LMFDB - Embedded newform 9.9.b.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,9,Mod(8,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	9.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:	$3.66640749055$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			8.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	9.8
Dual form			9.9.b.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.24264i q^{2} +238.000 q^{4} -988.535i q^{5} +1652.00 q^{7} -2095.86i q^{8} +O(q^{10})$	\(q-4.24264i q^{2} +238.000 q^{4} -988.535i q^{5} +1652.00 q^{7} -2095.86i q^{8} -4194.00 q^{10} +21365.9i q^{11} -26272.0 q^{13} -7008.84i q^{14} +52036.0 q^{16} -15184.4i q^{17} +46640.0 q^{19} -235271. i q^{20} +90648.0 q^{22} +328092. i q^{23} -586577. q^{25} +111463. i q^{26} +393176. q^{28} +614983. i q^{29} -196444. q^{31} -757311. i q^{32} -64422.0 q^{34} -1.63306e6i q^{35} +2.81941e6 q^{37} -197877. i q^{38} -2.07184e6 q^{40} +706429. i q^{41} -2.21346e6 q^{43} +5.08509e6i q^{44} +1.39198e6 q^{46} -1.63296e6i q^{47} -3.03570e6 q^{49} +2.48864e6i q^{50} -6.25274e6 q^{52} -5.18868e6i q^{53} +2.11210e7 q^{55} -3.46237e6i q^{56} +2.60915e6 q^{58} -1.17447e7i q^{59} -1.74053e7 q^{61} +833441. i q^{62} +1.01082e7 q^{64} +2.59708e7i q^{65} -1.43227e7 q^{67} -3.61389e6i q^{68} -6.92849e6 q^{70} +1.56456e7i q^{71} -8.90699e6 q^{73} -1.19618e7i q^{74} +1.11003e7 q^{76} +3.52965e7i q^{77} +3.27588e7 q^{79} -5.14394e7i q^{80} +2.99713e6 q^{82} -8.50888e7i q^{83} -1.50103e7 q^{85} +9.39093e6i q^{86} +4.47801e7 q^{88} +5.89361e7i q^{89} -4.34013e7 q^{91} +7.80859e7i q^{92} -6.92806e6 q^{94} -4.61053e7i q^{95} -2.44517e7 q^{97} +1.28794e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 476 q^{4} + 3304 q^{7}+O(q^{10}) $ 2 * q + 476 * q^4 + 3304 * q^7	$ 2 q + 476 q^{4} + 3304 q^{7} - 8388 q^{10} - 52544 q^{13} + 104072 q^{16} + 93280 q^{19} + 181296 q^{22} - 1173154 q^{25} + 786352 q^{28} - 392888 q^{31} - 128844 q^{34} + 5638828 q^{37} - 4143672 q^{40} - 4426928 q^{43} + 2783952 q^{46} - 6071394 q^{49} - 12505472 q^{52} + 42241968 q^{55} + 5218308 q^{58} - 34810604 q^{61} + 20216432 q^{64} - 28645328 q^{67} - 13856976 q^{70} - 17813984 q^{73} + 22200640 q^{76} + 65517688 q^{79} + 5994252 q^{82} - 30020652 q^{85} + 89560224 q^{88} - 86802688 q^{91} - 13856112 q^{94} - 48903488 q^{97}+O(q^{100}) $ 2 * q + 476 * q^4 + 3304 * q^7 - 8388 * q^10 - 52544 * q^13 + 104072 * q^16 + 93280 * q^19 + 181296 * q^22 - 1173154 * q^25 + 786352 * q^28 - 392888 * q^31 - 128844 * q^34 + 5638828 * q^37 - 4143672 * q^40 - 4426928 * q^43 + 2783952 * q^46 - 6071394 * q^49 - 12505472 * q^52 + 42241968 * q^55 + 5218308 * q^58 - 34810604 * q^61 + 20216432 * q^64 - 28645328 * q^67 - 13856976 * q^70 - 17813984 * q^73 + 22200640 * q^76 + 65517688 * q^79 + 5994252 * q^82 - 30020652 * q^85 + 89560224 * q^88 - 86802688 * q^91 - 13856112 * q^94 - 48903488 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 4.24264i	− 0.265165i	−0.991172	−	0.132583i	$-0.957673\pi$
$2$	− 4.24264i	− 0.265165i	0.991172	−	0.132583i	$-0.0423270\pi$
$3$	0	0
$3$	0	0
$4$	238.000	0.929688
$5$	− 988.535i	− 1.58166i	−0.612038	−	0.790828i	$-0.709650\pi$
$5$	− 988.535i	− 1.58166i	0.612038	−	0.790828i	$-0.290350\pi$
$6$	0	0
$7$	1652.00	0.688047	0.344023	−	0.938961i	$-0.388210\pi$
$7$	1652.00	0.688047	0.344023	+	0.938961i	$0.388210\pi$
$8$	− 2095.86i	− 0.511686i
$9$	0	0
$10$	−4194.00	−0.419400
$11$	21365.9i	1.45932i	0.683809	+	0.729661i	$0.260322\pi$
$11$	21365.9i	1.45932i	−0.683809	+	0.729661i	$0.739678\pi$
$12$	0	0
$13$	−26272.0	−0.919856	−0.459928	−	0.887956i	$-0.652125\pi$
$13$	−26272.0	−0.919856	−0.459928	+	0.887956i	$0.652125\pi$
$14$	− 7008.84i	− 0.182446i
$15$	0	0
$16$	52036.0	0.794006
$17$	− 15184.4i	− 0.181804i	−0.995860	−	0.0909018i	$-0.971025\pi$
$17$	− 15184.4i	− 0.181804i	0.995860	−	0.0909018i	$-0.0289749\pi$
$18$	0	0
$19$	46640.0	0.357886	0.178943	−	0.983859i	$-0.442732\pi$
$19$	46640.0	0.357886	0.178943	+	0.983859i	$0.442732\pi$
$20$	− 235271.i	− 1.47045i
$21$	0	0
$22$	90648.0	0.386961
$23$	328092.i	1.17242i	0.810158	+	0.586211i	$0.199381\pi$
$23$	328092.i	1.17242i	−0.810158	+	0.586211i	$0.800619\pi$
$24$	0	0
$25$	−586577.	−1.50164
$26$	111463.i	0.243914i
$27$	0	0
$28$	393176.	0.639668
$29$	614983.i	0.869504i	0.900550	+	0.434752i	$0.143164\pi$
$29$	614983.i	0.869504i	−0.900550	+	0.434752i	$0.856836\pi$
$30$	0	0
$31$	−196444.	−0.212712	−0.106356	−	0.994328i	$-0.533918\pi$
$31$	−196444.	−0.212712	−0.106356	+	0.994328i	$0.533918\pi$
$32$	− 757311.i	− 0.722228i
$33$	0	0
$34$	−64422.0	−0.0482079
$35$	− 1.63306e6i	− 1.08825i
$36$	0	0
$37$	2.81941e6	1.50436	0.752180	−	0.658957i	$-0.229002\pi$
$37$	2.81941e6	1.50436	0.752180	+	0.658957i	$0.229002\pi$
$38$	− 197877.i	− 0.0948987i
$39$	0	0
$40$	−2.07184e6	−0.809311
$41$	706429.i	0.249996i	0.992157	+	0.124998i	$0.0398925\pi$
$41$	706429.i	0.249996i	−0.992157	+	0.124998i	$0.960108\pi$
$42$	0	0
$43$	−2.21346e6	−0.647439	−0.323719	−	0.946153i	$-0.604933\pi$
$43$	−2.21346e6	−0.647439	−0.323719	+	0.946153i	$0.604933\pi$
$44$	5.08509e6i	1.35671i
$45$	0	0
$46$	1.39198e6	0.310885
$47$	− 1.63296e6i	− 0.334645i	−0.985902	−	0.167322i	$-0.946488\pi$
$47$	− 1.63296e6i	− 0.334645i	0.985902	−	0.167322i	$-0.0535120\pi$
$48$	0	0
$49$	−3.03570e6	−0.526592
$50$	2.48864e6i	0.398182i
$51$	0	0
$52$	−6.25274e6	−0.855178
$53$	− 5.18868e6i	− 0.657587i	−0.944402	−	0.328793i	$-0.893358\pi$
$53$	− 5.18868e6i	− 0.657587i	0.944402	−	0.328793i	$-0.106642\pi$
$54$	0	0
$55$	2.11210e7	2.30815
$56$	− 3.46237e6i	− 0.352064i
$57$	0	0
$58$	2.60915e6	0.230562
$59$	− 1.17447e7i	− 0.969250i	−0.874722	−	0.484625i	$-0.838956\pi$
$59$	− 1.17447e7i	− 0.969250i	0.874722	−	0.484625i	$-0.161044\pi$
$60$	0	0
$61$	−1.74053e7	−1.25708	−0.628539	−	0.777778i	$-0.716347\pi$
$61$	−1.74053e7	−1.25708	−0.628539	+	0.777778i	$0.716347\pi$
$62$	833441.i	0.0564038i
$63$	0	0
$64$	1.01082e7	0.602497
$65$	2.59708e7i	1.45490i
$66$	0	0
$67$	−1.43227e7	−0.710763	−0.355381	−	0.934721i	$-0.615649\pi$
$67$	−1.43227e7	−0.710763	−0.355381	+	0.934721i	$0.615649\pi$
$68$	− 3.61389e6i	− 0.169020i
$69$	0	0
$70$	−6.92849e6	−0.288567
$71$	1.56456e7i	0.615686i	0.951437	+	0.307843i	$0.0996072\pi$
$71$	1.56456e7i	0.615686i	−0.951437	+	0.307843i	$0.900393\pi$
$72$	0	0
$73$	−8.90699e6	−0.313646	−0.156823	−	0.987627i	$-0.550125\pi$
$73$	−8.90699e6	−0.313646	−0.156823	+	0.987627i	$0.550125\pi$
$74$	− 1.19618e7i	− 0.398904i
$75$	0	0
$76$	1.11003e7	0.332722
$77$	3.52965e7i	1.00408i
$78$	0	0
$79$	3.27588e7	0.841047	0.420523	−	0.907282i	$-0.361846\pi$
$79$	3.27588e7	0.841047	0.420523	+	0.907282i	$0.361846\pi$
$80$	− 5.14394e7i	− 1.25585i
$81$	0	0
$82$	2.99713e6	0.0662902
$83$	− 8.50888e7i	− 1.79292i	−0.443128	−	0.896458i	$-0.646131\pi$
$83$	− 8.50888e7i	− 1.79292i	0.443128	−	0.896458i	$-0.353869\pi$
$84$	0	0
$85$	−1.50103e7	−0.287551
$86$	9.39093e6i	0.171678i
$87$	0	0
$88$	4.47801e7	0.746714
$89$	5.89361e7i	0.939337i	0.882843	+	0.469668i	$0.155627\pi$
$89$	5.89361e7i	0.939337i	−0.882843	+	0.469668i	$0.844373\pi$
$90$	0	0
$91$	−4.34013e7	−0.632904
$92$	7.80859e7i	1.08999i
$93$	0	0
$94$	−6.92806e6	−0.0887360
$95$	− 4.61053e7i	− 0.566052i
$96$	0	0
$97$	−2.44517e7	−0.276200	−0.138100	−	0.990418i	$-0.544099\pi$
$97$	−2.44517e7	−0.276200	−0.138100	+	0.990418i	$0.544099\pi$
$98$	1.28794e7i	0.139634i
$99$	0	0
$100$	−1.39605e8	−1.39605
$101$	1.02159e8i	0.981733i	0.871235	+	0.490866i	$0.163320\pi$
$101$	1.02159e8i	0.981733i	−0.871235	+	0.490866i	$0.836680\pi$
$102$	0	0
$103$	1.64259e8	1.45942	0.729708	−	0.683759i	$-0.239656\pi$
$103$	1.64259e8	1.45942	0.729708	+	0.683759i	$0.239656\pi$
$104$	5.50626e7i	0.470677i
$105$	0	0
$106$	−2.20137e7	−0.174369
$107$	− 1.73028e8i	− 1.32002i	−0.751256	−	0.660011i	$-0.770551\pi$
$107$	− 1.73028e8i	− 1.32002i	0.751256	−	0.660011i	$-0.229449\pi$
$108$	0	0
$109$	−7.43430e7	−0.526665	−0.263332	−	0.964705i	$-0.584822\pi$
$109$	−7.43430e7	−0.526665	−0.263332	+	0.964705i	$0.584822\pi$
$110$	− 8.96087e7i	− 0.612040i
$111$	0	0
$112$	8.59635e7	0.546313
$113$	− 1.83570e8i	− 1.12587i	−0.826501	−	0.562935i	$-0.809672\pi$
$113$	− 1.83570e8i	− 1.12587i	0.826501	−	0.562935i	$-0.190328\pi$
$114$	0	0
$115$	3.24330e8	1.85437
$116$	1.46366e8i	0.808367i
$117$	0	0
$118$	−4.98288e7	−0.257011
$119$	− 2.50846e7i	− 0.125089i
$120$	0	0
$121$	−2.42144e8	−1.12962
$122$	7.38444e7i	0.333333i
$123$	0	0
$124$	−4.67537e7	−0.197756
$125$	1.93705e8i	0.793418i
$126$	0	0
$127$	−2.41939e8	−0.930016	−0.465008	−	0.885306i	$-0.653949\pi$
$127$	−2.41939e8	−0.930016	−0.465008	+	0.885306i	$0.653949\pi$
$128$	− 2.36757e8i	− 0.881989i
$129$	0	0
$130$	1.10185e8	0.385788
$131$	3.76211e8i	1.27746i	0.769432	+	0.638729i	$0.220539\pi$
$131$	3.76211e8i	1.27746i	−0.769432	+	0.638729i	$0.779461\pi$
$132$	0	0
$133$	7.70493e7	0.246242
$134$	6.07659e7i	0.188469i
$135$	0	0
$136$	−3.18245e7	−0.0930263
$137$	3.29613e8i	0.935670i	0.883816	+	0.467835i	$0.154966\pi$
$137$	3.29613e8i	0.935670i	−0.883816	+	0.467835i	$0.845034\pi$
$138$	0	0
$139$	−2.81930e8	−0.755235	−0.377618	−	0.925962i	$-0.623257\pi$
$139$	−2.81930e8	−0.755235	−0.377618	+	0.925962i	$0.623257\pi$
$140$	− 3.88668e8i	− 1.01174i
$141$	0	0
$142$	6.63787e7	0.163258
$143$	− 5.61326e8i	− 1.34237i
$144$	0	0
$145$	6.07933e8	1.37526
$146$	3.77892e7i	0.0831679i
$147$	0	0
$148$	6.71021e8	1.39859
$149$	− 2.86896e8i	− 0.582075i	−0.956712	−	0.291037i	$-0.906000\pi$
$149$	− 2.86896e8i	− 0.582075i	0.956712	−	0.291037i	$-0.0940004\pi$
$150$	0	0
$151$	−6.90036e8	−1.32729	−0.663643	−	0.748050i	$-0.730990\pi$
$151$	−6.90036e8	−1.32729	−0.663643	+	0.748050i	$0.730990\pi$
$152$	− 9.77511e7i	− 0.183125i
$153$	0	0
$154$	1.49750e8	0.266247
$155$	1.94192e8i	0.336437i
$156$	0	0
$157$	−4.38415e8	−0.721584	−0.360792	−	0.932646i	$-0.617494\pi$
$157$	−4.38415e8	−0.721584	−0.360792	+	0.932646i	$0.617494\pi$
$158$	− 1.38984e8i	− 0.223016i
$159$	0	0
$160$	−7.48629e8	−1.14232
$161$	5.42008e8i	0.806681i
$162$	0	0
$163$	1.20932e9	1.71313	0.856567	−	0.516036i	$-0.172593\pi$
$163$	1.20932e9	1.71313	0.856567	+	0.516036i	$0.172593\pi$
$164$	1.68130e8i	0.232418i
$165$	0	0
$166$	−3.61001e8	−0.475419
$167$	1.24766e9i	1.60409i	0.597262	+	0.802046i	$0.296255\pi$
$167$	1.24766e9i	1.60409i	−0.597262	+	0.802046i	$0.703745\pi$
$168$	0	0
$169$	−1.25513e8	−0.153865
$170$	6.36834e7i	0.0762484i
$171$	0	0
$172$	−5.26804e8	−0.601916
$173$	− 1.56770e9i	− 1.75016i	−0.483975	−	0.875082i	$-0.660808\pi$
$173$	− 1.56770e9i	− 1.75016i	0.483975	−	0.875082i	$-0.339192\pi$
$174$	0	0
$175$	−9.69025e8	−1.03320
$176$	1.11180e9i	1.15871i
$177$	0	0
$178$	2.50045e8	0.249079
$179$	− 1.91059e8i	− 0.186104i	−0.995661	−	0.0930520i	$-0.970338\pi$
$179$	− 1.91059e8i	− 0.186104i	0.995661	−	0.0930520i	$-0.0296623\pi$
$180$	0	0
$181$	1.53680e9	1.43187	0.715936	−	0.698166i	$-0.246000\pi$
$181$	1.53680e9	1.43187	0.715936	+	0.698166i	$0.246000\pi$
$182$	1.84136e8i	0.167824i
$183$	0	0
$184$	6.87636e8	0.599912
$185$	− 2.78709e9i	− 2.37938i
$186$	0	0
$187$	3.24429e8	0.265310
$188$	− 3.88644e8i	− 0.311115i
$189$	0	0
$190$	−1.95608e8	−0.150097
$191$	6.18990e8i	0.465104i	0.972584	+	0.232552i	$0.0747076\pi$
$191$	6.18990e8i	0.465104i	−0.972584	+	0.232552i	$0.925292\pi$
$192$	0	0
$193$	−3.29048e6	−0.00237154	−0.00118577	−	0.999999i	$-0.500377\pi$
$193$	−3.29048e6	−0.00237154	−0.00118577	+	0.999999i	$0.500377\pi$
$194$	1.03740e8i	0.0732385i
$195$	0	0
$196$	−7.22496e8	−0.489566
$197$	4.55140e8i	0.302190i	0.988519	+	0.151095i	$0.0482800\pi$
$197$	4.55140e8i	0.302190i	−0.988519	+	0.151095i	$0.951720\pi$
$198$	0	0
$199$	−2.01948e8	−0.128774	−0.0643869	−	0.997925i	$-0.520509\pi$
$199$	−2.01948e8	−0.128774	−0.0643869	+	0.997925i	$0.520509\pi$
$200$	1.22939e9i	0.768366i
$201$	0	0
$202$	4.33426e8	0.260321
$203$	1.01595e9i	0.598259i
$204$	0	0
$205$	6.98330e8	0.395408
$206$	− 6.96890e8i	− 0.386986i
$207$	0	0
$208$	−1.36709e9	−0.730371
$209$	9.96507e8i	0.522270i
$210$	0	0
$211$	−3.02679e9	−1.52705	−0.763524	−	0.645780i	$-0.776532\pi$
$211$	−3.02679e9	−1.52705	−0.763524	+	0.645780i	$0.776532\pi$
$212$	− 1.23491e9i	− 0.611350i
$213$	0	0
$214$	−7.34096e8	−0.350024
$215$	2.18809e9i	1.02403i
$216$	0	0
$217$	−3.24525e8	−0.146356
$218$	3.15411e8i	0.139653i
$219$	0	0
$220$	5.02679e9	2.14586
$221$	3.98925e8i	0.167233i
$222$	0	0
$223$	6.21079e8	0.251147	0.125573	−	0.992084i	$-0.459923\pi$
$223$	6.21079e8	0.251147	0.125573	+	0.992084i	$0.459923\pi$
$224$	− 1.25108e9i	− 0.496927i
$225$	0	0
$226$	−7.78822e8	−0.298541
$227$	− 3.81091e9i	− 1.43524i	−0.696434	−	0.717621i	$-0.745231\pi$
$227$	− 3.81091e9i	− 1.43524i	0.696434	−	0.717621i	$-0.254769\pi$
$228$	0	0
$229$	9.96529e8	0.362367	0.181183	−	0.983449i	$-0.442007\pi$
$229$	9.96529e8	0.362367	0.181183	+	0.983449i	$0.442007\pi$
$230$	− 1.37602e9i	− 0.491714i
$231$	0	0
$232$	1.28892e9	0.444913
$233$	− 7.27588e8i	− 0.246866i	−0.992353	−	0.123433i	$-0.960610\pi$
$233$	− 7.27588e8i	− 0.246866i	0.992353	−	0.123433i	$-0.0393904\pi$
$234$	0	0
$235$	−1.61424e9	−0.529293
$236$	− 2.79525e9i	− 0.901099i
$237$	0	0
$238$	−1.06425e8	−0.0331693
$239$	3.98682e9i	1.22190i	0.791670	+	0.610949i	$0.209212\pi$
$239$	3.98682e9i	1.22190i	−0.791670	+	0.610949i	$0.790788\pi$
$240$	0	0
$241$	3.71314e9	1.10071	0.550355	−	0.834931i	$-0.314492\pi$
$241$	3.71314e9	1.10071	0.550355	+	0.834931i	$0.314492\pi$
$242$	1.02733e9i	0.299536i
$243$	0	0
$244$	−4.14246e9	−1.16869
$245$	3.00089e9i	0.832887i
$246$	0	0
$247$	−1.22533e9	−0.329203
$248$	4.11720e8i	0.108842i
$249$	0	0
$250$	8.21823e8	0.210387
$251$	− 2.55588e9i	− 0.643940i	−0.946750	−	0.321970i	$-0.895655\pi$
$251$	− 2.55588e9i	− 0.643940i	0.946750	−	0.321970i	$-0.104345\pi$
$252$	0	0
$253$	−7.00999e9	−1.71094
$254$	1.02646e9i	0.246608i
$255$	0	0
$256$	1.58323e9	0.368624
$257$	7.81351e8i	0.179107i	0.995982	+	0.0895537i	$0.0285441\pi$
$257$	7.81351e8i	0.179107i	−0.995982	+	0.0895537i	$0.971456\pi$
$258$	0	0
$259$	4.65767e9	1.03507
$260$	6.18105e9i	1.35260i
$261$	0	0
$262$	1.59613e9	0.338737
$263$	4.40922e9i	0.921593i	0.887506	+	0.460796i	$0.152436\pi$
$263$	4.40922e9i	0.921593i	−0.887506	+	0.460796i	$0.847564\pi$
$264$	0	0
$265$	−5.12919e9	−1.04008
$266$	− 3.26892e8i	− 0.0652948i
$267$	0	0
$268$	−3.40879e9	−0.660787
$269$	− 8.30145e9i	− 1.58542i	−0.609598	−	0.792711i	$-0.708669\pi$
$269$	− 8.30145e9i	− 1.58542i	0.609598	−	0.792711i	$-0.291331\pi$
$270$	0	0
$271$	7.70047e9	1.42771	0.713855	−	0.700293i	$-0.246947\pi$
$271$	7.70047e9	1.42771	0.713855	+	0.700293i	$0.246947\pi$
$272$	− 7.90136e8i	− 0.144353i
$273$	0	0
$274$	1.39843e9	0.248107
$275$	− 1.25328e10i	− 2.19137i
$276$	0	0
$277$	9.65521e8	0.164000	0.0819998	−	0.996632i	$-0.473869\pi$
$277$	9.65521e8	0.164000	0.0819998	+	0.996632i	$0.473869\pi$
$278$	1.19613e9i	0.200262i
$279$	0	0
$280$	−3.42267e9	−0.556844
$281$	− 1.43642e9i	− 0.230386i	−0.993343	−	0.115193i	$-0.963251\pi$
$281$	− 1.43642e9i	− 0.230386i	0.993343	−	0.115193i	$-0.0367486\pi$
$282$	0	0
$283$	7.83057e9	1.22081	0.610405	−	0.792090i	$-0.291007\pi$
$283$	7.83057e9	1.22081	0.610405	+	0.792090i	$0.291007\pi$
$284$	3.72366e9i	0.572396i
$285$	0	0
$286$	−2.38150e9	−0.355949
$287$	1.16702e9i	0.172009i
$288$	0	0
$289$	6.74519e9	0.966947
$290$	− 2.57924e9i	− 0.364670i
$291$	0	0
$292$	−2.11986e9	−0.291593
$293$	1.46462e10i	1.98726i	0.112675	+	0.993632i	$0.464058\pi$
$293$	1.46462e10i	1.98726i	−0.112675	+	0.993632i	$0.535942\pi$
$294$	0	0
$295$	−1.16101e10	−1.53302
$296$	− 5.90911e9i	− 0.769760i
$297$	0	0
$298$	−1.21719e9	−0.154346
$299$	− 8.61963e9i	− 1.07846i
$300$	0	0
$301$	−3.65664e9	−0.445468
$302$	2.92758e9i	0.351950i
$303$	0	0
$304$	2.42696e9	0.284163
$305$	1.72058e10i	1.98827i
$306$	0	0
$307$	5.21094e9	0.586628	0.293314	−	0.956016i	$-0.405242\pi$
$307$	5.21094e9	0.586628	0.293314	+	0.956016i	$0.405242\pi$
$308$	8.40057e9i	0.933482i
$309$	0	0
$310$	8.23886e8	0.0892114
$311$	− 9.31283e9i	− 0.995498i	−0.867321	−	0.497749i	$-0.834160\pi$
$311$	− 9.31283e9i	− 0.995498i	0.867321	−	0.497749i	$-0.165840\pi$
$312$	0	0
$313$	−1.48794e10	−1.55027	−0.775137	−	0.631793i	$-0.782319\pi$
$313$	−1.48794e10	−1.55027	−0.775137	+	0.631793i	$0.782319\pi$
$314$	1.86004e9i	0.191339i
$315$	0	0
$316$	7.79660e9	0.781911
$317$	4.30922e8i	0.0426739i	0.999772	+	0.0213369i	$0.00679227\pi$
$317$	4.30922e8i	0.0426739i	−0.999772	+	0.0213369i	$0.993208\pi$
$318$	0	0
$319$	−1.31397e10	−1.26889
$320$	− 9.99233e9i	− 0.952943i
$321$	0	0
$322$	2.29954e9	0.213904
$323$	− 7.08201e8i	− 0.0650648i
$324$	0	0
$325$	1.54106e10	1.38129
$326$	− 5.13072e9i	− 0.454263i
$327$	0	0
$328$	1.48058e9	0.127919
$329$	− 2.69765e9i	− 0.230251i
$330$	0	0
$331$	2.10236e10	1.75144	0.875718	−	0.482823i	$-0.160389\pi$
$331$	2.10236e10	1.75144	0.875718	+	0.482823i	$0.160389\pi$
$332$	− 2.02511e10i	− 1.66685i
$333$	0	0
$334$	5.29336e9	0.425349
$335$	1.41585e10i	1.12418i
$336$	0	0
$337$	−4.29142e9	−0.332722	−0.166361	−	0.986065i	$-0.553202\pi$
$337$	−4.29142e9	−0.332722	−0.166361	+	0.986065i	$0.553202\pi$
$338$	5.32505e8i	0.0407997i
$339$	0	0
$340$	−3.57246e9	−0.267332
$341$	− 4.19721e9i	− 0.310415i
$342$	0	0
$343$	−1.45384e10	−1.05037
$344$	4.63912e9i	0.331285i
$345$	0	0
$346$	−6.65119e9	−0.464082
$347$	− 6.41858e8i	− 0.0442712i	−0.999755	−	0.0221356i	$-0.992953\pi$
$347$	− 6.41858e8i	− 0.0442712i	0.999755	−	0.0221356i	$-0.00704656\pi$
$348$	0	0
$349$	−1.90504e10	−1.28411	−0.642054	−	0.766660i	$-0.721917\pi$
$349$	−1.90504e10	−1.28411	−0.642054	+	0.766660i	$0.721917\pi$
$350$	4.11123e9i	0.273968i
$351$	0	0
$352$	1.61807e10	1.05396
$353$	− 2.10987e9i	− 0.135880i	−0.997689	−	0.0679401i	$-0.978357\pi$
$353$	− 2.10987e9i	− 0.135880i	0.997689	−	0.0679401i	$-0.0216427\pi$
$354$	0	0
$355$	1.54662e10	0.973804
$356$	1.40268e10i	0.873290i
$357$	0	0
$358$	−8.10595e8	−0.0493483
$359$	1.30698e10i	0.786846i	0.919358	+	0.393423i	$0.128709\pi$
$359$	1.30698e10i	0.786846i	−0.919358	+	0.393423i	$0.871291\pi$
$360$	0	0
$361$	−1.48083e10	−0.871918
$362$	− 6.52010e9i	− 0.379682i
$363$	0	0
$364$	−1.03295e10	−0.588403
$365$	8.80488e9i	0.496080i
$366$	0	0
$367$	−8.66221e9	−0.477490	−0.238745	−	0.971082i	$-0.576736\pi$
$367$	−8.66221e9	−0.477490	−0.238745	+	0.971082i	$0.576736\pi$
$368$	1.70726e10i	0.930911i
$369$	0	0
$370$	−1.18246e10	−0.630929
$371$	− 8.57170e9i	− 0.452451i
$372$	0	0
$373$	2.28526e10	1.18060	0.590298	−	0.807186i	$-0.299010\pi$
$373$	2.28526e10	1.18060	0.590298	+	0.807186i	$0.299010\pi$
$374$	− 1.37644e9i	− 0.0703509i
$375$	0	0
$376$	−3.42246e9	−0.171233
$377$	− 1.61568e10i	− 0.799818i
$378$	0	0
$379$	1.19395e10	0.578668	0.289334	−	0.957228i	$-0.406566\pi$
$379$	1.19395e10	0.578668	0.289334	+	0.957228i	$0.406566\pi$
$380$	− 1.09731e10i	− 0.526251i
$381$	0	0
$382$	2.62615e9	0.123329
$383$	− 2.82543e9i	− 0.131308i	−0.997842	−	0.0656538i	$-0.979087\pi$
$383$	− 2.82543e9i	− 0.131308i	0.997842	−	0.0656538i	$-0.0209133\pi$
$384$	0	0
$385$	3.48919e10	1.58811
$386$	1.39603e7i	0 0.000628849i
$387$	0	0
$388$	−5.81952e9	−0.256779
$389$	− 2.51686e10i	− 1.09916i	−0.835441	−	0.549580i	$-0.814788\pi$
$389$	− 2.51686e10i	− 1.09916i	0.835441	−	0.549580i	$-0.185212\pi$
$390$	0	0
$391$	4.98188e9	0.213151
$392$	6.36241e9i	0.269449i
$393$	0	0
$394$	1.93100e9	0.0801303
$395$	− 3.23833e10i	− 1.33025i
$396$	0	0
$397$	−2.22833e10	−0.897052	−0.448526	−	0.893770i	$-0.648051\pi$
$397$	−2.22833e10	−0.897052	−0.448526	+	0.893770i	$0.648051\pi$
$398$	8.56793e8i	0.0341463i
$399$	0	0
$400$	−3.05231e10	−1.19231
$401$	− 5.87601e9i	− 0.227251i	−0.993524	−	0.113625i	$-0.963754\pi$
$401$	− 5.87601e9i	− 0.227251i	0.993524	−	0.113625i	$-0.0362463\pi$
$402$	0	0
$403$	5.16098e9	0.195664
$404$	2.43140e10i	0.912705i
$405$	0	0
$406$	4.31032e9	0.158637
$407$	6.02394e10i	2.19535i
$408$	0	0
$409$	4.11930e10	1.47208	0.736039	−	0.676940i	$-0.236694\pi$
$409$	4.11930e10	1.47208	0.736039	+	0.676940i	$0.236694\pi$
$410$	− 2.96276e9i	− 0.104848i
$411$	0	0
$412$	3.90935e10	1.35680
$413$	− 1.94023e10i	− 0.666889i
$414$	0	0
$415$	−8.41133e10	−2.83578
$416$	1.98961e10i	0.664346i
$417$	0	0
$418$	4.22782e9	0.138488
$419$	− 5.63009e9i	− 0.182666i	−0.995820	−	0.0913332i	$-0.970887\pi$
$419$	− 5.63009e9i	− 0.182666i	0.995820	−	0.0913332i	$-0.0291128\pi$
$420$	0	0
$421$	−9.82721e9	−0.312825	−0.156413	−	0.987692i	$-0.549993\pi$
$421$	−9.82721e9	−0.312825	−0.156413	+	0.987692i	$0.549993\pi$
$422$	1.28416e10i	0.404920i
$423$	0	0
$424$	−1.08748e10	−0.336478
$425$	8.90683e9i	0.273003i
$426$	0	0
$427$	−2.87536e10	−0.864928
$428$	− 4.11807e10i	− 1.22721i
$429$	0	0
$430$	9.28327e9	0.271536
$431$	6.62106e10i	1.91875i	0.282135	+	0.959375i	$0.408957\pi$
$431$	6.62106e10i	1.91875i	−0.282135	+	0.959375i	$0.591043\pi$
$432$	0	0
$433$	2.02313e10	0.575537	0.287768	−	0.957700i	$-0.407087\pi$
$433$	2.02313e10	0.575537	0.287768	+	0.957700i	$0.407087\pi$
$434$	1.37685e9i	0.0388084i
$435$	0	0
$436$	−1.76936e10	−0.489634
$437$	1.53022e10i	0.419593i
$438$	0	0
$439$	2.82267e10	0.759981	0.379990	−	0.924990i	$-0.375927\pi$
$439$	2.82267e10	0.759981	0.379990	+	0.924990i	$0.375927\pi$
$440$	− 4.42667e10i	− 1.18105i
$441$	0	0
$442$	1.69249e9	0.0443443
$443$	− 6.41109e10i	− 1.66463i	−0.554305	−	0.832314i	$-0.687016\pi$
$443$	− 6.41109e10i	− 1.66463i	0.554305	−	0.832314i	$-0.312984\pi$
$444$	0	0
$445$	5.82604e10	1.48571
$446$	− 2.63501e9i	− 0.0665953i
$447$	0	0
$448$	1.66988e10	0.414546
$449$	− 3.14738e10i	− 0.774398i	−0.921996	−	0.387199i	$-0.873443\pi$
$449$	− 3.14738e10i	− 0.774398i	0.921996	−	0.387199i	$-0.126557\pi$
$450$	0	0
$451$	−1.50935e10	−0.364825
$452$	− 4.36897e10i	− 1.04671i
$453$	0	0
$454$	−1.61683e10	−0.380576
$455$	4.29038e10i	1.00104i
$456$	0	0
$457$	−6.49162e10	−1.48829	−0.744146	−	0.668017i	$-0.767143\pi$
$457$	−6.49162e10	−1.48829	−0.744146	+	0.668017i	$0.767143\pi$
$458$	− 4.22792e9i	− 0.0960870i
$459$	0	0
$460$	7.71906e10	1.72398
$461$	3.31042e9i	0.0732959i	0.999328	+	0.0366480i	$0.0116680\pi$
$461$	3.31042e9i	0.0732959i	−0.999328	+	0.0366480i	$0.988332\pi$
$462$	0	0
$463$	3.98533e10	0.867243	0.433621	−	0.901095i	$-0.357236\pi$
$463$	3.98533e10	0.867243	0.433621	+	0.901095i	$0.357236\pi$
$464$	3.20013e10i	0.690392i
$465$	0	0
$466$	−3.08689e9	−0.0654603
$467$	4.81612e10i	1.01258i	0.862363	+	0.506291i	$0.168984\pi$
$467$	4.81612e10i	1.01258i	−0.862363	+	0.506291i	$0.831016\pi$
$468$	0	0
$469$	−2.36610e10	−0.489038
$470$	6.84863e9i	0.140350i
$471$	0	0
$472$	−2.46154e10	−0.495951
$473$	− 4.72927e10i	− 0.944822i
$474$	0	0
$475$	−2.73580e10	−0.537414
$476$	− 5.97015e9i	− 0.116294i
$477$	0	0
$478$	1.69146e10	0.324005
$479$	4.57029e10i	0.868164i	0.900873	+	0.434082i	$0.142927\pi$
$479$	4.57029e10i	0.868164i	−0.900873	+	0.434082i	$0.857073\pi$
$480$	0	0
$481$	−7.40716e10	−1.38379
$482$	− 1.57535e10i	− 0.291870i
$483$	0	0
$484$	−5.76304e10	−1.05020
$485$	2.41714e10i	0.436853i
$486$	0	0
$487$	3.67295e10	0.652978	0.326489	−	0.945201i	$-0.394134\pi$
$487$	3.67295e10	0.652978	0.326489	+	0.945201i	$0.394134\pi$
$488$	3.64792e10i	0.643229i
$489$	0	0
$490$	1.27317e10	0.220853
$491$	1.16241e10i	0.200001i	0.994987	+	0.100001i	$0.0318845\pi$
$491$	1.16241e10i	0.200001i	−0.994987	+	0.100001i	$0.968116\pi$
$492$	0	0
$493$	9.33816e9	0.158079
$494$	5.19862e9i	0.0872931i
$495$	0	0
$496$	−1.02222e10	−0.168895
$497$	2.58466e10i	0.423621i
$498$	0	0
$499$	3.46311e10	0.558552	0.279276	−	0.960211i	$-0.409905\pi$
$499$	3.46311e10	0.558552	0.279276	+	0.960211i	$0.409905\pi$
$500$	4.61019e10i	0.737630i
$501$	0	0
$502$	−1.08437e10	−0.170750
$503$	− 8.31882e10i	− 1.29954i	−0.760130	−	0.649770i	$-0.774865\pi$
$503$	− 8.31882e10i	− 1.29954i	0.760130	−	0.649770i	$-0.225135\pi$
$504$	0	0
$505$	1.00988e11	1.55276
$506$	2.97409e10i	0.453682i
$507$	0	0
$508$	−5.75814e10	−0.864624
$509$	− 6.07300e10i	− 0.904758i	−0.891826	−	0.452379i	$-0.850575\pi$
$509$	− 6.07300e10i	− 0.904758i	0.891826	−	0.452379i	$-0.149425\pi$
$510$	0	0
$511$	−1.47144e10	−0.215803
$512$	− 6.73269e10i	− 0.979736i
$513$	0	0
$514$	3.31499e9	0.0474930
$515$	− 1.62375e11i	− 2.30829i
$516$	0	0
$517$	3.48897e10	0.488354
$518$	− 1.97608e10i	− 0.274464i
$519$	0	0
$520$	5.44313e10	0.744449
$521$	6.81755e10i	0.925289i	0.886544	+	0.462644i	$0.153099\pi$
$521$	6.81755e10i	0.925289i	−0.886544	+	0.462644i	$0.846901\pi$
$522$	0	0
$523$	4.73708e10	0.633147	0.316573	−	0.948568i	$-0.397468\pi$
$523$	4.73708e10	0.633147	0.316573	+	0.948568i	$0.397468\pi$
$524$	8.95382e10i	1.18764i
$525$	0	0
$526$	1.87067e10	0.244374
$527$	2.98289e9i	0.0386718i
$528$	0	0
$529$	−2.93333e10	−0.374575
$530$	2.17613e10i	0.275792i
$531$	0	0
$532$	1.83377e10	0.228928
$533$	− 1.85593e10i	− 0.229960i
$534$	0	0
$535$	−1.71044e11	−2.08782
$536$	3.00184e10i	0.363687i
$537$	0	0
$538$	−3.52201e10	−0.420398
$539$	− 6.48605e10i	− 0.768467i
$540$	0	0
$541$	1.63796e10	0.191212	0.0956059	−	0.995419i	$-0.469521\pi$
$541$	1.63796e10	0.191212	0.0956059	+	0.995419i	$0.469521\pi$
$542$	− 3.26703e10i	− 0.378579i
$543$	0	0
$544$	−1.14993e10	−0.131304
$545$	7.34907e10i	0.833003i
$546$	0	0
$547$	7.48606e10	0.836188	0.418094	−	0.908404i	$-0.362698\pi$
$547$	7.48606e10	0.836188	0.418094	+	0.908404i	$0.362698\pi$
$548$	7.84480e10i	0.869881i
$549$	0	0
$550$	−5.31720e10	−0.581075
$551$	2.86828e10i	0.311183i
$552$	0	0
$553$	5.41176e10	0.578679
$554$	− 4.09636e9i	− 0.0434869i
$555$	0	0
$556$	−6.70994e10	−0.702133
$557$	1.58080e11i	1.64231i	0.570705	+	0.821155i	$0.306670\pi$
$557$	1.58080e11i	1.64231i	−0.570705	+	0.821155i	$0.693330\pi$
$558$	0	0
$559$	5.81521e10	0.595550
$560$	− 8.49779e10i	− 0.864080i
$561$	0	0
$562$	−6.09421e9	−0.0610902
$563$	1.27798e11i	1.27201i	0.771687	+	0.636003i	$0.219413\pi$
$563$	1.27798e11i	1.27201i	−0.771687	+	0.636003i	$0.780587\pi$
$564$	0	0
$565$	−1.81465e11	−1.78074
$566$	− 3.32223e10i	− 0.323716i
$567$	0	0
$568$	3.27911e10	0.315038
$569$	5.42832e10i	0.517865i	0.965895	+	0.258933i	$0.0833707\pi$
$569$	5.42832e10i	0.517865i	−0.965895	+	0.258933i	$0.916629\pi$
$570$	0	0
$571$	1.20161e11	1.13037	0.565184	−	0.824965i	$-0.308805\pi$
$571$	1.20161e11	1.13037	0.565184	+	0.824965i	$0.308805\pi$
$572$	− 1.33596e11i	− 1.24798i
$573$	0	0
$574$	4.95125e9	0.0456108
$575$	− 1.92451e11i	− 1.76055i
$576$	0	0
$577$	−1.83000e11	−1.65101	−0.825503	−	0.564398i	$-0.809109\pi$
$577$	−1.83000e11	−1.65101	−0.825503	+	0.564398i	$0.809109\pi$
$578$	− 2.86174e10i	− 0.256401i
$579$	0	0
$580$	1.44688e11	1.27856
$581$	− 1.40567e11i	− 1.23361i
$582$	0	0
$583$	1.10861e11	0.959631
$584$	1.86678e10i	0.160488i
$585$	0	0
$586$	6.21387e10	0.526953
$587$	7.16104e10i	0.603148i	0.953443	+	0.301574i	$0.0975120\pi$
$587$	7.16104e10i	0.603148i	−0.953443	+	0.301574i	$0.902488\pi$
$588$	0	0
$589$	−9.16215e9	−0.0761265
$590$	4.92575e10i	0.406503i
$591$	0	0
$592$	1.46711e11	1.19447
$593$	6.84140e9i	0.0553256i	0.999617	+	0.0276628i	$0.00880647\pi$
$593$	6.84140e9i	0.0553256i	−0.999617	+	0.0276628i	$0.991194\pi$
$594$	0	0
$595$	−2.47971e10	−0.197848
$596$	− 6.82812e10i	− 0.541148i
$597$	0	0
$598$	−3.65700e10	−0.285970
$599$	− 1.61467e11i	− 1.25423i	−0.778927	−	0.627115i	$-0.784236\pi$
$599$	− 1.61467e11i	− 1.25423i	0.778927	−	0.627115i	$-0.215764\pi$
$600$	0	0
$601$	4.14207e10	0.317482	0.158741	−	0.987320i	$-0.449257\pi$
$601$	4.14207e10	0.317482	0.158741	+	0.987320i	$0.449257\pi$
$602$	1.55138e10i	0.118123i
$603$	0	0
$604$	−1.64229e11	−1.23396
$605$	2.39368e11i	1.78667i
$606$	0	0
$607$	−1.14644e11	−0.844492	−0.422246	−	0.906481i	$-0.638758\pi$
$607$	−1.14644e11	−0.844492	−0.422246	+	0.906481i	$0.638758\pi$
$608$	− 3.53210e10i	− 0.258475i
$609$	0	0
$610$	7.29978e10	0.527219
$611$	4.29011e10i	0.307825i
$612$	0	0
$613$	−1.23749e11	−0.876397	−0.438198	−	0.898878i	$-0.644383\pi$
$613$	−1.23749e11	−0.876397	−0.438198	+	0.898878i	$0.644383\pi$
$614$	− 2.21082e10i	− 0.155553i
$615$	0	0
$616$	7.39767e10	0.513774
$617$	6.29138e10i	0.434116i	0.976159	+	0.217058i	$0.0696460\pi$
$617$	6.29138e10i	0.434116i	−0.976159	+	0.217058i	$0.930354\pi$
$618$	0	0
$619$	1.39495e11	0.950156	0.475078	−	0.879944i	$-0.342420\pi$
$619$	1.39495e11	0.950156	0.475078	+	0.879944i	$0.342420\pi$
$620$	4.62177e10i	0.312782i
$621$	0	0
$622$	−3.95110e10	−0.263971
$623$	9.73624e10i	0.646308i
$624$	0	0
$625$	−3.76470e10	−0.246723
$626$	6.31280e10i	0.411079i
$627$	0	0
$628$	−1.04343e11	−0.670848
$629$	− 4.28111e10i	− 0.273498i
$630$	0	0
$631$	−8.25299e10	−0.520588	−0.260294	−	0.965529i	$-0.583819\pi$
$631$	−8.25299e10	−0.520588	−0.260294	+	0.965529i	$0.583819\pi$
$632$	− 6.86581e10i	− 0.430352i
$633$	0	0
$634$	1.82825e9	0.0113156
$635$	2.39165e11i	1.47097i
$636$	0	0
$637$	7.97538e10	0.484389
$638$	5.57470e10i	0.336464i
$639$	0	0
$640$	−2.34043e11	−1.39500
$641$	− 3.04379e11i	− 1.80295i	−0.432836	−	0.901473i	$-0.642487\pi$
$641$	− 3.04379e11i	− 1.80295i	0.432836	−	0.901473i	$-0.357513\pi$
$642$	0	0
$643$	−2.29544e11	−1.34283	−0.671416	−	0.741080i	$-0.734314\pi$
$643$	−2.29544e11	−1.34283	−0.671416	+	0.741080i	$0.734314\pi$
$644$	1.28998e11i	0.749962i
$645$	0	0
$646$	−3.00464e9	−0.0172529
$647$	− 1.03124e11i	− 0.588494i	−0.955729	−	0.294247i	$-0.904931\pi$
$647$	− 1.03124e11i	− 0.588494i	0.955729	−	0.294247i	$-0.0950688\pi$
$648$	0	0
$649$	2.50938e11	1.41445
$650$	− 6.53814e10i	− 0.366270i
$651$	0	0
$652$	2.87818e11	1.59268
$653$	1.38484e10i	0.0761633i	0.999275	+	0.0380816i	$0.0121247\pi$
$653$	1.38484e10i	0.0761633i	−0.999275	+	0.0380816i	$0.987875\pi$
$654$	0	0
$655$	3.71898e11	2.02050
$656$	3.67598e10i	0.198499i
$657$	0	0
$658$	−1.14451e10	−0.0610545
$659$	− 2.78234e11i	− 1.47526i	−0.675205	−	0.737630i	$-0.735945\pi$
$659$	− 2.78234e11i	− 1.47526i	0.675205	−	0.737630i	$-0.264055\pi$
$660$	0	0
$661$	2.00656e11	1.05111	0.525554	−	0.850761i	$-0.323858\pi$
$661$	2.00656e11	1.05111	0.525554	+	0.850761i	$0.323858\pi$
$662$	− 8.91954e10i	− 0.464419i
$663$	0	0
$664$	−1.78335e11	−0.917410
$665$	− 7.61659e10i	− 0.389470i
$666$	0	0
$667$	−2.01771e11	−1.01943
$668$	2.96942e11i	1.49130i
$669$	0	0
$670$	6.00693e10	0.298094
$671$	− 3.71881e11i	− 1.83448i
$672$	0	0
$673$	−1.93202e11	−0.941784	−0.470892	−	0.882191i	$-0.656068\pi$
$673$	−1.93202e11	−0.941784	−0.470892	+	0.882191i	$0.656068\pi$
$674$	1.82070e10i	0.0882263i
$675$	0	0
$676$	−2.98720e10	−0.143047
$677$	− 9.03093e9i	− 0.0429910i	−0.999769	−	0.0214955i	$-0.993157\pi$
$677$	− 9.03093e9i	− 0.0429910i	0.999769	−	0.0214955i	$-0.00684276\pi$
$678$	0	0
$679$	−4.03943e10	−0.190038
$680$	3.14596e10i	0.147136i
$681$	0	0
$682$	−1.78073e10	−0.0823113
$683$	2.79267e11i	1.28333i	0.766987	+	0.641663i	$0.221755\pi$
$683$	2.79267e11i	1.28333i	−0.766987	+	0.641663i	$0.778245\pi$
$684$	0	0
$685$	3.25835e11	1.47991
$686$	6.16813e10i	0.278520i
$687$	0	0
$688$	−1.15180e11	−0.514070
$689$	1.36317e11i	0.604885i
$690$	0	0
$691$	−1.41810e11	−0.622006	−0.311003	−	0.950409i	$-0.600665\pi$
$691$	−1.41810e11	−0.622006	−0.311003	+	0.950409i	$0.600665\pi$
$692$	− 3.73113e11i	− 1.62710i
$693$	0	0
$694$	−2.72317e9	−0.0117392
$695$	2.78698e11i	1.19452i
$696$	0	0
$697$	1.07267e10	0.0454502
$698$	8.08238e10i	0.340500i
$699$	0	0
$700$	−2.30628e11	−0.960550
$701$	− 1.72900e10i	− 0.0716017i	−0.999359	−	0.0358008i	$-0.988602\pi$
$701$	− 1.72900e10i	− 0.0716017i	0.999359	−	0.0358008i	$-0.0113982\pi$
$702$	0	0
$703$	1.31497e11	0.538389
$704$	2.15972e11i	0.879237i
$705$	0	0
$706$	−8.95141e9	−0.0360307
$707$	1.68767e11i	0.675478i
$708$	0	0
$709$	−2.29325e11	−0.907541	−0.453771	−	0.891118i	$-0.649921\pi$
$709$	−2.29325e11	−0.907541	−0.453771	+	0.891118i	$0.649921\pi$
$710$	− 6.56177e10i	− 0.258219i
$711$	0	0
$712$	1.23522e11	0.480645
$713$	− 6.44517e10i	− 0.249388i
$714$	0	0
$715$	−5.54890e11	−2.12316
$716$	− 4.54721e10i	− 0.173019i
$717$	0	0
$718$	5.54503e10	0.208644
$719$	2.34118e11i	0.876030i	0.898968	+	0.438015i	$0.144318\pi$
$719$	2.34118e11i	0.876030i	−0.898968	+	0.438015i	$0.855682\pi$
$720$	0	0
$721$	2.71355e11	1.00415
$722$	6.28262e10i	0.231202i
$723$	0	0
$724$	3.65759e11	1.33119
$725$	− 3.60735e11i	− 1.30568i
$726$	0	0
$727$	2.62995e11	0.941479	0.470740	−	0.882272i	$-0.343987\pi$
$727$	2.62995e11	0.941479	0.470740	+	0.882272i	$0.343987\pi$
$728$	9.09633e10i	0.323848i
$729$	0	0
$730$	3.73559e10	0.131543
$731$	3.36101e10i	0.117707i
$732$	0	0
$733$	−2.39665e11	−0.830213	−0.415106	−	0.909773i	$-0.636256\pi$
$733$	−2.39665e11	−0.830213	−0.415106	+	0.909773i	$0.636256\pi$
$734$	3.67506e10i	0.126614i
$735$	0	0
$736$	2.48468e11	0.846757
$737$	− 3.06017e11i	− 1.03723i
$738$	0	0
$739$	4.01061e10	0.134472	0.0672361	−	0.997737i	$-0.478582\pi$
$739$	4.01061e10	0.134472	0.0672361	+	0.997737i	$0.478582\pi$
$740$	− 6.63327e11i	− 2.21208i
$741$	0	0
$742$	−3.63666e10	−0.119974
$743$	− 5.15417e10i	− 0.169123i	−0.996418	−	0.0845617i	$-0.973051\pi$
$743$	− 5.15417e10i	− 0.169123i	0.996418	−	0.0845617i	$-0.0269490\pi$
$744$	0	0
$745$	−2.83606e11	−0.920642
$746$	− 9.69556e10i	− 0.313053i
$747$	0	0
$748$	7.72141e10	0.246655
$749$	− 2.85842e11i	− 0.908237i
$750$	0	0
$751$	1.45524e11	0.457484	0.228742	−	0.973487i	$-0.426539\pi$
$751$	1.45524e11	0.457484	0.228742	+	0.973487i	$0.426539\pi$
$752$	− 8.49726e10i	− 0.265710i
$753$	0	0
$754$	−6.85477e10	−0.212084
$755$	6.82125e11i	2.09931i
$756$	0	0
$757$	2.32953e11	0.709390	0.354695	−	0.934982i	$-0.384585\pi$
$757$	2.32953e11	0.709390	0.354695	+	0.934982i	$0.384585\pi$
$758$	− 5.06550e10i	− 0.153442i
$759$	0	0
$760$	−9.66304e10	−0.289641
$761$	3.56275e11i	1.06230i	0.847279	+	0.531149i	$0.178239\pi$
$761$	3.56275e11i	1.06230i	−0.847279	+	0.531149i	$0.821761\pi$
$762$	0	0
$763$	−1.22815e11	−0.362370
$764$	1.47320e11i	0.432401i
$765$	0	0
$766$	−1.19873e10	−0.0348182
$767$	3.08558e11i	0.891570i
$768$	0	0
$769$	1.68419e11	0.481599	0.240800	−	0.970575i	$-0.422590\pi$
$769$	1.68419e11	0.481599	0.240800	+	0.970575i	$0.422590\pi$
$770$	− 1.48034e11i	− 0.421112i
$771$	0	0
$772$	−7.83135e8	−0.00220479
$773$	− 3.15069e11i	− 0.882444i	−0.897398	−	0.441222i	$-0.854545\pi$
$773$	− 3.15069e11i	− 0.882444i	0.897398	−	0.441222i	$-0.145455\pi$
$774$	0	0
$775$	1.15230e11	0.319416
$776$	5.12475e10i	0.141327i
$777$	0	0
$778$	−1.06781e11	−0.291459
$779$	3.29479e10i	0.0894700i
$780$	0	0
$781$	−3.34283e11	−0.898485
$782$	− 2.11363e10i	− 0.0565201i
$783$	0	0
$784$	−1.57966e11	−0.418117
$785$	4.33389e11i	1.14130i
$786$	0	0
$787$	−6.25510e11	−1.63056	−0.815278	−	0.579070i	$-0.803416\pi$
$787$	−6.25510e11	−1.63056	−0.815278	+	0.579070i	$0.803416\pi$
$788$	1.08323e11i	0.280943i
$789$	0	0
$790$	−1.37391e11	−0.352735
$791$	− 3.03258e11i	− 0.774651i
$792$	0	0
$793$	4.57272e11	1.15633
$794$	9.45401e10i	0.237867i
$795$	0	0
$796$	−4.80636e10	−0.119719
$797$	5.74775e11i	1.42451i	0.701922	+	0.712254i	$0.252325\pi$
$797$	5.74775e11i	1.42451i	−0.701922	+	0.712254i	$0.747675\pi$
$798$	0	0
$799$	−2.47955e10	−0.0608395
$800$	4.44221e11i	1.08452i
$801$	0	0
$802$	−2.49298e10	−0.0602589
$803$	− 1.90306e11i	− 0.457710i
$804$	0	0
$805$	5.35794e11	1.27589
$806$	− 2.18962e10i	− 0.0518833i
$807$	0	0
$808$	2.14112e11	0.502339
$809$	− 5.68847e11i	− 1.32801i	−0.747728	−	0.664005i	$-0.768855\pi$
$809$	− 5.68847e11i	− 1.32801i	0.747728	−	0.664005i	$-0.231145\pi$
$810$	0	0
$811$	−6.39315e11	−1.47785	−0.738927	−	0.673785i	$-0.764667\pi$
$811$	−6.39315e11	−1.47785	−0.738927	+	0.673785i	$0.764667\pi$
$812$	2.41797e11i	0.556194i
$813$	0	0
$814$	2.55574e11	0.582129
$815$	− 1.19546e12i	− 2.70959i
$816$	0	0
$817$	−1.03236e11	−0.231709
$818$	− 1.74767e11i	− 0.390343i
$819$	0	0
$820$	1.66203e11	0.367606
$821$	− 7.38100e10i	− 0.162458i	−0.996695	−	0.0812292i	$-0.974115\pi$
$821$	− 7.38100e10i	− 0.162458i	0.996695	−	0.0812292i	$-0.0258846\pi$
$822$	0	0
$823$	4.34074e11	0.946159	0.473079	−	0.881020i	$-0.343142\pi$
$823$	4.34074e11	0.946159	0.473079	+	0.881020i	$0.343142\pi$
$824$	− 3.44264e11i	− 0.746762i
$825$	0	0
$826$	−8.23171e10	−0.176836
$827$	1.01622e11i	0.217253i	0.994083	+	0.108626i	$0.0346452\pi$
$827$	1.01622e11i	0.217253i	−0.994083	+	0.108626i	$0.965355\pi$
$828$	0	0
$829$	8.87841e10	0.187982	0.0939912	−	0.995573i	$-0.470037\pi$
$829$	8.87841e10	0.187982	0.0939912	+	0.995573i	$0.470037\pi$
$830$	3.56863e11i	0.751949i
$831$	0	0
$832$	−2.65563e11	−0.554210
$833$	4.60953e10i	0.0957362i
$834$	0	0
$835$	1.23335e12	2.53712
$836$	2.37169e11i	0.485548i
$837$	0	0
$838$	−2.38864e10	−0.0484368
$839$	− 3.88292e11i	− 0.783628i	−0.920044	−	0.391814i	$-0.871848\pi$
$839$	− 3.88292e11i	− 0.783628i	0.920044	−	0.391814i	$-0.128152\pi$
$840$	0	0
$841$	1.22042e11	0.243963
$842$	4.16933e10i	0.0829503i
$843$	0	0
$844$	−7.20376e11	−1.41968
$845$	1.24074e11i	0.243362i
$846$	0	0
$847$	−4.00023e11	−0.777232
$848$	− 2.69998e11i	− 0.522128i
$849$	0	0
$850$	3.77885e10	0.0723908
$851$	9.25027e11i	1.76375i
$852$	0	0
$853$	7.37267e10	0.139261	0.0696304	−	0.997573i	$-0.477818\pi$
$853$	7.37267e10	0.139261	0.0696304	+	0.997573i	$0.477818\pi$
$854$	1.21991e11i	0.229349i
$855$	0	0
$856$	−3.62643e11	−0.675437
$857$	− 5.60118e11i	− 1.03838i	−0.854659	−	0.519190i	$-0.826234\pi$
$857$	− 5.60118e11i	− 1.03838i	0.854659	−	0.519190i	$-0.173766\pi$
$858$	0	0
$859$	1.95095e11	0.358322	0.179161	−	0.983820i	$-0.442662\pi$
$859$	1.95095e11	0.358322	0.179161	+	0.983820i	$0.442662\pi$
$860$	5.20765e11i	0.952024i
$861$	0	0
$862$	2.80908e11	0.508785
$863$	− 7.69232e11i	− 1.38680i	−0.720552	−	0.693401i	$-0.756112\pi$
$863$	− 7.69232e11i	− 1.38680i	0.720552	−	0.693401i	$-0.243888\pi$
$864$	0	0
$865$	−1.54973e12	−2.76816
$866$	− 8.58343e10i	− 0.152612i
$867$	0	0
$868$	−7.72371e10	−0.136065
$869$	6.99923e11i	1.22736i
$870$	0	0
$871$	3.76285e11	0.653799
$872$	1.55813e11i	0.269487i
$873$	0	0
$874$	6.49218e10	0.111261
$875$	3.20001e11i	0.545908i
$876$	0	0
$877$	−2.58389e11	−0.436793	−0.218396	−	0.975860i	$-0.570083\pi$
$877$	−2.58389e11	−0.436793	−0.218396	+	0.975860i	$0.570083\pi$
$878$	− 1.19756e11i	− 0.201520i
$879$	0	0
$880$	1.09905e12	1.83268
$881$	1.16798e12i	1.93879i	0.245514	+	0.969393i	$0.421043\pi$
$881$	1.16798e12i	1.93879i	−0.245514	+	0.969393i	$0.578957\pi$
$882$	0	0
$883$	−6.16973e10	−0.101490	−0.0507450	−	0.998712i	$-0.516160\pi$
$883$	−6.16973e10	−0.101490	−0.0507450	+	0.998712i	$0.516160\pi$
$884$	9.49441e10i	0.155474i
$885$	0	0
$886$	−2.72000e11	−0.441401
$887$	− 1.45349e10i	− 0.0234811i	−0.999931	−	0.0117405i	$-0.996263\pi$
$887$	− 1.45349e10i	− 0.0234811i	0.999931	−	0.0117405i	$-0.00373722\pi$
$888$	0	0
$889$	−3.99683e11	−0.639894
$890$	− 2.47178e11i	− 0.393958i
$891$	0	0
$892$	1.47817e11	0.233488
$893$	− 7.61612e10i	− 0.119764i
$894$	0	0
$895$	−1.88869e11	−0.294353
$896$	− 3.91123e11i	− 0.606850i
$897$	0	0
$898$	−1.33532e11	−0.205343
$899$	− 1.20810e11i	− 0.184954i
$900$	0	0
$901$	−7.87870e10	−0.119552
$902$	6.40364e10i	0.0967388i
$903$	0	0
$904$	−3.84738e11	−0.576091
$905$	− 1.51918e12i	− 2.26473i
$906$	0	0
$907$	1.00686e12	1.48778	0.743891	−	0.668301i	$-0.232978\pi$
$907$	1.00686e12	1.48778	0.743891	+	0.668301i	$0.232978\pi$
$908$	− 9.06996e11i	− 1.33433i
$909$	0	0
$910$	1.82025e11	0.265440
$911$	2.55467e11i	0.370904i	0.982653	+	0.185452i	$0.0593749\pi$
$911$	2.55467e11i	0.370904i	−0.982653	+	0.185452i	$0.940625\pi$
$912$	0	0
$913$	1.81800e12	2.61644
$914$	2.75416e11i	0.394643i
$915$	0	0
$916$	2.37174e11	0.336888
$917$	6.21501e11i	0.878950i
$918$	0	0
$919$	−2.08241e11	−0.291947	−0.145973	−	0.989289i	$-0.546631\pi$
$919$	−2.08241e11	−0.291947	−0.145973	+	0.989289i	$0.546631\pi$
$920$	− 6.79753e11i	− 0.948854i
$921$	0	0
$922$	1.40449e10	0.0194355
$923$	− 4.11042e11i	− 0.566342i
$924$	0	0
$925$	−1.65380e12	−2.25900
$926$	− 1.69083e11i	− 0.229962i
$927$	0	0
$928$	4.65734e11	0.627980
$929$	1.32373e12i	1.77720i	0.458679	+	0.888602i	$0.348323\pi$
$929$	1.32373e12i	1.77720i	−0.458679	+	0.888602i	$0.651677\pi$
$930$	0	0
$931$	−1.41585e11	−0.188460
$932$	− 1.73166e11i	− 0.229508i
$933$	0	0
$934$	2.04331e11	0.268501
$935$	− 3.20710e11i	− 0.419629i
$936$	0	0
$937$	−3.83971e11	−0.498127	−0.249064	−	0.968487i	$-0.580123\pi$
$937$	−3.83971e11	−0.498127	−0.249064	+	0.968487i	$0.580123\pi$
$938$	1.00385e11i	0.129676i
$939$	0	0
$940$	−3.84188e11	−0.492077
$941$	1.24371e11i	0.158621i	0.996850	+	0.0793106i	$0.0252719\pi$
$941$	1.24371e11i	0.158621i	−0.996850	+	0.0793106i	$0.974728\pi$
$942$	0	0
$943$	−2.31774e11	−0.293101
$944$	− 6.11150e11i	− 0.769590i
$945$	0	0
$946$	−2.00646e11	−0.250534
$947$	− 5.07114e11i	− 0.630530i	−0.949004	−	0.315265i	$-0.897907\pi$
$947$	− 5.07114e11i	− 0.630530i	0.949004	−	0.315265i	$-0.102093\pi$
$948$	0	0
$949$	2.34004e11	0.288509
$950$	1.16070e11i	0.142503i
$951$	0	0
$952$	−5.25740e10	−0.0640064
$953$	1.41309e12i	1.71316i	0.516017	+	0.856578i	$0.327414\pi$
$953$	1.41309e12i	1.71316i	−0.516017	+	0.856578i	$0.672586\pi$
$954$	0	0
$955$	6.11893e11	0.735635
$956$	9.48863e11i	1.13598i
$957$	0	0
$958$	1.93901e11	0.230207
$959$	5.44521e11i	0.643785i
$960$	0	0
$961$	−8.14301e11	−0.954754
$962$	3.14259e11i	0.366934i
$963$	0	0
$964$	8.83726e11	1.02332
$965$	3.25276e9i	0.00375096i
$966$	0	0
$967$	−3.85172e11	−0.440503	−0.220252	−	0.975443i	$-0.570688\pi$
$967$	−3.85172e11	−0.440503	−0.220252	+	0.975443i	$0.570688\pi$
$968$	5.07502e11i	0.578011i
$969$	0	0
$970$	1.02551e11	0.115838
$971$	− 4.39991e11i	− 0.494957i	−0.968893	−	0.247478i	$-0.920398\pi$
$971$	− 4.39991e11i	− 0.494957i	0.968893	−	0.247478i	$-0.0796019\pi$
$972$	0	0
$973$	−4.65749e11	−0.519637
$974$	− 1.55830e11i	− 0.173147i
$975$	0	0
$976$	−9.05702e11	−0.998128
$977$	6.70267e10i	0.0735647i	0.999323	+	0.0367823i	$0.0117108\pi$
$977$	6.70267e10i	0.0735647i	−0.999323	+	0.0367823i	$0.988289\pi$
$978$	0	0
$979$	−1.25922e12	−1.37080
$980$	7.14213e11i	0.774325i
$981$	0	0
$982$	4.93168e10	0.0530333
$983$	− 1.28719e12i	− 1.37857i	−0.724489	−	0.689287i	$-0.757924\pi$
$983$	− 1.28719e12i	− 1.37857i	0.724489	−	0.689287i	$-0.242076\pi$
$984$	0	0
$985$	4.49922e11	0.477961
$986$	− 3.96185e10i	− 0.0419170i
$987$	0	0
$988$	−2.91628e11	−0.306056
$989$	− 7.26220e11i	− 0.759072i
$990$	0	0
$991$	1.01623e12	1.05365	0.526824	−	0.849974i	$-0.323383\pi$
$991$	1.01623e12	1.05365	0.526824	+	0.849974i	$0.323383\pi$
$992$	1.48769e11i	0.153627i
$993$	0	0
$994$	1.09658e11	0.112329
$995$	1.99633e11i	0.203676i
$996$	0	0
$997$	1.66136e12	1.68144	0.840721	−	0.541468i	$-0.182131\pi$
$997$	1.66136e12	1.68144	0.840721	+	0.541468i	$0.182131\pi$
$998$	− 1.46927e11i	− 0.148109i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.9.b.a.8.1	✓	2
3.2	odd	2	inner	9.9.b.a.8.2	yes	2
4.3	odd	2		144.9.e.a.17.1		2
5.2	odd	4		225.9.d.a.224.4		4
5.3	odd	4		225.9.d.a.224.1		4
5.4	even	2		225.9.c.a.26.2		2
9.2	odd	6		81.9.d.b.53.2		4
9.4	even	3		81.9.d.b.26.2		4
9.5	odd	6		81.9.d.b.26.1		4
9.7	even	3		81.9.d.b.53.1		4
12.11	even	2		144.9.e.a.17.2		2
15.2	even	4		225.9.d.a.224.2		4
15.8	even	4		225.9.d.a.224.3		4
15.14	odd	2		225.9.c.a.26.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.b.a.8.1	✓	2	1.1	even	1	trivial
9.9.b.a.8.2	yes	2	3.2	odd	2	inner
81.9.d.b.26.1		4	9.5	odd	6
81.9.d.b.26.2		4	9.4	even	3
81.9.d.b.53.1		4	9.7	even	3
81.9.d.b.53.2		4	9.2	odd	6
144.9.e.a.17.1		2	4.3	odd	2
144.9.e.a.17.2		2	12.11	even	2
225.9.c.a.26.1		2	15.14	odd	2
225.9.c.a.26.2		2	5.4	even	2
225.9.d.a.224.1		4	5.3	odd	4
225.9.d.a.224.2		4	15.2	even	4
225.9.d.a.224.3		4	15.8	even	4
225.9.d.a.224.4		4	5.2	odd	4

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

\(f(q)\)	\(=\)	\(q-4.24264i q^{2} +238.000 q^{4} -988.535i q^{5} +1652.00 q^{7} -2095.86i q^{8} +O(q^{10})\)	\(q-4.24264i q^{2} +238.000 q^{4} -988.535i q^{5} +1652.00 q^{7} -2095.86i q^{8} -4194.00 q^{10} +21365.9i q^{11} -26272.0 q^{13} -7008.84i q^{14} +52036.0 q^{16} -15184.4i q^{17} +46640.0 q^{19} -235271. i q^{20} +90648.0 q^{22} +328092. i q^{23} -586577. q^{25} +111463. i q^{26} +393176. q^{28} +614983. i q^{29} -196444. q^{31} -757311. i q^{32} -64422.0 q^{34} -1.63306e6i q^{35} +2.81941e6 q^{37} -197877. i q^{38} -2.07184e6 q^{40} +706429. i q^{41} -2.21346e6 q^{43} +5.08509e6i q^{44} +1.39198e6 q^{46} -1.63296e6i q^{47} -3.03570e6 q^{49} +2.48864e6i q^{50} -6.25274e6 q^{52} -5.18868e6i q^{53} +2.11210e7 q^{55} -3.46237e6i q^{56} +2.60915e6 q^{58} -1.17447e7i q^{59} -1.74053e7 q^{61} +833441. i q^{62} +1.01082e7 q^{64} +2.59708e7i q^{65} -1.43227e7 q^{67} -3.61389e6i q^{68} -6.92849e6 q^{70} +1.56456e7i q^{71} -8.90699e6 q^{73} -1.19618e7i q^{74} +1.11003e7 q^{76} +3.52965e7i q^{77} +3.27588e7 q^{79} -5.14394e7i q^{80} +2.99713e6 q^{82} -8.50888e7i q^{83} -1.50103e7 q^{85} +9.39093e6i q^{86} +4.47801e7 q^{88} +5.89361e7i q^{89} -4.34013e7 q^{91} +7.80859e7i q^{92} -6.92806e6 q^{94} -4.61053e7i q^{95} -2.44517e7 q^{97} +1.28794e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 476 q^{4} + 3304 q^{7}+O(q^{10}) \) 2 * q + 476 * q^4 + 3304 * q^7	\( 2 q + 476 q^{4} + 3304 q^{7} - 8388 q^{10} - 52544 q^{13} + 104072 q^{16} + 93280 q^{19} + 181296 q^{22} - 1173154 q^{25} + 786352 q^{28} - 392888 q^{31} - 128844 q^{34} + 5638828 q^{37} - 4143672 q^{40} - 4426928 q^{43} + 2783952 q^{46} - 6071394 q^{49} - 12505472 q^{52} + 42241968 q^{55} + 5218308 q^{58} - 34810604 q^{61} + 20216432 q^{64} - 28645328 q^{67} - 13856976 q^{70} - 17813984 q^{73} + 22200640 q^{76} + 65517688 q^{79} + 5994252 q^{82} - 30020652 q^{85} + 89560224 q^{88} - 86802688 q^{91} - 13856112 q^{94} - 48903488 q^{97}+O(q^{100}) \) 2 * q + 476 * q^4 + 3304 * q^7 - 8388 * q^10 - 52544 * q^13 + 104072 * q^16 + 93280 * q^19 + 181296 * q^22 - 1173154 * q^25 + 786352 * q^28 - 392888 * q^31 - 128844 * q^34 + 5638828 * q^37 - 4143672 * q^40 - 4426928 * q^43 + 2783952 * q^46 - 6071394 * q^49 - 12505472 * q^52 + 42241968 * q^55 + 5218308 * q^58 - 34810604 * q^61 + 20216432 * q^64 - 28645328 * q^67 - 13856976 * q^70 - 17813984 * q^73 + 22200640 * q^76 + 65517688 * q^79 + 5994252 * q^82 - 30020652 * q^85 + 89560224 * q^88 - 86802688 * q^91 - 13856112 * q^94 - 48903488 * q^97

Introduction

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