LMFDB - Embedded newform 48.22.c.c.47.15

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			47.15
Character	$\chi$	$=$	48.47
Dual form			48.22.c.c.47.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(554.307 - 102274. i) q^{3} -3.49802e7i q^{5} +7.47725e8i q^{7} +(-1.04597e10 - 1.13383e8i) q^{9} +O(q^{10})$	\(q+(554.307 - 102274. i) q^{3} -3.49802e7i q^{5} +7.47725e8i q^{7} +(-1.04597e10 - 1.13383e8i) q^{9} +1.00580e11 q^{11} +2.55401e11 q^{13} +(-3.57758e12 - 1.93898e10i) q^{15} -6.80713e12i q^{17} +4.43464e13i q^{19} +(7.64731e13 + 4.14469e11i) q^{21} +2.67379e14 q^{23} -7.46779e14 q^{25} +(-1.73941e13 + 1.06970e15i) q^{27} -4.19900e15i q^{29} -4.81995e15i q^{31} +(5.57521e13 - 1.02867e16i) q^{33} +2.61556e16 q^{35} +3.54159e16 q^{37} +(1.41571e14 - 2.61210e16i) q^{39} -1.43819e17i q^{41} -1.16710e17i q^{43} +(-3.96616e15 + 3.65884e17i) q^{45} -1.48520e17 q^{47} -5.46721e14 q^{49} +(-6.96195e17 - 3.77324e15i) q^{51} +1.61865e18i q^{53} -3.51830e18i q^{55} +(4.53550e18 + 2.45815e16i) q^{57} +1.11479e18 q^{59} +1.49449e18 q^{61} +(8.47792e16 - 7.82101e18i) q^{63} -8.93398e18i q^{65} -1.07807e19i q^{67} +(1.48210e17 - 2.73461e19i) q^{69} +2.20121e19 q^{71} -3.19922e19 q^{73} +(-4.13945e17 + 7.63763e19i) q^{75} +7.52060e19i q^{77} +2.21919e19i q^{79} +(1.09393e20 + 2.37191e18i) q^{81} -2.26654e19 q^{83} -2.38115e20 q^{85} +(-4.29450e20 - 2.32753e18i) q^{87} +2.74977e20i q^{89} +1.90970e20i q^{91} +(-4.92957e20 - 2.67173e18i) q^{93} +1.55125e21 q^{95} +3.33348e20 q^{97} +(-1.05204e21 - 1.14040e19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	554.307	−	102274.i	0.00541973	−	0.999985i
$3$	554.307	−	102274.i	0.00541973	−	0.999985i
$4$		0			0
$5$		−	3.49802e7i		−	1.60191i	−0.598726	−	0.800954i	$-0.704326\pi$
$5$		−	3.49802e7i		−	1.60191i	0.598726	−	0.800954i	$-0.295674\pi$
$6$		0			0
$7$			7.47725e8i			1.00049i	0.865884	+	0.500245i	$0.166757\pi$
$7$			7.47725e8i			1.00049i	−0.865884	+	0.500245i	$0.833243\pi$
$8$		0			0
$9$	−1.04597e10	−	1.13383e8i	−0.999941	−	0.0108393i
$10$		0			0
$11$	1.00580e11			1.16920			0.584598	−	0.811323i	$-0.301252\pi$
$11$	1.00580e11			1.16920			0.584598	+	0.811323i	$0.301252\pi$
$12$		0			0
$13$	2.55401e11			0.513828			0.256914	−	0.966434i	$-0.417294\pi$
$13$	2.55401e11			0.513828			0.256914	+	0.966434i	$0.417294\pi$
$14$		0			0
$15$	−3.57758e12	−	1.93898e10i	−1.60188	−	0.00868190i
$16$		0			0
$17$		−	6.80713e12i		−	0.818937i	−0.912324	−	0.409469i	$-0.865714\pi$
$17$		−	6.80713e12i		−	0.818937i	0.912324	−	0.409469i	$-0.134286\pi$
$18$		0			0
$19$			4.43464e13i			1.65938i	0.558226	+	0.829689i	$0.311482\pi$
$19$			4.43464e13i			1.65938i	−0.558226	+	0.829689i	$0.688518\pi$
$20$		0			0
$21$	7.64731e13	+	4.14469e11i	1.00047	+	0.00542238i
$22$		0			0
$23$	2.67379e14			1.34582			0.672908	−	0.739726i	$-0.265045\pi$
$23$	2.67379e14			1.34582			0.672908	+	0.739726i	$0.265045\pi$
$24$		0			0
$25$	−7.46779e14			−1.56611
$26$		0			0
$27$	−1.73941e13	+	1.06970e15i	−0.0162585	+	0.999868i
$28$		0			0
$29$		−	4.19900e15i		−	1.85339i	−0.375816	−	0.926694i	$-0.622638\pi$
$29$		−	4.19900e15i		−	1.85339i	0.375816	−	0.926694i	$-0.377362\pi$
$30$		0			0
$31$		−	4.81995e15i		−	1.05620i	−0.849183	−	0.528098i	$-0.822905\pi$
$31$		−	4.81995e15i		−	1.05620i	0.849183	−	0.528098i	$-0.177095\pi$
$32$		0			0
$33$	5.57521e13	−	1.02867e16i	0.00633673	−	1.16918i
$34$		0			0
$35$	2.61556e16			1.60269
$36$		0			0
$37$	3.54159e16			1.21082			0.605411	−	0.795913i	$-0.293009\pi$
$37$	3.54159e16			1.21082			0.605411	+	0.795913i	$0.293009\pi$
$38$		0			0
$39$	1.41571e14	−	2.61210e16i	0.00278481	−	0.513820i
$40$		0			0
$41$		−	1.43819e17i		−	1.67335i	−0.547702	−	0.836674i	$-0.684497\pi$
$41$		−	1.43819e17i		−	1.67335i	0.547702	−	0.836674i	$-0.315503\pi$
$42$		0			0
$43$		−	1.16710e17i		−	0.823546i	−0.911287	−	0.411773i	$-0.864910\pi$
$43$		−	1.16710e17i		−	0.823546i	0.911287	−	0.411773i	$-0.135090\pi$
$44$		0			0
$45$	−3.96616e15	+	3.65884e17i	−0.0173636	+	1.60181i
$46$		0			0
$47$	−1.48520e17			−0.411867			−0.205934	−	0.978566i	$-0.566023\pi$
$47$	−1.48520e17			−0.411867			−0.205934	+	0.978566i	$0.566023\pi$
$48$		0			0
$49$	−5.46721e14			−0.000978829
$50$		0			0
$51$	−6.96195e17	−	3.77324e15i	−0.818925	−	0.00443842i
$52$		0			0
$53$			1.61865e18i			1.27132i	0.771968	+	0.635661i	$0.219272\pi$
$53$			1.61865e18i			1.27132i	−0.771968	+	0.635661i	$0.780728\pi$
$54$		0			0
$55$		−	3.51830e18i		−	1.87295i
$56$		0			0
$57$	4.53550e18	+	2.45815e16i	1.65935	+	0.00899338i
$58$		0			0
$59$	1.11479e18			0.283953			0.141976	−	0.989870i	$-0.454654\pi$
$59$	1.11479e18			0.283953			0.141976	+	0.989870i	$0.454654\pi$
$60$		0			0
$61$	1.49449e18			0.268244			0.134122	−	0.990965i	$-0.457179\pi$
$61$	1.49449e18			0.268244			0.134122	+	0.990965i	$0.457179\pi$
$62$		0			0
$63$	8.47792e16	−	7.82101e18i	0.0108446	−	1.00043i
$64$		0			0
$65$		−	8.93398e18i		−	0.823104i
$66$		0			0
$67$		−	1.07807e19i		−	0.722539i	−0.932461	−	0.361270i	$-0.882343\pi$
$67$		−	1.07807e19i		−	0.722539i	0.932461	−	0.361270i	$-0.117657\pi$
$68$		0			0
$69$	1.48210e17	−	2.73461e19i	0.00729396	−	1.34580i
$70$		0			0
$71$	2.20121e19			0.802508			0.401254	−	0.915967i	$-0.368574\pi$
$71$	2.20121e19			0.802508			0.401254	+	0.915967i	$0.368574\pi$
$72$		0			0
$73$	−3.19922e19			−0.871271			−0.435636	−	0.900123i	$-0.643476\pi$
$73$	−3.19922e19			−0.871271			−0.435636	+	0.900123i	$0.643476\pi$
$74$		0			0
$75$	−4.13945e17	+	7.63763e19i	−0.00848788	+	1.56609i
$76$		0			0
$77$			7.52060e19i			1.16977i
$78$		0			0
$79$			2.21919e19i			0.263700i	0.991270	+	0.131850i	$0.0420918\pi$
$79$			2.21919e19i			0.263700i	−0.991270	+	0.131850i	$0.957908\pi$
$80$		0			0
$81$	1.09393e20	+	2.37191e18i	0.999765	+	0.0216773i
$82$		0			0
$83$	−2.26654e19			−0.160341			−0.0801704	−	0.996781i	$-0.525546\pi$
$83$	−2.26654e19			−0.160341			−0.0801704	+	0.996781i	$0.525546\pi$
$84$		0			0
$85$	−2.38115e20			−1.31186
$86$		0			0
$87$	−4.29450e20	−	2.32753e18i	−1.85336	−	0.0100449i
$88$		0			0
$89$			2.74977e20i			0.934762i	0.884056	+	0.467381i	$0.154802\pi$
$89$			2.74977e20i			0.934762i	−0.884056	+	0.467381i	$0.845198\pi$
$90$		0			0
$91$			1.90970e20i			0.514079i
$92$		0			0
$93$	−4.92957e20	−	2.67173e18i	−1.05618	−	0.00572430i
$94$		0			0
$95$	1.55125e21			2.65817
$96$		0			0
$97$	3.33348e20			0.458981			0.229490	−	0.973311i	$-0.426294\pi$
$97$	3.33348e20			0.458981			0.229490	+	0.973311i	$0.426294\pi$
$98$		0			0
$99$	−1.05204e21	−	1.14040e19i	−1.16913	−	0.0126733i
$100$		0			0
$101$		−	9.41944e20i		−	0.848498i	−0.905546	−	0.424249i	$-0.860538\pi$
$101$		−	9.41944e20i		−	0.848498i	0.905546	−	0.424249i	$-0.139462\pi$
$102$		0			0
$103$			5.76930e20i			0.422992i	0.977379	+	0.211496i	$0.0678335\pi$
$103$			5.76930e20i			0.422992i	−0.977379	+	0.211496i	$0.932166\pi$
$104$		0			0
$105$	1.44982e19	−	2.67505e21i	0.00868615	−	1.60267i
$106$		0			0
$107$	2.97194e20			0.146053			0.0730264	−	0.997330i	$-0.476734\pi$
$107$	2.97194e20			0.146053			0.0730264	+	0.997330i	$0.476734\pi$
$108$		0			0
$109$	1.05933e20			0.0428601			0.0214300	−	0.999770i	$-0.493178\pi$
$109$	1.05933e20			0.0428601			0.0214300	+	0.999770i	$0.493178\pi$
$110$		0			0
$111$	1.96313e19	−	3.62214e21i	0.00656233	−	1.21080i
$112$		0			0
$113$			5.87340e21i			1.62767i	0.581097	+	0.813834i	$0.302623\pi$
$113$			5.87340e21i			1.62767i	−0.581097	+	0.813834i	$0.697377\pi$
$114$		0			0
$115$		−	9.35299e21i		−	2.15587i
$116$		0			0
$117$	−2.67143e21	−	2.89581e19i	−0.513797	−	0.00556953i
$118$		0			0
$119$	5.08986e21			0.819338
$120$		0			0
$121$	2.71605e21			0.367021
$122$		0			0
$123$	−1.47090e22	−	7.97200e19i	−1.67332	−	0.00906909i
$124$		0			0
$125$			9.44261e21i			0.906853i
$126$		0			0
$127$			4.86885e21i			0.395811i	0.980221	+	0.197905i	$0.0634139\pi$
$127$			4.86885e21i			0.395811i	−0.980221	+	0.197905i	$0.936586\pi$
$128$		0			0
$129$	−1.19364e22	−	6.46930e19i	−0.823534	−	0.00446339i
$130$		0			0
$131$	−1.36566e22			−0.801667			−0.400833	−	0.916151i	$-0.631279\pi$
$131$	−1.36566e22			−0.801667			−0.400833	+	0.916151i	$0.631279\pi$
$132$		0			0
$133$	−3.31589e22			−1.66019
$134$		0			0
$135$	3.74184e22	+	6.08448e20i	1.60170	+	0.0260447i
$136$		0			0
$137$		−	4.35073e22i		−	1.59586i	−0.602747	−	0.797932i	$-0.705927\pi$
$137$		−	4.35073e22i		−	1.59586i	0.602747	−	0.797932i	$-0.294073\pi$
$138$		0			0
$139$			1.00355e22i			0.316144i	0.987428	+	0.158072i	$0.0505278\pi$
$139$			1.00355e22i			0.316144i	−0.987428	+	0.158072i	$0.949472\pi$
$140$		0			0
$141$	−8.23257e19	+	1.51898e22i	−0.00223221	+	0.411861i
$142$		0			0
$143$	2.56882e22			0.600766
$144$		0			0
$145$	−1.46882e23			−2.96896
$146$		0			0
$147$	−3.03051e17	+	5.59155e19i	−5.30499e−6	+	0.000978815i
$148$		0			0
$149$		−	7.87189e22i		−	1.19570i	−0.801607	−	0.597852i	$-0.796021\pi$
$149$		−	7.87189e22i		−	1.19570i	0.801607	−	0.597852i	$-0.203979\pi$
$150$		0			0
$151$		−	1.43792e23i		−	1.89879i	−0.314088	−	0.949394i	$-0.601699\pi$
$151$		−	1.43792e23i		−	1.89879i	0.314088	−	0.949394i	$-0.398301\pi$
$152$		0			0
$153$	−7.71812e20	+	7.12008e22i	−0.00887670	+	0.818889i
$154$		0			0
$155$	−1.68603e23			−1.69193
$156$		0			0
$157$	−6.87441e22			−0.602961			−0.301480	−	0.953472i	$-0.597481\pi$
$157$	−6.87441e22			−0.602961			−0.301480	+	0.953472i	$0.597481\pi$
$158$		0			0
$159$	1.65546e23	+	8.97228e20i	1.27130	+	0.00689022i
$160$		0			0
$161$			1.99926e23i			1.34647i
$162$		0			0
$163$		−	6.84150e22i		−	0.404745i	−0.979309	−	0.202373i	$-0.935135\pi$
$163$		−	6.84150e22i		−	0.404745i	0.979309	−	0.202373i	$-0.0648652\pi$
$164$		0			0
$165$	−3.59832e23	−	1.95022e21i	−1.87292	−	0.0101509i
$166$		0			0
$167$	−2.56288e23			−1.17545			−0.587727	−	0.809059i	$-0.699977\pi$
$167$	−2.56288e23			−1.17545			−0.587727	+	0.809059i	$0.699977\pi$
$168$		0			0
$169$	−1.81835e23			−0.735981
$170$		0			0
$171$	5.02812e21	−	4.63852e23i	0.0179865	−	1.65928i
$172$		0			0
$173$			9.26369e22i			0.293292i	0.989189	+	0.146646i	$0.0468478\pi$
$173$			9.26369e22i			0.293292i	−0.989189	+	0.146646i	$0.953152\pi$
$174$		0			0
$175$		−	5.58385e23i		−	1.56687i
$176$		0			0
$177$	6.17935e20	−	1.14014e23i	0.00153895	−	0.283949i
$178$		0			0
$179$	5.65105e23			1.25075			0.625377	−	0.780322i	$-0.284945\pi$
$179$	5.65105e23			1.25075			0.625377	+	0.780322i	$0.284945\pi$
$180$		0			0
$181$	−8.77402e23			−1.72812			−0.864059	−	0.503390i	$-0.832086\pi$
$181$	−8.77402e23			−1.72812			−0.864059	+	0.503390i	$0.832086\pi$
$182$		0			0
$183$	8.28409e20	−	1.52848e23i	0.00145381	−	0.268240i
$184$		0			0
$185$		−	1.23886e24i		−	1.93963i
$186$		0			0
$187$		−	6.84660e23i		−	0.957499i
$188$		0			0
$189$	−7.99842e23	−	1.30060e22i	−1.00036	−	0.0162665i
$190$		0			0
$191$	7.30255e21			0.00817757			0.00408879	−	0.999992i	$-0.498698\pi$
$191$	7.30255e21			0.00817757			0.00408879	+	0.999992i	$0.498698\pi$
$192$		0			0
$193$	4.77036e23			0.478850			0.239425	−	0.970915i	$-0.423041\pi$
$193$	4.77036e23			0.478850			0.239425	+	0.970915i	$0.423041\pi$
$194$		0			0
$195$	−9.13718e23	−	4.95217e21i	−0.823092	−	0.00446100i
$196$		0			0
$197$			1.14719e24i			0.928407i	0.885728	+	0.464204i	$0.153659\pi$
$197$			1.14719e24i			0.928407i	−0.885728	+	0.464204i	$0.846341\pi$
$198$		0			0
$199$			1.98955e24i			1.44810i	0.689749	+	0.724048i	$0.257721\pi$
$199$			1.98955e24i			1.44810i	−0.689749	+	0.724048i	$0.742279\pi$
$200$		0			0
$201$	−1.10259e24	−	5.97582e21i	−0.722529	−	0.00391597i
$202$		0			0
$203$	3.13969e24			1.85430
$204$		0			0
$205$	−5.03082e24			−2.68055
$206$		0			0
$207$	−2.79672e24	−	3.03163e22i	−1.34574	−	0.0145877i
$208$		0			0
$209$			4.46035e24i			1.94014i
$210$		0			0
$211$			5.41707e22i			0.0213205i	0.999943	+	0.0106603i	$0.00339333\pi$
$211$			5.41707e22i			0.0213205i	−0.999943	+	0.0106603i	$0.996607\pi$
$212$		0			0
$213$	1.22015e22	−	2.25128e24i	0.00434938	−	0.802496i
$214$		0			0
$215$	−4.08253e24			−1.31924
$216$		0			0
$217$	3.60400e24			1.05671
$218$		0			0
$219$	−1.77335e22	+	3.27198e24i	−0.00472205	+	0.871259i
$220$		0			0
$221$		−	1.73855e24i		−	0.420793i
$222$		0			0
$223$		−	7.60220e24i		−	1.67393i	−0.547254	−	0.836967i	$-0.684327\pi$
$223$		−	7.60220e24i		−	1.67393i	0.547254	−	0.836967i	$-0.315673\pi$
$224$		0			0
$225$	7.81111e24	+	8.46719e22i	1.56602	+	0.0169755i
$226$		0			0
$227$	5.20457e24			0.950854			0.475427	−	0.879755i	$-0.342294\pi$
$227$	5.20457e24			0.950854			0.475427	+	0.879755i	$0.342294\pi$
$228$		0			0
$229$	2.96569e24			0.494143			0.247071	−	0.968997i	$-0.420532\pi$
$229$	2.96569e24			0.494143			0.247071	+	0.968997i	$0.420532\pi$
$230$		0			0
$231$	7.69165e24	+	4.16873e22i	1.16975	+	0.00633983i
$232$		0			0
$233$		−	8.55617e24i		−	1.18862i	−0.804237	−	0.594309i	$-0.797426\pi$
$233$		−	8.55617e24i		−	1.18862i	0.804237	−	0.594309i	$-0.202574\pi$
$234$		0			0
$235$			5.19526e24i			0.659774i
$236$		0			0
$237$	2.26967e24	+	1.23012e22i	0.263696	+	0.00142918i
$238$		0			0
$239$	−1.38152e24			−0.146953			−0.0734767	−	0.997297i	$-0.523409\pi$
$239$	−1.38152e24			−0.146953			−0.0734767	+	0.997297i	$0.523409\pi$
$240$		0			0
$241$	1.04275e25			1.01625			0.508125	−	0.861283i	$-0.330339\pi$
$241$	1.04275e25			1.01625			0.508125	+	0.861283i	$0.330339\pi$
$242$		0			0
$243$	3.03223e23	−	1.11868e25i	0.0270955	−	0.999633i
$244$		0			0
$245$			1.91244e22i			0.00156799i
$246$		0			0
$247$			1.13261e25i			0.852634i
$248$		0			0
$249$	−1.25636e22	+	2.31809e24i	−0.000869004	+	0.160338i
$250$		0			0
$251$	−2.75170e25			−1.74995			−0.874977	−	0.484165i	$-0.839124\pi$
$251$	−2.75170e25			−1.74995			−0.874977	+	0.484165i	$0.839124\pi$
$252$		0			0
$253$	2.68930e25			1.57352
$254$		0			0
$255$	−1.31989e23	+	2.43531e25i	−0.00710993	+	1.31184i
$256$		0			0
$257$			2.13227e24i			0.105814i	0.998599	+	0.0529072i	$0.0168487\pi$
$257$			2.13227e24i			0.105814i	−0.998599	+	0.0529072i	$0.983151\pi$
$258$		0			0
$259$			2.64814e25i			1.21141i
$260$		0			0
$261$	−4.76094e23	+	4.39204e25i	−0.0200894	+	1.85328i
$262$		0			0
$263$	2.14616e25			0.835848			0.417924	−	0.908482i	$-0.362758\pi$
$263$	2.14616e25			0.835848			0.417924	+	0.908482i	$0.362758\pi$
$264$		0			0
$265$	5.66206e25			2.03654
$266$		0			0
$267$	2.81231e25	+	1.52422e23i	0.934748	+	0.00506616i
$268$		0			0
$269$		−	1.04389e25i		−	0.320815i	−0.987051	−	0.160408i	$-0.948719\pi$
$269$		−	1.04389e25i		−	0.320815i	0.987051	−	0.160408i	$-0.0512808\pi$
$270$		0			0
$271$			7.61617e23i			0.0216550i	0.999941	+	0.0108275i	$0.00344657\pi$
$271$			7.61617e23i			0.0216550i	−0.999941	+	0.0108275i	$0.996553\pi$
$272$		0			0
$273$	1.95313e25	+	1.05856e23i	0.514071	+	0.00278617i
$274$		0			0
$275$	−7.51109e25			−1.83109
$276$		0			0
$277$	−4.61108e25			−1.04175			−0.520877	−	0.853632i	$-0.674395\pi$
$277$	−4.61108e25			−1.04175			−0.520877	+	0.853632i	$0.674395\pi$
$278$		0			0
$279$	−5.46500e23	+	5.04154e25i	−0.0114484	+	1.05613i
$280$		0			0
$281$		−	1.94908e25i		−	0.378802i	−0.981900	−	0.189401i	$-0.939345\pi$
$281$		−	1.94908e25i		−	0.378802i	0.981900	−	0.189401i	$-0.0606547\pi$
$282$		0			0
$283$			7.01090e25i			1.26478i	0.774649	+	0.632391i	$0.217927\pi$
$283$			7.01090e25i			1.26478i	−0.774649	+	0.632391i	$0.782073\pi$
$284$		0			0
$285$	8.59867e23	−	1.58653e26i	0.0144066	−	2.65813i
$286$		0			0
$287$	1.07537e26			1.67417
$288$		0			0
$289$	2.27549e25			0.329342
$290$		0			0
$291$	1.84777e23	−	3.40929e25i	0.00248755	−	0.458974i
$292$		0			0
$293$			7.11825e25i			0.891791i	0.895085	+	0.445896i	$0.147115\pi$
$293$			7.11825e25i			0.891791i	−0.895085	+	0.445896i	$0.852885\pi$
$294$		0			0
$295$		−	3.89955e25i		−	0.454866i
$296$		0			0
$297$	−1.74949e24	+	1.07590e26i	−0.0190094	+	1.16904i
$298$		0			0
$299$	6.82890e25			0.691518
$300$		0			0
$301$	8.72667e25			0.823949
$302$		0			0
$303$	−9.63367e25	−	5.22126e23i	−0.848485	−	0.00459863i
$304$		0			0
$305$		−	5.22777e25i		−	0.429703i
$306$		0			0
$307$		−	1.88150e26i		−	1.44394i	−0.691922	−	0.721972i	$-0.743236\pi$
$307$		−	1.88150e26i		−	1.44394i	0.691922	−	0.721972i	$-0.256764\pi$
$308$		0			0
$309$	5.90051e25	+	3.19796e23i	0.422986	+	0.00229250i
$310$		0			0
$311$	−5.45675e25			−0.365553			−0.182776	−	0.983155i	$-0.558508\pi$
$311$	−5.45675e25			−0.365553			−0.182776	+	0.983155i	$0.558508\pi$
$312$		0			0
$313$	−2.02731e26			−1.26971			−0.634855	−	0.772632i	$-0.718940\pi$
$313$	−2.02731e26			−1.26971			−0.634855	+	0.772632i	$0.718940\pi$
$314$		0			0
$315$	−2.73581e26	−	2.96560e24i	−1.60260	−	0.0173721i
$316$		0			0
$317$			2.87563e26i			1.57620i	0.615547	+	0.788100i	$0.288935\pi$
$317$			2.87563e26i			1.57620i	−0.615547	+	0.788100i	$0.711065\pi$
$318$		0			0
$319$		−	4.22334e26i		−	2.16698i
$320$		0			0
$321$	1.64737e23	−	3.03953e25i	0.000791566	−	0.146051i
$322$		0			0
$323$	3.01872e26			1.35893
$324$		0			0
$325$	−1.90728e26			−0.804710
$326$		0			0
$327$	5.87194e22	−	1.08342e25i	0.000232290	−	0.0428595i
$328$		0			0
$329$		−	1.11052e26i		−	0.412069i
$330$		0			0
$331$			1.39437e26i			0.485494i	0.970090	+	0.242747i	$0.0780485\pi$
$331$			1.39437e26i			0.485494i	−0.970090	+	0.242747i	$0.921952\pi$
$332$		0			0
$333$	−3.70441e26	−	4.01556e24i	−1.21075	−	0.0131245i
$334$		0			0
$335$	−3.77111e26			−1.15744
$336$		0			0
$337$	−5.61456e26			−1.61883			−0.809416	−	0.587235i	$-0.800216\pi$
$337$	−5.61456e26			−1.61883			−0.809416	+	0.587235i	$0.800216\pi$
$338$		0			0
$339$	6.00698e26	+	3.25567e24i	1.62764	+	0.00882152i
$340$		0			0
$341$		−	4.84790e26i		−	1.23490i
$342$		0			0
$343$			4.17230e26i			0.999510i
$344$		0			0
$345$	−9.56571e26	−	5.18443e24i	−2.15584	−	0.0116842i
$346$		0			0
$347$	2.40237e26			0.509542			0.254771	−	0.967001i	$-0.418000\pi$
$347$	2.40237e26			0.509542			0.254771	+	0.967001i	$0.418000\pi$
$348$		0			0
$349$	7.99552e26			1.59654			0.798269	−	0.602301i	$-0.205749\pi$
$349$	7.99552e26			1.59654			0.798269	+	0.602301i	$0.205749\pi$
$350$		0			0
$351$	−4.44246e24	+	2.73203e26i	−0.00835409	+	0.513760i
$352$		0			0
$353$		−	1.64161e26i		−	0.290827i	−0.989371	−	0.145414i	$-0.953549\pi$
$353$		−	1.64161e26i		−	0.290827i	0.989371	−	0.145414i	$-0.0464513\pi$
$354$		0			0
$355$		−	7.69989e26i		−	1.28554i
$356$		0			0
$357$	2.82135e24	−	5.20563e26i	0.00444059	−	0.819326i
$358$		0			0
$359$	−4.77626e26			−0.708919			−0.354459	−	0.935071i	$-0.615335\pi$
$359$	−4.77626e26			−0.708919			−0.354459	+	0.935071i	$0.615335\pi$
$360$		0			0
$361$	−1.25239e27			−1.75354
$362$		0			0
$363$	1.50553e24	−	2.77782e26i	0.00198916	−	0.367016i
$364$		0			0
$365$			1.11909e27i			1.39570i
$366$		0			0
$367$		−	6.60572e26i		−	0.777905i	−0.921258	−	0.388953i	$-0.872837\pi$
$367$		−	6.60572e26i		−	0.777905i	0.921258	−	0.388953i	$-0.127163\pi$
$368$		0			0
$369$	−1.63066e25	+	1.50431e27i	−0.0181379	+	1.67325i
$370$		0			0
$371$	−1.21030e27			−1.27194
$372$		0			0
$373$	−5.29265e26			−0.525691			−0.262846	−	0.964838i	$-0.584661\pi$
$373$	−5.29265e26			−0.525691			−0.262846	+	0.964838i	$0.584661\pi$
$374$		0			0
$375$	9.65737e26	+	5.23411e24i	0.906840	+	0.00491490i
$376$		0			0
$377$		−	1.07243e27i		−	0.952322i
$378$		0			0
$379$		−	4.06272e26i		−	0.341276i	−0.985334	−	0.170638i	$-0.945417\pi$
$379$		−	4.06272e26i		−	0.341276i	0.985334	−	0.170638i	$-0.0545828\pi$
$380$		0			0
$381$	4.97959e26	+	2.69884e24i	0.395805	+	0.00214519i
$382$		0			0
$383$	−3.98177e26			−0.299564			−0.149782	−	0.988719i	$-0.547857\pi$
$383$	−3.98177e26			−0.299564			−0.149782	+	0.988719i	$0.547857\pi$
$384$		0			0
$385$	2.63072e27			1.87386
$386$		0			0
$387$	−1.32329e25	+	1.22075e27i	−0.00892666	+	0.823497i
$388$		0			0
$389$			7.30481e26i			0.466808i	0.972380	+	0.233404i	$0.0749865\pi$
$389$			7.30481e26i			0.466808i	−0.972380	+	0.233404i	$0.925014\pi$
$390$		0			0
$391$		−	1.82009e27i		−	1.10214i
$392$		0			0
$393$	−7.56995e24	+	1.39672e27i	−0.00434482	+	0.801655i
$394$		0			0
$395$	7.76279e26			0.422424
$396$		0			0
$397$	9.73510e26			0.502389			0.251194	−	0.967937i	$-0.419177\pi$
$397$	9.73510e26			0.502389			0.251194	+	0.967937i	$0.419177\pi$
$398$		0			0
$399$	−1.83802e25	+	3.39131e27i	−0.00899778	+	1.66017i
$400$		0			0
$401$		−	3.45875e27i		−	1.60658i	−0.595585	−	0.803292i	$-0.703080\pi$
$401$		−	3.45875e27i		−	1.60658i	0.595585	−	0.803292i	$-0.296920\pi$
$402$		0			0
$403$		−	1.23102e27i		−	0.542703i
$404$		0			0
$405$	8.29700e25	−	3.82660e27i	0.0347251	−	1.60153i
$406$		0			0
$407$	3.56213e27			1.41569
$408$		0			0
$409$	4.10563e27			1.54983			0.774917	−	0.632062i	$-0.217791\pi$
$409$	4.10563e27			1.54983			0.774917	+	0.632062i	$0.217791\pi$
$410$		0			0
$411$	−4.44968e27	−	2.41164e25i	−1.59584	−	0.00864915i
$412$		0			0
$413$			8.33555e26i			0.284092i
$414$		0			0
$415$			7.92842e26i			0.256851i
$416$		0			0
$417$	1.02638e27	+	5.56277e24i	0.316139	+	0.00171341i
$418$		0			0
$419$	1.73761e27			0.508986			0.254493	−	0.967075i	$-0.418091\pi$
$419$	1.73761e27			0.508986			0.254493	+	0.967075i	$0.418091\pi$
$420$		0			0
$421$	−4.45539e25			−0.0124144			−0.00620718	−	0.999981i	$-0.501976\pi$
$421$	−4.45539e25			−0.0124144			−0.00620718	+	0.999981i	$0.501976\pi$
$422$		0			0
$423$	1.55348e27	+	1.68396e25i	0.411843	+	0.00446435i
$424$		0			0
$425$			5.08342e27i			1.28254i
$426$		0			0
$427$			1.11747e27i			0.268376i
$428$		0			0
$429$	1.42392e25	−	2.62724e27i	0.00325599	−	0.600757i
$430$		0			0
$431$	9.73857e26			0.212072			0.106036	−	0.994362i	$-0.466184\pi$
$431$	9.73857e26			0.212072			0.106036	+	0.994362i	$0.466184\pi$
$432$		0			0
$433$	5.97484e27			1.23938			0.619689	−	0.784848i	$-0.287259\pi$
$433$	5.97484e27			1.23938			0.619689	+	0.784848i	$0.287259\pi$
$434$		0			0
$435$	−8.14177e25	+	1.50222e28i	−0.0160909	+	2.96891i
$436$		0			0
$437$			1.18573e28i			2.23322i
$438$		0			0
$439$			1.01308e28i			1.81873i	0.416004	+	0.909363i	$0.363430\pi$
$439$			1.01308e28i			1.81873i	−0.416004	+	0.909363i	$0.636570\pi$
$440$		0			0
$441$	5.71856e24	+	6.19888e22i	0.000978771	+	1.06098e-5i
$442$		0			0
$443$	−1.02381e28			−1.67101			−0.835506	−	0.549481i	$-0.814825\pi$
$443$	−1.02381e28			−1.67101			−0.835506	+	0.549481i	$0.814825\pi$
$444$		0			0
$445$	9.61875e27			1.49740
$446$		0			0
$447$	−8.05093e27	−	4.36345e25i	−1.19569	−	0.00648039i
$448$		0			0
$449$		−	1.14766e28i		−	1.62640i	−0.581983	−	0.813201i	$-0.697723\pi$
$449$		−	1.14766e28i		−	1.62640i	0.581983	−	0.813201i	$-0.302277\pi$
$450$		0			0
$451$		−	1.44653e28i		−	1.95647i
$452$		0			0
$453$	−1.47062e28	−	7.97049e25i	−1.89876	−	0.0102909i
$454$		0			0
$455$	6.68016e27			0.823507
$456$		0			0
$457$	5.13327e27			0.604330			0.302165	−	0.953256i	$-0.402291\pi$
$457$	5.13327e27			0.604330			0.302165	+	0.953256i	$0.402291\pi$
$458$		0			0
$459$	7.28159e27	+	1.18404e26i	0.818829	+	0.0133147i
$460$		0			0
$461$		−	4.40154e27i		−	0.472873i	−0.971647	−	0.236437i	$-0.924020\pi$
$461$		−	4.40154e27i		−	0.472873i	0.971647	−	0.236437i	$-0.0759795\pi$
$462$		0			0
$463$		−	9.61110e26i		−	0.0986672i	−0.998782	−	0.0493336i	$-0.984290\pi$
$463$		−	9.61110e26i		−	0.0986672i	0.998782	−	0.0493336i	$-0.0157097\pi$
$464$		0			0
$465$	−9.34578e25	+	1.72437e28i	−0.00916979	+	1.69190i
$466$		0			0
$467$	1.78197e28			1.67138			0.835688	−	0.549205i	$-0.185069\pi$
$467$	1.78197e28			1.67138			0.835688	+	0.549205i	$0.185069\pi$
$468$		0			0
$469$	8.06100e27			0.722893
$470$		0			0
$471$	−3.81054e25	+	7.03076e27i	−0.00326788	+	0.602952i
$472$		0			0
$473$		−	1.17386e28i		−	0.962887i
$474$		0			0
$475$		−	3.31169e28i		−	2.59877i
$476$		0			0
$477$	1.83527e26	−	1.69306e28i	0.0137802	−	1.27125i
$478$		0			0
$479$	−2.22352e28			−1.59778			−0.798892	−	0.601475i	$-0.794580\pi$
$479$	−2.22352e28			−1.59778			−0.798892	+	0.601475i	$0.794580\pi$
$480$		0			0
$481$	9.04526e27			0.622154
$482$		0			0
$483$	2.04473e28	+	1.10821e26i	1.34646	+	0.00729753i
$484$		0			0
$485$		−	1.16606e28i		−	0.735244i
$486$		0			0
$487$		−	2.75178e28i		−	1.66173i	−0.556477	−	0.830863i	$-0.687847\pi$
$487$		−	2.75178e28i		−	1.66173i	0.556477	−	0.830863i	$-0.312153\pi$
$488$		0			0
$489$	−6.99711e27	−	3.79230e25i	−0.404739	−	0.00219361i
$490$		0			0
$491$	−2.32096e28			−1.28621			−0.643106	−	0.765777i	$-0.722354\pi$
$491$	−2.32096e28			−1.28621			−0.643106	+	0.765777i	$0.722354\pi$
$492$		0			0
$493$	−2.85831e28			−1.51781
$494$		0			0
$495$	−3.98915e26	+	3.68005e28i	−0.0203014	+	1.87284i
$496$		0			0
$497$			1.64590e28i			0.802901i
$498$		0			0
$499$		−	1.14869e28i		−	0.537213i	−0.963250	−	0.268607i	$-0.913437\pi$
$499$		−	1.14869e28i		−	0.537213i	0.963250	−	0.268607i	$-0.0865632\pi$
$500$		0			0
$501$	−1.42062e26	+	2.62117e28i	−0.00637064	+	1.17544i
$502$		0			0
$503$	−6.47081e27			−0.278288			−0.139144	−	0.990272i	$-0.544435\pi$
$503$	−6.47081e27			−0.278288			−0.139144	+	0.990272i	$0.544435\pi$
$504$		0			0
$505$	−3.29494e28			−1.35921
$506$		0			0
$507$	−1.00792e26	+	1.85970e28i	−0.00398882	+	0.735970i
$508$		0			0
$509$			3.07298e28i			1.16687i	0.812159	+	0.583437i	$0.198292\pi$
$509$			3.07298e28i			1.16687i	−0.812159	+	0.583437i	$0.801708\pi$
$510$		0			0
$511$		−	2.39213e28i		−	0.871698i
$512$		0			0
$513$	−4.74373e28	−	7.71364e26i	−1.65916	−	0.0269791i
$514$		0			0
$515$	2.01811e28			0.677594
$516$		0			0
$517$	−1.49381e28			−0.481554
$518$		0			0
$519$	9.47438e27	+	5.13493e25i	0.293287	+	0.00158956i
$520$		0			0
$521$		−	2.85510e27i		−	0.0848838i	−0.999099	−	0.0424419i	$-0.986486\pi$
$521$		−	2.85510e27i		−	0.0848838i	0.999099	−	0.0424419i	$-0.0135137\pi$
$522$		0			0
$523$		−	2.26243e28i		−	0.646111i	−0.946380	−	0.323055i	$-0.895290\pi$
$523$		−	2.26243e28i		−	0.646111i	0.946380	−	0.323055i	$-0.104710\pi$
$524$		0			0
$525$	−5.71085e28	−	3.09517e26i	−1.56685	−	0.00849203i
$526$		0			0
$527$	−3.28100e28			−0.864958
$528$		0			0
$529$	3.20202e28			0.811222
$530$		0			0
$531$	−1.16604e28	−	1.26398e26i	−0.283936	−	0.00307785i
$532$		0			0
$533$		−	3.67316e28i		−	0.859812i
$534$		0			0
$535$		−	1.03959e28i		−	0.233963i
$536$		0			0
$537$	3.13242e26	−	5.77957e28i	0.00677875	−	1.25074i
$538$		0			0
$539$	−5.49891e25			−0.00114444
$540$		0			0
$541$	−2.78493e27			−0.0557498			−0.0278749	−	0.999611i	$-0.508874\pi$
$541$	−2.78493e27			−0.0557498			−0.0278749	+	0.999611i	$0.508874\pi$
$542$		0			0
$543$	−4.86350e26	+	8.97357e28i	−0.00936593	+	1.72809i
$544$		0			0
$545$		−	3.70556e27i		−	0.0686579i
$546$		0			0
$547$		−	8.91470e28i		−	1.58942i	−0.606986	−	0.794712i	$-0.707622\pi$
$547$		−	8.91470e28i		−	1.58942i	0.606986	−	0.794712i	$-0.292378\pi$
$548$		0			0
$549$	−1.56320e28	−	1.69450e26i	−0.268229	−	0.00290758i
$550$		0			0
$551$	1.86210e29			3.07547
$552$		0			0
$553$	−1.65935e28			−0.263829
$554$		0			0
$555$	−1.26703e29	−	6.86707e26i	−1.93960	−	0.0105122i
$556$		0			0
$557$			2.71342e27i			0.0399979i	0.999800	+	0.0199990i	$0.00636629\pi$
$557$			2.71342e27i			0.0399979i	−0.999800	+	0.0199990i	$0.993634\pi$
$558$		0			0
$559$		−	2.98077e28i		−	0.423160i
$560$		0			0
$561$	−7.00232e28	−	3.79512e26i	−0.957485	−	0.00518938i
$562$		0			0
$563$	8.45195e28			1.11332			0.556658	−	0.830742i	$-0.312083\pi$
$563$	8.45195e28			1.11332			0.556658	+	0.830742i	$0.312083\pi$
$564$		0			0
$565$	2.05453e29			2.60737
$566$		0			0
$567$	−1.77354e27	+	8.17961e28i	−0.0216879	+	1.00025i
$568$		0			0
$569$			6.37085e28i			0.750790i	0.926865	+	0.375395i	$0.122493\pi$
$569$			6.37085e28i			0.750790i	−0.926865	+	0.375395i	$0.877507\pi$
$570$		0			0
$571$		−	1.18041e29i		−	1.34077i	−0.742013	−	0.670385i	$-0.766129\pi$
$571$		−	1.18041e29i		−	1.34077i	0.742013	−	0.670385i	$-0.233871\pi$
$572$		0			0
$573$	4.04786e24	−	7.46864e26i	4.43202e−5	−	0.00817745i
$574$		0			0
$575$	−1.99673e29			−2.10769
$576$		0			0
$577$	−4.53533e28			−0.461597			−0.230798	−	0.973002i	$-0.574134\pi$
$577$	−4.53533e28			−0.461597			−0.230798	+	0.973002i	$0.574134\pi$
$578$		0			0
$579$	2.64425e26	−	4.87886e28i	0.00259524	−	0.478843i
$580$		0			0
$581$		−	1.69475e28i		−	0.160419i
$582$		0			0
$583$			1.62803e29i			1.48643i
$584$		0			0
$585$	−1.01296e27	+	9.34471e28i	−0.00892187	+	0.823056i
$586$		0			0
$587$	−1.79896e29			−1.52870			−0.764349	−	0.644803i	$-0.776939\pi$
$587$	−1.79896e29			−1.52870			−0.764349	+	0.644803i	$0.776939\pi$
$588$		0			0
$589$	2.13747e29			1.75263
$590$		0			0
$591$	1.17328e29	+	6.35894e26i	0.928394	+	0.00503172i
$592$		0			0
$593$			1.70822e29i			1.30458i	0.757971	+	0.652288i	$0.226191\pi$
$593$			1.70822e29i			1.30458i	−0.757971	+	0.652288i	$0.773809\pi$
$594$		0			0
$595$		−	1.78045e29i		−	1.31250i
$596$		0			0
$597$	2.03480e29	+	1.10282e27i	1.44808	+	0.00784829i
$598$		0			0
$599$	2.10298e29			1.44495			0.722476	−	0.691396i	$-0.243004\pi$
$599$	2.10298e29			1.44495			0.722476	+	0.691396i	$0.243004\pi$
$600$		0			0
$601$	2.42210e29			1.60698			0.803490	−	0.595318i	$-0.202974\pi$
$601$	2.42210e29			1.60698			0.803490	+	0.595318i	$0.202974\pi$
$602$		0			0
$603$	−1.22235e27	+	1.12763e29i	−0.00783182	+	0.722497i
$604$		0			0
$605$		−	9.50081e28i		−	0.587935i
$606$		0			0
$607$			1.05757e29i			0.632161i	0.948732	+	0.316080i	$0.102367\pi$
$607$			1.05757e29i			0.632161i	−0.948732	+	0.316080i	$0.897633\pi$
$608$		0			0
$609$	1.74036e27	−	3.21110e29i	0.0100498	−	1.85427i
$610$		0			0
$611$	−3.79322e28			−0.211629
$612$		0			0
$613$	−1.60853e29			−0.867151			−0.433576	−	0.901117i	$-0.642748\pi$
$613$	−1.60853e29			−0.867151			−0.433576	+	0.901117i	$0.642748\pi$
$614$		0			0
$615$	−2.78862e27	+	5.14524e29i	−0.0145278	+	2.68051i
$616$		0			0
$617$		−	1.47123e29i		−	0.740774i	−0.928878	−	0.370387i	$-0.879225\pi$
$617$		−	1.47123e29i		−	0.740774i	0.928878	−	0.370387i	$-0.120775\pi$
$618$		0			0
$619$			1.25054e29i			0.608618i	0.952573	+	0.304309i	$0.0984255\pi$
$619$			1.25054e29i			0.608618i	−0.952573	+	0.304309i	$0.901574\pi$
$620$		0			0
$621$	−4.65082e27	+	2.86016e29i	−0.0218810	+	1.34564i
$622$		0			0
$623$	−2.05607e29			−0.935219
$624$		0			0
$625$	−2.57871e28			−0.113413
$626$		0			0
$627$	4.56180e29	+	2.47241e27i	1.94011	+	0.0105150i
$628$		0			0
$629$		−	2.41081e29i		−	0.991587i
$630$		0			0
$631$			1.46578e28i			0.0583125i	0.999575	+	0.0291562i	$0.00928203\pi$
$631$			1.46578e28i			0.0583125i	−0.999575	+	0.0291562i	$0.990718\pi$
$632$		0			0
$633$	5.54027e27	+	3.00272e25i	0.0213202	+	0.000115552i
$634$		0			0
$635$	1.70314e29			0.634052
$636$		0			0
$637$	−1.39633e26			−0.000502949
$638$		0			0
$639$	−2.30241e29	−	2.49580e27i	−0.802461	−	0.00869862i
$640$		0			0
$641$		−	2.38597e29i		−	0.804740i	−0.915477	−	0.402370i	$-0.868187\pi$
$641$		−	2.38597e29i		−	0.804740i	0.915477	−	0.402370i	$-0.131813\pi$
$642$		0			0
$643$			1.53371e29i			0.500642i	0.968163	+	0.250321i	$0.0805361\pi$
$643$			1.53371e29i			0.500642i	−0.968163	+	0.250321i	$0.919464\pi$
$644$		0			0
$645$	−2.26297e27	+	4.17538e29i	−0.00714994	+	1.31922i
$646$		0			0
$647$	−3.14797e29			−0.962799			−0.481399	−	0.876501i	$-0.659871\pi$
$647$	−3.14797e29			−0.962799			−0.481399	+	0.876501i	$0.659871\pi$
$648$		0			0
$649$	1.12125e29			0.331997
$650$		0			0
$651$	1.99772e27	−	3.68596e29i	0.00572710	−	1.05670i
$652$		0			0
$653$		−	7.66658e28i		−	0.212820i	−0.994322	−	0.106410i	$-0.966064\pi$
$653$		−	7.66658e28i		−	0.212820i	0.994322	−	0.106410i	$-0.0339357\pi$
$654$		0			0
$655$			4.77711e29i			1.28420i
$656$		0			0
$657$	3.34630e29	+	3.62736e27i	0.871220	+	0.00944397i
$658$		0			0
$659$	−1.20379e29			−0.303567			−0.151783	−	0.988414i	$-0.548502\pi$
$659$	−1.20379e29			−0.303567			−0.151783	+	0.988414i	$0.548502\pi$
$660$		0			0
$661$	4.11592e29			1.00543			0.502715	−	0.864452i	$-0.332335\pi$
$661$	4.11592e29			1.00543			0.502715	+	0.864452i	$0.332335\pi$
$662$		0			0
$663$	−1.77809e29	−	9.63690e26i	−0.420786	−	0.00228058i
$664$		0			0
$665$			1.15991e30i			2.65947i
$666$		0			0
$667$		−	1.12273e30i		−	2.49432i
$668$		0			0
$669$	−7.77510e29	−	4.21396e27i	−1.67391	−	0.00907226i
$670$		0			0
$671$	1.50316e29			0.313630
$672$		0			0
$673$	5.22042e29			1.05572			0.527858	−	0.849332i	$-0.322995\pi$
$673$	5.22042e29			1.05572			0.527858	+	0.849332i	$0.322995\pi$
$674$		0			0
$675$	1.29895e28	−	7.98829e29i	0.0254626	−	1.56590i
$676$		0			0
$677$		−	2.40097e29i		−	0.456252i	−0.973632	−	0.228126i	$-0.926740\pi$
$677$		−	2.40097e29i		−	0.456252i	0.973632	−	0.228126i	$-0.0732599\pi$
$678$		0			0
$679$			2.49252e29i			0.459205i
$680$		0			0
$681$	2.88493e27	−	5.32295e29i	0.00515337	−	0.950840i
$682$		0			0
$683$	3.33314e29			0.577345			0.288673	−	0.957428i	$-0.406786\pi$
$683$	3.33314e29			0.577345			0.288673	+	0.957428i	$0.406786\pi$
$684$		0			0
$685$	−1.52189e30			−2.55643
$686$		0			0
$687$	1.64390e27	−	3.03314e29i	0.00267812	−	0.494136i
$688$		0			0
$689$			4.13404e29i			0.653240i
$690$		0			0
$691$		−	6.70770e29i		−	1.02814i	−0.857747	−	0.514072i	$-0.828136\pi$
$691$		−	6.70770e29i		−	1.02814i	0.857747	−	0.514072i	$-0.171864\pi$
$692$		0			0
$693$	8.52708e27	−	7.86636e29i	0.0126795	−	1.16970i
$694$		0			0
$695$	3.51045e29			0.506433
$696$		0			0
$697$	−9.78996e29			−1.37037
$698$		0			0
$699$	−8.75077e29	−	4.74275e27i	−1.18860	−	0.00644199i
$700$		0			0
$701$		−	7.56695e29i		−	0.997428i	−0.866766	−	0.498714i	$-0.833806\pi$
$701$		−	7.56695e29i		−	0.997428i	0.866766	−	0.498714i	$-0.166194\pi$
$702$		0			0
$703$			1.57057e30i			2.00921i
$704$		0			0
$705$	5.31342e29	+	2.87977e27i	0.659764	+	0.00357579i
$706$		0			0
$707$	7.04315e29			0.848913
$708$		0			0
$709$	−1.09551e30			−1.28183			−0.640913	−	0.767613i	$-0.721444\pi$
$709$	−1.09551e30			−1.28183			−0.640913	+	0.767613i	$0.721444\pi$
$710$		0			0
$711$	2.51619e27	−	2.32122e29i	0.00285833	−	0.263685i
$712$		0			0
$713$		−	1.28876e30i		−	1.42145i
$714$		0			0
$715$		−	8.98579e29i		−	0.962371i
$716$		0			0
$717$	−7.65788e26	+	1.41294e29i	−0.000796448	+	0.146951i
$718$		0			0
$719$	6.65035e29			0.671724			0.335862	−	0.941911i	$-0.390972\pi$
$719$	6.65035e29			0.671724			0.335862	+	0.941911i	$0.390972\pi$
$720$		0			0
$721$	−4.31385e29			−0.423199
$722$		0			0
$723$	5.78003e27	−	1.06646e30i	0.00550780	−	1.01624i
$724$		0			0
$725$			3.13572e30i			2.90261i
$726$		0			0
$727$			1.20051e30i			1.07958i	0.841799	+	0.539791i	$0.181497\pi$
$727$			1.20051e30i			1.07958i	−0.841799	+	0.539791i	$0.818503\pi$
$728$		0			0
$729$	−1.14396e30	−	3.72129e28i	−0.999471	−	0.0325128i
$730$		0			0
$731$	−7.94458e29			−0.674432
$732$		0			0
$733$	−6.89370e28			−0.0568670			−0.0284335	−	0.999596i	$-0.509052\pi$
$733$	−6.89370e28			−0.0568670			−0.0284335	+	0.999596i	$0.509052\pi$
$734$		0			0
$735$	1.95594e27	+	1.06008e25i	0.00156797	+	8.49810e-6i
$736$		0			0
$737$		−	1.08432e30i		−	0.844791i
$738$		0			0
$739$		−	4.29786e29i		−	0.325451i	−0.986671	−	0.162725i	$-0.947972\pi$
$739$		−	4.29786e29i		−	0.325451i	0.986671	−	0.162725i	$-0.0520284\pi$
$740$		0			0
$741$	1.15837e30	+	6.27815e27i	0.852622	+	0.00462105i
$742$		0			0
$743$	7.13498e29			0.510517			0.255259	−	0.966873i	$-0.417839\pi$
$743$	7.13498e29			0.510517			0.255259	+	0.966873i	$0.417839\pi$
$744$		0			0
$745$	−2.75361e30			−1.91541
$746$		0			0
$747$	2.37075e29	+	2.56987e27i	0.160331	+	0.00173798i
$748$		0			0
$749$			2.22219e29i			0.146124i
$750$		0			0
$751$			1.98079e30i			1.26654i	0.773932	+	0.633269i	$0.218287\pi$
$751$			1.98079e30i			1.26654i	−0.773932	+	0.633269i	$0.781713\pi$
$752$		0			0
$753$	−1.52529e28	+	2.81428e30i	−0.00948427	+	1.74993i
$754$		0			0
$755$	−5.02987e30			−3.04168
$756$		0			0
$757$	−1.86845e30			−1.09894			−0.549470	−	0.835513i	$-0.685170\pi$
$757$	−1.86845e30			−1.09894			−0.549470	+	0.835513i	$0.685170\pi$
$758$		0			0
$759$	1.49070e28	−	2.75046e30i	0.00852808	−	1.57350i
$760$		0			0
$761$		−	5.84584e29i		−	0.325318i	−0.986682	−	0.162659i	$-0.947993\pi$
$761$		−	5.84584e29i		−	0.325318i	0.986682	−	0.162659i	$-0.0520070\pi$
$762$		0			0
$763$			7.92087e28i			0.0428811i
$764$		0			0
$765$	2.49062e30	+	2.69982e28i	1.31178	+	0.0142197i
$766$		0			0
$767$	2.84718e29			0.145903
$768$		0			0
$769$	1.70264e30			0.848978			0.424489	−	0.905433i	$-0.360454\pi$
$769$	1.70264e30			0.848978			0.424489	+	0.905433i	$0.360454\pi$
$770$		0			0
$771$	2.18077e29	+	1.18193e27i	0.105813	+	0.000573485i
$772$		0			0
$773$		−	3.89141e30i		−	1.83748i	−0.394864	−	0.918740i	$-0.629208\pi$
$773$		−	3.89141e30i		−	1.83748i	0.394864	−	0.918740i	$-0.370792\pi$
$774$		0			0
$775$			3.59943e30i			1.65412i
$776$		0			0
$777$	2.70836e30	+	1.46788e28i	1.21140	+	0.00656554i
$778$		0			0
$779$	6.37786e30			2.77672
$780$		0			0
$781$	2.21398e30			0.938290
$782$		0			0
$783$	4.49167e30	+	7.30376e28i	1.85314	+	0.0301334i
$784$		0			0
$785$			2.40468e30i			0.965887i
$786$		0			0
$787$			5.77737e29i			0.225941i	0.993598	+	0.112971i	$0.0360366\pi$
$787$			5.77737e29i			0.225941i	−0.993598	+	0.112971i	$0.963963\pi$
$788$		0			0
$789$	1.18963e28	−	2.19497e30i	0.00453007	−	0.835835i
$790$		0			0
$791$	−4.39169e30			−1.62846
$792$		0			0
$793$	3.81695e29			0.137831
$794$		0			0
$795$	3.13852e28	−	5.79084e30i	0.0110375	−	2.03651i
$796$		0			0
$797$			8.69220e29i			0.297726i	0.988858	+	0.148863i	$0.0475614\pi$
$797$			8.69220e29i			0.297726i	−0.988858	+	0.148863i	$0.952439\pi$
$798$		0			0
$799$			1.01100e30i			0.337294i
$800$		0			0
$801$	3.11777e28	−	2.87619e30i	0.0101322	−	0.934707i
$802$		0			0
$803$	−3.21776e30			−1.01869
$804$		0			0
$805$	6.99347e30			2.15693
$806$		0			0
$807$	−1.06763e30	−	5.78634e27i	−0.320810	−	0.00173873i
$808$		0			0
$809$		−	4.64754e30i		−	1.36070i	−0.732886	−	0.680352i	$-0.761827\pi$
$809$		−	4.64754e30i		−	1.36070i	0.732886	−	0.680352i	$-0.238173\pi$
$810$		0			0
$811$			1.41993e29i			0.0405087i	0.999795	+	0.0202543i	$0.00644759\pi$
$811$			1.41993e29i			0.0405087i	−0.999795	+	0.0202543i	$0.993552\pi$
$812$		0			0
$813$	7.78939e28	+	4.22170e26i	0.0216547	+	0.000117364i
$814$		0			0
$815$	−2.39317e30			−0.648365
$816$		0			0
$817$	5.17565e30			1.36657
$818$		0			0
$819$	2.16527e28	−	1.99749e30i	0.00557226	−	0.514049i
$820$		0			0
$821$			5.05400e30i			1.26775i	0.773437	+	0.633873i	$0.218536\pi$
$821$			5.05400e30i			1.26775i	−0.773437	+	0.633873i	$0.781464\pi$
$822$		0			0
$823$			5.61530e30i			1.37301i	0.727124	+	0.686506i	$0.240857\pi$
$823$			5.61530e30i			1.37301i	−0.727124	+	0.686506i	$0.759143\pi$
$824$		0			0
$825$	−4.16345e28	+	7.68192e30i	−0.00992401	+	1.83106i
$826$		0			0
$827$	5.24661e30			1.21919			0.609594	−	0.792713i	$-0.291332\pi$
$827$	5.24661e30			1.21919			0.609594	+	0.792713i	$0.291332\pi$
$828$		0			0
$829$	−2.89648e30			−0.656218			−0.328109	−	0.944640i	$-0.606411\pi$
$829$	−2.89648e30			−0.656218			−0.328109	+	0.944640i	$0.606411\pi$
$830$		0			0
$831$	−2.55595e28	+	4.71595e30i	−0.00564602	+	1.04174i
$832$		0			0
$833$			3.72160e27i			0.000801599i
$834$		0			0
$835$			8.96502e30i			1.88297i
$836$		0			0
$837$	5.15590e30	+	8.38385e28i	1.05606	+	0.0171722i
$838$		0			0
$839$	−1.42250e30			−0.284152			−0.142076	−	0.989856i	$-0.545378\pi$
$839$	−1.42250e30			−0.284152			−0.142076	+	0.989856i	$0.545378\pi$
$840$		0			0
$841$	−1.24987e31			−2.43505
$842$		0			0
$843$	−1.99341e30	−	1.08039e28i	−0.378797	−	0.00205301i
$844$		0			0
$845$			6.36062e30i			1.17897i
$846$		0			0
$847$			2.03086e30i			0.367201i
$848$		0			0
$849$	7.17035e30	+	3.88619e28i	1.26476	+	0.00685478i
$850$		0			0
$851$	9.46949e30			1.62954
$852$		0			0
$853$	3.82137e30			0.641584			0.320792	−	0.947150i	$-0.396051\pi$
$853$	3.82137e30			0.641584			0.320792	+	0.947150i	$0.396051\pi$
$854$		0			0
$855$	−1.62256e31	−	1.75885e29i	−2.65801	−	0.0288127i
$856$		0			0
$857$		−	3.34205e30i		−	0.534212i	−0.963667	−	0.267106i	$-0.913933\pi$
$857$		−	3.34205e30i		−	0.534212i	0.963667	−	0.267106i	$-0.0860674\pi$
$858$		0			0
$859$			6.89441e30i			1.07540i	0.843137	+	0.537699i	$0.180706\pi$
$859$			6.89441e30i			1.07540i	−0.843137	+	0.537699i	$0.819294\pi$
$860$		0			0
$861$	5.96086e28	−	1.09983e31i	0.00907353	−	1.67414i
$862$		0			0
$863$	5.61828e30			0.834623			0.417311	−	0.908764i	$-0.362972\pi$
$863$	5.61828e30			0.834623			0.417311	+	0.908764i	$0.362972\pi$
$864$		0			0
$865$	3.24046e30			0.469826
$866$		0			0
$867$	1.26132e28	−	2.32724e30i	0.00178494	−	0.329337i
$868$		0			0
$869$			2.23206e30i			0.308318i
$870$		0			0
$871$		−	2.75340e30i		−	0.371261i
$872$		0			0
$873$	−3.48673e30	−	3.77959e28i	−0.458954	−	0.00497503i
$874$		0			0
$875$	−7.06048e30			−0.907297
$876$		0			0
$877$	−1.20149e31			−1.50738			−0.753692	−	0.657228i	$-0.771729\pi$
$877$	−1.20149e31			−1.50738			−0.753692	+	0.657228i	$0.771729\pi$
$878$		0			0
$879$	7.28015e30	+	3.94570e28i	0.891778	+	0.00483327i
$880$		0			0
$881$		−	1.08367e31i		−	1.29614i	−0.761582	−	0.648068i	$-0.775577\pi$
$881$		−	1.08367e31i		−	1.29614i	0.761582	−	0.648068i	$-0.224423\pi$
$882$		0			0
$883$		−	1.45236e31i		−	1.69624i	−0.529804	−	0.848120i	$-0.677734\pi$
$883$		−	1.45236e31i		−	1.69624i	0.529804	−	0.848120i	$-0.322266\pi$
$884$		0			0
$885$	−3.98824e30	−	2.16155e28i	−0.454860	−	0.00246525i
$886$		0			0
$887$	1.62800e31			1.81324			0.906621	−	0.421946i	$-0.138653\pi$
$887$	1.62800e31			1.81324			0.906621	+	0.421946i	$0.138653\pi$
$888$		0			0
$889$	−3.64056e30			−0.396004
$890$		0			0
$891$	1.10028e31	+	2.38566e29i	1.16892	+	0.0253451i
$892$		0			0
$893$		−	6.58632e30i		−	0.683444i
$894$		0			0
$895$		−	1.97675e31i		−	2.00359i
$896$		0			0
$897$	3.78531e28	−	6.98421e30i	0.00374784	−	0.691507i
$898$		0			0
$899$	−2.02389e31			−1.95754
$900$		0			0
$901$	1.10183e31			1.04113
$902$		0			0
$903$	4.83726e28	−	8.92514e30i	0.00446558	−	0.823937i
$904$		0			0
$905$			3.06917e31i			2.76829i
$906$		0			0
$907$			1.81303e30i			0.159782i	0.996804	+	0.0798911i	$0.0254573\pi$
$907$			1.81303e30i			0.159782i	−0.996804	+	0.0798911i	$0.974543\pi$
$908$		0			0
$909$	−1.06800e29	+	9.85249e30i	−0.00919712	+	0.848448i
$910$		0			0
$911$	−4.11199e30			−0.346026			−0.173013	−	0.984920i	$-0.555350\pi$
$911$	−4.11199e30			−0.346026			−0.173013	+	0.984920i	$0.555350\pi$
$912$		0			0
$913$	−2.27969e30			−0.187470
$914$		0			0
$915$	−5.34667e30	−	2.89779e28i	−0.429696	−	0.00232887i
$916$		0			0
$917$		−	1.02114e31i		−	0.802059i
$918$		0			0
$919$			4.28325e30i			0.328822i	0.986392	+	0.164411i	$0.0525723\pi$
$919$			4.28325e30i			0.328822i	−0.986392	+	0.164411i	$0.947428\pi$
$920$		0			0
$921$	−1.92429e31	−	1.04293e29i	−1.44392	−	0.00782578i
$922$		0			0
$923$	5.62192e30			0.412351
$924$		0			0
$925$	−2.64478e31			−1.89628
$926$		0			0
$927$	6.54140e28	−	6.03454e30i	0.00458494	−	0.422967i
$928$		0			0
$929$		−	1.09229e31i		−	0.748465i	−0.927335	−	0.374233i	$-0.877906\pi$
$929$		−	1.09229e31i		−	0.748465i	0.927335	−	0.374233i	$-0.122094\pi$
$930$		0			0
$931$		−	2.42451e28i		−	0.00162425i
$932$		0			0
$933$	−3.02472e28	+	5.58085e30i	−0.00198120	+	0.365547i
$934$		0			0
$935$	−2.39496e31			−1.53382
$936$		0			0
$937$	1.24009e31			0.776582			0.388291	−	0.921537i	$-0.373066\pi$
$937$	1.24009e31			0.776582			0.388291	+	0.921537i	$0.373066\pi$
$938$		0			0
$939$	−1.12375e29	+	2.07342e31i	−0.00688148	+	1.26969i
$940$		0			0
$941$			1.62316e31i			0.972009i	0.873956	+	0.486005i	$0.161546\pi$
$941$			1.62316e31i			0.972009i	−0.873956	+	0.486005i	$0.838454\pi$
$942$		0			0
$943$		−	3.84543e31i		−	2.25202i
$944$		0			0
$945$	−4.54952e29	+	2.79786e31i	−0.0260574	+	1.60248i
$946$		0			0
$947$	−1.64041e31			−0.918920			−0.459460	−	0.888199i	$-0.651957\pi$
$947$	−1.64041e31			−0.918920			−0.459460	+	0.888199i	$0.651957\pi$
$948$		0			0
$949$	−8.17083e30			−0.447683
$950$		0			0
$951$	2.94104e31	+	1.59399e29i	1.57618	+	0.00854258i
$952$		0			0
$953$		−	2.29653e31i		−	1.20392i	−0.798527	−	0.601959i	$-0.794387\pi$
$953$		−	2.29653e31i		−	1.20392i	0.798527	−	0.601959i	$-0.205613\pi$
$954$		0			0
$955$		−	2.55445e29i		−	0.0130997i
$956$		0			0
$957$	−4.31940e31	−	2.34103e29i	−2.16694	−	0.0117444i
$958$		0			0
$959$	3.25315e31			1.59665
$960$		0			0
$961$	−2.40640e30			−0.115550
$962$		0			0
$963$	−3.10857e30	−	3.36967e28i	−0.146044	−	0.00158311i
$964$		0			0
$965$		−	1.66868e31i		−	0.767074i
$966$		0			0
$967$		−	1.07315e31i		−	0.482708i	−0.970437	−	0.241354i	$-0.922409\pi$
$967$		−	1.07315e31i		−	0.482708i	0.970437	−	0.241354i	$-0.0775915\pi$
$968$		0			0
$969$	1.67330e29	−	3.08737e31i	0.00736501	−	1.35891i
$970$		0			0
$971$	−1.35451e31			−0.583419			−0.291709	−	0.956507i	$-0.594224\pi$
$971$	−1.35451e31			−0.583419			−0.291709	+	0.956507i	$0.594224\pi$
$972$		0			0
$973$	−7.50381e30			−0.316298
$974$		0			0
$975$	−1.05722e29	+	1.95066e31i	−0.00436131	+	0.804698i
$976$		0			0
$977$			4.05742e30i			0.163816i	0.996640	+	0.0819082i	$0.0261014\pi$
$977$			4.05742e30i			0.163816i	−0.996640	+	0.0819082i	$0.973899\pi$
$978$		0			0
$979$			2.76571e31i			1.09292i
$980$		0			0
$981$	−1.10803e30	−	1.20110e28i	−0.0428576	−	0.000464573i
$982$		0			0
$983$	8.95860e29			0.0339178			0.0169589	−	0.999856i	$-0.494602\pi$
$983$	8.95860e29			0.0339178			0.0169589	+	0.999856i	$0.494602\pi$
$984$		0			0
$985$	4.01288e31			1.48722
$986$		0			0
$987$	−1.13578e31	−	6.15570e28i	−0.412063	−	0.00223330i
$988$		0			0
$989$		−	3.12057e31i		−	1.10834i
$990$		0			0
$991$			1.88992e31i			0.657157i	0.944477	+	0.328579i	$0.106570\pi$
$991$			1.88992e31i			0.657157i	−0.944477	+	0.328579i	$0.893430\pi$
$992$		0			0
$993$	1.42608e31	+	7.72909e28i	0.485487	+	0.00263124i
$994$		0			0
$995$	6.95949e31			2.31972
$996$		0			0
$997$	7.83412e30			0.255677			0.127838	−	0.991795i	$-0.459196\pi$
$997$	7.83412e30			0.255677			0.127838	+	0.991795i	$0.459196\pi$
$998$		0			0
$999$	−6.16027e29	+	3.78844e31i	−0.0196862	+	1.21066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.22.c.c.47.15	yes	28
3.2	odd	2	inner	48.22.c.c.47.13	✓	28
4.3	odd	2	inner	48.22.c.c.47.14	yes	28
12.11	even	2	inner	48.22.c.c.47.16	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.22.c.c.47.13	✓	28	3.2	odd	2	inner
48.22.c.c.47.14	yes	28	4.3	odd	2	inner
48.22.c.c.47.15	yes	28	1.1	even	1	trivial
48.22.c.c.47.16	yes	28	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(554.307 - 102274. i) q^{3} -3.49802e7i q^{5} +7.47725e8i q^{7} +(-1.04597e10 - 1.13383e8i) q^{9} +O(q^{10})\)	\(q+(554.307 - 102274. i) q^{3} -3.49802e7i q^{5} +7.47725e8i q^{7} +(-1.04597e10 - 1.13383e8i) q^{9} +1.00580e11 q^{11} +2.55401e11 q^{13} +(-3.57758e12 - 1.93898e10i) q^{15} -6.80713e12i q^{17} +4.43464e13i q^{19} +(7.64731e13 + 4.14469e11i) q^{21} +2.67379e14 q^{23} -7.46779e14 q^{25} +(-1.73941e13 + 1.06970e15i) q^{27} -4.19900e15i q^{29} -4.81995e15i q^{31} +(5.57521e13 - 1.02867e16i) q^{33} +2.61556e16 q^{35} +3.54159e16 q^{37} +(1.41571e14 - 2.61210e16i) q^{39} -1.43819e17i q^{41} -1.16710e17i q^{43} +(-3.96616e15 + 3.65884e17i) q^{45} -1.48520e17 q^{47} -5.46721e14 q^{49} +(-6.96195e17 - 3.77324e15i) q^{51} +1.61865e18i q^{53} -3.51830e18i q^{55} +(4.53550e18 + 2.45815e16i) q^{57} +1.11479e18 q^{59} +1.49449e18 q^{61} +(8.47792e16 - 7.82101e18i) q^{63} -8.93398e18i q^{65} -1.07807e19i q^{67} +(1.48210e17 - 2.73461e19i) q^{69} +2.20121e19 q^{71} -3.19922e19 q^{73} +(-4.13945e17 + 7.63763e19i) q^{75} +7.52060e19i q^{77} +2.21919e19i q^{79} +(1.09393e20 + 2.37191e18i) q^{81} -2.26654e19 q^{83} -2.38115e20 q^{85} +(-4.29450e20 - 2.32753e18i) q^{87} +2.74977e20i q^{89} +1.90970e20i q^{91} +(-4.92957e20 - 2.67173e18i) q^{93} +1.55125e21 q^{95} +3.33348e20 q^{97} +(-1.05204e21 - 1.14040e19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 109254828 q^{9}+O(q^{10}) \) 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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