LMFDB - Embedded newform 48.22.c.c.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,22,Mod(47,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("48.47");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	48.c (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:	$134.149125258$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	48.47
Dual form			48.22.c.c.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-102214. - 3563.40i) q^{3} +3.58965e7i q^{5} -2.03455e8i q^{7} +(1.04350e10 + 7.28456e8i) q^{9} +O(q^{10})$	\(q+(-102214. - 3563.40i) q^{3} +3.58965e7i q^{5} -2.03455e8i q^{7} +(1.04350e10 + 7.28456e8i) q^{9} +1.20952e11 q^{11} +1.77218e11 q^{13} +(1.27914e11 - 3.66912e12i) q^{15} -1.07541e13i q^{17} +7.48860e12i q^{19} +(-7.24992e11 + 2.07959e13i) q^{21} +2.50481e14 q^{23} -8.11724e14 q^{25} +(-1.06400e15 - 1.11642e14i) q^{27} +1.36944e15i q^{29} -7.10692e15i q^{31} +(-1.23630e16 - 4.31000e14i) q^{33} +7.30334e15 q^{35} -5.30092e16 q^{37} +(-1.81141e16 - 6.31496e14i) q^{39} -1.12959e17i q^{41} +1.25061e17i q^{43} +(-2.61491e16 + 3.74579e17i) q^{45} +1.01711e17 q^{47} +5.17152e17 q^{49} +(-3.83210e16 + 1.09921e18i) q^{51} -6.36163e17i q^{53} +4.34176e18i q^{55} +(2.66849e16 - 7.65438e17i) q^{57} +1.08991e18 q^{59} -7.17405e18 q^{61} +(1.48208e17 - 2.12305e18i) q^{63} +6.36149e18i q^{65} -8.30973e17i q^{67} +(-2.56026e19 - 8.92561e17i) q^{69} -3.40906e19 q^{71} -6.94705e18 q^{73} +(8.29694e19 + 2.89249e18i) q^{75} -2.46083e19i q^{77} -5.54015e19i q^{79} +(1.08358e20 + 1.52028e19i) q^{81} -1.08266e20 q^{83} +3.86034e20 q^{85} +(4.87986e18 - 1.39976e20i) q^{87} -3.51807e20i q^{89} -3.60558e19i q^{91} +(-2.53248e19 + 7.26425e20i) q^{93} -2.68815e20 q^{95} -7.50983e20 q^{97} +(1.26213e21 + 8.81083e19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 109254828 q^{9}+O(q^{10}) $ 28 * q + 109254828 * q^9	$ 28 q + 109254828 q^{9} + 285248048392 q^{13} + 247146979606248 q^{21} - 31\!\cdots\!84 q^{25}+ \cdots + 16\!\cdots\!20 q^{97}+O(q^{100}) $ 28 * q + 109254828 * q^9 + 285248048392 * q^13 + 247146979606248 * q^21 - 3168527686741684 * q^25 - 7429429202649408 * q^33 + 33089121948065192 * q^37 - 121806830473453440 * q^45 - 569345069725368716 * q^49 + 10547854228195302552 * q^57 - 8280751575178739512 * q^61 - 22754055866538936960 * q^69 - 98548109928833394536 * q^73 + 563980976909609989500 * q^81 - 93841573689641488896 * q^85 - 1293830212233248374968 * q^93 + 1670728237822569097720 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−102214.	−	3563.40i	−0.999393	−	0.0348410i
$3$	−102214.	−	3563.40i	−0.999393	−	0.0348410i
$4$		0			0
$5$			3.58965e7i			1.64387i	0.569581	+	0.821935i	$0.307105\pi$
$5$			3.58965e7i			1.64387i	−0.569581	+	0.821935i	$0.692895\pi$
$6$		0			0
$7$		−	2.03455e8i		−	0.272232i	−0.990693	−	0.136116i	$-0.956538\pi$
$7$		−	2.03455e8i		−	0.272232i	0.990693	−	0.136116i	$-0.0434620\pi$
$8$		0			0
$9$	1.04350e10	+	7.28456e8i	0.997572	+	0.0696398i
$10$		0			0
$11$	1.20952e11			1.40602			0.703008	−	0.711182i	$-0.251840\pi$
$11$	1.20952e11			1.40602			0.703008	+	0.711182i	$0.251840\pi$
$12$		0			0
$13$	1.77218e11			0.356534			0.178267	−	0.983982i	$-0.442951\pi$
$13$	1.77218e11			0.356534			0.178267	+	0.983982i	$0.442951\pi$
$14$		0			0
$15$	1.27914e11	−	3.66912e12i	0.0572741	−	1.64287i
$16$		0			0
$17$		−	1.07541e13i		−	1.29378i	−0.762585	−	0.646888i	$-0.776070\pi$
$17$		−	1.07541e13i		−	1.29378i	0.762585	−	0.646888i	$-0.223930\pi$
$18$		0			0
$19$			7.48860e12i			0.280213i	0.990136	+	0.140106i	$0.0447445\pi$
$19$			7.48860e12i			0.280213i	−0.990136	+	0.140106i	$0.955256\pi$
$20$		0			0
$21$	−7.24992e11	+	2.07959e13i	−0.00948485	+	0.272067i
$22$		0			0
$23$	2.50481e14			1.26076			0.630379	−	0.776288i	$-0.282900\pi$
$23$	2.50481e14			1.26076			0.630379	+	0.776288i	$0.282900\pi$
$24$		0			0
$25$	−8.11724e14			−1.70231
$26$		0			0
$27$	−1.06400e15	−	1.11642e14i	−0.994540	−	0.104354i
$28$		0			0
$29$			1.36944e15i			0.604455i	0.953236	+	0.302228i	$0.0977303\pi$
$29$			1.36944e15i			0.604455i	−0.953236	+	0.302228i	$0.902270\pi$
$30$		0			0
$31$		−	7.10692e15i		−	1.55734i	−0.627434	−	0.778670i	$-0.715895\pi$
$31$		−	7.10692e15i		−	1.55734i	0.627434	−	0.778670i	$-0.284105\pi$
$32$		0			0
$33$	−1.23630e16	−	4.31000e14i	−1.40516	−	0.0489870i
$34$		0			0
$35$	7.30334e15			0.447514
$36$		0			0
$37$	−5.30092e16			−1.81231			−0.906156	−	0.422944i	$-0.860997\pi$
$37$	−5.30092e16			−1.81231			−0.906156	+	0.422944i	$0.860997\pi$
$38$		0			0
$39$	−1.81141e16	−	6.31496e14i	−0.356318	−	0.0124220i
$40$		0			0
$41$		−	1.12959e17i		−	1.31429i	−0.753763	−	0.657146i	$-0.771763\pi$
$41$		−	1.12959e17i		−	1.31429i	0.753763	−	0.657146i	$-0.228237\pi$
$42$		0			0
$43$			1.25061e17i			0.882478i	0.897390	+	0.441239i	$0.145461\pi$
$43$			1.25061e17i			0.882478i	−0.897390	+	0.441239i	$0.854539\pi$
$44$		0			0
$45$	−2.61491e16	+	3.74579e17i	−0.114479	+	1.63988i
$46$		0			0
$47$	1.01711e17			0.282058			0.141029	−	0.990005i	$-0.454959\pi$
$47$	1.01711e17			0.282058			0.141029	+	0.990005i	$0.454959\pi$
$48$		0			0
$49$	5.17152e17			0.925890
$50$		0			0
$51$	−3.83210e16	+	1.09921e18i	−0.0450765	+	1.29299i
$52$		0			0
$53$		−	6.36163e17i		−	0.499657i	−0.968290	−	0.249828i	$-0.919626\pi$
$53$		−	6.36163e17i		−	0.499657i	0.968290	−	0.249828i	$-0.0803742\pi$
$54$		0			0
$55$			4.34176e18i			2.31131i
$56$		0			0
$57$	2.66849e16	−	7.65438e17i	0.00976290	−	0.280043i
$58$		0			0
$59$	1.08991e18			0.277615			0.138807	−	0.990319i	$-0.455673\pi$
$59$	1.08991e18			0.277615			0.138807	+	0.990319i	$0.455673\pi$
$60$		0			0
$61$	−7.17405e18			−1.28766			−0.643830	−	0.765169i	$-0.722656\pi$
$61$	−7.17405e18			−1.28766			−0.643830	+	0.765169i	$0.722656\pi$
$62$		0			0
$63$	1.48208e17	−	2.12305e18i	0.0189582	−	0.271571i
$64$		0			0
$65$			6.36149e18i			0.586096i
$66$		0			0
$67$		−	8.30973e17i		−	0.0556931i	−0.999612	−	0.0278466i	$-0.991135\pi$
$67$		−	8.30973e17i		−	0.0556931i	0.999612	−	0.0278466i	$-0.00886498\pi$
$68$		0			0
$69$	−2.56026e19	−	8.92561e17i	−1.25999	−	0.0439261i
$70$		0			0
$71$	−3.40906e19			−1.24286			−0.621429	−	0.783470i	$-0.713448\pi$
$71$	−3.40906e19			−1.24286			−0.621429	+	0.783470i	$0.713448\pi$
$72$		0			0
$73$	−6.94705e18			−0.189195			−0.0945977	−	0.995516i	$-0.530156\pi$
$73$	−6.94705e18			−0.189195			−0.0945977	+	0.995516i	$0.530156\pi$
$74$		0			0
$75$	8.29694e19	+	2.89249e18i	1.70128	+	0.0593102i
$76$		0			0
$77$		−	2.46083e19i		−	0.382763i
$78$		0			0
$79$		−	5.54015e19i		−	0.658320i	−0.944274	−	0.329160i	$-0.893235\pi$
$79$		−	5.54015e19i		−	0.658320i	0.944274	−	0.329160i	$-0.106765\pi$
$80$		0			0
$81$	1.08358e20	+	1.52028e19i	0.990301	+	0.138941i
$82$		0			0
$83$	−1.08266e20			−0.765900			−0.382950	−	0.923769i	$-0.625092\pi$
$83$	−1.08266e20			−0.765900			−0.382950	+	0.923769i	$0.625092\pi$
$84$		0			0
$85$	3.86034e20			2.12680
$86$		0			0
$87$	4.87986e18	−	1.39976e20i	0.0210598	−	0.604088i
$88$		0			0
$89$		−	3.51807e20i		−	1.19594i	−0.801518	−	0.597970i	$-0.795974\pi$
$89$		−	3.51807e20i		−	1.19594i	0.801518	−	0.597970i	$-0.204026\pi$
$90$		0			0
$91$		−	3.60558e19i		−	0.0970601i
$92$		0			0
$93$	−2.53248e19	+	7.26425e20i	−0.0542593	+	1.55639i
$94$		0			0
$95$	−2.68815e20			−0.460633
$96$		0			0
$97$	−7.50983e20			−1.03402			−0.517008	−	0.855981i	$-0.672954\pi$
$97$	−7.50983e20			−1.03402			−0.517008	+	0.855981i	$0.672954\pi$
$98$		0			0
$99$	1.26213e21	+	8.81083e19i	1.40260	+	0.0979146i
$100$		0			0
$101$		−	1.49015e21i		−	1.34232i	−0.741315	−	0.671158i	$-0.765797\pi$
$101$		−	1.49015e21i		−	1.34232i	0.741315	−	0.671158i	$-0.234203\pi$
$102$		0			0
$103$		−	1.08571e21i		−	0.796020i	−0.917381	−	0.398010i	$-0.869701\pi$
$103$		−	1.08571e21i		−	0.796020i	0.917381	−	0.398010i	$-0.130299\pi$
$104$		0			0
$105$	−7.46502e20	−	2.60247e19i	−0.447243	−	0.0155919i
$106$		0			0
$107$	−3.12563e21			−1.53606			−0.768029	−	0.640416i	$-0.778762\pi$
$107$	−3.12563e21			−1.53606			−0.768029	+	0.640416i	$0.778762\pi$
$108$		0			0
$109$	−2.76108e21			−1.11712			−0.558560	−	0.829464i	$-0.688646\pi$
$109$	−2.76108e21			−1.11712			−0.558560	+	0.829464i	$0.688646\pi$
$110$		0			0
$111$	5.41827e21	+	1.88893e20i	1.81121	+	0.0631428i
$112$		0			0
$113$		−	3.97394e20i		−	0.110128i	−0.998483	−	0.0550640i	$-0.982464\pi$
$113$		−	3.97394e20i		−	0.110128i	0.998483	−	0.0550640i	$-0.0175363\pi$
$114$		0			0
$115$			8.99138e21i			2.07252i
$116$		0			0
$117$	1.84926e21	+	1.29095e20i	0.355669	+	0.0248290i
$118$		0			0
$119$	−2.18797e21			−0.352207
$120$		0			0
$121$	7.22915e21			0.976879
$122$		0			0
$123$	−4.02519e20	+	1.15460e22i	−0.0457913	+	1.31349i
$124$		0			0
$125$		−	1.20213e22i		−	1.15450i
$126$		0			0
$127$		−	1.33036e22i		−	1.08151i	−0.841181	−	0.540754i	$-0.818139\pi$
$127$		−	1.33036e22i		−	1.08151i	0.841181	−	0.540754i	$-0.181861\pi$
$128$		0			0
$129$	4.45642e20	−	1.27830e22i	0.0307464	−	0.881942i
$130$		0			0
$131$	2.67997e22			1.57319			0.786594	−	0.617470i	$-0.211842\pi$
$131$	2.67997e22			1.57319			0.786594	+	0.617470i	$0.211842\pi$
$132$		0			0
$133$	1.52360e21			0.0762829
$134$		0			0
$135$	4.00757e21	−	3.81939e22i	0.171544	−	1.63489i
$136$		0			0
$137$		−	2.37457e22i		−	0.871003i	−0.900188	−	0.435502i	$-0.856571\pi$
$137$		−	2.37457e22i		−	0.871003i	0.900188	−	0.435502i	$-0.143429\pi$
$138$		0			0
$139$		−	1.27944e21i		−	0.0403057i	−0.999797	−	0.0201528i	$-0.993585\pi$
$139$		−	1.27944e21i		−	0.0403057i	0.999797	−	0.0201528i	$-0.00641528\pi$
$140$		0			0
$141$	−1.03962e22	−	3.62436e20i	−0.281887	−	0.00982721i
$142$		0			0
$143$	2.14348e22			0.501293
$144$		0			0
$145$	−4.91582e22			−0.993646
$146$		0			0
$147$	−5.28600e22	−	1.84282e21i	−0.925328	−	0.0322589i
$148$		0			0
$149$		−	1.02541e23i		−	1.55754i	−0.627308	−	0.778771i	$-0.715843\pi$
$149$		−	1.02541e23i		−	1.55754i	0.627308	−	0.778771i	$-0.284157\pi$
$150$		0			0
$151$		−	1.10603e23i		−	1.46053i	−0.683165	−	0.730264i	$-0.739397\pi$
$151$		−	1.10603e23i		−	1.46053i	0.683165	−	0.730264i	$-0.260603\pi$
$152$		0			0
$153$	7.83387e21	−	1.12218e23i	0.0900982	−	1.29063i
$154$		0			0
$155$	2.55114e23			2.56006
$156$		0			0
$157$	1.91547e23			1.68008			0.840038	−	0.542527i	$-0.182532\pi$
$157$	1.91547e23			1.68008			0.840038	+	0.542527i	$0.182532\pi$
$158$		0			0
$159$	−2.26690e21	+	6.50246e22i	−0.0174086	+	0.499353i
$160$		0			0
$161$		−	5.09616e22i		−	0.343219i
$162$		0			0
$163$			3.26522e23i			1.93171i	0.259078	+	0.965856i	$0.416581\pi$
$163$			3.26522e23i			1.93171i	−0.259078	+	0.965856i	$0.583419\pi$
$164$		0			0
$165$	1.54714e22	−	4.43788e23i	0.0805283	−	2.30990i
$166$		0			0
$167$	2.03569e23			0.933661			0.466831	−	0.884347i	$-0.345396\pi$
$167$	2.03569e23			0.933661			0.466831	+	0.884347i	$0.345396\pi$
$168$		0			0
$169$	−2.15658e23			−0.872883
$170$		0			0
$171$	−5.45512e21	+	7.81433e22i	−0.0195140	+	0.279533i
$172$		0			0
$173$		−	1.30640e23i		−	0.413611i	−0.978382	−	0.206805i	$-0.933693\pi$
$173$		−	1.30640e23i		−	0.413611i	0.978382	−	0.206805i	$-0.0663067\pi$
$174$		0			0
$175$			1.65150e23i			0.463423i
$176$		0			0
$177$	−1.11403e23	−	3.88376e21i	−0.277446	−	0.00967239i
$178$		0			0
$179$	2.26063e23			0.500349			0.250174	−	0.968201i	$-0.419512\pi$
$179$	2.26063e23			0.500349			0.250174	+	0.968201i	$0.419512\pi$
$180$		0			0
$181$	−4.66173e23			−0.918167			−0.459084	−	0.888393i	$-0.651822\pi$
$181$	−4.66173e23			−0.918167			−0.459084	+	0.888393i	$0.651822\pi$
$182$		0			0
$183$	7.33287e23	+	2.55640e22i	1.28688	+	0.0448634i
$184$		0			0
$185$		−	1.90285e24i		−	2.97921i
$186$		0			0
$187$		−	1.30073e24i		−	1.81907i
$188$		0			0
$189$	−2.27142e22	+	2.16477e23i	−0.0284085	+	0.270746i
$190$		0			0
$191$	1.69482e22			0.0189790			0.00948948	−	0.999955i	$-0.496979\pi$
$191$	1.69482e22			0.0189790			0.00948948	+	0.999955i	$0.496979\pi$
$192$		0			0
$193$	−4.34811e23			−0.436464			−0.218232	−	0.975897i	$-0.570029\pi$
$193$	−4.34811e23			−0.436464			−0.218232	+	0.975897i	$0.570029\pi$
$194$		0			0
$195$	2.26685e22	−	6.50232e23i	0.0204202	−	0.585740i
$196$		0			0
$197$		−	1.48847e24i		−	1.20460i	−0.798269	−	0.602302i	$-0.794250\pi$
$197$		−	1.48847e24i		−	1.20460i	0.798269	−	0.602302i	$-0.205750\pi$
$198$		0			0
$199$			1.37317e24i			0.999466i	0.866179	+	0.499733i	$0.166569\pi$
$199$			1.37317e24i			0.999466i	−0.866179	+	0.499733i	$0.833431\pi$
$200$		0			0
$201$	−2.96109e21	+	8.49369e22i	−0.00194041	+	0.0556593i
$202$		0			0
$203$	2.78620e23			0.164552
$204$		0			0
$205$	4.05485e24			2.16053
$206$		0			0
$207$	2.61375e24	+	1.82464e23i	1.25770	+	0.0877989i
$208$		0			0
$209$			9.05762e23i			0.393983i
$210$		0			0
$211$		−	2.64484e24i		−	1.04096i	−0.853874	−	0.520480i	$-0.825753\pi$
$211$		−	2.64484e24i		−	1.04096i	0.853874	−	0.520480i	$-0.174247\pi$
$212$		0			0
$213$	3.48453e24	+	1.21478e23i	1.24210	+	0.0433025i
$214$		0			0
$215$	−4.48926e24			−1.45068
$216$		0			0
$217$	−1.44594e24			−0.423958
$218$		0			0
$219$	7.10084e23	+	2.47551e22i	0.189080	+	0.00659176i
$220$		0			0
$221$		−	1.90581e24i		−	0.461276i
$222$		0			0
$223$			2.41067e24i			0.530807i	0.964137	+	0.265404i	$0.0855052\pi$
$223$			2.41067e24i			0.530807i	−0.964137	+	0.265404i	$0.914495\pi$
$224$		0			0
$225$	−8.47031e24	−	5.91306e23i	−1.69818	−	0.118548i
$226$		0			0
$227$	1.37132e23			0.0250534			0.0125267	−	0.999922i	$-0.496013\pi$
$227$	1.37132e23			0.0250534			0.0125267	+	0.999922i	$0.496013\pi$
$228$		0			0
$229$	−2.74605e24			−0.457547			−0.228773	−	0.973480i	$-0.573471\pi$
$229$	−2.74605e24			−0.457547			−0.228773	+	0.973480i	$0.573471\pi$
$230$		0			0
$231$	−8.76892e22	+	2.51531e24i	−0.0133358	+	0.382530i
$232$		0			0
$233$			1.04316e25i			1.44915i	0.689196	+	0.724575i	$0.257964\pi$
$233$			1.04316e25i			1.44915i	−0.689196	+	0.724575i	$0.742036\pi$
$234$		0			0
$235$			3.65106e24i			0.463667i
$236$		0			0
$237$	−1.97417e23	+	5.66279e24i	−0.0229365	+	0.657920i
$238$		0			0
$239$	−2.51923e24			−0.267972			−0.133986	−	0.990983i	$-0.542778\pi$
$239$	−2.51923e24			−0.267972			−0.133986	+	0.990983i	$0.542778\pi$
$240$		0			0
$241$	−1.70486e25			−1.66154			−0.830768	−	0.556618i	$-0.812099\pi$
$241$	−1.70486e25			−1.66154			−0.830768	+	0.556618i	$0.812099\pi$
$242$		0			0
$243$	−1.10215e25	−	1.94006e24i	−0.984859	−	0.173360i
$244$		0			0
$245$			1.85640e25i			1.52204i
$246$		0			0
$247$			1.32711e24i			0.0999055i
$248$		0			0
$249$	1.10663e25	+	3.85794e23i	0.765435	+	0.0266847i
$250$		0			0
$251$	5.77644e24			0.367355			0.183678	−	0.982987i	$-0.441200\pi$
$251$	5.77644e24			0.367355			0.183678	+	0.982987i	$0.441200\pi$
$252$		0			0
$253$	3.02961e25			1.77264
$254$		0			0
$255$	−3.94580e25	−	1.37559e24i	−2.12551	−	0.0740999i
$256$		0			0
$257$			2.31218e25i			1.14743i	0.819056	+	0.573713i	$0.194498\pi$
$257$			2.31218e25i			1.14743i	−0.819056	+	0.573713i	$0.805502\pi$
$258$		0			0
$259$			1.07850e25i			0.493370i
$260$		0			0
$261$	−9.97578e23	+	1.42901e25i	−0.0420941	+	0.602988i
$262$		0			0
$263$	3.19050e25			1.24258			0.621289	−	0.783582i	$-0.286609\pi$
$263$	3.19050e25			1.24258			0.621289	+	0.783582i	$0.286609\pi$
$264$		0			0
$265$	2.28360e25			0.821371
$266$		0			0
$267$	−1.25363e24	+	3.59595e25i	−0.0416678	+	1.19521i
$268$		0			0
$269$			7.04856e24i			0.216621i	0.994117	+	0.108311i	$0.0345441\pi$
$269$			7.04856e24i			0.216621i	−0.994117	+	0.108311i	$0.965456\pi$
$270$		0			0
$271$		−	6.43765e25i		−	1.83041i	−0.402983	−	0.915207i	$-0.632027\pi$
$271$		−	6.43765e25i		−	1.83041i	0.402983	−	0.915207i	$-0.367973\pi$
$272$		0			0
$273$	−1.28481e23	+	3.68540e24i	−0.00338168	+	0.0970012i
$274$		0			0
$275$	−9.81797e25			−2.39347
$276$		0			0
$277$	−2.89529e25			−0.654115			−0.327058	−	0.945004i	$-0.606057\pi$
$277$	−2.89529e25			−0.654115			−0.327058	+	0.945004i	$0.606057\pi$
$278$		0			0
$279$	5.17708e24	−	7.41604e25i	0.108453	−	1.55356i
$280$		0			0
$281$			9.14738e25i			1.77779i	0.458111	+	0.888895i	$0.348526\pi$
$281$			9.14738e25i			1.77779i	−0.458111	+	0.888895i	$0.651474\pi$
$282$		0			0
$283$		−	9.23642e24i		−	0.166627i	−0.996523	−	0.0833137i	$-0.973450\pi$
$283$		−	9.23642e24i		−	0.166627i	0.996523	−	0.0833137i	$-0.0265503\pi$
$284$		0			0
$285$	2.74766e25	+	9.57894e23i	0.460354	+	0.0160489i
$286$		0			0
$287$	−2.29822e25			−0.357793
$288$		0			0
$289$	−4.65580e25			−0.673855
$290$		0			0
$291$	7.67608e25	+	2.67605e24i	1.03339	+	0.0360262i
$292$		0			0
$293$			1.92970e25i			0.241757i	0.992667	+	0.120879i	$0.0385712\pi$
$293$			1.92970e25i			0.241757i	−0.992667	+	0.120879i	$0.961429\pi$
$294$		0			0
$295$			3.91238e25i			0.456363i
$296$		0			0
$297$	−1.28693e26	−	1.35033e25i	−1.39834	−	0.146723i
$298$		0			0
$299$	4.43895e25			0.449504
$300$		0			0
$301$	2.54443e25			0.240239
$302$		0			0
$303$	−5.30998e24	+	1.52313e26i	−0.0467676	+	1.34150i
$304$		0			0
$305$		−	2.57524e26i		−	2.11675i
$306$		0			0
$307$			8.07277e25i			0.619540i	0.950811	+	0.309770i	$0.100252\pi$
$307$			8.07277e25i			0.619540i	−0.950811	+	0.309770i	$0.899748\pi$
$308$		0			0
$309$	−3.86882e24	+	1.10975e26i	−0.0277342	+	0.795537i
$310$		0			0
$311$	−7.70473e25			−0.516147			−0.258073	−	0.966125i	$-0.583088\pi$
$311$	−7.70473e25			−0.516147			−0.258073	+	0.966125i	$0.583088\pi$
$312$		0			0
$313$	1.73166e26			1.08454			0.542271	−	0.840204i	$-0.317565\pi$
$313$	1.73166e26			1.08454			0.542271	+	0.840204i	$0.317565\pi$
$314$		0			0
$315$	7.62100e25	+	5.32016e24i	0.446428	+	0.0311648i
$316$		0			0
$317$		−	2.26728e26i		−	1.24275i	−0.783515	−	0.621373i	$-0.786575\pi$
$317$		−	2.26728e26i		−	1.24275i	0.783515	−	0.621373i	$-0.213425\pi$
$318$		0			0
$319$			1.65637e26i			0.849873i
$320$		0			0
$321$	3.19482e26	+	1.11378e25i	1.53512	+	0.0535178i
$322$		0			0
$323$	8.05329e25			0.362532
$324$		0			0
$325$	−1.43852e26			−0.606932
$326$		0			0
$327$	2.82220e26	+	9.83881e24i	1.11644	+	0.0389216i
$328$		0			0
$329$		−	2.06936e25i		−	0.0767854i
$330$		0			0
$331$		−	4.43628e26i		−	1.54463i	−0.635239	−	0.772316i	$-0.719098\pi$
$331$		−	4.43628e26i		−	1.54463i	0.635239	−	0.772316i	$-0.280902\pi$
$332$		0			0
$333$	−5.53148e26	−	3.86149e25i	−1.80791	−	0.126209i
$334$		0			0
$335$	2.98291e25			0.0915523
$336$		0			0
$337$	5.57078e25			0.160621			0.0803105	−	0.996770i	$-0.474409\pi$
$337$	5.57078e25			0.160621			0.0803105	+	0.996770i	$0.474409\pi$
$338$		0			0
$339$	−1.41607e24	+	4.06192e25i	−0.00383698	+	0.110061i
$340$		0			0
$341$		−	8.59596e26i		−	2.18964i
$342$		0			0
$343$		−	2.18856e26i		−	0.524289i
$344$		0			0
$345$	3.20399e25	−	9.19043e26i	0.0722088	−	2.07126i
$346$		0			0
$347$	6.01455e26			1.27569			0.637843	−	0.770166i	$-0.279827\pi$
$347$	6.01455e26			1.27569			0.637843	+	0.770166i	$0.279827\pi$
$348$		0			0
$349$	−2.04257e26			−0.407858			−0.203929	−	0.978986i	$-0.565371\pi$
$349$	−2.04257e26			−0.407858			−0.203929	+	0.978986i	$0.565371\pi$
$350$		0			0
$351$	−1.88560e26	−	1.97849e25i	−0.354588	−	0.0372058i
$352$		0			0
$353$			7.31645e26i			1.29618i	0.761563	+	0.648091i	$0.224432\pi$
$353$			7.31645e26i			1.29618i	−0.761563	+	0.648091i	$0.775568\pi$
$354$		0			0
$355$		−	1.22373e27i		−	2.04310i
$356$		0			0
$357$	2.23641e26	+	7.79661e24i	0.351994	+	0.0122713i
$358$		0			0
$359$	9.08508e26			1.34846			0.674229	−	0.738523i	$-0.264476\pi$
$359$	9.08508e26			1.34846			0.674229	+	0.738523i	$0.264476\pi$
$360$		0			0
$361$	6.58130e26			0.921481
$362$		0			0
$363$	−7.38919e26	−	2.57603e25i	−0.976286	−	0.0340355i
$364$		0			0
$365$		−	2.49375e26i		−	0.311013i
$366$		0			0
$367$			6.72981e26i			0.792518i	0.918139	+	0.396259i	$0.129692\pi$
$367$			6.72981e26i			0.792518i	−0.918139	+	0.396259i	$0.870308\pi$
$368$		0			0
$369$	8.22861e25	−	1.17873e27i	0.0915270	−	1.31110i
$370$		0			0
$371$	−1.29431e26			−0.136023
$372$		0			0
$373$	2.56254e26			0.254524			0.127262	−	0.991869i	$-0.459381\pi$
$373$	2.56254e26			0.254524			0.127262	+	0.991869i	$0.459381\pi$
$374$		0			0
$375$	−4.28366e25	+	1.22874e27i	−0.0402241	+	1.15380i
$376$		0			0
$377$			2.42689e26i			0.215509i
$378$		0			0
$379$			2.08576e27i			1.75207i	0.482245	+	0.876036i	$0.339821\pi$
$379$			2.08576e27i			1.75207i	−0.482245	+	0.876036i	$0.660179\pi$
$380$		0			0
$381$	−4.74060e25	+	1.35981e27i	−0.0376809	+	1.08085i
$382$		0			0
$383$	3.50737e25			0.0263873			0.0131936	−	0.999913i	$-0.495800\pi$
$383$	3.50737e25			0.0263873			0.0131936	+	0.999913i	$0.495800\pi$
$384$		0			0
$385$	8.83354e26			0.629212
$386$		0			0
$387$	−9.11016e25	+	1.30501e27i	−0.0614555	+	0.880335i
$388$		0			0
$389$		−	7.44264e26i		−	0.475616i	−0.971312	−	0.237808i	$-0.923571\pi$
$389$		−	7.44264e26i		−	0.475616i	0.971312	−	0.237808i	$-0.0764289\pi$
$390$		0			0
$391$		−	2.69368e27i		−	1.63114i
$392$		0			0
$393$	−2.73929e27	−	9.54978e25i	−1.57223	−	0.0548115i
$394$		0			0
$395$	1.98872e27			1.08219
$396$		0			0
$397$	−1.09783e27			−0.566544			−0.283272	−	0.959040i	$-0.591420\pi$
$397$	−1.09783e27			−0.566544			−0.283272	+	0.959040i	$0.591420\pi$
$398$		0			0
$399$	−1.55732e26	−	5.42917e24i	−0.0762366	−	0.00265778i
$400$		0			0
$401$			2.11287e27i			0.981427i	0.871321	+	0.490713i	$0.163264\pi$
$401$			2.11287e27i			0.981427i	−0.871321	+	0.490713i	$0.836736\pi$
$402$		0			0
$403$		−	1.25947e27i		−	0.555245i
$404$		0			0
$405$	−5.45729e26	+	3.88967e27i	−0.228402	+	1.62793i
$406$		0			0
$407$	−6.41157e27			−2.54814
$408$		0			0
$409$	−9.92210e26			−0.374549			−0.187275	−	0.982308i	$-0.559965\pi$
$409$	−9.92210e26			−0.374549			−0.187275	+	0.982308i	$0.559965\pi$
$410$		0			0
$411$	−8.46155e25	+	2.42714e27i	−0.0303466	+	0.870474i
$412$		0			0
$413$		−	2.21747e26i		−	0.0755757i
$414$		0			0
$415$		−	3.88637e27i		−	1.25904i
$416$		0			0
$417$	−4.55917e24	+	1.30777e26i	−0.00140429	+	0.0402812i
$418$		0			0
$419$	−2.78660e27			−0.816257			−0.408129	−	0.912924i	$-0.633819\pi$
$419$	−2.78660e27			−0.816257			−0.408129	+	0.912924i	$0.633819\pi$
$420$		0			0
$421$	3.53971e27			0.986293			0.493146	−	0.869946i	$-0.335847\pi$
$421$	3.53971e27			0.986293			0.493146	+	0.869946i	$0.335847\pi$
$422$		0			0
$423$	1.06135e27	+	7.40918e25i	0.281374	+	0.0196425i
$424$		0			0
$425$			8.72933e27i			2.20241i
$426$		0			0
$427$			1.45960e27i			0.350542i
$428$		0			0
$429$	−2.19093e27	−	7.63808e25i	−0.500988	−	0.0174656i
$430$		0			0
$431$	−2.13545e27			−0.465028			−0.232514	−	0.972593i	$-0.574695\pi$
$431$	−2.13545e27			−0.465028			−0.232514	+	0.972593i	$0.574695\pi$
$432$		0			0
$433$	4.49869e27			0.933175			0.466587	−	0.884475i	$-0.345483\pi$
$433$	4.49869e27			0.933175			0.466587	+	0.884475i	$0.345483\pi$
$434$		0			0
$435$	5.02464e27	+	1.75170e26i	0.993043	+	0.0346196i
$436$		0			0
$437$			1.87575e27i			0.353280i
$438$		0			0
$439$		−	7.31030e27i		−	1.31237i	−0.754598	−	0.656187i	$-0.772168\pi$
$439$		−	7.31030e27i		−	1.31237i	0.754598	−	0.656187i	$-0.227832\pi$
$440$		0			0
$441$	5.39646e27	+	3.76723e26i	0.923642	+	0.0644787i
$442$		0			0
$443$	−9.40775e27			−1.53549			−0.767745	−	0.640756i	$-0.778621\pi$
$443$	−9.40775e27			−1.53549			−0.767745	+	0.640756i	$0.778621\pi$
$444$		0			0
$445$	1.26287e28			1.96597
$446$		0			0
$447$	−3.65393e26	+	1.04811e28i	−0.0542664	+	1.55660i
$448$		0			0
$449$		−	5.41424e27i		−	0.767275i	−0.923484	−	0.383638i	$-0.874671\pi$
$449$		−	5.41424e27i		−	0.767275i	0.923484	−	0.383638i	$-0.125329\pi$
$450$		0			0
$451$		−	1.36627e28i		−	1.84792i
$452$		0			0
$453$	−3.94123e26	+	1.13052e28i	−0.0508863	+	1.45964i
$454$		0			0
$455$	1.29428e27			0.159554
$456$		0			0
$457$	−1.03490e28			−1.21837			−0.609186	−	0.793027i	$-0.708504\pi$
$457$	−1.03490e28			−1.21837			−0.609186	+	0.793027i	$0.708504\pi$
$458$		0			0
$459$	−1.20061e27	+	1.14423e28i	−0.135011	+	1.28671i
$460$		0			0
$461$		−	1.18153e27i		−	0.126936i	−0.997984	−	0.0634682i	$-0.979784\pi$
$461$		−	1.18153e27i		−	0.126936i	0.997984	−	0.0634682i	$-0.0202161\pi$
$462$		0			0
$463$			7.65676e27i			0.786040i	0.919530	+	0.393020i	$0.128570\pi$
$463$			7.65676e27i			0.786040i	−0.919530	+	0.393020i	$0.871430\pi$
$464$		0			0
$465$	−2.60761e28	−	9.09071e26i	−2.55851	−	0.0891953i
$466$		0			0
$467$	1.17706e28			1.10401			0.552003	−	0.833842i	$-0.313864\pi$
$467$	1.17706e28			1.10401			0.552003	+	0.833842i	$0.313864\pi$
$468$		0			0
$469$	−1.69066e26			−0.0151615
$470$		0			0
$471$	−1.95787e28	−	6.82558e26i	−1.67906	−	0.0585356i
$472$		0			0
$473$			1.51264e28i			1.24078i
$474$		0			0
$475$		−	6.07868e27i		−	0.477009i
$476$		0			0
$477$	4.63417e26	−	6.63833e27i	0.0347960	−	0.498444i
$478$		0			0
$479$	1.89357e28			1.36068			0.680342	−	0.732895i	$-0.261831\pi$
$479$	1.89357e28			1.36068			0.680342	+	0.732895i	$0.261831\pi$
$480$		0			0
$481$	−9.39415e27			−0.646152
$482$		0			0
$483$	−1.81596e26	+	5.20897e27i	−0.0119581	+	0.343010i
$484$		0			0
$485$		−	2.69577e28i		−	1.69979i
$486$		0			0
$487$		−	1.16164e28i		−	0.701485i	−0.936472	−	0.350743i	$-0.885929\pi$
$487$		−	1.16164e28i		−	0.701485i	0.936472	−	0.350743i	$-0.114071\pi$
$488$		0			0
$489$	1.16353e27	−	3.33750e28i	0.0673029	−	1.93054i
$490$		0			0
$491$	1.16421e28			0.645172			0.322586	−	0.946540i	$-0.395448\pi$
$491$	1.16421e28			0.645172			0.322586	+	0.946540i	$0.395448\pi$
$492$		0			0
$493$	1.47270e28			0.782029
$494$		0			0
$495$	−3.16278e27	+	4.53061e28i	−0.160959	+	2.30570i
$496$		0			0
$497$			6.93591e27i			0.338346i
$498$		0			0
$499$		−	3.27872e28i		−	1.53337i	−0.642021	−	0.766687i	$-0.721904\pi$
$499$		−	3.27872e28i		−	1.53337i	0.642021	−	0.766687i	$-0.278096\pi$
$500$		0			0
$501$	−2.08076e28	−	7.25398e26i	−0.933094	−	0.0325297i
$502$		0			0
$503$	5.03645e27			0.216601			0.108301	−	0.994118i	$-0.465459\pi$
$503$	5.03645e27			0.216601			0.108301	+	0.994118i	$0.465459\pi$
$504$		0			0
$505$	5.34911e28			2.20659
$506$		0			0
$507$	2.20433e28	+	7.68477e26i	0.872353	+	0.0304122i
$508$		0			0
$509$		−	1.15020e28i		−	0.436755i	−0.975864	−	0.218377i	$-0.929924\pi$
$509$		−	1.15020e28i		−	0.436755i	0.975864	−	0.218377i	$-0.0700764\pi$
$510$		0			0
$511$			1.41341e27i			0.0515051i
$512$		0			0
$513$	8.36044e26	−	7.96788e27i	0.0292413	−	0.278683i
$514$		0			0
$515$	3.89733e28			1.30855
$516$		0			0
$517$	1.23021e28			0.396578
$518$		0			0
$519$	−4.65522e26	+	1.33532e28i	−0.0144106	+	0.413359i
$520$		0			0
$521$		−	3.48339e28i		−	1.03563i	−0.855491	−	0.517817i	$-0.826745\pi$
$521$		−	3.48339e28i		−	1.03563i	0.855491	−	0.517817i	$-0.173255\pi$
$522$		0			0
$523$		−	6.84610e27i		−	0.195513i	−0.995210	−	0.0977565i	$-0.968833\pi$
$523$		−	6.84610e27i		−	0.195513i	0.995210	−	0.0977565i	$-0.0311666\pi$
$524$		0			0
$525$	5.88493e26	−	1.68806e28i	0.0161461	−	0.463142i
$526$		0			0
$527$	−7.64282e28			−2.01485
$528$		0			0
$529$	2.32689e28			0.589510
$530$		0			0
$531$	1.13731e28	+	7.93948e26i	0.276941	+	0.0193330i
$532$		0			0
$533$		−	2.00184e28i		−	0.468591i
$534$		0			0
$535$		−	1.12199e29i		−	2.52508i
$536$		0			0
$537$	−2.31068e28	−	8.05552e26i	−0.500045	−	0.0174327i
$538$		0			0
$539$	6.25506e28			1.30181
$540$		0			0
$541$	−3.76889e28			−0.754470			−0.377235	−	0.926118i	$-0.623125\pi$
$541$	−3.76889e28			−0.754470			−0.377235	+	0.926118i	$0.623125\pi$
$542$		0			0
$543$	4.76493e28	+	1.66116e27i	0.917610	+	0.0319899i
$544$		0			0
$545$		−	9.91131e28i		−	1.83640i
$546$		0			0
$547$		−	9.96920e28i		−	1.77743i	−0.458457	−	0.888716i	$-0.651598\pi$
$547$		−	9.96920e28i		−	1.77743i	0.458457	−	0.888716i	$-0.348402\pi$
$548$		0			0
$549$	−7.48609e28	−	5.22598e27i	−1.28453	−	0.0896723i
$550$		0			0
$551$	−1.02552e28			−0.169376
$552$		0			0
$553$	−1.12717e28			−0.179216
$554$		0			0
$555$	−6.78059e27	+	1.94497e29i	−0.103799	+	2.97740i
$556$		0			0
$557$			7.34657e28i			1.08294i	0.840719	+	0.541471i	$0.182132\pi$
$557$			7.34657e28i			1.08294i	−0.840719	+	0.541471i	$0.817868\pi$
$558$		0			0
$559$			2.21630e28i			0.314634i
$560$		0			0
$561$	−4.63500e27	+	1.32952e29i	−0.0633782	+	1.81796i
$562$		0			0
$563$	−1.18267e28			−0.155785			−0.0778923	−	0.996962i	$-0.524819\pi$
$563$	−1.18267e28			−0.155785			−0.0778923	+	0.996962i	$0.524819\pi$
$564$		0			0
$565$	1.42651e28			0.181036
$566$		0			0
$567$	3.09309e27	−	2.20459e28i	0.0378243	−	0.269592i
$568$		0			0
$569$		−	3.72212e28i		−	0.438644i	−0.975653	−	0.219322i	$-0.929616\pi$
$569$		−	3.72212e28i		−	0.438644i	0.975653	−	0.219322i	$-0.0703845\pi$
$570$		0			0
$571$			1.59009e29i			1.80611i	0.429530	+	0.903053i	$0.358679\pi$
$571$			1.59009e29i			1.80611i	−0.429530	+	0.903053i	$0.641321\pi$
$572$		0			0
$573$	−1.73234e27	−	6.03931e25i	−0.0189674	−	0.000661247i
$574$		0			0
$575$	−2.03321e29			−2.14620
$576$		0			0
$577$	1.09230e29			1.11172			0.555861	−	0.831275i	$-0.312388\pi$
$577$	1.09230e29			1.11172			0.555861	+	0.831275i	$0.312388\pi$
$578$		0			0
$579$	4.44436e28	+	1.54940e27i	0.436199	+	0.0152069i
$580$		0			0
$581$			2.20273e28i			0.208503i
$582$		0			0
$583$		−	7.69452e28i		−	0.702525i
$584$		0			0
$585$	−4.63407e27	+	6.63819e28i	−0.0408156	+	0.584673i
$586$		0			0
$587$	8.28713e28			0.704213			0.352106	−	0.935960i	$-0.385466\pi$
$587$	8.28713e28			0.704213			0.352106	+	0.935960i	$0.385466\pi$
$588$		0			0
$589$	5.32209e28			0.436387
$590$		0			0
$591$	−5.30400e27	+	1.52142e29i	−0.0419696	+	1.20387i
$592$		0			0
$593$			2.17275e29i			1.65934i	0.558254	+	0.829670i	$0.311472\pi$
$593$			2.17275e29i			1.65934i	−0.558254	+	0.829670i	$0.688528\pi$
$594$		0			0
$595$		−	7.85406e28i		−	0.578983i
$596$		0			0
$597$	4.89316e27	−	1.40357e29i	0.0348224	−	0.998860i
$598$		0			0
$599$	−9.73795e28			−0.669092			−0.334546	−	0.942379i	$-0.608583\pi$
$599$	−9.73795e28			−0.669092			−0.334546	+	0.942379i	$0.608583\pi$
$600$		0			0
$601$	6.53048e28			0.433275			0.216637	−	0.976252i	$-0.430491\pi$
$601$	6.53048e28			0.433275			0.216637	+	0.976252i	$0.430491\pi$
$602$		0			0
$603$	6.05328e26	−	8.67117e27i	0.00387846	−	0.0555579i
$604$		0			0
$605$			2.59501e29i			1.60586i
$606$		0			0
$607$		−	6.16389e28i		−	0.368446i	−0.982885	−	0.184223i	$-0.941023\pi$
$607$		−	6.16389e28i		−	0.368446i	0.982885	−	0.184223i	$-0.0589768\pi$
$608$		0			0
$609$	−2.84788e28	−	9.92833e26i	−0.164452	−	0.00573317i
$610$		0			0
$611$	1.80249e28			0.100564
$612$		0			0
$613$	−1.21201e29			−0.653388			−0.326694	−	0.945130i	$-0.605935\pi$
$613$	−1.21201e29			−0.653388			−0.326694	+	0.945130i	$0.605935\pi$
$614$		0			0
$615$	−4.14462e29	−	1.44491e28i	−2.15922	−	0.0752750i
$616$		0			0
$617$			2.57529e28i			0.129668i	0.997896	+	0.0648340i	$0.0206518\pi$
$617$			2.57529e28i			0.129668i	−0.997896	+	0.0648340i	$0.979348\pi$
$618$		0			0
$619$		−	2.56300e29i		−	1.24738i	−0.781673	−	0.623688i	$-0.785634\pi$
$619$		−	2.56300e29i		−	1.24738i	0.781673	−	0.623688i	$-0.214366\pi$
$620$		0			0
$621$	−2.66511e29	−	2.79642e28i	−1.25387	−	0.131565i
$622$		0			0
$623$	−7.15770e28			−0.325573
$624$		0			0
$625$	4.44621e28			0.195546
$626$		0			0
$627$	3.22759e27	−	9.25813e28i	0.0137268	−	0.393744i
$628$		0			0
$629$			5.70064e29i			2.34472i
$630$		0			0
$631$		−	1.86450e29i		−	0.741745i	−0.928684	−	0.370873i	$-0.879059\pi$
$631$		−	1.86450e29i		−	0.741745i	0.928684	−	0.370873i	$-0.120941\pi$
$632$		0			0
$633$	−9.42463e27	+	2.70340e29i	−0.0362682	+	1.04033i
$634$		0			0
$635$	4.77553e29			1.77786
$636$		0			0
$637$	9.16484e28			0.330112
$638$		0			0
$639$	−3.55734e29	−	2.48335e28i	−1.23984	−	0.0865524i
$640$		0			0
$641$		−	3.54127e29i		−	1.19440i	−0.802093	−	0.597200i	$-0.796280\pi$
$641$		−	3.54127e29i		−	1.19440i	0.802093	−	0.597200i	$-0.203720\pi$
$642$		0			0
$643$		−	2.79067e29i		−	0.910947i	−0.890249	−	0.455474i	$-0.849470\pi$
$643$		−	2.79067e29i		−	0.910947i	0.890249	−	0.455474i	$-0.150530\pi$
$644$		0			0
$645$	4.58864e29	+	1.59970e28i	1.44980	+	0.0505431i
$646$		0			0
$647$	−7.28495e28			−0.222808			−0.111404	−	0.993775i	$-0.535535\pi$
$647$	−7.28495e28			−0.222808			−0.111404	+	0.993775i	$0.535535\pi$
$648$		0			0
$649$	1.31826e29			0.390331
$650$		0			0
$651$	1.47795e29	+	5.15246e27i	0.423701	+	0.0147711i
$652$		0			0
$653$		−	4.09267e29i		−	1.13611i	−0.822992	−	0.568053i	$-0.807697\pi$
$653$		−	4.09267e29i		−	1.13611i	0.822992	−	0.568053i	$-0.192303\pi$
$654$		0			0
$655$			9.62015e29i			2.58612i
$656$		0			0
$657$	−7.24922e28	−	5.06062e27i	−0.188736	−	0.0131755i
$658$		0			0
$659$	5.05774e28			0.127544			0.0637719	−	0.997964i	$-0.479687\pi$
$659$	5.05774e28			0.127544			0.0637719	+	0.997964i	$0.479687\pi$
$660$		0			0
$661$	1.09917e29			0.268502			0.134251	−	0.990947i	$-0.457137\pi$
$661$	1.09917e29			0.268502			0.134251	+	0.990947i	$0.457137\pi$
$662$		0			0
$663$	−6.79115e27	+	1.94800e29i	−0.0160713	+	0.460995i
$664$		0			0
$665$			5.46918e28i			0.125399i
$666$		0			0
$667$			3.43018e29i			0.762072i
$668$		0			0
$669$	8.59018e27	−	2.46404e29i	0.0184939	−	0.530485i
$670$		0			0
$671$	−8.67716e29			−1.81047
$672$		0			0
$673$	−8.55483e29			−1.73003			−0.865014	−	0.501747i	$-0.832691\pi$
$673$	−8.55483e29			−1.73003			−0.865014	+	0.501747i	$0.832691\pi$
$674$		0			0
$675$	8.63675e29	+	9.06226e28i	1.69301	+	0.177643i
$676$		0			0
$677$		−	2.45116e29i		−	0.465790i	−0.972502	−	0.232895i	$-0.925180\pi$
$677$		−	2.45116e29i		−	0.465790i	0.972502	−	0.232895i	$-0.0748198\pi$
$678$		0			0
$679$			1.52791e29i			0.281492i
$680$		0			0
$681$	−1.40168e28	−	4.88655e26i	−0.0250382	−	0.000872887i
$682$		0			0
$683$	7.74851e29			1.34215			0.671075	−	0.741390i	$-0.265833\pi$
$683$	7.74851e29			1.34215			0.671075	+	0.741390i	$0.265833\pi$
$684$		0			0
$685$	8.52390e29			1.43182
$686$		0			0
$687$	2.80684e29	+	9.78525e27i	0.457269	+	0.0159414i
$688$		0			0
$689$		−	1.12739e29i		−	0.178145i
$690$		0			0
$691$		−	1.75107e28i		−	0.0268401i	−0.999910	−	0.0134200i	$-0.995728\pi$
$691$		−	1.75107e28i		−	0.0268401i	0.999910	−	0.0134200i	$-0.00427186\pi$
$692$		0			0
$693$	1.79261e28	−	2.56787e29i	0.0266555	−	0.381833i
$694$		0			0
$695$	4.59276e28			0.0662573
$696$		0			0
$697$	−1.21477e30			−1.70040
$698$		0			0
$699$	3.71719e28	−	1.06625e30i	0.0504899	−	1.44827i
$700$		0			0
$701$		−	4.08682e29i		−	0.538700i	−0.963042	−	0.269350i	$-0.913191\pi$
$701$		−	4.08682e29i		−	0.538700i	0.963042	−	0.269350i	$-0.0868088\pi$
$702$		0			0
$703$		−	3.96965e29i		−	0.507833i
$704$		0			0
$705$	1.30102e28	−	3.73189e29i	0.0161546	−	0.463386i
$706$		0			0
$707$	−3.03178e29			−0.365421
$708$		0			0
$709$	−1.14485e30			−1.33957			−0.669783	−	0.742557i	$-0.733613\pi$
$709$	−1.14485e30			−1.33957			−0.669783	+	0.742557i	$0.733613\pi$
$710$		0			0
$711$	4.03576e28	−	5.78112e29i	0.0458452	−	0.656721i
$712$		0			0
$713$		−	1.78014e30i		−	1.96343i
$714$		0			0
$715$			7.69436e29i			0.824060i
$716$		0			0
$717$	2.57500e29	+	8.97701e27i	0.267809	+	0.00933642i
$718$		0			0
$719$	−6.08592e28			−0.0614714			−0.0307357	−	0.999528i	$-0.509785\pi$
$719$	−6.08592e28			−0.0614714			−0.0307357	+	0.999528i	$0.509785\pi$
$720$		0			0
$721$	−2.20894e29			−0.216702
$722$		0			0
$723$	1.74260e30	+	6.07510e28i	1.66053	+	0.0578897i
$724$		0			0
$725$		−	1.11161e30i		−	1.02897i
$726$		0			0
$727$		−	4.47721e29i		−	0.402621i	−0.979527	−	0.201311i	$-0.935480\pi$
$727$		−	4.47721e29i		−	0.402621i	0.979527	−	0.201311i	$-0.0645200\pi$
$728$		0			0
$729$	1.11963e30	+	2.37575e29i	0.978221	+	0.207568i
$730$		0			0
$731$	1.34492e30			1.14173
$732$		0			0
$733$	1.44013e30			1.18798			0.593992	−	0.804471i	$-0.297551\pi$
$733$	1.44013e30			1.18798			0.593992	+	0.804471i	$0.297551\pi$
$734$		0			0
$735$	6.61507e28	−	1.89749e30i	0.0530295	−	1.52112i
$736$		0			0
$737$		−	1.00508e29i		−	0.0783054i
$738$		0			0
$739$			2.29258e30i			1.73603i	0.496539	+	0.868015i	$0.334604\pi$
$739$			2.29258e30i			1.73603i	−0.496539	+	0.868015i	$0.665396\pi$
$740$		0			0
$741$	4.72902e27	−	1.35649e29i	0.00348081	−	0.0998449i
$742$		0			0
$743$	−2.58396e30			−1.84886			−0.924430	−	0.381352i	$-0.875459\pi$
$743$	−2.58396e30			−1.84886			−0.924430	+	0.381352i	$0.875459\pi$
$744$		0			0
$745$	3.68085e30			2.56040
$746$		0			0
$747$	−1.12975e30	−	7.88670e28i	−0.764040	−	0.0533371i
$748$		0			0
$749$			6.35925e29i			0.418164i
$750$		0			0
$751$		−	1.05049e30i		−	0.671697i	−0.941916	−	0.335849i	$-0.890977\pi$
$751$		−	1.05049e30i		−	0.671697i	0.941916	−	0.335849i	$-0.109023\pi$
$752$		0			0
$753$	−5.90432e29	−	2.05838e28i	−0.367132	−	0.0127990i
$754$		0			0
$755$	3.97027e30			2.40092
$756$		0			0
$757$	−3.03847e30			−1.78710			−0.893549	−	0.448965i	$-0.851793\pi$
$757$	−3.03847e30			−1.78710			−0.893549	+	0.448965i	$0.851793\pi$
$758$		0			0
$759$	−3.09668e30	−	1.07957e29i	−1.77157	−	0.0617608i
$760$		0			0
$761$			3.01503e29i			0.167785i	0.996475	+	0.0838925i	$0.0267352\pi$
$761$			3.01503e29i			0.167785i	−0.996475	+	0.0838925i	$0.973265\pi$
$762$		0			0
$763$			5.61755e29i			0.304116i
$764$		0			0
$765$	4.02824e30	+	2.81209e29i	2.12164	+	0.148110i
$766$		0			0
$767$	1.93150e29			0.0989792
$768$		0			0
$769$	−2.98421e30			−1.48800			−0.743999	−	0.668180i	$-0.767073\pi$
$769$	−2.98421e30			−1.48800			−0.743999	+	0.668180i	$0.767073\pi$
$770$		0			0
$771$	8.23923e28	−	2.36337e30i	0.0399775	−	1.14673i
$772$		0			0
$773$			2.98776e29i			0.141078i	0.997509	+	0.0705392i	$0.0224720\pi$
$773$			2.98776e29i			0.141078i	−0.997509	+	0.0705392i	$0.977528\pi$
$774$		0			0
$775$			5.76886e30i			2.65107i
$776$		0			0
$777$	3.84312e28	−	1.10237e30i	0.0171895	−	0.493070i
$778$		0			0
$779$	8.45909e29			0.368282
$780$		0			0
$781$	−4.12333e30			−1.74748
$782$		0			0
$783$	1.52887e29	−	1.45709e30i	0.0630773	−	0.601155i
$784$		0			0
$785$			6.87588e30i			2.76183i
$786$		0			0
$787$			2.46031e30i			0.962176i	0.876672	+	0.481088i	$0.159758\pi$
$787$			2.46031e30i			0.962176i	−0.876672	+	0.481088i	$0.840242\pi$
$788$		0			0
$789$	−3.26113e30	−	1.13690e29i	−1.24182	−	0.0432927i
$790$		0			0
$791$	−8.08520e28			−0.0299804
$792$		0			0
$793$	−1.27137e30			−0.459095
$794$		0			0
$795$	−2.33416e30	−	8.13739e28i	−0.820872	−	0.0286174i
$796$		0			0
$797$		−	9.83242e29i		−	0.336781i	−0.985720	−	0.168391i	$-0.946143\pi$
$797$		−	9.83242e29i		−	0.336781i	0.985720	−	0.168391i	$-0.0538570\pi$
$798$		0			0
$799$		−	1.09380e30i		−	0.364920i
$800$		0			0
$801$	2.56276e29	−	3.67109e30i	0.0832850	−	1.19304i
$802$		0			0
$803$	−8.40260e29			−0.266012
$804$		0			0
$805$	1.82934e30			0.564207
$806$		0			0
$807$	2.51168e28	−	7.20460e29i	0.00754731	−	0.216490i
$808$		0			0
$809$			5.20364e30i			1.52352i	0.647860	+	0.761759i	$0.275664\pi$
$809$			5.20364e30i			1.52352i	−0.647860	+	0.761759i	$0.724336\pi$
$810$		0			0
$811$		−	4.79519e30i		−	1.36800i	−0.729482	−	0.684001i	$-0.760239\pi$
$811$		−	4.79519e30i		−	1.36800i	0.729482	−	0.684001i	$-0.239761\pi$
$812$		0			0
$813$	−2.29399e29	+	6.58016e30i	−0.0637735	+	1.82930i
$814$		0			0
$815$	−1.17210e31			−3.17548
$816$		0			0
$817$	−9.36533e29			−0.247281
$818$		0			0
$819$	2.62651e28	−	3.76241e29i	0.00675924	−	0.0968245i
$820$		0			0
$821$			5.33920e30i			1.33929i	0.742683	+	0.669643i	$0.233553\pi$
$821$			5.33920e30i			1.33929i	−0.742683	+	0.669643i	$0.766447\pi$
$822$		0			0
$823$			6.52693e30i			1.59592i	0.602712	+	0.797959i	$0.294087\pi$
$823$			6.52693e30i			1.59592i	−0.602712	+	0.797959i	$0.705913\pi$
$824$		0			0
$825$	1.00353e31	+	3.49853e29i	2.39202	+	0.0833910i
$826$		0			0
$827$	3.19547e30			0.742552			0.371276	−	0.928523i	$-0.378920\pi$
$827$	3.19547e30			0.742552			0.371276	+	0.928523i	$0.378920\pi$
$828$		0			0
$829$	2.66285e30			0.603286			0.301643	−	0.953421i	$-0.402465\pi$
$829$	2.66285e30			0.603286			0.301643	+	0.953421i	$0.402465\pi$
$830$		0			0
$831$	2.95938e30	+	1.03171e29i	0.653718	+	0.0227901i
$832$		0			0
$833$		−	5.56148e30i		−	1.19789i
$834$		0			0
$835$			7.30743e30i			1.53482i
$836$		0			0
$837$	−7.93432e29	+	7.56176e30i	−0.162515	+	1.54884i
$838$		0			0
$839$	6.74423e30			1.34720			0.673600	−	0.739096i	$-0.264747\pi$
$839$	6.74423e30			1.34720			0.673600	+	0.739096i	$0.264747\pi$
$840$		0			0
$841$	3.25748e30			0.634634
$842$		0			0
$843$	3.25958e29	−	9.34989e30i	0.0619401	−	1.77671i
$844$		0			0
$845$		−	7.74139e30i		−	1.43491i
$846$		0			0
$847$		−	1.47081e30i		−	0.265938i
$848$		0			0
$849$	−3.29130e28	+	9.44090e29i	−0.00580547	+	0.166526i
$850$		0			0
$851$	−1.32778e31			−2.28489
$852$		0			0
$853$	−4.20403e30			−0.705831			−0.352916	−	0.935655i	$-0.614810\pi$
$853$	−4.20403e30			−0.705831			−0.352916	+	0.935655i	$0.614810\pi$
$854$		0			0
$855$	−2.80507e30	−	1.95820e29i	−0.459515	−	0.0320784i
$856$		0			0
$857$			5.44521e30i			0.870394i	0.900335	+	0.435197i	$0.143321\pi$
$857$			5.44521e30i			0.870394i	−0.900335	+	0.435197i	$0.856679\pi$
$858$		0			0
$859$		−	8.10886e30i		−	1.26483i	−0.774631	−	0.632414i	$-0.782064\pi$
$859$		−	8.10886e30i		−	1.26483i	0.774631	−	0.632414i	$-0.217936\pi$
$860$		0			0
$861$	2.34910e30	+	8.18947e28i	0.357576	+	0.0124659i
$862$		0			0
$863$	5.08376e30			0.755217			0.377609	−	0.925965i	$-0.376746\pi$
$863$	5.08376e30			0.755217			0.377609	+	0.925965i	$0.376746\pi$
$864$		0			0
$865$	4.68952e30			0.679922
$866$		0			0
$867$	4.75887e30	+	1.65905e29i	0.673446	+	0.0234778i
$868$		0			0
$869$		−	6.70092e30i		−	0.925607i
$870$		0			0
$871$		−	1.47263e29i		−	0.0198565i
$872$		0			0
$873$	−7.83648e30	−	5.47059e29i	−1.03151	−	0.0720086i
$874$		0			0
$875$	−2.44579e30			−0.314293
$876$		0			0
$877$	−7.61028e30			−0.954783			−0.477392	−	0.878691i	$-0.658418\pi$
$877$	−7.61028e30			−0.954783			−0.477392	+	0.878691i	$0.658418\pi$
$878$		0			0
$879$	6.87629e28	−	1.97242e30i	0.00842308	−	0.241611i
$880$		0			0
$881$			5.66908e30i			0.678055i	0.940776	+	0.339028i	$0.110098\pi$
$881$			5.66908e30i			0.678055i	−0.940776	+	0.339028i	$0.889902\pi$
$882$		0			0
$883$		−	4.51932e30i		−	0.527820i	−0.964547	−	0.263910i	$-0.914988\pi$
$883$		−	4.51932e30i		−	0.527820i	0.964547	−	0.263910i	$-0.0850122\pi$
$884$		0			0
$885$	1.39414e29	−	3.99899e30i	0.0159001	−	0.456086i
$886$		0			0
$887$	−8.74053e30			−0.973509			−0.486754	−	0.873539i	$-0.661819\pi$
$887$	−8.74053e30			−0.973509			−0.486754	+	0.873539i	$0.661819\pi$
$888$		0			0
$889$	−2.70669e30			−0.294421
$890$		0			0
$891$	1.31061e31	+	1.83881e30i	1.39238	+	0.195354i
$892$		0			0
$893$			7.61671e29i			0.0790364i
$894$		0			0
$895$			8.11488e30i			0.822508i
$896$		0			0
$897$	−4.53722e30	−	1.58178e29i	−0.449231	−	0.0156612i
$898$		0			0
$899$	9.73250e30			0.941342
$900$		0			0
$901$	−6.84134e30			−0.646444
$902$		0			0
$903$	−2.60076e30	−	9.06683e28i	−0.240093	−	0.00837017i
$904$		0			0
$905$		−	1.67340e31i		−	1.50935i
$906$		0			0
$907$			1.47863e31i			1.30311i	0.758601	+	0.651556i	$0.225883\pi$
$907$			1.47863e31i			1.30311i	−0.758601	+	0.651556i	$0.774117\pi$
$908$		0			0
$909$	1.08551e30	−	1.55496e31i	0.0934785	−	1.33906i
$910$		0			0
$911$	1.15676e31			0.973420			0.486710	−	0.873564i	$-0.338197\pi$
$911$	1.15676e31			0.973420			0.486710	+	0.873564i	$0.338197\pi$
$912$		0			0
$913$	−1.30950e31			−1.07687
$914$		0			0
$915$	−9.17659e29	+	2.63225e31i	−0.0737496	+	2.11546i
$916$		0			0
$917$		−	5.45253e30i		−	0.428272i
$918$		0			0
$919$		−	5.60794e30i		−	0.430517i	−0.976557	−	0.215259i	$-0.930941\pi$
$919$		−	5.60794e30i		−	0.430517i	0.976557	−	0.215259i	$-0.0690595\pi$
$920$		0			0
$921$	2.87665e29	−	8.25148e30i	0.0215854	−	0.619164i
$922$		0			0
$923$	−6.04145e30			−0.443122
$924$		0			0
$925$	4.30288e31			3.08511
$926$		0			0
$927$	7.90894e29	−	1.13294e31i	0.0554346	−	0.794087i
$928$		0			0
$929$		−	1.61159e31i		−	1.10431i	−0.833742	−	0.552154i	$-0.813806\pi$
$929$		−	1.61159e31i		−	1.10431i	0.833742	−	0.552154i	$-0.186194\pi$
$930$		0			0
$931$			3.87274e30i			0.259446i
$932$		0			0
$933$	7.87529e30	+	2.74550e29i	0.515833	+	0.0179831i
$934$		0			0
$935$	4.66916e31			2.99031
$936$		0			0
$937$	5.53868e30			0.346849			0.173424	−	0.984847i	$-0.444517\pi$
$937$	5.53868e30			0.346849			0.173424	+	0.984847i	$0.444517\pi$
$938$		0			0
$939$	−1.76999e31	−	6.17058e29i	−1.08388	−	0.0377865i
$940$		0			0
$941$			1.25619e31i			0.752256i	0.926568	+	0.376128i	$0.122745\pi$
$941$			1.25619e31i			0.752256i	−0.926568	+	0.376128i	$0.877255\pi$
$942$		0			0
$943$		−	2.82941e31i		−	1.65701i
$944$		0			0
$945$	−7.77076e30	−	8.15361e29i	−0.445071	−	0.0466999i
$946$		0			0
$947$	6.55060e30			0.366950			0.183475	−	0.983024i	$-0.441265\pi$
$947$	6.55060e30			0.366950			0.183475	+	0.983024i	$0.441265\pi$
$948$		0			0
$949$	−1.23114e30			−0.0674547
$950$		0			0
$951$	−8.07920e29	+	2.31747e31i	−0.0432985	+	1.24199i
$952$		0			0
$953$			5.42529e30i			0.284412i	0.989837	+	0.142206i	$0.0454195\pi$
$953$			5.42529e30i			0.284412i	−0.989837	+	0.142206i	$0.954581\pi$
$954$		0			0
$955$			6.08381e29i			0.0311990i
$956$		0			0
$957$	5.90229e29	−	1.69303e31i	0.0296105	−	0.849357i
$958$		0			0
$959$	−4.83119e30			−0.237115
$960$		0			0
$961$	−2.96828e31			−1.42531
$962$		0			0
$963$	−3.26158e31	−	2.27688e30i	−1.53233	−	0.106971i
$964$		0			0
$965$		−	1.56082e31i		−	0.717490i
$966$		0			0
$967$		−	3.23387e31i		−	1.45460i	−0.686318	−	0.727302i	$-0.740774\pi$
$967$		−	3.23387e31i		−	1.45460i	0.686318	−	0.727302i	$-0.259226\pi$
$968$		0			0
$969$	−8.23157e30	−	2.86971e29i	−0.362312	−	0.0126310i
$970$		0			0
$971$	5.79336e30			0.249533			0.124767	−	0.992186i	$-0.460182\pi$
$971$	5.79336e30			0.249533			0.124767	+	0.992186i	$0.460182\pi$
$972$		0			0
$973$	−2.60310e29			−0.0109725
$974$		0			0
$975$	1.47036e31	+	5.12601e29i	0.606563	+	0.0211461i
$976$		0			0
$977$		−	2.28906e31i		−	0.924197i	−0.886829	−	0.462098i	$-0.847097\pi$
$977$		−	2.28906e31i		−	0.924197i	0.886829	−	0.462098i	$-0.152903\pi$
$978$		0			0
$979$		−	4.25518e31i		−	1.68151i
$980$		0			0
$981$	−2.88117e31	−	2.01132e30i	−1.11441	−	0.0777960i
$982$		0			0
$983$	7.80676e30			0.295569			0.147784	−	0.989020i	$-0.452786\pi$
$983$	7.80676e30			0.295569			0.147784	+	0.989020i	$0.452786\pi$
$984$		0			0
$985$	5.34308e31			1.98021
$986$		0			0
$987$	−7.37394e28	+	2.11517e30i	−0.00267528	+	0.0767388i
$988$		0			0
$989$			3.13254e31i			1.11259i
$990$		0			0
$991$			4.36133e30i			0.151651i	0.997121	+	0.0758256i	$0.0241592\pi$
$991$			4.36133e30i			0.151651i	−0.997121	+	0.0758256i	$0.975841\pi$
$992$		0			0
$993$	−1.58082e30	+	4.53449e31i	−0.0538166	+	1.54369i
$994$		0			0
$995$	−4.92922e31			−1.64299
$996$		0			0
$997$	−1.02983e31			−0.336100			−0.168050	−	0.985779i	$-0.553747\pi$
$997$	−1.02983e31			−0.336100			−0.168050	+	0.985779i	$0.553747\pi$
$998$		0			0
$999$	5.64018e31	+	5.91806e30i	1.80242	+	0.189122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.22.c.c.47.3	✓	28
3.2	odd	2	inner	48.22.c.c.47.25	yes	28
4.3	odd	2	inner	48.22.c.c.47.26	yes	28
12.11	even	2	inner	48.22.c.c.47.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.22.c.c.47.3	✓	28	1.1	even	1	trivial
48.22.c.c.47.4	yes	28	12.11	even	2	inner
48.22.c.c.47.25	yes	28	3.2	odd	2	inner
48.22.c.c.47.26	yes	28	4.3	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-102214. - 3563.40i) q^{3} +3.58965e7i q^{5} -2.03455e8i q^{7} +(1.04350e10 + 7.28456e8i) q^{9} +O(q^{10})\)	\(q+(-102214. - 3563.40i) q^{3} +3.58965e7i q^{5} -2.03455e8i q^{7} +(1.04350e10 + 7.28456e8i) q^{9} +1.20952e11 q^{11} +1.77218e11 q^{13} +(1.27914e11 - 3.66912e12i) q^{15} -1.07541e13i q^{17} +7.48860e12i q^{19} +(-7.24992e11 + 2.07959e13i) q^{21} +2.50481e14 q^{23} -8.11724e14 q^{25} +(-1.06400e15 - 1.11642e14i) q^{27} +1.36944e15i q^{29} -7.10692e15i q^{31} +(-1.23630e16 - 4.31000e14i) q^{33} +7.30334e15 q^{35} -5.30092e16 q^{37} +(-1.81141e16 - 6.31496e14i) q^{39} -1.12959e17i q^{41} +1.25061e17i q^{43} +(-2.61491e16 + 3.74579e17i) q^{45} +1.01711e17 q^{47} +5.17152e17 q^{49} +(-3.83210e16 + 1.09921e18i) q^{51} -6.36163e17i q^{53} +4.34176e18i q^{55} +(2.66849e16 - 7.65438e17i) q^{57} +1.08991e18 q^{59} -7.17405e18 q^{61} +(1.48208e17 - 2.12305e18i) q^{63} +6.36149e18i q^{65} -8.30973e17i q^{67} +(-2.56026e19 - 8.92561e17i) q^{69} -3.40906e19 q^{71} -6.94705e18 q^{73} +(8.29694e19 + 2.89249e18i) q^{75} -2.46083e19i q^{77} -5.54015e19i q^{79} +(1.08358e20 + 1.52028e19i) q^{81} -1.08266e20 q^{83} +3.86034e20 q^{85} +(4.87986e18 - 1.39976e20i) q^{87} -3.51807e20i q^{89} -3.60558e19i q^{91} +(-2.53248e19 + 7.26425e20i) q^{93} -2.68815e20 q^{95} -7.50983e20 q^{97} +(1.26213e21 + 8.81083e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 109254828 q^{9}+O(q^{10}) \) 28 * q + 109254828 * q^9	\( 28 q + 109254828 q^{9} + 285248048392 q^{13} + 247146979606248 q^{21} - 31\!\cdots\!84 q^{25}+ \cdots + 16\!\cdots\!20 q^{97}+O(q^{100}) \) 28 * q + 109254828 * q^9 + 285248048392 * q^13 + 247146979606248 * q^21 - 3168527686741684 * q^25 - 7429429202649408 * q^33 + 33089121948065192 * q^37 - 121806830473453440 * q^45 - 569345069725368716 * q^49 + 10547854228195302552 * q^57 - 8280751575178739512 * q^61 - 22754055866538936960 * q^69 - 98548109928833394536 * q^73 + 563980976909609989500 * q^81 - 93841573689641488896 * q^85 - 1293830212233248374968 * q^93 + 1670728237822569097720 * q^97

Introduction

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