LMFDB - Embedded newform 48.22.c.c.47.19

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			47.19
Character	$\chi$	$=$	48.47
Dual form			48.22.c.c.47.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(51369.6 - 88439.3i) q^{3} +1.40544e6i q^{5} -5.11154e8i q^{7} +(-5.18267e9 - 9.08619e9i) q^{9} +O(q^{10})$	\(q+(51369.6 - 88439.3i) q^{3} +1.40544e6i q^{5} -5.11154e8i q^{7} +(-5.18267e9 - 9.08619e9i) q^{9} -1.07539e11 q^{11} +8.24942e11 q^{13} +(1.24296e11 + 7.21969e10i) q^{15} +1.34839e13i q^{17} +2.46747e13i q^{19} +(-4.52061e13 - 2.62578e13i) q^{21} +3.24677e14 q^{23} +4.74862e14 q^{25} +(-1.06981e15 - 8.40249e12i) q^{27} -3.04404e15i q^{29} +3.02120e15i q^{31} +(-5.52426e15 + 9.51072e15i) q^{33} +7.18396e14 q^{35} +1.03866e16 q^{37} +(4.23770e16 - 7.29573e16i) q^{39} -6.41368e16i q^{41} +2.36304e17i q^{43} +(1.27701e16 - 7.28393e15i) q^{45} +3.36773e16 q^{47} +2.97268e17 q^{49} +(1.19251e18 + 6.92665e17i) q^{51} -1.87274e18i q^{53} -1.51140e17i q^{55} +(2.18221e18 + 1.26753e18i) q^{57} +6.89692e18 q^{59} -3.93317e18 q^{61} +(-4.64444e18 + 2.64914e18i) q^{63} +1.15941e18i q^{65} +9.06671e18i q^{67} +(1.66785e19 - 2.87142e19i) q^{69} +2.00652e18 q^{71} -7.17450e18 q^{73} +(2.43935e19 - 4.19965e19i) q^{75} +5.49692e19i q^{77} +4.19951e19i q^{79} +(-5.56988e19 + 9.41815e19i) q^{81} -1.64190e20 q^{83} -1.89508e19 q^{85} +(-2.69213e20 - 1.56371e20i) q^{87} -1.53189e20i q^{89} -4.21672e20i q^{91} +(2.67193e20 + 1.55198e20i) q^{93} -3.46788e19 q^{95} -4.21220e20 q^{97} +(5.57342e20 + 9.77124e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	51369.6	−	88439.3i	0.502266	−	0.864713i
$3$	51369.6	−	88439.3i	0.502266	−	0.864713i
$4$		0			0
$5$			1.40544e6i			0.0643616i	0.999482	+	0.0321808i	$0.0102452\pi$
$5$			1.40544e6i			0.0643616i	−0.999482	+	0.0321808i	$0.989755\pi$
$6$		0			0
$7$		−	5.11154e8i		−	0.683947i	−0.939710	−	0.341973i	$-0.888905\pi$
$7$		−	5.11154e8i		−	0.683947i	0.939710	−	0.341973i	$-0.111095\pi$
$8$		0			0
$9$	−5.18267e9	−	9.08619e9i	−0.495459	−	0.868632i
$10$		0			0
$11$	−1.07539e11			−1.25010			−0.625050	−	0.780585i	$-0.714921\pi$
$11$	−1.07539e11			−1.25010			−0.625050	+	0.780585i	$0.714921\pi$
$12$		0			0
$13$	8.24942e11			1.65966			0.829828	−	0.558019i	$-0.188439\pi$
$13$	8.24942e11			1.65966			0.829828	+	0.558019i	$0.188439\pi$
$14$		0			0
$15$	1.24296e11	+	7.21969e10i	0.0556544	+	0.0323266i
$16$		0			0
$17$			1.34839e13i			1.62219i	0.584911	+	0.811097i	$0.301129\pi$
$17$			1.34839e13i			1.62219i	−0.584911	+	0.811097i	$0.698871\pi$
$18$		0			0
$19$			2.46747e13i			0.923292i	0.887064	+	0.461646i	$0.152741\pi$
$19$			2.46747e13i			0.923292i	−0.887064	+	0.461646i	$0.847259\pi$
$20$		0			0
$21$	−4.52061e13	−	2.62578e13i	−0.591418	−	0.343523i
$22$		0			0
$23$	3.24677e14			1.63421			0.817106	−	0.576487i	$-0.195577\pi$
$23$	3.24677e14			1.63421			0.817106	+	0.576487i	$0.195577\pi$
$24$		0			0
$25$	4.74862e14			0.995858
$26$		0			0
$27$	−1.06981e15	−	8.40249e12i	−0.999969	−	0.00785396i
$28$		0			0
$29$		−	3.04404e15i		−	1.34361i	−0.740730	−	0.671803i	$-0.765520\pi$
$29$		−	3.04404e15i		−	1.34361i	0.740730	−	0.671803i	$-0.234480\pi$
$30$		0			0
$31$			3.02120e15i			0.662037i	0.943624	+	0.331018i	$0.107392\pi$
$31$			3.02120e15i			0.662037i	−0.943624	+	0.331018i	$0.892608\pi$
$32$		0			0
$33$	−5.52426e15	+	9.51072e15i	−0.627882	+	1.08098i
$34$		0			0
$35$	7.18396e14			0.0440199
$36$		0			0
$37$	1.03866e16			0.355105			0.177552	−	0.984111i	$-0.443182\pi$
$37$	1.03866e16			0.355105			0.177552	+	0.984111i	$0.443182\pi$
$38$		0			0
$39$	4.23770e16	−	7.29573e16i	0.833588	−	1.43513i
$40$		0			0
$41$		−	6.41368e16i		−	0.746237i	−0.927784	−	0.373119i	$-0.878288\pi$
$41$		−	6.41368e16i		−	0.746237i	0.927784	−	0.373119i	$-0.121712\pi$
$42$		0			0
$43$			2.36304e17i			1.66744i	0.552184	+	0.833722i	$0.313795\pi$
$43$			2.36304e17i			1.66744i	−0.552184	+	0.833722i	$0.686205\pi$
$44$		0			0
$45$	1.27701e16	−	7.28393e15i	0.0559065	−	0.0318885i
$46$		0			0
$47$	3.36773e16			0.0933921			0.0466961	−	0.998909i	$-0.485131\pi$
$47$	3.36773e16			0.0933921			0.0466961	+	0.998909i	$0.485131\pi$
$48$		0			0
$49$	2.97268e17			0.532217
$50$		0			0
$51$	1.19251e18	+	6.92665e17i	1.40273	+	0.814772i
$52$		0			0
$53$		−	1.87274e18i		−	1.47089i	−0.677585	−	0.735444i	$-0.736973\pi$
$53$		−	1.87274e18i		−	1.47089i	0.677585	−	0.735444i	$-0.263027\pi$
$54$		0			0
$55$		−	1.51140e17i		−	0.0804584i
$56$		0			0
$57$	2.18221e18	+	1.26753e18i	0.798383	+	0.463738i
$58$		0			0
$59$	6.89692e18			1.75675			0.878373	−	0.477976i	$-0.158629\pi$
$59$	6.89692e18			1.75675			0.878373	+	0.477976i	$0.158629\pi$
$60$		0			0
$61$	−3.93317e18			−0.705958			−0.352979	−	0.935631i	$-0.614831\pi$
$61$	−3.93317e18			−0.705958			−0.352979	+	0.935631i	$0.614831\pi$
$62$		0			0
$63$	−4.64444e18	+	2.64914e18i	−0.594098	+	0.338867i
$64$		0			0
$65$			1.15941e18i			0.106818i
$66$		0			0
$67$			9.06671e18i			0.607665i	0.952725	+	0.303833i	$0.0982664\pi$
$67$			9.06671e18i			0.607665i	−0.952725	+	0.303833i	$0.901734\pi$
$68$		0			0
$69$	1.66785e19	−	2.87142e19i	0.820809	−	1.41313i
$70$		0			0
$71$	2.00652e18			0.0731529			0.0365765	−	0.999331i	$-0.488355\pi$
$71$	2.00652e18			0.0731529			0.0365765	+	0.999331i	$0.488355\pi$
$72$		0			0
$73$	−7.17450e18			−0.195390			−0.0976949	−	0.995216i	$-0.531147\pi$
$73$	−7.17450e18			−0.195390			−0.0976949	+	0.995216i	$0.531147\pi$
$74$		0			0
$75$	2.43935e19	−	4.19965e19i	0.500185	−	0.861131i
$76$		0			0
$77$			5.49692e19i			0.855002i
$78$		0			0
$79$			4.19951e19i			0.499016i	0.968373	+	0.249508i	$0.0802689\pi$
$79$			4.19951e19i			0.499016i	−0.968373	+	0.249508i	$0.919731\pi$
$80$		0			0
$81$	−5.56988e19	+	9.41815e19i	−0.509041	+	0.860742i
$82$		0			0
$83$	−1.64190e20			−1.16152			−0.580759	−	0.814076i	$-0.697244\pi$
$83$	−1.64190e20			−1.16152			−0.580759	+	0.814076i	$0.697244\pi$
$84$		0			0
$85$	−1.89508e19			−0.104407
$86$		0			0
$87$	−2.69213e20	−	1.56371e20i	−1.16183	−	0.674847i
$88$		0			0
$89$		−	1.53189e20i		−	0.520754i	−0.965507	−	0.260377i	$-0.916153\pi$
$89$		−	1.53189e20i		−	0.520754i	0.965507	−	0.260377i	$-0.0838469\pi$
$90$		0			0
$91$		−	4.21672e20i		−	1.13512i
$92$		0			0
$93$	2.67193e20	+	1.55198e20i	0.572472	+	0.332518i
$94$		0			0
$95$	−3.46788e19			−0.0594246
$96$		0			0
$97$	−4.21220e20			−0.579970			−0.289985	−	0.957031i	$-0.593650\pi$
$97$	−4.21220e20			−0.579970			−0.289985	+	0.957031i	$0.593650\pi$
$98$		0			0
$99$	5.57342e20	+	9.77124e20i	0.619373	+	1.08588i
$100$		0			0
$101$		−	1.79215e20i		−	0.161436i	−0.996737	−	0.0807180i	$-0.974279\pi$
$101$		−	1.79215e20i		−	0.161436i	0.996737	−	0.0807180i	$-0.0257213\pi$
$102$		0			0
$103$		−	5.07440e18i		−	0.00372044i	−0.999998	−	0.00186022i	$-0.999408\pi$
$103$		−	5.07440e18i		−	0.00372044i	0.999998	−	0.00186022i	$-0.000592126\pi$
$104$		0			0
$105$	3.69037e19	−	6.35344e19i	0.0221097	−	0.0380646i
$106$		0			0
$107$	1.80340e20			0.0886260			0.0443130	−	0.999018i	$-0.485890\pi$
$107$	1.80340e20			0.0886260			0.0443130	+	0.999018i	$0.485890\pi$
$108$		0			0
$109$	4.48595e21			1.81500			0.907498	−	0.420056i	$-0.137990\pi$
$109$	4.48595e21			1.81500			0.907498	+	0.420056i	$0.137990\pi$
$110$		0			0
$111$	5.33557e20	−	9.18586e20i	0.178357	−	0.307064i
$112$		0			0
$113$		−	1.75746e21i		−	0.487036i	−0.969896	−	0.243518i	$-0.921698\pi$
$113$		−	1.75746e21i		−	0.487036i	0.969896	−	0.243518i	$-0.0783016\pi$
$114$		0			0
$115$			4.56313e20i			0.105181i
$116$		0			0
$117$	−4.27540e21	−	7.49558e21i	−0.822291	−	1.44163i
$118$		0			0
$119$	6.89236e21			1.10949
$120$		0			0
$121$	4.16449e21			0.562749
$122$		0			0
$123$	−5.67222e21	−	3.29469e21i	−0.645282	−	0.374809i
$124$		0			0
$125$			1.33756e21i			0.128457i
$126$		0			0
$127$		−	3.97991e20i		−	0.0323545i	−0.999869	−	0.0161772i	$-0.994850\pi$
$127$		−	3.97991e20i		−	0.0323545i	0.999869	−	0.0161772i	$-0.00514960\pi$
$128$		0			0
$129$	2.08985e22	+	1.21388e22i	1.44186	+	0.837500i
$130$		0			0
$131$	−1.15770e22			−0.679592			−0.339796	−	0.940499i	$-0.610358\pi$
$131$	−1.15770e22			−0.679592			−0.339796	+	0.940499i	$0.610358\pi$
$132$		0			0
$133$	1.26126e22			0.631482
$134$		0			0
$135$	1.18092e19	−	1.50355e21i	0.000505493	−	0.0643596i
$136$		0			0
$137$		−	3.96087e22i		−	1.45286i	−0.687239	−	0.726432i	$-0.741177\pi$
$137$		−	3.96087e22i		−	1.45286i	0.687239	−	0.726432i	$-0.258823\pi$
$138$		0			0
$139$		−	4.61332e22i		−	1.45331i	−0.687002	−	0.726656i	$-0.741074\pi$
$139$		−	4.61332e22i		−	1.45331i	0.687002	−	0.726656i	$-0.258926\pi$
$140$		0			0
$141$	1.72999e21	−	2.97840e21i	0.0469076	−	0.0807574i
$142$		0			0
$143$	−8.87138e22			−2.07474
$144$		0			0
$145$	4.27822e21			0.0864766
$146$		0			0
$147$	1.52705e22	−	2.62901e22i	0.267314	−	0.460215i
$148$		0			0
$149$			3.11120e22i			0.472576i	0.971683	+	0.236288i	$0.0759309\pi$
$149$			3.11120e22i			0.472576i	−0.971683	+	0.236288i	$0.924069\pi$
$150$		0			0
$151$		−	8.07765e22i		−	1.06666i	−0.845906	−	0.533331i	$-0.820940\pi$
$151$		−	8.07765e22i		−	1.06666i	0.845906	−	0.533331i	$-0.179060\pi$
$152$		0			0
$153$	1.22518e23	−	6.98828e22i	1.40909	−	0.803730i
$154$		0			0
$155$	−4.24612e21			−0.0426098
$156$		0			0
$157$	1.92795e23			1.69102			0.845512	−	0.533956i	$-0.179295\pi$
$157$	1.92795e23			1.69102			0.845512	+	0.533956i	$0.179295\pi$
$158$		0			0
$159$	−1.65623e23	−	9.62018e22i	−1.27190	−	0.738777i
$160$		0			0
$161$		−	1.65960e23i		−	1.11771i
$162$		0			0
$163$			1.21106e23i			0.716468i	0.933632	+	0.358234i	$0.116621\pi$
$163$			1.21106e23i			0.716468i	−0.933632	+	0.358234i	$0.883379\pi$
$164$		0			0
$165$	−1.33667e22	−	7.76402e21i	−0.0695735	−	0.0404115i
$166$		0			0
$167$	3.42675e23			1.57166			0.785831	−	0.618442i	$-0.212236\pi$
$167$	3.42675e23			1.57166			0.785831	+	0.618442i	$0.212236\pi$
$168$		0			0
$169$	4.33464e23			1.75446
$170$		0			0
$171$	2.24199e23	−	1.27881e23i	0.802000	−	0.457453i
$172$		0			0
$173$		−	4.16980e23i		−	1.32018i	−0.751189	−	0.660088i	$-0.770519\pi$
$173$		−	4.16980e23i		−	1.32018i	0.751189	−	0.660088i	$-0.229481\pi$
$174$		0			0
$175$		−	2.42728e23i		−	0.681114i
$176$		0			0
$177$	3.54292e23	−	6.09959e23i	0.882353	−	1.51908i
$178$		0			0
$179$	−7.93089e23			−1.75536			−0.877678	−	0.479251i	$-0.840908\pi$
$179$	−7.93089e23			−1.75536			−0.877678	+	0.479251i	$0.840908\pi$
$180$		0			0
$181$	7.25735e23			1.42940			0.714699	−	0.699432i	$-0.246564\pi$
$181$	7.25735e23			1.42940			0.714699	+	0.699432i	$0.246564\pi$
$182$		0			0
$183$	−2.02045e23	+	3.47847e23i	−0.354579	+	0.610452i
$184$		0			0
$185$			1.45978e22i			0.0228551i
$186$		0			0
$187$		−	1.45005e24i		−	2.02790i
$188$		0			0
$189$	−4.29497e21	+	5.46837e23i	−0.00537169	+	0.683926i
$190$		0			0
$191$	7.66933e22			0.0858830			0.0429415	−	0.999078i	$-0.486327\pi$
$191$	7.66933e22			0.0858830			0.0429415	+	0.999078i	$0.486327\pi$
$192$		0			0
$193$	4.19198e23			0.420792			0.210396	−	0.977616i	$-0.432525\pi$
$193$	4.19198e23			0.420792			0.210396	+	0.977616i	$0.432525\pi$
$194$		0			0
$195$	1.02537e23	+	5.95582e22i	0.0923671	+	0.0536511i
$196$		0			0
$197$		−	6.59544e23i		−	0.533763i	−0.963729	−	0.266881i	$-0.914007\pi$
$197$		−	6.59544e23i		−	0.533763i	0.963729	−	0.266881i	$-0.0859932\pi$
$198$		0			0
$199$		−	9.16277e22i		−	0.0666913i	−0.999444	−	0.0333457i	$-0.989384\pi$
$199$		−	9.16277e22i		−	0.0666913i	0.999444	−	0.0333457i	$-0.0106162\pi$
$200$		0			0
$201$	8.01854e23	+	4.65754e23i	0.525456	+	0.305209i
$202$		0			0
$203$	−1.55597e24			−0.918954
$204$		0			0
$205$	9.01404e22			0.0480291
$206$		0			0
$207$	−1.68269e24	−	2.95007e24i	−0.809685	−	1.41953i
$208$		0			0
$209$		−	2.65350e24i		−	1.15421i
$210$		0			0
$211$			1.59546e24i			0.627943i	0.949432	+	0.313972i	$0.101660\pi$
$211$			1.59546e24i			0.627943i	−0.949432	+	0.313972i	$0.898340\pi$
$212$		0			0
$213$	1.03074e23	−	1.77456e23i	0.0367422	−	0.0632563i
$214$		0			0
$215$	−3.32110e23			−0.107319
$216$		0			0
$217$	1.54430e24			0.452798
$218$		0			0
$219$	−3.68552e23	+	6.34508e23i	−0.0981375	+	0.168956i
$220$		0			0
$221$			1.11235e25i			2.69228i
$222$		0			0
$223$			1.10716e24i			0.243786i	0.992543	+	0.121893i	$0.0388964\pi$
$223$			1.10716e24i			0.243786i	−0.992543	+	0.121893i	$0.961104\pi$
$224$		0			0
$225$	−2.46105e24	−	4.31469e24i	−0.493406	−	0.865033i
$226$		0			0
$227$	7.41440e24			1.35458			0.677289	−	0.735717i	$-0.263154\pi$
$227$	7.41440e24			1.35458			0.677289	+	0.735717i	$0.263154\pi$
$228$		0			0
$229$	−1.06094e25			−1.76775			−0.883874	−	0.467726i	$-0.845074\pi$
$229$	−1.06094e25			−1.76775			−0.883874	+	0.467726i	$0.845074\pi$
$230$		0			0
$231$	4.86144e24	+	2.82375e24i	0.739331	+	0.429438i
$232$		0			0
$233$		−	8.75310e24i		−	1.21598i	−0.793946	−	0.607988i	$-0.791977\pi$
$233$		−	8.75310e24i		−	1.21598i	0.793946	−	0.607988i	$-0.208023\pi$
$234$		0			0
$235$			4.73314e22i			0.00601087i
$236$		0			0
$237$	3.71402e24	+	2.15727e24i	0.431506	+	0.250639i
$238$		0			0
$239$	−1.84314e23			−0.0196056			−0.00980282	−	0.999952i	$-0.503120\pi$
$239$	−1.84314e23			−0.0196056			−0.00980282	+	0.999952i	$0.503120\pi$
$240$		0			0
$241$	5.21170e24			0.507926			0.253963	−	0.967214i	$-0.418266\pi$
$241$	5.21170e24			0.507926			0.253963	+	0.967214i	$0.418266\pi$
$242$		0			0
$243$	5.46812e24	+	9.76404e24i	0.488621	+	0.872496i
$244$		0			0
$245$			4.17791e23i			0.0342543i
$246$		0			0
$247$			2.03552e25i			1.53235i
$248$		0			0
$249$	−8.43437e24	+	1.45208e25i	−0.583391	+	1.00438i
$250$		0			0
$251$	4.76033e24			0.302735			0.151368	−	0.988478i	$-0.451632\pi$
$251$	4.76033e24			0.302735			0.151368	+	0.988478i	$0.451632\pi$
$252$		0			0
$253$	−3.49155e25			−2.04293
$254$		0			0
$255$	−9.73498e23	+	1.67600e24i	−0.0524401	+	0.0902822i
$256$		0			0
$257$			9.25622e24i			0.459342i	0.973268	+	0.229671i	$0.0737650\pi$
$257$			9.25622e24i			0.459342i	−0.973268	+	0.229671i	$0.926235\pi$
$258$		0			0
$259$		−	5.30916e24i		−	0.242873i
$260$		0			0
$261$	−2.76588e25	+	1.57763e25i	−1.16710	+	0.665701i
$262$		0			0
$263$	1.64146e25			0.639286			0.319643	−	0.947538i	$-0.396437\pi$
$263$	1.64146e25			0.639286			0.319643	+	0.947538i	$0.396437\pi$
$264$		0			0
$265$	2.63202e24			0.0946688
$266$		0			0
$267$	−1.35479e25	−	7.86927e24i	−0.450303	−	0.261557i
$268$		0			0
$269$			5.05201e25i			1.55262i	0.630351	+	0.776310i	$0.282911\pi$
$269$			5.05201e25i			1.55262i	−0.630351	+	0.776310i	$0.717089\pi$
$270$		0			0
$271$		−	4.29523e24i		−	0.122126i	−0.998134	−	0.0610631i	$-0.980551\pi$
$271$		−	4.29523e24i		−	0.122126i	0.998134	−	0.0610631i	$-0.0194491\pi$
$272$		0			0
$273$	−3.72924e25	−	2.16611e25i	−0.981550	−	0.570130i
$274$		0			0
$275$	−5.10664e25			−1.24492
$276$		0			0
$277$	−1.01355e24			−0.0228985			−0.0114492	−	0.999934i	$-0.503644\pi$
$277$	−1.01355e24			−0.0228985			−0.0114492	+	0.999934i	$0.503644\pi$
$278$		0			0
$279$	2.74512e25	−	1.56579e25i	0.575066	−	0.328012i
$280$		0			0
$281$			3.09179e25i			0.600888i	0.953800	+	0.300444i	$0.0971348\pi$
$281$			3.09179e25i			0.600888i	−0.953800	+	0.300444i	$0.902865\pi$
$282$		0			0
$283$			6.98486e25i			1.26009i	0.776560	+	0.630043i	$0.216963\pi$
$283$			6.98486e25i			1.26009i	−0.776560	+	0.630043i	$0.783037\pi$
$284$		0			0
$285$	−1.78144e24	+	3.06697e24i	−0.0298469	+	0.0513852i
$286$		0			0
$287$	−3.27838e25			−0.510387
$288$		0			0
$289$	−1.12725e26			−1.63151
$290$		0			0
$291$	−2.16379e25	+	3.72524e25i	−0.291299	+	0.501508i
$292$		0			0
$293$		−	5.50335e25i		−	0.689472i	−0.938700	−	0.344736i	$-0.887968\pi$
$293$		−	5.50335e25i		−	0.689472i	0.938700	−	0.344736i	$-0.112032\pi$
$294$		0			0
$295$			9.69320e24i			0.113067i
$296$		0			0
$297$	1.15047e26	+	9.03599e23i	1.25006	+	0.00981823i
$298$		0			0
$299$	2.67839e26			2.71223
$300$		0			0
$301$	1.20787e26			1.14044
$302$		0			0
$303$	−1.58497e25	−	9.20622e24i	−0.139596	−	0.0810837i
$304$		0			0
$305$		−	5.52783e24i		−	0.0454366i
$306$		0			0
$307$		−	1.74396e26i		−	1.33840i	−0.743084	−	0.669198i	$-0.766638\pi$
$307$		−	1.74396e26i		−	1.33840i	0.743084	−	0.669198i	$-0.233362\pi$
$308$		0			0
$309$	−4.48776e23	−	2.60670e23i	−0.00321711	−	0.00186865i
$310$		0			0
$311$	−8.80667e25			−0.589967			−0.294983	−	0.955502i	$-0.595314\pi$
$311$	−8.80667e25			−0.589967			−0.294983	+	0.955502i	$0.595314\pi$
$312$		0			0
$313$	−2.41524e25			−0.151267			−0.0756337	−	0.997136i	$-0.524098\pi$
$313$	−2.41524e25			−0.151267			−0.0756337	+	0.997136i	$0.524098\pi$
$314$		0			0
$315$	−3.72321e24	−	6.52748e24i	−0.0218100	−	0.0382371i
$316$		0			0
$317$		−	2.43934e26i		−	1.33706i	−0.743687	−	0.668528i	$-0.766925\pi$
$317$		−	2.43934e26i		−	1.33706i	0.743687	−	0.668528i	$-0.233075\pi$
$318$		0			0
$319$			3.27355e26i			1.67964i
$320$		0			0
$321$	9.26398e24	−	1.59491e25i	0.0445138	−	0.0766361i
$322$		0			0
$323$	−3.32712e26			−1.49776
$324$		0			0
$325$	3.91733e26			1.65278
$326$		0			0
$327$	2.30441e26	−	3.96734e26i	0.911610	−	1.56945i
$328$		0			0
$329$		−	1.72143e25i		−	0.0638752i
$330$		0			0
$331$		−	1.47895e26i		−	0.514943i	−0.966286	−	0.257471i	$-0.917111\pi$
$331$		−	1.47895e26i		−	0.514943i	0.966286	−	0.257471i	$-0.0828893\pi$
$332$		0			0
$333$	−5.38305e25	−	9.43749e25i	−0.175940	−	0.308455i
$334$		0			0
$335$	−1.27427e25			−0.0391103
$336$		0			0
$337$	6.03112e26			1.73894			0.869469	−	0.493988i	$-0.164461\pi$
$337$	6.03112e26			1.73894			0.869469	+	0.493988i	$0.164461\pi$
$338$		0			0
$339$	−1.55428e26	−	9.02800e25i	−0.421147	−	0.244622i
$340$		0			0
$341$		−	3.24899e26i		−	0.827612i
$342$		0			0
$343$		−	4.37452e26i		−	1.04795i
$344$		0			0
$345$	4.03560e25	+	2.34406e25i	0.0909511	+	0.0528286i
$346$		0			0
$347$	−1.39154e26			−0.295147			−0.147573	−	0.989051i	$-0.547146\pi$
$347$	−1.39154e26			−0.295147			−0.147573	+	0.989051i	$0.547146\pi$
$348$		0			0
$349$	−3.74620e25			−0.0748038			−0.0374019	−	0.999300i	$-0.511908\pi$
$349$	−3.74620e25			−0.0748038			−0.0374019	+	0.999300i	$0.511908\pi$
$350$		0			0
$351$	−8.82530e26	−	6.93156e24i	−1.65960	−	0.0130349i
$352$		0			0
$353$			7.71695e26i			1.36714i	0.729887	+	0.683568i	$0.239573\pi$
$353$			7.71695e26i			1.36714i	−0.729887	+	0.683568i	$0.760427\pi$
$354$		0			0
$355$			2.82005e24i			0.00470824i
$356$		0			0
$357$	3.54058e26	−	6.09556e26i	0.557261	−	0.959395i
$358$		0			0
$359$	4.07777e25			0.0605245			0.0302622	−	0.999542i	$-0.490366\pi$
$359$	4.07777e25			0.0605245			0.0302622	+	0.999542i	$0.490366\pi$
$360$		0			0
$361$	1.05369e26			0.147532
$362$		0			0
$363$	2.13928e26	−	3.68304e26i	0.282650	−	0.486617i
$364$		0			0
$365$		−	1.00833e25i		−	0.0125756i
$366$		0			0
$367$		−	6.39048e26i		−	0.752558i	−0.926507	−	0.376279i	$-0.877204\pi$
$367$		−	6.39048e26i		−	0.752558i	0.926507	−	0.376279i	$-0.122796\pi$
$368$		0			0
$369$	−5.82760e26	+	3.32400e26i	−0.648205	+	0.369730i
$370$		0			0
$371$	−9.57256e26			−1.00601
$372$		0			0
$373$	1.38047e27			1.37115			0.685575	−	0.728002i	$-0.259551\pi$
$373$	1.38047e27			1.37115			0.685575	+	0.728002i	$0.259551\pi$
$374$		0			0
$375$	1.18292e26	+	6.87097e25i	0.111078	+	0.0645193i
$376$		0			0
$377$		−	2.51116e27i		−	2.22992i
$378$		0			0
$379$			8.02896e26i			0.674447i	0.941425	+	0.337223i	$0.109488\pi$
$379$			8.02896e26i			0.674447i	−0.941425	+	0.337223i	$0.890512\pi$
$380$		0			0
$381$	−3.51980e25	−	2.04446e25i	−0.0279773	−	0.0162505i
$382$		0			0
$383$	2.02860e27			1.52619			0.763097	−	0.646284i	$-0.223678\pi$
$383$	2.02860e27			1.52619			0.763097	+	0.646284i	$0.223678\pi$
$384$		0			0
$385$	−7.72559e25			−0.0550293
$386$		0			0
$387$	2.14710e27	−	1.22468e27i	1.44839	−	0.826150i
$388$		0			0
$389$			1.35220e27i			0.864114i	0.901846	+	0.432057i	$0.142212\pi$
$389$			1.35220e27i			0.864114i	−0.901846	+	0.432057i	$0.857788\pi$
$390$		0			0
$391$			4.37792e27i			2.65101i
$392$		0			0
$393$	−5.94708e26	+	1.02386e27i	−0.341336	+	0.587653i
$394$		0			0
$395$	−5.90216e25			−0.0321175
$396$		0			0
$397$	−1.93193e27			−0.996993			−0.498496	−	0.866892i	$-0.666114\pi$
$397$	−1.93193e27			−0.996993			−0.498496	+	0.866892i	$0.666114\pi$
$398$		0			0
$399$	6.47903e26	−	1.11545e27i	0.317172	−	0.546051i
$400$		0			0
$401$			2.56252e27i			1.19029i	0.803619	+	0.595144i	$0.202905\pi$
$401$			2.56252e27i			1.19029i	−0.803619	+	0.595144i	$0.797095\pi$
$402$		0			0
$403$			2.49232e27i			1.09875i
$404$		0			0
$405$	−1.32366e26	−	7.82813e25i	−0.0553988	−	0.0327627i
$406$		0			0
$407$	−1.11697e27			−0.443916
$408$		0			0
$409$	1.04912e26			0.0396032			0.0198016	−	0.999804i	$-0.493697\pi$
$409$	1.04912e26			0.0396032			0.0198016	+	0.999804i	$0.493697\pi$
$410$		0			0
$411$	−3.50297e27	−	2.03469e27i	−1.25631	−	0.729723i
$412$		0			0
$413$		−	3.52539e27i		−	1.20152i
$414$		0			0
$415$		−	2.30759e26i		−	0.0747572i
$416$		0			0
$417$	−4.07999e27	−	2.36985e27i	−1.25670	−	0.729948i
$418$		0			0
$419$	4.69963e27			1.37663			0.688314	−	0.725413i	$-0.258351\pi$
$419$	4.69963e27			1.37663			0.688314	+	0.725413i	$0.258351\pi$
$420$		0			0
$421$	−3.30258e27			−0.920220			−0.460110	−	0.887862i	$-0.652190\pi$
$421$	−3.30258e27			−0.920220			−0.460110	+	0.887862i	$0.652190\pi$
$422$		0			0
$423$	−1.74539e26	−	3.05999e26i	−0.0462719	−	0.0811233i
$424$		0			0
$425$			6.40301e27i			1.61547i
$426$		0			0
$427$			2.01045e27i			0.482838i
$428$		0			0
$429$	−4.55719e27	+	7.84579e27i	−1.04207	+	1.79405i
$430$		0			0
$431$	−2.77600e27			−0.604517			−0.302259	−	0.953226i	$-0.597741\pi$
$431$	−2.77600e27			−0.604517			−0.302259	+	0.953226i	$0.597741\pi$
$432$		0			0
$433$	−1.62253e27			−0.336565			−0.168282	−	0.985739i	$-0.553822\pi$
$433$	−1.62253e27			−0.336565			−0.168282	+	0.985739i	$0.553822\pi$
$434$		0			0
$435$	2.19770e26	−	3.78362e26i	0.0434342	−	0.0747775i
$436$		0			0
$437$			8.01129e27i			1.50886i
$438$		0			0
$439$			3.59214e27i			0.644875i	0.946591	+	0.322437i	$0.104502\pi$
$439$			3.59214e27i			0.644875i	−0.946591	+	0.322437i	$0.895498\pi$
$440$		0			0
$441$	−1.54064e27	−	2.70103e27i	−0.263691	−	0.462300i
$442$		0			0
$443$	−2.03937e27			−0.332856			−0.166428	−	0.986054i	$-0.553223\pi$
$443$	−2.03937e27			−0.332856			−0.166428	+	0.986054i	$0.553223\pi$
$444$		0			0
$445$	2.15298e26			0.0335166
$446$		0			0
$447$	2.75152e27	+	1.59821e27i	0.408643	+	0.237359i
$448$		0			0
$449$		−	4.66097e27i		−	0.660526i	−0.943889	−	0.330263i	$-0.892863\pi$
$449$		−	4.66097e27i		−	0.660526i	0.943889	−	0.330263i	$-0.107137\pi$
$450$		0			0
$451$			6.89724e27i			0.932871i
$452$		0			0
$453$	−7.14382e27	−	4.14946e27i	−0.922358	−	0.535748i
$454$		0			0
$455$	5.92634e26			0.0730579
$456$		0			0
$457$	8.73817e27			1.02873			0.514364	−	0.857572i	$-0.328028\pi$
$457$	8.73817e27			1.02873			0.514364	+	0.857572i	$0.328028\pi$
$458$		0			0
$459$	1.13299e26	−	1.44252e28i	0.0127406	−	1.62214i
$460$		0			0
$461$			4.85355e27i			0.521434i	0.965415	+	0.260717i	$0.0839590\pi$
$461$			4.85355e27i			0.521434i	−0.965415	+	0.260717i	$0.916041\pi$
$462$		0			0
$463$			1.21821e28i			1.25061i	0.780382	+	0.625303i	$0.215025\pi$
$463$			1.21821e28i			1.25061i	−0.780382	+	0.625303i	$0.784975\pi$
$464$		0			0
$465$	−2.18122e26	+	3.75524e26i	−0.0214014	+	0.0368452i
$466$		0			0
$467$	−1.24198e27			−0.116490			−0.0582451	−	0.998302i	$-0.518550\pi$
$467$	−1.24198e27			−0.116490			−0.0582451	+	0.998302i	$0.518550\pi$
$468$		0			0
$469$	4.63449e27			0.415611
$470$		0			0
$471$	9.90382e27	−	1.70507e28i	0.849343	−	1.46225i
$472$		0			0
$473$		−	2.54120e28i		−	2.08447i
$474$		0			0
$475$			1.17171e28i			0.919467i
$476$		0			0
$477$	−1.70160e28	+	9.70578e27i	−1.27766	+	0.728765i
$478$		0			0
$479$	2.06433e28			1.48339			0.741696	−	0.670736i	$-0.234022\pi$
$479$	2.06433e28			1.48339			0.741696	+	0.670736i	$0.234022\pi$
$480$		0			0
$481$	8.56836e27			0.589351
$482$		0			0
$483$	−1.46774e28	−	8.52529e27i	−0.966503	−	0.561389i
$484$		0			0
$485$		−	5.91999e26i		−	0.0373278i
$486$		0			0
$487$			2.25561e28i			1.36210i	0.732236	+	0.681051i	$0.238477\pi$
$487$			2.25561e28i			1.36210i	−0.732236	+	0.681051i	$0.761523\pi$
$488$		0			0
$489$	1.07106e28	+	6.22119e27i	0.619540	+	0.359857i
$490$		0			0
$491$	−1.14770e28			−0.636024			−0.318012	−	0.948087i	$-0.603015\pi$
$491$	−1.14770e28			−0.636024			−0.318012	+	0.948087i	$0.603015\pi$
$492$		0			0
$493$	4.10457e28			2.17959
$494$		0			0
$495$	−1.37329e27	+	7.83310e26i	−0.0698887	+	0.0398638i
$496$		0			0
$497$		−	1.02564e27i		−	0.0500327i
$498$		0			0
$499$		−	2.42048e28i		−	1.13200i	−0.824406	−	0.565999i	$-0.808491\pi$
$499$		−	2.42048e28i		−	1.13200i	0.824406	−	0.565999i	$-0.191509\pi$
$500$		0			0
$501$	1.76031e28	−	3.03059e28i	0.789391	−	1.35904i
$502$		0			0
$503$	−1.81547e28			−0.780775			−0.390388	−	0.920651i	$-0.627659\pi$
$503$	−1.81547e28			−0.780775			−0.390388	+	0.920651i	$0.627659\pi$
$504$		0			0
$505$	2.51876e26			0.0103903
$506$		0			0
$507$	2.22669e28	−	3.83353e28i	0.881203	−	1.51710i
$508$		0			0
$509$			5.01271e27i			0.190343i	0.995461	+	0.0951713i	$0.0303399\pi$
$509$			5.01271e27i			0.190343i	−0.995461	+	0.0951713i	$0.969660\pi$
$510$		0			0
$511$			3.66727e27i			0.133636i
$512$		0			0
$513$	2.07329e26	−	2.63972e28i	0.00725149	−	0.923263i
$514$		0			0
$515$	7.13176e24			0.000239453
$516$		0			0
$517$	−3.62164e27			−0.116749
$518$		0			0
$519$	−3.68775e28	−	2.14201e28i	−1.14157	−	0.663078i
$520$		0			0
$521$			2.62286e28i			0.779792i	0.920859	+	0.389896i	$0.127489\pi$
$521$			2.62286e28i			0.779792i	−0.920859	+	0.389896i	$0.872511\pi$
$522$		0			0
$523$			3.26253e28i			0.931724i	0.884857	+	0.465862i	$0.154256\pi$
$523$			3.26253e28i			0.931724i	−0.884857	+	0.465862i	$0.845744\pi$
$524$		0			0
$525$	−2.14667e28	−	1.24688e28i	−0.588968	−	0.342100i
$526$		0			0
$527$	−4.07377e28			−1.07395
$528$		0			0
$529$	6.59433e28			1.67065
$530$		0			0
$531$	−3.57445e28	−	6.26667e28i	−0.870395	−	1.52597i
$532$		0			0
$533$		−	5.29091e28i		−	1.23850i
$534$		0			0
$535$			2.53456e26i			0.00570411i
$536$		0			0
$537$	−4.07407e28	+	7.01403e28i	−0.881655	+	1.51788i
$538$		0			0
$539$	−3.19680e28			−0.665324
$540$		0			0
$541$	7.42008e28			1.48538			0.742689	−	0.669636i	$-0.233550\pi$
$541$	7.42008e28			1.48538			0.742689	+	0.669636i	$0.233550\pi$
$542$		0			0
$543$	3.72808e28	−	6.41835e28i	0.717937	−	1.23602i
$544$		0			0
$545$			6.30472e27i			0.116816i
$546$		0			0
$547$			1.93453e27i			0.0344912i	0.999851	+	0.0172456i	$0.00548972\pi$
$547$			1.93453e27i			0.0344912i	−0.999851	+	0.0172456i	$0.994510\pi$
$548$		0			0
$549$	2.03843e28	+	3.57375e28i	0.349773	+	0.613218i
$550$		0			0
$551$	7.51108e28			1.24054
$552$		0			0
$553$	2.14660e28			0.341300
$554$		0			0
$555$	1.29102e27	+	7.49882e26i	0.0197631	+	0.0114793i
$556$		0			0
$557$		−	7.51169e28i		−	1.10728i	−0.832756	−	0.553641i	$-0.813238\pi$
$557$		−	7.51169e28i		−	1.10728i	0.832756	−	0.553641i	$-0.186762\pi$
$558$		0			0
$559$			1.94937e29i			2.76738i
$560$		0			0
$561$	−1.28242e29	−	7.44888e28i	−1.75356	−	1.01855i
$562$		0			0
$563$	−2.20802e28			−0.290847			−0.145423	−	0.989370i	$-0.546454\pi$
$563$	−2.20802e28			−0.290847			−0.145423	+	0.989370i	$0.546454\pi$
$564$		0			0
$565$	2.47000e27			0.0313465
$566$		0			0
$567$	4.81413e28	+	2.84707e28i	0.588702	+	0.348157i
$568$		0			0
$569$		−	1.06264e28i		−	0.125230i	−0.998038	−	0.0626151i	$-0.980056\pi$
$569$		−	1.06264e28i		−	0.125230i	0.998038	−	0.0626151i	$-0.0199441\pi$
$570$		0			0
$571$		−	9.99914e28i		−	1.13575i	−0.823114	−	0.567876i	$-0.807765\pi$
$571$		−	9.99914e28i		−	1.13575i	0.823114	−	0.567876i	$-0.192235\pi$
$572$		0			0
$573$	3.93971e27	−	6.78270e27i	0.0431361	−	0.0742642i
$574$		0			0
$575$	1.54177e29			1.62744
$576$		0			0
$577$	3.02156e28			0.307528			0.153764	−	0.988108i	$-0.450860\pi$
$577$	3.02156e28			0.307528			0.153764	+	0.988108i	$0.450860\pi$
$578$		0			0
$579$	2.15340e28	−	3.70736e28i	0.211349	−	0.363864i
$580$		0			0
$581$			8.39262e28i			0.794416i
$582$		0			0
$583$			2.01393e29i			1.83876i
$584$		0			0
$585$	1.05346e28	−	6.00882e27i	0.0927856	−	0.0529240i
$586$		0			0
$587$	−1.25542e29			−1.06681			−0.533405	−	0.845860i	$-0.679088\pi$
$587$	−1.25542e29			−1.06681			−0.533405	+	0.845860i	$0.679088\pi$
$588$		0			0
$589$	−7.45473e28			−0.611253
$590$		0			0
$591$	−5.83296e28	−	3.38805e28i	−0.461552	−	0.268091i
$592$		0			0
$593$			2.01726e29i			1.54059i	0.637685	+	0.770297i	$0.279892\pi$
$593$			2.01726e29i			1.54059i	−0.637685	+	0.770297i	$0.720108\pi$
$594$		0			0
$595$			9.68680e27i			0.0714089i
$596$		0			0
$597$	−8.10349e27	−	4.70688e27i	−0.0576689	−	0.0334968i
$598$		0			0
$599$	1.02750e29			0.705990			0.352995	−	0.935625i	$-0.385163\pi$
$599$	1.02750e29			0.705990			0.352995	+	0.935625i	$0.385163\pi$
$600$		0			0
$601$	−2.47773e29			−1.64388			−0.821942	−	0.569571i	$-0.807110\pi$
$601$	−2.47773e29			−1.64388			−0.821942	+	0.569571i	$0.807110\pi$
$602$		0			0
$603$	8.23819e28	−	4.69898e28i	0.527837	−	0.301073i
$604$		0			0
$605$			5.85293e27i			0.0362195i
$606$		0			0
$607$			1.55895e29i			0.931861i	0.884821	+	0.465931i	$0.154280\pi$
$607$			1.55895e29i			0.931861i	−0.884821	+	0.465931i	$0.845720\pi$
$608$		0			0
$609$	−7.99298e28	+	1.37609e29i	−0.461559	+	0.794632i
$610$		0			0
$611$	2.77818e28			0.154999
$612$		0			0
$613$	−2.43349e29			−1.31188			−0.655941	−	0.754812i	$-0.727728\pi$
$613$	−2.43349e29			−1.31188			−0.655941	+	0.754812i	$0.727728\pi$
$614$		0			0
$615$	4.63048e27	−	7.97196e27i	0.0241233	−	0.0415314i
$616$		0			0
$617$			2.61918e28i			0.131878i	0.997824	+	0.0659388i	$0.0210042\pi$
$617$			2.61918e28i			0.131878i	−0.997824	+	0.0659388i	$0.978996\pi$
$618$		0			0
$619$		−	4.43751e28i		−	0.215967i	−0.994153	−	0.107984i	$-0.965561\pi$
$619$		−	4.43751e28i		−	0.215967i	0.994153	−	0.107984i	$-0.0344394\pi$
$620$		0			0
$621$	−3.47342e29	−	2.72809e27i	−1.63416	−	0.0128350i
$622$		0			0
$623$	−7.83032e28			−0.356168
$624$		0			0
$625$	2.24552e29			0.987590
$626$		0			0
$627$	−2.34674e29	−	1.36310e29i	−0.998058	−	0.579718i
$628$		0			0
$629$			1.40053e29i			0.576049i
$630$		0			0
$631$			3.10159e29i			1.23389i	0.787007	+	0.616944i	$0.211630\pi$
$631$			3.10159e29i			1.23389i	−0.787007	+	0.616944i	$0.788370\pi$
$632$		0			0
$633$	1.41102e29	+	8.19583e28i	0.542991	+	0.315394i
$634$		0			0
$635$	5.59352e26			0.00208238
$636$		0			0
$637$	2.45228e29			0.883297
$638$		0			0
$639$	−1.03992e28	−	1.82317e28i	−0.0362442	−	0.0635429i
$640$		0			0
$641$		−	1.82657e29i		−	0.616065i	−0.951376	−	0.308032i	$-0.900329\pi$
$641$		−	1.82657e29i		−	0.616065i	0.951376	−	0.308032i	$-0.0996705\pi$
$642$		0			0
$643$			8.82717e28i			0.288142i	0.989567	+	0.144071i	$0.0460193\pi$
$643$			8.82717e28i			0.288142i	−0.989567	+	0.144071i	$0.953981\pi$
$644$		0			0
$645$	−1.70604e28	+	2.93716e28i	−0.0539029	+	0.0928006i
$646$		0			0
$647$	−8.30205e28			−0.253916			−0.126958	−	0.991908i	$-0.540521\pi$
$647$	−8.30205e28			−0.253916			−0.126958	+	0.991908i	$0.540521\pi$
$648$		0			0
$649$	−7.41691e29			−2.19611
$650$		0			0
$651$	7.93301e28	−	1.36577e29i	0.227425	−	0.391540i
$652$		0			0
$653$			1.51081e29i			0.419394i	0.977766	+	0.209697i	$0.0672478\pi$
$653$			1.51081e29i			0.419394i	−0.977766	+	0.209697i	$0.932752\pi$
$654$		0			0
$655$		−	1.62708e28i		−	0.0437397i
$656$		0			0
$657$	3.71831e28	+	6.51889e28i	0.0968075	+	0.169722i
$658$		0			0
$659$	−2.43677e29			−0.614494			−0.307247	−	0.951630i	$-0.599408\pi$
$659$	−2.43677e29			−0.614494			−0.307247	+	0.951630i	$0.599408\pi$
$660$		0			0
$661$	2.23572e29			0.546138			0.273069	−	0.961994i	$-0.411961\pi$
$661$	2.23572e29			0.546138			0.273069	+	0.961994i	$0.411961\pi$
$662$		0			0
$663$	9.83751e29	+	5.71408e29i	2.32805	+	1.35224i
$664$		0			0
$665$			1.77262e28i			0.0406432i
$666$		0			0
$667$		−	9.88329e29i		−	2.19574i
$668$		0			0
$669$	9.79162e28	+	5.68742e28i	0.210805	+	0.122445i
$670$		0			0
$671$	4.22971e29			0.882518
$672$		0			0
$673$	6.29275e29			1.27257			0.636286	−	0.771453i	$-0.280470\pi$
$673$	6.29275e29			1.27257			0.636286	+	0.771453i	$0.280470\pi$
$674$		0			0
$675$	−5.08011e29	−	3.99002e27i	−0.995827	−	0.00782142i
$676$		0			0
$677$		−	2.72729e29i		−	0.518263i	−0.965842	−	0.259131i	$-0.916564\pi$
$677$		−	2.72729e29i		−	0.518263i	0.965842	−	0.259131i	$-0.0834363\pi$
$678$		0			0
$679$			2.15308e29i			0.396669i
$680$		0			0
$681$	3.80875e29	−	6.55724e29i	0.680358	−	1.17132i
$682$		0			0
$683$	2.05854e29			0.356567			0.178284	−	0.983979i	$-0.442946\pi$
$683$	2.05854e29			0.356567			0.178284	+	0.983979i	$0.442946\pi$
$684$		0			0
$685$	5.56676e28			0.0935086
$686$		0			0
$687$	−5.45004e29	+	9.38292e29i	−0.887879	+	1.52859i
$688$		0			0
$689$		−	1.54490e30i		−	2.44117i
$690$		0			0
$691$		−	9.21840e29i		−	1.41298i	−0.707723	−	0.706490i	$-0.750278\pi$
$691$		−	9.21840e29i		−	1.41298i	0.707723	−	0.706490i	$-0.249722\pi$
$692$		0			0
$693$	4.99461e29	−	2.84887e29i	0.742681	−	0.423618i
$694$		0			0
$695$	6.48375e28			0.0935375
$696$		0			0
$697$	8.64817e29			1.21054
$698$		0			0
$699$	−7.74119e29	−	4.49644e29i	−1.05147	−	0.610743i
$700$		0			0
$701$			1.09827e30i			1.44767i	0.689975	+	0.723833i	$0.257621\pi$
$701$			1.09827e30i			1.44767i	−0.689975	+	0.723833i	$0.742379\pi$
$702$		0			0
$703$			2.56287e29i			0.327865i
$704$		0			0
$705$	4.18596e27	+	2.43140e27i	0.00519768	+	0.00301905i
$706$		0			0
$707$	−9.16065e28			−0.110414
$708$		0			0
$709$	1.14838e29			0.134369			0.0671844	−	0.997741i	$-0.478598\pi$
$709$	1.14838e29			0.134369			0.0671844	+	0.997741i	$0.478598\pi$
$710$		0			0
$711$	3.81576e29	−	2.17647e29i	0.433461	−	0.247242i
$712$		0			0
$713$			9.80914e29i			1.08191i
$714$		0			0
$715$		−	1.24682e29i		−	0.133533i
$716$		0			0
$717$	−9.46816e27	+	1.63006e28i	−0.00984724	+	0.0169533i
$718$		0			0
$719$	6.81668e29			0.688524			0.344262	−	0.938874i	$-0.388129\pi$
$719$	6.81668e29			0.688524			0.344262	+	0.938874i	$0.388129\pi$
$720$		0			0
$721$	−2.59380e27			−0.00254458
$722$		0			0
$723$	2.67723e29	−	4.60919e29i	0.255114	−	0.439211i
$724$		0			0
$725$		−	1.44550e30i		−	1.33804i
$726$		0			0
$727$		−	1.65534e30i		−	1.48860i	−0.667847	−	0.744298i	$-0.732784\pi$
$727$		−	1.65534e30i		−	1.48860i	0.667847	−	0.744298i	$-0.267216\pi$
$728$		0			0
$729$	1.14442e30	+	1.79781e28i	0.999877	+	0.0157074i
$730$		0			0
$731$	−3.18630e30			−2.70492
$732$		0			0
$733$	−1.09986e30			−0.907285			−0.453643	−	0.891184i	$-0.649876\pi$
$733$	−1.09986e30			−0.907285			−0.453643	+	0.891184i	$0.649876\pi$
$734$		0			0
$735$	3.69492e28	+	2.14618e28i	0.0296202	+	0.0172048i
$736$		0			0
$737$		−	9.75030e29i		−	0.759642i
$738$		0			0
$739$		−	2.45597e30i		−	1.85976i	−0.367861	−	0.929881i	$-0.619910\pi$
$739$		−	2.45597e30i		−	1.85976i	0.367861	−	0.929881i	$-0.380090\pi$
$740$		0			0
$741$	1.80020e30	+	1.04564e30i	1.32504	+	0.769645i
$742$		0			0
$743$	−1.95690e30			−1.40019			−0.700094	−	0.714051i	$-0.746859\pi$
$743$	−1.95690e30			−1.40019			−0.700094	+	0.714051i	$0.746859\pi$
$744$		0			0
$745$	−4.37260e28			−0.0304158
$746$		0			0
$747$	8.50941e29	+	1.49186e30i	0.575484	+	1.00893i
$748$		0			0
$749$		−	9.21812e28i		−	0.0606155i
$750$		0			0
$751$			8.06431e29i			0.515641i	0.966193	+	0.257821i	$0.0830044\pi$
$751$			8.06431e29i			0.515641i	−0.966193	+	0.257821i	$0.916996\pi$
$752$		0			0
$753$	2.44536e29	−	4.21000e29i	0.152053	−	0.261779i
$754$		0			0
$755$	1.13526e29			0.0686522
$756$		0			0
$757$	−1.68631e30			−0.991815			−0.495907	−	0.868375i	$-0.665164\pi$
$757$	−1.68631e30			−0.991815			−0.495907	+	0.868375i	$0.665164\pi$
$758$		0			0
$759$	−1.79360e30	+	3.08791e30i	−1.02609	+	1.76655i
$760$		0			0
$761$			2.46047e30i			1.36924i	0.728902	+	0.684618i	$0.240031\pi$
$761$			2.46047e30i			1.36924i	−0.728902	+	0.684618i	$0.759969\pi$
$762$		0			0
$763$		−	2.29301e30i		−	1.24136i
$764$		0			0
$765$	9.82160e28	+	1.72191e29i	0.0517294	+	0.0906913i
$766$		0			0
$767$	5.68956e30			2.91559
$768$		0			0
$769$	−4.10522e29			−0.204696			−0.102348	−	0.994749i	$-0.532636\pi$
$769$	−4.10522e29			−0.204696			−0.102348	+	0.994749i	$0.532636\pi$
$770$		0			0
$771$	8.18614e29	+	4.75489e29i	0.397199	+	0.230712i
$772$		0			0
$773$		−	2.50499e30i		−	1.18283i	−0.806369	−	0.591413i	$-0.798570\pi$
$773$		−	2.50499e30i		−	1.18283i	0.806369	−	0.591413i	$-0.201430\pi$
$774$		0			0
$775$			1.43465e30i			0.659294i
$776$		0			0
$777$	−4.69539e29	−	2.72730e29i	−0.210015	−	0.121987i
$778$		0			0
$779$	1.58256e30			0.688995
$780$		0			0
$781$	−2.15781e29			−0.0914485
$782$		0			0
$783$	−2.55775e28	+	3.25654e30i	−0.0105526	+	1.34356i
$784$		0			0
$785$			2.70962e29i			0.108837i
$786$		0			0
$787$		−	2.30494e30i		−	0.901417i	−0.892671	−	0.450708i	$-0.851171\pi$
$787$		−	2.30494e30i		−	0.901417i	0.892671	−	0.450708i	$-0.148829\pi$
$788$		0			0
$789$	8.43213e29	−	1.45170e30i	0.321091	−	0.552799i
$790$		0			0
$791$	−8.98332e29			−0.333107
$792$		0			0
$793$	−3.24463e30			−1.17165
$794$		0			0
$795$	1.35206e29	−	2.32774e29i	0.0475489	−	0.0818614i
$796$		0			0
$797$			4.88600e30i			1.67356i	0.547541	+	0.836779i	$0.315564\pi$
$797$			4.88600e30i			1.67356i	−0.547541	+	0.836779i	$0.684436\pi$
$798$		0			0
$799$			4.54103e29i			0.151500i
$800$		0			0
$801$	−1.39191e30	+	7.93929e29i	−0.452344	+	0.258012i
$802$		0			0
$803$	7.71542e29			0.244257
$804$		0			0
$805$	2.33246e29			0.0719379
$806$		0			0
$807$	4.46796e30	+	2.59520e30i	1.34257	+	0.779828i
$808$		0			0
$809$		−	1.05175e29i		−	0.0307932i	−0.999881	−	0.0153966i	$-0.995099\pi$
$809$		−	1.05175e29i		−	0.0307932i	0.999881	−	0.0153966i	$-0.00490108\pi$
$810$		0			0
$811$			3.09142e30i			0.881940i	0.897522	+	0.440970i	$0.145365\pi$
$811$			3.09142e30i			0.881940i	−0.897522	+	0.440970i	$0.854635\pi$
$812$		0			0
$813$	−3.79867e29	−	2.20644e29i	−0.105604	−	0.0613398i
$814$		0			0
$815$	−1.70208e29			−0.0461131
$816$		0			0
$817$	−5.83072e30			−1.53954
$818$		0			0
$819$	−3.83139e30	+	2.18539e30i	−0.985998	+	0.562403i
$820$		0			0
$821$		−	1.56458e30i		−	0.392460i	−0.980558	−	0.196230i	$-0.937130\pi$
$821$		−	1.56458e30i		−	0.392460i	0.980558	−	0.196230i	$-0.0628699\pi$
$822$		0			0
$823$		−	3.09284e30i		−	0.756240i	−0.925757	−	0.378120i	$-0.876571\pi$
$823$		−	3.09284e30i		−	0.756240i	0.925757	−	0.378120i	$-0.123429\pi$
$824$		0			0
$825$	−2.62326e30	+	4.51628e30i	−0.625281	+	1.07650i
$826$		0			0
$827$	−5.29501e30			−1.23043			−0.615217	−	0.788357i	$-0.710932\pi$
$827$	−5.29501e30			−1.23043			−0.615217	+	0.788357i	$0.710932\pi$
$828$		0			0
$829$	−2.28673e30			−0.518074			−0.259037	−	0.965867i	$-0.583405\pi$
$829$	−2.28673e30			−0.518074			−0.259037	+	0.965867i	$0.583405\pi$
$830$		0			0
$831$	−5.20655e28	+	8.96374e28i	−0.0115011	+	0.0198006i
$832$		0			0
$833$			4.00834e30i			0.863359i
$834$		0			0
$835$			4.81608e29i			0.101155i
$836$		0			0
$837$	2.53856e28	−	3.23211e30i	0.00519961	−	0.662016i
$838$		0			0
$839$	5.15532e30			1.02980			0.514902	−	0.857249i	$-0.327828\pi$
$839$	5.15532e30			1.02980			0.514902	+	0.857249i	$0.327828\pi$
$840$		0			0
$841$	−4.13335e30			−0.805275
$842$		0			0
$843$	2.73436e30	+	1.58824e30i	0.519596	+	0.301805i
$844$		0			0
$845$			6.09207e29i			0.112920i
$846$		0			0
$847$		−	2.12869e30i		−	0.384891i
$848$		0			0
$849$	6.17737e30	+	3.58810e30i	1.08961	+	0.632898i
$850$		0			0
$851$	3.37229e30			0.580317
$852$		0			0
$853$	1.07965e30			0.181267			0.0906335	−	0.995884i	$-0.471111\pi$
$853$	1.07965e30			0.181267			0.0906335	+	0.995884i	$0.471111\pi$
$854$		0			0
$855$	1.79729e29	+	3.15098e29i	0.0294424	+	0.0516180i
$856$		0			0
$857$			4.01505e30i			0.641788i	0.947115	+	0.320894i	$0.103983\pi$
$857$			4.01505e30i			0.641788i	−0.947115	+	0.320894i	$0.896017\pi$
$858$		0			0
$859$		−	1.03996e31i		−	1.62214i	−0.584948	−	0.811071i	$-0.698885\pi$
$859$		−	1.03996e31i		−	1.62214i	0.584948	−	0.811071i	$-0.301115\pi$
$860$		0			0
$861$	−1.68409e30	+	2.89938e30i	−0.256350	+	0.441338i
$862$		0			0
$863$	−1.12638e31			−1.67329			−0.836646	−	0.547744i	$-0.815487\pi$
$863$	−1.12638e31			−1.67329			−0.836646	+	0.547744i	$0.815487\pi$
$864$		0			0
$865$	5.86041e29			0.0849686
$866$		0			0
$867$	−5.79062e30	+	9.96928e30i	−0.819454	+	1.41079i
$868$		0			0
$869$		−	4.51613e30i		−	0.623820i
$870$		0			0
$871$			7.47951e30i			1.00852i
$872$		0			0
$873$	2.18305e30	+	3.82729e30i	0.287351	+	0.503781i
$874$		0			0
$875$	6.83696e29			0.0878575
$876$		0			0
$877$	−1.08953e31			−1.36692			−0.683459	−	0.729989i	$-0.739525\pi$
$877$	−1.08953e31			−1.36692			−0.683459	+	0.729989i	$0.739525\pi$
$878$		0			0
$879$	−4.86712e30	−	2.82705e30i	−0.596196	−	0.346298i
$880$		0			0
$881$		−	1.07706e31i		−	1.28822i	−0.764931	−	0.644112i	$-0.777227\pi$
$881$		−	1.07706e31i		−	1.28822i	0.764931	−	0.644112i	$-0.222773\pi$
$882$		0			0
$883$		−	5.70563e30i		−	0.666371i	−0.942861	−	0.333186i	$-0.891876\pi$
$883$		−	5.70563e30i		−	0.666371i	0.942861	−	0.333186i	$-0.108124\pi$
$884$		0			0
$885$	8.57260e29	+	4.97936e29i	0.0977706	+	0.0567897i
$886$		0			0
$887$	2.41549e30			0.269034			0.134517	−	0.990911i	$-0.457052\pi$
$887$	2.41549e30			0.269034			0.134517	+	0.990911i	$0.457052\pi$
$888$		0			0
$889$	−2.03435e29			−0.0221287
$890$		0			0
$891$	5.98982e30	−	1.01282e31i	0.636353	−	1.07601i
$892$		0			0
$893$			8.30978e29i			0.0862282i
$894$		0			0
$895$		−	1.11464e30i		−	0.112978i
$896$		0			0
$897$	1.37588e31	−	2.36875e31i	1.36226	−	2.34530i
$898$		0			0
$899$	9.19667e30			0.889516
$900$		0			0
$901$	2.52518e31			2.38607
$902$		0			0
$903$	6.20481e30	−	1.06824e31i	0.572805	−	0.986157i
$904$		0			0
$905$			1.01998e30i			0.0919984i
$906$		0			0
$907$			1.34805e31i			1.18804i	0.804452	+	0.594018i	$0.202459\pi$
$907$			1.34805e31i			1.18804i	−0.804452	+	0.594018i	$0.797541\pi$
$908$		0			0
$909$	−1.62838e30	+	9.28813e29i	−0.140228	+	0.0799848i
$910$		0			0
$911$	−3.61798e30			−0.304455			−0.152228	−	0.988345i	$-0.548645\pi$
$911$	−3.61798e30			−0.304455			−0.152228	+	0.988345i	$0.548645\pi$
$912$		0			0
$913$	1.76569e31			1.45201
$914$		0			0
$915$	−4.88877e29	−	2.83962e29i	−0.0392897	−	0.0228213i
$916$		0			0
$917$			5.91764e30i			0.464805i
$918$		0			0
$919$			4.85445e29i			0.0372673i	0.999826	+	0.0186336i	$0.00593161\pi$
$919$			4.85445e29i			0.0372673i	−0.999826	+	0.0186336i	$0.994068\pi$
$920$		0			0
$921$	−1.54235e31	−	8.95868e30i	−1.15733	−	0.672230i
$922$		0			0
$923$	1.65527e30			0.121409
$924$		0			0
$925$	4.93221e30			0.353634
$926$		0			0
$927$	−4.61070e28	+	2.62990e28i	−0.00323169	+	0.00184332i
$928$		0			0
$929$		−	1.75930e30i		−	0.120552i	−0.998182	−	0.0602762i	$-0.980802\pi$
$929$		−	1.75930e30i		−	0.120552i	0.998182	−	0.0602762i	$-0.0191981\pi$
$930$		0			0
$931$			7.33499e30i			0.491391i
$932$		0			0
$933$	−4.52395e30	+	7.78856e30i	−0.296320	+	0.510152i
$934$		0			0
$935$	2.03796e30			0.130519
$936$		0			0
$937$	2.55828e31			1.60207			0.801035	−	0.598617i	$-0.204283\pi$
$937$	2.55828e31			1.60207			0.801035	+	0.598617i	$0.204283\pi$
$938$		0			0
$939$	−1.24070e30	+	2.13603e30i	−0.0759764	+	0.130803i
$940$		0			0
$941$		−	1.91183e31i		−	1.14487i	−0.819949	−	0.572436i	$-0.805998\pi$
$941$		−	1.91183e31i		−	1.14487i	0.819949	−	0.572436i	$-0.194002\pi$
$942$		0			0
$943$		−	2.08237e31i		−	1.21951i
$944$		0			0
$945$	−7.68546e29	−	6.03631e27i	−0.0440186	−	0.000345731i
$946$		0			0
$947$	−1.51750e31			−0.850067			−0.425034	−	0.905178i	$-0.639738\pi$
$947$	−1.51750e31			−0.850067			−0.425034	+	0.905178i	$0.639738\pi$
$948$		0			0
$949$	−5.91854e30			−0.324280
$950$		0			0
$951$	−2.15733e31	−	1.25308e31i	−1.15617	−	0.671557i
$952$		0			0
$953$		−	2.32454e31i		−	1.21860i	−0.792940	−	0.609300i	$-0.791450\pi$
$953$		−	2.32454e31i		−	1.21860i	0.792940	−	0.609300i	$-0.208550\pi$
$954$		0			0
$955$			1.07788e29i			0.00552757i
$956$		0			0
$957$	2.89510e31	+	1.68161e31i	1.45241	+	0.843625i
$958$		0			0
$959$	−2.02461e31			−0.993681
$960$		0			0
$961$	1.16978e31			0.561707
$962$		0			0
$963$	−9.34641e29	−	1.63860e30i	−0.0439105	−	0.0769834i
$964$		0			0
$965$			5.89157e29i			0.0270828i
$966$		0			0
$967$		−	2.59341e31i		−	1.16652i	−0.812284	−	0.583262i	$-0.801776\pi$
$967$		−	2.59341e31i		−	1.16652i	0.812284	−	0.583262i	$-0.198224\pi$
$968$		0			0
$969$	−1.70913e31	+	2.94248e31i	−0.752273	+	1.29513i
$970$		0			0
$971$	1.79045e31			0.771189			0.385595	−	0.922668i	$-0.373996\pi$
$971$	1.79045e31			0.771189			0.385595	+	0.922668i	$0.373996\pi$
$972$		0			0
$973$	−2.35812e31			−0.993987
$974$		0			0
$975$	2.01232e31	−	3.46446e31i	0.830135	−	1.42918i
$976$		0			0
$977$		−	1.53173e31i		−	0.618427i	−0.950993	−	0.309214i	$-0.899934\pi$
$977$		−	1.53173e31i		−	0.618427i	0.950993	−	0.309214i	$-0.100066\pi$
$978$		0			0
$979$			1.64739e31i			0.650995i
$980$		0			0
$981$	−2.32492e31	−	4.07602e31i	−0.899256	−	1.57656i
$982$		0			0
$983$	−4.06296e31			−1.53826			−0.769131	−	0.639091i	$-0.779311\pi$
$983$	−4.06296e31			−1.53826			−0.769131	+	0.639091i	$0.779311\pi$
$984$		0			0
$985$	9.26949e29			0.0343538
$986$		0			0
$987$	−1.52242e30	−	8.84293e29i	−0.0552338	−	0.0320823i
$988$		0			0
$989$			7.67222e31i			2.72496i
$990$		0			0
$991$			3.93815e31i			1.36936i	0.728842	+	0.684682i	$0.240059\pi$
$991$			3.93815e31i			1.36936i	−0.728842	+	0.684682i	$0.759941\pi$
$992$		0			0
$993$	−1.30797e31	−	7.59731e30i	−0.445278	−	0.258638i
$994$		0			0
$995$	1.28777e29			0.00429236
$996$		0			0
$997$	1.01160e31			0.330149			0.165074	−	0.986281i	$-0.447214\pi$
$997$	1.01160e31			0.330149			0.165074	+	0.986281i	$0.447214\pi$
$998$		0			0
$999$	−1.11117e31	−	8.72735e28i	−0.355094	−	0.00278898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.22.c.c.47.19	yes	28
3.2	odd	2	inner	48.22.c.c.47.9	✓	28
4.3	odd	2	inner	48.22.c.c.47.10	yes	28
12.11	even	2	inner	48.22.c.c.47.20	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.22.c.c.47.9	✓	28	3.2	odd	2	inner
48.22.c.c.47.10	yes	28	4.3	odd	2	inner
48.22.c.c.47.19	yes	28	1.1	even	1	trivial
48.22.c.c.47.20	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)

\(f(q)\)	\(=\)	\(q+(51369.6 - 88439.3i) q^{3} +1.40544e6i q^{5} -5.11154e8i q^{7} +(-5.18267e9 - 9.08619e9i) q^{9} +O(q^{10})\)	\(q+(51369.6 - 88439.3i) q^{3} +1.40544e6i q^{5} -5.11154e8i q^{7} +(-5.18267e9 - 9.08619e9i) q^{9} -1.07539e11 q^{11} +8.24942e11 q^{13} +(1.24296e11 + 7.21969e10i) q^{15} +1.34839e13i q^{17} +2.46747e13i q^{19} +(-4.52061e13 - 2.62578e13i) q^{21} +3.24677e14 q^{23} +4.74862e14 q^{25} +(-1.06981e15 - 8.40249e12i) q^{27} -3.04404e15i q^{29} +3.02120e15i q^{31} +(-5.52426e15 + 9.51072e15i) q^{33} +7.18396e14 q^{35} +1.03866e16 q^{37} +(4.23770e16 - 7.29573e16i) q^{39} -6.41368e16i q^{41} +2.36304e17i q^{43} +(1.27701e16 - 7.28393e15i) q^{45} +3.36773e16 q^{47} +2.97268e17 q^{49} +(1.19251e18 + 6.92665e17i) q^{51} -1.87274e18i q^{53} -1.51140e17i q^{55} +(2.18221e18 + 1.26753e18i) q^{57} +6.89692e18 q^{59} -3.93317e18 q^{61} +(-4.64444e18 + 2.64914e18i) q^{63} +1.15941e18i q^{65} +9.06671e18i q^{67} +(1.66785e19 - 2.87142e19i) q^{69} +2.00652e18 q^{71} -7.17450e18 q^{73} +(2.43935e19 - 4.19965e19i) q^{75} +5.49692e19i q^{77} +4.19951e19i q^{79} +(-5.56988e19 + 9.41815e19i) q^{81} -1.64190e20 q^{83} -1.89508e19 q^{85} +(-2.69213e20 - 1.56371e20i) q^{87} -1.53189e20i q^{89} -4.21672e20i q^{91} +(2.67193e20 + 1.55198e20i) q^{93} -3.46788e19 q^{95} -4.21220e20 q^{97} +(5.57342e20 + 9.77124e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 109254828 q^{9}+O(q^{10}) \) 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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