LMFDB - Embedded newform 80.16.c.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,16,Mod(49,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("80.49");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	80.c (of order $2$, degree $1$, not 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:	$114.154804080$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 29397x^{4} + 153469728x^{2} + 65015354624 $ x^6 + 29397x^4 + 153469728x^2 + 65015354624
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{4}\cdot 5^{6} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$21.5470i$ of defining polynomial
Character	$\chi$	$=$	80.49
Dual form			80.16.c.a.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6725.99i q^{3} +(-160365. - 69286.1i) q^{5} -1.29717e6i q^{7} -3.08900e7 q^{9} +O(q^{10})$	\(q-6725.99i q^{3} +(-160365. - 69286.1i) q^{5} -1.29717e6i q^{7} -3.08900e7 q^{9} +2.48560e7 q^{11} -1.64842e8i q^{13} +(-4.66018e8 + 1.07862e9i) q^{15} +2.49651e9i q^{17} -3.47974e9 q^{19} -8.72472e9 q^{21} -1.39929e10i q^{23} +(2.09165e10 + 2.22222e10i) q^{25} +1.11256e11i q^{27} +7.33587e10 q^{29} -6.63708e9 q^{31} -1.67181e11i q^{33} +(-8.98755e10 + 2.08020e11i) q^{35} +8.47925e11i q^{37} -1.10873e12 q^{39} -7.77655e11 q^{41} +2.03959e12i q^{43} +(4.95369e12 + 2.14025e12i) q^{45} +3.83108e12i q^{47} +3.06492e12 q^{49} +1.67915e13 q^{51} -2.49472e12i q^{53} +(-3.98604e12 - 1.72217e12i) q^{55} +2.34047e13i q^{57} -1.33880e12 q^{59} +7.16455e12 q^{61} +4.00695e13i q^{63} +(-1.14213e13 + 2.64349e13i) q^{65} -6.61388e12i q^{67} -9.41158e13 q^{69} -1.42046e13 q^{71} -5.85350e13i q^{73} +(1.49466e14 - 1.40684e14i) q^{75} -3.22423e13i q^{77} -2.48505e14 q^{79} +3.05065e14 q^{81} +6.66100e13i q^{83} +(1.72973e14 - 4.00353e14i) q^{85} -4.93410e14i q^{87} -5.07426e14 q^{89} -2.13827e14 q^{91} +4.46409e13i q^{93} +(5.58029e14 + 2.41097e14i) q^{95} -1.18734e15i q^{97} -7.67802e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 238350 q^{5} - 11416662 q^{9}+O(q^{10}) $ 6 * q - 238350 * q^5 - 11416662 * q^9	$ 6 q - 238350 q^{5} - 11416662 q^{9} + 108590088 q^{11} - 297743400 q^{15} + 3630995640 q^{19} - 8917537608 q^{21} + 18250878750 q^{25} + 286168468740 q^{29} + 276236748288 q^{31} - 1171274911800 q^{35} - 2186980965936 q^{39} - 6153278882388 q^{41} + 10442765857950 q^{45} + 11613390856242 q^{49} + 43487373385728 q^{51} - 33977390365800 q^{55} - 14903258326680 q^{59} - 11352061428588 q^{61} - 50675287275600 q^{65} - 150489671962824 q^{69} - 131693145807312 q^{71} + 360965926890000 q^{75} + 26081853939360 q^{79} + 11\!\cdots\!46 q^{81}+ \cdots - 506999099666376 q^{99}+O(q^{100}) $ 6 * q - 238350 * q^5 - 11416662 * q^9 + 108590088 * q^11 - 297743400 * q^15 + 3630995640 * q^19 - 8917537608 * q^21 + 18250878750 * q^25 + 286168468740 * q^29 + 276236748288 * q^31 - 1171274911800 * q^35 - 2186980965936 * q^39 - 6153278882388 * q^41 + 10442765857950 * q^45 + 11613390856242 * q^49 + 43487373385728 * q^51 - 33977390365800 * q^55 - 14903258326680 * q^59 - 11352061428588 * q^61 - 50675287275600 * q^65 - 150489671962824 * q^69 - 131693145807312 * q^71 + 360965926890000 * q^75 + 26081853939360 * q^79 + 1148641568615646 * q^81 - 548221025491200 * q^85 + 59269690709820 * q^89 - 821206462566672 * q^91 - 232287694599000 * q^95 - 506999099666376 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$1$	$1$

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
$3$		−	6725.99i		−	1.77561i	−0.460223	−	0.887803i	$-0.652230\pi$
$3$		−	6725.99i		−	1.77561i	0.460223	−	0.887803i	$-0.347770\pi$
$4$		0			0
$5$	−160365.	−	69286.1i	−0.917984	−	0.396617i
$5$	−160365.	−	69286.1i	−0.917984	−	0.396617i
$6$		0			0
$7$		−	1.29717e6i		−	0.595333i	−0.954670	−	0.297667i	$-0.903792\pi$
$7$		−	1.29717e6i		−	0.595333i	0.954670	−	0.297667i	$-0.0962084\pi$
$8$		0			0
$9$	−3.08900e7			−2.15278
$10$		0			0
$11$	2.48560e7			0.384579			0.192290	−	0.981338i	$-0.438409\pi$
$11$	2.48560e7			0.384579			0.192290	+	0.981338i	$0.438409\pi$
$12$		0			0
$13$		−	1.64842e8i		−	0.728606i	−0.931281	−	0.364303i	$-0.881307\pi$
$13$		−	1.64842e8i		−	0.728606i	0.931281	−	0.364303i	$-0.118693\pi$
$14$		0			0
$15$	−4.66018e8	+	1.07862e9i	−0.704235	+	1.62998i
$16$		0			0
$17$			2.49651e9i			1.47559i	0.675024	+	0.737795i	$0.264133\pi$
$17$			2.49651e9i			1.47559i	−0.675024	+	0.737795i	$0.735867\pi$
$18$		0			0
$19$	−3.47974e9			−0.893088			−0.446544	−	0.894762i	$-0.647345\pi$
$19$	−3.47974e9			−0.893088			−0.446544	+	0.894762i	$0.647345\pi$
$20$		0			0
$21$	−8.72472e9			−1.05708
$22$		0			0
$23$		−	1.39929e10i		−	0.856934i	−0.903557	−	0.428467i	$-0.859054\pi$
$23$		−	1.39929e10i		−	0.856934i	0.903557	−	0.428467i	$-0.140946\pi$
$24$		0			0
$25$	2.09165e10	+	2.22222e10i	0.685390	+	0.728176i
$26$		0			0
$27$			1.11256e11i			2.04688i
$28$		0			0
$29$	7.33587e10			0.789709			0.394854	−	0.918744i	$-0.370795\pi$
$29$	7.33587e10			0.789709			0.394854	+	0.918744i	$0.370795\pi$
$30$		0			0
$31$	−6.63708e9			−0.0433276			−0.0216638	−	0.999765i	$-0.506896\pi$
$31$	−6.63708e9			−0.0433276			−0.0216638	+	0.999765i	$0.506896\pi$
$32$		0			0
$33$		−	1.67181e11i		−	0.682862i
$34$		0			0
$35$	−8.98755e10	+	2.08020e11i	−0.236119	+	0.546506i
$36$		0			0
$37$			8.47925e11i			1.46840i	0.678933	+	0.734201i	$0.262443\pi$
$37$			8.47925e11i			1.46840i	−0.678933	+	0.734201i	$0.737557\pi$
$38$		0			0
$39$	−1.10873e12			−1.29372
$40$		0			0
$41$	−7.77655e11			−0.623603			−0.311801	−	0.950147i	$-0.600932\pi$
$41$	−7.77655e11			−0.623603			−0.311801	+	0.950147i	$0.600932\pi$
$42$		0			0
$43$			2.03959e12i			1.14427i	0.820158	+	0.572137i	$0.193885\pi$
$43$			2.03959e12i			1.14427i	−0.820158	+	0.572137i	$0.806115\pi$
$44$		0			0
$45$	4.95369e12	+	2.14025e12i	1.97622	+	0.853828i
$46$		0			0
$47$			3.83108e12i			1.10303i	0.834165	+	0.551514i	$0.185950\pi$
$47$			3.83108e12i			1.10303i	−0.834165	+	0.551514i	$0.814050\pi$
$48$		0			0
$49$	3.06492e12			0.645578
$50$		0			0
$51$	1.67915e13			2.62007
$52$		0			0
$53$		−	2.49472e12i		−	0.291711i	−0.989306	−	0.145856i	$-0.953407\pi$
$53$		−	2.49472e12i		−	0.291711i	0.989306	−	0.145856i	$-0.0465935\pi$
$54$		0			0
$55$	−3.98604e12	−	1.72217e12i	−0.353038	−	0.152531i
$56$		0			0
$57$			2.34047e13i			1.58577i
$58$		0			0
$59$	−1.33880e12			−0.0700365			−0.0350183	−	0.999387i	$-0.511149\pi$
$59$	−1.33880e12			−0.0700365			−0.0350183	+	0.999387i	$0.511149\pi$
$60$		0			0
$61$	7.16455e12			0.291887			0.145944	−	0.989293i	$-0.453378\pi$
$61$	7.16455e12			0.291887			0.145944	+	0.989293i	$0.453378\pi$
$62$		0			0
$63$			4.00695e13i			1.28162i
$64$		0			0
$65$	−1.14213e13	+	2.64349e13i	−0.288977	+	0.668849i
$66$		0			0
$67$		−	6.61388e12i		−	0.133320i	−0.997776	−	0.0666600i	$-0.978766\pi$
$67$		−	6.61388e12i		−	0.133320i	0.997776	−	0.0666600i	$-0.0212343\pi$
$68$		0			0
$69$	−9.41158e13			−1.52158
$70$		0			0
$71$	−1.42046e13			−0.185349			−0.0926746	−	0.995696i	$-0.529542\pi$
$71$	−1.42046e13			−0.185349			−0.0926746	+	0.995696i	$0.529542\pi$
$72$		0			0
$73$		−	5.85350e13i		−	0.620147i	−0.950713	−	0.310073i	$-0.899646\pi$
$73$		−	5.85350e13i		−	0.620147i	0.950713	−	0.310073i	$-0.100354\pi$
$74$		0			0
$75$	1.49466e14	−	1.40684e14i	1.29295	−	1.21698i
$76$		0			0
$77$		−	3.22423e13i		−	0.228953i
$78$		0			0
$79$	−2.48505e14			−1.45590			−0.727950	−	0.685630i	$-0.759527\pi$
$79$	−2.48505e14			−1.45590			−0.727950	+	0.685630i	$0.759527\pi$
$80$		0			0
$81$	3.05065e14			1.48168
$82$		0			0
$83$			6.66100e13i			0.269435i	0.990884	+	0.134717i	$0.0430127\pi$
$83$			6.66100e13i			0.269435i	−0.990884	+	0.134717i	$0.956987\pi$
$84$		0			0
$85$	1.72973e14	−	4.00353e14i	0.585244	−	1.35457i
$86$		0			0
$87$		−	4.93410e14i		−	1.40221i
$88$		0			0
$89$	−5.07426e14			−1.21604			−0.608020	−	0.793922i	$-0.708036\pi$
$89$	−5.07426e14			−1.21604			−0.608020	+	0.793922i	$0.708036\pi$
$90$		0			0
$91$	−2.13827e14			−0.433763
$92$		0			0
$93$			4.46409e13i			0.0769327i
$94$		0			0
$95$	5.58029e14	+	2.41097e14i	0.819841	+	0.354214i
$96$		0			0
$97$		−	1.18734e15i		−	1.49206i	−0.665912	−	0.746030i	$-0.731957\pi$
$97$		−	1.18734e15i		−	1.49206i	0.665912	−	0.746030i	$-0.268043\pi$
$98$		0			0
$99$	−7.67802e14			−0.827915
$100$		0			0
$101$	1.97970e14			0.183734			0.0918671	−	0.995771i	$-0.470717\pi$
$101$	1.97970e14			0.183734			0.0918671	+	0.995771i	$0.470717\pi$
$102$		0			0
$103$		−	1.50015e15i		−	1.20186i	−0.799301	−	0.600931i	$-0.794797\pi$
$103$		−	1.50015e15i		−	1.20186i	0.799301	−	0.600931i	$-0.205203\pi$
$104$		0			0
$105$	1.39914e15	+	6.04502e14i	0.970381	+	0.419255i
$106$		0			0
$107$			6.89575e14i			0.415148i	0.978219	+	0.207574i	$0.0665568\pi$
$107$			6.89575e14i			0.415148i	−0.978219	+	0.207574i	$0.933443\pi$
$108$		0			0
$109$	1.35369e15			0.709287			0.354644	−	0.935002i	$-0.384602\pi$
$109$	1.35369e15			0.709287			0.354644	+	0.935002i	$0.384602\pi$
$110$		0			0
$111$	5.70314e15			2.60730
$112$		0			0
$113$			2.28009e15i			0.911726i	0.890050	+	0.455863i	$0.150669\pi$
$113$			2.28009e15i			0.911726i	−0.890050	+	0.455863i	$0.849331\pi$
$114$		0			0
$115$	−9.69510e14	+	2.24397e15i	−0.339874	+	0.786652i
$116$		0			0
$117$			5.09197e15i			1.56853i
$118$		0			0
$119$	3.23838e15			0.878468
$120$		0			0
$121$	−3.55943e15			−0.852099
$122$		0			0
$123$			5.23050e15i			1.10727i
$124$		0			0
$125$	−1.81459e15	−	5.01288e15i	−0.340371	−	0.940291i
$126$		0			0
$127$			2.82207e15i			0.469938i	0.972003	+	0.234969i	$0.0754988\pi$
$127$			2.82207e15i			0.469938i	−0.972003	+	0.234969i	$0.924501\pi$
$128$		0			0
$129$	1.37183e16			2.03178
$130$		0			0
$131$	−6.54539e15			−0.863775			−0.431888	−	0.901927i	$-0.642152\pi$
$131$	−6.54539e15			−0.863775			−0.431888	+	0.901927i	$0.642152\pi$
$132$		0			0
$133$			4.51379e15i			0.531685i
$134$		0			0
$135$	7.70846e15	−	1.78415e16i	0.811828	−	1.87901i
$136$		0			0
$137$		−	1.17625e16i		−	1.10941i	−0.832046	−	0.554707i	$-0.812830\pi$
$137$		−	1.17625e16i		−	1.10941i	0.832046	−	0.554707i	$-0.187170\pi$
$138$		0			0
$139$	2.03768e16			1.72395			0.861976	−	0.506949i	$-0.169227\pi$
$139$	2.03768e16			1.72395			0.861976	+	0.506949i	$0.169227\pi$
$140$		0			0
$141$	2.57678e16			1.95855
$142$		0			0
$143$		−	4.09731e15i		−	0.280207i
$144$		0			0
$145$	−1.17642e16	−	5.08274e15i	−0.724940	−	0.313212i
$146$		0			0
$147$		−	2.06146e16i		−	1.14629i
$148$		0			0
$149$	2.89572e16			1.45499			0.727493	−	0.686115i	$-0.240685\pi$
$149$	2.89572e16			1.45499			0.727493	+	0.686115i	$0.240685\pi$
$150$		0			0
$151$	−1.77226e13			−0.000805748			−0.000402874	−	1.00000i	$-0.500128\pi$
$151$	−1.77226e13			−0.000805748			−0.000402874		1.00000i	$0.500128\pi$
$152$		0			0
$153$		−	7.71172e16i		−	3.17662i
$154$		0			0
$155$	1.06436e15	+	4.59857e14i	0.0397740	+	0.0171844i
$156$		0			0
$157$			1.04137e16i			0.353475i	0.984258	+	0.176737i	$0.0565543\pi$
$157$			1.04137e16i			0.353475i	−0.984258	+	0.176737i	$0.943446\pi$
$158$		0			0
$159$	−1.67795e16			−0.517964
$160$		0			0
$161$	−1.81510e16			−0.510161
$162$		0			0
$163$		−	4.70622e16i		−	1.20577i	−0.797827	−	0.602886i	$-0.794017\pi$
$163$		−	4.70622e16i		−	1.20577i	0.797827	−	0.602886i	$-0.205983\pi$
$164$		0			0
$165$	−1.15833e16	+	2.68100e16i	−0.270834	+	0.626856i
$166$		0			0
$167$			3.97751e16i			0.849646i	0.905276	+	0.424823i	$0.139664\pi$
$167$			3.97751e16i			0.849646i	−0.905276	+	0.424823i	$0.860336\pi$
$168$		0			0
$169$	2.40130e16			0.469134
$170$		0			0
$171$	1.07489e17			1.92262
$172$		0			0
$173$			6.30223e16i			1.03311i	0.856253	+	0.516557i	$0.172787\pi$
$173$			6.30223e16i			1.03311i	−0.856253	+	0.516557i	$0.827213\pi$
$174$		0			0
$175$	2.88258e16	−	2.71321e16i	0.433507	−	0.408036i
$176$		0			0
$177$			9.00474e15i			0.124357i
$178$		0			0
$179$	−2.10684e16			−0.267445			−0.133722	−	0.991019i	$-0.542693\pi$
$179$	−2.10684e16			−0.267445			−0.133722	+	0.991019i	$0.542693\pi$
$180$		0			0
$181$	1.74536e16			0.203843			0.101922	−	0.994792i	$-0.467501\pi$
$181$	1.74536e16			0.203843			0.101922	+	0.994792i	$0.467501\pi$
$182$		0			0
$183$		−	4.81887e16i		−	0.518277i
$184$		0			0
$185$	5.87494e16	−	1.35978e17i	0.582392	−	1.34797i
$186$		0			0
$187$			6.20531e16i			0.567482i
$188$		0			0
$189$	1.44317e17			1.21858
$190$		0			0
$191$	1.82919e17			1.42728			0.713639	−	0.700514i	$-0.247046\pi$
$191$	1.82919e17			1.42728			0.713639	+	0.700514i	$0.247046\pi$
$192$		0			0
$193$		−	4.54299e16i		−	0.327840i	−0.986474	−	0.163920i	$-0.947586\pi$
$193$		−	4.54299e16i		−	0.327840i	0.986474	−	0.163920i	$-0.0524139\pi$
$194$		0			0
$195$	1.77801e17	+	7.68192e16i	1.18761	+	0.513110i
$196$		0			0
$197$			2.54430e17i			1.57425i	0.616797	+	0.787123i	$0.288430\pi$
$197$			2.54430e17i			1.57425i	−0.616797	+	0.787123i	$0.711570\pi$
$198$		0			0
$199$	−1.75148e17			−1.00463			−0.502316	−	0.864684i	$-0.667518\pi$
$199$	−1.75148e17			−1.00463			−0.502316	+	0.864684i	$0.667518\pi$
$200$		0			0
$201$	−4.44849e16			−0.236724
$202$		0			0
$203$		−	9.51584e16i		−	0.470140i
$204$		0			0
$205$	1.24709e17	+	5.38807e16i	0.572457	+	0.247331i
$206$		0			0
$207$			4.32240e17i			1.84479i
$208$		0			0
$209$	−8.64923e16			−0.343463
$210$		0			0
$211$	−3.58937e17			−1.32709			−0.663545	−	0.748137i	$-0.730949\pi$
$211$	−3.58937e17			−1.32709			−0.663545	+	0.748137i	$0.730949\pi$
$212$		0			0
$213$			9.55399e16i			0.329107i
$214$		0			0
$215$	1.41315e17	−	3.27080e17i	0.453838	−	1.05043i
$216$		0			0
$217$			8.60939e15i			0.0257943i
$218$		0			0
$219$	−3.93706e17			−1.10114
$220$		0			0
$221$	4.11529e17			1.07512
$222$		0			0
$223$			8.51111e16i			0.207826i	0.994586	+	0.103913i	$0.0331364\pi$
$223$			8.51111e16i			0.207826i	−0.994586	+	0.103913i	$0.966864\pi$
$224$		0			0
$225$	−6.46110e17	−	6.86443e17i	−1.47549	−	1.56760i
$226$		0			0
$227$			8.22273e16i			0.175720i	0.996133	+	0.0878602i	$0.0280029\pi$
$227$			8.22273e16i			0.175720i	−0.996133	+	0.0878602i	$0.971997\pi$
$228$		0			0
$229$	−3.91258e17			−0.782884			−0.391442	−	0.920203i	$-0.628024\pi$
$229$	−3.91258e17			−0.782884			−0.391442	+	0.920203i	$0.628024\pi$
$230$		0			0
$231$	−2.16862e17			−0.406530
$232$		0			0
$233$		−	9.50055e17i		−	1.66947i	−0.550650	−	0.834736i	$-0.685620\pi$
$233$		−	9.50055e17i		−	1.66947i	0.550650	−	0.834736i	$-0.314380\pi$
$234$		0			0
$235$	2.65440e17	−	6.14371e17i	0.437480	−	1.01256i
$236$		0			0
$237$			1.67144e18i			2.58511i
$238$		0			0
$239$	−3.05534e17			−0.443685			−0.221843	−	0.975082i	$-0.571207\pi$
$239$	−3.05534e17			−0.443685			−0.221843	+	0.975082i	$0.571207\pi$
$240$		0			0
$241$	−1.24585e18			−1.69956			−0.849780	−	0.527137i	$-0.823266\pi$
$241$	−1.24585e18			−1.69956			−0.849780	+	0.527137i	$0.823266\pi$
$242$		0			0
$243$		−	4.55471e17i		−	0.584001i
$244$		0			0
$245$	−4.91507e17	−	2.12357e17i	−0.592631	−	0.256047i
$246$		0			0
$247$			5.73606e17i			0.650709i
$248$		0			0
$249$	4.48018e17			0.478411
$250$		0			0
$251$	−3.78704e17			−0.380844			−0.190422	−	0.981702i	$-0.560986\pi$
$251$	−3.78704e17			−0.380844			−0.190422	+	0.981702i	$0.560986\pi$
$252$		0			0
$253$		−	3.47806e17i		−	0.329559i
$254$		0			0
$255$	−2.69277e18	−	1.16342e18i	−2.40518	−	1.03916i
$256$		0			0
$257$			6.98680e16i			0.0588545i	0.999567	+	0.0294273i	$0.00936834\pi$
$257$			6.98680e16i			0.0588545i	−0.999567	+	0.0294273i	$0.990632\pi$
$258$		0			0
$259$	1.09990e18			0.874188
$260$		0			0
$261$	−2.26605e18			−1.70007
$262$		0			0
$263$			6.94838e17i			0.492284i	0.969234	+	0.246142i	$0.0791629\pi$
$263$			6.94838e17i			0.492284i	−0.969234	+	0.246142i	$0.920837\pi$
$264$		0			0
$265$	−1.72849e17	+	4.00067e17i	−0.115698	+	0.267786i
$266$		0			0
$267$			3.41294e18i			2.15921i
$268$		0			0
$269$	1.75703e18			1.05108			0.525542	−	0.850768i	$-0.323863\pi$
$269$	1.75703e18			1.05108			0.525542	+	0.850768i	$0.323863\pi$
$270$		0			0
$271$	1.86384e18			1.05472			0.527362	−	0.849641i	$-0.323181\pi$
$271$	1.86384e18			1.05472			0.527362	+	0.849641i	$0.323181\pi$
$272$		0			0
$273$			1.43820e18i			0.770193i
$274$		0			0
$275$	5.19899e17	+	5.52354e17i	0.263587	+	0.280041i
$276$		0			0
$277$			3.28806e18i			1.57885i	0.613846	+	0.789425i	$0.289621\pi$
$277$			3.28806e18i			1.57885i	−0.613846	+	0.789425i	$0.710379\pi$
$278$		0			0
$279$	2.05020e17			0.0932747
$280$		0			0
$281$	2.41481e18			1.04132			0.520662	−	0.853763i	$-0.325685\pi$
$281$	2.41481e18			1.04132			0.520662	+	0.853763i	$0.325685\pi$
$282$		0			0
$283$		−	1.11571e17i		−	0.0456199i	−0.999740	−	0.0228099i	$-0.992739\pi$
$283$		−	1.11571e17i		−	0.0456199i	0.999740	−	0.0228099i	$-0.00726126\pi$
$284$		0			0
$285$	1.62162e18	−	3.75330e18i	0.628944	−	1.45571i
$286$		0			0
$287$			1.00875e18i			0.371251i
$288$		0			0
$289$	−3.37012e18			−1.17737
$290$		0			0
$291$	−7.98602e18			−2.64931
$292$		0			0
$293$			2.59868e18i			0.818927i	0.912327	+	0.409463i	$0.134284\pi$
$293$			2.59868e18i			0.818927i	−0.912327	+	0.409463i	$0.865716\pi$
$294$		0			0
$295$	2.14697e17	+	9.27600e16i	0.0642924	+	0.0277777i
$296$		0			0
$297$			2.76537e18i			0.787189i
$298$		0			0
$299$	−2.30661e18			−0.624367
$300$		0			0
$301$	2.64569e18			0.681224
$302$		0			0
$303$		−	1.33155e18i		−	0.326240i
$304$		0			0
$305$	−1.14895e18	−	4.96404e17i	−0.267948	−	0.115767i
$306$		0			0
$307$			7.96608e18i			1.76892i	0.466621	+	0.884458i	$0.345471\pi$
$307$			7.96608e18i			1.76892i	−0.466621	+	0.884458i	$0.654529\pi$
$308$		0			0
$309$	−1.00900e19			−2.13403
$310$		0			0
$311$	8.72923e18			1.75903			0.879515	−	0.475872i	$-0.157867\pi$
$311$	8.72923e18			1.75903			0.879515	+	0.475872i	$0.157867\pi$
$312$		0			0
$313$		−	3.04567e17i		−	0.0584926i	−0.999572	−	0.0292463i	$-0.990689\pi$
$313$		−	3.04567e17i		−	0.0584926i	0.999572	−	0.0292463i	$-0.00931071\pi$
$314$		0			0
$315$	2.77626e18	−	6.42575e18i	0.508312	−	1.17651i
$316$		0			0
$317$		−	5.64109e18i		−	0.984961i	−0.870324	−	0.492480i	$-0.836090\pi$
$317$		−	5.64109e18i		−	0.984961i	0.870324	−	0.492480i	$-0.163910\pi$
$318$		0			0
$319$	1.82340e18			0.303706
$320$		0			0
$321$	4.63807e18			0.737140
$322$		0			0
$323$		−	8.68718e18i		−	1.31783i
$324$		0			0
$325$	3.66314e18	−	3.44791e18i	0.530553	−	0.499379i
$326$		0			0
$327$		−	9.10494e18i		−	1.25941i
$328$		0			0
$329$	4.96954e18			0.656670
$330$		0			0
$331$	−6.05049e18			−0.763978			−0.381989	−	0.924167i	$-0.624761\pi$
$331$	−6.05049e18			−0.763978			−0.381989	+	0.924167i	$0.624761\pi$
$332$		0			0
$333$		−	2.61925e19i		−	3.16114i
$334$		0			0
$335$	−4.58250e17	+	1.06064e18i	−0.0528770	+	0.122386i
$336$		0			0
$337$			1.58672e19i			1.75096i	0.483254	+	0.875480i	$0.339455\pi$
$337$			1.58672e19i			1.75096i	−0.483254	+	0.875480i	$0.660545\pi$
$338$		0			0
$339$	1.53359e19			1.61887
$340$		0			0
$341$	−1.64971e17			−0.0166629
$342$		0			0
$343$		−	1.01341e19i		−	0.979667i
$344$		0			0
$345$	1.50929e19	+	6.52092e18i	1.39679	+	0.603484i
$346$		0			0
$347$		−	5.47026e18i		−	0.484771i	−0.970180	−	0.242386i	$-0.922070\pi$
$347$		−	5.47026e18i		−	0.484771i	0.970180	−	0.242386i	$-0.0779299\pi$
$348$		0			0
$349$	−7.51980e18			−0.638287			−0.319143	−	0.947706i	$-0.603395\pi$
$349$	−7.51980e18			−0.638287			−0.319143	+	0.947706i	$0.603395\pi$
$350$		0			0
$351$	1.83396e19			1.49137
$352$		0			0
$353$			3.96219e18i			0.308763i	0.988011	+	0.154382i	$0.0493385\pi$
$353$			3.96219e18i			0.308763i	−0.988011	+	0.154382i	$0.950662\pi$
$354$		0			0
$355$	2.27792e18	+	9.84179e17i	0.170148	+	0.0735126i
$356$		0			0
$357$		−	2.17813e19i		−	1.55981i
$358$		0			0
$359$	−1.88540e19			−1.29478			−0.647390	−	0.762159i	$-0.724140\pi$
$359$	−1.88540e19			−1.29478			−0.647390	+	0.762159i	$0.724140\pi$
$360$		0			0
$361$	−3.07257e18			−0.202394
$362$		0			0
$363$			2.39407e19i			1.51299i
$364$		0			0
$365$	−4.05566e18	+	9.38699e18i	−0.245961	+	0.569285i
$366$		0			0
$367$			1.02228e19i			0.595077i	0.954710	+	0.297538i	$0.0961656\pi$
$367$			1.02228e19i			0.595077i	−0.954710	+	0.297538i	$0.903834\pi$
$368$		0			0
$369$	2.40218e19			1.34248
$370$		0			0
$371$	−3.23607e18			−0.173665
$372$		0			0
$373$			1.86547e19i			0.961550i	0.876844	+	0.480775i	$0.159645\pi$
$373$			1.86547e19i			0.961550i	−0.876844	+	0.480775i	$0.840355\pi$
$374$		0			0
$375$	−3.37166e19	+	1.22049e19i	−1.66959	+	0.604365i
$376$		0			0
$377$		−	1.20926e19i		−	0.575386i
$378$		0			0
$379$	3.62923e19			1.65967			0.829833	−	0.558012i	$-0.188436\pi$
$379$	3.62923e19			1.65967			0.829833	+	0.558012i	$0.188436\pi$
$380$		0			0
$381$	1.89812e19			0.834425
$382$		0			0
$383$			3.39832e19i			1.43640i	0.695839	+	0.718198i	$0.255033\pi$
$383$			3.39832e19i			1.43640i	−0.695839	+	0.718198i	$0.744967\pi$
$384$		0			0
$385$	−2.23394e18	+	5.17055e18i	−0.0908065	+	0.210175i
$386$		0			0
$387$		−	6.30031e19i		−	2.46337i
$388$		0			0
$389$	4.43693e19			1.66902			0.834508	−	0.550996i	$-0.185752\pi$
$389$	4.43693e19			1.66902			0.834508	+	0.550996i	$0.185752\pi$
$390$		0			0
$391$	3.49333e19			1.26448
$392$		0			0
$393$			4.40242e19i			1.53373i
$394$		0			0
$395$	3.98516e19	+	1.72179e19i	1.33649	+	0.577434i
$396$		0			0
$397$			1.44302e19i			0.465953i	0.972482	+	0.232977i	$0.0748466\pi$
$397$			1.44302e19i			0.465953i	−0.972482	+	0.232977i	$0.925153\pi$
$398$		0			0
$399$	3.03597e19			0.944063
$400$		0			0
$401$	2.34827e19			0.703339			0.351669	−	0.936124i	$-0.385614\pi$
$401$	2.34827e19			0.703339			0.351669	+	0.936124i	$0.385614\pi$
$402$		0			0
$403$			1.09407e18i			0.0315687i
$404$		0			0
$405$	−4.89219e19	−	2.11368e19i	−1.36016	−	0.587660i
$406$		0			0
$407$			2.10760e19i			0.564717i
$408$		0			0
$409$	−3.99167e19			−1.03093			−0.515466	−	0.856910i	$-0.672381\pi$
$409$	−3.99167e19			−1.03093			−0.515466	+	0.856910i	$0.672381\pi$
$410$		0			0
$411$	−7.91142e19			−1.96988
$412$		0			0
$413$			1.73664e18i			0.0416951i
$414$		0			0
$415$	4.61515e18	−	1.06819e19i	0.106862	−	0.247337i
$416$		0			0
$417$		−	1.37054e20i		−	3.06106i
$418$		0			0
$419$	−7.16449e19			−1.54376			−0.771881	−	0.635767i	$-0.780684\pi$
$419$	−7.16449e19			−1.54376			−0.771881	+	0.635767i	$0.780684\pi$
$420$		0			0
$421$	−6.22202e18			−0.129365			−0.0646823	−	0.997906i	$-0.520603\pi$
$421$	−6.22202e18			−0.129365			−0.0646823	+	0.997906i	$0.520603\pi$
$422$		0			0
$423$		−	1.18342e20i		−	2.37458i
$424$		0			0
$425$	−5.54778e19	+	5.22181e19i	−1.07449	+	1.01136i
$426$		0			0
$427$		−	9.29361e18i		−	0.173770i
$428$		0			0
$429$	−2.75585e19			−0.497537
$430$		0			0
$431$	4.93032e19			0.859598			0.429799	−	0.902925i	$-0.358584\pi$
$431$	4.93032e19			0.859598			0.429799	+	0.902925i	$0.358584\pi$
$432$		0			0
$433$		−	1.59414e19i		−	0.268453i	−0.990951	−	0.134226i	$-0.957145\pi$
$433$		−	1.59414e19i		−	0.268453i	0.990951	−	0.134226i	$-0.0428549\pi$
$434$		0			0
$435$	−3.41865e19	+	7.91259e19i	−0.556141	+	1.28721i
$436$		0			0
$437$			4.86914e19i			0.765318i
$438$		0			0
$439$	1.26174e19			0.191640			0.0958201	−	0.995399i	$-0.469453\pi$
$439$	1.26174e19			0.191640			0.0958201	+	0.995399i	$0.469453\pi$
$440$		0			0
$441$	−9.46756e19			−1.38979
$442$		0			0
$443$			7.89961e19i			1.12093i	0.828179	+	0.560464i	$0.189377\pi$
$443$			7.89961e19i			1.12093i	−0.828179	+	0.560464i	$0.810623\pi$
$444$		0			0
$445$	8.13735e19	+	3.51576e19i	1.11630	+	0.482301i
$446$		0			0
$447$		−	1.94766e20i		−	2.58348i
$448$		0			0
$449$	4.36438e19			0.559854			0.279927	−	0.960021i	$-0.409690\pi$
$449$	4.36438e19			0.559854			0.279927	+	0.960021i	$0.409690\pi$
$450$		0			0
$451$	−1.93294e19			−0.239825
$452$		0			0
$453$			1.19202e17i			0.00143069i
$454$		0			0
$455$	3.42905e19	+	1.48153e19i	0.398188	+	0.172038i
$456$		0			0
$457$		−	1.00520e20i		−	1.12949i	−0.825266	−	0.564744i	$-0.808975\pi$
$457$		−	1.00520e20i		−	1.12949i	0.825266	−	0.564744i	$-0.191025\pi$
$458$		0			0
$459$	−2.77750e20			−3.02036
$460$		0			0
$461$	−1.09258e20			−1.15000			−0.574999	−	0.818154i	$-0.694998\pi$
$461$	−1.09258e20			−1.15000			−0.574999	+	0.818154i	$0.694998\pi$
$462$		0			0
$463$			1.81520e20i			1.84955i	0.380510	+	0.924777i	$0.375748\pi$
$463$			1.81520e20i			1.84955i	−0.380510	+	0.924777i	$0.624252\pi$
$464$		0			0
$465$	3.09299e18	−	7.15885e18i	0.0305128	−	0.0706230i
$466$		0			0
$467$			1.14048e20i			1.08946i	0.838611	+	0.544731i	$0.183368\pi$
$467$			1.14048e20i			1.08946i	−0.838611	+	0.544731i	$0.816632\pi$
$468$		0			0
$469$	−8.57930e18			−0.0793699
$470$		0			0
$471$	7.00425e19			0.627632
$472$		0			0
$473$			5.06961e19i			0.440064i
$474$		0			0
$475$	−7.27837e19	−	7.73272e19i	−0.612114	−	0.650325i
$476$		0			0
$477$			7.70621e19i			0.627990i
$478$		0			0
$479$	−1.21110e20			−0.956451			−0.478226	−	0.878237i	$-0.658720\pi$
$479$	−1.21110e20			−0.956451			−0.478226	+	0.878237i	$0.658720\pi$
$480$		0			0
$481$	1.39774e20			1.06989
$482$		0			0
$483$			1.22084e20i			0.905846i
$484$		0			0
$485$	−8.22660e19	+	1.90408e20i	−0.591776	+	1.36969i
$486$		0			0
$487$			1.00069e20i			0.697963i	0.937130	+	0.348982i	$0.113472\pi$
$487$			1.00069e20i			0.697963i	−0.937130	+	0.348982i	$0.886528\pi$
$488$		0			0
$489$	−3.16540e20			−2.14098
$490$		0			0
$491$	1.32724e20			0.870641			0.435321	−	0.900276i	$-0.356635\pi$
$491$	1.32724e20			0.870641			0.435321	+	0.900276i	$0.356635\pi$
$492$		0			0
$493$			1.83141e20i			1.16529i
$494$		0			0
$495$	1.23129e20	+	5.31980e19i	0.760013	+	0.328365i
$496$		0			0
$497$			1.84257e19i			0.110345i
$498$		0			0
$499$	9.34938e18			0.0543286			0.0271643	−	0.999631i	$-0.491352\pi$
$499$	9.34938e18			0.0543286			0.0271643	+	0.999631i	$0.491352\pi$
$500$		0			0
$501$	2.67527e20			1.50864
$502$		0			0
$503$		−	1.56622e20i		−	0.857223i	−0.903489	−	0.428612i	$-0.859003\pi$
$503$		−	1.56622e20i		−	0.857223i	0.903489	−	0.428612i	$-0.140997\pi$
$504$		0			0
$505$	−3.17476e19	−	1.37166e19i	−0.168665	−	0.0728720i
$506$		0			0
$507$		−	1.61511e20i		−	0.832997i
$508$		0			0
$509$	1.94050e20			0.971698			0.485849	−	0.874043i	$-0.338511\pi$
$509$	1.94050e20			0.971698			0.485849	+	0.874043i	$0.338511\pi$
$510$		0			0
$511$	−7.59296e19			−0.369194
$512$		0			0
$513$		−	3.87140e20i		−	1.82805i
$514$		0			0
$515$	−1.03939e20	+	2.40571e20i	−0.476678	+	1.10329i
$516$		0			0
$517$			9.52252e19i			0.424202i
$518$		0			0
$519$	4.23887e20			1.83441
$520$		0			0
$521$	−6.43719e19			−0.270653			−0.135327	−	0.990801i	$-0.543208\pi$
$521$	−6.43719e19			−0.270653			−0.135327	+	0.990801i	$0.543208\pi$
$522$		0			0
$523$		−	1.94571e20i		−	0.794904i	−0.917623	−	0.397452i	$-0.869895\pi$
$523$		−	1.94571e20i		−	0.794904i	0.917623	−	0.397452i	$-0.130105\pi$
$524$		0			0
$525$	−1.82490e20	−	1.93882e20i	−0.724511	−	0.769738i
$526$		0			0
$527$		−	1.65695e19i		−	0.0639337i
$528$		0			0
$529$	7.08352e19			0.265663
$530$		0			0
$531$	4.13555e19			0.150773
$532$		0			0
$533$			1.28190e20i			0.454360i
$534$		0			0
$535$	4.77779e19	−	1.10584e20i	0.164655	−	0.381099i
$536$		0			0
$537$			1.41706e20i			0.474877i
$538$		0			0
$539$	7.61817e19			0.248276
$540$		0			0
$541$	1.81403e19			0.0574996			0.0287498	−	0.999587i	$-0.490847\pi$
$541$	1.81403e19			0.0574996			0.0287498	+	0.999587i	$0.490847\pi$
$542$		0			0
$543$		−	1.17393e20i		−	0.361945i
$544$		0			0
$545$	−2.17086e20	−	9.37922e19i	−0.651114	−	0.281315i
$546$		0			0
$547$			6.00592e20i			1.75257i	0.481796	+	0.876283i	$0.339985\pi$
$547$			6.00592e20i			1.75257i	−0.481796	+	0.876283i	$0.660015\pi$
$548$		0			0
$549$	−2.21313e20			−0.628369
$550$		0			0
$551$	−2.55269e20			−0.705279
$552$		0			0
$553$			3.22352e20i			0.866746i
$554$		0			0
$555$	−9.14585e20	−	3.95148e20i	−2.39346	−	1.03410i
$556$		0			0
$557$		−	2.29611e20i		−	0.584895i	−0.956282	−	0.292447i	$-0.905530\pi$
$557$		−	2.29611e20i		−	0.584895i	0.956282	−	0.292447i	$-0.0944697\pi$
$558$		0			0
$559$	3.36210e20			0.833725
$560$		0			0
$561$	4.17369e20			1.00762
$562$		0			0
$563$		−	5.26651e20i		−	1.23797i	−0.785403	−	0.618985i	$-0.787544\pi$
$563$		−	5.26651e20i		−	1.23797i	0.785403	−	0.618985i	$-0.212456\pi$
$564$		0			0
$565$	1.57979e20	−	3.65648e20i	0.361606	−	0.836950i
$566$		0			0
$567$		−	3.95720e20i		−	0.882095i
$568$		0			0
$569$	5.86825e20			1.27399			0.636996	−	0.770868i	$-0.280177\pi$
$569$	5.86825e20			1.27399			0.636996	+	0.770868i	$0.280177\pi$
$570$		0			0
$571$	2.76080e20			0.583800			0.291900	−	0.956449i	$-0.405713\pi$
$571$	2.76080e20			0.583800			0.291900	+	0.956449i	$0.405713\pi$
$572$		0			0
$573$		−	1.23031e21i		−	2.53428i
$574$		0			0
$575$	3.10952e20	−	2.92681e20i	0.623999	−	0.587335i
$576$		0			0
$577$			1.42599e20i			0.278804i	0.990236	+	0.139402i	$0.0445180\pi$
$577$			1.42599e20i			0.278804i	−0.990236	+	0.139402i	$0.955482\pi$
$578$		0			0
$579$	−3.05561e20			−0.582115
$580$		0			0
$581$	8.64042e19			0.160404
$582$		0			0
$583$		−	6.20088e19i		−	0.112186i
$584$		0			0
$585$	3.52803e20	−	8.16576e20i	0.622104	−	1.43988i
$586$		0			0
$587$			7.48323e20i			1.28618i	0.765789	+	0.643092i	$0.222349\pi$
$587$			7.48323e20i			1.28618i	−0.765789	+	0.643092i	$0.777651\pi$
$588$		0			0
$589$	2.30953e19			0.0386953
$590$		0			0
$591$	1.71130e21			2.79524
$592$		0			0
$593$			3.21784e20i			0.512454i	0.966617	+	0.256227i	$0.0824794\pi$
$593$			3.21784e20i			0.512454i	−0.966617	+	0.256227i	$0.917521\pi$
$594$		0			0
$595$	−5.19324e20	−	2.24375e20i	−0.806420	−	0.348415i
$596$		0			0
$597$			1.17804e21i			1.78383i
$598$		0			0
$599$	1.08146e21			1.59702			0.798509	−	0.601983i	$-0.205623\pi$
$599$	1.08146e21			1.59702			0.798509	+	0.601983i	$0.205623\pi$
$600$		0			0
$601$	5.36803e20			0.773136			0.386568	−	0.922261i	$-0.373660\pi$
$601$	5.36803e20			0.773136			0.386568	+	0.922261i	$0.373660\pi$
$602$		0			0
$603$			2.04303e20i			0.287009i
$604$		0			0
$605$	5.70809e20	+	2.46619e20i	0.782213	+	0.337957i
$606$		0			0
$607$			4.11434e20i			0.550029i	0.961440	+	0.275014i	$0.0886826\pi$
$607$			4.11434e20i			0.550029i	−0.961440	+	0.275014i	$0.911317\pi$
$608$		0			0
$609$	−6.40035e20			−0.834783
$610$		0			0
$611$	6.31522e20			0.803673
$612$		0			0
$613$		−	5.44101e20i		−	0.675656i	−0.941208	−	0.337828i	$-0.890308\pi$
$613$		−	5.44101e20i		−	0.675656i	0.941208	−	0.337828i	$-0.109692\pi$
$614$		0			0
$615$	3.62401e20	−	8.38790e20i	0.439163	−	1.01646i
$616$		0			0
$617$			4.65828e20i			0.550918i	0.961313	+	0.275459i	$0.0888298\pi$
$617$			4.65828e20i			0.550918i	−0.961313	+	0.275459i	$0.911170\pi$
$618$		0			0
$619$	−1.51736e21			−1.75150			−0.875749	−	0.482767i	$-0.839632\pi$
$619$	−1.51736e21			−1.75150			−0.875749	+	0.482767i	$0.839632\pi$
$620$		0			0
$621$	1.55678e21			1.75405
$622$		0			0
$623$			6.58215e20i			0.723948i
$624$		0			0
$625$	−5.63262e19	+	9.29618e20i	−0.0604798	+	0.998169i
$626$		0			0
$627$			5.81746e20i			0.609855i
$628$		0			0
$629$	−2.11685e21			−2.16676
$630$		0			0
$631$	−5.94310e20			−0.594009			−0.297004	−	0.954876i	$-0.595988\pi$
$631$	−5.94310e20			−0.594009			−0.297004	+	0.954876i	$0.595988\pi$
$632$		0			0
$633$			2.41421e21i			2.35639i
$634$		0			0
$635$	1.95530e20	−	4.52563e20i	0.186385	−	0.431396i
$636$		0			0
$637$		−	5.05228e20i		−	0.470372i
$638$		0			0
$639$	4.38780e20			0.399016
$640$		0			0
$641$	9.48383e20			0.842458			0.421229	−	0.906954i	$-0.361599\pi$
$641$	9.48383e20			0.842458			0.421229	+	0.906954i	$0.361599\pi$
$642$		0			0
$643$			2.15909e21i			1.87365i	0.349800	+	0.936824i	$0.386250\pi$
$643$			2.15909e21i			1.87365i	−0.349800	+	0.936824i	$0.613750\pi$
$644$		0			0
$645$	−2.19994e21	−	9.50486e20i	−1.86514	−	0.805838i
$646$		0			0
$647$		−	2.26989e20i		−	0.188028i	−0.995571	−	0.0940139i	$-0.970030\pi$
$647$		−	2.26989e20i		−	0.188028i	0.995571	−	0.0940139i	$-0.0299698\pi$
$648$		0			0
$649$	−3.32771e19			−0.0269346
$650$		0			0
$651$	5.79067e19			0.0458006
$652$		0			0
$653$		−	2.12810e21i		−	1.64491i	−0.568830	−	0.822455i	$-0.692604\pi$
$653$		−	2.12810e21i		−	1.64491i	0.568830	−	0.822455i	$-0.307396\pi$
$654$		0			0
$655$	1.04965e21	+	4.53504e20i	0.792932	+	0.342588i
$656$		0			0
$657$			1.80815e21i			1.33504i
$658$		0			0
$659$	−3.97715e20			−0.287032			−0.143516	−	0.989648i	$-0.545841\pi$
$659$	−3.97715e20			−0.287032			−0.143516	+	0.989648i	$0.545841\pi$
$660$		0			0
$661$	1.97089e20			0.139044			0.0695218	−	0.997580i	$-0.477853\pi$
$661$	1.97089e20			0.139044			0.0695218	+	0.997580i	$0.477853\pi$
$662$		0			0
$663$		−	2.76794e21i		−	1.90900i
$664$		0			0
$665$	3.12743e20	−	7.23855e20i	0.210875	−	0.488078i
$666$		0			0
$667$		−	1.02650e21i		−	0.676729i
$668$		0			0
$669$	5.72457e20			0.369017
$670$		0			0
$671$	1.78082e20			0.112254
$672$		0			0
$673$		−	1.12563e21i		−	0.693876i	−0.937888	−	0.346938i	$-0.887221\pi$
$673$		−	1.12563e21i		−	0.693876i	0.937888	−	0.346938i	$-0.112779\pi$
$674$		0			0
$675$	−2.47234e21	+	2.32707e21i	−1.49049	+	1.40292i
$676$		0			0
$677$		−	2.01414e21i		−	1.18761i	−0.804608	−	0.593806i	$-0.797625\pi$
$677$		−	2.01414e21i		−	1.18761i	0.804608	−	0.593806i	$-0.202375\pi$
$678$		0			0
$679$	−1.54017e21			−0.888273
$680$		0			0
$681$	5.53060e20			0.312010
$682$		0			0
$683$		−	2.93860e21i		−	1.62176i	−0.585215	−	0.810878i	$-0.698990\pi$
$683$		−	2.93860e21i		−	1.62176i	0.585215	−	0.810878i	$-0.301010\pi$
$684$		0			0
$685$	−8.14974e20	+	1.88629e21i	−0.440012	+	1.01842i
$686$		0			0
$687$			2.63160e21i			1.39009i
$688$		0			0
$689$	−4.11235e20			−0.212542
$690$		0			0
$691$	1.85211e20			0.0936661			0.0468330	−	0.998903i	$-0.485087\pi$
$691$	1.85211e20			0.0936661			0.0468330	+	0.998903i	$0.485087\pi$
$692$		0			0
$693$			9.95967e20i			0.492885i
$694$		0			0
$695$	−3.26773e21	−	1.41183e21i	−1.58256	−	0.683748i
$696$		0			0
$697$		−	1.94142e21i		−	0.920182i
$698$		0			0
$699$	−6.39006e21			−2.96433
$700$		0			0
$701$	−1.53115e21			−0.695236			−0.347618	−	0.937636i	$-0.613009\pi$
$701$	−1.53115e21			−0.695236			−0.347618	+	0.937636i	$0.613009\pi$
$702$		0			0
$703$		−	2.95056e21i		−	1.31141i
$704$		0			0
$705$	−4.13226e21	−	1.78535e21i	−1.79791	−	0.776792i
$706$		0			0
$707$		−	2.56800e20i		−	0.109383i
$708$		0			0
$709$	−1.28361e19			−0.00535287			−0.00267643	−	0.999996i	$-0.500852\pi$
$709$	−1.28361e19			−0.00535287			−0.00267643	+	0.999996i	$0.500852\pi$
$710$		0			0
$711$	7.67633e21			3.13423
$712$		0			0
$713$			9.28717e19i			0.0371289i
$714$		0			0
$715$	−2.83886e20	+	6.57066e20i	−0.111135	+	0.257225i
$716$		0			0
$717$			2.05502e21i			0.787811i
$718$		0			0
$719$	3.14657e21			1.18133			0.590665	−	0.806917i	$-0.298866\pi$
$719$	3.14657e21			1.18133			0.590665	+	0.806917i	$0.298866\pi$
$720$		0			0
$721$	−1.94594e21			−0.715508
$722$		0			0
$723$			8.37955e21i			3.01775i
$724$		0			0
$725$	1.53440e21	+	1.63019e21i	0.541259	+	0.575047i
$726$		0			0
$727$		−	4.52609e21i		−	1.56392i	−0.623327	−	0.781962i	$-0.714219\pi$
$727$		−	4.52609e21i		−	1.56392i	0.623327	−	0.781962i	$-0.285781\pi$
$728$		0			0
$729$	1.31386e21			0.444726
$730$		0			0
$731$	−5.09186e21			−1.68848
$732$		0			0
$733$			2.68116e21i			0.871048i	0.900177	+	0.435524i	$0.143437\pi$
$733$			2.68116e21i			0.871048i	−0.900177	+	0.435524i	$0.856563\pi$
$734$		0			0
$735$	−1.42831e21	+	3.30587e21i	−0.454639	+	1.05228i
$736$		0			0
$737$		−	1.64395e20i		−	0.0512721i
$738$		0			0
$739$	1.15277e21			0.352298			0.176149	−	0.984364i	$-0.443636\pi$
$739$	1.15277e21			0.352298			0.176149	+	0.984364i	$0.443636\pi$
$740$		0			0
$741$	3.85807e21			1.15540
$742$		0			0
$743$			2.64683e21i			0.776801i	0.921491	+	0.388400i	$0.126972\pi$
$743$			2.64683e21i			0.776801i	−0.921491	+	0.388400i	$0.873028\pi$
$744$		0			0
$745$	−4.64372e21	−	2.00633e21i	−1.33565	−	0.577072i
$746$		0			0
$747$		−	2.05759e21i		−	0.580034i
$748$		0			0
$749$	8.94493e20			0.247151
$750$		0			0
$751$	4.36972e21			1.18346			0.591730	−	0.806136i	$-0.298445\pi$
$751$	4.36972e21			1.18346			0.591730	+	0.806136i	$0.298445\pi$
$752$		0			0
$753$			2.54716e21i			0.676229i
$754$		0			0
$755$	2.84208e18	+	1.22793e18i	0.000739664	+	0.000319573i
$756$		0			0
$757$		−	7.25274e20i		−	0.185047i	−0.995710	−	0.0925237i	$-0.970507\pi$
$757$		−	7.25274e20i		−	0.185047i	0.995710	−	0.0925237i	$-0.0294934\pi$
$758$		0			0
$759$	−2.33934e21			−0.585168
$760$		0			0
$761$	2.04957e21			0.502665			0.251333	−	0.967901i	$-0.419131\pi$
$761$	2.04957e21			0.502665			0.251333	+	0.967901i	$0.419131\pi$
$762$		0			0
$763$		−	1.75597e21i		−	0.422262i
$764$		0			0
$765$	−5.34315e21	+	1.23669e22i	−1.25990	+	2.91609i
$766$		0			0
$767$			2.20690e20i			0.0510290i
$768$		0			0
$769$	−2.52209e21			−0.571891			−0.285945	−	0.958246i	$-0.592308\pi$
$769$	−2.52209e21			−0.571891			−0.285945	+	0.958246i	$0.592308\pi$
$770$		0			0
$771$	4.69931e20			0.104503
$772$		0			0
$773$			2.53203e21i			0.552233i	0.961124	+	0.276117i	$0.0890476\pi$
$773$			2.53203e21i			0.552233i	−0.961124	+	0.276117i	$0.910952\pi$
$774$		0			0
$775$	−1.38824e20	−	1.47490e20i	−0.0296963	−	0.0315501i
$776$		0			0
$777$		−	7.39791e21i		−	1.55221i
$778$		0			0
$779$	2.70603e21			0.556932
$780$		0			0
$781$	−3.53069e20			−0.0712815
$782$		0			0
$783$			8.16157e21i			1.61644i
$784$		0			0
$785$	7.21525e20	−	1.67000e21i	0.140194	−	0.324484i
$786$		0			0
$787$			1.39343e21i			0.265629i	0.991141	+	0.132814i	$0.0424014\pi$
$787$			1.39343e21i			0.265629i	−0.991141	+	0.132814i	$0.957599\pi$
$788$		0			0
$789$	4.67347e21			0.874102
$790$		0			0
$791$	2.95766e21			0.542781
$792$		0			0
$793$		−	1.18102e21i		−	0.212671i
$794$		0			0
$795$	2.69085e21	+	1.16258e21i	0.475483	+	0.205433i
$796$		0			0
$797$		−	9.55241e20i		−	0.165644i	−0.996564	−	0.0828220i	$-0.973607\pi$
$797$		−	9.55241e20i		−	0.165644i	0.996564	−	0.0828220i	$-0.0263933\pi$
$798$		0			0
$799$	−9.56431e21			−1.62762
$800$		0			0
$801$	1.56744e22			2.61787
$802$		0			0
$803$		−	1.45495e21i		−	0.238496i
$804$		0			0
$805$	2.91080e21	+	1.25762e21i	0.468320	+	0.202339i
$806$		0			0
$807$		−	1.18178e22i		−	1.86631i
$808$		0			0
$809$	−9.73892e21			−1.50972			−0.754861	−	0.655885i	$-0.772296\pi$
$809$	−9.73892e21			−1.50972			−0.754861	+	0.655885i	$0.772296\pi$
$810$		0			0
$811$	−4.03949e20			−0.0614711			−0.0307355	−	0.999528i	$-0.509785\pi$
$811$	−4.03949e20			−0.0614711			−0.0307355	+	0.999528i	$0.509785\pi$
$812$		0			0
$813$		−	1.25362e22i		−	1.87277i
$814$		0			0
$815$	−3.26076e21	+	7.54715e21i	−0.478230	+	1.10688i
$816$		0			0
$817$		−	7.09724e21i		−	1.02194i
$818$		0			0
$819$	6.60513e21			0.933797
$820$		0			0
$821$	1.42068e22			1.97207			0.986034	−	0.166541i	$-0.0532599\pi$
$821$	1.42068e22			1.97207			0.986034	+	0.166541i	$0.0532599\pi$
$822$		0			0
$823$		−	6.03911e21i		−	0.823141i	−0.911378	−	0.411570i	$-0.864980\pi$
$823$		−	6.03911e21i		−	0.823141i	0.911378	−	0.411570i	$-0.135020\pi$
$824$		0			0
$825$	3.71513e21	−	3.49684e21i	0.497243	−	0.468027i
$826$		0			0
$827$		−	1.20995e22i		−	1.59029i	−0.606421	−	0.795144i	$-0.707395\pi$
$827$		−	1.20995e22i		−	1.59029i	0.606421	−	0.795144i	$-0.292605\pi$
$828$		0			0
$829$	−5.90195e21			−0.761792			−0.380896	−	0.924618i	$-0.624384\pi$
$829$	−5.90195e21			−0.761792			−0.380896	+	0.924618i	$0.624384\pi$
$830$		0			0
$831$	2.21154e22			2.80342
$832$		0			0
$833$			7.65160e21i			0.952610i
$834$		0			0
$835$	2.75586e21	−	6.37855e21i	0.336984	−	0.779962i
$836$		0			0
$837$		−	7.38412e20i		−	0.0886865i
$838$		0			0
$839$	−1.29661e22			−1.52966			−0.764831	−	0.644231i	$-0.777178\pi$
$839$	−1.29661e22			−1.52966			−0.764831	+	0.644231i	$0.777178\pi$
$840$		0			0
$841$	−3.24768e21			−0.376360
$842$		0			0
$843$		−	1.62420e22i		−	1.84898i
$844$		0			0
$845$	−3.85086e21	−	1.66377e21i	−0.430657	−	0.186066i
$846$		0			0
$847$			4.61717e21i			0.507283i
$848$		0			0
$849$	−7.50427e20			−0.0810029
$850$		0			0
$851$	1.18649e22			1.25832
$852$		0			0
$853$		−	9.05799e21i		−	0.943874i	−0.881632	−	0.471937i	$-0.843555\pi$
$853$		−	9.05799e21i		−	0.943874i	0.881632	−	0.471937i	$-0.156445\pi$
$854$		0			0
$855$	−1.72375e22	−	7.44750e21i	−1.76494	−	0.762544i
$856$		0			0
$857$		−	1.80435e22i		−	1.81536i	−0.419660	−	0.907682i	$-0.637851\pi$
$857$		−	1.80435e22i		−	1.81536i	0.419660	−	0.907682i	$-0.362149\pi$
$858$		0			0
$859$	2.44689e21			0.241916			0.120958	−	0.992658i	$-0.461403\pi$
$859$	2.44689e21			0.241916			0.120958	+	0.992658i	$0.461403\pi$
$860$		0			0
$861$	6.78482e21			0.659196
$862$		0			0
$863$			9.95152e21i			0.950185i	0.879936	+	0.475093i	$0.157585\pi$
$863$			9.95152e21i			0.950185i	−0.879936	+	0.475093i	$0.842415\pi$
$864$		0			0
$865$	4.36657e21	−	1.01066e22i	0.409750	−	0.948383i
$866$		0			0
$867$			2.26674e22i			2.09054i
$868$		0			0
$869$	−6.17683e21			−0.559909
$870$		0			0
$871$	−1.09025e21			−0.0971378
$872$		0			0
$873$			3.66769e22i			3.21208i
$874$		0			0
$875$	−6.50254e21	+	2.35382e21i	−0.559786	+	0.202634i
$876$		0			0
$877$			1.75476e22i			1.48498i	0.669855	+	0.742492i	$0.266356\pi$
$877$			1.75476e22i			1.48498i	−0.669855	+	0.742492i	$0.733644\pi$
$878$		0			0
$879$	1.74787e22			1.45409
$880$		0			0
$881$	−1.45628e22			−1.19104			−0.595520	−	0.803341i	$-0.703054\pi$
$881$	−1.45628e22			−1.19104			−0.595520	+	0.803341i	$0.703054\pi$
$882$		0			0
$883$			1.28619e22i			1.03419i	0.855928	+	0.517095i	$0.172987\pi$
$883$			1.28619e22i			1.03419i	−0.855928	+	0.517095i	$0.827013\pi$
$884$		0			0
$885$	6.23903e20	−	1.44405e21i	0.0493222	−	0.114158i
$886$		0			0
$887$		−	1.46337e22i		−	1.13743i	−0.822534	−	0.568716i	$-0.807440\pi$
$887$		−	1.46337e22i		−	1.13743i	0.822534	−	0.568716i	$-0.192560\pi$
$888$		0			0
$889$	3.66070e21			0.279770
$890$		0			0
$891$	7.58270e21			0.569824
$892$		0			0
$893$		−	1.33311e22i		−	0.985102i
$894$		0			0
$895$	3.37864e21	+	1.45975e21i	0.245510	+	0.106073i
$896$		0			0
$897$			1.55142e22i			1.10863i
$898$		0			0
$899$	−4.86888e20			−0.0342162
$900$		0			0
$901$	6.22809e21			0.430446
$902$		0			0
$903$		−	1.77949e22i		−	1.20959i
$904$		0			0
$905$	−2.79895e21	−	1.20929e21i	−0.187125	−	0.0808476i
$906$		0			0
$907$		−	4.06427e21i		−	0.267256i	−0.991032	−	0.133628i	$-0.957337\pi$
$907$		−	4.06427e21i		−	0.267256i	0.991032	−	0.133628i	$-0.0426627\pi$
$908$		0			0
$909$	−6.11531e21			−0.395539
$910$		0			0
$911$	−6.36749e21			−0.405117			−0.202558	−	0.979270i	$-0.564926\pi$
$911$	−6.36749e21			−0.405117			−0.202558	+	0.979270i	$0.564926\pi$
$912$		0			0
$913$			1.65566e21i			0.103619i
$914$		0			0
$915$	−3.33881e21	+	7.72780e21i	−0.205557	+	0.475770i
$916$		0			0
$917$			8.49045e21i			0.514234i
$918$		0			0
$919$	2.93596e22			1.74938			0.874690	−	0.484682i	$-0.161065\pi$
$919$	2.93596e22			1.74938			0.874690	+	0.484682i	$0.161065\pi$
$920$		0			0
$921$	5.35798e22			3.14090
$922$		0			0
$923$			2.34151e21i			0.135046i
$924$		0			0
$925$	−1.88427e22	+	1.77356e22i	−1.06925	+	1.00643i
$926$		0			0
$927$			4.63396e22i			2.58734i
$928$		0			0
$929$	3.30652e22			1.81658			0.908288	−	0.418347i	$-0.137390\pi$
$929$	3.30652e22			1.81658			0.908288	+	0.418347i	$0.137390\pi$
$930$		0			0
$931$	−1.06651e22			−0.576558
$932$		0			0
$933$		−	5.87127e22i		−	3.12334i
$934$		0			0
$935$	4.29942e21	−	9.95117e21i	0.225073	−	0.520939i
$936$		0			0
$937$			3.47429e22i			1.78986i	0.446205	+	0.894931i	$0.352775\pi$
$937$			3.47429e22i			1.78986i	−0.446205	+	0.894931i	$0.647225\pi$
$938$		0			0
$939$	−2.04852e21			−0.103860
$940$		0			0
$941$	−2.80935e21			−0.140179			−0.0700897	−	0.997541i	$-0.522329\pi$
$941$	−2.80935e21			−0.140179			−0.0700897	+	0.997541i	$0.522329\pi$
$942$		0			0
$943$			1.08816e22i			0.534387i
$944$		0			0
$945$	−2.31434e22	−	9.99915e21i	−1.11864	−	0.483308i
$946$		0			0
$947$			9.11666e21i			0.433722i	0.976203	+	0.216861i	$0.0695818\pi$
$947$			9.11666e21i			0.433722i	−0.976203	+	0.216861i	$0.930418\pi$
$948$		0			0
$949$	−9.64903e21			−0.451842
$950$		0			0
$951$	−3.79419e22			−1.74890
$952$		0			0
$953$			1.41863e22i			0.643682i	0.946794	+	0.321841i	$0.104302\pi$
$953$			1.41863e22i			0.643682i	−0.946794	+	0.321841i	$0.895698\pi$
$954$		0			0
$955$	−2.93338e22	−	1.26737e22i	−1.31022	−	0.566082i
$956$		0			0
$957$		−	1.22642e22i		−	0.539262i
$958$		0			0
$959$	−1.52578e22			−0.660471
$960$		0			0
$961$	−2.34212e22			−0.998123
$962$		0			0
$963$		−	2.13010e22i		−	0.893723i
$964$		0			0
$965$	−3.14766e21	+	7.28538e21i	−0.130027	+	0.300952i
$966$		0			0
$967$			1.40091e22i			0.569785i	0.958560	+	0.284892i	$0.0919578\pi$
$967$			1.40091e22i			0.569785i	−0.958560	+	0.284892i	$0.908042\pi$
$968$		0			0
$969$	−5.84299e22			−2.33995
$970$		0			0
$971$	3.55233e22			1.40078			0.700388	−	0.713762i	$-0.253010\pi$
$971$	3.55233e22			1.40078			0.700388	+	0.713762i	$0.253010\pi$
$972$		0			0
$973$		−	2.64321e22i		−	1.02633i
$974$		0			0
$975$	−2.31906e22	−	2.46383e22i	−0.886702	−	0.942054i
$976$		0			0
$977$			2.18841e22i			0.823985i	0.911187	+	0.411993i	$0.135167\pi$
$977$			2.18841e22i			0.823985i	−0.911187	+	0.411993i	$0.864833\pi$
$978$		0			0
$979$	−1.26126e22			−0.467663
$980$		0			0
$981$	−4.18157e22			−1.52694
$982$		0			0
$983$			6.12627e21i			0.220315i	0.993914	+	0.110158i	$0.0351356\pi$
$983$			6.12627e21i			0.220315i	−0.993914	+	0.110158i	$0.964864\pi$
$984$		0			0
$985$	1.76285e22	−	4.08018e22i	0.624372	−	1.44513i
$986$		0			0
$987$		−	3.34251e22i		−	1.16599i
$988$		0			0
$989$	2.85397e22			0.980568
$990$		0			0
$991$	−3.50331e22			−1.18557			−0.592784	−	0.805361i	$-0.701971\pi$
$991$	−3.50331e22			−1.18557			−0.592784	+	0.805361i	$0.701971\pi$
$992$		0			0
$993$			4.06956e22i			1.35652i
$994$		0			0
$995$	2.80876e22	+	1.21353e22i	0.922236	+	0.398453i
$996$		0			0
$997$			3.84796e22i			1.24456i	0.782793	+	0.622282i	$0.213794\pi$
$997$			3.84796e22i			1.24456i	−0.782793	+	0.622282i	$0.786206\pi$
$998$		0			0
$999$	−9.43364e22			−3.00565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.16.c.a.49.1		6
4.3	odd	2		5.16.b.a.4.4	yes	6
5.4	even	2	inner	80.16.c.a.49.6		6
12.11	even	2		45.16.b.b.19.3		6
20.3	even	4		25.16.a.f.1.4		6
20.7	even	4		25.16.a.f.1.3		6
20.19	odd	2		5.16.b.a.4.3	✓	6
60.59	even	2		45.16.b.b.19.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.16.b.a.4.3	✓	6	20.19	odd	2
5.16.b.a.4.4	yes	6	4.3	odd	2
25.16.a.f.1.3		6	20.7	even	4
25.16.a.f.1.4		6	20.3	even	4
45.16.b.b.19.3		6	12.11	even	2
45.16.b.b.19.4		6	60.59	even	2
80.16.c.a.49.1		6	1.1	even	1	trivial
80.16.c.a.49.6		6	5.4	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	80.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-6725.99i q^{3} +(-160365. - 69286.1i) q^{5} -1.29717e6i q^{7} -3.08900e7 q^{9} +O(q^{10})\)	\(q-6725.99i q^{3} +(-160365. - 69286.1i) q^{5} -1.29717e6i q^{7} -3.08900e7 q^{9} +2.48560e7 q^{11} -1.64842e8i q^{13} +(-4.66018e8 + 1.07862e9i) q^{15} +2.49651e9i q^{17} -3.47974e9 q^{19} -8.72472e9 q^{21} -1.39929e10i q^{23} +(2.09165e10 + 2.22222e10i) q^{25} +1.11256e11i q^{27} +7.33587e10 q^{29} -6.63708e9 q^{31} -1.67181e11i q^{33} +(-8.98755e10 + 2.08020e11i) q^{35} +8.47925e11i q^{37} -1.10873e12 q^{39} -7.77655e11 q^{41} +2.03959e12i q^{43} +(4.95369e12 + 2.14025e12i) q^{45} +3.83108e12i q^{47} +3.06492e12 q^{49} +1.67915e13 q^{51} -2.49472e12i q^{53} +(-3.98604e12 - 1.72217e12i) q^{55} +2.34047e13i q^{57} -1.33880e12 q^{59} +7.16455e12 q^{61} +4.00695e13i q^{63} +(-1.14213e13 + 2.64349e13i) q^{65} -6.61388e12i q^{67} -9.41158e13 q^{69} -1.42046e13 q^{71} -5.85350e13i q^{73} +(1.49466e14 - 1.40684e14i) q^{75} -3.22423e13i q^{77} -2.48505e14 q^{79} +3.05065e14 q^{81} +6.66100e13i q^{83} +(1.72973e14 - 4.00353e14i) q^{85} -4.93410e14i q^{87} -5.07426e14 q^{89} -2.13827e14 q^{91} +4.46409e13i q^{93} +(5.58029e14 + 2.41097e14i) q^{95} -1.18734e15i q^{97} -7.67802e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 238350 q^{5} - 11416662 q^{9}+O(q^{10}) \) 6 * q - 238350 * q^5 - 11416662 * q^9	\( 6 q - 238350 q^{5} - 11416662 q^{9} + 108590088 q^{11} - 297743400 q^{15} + 3630995640 q^{19} - 8917537608 q^{21} + 18250878750 q^{25} + 286168468740 q^{29} + 276236748288 q^{31} - 1171274911800 q^{35} - 2186980965936 q^{39} - 6153278882388 q^{41} + 10442765857950 q^{45} + 11613390856242 q^{49} + 43487373385728 q^{51} - 33977390365800 q^{55} - 14903258326680 q^{59} - 11352061428588 q^{61} - 50675287275600 q^{65} - 150489671962824 q^{69} - 131693145807312 q^{71} + 360965926890000 q^{75} + 26081853939360 q^{79} + 11\!\cdots\!46 q^{81}+ \cdots - 506999099666376 q^{99}+O(q^{100}) \) 6 * q - 238350 * q^5 - 11416662 * q^9 + 108590088 * q^11 - 297743400 * q^15 + 3630995640 * q^19 - 8917537608 * q^21 + 18250878750 * q^25 + 286168468740 * q^29 + 276236748288 * q^31 - 1171274911800 * q^35 - 2186980965936 * q^39 - 6153278882388 * q^41 + 10442765857950 * q^45 + 11613390856242 * q^49 + 43487373385728 * q^51 - 33977390365800 * q^55 - 14903258326680 * q^59 - 11352061428588 * q^61 - 50675287275600 * q^65 - 150489671962824 * q^69 - 131693145807312 * q^71 + 360965926890000 * q^75 + 26081853939360 * q^79 + 1148641568615646 * q^81 - 548221025491200 * q^85 + 59269690709820 * q^89 - 821206462566672 * q^91 - 232287694599000 * q^95 - 506999099666376 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more