$	−7.94373e9	−1.47281	−0.736406	−	0.676539i	$-0.763479\pi$
$271$	−7.94373e9	−1.47281	−0.736406	+	0.676539i	$0.763479\pi$
$272$	7.84167e8i	0.143263i
$273$	0	0
$274$	2.18207e9	0.387138
$275$	− 1.15261e10i	− 2.01535i
$276$	0	0
$277$	−4.99765e9	−0.848882	−0.424441	−	0.905456i	$-0.639529\pi$
$277$	−4.99765e9	−0.848882	−0.424441	+	0.905456i	$0.639529\pi$
$278$	3.84437e9i	0.643645i
$279$	0	0
$280$	1.59161e9	0.258944
$281$	7.01282e9i	1.12478i	0.826872	+	0.562390i	$0.190118\pi$
$281$	7.01282e9i	1.12478i	−0.826872	+	0.562390i	$0.809882\pi$
$282$	0	0
$283$	−1.00519e9	−0.156712	−0.0783562	−	0.996925i	$-0.524967\pi$
$283$	−1.00519e9	−0.156712	−0.0783562	+	0.996925i	$0.524967\pi$
$284$	2.45169e9i	0.376871i
$285$	0	0
$286$	1.64804e9	0.246322
$287$	− 1.55529e9i	− 0.229237i
$288$	0	0
$289$	4.68501e9	0.671613
$290$	− 1.63538e10i	− 2.31221i
$291$	0	0
$292$	3.70087e9	0.509064
$293$	8.29520e9i	1.12553i	0.826617	+	0.562764i	$0.190262\pi$
$293$	8.29520e9i	1.12553i	−0.826617	+	0.562764i	$0.809738\pi$
$294$	0	0
$295$	3.87946e9	0.512251
$296$	− 3.93767e9i	− 0.512947i
$297$	0	0
$298$	−5.02861e9	−0.637651
$299$	5.91589e9i	0.740176i
$300$	0	0
$301$	4.77422e9	0.581616
$302$	− 1.13133e8i	− 0.0136007i
$303$	0	0
$304$	3.99891e9	0.468218
$305$	2.40107e10i	2.77464i
$306$	0	0
$307$	−1.85484e7	−0.00208811	−0.00104406	−	0.999999i	$-0.500332\pi$
$307$	−1.85484e7	−0.00208811	−0.00104406	+	0.999999i	$0.500332\pi$
$308$	1.24414e9i	0.138250i
$309$	0	0
$310$	−4.13965e9	−0.448246
$311$	− 3.85678e9i	− 0.412272i	−0.978523	−	0.206136i	$-0.933911\pi$
$311$	− 3.85678e9i	− 0.412272i	0.978523	−	0.206136i	$-0.0660889\pi$
$312$	0	0
$313$	1.04702e10	1.09088	0.545440	−	0.838150i	$-0.316363\pi$
$313$	1.04702e10	1.09088	0.545440	+	0.838150i	$0.316363\pi$
$314$	− 1.01385e9i	− 0.104293i
$315$	0	0
$316$	6.89488e9	0.691478
$317$	1.37697e10i	1.36360i	0.731537	+	0.681802i	$0.238803\pi$
$317$	1.37697e10i	1.36360i	−0.731537	+	0.681802i	$0.761197\pi$
$318$	0	0
$319$	1.27835e10	1.23449
$320$	− 2.53986e9i	− 0.242220i
$321$	0	0
$322$	−4.46603e9	−0.415430
$323$	1.16818e10i	1.07325i
$324$	0	0
$325$	−1.46357e10	−1.31184
$326$	− 4.83286e9i	− 0.427891i
$327$	0	0
$328$	−2.48190e9	−0.214432
$329$	− 2.79743e9i	− 0.238768i
$330$	0	0
$331$	−2.26459e9	−0.188659	−0.0943296	−	0.995541i	$-0.530071\pi$
$331$	−2.26459e9	−0.188659	−0.0943296	+	0.995541i	$0.530071\pi$
$332$	1.04908e9i	0.0863489i
$333$	0	0
$334$	2.93661e9	0.235972
$335$	1.11160e10i	0.882613i
$336$	0	0
$337$	1.48341e10	1.15012	0.575060	−	0.818112i	$-0.304979\pi$
$337$	1.48341e10	1.15012	0.575060	+	0.818112i	$0.304979\pi$
$338$	7.13628e9i	0.546771i
$339$	0	0
$340$	7.41955e9	0.555216
$341$	− 3.23590e9i	− 0.239319i
$342$	0	0
$343$	−7.47359e8	−0.0539949
$344$	− 7.61858e9i	− 0.544052i
$345$	0	0
$346$	1.13082e9	0.0789022
$347$	2.02518e9i	0.139684i	0.997558	+	0.0698420i	$0.0222495\pi$
$347$	2.02518e9i	0.139684i	−0.997558	+	0.0698420i	$0.977751\pi$
$348$	0	0
$349$	−2.42477e10	−1.63444	−0.817218	−	0.576328i	$-0.804485\pi$
$349$	−2.42477e10	−1.63444	−0.817218	+	0.576328i	$0.804485\pi$
$350$	− 1.10488e10i	− 0.736279i
$351$	0	0
$352$	1.98536e9	0.129321
$353$	− 2.10151e10i	− 1.35342i	−0.736249	−	0.676711i	$-0.763405\pi$
$353$	− 2.10151e10i	− 1.35342i	0.736249	−	0.676711i	$-0.236595\pi$
$354$	0	0
$355$	2.31972e10	1.46057
$356$	− 1.18946e10i	− 0.740544i
$357$	0	0
$358$	−8.36467e9	−0.509233
$359$	− 1.09742e10i	− 0.660687i	−0.943861	−	0.330343i	$-0.892835\pi$
$359$	− 1.09742e10i	− 0.660687i	0.943861	−	0.330343i	$-0.107165\pi$
$360$	0	0
$361$	4.25887e10	2.50764
$362$	− 1.46397e10i	− 0.852510i
$363$	0	0
$364$	1.57979e9	0.0899900
$365$	− 3.50165e10i	− 1.97288i
$366$	0	0
$367$	−1.09600e10	−0.604151	−0.302076	−	0.953284i	$-0.597679\pi$
$367$	−1.09600e10	−0.604151	−0.302076	+	0.953284i	$0.597679\pi$
$368$	7.12678e9i	0.388599i
$369$	0	0
$370$	−3.72571e10	−1.98793
$371$	− 1.90105e9i	− 0.100346i
$372$	0	0
$373$	2.39996e10	1.23985	0.619924	−	0.784662i	$-0.287163\pi$
$373$	2.39996e10	1.23985	0.619924	+	0.784662i	$0.287163\pi$
$374$	5.79974e9i	0.296430i
$375$	0	0
$376$	−4.46407e9	−0.223347
$377$	− 1.62324e10i	− 0.803557i
$378$	0	0
$379$	5.79030e9	0.280636	0.140318	−	0.990106i	$-0.455187\pi$
$379$	5.79030e9	0.280636	0.140318	+	0.990106i	$0.455187\pi$
$380$	− 3.78366e10i	− 1.81458i
$381$	0	0
$382$	−3.52176e9	−0.165389
$383$	1.82408e10i	0.847713i	0.905729	+	0.423856i	$0.139324\pi$
$383$	1.82408e10i	0.847713i	−0.905729	+	0.423856i	$0.860676\pi$
$384$	0	0
$385$	1.17717e10	0.535790
$386$	1.29357e10i	0.582694i
$387$	0	0
$388$	2.45947e9	0.108521
$389$	2.99046e10i	1.30599i	0.757363	+	0.652994i	$0.226487\pi$
$389$	2.99046e10i	1.30599i	−0.757363	+	0.652994i	$0.773513\pi$
$390$	0	0
$391$	−2.08191e10	−0.890747
$392$	1.19262e9i	0.0505076i
$393$	0	0
$394$	2.51141e10	1.04216
$395$	− 6.52373e10i	− 2.67983i
$396$	0	0
$397$	1.00381e10	0.404102	0.202051	−	0.979375i	$-0.435239\pi$
$397$	1.00381e10	0.404102	0.202051	+	0.979375i	$0.435239\pi$
$398$	1.19752e10i	0.477254i
$399$	0	0
$400$	−1.76314e10	−0.688726
$401$	1.59491e10i	0.616819i	0.951254	+	0.308409i	$0.0997967\pi$
$401$	1.59491e10i	0.616819i	−0.951254	+	0.308409i	$0.900203\pi$
$402$	0	0
$403$	−4.10890e9	−0.155778
$404$	1.31748e10i	0.494560i
$405$	0	0
$406$	1.22542e10	0.451003
$407$	− 2.91232e10i	− 1.06136i
$408$	0	0
$409$	1.90060e10	0.679199	0.339600	−	0.940570i	$-0.389708\pi$
$409$	1.90060e10	0.679199	0.339600	+	0.940570i	$0.389708\pi$
$410$	2.34830e10i	0.831033i
$411$	0	0
$412$	1.76600e10	0.612918
$413$	2.90693e9i	0.0999158i
$414$	0	0
$415$	9.92611e9	0.334647
$416$	− 2.52099e9i	− 0.0841779i
$417$	0	0
$418$	2.95762e10	0.968807
$419$	2.05951e10i	0.668203i	0.942537	+	0.334102i	$0.108433\pi$
$419$	2.05951e10i	0.668203i	−0.942537	+	0.334102i	$0.891567\pi$
$420$	0	0
$421$	5.82351e10	1.85377	0.926886	−	0.375342i	$-0.122475\pi$
$421$	5.82351e10	1.85377	0.926886	+	0.375342i	$0.122475\pi$
$422$	5.34365e9i	0.168496i
$423$	0	0
$424$	−3.03365e9	−0.0938648
$425$	− 5.15057e10i	− 1.57870i
$426$	0	0
$427$	−1.79916e10	−0.541200
$428$	− 2.96347e9i	− 0.0883131i
$429$	0	0
$430$	−7.20848e10	−2.10848
$431$	6.30792e10i	1.82800i	0.405711	+	0.914002i	$0.367024\pi$
$431$	6.30792e10i	1.82800i	−0.405711	+	0.914002i	$0.632976\pi$
$432$	0	0
$433$	3.85552e10	1.09681	0.548405	−	0.836213i	$-0.315235\pi$
$433$	3.85552e10	1.09681	0.548405	+	0.836213i	$0.315235\pi$
$434$	− 3.10190e9i	− 0.0874316i
$435$	0	0
$436$	−2.02444e10	−0.560221
$437$	1.06168e11i	2.91118i
$438$	0	0
$439$	−3.97337e10	−1.06980	−0.534898	−	0.844917i	$-0.679650\pi$
$439$	−3.97337e10	−1.06980	−0.534898	+	0.844917i	$0.679650\pi$
$440$	− 1.87849e10i	− 0.501186i
$441$	0	0
$442$	7.36444e9	0.192953
$443$	− 3.70440e10i	− 0.961841i	−0.876764	−	0.480920i	$-0.840303\pi$
$443$	− 3.70440e10i	− 0.961841i	0.876764	−	0.480920i	$-0.159697\pi$
$444$	0	0
$445$	−1.12544e11	−2.86999
$446$	− 3.80751e10i	− 0.962281i
$447$	0	0
$448$	1.90315e9	0.0472456
$449$	− 6.33996e10i	− 1.55991i	−0.625833	−	0.779957i	$-0.715241\pi$
$449$	− 6.33996e10i	− 1.55991i	0.625833	−	0.779957i	$-0.284759\pi$
$450$	0	0
$451$	−1.83563e10	−0.443689
$452$	5.02037e9i	0.120277i
$453$	0	0
$454$	5.27280e10	1.24113
$455$	− 1.49475e10i	− 0.348758i
$456$	0	0
$457$	7.66752e9	0.175788	0.0878942	−	0.996130i	$-0.471986\pi$
$457$	7.66752e9	0.175788	0.0878942	+	0.996130i	$0.471986\pi$
$458$	− 6.66132e9i	− 0.151390i
$459$	0	0
$460$	6.74315e10	1.50602
$461$	7.49009e10i	1.65838i	0.558969	+	0.829188i	$0.311197\pi$
$461$	7.49009e10i	1.65838i	−0.558969	+	0.829188i	$0.688803\pi$
$462$	0	0
$463$	7.14524e9	0.155487	0.0777433	−	0.996973i	$-0.475229\pi$
$463$	7.14524e9	0.155487	0.0777433	+	0.996973i	$0.475229\pi$
$464$	− 1.95549e10i	− 0.421875i
$465$	0	0
$466$	−4.34985e10	−0.922425
$467$	− 1.03793e10i	− 0.218224i	−0.994029	−	0.109112i	$-0.965199\pi$
$467$	− 1.03793e10i	− 0.218224i	0.994029	−	0.109112i	$-0.0348007\pi$
$468$	0	0
$469$	−8.32939e9	−0.172156
$470$	4.22377e10i	0.865584i
$471$	0	0
$472$	4.63881e9	0.0934627
$473$	− 5.63475e10i	− 1.12572i
$474$	0	0
$475$	−2.62657e11	−5.15958
$476$	5.55957e9i	0.108296i
$477$	0	0
$478$	5.92950e10	1.13581
$479$	7.92703e10i	1.50580i	0.658132	+	0.752902i	$0.271347\pi$
$479$	7.92703e10i	1.50580i	−0.658132	+	0.752902i	$0.728653\pi$
$480$	0	0
$481$	−3.69803e10	−0.690861
$482$	4.19343e10i	0.776928i
$483$	0	0
$484$	−1.27541e10	−0.232417
$485$	− 2.32708e10i	− 0.420576i
$486$	0	0
$487$	−2.73830e10	−0.486816	−0.243408	−	0.969924i	$-0.578265\pi$
$487$	−2.73830e10	−0.486816	−0.243408	+	0.969924i	$0.578265\pi$
$488$	2.87105e10i	0.506246i
$489$	0	0
$490$	1.12842e10	0.195743
$491$	3.10188e10i	0.533703i	0.963738	+	0.266851i	$0.0859833\pi$
$491$	3.10188e10i	0.533703i	−0.963738	+	0.266851i	$0.914017\pi$
$492$	0	0
$493$	5.71247e10	0.967022
$494$	− 3.75555e10i	− 0.630617i
$495$	0	0
$496$	−4.94993e9	−0.0817848
$497$	1.73820e10i	0.284888i
$498$	0	0
$499$	8.87123e10	1.43081	0.715404	−	0.698711i	$-0.246243\pi$
$499$	8.87123e10	1.43081	0.715404	+	0.698711i	$0.246243\pi$
$500$	1.06268e11i	1.70029i
$501$	0	0
$502$	−3.78081e9	−0.0595346
$503$	7.98951e10i	1.24810i	0.781385	+	0.624049i	$0.214513\pi$
$503$	7.98951e10i	1.24810i	−0.781385	+	0.624049i	$0.785487\pi$
$504$	0	0
$505$	1.24656e11	1.91668
$506$	5.27101e10i	0.804065i
$507$	0	0
$508$	2.55896e9	0.0384246
$509$	6.44190e10i	0.959716i	0.877346	+	0.479858i	$0.159312\pi$
$509$	6.44190e10i	0.959716i	−0.877346	+	0.479858i	$0.840688\pi$
$510$	0	0
$511$	2.62384e10	0.384816
$512$	− 3.03700e9i	− 0.0441942i
$513$	0	0
$514$	2.13069e9	0.0305258
$515$	− 1.67094e11i	− 2.37537i
$516$	0	0
$517$	−3.30165e10	−0.462135
$518$	− 2.79172e10i	− 0.387751i
$519$	0	0
$520$	−2.38529e10	−0.326233
$521$	− 3.87777e10i	− 0.526298i	−0.964755	−	0.263149i	$-0.915239\pi$
$521$	− 3.87777e10i	− 0.526298i	0.964755	−	0.263149i	$-0.0847611\pi$
$522$	0	0
$523$	4.22312e10	0.564452	0.282226	−	0.959348i	$-0.408927\pi$
$523$	4.22312e10	0.564452	0.282226	+	0.959348i	$0.408927\pi$
$524$	6.53224e10i	0.866437i
$525$	0	0
$526$	−6.03960e10	−0.788978
$527$	− 1.44600e10i	− 0.187467i
$528$	0	0
$529$	−1.10900e11	−1.41615
$530$	2.87035e10i	0.363774i
$531$	0	0
$532$	2.83514e10	0.353939
$533$	2.33086e10i	0.288807i
$534$	0	0
$535$	−2.80395e10	−0.342259
$536$	1.32918e10i	0.161037i
$537$	0	0
$538$	2.14140e10	0.255604
$539$	8.82067e9i	0.104507i
$540$	0	0
$541$	−1.51749e11	−1.77148	−0.885739	−	0.464183i	$-0.846348\pi$
$541$	−1.51749e11	−1.77148	−0.885739	+	0.464183i	$0.846348\pi$
$542$	8.98731e10i	1.04144i
$543$	0	0
$544$	8.87183e9	0.101302
$545$	1.91547e11i	2.17114i
$546$	0	0
$547$	5.78467e10	0.646144	0.323072	−	0.946374i	$-0.395284\pi$
$547$	5.78467e10	0.646144	0.323072	+	0.946374i	$0.395284\pi$
$548$	− 2.46873e10i	− 0.273748i
$549$	0	0
$550$	−1.30403e11	−1.42507
$551$	− 2.91311e11i	− 3.16047i
$552$	0	0
$553$	4.88832e10	0.522708
$554$	5.65420e10i	0.600250i
$555$	0	0
$556$	4.34941e10	0.455126
$557$	6.08256e10i	0.631926i	0.948772	+	0.315963i	$0.102327\pi$
$557$	6.08256e10i	0.631926i	−0.948772	+	0.315963i	$0.897673\pi$
$558$	0	0
$559$	−7.15494e10	−0.732755
$560$	− 1.80070e10i	− 0.183101i
$561$	0	0
$562$	7.93410e10	0.795339
$563$	2.70129e10i	0.268867i	0.990923	+	0.134434i	$0.0429215\pi$
$563$	2.70129e10i	0.268867i	−0.990923	+	0.134434i	$0.957078\pi$
$564$	0	0
$565$	4.75012e10	0.466134
$566$	1.13725e10i	0.110812i
$567$	0	0
$568$	2.77377e10	0.266488
$569$	− 3.62472e10i	− 0.345800i	−0.984939	−	0.172900i	$-0.944686\pi$
$569$	− 3.62472e10i	− 0.345800i	0.984939	−	0.172900i	$-0.0553137\pi$
$570$	0	0
$571$	−4.82415e10	−0.453812	−0.226906	−	0.973917i	$-0.572861\pi$
$571$	−4.82415e10	−0.453812	−0.226906	+	0.973917i	$0.572861\pi$
$572$	− 1.86454e10i	− 0.174176i
$573$	0	0
$574$	−1.75961e10	−0.162095
$575$	− 4.68101e11i	− 4.28221i
$576$	0	0
$577$	6.36608e10	0.574340	0.287170	−	0.957880i	$-0.407286\pi$
$577$	6.36608e10	0.574340	0.287170	+	0.957880i	$0.407286\pi$
$578$	− 5.30049e10i	− 0.474902i
$579$	0	0
$580$	−1.85023e11	−1.63498
$581$	7.43777e9i	0.0652737i
$582$	0	0
$583$	−2.24371e10	−0.194219
$584$	− 4.18705e10i	− 0.359962i
$585$	0	0
$586$	9.38495e10	0.795869
$587$	− 1.28235e11i	− 1.08008i	−0.841641	−	0.540038i	$-0.818410\pi$
$587$	− 1.28235e11i	− 1.08008i	0.841641	−	0.540038i	$-0.181590\pi$
$588$	0	0
$589$	−7.37397e10	−0.612689
$590$	− 4.38910e10i	− 0.362216i
$591$	0	0
$592$	−4.45496e10	−0.362708
$593$	7.11877e10i	0.575687i	0.957678	+	0.287843i	$0.0929382\pi$
$593$	7.11877e10i	0.575687i	−0.957678	+	0.287843i	$0.907062\pi$
$594$	0	0
$595$	5.26031e10	0.419704
$596$	5.68923e10i	0.450887i
$597$	0	0
$598$	6.69306e10	0.523384
$599$	− 2.84426e10i	− 0.220934i	−0.993880	−	0.110467i	$-0.964765\pi$
$599$	− 2.84426e10i	− 0.220934i	0.993880	−	0.110467i	$-0.0352346\pi$
$600$	0	0
$601$	−9.50200e10	−0.728312	−0.364156	−	0.931338i	$-0.618642\pi$
$601$	−9.50200e10	−0.728312	−0.364156	+	0.931338i	$0.618642\pi$
$602$	− 5.40141e10i	− 0.411265i
$603$	0	0
$604$	−1.27995e9	−0.00961714
$605$	1.20675e11i	0.900734i
$606$	0	0
$607$	−2.42978e10	−0.178983	−0.0894915	−	0.995988i	$-0.528524\pi$
$607$	−2.42978e10	−0.178983	−0.0894915	+	0.995988i	$0.528524\pi$
$608$	− 4.52425e10i	− 0.331080i
$609$	0	0
$610$	2.71650e11	1.96196
$611$	4.19240e10i	0.300814i
$612$	0	0
$613$	−2.44906e11	−1.73443	−0.867217	−	0.497930i	$-0.834094\pi$
$613$	−2.44906e11	−1.73443	−0.867217	+	0.497930i	$0.834094\pi$
$614$	2.09851e8i	0.00147652i
$615$	0	0
$616$	1.40758e10	0.0977576
$617$	1.30161e11i	0.898130i	0.893499	+	0.449065i	$0.148243\pi$
$617$	1.30161e11i	0.898130i	−0.893499	+	0.449065i	$0.851757\pi$
$618$	0	0
$619$	1.13223e11	0.771211	0.385606	−	0.922664i	$-0.373993\pi$
$619$	1.13223e11	0.771211	0.385606	+	0.922664i	$0.373993\pi$
$620$	4.68348e10i	0.316958i
$621$	0	0
$622$	−4.36345e10	−0.291520
$623$	− 8.43304e10i	− 0.559799i
$624$	0	0
$625$	5.85113e11	3.83459
$626$	− 1.18457e11i	− 0.771369i
$627$	0	0
$628$	−1.14704e10	−0.0737464
$629$	− 1.30141e11i	− 0.831400i
$630$	0	0
$631$	−2.41602e11	−1.52400	−0.761998	−	0.647580i	$-0.775781\pi$
$631$	−2.41602e11	−1.52400	−0.761998	+	0.647580i	$0.775781\pi$
$632$	− 7.80067e10i	− 0.488949i
$633$	0	0
$634$	1.55787e11	0.964214
$635$	− 2.42122e10i	− 0.148915i
$636$	0	0
$637$	1.12004e10	0.0680260
$638$	− 1.44629e11i	− 0.872917i
$639$	0	0
$640$	−2.87352e10	−0.171275
$641$	1.59960e11i	0.947502i	0.880659	+	0.473751i	$0.157100\pi$
$641$	1.59960e11i	0.947502i	−0.880659	+	0.473751i	$0.842900\pi$
$642$	0	0
$643$	−2.05005e11	−1.19928	−0.599641	−	0.800269i	$-0.704690\pi$
$643$	−2.05005e11	−1.19928	−0.599641	+	0.800269i	$0.704690\pi$
$644$	5.05273e10i	0.293753i
$645$	0	0
$646$	1.32165e11	0.758901
$647$	2.92991e11i	1.67201i	0.548725	+	0.836003i	$0.315113\pi$
$647$	2.92991e11i	1.67201i	−0.548725	+	0.836003i	$0.684887\pi$
$648$	0	0
$649$	3.43089e10	0.193387
$650$	1.65584e11i	0.927609i
$651$	0	0
$652$	−5.46775e10	−0.302565
$653$	8.88422e10i	0.488615i	0.969698	+	0.244307i	$0.0785606\pi$
$653$	8.88422e10i	0.488615i	−0.969698	+	0.244307i	$0.921439\pi$
$654$	0	0
$655$	6.18062e11	3.35789
$656$	2.80795e10i	0.151626i
$657$	0	0
$658$	−3.16493e10	−0.168834
$659$	− 5.73364e10i	− 0.304011i	−0.988380	−	0.152005i	$-0.951427\pi$
$659$	− 5.73364e10i	− 0.304011i	0.988380	−	0.152005i	$-0.0485731\pi$
$660$	0	0
$661$	−2.69884e10	−0.141374	−0.0706872	−	0.997499i	$-0.522519\pi$
$661$	−2.69884e10	−0.141374	−0.0706872	+	0.997499i	$0.522519\pi$
$662$	2.56209e10i	0.133402i
$663$	0	0
$664$	1.18690e10	0.0610579
$665$	− 2.68253e11i	− 1.37170i
$666$	0	0
$667$	5.19169e11	2.62304
$668$	− 3.32239e10i	− 0.166857i
$669$	0	0
$670$	1.25763e11	0.624102
$671$	2.12345e11i	1.04749i
$672$	0	0
$673$	3.60125e11	1.75547	0.877735	−	0.479146i	$-0.159053\pi$
$673$	3.60125e11	1.75547	0.877735	+	0.479146i	$0.159053\pi$
$674$	− 1.67829e11i	− 0.813257i
$675$	0	0
$676$	8.07378e10	0.386625
$677$	1.55289e11i	0.739239i	0.929183	+	0.369619i	$0.120512\pi$
$677$	1.55289e11i	0.739239i	−0.929183	+	0.369619i	$0.879488\pi$
$678$	0	0
$679$	1.74371e10	0.0820343
$680$	− 8.39427e10i	− 0.392597i
$681$	0	0
$682$	−3.66100e10	−0.169224
$683$	− 1.17633e10i	− 0.0540565i	−0.999635	−	0.0270282i	$-0.991396\pi$
$683$	− 1.17633e10i	− 0.0540565i	0.999635	−	0.0270282i	$-0.00860440\pi$
$684$	0	0
$685$	−2.33584e11	−1.06092
$686$	8.45540e9i	0.0381802i
$687$	0	0
$688$	−8.61944e10	−0.384703
$689$	2.84903e10i	0.126421i
$690$	0	0
$691$	7.05538e10	0.309463	0.154731	−	0.987957i	$-0.450549\pi$
$691$	7.05538e10	0.309463	0.154731	+	0.987957i	$0.450549\pi$
$692$	− 1.27938e10i	− 0.0557923i
$693$	0	0
$694$	2.29123e10	0.0987714
$695$	− 4.11529e11i	− 1.76385i
$696$	0	0
$697$	−8.20272e10	−0.347557
$698$	2.74331e11i	1.15572i
$699$	0	0
$700$	−1.25003e11	−0.520628
$701$	− 2.52694e11i	− 1.04646i	−0.852191	−	0.523231i	$-0.824727\pi$
$701$	− 2.52694e11i	− 1.04646i	0.852191	−	0.523231i	$-0.175273\pi$
$702$	0	0
$703$	−6.63661e11	−2.71722
$704$	− 2.24618e10i	− 0.0914439i
$705$	0	0
$706$	−2.37759e11	−0.957013
$707$	9.34066e10i	0.373852i
$708$	0	0
$709$	1.12410e11	0.444856	0.222428	−	0.974949i	$-0.428602\pi$
$709$	1.12410e11	0.444856	0.222428	+	0.974949i	$0.428602\pi$
$710$	− 2.62446e11i	− 1.03278i
$711$	0	0
$712$	−1.34572e11	−0.523644
$713$	− 1.31417e11i	− 0.508504i
$714$	0	0
$715$	−1.76417e11	−0.675021
$716$	9.46354e10i	0.360082i
$717$	0	0
$718$	−1.24159e11	−0.467176
$719$	− 2.87571e11i	− 1.07604i	−0.842931	−	0.538022i	$-0.819172\pi$
$719$	− 2.87571e11i	− 1.07604i	0.842931	−	0.538022i	$-0.180828\pi$
$720$	0	0
$721$	1.25206e11	0.463322
$722$	− 4.81836e11i	− 1.77317i
$723$	0	0
$724$	−1.65630e11	−0.602815
$725$	1.28441e12i	4.64890i
$726$	0	0
$727$	−6.28461e10	−0.224978	−0.112489	−	0.993653i	$-0.535882\pi$
$727$	−6.28461e10	−0.224978	−0.112489	+	0.993653i	$0.535882\pi$
$728$	− 1.78733e10i	− 0.0636325i
$729$	0	0
$730$	−3.96167e11	−1.39504
$731$	− 2.51795e11i	− 0.881816i
$732$	0	0
$733$	4.36404e11	1.51172	0.755862	−	0.654731i	$-0.227218\pi$
$733$	4.36404e11	1.51172	0.755862	+	0.654731i	$0.227218\pi$
$734$	1.23998e11i	0.427199i
$735$	0	0
$736$	8.06303e10	0.274781
$737$	9.83072e10i	0.333208i
$738$	0	0
$739$	−2.95923e11	−0.992205	−0.496102	−	0.868264i	$-0.665236\pi$
$739$	−2.95923e11	−0.992205	−0.496102	+	0.868264i	$0.665236\pi$
$740$	4.21516e11i	1.40568i
$741$	0	0
$742$	−2.15080e10	−0.0709551
$743$	3.09788e11i	1.01651i	0.861208	+	0.508253i	$0.169708\pi$
$743$	3.09788e11i	1.01651i	−0.861208	+	0.508253i	$0.830292\pi$
$744$	0	0
$745$	5.38298e11	1.74742
$746$	− 2.71524e11i	− 0.876705i
$747$	0	0
$748$	6.56166e10	0.209608
$749$	− 2.10104e10i	− 0.0667584i
$750$	0	0
$751$	−3.97655e11	−1.25011	−0.625053	−	0.780583i	$-0.714922\pi$
$751$	−3.97655e11	−1.25011	−0.625053	+	0.780583i	$0.714922\pi$
$752$	5.05052e10i	0.157930i
$753$	0	0
$754$	−1.83648e11	−0.568201
$755$	1.21105e10i	0.0372714i
$756$	0	0
$757$	−1.25637e11	−0.382590	−0.191295	−	0.981533i	$-0.561269\pi$
$757$	−1.25637e11	−0.382590	−0.191295	+	0.981533i	$0.561269\pi$
$758$	− 6.55097e10i	− 0.198440i
$759$	0	0
$760$	−4.28072e11	−1.28310
$761$	− 9.54153e10i	− 0.284498i	−0.989831	−	0.142249i	$-0.954567\pi$
$761$	− 9.54153e10i	− 0.284498i	0.989831	−	0.142249i	$-0.0454334\pi$
$762$	0	0
$763$	−1.43529e11	−0.423487
$764$	3.98441e10i	0.116948i
$765$	0	0
$766$	2.06371e11	0.599423
$767$	− 4.35650e10i	− 0.125880i
$768$	0	0
$769$	2.45971e11	0.703362	0.351681	−	0.936120i	$-0.385610\pi$
$769$	2.45971e11	0.703362	0.351681	+	0.936120i	$0.385610\pi$
$770$	− 1.33181e11i	− 0.378861i
$771$	0	0
$772$	1.46351e11	0.412027
$773$	2.49685e10i	0.0699319i	0.999389	+	0.0349659i	$0.0111323\pi$
$773$	2.49685e10i	0.0699319i	−0.999389	+	0.0349659i	$0.988868\pi$
$774$	0	0
$775$	3.25122e11	0.901237
$776$	− 2.78257e10i	− 0.0767361i
$777$	0	0
$778$	3.38332e11	0.923473
$779$	4.18303e11i	1.13590i
$780$	0	0
$781$	2.05150e11	0.551401
$782$	2.35541e11i	0.629854i
$783$	0	0
$784$	1.34929e10	0.0357143
$785$	1.08530e11i	0.285805i
$786$	0	0
$787$	−5.86075e11	−1.52776	−0.763878	−	0.645360i	$-0.776707\pi$
$787$	−5.86075e11	−1.52776	−0.763878	+	0.645360i	$0.776707\pi$
$788$	− 2.84134e11i	− 0.736916i
$789$	0	0
$790$	−7.38076e11	−1.89493
$791$	3.55933e10i	0.0909207i
$792$	0	0
$793$	2.69633e11	0.681836
$794$	− 1.13568e11i	− 0.285743i
$795$	0	0
$796$	1.35484e11	0.337470
$797$	8.97034e10i	0.222318i	0.993803	+	0.111159i	$0.0354564\pi$
$797$	8.97034e10i	0.222318i	−0.993803	+	0.111159i	$0.964544\pi$
$798$	0	0
$799$	−1.47538e11	−0.362007
$800$	1.99476e11i	0.487003i
$801$	0	0
$802$	1.80443e11	0.436157
$803$	− 3.09677e11i	− 0.744812i
$804$	0	0
$805$	4.78075e11	1.13845
$806$	4.64869e10i	0.110152i
$807$	0	0
$808$	1.49056e11	0.349707
$809$	1.45741e11i	0.340242i	0.985423	+	0.170121i	$0.0544158\pi$
$809$	1.45741e11i	0.340242i	−0.985423	+	0.170121i	$0.945584\pi$
$810$	0	0
$811$	−8.42301e11	−1.94708	−0.973540	−	0.228516i	$-0.926613\pi$
$811$	−8.42301e11	−1.94708	−0.973540	+	0.228516i	$0.926613\pi$
$812$	− 1.38640e11i	− 0.318907i
$813$	0	0
$814$	−3.29492e11	−0.750494
$815$	5.17343e11i	1.17260i
$816$	0	0
$817$	−1.28405e12	−2.88199
$818$	− 2.15028e11i	− 0.480266i
$819$	0	0
$820$	2.65680e11	0.587629
$821$	2.27168e11i	0.500006i	0.968245	+	0.250003i	$0.0804315\pi$
$821$	2.27168e11i	0.500006i	−0.968245	+	0.250003i	$0.919568\pi$
$822$	0	0
$823$	−2.78306e11	−0.606629	−0.303315	−	0.952890i	$-0.598093\pi$
$823$	−2.78306e11	−0.606629	−0.303315	+	0.952890i	$0.598093\pi$
$824$	− 1.99800e11i	− 0.433398i
$825$	0	0
$826$	3.28882e10	0.0706512
$827$	8.65865e11i	1.85109i	0.378635	+	0.925546i	$0.376393\pi$
$827$	8.65865e11i	1.85109i	−0.378635	+	0.925546i	$0.623607\pi$
$828$	0	0
$829$	2.09129e11	0.442789	0.221395	−	0.975184i	$-0.428939\pi$
$829$	2.09129e11	0.442789	0.221395	+	0.975184i	$0.428939\pi$
$830$	− 1.12301e11i	− 0.236631i
$831$	0	0
$832$	−2.85218e10	−0.0595228
$833$	3.94162e10i	0.0818643i
$834$	0	0
$835$	−3.14355e11	−0.646658
$836$	− 3.34617e11i	− 0.685050i
$837$	0	0
$838$	2.33007e11	0.472491
$839$	8.44367e11i	1.70405i	0.523498	+	0.852027i	$0.324627\pi$
$839$	8.44367e11i	1.70405i	−0.523498	+	0.852027i	$0.675373\pi$
$840$	0	0
$841$	−9.24281e11	−1.84765
$842$	− 6.58855e11i	− 1.31082i
$843$	0	0
$844$	6.04565e10	0.119144
$845$	− 7.63918e11i	− 1.49837i
$846$	0	0
$847$	−9.04236e10	−0.175690
$848$	3.43219e10i	0.0663724i
$849$	0	0
$850$	−5.82720e11	−1.11631
$851$	− 1.18276e12i	− 2.25517i
$852$	0	0
$853$	3.48503e11	0.658279	0.329139	−	0.944281i	$-0.393241\pi$
$853$	3.48503e11	0.658279	0.329139	+	0.944281i	$0.393241\pi$
$854$	2.03551e11i	0.382686i
$855$	0	0
$856$	−3.35278e10	−0.0624468
$857$	− 2.74108e11i	− 0.508157i	−0.967184	−	0.254078i	$-0.918228\pi$
$857$	− 2.74108e11i	− 0.508157i	0.967184	−	0.254078i	$-0.0817721\pi$
$858$	0	0
$859$	6.53625e11	1.20048	0.600242	−	0.799819i	$-0.295071\pi$
$859$	6.53625e11	1.20048	0.600242	+	0.799819i	$0.295071\pi$
$860$	8.15546e11i	1.49092i
$861$	0	0
$862$	7.13659e11	1.29259
$863$	− 8.26447e11i	− 1.48995i	−0.667093	−	0.744975i	$-0.732461\pi$
$863$	− 8.26447e11i	− 1.48995i	0.667093	−	0.744975i	$-0.267539\pi$
$864$	0	0
$865$	−1.21051e11	−0.216224
$866$	− 4.36202e11i	− 0.775561i
$867$	0	0
$868$	−3.50940e10	−0.0618235
$869$	− 5.76942e11i	− 1.01170i
$870$	0	0
$871$	1.24829e11	0.216892
$872$	2.29039e11i	0.396136i
$873$	0	0
$874$	1.20116e12	2.05852
$875$	7.53418e11i	1.28530i
$876$	0	0
$877$	−3.78385e11	−0.639640	−0.319820	−	0.947478i	$-0.603622\pi$
$877$	−3.78385e11	−0.639640	−0.319820	+	0.947478i	$0.603622\pi$
$878$	4.49536e11i	0.756460i
$879$	0	0
$880$	−2.12527e11	−0.354392
$881$	− 1.13696e11i	− 0.188730i	−0.995538	−	0.0943648i	$-0.969918\pi$
$881$	− 1.13696e11i	− 0.188730i	0.995538	−	0.0943648i	$-0.0300820\pi$
$882$	0	0
$883$	−2.29515e11	−0.377545	−0.188772	−	0.982021i	$-0.560451\pi$
$883$	−2.29515e11	−0.377545	−0.188772	+	0.982021i	$0.560451\pi$
$884$	− 8.33192e10i	− 0.136438i
$885$	0	0
$886$	−4.19105e11	−0.680124
$887$	− 7.29173e11i	− 1.17798i	−0.808142	−	0.588988i	$-0.799527\pi$
$887$	− 7.29173e11i	− 1.17798i	0.808142	−	0.588988i	$-0.200473\pi$
$888$	0	0
$889$	1.81425e10	0.0290463
$890$	1.27328e12i	2.02939i
$891$	0	0
$892$	−4.30771e11	−0.680435
$893$	7.52382e11i	1.18313i
$894$	0	0
$895$	8.95413e11	1.39550
$896$	− 2.15317e10i	− 0.0334077i
$897$	0	0
$898$	−7.17284e11	−1.10303
$899$	3.60591e11i	0.552047i
$900$	0	0
$901$	−1.00263e11	−0.152139
$902$	2.07678e11i	0.313735i
$903$	0	0
$904$	5.67990e10	0.0850485
$905$	1.56714e12i	2.33622i
$906$	0	0
$907$	6.41849e10	0.0948427	0.0474214	−	0.998875i	$-0.484900\pi$
$907$	6.41849e10	0.0948427	0.0474214	+	0.998875i	$0.484900\pi$
$908$	− 5.96549e11i	− 0.877613i
$909$	0	0
$910$	−1.69112e11	−0.246609
$911$	− 4.41160e11i	− 0.640505i	−0.947332	−	0.320252i	$-0.896232\pi$
$911$	− 4.41160e11i	− 0.640505i	0.947332	−	0.320252i	$-0.103768\pi$
$912$	0	0
$913$	8.77839e10	0.126337
$914$	− 8.67481e10i	− 0.124301i
$915$	0	0
$916$	−7.53642e10	−0.107049
$917$	4.63122e11i	0.654965i
$918$	0	0
$919$	1.01965e12	1.42952	0.714758	−	0.699372i	$-0.246537\pi$
$919$	1.01965e12	1.42952	0.714758	+	0.699372i	$0.246537\pi$
$920$	− 7.62900e11i	− 1.06492i
$921$	0	0
$922$	8.47407e11	1.17265
$923$	− 2.60497e11i	− 0.358919i
$924$	0	0
$925$	2.92611e12	3.99691
$926$	− 8.08392e10i	− 0.109946i
$927$	0	0
$928$	−2.21238e11	−0.298310
$929$	1.84245e11i	0.247363i	0.992322	+	0.123681i	$0.0394700\pi$
$929$	1.84245e11i	0.247363i	−0.992322	+	0.123681i	$0.960530\pi$
$930$	0	0
$931$	2.01006e11	0.267553
$932$	4.92130e11i	0.652253i
$933$	0	0
$934$	−1.17429e11	−0.154307
$935$	− 6.20845e11i	− 0.812338i
$936$	0	0
$937$	1.47548e12	1.91414	0.957071	−	0.289855i	$-0.0936071\pi$
$937$	1.47548e12	1.91414	0.957071	+	0.289855i	$0.0936071\pi$
$938$	9.42363e10i	0.121733i
$939$	0	0
$940$	4.77865e11	0.612060
$941$	2.62336e11i	0.334580i	0.985908	+	0.167290i	$0.0535016\pi$
$941$	2.62336e11i	0.334580i	−0.985908	+	0.167290i	$0.946498\pi$
$942$	0	0
$943$	−7.45491e11	−0.942748
$944$	− 5.24821e10i	− 0.0660881i
$945$	0	0
$946$	−6.37499e11	−0.796003
$947$	− 7.76055e11i	− 0.964923i	−0.875917	−	0.482462i	$-0.839743\pi$
$947$	− 7.76055e11i	− 0.964923i	0.875917	−	0.482462i	$-0.160257\pi$
$948$	0	0
$949$	−3.93224e11	−0.484814
$950$	2.97162e12i	3.64837i
$951$	0	0
$952$	6.28994e10	0.0765771
$953$	− 2.12437e10i	− 0.0257548i	−0.999917	−	0.0128774i	$-0.995901\pi$
$953$	− 2.12437e10i	− 0.0257548i	0.999917	−	0.0128774i	$-0.00409911\pi$
$954$	0	0
$955$	3.76994e11	0.453232
$956$	− 6.70846e11i	− 0.803140i
$957$	0	0
$958$	8.96841e11	1.06476
$959$	− 1.75028e11i	− 0.206934i
$960$	0	0
$961$	−7.61615e11	−0.892980
$962$	4.18385e11i	0.488512i
$963$	0	0
$964$	4.74432e11	0.549371
$965$	− 1.38473e12i	− 1.59682i
$966$	0	0
$967$	−1.39651e11	−0.159712	−0.0798559	−	0.996806i	$-0.525446\pi$
$967$	−1.39651e11	−0.159712	−0.0798559	+	0.996806i	$0.525446\pi$
$968$	1.44296e11i	0.164343i
$969$	0	0
$970$	−2.63279e11	−0.297392
$971$	− 1.51279e12i	− 1.70177i	−0.525349	−	0.850887i	$-0.676065\pi$
$971$	− 1.51279e12i	− 1.70177i	0.525349	−	0.850887i	$-0.323935\pi$
$972$	0	0
$973$	3.08364e11	0.344043
$974$	3.09803e11i	0.344231i
$975$	0	0
$976$	3.24822e11	0.357970
$977$	9.69562e10i	0.106414i	0.998584	+	0.0532068i	$0.0169443\pi$
$977$	9.69562e10i	0.106414i	−0.998584	+	0.0532068i	$0.983056\pi$
$978$	0	0
$979$	−9.95306e11	−1.08349
$980$	− 1.27666e11i	− 0.138411i
$981$	0	0
$982$	3.50938e11	0.377385
$983$	− 1.25737e12i	− 1.34664i	−0.739353	−	0.673318i	$-0.764868\pi$
$983$	− 1.25737e12i	− 1.34664i	0.739353	−	0.673318i	$-0.235132\pi$
$984$	0	0
$985$	−2.68839e12	−2.85593
$986$	− 6.46292e11i	− 0.683787i
$987$	0	0
$988$	−4.24892e11	−0.445914
$989$	− 2.28840e12i	− 2.39192i
$990$	0	0
$991$	1.83414e12	1.90168	0.950839	−	0.309687i	$-0.100224\pi$
$991$	1.83414e12	1.90168	0.950839	+	0.309687i	$0.100224\pi$
$992$	5.60021e10i	0.0578306i
$993$	0	0
$994$	1.96655e11	0.201446
$995$	− 1.28191e12i	− 1.30787i
$996$	0	0
$997$	9.80469e11	0.992323	0.496162	−	0.868230i	$-0.334742\pi$
$997$	9.80469e11	0.992323	0.496162	+	0.868230i	$0.334742\pi$
$998$	− 1.00366e12i	− 1.01173i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.b.b.71.4	✓	8
3.2	odd	2	inner	126.9.b.b.71.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.b.b.71.4	✓	8	1.1	even	1	trivial
126.9.b.b.71.5	yes	8	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.3137i q^{2} -128.000 q^{4} +1211.10i q^{5} -907.493 q^{7} +1448.15i q^{8} +O(q^{10})\)	\(q-11.3137i q^{2} -128.000 q^{4} +1211.10i q^{5} -907.493 q^{7} +1448.15i q^{8} +13702.0 q^{10} +10710.6i q^{11} +13600.2 q^{13} +10267.1i q^{14} +16384.0 q^{16} +47861.7i q^{17} +244074. q^{19} -155021. i q^{20} +121177. q^{22} +434984. i q^{23} -1.07613e6 q^{25} -153869. i q^{26} +116159. q^{28} -1.19354e6i q^{29} -302120. q^{31} -185364. i q^{32} +541494. q^{34} -1.09906e6i q^{35} -2.71909e6 q^{37} -2.76139e6i q^{38} -1.75386e6 q^{40} +1.71384e6i q^{41} -5.26089e6 q^{43} -1.37096e6i q^{44} +4.92128e6 q^{46} +3.08259e6i q^{47} +823543. q^{49} +1.21751e7i q^{50} -1.74083e6 q^{52} +2.09484e6i q^{53} -1.29716e7 q^{55} -1.31419e6i q^{56} -1.35033e7 q^{58} -3.20325e6i q^{59} +1.98256e7 q^{61} +3.41810e6i q^{62} -2.09715e6 q^{64} +1.64712e7i q^{65} +9.17847e6 q^{67} -6.12630e6i q^{68} -1.24345e7 q^{70} -1.91539e7i q^{71} -2.89130e7 q^{73} +3.07630e7i q^{74} -3.12415e7 q^{76} -9.71982e6i q^{77} -5.38663e7 q^{79} +1.98426e7i q^{80} +1.93898e7 q^{82} -8.19595e6i q^{83} -5.79653e7 q^{85} +5.95202e7i q^{86} -1.55107e7 q^{88} +9.29268e7i q^{89} -1.23421e7 q^{91} -5.56779e7i q^{92} +3.48755e7 q^{94} +2.95598e8i q^{95} -1.92146e7 q^{97} -9.31733e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1024 q^{4}+O(q^{10}) \) 8 * q - 1024 * q^4	\( 8 q - 1024 q^{4} + 4480 q^{10} + 156632 q^{13} + 131072 q^{16} + 321160 q^{19} + 65216 q^{22} - 2280096 q^{25} - 2427880 q^{31} + 4914560 q^{34} + 2032696 q^{37} - 573440 q^{40} - 14076032 q^{43} + 13935680 q^{46} + 6588344 q^{49} - 20048896 q^{52} + 21354536 q^{55} - 4103168 q^{58} + 46591832 q^{61} - 16777216 q^{64} - 26848632 q^{67} - 39798976 q^{70} + 94257072 q^{73} - 41108480 q^{76} - 244539784 q^{79} + 10967040 q^{82} + 163925624 q^{85} - 8347648 q^{88} - 57547168 q^{91} - 28288512 q^{94} + 109673088 q^{97}+O(q^{100}) \) 8 * q - 1024 * q^4 + 4480 * q^10 + 156632 * q^13 + 131072 * q^16 + 321160 * q^19 + 65216 * q^22 - 2280096 * q^25 - 2427880 * q^31 + 4914560 * q^34 + 2032696 * q^37 - 573440 * q^40 - 14076032 * q^43 + 13935680 * q^46 + 6588344 * q^49 - 20048896 * q^52 + 21354536 * q^55 - 4103168 * q^58 + 46591832 * q^61 - 16777216 * q^64 - 26848632 * q^67 - 39798976 * q^70 + 94257072 * q^73 - 41108480 * q^76 - 244539784 * q^79 + 10967040 * q^82 + 163925624 * q^85 - 8347648 * q^88 - 57547168 * q^91 - 28288512 * q^94 + 109673088 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more